Subgroups — #72262379

Order 2048.

At least 30249 conjugacy classes of subgroups; only the 1640 normal subgroups are shown.

The subgroup lattice has 1109 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262377	C₂	1	1	yes	maximal, characteristic, complemented
2	#72262332	C₂	1	1	yes	maximal, characteristic, complemented
3	#72262306	C₂	1	1	yes	maximal, characteristic, complemented
4	#72262251	C₂	1	2	yes	maximal, complemented
5	#72262227	C₂	1	1	yes	maximal, characteristic, complemented
6	#72262193	C₂	1	2	yes	maximal, complemented
7	#72262125	C₂	1	1	yes	maximal, characteristic, complemented
8	#72249497	C₂	1	2	yes	maximal, complemented
9	C₂×#493635	C₂	1	1	yes	maximal, characteristic, complemented
10	#72237806	C₂	1	2	yes	maximal, complemented
11	#72234799	C₂	1	1	yes	maximal, characteristic, complemented
12	#72234696	C₂	1	1	yes	maximal, characteristic, complemented
13	#72234630	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#7622880	C₂	1	1	yes	maximal, characteristic, complemented
15	#72233087	C₂	1	2	yes	maximal, complemented
16	#72233086	C₂	1	2	yes	maximal, complemented
17	#72232895	C₂	1	1	yes	maximal, characteristic, complemented
18	#72232293	C₂	1	1	yes	maximal, characteristic, complemented
19	#72231228	C₂	1	2	yes	maximal, complemented
20	#72225802	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#493474	C₂	1	1	yes	maximal, characteristic, complemented
22	#72218099	C₂	1	2	yes	maximal, complemented
23	C₂×#6499874	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#63011	C₂²	1	1	yes	characteristic
25	C₂×#62817	C₂²	1	1	yes	characteristic
26	C₂×#60399	C₂²	1	1	yes	characteristic
27	C₂×#60399	C₂²	1	1	yes	characteristic, complemented
28	C₂×#60399	C₂²	1	1	yes	characteristic, complemented
29	C₂×#60399	C₂²	1	1	yes	characteristic, complemented
30	C₂×#60388	C₂²	1	1	yes	characteristic, complemented
31	#7819710	C₂²	1	1	yes	characteristic, complemented
32	#7819709	C₂²	1	1	yes	characteristic, complemented
33	#7791097	C₂²	1	1	yes	characteristic, complemented
34	#7785081	C₂²	1	1	yes	characteristic, complemented
35	#7733246	C₂²	1	1	yes	characteristic, complemented
36	#7733187	C₂²	1	1	yes	characteristic, complemented
37	#7708349	C₂²	1	1	yes	characteristic, complemented
38	C₂×#58990	C₂²	1	1	yes	characteristic, complemented
39	#7659307	C₂²	1	1	yes	characteristic
40	#7659296	C₂²	1	1	yes	characteristic
41	#7649984	C₂²	1	1	yes	characteristic
42	#7648640	C₂²	1	1	yes	characteristic
43	#7627266	C₂²	1	1	yes	characteristic
44	C₂×#33557	C₂²	1	2	yes	complemented
45	C₂×#33551	C₂²	1	2	yes	complemented
46	C₂×#33551	C₂²	1	2	yes	complemented
47	C₂²×#2196	C₂²	1	2	yes	complemented
48	C₂×#33359	C₂²	1	1	yes	characteristic, complemented
49	C₂×#33359	C₂²	1	1	yes	characteristic, complemented
50	C₂×#33348	C₂²	1	1	yes	characteristic
51	C₂×#33348	C₂²	1	1	yes	characteristic
52	C₂×#33348	C₂²	1	1	yes	characteristic, complemented
53	C₂×#33348	C₂²	1	1	yes	characteristic, complemented
54	C₂×#33348	C₂²	1	1	yes	characteristic, complemented
55	C₂×#33348	C₂²	1	1	yes	characteristic, complemented
56	C₂×#23996	C₂²	1	2	yes	complemented
57	C₂×#23996	C₂²	1	2	yes	complemented
58	C₂×#23895	C₂²	1	2	yes	complemented
59	C₂×#23900	C₂²	1	2	yes	complemented
60	C₂×#21782	C₂²	1	1	yes	characteristic, complemented
61	C₂×#21778	C₂²	1	1	yes	characteristic, complemented
62	C₂×#21776	C₂²	1	1	yes	characteristic
63	C₂×#21776	C₂²	1	1	yes	characteristic, complemented
64	C₂×#21776	C₂²	1	1	yes	characteristic, complemented
65	C₂×#21776	C₂²	1	1	yes	characteristic, complemented
66	C₂×#21776	C₂²	1	1	yes	characteristic, complemented
67	#6370747	C₂²	1	1	yes	characteristic, complemented
68	#6370735	C₂²	1	1	yes	characteristic, complemented
69	#498931	C₂²	1	2	yes	complemented
70	#498927	C₂²	1	2	yes	complemented
71	#498923	C₂²	1	2	yes	complemented
72	C₂×#13346	C₂²	1	2	yes	complemented
73	#498890	C₂²	1	2	yes	complemented
74	#498886	C₂²	1	2	yes	complemented
75	#498886	C₂²	1	2	yes	complemented
76	C₂×#13343	C₂²	1	2	yes	complemented
77	#494582	C₂²	1	2	yes	complemented
78	#494579	C₂²	1	2	yes	complemented
79	#494575	C₂²	1	2	yes	complemented
80	C₂×#13041	C₂²	1	2	yes	complemented
81	C₂×#12767	C₂²	1	2	yes	complemented
82	C₂×#12759	C₂²	1	2	yes	complemented
83	C₂×#12753	C₂²	1	2	yes	complemented
84	C₂×#12753	C₂²	1	2	yes	complemented
85	C₂×#12725	C₂²	1	2	yes	complemented
86	C₂×#12725	C₂²	1	2	yes	complemented
87	C₂×#12705	C₂²	1	2	yes	complemented
88	C₂×#12687	C₂²	1	2	yes	complemented
89	#492900	C₂²	1	1	yes	characteristic, complemented
90	#492900	C₂²	1	1	yes	characteristic, complemented
91	#492887	C₂²	1	1	yes	characteristic, complemented
92	#492887	C₂²	1	1	yes	characteristic, complemented
93	#405277	C₂²	1	2	yes	complemented
94	#405274	C₂²	1	2	yes	complemented
95	#405271	C₂²	1	2	yes	complemented
96	#405268	C₂²	1	2	yes	complemented
97	#394066	C₂²	1	2	yes	complemented
98	#394064	C₂²	1	2	yes	complemented
99	#393975	C₂²	1	2	yes	complemented
100	#393967	C₂²	1	2	yes	complemented
101	#355935	C₂²	1	1	yes	characteristic, complemented
102	#355922	C₂²	1	1	yes	characteristic, complemented
103	#147829	C₂²	1	2	yes	complemented
104	#147824	C₂²	1	2	yes	complemented
105	#147819	C₂²	1	2	yes	complemented
106	#147815	C₂²	1	2	yes	complemented
107	#147815	C₂²	1	2	yes	complemented
108	#147811	C₂²	1	2	yes	complemented
109	#147783	C₂²	1	2	yes	complemented
110	#147779	C₂²	1	2	yes	complemented
111	#147610	C₂²	1	2	yes	complemented
112	#147609	C₂²	1	2	yes	complemented
113	#147605	C₂²	1	2	yes	complemented
114	#147603	C₂²	1	2	yes	complemented
115	#147569	C₂²	1	2	yes	complemented
116	#147567	C₂²	1	2	yes	complemented
117	#147559	C₂²	1	2	yes	complemented
118	#147555	C₂²	1	2	yes	complemented
119	#146614	C₂²	1	2	yes	complemented
120	#146609	C₂²	1	2	yes	complemented
121	#146599	C₂²	1	2	yes	complemented
122	#146593	C₂²	1	2	yes	complemented
123	C₂×H(7,𝔽₂)	C₂³	1	1	yes	characteristic
124	C₂×#3498	C₂³	1	1	yes	characteristic
125	C₂×#3490	D₄	1	1	yes	characteristic, complemented
126	C₂×#3490	D₄	1	1	yes	characteristic, complemented
127	C₂×#3490	D₄	1	1	yes	characteristic, complemented
128	C₂×#3490	D₄	1	1	yes	characteristic, complemented
129	C₂×#3490	C₂³	1	1	yes	characteristic
130	C₂×#3490	C₂³	1	1	yes	characteristic
131	C₂×#3484	D₄	1	1	yes	characteristic, complemented
132	C₂×#3484	D₄	1	1	yes	characteristic, complemented
133	C₂×#3484	C₂³	1	1	yes	characteristic
134	C₂×#3484	C₂³	1	1	yes	characteristic
135	C₂×#3484	C₂³	1	1	yes	characteristic
136	C₂×#3484	C₂³	1	1	yes	characteristic
137	C₂×#3484	C₂³	1	1	yes	characteristic
138	C₂×#3484	C₂³	1	2	yes	complemented
139	C₂×#3549	D₄	1	1	yes	characteristic, complemented
140	C₂×#3543	D₄	1	1	yes	characteristic, complemented
141	C₂×#3543	C₂³	1	1	yes	characteristic
142	C₂×#3537	D₄	1	1	yes	characteristic, complemented
143	C₂×#3537	D₄	1	1	yes	characteristic, complemented
144	C₂×#3532	D₄	1	1	yes	characteristic, complemented
145	C₂×#3532	D₄	1	1	yes	characteristic, complemented
146	C₂×#3532	C₂³	1	1	yes	characteristic
147	C₂×#3532	C₂³	1	1	yes	characteristic
148	C₂×#3481	D₄	1	1	yes	characteristic, complemented
149	C₂²×D₄²	D₄	1	1	yes	characteristic, complemented
150	C₂²×D₄²	C₂³	1	1	yes	characteristic
151	C₂³×#120	D₄	1	1	yes	characteristic, complemented
152	C₂³×#120	D₄	1	1	yes	characteristic, complemented
153	C₂³×#120	C₂³	1	1	yes	characteristic
154	#60399	D₄	1	8	yes	complemented
155	C₂×#3026	C₂³	1	2	yes	—
156	C₂×#3026	C₂³	1	2	yes	—
157	C₂×#3026	C₂³	1	2	yes	complemented
158	C₂²×B(4,𝔽₂)	C₂³	1	2	yes	—
159	C₂²×B(4,𝔽₂)	C₂³	1	2	yes	—
160	C₂²×B(4,𝔽₂)	C₂³	1	2	yes	complemented
161	C₂×#3019	C₂³	1	2	yes	—
162	C₂²×#453	C₂³	1	2	yes	—
163	C₂×#2888	C₂³	1	1	yes	characteristic
164	C₂×#2888	C₂³	1	1	yes	characteristic
165	C₂×#2883	C₂³	1	1	yes	characteristic
166	C₂×#2883	C₂³	1	1	yes	characteristic
167	C₂×#2883	C₂³	1	1	yes	characteristic
168	C₂×#2883	C₂³	1	1	yes	characteristic
169	C₂×#2883	C₂³	1	1	yes	characteristic
170	C₂×#2883	C₂³	1	2	yes	complemented
171	#52165	D₄	1	1	yes	characteristic, complemented
172	#52163	D₄	1	1	yes	characteristic, complemented
173	C₂×#2679	D₄	1	1	yes	characteristic, complemented
174	C₂×#2679	C₂³	1	1	yes	characteristic
175	C₂×#2669	D₄	1	1	yes	characteristic, complemented
176	C₂×#2669	C₂³	1	1	yes	characteristic
177	#37297	D₄	1	1	yes	characteristic, complemented
178	#37297	D₄	1	1	yes	characteristic, complemented
179	#37273	D₄	1	1	yes	characteristic, complemented
180	#37269	D₄	1	1	yes	characteristic, complemented
181	#37269	D₄	1	1	yes	characteristic, complemented
182	#37269	D₄	1	1	yes	characteristic, complemented
183	#37232	D₄	1	1	yes	characteristic, complemented
184	#37232	C₂³	1	1	yes	characteristic
185	#37129	D₄	1	1	yes	characteristic, complemented
186	#37129	C₂³	1	1	yes	characteristic
187	#36737	D₄	1	1	yes	characteristic, complemented
188	#36737	C₂³	1	1	yes	characteristic
189	#36714	D₄	1	1	yes	characteristic, complemented
190	#36714	D₄	1	1	yes	characteristic, complemented
191	#36714	C₂³	1	1	yes	characteristic
192	#36714	C₂³	1	1	yes	characteristic
193	#36702	D₄	1	1	yes	characteristic, complemented
194	#36702	C₂³	1	1	yes	characteristic
195	#35563	D₄	1	1	yes	characteristic, complemented
196	#35554	C₂³	1	1	yes	characteristic
197	#35541	C₂³	1	1	yes	characteristic
198	#35533	D₄	1	1	yes	characteristic, complemented
199	#35527	D₄	1	1	yes	characteristic, complemented
200	#35512	D₄	1	1	yes	characteristic, complemented
201	#35360	D₄	1	1	yes	characteristic, complemented
202	#35360	C₂³	1	1	yes	characteristic
203	#35350	D₄	1	1	yes	characteristic, complemented
204	#35350	C₂³	1	1	yes	characteristic
205	#35348	D₄	1	1	yes	characteristic, complemented
206	#35348	D₄	1	1	yes	characteristic, complemented
207	#35272	D₄	1	1	yes	characteristic, complemented
208	#35254	D₄	1	1	yes	characteristic, complemented
209	#35222	C₂³	1	1	yes	characteristic
210	#34984	D₄	1	1	yes	characteristic, complemented
211	#34980	D₄	1	1	yes	characteristic, complemented
212	#34980	C₂³	1	1	yes	characteristic
213	#34743	D₄	1	1	yes	characteristic, complemented
214	#34742	D₄	1	1	yes	characteristic, complemented
215	C₂×#2433	C₂³	1	1	yes	characteristic
216	C₂×#2408	D₄	1	1	yes	characteristic, complemented
217	C₂×#2403	D₄	1	1	yes	characteristic, complemented
218	C₂×#2403	C₂³	1	1	yes	characteristic
219	#34415	D₄	1	1	yes	characteristic, complemented
220	#34411	D₄	1	1	yes	characteristic, complemented
221	#34408	D₄	1	1	yes	characteristic, complemented
222	#34408	C₂³	1	1	yes	characteristic
223	#34407	D₄	1	1	yes	characteristic, complemented
224	#34407	C₂³	1	1	yes	characteristic
225	#34360	D₄	1	1	yes	characteristic, complemented
226	#34356	D₄	1	1	yes	characteristic, complemented
227	#34356	C₂³	1	1	yes	characteristic
228	#34258	C₂³	1	1	yes	characteristic
229	#34256	C₂³	1	1	yes	characteristic
230	#34152	D₄	1	1	yes	characteristic, complemented
231	C₂×#2358	D₄	1	1	yes	characteristic, complemented
232	C₂×#2358	C₂³	1	1	yes	characteristic
233	C₂×#2127	C₂³	1	2	yes	—
234	C₂×#2127	C₂³	1	2	yes	—
235	C₂²×#353	C₂³	1	2	yes	—
236	C₂²×#353	C₂³	1	2	yes	—
237	#33348	D₄	1	8	yes	complemented
238	C₂×#2121	C₂³	1	2	yes	—
239	C₂×#2121	C₂³	1	2	yes	—
240	C₂×#2121	C₂³	1	2	yes	—
241	C₂×#2121	C₂³	1	2	yes	—
242	C₂×#2121	C₂³	1	2	yes	complemented
243	C₂×#2121	C₂³	1	2	yes	complemented
244	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
245	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
246	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
247	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
248	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	complemented
249	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	complemented
250	#21776	D₄	1	8	yes	complemented
251	C₂×#1913	C₂³	1	2	yes	—
252	C₂×#1913	C₂³	1	2	yes	—
253	C₂×#1913	C₂³	1	2	yes	complemented
254	C₂×#1911	C₂³	1	2	yes	—
255	C₂×#1889	C₂³	1	2	yes	—
256	C₂×#1889	C₂³	1	2	yes	—
257	C₂×#1889	C₂³	1	2	yes	complemented
258	C₂×#1887	C₂³	1	2	yes	—
259	C₂×#1829	C₂³	1	2	yes	complemented
260	C₂×#1828	C₂³	1	2	yes	complemented
261	C₂×#1828	C₂³	1	2	yes	complemented
262	#20616	C₂³	1	2	yes	complemented
263	C₂×#1792	C₂³	1	2	yes	complemented
264	#20609	C₂³	1	2	yes	complemented
265	C₂×#1790	C₂³	1	2	yes	complemented
266	C₂×#1783	C₂³	1	2	yes	complemented
267	C₂×#1781	C₂³	1	2	yes	complemented
268	C₂×#1781	C₂³	1	2	yes	complemented
269	#12582	C₂³	1	2	yes	complemented
270	#12582	C₂³	1	2	yes	complemented
271	C₂×#1393	C₂³	1	2	yes	complemented
272	C₂×#1393	C₂³	1	2	yes	complemented
273	#12574	C₂³	1	2	yes	complemented
274	#12574	C₂³	1	2	yes	complemented
275	C₂×#1390	C₂³	1	2	yes	complemented
276	C₂×#1390	C₂³	1	2	yes	complemented
277	#10754	C₂³	1	2	yes	complemented
278	#10749	C₂³	1	2	yes	complemented
279	#10745	C₂³	1	2	yes	complemented
280	#10740	C₂³	1	2	yes	complemented
281	C₂⁷	C₂×D₄	1	1	yes	characteristic, complemented
282	H(7,𝔽₂)	C₂×D₄	1	4	yes	complemented
283	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
284	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
285	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
286	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
287	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
288	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
289	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
290	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
291	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
292	C₂×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic, complemented
293	C₂×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic, complemented
294	C₂×#560	C₂×D₄	1	1	yes	characteristic, complemented
295	C₂×#560	C₂×D₄	1	1	yes	characteristic, complemented
296	C₂×#560	C₂×D₄	1	1	yes	characteristic, complemented
297	C₂×#560	C₂×D₄	1	1	yes	characteristic, complemented
298	#3484	C₂×D₄	1	4	yes	—
299	#3484	C₂×D₄	1	4	yes	—
300	#3484	C₂×D₄	1	4	yes	—
301	#3484	#41	1	4	yes	—
302	C₂×#559	C₂×D₄	1	1	yes	characteristic, complemented
303	C₂×#551	C₂×D₄	1	1	yes	characteristic, complemented
304	C₂×#551	C₂×D₄	1	1	yes	characteristic, complemented
305	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
306	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
307	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
308	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
309	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
310	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
311	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
312	C₂×#543	C₂×D₄	1	1	yes	characteristic, complemented
313	C₂×#543	C₂×D₄	1	1	yes	characteristic, complemented
314	C₂×#535	C₂×D₄	1	1	yes	characteristic
315	C₂×#535	C₂×D₄	1	1	yes	characteristic
316	C₂×#535	C₂×D₄	1	1	yes	characteristic
317	C₂×#535	C₂×D₄	1	1	yes	characteristic
318	C₂×#535	C₂×D₄	1	1	yes	characteristic
319	C₂×#535	C₂×D₄	1	1	yes	characteristic
320	C₂×#535	C₂×D₄	1	1	yes	characteristic
321	C₂×#535	C₂×D₄	1	1	yes	characteristic
322	C₂×#535	C₂×D₄	1	1	yes	characteristic
323	C₂×#535	C₂×D₄	1	1	yes	characteristic
324	C₂×#535	C₂×D₄	1	1	yes	characteristic
325	C₂×#535	C₂×D₄	1	1	yes	characteristic
326	C₂×#535	C₂×D₄	1	1	yes	characteristic
327	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
328	C₂×#535	C₂⁴	1	1	yes	characteristic
329	C₂×#534	C₂×D₄	1	1	yes	characteristic
330	C₂×#534	C₂×D₄	1	1	yes	characteristic
331	C₂×#534	C₂×D₄	1	1	yes	characteristic
332	C₂×#534	C₂×D₄	1	1	yes	characteristic
333	C₂×#534	C₂×D₄	1	1	yes	characteristic
334	C₂×#534	C₂×D₄	1	1	yes	characteristic
335	C₂×#534	C₂×D₄	1	1	yes	characteristic
336	C₂×#534	C₂×D₄	1	1	yes	characteristic
337	C₂×#534	C₂×D₄	1	1	yes	characteristic
338	C₂×#534	C₂×D₄	1	1	yes	characteristic
339	C₂×#534	C₂×D₄	1	1	yes	characteristic
340	C₂×#534	C₂×D₄	1	1	yes	characteristic
341	C₂×#534	C₂×D₄	1	1	yes	characteristic
342	C₂×#534	C₂×D₄	1	1	yes	characteristic, complemented
343	C₂×#534	C₂⁴	1	1	yes	characteristic
344	C₂×#534	C₂⁴	1	1	yes	characteristic
345	C₂×#534	C₂⁴	1	1	yes	characteristic
346	C₂×#532	C₂×D₄	1	1	yes	characteristic
347	C₂×#532	C₂×D₄	1	1	yes	characteristic
348	C₂×#532	C₂×D₄	1	1	yes	characteristic
349	C₂²×#127	C₂×D₄	1	1	yes	characteristic
350	C₂²×#127	C₂×D₄	1	1	yes	characteristic
351	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
352	C₂²×#127	C₂⁴	1	1	yes	characteristic
353	C₂×#525	C₂×D₄	1	1	yes	characteristic
354	C₂×#525	C₂×D₄	1	1	yes	characteristic
355	C₂×#525	C₂×D₄	1	1	yes	characteristic
356	C₂×#525	C₂×D₄	1	1	yes	characteristic
357	C₂×#525	C₂×D₄	1	1	yes	characteristic
358	C₂×#525	C₂×D₄	1	1	yes	characteristic
359	C₂×#525	C₂×D₄	1	1	yes	characteristic
360	C₂×#525	C₂×D₄	1	1	yes	characteristic
361	C₂×#525	C₂×D₄	1	1	yes	characteristic, complemented
362	C₂²×#121	C₂×D₄	1	1	yes	characteristic, complemented
363	C₂²×#120	C₂×D₄	1	1	yes	characteristic
364	C₂²×#120	C₂×D₄	1	1	yes	characteristic
365	C₂²×#120	C₂×D₄	1	1	yes	characteristic
366	C₂²×#120	C₂×D₄	1	1	yes	characteristic
367	C₂²×#120	C₂×D₄	1	1	yes	characteristic
368	C₂²×#120	C₂×D₄	1	1	yes	characteristic
369	C₂²×#120	C₂×D₄	1	1	yes	characteristic
370	C₂²×#120	C₂×D₄	1	1	yes	characteristic
371	C₂²×#120	C₂×D₄	1	1	yes	characteristic
372	C₂²×#120	C₂×D₄	1	1	yes	characteristic
373	C₂²×#120	C₂×D₄	1	1	yes	characteristic
374	C₂²×#120	C₂×D₄	1	1	yes	characteristic
375	C₂²×#120	C₂×D₄	1	1	yes	characteristic
376	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
377	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
378	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
379	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
380	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
381	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
382	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
383	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
384	C₂²×#120	C₂⁴	1	1	yes	characteristic
385	C₂²×#120	C₂⁴	1	1	yes	characteristic
386	C₂²×#120	C₂⁴	1	1	yes	characteristic
387	C₂×#520	C₂×D₄	1	1	yes	characteristic
388	C₂×#518	C₂×D₄	1	1	yes	characteristic
389	C₂×#518	C₂×D₄	1	1	yes	characteristic
390	C₂×#518	C₂×D₄	1	1	yes	characteristic
391	C₂×#518	C₂×D₄	1	1	yes	characteristic
392	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
393	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
394	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
395	C₂×#518	C₂⁴	1	2	yes	—
396	C₂×#518	C₂⁴	1	1	yes	characteristic
397	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
398	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
400	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
401	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
402	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
403	#3026	C₂×D₄	1	8	yes	complemented
404	C₂×B(4,𝔽₂)	C₂×D₄	1	8	yes	complemented
405	#2888	C₂×D₄	1	4	yes	complemented
406	C₂²×#100	C₂⁴	1	2	yes	—
407	C₂²×#100	C₂⁴	1	2	yes	—
408	#2883	C₂×D₄	1	4	yes	complemented
409	#2883	C₂×D₄	1	4	yes	complemented
410	#2883	C₂×D₄	1	4	yes	complemented
411	#2883	C₂×D₄	1	4	yes	complemented
412	C₂²×#99	C₂⁴	1	2	yes	—
413	C₂²×#99	C₂⁴	1	2	yes	—
414	C₂²×#99	C₂⁴	1	2	yes	—
415	C₂²×#99	C₂⁴	1	2	yes	—
416	#2724	C₂×D₄	1	1	yes	characteristic, complemented
417	#2717	C₂×D₄	1	1	yes	characteristic, complemented
418	#2709	C₂×D₄	1	1	yes	characteristic, complemented
419	#2709	C₂×D₄	1	1	yes	characteristic, complemented
420	#2709	C₂×D₄	1	1	yes	characteristic, complemented
421	#2697	C₂×D₄	1	1	yes	characteristic, complemented
422	#2697	C₂×D₄	1	1	yes	characteristic, complemented
423	#2697	C₂×D₄	1	1	yes	characteristic, complemented
424	#2697	C₂×D₄	1	1	yes	characteristic, complemented
425	#2697	C₂×D₄	1	1	yes	characteristic, complemented
426	#2697	C₂×D₄	1	1	yes	characteristic, complemented
427	#2684	C₂×D₄	1	1	yes	characteristic, complemented
428	#2684	C₂×D₄	1	1	yes	characteristic, complemented
429	#2684	C₂×D₄	1	1	yes	characteristic, complemented
430	#2679	C₂×D₄	1	1	yes	characteristic, complemented
431	#2679	C₂×D₄	1	1	yes	characteristic, complemented
432	#2679	C₂×D₄	1	1	yes	characteristic, complemented
433	#2679	C₂×D₄	1	1	yes	characteristic, complemented
434	#2679	C₂×D₄	1	1	yes	characteristic, complemented
435	#2679	C₂×D₄	1	1	yes	characteristic, complemented
436	#2679	C₂×D₄	1	1	yes	characteristic, complemented
437	#2679	C₂×D₄	1	1	yes	characteristic, complemented
438	#2679	C₂×D₄	1	1	yes	characteristic, complemented
439	#2669	C₂×D₄	1	1	yes	characteristic, complemented
440	#2669	C₂×D₄	1	1	yes	characteristic, complemented
441	#2669	C₂×D₄	1	1	yes	characteristic, complemented
442	#2669	C₂×D₄	1	1	yes	characteristic, complemented
443	#2669	C₂×D₄	1	1	yes	characteristic, complemented
444	#2669	C₂×D₄	1	1	yes	characteristic, complemented
445	#2669	C₂×D₄	1	1	yes	characteristic, complemented
446	#2669	C₂×D₄	1	1	yes	characteristic, complemented
447	#2669	C₂×D₄	1	1	yes	characteristic, complemented
448	#2376	C₂×D₄	1	1	yes	characteristic, complemented
449	#2376	C₂×D₄	1	1	yes	characteristic, complemented
450	#2375	C₂×D₄	1	1	yes	characteristic, complemented
451	#2375	C₂×D₄	1	1	yes	characteristic, complemented
452	#2375	C₂×D₄	1	1	yes	characteristic, complemented
453	#2375	C₂×D₄	1	1	yes	characteristic, complemented
454	#2374	C₂×D₄	1	1	yes	characteristic, complemented
455	#2374	C₂×D₄	1	1	yes	characteristic, complemented
456	#2358	C₂×D₄	1	1	yes	characteristic, complemented
457	#2358	C₂×D₄	1	1	yes	characteristic, complemented
458	#2358	C₂×D₄	1	1	yes	characteristic, complemented
459	#2358	C₂×D₄	1	1	yes	characteristic, complemented
460	#2358	C₂×D₄	1	1	yes	characteristic, complemented
461	#2358	C₂×D₄	1	1	yes	characteristic, complemented
462	#2358	C₂×D₄	1	1	yes	characteristic, complemented
463	#2358	C₂×D₄	1	1	yes	characteristic, complemented
464	#2316	C₂×D₄	1	1	yes	characteristic, complemented
465	#2315	C₂×D₄	1	1	yes	characteristic, complemented
466	#2315	C₂×D₄	1	1	yes	characteristic, complemented
467	#2315	C₂×D₄	1	1	yes	characteristic, complemented
468	#2311	C₂×D₄	1	1	yes	characteristic
469	#2311	C₂×D₄	1	1	yes	characteristic
470	#2311	C₂×D₄	1	1	yes	characteristic
471	#2311	C₂×D₄	1	1	yes	characteristic
472	#2311	C₂×D₄	1	1	yes	characteristic
473	#2311	C₂×D₄	1	1	yes	characteristic, complemented
474	#2309	C₂×D₄	1	1	yes	characteristic
475	#2309	C₂×D₄	1	1	yes	characteristic
476	#2309	C₂×D₄	1	1	yes	characteristic, complemented
477	#2309	C₂×D₄	1	1	yes	characteristic, complemented
478	#2309	C₂×D₄	1	1	yes	characteristic, complemented
479	#2309	C₂⁴	1	1	yes	characteristic
480	#2308	C₂×D₄	1	1	yes	characteristic
481	#2308	C₂×D₄	1	1	yes	characteristic
482	#2308	C₂×D₄	1	1	yes	characteristic
483	#2308	C₂×D₄	1	1	yes	characteristic, complemented
484	#2308	C₂×D₄	1	1	yes	characteristic, complemented
485	#2308	C₂⁴	1	1	yes	characteristic
486	#2297	C₂×D₄	1	1	yes	characteristic
487	#2297	C₂×D₄	1	1	yes	characteristic
488	#2297	C₂×D₄	1	1	yes	characteristic
489	#2297	C₂×D₄	1	1	yes	characteristic
490	#2297	C₂×D₄	1	1	yes	characteristic
491	#2297	C₂×D₄	1	1	yes	characteristic, complemented
492	#2296	C₂×D₄	1	1	yes	characteristic, complemented
493	#2296	C₂×D₄	1	1	yes	characteristic, complemented
494	C₂×#390	C₂×D₄	1	1	yes	characteristic
495	C₂×#390	C₂×D₄	1	1	yes	characteristic
496	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
497	C₂×#390	C₂⁴	1	1	yes	characteristic
498	C₂×#386	C₂×D₄	1	1	yes	characteristic
499	C₂×#386	C₂×D₄	1	1	yes	characteristic
500	C₂×#386	C₂×D₄	1	1	yes	characteristic
501	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
502	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
503	C₂×#386	C₂⁴	1	1	yes	characteristic
504	#2285	C₂×D₄	1	1	yes	characteristic, complemented
505	#2280	C₂×D₄	1	1	yes	characteristic, complemented
506	C₂×#380	C₂×D₄	1	1	yes	characteristic, complemented
507	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
508	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
509	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
510	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
511	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
512	#2121	C₂×D₄	1	8	yes	complemented
513	C₂×AΣL(1,𝔽₁₆)	C₂×D₄	1	8	yes	complemented
514	#1913	C₂×D₄	1	8	yes	complemented
515	#1889	C₂×D₄	1	8	yes	complemented
516	C₂⁶	#120	1	1	yes	characteristic
517	C₂⁶	#120	1	1	yes	characteristic
518	C₂⁶	#120	1	1	yes	characteristic, complemented
519	C₂⁶	C₂²×D₄	1	1	yes	characteristic
520	C₂⁶	C₂²×D₄	1	1	yes	characteristic
521	C₂⁶	C₂²×D₄	1	1	yes	characteristic
522	C₂⁶	C₂²×D₄	1	1	yes	characteristic
523	C₂⁶	C₂²×D₄	1	1	yes	characteristic
524	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
525	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
526	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
527	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
528	C₂×H(5,𝔽₂)	C₂×#41	1	2	yes	—
529	C₂×H(5,𝔽₂)	H(5,𝔽₂)	1	2	yes	—
530	C₂×H(5,𝔽₂)	H(5,𝔽₂)	1	2	yes	—
531	C₂×H(5,𝔽₂)	H(5,𝔽₂)	1	2	yes	—
532	C₂×H(5,𝔽₂)	H(5,𝔽₂)	1	2	yes	—
533	C₂²×#41	#120	1	1	yes	characteristic, complemented
534	C₂²×#41	#120	1	1	yes	characteristic, complemented
535	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
536	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
537	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
538	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
539	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
540	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
541	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
542	C₂³×D₄	#120	1	1	yes	characteristic
543	C₂³×D₄	#120	1	1	yes	characteristic
544	C₂³×D₄	#120	1	1	yes	characteristic
545	C₂³×D₄	#120	1	1	yes	characteristic
546	C₂³×D₄	#120	1	4	yes	—
547	C₂³×D₄	#120	1	1	yes	characteristic, complemented
548	C₂³×D₄	#120	1	1	yes	characteristic, complemented
549	C₂³×D₄	#120	1	1	yes	characteristic, complemented
550	C₂³×D₄	#120	1	1	yes	characteristic, complemented
551	C₂³×D₄	#121	1	4	yes	—
552	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
553	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
554	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
555	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
556	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
557	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
558	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
559	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
560	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
561	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
562	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
563	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
564	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
565	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
566	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
567	C₂³×D₄	C₂⁵	1	1	yes	characteristic
568	C₂⁴×C₄	#120	1	1	yes	characteristic
569	C₂⁴×C₄	#120	1	1	yes	characteristic
570	C₂⁴×C₄	#120	1	1	yes	characteristic, complemented
571	C₂⁴×C₄	#120	1	1	yes	characteristic, complemented
572	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
573	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
574	#535	#120	1	4	yes	—
575	#535	#121	1	4	yes	—
576	#535	#121	1	4	yes	—
577	#535	#127	1	4	yes	—
578	#534	#120	1	4	yes	—
579	#534	#120	1	4	yes	—
580	#534	#121	1	4	yes	—
581	#534	#121	1	4	yes	—
582	#534	#121	1	4	yes	—
583	#534	#127	1	4	yes	—
584	#534	C₂²×D₄	1	2	yes	—
585	#534	C₂²×D₄	1	2	yes	—
586	#534	C₂²×D₄	1	2	yes	—
587	#534	C₂×#41	1	2	yes	—
588	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic, complemented
589	C₂×#127	#120	1	1	yes	characteristic, complemented
590	C₂×#127	#120	1	1	yes	characteristic, complemented
591	C₂×#127	#120	1	1	yes	characteristic, complemented
592	C₂×#127	C₂²×D₄	1	1	yes	characteristic
593	C₂×#127	C₂²×D₄	1	1	yes	characteristic
594	C₂×#127	C₂²×D₄	1	1	yes	characteristic
595	C₂×#127	C₂²×D₄	1	1	yes	characteristic
596	C₂×#127	C₂²×D₄	1	1	yes	characteristic
597	C₂×#127	C₂²×D₄	1	1	yes	characteristic
598	C₂×#124	#120	1	1	yes	characteristic, complemented
599	C₂×#124	#120	1	1	yes	characteristic, complemented
600	C₂×#124	#120	1	1	yes	characteristic, complemented
601	C₂×#124	#120	1	1	yes	characteristic, complemented
602	C₂×#124	C₂²×D₄	1	1	yes	characteristic
603	C₂×#124	C₂²×D₄	1	1	yes	characteristic
604	#525	#120	1	4	yes	—
605	#525	#121	1	4	yes	—
606	#525	#121	1	4	yes	—
607	#525	#127	1	4	yes	—
608	C₂×#123	#120	1	1	yes	characteristic
609	C₂×#123	#120	1	1	yes	characteristic
610	C₂×#123	#120	1	1	yes	characteristic
611	C₂×#123	#120	1	1	yes	characteristic
612	C₂×#123	#120	1	1	yes	characteristic
613	C₂×#123	#120	1	1	yes	characteristic
614	C₂×#123	#120	1	1	yes	characteristic
615	C₂×#123	#120	1	1	yes	characteristic
616	C₂×#123	#120	1	1	yes	characteristic, complemented
617	C₂×#123	#120	1	1	yes	characteristic, complemented
618	C₂×#123	C₂²×D₄	1	1	yes	characteristic
619	C₂×#123	C₂²×D₄	1	1	yes	characteristic
620	C₂×#123	C₂²×D₄	1	1	yes	characteristic
621	C₂×#123	C₂²×D₄	1	1	yes	characteristic
622	C₂×#123	C₂²×D₄	1	1	yes	characteristic
623	C₂×#123	C₂²×D₄	1	1	yes	characteristic
624	C₂×#120	#120	1	1	yes	characteristic
625	C₂×#120	#120	1	1	yes	characteristic
626	C₂×#120	#120	1	1	yes	characteristic
627	C₂×#120	#120	1	1	yes	characteristic
628	C₂×#120	#120	1	1	yes	characteristic
629	C₂×#120	#120	1	1	yes	characteristic
630	C₂×#120	#120	1	1	yes	characteristic
631	C₂×#120	#120	1	1	yes	characteristic
632	C₂×#120	#120	1	1	yes	characteristic
633	C₂×#120	#120	1	1	yes	characteristic
634	C₂×#120	#120	1	1	yes	characteristic
635	C₂×#120	#120	1	1	yes	characteristic
636	C₂×#120	#120	1	1	yes	characteristic
637	C₂×#120	#120	1	1	yes	characteristic
638	C₂×#120	#120	1	1	yes	characteristic
639	C₂×#120	#120	1	1	yes	characteristic
640	C₂×#120	#120	1	1	yes	characteristic
641	C₂×#120	#120	1	1	yes	characteristic
642	C₂×#120	#120	1	1	yes	characteristic
643	C₂×#120	#120	1	1	yes	characteristic
644	C₂×#120	#120	1	1	yes	characteristic
645	C₂×#120	#120	1	1	yes	characteristic
646	C₂×#120	#120	1	1	yes	characteristic
647	C₂×#120	#120	1	1	yes	characteristic
648	C₂×#120	#120	1	4	yes	—
649	C₂×#120	#120	1	4	yes	—
650	C₂×#120	#120	1	1	yes	characteristic, complemented
651	C₂×#120	#120	1	1	yes	characteristic, complemented
652	C₂×#120	#120	1	1	yes	characteristic, complemented
653	C₂×#120	#120	1	1	yes	characteristic, complemented
654	C₂×#120	#120	1	1	yes	characteristic, complemented
655	C₂×#120	#120	1	1	yes	characteristic, complemented
656	C₂×#120	#121	1	4	yes	—
657	C₂×#120	#121	1	4	yes	—
658	C₂×#120	#121	1	4	yes	—
659	C₂×#120	#127	1	4	yes	—
660	C₂×#120	C₂²×D₄	1	1	yes	characteristic
661	C₂×#120	C₂²×D₄	1	1	yes	characteristic
662	C₂×#120	C₂²×D₄	1	1	yes	characteristic
663	C₂×#120	C₂²×D₄	1	1	yes	characteristic
664	C₂×#120	C₂²×D₄	1	1	yes	characteristic
665	C₂×#120	C₂²×D₄	1	1	yes	characteristic
666	C₂×#120	C₂²×D₄	1	1	yes	characteristic
667	C₂×#120	C₂²×D₄	1	1	yes	characteristic
668	C₂×#120	C₂²×D₄	1	1	yes	characteristic
669	C₂×#120	C₂²×D₄	1	1	yes	characteristic
670	C₂×#120	C₂²×D₄	1	1	yes	characteristic
671	C₂×#120	C₂²×D₄	1	1	yes	characteristic
672	C₂×#120	C₂²×D₄	1	1	yes	characteristic
673	C₂×#120	C₂²×D₄	1	1	yes	characteristic
674	C₂×#120	C₂²×D₄	1	1	yes	characteristic
675	C₂×#120	C₂²×D₄	1	2	yes	—
676	C₂×#120	C₂²×D₄	1	1	yes	characteristic
677	C₂×#120	C₂²×D₄	1	1	yes	characteristic
678	C₂×#120	C₂²×D₄	1	1	yes	characteristic
679	C₂×#120	C₂²×D₄	1	2	yes	—
680	C₂×#120	C₂²×D₄	1	2	yes	—
681	C₂×#120	C₂×#41	1	2	yes	—
682	#518	#120	1	4	yes	—
683	#518	#121	1	4	yes	—
684	#518	C₂²×D₄	1	4	yes	—
685	C₂×#117	#120	1	1	yes	characteristic
686	C₂×#117	#120	1	1	yes	characteristic
687	C₂×#117	#120	1	1	yes	characteristic
688	C₂×#117	#120	1	1	yes	characteristic
689	C₂×#117	#120	1	1	yes	characteristic, complemented
690	C₂×#117	#120	1	1	yes	characteristic, complemented
691	C₂×#117	#120	1	1	yes	characteristic, complemented
692	C₂×#117	#120	1	1	yes	characteristic, complemented
693	C₂×#117	#120	1	1	yes	characteristic, complemented
694	C₂×#117	#120	1	1	yes	characteristic, complemented
695	C₂×#117	#120	1	1	yes	characteristic, complemented
696	C₂×#117	#120	1	1	yes	characteristic, complemented
697	C₂×#117	#120	1	1	yes	characteristic, complemented
698	C₂×#117	#120	1	1	yes	characteristic, complemented
699	C₂×#117	C₂²×D₄	1	1	yes	characteristic
700	C₂×#117	C₂²×D₄	1	1	yes	characteristic
701	C₂×#117	C₂²×D₄	1	1	yes	characteristic
702	C₂×#117	C₂²×D₄	1	1	yes	characteristic
703	C₂×#117	C₂²×D₄	1	1	yes	characteristic
704	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic, complemented
705	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic, complemented
706	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic, complemented
707	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
708	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
709	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
710	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
711	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
712	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
713	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
714	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
715	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
716	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
717	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
718	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
719	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
720	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
721	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
722	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
723	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
724	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
725	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
726	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
727	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
728	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
729	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
730	C₂²×C₄²	#120	1	1	yes	characteristic, complemented
731	C₂²×C₄²	#120	1	1	yes	characteristic, complemented
732	C₂²×C₄²	#120	1	1	yes	characteristic, complemented
733	C₂²×C₄²	#120	1	1	yes	characteristic, complemented
734	C₂²×C₄²	#120	1	1	yes	characteristic, complemented
735	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
736	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
737	C₂×#100	C₂²×D₄	1	4	yes	—
738	C₂×#99	C₂²×D₄	1	4	yes	—
739	C₂×#99	C₂²×D₄	1	4	yes	—
740	C₂×#99	C₂²×D₄	1	4	yes	—
741	#391	#120	1	1	yes	characteristic, complemented
742	#391	#120	1	1	yes	characteristic, complemented
743	#391	#120	1	1	yes	characteristic, complemented
744	#391	#120	1	1	yes	characteristic, complemented
745	#390	#120	1	1	yes	characteristic, complemented
746	#390	#120	1	1	yes	characteristic, complemented
747	#390	#120	1	1	yes	characteristic, complemented
748	#390	#120	1	1	yes	characteristic, complemented
749	#390	C₂²×D₄	1	1	yes	characteristic
750	#390	C₂²×D₄	1	1	yes	characteristic
751	#390	C₂²×D₄	1	1	yes	characteristic
752	#390	C₂²×D₄	1	1	yes	characteristic
753	#390	C₂²×D₄	1	1	yes	characteristic
754	#390	C₂²×D₄	1	1	yes	characteristic
755	#390	C₂²×D₄	1	1	yes	characteristic
756	#390	C₂²×D₄	1	1	yes	characteristic
757	#386	#120	1	1	yes	characteristic, complemented
758	#386	#120	1	1	yes	characteristic, complemented
759	#386	#120	1	1	yes	characteristic, complemented
760	#386	#120	1	1	yes	characteristic, complemented
761	#386	#120	1	1	yes	characteristic, complemented
762	#386	#120	1	1	yes	characteristic, complemented
763	#386	#120	1	1	yes	characteristic, complemented
764	#386	#120	1	1	yes	characteristic, complemented
765	#386	C₂²×D₄	1	1	yes	characteristic
766	#386	C₂²×D₄	1	1	yes	characteristic
767	#386	C₂²×D₄	1	1	yes	characteristic
768	#386	C₂²×D₄	1	1	yes	characteristic
769	#386	C₂²×D₄	1	1	yes	characteristic
770	#386	C₂²×D₄	1	1	yes	characteristic
771	#386	C₂²×D₄	1	1	yes	characteristic
772	#386	C₂²×D₄	1	1	yes	characteristic
773	C₂⁵	#392	1	4	yes	complemented
774	C₂⁵	C₂×#120	1	1	yes	characteristic
775	C₂⁵	C₂×#120	1	1	yes	characteristic
776	C₂⁵	C₂×#120	1	1	yes	characteristic
777	C₂⁵	C₂×#120	1	1	yes	characteristic
778	C₂⁵	C₂×#120	1	1	yes	characteristic
779	C₂⁵	C₂×#120	1	1	yes	characteristic
780	C₂⁵	C₂×#120	1	1	yes	characteristic
781	C₂⁵	C₂×#120	1	1	yes	characteristic
782	C₂⁵	C₂×#120	1	1	yes	characteristic
783	C₂⁵	C₂×#120	1	1	yes	characteristic
784	C₂⁵	C₂×#120	1	1	yes	characteristic
785	C₂⁵	C₂×#120	1	1	yes	characteristic
786	C₂⁵	C₂×#120	1	2	yes	—
787	C₂⁵	C₂×#120	1	1	yes	characteristic
788	C₂⁵	C₂×#120	1	1	yes	characteristic
789	C₂⁵	C₂×#120	1	1	yes	characteristic
790	C₂⁵	C₂×#120	1	1	yes	characteristic
791	C₂⁵	C₂×#121	1	2	yes	—
792	C₂⁵	C₂³×D₄	1	1	yes	characteristic
793	C₂⁵	C₂³×D₄	1	1	yes	characteristic
794	C₂×#41	C₂×#120	1	2	yes	—
795	C₂×#41	C₂×#121	1	2	yes	—
796	C₂×#41	C₂×#121	1	2	yes	—
797	C₂×#41	C₂×#127	1	2	yes	—
798	C₂×#41	#534	1	2	yes	—
799	C₂×#41	#534	1	2	yes	—
800	C₂×#41	#535	1	2	yes	—
801	C₂×#41	#535	1	2	yes	—
802	C₂×#41	D₄²	1	2	yes	—
803	C₂×#41	D₄²	1	2	yes	—
804	C₂×#41	D₄²	1	2	yes	—
805	C₂×#41	D₄²	1	2	yes	—
806	C₂×#41	D₄²	1	2	yes	—
807	C₂×#41	D₄²	1	2	yes	—
808	C₂×#41	D₄²	1	2	yes	—
809	C₂×#41	D₄²	1	2	yes	—
810	C₂×#41	D₄²	1	2	yes	—
811	C₂×#41	D₄²	1	2	yes	—
812	C₂×#41	D₄²	1	2	yes	—
813	C₂×#41	D₄²	1	2	yes	—
814	C₂×#41	#546	1	2	yes	—
815	C₂×#41	#546	1	2	yes	—
816	C₂×#41	#546	1	2	yes	—
817	C₂×#41	#546	1	2	yes	—
818	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
819	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
820	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
821	C₂²×D₄	#392	1	4	yes	complemented
822	C₂²×D₄	#392	1	4	yes	complemented
823	C₂²×D₄	C₂×#120	1	1	yes	characteristic
824	C₂²×D₄	C₂×#120	1	1	yes	characteristic
825	C₂²×D₄	C₂×#120	1	1	yes	characteristic
826	C₂²×D₄	C₂×#120	1	1	yes	characteristic
827	C₂²×D₄	C₂×#120	1	1	yes	characteristic
828	C₂²×D₄	C₂×#120	1	1	yes	characteristic
829	C₂²×D₄	C₂×#120	1	1	yes	characteristic
830	C₂²×D₄	C₂×#120	1	1	yes	characteristic
831	C₂²×D₄	C₂×#120	1	1	yes	characteristic
832	C₂²×D₄	C₂×#120	1	1	yes	characteristic
833	C₂²×D₄	C₂×#120	1	1	yes	characteristic
834	C₂²×D₄	C₂×#120	1	1	yes	characteristic
835	C₂²×D₄	C₂×#120	1	2	yes	—
836	C₂²×D₄	C₂×#120	1	2	yes	—
837	C₂²×D₄	C₂×#120	1	2	yes	—
838	C₂²×D₄	C₂×#120	1	2	yes	—
839	C₂²×D₄	C₂×#120	1	1	yes	characteristic
840	C₂²×D₄	C₂×#120	1	1	yes	characteristic
841	C₂²×D₄	C₂×#120	1	1	yes	characteristic
842	C₂²×D₄	C₂×#120	1	1	yes	characteristic
843	C₂²×D₄	C₂×#120	1	1	yes	characteristic
844	C₂²×D₄	C₂×#121	1	2	yes	—
845	C₂²×D₄	C₂×#121	1	2	yes	—
846	C₂²×D₄	C₂×#121	1	2	yes	—
847	C₂²×D₄	C₂×#121	1	2	yes	—
848	C₂²×D₄	C₂×#121	1	2	yes	—
849	C₂²×D₄	C₂×#127	1	2	yes	—
850	C₂²×D₄	#534	1	2	yes	—
851	C₂²×D₄	#534	1	2	yes	—
852	C₂²×D₄	#534	1	2	yes	—
853	C₂²×D₄	#534	1	2	yes	—
854	C₂²×D₄	#534	1	2	yes	—
855	C₂²×D₄	#534	1	2	yes	—
856	C₂²×D₄	#535	1	2	yes	—
857	C₂²×D₄	#535	1	2	yes	—
858	C₂²×D₄	D₄²	1	2	yes	—
859	C₂²×D₄	D₄²	1	2	yes	—
860	C₂²×D₄	D₄²	1	2	yes	—
861	C₂²×D₄	D₄²	1	2	yes	—
862	C₂²×D₄	D₄²	1	2	yes	—
863	C₂²×D₄	D₄²	1	2	yes	—
864	C₂²×D₄	D₄²	1	2	yes	—
865	C₂²×D₄	D₄²	1	2	yes	—
866	C₂²×D₄	D₄²	1	2	yes	—
867	C₂²×D₄	D₄²	1	2	yes	—
868	C₂²×D₄	D₄²	1	2	yes	—
869	C₂²×D₄	D₄²	1	2	yes	—
870	C₂²×D₄	#546	1	2	yes	—
871	C₂²×D₄	#546	1	2	yes	—
872	C₂²×D₄	#546	1	2	yes	—
873	C₂²×D₄	#546	1	2	yes	—
874	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
875	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
876	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
877	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
878	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
879	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
880	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
881	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
882	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
883	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
884	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
885	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
886	C₂³×C₄	#392	1	4	yes	complemented
887	C₂³×C₄	C₂×#120	1	1	yes	characteristic
888	C₂³×C₄	C₂×#120	1	1	yes	characteristic
889	C₂³×C₄	C₂×#120	1	1	yes	characteristic
890	C₂³×C₄	C₂×#120	1	1	yes	characteristic
891	C₂³×C₄	C₂×#120	1	1	yes	characteristic
892	C₂³×C₄	C₂×#120	1	1	yes	characteristic
893	C₂³×C₄	C₂×#120	1	1	yes	characteristic
894	C₂³×C₄	C₂×#120	1	1	yes	characteristic
895	C₂³×C₄	C₂×#120	1	1	yes	characteristic
896	C₂³×C₄	C₂×#120	1	1	yes	characteristic
897	C₂³×C₄	C₂×#120	1	1	yes	characteristic
898	C₂³×C₄	C₂×#120	1	1	yes	characteristic
899	C₂³×C₄	C₂×#120	1	1	yes	characteristic
900	C₂³×C₄	C₂×#120	1	1	yes	characteristic
901	C₂³×C₄	C₂×#120	1	1	yes	characteristic
902	C₂³×C₄	C₂×#120	1	1	yes	characteristic
903	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
904	#123	#392	1	4	yes	complemented
905	#123	#392	1	4	yes	complemented
906	#123	C₂×#120	1	2	yes	—
907	#123	C₂×#121	1	2	yes	—
908	#123	C₂×#121	1	2	yes	—
909	#123	C₂×#127	1	2	yes	—
910	#120	#392	1	4	yes	complemented
911	#120	#392	1	4	yes	complemented
912	#120	#392	1	4	yes	complemented
913	#120	#392	1	4	yes	complemented
914	#120	#392	1	4	yes	complemented
915	#120	#392	1	4	yes	complemented
916	#120	C₂×#120	1	2	yes	—
917	#120	C₂×#120	1	2	yes	—
918	#120	C₂×#120	1	2	yes	—
919	#120	C₂×#121	1	2	yes	—
920	#120	C₂×#121	1	2	yes	—
921	#120	C₂×#121	1	2	yes	—
922	#120	C₂×#121	1	2	yes	—
923	#120	C₂×#121	1	2	yes	—
924	#120	C₂×#121	1	2	yes	—
925	#120	C₂×#127	1	2	yes	—
926	#120	C₂×#127	1	2	yes	—
927	#120	C₂×#127	1	2	yes	—
928	#117	#392	1	4	yes	complemented
929	#117	#392	1	4	yes	complemented
930	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
931	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
932	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
933	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
934	C₂×C₂²⋊C₄	#392	1	4	yes	complemented
935	C₂×C₂²⋊C₄	#392	1	4	yes	complemented
936	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
937	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
938	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
939	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
940	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
941	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
942	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
943	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
944	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
945	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
946	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
947	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
948	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
949	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
950	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
951	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
952	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
953	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
954	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
955	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
956	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
957	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
958	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
959	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
960	C₂×C₄²	C₂×#120	1	1	yes	characteristic
961	C₂×C₄²	C₂×#120	1	1	yes	characteristic
962	C₂×C₄²	C₂×#120	1	1	yes	characteristic
963	C₂×C₄²	C₂×#120	1	1	yes	characteristic
964	C₂×C₄²	C₂×#120	1	1	yes	characteristic
965	C₂×C₄²	C₂×#120	1	1	yes	characteristic
966	C₂×C₄²	C₂×#120	1	1	yes	characteristic
967	C₂×C₄²	C₂×#120	1	1	yes	characteristic
968	C₂⁴	C₂×#392	1	2	yes	—
969	C₂⁴	C₂×#392	1	2	yes	—
970	C₂⁴	C₂×#392	1	2	yes	—
971	C₂⁴	C₂×#392	1	2	yes	—
972	C₂⁴	#2403	1	2	yes	—
973	C₂⁴	#2403	1	2	yes	—
974	C₂⁴	#2408	1	2	yes	—
975	C₂⁴	#2410	1	2	yes	—
976	C₂⁴	#2410	1	2	yes	—
977	C₂⁴	#2433	1	2	yes	—
978	C₂⁴	#2613	1	2	yes	—
979	C₂⁴	#2846	1	1	yes	characteristic
980	C₂⁴	#2846	1	1	yes	characteristic
981	C₂⁴	#2846	1	1	yes	characteristic
982	C₂⁴	#2846	1	1	yes	characteristic
983	C₂⁴	C₂²×#120	1	1	yes	characteristic
984	C₂⁴	C₂²×#120	1	1	yes	characteristic
985	C₂⁴	C₂²×#120	1	1	yes	characteristic
986	C₂⁴	C₂²×#120	1	1	yes	characteristic
987	C₂⁴	C₂²×#120	1	1	yes	characteristic
988	C₂⁴	C₂²×#120	1	1	yes	characteristic
989	C₂⁴	C₂²×#121	1	1	yes	characteristic
990	C₂⁴	C₂×#534	1	1	yes	characteristic
991	C₂⁴	C₂×#534	1	1	yes	characteristic
992	C₂⁴	C₂×D₄²	1	1	yes	characteristic
993	C₂⁴	C₂×D₄²	1	1	yes	characteristic
994	C₂⁴	C₂×D₄²	1	1	yes	characteristic
995	C₂⁴	C₂×#546	1	1	yes	characteristic
996	C₂×Q₈	#2403	1	2	yes	—
997	C₂×Q₈	#2408	1	2	yes	—
998	C₂×Q₈	#2410	1	2	yes	—
999	C₂×Q₈	#2433	1	2	yes	—
1000	C₂×D₄	C₂×#392	1	2	yes	—
1001	C₂×D₄	C₂×#392	1	2	yes	—
1002	C₂×D₄	#2403	1	2	yes	—
1003	C₂×D₄	#2403	1	2	yes	—
1004	C₂×D₄	#2403	1	2	yes	—
1005	C₂×D₄	#2403	1	2	yes	—
1006	C₂×D₄	#2403	1	2	yes	—
1007	C₂×D₄	#2403	1	2	yes	—
1008	C₂×D₄	#2403	1	2	yes	—
1009	C₂×D₄	#2403	1	2	yes	—
1010	C₂×D₄	#2403	1	2	yes	—
1011	C₂×D₄	#2408	1	2	yes	—
1012	C₂×D₄	#2408	1	2	yes	—
1013	C₂×D₄	#2408	1	2	yes	—
1014	C₂×D₄	#2410	1	2	yes	—
1015	C₂×D₄	#2410	1	2	yes	—
1016	C₂×D₄	#2410	1	2	yes	—
1017	C₂×D₄	#2410	1	2	yes	—
1018	C₂×D₄	#2410	1	2	yes	—
1019	C₂×D₄	#2410	1	2	yes	—
1020	C₂×D₄	#2410	1	2	yes	—
1021	C₂×D₄	#2410	1	2	yes	—
1022	C₂×D₄	#2410	1	2	yes	—
1023	C₂×D₄	#2433	1	2	yes	—
1024	C₂×D₄	#2433	1	2	yes	—
1025	C₂×D₄	#2433	1	2	yes	—
1026	C₂×D₄	#2613	1	2	yes	—
1027	C₂×D₄	#2613	1	2	yes	—
1028	C₂×D₄	C₂²×#120	1	1	yes	characteristic
1029	C₂×D₄	C₂²×#121	1	1	yes	characteristic
1030	C₂×D₄	C₂²×#121	1	1	yes	characteristic
1031	C₂×D₄	C₂²×#127	1	1	yes	characteristic
1032	C₂×D₄	C₂×#534	1	1	yes	characteristic
1033	C₂×D₄	C₂×#534	1	1	yes	characteristic
1034	C₂×D₄	C₂×#535	1	1	yes	characteristic
1035	C₂×D₄	C₂×#535	1	1	yes	characteristic
1036	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
1037	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
1038	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
1039	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
1040	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
1041	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
1042	C₂×D₄	C₂×#546	1	1	yes	characteristic
1043	C₂×D₄	C₂×#546	1	1	yes	characteristic
1044	C₂²×C₄	C₂×#392	1	2	yes	—
1045	C₂²×C₄	C₂×#392	1	2	yes	—
1046	C₂²×C₄	#2403	1	2	yes	—
1047	C₂²×C₄	#2403	1	2	yes	—
1048	C₂²×C₄	#2403	1	2	yes	—
1049	C₂²×C₄	#2403	1	2	yes	—
1050	C₂²×C₄	#2408	1	2	yes	—
1051	C₂²×C₄	#2408	1	2	yes	—
1052	C₂²×C₄	#2408	1	2	yes	—
1053	C₂²×C₄	#2410	1	2	yes	—
1054	C₂²×C₄	#2410	1	2	yes	—
1055	C₂²×C₄	#2410	1	2	yes	—
1056	C₂²×C₄	#2410	1	2	yes	—
1057	C₂²×C₄	#2433	1	2	yes	—
1058	C₂²×C₄	#2433	1	2	yes	—
1059	C₂²×C₄	#2433	1	2	yes	—
1060	C₂²×C₄	#2613	1	2	yes	—
1061	C₂²×C₄	#2846	1	1	yes	characteristic
1062	C₂²×C₄	#2846	1	1	yes	characteristic
1063	C₂²×C₄	#2846	1	1	yes	characteristic
1064	C₂²×C₄	#2846	1	1	yes	characteristic
1065	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
1066	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
1067	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
1068	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
1069	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
1070	C₂²×C₄	C₂×#546	1	1	yes	characteristic
1071	C₂²⋊C₄	C₂×#392	1	2	yes	—
1072	C₂²⋊C₄	C₂×#392	1	2	yes	—
1073	C₂²⋊C₄	C₂×#392	1	2	yes	—
1074	C₂²⋊C₄	C₂×#392	1	2	yes	—
1075	C₂³	#14715	1	2	yes	—
1076	C₂³	#14715	1	2	yes	—
1077	C₂³	#14715	1	2	yes	—
1078	C₂³	#14715	1	2	yes	—
1079	C₂³	C₂²×#392	1	1	yes	characteristic
1080	C₂³	C₂×#2613	1	1	yes	characteristic
1081	C₂³	C₂×#2403	1	1	yes	characteristic
1082	C₂³	C₂×#2403	1	1	yes	characteristic
1083	C₂³	C₂×#2403	1	1	yes	characteristic
1084	C₂³	C₂×#2410	1	1	yes	characteristic
1085	C₂³	C₂×#2410	1	1	yes	characteristic
1086	C₂³	C₂×#2410	1	1	yes	characteristic
1087	C₂³	C₂×#2408	1	1	yes	characteristic
1088	C₂³	C₂×#2433	1	1	yes	characteristic
1089	C₂³	C₂×#2846	1	1	yes	characteristic
1090	C₂³	#60399	1	2	yes	—
1091	C₂³	#60399	1	2	yes	—
1092	C₂×C₄	#14715	1	2	yes	—
1093	C₂×C₄	#14715	1	2	yes	—
1094	C₂×C₄	#14715	1	2	yes	—
1095	C₂×C₄	#14715	1	2	yes	—
1096	C₂×C₄	C₂×#2403	1	1	yes	characteristic
1097	C₂×C₄	C₂×#2410	1	1	yes	characteristic
1098	C₂×C₄	C₂×#2408	1	1	yes	characteristic
1099	C₂×C₄	C₂×#2433	1	1	yes	characteristic
1100	C₂²	C₂×#14715	1	1	yes	characteristic
1101	C₂²	#6437632	1	2	yes	—
1102	C₂²	#6437999	1	2	yes	—
1103	C₂²	#6628896	1	1	yes	characteristic
1104	C₂²	#6628896	1	1	yes	characteristic
1105	C₂	#72216366	1	1	yes	characteristic
1106	C₂	#72233206	1	1	yes	characteristic
1107	C₂	#72238078	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#6628896
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂×#3484 ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #72262377	C₂	semidirect
2. #72262332	C₂	semidirect
3. #72262306	C₂	semidirect
4. #72262251	C₂	semidirect
5. #72262227	C₂	semidirect
6. #72262193	C₂	semidirect
7. #72262125	C₂	semidirect
8. #72249497	C₂	semidirect
9. C₂×#493635	C₂	semidirect
10. #72237806	C₂	semidirect
11. #72234799	C₂	semidirect
12. #72234696	C₂	semidirect
13. #72234630	C₂	semidirect
14. C₂×#7622880	C₂	semidirect
15. #72233087	C₂	semidirect
16. #72233086	C₂	semidirect
17. #72232895	C₂	semidirect
18. #72232293	C₂	semidirect
19. #72231228	C₂	semidirect
20. #72225802	C₂	semidirect
21. C₂×#493474	C₂	semidirect
22. #72218099	C₂	semidirect
23. C₂×#6499874	C₂	semidirect
27. C₂×#60399	C₂²	semidirect
28. C₂×#60399	C₂²	semidirect
29. C₂×#60399	C₂²	semidirect
30. C₂×#60388	C₂²	semidirect
31. #7819710	C₂²	semidirect
32. #7819709	C₂²	semidirect
33. #7791097	C₂²	semidirect
34. #7785081	C₂²	semidirect
35. #7733246	C₂²	semidirect
36. #7733187	C₂²	semidirect
37. #7708349	C₂²	semidirect
38. C₂×#58990	C₂²	semidirect
44. C₂×#33557	C₂²	semidirect
45. C₂×#33551	C₂²	semidirect
46. C₂×#33551	C₂²	semidirect
47. C₂²×#2196	C₂²	semidirect
48. C₂×#33359	C₂²	semidirect
49. C₂×#33359	C₂²	semidirect
52. C₂×#33348	C₂²	semidirect
53. C₂×#33348	C₂²	semidirect
54. C₂×#33348	C₂²	semidirect
55. C₂×#33348	C₂²	semidirect
56. C₂×#23996	C₂²	semidirect
57. C₂×#23996	C₂²	semidirect
58. C₂×#23895	C₂²	semidirect
59. C₂×#23900	C₂²	semidirect
60. C₂×#21782	C₂²	semidirect
61. C₂×#21778	C₂²	semidirect
63. C₂×#21776	C₂²	semidirect
64. C₂×#21776	C₂²	semidirect
65. C₂×#21776	C₂²	semidirect
66. C₂×#21776	C₂²	semidirect
67. #6370747	C₂²	semidirect
68. #6370735	C₂²	semidirect
69. #498931	C₂²	semidirect
70. #498927	C₂²	semidirect
71. #498923	C₂²	semidirect
72. C₂×#13346	C₂²	semidirect
73. #498890	C₂²	semidirect
74. #498886	C₂²	semidirect
75. #498886	C₂²	semidirect
76. C₂×#13343	C₂²	semidirect
77. #494582	C₂²	semidirect
78. #494579	C₂²	semidirect
79. #494575	C₂²	semidirect
80. C₂×#13041	C₂²	semidirect
81. C₂×#12767	C₂²	semidirect
82. C₂×#12759	C₂²	semidirect
83. C₂×#12753	C₂²	semidirect
84. C₂×#12753	C₂²	semidirect
85. C₂×#12725	C₂²	semidirect
86. C₂×#12725	C₂²	semidirect
87. C₂×#12705	C₂²	semidirect
88. C₂×#12687	C₂²	semidirect
89. #492900	C₂²	semidirect
90. #492900	C₂²	semidirect
91. #492887	C₂²	semidirect
92. #492887	C₂²	semidirect
93. #405277	C₂²	semidirect
94. #405274	C₂²	semidirect
95. #405271	C₂²	semidirect
96. #405268	C₂²	semidirect
97. #394066	C₂²	semidirect
98. #394064	C₂²	semidirect
99. #393975	C₂²	semidirect
100. #393967	C₂²	semidirect
101. #355935	C₂²	semidirect
102. #355922	C₂²	semidirect
103. #147829	C₂²	semidirect
104. #147824	C₂²	semidirect
105. #147819	C₂²	semidirect
106. #147815	C₂²	semidirect
107. #147815	C₂²	semidirect
108. #147811	C₂²	semidirect
109. #147783	C₂²	semidirect
110. #147779	C₂²	semidirect
111. #147610	C₂²	semidirect
112. #147609	C₂²	semidirect
113. #147605	C₂²	semidirect
114. #147603	C₂²	semidirect
115. #147569	C₂²	semidirect
116. #147567	C₂²	semidirect
117. #147559	C₂²	semidirect
118. #147555	C₂²	semidirect
119. #146614	C₂²	semidirect
120. #146609	C₂²	semidirect
121. #146599	C₂²	semidirect
122. #146593	C₂²	semidirect
125. C₂×#3490	D₄	semidirect
126. C₂×#3490	D₄	semidirect
127. C₂×#3490	D₄	semidirect
128. C₂×#3490	D₄	semidirect
131. C₂×#3484	D₄	semidirect
132. C₂×#3484	D₄	semidirect
138. C₂×#3484	C₂³	semidirect
139. C₂×#3549	D₄	semidirect
140. C₂×#3543	D₄	semidirect
142. C₂×#3537	D₄	semidirect
143. C₂×#3537	D₄	semidirect
144. C₂×#3532	D₄	semidirect
145. C₂×#3532	D₄	semidirect
148. C₂×#3481	D₄	semidirect
149. C₂²×D₄²	D₄	semidirect
151. C₂³×#120	D₄	semidirect
152. C₂³×#120	D₄	semidirect
154. #60399	D₄	semidirect
157. C₂×#3026	C₂³	semidirect
160. C₂²×B(4,𝔽₂)	C₂³	semidirect
170. C₂×#2883	C₂³	semidirect
171. #52165	D₄	semidirect
172. #52163	D₄	semidirect
173. C₂×#2679	D₄	semidirect
175. C₂×#2669	D₄	semidirect
177. #37297	D₄	semidirect
178. #37297	D₄	semidirect
179. #37273	D₄	semidirect
180. #37269	D₄	semidirect
181. #37269	D₄	semidirect
182. #37269	D₄	semidirect
183. #37232	D₄	semidirect
185. #37129	D₄	semidirect
187. #36737	D₄	semidirect
189. #36714	D₄	semidirect
190. #36714	D₄	semidirect
193. #36702	D₄	semidirect
195. #35563	D₄	semidirect
198. #35533	D₄	semidirect
199. #35527	D₄	semidirect
200. #35512	D₄	semidirect
201. #35360	D₄	semidirect
203. #35350	D₄	semidirect
205. #35348	D₄	semidirect
206. #35348	D₄	semidirect
207. #35272	D₄	semidirect
208. #35254	D₄	semidirect
210. #34984	D₄	semidirect
211. #34980	D₄	semidirect
213. #34743	D₄	semidirect
214. #34742	D₄	semidirect
216. C₂×#2408	D₄	semidirect
217. C₂×#2403	D₄	semidirect
219. #34415	D₄	semidirect
220. #34411	D₄	semidirect
221. #34408	D₄	semidirect
223. #34407	D₄	semidirect
225. #34360	D₄	semidirect
226. #34356	D₄	semidirect
230. #34152	D₄	semidirect
231. C₂×#2358	D₄	semidirect
237. #33348	D₄	semidirect
242. C₂×#2121	C₂³	semidirect
243. C₂×#2121	C₂³	semidirect
248. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
249. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
250. #21776	D₄	semidirect
253. C₂×#1913	C₂³	semidirect
257. C₂×#1889	C₂³	semidirect
259. C₂×#1829	C₂³	semidirect
260. C₂×#1828	C₂³	semidirect
261. C₂×#1828	C₂³	semidirect
262. #20616	C₂³	semidirect
263. C₂×#1792	C₂³	semidirect
264. #20609	C₂³	semidirect
265. C₂×#1790	C₂³	semidirect
266. C₂×#1783	C₂³	semidirect
267. C₂×#1781	C₂³	semidirect
268. C₂×#1781	C₂³	semidirect
269. #12582	C₂³	semidirect
270. #12582	C₂³	semidirect
271. C₂×#1393	C₂³	semidirect
272. C₂×#1393	C₂³	semidirect
273. #12574	C₂³	semidirect
274. #12574	C₂³	semidirect
275. C₂×#1390	C₂³	semidirect
276. C₂×#1390	C₂³	semidirect
277. #10754	C₂³	semidirect
278. #10749	C₂³	semidirect
279. #10745	C₂³	semidirect
280. #10740	C₂³	semidirect
281. C₂⁷	C₂×D₄	semidirect
282. H(7,𝔽₂)	C₂×D₄	semidirect
284. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
290. C₂⁴×D₄	C₂×D₄	semidirect
292. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
293. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
294. C₂×#560	C₂×D₄	semidirect
295. C₂×#560	C₂×D₄	semidirect
296. C₂×#560	C₂×D₄	semidirect
297. C₂×#560	C₂×D₄	semidirect
302. C₂×#559	C₂×D₄	semidirect
303. C₂×#551	C₂×D₄	semidirect
304. C₂×#551	C₂×D₄	semidirect
305. C₂×D₄²	C₂×D₄	semidirect
306. C₂×D₄²	C₂×D₄	semidirect
307. C₂×D₄²	C₂×D₄	semidirect
308. C₂×D₄²	C₂×D₄	semidirect
309. C₂×D₄²	C₂×D₄	semidirect
310. C₂×D₄²	C₂×D₄	semidirect
311. C₂×D₄²	C₂×D₄	semidirect
312. C₂×#543	C₂×D₄	semidirect
313. C₂×#543	C₂×D₄	semidirect
327. C₂×#535	C₂×D₄	semidirect
342. C₂×#534	C₂×D₄	semidirect
351. C₂²×#127	C₂×D₄	semidirect
361. C₂×#525	C₂×D₄	semidirect
362. C₂²×#121	C₂×D₄	semidirect
376. C₂²×#120	C₂×D₄	semidirect
377. C₂²×#120	C₂×D₄	semidirect
378. C₂²×#120	C₂×D₄	semidirect
379. C₂²×#120	C₂×D₄	semidirect
380. C₂²×#120	C₂×D₄	semidirect
381. C₂²×#120	C₂×D₄	semidirect
382. C₂²×#120	C₂×D₄	semidirect
383. C₂²×#120	C₂×D₄	semidirect
392. C₂×#518	C₂×D₄	semidirect
393. C₂×#518	C₂×D₄	semidirect
394. C₂×#518	C₂×D₄	semidirect
400. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
401. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
402. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
403. #3026	C₂×D₄	semidirect
404. C₂×B(4,𝔽₂)	C₂×D₄	semidirect
405. #2888	C₂×D₄	semidirect
408. #2883	C₂×D₄	semidirect
409. #2883	C₂×D₄	semidirect
410. #2883	C₂×D₄	semidirect
411. #2883	C₂×D₄	semidirect
416. #2724	C₂×D₄	semidirect
417. #2717	C₂×D₄	semidirect
418. #2709	C₂×D₄	semidirect
419. #2709	C₂×D₄	semidirect
420. #2709	C₂×D₄	semidirect
421. #2697	C₂×D₄	semidirect
422. #2697	C₂×D₄	semidirect
423. #2697	C₂×D₄	semidirect
424. #2697	C₂×D₄	semidirect
425. #2697	C₂×D₄	semidirect
426. #2697	C₂×D₄	semidirect
427. #2684	C₂×D₄	semidirect
428. #2684	C₂×D₄	semidirect
429. #2684	C₂×D₄	semidirect
430. #2679	C₂×D₄	semidirect
431. #2679	C₂×D₄	semidirect
432. #2679	C₂×D₄	semidirect
433. #2679	C₂×D₄	semidirect
434. #2679	C₂×D₄	semidirect
435. #2679	C₂×D₄	semidirect
436. #2679	C₂×D₄	semidirect
437. #2679	C₂×D₄	semidirect
438. #2679	C₂×D₄	semidirect
439. #2669	C₂×D₄	semidirect
440. #2669	C₂×D₄	semidirect
441. #2669	C₂×D₄	semidirect
442. #2669	C₂×D₄	semidirect
443. #2669	C₂×D₄	semidirect
444. #2669	C₂×D₄	semidirect
445. #2669	C₂×D₄	semidirect
446. #2669	C₂×D₄	semidirect
447. #2669	C₂×D₄	semidirect
448. #2376	C₂×D₄	semidirect
449. #2376	C₂×D₄	semidirect
450. #2375	C₂×D₄	semidirect
451. #2375	C₂×D₄	semidirect
452. #2375	C₂×D₄	semidirect
453. #2375	C₂×D₄	semidirect
454. #2374	C₂×D₄	semidirect
455. #2374	C₂×D₄	semidirect
456. #2358	C₂×D₄	semidirect
457. #2358	C₂×D₄	semidirect
458. #2358	C₂×D₄	semidirect
459. #2358	C₂×D₄	semidirect
460. #2358	C₂×D₄	semidirect
461. #2358	C₂×D₄	semidirect
462. #2358	C₂×D₄	semidirect
463. #2358	C₂×D₄	semidirect
464. #2316	C₂×D₄	semidirect
465. #2315	C₂×D₄	semidirect
466. #2315	C₂×D₄	semidirect
467. #2315	C₂×D₄	semidirect
473. #2311	C₂×D₄	semidirect
476. #2309	C₂×D₄	semidirect
477. #2309	C₂×D₄	semidirect
478. #2309	C₂×D₄	semidirect
483. #2308	C₂×D₄	semidirect
484. #2308	C₂×D₄	semidirect
491. #2297	C₂×D₄	semidirect
492. #2296	C₂×D₄	semidirect
493. #2296	C₂×D₄	semidirect
496. C₂×#390	C₂×D₄	semidirect
501. C₂×#386	C₂×D₄	semidirect
502. C₂×#386	C₂×D₄	semidirect
504. #2285	C₂×D₄	semidirect
505. #2280	C₂×D₄	semidirect
506. C₂×#380	C₂×D₄	semidirect
507. C₂×#379	C₂×D₄	semidirect
508. C₂×#379	C₂×D₄	semidirect
509. C₂×#379	C₂×D₄	semidirect
510. C₂×#379	C₂×D₄	semidirect
511. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
512. #2121	C₂×D₄	semidirect
513. C₂×AΣL(1,𝔽₁₆)	C₂×D₄	semidirect
514. #1913	C₂×D₄	semidirect
515. #1889	C₂×D₄	semidirect
518. C₂⁶	#120	semidirect
533. C₂²×#41	#120	semidirect
534. C₂²×#41	#120	semidirect
547. C₂³×D₄	#120	semidirect
548. C₂³×D₄	#120	semidirect
549. C₂³×D₄	#120	semidirect
550. C₂³×D₄	#120	semidirect
570. C₂⁴×C₄	#120	semidirect
571. C₂⁴×C₄	#120	semidirect
588. C₂×C₄⋊Q₈	#120	semidirect
589. C₂×#127	#120	semidirect
590. C₂×#127	#120	semidirect
591. C₂×#127	#120	semidirect
598. C₂×#124	#120	semidirect
599. C₂×#124	#120	semidirect
600. C₂×#124	#120	semidirect
601. C₂×#124	#120	semidirect
616. C₂×#123	#120	semidirect
617. C₂×#123	#120	semidirect
650. C₂×#120	#120	semidirect
651. C₂×#120	#120	semidirect
652. C₂×#120	#120	semidirect
653. C₂×#120	#120	semidirect
654. C₂×#120	#120	semidirect
655. C₂×#120	#120	semidirect
689. C₂×#117	#120	semidirect
690. C₂×#117	#120	semidirect
691. C₂×#117	#120	semidirect
692. C₂×#117	#120	semidirect
693. C₂×#117	#120	semidirect
694. C₂×#117	#120	semidirect
695. C₂×#117	#120	semidirect
696. C₂×#117	#120	semidirect
697. C₂×#117	#120	semidirect
698. C₂×#117	#120	semidirect
704. C₂²×C₄⋊C₄	#120	semidirect
705. C₂²×C₄⋊C₄	#120	semidirect
706. C₂²×C₄⋊C₄	#120	semidirect
712. C₂²×C₂²⋊C₄	#120	semidirect
713. C₂²×C₂²⋊C₄	#120	semidirect
714. C₂²×C₂²⋊C₄	#120	semidirect
715. C₂²×C₂²⋊C₄	#120	semidirect
716. C₂²×C₂²⋊C₄	#120	semidirect
730. C₂²×C₄²	#120	semidirect
731. C₂²×C₄²	#120	semidirect
732. C₂²×C₄²	#120	semidirect
733. C₂²×C₄²	#120	semidirect
734. C₂²×C₄²	#120	semidirect
741. #391	#120	semidirect
742. #391	#120	semidirect
743. #391	#120	semidirect
744. #391	#120	semidirect
745. #390	#120	semidirect
746. #390	#120	semidirect
747. #390	#120	semidirect
748. #390	#120	semidirect
757. #386	#120	semidirect
758. #386	#120	semidirect
759. #386	#120	semidirect
760. #386	#120	semidirect
761. #386	#120	semidirect
762. #386	#120	semidirect
763. #386	#120	semidirect
764. #386	#120	semidirect
773. C₂⁵	#392	semidirect
821. C₂²×D₄	#392	semidirect
822. C₂²×D₄	#392	semidirect
886. C₂³×C₄	#392	semidirect
904. #123	#392	semidirect
905. #123	#392	semidirect
910. #120	#392	semidirect
911. #120	#392	semidirect
912. #120	#392	semidirect
913. #120	#392	semidirect
914. #120	#392	semidirect
915. #120	#392	semidirect
928. #117	#392	semidirect
929. #117	#392	semidirect
934. C₂×C₂²⋊C₄	#392	semidirect
935. C₂×C₂²⋊C₄	#392	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#72262377	2
#72262332	2
#72262306	2
#72262251	2
#72262227	2
#72262193	2
#72262125	2
#72249497	2
C₂×#493635	2
#72237806	2
#72234799	2
#72234696	2
#72234630	2
C₂×#7622880	2
#72233087	2
#72233086	2
#72232895	2
#72232293	2
#72231228	2
#72225802	2
C₂×#493474	2
#72218099	2
C₂×#6499874	2