Subgroups — #72262374

Order 2048.

At least 30190 conjugacy classes of subgroups; only the 1250 normal subgroups are shown.

The subgroup lattice has 928 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262245	C₂	1	2	yes	maximal, complemented
2	#72262235	C₂	1	1	yes	maximal, characteristic, complemented
3	#72262188	C₂	1	2	yes	maximal, complemented
4	#72256796	C₂	1	1	yes	maximal, characteristic, complemented
5	#72242789	C₂	1	2	yes	maximal, complemented
6	#72241419	C₂	1	1	yes	maximal, characteristic, complemented
7	#72235270	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#33551	C₂	1	1	yes	maximal, characteristic, complemented
9	#72233807	C₂	1	1	yes	maximal, characteristic, complemented
10	#72233196	C₂	1	1	yes	maximal, characteristic, complemented
11	#72233183	C₂	1	1	yes	maximal, characteristic, complemented
12	#72233152	C₂	1	2	yes	maximal, complemented
13	#72233116	C₂	1	1	yes	maximal, characteristic, complemented
14	#72233086	C₂	1	2	yes	maximal, complemented
15	#72233069	C₂	1	1	yes	maximal, characteristic, complemented
16	#72232799	C₂	1	1	yes	maximal, characteristic, complemented
17	#72232755	C₂	1	1	yes	maximal, characteristic, complemented
18	#72218980	C₂	1	1	yes	maximal, characteristic, complemented
19	#72218099	C₂	1	2	yes	maximal, complemented
20	#72218077	C₂	1	1	yes	maximal, characteristic, complemented
21	#72216660	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#511790	C₂	1	2	yes	maximal, complemented
23	#72213329	C₂	1	2	yes	maximal, complemented
24	C₂×#62817	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#3532	C₂²	1	1	yes	characteristic
26	C₂²×#3026	C₂²	1	1	yes	characteristic, complemented
27	C₂³×B(4,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
28	C₂²×#3019	C₂²	1	1	yes	characteristic, complemented
29	#7792762	C₂²	1	1	yes	characteristic, complemented
30	#7792761	C₂²	1	1	yes	characteristic, complemented
31	#7785082	C₂²	1	1	yes	characteristic, complemented
32	#7785081	C₂²	1	1	yes	characteristic, complemented
33	#7772009	C₂²	1	1	yes	characteristic
34	#7763449	C₂²	1	1	yes	characteristic
35	#7708350	C₂²	1	1	yes	characteristic, complemented
36	#7708349	C₂²	1	1	yes	characteristic
37	#7708349	C₂²	1	1	yes	characteristic, complemented
38	#7677031	C₂²	1	1	yes	characteristic
39	#7675391	C₂²	1	1	yes	characteristic
40	#7631286	C₂²	1	1	yes	characteristic, complemented
41	C₂×D₄×#120	C₂²	1	1	yes	characteristic
42	#7626309	C₂²	1	1	yes	characteristic, complemented
43	C₂×#33551	C₂²	1	2	yes	—
44	C₂×#33551	C₂²	1	2	yes	complemented
45	C₂×#33551	C₂²	1	2	yes	complemented
46	C₂×#33551	C₂²	1	2	yes	complemented
47	C₂×#33551	C₂²	1	2	yes	complemented
48	C₂×#33551	C₂²	1	2	yes	complemented
49	C₂×#33551	C₂²	1	2	yes	complemented
50	C₂²×#2127	C₂²	1	1	yes	characteristic, complemented
51	C₂²×#2121	C₂²	1	1	yes	characteristic, complemented
52	C₂³×AΣL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic, complemented
53	#6628892	C₂²	1	1	yes	characteristic, complemented
54	C₂×#32898	C₂²	1	1	yes	characteristic, complemented
55	#6628867	C₂²	1	1	yes	characteristic, complemented
56	C₂×#23895	C₂²	1	2	yes	complemented
57	C₂×#23900	C₂²	1	2	yes	complemented
58	C₂×#23897	C₂²	1	2	yes	complemented
59	#498931	C₂²	1	2	yes	complemented
60	#498931	C₂²	1	2	yes	complemented
61	#498927	C₂²	1	2	yes	complemented
62	#498927	C₂²	1	2	yes	complemented
63	#498886	C₂²	1	2	yes	complemented
64	#498886	C₂²	1	2	yes	complemented
65	#494713	C₂²	1	1	yes	characteristic, complemented
66	#494713	C₂²	1	1	yes	characteristic, complemented
67	#494695	C₂²	1	1	yes	characteristic, complemented
68	C₂×#13086	C₂²	1	1	yes	characteristic, complemented
69	#494677	C₂²	1	1	yes	characteristic, complemented
70	C₂×#13082	C₂²	1	1	yes	characteristic, complemented
71	#494600	C₂²	1	2	yes	complemented
72	#494579	C₂²	1	2	yes	complemented
73	#494575	C₂²	1	2	yes	complemented
74	C₂×#12753	C₂²	1	2	yes	complemented
75	C₂×#12753	C₂²	1	2	yes	complemented
76	C₂×#12753	C₂²	1	2	yes	complemented
77	C₂×#12753	C₂²	1	2	yes	complemented
78	C₂×#12753	C₂²	1	2	yes	complemented
79	C₂×#12753	C₂²	1	2	yes	complemented
80	C₂×#12753	C₂²	1	2	yes	complemented
81	C₂×#12707	C₂²	1	2	yes	complemented
82	C₂×#12705	C₂²	1	2	yes	complemented
83	#493370	C₂²	1	1	yes	characteristic, complemented
84	#493357	C₂²	1	1	yes	characteristic, complemented
85	C₂×#12687	C₂²	1	2	yes	complemented
86	C₂×#12687	C₂²	1	1	yes	characteristic, complemented
87	#394174	C₂²	1	2	yes	complemented
88	#394173	C₂²	1	2	yes	complemented
89	#394165	C₂²	1	2	yes	complemented
90	#394066	C₂²	1	2	yes	complemented
91	#394064	C₂²	1	2	yes	complemented
92	#393975	C₂²	1	2	yes	complemented
93	#374058	C₂²	1	1	yes	characteristic, complemented
94	#374045	C₂²	1	1	yes	characteristic, complemented
95	#374038	C₂²	1	1	yes	characteristic, complemented
96	#364535	C₂²	1	2	yes	complemented
97	#364513	C₂²	1	2	yes	complemented
98	#364500	C₂²	1	2	yes	complemented
99	#359583	C₂²	1	1	yes	characteristic, complemented
100	#359579	C₂²	1	1	yes	characteristic, complemented
101	#359579	C₂²	1	1	yes	characteristic, complemented
102	#359509	C₂²	1	1	yes	characteristic, complemented
103	#359501	C₂²	1	1	yes	characteristic, complemented
104	#359442	C₂²	1	1	yes	characteristic, complemented
105	#147819	C₂²	1	2	yes	complemented
106	#147819	C₂²	1	2	yes	complemented
107	#147815	C₂²	1	2	yes	complemented
108	#147815	C₂²	1	2	yes	complemented
109	#147811	C₂²	1	2	yes	complemented
110	#147811	C₂²	1	2	yes	complemented
111	#147714	C₂²	1	2	yes	complemented
112	#147713	C₂²	1	2	yes	complemented
113	#147710	C₂²	1	2	yes	complemented
114	#147569	C₂²	1	2	yes	complemented
115	#147567	C₂²	1	2	yes	complemented
116	#147555	C₂²	1	2	yes	complemented
117	#146702	C₂²	1	2	yes	complemented
118	#146678	C₂²	1	2	yes	complemented
119	#146661	C₂²	1	2	yes	complemented
120	#146654	C₂²	1	2	yes	complemented
121	#146614	C₂²	1	2	yes	complemented
122	#146593	C₂²	1	2	yes	complemented
123	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic, complemented
124	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
125	C₂×#3488	D₄	1	1	yes	characteristic, complemented
126	C₂×#3484	D₄	1	1	yes	characteristic, complemented
127	C₂×#3484	C₂³	1	1	yes	characteristic
128	C₂×#3484	C₂³	1	1	yes	characteristic
129	C₂×#3484	C₂³	1	2	yes	complemented
130	C₂×#3532	D₄	1	1	yes	characteristic, complemented
131	C₂×#3532	D₄	1	1	yes	characteristic, complemented
132	C₂×#3532	D₄	1	1	yes	characteristic, complemented
133	C₂×#3532	D₄	1	1	yes	characteristic, complemented
134	C₂×#3532	C₂³	1	1	yes	characteristic
135	C₂×#3532	C₂³	1	1	yes	characteristic
136	C₂×#3532	C₂³	1	1	yes	characteristic
137	C₂×#3532	C₂³	1	1	yes	characteristic
138	C₂×#3532	C₂³	1	1	yes	characteristic
139	C₂×#3532	C₂³	1	1	yes	characteristic
140	C₂×#3532	C₂³	1	1	yes	characteristic
141	C₂²×#551	D₄	1	1	yes	characteristic, complemented
142	C₂²×D₄²	D₄	1	1	yes	characteristic, complemented
143	C₂²×D₄²	C₂³	1	1	yes	characteristic
144	C₂²×H(3,𝔽₄)	D₄	1	1	yes	characteristic, complemented
145	C₂²×#560	D₄	1	1	yes	characteristic, complemented
146	C₂²×#535	C₂³	1	1	yes	characteristic
147	C₂²×#534	C₂³	1	1	yes	characteristic
148	C₂³×#120	C₂³	1	1	yes	characteristic
149	C₂³×#120	C₂³	1	1	yes	characteristic
150	C₂×#3026	C₂³	1	2	yes	—
151	C₂×#3026	C₂³	1	2	yes	complemented
152	C₂×#3026	C₂³	1	2	yes	complemented
153	C₂²×B(4,𝔽₂)	C₂³	1	2	yes	—
154	C₂²×B(4,𝔽₂)	C₂³	1	2	yes	complemented
155	C₂²×B(4,𝔽₂)	C₂³	1	2	yes	complemented
156	C₂×#3019	C₂³	1	2	yes	—
157	C₂×#3019	C₂³	1	2	yes	complemented
158	C₂×#3019	C₂³	1	2	yes	complemented
159	C₂³×#100	C₂³	1	1	yes	characteristic, complemented
160	C₂³×#99	C₂³	1	1	yes	characteristic, complemented
161	C₂³×#99	C₂³	1	1	yes	characteristic, complemented
162	#59191	D₄	1	1	yes	characteristic, complemented
163	#59162	D₄	1	1	yes	characteristic, complemented
164	#59126	D₄	1	1	yes	characteristic, complemented
165	#59006	D₄	1	1	yes	characteristic, complemented
166	#59006	D₄	1	1	yes	characteristic, complemented
167	#58990	D₄	1	1	yes	characteristic, complemented
168	#58990	D₄	1	1	yes	characteristic, complemented
169	#58990	D₄	1	1	yes	characteristic, complemented
170	#52012	D₄	1	1	yes	characteristic, complemented
171	#52004	D₄	1	1	yes	characteristic, complemented
172	#51902	D₄	1	1	yes	characteristic, complemented
173	#51895	D₄	1	1	yes	characteristic, complemented
174	#50856	D₄	1	1	yes	characteristic, complemented
175	#50646	D₄	1	1	yes	characteristic, complemented
176	#47848	D₄	1	1	yes	characteristic, complemented
177	#47827	D₄	1	1	yes	characteristic, complemented
178	#46324	D₄	1	1	yes	characteristic, complemented
179	#45977	D₄	1	1	yes	characteristic, complemented
180	#45455	D₄	1	1	yes	characteristic, complemented
181	#45439	D₄	1	1	yes	characteristic, complemented
182	#45439	D₄	1	1	yes	characteristic, complemented
183	#45439	D₄	1	1	yes	characteristic, complemented
184	#45438	D₄	1	1	yes	characteristic, complemented
185	#45438	D₄	1	1	yes	characteristic, complemented
186	#36737	C₂³	1	1	yes	characteristic
187	#36737	C₂³	1	1	yes	characteristic
188	#36714	C₂³	1	1	yes	characteristic
189	#36714	C₂³	1	1	yes	characteristic
190	#36702	C₂³	1	1	yes	characteristic
191	#36702	C₂³	1	1	yes	characteristic
192	C₂×#2847	D₄	1	1	yes	characteristic, complemented
193	C₂×#2846	D₄	1	1	yes	characteristic, complemented
194	C₂×#2846	D₄	1	1	yes	characteristic, complemented
195	#35565	D₄	1	1	yes	characteristic, complemented
196	#35563	D₄	1	1	yes	characteristic, complemented
197	#35528	D₄	1	1	yes	characteristic, complemented
198	#35527	D₄	1	1	yes	characteristic, complemented
199	#35390	D₄	1	1	yes	characteristic, complemented
200	#35358	D₄	1	1	yes	characteristic, complemented
201	#35348	D₄	1	1	yes	characteristic, complemented
202	#35347	D₄	1	1	yes	characteristic, complemented
203	#35222	C₂³	1	1	yes	characteristic
204	#35222	C₂³	1	1	yes	characteristic
205	#35168	C₂³	1	1	yes	characteristic
206	#34984	C₂³	1	1	yes	characteristic
207	#34980	C₂³	1	1	yes	characteristic
208	#34980	C₂³	1	1	yes	characteristic
209	#34737	D₄	1	1	yes	characteristic, complemented
210	#34736	D₄	1	1	yes	characteristic, complemented
211	C₂×#2433	D₄	1	1	yes	characteristic, complemented
212	C₂×#2408	C₂³	1	1	yes	characteristic
213	C₂×#2410	D₄	1	1	yes	characteristic, complemented
214	C₂×#2410	D₄	1	1	yes	characteristic, complemented
215	C₂×#2410	D₄	1	1	yes	characteristic, complemented
216	C₂×#2403	D₄	1	1	yes	characteristic, complemented
217	C₂×#2403	C₂³	1	1	yes	characteristic
218	C₂×#2403	C₂³	1	1	yes	characteristic
219	#34407	C₂³	1	1	yes	characteristic
220	#34406	C₂³	1	1	yes	characteristic
221	#34356	C₂³	1	1	yes	characteristic
222	#34265	C₂³	1	1	yes	characteristic
223	#34264	C₂³	1	1	yes	characteristic
224	#34256	C₂³	1	2	yes	complemented
225	#34204	D₄	1	1	yes	characteristic, complemented
226	#34198	D₄	1	1	yes	characteristic, complemented
227	#34171	C₂³	1	1	yes	characteristic, complemented
228	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
229	C₂×C₄×#120	C₂³	1	1	yes	characteristic
230	#33551	D₄	1	16	yes	complemented
231	C₂×#2127	C₂³	1	2	yes	—
232	C₂×#2127	C₂³	1	2	yes	—
233	C₂×#2127	C₂³	1	2	yes	complemented
234	C₂×#2127	C₂³	1	2	yes	complemented
235	C₂×#2127	C₂³	1	2	yes	complemented
236	C₂×#2127	C₂³	1	2	yes	complemented
237	C₂×#2121	C₂³	1	2	yes	—
238	C₂×#2121	C₂³	1	2	yes	—
239	C₂×#2121	C₂³	1	2	yes	complemented
240	C₂×#2121	C₂³	1	2	yes	complemented
241	C₂×#2121	C₂³	1	2	yes	complemented
242	C₂×#2121	C₂³	1	2	yes	complemented
243	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
244	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
245	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	complemented
246	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	complemented
247	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	complemented
248	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	complemented
249	C₂×#1913	C₂³	1	2	yes	—
250	C₂×#1913	C₂³	1	2	yes	complemented
251	C₂×#1913	C₂³	1	2	yes	complemented
252	C₂×#1911	C₂³	1	2	yes	—
253	C₂×#1911	C₂³	1	2	yes	complemented
254	C₂×#1911	C₂³	1	2	yes	complemented
255	C₂×#1889	C₂³	1	2	yes	—
256	C₂×#1889	C₂³	1	2	yes	complemented
257	C₂×#1889	C₂³	1	2	yes	complemented
258	#20616	C₂³	1	2	yes	complemented
259	#20609	C₂³	1	2	yes	complemented
260	C₂×#1790	C₂³	1	2	yes	complemented
261	C₂×#1783	C₂³	1	1	yes	characteristic, complemented
262	C₂×#1783	C₂³	1	2	yes	complemented
263	C₂×#1781	C₂³	1	1	yes	characteristic, complemented
264	C₂×#1781	C₂³	1	1	yes	characteristic, complemented
265	C₂×#1781	C₂³	1	2	yes	complemented
266	C₂×#1781	C₂³	1	2	yes	complemented
267	#12582	C₂³	1	2	yes	complemented
268	#12582	C₂³	1	2	yes	complemented
269	#12574	C₂³	1	2	yes	complemented
270	#12574	C₂³	1	2	yes	complemented
271	C₂×#1390	C₂³	1	2	yes	complemented
272	C₂×#1390	C₂³	1	2	yes	complemented
273	#10762	C₂³	1	2	yes	complemented
274	#10761	C₂³	1	2	yes	complemented
275	#10761	C₂³	1	2	yes	complemented
276	#10754	C₂³	1	2	yes	complemented
277	#10745	C₂³	1	2	yes	complemented
278	#10740	C₂³	1	2	yes	complemented
279	C₂⁷	C₂×D₄	1	1	yes	characteristic
280	C₂⁷	C₂×D₄	1	1	yes	characteristic, complemented
281	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
282	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
283	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
284	C₂³×#41	C₂×D₄	1	1	yes	characteristic
285	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
286	C₂⁴×D₄	C₂×D₄	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, complemented
290	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
291	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
292	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
293	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
294	#3532	C₂×D₄	1	8	yes	—
295	C₂×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic
296	C₂×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic
297	C₂×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic
298	C₂×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic
299	C₂×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic, complemented
300	C₂×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic, complemented
301	C₂×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic, complemented
302	C₂×#560	C₂×D₄	1	1	yes	characteristic
303	C₂×#560	C₂×D₄	1	1	yes	characteristic
304	C₂×#560	C₂×D₄	1	1	yes	characteristic
305	C₂×#560	C₂×D₄	1	1	yes	characteristic
306	C₂×#560	C₂×D₄	1	1	yes	characteristic, complemented
307	C₂×#560	C₂×D₄	1	1	yes	characteristic, complemented
308	C₂×#560	C₂×D₄	1	1	yes	characteristic, complemented
309	C₂×#551	C₂×D₄	1	1	yes	characteristic
310	C₂×#551	C₂×D₄	1	1	yes	characteristic
311	C₂×#551	C₂×D₄	1	1	yes	characteristic
312	C₂×#551	C₂×D₄	1	1	yes	characteristic
313	C₂×#551	C₂×D₄	1	1	yes	characteristic, complemented
314	C₂×#551	C₂×D₄	1	1	yes	characteristic, complemented
315	C₂×#551	C₂×D₄	1	1	yes	characteristic, complemented
316	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
317	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
318	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
319	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
320	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
321	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
322	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
323	C₂×#537	C₂×D₄	1	1	yes	characteristic, complemented
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
328	C₂×#535	C₂×D₄	1	1	yes	characteristic
329	C₂×#535	C₂×D₄	1	1	yes	characteristic
330	C₂×#535	C₂×D₄	1	1	yes	characteristic
331	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
332	C₂×#535	C₂⁴	1	1	yes	characteristic
333	C₂×#535	C₂⁴	1	1	yes	characteristic
334	C₂×#535	C₂⁴	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	C₂×D₄	1	1	yes	characteristic, complemented
344	C₂×#534	C₂⁴	1	1	yes	characteristic
345	C₂×#534	C₂⁴	1	1	yes	characteristic
346	C₂×#534	C₂⁴	1	1	yes	characteristic
347	C₂²×#127	C₂×D₄	1	1	yes	characteristic
348	C₂²×#127	C₂×D₄	1	1	yes	characteristic
349	C₂²×#127	C₂×D₄	1	1	yes	characteristic
350	C₂²×#124	C₂×D₄	1	1	yes	characteristic
351	C₂²×#124	C₂×D₄	1	1	yes	characteristic
352	C₂×#525	C₂×D₄	1	1	yes	characteristic
353	C₂×#525	C₂×D₄	1	1	yes	characteristic, complemented
354	C₂×#525	C₂×D₄	1	1	yes	characteristic, complemented
355	C₂×#525	C₂×D₄	1	1	yes	characteristic, complemented
356	C₂²×#123	C₂×D₄	1	1	yes	characteristic
357	C₂²×#123	C₂×D₄	1	1	yes	characteristic
358	C₂²×#121	C₂×D₄	1	1	yes	characteristic
359	C₂²×#121	C₂×D₄	1	1	yes	characteristic
360	C₂²×#121	C₂×D₄	1	1	yes	characteristic
361	C₂²×#121	C₂×D₄	1	1	yes	characteristic
362	C₂²×#120	C₂×D₄	1	1	yes	characteristic
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
377	C₂²×#120	C₂×D₄	1	1	yes	characteristic
378	C₂²×#120	C₂×D₄	1	1	yes	characteristic
379	C₂²×#120	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic, complemented
385	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
386	C₂²×#120	C₂⁴	1	1	yes	characteristic
387	C₂²×#120	C₂⁴	1	1	yes	characteristic
388	C₂²×#120	C₂⁴	1	1	yes	characteristic
389	C₂×#520	C₂×D₄	1	1	yes	characteristic, complemented
390	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
391	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
392	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
393	C₂×#518	C₂⁴	1	2	yes	—
394	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
396	C₂²×#117	C₂×D₄	1	1	yes	characteristic
397	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
398	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
400	#3026	C₂×D₄	1	8	yes	complemented
401	C₂×B(4,𝔽₂)	C₂×D₄	1	8	yes	complemented
402	#3019	C₂×D₄	1	8	yes	complemented
403	C₂²×#100	C₂⁴	1	2	yes	—
404	C₂²×#100	C₂⁴	1	2	yes	—
405	C₂²×#99	C₂⁴	1	2	yes	—
406	C₂²×#99	C₂⁴	1	2	yes	—
407	C₂²×#99	C₂⁴	1	2	yes	—
408	C₂²×#99	C₂⁴	1	2	yes	—
409	#2717	C₂×D₄	1	1	yes	characteristic, complemented
410	#2717	C₂×D₄	1	1	yes	characteristic, complemented
411	#2709	C₂×D₄	1	1	yes	characteristic, complemented
412	#2709	C₂×D₄	1	1	yes	characteristic, complemented
413	#2697	C₂×D₄	1	1	yes	characteristic, complemented
414	#2697	C₂×D₄	1	1	yes	characteristic, complemented
415	#2697	C₂×D₄	1	1	yes	characteristic, complemented
416	#2697	C₂×D₄	1	1	yes	characteristic, complemented
417	#2684	C₂×D₄	1	1	yes	characteristic, complemented
418	#2684	C₂×D₄	1	1	yes	characteristic, complemented
419	#2684	C₂×D₄	1	1	yes	characteristic, complemented
420	#2684	C₂×D₄	1	1	yes	characteristic, complemented
421	#2684	C₂×D₄	1	1	yes	characteristic, complemented
422	#2684	C₂×D₄	1	1	yes	characteristic, complemented
423	#2679	C₂×D₄	1	1	yes	characteristic, complemented
424	#2679	C₂×D₄	1	1	yes	characteristic, complemented
425	#2679	C₂×D₄	1	1	yes	characteristic, complemented
426	#2679	C₂×D₄	1	1	yes	characteristic, complemented
427	#2669	C₂×D₄	1	1	yes	characteristic, complemented
428	#2669	C₂×D₄	1	1	yes	characteristic, complemented
429	#2669	C₂×D₄	1	1	yes	characteristic, complemented
430	#2669	C₂×D₄	1	1	yes	characteristic, complemented
431	#2669	C₂×D₄	1	1	yes	characteristic, complemented
432	#2669	C₂×D₄	1	1	yes	characteristic, complemented
433	#2435	C₂×D₄	1	1	yes	characteristic
434	#2435	C₂×D₄	1	1	yes	characteristic
435	#2435	C₂×D₄	1	1	yes	characteristic
436	#2435	C₂×D₄	1	1	yes	characteristic
437	#2433	C₂×D₄	1	1	yes	characteristic
438	#2433	C₂×D₄	1	1	yes	characteristic
439	#2433	C₂×D₄	1	1	yes	characteristic
440	#2433	C₂×D₄	1	1	yes	characteristic
441	#2405	C₂×D₄	1	1	yes	characteristic
442	#2405	C₂×D₄	1	1	yes	characteristic
443	#2405	C₂×D₄	1	1	yes	characteristic
444	#2405	C₂×D₄	1	1	yes	characteristic
445	#2403	C₂×D₄	1	1	yes	characteristic
446	#2403	C₂×D₄	1	1	yes	characteristic
447	#2403	C₂×D₄	1	1	yes	characteristic
448	#2403	C₂×D₄	1	1	yes	characteristic
449	#2403	C₂×D₄	1	1	yes	characteristic
450	#2403	C₂×D₄	1	1	yes	characteristic
451	#2403	C₂×D₄	1	1	yes	characteristic
452	#2403	C₂×D₄	1	1	yes	characteristic
453	#2403	C₂×D₄	1	1	yes	characteristic
454	#2403	C₂×D₄	1	1	yes	characteristic
455	#2403	C₂×D₄	1	1	yes	characteristic
456	#2403	C₂×D₄	1	1	yes	characteristic
457	#2380	C₂×D₄	1	1	yes	characteristic, complemented
458	#2379	C₂×D₄	1	1	yes	characteristic, complemented
459	#2376	C₂×D₄	1	1	yes	characteristic, complemented
460	#2375	C₂×D₄	1	1	yes	characteristic, complemented
461	#2375	C₂×D₄	1	1	yes	characteristic, complemented
462	#2375	C₂×D₄	1	1	yes	characteristic, complemented
463	#2374	C₂×D₄	1	1	yes	characteristic, complemented
464	#2372	C₂×D₄	1	1	yes	characteristic, complemented
465	#2366	C₂×D₄	1	1	yes	characteristic, complemented
466	#2358	C₂×D₄	1	1	yes	characteristic, complemented
467	#2358	C₂×D₄	1	1	yes	characteristic, complemented
468	#2358	C₂×D₄	1	1	yes	characteristic, complemented
469	#2316	C₂×D₄	1	1	yes	characteristic, complemented
470	#2315	C₂×D₄	1	1	yes	characteristic, complemented
471	#2309	C₂×D₄	1	1	yes	characteristic
472	#2309	C₂×D₄	1	1	yes	characteristic, complemented
473	#2309	C₂⁴	1	1	yes	characteristic
474	#2308	C₂×D₄	1	1	yes	characteristic
475	#2308	C₂×D₄	1	1	yes	characteristic, complemented
476	#2308	C₂⁴	1	1	yes	characteristic
477	#2297	C₂×D₄	1	1	yes	characteristic, complemented
478	#2297	C₂×D₄	1	1	yes	characteristic, complemented
479	#2297	C₂×D₄	1	1	yes	characteristic, complemented
480	#2296	C₂×D₄	1	1	yes	characteristic, complemented
481	C₂×#386	C₂×D₄	1	1	yes	characteristic
482	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
483	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
484	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
485	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
486	C₂×#386	C₂⁴	1	1	yes	characteristic
487	C₂×#385	C₂×D₄	1	1	yes	characteristic, complemented
488	C₂×#385	C₂×D₄	1	1	yes	characteristic, complemented
489	#2280	C₂×D₄	1	1	yes	characteristic
490	#2280	C₂×D₄	1	1	yes	characteristic, complemented
491	C₂×#380	C₂×D₄	1	1	yes	characteristic, complemented
492	C₂×#379	C₂×D₄	1	1	yes	characteristic
493	C₂×#379	C₂×D₄	1	1	yes	characteristic
494	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
495	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
496	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
497	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
498	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
499	#2274	C₂×D₄	1	1	yes	characteristic, complemented
500	#2273	C₂×D₄	1	1	yes	characteristic, complemented
501	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
502	#2127	C₂×D₄	1	8	yes	complemented
503	#2121	C₂×D₄	1	8	yes	complemented
504	C₂×AΣL(1,𝔽₁₆)	C₂×D₄	1	8	yes	complemented
505	C₂⁶	#120	1	1	yes	characteristic
506	C₂⁶	#120	1	1	yes	characteristic
507	C₂⁶	#120	1	1	yes	characteristic
508	C₂⁶	#120	1	1	yes	characteristic
509	C₂⁶	#120	1	1	yes	characteristic, complemented
510	C₂⁶	C₂²×D₄	1	1	yes	characteristic
511	C₂⁶	C₂²×D₄	1	1	yes	characteristic
512	C₂⁶	C₂²×D₄	1	1	yes	characteristic
513	C₂⁶	C₂²×D₄	1	1	yes	characteristic
514	C₂⁶	C₂²×D₄	1	1	yes	characteristic
515	C₂⁶	C₂²×D₄	1	1	yes	characteristic
516	C₂⁶	C₂²×D₄	1	1	yes	characteristic
517	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	complemented
518	C₂²×#41	#120	1	1	yes	characteristic, complemented
519	C₂²×#41	#120	1	1	yes	characteristic, complemented
520	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
521	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
522	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
523	C₂³×Q₈	#120	1	1	yes	characteristic, complemented
524	C₂³×D₄	#120	1	1	yes	characteristic
525	C₂³×D₄	#120	1	1	yes	characteristic
526	C₂³×D₄	#120	1	1	yes	characteristic
527	C₂³×D₄	#120	1	1	yes	characteristic
528	C₂³×D₄	#120	1	1	yes	characteristic
529	C₂³×D₄	#120	1	1	yes	characteristic
530	C₂³×D₄	#120	1	1	yes	characteristic
531	C₂³×D₄	#120	1	1	yes	characteristic
532	C₂³×D₄	#120	1	1	yes	characteristic
533	C₂³×D₄	#120	1	1	yes	characteristic
534	C₂³×D₄	#120	1	1	yes	characteristic
535	C₂³×D₄	#120	1	1	yes	characteristic
536	C₂³×D₄	#120	1	1	yes	characteristic
537	C₂³×D₄	#120	1	1	yes	characteristic, complemented
538	C₂³×D₄	#120	1	1	yes	characteristic, complemented
539	C₂³×D₄	#120	1	1	yes	characteristic, complemented
540	C₂³×D₄	#120	1	1	yes	characteristic, complemented
541	C₂³×D₄	#120	1	1	yes	characteristic, complemented
542	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
543	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
544	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
545	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
546	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
547	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
548	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
549	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
550	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
551	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
560	C₂⁴×C₄	#120	1	1	yes	characteristic, complemented
561	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
562	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
563	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
564	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
565	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
566	H(3,𝔽₄)	#120	1	4	yes	complemented
567	#560	#120	1	4	yes	complemented
568	#551	#120	1	4	yes	complemented
569	D₄²	#120	1	4	yes	complemented
570	#535	C₂²×D₄	1	4	yes	—
571	#535	H(5,𝔽₂)	1	4	yes	—
572	#534	C₂²×D₄	1	4	yes	—
573	#534	H(5,𝔽₂)	1	4	yes	—
574	C₂×#127	#120	1	1	yes	characteristic, complemented
575	C₂×#127	#120	1	1	yes	characteristic, complemented
576	C₂×#127	#120	1	1	yes	characteristic, complemented
577	C₂×#127	#120	1	1	yes	characteristic, complemented
578	C₂×#127	#120	1	1	yes	characteristic, complemented
579	C₂×#127	#120	1	1	yes	characteristic, complemented
580	C₂×#127	C₂²×D₄	1	1	yes	characteristic
581	C₂×#127	C₂²×D₄	1	1	yes	characteristic
582	C₂×#127	C₂²×D₄	1	1	yes	characteristic
583	C₂×#127	C₂²×D₄	1	1	yes	characteristic
584	C₂×#127	C₂²×D₄	1	1	yes	characteristic
585	C₂×#127	C₂²×D₄	1	1	yes	characteristic
586	C₂×#124	#120	1	1	yes	characteristic, complemented
587	C₂×#124	#120	1	1	yes	characteristic, complemented
588	C₂×#124	#120	1	1	yes	characteristic, complemented
589	C₂×#124	#120	1	1	yes	characteristic, complemented
590	C₂×#124	#120	1	1	yes	characteristic, complemented
591	C₂×#124	#120	1	1	yes	characteristic, complemented
592	C₂×#124	C₂²×D₄	1	1	yes	characteristic
593	C₂×#124	C₂²×D₄	1	1	yes	characteristic
594	C₂×#124	C₂²×D₄	1	1	yes	characteristic
595	C₂×#124	C₂²×D₄	1	1	yes	characteristic
596	C₂×#124	C₂²×D₄	1	1	yes	characteristic
597	C₂×#124	C₂²×D₄	1	1	yes	characteristic
598	C₂×#123	#120	1	1	yes	characteristic, complemented
599	C₂×#123	#120	1	1	yes	characteristic, complemented
600	C₂×#123	#120	1	1	yes	characteristic, complemented
601	C₂×#123	#120	1	1	yes	characteristic, complemented
602	C₂×#123	#120	1	1	yes	characteristic, complemented
603	C₂×#123	#120	1	1	yes	characteristic, complemented
604	C₂×#123	C₂²×D₄	1	1	yes	characteristic
605	C₂×#123	C₂²×D₄	1	1	yes	characteristic
606	C₂×#123	C₂²×D₄	1	1	yes	characteristic
607	C₂×#123	C₂²×D₄	1	1	yes	characteristic
608	C₂×#123	C₂²×D₄	1	1	yes	characteristic
609	C₂×#123	C₂²×D₄	1	1	yes	characteristic
610	C₂×C₂²⋊Q₈	#120	1	1	yes	characteristic, complemented
611	C₂×C₂²⋊Q₈	#120	1	1	yes	characteristic, complemented
612	C₂×#121	#120	1	1	yes	characteristic, complemented
613	C₂×#121	#120	1	1	yes	characteristic, complemented
614	C₂×#120	#120	1	1	yes	characteristic
615	C₂×#120	#120	1	1	yes	characteristic
616	C₂×#120	#120	1	1	yes	characteristic
617	C₂×#120	#120	1	1	yes	characteristic
618	C₂×#120	#120	1	1	yes	characteristic
619	C₂×#120	#120	1	1	yes	characteristic
620	C₂×#120	#120	1	1	yes	characteristic
621	C₂×#120	#120	1	1	yes	characteristic
622	C₂×#120	#120	1	1	yes	characteristic
623	C₂×#120	#120	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, complemented
627	C₂×#120	#120	1	1	yes	characteristic, complemented
628	C₂×#120	#120	1	1	yes	characteristic, complemented
629	C₂×#120	#120	1	1	yes	characteristic, complemented
630	C₂×#120	#120	1	1	yes	characteristic, complemented
631	C₂×#120	#120	1	1	yes	characteristic, complemented
632	C₂×#120	C₂²×D₄	1	1	yes	characteristic
633	C₂×#120	C₂²×D₄	1	1	yes	characteristic
634	C₂×#120	C₂²×D₄	1	1	yes	characteristic
635	C₂×#120	C₂²×D₄	1	1	yes	characteristic
636	C₂×#120	C₂²×D₄	1	1	yes	characteristic
637	C₂×#120	C₂²×D₄	1	1	yes	characteristic
638	C₂×#120	C₂²×D₄	1	1	yes	characteristic
639	C₂×#120	C₂²×D₄	1	1	yes	characteristic
640	C₂×#120	C₂²×D₄	1	1	yes	characteristic
641	C₂×#120	C₂²×D₄	1	1	yes	characteristic
642	C₂×#120	C₂²×D₄	1	1	yes	characteristic
643	C₂×#120	C₂²×D₄	1	1	yes	characteristic
644	C₂×#120	C₂²×D₄	1	1	yes	characteristic
645	C₂×#120	C₂²×D₄	1	1	yes	characteristic
646	C₂×#120	C₂²×D₄	1	1	yes	characteristic
647	C₂×#120	C₂²×D₄	1	1	yes	characteristic
648	C₂×#120	C₂²×D₄	1	1	yes	characteristic
649	C₂×#120	C₂²×D₄	1	1	yes	characteristic
650	C₂×#120	C₂²×D₄	1	4	yes	—
651	C₂×#120	H(5,𝔽₂)	1	4	yes	—
652	C₂×#117	#120	1	1	yes	characteristic, complemented
653	C₂×#117	#120	1	1	yes	characteristic, complemented
654	C₂×#117	C₂²×D₄	1	1	yes	characteristic
655	C₂×#117	C₂²×D₄	1	1	yes	characteristic
656	C₂×#117	C₂²×D₄	1	1	yes	characteristic
657	C₂×#117	C₂²×D₄	1	1	yes	characteristic
658	C₂×#117	C₂²×D₄	1	1	yes	characteristic
659	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
660	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
661	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
662	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
663	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
664	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
665	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
666	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
667	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
668	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
669	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
670	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
671	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
672	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
673	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
674	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
675	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
676	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
677	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
678	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
679	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
680	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
681	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
682	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
683	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
684	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
685	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
686	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
687	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
688	C₂²×C₄²	#120	1	1	yes	characteristic, complemented
689	C₂²×C₄²	#120	1	1	yes	characteristic, complemented
690	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
691	C₂×#100	C₂²×D₄	1	4	yes	complemented
692	C₂×#99	C₂²×D₄	1	4	yes	complemented
693	C₂×#99	C₂²×D₄	1	4	yes	complemented
694	#390	#120	1	1	yes	characteristic, complemented
695	#390	#120	1	1	yes	characteristic, complemented
696	#390	#120	1	1	yes	characteristic, complemented
697	#390	#120	1	1	yes	characteristic, complemented
698	#390	C₂²×D₄	1	1	yes	characteristic
699	#390	C₂²×D₄	1	1	yes	characteristic
700	#390	C₂²×D₄	1	1	yes	characteristic
701	#390	C₂²×D₄	1	1	yes	characteristic
702	#386	#120	1	1	yes	characteristic
703	#386	#120	1	1	yes	characteristic
704	#386	#120	1	1	yes	characteristic
705	#386	#120	1	1	yes	characteristic
706	#386	#120	1	1	yes	characteristic, complemented
707	#386	#120	1	1	yes	characteristic, complemented
708	#386	#120	1	1	yes	characteristic, complemented
709	#386	#120	1	1	yes	characteristic, complemented
710	#386	C₂²×D₄	1	1	yes	characteristic
711	#386	C₂²×D₄	1	1	yes	characteristic
712	#386	C₂²×D₄	1	1	yes	characteristic
713	#386	C₂²×D₄	1	1	yes	characteristic
714	#386	C₂²×D₄	1	1	yes	characteristic
715	#386	C₂²×D₄	1	1	yes	characteristic
716	#386	C₂²×D₄	1	1	yes	characteristic
717	#386	C₂²×D₄	1	1	yes	characteristic
718	#379	#120	1	1	yes	characteristic
719	#379	#120	1	1	yes	characteristic
720	#379	#120	1	1	yes	characteristic
721	#379	#120	1	1	yes	characteristic
722	#379	#120	1	1	yes	characteristic, complemented
723	#379	#120	1	1	yes	characteristic, complemented
724	#379	#120	1	1	yes	characteristic, complemented
725	#379	#120	1	1	yes	characteristic, complemented
726	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
727	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
728	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
729	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
730	C₂⁵	C₂×#120	1	1	yes	characteristic
731	C₂⁵	C₂×#120	1	1	yes	characteristic
732	C₂⁵	C₂×#120	1	1	yes	characteristic
733	C₂⁵	C₂×#120	1	1	yes	characteristic
734	C₂⁵	C₂×#120	1	1	yes	characteristic
735	C₂⁵	C₂×#120	1	1	yes	characteristic
736	C₂⁵	C₂×#120	1	1	yes	characteristic
737	C₂⁵	C₂×#120	1	1	yes	characteristic
738	C₂⁵	C₂×#120	1	1	yes	characteristic
739	C₂⁵	C₂×#120	1	1	yes	characteristic
740	C₂⁵	C₂×#120	1	1	yes	characteristic
741	C₂⁵	C₂×#120	1	1	yes	characteristic
742	C₂⁵	C₂×#120	1	1	yes	characteristic
743	C₂⁵	C₂×#120	1	1	yes	characteristic
744	C₂⁵	C₂×#120	1	1	yes	characteristic
745	C₂⁵	C₂×#120	1	1	yes	characteristic
746	C₂⁵	C₂×#120	1	1	yes	characteristic
747	C₂⁵	C₂×#120	1	1	yes	characteristic
748	C₂⁵	C₂×#120	1	1	yes	characteristic
749	C₂⁵	C₂×#120	1	1	yes	characteristic
750	C₂⁵	C₂×#120	1	1	yes	characteristic
751	C₂⁵	C₂×#120	1	1	yes	characteristic
752	C₂⁵	C₂×#120	1	1	yes	characteristic
753	C₂⁵	D₄²	1	4	yes	—
754	C₂⁵	C₂³×D₄	1	1	yes	characteristic
755	C₂⁵	C₂³×D₄	1	1	yes	characteristic
756	C₂×#41	D₄²	1	4	yes	—
757	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
758	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
759	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
760	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
761	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
762	C₂²×D₄	C₂×#120	1	1	yes	characteristic
763	C₂²×D₄	C₂×#120	1	1	yes	characteristic
764	C₂²×D₄	C₂×#120	1	1	yes	characteristic
765	C₂²×D₄	C₂×#120	1	1	yes	characteristic
766	C₂²×D₄	C₂×#120	1	1	yes	characteristic
767	C₂²×D₄	C₂×#120	1	1	yes	characteristic
768	C₂²×D₄	C₂×#120	1	1	yes	characteristic
769	C₂²×D₄	C₂×#120	1	1	yes	characteristic
770	C₂²×D₄	C₂×#120	1	1	yes	characteristic
771	C₂²×D₄	C₂×#120	1	1	yes	characteristic
772	C₂²×D₄	C₂×#120	1	1	yes	characteristic
773	C₂²×D₄	C₂×#120	1	1	yes	characteristic
774	C₂²×D₄	C₂×#120	1	1	yes	characteristic
775	C₂²×D₄	C₂×#120	1	1	yes	characteristic
776	C₂²×D₄	C₂×#120	1	1	yes	characteristic
777	C₂²×D₄	D₄²	1	4	yes	—
778	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
779	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
780	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
781	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
782	C₂²×D₄	C₂³×D₄	1	2	yes	—
783	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
784	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
785	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
786	C₂³×C₄	C₂×#120	1	1	yes	characteristic
787	C₂³×C₄	C₂×#120	1	1	yes	characteristic
788	C₂³×C₄	C₂×#120	1	1	yes	characteristic
789	C₂³×C₄	C₂×#120	1	1	yes	characteristic
790	C₂³×C₄	C₂×#120	1	1	yes	characteristic
791	C₂³×C₄	C₂×#120	1	1	yes	characteristic
792	C₂³×C₄	C₂×#120	1	1	yes	characteristic
793	C₂³×C₄	C₂×#120	1	1	yes	characteristic
794	C₂³×C₄	C₂×#120	1	1	yes	characteristic
795	C₂³×C₄	C₂×#120	1	1	yes	characteristic
796	C₂³×C₄	C₂×#120	1	1	yes	characteristic
797	C₂³×C₄	C₂×#120	1	1	yes	characteristic
798	C₂³×C₄	C₂×#120	1	1	yes	characteristic
799	C₂³×C₄	C₂×#120	1	1	yes	characteristic
800	C₂³×C₄	C₂×#120	1	1	yes	characteristic
801	C₂³×C₄	C₂×#120	1	1	yes	characteristic
802	C₂³×C₄	C₂×#120	1	1	yes	characteristic
803	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
804	#127	C₂×#120	1	2	yes	—
805	#127	#534	1	2	yes	—
806	#127	D₄²	1	4	yes	—
807	#124	C₂×#120	1	2	yes	—
808	#124	#534	1	2	yes	—
809	#124	D₄²	1	4	yes	—
810	#123	C₂×#120	1	2	yes	—
811	#123	#534	1	2	yes	—
812	#123	D₄²	1	4	yes	—
813	#120	C₂×#120	1	2	yes	—
814	#120	C₂×#120	1	2	yes	—
815	#120	C₂×#120	1	2	yes	—
816	#120	#534	1	2	yes	—
817	#120	#534	1	2	yes	—
818	#120	#534	1	2	yes	—
819	#120	D₄²	1	4	yes	—
820	#120	D₄²	1	4	yes	—
821	#120	D₄²	1	4	yes	—
822	#117	D₄²	1	4	yes	—
823	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
824	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
825	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
826	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
827	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
828	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
829	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
830	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
831	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
832	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
833	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
834	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
835	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
836	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
837	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
838	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
839	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
840	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
841	C₂×C₂²⋊C₄	D₄²	1	4	yes	—
842	C₂×C₂²⋊C₄	D₄²	1	4	yes	—
843	C₂×C₄²	C₂×#120	1	1	yes	characteristic
844	C₂×C₄²	C₂×#120	1	1	yes	characteristic
845	C₂×C₄²	C₂×#120	1	1	yes	characteristic
846	C₂×C₄²	C₂×#120	1	1	yes	characteristic
847	C₂×C₄²	C₂×#120	1	1	yes	characteristic
848	C₂×C₄²	C₂×#120	1	1	yes	characteristic
849	C₂×C₄²	C₂×#120	1	1	yes	characteristic
850	C₂×C₄²	C₂×#120	1	1	yes	characteristic
851	C₂⁴	#2403	1	2	yes	—
852	C₂⁴	#2403	1	2	yes	—
853	C₂⁴	#2403	1	2	yes	complemented
854	C₂⁴	#2846	1	1	yes	characteristic
855	C₂⁴	#2846	1	1	yes	characteristic
856	C₂⁴	#2846	1	1	yes	characteristic
857	C₂⁴	#2846	1	1	yes	characteristic
858	C₂⁴	#2846	1	1	yes	characteristic
859	C₂⁴	#2846	1	1	yes	characteristic
860	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
861	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
862	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
863	C₂⁴	#3026	1	1	yes	characteristic
864	C₂⁴	#3026	1	1	yes	characteristic
865	C₂⁴	C₂²×#120	1	1	yes	characteristic
866	C₂⁴	C₂²×#120	1	1	yes	characteristic
867	C₂⁴	C₂²×#120	1	1	yes	characteristic
868	C₂⁴	C₂²×#120	1	1	yes	characteristic
869	C₂⁴	C₂²×#120	1	1	yes	characteristic
870	C₂⁴	C₂×D₄²	1	2	yes	—
871	C₂⁴	C₂×D₄²	1	2	yes	—
872	C₂⁴	#3484	1	2	yes	—
873	C₂⁴	#3484	1	2	yes	—
874	C₂×Q₈	#2403	1	2	yes	complemented
875	C₂×D₄	#2403	1	2	yes	complemented
876	C₂×D₄	C₂²×#120	1	1	yes	characteristic
877	C₂×D₄	C₂×#534	1	1	yes	characteristic
878	C₂×D₄	C₂×#534	1	1	yes	characteristic
879	C₂×D₄	C₂×#534	1	1	yes	characteristic
880	C₂×D₄	C₂×D₄²	1	2	yes	—
881	C₂×D₄	C₂×D₄²	1	2	yes	—
882	C₂×D₄	C₂×D₄²	1	2	yes	—
883	C₂×D₄	#3484	1	2	yes	—
884	C₂×D₄	#3484	1	2	yes	—
885	C₂×D₄	#3484	1	2	yes	—
886	C₂²×C₄	#2403	1	2	yes	complemented
887	C₂²×C₄	#2846	1	1	yes	characteristic
888	C₂²×C₄	#2846	1	1	yes	characteristic
889	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
890	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
891	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
892	C₂²×C₄	C₂×D₄²	1	2	yes	—
893	C₂²×C₄	#3484	1	2	yes	—
894	C₂²⋊C₄	#2403	1	2	yes	—
895	C₂²⋊C₄	#2403	1	2	yes	—
896	C₂²⋊C₄	#2403	1	2	yes	complemented
897	C₂²⋊C₄	#2403	1	2	yes	complemented
898	C₄²	#2403	1	2	yes	complemented
899	C₄²	#2403	1	2	yes	complemented
900	C₂³	#32898	1	1	yes	characteristic
901	C₂³	#32898	1	1	yes	characteristic
902	C₂³	#32898	1	1	yes	characteristic
903	C₂³	#32898	1	1	yes	characteristic
904	C₂³	C₂×#2403	1	1	yes	characteristic
905	C₂³	C₂×#2403	1	1	yes	characteristic
906	C₂³	#34980	1	1	yes	characteristic
907	C₂³	#34980	1	1	yes	characteristic
908	C₂³	D₄×#120	1	2	yes	—
909	C₂³	D₄×#120	1	2	yes	—
910	C₂³	D₄×#120	1	2	yes	—
911	C₂³	C₂×#2846	1	1	yes	characteristic
912	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
913	C₂³	C₂×#3026	1	1	yes	characteristic
914	C₂³	#60399	1	2	yes	—
915	C₂×C₄	C₂×#2403	1	1	yes	characteristic
916	C₂×C₄	#34980	1	1	yes	characteristic
917	C₂×C₄	D₄×#120	1	2	yes	—
918	C₂²	#511790	1	2	yes	complemented
919	C₂²	#612424	1	1	yes	characteristic
920	C₂²	D₄×B(4,𝔽₂)	1	2	yes	—
921	C₂²	#6573715	1	2	yes	—
922	C₂²	C₂×#32898	1	1	yes	characteristic
923	C₂²	#6628896	1	1	yes	characteristic
924	C₂	C₂×#511790	1	1	yes	characteristic
925	C₂	#72225691	1	1	yes	characteristic
926	C₂	#72233205	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#32898
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂²×D₄² ◁ 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. #72262245	C₂	semidirect
2. #72262235	C₂	semidirect
3. #72262188	C₂	semidirect
4. #72256796	C₂	semidirect
5. #72242789	C₂	semidirect
6. #72241419	C₂	semidirect
7. #72235270	C₂	semidirect
8. C₂²×#33551	C₂	semidirect
9. #72233807	C₂	semidirect
10. #72233196	C₂	semidirect
11. #72233183	C₂	semidirect
12. #72233152	C₂	semidirect
13. #72233116	C₂	semidirect
14. #72233086	C₂	semidirect
15. #72233069	C₂	semidirect
16. #72232799	C₂	semidirect
17. #72232755	C₂	semidirect
18. #72218980	C₂	semidirect
19. #72218099	C₂	semidirect
20. #72218077	C₂	semidirect
21. #72216660	C₂	semidirect
22. C₂×#511790	C₂	semidirect
23. #72213329	C₂	semidirect
24. C₂×#62817	C₂²	semidirect
26. C₂²×#3026	C₂²	semidirect
27. C₂³×B(4,𝔽₂)	C₂²	semidirect
28. C₂²×#3019	C₂²	semidirect
29. #7792762	C₂²	semidirect
30. #7792761	C₂²	semidirect
31. #7785082	C₂²	semidirect
32. #7785081	C₂²	semidirect
35. #7708350	C₂²	semidirect
37. #7708349	C₂²	semidirect
40. #7631286	C₂²	semidirect
42. #7626309	C₂²	semidirect
44. C₂×#33551	C₂²	semidirect
45. C₂×#33551	C₂²	semidirect
46. C₂×#33551	C₂²	semidirect
47. C₂×#33551	C₂²	semidirect
48. C₂×#33551	C₂²	semidirect
49. C₂×#33551	C₂²	semidirect
50. C₂²×#2127	C₂²	semidirect
51. C₂²×#2121	C₂²	semidirect
52. C₂³×AΣL(1,𝔽₁₆)	C₂²	semidirect
53. #6628892	C₂²	semidirect
54. C₂×#32898	C₂²	semidirect
55. #6628867	C₂²	semidirect
56. C₂×#23895	C₂²	semidirect
57. C₂×#23900	C₂²	semidirect
58. C₂×#23897	C₂²	semidirect
59. #498931	C₂²	semidirect
60. #498931	C₂²	semidirect
61. #498927	C₂²	semidirect
62. #498927	C₂²	semidirect
63. #498886	C₂²	semidirect
64. #498886	C₂²	semidirect
65. #494713	C₂²	semidirect
66. #494713	C₂²	semidirect
67. #494695	C₂²	semidirect
68. C₂×#13086	C₂²	semidirect
69. #494677	C₂²	semidirect
70. C₂×#13082	C₂²	semidirect
71. #494600	C₂²	semidirect
72. #494579	C₂²	semidirect
73. #494575	C₂²	semidirect
74. C₂×#12753	C₂²	semidirect
75. C₂×#12753	C₂²	semidirect
76. C₂×#12753	C₂²	semidirect
77. C₂×#12753	C₂²	semidirect
78. C₂×#12753	C₂²	semidirect
79. C₂×#12753	C₂²	semidirect
80. C₂×#12753	C₂²	semidirect
81. C₂×#12707	C₂²	semidirect
82. C₂×#12705	C₂²	semidirect
83. #493370	C₂²	semidirect
84. #493357	C₂²	semidirect
85. C₂×#12687	C₂²	semidirect
86. C₂×#12687	C₂²	semidirect
87. #394174	C₂²	semidirect
88. #394173	C₂²	semidirect
89. #394165	C₂²	semidirect
90. #394066	C₂²	semidirect
91. #394064	C₂²	semidirect
92. #393975	C₂²	semidirect
93. #374058	C₂²	semidirect
94. #374045	C₂²	semidirect
95. #374038	C₂²	semidirect
96. #364535	C₂²	semidirect
97. #364513	C₂²	semidirect
98. #364500	C₂²	semidirect
99. #359583	C₂²	semidirect
100. #359579	C₂²	semidirect
101. #359579	C₂²	semidirect
102. #359509	C₂²	semidirect
103. #359501	C₂²	semidirect
104. #359442	C₂²	semidirect
105. #147819	C₂²	semidirect
106. #147819	C₂²	semidirect
107. #147815	C₂²	semidirect
108. #147815	C₂²	semidirect
109. #147811	C₂²	semidirect
110. #147811	C₂²	semidirect
111. #147714	C₂²	semidirect
112. #147713	C₂²	semidirect
113. #147710	C₂²	semidirect
114. #147569	C₂²	semidirect
115. #147567	C₂²	semidirect
116. #147555	C₂²	semidirect
117. #146702	C₂²	semidirect
118. #146678	C₂²	semidirect
119. #146661	C₂²	semidirect
120. #146654	C₂²	semidirect
121. #146614	C₂²	semidirect
122. #146593	C₂²	semidirect
123. C₂³×H(5,𝔽₂)	C₂³	semidirect
124. C₂⁵×D₄	D₄	semidirect
125. C₂×#3488	D₄	semidirect
126. C₂×#3484	D₄	semidirect
129. C₂×#3484	C₂³	semidirect
130. C₂×#3532	D₄	semidirect
131. C₂×#3532	D₄	semidirect
132. C₂×#3532	D₄	semidirect
133. C₂×#3532	D₄	semidirect
141. C₂²×#551	D₄	semidirect
142. C₂²×D₄²	D₄	semidirect
144. C₂²×H(3,𝔽₄)	D₄	semidirect
145. C₂²×#560	D₄	semidirect
151. C₂×#3026	C₂³	semidirect
152. C₂×#3026	C₂³	semidirect
154. C₂²×B(4,𝔽₂)	C₂³	semidirect
155. C₂²×B(4,𝔽₂)	C₂³	semidirect
157. C₂×#3019	C₂³	semidirect
158. C₂×#3019	C₂³	semidirect
159. C₂³×#100	C₂³	semidirect
160. C₂³×#99	C₂³	semidirect
161. C₂³×#99	C₂³	semidirect
162. #59191	D₄	semidirect
163. #59162	D₄	semidirect
164. #59126	D₄	semidirect
165. #59006	D₄	semidirect
166. #59006	D₄	semidirect
167. #58990	D₄	semidirect
168. #58990	D₄	semidirect
169. #58990	D₄	semidirect
170. #52012	D₄	semidirect
171. #52004	D₄	semidirect
172. #51902	D₄	semidirect
173. #51895	D₄	semidirect
174. #50856	D₄	semidirect
175. #50646	D₄	semidirect
176. #47848	D₄	semidirect
177. #47827	D₄	semidirect
178. #46324	D₄	semidirect
179. #45977	D₄	semidirect
180. #45455	D₄	semidirect
181. #45439	D₄	semidirect
182. #45439	D₄	semidirect
183. #45439	D₄	semidirect
184. #45438	D₄	semidirect
185. #45438	D₄	semidirect
192. C₂×#2847	D₄	semidirect
193. C₂×#2846	D₄	semidirect
194. C₂×#2846	D₄	semidirect
195. #35565	D₄	semidirect
196. #35563	D₄	semidirect
197. #35528	D₄	semidirect
198. #35527	D₄	semidirect
199. #35390	D₄	semidirect
200. #35358	D₄	semidirect
201. #35348	D₄	semidirect
202. #35347	D₄	semidirect
209. #34737	D₄	semidirect
210. #34736	D₄	semidirect
211. C₂×#2433	D₄	semidirect
213. C₂×#2410	D₄	semidirect
214. C₂×#2410	D₄	semidirect
215. C₂×#2410	D₄	semidirect
216. C₂×#2403	D₄	semidirect
224. #34256	C₂³	semidirect
225. #34204	D₄	semidirect
226. #34198	D₄	semidirect
227. #34171	C₂³	semidirect
228. C₂×D₄×C₂²⋊C₄	D₄	semidirect
230. #33551	D₄	semidirect
233. C₂×#2127	C₂³	semidirect
234. C₂×#2127	C₂³	semidirect
235. C₂×#2127	C₂³	semidirect
236. C₂×#2127	C₂³	semidirect
239. C₂×#2121	C₂³	semidirect
240. C₂×#2121	C₂³	semidirect
241. C₂×#2121	C₂³	semidirect
242. C₂×#2121	C₂³	semidirect
245. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
246. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
247. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
248. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
250. C₂×#1913	C₂³	semidirect
251. C₂×#1913	C₂³	semidirect
253. C₂×#1911	C₂³	semidirect
254. C₂×#1911	C₂³	semidirect
256. C₂×#1889	C₂³	semidirect
257. C₂×#1889	C₂³	semidirect
258. #20616	C₂³	semidirect
259. #20609	C₂³	semidirect
260. C₂×#1790	C₂³	semidirect
261. C₂×#1783	C₂³	semidirect
262. C₂×#1783	C₂³	semidirect
263. C₂×#1781	C₂³	semidirect
264. C₂×#1781	C₂³	semidirect
265. C₂×#1781	C₂³	semidirect
266. C₂×#1781	C₂³	semidirect
267. #12582	C₂³	semidirect
268. #12582	C₂³	semidirect
269. #12574	C₂³	semidirect
270. #12574	C₂³	semidirect
271. C₂×#1390	C₂³	semidirect
272. C₂×#1390	C₂³	semidirect
273. #10762	C₂³	semidirect
274. #10761	C₂³	semidirect
275. #10761	C₂³	semidirect
276. #10754	C₂³	semidirect
277. #10745	C₂³	semidirect
278. #10740	C₂³	semidirect
280. C₂⁷	C₂×D₄	semidirect
281. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
282. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
289. C₂⁴×D₄	C₂×D₄	semidirect
290. C₂⁴×D₄	C₂×D₄	semidirect
293. C₂⁵×C₄	C₂×D₄	semidirect
299. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
300. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
301. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
306. C₂×#560	C₂×D₄	semidirect
307. C₂×#560	C₂×D₄	semidirect
308. C₂×#560	C₂×D₄	semidirect
313. C₂×#551	C₂×D₄	semidirect
314. C₂×#551	C₂×D₄	semidirect
315. C₂×#551	C₂×D₄	semidirect
320. C₂×D₄²	C₂×D₄	semidirect
321. C₂×D₄²	C₂×D₄	semidirect
322. C₂×D₄²	C₂×D₄	semidirect
323. C₂×#537	C₂×D₄	semidirect
331. C₂×#535	C₂×D₄	semidirect
342. C₂×#534	C₂×D₄	semidirect
343. C₂×#534	C₂×D₄	semidirect
353. C₂×#525	C₂×D₄	semidirect
354. C₂×#525	C₂×D₄	semidirect
355. C₂×#525	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
384. C₂²×#120	C₂×D₄	semidirect
385. C₂²×#120	C₂×D₄	semidirect
389. C₂×#520	C₂×D₄	semidirect
390. C₂×#518	C₂×D₄	semidirect
391. C₂×#518	C₂×D₄	semidirect
392. C₂×#518	C₂×D₄	semidirect
399. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
400. #3026	C₂×D₄	semidirect
401. C₂×B(4,𝔽₂)	C₂×D₄	semidirect
402. #3019	C₂×D₄	semidirect
409. #2717	C₂×D₄	semidirect
410. #2717	C₂×D₄	semidirect
411. #2709	C₂×D₄	semidirect
412. #2709	C₂×D₄	semidirect
413. #2697	C₂×D₄	semidirect
414. #2697	C₂×D₄	semidirect
415. #2697	C₂×D₄	semidirect
416. #2697	C₂×D₄	semidirect
417. #2684	C₂×D₄	semidirect
418. #2684	C₂×D₄	semidirect
419. #2684	C₂×D₄	semidirect
420. #2684	C₂×D₄	semidirect
421. #2684	C₂×D₄	semidirect
422. #2684	C₂×D₄	semidirect
423. #2679	C₂×D₄	semidirect
424. #2679	C₂×D₄	semidirect
425. #2679	C₂×D₄	semidirect
426. #2679	C₂×D₄	semidirect
427. #2669	C₂×D₄	semidirect
428. #2669	C₂×D₄	semidirect
429. #2669	C₂×D₄	semidirect
430. #2669	C₂×D₄	semidirect
431. #2669	C₂×D₄	semidirect
432. #2669	C₂×D₄	semidirect
457. #2380	C₂×D₄	semidirect
458. #2379	C₂×D₄	semidirect
459. #2376	C₂×D₄	semidirect
460. #2375	C₂×D₄	semidirect
461. #2375	C₂×D₄	semidirect
462. #2375	C₂×D₄	semidirect
463. #2374	C₂×D₄	semidirect
464. #2372	C₂×D₄	semidirect
465. #2366	C₂×D₄	semidirect
466. #2358	C₂×D₄	semidirect
467. #2358	C₂×D₄	semidirect
468. #2358	C₂×D₄	semidirect
469. #2316	C₂×D₄	semidirect
470. #2315	C₂×D₄	semidirect
472. #2309	C₂×D₄	semidirect
475. #2308	C₂×D₄	semidirect
477. #2297	C₂×D₄	semidirect
478. #2297	C₂×D₄	semidirect
479. #2297	C₂×D₄	semidirect
480. #2296	C₂×D₄	semidirect
482. C₂×#386	C₂×D₄	semidirect
483. C₂×#386	C₂×D₄	semidirect
484. C₂×#386	C₂×D₄	semidirect
485. C₂×#386	C₂×D₄	semidirect
487. C₂×#385	C₂×D₄	semidirect
488. C₂×#385	C₂×D₄	semidirect
490. #2280	C₂×D₄	semidirect
491. C₂×#380	C₂×D₄	semidirect
494. C₂×#379	C₂×D₄	semidirect
495. C₂×#379	C₂×D₄	semidirect
496. C₂×#379	C₂×D₄	semidirect
497. C₂×#379	C₂×D₄	semidirect
498. C₂×#379	C₂×D₄	semidirect
499. #2274	C₂×D₄	semidirect
500. #2273	C₂×D₄	semidirect
501. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
502. #2127	C₂×D₄	semidirect
503. #2121	C₂×D₄	semidirect
504. C₂×AΣL(1,𝔽₁₆)	C₂×D₄	semidirect
509. C₂⁶	#120	semidirect
517. C₂×H(5,𝔽₂)	C₂²×D₄	semidirect
518. C₂²×#41	#120	semidirect
519. C₂²×#41	#120	semidirect
523. C₂³×Q₈	#120	semidirect
537. C₂³×D₄	#120	semidirect
538. C₂³×D₄	#120	semidirect
539. C₂³×D₄	#120	semidirect
540. C₂³×D₄	#120	semidirect
541. C₂³×D₄	#120	semidirect
560. C₂⁴×C₄	#120	semidirect
566. H(3,𝔽₄)	#120	semidirect
567. #560	#120	semidirect
568. #551	#120	semidirect
569. D₄²	#120	semidirect
574. C₂×#127	#120	semidirect
575. C₂×#127	#120	semidirect
576. C₂×#127	#120	semidirect
577. C₂×#127	#120	semidirect
578. C₂×#127	#120	semidirect
579. C₂×#127	#120	semidirect
586. C₂×#124	#120	semidirect
587. C₂×#124	#120	semidirect
588. C₂×#124	#120	semidirect
589. C₂×#124	#120	semidirect
590. C₂×#124	#120	semidirect
591. C₂×#124	#120	semidirect
598. C₂×#123	#120	semidirect
599. C₂×#123	#120	semidirect
600. C₂×#123	#120	semidirect
601. C₂×#123	#120	semidirect
602. C₂×#123	#120	semidirect
603. C₂×#123	#120	semidirect
610. C₂×C₂²⋊Q₈	#120	semidirect
611. C₂×C₂²⋊Q₈	#120	semidirect
612. C₂×#121	#120	semidirect
613. C₂×#121	#120	semidirect
626. C₂×#120	#120	semidirect
627. C₂×#120	#120	semidirect
628. C₂×#120	#120	semidirect
629. C₂×#120	#120	semidirect
630. C₂×#120	#120	semidirect
631. C₂×#120	#120	semidirect
652. C₂×#117	#120	semidirect
653. C₂×#117	#120	semidirect
671. C₂²×C₂²⋊C₄	#120	semidirect
672. C₂²×C₂²⋊C₄	#120	semidirect
673. C₂²×C₂²⋊C₄	#120	semidirect
674. C₂²×C₂²⋊C₄	#120	semidirect
675. C₂²×C₂²⋊C₄	#120	semidirect
676. C₂²×C₂²⋊C₄	#120	semidirect
688. C₂²×C₄²	#120	semidirect
689. C₂²×C₄²	#120	semidirect
691. C₂×#100	C₂²×D₄	semidirect
692. C₂×#99	C₂²×D₄	semidirect
693. C₂×#99	C₂²×D₄	semidirect
694. #390	#120	semidirect
695. #390	#120	semidirect
696. #390	#120	semidirect
697. #390	#120	semidirect
706. #386	#120	semidirect
707. #386	#120	semidirect
708. #386	#120	semidirect
709. #386	#120	semidirect
722. #379	#120	semidirect
723. #379	#120	semidirect
724. #379	#120	semidirect
725. #379	#120	semidirect
726. C₄×C₂²⋊C₄	#120	semidirect
727. C₄×C₂²⋊C₄	#120	semidirect
728. C₄×C₂²⋊C₄	#120	semidirect
729. C₄×C₂²⋊C₄	#120	semidirect
853. C₂⁴	#2403	semidirect
874. C₂×Q₈	#2403	semidirect
875. C₂×D₄	#2403	semidirect
886. C₂²×C₄	#2403	semidirect
896. C₂²⋊C₄	#2403	semidirect
897. C₂²⋊C₄	#2403	semidirect
898. C₄²	#2403	semidirect
899. C₄²	#2403	semidirect
918. C₂²	#511790	semidirect

Maximal subgroups

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

subgroup	index
#72262245	2
#72262235	2
#72262188	2
#72256796	2
#72242789	2
#72241419	2
#72235270	2
C₂²×#33551	2
#72233807	2
#72233196	2
#72233183	2
#72233152	2
#72233116	2
#72233086	2
#72233069	2
#72232799	2
#72232755	2
#72218980	2
#72218099	2
#72218077	2
#72216660	2
C₂×#511790	2
#72213329	2