Subgroups — #72256669

Order 2048.

At least 16598 conjugacy classes of subgroups; only the 1696 normal subgroups are shown.

The subgroup lattice has 795 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72256668	C₂	1	1	yes	maximal, characteristic, complemented
2	#72256665	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#493398	C₂	1	1	yes	maximal, characteristic, complemented
4	#72256654	C₂	1	1	yes	maximal, characteristic, complemented
5	#72256650	C₂	1	1	yes	maximal, characteristic, complemented
6	#72256648	C₂	1	1	yes	maximal, characteristic, complemented
7	#72256636	C₂	1	1	yes	maximal, characteristic, complemented
8	#72256630	C₂	1	1	yes	maximal, characteristic, complemented
9	#72256615	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#6437464	C₂	1	1	yes	maximal, characteristic, complemented
11	#72251160	C₂	1	1	yes	maximal, characteristic, complemented
12	#72250024	C₂	1	8	yes	maximal, complemented
13	C₂×#7622868	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#493561	C₂	1	1	yes	maximal, characteristic, complemented
15	#72238033	C₂	1	1	yes	maximal, characteristic, complemented
16	#72236774	C₂	1	1	yes	maximal, characteristic, complemented
17	#72213329	C₂	1	8	yes	maximal, complemented
18	C₂×#62729	C₂²	1	1	yes	characteristic
19	C₂×#62852	C₂²	1	1	yes	characteristic, complemented
20	C₂×#62842	C₂²	1	1	yes	characteristic
21	C₂×#60398	C₂²	1	1	yes	characteristic, complemented
22	C₂²×#3025	C₂²	1	1	yes	characteristic, complemented
23	C₂×#60387	C₂²	1	1	yes	characteristic
24	C₂×#60387	C₂²	1	1	yes	characteristic, complemented
25	#7793573	C₂²	1	4	yes	complemented
26	#7792761	C₂²	1	4	yes	complemented
27	#7642122	C₂²	1	1	yes	characteristic
28	#7634872	C₂²	1	1	yes	characteristic
29	#7630502	C₂²	1	1	yes	characteristic
30	C₂×#35512	C₂²	1	1	yes	characteristic
31	#7626378	C₂²	1	1	yes	characteristic
32	C₂×#33552	C₂²	1	4	yes	complemented
33	C₂×#33551	C₂²	1	4	yes	complemented
34	C₂×#33358	C₂²	1	1	yes	characteristic
35	C₂×#33358	C₂²	1	1	yes	characteristic
36	C₂×#33358	C₂²	1	1	yes	characteristic, complemented
37	C₂×#33358	C₂²	1	1	yes	characteristic, complemented
38	C₂×#33347	C₂²	1	1	yes	characteristic, complemented
39	C₂×#33347	C₂²	1	1	yes	characteristic, complemented
40	C₂²×#2120	C₂²	1	1	yes	characteristic, complemented
41	C₂²×#2120	C₂²	1	1	yes	characteristic, complemented
42	C₂×#23897	C₂²	1	8	yes	complemented
43	C₂×#21014	C₂²	1	1	yes	characteristic, complemented
44	C₂×#21012	C₂²	1	1	yes	characteristic
45	C₂×#21012	C₂²	1	1	yes	characteristic, complemented
46	C₂×#20959	C₂²	1	1	yes	characteristic, complemented
47	#6370734	C₂²	1	1	yes	characteristic, complemented
48	C₂×#20610	C₂²	1	1	yes	characteristic, complemented
49	C₂×#20592	C₂²	1	1	yes	characteristic, complemented
50	C₂×#20586	C₂²	1	1	yes	characteristic, complemented
51	C₂×#20586	C₂²	1	1	yes	characteristic, complemented
52	#498931	C₂²	1	8	yes	complemented
53	#498928	C₂²	1	4	yes	complemented
54	#498927	C₂²	1	4	yes	complemented
55	#494600	C₂²	1	8	yes	complemented
56	C₂×#12754	C₂²	1	4	yes	complemented
57	C₂×#12753	C₂²	1	4	yes	complemented
58	C₂×#12707	C₂²	1	8	yes	complemented
59	#492886	C₂²	1	1	yes	characteristic, complemented
60	#492886	C₂²	1	1	yes	characteristic, complemented
61	C₂×#12575	C₂²	1	1	yes	characteristic, complemented
62	C₂×#12575	C₂²	1	1	yes	characteristic, complemented
63	#394068	C₂²	1	4	yes	complemented
64	#394066	C₂²	1	4	yes	complemented
65	#394064	C₂²	1	8	yes	complemented
66	#353448	C₂²	1	1	yes	characteristic, complemented
67	#353428	C₂²	1	1	yes	characteristic, complemented
68	#147819	C₂²	1	8	yes	complemented
69	#147812	C₂²	1	4	yes	complemented
70	#147811	C₂²	1	4	yes	complemented
71	#147567	C₂²	1	8	yes	complemented
72	#147557	C₂²	1	4	yes	complemented
73	#147555	C₂²	1	4	yes	complemented
74	#146654	C₂²	1	8	yes	complemented
75	C₂²×#585	C₂³	1	1	yes	characteristic
76	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic, complemented
77	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
78	C₂×#3485	D₄	1	4	yes	complemented
79	C₂×#3484	C₂³	1	4	yes	—
80	C₂×#3484	C₂³	1	4	yes	—
81	C₂×#3540	D₄	1	1	yes	characteristic, complemented
82	C₂×#3540	D₄	1	1	yes	characteristic, complemented
83	C₂×#3533	C₂³	1	2	yes	—
84	C₂×#3538	D₄	1	1	yes	characteristic, complemented
85	C₂×#3537	D₄	1	1	yes	characteristic, complemented
86	C₂×#3532	C₂³	1	2	yes	—
87	C₂×#3481	D₄	1	2	yes	complemented
88	C₂×#3529	D₄	1	2	yes	complemented
89	C₂×#3449	D₄	1	1	yes	characteristic, complemented
90	C₂×#3449	D₄	1	1	yes	characteristic, complemented
91	C₂×#3449	D₄	1	1	yes	characteristic, complemented
92	C₂×#3449	C₂³	1	1	yes	characteristic
93	C₂×#3449	C₂³	1	1	yes	characteristic
94	C₂×#3449	C₂³	1	1	yes	characteristic
95	C₂²×#535	D₄	1	1	yes	characteristic, complemented
96	C₂²×#525	D₄	1	1	yes	characteristic, complemented
97	C₂²×#525	C₂³	1	1	yes	characteristic
98	C₂³×#121	D₄	1	1	yes	characteristic, complemented
99	C₂×#3428	C₂³	1	1	yes	characteristic
100	C₂²×#518	D₄	1	1	yes	characteristic, complemented
101	C₂×#3026	C₂³	1	4	yes	complemented
102	C₂²×#458	C₂³	1	2	yes	complemented
103	C₂²×B(4,𝔽₂)	C₂³	1	2	yes	complemented
104	#60387	D₄	1	8	yes	complemented
105	C₂×#3019	C₂³	1	4	yes	—
106	C₂×#3019	C₂³	1	4	yes	—
107	C₂²×#413	C₂³	1	1	yes	characteristic
108	C₂²×#413	C₂³	1	1	yes	characteristic
109	C₂²×#410	C₂³	1	1	yes	characteristic
110	C₂²×#410	C₂³	1	1	yes	characteristic
111	C₂²×#410	C₂³	1	1	yes	characteristic
112	C₂²×#410	C₂³	1	1	yes	characteristic
113	#52165	D₄	1	2	yes	complemented
114	#52165	D₄	1	2	yes	complemented
115	#37376	D₄	1	2	yes	complemented
116	#37374	D₄	1	2	yes	complemented
117	#37374	D₄	1	1	yes	characteristic, complemented
118	#37374	D₄	1	1	yes	characteristic, complemented
119	#37273	D₄	1	2	yes	complemented
120	#37269	D₄	1	2	yes	complemented
121	#37269	D₄	1	1	yes	characteristic, complemented
122	#37269	D₄	1	1	yes	characteristic, complemented
123	#36955	C₂³	1	2	yes	—
124	#36737	C₂³	1	4	yes	—
125	#36702	C₂³	1	2	yes	—
126	#34980	D₄	1	4	yes	complemented
127	#34980	C₂³	1	4	yes	—
128	C₂×#2405	D₄	1	2	yes	complemented
129	C₂×#2405	C₂³	1	2	yes	—
130	C₂×#2403	D₄	1	2	yes	complemented
131	C₂×#2403	C₂³	1	2	yes	—
132	#34412	D₄	1	2	yes	complemented
133	#34411	D₄	1	2	yes	complemented
134	#34406	C₂³	1	4	yes	—
135	#34369	D₄	1	2	yes	complemented
136	#34368	D₄	1	2	yes	complemented
137	#34044	D₄	1	1	yes	characteristic, complemented
138	#34044	C₂³	1	1	yes	characteristic
139	C₂×#2311	D₄	1	1	yes	characteristic, complemented
140	C₂×#2311	C₂³	1	1	yes	characteristic
141	C₂×#2309	D₄	1	1	yes	characteristic, complemented
142	C₂×#2309	D₄	1	1	yes	characteristic, complemented
143	#33358	D₄	1	8	yes	complemented
144	C₂×#2127	C₂³	1	4	yes	—
145	C₂×#2127	C₂³	1	4	yes	—
146	C₂×#2127	C₂³	1	4	yes	—
147	C₂×#2127	C₂³	1	4	yes	—
148	C₂×#2121	C₂³	1	4	yes	complemented
149	C₂×#2121	C₂³	1	4	yes	complemented
150	C₂²×#352	C₂³	1	2	yes	complemented
151	C₂²×#352	C₂³	1	2	yes	complemented
152	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	complemented
153	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	complemented
154	C₂×#1913	C₂³	1	4	yes	complemented
155	#21012	D₄	1	8	yes	complemented
156	C₂×#1911	C₂³	1	4	yes	—
157	C₂×#1911	C₂³	1	4	yes	—
158	C₂×#1890	C₂³	1	2	yes	complemented
159	C₂×#1889	C₂³	1	2	yes	complemented
160	#20609	C₂³	1	4	yes	complemented
161	C₂×#1790	C₂³	1	4	yes	complemented
162	C₂×#1783	C₂³	1	4	yes	—
163	C₂×#1781	C₂³	1	4	yes	—
164	C₂×#1781	C₂³	1	4	yes	—
165	#12574	C₂³	1	4	yes	complemented
166	#12574	C₂³	1	4	yes	complemented
167	C₂×#1390	C₂³	1	4	yes	complemented
168	C₂×#1390	C₂³	1	4	yes	complemented
169	#10754	C₂³	1	4	yes	complemented
170	#10745	C₂³	1	4	yes	complemented
171	C₂×#585	C₂×D₄	1	4	yes	complemented
172	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
173	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
174	C₂³×#41	C₂×D₄	1	1	yes	characteristic
175	C₂³×#41	C₂×D₄	1	1	yes	characteristic
176	C₂³×#41	C₂×D₄	1	2	yes	—
177	C₂³×#41	C₂×D₄	1	1	yes	characteristic
178	C₂³×#41	C₂×D₄	1	1	yes	characteristic
179	C₂³×#41	C₂×D₄	1	1	yes	characteristic
180	C₂³×#41	C₂×D₄	1	1	yes	characteristic
181	C₂³×#41	C₂⁴	1	1	yes	characteristic
182	C₂⁴×D₄	C₂×D₄	1	2	yes	—
183	C₂⁴×D₄	C₂×D₄	1	2	yes	—
184	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
185	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
186	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
187	C₂⁴×D₄	C₂×D₄	1	2	yes	—
188	C₂⁴×D₄	C₂⁴	1	2	yes	—
189	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
190	C₂×#563	C₂×D₄	1	2	yes	complemented
191	C₂×H(3,𝔽₄)	C₂×D₄	1	2	yes	complemented
192	C₂×#560	C₂×D₄	1	2	yes	complemented
193	C₂×#560	C₂×D₄	1	2	yes	complemented
194	C₂×#559	C₂×D₄	1	2	yes	complemented
195	C₂×#551	C₂×D₄	1	2	yes	complemented
196	C₂×#551	C₂×D₄	1	2	yes	complemented
197	C₂×D₄²	C₂×D₄	1	2	yes	complemented
198	#3449	C₂×D₄	1	4	yes	—
199	#3449	C₂×D₄	1	4	yes	—
200	#3449	C₂×D₄	1	4	yes	—
201	#3449	#41	1	4	yes	—
202	C₂×#536	C₂×D₄	1	1	yes	characteristic
203	C₂×#536	C₂×D₄	1	1	yes	characteristic
204	C₂×#536	C₂×D₄	1	1	yes	characteristic
205	C₂×#536	C₂×D₄	1	1	yes	characteristic
206	C₂×#536	C₂×D₄	1	1	yes	characteristic
207	C₂×#536	C₂×D₄	1	1	yes	characteristic
208	C₂×#536	C₂×D₄	1	2	yes	—
209	C₂×#536	C₂×D₄	1	2	yes	—
210	C₂×#535	C₂×D₄	1	1	yes	characteristic
211	C₂×#535	C₂×D₄	1	1	yes	characteristic
212	C₂×#535	C₂×D₄	1	1	yes	characteristic
213	C₂×#535	C₂×D₄	1	1	yes	characteristic
214	C₂×#535	C₂×D₄	1	1	yes	characteristic
215	C₂×#535	C₂×D₄	1	1	yes	characteristic
216	C₂×#535	C₂⁴	1	2	yes	—
217	C₂×#535	C₂⁴	1	2	yes	—
218	C₂×#534	C₂×D₄	1	4	yes	—
219	C₂×#534	C₂×D₄	1	2	yes	—
220	C₂×#534	C₂⁴	1	2	yes	—
221	C₂×#532	C₂×D₄	1	2	yes	—
222	C₂×#532	C₂×D₄	1	2	yes	—
223	C₂×#532	C₂×D₄	1	2	yes	—
224	C₂×#532	C₂×D₄	1	2	yes	—
225	C₂×#525	C₂×D₄	1	1	yes	characteristic
226	C₂×#525	C₂×D₄	1	1	yes	characteristic
227	C₂×#525	C₂×D₄	1	1	yes	characteristic
228	C₂×#525	C₂×D₄	1	1	yes	characteristic
229	C₂×#525	C₂×D₄	1	1	yes	characteristic
230	C₂×#525	C₂×D₄	1	1	yes	characteristic
231	C₂×#525	C₂×D₄	1	2	yes	—
232	C₂×#525	C₂×D₄	1	1	yes	characteristic
233	C₂×#525	C₂×D₄	1	1	yes	characteristic
234	C₂×#525	C₂×D₄	1	2	yes	—
235	C₂×#525	C₂×D₄	1	4	yes	—
236	C₂×#525	C₂×D₄	1	4	yes	—
237	C₂²×#123	C₂×D₄	1	1	yes	characteristic
238	C₂²×#123	C₂×D₄	1	2	yes	—
239	C₂²×#123	C₂⁴	1	1	yes	characteristic
240	C₂²×#120	C₂×D₄	1	1	yes	characteristic
241	C₂²×#120	C₂×D₄	1	2	yes	—
242	C₂²×#120	C₂×D₄	1	4	yes	—
243	C₂²×#120	C₂⁴	1	1	yes	characteristic
244	#3428	C₂×D₄	1	4	yes	complemented
245	C₂×#518	C₂×D₄	1	4	yes	—
246	C₂×#518	C₂⁴	1	2	yes	—
247	C₂²×#117	C₂×D₄	1	1	yes	characteristic
248	C₂²×#117	C₂×D₄	1	1	yes	characteristic
249	C₂²×#117	C₂×D₄	1	1	yes	characteristic
250	C₂²×#117	C₂×D₄	1	1	yes	characteristic
251	C₂²×#117	C₂×D₄	1	1	yes	characteristic
252	C₂²×#117	C₂×D₄	1	1	yes	characteristic
253	C₂²×#117	C₂×D₄	1	1	yes	characteristic
254	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
255	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
256	#3019	C₂×D₄	1	16	yes	complemented
257	C₂×#413	C₂×D₄	1	4	yes	complemented
258	C₂×#413	C₂×D₄	1	4	yes	complemented
259	C₂²×#100	C₂⁴	1	2	yes	—
260	C₂²×#100	C₂⁴	1	2	yes	—
261	C₂×#410	C₂×D₄	1	4	yes	complemented
262	C₂×#410	C₂×D₄	1	4	yes	complemented
263	C₂²×#99	C₂⁴	1	2	yes	—
264	C₂²×#99	C₂⁴	1	2	yes	—
265	C₂²×#99	C₂⁴	1	2	yes	—
266	C₂²×#99	C₂⁴	1	2	yes	—
267	#2717	C₂×D₄	1	4	yes	complemented
268	#2717	C₂×D₄	1	2	yes	complemented
269	#2717	C₂×D₄	1	2	yes	complemented
270	#2709	C₂×D₄	1	4	yes	complemented
271	#2709	C₂×D₄	1	2	yes	complemented
272	#2709	C₂×D₄	1	2	yes	complemented
273	#2684	C₂×D₄	1	4	yes	complemented
274	#2684	C₂×D₄	1	2	yes	complemented
275	#2684	C₂×D₄	1	2	yes	complemented
276	#2669	C₂×D₄	1	2	yes	complemented
277	#2669	C₂×D₄	1	2	yes	complemented
278	#2669	C₂×D₄	1	4	yes	complemented
279	#2380	C₂×D₄	1	4	yes	complemented
280	#2379	C₂×D₄	1	4	yes	complemented
281	#2372	C₂×D₄	1	4	yes	complemented
282	#2366	C₂×D₄	1	4	yes	complemented
283	#2311	C₂×D₄	1	2	yes	—
284	#2311	C₂×D₄	1	1	yes	characteristic
285	#2311	C₂×D₄	1	1	yes	characteristic
286	#2311	C₂×D₄	1	2	yes	—
287	#2311	C₂×D₄	1	1	yes	characteristic
288	#2311	C₂×D₄	1	2	yes	—
289	#2311	C₂×D₄	1	1	yes	characteristic
290	#2311	C₂×D₄	1	2	yes	—
291	#2308	C₂×D₄	1	4	yes	—
292	#2308	C₂×D₄	1	2	yes	—
293	#2308	C₂⁴	1	2	yes	—
294	#2297	C₂×D₄	1	2	yes	—
295	#2297	C₂×D₄	1	2	yes	—
296	C₂×#386	C₂×D₄	1	2	yes	—
297	C₂×#386	C₂×D₄	1	2	yes	—
298	C₂×#386	C₂×D₄	1	2	yes	—
299	C₂×#386	C₂⁴	1	2	yes	—
300	C₂×#379	C₂×D₄	1	2	yes	—
301	C₂×#379	C₂×D₄	1	2	yes	—
302	C₂×#379	C₂×D₄	1	4	yes	—
303	#2127	C₂×D₄	1	16	yes	complemented
304	#1911	C₂×D₄	1	16	yes	complemented
305	C₂⁶	#120	1	2	yes	—
306	C₂⁶	C₂²×D₄	1	2	yes	—
307	C₂⁶	C₂²×D₄	1	2	yes	—
308	C₂⁶	C₂²×D₄	1	1	yes	characteristic
309	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
310	C₂²×#41	#120	1	2	yes	—
311	C₂²×#41	#120	1	2	yes	—
312	C₂²×#41	#120	1	4	yes	—
313	C₂²×#41	#121	1	4	yes	—
314	C₂²×#41	C₂²×D₄	1	2	yes	—
315	C₂²×#41	C₂²×D₄	1	2	yes	—
316	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
317	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
318	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
319	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
320	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
321	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
322	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
323	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
324	C₂²×#41	C₂²×D₄	1	2	yes	—
325	C₂²×#41	C₂²×D₄	1	2	yes	—
326	C₂²×#41	C₂²×D₄	1	2	yes	—
327	C₂²×#41	C₂×#41	1	2	yes	—
328	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
329	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
330	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
331	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
332	C₂³×Q₈	#120	1	1	yes	characteristic
333	C₂³×Q₈	#120	1	1	yes	characteristic
334	C₂³×Q₈	#120	1	1	yes	characteristic
335	C₂³×Q₈	#120	1	1	yes	characteristic
336	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
337	C₂³×D₄	#120	1	2	yes	—
338	C₂³×D₄	#120	1	2	yes	—
339	C₂³×D₄	#120	1	2	yes	—
340	C₂³×D₄	#120	1	1	yes	characteristic
341	C₂³×D₄	#120	1	1	yes	characteristic
342	C₂³×D₄	#120	1	1	yes	characteristic
343	C₂³×D₄	#120	1	1	yes	characteristic
344	C₂³×D₄	#120	1	1	yes	characteristic
345	C₂³×D₄	#120	1	1	yes	characteristic
346	C₂³×D₄	C₂²×D₄	1	2	yes	—
347	C₂³×D₄	C₂²×D₄	1	2	yes	—
348	C₂³×D₄	C₂²×D₄	1	2	yes	—
349	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
350	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
351	C₂³×D₄	C₂²×D₄	1	2	yes	—
352	C₂³×D₄	C₂⁵	1	1	yes	characteristic
353	C₂⁴×C₄	#120	1	2	yes	—
354	C₂⁴×C₄	#120	1	2	yes	—
355	C₂⁴×C₄	#120	1	1	yes	characteristic
356	C₂⁴×C₄	#120	1	1	yes	characteristic
357	C₂⁴×C₄	#120	1	1	yes	characteristic
358	C₂⁴×C₄	#120	1	1	yes	characteristic
359	C₂⁴×C₄	#120	1	2	yes	—
360	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
361	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
362	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
363	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
364	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
365	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
366	#536	#120	1	8	yes	—
367	#536	#120	1	4	yes	—
368	#536	#121	1	8	yes	—
369	#536	#121	1	4	yes	—
370	#536	#121	1	4	yes	—
371	#536	#127	1	4	yes	—
372	#535	#120	1	4	yes	—
373	#535	#121	1	4	yes	—
374	#535	#121	1	4	yes	—
375	#535	#127	1	4	yes	—
376	#535	C₂²×D₄	1	4	yes	—
377	#535	C₂²×D₄	1	4	yes	—
378	#535	C₂²×D₄	1	4	yes	—
379	#535	C₂×#41	1	4	yes	—
380	#532	#120	1	8	yes	—
381	#532	#121	1	8	yes	—
382	#532	#121	1	8	yes	—
383	#532	#127	1	8	yes	—
384	C₂×C₄⋊Q₈	#120	1	2	yes	—
385	C₂×C₄⋊Q₈	#120	1	2	yes	—
386	C₂×C₄⋊Q₈	#120	1	2	yes	—
387	C₂×C₄⋊Q₈	#120	1	2	yes	—
388	C₂×#127	C₂²×D₄	1	2	yes	—
389	C₂×#127	C₂²×D₄	1	2	yes	—
390	C₂×#127	C₂²×D₄	1	2	yes	—
391	C₂×#127	C₂²×D₄	1	2	yes	—
392	C₂×#124	#120	1	2	yes	—
393	C₂×#124	#120	1	2	yes	—
394	C₂×#124	#120	1	2	yes	—
395	C₂×#124	#120	1	2	yes	—
396	C₂×#124	C₂²×D₄	1	2	yes	—
397	C₂×#124	C₂²×D₄	1	2	yes	—
398	C₂×#124	C₂²×D₄	1	2	yes	—
399	C₂×#124	C₂²×D₄	1	2	yes	—
400	C₂×#123	#120	1	1	yes	characteristic
401	C₂×#123	#120	1	1	yes	characteristic
402	C₂×#123	#120	1	1	yes	characteristic
403	C₂×#123	#120	1	1	yes	characteristic
404	C₂×#123	#120	1	2	yes	—
405	C₂×#123	#120	1	2	yes	—
406	C₂×#123	C₂²×D₄	1	1	yes	characteristic
407	C₂×#123	C₂²×D₄	1	1	yes	characteristic
408	C₂×#123	C₂²×D₄	1	1	yes	characteristic
409	C₂×#123	C₂²×D₄	1	1	yes	characteristic
410	C₂×#123	C₂²×D₄	1	2	yes	—
411	C₂×#123	C₂²×D₄	1	2	yes	—
412	C₂×#120	#120	1	1	yes	characteristic
413	C₂×#120	#120	1	1	yes	characteristic
414	C₂×#120	#120	1	1	yes	characteristic
415	C₂×#120	#120	1	1	yes	characteristic
416	C₂×#120	#120	1	2	yes	—
417	C₂×#120	#120	1	2	yes	—
418	C₂×#120	C₂²×D₄	1	1	yes	characteristic
419	C₂×#120	C₂²×D₄	1	1	yes	characteristic
420	C₂×#120	C₂²×D₄	1	1	yes	characteristic
421	C₂×#120	C₂²×D₄	1	1	yes	characteristic
422	C₂×#120	C₂²×D₄	1	2	yes	—
423	C₂×#120	C₂²×D₄	1	2	yes	—
424	#518	C₂²×D₄	1	4	yes	—
425	C₂×#117	#120	1	1	yes	characteristic
426	C₂×#117	#120	1	1	yes	characteristic
427	C₂×#117	#120	1	2	yes	—
428	C₂×#117	#120	1	1	yes	characteristic
429	C₂×#117	#120	1	1	yes	characteristic
430	C₂×#117	#120	1	1	yes	characteristic
431	C₂×#117	#120	1	1	yes	characteristic
432	C₂×#117	#120	1	2	yes	—
433	C₂×#117	#120	1	2	yes	—
434	C₂×#117	#120	1	2	yes	—
435	C₂×#117	#120	1	1	yes	characteristic
436	C₂×#117	#120	1	1	yes	characteristic
437	C₂×#117	#120	1	1	yes	characteristic
438	C₂×#117	#120	1	1	yes	characteristic
439	C₂×#117	#120	1	1	yes	characteristic
440	C₂×#117	#120	1	1	yes	characteristic
441	C₂×#117	#120	1	4	yes	—
442	C₂×#117	#121	1	4	yes	—
443	C₂×#117	C₂²×D₄	1	2	yes	—
444	C₂×#117	C₂²×D₄	1	2	yes	—
445	C₂²×C₄⋊C₄	#120	1	2	yes	—
446	C₂²×C₄⋊C₄	#120	1	2	yes	—
447	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
448	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
449	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
450	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
451	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
452	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
453	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
454	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
455	C₂²×C₄²	#120	1	2	yes	—
456	C₂²×C₄²	#120	1	2	yes	—
457	C₂²×C₄²	#120	1	2	yes	—
458	C₂×#100	C₂²×D₄	1	4	yes	—
459	C₂×#100	C₂²×D₄	1	4	yes	—
460	C₂×#99	C₂²×D₄	1	4	yes	—
461	C₂×#99	C₂²×D₄	1	4	yes	—
462	#386	#120	1	2	yes	—
463	#386	#120	1	2	yes	—
464	#386	#120	1	2	yes	—
465	#386	#120	1	2	yes	—
466	#386	#120	1	4	yes	—
467	#386	#120	1	4	yes	—
468	#386	C₂²×D₄	1	2	yes	—
469	#386	C₂²×D₄	1	2	yes	—
470	#386	C₂²×D₄	1	2	yes	—
471	#386	C₂²×D₄	1	2	yes	—
472	#386	C₂²×D₄	1	4	yes	—
473	#386	C₂²×D₄	1	4	yes	—
474	C₂⁵	C₂×#120	1	2	yes	—
475	C₂⁵	C₂×#120	1	2	yes	—
476	C₂⁵	C₂×#120	1	2	yes	—
477	C₂⁵	C₂×#120	1	1	yes	characteristic
478	C₂⁵	C₂×#120	1	1	yes	characteristic
479	C₂⁵	C₂×#120	1	2	yes	—
480	C₂⁵	C₂×#120	1	1	yes	characteristic
481	C₂⁵	C₂³×D₄	1	1	yes	characteristic
482	C₂⁵	C₂³×D₄	1	1	yes	characteristic
483	C₂×#41	#392	1	8	yes	complemented
484	C₂×#41	C₂×#120	1	4	yes	—
485	C₂×#41	C₂×#120	1	2	yes	—
486	C₂×#41	C₂×#120	1	2	yes	—
487	C₂×#41	C₂×#121	1	4	yes	—
488	C₂×#41	C₂×#121	1	2	yes	—
489	C₂×#41	C₂×#121	1	2	yes	—
490	C₂×#41	C₂×#121	1	2	yes	—
491	C₂×#41	C₂×#121	1	2	yes	—
492	C₂×#41	C₂×#127	1	2	yes	—
493	C₂×#41	C₂×#127	1	2	yes	—
494	C₂×#41	#534	1	2	yes	—
495	C₂×#41	#534	1	2	yes	—
496	C₂×#41	#534	1	2	yes	—
497	C₂×#41	#534	1	2	yes	—
498	C₂×#41	#535	1	2	yes	—
499	C₂×#41	#535	1	2	yes	—
500	C₂×#41	#535	1	2	yes	—
501	C₂×#41	#535	1	2	yes	—
502	C₂×#41	D₄²	1	2	yes	—
503	C₂×#41	D₄²	1	2	yes	—
504	C₂×#41	D₄²	1	2	yes	—
505	C₂×#41	D₄²	1	2	yes	—
506	C₂×#41	D₄²	1	2	yes	—
507	C₂×#41	D₄²	1	2	yes	—
508	C₂×#41	D₄²	1	2	yes	—
509	C₂×#41	D₄²	1	2	yes	—
510	C₂×#41	D₄²	1	2	yes	—
511	C₂×#41	D₄²	1	2	yes	—
512	C₂×#41	D₄²	1	2	yes	—
513	C₂×#41	D₄²	1	2	yes	—
514	C₂×#41	#546	1	2	yes	—
515	C₂×#41	#546	1	2	yes	—
516	C₂×#41	#546	1	2	yes	—
517	C₂×#41	#546	1	2	yes	—
518	C₂²×Q₈	#392	1	4	yes	complemented
519	C₂²×Q₈	C₂×#120	1	2	yes	—
520	C₂²×Q₈	C₂×#120	1	2	yes	—
521	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
522	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
523	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
524	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
525	C₂²×Q₈	C₂×#120	1	2	yes	—
526	C₂²×Q₈	C₂×#121	1	2	yes	—
527	C₂²×Q₈	#534	1	2	yes	—
528	C₂²×Q₈	#534	1	2	yes	—
529	C₂²×D₄	#392	1	4	yes	complemented
530	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
531	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
532	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
533	C₂²×D₄	C₂×#120	1	1	yes	characteristic
534	C₂²×D₄	C₂×#120	1	1	yes	characteristic
535	C₂²×D₄	C₂×#120	1	1	yes	characteristic
536	C₂²×D₄	C₂×#120	1	1	yes	characteristic
537	C₂²×D₄	C₂×#120	1	1	yes	characteristic
538	C₂²×D₄	C₂×#120	1	1	yes	characteristic
539	C₂²×D₄	C₂×#120	1	1	yes	characteristic
540	C₂²×D₄	C₂×#120	1	1	yes	characteristic
541	C₂²×D₄	C₂×#120	1	2	yes	—
542	C₂²×D₄	C₂×#120	1	2	yes	—
543	C₂²×D₄	D₄²	1	2	yes	—
544	C₂²×D₄	D₄²	1	2	yes	—
545	C₂²×D₄	D₄²	1	2	yes	—
546	C₂²×D₄	D₄²	1	2	yes	—
547	C₂²×D₄	D₄²	1	2	yes	—
548	C₂²×D₄	D₄²	1	2	yes	—
549	C₂²×D₄	#546	1	2	yes	—
550	C₂²×D₄	#546	1	2	yes	—
551	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
552	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
553	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
554	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
555	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
556	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
557	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
558	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
559	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
560	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
562	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
563	C₂³×C₄	C₂×#120	1	2	yes	—
564	C₂³×C₄	C₂×#120	1	1	yes	characteristic
565	C₂³×C₄	C₂×#120	1	1	yes	characteristic
566	C₂³×C₄	C₂×#120	1	1	yes	characteristic
567	C₂³×C₄	C₂×#120	1	1	yes	characteristic
568	C₂³×C₄	C₂×#120	1	1	yes	characteristic
569	C₂³×C₄	C₂×#120	1	1	yes	characteristic
570	C₂³×C₄	C₂×#120	1	1	yes	characteristic
571	C₂³×C₄	C₂×#120	1	1	yes	characteristic
572	C₂³×C₄	C₂×#120	1	1	yes	characteristic
573	C₂³×C₄	C₂×#120	1	1	yes	characteristic
574	C₂³×C₄	C₂×#120	1	1	yes	characteristic
575	C₂³×C₄	C₂×#120	1	1	yes	characteristic
576	C₂³×C₄	C₂×#120	1	1	yes	characteristic
577	C₂³×C₄	C₂×#120	1	1	yes	characteristic
578	C₂³×C₄	C₂×#120	1	2	yes	—
579	C₂³×C₄	C₂×#120	1	1	yes	characteristic
580	C₂³×C₄	C₂×#120	1	2	yes	—
581	C₂³×C₄	C₂×#120	1	1	yes	characteristic
582	C₂³×C₄	C₂×#120	1	2	yes	—
583	C₂³×C₄	C₂×#120	1	2	yes	—
584	C₂³×C₄	C₂×#120	1	4	yes	—
585	C₂³×C₄	C₂×#120	1	1	yes	characteristic
586	C₂³×C₄	C₂×#121	1	2	yes	—
587	C₂³×C₄	#534	1	2	yes	—
588	C₂³×C₄	#534	1	2	yes	—
589	C₂³×C₄	D₄²	1	2	yes	—
590	C₂³×C₄	D₄²	1	2	yes	—
591	C₂³×C₄	D₄²	1	2	yes	—
592	C₂³×C₄	D₄²	1	2	yes	—
593	C₂³×C₄	D₄²	1	2	yes	—
594	C₂³×C₄	D₄²	1	2	yes	—
595	C₂³×C₄	#546	1	2	yes	—
596	C₂³×C₄	#546	1	2	yes	—
597	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
598	C₄⋊Q₈	#392	1	8	yes	complemented
599	C₄⋊Q₈	#392	1	8	yes	complemented
600	#127	C₂×#120	1	4	yes	—
601	#127	C₂×#121	1	4	yes	—
602	#127	C₂×#121	1	4	yes	—
603	#127	C₂×#127	1	4	yes	—
604	#124	#392	1	8	yes	complemented
605	#124	#392	1	8	yes	complemented
606	#124	C₂×#120	1	4	yes	—
607	#124	C₂×#121	1	4	yes	—
608	#124	C₂×#121	1	4	yes	—
609	#124	C₂×#127	1	4	yes	—
610	#117	#392	1	4	yes	complemented
611	#117	#392	1	4	yes	complemented
612	#117	C₂×#120	1	4	yes	—
613	#117	C₂×#121	1	4	yes	—
614	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
616	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
619	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
620	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
623	C₂×C₄²	#392	1	8	yes	complemented
624	C₂×C₄²	C₂×#120	1	2	yes	—
625	C₂×C₄²	C₂×#120	1	2	yes	—
626	C₂×C₄²	C₂×#120	1	2	yes	—
627	C₂×C₄²	C₂×#120	1	2	yes	—
628	C₂⁴	#2403	1	2	yes	—
629	C₂⁴	#2410	1	2	yes	—
630	C₂⁴	#2846	1	1	yes	characteristic
631	C₂⁴	#2846	1	1	yes	characteristic
632	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
633	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
634	C₂⁴	C₂²×#120	1	1	yes	characteristic
635	C₂⁴	C₂²×#120	1	1	yes	characteristic
636	C₂⁴	C₂²×#120	1	1	yes	characteristic
637	C₂⁴	C₂²×#120	1	1	yes	characteristic
638	C₂⁴	C₂²×#120	1	1	yes	characteristic
639	C₂⁴	C₂×D₄²	1	1	yes	characteristic
640	C₂⁴	C₂×D₄²	1	1	yes	characteristic
641	C₂⁴	C₂×D₄²	1	1	yes	characteristic
642	C₂⁴	C₂×D₄²	1	1	yes	characteristic
643	C₂⁴	C₂×D₄²	1	1	yes	characteristic
644	C₂⁴	C₂×D₄²	1	1	yes	characteristic
645	C₂⁴	C₂×#546	1	1	yes	characteristic
646	C₂⁴	C₂×#546	1	1	yes	characteristic
647	C₂×Q₈	C₂×#392	1	4	yes	—
648	C₂×Q₈	C₂×#392	1	2	yes	—
649	C₂×Q₈	C₂×#392	1	2	yes	—
650	C₂×Q₈	#2403	1	2	yes	—
651	C₂×Q₈	#2403	1	2	yes	—
652	C₂×Q₈	#2410	1	2	yes	—
653	C₂×Q₈	#2410	1	2	yes	—
654	C₂×Q₈	#2613	1	2	yes	—
655	C₂×Q₈	#2613	1	2	yes	—
656	C₂×D₄	C₂×#392	1	4	yes	—
657	C₂×D₄	#2403	1	2	yes	—
658	C₂×D₄	#2403	1	2	yes	—
659	C₂×D₄	#2403	1	2	yes	—
660	C₂×D₄	#2403	1	2	yes	—
661	C₂×D₄	#2408	1	2	yes	—
662	C₂×D₄	#2408	1	2	yes	—
663	C₂×D₄	#2408	1	2	yes	—
664	C₂×D₄	#2408	1	2	yes	—
665	C₂×D₄	#2410	1	2	yes	—
666	C₂×D₄	#2410	1	2	yes	—
667	C₂×D₄	#2410	1	2	yes	—
668	C₂×D₄	#2410	1	2	yes	—
669	C₂×D₄	#2433	1	2	yes	—
670	C₂×D₄	#2433	1	2	yes	—
671	C₂×D₄	#2433	1	2	yes	—
672	C₂×D₄	#2433	1	2	yes	—
673	C₂×D₄	C₂²×#120	1	1	yes	characteristic
674	C₂×D₄	C₂²×#121	1	1	yes	characteristic
675	C₂×D₄	C₂²×#121	1	1	yes	characteristic
676	C₂×D₄	C₂²×#127	1	1	yes	characteristic
677	C₂×D₄	C₂×#534	1	1	yes	characteristic
678	C₂×D₄	C₂×#534	1	1	yes	characteristic
679	C₂×D₄	C₂×#535	1	1	yes	characteristic
680	C₂×D₄	C₂×#535	1	1	yes	characteristic
681	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
682	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
683	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
684	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
685	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
686	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
687	C₂×D₄	C₂×#546	1	1	yes	characteristic
688	C₂×D₄	C₂×#546	1	1	yes	characteristic
689	C₂²×C₄	C₂×#392	1	2	yes	—
690	C₂²×C₄	C₂×#392	1	2	yes	—
691	C₂²×C₄	#2403	1	2	yes	—
692	C₂²×C₄	#2403	1	2	yes	—
693	C₂²×C₄	#2403	1	2	yes	—
694	C₂²×C₄	#2403	1	2	yes	—
695	C₂²×C₄	#2403	1	2	yes	—
696	C₂²×C₄	#2403	1	2	yes	—
697	C₂²×C₄	#2403	1	2	yes	—
698	C₂²×C₄	#2403	1	2	yes	—
699	C₂²×C₄	#2403	1	2	yes	—
700	C₂²×C₄	#2408	1	2	yes	—
701	C₂²×C₄	#2408	1	2	yes	—
702	C₂²×C₄	#2408	1	2	yes	—
703	C₂²×C₄	#2408	1	2	yes	—
704	C₂²×C₄	#2410	1	2	yes	—
705	C₂²×C₄	#2410	1	2	yes	—
706	C₂²×C₄	#2410	1	2	yes	—
707	C₂²×C₄	#2410	1	2	yes	—
708	C₂²×C₄	#2410	1	2	yes	—
709	C₂²×C₄	#2410	1	2	yes	—
710	C₂²×C₄	#2410	1	2	yes	—
711	C₂²×C₄	#2410	1	2	yes	—
712	C₂²×C₄	#2410	1	2	yes	—
713	C₂²×C₄	#2433	1	2	yes	—
714	C₂²×C₄	#2433	1	2	yes	—
715	C₂²×C₄	#2433	1	2	yes	—
716	C₂²×C₄	#2433	1	2	yes	—
717	C₂²×C₄	#2613	1	2	yes	—
718	C₂²×C₄	#2613	1	2	yes	—
719	C₂²×C₄	#2846	1	1	yes	characteristic
720	C₂²×C₄	#2846	1	1	yes	characteristic
721	C₂²×C₄	#2846	1	1	yes	characteristic
722	C₂²×C₄	#2846	1	1	yes	characteristic
723	C₂²×C₄	#2846	1	1	yes	characteristic
724	C₂²×C₄	#2846	1	1	yes	characteristic
725	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
726	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
727	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
728	C₂²×C₄	#3026	1	2	yes	—
729	C₂²×C₄	#3026	1	1	yes	characteristic
730	C₂²×C₄	#3026	1	1	yes	characteristic
731	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
732	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
733	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
734	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
735	C₂²×C₄	C₂×#534	1	1	yes	characteristic
736	C₂²×C₄	C₂×#534	1	1	yes	characteristic
737	C₄²	C₂×#392	1	4	yes	—
738	C₄²	C₂×#392	1	4	yes	—
739	C₂³	#14715	1	2	yes	—
740	C₂³	#14715	1	2	yes	—
741	C₂³	C₂×#2403	1	1	yes	characteristic
742	C₂³	C₂×#2403	1	1	yes	characteristic
743	C₂³	C₂×#2403	1	1	yes	characteristic
744	C₂³	C₂×#2410	1	1	yes	characteristic
745	C₂³	C₂×#2410	1	1	yes	characteristic
746	C₂³	C₂×#2410	1	1	yes	characteristic
747	C₂³	C₂×#2408	1	1	yes	characteristic
748	C₂³	C₂×#2408	1	1	yes	characteristic
749	C₂³	C₂×#2433	1	1	yes	characteristic
750	C₂³	C₂×#2433	1	1	yes	characteristic
751	C₂³	C₂×#2846	1	1	yes	characteristic
752	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
753	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
754	C₂³	C₂×#3026	1	1	yes	characteristic
755	C₂³	C₂×#3026	1	1	yes	characteristic
756	C₂×C₄	#14715	1	2	yes	—
757	C₂×C₄	#14715	1	2	yes	—
758	C₂×C₄	#14715	1	2	yes	—
759	C₂×C₄	#14715	1	2	yes	—
760	C₂×C₄	#14715	1	2	yes	—
761	C₂×C₄	#14715	1	2	yes	—
762	C₂×C₄	#23900	1	2	yes	—
763	C₂×C₄	#23900	1	2	yes	—
764	C₂×C₄	#23903	1	2	yes	—
765	C₂×C₄	#23903	1	2	yes	—
766	C₂×C₄	#24404	1	2	yes	—
767	C₂×C₄	#24404	1	2	yes	—
768	C₂×C₄	#24404	1	2	yes	—
769	C₂×C₄	#24404	1	2	yes	—
770	C₂×C₄	#32898	1	2	yes	—
771	C₂×C₄	#32898	1	2	yes	—
772	C₂×C₄	#32898	1	1	yes	characteristic
773	C₂×C₄	#32898	1	1	yes	characteristic
774	C₂×C₄	#32898	1	1	yes	characteristic
775	C₂×C₄	#32898	1	1	yes	characteristic
776	C₂×C₄	C₂²×#392	1	1	yes	characteristic
777	C₂×C₄	C₂×#2613	1	1	yes	characteristic
778	C₂×C₄	C₂×#2403	1	1	yes	characteristic
779	C₂×C₄	C₂×#2410	1	1	yes	characteristic
780	C₂²	C₂×#14715	1	1	yes	characteristic
781	C₂²	C₂×#23900	1	1	yes	characteristic
782	C₂²	C₂×#23903	1	1	yes	characteristic
783	C₂²	C₂×#24404	1	1	yes	characteristic
784	C₂²	C₂×#24404	1	1	yes	characteristic
785	C₂²	C₂×#32898	1	1	yes	characteristic
786	C₂²	C₂×#32898	1	1	yes	characteristic
787	C₄	#394066	1	2	yes	—
788	C₄	#394066	1	2	yes	—
789	C₄	#394066	1	2	yes	—
790	C₄	#394066	1	2	yes	—
791	C₂	C₂×#394066	1	1	yes	characteristic
792	C₂	#72251112	1	1	yes	characteristic
793	C₂	#72256597	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 ◁ C₂³×C₄ ◁ C₂³×H(5,𝔽₂) ◁ 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. #72256668	C₂	semidirect
2. #72256665	C₂	semidirect
3. C₂×#493398	C₂	semidirect
4. #72256654	C₂	semidirect
5. #72256650	C₂	semidirect
6. #72256648	C₂	semidirect
7. #72256636	C₂	semidirect
8. #72256630	C₂	semidirect
9. #72256615	C₂	semidirect
10. C₂×#6437464	C₂	semidirect
11. #72251160	C₂	semidirect
12. #72250024	C₂	semidirect
13. C₂×#7622868	C₂	semidirect
14. C₂×#493561	C₂	semidirect
15. #72238033	C₂	semidirect
16. #72236774	C₂	semidirect
17. #72213329	C₂	semidirect
19. C₂×#62852	C₂²	semidirect
21. C₂×#60398	C₂²	semidirect
22. C₂²×#3025	C₂²	semidirect
24. C₂×#60387	C₂²	semidirect
25. #7793573	C₂²	semidirect
26. #7792761	C₂²	semidirect
32. C₂×#33552	C₂²	semidirect
33. C₂×#33551	C₂²	semidirect
36. C₂×#33358	C₂²	semidirect
37. C₂×#33358	C₂²	semidirect
38. C₂×#33347	C₂²	semidirect
39. C₂×#33347	C₂²	semidirect
40. C₂²×#2120	C₂²	semidirect
41. C₂²×#2120	C₂²	semidirect
42. C₂×#23897	C₂²	semidirect
43. C₂×#21014	C₂²	semidirect
45. C₂×#21012	C₂²	semidirect
46. C₂×#20959	C₂²	semidirect
47. #6370734	C₂²	semidirect
48. C₂×#20610	C₂²	semidirect
49. C₂×#20592	C₂²	semidirect
50. C₂×#20586	C₂²	semidirect
51. C₂×#20586	C₂²	semidirect
52. #498931	C₂²	semidirect
53. #498928	C₂²	semidirect
54. #498927	C₂²	semidirect
55. #494600	C₂²	semidirect
56. C₂×#12754	C₂²	semidirect
57. C₂×#12753	C₂²	semidirect
58. C₂×#12707	C₂²	semidirect
59. #492886	C₂²	semidirect
60. #492886	C₂²	semidirect
61. C₂×#12575	C₂²	semidirect
62. C₂×#12575	C₂²	semidirect
63. #394068	C₂²	semidirect
64. #394066	C₂²	semidirect
65. #394064	C₂²	semidirect
66. #353448	C₂²	semidirect
67. #353428	C₂²	semidirect
68. #147819	C₂²	semidirect
69. #147812	C₂²	semidirect
70. #147811	C₂²	semidirect
71. #147567	C₂²	semidirect
72. #147557	C₂²	semidirect
73. #147555	C₂²	semidirect
74. #146654	C₂²	semidirect
76. C₂³×H(5,𝔽₂)	D₄	semidirect
78. C₂×#3485	D₄	semidirect
81. C₂×#3540	D₄	semidirect
82. C₂×#3540	D₄	semidirect
84. C₂×#3538	D₄	semidirect
85. C₂×#3537	D₄	semidirect
87. C₂×#3481	D₄	semidirect
88. C₂×#3529	D₄	semidirect
89. C₂×#3449	D₄	semidirect
90. C₂×#3449	D₄	semidirect
91. C₂×#3449	D₄	semidirect
95. C₂²×#535	D₄	semidirect
96. C₂²×#525	D₄	semidirect
98. C₂³×#121	D₄	semidirect
100. C₂²×#518	D₄	semidirect
101. C₂×#3026	C₂³	semidirect
102. C₂²×#458	C₂³	semidirect
103. C₂²×B(4,𝔽₂)	C₂³	semidirect
104. #60387	D₄	semidirect
113. #52165	D₄	semidirect
114. #52165	D₄	semidirect
115. #37376	D₄	semidirect
116. #37374	D₄	semidirect
117. #37374	D₄	semidirect
118. #37374	D₄	semidirect
119. #37273	D₄	semidirect
120. #37269	D₄	semidirect
121. #37269	D₄	semidirect
122. #37269	D₄	semidirect
126. #34980	D₄	semidirect
128. C₂×#2405	D₄	semidirect
130. C₂×#2403	D₄	semidirect
132. #34412	D₄	semidirect
133. #34411	D₄	semidirect
135. #34369	D₄	semidirect
136. #34368	D₄	semidirect
137. #34044	D₄	semidirect
139. C₂×#2311	D₄	semidirect
141. C₂×#2309	D₄	semidirect
142. C₂×#2309	D₄	semidirect
143. #33358	D₄	semidirect
148. C₂×#2121	C₂³	semidirect
149. C₂×#2121	C₂³	semidirect
150. C₂²×#352	C₂³	semidirect
151. C₂²×#352	C₂³	semidirect
152. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
153. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
154. C₂×#1913	C₂³	semidirect
155. #21012	D₄	semidirect
158. C₂×#1890	C₂³	semidirect
159. C₂×#1889	C₂³	semidirect
160. #20609	C₂³	semidirect
161. C₂×#1790	C₂³	semidirect
165. #12574	C₂³	semidirect
166. #12574	C₂³	semidirect
167. C₂×#1390	C₂³	semidirect
168. C₂×#1390	C₂³	semidirect
169. #10754	C₂³	semidirect
170. #10745	C₂³	semidirect
171. C₂×#585	C₂×D₄	semidirect
190. C₂×#563	C₂×D₄	semidirect
191. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
192. C₂×#560	C₂×D₄	semidirect
193. C₂×#560	C₂×D₄	semidirect
194. C₂×#559	C₂×D₄	semidirect
195. C₂×#551	C₂×D₄	semidirect
196. C₂×#551	C₂×D₄	semidirect
197. C₂×D₄²	C₂×D₄	semidirect
244. #3428	C₂×D₄	semidirect
256. #3019	C₂×D₄	semidirect
257. C₂×#413	C₂×D₄	semidirect
258. C₂×#413	C₂×D₄	semidirect
261. C₂×#410	C₂×D₄	semidirect
262. C₂×#410	C₂×D₄	semidirect
267. #2717	C₂×D₄	semidirect
268. #2717	C₂×D₄	semidirect
269. #2717	C₂×D₄	semidirect
270. #2709	C₂×D₄	semidirect
271. #2709	C₂×D₄	semidirect
272. #2709	C₂×D₄	semidirect
273. #2684	C₂×D₄	semidirect
274. #2684	C₂×D₄	semidirect
275. #2684	C₂×D₄	semidirect
276. #2669	C₂×D₄	semidirect
277. #2669	C₂×D₄	semidirect
278. #2669	C₂×D₄	semidirect
279. #2380	C₂×D₄	semidirect
280. #2379	C₂×D₄	semidirect
281. #2372	C₂×D₄	semidirect
282. #2366	C₂×D₄	semidirect
303. #2127	C₂×D₄	semidirect
304. #1911	C₂×D₄	semidirect
483. C₂×#41	#392	semidirect
518. C₂²×Q₈	#392	semidirect
529. C₂²×D₄	#392	semidirect
598. C₄⋊Q₈	#392	semidirect
599. C₄⋊Q₈	#392	semidirect
604. #124	#392	semidirect
605. #124	#392	semidirect
610. #117	#392	semidirect
611. #117	#392	semidirect
623. C₂×C₄²	#392	semidirect

Maximal subgroups

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

subgroup	index
#72256668	2
#72256665	2
C₂×#493398	2
#72256654	2
#72256650	2
#72256648	2
#72256636	2
#72256630	2
#72256615	2
C₂×#6437464	2
#72251160	2
#72250024	2
C₂×#7622868	2
C₂×#493561	2
#72238033	2
#72236774	2
#72213329	2