Subgroups — #72318624

Order 2048.

At least 7186 conjugacy classes of subgroups; only the 3486 normal subgroups are shown.

The subgroup lattice has 966 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72318602	C₂	1	2	yes	maximal, complemented
2	#72318589	C₂	1	4	yes	maximal, complemented
3	#72318581	C₂	1	2	yes	maximal, complemented
4	#72318571	C₂	1	2	yes	maximal, complemented
5	#72318558	C₂	1	2	yes	maximal, complemented
6	#72318546	C₂	1	2	yes	maximal, complemented
7	#72318509	C₂	1	4	yes	maximal, complemented
8	#72318497	C₂	1	2	yes	maximal, complemented
9	#72318482	C₂	1	4	yes	maximal, complemented
10	#72318482	C₂	1	4	yes	maximal, complemented
11	#72318474	C₂	1	4	yes	maximal, complemented
12	#72318127	C₂	1	1	yes	maximal, characteristic, complemented
13	#72318063	C₂	1	2	yes	maximal, complemented
14	#72317961	C₂	1	2	yes	maximal, complemented
15	#72317872	C₂	1	2	yes	maximal, complemented
16	#72317848	C₂	1	2	yes	maximal, complemented
17	#72317787	C₂	1	2	yes	maximal, complemented
18	#72317769	C₂	1	1	yes	maximal, characteristic, complemented
19	#72306470	C₂	1	2	yes	maximal, complemented
20	#72286449	C₂	1	4	yes	maximal, complemented
21	#72286244	C₂	1	1	yes	maximal, characteristic, complemented
22	#72284607	C₂	1	4	yes	maximal, complemented
23	#72237054	C₂	1	4	yes	maximal, complemented
24	#72233775	C₂	1	2	yes	maximal, complemented
25	#72219689	C₂	1	2	yes	maximal, complemented
26	#10586091	C₂²	1	1	yes	characteristic, complemented
27	#10586066	C₂²	1	1	yes	characteristic, complemented
28	C₂×#62852	C₂²	1	1	yes	characteristic
29	#10574842	C₂²	1	2	yes	—
30	#10574840	C₂²	1	2	yes	—
31	C₂×#60389	C₂²	1	1	yes	characteristic, complemented
32	C₂×#60390	C₂²	1	1	yes	characteristic, complemented
33	C₂×#60390	C₂²	1	1	yes	characteristic, complemented
34	C₂×#60388	C₂²	1	1	yes	characteristic, complemented
35	#7503375	C₂²	1	4	yes	complemented
36	#7503371	C₂²	1	4	yes	complemented
37	#6628884	C₂²	1	4	yes	complemented
38	#6628883	C₂²	1	4	yes	complemented
39	#6437628	C₂²	1	2	yes	—
40	#6437585	C₂²	1	4	yes	complemented
41	#6437585	C₂²	1	4	yes	complemented
42	#6437577	C₂²	1	4	yes	complemented
43	#6437576	C₂²	1	4	yes	complemented
44	#6437463	C₂²	1	2	yes	—
45	#6437458	C₂²	1	2	yes	—
46	#6437458	C₂²	1	2	yes	complemented
47	#6437457	C₂²	1	2	yes	—
48	#6437456	C₂²	1	2	yes	complemented
49	#6437453	C₂²	1	2	yes	—
50	#6437452	C₂²	1	2	yes	—
51	#6437452	C₂²	1	2	yes	complemented
52	#6437452	C₂²	1	2	yes	complemented
53	#6437451	C₂²	1	2	yes	complemented
54	#6437449	C₂²	1	2	yes	complemented
55	#6437447	C₂²	1	2	yes	complemented
56	#6437445	C₂²	1	2	yes	complemented
57	#6437444	C₂²	1	2	yes	complemented
58	#6437444	C₂²	1	2	yes	complemented
59	C₂×#23915	C₂²	1	2	yes	complemented
60	C₂×#23912	C₂²	1	2	yes	complemented
61	#6433173	C₂²	1	4	yes	complemented
62	#6433173	C₂²	1	4	yes	complemented
63	#6431724	C₂²	1	2	yes	complemented
64	#6431723	C₂²	1	2	yes	complemented
65	#6431723	C₂²	1	2	yes	complemented
66	#6431723	C₂²	1	2	yes	complemented
67	#6374293	C₂²	1	2	yes	complemented
68	#6374281	C₂²	1	2	yes	complemented
69	#6371496	C₂²	1	2	yes	complemented
70	#6371496	C₂²	1	2	yes	complemented
71	#6371458	C₂²	1	1	yes	characteristic, complemented
72	#6371458	C₂²	1	1	yes	characteristic, complemented
73	#6371456	C₂²	1	1	yes	characteristic, complemented
74	#6371455	C₂²	1	1	yes	characteristic, complemented
75	#6370954	C₂²	1	1	yes	characteristic, complemented
76	#6370940	C₂²	1	1	yes	characteristic, complemented
77	#6370706	C₂²	1	1	yes	characteristic, complemented
78	#6370704	C₂²	1	1	yes	characteristic, complemented
79	#476291	C₂²	1	8	yes	complemented
80	#476291	C₂²	1	8	yes	complemented
81	#476289	C₂²	1	8	yes	complemented
82	#476289	C₂²	1	8	yes	complemented
83	#472032	C₂²	1	8	yes	complemented
84	#472029	C₂²	1	8	yes	complemented
85	#469682	C₂²	1	8	yes	complemented
86	#469680	C₂²	1	8	yes	complemented
87	#466727	C₂²	1	8	yes	complemented
88	#466726	C₂²	1	8	yes	complemented
89	#455836	C₂²	1	8	yes	complemented
90	#455836	C₂²	1	8	yes	complemented
91	#455833	C₂²	1	8	yes	complemented
92	#455832	C₂²	1	8	yes	complemented
93	#454695	C₂²	1	8	yes	complemented
94	#454694	C₂²	1	8	yes	complemented
95	#454675	C₂²	1	8	yes	complemented
96	#454675	C₂²	1	8	yes	complemented
97	#454094	C₂²	1	8	yes	complemented
98	#454093	C₂²	1	8	yes	complemented
99	#454087	C₂²	1	8	yes	complemented
100	#454087	C₂²	1	8	yes	complemented
101	#451784	C₂²	1	4	yes	complemented
102	#451783	C₂²	1	4	yes	complemented
103	#449491	C₂²	1	4	yes	complemented
104	#449490	C₂²	1	4	yes	complemented
105	#434421	C₂²	1	8	yes	complemented
106	#434418	C₂²	1	8	yes	complemented
107	#434415	C₂²	1	8	yes	complemented
108	#434415	C₂²	1	8	yes	complemented
109	#419060	C₂²	1	8	yes	complemented
110	#419057	C₂²	1	8	yes	complemented
111	#419045	C₂²	1	8	yes	complemented
112	#419045	C₂²	1	8	yes	complemented
113	#418773	C₂²	1	4	yes	complemented
114	#418772	C₂²	1	4	yes	complemented
115	#418771	C₂²	1	4	yes	complemented
116	#418770	C₂²	1	4	yes	complemented
117	#405948	C₂²	1	4	yes	complemented
118	#405948	C₂²	1	4	yes	complemented
119	#405945	C₂²	1	4	yes	complemented
120	#405945	C₂²	1	4	yes	complemented
121	#404106	C₂²	1	8	yes	complemented
122	#404041	C₂²	1	8	yes	complemented
123	#395791	C₂²	1	4	yes	complemented
124	#395791	C₂²	1	4	yes	complemented
125	#395790	C₂²	1	4	yes	complemented
126	#395789	C₂²	1	4	yes	complemented
127	#395528	C₂²	1	4	yes	complemented
128	#395528	C₂²	1	4	yes	complemented
129	#395527	C₂²	1	4	yes	complemented
130	#395527	C₂²	1	4	yes	complemented
131	#395434	C₂²	1	4	yes	complemented
132	#395434	C₂²	1	4	yes	complemented
133	#395433	C₂²	1	4	yes	complemented
134	#395432	C₂²	1	4	yes	complemented
135	#394601	C₂²	1	4	yes	complemented
136	#394600	C₂²	1	4	yes	complemented
137	#394599	C₂²	1	4	yes	complemented
138	#394598	C₂²	1	4	yes	complemented
139	#394108	C₂²	1	8	yes	complemented
140	#394108	C₂²	1	8	yes	complemented
141	#394103	C₂²	1	8	yes	complemented
142	#394102	C₂²	1	8	yes	complemented
143	#394086	C₂²	1	4	yes	complemented
144	#394086	C₂²	1	4	yes	complemented
145	#393986	C₂²	1	4	yes	complemented
146	#393986	C₂²	1	4	yes	complemented
147	#392730	C₂²	1	4	yes	complemented
148	#392729	C₂²	1	4	yes	complemented
149	#392134	C₂²	1	2	yes	complemented
150	#392132	C₂²	1	2	yes	complemented
151	#387629	C₂²	1	4	yes	complemented
152	#387625	C₂²	1	4	yes	complemented
153	#383066	C₂²	1	4	yes	complemented
154	#383066	C₂²	1	4	yes	complemented
155	#383060	C₂²	1	4	yes	complemented
156	#383059	C₂²	1	4	yes	complemented
157	#382416	C₂²	1	2	yes	complemented
158	#382414	C₂²	1	2	yes	complemented
159	#379829	C₂²	1	4	yes	complemented
160	#379829	C₂²	1	4	yes	complemented
161	#373643	C₂²	1	2	yes	complemented
162	#373639	C₂²	1	2	yes	complemented
163	#368555	C₂²	1	4	yes	complemented
164	#368555	C₂²	1	4	yes	complemented
165	#368550	C₂²	1	4	yes	complemented
166	#368550	C₂²	1	4	yes	complemented
167	#366630	C₂²	1	4	yes	complemented
168	#366630	C₂²	1	4	yes	complemented
169	#366624	C₂²	1	4	yes	complemented
170	#366624	C₂²	1	4	yes	complemented
171	#361636	C₂²	1	2	yes	complemented
172	#361636	C₂²	1	2	yes	complemented
173	#361634	C₂²	1	2	yes	complemented
174	#361634	C₂²	1	2	yes	complemented
175	#361633	C₂²	1	2	yes	complemented
176	#361633	C₂²	1	2	yes	complemented
177	#361631	C₂²	1	2	yes	complemented
178	#361631	C₂²	1	2	yes	complemented
179	#359665	C₂²	1	4	yes	complemented
180	#359665	C₂²	1	4	yes	complemented
181	#359651	C₂²	1	4	yes	complemented
182	#359650	C₂²	1	4	yes	complemented
183	#359562	C₂²	1	2	yes	complemented
184	#359562	C₂²	1	2	yes	complemented
185	#359551	C₂²	1	2	yes	complemented
186	#359551	C₂²	1	2	yes	complemented
187	C₂×2₋¹⁺⁶	C₂³	1	1	yes	characteristic, complemented
188	C₂×H(7,𝔽₂)	C₂³	1	1	yes	characteristic
189	C₂²×#585	C₂³	1	1	yes	characteristic
190	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
191	C₂×#3586	C₂³	1	2	yes	—
192	C₂×#3585	C₂³	1	2	yes	—
193	C₂×#3585	C₂³	1	2	yes	—
194	C₂×#3585	C₂³	1	2	yes	—
195	#62852	C₂³	1	2	yes	—
196	#62852	C₂³	1	2	yes	—
197	#62852	C₂³	1	2	yes	—
198	#62852	C₂³	1	2	yes	complemented
199	#62848	C₂³	1	2	yes	—
200	#62842	C₂³	1	2	yes	—
201	#62811	C₂³	1	2	yes	—
202	#62811	C₂³	1	2	yes	—
203	#62811	C₂³	1	2	yes	—
204	#62811	C₂³	1	2	yes	complemented
205	C₂×#3500	D₄	1	2	yes	complemented
206	C₂×#3500	D₄	1	2	yes	complemented
207	C₂×#3500	C₂³	1	1	yes	characteristic
208	C₂×#3500	C₂³	1	1	yes	characteristic
209	C₂×#3500	C₂³	1	1	yes	characteristic
210	C₂×#3500	C₂³	1	1	yes	characteristic
211	C₂×#3498	D₄	1	2	yes	complemented
212	C₂×#3498	D₄	1	2	yes	complemented
213	C₂×#3498	C₂³	1	1	yes	characteristic
214	C₂×#3498	C₂³	1	1	yes	characteristic
215	C₂×#3498	C₂³	1	1	yes	characteristic
216	C₂×#3498	C₂³	1	1	yes	characteristic
217	C₂×#3487	C₂³	1	2	yes	complemented
218	C₂×#3484	C₂³	1	2	yes	—
219	C₂×#3449	D₄	1	2	yes	complemented
220	C₂×#3449	D₄	1	2	yes	complemented
221	C₂×#3449	C₂³	1	1	yes	characteristic
222	C₂×#3449	C₂³	1	1	yes	characteristic
223	C₂²×#535	D₄	1	2	yes	complemented
224	C₂²×#535	D₄	1	2	yes	complemented
225	C₂²×#535	C₂³	1	1	yes	characteristic
226	C₂²×#535	C₂³	1	1	yes	characteristic
227	#62653	C₂³	1	1	yes	characteristic, complemented
228	#62652	C₂³	1	1	yes	characteristic
229	C₂×#3428	C₂³	1	1	yes	characteristic
230	#60398	C₂³	1	4	yes	—
231	#60398	C₂³	1	4	yes	—
232	#60387	C₂³	1	4	yes	—
233	#60387	C₂³	1	4	yes	—
234	#60387	C₂³	1	8	yes	—
235	#60387	C₂³	1	8	yes	complemented
236	C₂×#3022	C₂³	1	2	yes	—
237	C₂×#3021	C₂³	1	2	yes	—
238	C₂×#3021	C₂³	1	2	yes	—
239	C₂×#3021	C₂³	1	2	yes	complemented
240	C₂×#3020	C₂³	1	2	yes	—
241	C₂×#3020	C₂³	1	2	yes	complemented
242	C₂×#3019	C₂³	1	2	yes	—
243	C₂×#3019	C₂³	1	2	yes	—
244	C₂×#3018	C₂³	1	2	yes	—
245	C₂×#3018	C₂³	1	2	yes	—
246	C₂×#3018	C₂³	1	2	yes	—
247	C₂×#3018	C₂³	1	2	yes	complemented
248	C₂²×#454	C₂³	1	2	yes	—
249	C₂²×#454	C₂³	1	2	yes	complemented
250	C₂²×#455	C₂³	1	2	yes	—
251	C₂²×#453	C₂³	1	2	yes	—
252	#60368	C₂³	1	4	yes	—
253	#60368	C₂³	1	8	yes	complemented
254	#60367	C₂³	1	4	yes	—
255	#60367	C₂³	1	4	yes	—
256	#60367	C₂³	1	4	yes	—
257	#60367	C₂³	1	8	yes	—
258	#60359	C₂³	1	4	yes	—
259	#60359	C₂³	1	4	yes	—
260	C₂×#3005	C₂³	1	4	yes	—
261	C₂×#3003	C₂³	1	4	yes	—
262	C₂×#2921	C₂³	1	2	yes	complemented
263	C₂×#2901	C₂³	1	2	yes	—
264	C₂×#2901	C₂³	1	2	yes	—
265	C₂×#2901	C₂³	1	2	yes	complemented
266	C₂×#2901	C₂³	1	2	yes	complemented
267	#60088	C₂³	1	2	yes	—
268	#60087	C₂³	1	2	yes	—
269	#60087	C₂³	1	2	yes	—
270	#60087	C₂³	1	2	yes	—
271	C₂×#2889	C₂³	1	1	yes	characteristic, complemented
272	C₂×#2889	C₂³	1	1	yes	characteristic, complemented
273	C₂×#2888	C₂³	1	1	yes	characteristic
274	C₂×#2888	C₂³	1	1	yes	characteristic
275	C₂×#2888	C₂³	1	2	yes	—
276	C₂×#2888	C₂³	1	2	yes	complemented
277	#60064	C₂³	1	2	yes	—
278	#60064	C₂³	1	2	yes	—
279	#34048	C₂³	1	2	yes	complemented
280	C₂×#2081	C₂³	1	8	yes	complemented
281	C₂×#2081	C₂³	1	8	yes	complemented
282	#23649	C₂³	1	8	yes	complemented
283	#23649	C₂³	1	8	yes	complemented
284	#23532	C₂³	1	8	yes	complemented
285	#23531	C₂³	1	8	yes	—
286	#23527	C₂³	1	8	yes	—
287	#23527	C₂³	1	8	yes	complemented
288	C₂×#2050	C₂³	1	8	yes	complemented
289	#23525	C₂³	1	8	yes	complemented
290	#23525	C₂³	1	8	yes	complemented
291	#23521	C₂³	1	8	yes	complemented
292	#23521	C₂³	1	8	yes	complemented
293	#23498	C₂³	1	8	yes	complemented
294	#23443	C₂³	1	8	yes	—
295	#23414	C₂³	1	8	yes	—
296	#23414	C₂³	1	8	yes	complemented
297	C₂×#2010	C₂³	1	8	yes	—
298	#23412	C₂³	1	8	yes	—
299	#23412	C₂³	1	8	yes	complemented
300	C₂×#2008	C₂³	1	8	yes	—
301	C₂×#2008	C₂³	1	8	yes	complemented
302	#23402	C₂³	1	4	yes	—
303	#23402	C₂³	1	4	yes	—
304	#23402	C₂³	1	4	yes	—
305	#23402	C₂³	1	4	yes	complemented
306	#23401	C₂³	1	4	yes	—
307	#23400	C₂³	1	4	yes	—
308	#23400	C₂³	1	4	yes	—
309	#23400	C₂³	1	8	yes	—
310	#23400	C₂³	1	4	yes	complemented
311	#23400	C₂³	1	8	yes	complemented
312	#23399	C₂³	1	4	yes	—
313	#23399	C₂³	1	4	yes	—
314	#23399	C₂³	1	4	yes	—
315	#23399	C₂³	1	4	yes	complemented
316	C₂×#2004	C₂³	1	4	yes	—
317	C₂×#2002	C₂³	1	4	yes	—
318	C₂×#2002	C₂³	1	4	yes	—
319	C₂×#2002	C₂³	1	4	yes	complemented
320	#21261	C₂³	1	4	yes	complemented
321	#21260	C₂³	1	4	yes	—
322	#21252	C₂³	1	4	yes	—
323	#21252	C₂³	1	4	yes	complemented
324	#21241	C₂³	1	8	yes	complemented
325	#21210	C₂³	1	8	yes	complemented
326	#21209	C₂³	1	4	yes	—
327	#21209	C₂³	1	4	yes	complemented
328	#21204	C₂³	1	4	yes	—
329	#21203	C₂³	1	4	yes	complemented
330	#21017	C₂³	1	4	yes	—
331	#21017	C₂³	1	4	yes	—
332	#21014	C₂³	1	4	yes	—
333	#21014	C₂³	1	4	yes	—
334	#21012	C₂³	1	4	yes	—
335	#21012	C₂³	1	4	yes	—
336	#21009	C₂³	1	4	yes	—
337	#21009	C₂³	1	4	yes	—
338	#21000	C₂³	1	8	yes	—
339	#21000	C₂³	1	8	yes	complemented
340	C₂×#1905	C₂³	1	8	yes	complemented
341	C₂×#1904	C₂³	1	8	yes	—
342	#20980	C₂³	1	4	yes	—
343	#20980	C₂³	1	4	yes	—
344	#20980	C₂³	1	4	yes	—
345	#20980	C₂³	1	4	yes	—
346	#20979	C₂³	1	4	yes	—
347	#20979	C₂³	1	4	yes	complemented
348	C₂×#1897	C₂³	1	4	yes	—
349	C₂×#1897	C₂³	1	4	yes	complemented
350	#20964	C₂³	1	4	yes	—
351	#20964	C₂³	1	4	yes	—
352	#20956	C₂³	1	2	yes	—
353	#20956	C₂³	1	2	yes	—
354	#20956	C₂³	1	2	yes	complemented
355	#20955	C₂³	1	2	yes	—
356	#20954	C₂³	1	2	yes	—
357	#20954	C₂³	1	2	yes	complemented
358	#20953	C₂³	1	2	yes	—
359	#20953	C₂³	1	2	yes	—
360	#20952	C₂³	1	2	yes	—
361	#20952	C₂³	1	2	yes	—
362	#20952	C₂³	1	2	yes	—
363	#20952	C₂³	1	2	yes	complemented
364	C₂×#1888	C₂³	1	2	yes	—
365	C₂×#1888	C₂³	1	2	yes	complemented
366	C₂×#1887	C₂³	1	2	yes	—
367	C₂×#1885	C₂³	1	2	yes	—
368	#20947	C₂³	1	4	yes	—
369	#20947	C₂³	1	4	yes	—
370	#20892	C₂³	1	4	yes	—
371	#20892	C₂³	1	4	yes	complemented
372	#20860	C₂³	1	4	yes	—
373	#20860	C₂³	1	4	yes	complemented
374	#20694	C₂³	1	2	yes	complemented
375	#20688	C₂³	1	2	yes	complemented
376	#20637	C₂³	1	2	yes	—
377	#20637	C₂³	1	2	yes	complemented
378	#20632	C₂³	1	2	yes	—
379	#20632	C₂³	1	2	yes	complemented
380	C₂×#1796	C₂³	1	4	yes	—
381	C₂×#1796	C₂³	1	4	yes	complemented
382	C₂×#1796	C₂³	1	8	yes	complemented
383	C₂×#1795	C₂³	1	4	yes	—
384	C₂×#1795	C₂³	1	4	yes	—
385	C₂×#1795	C₂³	1	4	yes	—
386	C₂×#1795	C₂³	1	4	yes	—
387	C₂×#1795	C₂³	1	4	yes	—
388	C₂×#1795	C₂³	1	8	yes	—
389	C₂×#1795	C₂³	1	4	yes	complemented
390	#20620	C₂³	1	4	yes	—
391	#20620	C₂³	1	8	yes	—
392	#20620	C₂³	1	4	yes	complemented
393	#20620	C₂³	1	8	yes	complemented
394	#20612	C₂³	1	4	yes	—
395	#20612	C₂³	1	4	yes	complemented
396	#20605	C₂³	1	4	yes	—
397	#20605	C₂³	1	4	yes	complemented
398	#20600	C₂³	1	4	yes	complemented
399	#20598	C₂³	1	4	yes	—
400	#20593	C₂³	1	2	yes	—
401	#20592	C₂³	1	2	yes	—
402	#20592	C₂³	1	2	yes	—
403	#20592	C₂³	1	2	yes	—
404	#20591	C₂³	1	2	yes	—
405	#20591	C₂³	1	2	yes	—
406	#20591	C₂³	1	2	yes	complemented
407	C₂×#1785	C₂³	1	2	yes	complemented
408	C₂×#1783	C₂³	1	2	yes	—
409	#20584	C₂³	1	2	yes	—
410	C₄×#413	C₂³	1	2	yes	—
411	C₄×#413	C₂³	1	2	yes	complemented
412	C₄×#410	C₂³	1	2	yes	—
413	C₄×#410	C₂³	1	2	yes	complemented
414	#20343	C₂³	1	2	yes	—
415	#20343	C₂³	1	2	yes	—
416	#20343	C₂³	1	2	yes	complemented
417	#20343	C₂³	1	2	yes	complemented
418	#11307	C₂³	1	8	yes	complemented
419	#11307	C₂³	1	8	yes	complemented
420	#11302	C₂³	1	8	yes	complemented
421	#11302	C₂³	1	8	yes	complemented
422	#11244	C₂³	1	8	yes	complemented
423	#11212	C₂³	1	8	yes	complemented
424	#11187	C₂³	1	8	yes	complemented
425	#11187	C₂³	1	8	yes	complemented
426	#11180	C₂³	1	8	yes	complemented
427	#11180	C₂³	1	8	yes	complemented
428	#11179	C₂³	1	8	yes	complemented
429	#11179	C₂³	1	8	yes	complemented
430	#11159	C₂³	1	8	yes	complemented
431	#11159	C₂³	1	8	yes	complemented
432	#11158	C₂³	1	8	yes	complemented
433	#11157	C₂³	1	8	yes	—
434	#11153	C₂³	1	8	yes	—
435	#11153	C₂³	1	8	yes	complemented
436	#11118	C₂³	1	8	yes	complemented
437	#11118	C₂³	1	8	yes	complemented
438	#11116	C₂³	1	8	yes	—
439	#11116	C₂³	1	8	yes	complemented
440	#11101	C₂³	1	8	yes	complemented
441	#11094	C₂³	1	8	yes	complemented
442	#11094	C₂³	1	8	yes	complemented
443	#11081	C₂³	1	8	yes	complemented
444	#11081	C₂³	1	8	yes	complemented
445	#11080	C₂³	1	8	yes	complemented
446	#11080	C₂³	1	8	yes	complemented
447	#11071	C₂³	1	8	yes	complemented
448	#11059	C₂³	1	8	yes	complemented
449	#11058	C₂³	1	8	yes	—
450	#11037	C₂³	1	8	yes	—
451	#11037	C₂³	1	8	yes	complemented
452	#11035	C₂³	1	8	yes	complemented
453	#11034	C₂³	1	8	yes	—
454	#11032	C₂³	1	8	yes	complemented
455	#11032	C₂³	1	8	yes	complemented
456	#11032	C₂³	1	8	yes	complemented
457	#11032	C₂³	1	8	yes	complemented
458	#11014	C₂³	1	8	yes	complemented
459	#11014	C₂³	1	8	yes	complemented
460	#11007	C₂³	1	4	yes	—
461	#11007	C₂³	1	4	yes	complemented
462	#11006	C₂³	1	4	yes	—
463	#11006	C₂³	1	4	yes	—
464	#11006	C₂³	1	4	yes	—
465	#11006	C₂³	1	4	yes	complemented
466	#11006	C₂³	1	4	yes	complemented
467	#11006	C₂³	1	4	yes	complemented
468	#11004	C₂³	1	8	yes	—
469	#11004	C₂³	1	8	yes	complemented
470	#11003	C₂³	1	8	yes	—
471	#11003	C₂³	1	8	yes	complemented
472	#11003	C₂³	1	8	yes	complemented
473	#11003	C₂³	1	8	yes	complemented
474	#11000	C₂³	1	8	yes	—
475	#11000	C₂³	1	8	yes	complemented
476	#10994	C₂³	1	8	yes	—
477	#10994	C₂³	1	8	yes	complemented
478	#10993	C₂³	1	8	yes	—
479	#10993	C₂³	1	8	yes	complemented
480	#10987	C₂³	1	8	yes	—
481	#10987	C₂³	1	8	yes	complemented
482	#10946	C₂³	1	8	yes	complemented
483	#10946	C₂³	1	8	yes	complemented
484	#10945	C₂³	1	8	yes	complemented
485	#10945	C₂³	1	8	yes	complemented
486	#10816	C₂³	1	8	yes	complemented
487	#10805	C₂³	1	8	yes	complemented
488	#10792	C₂³	1	8	yes	—
489	#10792	C₂³	1	8	yes	complemented
490	#10786	C₂³	1	8	yes	complemented
491	#10785	C₂³	1	8	yes	—
492	#10757	C₂³	1	4	yes	—
493	#10757	C₂³	1	4	yes	complemented
494	#10756	C₂³	1	4	yes	—
495	#10756	C₂³	1	4	yes	complemented
496	#10744	C₂³	1	4	yes	—
497	#10744	C₂³	1	4	yes	complemented
498	#10743	C₂³	1	4	yes	—
499	#10743	C₂³	1	4	yes	complemented
500	C₂×#585	C₂⁴	1	2	yes	—
501	C₂×#585	C₂⁴	1	2	yes	—
502	C₂×#585	C₂⁴	1	2	yes	—
503	C₂×#585	C₂⁴	1	2	yes	—
504	C₂²×2₋¹⁺⁴	C₂×D₄	1	2	yes	—
505	C₂²×2₋¹⁺⁴	C₂⁴	1	2	yes	—
506	C₂²×2₋¹⁺⁴	C₂⁴	1	1	yes	characteristic
507	C₂²×2₋¹⁺⁴	C₂⁴	1	1	yes	characteristic
508	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
509	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
510	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
511	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
512	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
513	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
514	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
515	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
516	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
517	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
518	C₂³×#41	C₂×D₄	1	2	yes	—
519	C₂³×#41	C₂×D₄	1	2	yes	—
520	C₂³×#41	C₂×D₄	1	2	yes	—
521	C₂³×#41	C₂⁴	1	1	yes	characteristic
522	C₂³×#41	C₂⁴	1	1	yes	characteristic
523	C₂³×#41	C₂⁴	1	1	yes	characteristic
524	C₂³×#41	C₂⁴	1	1	yes	characteristic
525	C₂⁴×D₄	C₂×D₄	1	2	yes	—
526	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
527	C₂×#575	C₂⁴	1	4	yes	—
528	C₂×#575	C₂⁴	1	4	yes	—
529	C₂×#575	C₂⁴	1	4	yes	—
530	C₂×#575	C₂⁴	1	4	yes	—
531	C₂×#575	C₂⁴	1	8	yes	—
532	C₂²×#137	C₂⁴	1	4	yes	—
533	C₂²×AGL(1,ℤ/8)	C₂⁴	1	4	yes	—
534	C₂²×AGL(1,ℤ/8)	C₂⁴	1	4	yes	—
535	C₂²×AGL(1,ℤ/8)	C₂⁴	1	4	yes	—
536	C₂×#568	C₂⁴	1	2	yes	—
537	C₂×#568	C₂⁴	1	2	yes	—
538	C₂×#568	C₂⁴	1	2	yes	—
539	C₂×#568	C₂⁴	1	2	yes	—
540	#3449	C₂⁴	1	4	yes	—
541	#3449	C₂⁴	1	4	yes	—
542	#3449	C₂⁴	1	4	yes	—
543	#3449	C₂⁴	1	4	yes	—
544	#3449	C₂⁴	1	8	yes	—
545	C₂×#536	C₂×D₄	1	1	yes	characteristic
546	C₂×#536	C₂×D₄	1	1	yes	characteristic
547	C₂×#536	C₂×D₄	1	2	yes	—
548	C₂×#536	C₂×D₄	1	2	yes	—
549	C₂×#536	C₂×D₄	1	2	yes	—
550	C₂×#536	C₂×D₄	1	1	yes	characteristic
551	C₂×#536	C₂×D₄	1	1	yes	characteristic
552	C₂×#536	C₂×D₄	1	2	yes	—
553	C₂×#536	C₂×D₄	1	2	yes	—
554	C₂×#536	C₂⁴	1	1	yes	characteristic
555	C₂×#536	C₂⁴	1	1	yes	characteristic
556	C₂×#535	C₂×D₄	1	1	yes	characteristic
557	C₂×#535	C₂×D₄	1	1	yes	characteristic
558	C₂×#535	C₂×D₄	1	2	yes	—
559	C₂×#535	C₂×D₄	1	2	yes	—
560	C₂×#535	C₂×D₄	1	2	yes	—
561	C₂×#535	C₂×D₄	1	2	yes	—
562	C₂×#535	C₂×D₄	1	2	yes	—
563	C₂×#535	C₂×D₄	1	2	yes	—
564	C₂×#535	C₂×D₄	1	2	yes	—
565	C₂×#535	C₂×D₄	1	1	yes	characteristic
566	C₂×#535	C₂×D₄	1	1	yes	characteristic
567	C₂×#535	C₂×D₄	1	2	yes	—
568	C₂×#535	C₂×D₄	1	2	yes	—
569	C₂×#535	C₂×D₄	1	2	yes	—
570	C₂×#535	C₂×D₄	1	2	yes	—
571	C₂×#535	C₂×D₄	1	2	yes	—
572	C₂×#535	C₂×D₄	1	2	yes	—
573	C₂×#535	C₂×D₄	1	2	yes	—
574	C₂×#535	C₂×D₄	1	2	yes	—
575	C₂×#535	C₂×D₄	1	2	yes	—
576	C₂×#535	C₂×D₄	1	2	yes	—
577	C₂×#535	C₂×D₄	1	2	yes	—
578	C₂×#535	C₂×D₄	1	2	yes	—
579	C₂×#535	C₂⁴	1	4	yes	—
580	C₂×#535	C₂⁴	1	4	yes	—
581	C₂×#535	C₂⁴	1	1	yes	characteristic
582	C₂×#535	C₂⁴	1	1	yes	characteristic
583	C₂×#535	C₂⁴	1	1	yes	characteristic
584	C₂×#535	C₂⁴	1	1	yes	characteristic
585	C₂×#535	C₂⁴	1	1	yes	characteristic
586	C₂×#535	C₂⁴	1	1	yes	characteristic
587	C₂×#532	C₂×D₄	1	2	yes	—
588	C₂×#532	C₂×D₄	1	2	yes	—
589	C₂×#532	C₂×D₄	1	2	yes	—
590	C₂×#532	C₂×D₄	1	2	yes	—
591	C₂×#532	C₂×D₄	1	2	yes	—
592	C₂×#532	C₂×D₄	1	2	yes	—
593	C₂×#532	C₂×D₄	1	2	yes	—
594	C₂×#532	C₂×D₄	1	2	yes	—
595	C₂×#532	C₂×D₄	1	2	yes	—
596	C₂×#532	C₂×D₄	1	2	yes	—
597	C₂×#532	C₂⁴	1	1	yes	characteristic
598	C₂×#532	C₂⁴	1	1	yes	characteristic
599	C₂×#532	C₂⁴	1	1	yes	characteristic
600	C₂×#532	C₂⁴	1	1	yes	characteristic
601	C₂²×#127	C₂×D₄	1	2	yes	—
602	C₂²×#127	C₂×D₄	1	2	yes	—
603	C₂²×#127	C₂×D₄	1	2	yes	—
604	C₂²×#127	C₂×D₄	1	2	yes	—
605	C₂²×#127	C₂×D₄	1	2	yes	—
606	C₂²×#127	C₂⁴	1	1	yes	characteristic
607	C₂²×#127	C₂⁴	1	1	yes	characteristic
608	C₂²×#124	C₂×D₄	1	2	yes	—
609	C₂²×#124	C₂×D₄	1	2	yes	—
610	C₂²×#124	C₂×D₄	1	2	yes	—
611	C₂²×#124	C₂×D₄	1	2	yes	—
612	C₂²×#124	C₂×D₄	1	2	yes	—
613	C₂²×#124	C₂⁴	1	1	yes	characteristic
614	C₂²×#124	C₂⁴	1	1	yes	characteristic
615	C₂×#525	C₂⁴	1	4	yes	—
616	C₂×#525	C₂⁴	1	4	yes	—
617	#3428	C₂⁴	1	2	yes	—
618	#3428	C₂⁴	1	2	yes	—
619	#3428	C₂⁴	1	2	yes	—
620	#3428	C₂⁴	1	2	yes	—
621	C₂×#519	C₂⁴	1	2	yes	—
622	C₂×#518	C₂⁴	1	2	yes	—
623	C₂×C₄×#41	C₂×D₄	1	2	yes	—
624	C₂×C₄×#41	C₂×D₄	1	2	yes	—
625	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
626	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
627	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
628	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
629	C₂²×#117	C₂×D₄	1	2	yes	—
630	C₂²×#117	C₂×D₄	1	2	yes	—
631	C₂²×#117	C₂⁴	1	1	yes	characteristic
632	C₂²×#117	C₂⁴	1	1	yes	characteristic
633	C₂×#430	C₂⁴	1	8	yes	—
634	#2905	C₂⁴	1	8	yes	—
635	C₂×#423	C₂⁴	1	4	yes	—
636	C₂×#421	C₂⁴	1	8	yes	—
637	C₂×#421	C₂⁴	1	8	yes	—
638	C₂×#421	C₂⁴	1	4	yes	—
639	C₂×#421	C₂⁴	1	4	yes	—
640	C₂×#421	C₂⁴	1	4	yes	—
641	C₂×#421	C₂⁴	1	4	yes	—
642	C₂×#421	C₂⁴	1	8	yes	—
643	C₂×#421	C₂⁴	1	8	yes	—
644	C₂×#421	C₂⁴	1	8	yes	—
645	C₂×#421	C₂⁴	1	8	yes	—
646	C₂×#421	C₂⁴	1	8	yes	—
647	C₂×#421	C₂⁴	1	8	yes	—
648	C₂²×#104	C₂⁴	1	4	yes	—
649	C₂²×#104	C₂⁴	1	4	yes	—
650	C₂²×#104	C₂⁴	1	4	yes	—
651	C₂²×#104	C₂⁴	1	4	yes	—
652	#2896	C₂⁴	1	4	yes	—
653	#2896	C₂⁴	1	4	yes	—
654	#2896	C₂⁴	1	4	yes	—
655	#2896	C₂⁴	1	4	yes	—
656	#2896	C₂⁴	1	8	yes	—
657	#2896	C₂⁴	1	8	yes	—
658	C₂×#419	C₂⁴	1	8	yes	—
659	C₂×#419	C₂⁴	1	4	yes	—
660	C₂×#418	C₂⁴	1	8	yes	—
661	C₂×#418	C₂⁴	1	4	yes	—
662	C₂×#418	C₂⁴	1	4	yes	—
663	C₂×#418	C₂⁴	1	4	yes	—
664	C₂×#418	C₂⁴	1	8	yes	—
665	C₂×#418	C₂⁴	1	8	yes	—
666	C₂×#413	C₂⁴	1	4	yes	—
667	C₂×#413	C₂⁴	1	4	yes	—
668	C₂×#413	C₂⁴	1	2	yes	—
669	C₂×#413	C₂⁴	1	2	yes	—
670	C₂×#413	C₂⁴	1	4	yes	—
671	C₂×#413	C₂⁴	1	4	yes	—
672	C₂×#413	C₂⁴	1	8	yes	—
673	C₂×#413	C₂⁴	1	8	yes	—
674	C₂×#413	C₂⁴	1	2	yes	—
675	C₂×#413	C₂⁴	1	2	yes	—
676	C₂²×#101	C₂⁴	1	2	yes	—
677	C₂²×#101	C₂⁴	1	2	yes	—
678	C₂²×#100	C₂⁴	1	2	yes	—
679	C₂²×#100	C₂⁴	1	4	yes	—
680	C₂²×#100	C₂⁴	1	4	yes	—
681	C₂²×#100	C₂⁴	1	2	yes	—
682	C₂×#410	C₂⁴	1	4	yes	—
683	C₂×#410	C₂⁴	1	4	yes	—
684	C₂×#410	C₂⁴	1	8	yes	—
685	C₂×#410	C₂⁴	1	8	yes	—
686	#2879	C₂⁴	1	4	yes	—
687	#2879	C₂⁴	1	4	yes	—
688	#2879	C₂⁴	1	8	yes	—
689	#2879	C₂⁴	1	8	yes	—
690	C₂×#407	C₂⁴	1	4	yes	—
691	C₂×#407	C₂⁴	1	4	yes	—
692	C₂×#407	C₂⁴	1	4	yes	—
693	C₂×C₄×M₁₆	C₂⁴	1	4	yes	—
694	#2285	C₂⁴	1	4	yes	—
695	#2280	C₂⁴	1	4	yes	—
696	C₄×#117	C₂⁴	1	4	yes	—
697	C₂×#344	C₂⁴	1	8	yes	—
698	C₂×#344	C₂⁴	1	8	yes	—
699	C₂×#344	C₂⁴	1	8	yes	—
700	C₂×#344	C₂⁴	1	8	yes	—
701	C₂×#344	C₂⁴	1	8	yes	—
702	C₂×#344	C₂⁴	1	8	yes	—
703	#1742	C₂⁴	1	8	yes	—
704	#1742	C₂⁴	1	4	yes	—
705	#1742	C₂⁴	1	4	yes	—
706	#1740	C₂⁴	1	8	yes	—
707	#1740	C₂⁴	1	4	yes	—
708	#1740	C₂⁴	1	4	yes	—
709	#1738	C₂⁴	1	8	yes	—
710	#1738	C₂⁴	1	8	yes	—
711	#1733	C₂⁴	1	4	yes	—
712	#1733	C₂⁴	1	4	yes	—
713	#1733	C₂⁴	1	4	yes	—
714	#1733	C₂⁴	1	4	yes	—
715	#1733	C₂⁴	1	8	yes	—
716	#1733	C₂⁴	1	8	yes	—
717	C₂×#339	C₂⁴	1	4	yes	—
718	C₂×#339	C₂⁴	1	4	yes	—
719	C₂×#339	C₂⁴	1	4	yes	—
720	C₂×#339	C₂⁴	1	4	yes	—
721	C₂×#338	C₂⁴	1	8	yes	—
722	C₂×H(3,ℤ/4)	C₂⁴	1	8	yes	—
723	C₂×H(3,ℤ/4)	C₂⁴	1	8	yes	—
724	C₂×H(3,ℤ/4)	C₂⁴	1	8	yes	—
725	C₂²×#41	C₂²×D₄	1	2	yes	—
726	C₂²×#41	C₂²×D₄	1	2	yes	—
727	C₂²×#41	C₂²×D₄	1	2	yes	—
728	C₂²×#41	C₂²×D₄	1	2	yes	—
729	C₂²×#41	C₂²×D₄	1	2	yes	—
730	C₂²×#41	C₂²×D₄	1	2	yes	—
731	C₂²×#41	C₂²×D₄	1	2	yes	—
732	C₂²×#41	C₂²×D₄	1	2	yes	—
733	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
734	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
735	C₂²×#41	C₂²×D₄	1	2	yes	—
736	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
737	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
738	C₂²×#41	C₂²×D₄	1	2	yes	—
739	C₂²×#41	C₂²×D₄	1	2	yes	—
740	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
741	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
742	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
743	C₂²×#41	C₂⁵	1	1	yes	characteristic
744	C₂²×#41	C₂⁵	1	1	yes	characteristic
745	C₂²×#41	C₂⁵	1	1	yes	characteristic
746	C₂²×#41	C₂⁵	1	1	yes	characteristic
747	C₂²×#41	C₂⁵	1	4	yes	—
748	C₂²×#41	C₂⁵	1	4	yes	—
749	C₂²×#41	C₂⁵	1	1	yes	characteristic
750	C₂²×#41	C₂⁵	1	1	yes	characteristic
751	C₂³×Q₈	C₂²×D₄	1	2	yes	—
752	C₂³×Q₈	C₂²×D₄	1	2	yes	—
753	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
754	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
755	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
756	C₂³×Q₈	C₂⁵	1	1	yes	characteristic
757	C₂³×D₄	C₂²×D₄	1	2	yes	—
758	C₂³×D₄	C₂²×D₄	1	2	yes	—
759	C₂³×D₄	C₂²×D₄	1	2	yes	—
760	C₂³×D₄	C₂²×D₄	1	2	yes	—
761	C₂³×D₄	C₂²×D₄	1	2	yes	—
762	C₂³×D₄	C₂²×D₄	1	2	yes	—
763	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
764	C₂³×D₄	C₂²×D₄	1	2	yes	—
765	C₂³×D₄	C₂²×D₄	1	2	yes	—
766	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
767	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
768	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
769	C₂³×D₄	C₂⁵	1	1	yes	characteristic
770	C₂³×D₄	C₂⁵	1	1	yes	characteristic
771	C₂³×D₄	C₂⁵	1	1	yes	characteristic
772	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
773	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
774	C₂²×M₁₆	C₂⁵	1	8	yes	—
775	C₂²×M₁₆	C₂⁵	1	4	yes	—
776	C₂²×M₁₆	C₂⁵	1	4	yes	—
777	C₂²×M₁₆	C₂⁵	1	4	yes	—
778	C₂²×M₁₆	C₂⁵	1	4	yes	—
779	#536	H(5,𝔽₂)	1	8	yes	—
780	#536	H(5,𝔽₂)	1	8	yes	—
781	#535	H(5,𝔽₂)	1	8	yes	—
782	#535	H(5,𝔽₂)	1	8	yes	—
783	#532	H(5,𝔽₂)	1	8	yes	—
784	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
785	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
786	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
787	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
788	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
789	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
790	C₂×#127	C₂²×D₄	1	2	yes	—
791	C₂×#127	C₂²×D₄	1	1	yes	characteristic
792	C₂×#127	C₂²×D₄	1	1	yes	characteristic
793	C₂×#127	C₂²×D₄	1	2	yes	—
794	C₂×#127	C₂²×D₄	1	2	yes	—
795	C₂×#127	C₂²×D₄	1	2	yes	—
796	C₂×#127	C₂²×D₄	1	2	yes	—
797	C₂×#127	C₂²×D₄	1	2	yes	—
798	C₂×#127	C₂²×D₄	1	1	yes	characteristic
799	C₂×#127	C₂²×D₄	1	2	yes	—
800	C₂×#127	C₂²×D₄	1	2	yes	—
801	C₂×#127	C₂²×D₄	1	2	yes	—
802	C₂×#127	C₂²×D₄	1	2	yes	—
803	C₂×#127	C₂²×D₄	1	1	yes	characteristic
804	C₂×#124	C₂²×D₄	1	2	yes	—
805	C₂×#124	C₂²×D₄	1	2	yes	—
806	C₂×#124	C₂²×D₄	1	1	yes	characteristic
807	C₂×#124	C₂²×D₄	1	1	yes	characteristic
808	C₂×#124	C₂²×D₄	1	1	yes	characteristic
809	C₂×#124	C₂²×D₄	1	2	yes	—
810	C₂×#124	C₂²×D₄	1	2	yes	—
811	C₂×#124	C₂²×D₄	1	1	yes	characteristic
812	C₂×#124	C₂²×D₄	1	2	yes	—
813	C₂×#124	C₂²×D₄	1	2	yes	—
814	C₂×#124	C₂²×D₄	1	2	yes	—
815	C₂×#124	C₂²×D₄	1	2	yes	—
816	C₂×#124	C₂²×D₄	1	1	yes	characteristic
817	C₂×#124	C₂²×D₄	1	1	yes	characteristic
818	C₂×#124	C₂²×D₄	1	2	yes	—
819	C₂×#124	C₂²×D₄	1	2	yes	—
820	C₂×#124	C₂²×D₄	1	1	yes	characteristic
821	C₂×#124	C₂²×D₄	1	2	yes	—
822	C₂×#124	C₂²×D₄	1	2	yes	—
823	C₂×#124	C₂²×D₄	1	1	yes	characteristic
824	C₂×#124	H(5,𝔽₂)	1	8	yes	—
825	C₂×#117	C₂²×D₄	1	1	yes	characteristic
826	C₂×#117	C₂²×D₄	1	1	yes	characteristic
827	C₂×#117	C₂²×D₄	1	1	yes	characteristic
828	C₂×#117	C₂²×D₄	1	1	yes	characteristic
829	C₂×#117	C₂²×D₄	1	2	yes	—
830	C₂×#117	C₂²×D₄	1	2	yes	—
831	C₂×#117	C₂²×D₄	1	2	yes	—
832	C₂×#117	C₂²×D₄	1	2	yes	—
833	C₂×#117	C₂²×D₄	1	2	yes	—
834	C₂×#117	C₂⁵	1	8	yes	—
835	C₂×#117	C₂⁵	1	4	yes	—
836	C₂×#117	C₂⁵	1	4	yes	—
837	C₂×#117	C₂⁵	1	1	yes	characteristic
838	C₂×#117	C₂⁵	1	1	yes	characteristic
839	C₂²×C₄²	C₂²×D₄	1	2	yes	—
840	C₂²×C₄²	C₂²×D₄	1	2	yes	—
841	C₂²×C₄²	C₂²×D₄	1	2	yes	—
842	C₂²×C₄²	C₂²×D₄	1	2	yes	—
843	C₂²×C₄²	C₂²×D₄	1	2	yes	—
844	C₂²×C₄²	C₂⁵	1	1	yes	characteristic
845	C₂²×C₄²	C₂⁵	1	1	yes	characteristic
846	C₂⁵	#534	1	2	yes	—
847	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
848	C₂×#41	C₂×H(5,𝔽₂)	1	4	yes	—
849	C₂×#41	C₂×H(5,𝔽₂)	1	4	yes	—
850	C₂×#41	C₂×H(5,𝔽₂)	1	8	yes	—
851	C₂×#41	C₂×H(5,𝔽₂)	1	8	yes	—
852	C₂²×Q₈	#534	1	2	yes	—
853	C₂²×Q₈	C₂³×D₄	1	1	yes	characteristic
854	C₂²×Q₈	C₂³×D₄	1	1	yes	characteristic
855	C₂²×Q₈	C₂³×D₄	1	1	yes	characteristic
856	C₂²×Q₈	C₂³×D₄	1	2	yes	—
857	C₂²×Q₈	C₂³×D₄	1	1	yes	characteristic
858	C₂²×Q₈	C₂×H(5,𝔽₂)	1	4	yes	—
859	C₂²×Q₈	C₂×H(5,𝔽₂)	1	4	yes	—
860	C₂²×Q₈	C₂×H(5,𝔽₂)	1	4	yes	—
861	C₂²×Q₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
862	C₂²×Q₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
863	C₂²×D₄	#534	1	2	yes	—
864	C₂²×D₄	#534	1	2	yes	—
865	C₂²×D₄	#534	1	2	yes	—
866	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
867	C₂²×D₄	C₂³×D₄	1	2	yes	—
868	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
869	C₂²×D₄	C₂³×D₄	1	2	yes	—
870	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
871	C₂²×D₄	C₂³×D₄	1	2	yes	—
872	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
873	C₂²×D₄	C₂×H(5,𝔽₂)	1	4	yes	—
874	C₂²×D₄	C₂×H(5,𝔽₂)	1	4	yes	—
875	C₂²×D₄	C₂×H(5,𝔽₂)	1	4	yes	—
876	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
877	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
878	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
879	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
880	C₂³×C₄	#534	1	2	yes	—
881	C₂³×C₄	#534	1	2	yes	—
882	C₂³×C₄	#534	1	2	yes	—
883	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
884	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
885	C₂³×C₄	C₂³×D₄	1	2	yes	—
886	C₂³×C₄	C₂³×D₄	1	2	yes	—
887	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
888	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
889	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
890	C₂³×C₄	C₂⁶	1	1	yes	characteristic
891	C₄⋊Q₈	#534	1	4	yes	—
892	#127	#534	1	4	yes	—
893	#124	#534	1	4	yes	—
894	#124	#534	1	8	yes	—
895	#124	#534	1	8	yes	—
896	#124	#534	1	4	yes	—
897	#117	C₂×H(5,𝔽₂)	1	8	yes	—
898	#117	C₂×H(5,𝔽₂)	1	8	yes	—
899	C₂×C₄²	C₂³×D₄	1	2	yes	—
900	C₂×C₄²	C₂³×D₄	1	2	yes	—
901	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
902	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
903	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
904	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
905	C₂×C₄²	C₂×H(5,𝔽₂)	1	4	yes	—
906	C₂×C₄²	C₂×H(5,𝔽₂)	1	4	yes	—
907	C₂⁴	C₂×#534	1	1	yes	characteristic
908	C₂⁴	C₂×#534	1	1	yes	characteristic
909	C₂⁴	C₂×#534	1	2	yes	—
910	C₂⁴	C₂×#534	1	2	yes	—
911	C₂⁴	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
912	C₂×Q₈	C₂×#534	1	2	yes	—
913	C₂×Q₈	C₂×#534	1	4	yes	—
914	C₂×Q₈	C₂×#534	1	2	yes	—
915	C₂×Q₈	#3532	1	4	yes	—
916	C₂×Q₈	#3532	1	4	yes	—
917	C₂×D₄	C₂×#534	1	2	yes	—
918	C₂×D₄	C₂×#534	1	4	yes	—
919	C₂×D₄	C₂×#534	1	2	yes	—
920	C₂×D₄	#3532	1	8	yes	—
921	C₂×D₄	#3532	1	8	yes	—
922	C₂×D₄	#3532	1	4	yes	—
923	C₂×D₄	#3532	1	4	yes	—
924	C₂²×C₄	C₂×#534	1	1	yes	characteristic
925	C₂²×C₄	C₂×#534	1	1	yes	characteristic
926	C₂²×C₄	C₂×#534	1	2	yes	—
927	C₂²×C₄	C₂×#534	1	2	yes	—
928	C₂²×C₄	#3484	1	8	yes	—
929	C₂²×C₄	#3484	1	8	yes	—
930	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
931	C₂²×C₄	C₂²×H(5,𝔽₂)	1	4	yes	—
932	C₂²×C₄	C₂²×H(5,𝔽₂)	1	4	yes	—
933	C₂²×C₄	C₂²×H(5,𝔽₂)	1	2	yes	—
934	C₂²×C₄	C₂²×H(5,𝔽₂)	1	2	yes	—
935	C₂²×C₄	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
936	C₄²	C₂×#534	1	2	yes	—
937	C₄²	C₂×#534	1	2	yes	—
938	C₄²	C₂×#534	1	2	yes	—
939	C₄²	C₂×#534	1	2	yes	—
940	C₂³	#36714	1	4	yes	—
941	C₂³	#36714	1	4	yes	—
942	C₂³	C₂²×#534	1	1	yes	characteristic
943	C₂³	C₂×#3532	1	2	yes	—
944	C₂³	C₂×#3532	1	2	yes	—
945	C₂³	#62817	1	2	yes	—
946	C₂×C₄	#36714	1	4	yes	—
947	C₂×C₄	#36714	1	4	yes	—
948	C₂×C₄	C₂²×#534	1	1	yes	characteristic
949	C₂×C₄	C₂²×#534	1	1	yes	characteristic
950	C₂×C₄	C₂×#3532	1	2	yes	—
951	C₂×C₄	C₂×#3532	1	2	yes	—
952	C₂×C₄	C₂×#3484	1	2	yes	—
953	C₂×C₄	C₂×#3484	1	2	yes	—
954	C₂×C₄	#62817	1	2	yes	—
955	C₂×C₄	#63011	1	8	yes	—
956	C₂×C₄	#63011	1	8	yes	—
957	C₂²	C₂×#36714	1	1	yes	characteristic
958	C₂²	C₂×#36714	1	1	yes	characteristic
959	C₂²	#7641845	1	1	yes	characteristic
960	C₂²	#8181078	1	4	yes	—
961	C₄	#7652795	1	2	yes	—
962	C₄	#7652795	1	2	yes	—
963	C₄	#8181078	1	4	yes	—
964	C₂	#72317739	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72317739
commutator, Frattini, cosocle	C₂³×C₄	C₂⁶
LCS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂³×C₄ ◁ G
LECS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72318602	C₂	semidirect
2. #72318589	C₂	semidirect
3. #72318581	C₂	semidirect
4. #72318571	C₂	semidirect
5. #72318558	C₂	semidirect
6. #72318546	C₂	semidirect
7. #72318509	C₂	semidirect
8. #72318497	C₂	semidirect
9. #72318482	C₂	semidirect
10. #72318482	C₂	semidirect
11. #72318474	C₂	semidirect
12. #72318127	C₂	semidirect
13. #72318063	C₂	semidirect
14. #72317961	C₂	semidirect
15. #72317872	C₂	semidirect
16. #72317848	C₂	semidirect
17. #72317787	C₂	semidirect
18. #72317769	C₂	semidirect
19. #72306470	C₂	semidirect
20. #72286449	C₂	semidirect
21. #72286244	C₂	semidirect
22. #72284607	C₂	semidirect
23. #72237054	C₂	semidirect
24. #72233775	C₂	semidirect
25. #72219689	C₂	semidirect
26. #10586091	C₂²	semidirect
27. #10586066	C₂²	semidirect
31. C₂×#60389	C₂²	semidirect
32. C₂×#60390	C₂²	semidirect
33. C₂×#60390	C₂²	semidirect
34. C₂×#60388	C₂²	semidirect
35. #7503375	C₂²	semidirect
36. #7503371	C₂²	semidirect
37. #6628884	C₂²	semidirect
38. #6628883	C₂²	semidirect
40. #6437585	C₂²	semidirect
41. #6437585	C₂²	semidirect
42. #6437577	C₂²	semidirect
43. #6437576	C₂²	semidirect
46. #6437458	C₂²	semidirect
48. #6437456	C₂²	semidirect
51. #6437452	C₂²	semidirect
52. #6437452	C₂²	semidirect
53. #6437451	C₂²	semidirect
54. #6437449	C₂²	semidirect
55. #6437447	C₂²	semidirect
56. #6437445	C₂²	semidirect
57. #6437444	C₂²	semidirect
58. #6437444	C₂²	semidirect
59. C₂×#23915	C₂²	semidirect
60. C₂×#23912	C₂²	semidirect
61. #6433173	C₂²	semidirect
62. #6433173	C₂²	semidirect
63. #6431724	C₂²	semidirect
64. #6431723	C₂²	semidirect
65. #6431723	C₂²	semidirect
66. #6431723	C₂²	semidirect
67. #6374293	C₂²	semidirect
68. #6374281	C₂²	semidirect
69. #6371496	C₂²	semidirect
70. #6371496	C₂²	semidirect
71. #6371458	C₂²	semidirect
72. #6371458	C₂²	semidirect
73. #6371456	C₂²	semidirect
74. #6371455	C₂²	semidirect
75. #6370954	C₂²	semidirect
76. #6370940	C₂²	semidirect
77. #6370706	C₂²	semidirect
78. #6370704	C₂²	semidirect
79. #476291	C₂²	semidirect
80. #476291	C₂²	semidirect
81. #476289	C₂²	semidirect
82. #476289	C₂²	semidirect
83. #472032	C₂²	semidirect
84. #472029	C₂²	semidirect
85. #469682	C₂²	semidirect
86. #469680	C₂²	semidirect
87. #466727	C₂²	semidirect
88. #466726	C₂²	semidirect
89. #455836	C₂²	semidirect
90. #455836	C₂²	semidirect
91. #455833	C₂²	semidirect
92. #455832	C₂²	semidirect
93. #454695	C₂²	semidirect
94. #454694	C₂²	semidirect
95. #454675	C₂²	semidirect
96. #454675	C₂²	semidirect
97. #454094	C₂²	semidirect
98. #454093	C₂²	semidirect
99. #454087	C₂²	semidirect
100. #454087	C₂²	semidirect
101. #451784	C₂²	semidirect
102. #451783	C₂²	semidirect
103. #449491	C₂²	semidirect
104. #449490	C₂²	semidirect
105. #434421	C₂²	semidirect
106. #434418	C₂²	semidirect
107. #434415	C₂²	semidirect
108. #434415	C₂²	semidirect
109. #419060	C₂²	semidirect
110. #419057	C₂²	semidirect
111. #419045	C₂²	semidirect
112. #419045	C₂²	semidirect
113. #418773	C₂²	semidirect
114. #418772	C₂²	semidirect
115. #418771	C₂²	semidirect
116. #418770	C₂²	semidirect
117. #405948	C₂²	semidirect
118. #405948	C₂²	semidirect
119. #405945	C₂²	semidirect
120. #405945	C₂²	semidirect
121. #404106	C₂²	semidirect
122. #404041	C₂²	semidirect
123. #395791	C₂²	semidirect
124. #395791	C₂²	semidirect
125. #395790	C₂²	semidirect
126. #395789	C₂²	semidirect
127. #395528	C₂²	semidirect
128. #395528	C₂²	semidirect
129. #395527	C₂²	semidirect
130. #395527	C₂²	semidirect
131. #395434	C₂²	semidirect
132. #395434	C₂²	semidirect
133. #395433	C₂²	semidirect
134. #395432	C₂²	semidirect
135. #394601	C₂²	semidirect
136. #394600	C₂²	semidirect
137. #394599	C₂²	semidirect
138. #394598	C₂²	semidirect
139. #394108	C₂²	semidirect
140. #394108	C₂²	semidirect
141. #394103	C₂²	semidirect
142. #394102	C₂²	semidirect
143. #394086	C₂²	semidirect
144. #394086	C₂²	semidirect
145. #393986	C₂²	semidirect
146. #393986	C₂²	semidirect
147. #392730	C₂²	semidirect
148. #392729	C₂²	semidirect
149. #392134	C₂²	semidirect
150. #392132	C₂²	semidirect
151. #387629	C₂²	semidirect
152. #387625	C₂²	semidirect
153. #383066	C₂²	semidirect
154. #383066	C₂²	semidirect
155. #383060	C₂²	semidirect
156. #383059	C₂²	semidirect
157. #382416	C₂²	semidirect
158. #382414	C₂²	semidirect
159. #379829	C₂²	semidirect
160. #379829	C₂²	semidirect
161. #373643	C₂²	semidirect
162. #373639	C₂²	semidirect
163. #368555	C₂²	semidirect
164. #368555	C₂²	semidirect
165. #368550	C₂²	semidirect
166. #368550	C₂²	semidirect
167. #366630	C₂²	semidirect
168. #366630	C₂²	semidirect
169. #366624	C₂²	semidirect
170. #366624	C₂²	semidirect
171. #361636	C₂²	semidirect
172. #361636	C₂²	semidirect
173. #361634	C₂²	semidirect
174. #361634	C₂²	semidirect
175. #361633	C₂²	semidirect
176. #361633	C₂²	semidirect
177. #361631	C₂²	semidirect
178. #361631	C₂²	semidirect
179. #359665	C₂²	semidirect
180. #359665	C₂²	semidirect
181. #359651	C₂²	semidirect
182. #359650	C₂²	semidirect
183. #359562	C₂²	semidirect
184. #359562	C₂²	semidirect
185. #359551	C₂²	semidirect
186. #359551	C₂²	semidirect
187. C₂×2₋¹⁺⁶	C₂³	semidirect
198. #62852	C₂³	semidirect
204. #62811	C₂³	semidirect
205. C₂×#3500	D₄	semidirect
206. C₂×#3500	D₄	semidirect
211. C₂×#3498	D₄	semidirect
212. C₂×#3498	D₄	semidirect
217. C₂×#3487	C₂³	semidirect
219. C₂×#3449	D₄	semidirect
220. C₂×#3449	D₄	semidirect
223. C₂²×#535	D₄	semidirect
224. C₂²×#535	D₄	semidirect
227. #62653	C₂³	semidirect
235. #60387	C₂³	semidirect
239. C₂×#3021	C₂³	semidirect
241. C₂×#3020	C₂³	semidirect
247. C₂×#3018	C₂³	semidirect
249. C₂²×#454	C₂³	semidirect
253. #60368	C₂³	semidirect
262. C₂×#2921	C₂³	semidirect
265. C₂×#2901	C₂³	semidirect
266. C₂×#2901	C₂³	semidirect
271. C₂×#2889	C₂³	semidirect
272. C₂×#2889	C₂³	semidirect
276. C₂×#2888	C₂³	semidirect
279. #34048	C₂³	semidirect
280. C₂×#2081	C₂³	semidirect
281. C₂×#2081	C₂³	semidirect
282. #23649	C₂³	semidirect
283. #23649	C₂³	semidirect
284. #23532	C₂³	semidirect
287. #23527	C₂³	semidirect
288. C₂×#2050	C₂³	semidirect
289. #23525	C₂³	semidirect
290. #23525	C₂³	semidirect
291. #23521	C₂³	semidirect
292. #23521	C₂³	semidirect
293. #23498	C₂³	semidirect
296. #23414	C₂³	semidirect
299. #23412	C₂³	semidirect
301. C₂×#2008	C₂³	semidirect
305. #23402	C₂³	semidirect
310. #23400	C₂³	semidirect
311. #23400	C₂³	semidirect
315. #23399	C₂³	semidirect
319. C₂×#2002	C₂³	semidirect
320. #21261	C₂³	semidirect
323. #21252	C₂³	semidirect
324. #21241	C₂³	semidirect
325. #21210	C₂³	semidirect
327. #21209	C₂³	semidirect
329. #21203	C₂³	semidirect
339. #21000	C₂³	semidirect
340. C₂×#1905	C₂³	semidirect
347. #20979	C₂³	semidirect
349. C₂×#1897	C₂³	semidirect
354. #20956	C₂³	semidirect
357. #20954	C₂³	semidirect
363. #20952	C₂³	semidirect
365. C₂×#1888	C₂³	semidirect
371. #20892	C₂³	semidirect
373. #20860	C₂³	semidirect
374. #20694	C₂³	semidirect
375. #20688	C₂³	semidirect
377. #20637	C₂³	semidirect
379. #20632	C₂³	semidirect
381. C₂×#1796	C₂³	semidirect
382. C₂×#1796	C₂³	semidirect
389. C₂×#1795	C₂³	semidirect
392. #20620	C₂³	semidirect
393. #20620	C₂³	semidirect
395. #20612	C₂³	semidirect
397. #20605	C₂³	semidirect
398. #20600	C₂³	semidirect
406. #20591	C₂³	semidirect
407. C₂×#1785	C₂³	semidirect
411. C₄×#413	C₂³	semidirect
413. C₄×#410	C₂³	semidirect
416. #20343	C₂³	semidirect
417. #20343	C₂³	semidirect
418. #11307	C₂³	semidirect
419. #11307	C₂³	semidirect
420. #11302	C₂³	semidirect
421. #11302	C₂³	semidirect
422. #11244	C₂³	semidirect
423. #11212	C₂³	semidirect
424. #11187	C₂³	semidirect
425. #11187	C₂³	semidirect
426. #11180	C₂³	semidirect
427. #11180	C₂³	semidirect
428. #11179	C₂³	semidirect
429. #11179	C₂³	semidirect
430. #11159	C₂³	semidirect
431. #11159	C₂³	semidirect
432. #11158	C₂³	semidirect
435. #11153	C₂³	semidirect
436. #11118	C₂³	semidirect
437. #11118	C₂³	semidirect
439. #11116	C₂³	semidirect
440. #11101	C₂³	semidirect
441. #11094	C₂³	semidirect
442. #11094	C₂³	semidirect
443. #11081	C₂³	semidirect
444. #11081	C₂³	semidirect
445. #11080	C₂³	semidirect
446. #11080	C₂³	semidirect
447. #11071	C₂³	semidirect
448. #11059	C₂³	semidirect
451. #11037	C₂³	semidirect
452. #11035	C₂³	semidirect
454. #11032	C₂³	semidirect
455. #11032	C₂³	semidirect
456. #11032	C₂³	semidirect
457. #11032	C₂³	semidirect
458. #11014	C₂³	semidirect
459. #11014	C₂³	semidirect
461. #11007	C₂³	semidirect
465. #11006	C₂³	semidirect
466. #11006	C₂³	semidirect
467. #11006	C₂³	semidirect
469. #11004	C₂³	semidirect
471. #11003	C₂³	semidirect
472. #11003	C₂³	semidirect
473. #11003	C₂³	semidirect
475. #11000	C₂³	semidirect
477. #10994	C₂³	semidirect
479. #10993	C₂³	semidirect
481. #10987	C₂³	semidirect
482. #10946	C₂³	semidirect
483. #10946	C₂³	semidirect
484. #10945	C₂³	semidirect
485. #10945	C₂³	semidirect
486. #10816	C₂³	semidirect
487. #10805	C₂³	semidirect
489. #10792	C₂³	semidirect
490. #10786	C₂³	semidirect
493. #10757	C₂³	semidirect
495. #10756	C₂³	semidirect
497. #10744	C₂³	semidirect
499. #10743	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#72318602	2
#72318589	2
#72318581	2
#72318571	2
#72318558	2
#72318546	2
#72318509	2
#72318497	2
#72318482	2
#72318474	2
#72318127	2
#72318063	2
#72317961	2
#72317872	2
#72317848	2
#72317787	2
#72317769	2
#72306470	2
#72286449	2
#72286244	2
#72284607	2
#72237054	2
#72233775	2
#72219689	2