Subgroups — #72265950

Order 2048.

At least 24096 conjugacy classes of subgroups; only the 1080 normal subgroups are shown.

The subgroup lattice has 883 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72265949	C₂	1	1	yes	maximal, characteristic, complemented
2	#72265948	C₂	1	1	yes	maximal, characteristic, complemented
3	#72265947	C₂	1	1	yes	maximal, characteristic, complemented
4	#72265943	C₂	1	2	yes	maximal, complemented
5	#72265904	C₂	1	1	yes	maximal, characteristic, complemented
6	#72265195	C₂	1	1	yes	maximal, characteristic, complemented
7	#72261568	C₂	1	2	yes	maximal, complemented
8	#72258512	C₂	1	2	yes	maximal, complemented
9	#72258461	C₂	1	1	yes	maximal, characteristic, complemented
10	#72251466	C₂	1	2	yes	maximal, complemented
11	#72241329	C₂	1	1	yes	maximal, characteristic, complemented
12	#72234960	C₂	1	1	yes	maximal, characteristic, complemented
13	#72234959	C₂	1	2	yes	maximal, complemented
14	#72234958	C₂	1	2	yes	maximal, complemented
15	#72234957	C₂	1	1	yes	maximal, characteristic, complemented
16	#72234956	C₂	1	2	yes	maximal, complemented
17	#72234955	C₂	1	1	yes	maximal, characteristic, complemented
18	#72234644	C₂	1	1	yes	maximal, characteristic, complemented
19	#72233304	C₂	1	1	yes	maximal, characteristic, complemented
20	#72233069	C₂	1	1	yes	maximal, characteristic, complemented
21	#72233042	C₂	1	1	yes	maximal, characteristic, complemented
22	#72232934	C₂	1	2	yes	maximal, complemented
23	#72232821	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#3026	C₂²	1	1	yes	characteristic, complemented
25	#7806601	C₂²	1	1	yes	characteristic
26	#7806599	C₂²	1	1	yes	characteristic, complemented
27	#7752093	C₂²	1	1	yes	characteristic, complemented
28	#7752089	C₂²	1	1	yes	characteristic, complemented
29	#7733149	C₂²	1	1	yes	characteristic
30	#7733089	C₂²	1	1	yes	characteristic, complemented
31	#7721731	C₂²	1	1	yes	characteristic, complemented
32	#7721729	C₂²	1	1	yes	characteristic
33	C₂×#46996	C₂²	1	1	yes	characteristic, complemented
34	#7675392	C₂²	1	1	yes	characteristic
35	#7675391	C₂²	1	1	yes	characteristic
36	#7672777	C₂²	1	1	yes	characteristic
37	#7631286	C₂²	1	1	yes	characteristic
38	#7626663	C₂²	1	1	yes	characteristic, complemented
39	#7626568	C₂²	1	1	yes	characteristic
40	#7626386	C₂²	1	1	yes	characteristic, complemented
41	#6628892	C₂²	1	1	yes	characteristic, complemented
42	#6628892	C₂²	1	1	yes	characteristic, complemented
43	C₂×#32898	C₂²	1	1	yes	characteristic, complemented
44	#6470225	C₂²	1	2	yes	—
45	#6437621	C₂²	1	2	yes	—
46	#6385971	C₂²	1	1	yes	characteristic
47	#6370693	C₂²	1	1	yes	characteristic, complemented
48	#6370693	C₂²	1	1	yes	characteristic, complemented
49	#394470	C₂²	1	2	yes	complemented
50	#394470	C₂²	1	2	yes	complemented
51	#394267	C₂²	1	2	yes	complemented
52	#394061	C₂²	1	2	yes	complemented
53	#393929	C₂²	1	2	yes	complemented
54	#393929	C₂²	1	2	yes	complemented
55	#374058	C₂²	1	1	yes	characteristic, complemented
56	#374058	C₂²	1	1	yes	characteristic, complemented
57	#374038	C₂²	1	1	yes	characteristic, complemented
58	#364471	C₂²	1	2	yes	complemented
59	#364440	C₂²	1	2	yes	—
60	#364440	C₂²	1	2	yes	complemented
61	#359892	C₂²	1	1	yes	characteristic, complemented
62	#359892	C₂²	1	1	yes	characteristic, complemented
63	#359579	C₂²	1	1	yes	characteristic
64	#359504	C₂²	1	1	yes	characteristic, complemented
65	#359442	C₂²	1	1	yes	characteristic, complemented
66	#359442	C₂²	1	1	yes	characteristic, complemented
67	#359442	C₂²	1	2	yes	complemented
68	#359434	C₂²	1	2	yes	complemented
69	#238082	C₂²	1	2	yes	complemented
70	C₂×#10390	C₂²	1	2	yes	complemented
71	#233549	C₂²	1	2	yes	complemented
72	#233541	C₂²	1	2	yes	complemented
73	#233541	C₂²	1	2	yes	complemented
74	C₂×#10336	C₂²	1	2	yes	complemented
75	#201701	C₂²	1	1	yes	characteristic, complemented
76	#201701	C₂²	1	1	yes	characteristic, complemented
77	#201701	C₂²	1	1	yes	characteristic, complemented
78	#201701	C₂²	1	1	yes	characteristic, complemented
79	#201678	C₂²	1	2	yes	—
80	#201678	C₂²	1	2	yes	—
81	#201678	C₂²	1	2	yes	—
82	#201678	C₂²	1	2	yes	complemented
83	#201678	C₂²	1	2	yes	complemented
84	#201678	C₂²	1	2	yes	complemented
85	#201664	C₂²	1	1	yes	characteristic, complemented
86	#201664	C₂²	1	1	yes	characteristic, complemented
87	#201664	C₂²	1	2	yes	complemented
88	C₂×#9495	C₂²	1	2	yes	complemented
89	C₂×#9495	C₂²	1	2	yes	complemented
90	#190107	C₂²	1	1	yes	characteristic, complemented
91	#190107	C₂²	1	1	yes	characteristic, complemented
92	#188035	C₂²	1	1	yes	characteristic
93	#187944	C₂²	1	2	yes	complemented
94	#187928	C₂²	1	2	yes	complemented
95	#181344	C₂²	1	1	yes	characteristic, complemented
96	#181344	C₂²	1	1	yes	characteristic, complemented
97	#122191	C₂²	1	2	yes	complemented
98	#122187	C₂²	1	2	yes	complemented
99	#122187	C₂²	1	2	yes	complemented
100	#122038	C₂²	1	2	yes	complemented
101	#115631	C₂²	1	2	yes	complemented
102	#115204	C₂²	1	2	yes	complemented
103	#115204	C₂²	1	2	yes	complemented
104	#115163	C₂²	1	2	yes	complemented
105	#115133	C₂²	1	2	yes	complemented
106	#115133	C₂²	1	2	yes	complemented
107	#111467	C₂²	1	2	yes	complemented
108	#111458	C₂²	1	2	yes	complemented
109	#107194	C₂²	1	2	yes	complemented
110	#107194	C₂²	1	2	yes	complemented
111	#107194	C₂²	1	2	yes	complemented
112	#107194	C₂²	1	2	yes	complemented
113	#107194	C₂²	1	2	yes	complemented
114	#107194	C₂²	1	2	yes	complemented
115	#107114	C₂²	1	2	yes	complemented
116	#106766	C₂²	1	2	yes	complemented
117	#106654	C₂²	1	2	yes	complemented
118	#106542	C₂²	1	2	yes	complemented
119	#106542	C₂²	1	2	yes	complemented
120	#105808	C₂²	1	2	yes	complemented
121	#105752	C₂²	1	2	yes	complemented
122	#105752	C₂²	1	2	yes	complemented
123	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
124	C₂×#3490	D₄	1	1	yes	characteristic, complemented
125	C₂×#3490	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	C₂²×D₄²	C₂³	1	1	yes	characteristic
130	C₂²×#534	C₂³	1	2	yes	—
131	C₂²×#534	C₂³	1	1	yes	characteristic
132	C₂³×#99	C₂³	1	1	yes	characteristic
133	C₂³×#99	C₂³	1	2	yes	—
134	#47563	D₄	1	1	yes	characteristic, complemented
135	#46998	D₄	1	1	yes	characteristic, complemented
136	#46997	D₄	1	1	yes	characteristic, complemented
137	#46996	D₄	1	1	yes	characteristic, complemented
138	#46996	D₄	1	1	yes	characteristic, complemented
139	#46837	D₄	1	1	yes	characteristic, complemented
140	#46387	D₄	1	1	yes	characteristic, complemented
141	#46386	D₄	1	1	yes	characteristic, complemented
142	#46386	D₄	1	1	yes	characteristic, complemented
143	#46385	D₄	1	1	yes	characteristic, complemented
144	#46385	D₄	1	1	yes	characteristic, complemented
145	#46385	D₄	1	1	yes	characteristic, complemented
146	#46385	D₄	1	1	yes	characteristic, complemented
147	#46385	D₄	1	1	yes	characteristic, complemented
148	#46384	D₄	1	1	yes	characteristic, complemented
149	#46384	D₄	1	1	yes	characteristic, complemented
150	#37475	C₂³	1	1	yes	characteristic
151	#37436	C₂³	1	1	yes	characteristic
152	#37232	D₄	1	1	yes	characteristic, complemented
153	#36717	D₄	1	1	yes	characteristic, complemented
154	#36717	D₄	1	1	yes	characteristic, complemented
155	#36714	D₄	1	1	yes	characteristic, complemented
156	C₂×#2840	C₂³	1	1	yes	characteristic
157	#35527	D₄	1	1	yes	characteristic, complemented
158	#35455	D₄	1	1	yes	characteristic, complemented
159	#35448	D₄	1	1	yes	characteristic, complemented
160	#35447	D₄	1	1	yes	characteristic, complemented
161	#35447	D₄	1	1	yes	characteristic, complemented
162	#35390	D₄	1	1	yes	characteristic, complemented
163	#35360	D₄	1	1	yes	characteristic, complemented
164	#35360	D₄	1	1	yes	characteristic, complemented
165	#35358	D₄	1	1	yes	characteristic, complemented
166	#35355	D₄	1	1	yes	characteristic, complemented
167	#35355	D₄	1	1	yes	characteristic, complemented
168	#35348	D₄	1	1	yes	characteristic, complemented
169	#35348	D₄	1	1	yes	characteristic, complemented
170	#35348	D₄	1	1	yes	characteristic, complemented
171	#35347	D₄	1	1	yes	characteristic, complemented
172	#35346	D₄	1	1	yes	characteristic, complemented
173	#34993	D₄	1	1	yes	characteristic, complemented
174	#34992	D₄	1	1	yes	characteristic, complemented
175	#34984	D₄	1	1	yes	characteristic, complemented
176	#34982	C₂³	1	1	yes	characteristic
177	#34982	C₂³	1	1	yes	characteristic
178	#34981	D₄	1	1	yes	characteristic, complemented
179	#34981	D₄	1	1	yes	characteristic, complemented
180	#34980	D₄	1	1	yes	characteristic, complemented
181	#34980	C₂³	1	1	yes	characteristic
182	#34980	C₂³	1	1	yes	characteristic
183	#34980	C₂³	1	2	yes	—
184	#34980	C₂³	1	2	yes	—
185	#34980	C₂³	1	2	yes	—
186	#34980	C₂³	1	1	yes	characteristic
187	#34980	C₂³	1	1	yes	characteristic
188	C₂×#2410	C₂³	1	1	yes	characteristic
189	C₂×#2403	C₂³	1	1	yes	characteristic
190	C₂×#2403	C₂³	1	1	yes	characteristic
191	C₂×#2403	C₂³	1	1	yes	characteristic
192	C₂×#2403	C₂³	1	1	yes	characteristic
193	C₂×#2403	C₂³	1	2	yes	—
194	C₂×#2403	C₂³	1	2	yes	—
195	C₂×#2613	C₂³	1	1	yes	characteristic
196	#34363	D₄	1	1	yes	characteristic, complemented
197	#34363	D₄	1	1	yes	characteristic, complemented
198	#34356	D₄	1	1	yes	characteristic, complemented
199	#34356	D₄	1	1	yes	characteristic, complemented
200	#34356	C₂³	1	1	yes	characteristic
201	#34356	C₂³	1	1	yes	characteristic
202	#34356	C₂³	1	1	yes	characteristic
203	#34356	C₂³	1	1	yes	characteristic
204	#34356	C₂³	1	1	yes	characteristic
205	#34356	C₂³	1	1	yes	characteristic
206	#34273	D₄	1	1	yes	characteristic, complemented
207	#34264	D₄	1	1	yes	characteristic, complemented
208	#34198	D₄	1	1	yes	characteristic, complemented
209	#34198	C₂³	1	1	yes	characteristic
210	#34198	C₂³	1	1	yes	characteristic
211	#34185	D₄	1	1	yes	characteristic, complemented
212	#34171	D₄	1	1	yes	characteristic, complemented
213	#34171	C₂³	1	1	yes	characteristic
214	#34171	C₂³	1	1	yes	characteristic
215	#34171	C₂³	1	1	yes	characteristic
216	#34171	C₂³	1	1	yes	characteristic
217	#34171	C₂³	1	1	yes	characteristic
218	#34171	C₂³	1	1	yes	characteristic
219	#34171	C₂³	1	1	yes	characteristic
220	C₂×D₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
221	#34057	D₄	1	1	yes	characteristic, complemented
222	C₂×#2308	D₄	1	1	yes	characteristic, complemented
223	C₂×#2308	C₂³	1	1	yes	characteristic
224	C₂×#2308	C₂³	1	1	yes	characteristic
225	C₂×#2308	C₂³	1	1	yes	characteristic
226	#21746	C₂³	1	2	yes	—
227	#21746	C₂³	1	2	yes	—
228	#21746	C₂³	1	2	yes	—
229	#21746	C₂³	1	2	yes	—
230	#21746	C₂³	1	2	yes	—
231	#21746	C₂³	1	2	yes	—
232	C₂×#1898	C₂³	1	2	yes	—
233	C₂×#1898	C₂³	1	2	yes	—
234	C₂×#1898	C₂³	1	2	yes	—
235	C₂×#1781	C₂³	1	2	yes	—
236	C₂×#1781	C₂³	1	2	yes	—
237	C₂×#1781	C₂³	1	2	yes	—
238	C₂×#1781	C₂³	1	2	yes	—
239	C₂×#1781	C₂³	1	2	yes	—
240	C₂×#1781	C₂³	1	1	yes	characteristic
241	C₂×#1781	C₂³	1	1	yes	characteristic
242	C₂×#1781	C₂³	1	2	yes	—
243	C₂×#1781	C₂³	1	1	yes	characteristic
244	C₂×#1781	C₂³	1	2	yes	—
245	C₂×#1781	C₂³	1	2	yes	—
246	C₂×#1781	C₂³	1	2	yes	—
247	C₂×#1781	C₂³	1	2	yes	—
248	C₂×#1781	C₂³	1	2	yes	—
249	C₂×#1781	C₂³	1	2	yes	—
250	C₂×#1781	C₂³	1	2	yes	—
251	#14335	C₂³	1	2	yes	—
252	#13867	C₂³	1	2	yes	—
253	#13867	C₂³	1	2	yes	—
254	#10735	C₂³	1	2	yes	—
255	#10735	C₂³	1	2	yes	—
256	#10735	C₂³	1	2	yes	—
257	#10735	C₂³	1	2	yes	—
258	#10735	C₂³	1	2	yes	—
259	#10735	C₂³	1	2	yes	—
260	#10725	C₂³	1	2	yes	—
261	#10725	C₂³	1	2	yes	—
262	#10725	C₂³	1	2	yes	—
263	#10725	C₂³	1	2	yes	—
264	#8101	C₂³	1	2	yes	—
265	#8101	C₂³	1	2	yes	—
266	#8101	C₂³	1	2	yes	—
267	#8101	C₂³	1	2	yes	—
268	#8101	C₂³	1	2	yes	—
269	#8101	C₂³	1	2	yes	—
270	C₂×#1304	C₂³	1	2	yes	—
271	C₂×#1304	C₂³	1	2	yes	—
272	C₂×#1304	C₂³	1	2	yes	—
273	C₂×#1304	C₂³	1	2	yes	—
274	C₂×#1304	C₂³	1	2	yes	—
275	C₂×#1304	C₂³	1	2	yes	—
276	C₂×#1304	C₂³	1	2	yes	—
277	C₂×#1304	C₂³	1	2	yes	—
278	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
279	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
280	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
281	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
282	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
283	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
284	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
285	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
286	C₂⁴×D₄	C₂⁴	1	2	yes	—
287	C₂×#543	C₂×D₄	1	1	yes	characteristic, complemented
288	C₂×#543	C₂×D₄	1	1	yes	characteristic, complemented
289	C₂×#534	C₂×D₄	1	1	yes	characteristic
290	C₂×#534	C₂×D₄	1	1	yes	characteristic
291	C₂×#534	C₂×D₄	1	1	yes	characteristic
292	C₂×#534	C₂×D₄	1	1	yes	characteristic
293	C₂×#534	C₂×D₄	1	1	yes	characteristic
294	C₂×#534	C₂×D₄	1	1	yes	characteristic
295	C₂×#534	C₂×D₄	1	1	yes	characteristic
296	C₂×#534	C₂×D₄	1	1	yes	characteristic
297	C₂×#534	C₂×D₄	1	1	yes	characteristic
298	C₂×#534	C₂×D₄	1	1	yes	characteristic
299	C₂×#534	C₂×D₄	1	1	yes	characteristic
300	C₂×#534	C₂×D₄	1	1	yes	characteristic
301	C₂×#534	C₂×D₄	1	1	yes	characteristic
302	C₂×#534	C₂×D₄	1	1	yes	characteristic
303	C₂×#534	C₂×D₄	1	1	yes	characteristic
304	C₂×#534	C₂×D₄	1	1	yes	characteristic
305	C₂²×#127	C₂×D₄	1	1	yes	characteristic
306	C₂²×#123	C₂×D₄	1	1	yes	characteristic
307	C₂²×#123	C₂×D₄	1	1	yes	characteristic
308	C₂²×#123	C₂×D₄	1	1	yes	characteristic, complemented
309	C₂²×#121	C₂×D₄	1	1	yes	characteristic
310	C₂²×#121	C₂×D₄	1	1	yes	characteristic
311	C₂²×#121	C₂×D₄	1	1	yes	characteristic
312	C₂²×#121	C₂×D₄	1	1	yes	characteristic
313	C₂²×#120	C₂×D₄	1	1	yes	characteristic
314	C₂²×#120	C₂×D₄	1	1	yes	characteristic
315	C₂²×#120	C₂×D₄	1	1	yes	characteristic
316	C₂²×#120	C₂×D₄	1	1	yes	characteristic
317	C₂²×#120	C₂×D₄	1	1	yes	characteristic
318	C₂²×#120	C₂×D₄	1	1	yes	characteristic
319	C₂²×#120	C₂×D₄	1	1	yes	characteristic
320	C₂²×#120	C₂×D₄	1	1	yes	characteristic
321	C₂²×#120	C₂×D₄	1	1	yes	characteristic
322	C₂²×#120	C₂×D₄	1	1	yes	characteristic
323	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
324	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
325	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
326	C₂²×#120	C₂⁴	1	1	yes	characteristic
327	C₂²×#120	C₂⁴	1	1	yes	characteristic
328	C₂²×#120	C₂⁴	1	1	yes	characteristic
329	C₂×#518	C₂×D₄	1	1	yes	characteristic
330	C₂×#518	C₂×D₄	1	1	yes	characteristic
331	C₂×#518	C₂×D₄	1	1	yes	characteristic
332	C₂×#518	C₂×D₄	1	1	yes	characteristic
333	C₂×#518	C₂×D₄	1	1	yes	characteristic
334	C₂×#518	C₂×D₄	1	1	yes	characteristic
335	C₂×#518	C₂×D₄	1	1	yes	characteristic
336	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
337	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
338	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
339	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
341	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
342	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
343	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
344	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
345	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
346	#2849	#41	1	4	yes	complemented
347	#2846	#41	1	4	yes	complemented
348	#2842	C₂×D₄	1	1	yes	characteristic, complemented
349	#2842	C₂×D₄	1	1	yes	characteristic, complemented
350	#2842	C₂×D₄	1	1	yes	characteristic, complemented
351	#2840	C₂×D₄	1	1	yes	characteristic, complemented
352	#2840	C₂×D₄	1	1	yes	characteristic, complemented
353	#2840	C₂×D₄	1	1	yes	characteristic, complemented
354	#2840	C₂×D₄	1	1	yes	characteristic, complemented
355	#2840	C₂×D₄	1	1	yes	characteristic, complemented
356	#2483	C₂×D₄	1	1	yes	characteristic, complemented
357	#2405	C₂×D₄	1	1	yes	characteristic
358	#2405	C₂×D₄	1	1	yes	characteristic
359	#2405	C₂×D₄	1	1	yes	characteristic
360	#2405	C₂×D₄	1	1	yes	characteristic
361	#2405	C₂×D₄	1	1	yes	characteristic
362	#2405	C₂×D₄	1	1	yes	characteristic
363	#2405	C₂×D₄	1	1	yes	characteristic
364	#2405	C₂×D₄	1	1	yes	characteristic
365	#2405	C₂×D₄	1	1	yes	characteristic
366	#2405	C₂×D₄	1	1	yes	characteristic
367	#2405	C₂×D₄	1	1	yes	characteristic, complemented
368	#2405	C₂×D₄	1	1	yes	characteristic, complemented
369	#2405	C₂×D₄	1	1	yes	characteristic, complemented
370	#2405	C₂×D₄	1	1	yes	characteristic, complemented
371	#2403	C₂×D₄	1	1	yes	characteristic
372	#2403	C₂×D₄	1	1	yes	characteristic
373	#2403	C₂×D₄	1	1	yes	characteristic
374	#2403	C₂×D₄	1	1	yes	characteristic
375	#2403	C₂×D₄	1	1	yes	characteristic
376	#2403	C₂×D₄	1	1	yes	characteristic
377	#2403	C₂×D₄	1	1	yes	characteristic
378	#2403	C₂×D₄	1	1	yes	characteristic
379	#2403	C₂×D₄	1	1	yes	characteristic
380	#2403	C₂×D₄	1	1	yes	characteristic
381	#2403	C₂×D₄	1	1	yes	characteristic
382	#2403	C₂×D₄	1	1	yes	characteristic
383	#2403	C₂×D₄	1	1	yes	characteristic
384	#2403	C₂×D₄	1	1	yes	characteristic
385	#2403	C₂×D₄	1	1	yes	characteristic
386	#2403	C₂×D₄	1	1	yes	characteristic
387	#2403	C₂×D₄	1	1	yes	characteristic
388	#2403	C₂×D₄	1	1	yes	characteristic
389	#2403	C₂×D₄	1	1	yes	characteristic
390	#2403	C₂×D₄	1	1	yes	characteristic
391	#2403	C₂×D₄	1	1	yes	characteristic
392	#2403	C₂×D₄	1	1	yes	characteristic
393	#2403	C₂×D₄	1	1	yes	characteristic, complemented
394	#2403	C₂×D₄	1	1	yes	characteristic, complemented
395	#2403	C₂×D₄	1	1	yes	characteristic, complemented
396	#2315	C₂×D₄	1	1	yes	characteristic
397	#2315	C₂×D₄	1	1	yes	characteristic, complemented
398	#2315	C₂×D₄	1	1	yes	characteristic, complemented
399	#2315	C₂×D₄	1	1	yes	characteristic, complemented
400	#2315	C₂×D₄	1	1	yes	characteristic, complemented
401	#2315	C₂×D₄	1	1	yes	characteristic, complemented
402	#2315	C₂×D₄	1	1	yes	characteristic, complemented
403	#2315	C₂×D₄	1	1	yes	characteristic, complemented
404	#2312	C₂×D₄	1	1	yes	characteristic
405	#2312	C₂×D₄	1	1	yes	characteristic
406	#2312	C₂×D₄	1	1	yes	characteristic
407	#2312	C₂×D₄	1	1	yes	characteristic
408	#2312	C₂×D₄	1	1	yes	characteristic
409	#2312	C₂×D₄	1	1	yes	characteristic
410	#2312	C₂×D₄	1	1	yes	characteristic, complemented
411	#2312	C₂×D₄	1	1	yes	characteristic, complemented
412	#2312	C₂×D₄	1	1	yes	characteristic, complemented
413	#2312	C₂×D₄	1	1	yes	characteristic, complemented
414	#2312	C₂×D₄	1	1	yes	characteristic, complemented
415	#2312	C₂×D₄	1	1	yes	characteristic, complemented
416	#2309	C₂×D₄	1	1	yes	characteristic
417	#2309	C₂×D₄	1	1	yes	characteristic
418	#2309	C₂×D₄	1	1	yes	characteristic
419	#2309	C₂×D₄	1	1	yes	characteristic
420	#2309	C₂×D₄	1	1	yes	characteristic
421	#2309	C₂×D₄	1	1	yes	characteristic
422	#2309	C₂×D₄	1	1	yes	characteristic
423	#2309	C₂×D₄	1	1	yes	characteristic
424	#2309	C₂×D₄	1	1	yes	characteristic
425	#2309	C₂×D₄	1	1	yes	characteristic, complemented
426	#2309	C₂×D₄	1	1	yes	characteristic, complemented
427	#2309	C₂×D₄	1	1	yes	characteristic, complemented
428	#2308	C₂×D₄	1	1	yes	characteristic
429	#2308	C₂×D₄	1	1	yes	characteristic
430	#2308	C₂×D₄	1	1	yes	characteristic
431	#2308	C₂×D₄	1	1	yes	characteristic
432	#2308	C₂×D₄	1	1	yes	characteristic
433	#2308	C₂×D₄	1	1	yes	characteristic
434	#2308	C₂×D₄	1	1	yes	characteristic
435	#2308	C₂×D₄	1	1	yes	characteristic
436	#2308	C₂×D₄	1	1	yes	characteristic
437	#2308	C₂×D₄	1	1	yes	characteristic
438	#2308	C₂×D₄	1	1	yes	characteristic
439	#2308	C₂×D₄	1	1	yes	characteristic
440	#2308	C₂×D₄	1	1	yes	characteristic
441	#2308	C₂×D₄	1	1	yes	characteristic
442	#2308	C₂×D₄	1	1	yes	characteristic
443	#2308	C₂×D₄	1	1	yes	characteristic
444	#2308	C₂×D₄	1	1	yes	characteristic
445	#2308	C₂×D₄	1	1	yes	characteristic
446	#2308	C₂×D₄	1	1	yes	characteristic
447	#2308	C₂×D₄	1	1	yes	characteristic
448	#2308	C₂×D₄	1	1	yes	characteristic
449	#2308	C₂×D₄	1	1	yes	characteristic
450	#2308	C₂×D₄	1	1	yes	characteristic, complemented
451	#2308	C₂×D₄	1	1	yes	characteristic, complemented
452	#2308	C₂×D₄	1	1	yes	characteristic, complemented
453	#2308	C₂×D₄	1	1	yes	characteristic, complemented
454	#2308	C₂×D₄	1	1	yes	characteristic, complemented
455	#2308	C₂×D₄	1	1	yes	characteristic, complemented
456	#2308	C₂×D₄	1	1	yes	characteristic, complemented
457	#2308	C₂×D₄	1	1	yes	characteristic, complemented
458	#2308	C₂×D₄	1	1	yes	characteristic, complemented
459	#2308	C₂×D₄	1	1	yes	characteristic, complemented
460	C₂×#386	C₂×D₄	1	1	yes	characteristic
461	C₂×#386	C₂×D₄	1	1	yes	characteristic
462	C₂×#386	C₂×D₄	1	1	yes	characteristic
463	C₂×#386	C₂×D₄	1	1	yes	characteristic
464	C₂×#386	C₂×D₄	1	1	yes	characteristic
465	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
466	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
467	C₂×#385	C₂×D₄	1	1	yes	characteristic
468	#2280	C₂×D₄	1	1	yes	characteristic
469	#2280	C₂×D₄	1	1	yes	characteristic
470	#2280	C₂×D₄	1	1	yes	characteristic
471	#2280	C₂×D₄	1	1	yes	characteristic
472	C₂×#381	C₂×D₄	1	1	yes	characteristic, complemented
473	C₂×#381	C₂×D₄	1	1	yes	characteristic, complemented
474	C₂×#381	C₂×D₄	1	1	yes	characteristic, complemented
475	C₂×#380	C₂×D₄	1	1	yes	characteristic, complemented
476	C₂×#379	C₂×D₄	1	1	yes	characteristic
477	C₂×#379	C₂×D₄	1	1	yes	characteristic
478	C₂×#379	C₂×D₄	1	1	yes	characteristic
479	C₂×#379	C₂×D₄	1	1	yes	characteristic
480	C₂×#379	C₂×D₄	1	1	yes	characteristic
481	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
482	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
483	C₂×#379	C₂⁴	1	2	yes	—
484	C₂×#379	C₂⁴	1	2	yes	—
485	C₂×#379	C₂⁴	1	2	yes	—
486	C₂×#379	C₂⁴	1	2	yes	—
487	C₂×#379	C₂⁴	1	2	yes	—
488	C₂×#379	C₂⁴	1	2	yes	—
489	C₂×#379	C₂⁴	1	1	yes	characteristic
490	C₂×#379	C₂⁴	1	1	yes	characteristic
491	C₂×#379	C₂⁴	1	1	yes	characteristic
492	C₂×#379	C₂⁴	1	1	yes	characteristic
493	C₂×#379	C₂⁴	1	1	yes	characteristic
494	C₂×#379	C₂⁴	1	1	yes	characteristic
495	C₂×#379	C₂⁴	1	1	yes	characteristic
496	#2273	C₂×D₄	1	1	yes	characteristic
497	#2273	C₂×D₄	1	1	yes	characteristic, complemented
498	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
499	C₂⁶	#120	1	1	yes	characteristic
500	C₂⁶	C₂²×D₄	1	1	yes	characteristic
501	C₂⁶	C₂²×D₄	1	1	yes	characteristic
502	C₂⁶	C₂²×D₄	1	1	yes	characteristic
503	C₂⁶	C₂²×D₄	1	1	yes	characteristic
504	C₂⁶	C₂×#41	1	2	yes	complemented
505	C₂⁶	C₂⁵	1	1	yes	characteristic
506	C₂³×D₄	#120	1	1	yes	characteristic
507	C₂³×D₄	#120	1	1	yes	characteristic
508	C₂³×D₄	#120	1	1	yes	characteristic
509	C₂³×D₄	#120	1	1	yes	characteristic
510	C₂³×D₄	#120	1	1	yes	characteristic
511	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
512	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
513	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
514	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
515	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
516	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
517	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
518	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
519	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
520	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
521	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
522	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
523	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
524	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
525	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
526	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
527	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
528	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
529	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
530	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
531	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
532	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
533	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
534	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
535	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
536	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
537	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
538	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
539	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
540	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
541	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
542	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
543	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
544	C₂⁴×C₄	#120	1	1	yes	characteristic
545	C₂⁴×C₄	#120	1	1	yes	characteristic
546	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
547	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
548	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
549	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
550	C₂⁴×C₄	C₂×#41	1	2	yes	complemented
551	C₂×#123	#120	1	1	yes	characteristic
552	C₂×#123	#120	1	1	yes	characteristic
553	C₂×#123	#120	1	1	yes	characteristic
554	C₂×#123	#120	1	1	yes	characteristic
555	C₂×#123	#120	1	1	yes	characteristic
556	C₂×#123	#120	1	1	yes	characteristic
557	C₂×#123	#120	1	1	yes	characteristic
558	C₂×#123	#120	1	1	yes	characteristic
559	C₂×#123	#120	1	1	yes	characteristic
560	C₂×#123	#120	1	1	yes	characteristic
561	C₂×#123	#120	1	1	yes	characteristic
562	C₂×#123	#120	1	1	yes	characteristic
563	C₂×#123	#120	1	1	yes	characteristic
564	C₂×#123	#120	1	1	yes	characteristic
565	C₂×#123	#120	1	1	yes	characteristic
566	C₂×#123	#120	1	1	yes	characteristic
567	C₂×#120	#120	1	1	yes	characteristic
568	C₂×#120	#120	1	1	yes	characteristic
569	C₂×#120	#120	1	1	yes	characteristic
570	C₂×#120	#120	1	1	yes	characteristic
571	C₂×#120	#120	1	1	yes	characteristic
572	C₂×#120	#120	1	1	yes	characteristic
573	C₂×#120	#120	1	1	yes	characteristic
574	C₂×#120	#120	1	1	yes	characteristic
575	C₂×#120	#120	1	1	yes	characteristic
576	C₂×#120	#120	1	1	yes	characteristic
577	C₂×#120	#120	1	1	yes	characteristic
578	C₂×#120	#120	1	1	yes	characteristic
579	C₂×#120	#120	1	1	yes	characteristic
580	C₂×#120	#120	1	1	yes	characteristic
581	C₂×#120	#120	1	1	yes	characteristic
582	C₂×#120	#120	1	1	yes	characteristic
583	C₂×#120	#120	1	1	yes	characteristic
584	C₂×#120	#120	1	1	yes	characteristic
585	C₂×#120	#120	1	1	yes	characteristic
586	C₂×#120	#120	1	1	yes	characteristic
587	C₂×#120	#120	1	1	yes	characteristic
588	C₂×#120	#120	1	1	yes	characteristic
589	C₂×#120	#120	1	1	yes	characteristic
590	C₂×#120	#120	1	1	yes	characteristic
591	C₂×#120	C₂×#41	1	4	yes	—
592	C₂×#120	H(5,𝔽₂)	1	4	yes	—
593	C₂×#117	#120	1	1	yes	characteristic
594	C₂×#117	#120	1	1	yes	characteristic
595	C₂×#117	#120	1	1	yes	characteristic
596	C₂×#117	#120	1	1	yes	characteristic
597	C₂×#117	#120	1	1	yes	characteristic
598	C₂×#117	#120	1	1	yes	characteristic
599	C₂×#117	#120	1	1	yes	characteristic
600	C₂×#117	#120	1	1	yes	characteristic
601	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
602	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
603	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
604	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
605	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
606	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
607	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
608	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
609	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
610	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
611	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
612	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
613	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
614	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
615	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
616	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
617	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
618	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
619	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
620	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
621	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
622	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
623	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
624	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
625	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
626	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
627	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
628	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
629	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
630	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
631	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
632	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
633	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
634	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
635	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
636	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
637	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
638	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
639	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
640	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
641	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
642	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
643	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
644	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
645	C₂²×C₄²	#120	1	1	yes	characteristic
646	#386	#120	1	1	yes	characteristic
647	#386	#120	1	1	yes	characteristic
648	#386	#120	1	1	yes	characteristic
649	#386	#120	1	1	yes	characteristic
650	#386	#120	1	1	yes	characteristic
651	#386	#120	1	1	yes	characteristic
652	#386	#120	1	1	yes	characteristic
653	#386	#120	1	1	yes	characteristic
654	#386	#120	1	1	yes	characteristic
655	#386	#120	1	1	yes	characteristic
656	#386	#120	1	1	yes	characteristic
657	#386	#120	1	1	yes	characteristic
658	#386	#120	1	1	yes	characteristic
659	#386	#120	1	1	yes	characteristic
660	#386	#120	1	1	yes	characteristic
661	#386	#120	1	1	yes	characteristic
662	#386	#120	1	1	yes	characteristic
663	#386	#120	1	1	yes	characteristic
664	#386	#120	1	1	yes	characteristic
665	#386	#120	1	1	yes	characteristic
666	#386	#120	1	1	yes	characteristic
667	#386	#120	1	1	yes	characteristic
668	#386	#120	1	1	yes	characteristic
669	#386	#120	1	1	yes	characteristic
670	#381	#120	1	1	yes	characteristic
671	#381	#120	1	1	yes	characteristic
672	#381	#120	1	1	yes	characteristic
673	#381	#120	1	1	yes	characteristic
674	#381	#120	1	1	yes	characteristic
675	#381	#120	1	1	yes	characteristic
676	#381	#120	1	1	yes	characteristic
677	#381	#120	1	1	yes	characteristic
678	#379	#120	1	1	yes	characteristic
679	#379	#120	1	1	yes	characteristic
680	#379	#120	1	1	yes	characteristic
681	#379	#120	1	1	yes	characteristic
682	#379	#120	1	1	yes	characteristic
683	#379	#120	1	1	yes	characteristic
684	#379	#120	1	1	yes	characteristic
685	#379	#120	1	1	yes	characteristic
686	#379	C₂²×D₄	1	1	yes	characteristic
687	#379	C₂²×D₄	1	1	yes	characteristic
688	#379	C₂²×D₄	1	1	yes	characteristic
689	#379	C₂²×D₄	1	1	yes	characteristic
690	#379	C₂²×D₄	1	1	yes	characteristic
691	#379	C₂²×D₄	1	1	yes	characteristic
692	#379	C₂²×D₄	1	1	yes	characteristic
693	#379	C₂²×D₄	1	1	yes	characteristic
694	#379	C₂²×D₄	1	1	yes	characteristic
695	#379	C₂²×D₄	1	1	yes	characteristic
696	#379	C₂²×D₄	1	1	yes	characteristic
697	#379	C₂²×D₄	1	1	yes	characteristic
698	#379	C₂²×D₄	1	1	yes	characteristic
699	#379	C₂²×D₄	1	1	yes	characteristic
700	#379	C₂²×D₄	1	1	yes	characteristic
701	#379	C₂²×D₄	1	1	yes	characteristic
702	#379	C₂²×D₄	1	1	yes	characteristic
703	#379	C₂²×D₄	1	1	yes	characteristic
704	#379	C₂²×D₄	1	1	yes	characteristic
705	#379	C₂²×D₄	1	1	yes	characteristic
706	#379	C₂²×D₄	1	1	yes	characteristic
707	#379	C₂²×D₄	1	1	yes	characteristic
708	#379	C₂²×D₄	1	1	yes	characteristic
709	#379	C₂²×D₄	1	1	yes	characteristic
710	#379	C₂²×D₄	1	1	yes	characteristic
711	#379	C₂²×D₄	1	1	yes	characteristic
712	#379	C₂²×D₄	1	1	yes	characteristic
713	#379	C₂²×D₄	1	1	yes	characteristic
714	#379	C₂×#41	1	4	yes	complemented
715	C₂⁵	C₂×#120	1	1	yes	characteristic
716	C₂⁵	C₂×#120	1	1	yes	characteristic
717	C₂⁵	C₂×#120	1	1	yes	characteristic
718	C₂⁵	C₂×#120	1	1	yes	characteristic
719	C₂⁵	C₂×#120	1	1	yes	characteristic
720	C₂⁵	C₂×#120	1	1	yes	characteristic
721	C₂⁵	C₂×#120	1	1	yes	characteristic
722	C₂⁵	C₂×#120	1	1	yes	characteristic
723	C₂⁵	C₂×#120	1	1	yes	characteristic
724	C₂⁵	C₂×#120	1	1	yes	characteristic
725	C₂⁵	C₂×#120	1	1	yes	characteristic
726	C₂⁵	C₂×#120	1	1	yes	characteristic
727	C₂⁵	C₂×#120	1	1	yes	characteristic
728	C₂⁵	C₂×#120	1	1	yes	characteristic
729	C₂⁵	C₂×#120	1	1	yes	characteristic
730	C₂⁵	C₂³×D₄	1	1	yes	characteristic
731	C₂⁵	C₂³×D₄	1	1	yes	characteristic
732	C₂⁵	C₂³×D₄	1	1	yes	characteristic
733	C₂⁵	C₂³×D₄	1	1	yes	characteristic
734	C₂⁵	C₂³×D₄	1	1	yes	characteristic
735	C₂⁵	C₂³×D₄	1	1	yes	characteristic
736	C₂⁵	C₂³×D₄	1	1	yes	characteristic
737	C₂⁵	C₂²×#41	1	2	yes	—
738	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
739	C₂⁵	#585	1	2	yes	—
740	C₂⁵	#585	1	2	yes	—
741	C₂²×D₄	C₂×#120	1	1	yes	characteristic
742	C₂²×D₄	C₂×#120	1	1	yes	characteristic
743	C₂²×D₄	C₂×#120	1	1	yes	characteristic
744	C₂²×D₄	C₂×#120	1	1	yes	characteristic
745	C₂²×D₄	C₂×#120	1	1	yes	characteristic
746	C₂²×D₄	C₂×#120	1	1	yes	characteristic
747	C₂²×D₄	C₂×#120	1	1	yes	characteristic
748	C₂²×D₄	C₂×#120	1	1	yes	characteristic
749	C₂²×D₄	C₂×#120	1	1	yes	characteristic
750	C₂²×D₄	C₂×#120	1	1	yes	characteristic
751	C₂²×D₄	C₂×#120	1	1	yes	characteristic
752	C₂²×D₄	C₂×#120	1	1	yes	characteristic
753	C₂²×D₄	C₂×#120	1	1	yes	characteristic
754	C₂²×D₄	C₂×#120	1	1	yes	characteristic
755	C₂²×D₄	C₂×#120	1	1	yes	characteristic
756	C₂²×D₄	C₂×#120	1	1	yes	characteristic
757	C₂²×D₄	#525	1	2	yes	—
758	C₂²×D₄	#535	1	2	yes	—
759	C₂²×D₄	#546	1	4	yes	—
760	C₂²×D₄	#546	1	4	yes	—
761	C₂³×C₄	C₂×#120	1	1	yes	characteristic
762	C₂³×C₄	C₂×#120	1	1	yes	characteristic
763	C₂³×C₄	C₂×#120	1	1	yes	characteristic
764	C₂³×C₄	C₂×#120	1	1	yes	characteristic
765	C₂³×C₄	C₂×#120	1	1	yes	characteristic
766	C₂³×C₄	C₂×#120	1	1	yes	characteristic
767	C₂³×C₄	C₂×#120	1	1	yes	characteristic
768	C₂³×C₄	C₂×#120	1	1	yes	characteristic
769	C₂³×C₄	C₂×#120	1	1	yes	characteristic
770	C₂³×C₄	C₂×#120	1	1	yes	characteristic
771	C₂³×C₄	C₂×#120	1	1	yes	characteristic
772	C₂³×C₄	C₂×#120	1	1	yes	characteristic
773	C₂³×C₄	C₂×#120	1	1	yes	characteristic
774	C₂³×C₄	C₂×#120	1	1	yes	characteristic
775	C₂³×C₄	C₂×#120	1	1	yes	characteristic
776	C₂³×C₄	C₂×#120	1	1	yes	characteristic
777	C₂³×C₄	C₂×#120	1	1	yes	characteristic
778	C₂³×C₄	C₂×#120	1	1	yes	characteristic
779	C₂³×C₄	C₂×#120	1	1	yes	characteristic
780	C₂³×C₄	C₂×#120	1	1	yes	characteristic
781	C₂³×C₄	C₂×#120	1	1	yes	characteristic
782	#120	B(4,𝔽₂)	1	4	yes	complemented
783	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
784	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
785	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
786	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
787	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
788	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
789	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
790	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
791	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
792	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
793	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
794	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
795	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
796	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
797	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
798	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
799	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
800	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
801	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
802	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
803	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
804	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
805	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
806	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
807	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
808	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
809	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
810	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
811	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
812	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
813	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
814	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
815	C₂×C₂²⋊C₄	#525	1	2	yes	—
816	C₂×C₂²⋊C₄	#535	1	2	yes	—
817	C₂×C₂²⋊C₄	#546	1	4	yes	—
818	C₂×C₂²⋊C₄	#546	1	4	yes	—
819	C₂⁴	#2404	1	2	yes	—
820	C₂⁴	#2846	1	1	yes	characteristic
821	C₂⁴	#2846	1	1	yes	characteristic
822	C₂⁴	#2846	1	1	yes	characteristic
823	C₂⁴	#2846	1	1	yes	characteristic
824	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
825	C₂⁴	C₂²×#120	1	1	yes	characteristic
826	C₂⁴	C₂²×#120	1	1	yes	characteristic
827	C₂⁴	C₂²×#120	1	1	yes	characteristic
828	C₂⁴	C₂²×#120	1	1	yes	characteristic
829	C₂⁴	C₂²×#120	1	1	yes	characteristic
830	C₂⁴	C₂²×#120	1	1	yes	characteristic
831	C₂⁴	C₂²×#120	1	1	yes	characteristic
832	C₂⁴	C₂×#525	1	1	yes	characteristic
833	C₂⁴	C₂×#535	1	1	yes	characteristic
834	C₂⁴	#3449	1	1	yes	characteristic
835	C₂⁴	#3449	1	1	yes	characteristic
836	C₂⁴	C₂×#546	1	2	yes	—
837	C₂⁴	C₂×#546	1	2	yes	—
838	C₂⁴	D₄×#41	1	2	yes	—
839	C₂⁴	D₄×#41	1	2	yes	—
840	C₂⁴	D₄×#41	1	2	yes	—
841	C₂⁴	D₄×#41	1	2	yes	—
842	C₂⁴	#3485	1	2	yes	—
843	C₂⁴	#3485	1	2	yes	—
844	C₂⁴	#3488	1	2	yes	—
845	C₂⁴	#3488	1	2	yes	—
846	C₂⁴	#3488	1	2	yes	—
847	C₂⁴	#3488	1	2	yes	—
848	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
849	C₂×D₄	#3026	1	2	yes	—
850	C₂²×C₄	#2404	1	2	yes	—
851	C₂²×C₄	#2404	1	2	yes	—
852	C₂²×C₄	#2404	1	2	yes	—
853	C₂²×C₄	#2846	1	1	yes	characteristic
854	C₂²×C₄	#2846	1	1	yes	characteristic
855	C₂²×C₄	#2846	1	1	yes	characteristic
856	C₂²×C₄	#2846	1	1	yes	characteristic
857	C₂²⋊C₄	C₂×B(4,𝔽₂)	1	2	yes	—
858	C₂³	#32898	1	2	yes	—
859	C₂³	C₂×#2404	1	1	yes	characteristic
860	C₂³	#34736	1	1	yes	characteristic
861	C₂³	#34736	1	1	yes	characteristic
862	C₂³	#35088	1	1	yes	characteristic
863	C₂³	#35250	1	1	yes	characteristic
864	C₂³	#35250	1	1	yes	characteristic
865	C₂³	#36212	1	2	yes	—
866	C₂³	#36212	1	2	yes	—
867	C₂³	#36212	1	2	yes	—
868	C₂³	#36212	1	2	yes	—
869	C₂³	C₂×#2846	1	1	yes	characteristic
870	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
871	C₂³	C₂×#3026	1	1	yes	characteristic
872	C₂³	#60399	1	2	yes	—
873	C₂×C₄	#32898	1	2	yes	—
874	C₂²	#613188	1	1	yes	characteristic
875	C₂²	#6595772	1	2	yes	—
876	C₂²	#6595778	1	2	yes	—
877	C₂²	C₂×#32898	1	1	yes	characteristic
878	C₂²	#6628896	1	1	yes	characteristic
879	C₂	#72237919	1	1	yes	characteristic
880	C₂	#72240460	1	1	yes	characteristic
881	C₂	#72264896	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#613188
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁶ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72265949	C₂	semidirect
2. #72265948	C₂	semidirect
3. #72265947	C₂	semidirect
4. #72265943	C₂	semidirect
5. #72265904	C₂	semidirect
6. #72265195	C₂	semidirect
7. #72261568	C₂	semidirect
8. #72258512	C₂	semidirect
9. #72258461	C₂	semidirect
10. #72251466	C₂	semidirect
11. #72241329	C₂	semidirect
12. #72234960	C₂	semidirect
13. #72234959	C₂	semidirect
14. #72234958	C₂	semidirect
15. #72234957	C₂	semidirect
16. #72234956	C₂	semidirect
17. #72234955	C₂	semidirect
18. #72234644	C₂	semidirect
19. #72233304	C₂	semidirect
20. #72233069	C₂	semidirect
21. #72233042	C₂	semidirect
22. #72232934	C₂	semidirect
23. #72232821	C₂	semidirect
24. C₂²×#3026	C₂²	semidirect
26. #7806599	C₂²	semidirect
27. #7752093	C₂²	semidirect
28. #7752089	C₂²	semidirect
30. #7733089	C₂²	semidirect
31. #7721731	C₂²	semidirect
33. C₂×#46996	C₂²	semidirect
38. #7626663	C₂²	semidirect
40. #7626386	C₂²	semidirect
41. #6628892	C₂²	semidirect
42. #6628892	C₂²	semidirect
43. C₂×#32898	C₂²	semidirect
47. #6370693	C₂²	semidirect
48. #6370693	C₂²	semidirect
49. #394470	C₂²	semidirect
50. #394470	C₂²	semidirect
51. #394267	C₂²	semidirect
52. #394061	C₂²	semidirect
53. #393929	C₂²	semidirect
54. #393929	C₂²	semidirect
55. #374058	C₂²	semidirect
56. #374058	C₂²	semidirect
57. #374038	C₂²	semidirect
58. #364471	C₂²	semidirect
60. #364440	C₂²	semidirect
61. #359892	C₂²	semidirect
62. #359892	C₂²	semidirect
64. #359504	C₂²	semidirect
65. #359442	C₂²	semidirect
66. #359442	C₂²	semidirect
67. #359442	C₂²	semidirect
68. #359434	C₂²	semidirect
69. #238082	C₂²	semidirect
70. C₂×#10390	C₂²	semidirect
71. #233549	C₂²	semidirect
72. #233541	C₂²	semidirect
73. #233541	C₂²	semidirect
74. C₂×#10336	C₂²	semidirect
75. #201701	C₂²	semidirect
76. #201701	C₂²	semidirect
77. #201701	C₂²	semidirect
78. #201701	C₂²	semidirect
82. #201678	C₂²	semidirect
83. #201678	C₂²	semidirect
84. #201678	C₂²	semidirect
85. #201664	C₂²	semidirect
86. #201664	C₂²	semidirect
87. #201664	C₂²	semidirect
88. C₂×#9495	C₂²	semidirect
89. C₂×#9495	C₂²	semidirect
90. #190107	C₂²	semidirect
91. #190107	C₂²	semidirect
93. #187944	C₂²	semidirect
94. #187928	C₂²	semidirect
95. #181344	C₂²	semidirect
96. #181344	C₂²	semidirect
97. #122191	C₂²	semidirect
98. #122187	C₂²	semidirect
99. #122187	C₂²	semidirect
100. #122038	C₂²	semidirect
101. #115631	C₂²	semidirect
102. #115204	C₂²	semidirect
103. #115204	C₂²	semidirect
104. #115163	C₂²	semidirect
105. #115133	C₂²	semidirect
106. #115133	C₂²	semidirect
107. #111467	C₂²	semidirect
108. #111458	C₂²	semidirect
109. #107194	C₂²	semidirect
110. #107194	C₂²	semidirect
111. #107194	C₂²	semidirect
112. #107194	C₂²	semidirect
113. #107194	C₂²	semidirect
114. #107194	C₂²	semidirect
115. #107114	C₂²	semidirect
116. #106766	C₂²	semidirect
117. #106654	C₂²	semidirect
118. #106542	C₂²	semidirect
119. #106542	C₂²	semidirect
120. #105808	C₂²	semidirect
121. #105752	C₂²	semidirect
122. #105752	C₂²	semidirect
124. C₂×#3490	D₄	semidirect
125. C₂×#3490	D₄	semidirect
126. C₂×#3484	D₄	semidirect
134. #47563	D₄	semidirect
135. #46998	D₄	semidirect
136. #46997	D₄	semidirect
137. #46996	D₄	semidirect
138. #46996	D₄	semidirect
139. #46837	D₄	semidirect
140. #46387	D₄	semidirect
141. #46386	D₄	semidirect
142. #46386	D₄	semidirect
143. #46385	D₄	semidirect
144. #46385	D₄	semidirect
145. #46385	D₄	semidirect
146. #46385	D₄	semidirect
147. #46385	D₄	semidirect
148. #46384	D₄	semidirect
149. #46384	D₄	semidirect
152. #37232	D₄	semidirect
153. #36717	D₄	semidirect
154. #36717	D₄	semidirect
155. #36714	D₄	semidirect
157. #35527	D₄	semidirect
158. #35455	D₄	semidirect
159. #35448	D₄	semidirect
160. #35447	D₄	semidirect
161. #35447	D₄	semidirect
162. #35390	D₄	semidirect
163. #35360	D₄	semidirect
164. #35360	D₄	semidirect
165. #35358	D₄	semidirect
166. #35355	D₄	semidirect
167. #35355	D₄	semidirect
168. #35348	D₄	semidirect
169. #35348	D₄	semidirect
170. #35348	D₄	semidirect
171. #35347	D₄	semidirect
172. #35346	D₄	semidirect
173. #34993	D₄	semidirect
174. #34992	D₄	semidirect
175. #34984	D₄	semidirect
178. #34981	D₄	semidirect
179. #34981	D₄	semidirect
180. #34980	D₄	semidirect
196. #34363	D₄	semidirect
197. #34363	D₄	semidirect
198. #34356	D₄	semidirect
199. #34356	D₄	semidirect
206. #34273	D₄	semidirect
207. #34264	D₄	semidirect
208. #34198	D₄	semidirect
211. #34185	D₄	semidirect
212. #34171	D₄	semidirect
221. #34057	D₄	semidirect
222. C₂×#2308	D₄	semidirect
287. C₂×#543	C₂×D₄	semidirect
288. C₂×#543	C₂×D₄	semidirect
308. C₂²×#123	C₂×D₄	semidirect
323. C₂²×#120	C₂×D₄	semidirect
324. C₂²×#120	C₂×D₄	semidirect
325. C₂²×#120	C₂×D₄	semidirect
336. C₂×#518	C₂×D₄	semidirect
337. C₂×#518	C₂×D₄	semidirect
338. C₂×#518	C₂×D₄	semidirect
341. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
342. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
343. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
346. #2849	#41	semidirect
347. #2846	#41	semidirect
348. #2842	C₂×D₄	semidirect
349. #2842	C₂×D₄	semidirect
350. #2842	C₂×D₄	semidirect
351. #2840	C₂×D₄	semidirect
352. #2840	C₂×D₄	semidirect
353. #2840	C₂×D₄	semidirect
354. #2840	C₂×D₄	semidirect
355. #2840	C₂×D₄	semidirect
356. #2483	C₂×D₄	semidirect
367. #2405	C₂×D₄	semidirect
368. #2405	C₂×D₄	semidirect
369. #2405	C₂×D₄	semidirect
370. #2405	C₂×D₄	semidirect
393. #2403	C₂×D₄	semidirect
394. #2403	C₂×D₄	semidirect
395. #2403	C₂×D₄	semidirect
397. #2315	C₂×D₄	semidirect
398. #2315	C₂×D₄	semidirect
399. #2315	C₂×D₄	semidirect
400. #2315	C₂×D₄	semidirect
401. #2315	C₂×D₄	semidirect
402. #2315	C₂×D₄	semidirect
403. #2315	C₂×D₄	semidirect
410. #2312	C₂×D₄	semidirect
411. #2312	C₂×D₄	semidirect
412. #2312	C₂×D₄	semidirect
413. #2312	C₂×D₄	semidirect
414. #2312	C₂×D₄	semidirect
415. #2312	C₂×D₄	semidirect
425. #2309	C₂×D₄	semidirect
426. #2309	C₂×D₄	semidirect
427. #2309	C₂×D₄	semidirect
450. #2308	C₂×D₄	semidirect
451. #2308	C₂×D₄	semidirect
452. #2308	C₂×D₄	semidirect
453. #2308	C₂×D₄	semidirect
454. #2308	C₂×D₄	semidirect
455. #2308	C₂×D₄	semidirect
456. #2308	C₂×D₄	semidirect
457. #2308	C₂×D₄	semidirect
458. #2308	C₂×D₄	semidirect
459. #2308	C₂×D₄	semidirect
465. C₂×#386	C₂×D₄	semidirect
466. C₂×#386	C₂×D₄	semidirect
472. C₂×#381	C₂×D₄	semidirect
473. C₂×#381	C₂×D₄	semidirect
474. C₂×#381	C₂×D₄	semidirect
475. C₂×#380	C₂×D₄	semidirect
481. C₂×#379	C₂×D₄	semidirect
482. C₂×#379	C₂×D₄	semidirect
497. #2273	C₂×D₄	semidirect
498. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
504. C₂⁶	C₂×#41	semidirect
550. C₂⁴×C₄	C₂×#41	semidirect
714. #379	C₂×#41	semidirect
782. #120	B(4,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
#72265949	2
#72265948	2
#72265947	2
#72265943	2
#72265904	2
#72265195	2
#72261568	2
#72258512	2
#72258461	2
#72251466	2
#72241329	2
#72234960	2
#72234959	2
#72234958	2
#72234957	2
#72234956	2
#72234955	2
#72234644	2
#72233304	2
#72233069	2
#72233042	2
#72232934	2
#72232821	2