Subgroups — #72251990

Order 2048.

At least 21714 conjugacy classes of subgroups; only the 1270 normal subgroups are shown.

The subgroup lattice has 839 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72251987	C₂	1	1	yes	maximal, characteristic, complemented
2	#72251986	C₂	1	1	yes	maximal, characteristic, complemented
3	#72251883	C₂	1	1	yes	maximal, characteristic, complemented
4	#72251874	C₂	1	1	yes	maximal, characteristic, complemented
5	#72251839	C₂	1	1	yes	maximal, characteristic, complemented
6	#72251717	C₂	1	2	yes	maximal, complemented
7	#72238623	C₂	1	1	yes	maximal, characteristic, complemented
8	#72238620	C₂	1	1	yes	maximal, characteristic, complemented
9	#72238411	C₂	1	1	yes	maximal, characteristic, complemented
10	#72238397	C₂	1	2	yes	maximal, complemented
11	#72234794	C₂	1	1	yes	maximal, characteristic, complemented
12	#72234768	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#23882	C₂	1	1	yes	maximal, characteristic, complemented
14	#72232031	C₂	1	1	yes	maximal, characteristic, complemented
15	#72231758	C₂	1	2	yes	maximal, complemented
16	#72231756	C₂	1	2	yes	maximal, complemented
17	C₂×#511819	C₂	1	2	yes	maximal, complemented
18	#72219502	C₂	1	2	yes	maximal, complemented
19	#72219483	C₂	1	1	yes	maximal, characteristic, complemented
20	#72215601	C₂	1	2	yes	maximal, complemented
21	#72214896	C₂	1	1	yes	maximal, characteristic, complemented
22	#72214565	C₂	1	2	yes	maximal, complemented
23	#72214353	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#3585	C₂²	1	1	yes	characteristic, complemented
25	C₂×#63011	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#3484	C₂²	1	1	yes	characteristic
27	C₂²×#3025	C₂²	1	1	yes	characteristic, complemented
28	C₂²×#3021	C₂²	1	1	yes	characteristic, complemented
29	#7837030	C₂²	1	1	yes	characteristic, complemented
30	#7837029	C₂²	1	1	yes	characteristic, complemented
31	#7783989	C₂²	1	1	yes	characteristic
32	#7779441	C₂²	1	1	yes	characteristic
33	#7737956	C₂²	1	1	yes	characteristic, complemented
34	#7737955	C₂²	1	1	yes	characteristic, complemented
35	#7712649	C₂²	1	1	yes	characteristic
36	#7665748	C₂²	1	1	yes	characteristic
37	#7659307	C₂²	1	1	yes	characteristic, complemented
38	#7659296	C₂²	1	1	yes	characteristic, complemented
39	#7633039	C₂²	1	1	yes	characteristic
40	#7631286	C₂²	1	1	yes	characteristic
41	#7627266	C₂²	1	1	yes	characteristic, complemented
42	C₂×#33570	C₂²	1	2	yes	complemented
43	C₂×#33553	C₂²	1	2	yes	complemented
44	C₂×#33553	C₂²	1	2	yes	complemented
45	C₂×#33546	C₂²	1	2	yes	complemented
46	#6628894	C₂²	1	1	yes	characteristic, complemented
47	#6628891	C₂²	1	1	yes	characteristic, complemented
48	#6628870	C₂²	1	1	yes	characteristic, complemented
49	#6628866	C₂²	1	1	yes	characteristic, complemented
50	C₂×#23872	C₂²	1	2	yes	complemented
51	C₂×#23882	C₂²	1	2	yes	—
52	C₂×#23882	C₂²	1	2	yes	complemented
53	C₂×#23882	C₂²	1	2	yes	complemented
54	C₂×#23882	C₂²	1	2	yes	complemented
55	C₂×#23882	C₂²	1	2	yes	complemented
56	C₂²×#1910	C₂²	1	1	yes	characteristic, complemented
57	C₂²×#1891	C₂²	1	1	yes	characteristic, complemented
58	C₂²×#1795	C₂²	1	1	yes	characteristic, complemented
59	#498932	C₂²	1	2	yes	complemented
60	#498929	C₂²	1	2	yes	complemented
61	#498929	C₂²	1	2	yes	complemented
62	#498922	C₂²	1	2	yes	complemented
63	#498909	C₂²	1	2	yes	complemented
64	#498906	C₂²	1	2	yes	complemented
65	#498888	C₂²	1	2	yes	complemented
66	#498885	C₂²	1	2	yes	complemented
67	#494733	C₂²	1	1	yes	characteristic, complemented
68	#494730	C₂²	1	1	yes	characteristic, complemented
69	#494715	C₂²	1	1	yes	characteristic, complemented
70	#494712	C₂²	1	1	yes	characteristic, complemented
71	#494698	C₂²	1	1	yes	characteristic, complemented
72	#494694	C₂²	1	1	yes	characteristic, complemented
73	#494680	C₂²	1	1	yes	characteristic, complemented
74	#494676	C₂²	1	1	yes	characteristic, complemented
75	#494622	C₂²	1	2	yes	complemented
76	#494601	C₂²	1	2	yes	complemented
77	#494577	C₂²	1	2	yes	complemented
78	#494571	C₂²	1	2	yes	complemented
79	C₂×#12778	C₂²	1	2	yes	complemented
80	C₂×#12765	C₂²	1	2	yes	complemented
81	C₂×#12755	C₂²	1	2	yes	complemented
82	C₂×#12755	C₂²	1	2	yes	complemented
83	C₂×#12718	C₂²	1	2	yes	complemented
84	C₂×#12711	C₂²	1	2	yes	complemented
85	C₂×#12711	C₂²	1	2	yes	complemented
86	C₂×#12711	C₂²	1	2	yes	complemented
87	C₂×#12711	C₂²	1	2	yes	complemented
88	C₂×#12711	C₂²	1	2	yes	complemented
89	#493385	C₂²	1	1	yes	characteristic, complemented
90	#493372	C₂²	1	1	yes	characteristic, complemented
91	#493352	C₂²	1	1	yes	characteristic, complemented
92	#493352	C₂²	1	1	yes	characteristic, complemented
93	#394080	C₂²	1	2	yes	complemented
94	#394076	C₂²	1	2	yes	complemented
95	#394022	C₂²	1	2	yes	complemented
96	#394020	C₂²	1	2	yes	complemented
97	#392701	C₂²	1	1	yes	characteristic, complemented
98	#392695	C₂²	1	1	yes	characteristic, complemented
99	#392662	C₂²	1	1	yes	characteristic, complemented
100	#392646	C₂²	1	1	yes	characteristic, complemented
101	#392132	C₂²	1	1	yes	characteristic, complemented
102	#392132	C₂²	1	1	yes	characteristic, complemented
103	#359576	C₂²	1	2	yes	complemented
104	#359573	C₂²	1	2	yes	complemented
105	#147833	C₂²	1	2	yes	complemented
106	#147828	C₂²	1	2	yes	complemented
107	#147820	C₂²	1	2	yes	complemented
108	#147817	C₂²	1	2	yes	complemented
109	#147813	C₂²	1	2	yes	complemented
110	#147813	C₂²	1	2	yes	complemented
111	#147787	C₂²	1	2	yes	complemented
112	#147782	C₂²	1	2	yes	complemented
113	#147582	C₂²	1	2	yes	complemented
114	#147577	C₂²	1	2	yes	complemented
115	#147576	C₂²	1	2	yes	complemented
116	#147573	C₂²	1	2	yes	complemented
117	#146656	C₂²	1	2	yes	complemented
118	#146651	C₂²	1	2	yes	complemented
119	#146605	C₂²	1	2	yes	complemented
120	#146596	C₂²	1	2	yes	complemented
121	#146488	C₂²	1	2	yes	complemented
122	#146484	C₂²	1	2	yes	complemented
123	C₂²×#585	C₂³	1	1	yes	characteristic, complemented
124	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
125	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
126	C₂×#3585	C₂³	1	2	yes	—
127	C₂×#3585	C₂³	1	2	yes	complemented
128	C₂²×#568	C₂³	1	1	yes	characteristic, complemented
129	C₂×#3498	D₄	1	1	yes	characteristic, complemented
130	C₂×#3498	C₂³	1	1	yes	characteristic
131	C₂×#3488	D₄	1	1	yes	characteristic, complemented
132	C₂×#3484	D₄	1	1	yes	characteristic, complemented
133	C₂×#3484	D₄	1	1	yes	characteristic, complemented
134	C₂×#3484	D₄	1	1	yes	characteristic, complemented
135	C₂×#3484	D₄	1	1	yes	characteristic, complemented
136	C₂×#3484	D₄	1	1	yes	characteristic, complemented
137	C₂×#3484	C₂³	1	1	yes	characteristic
138	C₂×#3484	C₂³	1	1	yes	characteristic
139	C₂×#3484	C₂³	1	1	yes	characteristic
140	C₂×#3484	C₂³	1	1	yes	characteristic
141	C₂×#3484	C₂³	1	1	yes	characteristic
142	C₂×#3549	C₂³	1	1	yes	characteristic
143	C₂×#3537	C₂³	1	1	yes	characteristic
144	C₂×#3537	C₂³	1	1	yes	characteristic
145	C₂×#3481	C₂³	1	1	yes	characteristic
146	C₂²×D₄²	D₄	1	1	yes	characteristic, complemented
147	C₂²×#535	D₄	1	1	yes	characteristic, complemented
148	C₂²×#535	C₂³	1	1	yes	characteristic
149	C₂²×#525	D₄	1	1	yes	characteristic, complemented
150	C₂²×#525	C₂³	1	1	yes	characteristic
151	C₂²×#518	D₄	1	1	yes	characteristic, complemented
152	C₂×#3027	C₂³	1	2	yes	complemented
153	C₂×#3025	C₂³	1	2	yes	—
154	C₂×#3025	C₂³	1	2	yes	complemented
155	C₂×#3025	C₂³	1	2	yes	complemented
156	C₂×#3021	C₂³	1	2	yes	—
157	C₂×#3021	C₂³	1	2	yes	complemented
158	C₂×#3021	C₂³	1	2	yes	complemented
159	C₂×#3018	C₂³	1	2	yes	complemented
160	C₂²×#413	C₂³	1	1	yes	characteristic, complemented
161	C₂²×#410	C₂³	1	1	yes	characteristic, complemented
162	#59191	D₄	1	1	yes	characteristic, complemented
163	#59189	D₄	1	1	yes	characteristic, complemented
164	#59179	D₄	1	1	yes	characteristic, complemented
165	#59173	D₄	1	1	yes	characteristic, complemented
166	#59160	D₄	1	2	yes	complemented
167	#59126	D₄	1	2	yes	complemented
168	#59107	D₄	1	1	yes	characteristic, complemented
169	#59089	D₄	1	1	yes	characteristic, complemented
170	#59089	D₄	1	2	yes	complemented
171	#59006	D₄	1	1	yes	characteristic, complemented
172	#58990	D₄	1	1	yes	characteristic, complemented
173	#58990	D₄	1	2	yes	complemented
174	#52165	C₂³	1	1	yes	characteristic
175	#52163	C₂³	1	1	yes	characteristic
176	#52013	D₄	1	2	yes	complemented
177	#52004	D₄	1	2	yes	complemented
178	#51902	D₄	1	2	yes	complemented
179	#51896	D₄	1	2	yes	complemented
180	#46324	D₄	1	2	yes	complemented
181	#45977	D₄	1	2	yes	complemented
182	#45455	D₄	1	2	yes	complemented
183	#45452	D₄	1	2	yes	complemented
184	#37297	C₂³	1	1	yes	characteristic
185	#37297	C₂³	1	1	yes	characteristic
186	#37273	C₂³	1	1	yes	characteristic
187	#37269	C₂³	1	1	yes	characteristic
188	#37269	C₂³	1	1	yes	characteristic
189	#37269	C₂³	1	1	yes	characteristic
190	#35527	D₄	1	1	yes	characteristic, complemented
191	#35527	D₄	1	1	yes	characteristic, complemented
192	#35527	C₂³	1	1	yes	characteristic
193	#35527	C₂³	1	1	yes	characteristic
194	#35513	D₄	1	1	yes	characteristic, complemented
195	#35513	C₂³	1	1	yes	characteristic
196	#35512	D₄	1	1	yes	characteristic, complemented
197	#35512	C₂³	1	1	yes	characteristic
198	#35250	D₄	1	1	yes	characteristic, complemented
199	#35250	C₂³	1	1	yes	characteristic
200	#35250	C₂³	1	1	yes	characteristic
201	#35222	D₄	1	1	yes	characteristic, complemented
202	#34738	C₂³	1	1	yes	characteristic
203	#34736	D₄	1	1	yes	characteristic, complemented
204	#34736	C₂³	1	1	yes	characteristic
205	C₂×#2433	D₄	1	1	yes	characteristic, complemented
206	#34415	C₂³	1	1	yes	characteristic
207	#34411	C₂³	1	1	yes	characteristic
208	#34360	C₂³	1	1	yes	characteristic
209	#34258	D₄	1	1	yes	characteristic, complemented
210	#34258	C₂³	1	1	yes	characteristic
211	#34256	D₄	1	1	yes	characteristic, complemented
212	#34256	C₂³	1	1	yes	characteristic
213	#34171	D₄	1	1	yes	characteristic, complemented
214	#34152	C₂³	1	1	yes	characteristic
215	C₂²⋊C₄×#41	D₄	1	1	yes	characteristic, complemented
216	C₂×#2134	C₂³	1	2	yes	—
217	C₂×#2134	C₂³	1	2	yes	complemented
218	C₂×#2134	C₂³	1	2	yes	complemented
219	C₂×#2132	C₂³	1	2	yes	complemented
220	C₂×#2128	C₂³	1	2	yes	—
221	C₂×#2128	C₂³	1	2	yes	complemented
222	C₂×#2128	C₂³	1	2	yes	complemented
223	C₂×#2126	C₂³	1	2	yes	complemented
224	C₂×#2122	C₂³	1	2	yes	complemented
225	C₂×#2122	C₂³	1	2	yes	complemented
226	C₂×#2120	C₂³	1	2	yes	—
227	C₂×#2120	C₂³	1	2	yes	—
228	C₂×#2120	C₂³	1	2	yes	complemented
229	C₂×#2120	C₂³	1	2	yes	complemented
230	C₂×#2120	C₂³	1	2	yes	complemented
231	C₂×#2120	C₂³	1	2	yes	complemented
232	#23882	D₄	1	16	yes	complemented
233	C₂×#1914	C₂³	1	2	yes	complemented
234	C₂×#1910	C₂³	1	2	yes	—
235	C₂×#1910	C₂³	1	2	yes	complemented
236	C₂×#1910	C₂³	1	2	yes	complemented
237	C₂×#1891	C₂³	1	2	yes	—
238	C₂×#1891	C₂³	1	2	yes	complemented
239	C₂×#1891	C₂³	1	2	yes	complemented
240	C₂×#1884	C₂³	1	2	yes	complemented
241	C₂×#1795	C₂³	1	2	yes	—
242	C₂×#1795	C₂³	1	2	yes	—
243	C₂×#1795	C₂³	1	2	yes	—
244	C₂×#1795	C₂³	1	2	yes	complemented
245	C₂×#1795	C₂³	1	2	yes	complemented
246	C₂×#1795	C₂³	1	2	yes	complemented
247	#20618	C₂³	1	2	yes	complemented
248	#20615	C₂³	1	2	yes	complemented
249	#20610	C₂³	1	2	yes	complemented
250	#20608	C₂³	1	2	yes	complemented
251	#20591	C₂³	1	1	yes	characteristic, complemented
252	#20591	C₂³	1	1	yes	characteristic, complemented
253	#20584	C₂³	1	1	yes	characteristic, complemented
254	#20584	C₂³	1	1	yes	characteristic, complemented
255	#12587	C₂³	1	2	yes	complemented
256	#12585	C₂³	1	2	yes	complemented
257	#12583	C₂³	1	2	yes	complemented
258	#12581	C₂³	1	2	yes	complemented
259	#12575	C₂³	1	2	yes	complemented
260	#12575	C₂³	1	2	yes	complemented
261	#12573	C₂³	1	2	yes	complemented
262	#12573	C₂³	1	2	yes	complemented
263	#10755	C₂³	1	2	yes	complemented
264	#10751	C₂³	1	2	yes	complemented
265	#10746	C₂³	1	2	yes	complemented
266	#10742	C₂³	1	2	yes	complemented
267	C₂×#585	C₂⁴	1	2	yes	—
268	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
269	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
270	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
271	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
272	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
273	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
274	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
275	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
276	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
277	C₂³×#41	C₂×D₄	1	1	yes	characteristic
278	C₂³×#41	C₂×D₄	1	1	yes	characteristic
279	C₂³×#41	C₂×D₄	1	1	yes	characteristic
280	C₂³×#41	C₂⁴	1	1	yes	characteristic
281	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
282	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
283	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
284	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
285	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
286	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
287	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
288	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
289	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
290	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
291	#3585	C₂×D₄	1	8	yes	complemented
292	C₂×#568	C₂⁴	1	2	yes	—
293	C₂×H(3,𝔽₄)	C₂×D₄	1	2	yes	complemented
294	C₂×#560	C₂×D₄	1	2	yes	—
295	C₂×#560	C₂×D₄	1	2	yes	complemented
296	#3484	C₂×D₄	1	8	yes	—
297	C₂×#559	C₂×D₄	1	1	yes	characteristic
298	C₂×#555	C₂×D₄	1	2	yes	complemented
299	C₂×#551	C₂×D₄	1	1	yes	characteristic
300	C₂×#551	C₂×D₄	1	1	yes	characteristic
301	C₂×D₄²	C₂×D₄	1	2	yes	—
302	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
303	C₂×D₄²	C₂×D₄	1	2	yes	complemented
304	C₂×#537	C₂×D₄	1	1	yes	characteristic, complemented
305	C₂×#535	C₂×D₄	1	2	yes	—
306	C₂×#535	C₂×D₄	1	2	yes	—
307	C₂×#535	C₂×D₄	1	1	yes	characteristic
308	C₂×#535	C₂×D₄	1	1	yes	characteristic
309	C₂×#535	C₂×D₄	1	1	yes	characteristic
310	C₂×#535	C₂×D₄	1	1	yes	characteristic
311	C₂×#535	C₂×D₄	1	1	yes	characteristic
312	C₂×#535	C₂×D₄	1	1	yes	characteristic
313	C₂×#535	C₂×D₄	1	1	yes	characteristic
314	C₂×#535	C₂×D₄	1	1	yes	characteristic
315	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
316	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
317	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
318	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
319	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
320	C₂×#535	C₂⁴	1	1	yes	characteristic
321	C₂×#535	C₂⁴	1	1	yes	characteristic
322	C₂×#535	C₂⁴	1	1	yes	characteristic
323	C₂×#535	C₂⁴	1	1	yes	characteristic
324	C₂×#532	C₂×D₄	1	1	yes	characteristic
325	C₂×#532	C₂⁴	1	1	yes	characteristic
326	C₂²×#127	C₂×D₄	1	2	yes	—
327	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
328	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
329	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
330	C₂²×#124	C₂×D₄	1	2	yes	—
331	C₂×#525	C₂×D₄	1	1	yes	characteristic
332	C₂×#525	C₂×D₄	1	1	yes	characteristic
333	C₂×#525	C₂×D₄	1	1	yes	characteristic
334	C₂×#525	C₂×D₄	1	1	yes	characteristic
335	C₂×#525	C₂×D₄	1	1	yes	characteristic
336	C₂×#525	C₂×D₄	1	1	yes	characteristic
337	C₂×#525	C₂×D₄	1	1	yes	characteristic
338	C₂×#525	C₂×D₄	1	1	yes	characteristic
339	C₂×#525	C₂×D₄	1	1	yes	characteristic
340	C₂×#525	C₂×D₄	1	1	yes	characteristic
341	C₂×#525	C₂×D₄	1	1	yes	characteristic
342	C₂×#525	C₂×D₄	1	1	yes	characteristic
343	C₂×#525	C₂×D₄	1	1	yes	characteristic, complemented
344	C₂×#525	C₂×D₄	1	1	yes	characteristic, complemented
345	C₂×#525	C₂⁴	1	1	yes	characteristic
346	C₂×#525	C₂⁴	1	1	yes	characteristic
347	C₂×#525	C₂⁴	1	1	yes	characteristic
348	C₂²×#123	C₂×D₄	1	1	yes	characteristic
349	C₂²×#123	C₂×D₄	1	1	yes	characteristic
350	C₂²×#121	C₂×D₄	1	1	yes	characteristic
351	C₂²×#121	C₂×D₄	1	1	yes	characteristic
352	C₂²×#121	C₂×D₄	1	1	yes	characteristic, complemented
353	C₂²×#120	C₂×D₄	1	1	yes	characteristic
354	C₂²×#120	C₂×D₄	1	1	yes	characteristic
355	C₂×#520	C₂×D₄	1	1	yes	characteristic, complemented
356	C₂×#518	C₂×D₄	1	1	yes	characteristic
357	C₂×#518	C₂×D₄	1	1	yes	characteristic
358	C₂×#518	C₂×D₄	1	1	yes	characteristic
359	C₂×#518	C₂×D₄	1	1	yes	characteristic
360	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
361	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
362	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
363	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
364	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic, complemented
366	C₂²×#117	C₂×D₄	1	1	yes	characteristic
367	C₂²×#117	C₂×D₄	1	1	yes	characteristic
368	#3025	C₂×D₄	1	8	yes	complemented
369	#3021	C₂×D₄	1	8	yes	complemented
370	C₂×#413	C₂⁴	1	2	yes	—
371	C₂×#413	C₂⁴	1	2	yes	—
372	C₂×#413	C₂⁴	1	2	yes	—
373	C₂×#410	C₂⁴	1	2	yes	—
374	C₂×#410	C₂⁴	1	2	yes	—
375	C₂×#410	C₂⁴	1	2	yes	—
376	#2733	C₂×D₄	1	2	yes	complemented
377	#2733	C₂×D₄	1	2	yes	complemented
378	#2733	C₂×D₄	1	2	yes	complemented
379	#2731	C₂×D₄	1	2	yes	complemented
380	#2724	C₂×D₄	1	1	yes	characteristic
381	#2717	C₂×D₄	1	1	yes	characteristic
382	#2709	C₂×D₄	1	2	yes	—
383	#2709	C₂×D₄	1	1	yes	characteristic
384	#2709	C₂×D₄	1	2	yes	complemented
385	#2697	C₂×D₄	1	2	yes	—
386	#2697	C₂×D₄	1	1	yes	characteristic
387	#2697	C₂×D₄	1	1	yes	characteristic
388	#2684	C₂×D₄	1	1	yes	characteristic
389	#2679	C₂×D₄	1	2	yes	—
390	#2679	C₂×D₄	1	1	yes	characteristic
391	#2669	C₂×D₄	1	2	yes	—
392	#2669	C₂×D₄	1	1	yes	characteristic
393	#2669	C₂×D₄	1	2	yes	complemented
394	#2669	C₂×D₄	1	2	yes	complemented
395	#2669	C₂×D₄	1	2	yes	complemented
396	#2436	C₂×D₄	1	2	yes	—
397	#2436	C₂×D₄	1	1	yes	characteristic
398	#2435	C₂×D₄	1	1	yes	characteristic
399	#2434	C₂×D₄	1	1	yes	characteristic
400	#2433	C₂×D₄	1	2	yes	—
401	#2433	C₂×D₄	1	1	yes	characteristic
402	#2432	C₂×D₄	1	1	yes	characteristic
403	#2432	C₂×D₄	1	1	yes	characteristic
404	#2431	C₂×D₄	1	1	yes	characteristic
405	#2431	C₂×D₄	1	2	yes	—
406	#2431	C₂×D₄	1	2	yes	—
407	#2431	C₂×D₄	1	1	yes	characteristic
408	#2406	C₂×D₄	1	1	yes	characteristic
409	#2406	C₂×D₄	1	1	yes	characteristic
410	#2405	C₂×D₄	1	1	yes	characteristic
411	#2405	C₂×D₄	1	1	yes	characteristic
412	#2404	C₂×D₄	1	2	yes	—
413	#2404	C₂×D₄	1	1	yes	characteristic
414	#2404	C₂×D₄	1	1	yes	characteristic
415	#2404	C₂×D₄	1	2	yes	—
416	#2403	C₂×D₄	1	2	yes	—
417	#2403	C₂×D₄	1	2	yes	—
418	#2403	C₂×D₄	1	1	yes	characteristic
419	#2403	C₂×D₄	1	1	yes	characteristic
420	#2380	C₂×D₄	1	2	yes	complemented
421	#2379	C₂×D₄	1	2	yes	complemented
422	#2376	C₂×D₄	1	2	yes	—
423	#2374	C₂×D₄	1	1	yes	characteristic
424	#2374	C₂×D₄	1	1	yes	characteristic
425	#2372	C₂×D₄	1	2	yes	complemented
426	#2366	C₂×D₄	1	2	yes	complemented
427	#2358	C₂×D₄	1	1	yes	characteristic
428	#2358	C₂×D₄	1	2	yes	—
429	#2358	C₂×D₄	1	1	yes	characteristic
430	#2311	C₂×D₄	1	1	yes	characteristic
431	#2311	C₂×D₄	1	1	yes	characteristic
432	#2311	C₂×D₄	1	1	yes	characteristic, complemented
433	#2311	C₂×D₄	1	1	yes	characteristic, complemented
434	#2311	C₂⁴	1	1	yes	characteristic
435	#2311	C₂⁴	1	1	yes	characteristic
436	#2309	C₂×D₄	1	1	yes	characteristic, complemented
437	#2309	C₂×D₄	1	1	yes	characteristic, complemented
438	#2309	C₂×D₄	1	1	yes	characteristic, complemented
439	#2309	C₂×D₄	1	1	yes	characteristic, complemented
440	#2297	C₂×D₄	1	1	yes	characteristic
441	#2297	C₂×D₄	1	1	yes	characteristic
442	#2297	C₂×D₄	1	1	yes	characteristic, complemented
443	#2297	C₂×D₄	1	1	yes	characteristic, complemented
444	#2297	C₂×D₄	1	1	yes	characteristic, complemented
445	#2297	C₂×D₄	1	1	yes	characteristic, complemented
446	#2297	C₂⁴	1	1	yes	characteristic
447	#2297	C₂⁴	1	1	yes	characteristic
448	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
449	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
450	#2280	C₂×D₄	1	1	yes	characteristic
451	#2280	C₂×D₄	1	1	yes	characteristic
452	#2280	C₂×D₄	1	1	yes	characteristic
453	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
454	#1910	C₂×D₄	1	8	yes	complemented
455	#1891	C₂×D₄	1	8	yes	complemented
456	#1795	C₂×D₄	1	8	yes	complemented
457	C₂⁶	#120	1	1	yes	characteristic
458	#585	C₂²×D₄	1	4	yes	complemented
459	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
460	C₂×H(5,𝔽₂)	H(5,𝔽₂)	1	4	yes	—
461	C₂²×#41	#120	1	1	yes	characteristic
462	C₂²×#41	#120	1	1	yes	characteristic
463	C₂²×#41	#120	1	1	yes	characteristic
464	C₂²×#41	#120	1	1	yes	characteristic
465	C₂²×#41	#120	1	1	yes	characteristic
466	C₂²×#41	#120	1	1	yes	characteristic
467	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
468	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
469	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
470	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
471	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
472	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
473	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
474	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
475	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
476	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
477	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
478	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
479	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
480	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
481	C₂²×#41	C₂⁵	1	1	yes	characteristic
482	C₂³×Q₈	#120	1	1	yes	characteristic
483	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
484	C₂³×D₄	#120	1	1	yes	characteristic
485	C₂³×D₄	#120	1	1	yes	characteristic
486	C₂³×D₄	#120	1	1	yes	characteristic
487	C₂³×D₄	#120	1	1	yes	characteristic
488	C₂³×D₄	#120	1	1	yes	characteristic
489	C₂³×D₄	#120	1	2	yes	—
490	C₂³×D₄	#120	1	2	yes	—
491	C₂³×D₄	#120	1	1	yes	characteristic
492	C₂³×D₄	#120	1	1	yes	characteristic
493	C₂³×D₄	#120	1	2	yes	—
494	C₂³×D₄	#120	1	1	yes	characteristic
495	C₂³×D₄	#120	1	1	yes	characteristic
496	C₂³×D₄	#120	1	1	yes	characteristic
497	C₂³×D₄	#120	1	4	yes	complemented
498	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
499	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
500	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
501	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
502	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
503	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
504	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
505	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
506	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
507	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
508	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
509	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
510	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
511	C₂⁴×C₄	#120	1	1	yes	characteristic
512	C₂⁴×C₄	#120	1	1	yes	characteristic
513	C₂⁴×C₄	#120	1	1	yes	characteristic
514	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
515	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
516	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
517	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
518	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
519	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
520	#568	C₂²×D₄	1	4	yes	complemented
521	#535	#120	1	4	yes	complemented
522	#535	C₂²×D₄	1	4	yes	—
523	#535	H(5,𝔽₂)	1	4	yes	—
524	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
525	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
526	C₂×#127	#120	1	2	yes	—
527	C₂×#127	#120	1	2	yes	—
528	C₂×#127	#120	1	2	yes	—
529	C₂×#127	#120	1	1	yes	characteristic
530	C₂×#127	C₂²×D₄	1	1	yes	characteristic
531	C₂×#127	C₂²×D₄	1	2	yes	—
532	C₂×#127	C₂²×D₄	1	2	yes	—
533	C₂×#127	C₂²×D₄	1	2	yes	—
534	C₂×#124	#120	1	2	yes	—
535	C₂×#124	#120	1	2	yes	—
536	C₂×#124	#120	1	1	yes	characteristic
537	C₂×#124	#120	1	1	yes	characteristic
538	C₂×#124	#120	1	2	yes	—
539	C₂×#124	C₂²×D₄	1	2	yes	—
540	C₂×#124	C₂²×D₄	1	1	yes	characteristic
541	C₂×#124	C₂²×D₄	1	2	yes	—
542	C₂×#124	C₂²×D₄	1	1	yes	characteristic
543	C₂×#124	C₂²×D₄	1	2	yes	—
544	#525	#120	1	4	yes	complemented
545	#525	C₂²×D₄	1	4	yes	—
546	#525	H(5,𝔽₂)	1	4	yes	—
547	C₂×#123	#120	1	1	yes	characteristic
548	C₂×#123	#120	1	1	yes	characteristic
549	C₂×#123	#120	1	1	yes	characteristic
550	C₂×#123	#120	1	1	yes	characteristic
551	C₂×#123	#120	1	1	yes	characteristic
552	C₂×#123	#120	1	1	yes	characteristic
553	C₂×#123	C₂²×D₄	1	1	yes	characteristic
554	C₂×#123	C₂²×D₄	1	1	yes	characteristic
555	C₂×#123	C₂²×D₄	1	1	yes	characteristic
556	C₂×#123	C₂²×D₄	1	1	yes	characteristic
557	C₂×#123	C₂²×D₄	1	1	yes	characteristic
558	C₂×#123	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₂²⋊Q₈	#120	1	1	yes	characteristic
560	C₂×C₂²⋊Q₈	#120	1	1	yes	characteristic
561	C₂×#121	#120	1	2	yes	—
562	C₂×#121	#120	1	2	yes	—
563	C₂×#121	#120	1	1	yes	characteristic
564	C₂×#121	#120	1	1	yes	characteristic
565	C₂×#120	#120	1	1	yes	characteristic
566	C₂×#120	#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	2	yes	—
571	C₂×#120	#120	1	1	yes	characteristic
572	C₂×#120	#120	1	2	yes	—
573	C₂×#120	C₂²×D₄	1	1	yes	characteristic
574	C₂×#120	C₂²×D₄	1	1	yes	characteristic
575	C₂×#120	C₂²×D₄	1	2	yes	—
576	C₂×#120	C₂²×D₄	1	2	yes	—
577	C₂×#120	C₂²×D₄	1	1	yes	characteristic
578	C₂×#120	C₂²×D₄	1	1	yes	characteristic
579	C₂×#120	C₂²×D₄	1	1	yes	characteristic
580	C₂×#120	C₂²×D₄	1	1	yes	characteristic
581	#518	#120	1	4	yes	complemented
582	C₂×#117	#120	1	1	yes	characteristic
583	C₂×#117	#120	1	1	yes	characteristic
584	C₂×#117	#120	1	2	yes	—
585	C₂×#117	C₂²×D₄	1	1	yes	characteristic
586	C₂×#117	C₂²×D₄	1	1	yes	characteristic
587	C₂×#117	C₂²×D₄	1	1	yes	characteristic
588	C₂×#117	C₂²×D₄	1	1	yes	characteristic
589	C₂×#117	C₂²×D₄	1	1	yes	characteristic
590	C₂×#117	C₂²×D₄	1	1	yes	characteristic
591	C₂×#117	C₂²×D₄	1	1	yes	characteristic
592	C₂×#117	C₂²×D₄	1	1	yes	characteristic
593	C₂×#117	C₂²×D₄	1	1	yes	characteristic
594	C₂×#117	C₂²×D₄	1	1	yes	characteristic
595	C₂×#117	C₂²×D₄	1	1	yes	characteristic
596	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
597	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
598	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
599	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
600	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
601	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
602	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
603	C₂²×C₂²⋊C₄	#120	1	2	yes	—
604	C₂²×C₄²	#120	1	2	yes	—
605	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
606	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
607	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
608	#413	C₂²×D₄	1	4	yes	complemented
609	#410	C₂²×D₄	1	4	yes	complemented
610	#391	#120	1	1	yes	characteristic
611	#391	#120	1	2	yes	—
612	#391	#120	1	1	yes	characteristic
613	#391	C₂²×D₄	1	1	yes	characteristic
614	#391	C₂²×D₄	1	2	yes	—
615	#391	C₂²×D₄	1	1	yes	characteristic
616	#390	#120	1	1	yes	characteristic
617	#390	#120	1	2	yes	—
618	#390	#120	1	1	yes	characteristic
619	#390	C₂²×D₄	1	1	yes	characteristic
620	#390	C₂²×D₄	1	2	yes	—
621	#390	C₂²×D₄	1	1	yes	characteristic
622	#386	#120	1	1	yes	characteristic
623	#386	#120	1	1	yes	characteristic
624	#386	#120	1	2	yes	—
625	#386	#120	1	2	yes	—
626	#386	#120	1	1	yes	characteristic
627	#386	#120	1	1	yes	characteristic
628	#386	C₂²×D₄	1	1	yes	characteristic
629	#386	C₂²×D₄	1	1	yes	characteristic
630	#386	C₂²×D₄	1	2	yes	—
631	#386	C₂²×D₄	1	2	yes	—
632	#386	C₂²×D₄	1	1	yes	characteristic
633	#386	C₂²×D₄	1	1	yes	characteristic
634	#381	#120	1	1	yes	characteristic
635	#381	#120	1	1	yes	characteristic
636	#381	#120	1	2	yes	—
637	#379	#120	1	2	yes	—
638	#379	#120	1	1	yes	characteristic
639	#379	#120	1	1	yes	characteristic
640	C₄×C₂²⋊C₄	#120	1	2	yes	—
641	C₄×C₂²⋊C₄	#120	1	2	yes	—
642	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic
643	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic
644	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic
645	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic
646	C₂⁵	C₂×#120	1	1	yes	characteristic
647	C₂⁵	C₂×#120	1	1	yes	characteristic
648	C₂⁵	C₂×#120	1	1	yes	characteristic
649	C₂⁵	C₂×#120	1	1	yes	characteristic
650	C₂⁵	C₂×#120	1	1	yes	characteristic
651	C₂⁵	C₂×#120	1	2	yes	—
652	C₂⁵	C₂×#120	1	1	yes	characteristic
653	C₂×#41	C₂×#120	1	2	yes	—
654	C₂×#41	#534	1	2	yes	—
655	C₂×#41	D₄²	1	4	yes	—
656	C₂×#41	D₄²	1	4	yes	—
657	C₂×#41	C₂³×D₄	1	2	yes	—
658	C₂×#41	C₂×H(5,𝔽₂)	1	2	yes	—
659	C₂×#41	C₂×H(5,𝔽₂)	1	2	yes	—
660	C₂×#41	C₂×H(5,𝔽₂)	1	2	yes	—
661	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
662	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
663	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
664	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
665	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
666	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
667	C₂²×Q₈	C₂³×D₄	1	1	yes	characteristic
668	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
669	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
670	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
671	C₂²×D₄	C₂×#120	1	1	yes	characteristic
672	C₂²×D₄	C₂×#120	1	1	yes	characteristic
673	C₂²×D₄	C₂×#120	1	1	yes	characteristic
674	C₂²×D₄	C₂×#120	1	1	yes	characteristic
675	C₂²×D₄	C₂×#120	1	1	yes	characteristic
676	C₂²×D₄	C₂×#120	1	1	yes	characteristic
677	C₂²×D₄	C₂×#120	1	1	yes	characteristic
678	C₂²×D₄	C₂×#120	1	1	yes	characteristic
679	C₂²×D₄	C₂×#120	1	1	yes	characteristic
680	C₂²×D₄	C₂×#120	1	1	yes	characteristic
681	C₂²×D₄	C₂×#120	1	1	yes	characteristic
682	C₂²×D₄	C₂×#120	1	1	yes	characteristic
683	C₂²×D₄	C₂×#120	1	1	yes	characteristic
684	C₂²×D₄	C₂×#120	1	2	yes	—
685	C₂²×D₄	C₂×#120	1	1	yes	characteristic
686	C₂²×D₄	C₂×#120	1	1	yes	characteristic
687	C₂²×D₄	C₂×#120	1	2	yes	—
688	C₂²×D₄	C₂×#120	1	2	yes	—
689	C₂²×D₄	C₂×#120	1	1	yes	characteristic
690	C₂²×D₄	C₂×#120	1	2	yes	—
691	C₂²×D₄	C₂×#120	1	2	yes	—
692	C₂²×D₄	#534	1	2	yes	—
693	C₂²×D₄	#534	1	2	yes	—
694	C₂²×D₄	D₄²	1	4	yes	—
695	C₂²×D₄	D₄²	1	4	yes	—
696	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
697	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
698	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
699	C₂³×C₄	C₂×#120	1	1	yes	characteristic
700	C₂³×C₄	C₂×#120	1	1	yes	characteristic
701	C₂³×C₄	C₂×#120	1	1	yes	characteristic
702	C₂³×C₄	C₂×#120	1	1	yes	characteristic
703	C₂³×C₄	C₂×#120	1	1	yes	characteristic
704	C₂³×C₄	C₂×#120	1	1	yes	characteristic
705	C₂³×C₄	C₂×#120	1	1	yes	characteristic
706	C₂³×C₄	C₂×#120	1	1	yes	characteristic
707	C₂³×C₄	C₂×#120	1	1	yes	characteristic
708	C₂³×C₄	C₂×#120	1	1	yes	characteristic
709	C₂³×C₄	C₂×#120	1	1	yes	characteristic
710	C₂³×C₄	C₂×#120	1	1	yes	characteristic
711	C₂³×C₄	C₂×#120	1	1	yes	characteristic
712	C₂³×C₄	C₂×#120	1	1	yes	characteristic
713	C₂³×C₄	C₂×#120	1	1	yes	characteristic
714	C₂³×C₄	C₂×#120	1	2	yes	—
715	C₂³×C₄	C₂×#120	1	1	yes	characteristic
716	C₂³×C₄	C₂×#120	1	2	yes	—
717	C₂³×C₄	C₂×#120	1	1	yes	characteristic
718	C₂³×C₄	C₂×#120	1	1	yes	characteristic
719	C₂³×C₄	#534	1	2	yes	—
720	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
721	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
722	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
723	#127	D₄²	1	8	yes	—
724	#124	D₄²	1	8	yes	—
725	#123	D₄²	1	4	yes	—
726	#123	D₄²	1	4	yes	—
727	#120	D₄²	1	4	yes	—
728	#120	D₄²	1	4	yes	—
729	#117	C₂×#120	1	2	yes	—
730	#117	C₂×#120	1	2	yes	—
731	#117	#534	1	2	yes	—
732	#117	#534	1	2	yes	—
733	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
735	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
736	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
737	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
738	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
739	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
740	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
742	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
743	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
744	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
745	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
746	C₂×C₄²	C₂×#120	1	1	yes	characteristic
747	C₂×C₄²	C₂×#120	1	2	yes	—
748	C₂×C₄²	C₂×#120	1	2	yes	—
749	C₂×C₄²	C₂×#120	1	1	yes	characteristic
750	C₂×C₄²	C₂×#120	1	2	yes	—
751	C₂×C₄²	C₂×#120	1	1	yes	characteristic
752	C₂×C₄²	C₂×#120	1	2	yes	—
753	C₂×C₄²	C₂×#120	1	1	yes	characteristic
754	C₂⁴	#2403	1	2	yes	—
755	C₂⁴	#2846	1	1	yes	characteristic
756	C₂⁴	#2846	1	1	yes	characteristic
757	C₂⁴	#2846	1	1	yes	characteristic
758	C₂⁴	#2846	1	1	yes	characteristic
759	C₂⁴	C₂²×#120	1	1	yes	characteristic
760	C₂⁴	C₂²×#120	1	1	yes	characteristic
761	C₂⁴	C₂²×#120	1	1	yes	characteristic
762	C₂×Q₈	#2403	1	2	yes	—
763	C₂×Q₈	C₂×D₄²	1	2	yes	—
764	C₂×Q₈	#3484	1	2	yes	—
765	C₂×D₄	#2403	1	2	yes	—
766	C₂×D₄	#2403	1	2	yes	—
767	C₂×D₄	#2403	1	2	yes	—
768	C₂×D₄	#2403	1	4	yes	—
769	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
770	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
771	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
772	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
773	C₂×D₄	C₂×D₄²	1	2	yes	—
774	C₂×D₄	C₂×D₄²	1	2	yes	—
775	C₂×D₄	C₂×D₄²	1	2	yes	—
776	C₂×D₄	#3484	1	2	yes	—
777	C₂×D₄	#3484	1	2	yes	—
778	C₂×D₄	#3484	1	2	yes	—
779	C₂²×C₄	#2403	1	2	yes	—
780	C₂²×C₄	#2846	1	1	yes	characteristic
781	C₂²×C₄	#2846	1	1	yes	characteristic
782	C₂²×C₄	#2846	1	1	yes	characteristic
783	C₂²×C₄	#2846	1	1	yes	characteristic
784	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
785	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
786	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
787	C₂²×C₄	#3026	1	1	yes	characteristic
788	C₂²×C₄	#3026	1	1	yes	characteristic
789	C₂²×C₄	#3026	1	2	yes	—
790	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
791	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
792	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
793	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
794	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
795	C₂²×C₄	C₂×#534	1	1	yes	characteristic
796	C₂²×C₄	C₂×#534	1	1	yes	characteristic
797	C₂²×C₄	C₂×#534	1	1	yes	characteristic
798	C₂²×C₄	C₂×D₄²	1	2	yes	—
799	C₂²×C₄	C₂×D₄²	1	2	yes	—
800	C₂²×C₄	#3484	1	2	yes	—
801	C₂²×C₄	#3484	1	2	yes	—
802	C₂²⋊C₄	#2403	1	2	yes	—
803	C₂²⋊C₄	#2403	1	2	yes	—
804	C₄²	#2403	1	4	yes	—
805	C₂³	#32898	1	1	yes	characteristic
806	C₂³	#32898	1	1	yes	characteristic
807	C₂³	#32898	1	2	yes	—
808	C₂³	C₂×#2403	1	1	yes	characteristic
809	C₂³	#34980	1	1	yes	characteristic
810	C₂³	D₄×#120	1	2	yes	—
811	C₂³	D₄×#120	1	2	yes	—
812	C₂³	C₂×#2846	1	1	yes	characteristic
813	D₄	#23900	1	4	yes	—
814	C₂×C₄	#32898	1	2	yes	—
815	C₂×C₄	#32898	1	1	yes	characteristic
816	C₂×C₄	#32898	1	1	yes	characteristic
817	C₂×C₄	C₂×#2403	1	1	yes	characteristic
818	C₂×C₄	C₂×#2403	1	1	yes	characteristic
819	C₂×C₄	#34980	1	1	yes	characteristic
820	C₂×C₄	#34980	1	1	yes	characteristic
821	C₂×C₄	D₄×#120	1	2	yes	—
822	C₂×C₄	D₄×#120	1	2	yes	—
823	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
824	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
825	C₂×C₄	C₂×#3026	1	1	yes	characteristic
826	C₂×C₄	C₂×#3026	1	1	yes	characteristic
827	C₂²	#511819	1	2	yes	complemented
828	C₂²	#612424	1	1	yes	characteristic
829	C₂²	C₂×#32898	1	1	yes	characteristic
830	C₂²	C₂×#32898	1	1	yes	characteristic
831	C₄	C₂×#23900	1	1	yes	characteristic
832	C₄	#6437621	1	1	yes	characteristic
833	C₄	#6470225	1	1	yes	characteristic
834	C₄	#6470225	1	1	yes	characteristic
835	C₂	#72214832	1	1	yes	characteristic
836	C₂	C₂×#511819	1	1	yes	characteristic
837	C₂	#72234211	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#32898
commutator, Frattini, cosocle	C₂²×#41	C₂⁵
LCS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72251987	C₂	semidirect
2. #72251986	C₂	semidirect
3. #72251883	C₂	semidirect
4. #72251874	C₂	semidirect
5. #72251839	C₂	semidirect
6. #72251717	C₂	semidirect
7. #72238623	C₂	semidirect
8. #72238620	C₂	semidirect
9. #72238411	C₂	semidirect
10. #72238397	C₂	semidirect
11. #72234794	C₂	semidirect
12. #72234768	C₂	semidirect
13. C₂²×#23882	C₂	semidirect
14. #72232031	C₂	semidirect
15. #72231758	C₂	semidirect
16. #72231756	C₂	semidirect
17. C₂×#511819	C₂	semidirect
18. #72219502	C₂	semidirect
19. #72219483	C₂	semidirect
20. #72215601	C₂	semidirect
21. #72214896	C₂	semidirect
22. #72214565	C₂	semidirect
23. #72214353	C₂	semidirect
24. C₂²×#3585	C₂²	semidirect
25. C₂×#63011	C₂²	semidirect
27. C₂²×#3025	C₂²	semidirect
28. C₂²×#3021	C₂²	semidirect
29. #7837030	C₂²	semidirect
30. #7837029	C₂²	semidirect
33. #7737956	C₂²	semidirect
34. #7737955	C₂²	semidirect
37. #7659307	C₂²	semidirect
38. #7659296	C₂²	semidirect
41. #7627266	C₂²	semidirect
42. C₂×#33570	C₂²	semidirect
43. C₂×#33553	C₂²	semidirect
44. C₂×#33553	C₂²	semidirect
45. C₂×#33546	C₂²	semidirect
46. #6628894	C₂²	semidirect
47. #6628891	C₂²	semidirect
48. #6628870	C₂²	semidirect
49. #6628866	C₂²	semidirect
50. C₂×#23872	C₂²	semidirect
52. C₂×#23882	C₂²	semidirect
53. C₂×#23882	C₂²	semidirect
54. C₂×#23882	C₂²	semidirect
55. C₂×#23882	C₂²	semidirect
56. C₂²×#1910	C₂²	semidirect
57. C₂²×#1891	C₂²	semidirect
58. C₂²×#1795	C₂²	semidirect
59. #498932	C₂²	semidirect
60. #498929	C₂²	semidirect
61. #498929	C₂²	semidirect
62. #498922	C₂²	semidirect
63. #498909	C₂²	semidirect
64. #498906	C₂²	semidirect
65. #498888	C₂²	semidirect
66. #498885	C₂²	semidirect
67. #494733	C₂²	semidirect
68. #494730	C₂²	semidirect
69. #494715	C₂²	semidirect
70. #494712	C₂²	semidirect
71. #494698	C₂²	semidirect
72. #494694	C₂²	semidirect
73. #494680	C₂²	semidirect
74. #494676	C₂²	semidirect
75. #494622	C₂²	semidirect
76. #494601	C₂²	semidirect
77. #494577	C₂²	semidirect
78. #494571	C₂²	semidirect
79. C₂×#12778	C₂²	semidirect
80. C₂×#12765	C₂²	semidirect
81. C₂×#12755	C₂²	semidirect
82. C₂×#12755	C₂²	semidirect
83. C₂×#12718	C₂²	semidirect
84. C₂×#12711	C₂²	semidirect
85. C₂×#12711	C₂²	semidirect
86. C₂×#12711	C₂²	semidirect
87. C₂×#12711	C₂²	semidirect
88. C₂×#12711	C₂²	semidirect
89. #493385	C₂²	semidirect
90. #493372	C₂²	semidirect
91. #493352	C₂²	semidirect
92. #493352	C₂²	semidirect
93. #394080	C₂²	semidirect
94. #394076	C₂²	semidirect
95. #394022	C₂²	semidirect
96. #394020	C₂²	semidirect
97. #392701	C₂²	semidirect
98. #392695	C₂²	semidirect
99. #392662	C₂²	semidirect
100. #392646	C₂²	semidirect
101. #392132	C₂²	semidirect
102. #392132	C₂²	semidirect
103. #359576	C₂²	semidirect
104. #359573	C₂²	semidirect
105. #147833	C₂²	semidirect
106. #147828	C₂²	semidirect
107. #147820	C₂²	semidirect
108. #147817	C₂²	semidirect
109. #147813	C₂²	semidirect
110. #147813	C₂²	semidirect
111. #147787	C₂²	semidirect
112. #147782	C₂²	semidirect
113. #147582	C₂²	semidirect
114. #147577	C₂²	semidirect
115. #147576	C₂²	semidirect
116. #147573	C₂²	semidirect
117. #146656	C₂²	semidirect
118. #146651	C₂²	semidirect
119. #146605	C₂²	semidirect
120. #146596	C₂²	semidirect
121. #146488	C₂²	semidirect
122. #146484	C₂²	semidirect
123. C₂²×#585	C₂³	semidirect
125. C₂⁵×D₄	D₄	semidirect
127. C₂×#3585	C₂³	semidirect
128. C₂²×#568	C₂³	semidirect
129. C₂×#3498	D₄	semidirect
131. C₂×#3488	D₄	semidirect
132. C₂×#3484	D₄	semidirect
133. C₂×#3484	D₄	semidirect
134. C₂×#3484	D₄	semidirect
135. C₂×#3484	D₄	semidirect
136. C₂×#3484	D₄	semidirect
146. C₂²×D₄²	D₄	semidirect
147. C₂²×#535	D₄	semidirect
149. C₂²×#525	D₄	semidirect
151. C₂²×#518	D₄	semidirect
152. C₂×#3027	C₂³	semidirect
154. C₂×#3025	C₂³	semidirect
155. C₂×#3025	C₂³	semidirect
157. C₂×#3021	C₂³	semidirect
158. C₂×#3021	C₂³	semidirect
159. C₂×#3018	C₂³	semidirect
160. C₂²×#413	C₂³	semidirect
161. C₂²×#410	C₂³	semidirect
162. #59191	D₄	semidirect
163. #59189	D₄	semidirect
164. #59179	D₄	semidirect
165. #59173	D₄	semidirect
166. #59160	D₄	semidirect
167. #59126	D₄	semidirect
168. #59107	D₄	semidirect
169. #59089	D₄	semidirect
170. #59089	D₄	semidirect
171. #59006	D₄	semidirect
172. #58990	D₄	semidirect
173. #58990	D₄	semidirect
176. #52013	D₄	semidirect
177. #52004	D₄	semidirect
178. #51902	D₄	semidirect
179. #51896	D₄	semidirect
180. #46324	D₄	semidirect
181. #45977	D₄	semidirect
182. #45455	D₄	semidirect
183. #45452	D₄	semidirect
190. #35527	D₄	semidirect
191. #35527	D₄	semidirect
194. #35513	D₄	semidirect
196. #35512	D₄	semidirect
198. #35250	D₄	semidirect
201. #35222	D₄	semidirect
203. #34736	D₄	semidirect
205. C₂×#2433	D₄	semidirect
209. #34258	D₄	semidirect
211. #34256	D₄	semidirect
213. #34171	D₄	semidirect
215. C₂²⋊C₄×#41	D₄	semidirect
217. C₂×#2134	C₂³	semidirect
218. C₂×#2134	C₂³	semidirect
219. C₂×#2132	C₂³	semidirect
221. C₂×#2128	C₂³	semidirect
222. C₂×#2128	C₂³	semidirect
223. C₂×#2126	C₂³	semidirect
224. C₂×#2122	C₂³	semidirect
225. C₂×#2122	C₂³	semidirect
228. C₂×#2120	C₂³	semidirect
229. C₂×#2120	C₂³	semidirect
230. C₂×#2120	C₂³	semidirect
231. C₂×#2120	C₂³	semidirect
232. #23882	D₄	semidirect
233. C₂×#1914	C₂³	semidirect
235. C₂×#1910	C₂³	semidirect
236. C₂×#1910	C₂³	semidirect
238. C₂×#1891	C₂³	semidirect
239. C₂×#1891	C₂³	semidirect
240. C₂×#1884	C₂³	semidirect
244. C₂×#1795	C₂³	semidirect
245. C₂×#1795	C₂³	semidirect
246. C₂×#1795	C₂³	semidirect
247. #20618	C₂³	semidirect
248. #20615	C₂³	semidirect
249. #20610	C₂³	semidirect
250. #20608	C₂³	semidirect
251. #20591	C₂³	semidirect
252. #20591	C₂³	semidirect
253. #20584	C₂³	semidirect
254. #20584	C₂³	semidirect
255. #12587	C₂³	semidirect
256. #12585	C₂³	semidirect
257. #12583	C₂³	semidirect
258. #12581	C₂³	semidirect
259. #12575	C₂³	semidirect
260. #12575	C₂³	semidirect
261. #12573	C₂³	semidirect
262. #12573	C₂³	semidirect
263. #10755	C₂³	semidirect
264. #10751	C₂³	semidirect
265. #10746	C₂³	semidirect
266. #10742	C₂³	semidirect
274. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
289. C₂⁴×D₄	C₂×D₄	semidirect
291. #3585	C₂×D₄	semidirect
293. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
295. C₂×#560	C₂×D₄	semidirect
298. C₂×#555	C₂×D₄	semidirect
303. C₂×D₄²	C₂×D₄	semidirect
304. C₂×#537	C₂×D₄	semidirect
315. C₂×#535	C₂×D₄	semidirect
316. C₂×#535	C₂×D₄	semidirect
317. C₂×#535	C₂×D₄	semidirect
318. C₂×#535	C₂×D₄	semidirect
319. C₂×#535	C₂×D₄	semidirect
327. C₂²×#127	C₂×D₄	semidirect
328. C₂²×#127	C₂×D₄	semidirect
329. C₂²×#127	C₂×D₄	semidirect
343. C₂×#525	C₂×D₄	semidirect
344. C₂×#525	C₂×D₄	semidirect
352. C₂²×#121	C₂×D₄	semidirect
355. C₂×#520	C₂×D₄	semidirect
360. C₂×#518	C₂×D₄	semidirect
361. C₂×#518	C₂×D₄	semidirect
362. C₂×C₄×#41	C₂×D₄	semidirect
363. C₂×C₄×#41	C₂×D₄	semidirect
365. C₂²×C₄×D₄	C₂×D₄	semidirect
368. #3025	C₂×D₄	semidirect
369. #3021	C₂×D₄	semidirect
376. #2733	C₂×D₄	semidirect
377. #2733	C₂×D₄	semidirect
378. #2733	C₂×D₄	semidirect
379. #2731	C₂×D₄	semidirect
384. #2709	C₂×D₄	semidirect
393. #2669	C₂×D₄	semidirect
394. #2669	C₂×D₄	semidirect
395. #2669	C₂×D₄	semidirect
420. #2380	C₂×D₄	semidirect
421. #2379	C₂×D₄	semidirect
425. #2372	C₂×D₄	semidirect
426. #2366	C₂×D₄	semidirect
432. #2311	C₂×D₄	semidirect
433. #2311	C₂×D₄	semidirect
436. #2309	C₂×D₄	semidirect
437. #2309	C₂×D₄	semidirect
438. #2309	C₂×D₄	semidirect
439. #2309	C₂×D₄	semidirect
442. #2297	C₂×D₄	semidirect
443. #2297	C₂×D₄	semidirect
444. #2297	C₂×D₄	semidirect
445. #2297	C₂×D₄	semidirect
448. C₂×#390	C₂×D₄	semidirect
449. C₂×#390	C₂×D₄	semidirect
454. #1910	C₂×D₄	semidirect
455. #1891	C₂×D₄	semidirect
456. #1795	C₂×D₄	semidirect
458. #585	C₂²×D₄	semidirect
497. C₂³×D₄	#120	semidirect
520. #568	C₂²×D₄	semidirect
521. #535	#120	semidirect
544. #525	#120	semidirect
581. #518	#120	semidirect
608. #413	C₂²×D₄	semidirect
609. #410	C₂²×D₄	semidirect
827. C₂²	#511819	semidirect

Maximal subgroups

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

subgroup	index
#72251987	2
#72251986	2
#72251883	2
#72251874	2
#72251839	2
#72251717	2
#72238623	2
#72238620	2
#72238411	2
#72238397	2
#72234794	2
#72234768	2
C₂²×#23882	2
#72232031	2
#72231758	2
#72231756	2
C₂×#511819	2
#72219502	2
#72219483	2
#72215601	2
#72214896	2
#72214565	2
#72214353	2