Subgroups — #72302913

Order 2048.

At least 8844 conjugacy classes of subgroups; only the 8268 normal subgroups are shown.

The subgroup lattice has 903 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72302895	C₂	1	1	yes	maximal, characteristic, complemented
2	#72302893	C₂	1	4	yes	maximal, complemented
3	#72302890	C₂	1	4	yes	maximal, complemented
4	#72302888	C₂	1	4	yes	maximal, complemented
5	#72302882	C₂	1	8	yes	maximal, complemented
6	#72302358	C₂	1	2	yes	maximal, complemented
7	#72302333	C₂	1	2	yes	maximal, complemented
8	#72302285	C₂	1	4	yes	maximal, complemented
9	#72280406	C₂	1	2	yes	maximal, complemented
10	C₂²×#62811	C₂	1	1	yes	maximal, characteristic, complemented
11	#72259172	C₂	1	1	yes	maximal, characteristic, complemented
12	#72258211	C₂	1	2	yes	maximal, complemented
13	#72255937	C₂	1	8	yes	maximal, complemented
14	#72249727	C₂	1	8	yes	maximal, complemented
15	C₂×#6437463	C₂	1	4	yes	maximal, complemented
16	C₂×#393988	C₂	1	4	yes	maximal, complemented
17	#72210511	C₂	1	4	yes	maximal, complemented
18	C₂³×#585	C₂²	1	1	yes	characteristic, complemented
19	C₂⁵×#41	C₂²	1	1	yes	characteristic
20	C₂×#62811	C₂²	1	4	yes	—
21	C₂×#62811	C₂²	1	4	yes	complemented
22	C₂×#62811	C₂²	1	4	yes	complemented
23	C₂×#62811	C₂²	1	4	yes	complemented
24	C₂×#62811	C₂²	1	1	yes	characteristic, complemented
25	C₂×#62811	C₂²	1	2	yes	complemented
26	C₂²×#3487	C₂²	1	2	yes	complemented
27	C₂²×#3486	C₂²	1	2	yes	complemented
28	C₂²×#3485	C₂²	1	2	yes	complemented
29	C₂²×#3484	C₂²	1	2	yes	complemented
30	C₂²×#3449	C₂²	1	2	yes	—
31	C₂³×#525	C₂²	1	2	yes	complemented
32	C₂²×#3428	C₂²	1	1	yes	characteristic, complemented
33	C₂×#60387	C₂²	1	8	yes	complemented
34	C₂×#60387	C₂²	1	4	yes	complemented
35	C₂×#60359	C₂²	1	4	yes	complemented
36	C₂×#36614	C₂²	1	2	yes	complemented
37	#7631198	C₂²	1	2	yes	complemented
38	#7631153	C₂²	1	2	yes	complemented
39	#7631153	C₂²	1	4	yes	complemented
40	#7631032	C₂²	1	2	yes	complemented
41	#7631032	C₂²	1	4	yes	complemented
42	#7630939	C₂²	1	2	yes	complemented
43	#7628649	C₂²	1	2	yes	—
44	#7628649	C₂²	1	4	yes	complemented
45	#7625442	C₂²	1	1	yes	characteristic, complemented
46	#7625442	C₂²	1	2	yes	complemented
47	#6628869	C₂²	1	16	yes	complemented
48	#6628868	C₂²	1	8	yes	complemented
49	#6628867	C₂²	1	8	yes	complemented
50	C₂×#23899	C₂²	1	16	yes	complemented
51	C₂×#23898	C₂²	1	16	yes	complemented
52	C₂×#23898	C₂²	1	16	yes	complemented
53	C₂×#23897	C₂²	1	16	yes	complemented
54	#6437448	C₂²	1	8	yes	complemented
55	#6437447	C₂²	1	8	yes	complemented
56	#6437446	C₂²	1	8	yes	complemented
57	#6437445	C₂²	1	8	yes	complemented
58	C₂²×#2010	C₂²	1	16	yes	complemented
59	#6431722	C₂²	1	8	yes	complemented
60	C₂×#21012	C₂²	1	8	yes	complemented
61	C₂×#21012	C₂²	1	8	yes	complemented
62	C₂×#20979	C₂²	1	4	yes	complemented
63	#6371454	C₂²	1	4	yes	complemented
64	#6370746	C₂²	1	8	yes	complemented
65	C₂×#20605	C₂²	1	4	yes	complemented
66	C₂×#20591	C₂²	1	2	yes	complemented
67	C₂×#20591	C₂²	1	2	yes	complemented
68	C₂×#20591	C₂²	1	4	yes	complemented
69	C₂×#20591	C₂²	1	4	yes	complemented
70	C₂×#20579	C₂²	1	2	yes	complemented
71	#393988	C₂²	1	16	yes	complemented
72	#393988	C₂²	1	16	yes	complemented
73	#393988	C₂²	1	32	yes	complemented
74	#393978	C₂²	1	32	yes	complemented
75	#393977	C₂²	1	32	yes	complemented
76	#393976	C₂²	1	32	yes	complemented
77	#393975	C₂²	1	32	yes	complemented
78	#392698	C₂²	1	16	yes	complemented
79	#392697	C₂²	1	8	yes	complemented
80	#392696	C₂²	1	8	yes	complemented
81	#392115	C₂²	1	2	yes	complemented
82	#392115	C₂²	1	2	yes	complemented
83	#392115	C₂²	1	4	yes	complemented
84	#392115	C₂²	1	4	yes	complemented
85	#392114	C₂²	1	2	yes	complemented
86	#392113	C₂²	1	2	yes	complemented
87	#359561	C₂²	1	16	yes	complemented
88	#359560	C₂²	1	16	yes	complemented
89	#359559	C₂²	1	16	yes	complemented
90	#359558	C₂²	1	16	yes	complemented
91	#359512	C₂²	1	8	yes	complemented
92	#359511	C₂²	1	8	yes	complemented
93	#359510	C₂²	1	8	yes	complemented
94	#359509	C₂²	1	8	yes	complemented
95	C₂×#10994	C₂²	1	16	yes	complemented
96	#357478	C₂²	1	8	yes	complemented
97	#353420	C₂²	1	8	yes	complemented
98	C₂×#10716	C₂²	1	4	yes	complemented
99	C₂²×#585	C₂³	1	4	yes	—
100	C₂²×#585	C₂³	1	4	yes	—
101	C₂²×#585	C₂³	1	1	yes	characteristic, complemented
102	C₂³×2₋¹⁺⁴	C₂³	1	2	yes	—
103	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
104	C₂⁴×#41	D₄	1	2	yes	—
105	C₂⁴×#41	D₄	1	2	yes	—
106	C₂⁴×#41	D₄	1	4	yes	—
107	C₂⁴×#41	D₄	1	4	yes	—
108	C₂⁴×#41	C₂³	1	2	yes	—
109	C₂⁴×#41	C₂³	1	2	yes	—
110	C₂⁴×#41	C₂³	1	1	yes	characteristic
111	C₂⁴×#41	C₂³	1	2	yes	—
112	C₂⁴×#41	C₂³	1	1	yes	characteristic
113	C₂⁴×#41	C₂³	1	2	yes	—
114	C₂⁴×#41	C₂³	1	2	yes	—
115	C₂⁴×#41	C₂³	1	1	yes	characteristic
116	C₂⁴×#41	C₂³	1	1	yes	characteristic
117	C₂⁵×Q₈	C₂³	1	1	yes	characteristic
118	C₂⁵×D₄	D₄	1	2	yes	—
119	C₂⁵×D₄	C₂³	1	1	yes	characteristic
120	C₂⁶×C₄	D₄	1	2	yes	—
121	C₂⁶×C₄	C₂³	1	1	yes	characteristic
122	C₂²×#575	C₂³	1	8	yes	complemented
123	#62811	D₄	1	64	yes	complemented
124	C₂×#3487	C₂³	1	8	yes	—
125	C₂×#3487	C₂³	1	8	yes	—
126	C₂×#3487	C₂³	1	2	yes	complemented
127	C₂×#3487	C₂³	1	4	yes	complemented
128	C₂×#3486	C₂³	1	8	yes	—
129	C₂×#3486	C₂³	1	8	yes	—
130	C₂×#3486	C₂³	1	2	yes	—
131	C₂×#3486	C₂³	1	4	yes	complemented
132	C₂×#3485	C₂³	1	8	yes	—
133	C₂×#3485	C₂³	1	8	yes	—
134	C₂×#3485	C₂³	1	2	yes	complemented
135	C₂×#3485	C₂³	1	4	yes	complemented
136	C₂×#3484	C₂³	1	8	yes	—
137	C₂×#3484	C₂³	1	8	yes	—
138	C₂×#3484	C₂³	1	2	yes	—
139	C₂×#3484	C₂³	1	4	yes	complemented
140	C₂×#3449	D₄	1	8	yes	complemented
141	C₂×#3449	D₄	1	8	yes	complemented
142	C₂×#3449	C₂³	1	4	yes	—
143	C₂×#3449	C₂³	1	4	yes	—
144	C₂×#3449	C₂³	1	4	yes	—
145	C₂×#3449	C₂³	1	4	yes	—
146	C₂×#3449	C₂³	1	4	yes	—
147	C₂×#3449	C₂³	1	2	yes	complemented
148	C₂²×#536	D₄	1	4	yes	complemented
149	C₂²×#536	C₂³	1	4	yes	—
150	C₂²×#535	D₄	1	4	yes	complemented
151	C₂²×#535	C₂³	1	4	yes	—
152	C₂²×#532	D₄	1	8	yes	complemented
153	C₂²×#525	C₂³	1	4	yes	—
154	C₂²×#525	C₂³	1	4	yes	—
155	C₂²×#525	C₂³	1	8	yes	—
156	C₂²×#525	C₂³	1	8	yes	—
157	C₂²×#525	C₂³	1	2	yes	—
158	C₂²×#525	C₂³	1	4	yes	complemented
159	C₂×#3428	C₂³	1	4	yes	—
160	C₂×#3428	C₂³	1	4	yes	—
161	C₂×#3428	C₂³	1	1	yes	characteristic, complemented
162	C₂×#3428	C₂³	1	2	yes	complemented
163	C₂²×#519	C₂³	1	2	yes	—
164	C₂²×#518	C₂³	1	2	yes	—
165	C₂³×#117	C₂³	1	2	yes	—
166	C₂×#3020	C₂³	1	16	yes	complemented
167	C₂×#3020	C₂³	1	32	yes	complemented
168	C₂×#3019	C₂³	1	16	yes	complemented
169	C₂×#3019	C₂³	1	32	yes	complemented
170	#60359	C₂³	1	16	yes	—
171	#60359	C₂³	1	16	yes	complemented
172	C₂²×#421	C₂³	1	8	yes	complemented
173	C₂²×#421	C₂³	1	16	yes	complemented
174	C₂×#2896	C₂³	1	8	yes	complemented
175	C₂²×#413	C₂³	1	8	yes	—
176	C₂²×#413	C₂³	1	4	yes	complemented
177	C₂²×#413	C₂³	1	4	yes	complemented
178	C₂²×#407	C₂³	1	4	yes	—
179	C₂²×#407	C₂³	1	8	yes	complemented
180	#36614	C₂³	1	4	yes	—
181	#36614	C₂³	1	4	yes	—
182	#36614	C₂³	1	8	yes	complemented
183	#35305	D₄	1	8	yes	complemented
184	#35250	D₄	1	8	yes	complemented
185	#35242	C₂³	1	4	yes	—
186	#35242	C₂³	1	8	yes	complemented
187	#35222	C₂³	1	4	yes	—
188	#35222	C₂³	1	8	yes	complemented
189	#35149	C₂³	1	8	yes	—
190	#35149	C₂³	1	8	yes	complemented
191	#35149	C₂³	1	8	yes	complemented
192	#34738	D₄	1	16	yes	complemented
193	#34174	C₂³	1	2	yes	complemented
194	#34174	C₂³	1	4	yes	complemented
195	#34173	C₂³	1	2	yes	—
196	#34173	C₂³	1	4	yes	complemented
197	#34172	C₂³	1	2	yes	complemented
198	#34172	C₂³	1	4	yes	complemented
199	#34171	C₂³	1	2	yes	—
200	#34171	C₂³	1	4	yes	complemented
201	#34044	C₂³	1	4	yes	—
202	#34044	C₂³	1	2	yes	complemented
203	C₂×#2280	C₂³	1	2	yes	—
204	C₂×#2280	C₂³	1	4	yes	complemented
205	C₂×#2010	C₂³	1	64	yes	complemented
206	C₂×#2010	C₂³	1	64	yes	complemented
207	#23403	C₂³	1	32	yes	complemented
208	#23402	C₂³	1	32	yes	complemented
209	C₂×#1912	C₂³	1	32	yes	complemented
210	C₂×#1912	C₂³	1	32	yes	complemented
211	C₂×#1911	C₂³	1	32	yes	complemented
212	C₂×#1911	C₂³	1	32	yes	complemented
213	#20979	C₂³	1	16	yes	—
214	#20979	C₂³	1	16	yes	complemented
215	#20954	C₂³	1	16	yes	complemented
216	#20953	C₂³	1	16	yes	complemented
217	#20617	C₂³	1	32	yes	complemented
218	#20616	C₂³	1	32	yes	complemented
219	#20605	C₂³	1	16	yes	—
220	#20605	C₂³	1	16	yes	complemented
221	C₂×#1785	C₂³	1	8	yes	—
222	C₂×#1785	C₂³	1	4	yes	complemented
223	C₂×#1785	C₂³	1	4	yes	complemented
224	C₂×#1785	C₂³	1	8	yes	complemented
225	C₂×#1785	C₂³	1	8	yes	complemented
226	C₂×#1785	C₂³	1	8	yes	complemented
227	C₂×#1785	C₂³	1	8	yes	complemented
228	C₂×#1784	C₂³	1	4	yes	—
229	C₂×#1784	C₂³	1	4	yes	—
230	C₂×#1784	C₂³	1	8	yes	complemented
231	C₂×#1784	C₂³	1	8	yes	complemented
232	C₂×#1783	C₂³	1	4	yes	—
233	C₂×#1783	C₂³	1	4	yes	—
234	C₂×#1783	C₂³	1	8	yes	complemented
235	C₂×#1783	C₂³	1	8	yes	complemented
236	#20579	C₂³	1	4	yes	—
237	#20579	C₂³	1	4	yes	—
238	#20579	C₂³	1	8	yes	complemented
239	C₂×#1733	C₂³	1	8	yes	complemented
240	C₂²×H(3,ℤ/4)	C₂³	1	16	yes	complemented
241	#10994	C₂³	1	64	yes	complemented
242	#10994	C₂³	1	64	yes	complemented
243	#10990	C₂³	1	32	yes	complemented
244	#10989	C₂³	1	32	yes	complemented
245	#10741	C₂³	1	32	yes	complemented
246	#10740	C₂³	1	32	yes	complemented
247	#10716	C₂³	1	16	yes	—
248	#10716	C₂³	1	16	yes	complemented
249	C₂⁷	C₂×D₄	1	1	yes	characteristic
250	C₂⁷	C₂×D₄	1	2	yes	—
251	C₂×#585	C₂×D₄	1	32	yes	complemented
252	C₂²×2₋¹⁺⁴	C₂⁴	1	8	yes	—
253	C₂²×2₋¹⁺⁴	C₂⁴	1	2	yes	—
254	C₂²×H(5,𝔽₂)	C₂⁴	1	8	yes	—
255	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
256	C₂³×#41	C₂×D₄	1	8	yes	—
257	C₂³×#41	C₂×D₄	1	8	yes	—
258	C₂³×#41	C₂×D₄	1	32	yes	—
259	C₂³×#41	C₂×D₄	1	4	yes	—
260	C₂³×#41	C₂×D₄	1	4	yes	—
261	C₂³×#41	C₂×D₄	1	4	yes	—
262	C₂³×#41	C₂×D₄	1	4	yes	—
263	C₂³×#41	C₂×D₄	1	2	yes	—
264	C₂³×#41	C₂×D₄	1	2	yes	—
265	C₂³×#41	C₂×D₄	1	4	yes	—
266	C₂³×#41	C₂×D₄	1	4	yes	—
267	C₂³×#41	C₂×D₄	1	4	yes	—
268	C₂³×#41	C₂×D₄	1	4	yes	—
269	C₂³×#41	C₂×D₄	1	4	yes	—
270	C₂³×#41	C₂×D₄	1	4	yes	—
271	C₂³×#41	C₂×D₄	1	4	yes	—
272	C₂³×#41	C₂×D₄	1	4	yes	—
273	C₂³×#41	C₂×D₄	1	4	yes	—
274	C₂³×#41	C₂×D₄	1	2	yes	—
275	C₂³×#41	C₂×D₄	1	2	yes	—
276	C₂³×#41	C₂×D₄	1	4	yes	—
277	C₂³×#41	C₂×D₄	1	4	yes	complemented
278	C₂³×#41	C₂×D₄	1	4	yes	complemented
279	C₂³×#41	C₂×D₄	1	4	yes	complemented
280	C₂³×#41	C₂⁴	1	4	yes	—
281	C₂³×#41	C₂⁴	1	4	yes	—
282	C₂³×#41	C₂⁴	1	4	yes	—
283	C₂³×#41	C₂⁴	1	2	yes	—
284	C₂³×#41	C₂⁴	1	2	yes	—
285	C₂³×#41	C₂⁴	1	1	yes	characteristic
286	C₂³×#41	C₂⁴	1	2	yes	—
287	C₂³×#41	C₂⁴	1	2	yes	—
288	C₂³×#41	C₂⁴	1	2	yes	—
289	C₂³×#41	C₂⁴	1	2	yes	—
290	C₂³×#41	C₂⁴	1	1	yes	characteristic
291	C₂³×#41	C₂⁴	1	1	yes	characteristic
292	C₂³×#41	C₂⁴	1	1	yes	characteristic
293	C₂³×#41	C₂⁴	1	2	yes	—
294	C₂⁴×Q₈	C₂×D₄	1	4	yes	—
295	C₂⁴×Q₈	C₂×D₄	1	2	yes	—
296	C₂⁴×Q₈	C₂×D₄	1	2	yes	complemented
297	C₂⁴×Q₈	C₂⁴	1	1	yes	characteristic
298	C₂⁴×Q₈	C₂⁴	1	2	yes	—
299	C₂⁴×Q₈	C₂⁴	1	2	yes	—
300	C₂⁴×Q₈	C₂⁴	1	1	yes	characteristic
301	C₂⁴×D₄	C₂×D₄	1	2	yes	—
302	C₂⁴×D₄	C₂×D₄	1	4	yes	—
303	C₂⁴×D₄	C₂×D₄	1	4	yes	—
304	C₂⁴×D₄	C₂×D₄	1	4	yes	—
305	C₂⁴×D₄	C₂×D₄	1	4	yes	—
306	C₂⁴×D₄	C₂×D₄	1	2	yes	—
307	C₂⁴×D₄	C₂×D₄	1	2	yes	—
308	C₂⁴×D₄	C₂×D₄	1	2	yes	—
309	C₂⁴×D₄	C₂×D₄	1	4	yes	—
310	C₂⁴×D₄	C₂×D₄	1	2	yes	—
311	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
312	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
313	C₂⁴×D₄	C₂⁴	1	2	yes	—
314	C₂⁴×D₄	C₂⁴	1	2	yes	—
315	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
316	C₂⁵×C₄	C₂×D₄	1	2	yes	—
317	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
318	C₂⁵×C₄	C₂×D₄	1	2	yes	—
319	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
320	C₂⁵×C₄	C₂×D₄	1	4	yes	—
321	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
322	C₂⁵×C₄	C₂×D₄	1	2	yes	—
323	C₂⁵×C₄	C₂×D₄	1	2	yes	—
324	C₂⁵×C₄	C₂×D₄	1	4	yes	—
325	C₂⁵×C₄	C₂×D₄	1	2	yes	—
326	C₂⁵×C₄	C₂×D₄	1	2	yes	—
327	C₂⁵×C₄	C₂×D₄	1	4	yes	—
328	C₂⁵×C₄	C₂×D₄	1	4	yes	—
329	C₂⁵×C₄	C₂×D₄	1	2	yes	—
330	C₂⁵×C₄	C₂⁴	1	2	yes	—
331	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
332	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
333	C₂⁵×C₄	C₂⁴	1	2	yes	—
334	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
335	C₂×#575	C₂⁴	1	32	yes	—
336	C₂³×M₁₆	C₂⁴	1	8	yes	—
337	#3487	C₂×D₄	1	64	yes	complemented
338	#3486	C₂×D₄	1	64	yes	complemented
339	#3485	C₂×D₄	1	64	yes	complemented
340	#3484	C₂×D₄	1	64	yes	complemented
341	#3449	C₂×D₄	1	64	yes	—
342	C₂×#536	C₂×D₄	1	8	yes	—
343	C₂×#536	C₂×D₄	1	16	yes	complemented
344	C₂×#536	C₂×D₄	1	8	yes	complemented
345	C₂×#536	C₂×D₄	1	8	yes	complemented
346	C₂×#536	C₂×D₄	1	8	yes	complemented
347	C₂×#536	C₂×D₄	1	8	yes	complemented
348	C₂×#536	C₂⁴	1	4	yes	—
349	C₂×#536	C₂⁴	1	8	yes	—
350	C₂×#536	C₂⁴	1	8	yes	—
351	C₂×#536	C₂⁴	1	8	yes	—
352	C₂×#535	C₂×D₄	1	8	yes	—
353	C₂×#535	C₂×D₄	1	16	yes	complemented
354	C₂×#535	C₂×D₄	1	8	yes	complemented
355	C₂×#535	C₂×D₄	1	8	yes	complemented
356	C₂×#535	C₂×D₄	1	8	yes	complemented
357	C₂×#535	C₂×D₄	1	8	yes	complemented
358	C₂×#535	C₂⁴	1	4	yes	—
359	C₂×#535	C₂⁴	1	8	yes	—
360	C₂×#535	C₂⁴	1	8	yes	—
361	C₂×#535	C₂⁴	1	8	yes	—
362	C₂×#532	C₂×D₄	1	16	yes	—
363	C₂×#532	C₂×D₄	1	16	yes	complemented
364	C₂×#532	C₂×D₄	1	16	yes	complemented
365	C₂×#532	C₂×D₄	1	16	yes	complemented
366	C₂×#532	C₂×D₄	1	16	yes	complemented
367	C₂²×C₄⋊Q₈	C₂×D₄	1	8	yes	complemented
368	C₂²×#127	C₂×D₄	1	8	yes	complemented
369	C₂²×#124	C₂×D₄	1	8	yes	complemented
370	C₂²×#124	C₂×D₄	1	8	yes	complemented
371	C₂×#525	C₂×D₄	1	64	yes	complemented
372	C₂×#525	C₂×D₄	1	8	yes	complemented
373	C₂×#525	C₂⁴	1	16	yes	—
374	C₂×#525	C₂⁴	1	16	yes	—
375	C₂×#525	C₂⁴	1	8	yes	—
376	C₂×#525	C₂⁴	1	8	yes	—
377	C₂×#525	C₂⁴	1	4	yes	—
378	C₂×#525	C₂⁴	1	4	yes	—
379	C₂²×C₂²⋊Q₈	C₂×D₄	1	4	yes	complemented
380	C₂²×#121	C₂×D₄	1	4	yes	complemented
381	#3428	C₂×D₄	1	32	yes	complemented
382	C₂×#519	C₂⁴	1	8	yes	—
383	C₂×#519	C₂⁴	1	4	yes	—
384	C₂×#519	C₂⁴	1	2	yes	—
385	C₂×#518	C₂⁴	1	8	yes	—
386	C₂×#518	C₂⁴	1	4	yes	—
387	C₂×#518	C₂⁴	1	2	yes	—
388	C₂²×#117	C₂×D₄	1	4	yes	complemented
389	C₂²×#117	C₂×D₄	1	4	yes	complemented
390	C₂²×#117	C₂×D₄	1	4	yes	complemented
391	C₂²×#117	C₂⁴	1	4	yes	—
392	C₂²×#117	C₂⁴	1	4	yes	—
393	C₂²×#117	C₂⁴	1	4	yes	—
394	C₂²×#117	C₂⁴	1	4	yes	—
395	C₂²×#117	C₂⁴	1	2	yes	—
396	C₂³×C₄²	C₂×D₄	1	4	yes	complemented
397	C₂×#421	C₂⁴	1	32	yes	—
398	C₂×#421	C₂⁴	1	64	yes	—
399	#2896	C₂⁴	1	32	yes	—
400	C₂²×#101	C₂⁴	1	8	yes	—
401	C₂²×#101	C₂⁴	1	16	yes	—
402	C₂²×#101	C₂⁴	1	8	yes	—
403	C₂²×#100	C₂⁴	1	8	yes	—
404	C₂²×#100	C₂⁴	1	16	yes	—
405	C₂²×#100	C₂⁴	1	8	yes	—
406	C₂×#407	C₂⁴	1	8	yes	—
407	C₂×#407	C₂⁴	1	8	yes	—
408	C₂×#407	C₂⁴	1	16	yes	—
409	C₂×#407	C₂⁴	1	16	yes	—
410	#2436	C₂×D₄	1	16	yes	complemented
411	#2435	C₂×D₄	1	16	yes	complemented
412	#2434	C₂×D₄	1	16	yes	complemented
413	#2433	C₂×D₄	1	16	yes	complemented
414	#2432	C₂×D₄	1	32	yes	complemented
415	#2431	C₂×D₄	1	32	yes	complemented
416	#2311	C₂×D₄	1	16	yes	complemented
417	#2310	C₂⁴	1	4	yes	—
418	#2310	C₂⁴	1	8	yes	—
419	#2309	C₂⁴	1	4	yes	—
420	#2309	C₂⁴	1	8	yes	—
421	#2297	C₂×D₄	1	16	yes	complemented
422	#2280	C₂×D₄	1	8	yes	complemented
423	#2280	C₂⁴	1	8	yes	—
424	#2280	C₂⁴	1	8	yes	—
425	#2280	C₂⁴	1	4	yes	—
426	#2280	C₂⁴	1	4	yes	—
427	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
428	#1733	C₂⁴	1	32	yes	—
429	C₂×H(3,ℤ/4)	C₂⁴	1	64	yes	—
430	C₂⁶	C₂²×D₄	1	2	yes	—
431	C₂⁶	C₂²×D₄	1	2	yes	—
432	C₂⁶	C₂²×D₄	1	1	yes	characteristic
433	C₂⁶	C₂²×D₄	1	4	yes	—
434	C₂⁶	C₂²×D₄	1	1	yes	characteristic
435	C₂⁶	C₂²×D₄	1	2	yes	—
436	C₂⁶	C₂²×D₄	1	4	yes	—
437	C₂⁶	C₂²×D₄	1	2	yes	—
438	C₂⁶	C₂²×D₄	1	1	yes	characteristic
439	C₂×2₋¹⁺⁴	C₂²×D₄	1	32	yes	—
440	C₂×H(5,𝔽₂)	C₂²×D₄	1	32	yes	—
441	C₂²×#41	#120	1	8	yes	—
442	C₂²×#41	#120	1	8	yes	—
443	C₂²×#41	#120	1	16	yes	—
444	C₂²×#41	#120	1	8	yes	—
445	C₂²×#41	#120	1	8	yes	—
446	C₂²×#41	#120	1	8	yes	—
447	C₂²×#41	#120	1	8	yes	—
448	C₂²×#41	#120	1	32	yes	—
449	C₂²×#41	#120	1	32	yes	—
450	C₂²×#41	C₂²×D₄	1	32	yes	—
451	C₂²×#41	C₂²×D₄	1	8	yes	—
452	C₂²×#41	C₂²×D₄	1	8	yes	—
453	C₂²×#41	C₂²×D₄	1	8	yes	—
454	C₂²×#41	C₂²×D₄	1	16	yes	—
455	C₂²×#41	C₂²×D₄	1	4	yes	—
456	C₂²×#41	C₂²×D₄	1	4	yes	—
457	C₂²×#41	C₂²×D₄	1	4	yes	—
458	C₂²×#41	C₂²×D₄	1	4	yes	—
459	C₂²×#41	C₂²×D₄	1	4	yes	—
460	C₂²×#41	C₂²×D₄	1	4	yes	—
461	C₂²×#41	C₂²×D₄	1	16	yes	—
462	C₂²×#41	C₂²×D₄	1	16	yes	—
463	C₂²×#41	C₂²×D₄	1	4	yes	—
464	C₂²×#41	C₂²×D₄	1	4	yes	—
465	C₂²×#41	C₂²×D₄	1	16	yes	—
466	C₂²×#41	C₂²×D₄	1	8	yes	—
467	C₂²×#41	C₂²×D₄	1	8	yes	—
468	C₂²×#41	C₂²×D₄	1	16	yes	—
469	C₂²×#41	C₂²×D₄	1	4	yes	complemented
470	C₂²×#41	H(5,𝔽₂)	1	16	yes	—
471	C₂²×#41	C₂⁵	1	4	yes	—
472	C₂²×#41	C₂⁵	1	8	yes	—
473	C₂³×Q₈	C₂²×D₄	1	4	yes	—
474	C₂³×Q₈	C₂²×D₄	1	4	yes	—
475	C₂³×Q₈	C₂²×D₄	1	4	yes	—
476	C₂³×Q₈	C₂²×D₄	1	8	yes	—
477	C₂³×Q₈	C₂²×D₄	1	4	yes	—
478	C₂³×Q₈	C₂²×D₄	1	4	yes	—
479	C₂³×Q₈	C₂²×D₄	1	16	yes	—
480	C₂³×Q₈	C₂²×D₄	1	2	yes	—
481	C₂³×Q₈	C₂²×D₄	1	4	yes	—
482	C₂³×Q₈	C₂²×D₄	1	2	yes	—
483	C₂³×Q₈	C₂²×D₄	1	4	yes	—
484	C₂³×Q₈	C₂²×D₄	1	2	yes	complemented
485	C₂³×Q₈	C₂⁵	1	1	yes	characteristic
486	C₂³×Q₈	C₂⁵	1	1	yes	characteristic
487	C₂³×Q₈	C₂⁵	1	2	yes	—
488	C₂³×D₄	#120	1	16	yes	—
489	C₂³×D₄	#120	1	8	yes	—
490	C₂³×D₄	#120	1	8	yes	—
491	C₂³×D₄	#120	1	32	yes	—
492	C₂³×D₄	C₂²×D₄	1	2	yes	—
493	C₂³×D₄	C₂²×D₄	1	4	yes	—
494	C₂³×D₄	C₂²×D₄	1	2	yes	—
495	C₂³×D₄	C₂²×D₄	1	8	yes	—
496	C₂³×D₄	C₂²×D₄	1	4	yes	—
497	C₂³×D₄	C₂²×D₄	1	4	yes	—
498	C₂³×D₄	C₂²×D₄	1	4	yes	—
499	C₂³×D₄	C₂²×D₄	1	4	yes	—
500	C₂³×D₄	C₂²×D₄	1	4	yes	—
501	C₂³×D₄	C₂²×D₄	1	4	yes	—
502	C₂³×D₄	C₂²×D₄	1	2	yes	—
503	C₂³×D₄	C₂²×D₄	1	4	yes	—
504	C₂³×D₄	C₂²×D₄	1	4	yes	—
505	C₂³×D₄	C₂²×D₄	1	2	yes	—
506	C₂³×D₄	C₂²×D₄	1	4	yes	—
507	C₂³×D₄	C₂²×D₄	1	2	yes	—
508	C₂³×D₄	C₂²×D₄	1	4	yes	—
509	C₂³×D₄	C₂²×D₄	1	4	yes	—
510	C₂³×D₄	C₂²×D₄	1	16	yes	—
511	C₂³×D₄	C₂²×D₄	1	2	yes	—
512	C₂³×D₄	C₂²×D₄	1	4	yes	—
513	C₂³×D₄	C₂²×D₄	1	2	yes	complemented
514	C₂³×D₄	C₂⁵	1	1	yes	characteristic
515	C₂³×D₄	C₂⁵	1	1	yes	characteristic
516	C₂³×D₄	C₂⁵	1	2	yes	—
517	C₂⁴×C₄	#120	1	8	yes	—
518	C₂⁴×C₄	#120	1	8	yes	—
519	C₂⁴×C₄	#120	1	4	yes	—
520	C₂⁴×C₄	#120	1	4	yes	—
521	C₂⁴×C₄	#120	1	32	yes	—
522	C₂⁴×C₄	#120	1	4	yes	—
523	C₂⁴×C₄	#120	1	4	yes	—
524	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
525	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
526	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
527	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
528	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
529	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
530	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
531	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
532	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
533	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
534	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
535	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
536	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
537	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
538	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
539	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
540	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
541	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
542	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
543	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
544	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
545	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
546	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
547	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
548	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
549	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
550	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
551	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
552	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
553	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
554	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
555	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
556	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
557	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
558	C₂⁴×C₄	H(5,𝔽₂)	1	4	yes	—
559	C₂⁴×C₄	H(5,𝔽₂)	1	4	yes	—
560	C₂⁴×C₄	C₂⁵	1	2	yes	—
561	C₂⁴×C₄	C₂⁵	1	2	yes	—
562	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
563	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
564	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
565	C₂²×M₁₆	C₂⁵	1	16	yes	—
566	#536	#120	1	64	yes	complemented
567	#536	C₂²×D₄	1	64	yes	—
568	#535	#120	1	64	yes	complemented
569	#535	C₂²×D₄	1	64	yes	—
570	#532	#120	1	128	yes	complemented
571	C₂×C₄⋊Q₈	C₂²×D₄	1	16	yes	—
572	C₂×C₄⋊Q₈	C₂²×D₄	1	16	yes	—
573	C₂×C₄⋊Q₈	C₂²×D₄	1	16	yes	complemented
574	C₂×#127	C₂²×D₄	1	16	yes	—
575	C₂×#127	C₂²×D₄	1	16	yes	—
576	C₂×#127	C₂²×D₄	1	16	yes	complemented
577	C₂×#124	C₂²×D₄	1	16	yes	—
578	C₂×#124	C₂²×D₄	1	16	yes	—
579	C₂×#124	C₂²×D₄	1	16	yes	—
580	C₂×#124	C₂²×D₄	1	16	yes	—
581	C₂×#124	C₂²×D₄	1	16	yes	complemented
582	C₂×#124	C₂²×D₄	1	16	yes	complemented
583	#525	C₂²×D₄	1	64	yes	—
584	#525	C₂²×D₄	1	64	yes	—
585	C₂×C₂²⋊Q₈	C₂²×D₄	1	8	yes	—
586	C₂×C₂²⋊Q₈	C₂²×D₄	1	8	yes	complemented
587	C₂×#121	C₂²×D₄	1	8	yes	—
588	C₂×#121	C₂²×D₄	1	8	yes	complemented
589	#519	C₂²×D₄	1	32	yes	—
590	#518	C₂²×D₄	1	32	yes	—
591	C₂×#117	C₂²×D₄	1	32	yes	—
592	C₂×#117	C₂²×D₄	1	8	yes	—
593	C₂×#117	C₂²×D₄	1	8	yes	—
594	C₂×#117	C₂²×D₄	1	8	yes	—
595	C₂×#117	C₂²×D₄	1	4	yes	complemented
596	C₂×#117	C₂²×D₄	1	8	yes	complemented
597	C₂×#117	C₂⁵	1	4	yes	—
598	C₂×#117	C₂⁵	1	8	yes	—
599	C₂×#117	C₂⁵	1	8	yes	—
600	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	complemented
601	C₂²×C₄²	C₂²×D₄	1	8	yes	—
602	C₂²×C₄²	C₂²×D₄	1	8	yes	—
603	C₂²×C₄²	C₂²×D₄	1	8	yes	—
604	C₂²×C₄²	C₂²×D₄	1	8	yes	complemented
605	#391	C₂²×D₄	1	32	yes	complemented
606	#390	C₂²×D₄	1	32	yes	complemented
607	C₄×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
608	C₄×C₂²⋊C₄	C₂²×D₄	1	16	yes	complemented
609	C₂⁵	C₂×#120	1	8	yes	—
610	C₂⁵	C₂×#120	1	8	yes	—
611	C₂⁵	C₂×#120	1	4	yes	—
612	C₂⁵	C₂×#120	1	2	yes	—
613	C₂⁵	C₂×#120	1	4	yes	—
614	C₂⁵	C₂×#120	1	16	yes	—
615	C₂⁵	C₂×#120	1	4	yes	—
616	C₂⁵	C₂×#120	1	2	yes	—
617	C₂⁵	#534	1	4	yes	—
618	C₂⁵	C₂³×D₄	1	2	yes	—
619	C₂⁵	C₂³×D₄	1	2	yes	—
620	C₂⁵	C₂³×D₄	1	2	yes	—
621	C₂⁵	C₂³×D₄	1	1	yes	characteristic
622	C₂⁵	C₂³×D₄	1	2	yes	—
623	C₂⁵	C₂³×D₄	1	4	yes	—
624	C₂⁵	C₂³×D₄	1	1	yes	characteristic
625	C₂⁵	C₂³×D₄	1	1	yes	characteristic
626	C₂×#41	C₂×#120	1	32	yes	—
627	C₂×#41	C₂×#120	1	32	yes	—
628	C₂×#41	C₂×#120	1	32	yes	complemented
629	C₂×#41	D₄²	1	64	yes	—
630	C₂×#41	D₄²	1	64	yes	—
631	C₂×#41	C₂³×D₄	1	32	yes	—
632	C₂²×Q₈	C₂×#120	1	8	yes	—
633	C₂²×Q₈	C₂×#120	1	8	yes	—
634	C₂²×Q₈	C₂×#120	1	16	yes	—
635	C₂²×Q₈	C₂×#120	1	16	yes	complemented
636	C₂²×Q₈	C₂³×D₄	1	4	yes	—
637	C₂²×Q₈	C₂³×D₄	1	8	yes	—
638	C₂²×Q₈	C₂³×D₄	1	4	yes	—
639	C₂²×Q₈	C₂³×D₄	1	4	yes	—
640	C₂²×Q₈	C₂³×D₄	1	8	yes	—
641	C₂²×Q₈	C₂³×D₄	1	8	yes	—
642	C₂²×Q₈	C₂³×D₄	1	8	yes	—
643	C₂²×Q₈	C₂×H(5,𝔽₂)	1	8	yes	—
644	C₂²×D₄	C₂×#120	1	8	yes	—
645	C₂²×D₄	C₂×#120	1	16	yes	—
646	C₂²×D₄	C₂×#120	1	8	yes	—
647	C₂²×D₄	C₂×#120	1	8	yes	—
648	C₂²×D₄	C₂×#120	1	8	yes	—
649	C₂²×D₄	C₂×#120	1	8	yes	—
650	C₂²×D₄	C₂×#120	1	16	yes	—
651	C₂²×D₄	C₂×#120	1	16	yes	—
652	C₂²×D₄	C₂×#120	1	16	yes	—
653	C₂²×D₄	C₂×#120	1	8	yes	—
654	C₂²×D₄	C₂×#120	1	16	yes	—
655	C₂²×D₄	C₂×#120	1	16	yes	—
656	C₂²×D₄	C₂×#120	1	16	yes	—
657	C₂²×D₄	C₂×#120	1	16	yes	complemented
658	C₂²×D₄	#534	1	16	yes	—
659	C₂²×D₄	C₂³×D₄	1	4	yes	—
660	C₂²×D₄	C₂³×D₄	1	4	yes	—
661	C₂²×D₄	C₂³×D₄	1	8	yes	—
662	C₂²×D₄	C₂³×D₄	1	4	yes	—
663	C₂²×D₄	C₂³×D₄	1	8	yes	—
664	C₂²×D₄	C₂³×D₄	1	8	yes	—
665	C₂²×D₄	C₂³×D₄	1	8	yes	—
666	C₂²×D₄	C₂×H(5,𝔽₂)	1	8	yes	—
667	C₂³×C₄	C₂×#120	1	4	yes	—
668	C₂³×C₄	C₂×#120	1	4	yes	—
669	C₂³×C₄	C₂×#120	1	8	yes	—
670	C₂³×C₄	C₂×#120	1	8	yes	—
671	C₂³×C₄	C₂×#120	1	8	yes	—
672	C₂³×C₄	C₂×#120	1	8	yes	—
673	C₂³×C₄	C₂×#120	1	16	yes	—
674	C₂³×C₄	C₂×#120	1	4	yes	—
675	C₂³×C₄	C₂×#120	1	4	yes	—
676	C₂³×C₄	C₂×#120	1	4	yes	—
677	C₂³×C₄	C₂×#120	1	4	yes	—
678	C₂³×C₄	C₂×#120	1	4	yes	—
679	C₂³×C₄	C₂×#120	1	4	yes	—
680	C₂³×C₄	C₂×#120	1	16	yes	—
681	C₂³×C₄	C₂×#120	1	16	yes	—
682	C₂³×C₄	C₂×#120	1	16	yes	—
683	C₂³×C₄	C₂×#120	1	4	yes	—
684	C₂³×C₄	C₂×#120	1	4	yes	—
685	C₂³×C₄	C₂×#120	1	16	yes	—
686	C₂³×C₄	C₂×#120	1	4	yes	—
687	C₂³×C₄	C₂×#120	1	1	yes	characteristic
688	C₂³×C₄	C₂×#120	1	2	yes	—
689	C₂³×C₄	C₂×#120	1	2	yes	—
690	C₂³×C₄	C₂×#120	1	1	yes	characteristic
691	C₂³×C₄	C₂×#120	1	1	yes	characteristic
692	C₂³×C₄	C₂×#120	1	16	yes	—
693	C₂³×C₄	C₂×#120	1	2	yes	—
694	C₂³×C₄	C₂×#120	1	2	yes	—
695	C₂³×C₄	C₂×#120	1	2	yes	—
696	C₂³×C₄	C₂×#120	1	8	yes	—
697	C₂³×C₄	C₂×#120	1	2	yes	—
698	C₂³×C₄	C₂×#120	1	2	yes	—
699	C₂³×C₄	C₂×#120	1	8	yes	—
700	C₂³×C₄	C₂×#120	1	2	yes	—
701	C₂³×C₄	C₂×#120	1	1	yes	characteristic
702	C₂³×C₄	#534	1	4	yes	—
703	C₂³×C₄	#534	1	2	yes	—
704	C₂³×C₄	#534	1	2	yes	—
705	C₂³×C₄	#534	1	16	yes	—
706	C₂³×C₄	#534	1	2	yes	—
707	C₂³×C₄	#534	1	2	yes	—
708	C₂³×C₄	D₄²	1	8	yes	—
709	C₂³×C₄	D₄²	1	8	yes	—
710	C₂³×C₄	D₄²	1	8	yes	—
711	C₂³×C₄	D₄²	1	8	yes	—
712	C₂³×C₄	D₄²	1	8	yes	—
713	C₂³×C₄	D₄²	1	8	yes	—
714	C₂³×C₄	D₄²	1	8	yes	—
715	C₂³×C₄	D₄²	1	8	yes	—
716	C₂³×C₄	C₂³×D₄	1	8	yes	—
717	C₂³×C₄	C₂³×D₄	1	8	yes	—
718	C₂³×C₄	C₂³×D₄	1	2	yes	—
719	C₂³×C₄	C₂³×D₄	1	2	yes	—
720	C₂³×C₄	C₂³×D₄	1	2	yes	—
721	C₂³×C₄	C₂³×D₄	1	2	yes	—
722	C₂³×C₄	C₂³×D₄	1	2	yes	—
723	C₂³×C₄	C₂³×D₄	1	2	yes	—
724	C₂³×C₄	C₂³×D₄	1	2	yes	—
725	C₂³×C₄	C₂³×D₄	1	4	yes	—
726	C₂³×C₄	C₂³×D₄	1	4	yes	—
727	C₂³×C₄	C₂³×D₄	1	2	yes	—
728	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
729	C₂³×C₄	C₂³×D₄	1	4	yes	—
730	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
731	C₂³×C₄	C₂³×D₄	1	2	yes	—
732	C₂³×C₄	C₂³×D₄	1	8	yes	—
733	C₂³×C₄	C₂³×D₄	1	2	yes	—
734	C₂³×C₄	C₂³×D₄	1	2	yes	—
735	C₂³×C₄	C₂³×D₄	1	2	yes	—
736	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
737	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
738	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
739	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
740	C₂³×C₄	C₂×H(5,𝔽₂)	1	8	yes	—
741	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
742	C₂³×C₄	C₂⁶	1	1	yes	characteristic
743	C₄⋊Q₈	C₂×#120	1	64	yes	complemented
744	#127	C₂×#120	1	64	yes	complemented
745	#124	C₂×#120	1	64	yes	complemented
746	#124	C₂×#120	1	64	yes	complemented
747	#117	C₂×#120	1	32	yes	complemented
748	#117	C₂³×D₄	1	32	yes	—
749	C₂×C₄⋊C₄	C₂³×D₄	1	8	yes	—
750	C₂×C₄²	C₂×#120	1	32	yes	complemented
751	C₂×C₄²	C₂³×D₄	1	16	yes	—
752	C₂×C₄²	C₂³×D₄	1	16	yes	—
753	C₂⁴	#2403	1	8	yes	—
754	C₂⁴	#2403	1	8	yes	—
755	C₂⁴	C₂²×#120	1	1	yes	characteristic
756	C₂⁴	C₂²×#120	1	2	yes	—
757	C₂⁴	C₂²×#120	1	4	yes	—
758	C₂⁴	C₂²×#120	1	4	yes	—
759	C₂⁴	C₂²×#120	1	4	yes	—
760	C₂⁴	C₂²×#120	1	4	yes	—
761	C₂⁴	C₂²×#120	1	8	yes	—
762	C₂⁴	C₂²×#120	1	2	yes	—
763	C₂⁴	C₂²×#120	1	1	yes	characteristic
764	C₂⁴	C₂²×#120	1	2	yes	—
765	C₂⁴	C₂²×#120	1	8	yes	—
766	C₂⁴	C₂²×#120	1	8	yes	—
767	C₂⁴	C₂²×#120	1	2	yes	—
768	C₂⁴	C₂²×#120	1	2	yes	—
769	C₂⁴	C₂²×#120	1	4	yes	—
770	C₂⁴	C₂×#534	1	2	yes	—
771	C₂⁴	C₂×#534	1	2	yes	—
772	C₂⁴	C₂×#534	1	8	yes	—
773	C₂⁴	C₂×#534	1	2	yes	—
774	C₂⁴	C₂×#534	1	4	yes	—
775	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
776	C₂×Q₈	C₂²×#120	1	16	yes	—
777	C₂×Q₈	C₂²×#120	1	16	yes	—
778	C₂×Q₈	C₂×D₄²	1	32	yes	—
779	C₂×D₄	#2403	1	64	yes	—
780	C₂×D₄	#2846	1	32	yes	—
781	C₂×D₄	C₂²×#120	1	16	yes	—
782	C₂×D₄	C₂²×#120	1	16	yes	—
783	C₂×D₄	C₂×D₄²	1	32	yes	—
784	C₂²×C₄	#2403	1	8	yes	—
785	C₂²×C₄	#2403	1	8	yes	—
786	C₂²×C₄	#2403	1	2	yes	—
787	C₂²×C₄	#2403	1	2	yes	—
788	C₂²×C₄	#2403	1	32	yes	—
789	C₂²×C₄	#2403	1	4	yes	—
790	C₂²×C₄	#2403	1	2	yes	—
791	C₂²×C₄	#2403	1	2	yes	—
792	C₂²×C₄	#2403	1	2	yes	—
793	C₂²×C₄	#2403	1	2	yes	—
794	C₂²×C₄	#2403	1	32	yes	—
795	C₂²×C₄	#2403	1	4	yes	—
796	C₂²×C₄	#2403	1	4	yes	—
797	C₂²×C₄	#2403	1	2	yes	—
798	C₂²×C₄	#2403	1	2	yes	—
799	C₂²×C₄	#2403	1	4	yes	—
800	C₂²×C₄	#2846	1	16	yes	—
801	C₂²×C₄	#2846	1	16	yes	—
802	C₂²×C₄	C₂²×#120	1	4	yes	—
803	C₂²×C₄	C₂²×#120	1	4	yes	—
804	C₂²×C₄	C₂²×#120	1	4	yes	—
805	C₂²×C₄	C₂²×#120	1	4	yes	—
806	C₂²×C₄	C₂²×#120	1	8	yes	—
807	C₂²×C₄	C₂²×#120	1	2	yes	—
808	C₂²×C₄	C₂²×#120	1	8	yes	—
809	C₂²×C₄	C₂²×#120	1	2	yes	—
810	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
811	C₂²×C₄	C₂²×#120	1	2	yes	—
812	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
813	C₂²×C₄	C₂²×#120	1	8	yes	—
814	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
815	C₂²×C₄	C₂²×#120	1	4	yes	—
816	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
817	C₂²×C₄	C₂²×#120	1	8	yes	—
818	C₂²×C₄	C₂²×#120	1	8	yes	—
819	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
820	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
821	C₂²×C₄	C₂×#534	1	2	yes	—
822	C₂²×C₄	C₂×#534	1	8	yes	—
823	C₂²×C₄	C₂×#534	1	2	yes	—
824	C₂²×C₄	C₂×#534	1	1	yes	characteristic
825	C₂²×C₄	C₂×#534	1	4	yes	—
826	C₂²×C₄	C₂×#534	1	1	yes	characteristic
827	C₂²×C₄	C₂×D₄²	1	8	yes	—
828	C₂²×C₄	C₂×D₄²	1	8	yes	—
829	C₂²×C₄	C₂×D₄²	1	8	yes	—
830	C₂²×C₄	C₂×D₄²	1	8	yes	—
831	C₂²×C₄	C₂×D₄²	1	16	yes	—
832	C₂²×C₄	C₂×D₄²	1	4	yes	—
833	C₂²×C₄	C₂×D₄²	1	4	yes	—
834	C₂²×C₄	C₂×D₄²	1	4	yes	—
835	C₂²×C₄	C₂×D₄²	1	16	yes	—
836	C₂²×C₄	C₂×D₄²	1	4	yes	—
837	C₂²×C₄	#3484	1	16	yes	—
838	C₂²×C₄	#3484	1	16	yes	—
839	C₂²×C₄	#3484	1	8	yes	—
840	C₂²×C₄	#3484	1	8	yes	—
841	C₂²×C₄	C₂⁴×D₄	1	2	yes	—
842	C₂²×C₄	C₂⁴×D₄	1	4	yes	—
843	C₂²×C₄	C₂⁴×D₄	1	2	yes	—
844	C₂²×C₄	C₂²×H(5,𝔽₂)	1	2	yes	—
845	C₂²×C₄	C₂²×H(5,𝔽₂)	1	4	yes	—
846	C₄²	C₂²×#120	1	32	yes	—
847	C₂³	C₂×#2403	1	2	yes	—
848	C₂³	C₂×#2403	1	4	yes	—
849	C₂³	C₂×#2403	1	4	yes	—
850	C₂³	C₂×#2403	1	2	yes	—
851	C₂³	C₂×#2403	1	16	yes	—
852	C₂³	C₂×#2403	1	8	yes	—
853	C₂³	#34980	1	8	yes	—
854	C₂³	#34980	1	4	yes	—
855	C₂³	C₂×#2846	1	8	yes	—
856	C₂³	C₂×#2846	1	4	yes	—
857	C₂³	C₂³×#120	1	1	yes	characteristic
858	C₂³	C₂³×#120	1	1	yes	characteristic
859	C₂³	C₂³×#120	1	2	yes	—
860	C₂³	C₂²×#534	1	1	yes	characteristic
861	C₂³	C₂²×#534	1	2	yes	—
862	C₂×C₄	C₂×#2403	1	2	yes	—
863	C₂×C₄	C₂×#2403	1	2	yes	—
864	C₂×C₄	C₂×#2403	1	16	yes	—
865	C₂×C₄	C₂×#2403	1	4	yes	—
866	C₂×C₄	C₂×#2403	1	1	yes	characteristic
867	C₂×C₄	C₂×#2403	1	4	yes	—
868	C₂×C₄	C₂×#2403	1	1	yes	characteristic
869	C₂×C₄	C₂×#2403	1	1	yes	characteristic
870	C₂×C₄	C₂×#2403	1	4	yes	—
871	C₂×C₄	C₂×#2403	1	1	yes	characteristic
872	C₂×C₄	#34980	1	2	yes	—
873	C₂×C₄	#34980	1	2	yes	—
874	C₂×C₄	#34980	1	4	yes	—
875	C₂×C₄	#34980	1	4	yes	—
876	C₂×C₄	D₄×#120	1	16	yes	—
877	C₂×C₄	D₄×#120	1	16	yes	—
878	C₂×C₄	D₄×#120	1	16	yes	—
879	C₂×C₄	D₄×#120	1	16	yes	—
880	C₂×C₄	C₂×#2846	1	8	yes	—
881	C₂×C₄	C₂×#2846	1	2	yes	—
882	C₂×C₄	C₂×#2846	1	2	yes	—
883	C₂×C₄	C₂³×#120	1	4	yes	—
884	C₂×C₄	C₂²×D₄²	1	8	yes	—
885	C₂×C₄	C₂²×D₄²	1	4	yes	—
886	C₂×C₄	C₂×#3484	1	8	yes	—
887	C₂×C₄	C₂×#3484	1	4	yes	—
888	C₂²	#612424	1	8	yes	—
889	C₂²	#6437463	1	4	yes	complemented
890	C₂²	C₂²×#2403	1	2	yes	—
891	C₂²	C₂²×#2403	1	1	yes	characteristic
892	C₂²	C₂×#34980	1	1	yes	characteristic
893	C₂²	C₂×#34980	1	2	yes	—
894	C₂²	C₂²×#2846	1	1	yes	characteristic
895	C₄	#612424	1	2	yes	—
896	C₄	#612424	1	2	yes	—
897	C₄	#612424	1	2	yes	—
898	C₄	#612424	1	2	yes	—
899	C₄	C₂×D₄×#120	1	8	yes	—
900	C₂	C₂×#612424	1	1	yes	characteristic
901	C₂	C₂×#6437463	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×#2403
commutator, Frattini, cosocle	C₂³×C₄	C₂⁶
socle	C₂²	C₂²×#2403
LCS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂⁵×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. #72302895	C₂	semidirect
2. #72302893	C₂	semidirect
3. #72302890	C₂	semidirect
4. #72302888	C₂	semidirect
5. #72302882	C₂	semidirect
6. #72302358	C₂	semidirect
7. #72302333	C₂	semidirect
8. #72302285	C₂	semidirect
9. #72280406	C₂	semidirect
10. C₂²×#62811	C₂	semidirect
11. #72259172	C₂	semidirect
12. #72258211	C₂	semidirect
13. #72255937	C₂	semidirect
14. #72249727	C₂	semidirect
15. C₂×#6437463	C₂	semidirect
16. C₂×#393988	C₂	semidirect
17. #72210511	C₂	semidirect
18. C₂³×#585	C₂²	semidirect
21. C₂×#62811	C₂²	semidirect
22. C₂×#62811	C₂²	semidirect
23. C₂×#62811	C₂²	semidirect
24. C₂×#62811	C₂²	semidirect
25. C₂×#62811	C₂²	semidirect
26. C₂²×#3487	C₂²	semidirect
27. C₂²×#3486	C₂²	semidirect
28. C₂²×#3485	C₂²	semidirect
29. C₂²×#3484	C₂²	semidirect
31. C₂³×#525	C₂²	semidirect
32. C₂²×#3428	C₂²	semidirect
33. C₂×#60387	C₂²	semidirect
34. C₂×#60387	C₂²	semidirect
35. C₂×#60359	C₂²	semidirect
36. C₂×#36614	C₂²	semidirect
37. #7631198	C₂²	semidirect
38. #7631153	C₂²	semidirect
39. #7631153	C₂²	semidirect
40. #7631032	C₂²	semidirect
41. #7631032	C₂²	semidirect
42. #7630939	C₂²	semidirect
44. #7628649	C₂²	semidirect
45. #7625442	C₂²	semidirect
46. #7625442	C₂²	semidirect
47. #6628869	C₂²	semidirect
48. #6628868	C₂²	semidirect
49. #6628867	C₂²	semidirect
50. C₂×#23899	C₂²	semidirect
51. C₂×#23898	C₂²	semidirect
52. C₂×#23898	C₂²	semidirect
53. C₂×#23897	C₂²	semidirect
54. #6437448	C₂²	semidirect
55. #6437447	C₂²	semidirect
56. #6437446	C₂²	semidirect
57. #6437445	C₂²	semidirect
58. C₂²×#2010	C₂²	semidirect
59. #6431722	C₂²	semidirect
60. C₂×#21012	C₂²	semidirect
61. C₂×#21012	C₂²	semidirect
62. C₂×#20979	C₂²	semidirect
63. #6371454	C₂²	semidirect
64. #6370746	C₂²	semidirect
65. C₂×#20605	C₂²	semidirect
66. C₂×#20591	C₂²	semidirect
67. C₂×#20591	C₂²	semidirect
68. C₂×#20591	C₂²	semidirect
69. C₂×#20591	C₂²	semidirect
70. C₂×#20579	C₂²	semidirect
71. #393988	C₂²	semidirect
72. #393988	C₂²	semidirect
73. #393988	C₂²	semidirect
74. #393978	C₂²	semidirect
75. #393977	C₂²	semidirect
76. #393976	C₂²	semidirect
77. #393975	C₂²	semidirect
78. #392698	C₂²	semidirect
79. #392697	C₂²	semidirect
80. #392696	C₂²	semidirect
81. #392115	C₂²	semidirect
82. #392115	C₂²	semidirect
83. #392115	C₂²	semidirect
84. #392115	C₂²	semidirect
85. #392114	C₂²	semidirect
86. #392113	C₂²	semidirect
87. #359561	C₂²	semidirect
88. #359560	C₂²	semidirect
89. #359559	C₂²	semidirect
90. #359558	C₂²	semidirect
91. #359512	C₂²	semidirect
92. #359511	C₂²	semidirect
93. #359510	C₂²	semidirect
94. #359509	C₂²	semidirect
95. C₂×#10994	C₂²	semidirect
96. #357478	C₂²	semidirect
97. #353420	C₂²	semidirect
98. C₂×#10716	C₂²	semidirect
101. C₂²×#585	C₂³	semidirect
122. C₂²×#575	C₂³	semidirect
123. #62811	D₄	semidirect
126. C₂×#3487	C₂³	semidirect
127. C₂×#3487	C₂³	semidirect
131. C₂×#3486	C₂³	semidirect
134. C₂×#3485	C₂³	semidirect
135. C₂×#3485	C₂³	semidirect
139. C₂×#3484	C₂³	semidirect
140. C₂×#3449	D₄	semidirect
141. C₂×#3449	D₄	semidirect
147. C₂×#3449	C₂³	semidirect
148. C₂²×#536	D₄	semidirect
150. C₂²×#535	D₄	semidirect
152. C₂²×#532	D₄	semidirect
158. C₂²×#525	C₂³	semidirect
161. C₂×#3428	C₂³	semidirect
162. C₂×#3428	C₂³	semidirect
166. C₂×#3020	C₂³	semidirect
167. C₂×#3020	C₂³	semidirect
168. C₂×#3019	C₂³	semidirect
169. C₂×#3019	C₂³	semidirect
171. #60359	C₂³	semidirect
172. C₂²×#421	C₂³	semidirect
173. C₂²×#421	C₂³	semidirect
174. C₂×#2896	C₂³	semidirect
176. C₂²×#413	C₂³	semidirect
177. C₂²×#413	C₂³	semidirect
179. C₂²×#407	C₂³	semidirect
182. #36614	C₂³	semidirect
183. #35305	D₄	semidirect
184. #35250	D₄	semidirect
186. #35242	C₂³	semidirect
188. #35222	C₂³	semidirect
190. #35149	C₂³	semidirect
191. #35149	C₂³	semidirect
192. #34738	D₄	semidirect
193. #34174	C₂³	semidirect
194. #34174	C₂³	semidirect
196. #34173	C₂³	semidirect
197. #34172	C₂³	semidirect
198. #34172	C₂³	semidirect
200. #34171	C₂³	semidirect
202. #34044	C₂³	semidirect
204. C₂×#2280	C₂³	semidirect
205. C₂×#2010	C₂³	semidirect
206. C₂×#2010	C₂³	semidirect
207. #23403	C₂³	semidirect
208. #23402	C₂³	semidirect
209. C₂×#1912	C₂³	semidirect
210. C₂×#1912	C₂³	semidirect
211. C₂×#1911	C₂³	semidirect
212. C₂×#1911	C₂³	semidirect
214. #20979	C₂³	semidirect
215. #20954	C₂³	semidirect
216. #20953	C₂³	semidirect
217. #20617	C₂³	semidirect
218. #20616	C₂³	semidirect
220. #20605	C₂³	semidirect
222. C₂×#1785	C₂³	semidirect
223. C₂×#1785	C₂³	semidirect
224. C₂×#1785	C₂³	semidirect
225. C₂×#1785	C₂³	semidirect
226. C₂×#1785	C₂³	semidirect
227. C₂×#1785	C₂³	semidirect
230. C₂×#1784	C₂³	semidirect
231. C₂×#1784	C₂³	semidirect
234. C₂×#1783	C₂³	semidirect
235. C₂×#1783	C₂³	semidirect
238. #20579	C₂³	semidirect
239. C₂×#1733	C₂³	semidirect
240. C₂²×H(3,ℤ/4)	C₂³	semidirect
241. #10994	C₂³	semidirect
242. #10994	C₂³	semidirect
243. #10990	C₂³	semidirect
244. #10989	C₂³	semidirect
245. #10741	C₂³	semidirect
246. #10740	C₂³	semidirect
248. #10716	C₂³	semidirect
251. C₂×#585	C₂×D₄	semidirect
277. C₂³×#41	C₂×D₄	semidirect
278. C₂³×#41	C₂×D₄	semidirect
279. C₂³×#41	C₂×D₄	semidirect
296. C₂⁴×Q₈	C₂×D₄	semidirect
311. C₂⁴×D₄	C₂×D₄	semidirect
337. #3487	C₂×D₄	semidirect
338. #3486	C₂×D₄	semidirect
339. #3485	C₂×D₄	semidirect
340. #3484	C₂×D₄	semidirect
343. C₂×#536	C₂×D₄	semidirect
344. C₂×#536	C₂×D₄	semidirect
345. C₂×#536	C₂×D₄	semidirect
346. C₂×#536	C₂×D₄	semidirect
347. C₂×#536	C₂×D₄	semidirect
353. C₂×#535	C₂×D₄	semidirect
354. C₂×#535	C₂×D₄	semidirect
355. C₂×#535	C₂×D₄	semidirect
356. C₂×#535	C₂×D₄	semidirect
357. C₂×#535	C₂×D₄	semidirect
363. C₂×#532	C₂×D₄	semidirect
364. C₂×#532	C₂×D₄	semidirect
365. C₂×#532	C₂×D₄	semidirect
366. C₂×#532	C₂×D₄	semidirect
367. C₂²×C₄⋊Q₈	C₂×D₄	semidirect
368. C₂²×#127	C₂×D₄	semidirect
369. C₂²×#124	C₂×D₄	semidirect
370. C₂²×#124	C₂×D₄	semidirect
371. C₂×#525	C₂×D₄	semidirect
372. C₂×#525	C₂×D₄	semidirect
379. C₂²×C₂²⋊Q₈	C₂×D₄	semidirect
380. C₂²×#121	C₂×D₄	semidirect
381. #3428	C₂×D₄	semidirect
388. C₂²×#117	C₂×D₄	semidirect
389. C₂²×#117	C₂×D₄	semidirect
390. C₂²×#117	C₂×D₄	semidirect
396. C₂³×C₄²	C₂×D₄	semidirect
410. #2436	C₂×D₄	semidirect
411. #2435	C₂×D₄	semidirect
412. #2434	C₂×D₄	semidirect
413. #2433	C₂×D₄	semidirect
414. #2432	C₂×D₄	semidirect
415. #2431	C₂×D₄	semidirect
416. #2311	C₂×D₄	semidirect
421. #2297	C₂×D₄	semidirect
422. #2280	C₂×D₄	semidirect
427. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
469. C₂²×#41	C₂²×D₄	semidirect
484. C₂³×Q₈	C₂²×D₄	semidirect
513. C₂³×D₄	C₂²×D₄	semidirect
566. #536	#120	semidirect
568. #535	#120	semidirect
570. #532	#120	semidirect
573. C₂×C₄⋊Q₈	C₂²×D₄	semidirect
576. C₂×#127	C₂²×D₄	semidirect
581. C₂×#124	C₂²×D₄	semidirect
582. C₂×#124	C₂²×D₄	semidirect
586. C₂×C₂²⋊Q₈	C₂²×D₄	semidirect
588. C₂×#121	C₂²×D₄	semidirect
595. C₂×#117	C₂²×D₄	semidirect
596. C₂×#117	C₂²×D₄	semidirect
600. C₂²×C₄⋊C₄	C₂²×D₄	semidirect
604. C₂²×C₄²	C₂²×D₄	semidirect
605. #391	C₂²×D₄	semidirect
606. #390	C₂²×D₄	semidirect
608. C₄×C₂²⋊C₄	C₂²×D₄	semidirect
628. C₂×#41	C₂×#120	semidirect
635. C₂²×Q₈	C₂×#120	semidirect
657. C₂²×D₄	C₂×#120	semidirect
743. C₄⋊Q₈	C₂×#120	semidirect
744. #127	C₂×#120	semidirect
745. #124	C₂×#120	semidirect
746. #124	C₂×#120	semidirect
747. #117	C₂×#120	semidirect
750. C₂×C₄²	C₂×#120	semidirect
889. C₂²	#6437463	semidirect

Maximal subgroups

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

subgroup	index
#72302895	2
#72302893	2
#72302890	2
#72302888	2
#72302882	2
#72302358	2
#72302333	2
#72302285	2
#72280406	2
C₂²×#62811	2
#72259172	2
#72258211	2
#72255937	2
#72249727	2
C₂×#6437463	2
C₂×#393988	2
#72210511	2