Subgroups — #72279981

Order 2048.

At least 14231 conjugacy classes of subgroups; only the 2196 normal subgroups are shown.

The subgroup lattice has 907 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72279945	C₂	1	1	yes	maximal, characteristic, complemented
2	#72279925	C₂	1	2	yes	maximal, complemented
3	#72279907	C₂	1	1	yes	maximal, characteristic, complemented
4	#72279624	C₂	1	2	yes	maximal, complemented
5	#72279500	C₂	1	2	yes	maximal, complemented
6	#72279469	C₂	1	1	yes	maximal, characteristic, complemented
7	#72279412	C₂	1	1	yes	maximal, characteristic, complemented
8	#72279381	C₂	1	2	yes	maximal, complemented
9	#72279346	C₂	1	2	yes	maximal, complemented
10	#72268516	C₂	1	1	yes	maximal, characteristic, complemented
11	#72256165	C₂	1	1	yes	maximal, characteristic, complemented
12	#72256073	C₂	1	2	yes	maximal, complemented
13	#72249727	C₂	1	1	yes	maximal, characteristic, complemented
14	#72239343	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#359649	C₂	1	1	yes	maximal, characteristic, complemented
16	#72239326	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#6437575	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#6431743	C₂	1	1	yes	maximal, characteristic, complemented
19	#72237261	C₂	1	2	yes	maximal, complemented
20	#72237193	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#6437616	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#359507	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#393988	C₂	1	2	yes	maximal, complemented
24	C₂×#63090	C₂²	1	1	yes	characteristic, complemented
25	C₂×#62811	C₂²	1	1	yes	characteristic
26	C₂×#62811	C₂²	1	1	yes	characteristic
27	C₂×#62811	C₂²	1	1	yes	characteristic, complemented
28	C₂³×#525	C₂²	1	1	yes	characteristic
29	C₂³×#525	C₂²	1	1	yes	characteristic, complemented
30	C₂²×#3025	C₂²	1	1	yes	characteristic
31	C₂²×#3025	C₂²	1	1	yes	characteristic, complemented
32	C₂×#60387	C₂²	1	1	yes	characteristic, complemented
33	C₂×#60359	C₂²	1	2	yes	complemented
34	C₂×#60064	C₂²	1	1	yes	characteristic, complemented
35	C₂×#60093	C₂²	1	1	yes	characteristic, complemented
36	C₂×#60093	C₂²	1	1	yes	characteristic, complemented
37	C₂×#36614	C₂²	1	1	yes	characteristic, complemented
38	C₂×#36614	C₂²	1	2	yes	complemented
39	#7629144	C₂²	1	1	yes	characteristic, complemented
40	#7629122	C₂²	1	1	yes	characteristic
41	#7629122	C₂²	1	1	yes	characteristic, complemented
42	#7629120	C₂²	1	1	yes	characteristic
43	#7628650	C₂²	1	1	yes	characteristic, complemented
44	#7628650	C₂²	1	1	yes	characteristic, complemented
45	#7628649	C₂²	1	1	yes	characteristic
46	#7628649	C₂²	1	1	yes	characteristic, complemented
47	#7625530	C₂²	1	1	yes	characteristic
48	#7625530	C₂²	1	1	yes	characteristic, complemented
49	C₂×#23443	C₂²	1	2	yes	complemented
50	C₂×#23443	C₂²	1	2	yes	complemented
51	C₂×#23414	C₂²	1	2	yes	complemented
52	C₂×#23414	C₂²	1	2	yes	complemented
53	C₂²×#2010	C₂²	1	2	yes	—
54	C₂²×#2010	C₂²	1	2	yes	complemented
55	C₂²×#2010	C₂²	1	2	yes	complemented
56	C₂²×#2010	C₂²	1	2	yes	complemented
57	C₂²×#2010	C₂²	1	2	yes	complemented
58	C₂²×#2010	C₂²	1	2	yes	complemented
59	C₂×#23412	C₂²	1	2	yes	complemented
60	#6431722	C₂²	1	2	yes	complemented
61	#6431698	C₂²	1	2	yes	complemented
62	C₂×#21012	C₂²	1	1	yes	characteristic, complemented
63	C₂×#21009	C₂²	1	1	yes	characteristic, complemented
64	C₂×#20998	C₂²	1	2	yes	complemented
65	C₂×#20983	C₂²	1	2	yes	complemented
66	C₂×#20979	C₂²	1	2	yes	complemented
67	C₂²×#1891	C₂²	1	1	yes	characteristic
68	C₂²×#1891	C₂²	1	1	yes	characteristic
69	C₂²×#1891	C₂²	1	1	yes	characteristic, complemented
70	C₂²×#1891	C₂²	1	1	yes	characteristic, complemented
71	C₂×#20959	C₂²	1	1	yes	characteristic
72	C₂×#20959	C₂²	1	1	yes	characteristic, complemented
73	C₂×#20947	C₂²	1	1	yes	characteristic, complemented
74	C₂×#20623	C₂²	1	1	yes	characteristic, complemented
75	C₂×#20623	C₂²	1	1	yes	characteristic, complemented
76	#6370746	C₂²	1	1	yes	characteristic, complemented
77	C₂×#20605	C₂²	1	2	yes	complemented
78	C₂×#20591	C₂²	1	1	yes	characteristic, complemented
79	C₂×#20584	C₂²	1	1	yes	characteristic, complemented
80	C₂×#20579	C₂²	1	2	yes	complemented
81	C₂×#20338	C₂²	1	1	yes	characteristic, complemented
82	#357769	C₂²	1	2	yes	complemented
83	#357756	C₂²	1	2	yes	complemented
84	#357593	C₂²	1	2	yes	complemented
85	#357577	C₂²	1	2	yes	complemented
86	#357564	C₂²	1	2	yes	complemented
87	C₂×#11003	C₂²	1	2	yes	complemented
88	C₂×#11000	C₂²	1	2	yes	complemented
89	C₂×#11000	C₂²	1	2	yes	complemented
90	#357556	C₂²	1	2	yes	complemented
91	C₂×#10994	C₂²	1	2	yes	complemented
92	C₂×#10994	C₂²	1	2	yes	complemented
93	C₂×#10994	C₂²	1	2	yes	complemented
94	C₂×#10994	C₂²	1	2	yes	complemented
95	C₂×#10994	C₂²	1	2	yes	complemented
96	C₂×#10994	C₂²	1	2	yes	complemented
97	C₂×#10994	C₂²	1	2	yes	complemented
98	C₂×#10994	C₂²	1	2	yes	complemented
99	C₂×#10993	C₂²	1	2	yes	complemented
100	C₂×#10993	C₂²	1	2	yes	complemented
101	#357478	C₂²	1	2	yes	complemented
102	#357440	C₂²	1	2	yes	complemented
103	#357440	C₂²	1	2	yes	complemented
104	#354116	C₂²	1	2	yes	complemented
105	C₂×#10783	C₂²	1	2	yes	complemented
106	#353442	C₂²	1	1	yes	characteristic, complemented
107	#353422	C₂²	1	1	yes	characteristic, complemented
108	#353420	C₂²	1	1	yes	characteristic, complemented
109	C₂×#10738	C₂²	1	2	yes	complemented
110	#353324	C₂²	1	1	yes	characteristic, complemented
111	#353324	C₂²	1	1	yes	characteristic, complemented
112	C₂×#10716	C₂²	1	2	yes	complemented
113	#124041	C₂²	1	2	yes	complemented
114	#123916	C₂²	1	2	yes	complemented
115	#123610	C₂²	1	2	yes	complemented
116	#123598	C₂²	1	2	yes	complemented
117	#123586	C₂²	1	2	yes	complemented
118	#123568	C₂²	1	2	yes	complemented
119	#123531	C₂²	1	2	yes	complemented
120	#123531	C₂²	1	2	yes	complemented
121	#123508	C₂²	1	2	yes	complemented
122	#123457	C₂²	1	2	yes	complemented
123	C₂²×#585	C₂³	1	1	yes	characteristic
124	C₂²×#585	C₂³	1	1	yes	characteristic
125	C₂⁴×#41	C₂³	1	1	yes	characteristic
126	C₂⁴×#41	C₂³	1	1	yes	characteristic
127	C₂⁶×C₄	C₂³	1	1	yes	characteristic
128	C₂²×#575	C₂³	1	2	yes	—
129	C₂²×#575	C₂³	1	2	yes	—
130	C₂²×#575	C₂³	1	2	yes	—
131	C₂²×#568	C₂³	1	1	yes	characteristic
132	C₂²×#568	C₂³	1	1	yes	characteristic
133	C₂×#3487	D₄	1	2	yes	complemented
134	C₂×#3486	D₄	1	2	yes	complemented
135	C₂×#3485	D₄	1	2	yes	complemented
136	C₂×#3484	D₄	1	2	yes	complemented
137	C₂×#3449	D₄	1	4	yes	complemented
138	C₂×#3449	C₂³	1	1	yes	characteristic
139	C₂×#3449	C₂³	1	1	yes	characteristic
140	C₂×#3449	C₂³	1	1	yes	characteristic
141	C₂×#3449	C₂³	1	2	yes	—
142	C₂×#3449	C₂³	1	1	yes	characteristic
143	C₂×#3449	C₂³	1	1	yes	characteristic
144	C₂²×#525	D₄	1	2	yes	—
145	C₂²×#525	D₄	1	2	yes	—
146	C₂²×#525	D₄	1	4	yes	complemented
147	C₂²×#525	C₂³	1	1	yes	characteristic
148	C₂²×#525	C₂³	1	1	yes	characteristic
149	C₂²×#525	C₂³	1	1	yes	characteristic
150	C₂²×#525	C₂³	1	1	yes	characteristic
151	C₂²×#525	C₂³	1	1	yes	characteristic
152	C₂²×#525	C₂³	1	1	yes	characteristic
153	C₂²×#525	C₂³	1	2	yes	—
154	C₂²×#525	C₂³	1	1	yes	characteristic
155	C₂²×#525	C₂³	1	1	yes	characteristic
156	C₂²×#525	C₂³	1	1	yes	characteristic
157	C₂²×#525	C₂³	1	1	yes	characteristic
158	C₂²×#525	C₂³	1	1	yes	characteristic
159	C₂²×#525	C₂³	1	2	yes	—
160	C₂²×#525	C₂³	1	2	yes	—
161	C₂³×#123	D₄	1	2	yes	—
162	C₂³×#120	D₄	1	2	yes	—
163	C₂×#3428	C₂³	1	1	yes	characteristic
164	C₂×#3428	C₂³	1	1	yes	characteristic
165	C₂×#3428	C₂³	1	1	yes	characteristic
166	C₂³×#117	C₂³	1	1	yes	characteristic
167	C₂³×#117	C₂³	1	1	yes	characteristic
168	C₂×#3025	D₄	1	8	yes	complemented
169	C₂²×#421	C₂³	1	2	yes	—
170	C₂²×#421	C₂³	1	2	yes	—
171	C₂²×#421	C₂³	1	2	yes	—
172	C₂²×#421	C₂³	1	2	yes	—
173	C₂²×#421	C₂³	1	2	yes	—
174	C₂²×#421	C₂³	1	2	yes	—
175	C₂²×#421	C₂³	1	2	yes	—
176	C₂²×#421	C₂³	1	2	yes	—
177	C₂²×#421	C₂³	1	2	yes	—
178	C₂²×#421	C₂³	1	2	yes	—
179	C₂×#2896	C₂³	1	2	yes	—
180	C₂×#2896	C₂³	1	2	yes	—
181	C₂×#2896	C₂³	1	2	yes	—
182	C₂×#2896	C₂³	1	2	yes	—
183	C₂²×#413	C₂³	1	1	yes	characteristic
184	C₂²×#413	C₂³	1	1	yes	characteristic
185	C₂²×#413	C₂³	1	2	yes	—
186	C₂²×#410	C₂³	1	1	yes	characteristic
187	C₂²×#410	C₂³	1	2	yes	—
188	C₂²×#410	C₂³	1	1	yes	characteristic
189	C₂²×#410	C₂³	1	2	yes	—
190	C₂²×#410	C₂³	1	2	yes	—
191	C₂×#2879	C₂³	1	2	yes	—
192	C₂²×#407	C₂³	1	2	yes	—
193	C₂²×#407	C₂³	1	2	yes	—
194	C₂²×#407	C₂³	1	2	yes	—
195	C₂²×#407	C₂³	1	2	yes	—
196	C₂²×#407	C₂³	1	2	yes	—
197	C₂²×#407	C₂³	1	2	yes	—
198	#35659	D₄	1	4	yes	complemented
199	#35512	D₄	1	4	yes	complemented
200	#35242	D₄	1	2	yes	complemented
201	#35222	D₄	1	2	yes	complemented
202	#35149	D₄	1	2	yes	complemented
203	#35149	D₄	1	2	yes	complemented
204	#34743	D₄	1	8	yes	complemented
205	#34065	D₄	1	4	yes	complemented
206	#34052	C₂³	1	1	yes	characteristic
207	#34052	C₂³	1	1	yes	characteristic
208	#34044	C₂³	1	1	yes	characteristic
209	#34044	C₂³	1	1	yes	characteristic
210	#34044	C₂³	1	1	yes	characteristic
211	#34044	C₂³	1	1	yes	characteristic
212	#34044	C₂³	1	1	yes	characteristic
213	C₄×#525	D₄	1	4	yes	complemented
214	C₂×#2280	C₂³	1	1	yes	characteristic
215	C₂×#2280	C₂³	1	1	yes	characteristic
216	C₂×#2280	C₂³	1	2	yes	—
217	C₂×#2280	C₂³	1	2	yes	—
218	C₂×#2280	C₂³	1	2	yes	—
219	C₂×#2280	C₂³	1	1	yes	characteristic
220	#33996	C₂³	1	1	yes	characteristic
221	C₂×#2010	D₄	1	16	yes	complemented
222	C₂×#1891	D₄	1	8	yes	complemented
223	#20959	D₄	1	8	yes	complemented
224	C₂²×#344	C₂³	1	2	yes	—
225	C₂²×#344	C₂³	1	2	yes	—
226	C₂²×#344	C₂³	1	2	yes	—
227	C₂²×#344	C₂³	1	2	yes	—
228	C₂×#1740	C₂³	1	2	yes	—
229	C₂×#1740	C₂³	1	2	yes	—
230	#20347	C₂³	1	2	yes	—
231	C₂×#1733	C₂³	1	2	yes	—
232	C₂×#1733	C₂³	1	2	yes	—
233	C₂×#1733	C₂³	1	2	yes	—
234	C₂×#1733	C₂³	1	2	yes	—
235	C₂×#1733	C₂³	1	2	yes	—
236	C₂×#1733	C₂³	1	2	yes	—
237	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
238	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
239	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
240	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
241	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
242	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
243	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
244	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
245	C₂⁷	C₂×D₄	1	1	yes	characteristic
246	C₂×#585	C₂×D₄	1	4	yes	complemented
247	C₂²×2₋¹⁺⁴	C₂×D₄	1	2	yes	—
248	C₂²×2₋¹⁺⁴	C₂×D₄	1	2	yes	—
249	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
250	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
251	C₂³×#41	C₂×D₄	1	4	yes	—
252	C₂³×#41	C₂×D₄	1	1	yes	characteristic
253	C₂³×#41	C₂×D₄	1	1	yes	characteristic
254	C₂³×#41	C₂×D₄	1	2	yes	—
255	C₂³×#41	C₂×D₄	1	2	yes	—
256	C₂³×#41	C₂×D₄	1	1	yes	characteristic, complemented
257	C₂³×#41	C₂×D₄	1	1	yes	characteristic, complemented
258	C₂³×#41	C₂⁴	1	1	yes	characteristic
259	C₂³×#41	C₂⁴	1	1	yes	characteristic
260	C₂³×#41	C₂⁴	1	1	yes	characteristic
261	C₂³×#41	C₂⁴	1	2	yes	—
262	C₂³×#41	C₂⁴	1	1	yes	characteristic
263	C₂³×#41	C₂⁴	1	1	yes	characteristic
264	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
265	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic, complemented
266	C₂⁴×D₄	C₂×D₄	1	2	yes	—
267	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
268	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
269	C₂⁵×C₄	C₂×D₄	1	2	yes	—
270	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
271	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
272	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
273	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
274	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
275	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
276	C₂×#575	C₂×D₄	1	8	yes	complemented
277	C₂×#568	C₂×D₄	1	4	yes	complemented
278	C₂³×M₁₆	C₂⁴	1	2	yes	—
279	C₂³×M₁₆	C₂⁴	1	2	yes	—
280	C₂³×M₁₆	C₂⁴	1	2	yes	—
281	C₂³×M₁₆	C₂⁴	1	2	yes	—
282	C₂×#536	C₂×D₄	1	2	yes	—
283	C₂×#536	C₂×D₄	1	2	yes	—
284	C₂×#536	C₂×D₄	1	2	yes	—
285	C₂×#536	C₂×D₄	1	2	yes	complemented
286	C₂×#535	C₂×D₄	1	2	yes	—
287	C₂×#535	C₂×D₄	1	2	yes	—
288	C₂×#535	C₂×D₄	1	2	yes	—
289	C₂×#535	C₂×D₄	1	2	yes	complemented
290	C₂×#532	C₂×D₄	1	4	yes	—
291	C₂×#525	C₂×D₄	1	2	yes	—
292	C₂×#525	C₂×D₄	1	8	yes	—
293	C₂×#525	C₂×D₄	1	2	yes	—
294	C₂×#525	C₂×D₄	1	2	yes	—
295	C₂×#525	C₂×D₄	1	2	yes	—
296	C₂×#525	C₂×D₄	1	2	yes	—
297	C₂×#525	C₂×D₄	1	4	yes	—
298	C₂×#525	C₂×D₄	1	4	yes	—
299	C₂×#525	C₂×D₄	1	2	yes	—
300	C₂×#525	C₂×D₄	1	4	yes	—
301	C₂×#525	C₂×D₄	1	4	yes	—
302	C₂×#525	C₂×D₄	1	2	yes	—
303	C₂×#525	C₂×D₄	1	2	yes	—
304	C₂×#525	C₂×D₄	1	4	yes	—
305	C₂×#525	C₂×D₄	1	2	yes	—
306	C₂×#525	C₂×D₄	1	4	yes	—
307	C₂×#525	C₂×D₄	1	2	yes	—
308	C₂×#525	C₂×D₄	1	4	yes	—
309	C₂×#525	C₂×D₄	1	2	yes	complemented
310	C₂×#525	C₂×D₄	1	2	yes	complemented
311	C₂×#525	C₂×D₄	1	8	yes	complemented
312	C₂×#525	C₂×D₄	1	4	yes	complemented
313	C₂×#525	C₂×D₄	1	4	yes	complemented
314	C₂×#525	C₂×D₄	1	8	yes	complemented
315	C₂×#525	#41	1	4	yes	—
316	C₂²×#123	C₂×D₄	1	2	yes	—
317	C₂²×#123	C₂×D₄	1	2	yes	—
318	C₂²×#123	C₂×D₄	1	2	yes	—
319	C₂²×#123	C₂×D₄	1	2	yes	—
320	C₂²×C₂²⋊Q₈	C₂×D₄	1	2	yes	complemented
321	C₂²×#121	C₂×D₄	1	2	yes	complemented
322	C₂²×#120	C₂×D₄	1	2	yes	—
323	C₂²×#120	C₂×D₄	1	2	yes	—
324	C₂²×#120	C₂×D₄	1	2	yes	—
325	C₂²×#120	C₂×D₄	1	2	yes	—
326	#3428	C₂×D₄	1	4	yes	complemented
327	C₂×#519	C₂×D₄	1	2	yes	complemented
328	C₂×#518	C₂×D₄	1	2	yes	complemented
329	C₂×C₄×#41	C₂×D₄	1	4	yes	—
330	C₂×C₄×#41	C₂×D₄	1	4	yes	—
331	C₂²×#117	C₂×D₄	1	4	yes	—
332	C₂²×#117	C₂×D₄	1	2	yes	—
333	C₂²×#117	C₂×D₄	1	2	yes	complemented
334	C₂²×#117	C₂⁴	1	2	yes	—
335	C₂²×#117	C₂⁴	1	2	yes	—
336	C₂²×#117	C₂⁴	1	1	yes	characteristic
337	C₂²×#117	C₂⁴	1	1	yes	characteristic
338	C₂²×#117	C₂⁴	1	1	yes	characteristic
339	C₂²×#117	C₂⁴	1	2	yes	—
340	C₂²×#117	C₂⁴	1	1	yes	characteristic
341	C₂²×#117	C₂⁴	1	1	yes	characteristic
342	C₂²×#117	C₂⁴	1	1	yes	characteristic
343	C₂²×#117	C₂⁴	1	1	yes	characteristic
344	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
345	C₂³×C₄²	C₂×D₄	1	2	yes	complemented
346	C₂×#421	C₂×D₄	1	8	yes	complemented
347	C₂×#421	C₂×D₄	1	8	yes	complemented
348	C₂×#413	C₂×D₄	1	4	yes	complemented
349	C₂×#410	C₂×D₄	1	8	yes	complemented
350	C₂×#410	C₂×D₄	1	4	yes	complemented
351	C₂×#410	C₂×D₄	1	4	yes	complemented
352	C₂×#407	C₂×D₄	1	8	yes	complemented
353	C₂×#407	C₂×D₄	1	8	yes	complemented
354	#2311	C₂×D₄	1	4	yes	—
355	#2311	C₂×D₄	1	4	yes	complemented
356	#2310	C₂×D₄	1	2	yes	—
357	#2310	C₂×D₄	1	2	yes	—
358	#2310	C₂×D₄	1	2	yes	complemented
359	#2309	C₂×D₄	1	2	yes	—
360	#2309	C₂×D₄	1	2	yes	—
361	#2309	C₂×D₄	1	2	yes	complemented
362	#2297	C₂×D₄	1	4	yes	—
363	#2297	C₂×D₄	1	4	yes	complemented
364	#2296	C₂×D₄	1	4	yes	complemented
365	#2296	C₂×D₄	1	4	yes	complemented
366	#2280	C₂×D₄	1	2	yes	—
367	#2280	C₂×D₄	1	2	yes	—
368	#2280	C₂×D₄	1	2	yes	complemented
369	#2280	C₂×D₄	1	2	yes	complemented
370	#2280	C₂×D₄	1	8	yes	complemented
371	C₄×#117	C₂×D₄	1	4	yes	complemented
372	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
373	C₂×#344	C₂×D₄	1	8	yes	complemented
374	#1740	C₂×D₄	1	8	yes	complemented
375	C₂×H(3,ℤ/4)	C₂×D₄	1	8	yes	complemented
376	C₂⁶	#120	1	2	yes	—
377	C₂⁶	C₂²×D₄	1	1	yes	characteristic
378	C₂⁶	C₂²×D₄	1	1	yes	characteristic
379	C₂⁶	C₂²×D₄	1	1	yes	characteristic
380	C₂²×#41	#120	1	4	yes	complemented
381	C₂²×#41	#120	1	4	yes	complemented
382	C₂²×#41	C₂²×D₄	1	2	yes	—
383	C₂²×#41	C₂²×D₄	1	2	yes	—
384	C₂²×#41	C₂²×D₄	1	2	yes	—
385	C₂²×#41	C₂²×D₄	1	2	yes	—
386	C₂²×#41	C₂²×D₄	1	2	yes	—
387	C₂²×#41	C₂²×D₄	1	2	yes	—
388	C₂²×#41	C₂²×D₄	1	4	yes	—
389	C₂²×#41	C₂²×D₄	1	4	yes	—
390	C₂²×#41	C₂²×D₄	1	4	yes	—
391	C₂²×#41	C₂²×D₄	1	2	yes	—
392	C₂²×#41	C₂²×D₄	1	2	yes	—
393	C₂²×#41	C₂²×D₄	1	2	yes	—
394	C₂²×#41	C₂²×D₄	1	2	yes	—
395	C₂²×#41	C₂²×D₄	1	2	yes	—
396	C₂²×#41	C₂²×D₄	1	2	yes	—
397	C₂²×#41	C₂²×D₄	1	2	yes	—
398	C₂²×#41	C₂×#41	1	2	yes	—
399	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
400	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
401	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
402	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
403	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
404	C₂³×Q₈	#120	1	2	yes	—
405	C₂³×Q₈	#120	1	4	yes	complemented
406	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
407	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
408	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
409	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
410	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
411	C₂³×Q₈	H(5,𝔽₂)	1	2	yes	—
412	C₂³×D₄	#120	1	2	yes	—
413	C₂³×D₄	#120	1	2	yes	—
414	C₂³×D₄	#120	1	2	yes	—
415	C₂³×D₄	#120	1	4	yes	complemented
416	C₂³×D₄	C₂²×D₄	1	2	yes	—
417	C₂³×D₄	C₂²×D₄	1	2	yes	—
418	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
419	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
420	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
421	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
422	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
423	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
424	C₂⁴×C₄	#120	1	2	yes	—
425	C₂⁴×C₄	#120	1	2	yes	—
426	C₂⁴×C₄	#120	1	2	yes	—
427	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
428	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
429	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
430	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
431	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
432	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
433	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
434	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
435	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
436	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
437	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
438	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
439	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
440	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
441	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
442	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
443	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
444	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
445	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
446	C₂⁴×C₄	C₂×#41	1	2	yes	—
447	C₂⁴×C₄	H(5,𝔽₂)	1	4	yes	—
448	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
449	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
450	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
451	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
452	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
453	C₂³×C₈	H(5,𝔽₂)	1	4	yes	—
454	C₂×C₄⋊Q₈	#120	1	4	yes	complemented
455	C₂×#127	#120	1	4	yes	complemented
456	C₂×#124	#120	1	4	yes	complemented
457	C₂×#124	#120	1	4	yes	complemented
458	#525	#120	1	8	yes	—
459	#525	#120	1	8	yes	—
460	#525	#120	1	8	yes	—
461	#525	#120	1	8	yes	—
462	#525	#121	1	8	yes	—
463	#525	#121	1	8	yes	—
464	#525	#121	1	8	yes	—
465	#525	#121	1	8	yes	—
466	#525	#127	1	8	yes	—
467	#525	#127	1	8	yes	—
468	C₂×#123	#120	1	8	yes	—
469	C₂×#123	#120	1	4	yes	—
470	C₂×#123	#120	1	8	yes	—
471	C₂×#123	#120	1	4	yes	—
472	C₂×#123	#121	1	8	yes	—
473	C₂×#120	#120	1	8	yes	—
474	C₂×#120	#120	1	4	yes	—
475	C₂×#120	#120	1	8	yes	—
476	C₂×#120	#120	1	4	yes	—
477	C₂×#120	#121	1	8	yes	—
478	C₂×#117	#120	1	8	yes	complemented
479	C₂×#117	C₂²×D₄	1	4	yes	—
480	C₂×#117	C₂²×D₄	1	4	yes	—
481	C₂×#117	C₂²×D₄	1	2	yes	—
482	C₂×#117	C₂²×D₄	1	2	yes	—
483	C₂×#117	C₂²×D₄	1	2	yes	—
484	C₂×#117	C₂²×D₄	1	2	yes	—
485	C₂×#117	C₂²×D₄	1	2	yes	—
486	C₂×#117	C₂²×D₄	1	2	yes	—
487	C₂×#117	C₂²×D₄	1	2	yes	—
488	C₂×#117	C₂²×D₄	1	2	yes	—
489	C₂×#117	C₂²×D₄	1	2	yes	—
490	C₂×#117	C₂²×D₄	1	2	yes	—
491	C₂×#117	C₂²×D₄	1	2	yes	—
492	C₂×#117	C₂²×D₄	1	2	yes	—
493	C₂×#117	C₂²×D₄	1	2	yes	—
494	C₂×#117	C₂²×D₄	1	2	yes	—
495	C₂×#117	C₂²×D₄	1	2	yes	—
496	C₂×#117	C₂²×D₄	1	2	yes	—
497	C₂×#117	C₂²×D₄	1	2	yes	—
498	C₂×#117	C₂²×D₄	1	4	yes	—
499	C₂×#117	C₂²×D₄	1	4	yes	—
500	C₂×#117	C₂²×D₄	1	4	yes	—
501	C₂×#117	C₂×#41	1	2	yes	—
502	C₂×#117	H(5,𝔽₂)	1	4	yes	—
503	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
504	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
505	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
506	C₂²×C₄²	#120	1	8	yes	complemented
507	C₂²×C₄²	C₂²×D₄	1	2	yes	—
508	C₂²×C₄²	C₂²×D₄	1	2	yes	—
509	C₂²×C₄²	C₂²×D₄	1	2	yes	—
510	C₂²×C₄²	C₂²×D₄	1	2	yes	—
511	C₂²×C₄²	H(5,𝔽₂)	1	4	yes	—
512	#391	#120	1	8	yes	complemented
513	#390	#120	1	8	yes	complemented
514	C₂⁵	C₂×#120	1	2	yes	—
515	C₂⁵	C₂×#120	1	2	yes	—
516	C₂⁵	C₂×#120	1	1	yes	characteristic
517	C₂⁵	C₂×#120	1	1	yes	characteristic
518	C₂⁵	C₂×#120	1	1	yes	characteristic
519	C₂⁵	C₂×#120	1	2	yes	—
520	C₂⁵	C₂×#120	1	1	yes	characteristic
521	C₂⁵	C₂×#120	1	2	yes	—
522	C₂⁵	C₂×#121	1	2	yes	—
523	C₂⁵	D₄²	1	4	yes	—
524	C₂⁵	C₂³×D₄	1	1	yes	characteristic
525	C₂×#41	C₂×#120	1	4	yes	—
526	C₂×#41	C₂×#120	1	4	yes	—
527	C₂×#41	C₂×#121	1	4	yes	—
528	C₂×#41	C₂×#121	1	4	yes	—
529	C₂×#41	C₂×#127	1	4	yes	—
530	C₂×#41	#534	1	4	yes	—
531	C₂×#41	#534	1	4	yes	—
532	C₂×#41	#534	1	4	yes	—
533	C₂×#41	#535	1	4	yes	—
534	C₂×#41	#535	1	4	yes	—
535	C₂×#41	D₄²	1	8	yes	—
536	C₂×#41	D₄²	1	4	yes	—
537	C₂×#41	D₄²	1	4	yes	—
538	C₂×#41	D₄²	1	4	yes	—
539	C₂×#41	D₄²	1	4	yes	—
540	C₂×#41	D₄²	1	4	yes	—
541	C₂×#41	D₄²	1	4	yes	—
542	C₂×#41	#546	1	4	yes	—
543	C₂×#41	#546	1	4	yes	—
544	C₂²×Q₈	C₂×#120	1	2	yes	—
545	C₂²×Q₈	C₂×#120	1	2	yes	—
546	C₂²×Q₈	C₂×#120	1	2	yes	—
547	C₂²×Q₈	C₂×#120	1	2	yes	—
548	C₂²×Q₈	C₂×#120	1	2	yes	—
549	C₂²×Q₈	D₄²	1	4	yes	—
550	C₂²×Q₈	D₄²	1	2	yes	—
551	C₂²×Q₈	D₄²	1	2	yes	—
552	C₂²×Q₈	D₄²	1	2	yes	—
553	C₂²×Q₈	D₄²	1	4	yes	complemented
554	C₂²×Q₈	#546	1	2	yes	—
555	C₂²×D₄	C₂×#120	1	4	yes	—
556	C₂²×D₄	C₂×#120	1	4	yes	—
557	C₂²×D₄	C₂×#120	1	4	yes	—
558	C₂²×D₄	C₂×#120	1	2	yes	—
559	C₂²×D₄	C₂×#120	1	2	yes	—
560	C₂²×D₄	C₂×#120	1	2	yes	—
561	C₂²×D₄	C₂×#120	1	2	yes	—
562	C₂²×D₄	C₂×#120	1	2	yes	—
563	C₂²×D₄	C₂×#121	1	4	yes	—
564	C₂²×D₄	#534	1	4	yes	—
565	C₂²×D₄	#534	1	4	yes	—
566	C₂²×D₄	D₄²	1	4	yes	—
567	C₂²×D₄	D₄²	1	2	yes	—
568	C₂²×D₄	D₄²	1	2	yes	—
569	C₂²×D₄	D₄²	1	2	yes	—
570	C₂²×D₄	D₄²	1	4	yes	complemented
571	C₂²×D₄	#546	1	2	yes	—
572	C₂³×C₄	C₂×#120	1	2	yes	—
573	C₂³×C₄	C₂×#120	1	2	yes	—
574	C₂³×C₄	C₂×#120	1	1	yes	characteristic
575	C₂³×C₄	C₂×#120	1	2	yes	—
576	C₂³×C₄	C₂×#120	1	1	yes	characteristic
577	C₂³×C₄	C₂×#120	1	2	yes	—
578	C₂³×C₄	C₂×#120	1	2	yes	—
579	C₂³×C₄	C₂×#120	1	1	yes	characteristic
580	C₂³×C₄	C₂×#120	1	1	yes	characteristic
581	C₂³×C₄	C₂×#120	1	2	yes	—
582	C₂³×C₄	C₂×#120	1	2	yes	—
583	C₂³×C₄	C₂×#120	1	2	yes	—
584	C₂³×C₄	C₂×#120	1	4	yes	—
585	C₂³×C₄	C₂×#120	1	4	yes	—
586	C₂³×C₄	C₂×#121	1	2	yes	—
587	C₂³×C₄	C₂×#121	1	2	yes	—
588	C₂³×C₄	C₂×#121	1	2	yes	—
589	C₂³×C₄	C₂×#121	1	2	yes	—
590	C₂³×C₄	C₂×#121	1	2	yes	—
591	C₂³×C₄	C₂×#127	1	2	yes	—
592	C₂³×C₄	C₂×#127	1	2	yes	—
593	C₂³×C₄	#534	1	2	yes	—
594	C₂³×C₄	#534	1	2	yes	—
595	C₂³×C₄	D₄²	1	4	yes	—
596	C₂³×C₄	D₄²	1	4	yes	—
597	C₂³×C₄	D₄²	1	4	yes	—
598	C₂³×C₄	D₄²	1	4	yes	—
599	C₂³×C₄	D₄²	1	4	yes	—
600	C₂³×C₄	D₄²	1	4	yes	—
601	C₂³×C₄	#546	1	4	yes	—
602	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
603	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
604	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
605	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
606	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
607	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
608	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
609	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
610	C₂³×C₄	C₂³×D₄	1	2	yes	—
611	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
612	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
613	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
614	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
615	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
616	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
617	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
618	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
619	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
620	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
621	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
622	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
623	C₂³×C₄	#585	1	2	yes	—
624	C₂²×C₈	D₄²	1	8	yes	complemented
625	#123	#392	1	16	yes	—
626	#123	#392	1	16	yes	—
627	#120	#392	1	16	yes	—
628	#120	#392	1	16	yes	—
629	#117	C₂×#120	1	4	yes	—
630	#117	C₂×#120	1	4	yes	—
631	#117	C₂×#121	1	4	yes	—
632	#117	C₂×#121	1	4	yes	—
633	#117	C₂×#127	1	4	yes	—
634	#117	#534	1	4	yes	—
635	#117	D₄²	1	8	yes	—
636	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
637	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
638	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
639	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
640	C₂×C₂²⋊C₄	C₂×#121	1	4	yes	—
641	C₂×C₄²	C₂×#120	1	4	yes	—
642	C₂×C₄²	C₂×#120	1	4	yes	—
643	C₂×C₄²	C₂×#120	1	4	yes	—
644	C₂×C₄²	C₂×#120	1	4	yes	—
645	C₂×C₄²	D₄²	1	8	yes	—
646	C₂×C₄²	D₄²	1	8	yes	complemented
647	C₂⁴	C₂×#392	1	2	yes	—
648	C₂⁴	C₂×#392	1	2	yes	—
649	C₂⁴	#2403	1	2	yes	—
650	C₂⁴	#2403	1	2	yes	—
651	C₂⁴	#2403	1	4	yes	—
652	C₂⁴	#2410	1	4	yes	—
653	C₂⁴	#2846	1	4	yes	—
654	C₂⁴	C₂²×#120	1	1	yes	characteristic
655	C₂⁴	C₂²×#120	1	1	yes	characteristic
656	C₂⁴	C₂²×#120	1	1	yes	characteristic
657	C₂⁴	C₂²×#120	1	1	yes	characteristic
658	C₂⁴	C₂²×#121	1	1	yes	characteristic
659	C₂⁴	C₂×#534	1	1	yes	characteristic
660	C₂⁴	C₂×#534	1	1	yes	characteristic
661	C₂⁴	C₂×D₄²	1	2	yes	—
662	C₂⁴	#3484	1	2	yes	—
663	C₂⁴	#3484	1	2	yes	—
664	C₂⁴	#3496	1	2	yes	—
665	C₂×Q₈	#2403	1	4	yes	—
666	C₂×Q₈	#2403	1	4	yes	—
667	C₂×Q₈	#2408	1	4	yes	—
668	C₂×Q₈	#2410	1	4	yes	—
669	C₂×Q₈	#2433	1	4	yes	—
670	C₂×D₄	C₂×#392	1	8	yes	—
671	C₂×D₄	#2403	1	4	yes	—
672	C₂×D₄	#2403	1	4	yes	—
673	C₂×D₄	#2403	1	8	yes	—
674	C₂×D₄	#2408	1	4	yes	—
675	C₂×D₄	#2410	1	4	yes	—
676	C₂×D₄	#2410	1	8	yes	—
677	C₂×D₄	#2433	1	4	yes	—
678	C₂×D₄	#2613	1	8	yes	—
679	C₂²×C₄	C₂×#392	1	2	yes	—
680	C₂²×C₄	C₂×#392	1	2	yes	—
681	C₂²×C₄	#2403	1	2	yes	—
682	C₂²×C₄	#2403	1	2	yes	—
683	C₂²×C₄	#2403	1	8	yes	—
684	C₂²×C₄	#2403	1	4	yes	—
685	C₂²×C₄	#2408	1	8	yes	—
686	C₂²×C₄	#2410	1	8	yes	—
687	C₂²×C₄	#2410	1	4	yes	—
688	C₂²×C₄	#2433	1	8	yes	—
689	C₂²×C₄	#2846	1	4	yes	—
690	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
691	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
692	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
693	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
694	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
695	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
696	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
697	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
698	C₂²×C₄	C₂²×#127	1	1	yes	characteristic
699	C₂²×C₄	C₂×#534	1	1	yes	characteristic
700	C₂²×C₄	C₂×#534	1	1	yes	characteristic
701	C₂²×C₄	C₂×#534	1	1	yes	characteristic
702	C₂²×C₄	C₂×#534	1	1	yes	characteristic
703	C₂²×C₄	C₂×#534	1	1	yes	characteristic
704	C₂²×C₄	C₂×#535	1	1	yes	characteristic
705	C₂²×C₄	C₂×#535	1	1	yes	characteristic
706	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄²	1	2	yes	—
710	C₂²×C₄	C₂×D₄²	1	2	yes	—
711	C₂²×C₄	C₂×D₄²	1	2	yes	—
712	C₂²×C₄	C₂×D₄²	1	2	yes	—
713	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
714	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
715	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄²	1	2	yes	—
718	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
719	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄²	1	2	yes	—
721	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
722	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
723	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
724	C₂²×C₄	C₂×D₄²	1	2	yes	—
725	C₂²×C₄	C₂×D₄²	1	2	yes	—
726	C₂²×C₄	C₂×#546	1	1	yes	characteristic
727	C₂²×C₄	C₂×#546	1	1	yes	characteristic
728	C₂²×C₄	C₂×#546	1	1	yes	characteristic
729	C₂²×C₄	C₂×#546	1	1	yes	characteristic
730	C₂²×C₄	D₄×#41	1	2	yes	—
731	C₂²×C₄	#3484	1	1	yes	characteristic
732	C₂²×C₄	#3484	1	2	yes	—
733	C₂²×C₄	#3484	1	1	yes	characteristic
734	C₂²×C₄	#3484	1	2	yes	—
735	C₂²×C₄	#3484	1	1	yes	characteristic
736	C₂²×C₄	#3484	1	2	yes	—
737	C₂²×C₄	#3484	1	2	yes	—
738	C₂²×C₄	#3484	1	2	yes	—
739	C₂²×C₄	#3484	1	2	yes	—
740	C₂²×C₄	#3484	1	2	yes	—
741	C₂²×C₄	#3484	1	2	yes	—
742	C₂²×C₄	#3484	1	2	yes	—
743	C₂²×C₄	#3484	1	2	yes	—
744	C₂²×C₄	#3484	1	2	yes	—
745	C₂²×C₄	#3484	1	2	yes	—
746	C₂²×C₄	#3484	1	2	yes	—
747	C₂²×C₄	#3484	1	2	yes	—
748	C₂²×C₄	#3484	1	2	yes	—
749	C₂²×C₄	#3485	1	1	yes	characteristic
750	C₂²×C₄	#3488	1	2	yes	—
751	C₂²×C₄	#3488	1	2	yes	—
752	C₂²×C₄	#3488	1	2	yes	—
753	C₂²×C₄	#3488	1	2	yes	—
754	C₂²×C₄	#3488	1	2	yes	—
755	C₂²×C₄	#3496	1	2	yes	—
756	C₂²×C₄	#3496	1	2	yes	—
757	C₂²×C₄	#3496	1	2	yes	—
758	C₂²×C₄	#3496	1	2	yes	—
759	C₂²×C₄	#3498	1	2	yes	—
760	C₂²×C₄	#3498	1	2	yes	—
761	C₂²×C₄	#3498	1	2	yes	—
762	C₂²×C₄	#3498	1	2	yes	—
763	C₂²×C₄	#3519	1	2	yes	—
764	C₂²×C₄	#3519	1	2	yes	—
765	C₂²×C₄	#3519	1	2	yes	—
766	C₂²×C₄	#3532	1	2	yes	—
767	C₂²×C₄	#3532	1	2	yes	—
768	C₂²×C₄	#3532	1	2	yes	—
769	C₂²×C₄	#3532	1	2	yes	—
770	C₂²×C₄	#3534	1	2	yes	—
771	C₂²×C₄	#3534	1	2	yes	—
772	C₂²×C₄	#3537	1	2	yes	—
773	C₂²×C₄	#3537	1	2	yes	—
774	C₂²×C₄	#3537	1	2	yes	—
775	C₂²×C₄	#3542	1	2	yes	—
776	C₂²×C₄	#3543	1	2	yes	—
777	C₂²×C₄	#3543	1	2	yes	—
778	C₂²⋊C₄	C₂×#392	1	8	yes	—
779	C₄²	#2403	1	8	yes	—
780	C₂³	#14715	1	8	yes	—
781	C₂³	C₂²×#392	1	1	yes	characteristic
782	C₂³	C₂×#2613	1	1	yes	characteristic
783	C₂³	C₂×#2403	1	1	yes	characteristic
784	C₂³	C₂×#2403	1	1	yes	characteristic
785	C₂³	C₂×#2403	1	1	yes	characteristic
786	C₂³	C₂×#2410	1	1	yes	characteristic
787	C₂³	C₂×#2410	1	1	yes	characteristic
788	C₂³	#34980	1	1	yes	characteristic
789	C₂³	#35346	1	1	yes	characteristic
790	C₂³	#35347	1	1	yes	characteristic
791	C₂³	#35680	1	2	yes	—
792	C₂³	#35680	1	2	yes	—
793	C₂³	#35680	1	2	yes	—
794	C₂³	#35691	1	2	yes	—
795	C₂³	D₄×#120	1	2	yes	—
796	C₂³	D₄×#120	1	2	yes	—
797	C₂³	D₄×#120	1	2	yes	—
798	C₂³	D₄×#121	1	2	yes	—
799	C₂³	C₂×#2846	1	1	yes	characteristic
800	C₂³	#37644	1	2	yes	—
801	C₂³	#37672	1	2	yes	—
802	C₂³	#40484	1	2	yes	—
803	C₂³	#40584	1	2	yes	—
804	C₂×C₄	#14715	1	8	yes	—
805	C₂×C₄	C₂×#2403	1	1	yes	characteristic
806	C₂×C₄	C₂×#2403	1	1	yes	characteristic
807	C₂×C₄	C₂×#2403	1	1	yes	characteristic
808	C₂×C₄	C₂×#2403	1	1	yes	characteristic
809	C₂×C₄	C₂×#2410	1	1	yes	characteristic
810	C₂×C₄	C₂×#2410	1	1	yes	characteristic
811	C₂×C₄	C₂×#2408	1	1	yes	characteristic
812	C₂×C₄	C₂×#2408	1	1	yes	characteristic
813	C₂×C₄	C₂×#2433	1	1	yes	characteristic
814	C₂×C₄	C₂×#2433	1	1	yes	characteristic
815	C₂×C₄	#34980	1	1	yes	characteristic
816	C₂×C₄	#34980	1	1	yes	characteristic
817	C₂×C₄	#35346	1	1	yes	characteristic
818	C₂×C₄	#35347	1	1	yes	characteristic
819	C₂×C₄	#35512	1	1	yes	characteristic
820	C₂×C₄	#35527	1	1	yes	characteristic
821	C₂×C₄	#35680	1	2	yes	—
822	C₂×C₄	#35680	1	2	yes	—
823	C₂×C₄	#35680	1	2	yes	—
824	C₂×C₄	#35691	1	2	yes	—
825	C₂×C₄	#35691	1	2	yes	—
826	C₂×C₄	#35921	1	2	yes	—
827	C₂×C₄	D₄×#120	1	1	yes	characteristic
828	C₂×C₄	D₄×#120	1	1	yes	characteristic
829	C₂×C₄	D₄×#120	1	2	yes	—
830	C₂×C₄	D₄×#120	1	2	yes	—
831	C₂×C₄	D₄×#120	1	2	yes	—
832	C₂×C₄	D₄×#120	1	1	yes	characteristic
833	C₂×C₄	D₄×#121	1	2	yes	—
834	C₂×C₄	D₄×#121	1	2	yes	—
835	C₂×C₄	D₄×#127	1	2	yes	—
836	C₂×C₄	#36212	1	1	yes	characteristic
837	C₂×C₄	#37644	1	1	yes	characteristic
838	C₂×C₄	#37644	1	1	yes	characteristic
839	C₂×C₄	#37644	1	1	yes	characteristic
840	C₂×C₄	#37644	1	2	yes	—
841	C₂×C₄	#37644	1	1	yes	characteristic
842	C₂×C₄	#37646	1	1	yes	characteristic
843	C₂×C₄	#37646	1	1	yes	characteristic
844	C₂×C₄	#37650	1	2	yes	—
845	C₂×C₄	#37672	1	2	yes	—
846	C₂×C₄	#37674	1	2	yes	—
847	C₂×C₄	#38020	1	1	yes	characteristic
848	C₂×C₄	#38020	1	1	yes	characteristic
849	C₂×C₄	#38904	1	1	yes	characteristic
850	C₂×C₄	#39336	1	1	yes	characteristic
851	C₂×C₄	#39336	1	1	yes	characteristic
852	C₂×C₄	#39338	1	1	yes	characteristic
853	C₂×C₄	#40484	1	2	yes	—
854	C₂×C₄	#40490	1	2	yes	—
855	C₂×C₄	#40584	1	2	yes	—
856	C₂×C₄	#40590	1	2	yes	—
857	C₂×C₄	#42996	1	2	yes	—
858	C₂×C₄	#42996	1	2	yes	—
859	C₂×C₄	#43001	1	2	yes	—
860	C₂×C₄	#43001	1	2	yes	—
861	C₂×C₄	#43001	1	2	yes	—
862	C₂×C₄	#43095	1	2	yes	—
863	C₂×C₄	#43095	1	2	yes	—
864	C₂×C₄	#43098	1	2	yes	—
865	C₂×C₄	#43098	1	2	yes	—
866	C₂×C₄	#43886	1	2	yes	—
867	C₂×C₄	#43886	1	2	yes	—
868	C₂×C₄	#43893	1	2	yes	—
869	C₂×C₄	#58990	1	2	yes	—
870	C₂×C₄	#58990	1	2	yes	—
871	C₂×C₄	#58990	1	2	yes	—
872	C₂×C₄	#58990	1	2	yes	—
873	C₂×C₄	#58997	1	2	yes	—
874	C₂×C₄	#58997	1	2	yes	—
875	C₂×C₄	#58997	1	2	yes	—
876	C₂×C₄	#59004	1	2	yes	—
877	C₂×C₄	#59123	1	2	yes	—
878	C₂×C₄	#59123	1	2	yes	—
879	C₂×C₄	#59126	1	2	yes	—
880	C₂×C₄	#59126	1	2	yes	—
881	C₂²	C₂×#14715	1	1	yes	characteristic
882	C₂²	#612424	1	1	yes	characteristic
883	C₂²	#647656	1	1	yes	characteristic
884	C₂²	#647714	1	1	yes	characteristic
885	C₂²	#686200	1	1	yes	characteristic
886	C₂²	#686258	1	1	yes	characteristic
887	C₂²	#772778	1	2	yes	—
888	C₂²	#772794	1	2	yes	—
889	C₂²	#1393169	1	2	yes	—
890	C₂²	D₄×#392	1	2	yes	—
891	C₂²	#4928938	1	1	yes	characteristic
892	C₄	#647656	1	1	yes	characteristic
893	C₄	#647663	1	1	yes	characteristic
894	C₄	#647714	1	1	yes	characteristic
895	C₄	#649038	1	1	yes	characteristic
896	C₄	#686200	1	1	yes	characteristic
897	C₄	#686258	1	1	yes	characteristic
898	C₄	#719096	1	1	yes	characteristic
899	C₄	#719140	1	1	yes	characteristic
900	C₄	#772778	1	2	yes	—
901	C₄	#772794	1	2	yes	—
902	C₄	#773762	1	2	yes	—
903	C₄	#773780	1	2	yes	—
904	C₂	#72216294	1	2	yes	—
905	C₂	#72233926	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#35527
commutator, Frattini, cosocle	C₂⁴×C₄	C₂⁵
socle	C₂²	#4928938
LCS	G ▷ C₂⁴×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72279945	C₂	semidirect
2. #72279925	C₂	semidirect
3. #72279907	C₂	semidirect
4. #72279624	C₂	semidirect
5. #72279500	C₂	semidirect
6. #72279469	C₂	semidirect
7. #72279412	C₂	semidirect
8. #72279381	C₂	semidirect
9. #72279346	C₂	semidirect
10. #72268516	C₂	semidirect
11. #72256165	C₂	semidirect
12. #72256073	C₂	semidirect
13. #72249727	C₂	semidirect
14. #72239343	C₂	semidirect
15. C₂×#359649	C₂	semidirect
16. #72239326	C₂	semidirect
17. C₂×#6437575	C₂	semidirect
18. C₂×#6431743	C₂	semidirect
19. #72237261	C₂	semidirect
20. #72237193	C₂	semidirect
21. C₂×#6437616	C₂	semidirect
22. C₂×#359507	C₂	semidirect
23. C₂×#393988	C₂	semidirect
24. C₂×#63090	C₂²	semidirect
27. C₂×#62811	C₂²	semidirect
29. C₂³×#525	C₂²	semidirect
31. C₂²×#3025	C₂²	semidirect
32. C₂×#60387	C₂²	semidirect
33. C₂×#60359	C₂²	semidirect
34. C₂×#60064	C₂²	semidirect
35. C₂×#60093	C₂²	semidirect
36. C₂×#60093	C₂²	semidirect
37. C₂×#36614	C₂²	semidirect
38. C₂×#36614	C₂²	semidirect
39. #7629144	C₂²	semidirect
41. #7629122	C₂²	semidirect
43. #7628650	C₂²	semidirect
44. #7628650	C₂²	semidirect
46. #7628649	C₂²	semidirect
48. #7625530	C₂²	semidirect
49. C₂×#23443	C₂²	semidirect
50. C₂×#23443	C₂²	semidirect
51. C₂×#23414	C₂²	semidirect
52. C₂×#23414	C₂²	semidirect
54. C₂²×#2010	C₂²	semidirect
55. C₂²×#2010	C₂²	semidirect
56. C₂²×#2010	C₂²	semidirect
57. C₂²×#2010	C₂²	semidirect
58. C₂²×#2010	C₂²	semidirect
59. C₂×#23412	C₂²	semidirect
60. #6431722	C₂²	semidirect
61. #6431698	C₂²	semidirect
62. C₂×#21012	C₂²	semidirect
63. C₂×#21009	C₂²	semidirect
64. C₂×#20998	C₂²	semidirect
65. C₂×#20983	C₂²	semidirect
66. C₂×#20979	C₂²	semidirect
69. C₂²×#1891	C₂²	semidirect
70. C₂²×#1891	C₂²	semidirect
72. C₂×#20959	C₂²	semidirect
73. C₂×#20947	C₂²	semidirect
74. C₂×#20623	C₂²	semidirect
75. C₂×#20623	C₂²	semidirect
76. #6370746	C₂²	semidirect
77. C₂×#20605	C₂²	semidirect
78. C₂×#20591	C₂²	semidirect
79. C₂×#20584	C₂²	semidirect
80. C₂×#20579	C₂²	semidirect
81. C₂×#20338	C₂²	semidirect
82. #357769	C₂²	semidirect
83. #357756	C₂²	semidirect
84. #357593	C₂²	semidirect
85. #357577	C₂²	semidirect
86. #357564	C₂²	semidirect
87. C₂×#11003	C₂²	semidirect
88. C₂×#11000	C₂²	semidirect
89. C₂×#11000	C₂²	semidirect
90. #357556	C₂²	semidirect
91. C₂×#10994	C₂²	semidirect
92. C₂×#10994	C₂²	semidirect
93. C₂×#10994	C₂²	semidirect
94. C₂×#10994	C₂²	semidirect
95. C₂×#10994	C₂²	semidirect
96. C₂×#10994	C₂²	semidirect
97. C₂×#10994	C₂²	semidirect
98. C₂×#10994	C₂²	semidirect
99. C₂×#10993	C₂²	semidirect
100. C₂×#10993	C₂²	semidirect
101. #357478	C₂²	semidirect
102. #357440	C₂²	semidirect
103. #357440	C₂²	semidirect
104. #354116	C₂²	semidirect
105. C₂×#10783	C₂²	semidirect
106. #353442	C₂²	semidirect
107. #353422	C₂²	semidirect
108. #353420	C₂²	semidirect
109. C₂×#10738	C₂²	semidirect
110. #353324	C₂²	semidirect
111. #353324	C₂²	semidirect
112. C₂×#10716	C₂²	semidirect
113. #124041	C₂²	semidirect
114. #123916	C₂²	semidirect
115. #123610	C₂²	semidirect
116. #123598	C₂²	semidirect
117. #123586	C₂²	semidirect
118. #123568	C₂²	semidirect
119. #123531	C₂²	semidirect
120. #123531	C₂²	semidirect
121. #123508	C₂²	semidirect
122. #123457	C₂²	semidirect
133. C₂×#3487	D₄	semidirect
134. C₂×#3486	D₄	semidirect
135. C₂×#3485	D₄	semidirect
136. C₂×#3484	D₄	semidirect
137. C₂×#3449	D₄	semidirect
146. C₂²×#525	D₄	semidirect
168. C₂×#3025	D₄	semidirect
198. #35659	D₄	semidirect
199. #35512	D₄	semidirect
200. #35242	D₄	semidirect
201. #35222	D₄	semidirect
202. #35149	D₄	semidirect
203. #35149	D₄	semidirect
204. #34743	D₄	semidirect
205. #34065	D₄	semidirect
213. C₄×#525	D₄	semidirect
221. C₂×#2010	D₄	semidirect
222. C₂×#1891	D₄	semidirect
223. #20959	D₄	semidirect
246. C₂×#585	C₂×D₄	semidirect
256. C₂³×#41	C₂×D₄	semidirect
257. C₂³×#41	C₂×D₄	semidirect
265. C₂⁴×Q₈	C₂×D₄	semidirect
268. C₂⁴×D₄	C₂×D₄	semidirect
276. C₂×#575	C₂×D₄	semidirect
277. C₂×#568	C₂×D₄	semidirect
285. C₂×#536	C₂×D₄	semidirect
289. C₂×#535	C₂×D₄	semidirect
309. C₂×#525	C₂×D₄	semidirect
310. C₂×#525	C₂×D₄	semidirect
311. C₂×#525	C₂×D₄	semidirect
312. C₂×#525	C₂×D₄	semidirect
313. C₂×#525	C₂×D₄	semidirect
314. C₂×#525	C₂×D₄	semidirect
320. C₂²×C₂²⋊Q₈	C₂×D₄	semidirect
321. C₂²×#121	C₂×D₄	semidirect
326. #3428	C₂×D₄	semidirect
327. C₂×#519	C₂×D₄	semidirect
328. C₂×#518	C₂×D₄	semidirect
333. C₂²×#117	C₂×D₄	semidirect
345. C₂³×C₄²	C₂×D₄	semidirect
346. C₂×#421	C₂×D₄	semidirect
347. C₂×#421	C₂×D₄	semidirect
348. C₂×#413	C₂×D₄	semidirect
349. C₂×#410	C₂×D₄	semidirect
350. C₂×#410	C₂×D₄	semidirect
351. C₂×#410	C₂×D₄	semidirect
352. C₂×#407	C₂×D₄	semidirect
353. C₂×#407	C₂×D₄	semidirect
355. #2311	C₂×D₄	semidirect
358. #2310	C₂×D₄	semidirect
361. #2309	C₂×D₄	semidirect
363. #2297	C₂×D₄	semidirect
364. #2296	C₂×D₄	semidirect
365. #2296	C₂×D₄	semidirect
368. #2280	C₂×D₄	semidirect
369. #2280	C₂×D₄	semidirect
370. #2280	C₂×D₄	semidirect
371. C₄×#117	C₂×D₄	semidirect
372. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
373. C₂×#344	C₂×D₄	semidirect
374. #1740	C₂×D₄	semidirect
375. C₂×H(3,ℤ/4)	C₂×D₄	semidirect
380. C₂²×#41	#120	semidirect
381. C₂²×#41	#120	semidirect
405. C₂³×Q₈	#120	semidirect
415. C₂³×D₄	#120	semidirect
454. C₂×C₄⋊Q₈	#120	semidirect
455. C₂×#127	#120	semidirect
456. C₂×#124	#120	semidirect
457. C₂×#124	#120	semidirect
478. C₂×#117	#120	semidirect
506. C₂²×C₄²	#120	semidirect
512. #391	#120	semidirect
513. #390	#120	semidirect
553. C₂²×Q₈	D₄²	semidirect
570. C₂²×D₄	D₄²	semidirect
624. C₂²×C₈	D₄²	semidirect
646. C₂×C₄²	D₄²	semidirect

Maximal subgroups

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

subgroup	index
#72279945	2
#72279925	2
#72279907	2
#72279624	2
#72279500	2
#72279469	2
#72279412	2
#72279381	2
#72279346	2
#72268516	2
#72256165	2
#72256073	2
#72249727	2
#72239343	2
C₂×#359649	2
#72239326	2
C₂×#6437575	2
C₂×#6431743	2
#72237261	2
#72237193	2
C₂×#6437616	2
C₂×#359507	2
C₂×#393988	2