Subgroups — #72335068

Order 2048.

At least 6066 conjugacy classes of subgroups; only the 8264 normal subgroups are shown.

The subgroup lattice has 789 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72335060	C₂	1	1	yes	maximal, characteristic, complemented
2	#72335059	C₂	1	1	yes	maximal, characteristic, complemented
3	#72334957	C₂	1	2	yes	maximal, complemented
4	C₂×#636791	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#613191	C₂	1	1	yes	maximal, characteristic, complemented
6	#72323673	C₂	1	2	yes	maximal, complemented
7	#72323618	C₂	1	4	yes	maximal, complemented
8	#72323618	C₂	1	2	yes	maximal, complemented
9	#72317006	C₂	1	8	yes	maximal, complemented
10	#72302231	C₂	1	1	yes	maximal, characteristic, complemented
11	#72287890	C₂	1	2	yes	maximal, complemented
12	#72287889	C₂	1	4	yes	maximal, complemented
13	C₂×#635984	C₂	1	2	yes	maximal, complemented
14	#72251033	C₂	1	16	yes	maximal, complemented
15	#72250308	C₂	1	2	yes	maximal, complemented
16	C₂²×#14715	C₂	1	1	yes	maximal, characteristic, complemented
17	#72240113	C₂	1	2	yes	maximal, complemented
18	#72233926	C₂	1	8	yes	maximal, complemented
19	C₂×#612424	C₂	1	2	yes	maximal, complemented
20	C₂⁴×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂⁶×D₄	C₂²	1	1	yes	characteristic
22	C₂⁶×D₄	C₂²	1	2	yes	—
23	C₂⁶×D₄	C₂²	1	1	yes	characteristic, complemented
24	C₂³×D₄²	C₂²	1	8	yes	—
25	C₂³×D₄²	C₂²	1	8	yes	complemented
26	C₂⁴×#127	C₂²	1	1	yes	characteristic, complemented
27	C₂⁴×#121	C₂²	1	1	yes	characteristic
28	C₂⁴×#121	C₂²	1	1	yes	characteristic, complemented
29	C₂⁴×#121	C₂²	1	2	yes	complemented
30	C₂⁴×#120	C₂²	1	2	yes	—
31	C₂⁴×#120	C₂²	1	2	yes	complemented
32	C₂⁴×#120	C₂²	1	2	yes	complemented
33	C₂⁴×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂⁴×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
35	C₂²×#2846	C₂²	1	4	yes	complemented
36	C₂²×#2405	C₂²	1	1	yes	characteristic, complemented
37	C₂²×#2403	C₂²	1	1	yes	characteristic
38	C₂²×#2403	C₂²	1	2	yes	complemented
39	C₂²×#2403	C₂²	1	8	yes	complemented
40	C₂²×#2613	C₂²	1	4	yes	complemented
41	C₂³×#392	C₂²	1	4	yes	complemented
42	C₂³×#386	C₂²	1	1	yes	characteristic, complemented
43	C₂³×#379	C₂²	1	2	yes	complemented
44	C₂×#16258	C₂²	1	8	yes	complemented
45	C₂×#16249	C₂²	1	16	yes	complemented
46	C₂×#15091	C₂²	1	2	yes	complemented
47	C₂×#15091	C₂²	1	2	yes	complemented
48	C₂×#14913	C₂²	1	4	yes	complemented
49	C₂×#14911	C₂²	1	2	yes	complemented
50	C₂×#14911	C₂²	1	4	yes	complemented
51	C₂×#14730	C₂²	1	8	yes	complemented
52	C₂×#14718	C₂²	1	8	yes	complemented
53	C₂×#14716	C₂²	1	4	yes	complemented
54	C₂×#14715	C₂²	1	2	yes	—
55	C₂×#14715	C₂²	1	8	yes	complemented
56	C₂×#14715	C₂²	1	16	yes	complemented
57	C₂×#14715	C₂²	1	16	yes	complemented
58	C₂×#14715	C₂²	1	2	yes	complemented
59	C₂×#14715	C₂²	1	4	yes	complemented
60	C₂×#14715	C₂²	1	4	yes	complemented
61	C₂×#14715	C₂²	1	4	yes	complemented
62	C₂×#14715	C₂²	1	4	yes	complemented
63	C₂×#14715	C₂²	1	2	yes	complemented
64	C₂×#14715	C₂²	1	8	yes	complemented
65	C₂×#14706	C₂²	1	2	yes	complemented
66	C₂×#14694	C₂²	1	2	yes	complemented
67	C₂×#14694	C₂²	1	4	yes	complemented
68	C₂×#14681	C₂²	1	1	yes	characteristic, complemented
69	C₂×#14681	C₂²	1	1	yes	characteristic, complemented
70	C₂×#14679	C₂²	1	2	yes	complemented
71	C₂×#14679	C₂²	1	2	yes	complemented
72	C₂×#14679	C₂²	1	4	yes	complemented
73	C₂×#14335	C₂²	1	8	yes	complemented
74	C₂×#14335	C₂²	1	4	yes	complemented
75	C₂×#14255	C₂²	1	4	yes	complemented
76	C₂×#14255	C₂²	1	4	yes	complemented
77	C₂×#14016	C₂²	1	4	yes	complemented
78	C₂×#13967	C₂²	1	4	yes	complemented
79	C₂×#13869	C₂²	1	1	yes	characteristic, complemented
80	C₂×#13869	C₂²	1	2	yes	complemented
81	C₂×#13867	C₂²	1	1	yes	characteristic
82	C₂×#13867	C₂²	1	2	yes	—
83	C₂×#13867	C₂²	1	2	yes	complemented
84	C₂×#13867	C₂²	1	2	yes	complemented
85	C₂×#13867	C₂²	1	2	yes	complemented
86	C₂×#13867	C₂²	1	8	yes	complemented
87	C₂×#13867	C₂²	1	16	yes	complemented
88	C₂²×#1438	C₂²	1	4	yes	complemented
89	C₂²×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
90	#158327	C₂²	1	16	yes	complemented
91	#158314	C₂²	1	16	yes	complemented
92	#156854	C₂²	1	32	yes	complemented
93	#156854	C₂²	1	16	yes	complemented
94	#156706	C₂²	1	32	yes	complemented
95	#156706	C₂²	1	16	yes	complemented
96	#156688	C₂²	1	32	yes	complemented
97	#156684	C₂²	1	32	yes	complemented
98	#155624	C₂²	1	8	yes	complemented
99	#155622	C₂²	1	16	yes	complemented
100	#154634	C₂²	1	16	yes	complemented
101	#154467	C₂²	1	16	yes	complemented
102	#154255	C₂²	1	8	yes	complemented
103	#154195	C₂²	1	16	yes	complemented
104	#154160	C₂²	1	2	yes	complemented
105	#154160	C₂²	1	2	yes	complemented
106	#154130	C₂²	1	4	yes	complemented
107	#154130	C₂²	1	2	yes	complemented
108	#154098	C₂²	1	8	yes	complemented
109	#154094	C₂²	1	2	yes	complemented
110	#154094	C₂²	1	8	yes	complemented
111	#154094	C₂²	1	16	yes	complemented
112	#154094	C₂²	1	16	yes	complemented
113	#154094	C₂²	1	2	yes	complemented
114	#154094	C₂²	1	4	yes	complemented
115	#154094	C₂²	1	4	yes	complemented
116	#154094	C₂²	1	4	yes	complemented
117	#154094	C₂²	1	4	yes	complemented
118	#154094	C₂²	1	2	yes	complemented
119	#154082	C₂²	1	2	yes	complemented
120	#154077	C₂²	1	4	yes	complemented
121	#154077	C₂²	1	2	yes	complemented
122	#153931	C₂²	1	4	yes	complemented
123	#153931	C₂²	1	4	yes	complemented
124	#153827	C₂²	1	8	yes	complemented
125	C₂⁸	C₂³	1	2	yes	—
126	C₂⁸	C₂³	1	2	yes	—
127	C₂⁵×D₄	D₄	1	16	yes	complemented
128	C₂⁵×D₄	D₄	1	32	yes	complemented
129	C₂⁵×D₄	C₂³	1	1	yes	characteristic
130	C₂⁵×D₄	C₂³	1	1	yes	characteristic
131	C₂⁵×D₄	C₂³	1	8	yes	—
132	C₂⁵×D₄	C₂³	1	1	yes	characteristic
133	C₂⁵×D₄	C₂³	1	8	yes	—
134	C₂⁵×D₄	C₂³	1	4	yes	—
135	C₂⁵×D₄	C₂³	1	4	yes	—
136	C₂⁵×D₄	C₂³	1	2	yes	—
137	C₂⁵×D₄	C₂³	1	1	yes	characteristic
138	C₂⁵×D₄	C₂³	1	2	yes	—
139	C₂⁵×D₄	C₂³	1	2	yes	—
140	C₂⁵×D₄	C₂³	1	2	yes	—
141	C₂⁵×D₄	C₂³	1	1	yes	characteristic
142	C₂⁵×D₄	C₂³	1	2	yes	—
143	C₂⁵×D₄	C₂³	1	8	yes	—
144	C₂⁵×D₄	C₂³	1	2	yes	—
145	C₂⁵×D₄	C₂³	1	4	yes	complemented
146	C₂⁶×C₄	C₂³	1	1	yes	characteristic
147	C₂⁶×C₄	C₂³	1	2	yes	—
148	C₂⁶×C₄	C₂³	1	1	yes	characteristic
149	C₂³×#127	C₂³	1	8	yes	—
150	C₂³×#123	C₂³	1	2	yes	—
151	C₂³×#121	D₄	1	16	yes	complemented
152	C₂³×#121	C₂³	1	16	yes	—
153	C₂³×#121	C₂³	1	8	yes	—
154	C₂³×#121	C₂³	1	4	yes	—
155	C₂³×#121	C₂³	1	4	yes	—
156	C₂³×#120	D₄	1	32	yes	complemented
157	C₂³×#120	C₂³	1	16	yes	—
158	C₂³×#120	C₂³	1	2	yes	—
159	C₂³×#120	C₂³	1	8	yes	—
160	C₂³×#120	C₂³	1	8	yes	—
161	C₂³×#120	C₂³	1	4	yes	—
162	C₂³×#120	C₂³	1	4	yes	—
163	C₂³×#120	C₂³	1	2	yes	—
164	C₂³×#120	C₂³	1	4	yes	—
165	C₂³×#120	C₂³	1	8	yes	complemented
166	C₂³×#120	C₂³	1	4	yes	complemented
167	C₂³×#120	C₂³	1	16	yes	complemented
168	C₂³×C₄×D₄	D₄	1	16	yes	complemented
169	C₂³×C₄×D₄	C₂³	1	8	yes	—
170	C₂³×C₄×D₄	C₂³	1	4	yes	—
171	C₂³×C₄×D₄	C₂³	1	4	yes	—
172	C₂⁴×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂⁴×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	complemented
182	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	complemented
183	C₂⁴×C₂²⋊C₄	C₂³	1	8	yes	complemented
184	C₂⁴×C₄²	C₂³	1	1	yes	characteristic
185	C₂²×#394	C₂³	1	4	yes	complemented
186	C₂²×#394	C₂³	1	16	yes	complemented
187	C₂²×#392	C₂³	1	8	yes	—
188	C₂²×#392	C₂³	1	4	yes	—
189	C₂²×#392	C₂³	1	8	yes	complemented
190	C₂²×#392	C₂³	1	16	yes	complemented
191	C₂²×#392	C₂³	1	16	yes	complemented
192	C₂²×#392	C₂³	1	16	yes	complemented
193	C₂²×#392	C₂³	1	16	yes	complemented
194	C₂²×#392	C₂³	1	8	yes	complemented
195	C₂²×#392	C₂³	1	16	yes	complemented
196	C₂²×#392	C₂³	1	8	yes	complemented
197	C₂²×#386	C₂³	1	2	yes	—
198	C₂²×#386	C₂³	1	4	yes	—
199	C₂²×#386	C₂³	1	2	yes	—
200	C₂²×#386	C₂³	1	2	yes	—
201	C₂²×#386	C₂³	1	2	yes	—
202	C₂²×#386	C₂³	1	4	yes	—
203	C₂²×#386	C₂³	1	8	yes	—
204	C₂²×#386	C₂³	1	2	yes	—
205	C₂²×#386	C₂³	1	4	yes	complemented
206	C₂²×#386	C₂³	1	4	yes	complemented
207	C₂²×#386	C₂³	1	16	yes	complemented
208	C₂²×#386	C₂³	1	8	yes	complemented
209	C₂²×#386	C₂³	1	8	yes	complemented
210	C₂²×#386	C₂³	1	8	yes	complemented
211	C₂²×#386	C₂³	1	8	yes	complemented
212	C₂²×#385	C₂³	1	2	yes	complemented
213	C₂²×#381	C₂³	1	4	yes	—
214	C₂²×#381	C₂³	1	2	yes	—
215	C₂²×#381	C₂³	1	4	yes	complemented
216	C₂²×#381	C₂³	1	4	yes	complemented
217	C₂²×#379	C₂³	1	1	yes	characteristic
218	C₂²×#379	C₂³	1	2	yes	—
219	C₂²×#379	C₂³	1	1	yes	characteristic
220	C₂²×#379	C₂³	1	4	yes	—
221	C₂²×#379	C₂³	1	4	yes	—
222	C₂²×#379	C₂³	1	4	yes	—
223	C₂²×#379	C₂³	1	4	yes	—
224	C₂²×#379	C₂³	1	4	yes	—
225	C₂²×#379	C₂³	1	4	yes	—
226	C₂²×#379	C₂³	1	2	yes	—
227	C₂²×#379	C₂³	1	4	yes	—
228	C₂²×#379	C₂³	1	4	yes	—
229	C₂²×#379	C₂³	1	4	yes	—
230	C₂²×#379	C₂³	1	4	yes	—
231	C₂²×#379	C₂³	1	2	yes	complemented
232	C₂²×#379	C₂³	1	8	yes	complemented
233	C₂²×#379	C₂³	1	16	yes	complemented
234	C₂²×#379	C₂³	1	8	yes	complemented
235	C₂²×#379	C₂³	1	8	yes	complemented
236	C₂²×#379	C₂³	1	8	yes	complemented
237	C₂²×#379	C₂³	1	8	yes	complemented
238	C₂²×#379	C₂³	1	32	yes	complemented
239	C₂³×#95	C₂³	1	2	yes	complemented
240	C₂³×#95	C₂³	1	4	yes	complemented
241	C₂×#1442	C₂³	1	8	yes	complemented
242	C₂×#1442	C₂³	1	8	yes	complemented
243	C₂×#1440	C₂³	1	8	yes	complemented
244	C₂×#1440	C₂³	1	4	yes	complemented
245	C₂×#1440	C₂³	1	16	yes	complemented
246	C₂×#1440	C₂³	1	16	yes	complemented
247	C₂×#1439	C₂³	1	8	yes	complemented
248	C₂×#1439	C₂³	1	8	yes	complemented
249	C₂×#1439	C₂³	1	16	yes	complemented
250	C₂×#1439	C₂³	1	8	yes	complemented
251	C₂×#1438	C₂³	1	16	yes	—
252	C₂×#1438	C₂³	1	8	yes	—
253	C₂×#1438	C₂³	1	8	yes	—
254	C₂×#1438	C₂³	1	4	yes	—
255	C₂×#1438	C₂³	1	16	yes	complemented
256	C₂×#1438	C₂³	1	8	yes	complemented
257	C₂×#1438	C₂³	1	16	yes	complemented
258	C₂×#1438	C₂³	1	16	yes	complemented
259	C₂×#1438	C₂³	1	16	yes	complemented
260	C₂×#1438	C₂³	1	16	yes	complemented
261	C₂×#1438	C₂³	1	8	yes	complemented
262	C₂×#1438	C₂³	1	16	yes	complemented
263	C₂×#1438	C₂³	1	8	yes	complemented
264	C₂×#1438	C₂³	1	8	yes	complemented
265	C₂×#1438	C₂³	1	16	yes	complemented
266	C₂×#1438	C₂³	1	8	yes	complemented
267	C₂×#1438	C₂³	1	8	yes	complemented
268	C₂×#1438	C₂³	1	32	yes	complemented
269	C₂×#1438	C₂³	1	32	yes	complemented
270	C₂×#1438	C₂³	1	32	yes	complemented
271	C₂×#1438	C₂³	1	32	yes	complemented
272	C₂×#1438	C₂³	1	16	yes	complemented
273	C₂×#1438	C₂³	1	32	yes	complemented
274	C₂×#1438	C₂³	1	16	yes	complemented
275	C₂×#1437	C₂³	1	8	yes	complemented
276	C₂×#1436	C₂³	1	8	yes	complemented
277	C₂×C₂²⋊#95	C₂³	1	4	yes	—
278	C₂×C₂²⋊#95	C₂³	1	2	yes	—
279	C₂×C₂²⋊#95	C₂³	1	2	yes	—
280	C₂×C₂²⋊#95	C₂³	1	2	yes	—
281	C₂×C₂²⋊#95	C₂³	1	4	yes	—
282	C₂×C₂²⋊#95	C₂³	1	4	yes	—
283	C₂×C₂²⋊#95	C₂³	1	2	yes	—
284	C₂×C₂²⋊#95	C₂³	1	2	yes	—
285	C₂×C₂²⋊#95	C₂³	1	4	yes	—
286	C₂×C₂²⋊#95	C₂³	1	4	yes	—
287	C₂×C₂²⋊#95	C₂³	1	2	yes	—
288	C₂×C₂²⋊#95	C₂³	1	2	yes	—
289	C₂×C₂²⋊#95	C₂³	1	2	yes	—
290	C₂×C₂²⋊#95	C₂³	1	4	yes	complemented
291	C₂×C₂²⋊#95	C₂³	1	8	yes	complemented
292	C₂×C₂²⋊#95	C₂³	1	4	yes	complemented
293	C₂×C₂²⋊#95	C₂³	1	8	yes	complemented
294	C₂×C₂²⋊#95	C₂³	1	4	yes	complemented
295	C₂×C₂²⋊#95	C₂³	1	4	yes	complemented
296	C₂×C₂²⋊#95	C₂³	1	16	yes	complemented
297	C₂×C₂²⋊#95	C₂³	1	32	yes	complemented
298	C₂×C₂²⋊#95	C₂³	1	16	yes	complemented
299	#7557	C₂³	1	16	yes	complemented
300	#7557	C₂³	1	16	yes	complemented
301	#7555	C₂³	1	32	yes	complemented
302	#7555	C₂³	1	16	yes	complemented
303	#7555	C₂³	1	32	yes	complemented
304	#7555	C₂³	1	32	yes	complemented
305	#7554	C₂³	1	16	yes	complemented
306	C₂⁷	C₂×D₄	1	16	yes	—
307	C₂⁷	C₂×D₄	1	16	yes	—
308	C₂⁷	C₂×D₄	1	16	yes	—
309	C₂⁷	C₂×D₄	1	16	yes	complemented
310	C₂⁷	C₂⁴	1	2	yes	—
311	C₂⁷	C₂⁴	1	1	yes	characteristic
312	C₂⁷	C₂⁴	1	1	yes	characteristic
313	C₂⁷	C₂⁴	1	4	yes	—
314	C₂⁷	C₂⁴	1	1	yes	characteristic
315	C₂⁷	C₂⁴	1	8	yes	—
316	C₂⁷	C₂⁴	1	2	yes	—
317	C₂⁷	C₂⁴	1	2	yes	—
318	C₂⁷	C₂⁴	1	4	yes	—
319	C₂⁴×D₄	C₂×D₄	1	8	yes	—
320	C₂⁴×D₄	C₂×D₄	1	8	yes	—
321	C₂⁴×D₄	C₂×D₄	1	16	yes	—
322	C₂⁴×D₄	C₂×D₄	1	64	yes	—
323	C₂⁴×D₄	C₂×D₄	1	32	yes	—
324	C₂⁴×D₄	C₂×D₄	1	32	yes	—
325	C₂⁴×D₄	C₂×D₄	1	16	yes	—
326	C₂⁴×D₄	C₂×D₄	1	8	yes	—
327	C₂⁴×D₄	C₂×D₄	1	16	yes	—
328	C₂⁴×D₄	C₂×D₄	1	16	yes	—
329	C₂⁴×D₄	C₂×D₄	1	16	yes	—
330	C₂⁴×D₄	C₂×D₄	1	16	yes	complemented
331	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
332	C₂⁴×D₄	C₂×D₄	1	16	yes	complemented
333	C₂⁴×D₄	C₂×D₄	1	16	yes	complemented
334	C₂⁴×D₄	C₂×D₄	1	64	yes	complemented
335	C₂⁴×D₄	C₂×D₄	1	16	yes	complemented
336	C₂⁴×D₄	C₂⁴	1	2	yes	—
337	C₂⁴×D₄	C₂⁴	1	2	yes	—
338	C₂⁴×D₄	C₂⁴	1	4	yes	—
339	C₂⁴×D₄	C₂⁴	1	4	yes	—
340	C₂⁴×D₄	C₂⁴	1	8	yes	—
341	C₂⁴×D₄	C₂⁴	1	8	yes	—
342	C₂⁴×D₄	C₂⁴	1	8	yes	—
343	C₂⁴×D₄	C₂⁴	1	4	yes	—
344	C₂⁴×D₄	C₂⁴	1	8	yes	—
345	C₂⁴×D₄	C₂⁴	1	4	yes	—
346	C₂⁴×D₄	C₂⁴	1	8	yes	—
347	C₂⁴×D₄	C₂⁴	1	2	yes	—
348	C₂⁴×D₄	C₂⁴	1	4	yes	—
349	C₂⁴×D₄	C₂⁴	1	2	yes	—
350	C₂⁴×D₄	C₂⁴	1	8	yes	—
351	C₂⁴×D₄	C₂⁴	1	8	yes	—
352	C₂⁴×D₄	C₂⁴	1	8	yes	—
353	C₂⁴×D₄	C₂⁴	1	4	yes	—
354	C₂⁵×C₄	C₂×D₄	1	8	yes	—
355	C₂⁵×C₄	C₂×D₄	1	8	yes	—
356	C₂⁵×C₄	C₂×D₄	1	8	yes	—
357	C₂⁵×C₄	C₂×D₄	1	8	yes	complemented
358	C₂⁵×C₄	C₂×D₄	1	16	yes	complemented
359	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
360	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
361	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
362	C₂⁵×C₄	C₂⁴	1	8	yes	—
363	C₂⁵×C₄	C₂⁴	1	4	yes	—
364	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
365	C₂⁵×C₄	C₂⁴	1	4	yes	—
366	C₂⁵×C₄	C₂⁴	1	2	yes	—
367	C₂⁵×C₄	C₂⁴	1	2	yes	—
368	C₂⁵×C₄	C₂⁴	1	2	yes	—
369	C₂⁵×C₄	C₂⁴	1	2	yes	—
370	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
371	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
372	C₂²×#121	C₂×D₄	1	32	yes	—
373	C₂²×#121	C₂×D₄	1	32	yes	complemented
374	C₂²×#120	C₂×D₄	1	64	yes	—
375	C₂²×#120	C₂×D₄	1	64	yes	complemented
376	C₂²×C₄×D₄	C₂×D₄	1	32	yes	—
377	C₂²×C₄×D₄	C₂×D₄	1	32	yes	complemented
378	C₂³×C₄⋊C₄	C₂×D₄	1	8	yes	complemented
379	C₂³×C₄⋊C₄	C₂×D₄	1	8	yes	complemented
380	C₂³×C₄⋊C₄	C₂⁴	1	4	yes	—
381	C₂³×C₄⋊C₄	C₂⁴	1	4	yes	—
382	C₂³×C₄⋊C₄	C₂⁴	1	4	yes	—
383	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	—
384	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
385	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	complemented
386	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
387	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	complemented
388	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	complemented
389	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
390	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
391	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
392	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
393	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
394	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
395	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
396	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
397	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
398	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
399	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
400	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
401	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
402	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
403	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
404	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
405	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
406	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
407	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
408	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
409	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
410	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
411	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
412	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
413	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
414	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
415	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
416	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
417	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
418	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
419	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
420	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
421	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
422	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
423	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
424	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
425	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
426	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
427	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
428	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
429	C₂³×C₄²	C₂×D₄	1	8	yes	complemented
430	C₂³×C₄²	C₂⁴	1	4	yes	—
431	C₂²×#95	C₂⁴	1	4	yes	—
432	C₂²×#95	C₂⁴	1	8	yes	—
433	C₂²×#95	C₂⁴	1	8	yes	—
434	C₂²×#95	C₂⁴	1	8	yes	—
435	C₂²×#95	C₂⁴	1	8	yes	—
436	C₂²×#95	C₂⁴	1	16	yes	—
437	C₂²×#95	C₂⁴	1	4	yes	—
438	C₂²×#95	C₂⁴	1	4	yes	—
439	C₂²×#95	C₂⁴	1	4	yes	—
440	C₂²×#95	C₂⁴	1	8	yes	—
441	C₂²×#95	C₂⁴	1	16	yes	—
442	C₂²×#95	C₂⁴	1	8	yes	—
443	C₂²×#95	C₂⁴	1	8	yes	—
444	C₂²×#95	C₂⁴	1	8	yes	—
445	C₂²×#95	C₂⁴	1	16	yes	—
446	C₂²×#95	C₂⁴	1	8	yes	—
447	C₂²×#95	C₂⁴	1	16	yes	—
448	C₂²×#95	C₂⁴	1	16	yes	—
449	C₂²×#95	C₂⁴	1	8	yes	—
450	C₂²×#95	C₂⁴	1	16	yes	—
451	C₂⁶	#120	1	128	yes	complemented
452	C₂⁶	C₂²×D₄	1	8	yes	—
453	C₂⁶	C₂²×D₄	1	8	yes	—
454	C₂⁶	C₂²×D₄	1	8	yes	—
455	C₂⁶	C₂²×D₄	1	8	yes	—
456	C₂⁶	C₂²×D₄	1	4	yes	—
457	C₂⁶	C₂²×D₄	1	16	yes	—
458	C₂⁶	C₂²×D₄	1	16	yes	—
459	C₂⁶	C₂²×D₄	1	16	yes	—
460	C₂⁶	C₂²×D₄	1	8	yes	—
461	C₂⁶	C₂²×D₄	1	8	yes	—
462	C₂⁶	C₂²×D₄	1	4	yes	—
463	C₂⁶	C₂²×D₄	1	4	yes	—
464	C₂⁶	C₂²×D₄	1	4	yes	—
465	C₂⁶	C₂²×D₄	1	32	yes	—
466	C₂⁶	C₂²×D₄	1	8	yes	—
467	C₂⁶	C₂²×D₄	1	8	yes	—
468	C₂⁶	C₂²×D₄	1	8	yes	—
469	C₂⁶	C₂²×D₄	1	8	yes	—
470	C₂⁶	C₂²×D₄	1	8	yes	—
471	C₂⁶	C₂²×D₄	1	8	yes	—
472	C₂⁶	C₂²×D₄	1	16	yes	—
473	C₂⁶	C₂²×D₄	1	16	yes	—
474	C₂⁶	C₂²×D₄	1	16	yes	—
475	C₂⁶	C₂⁵	1	2	yes	—
476	C₂⁶	C₂⁵	1	4	yes	—
477	C₂⁶	C₂⁵	1	4	yes	—
478	C₂⁶	C₂⁵	1	1	yes	characteristic
479	C₂⁶	C₂⁵	1	4	yes	—
480	C₂⁶	C₂⁵	1	2	yes	—
481	C₂⁶	C₂⁵	1	1	yes	characteristic
482	C₂⁶	C₂⁵	1	1	yes	characteristic
483	C₂³×D₄	#120	1	64	yes	—
484	C₂³×D₄	#120	1	128	yes	complemented
485	C₂³×D₄	C₂²×D₄	1	8	yes	—
486	C₂³×D₄	C₂²×D₄	1	16	yes	—
487	C₂³×D₄	C₂²×D₄	1	16	yes	—
488	C₂³×D₄	C₂²×D₄	1	16	yes	—
489	C₂³×D₄	C₂²×D₄	1	16	yes	—
490	C₂³×D₄	C₂²×D₄	1	16	yes	—
491	C₂³×D₄	C₂²×D₄	1	32	yes	—
492	C₂³×D₄	C₂²×D₄	1	16	yes	—
493	C₂³×D₄	C₂²×D₄	1	32	yes	—
494	C₂³×D₄	C₂²×D₄	1	16	yes	—
495	C₂³×D₄	C₂²×D₄	1	32	yes	—
496	C₂³×D₄	C₂²×D₄	1	32	yes	—
497	C₂³×D₄	C₂²×D₄	1	16	yes	—
498	C₂³×D₄	C₂²×D₄	1	8	yes	—
499	C₂³×D₄	C₂²×D₄	1	32	yes	—
500	C₂³×D₄	C₂²×D₄	1	16	yes	—
501	C₂³×D₄	C₂²×D₄	1	16	yes	—
502	C₂³×D₄	C₂²×D₄	1	16	yes	—
503	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
504	C₂³×D₄	H(5,𝔽₂)	1	32	yes	—
505	C₂³×D₄	H(5,𝔽₂)	1	32	yes	—
506	C₂⁴×C₄	#120	1	64	yes	complemented
507	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
508	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
509	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
510	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
511	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
512	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
513	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
514	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
515	C₂⁴×C₄	C₂²×D₄	1	32	yes	—
516	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
517	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
518	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
519	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
520	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
521	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
522	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
523	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
524	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
525	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
526	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
527	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
528	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
529	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
530	C₂⁴×C₄	C₂⁵	1	4	yes	—
531	C₂⁴×C₄	C₂⁵	1	4	yes	—
532	C₂⁴×C₄	C₂⁵	1	8	yes	—
533	C₂⁴×C₄	C₂⁵	1	4	yes	—
534	C₂⁴×C₄	C₂⁵	1	2	yes	—
535	C₂⁴×C₄	C₂⁵	1	8	yes	—
536	C₂⁴×C₄	C₂⁵	1	4	yes	—
537	C₂⁴×C₄	C₂⁵	1	2	yes	—
538	C₂⁴×C₄	C₂⁵	1	2	yes	—
539	C₂⁴×C₄	C₂⁵	1	2	yes	—
540	C₂⁴×C₄	C₂⁵	1	2	yes	—
541	C₂⁴×C₄	C₂⁵	1	2	yes	—
542	C₂²×C₄⋊C₄	C₂²×D₄	1	16	yes	—
543	C₂²×C₄⋊C₄	C₂²×D₄	1	16	yes	—
544	C₂²×C₂²⋊C₄	#120	1	64	yes	complemented
545	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
546	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
547	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
548	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
549	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
550	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
551	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
552	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
553	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	16	yes	—
554	C₂²×C₄²	C₂²×D₄	1	16	yes	—
555	C₂⁵	C₂×#120	1	32	yes	—
556	C₂⁵	C₂×#120	1	16	yes	—
557	C₂⁵	C₂×#120	1	64	yes	—
558	C₂⁵	C₂×#120	1	32	yes	—
559	C₂⁵	C₂×#120	1	16	yes	—
560	C₂⁵	C₂×#120	1	16	yes	—
561	C₂⁵	C₂×#120	1	32	yes	—
562	C₂⁵	C₂×#120	1	16	yes	—
563	C₂⁵	C₂×#120	1	32	yes	—
564	C₂⁵	C₂×#120	1	32	yes	—
565	C₂⁵	C₂×#120	1	64	yes	—
566	C₂⁵	C₂³×D₄	1	8	yes	—
567	C₂⁵	C₂³×D₄	1	8	yes	—
568	C₂⁵	C₂³×D₄	1	8	yes	—
569	C₂⁵	C₂³×D₄	1	8	yes	—
570	C₂⁵	C₂³×D₄	1	8	yes	—
571	C₂⁵	C₂³×D₄	1	8	yes	—
572	C₂⁵	C₂³×D₄	1	4	yes	—
573	C₂⁵	C₂³×D₄	1	2	yes	—
574	C₂⁵	C₂³×D₄	1	2	yes	—
575	C₂⁵	C₂³×D₄	1	4	yes	—
576	C₂⁵	C₂³×D₄	1	2	yes	—
577	C₂⁵	C₂³×D₄	1	8	yes	—
578	C₂⁵	C₂³×D₄	1	8	yes	—
579	C₂⁵	C₂³×D₄	1	4	yes	—
580	C₂⁵	C₂³×D₄	1	8	yes	—
581	C₂⁵	C₂³×D₄	1	8	yes	—
582	C₂⁵	C₂³×D₄	1	4	yes	—
583	C₂⁵	C₂³×D₄	1	2	yes	—
584	C₂⁵	C₂³×D₄	1	2	yes	—
585	C₂⁵	C₂³×D₄	1	4	yes	—
586	C₂⁵	C₂³×D₄	1	2	yes	—
587	C₂⁵	C₂³×D₄	1	2	yes	—
588	C₂⁵	C₂³×D₄	1	4	yes	—
589	C₂⁵	C₂³×D₄	1	4	yes	—
590	C₂⁵	C₂³×D₄	1	2	yes	—
591	C₂⁵	C₂³×D₄	1	2	yes	—
592	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
593	C₂⁵	C₂×H(5,𝔽₂)	1	16	yes	—
594	C₂⁵	C₂×H(5,𝔽₂)	1	32	yes	—
595	C₂⁵	C₂×H(5,𝔽₂)	1	16	yes	—
596	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
597	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
598	C₂⁵	#585	1	4	yes	—
599	C₂⁵	C₂⁶	1	1	yes	characteristic
600	C₂²×D₄	C₂×#120	1	32	yes	—
601	C₂²×D₄	C₂×#120	1	64	yes	—
602	C₂²×D₄	C₂×#120	1	32	yes	—
603	C₂²×D₄	C₂×#120	1	64	yes	—
604	C₂²×D₄	#534	1	64	yes	—
605	C₂²×D₄	#534	1	128	yes	—
606	C₂²×D₄	#535	1	64	yes	—
607	C₂³×C₄	C₂×#120	1	16	yes	—
608	C₂³×C₄	C₂×#120	1	16	yes	—
609	C₂³×C₄	C₂×#120	1	16	yes	—
610	C₂³×C₄	C₂×#120	1	32	yes	—
611	C₂³×C₄	C₂×#120	1	32	yes	—
612	C₂³×C₄	C₂×#120	1	32	yes	—
613	C₂³×C₄	C₂×#120	1	16	yes	—
614	C₂³×C₄	C₂×#120	1	16	yes	—
615	C₂³×C₄	C₂³×D₄	1	8	yes	—
616	C₂³×C₄	C₂³×D₄	1	4	yes	—
617	C₂³×C₄	C₂³×D₄	1	4	yes	—
618	C₂³×C₄	C₂³×D₄	1	8	yes	—
619	C₂³×C₄	C₂³×D₄	1	8	yes	—
620	C₂³×C₄	C₂³×D₄	1	4	yes	—
621	C₂³×C₄	C₂³×D₄	1	4	yes	—
622	C₂³×C₄	C₂³×D₄	1	8	yes	—
623	C₂³×C₄	C₂³×D₄	1	8	yes	—
624	C₂³×C₄	C₂³×D₄	1	4	yes	—
625	C₂³×C₄	C₂³×D₄	1	4	yes	—
626	C₂³×C₄	C₂³×D₄	1	8	yes	—
627	C₂³×C₄	C₂³×D₄	1	4	yes	—
628	C₂³×C₄	C₂³×D₄	1	4	yes	—
629	C₂³×C₄	C₂³×D₄	1	4	yes	—
630	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
631	C₂³×C₄	C₂×H(5,𝔽₂)	1	16	yes	—
632	C₂³×C₄	C₂×H(5,𝔽₂)	1	16	yes	—
633	C₂³×C₄	C₂×H(5,𝔽₂)	1	16	yes	—
634	C₂×C₂²⋊C₄	C₂×#120	1	32	yes	—
635	C₂×C₂²⋊C₄	C₂×#120	1	32	yes	—
636	C₂⁴	#2846	1	64	yes	—
637	C₂⁴	C₂²×#120	1	16	yes	—
638	C₂⁴	C₂²×#120	1	16	yes	—
639	C₂⁴	C₂²×#120	1	8	yes	—
640	C₂⁴	C₂²×#120	1	8	yes	—
641	C₂⁴	C₂²×#120	1	4	yes	—
642	C₂⁴	C₂²×#120	1	4	yes	—
643	C₂⁴	C₂²×#120	1	4	yes	—
644	C₂⁴	C₂²×#120	1	16	yes	—
645	C₂⁴	C₂²×#120	1	8	yes	—
646	C₂⁴	C₂²×#120	1	8	yes	—
647	C₂⁴	C₂²×#120	1	8	yes	—
648	C₂⁴	C₂²×#120	1	4	yes	—
649	C₂⁴	C₂²×#120	1	4	yes	—
650	C₂⁴	C₂²×#120	1	4	yes	—
651	C₂⁴	C₂²×#120	1	4	yes	—
652	C₂⁴	C₂²×#120	1	8	yes	—
653	C₂⁴	C₂²×#120	1	8	yes	—
654	C₂⁴	C₂²×#120	1	4	yes	—
655	C₂⁴	C₂²×#120	1	4	yes	—
656	C₂⁴	C₂×#534	1	32	yes	—
657	C₂⁴	C₂×#534	1	32	yes	—
658	C₂⁴	C₂×#534	1	32	yes	—
659	C₂⁴	C₂×#535	1	16	yes	—
660	C₂⁴	C₂×#535	1	16	yes	—
661	C₂⁴	#3484	1	32	yes	—
662	C₂⁴	#3484	1	32	yes	—
663	C₂⁴	#3484	1	4	yes	—
664	C₂⁴	#3484	1	8	yes	—
665	C₂⁴	#3484	1	16	yes	—
666	C₂⁴	#3484	1	16	yes	—
667	C₂⁴	#3484	1	16	yes	—
668	C₂⁴	#3484	1	32	yes	—
669	C₂⁴	#3484	1	16	yes	—
670	C₂⁴	#3485	1	4	yes	—
671	C₂⁴	#3488	1	8	yes	—
672	C₂⁴	#3488	1	8	yes	—
673	C₂⁴	#3496	1	16	yes	—
674	C₂⁴	#3496	1	16	yes	—
675	C₂⁴	#3498	1	8	yes	—
676	C₂⁴	#3498	1	8	yes	—
677	C₂⁴	C₂⁴×D₄	1	2	yes	—
678	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
679	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
680	C₂⁴	C₂⁴×D₄	1	2	yes	—
681	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
682	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
683	C₂⁴	C₂²×H(5,𝔽₂)	1	4	yes	—
684	C₂⁴	C₂²×H(5,𝔽₂)	1	8	yes	—
685	C₂⁴	C₂²×H(5,𝔽₂)	1	8	yes	—
686	C₂⁴	C₂×#585	1	2	yes	—
687	C₂×D₄	#2613	1	128	yes	complemented
688	C₂²×C₄	C₂²×#120	1	16	yes	—
689	C₂²×C₄	C₂²×#120	1	8	yes	—
690	C₂²×C₄	C₂²×#120	1	8	yes	—
691	C₂²×C₄	C₂²×#120	1	8	yes	—
692	C₂²×C₄	C₂²×#120	1	8	yes	—
693	C₂²×C₄	C₂²×#120	1	8	yes	—
694	C₂²×C₄	C₂×#534	1	16	yes	—
695	C₂²×C₄	C₂×#534	1	32	yes	—
696	C₂²×C₄	C₂×#535	1	16	yes	—
697	C₂²×C₄	#3484	1	16	yes	—
698	C₂²×C₄	#3484	1	16	yes	—
699	C₂³	C₂×#2613	1	16	yes	—
700	C₂³	C₂×#2613	1	16	yes	—
701	C₂³	#34980	1	32	yes	—
702	C₂³	#34980	1	32	yes	—
703	C₂³	#34980	1	32	yes	—
704	C₂³	#35222	1	16	yes	—
705	C₂³	#35222	1	16	yes	—
706	C₂³	#35346	1	16	yes	—
707	C₂³	#35347	1	16	yes	—
708	C₂³	#35512	1	8	yes	—
709	C₂³	#35527	1	8	yes	—
710	C₂³	#35680	1	16	yes	—
711	C₂³	#35680	1	16	yes	—
712	C₂³	#35680	1	32	yes	—
713	C₂³	C₂×#2846	1	8	yes	—
714	C₂³	C₂×#2846	1	8	yes	—
715	C₂³	C₂×#2846	1	8	yes	—
716	C₂³	C₂³×#120	1	1	yes	characteristic
717	C₂³	C₂³×#120	1	2	yes	—
718	C₂³	C₂³×#120	1	1	yes	characteristic
719	C₂³	C₂³×#120	1	1	yes	characteristic
720	C₂³	C₂³×#120	1	2	yes	—
721	C₂³	C₂²×#534	1	4	yes	—
722	C₂³	C₂²×#534	1	8	yes	—
723	C₂³	C₂²×#535	1	4	yes	—
724	C₂³	C₂×#3484	1	4	yes	—
725	C₂³	C₂×#3484	1	1	yes	characteristic
726	C₂³	C₂×#3484	1	4	yes	—
727	C₂³	C₂×#3484	1	4	yes	—
728	C₂³	C₂×#3484	1	8	yes	—
729	C₂³	C₂×#3484	1	8	yes	—
730	C₂³	C₂×#3484	1	4	yes	—
731	C₂³	C₂×#3484	1	4	yes	—
732	C₂³	C₂×#3484	1	4	yes	—
733	C₂³	C₂×#3484	1	2	yes	—
734	C₂³	C₂×#3484	1	8	yes	—
735	C₂³	C₂×#3496	1	4	yes	—
736	C₂³	C₂×#3496	1	4	yes	—
737	C₂³	C₂×#3485	1	1	yes	characteristic
738	C₂³	C₂×#3488	1	2	yes	—
739	C₂³	C₂×#3488	1	2	yes	—
740	C₂³	C₂×#3498	1	2	yes	—
741	C₂³	C₂×#3498	1	2	yes	—
742	C₂³	#63011	1	16	yes	—
743	C₂³	#63011	1	32	yes	—
744	C₂³	#63012	1	16	yes	—
745	C₂×C₄	C₂×#2613	1	16	yes	—
746	C₂×C₄	#34980	1	16	yes	—
747	C₂²	#4307937	1	16	yes	—
748	C₂²	#4928938	1	16	yes	—
749	C₂²	C₂²×#2613	1	2	yes	—
750	C₂²	C₂×#34980	1	2	yes	—
751	C₂²	C₂×#34980	1	4	yes	—
752	C₂²	C₂×#34980	1	4	yes	—
753	C₂²	C₂×#34980	1	4	yes	—
754	C₂²	C₂×#35222	1	2	yes	—
755	C₂²	C₂×#35222	1	2	yes	—
756	C₂²	C₂×#35346	1	2	yes	—
757	C₂²	C₂×#35347	1	2	yes	—
758	C₂²	C₂×#35512	1	1	yes	characteristic
759	C₂²	C₂×#35527	1	1	yes	characteristic
760	C₂²	C₂×#35680	1	2	yes	—
761	C₂²	C₂×#35680	1	2	yes	—
762	C₂²	C₂×#35680	1	4	yes	—
763	C₂²	#7630939	1	2	yes	—
764	C₂²	#7630939	1	2	yes	—
765	C₂²	#7630939	1	4	yes	—
766	C₂²	C₂²×#2846	1	1	yes	characteristic
767	C₂²	#7652795	1	16	yes	—
768	C₂²	#7652795	1	8	yes	—
769	C₂²	#7652795	1	4	yes	—
770	C₂²	#7652802	1	16	yes	—
771	C₂²	#7652921	1	4	yes	—
772	C₂²	#7653764	1	8	yes	—
773	C₂²	#7653790	1	8	yes	—
774	C₂²	#7733149	1	16	yes	—
775	C₂²	#7733150	1	16	yes	—
776	C₂²	#7733601	1	8	yes	—
777	C₂²	#7733603	1	8	yes	—
778	C₂	#72225665	1	4	yes	—
779	C₂	C₂×#4928938	1	1	yes	characteristic
780	C₂	#72232405	1	8	yes	—
781	C₂	#72233691	1	1	yes	characteristic
782	C₂	#72236761	1	4	yes	—
783	C₂	#72236777	1	2	yes	—
784	C₂	#72237104	1	4	yes	—
785	C₂	#72237105	1	2	yes	—
786	C₂	#72237465	1	4	yes	—
787	C₂	C₂×#4307937	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. #72335060	C₂	semidirect
2. #72335059	C₂	semidirect
3. #72334957	C₂	semidirect
4. C₂×#636791	C₂	semidirect
5. C₂×#613191	C₂	semidirect
6. #72323673	C₂	semidirect
7. #72323618	C₂	semidirect
8. #72323618	C₂	semidirect
9. #72317006	C₂	semidirect
10. #72302231	C₂	semidirect
11. #72287890	C₂	semidirect
12. #72287889	C₂	semidirect
13. C₂×#635984	C₂	semidirect
14. #72251033	C₂	semidirect
15. #72250308	C₂	semidirect
16. C₂²×#14715	C₂	semidirect
17. #72240113	C₂	semidirect
18. #72233926	C₂	semidirect
19. C₂×#612424	C₂	semidirect
20. C₂⁴×D₄²	C₂	semidirect
23. C₂⁶×D₄	C₂²	semidirect
25. C₂³×D₄²	C₂²	semidirect
26. C₂⁴×#127	C₂²	semidirect
28. C₂⁴×#121	C₂²	semidirect
29. C₂⁴×#121	C₂²	semidirect
31. C₂⁴×#120	C₂²	semidirect
32. C₂⁴×#120	C₂²	semidirect
34. C₂⁴×C₄×D₄	C₂²	semidirect
35. C₂²×#2846	C₂²	semidirect
36. C₂²×#2405	C₂²	semidirect
38. C₂²×#2403	C₂²	semidirect
39. C₂²×#2403	C₂²	semidirect
40. C₂²×#2613	C₂²	semidirect
41. C₂³×#392	C₂²	semidirect
42. C₂³×#386	C₂²	semidirect
43. C₂³×#379	C₂²	semidirect
44. C₂×#16258	C₂²	semidirect
45. C₂×#16249	C₂²	semidirect
46. C₂×#15091	C₂²	semidirect
47. C₂×#15091	C₂²	semidirect
48. C₂×#14913	C₂²	semidirect
49. C₂×#14911	C₂²	semidirect
50. C₂×#14911	C₂²	semidirect
51. C₂×#14730	C₂²	semidirect
52. C₂×#14718	C₂²	semidirect
53. C₂×#14716	C₂²	semidirect
55. C₂×#14715	C₂²	semidirect
56. C₂×#14715	C₂²	semidirect
57. C₂×#14715	C₂²	semidirect
58. C₂×#14715	C₂²	semidirect
59. C₂×#14715	C₂²	semidirect
60. C₂×#14715	C₂²	semidirect
61. C₂×#14715	C₂²	semidirect
62. C₂×#14715	C₂²	semidirect
63. C₂×#14715	C₂²	semidirect
64. C₂×#14715	C₂²	semidirect
65. C₂×#14706	C₂²	semidirect
66. C₂×#14694	C₂²	semidirect
67. C₂×#14694	C₂²	semidirect
68. C₂×#14681	C₂²	semidirect
69. C₂×#14681	C₂²	semidirect
70. C₂×#14679	C₂²	semidirect
71. C₂×#14679	C₂²	semidirect
72. C₂×#14679	C₂²	semidirect
73. C₂×#14335	C₂²	semidirect
74. C₂×#14335	C₂²	semidirect
75. C₂×#14255	C₂²	semidirect
76. C₂×#14255	C₂²	semidirect
77. C₂×#14016	C₂²	semidirect
78. C₂×#13967	C₂²	semidirect
79. C₂×#13869	C₂²	semidirect
80. C₂×#13869	C₂²	semidirect
83. C₂×#13867	C₂²	semidirect
84. C₂×#13867	C₂²	semidirect
85. C₂×#13867	C₂²	semidirect
86. C₂×#13867	C₂²	semidirect
87. C₂×#13867	C₂²	semidirect
88. C₂²×#1438	C₂²	semidirect
89. C₂²×C₂²⋊#95	C₂²	semidirect
90. #158327	C₂²	semidirect
91. #158314	C₂²	semidirect
92. #156854	C₂²	semidirect
93. #156854	C₂²	semidirect
94. #156706	C₂²	semidirect
95. #156706	C₂²	semidirect
96. #156688	C₂²	semidirect
97. #156684	C₂²	semidirect
98. #155624	C₂²	semidirect
99. #155622	C₂²	semidirect
100. #154634	C₂²	semidirect
101. #154467	C₂²	semidirect
102. #154255	C₂²	semidirect
103. #154195	C₂²	semidirect
104. #154160	C₂²	semidirect
105. #154160	C₂²	semidirect
106. #154130	C₂²	semidirect
107. #154130	C₂²	semidirect
108. #154098	C₂²	semidirect
109. #154094	C₂²	semidirect
110. #154094	C₂²	semidirect
111. #154094	C₂²	semidirect
112. #154094	C₂²	semidirect
113. #154094	C₂²	semidirect
114. #154094	C₂²	semidirect
115. #154094	C₂²	semidirect
116. #154094	C₂²	semidirect
117. #154094	C₂²	semidirect
118. #154094	C₂²	semidirect
119. #154082	C₂²	semidirect
120. #154077	C₂²	semidirect
121. #154077	C₂²	semidirect
122. #153931	C₂²	semidirect
123. #153931	C₂²	semidirect
124. #153827	C₂²	semidirect
127. C₂⁵×D₄	D₄	semidirect
128. C₂⁵×D₄	D₄	semidirect
145. C₂⁵×D₄	C₂³	semidirect
151. C₂³×#121	D₄	semidirect
156. C₂³×#120	D₄	semidirect
165. C₂³×#120	C₂³	semidirect
166. C₂³×#120	C₂³	semidirect
167. C₂³×#120	C₂³	semidirect
168. C₂³×C₄×D₄	D₄	semidirect
181. C₂⁴×C₂²⋊C₄	C₂³	semidirect
182. C₂⁴×C₂²⋊C₄	C₂³	semidirect
183. C₂⁴×C₂²⋊C₄	C₂³	semidirect
185. C₂²×#394	C₂³	semidirect
186. C₂²×#394	C₂³	semidirect
189. C₂²×#392	C₂³	semidirect
190. C₂²×#392	C₂³	semidirect
191. C₂²×#392	C₂³	semidirect
192. C₂²×#392	C₂³	semidirect
193. C₂²×#392	C₂³	semidirect
194. C₂²×#392	C₂³	semidirect
195. C₂²×#392	C₂³	semidirect
196. C₂²×#392	C₂³	semidirect
205. C₂²×#386	C₂³	semidirect
206. C₂²×#386	C₂³	semidirect
207. C₂²×#386	C₂³	semidirect
208. C₂²×#386	C₂³	semidirect
209. C₂²×#386	C₂³	semidirect
210. C₂²×#386	C₂³	semidirect
211. C₂²×#386	C₂³	semidirect
212. C₂²×#385	C₂³	semidirect
215. C₂²×#381	C₂³	semidirect
216. C₂²×#381	C₂³	semidirect
231. C₂²×#379	C₂³	semidirect
232. C₂²×#379	C₂³	semidirect
233. C₂²×#379	C₂³	semidirect
234. C₂²×#379	C₂³	semidirect
235. C₂²×#379	C₂³	semidirect
236. C₂²×#379	C₂³	semidirect
237. C₂²×#379	C₂³	semidirect
238. C₂²×#379	C₂³	semidirect
239. C₂³×#95	C₂³	semidirect
240. C₂³×#95	C₂³	semidirect
241. C₂×#1442	C₂³	semidirect
242. C₂×#1442	C₂³	semidirect
243. C₂×#1440	C₂³	semidirect
244. C₂×#1440	C₂³	semidirect
245. C₂×#1440	C₂³	semidirect
246. C₂×#1440	C₂³	semidirect
247. C₂×#1439	C₂³	semidirect
248. C₂×#1439	C₂³	semidirect
249. C₂×#1439	C₂³	semidirect
250. C₂×#1439	C₂³	semidirect
255. C₂×#1438	C₂³	semidirect
256. C₂×#1438	C₂³	semidirect
257. C₂×#1438	C₂³	semidirect
258. C₂×#1438	C₂³	semidirect
259. C₂×#1438	C₂³	semidirect
260. C₂×#1438	C₂³	semidirect
261. C₂×#1438	C₂³	semidirect
262. C₂×#1438	C₂³	semidirect
263. C₂×#1438	C₂³	semidirect
264. C₂×#1438	C₂³	semidirect
265. C₂×#1438	C₂³	semidirect
266. C₂×#1438	C₂³	semidirect
267. C₂×#1438	C₂³	semidirect
268. C₂×#1438	C₂³	semidirect
269. C₂×#1438	C₂³	semidirect
270. C₂×#1438	C₂³	semidirect
271. C₂×#1438	C₂³	semidirect
272. C₂×#1438	C₂³	semidirect
273. C₂×#1438	C₂³	semidirect
274. C₂×#1438	C₂³	semidirect
275. C₂×#1437	C₂³	semidirect
276. C₂×#1436	C₂³	semidirect
290. C₂×C₂²⋊#95	C₂³	semidirect
291. C₂×C₂²⋊#95	C₂³	semidirect
292. C₂×C₂²⋊#95	C₂³	semidirect
293. C₂×C₂²⋊#95	C₂³	semidirect
294. C₂×C₂²⋊#95	C₂³	semidirect
295. C₂×C₂²⋊#95	C₂³	semidirect
296. C₂×C₂²⋊#95	C₂³	semidirect
297. C₂×C₂²⋊#95	C₂³	semidirect
298. C₂×C₂²⋊#95	C₂³	semidirect
299. #7557	C₂³	semidirect
300. #7557	C₂³	semidirect
301. #7555	C₂³	semidirect
302. #7555	C₂³	semidirect
303. #7555	C₂³	semidirect
304. #7555	C₂³	semidirect
305. #7554	C₂³	semidirect
309. C₂⁷	C₂×D₄	semidirect
330. C₂⁴×D₄	C₂×D₄	semidirect
331. C₂⁴×D₄	C₂×D₄	semidirect
332. C₂⁴×D₄	C₂×D₄	semidirect
333. C₂⁴×D₄	C₂×D₄	semidirect
334. C₂⁴×D₄	C₂×D₄	semidirect
335. C₂⁴×D₄	C₂×D₄	semidirect
357. C₂⁵×C₄	C₂×D₄	semidirect
358. C₂⁵×C₄	C₂×D₄	semidirect
373. C₂²×#121	C₂×D₄	semidirect
375. C₂²×#120	C₂×D₄	semidirect
377. C₂²×C₄×D₄	C₂×D₄	semidirect
378. C₂³×C₄⋊C₄	C₂×D₄	semidirect
379. C₂³×C₄⋊C₄	C₂×D₄	semidirect
385. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
386. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
387. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
388. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
429. C₂³×C₄²	C₂×D₄	semidirect
451. C₂⁶	#120	semidirect
484. C₂³×D₄	#120	semidirect
506. C₂⁴×C₄	#120	semidirect
544. C₂²×C₂²⋊C₄	#120	semidirect
687. C₂×D₄	#2613	semidirect

Maximal subgroups

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

subgroup	index
#72335060	2
#72335059	2
#72334957	2
C₂×#636791	2
C₂×#613191	2
#72323673	2
#72323618	2
#72317006	2
#72302231	2
#72287890	2
#72287889	2
C₂×#635984	2
#72251033	2
#72250308	2
C₂²×#14715	2
#72240113	2
#72233926	2
C₂×#612424	2
C₂⁴×D₄²	2