Subgroups — #72331313

Order 1024.

At least 8876 conjugacy classes of subgroups; only the 1345 normal subgroups are shown.

The subgroup lattice has 917 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#2456	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15273	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15257	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14911	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14715	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14715	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13967	C₂	1	1	yes	maximal, characteristic, complemented
9	#158361	C₂	1	1	yes	maximal, characteristic, complemented
10	#158282	C₂	1	1	yes	maximal, characteristic, complemented
11	#156829	C₂	1	1	yes	maximal, characteristic, complemented
12	#156742	C₂	1	1	yes	maximal, characteristic, complemented
13	#156741	C₂	1	1	yes	maximal, characteristic, complemented
14	#156709	C₂	1	1	yes	maximal, characteristic, complemented
15	#156689	C₂	1	1	yes	maximal, characteristic, complemented
16	#156684	C₂	1	1	yes	maximal, characteristic, complemented
17	#155875	C₂	1	1	yes	maximal, characteristic, complemented
18	#155258	C₂	1	1	yes	maximal, characteristic, complemented
19	#155116	C₂	1	1	yes	maximal, characteristic, complemented
20	#154737	C₂	1	1	yes	maximal, characteristic, complemented
21	#154712	C₂	1	1	yes	maximal, characteristic, complemented
22	#154684	C₂	1	1	yes	maximal, characteristic, complemented
23	#154676	C₂	1	1	yes	maximal, characteristic, complemented
24	#154635	C₂	1	1	yes	maximal, characteristic, complemented
25	#154634	C₂	1	1	yes	maximal, characteristic, complemented
26	#154634	C₂	1	1	yes	maximal, characteristic, complemented
27	#154634	C₂	1	1	yes	maximal, characteristic, complemented
28	#154487	C₂	1	1	yes	maximal, characteristic, complemented
29	#154195	C₂	1	1	yes	maximal, characteristic, complemented
30	#154195	C₂	1	1	yes	maximal, characteristic, complemented
31	#154098	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂⁵×D₄	C₂²	1	1	yes	characteristic
33	C₂³×#123	C₂²	1	1	yes	characteristic, complemented
34	C₂³×#121	C₂²	1	1	yes	characteristic, complemented
35	C₂³×#120	C₂²	1	1	yes	characteristic
36	C₂³×#120	C₂²	1	1	yes	characteristic
37	C₂³×#120	C₂²	1	1	yes	characteristic
38	C₂³×#120	C₂²	1	1	yes	characteristic
39	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic
40	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic
41	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
42	C₂⁴×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂⁴×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×#396	C₂²	1	1	yes	characteristic, complemented
45	C₂²×#392	C₂²	1	1	yes	characteristic
46	C₂²×#392	C₂²	1	1	yes	characteristic
47	C₂²×#392	C₂²	1	1	yes	characteristic
48	C₂²×#392	C₂²	1	1	yes	characteristic
49	C₂²×#392	C₂²	1	1	yes	characteristic
50	C₂²×#392	C₂²	1	1	yes	characteristic
51	C₂²×#392	C₂²	1	1	yes	characteristic
52	C₂²×#392	C₂²	1	1	yes	characteristic
53	C₂²×#392	C₂²	1	1	yes	characteristic
54	C₂²×#392	C₂²	1	1	yes	characteristic, complemented
55	C₂²×#392	C₂²	1	1	yes	characteristic, complemented
56	C₂²×#392	C₂²	1	1	yes	characteristic, complemented
57	C₂²×#390	C₂²	1	1	yes	characteristic
58	C₂²×#390	C₂²	1	1	yes	characteristic
59	C₂²×#390	C₂²	1	1	yes	characteristic, complemented
60	C₂²×#388	C₂²	1	1	yes	characteristic, complemented
61	C₂²×#388	C₂²	1	1	yes	characteristic, complemented
62	C₂²×#387	C₂²	1	1	yes	characteristic, complemented
63	C₂²×#386	C₂²	1	1	yes	characteristic
64	C₂²×#386	C₂²	1	1	yes	characteristic
65	C₂²×#386	C₂²	1	1	yes	characteristic
66	C₂²×#386	C₂²	1	1	yes	characteristic
67	C₂²×#386	C₂²	1	1	yes	characteristic
68	C₂²×#386	C₂²	1	1	yes	characteristic
69	C₂²×#386	C₂²	1	1	yes	characteristic
70	C₂²×#386	C₂²	1	1	yes	characteristic, complemented
71	C₂²×#386	C₂²	1	1	yes	characteristic, complemented
72	C₂²×#386	C₂²	1	1	yes	characteristic, complemented
73	C₂²×#386	C₂²	1	1	yes	characteristic, complemented
74	C₂²×#386	C₂²	1	1	yes	characteristic, complemented
75	C₂²×#386	C₂²	1	1	yes	characteristic, complemented
76	C₂²×#386	C₂²	1	1	yes	characteristic, complemented
77	C₂²×#386	C₂²	1	1	yes	characteristic, complemented
78	C₂²×#385	C₂²	1	1	yes	characteristic, complemented
79	C₂²×#381	C₂²	1	1	yes	characteristic, complemented
80	C₂²×#380	C₂²	1	1	yes	characteristic
81	C₂²×#379	C₂²	1	1	yes	characteristic
82	C₂²×#379	C₂²	1	1	yes	characteristic
83	C₂²×#379	C₂²	1	1	yes	characteristic
84	C₂²×#379	C₂²	1	1	yes	characteristic
85	C₂²×#379	C₂²	1	1	yes	characteristic
86	C₂²×#379	C₂²	1	1	yes	characteristic
87	C₂²×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
88	C₂×#1442	C₂²	1	1	yes	characteristic, complemented
89	C₂×#1440	C₂²	1	1	yes	characteristic, complemented
90	C₂×#1440	C₂²	1	1	yes	characteristic, complemented
91	C₂×#1440	C₂²	1	1	yes	characteristic, complemented
92	C₂×#1439	C₂²	1	1	yes	characteristic
93	C₂×#1439	C₂²	1	1	yes	characteristic
94	C₂×#1439	C₂²	1	1	yes	characteristic
95	C₂×#1439	C₂²	1	1	yes	characteristic
96	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
97	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
98	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
99	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
100	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
101	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
102	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
103	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
104	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
105	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
106	C₂×#1438	C₂²	1	1	yes	characteristic
107	C₂×#1438	C₂²	1	1	yes	characteristic
108	C₂×#1438	C₂²	1	1	yes	characteristic
109	C₂×#1438	C₂²	1	1	yes	characteristic
110	C₂×#1438	C₂²	1	1	yes	characteristic
111	C₂×#1438	C₂²	1	1	yes	characteristic
112	C₂×#1438	C₂²	1	1	yes	characteristic
113	C₂×#1438	C₂²	1	1	yes	characteristic
114	C₂×#1438	C₂²	1	1	yes	characteristic
115	C₂×#1438	C₂²	1	1	yes	characteristic
116	C₂×#1438	C₂²	1	1	yes	characteristic
117	C₂×#1438	C₂²	1	1	yes	characteristic
118	C₂×#1438	C₂²	1	1	yes	characteristic
119	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
120	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
121	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
122	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
123	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
124	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
125	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
126	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
127	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
128	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
129	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
130	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
131	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
132	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
133	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
134	C₂×#1437	C₂²	1	1	yes	characteristic
135	C₂×#1437	C₂²	1	1	yes	characteristic, complemented
136	C₂×#1437	C₂²	1	1	yes	characteristic, complemented
137	C₂×#1437	C₂²	1	1	yes	characteristic, complemented
138	C₂×#1437	C₂²	1	1	yes	characteristic, complemented
139	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
140	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
141	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
142	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
143	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
144	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
145	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
146	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
147	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
148	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
149	#7557	C₂²	1	1	yes	characteristic, complemented
150	#7557	C₂²	1	1	yes	characteristic, complemented
151	#7557	C₂²	1	1	yes	characteristic, complemented
152	#7557	C₂²	1	1	yes	characteristic, complemented
153	#7557	C₂²	1	1	yes	characteristic, complemented
154	#7557	C₂²	1	1	yes	characteristic, complemented
155	#7557	C₂²	1	1	yes	characteristic, complemented
156	#7556	C₂²	1	1	yes	characteristic, complemented
157	#7556	C₂²	1	1	yes	characteristic, complemented
158	#7556	C₂²	1	1	yes	characteristic, complemented
159	#7556	C₂²	1	1	yes	characteristic, complemented
160	#7555	C₂²	1	1	yes	characteristic
161	#7555	C₂²	1	1	yes	characteristic
162	#7555	C₂²	1	1	yes	characteristic
163	#7555	C₂²	1	1	yes	characteristic
164	#7555	C₂²	1	1	yes	characteristic, complemented
165	#7555	C₂²	1	1	yes	characteristic, complemented
166	#7555	C₂²	1	1	yes	characteristic, complemented
167	#7555	C₂²	1	1	yes	characteristic, complemented
168	#7555	C₂²	1	1	yes	characteristic, complemented
169	#7555	C₂²	1	1	yes	characteristic, complemented
170	#7555	C₂²	1	1	yes	characteristic, complemented
171	#7555	C₂²	1	1	yes	characteristic, complemented
172	#7555	C₂²	1	1	yes	characteristic, complemented
173	#7555	C₂²	1	1	yes	characteristic, complemented
174	#7555	C₂²	1	1	yes	characteristic, complemented
175	#7555	C₂²	1	1	yes	characteristic, complemented
176	#7555	C₂²	1	1	yes	characteristic, complemented
177	#7555	C₂²	1	1	yes	characteristic, complemented
178	#7555	C₂²	1	1	yes	characteristic, complemented
179	#7555	C₂²	1	1	yes	characteristic, complemented
180	#7555	C₂²	1	1	yes	characteristic, complemented
181	#7555	C₂²	1	1	yes	characteristic, complemented
182	#7554	C₂²	1	1	yes	characteristic, complemented
183	#7554	C₂²	1	1	yes	characteristic, complemented
184	#7554	C₂²	1	1	yes	characteristic, complemented
185	#7554	C₂²	1	1	yes	characteristic, complemented
186	#7554	C₂²	1	1	yes	characteristic, complemented
187	C₂⁷	C₂³	1	1	yes	characteristic
188	C₂⁷	C₂³	1	1	yes	characteristic
189	C₂⁴×D₄	C₂³	1	1	yes	characteristic
190	C₂⁴×D₄	C₂³	1	1	yes	characteristic
191	C₂⁴×D₄	C₂³	1	1	yes	characteristic
192	C₂⁴×D₄	C₂³	1	1	yes	characteristic
193	C₂⁴×D₄	C₂³	1	1	yes	characteristic
194	C₂⁴×D₄	C₂³	1	1	yes	characteristic
195	C₂⁴×D₄	C₂³	1	1	yes	characteristic
196	C₂⁴×D₄	C₂³	1	1	yes	characteristic
197	C₂⁴×D₄	C₂³	1	1	yes	characteristic
198	C₂⁴×D₄	C₂³	1	1	yes	characteristic
199	C₂⁴×D₄	C₂³	1	1	yes	characteristic
200	C₂⁴×D₄	C₂³	1	1	yes	characteristic
201	C₂⁴×D₄	C₂³	1	1	yes	characteristic
202	C₂⁴×D₄	C₂³	1	1	yes	characteristic
203	C₂⁴×D₄	C₂³	1	1	yes	characteristic
204	C₂⁵×C₄	C₂³	1	1	yes	characteristic
205	C₂⁵×C₄	C₂³	1	1	yes	characteristic
206	C₂⁵×C₄	C₂³	1	1	yes	characteristic
207	C₂⁵×C₄	C₂³	1	1	yes	characteristic
208	C₂⁵×C₄	C₂³	1	1	yes	characteristic
209	C₂⁵×C₄	C₂³	1	1	yes	characteristic
210	C₂²×C₄×D₄	D₄	1	8	yes	complemented
211	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
212	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
215	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
216	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
217	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
218	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
219	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
220	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
221	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
222	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
223	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
224	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
225	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
226	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
227	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
228	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
229	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
230	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
231	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
232	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
233	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
234	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
235	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
236	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
237	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
238	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
239	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
240	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
241	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
242	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
244	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
245	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
246	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
247	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
248	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
249	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
250	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
251	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
252	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
253	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
254	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
255	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
256	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
257	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
258	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
259	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
260	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
261	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
263	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
264	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
265	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
266	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
270	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
271	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
272	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
273	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
274	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
275	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
276	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
277	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
278	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
279	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
280	C₂³×C₄²	C₂³	1	1	yes	characteristic
281	C₂³×C₄²	C₂³	1	1	yes	characteristic
282	C₂³×C₄²	C₂³	1	1	yes	characteristic
283	C₂×#392	D₄	1	8	yes	complemented
284	C₂×#392	D₄	1	8	yes	complemented
285	C₂×#386	D₄	1	8	yes	complemented
286	C₂×#379	D₄	1	8	yes	complemented
287	C₂²×#95	C₂³	1	1	yes	characteristic
288	C₂²×#95	C₂³	1	1	yes	characteristic
289	C₂²×#95	C₂³	1	1	yes	characteristic
290	C₂²×#95	C₂³	1	1	yes	characteristic
291	C₂²×#95	C₂³	1	1	yes	characteristic
292	C₂²×#95	C₂³	1	1	yes	characteristic
293	C₂²×#95	C₂³	1	1	yes	characteristic
294	C₂²×#95	C₂³	1	1	yes	characteristic
295	C₂²×#95	C₂³	1	1	yes	characteristic
296	C₂²×#95	C₂³	1	1	yes	characteristic
297	C₂²×#95	C₂³	1	1	yes	characteristic
298	C₂²×#95	C₂³	1	1	yes	characteristic
299	C₂²×#95	C₂³	1	1	yes	characteristic
300	C₂²×#95	C₂³	1	1	yes	characteristic
301	C₂²×#95	C₂³	1	1	yes	characteristic
302	C₂²×#95	C₂³	1	1	yes	characteristic
303	C₂²×#95	C₂³	1	1	yes	characteristic
304	C₂²×#95	C₂³	1	1	yes	characteristic
305	C₂²×#95	C₂³	1	1	yes	characteristic
306	C₂²×#95	C₂³	1	1	yes	characteristic
307	C₂²×#95	C₂³	1	1	yes	characteristic
308	C₂²×#95	C₂³	1	1	yes	characteristic
309	C₂²×#95	C₂³	1	1	yes	characteristic
310	C₂²×#95	C₂³	1	1	yes	characteristic
311	C₂²×#95	C₂³	1	1	yes	characteristic
312	C₂²×#95	C₂³	1	1	yes	characteristic
313	C₂²×#95	C₂³	1	1	yes	characteristic
314	C₂²×#95	C₂³	1	1	yes	characteristic
315	C₂²×#95	C₂³	1	1	yes	characteristic
316	C₂²×#95	C₂³	1	1	yes	characteristic
317	C₂²×#95	C₂³	1	1	yes	characteristic
318	C₂²×#95	C₂³	1	1	yes	characteristic
319	C₂²×#95	C₂³	1	1	yes	characteristic
320	C₂²×#95	C₂³	1	1	yes	characteristic
321	C₂²×#95	C₂³	1	1	yes	characteristic
322	C₂²×#95	C₂³	1	1	yes	characteristic
323	C₂²×#95	C₂³	1	1	yes	characteristic
324	C₂²×#95	C₂³	1	1	yes	characteristic
325	C₂²×#95	C₂³	1	1	yes	characteristic
326	C₂²×#95	C₂³	1	1	yes	characteristic
327	C₂²×#95	C₂³	1	1	yes	characteristic
328	C₂²×#95	C₂³	1	1	yes	characteristic
329	C₂²×#95	C₂³	1	1	yes	characteristic
330	C₂²×#95	C₂³	1	1	yes	characteristic
331	C₂²×#95	C₂³	1	1	yes	characteristic
332	C₂²×#95	C₂³	1	1	yes	characteristic
333	C₂²×#95	C₂³	1	1	yes	characteristic
334	C₂²×#95	C₂³	1	1	yes	characteristic
335	C₂²×#95	C₂³	1	1	yes	characteristic
336	C₂²×#95	C₂³	1	1	yes	characteristic
337	C₂²×#95	C₂³	1	1	yes	characteristic
338	C₂²×#95	C₂³	1	1	yes	characteristic
339	C₂²×#95	C₂³	1	1	yes	characteristic
340	C₂²×#95	C₂³	1	1	yes	characteristic
341	C₂²×#95	C₂³	1	1	yes	characteristic
342	C₂²×#95	C₂³	1	1	yes	characteristic
343	C₂²×#95	C₂³	1	1	yes	characteristic
344	C₂²×#95	C₂³	1	1	yes	characteristic
345	C₂²×#95	C₂³	1	1	yes	characteristic
346	C₂²×#95	C₂³	1	1	yes	characteristic
347	#1439	D₄	1	8	yes	complemented
348	C₂⁶	C₂×D₄	1	4	yes	—
349	C₂⁶	#41	1	4	yes	—
350	C₂⁶	C₂⁴	1	1	yes	characteristic
351	C₂⁶	C₂⁴	1	1	yes	characteristic
352	C₂⁶	C₂⁴	1	1	yes	characteristic
353	C₂⁶	C₂⁴	1	1	yes	characteristic
354	C₂⁶	C₂⁴	1	1	yes	characteristic
355	C₂⁶	C₂⁴	1	1	yes	characteristic
356	C₂⁶	C₂⁴	1	1	yes	characteristic
357	C₂³×D₄	C₂×D₄	1	4	yes	—
358	C₂³×D₄	C₂×D₄	1	4	yes	—
359	C₂³×D₄	C₂×D₄	1	4	yes	—
360	C₂³×D₄	C₂×D₄	1	4	yes	—
361	C₂³×D₄	C₂×D₄	1	4	yes	—
362	C₂³×D₄	C₂×D₄	1	4	yes	—
363	C₂³×D₄	C₂×D₄	1	4	yes	—
364	C₂³×D₄	C₂×D₄	1	4	yes	—
365	C₂³×D₄	#41	1	4	yes	—
366	C₂³×D₄	#41	1	4	yes	—
367	C₂³×D₄	#41	1	4	yes	—
368	C₂⁴×C₄	C₂×D₄	1	4	yes	—
369	C₂⁴×C₄	C₂×D₄	1	4	yes	—
370	C₂⁴×C₄	C₂×D₄	1	4	yes	—
371	C₂⁴×C₄	#41	1	4	yes	—
372	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
373	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
374	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
375	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
376	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
377	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
378	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
379	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
380	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
381	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
382	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
383	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
384	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
385	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
386	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
387	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
388	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
389	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
390	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
391	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
392	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
393	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
394	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
395	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄⋊C₄	C₂×D₄	1	4	yes	—
397	C₂²×C₄⋊C₄	C₂×D₄	1	4	yes	complemented
398	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
399	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
400	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
401	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
402	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
403	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
404	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
405	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
406	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
407	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
408	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
409	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
410	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
411	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
412	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
413	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
414	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
415	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
416	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
417	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
418	C₂²×C₄²	C₂×D₄	1	4	yes	—
419	C₂×#95	C₂×D₄	1	4	yes	—
420	C₂×#95	C₂×D₄	1	4	yes	—
421	C₂×#95	C₂×D₄	1	4	yes	—
422	C₂×#95	C₂×D₄	1	4	yes	—
423	C₂×#95	C₂×D₄	1	4	yes	complemented
424	C₂×#95	C₂×D₄	1	4	yes	complemented
425	C₂×#95	C₂×D₄	1	4	yes	complemented
426	C₂⁵	C₂²×D₄	1	2	yes	—
427	C₂⁵	C₂²×D₄	1	2	yes	—
428	C₂⁵	C₂²×D₄	1	2	yes	—
429	C₂⁵	C₂²×D₄	1	2	yes	—
430	C₂⁵	C₂²×D₄	1	2	yes	—
431	C₂⁵	C₂²×D₄	1	2	yes	—
432	C₂⁵	C₂²×D₄	1	2	yes	—
433	C₂⁵	C₂²×D₄	1	2	yes	—
434	C₂⁵	C₂²×D₄	1	2	yes	—
435	C₂⁵	C₂²×D₄	1	2	yes	—
436	C₂⁵	C₂²×D₄	1	2	yes	—
437	C₂⁵	C₂²×D₄	1	2	yes	—
438	C₂⁵	C₂²×D₄	1	2	yes	—
439	C₂⁵	C₂²×D₄	1	2	yes	—
440	C₂⁵	C₂×#41	1	2	yes	—
441	C₂⁵	C₂×#41	1	2	yes	—
442	C₂⁵	C₂×#41	1	2	yes	—
443	C₂⁵	C₂×#41	1	2	yes	—
444	C₂⁵	C₂×#41	1	2	yes	—
445	C₂⁵	C₂×#41	1	2	yes	—
446	C₂⁵	C₂×#41	1	2	yes	—
447	C₂⁵	C₂×#41	1	2	yes	—
448	C₂⁵	C₂×#41	1	2	yes	—
449	C₂⁵	C₂×#41	1	2	yes	—
450	C₂⁵	H(5,𝔽₂)	1	2	yes	—
451	C₂⁵	H(5,𝔽₂)	1	2	yes	—
452	C₂⁵	H(5,𝔽₂)	1	2	yes	—
453	C₂⁵	H(5,𝔽₂)	1	2	yes	—
454	C₂⁵	H(5,𝔽₂)	1	2	yes	—
455	C₂⁵	H(5,𝔽₂)	1	2	yes	—
456	C₂⁵	H(5,𝔽₂)	1	2	yes	—
457	C₂⁵	C₂⁵	1	1	yes	characteristic
458	C₂²×D₄	#120	1	16	yes	—
459	C₂³×C₄	C₂²×D₄	1	2	yes	—
460	C₂³×C₄	C₂²×D₄	1	2	yes	—
461	C₂³×C₄	C₂²×D₄	1	2	yes	—
462	C₂³×C₄	C₂²×D₄	1	2	yes	—
463	C₂³×C₄	C₂²×D₄	1	2	yes	—
464	C₂³×C₄	C₂²×D₄	1	2	yes	—
465	C₂³×C₄	C₂²×D₄	1	2	yes	—
466	C₂³×C₄	C₂²×D₄	1	2	yes	—
467	C₂³×C₄	C₂²×D₄	1	2	yes	—
468	C₂³×C₄	C₂²×D₄	1	2	yes	—
469	C₂³×C₄	C₂²×D₄	1	2	yes	—
470	C₂³×C₄	C₂²×D₄	1	2	yes	—
471	C₂³×C₄	C₂²×D₄	1	2	yes	—
472	C₂³×C₄	C₂²×D₄	1	2	yes	—
473	C₂³×C₄	C₂²×D₄	1	2	yes	—
474	C₂³×C₄	C₂²×D₄	1	2	yes	—
475	C₂³×C₄	C₂²×D₄	1	2	yes	—
476	C₂³×C₄	C₂²×D₄	1	2	yes	—
477	C₂³×C₄	C₂²×D₄	1	2	yes	—
478	C₂³×C₄	C₂²×D₄	1	2	yes	—
479	C₂³×C₄	C₂²×D₄	1	2	yes	—
480	C₂³×C₄	C₂²×D₄	1	2	yes	—
481	C₂³×C₄	C₂²×D₄	1	2	yes	—
482	C₂³×C₄	C₂²×D₄	1	2	yes	—
483	C₂³×C₄	C₂²×D₄	1	2	yes	—
484	C₂³×C₄	C₂²×D₄	1	2	yes	—
485	C₂³×C₄	C₂²×D₄	1	2	yes	—
486	C₂³×C₄	C₂²×D₄	1	2	yes	—
487	C₂³×C₄	C₂×#41	1	2	yes	—
488	C₂³×C₄	C₂×#41	1	2	yes	—
489	C₂³×C₄	C₂×#41	1	2	yes	—
490	C₂³×C₄	C₂×#41	1	2	yes	—
491	C₂³×C₄	C₂×#41	1	2	yes	—
492	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
493	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
494	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
495	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
496	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
497	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
498	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
499	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
500	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
501	C₂×C₂²⋊C₄	#120	1	16	yes	complemented
502	C₂⁴	C₂×#120	1	4	yes	—
503	C₂⁴	C₂×#120	1	4	yes	—
504	C₂⁴	C₂×#120	1	4	yes	—
505	C₂⁴	#525	1	4	yes	—
506	C₂⁴	#525	1	4	yes	—
507	C₂⁴	#525	1	4	yes	—
508	C₂⁴	#525	1	4	yes	—
509	C₂⁴	#525	1	4	yes	—
510	C₂⁴	#534	1	4	yes	—
511	C₂⁴	#535	1	4	yes	—
512	C₂⁴	#538	1	4	yes	—
513	C₂⁴	D₄²	1	4	yes	—
514	C₂⁴	D₄²	1	4	yes	—
515	C₂⁴	D₄²	1	4	yes	—
516	C₂⁴	D₄²	1	4	yes	—
517	C₂⁴	D₄²	1	4	yes	—
518	C₂⁴	#546	1	4	yes	—
519	C₂⁴	#546	1	4	yes	—
520	C₂⁴	#546	1	4	yes	—
521	C₂⁴	#546	1	4	yes	—
522	C₂⁴	#546	1	4	yes	—
523	C₂⁴	#546	1	4	yes	—
524	C₂⁴	#550	1	4	yes	—
525	C₂⁴	#553	1	4	yes	—
526	C₂⁴	C₂³×D₄	1	1	yes	characteristic
527	C₂⁴	C₂³×D₄	1	1	yes	characteristic
528	C₂⁴	C₂³×D₄	1	1	yes	characteristic
529	C₂⁴	C₂³×D₄	1	1	yes	characteristic
530	C₂⁴	C₂³×D₄	1	1	yes	characteristic
531	C₂⁴	C₂³×D₄	1	1	yes	characteristic
532	C₂⁴	C₂²×#41	1	1	yes	characteristic
533	C₂⁴	C₂²×#41	1	1	yes	characteristic
534	C₂⁴	C₂²×#41	1	1	yes	characteristic
535	C₂⁴	C₂²×#41	1	1	yes	characteristic
536	C₂⁴	C₂²×#41	1	1	yes	characteristic
537	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
538	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
539	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
540	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
541	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
542	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
543	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
544	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
545	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
546	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
547	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
549	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
550	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
551	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
552	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
553	C₂⁴	#585	1	1	yes	characteristic
554	C₂⁴	#585	1	1	yes	characteristic
555	C₂⁴	#585	1	1	yes	characteristic
556	C₂⁴	#585	1	1	yes	characteristic
557	C₂²×C₄	C₂×#120	1	4	yes	—
558	C₂²×C₄	C₂×#120	1	4	yes	—
559	C₂²×C₄	C₂×#120	1	4	yes	—
560	C₂²×C₄	#525	1	4	yes	—
561	C₂²×C₄	#525	1	4	yes	—
562	C₂²×C₄	#535	1	4	yes	—
563	C₂²×C₄	D₄²	1	4	yes	—
564	C₂²×C₄	D₄²	1	4	yes	—
565	C₂²×C₄	D₄²	1	4	yes	—
566	C₂²×C₄	D₄²	1	4	yes	—
567	C₂²×C₄	#546	1	4	yes	—
568	C₂²×C₄	#546	1	4	yes	—
569	C₂²×C₄	#546	1	4	yes	—
570	C₂²×C₄	#546	1	4	yes	—
571	C₂³	#2403	1	8	yes	—
572	C₂³	#2404	1	8	yes	—
573	C₂³	#2456	1	8	yes	complemented
574	C₂³	C₂²×#120	1	1	yes	characteristic
575	C₂³	C₂²×#120	1	1	yes	characteristic
576	C₂³	C₂×#525	1	1	yes	characteristic
577	C₂³	C₂×#525	1	1	yes	characteristic
578	C₂³	C₂×#525	1	1	yes	characteristic
579	C₂³	C₂×#525	1	1	yes	characteristic
580	C₂³	C₂×#525	1	1	yes	characteristic
581	C₂³	C₂×#525	1	1	yes	characteristic
582	C₂³	C₂×#525	1	1	yes	characteristic
583	C₂³	C₂×#534	1	1	yes	characteristic
584	C₂³	C₂×#535	1	1	yes	characteristic
585	C₂³	C₂×#535	1	1	yes	characteristic
586	C₂³	C₂×#538	1	1	yes	characteristic
587	C₂³	#3459	1	1	yes	characteristic
588	C₂³	#3459	1	1	yes	characteristic
589	C₂³	C₂×D₄²	1	1	yes	characteristic
590	C₂³	C₂×D₄²	1	1	yes	characteristic
591	C₂³	C₂×D₄²	1	1	yes	characteristic
592	C₂³	C₂×D₄²	1	1	yes	characteristic
593	C₂³	C₂×D₄²	1	1	yes	characteristic
594	C₂³	C₂×D₄²	1	1	yes	characteristic
595	C₂³	C₂×D₄²	1	1	yes	characteristic
596	C₂³	C₂×D₄²	1	1	yes	characteristic
597	C₂³	C₂×D₄²	1	1	yes	characteristic
598	C₂³	C₂×#546	1	1	yes	characteristic
599	C₂³	C₂×#546	1	1	yes	characteristic
600	C₂³	C₂×#546	1	1	yes	characteristic
601	C₂³	C₂×#546	1	1	yes	characteristic
602	C₂³	C₂×#546	1	1	yes	characteristic
603	C₂³	C₂×#546	1	1	yes	characteristic
604	C₂³	C₂×#546	1	1	yes	characteristic
605	C₂³	C₂×#546	1	1	yes	characteristic
606	C₂³	C₂×#546	1	1	yes	characteristic
607	C₂³	C₂×#546	1	1	yes	characteristic
608	C₂³	C₂×#550	1	1	yes	characteristic
609	C₂³	D₄×#41	1	1	yes	characteristic
610	C₂³	D₄×#41	1	1	yes	characteristic
611	C₂³	D₄×#41	1	1	yes	characteristic
612	C₂³	D₄×#41	1	1	yes	characteristic
613	C₂³	D₄×#41	1	1	yes	characteristic
614	C₂³	C₂×#553	1	1	yes	characteristic
615	C₂³	#3481	1	1	yes	characteristic
616	C₂³	#3481	1	1	yes	characteristic
617	C₂³	#3484	1	1	yes	characteristic
618	C₂³	#3484	1	1	yes	characteristic
619	C₂³	#3484	1	1	yes	characteristic
620	C₂³	#3484	1	1	yes	characteristic
621	C₂³	#3484	1	1	yes	characteristic
622	C₂³	#3484	1	1	yes	characteristic
623	C₂³	#3484	1	1	yes	characteristic
624	C₂³	#3484	1	1	yes	characteristic
625	C₂³	#3484	1	1	yes	characteristic
626	C₂³	#3484	1	1	yes	characteristic
627	C₂³	#3484	1	1	yes	characteristic
628	C₂³	#3484	1	1	yes	characteristic
629	C₂³	#3484	1	1	yes	characteristic
630	C₂³	#3484	1	1	yes	characteristic
631	C₂³	#3484	1	1	yes	characteristic
632	C₂³	#3484	1	1	yes	characteristic
633	C₂³	#3484	1	1	yes	characteristic
634	C₂³	#3484	1	1	yes	characteristic
635	C₂³	#3485	1	1	yes	characteristic
636	C₂³	#3485	1	1	yes	characteristic
637	C₂³	#3488	1	1	yes	characteristic
638	C₂³	#3488	1	1	yes	characteristic
639	C₂³	#3488	1	1	yes	characteristic
640	C₂³	#3488	1	1	yes	characteristic
641	C₂³	#3488	1	1	yes	characteristic
642	C₂³	#3488	1	1	yes	characteristic
643	C₂³	#3488	1	1	yes	characteristic
644	C₂³	#3488	1	1	yes	characteristic
645	C₂³	#3490	1	1	yes	characteristic
646	C₂³	#3490	1	1	yes	characteristic
647	C₂³	#3490	1	1	yes	characteristic
648	C₂³	#3490	1	1	yes	characteristic
649	C₂³	#3490	1	1	yes	characteristic
650	C₂³	#3490	1	1	yes	characteristic
651	C₂³	#3490	1	1	yes	characteristic
652	C₂³	#3490	1	1	yes	characteristic
653	C₂³	#3490	1	1	yes	characteristic
654	C₂³	#3490	1	1	yes	characteristic
655	C₂³	#3490	1	1	yes	characteristic
656	C₂³	#3490	1	1	yes	characteristic
657	C₂³	#3494	1	1	yes	characteristic
658	C₂³	#3494	1	1	yes	characteristic
659	C₂³	#3496	1	1	yes	characteristic
660	C₂³	#3496	1	1	yes	characteristic
661	C₂³	#3496	1	1	yes	characteristic
662	C₂³	#3496	1	1	yes	characteristic
663	C₂³	#3496	1	1	yes	characteristic
664	C₂³	#3496	1	1	yes	characteristic
665	C₂³	#3496	1	1	yes	characteristic
666	C₂³	#3498	1	1	yes	characteristic
667	C₂³	#3498	1	1	yes	characteristic
668	C₂³	#3498	1	1	yes	characteristic
669	C₂³	#3498	1	1	yes	characteristic
670	C₂³	#3498	1	1	yes	characteristic
671	C₂³	#3505	1	1	yes	characteristic
672	C₂³	#3505	1	1	yes	characteristic
673	C₂³	#3505	1	1	yes	characteristic
674	C₂³	#3506	1	1	yes	characteristic
675	C₂³	#3506	1	1	yes	characteristic
676	C₂³	#3508	1	1	yes	characteristic
677	C₂³	#3508	1	1	yes	characteristic
678	C₂³	#3513	1	1	yes	characteristic
679	C₂³	#3513	1	1	yes	characteristic
680	C₂³	#3513	1	1	yes	characteristic
681	C₂³	#3514	1	1	yes	characteristic
682	C₂³	#3519	1	1	yes	characteristic
683	C₂³	#3519	1	1	yes	characteristic
684	C₂³	#3519	1	1	yes	characteristic
685	C₂³	#3519	1	1	yes	characteristic
686	C₂³	#3519	1	1	yes	characteristic
687	C₂³	#3519	1	1	yes	characteristic
688	C₂³	#3519	1	1	yes	characteristic
689	C₂³	#3519	1	1	yes	characteristic
690	C₂³	#3519	1	1	yes	characteristic
691	C₂³	#3519	1	1	yes	characteristic
692	C₂³	#3521	1	1	yes	characteristic
693	C₂³	#3532	1	1	yes	characteristic
694	C₂³	#3532	1	1	yes	characteristic
695	C₂³	#3532	1	1	yes	characteristic
696	C₂³	#3532	1	1	yes	characteristic
697	C₂³	#3532	1	1	yes	characteristic
698	C₂³	#3533	1	1	yes	characteristic
699	C₂³	#3534	1	1	yes	characteristic
700	C₂³	#3534	1	1	yes	characteristic
701	C₂³	#3534	1	1	yes	characteristic
702	C₂³	#3534	1	1	yes	characteristic
703	C₂³	#3534	1	1	yes	characteristic
704	C₂³	#3534	1	1	yes	characteristic
705	C₂³	#3537	1	1	yes	characteristic
706	C₂³	#3537	1	1	yes	characteristic
707	C₂³	#3537	1	1	yes	characteristic
708	C₂³	#3537	1	1	yes	characteristic
709	C₂³	#3537	1	1	yes	characteristic
710	C₂³	#3537	1	1	yes	characteristic
711	C₂³	#3537	1	1	yes	characteristic
712	C₂³	#3537	1	1	yes	characteristic
713	C₂³	#3542	1	1	yes	characteristic
714	C₂³	#3542	1	1	yes	characteristic
715	C₂³	#3542	1	1	yes	characteristic
716	C₂³	#3542	1	1	yes	characteristic
717	C₂³	#3543	1	1	yes	characteristic
718	C₂³	#3543	1	1	yes	characteristic
719	C₂³	#3543	1	1	yes	characteristic
720	C₂³	#3543	1	1	yes	characteristic
721	C₂³	#3543	1	1	yes	characteristic
722	C₂³	#3545	1	1	yes	characteristic
723	C₂³	#3546	1	1	yes	characteristic
724	C₂³	#3546	1	1	yes	characteristic
725	C₂³	#3546	1	1	yes	characteristic
726	C₂³	#3551	1	1	yes	characteristic
727	C₂³	#3558	1	1	yes	characteristic
728	C₂³	#3558	1	1	yes	characteristic
729	C₂×C₄	#2404	1	8	yes	—
730	C₂²	C₂×#2403	1	1	yes	characteristic
731	C₂²	C₂×#2456	1	1	yes	characteristic
732	C₂²	#34655	1	1	yes	characteristic
733	C₂²	#34655	1	1	yes	characteristic
734	C₂²	C₂×#2404	1	1	yes	characteristic
735	C₂²	C₂×#2404	1	1	yes	characteristic
736	C₂²	#34986	1	1	yes	characteristic
737	C₂²	#34990	1	1	yes	characteristic
738	C₂²	#34990	1	1	yes	characteristic
739	C₂²	#35050	1	1	yes	characteristic
740	C₂²	#35050	1	1	yes	characteristic
741	C₂²	#35222	1	1	yes	characteristic
742	C₂²	#35352	1	1	yes	characteristic
743	C₂²	#35355	1	1	yes	characteristic
744	C₂²	#35361	1	1	yes	characteristic
745	C₂²	#35365	1	1	yes	characteristic
746	C₂²	#35524	1	1	yes	characteristic
747	C₂²	#35538	1	1	yes	characteristic
748	C₂²	#35680	1	1	yes	characteristic
749	C₂²	#35680	1	1	yes	characteristic
750	C₂²	#35680	1	1	yes	characteristic
751	C₂²	#35680	1	1	yes	characteristic
752	C₂²	#35681	1	1	yes	characteristic
753	C₂²	#35681	1	1	yes	characteristic
754	C₂²	#35683	1	1	yes	characteristic
755	C₂²	#35692	1	1	yes	characteristic
756	C₂²	#35692	1	1	yes	characteristic
757	C₂²	#35741	1	1	yes	characteristic
758	C₂²	#35777	1	1	yes	characteristic
759	C₂²	#35823	1	1	yes	characteristic
760	C₂²	D₄×#120	1	1	yes	characteristic
761	C₂²	D₄×#120	1	1	yes	characteristic
762	C₂²	#36096	1	1	yes	characteristic
763	C₂²	#36098	1	1	yes	characteristic
764	C₂²	#36098	1	1	yes	characteristic
765	C₂²	#36098	1	1	yes	characteristic
766	C₂²	#36098	1	1	yes	characteristic
767	C₂²	#36098	1	1	yes	characteristic
768	C₂²	#36098	1	1	yes	characteristic
769	C₂²	#36098	1	1	yes	characteristic
770	C₂²	#36098	1	1	yes	characteristic
771	C₂²	#36098	1	1	yes	characteristic
772	C₂²	#36099	1	1	yes	characteristic
773	C₂²	#36101	1	1	yes	characteristic
774	C₂²	#36101	1	1	yes	characteristic
775	C₂²	#36212	1	1	yes	characteristic
776	C₂²	#36212	1	1	yes	characteristic
777	C₂²	#36316	1	1	yes	characteristic
778	C₂²	#36440	1	1	yes	characteristic
779	C₂²	#36440	1	1	yes	characteristic
780	C₂²	#36614	1	1	yes	characteristic
781	C₂²	#37650	1	1	yes	characteristic
782	C₂²	#37660	1	1	yes	characteristic
783	C₂²	#37672	1	1	yes	characteristic
784	C₂²	#37693	1	1	yes	characteristic
785	C₂²	#37744	1	1	yes	characteristic
786	C₂²	#37776	1	1	yes	characteristic
787	C₂²	#38358	1	1	yes	characteristic
788	C₂²	#38424	1	1	yes	characteristic
789	C₂²	#39361	1	1	yes	characteristic
790	C₂²	#39412	1	1	yes	characteristic
791	C₂²	#39428	1	1	yes	characteristic
792	C₂²	#39948	1	1	yes	characteristic
793	C₂²	#40490	1	1	yes	characteristic
794	C₂²	#40512	1	1	yes	characteristic
795	C₂²	#40536	1	1	yes	characteristic
796	C₂²	#40584	1	1	yes	characteristic
797	C₂²	#40640	1	1	yes	characteristic
798	C₂²	#40917	1	1	yes	characteristic
799	C₂²	#40917	1	1	yes	characteristic
800	C₂²	#41029	1	1	yes	characteristic
801	C₂²	#41032	1	1	yes	characteristic
802	C₂²	#41981	1	1	yes	characteristic
803	C₂²	#42480	1	1	yes	characteristic
804	C₂²	#42483	1	1	yes	characteristic
805	C₂²	#42996	1	1	yes	characteristic
806	C₂²	#42997	1	1	yes	characteristic
807	C₂²	#42998	1	1	yes	characteristic
808	C₂²	#43001	1	1	yes	characteristic
809	C₂²	#43001	1	1	yes	characteristic
810	C₂²	#43001	1	1	yes	characteristic
811	C₂²	#43001	1	1	yes	characteristic
812	C₂²	#43010	1	1	yes	characteristic
813	C₂²	#43010	1	1	yes	characteristic
814	C₂²	#43017	1	1	yes	characteristic
815	C₂²	#43019	1	1	yes	characteristic
816	C₂²	#43023	1	1	yes	characteristic
817	C₂²	#43023	1	1	yes	characteristic
818	C₂²	#43080	1	1	yes	characteristic
819	C₂²	#43095	1	1	yes	characteristic
820	C₂²	#43098	1	1	yes	characteristic
821	C₂²	#43098	1	1	yes	characteristic
822	C₂²	#43099	1	1	yes	characteristic
823	C₂²	#43099	1	1	yes	characteristic
824	C₂²	#43111	1	1	yes	characteristic
825	C₂²	#43118	1	1	yes	characteristic
826	C₂²	#43363	1	1	yes	characteristic
827	C₂²	#43363	1	1	yes	characteristic
828	C₂²	#43797	1	1	yes	characteristic
829	C₂²	#43886	1	1	yes	characteristic
830	C₂²	#43886	1	1	yes	characteristic
831	C₂²	#43893	1	1	yes	characteristic
832	C₂²	#43910	1	1	yes	characteristic
833	C₂²	#43964	1	1	yes	characteristic
834	C₂²	#44138	1	1	yes	characteristic
835	C₂²	#44143	1	1	yes	characteristic
836	C₂²	#44241	1	1	yes	characteristic
837	C₂²	#44876	1	1	yes	characteristic
838	C₂²	#44876	1	1	yes	characteristic
839	C₂²	#44899	1	1	yes	characteristic
840	C₂²	#44936	1	1	yes	characteristic
841	C₂²	#44936	1	1	yes	characteristic
842	C₂²	#45010	1	1	yes	characteristic
843	C₂²	#45105	1	1	yes	characteristic
844	C₂²	#45352	1	1	yes	characteristic
845	C₂²	#47827	1	1	yes	characteristic
846	C₂²	#47827	1	1	yes	characteristic
847	C₂²	#47891	1	1	yes	characteristic
848	C₂²	#47931	1	1	yes	characteristic
849	C₂²	#47932	1	1	yes	characteristic
850	C₂²	#47932	1	1	yes	characteristic
851	C₂²	#47952	1	1	yes	characteristic
852	C₂²	#48005	1	1	yes	characteristic
853	C₂²	#48007	1	1	yes	characteristic
854	C₂²	#48454	1	1	yes	characteristic
855	C₂²	#48487	1	1	yes	characteristic
856	C₂²	#48563	1	1	yes	characteristic
857	C₂²	#48667	1	1	yes	characteristic
858	C₂²	#49544	1	1	yes	characteristic
859	C₂²	#49559	1	1	yes	characteristic
860	C₂²	#49599	1	1	yes	characteristic
861	C₂²	#49838	1	1	yes	characteristic
862	C₂²	#49863	1	1	yes	characteristic
863	C₂²	#50015	1	1	yes	characteristic
864	C₂²	#50091	1	1	yes	characteristic
865	C₂²	#58990	1	1	yes	characteristic
866	C₂²	#58991	1	1	yes	characteristic
867	C₂²	#58994	1	1	yes	characteristic
868	C₂²	#58997	1	1	yes	characteristic
869	C₂²	#58997	1	1	yes	characteristic
870	C₂²	#59004	1	1	yes	characteristic
871	C₂²	#59013	1	1	yes	characteristic
872	C₂²	#59028	1	1	yes	characteristic
873	C₂²	#59029	1	1	yes	characteristic
874	C₂²	#59089	1	1	yes	characteristic
875	C₂²	#59123	1	1	yes	characteristic
876	C₂²	#59123	1	1	yes	characteristic
877	C₂²	#59124	1	1	yes	characteristic
878	C₂²	#59124	1	1	yes	characteristic
879	C₂²	#59126	1	1	yes	characteristic
880	C₂²	#59408	1	1	yes	characteristic
881	C₂²	#59412	1	1	yes	characteristic
882	C₂²	#59412	1	1	yes	characteristic
883	C₂²	#59812	1	1	yes	characteristic
884	C₂²	#59814	1	1	yes	characteristic
885	C₂	#612425	1	1	yes	characteristic
886	C₂	#612517	1	1	yes	characteristic
887	C₂	#647938	1	1	yes	characteristic
888	C₂	#687931	1	1	yes	characteristic
889	C₂	#688968	1	1	yes	characteristic
890	C₂	#772778	1	1	yes	characteristic
891	C₂	#772780	1	1	yes	characteristic
892	C₂	#772946	1	1	yes	characteristic
893	C₂	#773003	1	1	yes	characteristic
894	C₂	#775162	1	1	yes	characteristic
895	C₂	#775331	1	1	yes	characteristic
896	C₂	#777327	1	1	yes	characteristic
897	C₂	#779705	1	1	yes	characteristic
898	C₂	#1258522	1	1	yes	characteristic
899	C₂	#1259513	1	1	yes	characteristic
900	C₂	#1264673	1	1	yes	characteristic
901	C₂	#1266209	1	1	yes	characteristic
902	C₂	#1269265	1	1	yes	characteristic
903	C₂	#1277459	1	1	yes	characteristic
904	C₂	#1285141	1	1	yes	characteristic
905	C₂	#1286161	1	1	yes	characteristic
906	C₂	#1418405	1	1	yes	characteristic
907	C₂	#1418439	1	1	yes	characteristic
908	C₂	#1419202	1	1	yes	characteristic
909	C₂	#1420357	1	1	yes	characteristic
910	C₂	#1426628	1	1	yes	characteristic
911	C₂	#1426659	1	1	yes	characteristic
912	C₂	#1427390	1	1	yes	characteristic
913	C₂	#1428498	1	1	yes	characteristic
914	C₂	#4420924	1	1	yes	characteristic
915	C₂	#4931464	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂⁵	C₂⁵
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. C₂²×#2456	C₂	semidirect
2. C₂²×D₄×C₂²⋊C₄	C₂	semidirect
3. C₂×#15273	C₂	semidirect
4. C₂×#15257	C₂	semidirect
5. C₂×#14911	C₂	semidirect
6. C₂×#14715	C₂	semidirect
7. C₂×#14715	C₂	semidirect
8. C₂×#13967	C₂	semidirect
9. #158361	C₂	semidirect
10. #158282	C₂	semidirect
11. #156829	C₂	semidirect
12. #156742	C₂	semidirect
13. #156741	C₂	semidirect
14. #156709	C₂	semidirect
15. #156689	C₂	semidirect
16. #156684	C₂	semidirect
17. #155875	C₂	semidirect
18. #155258	C₂	semidirect
19. #155116	C₂	semidirect
20. #154737	C₂	semidirect
21. #154712	C₂	semidirect
22. #154684	C₂	semidirect
23. #154676	C₂	semidirect
24. #154635	C₂	semidirect
25. #154634	C₂	semidirect
26. #154634	C₂	semidirect
27. #154634	C₂	semidirect
28. #154487	C₂	semidirect
29. #154195	C₂	semidirect
30. #154195	C₂	semidirect
31. #154098	C₂	semidirect
33. C₂³×#123	C₂²	semidirect
34. C₂³×#121	C₂²	semidirect
41. C₂³×C₄×D₄	C₂²	semidirect
44. C₂²×#396	C₂²	semidirect
54. C₂²×#392	C₂²	semidirect
55. C₂²×#392	C₂²	semidirect
56. C₂²×#392	C₂²	semidirect
59. C₂²×#390	C₂²	semidirect
60. C₂²×#388	C₂²	semidirect
61. C₂²×#388	C₂²	semidirect
62. C₂²×#387	C₂²	semidirect
70. C₂²×#386	C₂²	semidirect
71. C₂²×#386	C₂²	semidirect
72. C₂²×#386	C₂²	semidirect
73. C₂²×#386	C₂²	semidirect
74. C₂²×#386	C₂²	semidirect
75. C₂²×#386	C₂²	semidirect
76. C₂²×#386	C₂²	semidirect
77. C₂²×#386	C₂²	semidirect
78. C₂²×#385	C₂²	semidirect
79. C₂²×#381	C₂²	semidirect
88. C₂×#1442	C₂²	semidirect
89. C₂×#1440	C₂²	semidirect
90. C₂×#1440	C₂²	semidirect
91. C₂×#1440	C₂²	semidirect
96. C₂×#1439	C₂²	semidirect
97. C₂×#1439	C₂²	semidirect
98. C₂×#1439	C₂²	semidirect
99. C₂×#1439	C₂²	semidirect
100. C₂×#1439	C₂²	semidirect
101. C₂×#1439	C₂²	semidirect
102. C₂×#1439	C₂²	semidirect
103. C₂×#1439	C₂²	semidirect
104. C₂×#1439	C₂²	semidirect
105. C₂×#1439	C₂²	semidirect
119. C₂×#1438	C₂²	semidirect
120. C₂×#1438	C₂²	semidirect
121. C₂×#1438	C₂²	semidirect
122. C₂×#1438	C₂²	semidirect
123. C₂×#1438	C₂²	semidirect
124. C₂×#1438	C₂²	semidirect
125. C₂×#1438	C₂²	semidirect
126. C₂×#1438	C₂²	semidirect
127. C₂×#1438	C₂²	semidirect
128. C₂×#1438	C₂²	semidirect
129. C₂×#1438	C₂²	semidirect
130. C₂×#1438	C₂²	semidirect
131. C₂×#1438	C₂²	semidirect
132. C₂×#1438	C₂²	semidirect
133. C₂×#1438	C₂²	semidirect
135. C₂×#1437	C₂²	semidirect
136. C₂×#1437	C₂²	semidirect
137. C₂×#1437	C₂²	semidirect
138. C₂×#1437	C₂²	semidirect
141. C₂×C₂²⋊#95	C₂²	semidirect
142. C₂×C₂²⋊#95	C₂²	semidirect
143. C₂×C₂²⋊#95	C₂²	semidirect
144. C₂×C₂²⋊#95	C₂²	semidirect
145. C₂×C₂²⋊#95	C₂²	semidirect
146. C₂×C₂²⋊#95	C₂²	semidirect
147. C₂×C₂²⋊#95	C₂²	semidirect
148. C₂×C₂²⋊#95	C₂²	semidirect
149. #7557	C₂²	semidirect
150. #7557	C₂²	semidirect
151. #7557	C₂²	semidirect
152. #7557	C₂²	semidirect
153. #7557	C₂²	semidirect
154. #7557	C₂²	semidirect
155. #7557	C₂²	semidirect
156. #7556	C₂²	semidirect
157. #7556	C₂²	semidirect
158. #7556	C₂²	semidirect
159. #7556	C₂²	semidirect
164. #7555	C₂²	semidirect
165. #7555	C₂²	semidirect
166. #7555	C₂²	semidirect
167. #7555	C₂²	semidirect
168. #7555	C₂²	semidirect
169. #7555	C₂²	semidirect
170. #7555	C₂²	semidirect
171. #7555	C₂²	semidirect
172. #7555	C₂²	semidirect
173. #7555	C₂²	semidirect
174. #7555	C₂²	semidirect
175. #7555	C₂²	semidirect
176. #7555	C₂²	semidirect
177. #7555	C₂²	semidirect
178. #7555	C₂²	semidirect
179. #7555	C₂²	semidirect
180. #7555	C₂²	semidirect
181. #7555	C₂²	semidirect
182. #7554	C₂²	semidirect
183. #7554	C₂²	semidirect
184. #7554	C₂²	semidirect
185. #7554	C₂²	semidirect
186. #7554	C₂²	semidirect
210. C₂²×C₄×D₄	D₄	semidirect
283. C₂×#392	D₄	semidirect
284. C₂×#392	D₄	semidirect
285. C₂×#386	D₄	semidirect
286. C₂×#379	D₄	semidirect
347. #1439	D₄	semidirect
397. C₂²×C₄⋊C₄	C₂×D₄	semidirect
423. C₂×#95	C₂×D₄	semidirect
424. C₂×#95	C₂×D₄	semidirect
425. C₂×#95	C₂×D₄	semidirect
501. C₂×C₂²⋊C₄	#120	semidirect
573. C₂³	#2456	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#2456	2
C₂²×D₄×C₂²⋊C₄	2
C₂×#15273	2
C₂×#15257	2
C₂×#14911	2
C₂×#14715	2
C₂×#13967	2
#158361	2
#158282	2
#156829	2
#156742	2
#156741	2
#156709	2
#156689	2
#156684	2
#155875	2
#155258	2
#155116	2
#154737	2
#154712	2
#154684	2
#154676	2
#154635	2
#154634	2
#154487	2
#154195	2
#154098	2