Subgroups — #72333283

Order 1024.

At least 8035 conjugacy classes of subgroups; only the 1245 normal subgroups are shown.

The subgroup lattice has 888 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×#2358	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15947	C₂	1	1	yes	maximal, characteristic
4	C₂×#14911	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#13967	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13967	C₂	1	1	yes	maximal, characteristic, complemented
7	#157952	C₂	1	1	yes	maximal, characteristic, complemented
8	#157922	C₂	1	1	yes	maximal, characteristic, complemented
9	#157737	C₂	1	1	yes	maximal, characteristic, complemented
10	#157737	C₂	1	1	yes	maximal, characteristic, complemented
11	#157465	C₂	1	1	yes	maximal, characteristic, complemented
12	#156891	C₂	1	1	yes	maximal, characteristic, complemented
13	#156858	C₂	1	1	yes	maximal, characteristic, complemented
14	#156841	C₂	1	1	yes	maximal, characteristic, complemented
15	#155887	C₂	1	1	yes	maximal, characteristic, complemented
16	#154700	C₂	1	1	yes	maximal, characteristic, complemented
17	#154687	C₂	1	1	yes	maximal, characteristic, complemented
18	#154686	C₂	1	1	yes	maximal, characteristic, complemented
19	#154671	C₂	1	1	yes	maximal, characteristic, complemented
20	#154670	C₂	1	1	yes	maximal, characteristic, complemented
21	#154670	C₂	1	1	yes	maximal, characteristic, complemented
22	#154599	C₂	1	1	yes	maximal, characteristic, complemented
23	#154467	C₂	1	1	yes	maximal, characteristic, complemented
24	#154299	C₂	1	1	yes	maximal, characteristic, complemented
25	#154226	C₂	1	1	yes	maximal, characteristic, complemented
26	#154222	C₂	1	1	yes	maximal, characteristic, complemented
27	#154195	C₂	1	1	yes	maximal, characteristic, complemented
28	#154195	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	#154115	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂³×#123	C₂²	1	1	yes	characteristic
33	C₂³×#120	C₂²	1	1	yes	characteristic
34	C₂³×#120	C₂²	1	1	yes	characteristic
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	C₂⁴×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₂⁴×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	C₂⁴×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	C₂²×#390	C₂²	1	1	yes	characteristic
45	C₂²×#388	C₂²	1	1	yes	characteristic, complemented
46	C₂²×#388	C₂²	1	1	yes	characteristic, complemented
47	C₂²×#386	C₂²	1	1	yes	characteristic
48	C₂²×#386	C₂²	1	1	yes	characteristic
49	C₂²×#386	C₂²	1	1	yes	characteristic
50	C₂²×#386	C₂²	1	1	yes	characteristic
51	C₂²×#386	C₂²	1	1	yes	characteristic
52	C₂²×#386	C₂²	1	1	yes	characteristic
53	C₂²×#386	C₂²	1	1	yes	characteristic
54	C₂²×#386	C₂²	1	1	yes	characteristic
55	C₂²×#386	C₂²	1	1	yes	characteristic
56	C₂²×#386	C₂²	1	1	yes	characteristic
57	C₂²×#386	C₂²	1	1	yes	characteristic
58	C₂²×#386	C₂²	1	1	yes	characteristic
59	C₂²×#386	C₂²	1	1	yes	characteristic
60	C₂²×#385	C₂²	1	1	yes	characteristic, complemented
61	C₂²×#385	C₂²	1	1	yes	characteristic, complemented
62	C₂²×#381	C₂²	1	1	yes	characteristic, complemented
63	C₂²×#379	C₂²	1	1	yes	characteristic, complemented
64	C₂²×#379	C₂²	1	1	yes	characteristic, complemented
65	C₂²×#379	C₂²	1	1	yes	characteristic, complemented
66	C₂²×#379	C₂²	1	1	yes	characteristic, complemented
67	C₂²×#379	C₂²	1	1	yes	characteristic, complemented
68	C₂²×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
69	C₂²×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
70	C₂×#1445	C₂²	1	1	yes	characteristic, complemented
71	C₂×#1445	C₂²	1	1	yes	characteristic, complemented
72	C₂×#1442	C₂²	1	1	yes	characteristic, complemented
73	C₂×#1442	C₂²	1	1	yes	characteristic, complemented
74	C₂×#1440	C₂²	1	1	yes	characteristic, complemented
75	C₂×#1440	C₂²	1	1	yes	characteristic, complemented
76	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
77	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
78	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
79	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
80	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
81	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
82	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
83	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
84	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
85	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
86	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
87	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
88	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
89	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
90	C₂×#1438	C₂²	1	1	yes	characteristic
91	C₂×#1438	C₂²	1	1	yes	characteristic
92	C₂×#1438	C₂²	1	1	yes	characteristic
93	C₂×#1438	C₂²	1	1	yes	characteristic
94	C₂×#1438	C₂²	1	1	yes	characteristic
95	C₂×#1438	C₂²	1	1	yes	characteristic
96	C₂×#1438	C₂²	1	1	yes	characteristic
97	C₂×#1438	C₂²	1	1	yes	characteristic
98	C₂×#1438	C₂²	1	1	yes	characteristic
99	C₂×#1438	C₂²	1	1	yes	characteristic
100	C₂×#1438	C₂²	1	1	yes	characteristic
101	C₂×#1438	C₂²	1	1	yes	characteristic
102	C₂×#1438	C₂²	1	1	yes	characteristic
103	C₂×#1438	C₂²	1	1	yes	characteristic
104	C₂×#1438	C₂²	1	1	yes	characteristic
105	C₂×#1438	C₂²	1	1	yes	characteristic
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×#1437	C₂²	1	1	yes	characteristic, complemented
119	C₂×#1437	C₂²	1	1	yes	characteristic, complemented
120	C₂×#1437	C₂²	1	1	yes	characteristic, complemented
121	C₂×#1437	C₂²	1	1	yes	characteristic, complemented
122	C₂×#1437	C₂²	1	1	yes	characteristic, complemented
123	C₂×#1437	C₂²	1	1	yes	characteristic, complemented
124	C₂×#1436	C₂²	1	1	yes	characteristic, complemented
125	C₂×#1436	C₂²	1	1	yes	characteristic, complemented
126	C₂×#1434	C₂²	1	1	yes	characteristic, complemented
127	C₂×#1434	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
136	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
137	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
138	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
139	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
140	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
141	#7557	C₂²	1	1	yes	characteristic, complemented
142	#7557	C₂²	1	1	yes	characteristic, complemented
143	#7557	C₂²	1	1	yes	characteristic, complemented
144	#7557	C₂²	1	1	yes	characteristic, complemented
145	#7556	C₂²	1	1	yes	characteristic, complemented
146	#7556	C₂²	1	1	yes	characteristic, complemented
147	#7556	C₂²	1	1	yes	characteristic, complemented
148	#7556	C₂²	1	1	yes	characteristic, complemented
149	#7556	C₂²	1	1	yes	characteristic, complemented
150	#7556	C₂²	1	1	yes	characteristic, complemented
151	#7556	C₂²	1	1	yes	characteristic, complemented
152	#7556	C₂²	1	1	yes	characteristic, complemented
153	#7556	C₂²	1	1	yes	characteristic, complemented
154	#7556	C₂²	1	1	yes	characteristic, complemented
155	#7555	C₂²	1	1	yes	characteristic, complemented
156	#7555	C₂²	1	1	yes	characteristic, complemented
157	#7555	C₂²	1	1	yes	characteristic, complemented
158	#7555	C₂²	1	1	yes	characteristic, complemented
159	#7555	C₂²	1	1	yes	characteristic, complemented
160	#7555	C₂²	1	1	yes	characteristic, complemented
161	#7555	C₂²	1	1	yes	characteristic, complemented
162	#7555	C₂²	1	1	yes	characteristic, complemented
163	#7555	C₂²	1	1	yes	characteristic, complemented
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	#7555	C₂²	1	1	yes	characteristic, complemented
183	#7555	C₂²	1	1	yes	characteristic, complemented
184	#7555	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	C₂⁵×C₄	C₂³	1	1	yes	characteristic
199	C₂⁵×C₄	C₂³	1	1	yes	characteristic
200	C₂⁵×C₄	C₂³	1	1	yes	characteristic
201	C₂⁵×C₄	C₂³	1	1	yes	characteristic
202	C₂⁵×C₄	C₂³	1	1	yes	characteristic
203	C₂⁵×C₄	C₂³	1	1	yes	characteristic
204	C₂²×#120	D₄	1	8	yes	—
205	C₂²×C₄×D₄	D₄	1	8	yes	complemented
206	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
209	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
212	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
215	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
216	C₂³×C₂²⋊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×C₄²	C₂³	1	1	yes	characteristic
272	C₂³×C₄²	C₂³	1	1	yes	characteristic
273	C₂³×C₄²	C₂³	1	1	yes	characteristic
274	C₂×#386	D₄	1	8	yes	complemented
275	C₂²×#95	C₂³	1	1	yes	characteristic
276	C₂²×#95	C₂³	1	1	yes	characteristic
277	C₂²×#95	C₂³	1	1	yes	characteristic
278	C₂²×#95	C₂³	1	1	yes	characteristic
279	C₂²×#95	C₂³	1	1	yes	characteristic
280	C₂²×#95	C₂³	1	1	yes	characteristic
281	C₂²×#95	C₂³	1	1	yes	characteristic
282	C₂²×#95	C₂³	1	1	yes	characteristic
283	C₂²×#95	C₂³	1	1	yes	characteristic
284	C₂²×#95	C₂³	1	1	yes	characteristic
285	C₂²×#95	C₂³	1	1	yes	characteristic
286	C₂²×#95	C₂³	1	1	yes	characteristic
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	#1438	D₄	1	8	yes	complemented
346	C₂⁶	C₂×D₄	1	4	yes	—
347	C₂⁶	C₂⁴	1	1	yes	characteristic
348	C₂⁶	C₂⁴	1	1	yes	characteristic
349	C₂⁶	C₂⁴	1	1	yes	characteristic
350	C₂⁶	C₂⁴	1	1	yes	characteristic
351	C₂⁶	C₂⁴	1	1	yes	characteristic
352	C₂⁶	C₂⁴	1	1	yes	characteristic
353	C₂³×D₄	C₂×D₄	1	4	yes	—
354	C₂³×D₄	C₂×D₄	1	4	yes	—
355	C₂³×D₄	C₂×D₄	1	4	yes	—
356	C₂³×D₄	C₂×D₄	1	4	yes	—
357	C₂³×D₄	C₂×D₄	1	4	yes	—
358	C₂³×D₄	C₂×D₄	1	4	yes	—
359	C₂³×D₄	#41	1	4	yes	—
360	C₂³×D₄	#41	1	4	yes	—
361	C₂³×D₄	#41	1	4	yes	—
362	C₂³×D₄	#41	1	4	yes	—
363	C₂³×D₄	#41	1	4	yes	—
364	C₂³×D₄	#41	1	4	yes	—
365	C₂³×D₄	#41	1	4	yes	—
366	C₂⁴×C₄	C₂×D₄	1	4	yes	—
367	C₂⁴×C₄	C₂×D₄	1	4	yes	—
368	C₂⁴×C₄	C₂×D₄	1	4	yes	—
369	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
370	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
371	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄⋊C₄	C₂×D₄	1	4	yes	—
395	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
396	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
397	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
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×C₄²	C₂×D₄	1	4	yes	—
408	C₂×#95	C₂×D₄	1	4	yes	—
409	C₂×#95	C₂×D₄	1	4	yes	—
410	C₂×#95	C₂×D₄	1	4	yes	—
411	C₂×#95	C₂×D₄	1	4	yes	—
412	C₂⁵	C₂²×D₄	1	2	yes	—
413	C₂⁵	C₂²×D₄	1	2	yes	—
414	C₂⁵	C₂²×D₄	1	2	yes	—
415	C₂⁵	C₂²×D₄	1	2	yes	—
416	C₂⁵	C₂²×D₄	1	2	yes	—
417	C₂⁵	C₂²×D₄	1	2	yes	—
418	C₂⁵	C₂²×D₄	1	2	yes	—
419	C₂⁵	C₂²×D₄	1	2	yes	—
420	C₂⁵	C₂²×D₄	1	2	yes	—
421	C₂⁵	C₂²×D₄	1	2	yes	—
422	C₂⁵	C₂×#41	1	2	yes	—
423	C₂⁵	C₂×#41	1	2	yes	—
424	C₂⁵	C₂×#41	1	2	yes	—
425	C₂⁵	C₂×#41	1	2	yes	—
426	C₂⁵	C₂×#41	1	2	yes	—
427	C₂⁵	C₂×#41	1	2	yes	—
428	C₂⁵	C₂×#41	1	2	yes	—
429	C₂⁵	C₂×#41	1	2	yes	—
430	C₂⁵	C₂×#41	1	2	yes	—
431	C₂⁵	C₂×#41	1	2	yes	—
432	C₂⁵	C₂×#41	1	2	yes	—
433	C₂⁵	C₂×#41	1	2	yes	—
434	C₂⁵	C₂×#41	1	2	yes	—
435	C₂⁵	C₂×#41	1	2	yes	—
436	C₂⁵	H(5,𝔽₂)	1	2	yes	—
437	C₂⁵	H(5,𝔽₂)	1	2	yes	—
438	C₂⁵	H(5,𝔽₂)	1	2	yes	—
439	C₂⁵	H(5,𝔽₂)	1	2	yes	—
440	C₂⁵	H(5,𝔽₂)	1	2	yes	—
441	C₂⁵	H(5,𝔽₂)	1	2	yes	—
442	C₂⁵	C₂⁵	1	1	yes	characteristic
443	C₂²×D₄	#120	1	16	yes	—
444	C₂²×D₄	#123	1	16	yes	complemented
445	C₂²×D₄	#123	1	16	yes	complemented
446	C₂³×C₄	C₂²×D₄	1	2	yes	—
447	C₂³×C₄	C₂²×D₄	1	2	yes	—
448	C₂³×C₄	C₂²×D₄	1	2	yes	—
449	C₂³×C₄	C₂²×D₄	1	2	yes	—
450	C₂³×C₄	C₂²×D₄	1	2	yes	—
451	C₂³×C₄	C₂²×D₄	1	2	yes	—
452	C₂³×C₄	C₂²×D₄	1	2	yes	—
453	C₂³×C₄	C₂²×D₄	1	2	yes	—
454	C₂³×C₄	C₂²×D₄	1	2	yes	—
455	C₂³×C₄	C₂²×D₄	1	2	yes	—
456	C₂³×C₄	C₂²×D₄	1	2	yes	—
457	C₂³×C₄	C₂²×D₄	1	2	yes	—
458	C₂³×C₄	C₂²×D₄	1	2	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	C₂×#41	1	2	yes	—
465	C₂³×C₄	C₂×#41	1	2	yes	—
466	C₂³×C₄	C₂×#41	1	2	yes	—
467	C₂³×C₄	C₂×#41	1	2	yes	—
468	C₂³×C₄	C₂×#41	1	2	yes	—
469	C₂³×C₄	C₂×#41	1	2	yes	—
470	C₂³×C₄	C₂×#41	1	2	yes	—
471	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
472	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
473	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
474	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
475	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
476	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
477	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
478	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
479	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
480	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
481	C₂⁴	C₂×#120	1	4	yes	—
482	C₂⁴	C₂×#120	1	4	yes	—
483	C₂⁴	C₂×#123	1	4	yes	—
484	C₂⁴	C₂×#123	1	4	yes	—
485	C₂⁴	C₂×#123	1	4	yes	—
486	C₂⁴	C₂×#123	1	4	yes	—
487	C₂⁴	#525	1	4	yes	—
488	C₂⁴	#525	1	4	yes	—
489	C₂⁴	#525	1	4	yes	—
490	C₂⁴	#525	1	4	yes	—
491	C₂⁴	#525	1	4	yes	—
492	C₂⁴	#525	1	4	yes	—
493	C₂⁴	#535	1	4	yes	—
494	C₂⁴	#538	1	4	yes	—
495	C₂⁴	D₄²	1	4	yes	—
496	C₂⁴	#546	1	4	yes	—
497	C₂⁴	#546	1	4	yes	—
498	C₂⁴	#546	1	4	yes	—
499	C₂⁴	#546	1	4	yes	—
500	C₂⁴	#546	1	4	yes	—
501	C₂⁴	#546	1	4	yes	—
502	C₂⁴	#546	1	4	yes	—
503	C₂⁴	#551	1	4	yes	—
504	C₂⁴	#551	1	4	yes	—
505	C₂⁴	C₂³×D₄	1	1	yes	characteristic
506	C₂⁴	C₂³×D₄	1	1	yes	characteristic
507	C₂⁴	C₂³×D₄	1	1	yes	characteristic
508	C₂⁴	C₂³×D₄	1	1	yes	characteristic
509	C₂⁴	C₂²×#41	1	1	yes	characteristic
510	C₂⁴	C₂²×#41	1	1	yes	characteristic
511	C₂⁴	C₂²×#41	1	1	yes	characteristic
512	C₂⁴	C₂²×#41	1	1	yes	characteristic
513	C₂⁴	C₂²×#41	1	1	yes	characteristic
514	C₂⁴	C₂²×#41	1	1	yes	characteristic
515	C₂⁴	C₂²×#41	1	1	yes	characteristic
516	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
517	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
518	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
519	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
520	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
521	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
522	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
523	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
525	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
526	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
527	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
528	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
529	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
530	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
531	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂⁴	#585	1	1	yes	characteristic
533	C₂⁴	#585	1	1	yes	characteristic
534	C₂⁴	#585	1	1	yes	characteristic
535	C₂⁴	#585	1	1	yes	characteristic
536	C₂²×C₄	C₂×#120	1	4	yes	—
537	C₂²×C₄	C₂×#123	1	4	yes	—
538	C₂²×C₄	C₂×#123	1	4	yes	—
539	C₂²×C₄	#534	1	4	yes	—
540	C₂²×C₄	#534	1	4	yes	—
541	C₂²×C₄	D₄²	1	4	yes	—
542	C₂²×C₄	D₄²	1	4	yes	—
543	C₂³	#2404	1	8	yes	—
544	C₂³	#2418	1	8	yes	—
545	C₂³	#2849	1	8	yes	—
546	C₂³	C₂²×#120	1	1	yes	characteristic
547	C₂³	C₂²×#123	1	1	yes	characteristic
548	C₂³	C₂²×#123	1	1	yes	characteristic
549	C₂³	C₂×#525	1	1	yes	characteristic
550	C₂³	C₂×#525	1	1	yes	characteristic
551	C₂³	C₂×#525	1	1	yes	characteristic
552	C₂³	C₂×#525	1	1	yes	characteristic
553	C₂³	C₂×#525	1	1	yes	characteristic
554	C₂³	C₂×#525	1	1	yes	characteristic
555	C₂³	C₂×#534	1	1	yes	characteristic
556	C₂³	C₂×#534	1	1	yes	characteristic
557	C₂³	C₂×#535	1	1	yes	characteristic
558	C₂³	C₂×#538	1	1	yes	characteristic
559	C₂³	#3459	1	1	yes	characteristic
560	C₂³	#3459	1	1	yes	characteristic
561	C₂³	C₂×D₄²	1	1	yes	characteristic
562	C₂³	C₂×D₄²	1	1	yes	characteristic
563	C₂³	C₂×D₄²	1	1	yes	characteristic
564	C₂³	C₂×#546	1	1	yes	characteristic
565	C₂³	C₂×#546	1	1	yes	characteristic
566	C₂³	C₂×#546	1	1	yes	characteristic
567	C₂³	C₂×#546	1	1	yes	characteristic
568	C₂³	C₂×#546	1	1	yes	characteristic
569	C₂³	C₂×#546	1	1	yes	characteristic
570	C₂³	C₂×#546	1	1	yes	characteristic
571	C₂³	D₄×#41	1	1	yes	characteristic
572	C₂³	D₄×#41	1	1	yes	characteristic
573	C₂³	D₄×#41	1	1	yes	characteristic
574	C₂³	D₄×#41	1	1	yes	characteristic
575	C₂³	D₄×#41	1	1	yes	characteristic
576	C₂³	C₂×#551	1	1	yes	characteristic
577	C₂³	C₂×#551	1	1	yes	characteristic
578	C₂³	#3481	1	1	yes	characteristic
579	C₂³	#3481	1	1	yes	characteristic
580	C₂³	#3481	1	1	yes	characteristic
581	C₂³	#3481	1	1	yes	characteristic
582	C₂³	#3481	1	1	yes	characteristic
583	C₂³	#3481	1	1	yes	characteristic
584	C₂³	#3481	1	1	yes	characteristic
585	C₂³	#3481	1	1	yes	characteristic
586	C₂³	#3481	1	1	yes	characteristic
587	C₂³	#3481	1	1	yes	characteristic
588	C₂³	#3481	1	1	yes	characteristic
589	C₂³	#3484	1	1	yes	characteristic
590	C₂³	#3484	1	1	yes	characteristic
591	C₂³	#3484	1	1	yes	characteristic
592	C₂³	#3484	1	1	yes	characteristic
593	C₂³	#3484	1	1	yes	characteristic
594	C₂³	#3484	1	1	yes	characteristic
595	C₂³	#3484	1	1	yes	characteristic
596	C₂³	#3484	1	1	yes	characteristic
597	C₂³	#3484	1	1	yes	characteristic
598	C₂³	#3484	1	1	yes	characteristic
599	C₂³	#3484	1	1	yes	characteristic
600	C₂³	#3484	1	1	yes	characteristic
601	C₂³	#3484	1	1	yes	characteristic
602	C₂³	#3484	1	1	yes	characteristic
603	C₂³	#3484	1	1	yes	characteristic
604	C₂³	#3485	1	1	yes	characteristic
605	C₂³	#3488	1	1	yes	characteristic
606	C₂³	#3488	1	1	yes	characteristic
607	C₂³	#3488	1	1	yes	characteristic
608	C₂³	#3488	1	1	yes	characteristic
609	C₂³	#3490	1	1	yes	characteristic
610	C₂³	#3490	1	1	yes	characteristic
611	C₂³	#3490	1	1	yes	characteristic
612	C₂³	#3490	1	1	yes	characteristic
613	C₂³	#3490	1	1	yes	characteristic
614	C₂³	#3490	1	1	yes	characteristic
615	C₂³	#3490	1	1	yes	characteristic
616	C₂³	#3490	1	1	yes	characteristic
617	C₂³	#3490	1	1	yes	characteristic
618	C₂³	#3490	1	1	yes	characteristic
619	C₂³	#3491	1	1	yes	characteristic
620	C₂³	#3491	1	1	yes	characteristic
621	C₂³	#3496	1	1	yes	characteristic
622	C₂³	#3496	1	1	yes	characteristic
623	C₂³	#3496	1	1	yes	characteristic
624	C₂³	#3496	1	1	yes	characteristic
625	C₂³	#3496	1	1	yes	characteristic
626	C₂³	#3498	1	1	yes	characteristic
627	C₂³	#3498	1	1	yes	characteristic
628	C₂³	#3498	1	1	yes	characteristic
629	C₂³	#3505	1	1	yes	characteristic
630	C₂³	#3505	1	1	yes	characteristic
631	C₂³	#3505	1	1	yes	characteristic
632	C₂³	#3505	1	1	yes	characteristic
633	C₂³	#3505	1	1	yes	characteristic
634	C₂³	#3505	1	1	yes	characteristic
635	C₂³	#3505	1	1	yes	characteristic
636	C₂³	#3513	1	1	yes	characteristic
637	C₂³	#3513	1	1	yes	characteristic
638	C₂³	#3513	1	1	yes	characteristic
639	C₂³	#3513	1	1	yes	characteristic
640	C₂³	#3513	1	1	yes	characteristic
641	C₂³	#3513	1	1	yes	characteristic
642	C₂³	#3513	1	1	yes	characteristic
643	C₂³	#3514	1	1	yes	characteristic
644	C₂³	#3514	1	1	yes	characteristic
645	C₂³	#3514	1	1	yes	characteristic
646	C₂³	#3519	1	1	yes	characteristic
647	C₂³	#3519	1	1	yes	characteristic
648	C₂³	#3519	1	1	yes	characteristic
649	C₂³	#3519	1	1	yes	characteristic
650	C₂³	#3519	1	1	yes	characteristic
651	C₂³	#3519	1	1	yes	characteristic
652	C₂³	#3519	1	1	yes	characteristic
653	C₂³	#3519	1	1	yes	characteristic
654	C₂³	#3519	1	1	yes	characteristic
655	C₂³	#3519	1	1	yes	characteristic
656	C₂³	#3519	1	1	yes	characteristic
657	C₂³	#3519	1	1	yes	characteristic
658	C₂³	#3519	1	1	yes	characteristic
659	C₂³	#3519	1	1	yes	characteristic
660	C₂³	#3519	1	1	yes	characteristic
661	C₂³	#3519	1	1	yes	characteristic
662	C₂³	#3519	1	1	yes	characteristic
663	C₂³	#3519	1	1	yes	characteristic
664	C₂³	#3519	1	1	yes	characteristic
665	C₂³	#3532	1	1	yes	characteristic
666	C₂³	#3532	1	1	yes	characteristic
667	C₂³	#3532	1	1	yes	characteristic
668	C₂³	#3532	1	1	yes	characteristic
669	C₂³	#3532	1	1	yes	characteristic
670	C₂³	#3532	1	1	yes	characteristic
671	C₂³	#3532	1	1	yes	characteristic
672	C₂³	#3534	1	1	yes	characteristic
673	C₂³	#3534	1	1	yes	characteristic
674	C₂³	#3534	1	1	yes	characteristic
675	C₂³	#3534	1	1	yes	characteristic
676	C₂³	#3534	1	1	yes	characteristic
677	C₂³	#3534	1	1	yes	characteristic
678	C₂³	#3534	1	1	yes	characteristic
679	C₂³	#3534	1	1	yes	characteristic
680	C₂³	#3537	1	1	yes	characteristic
681	C₂³	#3537	1	1	yes	characteristic
682	C₂³	#3537	1	1	yes	characteristic
683	C₂³	#3537	1	1	yes	characteristic
684	C₂³	#3540	1	1	yes	characteristic
685	C₂³	#3542	1	1	yes	characteristic
686	C₂³	#3542	1	1	yes	characteristic
687	C₂³	#3543	1	1	yes	characteristic
688	C₂³	#3543	1	1	yes	characteristic
689	C₂³	#3543	1	1	yes	characteristic
690	C₂³	#3543	1	1	yes	characteristic
691	C₂³	#3543	1	1	yes	characteristic
692	C₂³	#3543	1	1	yes	characteristic
693	C₂³	#3545	1	1	yes	characteristic
694	C₂³	#3545	1	1	yes	characteristic
695	C₂³	#3549	1	1	yes	characteristic
696	C₂³	#3558	1	1	yes	characteristic
697	C₂³	#3558	1	1	yes	characteristic
698	C₂³	#3558	1	1	yes	characteristic
699	C₂³	#3558	1	1	yes	characteristic
700	C₂³	#3558	1	1	yes	characteristic
701	C₂²	C₂×#2418	1	1	yes	characteristic
702	C₂²	#34655	1	1	yes	characteristic
703	C₂²	#34655	1	1	yes	characteristic
704	C₂²	C₂×#2404	1	1	yes	characteristic
705	C₂²	#34956	1	1	yes	characteristic
706	C₂²	#34956	1	1	yes	characteristic
707	C₂²	#34980	1	1	yes	characteristic
708	C₂²	#34983	1	1	yes	characteristic
709	C₂²	#34990	1	1	yes	characteristic
710	C₂²	#34990	1	1	yes	characteristic
711	C₂²	#35076	1	1	yes	characteristic
712	C₂²	#35076	1	1	yes	characteristic
713	C₂²	#35350	1	1	yes	characteristic
714	C₂²	#35352	1	1	yes	characteristic
715	C₂²	#35352	1	1	yes	characteristic
716	C₂²	#35360	1	1	yes	characteristic
717	C₂²	#35361	1	1	yes	characteristic
718	C₂²	#35361	1	1	yes	characteristic
719	C₂²	#35680	1	1	yes	characteristic
720	C₂²	#35680	1	1	yes	characteristic
721	C₂²	#35692	1	1	yes	characteristic
722	C₂²	#35692	1	1	yes	characteristic
723	C₂²	#35692	1	1	yes	characteristic
724	C₂²	#35692	1	1	yes	characteristic
725	C₂²	#35713	1	1	yes	characteristic
726	C₂²	#35713	1	1	yes	characteristic
727	C₂²	#35714	1	1	yes	characteristic
728	C₂²	#35762	1	1	yes	characteristic
729	C₂²	#35762	1	1	yes	characteristic
730	C₂²	#35762	1	1	yes	characteristic
731	C₂²	D₄×#120	1	1	yes	characteristic
732	C₂²	D₄×#123	1	1	yes	characteristic
733	C₂²	#36096	1	1	yes	characteristic
734	C₂²	#36096	1	1	yes	characteristic
735	C₂²	#36096	1	1	yes	characteristic
736	C₂²	#36212	1	1	yes	characteristic
737	C₂²	#36220	1	1	yes	characteristic
738	C₂²	#36220	1	1	yes	characteristic
739	C₂²	#36220	1	1	yes	characteristic
740	C₂²	#36220	1	1	yes	characteristic
741	C₂²	#36236	1	1	yes	characteristic
742	C₂²	#36236	1	1	yes	characteristic
743	C₂²	#36236	1	1	yes	characteristic
744	C₂²	#36236	1	1	yes	characteristic
745	C₂²	#36236	1	1	yes	characteristic
746	C₂²	#36316	1	1	yes	characteristic
747	C₂²	#36316	1	1	yes	characteristic
748	C₂²	#36316	1	1	yes	characteristic
749	C₂²	#36316	1	1	yes	characteristic
750	C₂²	#36316	1	1	yes	characteristic
751	C₂²	C₂×#2849	1	1	yes	characteristic
752	C₂²	#37644	1	1	yes	characteristic
753	C₂²	#37674	1	1	yes	characteristic
754	C₂²	#38420	1	1	yes	characteristic
755	C₂²	#38424	1	1	yes	characteristic
756	C₂²	#38564	1	1	yes	characteristic
757	C₂²	#38572	1	1	yes	characteristic
758	C₂²	#38760	1	1	yes	characteristic
759	C₂²	#38768	1	1	yes	characteristic
760	C₂²	#39358	1	1	yes	characteristic
761	C₂²	#39885	1	1	yes	characteristic
762	C₂²	#40389	1	1	yes	characteristic
763	C₂²	#40413	1	1	yes	characteristic
764	C₂²	#40486	1	1	yes	characteristic
765	C₂²	#40588	1	1	yes	characteristic
766	C₂²	#40590	1	1	yes	characteristic
767	C₂²	#40725	1	1	yes	characteristic
768	C₂²	#40728	1	1	yes	characteristic
769	C₂²	#41237	1	1	yes	characteristic
770	C₂²	#41260	1	1	yes	characteristic
771	C₂²	#41981	1	1	yes	characteristic
772	C₂²	#42091	1	1	yes	characteristic
773	C₂²	#42103	1	1	yes	characteristic
774	C₂²	#42475	1	1	yes	characteristic
775	C₂²	#42966	1	1	yes	characteristic
776	C₂²	#42996	1	1	yes	characteristic
777	C₂²	#42997	1	1	yes	characteristic
778	C₂²	#42997	1	1	yes	characteristic
779	C₂²	#42997	1	1	yes	characteristic
780	C₂²	#43001	1	1	yes	characteristic
781	C₂²	#43016	1	1	yes	characteristic
782	C₂²	#43038	1	1	yes	characteristic
783	C₂²	#43038	1	1	yes	characteristic
784	C₂²	#43050	1	1	yes	characteristic
785	C₂²	#43094	1	1	yes	characteristic
786	C₂²	#43095	1	1	yes	characteristic
787	C₂²	#43095	1	1	yes	characteristic
788	C₂²	#43095	1	1	yes	characteristic
789	C₂²	#43095	1	1	yes	characteristic
790	C₂²	#43095	1	1	yes	characteristic
791	C₂²	#43118	1	1	yes	characteristic
792	C₂²	#43118	1	1	yes	characteristic
793	C₂²	#43118	1	1	yes	characteristic
794	C₂²	#43197	1	1	yes	characteristic
795	C₂²	#43363	1	1	yes	characteristic
796	C₂²	#43363	1	1	yes	characteristic
797	C₂²	#43367	1	1	yes	characteristic
798	C₂²	#43367	1	1	yes	characteristic
799	C₂²	#43367	1	1	yes	characteristic
800	C₂²	#43367	1	1	yes	characteristic
801	C₂²	#43368	1	1	yes	characteristic
802	C₂²	#43372	1	1	yes	characteristic
803	C₂²	#43478	1	1	yes	characteristic
804	C₂²	#43791	1	1	yes	characteristic
805	C₂²	#43795	1	1	yes	characteristic
806	C₂²	#43795	1	1	yes	characteristic
807	C₂²	#43795	1	1	yes	characteristic
808	C₂²	#43795	1	1	yes	characteristic
809	C₂²	#43932	1	1	yes	characteristic
810	C₂²	#44001	1	1	yes	characteristic
811	C₂²	#44228	1	1	yes	characteristic
812	C₂²	#44241	1	1	yes	characteristic
813	C₂²	#44241	1	1	yes	characteristic
814	C₂²	#44870	1	1	yes	characteristic
815	C₂²	#44877	1	1	yes	characteristic
816	C₂²	#47826	1	1	yes	characteristic
817	C₂²	#47827	1	1	yes	characteristic
818	C₂²	#47838	1	1	yes	characteristic
819	C₂²	#47929	1	1	yes	characteristic
820	C₂²	#47933	1	1	yes	characteristic
821	C₂²	#47942	1	1	yes	characteristic
822	C₂²	#48082	1	1	yes	characteristic
823	C₂²	#48088	1	1	yes	characteristic
824	C₂²	#48392	1	1	yes	characteristic
825	C₂²	#48396	1	1	yes	characteristic
826	C₂²	#48405	1	1	yes	characteristic
827	C₂²	#48405	1	1	yes	characteristic
828	C₂²	#49748	1	1	yes	characteristic
829	C₂²	#49750	1	1	yes	characteristic
830	C₂²	#51776	1	1	yes	characteristic
831	C₂²	#51823	1	1	yes	characteristic
832	C₂²	#51889	1	1	yes	characteristic
833	C₂²	#51937	1	1	yes	characteristic
834	C₂²	#51940	1	1	yes	characteristic
835	C₂²	#51940	1	1	yes	characteristic
836	C₂²	#58991	1	1	yes	characteristic
837	C₂²	#58991	1	1	yes	characteristic
838	C₂²	#59006	1	1	yes	characteristic
839	C₂²	#59011	1	1	yes	characteristic
840	C₂²	#59029	1	1	yes	characteristic
841	C₂²	#59123	1	1	yes	characteristic
842	C₂²	#59123	1	1	yes	characteristic
843	C₂²	#59179	1	1	yes	characteristic
844	C₂²	#59267	1	1	yes	characteristic
845	C₂²	#59370	1	1	yes	characteristic
846	C₂²	#59800	1	1	yes	characteristic
847	C₂²	#59800	1	1	yes	characteristic
848	C₂²	#59800	1	1	yes	characteristic
849	C₂²	#59802	1	1	yes	characteristic
850	C₂²	#59803	1	1	yes	characteristic
851	C₂²	#59836	1	1	yes	characteristic
852	C₂²	#59940	1	1	yes	characteristic
853	C₂²	#59940	1	1	yes	characteristic
854	C₂²	#60037	1	1	yes	characteristic
855	C₂²	#60045	1	1	yes	characteristic
856	C₂	#612493	1	1	yes	characteristic
857	C₂	#613191	1	1	yes	characteristic
858	C₂	#648027	1	1	yes	characteristic
859	C₂	#688016	1	1	yes	characteristic
860	C₂	#759224	1	1	yes	characteristic
861	C₂	#772820	1	1	yes	characteristic
862	C₂	#773072	1	1	yes	characteristic
863	C₂	#775096	1	1	yes	characteristic
864	C₂	#775512	1	1	yes	characteristic
865	C₂	#777314	1	1	yes	characteristic
866	C₂	#777316	1	1	yes	characteristic
867	C₂	#843528	1	1	yes	characteristic
868	C₂	#843536	1	1	yes	characteristic
869	C₂	#1258513	1	1	yes	characteristic
870	C₂	#1259617	1	1	yes	characteristic
871	C₂	#1266705	1	1	yes	characteristic
872	C₂	#1267409	1	1	yes	characteristic
873	C₂	#1361330	1	1	yes	characteristic
874	C₂	#1361347	1	1	yes	characteristic
875	C₂	#1385970	1	1	yes	characteristic
876	C₂	#1385989	1	1	yes	characteristic
877	C₂	#1418637	1	1	yes	characteristic
878	C₂	#1419104	1	1	yes	characteristic
879	C₂	#1422211	1	1	yes	characteristic
880	C₂	#1422305	1	1	yes	characteristic
881	C₂	#1426826	1	1	yes	characteristic
882	C₂	#1427353	1	1	yes	characteristic
883	C₂	#1430828	1	1	yes	characteristic
884	C₂	#1430912	1	1	yes	characteristic
885	C₂	#4421038	1	1	yes	characteristic
886	C₂	#4929121	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂⁵	C₂⁵
prime radical	C₂×#15947	C₂
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×#2358	C₂	semidirect
2. C₂×#15948	C₂	semidirect
4. C₂×#14911	C₂	semidirect
5. C₂×#13967	C₂	semidirect
6. C₂×#13967	C₂	semidirect
7. #157952	C₂	semidirect
8. #157922	C₂	semidirect
9. #157737	C₂	semidirect
10. #157737	C₂	semidirect
11. #157465	C₂	semidirect
12. #156891	C₂	semidirect
13. #156858	C₂	semidirect
14. #156841	C₂	semidirect
15. #155887	C₂	semidirect
16. #154700	C₂	semidirect
17. #154687	C₂	semidirect
18. #154686	C₂	semidirect
19. #154671	C₂	semidirect
20. #154670	C₂	semidirect
21. #154670	C₂	semidirect
22. #154599	C₂	semidirect
23. #154467	C₂	semidirect
24. #154299	C₂	semidirect
25. #154226	C₂	semidirect
26. #154222	C₂	semidirect
27. #154195	C₂	semidirect
28. #154195	C₂	semidirect
29. #154195	C₂	semidirect
30. #154195	C₂	semidirect
31. #154115	C₂	semidirect
41. C₂⁴×C₂²⋊C₄	C₂²	semidirect
42. C₂⁴×C₂²⋊C₄	C₂²	semidirect
43. C₂⁴×C₂²⋊C₄	C₂²	semidirect
45. C₂²×#388	C₂²	semidirect
46. C₂²×#388	C₂²	semidirect
60. C₂²×#385	C₂²	semidirect
61. C₂²×#385	C₂²	semidirect
62. C₂²×#381	C₂²	semidirect
63. C₂²×#379	C₂²	semidirect
64. C₂²×#379	C₂²	semidirect
65. C₂²×#379	C₂²	semidirect
66. C₂²×#379	C₂²	semidirect
67. C₂²×#379	C₂²	semidirect
68. C₂²×C₄×C₂²⋊C₄	C₂²	semidirect
69. C₂²×C₄×C₂²⋊C₄	C₂²	semidirect
70. C₂×#1445	C₂²	semidirect
71. C₂×#1445	C₂²	semidirect
72. C₂×#1442	C₂²	semidirect
73. C₂×#1442	C₂²	semidirect
74. C₂×#1440	C₂²	semidirect
75. C₂×#1440	C₂²	semidirect
76. C₂×#1439	C₂²	semidirect
77. C₂×#1439	C₂²	semidirect
78. C₂×#1439	C₂²	semidirect
79. C₂×#1439	C₂²	semidirect
80. C₂×#1439	C₂²	semidirect
81. C₂×#1439	C₂²	semidirect
82. C₂×#1439	C₂²	semidirect
83. C₂×#1439	C₂²	semidirect
84. C₂×#1439	C₂²	semidirect
85. C₂×#1439	C₂²	semidirect
86. C₂×#1439	C₂²	semidirect
87. C₂×#1439	C₂²	semidirect
88. C₂×#1439	C₂²	semidirect
89. C₂×#1439	C₂²	semidirect
118. C₂×#1437	C₂²	semidirect
119. C₂×#1437	C₂²	semidirect
120. C₂×#1437	C₂²	semidirect
121. C₂×#1437	C₂²	semidirect
122. C₂×#1437	C₂²	semidirect
123. C₂×#1437	C₂²	semidirect
124. C₂×#1436	C₂²	semidirect
125. C₂×#1436	C₂²	semidirect
126. C₂×#1434	C₂²	semidirect
127. C₂×#1434	C₂²	semidirect
128. C₂×C₂²⋊#95	C₂²	semidirect
129. C₂×C₂²⋊#95	C₂²	semidirect
130. C₂×C₂²⋊#95	C₂²	semidirect
131. C₂×C₂²⋊#95	C₂²	semidirect
132. C₂×C₂²⋊#95	C₂²	semidirect
133. C₂×C₂²⋊#95	C₂²	semidirect
134. C₂×C₂²⋊#95	C₂²	semidirect
135. C₂×C₂²⋊#95	C₂²	semidirect
136. C₂×C₂²⋊#95	C₂²	semidirect
137. C₂×C₂²⋊#95	C₂²	semidirect
138. C₂×C₂²⋊#95	C₂²	semidirect
139. C₂×C₂²⋊#95	C₂²	semidirect
140. C₂×C₂²⋊#95	C₂²	semidirect
141. #7557	C₂²	semidirect
142. #7557	C₂²	semidirect
143. #7557	C₂²	semidirect
144. #7557	C₂²	semidirect
145. #7556	C₂²	semidirect
146. #7556	C₂²	semidirect
147. #7556	C₂²	semidirect
148. #7556	C₂²	semidirect
149. #7556	C₂²	semidirect
150. #7556	C₂²	semidirect
151. #7556	C₂²	semidirect
152. #7556	C₂²	semidirect
153. #7556	C₂²	semidirect
154. #7556	C₂²	semidirect
155. #7555	C₂²	semidirect
156. #7555	C₂²	semidirect
157. #7555	C₂²	semidirect
158. #7555	C₂²	semidirect
159. #7555	C₂²	semidirect
160. #7555	C₂²	semidirect
161. #7555	C₂²	semidirect
162. #7555	C₂²	semidirect
163. #7555	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. #7555	C₂²	semidirect
183. #7555	C₂²	semidirect
184. #7555	C₂²	semidirect
185. #7554	C₂²	semidirect
186. #7554	C₂²	semidirect
205. C₂²×C₄×D₄	D₄	semidirect
274. C₂×#386	D₄	semidirect
345. #1438	D₄	semidirect
444. C₂²×D₄	#123	semidirect
445. C₂²×D₄	#123	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#2358	2
C₂×#15948	2
C₂×#15947	2
C₂×#14911	2
C₂×#13967	2
#157952	2
#157922	2
#157737	2
#157465	2
#156891	2
#156858	2
#156841	2
#155887	2
#154700	2
#154687	2
#154686	2
#154671	2
#154670	2
#154599	2
#154467	2
#154299	2
#154226	2
#154222	2
#154195	2
#154115	2