Subgroups — #72332713

Order 1024.

At least 7246 conjugacy classes of subgroups; only the 1577 normal subgroups are shown.

The subgroup lattice has 951 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×#2364	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15257	C₂	1	1	yes	maximal, characteristic
3	C₂×#14171	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14134	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#13991	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13967	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#13967	C₂	1	1	yes	maximal, characteristic, complemented
8	#155534	C₂	1	1	yes	maximal, characteristic, complemented
9	#155384	C₂	1	1	yes	maximal, characteristic, complemented
10	#155365	C₂	1	1	yes	maximal, characteristic, complemented
11	#155335	C₂	1	1	yes	maximal, characteristic, complemented
12	#155095	C₂	1	1	yes	maximal, characteristic, complemented
13	#155088	C₂	1	1	yes	maximal, characteristic, complemented
14	#155079	C₂	1	1	yes	maximal, characteristic, complemented
15	#155065	C₂	1	1	yes	maximal, characteristic, complemented
16	#155052	C₂	1	1	yes	maximal, characteristic, complemented
17	#154674	C₂	1	1	yes	maximal, characteristic, complemented
18	#154670	C₂	1	1	yes	maximal, characteristic, complemented
19	#154634	C₂	1	1	yes	maximal, characteristic, complemented
20	#154483	C₂	1	1	yes	maximal, characteristic, complemented
21	#154467	C₂	1	1	yes	maximal, characteristic, complemented
22	#154455	C₂	1	1	yes	maximal, characteristic, complemented
23	#154199	C₂	1	1	yes	maximal, characteristic, complemented
24	#154197	C₂	1	1	yes	maximal, characteristic, complemented
25	#154007	C₂	1	1	yes	maximal, characteristic, complemented
26	#154003	C₂	1	1	yes	maximal, characteristic, complemented
27	#153970	C₂	1	1	yes	maximal, characteristic, complemented
28	#153827	C₂	1	1	yes	maximal, characteristic, complemented
29	#153793	C₂	1	1	yes	maximal, characteristic, complemented
30	#153793	C₂	1	1	yes	maximal, characteristic, complemented
31	#153749	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂³×#121	C₂²	1	1	yes	characteristic
33	C₂³×#120	C₂²	1	1	yes	characteristic
34	C₂³×#120	C₂²	1	1	yes	characteristic
35	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic
37	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
38	C₂⁴×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂⁴×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×#392	C₂²	1	1	yes	characteristic
41	C₂²×#392	C₂²	1	1	yes	characteristic
42	C₂²×#388	C₂²	1	1	yes	characteristic
43	C₂²×#388	C₂²	1	1	yes	characteristic
44	C₂²×#388	C₂²	1	1	yes	characteristic, complemented
45	C₂²×#387	C₂²	1	1	yes	characteristic, complemented
46	C₂²×#387	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×#386	C₂²	1	1	yes	characteristic
61	C₂²×#386	C₂²	1	1	yes	characteristic
62	C₂²×#386	C₂²	1	1	yes	characteristic, complemented
63	C₂²×#385	C₂²	1	1	yes	characteristic
64	C₂²×#385	C₂²	1	1	yes	characteristic, complemented
65	C₂²×#379	C₂²	1	1	yes	characteristic
66	C₂²×#379	C₂²	1	1	yes	characteristic
67	C₂²×#379	C₂²	1	1	yes	characteristic
68	C₂²×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
69	C₂²×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
70	C₂²×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
71	C₂²×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
72	C₂³×#95	C₂²	1	1	yes	characteristic, complemented
73	#15257	C₄	1	16	yes	complemented
74	C₂×#1442	C₂²	1	1	yes	characteristic, complemented
75	C₂×#1440	C₂²	1	1	yes	characteristic
76	C₂×#1440	C₂²	1	1	yes	characteristic
77	C₂×#1440	C₂²	1	1	yes	characteristic
78	C₂×#1440	C₂²	1	1	yes	characteristic
79	C₂×#1440	C₂²	1	1	yes	characteristic
80	C₂×#1439	C₂²	1	1	yes	characteristic
81	C₂×#1439	C₂²	1	1	yes	characteristic
82	C₂×#1439	C₂²	1	1	yes	characteristic
83	C₂×#1439	C₂²	1	1	yes	characteristic
84	C₂×#1439	C₂²	1	1	yes	characteristic
85	C₂×#1439	C₂²	1	1	yes	characteristic
86	C₂×#1439	C₂²	1	1	yes	characteristic
87	C₂×#1439	C₂²	1	1	yes	characteristic
88	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
89	C₂×#1438	C₂²	1	1	yes	characteristic
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, complemented
103	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
104	C₂×#1437	C₂²	1	1	yes	characteristic
105	C₂×#1437	C₂²	1	1	yes	characteristic
106	C₂×#1437	C₂²	1	1	yes	characteristic
107	C₂×#1437	C₂²	1	1	yes	characteristic
108	C₂×#1437	C₂²	1	1	yes	characteristic
109	C₂×#1437	C₂²	1	1	yes	characteristic
110	C₂×#1437	C₂²	1	1	yes	characteristic
111	C₂×#1437	C₂²	1	1	yes	characteristic
112	C₂×#1437	C₂²	1	1	yes	characteristic
113	C₂×#1437	C₂²	1	1	yes	characteristic
114	C₂×#1437	C₂²	1	1	yes	characteristic, complemented
115	C₂×#1437	C₂²	1	1	yes	characteristic, complemented
116	C₂×#1437	C₂²	1	1	yes	characteristic, complemented
117	C₂×#1436	C₂²	1	1	yes	characteristic, complemented
118	C₂×#1436	C₂²	1	1	yes	characteristic, complemented
119	C₂×#1436	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
121	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
122	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
123	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
124	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
125	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
126	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
127	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
128	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
129	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
130	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
131	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
132	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
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	#7557	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	#7557	C₂²	1	1	yes	characteristic, complemented
146	#7557	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	#7556	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
165	#7555	C₂²	1	1	yes	characteristic
166	#7555	C₂²	1	1	yes	characteristic
167	#7555	C₂²	1	1	yes	characteristic
168	#7555	C₂²	1	1	yes	characteristic
169	#7555	C₂²	1	1	yes	characteristic
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	#7554	C₂²	1	1	yes	characteristic, complemented
179	#7554	C₂²	1	1	yes	characteristic, complemented
180	#7554	C₂²	1	1	yes	characteristic, complemented
181	#7554	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	#7554	C₂²	1	1	yes	characteristic, complemented
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	C₂⁵×C₄	C₂³	1	1	yes	characteristic
197	C₂⁵×C₄	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×#121	C₂×C₄	1	8	yes	complemented
205	C₂²×#120	C₂×C₄	1	8	yes	complemented
206	C₂²×#120	C₂×C₄	1	8	yes	complemented
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×C₄⋊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×C₄²	C₂³	1	1	yes	characteristic
263	C₂³×C₄²	C₂³	1	1	yes	characteristic
264	C₂³×C₄²	C₂³	1	1	yes	characteristic
265	C₂³×C₄²	C₂³	1	1	yes	characteristic
266	C₂³×C₄²	C₂³	1	1	yes	characteristic
267	C₂³×C₄²	C₂³	1	1	yes	characteristic
268	C₂×#392	C₂×C₄	1	8	yes	complemented
269	C₂×#392	C₂×C₄	1	8	yes	complemented
270	C₂×#388	D₄	1	8	yes	complemented
271	C₂×#386	C₂×C₄	1	8	yes	complemented
272	C₂×#386	C₂×C₄	1	8	yes	complemented
273	C₂×#386	D₄	1	8	yes	complemented
274	C₂×#386	D₄	1	8	yes	complemented
275	C₂×#379	C₂×C₄	1	8	yes	complemented
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	C₂²×#95	C₂³	1	1	yes	characteristic
346	C₂²×#95	C₂³	1	1	yes	characteristic
347	C₂²×#95	C₂³	1	1	yes	characteristic
348	C₂²×#95	C₂³	1	1	yes	characteristic
349	C₂²×#95	C₂³	1	1	yes	characteristic
350	C₂²×#95	C₂³	1	1	yes	characteristic
351	C₂²×#95	C₂³	1	1	yes	characteristic
352	C₂²×#95	C₂³	1	1	yes	characteristic
353	C₂²×#95	C₂³	1	1	yes	characteristic
354	#1440	C₂×C₄	1	8	yes	complemented
355	#1439	C₂×C₄	1	8	yes	complemented
356	#1439	C₂×C₄	1	8	yes	complemented
357	#1438	C₂×C₄	1	8	yes	complemented
358	#1438	C₂×C₄	1	8	yes	complemented
359	#1438	C₂×C₄	1	8	yes	complemented
360	#1438	C₂×C₄	1	8	yes	complemented
361	#1438	D₄	1	8	yes	complemented
362	C₂⁶	C₂²×C₄	1	4	yes	—
363	C₂⁶	C₂⁴	1	1	yes	characteristic
364	C₂⁶	C₂⁴	1	1	yes	characteristic
365	C₂⁶	C₂⁴	1	1	yes	characteristic
366	C₂⁶	C₂⁴	1	1	yes	characteristic
367	C₂⁶	C₂⁴	1	1	yes	characteristic
368	C₂³×D₄	C₂²×C₄	1	4	yes	—
369	C₂³×D₄	C₂²×C₄	1	4	yes	—
370	C₂³×D₄	C₂²×C₄	1	4	yes	—
371	C₂³×D₄	C₂²×C₄	1	4	yes	—
372	C₂³×D₄	C₂²×C₄	1	4	yes	—
373	C₂³×D₄	C₂²×C₄	1	4	yes	—
374	C₂³×D₄	C₂²×C₄	1	4	yes	—
375	C₂³×D₄	C₂×D₄	1	4	yes	—
376	C₂³×D₄	C₂×D₄	1	4	yes	—
377	C₂³×D₄	C₂×D₄	1	4	yes	—
378	C₂³×D₄	#41	1	4	yes	—
379	C₂³×D₄	#41	1	4	yes	—
380	C₂³×D₄	#41	1	4	yes	—
381	C₂⁴×C₄	C₂²×C₄	1	4	yes	—
382	C₂⁴×C₄	C₂×D₄	1	4	yes	—
383	C₂⁴×C₄	C₂×D₄	1	4	yes	—
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	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
397	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
398	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
399	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
400	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
401	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
402	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
403	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
404	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
405	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
406	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
407	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
408	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
409	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄⋊C₄	C₂²×C₄	1	4	yes	—
411	C₂²×C₄⋊C₄	C₂×D₄	1	4	yes	—
412	C₂²×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
413	C₂²×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
414	C₂²×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
415	C₂²×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
416	C₂²×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
417	C₂²×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
418	C₂²×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
419	C₂²×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
420	C₂²×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
421	C₂²×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
422	C₂²×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
423	C₂²×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
424	C₂²×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
425	C₂²×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
426	C₂²×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
427	C₂²×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
428	C₂²×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
429	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
430	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
431	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
432	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
433	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
434	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
435	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
436	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
437	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
438	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
439	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
440	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
441	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
442	C₂²×C₂²⋊C₄	#41	1	4	yes	—
443	C₂²×C₂²⋊C₄	#41	1	4	yes	—
444	C₂²×C₂²⋊C₄	#41	1	4	yes	—
445	C₂²×C₄²	C₂×D₄	1	4	yes	—
446	C₂×#95	C₂²×C₄	1	4	yes	—
447	C₂×#95	C₂²×C₄	1	4	yes	—
448	C₂×#95	C₂²×C₄	1	4	yes	—
449	C₂×#95	C₂²×C₄	1	4	yes	—
450	C₂×#95	C₂²×C₄	1	4	yes	—
451	C₂×#95	C₂²×C₄	1	4	yes	—
452	C₂×#95	C₂²×C₄	1	4	yes	—
453	C₂×#95	C₂²×C₄	1	4	yes	—
454	C₂×#95	C₂×D₄	1	4	yes	—
455	C₂×#95	C₂×D₄	1	4	yes	—
456	C₂×#95	C₂×D₄	1	4	yes	—
457	C₂×#95	C₂×D₄	1	4	yes	—
458	C₂×#95	C₂×D₄	1	4	yes	—
459	C₂×#95	C₂×D₄	1	4	yes	—
460	C₂×#95	C₂×D₄	1	4	yes	—
461	C₂×#95	C₂×D₄	1	4	yes	—
462	C₂⁵	C₂³×C₄	1	2	yes	—
463	C₂⁵	C₂³×C₄	1	2	yes	—
464	C₂⁵	C₂³×C₄	1	2	yes	—
465	C₂⁵	C₂³×C₄	1	2	yes	—
466	C₂⁵	C₂³×C₄	1	2	yes	—
467	C₂⁵	C₂²×D₄	1	2	yes	—
468	C₂⁵	C₂²×D₄	1	2	yes	—
469	C₂⁵	C₂²×D₄	1	2	yes	—
470	C₂⁵	C₂²×D₄	1	2	yes	—
471	C₂⁵	C₂²×D₄	1	2	yes	—
472	C₂⁵	C₂²×D₄	1	2	yes	—
473	C₂⁵	C₂²×D₄	1	2	yes	—
474	C₂⁵	C₂×#41	1	2	yes	—
475	C₂⁵	C₂×#41	1	2	yes	—
476	C₂⁵	C₂×#41	1	2	yes	—
477	C₂⁵	C₂×#41	1	2	yes	—
478	C₂⁵	C₂×#41	1	2	yes	—
479	C₂⁵	C₂×#41	1	2	yes	—
480	C₂⁵	C₂×#41	1	2	yes	—
481	C₂⁵	C₂×#41	1	2	yes	—
482	C₂⁵	C₂×#41	1	2	yes	—
483	C₂⁵	H(5,𝔽₂)	1	2	yes	—
484	C₂⁵	H(5,𝔽₂)	1	2	yes	—
485	C₂⁵	H(5,𝔽₂)	1	2	yes	—
486	C₂⁵	H(5,𝔽₂)	1	2	yes	—
487	C₂⁵	H(5,𝔽₂)	1	2	yes	—
488	C₂⁵	H(5,𝔽₂)	1	2	yes	—
489	C₂⁵	C₂⁵	1	1	yes	characteristic
490	C₂²×D₄	C₄×D₄	1	16	yes	—
491	C₂²×D₄	C₄×D₄	1	16	yes	—
492	C₂²×D₄	C₄×D₄	1	16	yes	complemented
493	C₂³×C₄	C₂³×C₄	1	2	yes	—
494	C₂³×C₄	C₂³×C₄	1	2	yes	—
495	C₂³×C₄	C₂³×C₄	1	2	yes	—
496	C₂³×C₄	C₂³×C₄	1	2	yes	—
497	C₂³×C₄	C₂³×C₄	1	2	yes	—
498	C₂³×C₄	C₂³×C₄	1	2	yes	—
499	C₂³×C₄	C₂³×C₄	1	2	yes	—
500	C₂³×C₄	C₂³×C₄	1	2	yes	—
501	C₂³×C₄	C₂³×C₄	1	2	yes	—
502	C₂³×C₄	C₂³×C₄	1	2	yes	—
503	C₂³×C₄	C₂²×D₄	1	2	yes	—
504	C₂³×C₄	C₂²×D₄	1	2	yes	—
505	C₂³×C₄	C₂²×D₄	1	2	yes	—
506	C₂³×C₄	C₂²×D₄	1	2	yes	—
507	C₂³×C₄	C₂²×D₄	1	2	yes	—
508	C₂³×C₄	C₂²×D₄	1	2	yes	—
509	C₂³×C₄	C₂²×D₄	1	2	yes	—
510	C₂³×C₄	C₂²×D₄	1	2	yes	—
511	C₂³×C₄	C₂²×D₄	1	2	yes	—
512	C₂³×C₄	C₂²×D₄	1	2	yes	—
513	C₂³×C₄	C₂²×D₄	1	2	yes	—
514	C₂³×C₄	C₂²×D₄	1	2	yes	—
515	C₂³×C₄	C₂²×D₄	1	2	yes	—
516	C₂³×C₄	C₂²×D₄	1	2	yes	—
517	C₂³×C₄	C₂²×D₄	1	2	yes	—
518	C₂³×C₄	C₂²×D₄	1	2	yes	—
519	C₂³×C₄	C₂²×D₄	1	2	yes	—
520	C₂³×C₄	C₂²×D₄	1	2	yes	—
521	C₂³×C₄	C₂²×D₄	1	2	yes	—
522	C₂³×C₄	C₂²×D₄	1	2	yes	—
523	C₂³×C₄	C₂²×D₄	1	2	yes	—
524	C₂³×C₄	C₂×#41	1	2	yes	—
525	C₂³×C₄	C₂×#41	1	2	yes	—
526	C₂³×C₄	C₂×#41	1	2	yes	—
527	C₂³×C₄	C₂×#41	1	2	yes	—
528	C₂³×C₄	C₂×#41	1	2	yes	—
529	C₂³×C₄	C₂×#41	1	2	yes	—
530	C₂³×C₄	C₂×#41	1	2	yes	—
531	C₂³×C₄	C₂×#41	1	2	yes	—
532	C₂³×C₄	C₂×#41	1	2	yes	—
533	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
534	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
535	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
536	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
537	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
538	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
539	C₂×C₂²⋊C₄	C₄×D₄	1	16	yes	complemented
540	C₂×C₂²⋊C₄	#120	1	16	yes	—
541	C₂⁴	C₂×C₄×D₄	1	4	yes	—
542	C₂⁴	C₂×C₄×D₄	1	4	yes	—
543	C₂⁴	C₂×C₄×D₄	1	4	yes	—
544	C₂⁴	C₂×C₄×D₄	1	4	yes	—
545	C₂⁴	C₂×C₄×D₄	1	4	yes	—
546	C₂⁴	C₂×C₄×D₄	1	4	yes	—
547	C₂⁴	C₂×C₄×D₄	1	4	yes	—
548	C₂⁴	C₄×#41	1	4	yes	—
549	C₂⁴	#518	1	4	yes	—
550	C₂⁴	#518	1	4	yes	—
551	C₂⁴	#518	1	4	yes	—
552	C₂⁴	C₂×#120	1	4	yes	—
553	C₂⁴	#525	1	4	yes	—
554	C₂⁴	#525	1	4	yes	—
555	C₂⁴	#525	1	4	yes	—
556	C₂⁴	D₄²	1	4	yes	—
557	C₂⁴	#546	1	4	yes	—
558	C₂⁴	#546	1	4	yes	—
559	C₂⁴	#546	1	4	yes	—
560	C₂⁴	#546	1	4	yes	—
561	C₂⁴	#551	1	4	yes	—
562	C₂⁴	#553	1	4	yes	—
563	C₂⁴	#553	1	4	yes	—
564	C₂⁴	C₂⁴×C₄	1	1	yes	characteristic
565	C₂⁴	C₂³×D₄	1	1	yes	characteristic
566	C₂⁴	C₂³×D₄	1	1	yes	characteristic
567	C₂⁴	C₂³×D₄	1	1	yes	characteristic
568	C₂⁴	C₂³×D₄	1	1	yes	characteristic
569	C₂⁴	C₂²×#41	1	1	yes	characteristic
570	C₂⁴	C₂²×#41	1	1	yes	characteristic
571	C₂⁴	C₂²×#41	1	1	yes	characteristic
572	C₂⁴	C₂²×#41	1	1	yes	characteristic
573	C₂⁴	C₂²×#41	1	1	yes	characteristic
574	C₂⁴	C₂²×#41	1	1	yes	characteristic
575	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
576	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
577	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
578	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
579	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
580	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
581	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
582	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
583	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
584	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
585	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
586	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
587	C₂⁴	#585	1	1	yes	characteristic
588	C₂⁴	#585	1	1	yes	characteristic
589	C₂⁴	#585	1	1	yes	characteristic
590	C₂⁴	#585	1	1	yes	characteristic
591	C₂⁴	#585	1	1	yes	characteristic
592	C₂⁴	#585	1	1	yes	characteristic
593	C₂⁴	#585	1	1	yes	characteristic
594	C₂⁴	#585	1	1	yes	characteristic
595	C₂²×C₄	C₂×C₄×D₄	1	4	yes	—
596	C₂²×C₄	C₂×C₄×D₄	1	4	yes	—
597	C₂²×C₄	C₂×C₄×D₄	1	4	yes	—
598	C₂²×C₄	C₂×C₄×D₄	1	4	yes	—
599	C₂²×C₄	C₂×C₄×D₄	1	4	yes	—
600	C₂²×C₄	C₂×#120	1	4	yes	—
601	C₂²×C₄	C₂×#120	1	4	yes	—
602	C₂²×C₄	D₄²	1	4	yes	—
603	C₂²×C₄	D₄²	1	4	yes	—
604	C₂²×C₄	#546	1	4	yes	—
605	C₂²×C₄	#546	1	4	yes	—
606	C₂³	C₄×#120	1	8	yes	—
607	C₂³	#2358	1	8	yes	—
608	C₂³	#2364	1	8	yes	complemented
609	C₂³	C₂²×C₄×D₄	1	1	yes	characteristic
610	C₂³	C₂²×C₄×D₄	1	1	yes	characteristic
611	C₂³	C₂²×C₄×D₄	1	1	yes	characteristic
612	C₂³	C₂²×C₄×D₄	1	1	yes	characteristic
613	C₂³	C₂×C₄×#41	1	1	yes	characteristic
614	C₂³	C₂×#518	1	1	yes	characteristic
615	C₂³	C₂×#518	1	1	yes	characteristic
616	C₂³	C₂×#518	1	1	yes	characteristic
617	C₂³	#3428	1	1	yes	characteristic
618	C₂³	C₄×H(5,𝔽₂)	1	1	yes	characteristic
619	C₂³	C₄×H(5,𝔽₂)	1	1	yes	characteristic
620	C₂³	C₄×H(5,𝔽₂)	1	1	yes	characteristic
621	C₂³	C₄×H(5,𝔽₂)	1	1	yes	characteristic
622	C₂³	C₄×H(5,𝔽₂)	1	1	yes	characteristic
623	C₂³	C₄×H(5,𝔽₂)	1	1	yes	characteristic
624	C₂³	C₂²×#120	1	1	yes	characteristic
625	C₂³	C₂×#525	1	1	yes	characteristic
626	C₂³	C₂×#525	1	1	yes	characteristic
627	C₂³	C₂×#525	1	1	yes	characteristic
628	C₂³	C₂×D₄²	1	1	yes	characteristic
629	C₂³	C₂×D₄²	1	1	yes	characteristic
630	C₂³	C₂×D₄²	1	1	yes	characteristic
631	C₂³	C₂×#546	1	1	yes	characteristic
632	C₂³	C₂×#546	1	1	yes	characteristic
633	C₂³	C₂×#546	1	1	yes	characteristic
634	C₂³	C₂×#546	1	1	yes	characteristic
635	C₂³	C₂×#546	1	1	yes	characteristic
636	C₂³	C₂×#546	1	1	yes	characteristic
637	C₂³	D₄×#41	1	1	yes	characteristic
638	C₂³	D₄×#41	1	1	yes	characteristic
639	C₂³	D₄×#41	1	1	yes	characteristic
640	C₂³	D₄×#41	1	1	yes	characteristic
641	C₂³	D₄×#41	1	1	yes	characteristic
642	C₂³	D₄×#41	1	1	yes	characteristic
643	C₂³	D₄×#41	1	1	yes	characteristic
644	C₂³	D₄×#41	1	1	yes	characteristic
645	C₂³	C₂×#551	1	1	yes	characteristic
646	C₂³	C₂×#553	1	1	yes	characteristic
647	C₂³	C₂×#553	1	1	yes	characteristic
648	C₂³	#3475	1	1	yes	characteristic
649	C₂³	#3475	1	1	yes	characteristic
650	C₂³	#3475	1	1	yes	characteristic
651	C₂³	#3475	1	1	yes	characteristic
652	C₂³	#3481	1	1	yes	characteristic
653	C₂³	#3481	1	1	yes	characteristic
654	C₂³	#3481	1	1	yes	characteristic
655	C₂³	#3481	1	1	yes	characteristic
656	C₂³	#3484	1	1	yes	characteristic
657	C₂³	#3484	1	1	yes	characteristic
658	C₂³	#3484	1	1	yes	characteristic
659	C₂³	#3484	1	1	yes	characteristic
660	C₂³	#3484	1	1	yes	characteristic
661	C₂³	#3484	1	1	yes	characteristic
662	C₂³	#3484	1	1	yes	characteristic
663	C₂³	#3484	1	1	yes	characteristic
664	C₂³	#3484	1	1	yes	characteristic
665	C₂³	#3484	1	1	yes	characteristic
666	C₂³	#3484	1	1	yes	characteristic
667	C₂³	#3484	1	1	yes	characteristic
668	C₂³	#3485	1	1	yes	characteristic
669	C₂³	#3485	1	1	yes	characteristic
670	C₂³	#3485	1	1	yes	characteristic
671	C₂³	#3485	1	1	yes	characteristic
672	C₂³	#3485	1	1	yes	characteristic
673	C₂³	#3488	1	1	yes	characteristic
674	C₂³	#3488	1	1	yes	characteristic
675	C₂³	#3488	1	1	yes	characteristic
676	C₂³	#3488	1	1	yes	characteristic
677	C₂³	#3488	1	1	yes	characteristic
678	C₂³	#3488	1	1	yes	characteristic
679	C₂³	#3488	1	1	yes	characteristic
680	C₂³	#3488	1	1	yes	characteristic
681	C₂³	#3488	1	1	yes	characteristic
682	C₂³	#3488	1	1	yes	characteristic
683	C₂³	#3488	1	1	yes	characteristic
684	C₂³	#3490	1	1	yes	characteristic
685	C₂³	#3490	1	1	yes	characteristic
686	C₂³	#3490	1	1	yes	characteristic
687	C₂³	#3490	1	1	yes	characteristic
688	C₂³	#3494	1	1	yes	characteristic
689	C₂³	#3494	1	1	yes	characteristic
690	C₂³	#3496	1	1	yes	characteristic
691	C₂³	#3500	1	1	yes	characteristic
692	C₂³	#3505	1	1	yes	characteristic
693	C₂³	#3505	1	1	yes	characteristic
694	C₂³	#3505	1	1	yes	characteristic
695	C₂³	#3505	1	1	yes	characteristic
696	C₂³	#3505	1	1	yes	characteristic
697	C₂³	#3505	1	1	yes	characteristic
698	C₂³	#3508	1	1	yes	characteristic
699	C₂³	#3510	1	1	yes	characteristic
700	C₂³	#3513	1	1	yes	characteristic
701	C₂³	#3513	1	1	yes	characteristic
702	C₂³	#3513	1	1	yes	characteristic
703	C₂³	#3513	1	1	yes	characteristic
704	C₂³	#3513	1	1	yes	characteristic
705	C₂³	#3513	1	1	yes	characteristic
706	C₂³	#3513	1	1	yes	characteristic
707	C₂³	#3513	1	1	yes	characteristic
708	C₂³	#3513	1	1	yes	characteristic
709	C₂³	#3513	1	1	yes	characteristic
710	C₂³	#3513	1	1	yes	characteristic
711	C₂³	#3514	1	1	yes	characteristic
712	C₂³	#3514	1	1	yes	characteristic
713	C₂³	#3514	1	1	yes	characteristic
714	C₂³	#3519	1	1	yes	characteristic
715	C₂³	#3519	1	1	yes	characteristic
716	C₂³	#3519	1	1	yes	characteristic
717	C₂³	#3519	1	1	yes	characteristic
718	C₂³	#3519	1	1	yes	characteristic
719	C₂³	#3519	1	1	yes	characteristic
720	C₂³	#3519	1	1	yes	characteristic
721	C₂³	#3519	1	1	yes	characteristic
722	C₂³	#3519	1	1	yes	characteristic
723	C₂³	#3519	1	1	yes	characteristic
724	C₂³	#3521	1	1	yes	characteristic
725	C₂³	#3521	1	1	yes	characteristic
726	C₂³	#3521	1	1	yes	characteristic
727	C₂³	#3521	1	1	yes	characteristic
728	C₂³	#3532	1	1	yes	characteristic
729	C₂³	#3532	1	1	yes	characteristic
730	C₂³	#3532	1	1	yes	characteristic
731	C₂³	#3533	1	1	yes	characteristic
732	C₂³	#3533	1	1	yes	characteristic
733	C₂³	#3533	1	1	yes	characteristic
734	C₂³	#3534	1	1	yes	characteristic
735	C₂³	#3534	1	1	yes	characteristic
736	C₂³	#3534	1	1	yes	characteristic
737	C₂³	#3534	1	1	yes	characteristic
738	C₂³	#3534	1	1	yes	characteristic
739	C₂³	#3534	1	1	yes	characteristic
740	C₂³	#3534	1	1	yes	characteristic
741	C₂³	#3534	1	1	yes	characteristic
742	C₂³	#3534	1	1	yes	characteristic
743	C₂³	#3537	1	1	yes	characteristic
744	C₂³	#3537	1	1	yes	characteristic
745	C₂³	#3542	1	1	yes	characteristic
746	C₂³	#3542	1	1	yes	characteristic
747	C₂³	#3542	1	1	yes	characteristic
748	C₂³	#3542	1	1	yes	characteristic
749	C₂³	#3542	1	1	yes	characteristic
750	C₂³	#3543	1	1	yes	characteristic
751	C₂³	#3546	1	1	yes	characteristic
752	C₂³	#3551	1	1	yes	characteristic
753	C₂³	#3558	1	1	yes	characteristic
754	C₂³	#3558	1	1	yes	characteristic
755	C₂³	#3558	1	1	yes	characteristic
756	C₂³	#3560	1	1	yes	characteristic
757	C₂³	#3560	1	1	yes	characteristic
758	C₂³	#3560	1	1	yes	characteristic
759	C₂³	#3560	1	1	yes	characteristic
760	C₂³	#3560	1	1	yes	characteristic
761	C₂³	#3562	1	1	yes	characteristic
762	C₂³	#3566	1	1	yes	characteristic
763	C₂³	#3566	1	1	yes	characteristic
764	C₂²	C₂×C₄×#120	1	1	yes	characteristic
765	C₂²	C₂×#2358	1	1	yes	characteristic
766	C₂²	#34136	1	1	yes	characteristic
767	C₂²	C₂×#2364	1	1	yes	characteristic
768	C₂²	C₄×D₄²	1	1	yes	characteristic
769	C₂²	C₄×D₄²	1	1	yes	characteristic
770	C₂²	C₄×#546	1	1	yes	characteristic
771	C₂²	C₄×#546	1	1	yes	characteristic
772	C₂²	#34198	1	1	yes	characteristic
773	C₂²	#34264	1	1	yes	characteristic
774	C₂²	#34264	1	1	yes	characteristic
775	C₂²	#34264	1	1	yes	characteristic
776	C₂²	#34269	1	1	yes	characteristic
777	C₂²	#34283	1	1	yes	characteristic
778	C₂²	#34290	1	1	yes	characteristic
779	C₂²	#34290	1	1	yes	characteristic
780	C₂²	#34290	1	1	yes	characteristic
781	C₂²	#34290	1	1	yes	characteristic
782	C₂²	#34290	1	1	yes	characteristic
783	C₂²	#34290	1	1	yes	characteristic
784	C₂²	#34290	1	1	yes	characteristic
785	C₂²	#34292	1	1	yes	characteristic
786	C₂²	#34292	1	1	yes	characteristic
787	C₂²	#34302	1	1	yes	characteristic
788	C₂²	#34302	1	1	yes	characteristic
789	C₂²	#34309	1	1	yes	characteristic
790	C₂²	#34358	1	1	yes	characteristic
791	C₂²	#34406	1	1	yes	characteristic
792	C₂²	#34406	1	1	yes	characteristic
793	C₂²	#34437	1	1	yes	characteristic
794	C₂²	#34454	1	1	yes	characteristic
795	C₂²	#34468	1	1	yes	characteristic
796	C₂²	#34470	1	1	yes	characteristic
797	C₂²	#34517	1	1	yes	characteristic
798	C₂²	#34520	1	1	yes	characteristic
799	C₂²	#35346	1	1	yes	characteristic
800	C₂²	#35352	1	1	yes	characteristic
801	C₂²	#35352	1	1	yes	characteristic
802	C₂²	#35352	1	1	yes	characteristic
803	C₂²	#35352	1	1	yes	characteristic
804	C₂²	#35354	1	1	yes	characteristic
805	C₂²	#35355	1	1	yes	characteristic
806	C₂²	#35512	1	1	yes	characteristic
807	C₂²	D₄×#120	1	1	yes	characteristic
808	C₂²	#36096	1	1	yes	characteristic
809	C₂²	#36096	1	1	yes	characteristic
810	C₂²	#36099	1	1	yes	characteristic
811	C₂²	#36212	1	1	yes	characteristic
812	C₂²	#36212	1	1	yes	characteristic
813	C₂²	#36212	1	1	yes	characteristic
814	C₂²	#36220	1	1	yes	characteristic
815	C₂²	#36220	1	1	yes	characteristic
816	C₂²	#36224	1	1	yes	characteristic
817	C₂²	#36224	1	1	yes	characteristic
818	C₂²	#36226	1	1	yes	characteristic
819	C₂²	#36226	1	1	yes	characteristic
820	C₂²	#36316	1	1	yes	characteristic
821	C₂²	#36360	1	1	yes	characteristic
822	C₂²	#36360	1	1	yes	characteristic
823	C₂²	#43019	1	1	yes	characteristic
824	C₂²	#43023	1	1	yes	characteristic
825	C₂²	#43095	1	1	yes	characteristic
826	C₂²	#43096	1	1	yes	characteristic
827	C₂²	#43098	1	1	yes	characteristic
828	C₂²	#43102	1	1	yes	characteristic
829	C₂²	#43107	1	1	yes	characteristic
830	C₂²	#43109	1	1	yes	characteristic
831	C₂²	#43111	1	1	yes	characteristic
832	C₂²	#43113	1	1	yes	characteristic
833	C₂²	#43114	1	1	yes	characteristic
834	C₂²	#43118	1	1	yes	characteristic
835	C₂²	#43118	1	1	yes	characteristic
836	C₂²	#43212	1	1	yes	characteristic
837	C₂²	#43252	1	1	yes	characteristic
838	C₂²	#43267	1	1	yes	characteristic
839	C₂²	#43272	1	1	yes	characteristic
840	C₂²	#43276	1	1	yes	characteristic
841	C₂²	#43283	1	1	yes	characteristic
842	C₂²	#43362	1	1	yes	characteristic
843	C₂²	#43421	1	1	yes	characteristic
844	C₂²	#43434	1	1	yes	characteristic
845	C₂²	#43492	1	1	yes	characteristic
846	C₂²	#43503	1	1	yes	characteristic
847	C₂²	#43530	1	1	yes	characteristic
848	C₂²	#43535	1	1	yes	characteristic
849	C₂²	#43539	1	1	yes	characteristic
850	C₂²	#43546	1	1	yes	characteristic
851	C₂²	#43662	1	1	yes	characteristic
852	C₂²	#43668	1	1	yes	characteristic
853	C₂²	#43793	1	1	yes	characteristic
854	C₂²	#43796	1	1	yes	characteristic
855	C₂²	#43889	1	1	yes	characteristic
856	C₂²	#43998	1	1	yes	characteristic
857	C₂²	#44008	1	1	yes	characteristic
858	C₂²	#44013	1	1	yes	characteristic
859	C₂²	#44165	1	1	yes	characteristic
860	C₂²	#44172	1	1	yes	characteristic
861	C₂²	#44178	1	1	yes	characteristic
862	C₂²	#44231	1	1	yes	characteristic
863	C₂²	#44328	1	1	yes	characteristic
864	C₂²	#44333	1	1	yes	characteristic
865	C₂²	#44401	1	1	yes	characteristic
866	C₂²	#44649	1	1	yes	characteristic
867	C₂²	#44877	1	1	yes	characteristic
868	C₂²	#44932	1	1	yes	characteristic
869	C₂²	#45010	1	1	yes	characteristic
870	C₂²	#45352	1	1	yes	characteristic
871	C₂²	#47826	1	1	yes	characteristic
872	C₂²	#47826	1	1	yes	characteristic
873	C₂²	#47830	1	1	yes	characteristic
874	C₂²	#47844	1	1	yes	characteristic
875	C₂²	#48049	1	1	yes	characteristic
876	C₂²	#48057	1	1	yes	characteristic
877	C₂²	#48144	1	1	yes	characteristic
878	C₂²	#48149	1	1	yes	characteristic
879	C₂²	#48578	1	1	yes	characteristic
880	C₂²	#48600	1	1	yes	characteristic
881	C₂²	#48689	1	1	yes	characteristic
882	C₂²	#48715	1	1	yes	characteristic
883	C₂²	#48776	1	1	yes	characteristic
884	C₂²	#48784	1	1	yes	characteristic
885	C₂²	#50634	1	1	yes	characteristic
886	C₂²	#50634	1	1	yes	characteristic
887	C₂²	#50640	1	1	yes	characteristic
888	C₂²	#50738	1	1	yes	characteristic
889	C₂²	#50746	1	1	yes	characteristic
890	C₂²	#50864	1	1	yes	characteristic
891	C₂²	#51035	1	1	yes	characteristic
892	C₂²	#51165	1	1	yes	characteristic
893	C₂²	#51889	1	1	yes	characteristic
894	C₂²	#51890	1	1	yes	characteristic
895	C₂²	#58991	1	1	yes	characteristic
896	C₂²	#58991	1	1	yes	characteristic
897	C₂²	#58994	1	1	yes	characteristic
898	C₂²	#59004	1	1	yes	characteristic
899	C₂²	#59007	1	1	yes	characteristic
900	C₂²	#59009	1	1	yes	characteristic
901	C₂²	#59013	1	1	yes	characteristic
902	C₂²	#59028	1	1	yes	characteristic
903	C₂²	#59029	1	1	yes	characteristic
904	C₂²	#59089	1	1	yes	characteristic
905	C₂²	#59123	1	1	yes	characteristic
906	C₂²	#59131	1	1	yes	characteristic
907	C₂²	#59142	1	1	yes	characteristic
908	C₂²	#59167	1	1	yes	characteristic
909	C₂²	#59190	1	1	yes	characteristic
910	C₂²	#59190	1	1	yes	characteristic
911	C₂²	#59207	1	1	yes	characteristic
912	C₂²	#59301	1	1	yes	characteristic
913	C₂²	#59384	1	1	yes	characteristic
914	C₂²	#59386	1	1	yes	characteristic
915	C₂²	#59407	1	1	yes	characteristic
916	C₂²	#59689	1	1	yes	characteristic
917	C₂²	#59805	1	1	yes	characteristic
918	C₂²	#59851	1	1	yes	characteristic
919	C₂	#515667	1	1	yes	characteristic
920	C₂	#519563	1	1	yes	characteristic
921	C₂	#519565	1	1	yes	characteristic
922	C₂	#532351	1	1	yes	characteristic
923	C₂	#532634	1	1	yes	characteristic
924	C₂	#533222	1	1	yes	characteristic
925	C₂	#537754	1	1	yes	characteristic
926	C₂	#538095	1	1	yes	characteristic
927	C₂	#542279	1	1	yes	characteristic
928	C₂	#542689	1	1	yes	characteristic
929	C₂	#542747	1	1	yes	characteristic
930	C₂	#542794	1	1	yes	characteristic
931	C₂	#562612	1	1	yes	characteristic
932	C₂	#562695	1	1	yes	characteristic
933	C₂	#570829	1	1	yes	characteristic
934	C₂	#1418387	1	1	yes	characteristic
935	C₂	#1418391	1	1	yes	characteristic
936	C₂	#1418757	1	1	yes	characteristic
937	C₂	#1418761	1	1	yes	characteristic
938	C₂	#1419035	1	1	yes	characteristic
939	C₂	#1419054	1	1	yes	characteristic
940	C₂	#1420557	1	1	yes	characteristic
941	C₂	#1420573	1	1	yes	characteristic
942	C₂	#1422032	1	1	yes	characteristic
943	C₂	#1422034	1	1	yes	characteristic
944	C₂	#1422526	1	1	yes	characteristic
945	C₂	#1422570	1	1	yes	characteristic
946	C₂	#1423558	1	1	yes	characteristic
947	C₂	#1425263	1	1	yes	characteristic
948	C₂	#1426397	1	1	yes	characteristic
949	C₂	#1426482	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle, cosocle	C₂⁵	C₂⁵
commutator	C₂⁴	C₂⁴×C₄
prime radical	C₂×#15257	C₂
LCS	G ▷ C₂⁴ ▷ 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×#2364	C₂	semidirect
3. C₂×#14171	C₂	semidirect
4. C₂×#14134	C₂	semidirect
5. C₂×#13991	C₂	semidirect
6. C₂×#13967	C₂	semidirect
7. C₂×#13967	C₂	semidirect
8. #155534	C₂	semidirect
9. #155384	C₂	semidirect
10. #155365	C₂	semidirect
11. #155335	C₂	semidirect
12. #155095	C₂	semidirect
13. #155088	C₂	semidirect
14. #155079	C₂	semidirect
15. #155065	C₂	semidirect
16. #155052	C₂	semidirect
17. #154674	C₂	semidirect
18. #154670	C₂	semidirect
19. #154634	C₂	semidirect
20. #154483	C₂	semidirect
21. #154467	C₂	semidirect
22. #154455	C₂	semidirect
23. #154199	C₂	semidirect
24. #154197	C₂	semidirect
25. #154007	C₂	semidirect
26. #154003	C₂	semidirect
27. #153970	C₂	semidirect
28. #153827	C₂	semidirect
29. #153793	C₂	semidirect
30. #153793	C₂	semidirect
31. #153749	C₂	semidirect
37. C₂³×C₄×D₄	C₂²	semidirect
44. C₂²×#388	C₂²	semidirect
45. C₂²×#387	C₂²	semidirect
46. C₂²×#387	C₂²	semidirect
62. C₂²×#386	C₂²	semidirect
64. C₂²×#385	C₂²	semidirect
70. C₂²×C₄×C₂²⋊C₄	C₂²	semidirect
71. C₂²×C₄×C₂²⋊C₄	C₂²	semidirect
72. C₂³×#95	C₂²	semidirect
73. #15257	C₄	semidirect
74. C₂×#1442	C₂²	semidirect
88. C₂×#1439	C₂²	semidirect
102. C₂×#1438	C₂²	semidirect
103. C₂×#1438	C₂²	semidirect
114. C₂×#1437	C₂²	semidirect
115. C₂×#1437	C₂²	semidirect
116. C₂×#1437	C₂²	semidirect
117. C₂×#1436	C₂²	semidirect
118. C₂×#1436	C₂²	semidirect
119. C₂×#1436	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. #7557	C₂²	semidirect
141. #7557	C₂²	semidirect
142. #7557	C₂²	semidirect
143. #7557	C₂²	semidirect
144. #7557	C₂²	semidirect
145. #7557	C₂²	semidirect
146. #7557	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. #7556	C₂²	semidirect
156. #7556	C₂²	semidirect
157. #7556	C₂²	semidirect
158. #7556	C₂²	semidirect
159. #7556	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. #7554	C₂²	semidirect
179. #7554	C₂²	semidirect
180. #7554	C₂²	semidirect
181. #7554	C₂²	semidirect
182. #7554	C₂²	semidirect
183. #7554	C₂²	semidirect
184. #7554	C₂²	semidirect
185. #7554	C₂²	semidirect
186. #7554	C₂²	semidirect
187. #7554	C₂²	semidirect
204. C₂²×#121	C₂×C₄	semidirect
205. C₂²×#120	C₂×C₄	semidirect
206. C₂²×#120	C₂×C₄	semidirect
268. C₂×#392	C₂×C₄	semidirect
269. C₂×#392	C₂×C₄	semidirect
270. C₂×#388	D₄	semidirect
271. C₂×#386	C₂×C₄	semidirect
272. C₂×#386	C₂×C₄	semidirect
273. C₂×#386	D₄	semidirect
274. C₂×#386	D₄	semidirect
275. C₂×#379	C₂×C₄	semidirect
354. #1440	C₂×C₄	semidirect
355. #1439	C₂×C₄	semidirect
356. #1439	C₂×C₄	semidirect
357. #1438	C₂×C₄	semidirect
358. #1438	C₂×C₄	semidirect
359. #1438	C₂×C₄	semidirect
360. #1438	C₂×C₄	semidirect
361. #1438	D₄	semidirect
492. C₂²×D₄	C₄×D₄	semidirect
539. C₂×C₂²⋊C₄	C₄×D₄	semidirect
608. C₂³	#2364	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#2364	2
C₂×#15257	2
C₂×#14171	2
C₂×#14134	2
C₂×#13991	2
C₂×#13967	2
#155534	2
#155384	2
#155365	2
#155335	2
#155095	2
#155088	2
#155079	2
#155065	2
#155052	2
#154674	2
#154670	2
#154634	2
#154483	2
#154467	2
#154455	2
#154199	2
#154197	2
#154007	2
#154003	2
#153970	2
#153827	2
#153793	2
#153749	2