Subgroups — #72298413

Order 1024.

At least 6332 conjugacy classes of subgroups; only the 1557 normal subgroups are shown.

The subgroup lattice has 797 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×#2433	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#2408	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16249	C₂	1	2	yes	maximal, complemented
4	C₂×#15140	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15126	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15124	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15124	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15123	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13902	C₂	1	1	yes	maximal, characteristic, complemented
10	#158830	C₂	1	2	yes	maximal, complemented
11	#158819	C₂	1	2	yes	maximal, complemented
12	#158818	C₂	1	2	yes	maximal, complemented
13	#158815	C₂	1	2	yes	maximal, complemented
14	#156688	C₂	1	2	yes	maximal, complemented
15	#156684	C₂	1	2	yes	maximal, complemented
16	#155622	C₂	1	2	yes	maximal, complemented
17	#154402	C₂	1	1	yes	maximal, characteristic, complemented
18	#154386	C₂	1	1	yes	maximal, characteristic, complemented
19	#154386	C₂	1	1	yes	maximal, characteristic, complemented
20	#154384	C₂	1	1	yes	maximal, characteristic, complemented
21	#154384	C₂	1	1	yes	maximal, characteristic, complemented
22	#154383	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#1438	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂⁵×D₄	C₂²	1	1	yes	characteristic
25	C₂³×#127	C₂²	1	1	yes	characteristic
26	C₂³×#127	C₂²	1	1	yes	characteristic
27	C₂³×#121	C₂²	1	1	yes	characteristic
28	C₂³×#121	C₂²	1	1	yes	characteristic
29	C₂³×#121	C₂²	1	1	yes	characteristic
30	C₂³×#121	C₂²	1	1	yes	characteristic, complemented
31	C₂³×#120	C₂²	1	2	yes	—
32	C₂³×#120	C₂²	1	2	yes	—
33	C₂³×#120	C₂²	1	2	yes	—
34	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic
35	C₂²×#394	C₂²	1	2	yes	—
36	C₂²×#394	C₂²	1	2	yes	complemented
37	C₂²×#394	C₂²	1	2	yes	complemented
38	C₂²×#394	C₂²	1	2	yes	complemented
39	C₂²×#392	C₂²	1	2	yes	—
40	C₂²×#392	C₂²	1	2	yes	—
41	C₂²×#392	C₂²	1	2	yes	—
42	C₂²×#392	C₂²	1	2	yes	—
43	C₂²×#392	C₂²	1	2	yes	complemented
44	C₂²×#392	C₂²	1	2	yes	complemented
45	C₂²×#392	C₂²	1	2	yes	complemented
46	C₂²×#392	C₂²	1	2	yes	complemented
47	C₂²×#390	C₂²	1	1	yes	characteristic
48	C₂²×#390	C₂²	1	1	yes	characteristic
49	C₂²×#390	C₂²	1	1	yes	characteristic
50	C₂²×#390	C₂²	1	1	yes	characteristic
51	C₂²×#390	C₂²	1	1	yes	characteristic
52	C₂²×#390	C₂²	1	1	yes	characteristic
53	C₂²×#390	C₂²	1	1	yes	characteristic
54	C₂²×#390	C₂²	1	1	yes	characteristic
55	C₂²×#390	C₂²	1	1	yes	characteristic, complemented
56	C₂²×#390	C₂²	1	1	yes	characteristic, complemented
57	C₂²×#390	C₂²	1	1	yes	characteristic, complemented
58	C₂²×#389	C₂²	1	1	yes	characteristic, complemented
59	C₂²×#380	C₂²	1	1	yes	characteristic
60	C₂²×#380	C₂²	1	1	yes	characteristic
61	C₂²×#380	C₂²	1	1	yes	characteristic, complemented
62	C₂²×#379	C₂²	1	2	yes	—
63	C₂²×#379	C₂²	1	2	yes	—
64	C₂²×#379	C₂²	1	2	yes	—
65	C₂²×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
66	C₂²×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
67	C₂²×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
68	C₂²×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
69	C₂×#1440	C₂²	1	2	yes	complemented
70	C₂×#1440	C₂²	1	2	yes	complemented
71	C₂×#1440	C₂²	1	2	yes	complemented
72	C₂×#1440	C₂²	1	2	yes	complemented
73	C₂×#1440	C₂²	1	2	yes	complemented
74	C₂×#1439	C₂²	1	2	yes	—
75	C₂×#1439	C₂²	1	2	yes	complemented
76	C₂×#1439	C₂²	1	2	yes	complemented
77	C₂×#1438	C₂²	1	1	yes	characteristic
78	C₂×#1438	C₂²	1	2	yes	—
79	C₂×#1438	C₂²	1	2	yes	—
80	C₂×#1438	C₂²	1	2	yes	—
81	C₂×#1438	C₂²	1	2	yes	—
82	C₂×#1438	C₂²	1	2	yes	—
83	C₂×#1438	C₂²	1	1	yes	characteristic
84	C₂×#1438	C₂²	1	2	yes	complemented
85	C₂×#1438	C₂²	1	2	yes	complemented
86	C₂×#1438	C₂²	1	2	yes	complemented
87	C₂×#1438	C₂²	1	2	yes	complemented
88	C₂×#1438	C₂²	1	2	yes	complemented
89	C₂×#1438	C₂²	1	2	yes	complemented
90	C₂×#1438	C₂²	1	2	yes	complemented
91	C₂×#1438	C₂²	1	2	yes	complemented
92	C₂×#1438	C₂²	1	2	yes	complemented
93	C₂×#1438	C₂²	1	2	yes	complemented
94	C₂×#1438	C₂²	1	2	yes	complemented
95	C₂×#1438	C₂²	1	2	yes	complemented
96	C₂×#1438	C₂²	1	2	yes	complemented
97	C₂×#1438	C₂²	1	2	yes	complemented
98	C₂×C₄⋊#95	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₄⋊#95	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄⋊#95	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₄⋊#95	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₄⋊#95	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₄⋊#95	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₄×#95	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₄×#95	C₂²	1	1	yes	characteristic, complemented
106	#7557	C₂²	1	2	yes	complemented
107	#7557	C₂²	1	1	yes	characteristic, complemented
108	#7557	C₂²	1	1	yes	characteristic, complemented
109	#7556	C₂²	1	2	yes	complemented
110	#7555	C₂²	1	2	yes	—
111	#7555	C₂²	1	1	yes	characteristic
112	#7555	C₂²	1	1	yes	characteristic
113	#7555	C₂²	1	2	yes	complemented
114	#7555	C₂²	1	2	yes	complemented
115	#7555	C₂²	1	2	yes	complemented
116	#7555	C₂²	1	2	yes	complemented
117	#7555	C₂²	1	2	yes	complemented
118	#7555	C₂²	1	2	yes	complemented
119	#7555	C₂²	1	2	yes	complemented
120	#7555	C₂²	1	2	yes	complemented
121	#7555	C₂²	1	1	yes	characteristic, complemented
122	#7555	C₂²	1	1	yes	characteristic, complemented
123	C₂⁷	C₂³	1	2	yes	—
124	C₂⁴×D₄	D₄	1	8	yes	complemented
125	C₂⁴×D₄	C₂³	1	1	yes	characteristic
126	C₂⁴×D₄	C₂³	1	1	yes	characteristic
127	C₂⁴×D₄	C₂³	1	1	yes	characteristic
128	C₂⁴×D₄	C₂³	1	1	yes	characteristic
129	C₂⁴×D₄	C₂³	1	2	yes	—
130	C₂⁴×D₄	C₂³	1	2	yes	—
131	C₂⁴×D₄	C₂³	1	2	yes	—
132	C₂⁴×D₄	C₂³	1	2	yes	—
133	C₂⁴×D₄	C₂³	1	2	yes	—
134	C₂⁴×D₄	C₂³	1	2	yes	—
135	C₂⁴×D₄	C₂³	1	2	yes	—
136	C₂⁴×D₄	C₂³	1	2	yes	—
137	C₂⁴×D₄	C₂³	1	2	yes	—
138	C₂⁵×C₄	C₂³	1	1	yes	characteristic
139	C₂⁵×C₄	C₂³	1	1	yes	characteristic
140	C₂²×#127	D₄	1	8	yes	complemented
141	C₂²×#121	D₄	1	8	yes	complemented
142	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
150	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
151	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
152	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
154	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
155	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
156	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
159	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
167	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
188	C₂³×C₄²	C₂³	1	1	yes	characteristic
189	C₂³×C₄²	C₂³	1	1	yes	characteristic
190	C₂³×C₄²	C₂³	1	1	yes	characteristic
191	C₂³×C₄²	C₂³	1	1	yes	characteristic
192	C₂³×C₄²	C₂³	1	1	yes	characteristic
193	C₂×#390	D₄	1	8	yes	complemented
194	C₂×#390	D₄	1	8	yes	complemented
195	C₂×#380	D₄	1	8	yes	complemented
196	C₂²×#95	C₂³	1	2	yes	—
197	C₂²×#95	C₂³	1	1	yes	characteristic
198	C₂²×#95	C₂³	1	2	yes	—
199	C₂²×#95	C₂³	1	1	yes	characteristic
200	C₂²×#95	C₂³	1	1	yes	characteristic
201	C₂²×#95	C₂³	1	1	yes	characteristic
202	C₂²×#95	C₂³	1	1	yes	characteristic
203	C₂²×#95	C₂³	1	2	yes	—
204	C₂²×#95	C₂³	1	2	yes	—
205	C₂²×#95	C₂³	1	2	yes	—
206	C₂²×#95	C₂³	1	1	yes	characteristic
207	C₂²×#95	C₂³	1	1	yes	characteristic
208	C₂²×#95	C₂³	1	1	yes	characteristic
209	C₂²×#95	C₂³	1	1	yes	characteristic
210	C₂²×#95	C₂³	1	2	yes	—
211	C₂²×#95	C₂³	1	2	yes	—
212	C₂²×#95	C₂³	1	2	yes	—
213	C₂²×#95	C₂³	1	1	yes	characteristic
214	C₂²×#95	C₂³	1	1	yes	characteristic
215	C₂²×#95	C₂³	1	1	yes	characteristic
216	C₂²×#95	C₂³	1	2	yes	—
217	C₂²×#95	C₂³	1	2	yes	—
218	C₂²×#95	C₂³	1	2	yes	—
219	C₂²×#95	C₂³	1	2	yes	—
220	C₂²×#95	C₂³	1	2	yes	—
221	C₂²×#95	C₂³	1	1	yes	characteristic
222	C₂²×#95	C₂³	1	1	yes	characteristic
223	C₂²×#95	C₂³	1	1	yes	characteristic
224	C₂²×#95	C₂³	1	2	yes	—
225	C₂²×#95	C₂³	1	2	yes	—
226	C₂²×#95	C₂³	1	2	yes	—
227	C₂²×#95	C₂³	1	1	yes	characteristic
228	#1438	D₄	1	8	yes	complemented
229	C₂⁶	C₂×D₄	1	8	yes	—
230	C₂⁶	C₂⁴	1	2	yes	—
231	C₂⁶	C₂⁴	1	2	yes	—
232	C₂⁶	C₂⁴	1	2	yes	—
233	C₂⁶	C₂⁴	1	1	yes	characteristic
234	C₂⁶	C₂⁴	1	1	yes	characteristic
235	C₂³×D₄	C₂×D₄	1	4	yes	—
236	C₂³×D₄	C₂×D₄	1	4	yes	—
237	C₂³×D₄	C₂×D₄	1	4	yes	—
238	C₂³×D₄	C₂×D₄	1	4	yes	—
239	C₂³×D₄	C₂×D₄	1	4	yes	—
240	C₂³×D₄	C₂×D₄	1	4	yes	—
241	C₂³×D₄	C₂×D₄	1	4	yes	—
242	C₂³×D₄	C₂×D₄	1	4	yes	—
243	C₂³×D₄	C₂×D₄	1	8	yes	—
244	C₂³×D₄	C₂×D₄	1	8	yes	—
245	C₂³×D₄	C₂×D₄	1	8	yes	—
246	C₂³×D₄	C₂×D₄	1	8	yes	—
247	C₂⁴×C₄	C₂×D₄	1	4	yes	—
248	C₂⁴×C₄	C₂×D₄	1	4	yes	—
249	C₂⁴×C₄	C₂×D₄	1	4	yes	—
250	C₂⁴×C₄	#41	1	4	yes	—
251	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
252	C₂⁴×C₄	C₂⁴	1	2	yes	—
253	C₂⁴×C₄	C₂⁴	1	2	yes	—
254	C₂⁴×C₄	C₂⁴	1	2	yes	—
255	C₂⁴×C₄	C₂⁴	1	2	yes	—
256	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
257	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
258	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
259	C₂⁴×C₄	C₂⁴	1	2	yes	—
260	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
261	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
262	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
263	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
264	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
265	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
266	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
267	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
268	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄⋊C₄	C₂×D₄	1	4	yes	—
270	C₂²×C₄⋊C₄	C₂×D₄	1	4	yes	—
271	C₂²×C₄⋊C₄	C₂×D₄	1	4	yes	—
272	C₂²×C₄⋊C₄	C₂×D₄	1	4	yes	—
273	C₂²×C₄⋊C₄	C₂×D₄	1	4	yes	—
274	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
275	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
276	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
277	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
278	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
279	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
280	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
281	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
282	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
283	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
284	C₂²×C₂²⋊C₄	#41	1	4	yes	—
285	C₂²×C₄²	C₂×D₄	1	4	yes	—
286	C₂²×C₄²	C₂×D₄	1	4	yes	—
287	C₂²×C₄²	C₂×D₄	1	4	yes	—
288	C₂×#95	C₂×D₄	1	8	yes	—
289	C₂×#95	C₂×D₄	1	4	yes	complemented
290	C₂×#95	C₂×D₄	1	4	yes	complemented
291	C₂⁵	C₂²×D₄	1	4	yes	—
292	C₂⁵	C₂²×D₄	1	4	yes	—
293	C₂⁵	C₂²×D₄	1	4	yes	—
294	C₂⁵	C₂²×D₄	1	4	yes	—
295	C₂⁵	C₂²×D₄	1	4	yes	—
296	C₂⁵	C₂²×D₄	1	4	yes	—
297	C₂⁵	C₂²×D₄	1	4	yes	—
298	C₂⁵	C₂²×D₄	1	2	yes	—
299	C₂⁵	C₂²×D₄	1	2	yes	—
300	C₂⁵	C₂²×D₄	1	2	yes	—
301	C₂⁵	C₂²×D₄	1	2	yes	—
302	C₂⁵	C₂²×D₄	1	2	yes	—
303	C₂⁵	C₂×#41	1	2	yes	—
304	C₂⁵	C₂×#41	1	2	yes	—
305	C₂⁵	H(5,𝔽₂)	1	2	yes	—
306	C₂⁵	H(5,𝔽₂)	1	2	yes	—
307	C₂⁵	H(5,𝔽₂)	1	2	yes	—
308	C₂⁵	C₂⁵	1	1	yes	characteristic
309	C₂²×D₄	#120	1	16	yes	—
310	C₂²×D₄	#120	1	16	yes	—
311	C₂³×C₄	#121	1	16	yes	—
312	C₂³×C₄	C₂²×D₄	1	4	yes	—
313	C₂³×C₄	C₂²×D₄	1	2	yes	—
314	C₂³×C₄	C₂²×D₄	1	2	yes	—
315	C₂³×C₄	C₂²×D₄	1	2	yes	—
316	C₂³×C₄	C₂²×D₄	1	2	yes	—
317	C₂³×C₄	C₂²×D₄	1	4	yes	—
318	C₂³×C₄	C₂²×D₄	1	4	yes	—
319	C₂³×C₄	C₂²×D₄	1	4	yes	—
320	C₂³×C₄	C₂²×D₄	1	4	yes	—
321	C₂³×C₄	C₂²×D₄	1	2	yes	—
322	C₂³×C₄	C₂²×D₄	1	2	yes	—
323	C₂³×C₄	C₂²×D₄	1	2	yes	—
324	C₂³×C₄	C₂²×D₄	1	2	yes	—
325	C₂³×C₄	C₂²×D₄	1	2	yes	—
326	C₂³×C₄	C₂²×D₄	1	2	yes	—
327	C₂³×C₄	C₂²×D₄	1	2	yes	—
328	C₂³×C₄	C₂²×D₄	1	2	yes	—
329	C₂³×C₄	C₂²×D₄	1	2	yes	—
330	C₂³×C₄	C₂²×D₄	1	2	yes	—
331	C₂³×C₄	C₂²×D₄	1	2	yes	—
332	C₂³×C₄	C₂²×D₄	1	2	yes	—
333	C₂³×C₄	C₂²×D₄	1	2	yes	—
334	C₂³×C₄	C₂²×D₄	1	2	yes	—
335	C₂³×C₄	C₂²×D₄	1	2	yes	—
336	C₂³×C₄	C₂²×D₄	1	2	yes	—
337	C₂³×C₄	C₂×#41	1	2	yes	—
338	C₂³×C₄	C₂×#41	1	2	yes	—
339	C₂³×C₄	C₂×#41	1	2	yes	—
340	C₂³×C₄	C₂×#41	1	2	yes	—
341	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
342	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
343	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
344	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
345	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
346	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
347	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
348	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
349	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
350	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
351	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
352	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
353	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
354	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
355	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
356	C₂⁴	C₂×#120	1	8	yes	—
357	C₂⁴	C₂×#120	1	8	yes	—
358	C₂⁴	C₂×#121	1	4	yes	—
359	C₂⁴	#532	1	4	yes	—
360	C₂⁴	#540	1	4	yes	—
361	C₂⁴	D₄²	1	4	yes	—
362	C₂⁴	D₄²	1	4	yes	—
363	C₂⁴	D₄²	1	4	yes	—
364	C₂⁴	#546	1	4	yes	—
365	C₂⁴	#550	1	4	yes	—
366	C₂⁴	C₂³×D₄	1	1	yes	characteristic
367	C₂⁴	C₂³×D₄	1	1	yes	characteristic
368	C₂⁴	C₂³×D₄	1	1	yes	characteristic
369	C₂⁴	C₂³×D₄	1	1	yes	characteristic
370	C₂⁴	C₂³×D₄	1	1	yes	characteristic
371	C₂⁴	C₂³×D₄	1	1	yes	characteristic
372	C₂⁴	C₂³×D₄	1	1	yes	characteristic
373	C₂⁴	C₂²×#41	1	1	yes	characteristic
374	C₂⁴	C₂²×#41	1	1	yes	characteristic
375	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
376	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
377	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
379	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
380	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
381	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
383	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
384	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
385	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
386	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
387	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
388	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
389	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
390	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
391	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
392	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
393	C₂⁴	#585	1	1	yes	characteristic
394	C₂⁴	#585	1	1	yes	characteristic
395	C₂⁴	#585	1	1	yes	characteristic
396	C₂⁴	#585	1	1	yes	characteristic
397	C₂²×C₄	C₂×#120	1	4	yes	—
398	C₂²×C₄	C₂×#120	1	4	yes	—
399	C₂²×C₄	C₂×#121	1	4	yes	—
400	C₂²×C₄	C₂×#121	1	4	yes	—
401	C₂²×C₄	#534	1	4	yes	—
402	C₂²×C₄	#534	1	4	yes	—
403	C₂²×C₄	#534	1	4	yes	—
404	C₂²×C₄	#534	1	4	yes	—
405	C₂²×C₄	#534	1	4	yes	—
406	C₂²×C₄	#534	1	4	yes	—
407	C₂²×C₄	#534	1	4	yes	—
408	C₂²×C₄	#534	1	4	yes	—
409	C₂²×C₄	#534	1	4	yes	—
410	C₂²×C₄	#535	1	4	yes	—
411	C₂²×C₄	#535	1	4	yes	—
412	C₂²×C₄	#535	1	4	yes	—
413	C₂²×C₄	#535	1	4	yes	—
414	C₂²×C₄	#535	1	4	yes	—
415	C₂²×C₄	#538	1	4	yes	—
416	C₂²×C₄	#538	1	4	yes	—
417	C₂²×C₄	D₄²	1	4	yes	—
418	C₂²×C₄	D₄²	1	4	yes	—
419	C₂²×C₄	D₄²	1	4	yes	—
420	C₂²×C₄	D₄²	1	4	yes	—
421	C₂²×C₄	D₄²	1	4	yes	—
422	C₂²×C₄	D₄²	1	4	yes	—
423	C₂²×C₄	D₄²	1	4	yes	—
424	C₂²×C₄	D₄²	1	4	yes	—
425	C₂²×C₄	D₄²	1	4	yes	—
426	C₂²×C₄	D₄²	1	4	yes	—
427	C₂²×C₄	D₄²	1	4	yes	—
428	C₂²×C₄	#546	1	4	yes	—
429	C₂²×C₄	#546	1	4	yes	—
430	C₂²×C₄	#546	1	4	yes	—
431	C₂²×C₄	#546	1	4	yes	—
432	C₂²×C₄	#546	1	4	yes	—
433	C₂²×C₄	#546	1	4	yes	—
434	C₂²×C₄	#560	1	4	yes	—
435	C₂²×C₄	#560	1	4	yes	—
436	C₂²×C₄	#560	1	4	yes	—
437	C₂²×C₄	H(3,𝔽₄)	1	4	yes	—
438	C₂³	#2428	1	8	yes	—
439	C₂³	C₂²×#120	1	1	yes	characteristic
440	C₂³	C₂²×#120	1	1	yes	characteristic
441	C₂³	C₂²×#121	1	1	yes	characteristic
442	C₂³	C₂×#532	1	1	yes	characteristic
443	C₂³	C₂×#534	1	1	yes	characteristic
444	C₂³	C₂×#534	1	1	yes	characteristic
445	C₂³	C₂×#534	1	1	yes	characteristic
446	C₂³	C₂×#534	1	1	yes	characteristic
447	C₂³	C₂×#534	1	1	yes	characteristic
448	C₂³	C₂×#534	1	1	yes	characteristic
449	C₂³	C₂×#534	1	1	yes	characteristic
450	C₂³	C₂×#534	1	1	yes	characteristic
451	C₂³	C₂×#534	1	1	yes	characteristic
452	C₂³	C₂×#535	1	1	yes	characteristic
453	C₂³	C₂×#535	1	1	yes	characteristic
454	C₂³	C₂×#535	1	1	yes	characteristic
455	C₂³	C₂×#535	1	1	yes	characteristic
456	C₂³	C₂×#535	1	1	yes	characteristic
457	C₂³	C₂×#538	1	1	yes	characteristic
458	C₂³	C₂×#538	1	1	yes	characteristic
459	C₂³	C₂×#540	1	1	yes	characteristic
460	C₂³	#3460	1	1	yes	characteristic
461	C₂³	#3460	1	1	yes	characteristic
462	C₂³	C₂×D₄²	1	1	yes	characteristic
463	C₂³	C₂×D₄²	1	1	yes	characteristic
464	C₂³	C₂×D₄²	1	1	yes	characteristic
465	C₂³	C₂×D₄²	1	1	yes	characteristic
466	C₂³	C₂×D₄²	1	1	yes	characteristic
467	C₂³	C₂×D₄²	1	1	yes	characteristic
468	C₂³	C₂×D₄²	1	1	yes	characteristic
469	C₂³	C₂×D₄²	1	1	yes	characteristic
470	C₂³	C₂×D₄²	1	1	yes	characteristic
471	C₂³	C₂×D₄²	1	1	yes	characteristic
472	C₂³	C₂×D₄²	1	1	yes	characteristic
473	C₂³	C₂×D₄²	1	1	yes	characteristic
474	C₂³	C₂×D₄²	1	1	yes	characteristic
475	C₂³	C₂×D₄²	1	1	yes	characteristic
476	C₂³	C₂×#546	1	1	yes	characteristic
477	C₂³	C₂×#546	1	1	yes	characteristic
478	C₂³	C₂×#546	1	1	yes	characteristic
479	C₂³	C₂×#546	1	1	yes	characteristic
480	C₂³	C₂×#546	1	1	yes	characteristic
481	C₂³	C₂×#546	1	1	yes	characteristic
482	C₂³	C₂×#546	1	1	yes	characteristic
483	C₂³	C₂×#550	1	1	yes	characteristic
484	C₂³	D₄×#41	1	1	yes	characteristic
485	C₂³	D₄×#41	1	1	yes	characteristic
486	C₂³	#3484	1	1	yes	characteristic
487	C₂³	#3484	1	1	yes	characteristic
488	C₂³	#3484	1	1	yes	characteristic
489	C₂³	#3484	1	1	yes	characteristic
490	C₂³	#3484	1	1	yes	characteristic
491	C₂³	#3484	1	1	yes	characteristic
492	C₂³	#3484	1	1	yes	characteristic
493	C₂³	#3484	1	1	yes	characteristic
494	C₂³	#3484	1	1	yes	characteristic
495	C₂³	#3484	1	1	yes	characteristic
496	C₂³	#3484	1	1	yes	characteristic
497	C₂³	#3484	1	1	yes	characteristic
498	C₂³	#3484	1	1	yes	characteristic
499	C₂³	#3485	1	1	yes	characteristic
500	C₂³	#3485	1	1	yes	characteristic
501	C₂³	#3487	1	1	yes	characteristic
502	C₂³	#3488	1	1	yes	characteristic
503	C₂³	#3488	1	1	yes	characteristic
504	C₂³	#3488	1	1	yes	characteristic
505	C₂³	#3488	1	1	yes	characteristic
506	C₂³	#3488	1	1	yes	characteristic
507	C₂³	#3488	1	1	yes	characteristic
508	C₂³	#3488	1	1	yes	characteristic
509	C₂³	#3488	1	1	yes	characteristic
510	C₂³	#3494	1	1	yes	characteristic
511	C₂³	#3494	1	1	yes	characteristic
512	C₂³	#3496	1	1	yes	characteristic
513	C₂³	#3496	1	1	yes	characteristic
514	C₂³	#3496	1	1	yes	characteristic
515	C₂³	#3496	1	1	yes	characteristic
516	C₂³	#3496	1	1	yes	characteristic
517	C₂³	#3496	1	1	yes	characteristic
518	C₂³	#3496	1	1	yes	characteristic
519	C₂³	#3496	1	1	yes	characteristic
520	C₂³	#3496	1	1	yes	characteristic
521	C₂³	#3496	1	1	yes	characteristic
522	C₂³	#3498	1	1	yes	characteristic
523	C₂³	#3498	1	1	yes	characteristic
524	C₂³	#3498	1	1	yes	characteristic
525	C₂³	#3498	1	1	yes	characteristic
526	C₂³	#3498	1	1	yes	characteristic
527	C₂³	#3498	1	1	yes	characteristic
528	C₂³	#3498	1	1	yes	characteristic
529	C₂³	#3498	1	1	yes	characteristic
530	C₂³	#3498	1	1	yes	characteristic
531	C₂³	#3500	1	1	yes	characteristic
532	C₂³	#3508	1	1	yes	characteristic
533	C₂³	#3508	1	1	yes	characteristic
534	C₂³	#3508	1	1	yes	characteristic
535	C₂³	#3508	1	1	yes	characteristic
536	C₂³	#3514	1	1	yes	characteristic
537	C₂³	#3514	1	1	yes	characteristic
538	C₂³	#3519	1	1	yes	characteristic
539	C₂³	#3519	1	1	yes	characteristic
540	C₂³	#3519	1	1	yes	characteristic
541	C₂³	#3519	1	1	yes	characteristic
542	C₂³	C₂×#560	1	1	yes	characteristic
543	C₂³	C₂×#560	1	1	yes	characteristic
544	C₂³	C₂×#560	1	1	yes	characteristic
545	C₂³	C₂×H(3,𝔽₄)	1	1	yes	characteristic
546	C₂³	#3537	1	1	yes	characteristic
547	C₂³	#3537	1	1	yes	characteristic
548	C₂³	#3537	1	1	yes	characteristic
549	C₂³	#3537	1	1	yes	characteristic
550	C₂³	#3537	1	1	yes	characteristic
551	C₂³	#3537	1	1	yes	characteristic
552	C₂³	#3537	1	1	yes	characteristic
553	C₂³	#3537	1	1	yes	characteristic
554	C₂³	#3542	1	1	yes	characteristic
555	C₂³	#3542	1	1	yes	characteristic
556	C₂³	#3542	1	1	yes	characteristic
557	C₂³	#3542	1	1	yes	characteristic
558	C₂³	#3542	1	1	yes	characteristic
559	C₂³	#3542	1	1	yes	characteristic
560	C₂³	#3542	1	1	yes	characteristic
561	C₂³	#3542	1	1	yes	characteristic
562	C₂³	#3543	1	1	yes	characteristic
563	C₂³	#3543	1	1	yes	characteristic
564	C₂³	#3543	1	1	yes	characteristic
565	C₂³	#3543	1	1	yes	characteristic
566	C₂³	#3543	1	1	yes	characteristic
567	C₂³	#3543	1	1	yes	characteristic
568	C₂³	#3543	1	1	yes	characteristic
569	C₂³	#3543	1	1	yes	characteristic
570	C₂³	#3543	1	1	yes	characteristic
571	C₂³	#3543	1	1	yes	characteristic
572	C₂³	#3543	1	1	yes	characteristic
573	C₂³	#3543	1	1	yes	characteristic
574	C₂³	#3546	1	1	yes	characteristic
575	C₂³	#3546	1	1	yes	characteristic
576	C₂³	#3546	1	1	yes	characteristic
577	C₂³	#3546	1	1	yes	characteristic
578	C₂³	#3546	1	1	yes	characteristic
579	C₂³	#3546	1	1	yes	characteristic
580	C₂³	#3546	1	1	yes	characteristic
581	C₂³	#3546	1	1	yes	characteristic
582	C₂³	#3549	1	1	yes	characteristic
583	C₂³	#3549	1	1	yes	characteristic
584	C₂³	#3549	1	1	yes	characteristic
585	C₂³	#3549	1	1	yes	characteristic
586	C₂³	#3558	1	1	yes	characteristic
587	C₂³	#3558	1	1	yes	characteristic
588	C₂³	#3558	1	1	yes	characteristic
589	C₂³	#3558	1	1	yes	characteristic
590	C₂³	#3558	1	1	yes	characteristic
591	C₂³	#3558	1	1	yes	characteristic
592	C₂³	#3562	1	1	yes	characteristic
593	C₂³	#3562	1	1	yes	characteristic
594	C₂×C₄	#2403	1	8	yes	—
595	C₂×C₄	#2410	1	8	yes	—
596	C₂×C₄	#2410	1	8	yes	—
597	C₂×C₄	#2613	1	8	yes	—
598	C₂×C₄	#2613	1	8	yes	—
599	C₂×C₄	#2617	1	8	yes	—
600	C₂×C₄	#2668	1	8	yes	—
601	C₂×C₄	#2669	1	8	yes	—
602	C₂×C₄	#2669	1	8	yes	—
603	C₂×C₄	#2669	1	8	yes	—
604	C₂×C₄	#2670	1	8	yes	—
605	C₂×C₄	#2678	1	8	yes	—
606	C₂×C₄	#2678	1	8	yes	—
607	C₂×C₄	#2679	1	8	yes	—
608	C₂×C₄	#2812	1	8	yes	—
609	C₂²	C₂×#2613	1	1	yes	characteristic
610	C₂²	C₂×#2613	1	1	yes	characteristic
611	C₂²	C₂×#2617	1	1	yes	characteristic
612	C₂²	C₂×#2403	1	1	yes	characteristic
613	C₂²	C₂×#2410	1	1	yes	characteristic
614	C₂²	C₂×#2410	1	1	yes	characteristic
615	C₂²	C₂×#2428	1	1	yes	characteristic
616	C₂²	#35007	1	1	yes	characteristic
617	C₂²	#35007	1	1	yes	characteristic
618	C₂²	#35168	1	1	yes	characteristic
619	C₂²	#35514	1	1	yes	characteristic
620	C₂²	#35528	1	1	yes	characteristic
621	C₂²	#35680	1	1	yes	characteristic
622	C₂²	#35680	1	1	yes	characteristic
623	C₂²	#35680	1	1	yes	characteristic
624	C₂²	#35750	1	1	yes	characteristic
625	C₂²	D₄×#120	1	1	yes	characteristic
626	C₂²	D₄×#120	1	1	yes	characteristic
627	C₂²	#36121	1	1	yes	characteristic
628	C₂²	#36121	1	1	yes	characteristic
629	C₂²	#36123	1	1	yes	characteristic
630	C₂²	#36123	1	1	yes	characteristic
631	C₂²	#36152	1	1	yes	characteristic
632	C₂²	#36212	1	1	yes	characteristic
633	C₂²	C₂×#2812	1	1	yes	characteristic
634	C₂²	#37331	1	1	yes	characteristic
635	C₂²	#37331	1	1	yes	characteristic
636	C₂²	#37334	1	1	yes	characteristic
637	C₂²	#37334	1	1	yes	characteristic
638	C₂²	#37493	1	1	yes	characteristic
639	C₂²	#37493	1	1	yes	characteristic
640	C₂²	#37662	1	1	yes	characteristic
641	C₂²	#37662	1	1	yes	characteristic
642	C₂²	#37694	1	1	yes	characteristic
643	C₂²	#37694	1	1	yes	characteristic
644	C₂²	#37748	1	1	yes	characteristic
645	C₂²	#37751	1	1	yes	characteristic
646	C₂²	#37782	1	1	yes	characteristic
647	C₂²	#37782	1	1	yes	characteristic
648	C₂²	#38904	1	1	yes	characteristic
649	C₂²	#38904	1	1	yes	characteristic
650	C₂²	#38910	1	1	yes	characteristic
651	C₂²	#38949	1	1	yes	characteristic
652	C₂²	#38949	1	1	yes	characteristic
653	C₂²	#38949	1	1	yes	characteristic
654	C₂²	#38953	1	1	yes	characteristic
655	C₂²	#39132	1	1	yes	characteristic
656	C₂²	#39135	1	1	yes	characteristic
657	C₂²	#39336	1	1	yes	characteristic
658	C₂²	#39336	1	1	yes	characteristic
659	C₂²	#39336	1	1	yes	characteristic
660	C₂²	#39338	1	1	yes	characteristic
661	C₂²	#39338	1	1	yes	characteristic
662	C₂²	#39339	1	1	yes	characteristic
663	C₂²	#39342	1	1	yes	characteristic
664	C₂²	#39342	1	1	yes	characteristic
665	C₂²	#39358	1	1	yes	characteristic
666	C₂²	#39358	1	1	yes	characteristic
667	C₂²	#39358	1	1	yes	characteristic
668	C₂²	#39358	1	1	yes	characteristic
669	C₂²	#39361	1	1	yes	characteristic
670	C₂²	#39362	1	1	yes	characteristic
671	C₂²	#39416	1	1	yes	characteristic
672	C₂²	#39419	1	1	yes	characteristic
673	C₂²	#39434	1	1	yes	characteristic
674	C₂²	#39434	1	1	yes	characteristic
675	C₂²	#39464	1	1	yes	characteristic
676	C₂²	#39876	1	1	yes	characteristic
677	C₂²	#39888	1	1	yes	characteristic
678	C₂²	#39953	1	1	yes	characteristic
679	C₂²	#39957	1	1	yes	characteristic
680	C₂²	#42420	1	1	yes	characteristic
681	C₂²	#42420	1	1	yes	characteristic
682	C₂²	#42420	1	1	yes	characteristic
683	C₂²	#42420	1	1	yes	characteristic
684	C₂²	#42422	1	1	yes	characteristic
685	C₂²	#42422	1	1	yes	characteristic
686	C₂²	#42426	1	1	yes	characteristic
687	C₂²	#42430	1	1	yes	characteristic
688	C₂²	#42430	1	1	yes	characteristic
689	C₂²	#42435	1	1	yes	characteristic
690	C₂²	#42438	1	1	yes	characteristic
691	C₂²	#42474	1	1	yes	characteristic
692	C₂²	#42474	1	1	yes	characteristic
693	C₂²	#42474	1	1	yes	characteristic
694	C₂²	#42475	1	1	yes	characteristic
695	C₂²	#42475	1	1	yes	characteristic
696	C₂²	#42475	1	1	yes	characteristic
697	C₂²	#42475	1	1	yes	characteristic
698	C₂²	#42480	1	1	yes	characteristic
699	C₂²	#42480	1	1	yes	characteristic
700	C₂²	#42483	1	1	yes	characteristic
701	C₂²	#42484	1	1	yes	characteristic
702	C₂²	#42951	1	1	yes	characteristic
703	C₂²	#42963	1	1	yes	characteristic
704	C₂²	#42966	1	1	yes	characteristic
705	C₂²	#42966	1	1	yes	characteristic
706	C₂²	#42969	1	1	yes	characteristic
707	C₂²	#42986	1	1	yes	characteristic
708	C₂²	#44868	1	1	yes	characteristic
709	C₂²	#44870	1	1	yes	characteristic
710	C₂²	#44870	1	1	yes	characteristic
711	C₂²	#44870	1	1	yes	characteristic
712	C₂²	#44877	1	1	yes	characteristic
713	C₂²	#44877	1	1	yes	characteristic
714	C₂²	#44877	1	1	yes	characteristic
715	C₂²	#44877	1	1	yes	characteristic
716	C₂²	#44886	1	1	yes	characteristic
717	C₂²	#44886	1	1	yes	characteristic
718	C₂²	#44892	1	1	yes	characteristic
719	C₂²	#44927	1	1	yes	characteristic
720	C₂²	#44927	1	1	yes	characteristic
721	C₂²	#44932	1	1	yes	characteristic
722	C₂²	#45263	1	1	yes	characteristic
723	C₂²	#45355	1	1	yes	characteristic
724	C₂²	#45483	1	1	yes	characteristic
725	C₂²	#45483	1	1	yes	characteristic
726	C₂²	#45487	1	1	yes	characteristic
727	C₂²	#45647	1	1	yes	characteristic
728	C₂²	#45655	1	1	yes	characteristic
729	C₂²	#45655	1	1	yes	characteristic
730	C₂²	#45996	1	1	yes	characteristic
731	C₂²	#46054	1	1	yes	characteristic
732	C₂²	C₂×#2668	1	1	yes	characteristic
733	C₂²	C₂×#2669	1	1	yes	characteristic
734	C₂²	C₂×#2669	1	1	yes	characteristic
735	C₂²	C₂×#2669	1	1	yes	characteristic
736	C₂²	C₂×#2670	1	1	yes	characteristic
737	C₂²	C₂×#2678	1	1	yes	characteristic
738	C₂²	C₂×#2678	1	1	yes	characteristic
739	C₂²	C₂×#2679	1	1	yes	characteristic
740	C₂²	#52969	1	1	yes	characteristic
741	C₂²	#52971	1	1	yes	characteristic
742	C₂²	#52971	1	1	yes	characteristic
743	C₂²	#52977	1	1	yes	characteristic
744	C₂²	#52986	1	1	yes	characteristic
745	C₂²	#53102	1	1	yes	characteristic
746	C₂²	#53102	1	1	yes	characteristic
747	C₂²	#53116	1	1	yes	characteristic
748	C₂²	#58997	1	1	yes	characteristic
749	C₂²	#58997	1	1	yes	characteristic
750	C₂²	#58997	1	1	yes	characteristic
751	C₂²	#59003	1	1	yes	characteristic
752	C₂²	#59003	1	1	yes	characteristic
753	C₂²	#59004	1	1	yes	characteristic
754	C₂²	#59035	1	1	yes	characteristic
755	C₂²	#59124	1	1	yes	characteristic
756	C₂²	#59124	1	1	yes	characteristic
757	C₂²	#59126	1	1	yes	characteristic
758	C₂²	#59126	1	1	yes	characteristic
759	C₂²	#59126	1	1	yes	characteristic
760	C₂²	#59126	1	1	yes	characteristic
761	C₂²	#59131	1	1	yes	characteristic
762	C₂²	#59412	1	1	yes	characteristic
763	C₂²	#59816	1	1	yes	characteristic
764	C₄	#16249	1	16	yes	complemented
765	C₂	C₂×#16249	1	1	yes	characteristic
766	C₂	#636433	1	1	yes	characteristic
767	C₂	#648046	1	1	yes	characteristic
768	C₂	#649480	1	1	yes	characteristic
769	C₂	#686591	1	1	yes	characteristic
770	C₂	#688036	1	1	yes	characteristic
771	C₂	#772784	1	1	yes	characteristic
772	C₂	#772785	1	1	yes	characteristic
773	C₂	#855287	1	1	yes	characteristic
774	C₂	#855335	1	1	yes	characteristic
775	C₂	#856519	1	1	yes	characteristic
776	C₂	#856663	1	1	yes	characteristic
777	C₂	#927163	1	1	yes	characteristic
778	C₂	#927211	1	1	yes	characteristic
779	C₂	#928395	1	1	yes	characteristic
780	C₂	#928539	1	1	yes	characteristic
781	C₂	#988792	1	1	yes	characteristic
782	C₂	#988793	1	1	yes	characteristic
783	C₂	#988858	1	1	yes	characteristic
784	C₂	#988859	1	1	yes	characteristic
785	C₂	#989801	1	1	yes	characteristic
786	C₂	#989802	1	1	yes	characteristic
787	C₂	#991067	1	1	yes	characteristic
788	C₂	#991071	1	1	yes	characteristic
789	C₂	#1393921	1	1	yes	characteristic
790	C₂	#1393922	1	1	yes	characteristic
791	C₂	#1394155	1	1	yes	characteristic
792	C₂	#1395626	1	1	yes	characteristic
793	C₂	#2736534	1	1	yes	characteristic
794	C₂	#2736721	1	1	yes	characteristic
795	C₂	#4456939	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×#2433	C₂	semidirect
2. C₂²×#2408	C₂	semidirect
3. C₂×#16249	C₂	semidirect
4. C₂×#15140	C₂	semidirect
5. C₂×#15126	C₂	semidirect
6. C₂×#15124	C₂	semidirect
7. C₂×#15124	C₂	semidirect
8. C₂×#15123	C₂	semidirect
9. C₂×#13902	C₂	semidirect
10. #158830	C₂	semidirect
11. #158819	C₂	semidirect
12. #158818	C₂	semidirect
13. #158815	C₂	semidirect
14. #156688	C₂	semidirect
15. #156684	C₂	semidirect
16. #155622	C₂	semidirect
17. #154402	C₂	semidirect
18. #154386	C₂	semidirect
19. #154386	C₂	semidirect
20. #154384	C₂	semidirect
21. #154384	C₂	semidirect
22. #154383	C₂	semidirect
23. C₄×#1438	C₂	semidirect
30. C₂³×#121	C₂²	semidirect
36. C₂²×#394	C₂²	semidirect
37. C₂²×#394	C₂²	semidirect
38. C₂²×#394	C₂²	semidirect
43. C₂²×#392	C₂²	semidirect
44. C₂²×#392	C₂²	semidirect
45. C₂²×#392	C₂²	semidirect
46. C₂²×#392	C₂²	semidirect
55. C₂²×#390	C₂²	semidirect
56. C₂²×#390	C₂²	semidirect
57. C₂²×#390	C₂²	semidirect
58. C₂²×#389	C₂²	semidirect
61. C₂²×#380	C₂²	semidirect
67. C₂²×C₄×C₂²⋊C₄	C₂²	semidirect
68. C₂²×C₄×C₂²⋊C₄	C₂²	semidirect
69. C₂×#1440	C₂²	semidirect
70. C₂×#1440	C₂²	semidirect
71. C₂×#1440	C₂²	semidirect
72. C₂×#1440	C₂²	semidirect
73. C₂×#1440	C₂²	semidirect
75. C₂×#1439	C₂²	semidirect
76. C₂×#1439	C₂²	semidirect
84. C₂×#1438	C₂²	semidirect
85. C₂×#1438	C₂²	semidirect
86. C₂×#1438	C₂²	semidirect
87. C₂×#1438	C₂²	semidirect
88. C₂×#1438	C₂²	semidirect
89. C₂×#1438	C₂²	semidirect
90. C₂×#1438	C₂²	semidirect
91. C₂×#1438	C₂²	semidirect
92. C₂×#1438	C₂²	semidirect
93. C₂×#1438	C₂²	semidirect
94. C₂×#1438	C₂²	semidirect
95. C₂×#1438	C₂²	semidirect
96. C₂×#1438	C₂²	semidirect
97. C₂×#1438	C₂²	semidirect
98. C₂×C₄⋊#95	C₂²	semidirect
99. C₂×C₄⋊#95	C₂²	semidirect
100. C₂×C₄⋊#95	C₂²	semidirect
101. C₂×C₄⋊#95	C₂²	semidirect
102. C₂×C₄⋊#95	C₂²	semidirect
103. C₂×C₄⋊#95	C₂²	semidirect
104. C₂×C₄×#95	C₂²	semidirect
105. C₂×C₄×#95	C₂²	semidirect
106. #7557	C₂²	semidirect
107. #7557	C₂²	semidirect
108. #7557	C₂²	semidirect
109. #7556	C₂²	semidirect
113. #7555	C₂²	semidirect
114. #7555	C₂²	semidirect
115. #7555	C₂²	semidirect
116. #7555	C₂²	semidirect
117. #7555	C₂²	semidirect
118. #7555	C₂²	semidirect
119. #7555	C₂²	semidirect
120. #7555	C₂²	semidirect
121. #7555	C₂²	semidirect
122. #7555	C₂²	semidirect
124. C₂⁴×D₄	D₄	semidirect
140. C₂²×#127	D₄	semidirect
141. C₂²×#121	D₄	semidirect
193. C₂×#390	D₄	semidirect
194. C₂×#390	D₄	semidirect
195. C₂×#380	D₄	semidirect
228. #1438	D₄	semidirect
282. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
283. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
289. C₂×#95	C₂×D₄	semidirect
290. C₂×#95	C₂×D₄	semidirect
764. C₄	#16249	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#2433	2
C₂²×#2408	2
C₂×#16249	2
C₂×#15140	2
C₂×#15126	2
C₂×#15124	2
C₂×#15123	2
C₂×#13902	2
#158830	2
#158819	2
#158818	2
#158815	2
#156688	2
#156684	2
#155622	2
#154402	2
#154386	2
#154384	2
#154383	2
C₄×#1438	2