Subgroups — C₂×#72250287 #72334632

Order 2048.

At least 7964 conjugacy classes of subgroups; only the 12312 normal subgroups are shown.

The subgroup lattice has 808 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#154674	C₂	1	2	yes	maximal, complemented
2	C₂×#154763	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#15258	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#15257	C₂	1	2	yes	maximal, complemented
5	C₂×#155622	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#154670	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#154094	C₂	1	2	yes	maximal, complemented
8	C₂×#156684	C₂	1	4	yes	maximal, complemented
9	C₂×#156706	C₂	1	4	yes	maximal, complemented
10	C₂×#154634	C₂	1	4	yes	maximal, complemented
11	#72250287	C₂	1	32	yes	maximal, direct product factor
12	C₂²×#14715	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#14715	C₂	1	4	yes	maximal, complemented
14	C₂³×#2403	C₂	1	2	yes	maximal, complemented
15	C₂⁴×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#15947	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁶×D₄	C₂²	1	2	yes	—
18	C₂⁶×D₄	C₂²	1	2	yes	complemented
19	C₂⁶×D₄	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄²	C₂²	1	16	yes	complemented
21	C₂⁴×#127	C₂²	1	1	yes	characteristic
22	C₂⁴×#121	C₂²	1	2	yes	—
23	C₂⁴×#121	C₂²	1	2	yes	complemented
24	C₂⁴×#120	C₂²	1	1	yes	characteristic
25	C₂⁴×#120	C₂²	1	1	yes	characteristic
26	C₂⁴×#120	C₂²	1	2	yes	complemented
27	C₂⁴×#120	C₂²	1	2	yes	complemented
28	C₂⁴×#120	C₂²	1	2	yes	complemented
29	C₂⁴×#120	C₂²	1	4	yes	complemented
30	C₂⁴×#120	C₂²	1	2	yes	complemented
31	C₂⁴×#120	C₂²	1	1	yes	characteristic, complemented
32	C₂⁴×C₄×D₄	C₂²	1	2	yes	complemented
33	C₂²×#2403	C₂²	1	32	yes	complemented
34	C₂³×#392	C₂²	1	4	yes	—
35	C₂³×#392	C₂²	1	4	yes	complemented
36	C₂³×#392	C₂²	1	4	yes	complemented
37	C₂³×#392	C₂²	1	4	yes	complemented
38	C₂³×#392	C₂²	1	4	yes	complemented
39	C₂³×#392	C₂²	1	2	yes	complemented
40	C₂³×#386	C₂²	1	2	yes	complemented
41	C₂³×#386	C₂²	1	2	yes	complemented
42	C₂³×#386	C₂²	1	4	yes	complemented
43	C₂³×#386	C₂²	1	4	yes	complemented
44	C₂³×#386	C₂²	1	1	yes	characteristic, complemented
45	C₂³×#379	C₂²	1	1	yes	characteristic, complemented
46	C₂³×#379	C₂²	1	2	yes	complemented
47	C₂³×#379	C₂²	1	2	yes	complemented
48	C₂³×#379	C₂²	1	4	yes	complemented
49	C₂³×#379	C₂²	1	1	yes	characteristic, complemented
50	C₂×#15947	C₂²	1	16	yes	complemented
51	C₂×#15258	C₂²	1	16	yes	complemented
52	C₂×#15257	C₂²	1	32	yes	complemented
53	C₂×#14715	C₂²	1	16	yes	complemented
54	C₂×#14715	C₂²	1	64	yes	complemented
55	C₂²×#1440	C₂²	1	2	yes	complemented
56	C₂²×#1439	C₂²	1	4	yes	complemented
57	C₂²×#1438	C₂²	1	2	yes	complemented
58	C₂²×#1438	C₂²	1	2	yes	complemented
59	C₂²×#1438	C₂²	1	4	yes	complemented
60	C₂²×#1438	C₂²	1	4	yes	complemented
61	C₂²×#1438	C₂²	1	4	yes	complemented
62	C₂²×#1438	C₂²	1	4	yes	complemented
63	C₂²×#1438	C₂²	1	4	yes	complemented
64	C₂²×#1438	C₂²	1	4	yes	complemented
65	C₂²×#1438	C₂²	1	2	yes	complemented
66	C₂²×#1438	C₂²	1	1	yes	characteristic, complemented
67	C₂²×#1438	C₂²	1	1	yes	characteristic, complemented
68	C₂²×#1438	C₂²	1	2	yes	complemented
69	C₂²×#1438	C₂²	1	4	yes	complemented
70	C₂²×#1438	C₂²	1	2	yes	complemented
71	C₂²×#1438	C₂²	1	2	yes	complemented
72	C₂²×#1438	C₂²	1	4	yes	complemented
73	C₂²×#1437	C₂²	1	2	yes	complemented
74	C₂²×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
75	C₂²×C₂²⋊#95	C₂²	1	4	yes	complemented
76	C₂²×C₂²⋊#95	C₂²	1	4	yes	complemented
77	#156706	C₂²	1	64	yes	complemented
78	#156684	C₂²	1	64	yes	complemented
79	#155622	C₂²	1	16	yes	complemented
80	#154763	C₂²	1	16	yes	complemented
81	#154674	C₂²	1	32	yes	complemented
82	#154670	C₂²	1	16	yes	complemented
83	#154634	C₂²	1	64	yes	complemented
84	#154094	C₂²	1	32	yes	complemented
85	C₂×#7557	C₂²	1	4	yes	complemented
86	C₂×#7555	C₂²	1	4	yes	complemented
87	C₂×#7555	C₂²	1	4	yes	complemented
88	C₂×#7555	C₂²	1	2	yes	complemented
89	C₂×#7555	C₂²	1	4	yes	complemented
90	C₂×#7554	C₂²	1	2	yes	complemented
91	C₂⁸	C₂³	1	2	yes	—
92	C₂⁸	C₂³	1	1	yes	characteristic
93	C₂⁸	C₂³	1	1	yes	characteristic
94	C₂⁸	C₂³	1	1	yes	characteristic
95	C₂⁵×D₄	D₄	1	32	yes	complemented
96	C₂⁵×D₄	C₂³	1	2	yes	—
97	C₂⁵×D₄	C₂³	1	2	yes	—
98	C₂⁵×D₄	C₂³	1	2	yes	—
99	C₂⁵×D₄	C₂³	1	4	yes	—
100	C₂⁵×D₄	C₂³	1	2	yes	—
101	C₂⁵×D₄	C₂³	1	2	yes	—
102	C₂⁵×D₄	C₂³	1	4	yes	—
103	C₂⁵×D₄	C₂³	1	16	yes	—
104	C₂⁵×D₄	C₂³	1	2	yes	—
105	C₂⁵×D₄	C₂³	1	2	yes	—
106	C₂⁵×D₄	C₂³	1	4	yes	—
107	C₂⁵×D₄	C₂³	1	2	yes	—
108	C₂⁵×D₄	C₂³	1	1	yes	characteristic
109	C₂⁵×D₄	C₂³	1	1	yes	characteristic
110	C₂⁵×D₄	C₂³	1	16	yes	complemented
111	C₂⁵×D₄	C₂³	1	8	yes	complemented
112	C₂⁶×C₄	C₂³	1	2	yes	—
113	C₂⁶×C₄	C₂³	1	2	yes	—
114	C₂⁶×C₄	C₂³	1	1	yes	characteristic
115	C₂³×#127	D₄	1	16	yes	complemented
116	C₂³×#127	C₂³	1	8	yes	—
117	C₂³×#121	D₄	1	32	yes	complemented
118	C₂³×#121	C₂³	1	16	yes	—
119	C₂³×#121	C₂³	1	16	yes	complemented
120	C₂³×#120	D₄	1	16	yes	complemented
121	C₂³×#120	D₄	1	16	yes	complemented
122	C₂³×#120	C₂³	1	8	yes	—
123	C₂³×#120	C₂³	1	8	yes	—
124	C₂³×#120	C₂³	1	16	yes	complemented
125	C₂³×#120	C₂³	1	16	yes	complemented
126	C₂³×#120	C₂³	1	16	yes	complemented
127	C₂³×#120	C₂³	1	32	yes	complemented
128	C₂³×#120	C₂³	1	8	yes	complemented
129	C₂³×#120	C₂³	1	16	yes	complemented
130	C₂³×C₄×D₄	C₂³	1	16	yes	complemented
131	C₂⁴×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
136	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
142	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
151	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
152	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
157	C₂⁴×C₄²	C₂³	1	1	yes	characteristic
158	C₂²×#392	D₄	1	64	yes	complemented
159	C₂²×#392	C₂³	1	32	yes	—
160	C₂²×#392	C₂³	1	32	yes	complemented
161	C₂²×#392	C₂³	1	32	yes	complemented
162	C₂²×#392	C₂³	1	32	yes	complemented
163	C₂²×#392	C₂³	1	32	yes	complemented
164	C₂²×#392	C₂³	1	16	yes	complemented
165	C₂²×#386	C₂³	1	32	yes	complemented
166	C₂²×#386	C₂³	1	16	yes	complemented
167	C₂²×#386	C₂³	1	16	yes	complemented
168	C₂²×#386	C₂³	1	32	yes	complemented
169	C₂²×#386	C₂³	1	8	yes	complemented
170	C₂²×#379	C₂³	1	8	yes	complemented
171	C₂²×#379	C₂³	1	16	yes	complemented
172	C₂²×#379	C₂³	1	16	yes	complemented
173	C₂²×#379	C₂³	1	32	yes	complemented
174	C₂²×#379	C₂³	1	8	yes	complemented
175	C₂³×#95	C₂³	1	4	yes	—
176	C₂³×#95	C₂³	1	4	yes	—
177	C₂³×#95	C₂³	1	4	yes	—
178	C₂³×#95	C₂³	1	2	yes	—
179	C₂³×#95	C₂³	1	4	yes	—
180	C₂³×#95	C₂³	1	4	yes	—
181	C₂³×#95	C₂³	1	4	yes	—
182	C₂³×#95	C₂³	1	4	yes	—
183	C₂³×#95	C₂³	1	4	yes	—
184	C₂³×#95	C₂³	1	4	yes	—
185	C₂³×#95	C₂³	1	2	yes	—
186	C₂³×#95	C₂³	1	2	yes	—
187	C₂×#1440	C₂³	1	16	yes	complemented
188	C₂×#1439	C₂³	1	32	yes	complemented
189	C₂×#1438	C₂³	1	32	yes	complemented
190	C₂×#1438	C₂³	1	32	yes	complemented
191	C₂×#1438	C₂³	1	32	yes	complemented
192	C₂×#1438	C₂³	1	32	yes	complemented
193	C₂×#1438	C₂³	1	32	yes	complemented
194	C₂×#1438	C₂³	1	16	yes	complemented
195	C₂×#1438	C₂³	1	16	yes	complemented
196	C₂×#1438	C₂³	1	8	yes	complemented
197	C₂×#1438	C₂³	1	16	yes	complemented
198	C₂×#1438	C₂³	1	16	yes	complemented
199	C₂×#1438	C₂³	1	32	yes	complemented
200	C₂×#1438	C₂³	1	32	yes	complemented
201	C₂×#1438	C₂³	1	16	yes	complemented
202	C₂×#1438	C₂³	1	8	yes	complemented
203	C₂×#1438	C₂³	1	16	yes	complemented
204	C₂×#1438	C₂³	1	32	yes	complemented
205	C₂×#1437	C₂³	1	16	yes	complemented
206	C₂×C₂²⋊#95	C₂³	1	32	yes	complemented
207	C₂×C₂²⋊#95	C₂³	1	8	yes	complemented
208	C₂×C₂²⋊#95	C₂³	1	32	yes	complemented
209	#7557	C₂³	1	32	yes	complemented
210	#7555	C₂³	1	32	yes	complemented
211	#7555	C₂³	1	32	yes	complemented
212	#7555	C₂³	1	32	yes	complemented
213	#7555	C₂³	1	16	yes	complemented
214	#7554	C₂³	1	16	yes	complemented
215	C₂⁷	C₂×D₄	1	16	yes	—
216	C₂⁷	C₂×D₄	1	8	yes	—
217	C₂⁷	C₂×D₄	1	16	yes	—
218	C₂⁷	C₂×D₄	1	8	yes	complemented
219	C₂⁷	C₂⁴	1	2	yes	—
220	C₂⁷	C₂⁴	1	1	yes	characteristic
221	C₂⁷	C₂⁴	1	2	yes	—
222	C₂⁷	C₂⁴	1	1	yes	characteristic
223	C₂⁷	C₂⁴	1	2	yes	—
224	C₂⁷	C₂⁴	1	2	yes	—
225	C₂⁷	C₂⁴	1	8	yes	—
226	C₂⁷	C₂⁴	1	4	yes	—
227	C₂⁷	C₂⁴	1	4	yes	—
228	C₂⁷	C₂⁴	1	4	yes	—
229	C₂⁴×D₄	C₂×D₄	1	32	yes	—
230	C₂⁴×D₄	C₂×D₄	1	16	yes	—
231	C₂⁴×D₄	C₂×D₄	1	16	yes	—
232	C₂⁴×D₄	C₂×D₄	1	16	yes	—
233	C₂⁴×D₄	C₂×D₄	1	16	yes	—
234	C₂⁴×D₄	C₂×D₄	1	16	yes	—
235	C₂⁴×D₄	C₂×D₄	1	16	yes	—
236	C₂⁴×D₄	C₂×D₄	1	16	yes	—
237	C₂⁴×D₄	C₂×D₄	1	16	yes	—
238	C₂⁴×D₄	C₂×D₄	1	16	yes	—
239	C₂⁴×D₄	C₂×D₄	1	8	yes	—
240	C₂⁴×D₄	C₂×D₄	1	8	yes	—
241	C₂⁴×D₄	C₂×D₄	1	8	yes	—
242	C₂⁴×D₄	C₂×D₄	1	16	yes	complemented
243	C₂⁴×D₄	C₂×D₄	1	32	yes	complemented
244	C₂⁴×D₄	C₂×D₄	1	16	yes	complemented
245	C₂⁴×D₄	C₂×D₄	1	128	yes	complemented
246	C₂⁴×D₄	C₂×D₄	1	32	yes	complemented
247	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
248	C₂⁴×D₄	C₂⁴	1	8	yes	—
249	C₂⁴×D₄	C₂⁴	1	8	yes	—
250	C₂⁴×D₄	C₂⁴	1	8	yes	—
251	C₂⁴×D₄	C₂⁴	1	8	yes	—
252	C₂⁴×D₄	C₂⁴	1	8	yes	—
253	C₂⁴×D₄	C₂⁴	1	16	yes	—
254	C₂⁴×D₄	C₂⁴	1	16	yes	—
255	C₂⁴×D₄	C₂⁴	1	8	yes	—
256	C₂⁴×D₄	C₂⁴	1	8	yes	—
257	C₂⁴×D₄	C₂⁴	1	16	yes	—
258	C₂⁴×D₄	C₂⁴	1	8	yes	—
259	C₂⁴×D₄	C₂⁴	1	4	yes	—
260	C₂⁴×D₄	C₂⁴	1	4	yes	—
261	C₂⁵×C₄	C₂×D₄	1	16	yes	—
262	C₂⁵×C₄	C₂×D₄	1	16	yes	complemented
263	C₂⁵×C₄	C₂⁴	1	2	yes	—
264	C₂⁵×C₄	C₂⁴	1	4	yes	—
265	C₂⁵×C₄	C₂⁴	1	4	yes	—
266	C₂⁵×C₄	C₂⁴	1	2	yes	—
267	C₂⁵×C₄	C₂⁴	1	2	yes	—
268	C₂⁵×C₄	C₂⁴	1	2	yes	—
269	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
270	C₂⁵×C₄	C₂⁴	1	2	yes	—
271	C₂⁵×C₄	C₂⁴	1	8	yes	—
272	C₂⁵×C₄	C₂⁴	1	8	yes	—
273	C₂⁵×C₄	C₂⁴	1	4	yes	—
274	C₂⁵×C₄	C₂⁴	1	2	yes	—
275	C₂²×#127	C₂×D₄	1	64	yes	complemented
276	C₂²×#121	C₂×D₄	1	128	yes	complemented
277	C₂²×#120	C₂×D₄	1	64	yes	complemented
278	C₂²×#120	C₂×D₄	1	64	yes	complemented
279	C₂³×C₄⋊C₄	C₂×D₄	1	16	yes	complemented
280	C₂³×C₄⋊C₄	C₂⁴	1	8	yes	—
281	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	—
282	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	—
283	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
284	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	complemented
285	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	complemented
286	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
287	C₂³×C₂²⋊C₄	C₂×D₄	1	32	yes	complemented
288	C₂³×C₂²⋊C₄	C₂×D₄	1	32	yes	complemented
289	C₂³×C₂²⋊C₄	C₂×D₄	1	32	yes	complemented
290	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
291	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
292	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
293	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
294	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
295	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
296	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
297	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
298	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
299	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
300	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
301	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
302	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
303	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
304	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
305	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
306	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
307	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
308	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
309	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
310	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
311	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
312	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
313	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
314	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
315	C₂³×C₄²	C₂×D₄	1	8	yes	complemented
316	C₂³×C₄²	C₂⁴	1	4	yes	—
317	C₂×#392	C₂×D₄	1	256	yes	complemented
318	C₂²×#95	C₂×D₄	1	32	yes	complemented
319	C₂²×#95	C₂⁴	1	16	yes	—
320	C₂²×#95	C₂⁴	1	16	yes	—
321	C₂²×#95	C₂⁴	1	16	yes	—
322	C₂²×#95	C₂⁴	1	16	yes	—
323	C₂²×#95	C₂⁴	1	8	yes	—
324	C₂²×#95	C₂⁴	1	16	yes	—
325	C₂²×#95	C₂⁴	1	16	yes	—
326	C₂²×#95	C₂⁴	1	16	yes	—
327	C₂²×#95	C₂⁴	1	8	yes	—
328	C₂²×#95	C₂⁴	1	16	yes	—
329	C₂²×#95	C₂⁴	1	16	yes	—
330	C₂²×#95	C₂⁴	1	8	yes	—
331	C₂⁶	#120	1	64	yes	complemented
332	C₂⁶	C₂²×D₄	1	4	yes	—
333	C₂⁶	C₂²×D₄	1	8	yes	—
334	C₂⁶	C₂²×D₄	1	8	yes	—
335	C₂⁶	C₂²×D₄	1	4	yes	—
336	C₂⁶	C₂²×D₄	1	4	yes	—
337	C₂⁶	C₂²×D₄	1	8	yes	—
338	C₂⁶	C₂²×D₄	1	16	yes	—
339	C₂⁶	C₂²×D₄	1	4	yes	—
340	C₂⁶	C₂²×D₄	1	8	yes	—
341	C₂⁶	C₂²×D₄	1	8	yes	—
342	C₂⁶	C₂²×D₄	1	4	yes	—
343	C₂⁶	C₂²×D₄	1	4	yes	—
344	C₂⁶	C₂²×D₄	1	8	yes	—
345	C₂⁶	C₂²×D₄	1	8	yes	—
346	C₂⁶	C₂²×D₄	1	8	yes	—
347	C₂⁶	C₂²×D₄	1	8	yes	—
348	C₂⁶	C₂²×D₄	1	8	yes	—
349	C₂⁶	C₂²×D₄	1	8	yes	—
350	C₂⁶	C₂²×D₄	1	16	yes	—
351	C₂⁶	C₂²×D₄	1	16	yes	—
352	C₂⁶	C₂²×D₄	1	32	yes	—
353	C₂⁶	C₂²×D₄	1	16	yes	—
354	C₂⁶	C₂²×D₄	1	32	yes	—
355	C₂⁶	C₂²×D₄	1	16	yes	complemented
356	C₂⁶	H(5,𝔽₂)	1	8	yes	—
357	C₂⁶	H(5,𝔽₂)	1	16	yes	—
358	C₂⁶	H(5,𝔽₂)	1	16	yes	—
359	C₂⁶	C₂⁵	1	2	yes	—
360	C₂⁶	C₂⁵	1	4	yes	—
361	C₂⁶	C₂⁵	1	4	yes	—
362	C₂⁶	C₂⁵	1	2	yes	—
363	C₂⁶	C₂⁵	1	4	yes	—
364	C₂⁶	C₂⁵	1	4	yes	—
365	C₂⁶	C₂⁵	1	1	yes	characteristic
366	C₂³×D₄	#120	1	128	yes	complemented
367	C₂³×D₄	#120	1	128	yes	complemented
368	C₂³×D₄	#120	1	128	yes	complemented
369	C₂³×D₄	#120	1	64	yes	complemented
370	C₂³×D₄	C₂²×D₄	1	64	yes	—
371	C₂³×D₄	C₂²×D₄	1	32	yes	—
372	C₂³×D₄	C₂²×D₄	1	32	yes	—
373	C₂³×D₄	C₂²×D₄	1	32	yes	—
374	C₂³×D₄	C₂²×D₄	1	32	yes	—
375	C₂³×D₄	C₂²×D₄	1	32	yes	—
376	C₂³×D₄	C₂²×D₄	1	32	yes	—
377	C₂³×D₄	C₂²×D₄	1	32	yes	—
378	C₂³×D₄	C₂²×D₄	1	32	yes	—
379	C₂³×D₄	C₂²×D₄	1	32	yes	—
380	C₂³×D₄	C₂²×D₄	1	16	yes	—
381	C₂³×D₄	C₂²×D₄	1	16	yes	—
382	C₂³×D₄	C₂²×D₄	1	16	yes	—
383	C₂³×D₄	C₂²×D₄	1	64	yes	complemented
384	C₂³×D₄	C₂²×D₄	1	32	yes	complemented
385	C₂³×D₄	C₂²×D₄	1	32	yes	complemented
386	C₂³×D₄	C₂²×D₄	1	64	yes	complemented
387	C₂³×D₄	C₂²×D₄	1	16	yes	complemented
388	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
389	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
390	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
391	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
392	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
393	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
394	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
395	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
396	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
397	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
398	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
399	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
400	C₂⁴×C₄	C₂²×D₄	1	32	yes	—
401	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
402	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
403	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
404	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
405	C₂⁴×C₄	C₂²×D₄	1	32	yes	complemented
406	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
407	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
408	C₂⁴×C₄	H(5,𝔽₂)	1	16	yes	—
409	C₂⁴×C₄	C₂⁵	1	4	yes	—
410	C₂⁴×C₄	C₂⁵	1	8	yes	—
411	C₂⁴×C₄	C₂⁵	1	8	yes	—
412	C₂⁴×C₄	C₂⁵	1	4	yes	—
413	C₂⁴×C₄	C₂⁵	1	4	yes	—
414	C₂⁴×C₄	C₂⁵	1	4	yes	—
415	C₂⁴×C₄	C₂⁵	1	2	yes	—
416	C₂⁴×C₄	C₂⁵	1	4	yes	—
417	C₂⁴×C₄	C₂⁵	1	4	yes	—
418	C₂²×C₄⋊C₄	C₂²×D₄	1	32	yes	complemented
419	C₂²×C₂²⋊C₄	#120	1	64	yes	complemented
420	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
421	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
422	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
423	C₂²×C₂²⋊C₄	C₂²×D₄	1	64	yes	complemented
424	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	complemented
425	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	complemented
426	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	complemented
427	C₂²×C₂²⋊C₄	C₂²×D₄	1	64	yes	complemented
428	C₂²×C₂²⋊C₄	C₂²×D₄	1	64	yes	complemented
429	C₂²×C₄²	C₂²×D₄	1	16	yes	complemented
430	C₂×#95	C₂²×D₄	1	64	yes	complemented
431	C₂⁵	C₂×#120	1	16	yes	—
432	C₂⁵	C₂×#120	1	32	yes	—
433	C₂⁵	C₂×#120	1	16	yes	—
434	C₂⁵	C₂×#120	1	32	yes	—
435	C₂⁵	C₂×#120	1	32	yes	—
436	C₂⁵	C₂×#120	1	16	yes	—
437	C₂⁵	C₂×#120	1	16	yes	—
438	C₂⁵	C₂×#120	1	32	yes	—
439	C₂⁵	C₂×#120	1	32	yes	—
440	C₂⁵	C₂×#120	1	32	yes	—
441	C₂⁵	C₂×#120	1	32	yes	—
442	C₂⁵	C₂×#120	1	64	yes	complemented
443	C₂⁵	#534	1	32	yes	—
444	C₂⁵	#534	1	32	yes	—
445	C₂⁵	D₄²	1	64	yes	—
446	C₂⁵	D₄²	1	64	yes	—
447	C₂⁵	D₄²	1	64	yes	—
448	C₂⁵	D₄²	1	64	yes	—
449	C₂⁵	D₄²	1	32	yes	complemented
450	C₂⁵	C₂³×D₄	1	8	yes	—
451	C₂⁵	C₂³×D₄	1	4	yes	—
452	C₂⁵	C₂³×D₄	1	8	yes	—
453	C₂⁵	C₂³×D₄	1	4	yes	—
454	C₂⁵	C₂³×D₄	1	4	yes	—
455	C₂⁵	C₂³×D₄	1	8	yes	—
456	C₂⁵	C₂³×D₄	1	16	yes	—
457	C₂⁵	C₂³×D₄	1	4	yes	—
458	C₂⁵	C₂³×D₄	1	4	yes	—
459	C₂⁵	C₂³×D₄	1	8	yes	—
460	C₂⁵	C₂³×D₄	1	8	yes	—
461	C₂⁵	C₂³×D₄	1	4	yes	—
462	C₂⁵	C₂³×D₄	1	8	yes	—
463	C₂⁵	C₂³×D₄	1	8	yes	—
464	C₂⁵	C₂³×D₄	1	16	yes	—
465	C₂⁵	C₂³×D₄	1	16	yes	—
466	C₂⁵	C₂³×D₄	1	8	yes	—
467	C₂⁵	C₂³×D₄	1	8	yes	—
468	C₂⁵	C₂³×D₄	1	8	yes	—
469	C₂⁵	C₂³×D₄	1	8	yes	—
470	C₂⁵	C₂³×D₄	1	4	yes	—
471	C₂⁵	C₂³×D₄	1	2	yes	—
472	C₂⁵	C₂³×D₄	1	2	yes	—
473	C₂⁵	C₂³×D₄	1	2	yes	—
474	C₂⁵	C₂³×D₄	1	4	yes	—
475	C₂⁵	C₂³×D₄	1	8	yes	—
476	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
477	C₂⁵	C₂×H(5,𝔽₂)	1	16	yes	—
478	C₂⁵	C₂×H(5,𝔽₂)	1	16	yes	—
479	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
480	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
481	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
482	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
483	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
484	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
485	C₂⁵	#585	1	4	yes	—
486	C₂⁵	C₂⁶	1	1	yes	characteristic
487	C₂²×D₄	C₂×#120	1	128	yes	complemented
488	C₂²×D₄	C₂×#120	1	128	yes	complemented
489	C₂²×D₄	C₂×#120	1	128	yes	complemented
490	C₂²×D₄	C₂×#120	1	64	yes	complemented
491	C₂³×C₄	C₂×#120	1	16	yes	—
492	C₂³×C₄	C₂×#120	1	32	yes	—
493	C₂³×C₄	C₂×#120	1	32	yes	—
494	C₂³×C₄	C₂×#120	1	32	yes	—
495	C₂³×C₄	C₂×#120	1	32	yes	—
496	C₂³×C₄	#534	1	32	yes	—
497	C₂³×C₄	D₄²	1	64	yes	—
498	C₂³×C₄	D₄²	1	64	yes	—
499	C₂³×C₄	D₄²	1	32	yes	complemented
500	C₂³×C₄	C₂³×D₄	1	16	yes	—
501	C₂³×C₄	C₂³×D₄	1	16	yes	—
502	C₂³×C₄	C₂³×D₄	1	4	yes	—
503	C₂³×C₄	C₂³×D₄	1	8	yes	—
504	C₂³×C₄	C₂³×D₄	1	4	yes	—
505	C₂³×C₄	C₂³×D₄	1	8	yes	—
506	C₂³×C₄	C₂³×D₄	1	4	yes	—
507	C₂³×C₄	C₂³×D₄	1	8	yes	—
508	C₂³×C₄	C₂³×D₄	1	8	yes	—
509	C₂³×C₄	C₂³×D₄	1	8	yes	—
510	C₂³×C₄	C₂³×D₄	1	8	yes	—
511	C₂³×C₄	C₂³×D₄	1	16	yes	—
512	C₂³×C₄	C₂³×D₄	1	8	yes	—
513	C₂³×C₄	C₂³×D₄	1	8	yes	—
514	C₂³×C₄	C₂³×D₄	1	8	yes	—
515	C₂³×C₄	C₂³×D₄	1	16	yes	—
516	C₂³×C₄	C₂×H(5,𝔽₂)	1	8	yes	—
517	C₂³×C₄	C₂×H(5,𝔽₂)	1	8	yes	—
518	C₂³×C₄	C₂×H(5,𝔽₂)	1	16	yes	—
519	C₂×C₂²⋊C₄	C₂×#120	1	64	yes	complemented
520	C₂⁴	#2403	1	128	yes	—
521	C₂⁴	#2403	1	128	yes	complemented
522	C₂⁴	#2846	1	64	yes	—
523	C₂⁴	C₂²×#120	1	16	yes	—
524	C₂⁴	C₂²×#120	1	8	yes	—
525	C₂⁴	C₂²×#120	1	16	yes	—
526	C₂⁴	C₂²×#120	1	16	yes	—
527	C₂⁴	C₂²×#120	1	8	yes	—
528	C₂⁴	C₂²×#120	1	8	yes	—
529	C₂⁴	C₂²×#120	1	8	yes	—
530	C₂⁴	C₂²×#120	1	16	yes	—
531	C₂⁴	C₂²×#120	1	16	yes	—
532	C₂⁴	C₂²×#120	1	16	yes	—
533	C₂⁴	C₂²×#120	1	16	yes	—
534	C₂⁴	C₂²×#120	1	4	yes	—
535	C₂⁴	C₂²×#120	1	4	yes	—
536	C₂⁴	C₂²×#120	1	8	yes	—
537	C₂⁴	C₂²×#120	1	8	yes	—
538	C₂⁴	C₂²×#120	1	4	yes	—
539	C₂⁴	C₂²×#120	1	8	yes	—
540	C₂⁴	C₂×#534	1	16	yes	—
541	C₂⁴	C₂×#534	1	16	yes	—
542	C₂⁴	C₂×#534	1	8	yes	—
543	C₂⁴	C₂×#534	1	8	yes	—
544	C₂⁴	C₂×#534	1	8	yes	—
545	C₂⁴	C₂×D₄²	1	32	yes	—
546	C₂⁴	C₂×D₄²	1	32	yes	—
547	C₂⁴	C₂×D₄²	1	32	yes	—
548	C₂⁴	C₂×D₄²	1	32	yes	—
549	C₂⁴	C₂×D₄²	1	16	yes	—
550	C₂⁴	C₂×D₄²	1	16	yes	—
551	C₂⁴	C₂×D₄²	1	16	yes	—
552	C₂⁴	C₂×D₄²	1	16	yes	—
553	C₂⁴	C₂×D₄²	1	16	yes	—
554	C₂⁴	C₂×D₄²	1	16	yes	—
555	C₂⁴	C₂×D₄²	1	8	yes	—
556	C₂⁴	C₂×D₄²	1	8	yes	—
557	C₂⁴	C₂×D₄²	1	16	yes	complemented
558	C₂⁴	#3484	1	16	yes	—
559	C₂⁴	#3484	1	16	yes	—
560	C₂⁴	#3484	1	16	yes	—
561	C₂⁴	#3484	1	16	yes	—
562	C₂⁴	#3484	1	4	yes	—
563	C₂⁴	#3484	1	4	yes	—
564	C₂⁴	#3484	1	4	yes	—
565	C₂⁴	#3484	1	8	yes	—
566	C₂⁴	#3484	1	8	yes	—
567	C₂⁴	#3484	1	16	yes	—
568	C₂⁴	#3484	1	16	yes	—
569	C₂⁴	#3484	1	16	yes	—
570	C₂⁴	#3484	1	16	yes	—
571	C₂⁴	#3484	1	16	yes	—
572	C₂⁴	#3484	1	16	yes	—
573	C₂⁴	#3485	1	4	yes	—
574	C₂⁴	#3488	1	16	yes	—
575	C₂⁴	#3488	1	16	yes	—
576	C₂⁴	#3496	1	16	yes	—
577	C₂⁴	#3496	1	16	yes	—
578	C₂⁴	#3496	1	8	yes	—
579	C₂⁴	#3496	1	8	yes	—
580	C₂⁴	#3498	1	16	yes	—
581	C₂⁴	#3498	1	16	yes	—
582	C₂⁴	#3532	1	8	yes	—
583	C₂⁴	#3532	1	8	yes	—
584	C₂⁴	#3532	1	8	yes	—
585	C₂⁴	#3534	1	16	yes	—
586	C₂⁴	#3537	1	16	yes	—
587	C₂⁴	#3537	1	16	yes	—
588	C₂⁴	#3537	1	16	yes	—
589	C₂⁴	#3537	1	8	yes	—
590	C₂⁴	#3543	1	16	yes	—
591	C₂⁴	#3543	1	8	yes	—
592	C₂⁴	#3549	1	8	yes	—
593	C₂⁴	#3558	1	16	yes	—
594	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
595	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
596	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
597	C₂⁴	C₂⁴×D₄	1	2	yes	—
598	C₂⁴	C₂⁴×D₄	1	2	yes	—
599	C₂⁴	C₂⁴×D₄	1	4	yes	—
600	C₂⁴	C₂²×H(5,𝔽₂)	1	4	yes	—
601	C₂⁴	C₂²×H(5,𝔽₂)	1	4	yes	—
602	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
603	C₂⁴	C₂²×H(5,𝔽₂)	1	4	yes	—
604	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
605	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
606	C₂⁴	C₂×#585	1	2	yes	—
607	C₂²×C₄	#2403	1	128	yes	complemented
608	C₂²×C₄	C₂²×#120	1	8	yes	—
609	C₂²×C₄	C₂²×#120	1	16	yes	—
610	C₂²×C₄	C₂²×#120	1	16	yes	—
611	C₂²×C₄	C₂²×#120	1	16	yes	—
612	C₂²×C₄	C₂²×#120	1	16	yes	—
613	C₂²×C₄	C₂×#534	1	16	yes	—
614	C₂²×C₄	C₂×D₄²	1	32	yes	—
615	C₂²×C₄	C₂×D₄²	1	32	yes	—
616	C₂²×C₄	C₂×D₄²	1	16	yes	complemented
617	C₂³	C₂×#2403	1	32	yes	—
618	C₂³	C₂×#2403	1	16	yes	—
619	C₂³	C₂×#2403	1	16	yes	—
620	C₂³	C₂×#2403	1	16	yes	—
621	C₂³	C₂×#2403	1	32	yes	complemented
622	C₂³	#34980	1	16	yes	—
623	C₂³	#34980	1	16	yes	—
624	C₂³	#34980	1	16	yes	—
625	C₂³	#35346	1	8	yes	—
626	C₂³	#35346	1	8	yes	—
627	C₂³	#35347	1	8	yes	—
628	C₂³	#35347	1	8	yes	—
629	C₂³	#35512	1	8	yes	—
630	C₂³	#35527	1	8	yes	—
631	C₂³	#35680	1	32	yes	—
632	C₂³	#35680	1	32	yes	—
633	C₂³	#35680	1	32	yes	—
634	C₂³	D₄×#120	1	32	yes	—
635	C₂³	D₄×#120	1	32	yes	—
636	C₂³	D₄×#120	1	32	yes	—
637	C₂³	D₄×#120	1	32	yes	—
638	C₂³	D₄×#120	1	32	yes	—
639	C₂³	C₂×#2846	1	16	yes	—
640	C₂³	C₂×#2846	1	8	yes	—
641	C₂³	#37644	1	32	yes	—
642	C₂³	#37672	1	32	yes	—
643	C₂³	#39358	1	32	yes	—
644	C₂³	#40486	1	32	yes	—
645	C₂³	#40584	1	32	yes	—
646	C₂³	#42475	1	32	yes	—
647	C₂³	#42996	1	32	yes	—
648	C₂³	#43001	1	32	yes	—
649	C₂³	#43001	1	32	yes	—
650	C₂³	#43001	1	32	yes	—
651	C₂³	#43023	1	32	yes	—
652	C₂³	#43098	1	32	yes	—
653	C₂³	#44870	1	32	yes	—
654	C₂³	#44877	1	32	yes	—
655	C₂³	#44877	1	32	yes	—
656	C₂³	#45355	1	32	yes	—
657	C₂³	#47827	1	16	yes	—
658	C₂³	#47827	1	16	yes	—
659	C₂³	#47838	1	32	yes	—
660	C₂³	#47929	1	16	yes	—
661	C₂³	#47942	1	32	yes	—
662	C₂³	#49545	1	16	yes	—
663	C₂³	#52004	1	16	yes	—
664	C₂³	#52031	1	16	yes	—
665	C₂³	#58990	1	16	yes	—
666	C₂³	#58990	1	16	yes	—
667	C₂³	#58990	1	16	yes	—
668	C₂³	#58997	1	16	yes	—
669	C₂³	#58997	1	32	yes	—
670	C₂³	#59126	1	32	yes	—
671	C₂³	#59126	1	16	yes	—
672	C₂³	#59816	1	16	yes	—
673	C₂³	C₂³×#120	1	2	yes	—
674	C₂³	C₂³×#120	1	1	yes	characteristic
675	C₂³	C₂³×#120	1	2	yes	—
676	C₂³	C₂³×#120	1	2	yes	—
677	C₂³	C₂³×#120	1	1	yes	characteristic
678	C₂³	C₂³×#120	1	1	yes	characteristic
679	C₂³	C₂²×#534	1	2	yes	—
680	C₂³	C₂²×#534	1	2	yes	—
681	C₂³	C₂²×#534	1	2	yes	—
682	C₂³	C₂²×D₄²	1	2	yes	—
683	C₂³	C₂²×D₄²	1	4	yes	—
684	C₂³	C₂²×D₄²	1	4	yes	—
685	C₂³	C₂²×D₄²	1	4	yes	—
686	C₂³	C₂²×D₄²	1	2	yes	—
687	C₂³	C₂²×D₄²	1	4	yes	—
688	C₂³	C₂²×D₄²	1	4	yes	—
689	C₂³	C₂²×D₄²	1	4	yes	—
690	C₂³	C₂×#3532	1	2	yes	—
691	C₂³	C₂×#3532	1	2	yes	—
692	C₂³	C₂×#3532	1	2	yes	—
693	C₂³	C₂×#3534	1	4	yes	—
694	C₂³	C₂×#3537	1	4	yes	—
695	C₂³	C₂×#3537	1	4	yes	—
696	C₂³	C₂×#3537	1	4	yes	—
697	C₂³	C₂×#3537	1	2	yes	—
698	C₂³	C₂×#3558	1	4	yes	—
699	C₂³	C₂×#3543	1	4	yes	—
700	C₂³	C₂×#3543	1	2	yes	—
701	C₂³	C₂×#3549	1	2	yes	—
702	C₂³	C₂×#3484	1	2	yes	—
703	C₂³	C₂×#3484	1	4	yes	—
704	C₂³	C₂×#3484	1	4	yes	—
705	C₂³	C₂×#3484	1	4	yes	—
706	C₂³	C₂×#3484	1	4	yes	—
707	C₂³	C₂×#3484	1	4	yes	—
708	C₂³	C₂×#3484	1	4	yes	—
709	C₂³	C₂×#3484	1	1	yes	characteristic
710	C₂³	C₂×#3484	1	1	yes	characteristic
711	C₂³	C₂×#3484	1	2	yes	—
712	C₂³	C₂×#3484	1	4	yes	—
713	C₂³	C₂×#3484	1	4	yes	—
714	C₂³	C₂×#3484	1	4	yes	—
715	C₂³	C₂×#3484	1	4	yes	—
716	C₂³	C₂×#3484	1	1	yes	characteristic
717	C₂³	C₂×#3496	1	4	yes	—
718	C₂³	C₂×#3496	1	2	yes	—
719	C₂³	C₂×#3496	1	4	yes	—
720	C₂³	C₂×#3496	1	2	yes	—
721	C₂³	C₂×#3485	1	1	yes	characteristic
722	C₂³	C₂×#3488	1	4	yes	—
723	C₂³	C₂×#3488	1	4	yes	—
724	C₂³	C₂×#3498	1	4	yes	—
725	C₂³	C₂×#3498	1	4	yes	—
726	C₂×C₄	C₂×#2403	1	32	yes	complemented
727	C₂²	#612424	1	32	yes	—
728	C₂²	#647656	1	16	yes	—
729	C₂²	#687584	1	32	yes	—
730	C₂²	#772778	1	64	yes	—
731	C₂²	#772785	1	64	yes	—
732	C₂²	#1258513	1	64	yes	—
733	C₂²	#1259281	1	64	yes	—
734	C₂²	#1418353	1	32	yes	—
735	C₂²	#1418363	1	32	yes	—
736	C₂²	#1418385	1	32	yes	—
737	C₂²	#1418393	1	32	yes	—
738	C₂²	#4420586	1	16	yes	—
739	C₂²	#4928938	1	16	yes	—
740	C₂²	C₂²×#2403	1	2	yes	—
741	C₂²	C₂²×#2403	1	2	yes	—
742	C₂²	C₂²×#2403	1	2	yes	—
743	C₂²	C₂×#34980	1	2	yes	—
744	C₂²	C₂×#34980	1	2	yes	—
745	C₂²	C₂×#34980	1	2	yes	—
746	C₂²	C₂×#35346	1	1	yes	characteristic
747	C₂²	C₂×#35346	1	1	yes	characteristic
748	C₂²	C₂×#35347	1	1	yes	characteristic
749	C₂²	C₂×#35347	1	1	yes	characteristic
750	C₂²	C₂×#35512	1	1	yes	characteristic
751	C₂²	C₂×#35527	1	1	yes	characteristic
752	C₂²	C₂×#35680	1	4	yes	—
753	C₂²	C₂×#35680	1	4	yes	—
754	C₂²	C₂×#35680	1	4	yes	—
755	C₂²	C₂×D₄×#120	1	4	yes	—
756	C₂²	C₂×D₄×#120	1	4	yes	—
757	C₂²	C₂×D₄×#120	1	4	yes	—
758	C₂²	C₂×D₄×#120	1	4	yes	—
759	C₂²	C₂×D₄×#120	1	4	yes	—
760	C₂²	C₂²×#2846	1	1	yes	characteristic
761	C₂²	C₂×#37644	1	4	yes	—
762	C₂²	C₂×#37672	1	4	yes	—
763	C₂²	C₂×#39358	1	4	yes	—
764	C₂²	C₂×#40584	1	4	yes	—
765	C₂²	C₂×#40486	1	4	yes	—
766	C₂²	C₂×#42475	1	4	yes	—
767	C₂²	C₂×#58990	1	2	yes	—
768	C₂²	C₂×#58990	1	2	yes	—
769	C₂²	C₂×#58990	1	2	yes	—
770	C₂²	C₂×#58997	1	2	yes	—
771	C₂²	C₂×#58997	1	4	yes	—
772	C₂²	C₂×#59126	1	4	yes	—
773	C₂²	C₂×#59126	1	2	yes	—
774	C₂²	C₂×#59816	1	2	yes	—
775	C₂²	C₂×#42996	1	4	yes	—
776	C₂²	C₂×#43001	1	4	yes	—
777	C₂²	C₂×#43001	1	4	yes	—
778	C₂²	C₂×#43001	1	4	yes	—
779	C₂²	C₂×#43023	1	4	yes	—
780	C₂²	C₂×#43098	1	4	yes	—
781	C₂²	C₂×#44870	1	4	yes	—
782	C₂²	C₂×#44877	1	4	yes	—
783	C₂²	C₂×#44877	1	4	yes	—
784	C₂²	C₂×#45355	1	4	yes	—
785	C₂²	C₂×#47827	1	2	yes	—
786	C₂²	C₂×#47827	1	2	yes	—
787	C₂²	C₂×#47929	1	2	yes	—
788	C₂²	C₂×#47838	1	4	yes	—
789	C₂²	C₂×#47942	1	4	yes	—
790	C₂²	C₂×#49545	1	2	yes	—
791	C₂²	C₂×#52004	1	2	yes	—
792	C₂²	C₂×#52031	1	2	yes	—
793	C₂	C₂×#647656	1	1	yes	characteristic
794	C₂	C₂×#612424	1	2	yes	—
795	C₂	C₂×#1259281	1	4	yes	—
796	C₂	C₂×#4928938	1	1	yes	characteristic
797	C₂	C₂×#772778	1	4	yes	—
798	C₂	C₂×#687584	1	2	yes	—
799	C₂	C₂×#772785	1	4	yes	—
800	C₂	#72250287	1	32	yes	direct product factor
801	C₂	C₂×#1418385	1	2	yes	—
802	C₂	C₂×#1258513	1	4	yes	—
803	C₂	C₂×#1418363	1	2	yes	—
804	C₂	C₂×#1418393	1	2	yes	—
805	C₂	C₂×#1418353	1	2	yes	—
806	C₂	C₂×#4420586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#154674	C₂	semidirect
2. C₂×#154763	C₂	semidirect
3. C₂²×#15258	C₂	semidirect
4. C₂²×#15257	C₂	semidirect
5. C₂×#155622	C₂	semidirect
6. C₂×#154670	C₂	semidirect
7. C₂×#154094	C₂	semidirect
8. C₂×#156684	C₂	semidirect
9. C₂×#156706	C₂	semidirect
10. C₂×#154634	C₂	semidirect
11. #72250287	C₂	direct (N × H)
12. C₂²×#14715	C₂	semidirect
13. C₂²×#14715	C₂	semidirect
14. C₂³×#2403	C₂	semidirect
15. C₂⁴×D₄²	C₂	semidirect
16. C₂²×#15947	C₂	semidirect
18. C₂⁶×D₄	C₂²	semidirect
19. C₂⁶×D₄	C₂²	semidirect
20. C₂³×D₄²	C₂²	semidirect
23. C₂⁴×#121	C₂²	semidirect
26. C₂⁴×#120	C₂²	semidirect
27. C₂⁴×#120	C₂²	semidirect
28. C₂⁴×#120	C₂²	semidirect
29. C₂⁴×#120	C₂²	semidirect
30. C₂⁴×#120	C₂²	semidirect
31. C₂⁴×#120	C₂²	semidirect
32. C₂⁴×C₄×D₄	C₂²	semidirect
33. C₂²×#2403	C₂²	semidirect
35. C₂³×#392	C₂²	semidirect
36. C₂³×#392	C₂²	semidirect
37. C₂³×#392	C₂²	semidirect
38. C₂³×#392	C₂²	semidirect
39. C₂³×#392	C₂²	semidirect
40. C₂³×#386	C₂²	semidirect
41. C₂³×#386	C₂²	semidirect
42. C₂³×#386	C₂²	semidirect
43. C₂³×#386	C₂²	semidirect
44. C₂³×#386	C₂²	semidirect
45. C₂³×#379	C₂²	semidirect
46. C₂³×#379	C₂²	semidirect
47. C₂³×#379	C₂²	semidirect
48. C₂³×#379	C₂²	semidirect
49. C₂³×#379	C₂²	semidirect
50. C₂×#15947	C₂²	semidirect
51. C₂×#15258	C₂²	semidirect
52. C₂×#15257	C₂²	semidirect
53. C₂×#14715	C₂²	semidirect
54. C₂×#14715	C₂²	semidirect
55. C₂²×#1440	C₂²	semidirect
56. C₂²×#1439	C₂²	semidirect
57. C₂²×#1438	C₂²	semidirect
58. C₂²×#1438	C₂²	semidirect
59. C₂²×#1438	C₂²	semidirect
60. C₂²×#1438	C₂²	semidirect
61. C₂²×#1438	C₂²	semidirect
62. C₂²×#1438	C₂²	semidirect
63. C₂²×#1438	C₂²	semidirect
64. C₂²×#1438	C₂²	semidirect
65. C₂²×#1438	C₂²	semidirect
66. C₂²×#1438	C₂²	semidirect
67. C₂²×#1438	C₂²	semidirect
68. C₂²×#1438	C₂²	semidirect
69. C₂²×#1438	C₂²	semidirect
70. C₂²×#1438	C₂²	semidirect
71. C₂²×#1438	C₂²	semidirect
72. C₂²×#1438	C₂²	semidirect
73. C₂²×#1437	C₂²	semidirect
74. C₂²×C₂²⋊#95	C₂²	semidirect
75. C₂²×C₂²⋊#95	C₂²	semidirect
76. C₂²×C₂²⋊#95	C₂²	semidirect
77. #156706	C₂²	semidirect
78. #156684	C₂²	semidirect
79. #155622	C₂²	semidirect
80. #154763	C₂²	semidirect
81. #154674	C₂²	semidirect
82. #154670	C₂²	semidirect
83. #154634	C₂²	semidirect
84. #154094	C₂²	semidirect
85. C₂×#7557	C₂²	semidirect
86. C₂×#7555	C₂²	semidirect
87. C₂×#7555	C₂²	semidirect
88. C₂×#7555	C₂²	semidirect
89. C₂×#7555	C₂²	semidirect
90. C₂×#7554	C₂²	semidirect
95. C₂⁵×D₄	D₄	semidirect
110. C₂⁵×D₄	C₂³	semidirect
111. C₂⁵×D₄	C₂³	semidirect
115. C₂³×#127	D₄	semidirect
117. C₂³×#121	D₄	semidirect
119. C₂³×#121	C₂³	semidirect
120. C₂³×#120	D₄	semidirect
121. C₂³×#120	D₄	semidirect
124. C₂³×#120	C₂³	semidirect
125. C₂³×#120	C₂³	semidirect
126. C₂³×#120	C₂³	semidirect
127. C₂³×#120	C₂³	semidirect
128. C₂³×#120	C₂³	semidirect
129. C₂³×#120	C₂³	semidirect
130. C₂³×C₄×D₄	C₂³	semidirect
158. C₂²×#392	D₄	semidirect
160. C₂²×#392	C₂³	semidirect
161. C₂²×#392	C₂³	semidirect
162. C₂²×#392	C₂³	semidirect
163. C₂²×#392	C₂³	semidirect
164. C₂²×#392	C₂³	semidirect
165. C₂²×#386	C₂³	semidirect
166. C₂²×#386	C₂³	semidirect
167. C₂²×#386	C₂³	semidirect
168. C₂²×#386	C₂³	semidirect
169. C₂²×#386	C₂³	semidirect
170. C₂²×#379	C₂³	semidirect
171. C₂²×#379	C₂³	semidirect
172. C₂²×#379	C₂³	semidirect
173. C₂²×#379	C₂³	semidirect
174. C₂²×#379	C₂³	semidirect
187. C₂×#1440	C₂³	semidirect
188. C₂×#1439	C₂³	semidirect
189. C₂×#1438	C₂³	semidirect
190. C₂×#1438	C₂³	semidirect
191. C₂×#1438	C₂³	semidirect
192. C₂×#1438	C₂³	semidirect
193. C₂×#1438	C₂³	semidirect
194. C₂×#1438	C₂³	semidirect
195. C₂×#1438	C₂³	semidirect
196. C₂×#1438	C₂³	semidirect
197. C₂×#1438	C₂³	semidirect
198. C₂×#1438	C₂³	semidirect
199. C₂×#1438	C₂³	semidirect
200. C₂×#1438	C₂³	semidirect
201. C₂×#1438	C₂³	semidirect
202. C₂×#1438	C₂³	semidirect
203. C₂×#1438	C₂³	semidirect
204. C₂×#1438	C₂³	semidirect
205. C₂×#1437	C₂³	semidirect
206. C₂×C₂²⋊#95	C₂³	semidirect
207. C₂×C₂²⋊#95	C₂³	semidirect
208. C₂×C₂²⋊#95	C₂³	semidirect
209. #7557	C₂³	semidirect
210. #7555	C₂³	semidirect
211. #7555	C₂³	semidirect
212. #7555	C₂³	semidirect
213. #7555	C₂³	semidirect
214. #7554	C₂³	semidirect
218. C₂⁷	C₂×D₄	semidirect
242. C₂⁴×D₄	C₂×D₄	semidirect
243. C₂⁴×D₄	C₂×D₄	semidirect
244. C₂⁴×D₄	C₂×D₄	semidirect
245. C₂⁴×D₄	C₂×D₄	semidirect
246. C₂⁴×D₄	C₂×D₄	semidirect
247. C₂⁴×D₄	C₂×D₄	semidirect
262. C₂⁵×C₄	C₂×D₄	semidirect
275. C₂²×#127	C₂×D₄	semidirect
276. C₂²×#121	C₂×D₄	semidirect
277. C₂²×#120	C₂×D₄	semidirect
278. C₂²×#120	C₂×D₄	semidirect
279. C₂³×C₄⋊C₄	C₂×D₄	semidirect
284. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
285. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
286. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
287. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
288. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
289. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
315. C₂³×C₄²	C₂×D₄	semidirect
317. C₂×#392	C₂×D₄	semidirect
318. C₂²×#95	C₂×D₄	semidirect
331. C₂⁶	#120	semidirect
355. C₂⁶	C₂²×D₄	semidirect
366. C₂³×D₄	#120	semidirect
367. C₂³×D₄	#120	semidirect
368. C₂³×D₄	#120	semidirect
369. C₂³×D₄	#120	semidirect
383. C₂³×D₄	C₂²×D₄	semidirect
384. C₂³×D₄	C₂²×D₄	semidirect
385. C₂³×D₄	C₂²×D₄	semidirect
386. C₂³×D₄	C₂²×D₄	semidirect
387. C₂³×D₄	C₂²×D₄	semidirect
405. C₂⁴×C₄	C₂²×D₄	semidirect
418. C₂²×C₄⋊C₄	C₂²×D₄	semidirect
419. C₂²×C₂²⋊C₄	#120	semidirect
423. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
424. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
425. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
426. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
427. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
428. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
429. C₂²×C₄²	C₂²×D₄	semidirect
430. C₂×#95	C₂²×D₄	semidirect
442. C₂⁵	C₂×#120	semidirect
449. C₂⁵	D₄²	semidirect
487. C₂²×D₄	C₂×#120	semidirect
488. C₂²×D₄	C₂×#120	semidirect
489. C₂²×D₄	C₂×#120	semidirect
490. C₂²×D₄	C₂×#120	semidirect
499. C₂³×C₄	D₄²	semidirect
519. C₂×C₂²⋊C₄	C₂×#120	semidirect
521. C₂⁴	#2403	semidirect
557. C₂⁴	C₂×D₄²	semidirect
607. C₂²×C₄	#2403	semidirect
616. C₂²×C₄	C₂×D₄²	semidirect
621. C₂³	C₂×#2403	semidirect
726. C₂×C₄	C₂×#2403	semidirect
800. C₂	#72250287	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#154674	2
C₂×#154763	2
C₂²×#15258	2
C₂²×#15257	2
C₂×#155622	2
C₂×#154670	2
C₂×#154094	2
C₂×#156684	2
C₂×#156706	2
C₂×#154634	2
#72250287	2
C₂²×#14715	2
C₂³×#2403	2
C₂⁴×D₄²	2
C₂²×#15947	2

Subgroups — C2×#72250287 #72334632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72250287 #72334632