Subgroups — C₂×#72278194 #72296469

Order 2048.

At least 9188 conjugacy classes of subgroups; only the 8288 normal subgroups are shown.

The subgroup lattice has 1020 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×#155935	C₂	1	2	yes	maximal, complemented
2	C₂×#158869	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#159030	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#156710	C₂	1	2	yes	maximal, complemented
5	C₂×#159029	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#155875	C₂	1	2	yes	maximal, complemented
7	C₂×#154686	C₂	1	2	yes	maximal, complemented
8	C₂×#157223	C₂	1	2	yes	maximal, complemented
9	C₂×#155941	C₂	1	2	yes	maximal, complemented
10	C₂²×#14885	C₂	1	2	yes	maximal, complemented
11	C₂²×#15273	C₂	1	2	yes	maximal, complemented
12	C₂×#153851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×#2404	C₂	1	1	yes	maximal, characteristic, complemented
14	#72278194	C₂	1	32	yes	maximal, direct product factor
15	C₂²×#14716	C₂	1	2	yes	maximal, complemented
16	C₂²×#14716	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#156684	C₂	1	2	yes	maximal, complemented
18	C₂×#156706	C₂	1	2	yes	maximal, complemented
19	C₂×#156706	C₂	1	2	yes	maximal, complemented
20	C₂×#158995	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂⁵×#41	C₂²	1	1	yes	characteristic
22	C₂⁴×#121	C₂²	1	2	yes	—
23	C₂⁴×#121	C₂²	1	1	yes	characteristic
24	C₂⁴×#120	C₂²	1	2	yes	—
25	C₂⁴×#120	C₂²	1	2	yes	—
26	C₂⁵×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂⁵×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×#2404	C₂²	1	16	yes	complemented
29	C₂³×#393	C₂²	1	1	yes	characteristic
30	C₂³×#393	C₂²	1	1	yes	characteristic
31	C₂³×#393	C₂²	1	2	yes	complemented
32	C₂³×#392	C₂²	1	1	yes	characteristic
33	C₂³×#392	C₂²	1	1	yes	characteristic
34	C₂³×#392	C₂²	1	1	yes	characteristic
35	C₂³×#392	C₂²	1	2	yes	—
36	C₂³×#392	C₂²	1	2	yes	—
37	C₂³×#392	C₂²	1	1	yes	characteristic
38	C₂³×#392	C₂²	1	2	yes	—
39	C₂³×#392	C₂²	1	2	yes	—
40	C₂³×#392	C₂²	1	2	yes	—
41	C₂³×#392	C₂²	1	2	yes	complemented
42	C₂³×#392	C₂²	1	2	yes	complemented
43	C₂³×#386	C₂²	1	2	yes	—
44	C₂³×#386	C₂²	1	2	yes	—
45	C₂³×#386	C₂²	1	2	yes	—
46	C₂³×#386	C₂²	1	2	yes	—
47	C₂³×#386	C₂²	1	2	yes	—
48	C₂³×#386	C₂²	1	2	yes	—
49	C₂³×#386	C₂²	1	2	yes	complemented
50	C₂³×#386	C₂²	1	2	yes	complemented
51	C₂³×#381	C₂²	1	1	yes	characteristic
52	C₂³×#379	C₂²	1	1	yes	characteristic
53	C₂×#15273	C₂²	1	32	yes	complemented
54	C₂×#14885	C₂²	1	32	yes	complemented
55	C₂×#14716	C₂²	1	16	yes	complemented
56	C₂×#14716	C₂²	1	32	yes	complemented
57	C₂²×#1446	C₂²	1	2	yes	complemented
58	C₂²×#1442	C₂²	1	2	yes	complemented
59	C₂²×#1440	C₂²	1	2	yes	complemented
60	C₂²×#1440	C₂²	1	2	yes	complemented
61	C₂²×#1439	C₂²	1	1	yes	characteristic
62	C₂²×#1439	C₂²	1	2	yes	—
63	C₂²×#1439	C₂²	1	2	yes	—
64	C₂²×#1439	C₂²	1	1	yes	characteristic
65	C₂²×#1439	C₂²	1	2	yes	complemented
66	C₂²×#1439	C₂²	1	2	yes	complemented
67	C₂²×#1439	C₂²	1	2	yes	complemented
68	C₂²×#1438	C₂²	1	2	yes	—
69	C₂²×#1438	C₂²	1	2	yes	—
70	C₂²×#1438	C₂²	1	2	yes	—
71	C₂²×#1438	C₂²	1	2	yes	—
72	C₂²×#1438	C₂²	1	2	yes	—
73	C₂²×#1438	C₂²	1	2	yes	—
74	C₂²×#1438	C₂²	1	2	yes	—
75	C₂²×#1438	C₂²	1	2	yes	—
76	C₂²×#1438	C₂²	1	2	yes	—
77	C₂²×#1438	C₂²	1	2	yes	—
78	C₂²×#1438	C₂²	1	2	yes	—
79	C₂²×#1438	C₂²	1	2	yes	—
80	C₂²×#1438	C₂²	1	2	yes	complemented
81	C₂²×#1438	C₂²	1	2	yes	complemented
82	C₂²×#1438	C₂²	1	2	yes	complemented
83	C₂²×#1438	C₂²	1	2	yes	complemented
84	C₂²×C₂²⋊#95	C₂²	1	2	yes	—
85	C₂²×C₂²⋊#95	C₂²	1	1	yes	characteristic
86	C₂²×C₂²⋊#95	C₂²	1	2	yes	—
87	C₂²×C₂²⋊#95	C₂²	1	2	yes	—
88	C₂²×C₂²⋊#95	C₂²	1	2	yes	—
89	C₂²×C₂²⋊#95	C₂²	1	2	yes	—
90	C₂²×C₂²⋊#95	C₂²	1	2	yes	complemented
91	C₂²×C₂²⋊#95	C₂²	1	2	yes	complemented
92	#159030	C₂²	1	16	yes	complemented
93	#159029	C₂²	1	16	yes	complemented
94	#158995	C₂²	1	16	yes	complemented
95	#158869	C₂²	1	16	yes	complemented
96	#157223	C₂²	1	32	yes	complemented
97	#156710	C₂²	1	32	yes	complemented
98	#156706	C₂²	1	32	yes	complemented
99	#156706	C₂²	1	32	yes	complemented
100	#156684	C₂²	1	32	yes	complemented
101	#155941	C₂²	1	32	yes	complemented
102	#155935	C₂²	1	32	yes	complemented
103	#155875	C₂²	1	32	yes	complemented
104	#154686	C₂²	1	32	yes	complemented
105	#153851	C₂²	1	16	yes	complemented
106	C₂×#7557	C₂²	1	2	yes	complemented
107	C₂×#7557	C₂²	1	2	yes	complemented
108	C₂×#7556	C₂²	1	2	yes	complemented
109	C₂×#7556	C₂²	1	2	yes	complemented
110	C₂×#7556	C₂²	1	2	yes	complemented
111	C₂×#7556	C₂²	1	2	yes	complemented
112	C₂×#7556	C₂²	1	2	yes	complemented
113	C₂×#7556	C₂²	1	2	yes	complemented
114	C₂×#7555	C₂²	1	2	yes	—
115	C₂×#7555	C₂²	1	2	yes	—
116	C₂×#7555	C₂²	1	1	yes	characteristic
117	C₂×#7555	C₂²	1	1	yes	characteristic
118	C₂×#7555	C₂²	1	2	yes	—
119	C₂×#7555	C₂²	1	1	yes	characteristic
120	C₂×#7555	C₂²	1	1	yes	characteristic
121	C₂×#7555	C₂²	1	2	yes	complemented
122	C₂×#7555	C₂²	1	2	yes	complemented
123	C₂×#7555	C₂²	1	2	yes	complemented
124	C₂×#7555	C₂²	1	2	yes	complemented
125	C₂×#7555	C₂²	1	2	yes	complemented
126	C₂×#7555	C₂²	1	2	yes	complemented
127	C₂⁸	C₂³	1	1	yes	characteristic
128	C₂⁴×#41	C₂³	1	8	yes	—
129	C₂⁵×Q₈	C₂³	1	1	yes	characteristic
130	C₂⁵×D₄	C₂³	1	2	yes	—
131	C₂⁵×D₄	C₂³	1	2	yes	—
132	C₂⁵×D₄	C₂³	1	2	yes	—
133	C₂⁵×D₄	C₂³	1	1	yes	characteristic
134	C₂⁵×D₄	C₂³	1	2	yes	—
135	C₂⁵×D₄	C₂³	1	2	yes	—
136	C₂⁵×D₄	C₂³	1	2	yes	—
137	C₂⁵×D₄	C₂³	1	2	yes	—
138	C₂⁵×D₄	C₂³	1	2	yes	—
139	C₂⁵×D₄	C₂³	1	1	yes	characteristic
140	C₂⁶×C₄	C₂³	1	1	yes	characteristic
141	C₂⁶×C₄	C₂³	1	2	yes	—
142	C₂⁶×C₄	C₂³	1	2	yes	—
143	C₂⁶×C₄	C₂³	1	1	yes	characteristic
144	C₂³×#121	C₂³	1	16	yes	—
145	C₂³×#121	C₂³	1	8	yes	—
146	C₂³×#120	C₂³	1	16	yes	—
147	C₂³×#120	C₂³	1	16	yes	—
148	C₂⁴×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂⁴×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂⁴×C₂²⋊C₄	D₄	1	16	yes	complemented
151	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
161	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
163	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₂⁴×C₂²⋊C₄	C₂³	1	8	yes	—
167	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂⁴×C₂²⋊C₄	C₂³	1	8	yes	—
183	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₂²×#393	C₂³	1	8	yes	—
188	C₂²×#393	C₂³	1	8	yes	—
189	C₂²×#393	C₂³	1	16	yes	complemented
190	C₂²×#392	C₂³	1	8	yes	—
191	C₂²×#392	C₂³	1	8	yes	—
192	C₂²×#392	C₂³	1	8	yes	—
193	C₂²×#392	C₂³	1	16	yes	—
194	C₂²×#392	C₂³	1	16	yes	—
195	C₂²×#392	C₂³	1	16	yes	—
196	C₂²×#392	C₂³	1	16	yes	—
197	C₂²×#392	C₂³	1	16	yes	—
198	C₂²×#392	C₂³	1	8	yes	—
199	C₂²×#392	C₂³	1	16	yes	complemented
200	C₂²×#392	C₂³	1	16	yes	complemented
201	C₂²×#386	D₄	1	32	yes	complemented
202	C₂²×#386	C₂³	1	16	yes	—
203	C₂²×#386	C₂³	1	16	yes	—
204	C₂²×#386	C₂³	1	16	yes	—
205	C₂²×#386	C₂³	1	16	yes	—
206	C₂²×#386	C₂³	1	16	yes	—
207	C₂²×#386	C₂³	1	16	yes	—
208	C₂²×#386	C₂³	1	16	yes	complemented
209	C₂²×#386	C₂³	1	16	yes	complemented
210	C₂²×#381	C₂³	1	8	yes	—
211	C₂²×#379	C₂³	1	8	yes	—
212	C₂³×#95	C₂³	1	1	yes	characteristic
213	C₂³×#95	C₂³	1	1	yes	characteristic
214	C₂³×#95	C₂³	1	2	yes	—
215	C₂³×#95	C₂³	1	1	yes	characteristic
216	C₂³×#95	C₂³	1	2	yes	—
217	C₂³×#95	C₂³	1	2	yes	—
218	C₂³×#95	C₂³	1	2	yes	—
219	C₂³×#95	C₂³	1	2	yes	—
220	C₂³×#95	C₂³	1	2	yes	—
221	C₂³×#95	C₂³	1	2	yes	—
222	C₂³×#95	C₂³	1	2	yes	—
223	C₂³×#95	C₂³	1	2	yes	—
224	C₂³×#95	C₂³	1	2	yes	—
225	C₂³×#95	C₂³	1	2	yes	—
226	C₂³×#95	C₂³	1	2	yes	—
227	C₂³×#95	C₂³	1	2	yes	—
228	C₂³×#95	C₂³	1	2	yes	—
229	C₂³×#95	C₂³	1	2	yes	—
230	C₂³×#95	C₂³	1	2	yes	—
231	C₂³×#95	C₂³	1	2	yes	—
232	C₂³×#95	C₂³	1	2	yes	—
233	C₂³×#95	C₂³	1	2	yes	—
234	C₂³×#95	C₂³	1	2	yes	—
235	C₂³×#95	C₂³	1	1	yes	characteristic
236	C₂³×#95	C₂³	1	2	yes	—
237	C₂³×#95	C₂³	1	2	yes	—
238	C₂³×#95	C₂³	1	2	yes	—
239	C₂³×#95	C₂³	1	2	yes	—
240	C₂³×#95	C₂³	1	2	yes	—
241	C₂³×#95	C₂³	1	2	yes	—
242	C₂³×#95	C₂³	1	2	yes	—
243	C₂³×#95	C₂³	1	2	yes	—
244	C₂³×#95	C₂³	1	2	yes	—
245	C₂³×#95	C₂³	1	2	yes	—
246	C₂³×#95	C₂³	1	2	yes	—
247	C₂×#1446	C₂³	1	16	yes	complemented
248	C₂×#1442	C₂³	1	16	yes	complemented
249	C₂×#1440	C₂³	1	16	yes	complemented
250	C₂×#1440	C₂³	1	16	yes	complemented
251	C₂×#1439	C₂³	1	16	yes	—
252	C₂×#1439	C₂³	1	16	yes	—
253	C₂×#1439	C₂³	1	8	yes	—
254	C₂×#1439	C₂³	1	8	yes	—
255	C₂×#1439	C₂³	1	16	yes	complemented
256	C₂×#1439	C₂³	1	16	yes	complemented
257	C₂×#1439	C₂³	1	16	yes	complemented
258	C₂×#1438	D₄	1	32	yes	complemented
259	C₂×#1438	C₂³	1	16	yes	—
260	C₂×#1438	C₂³	1	16	yes	—
261	C₂×#1438	C₂³	1	16	yes	—
262	C₂×#1438	C₂³	1	16	yes	—
263	C₂×#1438	C₂³	1	16	yes	—
264	C₂×#1438	C₂³	1	16	yes	—
265	C₂×#1438	C₂³	1	16	yes	—
266	C₂×#1438	C₂³	1	16	yes	—
267	C₂×#1438	C₂³	1	16	yes	—
268	C₂×#1438	C₂³	1	16	yes	—
269	C₂×#1438	C₂³	1	16	yes	—
270	C₂×#1438	C₂³	1	16	yes	—
271	C₂×#1438	C₂³	1	16	yes	complemented
272	C₂×#1438	C₂³	1	16	yes	complemented
273	C₂×#1438	C₂³	1	16	yes	complemented
274	C₂×#1438	C₂³	1	16	yes	complemented
275	C₂×C₂²⋊#95	C₂³	1	16	yes	—
276	C₂×C₂²⋊#95	C₂³	1	8	yes	—
277	C₂×C₂²⋊#95	C₂³	1	16	yes	—
278	C₂×C₂²⋊#95	C₂³	1	16	yes	—
279	C₂×C₂²⋊#95	C₂³	1	16	yes	—
280	C₂×C₂²⋊#95	C₂³	1	16	yes	—
281	C₂×C₂²⋊#95	C₂³	1	16	yes	complemented
282	C₂×C₂²⋊#95	C₂³	1	16	yes	complemented
283	#7557	C₂³	1	16	yes	complemented
284	#7557	C₂³	1	16	yes	complemented
285	#7556	C₂³	1	16	yes	complemented
286	#7556	C₂³	1	16	yes	complemented
287	#7556	C₂³	1	16	yes	complemented
288	#7556	C₂³	1	16	yes	complemented
289	#7556	C₂³	1	16	yes	complemented
290	#7556	C₂³	1	16	yes	complemented
291	#7555	C₂³	1	16	yes	—
292	#7555	C₂³	1	16	yes	—
293	#7555	C₂³	1	16	yes	—
294	#7555	C₂³	1	8	yes	—
295	#7555	C₂³	1	8	yes	—
296	#7555	C₂³	1	8	yes	—
297	#7555	C₂³	1	8	yes	—
298	#7555	C₂³	1	16	yes	complemented
299	#7555	C₂³	1	16	yes	complemented
300	#7555	C₂³	1	16	yes	complemented
301	#7555	C₂³	1	16	yes	complemented
302	#7555	C₂³	1	16	yes	complemented
303	#7555	C₂³	1	16	yes	complemented
304	C₂⁷	C₂×D₄	1	8	yes	—
305	C₂⁷	C₂⁴	1	2	yes	—
306	C₂⁷	C₂⁴	1	2	yes	—
307	C₂⁷	C₂⁴	1	1	yes	characteristic
308	C₂⁷	C₂⁴	1	1	yes	characteristic
309	C₂⁷	C₂⁴	1	1	yes	characteristic
310	C₂⁷	C₂⁴	1	4	yes	—
311	C₂⁴×Q₈	C₂⁴	1	4	yes	—
312	C₂⁴×D₄	C₂×D₄	1	16	yes	—
313	C₂⁴×D₄	C₂×D₄	1	16	yes	—
314	C₂⁴×D₄	C₂⁴	1	8	yes	—
315	C₂⁴×D₄	C₂⁴	1	8	yes	—
316	C₂⁴×D₄	C₂⁴	1	8	yes	—
317	C₂⁴×D₄	C₂⁴	1	4	yes	—
318	C₂⁴×D₄	C₂⁴	1	8	yes	—
319	C₂⁴×D₄	C₂⁴	1	8	yes	—
320	C₂⁴×D₄	C₂⁴	1	8	yes	—
321	C₂⁴×D₄	C₂⁴	1	8	yes	—
322	C₂⁴×D₄	C₂⁴	1	4	yes	—
323	C₂⁴×D₄	C₂⁴	1	8	yes	—
324	C₂⁵×C₄	C₂×D₄	1	8	yes	—
325	C₂⁵×C₄	C₂×D₄	1	16	yes	—
326	C₂⁵×C₄	C₂×D₄	1	8	yes	—
327	C₂⁵×C₄	C₂⁴	1	2	yes	—
328	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
329	C₂⁵×C₄	C₂⁴	1	2	yes	—
330	C₂⁵×C₄	C₂⁴	1	2	yes	—
331	C₂⁵×C₄	C₂⁴	1	2	yes	—
332	C₂⁵×C₄	C₂⁴	1	2	yes	—
333	C₂⁵×C₄	C₂⁴	1	2	yes	—
334	C₂⁵×C₄	C₂⁴	1	2	yes	—
335	C₂⁵×C₄	C₂⁴	1	2	yes	—
336	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
337	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
338	C₂⁵×C₄	C₂⁴	1	2	yes	—
339	C₂⁵×C₄	C₂⁴	1	2	yes	—
340	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
341	C₂⁵×C₄	C₂⁴	1	4	yes	—
342	C₂⁵×C₄	C₂⁴	1	8	yes	—
343	C₂⁵×C₄	C₂⁴	1	8	yes	—
344	C₂⁵×C₄	C₂⁴	1	4	yes	—
345	C₂³×C₄⋊C₄	C₂⁴	1	8	yes	—
346	C₂³×C₄⋊C₄	C₂⁴	1	4	yes	—
347	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
348	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	—
349	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	—
350	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
351	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	—
352	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
353	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	—
354	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	—
355	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	—
356	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
357	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	—
358	C₂³×C₂²⋊C₄	C₂×D₄	1	64	yes	complemented
359	C₂³×C₂²⋊C₄	#41	1	8	yes	complemented
360	C₂³×C₂²⋊C₄	#41	1	8	yes	complemented
361	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
362	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
363	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
364	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
365	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
366	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
367	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
368	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
369	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
370	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
371	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
372	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
373	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
374	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
375	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
376	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
377	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
378	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
379	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
380	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
381	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
382	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
383	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
384	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
385	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
386	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
387	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
388	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
389	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
390	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
391	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
392	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
393	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
394	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
395	C₂×#386	C₂×D₄	1	128	yes	complemented
396	C₂²×#95	C₂×D₄	1	16	yes	—
397	C₂²×#95	C₂×D₄	1	16	yes	—
398	C₂²×#95	C₂×D₄	1	16	yes	—
399	C₂²×#95	C₂×D₄	1	16	yes	—
400	C₂²×#95	C₂⁴	1	4	yes	—
401	C₂²×#95	C₂⁴	1	4	yes	—
402	C₂²×#95	C₂⁴	1	8	yes	—
403	C₂²×#95	C₂⁴	1	4	yes	—
404	C₂²×#95	C₂⁴	1	8	yes	—
405	C₂²×#95	C₂⁴	1	8	yes	—
406	C₂²×#95	C₂⁴	1	8	yes	—
407	C₂²×#95	C₂⁴	1	8	yes	—
408	C₂²×#95	C₂⁴	1	8	yes	—
409	C₂²×#95	C₂⁴	1	8	yes	—
410	C₂²×#95	C₂⁴	1	8	yes	—
411	C₂²×#95	C₂⁴	1	8	yes	—
412	C₂²×#95	C₂⁴	1	8	yes	—
413	C₂²×#95	C₂⁴	1	8	yes	—
414	C₂²×#95	C₂⁴	1	8	yes	—
415	C₂²×#95	C₂⁴	1	8	yes	—
416	C₂²×#95	C₂⁴	1	8	yes	—
417	C₂²×#95	C₂⁴	1	8	yes	—
418	C₂²×#95	C₂⁴	1	8	yes	—
419	C₂²×#95	C₂⁴	1	8	yes	—
420	C₂²×#95	C₂⁴	1	8	yes	—
421	C₂²×#95	C₂⁴	1	8	yes	—
422	C₂²×#95	C₂⁴	1	8	yes	—
423	C₂²×#95	C₂⁴	1	8	yes	—
424	C₂²×#95	C₂⁴	1	8	yes	—
425	C₂²×#95	C₂⁴	1	8	yes	—
426	C₂²×#95	C₂⁴	1	8	yes	—
427	C₂²×#95	C₂⁴	1	4	yes	—
428	C₂²×#95	C₂⁴	1	8	yes	—
429	C₂²×#95	C₂⁴	1	8	yes	—
430	C₂²×#95	C₂⁴	1	8	yes	—
431	C₂²×#95	C₂⁴	1	8	yes	—
432	C₂²×#95	C₂⁴	1	8	yes	—
433	C₂²×#95	C₂⁴	1	8	yes	—
434	C₂²×#95	C₂⁴	1	8	yes	—
435	#1438	C₂×D₄	1	128	yes	complemented
436	C₂⁶	C₂²×D₄	1	4	yes	—
437	C₂⁶	C₂²×D₄	1	8	yes	—
438	C₂⁶	C₂²×D₄	1	8	yes	—
439	C₂⁶	C₂²×D₄	1	8	yes	—
440	C₂⁶	C₂²×D₄	1	4	yes	—
441	C₂⁶	C₂²×D₄	1	4	yes	—
442	C₂⁶	C₂²×D₄	1	8	yes	—
443	C₂⁶	C₂²×D₄	1	16	yes	—
444	C₂⁶	C₂×#41	1	4	yes	—
445	C₂⁶	C₂×#41	1	4	yes	—
446	C₂⁶	H(5,𝔽₂)	1	8	yes	—
447	C₂⁶	H(5,𝔽₂)	1	8	yes	—
448	C₂⁶	H(5,𝔽₂)	1	4	yes	—
449	C₂⁶	H(5,𝔽₂)	1	4	yes	—
450	C₂⁶	H(5,𝔽₂)	1	4	yes	—
451	C₂⁶	H(5,𝔽₂)	1	8	yes	—
452	C₂⁶	H(5,𝔽₂)	1	8	yes	—
453	C₂⁶	2₋¹⁺⁴	1	4	yes	—
454	C₂⁶	C₂⁵	1	4	yes	—
455	C₂⁶	C₂⁵	1	4	yes	—
456	C₂⁶	C₂⁵	1	2	yes	—
457	C₂⁶	C₂⁵	1	2	yes	—
458	C₂⁶	C₂⁵	1	2	yes	—
459	C₂⁶	C₂⁵	1	1	yes	characteristic
460	C₂³×D₄	C₂²×D₄	1	32	yes	—
461	C₂³×D₄	C₂²×D₄	1	32	yes	—
462	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
463	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
464	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
465	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
466	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
467	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
468	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
469	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
470	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
471	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
472	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
473	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
474	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
475	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
476	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
477	C₂⁴×C₄	C₂²×D₄	1	32	yes	—
478	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
479	C₂⁴×C₄	C₂×#41	1	8	yes	—
480	C₂⁴×C₄	C₂×#41	1	8	yes	—
481	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
482	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
483	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
484	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
485	C₂⁴×C₄	C₂⁵	1	4	yes	—
486	C₂⁴×C₄	C₂⁵	1	2	yes	—
487	C₂⁴×C₄	C₂⁵	1	4	yes	—
488	C₂⁴×C₄	C₂⁵	1	4	yes	—
489	C₂⁴×C₄	C₂⁵	1	4	yes	—
490	C₂⁴×C₄	C₂⁵	1	4	yes	—
491	C₂⁴×C₄	C₂⁵	1	4	yes	—
492	C₂⁴×C₄	C₂⁵	1	4	yes	—
493	C₂⁴×C₄	C₂⁵	1	4	yes	—
494	C₂⁴×C₄	C₂⁵	1	2	yes	—
495	C₂⁴×C₄	C₂⁵	1	2	yes	—
496	C₂⁴×C₄	C₂⁵	1	4	yes	—
497	C₂⁴×C₄	C₂⁵	1	4	yes	—
498	C₂⁴×C₄	C₂⁵	1	2	yes	—
499	C₂²×C₂²⋊C₄	#120	1	64	yes	—
500	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
501	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
502	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
503	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
504	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
505	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
506	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
507	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
508	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
509	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
510	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
511	C₂²×C₂²⋊C₄	C₂×#41	1	16	yes	complemented
512	C₂²×C₂²⋊C₄	C₂×#41	1	16	yes	complemented
513	C₂×#95	C₂²×D₄	1	32	yes	—
514	C₂×#95	C₂²×D₄	1	32	yes	—
515	C₂×#95	C₂²×D₄	1	32	yes	—
516	C₂×#95	C₂²×D₄	1	32	yes	—
517	C₂⁵	C₂×#120	1	16	yes	—
518	C₂⁵	#532	1	16	yes	—
519	C₂⁵	#534	1	16	yes	—
520	C₂⁵	#535	1	16	yes	—
521	C₂⁵	#535	1	32	yes	—
522	C₂⁵	#535	1	32	yes	—
523	C₂⁵	#537	1	32	yes	—
524	C₂⁵	#537	1	16	yes	—
525	C₂⁵	D₄²	1	32	yes	—
526	C₂⁵	D₄²	1	16	yes	—
527	C₂⁵	D₄²	1	32	yes	—
528	C₂⁵	#560	1	16	yes	—
529	C₂⁵	C₂³×D₄	1	4	yes	—
530	C₂⁵	C₂³×D₄	1	8	yes	—
531	C₂⁵	C₂³×D₄	1	8	yes	—
532	C₂⁵	C₂³×D₄	1	4	yes	—
533	C₂⁵	C₂³×D₄	1	8	yes	—
534	C₂⁵	C₂³×D₄	1	4	yes	—
535	C₂⁵	C₂³×D₄	1	8	yes	—
536	C₂⁵	C₂³×D₄	1	2	yes	—
537	C₂⁵	C₂³×D₄	1	4	yes	—
538	C₂⁵	C₂³×D₄	1	4	yes	—
539	C₂⁵	C₂²×#41	1	4	yes	—
540	C₂⁵	C₂²×#41	1	4	yes	—
541	C₂⁵	C₂²×#41	1	2	yes	—
542	C₂⁵	C₂²×#41	1	2	yes	—
543	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
544	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
545	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
546	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
547	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
548	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
549	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
550	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
551	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
552	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
553	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
554	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
555	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
556	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
557	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
558	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
559	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
560	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
561	C₂⁵	C₂×2₋¹⁺⁴	1	4	yes	—
562	C₂⁵	C₂×2₋¹⁺⁴	1	2	yes	—
563	C₂⁵	#585	1	4	yes	—
564	C₂⁵	#585	1	4	yes	—
565	C₂⁵	C₂⁶	1	1	yes	characteristic
566	C₂³×C₄	C₂×#120	1	16	yes	—
567	C₂³×C₄	C₂×#120	1	16	yes	—
568	C₂³×C₄	#534	1	16	yes	—
569	C₂³×C₄	D₄²	1	32	yes	—
570	C₂³×C₄	#546	1	32	yes	—
571	C₂³×C₄	C₂³×D₄	1	8	yes	—
572	C₂³×C₄	C₂³×D₄	1	8	yes	—
573	C₂³×C₄	C₂³×D₄	1	4	yes	—
574	C₂³×C₄	C₂³×D₄	1	8	yes	—
575	C₂³×C₄	C₂³×D₄	1	8	yes	—
576	C₂³×C₄	C₂³×D₄	1	8	yes	—
577	C₂³×C₄	C₂³×D₄	1	8	yes	—
578	C₂³×C₄	C₂³×D₄	1	4	yes	—
579	C₂³×C₄	C₂³×D₄	1	4	yes	—
580	C₂³×C₄	C₂³×D₄	1	8	yes	—
581	C₂³×C₄	C₂³×D₄	1	4	yes	—
582	C₂³×C₄	C₂³×D₄	1	8	yes	—
583	C₂³×C₄	C₂³×D₄	1	8	yes	—
584	C₂³×C₄	C₂³×D₄	1	8	yes	—
585	C₂³×C₄	C₂²×#41	1	8	yes	—
586	C₂³×C₄	C₂²×#41	1	8	yes	—
587	C₂³×C₄	C₂×H(5,𝔽₂)	1	8	yes	—
588	C₂³×C₄	C₂×H(5,𝔽₂)	1	8	yes	—
589	C₂³×C₄	C₂×H(5,𝔽₂)	1	8	yes	—
590	C₂³×C₄	C₂×H(5,𝔽₂)	1	8	yes	—
591	C₂×C₂²⋊C₄	C₂×#120	1	64	yes	—
592	C₂⁴	#2615	1	64	yes	—
593	C₂⁴	#2669	1	64	yes	—
594	C₂⁴	C₂²×#120	1	8	yes	—
595	C₂⁴	C₂²×#120	1	4	yes	—
596	C₂⁴	C₂×#532	1	8	yes	—
597	C₂⁴	C₂×#532	1	4	yes	—
598	C₂⁴	C₂×#534	1	8	yes	—
599	C₂⁴	C₂×#534	1	4	yes	—
600	C₂⁴	C₂×#534	1	4	yes	—
601	C₂⁴	C₂×#535	1	8	yes	—
602	C₂⁴	C₂×#535	1	16	yes	—
603	C₂⁴	C₂×#535	1	16	yes	—
604	C₂⁴	C₂×#535	1	4	yes	—
605	C₂⁴	C₂×#535	1	8	yes	—
606	C₂⁴	C₂×#535	1	8	yes	—
607	C₂⁴	C₂×#537	1	16	yes	—
608	C₂⁴	C₂×#537	1	8	yes	—
609	C₂⁴	C₂×#537	1	8	yes	—
610	C₂⁴	C₂×#537	1	4	yes	—
611	C₂⁴	#3449	1	4	yes	—
612	C₂⁴	C₂×D₄²	1	16	yes	—
613	C₂⁴	C₂×D₄²	1	8	yes	—
614	C₂⁴	C₂×D₄²	1	16	yes	—
615	C₂⁴	C₂×D₄²	1	8	yes	—
616	C₂⁴	C₂×D₄²	1	8	yes	—
617	C₂⁴	C₂×D₄²	1	8	yes	—
618	C₂⁴	C₂×D₄²	1	4	yes	—
619	C₂⁴	C₂×#546	1	8	yes	—
620	C₂⁴	D₄×#41	1	8	yes	—
621	C₂⁴	D₄×#41	1	8	yes	—
622	C₂⁴	D₄×#41	1	8	yes	—
623	C₂⁴	#3484	1	8	yes	—
624	C₂⁴	#3484	1	8	yes	—
625	C₂⁴	#3484	1	8	yes	—
626	C₂⁴	#3484	1	8	yes	—
627	C₂⁴	#3484	1	8	yes	—
628	C₂⁴	#3484	1	8	yes	—
629	C₂⁴	#3484	1	8	yes	—
630	C₂⁴	#3484	1	8	yes	—
631	C₂⁴	#3484	1	8	yes	—
632	C₂⁴	#3484	1	8	yes	—
633	C₂⁴	#3484	1	8	yes	—
634	C₂⁴	#3484	1	8	yes	—
635	C₂⁴	#3488	1	8	yes	—
636	C₂⁴	#3488	1	8	yes	—
637	C₂⁴	#3488	1	8	yes	—
638	C₂⁴	#3489	1	8	yes	—
639	C₂⁴	#3490	1	8	yes	—
640	C₂⁴	#3490	1	4	yes	—
641	C₂⁴	#3490	1	4	yes	—
642	C₂⁴	#3492	1	4	yes	—
643	C₂⁴	#3492	1	4	yes	—
644	C₂⁴	#3494	1	8	yes	—
645	C₂⁴	#3496	1	8	yes	—
646	C₂⁴	#3496	1	8	yes	—
647	C₂⁴	#3498	1	8	yes	—
648	C₂⁴	#3508	1	8	yes	—
649	C₂⁴	#3519	1	8	yes	—
650	C₂⁴	#3519	1	8	yes	—
651	C₂⁴	#3519	1	8	yes	—
652	C₂⁴	#3519	1	8	yes	—
653	C₂⁴	#3519	1	8	yes	—
654	C₂⁴	C₂×#560	1	8	yes	—
655	C₂⁴	C₂×#560	1	4	yes	—
656	C₂⁴	#3532	1	4	yes	—
657	C₂⁴	#3532	1	8	yes	—
658	C₂⁴	#3532	1	8	yes	—
659	C₂⁴	#3532	1	8	yes	—
660	C₂⁴	#3532	1	8	yes	—
661	C₂⁴	#3532	1	8	yes	—
662	C₂⁴	#3532	1	8	yes	—
663	C₂⁴	#3532	1	4	yes	—
664	C₂⁴	#3532	1	8	yes	—
665	C₂⁴	#3532	1	8	yes	—
666	C₂⁴	#3532	1	4	yes	—
667	C₂⁴	#3532	1	4	yes	—
668	C₂⁴	#3532	1	4	yes	—
669	C₂⁴	#3533	1	8	yes	—
670	C₂⁴	#3533	1	4	yes	—
671	C₂⁴	#3534	1	8	yes	—
672	C₂⁴	#3534	1	8	yes	—
673	C₂⁴	#3534	1	8	yes	—
674	C₂⁴	#3534	1	8	yes	—
675	C₂⁴	#3534	1	8	yes	—
676	C₂⁴	#3534	1	8	yes	—
677	C₂⁴	#3536	1	8	yes	—
678	C₂⁴	#3536	1	8	yes	—
679	C₂⁴	#3536	1	8	yes	—
680	C₂⁴	#3541	1	8	yes	—
681	C₂⁴	#3542	1	8	yes	—
682	C₂⁴	#3542	1	8	yes	—
683	C₂⁴	#3542	1	8	yes	—
684	C₂⁴	#3542	1	8	yes	—
685	C₂⁴	#3543	1	8	yes	—
686	C₂⁴	#3543	1	8	yes	—
687	C₂⁴	#3543	1	8	yes	—
688	C₂⁴	#3543	1	8	yes	—
689	C₂⁴	#3546	1	8	yes	—
690	C₂⁴	#3558	1	8	yes	—
691	C₂⁴	#3558	1	8	yes	—
692	C₂⁴	#3562	1	8	yes	—
693	C₂⁴	C₂⁴×D₄	1	2	yes	—
694	C₂⁴	C₂⁴×D₄	1	2	yes	—
695	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
696	C₂⁴	C₂³×#41	1	1	yes	characteristic
697	C₂⁴	C₂³×#41	1	1	yes	characteristic
698	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
699	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
700	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
701	C₂⁴	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
702	C₂⁴	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
703	C₂⁴	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
705	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
706	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
707	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
708	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
709	C₂⁴	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
710	C₂⁴	C₂×#585	1	2	yes	—
711	C₂⁴	C₂×#585	1	2	yes	—
712	C₂²×C₄	C₂²×#120	1	8	yes	—
713	C₂²×C₄	C₂²×#120	1	8	yes	—
714	C₂²×C₄	C₂×#534	1	8	yes	—
715	C₂²×C₄	C₂×D₄²	1	16	yes	—
716	C₂²×C₄	C₂×#546	1	16	yes	—
717	C₂³	C₂×#2615	1	16	yes	—
718	C₂³	C₂×#2615	1	8	yes	—
719	C₂³	#34738	1	8	yes	—
720	C₂³	#34980	1	8	yes	—
721	C₂³	#35051	1	8	yes	—
722	C₂³	#35078	1	8	yes	—
723	C₂³	#35680	1	16	yes	—
724	C₂³	#35694	1	16	yes	—
725	C₂³	D₄×#120	1	16	yes	—
726	C₂³	#36123	1	16	yes	—
727	C₂³	#36702	1	8	yes	—
728	C₂³	#36702	1	8	yes	—
729	C₂³	#36737	1	8	yes	—
730	C₂³	#37444	1	8	yes	—
731	C₂³	#37446	1	8	yes	—
732	C₂³	#37644	1	16	yes	—
733	C₂³	#37645	1	16	yes	—
734	C₂³	#37645	1	16	yes	—
735	C₂³	#37645	1	16	yes	—
736	C₂³	#37645	1	16	yes	—
737	C₂³	#37648	1	16	yes	—
738	C₂³	#37652	1	16	yes	—
739	C₂³	#37673	1	16	yes	—
740	C₂³	#37673	1	16	yes	—
741	C₂³	#37674	1	16	yes	—
742	C₂³	#37839	1	16	yes	—
743	C₂³	#38357	1	16	yes	—
744	C₂³	#38357	1	16	yes	—
745	C₂³	#38358	1	16	yes	—
746	C₂³	#38358	1	16	yes	—
747	C₂³	#38358	1	16	yes	—
748	C₂³	#40485	1	16	yes	—
749	C₂³	#40485	1	16	yes	—
750	C₂³	#40488	1	16	yes	—
751	C₂³	#40496	1	16	yes	—
752	C₂³	#40586	1	16	yes	—
753	C₂³	#40586	1	16	yes	—
754	C₂³	#40588	1	16	yes	—
755	C₂³	#40588	1	16	yes	—
756	C₂³	#40588	1	16	yes	—
757	C₂³	#42422	1	16	yes	—
758	C₂³	#43095	1	16	yes	—
759	C₂³	#43098	1	16	yes	—
760	C₂³	#43107	1	16	yes	—
761	C₂³	#43113	1	16	yes	—
762	C₂³	#43118	1	16	yes	—
763	C₂³	#43118	1	16	yes	—
764	C₂³	#43896	1	16	yes	—
765	C₂³	#43901	1	16	yes	—
766	C₂³	#44936	1	16	yes	—
767	C₂³	#45438	1	16	yes	—
768	C₂³	#45473	1	8	yes	—
769	C₂³	#45743	1	8	yes	—
770	C₂³	#46355	1	16	yes	—
771	C₂³	#46367	1	16	yes	—
772	C₂³	#46996	1	8	yes	—
773	C₂³	#47031	1	8	yes	—
774	C₂³	#47063	1	8	yes	—
775	C₂³	#47063	1	8	yes	—
776	C₂³	#47831	1	16	yes	—
777	C₂³	#47845	1	16	yes	—
778	C₂³	#47881	1	16	yes	—
779	C₂³	#48088	1	16	yes	—
780	C₂³	#48088	1	16	yes	—
781	C₂³	#48461	1	16	yes	—
782	C₂³	#49763	1	16	yes	—
783	C₂³	#50642	1	16	yes	—
784	C₂³	#51137	1	16	yes	—
785	C₂³	#51889	1	16	yes	—
786	C₂³	#51889	1	16	yes	—
787	C₂³	#51899	1	16	yes	—
788	C₂³	C₂×#2669	1	16	yes	—
789	C₂³	C₂×#2669	1	8	yes	—
790	C₂³	#52398	1	16	yes	—
791	C₂³	#55684	1	16	yes	—
792	C₂³	#55695	1	16	yes	—
793	C₂³	#56324	1	16	yes	—
794	C₂³	#56324	1	16	yes	—
795	C₂³	#56401	1	16	yes	—
796	C₂³	#56614	1	16	yes	—
797	C₂³	#57974	1	16	yes	—
798	C₂³	#57975	1	16	yes	—
799	C₂³	#58990	1	16	yes	—
800	C₂³	#58991	1	8	yes	—
801	C₂³	#58992	1	16	yes	—
802	C₂³	#58993	1	8	yes	—
803	C₂³	#59004	1	16	yes	—
804	C₂³	#59095	1	16	yes	—
805	C₂³	#59129	1	16	yes	—
806	C₂³	C₂³×#120	1	1	yes	characteristic
807	C₂³	C₂²×#532	1	1	yes	characteristic
808	C₂³	C₂²×#534	1	1	yes	characteristic
809	C₂³	C₂²×#534	1	1	yes	characteristic
810	C₂³	C₂²×#535	1	2	yes	—
811	C₂³	C₂²×#535	1	1	yes	characteristic
812	C₂³	C₂²×#535	1	2	yes	—
813	C₂³	C₂²×#537	1	1	yes	characteristic
814	C₂³	C₂²×#537	1	2	yes	—
815	C₂³	C₂×#3449	1	1	yes	characteristic
816	C₂³	C₂²×#560	1	1	yes	characteristic
817	C₂³	C₂²×D₄²	1	2	yes	—
818	C₂³	C₂²×D₄²	1	2	yes	—
819	C₂³	C₂²×D₄²	1	2	yes	—
820	C₂³	C₂²×D₄²	1	1	yes	characteristic
821	C₂³	C₂²×#546	1	2	yes	—
822	C₂³	C₂×D₄×#41	1	2	yes	—
823	C₂³	C₂×D₄×#41	1	2	yes	—
824	C₂³	C₂×D₄×#41	1	2	yes	—
825	C₂³	C₂×#3532	1	1	yes	characteristic
826	C₂³	C₂×#3532	1	2	yes	—
827	C₂³	C₂×#3532	1	2	yes	—
828	C₂³	C₂×#3532	1	1	yes	characteristic
829	C₂³	C₂×#3532	1	1	yes	characteristic
830	C₂³	C₂×#3532	1	2	yes	—
831	C₂³	C₂×#3532	1	2	yes	—
832	C₂³	C₂×#3532	1	2	yes	—
833	C₂³	C₂×#3532	1	2	yes	—
834	C₂³	C₂×#3532	1	2	yes	—
835	C₂³	C₂×#3532	1	2	yes	—
836	C₂³	C₂×#3532	1	1	yes	characteristic
837	C₂³	C₂×#3532	1	1	yes	characteristic
838	C₂³	C₂×#3542	1	2	yes	—
839	C₂³	C₂×#3542	1	2	yes	—
840	C₂³	C₂×#3542	1	2	yes	—
841	C₂³	C₂×#3542	1	2	yes	—
842	C₂³	C₂×#3541	1	2	yes	—
843	C₂³	C₂×#3534	1	2	yes	—
844	C₂³	C₂×#3534	1	2	yes	—
845	C₂³	C₂×#3534	1	2	yes	—
846	C₂³	C₂×#3534	1	2	yes	—
847	C₂³	C₂×#3534	1	2	yes	—
848	C₂³	C₂×#3534	1	2	yes	—
849	C₂³	C₂×#3536	1	2	yes	—
850	C₂³	C₂×#3536	1	2	yes	—
851	C₂³	C₂×#3536	1	2	yes	—
852	C₂³	C₂×#3533	1	1	yes	characteristic
853	C₂³	C₂×#3533	1	2	yes	—
854	C₂³	C₂×#3558	1	2	yes	—
855	C₂³	C₂×#3558	1	2	yes	—
856	C₂³	C₂×#3562	1	2	yes	—
857	C₂³	C₂×#3543	1	2	yes	—
858	C₂³	C₂×#3543	1	2	yes	—
859	C₂³	C₂×#3543	1	2	yes	—
860	C₂³	C₂×#3543	1	2	yes	—
861	C₂³	C₂×#3546	1	2	yes	—
862	C₂³	C₂×#3484	1	2	yes	—
863	C₂³	C₂×#3484	1	2	yes	—
864	C₂³	C₂×#3484	1	2	yes	—
865	C₂³	C₂×#3484	1	2	yes	—
866	C₂³	C₂×#3484	1	2	yes	—
867	C₂³	C₂×#3484	1	2	yes	—
868	C₂³	C₂×#3484	1	2	yes	—
869	C₂³	C₂×#3484	1	2	yes	—
870	C₂³	C₂×#3484	1	2	yes	—
871	C₂³	C₂×#3484	1	2	yes	—
872	C₂³	C₂×#3484	1	2	yes	—
873	C₂³	C₂×#3484	1	2	yes	—
874	C₂³	C₂×#3496	1	2	yes	—
875	C₂³	C₂×#3496	1	2	yes	—
876	C₂³	C₂×#3490	1	1	yes	characteristic
877	C₂³	C₂×#3490	1	1	yes	characteristic
878	C₂³	C₂×#3490	1	2	yes	—
879	C₂³	C₂×#3492	1	1	yes	characteristic
880	C₂³	C₂×#3492	1	1	yes	characteristic
881	C₂³	C₂×#3519	1	2	yes	—
882	C₂³	C₂×#3519	1	2	yes	—
883	C₂³	C₂×#3519	1	2	yes	—
884	C₂³	C₂×#3519	1	2	yes	—
885	C₂³	C₂×#3519	1	2	yes	—
886	C₂³	C₂×#3488	1	2	yes	—
887	C₂³	C₂×#3488	1	2	yes	—
888	C₂³	C₂×#3488	1	2	yes	—
889	C₂³	C₂×#3498	1	2	yes	—
890	C₂³	C₂×#3494	1	2	yes	—
891	C₂³	C₂×#3508	1	2	yes	—
892	C₂³	C₂×#3489	1	2	yes	—
893	C₂²	#637534	1	16	yes	—
894	C₂²	#781994	1	32	yes	—
895	C₂²	#846057	1	16	yes	—
896	C₂²	#873826	1	16	yes	—
897	C₂²	#918662	1	16	yes	—
898	C₂²	#1294119	1	32	yes	—
899	C₂²	#1393171	1	32	yes	—
900	C₂²	#2108839	1	32	yes	—
901	C₂²	#2108851	1	32	yes	—
902	C₂²	#2110394	1	32	yes	—
903	C₂²	#2110406	1	32	yes	—
904	C₂²	#2601298	1	32	yes	—
905	C₂²	#3362302	1	32	yes	—
906	C₂²	#3365471	1	32	yes	—
907	C₂²	#3860124	1	32	yes	—
908	C₂²	#3860698	1	32	yes	—
909	C₂²	#4312024	1	16	yes	—
910	C₂²	#4320282	1	16	yes	—
911	C₂²	#4861908	1	16	yes	—
912	C₂²	C₂²×#2615	1	1	yes	characteristic
913	C₂²	C₂×#34738	1	1	yes	characteristic
914	C₂²	C₂×#34980	1	1	yes	characteristic
915	C₂²	C₂×#35051	1	1	yes	characteristic
916	C₂²	C₂×#35078	1	1	yes	characteristic
917	C₂²	C₂×#35680	1	2	yes	—
918	C₂²	C₂×#35694	1	2	yes	—
919	C₂²	C₂×D₄×#120	1	2	yes	—
920	C₂²	C₂×#36123	1	2	yes	—
921	C₂²	C₂²×#2669	1	1	yes	characteristic
922	C₂²	C₂×#37444	1	1	yes	characteristic
923	C₂²	C₂×#37446	1	1	yes	characteristic
924	C₂²	C₂×#36702	1	1	yes	characteristic
925	C₂²	C₂×#36702	1	1	yes	characteristic
926	C₂²	C₂×#36737	1	1	yes	characteristic
927	C₂²	C₂×#37644	1	2	yes	—
928	C₂²	C₂×#37645	1	2	yes	—
929	C₂²	C₂×#37645	1	2	yes	—
930	C₂²	C₂×#37645	1	2	yes	—
931	C₂²	C₂×#37645	1	2	yes	—
932	C₂²	C₂×#37673	1	2	yes	—
933	C₂²	C₂×#37673	1	2	yes	—
934	C₂²	C₂×#37648	1	2	yes	—
935	C₂²	C₂×#37674	1	2	yes	—
936	C₂²	C₂×#37652	1	2	yes	—
937	C₂²	C₂×#37839	1	2	yes	—
938	C₂²	C₂×#38358	1	2	yes	—
939	C₂²	C₂×#38358	1	2	yes	—
940	C₂²	C₂×#38358	1	2	yes	—
941	C₂²	C₂×#38357	1	2	yes	—
942	C₂²	C₂×#38357	1	2	yes	—
943	C₂²	C₂×#40485	1	2	yes	—
944	C₂²	C₂×#40485	1	2	yes	—
945	C₂²	C₂×#40586	1	2	yes	—
946	C₂²	C₂×#40586	1	2	yes	—
947	C₂²	C₂×#40488	1	2	yes	—
948	C₂²	C₂×#40588	1	2	yes	—
949	C₂²	C₂×#40588	1	2	yes	—
950	C₂²	C₂×#40588	1	2	yes	—
951	C₂²	C₂×#40496	1	2	yes	—
952	C₂²	C₂×#42422	1	2	yes	—
953	C₂²	C₂×#58990	1	2	yes	—
954	C₂²	C₂×#58991	1	1	yes	characteristic
955	C₂²	C₂×#59004	1	2	yes	—
956	C₂²	C₂×#58992	1	2	yes	—
957	C₂²	C₂×#58993	1	1	yes	characteristic
958	C₂²	C₂×#59095	1	2	yes	—
959	C₂²	C₂×#59129	1	2	yes	—
960	C₂²	C₂×#43095	1	2	yes	—
961	C₂²	C₂×#43098	1	2	yes	—
962	C₂²	C₂×#43118	1	2	yes	—
963	C₂²	C₂×#43118	1	2	yes	—
964	C₂²	C₂×#43107	1	2	yes	—
965	C₂²	C₂×#43113	1	2	yes	—
966	C₂²	C₂×#43896	1	2	yes	—
967	C₂²	C₂×#43901	1	2	yes	—
968	C₂²	C₂×#44936	1	2	yes	—
969	C₂²	C₂×#46355	1	2	yes	—
970	C₂²	C₂×#46367	1	2	yes	—
971	C₂²	C₂×#46996	1	1	yes	characteristic
972	C₂²	C₂×#47063	1	1	yes	characteristic
973	C₂²	C₂×#47063	1	1	yes	characteristic
974	C₂²	C₂×#47031	1	1	yes	characteristic
975	C₂²	C₂×#45438	1	2	yes	—
976	C₂²	C₂×#45743	1	1	yes	characteristic
977	C₂²	C₂×#45473	1	1	yes	characteristic
978	C₂²	C₂×#47881	1	2	yes	—
979	C₂²	C₂×#48088	1	2	yes	—
980	C₂²	C₂×#48088	1	2	yes	—
981	C₂²	C₂×#48461	1	2	yes	—
982	C₂²	C₂×#47831	1	2	yes	—
983	C₂²	C₂×#47845	1	2	yes	—
984	C₂²	C₂×#49763	1	2	yes	—
985	C₂²	C₂×#50642	1	2	yes	—
986	C₂²	C₂×#51137	1	2	yes	—
987	C₂²	C₂×#51889	1	2	yes	—
988	C₂²	C₂×#51889	1	2	yes	—
989	C₂²	C₂×#51899	1	2	yes	—
990	C₂²	C₂×#52398	1	2	yes	—
991	C₂²	C₂×#56324	1	2	yes	—
992	C₂²	C₂×#56324	1	2	yes	—
993	C₂²	C₂×#56401	1	2	yes	—
994	C₂²	C₂×#55684	1	2	yes	—
995	C₂²	C₂×#55695	1	2	yes	—
996	C₂²	C₂×#56614	1	2	yes	—
997	C₂²	C₂×#57974	1	2	yes	—
998	C₂²	C₂×#57975	1	2	yes	—
999	C₂	C₂×#4312024	1	1	yes	characteristic
1000	C₂	C₂×#1393171	1	2	yes	—
1001	C₂	C₂×#3860124	1	2	yes	—
1002	C₂	C₂×#918662	1	1	yes	characteristic
1003	C₂	#72278194	1	32	yes	direct product factor
1004	C₂	C₂×#2108839	1	2	yes	—
1005	C₂	C₂×#846057	1	1	yes	characteristic
1006	C₂	C₂×#3362302	1	2	yes	—
1007	C₂	C₂×#3365471	1	2	yes	—
1008	C₂	C₂×#4320282	1	1	yes	characteristic
1009	C₂	C₂×#2110406	1	2	yes	—
1010	C₂	C₂×#781994	1	2	yes	—
1011	C₂	C₂×#2108851	1	2	yes	—
1012	C₂	C₂×#2601298	1	2	yes	—
1013	C₂	C₂×#2110394	1	2	yes	—
1014	C₂	C₂×#1294119	1	2	yes	—
1015	C₂	C₂×#637534	1	1	yes	characteristic
1016	C₂	C₂×#4861908	1	1	yes	characteristic
1017	C₂	C₂×#3860698	1	2	yes	—
1018	C₂	C₂×#873826	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×#155935	C₂	semidirect
2. C₂×#158869	C₂	semidirect
3. C₂×#159030	C₂	semidirect
4. C₂×#156710	C₂	semidirect
5. C₂×#159029	C₂	semidirect
6. C₂×#155875	C₂	semidirect
7. C₂×#154686	C₂	semidirect
8. C₂×#157223	C₂	semidirect
9. C₂×#155941	C₂	semidirect
10. C₂²×#14885	C₂	semidirect
11. C₂²×#15273	C₂	semidirect
12. C₂×#153851	C₂	semidirect
13. C₂³×#2404	C₂	semidirect
14. #72278194	C₂	direct (N × H)
15. C₂²×#14716	C₂	semidirect
16. C₂²×#14716	C₂	semidirect
17. C₂×#156684	C₂	semidirect
18. C₂×#156706	C₂	semidirect
19. C₂×#156706	C₂	semidirect
20. C₂×#158995	C₂	semidirect
28. C₂²×#2404	C₂²	semidirect
31. C₂³×#393	C₂²	semidirect
41. C₂³×#392	C₂²	semidirect
42. C₂³×#392	C₂²	semidirect
49. C₂³×#386	C₂²	semidirect
50. C₂³×#386	C₂²	semidirect
53. C₂×#15273	C₂²	semidirect
54. C₂×#14885	C₂²	semidirect
55. C₂×#14716	C₂²	semidirect
56. C₂×#14716	C₂²	semidirect
57. C₂²×#1446	C₂²	semidirect
58. C₂²×#1442	C₂²	semidirect
59. C₂²×#1440	C₂²	semidirect
60. C₂²×#1440	C₂²	semidirect
65. C₂²×#1439	C₂²	semidirect
66. C₂²×#1439	C₂²	semidirect
67. C₂²×#1439	C₂²	semidirect
80. C₂²×#1438	C₂²	semidirect
81. C₂²×#1438	C₂²	semidirect
82. C₂²×#1438	C₂²	semidirect
83. C₂²×#1438	C₂²	semidirect
90. C₂²×C₂²⋊#95	C₂²	semidirect
91. C₂²×C₂²⋊#95	C₂²	semidirect
92. #159030	C₂²	semidirect
93. #159029	C₂²	semidirect
94. #158995	C₂²	semidirect
95. #158869	C₂²	semidirect
96. #157223	C₂²	semidirect
97. #156710	C₂²	semidirect
98. #156706	C₂²	semidirect
99. #156706	C₂²	semidirect
100. #156684	C₂²	semidirect
101. #155941	C₂²	semidirect
102. #155935	C₂²	semidirect
103. #155875	C₂²	semidirect
104. #154686	C₂²	semidirect
105. #153851	C₂²	semidirect
106. C₂×#7557	C₂²	semidirect
107. C₂×#7557	C₂²	semidirect
108. C₂×#7556	C₂²	semidirect
109. C₂×#7556	C₂²	semidirect
110. C₂×#7556	C₂²	semidirect
111. C₂×#7556	C₂²	semidirect
112. C₂×#7556	C₂²	semidirect
113. C₂×#7556	C₂²	semidirect
121. C₂×#7555	C₂²	semidirect
122. C₂×#7555	C₂²	semidirect
123. C₂×#7555	C₂²	semidirect
124. C₂×#7555	C₂²	semidirect
125. C₂×#7555	C₂²	semidirect
126. C₂×#7555	C₂²	semidirect
150. C₂⁴×C₂²⋊C₄	D₄	semidirect
189. C₂²×#393	C₂³	semidirect
199. C₂²×#392	C₂³	semidirect
200. C₂²×#392	C₂³	semidirect
201. C₂²×#386	D₄	semidirect
208. C₂²×#386	C₂³	semidirect
209. C₂²×#386	C₂³	semidirect
247. C₂×#1446	C₂³	semidirect
248. C₂×#1442	C₂³	semidirect
249. C₂×#1440	C₂³	semidirect
250. C₂×#1440	C₂³	semidirect
255. C₂×#1439	C₂³	semidirect
256. C₂×#1439	C₂³	semidirect
257. C₂×#1439	C₂³	semidirect
258. C₂×#1438	D₄	semidirect
271. C₂×#1438	C₂³	semidirect
272. C₂×#1438	C₂³	semidirect
273. C₂×#1438	C₂³	semidirect
274. C₂×#1438	C₂³	semidirect
281. C₂×C₂²⋊#95	C₂³	semidirect
282. C₂×C₂²⋊#95	C₂³	semidirect
283. #7557	C₂³	semidirect
284. #7557	C₂³	semidirect
285. #7556	C₂³	semidirect
286. #7556	C₂³	semidirect
287. #7556	C₂³	semidirect
288. #7556	C₂³	semidirect
289. #7556	C₂³	semidirect
290. #7556	C₂³	semidirect
298. #7555	C₂³	semidirect
299. #7555	C₂³	semidirect
300. #7555	C₂³	semidirect
301. #7555	C₂³	semidirect
302. #7555	C₂³	semidirect
303. #7555	C₂³	semidirect
358. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
359. C₂³×C₂²⋊C₄	#41	semidirect
360. C₂³×C₂²⋊C₄	#41	semidirect
395. C₂×#386	C₂×D₄	semidirect
435. #1438	C₂×D₄	semidirect
511. C₂²×C₂²⋊C₄	C₂×#41	semidirect
512. C₂²×C₂²⋊C₄	C₂×#41	semidirect
1003. C₂	#72278194	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×#155935	2
C₂×#158869	2
C₂×#159030	2
C₂×#156710	2
C₂×#159029	2
C₂×#155875	2
C₂×#154686	2
C₂×#157223	2
C₂×#155941	2
C₂²×#14885	2
C₂²×#15273	2
C₂×#153851	2
C₂³×#2404	2
#72278194	2
C₂²×#14716	2
C₂×#156684	2
C₂×#156706	2
C₂×#158995	2

Subgroups — C2×#72278194 #72296469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72278194 #72296469