Subgroups — C₂×C₆₁×#3257 #29564341

Order 15616.

1946 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#540	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3257	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₆₁×#479	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×#478	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₆₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₆₁×#474	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₆₁×#469	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₆₁×#468	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₆₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×#465	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₆₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₆₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₆₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₆₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₆₁×#424	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₆₁×#542	—	2	4	no	—
24	C₆₁×#542	C₂²	1	8	yes	complemented
25	C₆₁×#540	—	2	4	no	—
26	C₆₁×#540	C₂²	1	8	yes	complemented
27	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#126×C₆₁	—	2	1	no	—
30	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#124×C₆₁	—	2	1	no	—
32	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#123×C₆₁	—	2	1	no	—
34	C₂×#123×C₆₁	—	2	1	no	—
35	C₂×#123×C₆₁	—	2	1	no	—
36	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
37	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×#121×C₆₁	—	2	1	no	—
39	C₂×#121×C₆₁	—	2	1	no	—
40	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
48	C₆₁×#479	C₂²	1	8	yes	complemented
49	C₆₁×#478	C₂²	1	8	yes	complemented
50	C₆₁×#476	C₂²	1	8	yes	complemented
51	C₆₁×#474	C₂²	1	8	yes	complemented
52	C₆₁×#469	C₂²	1	8	yes	complemented
53	C₆₁×#468	C₂²	1	8	yes	complemented
54	C₆₁×#466	C₂²	1	8	yes	complemented
55	C₆₁×#465	C₂²	1	8	yes	complemented
56	C₆₁×#463	C₂²	1	8	yes	complemented
57	C₆₁×#463	C₂²	1	8	yes	complemented
58	C₆₁×#460	C₂²	1	8	yes	complemented
59	C₆₁×#459	C₂²	1	8	yes	complemented
60	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
61	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
62	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
63	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
64	C₆₁×#424	C₂²	1	8	yes	complemented
65	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
66	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
67	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
68	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
69	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
70	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
71	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
72	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
73	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
74	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
75	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
76	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₆₁	—	2	1	no	—
78	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₆₁	—	2	1	no	—
80	C₂²×D₄×C₆₁	—	2	1	no	—
81	C₂²×D₄×C₆₁	—	2	1	no	—
82	C₂²×D₄×C₆₁	—	2	1	no	—
83	C₂²×D₄×C₆₁	—	2	1	no	—
84	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₆₁	—	2	1	no	—
88	C₂³×C₄×C₆₁	—	2	1	no	—
89	C₂³×C₄×C₆₁	—	2	1	no	—
90	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
91	C₂×SD₁₆×C₆₁	—	4	2	no	—
92	C₂×SD₁₆×C₆₁	—	4	2	no	—
93	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
95	C₂×D₈×C₆₁	—	4	2	no	—
96	C₂×D₈×C₆₁	—	4	2	no	—
97	C₂×D₈×C₆₁	C₂³	1	4	yes	—
98	C₂×D₈×C₆₁	C₂³	1	4	yes	—
99	C₂×M₁₆×C₆₁	—	4	2	no	—
100	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
101	C₂²×C₈×C₆₁	—	4	2	no	—
102	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
107	C₄⋊Q₈×C₆₁	—	2	2	no	—
108	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
109	#127×C₆₁	—	2	2	no	—
110	#127×C₆₁	C₂³	1	4	yes	—
111	#126×C₆₁	—	2	8	no	—
112	#125×C₆₁	—	2	2	no	—
113	#125×C₆₁	C₂³	1	4	yes	—
114	#124×C₆₁	—	2	8	no	—
115	#124×C₆₁	—	2	2	no	—
116	#124×C₆₁	C₂³	1	4	yes	—
117	#123×C₆₁	—	2	8	no	—
118	#123×C₆₁	—	2	8	no	—
119	#123×C₆₁	—	2	8	no	—
120	C₂²⋊Q₈×C₆₁	—	2	2	no	—
121	C₂²⋊Q₈×C₆₁	—	2	8	no	—
122	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
123	#121×C₆₁	—	2	2	no	—
124	#121×C₆₁	—	2	2	no	—
125	#121×C₆₁	—	2	2	no	—
126	#121×C₆₁	—	2	8	no	—
127	#121×C₆₁	—	2	8	no	—
128	#121×C₆₁	C₂³	1	4	yes	—
129	#121×C₆₁	C₂³	1	4	yes	—
130	#121×C₆₁	C₂³	1	4	yes	—
131	C₄×Q₈×C₆₁	—	2	2	no	—
132	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
133	C₄×D₄×C₆₁	—	2	2	no	—
134	C₄×D₄×C₆₁	—	2	2	no	—
135	C₄×D₄×C₆₁	—	2	2	no	—
136	C₄×D₄×C₆₁	C₂³	1	4	yes	—
137	C₄×D₄×C₆₁	C₂³	1	4	yes	—
138	C₄×D₄×C₆₁	C₂³	1	4	yes	—
139	#117×C₆₁	D₄	1	4	yes	—
140	#117×C₆₁	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
142	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
143	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
144	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
145	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
146	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
155	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
163	C₂×C₄²×C₆₁	—	2	1	no	—
164	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
166	#107×C₆₁	C₂³	1	4	yes	—
167	#107×C₆₁	C₂³	1	4	yes	—
168	#106×C₆₁	C₂³	1	4	yes	—
169	#106×C₆₁	C₂³	1	4	yes	—
170	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
171	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
172	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
173	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
174	#103×C₆₁	C₂³	1	4	yes	—
175	#103×C₆₁	C₂³	1	4	yes	—
176	#102×C₆₁	C₂³	1	4	yes	—
177	#102×C₆₁	C₂³	1	4	yes	—
178	#102×C₆₁	C₂³	1	4	yes	—
179	#102×C₆₁	C₂³	1	4	yes	—
180	#102×C₆₁	C₂³	1	4	yes	—
181	#102×C₆₁	C₂³	1	4	yes	—
182	C₂⁴×C₆₁	—	2	1	no	—
183	C₂⁴×C₆₁	—	2	1	no	—
184	C₂⁴×C₆₁	—	2	1	no	—
185	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
186	C₂×Q₈×C₆₁	—	2	1	no	—
187	C₂×Q₈×C₆₁	—	2	4	no	—
188	C₂×Q₈×C₆₁	—	2	2	no	—
189	C₂×Q₈×C₆₁	—	2	2	no	—
190	C₂×Q₈×C₆₁	—	8	2	no	—
191	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
192	C₂×D₄×C₆₁	—	2	4	no	—
193	C₂×D₄×C₆₁	—	2	4	no	—
194	C₂×D₄×C₆₁	—	2	4	no	—
195	C₂×D₄×C₆₁	—	2	1	no	—
196	C₂×D₄×C₆₁	—	2	1	no	—
197	C₂×D₄×C₆₁	—	2	1	no	—
198	C₂×D₄×C₆₁	—	2	4	no	—
199	C₂×D₄×C₆₁	—	2	4	no	—
200	C₂×D₄×C₆₁	—	2	2	no	—
201	C₂×D₄×C₆₁	—	2	2	no	—
202	C₂×D₄×C₆₁	—	2	2	no	—
203	C₂×D₄×C₆₁	—	2	2	no	—
204	C₂×D₄×C₆₁	—	2	2	no	—
205	C₂×D₄×C₆₁	—	2	2	no	—
206	C₂×D₄×C₆₁	—	8	2	no	—
207	C₂×D₄×C₆₁	—	8	2	no	—
208	C₂×D₄×C₆₁	—	8	2	no	—
209	C₂×D₄×C₆₁	—	8	2	no	—
210	C₂×D₄×C₆₁	—	8	2	no	—
211	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
212	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
213	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₆₁	—	2	2	no	—
215	C₂²×C₄×C₆₁	—	2	2	no	—
216	C₂²×C₄×C₆₁	—	2	1	no	—
217	C₂²×C₄×C₆₁	—	2	1	no	—
218	C₂²×C₄×C₆₁	—	2	1	no	—
219	C₂²×C₄×C₆₁	—	2	1	no	—
220	C₂²×C₄×C₆₁	—	2	1	no	—
221	C₂²×C₄×C₆₁	—	2	4	no	—
222	C₂²×C₄×C₆₁	—	2	4	no	—
223	C₂²×C₄×C₆₁	—	2	4	no	—
224	C₂²×C₄×C₆₁	—	8	2	no	—
225	C₂²×C₄×C₆₁	—	8	2	no	—
226	C₂²×C₄×C₆₁	—	8	2	no	—
227	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
235	SD₁₆×C₆₁	—	4	4	no	—
236	SD₁₆×C₆₁	—	4	4	no	—
237	D₈×C₆₁	—	4	4	no	—
238	D₈×C₆₁	—	4	4	no	—
239	M₁₆×C₆₁	—	4	4	no	—
240	C₂×C₈×C₆₁	—	2	2	no	—
241	C₂×C₈×C₆₁	—	2	2	no	—
242	C₂×C₈×C₆₁	—	2	2	no	—
243	C₂×C₈×C₆₁	—	2	2	no	—
244	C₂×C₈×C₆₁	—	4	4	no	—
245	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
246	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
247	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
248	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
249	C₄⋊C₄×C₆₁	—	2	4	no	—
250	C₄⋊C₄×C₆₁	—	2	4	no	—
251	C₄⋊C₄×C₆₁	—	2	4	no	—
252	C₄⋊C₄×C₆₁	—	2	4	no	—
253	C₄⋊C₄×C₆₁	—	2	4	no	—
254	C₄⋊C₄×C₆₁	—	2	1	no	—
255	C₄⋊C₄×C₆₁	—	2	1	no	—
256	C₄⋊C₄×C₆₁	—	2	1	no	—
257	C₄⋊C₄×C₆₁	—	2	1	no	—
258	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
259	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
260	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
264	C₂²⋊C₄×C₆₁	—	2	4	no	—
265	C₂²⋊C₄×C₆₁	—	2	4	no	—
266	C₂²⋊C₄×C₆₁	—	2	4	no	—
267	C₂²⋊C₄×C₆₁	—	2	4	no	—
268	C₂²⋊C₄×C₆₁	—	2	4	no	—
269	C₂²⋊C₄×C₆₁	—	2	4	no	—
270	C₂²⋊C₄×C₆₁	—	2	4	no	—
271	C₂²⋊C₄×C₆₁	—	2	4	no	—
272	C₂²⋊C₄×C₆₁	—	2	4	no	—
273	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
274	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
275	C₄²×C₆₁	—	2	4	no	—
276	C₄²×C₆₁	C₂×D₄	1	2	yes	—
277	C₄²×C₆₁	C₂×D₄	1	2	yes	—
278	C₄²×C₆₁	C₂⁴	1	2	yes	—
279	C₄²×C₆₁	C₂⁴	1	2	yes	—
280	C₂³×C₆₁	—	2	2	no	—
281	C₂³×C₆₁	—	2	2	no	—
282	C₂³×C₆₁	—	2	2	no	—
283	C₂³×C₆₁	—	2	2	no	—
284	C₂³×C₆₁	—	2	2	no	—
285	C₂³×C₆₁	—	2	2	no	—
286	C₂³×C₆₁	—	4	2	no	—
287	C₂³×C₆₁	—	4	2	no	—
288	C₂³×C₆₁	—	4	2	no	—
289	C₂³×C₆₁	—	4	2	no	—
290	C₂³×C₆₁	—	4	2	no	—
291	C₂³×C₆₁	—	4	2	no	—
292	C₂³×C₆₁	—	4	2	no	—
293	C₂³×C₆₁	—	4	2	no	—
294	C₂³×C₆₁	—	4	2	no	—
295	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
296	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
297	Q₈×C₆₁	—	2	2	no	—
298	Q₈×C₆₁	—	2	2	no	—
299	Q₈×C₆₁	—	4	2	no	—
300	Q₈×C₆₁	—	8	4	no	—
301	D₄×C₆₁	—	2	2	no	—
302	D₄×C₆₁	—	2	2	no	—
303	D₄×C₆₁	—	2	2	no	—
304	D₄×C₆₁	—	2	2	no	—
305	D₄×C₆₁	—	2	2	no	—
306	D₄×C₆₁	—	2	2	no	—
307	D₄×C₆₁	—	4	2	no	—
308	D₄×C₆₁	—	4	2	no	—
309	D₄×C₆₁	—	4	2	no	—
310	D₄×C₆₁	—	8	4	no	—
311	D₄×C₆₁	—	8	4	no	—
312	D₄×C₆₁	—	8	4	no	—
313	D₄×C₆₁	—	8	4	no	—
314	D₄×C₆₁	—	8	4	no	—
315	C₂×C₄×C₆₁	—	2	2	no	—
316	C₂×C₄×C₆₁	—	2	2	no	—
317	C₂×C₄×C₆₁	—	2	2	no	—
318	C₂×C₄×C₆₁	—	2	2	no	—
319	C₂×C₄×C₆₁	—	2	2	no	—
320	C₂×C₄×C₆₁	—	2	4	no	—
321	C₂×C₄×C₆₁	—	2	2	no	—
322	C₂×C₄×C₆₁	—	2	2	no	—
323	C₂×C₄×C₆₁	—	2	2	no	—
324	C₂×C₄×C₆₁	—	2	2	no	—
325	C₂×C₄×C₆₁	—	2	2	no	—
326	C₂×C₄×C₆₁	—	2	2	no	—
327	C₂×C₄×C₆₁	—	2	2	no	—
328	C₂×C₄×C₆₁	—	4	2	no	—
329	C₂×C₄×C₆₁	—	4	2	no	—
330	C₂×C₄×C₆₁	—	4	2	no	—
331	C₂×C₄×C₆₁	—	4	2	no	—
332	C₂×C₄×C₆₁	—	4	2	no	—
333	C₂×C₄×C₆₁	—	8	4	no	—
334	C₂×C₄×C₆₁	—	8	4	no	—
335	C₂×C₄×C₆₁	—	8	4	no	—
336	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
343	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
344	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
345	C₈×C₆₁	—	2	2	no	—
346	C₈×C₆₁	—	2	2	no	—
347	C₈×C₆₁	—	2	2	no	—
348	C₈×C₆₁	—	2	2	no	—
349	C₂×#3257	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
350	C₂²×C₆₁	—	2	2	no	—
351	C₂²×C₆₁	—	2	2	no	—
352	C₂²×C₆₁	—	2	2	no	—
353	C₂²×C₆₁	—	4	4	no	—
354	C₂²×C₆₁	—	4	2	no	—
355	C₂²×C₆₁	—	4	2	no	—
356	C₂²×C₆₁	—	4	2	no	—
357	C₂²×C₆₁	—	4	2	no	—
358	C₂²×C₆₁	—	4	2	no	—
359	C₂²×C₆₁	—	4	2	no	—
360	C₂²×C₆₁	—	4	2	no	—
361	C₂²×C₆₁	—	4	2	no	—
362	C₂²×C₆₁	—	4	2	no	—
363	C₂²×C₆₁	—	8	4	no	—
364	C₂²×C₆₁	—	8	4	no	—
365	C₂²×C₆₁	—	8	4	no	—
366	C₂²×C₆₁	#537	1	2	yes	—
367	C₂²×C₆₁	#576	1	2	yes	—
368	C₂²×C₆₁	#577	1	2	yes	—
369	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
370	C₄×C₆₁	—	2	2	no	—
371	C₄×C₆₁	—	2	2	no	—
372	C₄×C₆₁	—	2	2	no	—
373	C₄×C₆₁	—	2	2	no	—
374	C₄×C₆₁	—	2	2	no	—
375	C₄×C₆₁	—	4	2	no	—
376	C₄×C₆₁	—	4	2	no	—
377	C₄×C₆₁	—	4	2	no	—
378	C₄×C₆₁	—	4	2	no	—
379	C₄×C₆₁	—	4	2	no	—
380	C₄×C₆₁	#537	1	2	yes	—
381	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
382	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
383	C₂×#542	C₂×C₆₁	1	1	yes	characteristic, complemented
384	C₂×#540	C₂×C₆₁	1	1	yes	characteristic, complemented
385	#3257	C₂×C₆₁	1	16	yes	direct product factor
386	C₂×#479	C₂×C₆₁	1	1	yes	characteristic, complemented
387	C₂×#478	C₂×C₆₁	1	1	yes	characteristic, complemented
388	C₂×#476	C₂×C₆₁	1	1	yes	characteristic, complemented
389	C₂×#474	C₂×C₆₁	1	1	yes	characteristic, complemented
390	C₂×#469	C₂×C₆₁	1	1	yes	characteristic, complemented
391	C₂×#468	C₂×C₆₁	1	1	yes	characteristic, complemented
392	C₂×#466	C₂×C₆₁	1	1	yes	characteristic, complemented
393	C₂×#465	C₂×C₆₁	1	1	yes	characteristic, complemented
394	C₂×#460	C₂×C₆₁	1	1	yes	characteristic, complemented
395	C₂×#463	C₂×C₆₁	1	1	yes	characteristic, complemented
396	C₂×#463	C₂×C₆₁	1	1	yes	characteristic, complemented
397	C₂×#459	C₂×C₆₁	1	1	yes	characteristic, complemented
398	C₂×#424	C₂×C₆₁	1	1	yes	characteristic, complemented
399	C₂×C₆₁	—	4	2	no	—
400	C₂×C₆₁	—	8	2	no	—
401	C₂×C₆₁	—	8	2	no	—
402	C₂×C₆₁	—	8	2	no	—
403	C₂×C₆₁	#3257	1	4	yes	direct product factor
404	C₂×C₆₁	C₂×#537	1	1	yes	characteristic
405	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
406	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
407	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
408	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
409	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
410	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
411	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
412	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
413	#542	—	2	4	no	—
414	#542	C₂²×C₆₁	1	8	yes	complemented
415	#540	—	2	4	no	—
416	#540	C₂²×C₆₁	1	8	yes	complemented
417	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
418	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
419	C₂×#126	—	2	1	no	—
420	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
421	C₂×#124	—	2	1	no	—
422	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
423	C₂×#123	—	2	1	no	—
424	C₂×#123	—	2	1	no	—
425	C₂×#123	—	2	1	no	—
426	C₂×C₂²⋊Q₈	—	2	1	no	—
427	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
428	C₂×#121	—	2	1	no	—
429	C₂×#121	—	2	1	no	—
430	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
431	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
432	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
433	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
434	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
435	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
436	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
437	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
438	#479	C₂²×C₆₁	1	8	yes	complemented
439	#478	C₂²×C₆₁	1	8	yes	complemented
440	#476	C₂²×C₆₁	1	8	yes	complemented
441	#474	C₂²×C₆₁	1	8	yes	complemented
442	#469	C₂²×C₆₁	1	8	yes	complemented
443	#468	C₂²×C₆₁	1	8	yes	complemented
444	#466	C₂²×C₆₁	1	8	yes	complemented
445	#465	C₂²×C₆₁	1	8	yes	complemented
446	#463	C₂²×C₆₁	1	8	yes	complemented
447	#463	C₂²×C₆₁	1	8	yes	complemented
448	#460	C₂²×C₆₁	1	8	yes	complemented
449	#459	C₂²×C₆₁	1	8	yes	complemented
450	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
451	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
452	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
453	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
454	#424	C₂²×C₆₁	1	8	yes	complemented
455	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
456	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
457	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
458	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
459	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
460	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
461	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
462	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
463	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
464	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
465	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
466	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
467	C₆₁	C₂×#3257	1	1	yes	characteristic, direct product factor, Sylow
468	C₂²×Q₈	—	2	1	no	—
469	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
470	C₂²×D₄	—	2	1	no	—
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	—	2	1	no	—
473	C₂²×D₄	—	2	1	no	—
474	C₂²×D₄	—	2	1	no	—
475	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
476	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
477	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
478	C₂³×C₄	—	2	1	no	—
479	C₂³×C₄	—	2	1	no	—
480	C₂³×C₄	—	2	1	no	—
481	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
482	C₂×SD₁₆	—	4	2	no	—
483	C₂×SD₁₆	—	4	2	no	—
484	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
485	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
486	C₂×D₈	—	4	2	no	—
487	C₂×D₈	—	4	2	no	—
488	C₂×D₈	C₂³×C₆₁	1	4	yes	—
489	C₂×D₈	C₂³×C₆₁	1	4	yes	—
490	C₂×M₁₆	—	4	2	no	—
491	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
492	C₂²×C₈	—	4	2	no	—
493	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
496	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
497	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
498	C₄⋊Q₈	—	2	2	no	—
499	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
500	#127	—	2	2	no	—
501	#127	C₂³×C₆₁	1	4	yes	—
502	#126	—	2	8	no	—
503	#125	—	2	2	no	—
504	#125	C₂³×C₆₁	1	4	yes	—
505	#124	—	2	8	no	—
506	#124	—	2	2	no	—
507	#124	C₂³×C₆₁	1	4	yes	—
508	#123	—	2	8	no	—
509	#123	—	2	8	no	—
510	#123	—	2	8	no	—
511	C₂²⋊Q₈	—	2	2	no	—
512	C₂²⋊Q₈	—	2	8	no	—
513	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
514	#121	—	2	2	no	—
515	#121	—	2	2	no	—
516	#121	—	2	2	no	—
517	#121	—	2	8	no	—
518	#121	—	2	8	no	—
519	#121	C₂³×C₆₁	1	4	yes	—
520	#121	C₂³×C₆₁	1	4	yes	—
521	#121	C₂³×C₆₁	1	4	yes	—
522	C₄×Q₈	—	2	2	no	—
523	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	C₂³×C₆₁	1	4	yes	—
528	C₄×D₄	C₂³×C₆₁	1	4	yes	—
529	C₄×D₄	C₂³×C₆₁	1	4	yes	—
530	#117	D₄×C₆₁	1	4	yes	—
531	#117	C₂³×C₆₁	1	4	yes	—
532	C₂×C₄⋊C₄	—	2	1	no	—
533	C₂×C₄⋊C₄	—	2	1	no	—
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
538	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
543	C₂×C₂²⋊C₄	—	2	1	no	—
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
554	C₂×C₄²	—	2	1	no	—
555	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
557	#107	C₂³×C₆₁	1	4	yes	—
558	#107	C₂³×C₆₁	1	4	yes	—
559	#106	C₂³×C₆₁	1	4	yes	—
560	#106	C₂³×C₆₁	1	4	yes	—
561	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
562	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
563	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
564	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
565	#103	C₂³×C₆₁	1	4	yes	—
566	#103	C₂³×C₆₁	1	4	yes	—
567	#102	C₂³×C₆₁	1	4	yes	—
568	#102	C₂³×C₆₁	1	4	yes	—
569	#102	C₂³×C₆₁	1	4	yes	—
570	#102	C₂³×C₆₁	1	4	yes	—
571	#102	C₂³×C₆₁	1	4	yes	—
572	#102	C₂³×C₆₁	1	4	yes	—
573	C₂⁴	—	2	1	no	—
574	C₂⁴	—	2	1	no	—
575	C₂⁴	—	2	1	no	—
576	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	4	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	—	2	2	no	—
581	C₂×Q₈	—	8	2	no	—
582	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	8	2	no	—
598	C₂×D₄	—	8	2	no	—
599	C₂×D₄	—	8	2	no	—
600	C₂×D₄	—	8	2	no	—
601	C₂×D₄	—	8	2	no	—
602	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
603	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
604	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	8	2	no	—
616	C₂²×C₄	—	8	2	no	—
617	C₂²×C₄	—	8	2	no	—
618	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
626	SD₁₆	—	4	4	no	—
627	SD₁₆	—	4	4	no	—
628	D₈	—	4	4	no	—
629	D₈	—	4	4	no	—
630	M₁₆	—	4	4	no	—
631	C₂×C₈	—	2	2	no	—
632	C₂×C₈	—	2	2	no	—
633	C₂×C₈	—	2	2	no	—
634	C₂×C₈	—	2	2	no	—
635	C₂×C₈	—	4	4	no	—
636	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
637	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
638	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
639	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
650	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
651	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
652	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
665	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
666	C₄²	—	2	4	no	—
667	C₄²	C₂×D₄×C₆₁	1	2	yes	—
668	C₄²	C₂×D₄×C₆₁	1	2	yes	—
669	C₄²	C₂⁴×C₆₁	1	2	yes	—
670	C₄²	C₂⁴×C₆₁	1	2	yes	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	4	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	—	4	2	no	—
680	C₂³	—	4	2	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	4	2	no	—
683	C₂³	—	4	2	no	—
684	C₂³	—	4	2	no	—
685	C₂³	—	4	2	no	—
686	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
687	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
688	Q₈	—	2	2	no	—
689	Q₈	—	2	2	no	—
690	Q₈	—	4	2	no	—
691	Q₈	—	8	4	no	—
692	D₄	—	2	2	no	—
693	D₄	—	2	2	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	2	no	—
697	D₄	—	2	2	no	—
698	D₄	—	4	2	no	—
699	D₄	—	4	2	no	—
700	D₄	—	4	2	no	—
701	D₄	—	8	4	no	—
702	D₄	—	8	4	no	—
703	D₄	—	8	4	no	—
704	D₄	—	8	4	no	—
705	D₄	—	8	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	8	4	no	—
725	C₂×C₄	—	8	4	no	—
726	C₂×C₄	—	8	4	no	—
727	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
730	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
731	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
732	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
733	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
734	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
735	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
736	C₈	—	2	2	no	—
737	C₈	—	2	2	no	—
738	C₈	—	2	2	no	—
739	C₈	—	2	2	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	4	4	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	8	4	no	—
754	C₂²	—	8	4	no	—
755	C₂²	—	8	4	no	—
756	C₂²	C₆₁×#537	1	2	yes	—
757	C₂²	C₆₁×#576	1	2	yes	—
758	C₂²	C₆₁×#577	1	2	yes	—
759	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
760	C₄	—	2	2	no	—
761	C₄	—	2	2	no	—
762	C₄	—	2	2	no	—
763	C₄	—	2	2	no	—
764	C₄	—	2	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	C₆₁×#537	1	2	yes	—
771	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
772	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
773	C₂	—	4	2	no	—
774	C₂	—	8	2	no	—
775	C₂	—	8	2	no	—
776	C₂	—	8	2	no	—
777	C₂	C₆₁×#3257	1	4	yes	direct product factor
778	C₂	C₂×C₆₁×#537	1	1	yes	characteristic
779	C₂	C₂×C₆₁×#576	1	1	yes	characteristic
780	C₂	C₂×C₆₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×#117×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#542	C₂	semidirect
2. C₂×C₆₁×#540	C₂	semidirect
3. C₆₁×#3257	C₂	direct (N × H)
4. C₂×C₆₁×#479	C₂	semidirect
5. C₂×C₆₁×#478	C₂	semidirect
6. C₂×C₆₁×#476	C₂	semidirect
7. C₂×C₆₁×#474	C₂	semidirect
8. C₂×C₆₁×#469	C₂	semidirect
9. C₂×C₆₁×#468	C₂	semidirect
10. C₂×C₆₁×#466	C₂	semidirect
11. C₂×C₆₁×#465	C₂	semidirect
12. C₂×C₆₁×#460	C₂	semidirect
13. C₂×C₆₁×#463	C₂	semidirect
14. C₂×C₆₁×#463	C₂	semidirect
15. C₂×C₆₁×#459	C₂	semidirect
16. C₂×C₆₁×#424	C₂	semidirect
24. C₆₁×#542	C₂²	semidirect
26. C₆₁×#540	C₂²	semidirect
48. C₆₁×#479	C₂²	semidirect
49. C₆₁×#478	C₂²	semidirect
50. C₆₁×#476	C₂²	semidirect
51. C₆₁×#474	C₂²	semidirect
52. C₆₁×#469	C₂²	semidirect
53. C₆₁×#468	C₂²	semidirect
54. C₆₁×#466	C₂²	semidirect
55. C₆₁×#465	C₂²	semidirect
56. C₆₁×#463	C₂²	semidirect
57. C₆₁×#463	C₂²	semidirect
58. C₆₁×#460	C₂²	semidirect
59. C₆₁×#459	C₂²	semidirect
64. C₆₁×#424	C₂²	semidirect
349. C₂×#3257	C₆₁	direct (N × H)
383. C₂×#542	C₂×C₆₁	semidirect
384. C₂×#540	C₂×C₆₁	semidirect
385. #3257	C₂×C₆₁	direct (N × H)
386. C₂×#479	C₂×C₆₁	semidirect
387. C₂×#478	C₂×C₆₁	semidirect
388. C₂×#476	C₂×C₆₁	semidirect
389. C₂×#474	C₂×C₆₁	semidirect
390. C₂×#469	C₂×C₆₁	semidirect
391. C₂×#468	C₂×C₆₁	semidirect
392. C₂×#466	C₂×C₆₁	semidirect
393. C₂×#465	C₂×C₆₁	semidirect
394. C₂×#460	C₂×C₆₁	semidirect
395. C₂×#463	C₂×C₆₁	semidirect
396. C₂×#463	C₂×C₆₁	semidirect
397. C₂×#459	C₂×C₆₁	semidirect
398. C₂×#424	C₂×C₆₁	semidirect
403. C₂×C₆₁	#3257	direct (N × H)
414. #542	C₂²×C₆₁	semidirect
416. #540	C₂²×C₆₁	semidirect
438. #479	C₂²×C₆₁	semidirect
439. #478	C₂²×C₆₁	semidirect
440. #476	C₂²×C₆₁	semidirect
441. #474	C₂²×C₆₁	semidirect
442. #469	C₂²×C₆₁	semidirect
443. #468	C₂²×C₆₁	semidirect
444. #466	C₂²×C₆₁	semidirect
445. #465	C₂²×C₆₁	semidirect
446. #463	C₂²×C₆₁	semidirect
447. #463	C₂²×C₆₁	semidirect
448. #460	C₂²×C₆₁	semidirect
449. #459	C₂²×C₆₁	semidirect
454. #424	C₂²×C₆₁	semidirect
467. C₆₁	C₂×#3257	direct (N × H)
777. C₂	C₆₁×#3257	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×C₆₁×#542	2
C₂×C₆₁×#540	2
C₆₁×#3257	2
C₂×C₆₁×#479	2
C₂×C₆₁×#478	2
C₂×C₆₁×#476	2
C₂×C₆₁×#474	2
C₂×C₆₁×#469	2
C₂×C₆₁×#468	2
C₂×C₆₁×#466	2
C₂×C₆₁×#465	2
C₂×C₆₁×#460	2
C₂×C₆₁×#463	2
C₂×C₆₁×#459	2
C₂×C₆₁×#424	2
C₂×#3257	61

Subgroups — C2×C61×#3257 #29564341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3257 #29564341