Subgroups — C₆₁×#60860 #29564293

Order 15616.

2006 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3239	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3238	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3230	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3229	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3227	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3226	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3165	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3141	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3092	C₂	1	4	yes	maximal, complemented
12	C₆₁×#3079	C₂	1	4	yes	maximal, complemented
13	C₆₁×#2920	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×Q₈×C₆₁	—	2	1	no	—
15	C₆₁×#533	C₂²	1	1	yes	characteristic
16	C₆₁×#533	C₂²	1	1	yes	characteristic
17	C₆₁×#533	C₂²	1	1	yes	characteristic
18	C₆₁×#532	C₂²	1	1	yes	characteristic
19	C₆₁×#532	C₂²	1	1	yes	characteristic
20	C₆₁×#532	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
22	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
23	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
24	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
25	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
26	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
27	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
28	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
29	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
30	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
31	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
32	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
33	C₆₁×#529	—	2	1	no	—
34	C₆₁×#529	—	2	1	no	—
35	C₆₁×#529	—	2	1	no	—
36	C₆₁×#529	—	2	1	no	—
37	C₆₁×#529	C₂²	1	2	yes	—
38	C₆₁×#529	C₂²	1	2	yes	—
39	C₆₁×#525	—	2	1	no	—
40	C₆₁×#525	—	2	1	no	—
41	C₆₁×#525	C₂²	1	2	yes	—
42	C₄×#41×C₆₁	—	2	1	no	—
43	C₄×#41×C₆₁	—	2	1	no	—
44	C₄×#41×C₆₁	C₂²	1	2	yes	—
45	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
46	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
47	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
48	C₆₁×#501	C₂²	1	8	yes	complemented
49	C₆₁×#500	C₂²	1	4	yes	complemented
50	C₆₁×#498	C₂²	1	4	yes	complemented
51	C₆₁×#489	C₂²	1	8	yes	complemented
52	C₆₁×#487	C₂²	1	4	yes	complemented
53	C₆₁×#486	C₂²	1	4	yes	complemented
54	C₆₁×#484	C₂²	1	8	yes	—
55	C₆₁×#483	C₂²	1	8	yes	—
56	C₆₁×#481	C₂²	1	8	yes	—
57	C₆₁×#480	C₂²	1	8	yes	—
58	C₆₁×#477	C₂²	1	8	yes	complemented
59	C₆₁×#476	C₂²	1	8	yes	complemented
60	C₆₁×#475	C₂²	1	8	yes	complemented
61	C₆₁×#474	C₂²	1	8	yes	complemented
62	C₆₁×#432	C₂²	1	2	yes	—
63	C₆₁×#432	C₂²	1	2	yes	—
64	C₆₁×#431	C₂²	1	2	yes	—
65	C₆₁×#431	C₂²	1	2	yes	—
66	C₆₁×#428	C₂²	1	8	yes	—
67	C₆₁×#423	C₂²	1	2	yes	—
68	C₆₁×#417	C₂²	1	8	yes	—
69	C₆₁×#407	C₂²	1	2	yes	—
70	C₄×M₁₆×C₆₁	C₂²	1	2	yes	—
71	C₂×#41×C₆₁	—	2	1	no	—
72	C₂×#41×C₆₁	—	2	1	no	—
73	C₂×#41×C₆₁	C₂³	1	2	yes	—
74	C₂²×Q₈×C₆₁	—	2	2	no	—
75	C₂²×Q₈×C₆₁	—	2	2	no	—
76	C₂²×Q₈×C₆₁	—	2	2	no	—
77	C₂²×Q₈×C₆₁	—	2	2	no	—
78	C₂²×Q₈×C₆₁	—	2	2	no	—
79	C₂²×Q₈×C₆₁	—	2	2	no	—
80	C₂²×Q₈×C₆₁	—	4	8	no	—
81	C₂³×C₄×C₆₁	—	2	2	no	—
82	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
83	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
84	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
86	C₄⋊Q₈×C₆₁	—	2	2	no	—
87	C₄⋊Q₈×C₆₁	—	2	2	no	—
88	C₄⋊Q₈×C₆₁	—	2	2	no	—
89	C₄⋊Q₈×C₆₁	—	2	2	no	—
90	C₄⋊Q₈×C₆₁	—	2	2	no	—
91	C₄⋊Q₈×C₆₁	—	2	2	no	—
92	C₄⋊Q₈×C₆₁	—	2	2	no	—
93	C₄⋊Q₈×C₆₁	—	2	2	no	—
94	C₄⋊Q₈×C₆₁	—	2	2	no	—
95	C₄⋊Q₈×C₆₁	—	2	2	no	—
96	C₄⋊Q₈×C₆₁	—	2	2	no	—
97	C₄⋊Q₈×C₆₁	—	2	2	no	—
98	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
99	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
100	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
101	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
102	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
103	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
104	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
105	#127×C₆₁	C₂³	1	1	yes	characteristic
106	#126×C₆₁	—	2	2	no	—
107	#126×C₆₁	—	2	2	no	—
108	#125×C₆₁	—	2	1	no	—
109	#125×C₆₁	—	2	1	no	—
110	#125×C₆₁	C₂³	1	2	yes	—
111	#124×C₆₁	—	2	1	no	—
112	#124×C₆₁	—	2	1	no	—
113	#124×C₆₁	C₂³	1	2	yes	—
114	#123×C₆₁	—	2	2	no	—
115	#123×C₆₁	—	2	2	no	—
116	#123×C₆₁	—	2	2	no	—
117	C₂²⋊Q₈×C₆₁	—	2	1	no	—
118	C₂²⋊Q₈×C₆₁	—	2	1	no	—
119	C₂²⋊Q₈×C₆₁	—	2	1	no	—
120	C₂²⋊Q₈×C₆₁	—	2	1	no	—
121	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
122	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
123	#121×C₆₁	—	2	1	no	—
124	#121×C₆₁	—	2	1	no	—
125	#121×C₆₁	—	2	1	no	—
126	#121×C₆₁	—	2	1	no	—
127	#121×C₆₁	C₂³	1	2	yes	—
128	#121×C₆₁	C₂³	1	2	yes	—
129	#120×C₆₁	—	2	2	no	—
130	C₄×Q₈×C₆₁	—	2	1	no	—
131	C₄×Q₈×C₆₁	—	2	1	no	—
132	C₄×Q₈×C₆₁	—	2	1	no	—
133	C₄×Q₈×C₆₁	—	2	1	no	—
134	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
135	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
136	C₄×D₄×C₆₁	—	2	2	no	—
137	C₄×D₄×C₆₁	—	2	2	no	—
138	C₄×D₄×C₆₁	—	2	2	no	—
139	C₄×D₄×C₆₁	—	2	2	no	—
140	C₄×D₄×C₆₁	—	2	2	no	—
141	C₄×D₄×C₆₁	—	2	2	no	—
142	C₄×D₄×C₆₁	—	2	1	no	—
143	C₄×D₄×C₆₁	—	2	1	no	—
144	C₄×D₄×C₆₁	—	2	1	no	—
145	C₄×D₄×C₆₁	—	2	1	no	—
146	C₄×D₄×C₆₁	C₂³	1	2	yes	—
147	C₄×D₄×C₆₁	C₂³	1	2	yes	—
148	#117×C₆₁	—	2	1	no	—
149	#117×C₆₁	—	2	1	no	—
150	#117×C₆₁	—	2	2	no	—
151	#117×C₆₁	—	2	2	no	—
152	#117×C₆₁	—	2	2	no	—
153	#117×C₆₁	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
155	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
156	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
157	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
158	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
159	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
160	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
161	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
162	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
163	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
164	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
165	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
166	C₂×C₄²×C₆₁	—	2	2	no	—
167	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
168	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
169	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
170	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
171	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
172	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
173	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
179	#107×C₆₁	C₂³	1	16	yes	—
180	#106×C₆₁	C₂³	1	16	yes	—
181	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
182	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
183	#103×C₆₁	C₂³	1	16	yes	—
184	#102×C₆₁	C₂³	1	16	yes	—
185	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
186	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
187	#97×C₆₁	C₂³	1	4	yes	—
188	C₄×C₈×C₆₁	C₂³	1	4	yes	—
189	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
190	#41×C₆₁	—	2	8	no	—
191	#41×C₆₁	—	4	4	no	—
192	#41×C₆₁	—	4	4	no	—
193	C₂×Q₈×C₆₁	—	2	1	no	—
194	C₂×Q₈×C₆₁	—	2	1	no	—
195	C₂×Q₈×C₆₁	—	2	4	no	—
196	C₂×Q₈×C₆₁	—	2	4	no	—
197	C₂×Q₈×C₆₁	—	2	4	no	—
198	C₂×Q₈×C₆₁	—	2	4	no	—
199	C₂×Q₈×C₆₁	—	4	8	no	—
200	C₂×Q₈×C₆₁	—	4	8	no	—
201	C₂×Q₈×C₆₁	—	4	8	no	—
202	C₂×Q₈×C₆₁	—	4	8	no	—
203	C₂×Q₈×C₆₁	—	4	8	no	—
204	C₂×Q₈×C₆₁	—	4	8	no	—
205	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
206	C₂×D₄×C₆₁	—	2	2	no	—
207	C₂×D₄×C₆₁	—	2	2	no	—
208	C₂×D₄×C₆₁	—	2	2	no	—
209	C₂×D₄×C₆₁	—	2	1	no	—
210	C₂×D₄×C₆₁	—	2	1	no	—
211	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₆₁	—	2	4	no	—
213	C₂²×C₄×C₆₁	—	2	4	no	—
214	C₂²×C₄×C₆₁	—	2	4	no	—
215	C₂²×C₄×C₆₁	—	2	4	no	—
216	C₂²×C₄×C₆₁	—	2	4	no	—
217	C₂²×C₄×C₆₁	—	2	4	no	—
218	C₂²×C₄×C₆₁	—	2	2	no	—
219	C₂²×C₄×C₆₁	—	2	2	no	—
220	C₂²×C₄×C₆₁	—	2	2	no	—
221	C₂²×C₄×C₆₁	—	4	8	no	—
222	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
240	M₁₆×C₆₁	—	2	8	no	—
241	C₂×C₈×C₆₁	C₂⁴	1	8	yes	—
242	C₄⋊C₄×C₆₁	—	2	4	no	—
243	C₄⋊C₄×C₆₁	—	2	4	no	—
244	C₄⋊C₄×C₆₁	—	2	4	no	—
245	C₄⋊C₄×C₆₁	—	2	4	no	—
246	C₄⋊C₄×C₆₁	—	2	4	no	—
247	C₄⋊C₄×C₆₁	—	2	4	no	—
248	C₄⋊C₄×C₆₁	—	2	4	no	—
249	C₄⋊C₄×C₆₁	—	2	1	no	—
250	C₄⋊C₄×C₆₁	—	2	1	no	—
251	C₄⋊C₄×C₆₁	—	2	1	no	—
252	C₄⋊C₄×C₆₁	—	2	1	no	—
253	C₄⋊C₄×C₆₁	—	2	2	no	—
254	C₄⋊C₄×C₆₁	—	2	2	no	—
255	C₄⋊C₄×C₆₁	—	2	2	no	—
256	C₄⋊C₄×C₆₁	—	2	2	no	—
257	C₄⋊C₄×C₆₁	—	2	2	no	—
258	C₄⋊C₄×C₆₁	—	2	2	no	—
259	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
260	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
262	C₂²⋊C₄×C₆₁	—	2	2	no	—
263	C₂²⋊C₄×C₆₁	—	2	2	no	—
264	C₂²⋊C₄×C₆₁	—	2	2	no	—
265	C₂²⋊C₄×C₆₁	—	2	2	no	—
266	C₂²⋊C₄×C₆₁	—	2	2	no	—
267	C₂²⋊C₄×C₆₁	—	2	2	no	—
268	C₂²⋊C₄×C₆₁	—	2	2	no	—
269	C₂²⋊C₄×C₆₁	—	2	2	no	—
270	C₂²⋊C₄×C₆₁	—	2	2	no	—
271	C₄²×C₆₁	—	2	2	no	—
272	C₄²×C₆₁	—	2	2	no	—
273	C₄²×C₆₁	—	2	2	no	—
274	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
287	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
288	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
289	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
290	C₂³×C₆₁	—	2	2	no	—
291	C₂³×C₆₁	—	2	2	no	—
292	C₂³×C₆₁	—	2	2	no	—
293	C₂³×C₆₁	—	2	2	no	—
294	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
295	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
296	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
297	Q₈×C₆₁	—	2	4	no	—
298	Q₈×C₆₁	—	4	8	no	—
299	Q₈×C₆₁	—	4	8	no	—
300	Q₈×C₆₁	—	4	8	no	—
301	Q₈×C₆₁	—	4	8	no	—
302	Q₈×C₆₁	—	4	2	no	—
303	Q₈×C₆₁	—	4	2	no	—
304	D₄×C₆₁	—	2	4	no	—
305	D₄×C₆₁	—	4	4	no	—
306	D₄×C₆₁	—	4	4	no	—
307	D₄×C₆₁	—	4	4	no	—
308	D₄×C₆₁	—	4	2	no	—
309	D₄×C₆₁	—	4	2	no	—
310	C₂×C₄×C₆₁	—	2	2	no	—
311	C₂×C₄×C₆₁	—	2	2	no	—
312	C₂×C₄×C₆₁	—	2	2	no	—
313	C₂×C₄×C₆₁	—	2	2	no	—
314	C₂×C₄×C₆₁	—	2	2	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	2	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	—	2	8	no	—
329	C₂×C₄×C₆₁	—	4	8	no	—
330	C₂×C₄×C₆₁	—	4	8	no	—
331	C₂×C₄×C₆₁	—	4	8	no	—
332	C₂×C₄×C₆₁	—	4	4	no	—
333	C₂×C₄×C₆₁	—	4	4	no	—
334	C₂×C₄×C₆₁	—	4	4	no	—
335	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
336	C₂×C₄×C₆₁	#137	1	4	yes	—
337	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₆₁	2₋¹⁺⁴	1	4	yes	—
349	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
350	C₈×C₆₁	—	2	8	no	—
351	#60860	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
352	C₂²×C₆₁	—	2	8	no	—
353	C₂²×C₆₁	—	2	1	no	—
354	C₂²×C₆₁	—	2	1	no	—
355	C₂²×C₆₁	—	2	1	no	—
356	C₂²×C₆₁	—	2	1	no	—
357	C₂²×C₆₁	—	2	1	no	—
358	C₂²×C₆₁	—	2	1	no	—
359	C₂²×C₆₁	—	4	2	no	—
360	C₂²×C₆₁	—	4	2	no	—
361	C₂²×C₆₁	—	4	2	no	—
362	C₂²×C₆₁	#536	1	2	yes	—
363	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
364	C₂²×C₆₁	C₂×#137	1	2	yes	—
365	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
366	C₄×C₆₁	—	2	1	no	—
367	C₄×C₆₁	—	2	1	no	—
368	C₄×C₆₁	—	2	1	no	—
369	C₄×C₆₁	—	2	1	no	—
370	C₄×C₆₁	—	2	1	no	—
371	C₄×C₆₁	—	2	1	no	—
372	C₄×C₆₁	—	4	2	no	—
373	C₄×C₆₁	—	4	8	no	—
374	C₄×C₆₁	—	4	2	no	—
375	C₄×C₆₁	—	4	2	no	—
376	C₄×C₆₁	#536	1	2	yes	—
377	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
378	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
379	C₄×C₆₁	C₂×#137	1	2	yes	—
380	C₄×C₆₁	C₂×#137	1	2	yes	—
381	C₄×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
382	#3444	C₂×C₆₁	1	1	yes	characteristic
383	C₂²×C₄⋊Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
384	#3239	C₂×C₆₁	1	4	yes	complemented
385	#3238	C₂×C₆₁	1	4	yes	complemented
386	#3230	C₂×C₆₁	1	2	yes	complemented
387	#3229	C₂×C₆₁	1	2	yes	complemented
388	#3227	C₂×C₆₁	1	2	yes	complemented
389	#3226	C₂×C₆₁	1	2	yes	complemented
390	#3165	C₂×C₆₁	1	2	yes	complemented
391	#3141	C₂×C₆₁	1	2	yes	complemented
392	#3092	C₂×C₆₁	1	4	yes	complemented
393	#3079	C₂×C₆₁	1	4	yes	complemented
394	#2920	C₂×C₆₁	1	1	yes	characteristic, complemented
395	C₂×C₆₁	—	2	2	no	—
396	C₂×C₆₁	—	2	2	no	—
397	C₂×C₆₁	—	2	2	no	—
398	C₂×C₆₁	—	8	2	no	—
399	C₂×C₆₁	C₂×#536	1	1	yes	characteristic
400	C₂×C₆₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
401	C₂×C₆₁	C₂²×#137	1	1	yes	characteristic
402	C₂³×Q₈	—	2	1	no	—
403	#533	C₂²×C₆₁	1	1	yes	characteristic
404	#533	C₂²×C₆₁	1	1	yes	characteristic
405	#533	C₂²×C₆₁	1	1	yes	characteristic
406	#532	C₂²×C₆₁	1	1	yes	characteristic
407	#532	C₂²×C₆₁	1	1	yes	characteristic
408	#532	C₂²×C₆₁	1	1	yes	characteristic
409	C₂×C₄⋊Q₈	—	2	1	no	—
410	C₂×C₄⋊Q₈	—	2	1	no	—
411	C₂×C₄⋊Q₈	—	2	1	no	—
412	C₂×C₄⋊Q₈	—	2	1	no	—
413	C₂×C₄⋊Q₈	—	2	1	no	—
414	C₂×C₄⋊Q₈	—	2	1	no	—
415	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
416	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
417	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
418	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
419	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
420	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
421	#529	—	2	1	no	—
422	#529	—	2	1	no	—
423	#529	—	2	1	no	—
424	#529	—	2	1	no	—
425	#529	C₂²×C₆₁	1	2	yes	—
426	#529	C₂²×C₆₁	1	2	yes	—
427	#525	—	2	1	no	—
428	#525	—	2	1	no	—
429	#525	C₂²×C₆₁	1	2	yes	—
430	C₄×#41	—	2	1	no	—
431	C₄×#41	—	2	1	no	—
432	C₄×#41	C₂²×C₆₁	1	2	yes	—
433	C₂²×C₄⋊C₄	—	2	1	no	—
434	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
435	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
436	#501	C₂²×C₆₁	1	8	yes	complemented
437	#500	C₂²×C₆₁	1	4	yes	complemented
438	#498	C₂²×C₆₁	1	4	yes	complemented
439	#489	C₂²×C₆₁	1	8	yes	complemented
440	#487	C₂²×C₆₁	1	4	yes	complemented
441	#486	C₂²×C₆₁	1	4	yes	complemented
442	#484	C₂²×C₆₁	1	8	yes	—
443	#483	C₂²×C₆₁	1	8	yes	—
444	#481	C₂²×C₆₁	1	8	yes	—
445	#480	C₂²×C₆₁	1	8	yes	—
446	#477	C₂²×C₆₁	1	8	yes	complemented
447	#476	C₂²×C₆₁	1	8	yes	complemented
448	#475	C₂²×C₆₁	1	8	yes	complemented
449	#474	C₂²×C₆₁	1	8	yes	complemented
450	#432	C₂²×C₆₁	1	2	yes	—
451	#432	C₂²×C₆₁	1	2	yes	—
452	#431	C₂²×C₆₁	1	2	yes	—
453	#431	C₂²×C₆₁	1	2	yes	—
454	#428	C₂²×C₆₁	1	8	yes	—
455	#423	C₂²×C₆₁	1	2	yes	—
456	#417	C₂²×C₆₁	1	8	yes	—
457	#407	C₂²×C₆₁	1	2	yes	—
458	C₄×M₁₆	C₂²×C₆₁	1	2	yes	—
459	C₆₁	#60860	1	1	yes	characteristic, direct product factor, Sylow
460	C₂×#41	—	2	1	no	—
461	C₂×#41	—	2	1	no	—
462	C₂×#41	C₂³×C₆₁	1	2	yes	—
463	C₂²×Q₈	—	2	2	no	—
464	C₂²×Q₈	—	2	2	no	—
465	C₂²×Q₈	—	2	2	no	—
466	C₂²×Q₈	—	2	2	no	—
467	C₂²×Q₈	—	2	2	no	—
468	C₂²×Q₈	—	2	2	no	—
469	C₂²×Q₈	—	4	8	no	—
470	C₂³×C₄	—	2	2	no	—
471	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
472	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
474	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
475	C₄⋊Q₈	—	2	2	no	—
476	C₄⋊Q₈	—	2	2	no	—
477	C₄⋊Q₈	—	2	2	no	—
478	C₄⋊Q₈	—	2	2	no	—
479	C₄⋊Q₈	—	2	2	no	—
480	C₄⋊Q₈	—	2	2	no	—
481	C₄⋊Q₈	—	2	2	no	—
482	C₄⋊Q₈	—	2	2	no	—
483	C₄⋊Q₈	—	2	2	no	—
484	C₄⋊Q₈	—	2	2	no	—
485	C₄⋊Q₈	—	2	2	no	—
486	C₄⋊Q₈	—	2	2	no	—
487	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
488	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
489	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
490	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
491	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
492	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
493	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
494	#127	C₂³×C₆₁	1	1	yes	characteristic
495	#126	—	2	2	no	—
496	#126	—	2	2	no	—
497	#125	—	2	1	no	—
498	#125	—	2	1	no	—
499	#125	C₂³×C₆₁	1	2	yes	—
500	#124	—	2	1	no	—
501	#124	—	2	1	no	—
502	#124	C₂³×C₆₁	1	2	yes	—
503	#123	—	2	2	no	—
504	#123	—	2	2	no	—
505	#123	—	2	2	no	—
506	C₂²⋊Q₈	—	2	1	no	—
507	C₂²⋊Q₈	—	2	1	no	—
508	C₂²⋊Q₈	—	2	1	no	—
509	C₂²⋊Q₈	—	2	1	no	—
510	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
511	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
512	#121	—	2	1	no	—
513	#121	—	2	1	no	—
514	#121	—	2	1	no	—
515	#121	—	2	1	no	—
516	#121	C₂³×C₆₁	1	2	yes	—
517	#121	C₂³×C₆₁	1	2	yes	—
518	#120	—	2	2	no	—
519	C₄×Q₈	—	2	1	no	—
520	C₄×Q₈	—	2	1	no	—
521	C₄×Q₈	—	2	1	no	—
522	C₄×Q₈	—	2	1	no	—
523	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
524	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	1	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	—	2	1	no	—
534	C₄×D₄	—	2	1	no	—
535	C₄×D₄	C₂³×C₆₁	1	2	yes	—
536	C₄×D₄	C₂³×C₆₁	1	2	yes	—
537	#117	—	2	1	no	—
538	#117	—	2	1	no	—
539	#117	—	2	2	no	—
540	#117	—	2	2	no	—
541	#117	—	2	2	no	—
542	#117	C₂³×C₆₁	1	2	yes	—
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₄⋊C₄	—	2	2	no	—
545	C₂×C₄⋊C₄	—	2	2	no	—
546	C₂×C₄⋊C₄	—	2	2	no	—
547	C₂×C₄⋊C₄	—	2	2	no	—
548	C₂×C₄⋊C₄	—	2	2	no	—
549	C₂×C₄⋊C₄	—	2	2	no	—
550	C₂×C₄⋊C₄	—	2	2	no	—
551	C₂×C₄⋊C₄	—	2	2	no	—
552	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
553	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
554	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
555	C₂×C₄²	—	2	2	no	—
556	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
557	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
558	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
559	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
560	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
561	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
565	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
568	#107	C₂³×C₆₁	1	16	yes	—
569	#106	C₂³×C₆₁	1	16	yes	—
570	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
571	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
572	#103	C₂³×C₆₁	1	16	yes	—
573	#102	C₂³×C₆₁	1	16	yes	—
574	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
575	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
576	#97	C₂³×C₆₁	1	4	yes	—
577	C₄×C₈	C₂³×C₆₁	1	4	yes	—
578	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
579	#41	—	2	8	no	—
580	#41	—	4	4	no	—
581	#41	—	4	4	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	4	no	—
585	C₂×Q₈	—	2	4	no	—
586	C₂×Q₈	—	2	4	no	—
587	C₂×Q₈	—	2	4	no	—
588	C₂×Q₈	—	4	8	no	—
589	C₂×Q₈	—	4	8	no	—
590	C₂×Q₈	—	4	8	no	—
591	C₂×Q₈	—	4	8	no	—
592	C₂×Q₈	—	4	8	no	—
593	C₂×Q₈	—	4	8	no	—
594	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	4	8	no	—
611	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
613	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
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	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
629	M₁₆	—	2	8	no	—
630	C₂×C₈	C₂⁴×C₆₁	1	8	yes	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
649	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
650	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₄²	—	2	2	no	—
661	C₄²	—	2	2	no	—
662	C₄²	—	2	2	no	—
663	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
664	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
665	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
666	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
667	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
668	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
669	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
670	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
671	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
672	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
673	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
674	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
675	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
676	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
677	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
678	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
684	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
685	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
686	Q₈	—	2	4	no	—
687	Q₈	—	4	8	no	—
688	Q₈	—	4	8	no	—
689	Q₈	—	4	8	no	—
690	Q₈	—	4	8	no	—
691	Q₈	—	4	2	no	—
692	Q₈	—	4	2	no	—
693	D₄	—	2	4	no	—
694	D₄	—	4	4	no	—
695	D₄	—	4	4	no	—
696	D₄	—	4	4	no	—
697	D₄	—	4	2	no	—
698	D₄	—	4	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	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	2	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	8	no	—
718	C₂×C₄	—	4	8	no	—
719	C₂×C₄	—	4	8	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	4	no	—
722	C₂×C₄	—	4	4	no	—
723	C₂×C₄	—	4	4	no	—
724	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	4	yes	—
725	C₂×C₄	#137×C₆₁	1	4	yes	—
726	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
727	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
731	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
733	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
734	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
735	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
736	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
737	C₂×C₄	2₋¹⁺⁴×C₆₁	1	4	yes	—
738	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
739	C₈	—	2	8	no	—
740	C₂²	—	2	8	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	1	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	C₆₁×#536	1	2	yes	—
751	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
752	C₂²	C₂×#137×C₆₁	1	2	yes	—
753	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
754	C₄	—	2	1	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	1	no	—
759	C₄	—	2	1	no	—
760	C₄	—	4	8	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	C₆₁×#536	1	2	yes	—
765	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
766	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
767	C₄	C₂×#137×C₆₁	1	2	yes	—
768	C₄	C₂×#137×C₆₁	1	2	yes	—
769	C₄	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
770	C₂	—	2	2	no	—
771	C₂	—	2	2	no	—
772	C₂	—	2	2	no	—
773	C₂	—	8	2	no	—
774	C₂	C₂×C₆₁×#536	1	1	yes	characteristic
775	C₂	C₂²×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
776	C₂	C₂²×#137×C₆₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊Q₈×C₆₁	C₂	semidirect
3. C₆₁×#3239	C₂	semidirect
4. C₆₁×#3238	C₂	semidirect
5. C₆₁×#3230	C₂	semidirect
6. C₆₁×#3229	C₂	semidirect
7. C₆₁×#3227	C₂	semidirect
8. C₆₁×#3226	C₂	semidirect
9. C₆₁×#3165	C₂	semidirect
10. C₆₁×#3141	C₂	semidirect
11. C₆₁×#3092	C₂	semidirect
12. C₆₁×#3079	C₂	semidirect
13. C₆₁×#2920	C₂	semidirect
48. C₆₁×#501	C₂²	semidirect
49. C₆₁×#500	C₂²	semidirect
50. C₆₁×#498	C₂²	semidirect
51. C₆₁×#489	C₂²	semidirect
52. C₆₁×#487	C₂²	semidirect
53. C₆₁×#486	C₂²	semidirect
58. C₆₁×#477	C₂²	semidirect
59. C₆₁×#476	C₂²	semidirect
60. C₆₁×#475	C₂²	semidirect
61. C₆₁×#474	C₂²	semidirect
351. #60860	C₆₁	direct (N × H)
383. C₂²×C₄⋊Q₈	C₂×C₆₁	semidirect
384. #3239	C₂×C₆₁	semidirect
385. #3238	C₂×C₆₁	semidirect
386. #3230	C₂×C₆₁	semidirect
387. #3229	C₂×C₆₁	semidirect
388. #3227	C₂×C₆₁	semidirect
389. #3226	C₂×C₆₁	semidirect
390. #3165	C₂×C₆₁	semidirect
391. #3141	C₂×C₆₁	semidirect
392. #3092	C₂×C₆₁	semidirect
393. #3079	C₂×C₆₁	semidirect
394. #2920	C₂×C₆₁	semidirect
436. #501	C₂²×C₆₁	semidirect
437. #500	C₂²×C₆₁	semidirect
438. #498	C₂²×C₆₁	semidirect
439. #489	C₂²×C₆₁	semidirect
440. #487	C₂²×C₆₁	semidirect
441. #486	C₂²×C₆₁	semidirect
446. #477	C₂²×C₆₁	semidirect
447. #476	C₂²×C₆₁	semidirect
448. #475	C₂²×C₆₁	semidirect
449. #474	C₂²×C₆₁	semidirect
459. C₆₁	#60860	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#3444	2
C₂²×C₄⋊Q₈×C₆₁	2
C₆₁×#3239	2
C₆₁×#3238	2
C₆₁×#3230	2
C₆₁×#3229	2
C₆₁×#3227	2
C₆₁×#3226	2
C₆₁×#3165	2
C₆₁×#3141	2
C₆₁×#3092	2
C₆₁×#3079	2
C₆₁×#2920	2
#60860	61

Subgroups — C61×#60860 #29564293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60860 #29564293