Subgroups — C₆₁×#61371 #29564804

Order 15616.

1750 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3502	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3501	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3388	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3386	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3385	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3381	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3381	C₂	1	4	yes	maximal, complemented
8	Q₈×SD₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3163	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3160	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3082	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3081	C₂	1	2	yes	maximal
13	C₆₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3077	C₂	1	1	yes	maximal, characteristic
15	C₆₁×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#2949	C₂	1	2	yes	maximal
17	C₂×C₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
18	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	Q₈²×C₆₁	—	2	1	no	—
20	Q₈²×C₆₁	C₂²	1	2	yes	complemented
21	C₆₁×#557	—	2	1	no	—
22	C₆₁×#557	—	2	2	no	—
23	C₆₁×#557	C₂²	1	2	yes	complemented
24	C₆₁×#557	C₂²	1	4	yes	complemented
25	C₆₁×#554	—	2	1	no	—
26	C₆₁×#554	—	2	2	no	—
27	C₆₁×#554	C₂²	1	2	yes	—
28	C₆₁×#554	C₂²	1	4	yes	—
29	D₄×Q₈×C₆₁	—	2	1	no	—
30	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
31	C₆₁×#544	—	2	2	no	—
32	C₆₁×#544	C₂²	1	2	yes	—
33	C₆₁×#544	C₂²	1	2	yes	—
34	C₆₁×#543	—	2	2	no	—
35	C₆₁×#533	—	2	2	no	—
36	C₆₁×#533	C₂²	1	1	yes	characteristic
37	C₆₁×#533	C₂²	1	1	yes	characteristic
38	C₆₁×#533	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₆₁	—	2	2	no	—
40	C₆₁×#519	C₂²	1	2	yes	—
41	C₆₁×#518	C₂²	1	2	yes	—
42	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
44	C₆₁×#501	C₂²	1	4	yes	complemented
45	C₆₁×#501	C₂²	1	4	yes	complemented
46	C₆₁×#500	C₂²	1	1	yes	characteristic, complemented
47	C₆₁×#500	C₂²	1	1	yes	characteristic, complemented
48	C₆₁×#499	C₂²	1	2	yes	complemented
49	C₆₁×#499	C₂²	1	4	yes	complemented
50	C₆₁×#499	C₂²	1	2	yes	complemented
51	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
52	C₆₁×#498	C₂²	1	4	yes	complemented
53	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
54	C₆₁×#479	C₂²	1	4	yes	complemented
55	C₆₁×#479	C₂²	1	4	yes	complemented
56	C₆₁×#479	C₂²	1	4	yes	complemented
57	C₆₁×#478	C₂²	1	4	yes	—
58	C₆₁×#478	C₂²	1	4	yes	—
59	C₆₁×#478	C₂²	1	4	yes	—
60	C₆₁×#477	C₂²	1	2	yes	complemented
61	C₆₁×#477	C₂²	1	4	yes	complemented
62	C₆₁×#476	C₂²	1	2	yes	—
63	C₆₁×#476	C₂²	1	4	yes	—
64	C₆₁×#475	C₂²	1	2	yes	complemented
65	C₆₁×#475	C₂²	1	4	yes	complemented
66	C₆₁×#474	C₂²	1	2	yes	—
67	C₆₁×#474	C₂²	1	4	yes	—
68	C₆₁×#446	C₂²	1	2	yes	complemented
69	C₆₁×#446	C₂²	1	2	yes	complemented
70	C₈×Q₈×C₆₁	C₂²	1	2	yes	complemented
71	C₈×Q₈×C₆₁	C₂²	1	2	yes	complemented
72	C₆₁×#440	C₂²	1	4	yes	—
73	C₆₁×#440	C₂²	1	4	yes	—
74	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
75	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	—
76	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
77	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	—
78	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
79	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
80	C₆₁×#428	C₂²	1	2	yes	—
81	C₆₁×#428	C₂²	1	2	yes	—
82	C₆₁×#427	C₂²	1	2	yes	—
83	C₆₁×#427	C₂²	1	2	yes	—
84	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
85	C₆₁×#424	C₂²	1	2	yes	—
86	C₆₁×#423	C₂²	1	1	yes	characteristic
87	C₆₁×#419	C₂²	1	2	yes	—
88	C₆₁×#418	C₂²	1	2	yes	—
89	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
90	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
91	C₆₁×#405	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
93	C₂²×Q₈×C₆₁	—	2	2	no	—
94	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₆₁	—	2	1	no	—
97	C₂×SD₁₆×C₆₁	Q₈	1	8	yes	complemented
98	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
99	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
100	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
101	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₆₁	—	2	2	no	—
104	C₄⋊Q₈×C₆₁	—	2	4	no	—
105	C₄⋊Q₈×C₆₁	—	2	2	no	—
106	C₄⋊Q₈×C₆₁	—	2	4	no	—
107	C₄⋊Q₈×C₆₁	—	2	2	no	—
108	C₄⋊Q₈×C₆₁	—	2	2	no	—
109	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
110	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
116	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
117	#125×C₆₁	—	2	4	no	—
118	#125×C₆₁	—	2	4	no	—
119	#125×C₆₁	—	2	4	no	—
120	#125×C₆₁	—	2	2	no	—
121	#125×C₆₁	—	2	2	no	—
122	#125×C₆₁	D₄	1	2	yes	—
123	#125×C₆₁	C₂³	1	2	yes	—
124	#125×C₆₁	C₂³	1	2	yes	—
125	#125×C₆₁	C₂³	1	4	yes	—
126	#125×C₆₁	C₂³	1	4	yes	—
127	C₂²⋊Q₈×C₆₁	—	2	4	no	—
128	C₂²⋊Q₈×C₆₁	—	2	2	no	—
129	C₂²⋊Q₈×C₆₁	—	2	1	no	—
130	C₂²⋊Q₈×C₆₁	—	2	1	no	—
131	C₂²⋊Q₈×C₆₁	—	2	1	no	—
132	C₂²⋊Q₈×C₆₁	—	2	1	no	—
133	C₂²⋊Q₈×C₆₁	—	2	4	no	—
134	C₂²⋊Q₈×C₆₁	—	2	4	no	—
135	C₂²⋊Q₈×C₆₁	—	2	4	no	—
136	C₂²⋊Q₈×C₆₁	—	2	2	no	—
137	C₂²⋊Q₈×C₆₁	—	2	4	no	—
138	C₂²⋊Q₈×C₆₁	—	2	4	no	—
139	C₂²⋊Q₈×C₆₁	—	2	4	no	—
140	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
141	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
142	C₄×Q₈×C₆₁	—	2	2	no	—
143	C₄×Q₈×C₆₁	—	2	4	no	—
144	C₄×Q₈×C₆₁	—	2	2	no	—
145	C₄×Q₈×C₆₁	—	2	2	no	—
146	C₄×Q₈×C₆₁	—	2	2	no	—
147	C₄×Q₈×C₆₁	—	2	1	no	—
148	C₄×Q₈×C₆₁	—	2	1	no	—
149	C₄×Q₈×C₆₁	—	2	1	no	—
150	C₄×Q₈×C₆₁	—	2	1	no	—
151	C₄×Q₈×C₆₁	—	2	1	no	—
152	C₄×Q₈×C₆₁	—	2	1	no	—
153	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
154	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
155	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
156	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
157	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
158	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
159	C₄×D₄×C₆₁	—	2	2	no	—
160	C₄×D₄×C₆₁	—	2	2	no	—
161	C₄×D₄×C₆₁	—	2	1	no	—
162	C₄×D₄×C₆₁	—	2	1	no	—
163	C₄×D₄×C₆₁	C₂³	1	2	yes	—
164	C₄×D₄×C₆₁	C₂³	1	4	yes	—
165	C₄×D₄×C₆₁	C₂³	1	2	yes	—
166	C₄×D₄×C₆₁	C₂³	1	4	yes	—
167	#117×C₆₁	—	2	4	no	—
168	#117×C₆₁	C₂³	1	2	yes	—
169	#117×C₆₁	C₂³	1	2	yes	—
170	#117×C₆₁	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
172	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
173	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
174	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
177	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
178	C₂×C₄²×C₆₁	—	2	1	no	—
179	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
180	#107×C₆₁	C₂³	1	2	yes	—
181	#107×C₆₁	C₂³	1	2	yes	—
182	#107×C₆₁	C₂³	1	2	yes	—
183	#107×C₆₁	C₂³	1	2	yes	—
184	#107×C₆₁	C₂³	1	4	yes	—
185	#107×C₆₁	C₂³	1	4	yes	—
186	#106×C₆₁	C₂³	1	2	yes	—
187	#106×C₆₁	C₂³	1	2	yes	—
188	#106×C₆₁	C₂³	1	2	yes	—
189	#106×C₆₁	C₂³	1	2	yes	—
190	#106×C₆₁	C₂³	1	2	yes	—
191	#106×C₆₁	C₂³	1	2	yes	—
192	#106×C₆₁	C₂³	1	4	yes	—
193	#106×C₆₁	C₂³	1	4	yes	—
194	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
195	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
196	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
197	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
198	#103×C₆₁	C₂³	1	2	yes	—
199	#103×C₆₁	C₂³	1	2	yes	—
200	#103×C₆₁	C₂³	1	4	yes	—
201	#103×C₆₁	C₂³	1	4	yes	—
202	#102×C₆₁	C₂³	1	2	yes	—
203	#102×C₆₁	C₂³	1	2	yes	—
204	#102×C₆₁	C₂³	1	4	yes	—
205	#102×C₆₁	C₂³	1	4	yes	—
206	#97×C₆₁	C₂³	1	4	yes	—
207	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
208	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
209	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₆₁	C₂³	1	4	yes	—
212	C₂⁴×C₆₁	—	2	1	no	—
213	C₂×Q₈×C₆₁	—	2	1	no	—
214	C₂×Q₈×C₆₁	—	2	1	no	—
215	C₂×Q₈×C₆₁	—	2	1	no	—
216	C₂×Q₈×C₆₁	—	2	1	no	—
217	C₂×Q₈×C₆₁	—	2	1	no	—
218	C₂×Q₈×C₆₁	—	2	4	no	—
219	C₂×Q₈×C₆₁	—	2	4	no	—
220	C₂×Q₈×C₆₁	—	2	2	no	—
221	C₂×Q₈×C₆₁	—	8	4	no	—
222	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
223	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₆₁	C₂×Q₈	1	4	yes	complemented
225	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
226	C₂×D₄×C₆₁	—	2	1	no	—
227	C₂×D₄×C₆₁	—	2	2	no	—
228	C₂×D₄×C₆₁	C₂×Q₈	1	4	yes	—
229	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₆₁	—	2	1	no	—
231	C₂²×C₄×C₆₁	—	2	1	no	—
232	C₂²×C₄×C₆₁	—	2	1	no	—
233	C₂²×C₄×C₆₁	—	2	2	no	—
234	C₂²×C₄×C₆₁	—	2	4	no	—
235	C₂²×C₄×C₆₁	—	2	4	no	—
236	C₂²×C₄×C₆₁	—	2	2	no	—
237	C₂²×C₄×C₆₁	—	8	2	no	—
238	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
241	SD₁₆×C₆₁	C₂×Q₈	1	8	yes	complemented
242	SD₁₆×C₆₁	C₂×Q₈	1	8	yes	complemented
243	M₁₆×C₆₁	—	2	4	no	—
244	C₂×C₈×C₆₁	—	2	2	no	—
245	C₂×C₈×C₆₁	C₂×Q₈	1	4	yes	complemented
246	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
248	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
249	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
251	C₄⋊C₄×C₆₁	—	2	2	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	4	no	—
256	C₄⋊C₄×C₆₁	—	2	4	no	—
257	C₄⋊C₄×C₆₁	—	2	4	no	—
258	C₄⋊C₄×C₆₁	—	2	1	no	—
259	C₄⋊C₄×C₆₁	—	2	1	no	—
260	C₄⋊C₄×C₆₁	—	2	4	no	—
261	C₄⋊C₄×C₆₁	—	2	4	no	—
262	C₄⋊C₄×C₆₁	—	2	2	no	—
263	C₄⋊C₄×C₆₁	—	2	1	no	—
264	C₄⋊C₄×C₆₁	—	2	2	no	—
265	C₄⋊C₄×C₆₁	—	2	1	no	—
266	C₄⋊C₄×C₆₁	—	2	1	no	—
267	C₄⋊C₄×C₆₁	—	2	4	no	—
268	C₄⋊C₄×C₆₁	—	2	4	no	—
269	C₄⋊C₄×C₆₁	—	2	2	no	—
270	C₄⋊C₄×C₆₁	—	2	4	no	—
271	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
272	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
273	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
274	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
277	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
283	C₂²⋊C₄×C₆₁	—	2	2	no	—
284	C₂²⋊C₄×C₆₁	—	2	2	no	—
285	C₂²⋊C₄×C₆₁	—	2	4	no	—
286	C₂²⋊C₄×C₆₁	—	2	4	no	—
287	C₂²⋊C₄×C₆₁	—	2	2	no	—
288	C₂²⋊C₄×C₆₁	—	2	2	no	—
289	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
290	C₄²×C₆₁	—	2	2	no	—
291	C₄²×C₆₁	—	2	2	no	—
292	C₄²×C₆₁	—	2	4	no	—
293	C₄²×C₆₁	—	2	4	no	—
294	C₄²×C₆₁	—	2	2	no	—
295	C₄²×C₆₁	—	2	2	no	—
296	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
297	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
299	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
300	C₄²×C₆₁	C₂⁴	1	4	yes	—
301	C₂³×C₆₁	—	2	2	no	—
302	C₂³×C₆₁	—	2	4	no	—
303	C₂³×C₆₁	—	8	1	no	—
304	C₂³×C₆₁	—	8	1	no	—
305	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
306	Q₈×C₆₁	—	2	4	no	—
307	Q₈×C₆₁	—	2	4	no	—
308	Q₈×C₆₁	—	2	2	no	—
309	Q₈×C₆₁	—	4	2	no	—
310	Q₈×C₆₁	—	4	2	no	—
311	Q₈×C₆₁	—	4	2	no	—
312	Q₈×C₆₁	—	8	1	no	—
313	Q₈×C₆₁	—	8	1	no	—
314	Q₈×C₆₁	—	8	4	no	—
315	Q₈×C₆₁	—	8	4	no	—
316	Q₈×C₆₁	C₂²×Q₈	1	4	yes	—
317	D₄×C₆₁	—	2	4	no	—
318	D₄×C₆₁	—	2	2	no	—
319	D₄×C₆₁	C₂²×Q₈	1	4	yes	—
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	—	2	2	no	—
329	C₂×C₄×C₆₁	—	4	1	no	—
330	C₂×C₄×C₆₁	—	4	4	no	—
331	C₂×C₄×C₆₁	—	8	4	no	—
332	C₂×C₄×C₆₁	—	8	2	no	—
333	C₂×C₄×C₆₁	—	8	4	no	—
334	C₂×C₄×C₆₁	—	8	1	no	—
335	C₂×C₄×C₆₁	—	8	1	no	—
336	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
338	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
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×Q₈	1	2	yes	—
344	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
345	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
346	C₈×C₆₁	—	2	1	no	—
347	C₈×C₆₁	—	2	1	no	—
348	C₈×C₆₁	—	2	4	no	—
349	C₈×C₆₁	C₂²×Q₈	1	2	yes	—
350	C₈×C₆₁	C₂²×Q₈	1	2	yes	—
351	#61371	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
352	C₂²×C₆₁	—	2	1	no	—
353	C₂²×C₆₁	—	2	1	no	—
354	C₂²×C₆₁	—	2	4	no	—
355	C₂²×C₆₁	—	4	2	no	—
356	C₂²×C₆₁	—	4	2	no	—
357	C₂²×C₆₁	—	8	4	no	—
358	C₂²×C₆₁	D₄×Q₈	1	2	yes	—
359	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
360	C₄×C₆₁	—	2	1	no	—
361	C₄×C₆₁	—	2	1	no	—
362	C₄×C₆₁	—	2	4	no	—
363	C₄×C₆₁	—	2	4	no	—
364	C₄×C₆₁	—	2	1	no	—
365	C₄×C₆₁	—	2	4	no	—
366	C₄×C₆₁	—	4	2	no	—
367	C₄×C₆₁	—	4	2	no	—
368	C₄×C₆₁	—	4	2	no	—
369	C₄×C₆₁	—	4	2	no	—
370	C₄×C₆₁	—	4	2	no	—
371	C₄×C₆₁	—	4	2	no	—
372	C₄×C₆₁	D₄×Q₈	1	2	yes	—
373	C₄×C₆₁	#577	1	2	yes	—
374	C₄×C₆₁	C₂³×Q₈	1	1	yes	characteristic
375	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
376	#3502	C₂×C₆₁	1	1	yes	characteristic, complemented
377	#3501	C₂×C₆₁	1	1	yes	characteristic
378	#3388	C₂×C₆₁	1	4	yes	complemented
379	#3386	C₂×C₆₁	1	2	yes	complemented
380	#3385	C₂×C₆₁	1	2	yes	complemented
381	#3381	C₂×C₆₁	1	2	yes	complemented
382	#3381	C₂×C₆₁	1	4	yes	complemented
383	Q₈×SD₁₆	C₂×C₆₁	1	2	yes	complemented
384	#3163	C₂×C₆₁	1	2	yes	complemented
385	#3160	C₂×C₆₁	1	1	yes	characteristic, complemented
386	#3082	C₂×C₆₁	1	2	yes	complemented
387	#3081	C₂×C₆₁	1	2	yes	—
388	#3078	C₂×C₆₁	1	1	yes	characteristic, complemented
389	#3077	C₂×C₆₁	1	1	yes	characteristic
390	#2960	C₂×C₆₁	1	1	yes	characteristic, complemented
391	#2949	C₂×C₆₁	1	2	yes	—
392	C₂×C₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic
393	C₂×C₆₁	—	2	2	no	—
394	C₂×C₆₁	—	4	4	no	—
395	C₂×C₆₁	C₂×D₄×Q₈	1	1	yes	characteristic
396	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
397	C₂×C₆₁	#3584	1	1	yes	characteristic
398	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
399	Q₈²	—	2	1	no	—
400	Q₈²	C₂²×C₆₁	1	2	yes	complemented
401	#557	—	2	1	no	—
402	#557	—	2	2	no	—
403	#557	C₂²×C₆₁	1	2	yes	complemented
404	#557	C₂²×C₆₁	1	4	yes	complemented
405	#554	—	2	1	no	—
406	#554	—	2	2	no	—
407	#554	C₂²×C₆₁	1	2	yes	—
408	#554	C₂²×C₆₁	1	4	yes	—
409	D₄×Q₈	—	2	1	no	—
410	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
411	#544	—	2	2	no	—
412	#544	C₂²×C₆₁	1	2	yes	—
413	#544	C₂²×C₆₁	1	2	yes	—
414	#543	—	2	2	no	—
415	#533	—	2	2	no	—
416	#533	C₂²×C₆₁	1	1	yes	characteristic
417	#533	C₂²×C₆₁	1	1	yes	characteristic
418	#533	C₂²×C₆₁	1	1	yes	characteristic
419	C₂×C₂²⋊Q₈	—	2	2	no	—
420	#519	C₂²×C₆₁	1	2	yes	—
421	#518	C₂²×C₆₁	1	2	yes	—
422	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
423	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
424	#501	C₂²×C₆₁	1	4	yes	complemented
425	#501	C₂²×C₆₁	1	4	yes	complemented
426	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
427	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
428	#499	C₂²×C₆₁	1	2	yes	complemented
429	#499	C₂²×C₆₁	1	4	yes	complemented
430	#499	C₂²×C₆₁	1	2	yes	complemented
431	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
432	#498	C₂²×C₆₁	1	4	yes	complemented
433	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
434	#479	C₂²×C₆₁	1	4	yes	complemented
435	#479	C₂²×C₆₁	1	4	yes	complemented
436	#479	C₂²×C₆₁	1	4	yes	complemented
437	#478	C₂²×C₆₁	1	4	yes	—
438	#478	C₂²×C₆₁	1	4	yes	—
439	#478	C₂²×C₆₁	1	4	yes	—
440	#477	C₂²×C₆₁	1	2	yes	complemented
441	#477	C₂²×C₆₁	1	4	yes	complemented
442	#476	C₂²×C₆₁	1	2	yes	—
443	#476	C₂²×C₆₁	1	4	yes	—
444	#475	C₂²×C₆₁	1	2	yes	complemented
445	#475	C₂²×C₆₁	1	4	yes	complemented
446	#474	C₂²×C₆₁	1	2	yes	—
447	#474	C₂²×C₆₁	1	4	yes	—
448	#446	C₂²×C₆₁	1	2	yes	complemented
449	#446	C₂²×C₆₁	1	2	yes	complemented
450	C₈×Q₈	C₂²×C₆₁	1	2	yes	complemented
451	C₈×Q₈	C₂²×C₆₁	1	2	yes	complemented
452	#440	C₂²×C₆₁	1	4	yes	—
453	#440	C₂²×C₆₁	1	4	yes	—
454	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
455	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	—
456	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
457	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	—
458	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
459	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
460	#428	C₂²×C₆₁	1	2	yes	—
461	#428	C₂²×C₆₁	1	2	yes	—
462	#427	C₂²×C₆₁	1	2	yes	—
463	#427	C₂²×C₆₁	1	2	yes	—
464	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
465	#424	C₂²×C₆₁	1	2	yes	—
466	#423	C₂²×C₆₁	1	1	yes	characteristic
467	#419	C₂²×C₆₁	1	2	yes	—
468	#418	C₂²×C₆₁	1	2	yes	—
469	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
470	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
471	#405	C₂²×C₆₁	1	2	yes	—
472	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
473	C₆₁	#61371	1	1	yes	characteristic, direct product factor, Sylow
474	C₂²×Q₈	—	2	2	no	—
475	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
476	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
477	C₂³×C₄	—	2	1	no	—
478	C₂×SD₁₆	Q₈×C₆₁	1	8	yes	complemented
479	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
480	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
481	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
482	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
483	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
484	C₄⋊Q₈	—	2	2	no	—
485	C₄⋊Q₈	—	2	4	no	—
486	C₄⋊Q₈	—	2	2	no	—
487	C₄⋊Q₈	—	2	4	no	—
488	C₄⋊Q₈	—	2	2	no	—
489	C₄⋊Q₈	—	2	2	no	—
490	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
491	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
492	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
493	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
494	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
495	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
496	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
497	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
498	#125	—	2	4	no	—
499	#125	—	2	4	no	—
500	#125	—	2	4	no	—
501	#125	—	2	2	no	—
502	#125	—	2	2	no	—
503	#125	D₄×C₆₁	1	2	yes	—
504	#125	C₂³×C₆₁	1	2	yes	—
505	#125	C₂³×C₆₁	1	2	yes	—
506	#125	C₂³×C₆₁	1	4	yes	—
507	#125	C₂³×C₆₁	1	4	yes	—
508	C₂²⋊Q₈	—	2	2	no	—
509	C₂²⋊Q₈	—	2	4	no	—
510	C₂²⋊Q₈	—	2	1	no	—
511	C₂²⋊Q₈	—	2	1	no	—
512	C₂²⋊Q₈	—	2	1	no	—
513	C₂²⋊Q₈	—	2	1	no	—
514	C₂²⋊Q₈	—	2	2	no	—
515	C₂²⋊Q₈	—	2	4	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	—	2	4	no	—
518	C₂²⋊Q₈	—	2	4	no	—
519	C₂²⋊Q₈	—	2	4	no	—
520	C₂²⋊Q₈	—	2	4	no	—
521	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
522	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
523	C₄×Q₈	—	2	2	no	—
524	C₄×Q₈	—	2	2	no	—
525	C₄×Q₈	—	2	2	no	—
526	C₄×Q₈	—	2	4	no	—
527	C₄×Q₈	—	2	2	no	—
528	C₄×Q₈	—	2	1	no	—
529	C₄×Q₈	—	2	1	no	—
530	C₄×Q₈	—	2	1	no	—
531	C₄×Q₈	—	2	1	no	—
532	C₄×Q₈	—	2	1	no	—
533	C₄×Q₈	—	2	1	no	—
534	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
535	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
536	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
537	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
538	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
539	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	1	no	—
543	C₄×D₄	—	2	1	no	—
544	C₄×D₄	C₂³×C₆₁	1	2	yes	—
545	C₄×D₄	C₂³×C₆₁	1	2	yes	—
546	C₄×D₄	C₂³×C₆₁	1	4	yes	—
547	C₄×D₄	C₂³×C₆₁	1	4	yes	—
548	#117	—	2	4	no	—
549	#117	C₂³×C₆₁	1	2	yes	—
550	#117	C₂³×C₆₁	1	2	yes	—
551	#117	C₂³×C₆₁	1	2	yes	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	4	no	—
554	C₂×C₄⋊C₄	—	2	2	no	—
555	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₂²⋊C₄	—	2	4	no	—
559	C₂×C₄²	—	2	1	no	—
560	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
561	#107	C₂³×C₆₁	1	2	yes	—
562	#107	C₂³×C₆₁	1	2	yes	—
563	#107	C₂³×C₆₁	1	2	yes	—
564	#107	C₂³×C₆₁	1	2	yes	—
565	#107	C₂³×C₆₁	1	4	yes	—
566	#107	C₂³×C₆₁	1	4	yes	—
567	#106	C₂³×C₆₁	1	2	yes	—
568	#106	C₂³×C₆₁	1	2	yes	—
569	#106	C₂³×C₆₁	1	2	yes	—
570	#106	C₂³×C₆₁	1	2	yes	—
571	#106	C₂³×C₆₁	1	2	yes	—
572	#106	C₂³×C₆₁	1	2	yes	—
573	#106	C₂³×C₆₁	1	4	yes	—
574	#106	C₂³×C₆₁	1	4	yes	—
575	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
576	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
577	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
578	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
579	#103	C₂³×C₆₁	1	2	yes	—
580	#103	C₂³×C₆₁	1	2	yes	—
581	#103	C₂³×C₆₁	1	4	yes	—
582	#103	C₂³×C₆₁	1	4	yes	—
583	#102	C₂³×C₆₁	1	2	yes	—
584	#102	C₂³×C₆₁	1	2	yes	—
585	#102	C₂³×C₆₁	1	4	yes	—
586	#102	C₂³×C₆₁	1	4	yes	—
587	#97	C₂³×C₆₁	1	4	yes	—
588	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
589	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
590	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
591	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
592	C₄×C₈	C₂³×C₆₁	1	4	yes	—
593	C₂⁴	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	4	no	—
600	C₂×Q₈	—	2	4	no	—
601	C₂×Q₈	—	2	2	no	—
602	C₂×Q₈	—	8	4	no	—
603	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
604	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
605	C₂×Q₈	C₂×Q₈×C₆₁	1	4	yes	complemented
606	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	C₂×Q₈×C₆₁	1	4	yes	—
610	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	8	2	no	—
619	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
622	SD₁₆	C₂×Q₈×C₆₁	1	8	yes	complemented
623	SD₁₆	C₂×Q₈×C₆₁	1	8	yes	complemented
624	M₁₆	—	2	4	no	—
625	C₂×C₈	—	2	2	no	—
626	C₂×C₈	C₂×Q₈×C₆₁	1	4	yes	complemented
627	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
628	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
629	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
630	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
631	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
653	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
654	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
655	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
656	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
657	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
658	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
659	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
660	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
661	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
662	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
663	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
671	C₄²	—	2	2	no	—
672	C₄²	—	2	2	no	—
673	C₄²	—	2	4	no	—
674	C₄²	—	2	4	no	—
675	C₄²	—	2	2	no	—
676	C₄²	—	2	2	no	—
677	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
678	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
679	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
680	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
681	C₄²	C₂⁴×C₆₁	1	4	yes	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	4	no	—
684	C₂³	—	8	1	no	—
685	C₂³	—	8	1	no	—
686	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
687	Q₈	—	2	4	no	—
688	Q₈	—	2	4	no	—
689	Q₈	—	2	2	no	—
690	Q₈	—	4	2	no	—
691	Q₈	—	4	2	no	—
692	Q₈	—	4	2	no	—
693	Q₈	—	8	1	no	—
694	Q₈	—	8	1	no	—
695	Q₈	—	8	4	no	—
696	Q₈	—	8	4	no	—
697	Q₈	C₂²×Q₈×C₆₁	1	4	yes	—
698	D₄	—	2	4	no	—
699	D₄	—	2	2	no	—
700	D₄	C₂²×Q₈×C₆₁	1	4	yes	—
701	C₂×C₄	—	2	4	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	—	4	1	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	—	8	2	no	—
714	C₂×C₄	—	8	4	no	—
715	C₂×C₄	—	8	1	no	—
716	C₂×C₄	—	8	1	no	—
717	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
718	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
719	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
720	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
721	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
722	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
723	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
724	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
725	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
726	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
727	C₈	—	2	1	no	—
728	C₈	—	2	1	no	—
729	C₈	—	2	4	no	—
730	C₈	C₂²×Q₈×C₆₁	1	2	yes	—
731	C₈	C₂²×Q₈×C₆₁	1	2	yes	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	8	4	no	—
738	C₂²	D₄×Q₈×C₆₁	1	2	yes	—
739	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
740	C₄	—	2	1	no	—
741	C₄	—	2	4	no	—
742	C₄	—	2	1	no	—
743	C₄	—	2	1	no	—
744	C₄	—	2	4	no	—
745	C₄	—	2	4	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	D₄×Q₈×C₆₁	1	2	yes	—
753	C₄	C₆₁×#577	1	2	yes	—
754	C₄	C₂³×Q₈×C₆₁	1	1	yes	characteristic
755	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
756	C₂	—	2	2	no	—
757	C₂	—	4	4	no	—
758	C₂	C₂×D₄×Q₈×C₆₁	1	1	yes	characteristic
759	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
760	C₂	C₆₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₂²×D₄×C₆₁	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3502	C₂	semidirect
3. C₆₁×#3388	C₂	semidirect
4. C₆₁×#3386	C₂	semidirect
5. C₆₁×#3385	C₂	semidirect
6. C₆₁×#3381	C₂	semidirect
7. C₆₁×#3381	C₂	semidirect
8. Q₈×SD₁₆×C₆₁	C₂	semidirect
9. C₆₁×#3163	C₂	semidirect
10. C₆₁×#3160	C₂	semidirect
11. C₆₁×#3082	C₂	semidirect
13. C₆₁×#3078	C₂	semidirect
15. C₆₁×#2960	C₂	semidirect
20. Q₈²×C₆₁	C₂²	semidirect
23. C₆₁×#557	C₂²	semidirect
24. C₆₁×#557	C₂²	semidirect
44. C₆₁×#501	C₂²	semidirect
45. C₆₁×#501	C₂²	semidirect
46. C₆₁×#500	C₂²	semidirect
47. C₆₁×#500	C₂²	semidirect
48. C₆₁×#499	C₂²	semidirect
49. C₆₁×#499	C₂²	semidirect
50. C₆₁×#499	C₂²	semidirect
51. C₆₁×#498	C₂²	semidirect
52. C₆₁×#498	C₂²	semidirect
53. C₆₁×#498	C₂²	semidirect
54. C₆₁×#479	C₂²	semidirect
55. C₆₁×#479	C₂²	semidirect
56. C₆₁×#479	C₂²	semidirect
60. C₆₁×#477	C₂²	semidirect
61. C₆₁×#477	C₂²	semidirect
64. C₆₁×#475	C₂²	semidirect
65. C₆₁×#475	C₂²	semidirect
68. C₆₁×#446	C₂²	semidirect
69. C₆₁×#446	C₂²	semidirect
70. C₈×Q₈×C₆₁	C₂²	semidirect
71. C₈×Q₈×C₆₁	C₂²	semidirect
97. C₂×SD₁₆×C₆₁	Q₈	semidirect
224. C₂×Q₈×C₆₁	C₂×Q₈	semidirect
241. SD₁₆×C₆₁	C₂×Q₈	semidirect
242. SD₁₆×C₆₁	C₂×Q₈	semidirect
245. C₂×C₈×C₆₁	C₂×Q₈	semidirect
351. #61371	C₆₁	direct (N × H)
376. #3502	C₂×C₆₁	semidirect
378. #3388	C₂×C₆₁	semidirect
379. #3386	C₂×C₆₁	semidirect
380. #3385	C₂×C₆₁	semidirect
381. #3381	C₂×C₆₁	semidirect
382. #3381	C₂×C₆₁	semidirect
383. Q₈×SD₁₆	C₂×C₆₁	semidirect
384. #3163	C₂×C₆₁	semidirect
385. #3160	C₂×C₆₁	semidirect
386. #3082	C₂×C₆₁	semidirect
388. #3078	C₂×C₆₁	semidirect
390. #2960	C₂×C₆₁	semidirect
400. Q₈²	C₂²×C₆₁	semidirect
403. #557	C₂²×C₆₁	semidirect
404. #557	C₂²×C₆₁	semidirect
424. #501	C₂²×C₆₁	semidirect
425. #501	C₂²×C₆₁	semidirect
426. #500	C₂²×C₆₁	semidirect
427. #500	C₂²×C₆₁	semidirect
428. #499	C₂²×C₆₁	semidirect
429. #499	C₂²×C₆₁	semidirect
430. #499	C₂²×C₆₁	semidirect
431. #498	C₂²×C₆₁	semidirect
432. #498	C₂²×C₆₁	semidirect
433. #498	C₂²×C₆₁	semidirect
434. #479	C₂²×C₆₁	semidirect
435. #479	C₂²×C₆₁	semidirect
436. #479	C₂²×C₆₁	semidirect
440. #477	C₂²×C₆₁	semidirect
441. #477	C₂²×C₆₁	semidirect
444. #475	C₂²×C₆₁	semidirect
445. #475	C₂²×C₆₁	semidirect
448. #446	C₂²×C₆₁	semidirect
449. #446	C₂²×C₆₁	semidirect
450. C₈×Q₈	C₂²×C₆₁	semidirect
451. C₈×Q₈	C₂²×C₆₁	semidirect
473. C₆₁	#61371	direct (N × H)
478. C₂×SD₁₆	Q₈×C₆₁	semidirect
605. C₂×Q₈	C₂×Q₈×C₆₁	semidirect
622. SD₁₆	C₂×Q₈×C₆₁	semidirect
623. SD₁₆	C₂×Q₈×C₆₁	semidirect
626. C₂×C₈	C₂×Q₈×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3502	2
C₆₁×#3501	2
C₆₁×#3388	2
C₆₁×#3386	2
C₆₁×#3385	2
C₆₁×#3381	2
Q₈×SD₁₆×C₆₁	2
C₆₁×#3163	2
C₆₁×#3160	2
C₆₁×#3082	2
C₆₁×#3081	2
C₆₁×#3078	2
C₆₁×#3077	2
C₆₁×#2960	2
C₆₁×#2949	2
C₂×C₄×SD₁₆×C₆₁	2
#61371	61

Subgroups — C61×#61371 #29564804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61371 #29564804