Subgroups — C₆₁×#61792 #29565225

Order 15616.

1774 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3356	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3354	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3335	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3335	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3332	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3331	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3304	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3303	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3204	C₂	1	4	yes	maximal, complemented
14	C₆₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3099	C₂	1	4	yes	maximal, complemented
17	C₆₁×#2979	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#562	—	2	2	no	—
19	C₆₁×#556	C₂²	1	2	yes	—
20	C₆₁×#555	C₂²	1	2	yes	—
21	C₆₁×#554	—	2	1	no	—
22	C₆₁×#554	C₂²	1	2	yes	—
23	C₆₁×#554	C₂²	1	2	yes	—
24	C₆₁×#553	—	2	2	no	—
25	C₆₁×#550	—	2	1	no	—
26	C₆₁×#550	C₂²	1	2	yes	—
27	C₆₁×#548	—	2	2	no	—
28	C₆₁×#547	C₂²	1	2	yes	—
29	C₆₁×#547	C₂²	1	2	yes	—
30	C₆₁×#547	C₂²	1	2	yes	—
31	C₆₁×#542	—	2	2	no	—
32	C₆₁×#540	—	2	2	no	—
33	C₆₁×#537	—	2	2	no	—
34	C₆₁×#537	C₂²	1	4	yes	—
35	C₆₁×#537	C₂²	1	2	yes	—
36	C₆₁×#533	—	2	1	no	—
37	C₆₁×#533	C₂²	1	1	yes	characteristic
38	C₆₁×#532	—	2	1	no	—
39	C₆₁×#532	C₂²	1	1	yes	characteristic
40	C₆₁×#532	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#520	C₂²	1	2	yes	—
43	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
44	C₆₁×#498	C₂²	1	2	yes	—
45	C₆₁×#498	C₂²	1	2	yes	—
46	C₆₁×#487	C₂²	1	2	yes	—
47	C₆₁×#486	C₂²	1	2	yes	—
48	C₆₁×#485	C₂²	1	4	yes	—
49	C₆₁×#485	C₂²	1	2	yes	—
50	C₆₁×#483	C₂²	1	4	yes	—
51	C₆₁×#483	C₂²	1	4	yes	—
52	C₆₁×#483	C₂²	1	4	yes	—
53	C₆₁×#482	C₂²	1	4	yes	—
54	C₆₁×#482	C₂²	1	2	yes	—
55	C₆₁×#481	C₂²	1	4	yes	—
56	C₆₁×#481	C₂²	1	4	yes	—
57	C₆₁×#481	C₂²	1	4	yes	—
58	C₆₁×#477	C₂²	1	1	yes	characteristic
59	C₆₁×#476	C₂²	1	2	yes	—
60	C₆₁×#476	C₂²	1	2	yes	—
61	C₆₁×#476	C₂²	1	1	yes	characteristic
62	C₆₁×#475	C₂²	1	2	yes	—
63	C₆₁×#475	C₂²	1	2	yes	—
64	C₆₁×#475	C₂²	1	1	yes	characteristic
65	C₆₁×#474	C₂²	1	1	yes	characteristic
66	C₆₁×#470	C₂²	1	4	yes	—
67	C₆₁×#469	C₂²	1	4	yes	—
68	C₆₁×#465	C₂²	1	4	yes	—
69	C₆₁×#465	C₂²	1	4	yes	—
70	C₆₁×#462	C₂²	1	1	yes	characteristic
71	C₆₁×#461	C₂²	1	1	yes	characteristic
72	C₆₁×#460	C₂²	1	1	yes	characteristic
73	C₆₁×#459	C₂²	1	1	yes	characteristic
74	C₆₁×#452	C₂²	1	4	yes	—
75	C₆₁×#452	C₂²	1	2	yes	—
76	C₆₁×#449	C₂²	1	4	yes	—
77	C₆₁×#449	C₂²	1	2	yes	—
78	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
79	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
80	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
81	C₄×D₈×C₆₁	C₂²	1	2	yes	—
82	C₆₁×#436	C₂²	1	2	yes	—
83	C₆₁×#436	C₂²	1	2	yes	—
84	C₈×D₄×C₆₁	C₂²	1	2	yes	—
85	C₈×D₄×C₆₁	C₂²	1	2	yes	—
86	C₆₁×#431	C₂²	1	1	yes	characteristic
87	C₆₁×#431	C₂²	1	1	yes	characteristic
88	C₆₁×#428	C₂²	1	4	yes	—
89	C₂×#106×C₆₁	C₂²	1	4	yes	—
90	C₆₁×#417	C₂²	1	4	yes	—
91	C₆₁×#416	C₂²	1	4	yes	—
92	C₆₁×#408	C₂²	1	4	yes	—
93	C₂×#41×C₆₁	—	2	2	no	—
94	C₂×#41×C₆₁	—	2	2	no	—
95	C₂×#41×C₆₁	—	2	1	no	—
96	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
97	C₂×#41×C₆₁	C₂³	1	4	yes	—
98	C₂×#41×C₆₁	C₂³	1	2	yes	—
99	C₂²×Q₈×C₆₁	—	2	1	no	—
100	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
101	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
103	C₂×D₈×C₆₁	C₂³	1	2	yes	—
104	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
105	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
106	C₄⋊Q₈×C₆₁	—	2	1	no	—
107	C₄⋊Q₈×C₆₁	—	2	1	no	—
108	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
109	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
114	#127×C₆₁	—	2	2	no	—
115	#127×C₆₁	D₄	1	1	yes	characteristic
116	#127×C₆₁	C₂³	1	1	yes	characteristic
117	#126×C₆₁	—	2	4	no	—
118	#125×C₆₁	—	2	2	no	—
119	#125×C₆₁	—	2	2	no	—
120	#125×C₆₁	—	2	1	no	—
121	#124×C₆₁	—	2	2	no	—
122	#124×C₆₁	—	2	4	no	—
123	#124×C₆₁	—	2	1	no	—
124	#124×C₆₁	D₄	1	2	yes	—
125	#123×C₆₁	—	2	4	no	—
126	#123×C₆₁	—	2	4	no	—
127	#123×C₆₁	—	2	4	no	—
128	C₂²⋊Q₈×C₆₁	—	2	2	no	—
129	C₂²⋊Q₈×C₆₁	—	2	4	no	—
130	C₂²⋊Q₈×C₆₁	—	2	1	no	—
131	C₂²⋊Q₈×C₆₁	—	2	2	no	—
132	C₂²⋊Q₈×C₆₁	—	2	2	no	—
133	C₂²⋊Q₈×C₆₁	—	2	4	no	—
134	C₂²⋊Q₈×C₆₁	—	2	4	no	—
135	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
136	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
137	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
138	#121×C₆₁	—	2	2	no	—
139	#121×C₆₁	—	2	2	no	—
140	#121×C₆₁	—	2	4	no	—
141	#121×C₆₁	—	2	4	no	—
142	#121×C₆₁	—	2	2	no	—
143	#121×C₆₁	—	2	4	no	—
144	#121×C₆₁	—	2	4	no	—
145	#121×C₆₁	—	2	1	no	—
146	#121×C₆₁	—	2	4	no	—
147	#121×C₆₁	D₄	1	2	yes	—
148	#121×C₆₁	D₄	1	2	yes	—
149	#121×C₆₁	C₂³	1	2	yes	—
150	#121×C₆₁	C₂³	1	4	yes	—
151	#121×C₆₁	C₂³	1	4	yes	—
152	C₄×Q₈×C₆₁	—	2	2	no	—
153	C₄×Q₈×C₆₁	—	2	2	no	—
154	C₄×Q₈×C₆₁	—	2	1	no	—
155	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
156	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
158	C₄×D₄×C₆₁	—	2	2	no	—
159	C₄×D₄×C₆₁	—	2	2	no	—
160	C₄×D₄×C₆₁	—	2	2	no	—
161	C₄×D₄×C₆₁	—	2	4	no	—
162	C₄×D₄×C₆₁	—	2	1	no	—
163	C₄×D₄×C₆₁	—	2	1	no	—
164	C₄×D₄×C₆₁	—	2	2	no	—
165	C₄×D₄×C₆₁	—	2	1	no	—
166	C₄×D₄×C₆₁	C₂³	1	2	yes	—
167	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₆₁	C₂³	1	2	yes	—
170	C₄×D₄×C₆₁	C₂³	1	2	yes	—
171	#117×C₆₁	—	2	1	no	—
172	#117×C₆₁	—	2	2	no	—
173	#117×C₆₁	—	2	1	no	—
174	#117×C₆₁	C₂³	1	4	yes	—
175	#117×C₆₁	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
177	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
178	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
180	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
181	C₂×C₄²×C₆₁	—	2	1	no	—
182	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
183	#107×C₆₁	C₂³	1	2	yes	—
184	#107×C₆₁	C₂³	1	2	yes	—
185	#106×C₆₁	C₂³	1	2	yes	—
186	#106×C₆₁	C₂³	1	2	yes	—
187	#106×C₆₁	C₂³	1	4	yes	—
188	#106×C₆₁	C₂³	1	4	yes	—
189	#106×C₆₁	C₂³	1	4	yes	—
190	#106×C₆₁	C₂³	1	4	yes	—
191	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
192	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
193	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
194	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
195	#103×C₆₁	C₂³	1	2	yes	—
196	#103×C₆₁	C₂³	1	4	yes	—
197	#103×C₆₁	C₂³	1	2	yes	—
198	#103×C₆₁	C₂³	1	4	yes	—
199	#103×C₆₁	C₂³	1	2	yes	—
200	#103×C₆₁	C₂³	1	2	yes	—
201	#102×C₆₁	C₂³	1	2	yes	—
202	#102×C₆₁	C₂³	1	4	yes	—
203	#102×C₆₁	C₂³	1	2	yes	—
204	#102×C₆₁	C₂³	1	4	yes	—
205	#102×C₆₁	C₂³	1	2	yes	—
206	#102×C₆₁	C₂³	1	2	yes	—
207	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
208	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
209	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
210	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
211	C₄×C₈×C₆₁	C₂³	1	2	yes	—
212	C₄×C₈×C₆₁	C₂³	1	2	yes	—
213	#41×C₆₁	—	4	2	no	—
214	#41×C₆₁	—	4	2	no	—
215	#41×C₆₁	—	4	1	no	—
216	#41×C₆₁	—	4	1	no	—
217	#41×C₆₁	—	4	4	no	—
218	#41×C₆₁	—	4	4	no	—
219	#41×C₆₁	—	8	2	no	—
220	#41×C₆₁	—	8	4	no	—
221	#41×C₆₁	—	8	4	no	—
222	C₂×Q₈×C₆₁	—	2	1	no	—
223	C₂×Q₈×C₆₁	—	2	2	no	—
224	C₂×Q₈×C₆₁	—	2	1	no	—
225	C₂×Q₈×C₆₁	—	2	2	no	—
226	C₂×Q₈×C₆₁	—	8	2	no	—
227	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
229	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
230	C₂×D₄×C₆₁	—	2	1	no	—
231	C₂×D₄×C₆₁	—	2	2	no	—
232	C₂×D₄×C₆₁	—	2	4	no	—
233	C₂×D₄×C₆₁	—	2	4	no	—
234	C₂×D₄×C₆₁	—	2	4	no	—
235	C₂×D₄×C₆₁	—	2	1	no	—
236	C₂×D₄×C₆₁	—	2	1	no	—
237	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
239	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
240	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
241	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
242	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₆₁	—	2	2	no	—
244	C₂²×C₄×C₆₁	—	2	4	no	—
245	C₂²×C₄×C₆₁	—	2	4	no	—
246	C₂²×C₄×C₆₁	—	2	1	no	—
247	C₂²×C₄×C₆₁	—	2	1	no	—
248	C₂²×C₄×C₆₁	—	2	1	no	—
249	C₂²×C₄×C₆₁	—	2	2	no	—
250	C₂²×C₄×C₆₁	—	2	4	no	—
251	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
255	Q₁₆×C₆₁	—	4	2	no	—
256	SD₁₆×C₆₁	—	4	2	no	—
257	SD₁₆×C₆₁	—	4	2	no	—
258	D₈×C₆₁	—	4	2	no	—
259	M₁₆×C₆₁	—	4	4	no	—
260	C₂×C₈×C₆₁	—	4	4	no	—
261	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
262	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
263	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
264	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₆₁	—	2	1	no	—
266	C₄⋊C₄×C₆₁	—	2	2	no	—
267	C₄⋊C₄×C₆₁	—	2	4	no	—
268	C₄⋊C₄×C₆₁	—	2	2	no	—
269	C₄⋊C₄×C₆₁	—	2	2	no	—
270	C₄⋊C₄×C₆₁	—	2	4	no	—
271	C₄⋊C₄×C₆₁	—	2	4	no	—
272	C₄⋊C₄×C₆₁	—	2	1	no	—
273	C₄⋊C₄×C₆₁	—	2	1	no	—
274	C₄⋊C₄×C₆₁	—	2	1	no	—
275	C₄⋊C₄×C₆₁	—	2	1	no	—
276	C₄⋊C₄×C₆₁	—	2	1	no	—
277	C₄⋊C₄×C₆₁	—	2	2	no	—
278	C₄⋊C₄×C₆₁	—	2	4	no	—
279	C₄⋊C₄×C₆₁	—	2	2	no	—
280	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
283	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
284	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
285	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
287	C₂²⋊C₄×C₆₁	—	2	2	no	—
288	C₂²⋊C₄×C₆₁	—	2	1	no	—
289	C₂²⋊C₄×C₆₁	—	2	4	no	—
290	C₂²⋊C₄×C₆₁	—	2	4	no	—
291	C₂²⋊C₄×C₆₁	—	2	4	no	—
292	C₂²⋊C₄×C₆₁	—	2	1	no	—
293	C₂²⋊C₄×C₆₁	—	2	1	no	—
294	C₂²⋊C₄×C₆₁	—	2	4	no	—
295	C₂²⋊C₄×C₆₁	—	2	4	no	—
296	C₂²⋊C₄×C₆₁	—	2	2	no	—
297	C₂²⋊C₄×C₆₁	—	2	2	no	—
298	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
299	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
300	C₄²×C₆₁	—	2	1	no	—
301	C₄²×C₆₁	—	2	1	no	—
302	C₄²×C₆₁	—	2	1	no	—
303	C₄²×C₆₁	—	2	4	no	—
304	C₄²×C₆₁	—	2	2	no	—
305	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
308	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
309	C₂³×C₆₁	—	2	1	no	—
310	C₂³×C₆₁	—	2	2	no	—
311	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
312	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
313	Q₈×C₆₁	—	2	1	no	—
314	Q₈×C₆₁	—	2	2	no	—
315	Q₈×C₆₁	—	2	1	no	—
316	Q₈×C₆₁	—	2	2	no	—
317	Q₈×C₆₁	—	4	2	no	—
318	Q₈×C₆₁	—	4	4	no	—
319	Q₈×C₆₁	—	4	2	no	—
320	Q₈×C₆₁	—	8	2	no	—
321	Q₈×C₆₁	—	8	1	no	—
322	D₄×C₆₁	—	2	4	no	—
323	D₄×C₆₁	—	2	4	no	—
324	D₄×C₆₁	—	2	1	no	—
325	D₄×C₆₁	—	2	2	no	—
326	D₄×C₆₁	—	2	1	no	—
327	D₄×C₆₁	—	2	2	no	—
328	D₄×C₆₁	—	4	2	no	—
329	D₄×C₆₁	—	4	4	no	—
330	D₄×C₆₁	—	4	2	no	—
331	D₄×C₆₁	—	4	2	no	—
332	D₄×C₆₁	—	8	1	no	—
333	D₄×C₆₁	—	8	4	no	—
334	D₄×C₆₁	—	8	2	no	—
335	D₄×C₆₁	—	8	4	no	—
336	D₄×C₆₁	—	8	4	no	—
337	C₂×C₄×C₆₁	—	2	2	no	—
338	C₂×C₄×C₆₁	—	2	2	no	—
339	C₂×C₄×C₆₁	—	2	4	no	—
340	C₂×C₄×C₆₁	—	2	4	no	—
341	C₂×C₄×C₆₁	—	2	1	no	—
342	C₂×C₄×C₆₁	—	2	1	no	—
343	C₂×C₄×C₆₁	—	2	1	no	—
344	C₂×C₄×C₆₁	—	2	1	no	—
345	C₂×C₄×C₆₁	—	2	1	no	—
346	C₂×C₄×C₆₁	—	2	2	no	—
347	C₂×C₄×C₆₁	—	2	2	no	—
348	C₂×C₄×C₆₁	—	2	4	no	—
349	C₂×C₄×C₆₁	—	2	2	no	—
350	C₂×C₄×C₆₁	—	4	2	no	—
351	C₂×C₄×C₆₁	—	4	2	no	—
352	C₂×C₄×C₆₁	—	4	2	no	—
353	C₂×C₄×C₆₁	—	4	4	no	—
354	C₂×C₄×C₆₁	—	8	4	no	—
355	C₂×C₄×C₆₁	—	8	2	no	—
356	C₂×C₄×C₆₁	—	8	4	no	—
357	C₂×C₄×C₆₁	—	8	4	no	—
358	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
360	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
365	C₈×C₆₁	—	2	2	no	—
366	C₈×C₆₁	—	2	2	no	—
367	C₈×C₆₁	—	2	2	no	—
368	C₈×C₆₁	—	2	2	no	—
369	#61792	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
370	C₂²×C₆₁	—	2	1	no	—
371	C₂²×C₆₁	—	2	4	no	—
372	C₂²×C₆₁	—	2	1	no	—
373	C₂²×C₆₁	—	2	1	no	—
374	C₂²×C₆₁	—	2	4	no	—
375	C₂²×C₆₁	—	2	4	no	—
376	C₂²×C₆₁	—	4	1	no	—
377	C₂²×C₆₁	—	4	2	no	—
378	C₂²×C₆₁	—	4	2	no	—
379	C₂²×C₆₁	—	4	1	no	—
380	C₂²×C₆₁	—	4	1	no	—
381	C₂²×C₆₁	—	4	2	no	—
382	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
383	C₄×C₆₁	—	2	1	no	—
384	C₄×C₆₁	—	2	4	no	—
385	C₄×C₆₁	—	2	1	no	—
386	C₄×C₆₁	—	2	1	no	—
387	C₄×C₆₁	—	4	1	no	—
388	C₄×C₆₁	—	4	2	no	—
389	C₄×C₆₁	—	4	1	no	—
390	C₄×C₆₁	—	4	1	no	—
391	C₄×C₆₁	—	4	2	no	—
392	C₄×C₆₁	—	4	2	no	—
393	C₄×C₆₁	—	4	4	no	—
394	C₄×C₆₁	#577	1	2	yes	—
395	C₄×C₆₁	#577	1	2	yes	—
396	C₄×C₆₁	#585	1	1	yes	characteristic
397	C₄×C₆₁	#585	1	1	yes	characteristic
398	#3548	C₂×C₆₁	1	1	yes	characteristic, complemented
399	#3511	C₂×C₆₁	1	1	yes	characteristic, complemented
400	#3356	C₂×C₆₁	1	2	yes	complemented
401	#3354	C₂×C₆₁	1	2	yes	complemented
402	#3335	C₂×C₆₁	1	2	yes	complemented
403	#3335	C₂×C₆₁	1	2	yes	complemented
404	#3332	C₂×C₆₁	1	2	yes	complemented
405	#3331	C₂×C₆₁	1	2	yes	complemented
406	#3304	C₂×C₆₁	1	2	yes	complemented
407	#3303	C₂×C₆₁	1	2	yes	complemented
408	#3229	C₂×C₆₁	1	1	yes	characteristic, complemented
409	#3227	C₂×C₆₁	1	1	yes	characteristic, complemented
410	#3204	C₂×C₆₁	1	4	yes	complemented
411	#3107	C₂×C₆₁	1	1	yes	characteristic, complemented
412	#3106	C₂×C₆₁	1	1	yes	characteristic, complemented
413	#3099	C₂×C₆₁	1	4	yes	complemented
414	#2979	C₂×C₆₁	1	1	yes	characteristic, complemented
415	C₂×C₆₁	—	4	1	no	—
416	C₂×C₆₁	—	4	4	no	—
417	C₂×C₆₁	—	8	1	no	—
418	C₂×C₆₁	—	8	2	no	—
419	C₂×C₆₁	#3485	1	1	yes	characteristic
420	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
421	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
422	#562	—	2	2	no	—
423	#556	C₂²×C₆₁	1	2	yes	—
424	#555	C₂²×C₆₁	1	2	yes	—
425	#554	—	2	1	no	—
426	#554	C₂²×C₆₁	1	2	yes	—
427	#554	C₂²×C₆₁	1	2	yes	—
428	#553	—	2	2	no	—
429	#550	—	2	1	no	—
430	#550	C₂²×C₆₁	1	2	yes	—
431	#548	—	2	2	no	—
432	#547	C₂²×C₆₁	1	2	yes	—
433	#547	C₂²×C₆₁	1	2	yes	—
434	#547	C₂²×C₆₁	1	2	yes	—
435	#542	—	2	2	no	—
436	#540	—	2	2	no	—
437	#537	—	2	2	no	—
438	#537	C₂²×C₆₁	1	4	yes	—
439	#537	C₂²×C₆₁	1	2	yes	—
440	#533	—	2	1	no	—
441	#533	C₂²×C₆₁	1	1	yes	characteristic
442	#532	—	2	1	no	—
443	#532	C₂²×C₆₁	1	1	yes	characteristic
444	#532	C₂²×C₆₁	1	1	yes	characteristic
445	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
446	#520	C₂²×C₆₁	1	2	yes	—
447	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
448	#498	C₂²×C₆₁	1	2	yes	—
449	#498	C₂²×C₆₁	1	2	yes	—
450	#487	C₂²×C₆₁	1	2	yes	—
451	#486	C₂²×C₆₁	1	2	yes	—
452	#485	C₂²×C₆₁	1	2	yes	—
453	#485	C₂²×C₆₁	1	4	yes	—
454	#483	C₂²×C₆₁	1	4	yes	—
455	#483	C₂²×C₆₁	1	4	yes	—
456	#483	C₂²×C₆₁	1	4	yes	—
457	#482	C₂²×C₆₁	1	4	yes	—
458	#482	C₂²×C₆₁	1	2	yes	—
459	#481	C₂²×C₆₁	1	4	yes	—
460	#481	C₂²×C₆₁	1	4	yes	—
461	#481	C₂²×C₆₁	1	4	yes	—
462	#477	C₂²×C₆₁	1	1	yes	characteristic
463	#476	C₂²×C₆₁	1	2	yes	—
464	#476	C₂²×C₆₁	1	1	yes	characteristic
465	#476	C₂²×C₆₁	1	2	yes	—
466	#475	C₂²×C₆₁	1	2	yes	—
467	#475	C₂²×C₆₁	1	1	yes	characteristic
468	#475	C₂²×C₆₁	1	2	yes	—
469	#474	C₂²×C₆₁	1	1	yes	characteristic
470	#470	C₂²×C₆₁	1	4	yes	—
471	#469	C₂²×C₆₁	1	4	yes	—
472	#465	C₂²×C₆₁	1	4	yes	—
473	#465	C₂²×C₆₁	1	4	yes	—
474	#462	C₂²×C₆₁	1	1	yes	characteristic
475	#461	C₂²×C₆₁	1	1	yes	characteristic
476	#460	C₂²×C₆₁	1	1	yes	characteristic
477	#459	C₂²×C₆₁	1	1	yes	characteristic
478	#452	C₂²×C₆₁	1	4	yes	—
479	#452	C₂²×C₆₁	1	2	yes	—
480	#449	C₂²×C₆₁	1	4	yes	—
481	#449	C₂²×C₆₁	1	2	yes	—
482	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
483	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
484	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
485	C₄×D₈	C₂²×C₆₁	1	2	yes	—
486	#436	C₂²×C₆₁	1	2	yes	—
487	#436	C₂²×C₆₁	1	2	yes	—
488	C₈×D₄	C₂²×C₆₁	1	2	yes	—
489	C₈×D₄	C₂²×C₆₁	1	2	yes	—
490	#431	C₂²×C₆₁	1	1	yes	characteristic
491	#431	C₂²×C₆₁	1	1	yes	characteristic
492	#428	C₂²×C₆₁	1	4	yes	—
493	C₂×#106	C₂²×C₆₁	1	4	yes	—
494	#417	C₂²×C₆₁	1	4	yes	—
495	#416	C₂²×C₆₁	1	4	yes	—
496	#408	C₂²×C₆₁	1	4	yes	—
497	C₆₁	#61792	1	1	yes	characteristic, direct product factor, Sylow
498	C₂×#41	—	2	2	no	—
499	C₂×#41	—	2	2	no	—
500	C₂×#41	—	2	1	no	—
501	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
502	C₂×#41	C₂³×C₆₁	1	4	yes	—
503	C₂×#41	C₂³×C₆₁	1	2	yes	—
504	C₂²×Q₈	—	2	1	no	—
505	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
506	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
507	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
508	C₂×D₈	C₂³×C₆₁	1	2	yes	—
509	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
510	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
511	C₄⋊Q₈	—	2	1	no	—
512	C₄⋊Q₈	—	2	1	no	—
513	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
516	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
517	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
518	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
519	#127	—	2	2	no	—
520	#127	D₄×C₆₁	1	1	yes	characteristic
521	#127	C₂³×C₆₁	1	1	yes	characteristic
522	#126	—	2	4	no	—
523	#125	—	2	2	no	—
524	#125	—	2	2	no	—
525	#125	—	2	1	no	—
526	#124	—	2	2	no	—
527	#124	—	2	4	no	—
528	#124	—	2	1	no	—
529	#124	D₄×C₆₁	1	2	yes	—
530	#123	—	2	4	no	—
531	#123	—	2	4	no	—
532	#123	—	2	4	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	—	2	1	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	4	no	—
539	C₂²⋊Q₈	—	2	4	no	—
540	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
541	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
542	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
543	#121	—	2	2	no	—
544	#121	—	2	2	no	—
545	#121	—	2	4	no	—
546	#121	—	2	4	no	—
547	#121	—	2	2	no	—
548	#121	—	2	4	no	—
549	#121	—	2	4	no	—
550	#121	—	2	1	no	—
551	#121	—	2	4	no	—
552	#121	D₄×C₆₁	1	2	yes	—
553	#121	D₄×C₆₁	1	2	yes	—
554	#121	C₂³×C₆₁	1	2	yes	—
555	#121	C₂³×C₆₁	1	4	yes	—
556	#121	C₂³×C₆₁	1	4	yes	—
557	C₄×Q₈	—	2	2	no	—
558	C₄×Q₈	—	2	2	no	—
559	C₄×Q₈	—	2	1	no	—
560	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
561	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
562	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	4	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
572	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
573	C₄×D₄	C₂³×C₆₁	1	2	yes	—
574	C₄×D₄	C₂³×C₆₁	1	2	yes	—
575	C₄×D₄	C₂³×C₆₁	1	2	yes	—
576	#117	—	2	1	no	—
577	#117	—	2	2	no	—
578	#117	—	2	1	no	—
579	#117	C₂³×C₆₁	1	1	yes	characteristic
580	#117	C₂³×C₆₁	1	4	yes	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	2	no	—
583	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
585	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
586	C₂×C₄²	—	2	1	no	—
587	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
588	#107	C₂³×C₆₁	1	2	yes	—
589	#107	C₂³×C₆₁	1	2	yes	—
590	#106	C₂³×C₆₁	1	2	yes	—
591	#106	C₂³×C₆₁	1	2	yes	—
592	#106	C₂³×C₆₁	1	4	yes	—
593	#106	C₂³×C₆₁	1	4	yes	—
594	#106	C₂³×C₆₁	1	4	yes	—
595	#106	C₂³×C₆₁	1	4	yes	—
596	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
597	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
598	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
599	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
600	#103	C₂³×C₆₁	1	2	yes	—
601	#103	C₂³×C₆₁	1	4	yes	—
602	#103	C₂³×C₆₁	1	2	yes	—
603	#103	C₂³×C₆₁	1	4	yes	—
604	#103	C₂³×C₆₁	1	2	yes	—
605	#103	C₂³×C₆₁	1	2	yes	—
606	#102	C₂³×C₆₁	1	2	yes	—
607	#102	C₂³×C₆₁	1	4	yes	—
608	#102	C₂³×C₆₁	1	2	yes	—
609	#102	C₂³×C₆₁	1	4	yes	—
610	#102	C₂³×C₆₁	1	2	yes	—
611	#102	C₂³×C₆₁	1	2	yes	—
612	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
613	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
614	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
615	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
616	C₄×C₈	C₂³×C₆₁	1	2	yes	—
617	C₄×C₈	C₂³×C₆₁	1	2	yes	—
618	#41	—	4	2	no	—
619	#41	—	4	2	no	—
620	#41	—	4	1	no	—
621	#41	—	4	1	no	—
622	#41	—	4	4	no	—
623	#41	—	4	4	no	—
624	#41	—	8	2	no	—
625	#41	—	8	4	no	—
626	#41	—	8	4	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	2	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	2	no	—
631	C₂×Q₈	—	8	2	no	—
632	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
633	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
634	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	2	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
643	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
644	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
645	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
646	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
647	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
660	Q₁₆	—	4	2	no	—
661	SD₁₆	—	4	2	no	—
662	SD₁₆	—	4	2	no	—
663	D₈	—	4	2	no	—
664	M₁₆	—	4	4	no	—
665	C₂×C₈	—	4	4	no	—
666	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
667	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
668	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
669	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
686	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
687	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
688	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
689	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
690	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
691	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	1	no	—
698	C₂²⋊C₄	—	2	1	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
704	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
705	C₄²	—	2	1	no	—
706	C₄²	—	2	1	no	—
707	C₄²	—	2	1	no	—
708	C₄²	—	2	4	no	—
709	C₄²	—	2	2	no	—
710	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
711	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
712	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
713	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
714	C₂³	—	2	1	no	—
715	C₂³	—	2	2	no	—
716	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
717	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
718	Q₈	—	2	1	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	2	1	no	—
721	Q₈	—	2	2	no	—
722	Q₈	—	4	2	no	—
723	Q₈	—	4	4	no	—
724	Q₈	—	4	2	no	—
725	Q₈	—	8	2	no	—
726	Q₈	—	8	1	no	—
727	D₄	—	2	4	no	—
728	D₄	—	2	4	no	—
729	D₄	—	2	1	no	—
730	D₄	—	2	2	no	—
731	D₄	—	2	1	no	—
732	D₄	—	2	2	no	—
733	D₄	—	4	2	no	—
734	D₄	—	4	4	no	—
735	D₄	—	4	2	no	—
736	D₄	—	4	2	no	—
737	D₄	—	8	1	no	—
738	D₄	—	8	4	no	—
739	D₄	—	8	2	no	—
740	D₄	—	8	4	no	—
741	D₄	—	8	4	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	—	4	4	no	—
759	C₂×C₄	—	8	4	no	—
760	C₂×C₄	—	8	2	no	—
761	C₂×C₄	—	8	4	no	—
762	C₂×C₄	—	8	4	no	—
763	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
764	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
765	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
766	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
767	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
768	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
769	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
770	C₈	—	2	2	no	—
771	C₈	—	2	2	no	—
772	C₈	—	2	2	no	—
773	C₈	—	2	2	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	2	no	—
786	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
787	C₄	—	2	1	no	—
788	C₄	—	2	1	no	—
789	C₄	—	2	1	no	—
790	C₄	—	2	4	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	4	no	—
796	C₄	—	4	1	no	—
797	C₄	—	4	2	no	—
798	C₄	C₆₁×#577	1	2	yes	—
799	C₄	C₆₁×#577	1	2	yes	—
800	C₄	C₆₁×#585	1	1	yes	characteristic
801	C₄	C₆₁×#585	1	1	yes	characteristic
802	C₂	—	4	1	no	—
803	C₂	—	4	4	no	—
804	C₂	—	8	1	no	—
805	C₂	—	8	2	no	—
806	C₂	C₆₁×#3485	1	1	yes	characteristic
807	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
808	C₂	C₂×C₆₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3548	C₂	semidirect
2. C₆₁×#3511	C₂	semidirect
3. C₆₁×#3356	C₂	semidirect
4. C₆₁×#3354	C₂	semidirect
5. C₆₁×#3335	C₂	semidirect
6. C₆₁×#3335	C₂	semidirect
7. C₆₁×#3332	C₂	semidirect
8. C₆₁×#3331	C₂	semidirect
9. C₆₁×#3304	C₂	semidirect
10. C₆₁×#3303	C₂	semidirect
11. C₆₁×#3229	C₂	semidirect
12. C₆₁×#3227	C₂	semidirect
13. C₆₁×#3204	C₂	semidirect
14. C₆₁×#3107	C₂	semidirect
15. C₆₁×#3106	C₂	semidirect
16. C₆₁×#3099	C₂	semidirect
17. C₆₁×#2979	C₂	semidirect
369. #61792	C₆₁	direct (N × H)
398. #3548	C₂×C₆₁	semidirect
399. #3511	C₂×C₆₁	semidirect
400. #3356	C₂×C₆₁	semidirect
401. #3354	C₂×C₆₁	semidirect
402. #3335	C₂×C₆₁	semidirect
403. #3335	C₂×C₆₁	semidirect
404. #3332	C₂×C₆₁	semidirect
405. #3331	C₂×C₆₁	semidirect
406. #3304	C₂×C₆₁	semidirect
407. #3303	C₂×C₆₁	semidirect
408. #3229	C₂×C₆₁	semidirect
409. #3227	C₂×C₆₁	semidirect
410. #3204	C₂×C₆₁	semidirect
411. #3107	C₂×C₆₁	semidirect
412. #3106	C₂×C₆₁	semidirect
413. #3099	C₂×C₆₁	semidirect
414. #2979	C₂×C₆₁	semidirect
497. C₆₁	#61792	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×#3548	2
C₆₁×#3511	2
C₆₁×#3356	2
C₆₁×#3354	2
C₆₁×#3335	2
C₆₁×#3332	2
C₆₁×#3331	2
C₆₁×#3304	2
C₆₁×#3303	2
C₆₁×#3229	2
C₆₁×#3227	2
C₆₁×#3204	2
C₆₁×#3107	2
C₆₁×#3106	2
C₆₁×#3099	2
C₆₁×#2979	2
#61792	61

Subgroups — C61×#61792 #29565225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61792 #29565225