Subgroups — C₆₁×#61868 #29565301

Order 15616.

1756 conjugacy classes of subgroups.

The subgroup lattice has 800 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×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3385	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3384	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3381	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3380	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3368	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3366	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3362	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3358	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3241	C₂	1	4	yes	maximal, complemented
12	C₆₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3119	C₂	1	4	yes	maximal, complemented
15	C₆₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#562	—	2	2	no	—
19	Q₈²×C₆₁	C₂²	1	2	yes	—
20	C₆₁×#557	C₂²	1	2	yes	—
21	C₆₁×#554	—	2	2	no	—
22	C₆₁×#554	C₂²	1	2	yes	—
23	C₆₁×#554	C₂²	1	2	yes	—
24	C₆₁×#554	C₂²	1	2	yes	—
25	C₆₁×#550	C₂²	1	2	yes	—
26	C₆₁×#550	C₂²	1	2	yes	—
27	D₄×Q₈×C₆₁	—	2	2	no	—
28	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
29	C₆₁×#547	—	2	1	no	—
30	C₆₁×#547	—	2	1	no	—
31	C₆₁×#544	—	2	2	no	—
32	C₆₁×#544	C₂²	1	2	yes	—
33	C₆₁×#540	C₂²	1	4	yes	—
34	C₆₁×#537	—	2	2	no	—
35	C₆₁×#537	—	2	2	no	—
36	C₆₁×#533	—	2	1	no	—
37	C₆₁×#533	C₂²	1	1	yes	characteristic
38	C₆₁×#532	C₂²	1	1	yes	characteristic
39	C₆₁×#532	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
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×#501	C₂²	1	4	yes	—
45	C₆₁×#500	C₂²	1	2	yes	—
46	C₆₁×#499	C₂²	1	4	yes	—
47	C₆₁×#498	C₂²	1	2	yes	—
48	C₆₁×#490	C₂²	1	4	yes	—
49	C₆₁×#486	C₂²	1	4	yes	—
50	C₆₁×#486	C₂²	1	2	yes	—
51	C₆₁×#486	C₂²	1	2	yes	—
52	C₆₁×#482	C₂²	1	2	yes	—
53	C₆₁×#482	C₂²	1	2	yes	—
54	C₆₁×#481	C₂²	1	4	yes	—
55	C₆₁×#480	C₂²	1	4	yes	—
56	C₆₁×#479	C₂²	1	4	yes	—
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	1	yes	characteristic
61	C₆₁×#477	C₂²	1	1	yes	characteristic
62	C₆₁×#476	C₂²	1	1	yes	characteristic
63	C₆₁×#476	C₂²	1	1	yes	characteristic
64	C₆₁×#476	C₂²	1	2	yes	—
65	C₆₁×#476	C₂²	1	4	yes	—
66	C₆₁×#476	C₂²	1	2	yes	—
67	C₆₁×#474	C₂²	1	2	yes	—
68	C₆₁×#474	C₂²	1	4	yes	—
69	C₆₁×#474	C₂²	1	2	yes	—
70	C₆₁×#460	C₂²	1	1	yes	characteristic
71	C₆₁×#460	C₂²	1	1	yes	characteristic
72	C₆₁×#460	C₂²	1	4	yes	—
73	C₆₁×#459	C₂²	1	1	yes	characteristic
74	C₆₁×#459	C₂²	1	4	yes	—
75	C₆₁×#459	C₂²	1	1	yes	characteristic
76	C₆₁×#449	C₂²	1	2	yes	—
77	C₆₁×#449	C₂²	1	2	yes	—
78	C₆₁×#446	C₂²	1	2	yes	—
79	C₆₁×#446	C₂²	1	2	yes	—
80	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
81	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
82	C₆₁×#442	C₂²	1	4	yes	—
83	C₆₁×#440	C₂²	1	4	yes	—
84	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
85	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
86	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	—
87	C₄×D₈×C₆₁	C₂²	1	2	yes	—
88	C₄×D₈×C₆₁	C₂²	1	4	yes	—
89	C₄×D₈×C₆₁	C₂²	1	2	yes	—
90	C₆₁×#433	C₂²	1	4	yes	—
91	C₆₁×#431	C₂²	1	1	yes	characteristic
92	C₆₁×#431	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
97	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₆₁	—	2	2	no	—
99	C₂²×Q₈×C₆₁	—	2	1	no	—
100	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
101	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
102	C₂×D₈×C₆₁	C₂³	1	2	yes	—
103	C₂×D₈×C₆₁	C₂³	1	2	yes	—
104	C₄⋊Q₈×C₆₁	—	2	2	no	—
105	C₄⋊Q₈×C₆₁	—	2	2	no	—
106	C₄⋊Q₈×C₆₁	—	2	2	no	—
107	C₄⋊Q₈×C₆₁	—	2	4	no	—
108	C₄⋊Q₈×C₆₁	—	2	1	no	—
109	C₄⋊Q₈×C₆₁	—	2	1	no	—
110	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
117	#127×C₆₁	C₂³	1	1	yes	characteristic
118	#127×C₆₁	C₂³	1	1	yes	characteristic
119	#127×C₆₁	C₂³	1	4	yes	—
120	#125×C₆₁	—	2	2	no	—
121	#125×C₆₁	—	2	4	no	—
122	#125×C₆₁	D₄	1	2	yes	—
123	#125×C₆₁	C₂³	1	4	yes	—
124	#125×C₆₁	C₂³	1	4	yes	—
125	#124×C₆₁	—	2	1	no	—
126	#124×C₆₁	—	2	1	no	—
127	#123×C₆₁	—	2	4	no	—
128	#123×C₆₁	—	2	4	no	—
129	C₂²⋊Q₈×C₆₁	—	2	2	no	—
130	C₂²⋊Q₈×C₆₁	—	2	2	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	—	2	4	no	—
136	C₂²⋊Q₈×C₆₁	—	2	4	no	—
137	C₂²⋊Q₈×C₆₁	—	2	4	no	—
138	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
139	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
140	#121×C₆₁	—	2	1	no	—
141	#121×C₆₁	—	2	1	no	—
142	#121×C₆₁	—	2	2	no	—
143	#121×C₆₁	—	2	2	no	—
144	#121×C₆₁	—	2	4	no	—
145	#121×C₆₁	—	2	4	no	—
146	#121×C₆₁	—	2	4	no	—
147	#121×C₆₁	—	2	4	no	—
148	#121×C₆₁	C₂³	1	2	yes	—
149	#121×C₆₁	C₂³	1	2	yes	—
150	C₄×Q₈×C₆₁	—	2	2	no	—
151	C₄×Q₈×C₆₁	—	2	2	no	—
152	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
153	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
154	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
155	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
156	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
157	C₄×D₄×C₆₁	—	2	1	no	—
158	C₄×D₄×C₆₁	—	2	1	no	—
159	C₄×D₄×C₆₁	—	2	4	no	—
160	C₄×D₄×C₆₁	—	2	1	no	—
161	C₄×D₄×C₆₁	—	2	1	no	—
162	C₄×D₄×C₆₁	C₂³	1	2	yes	—
163	C₄×D₄×C₆₁	C₂³	1	2	yes	—
164	C₄×D₄×C₆₁	C₂³	1	4	yes	—
165	C₄×D₄×C₆₁	C₂³	1	4	yes	—
166	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₆₁	C₂³	1	4	yes	—
168	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
169	#117×C₆₁	—	2	2	no	—
170	#117×C₆₁	—	2	1	no	—
171	#117×C₆₁	C₂³	1	1	yes	characteristic
172	#117×C₆₁	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
174	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
175	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
176	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
177	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
178	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
179	C₂×C₄²×C₆₁	—	2	1	no	—
180	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
181	#107×C₆₁	C₂³	1	2	yes	—
182	#107×C₆₁	C₂³	1	4	yes	—
183	#107×C₆₁	C₂³	1	2	yes	—
184	#107×C₆₁	C₂³	1	4	yes	—
185	#106×C₆₁	C₂³	1	2	yes	—
186	#106×C₆₁	C₂³	1	4	yes	—
187	#106×C₆₁	C₂³	1	2	yes	—
188	#106×C₆₁	C₂³	1	4	yes	—
189	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
190	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
191	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
192	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
193	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
194	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
195	#103×C₆₁	C₂³	1	2	yes	—
196	#103×C₆₁	C₂³	1	2	yes	—
197	#102×C₆₁	C₂³	1	2	yes	—
198	#102×C₆₁	C₂³	1	2	yes	—
199	#102×C₆₁	C₂³	1	2	yes	—
200	#102×C₆₁	C₂³	1	4	yes	—
201	#102×C₆₁	C₂³	1	2	yes	—
202	#102×C₆₁	C₂³	1	2	yes	—
203	#102×C₆₁	C₂³	1	4	yes	—
204	#102×C₆₁	C₂³	1	2	yes	—
205	#102×C₆₁	C₂³	1	4	yes	—
206	#102×C₆₁	C₂³	1	4	yes	—
207	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
208	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
209	#97×C₆₁	C₂³	1	4	yes	—
210	C₄×C₈×C₆₁	C₂³	1	2	yes	—
211	C₄×C₈×C₆₁	C₂³	1	2	yes	—
212	C₄×C₈×C₆₁	C₂³	1	4	yes	—
213	#41×C₆₁	—	2	2	no	—
214	#41×C₆₁	—	2	2	no	—
215	#41×C₆₁	—	8	2	no	—
216	#41×C₆₁	—	8	2	no	—
217	#41×C₆₁	—	8	4	no	—
218	#41×C₆₁	—	8	4	no	—
219	C₂×Q₈×C₆₁	—	2	2	no	—
220	C₂×Q₈×C₆₁	—	2	1	no	—
221	C₂×Q₈×C₆₁	—	2	1	no	—
222	C₂×Q₈×C₆₁	—	2	4	no	—
223	C₂×Q₈×C₆₁	—	2	2	no	—
224	C₂×Q₈×C₆₁	—	8	2	no	—
225	C₂×Q₈×C₆₁	—	8	4	no	—
226	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
229	C₂×D₄×C₆₁	—	2	1	no	—
230	C₂×D₄×C₆₁	—	2	2	no	—
231	C₂×D₄×C₆₁	—	2	2	no	—
232	C₂×D₄×C₆₁	—	2	1	no	—
233	C₂×D₄×C₆₁	—	2	1	no	—
234	C₂×D₄×C₆₁	—	2	4	no	—
235	C₂×D₄×C₆₁	—	2	4	no	—
236	C₂×D₄×C₆₁	—	2	1	no	—
237	C₂×D₄×C₆₁	—	2	1	no	—
238	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
239	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
240	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₆₁	—	2	1	no	—
242	C₂²×C₄×C₆₁	—	2	2	no	—
243	C₂²×C₄×C₆₁	—	2	1	no	—
244	C₂²×C₄×C₆₁	—	2	1	no	—
245	C₂²×C₄×C₆₁	—	2	2	no	—
246	C₂²×C₄×C₆₁	—	2	2	no	—
247	C₂²×C₄×C₆₁	—	2	4	no	—
248	C₂²×C₄×C₆₁	—	2	4	no	—
249	C₂²×C₄×C₆₁	—	2	4	no	—
250	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
253	SD₁₆×C₆₁	—	2	4	no	—
254	SD₁₆×C₆₁	—	2	4	no	—
255	D₈×C₆₁	—	2	4	no	—
256	D₈×C₆₁	—	2	4	no	—
257	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
258	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
259	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
260	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₆₁	—	2	1	no	—
262	C₄⋊C₄×C₆₁	—	2	1	no	—
263	C₄⋊C₄×C₆₁	—	2	2	no	—
264	C₄⋊C₄×C₆₁	—	2	2	no	—
265	C₄⋊C₄×C₆₁	—	2	4	no	—
266	C₄⋊C₄×C₆₁	—	2	4	no	—
267	C₄⋊C₄×C₆₁	—	2	4	no	—
268	C₄⋊C₄×C₆₁	—	2	2	no	—
269	C₄⋊C₄×C₆₁	—	2	4	no	—
270	C₄⋊C₄×C₆₁	—	2	1	no	—
271	C₄⋊C₄×C₆₁	—	2	1	no	—
272	C₄⋊C₄×C₆₁	—	2	4	no	—
273	C₄⋊C₄×C₆₁	—	2	4	no	—
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	2	yes	—
277	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
279	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
280	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
281	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
282	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
283	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
285	C₂²⋊C₄×C₆₁	—	2	1	no	—
286	C₂²⋊C₄×C₆₁	—	2	1	no	—
287	C₂²⋊C₄×C₆₁	—	2	1	no	—
288	C₂²⋊C₄×C₆₁	—	2	4	no	—
289	C₂²⋊C₄×C₆₁	—	2	2	no	—
290	C₂²⋊C₄×C₆₁	—	2	2	no	—
291	C₂²⋊C₄×C₆₁	—	2	4	no	—
292	C₂²⋊C₄×C₆₁	—	2	4	no	—
293	C₂²⋊C₄×C₆₁	—	2	2	no	—
294	C₂²⋊C₄×C₆₁	—	2	2	no	—
295	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
296	C₄²×C₆₁	—	2	1	no	—
297	C₄²×C₆₁	—	2	1	no	—
298	C₄²×C₆₁	—	2	1	no	—
299	C₄²×C₆₁	—	2	4	no	—
300	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
303	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
304	C₄²×C₆₁	C₂⁴	1	4	yes	—
305	C₂³×C₆₁	—	2	1	no	—
306	C₂³×C₆₁	—	2	2	no	—
307	C₂³×C₆₁	—	2	2	no	—
308	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
309	Q₈×C₆₁	—	2	4	no	—
310	Q₈×C₆₁	—	2	4	no	—
311	Q₈×C₆₁	—	2	1	no	—
312	Q₈×C₆₁	—	4	4	no	—
313	Q₈×C₆₁	—	8	2	no	—
314	Q₈×C₆₁	—	8	4	no	—
315	Q₈×C₆₁	—	8	1	no	—
316	Q₈×C₆₁	—	8	1	no	—
317	Q₈×C₆₁	2₋¹⁺⁴	1	2	yes	—
318	D₄×C₆₁	—	2	4	no	—
319	D₄×C₆₁	—	2	1	no	—
320	D₄×C₆₁	—	2	2	no	—
321	D₄×C₆₁	—	2	2	no	—
322	D₄×C₆₁	—	2	2	no	—
323	D₄×C₆₁	—	2	2	no	—
324	D₄×C₆₁	—	4	2	no	—
325	D₄×C₆₁	—	4	2	no	—
326	D₄×C₆₁	—	8	1	no	—
327	D₄×C₆₁	—	8	4	no	—
328	D₄×C₆₁	—	8	1	no	—
329	D₄×C₆₁	—	8	4	no	—
330	D₄×C₆₁	—	8	2	no	—
331	D₄×C₆₁	—	8	2	no	—
332	D₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
333	C₂×C₄×C₆₁	—	2	4	no	—
334	C₂×C₄×C₆₁	—	2	1	no	—
335	C₂×C₄×C₆₁	—	2	2	no	—
336	C₂×C₄×C₆₁	—	2	2	no	—
337	C₂×C₄×C₆₁	—	2	1	no	—
338	C₂×C₄×C₆₁	—	2	1	no	—
339	C₂×C₄×C₆₁	—	2	1	no	—
340	C₂×C₄×C₆₁	—	2	1	no	—
341	C₂×C₄×C₆₁	—	2	4	no	—
342	C₂×C₄×C₆₁	—	2	2	no	—
343	C₂×C₄×C₆₁	—	2	2	no	—
344	C₂×C₄×C₆₁	—	4	2	no	—
345	C₂×C₄×C₆₁	—	4	4	no	—
346	C₂×C₄×C₆₁	—	4	2	no	—
347	C₂×C₄×C₆₁	—	4	4	no	—
348	C₂×C₄×C₆₁	—	8	4	no	—
349	C₂×C₄×C₆₁	—	8	4	no	—
350	C₂×C₄×C₆₁	—	8	4	no	—
351	C₂×C₄×C₆₁	—	8	2	no	—
352	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
354	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
357	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
360	C₈×C₆₁	—	2	2	no	—
361	C₈×C₆₁	—	2	2	no	—
362	C₈×C₆₁	—	2	2	no	—
363	C₈×C₆₁	—	2	2	no	—
364	#61868	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
365	C₂²×C₆₁	—	2	1	no	—
366	C₂²×C₆₁	—	2	2	no	—
367	C₂²×C₆₁	—	2	1	no	—
368	C₂²×C₆₁	—	2	1	no	—
369	C₂²×C₆₁	—	4	1	no	—
370	C₂²×C₆₁	—	4	1	no	—
371	C₂²×C₆₁	—	4	2	no	—
372	C₂²×C₆₁	—	4	2	no	—
373	C₂²×C₆₁	—	4	2	no	—
374	C₂²×C₆₁	—	4	2	no	—
375	C₂²×C₆₁	—	4	2	no	—
376	C₂²×C₆₁	—	4	2	no	—
377	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
378	C₄×C₆₁	—	2	1	no	—
379	C₄×C₆₁	—	2	2	no	—
380	C₄×C₆₁	—	2	1	no	—
381	C₄×C₆₁	—	2	4	no	—
382	C₄×C₆₁	—	2	1	no	—
383	C₄×C₆₁	—	2	4	no	—
384	C₄×C₆₁	—	4	2	no	—
385	C₄×C₆₁	—	4	1	no	—
386	C₄×C₆₁	—	4	4	no	—
387	C₄×C₆₁	—	4	1	no	—
388	C₄×C₆₁	—	4	2	no	—
389	C₄×C₆₁	#576	1	2	yes	—
390	C₄×C₆₁	#577	1	2	yes	—
391	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
392	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
393	#3548	C₂×C₆₁	1	1	yes	characteristic, complemented
394	#3503	C₂×C₆₁	1	1	yes	characteristic, complemented
395	#3385	C₂×C₆₁	1	2	yes	complemented
396	#3384	C₂×C₆₁	1	2	yes	complemented
397	#3381	C₂×C₆₁	1	2	yes	complemented
398	#3380	C₂×C₆₁	1	2	yes	complemented
399	#3368	C₂×C₆₁	1	2	yes	complemented
400	#3366	C₂×C₆₁	1	2	yes	complemented
401	#3362	C₂×C₆₁	1	2	yes	complemented
402	#3358	C₂×C₆₁	1	2	yes	complemented
403	#3241	C₂×C₆₁	1	4	yes	complemented
404	#3227	C₂×C₆₁	1	1	yes	characteristic, complemented
405	#3226	C₂×C₆₁	1	1	yes	characteristic, complemented
406	#3119	C₂×C₆₁	1	4	yes	complemented
407	#3106	C₂×C₆₁	1	1	yes	characteristic, complemented
408	#3106	C₂×C₆₁	1	1	yes	characteristic, complemented
409	#2986	C₂×C₆₁	1	1	yes	characteristic, complemented
410	C₂×C₆₁	—	4	1	no	—
411	C₂×C₆₁	—	4	2	no	—
412	C₂×C₆₁	—	8	2	no	—
413	C₂×C₆₁	—	8	2	no	—
414	C₂×C₆₁	#3486	1	1	yes	characteristic
415	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
416	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
417	#562	—	2	2	no	—
418	Q₈²	C₂²×C₆₁	1	2	yes	—
419	#557	C₂²×C₆₁	1	2	yes	—
420	#554	—	2	2	no	—
421	#554	C₂²×C₆₁	1	2	yes	—
422	#554	C₂²×C₆₁	1	2	yes	—
423	#554	C₂²×C₆₁	1	2	yes	—
424	#550	C₂²×C₆₁	1	2	yes	—
425	#550	C₂²×C₆₁	1	2	yes	—
426	D₄×Q₈	—	2	2	no	—
427	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
428	#547	—	2	1	no	—
429	#547	—	2	1	no	—
430	#544	—	2	2	no	—
431	#544	C₂²×C₆₁	1	2	yes	—
432	#540	C₂²×C₆₁	1	4	yes	—
433	#537	—	2	2	no	—
434	#537	—	2	2	no	—
435	#533	—	2	1	no	—
436	#533	C₂²×C₆₁	1	1	yes	characteristic
437	#532	C₂²×C₆₁	1	1	yes	characteristic
438	#532	C₂²×C₆₁	1	1	yes	characteristic
439	C₂×C₄⋊Q₈	—	2	1	no	—
440	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
441	#520	C₂²×C₆₁	1	2	yes	—
442	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
443	#501	C₂²×C₆₁	1	4	yes	—
444	#500	C₂²×C₆₁	1	2	yes	—
445	#499	C₂²×C₆₁	1	4	yes	—
446	#498	C₂²×C₆₁	1	2	yes	—
447	#490	C₂²×C₆₁	1	4	yes	—
448	#486	C₂²×C₆₁	1	4	yes	—
449	#486	C₂²×C₆₁	1	2	yes	—
450	#486	C₂²×C₆₁	1	2	yes	—
451	#482	C₂²×C₆₁	1	2	yes	—
452	#482	C₂²×C₆₁	1	2	yes	—
453	#481	C₂²×C₆₁	1	4	yes	—
454	#480	C₂²×C₆₁	1	4	yes	—
455	#479	C₂²×C₆₁	1	4	yes	—
456	#478	C₂²×C₆₁	1	4	yes	—
457	#478	C₂²×C₆₁	1	4	yes	—
458	#478	C₂²×C₆₁	1	4	yes	—
459	#477	C₂²×C₆₁	1	1	yes	characteristic
460	#477	C₂²×C₆₁	1	1	yes	characteristic
461	#476	C₂²×C₆₁	1	1	yes	characteristic
462	#476	C₂²×C₆₁	1	1	yes	characteristic
463	#476	C₂²×C₆₁	1	2	yes	—
464	#476	C₂²×C₆₁	1	4	yes	—
465	#476	C₂²×C₆₁	1	2	yes	—
466	#474	C₂²×C₆₁	1	2	yes	—
467	#474	C₂²×C₆₁	1	4	yes	—
468	#474	C₂²×C₆₁	1	2	yes	—
469	#460	C₂²×C₆₁	1	1	yes	characteristic
470	#460	C₂²×C₆₁	1	1	yes	characteristic
471	#460	C₂²×C₆₁	1	4	yes	—
472	#459	C₂²×C₆₁	1	1	yes	characteristic
473	#459	C₂²×C₆₁	1	4	yes	—
474	#459	C₂²×C₆₁	1	1	yes	characteristic
475	#449	C₂²×C₆₁	1	2	yes	—
476	#449	C₂²×C₆₁	1	2	yes	—
477	#446	C₂²×C₆₁	1	2	yes	—
478	#446	C₂²×C₆₁	1	2	yes	—
479	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
480	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
481	#442	C₂²×C₆₁	1	4	yes	—
482	#440	C₂²×C₆₁	1	4	yes	—
483	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
484	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
485	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	—
486	C₄×D₈	C₂²×C₆₁	1	2	yes	—
487	C₄×D₈	C₂²×C₆₁	1	4	yes	—
488	C₄×D₈	C₂²×C₆₁	1	2	yes	—
489	#433	C₂²×C₆₁	1	4	yes	—
490	#431	C₂²×C₆₁	1	1	yes	characteristic
491	#431	C₂²×C₆₁	1	1	yes	characteristic
492	C₆₁	#61868	1	1	yes	characteristic, direct product factor, Sylow
493	C₂×#41	—	2	2	no	—
494	C₂×#41	—	2	2	no	—
495	C₂×#41	—	2	1	no	—
496	C₂×#41	—	2	1	no	—
497	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
498	C₂²×Q₈	—	2	2	no	—
499	C₂²×Q₈	—	2	1	no	—
500	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
501	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
502	C₂×D₈	C₂³×C₆₁	1	2	yes	—
503	C₂×D₈	C₂³×C₆₁	1	2	yes	—
504	C₄⋊Q₈	—	2	2	no	—
505	C₄⋊Q₈	—	2	2	no	—
506	C₄⋊Q₈	—	2	2	no	—
507	C₄⋊Q₈	—	2	4	no	—
508	C₄⋊Q₈	—	2	1	no	—
509	C₄⋊Q₈	—	2	1	no	—
510	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
511	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
512	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
513	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
514	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
517	#127	C₂³×C₆₁	1	1	yes	characteristic
518	#127	C₂³×C₆₁	1	1	yes	characteristic
519	#127	C₂³×C₆₁	1	4	yes	—
520	#125	—	2	2	no	—
521	#125	—	2	4	no	—
522	#125	D₄×C₆₁	1	2	yes	—
523	#125	C₂³×C₆₁	1	4	yes	—
524	#125	C₂³×C₆₁	1	4	yes	—
525	#124	—	2	1	no	—
526	#124	—	2	1	no	—
527	#123	—	2	4	no	—
528	#123	—	2	4	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	4	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	—	2	4	no	—
536	C₂²⋊Q₈	—	2	4	no	—
537	C₂²⋊Q₈	—	2	4	no	—
538	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
539	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
540	#121	—	2	1	no	—
541	#121	—	2	1	no	—
542	#121	—	2	2	no	—
543	#121	—	2	2	no	—
544	#121	—	2	4	no	—
545	#121	—	2	4	no	—
546	#121	—	2	4	no	—
547	#121	—	2	4	no	—
548	#121	C₂³×C₆₁	1	2	yes	—
549	#121	C₂³×C₆₁	1	2	yes	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
553	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
554	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
555	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
556	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	—	2	4	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
563	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
564	C₄×D₄	C₂³×C₆₁	1	4	yes	—
565	C₄×D₄	C₂³×C₆₁	1	2	yes	—
566	C₄×D₄	C₂³×C₆₁	1	2	yes	—
567	C₄×D₄	C₂³×C₆₁	1	4	yes	—
568	C₄×D₄	C₂³×C₆₁	1	4	yes	—
569	#117	—	2	2	no	—
570	#117	—	2	1	no	—
571	#117	C₂³×C₆₁	1	1	yes	characteristic
572	#117	C₂³×C₆₁	1	2	yes	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	2	no	—
575	C₂×C₄⋊C₄	—	2	2	no	—
576	C₂×C₄⋊C₄	—	2	2	no	—
577	C₂×C₄⋊C₄	—	2	2	no	—
578	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
579	C₂×C₄²	—	2	1	no	—
580	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
581	#107	C₂³×C₆₁	1	2	yes	—
582	#107	C₂³×C₆₁	1	4	yes	—
583	#107	C₂³×C₆₁	1	2	yes	—
584	#107	C₂³×C₆₁	1	4	yes	—
585	#106	C₂³×C₆₁	1	2	yes	—
586	#106	C₂³×C₆₁	1	4	yes	—
587	#106	C₂³×C₆₁	1	2	yes	—
588	#106	C₂³×C₆₁	1	4	yes	—
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	1	yes	characteristic
593	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
594	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
595	#103	C₂³×C₆₁	1	2	yes	—
596	#103	C₂³×C₆₁	1	2	yes	—
597	#102	C₂³×C₆₁	1	2	yes	—
598	#102	C₂³×C₆₁	1	2	yes	—
599	#102	C₂³×C₆₁	1	2	yes	—
600	#102	C₂³×C₆₁	1	4	yes	—
601	#102	C₂³×C₆₁	1	2	yes	—
602	#102	C₂³×C₆₁	1	2	yes	—
603	#102	C₂³×C₆₁	1	4	yes	—
604	#102	C₂³×C₆₁	1	2	yes	—
605	#102	C₂³×C₆₁	1	4	yes	—
606	#102	C₂³×C₆₁	1	4	yes	—
607	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
608	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
609	#97	C₂³×C₆₁	1	4	yes	—
610	C₄×C₈	C₂³×C₆₁	1	2	yes	—
611	C₄×C₈	C₂³×C₆₁	1	2	yes	—
612	C₄×C₈	C₂³×C₆₁	1	4	yes	—
613	#41	—	2	2	no	—
614	#41	—	2	2	no	—
615	#41	—	8	2	no	—
616	#41	—	8	2	no	—
617	#41	—	8	4	no	—
618	#41	—	8	4	no	—
619	C₂×Q₈	—	2	2	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	—	2	4	no	—
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	8	2	no	—
625	C₂×Q₈	—	8	4	no	—
626	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
627	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
628	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
639	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
640	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
653	SD₁₆	—	2	4	no	—
654	SD₁₆	—	2	4	no	—
655	D₈	—	2	4	no	—
656	D₈	—	2	4	no	—
657	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
658	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
659	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
660	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
675	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
676	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
677	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
678	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
679	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
680	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
681	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
682	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
683	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
684	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
685	C₂²⋊C₄	—	2	1	no	—
686	C₂²⋊C₄	—	2	1	no	—
687	C₂²⋊C₄	—	2	1	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
696	C₄²	—	2	1	no	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	4	no	—
700	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
701	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
702	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
703	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
704	C₄²	C₂⁴×C₆₁	1	4	yes	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
709	Q₈	—	2	4	no	—
710	Q₈	—	2	4	no	—
711	Q₈	—	2	1	no	—
712	Q₈	—	4	4	no	—
713	Q₈	—	8	2	no	—
714	Q₈	—	8	4	no	—
715	Q₈	—	8	1	no	—
716	Q₈	—	8	1	no	—
717	Q₈	2₋¹⁺⁴×C₆₁	1	2	yes	—
718	D₄	—	2	4	no	—
719	D₄	—	2	1	no	—
720	D₄	—	2	2	no	—
721	D₄	—	2	2	no	—
722	D₄	—	2	2	no	—
723	D₄	—	2	2	no	—
724	D₄	—	4	2	no	—
725	D₄	—	4	2	no	—
726	D₄	—	8	1	no	—
727	D₄	—	8	4	no	—
728	D₄	—	8	1	no	—
729	D₄	—	8	4	no	—
730	D₄	—	8	2	no	—
731	D₄	—	8	2	no	—
732	D₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	4	2	no	—
745	C₂×C₄	—	4	4	no	—
746	C₂×C₄	—	4	2	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	8	4	no	—
749	C₂×C₄	—	8	4	no	—
750	C₂×C₄	—	8	4	no	—
751	C₂×C₄	—	8	2	no	—
752	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
754	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
756	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
757	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
759	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
760	C₈	—	2	2	no	—
761	C₈	—	2	2	no	—
762	C₈	—	2	2	no	—
763	C₈	—	2	2	no	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	2	1	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
777	C₄	—	2	1	no	—
778	C₄	—	2	4	no	—
779	C₄	—	2	1	no	—
780	C₄	—	2	4	no	—
781	C₄	—	2	1	no	—
782	C₄	—	2	2	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	1	no	—
785	C₄	—	4	4	no	—
786	C₄	—	4	1	no	—
787	C₄	—	4	2	no	—
788	C₄	C₆₁×#576	1	2	yes	—
789	C₄	C₆₁×#577	1	2	yes	—
790	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
791	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
792	C₂	—	4	1	no	—
793	C₂	—	4	2	no	—
794	C₂	—	8	2	no	—
795	C₂	—	8	2	no	—
796	C₂	C₆₁×#3486	1	1	yes	characteristic
797	C₂	C₂×C₆₁×#576	1	1	yes	characteristic
798	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3548	C₂	semidirect
2. C₆₁×#3503	C₂	semidirect
3. C₆₁×#3385	C₂	semidirect
4. C₆₁×#3384	C₂	semidirect
5. C₆₁×#3381	C₂	semidirect
6. C₆₁×#3380	C₂	semidirect
7. C₆₁×#3368	C₂	semidirect
8. C₆₁×#3366	C₂	semidirect
9. C₆₁×#3362	C₂	semidirect
10. C₆₁×#3358	C₂	semidirect
11. C₆₁×#3241	C₂	semidirect
12. C₆₁×#3227	C₂	semidirect
13. C₆₁×#3226	C₂	semidirect
14. C₆₁×#3119	C₂	semidirect
15. C₆₁×#3106	C₂	semidirect
16. C₆₁×#3106	C₂	semidirect
17. C₆₁×#2986	C₂	semidirect
364. #61868	C₆₁	direct (N × H)
393. #3548	C₂×C₆₁	semidirect
394. #3503	C₂×C₆₁	semidirect
395. #3385	C₂×C₆₁	semidirect
396. #3384	C₂×C₆₁	semidirect
397. #3381	C₂×C₆₁	semidirect
398. #3380	C₂×C₆₁	semidirect
399. #3368	C₂×C₆₁	semidirect
400. #3366	C₂×C₆₁	semidirect
401. #3362	C₂×C₆₁	semidirect
402. #3358	C₂×C₆₁	semidirect
403. #3241	C₂×C₆₁	semidirect
404. #3227	C₂×C₆₁	semidirect
405. #3226	C₂×C₆₁	semidirect
406. #3119	C₂×C₆₁	semidirect
407. #3106	C₂×C₆₁	semidirect
408. #3106	C₂×C₆₁	semidirect
409. #2986	C₂×C₆₁	semidirect
492. C₆₁	#61868	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×#3503	2
C₆₁×#3385	2
C₆₁×#3384	2
C₆₁×#3381	2
C₆₁×#3380	2
C₆₁×#3368	2
C₆₁×#3366	2
C₆₁×#3362	2
C₆₁×#3358	2
C₆₁×#3241	2
C₆₁×#3227	2
C₆₁×#3226	2
C₆₁×#3119	2
C₆₁×#3106	2
C₆₁×#2986	2
#61868	61

Subgroups — C61×#61868 #29565301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61868 #29565301