Subgroups — C₆₁×#61897 #29565330

Order 15616.

1720 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3402	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3401	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3377	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3371	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3219	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3216	C₂	1	2	yes	maximal, complemented
17	C₆₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3116	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3111	C₂	1	2	yes	maximal, complemented
21	C₆₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2983	C₂	1	1	yes	maximal, characteristic, complemented
24	C₆₁×#559	C₂²	1	2	yes	—
25	C₆₁×#559	C₂²	1	1	yes	characteristic
26	C₆₁×#557	C₂²	1	1	yes	characteristic
27	C₆₁×#557	C₂²	1	1	yes	characteristic
28	C₆₁×#557	C₂²	1	1	yes	characteristic
29	C₆₁×#557	C₂²	1	2	yes	—
30	C₆₁×#556	C₂²	1	1	yes	characteristic
31	C₆₁×#556	C₂²	1	2	yes	—
32	C₆₁×#556	C₂²	1	1	yes	characteristic
33	C₆₁×#556	C₂²	1	2	yes	—
34	C₆₁×#553	—	2	1	no	—
35	C₆₁×#553	—	2	2	no	—
36	C₆₁×#552	—	2	1	no	—
37	C₆₁×#552	—	2	2	no	—
38	C₆₁×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₆₁	—	2	1	no	—
40	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#548	—	2	1	no	—
42	C₆₁×#541	—	2	1	no	—
43	C₆₁×#541	—	2	2	no	—
44	C₆₁×#533	C₂²	1	1	yes	characteristic
45	C₆₁×#533	C₂²	1	2	yes	—
46	C₆₁×#532	C₂²	1	1	yes	characteristic
47	C₆₁×#532	C₂²	1	2	yes	—
48	C₆₁×#529	—	2	2	no	—
49	C₆₁×#529	—	2	1	no	—
50	C₆₁×#529	C₂²	1	1	yes	characteristic
51	C₆₁×#529	C₂²	1	2	yes	—
52	C₆₁×#519	—	2	1	no	—
53	C₄×#41×C₆₁	—	2	1	no	—
54	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
55	C₄×#41×C₆₁	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
57	C₆₁×#497	C₂²	1	2	yes	—
58	C₆₁×#497	C₂²	1	2	yes	—
59	C₆₁×#497	C₂²	1	2	yes	—
60	C₆₁×#496	C₂²	1	2	yes	—
61	C₆₁×#495	C₂²	1	2	yes	—
62	C₆₁×#494	C₂²	1	1	yes	characteristic
63	C₆₁×#492	C₂²	1	1	yes	characteristic
64	C₆₁×#491	C₂²	1	2	yes	—
65	C₆₁×#490	C₂²	1	2	yes	—
66	C₆₁×#489	C₂²	1	2	yes	—
67	C₆₁×#489	C₂²	1	2	yes	—
68	C₆₁×#488	C₂²	1	2	yes	—
69	C₆₁×#487	C₂²	1	1	yes	characteristic
70	C₆₁×#486	C₂²	1	1	yes	characteristic
71	C₆₁×#485	C₂²	1	1	yes	characteristic
72	C₆₁×#485	C₂²	1	2	yes	—
73	C₆₁×#482	C₂²	1	1	yes	characteristic
74	C₆₁×#479	C₂²	1	1	yes	characteristic
75	C₆₁×#479	C₂²	1	2	yes	—
76	C₆₁×#478	C₂²	1	1	yes	characteristic
77	C₆₁×#478	C₂²	1	2	yes	—
78	C₆₁×#477	C₂²	1	2	yes	—
79	C₆₁×#476	C₂²	1	2	yes	—
80	C₆₁×#475	C₂²	1	1	yes	characteristic
81	C₆₁×#474	C₂²	1	1	yes	characteristic
82	C₆₁×#464	C₂²	1	1	yes	characteristic
83	C₆₁×#464	C₂²	1	2	yes	—
84	C₆₁×#464	C₂²	1	2	yes	—
85	C₆₁×#464	C₂²	1	2	yes	—
86	C₆₁×#464	C₂²	1	2	yes	—
87	C₆₁×#464	C₂²	1	2	yes	—
88	C₆₁×#463	C₂²	1	1	yes	characteristic
89	C₆₁×#463	C₂²	1	2	yes	—
90	C₆₁×#463	C₂²	1	2	yes	—
91	C₆₁×#463	C₂²	1	2	yes	—
92	C₆₁×#462	C₂²	1	1	yes	characteristic
93	C₆₁×#462	C₂²	1	2	yes	—
94	C₆₁×#462	C₂²	1	1	yes	characteristic
95	C₆₁×#462	C₂²	1	2	yes	—
96	C₆₁×#462	C₂²	1	2	yes	—
97	C₆₁×#461	C₂²	1	1	yes	characteristic
98	C₆₁×#461	C₂²	1	1	yes	characteristic
99	C₆₁×#461	C₂²	1	2	yes	—
100	C₆₁×#460	C₂²	1	1	yes	characteristic
101	C₆₁×#460	C₂²	1	2	yes	—
102	C₆₁×#460	C₂²	1	2	yes	—
103	C₆₁×#459	C₂²	1	1	yes	characteristic
104	C₆₁×#452	C₂²	1	1	yes	characteristic
105	C₆₁×#452	C₂²	1	2	yes	—
106	C₆₁×#452	C₂²	1	2	yes	—
107	C₆₁×#452	C₂²	1	2	yes	—
108	C₆₁×#452	C₂²	1	2	yes	—
109	C₆₁×#449	C₂²	1	1	yes	characteristic
110	C₆₁×#449	C₂²	1	2	yes	—
111	C₆₁×#446	C₂²	1	1	yes	characteristic
112	C₆₁×#446	C₂²	1	1	yes	characteristic
113	C₆₁×#446	C₂²	1	2	yes	—
114	C₆₁×#446	C₂²	1	1	yes	characteristic
115	C₆₁×#446	C₂²	1	1	yes	characteristic
116	C₆₁×#446	C₂²	1	2	yes	—
117	C₆₁×#442	C₂²	1	2	yes	—
118	C₆₁×#441	C₂²	1	2	yes	—
119	C₆₁×#441	C₂²	1	2	yes	—
120	C₆₁×#441	C₂²	1	2	yes	—
121	C₆₁×#440	C₂²	1	2	yes	—
122	C₆₁×#440	C₂²	1	2	yes	—
123	C₆₁×#440	C₂²	1	2	yes	—
124	C₆₁×#440	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
126	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
129	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
130	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
131	C₆₁×#432	C₂²	1	2	yes	—
132	C₆₁×#432	C₂²	1	2	yes	—
133	C₆₁×#431	C₂²	1	1	yes	characteristic
134	C₆₁×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	C₂³	1	2	yes	—
137	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₆₁	—	2	1	no	—
139	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
140	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
143	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
152	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₆₁	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₆₁	—	2	1	no	—
155	C₄⋊Q₈×C₆₁	—	2	2	no	—
156	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
162	#127×C₆₁	C₂³	1	1	yes	characteristic
163	#127×C₆₁	C₂³	1	2	yes	—
164	#126×C₆₁	—	2	2	no	—
165	#126×C₆₁	—	2	2	no	—
166	#126×C₆₁	—	2	2	no	—
167	#126×C₆₁	—	2	2	no	—
168	#126×C₆₁	—	2	2	no	—
169	#126×C₆₁	—	2	2	no	—
170	#126×C₆₁	—	2	2	no	—
171	#126×C₆₁	—	2	1	no	—
172	#125×C₆₁	—	2	2	no	—
173	#125×C₆₁	—	2	2	no	—
174	#125×C₆₁	—	2	2	no	—
175	#125×C₆₁	—	2	1	no	—
176	#125×C₆₁	—	2	2	no	—
177	#125×C₆₁	—	2	1	no	—
178	#125×C₆₁	—	2	2	no	—
179	#125×C₆₁	—	2	2	no	—
180	#125×C₆₁	—	2	1	no	—
181	#125×C₆₁	C₂³	1	1	yes	characteristic
182	#125×C₆₁	C₂³	1	2	yes	—
183	#124×C₆₁	—	2	1	no	—
184	#124×C₆₁	—	2	2	no	—
185	#124×C₆₁	C₂³	1	2	yes	—
186	#124×C₆₁	C₂³	1	2	yes	—
187	#124×C₆₁	C₂³	1	2	yes	—
188	#124×C₆₁	C₂³	1	1	yes	characteristic
189	#124×C₆₁	C₂³	1	2	yes	—
190	#123×C₆₁	—	2	1	no	—
191	#123×C₆₁	—	2	2	no	—
192	#123×C₆₁	—	2	2	no	—
193	#123×C₆₁	—	2	2	no	—
194	#123×C₆₁	—	2	2	no	—
195	C₂²⋊Q₈×C₆₁	—	2	1	no	—
196	C₂²⋊Q₈×C₆₁	—	2	2	no	—
197	C₂²⋊Q₈×C₆₁	—	2	1	no	—
198	C₂²⋊Q₈×C₆₁	—	2	2	no	—
199	C₂²⋊Q₈×C₆₁	—	2	1	no	—
200	C₂²⋊Q₈×C₆₁	—	2	2	no	—
201	C₂²⋊Q₈×C₆₁	—	2	1	no	—
202	C₂²⋊Q₈×C₆₁	—	2	2	no	—
203	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
204	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
205	#121×C₆₁	—	2	1	no	—
206	#121×C₆₁	—	2	2	no	—
207	#121×C₆₁	—	2	1	no	—
208	#121×C₆₁	—	2	2	no	—
209	#121×C₆₁	—	2	1	no	—
210	#121×C₆₁	—	2	2	no	—
211	#121×C₆₁	C₂³	1	1	yes	characteristic
212	C₄×Q₈×C₆₁	—	2	1	no	—
213	C₄×Q₈×C₆₁	—	2	1	no	—
214	C₄×Q₈×C₆₁	—	2	1	no	—
215	C₄×Q₈×C₆₁	—	2	2	no	—
216	C₄×Q₈×C₆₁	—	2	1	no	—
217	C₄×Q₈×C₆₁	—	2	2	no	—
218	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
219	C₄×Q₈×C₆₁	D₄	1	2	yes	—
220	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
221	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
222	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
223	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
224	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
228	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
233	C₄×D₄×C₆₁	—	2	1	no	—
234	C₄×D₄×C₆₁	—	2	2	no	—
235	C₄×D₄×C₆₁	—	2	1	no	—
236	C₄×D₄×C₆₁	—	2	2	no	—
237	C₄×D₄×C₆₁	—	2	1	no	—
238	C₄×D₄×C₆₁	—	2	2	no	—
239	C₄×D₄×C₆₁	—	2	1	no	—
240	C₄×D₄×C₆₁	—	2	2	no	—
241	C₄×D₄×C₆₁	—	2	1	no	—
242	C₄×D₄×C₆₁	—	2	2	no	—
243	C₄×D₄×C₆₁	—	2	2	no	—
244	C₄×D₄×C₆₁	—	2	1	no	—
245	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₆₁	C₂³	1	2	yes	—
247	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₆₁	C₂³	1	2	yes	—
249	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₆₁	C₂³	1	2	yes	—
251	#117×C₆₁	—	2	1	no	—
252	#117×C₆₁	—	2	2	no	—
253	#117×C₆₁	—	2	1	no	—
254	#117×C₆₁	—	2	2	no	—
255	#117×C₆₁	—	2	1	no	—
256	#117×C₆₁	—	2	2	no	—
257	#117×C₆₁	—	2	1	no	—
258	#117×C₆₁	—	2	2	no	—
259	#117×C₆₁	—	2	2	no	—
260	#117×C₆₁	—	2	1	no	—
261	#117×C₆₁	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
264	C₂×C₄²×C₆₁	—	2	1	no	—
265	C₂×C₄²×C₆₁	—	2	2	no	—
266	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
267	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
268	#107×C₆₁	C₂³	1	1	yes	characteristic
269	#107×C₆₁	C₂³	1	2	yes	—
270	#107×C₆₁	C₂³	1	1	yes	characteristic
271	#106×C₆₁	C₂³	1	1	yes	characteristic
272	#106×C₆₁	C₂³	1	1	yes	characteristic
273	#106×C₆₁	C₂³	1	2	yes	—
274	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
279	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
282	#103×C₆₁	C₂³	1	1	yes	characteristic
283	#103×C₆₁	C₂³	1	2	yes	—
284	#103×C₆₁	C₂³	1	1	yes	characteristic
285	#103×C₆₁	C₂³	1	2	yes	—
286	#103×C₆₁	C₂³	1	1	yes	characteristic
287	#103×C₆₁	C₂³	1	1	yes	characteristic
288	#103×C₆₁	C₂³	1	2	yes	—
289	#103×C₆₁	C₂³	1	2	yes	—
290	#103×C₆₁	C₂³	1	2	yes	—
291	#103×C₆₁	C₂³	1	2	yes	—
292	#103×C₆₁	C₂³	1	2	yes	—
293	#102×C₆₁	C₂³	1	1	yes	characteristic
294	#102×C₆₁	C₂³	1	1	yes	characteristic
295	#102×C₆₁	C₂³	1	1	yes	characteristic
296	#102×C₆₁	C₂³	1	1	yes	characteristic
297	#102×C₆₁	C₂³	1	2	yes	—
298	#102×C₆₁	C₂³	1	2	yes	—
299	#102×C₆₁	C₂³	1	2	yes	—
300	#102×C₆₁	C₂³	1	2	yes	—
301	#102×C₆₁	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
305	#97×C₆₁	C₂³	1	2	yes	—
306	#97×C₆₁	C₂³	1	2	yes	—
307	#97×C₆₁	C₂³	1	2	yes	—
308	#97×C₆₁	C₂³	1	2	yes	—
309	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₁	C₂³	1	2	yes	—
312	#41×C₆₁	—	4	2	no	—
313	#41×C₆₁	—	4	1	no	—
314	#41×C₆₁	—	4	2	no	—
315	#41×C₆₁	—	4	1	no	—
316	#41×C₆₁	—	4	4	no	—
317	C₂×Q₈×C₆₁	—	2	2	no	—
318	C₂×Q₈×C₆₁	—	2	1	no	—
319	C₂×Q₈×C₆₁	—	4	2	no	—
320	C₂×Q₈×C₆₁	—	4	4	no	—
321	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
324	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
328	C₂×D₄×C₆₁	—	2	1	no	—
329	C₂×D₄×C₆₁	—	2	1	no	—
330	C₂×D₄×C₆₁	—	2	2	no	—
331	C₂×D₄×C₆₁	—	2	2	no	—
332	C₂×D₄×C₆₁	—	2	1	no	—
333	C₂×D₄×C₆₁	—	2	2	no	—
334	C₂×D₄×C₆₁	—	2	1	no	—
335	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
337	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₆₁	—	2	1	no	—
339	C₂²×C₄×C₆₁	—	2	2	no	—
340	C₂²×C₄×C₆₁	—	2	2	no	—
341	C₂²×C₄×C₆₁	—	2	1	no	—
342	C₂²×C₄×C₆₁	—	2	2	no	—
343	C₂²×C₄×C₆₁	—	2	1	no	—
344	C₂²×C₄×C₆₁	—	2	1	no	—
345	C₂²×C₄×C₆₁	—	2	2	no	—
346	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
349	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
350	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
351	Q₁₆×C₆₁	—	4	2	no	—
352	Q₁₆×C₆₁	—	4	2	no	—
353	Q₁₆×C₆₁	—	4	1	no	—
354	Q₁₆×C₆₁	—	4	2	no	—
355	Q₁₆×C₆₁	—	4	2	no	—
356	SD₁₆×C₆₁	—	4	2	no	—
357	SD₁₆×C₆₁	—	4	2	no	—
358	SD₁₆×C₆₁	—	4	2	no	—
359	SD₁₆×C₆₁	—	4	2	no	—
360	SD₁₆×C₆₁	—	4	2	no	—
361	SD₁₆×C₆₁	—	4	1	no	—
362	SD₁₆×C₆₁	—	4	1	no	—
363	D₈×C₆₁	—	4	1	no	—
364	D₈×C₆₁	—	4	2	no	—
365	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
369	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
370	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄×C₆₁	—	2	2	no	—
372	C₄⋊C₄×C₆₁	—	2	1	no	—
373	C₄⋊C₄×C₆₁	—	2	2	no	—
374	C₄⋊C₄×C₆₁	—	2	1	no	—
375	C₄⋊C₄×C₆₁	—	2	2	no	—
376	C₄⋊C₄×C₆₁	—	2	1	no	—
377	C₄⋊C₄×C₆₁	—	2	2	no	—
378	C₄⋊C₄×C₆₁	—	2	1	no	—
379	C₄⋊C₄×C₆₁	—	2	1	no	—
380	C₄⋊C₄×C₆₁	—	2	2	no	—
381	C₄⋊C₄×C₆₁	—	2	1	no	—
382	C₄⋊C₄×C₆₁	—	2	2	no	—
383	C₄⋊C₄×C₆₁	—	2	2	no	—
384	C₄⋊C₄×C₆₁	—	2	1	no	—
385	C₄⋊C₄×C₆₁	—	2	2	no	—
386	C₄⋊C₄×C₆₁	—	2	1	no	—
387	C₄⋊C₄×C₆₁	—	2	2	no	—
388	C₄⋊C₄×C₆₁	—	2	1	no	—
389	C₄⋊C₄×C₆₁	—	2	2	no	—
390	C₄⋊C₄×C₆₁	—	2	1	no	—
391	C₄⋊C₄×C₆₁	—	2	2	no	—
392	C₄⋊C₄×C₆₁	—	2	2	no	—
393	C₄⋊C₄×C₆₁	—	2	2	no	—
394	C₄⋊C₄×C₆₁	—	2	2	no	—
395	C₄⋊C₄×C₆₁	—	2	1	no	—
396	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
408	C₂²⋊C₄×C₆₁	—	2	2	no	—
409	C₂²⋊C₄×C₆₁	—	2	1	no	—
410	C₂²⋊C₄×C₆₁	—	2	1	no	—
411	C₂²⋊C₄×C₆₁	—	2	1	no	—
412	C₂²⋊C₄×C₆₁	—	2	1	no	—
413	C₂²⋊C₄×C₆₁	—	2	2	no	—
414	C₂²⋊C₄×C₆₁	—	2	2	no	—
415	C₂²⋊C₄×C₆₁	—	2	2	no	—
416	C₂²⋊C₄×C₆₁	—	2	2	no	—
417	C₂²⋊C₄×C₆₁	—	2	2	no	—
418	C₂²⋊C₄×C₆₁	—	2	1	no	—
419	C₂²⋊C₄×C₆₁	—	2	2	no	—
420	C₂²⋊C₄×C₆₁	—	2	1	no	—
421	C₂²⋊C₄×C₆₁	—	2	2	no	—
422	C₂²⋊C₄×C₆₁	—	2	2	no	—
423	C₂²⋊C₄×C₆₁	—	2	2	no	—
424	C₂²⋊C₄×C₆₁	—	2	2	no	—
425	C₂²⋊C₄×C₆₁	—	2	1	no	—
426	C₂²⋊C₄×C₆₁	—	2	2	no	—
427	C₂²⋊C₄×C₆₁	—	2	1	no	—
428	C₄²×C₆₁	—	2	1	no	—
429	C₄²×C₆₁	—	2	1	no	—
430	C₄²×C₆₁	—	2	2	no	—
431	C₄²×C₆₁	—	2	2	no	—
432	C₄²×C₆₁	—	2	1	no	—
433	C₄²×C₆₁	—	2	2	no	—
434	C₄²×C₆₁	—	2	2	no	—
435	C₄²×C₆₁	—	2	2	no	—
436	C₄²×C₆₁	—	2	2	no	—
437	C₄²×C₆₁	—	2	1	no	—
438	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₆₁	C₂×D₄	1	2	yes	—
440	C₄²×C₆₁	C₂×D₄	1	2	yes	—
441	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
443	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
444	C₄²×C₆₁	C₂⁴	1	2	yes	—
445	C₄²×C₆₁	C₂⁴	1	2	yes	—
446	C₂³×C₆₁	—	2	1	no	—
447	C₂³×C₆₁	—	2	2	no	—
448	C₂³×C₆₁	—	2	1	no	—
449	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
450	Q₈×C₆₁	—	2	2	no	—
451	Q₈×C₆₁	—	2	2	no	—
452	Q₈×C₆₁	—	2	1	no	—
453	Q₈×C₆₁	—	2	2	no	—
454	Q₈×C₆₁	—	2	2	no	—
455	Q₈×C₆₁	—	2	2	no	—
456	Q₈×C₆₁	—	2	1	no	—
457	Q₈×C₆₁	—	2	1	no	—
458	Q₈×C₆₁	—	2	1	no	—
459	Q₈×C₆₁	—	2	2	no	—
460	Q₈×C₆₁	—	4	2	no	—
461	Q₈×C₆₁	—	4	4	no	—
462	Q₈×C₆₁	—	4	2	no	—
463	D₄×C₆₁	—	2	1	no	—
464	D₄×C₆₁	—	2	1	no	—
465	D₄×C₆₁	—	2	1	no	—
466	D₄×C₆₁	—	2	2	no	—
467	D₄×C₆₁	—	2	2	no	—
468	D₄×C₆₁	—	2	1	no	—
469	D₄×C₆₁	—	4	4	no	—
470	D₄×C₆₁	—	4	2	no	—
471	D₄×C₆₁	—	4	2	no	—
472	D₄×C₆₁	—	4	4	no	—
473	D₄×C₆₁	—	4	2	no	—
474	D₄×C₆₁	—	8	2	no	—
475	D₄×C₆₁	—	8	1	no	—
476	C₂×C₄×C₆₁	—	2	2	no	—
477	C₂×C₄×C₆₁	—	2	1	no	—
478	C₂×C₄×C₆₁	—	2	1	no	—
479	C₂×C₄×C₆₁	—	2	1	no	—
480	C₂×C₄×C₆₁	—	2	1	no	—
481	C₂×C₄×C₆₁	—	2	1	no	—
482	C₂×C₄×C₆₁	—	2	2	no	—
483	C₂×C₄×C₆₁	—	2	1	no	—
484	C₂×C₄×C₆₁	—	2	1	no	—
485	C₂×C₄×C₆₁	—	2	2	no	—
486	C₂×C₄×C₆₁	—	2	2	no	—
487	C₂×C₄×C₆₁	—	2	1	no	—
488	C₂×C₄×C₆₁	—	4	1	no	—
489	C₂×C₄×C₆₁	—	4	2	no	—
490	C₂×C₄×C₆₁	—	4	2	no	—
491	C₂×C₄×C₆₁	—	4	4	no	—
492	C₂×C₄×C₆₁	—	4	2	no	—
493	C₂×C₄×C₆₁	—	4	4	no	—
494	C₂×C₄×C₆₁	—	4	4	no	—
495	C₂×C₄×C₆₁	—	4	2	no	—
496	C₂×C₄×C₆₁	—	4	2	no	—
497	C₂×C₄×C₆₁	—	8	1	no	—
498	C₂×C₄×C₆₁	—	8	2	no	—
499	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
509	C₈×C₆₁	—	2	1	no	—
510	C₈×C₆₁	—	2	2	no	—
511	C₈×C₆₁	—	2	2	no	—
512	C₈×C₆₁	—	2	1	no	—
513	C₈×C₆₁	—	2	1	no	—
514	C₈×C₆₁	—	2	1	no	—
515	#61897	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
516	C₂²×C₆₁	—	2	1	no	—
517	C₂²×C₆₁	—	2	1	no	—
518	C₂²×C₆₁	—	2	1	no	—
519	C₂²×C₆₁	—	4	2	no	—
520	C₂²×C₆₁	—	4	1	no	—
521	C₂²×C₆₁	—	4	1	no	—
522	C₂²×C₆₁	—	4	2	no	—
523	C₂²×C₆₁	—	4	1	no	—
524	C₂²×C₆₁	—	4	1	no	—
525	C₂²×C₆₁	—	4	1	no	—
526	C₂²×C₆₁	—	4	2	no	—
527	C₂²×C₆₁	—	4	1	no	—
528	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
529	C₄×C₆₁	—	2	1	no	—
530	C₄×C₆₁	—	2	2	no	—
531	C₄×C₆₁	—	2	2	no	—
532	C₄×C₆₁	—	2	1	no	—
533	C₄×C₆₁	—	2	1	no	—
534	C₄×C₆₁	—	2	1	no	—
535	C₄×C₆₁	—	2	2	no	—
536	C₄×C₆₁	—	2	2	no	—
537	C₄×C₆₁	—	4	1	no	—
538	C₄×C₆₁	—	4	1	no	—
539	C₄×C₆₁	—	4	1	no	—
540	C₄×C₆₁	—	4	2	no	—
541	C₄×C₆₁	—	4	1	no	—
542	C₄×C₆₁	—	4	2	no	—
543	C₄×C₆₁	—	4	1	no	—
544	C₄×C₆₁	—	4	2	no	—
545	C₄×C₆₁	—	4	1	no	—
546	C₄×C₆₁	#575	1	2	yes	—
547	C₄×C₆₁	#585	1	1	yes	characteristic
548	C₄×C₆₁	#585	1	1	yes	characteristic
549	#3523	C₂×C₆₁	1	1	yes	characteristic, complemented
550	#3480	C₂×C₆₁	1	1	yes	characteristic, complemented
551	#3402	C₂×C₆₁	1	2	yes	complemented
552	#3401	C₂×C₆₁	1	2	yes	complemented
553	#3400	C₂×C₆₁	1	1	yes	characteristic, complemented
554	#3398	C₂×C₆₁	1	1	yes	characteristic, complemented
555	#3398	C₂×C₆₁	1	1	yes	characteristic, complemented
556	#3397	C₂×C₆₁	1	1	yes	characteristic, complemented
557	#3377	C₂×C₆₁	1	2	yes	complemented
558	#3374	C₂×C₆₁	1	1	yes	characteristic, complemented
559	#3373	C₂×C₆₁	1	1	yes	characteristic, complemented
560	#3371	C₂×C₆₁	1	2	yes	complemented
561	#3368	C₂×C₆₁	1	1	yes	characteristic, complemented
562	#3367	C₂×C₆₁	1	1	yes	characteristic, complemented
563	#3219	C₂×C₆₁	1	2	yes	complemented
564	#3216	C₂×C₆₁	1	2	yes	complemented
565	#3212	C₂×C₆₁	1	1	yes	characteristic, complemented
566	#3210	C₂×C₆₁	1	1	yes	characteristic, complemented
567	#3116	C₂×C₆₁	1	2	yes	complemented
568	#3111	C₂×C₆₁	1	2	yes	complemented
569	#3107	C₂×C₆₁	1	1	yes	characteristic, complemented
570	#3102	C₂×C₆₁	1	1	yes	characteristic, complemented
571	#2983	C₂×C₆₁	1	1	yes	characteristic, complemented
572	C₂×C₆₁	—	4	1	no	—
573	C₂×C₆₁	—	8	2	no	—
574	C₂×C₆₁	—	8	1	no	—
575	C₂×C₆₁	—	8	1	no	—
576	C₂×C₆₁	#3487	1	1	yes	characteristic
577	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
578	C₂×C₆₁	#3586	1	1	yes	characteristic
579	#559	C₂²×C₆₁	1	2	yes	—
580	#559	C₂²×C₆₁	1	1	yes	characteristic
581	#557	C₂²×C₆₁	1	1	yes	characteristic
582	#557	C₂²×C₆₁	1	1	yes	characteristic
583	#557	C₂²×C₆₁	1	1	yes	characteristic
584	#557	C₂²×C₆₁	1	2	yes	—
585	#556	C₂²×C₆₁	1	1	yes	characteristic
586	#556	C₂²×C₆₁	1	2	yes	—
587	#556	C₂²×C₆₁	1	1	yes	characteristic
588	#556	C₂²×C₆₁	1	2	yes	—
589	#553	—	2	1	no	—
590	#553	—	2	2	no	—
591	#552	—	2	1	no	—
592	#552	—	2	2	no	—
593	#550	C₂²×C₆₁	1	1	yes	characteristic
594	D₄×Q₈	—	2	1	no	—
595	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
596	#548	—	2	1	no	—
597	#541	—	2	1	no	—
598	#541	—	2	2	no	—
599	#533	C₂²×C₆₁	1	1	yes	characteristic
600	#533	C₂²×C₆₁	1	2	yes	—
601	#532	C₂²×C₆₁	1	1	yes	characteristic
602	#532	C₂²×C₆₁	1	2	yes	—
603	#529	—	2	1	no	—
604	#529	—	2	2	no	—
605	#529	C₂²×C₆₁	1	1	yes	characteristic
606	#529	C₂²×C₆₁	1	2	yes	—
607	#519	—	2	1	no	—
608	C₄×#41	—	2	1	no	—
609	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
610	C₄×#41	C₂²×C₆₁	1	2	yes	—
611	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
612	#497	C₂²×C₆₁	1	2	yes	—
613	#497	C₂²×C₆₁	1	2	yes	—
614	#497	C₂²×C₆₁	1	2	yes	—
615	#496	C₂²×C₆₁	1	2	yes	—
616	#495	C₂²×C₆₁	1	2	yes	—
617	#494	C₂²×C₆₁	1	1	yes	characteristic
618	#492	C₂²×C₆₁	1	1	yes	characteristic
619	#491	C₂²×C₆₁	1	2	yes	—
620	#490	C₂²×C₆₁	1	2	yes	—
621	#489	C₂²×C₆₁	1	2	yes	—
622	#489	C₂²×C₆₁	1	2	yes	—
623	#488	C₂²×C₆₁	1	2	yes	—
624	#487	C₂²×C₆₁	1	1	yes	characteristic
625	#486	C₂²×C₆₁	1	1	yes	characteristic
626	#485	C₂²×C₆₁	1	1	yes	characteristic
627	#485	C₂²×C₆₁	1	2	yes	—
628	#482	C₂²×C₆₁	1	1	yes	characteristic
629	#479	C₂²×C₆₁	1	1	yes	characteristic
630	#479	C₂²×C₆₁	1	2	yes	—
631	#478	C₂²×C₆₁	1	1	yes	characteristic
632	#478	C₂²×C₆₁	1	2	yes	—
633	#477	C₂²×C₆₁	1	2	yes	—
634	#476	C₂²×C₆₁	1	2	yes	—
635	#475	C₂²×C₆₁	1	1	yes	characteristic
636	#474	C₂²×C₆₁	1	1	yes	characteristic
637	#464	C₂²×C₆₁	1	1	yes	characteristic
638	#464	C₂²×C₆₁	1	2	yes	—
639	#464	C₂²×C₆₁	1	2	yes	—
640	#464	C₂²×C₆₁	1	2	yes	—
641	#464	C₂²×C₆₁	1	2	yes	—
642	#464	C₂²×C₆₁	1	2	yes	—
643	#463	C₂²×C₆₁	1	1	yes	characteristic
644	#463	C₂²×C₆₁	1	2	yes	—
645	#463	C₂²×C₆₁	1	2	yes	—
646	#463	C₂²×C₆₁	1	2	yes	—
647	#462	C₂²×C₆₁	1	1	yes	characteristic
648	#462	C₂²×C₆₁	1	2	yes	—
649	#462	C₂²×C₆₁	1	1	yes	characteristic
650	#462	C₂²×C₆₁	1	2	yes	—
651	#462	C₂²×C₆₁	1	2	yes	—
652	#461	C₂²×C₆₁	1	1	yes	characteristic
653	#461	C₂²×C₆₁	1	1	yes	characteristic
654	#461	C₂²×C₆₁	1	2	yes	—
655	#460	C₂²×C₆₁	1	1	yes	characteristic
656	#460	C₂²×C₆₁	1	2	yes	—
657	#460	C₂²×C₆₁	1	2	yes	—
658	#459	C₂²×C₆₁	1	1	yes	characteristic
659	#452	C₂²×C₆₁	1	1	yes	characteristic
660	#452	C₂²×C₆₁	1	2	yes	—
661	#452	C₂²×C₆₁	1	2	yes	—
662	#452	C₂²×C₆₁	1	2	yes	—
663	#452	C₂²×C₆₁	1	2	yes	—
664	#449	C₂²×C₆₁	1	1	yes	characteristic
665	#449	C₂²×C₆₁	1	2	yes	—
666	#446	C₂²×C₆₁	1	1	yes	characteristic
667	#446	C₂²×C₆₁	1	1	yes	characteristic
668	#446	C₂²×C₆₁	1	2	yes	—
669	#446	C₂²×C₆₁	1	1	yes	characteristic
670	#446	C₂²×C₆₁	1	1	yes	characteristic
671	#446	C₂²×C₆₁	1	2	yes	—
672	#442	C₂²×C₆₁	1	2	yes	—
673	#441	C₂²×C₆₁	1	2	yes	—
674	#441	C₂²×C₆₁	1	2	yes	—
675	#441	C₂²×C₆₁	1	2	yes	—
676	#440	C₂²×C₆₁	1	2	yes	—
677	#440	C₂²×C₆₁	1	2	yes	—
678	#440	C₂²×C₆₁	1	2	yes	—
679	#440	C₂²×C₆₁	1	2	yes	—
680	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
681	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
682	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
683	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
684	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
685	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
686	#432	C₂²×C₆₁	1	2	yes	—
687	#432	C₂²×C₆₁	1	2	yes	—
688	#431	C₂²×C₆₁	1	1	yes	characteristic
689	#431	C₂²×C₆₁	1	1	yes	characteristic
690	C₆₁	#61897	1	1	yes	characteristic, direct product factor, Sylow
691	C₂×#41	—	2	1	no	—
692	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
693	C₂×#41	C₂³×C₆₁	1	2	yes	—
694	C₂²×Q₈	—	2	1	no	—
695	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
696	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
697	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
698	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
699	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
700	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
701	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
702	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
703	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
704	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
705	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
706	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
707	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
708	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
709	C₂×D₈	C₂³×C₆₁	1	2	yes	—
710	C₄⋊Q₈	—	2	1	no	—
711	C₄⋊Q₈	—	2	2	no	—
712	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
713	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
714	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
715	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
716	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
717	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
718	#127	C₂³×C₆₁	1	1	yes	characteristic
719	#127	C₂³×C₆₁	1	2	yes	—
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#126	—	2	2	no	—
723	#126	—	2	2	no	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	1	no	—
728	#125	—	2	1	no	—
729	#125	—	2	2	no	—
730	#125	—	2	2	no	—
731	#125	—	2	2	no	—
732	#125	—	2	2	no	—
733	#125	—	2	1	no	—
734	#125	—	2	2	no	—
735	#125	—	2	2	no	—
736	#125	—	2	1	no	—
737	#125	C₂³×C₆₁	1	1	yes	characteristic
738	#125	C₂³×C₆₁	1	2	yes	—
739	#124	—	2	1	no	—
740	#124	—	2	2	no	—
741	#124	C₂³×C₆₁	1	1	yes	characteristic
742	#124	C₂³×C₆₁	1	2	yes	—
743	#124	C₂³×C₆₁	1	2	yes	—
744	#124	C₂³×C₆₁	1	2	yes	—
745	#124	C₂³×C₆₁	1	2	yes	—
746	#123	—	2	1	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	1	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
760	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
761	#121	—	2	1	no	—
762	#121	—	2	2	no	—
763	#121	—	2	1	no	—
764	#121	—	2	2	no	—
765	#121	—	2	1	no	—
766	#121	—	2	2	no	—
767	#121	C₂³×C₆₁	1	1	yes	characteristic
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	1	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	2	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	2	no	—
774	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
775	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
776	C₄×Q₈	D₄×C₆₁	1	2	yes	—
777	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
778	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
779	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
781	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
783	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
784	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
785	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
786	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₆₁	1	2	yes	—
803	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₆₁	1	2	yes	—
805	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
806	C₄×D₄	C₂³×C₆₁	1	2	yes	—
807	#117	—	2	1	no	—
808	#117	—	2	2	no	—
809	#117	—	2	1	no	—
810	#117	—	2	2	no	—
811	#117	—	2	1	no	—
812	#117	—	2	2	no	—
813	#117	—	2	2	no	—
814	#117	—	2	1	no	—
815	#117	—	2	1	no	—
816	#117	—	2	2	no	—
817	#117	C₂³×C₆₁	1	1	yes	characteristic
818	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
819	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
820	C₂×C₄²	—	2	1	no	—
821	C₂×C₄²	—	2	2	no	—
822	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
823	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
824	#107	C₂³×C₆₁	1	1	yes	characteristic
825	#107	C₂³×C₆₁	1	2	yes	—
826	#107	C₂³×C₆₁	1	1	yes	characteristic
827	#106	C₂³×C₆₁	1	1	yes	characteristic
828	#106	C₂³×C₆₁	1	1	yes	characteristic
829	#106	C₂³×C₆₁	1	2	yes	—
830	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
831	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
832	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
833	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
834	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
835	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
836	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
837	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
838	#103	C₂³×C₆₁	1	1	yes	characteristic
839	#103	C₂³×C₆₁	1	2	yes	—
840	#103	C₂³×C₆₁	1	1	yes	characteristic
841	#103	C₂³×C₆₁	1	2	yes	—
842	#103	C₂³×C₆₁	1	1	yes	characteristic
843	#103	C₂³×C₆₁	1	1	yes	characteristic
844	#103	C₂³×C₆₁	1	2	yes	—
845	#103	C₂³×C₆₁	1	2	yes	—
846	#103	C₂³×C₆₁	1	2	yes	—
847	#103	C₂³×C₆₁	1	2	yes	—
848	#103	C₂³×C₆₁	1	2	yes	—
849	#102	C₂³×C₆₁	1	1	yes	characteristic
850	#102	C₂³×C₆₁	1	1	yes	characteristic
851	#102	C₂³×C₆₁	1	1	yes	characteristic
852	#102	C₂³×C₆₁	1	1	yes	characteristic
853	#102	C₂³×C₆₁	1	2	yes	—
854	#102	C₂³×C₆₁	1	2	yes	—
855	#102	C₂³×C₆₁	1	2	yes	—
856	#102	C₂³×C₆₁	1	2	yes	—
857	#102	C₂³×C₆₁	1	2	yes	—
858	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
859	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
860	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
861	#97	C₂³×C₆₁	1	2	yes	—
862	#97	C₂³×C₆₁	1	2	yes	—
863	#97	C₂³×C₆₁	1	2	yes	—
864	#97	C₂³×C₆₁	1	2	yes	—
865	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
866	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
867	C₄×C₈	C₂³×C₆₁	1	2	yes	—
868	#41	—	4	1	no	—
869	#41	—	4	2	no	—
870	#41	—	4	1	no	—
871	#41	—	4	2	no	—
872	#41	—	4	4	no	—
873	C₂×Q₈	—	2	2	no	—
874	C₂×Q₈	—	2	1	no	—
875	C₂×Q₈	—	4	2	no	—
876	C₂×Q₈	—	4	4	no	—
877	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
878	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
879	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
880	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
881	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
882	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
883	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
884	C₂×D₄	—	2	1	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
892	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
893	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	2	1	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
903	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
904	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
905	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
906	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
907	Q₁₆	—	4	2	no	—
908	Q₁₆	—	4	2	no	—
909	Q₁₆	—	4	1	no	—
910	Q₁₆	—	4	2	no	—
911	Q₁₆	—	4	2	no	—
912	SD₁₆	—	4	2	no	—
913	SD₁₆	—	4	2	no	—
914	SD₁₆	—	4	2	no	—
915	SD₁₆	—	4	2	no	—
916	SD₁₆	—	4	2	no	—
917	SD₁₆	—	4	1	no	—
918	SD₁₆	—	4	1	no	—
919	D₈	—	4	1	no	—
920	D₈	—	4	2	no	—
921	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
922	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
923	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
924	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
925	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
926	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
953	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
954	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
955	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
956	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
957	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
958	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
959	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
960	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
961	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
962	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
963	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	1	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	1	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	1	no	—
994	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
995	C₄²	C₂×D₄×C₆₁	1	2	yes	—
996	C₄²	C₂×D₄×C₆₁	1	2	yes	—
997	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
998	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
999	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1000	C₄²	C₂⁴×C₆₁	1	2	yes	—
1001	C₄²	C₂⁴×C₆₁	1	2	yes	—
1002	C₂³	—	2	1	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	2	1	no	—
1005	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1006	Q₈	—	2	2	no	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	1	no	—
1009	Q₈	—	2	2	no	—
1010	Q₈	—	2	2	no	—
1011	Q₈	—	2	2	no	—
1012	Q₈	—	2	1	no	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	2	no	—
1016	Q₈	—	4	2	no	—
1017	Q₈	—	4	4	no	—
1018	Q₈	—	4	2	no	—
1019	D₄	—	2	1	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	2	1	no	—
1022	D₄	—	2	2	no	—
1023	D₄	—	2	2	no	—
1024	D₄	—	2	1	no	—
1025	D₄	—	4	4	no	—
1026	D₄	—	4	2	no	—
1027	D₄	—	4	2	no	—
1028	D₄	—	4	4	no	—
1029	D₄	—	4	2	no	—
1030	D₄	—	8	2	no	—
1031	D₄	—	8	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	4	1	no	—
1045	C₂×C₄	—	4	2	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	4	no	—
1048	C₂×C₄	—	4	4	no	—
1049	C₂×C₄	—	4	2	no	—
1050	C₂×C₄	—	4	4	no	—
1051	C₂×C₄	—	4	2	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	8	1	no	—
1054	C₂×C₄	—	8	2	no	—
1055	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1056	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1057	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1058	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1059	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1060	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1061	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1062	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1063	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1064	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1065	C₈	—	2	1	no	—
1066	C₈	—	2	2	no	—
1067	C₈	—	2	2	no	—
1068	C₈	—	2	1	no	—
1069	C₈	—	2	1	no	—
1070	C₈	—	2	1	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	1	no	—
1074	C₂²	—	4	1	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	2	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1084	C₄	—	2	1	no	—
1085	C₄	—	2	2	no	—
1086	C₄	—	2	2	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	2	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	2	no	—
1101	C₄	C₆₁×#575	1	2	yes	—
1102	C₄	C₆₁×#585	1	1	yes	characteristic
1103	C₄	C₆₁×#585	1	1	yes	characteristic
1104	C₂	—	4	1	no	—
1105	C₂	—	8	1	no	—
1106	C₂	—	8	2	no	—
1107	C₂	—	8	1	no	—
1108	C₂	C₆₁×#3487	1	1	yes	characteristic
1109	C₂	C₂×C₆₁×#575	1	1	yes	characteristic
1110	C₂	C₆₁×#3586	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 ◁ C₂×C₄×Q₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3523	C₂	semidirect
2. C₆₁×#3480	C₂	semidirect
3. C₆₁×#3402	C₂	semidirect
4. C₆₁×#3401	C₂	semidirect
5. C₆₁×#3400	C₂	semidirect
6. C₆₁×#3398	C₂	semidirect
7. C₆₁×#3398	C₂	semidirect
8. C₆₁×#3397	C₂	semidirect
9. C₆₁×#3377	C₂	semidirect
10. C₆₁×#3374	C₂	semidirect
11. C₆₁×#3373	C₂	semidirect
12. C₆₁×#3371	C₂	semidirect
13. C₆₁×#3368	C₂	semidirect
14. C₆₁×#3367	C₂	semidirect
15. C₆₁×#3219	C₂	semidirect
16. C₆₁×#3216	C₂	semidirect
17. C₆₁×#3212	C₂	semidirect
18. C₆₁×#3210	C₂	semidirect
19. C₆₁×#3116	C₂	semidirect
20. C₆₁×#3111	C₂	semidirect
21. C₆₁×#3107	C₂	semidirect
22. C₆₁×#3102	C₂	semidirect
23. C₆₁×#2983	C₂	semidirect
515. #61897	C₆₁	direct (N × H)
549. #3523	C₂×C₆₁	semidirect
550. #3480	C₂×C₆₁	semidirect
551. #3402	C₂×C₆₁	semidirect
552. #3401	C₂×C₆₁	semidirect
553. #3400	C₂×C₆₁	semidirect
554. #3398	C₂×C₆₁	semidirect
555. #3398	C₂×C₆₁	semidirect
556. #3397	C₂×C₆₁	semidirect
557. #3377	C₂×C₆₁	semidirect
558. #3374	C₂×C₆₁	semidirect
559. #3373	C₂×C₆₁	semidirect
560. #3371	C₂×C₆₁	semidirect
561. #3368	C₂×C₆₁	semidirect
562. #3367	C₂×C₆₁	semidirect
563. #3219	C₂×C₆₁	semidirect
564. #3216	C₂×C₆₁	semidirect
565. #3212	C₂×C₆₁	semidirect
566. #3210	C₂×C₆₁	semidirect
567. #3116	C₂×C₆₁	semidirect
568. #3111	C₂×C₆₁	semidirect
569. #3107	C₂×C₆₁	semidirect
570. #3102	C₂×C₆₁	semidirect
571. #2983	C₂×C₆₁	semidirect
690. C₆₁	#61897	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×#3523	2
C₆₁×#3480	2
C₆₁×#3402	2
C₆₁×#3401	2
C₆₁×#3400	2
C₆₁×#3398	2
C₆₁×#3397	2
C₆₁×#3377	2
C₆₁×#3374	2
C₆₁×#3373	2
C₆₁×#3371	2
C₆₁×#3368	2
C₆₁×#3367	2
C₆₁×#3219	2
C₆₁×#3216	2
C₆₁×#3212	2
C₆₁×#3210	2
C₆₁×#3116	2
C₆₁×#3111	2
C₆₁×#3107	2
C₆₁×#3102	2
C₆₁×#2983	2
#61897	61

Subgroups — C61×#61897 #29565330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61897 #29565330