Subgroups — C₆₁×#62092 #29565525

Order 15616.

1840 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3558	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3401	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3375	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3324	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3319	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3313	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3277	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3266	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3265	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3262	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3224	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3121	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3043	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3040	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#2995	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#137×C₆₁	C₂²	1	1	yes	characteristic, complemented
21	C₂×#137×C₆₁	C₂²	1	2	yes	complemented
22	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
24	C₆₁×#562	—	2	1	no	—
25	C₆₁×H(3,𝔽₄)	—	2	1	no	—
26	C₆₁×#559	C₂²	1	2	yes	—
27	Q₈²×C₆₁	C₂²	1	1	yes	characteristic, complemented
28	C₆₁×#556	—	2	2	no	—
29	C₆₁×#556	—	2	1	no	—
30	C₆₁×#556	C₂²	1	1	yes	characteristic, complemented
31	C₆₁×#556	C₂²	1	2	yes	complemented
32	C₆₁×#555	—	2	1	no	—
33	C₆₁×#555	C₂²	1	1	yes	characteristic, complemented
34	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
35	C₆₁×#548	C₂²	1	2	yes	—
36	C₆₁×#548	C₂²	1	2	yes	complemented
37	C₆₁×#546	—	2	2	no	—
38	C₆₁×#546	C₂²	1	2	yes	—
39	D₄²×C₆₁	C₂²	1	2	yes	—
40	C₆₁×#542	—	2	2	no	—
41	C₆₁×#542	C₂²	1	2	yes	—
42	C₆₁×#542	C₂²	1	2	yes	complemented
43	C₆₁×#538	—	2	2	no	—
44	C₆₁×#538	—	2	1	no	—
45	C₆₁×#535	C₂²	1	2	yes	—
46	C₆₁×#534	—	2	1	no	—
47	C₆₁×#533	—	2	1	no	—
48	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
49	C₆₁×#532	C₂²	1	1	yes	characteristic
50	C₆₁×#529	—	2	1	no	—
51	C₆₁×#529	C₂²	1	1	yes	characteristic
52	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
53	C₆₁×#519	C₂²	1	2	yes	complemented
54	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic, complemented
55	C₆₁×#497	C₂²	1	2	yes	complemented
56	C₆₁×#496	C₂²	1	2	yes	—
57	C₆₁×#495	C₂²	1	2	yes	complemented
58	C₆₁×#489	C₂²	1	2	yes	complemented
59	C₆₁×#489	C₂²	1	2	yes	complemented
60	C₆₁×#486	C₂²	1	2	yes	—
61	C₆₁×#485	C₂²	1	2	yes	complemented
62	C₆₁×#482	C₂²	1	2	yes	—
63	C₆₁×#482	C₂²	1	2	yes	complemented
64	C₆₁×#477	C₂²	1	2	yes	complemented
65	C₆₁×#477	C₂²	1	2	yes	complemented
66	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
67	C₆₁×#474	C₂²	1	2	yes	complemented
68	C₆₁×#474	C₂²	1	2	yes	complemented
69	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
70	C₆₁×#468	C₂²	1	2	yes	—
71	C₆₁×#468	C₂²	1	2	yes	complemented
72	C₆₁×#468	C₂²	1	2	yes	complemented
73	C₆₁×#468	C₂²	1	2	yes	complemented
74	C₆₁×#467	C₂²	1	2	yes	complemented
75	C₆₁×#466	C₂²	1	2	yes	—
76	C₆₁×#464	C₂²	1	2	yes	complemented
77	C₆₁×#464	C₂²	1	2	yes	complemented
78	C₆₁×#464	C₂²	1	2	yes	complemented
79	C₆₁×#464	C₂²	1	2	yes	complemented
80	C₆₁×#464	C₂²	1	2	yes	complemented
81	C₆₁×#464	C₂²	1	2	yes	complemented
82	C₆₁×#464	C₂²	1	2	yes	complemented
83	C₆₁×#463	C₂²	1	2	yes	complemented
84	C₆₁×#463	C₂²	1	2	yes	complemented
85	C₆₁×#463	C₂²	1	2	yes	complemented
86	C₆₁×#461	C₂²	1	2	yes	complemented
87	C₆₁×#460	C₂²	1	2	yes	—
88	C₆₁×#460	C₂²	1	2	yes	—
89	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
90	C₆₁×#460	C₂²	1	2	yes	complemented
91	C₆₁×#459	C₂²	1	1	yes	characteristic, complemented
92	C₆₁×#452	C₂²	1	2	yes	complemented
93	C₆₁×#451	C₂²	1	2	yes	complemented
94	C₆₁×#451	C₂²	1	2	yes	complemented
95	C₆₁×#450	C₂²	1	2	yes	—
96	C₆₁×#450	C₂²	1	2	yes	complemented
97	C₆₁×#449	C₂²	1	2	yes	complemented
98	C₆₁×#449	C₂²	1	2	yes	complemented
99	C₆₁×#448	C₂²	1	2	yes	—
100	C₆₁×#447	C₂²	1	2	yes	complemented
101	C₆₁×#446	C₂²	1	2	yes	complemented
102	C₆₁×#442	C₂²	1	2	yes	complemented
103	C₆₁×#441	C₂²	1	2	yes	complemented
104	C₆₁×#440	C₂²	1	2	yes	complemented
105	C₆₁×#440	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
108	C₆₁×#436	C₂²	1	2	yes	complemented
109	C₆₁×#435	C₂²	1	2	yes	complemented
110	C₆₁×#435	C₂²	1	2	yes	complemented
111	C₆₁×#433	C₂²	1	2	yes	complemented
112	C₆₁×#432	C₂²	1	1	yes	characteristic, complemented
113	C₆₁×#424	C₂²	1	2	yes	complemented
114	C₆₁×#423	C₂²	1	1	yes	characteristic, complemented
115	C₆₁×#419	C₂²	1	1	yes	characteristic, complemented
116	C₆₁×#418	C₂²	1	1	yes	characteristic
117	C₆₁×#418	C₂²	1	2	yes	complemented
118	C₆₁×#416	C₂²	1	2	yes	complemented
119	C₂×#41×C₆₁	—	2	1	no	—
120	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
121	C₂×#41×C₆₁	C₂³	1	2	yes	—
122	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
123	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₆₁	—	2	2	no	—
125	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
126	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
127	#137×C₆₁	—	4	4	no	—
128	#137×C₆₁	—	4	2	no	—
129	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
130	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
131	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
132	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
133	C₂×SD₁₆×C₆₁	—	4	4	no	—
134	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
135	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
136	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
137	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
138	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
141	C₂×D₈×C₆₁	C₂³	1	2	yes	—
142	C₂×D₈×C₆₁	C₂³	1	2	yes	—
143	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
145	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
146	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
147	C₄⋊Q₈×C₆₁	—	2	1	no	—
148	C₄⋊Q₈×C₆₁	—	2	1	no	—
149	C₄⋊Q₈×C₆₁	—	2	2	no	—
150	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
154	#127×C₆₁	C₂³	1	1	yes	characteristic
155	#127×C₆₁	C₂³	1	2	yes	—
156	#126×C₆₁	—	2	2	no	—
157	#126×C₆₁	—	2	2	no	—
158	#126×C₆₁	—	2	2	no	—
159	#126×C₆₁	—	2	2	no	—
160	#126×C₆₁	—	2	2	no	—
161	#126×C₆₁	D₄	1	2	yes	—
162	#125×C₆₁	—	2	1	no	—
163	#125×C₆₁	D₄	1	1	yes	characteristic
164	#124×C₆₁	—	2	2	no	—
165	#124×C₆₁	—	2	2	no	—
166	#124×C₆₁	—	2	2	no	—
167	#124×C₆₁	—	2	2	no	—
168	#124×C₆₁	—	2	2	no	—
169	#124×C₆₁	—	2	2	no	—
170	#124×C₆₁	—	2	2	no	—
171	#124×C₆₁	—	2	1	no	—
172	#124×C₆₁	—	2	1	no	—
173	#124×C₆₁	—	2	1	no	—
174	#124×C₆₁	D₄	1	1	yes	characteristic
175	#124×C₆₁	C₂³	1	2	yes	—
176	#124×C₆₁	C₂³	1	2	yes	—
177	#124×C₆₁	C₂³	1	2	yes	—
178	#124×C₆₁	C₂³	1	2	yes	—
179	#123×C₆₁	—	2	2	no	—
180	#123×C₆₁	—	2	2	no	—
181	#123×C₆₁	—	2	2	no	—
182	#123×C₆₁	—	2	2	no	—
183	#123×C₆₁	—	2	2	no	—
184	#123×C₆₁	D₄	1	2	yes	—
185	C₂²⋊Q₈×C₆₁	—	2	1	no	—
186	C₂²⋊Q₈×C₆₁	—	2	1	no	—
187	C₂²⋊Q₈×C₆₁	—	2	2	no	—
188	C₂²⋊Q₈×C₆₁	—	2	2	no	—
189	C₂²⋊Q₈×C₆₁	—	2	2	no	—
190	C₂²⋊Q₈×C₆₁	—	2	2	no	—
191	C₂²⋊Q₈×C₆₁	—	2	2	no	—
192	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
193	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
194	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
196	#121×C₆₁	—	2	2	no	—
197	#121×C₆₁	—	2	2	no	—
198	#121×C₆₁	—	2	1	no	—
199	#121×C₆₁	—	2	1	no	—
200	#121×C₆₁	—	2	2	no	—
201	#121×C₆₁	—	2	2	no	—
202	#121×C₆₁	—	2	2	no	—
203	#121×C₆₁	—	2	2	no	—
204	#121×C₆₁	D₄	1	1	yes	characteristic
205	#121×C₆₁	C₂³	1	2	yes	—
206	#121×C₆₁	C₂³	1	2	yes	—
207	#121×C₆₁	C₂³	1	2	yes	—
208	#120×C₆₁	—	2	2	no	—
209	#120×C₆₁	—	2	2	no	—
210	#120×C₆₁	—	2	2	no	—
211	#120×C₆₁	—	2	2	no	—
212	#120×C₆₁	—	2	2	no	—
213	C₄×Q₈×C₆₁	—	2	1	no	—
214	C₄×Q₈×C₆₁	—	2	2	no	—
215	C₄×Q₈×C₆₁	—	2	2	no	—
216	C₄×Q₈×C₆₁	—	2	2	no	—
217	C₄×Q₈×C₆₁	—	2	1	no	—
218	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
221	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
223	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₆₁	—	2	1	no	—
226	C₄×D₄×C₆₁	—	2	1	no	—
227	C₄×D₄×C₆₁	—	2	1	no	—
228	C₄×D₄×C₆₁	—	2	2	no	—
229	C₄×D₄×C₆₁	—	2	2	no	—
230	C₄×D₄×C₆₁	—	2	2	no	—
231	C₄×D₄×C₆₁	—	2	1	no	—
232	C₄×D₄×C₆₁	C₂³	1	2	yes	—
233	C₄×D₄×C₆₁	C₂³	1	2	yes	—
234	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₆₁	C₂³	1	2	yes	—
237	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
238	#117×C₆₁	—	2	1	no	—
239	#117×C₆₁	—	2	1	no	—
240	#117×C₆₁	—	2	1	no	—
241	#117×C₆₁	—	2	2	no	—
242	#117×C₆₁	—	2	2	no	—
243	#117×C₆₁	—	2	1	no	—
244	#117×C₆₁	C₂³	1	2	yes	—
245	#117×C₆₁	C₂³	1	1	yes	characteristic
246	#117×C₆₁	C₂³	1	2	yes	—
247	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
248	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
249	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
250	C₂×C₄²×C₆₁	—	2	1	no	—
251	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
252	#107×C₆₁	C₂³	1	2	yes	—
253	#107×C₆₁	C₂³	1	2	yes	—
254	#107×C₆₁	C₂³	1	2	yes	—
255	#106×C₆₁	C₂³	1	2	yes	—
256	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
257	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
258	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
259	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
260	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
261	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
262	#103×C₆₁	C₂³	1	2	yes	—
263	#103×C₆₁	C₂³	1	2	yes	—
264	#103×C₆₁	C₂³	1	2	yes	—
265	#103×C₆₁	C₂³	1	2	yes	—
266	#103×C₆₁	C₂³	1	2	yes	—
267	#103×C₆₁	C₂³	1	2	yes	—
268	#103×C₆₁	C₂³	1	2	yes	—
269	#102×C₆₁	C₂³	1	2	yes	—
270	#102×C₆₁	C₂³	1	2	yes	—
271	#102×C₆₁	C₂³	1	2	yes	—
272	#102×C₆₁	C₂³	1	2	yes	—
273	#102×C₆₁	C₂³	1	2	yes	—
274	#102×C₆₁	C₂³	1	2	yes	—
275	#102×C₆₁	C₂³	1	2	yes	—
276	#102×C₆₁	C₂³	1	2	yes	—
277	#102×C₆₁	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
279	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
280	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
281	#97×C₆₁	C₂³	1	2	yes	—
282	#97×C₆₁	C₂³	1	2	yes	—
283	C₄×C₈×C₆₁	C₂³	1	2	yes	—
284	C₂⁴×C₆₁	—	2	1	no	—
285	C₂⁴×C₆₁	—	2	2	no	—
286	#41×C₆₁	—	2	2	no	—
287	#41×C₆₁	—	4	1	no	—
288	#41×C₆₁	—	4	2	no	—
289	#41×C₆₁	—	4	2	no	—
290	#41×C₆₁	—	8	2	no	—
291	C₂×Q₈×C₆₁	—	2	2	no	—
292	C₂×Q₈×C₆₁	—	2	1	no	—
293	C₂×Q₈×C₆₁	—	2	2	no	—
294	C₂×Q₈×C₆₁	—	2	1	no	—
295	C₂×Q₈×C₆₁	—	2	1	no	—
296	C₂×Q₈×C₆₁	—	2	4	no	—
297	C₂×Q₈×C₆₁	—	4	2	no	—
298	C₂×Q₈×C₆₁	—	4	1	no	—
299	C₂×Q₈×C₆₁	—	4	1	no	—
300	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
301	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
302	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
303	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
304	C₂×D₄×C₆₁	—	2	1	no	—
305	C₂×D₄×C₆₁	—	2	2	no	—
306	C₂×D₄×C₆₁	—	2	2	no	—
307	C₂×D₄×C₆₁	—	2	2	no	—
308	C₂×D₄×C₆₁	—	2	2	no	—
309	C₂×D₄×C₆₁	—	2	2	no	—
310	C₂×D₄×C₆₁	—	2	1	no	—
311	C₂×D₄×C₆₁	—	2	1	no	—
312	C₂×D₄×C₆₁	—	2	1	no	—
313	C₂×D₄×C₆₁	—	2	2	no	—
314	C₂×D₄×C₆₁	—	2	2	no	—
315	C₂×D₄×C₆₁	—	4	2	no	—
316	C₂×D₄×C₆₁	—	4	1	no	—
317	C₂×D₄×C₆₁	—	4	2	no	—
318	C₂×D₄×C₆₁	—	4	1	no	—
319	C₂×D₄×C₆₁	—	8	4	no	—
320	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
321	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
322	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
323	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
324	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₆₁	—	2	2	no	—
326	C₂²×C₄×C₆₁	—	2	1	no	—
327	C₂²×C₄×C₆₁	—	2	1	no	—
328	C₂²×C₄×C₆₁	—	2	1	no	—
329	C₂²×C₄×C₆₁	—	2	1	no	—
330	C₂²×C₄×C₆₁	—	2	2	no	—
331	C₂²×C₄×C₆₁	—	2	2	no	—
332	C₂²×C₄×C₆₁	—	2	2	no	—
333	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
337	Q₁₆×C₆₁	—	2	4	no	—
338	Q₁₆×C₆₁	—	4	2	no	—
339	Q₁₆×C₆₁	—	4	2	no	—
340	SD₁₆×C₆₁	—	2	4	no	—
341	SD₁₆×C₆₁	—	2	4	no	—
342	SD₁₆×C₆₁	—	4	2	no	—
343	SD₁₆×C₆₁	—	4	2	no	—
344	SD₁₆×C₆₁	—	4	2	no	—
345	SD₁₆×C₆₁	—	4	2	no	—
346	SD₁₆×C₆₁	—	4	2	no	—
347	D₈×C₆₁	—	4	2	no	—
348	D₈×C₆₁	—	4	2	no	—
349	M₁₆×C₆₁	—	4	1	no	—
350	M₁₆×C₆₁	—	4	2	no	—
351	M₁₆×C₆₁	—	4	1	no	—
352	C₂×C₈×C₆₁	—	4	2	no	—
353	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
354	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
355	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
356	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
357	C₄⋊C₄×C₆₁	—	2	1	no	—
358	C₄⋊C₄×C₆₁	—	2	1	no	—
359	C₄⋊C₄×C₆₁	—	2	1	no	—
360	C₄⋊C₄×C₆₁	—	2	1	no	—
361	C₄⋊C₄×C₆₁	—	2	2	no	—
362	C₄⋊C₄×C₆₁	—	2	2	no	—
363	C₄⋊C₄×C₆₁	—	2	2	no	—
364	C₄⋊C₄×C₆₁	—	2	2	no	—
365	C₄⋊C₄×C₆₁	—	2	2	no	—
366	C₄⋊C₄×C₆₁	—	2	1	no	—
367	C₄⋊C₄×C₆₁	—	2	1	no	—
368	C₄⋊C₄×C₆₁	—	2	2	no	—
369	C₄⋊C₄×C₆₁	—	2	2	no	—
370	C₄⋊C₄×C₆₁	—	2	2	no	—
371	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
372	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
373	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
375	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
377	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
379	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
380	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
381	C₂²⋊C₄×C₆₁	—	2	2	no	—
382	C₂²⋊C₄×C₆₁	—	2	2	no	—
383	C₂²⋊C₄×C₆₁	—	2	2	no	—
384	C₂²⋊C₄×C₆₁	—	2	1	no	—
385	C₂²⋊C₄×C₆₁	—	2	2	no	—
386	C₂²⋊C₄×C₆₁	—	2	2	no	—
387	C₂²⋊C₄×C₆₁	—	2	2	no	—
388	C₂²⋊C₄×C₆₁	—	2	2	no	—
389	C₂²⋊C₄×C₆₁	—	2	2	no	—
390	C₂²⋊C₄×C₆₁	—	2	2	no	—
391	C₂²⋊C₄×C₆₁	—	2	1	no	—
392	C₂²⋊C₄×C₆₁	—	2	1	no	—
393	C₂²⋊C₄×C₆₁	—	2	2	no	—
394	C₂²⋊C₄×C₆₁	—	2	2	no	—
395	C₂²⋊C₄×C₆₁	—	2	2	no	—
396	C₂²⋊C₄×C₆₁	—	2	2	no	—
397	C₂²⋊C₄×C₆₁	—	2	2	no	—
398	C₂²⋊C₄×C₆₁	—	2	2	no	—
399	C₂²⋊C₄×C₆₁	—	2	2	no	—
400	C₂²⋊C₄×C₆₁	—	2	2	no	—
401	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
402	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
403	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
404	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
405	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
406	C₄²×C₆₁	—	2	1	no	—
407	C₄²×C₆₁	—	2	1	no	—
408	C₄²×C₆₁	—	2	1	no	—
409	C₄²×C₆₁	—	2	2	no	—
410	C₄²×C₆₁	—	2	2	no	—
411	C₄²×C₆₁	—	2	2	no	—
412	C₄²×C₆₁	—	2	2	no	—
413	C₄²×C₆₁	—	2	2	no	—
414	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
415	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
416	C₄²×C₆₁	C₂⁴	1	2	yes	—
417	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
418	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
419	C₂³×C₆₁	—	2	1	no	—
420	C₂³×C₆₁	—	2	2	no	—
421	C₂³×C₆₁	—	2	2	no	—
422	C₂³×C₆₁	—	4	2	no	—
423	C₂³×C₆₁	—	8	2	no	—
424	C₂³×C₆₁	—	8	1	no	—
425	C₂³×C₆₁	—	8	2	no	—
426	C₂³×C₆₁	—	8	1	no	—
427	C₂³×C₆₁	—	8	2	no	—
428	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
429	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
430	Q₈×C₆₁	—	2	1	no	—
431	Q₈×C₆₁	—	2	2	no	—
432	Q₈×C₆₁	—	2	2	no	—
433	Q₈×C₆₁	—	2	2	no	—
434	Q₈×C₆₁	—	2	2	no	—
435	Q₈×C₆₁	—	4	1	no	—
436	Q₈×C₆₁	—	4	4	no	—
437	Q₈×C₆₁	—	8	1	no	—
438	Q₈×C₆₁	—	8	2	no	—
439	Q₈×C₆₁	—	8	1	no	—
440	Q₈×C₆₁	—	8	1	no	—
441	Q₈×C₆₁	H(5,𝔽₂)	1	2	yes	—
442	D₄×C₆₁	—	2	1	no	—
443	D₄×C₆₁	—	2	2	no	—
444	D₄×C₆₁	—	2	2	no	—
445	D₄×C₆₁	—	2	1	no	—
446	D₄×C₆₁	—	2	2	no	—
447	D₄×C₆₁	—	2	2	no	—
448	D₄×C₆₁	—	4	2	no	—
449	D₄×C₆₁	—	4	1	no	—
450	D₄×C₆₁	—	4	2	no	—
451	D₄×C₆₁	—	4	4	no	—
452	D₄×C₆₁	—	8	1	no	—
453	D₄×C₆₁	—	8	2	no	—
454	D₄×C₆₁	—	8	1	no	—
455	D₄×C₆₁	—	8	2	no	—
456	D₄×C₆₁	—	8	2	no	—
457	D₄×C₆₁	—	8	1	no	—
458	D₄×C₆₁	—	8	2	no	—
459	D₄×C₆₁	—	8	2	no	—
460	D₄×C₆₁	—	8	2	no	—
461	C₂×C₄×C₆₁	—	2	1	no	—
462	C₂×C₄×C₆₁	—	2	2	no	—
463	C₂×C₄×C₆₁	—	2	1	no	—
464	C₂×C₄×C₆₁	—	2	1	no	—
465	C₂×C₄×C₆₁	—	2	2	no	—
466	C₂×C₄×C₆₁	—	2	1	no	—
467	C₂×C₄×C₆₁	—	2	2	no	—
468	C₂×C₄×C₆₁	—	2	2	no	—
469	C₂×C₄×C₆₁	—	2	1	no	—
470	C₂×C₄×C₆₁	—	2	2	no	—
471	C₂×C₄×C₆₁	—	2	2	no	—
472	C₂×C₄×C₆₁	—	4	1	no	—
473	C₂×C₄×C₆₁	—	4	1	no	—
474	C₂×C₄×C₆₁	—	4	2	no	—
475	C₂×C₄×C₆₁	—	4	4	no	—
476	C₂×C₄×C₆₁	—	4	2	no	—
477	C₂×C₄×C₆₁	—	8	1	no	—
478	C₂×C₄×C₆₁	—	8	2	no	—
479	C₂×C₄×C₆₁	—	8	2	no	—
480	C₂×C₄×C₆₁	—	8	2	no	—
481	C₂×C₄×C₆₁	—	8	1	no	—
482	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
491	C₈×C₆₁	—	2	2	no	—
492	C₈×C₆₁	—	2	2	no	—
493	C₈×C₆₁	—	2	2	no	—
494	C₈×C₆₁	—	2	2	no	—
495	#62092	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
496	C₂²×C₆₁	—	2	1	no	—
497	C₂²×C₆₁	—	2	2	no	—
498	C₂²×C₆₁	—	2	1	no	—
499	C₂²×C₆₁	—	2	2	no	—
500	C₂²×C₆₁	—	2	2	no	—
501	C₂²×C₆₁	—	2	1	no	—
502	C₂²×C₆₁	—	4	2	no	—
503	C₂²×C₆₁	—	4	1	no	—
504	C₂²×C₆₁	—	4	2	no	—
505	C₂²×C₆₁	—	4	1	no	—
506	C₂²×C₆₁	—	4	2	no	—
507	C₂²×C₆₁	—	4	2	no	—
508	C₂²×C₆₁	—	4	1	no	—
509	C₂²×C₆₁	—	4	2	no	—
510	C₂²×C₆₁	—	4	2	no	—
511	C₂²×C₆₁	—	16	2	no	—
512	C₂²×C₆₁	—	16	4	no	—
513	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
514	C₄×C₆₁	—	2	1	no	—
515	C₄×C₆₁	—	2	1	no	—
516	C₄×C₆₁	—	2	2	no	—
517	C₄×C₆₁	—	2	1	no	—
518	C₄×C₆₁	—	2	1	no	—
519	C₄×C₆₁	—	2	2	no	—
520	C₄×C₆₁	—	2	1	no	—
521	C₄×C₆₁	—	2	2	no	—
522	C₄×C₆₁	—	2	2	no	—
523	C₄×C₆₁	—	4	2	no	—
524	C₄×C₆₁	—	4	1	no	—
525	C₄×C₆₁	—	4	2	no	—
526	C₄×C₆₁	—	4	1	no	—
527	C₄×C₆₁	—	4	2	no	—
528	C₄×C₆₁	—	4	2	no	—
529	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
530	C₄×C₆₁	#585	1	1	yes	characteristic
531	#3558	C₂×C₆₁	1	1	yes	characteristic, complemented
532	#3518	C₂×C₆₁	1	1	yes	characteristic, complemented
533	#3401	C₂×C₆₁	1	2	yes	complemented
534	#3375	C₂×C₆₁	1	2	yes	complemented
535	#3324	C₂×C₆₁	1	2	yes	complemented
536	#3319	C₂×C₆₁	1	2	yes	complemented
537	#3313	C₂×C₆₁	1	2	yes	complemented
538	#3277	C₂×C₆₁	1	2	yes	complemented
539	#3266	C₂×C₆₁	1	2	yes	complemented
540	#3265	C₂×C₆₁	1	2	yes	complemented
541	#3262	C₂×C₆₁	1	2	yes	complemented
542	#3254	C₂×C₆₁	1	1	yes	characteristic, complemented
543	#3224	C₂×C₆₁	1	2	yes	complemented
544	#3215	C₂×C₆₁	1	1	yes	characteristic, complemented
545	#3121	C₂×C₆₁	1	2	yes	complemented
546	#3115	C₂×C₆₁	1	1	yes	characteristic, complemented
547	#3043	C₂×C₆₁	1	2	yes	complemented
548	#3040	C₂×C₆₁	1	1	yes	characteristic, complemented
549	#2995	C₂×C₆₁	1	1	yes	characteristic, complemented
550	C₂×C₆₁	—	4	1	no	—
551	C₂×C₆₁	—	4	2	no	—
552	C₂×C₆₁	—	8	1	no	—
553	C₂×C₆₁	—	8	2	no	—
554	C₂×C₆₁	—	8	2	no	—
555	C₂×C₆₁	#3488	1	1	yes	characteristic
556	C₂×C₆₁	#3585	1	1	yes	characteristic
557	C₂×C₆₁	#3586	1	1	yes	characteristic
558	C₂×#137	C₂²×C₆₁	1	2	yes	complemented
559	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic, complemented
560	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
561	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
562	#562	—	2	1	no	—
563	H(3,𝔽₄)	—	2	1	no	—
564	#559	C₂²×C₆₁	1	2	yes	—
565	Q₈²	C₂²×C₆₁	1	1	yes	characteristic, complemented
566	#556	—	2	2	no	—
567	#556	—	2	1	no	—
568	#556	C₂²×C₆₁	1	1	yes	characteristic, complemented
569	#556	C₂²×C₆₁	1	2	yes	complemented
570	#555	—	2	1	no	—
571	#555	C₂²×C₆₁	1	1	yes	characteristic, complemented
572	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
573	#548	C₂²×C₆₁	1	2	yes	—
574	#548	C₂²×C₆₁	1	2	yes	complemented
575	#546	—	2	2	no	—
576	#546	C₂²×C₆₁	1	2	yes	—
577	D₄²	C₂²×C₆₁	1	2	yes	—
578	#542	—	2	2	no	—
579	#542	C₂²×C₆₁	1	2	yes	—
580	#542	C₂²×C₆₁	1	2	yes	complemented
581	#538	—	2	2	no	—
582	#538	—	2	1	no	—
583	#535	C₂²×C₆₁	1	2	yes	—
584	#534	—	2	1	no	—
585	#533	—	2	1	no	—
586	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
587	#532	C₂²×C₆₁	1	1	yes	characteristic
588	#529	—	2	1	no	—
589	#529	C₂²×C₆₁	1	1	yes	characteristic
590	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
591	#519	C₂²×C₆₁	1	2	yes	complemented
592	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic, complemented
593	#497	C₂²×C₆₁	1	2	yes	complemented
594	#496	C₂²×C₆₁	1	2	yes	—
595	#495	C₂²×C₆₁	1	2	yes	complemented
596	#489	C₂²×C₆₁	1	2	yes	complemented
597	#489	C₂²×C₆₁	1	2	yes	complemented
598	#486	C₂²×C₆₁	1	2	yes	—
599	#485	C₂²×C₆₁	1	2	yes	complemented
600	#482	C₂²×C₆₁	1	2	yes	—
601	#482	C₂²×C₆₁	1	2	yes	complemented
602	#477	C₂²×C₆₁	1	2	yes	complemented
603	#477	C₂²×C₆₁	1	2	yes	complemented
604	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
605	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
606	#474	C₂²×C₆₁	1	2	yes	complemented
607	#474	C₂²×C₆₁	1	2	yes	complemented
608	#468	C₂²×C₆₁	1	2	yes	—
609	#468	C₂²×C₆₁	1	2	yes	complemented
610	#468	C₂²×C₆₁	1	2	yes	complemented
611	#468	C₂²×C₆₁	1	2	yes	complemented
612	#467	C₂²×C₆₁	1	2	yes	complemented
613	#466	C₂²×C₆₁	1	2	yes	—
614	#464	C₂²×C₆₁	1	2	yes	complemented
615	#464	C₂²×C₆₁	1	2	yes	complemented
616	#464	C₂²×C₆₁	1	2	yes	complemented
617	#464	C₂²×C₆₁	1	2	yes	complemented
618	#464	C₂²×C₆₁	1	2	yes	complemented
619	#464	C₂²×C₆₁	1	2	yes	complemented
620	#464	C₂²×C₆₁	1	2	yes	complemented
621	#463	C₂²×C₆₁	1	2	yes	complemented
622	#463	C₂²×C₆₁	1	2	yes	complemented
623	#463	C₂²×C₆₁	1	2	yes	complemented
624	#461	C₂²×C₆₁	1	2	yes	complemented
625	#460	C₂²×C₆₁	1	2	yes	—
626	#460	C₂²×C₆₁	1	2	yes	—
627	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
628	#460	C₂²×C₆₁	1	2	yes	complemented
629	#459	C₂²×C₆₁	1	1	yes	characteristic, complemented
630	#452	C₂²×C₆₁	1	2	yes	complemented
631	#451	C₂²×C₆₁	1	2	yes	complemented
632	#451	C₂²×C₆₁	1	2	yes	complemented
633	#450	C₂²×C₆₁	1	2	yes	—
634	#450	C₂²×C₆₁	1	2	yes	complemented
635	#449	C₂²×C₆₁	1	2	yes	complemented
636	#449	C₂²×C₆₁	1	2	yes	complemented
637	#448	C₂²×C₆₁	1	2	yes	—
638	#447	C₂²×C₆₁	1	2	yes	complemented
639	#446	C₂²×C₆₁	1	2	yes	complemented
640	#442	C₂²×C₆₁	1	2	yes	complemented
641	#441	C₂²×C₆₁	1	2	yes	complemented
642	#440	C₂²×C₆₁	1	2	yes	complemented
643	#440	C₂²×C₆₁	1	2	yes	complemented
644	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
645	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
646	#436	C₂²×C₆₁	1	2	yes	complemented
647	#435	C₂²×C₆₁	1	2	yes	complemented
648	#435	C₂²×C₆₁	1	2	yes	complemented
649	#433	C₂²×C₆₁	1	2	yes	complemented
650	#432	C₂²×C₆₁	1	1	yes	characteristic, complemented
651	#424	C₂²×C₆₁	1	2	yes	complemented
652	#423	C₂²×C₆₁	1	1	yes	characteristic, complemented
653	#419	C₂²×C₆₁	1	1	yes	characteristic, complemented
654	#418	C₂²×C₆₁	1	1	yes	characteristic
655	#418	C₂²×C₆₁	1	2	yes	complemented
656	#416	C₂²×C₆₁	1	2	yes	complemented
657	C₆₁	#62092	1	1	yes	characteristic, direct product factor, Sylow
658	C₂×#41	—	2	1	no	—
659	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
660	C₂×#41	C₂³×C₆₁	1	2	yes	—
661	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
662	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
663	C₂²×D₄	—	2	2	no	—
664	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
665	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
666	#137	—	4	4	no	—
667	#137	—	4	2	no	—
668	AGL(1,ℤ/8)	—	4	2	no	—
669	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
670	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
671	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
672	C₂×SD₁₆	—	4	4	no	—
673	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
674	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
675	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
676	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
677	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
678	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
679	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
680	C₂×D₈	C₂³×C₆₁	1	2	yes	—
681	C₂×D₈	C₂³×C₆₁	1	2	yes	—
682	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
683	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
684	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
685	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
686	C₄⋊Q₈	—	2	1	no	—
687	C₄⋊Q₈	—	2	1	no	—
688	C₄⋊Q₈	—	2	2	no	—
689	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
690	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
691	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
692	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
693	#127	C₂³×C₆₁	1	1	yes	characteristic
694	#127	C₂³×C₆₁	1	2	yes	—
695	#126	—	2	2	no	—
696	#126	—	2	2	no	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	D₄×C₆₁	1	2	yes	—
701	#125	—	2	1	no	—
702	#125	D₄×C₆₁	1	1	yes	characteristic
703	#124	—	2	2	no	—
704	#124	—	2	2	no	—
705	#124	—	2	2	no	—
706	#124	—	2	2	no	—
707	#124	—	2	2	no	—
708	#124	—	2	2	no	—
709	#124	—	2	2	no	—
710	#124	—	2	1	no	—
711	#124	—	2	1	no	—
712	#124	—	2	1	no	—
713	#124	D₄×C₆₁	1	1	yes	characteristic
714	#124	C₂³×C₆₁	1	2	yes	—
715	#124	C₂³×C₆₁	1	2	yes	—
716	#124	C₂³×C₆₁	1	2	yes	—
717	#124	C₂³×C₆₁	1	2	yes	—
718	#123	—	2	2	no	—
719	#123	—	2	2	no	—
720	#123	—	2	2	no	—
721	#123	—	2	2	no	—
722	#123	—	2	2	no	—
723	#123	D₄×C₆₁	1	2	yes	—
724	C₂²⋊Q₈	—	2	1	no	—
725	C₂²⋊Q₈	—	2	1	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
732	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
733	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
734	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
735	#121	—	2	1	no	—
736	#121	—	2	2	no	—
737	#121	—	2	2	no	—
738	#121	—	2	1	no	—
739	#121	—	2	2	no	—
740	#121	—	2	2	no	—
741	#121	—	2	2	no	—
742	#121	—	2	2	no	—
743	#121	D₄×C₆₁	1	1	yes	characteristic
744	#121	C₂³×C₆₁	1	2	yes	—
745	#121	C₂³×C₆₁	1	2	yes	—
746	#121	C₂³×C₆₁	1	2	yes	—
747	#120	—	2	2	no	—
748	#120	—	2	2	no	—
749	#120	—	2	2	no	—
750	#120	—	2	2	no	—
751	#120	—	2	2	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	—	2	2	no	—
754	C₄×Q₈	—	2	2	no	—
755	C₄×Q₈	—	2	2	no	—
756	C₄×Q₈	—	2	1	no	—
757	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
758	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
759	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
760	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
761	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
762	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
763	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
764	C₄×D₄	—	2	1	no	—
765	C₄×D₄	—	2	1	no	—
766	C₄×D₄	—	2	1	no	—
767	C₄×D₄	—	2	2	no	—
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	2	2	no	—
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
772	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
773	C₄×D₄	C₂³×C₆₁	1	2	yes	—
774	C₄×D₄	C₂³×C₆₁	1	2	yes	—
775	C₄×D₄	C₂³×C₆₁	1	2	yes	—
776	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
777	#117	—	2	1	no	—
778	#117	—	2	1	no	—
779	#117	—	2	1	no	—
780	#117	—	2	2	no	—
781	#117	—	2	2	no	—
782	#117	—	2	1	no	—
783	#117	C₂³×C₆₁	1	1	yes	characteristic
784	#117	C₂³×C₆₁	1	2	yes	—
785	#117	C₂³×C₆₁	1	2	yes	—
786	C₂×C₂²⋊C₄	—	2	1	no	—
787	C₂×C₂²⋊C₄	—	2	1	no	—
788	C₂×C₂²⋊C₄	—	2	2	no	—
789	C₂×C₄²	—	2	1	no	—
790	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
791	#107	C₂³×C₆₁	1	2	yes	—
792	#107	C₂³×C₆₁	1	2	yes	—
793	#107	C₂³×C₆₁	1	2	yes	—
794	#106	C₂³×C₆₁	1	2	yes	—
795	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
796	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
797	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
798	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
799	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
800	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
801	#103	C₂³×C₆₁	1	2	yes	—
802	#103	C₂³×C₆₁	1	2	yes	—
803	#103	C₂³×C₆₁	1	2	yes	—
804	#103	C₂³×C₆₁	1	2	yes	—
805	#103	C₂³×C₆₁	1	2	yes	—
806	#103	C₂³×C₆₁	1	2	yes	—
807	#103	C₂³×C₆₁	1	2	yes	—
808	#102	C₂³×C₆₁	1	2	yes	—
809	#102	C₂³×C₆₁	1	2	yes	—
810	#102	C₂³×C₆₁	1	2	yes	—
811	#102	C₂³×C₆₁	1	2	yes	—
812	#102	C₂³×C₆₁	1	2	yes	—
813	#102	C₂³×C₆₁	1	2	yes	—
814	#102	C₂³×C₆₁	1	2	yes	—
815	#102	C₂³×C₆₁	1	2	yes	—
816	#102	C₂³×C₆₁	1	2	yes	—
817	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
818	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
819	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
820	#97	C₂³×C₆₁	1	2	yes	—
821	#97	C₂³×C₆₁	1	2	yes	—
822	C₄×C₈	C₂³×C₆₁	1	2	yes	—
823	C₂⁴	—	2	1	no	—
824	C₂⁴	—	2	2	no	—
825	#41	—	2	2	no	—
826	#41	—	4	1	no	—
827	#41	—	4	2	no	—
828	#41	—	4	2	no	—
829	#41	—	8	2	no	—
830	C₂×Q₈	—	2	2	no	—
831	C₂×Q₈	—	2	1	no	—
832	C₂×Q₈	—	2	2	no	—
833	C₂×Q₈	—	2	1	no	—
834	C₂×Q₈	—	2	1	no	—
835	C₂×Q₈	—	2	4	no	—
836	C₂×Q₈	—	4	2	no	—
837	C₂×Q₈	—	4	1	no	—
838	C₂×Q₈	—	4	1	no	—
839	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
840	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
841	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
842	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
843	C₂×D₄	—	2	1	no	—
844	C₂×D₄	—	2	2	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	1	no	—
850	C₂×D₄	—	2	1	no	—
851	C₂×D₄	—	2	1	no	—
852	C₂×D₄	—	2	2	no	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	4	2	no	—
855	C₂×D₄	—	4	1	no	—
856	C₂×D₄	—	4	2	no	—
857	C₂×D₄	—	4	1	no	—
858	C₂×D₄	—	8	4	no	—
859	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
860	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
861	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
862	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
863	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
873	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
876	Q₁₆	—	2	4	no	—
877	Q₁₆	—	4	2	no	—
878	Q₁₆	—	4	2	no	—
879	SD₁₆	—	2	4	no	—
880	SD₁₆	—	2	4	no	—
881	SD₁₆	—	4	2	no	—
882	SD₁₆	—	4	2	no	—
883	SD₁₆	—	4	2	no	—
884	SD₁₆	—	4	2	no	—
885	SD₁₆	—	4	2	no	—
886	D₈	—	4	2	no	—
887	D₈	—	4	2	no	—
888	M₁₆	—	4	1	no	—
889	M₁₆	—	4	2	no	—
890	M₁₆	—	4	1	no	—
891	C₂×C₈	—	4	2	no	—
892	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
893	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
894	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
895	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
911	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
912	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
913	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
914	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
915	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
916	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
917	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
918	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
919	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	1	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	1	no	—
931	C₂²⋊C₄	—	2	1	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
941	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
942	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
943	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
944	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
945	C₄²	—	2	1	no	—
946	C₄²	—	2	1	no	—
947	C₄²	—	2	1	no	—
948	C₄²	—	2	2	no	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
954	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
955	C₄²	C₂⁴×C₆₁	1	2	yes	—
956	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
957	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
958	C₂³	—	2	1	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	4	2	no	—
962	C₂³	—	8	2	no	—
963	C₂³	—	8	1	no	—
964	C₂³	—	8	2	no	—
965	C₂³	—	8	1	no	—
966	C₂³	—	8	2	no	—
967	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
968	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
969	Q₈	—	2	1	no	—
970	Q₈	—	2	2	no	—
971	Q₈	—	2	2	no	—
972	Q₈	—	2	2	no	—
973	Q₈	—	2	2	no	—
974	Q₈	—	4	1	no	—
975	Q₈	—	4	4	no	—
976	Q₈	—	8	1	no	—
977	Q₈	—	8	2	no	—
978	Q₈	—	8	1	no	—
979	Q₈	—	8	1	no	—
980	Q₈	H(5,𝔽₂)×C₆₁	1	2	yes	—
981	D₄	—	2	1	no	—
982	D₄	—	2	2	no	—
983	D₄	—	2	2	no	—
984	D₄	—	2	1	no	—
985	D₄	—	2	2	no	—
986	D₄	—	2	2	no	—
987	D₄	—	4	2	no	—
988	D₄	—	4	1	no	—
989	D₄	—	4	2	no	—
990	D₄	—	4	4	no	—
991	D₄	—	8	1	no	—
992	D₄	—	8	2	no	—
993	D₄	—	8	1	no	—
994	D₄	—	8	2	no	—
995	D₄	—	8	2	no	—
996	D₄	—	8	1	no	—
997	D₄	—	8	2	no	—
998	D₄	—	8	2	no	—
999	D₄	—	8	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	4	1	no	—
1012	C₂×C₄	—	4	1	no	—
1013	C₂×C₄	—	4	2	no	—
1014	C₂×C₄	—	4	4	no	—
1015	C₂×C₄	—	4	2	no	—
1016	C₂×C₄	—	8	1	no	—
1017	C₂×C₄	—	8	2	no	—
1018	C₂×C₄	—	8	2	no	—
1019	C₂×C₄	—	8	2	no	—
1020	C₂×C₄	—	8	1	no	—
1021	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1022	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1023	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1024	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1025	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1026	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1027	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1028	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1029	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1030	C₈	—	2	2	no	—
1031	C₈	—	2	2	no	—
1032	C₈	—	2	2	no	—
1033	C₈	—	2	2	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	2	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	4	2	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	2	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	2	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	16	2	no	—
1050	C₂²	—	16	4	no	—
1051	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	2	2	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	4	2	no	—
1062	C₄	—	4	1	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	2	no	—
1067	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1068	C₄	C₆₁×#585	1	1	yes	characteristic
1069	C₂	—	4	1	no	—
1070	C₂	—	4	2	no	—
1071	C₂	—	8	2	no	—
1072	C₂	—	8	2	no	—
1073	C₂	—	8	1	no	—
1074	C₂	C₆₁×#3488	1	1	yes	characteristic
1075	C₂	C₆₁×#3585	1	1	yes	characteristic
1076	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 ◁ C₆₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3558	C₂	semidirect
2. C₆₁×#3518	C₂	semidirect
3. C₆₁×#3401	C₂	semidirect
4. C₆₁×#3375	C₂	semidirect
5. C₆₁×#3324	C₂	semidirect
6. C₆₁×#3319	C₂	semidirect
7. C₆₁×#3313	C₂	semidirect
8. C₆₁×#3277	C₂	semidirect
9. C₆₁×#3266	C₂	semidirect
10. C₆₁×#3265	C₂	semidirect
11. C₆₁×#3262	C₂	semidirect
12. C₆₁×#3254	C₂	semidirect
13. C₆₁×#3224	C₂	semidirect
14. C₆₁×#3215	C₂	semidirect
15. C₆₁×#3121	C₂	semidirect
16. C₆₁×#3115	C₂	semidirect
17. C₆₁×#3043	C₂	semidirect
18. C₆₁×#3040	C₂	semidirect
19. C₆₁×#2995	C₂	semidirect
20. C₂×#137×C₆₁	C₂²	semidirect
21. C₂×#137×C₆₁	C₂²	semidirect
23. C₂²×SD₁₆×C₆₁	C₂²	semidirect
27. Q₈²×C₆₁	C₂²	semidirect
30. C₆₁×#556	C₂²	semidirect
31. C₆₁×#556	C₂²	semidirect
33. C₆₁×#555	C₂²	semidirect
34. D₄×Q₈×C₆₁	C₂²	semidirect
36. C₆₁×#548	C₂²	semidirect
42. C₆₁×#542	C₂²	semidirect
48. C₆₁×#533	C₂²	semidirect
53. C₆₁×#519	C₂²	semidirect
54. C₄×#41×C₆₁	C₂²	semidirect
55. C₆₁×#497	C₂²	semidirect
57. C₆₁×#495	C₂²	semidirect
58. C₆₁×#489	C₂²	semidirect
59. C₆₁×#489	C₂²	semidirect
61. C₆₁×#485	C₂²	semidirect
63. C₆₁×#482	C₂²	semidirect
64. C₆₁×#477	C₂²	semidirect
65. C₆₁×#477	C₂²	semidirect
66. C₆₁×#475	C₂²	semidirect
67. C₆₁×#474	C₂²	semidirect
68. C₆₁×#474	C₂²	semidirect
69. C₆₁×#474	C₂²	semidirect
71. C₆₁×#468	C₂²	semidirect
72. C₆₁×#468	C₂²	semidirect
73. C₆₁×#468	C₂²	semidirect
74. C₆₁×#467	C₂²	semidirect
76. C₆₁×#464	C₂²	semidirect
77. C₆₁×#464	C₂²	semidirect
78. C₆₁×#464	C₂²	semidirect
79. C₆₁×#464	C₂²	semidirect
80. C₆₁×#464	C₂²	semidirect
81. C₆₁×#464	C₂²	semidirect
82. C₆₁×#464	C₂²	semidirect
83. C₆₁×#463	C₂²	semidirect
84. C₆₁×#463	C₂²	semidirect
85. C₆₁×#463	C₂²	semidirect
86. C₆₁×#461	C₂²	semidirect
89. C₆₁×#460	C₂²	semidirect
90. C₆₁×#460	C₂²	semidirect
91. C₆₁×#459	C₂²	semidirect
92. C₆₁×#452	C₂²	semidirect
93. C₆₁×#451	C₂²	semidirect
94. C₆₁×#451	C₂²	semidirect
96. C₆₁×#450	C₂²	semidirect
97. C₆₁×#449	C₂²	semidirect
98. C₆₁×#449	C₂²	semidirect
100. C₆₁×#447	C₂²	semidirect
101. C₆₁×#446	C₂²	semidirect
102. C₆₁×#442	C₂²	semidirect
103. C₆₁×#441	C₂²	semidirect
104. C₆₁×#440	C₂²	semidirect
105. C₆₁×#440	C₂²	semidirect
106. C₄×Q₁₆×C₆₁	C₂²	semidirect
107. C₄×SD₁₆×C₆₁	C₂²	semidirect
108. C₆₁×#436	C₂²	semidirect
109. C₆₁×#435	C₂²	semidirect
110. C₆₁×#435	C₂²	semidirect
111. C₆₁×#433	C₂²	semidirect
112. C₆₁×#432	C₂²	semidirect
113. C₆₁×#424	C₂²	semidirect
114. C₆₁×#423	C₂²	semidirect
115. C₆₁×#419	C₂²	semidirect
117. C₆₁×#418	C₂²	semidirect
118. C₆₁×#416	C₂²	semidirect
495. #62092	C₆₁	direct (N × H)
531. #3558	C₂×C₆₁	semidirect
532. #3518	C₂×C₆₁	semidirect
533. #3401	C₂×C₆₁	semidirect
534. #3375	C₂×C₆₁	semidirect
535. #3324	C₂×C₆₁	semidirect
536. #3319	C₂×C₆₁	semidirect
537. #3313	C₂×C₆₁	semidirect
538. #3277	C₂×C₆₁	semidirect
539. #3266	C₂×C₆₁	semidirect
540. #3265	C₂×C₆₁	semidirect
541. #3262	C₂×C₆₁	semidirect
542. #3254	C₂×C₆₁	semidirect
543. #3224	C₂×C₆₁	semidirect
544. #3215	C₂×C₆₁	semidirect
545. #3121	C₂×C₆₁	semidirect
546. #3115	C₂×C₆₁	semidirect
547. #3043	C₂×C₆₁	semidirect
548. #3040	C₂×C₆₁	semidirect
549. #2995	C₂×C₆₁	semidirect
558. C₂×#137	C₂²×C₆₁	semidirect
559. C₂×#137	C₂²×C₆₁	semidirect
561. C₂²×SD₁₆	C₂²×C₆₁	semidirect
565. Q₈²	C₂²×C₆₁	semidirect
568. #556	C₂²×C₆₁	semidirect
569. #556	C₂²×C₆₁	semidirect
571. #555	C₂²×C₆₁	semidirect
572. D₄×Q₈	C₂²×C₆₁	semidirect
574. #548	C₂²×C₆₁	semidirect
580. #542	C₂²×C₆₁	semidirect
586. #533	C₂²×C₆₁	semidirect
591. #519	C₂²×C₆₁	semidirect
592. C₄×#41	C₂²×C₆₁	semidirect
593. #497	C₂²×C₆₁	semidirect
595. #495	C₂²×C₆₁	semidirect
596. #489	C₂²×C₆₁	semidirect
597. #489	C₂²×C₆₁	semidirect
599. #485	C₂²×C₆₁	semidirect
601. #482	C₂²×C₆₁	semidirect
602. #477	C₂²×C₆₁	semidirect
603. #477	C₂²×C₆₁	semidirect
604. #475	C₂²×C₆₁	semidirect
605. #474	C₂²×C₆₁	semidirect
606. #474	C₂²×C₆₁	semidirect
607. #474	C₂²×C₆₁	semidirect
609. #468	C₂²×C₆₁	semidirect
610. #468	C₂²×C₆₁	semidirect
611. #468	C₂²×C₆₁	semidirect
612. #467	C₂²×C₆₁	semidirect
614. #464	C₂²×C₆₁	semidirect
615. #464	C₂²×C₆₁	semidirect
616. #464	C₂²×C₆₁	semidirect
617. #464	C₂²×C₆₁	semidirect
618. #464	C₂²×C₆₁	semidirect
619. #464	C₂²×C₆₁	semidirect
620. #464	C₂²×C₆₁	semidirect
621. #463	C₂²×C₆₁	semidirect
622. #463	C₂²×C₆₁	semidirect
623. #463	C₂²×C₆₁	semidirect
624. #461	C₂²×C₆₁	semidirect
627. #460	C₂²×C₆₁	semidirect
628. #460	C₂²×C₆₁	semidirect
629. #459	C₂²×C₆₁	semidirect
630. #452	C₂²×C₆₁	semidirect
631. #451	C₂²×C₆₁	semidirect
632. #451	C₂²×C₆₁	semidirect
634. #450	C₂²×C₆₁	semidirect
635. #449	C₂²×C₆₁	semidirect
636. #449	C₂²×C₆₁	semidirect
638. #447	C₂²×C₆₁	semidirect
639. #446	C₂²×C₆₁	semidirect
640. #442	C₂²×C₆₁	semidirect
641. #441	C₂²×C₆₁	semidirect
642. #440	C₂²×C₆₁	semidirect
643. #440	C₂²×C₆₁	semidirect
644. C₄×Q₁₆	C₂²×C₆₁	semidirect
645. C₄×SD₁₆	C₂²×C₆₁	semidirect
646. #436	C₂²×C₆₁	semidirect
647. #435	C₂²×C₆₁	semidirect
648. #435	C₂²×C₆₁	semidirect
649. #433	C₂²×C₆₁	semidirect
650. #432	C₂²×C₆₁	semidirect
651. #424	C₂²×C₆₁	semidirect
652. #423	C₂²×C₆₁	semidirect
653. #419	C₂²×C₆₁	semidirect
655. #418	C₂²×C₆₁	semidirect
656. #416	C₂²×C₆₁	semidirect
657. C₆₁	#62092	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×#3558	2
C₆₁×#3518	2
C₆₁×#3401	2
C₆₁×#3375	2
C₆₁×#3324	2
C₆₁×#3319	2
C₆₁×#3313	2
C₆₁×#3277	2
C₆₁×#3266	2
C₆₁×#3265	2
C₆₁×#3262	2
C₆₁×#3254	2
C₆₁×#3224	2
C₆₁×#3215	2
C₆₁×#3121	2
C₆₁×#3115	2
C₆₁×#3043	2
C₆₁×#3040	2
C₆₁×#2995	2
#62092	61

Subgroups — C61×#62092 #29565525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62092 #29565525