Subgroups — C₆₁×#62929 #29566362

Order 15616.

6566 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3565	C₂	1	8	yes	maximal, complemented
2	C₆₁×#3561	C₂	1	8	yes	maximal, complemented
3	C₆₁×#3547	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3547	C₂	1	8	yes	maximal, complemented
5	C₆₁×#3544	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3536	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3518	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3511	C₂	1	4	yes	maximal, complemented
9	C₆₁×#3503	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3501	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3495	C₂	1	4	yes	maximal, complemented
12	C₆₁×#3494	C₂	1	4	yes	maximal, complemented
13	C₆₁×#3493	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3475	C₂	1	2	yes	maximal, complemented
15	C₂×C₆₁×#555	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3460	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3458	C₂	1	2	yes	maximal, complemented
18	C₆₁×#563	C₂²	1	16	yes	complemented
19	C₆₁×#562	C₂²	1	16	yes	complemented
20	C₆₁×#562	C₂²	1	16	yes	complemented
21	Q₈²×C₆₁	C₂²	1	4	yes	complemented
22	C₆₁×#557	C₂²	1	4	yes	complemented
23	C₆₁×#556	C₂²	1	16	yes	complemented
24	C₆₁×#556	C₂²	1	8	yes	complemented
25	C₆₁×#556	C₂²	1	2	yes	complemented
26	C₆₁×#556	C₂²	1	8	yes	complemented
27	C₆₁×#555	C₂²	1	4	yes	—
28	C₆₁×#555	C₂²	1	8	yes	—
29	C₆₁×#555	C₂²	1	4	yes	—
30	C₆₁×#555	C₂²	1	8	yes	complemented
31	C₆₁×#555	C₂²	1	8	yes	complemented
32	C₆₁×#555	C₂²	1	2	yes	complemented
33	C₆₁×#554	C₂²	1	8	yes	—
34	C₆₁×#554	C₂²	1	2	yes	complemented
35	C₆₁×#554	C₂²	1	4	yes	complemented
36	C₆₁×#554	C₂²	1	8	yes	complemented
37	C₆₁×#554	C₂²	1	4	yes	complemented
38	C₆₁×#553	C₂²	1	4	yes	complemented
39	C₆₁×#553	C₂²	1	8	yes	complemented
40	C₆₁×#553	C₂²	1	8	yes	complemented
41	C₆₁×#553	C₂²	1	8	yes	complemented
42	C₆₁×#552	C₂²	1	4	yes	—
43	C₆₁×#552	C₂²	1	8	yes	complemented
44	C₆₁×#552	C₂²	1	8	yes	complemented
45	C₆₁×#552	C₂²	1	16	yes	complemented
46	C₆₁×#552	C₂²	1	4	yes	complemented
47	C₆₁×#551	C₂²	1	8	yes	—
48	C₆₁×#551	C₂²	1	16	yes	—
49	D₄×Q₈×C₆₁	C₂²	1	8	yes	—
50	D₄×Q₈×C₆₁	C₂²	1	4	yes	complemented
51	D₄×Q₈×C₆₁	C₂²	1	4	yes	complemented
52	C₆₁×#548	C₂²	1	16	yes	complemented
53	C₆₁×#548	C₂²	1	8	yes	complemented
54	C₆₁×#547	C₂²	1	8	yes	complemented
55	C₆₁×#547	C₂²	1	8	yes	complemented
56	C₆₁×#547	C₂²	1	2	yes	complemented
57	C₆₁×#546	C₂²	1	16	yes	—
58	C₆₁×#546	C₂²	1	4	yes	—
59	C₆₁×#544	C₂²	1	1	yes	characteristic
60	C₆₁×#544	C₂²	1	2	yes	—
61	C₆₁×#544	C₂²	1	4	yes	—
62	C₆₁×#544	C₂²	1	4	yes	complemented
63	C₆₁×#544	C₂²	1	8	yes	complemented
64	C₆₁×#544	C₂²	1	8	yes	complemented
65	C₆₁×#544	C₂²	1	8	yes	complemented
66	C₆₁×#543	C₂²	1	4	yes	—
67	C₆₁×#543	C₂²	1	8	yes	—
68	C₆₁×#542	C₂²	1	8	yes	complemented
69	C₆₁×#542	C₂²	1	8	yes	complemented
70	C₆₁×#542	C₂²	1	8	yes	complemented
71	C₆₁×#542	C₂²	1	16	yes	complemented
72	C₆₁×#542	C₂²	1	16	yes	complemented
73	C₆₁×#542	C₂²	1	16	yes	complemented
74	C₆₁×#542	C₂²	1	4	yes	complemented
75	C₆₁×#541	C₂²	1	8	yes	complemented
76	C₆₁×#540	C₂²	1	4	yes	complemented
77	C₆₁×#540	C₂²	1	8	yes	complemented
78	C₆₁×#539	C₂²	1	8	yes	complemented
79	C₆₁×#538	C₂²	1	4	yes	—
80	C₆₁×#538	C₂²	1	8	yes	—
81	C₆₁×#537	C₂²	1	1	yes	characteristic
82	C₆₁×#537	C₂²	1	8	yes	complemented
83	C₆₁×#537	C₂²	1	8	yes	complemented
84	C₆₁×#536	C₂²	1	16	yes	complemented
85	C₆₁×#536	C₂²	1	4	yes	complemented
86	C₆₁×#535	C₂²	1	2	yes	—
87	C₆₁×#533	C₂²	1	8	yes	—
88	C₆₁×#533	C₂²	1	2	yes	—
89	C₆₁×#533	C₂²	1	8	yes	complemented
90	C₆₁×#533	C₂²	1	4	yes	complemented
91	C₆₁×#533	C₂²	1	8	yes	complemented
92	C₆₁×#532	C₂²	1	4	yes	complemented
93	C₆₁×#532	C₂²	1	8	yes	complemented
94	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
95	C₂×C₄⋊Q₈×C₆₁	C₂²	1	4	yes	complemented
96	C₆₁×#529	C₂²	1	8	yes	—
97	C₆₁×#529	C₂²	1	4	yes	complemented
98	C₆₁×#529	C₂²	1	4	yes	complemented
99	C₆₁×#529	C₂²	1	8	yes	complemented
100	C₆₁×#529	C₂²	1	8	yes	complemented
101	C₂×#124×C₆₁	C₂²	1	4	yes	—
102	C₆₁×#525	C₂²	1	4	yes	—
103	C₆₁×#525	C₂²	1	4	yes	—
104	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	4	yes	—
105	C₂×#121×C₆₁	C₂²	1	2	yes	—
106	C₂×#121×C₆₁	C₂²	1	2	yes	—
107	C₆₁×#520	C₂²	1	4	yes	—
108	C₆₁×#520	C₂²	1	4	yes	complemented
109	C₆₁×#519	C₂²	1	4	yes	complemented
110	C₆₁×#518	C₂²	1	2	yes	—
111	C₄×#41×C₆₁	C₂²	1	2	yes	—
112	C₄×#41×C₆₁	C₂²	1	4	yes	complemented
113	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
114	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
115	C₂×#117×C₆₁	C₂²	1	2	yes	—
116	C₂×#117×C₆₁	C₂²	1	4	yes	—
117	C₂×#117×C₆₁	C₂²	1	2	yes	—
118	C₂×#41×C₆₁	C₂³	1	2	yes	—
119	C₂×#41×C₆₁	C₂³	1	4	yes	—
120	C₂×#41×C₆₁	C₂³	1	4	yes	—
121	C₂×#41×C₆₁	C₂³	1	16	yes	—
122	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
123	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
124	C₂²×Q₈×C₆₁	C₂³	1	8	yes	—
125	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
128	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
129	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
130	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
131	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
132	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
133	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
134	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
135	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
136	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
137	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
138	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
139	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
140	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
141	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
142	C₄⋊Q₈×C₆₁	C₂³	1	16	yes	—
143	#127×C₆₁	C₂³	1	4	yes	—
144	#126×C₆₁	C₂³	1	16	yes	—
145	#126×C₆₁	C₂³	1	8	yes	—
146	#126×C₆₁	C₂³	1	16	yes	—
147	#126×C₆₁	C₂³	1	16	yes	—
148	#126×C₆₁	C₂³	1	8	yes	—
149	#126×C₆₁	C₂³	1	8	yes	—
150	#126×C₆₁	C₂³	1	8	yes	—
151	#126×C₆₁	C₂³	1	16	yes	—
152	#125×C₆₁	C₂³	1	16	yes	—
153	#125×C₆₁	C₂³	1	4	yes	—
154	#125×C₆₁	C₂³	1	4	yes	—
155	#125×C₆₁	C₂³	1	8	yes	—
156	#125×C₆₁	C₂³	1	8	yes	—
157	#125×C₆₁	C₂³	1	8	yes	—
158	#125×C₆₁	C₂³	1	16	yes	—
159	#125×C₆₁	C₂³	1	8	yes	—
160	#125×C₆₁	C₂³	1	8	yes	—
161	#125×C₆₁	C₂³	1	4	yes	—
162	#124×C₆₁	C₂³	1	8	yes	—
163	#124×C₆₁	C₂³	1	16	yes	—
164	#124×C₆₁	C₂³	1	4	yes	—
165	#124×C₆₁	C₂³	1	16	yes	—
166	#124×C₆₁	C₂³	1	16	yes	—
167	#124×C₆₁	C₂³	1	8	yes	—
168	#124×C₆₁	C₂³	1	16	yes	—
169	#124×C₆₁	C₂³	1	4	yes	—
170	#124×C₆₁	C₂³	1	8	yes	—
171	#124×C₆₁	C₂³	1	16	yes	—
172	#123×C₆₁	C₂³	1	8	yes	—
173	#123×C₆₁	C₂³	1	8	yes	—
174	#123×C₆₁	C₂³	1	16	yes	—
175	#123×C₆₁	C₂³	1	16	yes	—
176	#123×C₆₁	C₂³	1	16	yes	—
177	#123×C₆₁	C₂³	1	8	yes	—
178	#123×C₆₁	C₂³	1	16	yes	—
179	#123×C₆₁	C₂³	1	8	yes	—
180	#123×C₆₁	C₂³	1	16	yes	—
181	#123×C₆₁	C₂³	1	8	yes	—
182	#123×C₆₁	C₂³	1	8	yes	—
183	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
184	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
185	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
186	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
187	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
188	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
189	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
190	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
191	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
192	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
193	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
194	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
195	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
196	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
197	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
198	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
199	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
200	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
201	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
202	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
203	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
204	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
205	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
206	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
207	#121×C₆₁	C₂³	1	4	yes	—
208	#121×C₆₁	C₂³	1	4	yes	—
209	#121×C₆₁	C₂³	1	4	yes	—
210	#121×C₆₁	C₂³	1	16	yes	—
211	#121×C₆₁	C₂³	1	8	yes	—
212	#121×C₆₁	C₂³	1	8	yes	—
213	#121×C₆₁	C₂³	1	4	yes	—
214	#121×C₆₁	C₂³	1	4	yes	—
215	#121×C₆₁	C₂³	1	16	yes	—
216	#121×C₆₁	C₂³	1	4	yes	—
217	#121×C₆₁	C₂³	1	4	yes	—
218	#121×C₆₁	C₂³	1	8	yes	—
219	#121×C₆₁	C₂³	1	8	yes	—
220	#121×C₆₁	C₂³	1	16	yes	—
221	#121×C₆₁	C₂³	1	16	yes	—
222	#121×C₆₁	C₂³	1	8	yes	—
223	#121×C₆₁	C₂³	1	4	yes	—
224	#121×C₆₁	C₂³	1	8	yes	—
225	#120×C₆₁	C₂³	1	8	yes	—
226	#120×C₆₁	C₂³	1	8	yes	—
227	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
228	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
229	C₄×Q₈×C₆₁	C₂³	1	16	yes	—
230	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
231	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
232	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
233	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
234	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
235	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
236	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
237	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
238	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
239	C₄×D₄×C₆₁	C₂³	1	2	yes	—
240	C₄×D₄×C₆₁	C₂³	1	8	yes	—
241	C₄×D₄×C₆₁	C₂³	1	8	yes	—
242	C₄×D₄×C₆₁	C₂³	1	16	yes	—
243	C₄×D₄×C₆₁	C₂³	1	8	yes	—
244	C₄×D₄×C₆₁	C₂³	1	4	yes	—
245	C₄×D₄×C₆₁	C₂³	1	4	yes	—
246	C₄×D₄×C₆₁	C₂³	1	16	yes	—
247	C₄×D₄×C₆₁	C₂³	1	16	yes	—
248	C₄×D₄×C₆₁	C₂³	1	2	yes	—
249	C₄×D₄×C₆₁	C₂³	1	4	yes	—
250	C₄×D₄×C₆₁	C₂³	1	8	yes	—
251	C₄×D₄×C₆₁	C₂³	1	4	yes	—
252	C₄×D₄×C₆₁	C₂³	1	8	yes	—
253	C₄×D₄×C₆₁	C₂³	1	8	yes	—
254	C₄×D₄×C₆₁	C₂³	1	4	yes	—
255	C₄×D₄×C₆₁	C₂³	1	8	yes	—
256	C₄×D₄×C₆₁	C₂³	1	2	yes	—
257	C₄×D₄×C₆₁	C₂³	1	4	yes	—
258	C₄×D₄×C₆₁	C₂³	1	8	yes	—
259	C₄×D₄×C₆₁	C₂³	1	2	yes	—
260	#117×C₆₁	C₂³	1	8	yes	—
261	#117×C₆₁	C₂³	1	4	yes	—
262	#117×C₆₁	C₂³	1	4	yes	—
263	#117×C₆₁	C₂³	1	8	yes	—
264	#117×C₆₁	C₂³	1	4	yes	—
265	#117×C₆₁	C₂³	1	8	yes	—
266	#117×C₆₁	C₂³	1	2	yes	—
267	#117×C₆₁	C₂³	1	16	yes	—
268	#117×C₆₁	C₂³	1	4	yes	—
269	#117×C₆₁	C₂³	1	8	yes	—
270	#117×C₆₁	C₂³	1	4	yes	—
271	#117×C₆₁	C₂³	1	8	yes	—
272	#117×C₆₁	C₂³	1	4	yes	—
273	#117×C₆₁	C₂³	1	8	yes	—
274	#117×C₆₁	C₂³	1	16	yes	—
275	#117×C₆₁	C₂³	1	8	yes	—
276	#117×C₆₁	C₂³	1	4	yes	—
277	#117×C₆₁	C₂³	1	4	yes	—
278	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
279	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
280	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
281	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
282	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
283	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
284	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
285	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
286	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
287	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
289	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
290	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
291	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
292	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
293	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
294	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
296	C₂×C₄²×C₆₁	C₂³	1	8	yes	—
297	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
298	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
299	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
300	#41×C₆₁	—	2	8	no	—
301	#41×C₆₁	—	4	8	no	—
302	#41×C₆₁	—	4	8	no	—
303	#41×C₆₁	—	8	16	no	—
304	C₂×Q₈×C₆₁	—	4	8	no	—
305	C₂×Q₈×C₆₁	—	8	2	no	—
306	C₂×Q₈×C₆₁	—	8	8	no	—
307	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
308	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
309	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
310	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
311	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
312	C₂×Q₈×C₆₁	C₂⁴	1	16	yes	—
313	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
314	C₂×D₄×C₆₁	—	2	4	no	—
315	C₂×D₄×C₆₁	—	4	2	no	—
316	C₂×D₄×C₆₁	—	8	4	no	—
317	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
318	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
319	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
320	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
321	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
322	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
323	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
324	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
325	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
326	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
327	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
328	C₂²×C₄×C₆₁	—	2	8	no	—
329	C₂²×C₄×C₆₁	—	4	4	no	—
330	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
332	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
334	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
335	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
336	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
337	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
340	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
341	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
342	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
343	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
344	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
345	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
346	C₂²×C₄×C₆₁	C₂⁴	1	16	yes	—
347	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
348	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
349	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
350	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
351	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
352	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
353	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
354	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
355	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
356	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
357	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
358	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
359	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
361	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
362	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
363	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
364	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
365	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
366	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
367	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
368	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
369	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
370	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
371	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
372	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
373	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
374	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
375	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
376	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
377	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
378	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
379	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
380	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
381	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
382	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
383	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
384	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
385	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
386	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
387	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
388	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
389	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
390	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
391	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
392	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
393	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
394	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
395	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
396	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
397	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
398	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
399	C₄²×C₆₁	C₂⁴	1	4	yes	—
400	C₄²×C₆₁	C₂⁴	1	2	yes	—
401	C₄²×C₆₁	C₂⁴	1	8	yes	—
402	C₄²×C₆₁	C₂⁴	1	8	yes	—
403	C₄²×C₆₁	C₂⁴	1	8	yes	—
404	C₄²×C₆₁	C₂⁴	1	8	yes	—
405	C₄²×C₆₁	C₂⁴	1	2	yes	—
406	C₄²×C₆₁	C₂⁴	1	8	yes	—
407	C₄²×C₆₁	C₂⁴	1	4	yes	—
408	C₄²×C₆₁	C₂⁴	1	4	yes	—
409	C₄²×C₆₁	C₂⁴	1	16	yes	—
410	C₂³×C₆₁	—	2	4	no	—
411	C₂³×C₆₁	—	2	4	no	—
412	C₂³×C₆₁	—	4	2	no	—
413	C₂³×C₆₁	—	4	2	no	—
414	C₂³×C₆₁	—	4	2	no	—
415	C₂³×C₆₁	—	4	2	no	—
416	C₂³×C₆₁	C₂⁵	1	4	yes	—
417	C₂³×C₆₁	C₂⁵	1	4	yes	—
418	C₂³×C₆₁	C₂⁵	1	4	yes	—
419	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
420	Q₈×C₆₁	—	2	4	no	—
421	Q₈×C₆₁	—	2	8	no	—
422	Q₈×C₆₁	—	4	8	no	—
423	Q₈×C₆₁	—	4	4	no	—
424	Q₈×C₆₁	—	4	8	no	—
425	Q₈×C₆₁	—	4	16	no	—
426	Q₈×C₆₁	—	4	4	no	—
427	D₄×C₆₁	—	2	8	no	—
428	D₄×C₆₁	—	2	8	no	—
429	D₄×C₆₁	—	2	4	no	—
430	D₄×C₆₁	—	2	4	no	—
431	D₄×C₆₁	—	4	2	no	—
432	D₄×C₆₁	—	4	16	no	—
433	D₄×C₆₁	—	4	8	no	—
434	D₄×C₆₁	—	4	4	no	—
435	D₄×C₆₁	—	4	8	no	—
436	D₄×C₆₁	—	4	8	no	—
437	D₄×C₆₁	—	4	8	no	—
438	C₂×C₄×C₆₁	—	2	4	no	—
439	C₂×C₄×C₆₁	—	2	8	no	—
440	C₂×C₄×C₆₁	—	2	8	no	—
441	C₂×C₄×C₆₁	—	2	8	no	—
442	C₂×C₄×C₆₁	—	2	2	no	—
443	C₂×C₄×C₆₁	—	2	8	no	—
444	C₂×C₄×C₆₁	—	2	8	no	—
445	C₂×C₄×C₆₁	—	4	4	no	—
446	C₂×C₄×C₆₁	—	4	2	no	—
447	C₂×C₄×C₆₁	—	4	4	no	—
448	C₂×C₄×C₆₁	—	4	8	no	—
449	C₂×C₄×C₆₁	—	4	4	no	—
450	C₂×C₄×C₆₁	—	4	1	no	—
451	C₂×C₄×C₆₁	—	4	16	no	—
452	C₂×C₄×C₆₁	—	4	8	no	—
453	C₂×C₄×C₆₁	—	4	8	no	—
454	C₂×C₄×C₆₁	—	4	8	no	—
455	C₂×C₄×C₆₁	2₋¹⁺⁴	1	4	yes	—
456	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
457	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
458	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
459	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
460	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
461	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
462	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
463	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
464	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
465	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
466	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
467	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
468	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
469	#62929	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
470	C₂²×C₆₁	—	2	1	no	—
471	C₂²×C₆₁	—	2	1	no	—
472	C₂²×C₆₁	—	2	4	no	—
473	C₂²×C₆₁	—	2	4	no	—
474	C₂²×C₆₁	—	2	4	no	—
475	C₂²×C₆₁	—	2	4	no	—
476	C₂²×C₆₁	—	2	4	no	—
477	C₂²×C₆₁	—	2	4	no	—
478	C₂²×C₆₁	—	2	4	no	—
479	C₂²×C₆₁	—	2	4	no	—
480	C₂²×C₆₁	—	2	4	no	—
481	C₂²×C₆₁	—	8	4	no	—
482	C₂²×C₆₁	—	8	4	no	—
483	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
484	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
485	C₄×C₆₁	—	2	2	no	—
486	C₄×C₆₁	—	2	2	no	—
487	C₄×C₆₁	—	2	4	no	—
488	C₄×C₆₁	—	2	1	no	—
489	C₄×C₆₁	—	2	4	no	—
490	C₄×C₆₁	—	2	4	no	—
491	C₄×C₆₁	—	2	8	no	—
492	C₄×C₆₁	—	2	8	no	—
493	C₄×C₆₁	—	2	8	no	—
494	C₄×C₆₁	—	2	4	no	—
495	C₄×C₆₁	—	2	2	no	—
496	C₄×C₆₁	C₂×2₋¹⁺⁴	1	4	yes	—
497	C₄×C₆₁	#585	1	2	yes	—
498	#3565	C₂×C₆₁	1	8	yes	complemented
499	#3561	C₂×C₆₁	1	8	yes	complemented
500	#3547	C₂×C₆₁	1	4	yes	complemented
501	#3547	C₂×C₆₁	1	8	yes	complemented
502	#3544	C₂×C₆₁	1	4	yes	complemented
503	#3536	C₂×C₆₁	1	4	yes	complemented
504	#3518	C₂×C₆₁	1	4	yes	complemented
505	#3511	C₂×C₆₁	1	4	yes	complemented
506	#3503	C₂×C₆₁	1	2	yes	complemented
507	#3501	C₂×C₆₁	1	1	yes	characteristic, complemented
508	#3495	C₂×C₆₁	1	4	yes	complemented
509	#3494	C₂×C₆₁	1	4	yes	complemented
510	#3493	C₂×C₆₁	1	2	yes	complemented
511	#3475	C₂×C₆₁	1	2	yes	complemented
512	C₂×#555	C₂×C₆₁	1	1	yes	characteristic, complemented
513	#3460	C₂×C₆₁	1	1	yes	characteristic, complemented
514	#3458	C₂×C₆₁	1	2	yes	complemented
515	C₂×C₆₁	—	2	2	no	—
516	C₂×C₆₁	—	4	4	no	—
517	C₂×C₆₁	—	4	4	no	—
518	C₂×C₆₁	—	4	4	no	—
519	C₂×C₆₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
520	C₂×C₆₁	C₂×#585	1	1	yes	characteristic
521	C₂×C₆₁	H(7,𝔽₂)	1	1	yes	characteristic
522	#563	C₂²×C₆₁	1	16	yes	complemented
523	#562	C₂²×C₆₁	1	16	yes	complemented
524	#562	C₂²×C₆₁	1	16	yes	complemented
525	Q₈²	C₂²×C₆₁	1	4	yes	complemented
526	#557	C₂²×C₆₁	1	4	yes	complemented
527	#556	C₂²×C₆₁	1	2	yes	complemented
528	#556	C₂²×C₆₁	1	8	yes	complemented
529	#556	C₂²×C₆₁	1	8	yes	complemented
530	#556	C₂²×C₆₁	1	16	yes	complemented
531	#555	C₂²×C₆₁	1	4	yes	—
532	#555	C₂²×C₆₁	1	4	yes	—
533	#555	C₂²×C₆₁	1	8	yes	—
534	#555	C₂²×C₆₁	1	2	yes	complemented
535	#555	C₂²×C₆₁	1	8	yes	complemented
536	#555	C₂²×C₆₁	1	8	yes	complemented
537	#554	C₂²×C₆₁	1	8	yes	—
538	#554	C₂²×C₆₁	1	2	yes	complemented
539	#554	C₂²×C₆₁	1	4	yes	complemented
540	#554	C₂²×C₆₁	1	8	yes	complemented
541	#554	C₂²×C₆₁	1	4	yes	complemented
542	#553	C₂²×C₆₁	1	4	yes	complemented
543	#553	C₂²×C₆₁	1	8	yes	complemented
544	#553	C₂²×C₆₁	1	8	yes	complemented
545	#553	C₂²×C₆₁	1	8	yes	complemented
546	#552	C₂²×C₆₁	1	4	yes	—
547	#552	C₂²×C₆₁	1	4	yes	complemented
548	#552	C₂²×C₆₁	1	8	yes	complemented
549	#552	C₂²×C₆₁	1	8	yes	complemented
550	#552	C₂²×C₆₁	1	16	yes	complemented
551	#551	C₂²×C₆₁	1	8	yes	—
552	#551	C₂²×C₆₁	1	16	yes	—
553	D₄×Q₈	C₂²×C₆₁	1	8	yes	—
554	D₄×Q₈	C₂²×C₆₁	1	4	yes	complemented
555	D₄×Q₈	C₂²×C₆₁	1	4	yes	complemented
556	#548	C₂²×C₆₁	1	16	yes	complemented
557	#548	C₂²×C₆₁	1	8	yes	complemented
558	#547	C₂²×C₆₁	1	2	yes	complemented
559	#547	C₂²×C₆₁	1	8	yes	complemented
560	#547	C₂²×C₆₁	1	8	yes	complemented
561	#546	C₂²×C₆₁	1	4	yes	—
562	#546	C₂²×C₆₁	1	16	yes	—
563	#544	C₂²×C₆₁	1	1	yes	characteristic
564	#544	C₂²×C₆₁	1	2	yes	—
565	#544	C₂²×C₆₁	1	4	yes	—
566	#544	C₂²×C₆₁	1	8	yes	complemented
567	#544	C₂²×C₆₁	1	8	yes	complemented
568	#544	C₂²×C₆₁	1	4	yes	complemented
569	#544	C₂²×C₆₁	1	8	yes	complemented
570	#543	C₂²×C₆₁	1	8	yes	—
571	#543	C₂²×C₆₁	1	4	yes	—
572	#542	C₂²×C₆₁	1	4	yes	complemented
573	#542	C₂²×C₆₁	1	8	yes	complemented
574	#542	C₂²×C₆₁	1	8	yes	complemented
575	#542	C₂²×C₆₁	1	16	yes	complemented
576	#542	C₂²×C₆₁	1	8	yes	complemented
577	#542	C₂²×C₆₁	1	16	yes	complemented
578	#542	C₂²×C₆₁	1	16	yes	complemented
579	#541	C₂²×C₆₁	1	8	yes	complemented
580	#540	C₂²×C₆₁	1	4	yes	complemented
581	#540	C₂²×C₆₁	1	8	yes	complemented
582	#539	C₂²×C₆₁	1	8	yes	complemented
583	#538	C₂²×C₆₁	1	4	yes	—
584	#538	C₂²×C₆₁	1	8	yes	—
585	#537	C₂²×C₆₁	1	1	yes	characteristic
586	#537	C₂²×C₆₁	1	8	yes	complemented
587	#537	C₂²×C₆₁	1	8	yes	complemented
588	#536	C₂²×C₆₁	1	4	yes	complemented
589	#536	C₂²×C₆₁	1	16	yes	complemented
590	#535	C₂²×C₆₁	1	2	yes	—
591	#533	C₂²×C₆₁	1	8	yes	—
592	#533	C₂²×C₆₁	1	2	yes	—
593	#533	C₂²×C₆₁	1	8	yes	complemented
594	#533	C₂²×C₆₁	1	8	yes	complemented
595	#533	C₂²×C₆₁	1	4	yes	complemented
596	#532	C₂²×C₆₁	1	4	yes	complemented
597	#532	C₂²×C₆₁	1	8	yes	complemented
598	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
599	C₂×C₄⋊Q₈	C₂²×C₆₁	1	4	yes	complemented
600	#529	C₂²×C₆₁	1	8	yes	—
601	#529	C₂²×C₆₁	1	4	yes	complemented
602	#529	C₂²×C₆₁	1	4	yes	complemented
603	#529	C₂²×C₆₁	1	8	yes	complemented
604	#529	C₂²×C₆₁	1	8	yes	complemented
605	C₂×#124	C₂²×C₆₁	1	4	yes	—
606	#525	C₂²×C₆₁	1	4	yes	—
607	#525	C₂²×C₆₁	1	4	yes	—
608	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	4	yes	—
609	C₂×#121	C₂²×C₆₁	1	2	yes	—
610	C₂×#121	C₂²×C₆₁	1	2	yes	—
611	#520	C₂²×C₆₁	1	4	yes	—
612	#520	C₂²×C₆₁	1	4	yes	complemented
613	#519	C₂²×C₆₁	1	4	yes	complemented
614	#518	C₂²×C₆₁	1	2	yes	—
615	C₄×#41	C₂²×C₆₁	1	2	yes	—
616	C₄×#41	C₂²×C₆₁	1	4	yes	complemented
617	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
618	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
619	C₂×#117	C₂²×C₆₁	1	2	yes	—
620	C₂×#117	C₂²×C₆₁	1	4	yes	—
621	C₂×#117	C₂²×C₆₁	1	2	yes	—
622	C₆₁	#62929	1	1	yes	characteristic, direct product factor, Sylow
623	C₂×#41	C₂³×C₆₁	1	2	yes	—
624	C₂×#41	C₂³×C₆₁	1	4	yes	—
625	C₂×#41	C₂³×C₆₁	1	4	yes	—
626	C₂×#41	C₂³×C₆₁	1	16	yes	—
627	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
628	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
629	C₂²×Q₈	C₂³×C₆₁	1	8	yes	—
630	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
631	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
632	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
633	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
634	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
635	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
636	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
637	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
638	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
639	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
640	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
641	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
642	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
643	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
644	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
645	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
646	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
647	C₄⋊Q₈	C₂³×C₆₁	1	16	yes	—
648	#127	C₂³×C₆₁	1	4	yes	—
649	#126	C₂³×C₆₁	1	16	yes	—
650	#126	C₂³×C₆₁	1	8	yes	—
651	#126	C₂³×C₆₁	1	16	yes	—
652	#126	C₂³×C₆₁	1	8	yes	—
653	#126	C₂³×C₆₁	1	8	yes	—
654	#126	C₂³×C₆₁	1	8	yes	—
655	#126	C₂³×C₆₁	1	16	yes	—
656	#126	C₂³×C₆₁	1	16	yes	—
657	#125	C₂³×C₆₁	1	8	yes	—
658	#125	C₂³×C₆₁	1	4	yes	—
659	#125	C₂³×C₆₁	1	8	yes	—
660	#125	C₂³×C₆₁	1	8	yes	—
661	#125	C₂³×C₆₁	1	4	yes	—
662	#125	C₂³×C₆₁	1	16	yes	—
663	#125	C₂³×C₆₁	1	4	yes	—
664	#125	C₂³×C₆₁	1	8	yes	—
665	#125	C₂³×C₆₁	1	8	yes	—
666	#125	C₂³×C₆₁	1	16	yes	—
667	#124	C₂³×C₆₁	1	16	yes	—
668	#124	C₂³×C₆₁	1	16	yes	—
669	#124	C₂³×C₆₁	1	8	yes	—
670	#124	C₂³×C₆₁	1	4	yes	—
671	#124	C₂³×C₆₁	1	4	yes	—
672	#124	C₂³×C₆₁	1	8	yes	—
673	#124	C₂³×C₆₁	1	8	yes	—
674	#124	C₂³×C₆₁	1	16	yes	—
675	#124	C₂³×C₆₁	1	16	yes	—
676	#124	C₂³×C₆₁	1	16	yes	—
677	#123	C₂³×C₆₁	1	8	yes	—
678	#123	C₂³×C₆₁	1	8	yes	—
679	#123	C₂³×C₆₁	1	8	yes	—
680	#123	C₂³×C₆₁	1	8	yes	—
681	#123	C₂³×C₆₁	1	8	yes	—
682	#123	C₂³×C₆₁	1	16	yes	—
683	#123	C₂³×C₆₁	1	8	yes	—
684	#123	C₂³×C₆₁	1	16	yes	—
685	#123	C₂³×C₆₁	1	16	yes	—
686	#123	C₂³×C₆₁	1	16	yes	—
687	#123	C₂³×C₆₁	1	16	yes	—
688	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
689	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
690	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
691	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
692	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
693	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
694	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
695	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
696	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
697	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
698	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
699	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
700	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
701	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
702	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
703	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
704	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
705	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
706	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
707	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
708	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
709	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
710	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
711	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
712	#121	C₂³×C₆₁	1	8	yes	—
713	#121	C₂³×C₆₁	1	8	yes	—
714	#121	C₂³×C₆₁	1	8	yes	—
715	#121	C₂³×C₆₁	1	8	yes	—
716	#121	C₂³×C₆₁	1	4	yes	—
717	#121	C₂³×C₆₁	1	4	yes	—
718	#121	C₂³×C₆₁	1	4	yes	—
719	#121	C₂³×C₆₁	1	4	yes	—
720	#121	C₂³×C₆₁	1	4	yes	—
721	#121	C₂³×C₆₁	1	4	yes	—
722	#121	C₂³×C₆₁	1	8	yes	—
723	#121	C₂³×C₆₁	1	4	yes	—
724	#121	C₂³×C₆₁	1	4	yes	—
725	#121	C₂³×C₆₁	1	16	yes	—
726	#121	C₂³×C₆₁	1	8	yes	—
727	#121	C₂³×C₆₁	1	16	yes	—
728	#121	C₂³×C₆₁	1	16	yes	—
729	#121	C₂³×C₆₁	1	16	yes	—
730	#120	C₂³×C₆₁	1	8	yes	—
731	#120	C₂³×C₆₁	1	8	yes	—
732	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
733	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
734	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
735	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
736	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
737	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
738	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
739	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
740	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
741	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
742	C₄×Q₈	C₂³×C₆₁	1	16	yes	—
743	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
744	C₄×D₄	C₂³×C₆₁	1	2	yes	—
745	C₄×D₄	C₂³×C₆₁	1	2	yes	—
746	C₄×D₄	C₂³×C₆₁	1	4	yes	—
747	C₄×D₄	C₂³×C₆₁	1	4	yes	—
748	C₄×D₄	C₂³×C₆₁	1	4	yes	—
749	C₄×D₄	C₂³×C₆₁	1	4	yes	—
750	C₄×D₄	C₂³×C₆₁	1	2	yes	—
751	C₄×D₄	C₂³×C₆₁	1	4	yes	—
752	C₄×D₄	C₂³×C₆₁	1	2	yes	—
753	C₄×D₄	C₂³×C₆₁	1	8	yes	—
754	C₄×D₄	C₂³×C₆₁	1	4	yes	—
755	C₄×D₄	C₂³×C₆₁	1	8	yes	—
756	C₄×D₄	C₂³×C₆₁	1	8	yes	—
757	C₄×D₄	C₂³×C₆₁	1	8	yes	—
758	C₄×D₄	C₂³×C₆₁	1	16	yes	—
759	C₄×D₄	C₂³×C₆₁	1	8	yes	—
760	C₄×D₄	C₂³×C₆₁	1	8	yes	—
761	C₄×D₄	C₂³×C₆₁	1	16	yes	—
762	C₄×D₄	C₂³×C₆₁	1	8	yes	—
763	C₄×D₄	C₂³×C₆₁	1	8	yes	—
764	C₄×D₄	C₂³×C₆₁	1	16	yes	—
765	#117	C₂³×C₆₁	1	2	yes	—
766	#117	C₂³×C₆₁	1	4	yes	—
767	#117	C₂³×C₆₁	1	4	yes	—
768	#117	C₂³×C₆₁	1	8	yes	—
769	#117	C₂³×C₆₁	1	8	yes	—
770	#117	C₂³×C₆₁	1	4	yes	—
771	#117	C₂³×C₆₁	1	8	yes	—
772	#117	C₂³×C₆₁	1	4	yes	—
773	#117	C₂³×C₆₁	1	4	yes	—
774	#117	C₂³×C₆₁	1	8	yes	—
775	#117	C₂³×C₆₁	1	8	yes	—
776	#117	C₂³×C₆₁	1	4	yes	—
777	#117	C₂³×C₆₁	1	4	yes	—
778	#117	C₂³×C₆₁	1	8	yes	—
779	#117	C₂³×C₆₁	1	4	yes	—
780	#117	C₂³×C₆₁	1	16	yes	—
781	#117	C₂³×C₆₁	1	8	yes	—
782	#117	C₂³×C₆₁	1	16	yes	—
783	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
784	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
785	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
786	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
787	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
788	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
789	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
790	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
791	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
792	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
794	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
795	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
796	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
797	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
798	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
799	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
800	C₂×C₄²	C₂³×C₆₁	1	8	yes	—
801	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
802	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
803	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
804	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
805	#41	—	2	8	no	—
806	#41	—	4	8	no	—
807	#41	—	4	8	no	—
808	#41	—	8	16	no	—
809	C₂×Q₈	—	4	8	no	—
810	C₂×Q₈	—	8	2	no	—
811	C₂×Q₈	—	8	8	no	—
812	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
813	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
814	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
815	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
816	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
817	C₂×Q₈	C₂⁴×C₆₁	1	16	yes	—
818	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
819	C₂×D₄	—	2	4	no	—
820	C₂×D₄	—	4	2	no	—
821	C₂×D₄	—	8	4	no	—
822	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
823	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
824	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
825	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
826	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
827	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
828	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
829	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
830	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
831	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
832	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
833	C₂²×C₄	—	2	8	no	—
834	C₂²×C₄	—	4	4	no	—
835	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
836	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
837	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
839	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
840	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
841	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
842	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
843	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
845	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
846	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
847	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
848	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
849	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
850	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
851	C₂²×C₄	C₂⁴×C₆₁	1	16	yes	—
852	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
853	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
854	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
855	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
856	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
857	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
858	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
859	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
860	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
861	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
862	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
863	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
864	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
865	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
866	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
867	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
868	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
869	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
870	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
871	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
872	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
873	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
874	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
875	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
876	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
877	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
878	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
879	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
880	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
881	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
882	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
883	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
884	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
885	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
886	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
887	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
888	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
889	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
890	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
891	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
892	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
893	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
894	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
895	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
896	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
897	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
898	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
899	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
900	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
901	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
902	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
903	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
904	C₄²	C₂⁴×C₆₁	1	4	yes	—
905	C₄²	C₂⁴×C₆₁	1	2	yes	—
906	C₄²	C₂⁴×C₆₁	1	8	yes	—
907	C₄²	C₂⁴×C₆₁	1	8	yes	—
908	C₄²	C₂⁴×C₆₁	1	8	yes	—
909	C₄²	C₂⁴×C₆₁	1	8	yes	—
910	C₄²	C₂⁴×C₆₁	1	2	yes	—
911	C₄²	C₂⁴×C₆₁	1	8	yes	—
912	C₄²	C₂⁴×C₆₁	1	4	yes	—
913	C₄²	C₂⁴×C₆₁	1	4	yes	—
914	C₄²	C₂⁴×C₆₁	1	16	yes	—
915	C₂³	—	2	4	no	—
916	C₂³	—	2	4	no	—
917	C₂³	—	4	2	no	—
918	C₂³	—	4	2	no	—
919	C₂³	—	4	2	no	—
920	C₂³	—	4	2	no	—
921	C₂³	C₂⁵×C₆₁	1	4	yes	—
922	C₂³	C₂⁵×C₆₁	1	4	yes	—
923	C₂³	C₂⁵×C₆₁	1	4	yes	—
924	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
925	Q₈	—	2	4	no	—
926	Q₈	—	2	8	no	—
927	Q₈	—	4	8	no	—
928	Q₈	—	4	4	no	—
929	Q₈	—	4	8	no	—
930	Q₈	—	4	16	no	—
931	Q₈	—	4	4	no	—
932	D₄	—	2	8	no	—
933	D₄	—	2	8	no	—
934	D₄	—	2	4	no	—
935	D₄	—	2	4	no	—
936	D₄	—	4	2	no	—
937	D₄	—	4	16	no	—
938	D₄	—	4	8	no	—
939	D₄	—	4	4	no	—
940	D₄	—	4	8	no	—
941	D₄	—	4	8	no	—
942	D₄	—	4	8	no	—
943	C₂×C₄	—	2	4	no	—
944	C₂×C₄	—	2	8	no	—
945	C₂×C₄	—	2	8	no	—
946	C₂×C₄	—	2	8	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	8	no	—
949	C₂×C₄	—	2	8	no	—
950	C₂×C₄	—	4	4	no	—
951	C₂×C₄	—	4	2	no	—
952	C₂×C₄	—	4	4	no	—
953	C₂×C₄	—	4	8	no	—
954	C₂×C₄	—	4	4	no	—
955	C₂×C₄	—	4	1	no	—
956	C₂×C₄	—	4	16	no	—
957	C₂×C₄	—	4	8	no	—
958	C₂×C₄	—	4	8	no	—
959	C₂×C₄	—	4	8	no	—
960	C₂×C₄	2₋¹⁺⁴×C₆₁	1	4	yes	—
961	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
962	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
963	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
964	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
965	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
966	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
967	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
968	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
969	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
970	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
971	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
972	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
973	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
974	C₂²	—	2	1	no	—
975	C₂²	—	2	1	no	—
976	C₂²	—	2	4	no	—
977	C₂²	—	2	4	no	—
978	C₂²	—	2	4	no	—
979	C₂²	—	2	4	no	—
980	C₂²	—	2	4	no	—
981	C₂²	—	2	4	no	—
982	C₂²	—	2	4	no	—
983	C₂²	—	2	4	no	—
984	C₂²	—	2	4	no	—
985	C₂²	—	8	4	no	—
986	C₂²	—	8	4	no	—
987	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
988	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
989	C₄	—	2	2	no	—
990	C₄	—	2	2	no	—
991	C₄	—	2	4	no	—
992	C₄	—	2	1	no	—
993	C₄	—	2	4	no	—
994	C₄	—	2	4	no	—
995	C₄	—	2	8	no	—
996	C₄	—	2	8	no	—
997	C₄	—	2	8	no	—
998	C₄	—	2	4	no	—
999	C₄	—	2	2	no	—
1000	C₄	C₂×2₋¹⁺⁴×C₆₁	1	4	yes	—
1001	C₄	C₆₁×#585	1	2	yes	—
1002	C₂	—	2	2	no	—
1003	C₂	—	4	4	no	—
1004	C₂	—	4	4	no	—
1005	C₂	—	4	4	no	—
1006	C₂	C₂²×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1007	C₂	C₂×C₆₁×#585	1	1	yes	characteristic
1008	C₂	C₆₁×H(7,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3565	C₂	semidirect
2. C₆₁×#3561	C₂	semidirect
3. C₆₁×#3547	C₂	semidirect
4. C₆₁×#3547	C₂	semidirect
5. C₆₁×#3544	C₂	semidirect
6. C₆₁×#3536	C₂	semidirect
7. C₆₁×#3518	C₂	semidirect
8. C₆₁×#3511	C₂	semidirect
9. C₆₁×#3503	C₂	semidirect
10. C₆₁×#3501	C₂	semidirect
11. C₆₁×#3495	C₂	semidirect
12. C₆₁×#3494	C₂	semidirect
13. C₆₁×#3493	C₂	semidirect
14. C₆₁×#3475	C₂	semidirect
15. C₂×C₆₁×#555	C₂	semidirect
16. C₆₁×#3460	C₂	semidirect
17. C₆₁×#3458	C₂	semidirect
18. C₆₁×#563	C₂²	semidirect
19. C₆₁×#562	C₂²	semidirect
20. C₆₁×#562	C₂²	semidirect
21. Q₈²×C₆₁	C₂²	semidirect
22. C₆₁×#557	C₂²	semidirect
23. C₆₁×#556	C₂²	semidirect
24. C₆₁×#556	C₂²	semidirect
25. C₆₁×#556	C₂²	semidirect
26. C₆₁×#556	C₂²	semidirect
30. C₆₁×#555	C₂²	semidirect
31. C₆₁×#555	C₂²	semidirect
32. C₆₁×#555	C₂²	semidirect
34. C₆₁×#554	C₂²	semidirect
35. C₆₁×#554	C₂²	semidirect
36. C₆₁×#554	C₂²	semidirect
37. C₆₁×#554	C₂²	semidirect
38. C₆₁×#553	C₂²	semidirect
39. C₆₁×#553	C₂²	semidirect
40. C₆₁×#553	C₂²	semidirect
41. C₆₁×#553	C₂²	semidirect
43. C₆₁×#552	C₂²	semidirect
44. C₆₁×#552	C₂²	semidirect
45. C₆₁×#552	C₂²	semidirect
46. C₆₁×#552	C₂²	semidirect
50. D₄×Q₈×C₆₁	C₂²	semidirect
51. D₄×Q₈×C₆₁	C₂²	semidirect
52. C₆₁×#548	C₂²	semidirect
53. C₆₁×#548	C₂²	semidirect
54. C₆₁×#547	C₂²	semidirect
55. C₆₁×#547	C₂²	semidirect
56. C₆₁×#547	C₂²	semidirect
62. C₆₁×#544	C₂²	semidirect
63. C₆₁×#544	C₂²	semidirect
64. C₆₁×#544	C₂²	semidirect
65. C₆₁×#544	C₂²	semidirect
68. C₆₁×#542	C₂²	semidirect
69. C₆₁×#542	C₂²	semidirect
70. C₆₁×#542	C₂²	semidirect
71. C₆₁×#542	C₂²	semidirect
72. C₆₁×#542	C₂²	semidirect
73. C₆₁×#542	C₂²	semidirect
74. C₆₁×#542	C₂²	semidirect
75. C₆₁×#541	C₂²	semidirect
76. C₆₁×#540	C₂²	semidirect
77. C₆₁×#540	C₂²	semidirect
78. C₆₁×#539	C₂²	semidirect
82. C₆₁×#537	C₂²	semidirect
83. C₆₁×#537	C₂²	semidirect
84. C₆₁×#536	C₂²	semidirect
85. C₆₁×#536	C₂²	semidirect
89. C₆₁×#533	C₂²	semidirect
90. C₆₁×#533	C₂²	semidirect
91. C₆₁×#533	C₂²	semidirect
92. C₆₁×#532	C₂²	semidirect
93. C₆₁×#532	C₂²	semidirect
95. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
97. C₆₁×#529	C₂²	semidirect
98. C₆₁×#529	C₂²	semidirect
99. C₆₁×#529	C₂²	semidirect
100. C₆₁×#529	C₂²	semidirect
108. C₆₁×#520	C₂²	semidirect
109. C₆₁×#519	C₂²	semidirect
112. C₄×#41×C₆₁	C₂²	semidirect
469. #62929	C₆₁	direct (N × H)
498. #3565	C₂×C₆₁	semidirect
499. #3561	C₂×C₆₁	semidirect
500. #3547	C₂×C₆₁	semidirect
501. #3547	C₂×C₆₁	semidirect
502. #3544	C₂×C₆₁	semidirect
503. #3536	C₂×C₆₁	semidirect
504. #3518	C₂×C₆₁	semidirect
505. #3511	C₂×C₆₁	semidirect
506. #3503	C₂×C₆₁	semidirect
507. #3501	C₂×C₆₁	semidirect
508. #3495	C₂×C₆₁	semidirect
509. #3494	C₂×C₆₁	semidirect
510. #3493	C₂×C₆₁	semidirect
511. #3475	C₂×C₆₁	semidirect
512. C₂×#555	C₂×C₆₁	semidirect
513. #3460	C₂×C₆₁	semidirect
514. #3458	C₂×C₆₁	semidirect
522. #563	C₂²×C₆₁	semidirect
523. #562	C₂²×C₆₁	semidirect
524. #562	C₂²×C₆₁	semidirect
525. Q₈²	C₂²×C₆₁	semidirect
526. #557	C₂²×C₆₁	semidirect
527. #556	C₂²×C₆₁	semidirect
528. #556	C₂²×C₆₁	semidirect
529. #556	C₂²×C₆₁	semidirect
530. #556	C₂²×C₆₁	semidirect
534. #555	C₂²×C₆₁	semidirect
535. #555	C₂²×C₆₁	semidirect
536. #555	C₂²×C₆₁	semidirect
538. #554	C₂²×C₆₁	semidirect
539. #554	C₂²×C₆₁	semidirect
540. #554	C₂²×C₆₁	semidirect
541. #554	C₂²×C₆₁	semidirect
542. #553	C₂²×C₆₁	semidirect
543. #553	C₂²×C₆₁	semidirect
544. #553	C₂²×C₆₁	semidirect
545. #553	C₂²×C₆₁	semidirect
547. #552	C₂²×C₆₁	semidirect
548. #552	C₂²×C₆₁	semidirect
549. #552	C₂²×C₆₁	semidirect
550. #552	C₂²×C₆₁	semidirect
554. D₄×Q₈	C₂²×C₆₁	semidirect
555. D₄×Q₈	C₂²×C₆₁	semidirect
556. #548	C₂²×C₆₁	semidirect
557. #548	C₂²×C₆₁	semidirect
558. #547	C₂²×C₆₁	semidirect
559. #547	C₂²×C₆₁	semidirect
560. #547	C₂²×C₆₁	semidirect
566. #544	C₂²×C₆₁	semidirect
567. #544	C₂²×C₆₁	semidirect
568. #544	C₂²×C₆₁	semidirect
569. #544	C₂²×C₆₁	semidirect
572. #542	C₂²×C₆₁	semidirect
573. #542	C₂²×C₆₁	semidirect
574. #542	C₂²×C₆₁	semidirect
575. #542	C₂²×C₆₁	semidirect
576. #542	C₂²×C₆₁	semidirect
577. #542	C₂²×C₆₁	semidirect
578. #542	C₂²×C₆₁	semidirect
579. #541	C₂²×C₆₁	semidirect
580. #540	C₂²×C₆₁	semidirect
581. #540	C₂²×C₆₁	semidirect
582. #539	C₂²×C₆₁	semidirect
586. #537	C₂²×C₆₁	semidirect
587. #537	C₂²×C₆₁	semidirect
588. #536	C₂²×C₆₁	semidirect
589. #536	C₂²×C₆₁	semidirect
593. #533	C₂²×C₆₁	semidirect
594. #533	C₂²×C₆₁	semidirect
595. #533	C₂²×C₆₁	semidirect
596. #532	C₂²×C₆₁	semidirect
597. #532	C₂²×C₆₁	semidirect
599. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
601. #529	C₂²×C₆₁	semidirect
602. #529	C₂²×C₆₁	semidirect
603. #529	C₂²×C₆₁	semidirect
604. #529	C₂²×C₆₁	semidirect
612. #520	C₂²×C₆₁	semidirect
613. #519	C₂²×C₆₁	semidirect
616. C₄×#41	C₂²×C₆₁	semidirect
622. C₆₁	#62929	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×#3565	2
C₆₁×#3561	2
C₆₁×#3547	2
C₆₁×#3544	2
C₆₁×#3536	2
C₆₁×#3518	2
C₆₁×#3511	2
C₆₁×#3503	2
C₆₁×#3501	2
C₆₁×#3495	2
C₆₁×#3494	2
C₆₁×#3493	2
C₆₁×#3475	2
C₂×C₆₁×#555	2
C₆₁×#3460	2
C₆₁×#3458	2
#62929	61

Subgroups — C61×#62929 #29566362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62929 #29566362