Subgroups — C₆₁×#62944 #29566377

Order 15616.

7214 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3559	C₂	1	4	yes	maximal, complemented
2	C₆₁×#3548	C₂	1	4	yes	maximal, complemented
3	C₆₁×#3547	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3541	C₂	1	8	yes	maximal, complemented
5	C₆₁×#3536	C₂	1	8	yes	maximal, complemented
6	C₆₁×#3536	C₂	1	8	yes	maximal, complemented
7	C₆₁×#3519	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3519	C₂	1	4	yes	maximal, complemented
9	C₆₁×#3511	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3501	C₂	1	4	yes	maximal, complemented
11	C₆₁×#3497	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3492	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3489	C₂	1	4	yes	maximal, complemented
14	C₂×C₆₁×#554	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×#41×C₆₁	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3461	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₆₁×#537	C₂	1	2	yes	maximal, complemented
18	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	2	yes	complemented
19	C₂²×#41×C₆₁	C₂²	1	4	yes	complemented
20	C₆₁×#563	C₂²	1	8	yes	complemented
21	C₆₁×#562	C₂²	1	16	yes	complemented
22	C₆₁×#562	C₂²	1	16	yes	complemented
23	C₆₁×#562	C₂²	1	8	yes	complemented
24	C₆₁×#556	C₂²	1	4	yes	complemented
25	C₆₁×#555	C₂²	1	4	yes	complemented
26	C₆₁×#555	C₂²	1	4	yes	complemented
27	C₆₁×#554	C₂²	1	4	yes	—
28	C₆₁×#554	C₂²	1	4	yes	—
29	C₆₁×#554	C₂²	1	4	yes	complemented
30	C₆₁×#554	C₂²	1	8	yes	complemented
31	C₆₁×#554	C₂²	1	4	yes	complemented
32	C₆₁×#554	C₂²	1	8	yes	complemented
33	C₆₁×#554	C₂²	1	8	yes	complemented
34	C₆₁×#554	C₂²	1	16	yes	complemented
35	C₆₁×#553	C₂²	1	8	yes	complemented
36	C₆₁×#553	C₂²	1	8	yes	complemented
37	C₆₁×#553	C₂²	1	8	yes	complemented
38	C₆₁×#553	C₂²	1	8	yes	complemented
39	C₆₁×#552	C₂²	1	8	yes	complemented
40	C₆₁×#550	C₂²	1	2	yes	complemented
41	C₆₁×#550	C₂²	1	4	yes	complemented
42	C₆₁×#550	C₂²	1	4	yes	complemented
43	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
44	D₄×Q₈×C₆₁	C₂²	1	4	yes	complemented
45	D₄×Q₈×C₆₁	C₂²	1	8	yes	complemented
46	C₆₁×#548	C₂²	1	8	yes	complemented
47	C₆₁×#548	C₂²	1	4	yes	complemented
48	C₆₁×#548	C₂²	1	8	yes	complemented
49	C₆₁×#548	C₂²	1	8	yes	complemented
50	C₆₁×#547	C₂²	1	2	yes	complemented
51	C₆₁×#547	C₂²	1	8	yes	complemented
52	C₆₁×#547	C₂²	1	8	yes	complemented
53	C₆₁×#547	C₂²	1	4	yes	complemented
54	C₆₁×#547	C₂²	1	16	yes	complemented
55	C₆₁×#547	C₂²	1	4	yes	complemented
56	C₆₁×#546	C₂²	1	4	yes	complemented
57	C₆₁×#546	C₂²	1	8	yes	complemented
58	C₆₁×#546	C₂²	1	8	yes	complemented
59	C₆₁×#546	C₂²	1	16	yes	complemented
60	C₆₁×#546	C₂²	1	16	yes	complemented
61	C₆₁×#546	C₂²	1	8	yes	complemented
62	D₄²×C₆₁	C₂²	1	4	yes	—
63	D₄²×C₆₁	C₂²	1	2	yes	—
64	D₄²×C₆₁	C₂²	1	4	yes	—
65	C₆₁×#544	C₂²	1	8	yes	complemented
66	C₆₁×#544	C₂²	1	1	yes	characteristic, complemented
67	C₆₁×#543	C₂²	1	16	yes	complemented
68	C₆₁×#542	C₂²	1	16	yes	complemented
69	C₆₁×#542	C₂²	1	4	yes	complemented
70	C₆₁×#542	C₂²	1	8	yes	complemented
71	C₆₁×#541	C₂²	1	4	yes	complemented
72	C₆₁×#540	C₂²	1	8	yes	complemented
73	C₆₁×#540	C₂²	1	8	yes	complemented
74	C₆₁×#539	C₂²	1	8	yes	complemented
75	C₆₁×#539	C₂²	1	16	yes	complemented
76	C₆₁×#539	C₂²	1	4	yes	complemented
77	C₆₁×#538	C₂²	1	16	yes	complemented
78	C₆₁×#538	C₂²	1	16	yes	complemented
79	C₆₁×#537	C₂²	1	1	yes	characteristic
80	C₆₁×#537	C₂²	1	8	yes	complemented
81	C₆₁×#537	C₂²	1	8	yes	complemented
82	C₆₁×#537	C₂²	1	8	yes	complemented
83	C₆₁×#537	C₂²	1	16	yes	complemented
84	C₆₁×#537	C₂²	1	8	yes	complemented
85	C₆₁×#537	C₂²	1	4	yes	complemented
86	C₆₁×#537	C₂²	1	2	yes	complemented
87	C₆₁×#537	C₂²	1	4	yes	complemented
88	C₆₁×#536	C₂²	1	8	yes	complemented
89	C₆₁×#536	C₂²	1	2	yes	complemented
90	C₆₁×#533	C₂²	1	4	yes	complemented
91	C₆₁×#533	C₂²	1	4	yes	complemented
92	C₆₁×#532	C₂²	1	4	yes	complemented
93	C₆₁×#532	C₂²	1	4	yes	complemented
94	C₆₁×#532	C₂²	1	4	yes	complemented
95	C₆₁×#532	C₂²	1	2	yes	complemented
96	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
97	C₆₁×#529	C₂²	1	4	yes	complemented
98	C₆₁×#529	C₂²	1	4	yes	complemented
99	C₂×#125×C₆₁	C₂²	1	2	yes	complemented
100	C₆₁×#525	C₂²	1	4	yes	complemented
101	C₆₁×#525	C₂²	1	8	yes	complemented
102	C₆₁×#525	C₂²	1	8	yes	complemented
103	C₆₁×#525	C₂²	1	8	yes	complemented
104	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	8	yes	complemented
105	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	4	yes	complemented
107	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	8	yes	complemented
108	C₂×#121×C₆₁	C₂²	1	8	yes	complemented
109	C₂×#121×C₆₁	C₂²	1	8	yes	complemented
110	C₆₁×#520	C₂²	1	4	yes	complemented
111	C₆₁×#518	C₂²	1	8	yes	—
112	C₄×#41×C₆₁	C₂²	1	2	yes	complemented
113	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
115	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	—
116	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
117	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	complemented
118	2₋¹⁺⁴×C₆₁	—	4	8	no	—
119	C₂×#41×C₆₁	—	4	16	no	—
120	C₂×#41×C₆₁	C₂³	1	4	yes	—
121	C₂×#41×C₆₁	C₂³	1	2	yes	—
122	C₂×#41×C₆₁	C₂³	1	8	yes	—
123	C₂×#41×C₆₁	C₂³	1	8	yes	—
124	C₂×#41×C₆₁	C₂³	1	8	yes	—
125	C₂×#41×C₆₁	C₂³	1	4	yes	—
126	C₂×#41×C₆₁	C₂³	1	4	yes	—
127	C₂×#41×C₆₁	C₂³	1	8	yes	—
128	C₂×#41×C₆₁	C₂³	1	8	yes	—
129	C₂×#41×C₆₁	C₂³	1	8	yes	—
130	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₆₁	C₂³	1	8	yes	—
132	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
133	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
134	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
136	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
137	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
138	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
139	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
140	C₂³×C₄×C₆₁	C₂³	1	8	yes	—
141	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
142	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
143	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
144	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
145	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
146	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
147	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
148	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
149	C₄⋊Q₈×C₆₁	C₂³	1	16	yes	—
150	#127×C₆₁	C₂³	1	2	yes	—
151	#127×C₆₁	C₂³	1	4	yes	—
152	#127×C₆₁	C₂³	1	4	yes	—
153	#126×C₆₁	C₂³	1	8	yes	—
154	#126×C₆₁	C₂³	1	8	yes	—
155	#126×C₆₁	C₂³	1	16	yes	—
156	#126×C₆₁	C₂³	1	16	yes	—
157	#125×C₆₁	C₂³	1	8	yes	—
158	#125×C₆₁	C₂³	1	8	yes	—
159	#125×C₆₁	C₂³	1	16	yes	—
160	#125×C₆₁	C₂³	1	8	yes	—
161	#125×C₆₁	C₂³	1	8	yes	—
162	#125×C₆₁	C₂³	1	4	yes	—
163	#125×C₆₁	C₂³	1	4	yes	—
164	#124×C₆₁	C₂³	1	8	yes	—
165	#124×C₆₁	C₂³	1	8	yes	—
166	#124×C₆₁	C₂³	1	4	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	16	yes	—
171	#124×C₆₁	C₂³	1	4	yes	—
172	#123×C₆₁	C₂³	1	16	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	16	yes	—
178	#123×C₆₁	C₂³	1	16	yes	—
179	#123×C₆₁	C₂³	1	8	yes	—
180	#123×C₆₁	C₂³	1	8	yes	—
181	#123×C₆₁	C₂³	1	8	yes	—
182	#123×C₆₁	C₂³	1	8	yes	—
183	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
184	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
185	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
186	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
187	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
188	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
189	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
190	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
191	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
192	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
193	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
194	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
195	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
196	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
197	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
198	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
199	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
200	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
201	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
202	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
203	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
204	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
205	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
206	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
207	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
208	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
209	#121×C₆₁	C₂³	1	4	yes	—
210	#121×C₆₁	C₂³	1	8	yes	—
211	#121×C₆₁	C₂³	1	8	yes	—
212	#121×C₆₁	C₂³	1	4	yes	—
213	#121×C₆₁	C₂³	1	8	yes	—
214	#121×C₆₁	C₂³	1	4	yes	—
215	#121×C₆₁	C₂³	1	4	yes	—
216	#121×C₆₁	C₂³	1	8	yes	—
217	#121×C₆₁	C₂³	1	4	yes	—
218	#121×C₆₁	C₂³	1	4	yes	—
219	#121×C₆₁	C₂³	1	16	yes	—
220	#121×C₆₁	C₂³	1	16	yes	—
221	#121×C₆₁	C₂³	1	16	yes	—
222	#121×C₆₁	C₂³	1	16	yes	—
223	#121×C₆₁	C₂³	1	16	yes	—
224	#121×C₆₁	C₂³	1	16	yes	—
225	#121×C₆₁	C₂³	1	4	yes	—
226	#121×C₆₁	C₂³	1	16	yes	—
227	#121×C₆₁	C₂³	1	8	yes	—
228	#121×C₆₁	C₂³	1	8	yes	—
229	#121×C₆₁	C₂³	1	16	yes	—
230	#121×C₆₁	C₂³	1	8	yes	—
231	#121×C₆₁	C₂³	1	8	yes	—
232	#121×C₆₁	C₂³	1	8	yes	—
233	#121×C₆₁	C₂³	1	8	yes	—
234	#121×C₆₁	C₂³	1	8	yes	—
235	#121×C₆₁	C₂³	1	4	yes	—
236	#120×C₆₁	C₂³	1	8	yes	—
237	#120×C₆₁	C₂³	1	8	yes	—
238	#120×C₆₁	C₂³	1	16	yes	—
239	#120×C₆₁	C₂³	1	8	yes	—
240	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
241	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
242	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
243	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
244	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
245	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
246	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
247	C₄×D₄×C₆₁	C₂³	1	2	yes	—
248	C₄×D₄×C₆₁	C₂³	1	4	yes	—
249	C₄×D₄×C₆₁	C₂³	1	8	yes	—
250	C₄×D₄×C₆₁	C₂³	1	8	yes	—
251	C₄×D₄×C₆₁	C₂³	1	8	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	8	yes	—
257	C₄×D₄×C₆₁	C₂³	1	16	yes	—
258	C₄×D₄×C₆₁	C₂³	1	16	yes	—
259	C₄×D₄×C₆₁	C₂³	1	4	yes	—
260	C₄×D₄×C₆₁	C₂³	1	16	yes	—
261	C₄×D₄×C₆₁	C₂³	1	16	yes	—
262	C₄×D₄×C₆₁	C₂³	1	4	yes	—
263	C₄×D₄×C₆₁	C₂³	1	4	yes	—
264	C₄×D₄×C₆₁	C₂³	1	2	yes	—
265	C₄×D₄×C₆₁	C₂³	1	4	yes	—
266	C₄×D₄×C₆₁	C₂³	1	2	yes	—
267	C₄×D₄×C₆₁	C₂³	1	2	yes	—
268	C₄×D₄×C₆₁	C₂³	1	4	yes	—
269	C₄×D₄×C₆₁	C₂³	1	4	yes	—
270	C₄×D₄×C₆₁	C₂³	1	4	yes	—
271	C₄×D₄×C₆₁	C₂³	1	4	yes	—
272	C₄×D₄×C₆₁	C₂³	1	8	yes	—
273	#117×C₆₁	C₂³	1	8	yes	—
274	#117×C₆₁	C₂³	1	8	yes	—
275	#117×C₆₁	C₂³	1	2	yes	—
276	#117×C₆₁	C₂³	1	8	yes	—
277	#117×C₆₁	C₂³	1	4	yes	—
278	#117×C₆₁	C₂³	1	8	yes	—
279	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
280	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
281	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
282	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
283	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
284	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
285	C₂×C₄⋊C₄×C₆₁	C₂³	1	16	yes	—
286	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
287	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
288	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
290	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
291	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
292	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	—
293	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
294	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	—
295	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
296	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
297	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
298	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
299	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
300	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
301	C₂⁴×C₆₁	C₂⁴	1	8	yes	—
302	#41×C₆₁	—	2	8	no	—
303	#41×C₆₁	—	2	16	no	—
304	#41×C₆₁	—	4	16	no	—
305	#41×C₆₁	—	4	16	no	—
306	#41×C₆₁	—	4	16	no	—
307	#41×C₆₁	—	4	8	no	—
308	#41×C₆₁	—	4	8	no	—
309	#41×C₆₁	—	4	16	no	—
310	#41×C₆₁	—	8	8	no	—
311	#41×C₆₁	—	8	8	no	—
312	C₂×Q₈×C₆₁	—	2	4	no	—
313	C₂×Q₈×C₆₁	—	4	8	no	—
314	C₂×Q₈×C₆₁	—	4	16	no	—
315	C₂×Q₈×C₆₁	—	8	2	no	—
316	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
317	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
318	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
319	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
320	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
321	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
322	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
323	C₂×D₄×C₆₁	—	2	4	no	—
324	C₂×D₄×C₆₁	—	2	16	no	—
325	C₂×D₄×C₆₁	—	4	8	no	—
326	C₂×D₄×C₆₁	—	4	16	no	—
327	C₂×D₄×C₆₁	—	8	8	no	—
328	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
329	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
330	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
332	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
333	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
334	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
335	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
336	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
337	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
338	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
339	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
340	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
341	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
342	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
343	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
344	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
345	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₆₁	—	2	8	no	—
347	C₂²×C₄×C₆₁	—	4	16	no	—
348	C₂²×C₄×C₆₁	—	8	4	no	—
349	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
352	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
353	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
355	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
356	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
357	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
359	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
360	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
361	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
362	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
363	C₂²×C₄×C₆₁	C₂⁴	1	16	yes	—
364	C₂²×C₄×C₆₁	C₂⁴	1	16	yes	—
365	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
366	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
367	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
368	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
370	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
371	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
372	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
373	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
374	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
375	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
376	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
377	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
378	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
379	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
380	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
381	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
382	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
383	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
384	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
385	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
386	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
387	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
388	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
389	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
390	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
391	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
392	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
393	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
394	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
395	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
396	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
397	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
398	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
399	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
400	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
401	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
402	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
403	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
404	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
405	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
406	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
407	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
408	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
409	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
410	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
411	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
412	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
413	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
414	C₄²×C₆₁	C₂⁴	1	2	yes	—
415	C₄²×C₆₁	C₂⁴	1	4	yes	—
416	C₄²×C₆₁	C₂⁴	1	2	yes	—
417	C₄²×C₆₁	C₂⁴	1	4	yes	—
418	C₄²×C₆₁	C₂⁴	1	4	yes	—
419	C₄²×C₆₁	C₂⁴	1	4	yes	—
420	C₄²×C₆₁	C₂⁴	1	4	yes	—
421	C₄²×C₆₁	C₂⁴	1	16	yes	—
422	C₂³×C₆₁	—	2	4	no	—
423	C₂³×C₆₁	—	2	4	no	—
424	C₂³×C₆₁	—	2	16	no	—
425	C₂³×C₆₁	—	4	2	no	—
426	C₂³×C₆₁	—	4	8	no	—
427	C₂³×C₆₁	—	4	8	no	—
428	C₂³×C₆₁	C₂⁵	1	4	yes	—
429	C₂³×C₆₁	C₂⁵	1	2	yes	—
430	C₂³×C₆₁	C₂⁵	1	8	yes	—
431	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
432	C₂³×C₆₁	C₂⁵	1	2	yes	—
433	Q₈×C₆₁	—	2	8	no	—
434	Q₈×C₆₁	—	2	8	no	—
435	Q₈×C₆₁	—	2	4	no	—
436	Q₈×C₆₁	—	4	8	no	—
437	Q₈×C₆₁	—	4	8	no	—
438	Q₈×C₆₁	—	4	8	no	—
439	Q₈×C₆₁	—	4	4	no	—
440	D₄×C₆₁	—	2	8	no	—
441	D₄×C₆₁	—	2	16	no	—
442	D₄×C₆₁	—	2	4	no	—
443	D₄×C₆₁	—	2	16	no	—
444	D₄×C₆₁	—	2	4	no	—
445	D₄×C₆₁	—	2	8	no	—
446	D₄×C₆₁	—	2	2	no	—
447	D₄×C₆₁	—	2	8	no	—
448	D₄×C₆₁	—	4	8	no	—
449	D₄×C₆₁	—	4	8	no	—
450	D₄×C₆₁	—	4	8	no	—
451	D₄×C₆₁	—	4	4	no	—
452	D₄×C₆₁	—	4	8	no	—
453	D₄×C₆₁	—	4	16	no	—
454	D₄×C₆₁	—	4	8	no	—
455	D₄×C₆₁	—	4	8	no	—
456	D₄×C₆₁	—	4	4	no	—
457	D₄×C₆₁	2₋¹⁺⁴	1	4	yes	complemented
458	C₂×C₄×C₆₁	—	2	4	no	—
459	C₂×C₄×C₆₁	—	2	4	no	—
460	C₂×C₄×C₆₁	—	2	8	no	—
461	C₂×C₄×C₆₁	—	2	8	no	—
462	C₂×C₄×C₆₁	—	2	8	no	—
463	C₂×C₄×C₆₁	—	2	16	no	—
464	C₂×C₄×C₆₁	—	2	2	no	—
465	C₂×C₄×C₆₁	—	2	8	no	—
466	C₂×C₄×C₆₁	—	4	8	no	—
467	C₂×C₄×C₆₁	—	4	8	no	—
468	C₂×C₄×C₆₁	—	4	8	no	—
469	C₂×C₄×C₆₁	—	4	2	no	—
470	C₂×C₄×C₆₁	—	4	8	no	—
471	C₂×C₄×C₆₁	—	4	4	no	—
472	C₂×C₄×C₆₁	—	4	8	no	—
473	C₂×C₄×C₆₁	—	4	16	no	—
474	C₂×C₄×C₆₁	—	4	1	no	—
475	C₂×C₄×C₆₁	—	4	16	no	—
476	C₂×C₄×C₆₁	—	4	4	no	—
477	C₂×C₄×C₆₁	H(5,𝔽₂)	1	4	yes	—
478	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
479	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
480	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
481	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
482	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
483	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
484	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
485	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
486	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
487	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
488	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
489	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
490	#62944	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
491	C₂²×C₆₁	—	2	2	no	—
492	C₂²×C₆₁	—	2	1	no	—
493	C₂²×C₆₁	—	2	1	no	—
494	C₂²×C₆₁	—	2	2	no	—
495	C₂²×C₆₁	—	2	2	no	—
496	C₂²×C₆₁	—	2	8	no	—
497	C₂²×C₆₁	—	2	4	no	—
498	C₂²×C₆₁	—	2	4	no	—
499	C₂²×C₆₁	—	2	2	no	—
500	C₂²×C₆₁	—	2	8	no	—
501	C₂²×C₆₁	—	2	2	no	—
502	C₂²×C₆₁	—	2	8	no	—
503	C₂²×C₆₁	—	2	4	no	—
504	C₂²×C₆₁	—	4	8	no	—
505	C₂²×C₆₁	—	8	16	no	—
506	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
507	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	4	yes	—
508	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
509	C₄×C₆₁	—	2	4	no	—
510	C₄×C₆₁	—	2	4	no	—
511	C₄×C₆₁	—	2	8	no	—
512	C₄×C₆₁	—	2	4	no	—
513	C₄×C₆₁	—	2	1	no	—
514	C₄×C₆₁	—	2	4	no	—
515	C₄×C₆₁	—	2	4	no	—
516	C₄×C₆₁	—	2	8	no	—
517	C₄×C₆₁	—	2	4	no	—
518	C₄×C₆₁	—	2	2	no	—
519	C₄×C₆₁	C₂×H(5,𝔽₂)	1	4	yes	—
520	C₄×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
521	#3559	C₂×C₆₁	1	4	yes	complemented
522	#3548	C₂×C₆₁	1	4	yes	complemented
523	#3547	C₂×C₆₁	1	4	yes	complemented
524	#3541	C₂×C₆₁	1	8	yes	complemented
525	#3536	C₂×C₆₁	1	8	yes	complemented
526	#3536	C₂×C₆₁	1	8	yes	complemented
527	#3519	C₂×C₆₁	1	4	yes	complemented
528	#3519	C₂×C₆₁	1	4	yes	complemented
529	#3511	C₂×C₆₁	1	2	yes	complemented
530	#3501	C₂×C₆₁	1	4	yes	complemented
531	#3497	C₂×C₆₁	1	1	yes	characteristic, complemented
532	#3492	C₂×C₆₁	1	2	yes	complemented
533	#3489	C₂×C₆₁	1	4	yes	complemented
534	C₂×#554	C₂×C₆₁	1	1	yes	characteristic, complemented
535	D₄×#41	C₂×C₆₁	1	2	yes	complemented
536	#3461	C₂×C₆₁	1	1	yes	characteristic, complemented
537	C₂×#537	C₂×C₆₁	1	2	yes	complemented
538	C₂×C₆₁	—	2	2	no	—
539	C₂×C₆₁	—	2	4	no	—
540	C₂×C₆₁	—	4	2	no	—
541	C₂×C₆₁	—	4	8	no	—
542	C₂×C₆₁	—	4	4	no	—
543	C₂×C₆₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
544	C₂×C₆₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
545	C₂×C₆₁	H(7,𝔽₂)	1	1	yes	characteristic
546	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	2	yes	complemented
547	C₂²×#41	C₂²×C₆₁	1	4	yes	complemented
548	#563	C₂²×C₆₁	1	8	yes	complemented
549	#562	C₂²×C₆₁	1	16	yes	complemented
550	#562	C₂²×C₆₁	1	8	yes	complemented
551	#562	C₂²×C₆₁	1	16	yes	complemented
552	#556	C₂²×C₆₁	1	4	yes	complemented
553	#555	C₂²×C₆₁	1	4	yes	complemented
554	#555	C₂²×C₆₁	1	4	yes	complemented
555	#554	C₂²×C₆₁	1	4	yes	—
556	#554	C₂²×C₆₁	1	4	yes	—
557	#554	C₂²×C₆₁	1	8	yes	complemented
558	#554	C₂²×C₆₁	1	4	yes	complemented
559	#554	C₂²×C₆₁	1	8	yes	complemented
560	#554	C₂²×C₆₁	1	4	yes	complemented
561	#554	C₂²×C₆₁	1	16	yes	complemented
562	#554	C₂²×C₆₁	1	8	yes	complemented
563	#553	C₂²×C₆₁	1	8	yes	complemented
564	#553	C₂²×C₆₁	1	8	yes	complemented
565	#553	C₂²×C₆₁	1	8	yes	complemented
566	#553	C₂²×C₆₁	1	8	yes	complemented
567	#552	C₂²×C₆₁	1	8	yes	complemented
568	#550	C₂²×C₆₁	1	2	yes	complemented
569	#550	C₂²×C₆₁	1	4	yes	complemented
570	#550	C₂²×C₆₁	1	4	yes	complemented
571	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
572	D₄×Q₈	C₂²×C₆₁	1	8	yes	complemented
573	D₄×Q₈	C₂²×C₆₁	1	4	yes	complemented
574	#548	C₂²×C₆₁	1	4	yes	complemented
575	#548	C₂²×C₆₁	1	8	yes	complemented
576	#548	C₂²×C₆₁	1	8	yes	complemented
577	#548	C₂²×C₆₁	1	8	yes	complemented
578	#547	C₂²×C₆₁	1	2	yes	complemented
579	#547	C₂²×C₆₁	1	4	yes	complemented
580	#547	C₂²×C₆₁	1	16	yes	complemented
581	#547	C₂²×C₆₁	1	8	yes	complemented
582	#547	C₂²×C₆₁	1	8	yes	complemented
583	#547	C₂²×C₆₁	1	4	yes	complemented
584	#546	C₂²×C₆₁	1	8	yes	complemented
585	#546	C₂²×C₆₁	1	4	yes	complemented
586	#546	C₂²×C₆₁	1	16	yes	complemented
587	#546	C₂²×C₆₁	1	8	yes	complemented
588	#546	C₂²×C₆₁	1	16	yes	complemented
589	#546	C₂²×C₆₁	1	8	yes	complemented
590	D₄²	C₂²×C₆₁	1	2	yes	—
591	D₄²	C₂²×C₆₁	1	4	yes	—
592	D₄²	C₂²×C₆₁	1	4	yes	—
593	#544	C₂²×C₆₁	1	1	yes	characteristic, complemented
594	#544	C₂²×C₆₁	1	8	yes	complemented
595	#543	C₂²×C₆₁	1	16	yes	complemented
596	#542	C₂²×C₆₁	1	4	yes	complemented
597	#542	C₂²×C₆₁	1	8	yes	complemented
598	#542	C₂²×C₆₁	1	16	yes	complemented
599	#541	C₂²×C₆₁	1	4	yes	complemented
600	#540	C₂²×C₆₁	1	8	yes	complemented
601	#540	C₂²×C₆₁	1	8	yes	complemented
602	#539	C₂²×C₆₁	1	4	yes	complemented
603	#539	C₂²×C₆₁	1	8	yes	complemented
604	#539	C₂²×C₆₁	1	16	yes	complemented
605	#538	C₂²×C₆₁	1	16	yes	complemented
606	#538	C₂²×C₆₁	1	16	yes	complemented
607	#537	C₂²×C₆₁	1	1	yes	characteristic
608	#537	C₂²×C₆₁	1	4	yes	complemented
609	#537	C₂²×C₆₁	1	2	yes	complemented
610	#537	C₂²×C₆₁	1	8	yes	complemented
611	#537	C₂²×C₆₁	1	8	yes	complemented
612	#537	C₂²×C₆₁	1	8	yes	complemented
613	#537	C₂²×C₆₁	1	8	yes	complemented
614	#537	C₂²×C₆₁	1	4	yes	complemented
615	#537	C₂²×C₆₁	1	16	yes	complemented
616	#536	C₂²×C₆₁	1	2	yes	complemented
617	#536	C₂²×C₆₁	1	8	yes	complemented
618	#533	C₂²×C₆₁	1	4	yes	complemented
619	#533	C₂²×C₆₁	1	4	yes	complemented
620	#532	C₂²×C₆₁	1	2	yes	complemented
621	#532	C₂²×C₆₁	1	4	yes	complemented
622	#532	C₂²×C₆₁	1	4	yes	complemented
623	#532	C₂²×C₆₁	1	4	yes	complemented
624	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
625	#529	C₂²×C₆₁	1	4	yes	complemented
626	#529	C₂²×C₆₁	1	4	yes	complemented
627	C₂×#125	C₂²×C₆₁	1	2	yes	complemented
628	#525	C₂²×C₆₁	1	4	yes	complemented
629	#525	C₂²×C₆₁	1	8	yes	complemented
630	#525	C₂²×C₆₁	1	8	yes	complemented
631	#525	C₂²×C₆₁	1	8	yes	complemented
632	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	8	yes	complemented
633	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	complemented
634	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	4	yes	complemented
635	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	8	yes	complemented
636	C₂×#121	C₂²×C₆₁	1	8	yes	complemented
637	C₂×#121	C₂²×C₆₁	1	8	yes	complemented
638	#520	C₂²×C₆₁	1	4	yes	complemented
639	#518	C₂²×C₆₁	1	8	yes	—
640	C₄×#41	C₂²×C₆₁	1	2	yes	complemented
641	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
642	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
643	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	—
644	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
645	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	complemented
646	C₆₁	#62944	1	1	yes	characteristic, direct product factor, Sylow
647	2₋¹⁺⁴	—	4	8	no	—
648	C₂×#41	—	4	16	no	—
649	C₂×#41	C₂³×C₆₁	1	2	yes	—
650	C₂×#41	C₂³×C₆₁	1	4	yes	—
651	C₂×#41	C₂³×C₆₁	1	8	yes	—
652	C₂×#41	C₂³×C₆₁	1	8	yes	—
653	C₂×#41	C₂³×C₆₁	1	8	yes	—
654	C₂×#41	C₂³×C₆₁	1	8	yes	—
655	C₂×#41	C₂³×C₆₁	1	4	yes	—
656	C₂×#41	C₂³×C₆₁	1	4	yes	—
657	C₂×#41	C₂³×C₆₁	1	8	yes	—
658	C₂×#41	C₂³×C₆₁	1	8	yes	—
659	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
660	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
661	C₂²×Q₈	C₂³×C₆₁	1	8	yes	—
662	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
663	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
664	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
665	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
666	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
667	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
668	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
669	C₂³×C₄	C₂³×C₆₁	1	8	yes	—
670	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
671	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
672	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
673	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
674	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
675	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
676	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
677	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
678	C₄⋊Q₈	C₂³×C₆₁	1	16	yes	—
679	#127	C₂³×C₆₁	1	2	yes	—
680	#127	C₂³×C₆₁	1	4	yes	—
681	#127	C₂³×C₆₁	1	4	yes	—
682	#126	C₂³×C₆₁	1	8	yes	—
683	#126	C₂³×C₆₁	1	8	yes	—
684	#126	C₂³×C₆₁	1	16	yes	—
685	#126	C₂³×C₆₁	1	16	yes	—
686	#125	C₂³×C₆₁	1	8	yes	—
687	#125	C₂³×C₆₁	1	8	yes	—
688	#125	C₂³×C₆₁	1	4	yes	—
689	#125	C₂³×C₆₁	1	4	yes	—
690	#125	C₂³×C₆₁	1	8	yes	—
691	#125	C₂³×C₆₁	1	8	yes	—
692	#125	C₂³×C₆₁	1	16	yes	—
693	#124	C₂³×C₆₁	1	4	yes	—
694	#124	C₂³×C₆₁	1	4	yes	—
695	#124	C₂³×C₆₁	1	8	yes	—
696	#124	C₂³×C₆₁	1	8	yes	—
697	#124	C₂³×C₆₁	1	4	yes	—
698	#124	C₂³×C₆₁	1	8	yes	—
699	#124	C₂³×C₆₁	1	16	yes	—
700	#124	C₂³×C₆₁	1	16	yes	—
701	#123	C₂³×C₆₁	1	16	yes	—
702	#123	C₂³×C₆₁	1	16	yes	—
703	#123	C₂³×C₆₁	1	8	yes	—
704	#123	C₂³×C₆₁	1	8	yes	—
705	#123	C₂³×C₆₁	1	8	yes	—
706	#123	C₂³×C₆₁	1	8	yes	—
707	#123	C₂³×C₆₁	1	8	yes	—
708	#123	C₂³×C₆₁	1	16	yes	—
709	#123	C₂³×C₆₁	1	16	yes	—
710	#123	C₂³×C₆₁	1	16	yes	—
711	#123	C₂³×C₆₁	1	16	yes	—
712	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
713	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
714	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
715	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
716	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
717	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
718	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
719	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
720	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
721	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
722	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
723	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
724	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
725	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
726	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
727	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
728	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
729	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
730	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
731	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
732	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
733	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
734	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
735	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
736	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
737	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
738	#121	C₂³×C₆₁	1	4	yes	—
739	#121	C₂³×C₆₁	1	4	yes	—
740	#121	C₂³×C₆₁	1	8	yes	—
741	#121	C₂³×C₆₁	1	8	yes	—
742	#121	C₂³×C₆₁	1	16	yes	—
743	#121	C₂³×C₆₁	1	16	yes	—
744	#121	C₂³×C₆₁	1	16	yes	—
745	#121	C₂³×C₆₁	1	8	yes	—
746	#121	C₂³×C₆₁	1	16	yes	—
747	#121	C₂³×C₆₁	1	8	yes	—
748	#121	C₂³×C₆₁	1	8	yes	—
749	#121	C₂³×C₆₁	1	8	yes	—
750	#121	C₂³×C₆₁	1	4	yes	—
751	#121	C₂³×C₆₁	1	4	yes	—
752	#121	C₂³×C₆₁	1	8	yes	—
753	#121	C₂³×C₆₁	1	8	yes	—
754	#121	C₂³×C₆₁	1	8	yes	—
755	#121	C₂³×C₆₁	1	4	yes	—
756	#121	C₂³×C₆₁	1	4	yes	—
757	#121	C₂³×C₆₁	1	8	yes	—
758	#121	C₂³×C₆₁	1	4	yes	—
759	#121	C₂³×C₆₁	1	4	yes	—
760	#121	C₂³×C₆₁	1	8	yes	—
761	#121	C₂³×C₆₁	1	16	yes	—
762	#121	C₂³×C₆₁	1	16	yes	—
763	#121	C₂³×C₆₁	1	16	yes	—
764	#121	C₂³×C₆₁	1	16	yes	—
765	#120	C₂³×C₆₁	1	8	yes	—
766	#120	C₂³×C₆₁	1	8	yes	—
767	#120	C₂³×C₆₁	1	8	yes	—
768	#120	C₂³×C₆₁	1	16	yes	—
769	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
770	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
771	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
772	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
773	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
774	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
775	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
776	C₄×D₄	C₂³×C₆₁	1	2	yes	—
777	C₄×D₄	C₂³×C₆₁	1	4	yes	—
778	C₄×D₄	C₂³×C₆₁	1	4	yes	—
779	C₄×D₄	C₂³×C₆₁	1	4	yes	—
780	C₄×D₄	C₂³×C₆₁	1	8	yes	—
781	C₄×D₄	C₂³×C₆₁	1	2	yes	—
782	C₄×D₄	C₂³×C₆₁	1	4	yes	—
783	C₄×D₄	C₂³×C₆₁	1	8	yes	—
784	C₄×D₄	C₂³×C₆₁	1	8	yes	—
785	C₄×D₄	C₂³×C₆₁	1	4	yes	—
786	C₄×D₄	C₂³×C₆₁	1	4	yes	—
787	C₄×D₄	C₂³×C₆₁	1	4	yes	—
788	C₄×D₄	C₂³×C₆₁	1	2	yes	—
789	C₄×D₄	C₂³×C₆₁	1	4	yes	—
790	C₄×D₄	C₂³×C₆₁	1	2	yes	—
791	C₄×D₄	C₂³×C₆₁	1	16	yes	—
792	C₄×D₄	C₂³×C₆₁	1	16	yes	—
793	C₄×D₄	C₂³×C₆₁	1	8	yes	—
794	C₄×D₄	C₂³×C₆₁	1	8	yes	—
795	C₄×D₄	C₂³×C₆₁	1	16	yes	—
796	C₄×D₄	C₂³×C₆₁	1	8	yes	—
797	C₄×D₄	C₂³×C₆₁	1	8	yes	—
798	C₄×D₄	C₂³×C₆₁	1	4	yes	—
799	C₄×D₄	C₂³×C₆₁	1	16	yes	—
800	C₄×D₄	C₂³×C₆₁	1	4	yes	—
801	C₄×D₄	C₂³×C₆₁	1	8	yes	—
802	#117	C₂³×C₆₁	1	2	yes	—
803	#117	C₂³×C₆₁	1	4	yes	—
804	#117	C₂³×C₆₁	1	8	yes	—
805	#117	C₂³×C₆₁	1	8	yes	—
806	#117	C₂³×C₆₁	1	8	yes	—
807	#117	C₂³×C₆₁	1	8	yes	—
808	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
809	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
810	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
811	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
812	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
813	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
814	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
815	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
816	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
817	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
818	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
819	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
820	C₂×C₄⋊C₄	C₂³×C₆₁	1	16	yes	—
821	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
822	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
823	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
824	C₂×C₂²⋊C₄	C₂³×C₆₁	1	16	yes	—
825	C₂×C₂²⋊C₄	C₂³×C₆₁	1	16	yes	—
826	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
827	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
828	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
829	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
830	C₂⁴	C₂⁴×C₆₁	1	8	yes	—
831	#41	—	2	8	no	—
832	#41	—	2	16	no	—
833	#41	—	4	16	no	—
834	#41	—	4	16	no	—
835	#41	—	4	16	no	—
836	#41	—	4	8	no	—
837	#41	—	4	8	no	—
838	#41	—	4	16	no	—
839	#41	—	8	8	no	—
840	#41	—	8	8	no	—
841	C₂×Q₈	—	2	4	no	—
842	C₂×Q₈	—	4	8	no	—
843	C₂×Q₈	—	4	16	no	—
844	C₂×Q₈	—	8	2	no	—
845	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
846	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
847	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
848	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
849	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
850	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
851	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
852	C₂×D₄	—	2	4	no	—
853	C₂×D₄	—	2	16	no	—
854	C₂×D₄	—	4	8	no	—
855	C₂×D₄	—	4	16	no	—
856	C₂×D₄	—	8	8	no	—
857	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
858	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
859	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
860	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
861	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
862	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
863	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
864	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
865	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
866	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
867	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
868	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
869	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
870	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
871	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
872	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
873	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
874	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
875	C₂²×C₄	—	2	8	no	—
876	C₂²×C₄	—	4	16	no	—
877	C₂²×C₄	—	8	4	no	—
878	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
880	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
881	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
882	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
883	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
884	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
885	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
886	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
888	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
889	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
890	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
891	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
892	C₂²×C₄	C₂⁴×C₆₁	1	16	yes	—
893	C₂²×C₄	C₂⁴×C₆₁	1	16	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	1	yes	characteristic
898	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
899	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
900	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
901	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
902	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
903	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
904	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
905	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
906	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
907	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
908	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
909	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
910	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
911	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
912	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
913	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
914	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
915	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
916	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
917	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
918	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
919	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
920	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
921	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
922	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
923	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
924	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
925	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
926	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
927	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
928	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
929	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
930	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
931	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
932	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
933	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
934	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
935	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
936	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
937	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
938	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
939	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
940	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
941	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
942	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
943	C₄²	C₂⁴×C₆₁	1	2	yes	—
944	C₄²	C₂⁴×C₆₁	1	4	yes	—
945	C₄²	C₂⁴×C₆₁	1	2	yes	—
946	C₄²	C₂⁴×C₆₁	1	4	yes	—
947	C₄²	C₂⁴×C₆₁	1	4	yes	—
948	C₄²	C₂⁴×C₆₁	1	4	yes	—
949	C₄²	C₂⁴×C₆₁	1	4	yes	—
950	C₄²	C₂⁴×C₆₁	1	16	yes	—
951	C₂³	—	2	4	no	—
952	C₂³	—	2	4	no	—
953	C₂³	—	2	16	no	—
954	C₂³	—	4	2	no	—
955	C₂³	—	4	8	no	—
956	C₂³	—	4	8	no	—
957	C₂³	C₂⁵×C₆₁	1	4	yes	—
958	C₂³	C₂⁵×C₆₁	1	2	yes	—
959	C₂³	C₂⁵×C₆₁	1	8	yes	—
960	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
961	C₂³	C₂⁵×C₆₁	1	2	yes	—
962	Q₈	—	2	8	no	—
963	Q₈	—	2	8	no	—
964	Q₈	—	2	4	no	—
965	Q₈	—	4	8	no	—
966	Q₈	—	4	8	no	—
967	Q₈	—	4	8	no	—
968	Q₈	—	4	4	no	—
969	D₄	—	2	8	no	—
970	D₄	—	2	16	no	—
971	D₄	—	2	4	no	—
972	D₄	—	2	16	no	—
973	D₄	—	2	4	no	—
974	D₄	—	2	8	no	—
975	D₄	—	2	2	no	—
976	D₄	—	2	8	no	—
977	D₄	—	4	8	no	—
978	D₄	—	4	8	no	—
979	D₄	—	4	8	no	—
980	D₄	—	4	4	no	—
981	D₄	—	4	8	no	—
982	D₄	—	4	16	no	—
983	D₄	—	4	8	no	—
984	D₄	—	4	8	no	—
985	D₄	—	4	4	no	—
986	D₄	2₋¹⁺⁴×C₆₁	1	4	yes	complemented
987	C₂×C₄	—	2	4	no	—
988	C₂×C₄	—	2	4	no	—
989	C₂×C₄	—	2	8	no	—
990	C₂×C₄	—	2	8	no	—
991	C₂×C₄	—	2	8	no	—
992	C₂×C₄	—	2	16	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	8	no	—
995	C₂×C₄	—	4	8	no	—
996	C₂×C₄	—	4	8	no	—
997	C₂×C₄	—	4	8	no	—
998	C₂×C₄	—	4	2	no	—
999	C₂×C₄	—	4	8	no	—
1000	C₂×C₄	—	4	4	no	—
1001	C₂×C₄	—	4	8	no	—
1002	C₂×C₄	—	4	16	no	—
1003	C₂×C₄	—	4	1	no	—
1004	C₂×C₄	—	4	16	no	—
1005	C₂×C₄	—	4	4	no	—
1006	C₂×C₄	H(5,𝔽₂)×C₆₁	1	4	yes	—
1007	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
1008	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1009	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
1010	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
1011	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
1012	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
1013	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
1014	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
1015	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
1016	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
1017	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
1018	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1019	C₂²	—	2	2	no	—
1020	C₂²	—	2	1	no	—
1021	C₂²	—	2	1	no	—
1022	C₂²	—	2	2	no	—
1023	C₂²	—	2	2	no	—
1024	C₂²	—	2	8	no	—
1025	C₂²	—	2	4	no	—
1026	C₂²	—	2	4	no	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	8	no	—
1029	C₂²	—	2	2	no	—
1030	C₂²	—	2	8	no	—
1031	C₂²	—	2	4	no	—
1032	C₂²	—	4	8	no	—
1033	C₂²	—	8	16	no	—
1034	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
1035	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	4	yes	—
1036	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
1037	C₄	—	2	4	no	—
1038	C₄	—	2	4	no	—
1039	C₄	—	2	8	no	—
1040	C₄	—	2	4	no	—
1041	C₄	—	2	1	no	—
1042	C₄	—	2	4	no	—
1043	C₄	—	2	4	no	—
1044	C₄	—	2	8	no	—
1045	C₄	—	2	4	no	—
1046	C₄	—	2	2	no	—
1047	C₄	C₂×H(5,𝔽₂)×C₆₁	1	4	yes	—
1048	C₄	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
1049	C₂	—	2	2	no	—
1050	C₂	—	2	4	no	—
1051	C₂	—	4	2	no	—
1052	C₂	—	4	4	no	—
1053	C₂	—	4	8	no	—
1054	C₂	C₂²×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1055	C₂	C₂²×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1056	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×#3559	C₂	semidirect
2. C₆₁×#3548	C₂	semidirect
3. C₆₁×#3547	C₂	semidirect
4. C₆₁×#3541	C₂	semidirect
5. C₆₁×#3536	C₂	semidirect
6. C₆₁×#3536	C₂	semidirect
7. C₆₁×#3519	C₂	semidirect
8. C₆₁×#3519	C₂	semidirect
9. C₆₁×#3511	C₂	semidirect
10. C₆₁×#3501	C₂	semidirect
11. C₆₁×#3497	C₂	semidirect
12. C₆₁×#3492	C₂	semidirect
13. C₆₁×#3489	C₂	semidirect
14. C₂×C₆₁×#554	C₂	semidirect
15. D₄×#41×C₆₁	C₂	semidirect
16. C₆₁×#3461	C₂	semidirect
17. C₂×C₆₁×#537	C₂	semidirect
18. C₂×2₋¹⁺⁴×C₆₁	C₂²	semidirect
19. C₂²×#41×C₆₁	C₂²	semidirect
20. C₆₁×#563	C₂²	semidirect
21. C₆₁×#562	C₂²	semidirect
22. C₆₁×#562	C₂²	semidirect
23. C₆₁×#562	C₂²	semidirect
24. C₆₁×#556	C₂²	semidirect
25. C₆₁×#555	C₂²	semidirect
26. C₆₁×#555	C₂²	semidirect
29. C₆₁×#554	C₂²	semidirect
30. C₆₁×#554	C₂²	semidirect
31. C₆₁×#554	C₂²	semidirect
32. C₆₁×#554	C₂²	semidirect
33. C₆₁×#554	C₂²	semidirect
34. C₆₁×#554	C₂²	semidirect
35. C₆₁×#553	C₂²	semidirect
36. C₆₁×#553	C₂²	semidirect
37. C₆₁×#553	C₂²	semidirect
38. C₆₁×#553	C₂²	semidirect
39. C₆₁×#552	C₂²	semidirect
40. C₆₁×#550	C₂²	semidirect
41. C₆₁×#550	C₂²	semidirect
42. C₆₁×#550	C₂²	semidirect
44. D₄×Q₈×C₆₁	C₂²	semidirect
45. D₄×Q₈×C₆₁	C₂²	semidirect
46. C₆₁×#548	C₂²	semidirect
47. C₆₁×#548	C₂²	semidirect
48. C₆₁×#548	C₂²	semidirect
49. C₆₁×#548	C₂²	semidirect
50. C₆₁×#547	C₂²	semidirect
51. C₆₁×#547	C₂²	semidirect
52. C₆₁×#547	C₂²	semidirect
53. C₆₁×#547	C₂²	semidirect
54. C₆₁×#547	C₂²	semidirect
55. C₆₁×#547	C₂²	semidirect
56. C₆₁×#546	C₂²	semidirect
57. C₆₁×#546	C₂²	semidirect
58. C₆₁×#546	C₂²	semidirect
59. C₆₁×#546	C₂²	semidirect
60. C₆₁×#546	C₂²	semidirect
61. C₆₁×#546	C₂²	semidirect
65. C₆₁×#544	C₂²	semidirect
66. C₆₁×#544	C₂²	semidirect
67. C₆₁×#543	C₂²	semidirect
68. C₆₁×#542	C₂²	semidirect
69. C₆₁×#542	C₂²	semidirect
70. C₆₁×#542	C₂²	semidirect
71. C₆₁×#541	C₂²	semidirect
72. C₆₁×#540	C₂²	semidirect
73. C₆₁×#540	C₂²	semidirect
74. C₆₁×#539	C₂²	semidirect
75. C₆₁×#539	C₂²	semidirect
76. C₆₁×#539	C₂²	semidirect
77. C₆₁×#538	C₂²	semidirect
78. C₆₁×#538	C₂²	semidirect
80. C₆₁×#537	C₂²	semidirect
81. C₆₁×#537	C₂²	semidirect
82. C₆₁×#537	C₂²	semidirect
83. C₆₁×#537	C₂²	semidirect
84. C₆₁×#537	C₂²	semidirect
85. C₆₁×#537	C₂²	semidirect
86. C₆₁×#537	C₂²	semidirect
87. C₆₁×#537	C₂²	semidirect
88. C₆₁×#536	C₂²	semidirect
89. C₆₁×#536	C₂²	semidirect
90. C₆₁×#533	C₂²	semidirect
91. C₆₁×#533	C₂²	semidirect
92. C₆₁×#532	C₂²	semidirect
93. C₆₁×#532	C₂²	semidirect
94. C₆₁×#532	C₂²	semidirect
95. C₆₁×#532	C₂²	semidirect
96. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
97. C₆₁×#529	C₂²	semidirect
98. C₆₁×#529	C₂²	semidirect
99. C₂×#125×C₆₁	C₂²	semidirect
100. C₆₁×#525	C₂²	semidirect
101. C₆₁×#525	C₂²	semidirect
102. C₆₁×#525	C₂²	semidirect
103. C₆₁×#525	C₂²	semidirect
104. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
105. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
106. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
107. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
108. C₂×#121×C₆₁	C₂²	semidirect
109. C₂×#121×C₆₁	C₂²	semidirect
110. C₆₁×#520	C₂²	semidirect
112. C₄×#41×C₆₁	C₂²	semidirect
113. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
117. C₂²×C₄⋊C₄×C₆₁	C₂²	semidirect
457. D₄×C₆₁	2₋¹⁺⁴	semidirect
490. #62944	C₆₁	direct (N × H)
521. #3559	C₂×C₆₁	semidirect
522. #3548	C₂×C₆₁	semidirect
523. #3547	C₂×C₆₁	semidirect
524. #3541	C₂×C₆₁	semidirect
525. #3536	C₂×C₆₁	semidirect
526. #3536	C₂×C₆₁	semidirect
527. #3519	C₂×C₆₁	semidirect
528. #3519	C₂×C₆₁	semidirect
529. #3511	C₂×C₆₁	semidirect
530. #3501	C₂×C₆₁	semidirect
531. #3497	C₂×C₆₁	semidirect
532. #3492	C₂×C₆₁	semidirect
533. #3489	C₂×C₆₁	semidirect
534. C₂×#554	C₂×C₆₁	semidirect
535. D₄×#41	C₂×C₆₁	semidirect
536. #3461	C₂×C₆₁	semidirect
537. C₂×#537	C₂×C₆₁	semidirect
546. C₂×2₋¹⁺⁴	C₂²×C₆₁	semidirect
547. C₂²×#41	C₂²×C₆₁	semidirect
548. #563	C₂²×C₆₁	semidirect
549. #562	C₂²×C₆₁	semidirect
550. #562	C₂²×C₆₁	semidirect
551. #562	C₂²×C₆₁	semidirect
552. #556	C₂²×C₆₁	semidirect
553. #555	C₂²×C₆₁	semidirect
554. #555	C₂²×C₆₁	semidirect
557. #554	C₂²×C₆₁	semidirect
558. #554	C₂²×C₆₁	semidirect
559. #554	C₂²×C₆₁	semidirect
560. #554	C₂²×C₆₁	semidirect
561. #554	C₂²×C₆₁	semidirect
562. #554	C₂²×C₆₁	semidirect
563. #553	C₂²×C₆₁	semidirect
564. #553	C₂²×C₆₁	semidirect
565. #553	C₂²×C₆₁	semidirect
566. #553	C₂²×C₆₁	semidirect
567. #552	C₂²×C₆₁	semidirect
568. #550	C₂²×C₆₁	semidirect
569. #550	C₂²×C₆₁	semidirect
570. #550	C₂²×C₆₁	semidirect
572. D₄×Q₈	C₂²×C₆₁	semidirect
573. D₄×Q₈	C₂²×C₆₁	semidirect
574. #548	C₂²×C₆₁	semidirect
575. #548	C₂²×C₆₁	semidirect
576. #548	C₂²×C₆₁	semidirect
577. #548	C₂²×C₆₁	semidirect
578. #547	C₂²×C₆₁	semidirect
579. #547	C₂²×C₆₁	semidirect
580. #547	C₂²×C₆₁	semidirect
581. #547	C₂²×C₆₁	semidirect
582. #547	C₂²×C₆₁	semidirect
583. #547	C₂²×C₆₁	semidirect
584. #546	C₂²×C₆₁	semidirect
585. #546	C₂²×C₆₁	semidirect
586. #546	C₂²×C₆₁	semidirect
587. #546	C₂²×C₆₁	semidirect
588. #546	C₂²×C₆₁	semidirect
589. #546	C₂²×C₆₁	semidirect
593. #544	C₂²×C₆₁	semidirect
594. #544	C₂²×C₆₁	semidirect
595. #543	C₂²×C₆₁	semidirect
596. #542	C₂²×C₆₁	semidirect
597. #542	C₂²×C₆₁	semidirect
598. #542	C₂²×C₆₁	semidirect
599. #541	C₂²×C₆₁	semidirect
600. #540	C₂²×C₆₁	semidirect
601. #540	C₂²×C₆₁	semidirect
602. #539	C₂²×C₆₁	semidirect
603. #539	C₂²×C₆₁	semidirect
604. #539	C₂²×C₆₁	semidirect
605. #538	C₂²×C₆₁	semidirect
606. #538	C₂²×C₆₁	semidirect
608. #537	C₂²×C₆₁	semidirect
609. #537	C₂²×C₆₁	semidirect
610. #537	C₂²×C₆₁	semidirect
611. #537	C₂²×C₆₁	semidirect
612. #537	C₂²×C₆₁	semidirect
613. #537	C₂²×C₆₁	semidirect
614. #537	C₂²×C₆₁	semidirect
615. #537	C₂²×C₆₁	semidirect
616. #536	C₂²×C₆₁	semidirect
617. #536	C₂²×C₆₁	semidirect
618. #533	C₂²×C₆₁	semidirect
619. #533	C₂²×C₆₁	semidirect
620. #532	C₂²×C₆₁	semidirect
621. #532	C₂²×C₆₁	semidirect
622. #532	C₂²×C₆₁	semidirect
623. #532	C₂²×C₆₁	semidirect
624. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
625. #529	C₂²×C₆₁	semidirect
626. #529	C₂²×C₆₁	semidirect
627. C₂×#125	C₂²×C₆₁	semidirect
628. #525	C₂²×C₆₁	semidirect
629. #525	C₂²×C₆₁	semidirect
630. #525	C₂²×C₆₁	semidirect
631. #525	C₂²×C₆₁	semidirect
632. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
633. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
634. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
635. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
636. C₂×#121	C₂²×C₆₁	semidirect
637. C₂×#121	C₂²×C₆₁	semidirect
638. #520	C₂²×C₆₁	semidirect
640. C₄×#41	C₂²×C₆₁	semidirect
641. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
645. C₂²×C₄⋊C₄	C₂²×C₆₁	semidirect
646. C₆₁	#62944	direct (N × H)
986. D₄	2₋¹⁺⁴×C₆₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₁×#3559	2
C₆₁×#3548	2
C₆₁×#3547	2
C₆₁×#3541	2
C₆₁×#3536	2
C₆₁×#3519	2
C₆₁×#3511	2
C₆₁×#3501	2
C₆₁×#3497	2
C₆₁×#3492	2
C₆₁×#3489	2
C₂×C₆₁×#554	2
D₄×#41×C₆₁	2
C₆₁×#3461	2
C₂×C₆₁×#537	2
#62944	61

Subgroups — C61×#62944 #29566377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62944 #29566377