Subgroups — C₆₁×#62761 #29566194

Order 15616.

6518 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3557	C₂	1	4	yes	maximal, complemented
2	C₆₁×#3556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3555	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3554	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3553	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3552	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3550	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3548	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3541	C₂	1	8	yes	maximal, complemented
10	C₆₁×#3531	C₂	1	4	yes	maximal, complemented
11	C₆₁×#3482	C₂	1	4	yes	maximal, complemented
12	C₆₁×#3480	C₂	1	4	yes	maximal, complemented
13	Q₈×#41×C₆₁	C₂	1	4	yes	maximal, complemented
14	C₆₁×#3461	C₂	1	8	yes	maximal, complemented
15	C₆₁×#3455	C₂	1	4	yes	maximal, complemented
16	C₆₁×#3444	C₂	1	2	yes	maximal, complemented
17	C₂×C₆₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#564	C₂²	1	4	yes	complemented
19	C₆₁×#563	C₂²	1	16	yes	—
20	C₆₁×#563	C₂²	1	8	yes	complemented
21	C₆₁×#563	C₂²	1	16	yes	complemented
22	C₆₁×#562	C₂²	1	16	yes	—
23	C₆₁×#562	C₂²	1	4	yes	complemented
24	C₆₁×#559	C₂²	1	4	yes	complemented
25	C₆₁×#559	C₂²	1	8	yes	complemented
26	Q₈²×C₆₁	C₂²	1	4	yes	complemented
27	C₆₁×#557	C₂²	1	4	yes	complemented
28	C₆₁×#557	C₂²	1	4	yes	complemented
29	C₆₁×#557	C₂²	1	4	yes	complemented
30	C₆₁×#557	C₂²	1	8	yes	complemented
31	C₆₁×#556	C₂²	1	8	yes	—
32	C₆₁×#556	C₂²	1	4	yes	complemented
33	C₆₁×#556	C₂²	1	4	yes	complemented
34	C₆₁×#556	C₂²	1	8	yes	complemented
35	C₆₁×#554	C₂²	1	8	yes	—
36	C₆₁×#554	C₂²	1	16	yes	—
37	C₆₁×#554	C₂²	1	4	yes	complemented
38	C₆₁×#554	C₂²	1	8	yes	complemented
39	C₆₁×#553	C₂²	1	8	yes	—
40	C₆₁×#553	C₂²	1	16	yes	—
41	C₆₁×#552	C₂²	1	8	yes	—
42	C₆₁×#552	C₂²	1	16	yes	complemented
43	C₆₁×#550	C₂²	1	4	yes	complemented
44	D₄×Q₈×C₆₁	C₂²	1	8	yes	—
45	D₄×Q₈×C₆₁	C₂²	1	4	yes	complemented
46	D₄×Q₈×C₆₁	C₂²	1	4	yes	complemented
47	C₆₁×#548	C₂²	1	8	yes	—
48	C₆₁×#548	C₂²	1	8	yes	—
49	C₆₁×#547	C₂²	1	8	yes	—
50	C₆₁×#547	C₂²	1	4	yes	complemented
51	C₆₁×#544	C₂²	1	8	yes	complemented
52	C₆₁×#542	C₂²	1	8	yes	—
53	C₆₁×#542	C₂²	1	8	yes	—
54	C₆₁×#542	C₂²	1	8	yes	—
55	C₆₁×#542	C₂²	1	16	yes	—
56	C₆₁×#542	C₂²	1	8	yes	complemented
57	C₆₁×#541	C₂²	1	4	yes	—
58	C₆₁×#541	C₂²	1	4	yes	—
59	C₆₁×#541	C₂²	1	8	yes	—
60	C₆₁×#541	C₂²	1	8	yes	complemented
61	C₆₁×#541	C₂²	1	16	yes	complemented
62	C₆₁×#540	C₂²	1	4	yes	—
63	C₆₁×#540	C₂²	1	4	yes	—
64	C₆₁×#539	C₂²	1	16	yes	—
65	C₆₁×#539	C₂²	1	16	yes	—
66	C₆₁×#539	C₂²	1	16	yes	complemented
67	C₆₁×#538	C₂²	1	16	yes	—
68	C₆₁×#537	C₂²	1	8	yes	—
69	C₆₁×#536	C₂²	1	8	yes	—
70	C₆₁×#536	C₂²	1	8	yes	complemented
71	C₆₁×#533	C₂²	1	1	yes	characteristic
72	C₆₁×#533	C₂²	1	1	yes	characteristic
73	C₆₁×#533	C₂²	1	2	yes	—
74	C₆₁×#533	C₂²	1	4	yes	—
75	C₆₁×#533	C₂²	1	2	yes	—
76	C₆₁×#533	C₂²	1	2	yes	—
77	C₆₁×#533	C₂²	1	4	yes	—
78	C₆₁×#533	C₂²	1	2	yes	—
79	C₆₁×#533	C₂²	1	2	yes	—
80	C₆₁×#533	C₂²	1	2	yes	—
81	C₆₁×#533	C₂²	1	4	yes	—
82	C₆₁×#533	C₂²	1	8	yes	complemented
83	C₆₁×#533	C₂²	1	16	yes	complemented
84	C₆₁×#532	C₂²	1	2	yes	—
85	C₆₁×#532	C₂²	1	2	yes	—
86	C₆₁×#532	C₂²	1	2	yes	—
87	C₆₁×#532	C₂²	1	4	yes	—
88	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
89	C₆₁×#529	C₂²	1	4	yes	—
90	C₆₁×#529	C₂²	1	4	yes	—
91	C₆₁×#529	C₂²	1	4	yes	—
92	C₆₁×#529	C₂²	1	4	yes	—
93	C₆₁×#529	C₂²	1	4	yes	—
94	C₆₁×#529	C₂²	1	4	yes	—
95	C₆₁×#529	C₂²	1	16	yes	—
96	C₆₁×#529	C₂²	1	16	yes	—
97	C₆₁×#529	C₂²	1	8	yes	complemented
98	C₆₁×#529	C₂²	1	16	yes	complemented
99	C₂×#125×C₆₁	C₂²	1	2	yes	—
100	C₆₁×#525	C₂²	1	4	yes	—
101	C₆₁×#525	C₂²	1	4	yes	—
102	C₆₁×#525	C₂²	1	4	yes	—
103	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	4	yes	—
104	C₄×#41×C₆₁	C₂²	1	4	yes	—
105	C₄×#41×C₆₁	C₂²	1	4	yes	—
106	C₄×#41×C₆₁	C₂²	1	4	yes	—
107	C₄×#41×C₆₁	C₂²	1	8	yes	—
108	C₄×#41×C₆₁	C₂²	1	8	yes	complemented
109	C₂×C₄×Q₈×C₆₁	C₂²	1	4	yes	—
110	C₂×C₄×Q₈×C₆₁	C₂²	1	8	yes	complemented
111	C₂×#117×C₆₁	C₂²	1	2	yes	—
112	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
113	C₂×#41×C₆₁	C₂³	1	4	yes	—
114	C₂×#41×C₆₁	C₂³	1	4	yes	—
115	C₂×#41×C₆₁	C₂³	1	4	yes	—
116	C₂×#41×C₆₁	C₂³	1	8	yes	—
117	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
118	C₂²×Q₈×C₆₁	C₂³	1	8	yes	—
119	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
121	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
122	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
123	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
124	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
125	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
126	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
127	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
128	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
129	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
130	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
131	C₄⋊Q₈×C₆₁	C₂³	1	16	yes	—
132	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
133	C₄⋊Q₈×C₆₁	C₂³	1	16	yes	—
134	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
135	#127×C₆₁	C₂³	1	2	yes	—
136	#127×C₆₁	C₂³	1	4	yes	—
137	#126×C₆₁	C₂³	1	16	yes	—
138	#126×C₆₁	C₂³	1	16	yes	—
139	#126×C₆₁	C₂³	1	16	yes	—
140	#126×C₆₁	C₂³	1	16	yes	—
141	#126×C₆₁	C₂³	1	16	yes	—
142	#126×C₆₁	C₂³	1	8	yes	—
143	#126×C₆₁	C₂³	1	16	yes	—
144	#126×C₆₁	C₂³	1	16	yes	—
145	#126×C₆₁	C₂³	1	8	yes	—
146	#125×C₆₁	C₂³	1	8	yes	—
147	#125×C₆₁	C₂³	1	4	yes	—
148	#125×C₆₁	C₂³	1	2	yes	—
149	#125×C₆₁	C₂³	1	2	yes	—
150	#125×C₆₁	C₂³	1	4	yes	—
151	#125×C₆₁	C₂³	1	4	yes	—
152	#125×C₆₁	C₂³	1	4	yes	—
153	#125×C₆₁	C₂³	1	4	yes	—
154	#125×C₆₁	C₂³	1	4	yes	—
155	#125×C₆₁	C₂³	1	16	yes	—
156	#125×C₆₁	C₂³	1	16	yes	—
157	#125×C₆₁	C₂³	1	16	yes	—
158	#125×C₆₁	C₂³	1	16	yes	—
159	#125×C₆₁	C₂³	1	16	yes	—
160	#125×C₆₁	C₂³	1	16	yes	—
161	#125×C₆₁	C₂³	1	8	yes	—
162	#124×C₆₁	C₂³	1	4	yes	—
163	#124×C₆₁	C₂³	1	8	yes	—
164	#124×C₆₁	C₂³	1	4	yes	—
165	#124×C₆₁	C₂³	1	4	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	16	yes	—
170	#123×C₆₁	C₂³	1	16	yes	—
171	#123×C₆₁	C₂³	1	16	yes	—
172	#123×C₆₁	C₂³	1	16	yes	—
173	#123×C₆₁	C₂³	1	16	yes	—
174	#123×C₆₁	C₂³	1	16	yes	—
175	#123×C₆₁	C₂³	1	8	yes	—
176	#123×C₆₁	C₂³	1	8	yes	—
177	#123×C₆₁	C₂³	1	16	yes	—
178	#123×C₆₁	C₂³	1	16	yes	—
179	#123×C₆₁	C₂³	1	8	yes	—
180	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
181	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
182	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
183	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
184	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
185	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
186	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
187	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
188	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
189	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
190	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
191	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
192	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
193	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
194	C₂²⋊Q₈×C₆₁	C₂³	1	16	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	16	yes	—
199	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
200	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
201	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
202	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
203	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
204	#121×C₆₁	C₂³	1	4	yes	—
205	#121×C₆₁	C₂³	1	16	yes	—
206	#121×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	4	yes	—
211	#121×C₆₁	C₂³	1	16	yes	—
212	#121×C₆₁	C₂³	1	16	yes	—
213	#121×C₆₁	C₂³	1	8	yes	—
214	#121×C₆₁	C₂³	1	16	yes	—
215	#120×C₆₁	C₂³	1	8	yes	—
216	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
217	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
218	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
219	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
220	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
221	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
222	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
223	C₄×Q₈×C₆₁	C₂³	1	16	yes	—
224	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
225	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
226	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
227	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
228	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
229	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
230	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
231	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
232	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
233	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
234	C₄×Q₈×C₆₁	C₂³	1	16	yes	—
235	C₄×D₄×C₆₁	C₂³	1	4	yes	—
236	C₄×D₄×C₆₁	C₂³	1	4	yes	—
237	C₄×D₄×C₆₁	C₂³	1	4	yes	—
238	C₄×D₄×C₆₁	C₂³	1	4	yes	—
239	C₄×D₄×C₆₁	C₂³	1	4	yes	—
240	C₄×D₄×C₆₁	C₂³	1	4	yes	—
241	C₄×D₄×C₆₁	C₂³	1	16	yes	—
242	C₄×D₄×C₆₁	C₂³	1	16	yes	—
243	C₄×D₄×C₆₁	C₂³	1	16	yes	—
244	C₄×D₄×C₆₁	C₂³	1	8	yes	—
245	C₄×D₄×C₆₁	C₂³	1	16	yes	—
246	C₄×D₄×C₆₁	C₂³	1	8	yes	—
247	C₄×D₄×C₆₁	C₂³	1	8	yes	—
248	C₄×D₄×C₆₁	C₂³	1	8	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	#117×C₆₁	C₂³	1	4	yes	—
255	#117×C₆₁	C₂³	1	2	yes	—
256	#117×C₆₁	C₂³	1	4	yes	—
257	#117×C₆₁	C₂³	1	2	yes	—
258	#117×C₆₁	C₂³	1	4	yes	—
259	#117×C₆₁	C₂³	1	4	yes	—
260	#117×C₆₁	C₂³	1	4	yes	—
261	#117×C₆₁	C₂³	1	4	yes	—
262	#117×C₆₁	C₂³	1	16	yes	—
263	#117×C₆₁	C₂³	1	8	yes	—
264	#117×C₆₁	C₂³	1	8	yes	—
265	#117×C₆₁	C₂³	1	8	yes	—
266	#117×C₆₁	C₂³	1	16	yes	—
267	#117×C₆₁	C₂³	1	8	yes	—
268	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
269	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
270	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
271	C₂×C₄⋊C₄×C₆₁	C₂³	1	16	yes	—
272	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
273	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
274	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
275	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
276	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
277	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
278	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
279	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
280	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
281	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
282	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
283	C₂×C₄²×C₆₁	C₂³	1	8	yes	—
284	C₂×C₄²×C₆₁	C₂³	1	16	yes	—
285	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
286	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
287	#41×C₆₁	—	2	16	no	—
288	#41×C₆₁	—	4	8	no	—
289	#41×C₆₁	—	4	8	no	—
290	#41×C₆₁	—	4	16	no	—
291	C₂×Q₈×C₆₁	—	4	8	no	—
292	C₂×Q₈×C₆₁	—	4	16	no	—
293	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
294	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
295	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
296	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
297	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
298	C₂×Q₈×C₆₁	C₂⁴	1	16	yes	—
299	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
300	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
301	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
302	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
303	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
304	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
305	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
306	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
307	C₂²×C₄×C₆₁	—	2	4	no	—
308	C₂²×C₄×C₆₁	—	4	4	no	—
309	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
316	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
317	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
323	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
324	C₂²×C₄×C₆₁	C₂⁴	1	16	yes	—
325	C₂²×C₄×C₆₁	C₂⁴	1	16	yes	—
326	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
327	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
328	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
329	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
330	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
331	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
332	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
333	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
334	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
335	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
336	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
337	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
338	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
339	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
340	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
341	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
342	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
343	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
344	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
345	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
346	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
347	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
348	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
349	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
350	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
351	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
352	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
353	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
354	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
355	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
356	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
357	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
358	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
359	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
360	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
361	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
362	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
363	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
364	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
365	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
366	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
367	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
368	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
369	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
370	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
371	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
372	C₄²×C₆₁	C₂⁴	1	2	yes	—
373	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
374	C₄²×C₆₁	C₂⁴	1	2	yes	—
375	C₄²×C₆₁	C₂⁴	1	2	yes	—
376	C₄²×C₆₁	C₂⁴	1	2	yes	—
377	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
378	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
379	C₄²×C₆₁	C₂⁴	1	8	yes	—
380	C₄²×C₆₁	C₂⁴	1	8	yes	—
381	C₄²×C₆₁	C₂⁴	1	4	yes	—
382	C₄²×C₆₁	C₂⁴	1	4	yes	—
383	C₄²×C₆₁	C₂⁴	1	16	yes	—
384	C₄²×C₆₁	C₂⁴	1	16	yes	—
385	C₄²×C₆₁	C₂⁴	1	2	yes	—
386	C₄²×C₆₁	C₂⁴	1	2	yes	—
387	C₄²×C₆₁	C₂⁴	1	8	yes	—
388	C₄²×C₆₁	C₂⁴	1	8	yes	—
389	C₂³×C₆₁	—	2	2	no	—
390	C₂³×C₆₁	—	4	2	no	—
391	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
392	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
393	C₂³×C₆₁	C₂⁵	1	8	yes	—
394	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
395	Q₈×C₆₁	—	2	8	no	—
396	Q₈×C₆₁	—	2	8	no	—
397	Q₈×C₆₁	—	2	8	no	—
398	Q₈×C₆₁	—	2	8	no	—
399	Q₈×C₆₁	—	4	16	no	—
400	Q₈×C₆₁	—	4	8	no	—
401	Q₈×C₆₁	—	4	4	no	—
402	D₄×C₆₁	—	2	16	no	—
403	D₄×C₆₁	—	2	8	no	—
404	D₄×C₆₁	—	2	8	no	—
405	D₄×C₆₁	—	4	4	no	—
406	D₄×C₆₁	—	4	8	no	—
407	D₄×C₆₁	—	4	16	no	—
408	D₄×C₆₁	—	4	8	no	—
409	C₂×C₄×C₆₁	—	2	2	no	—
410	C₂×C₄×C₆₁	—	2	2	no	—
411	C₂×C₄×C₆₁	—	2	2	no	—
412	C₂×C₄×C₆₁	—	2	2	no	—
413	C₂×C₄×C₆₁	—	2	2	no	—
414	C₂×C₄×C₆₁	—	2	16	no	—
415	C₂×C₄×C₆₁	—	2	4	no	—
416	C₂×C₄×C₆₁	—	2	4	no	—
417	C₂×C₄×C₆₁	—	2	4	no	—
418	C₂×C₄×C₆₁	—	2	16	no	—
419	C₂×C₄×C₆₁	—	4	2	no	—
420	C₂×C₄×C₆₁	—	4	2	no	—
421	C₂×C₄×C₆₁	—	4	2	no	—
422	C₂×C₄×C₆₁	—	4	8	no	—
423	C₂×C₄×C₆₁	—	4	16	no	—
424	C₂×C₄×C₆₁	—	4	8	no	—
425	C₂×C₄×C₆₁	—	4	16	no	—
426	C₂×C₄×C₆₁	2₋¹⁺⁴	1	4	yes	—
427	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
428	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
429	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
430	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
431	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
432	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
433	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
434	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
435	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
436	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
437	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
438	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
439	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
440	#62761	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
441	C₂²×C₆₁	—	2	2	no	—
442	C₂²×C₆₁	—	2	1	no	—
443	C₂²×C₆₁	—	2	1	no	—
444	C₂²×C₆₁	—	2	8	no	—
445	C₂²×C₆₁	—	2	8	no	—
446	C₂²×C₆₁	—	2	2	no	—
447	C₂²×C₆₁	—	2	2	no	—
448	C₂²×C₆₁	—	2	8	no	—
449	C₂²×C₆₁	—	4	4	no	—
450	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
451	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
452	C₄×C₆₁	—	2	1	no	—
453	C₄×C₆₁	—	2	1	no	—
454	C₄×C₆₁	—	2	8	no	—
455	C₄×C₆₁	—	2	2	no	—
456	C₄×C₆₁	—	2	2	no	—
457	C₄×C₆₁	—	2	8	no	—
458	C₄×C₆₁	—	2	2	no	—
459	C₄×C₆₁	—	2	8	no	—
460	C₄×C₆₁	—	2	8	no	—
461	C₄×C₆₁	—	2	8	no	—
462	C₄×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
463	C₄×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
464	C₄×C₆₁	#585	1	4	yes	—
465	#3557	C₂×C₆₁	1	4	yes	complemented
466	#3556	C₂×C₆₁	1	1	yes	characteristic, complemented
467	#3555	C₂×C₆₁	1	4	yes	complemented
468	#3554	C₂×C₆₁	1	4	yes	complemented
469	#3553	C₂×C₆₁	1	4	yes	complemented
470	#3552	C₂×C₆₁	1	4	yes	complemented
471	#3550	C₂×C₆₁	1	2	yes	complemented
472	#3548	C₂×C₆₁	1	1	yes	characteristic, complemented
473	#3541	C₂×C₆₁	1	8	yes	complemented
474	#3531	C₂×C₆₁	1	4	yes	complemented
475	#3482	C₂×C₆₁	1	4	yes	complemented
476	#3480	C₂×C₆₁	1	4	yes	complemented
477	Q₈×#41	C₂×C₆₁	1	4	yes	complemented
478	#3461	C₂×C₆₁	1	8	yes	complemented
479	#3455	C₂×C₆₁	1	4	yes	complemented
480	#3444	C₂×C₆₁	1	2	yes	complemented
481	C₂×#533	C₂×C₆₁	1	1	yes	characteristic, complemented
482	C₂×C₆₁	—	2	2	no	—
483	C₂×C₆₁	—	4	8	no	—
484	C₂×C₆₁	—	4	1	no	—
485	C₂×C₆₁	—	4	1	no	—
486	C₂×C₆₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
487	C₂×C₆₁	C₂×#585	1	2	yes	—
488	#564	C₂²×C₆₁	1	4	yes	complemented
489	#563	C₂²×C₆₁	1	16	yes	—
490	#563	C₂²×C₆₁	1	8	yes	complemented
491	#563	C₂²×C₆₁	1	16	yes	complemented
492	#562	C₂²×C₆₁	1	16	yes	—
493	#562	C₂²×C₆₁	1	4	yes	complemented
494	#559	C₂²×C₆₁	1	4	yes	complemented
495	#559	C₂²×C₆₁	1	8	yes	complemented
496	Q₈²	C₂²×C₆₁	1	4	yes	complemented
497	#557	C₂²×C₆₁	1	4	yes	complemented
498	#557	C₂²×C₆₁	1	8	yes	complemented
499	#557	C₂²×C₆₁	1	4	yes	complemented
500	#557	C₂²×C₆₁	1	4	yes	complemented
501	#556	C₂²×C₆₁	1	8	yes	—
502	#556	C₂²×C₆₁	1	4	yes	complemented
503	#556	C₂²×C₆₁	1	8	yes	complemented
504	#556	C₂²×C₆₁	1	4	yes	complemented
505	#554	C₂²×C₆₁	1	8	yes	—
506	#554	C₂²×C₆₁	1	16	yes	—
507	#554	C₂²×C₆₁	1	4	yes	complemented
508	#554	C₂²×C₆₁	1	8	yes	complemented
509	#553	C₂²×C₆₁	1	8	yes	—
510	#553	C₂²×C₆₁	1	16	yes	—
511	#552	C₂²×C₆₁	1	8	yes	—
512	#552	C₂²×C₆₁	1	16	yes	complemented
513	#550	C₂²×C₆₁	1	4	yes	complemented
514	D₄×Q₈	C₂²×C₆₁	1	8	yes	—
515	D₄×Q₈	C₂²×C₆₁	1	4	yes	complemented
516	D₄×Q₈	C₂²×C₆₁	1	4	yes	complemented
517	#548	C₂²×C₆₁	1	8	yes	—
518	#548	C₂²×C₆₁	1	8	yes	—
519	#547	C₂²×C₆₁	1	8	yes	—
520	#547	C₂²×C₆₁	1	4	yes	complemented
521	#544	C₂²×C₆₁	1	8	yes	complemented
522	#542	C₂²×C₆₁	1	8	yes	—
523	#542	C₂²×C₆₁	1	8	yes	—
524	#542	C₂²×C₆₁	1	8	yes	—
525	#542	C₂²×C₆₁	1	16	yes	—
526	#542	C₂²×C₆₁	1	8	yes	complemented
527	#541	C₂²×C₆₁	1	4	yes	—
528	#541	C₂²×C₆₁	1	4	yes	—
529	#541	C₂²×C₆₁	1	8	yes	—
530	#541	C₂²×C₆₁	1	8	yes	complemented
531	#541	C₂²×C₆₁	1	16	yes	complemented
532	#540	C₂²×C₆₁	1	4	yes	—
533	#540	C₂²×C₆₁	1	4	yes	—
534	#539	C₂²×C₆₁	1	16	yes	—
535	#539	C₂²×C₆₁	1	16	yes	—
536	#539	C₂²×C₆₁	1	16	yes	complemented
537	#538	C₂²×C₆₁	1	16	yes	—
538	#537	C₂²×C₆₁	1	8	yes	—
539	#536	C₂²×C₆₁	1	8	yes	—
540	#536	C₂²×C₆₁	1	8	yes	complemented
541	#533	C₂²×C₆₁	1	4	yes	—
542	#533	C₂²×C₆₁	1	2	yes	—
543	#533	C₂²×C₆₁	1	2	yes	—
544	#533	C₂²×C₆₁	1	1	yes	characteristic
545	#533	C₂²×C₆₁	1	1	yes	characteristic
546	#533	C₂²×C₆₁	1	4	yes	—
547	#533	C₂²×C₆₁	1	2	yes	—
548	#533	C₂²×C₆₁	1	2	yes	—
549	#533	C₂²×C₆₁	1	2	yes	—
550	#533	C₂²×C₆₁	1	2	yes	—
551	#533	C₂²×C₆₁	1	4	yes	—
552	#533	C₂²×C₆₁	1	8	yes	complemented
553	#533	C₂²×C₆₁	1	16	yes	complemented
554	#532	C₂²×C₆₁	1	2	yes	—
555	#532	C₂²×C₆₁	1	2	yes	—
556	#532	C₂²×C₆₁	1	2	yes	—
557	#532	C₂²×C₆₁	1	4	yes	—
558	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
559	#529	C₂²×C₆₁	1	4	yes	—
560	#529	C₂²×C₆₁	1	4	yes	—
561	#529	C₂²×C₆₁	1	4	yes	—
562	#529	C₂²×C₆₁	1	4	yes	—
563	#529	C₂²×C₆₁	1	4	yes	—
564	#529	C₂²×C₆₁	1	4	yes	—
565	#529	C₂²×C₆₁	1	16	yes	—
566	#529	C₂²×C₆₁	1	16	yes	—
567	#529	C₂²×C₆₁	1	8	yes	complemented
568	#529	C₂²×C₆₁	1	16	yes	complemented
569	C₂×#125	C₂²×C₆₁	1	2	yes	—
570	#525	C₂²×C₆₁	1	4	yes	—
571	#525	C₂²×C₆₁	1	4	yes	—
572	#525	C₂²×C₆₁	1	4	yes	—
573	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	4	yes	—
574	C₄×#41	C₂²×C₆₁	1	4	yes	—
575	C₄×#41	C₂²×C₆₁	1	4	yes	—
576	C₄×#41	C₂²×C₆₁	1	4	yes	—
577	C₄×#41	C₂²×C₆₁	1	8	yes	—
578	C₄×#41	C₂²×C₆₁	1	8	yes	complemented
579	C₂×C₄×Q₈	C₂²×C₆₁	1	4	yes	—
580	C₂×C₄×Q₈	C₂²×C₆₁	1	8	yes	complemented
581	C₂×#117	C₂²×C₆₁	1	2	yes	—
582	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
583	C₆₁	#62761	1	1	yes	characteristic, direct product factor, Sylow
584	C₂×#41	C₂³×C₆₁	1	4	yes	—
585	C₂×#41	C₂³×C₆₁	1	4	yes	—
586	C₂×#41	C₂³×C₆₁	1	4	yes	—
587	C₂×#41	C₂³×C₆₁	1	8	yes	—
588	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
589	C₂²×Q₈	C₂³×C₆₁	1	8	yes	—
590	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
591	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
592	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
593	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
594	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
595	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
596	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
597	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
598	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
599	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
600	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
601	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
602	C₄⋊Q₈	C₂³×C₆₁	1	16	yes	—
603	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
604	C₄⋊Q₈	C₂³×C₆₁	1	16	yes	—
605	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
606	#127	C₂³×C₆₁	1	2	yes	—
607	#127	C₂³×C₆₁	1	4	yes	—
608	#126	C₂³×C₆₁	1	8	yes	—
609	#126	C₂³×C₆₁	1	8	yes	—
610	#126	C₂³×C₆₁	1	16	yes	—
611	#126	C₂³×C₆₁	1	16	yes	—
612	#126	C₂³×C₆₁	1	16	yes	—
613	#126	C₂³×C₆₁	1	16	yes	—
614	#126	C₂³×C₆₁	1	16	yes	—
615	#126	C₂³×C₆₁	1	16	yes	—
616	#126	C₂³×C₆₁	1	16	yes	—
617	#125	C₂³×C₆₁	1	8	yes	—
618	#125	C₂³×C₆₁	1	4	yes	—
619	#125	C₂³×C₆₁	1	2	yes	—
620	#125	C₂³×C₆₁	1	2	yes	—
621	#125	C₂³×C₆₁	1	4	yes	—
622	#125	C₂³×C₆₁	1	4	yes	—
623	#125	C₂³×C₆₁	1	4	yes	—
624	#125	C₂³×C₆₁	1	16	yes	—
625	#125	C₂³×C₆₁	1	16	yes	—
626	#125	C₂³×C₆₁	1	16	yes	—
627	#125	C₂³×C₆₁	1	8	yes	—
628	#125	C₂³×C₆₁	1	4	yes	—
629	#125	C₂³×C₆₁	1	4	yes	—
630	#125	C₂³×C₆₁	1	16	yes	—
631	#125	C₂³×C₆₁	1	16	yes	—
632	#125	C₂³×C₆₁	1	16	yes	—
633	#124	C₂³×C₆₁	1	4	yes	—
634	#124	C₂³×C₆₁	1	4	yes	—
635	#124	C₂³×C₆₁	1	4	yes	—
636	#124	C₂³×C₆₁	1	16	yes	—
637	#124	C₂³×C₆₁	1	16	yes	—
638	#124	C₂³×C₆₁	1	8	yes	—
639	#124	C₂³×C₆₁	1	16	yes	—
640	#124	C₂³×C₆₁	1	8	yes	—
641	#123	C₂³×C₆₁	1	8	yes	—
642	#123	C₂³×C₆₁	1	8	yes	—
643	#123	C₂³×C₆₁	1	8	yes	—
644	#123	C₂³×C₆₁	1	16	yes	—
645	#123	C₂³×C₆₁	1	16	yes	—
646	#123	C₂³×C₆₁	1	16	yes	—
647	#123	C₂³×C₆₁	1	16	yes	—
648	#123	C₂³×C₆₁	1	16	yes	—
649	#123	C₂³×C₆₁	1	16	yes	—
650	#123	C₂³×C₆₁	1	16	yes	—
651	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
652	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
653	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
654	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
655	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
656	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
657	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
658	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
659	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
660	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
661	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
662	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
663	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
664	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
665	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
666	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
667	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
668	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
669	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
670	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
671	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
672	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
673	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
674	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
675	#121	C₂³×C₆₁	1	4	yes	—
676	#121	C₂³×C₆₁	1	4	yes	—
677	#121	C₂³×C₆₁	1	4	yes	—
678	#121	C₂³×C₆₁	1	4	yes	—
679	#121	C₂³×C₆₁	1	4	yes	—
680	#121	C₂³×C₆₁	1	4	yes	—
681	#121	C₂³×C₆₁	1	16	yes	—
682	#121	C₂³×C₆₁	1	16	yes	—
683	#121	C₂³×C₆₁	1	16	yes	—
684	#121	C₂³×C₆₁	1	8	yes	—
685	#121	C₂³×C₆₁	1	16	yes	—
686	#120	C₂³×C₆₁	1	8	yes	—
687	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
688	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
689	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
690	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
691	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
692	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
693	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
694	C₄×Q₈	C₂³×C₆₁	1	16	yes	—
695	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
696	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
697	C₄×Q₈	C₂³×C₆₁	1	16	yes	—
698	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
699	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
700	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
701	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
702	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
703	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
704	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
705	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
706	C₄×D₄	C₂³×C₆₁	1	4	yes	—
707	C₄×D₄	C₂³×C₆₁	1	8	yes	—
708	C₄×D₄	C₂³×C₆₁	1	8	yes	—
709	C₄×D₄	C₂³×C₆₁	1	8	yes	—
710	C₄×D₄	C₂³×C₆₁	1	8	yes	—
711	C₄×D₄	C₂³×C₆₁	1	8	yes	—
712	C₄×D₄	C₂³×C₆₁	1	8	yes	—
713	C₄×D₄	C₂³×C₆₁	1	4	yes	—
714	C₄×D₄	C₂³×C₆₁	1	4	yes	—
715	C₄×D₄	C₂³×C₆₁	1	4	yes	—
716	C₄×D₄	C₂³×C₆₁	1	4	yes	—
717	C₄×D₄	C₂³×C₆₁	1	4	yes	—
718	C₄×D₄	C₂³×C₆₁	1	16	yes	—
719	C₄×D₄	C₂³×C₆₁	1	16	yes	—
720	C₄×D₄	C₂³×C₆₁	1	8	yes	—
721	C₄×D₄	C₂³×C₆₁	1	8	yes	—
722	C₄×D₄	C₂³×C₆₁	1	16	yes	—
723	C₄×D₄	C₂³×C₆₁	1	16	yes	—
724	C₄×D₄	C₂³×C₆₁	1	8	yes	—
725	#117	C₂³×C₆₁	1	4	yes	—
726	#117	C₂³×C₆₁	1	4	yes	—
727	#117	C₂³×C₆₁	1	2	yes	—
728	#117	C₂³×C₆₁	1	4	yes	—
729	#117	C₂³×C₆₁	1	2	yes	—
730	#117	C₂³×C₆₁	1	4	yes	—
731	#117	C₂³×C₆₁	1	4	yes	—
732	#117	C₂³×C₆₁	1	4	yes	—
733	#117	C₂³×C₆₁	1	8	yes	—
734	#117	C₂³×C₆₁	1	16	yes	—
735	#117	C₂³×C₆₁	1	8	yes	—
736	#117	C₂³×C₆₁	1	8	yes	—
737	#117	C₂³×C₆₁	1	8	yes	—
738	#117	C₂³×C₆₁	1	16	yes	—
739	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
740	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
741	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
742	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
743	C₂×C₄⋊C₄	C₂³×C₆₁	1	16	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
745	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
746	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
747	C₂×C₄²	C₂³×C₆₁	1	8	yes	—
748	C₂×C₄²	C₂³×C₆₁	1	16	yes	—
749	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
750	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
751	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
752	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
753	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
754	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
755	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
756	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
757	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
758	#41	—	2	16	no	—
759	#41	—	4	8	no	—
760	#41	—	4	8	no	—
761	#41	—	4	16	no	—
762	C₂×Q₈	—	4	8	no	—
763	C₂×Q₈	—	4	16	no	—
764	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
765	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
766	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
767	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
768	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
769	C₂×Q₈	C₂⁴×C₆₁	1	16	yes	—
770	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
771	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
772	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
773	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
774	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
775	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
776	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
777	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
778	C₂²×C₄	—	2	4	no	—
779	C₂²×C₄	—	4	4	no	—
780	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
781	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
790	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
794	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
795	C₂²×C₄	C₂⁴×C₆₁	1	16	yes	—
796	C₂²×C₄	C₂⁴×C₆₁	1	16	yes	—
797	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
798	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
799	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
800	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
801	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
802	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
803	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
804	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
805	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
806	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
807	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
808	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
809	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
810	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
811	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
812	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
813	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
814	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
815	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
816	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
817	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
818	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
819	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
820	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
821	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
822	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
823	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
824	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
825	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
826	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
827	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
828	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
829	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
830	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
831	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
832	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
833	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
834	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
835	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
836	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
837	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
838	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
839	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
840	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
841	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
842	C₄²	C₂⁴×C₆₁	1	2	yes	—
843	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
844	C₄²	C₂⁴×C₆₁	1	8	yes	—
845	C₄²	C₂⁴×C₆₁	1	2	yes	—
846	C₄²	C₂⁴×C₆₁	1	8	yes	—
847	C₄²	C₂⁴×C₆₁	1	2	yes	—
848	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
849	C₄²	C₂⁴×C₆₁	1	2	yes	—
850	C₄²	C₂⁴×C₆₁	1	2	yes	—
851	C₄²	C₂⁴×C₆₁	1	2	yes	—
852	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
853	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
854	C₄²	C₂⁴×C₆₁	1	8	yes	—
855	C₄²	C₂⁴×C₆₁	1	8	yes	—
856	C₄²	C₂⁴×C₆₁	1	4	yes	—
857	C₄²	C₂⁴×C₆₁	1	4	yes	—
858	C₄²	C₂⁴×C₆₁	1	16	yes	—
859	C₄²	C₂⁴×C₆₁	1	16	yes	—
860	C₂³	—	2	2	no	—
861	C₂³	—	4	2	no	—
862	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
863	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
864	C₂³	C₂⁵×C₆₁	1	8	yes	—
865	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
866	Q₈	—	2	8	no	—
867	Q₈	—	2	8	no	—
868	Q₈	—	2	8	no	—
869	Q₈	—	2	8	no	—
870	Q₈	—	4	16	no	—
871	Q₈	—	4	8	no	—
872	Q₈	—	4	4	no	—
873	D₄	—	2	16	no	—
874	D₄	—	2	8	no	—
875	D₄	—	2	8	no	—
876	D₄	—	4	4	no	—
877	D₄	—	4	8	no	—
878	D₄	—	4	16	no	—
879	D₄	—	4	8	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	16	no	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	4	no	—
888	C₂×C₄	—	2	4	no	—
889	C₂×C₄	—	2	16	no	—
890	C₂×C₄	—	4	2	no	—
891	C₂×C₄	—	4	2	no	—
892	C₂×C₄	—	4	2	no	—
893	C₂×C₄	—	4	8	no	—
894	C₂×C₄	—	4	16	no	—
895	C₂×C₄	—	4	8	no	—
896	C₂×C₄	—	4	16	no	—
897	C₂×C₄	2₋¹⁺⁴×C₆₁	1	4	yes	—
898	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
899	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
900	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
901	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
902	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
903	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
904	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
905	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
906	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
907	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
908	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
909	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
910	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	8	no	—
915	C₂²	—	2	8	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	8	no	—
919	C₂²	—	4	4	no	—
920	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
921	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	8	no	—
925	C₄	—	2	2	no	—
926	C₄	—	2	2	no	—
927	C₄	—	2	8	no	—
928	C₄	—	2	2	no	—
929	C₄	—	2	8	no	—
930	C₄	—	2	8	no	—
931	C₄	—	2	8	no	—
932	C₄	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
933	C₄	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
934	C₄	C₆₁×#585	1	4	yes	—
935	C₂	—	2	2	no	—
936	C₂	—	4	1	no	—
937	C₂	—	4	1	no	—
938	C₂	—	4	8	no	—
939	C₂	C₂²×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
940	C₂	C₂×C₆₁×#585	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₁
socle	C₂²×C₆₁	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3557	C₂	semidirect
2. C₆₁×#3556	C₂	semidirect
3. C₆₁×#3555	C₂	semidirect
4. C₆₁×#3554	C₂	semidirect
5. C₆₁×#3553	C₂	semidirect
6. C₆₁×#3552	C₂	semidirect
7. C₆₁×#3550	C₂	semidirect
8. C₆₁×#3548	C₂	semidirect
9. C₆₁×#3541	C₂	semidirect
10. C₆₁×#3531	C₂	semidirect
11. C₆₁×#3482	C₂	semidirect
12. C₆₁×#3480	C₂	semidirect
13. Q₈×#41×C₆₁	C₂	semidirect
14. C₆₁×#3461	C₂	semidirect
15. C₆₁×#3455	C₂	semidirect
16. C₆₁×#3444	C₂	semidirect
17. C₂×C₆₁×#533	C₂	semidirect
18. C₆₁×#564	C₂²	semidirect
20. C₆₁×#563	C₂²	semidirect
21. C₆₁×#563	C₂²	semidirect
23. C₆₁×#562	C₂²	semidirect
24. C₆₁×#559	C₂²	semidirect
25. C₆₁×#559	C₂²	semidirect
26. Q₈²×C₆₁	C₂²	semidirect
27. C₆₁×#557	C₂²	semidirect
28. C₆₁×#557	C₂²	semidirect
29. C₆₁×#557	C₂²	semidirect
30. C₆₁×#557	C₂²	semidirect
32. C₆₁×#556	C₂²	semidirect
33. C₆₁×#556	C₂²	semidirect
34. C₆₁×#556	C₂²	semidirect
37. C₆₁×#554	C₂²	semidirect
38. C₆₁×#554	C₂²	semidirect
42. C₆₁×#552	C₂²	semidirect
43. C₆₁×#550	C₂²	semidirect
45. D₄×Q₈×C₆₁	C₂²	semidirect
46. D₄×Q₈×C₆₁	C₂²	semidirect
50. C₆₁×#547	C₂²	semidirect
51. C₆₁×#544	C₂²	semidirect
56. C₆₁×#542	C₂²	semidirect
60. C₆₁×#541	C₂²	semidirect
61. C₆₁×#541	C₂²	semidirect
66. C₆₁×#539	C₂²	semidirect
70. C₆₁×#536	C₂²	semidirect
82. C₆₁×#533	C₂²	semidirect
83. C₆₁×#533	C₂²	semidirect
97. C₆₁×#529	C₂²	semidirect
98. C₆₁×#529	C₂²	semidirect
108. C₄×#41×C₆₁	C₂²	semidirect
110. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
440. #62761	C₆₁	direct (N × H)
465. #3557	C₂×C₆₁	semidirect
466. #3556	C₂×C₆₁	semidirect
467. #3555	C₂×C₆₁	semidirect
468. #3554	C₂×C₆₁	semidirect
469. #3553	C₂×C₆₁	semidirect
470. #3552	C₂×C₆₁	semidirect
471. #3550	C₂×C₆₁	semidirect
472. #3548	C₂×C₆₁	semidirect
473. #3541	C₂×C₆₁	semidirect
474. #3531	C₂×C₆₁	semidirect
475. #3482	C₂×C₆₁	semidirect
476. #3480	C₂×C₆₁	semidirect
477. Q₈×#41	C₂×C₆₁	semidirect
478. #3461	C₂×C₆₁	semidirect
479. #3455	C₂×C₆₁	semidirect
480. #3444	C₂×C₆₁	semidirect
481. C₂×#533	C₂×C₆₁	semidirect
488. #564	C₂²×C₆₁	semidirect
490. #563	C₂²×C₆₁	semidirect
491. #563	C₂²×C₆₁	semidirect
493. #562	C₂²×C₆₁	semidirect
494. #559	C₂²×C₆₁	semidirect
495. #559	C₂²×C₆₁	semidirect
496. Q₈²	C₂²×C₆₁	semidirect
497. #557	C₂²×C₆₁	semidirect
498. #557	C₂²×C₆₁	semidirect
499. #557	C₂²×C₆₁	semidirect
500. #557	C₂²×C₆₁	semidirect
502. #556	C₂²×C₆₁	semidirect
503. #556	C₂²×C₆₁	semidirect
504. #556	C₂²×C₆₁	semidirect
507. #554	C₂²×C₆₁	semidirect
508. #554	C₂²×C₆₁	semidirect
512. #552	C₂²×C₆₁	semidirect
513. #550	C₂²×C₆₁	semidirect
515. D₄×Q₈	C₂²×C₆₁	semidirect
516. D₄×Q₈	C₂²×C₆₁	semidirect
520. #547	C₂²×C₆₁	semidirect
521. #544	C₂²×C₆₁	semidirect
526. #542	C₂²×C₆₁	semidirect
530. #541	C₂²×C₆₁	semidirect
531. #541	C₂²×C₆₁	semidirect
536. #539	C₂²×C₆₁	semidirect
540. #536	C₂²×C₆₁	semidirect
552. #533	C₂²×C₆₁	semidirect
553. #533	C₂²×C₆₁	semidirect
567. #529	C₂²×C₆₁	semidirect
568. #529	C₂²×C₆₁	semidirect
578. C₄×#41	C₂²×C₆₁	semidirect
580. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
583. C₆₁	#62761	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×#3557	2
C₆₁×#3556	2
C₆₁×#3555	2
C₆₁×#3554	2
C₆₁×#3553	2
C₆₁×#3552	2
C₆₁×#3550	2
C₆₁×#3548	2
C₆₁×#3541	2
C₆₁×#3531	2
C₆₁×#3482	2
C₆₁×#3480	2
Q₈×#41×C₆₁	2
C₆₁×#3461	2
C₆₁×#3455	2
C₆₁×#3444	2
C₂×C₆₁×#533	2
#62761	61

Subgroups — C61×#62761 #29566194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62761 #29566194