Subgroups — C₆₁×#61017 #29564450

Order 15616.

1792 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3257	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3240	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3235	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3217	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3213	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3200	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3199	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3180	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3171	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3126	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3122	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3118	C₂	1	4	yes	maximal, complemented
15	C₆₁×#2923	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#559	—	2	2	no	—
17	C₆₁×#559	—	2	2	no	—
18	C₆₁×#556	—	2	2	no	—
19	C₆₁×#551	—	2	2	no	—
20	C₆₁×#551	—	2	2	no	—
21	C₆₁×#550	—	2	2	no	—
22	C₆₁×#546	—	2	2	no	—
23	C₆₁×#546	—	2	2	no	—
24	C₆₁×#542	C₂²	1	2	yes	—
25	C₆₁×#542	C₂²	1	2	yes	complemented
26	C₆₁×#540	C₂²	1	2	yes	—
27	C₆₁×#540	C₂²	1	2	yes	complemented
28	C₆₁×#536	C₂²	1	1	yes	characteristic
29	C₆₁×#535	C₂²	1	1	yes	characteristic
30	C₆₁×#535	C₂²	1	2	yes	—
31	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
32	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
33	C₆₁×#532	C₂²	1	2	yes	—
34	C₆₁×#532	C₂²	1	2	yes	complemented
35	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic, complemented
36	C₆₁×#529	C₂²	1	2	yes	—
37	C₆₁×#529	C₂²	1	2	yes	complemented
38	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic, complemented
39	C₆₁×#519	C₂²	1	1	yes	characteristic, complemented
40	C₆₁×#518	C₂²	1	2	yes	complemented
41	C₆₁×#518	C₂²	1	1	yes	characteristic, complemented
42	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
43	C₆₁×#501	C₂²	1	2	yes	complemented
44	C₆₁×#501	C₂²	1	2	yes	complemented
45	C₆₁×#496	C₂²	1	2	yes	—
46	C₆₁×#496	C₂²	1	2	yes	—
47	C₆₁×#490	C₂²	1	2	yes	complemented
48	C₆₁×#490	C₂²	1	2	yes	complemented
49	C₆₁×#489	C₂²	1	2	yes	complemented
50	C₆₁×#489	C₂²	1	2	yes	complemented
51	C₆₁×#485	C₂²	1	4	yes	complemented
52	C₆₁×#482	C₂²	1	4	yes	—
53	C₆₁×#482	C₂²	1	4	yes	complemented
54	C₆₁×#482	C₂²	1	4	yes	complemented
55	C₆₁×#479	C₂²	1	4	yes	complemented
56	C₆₁×#478	C₂²	1	4	yes	complemented
57	C₆₁×#476	C₂²	1	4	yes	complemented
58	C₆₁×#474	C₂²	1	4	yes	complemented
59	C₆₁×#469	C₂²	1	4	yes	complemented
60	C₆₁×#468	C₂²	1	4	yes	complemented
61	C₆₁×#466	C₂²	1	4	yes	complemented
62	C₆₁×#465	C₂²	1	4	yes	complemented
63	C₆₁×#463	C₂²	1	4	yes	complemented
64	C₆₁×#463	C₂²	1	4	yes	complemented
65	C₆₁×#460	C₂²	1	4	yes	complemented
66	C₆₁×#459	C₂²	1	4	yes	—
67	C₆₁×#450	C₂²	1	4	yes	complemented
68	C₆₁×#448	C₂²	1	4	yes	complemented
69	C₆₁×#447	C₂²	1	4	yes	—
70	C₆₁×#447	C₂²	1	4	yes	complemented
71	C₆₁×#442	C₂²	1	4	yes	complemented
72	C₆₁×#440	C₂²	1	4	yes	complemented
73	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	complemented
74	C₄×D₈×C₆₁	C₂²	1	4	yes	complemented
75	C₆₁×#433	C₂²	1	2	yes	complemented
76	C₆₁×#433	C₂²	1	2	yes	complemented
77	C₆₁×#432	C₂²	1	2	yes	complemented
78	C₆₁×#432	C₂²	1	2	yes	complemented
79	C₆₁×#424	C₂²	1	2	yes	complemented
80	C₆₁×#408	C₂²	1	2	yes	—
81	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
82	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic, complemented
83	C₂×#41×C₆₁	—	2	2	no	—
84	C₂×#41×C₆₁	—	2	2	no	—
85	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₆₁	—	2	2	no	—
88	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
89	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
90	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
91	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
92	C₂×D₈×C₆₁	C₂³	1	4	yes	—
93	C₂×D₈×C₆₁	C₂³	1	4	yes	—
94	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
95	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
96	C₄⋊Q₈×C₆₁	—	2	1	no	—
97	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
98	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
99	#127×C₆₁	—	2	2	no	—
100	#127×C₆₁	—	2	1	no	—
101	#127×C₆₁	—	2	2	no	—
102	#127×C₆₁	C₂³	1	2	yes	—
103	#127×C₆₁	C₂³	1	2	yes	—
104	#126×C₆₁	—	2	2	no	—
105	#126×C₆₁	—	2	2	no	—
106	#126×C₆₁	—	2	2	no	—
107	#126×C₆₁	—	2	2	no	—
108	#125×C₆₁	C₂³	1	2	yes	—
109	#125×C₆₁	C₂³	1	2	yes	—
110	#124×C₆₁	—	2	1	no	—
111	#124×C₆₁	—	2	2	no	—
112	#124×C₆₁	—	2	1	no	—
113	#124×C₆₁	—	2	2	no	—
114	#124×C₆₁	—	2	2	no	—
115	#124×C₆₁	—	2	2	no	—
116	#124×C₆₁	—	2	2	no	—
117	#124×C₆₁	—	2	2	no	—
118	#124×C₆₁	C₂³	1	2	yes	—
119	#124×C₆₁	C₂³	1	2	yes	—
120	#123×C₆₁	—	2	1	no	—
121	#123×C₆₁	—	2	1	no	—
122	#123×C₆₁	—	2	2	no	—
123	#123×C₆₁	—	2	2	no	—
124	#123×C₆₁	—	2	4	no	—
125	#123×C₆₁	—	2	4	no	—
126	#123×C₆₁	—	2	2	no	—
127	#123×C₆₁	—	2	2	no	—
128	C₂²⋊Q₈×C₆₁	—	2	2	no	—
129	C₂²⋊Q₈×C₆₁	—	2	2	no	—
130	C₂²⋊Q₈×C₆₁	—	2	2	no	—
131	C₂²⋊Q₈×C₆₁	—	2	2	no	—
132	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
133	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
134	#121×C₆₁	—	2	2	no	—
135	#121×C₆₁	—	2	2	no	—
136	#121×C₆₁	—	2	4	no	—
137	#121×C₆₁	—	2	4	no	—
138	#121×C₆₁	C₂³	1	4	yes	—
139	#121×C₆₁	C₂³	1	4	yes	—
140	#121×C₆₁	C₂³	1	2	yes	—
141	#121×C₆₁	C₂³	1	2	yes	—
142	#120×C₆₁	—	2	2	no	—
143	#120×C₆₁	—	2	2	no	—
144	#120×C₆₁	—	2	1	no	—
145	#120×C₆₁	—	2	1	no	—
146	C₄×Q₈×C₆₁	—	2	2	no	—
147	C₄×Q₈×C₆₁	—	2	2	no	—
148	C₄×Q₈×C₆₁	—	2	2	no	—
149	C₄×Q₈×C₆₁	D₄	1	2	yes	—
150	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
151	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
152	C₄×D₄×C₆₁	—	2	2	no	—
153	C₄×D₄×C₆₁	—	2	2	no	—
154	C₄×D₄×C₆₁	—	2	4	no	—
155	C₄×D₄×C₆₁	—	2	2	no	—
156	C₄×D₄×C₆₁	—	2	2	no	—
157	C₄×D₄×C₆₁	—	2	2	no	—
158	C₄×D₄×C₆₁	D₄	1	2	yes	—
159	C₄×D₄×C₆₁	D₄	1	2	yes	—
160	C₄×D₄×C₆₁	D₄	1	2	yes	—
161	C₄×D₄×C₆₁	C₂³	1	4	yes	—
162	C₄×D₄×C₆₁	C₂³	1	4	yes	—
163	C₄×D₄×C₆₁	C₂³	1	2	yes	—
164	C₄×D₄×C₆₁	C₂³	1	2	yes	—
165	#117×C₆₁	—	2	2	no	—
166	#117×C₆₁	—	2	2	no	—
167	#117×C₆₁	—	2	2	no	—
168	#117×C₆₁	C₂³	1	2	yes	—
169	#117×C₆₁	C₂³	1	1	yes	characteristic
170	#117×C₆₁	C₂³	1	1	yes	characteristic
171	#117×C₆₁	C₂³	1	1	yes	characteristic
172	#117×C₆₁	C₂³	1	1	yes	characteristic
173	#117×C₆₁	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
175	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
176	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
177	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
180	#107×C₆₁	C₂³	1	4	yes	—
181	#107×C₆₁	C₂³	1	4	yes	—
182	#106×C₆₁	C₂³	1	4	yes	—
183	#106×C₆₁	C₂³	1	4	yes	—
184	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
185	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
186	#103×C₆₁	C₂³	1	4	yes	—
187	#103×C₆₁	C₂³	1	4	yes	—
188	#102×C₆₁	C₂³	1	4	yes	—
189	#102×C₆₁	C₂³	1	4	yes	—
190	#102×C₆₁	C₂³	1	4	yes	—
191	#102×C₆₁	C₂³	1	4	yes	—
192	#102×C₆₁	C₂³	1	4	yes	—
193	#102×C₆₁	C₂³	1	4	yes	—
194	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
195	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
196	#97×C₆₁	C₂³	1	2	yes	—
197	#97×C₆₁	C₂³	1	2	yes	—
198	#97×C₆₁	C₂³	1	2	yes	—
199	C₄×C₈×C₆₁	C₂³	1	2	yes	—
200	C₂⁴×C₆₁	—	2	1	no	—
201	C₂⁴×C₆₁	—	2	2	no	—
202	#41×C₆₁	—	4	2	no	—
203	#41×C₆₁	—	8	4	no	—
204	#41×C₆₁	—	8	4	no	—
205	C₂×Q₈×C₆₁	—	2	1	no	—
206	C₂×Q₈×C₆₁	—	2	2	no	—
207	C₂×Q₈×C₆₁	—	2	2	no	—
208	C₂×Q₈×C₆₁	—	4	2	no	—
209	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
210	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
211	C₂×D₄×C₆₁	—	2	2	no	—
212	C₂×D₄×C₆₁	—	2	2	no	—
213	C₂×D₄×C₆₁	—	2	4	no	—
214	C₂×D₄×C₆₁	—	2	4	no	—
215	C₂×D₄×C₆₁	—	2	1	no	—
216	C₂×D₄×C₆₁	—	2	2	no	—
217	C₂×D₄×C₆₁	—	2	2	no	—
218	C₂×D₄×C₆₁	—	2	2	no	—
219	C₂×D₄×C₆₁	—	2	4	no	—
220	C₂×D₄×C₆₁	—	4	2	no	—
221	C₂×D₄×C₆₁	—	4	2	no	—
222	C₂×D₄×C₆₁	—	4	2	no	—
223	C₂×D₄×C₆₁	—	8	4	no	—
224	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
225	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
226	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
227	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
228	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
229	C₂²×C₄×C₆₁	—	2	1	no	—
230	C₂²×C₄×C₆₁	—	2	2	no	—
231	C₂²×C₄×C₆₁	—	2	2	no	—
232	C₂²×C₄×C₆₁	—	2	4	no	—
233	C₂²×C₄×C₆₁	—	2	4	no	—
234	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
237	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
240	SD₁₆×C₆₁	—	4	4	no	—
241	SD₁₆×C₆₁	—	4	4	no	—
242	D₈×C₆₁	—	4	4	no	—
243	D₈×C₆₁	—	4	4	no	—
244	M₁₆×C₆₁	—	4	2	no	—
245	C₂×C₈×C₆₁	—	4	2	no	—
246	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
247	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
248	C₄⋊C₄×C₆₁	—	2	2	no	—
249	C₄⋊C₄×C₆₁	—	2	2	no	—
250	C₄⋊C₄×C₆₁	—	2	2	no	—
251	C₄⋊C₄×C₆₁	—	2	2	no	—
252	C₄⋊C₄×C₆₁	—	2	2	no	—
253	C₄⋊C₄×C₆₁	—	2	2	no	—
254	C₄⋊C₄×C₆₁	—	2	2	no	—
255	C₄⋊C₄×C₆₁	—	2	4	no	—
256	C₄⋊C₄×C₆₁	—	2	2	no	—
257	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
263	C₂²⋊C₄×C₆₁	—	2	2	no	—
264	C₂²⋊C₄×C₆₁	—	2	1	no	—
265	C₂²⋊C₄×C₆₁	—	2	1	no	—
266	C₂²⋊C₄×C₆₁	—	2	2	no	—
267	C₂²⋊C₄×C₆₁	—	2	2	no	—
268	C₂²⋊C₄×C₆₁	—	2	2	no	—
269	C₂²⋊C₄×C₆₁	—	2	2	no	—
270	C₂²⋊C₄×C₆₁	—	2	4	no	—
271	C₂²⋊C₄×C₆₁	—	2	4	no	—
272	C₂²⋊C₄×C₆₁	—	2	2	no	—
273	C₂²⋊C₄×C₆₁	—	2	2	no	—
274	C₂²⋊C₄×C₆₁	—	2	2	no	—
275	C₂²⋊C₄×C₆₁	—	2	2	no	—
276	C₂²⋊C₄×C₆₁	—	2	2	no	—
277	C₂²⋊C₄×C₆₁	—	2	2	no	—
278	C₂²⋊C₄×C₆₁	—	2	4	no	—
279	C₂²⋊C₄×C₆₁	—	2	4	no	—
280	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
281	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
282	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
283	C₄²×C₆₁	—	2	2	no	—
284	C₄²×C₆₁	—	2	2	no	—
285	C₄²×C₆₁	—	2	2	no	—
286	C₄²×C₆₁	—	2	1	no	—
287	C₄²×C₆₁	—	2	1	no	—
288	C₄²×C₆₁	C₂×D₄	1	2	yes	—
289	C₄²×C₆₁	C₂×D₄	1	2	yes	—
290	C₄²×C₆₁	C₂×D₄	1	2	yes	—
291	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
292	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
293	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
294	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
295	C₂³×C₆₁	—	2	2	no	—
296	C₂³×C₆₁	—	2	4	no	—
297	C₂³×C₆₁	—	4	2	no	—
298	C₂³×C₆₁	—	4	4	no	—
299	C₂³×C₆₁	—	8	4	no	—
300	C₂³×C₆₁	—	8	2	no	—
301	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
302	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
303	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
304	Q₈×C₆₁	—	2	4	no	—
305	Q₈×C₆₁	—	4	1	no	—
306	Q₈×C₆₁	—	4	2	no	—
307	Q₈×C₆₁	—	4	4	no	—
308	Q₈×C₆₁	—	8	2	no	—
309	D₄×C₆₁	—	2	4	no	—
310	D₄×C₆₁	—	2	4	no	—
311	D₄×C₆₁	—	2	4	no	—
312	D₄×C₆₁	—	4	1	no	—
313	D₄×C₆₁	—	4	1	no	—
314	D₄×C₆₁	—	4	1	no	—
315	D₄×C₆₁	—	4	4	no	—
316	D₄×C₆₁	—	4	2	no	—
317	D₄×C₆₁	—	4	4	no	—
318	D₄×C₆₁	—	4	4	no	—
319	D₄×C₆₁	—	8	4	no	—
320	D₄×C₆₁	—	8	2	no	—
321	D₄×C₆₁	—	8	2	no	—
322	D₄×C₆₁	—	8	4	no	—
323	D₄×C₆₁	—	8	4	no	—
324	C₂×C₄×C₆₁	—	2	2	no	—
325	C₂×C₄×C₆₁	—	2	2	no	—
326	C₂×C₄×C₆₁	—	2	2	no	—
327	C₂×C₄×C₆₁	—	2	2	no	—
328	C₂×C₄×C₆₁	—	2	2	no	—
329	C₂×C₄×C₆₁	—	2	2	no	—
330	C₂×C₄×C₆₁	—	2	4	no	—
331	C₂×C₄×C₆₁	—	4	2	no	—
332	C₂×C₄×C₆₁	—	4	2	no	—
333	C₂×C₄×C₆₁	—	4	2	no	—
334	C₂×C₄×C₆₁	—	4	2	no	—
335	C₂×C₄×C₆₁	—	8	2	no	—
336	C₂×C₄×C₆₁	—	8	2	no	—
337	C₂×C₄×C₆₁	—	8	4	no	—
338	C₂×C₄×C₆₁	—	8	4	no	—
339	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
347	C₈×C₆₁	—	2	4	no	—
348	C₈×C₆₁	—	2	4	no	—
349	#61017	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
350	C₂²×C₆₁	—	2	2	no	—
351	C₂²×C₆₁	—	2	2	no	—
352	C₂²×C₆₁	—	2	2	no	—
353	C₂²×C₆₁	—	2	1	no	—
354	C₂²×C₆₁	—	2	1	no	—
355	C₂²×C₆₁	—	2	1	no	—
356	C₂²×C₆₁	—	4	4	no	—
357	C₂²×C₆₁	—	4	4	no	—
358	C₂²×C₆₁	—	4	2	no	—
359	C₂²×C₆₁	—	4	2	no	—
360	C₂²×C₆₁	—	4	2	no	—
361	C₂²×C₆₁	—	4	4	no	—
362	C₂²×C₆₁	—	16	2	no	—
363	C₂²×C₆₁	—	16	4	no	—
364	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
365	C₄×C₆₁	—	2	2	no	—
366	C₄×C₆₁	—	2	2	no	—
367	C₄×C₆₁	—	2	2	no	—
368	C₄×C₆₁	—	2	2	no	—
369	C₄×C₆₁	—	2	1	no	—
370	C₄×C₆₁	—	2	1	no	—
371	C₄×C₆₁	—	2	1	no	—
372	C₄×C₆₁	—	4	4	no	—
373	C₄×C₆₁	—	4	2	no	—
374	C₄×C₆₁	—	4	2	no	—
375	C₄×C₆₁	—	4	2	no	—
376	C₄×C₆₁	#585	1	2	yes	—
377	#3510	C₂×C₆₁	1	1	yes	characteristic, complemented
378	#3508	C₂×C₆₁	1	1	yes	characteristic, complemented
379	#3257	C₂×C₆₁	1	4	yes	complemented
380	#3240	C₂×C₆₁	1	2	yes	complemented
381	#3235	C₂×C₆₁	1	2	yes	complemented
382	#3217	C₂×C₆₁	1	2	yes	complemented
383	#3213	C₂×C₆₁	1	2	yes	complemented
384	#3200	C₂×C₆₁	1	2	yes	complemented
385	#3199	C₂×C₆₁	1	2	yes	complemented
386	#3180	C₂×C₆₁	1	2	yes	complemented
387	#3171	C₂×C₆₁	1	2	yes	complemented
388	#3126	C₂×C₆₁	1	2	yes	complemented
389	#3122	C₂×C₆₁	1	2	yes	complemented
390	#3118	C₂×C₆₁	1	4	yes	complemented
391	#2923	C₂×C₆₁	1	1	yes	characteristic, complemented
392	C₂×C₆₁	—	4	1	no	—
393	C₂×C₆₁	—	4	1	no	—
394	C₂×C₆₁	—	4	1	no	—
395	C₂×C₆₁	—	8	4	no	—
396	C₂×C₆₁	—	8	2	no	—
397	C₂×C₆₁	#3449	1	1	yes	characteristic
398	C₂×C₆₁	#3585	1	2	yes	—
399	#559	—	2	2	no	—
400	#559	—	2	2	no	—
401	#556	—	2	2	no	—
402	#551	—	2	2	no	—
403	#551	—	2	2	no	—
404	#550	—	2	2	no	—
405	#546	—	2	2	no	—
406	#546	—	2	2	no	—
407	#542	C₂²×C₆₁	1	2	yes	—
408	#542	C₂²×C₆₁	1	2	yes	complemented
409	#540	C₂²×C₆₁	1	2	yes	—
410	#540	C₂²×C₆₁	1	2	yes	complemented
411	#536	C₂²×C₆₁	1	1	yes	characteristic
412	#535	C₂²×C₆₁	1	1	yes	characteristic
413	#535	C₂²×C₆₁	1	2	yes	—
414	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
415	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
416	#532	C₂²×C₆₁	1	2	yes	—
417	#532	C₂²×C₆₁	1	2	yes	complemented
418	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic, complemented
419	#529	C₂²×C₆₁	1	2	yes	—
420	#529	C₂²×C₆₁	1	2	yes	complemented
421	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic, complemented
422	#519	C₂²×C₆₁	1	1	yes	characteristic, complemented
423	#518	C₂²×C₆₁	1	2	yes	complemented
424	#518	C₂²×C₆₁	1	1	yes	characteristic, complemented
425	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
426	#501	C₂²×C₆₁	1	2	yes	complemented
427	#501	C₂²×C₆₁	1	2	yes	complemented
428	#496	C₂²×C₆₁	1	2	yes	—
429	#496	C₂²×C₆₁	1	2	yes	—
430	#490	C₂²×C₆₁	1	2	yes	complemented
431	#490	C₂²×C₆₁	1	2	yes	complemented
432	#489	C₂²×C₆₁	1	2	yes	complemented
433	#489	C₂²×C₆₁	1	2	yes	complemented
434	#485	C₂²×C₆₁	1	4	yes	complemented
435	#482	C₂²×C₆₁	1	4	yes	—
436	#482	C₂²×C₆₁	1	4	yes	complemented
437	#482	C₂²×C₆₁	1	4	yes	complemented
438	#479	C₂²×C₆₁	1	4	yes	complemented
439	#478	C₂²×C₆₁	1	4	yes	complemented
440	#476	C₂²×C₆₁	1	4	yes	complemented
441	#474	C₂²×C₆₁	1	4	yes	complemented
442	#469	C₂²×C₆₁	1	4	yes	complemented
443	#468	C₂²×C₆₁	1	4	yes	complemented
444	#466	C₂²×C₆₁	1	4	yes	complemented
445	#465	C₂²×C₆₁	1	4	yes	complemented
446	#463	C₂²×C₆₁	1	4	yes	complemented
447	#463	C₂²×C₆₁	1	4	yes	complemented
448	#460	C₂²×C₆₁	1	4	yes	complemented
449	#459	C₂²×C₆₁	1	4	yes	—
450	#450	C₂²×C₆₁	1	4	yes	complemented
451	#448	C₂²×C₆₁	1	4	yes	complemented
452	#447	C₂²×C₆₁	1	4	yes	—
453	#447	C₂²×C₆₁	1	4	yes	complemented
454	#442	C₂²×C₆₁	1	4	yes	complemented
455	#440	C₂²×C₆₁	1	4	yes	complemented
456	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	complemented
457	C₄×D₈	C₂²×C₆₁	1	4	yes	complemented
458	#433	C₂²×C₆₁	1	2	yes	complemented
459	#433	C₂²×C₆₁	1	2	yes	complemented
460	#432	C₂²×C₆₁	1	2	yes	complemented
461	#432	C₂²×C₆₁	1	2	yes	complemented
462	#424	C₂²×C₆₁	1	2	yes	complemented
463	#408	C₂²×C₆₁	1	2	yes	—
464	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
465	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic, complemented
466	C₆₁	#61017	1	1	yes	characteristic, direct product factor, Sylow
467	C₂×#41	—	2	2	no	—
468	C₂×#41	—	2	2	no	—
469	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
470	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
471	C₂²×D₄	—	2	2	no	—
472	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
473	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
474	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
475	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
476	C₂×D₈	C₂³×C₆₁	1	4	yes	—
477	C₂×D₈	C₂³×C₆₁	1	4	yes	—
478	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
479	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
480	C₄⋊Q₈	—	2	1	no	—
481	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
482	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
483	#127	—	2	2	no	—
484	#127	—	2	1	no	—
485	#127	—	2	2	no	—
486	#127	C₂³×C₆₁	1	2	yes	—
487	#127	C₂³×C₆₁	1	2	yes	—
488	#126	—	2	2	no	—
489	#126	—	2	2	no	—
490	#126	—	2	2	no	—
491	#126	—	2	2	no	—
492	#125	C₂³×C₆₁	1	2	yes	—
493	#125	C₂³×C₆₁	1	2	yes	—
494	#124	—	2	1	no	—
495	#124	—	2	2	no	—
496	#124	—	2	1	no	—
497	#124	—	2	2	no	—
498	#124	—	2	2	no	—
499	#124	—	2	2	no	—
500	#124	—	2	2	no	—
501	#124	—	2	2	no	—
502	#124	C₂³×C₆₁	1	2	yes	—
503	#124	C₂³×C₆₁	1	2	yes	—
504	#123	—	2	1	no	—
505	#123	—	2	1	no	—
506	#123	—	2	2	no	—
507	#123	—	2	2	no	—
508	#123	—	2	4	no	—
509	#123	—	2	4	no	—
510	#123	—	2	2	no	—
511	#123	—	2	2	no	—
512	C₂²⋊Q₈	—	2	2	no	—
513	C₂²⋊Q₈	—	2	2	no	—
514	C₂²⋊Q₈	—	2	2	no	—
515	C₂²⋊Q₈	—	2	2	no	—
516	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
517	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
518	#121	—	2	2	no	—
519	#121	—	2	2	no	—
520	#121	—	2	4	no	—
521	#121	—	2	4	no	—
522	#121	C₂³×C₆₁	1	2	yes	—
523	#121	C₂³×C₆₁	1	2	yes	—
524	#121	C₂³×C₆₁	1	4	yes	—
525	#121	C₂³×C₆₁	1	4	yes	—
526	#120	—	2	2	no	—
527	#120	—	2	2	no	—
528	#120	—	2	1	no	—
529	#120	—	2	1	no	—
530	C₄×Q₈	—	2	2	no	—
531	C₄×Q₈	—	2	2	no	—
532	C₄×Q₈	—	2	2	no	—
533	C₄×Q₈	D₄×C₆₁	1	2	yes	—
534	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
535	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
536	C₄×D₄	—	2	2	no	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	4	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	D₄×C₆₁	1	2	yes	—
543	C₄×D₄	D₄×C₆₁	1	2	yes	—
544	C₄×D₄	D₄×C₆₁	1	2	yes	—
545	C₄×D₄	C₂³×C₆₁	1	2	yes	—
546	C₄×D₄	C₂³×C₆₁	1	2	yes	—
547	C₄×D₄	C₂³×C₆₁	1	4	yes	—
548	C₄×D₄	C₂³×C₆₁	1	4	yes	—
549	#117	—	2	2	no	—
550	#117	—	2	2	no	—
551	#117	—	2	2	no	—
552	#117	C₂³×C₆₁	1	2	yes	—
553	#117	C₂³×C₆₁	1	1	yes	characteristic
554	#117	C₂³×C₆₁	1	1	yes	characteristic
555	#117	C₂³×C₆₁	1	1	yes	characteristic
556	#117	C₂³×C₆₁	1	1	yes	characteristic
557	#117	C₂³×C₆₁	1	1	yes	characteristic
558	C₂×C₂²⋊C₄	—	2	2	no	—
559	C₂×C₂²⋊C₄	—	2	4	no	—
560	C₂×C₂²⋊C₄	—	2	2	no	—
561	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
564	#107	C₂³×C₆₁	1	4	yes	—
565	#107	C₂³×C₆₁	1	4	yes	—
566	#106	C₂³×C₆₁	1	4	yes	—
567	#106	C₂³×C₆₁	1	4	yes	—
568	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
569	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
570	#103	C₂³×C₆₁	1	4	yes	—
571	#103	C₂³×C₆₁	1	4	yes	—
572	#102	C₂³×C₆₁	1	4	yes	—
573	#102	C₂³×C₆₁	1	4	yes	—
574	#102	C₂³×C₆₁	1	4	yes	—
575	#102	C₂³×C₆₁	1	4	yes	—
576	#102	C₂³×C₆₁	1	4	yes	—
577	#102	C₂³×C₆₁	1	4	yes	—
578	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
579	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
580	#97	C₂³×C₆₁	1	2	yes	—
581	#97	C₂³×C₆₁	1	2	yes	—
582	#97	C₂³×C₆₁	1	2	yes	—
583	C₄×C₈	C₂³×C₆₁	1	2	yes	—
584	C₂⁴	—	2	1	no	—
585	C₂⁴	—	2	2	no	—
586	#41	—	4	2	no	—
587	#41	—	8	4	no	—
588	#41	—	8	4	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	2	no	—
591	C₂×Q₈	—	2	2	no	—
592	C₂×Q₈	—	4	2	no	—
593	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
594	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	4	2	no	—
605	C₂×D₄	—	4	2	no	—
606	C₂×D₄	—	4	2	no	—
607	C₂×D₄	—	8	4	no	—
608	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
609	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
610	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
611	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
612	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
619	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
620	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
623	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
624	SD₁₆	—	4	4	no	—
625	SD₁₆	—	4	4	no	—
626	D₈	—	4	4	no	—
627	D₈	—	4	4	no	—
628	M₁₆	—	4	2	no	—
629	C₂×C₈	—	4	2	no	—
630	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
631	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
642	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
643	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
644	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
645	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
646	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₂²⋊C₄	—	2	1	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
665	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
666	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
667	C₄²	—	2	2	no	—
668	C₄²	—	2	2	no	—
669	C₄²	—	2	2	no	—
670	C₄²	—	2	1	no	—
671	C₄²	—	2	1	no	—
672	C₄²	C₂×D₄×C₆₁	1	2	yes	—
673	C₄²	C₂×D₄×C₆₁	1	2	yes	—
674	C₄²	C₂×D₄×C₆₁	1	2	yes	—
675	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
676	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
677	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
678	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
679	C₂³	—	2	2	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	4	4	no	—
683	C₂³	—	8	4	no	—
684	C₂³	—	8	2	no	—
685	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
686	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
687	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
688	Q₈	—	2	4	no	—
689	Q₈	—	4	1	no	—
690	Q₈	—	4	2	no	—
691	Q₈	—	4	4	no	—
692	Q₈	—	8	2	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	4	no	—
695	D₄	—	2	4	no	—
696	D₄	—	4	1	no	—
697	D₄	—	4	1	no	—
698	D₄	—	4	1	no	—
699	D₄	—	4	4	no	—
700	D₄	—	4	2	no	—
701	D₄	—	4	4	no	—
702	D₄	—	4	4	no	—
703	D₄	—	8	4	no	—
704	D₄	—	8	2	no	—
705	D₄	—	8	2	no	—
706	D₄	—	8	4	no	—
707	D₄	—	8	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	4	2	no	—
718	C₂×C₄	—	4	2	no	—
719	C₂×C₄	—	8	2	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	—	8	4	no	—
723	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
724	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
726	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
730	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
731	C₈	—	2	4	no	—
732	C₈	—	2	4	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	4	4	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	4	no	—
745	C₂²	—	16	4	no	—
746	C₂²	—	16	2	no	—
747	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	1	no	—
754	C₄	—	2	1	no	—
755	C₄	—	4	4	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	C₆₁×#585	1	2	yes	—
760	C₂	—	4	1	no	—
761	C₂	—	4	1	no	—
762	C₂	—	4	1	no	—
763	C₂	—	8	4	no	—
764	C₂	—	8	2	no	—
765	C₂	C₆₁×#3449	1	1	yes	characteristic
766	C₂	C₆₁×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3510	C₂	semidirect
2. C₆₁×#3508	C₂	semidirect
3. C₆₁×#3257	C₂	semidirect
4. C₆₁×#3240	C₂	semidirect
5. C₆₁×#3235	C₂	semidirect
6. C₆₁×#3217	C₂	semidirect
7. C₆₁×#3213	C₂	semidirect
8. C₆₁×#3200	C₂	semidirect
9. C₆₁×#3199	C₂	semidirect
10. C₆₁×#3180	C₂	semidirect
11. C₆₁×#3171	C₂	semidirect
12. C₆₁×#3126	C₂	semidirect
13. C₆₁×#3122	C₂	semidirect
14. C₆₁×#3118	C₂	semidirect
15. C₆₁×#2923	C₂	semidirect
25. C₆₁×#542	C₂²	semidirect
27. C₆₁×#540	C₂²	semidirect
31. C₆₁×#533	C₂²	semidirect
32. C₆₁×#533	C₂²	semidirect
34. C₆₁×#532	C₂²	semidirect
35. C₂×#127×C₆₁	C₂²	semidirect
37. C₆₁×#529	C₂²	semidirect
38. C₂×#124×C₆₁	C₂²	semidirect
39. C₆₁×#519	C₂²	semidirect
40. C₆₁×#518	C₂²	semidirect
41. C₆₁×#518	C₂²	semidirect
43. C₆₁×#501	C₂²	semidirect
44. C₆₁×#501	C₂²	semidirect
47. C₆₁×#490	C₂²	semidirect
48. C₆₁×#490	C₂²	semidirect
49. C₆₁×#489	C₂²	semidirect
50. C₆₁×#489	C₂²	semidirect
51. C₆₁×#485	C₂²	semidirect
53. C₆₁×#482	C₂²	semidirect
54. C₆₁×#482	C₂²	semidirect
55. C₆₁×#479	C₂²	semidirect
56. C₆₁×#478	C₂²	semidirect
57. C₆₁×#476	C₂²	semidirect
58. C₆₁×#474	C₂²	semidirect
59. C₆₁×#469	C₂²	semidirect
60. C₆₁×#468	C₂²	semidirect
61. C₆₁×#466	C₂²	semidirect
62. C₆₁×#465	C₂²	semidirect
63. C₆₁×#463	C₂²	semidirect
64. C₆₁×#463	C₂²	semidirect
65. C₆₁×#460	C₂²	semidirect
67. C₆₁×#450	C₂²	semidirect
68. C₆₁×#448	C₂²	semidirect
70. C₆₁×#447	C₂²	semidirect
71. C₆₁×#442	C₂²	semidirect
72. C₆₁×#440	C₂²	semidirect
73. C₄×SD₁₆×C₆₁	C₂²	semidirect
74. C₄×D₈×C₆₁	C₂²	semidirect
75. C₆₁×#433	C₂²	semidirect
76. C₆₁×#433	C₂²	semidirect
77. C₆₁×#432	C₂²	semidirect
78. C₆₁×#432	C₂²	semidirect
79. C₆₁×#424	C₂²	semidirect
81. C₄×M₁₆×C₆₁	C₂²	semidirect
82. C₂×#97×C₆₁	C₂²	semidirect
349. #61017	C₆₁	direct (N × H)
377. #3510	C₂×C₆₁	semidirect
378. #3508	C₂×C₆₁	semidirect
379. #3257	C₂×C₆₁	semidirect
380. #3240	C₂×C₆₁	semidirect
381. #3235	C₂×C₆₁	semidirect
382. #3217	C₂×C₆₁	semidirect
383. #3213	C₂×C₆₁	semidirect
384. #3200	C₂×C₆₁	semidirect
385. #3199	C₂×C₆₁	semidirect
386. #3180	C₂×C₆₁	semidirect
387. #3171	C₂×C₆₁	semidirect
388. #3126	C₂×C₆₁	semidirect
389. #3122	C₂×C₆₁	semidirect
390. #3118	C₂×C₆₁	semidirect
391. #2923	C₂×C₆₁	semidirect
408. #542	C₂²×C₆₁	semidirect
410. #540	C₂²×C₆₁	semidirect
414. #533	C₂²×C₆₁	semidirect
415. #533	C₂²×C₆₁	semidirect
417. #532	C₂²×C₆₁	semidirect
418. C₂×#127	C₂²×C₆₁	semidirect
420. #529	C₂²×C₆₁	semidirect
421. C₂×#124	C₂²×C₆₁	semidirect
422. #519	C₂²×C₆₁	semidirect
423. #518	C₂²×C₆₁	semidirect
424. #518	C₂²×C₆₁	semidirect
426. #501	C₂²×C₆₁	semidirect
427. #501	C₂²×C₆₁	semidirect
430. #490	C₂²×C₆₁	semidirect
431. #490	C₂²×C₆₁	semidirect
432. #489	C₂²×C₆₁	semidirect
433. #489	C₂²×C₆₁	semidirect
434. #485	C₂²×C₆₁	semidirect
436. #482	C₂²×C₆₁	semidirect
437. #482	C₂²×C₆₁	semidirect
438. #479	C₂²×C₆₁	semidirect
439. #478	C₂²×C₆₁	semidirect
440. #476	C₂²×C₆₁	semidirect
441. #474	C₂²×C₆₁	semidirect
442. #469	C₂²×C₆₁	semidirect
443. #468	C₂²×C₆₁	semidirect
444. #466	C₂²×C₆₁	semidirect
445. #465	C₂²×C₆₁	semidirect
446. #463	C₂²×C₆₁	semidirect
447. #463	C₂²×C₆₁	semidirect
448. #460	C₂²×C₆₁	semidirect
450. #450	C₂²×C₆₁	semidirect
451. #448	C₂²×C₆₁	semidirect
453. #447	C₂²×C₆₁	semidirect
454. #442	C₂²×C₆₁	semidirect
455. #440	C₂²×C₆₁	semidirect
456. C₄×SD₁₆	C₂²×C₆₁	semidirect
457. C₄×D₈	C₂²×C₆₁	semidirect
458. #433	C₂²×C₆₁	semidirect
459. #433	C₂²×C₆₁	semidirect
460. #432	C₂²×C₆₁	semidirect
461. #432	C₂²×C₆₁	semidirect
462. #424	C₂²×C₆₁	semidirect
464. C₄×M₁₆	C₂²×C₆₁	semidirect
465. C₂×#97	C₂²×C₆₁	semidirect
466. C₆₁	#61017	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×#3510	2
C₆₁×#3508	2
C₆₁×#3257	2
C₆₁×#3240	2
C₆₁×#3235	2
C₆₁×#3217	2
C₆₁×#3213	2
C₆₁×#3200	2
C₆₁×#3199	2
C₆₁×#3180	2
C₆₁×#3171	2
C₆₁×#3126	2
C₆₁×#3122	2
C₆₁×#3118	2
C₆₁×#2923	2
#61017	61

Subgroups — C61×#61017 #29564450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61017 #29564450