Subgroups — C₆₁×#61018 #29564451

Order 15616.

1672 conjugacy classes of subgroups.

The subgroup lattice has 738 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
2	C₆₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3258	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3240	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3237	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3218	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3215	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3202	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3200	C₂	1	2	yes	maximal
10	C₆₁×#3181	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3172	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3127	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3123	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3121	C₂	1	4	yes	maximal, complemented
15	C₆₁×#2923	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#559	—	2	2	no	—
17	C₆₁×#557	—	2	2	no	—
18	C₆₁×#556	—	2	2	no	—
19	C₆₁×#556	—	2	2	no	—
20	C₆₁×#552	—	2	2	no	—
21	C₆₁×#552	—	2	2	no	—
22	C₆₁×#551	—	2	2	no	—
23	C₆₁×#551	—	2	2	no	—
24	C₆₁×#542	C₂²	1	2	yes	—
25	C₆₁×#542	C₂²	1	2	yes	—
26	C₆₁×#541	C₂²	1	2	yes	—
27	C₆₁×#541	C₂²	1	2	yes	complemented
28	C₆₁×#536	C₂²	1	2	yes	—
29	C₆₁×#536	C₂²	1	1	yes	characteristic
30	C₆₁×#535	C₂²	1	1	yes	characteristic
31	C₆₁×#533	C₂²	1	2	yes	—
32	C₆₁×#533	C₂²	1	1	yes	characteristic
33	C₆₁×#533	C₂²	1	2	yes	complemented
34	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
36	C₆₁×#529	C₂²	1	2	yes	—
37	C₆₁×#529	C₂²	1	2	yes	—
38	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×#519	C₂²	1	1	yes	characteristic
40	C₆₁×#519	C₂²	1	2	yes	complemented
41	C₆₁×#518	C₂²	1	1	yes	characteristic
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×#497	C₂²	1	2	yes	—
46	C₆₁×#497	C₂²	1	2	yes	—
47	C₆₁×#491	C₂²	1	2	yes	complemented
48	C₆₁×#491	C₂²	1	2	yes	complemented
49	C₆₁×#489	C₂²	1	2	yes	—
50	C₆₁×#489	C₂²	1	2	yes	—
51	C₆₁×#485	C₂²	1	4	yes	—
52	C₆₁×#485	C₂²	1	4	yes	—
53	C₆₁×#485	C₂²	1	4	yes	complemented
54	C₆₁×#482	C₂²	1	4	yes	—
55	C₆₁×#479	C₂²	1	4	yes	complemented
56	C₆₁×#478	C₂²	1	4	yes	—
57	C₆₁×#477	C₂²	1	4	yes	complemented
58	C₆₁×#475	C₂²	1	4	yes	complemented
59	C₆₁×#470	C₂²	1	4	yes	complemented
60	C₆₁×#468	C₂²	1	4	yes	—
61	C₆₁×#467	C₂²	1	4	yes	complemented
62	C₆₁×#465	C₂²	1	4	yes	—
63	C₆₁×#464	C₂²	1	4	yes	—
64	C₆₁×#464	C₂²	1	4	yes	—
65	C₆₁×#462	C₂²	1	4	yes	complemented
66	C₆₁×#461	C₂²	1	4	yes	—
67	C₆₁×#451	C₂²	1	4	yes	—
68	C₆₁×#451	C₂²	1	4	yes	complemented
69	C₆₁×#450	C₂²	1	4	yes	—
70	C₆₁×#448	C₂²	1	4	yes	—
71	C₆₁×#441	C₂²	1	4	yes	complemented
72	C₆₁×#440	C₂²	1	4	yes	—
73	C₄×Q₁₆×C₆₁	C₂²	1	4	yes	complemented
74	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	—
75	C₆₁×#433	C₂²	1	2	yes	—
76	C₆₁×#433	C₂²	1	2	yes	complemented
77	C₆₁×#432	C₂²	1	2	yes	—
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	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
85	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
87	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
88	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
89	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
90	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
91	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
92	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
93	C₄⋊Q₈×C₆₁	—	2	1	no	—
94	C₄⋊Q₈×C₆₁	—	2	2	no	—
95	C₄⋊Q₈×C₆₁	—	2	2	no	—
96	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
97	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
98	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
99	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
100	#127×C₆₁	—	2	1	no	—
101	#126×C₆₁	—	2	2	no	—
102	#126×C₆₁	—	2	2	no	—
103	#126×C₆₁	—	2	4	no	—
104	#126×C₆₁	—	2	4	no	—
105	#126×C₆₁	—	2	2	no	—
106	#126×C₆₁	—	2	2	no	—
107	#125×C₆₁	—	2	4	no	—
108	#125×C₆₁	—	2	4	no	—
109	#125×C₆₁	—	2	2	no	—
110	#125×C₆₁	—	2	2	no	—
111	#125×C₆₁	C₂³	1	2	yes	—
112	#125×C₆₁	C₂³	1	2	yes	—
113	#124×C₆₁	—	2	1	no	—
114	#124×C₆₁	—	2	2	no	—
115	#124×C₆₁	—	2	1	no	—
116	#124×C₆₁	—	2	2	no	—
117	#124×C₆₁	—	2	2	no	—
118	#124×C₆₁	—	2	2	no	—
119	#124×C₆₁	C₂³	1	2	yes	—
120	#124×C₆₁	C₂³	1	2	yes	—
121	#123×C₆₁	—	2	1	no	—
122	#123×C₆₁	—	2	1	no	—
123	#123×C₆₁	—	2	2	no	—
124	#123×C₆₁	—	2	2	no	—
125	#123×C₆₁	—	2	2	no	—
126	#123×C₆₁	—	2	2	no	—
127	#123×C₆₁	—	2	2	no	—
128	#123×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	—	2	2	no	—
133	C₂²⋊Q₈×C₆₁	—	2	2	no	—
134	C₂²⋊Q₈×C₆₁	—	2	2	no	—
135	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
136	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
137	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
138	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
139	#121×C₆₁	C₂³	1	2	yes	—
140	#121×C₆₁	C₂³	1	2	yes	—
141	#120×C₆₁	—	2	1	no	—
142	#120×C₆₁	—	2	1	no	—
143	C₄×Q₈×C₆₁	—	2	4	no	—
144	C₄×Q₈×C₆₁	—	2	2	no	—
145	C₄×Q₈×C₆₁	—	2	2	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	4	yes	—
151	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
152	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
153	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
154	C₄×D₄×C₆₁	—	2	2	no	—
155	C₄×D₄×C₆₁	—	2	2	no	—
156	C₄×D₄×C₆₁	—	2	2	no	—
157	C₄×D₄×C₆₁	D₄	1	2	yes	—
158	C₄×D₄×C₆₁	D₄	1	2	yes	—
159	C₄×D₄×C₆₁	D₄	1	2	yes	—
160	C₄×D₄×C₆₁	C₂³	1	2	yes	—
161	C₄×D₄×C₆₁	C₂³	1	2	yes	—
162	#117×C₆₁	—	2	2	no	—
163	#117×C₆₁	—	2	2	no	—
164	#117×C₆₁	—	2	2	no	—
165	#117×C₆₁	—	2	4	no	—
166	#117×C₆₁	—	2	2	no	—
167	#117×C₆₁	—	2	2	no	—
168	#117×C₆₁	C₂³	1	1	yes	characteristic
169	#117×C₆₁	C₂³	1	1	yes	characteristic
170	#117×C₆₁	C₂³	1	2	yes	—
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×C₄⋊C₄×C₆₁	—	2	2	no	—
175	C₂×C₂²⋊C₄×C₆₁	—	2	2	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	#103×C₆₁	C₂³	1	4	yes	—
189	#103×C₆₁	C₂³	1	4	yes	—
190	#103×C₆₁	C₂³	1	4	yes	—
191	#103×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	#41×C₆₁	—	4	2	no	—
202	C₂×Q₈×C₆₁	—	2	2	no	—
203	C₂×Q₈×C₆₁	—	2	1	no	—
204	C₂×Q₈×C₆₁	—	2	2	no	—
205	C₂×Q₈×C₆₁	—	2	2	no	—
206	C₂×Q₈×C₆₁	—	4	2	no	—
207	C₂×Q₈×C₆₁	—	4	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×Q₈×C₆₁	C₂⁴	1	4	yes	—
212	C₂×D₄×C₆₁	—	2	2	no	—
213	C₂×D₄×C₆₁	—	2	2	no	—
214	C₂×D₄×C₆₁	—	2	1	no	—
215	C₂×D₄×C₆₁	—	4	2	no	—
216	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
217	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
218	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
219	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₆₁	—	2	1	no	—
221	C₂²×C₄×C₆₁	—	2	2	no	—
222	C₂²×C₄×C₆₁	—	2	2	no	—
223	C₂²×C₄×C₆₁	—	2	2	no	—
224	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
230	Q₁₆×C₆₁	—	4	4	no	—
231	Q₁₆×C₆₁	—	4	4	no	—
232	SD₁₆×C₆₁	—	4	4	no	—
233	SD₁₆×C₆₁	—	4	4	no	—
234	M₁₆×C₆₁	—	4	2	no	—
235	C₂×C₈×C₆₁	—	4	2	no	—
236	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
237	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
238	C₄⋊C₄×C₆₁	—	2	2	no	—
239	C₄⋊C₄×C₆₁	—	2	2	no	—
240	C₄⋊C₄×C₆₁	—	2	4	no	—
241	C₄⋊C₄×C₆₁	—	2	2	no	—
242	C₄⋊C₄×C₆₁	—	2	2	no	—
243	C₄⋊C₄×C₆₁	—	2	2	no	—
244	C₄⋊C₄×C₆₁	—	2	2	no	—
245	C₄⋊C₄×C₆₁	—	2	4	no	—
246	C₄⋊C₄×C₆₁	—	2	4	no	—
247	C₄⋊C₄×C₆₁	—	2	2	no	—
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	4	no	—
252	C₄⋊C₄×C₆₁	—	2	4	no	—
253	C₄⋊C₄×C₆₁	—	2	4	no	—
254	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
258	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
260	C₂²⋊C₄×C₆₁	—	2	1	no	—
261	C₂²⋊C₄×C₆₁	—	2	1	no	—
262	C₂²⋊C₄×C₆₁	—	2	2	no	—
263	C₂²⋊C₄×C₆₁	—	2	4	no	—
264	C₂²⋊C₄×C₆₁	—	2	4	no	—
265	C₂²⋊C₄×C₆₁	—	2	2	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	2	no	—
271	C₂²⋊C₄×C₆₁	—	2	2	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	C₂×D₄	1	2	yes	—
276	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
277	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
278	C₄²×C₆₁	—	2	2	no	—
279	C₄²×C₆₁	—	2	2	no	—
280	C₄²×C₆₁	—	2	4	no	—
281	C₄²×C₆₁	—	2	4	no	—
282	C₄²×C₆₁	—	2	1	no	—
283	C₄²×C₆₁	—	2	1	no	—
284	C₄²×C₆₁	—	2	2	no	—
285	C₄²×C₆₁	C₂×D₄	1	2	yes	—
286	C₄²×C₆₁	C₂×D₄	1	2	yes	—
287	C₄²×C₆₁	C₂×D₄	1	2	yes	—
288	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
289	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
290	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
291	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
292	C₂³×C₆₁	—	2	2	no	—
293	C₂³×C₆₁	—	4	2	no	—
294	C₂³×C₆₁	—	8	2	no	—
295	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
296	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
297	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
298	Q₈×C₆₁	—	2	4	no	—
299	Q₈×C₆₁	—	2	4	no	—
300	Q₈×C₆₁	—	2	4	no	—
301	Q₈×C₆₁	—	4	1	no	—
302	Q₈×C₆₁	—	4	4	no	—
303	Q₈×C₆₁	—	4	2	no	—
304	Q₈×C₆₁	—	4	4	no	—
305	Q₈×C₆₁	—	8	2	no	—
306	D₄×C₆₁	—	2	4	no	—
307	D₄×C₆₁	—	4	1	no	—
308	D₄×C₆₁	—	4	1	no	—
309	D₄×C₆₁	—	4	1	no	—
310	D₄×C₆₁	—	4	2	no	—
311	D₄×C₆₁	—	8	2	no	—
312	D₄×C₆₁	—	8	2	no	—
313	C₂×C₄×C₆₁	—	2	2	no	—
314	C₂×C₄×C₆₁	—	2	2	no	—
315	C₂×C₄×C₆₁	—	2	2	no	—
316	C₂×C₄×C₆₁	—	2	4	no	—
317	C₂×C₄×C₆₁	—	2	2	no	—
318	C₂×C₄×C₆₁	—	2	2	no	—
319	C₂×C₄×C₆₁	—	2	4	no	—
320	C₂×C₄×C₆₁	—	2	2	no	—
321	C₂×C₄×C₆₁	—	4	2	no	—
322	C₂×C₄×C₆₁	—	4	2	no	—
323	C₂×C₄×C₆₁	—	4	2	no	—
324	C₂×C₄×C₆₁	—	4	4	no	—
325	C₂×C₄×C₆₁	—	4	2	no	—
326	C₂×C₄×C₆₁	—	8	2	no	—
327	C₂×C₄×C₆₁	—	8	2	no	—
328	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
336	C₈×C₆₁	—	2	4	no	—
337	C₈×C₆₁	—	2	4	no	—
338	#61018	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
339	C₂²×C₆₁	—	2	2	no	—
340	C₂²×C₆₁	—	2	2	no	—
341	C₂²×C₆₁	—	2	2	no	—
342	C₂²×C₆₁	—	2	1	no	—
343	C₂²×C₆₁	—	2	1	no	—
344	C₂²×C₆₁	—	2	1	no	—
345	C₂²×C₆₁	—	4	2	no	—
346	C₂²×C₆₁	—	4	2	no	—
347	C₂²×C₆₁	—	4	2	no	—
348	C₂²×C₆₁	—	16	2	no	—
349	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
350	C₄×C₆₁	—	2	2	no	—
351	C₄×C₆₁	—	2	2	no	—
352	C₄×C₆₁	—	2	2	no	—
353	C₄×C₆₁	—	2	2	no	—
354	C₄×C₆₁	—	2	1	no	—
355	C₄×C₆₁	—	2	1	no	—
356	C₄×C₆₁	—	2	1	no	—
357	C₄×C₆₁	—	4	2	no	—
358	C₄×C₆₁	—	4	2	no	—
359	C₄×C₆₁	—	4	4	no	—
360	C₄×C₆₁	—	4	2	no	—
361	C₄×C₆₁	—	4	4	no	—
362	C₄×C₆₁	#585	1	2	yes	—
363	#3510	C₂×C₆₁	1	1	yes	characteristic
364	#3509	C₂×C₆₁	1	1	yes	characteristic, complemented
365	#3258	C₂×C₆₁	1	4	yes	complemented
366	#3240	C₂×C₆₁	1	2	yes	complemented
367	#3237	C₂×C₆₁	1	2	yes	complemented
368	#3218	C₂×C₆₁	1	2	yes	complemented
369	#3215	C₂×C₆₁	1	2	yes	complemented
370	#3202	C₂×C₆₁	1	2	yes	complemented
371	#3200	C₂×C₆₁	1	2	yes	—
372	#3181	C₂×C₆₁	1	2	yes	complemented
373	#3172	C₂×C₆₁	1	2	yes	complemented
374	#3127	C₂×C₆₁	1	2	yes	complemented
375	#3123	C₂×C₆₁	1	2	yes	complemented
376	#3121	C₂×C₆₁	1	4	yes	complemented
377	#2923	C₂×C₆₁	1	1	yes	characteristic, complemented
378	C₂×C₆₁	—	4	1	no	—
379	C₂×C₆₁	—	4	1	no	—
380	C₂×C₆₁	—	4	1	no	—
381	C₂×C₆₁	—	8	2	no	—
382	C₂×C₆₁	#3449	1	1	yes	characteristic
383	C₂×C₆₁	#3586	1	2	yes	—
384	#559	—	2	2	no	—
385	#557	—	2	2	no	—
386	#556	—	2	2	no	—
387	#556	—	2	2	no	—
388	#552	—	2	2	no	—
389	#552	—	2	2	no	—
390	#551	—	2	2	no	—
391	#551	—	2	2	no	—
392	#542	C₂²×C₆₁	1	2	yes	—
393	#542	C₂²×C₆₁	1	2	yes	—
394	#541	C₂²×C₆₁	1	2	yes	—
395	#541	C₂²×C₆₁	1	2	yes	complemented
396	#536	C₂²×C₆₁	1	2	yes	—
397	#536	C₂²×C₆₁	1	1	yes	characteristic
398	#535	C₂²×C₆₁	1	1	yes	characteristic
399	#533	C₂²×C₆₁	1	2	yes	—
400	#533	C₂²×C₆₁	1	1	yes	characteristic
401	#533	C₂²×C₆₁	1	2	yes	complemented
402	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
403	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
404	#529	C₂²×C₆₁	1	2	yes	—
405	#529	C₂²×C₆₁	1	2	yes	—
406	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
407	#519	C₂²×C₆₁	1	1	yes	characteristic
408	#519	C₂²×C₆₁	1	2	yes	complemented
409	#518	C₂²×C₆₁	1	1	yes	characteristic
410	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
411	#501	C₂²×C₆₁	1	2	yes	complemented
412	#501	C₂²×C₆₁	1	2	yes	complemented
413	#497	C₂²×C₆₁	1	2	yes	—
414	#497	C₂²×C₆₁	1	2	yes	—
415	#491	C₂²×C₆₁	1	2	yes	complemented
416	#491	C₂²×C₆₁	1	2	yes	complemented
417	#489	C₂²×C₆₁	1	2	yes	—
418	#489	C₂²×C₆₁	1	2	yes	—
419	#485	C₂²×C₆₁	1	4	yes	—
420	#485	C₂²×C₆₁	1	4	yes	—
421	#485	C₂²×C₆₁	1	4	yes	complemented
422	#482	C₂²×C₆₁	1	4	yes	—
423	#479	C₂²×C₆₁	1	4	yes	complemented
424	#478	C₂²×C₆₁	1	4	yes	—
425	#477	C₂²×C₆₁	1	4	yes	complemented
426	#475	C₂²×C₆₁	1	4	yes	complemented
427	#470	C₂²×C₆₁	1	4	yes	complemented
428	#468	C₂²×C₆₁	1	4	yes	—
429	#467	C₂²×C₆₁	1	4	yes	complemented
430	#465	C₂²×C₆₁	1	4	yes	—
431	#464	C₂²×C₆₁	1	4	yes	—
432	#464	C₂²×C₆₁	1	4	yes	—
433	#462	C₂²×C₆₁	1	4	yes	complemented
434	#461	C₂²×C₆₁	1	4	yes	—
435	#451	C₂²×C₆₁	1	4	yes	—
436	#451	C₂²×C₆₁	1	4	yes	complemented
437	#450	C₂²×C₆₁	1	4	yes	—
438	#448	C₂²×C₆₁	1	4	yes	—
439	#441	C₂²×C₆₁	1	4	yes	complemented
440	#440	C₂²×C₆₁	1	4	yes	—
441	C₄×Q₁₆	C₂²×C₆₁	1	4	yes	complemented
442	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	—
443	#433	C₂²×C₆₁	1	2	yes	—
444	#433	C₂²×C₆₁	1	2	yes	complemented
445	#432	C₂²×C₆₁	1	2	yes	—
446	#432	C₂²×C₆₁	1	2	yes	complemented
447	#424	C₂²×C₆₁	1	2	yes	complemented
448	#408	C₂²×C₆₁	1	2	yes	—
449	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
450	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic, complemented
451	C₆₁	#61018	1	1	yes	characteristic, direct product factor, Sylow
452	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
453	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
454	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
455	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
456	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
457	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
458	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
459	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
460	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
461	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
462	C₄⋊Q₈	—	2	1	no	—
463	C₄⋊Q₈	—	2	2	no	—
464	C₄⋊Q₈	—	2	2	no	—
465	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
466	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
467	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
468	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
469	#127	—	2	1	no	—
470	#126	—	2	2	no	—
471	#126	—	2	2	no	—
472	#126	—	2	4	no	—
473	#126	—	2	4	no	—
474	#126	—	2	2	no	—
475	#126	—	2	2	no	—
476	#125	—	2	4	no	—
477	#125	—	2	4	no	—
478	#125	—	2	2	no	—
479	#125	—	2	2	no	—
480	#125	C₂³×C₆₁	1	2	yes	—
481	#125	C₂³×C₆₁	1	2	yes	—
482	#124	—	2	1	no	—
483	#124	—	2	2	no	—
484	#124	—	2	1	no	—
485	#124	—	2	2	no	—
486	#124	—	2	2	no	—
487	#124	—	2	2	no	—
488	#124	C₂³×C₆₁	1	2	yes	—
489	#124	C₂³×C₆₁	1	2	yes	—
490	#123	—	2	1	no	—
491	#123	—	2	1	no	—
492	#123	—	2	2	no	—
493	#123	—	2	2	no	—
494	#123	—	2	2	no	—
495	#123	—	2	2	no	—
496	#123	—	2	2	no	—
497	#123	—	2	2	no	—
498	C₂²⋊Q₈	—	2	2	no	—
499	C₂²⋊Q₈	—	2	2	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	—	2	2	no	—
504	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
505	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
506	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
507	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
508	#121	C₂³×C₆₁	1	2	yes	—
509	#121	C₂³×C₆₁	1	2	yes	—
510	#120	—	2	1	no	—
511	#120	—	2	1	no	—
512	C₄×Q₈	—	2	2	no	—
513	C₄×Q₈	—	2	4	no	—
514	C₄×Q₈	—	2	2	no	—
515	C₄×Q₈	—	2	2	no	—
516	C₄×Q₈	—	2	2	no	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	D₄×C₆₁	1	2	yes	—
519	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
520	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
521	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
522	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	D₄×C₆₁	1	2	yes	—
527	C₄×D₄	D₄×C₆₁	1	2	yes	—
528	C₄×D₄	D₄×C₆₁	1	2	yes	—
529	C₄×D₄	C₂³×C₆₁	1	2	yes	—
530	C₄×D₄	C₂³×C₆₁	1	2	yes	—
531	#117	—	2	2	no	—
532	#117	—	2	2	no	—
533	#117	—	2	2	no	—
534	#117	—	2	4	no	—
535	#117	—	2	2	no	—
536	#117	—	2	2	no	—
537	#117	C₂³×C₆₁	1	1	yes	characteristic
538	#117	C₂³×C₆₁	1	1	yes	characteristic
539	#117	C₂³×C₆₁	1	2	yes	—
540	#117	C₂³×C₆₁	1	1	yes	characteristic
541	#117	C₂³×C₆₁	1	1	yes	characteristic
542	#117	C₂³×C₆₁	1	1	yes	characteristic
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₂²⋊C₄	—	2	2	no	—
545	C₂×C₂²⋊C₄	—	2	2	no	—
546	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
549	#107	C₂³×C₆₁	1	4	yes	—
550	#107	C₂³×C₆₁	1	4	yes	—
551	#106	C₂³×C₆₁	1	4	yes	—
552	#106	C₂³×C₆₁	1	4	yes	—
553	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
554	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
555	#103	C₂³×C₆₁	1	4	yes	—
556	#103	C₂³×C₆₁	1	4	yes	—
557	#103	C₂³×C₆₁	1	4	yes	—
558	#103	C₂³×C₆₁	1	4	yes	—
559	#103	C₂³×C₆₁	1	4	yes	—
560	#103	C₂³×C₆₁	1	4	yes	—
561	#102	C₂³×C₆₁	1	4	yes	—
562	#102	C₂³×C₆₁	1	4	yes	—
563	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
564	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
565	#97	C₂³×C₆₁	1	2	yes	—
566	#97	C₂³×C₆₁	1	2	yes	—
567	#97	C₂³×C₆₁	1	2	yes	—
568	C₄×C₈	C₂³×C₆₁	1	2	yes	—
569	C₂⁴	—	2	1	no	—
570	#41	—	4	2	no	—
571	C₂×Q₈	—	2	2	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	—	4	2	no	—
576	C₂×Q₈	—	4	2	no	—
577	C₂×Q₈	—	4	2	no	—
578	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
579	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
580	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	4	2	no	—
585	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
586	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
587	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
588	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
594	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
595	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
599	Q₁₆	—	4	4	no	—
600	Q₁₆	—	4	4	no	—
601	SD₁₆	—	4	4	no	—
602	SD₁₆	—	4	4	no	—
603	M₁₆	—	4	2	no	—
604	C₂×C₈	—	4	2	no	—
605	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
606	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
624	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
625	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
627	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
645	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
646	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
647	C₄²	—	2	2	no	—
648	C₄²	—	2	2	no	—
649	C₄²	—	2	4	no	—
650	C₄²	—	2	4	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	2	2	no	—
654	C₄²	C₂×D₄×C₆₁	1	2	yes	—
655	C₄²	C₂×D₄×C₆₁	1	2	yes	—
656	C₄²	C₂×D₄×C₆₁	1	2	yes	—
657	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
658	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
659	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
660	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
661	C₂³	—	2	2	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	8	2	no	—
664	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
665	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
666	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
667	Q₈	—	2	4	no	—
668	Q₈	—	2	4	no	—
669	Q₈	—	2	4	no	—
670	Q₈	—	4	1	no	—
671	Q₈	—	4	4	no	—
672	Q₈	—	4	2	no	—
673	Q₈	—	4	4	no	—
674	Q₈	—	8	2	no	—
675	D₄	—	2	4	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	4	1	no	—
679	D₄	—	4	2	no	—
680	D₄	—	8	2	no	—
681	D₄	—	8	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	2	no	—
695	C₂×C₄	—	8	2	no	—
696	C₂×C₄	—	8	2	no	—
697	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
698	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
699	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
704	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
705	C₈	—	2	4	no	—
706	C₈	—	2	4	no	—
707	C₂²	—	2	2	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	1	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	16	2	no	—
717	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	1	no	—
723	C₄	—	2	1	no	—
724	C₄	—	2	1	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	4	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	4	no	—
730	C₄	C₆₁×#585	1	2	yes	—
731	C₂	—	4	1	no	—
732	C₂	—	4	1	no	—
733	C₂	—	4	1	no	—
734	C₂	—	8	2	no	—
735	C₂	C₆₁×#3449	1	1	yes	characteristic
736	C₂	C₆₁×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#535	C₂²
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
2. C₆₁×#3509	C₂	semidirect
3. C₆₁×#3258	C₂	semidirect
4. C₆₁×#3240	C₂	semidirect
5. C₆₁×#3237	C₂	semidirect
6. C₆₁×#3218	C₂	semidirect
7. C₆₁×#3215	C₂	semidirect
8. C₆₁×#3202	C₂	semidirect
10. C₆₁×#3181	C₂	semidirect
11. C₆₁×#3172	C₂	semidirect
12. C₆₁×#3127	C₂	semidirect
13. C₆₁×#3123	C₂	semidirect
14. C₆₁×#3121	C₂	semidirect
15. C₆₁×#2923	C₂	semidirect
27. C₆₁×#541	C₂²	semidirect
33. C₆₁×#533	C₂²	semidirect
34. C₆₁×#533	C₂²	semidirect
35. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
40. C₆₁×#519	C₂²	semidirect
43. C₆₁×#501	C₂²	semidirect
44. C₆₁×#501	C₂²	semidirect
47. C₆₁×#491	C₂²	semidirect
48. C₆₁×#491	C₂²	semidirect
53. C₆₁×#485	C₂²	semidirect
55. C₆₁×#479	C₂²	semidirect
57. C₆₁×#477	C₂²	semidirect
58. C₆₁×#475	C₂²	semidirect
59. C₆₁×#470	C₂²	semidirect
61. C₆₁×#467	C₂²	semidirect
65. C₆₁×#462	C₂²	semidirect
68. C₆₁×#451	C₂²	semidirect
71. C₆₁×#441	C₂²	semidirect
73. C₄×Q₁₆×C₆₁	C₂²	semidirect
76. C₆₁×#433	C₂²	semidirect
78. C₆₁×#432	C₂²	semidirect
79. C₆₁×#424	C₂²	semidirect
81. C₄×M₁₆×C₆₁	C₂²	semidirect
82. C₂×#97×C₆₁	C₂²	semidirect
338. #61018	C₆₁	direct (N × H)
364. #3509	C₂×C₆₁	semidirect
365. #3258	C₂×C₆₁	semidirect
366. #3240	C₂×C₆₁	semidirect
367. #3237	C₂×C₆₁	semidirect
368. #3218	C₂×C₆₁	semidirect
369. #3215	C₂×C₆₁	semidirect
370. #3202	C₂×C₆₁	semidirect
372. #3181	C₂×C₆₁	semidirect
373. #3172	C₂×C₆₁	semidirect
374. #3127	C₂×C₆₁	semidirect
375. #3123	C₂×C₆₁	semidirect
376. #3121	C₂×C₆₁	semidirect
377. #2923	C₂×C₆₁	semidirect
395. #541	C₂²×C₆₁	semidirect
401. #533	C₂²×C₆₁	semidirect
402. #533	C₂²×C₆₁	semidirect
403. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
408. #519	C₂²×C₆₁	semidirect
411. #501	C₂²×C₆₁	semidirect
412. #501	C₂²×C₆₁	semidirect
415. #491	C₂²×C₆₁	semidirect
416. #491	C₂²×C₆₁	semidirect
421. #485	C₂²×C₆₁	semidirect
423. #479	C₂²×C₆₁	semidirect
425. #477	C₂²×C₆₁	semidirect
426. #475	C₂²×C₆₁	semidirect
427. #470	C₂²×C₆₁	semidirect
429. #467	C₂²×C₆₁	semidirect
433. #462	C₂²×C₆₁	semidirect
436. #451	C₂²×C₆₁	semidirect
439. #441	C₂²×C₆₁	semidirect
441. C₄×Q₁₆	C₂²×C₆₁	semidirect
444. #433	C₂²×C₆₁	semidirect
446. #432	C₂²×C₆₁	semidirect
447. #424	C₂²×C₆₁	semidirect
449. C₄×M₁₆	C₂²×C₆₁	semidirect
450. C₂×#97	C₂²×C₆₁	semidirect
451. C₆₁	#61018	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×#3509	2
C₆₁×#3258	2
C₆₁×#3240	2
C₆₁×#3237	2
C₆₁×#3218	2
C₆₁×#3215	2
C₆₁×#3202	2
C₆₁×#3200	2
C₆₁×#3181	2
C₆₁×#3172	2
C₆₁×#3127	2
C₆₁×#3123	2
C₆₁×#3121	2
C₆₁×#2923	2
#61018	61

Subgroups — C61×#61018 #29564451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61018 #29564451