Subgroups — C₆₁×#61334 #29564767

Order 15616.

1794 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3506	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3377	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3375	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3371	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3368	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3136	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3135	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3083	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3043	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#2947	C₂	1	2	yes	maximal, complemented
15	C₂×C₆₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#137×C₆₁	C₂²	1	2	yes	—
17	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#559	C₂²	1	4	yes	—
19	Q₈²×C₆₁	—	2	1	no	—
20	Q₈²×C₆₁	C₂²	1	2	yes	complemented
21	C₆₁×#557	—	2	1	no	—
22	C₆₁×#557	—	2	2	no	—
23	C₆₁×#557	C₂²	1	4	yes	complemented
24	C₆₁×#557	C₂²	1	2	yes	complemented
25	C₆₁×#556	C₂²	1	2	yes	—
26	C₆₁×#555	—	2	1	no	—
27	C₆₁×#553	—	2	2	no	—
28	C₆₁×#550	C₂²	1	2	yes	—
29	C₆₁×#547	—	2	1	no	—
30	C₆₁×#544	—	2	2	no	—
31	C₆₁×#544	C₂²	1	2	yes	—
32	C₆₁×#538	—	2	2	no	—
33	C₆₁×#535	C₂²	1	2	yes	—
34	C₆₁×#533	—	2	2	no	—
35	C₆₁×#533	C₂²	1	1	yes	characteristic
36	C₆₁×#533	C₂²	1	1	yes	characteristic
37	C₆₁×#532	C₂²	1	1	yes	characteristic
38	C₆₁×#525	—	2	2	no	—
39	C₆₁×#520	C₂²	1	2	yes	—
40	C₆₁×#519	C₂²	1	2	yes	—
41	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
43	C₆₁×#491	C₂²	1	2	yes	complemented
44	C₆₁×#490	C₂²	1	4	yes	—
45	C₆₁×#490	C₂²	1	2	yes	complemented
46	C₆₁×#489	C₂²	1	4	yes	—
47	C₆₁×#489	C₂²	1	2	yes	complemented
48	C₆₁×#489	C₂²	1	2	yes	complemented
49	C₆₁×#488	C₂²	1	4	yes	—
50	C₆₁×#486	C₂²	1	4	yes	—
51	C₆₁×#479	C₂²	1	4	yes	complemented
52	C₆₁×#478	C₂²	1	4	yes	—
53	C₆₁×#478	C₂²	1	4	yes	complemented
54	C₆₁×#477	C₂²	1	4	yes	complemented
55	C₆₁×#476	C₂²	1	2	yes	—
56	C₆₁×#474	C₂²	1	2	yes	—
57	C₆₁×#474	C₂²	1	4	yes	complemented
58	C₆₁×#464	C₂²	1	4	yes	—
59	C₆₁×#464	C₂²	1	4	yes	—
60	C₆₁×#464	C₂²	1	4	yes	complemented
61	C₆₁×#462	C₂²	1	2	yes	complemented
62	C₆₁×#460	C₂²	1	4	yes	—
63	C₆₁×#460	C₂²	1	4	yes	—
64	C₆₁×#460	C₂²	1	2	yes	complemented
65	C₆₁×#446	C₂²	1	4	yes	complemented
66	C₆₁×#446	C₂²	1	4	yes	complemented
67	C₆₁×#441	C₂²	1	4	yes	complemented
68	C₆₁×#440	C₂²	1	4	yes	—
69	C₆₁×#440	C₂²	1	4	yes	—
70	C₆₁×#440	C₂²	1	4	yes	complemented
71	C₄×Q₁₆×C₆₁	C₂²	1	4	yes	complemented
72	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	complemented
73	C₆₁×#428	C₂²	1	2	yes	—
74	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
75	C₆₁×#424	C₂²	1	2	yes	—
76	C₆₁×#423	C₂²	1	1	yes	characteristic
77	C₆₁×#418	C₂²	1	2	yes	—
78	C₆₁×#417	C₂²	1	2	yes	—
79	C₆₁×#416	C₂²	1	2	yes	—
80	C₆₁×#416	C₂²	1	2	yes	—
81	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
82	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
83	C₆₁×#405	C₂²	1	2	yes	—
84	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
85	C₂×#41×C₆₁	—	2	2	no	—
86	C₂×#41×C₆₁	C₂³	1	2	yes	—
87	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₆₁	—	2	1	no	—
90	#137×C₆₁	—	2	8	no	—
91	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
92	C₂×SD₁₆×C₆₁	—	2	4	no	—
93	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
95	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
96	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₆₁	—	2	2	no	—
99	C₄⋊Q₈×C₆₁	—	2	4	no	—
100	C₄⋊Q₈×C₆₁	—	2	2	no	—
101	C₄⋊Q₈×C₆₁	—	2	4	no	—
102	C₄⋊Q₈×C₆₁	—	2	2	no	—
103	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
104	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
105	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
106	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
107	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
108	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
109	#127×C₆₁	C₂³	1	1	yes	characteristic
110	#127×C₆₁	C₂³	1	4	yes	—
111	#126×C₆₁	—	2	4	no	—
112	#125×C₆₁	—	2	4	no	—
113	#125×C₆₁	—	2	4	no	—
114	#125×C₆₁	—	2	4	no	—
115	#125×C₆₁	—	2	2	no	—
116	#125×C₆₁	D₄	1	2	yes	—
117	#125×C₆₁	C₂³	1	2	yes	—
118	#125×C₆₁	C₂³	1	4	yes	—
119	#124×C₆₁	—	2	4	no	—
120	#124×C₆₁	C₂³	1	2	yes	—
121	#124×C₆₁	C₂³	1	4	yes	—
122	#123×C₆₁	—	2	4	no	—
123	#123×C₆₁	—	2	4	no	—
124	C₂²⋊Q₈×C₆₁	—	2	2	no	—
125	C₂²⋊Q₈×C₆₁	—	2	1	no	—
126	C₂²⋊Q₈×C₆₁	—	2	1	no	—
127	C₂²⋊Q₈×C₆₁	—	2	4	no	—
128	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
129	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
130	#121×C₆₁	—	2	1	no	—
131	#121×C₆₁	—	2	1	no	—
132	#121×C₆₁	—	2	2	no	—
133	#121×C₆₁	—	2	2	no	—
134	#121×C₆₁	—	2	4	no	—
135	#121×C₆₁	—	2	2	no	—
136	#120×C₆₁	—	2	4	no	—
137	C₄×Q₈×C₆₁	—	2	2	no	—
138	C₄×Q₈×C₆₁	—	2	4	no	—
139	C₄×Q₈×C₆₁	—	2	2	no	—
140	C₄×Q₈×C₆₁	—	2	2	no	—
141	C₄×Q₈×C₆₁	—	2	2	no	—
142	C₄×Q₈×C₆₁	—	2	1	no	—
143	C₄×Q₈×C₆₁	—	2	1	no	—
144	C₄×Q₈×C₆₁	—	2	1	no	—
145	C₄×Q₈×C₆₁	—	2	1	no	—
146	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
147	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
148	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
149	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
150	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
151	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
152	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
153	C₄×D₄×C₆₁	—	2	4	no	—
154	C₄×D₄×C₆₁	—	2	4	no	—
155	C₄×D₄×C₆₁	—	2	1	no	—
156	C₄×D₄×C₆₁	—	2	1	no	—
157	C₄×D₄×C₆₁	—	2	1	no	—
158	C₄×D₄×C₆₁	—	2	1	no	—
159	C₄×D₄×C₆₁	C₂³	1	2	yes	—
160	C₄×D₄×C₆₁	C₂³	1	4	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	4	no	—
165	#117×C₆₁	C₂³	1	2	yes	—
166	#117×C₆₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
168	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
169	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
172	C₂×C₄²×C₆₁	—	2	1	no	—
173	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
174	#107×C₆₁	C₂³	1	4	yes	—
175	#107×C₆₁	C₂³	1	4	yes	—
176	#106×C₆₁	C₂³	1	4	yes	—
177	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
178	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
179	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
180	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
181	#103×C₆₁	C₂³	1	4	yes	—
182	#103×C₆₁	C₂³	1	2	yes	—
183	#103×C₆₁	C₂³	1	2	yes	—
184	#103×C₆₁	C₂³	1	2	yes	—
185	#103×C₆₁	C₂³	1	2	yes	—
186	#103×C₆₁	C₂³	1	4	yes	—
187	#102×C₆₁	C₂³	1	4	yes	—
188	#102×C₆₁	C₂³	1	2	yes	—
189	#102×C₆₁	C₂³	1	2	yes	—
190	#102×C₆₁	C₂³	1	2	yes	—
191	#102×C₆₁	C₂³	1	2	yes	—
192	#102×C₆₁	C₂³	1	4	yes	—
193	#102×C₆₁	C₂³	1	4	yes	—
194	#102×C₆₁	C₂³	1	4	yes	—
195	#97×C₆₁	C₂³	1	2	yes	—
196	#97×C₆₁	C₂³	1	2	yes	—
197	#97×C₆₁	C₂³	1	4	yes	—
198	C₄×C₈×C₆₁	C₂³	1	4	yes	—
199	C₂⁴×C₆₁	—	2	1	no	—
200	#41×C₆₁	—	2	4	no	—
201	#41×C₆₁	—	2	4	no	—
202	#41×C₆₁	—	8	4	no	—
203	C₂×Q₈×C₆₁	—	2	1	no	—
204	C₂×Q₈×C₆₁	—	2	1	no	—
205	C₂×Q₈×C₆₁	—	2	1	no	—
206	C₂×Q₈×C₆₁	—	2	4	no	—
207	C₂×Q₈×C₆₁	—	2	2	no	—
208	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
210	C₂×Q₈×C₆₁	#41	1	4	yes	complemented
211	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
212	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
213	C₂×D₄×C₆₁	—	2	2	no	—
214	C₂×D₄×C₆₁	—	2	1	no	—
215	C₂×D₄×C₆₁	—	2	1	no	—
216	C₂×D₄×C₆₁	—	2	4	no	—
217	C₂×D₄×C₆₁	—	2	1	no	—
218	C₂×D₄×C₆₁	—	2	4	no	—
219	C₂×D₄×C₆₁	—	2	2	no	—
220	C₂×D₄×C₆₁	—	2	2	no	—
221	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
222	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₆₁	—	2	1	no	—
224	C₂²×C₄×C₆₁	—	2	1	no	—
225	C₂²×C₄×C₆₁	—	2	1	no	—
226	C₂²×C₄×C₆₁	—	2	2	no	—
227	C₂²×C₄×C₆₁	—	2	2	no	—
228	C₂²×C₄×C₆₁	—	2	4	no	—
229	C₂²×C₄×C₆₁	—	2	2	no	—
230	C₂²×C₄×C₆₁	—	8	2	no	—
231	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
234	Q₁₆×C₆₁	—	2	8	no	—
235	SD₁₆×C₆₁	—	2	8	no	—
236	SD₁₆×C₆₁	—	2	8	no	—
237	M₁₆×C₆₁	—	2	4	no	—
238	C₂×C₈×C₆₁	—	2	2	no	—
239	C₂×C₈×C₆₁	—	2	2	no	—
240	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
241	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
242	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
243	C₄⋊C₄×C₆₁	—	2	1	no	—
244	C₄⋊C₄×C₆₁	—	2	4	no	—
245	C₄⋊C₄×C₆₁	—	2	2	no	—
246	C₄⋊C₄×C₆₁	—	2	2	no	—
247	C₄⋊C₄×C₆₁	—	2	1	no	—
248	C₄⋊C₄×C₆₁	—	2	1	no	—
249	C₄⋊C₄×C₆₁	—	2	4	no	—
250	C₄⋊C₄×C₆₁	—	2	4	no	—
251	C₄⋊C₄×C₆₁	—	2	1	no	—
252	C₄⋊C₄×C₆₁	—	2	2	no	—
253	C₄⋊C₄×C₆₁	—	2	1	no	—
254	C₄⋊C₄×C₆₁	—	2	1	no	—
255	C₄⋊C₄×C₆₁	—	2	4	no	—
256	C₄⋊C₄×C₆₁	—	2	4	no	—
257	C₄⋊C₄×C₆₁	—	2	2	no	—
258	C₄⋊C₄×C₆₁	—	2	4	no	—
259	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
263	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
264	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
265	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
267	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
268	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
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	4	no	—
273	C₂²⋊C₄×C₆₁	—	2	4	no	—
274	C₂²⋊C₄×C₆₁	—	2	2	no	—
275	C₂²⋊C₄×C₆₁	—	2	4	no	—
276	C₂²⋊C₄×C₆₁	—	2	2	no	—
277	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	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	4	no	—
283	C₄²×C₆₁	—	2	2	no	—
284	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₆₁	C₂⁴	1	4	yes	—
287	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
288	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
289	C₂³×C₆₁	—	2	2	no	—
290	C₂³×C₆₁	—	2	2	no	—
291	C₂³×C₆₁	—	4	2	no	—
292	C₂³×C₆₁	—	8	1	no	—
293	C₂³×C₆₁	—	8	1	no	—
294	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
295	Q₈×C₆₁	—	2	4	no	—
296	Q₈×C₆₁	—	2	2	no	—
297	Q₈×C₆₁	—	2	2	no	—
298	Q₈×C₆₁	—	2	2	no	—
299	Q₈×C₆₁	—	4	2	no	—
300	Q₈×C₆₁	—	4	2	no	—
301	Q₈×C₆₁	—	4	2	no	—
302	Q₈×C₆₁	—	8	1	no	—
303	Q₈×C₆₁	—	8	4	no	—
304	Q₈×C₆₁	C₂×#41	1	4	yes	—
305	D₄×C₆₁	—	2	2	no	—
306	D₄×C₆₁	—	2	2	no	—
307	D₄×C₆₁	—	2	2	no	—
308	D₄×C₆₁	—	2	2	no	—
309	D₄×C₆₁	—	4	2	no	—
310	D₄×C₆₁	—	4	4	no	—
311	D₄×C₆₁	—	4	2	no	—
312	D₄×C₆₁	—	8	1	no	—
313	D₄×C₆₁	—	8	4	no	—
314	D₄×C₆₁	—	8	4	no	—
315	C₂×C₄×C₆₁	—	2	4	no	—
316	C₂×C₄×C₆₁	—	2	2	no	—
317	C₂×C₄×C₆₁	—	2	2	no	—
318	C₂×C₄×C₆₁	—	2	2	no	—
319	C₂×C₄×C₆₁	—	2	2	no	—
320	C₂×C₄×C₆₁	—	2	2	no	—
321	C₂×C₄×C₆₁	—	2	2	no	—
322	C₂×C₄×C₆₁	—	4	1	no	—
323	C₂×C₄×C₆₁	—	4	1	no	—
324	C₂×C₄×C₆₁	—	4	4	no	—
325	C₂×C₄×C₆₁	—	4	4	no	—
326	C₂×C₄×C₆₁	—	8	2	no	—
327	C₂×C₄×C₆₁	—	8	4	no	—
328	C₂×C₄×C₆₁	—	8	1	no	—
329	C₂×C₄×C₆₁	—	8	1	no	—
330	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
333	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
334	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
338	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
339	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
340	C₈×C₆₁	—	2	2	no	—
341	C₈×C₆₁	—	2	4	no	—
342	C₈×C₆₁	—	2	2	no	—
343	#61334	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₂²×C₆₁	—	2	1	no	—
345	C₂²×C₆₁	—	2	1	no	—
346	C₂²×C₆₁	—	4	2	no	—
347	C₂²×C₆₁	—	4	2	no	—
348	C₂²×C₆₁	—	4	2	no	—
349	C₂²×C₆₁	—	4	2	no	—
350	C₂²×C₆₁	—	4	2	no	—
351	C₂²×C₆₁	—	4	2	no	—
352	C₂²×C₆₁	—	8	4	no	—
353	C₂²×C₆₁	#548	1	2	yes	—
354	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
355	C₄×C₆₁	—	2	1	no	—
356	C₄×C₆₁	—	2	1	no	—
357	C₄×C₆₁	—	2	4	no	—
358	C₄×C₆₁	—	2	1	no	—
359	C₄×C₆₁	—	2	1	no	—
360	C₄×C₆₁	—	2	4	no	—
361	C₄×C₆₁	—	2	4	no	—
362	C₄×C₆₁	—	4	2	no	—
363	C₄×C₆₁	—	4	2	no	—
364	C₄×C₆₁	—	4	2	no	—
365	C₄×C₆₁	—	4	2	no	—
366	C₄×C₆₁	—	4	2	no	—
367	C₄×C₆₁	#548	1	2	yes	—
368	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
369	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
370	#3506	C₂×C₆₁	1	1	yes	characteristic
371	#3502	C₂×C₆₁	1	1	yes	characteristic, complemented
372	#3377	C₂×C₆₁	1	4	yes	complemented
373	#3375	C₂×C₆₁	1	4	yes	complemented
374	#3371	C₂×C₆₁	1	4	yes	complemented
375	#3368	C₂×C₆₁	1	4	yes	complemented
376	#3136	C₂×C₆₁	1	2	yes	complemented
377	#3135	C₂×C₆₁	1	1	yes	characteristic, complemented
378	#3083	C₂×C₆₁	1	2	yes	complemented
379	#3077	C₂×C₆₁	1	1	yes	characteristic, complemented
380	#3043	C₂×C₆₁	1	2	yes	complemented
381	#3037	C₂×C₆₁	1	1	yes	characteristic, complemented
382	#2961	C₂×C₆₁	1	1	yes	characteristic, complemented
383	#2947	C₂×C₆₁	1	2	yes	complemented
384	C₂×#440	C₂×C₆₁	1	1	yes	characteristic, complemented
385	C₂×C₆₁	—	2	2	no	—
386	C₂×C₆₁	—	8	2	no	—
387	C₂×C₆₁	—	8	2	no	—
388	C₂×C₆₁	C₂×#548	1	1	yes	characteristic
389	C₂×C₆₁	#3585	1	1	yes	characteristic
390	C₂×C₆₁	#3586	1	1	yes	characteristic
391	C₂×#137	C₂²×C₆₁	1	2	yes	—
392	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
393	#559	C₂²×C₆₁	1	4	yes	—
394	Q₈²	—	2	1	no	—
395	Q₈²	C₂²×C₆₁	1	2	yes	complemented
396	#557	—	2	1	no	—
397	#557	—	2	2	no	—
398	#557	C₂²×C₆₁	1	4	yes	complemented
399	#557	C₂²×C₆₁	1	2	yes	complemented
400	#556	C₂²×C₆₁	1	2	yes	—
401	#555	—	2	1	no	—
402	#553	—	2	2	no	—
403	#550	C₂²×C₆₁	1	2	yes	—
404	#547	—	2	1	no	—
405	#544	—	2	2	no	—
406	#544	C₂²×C₆₁	1	2	yes	—
407	#538	—	2	2	no	—
408	#535	C₂²×C₆₁	1	2	yes	—
409	#533	—	2	2	no	—
410	#533	C₂²×C₆₁	1	1	yes	characteristic
411	#533	C₂²×C₆₁	1	1	yes	characteristic
412	#532	C₂²×C₆₁	1	1	yes	characteristic
413	#525	—	2	2	no	—
414	#520	C₂²×C₆₁	1	2	yes	—
415	#519	C₂²×C₆₁	1	2	yes	—
416	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
418	#491	C₂²×C₆₁	1	2	yes	complemented
419	#490	C₂²×C₆₁	1	4	yes	—
420	#490	C₂²×C₆₁	1	2	yes	complemented
421	#489	C₂²×C₆₁	1	4	yes	—
422	#489	C₂²×C₆₁	1	2	yes	complemented
423	#489	C₂²×C₆₁	1	2	yes	complemented
424	#488	C₂²×C₆₁	1	4	yes	—
425	#486	C₂²×C₆₁	1	4	yes	—
426	#479	C₂²×C₆₁	1	4	yes	complemented
427	#478	C₂²×C₆₁	1	4	yes	—
428	#478	C₂²×C₆₁	1	4	yes	complemented
429	#477	C₂²×C₆₁	1	4	yes	complemented
430	#476	C₂²×C₆₁	1	2	yes	—
431	#474	C₂²×C₆₁	1	2	yes	—
432	#474	C₂²×C₆₁	1	4	yes	complemented
433	#464	C₂²×C₆₁	1	4	yes	—
434	#464	C₂²×C₆₁	1	4	yes	—
435	#464	C₂²×C₆₁	1	4	yes	complemented
436	#462	C₂²×C₆₁	1	2	yes	complemented
437	#460	C₂²×C₆₁	1	4	yes	—
438	#460	C₂²×C₆₁	1	4	yes	—
439	#460	C₂²×C₆₁	1	2	yes	complemented
440	#446	C₂²×C₆₁	1	4	yes	complemented
441	#446	C₂²×C₆₁	1	4	yes	complemented
442	#441	C₂²×C₆₁	1	4	yes	complemented
443	#440	C₂²×C₆₁	1	4	yes	—
444	#440	C₂²×C₆₁	1	4	yes	—
445	#440	C₂²×C₆₁	1	4	yes	complemented
446	C₄×Q₁₆	C₂²×C₆₁	1	4	yes	complemented
447	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	complemented
448	#428	C₂²×C₆₁	1	2	yes	—
449	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
450	#424	C₂²×C₆₁	1	2	yes	—
451	#423	C₂²×C₆₁	1	1	yes	characteristic
452	#418	C₂²×C₆₁	1	2	yes	—
453	#417	C₂²×C₆₁	1	2	yes	—
454	#416	C₂²×C₆₁	1	2	yes	—
455	#416	C₂²×C₆₁	1	2	yes	—
456	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
457	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
458	#405	C₂²×C₆₁	1	2	yes	—
459	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
460	C₆₁	#61334	1	1	yes	characteristic, direct product factor, Sylow
461	C₂×#41	—	2	2	no	—
462	C₂×#41	C₂³×C₆₁	1	2	yes	—
463	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
464	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
465	C₂³×C₄	—	2	1	no	—
466	#137	—	2	8	no	—
467	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
468	C₂×SD₁₆	—	2	4	no	—
469	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
470	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
471	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
472	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
474	C₄⋊Q₈	—	2	2	no	—
475	C₄⋊Q₈	—	2	4	no	—
476	C₄⋊Q₈	—	2	2	no	—
477	C₄⋊Q₈	—	2	4	no	—
478	C₄⋊Q₈	—	2	2	no	—
479	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
480	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
481	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
482	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
483	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
484	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
485	#127	C₂³×C₆₁	1	1	yes	characteristic
486	#127	C₂³×C₆₁	1	4	yes	—
487	#126	—	2	4	no	—
488	#125	—	2	4	no	—
489	#125	—	2	4	no	—
490	#125	—	2	4	no	—
491	#125	—	2	2	no	—
492	#125	D₄×C₆₁	1	2	yes	—
493	#125	C₂³×C₆₁	1	2	yes	—
494	#125	C₂³×C₆₁	1	4	yes	—
495	#124	—	2	4	no	—
496	#124	C₂³×C₆₁	1	2	yes	—
497	#124	C₂³×C₆₁	1	4	yes	—
498	#123	—	2	4	no	—
499	#123	—	2	4	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	1	no	—
502	C₂²⋊Q₈	—	2	1	no	—
503	C₂²⋊Q₈	—	2	4	no	—
504	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
505	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
506	#121	—	2	1	no	—
507	#121	—	2	1	no	—
508	#121	—	2	2	no	—
509	#121	—	2	2	no	—
510	#121	—	2	2	no	—
511	#121	—	2	4	no	—
512	#120	—	2	4	no	—
513	C₄×Q₈	—	2	2	no	—
514	C₄×Q₈	—	2	2	no	—
515	C₄×Q₈	—	2	2	no	—
516	C₄×Q₈	—	2	4	no	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	—	2	1	no	—
519	C₄×Q₈	—	2	1	no	—
520	C₄×Q₈	—	2	1	no	—
521	C₄×Q₈	—	2	1	no	—
522	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
523	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
524	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
525	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
526	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
527	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
528	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
529	C₄×D₄	—	2	4	no	—
530	C₄×D₄	—	2	4	no	—
531	C₄×D₄	—	2	1	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	—	2	1	no	—
534	C₄×D₄	—	2	1	no	—
535	C₄×D₄	C₂³×C₆₁	1	2	yes	—
536	C₄×D₄	C₂³×C₆₁	1	2	yes	—
537	C₄×D₄	C₂³×C₆₁	1	4	yes	—
538	#117	—	2	2	no	—
539	#117	—	2	2	no	—
540	#117	—	2	4	no	—
541	#117	C₂³×C₆₁	1	2	yes	—
542	#117	C₂³×C₆₁	1	2	yes	—
543	C₂×C₄⋊C₄	—	2	1	no	—
544	C₂×C₄⋊C₄	—	2	2	no	—
545	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₄²	—	2	1	no	—
549	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
550	#107	C₂³×C₆₁	1	4	yes	—
551	#107	C₂³×C₆₁	1	4	yes	—
552	#106	C₂³×C₆₁	1	4	yes	—
553	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
554	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
555	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
556	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
557	#103	C₂³×C₆₁	1	4	yes	—
558	#103	C₂³×C₆₁	1	2	yes	—
559	#103	C₂³×C₆₁	1	2	yes	—
560	#103	C₂³×C₆₁	1	2	yes	—
561	#103	C₂³×C₆₁	1	2	yes	—
562	#103	C₂³×C₆₁	1	4	yes	—
563	#102	C₂³×C₆₁	1	4	yes	—
564	#102	C₂³×C₆₁	1	2	yes	—
565	#102	C₂³×C₆₁	1	2	yes	—
566	#102	C₂³×C₆₁	1	2	yes	—
567	#102	C₂³×C₆₁	1	2	yes	—
568	#102	C₂³×C₆₁	1	4	yes	—
569	#102	C₂³×C₆₁	1	4	yes	—
570	#102	C₂³×C₆₁	1	4	yes	—
571	#97	C₂³×C₆₁	1	2	yes	—
572	#97	C₂³×C₆₁	1	2	yes	—
573	#97	C₂³×C₆₁	1	4	yes	—
574	C₄×C₈	C₂³×C₆₁	1	4	yes	—
575	C₂⁴	—	2	1	no	—
576	#41	—	2	4	no	—
577	#41	—	2	4	no	—
578	#41	—	8	4	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	4	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
585	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
586	C₂×Q₈	#41×C₆₁	1	4	yes	complemented
587	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
588	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
598	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	8	2	no	—
607	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
610	Q₁₆	—	2	8	no	—
611	SD₁₆	—	2	8	no	—
612	SD₁₆	—	2	8	no	—
613	M₁₆	—	2	4	no	—
614	C₂×C₈	—	2	2	no	—
615	C₂×C₈	—	2	2	no	—
616	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
617	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
618	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
636	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
637	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
638	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
639	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
640	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
642	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
643	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
644	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	2	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	2	no	—
660	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
661	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
662	C₄²	C₂⁴×C₆₁	1	4	yes	—
663	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
664	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	4	2	no	—
668	C₂³	—	8	1	no	—
669	C₂³	—	8	1	no	—
670	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
671	Q₈	—	2	4	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	2	2	no	—
674	Q₈	—	2	2	no	—
675	Q₈	—	4	2	no	—
676	Q₈	—	4	2	no	—
677	Q₈	—	4	2	no	—
678	Q₈	—	8	1	no	—
679	Q₈	—	8	4	no	—
680	Q₈	C₂×#41×C₆₁	1	4	yes	—
681	D₄	—	2	2	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	2	no	—
684	D₄	—	2	2	no	—
685	D₄	—	4	2	no	—
686	D₄	—	4	4	no	—
687	D₄	—	4	2	no	—
688	D₄	—	8	1	no	—
689	D₄	—	8	4	no	—
690	D₄	—	8	4	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	4	no	—
702	C₂×C₄	—	8	2	no	—
703	C₂×C₄	—	8	4	no	—
704	C₂×C₄	—	8	1	no	—
705	C₂×C₄	—	8	1	no	—
706	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
709	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
710	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
711	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
713	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
714	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
715	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
716	C₈	—	2	2	no	—
717	C₈	—	2	4	no	—
718	C₈	—	2	2	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	8	4	no	—
728	C₂²	C₆₁×#548	1	2	yes	—
729	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
730	C₄	—	2	1	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	4	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	4	no	—
736	C₄	—	2	4	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	C₆₁×#548	1	2	yes	—
743	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
744	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
745	C₂	—	2	2	no	—
746	C₂	—	8	2	no	—
747	C₂	—	8	2	no	—
748	C₂	C₂×C₆₁×#548	1	1	yes	characteristic
749	C₂	C₆₁×#3585	1	1	yes	characteristic
750	C₂	C₆₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3506	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#3502	C₂	semidirect
3. C₆₁×#3377	C₂	semidirect
4. C₆₁×#3375	C₂	semidirect
5. C₆₁×#3371	C₂	semidirect
6. C₆₁×#3368	C₂	semidirect
7. C₆₁×#3136	C₂	semidirect
8. C₆₁×#3135	C₂	semidirect
9. C₆₁×#3083	C₂	semidirect
10. C₆₁×#3077	C₂	semidirect
11. C₆₁×#3043	C₂	semidirect
12. C₆₁×#3037	C₂	semidirect
13. C₆₁×#2961	C₂	semidirect
14. C₆₁×#2947	C₂	semidirect
15. C₂×C₆₁×#440	C₂	semidirect
20. Q₈²×C₆₁	C₂²	semidirect
23. C₆₁×#557	C₂²	semidirect
24. C₆₁×#557	C₂²	semidirect
43. C₆₁×#491	C₂²	semidirect
45. C₆₁×#490	C₂²	semidirect
47. C₆₁×#489	C₂²	semidirect
48. C₆₁×#489	C₂²	semidirect
51. C₆₁×#479	C₂²	semidirect
53. C₆₁×#478	C₂²	semidirect
54. C₆₁×#477	C₂²	semidirect
57. C₆₁×#474	C₂²	semidirect
60. C₆₁×#464	C₂²	semidirect
61. C₆₁×#462	C₂²	semidirect
64. C₆₁×#460	C₂²	semidirect
65. C₆₁×#446	C₂²	semidirect
66. C₆₁×#446	C₂²	semidirect
67. C₆₁×#441	C₂²	semidirect
70. C₆₁×#440	C₂²	semidirect
71. C₄×Q₁₆×C₆₁	C₂²	semidirect
72. C₄×SD₁₆×C₆₁	C₂²	semidirect
210. C₂×Q₈×C₆₁	#41	semidirect
343. #61334	C₆₁	direct (N × H)
371. #3502	C₂×C₆₁	semidirect
372. #3377	C₂×C₆₁	semidirect
373. #3375	C₂×C₆₁	semidirect
374. #3371	C₂×C₆₁	semidirect
375. #3368	C₂×C₆₁	semidirect
376. #3136	C₂×C₆₁	semidirect
377. #3135	C₂×C₆₁	semidirect
378. #3083	C₂×C₆₁	semidirect
379. #3077	C₂×C₆₁	semidirect
380. #3043	C₂×C₆₁	semidirect
381. #3037	C₂×C₆₁	semidirect
382. #2961	C₂×C₆₁	semidirect
383. #2947	C₂×C₆₁	semidirect
384. C₂×#440	C₂×C₆₁	semidirect
395. Q₈²	C₂²×C₆₁	semidirect
398. #557	C₂²×C₆₁	semidirect
399. #557	C₂²×C₆₁	semidirect
418. #491	C₂²×C₆₁	semidirect
420. #490	C₂²×C₆₁	semidirect
422. #489	C₂²×C₆₁	semidirect
423. #489	C₂²×C₆₁	semidirect
426. #479	C₂²×C₆₁	semidirect
428. #478	C₂²×C₆₁	semidirect
429. #477	C₂²×C₆₁	semidirect
432. #474	C₂²×C₆₁	semidirect
435. #464	C₂²×C₆₁	semidirect
436. #462	C₂²×C₆₁	semidirect
439. #460	C₂²×C₆₁	semidirect
440. #446	C₂²×C₆₁	semidirect
441. #446	C₂²×C₆₁	semidirect
442. #441	C₂²×C₆₁	semidirect
445. #440	C₂²×C₆₁	semidirect
446. C₄×Q₁₆	C₂²×C₆₁	semidirect
447. C₄×SD₁₆	C₂²×C₆₁	semidirect
460. C₆₁	#61334	direct (N × H)
586. C₂×Q₈	#41×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3506	2
C₆₁×#3502	2
C₆₁×#3377	2
C₆₁×#3375	2
C₆₁×#3371	2
C₆₁×#3368	2
C₆₁×#3136	2
C₆₁×#3135	2
C₆₁×#3083	2
C₆₁×#3077	2
C₆₁×#3043	2
C₆₁×#3037	2
C₆₁×#2961	2
C₆₁×#2947	2
C₂×C₆₁×#440	2
#61334	61

Subgroups — C61×#61334 #29564767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61334 #29564767