Subgroups — C₆₁×#61377 #29564810

Order 15616.

1742 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3502	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3501	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3388	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3388	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3386	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3385	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3164	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3162	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3082	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3081	C₂	1	2	yes	maximal
11	C₆₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3077	C₂	1	1	yes	maximal, characteristic
13	C₆₁×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#2949	C₂	1	2	yes	maximal
15	C₂×C₆₁×#440	C₂	1	1	yes	maximal, characteristic
16	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	Q₈²×C₆₁	—	2	1	no	—
18	Q₈²×C₆₁	C₂²	1	2	yes	complemented
19	C₆₁×#557	—	2	1	no	—
20	C₆₁×#557	—	2	2	no	—
21	C₆₁×#557	C₂²	1	4	yes	complemented
22	C₆₁×#557	C₂²	1	2	yes	complemented
23	C₆₁×#554	—	2	1	no	—
24	C₆₁×#554	—	2	2	no	—
25	C₆₁×#554	C₂²	1	4	yes	—
26	C₆₁×#554	C₂²	1	2	yes	—
27	D₄×Q₈×C₆₁	—	2	1	no	—
28	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
29	C₆₁×#544	—	2	2	no	—
30	C₆₁×#544	C₂²	1	2	yes	—
31	C₆₁×#544	C₂²	1	2	yes	—
32	C₆₁×#543	—	2	2	no	—
33	C₆₁×#533	—	2	2	no	—
34	C₆₁×#533	C₂²	1	1	yes	characteristic
35	C₆₁×#533	C₂²	1	1	yes	characteristic
36	C₆₁×#533	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₆₁	—	2	2	no	—
38	C₆₁×#519	C₂²	1	2	yes	—
39	C₆₁×#518	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#501	C₂²	1	2	yes	complemented
43	C₆₁×#501	C₂²	1	4	yes	complemented
44	C₆₁×#501	C₂²	1	2	yes	complemented
45	C₆₁×#501	C₂²	1	4	yes	complemented
46	C₆₁×#501	C₂²	1	2	yes	complemented
47	C₆₁×#501	C₂²	1	2	yes	complemented
48	C₆₁×#500	C₂²	1	4	yes	complemented
49	C₆₁×#499	C₂²	1	4	yes	complemented
50	C₆₁×#479	C₂²	1	4	yes	complemented
51	C₆₁×#479	C₂²	1	4	yes	complemented
52	C₆₁×#479	C₂²	1	4	yes	complemented
53	C₆₁×#478	C₂²	1	4	yes	—
54	C₆₁×#478	C₂²	1	4	yes	—
55	C₆₁×#478	C₂²	1	4	yes	—
56	C₆₁×#477	C₂²	1	2	yes	complemented
57	C₆₁×#477	C₂²	1	4	yes	complemented
58	C₆₁×#476	C₂²	1	2	yes	—
59	C₆₁×#476	C₂²	1	4	yes	—
60	C₆₁×#475	C₂²	1	2	yes	complemented
61	C₆₁×#475	C₂²	1	4	yes	complemented
62	C₆₁×#474	C₂²	1	2	yes	—
63	C₆₁×#474	C₂²	1	4	yes	—
64	C₆₁×#446	C₂²	1	4	yes	complemented
65	C₆₁×#446	C₂²	1	4	yes	complemented
66	C₆₁×#440	C₂²	1	4	yes	—
67	C₆₁×#440	C₂²	1	4	yes	—
68	C₆₁×#440	C₂²	1	4	yes	—
69	C₆₁×#440	C₂²	1	4	yes	—
70	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	—
71	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	—
72	C₆₁×#428	C₂²	1	2	yes	—
73	C₆₁×#428	C₂²	1	2	yes	—
74	C₆₁×#427	C₂²	1	2	yes	—
75	C₆₁×#427	C₂²	1	2	yes	—
76	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
77	C₆₁×#424	C₂²	1	2	yes	—
78	C₆₁×#423	C₂²	1	1	yes	characteristic
79	C₆₁×#419	C₂²	1	2	yes	—
80	C₆₁×#418	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	C₂²×Q₈×C₆₁	—	2	2	no	—
86	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₆₁	—	2	1	no	—
89	C₂×SD₁₆×C₆₁	Q₈	1	8	yes	complemented
90	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
91	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
92	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
94	C₄⋊Q₈×C₆₁	—	2	2	no	—
95	C₄⋊Q₈×C₆₁	—	2	4	no	—
96	C₄⋊Q₈×C₆₁	—	2	2	no	—
97	C₄⋊Q₈×C₆₁	—	2	4	no	—
98	C₄⋊Q₈×C₆₁	—	2	2	no	—
99	C₄⋊Q₈×C₆₁	—	2	2	no	—
100	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
101	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
102	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
104	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
105	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
106	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
107	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
108	#125×C₆₁	—	2	4	no	—
109	#125×C₆₁	—	2	4	no	—
110	#125×C₆₁	—	2	4	no	—
111	#125×C₆₁	—	2	2	no	—
112	#125×C₆₁	—	2	2	no	—
113	#125×C₆₁	D₄	1	2	yes	—
114	#125×C₆₁	C₂³	1	2	yes	—
115	#125×C₆₁	C₂³	1	2	yes	—
116	#125×C₆₁	C₂³	1	4	yes	—
117	#125×C₆₁	C₂³	1	4	yes	—
118	C₂²⋊Q₈×C₆₁	—	2	4	no	—
119	C₂²⋊Q₈×C₆₁	—	2	2	no	—
120	C₂²⋊Q₈×C₆₁	—	2	1	no	—
121	C₂²⋊Q₈×C₆₁	—	2	1	no	—
122	C₂²⋊Q₈×C₆₁	—	2	1	no	—
123	C₂²⋊Q₈×C₆₁	—	2	1	no	—
124	C₂²⋊Q₈×C₆₁	—	2	4	no	—
125	C₂²⋊Q₈×C₆₁	—	2	4	no	—
126	C₂²⋊Q₈×C₆₁	—	2	4	no	—
127	C₂²⋊Q₈×C₆₁	—	2	2	no	—
128	C₂²⋊Q₈×C₆₁	—	2	4	no	—
129	C₂²⋊Q₈×C₆₁	—	2	4	no	—
130	C₂²⋊Q₈×C₆₁	—	2	4	no	—
131	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
132	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
133	C₄×Q₈×C₆₁	—	2	2	no	—
134	C₄×Q₈×C₆₁	—	2	4	no	—
135	C₄×Q₈×C₆₁	—	2	2	no	—
136	C₄×Q₈×C₆₁	—	2	2	no	—
137	C₄×Q₈×C₆₁	—	2	2	no	—
138	C₄×Q₈×C₆₁	—	2	1	no	—
139	C₄×Q₈×C₆₁	—	2	1	no	—
140	C₄×Q₈×C₆₁	—	2	1	no	—
141	C₄×Q₈×C₆₁	—	2	1	no	—
142	C₄×Q₈×C₆₁	—	2	1	no	—
143	C₄×Q₈×C₆₁	—	2	1	no	—
144	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
145	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
146	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
147	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
148	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
149	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
150	C₄×D₄×C₆₁	—	2	2	no	—
151	C₄×D₄×C₆₁	—	2	2	no	—
152	C₄×D₄×C₆₁	—	2	1	no	—
153	C₄×D₄×C₆₁	—	2	1	no	—
154	C₄×D₄×C₆₁	C₂³	1	4	yes	—
155	C₄×D₄×C₆₁	C₂³	1	2	yes	—
156	C₄×D₄×C₆₁	C₂³	1	4	yes	—
157	C₄×D₄×C₆₁	C₂³	1	2	yes	—
158	#117×C₆₁	—	2	4	no	—
159	#117×C₆₁	C₂³	1	2	yes	—
160	#117×C₆₁	C₂³	1	2	yes	—
161	#117×C₆₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
163	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
164	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
165	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
168	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
169	C₂×C₄²×C₆₁	—	2	1	no	—
170	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
171	#107×C₆₁	C₂³	1	4	yes	—
172	#107×C₆₁	C₂³	1	2	yes	—
173	#107×C₆₁	C₂³	1	2	yes	—
174	#107×C₆₁	C₂³	1	2	yes	—
175	#107×C₆₁	C₂³	1	2	yes	—
176	#107×C₆₁	C₂³	1	4	yes	—
177	#107×C₆₁	C₂³	1	4	yes	—
178	#106×C₆₁	C₂³	1	2	yes	—
179	#106×C₆₁	C₂³	1	2	yes	—
180	#106×C₆₁	C₂³	1	2	yes	—
181	#106×C₆₁	C₂³	1	2	yes	—
182	#106×C₆₁	C₂³	1	4	yes	—
183	#106×C₆₁	C₂³	1	4	yes	—
184	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
185	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
186	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
187	C₄⋊C₈×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	#102×C₆₁	C₂³	1	4	yes	—
192	#102×C₆₁	C₂³	1	4	yes	—
193	#102×C₆₁	C₂³	1	4	yes	—
194	#97×C₆₁	C₂³	1	2	yes	—
195	#97×C₆₁	C₂³	1	2	yes	—
196	#97×C₆₁	C₂³	1	4	yes	—
197	C₄×C₈×C₆₁	C₂³	1	4	yes	—
198	C₂⁴×C₆₁	—	2	1	no	—
199	C₂×Q₈×C₆₁	—	2	1	no	—
200	C₂×Q₈×C₆₁	—	2	1	no	—
201	C₂×Q₈×C₆₁	—	2	1	no	—
202	C₂×Q₈×C₆₁	—	2	1	no	—
203	C₂×Q₈×C₆₁	—	2	1	no	—
204	C₂×Q₈×C₆₁	—	2	4	no	—
205	C₂×Q₈×C₆₁	—	2	4	no	—
206	C₂×Q₈×C₆₁	—	2	2	no	—
207	C₂×Q₈×C₆₁	—	8	4	no	—
208	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
210	C₂×Q₈×C₆₁	C₂×Q₈	1	4	yes	complemented
211	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
212	C₂×D₄×C₆₁	—	2	1	no	—
213	C₂×D₄×C₆₁	—	2	2	no	—
214	C₂×D₄×C₆₁	C₂×Q₈	1	4	yes	—
215	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₆₁	—	2	1	no	—
217	C₂²×C₄×C₆₁	—	2	1	no	—
218	C₂²×C₄×C₆₁	—	2	1	no	—
219	C₂²×C₄×C₆₁	—	2	2	no	—
220	C₂²×C₄×C₆₁	—	2	4	no	—
221	C₂²×C₄×C₆₁	—	2	4	no	—
222	C₂²×C₄×C₆₁	—	2	2	no	—
223	C₂²×C₄×C₆₁	—	8	2	no	—
224	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
227	SD₁₆×C₆₁	C₂×Q₈	1	16	yes	complemented
228	M₁₆×C₆₁	—	2	4	no	—
229	C₂×C₈×C₆₁	—	2	2	no	—
230	C₂×C₈×C₆₁	C₂×Q₈	1	4	yes	complemented
231	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
232	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
233	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
234	C₄⋊C₄×C₆₁	—	2	2	no	—
235	C₄⋊C₄×C₆₁	—	2	1	no	—
236	C₄⋊C₄×C₆₁	—	2	2	no	—
237	C₄⋊C₄×C₆₁	—	2	2	no	—
238	C₄⋊C₄×C₆₁	—	2	4	no	—
239	C₄⋊C₄×C₆₁	—	2	4	no	—
240	C₄⋊C₄×C₆₁	—	2	4	no	—
241	C₄⋊C₄×C₆₁	—	2	1	no	—
242	C₄⋊C₄×C₆₁	—	2	1	no	—
243	C₄⋊C₄×C₆₁	—	2	4	no	—
244	C₄⋊C₄×C₆₁	—	2	4	no	—
245	C₄⋊C₄×C₆₁	—	2	2	no	—
246	C₄⋊C₄×C₆₁	—	2	1	no	—
247	C₄⋊C₄×C₆₁	—	2	2	no	—
248	C₄⋊C₄×C₆₁	—	2	1	no	—
249	C₄⋊C₄×C₆₁	—	2	1	no	—
250	C₄⋊C₄×C₆₁	—	2	4	no	—
251	C₄⋊C₄×C₆₁	—	2	4	no	—
252	C₄⋊C₄×C₆₁	—	2	2	no	—
253	C₄⋊C₄×C₆₁	—	2	4	no	—
254	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
256	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₆₁	C₂×D₄	1	4	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	2	yes	—
263	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
266	C₂²⋊C₄×C₆₁	—	2	2	no	—
267	C₂²⋊C₄×C₆₁	—	2	2	no	—
268	C₂²⋊C₄×C₆₁	—	2	4	no	—
269	C₂²⋊C₄×C₆₁	—	2	4	no	—
270	C₂²⋊C₄×C₆₁	—	2	2	no	—
271	C₂²⋊C₄×C₆₁	—	2	2	no	—
272	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
273	C₄²×C₆₁	—	2	2	no	—
274	C₄²×C₆₁	—	2	2	no	—
275	C₄²×C₆₁	—	2	4	no	—
276	C₄²×C₆₁	—	2	4	no	—
277	C₄²×C₆₁	—	2	2	no	—
278	C₄²×C₆₁	—	2	2	no	—
279	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₆₁	C₂⁴	1	4	yes	—
282	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
283	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
284	C₂³×C₆₁	—	2	2	no	—
285	C₂³×C₆₁	—	2	4	no	—
286	C₂³×C₆₁	—	8	1	no	—
287	C₂³×C₆₁	—	8	1	no	—
288	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
289	Q₈×C₆₁	—	2	4	no	—
290	Q₈×C₆₁	—	2	2	no	—
291	Q₈×C₆₁	—	4	2	no	—
292	Q₈×C₆₁	—	4	2	no	—
293	Q₈×C₆₁	—	4	2	no	—
294	Q₈×C₆₁	—	4	2	no	—
295	Q₈×C₆₁	—	8	1	no	—
296	Q₈×C₆₁	—	8	4	no	—
297	Q₈×C₆₁	—	8	1	no	—
298	Q₈×C₆₁	—	8	4	no	—
299	Q₈×C₆₁	C₂²×Q₈	1	4	yes	—
300	D₄×C₆₁	—	2	4	no	—
301	D₄×C₆₁	—	2	2	no	—
302	D₄×C₆₁	C₂²×Q₈	1	4	yes	—
303	C₂×C₄×C₆₁	—	2	4	no	—
304	C₂×C₄×C₆₁	—	2	2	no	—
305	C₂×C₄×C₆₁	—	2	2	no	—
306	C₂×C₄×C₆₁	—	2	2	no	—
307	C₂×C₄×C₆₁	—	2	2	no	—
308	C₂×C₄×C₆₁	—	2	2	no	—
309	C₂×C₄×C₆₁	—	2	2	no	—
310	C₂×C₄×C₆₁	—	2	2	no	—
311	C₂×C₄×C₆₁	—	4	1	no	—
312	C₂×C₄×C₆₁	—	4	1	no	—
313	C₂×C₄×C₆₁	—	4	4	no	—
314	C₂×C₄×C₆₁	—	8	4	no	—
315	C₂×C₄×C₆₁	—	8	2	no	—
316	C₂×C₄×C₆₁	—	8	4	no	—
317	C₂×C₄×C₆₁	—	8	1	no	—
318	C₂×C₄×C₆₁	—	8	1	no	—
319	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
322	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
323	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
327	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
328	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
329	C₈×C₆₁	—	2	2	no	—
330	C₈×C₆₁	—	2	4	no	—
331	C₈×C₆₁	C₂²×Q₈	1	4	yes	—
332	#61377	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
333	C₂²×C₆₁	—	2	1	no	—
334	C₂²×C₆₁	—	2	1	no	—
335	C₂²×C₆₁	—	2	4	no	—
336	C₂²×C₆₁	—	4	2	no	—
337	C₂²×C₆₁	—	4	2	no	—
338	C₂²×C₆₁	—	8	4	no	—
339	C₂²×C₆₁	D₄×Q₈	1	2	yes	—
340	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
341	C₄×C₆₁	—	2	1	no	—
342	C₄×C₆₁	—	2	1	no	—
343	C₄×C₆₁	—	2	4	no	—
344	C₄×C₆₁	—	2	1	no	—
345	C₄×C₆₁	—	2	1	no	—
346	C₄×C₆₁	—	2	4	no	—
347	C₄×C₆₁	—	2	4	no	—
348	C₄×C₆₁	—	4	2	no	—
349	C₄×C₆₁	—	4	2	no	—
350	C₄×C₆₁	—	4	2	no	—
351	C₄×C₆₁	—	4	2	no	—
352	C₄×C₆₁	—	4	2	no	—
353	C₄×C₆₁	—	4	2	no	—
354	C₄×C₆₁	D₄×Q₈	1	2	yes	—
355	C₄×C₆₁	C₂³×Q₈	1	1	yes	characteristic
356	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
357	#3502	C₂×C₆₁	1	1	yes	characteristic, complemented
358	#3501	C₂×C₆₁	1	1	yes	characteristic
359	#3388	C₂×C₆₁	1	4	yes	complemented
360	#3388	C₂×C₆₁	1	4	yes	complemented
361	#3386	C₂×C₆₁	1	4	yes	complemented
362	#3385	C₂×C₆₁	1	4	yes	complemented
363	#3164	C₂×C₆₁	1	2	yes	complemented
364	#3162	C₂×C₆₁	1	1	yes	characteristic, complemented
365	#3082	C₂×C₆₁	1	2	yes	complemented
366	#3081	C₂×C₆₁	1	2	yes	—
367	#3078	C₂×C₆₁	1	1	yes	characteristic, complemented
368	#3077	C₂×C₆₁	1	1	yes	characteristic
369	#2961	C₂×C₆₁	1	1	yes	characteristic, complemented
370	#2949	C₂×C₆₁	1	2	yes	—
371	C₂×#440	C₂×C₆₁	1	1	yes	characteristic
372	C₂×C₆₁	—	2	2	no	—
373	C₂×C₆₁	—	4	4	no	—
374	C₂×C₆₁	C₂×D₄×Q₈	1	1	yes	characteristic
375	C₂×C₆₁	#3585	1	1	yes	characteristic
376	C₂×C₆₁	#3586	1	1	yes	characteristic
377	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
378	Q₈²	—	2	1	no	—
379	Q₈²	C₂²×C₆₁	1	2	yes	complemented
380	#557	—	2	1	no	—
381	#557	—	2	2	no	—
382	#557	C₂²×C₆₁	1	4	yes	complemented
383	#557	C₂²×C₆₁	1	2	yes	complemented
384	#554	—	2	1	no	—
385	#554	—	2	2	no	—
386	#554	C₂²×C₆₁	1	4	yes	—
387	#554	C₂²×C₆₁	1	2	yes	—
388	D₄×Q₈	—	2	1	no	—
389	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
390	#544	—	2	2	no	—
391	#544	C₂²×C₆₁	1	2	yes	—
392	#544	C₂²×C₆₁	1	2	yes	—
393	#543	—	2	2	no	—
394	#533	—	2	2	no	—
395	#533	C₂²×C₆₁	1	1	yes	characteristic
396	#533	C₂²×C₆₁	1	1	yes	characteristic
397	#533	C₂²×C₆₁	1	1	yes	characteristic
398	C₂×C₂²⋊Q₈	—	2	2	no	—
399	#519	C₂²×C₆₁	1	2	yes	—
400	#518	C₂²×C₆₁	1	2	yes	—
401	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
402	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
403	#501	C₂²×C₆₁	1	2	yes	complemented
404	#501	C₂²×C₆₁	1	4	yes	complemented
405	#501	C₂²×C₆₁	1	2	yes	complemented
406	#501	C₂²×C₆₁	1	4	yes	complemented
407	#501	C₂²×C₆₁	1	2	yes	complemented
408	#501	C₂²×C₆₁	1	2	yes	complemented
409	#500	C₂²×C₆₁	1	4	yes	complemented
410	#499	C₂²×C₆₁	1	4	yes	complemented
411	#479	C₂²×C₆₁	1	4	yes	complemented
412	#479	C₂²×C₆₁	1	4	yes	complemented
413	#479	C₂²×C₆₁	1	4	yes	complemented
414	#478	C₂²×C₆₁	1	4	yes	—
415	#478	C₂²×C₆₁	1	4	yes	—
416	#478	C₂²×C₆₁	1	4	yes	—
417	#477	C₂²×C₆₁	1	2	yes	complemented
418	#477	C₂²×C₆₁	1	4	yes	complemented
419	#476	C₂²×C₆₁	1	2	yes	—
420	#476	C₂²×C₆₁	1	4	yes	—
421	#475	C₂²×C₆₁	1	2	yes	complemented
422	#475	C₂²×C₆₁	1	4	yes	complemented
423	#474	C₂²×C₆₁	1	2	yes	—
424	#474	C₂²×C₆₁	1	4	yes	—
425	#446	C₂²×C₆₁	1	4	yes	complemented
426	#446	C₂²×C₆₁	1	4	yes	complemented
427	#440	C₂²×C₆₁	1	4	yes	—
428	#440	C₂²×C₆₁	1	4	yes	—
429	#440	C₂²×C₆₁	1	4	yes	—
430	#440	C₂²×C₆₁	1	4	yes	—
431	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	—
432	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	—
433	#428	C₂²×C₆₁	1	2	yes	—
434	#428	C₂²×C₆₁	1	2	yes	—
435	#427	C₂²×C₆₁	1	2	yes	—
436	#427	C₂²×C₆₁	1	2	yes	—
437	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
438	#424	C₂²×C₆₁	1	2	yes	—
439	#423	C₂²×C₆₁	1	1	yes	characteristic
440	#419	C₂²×C₆₁	1	2	yes	—
441	#418	C₂²×C₆₁	1	2	yes	—
442	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
443	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
444	#405	C₂²×C₆₁	1	2	yes	—
445	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
446	C₆₁	#61377	1	1	yes	characteristic, direct product factor, Sylow
447	C₂²×Q₈	—	2	2	no	—
448	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
449	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
450	C₂³×C₄	—	2	1	no	—
451	C₂×SD₁₆	Q₈×C₆₁	1	8	yes	complemented
452	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
453	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
454	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
455	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
456	C₄⋊Q₈	—	2	2	no	—
457	C₄⋊Q₈	—	2	4	no	—
458	C₄⋊Q₈	—	2	2	no	—
459	C₄⋊Q₈	—	2	4	no	—
460	C₄⋊Q₈	—	2	2	no	—
461	C₄⋊Q₈	—	2	2	no	—
462	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
463	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
464	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
465	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
466	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
467	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
468	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
469	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
470	#125	—	2	4	no	—
471	#125	—	2	4	no	—
472	#125	—	2	4	no	—
473	#125	—	2	2	no	—
474	#125	—	2	2	no	—
475	#125	D₄×C₆₁	1	2	yes	—
476	#125	C₂³×C₆₁	1	2	yes	—
477	#125	C₂³×C₆₁	1	2	yes	—
478	#125	C₂³×C₆₁	1	4	yes	—
479	#125	C₂³×C₆₁	1	4	yes	—
480	C₂²⋊Q₈	—	2	2	no	—
481	C₂²⋊Q₈	—	2	4	no	—
482	C₂²⋊Q₈	—	2	1	no	—
483	C₂²⋊Q₈	—	2	1	no	—
484	C₂²⋊Q₈	—	2	1	no	—
485	C₂²⋊Q₈	—	2	1	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	4	no	—
488	C₂²⋊Q₈	—	2	4	no	—
489	C₂²⋊Q₈	—	2	4	no	—
490	C₂²⋊Q₈	—	2	4	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	2	4	no	—
493	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
494	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
495	C₄×Q₈	—	2	2	no	—
496	C₄×Q₈	—	2	2	no	—
497	C₄×Q₈	—	2	2	no	—
498	C₄×Q₈	—	2	4	no	—
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	—	2	1	no	—
501	C₄×Q₈	—	2	1	no	—
502	C₄×Q₈	—	2	1	no	—
503	C₄×Q₈	—	2	1	no	—
504	C₄×Q₈	—	2	1	no	—
505	C₄×Q₈	—	2	1	no	—
506	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
507	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
508	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
509	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
510	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
511	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	—	2	1	no	—
515	C₄×D₄	—	2	1	no	—
516	C₄×D₄	C₂³×C₆₁	1	2	yes	—
517	C₄×D₄	C₂³×C₆₁	1	2	yes	—
518	C₄×D₄	C₂³×C₆₁	1	4	yes	—
519	C₄×D₄	C₂³×C₆₁	1	4	yes	—
520	#117	—	2	4	no	—
521	#117	C₂³×C₆₁	1	2	yes	—
522	#117	C₂³×C₆₁	1	2	yes	—
523	#117	C₂³×C₆₁	1	2	yes	—
524	C₂×C₄⋊C₄	—	2	1	no	—
525	C₂×C₄⋊C₄	—	2	4	no	—
526	C₂×C₄⋊C₄	—	2	2	no	—
527	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₂²⋊C₄	—	2	4	no	—
531	C₂×C₄²	—	2	1	no	—
532	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
533	#107	C₂³×C₆₁	1	4	yes	—
534	#107	C₂³×C₆₁	1	2	yes	—
535	#107	C₂³×C₆₁	1	2	yes	—
536	#107	C₂³×C₆₁	1	2	yes	—
537	#107	C₂³×C₆₁	1	2	yes	—
538	#107	C₂³×C₆₁	1	4	yes	—
539	#107	C₂³×C₆₁	1	4	yes	—
540	#106	C₂³×C₆₁	1	2	yes	—
541	#106	C₂³×C₆₁	1	2	yes	—
542	#106	C₂³×C₆₁	1	2	yes	—
543	#106	C₂³×C₆₁	1	2	yes	—
544	#106	C₂³×C₆₁	1	4	yes	—
545	#106	C₂³×C₆₁	1	4	yes	—
546	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
547	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
548	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
549	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
550	#103	C₂³×C₆₁	1	4	yes	—
551	#103	C₂³×C₆₁	1	4	yes	—
552	#103	C₂³×C₆₁	1	4	yes	—
553	#102	C₂³×C₆₁	1	4	yes	—
554	#102	C₂³×C₆₁	1	4	yes	—
555	#102	C₂³×C₆₁	1	4	yes	—
556	#97	C₂³×C₆₁	1	2	yes	—
557	#97	C₂³×C₆₁	1	2	yes	—
558	#97	C₂³×C₆₁	1	4	yes	—
559	C₄×C₈	C₂³×C₆₁	1	4	yes	—
560	C₂⁴	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	4	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	8	4	no	—
570	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
571	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
572	C₂×Q₈	C₂×Q₈×C₆₁	1	4	yes	complemented
573	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	C₂×Q₈×C₆₁	1	4	yes	—
577	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	8	2	no	—
586	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
589	SD₁₆	C₂×Q₈×C₆₁	1	16	yes	complemented
590	M₁₆	—	2	4	no	—
591	C₂×C₈	—	2	2	no	—
592	C₂×C₈	C₂×Q₈×C₆₁	1	4	yes	complemented
593	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
594	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
595	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
617	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
618	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
619	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
620	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
621	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
622	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
623	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
624	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
625	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
635	C₄²	—	2	2	no	—
636	C₄²	—	2	2	no	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	4	no	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	2	no	—
641	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
642	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
643	C₄²	C₂⁴×C₆₁	1	4	yes	—
644	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
645	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
646	C₂³	—	2	2	no	—
647	C₂³	—	2	4	no	—
648	C₂³	—	8	1	no	—
649	C₂³	—	8	1	no	—
650	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
651	Q₈	—	2	4	no	—
652	Q₈	—	2	2	no	—
653	Q₈	—	4	2	no	—
654	Q₈	—	4	2	no	—
655	Q₈	—	4	2	no	—
656	Q₈	—	4	2	no	—
657	Q₈	—	8	1	no	—
658	Q₈	—	8	4	no	—
659	Q₈	—	8	1	no	—
660	Q₈	—	8	4	no	—
661	Q₈	C₂²×Q₈×C₆₁	1	4	yes	—
662	D₄	—	2	4	no	—
663	D₄	—	2	2	no	—
664	D₄	C₂²×Q₈×C₆₁	1	4	yes	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	4	no	—
676	C₂×C₄	—	8	4	no	—
677	C₂×C₄	—	8	2	no	—
678	C₂×C₄	—	8	4	no	—
679	C₂×C₄	—	8	1	no	—
680	C₂×C₄	—	8	1	no	—
681	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
682	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
683	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
684	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
685	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
686	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
687	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
688	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
689	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
690	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
691	C₈	—	2	2	no	—
692	C₈	—	2	4	no	—
693	C₈	C₂²×Q₈×C₆₁	1	4	yes	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	8	4	no	—
700	C₂²	D₄×Q₈×C₆₁	1	2	yes	—
701	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
702	C₄	—	2	1	no	—
703	C₄	—	2	1	no	—
704	C₄	—	2	4	no	—
705	C₄	—	2	1	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	4	no	—
708	C₄	—	2	4	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	D₄×Q₈×C₆₁	1	2	yes	—
716	C₄	C₂³×Q₈×C₆₁	1	1	yes	characteristic
717	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
718	C₂	—	2	2	no	—
719	C₂	—	4	4	no	—
720	C₂	C₂×D₄×Q₈×C₆₁	1	1	yes	characteristic
721	C₂	C₆₁×#3585	1	1	yes	characteristic
722	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	C₂²×D₄×C₆₁	C₂³
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
1. C₆₁×#3502	C₂	semidirect
3. C₆₁×#3388	C₂	semidirect
4. C₆₁×#3388	C₂	semidirect
5. C₆₁×#3386	C₂	semidirect
6. C₆₁×#3385	C₂	semidirect
7. C₆₁×#3164	C₂	semidirect
8. C₆₁×#3162	C₂	semidirect
9. C₆₁×#3082	C₂	semidirect
11. C₆₁×#3078	C₂	semidirect
13. C₆₁×#2961	C₂	semidirect
18. Q₈²×C₆₁	C₂²	semidirect
21. C₆₁×#557	C₂²	semidirect
22. C₆₁×#557	C₂²	semidirect
42. C₆₁×#501	C₂²	semidirect
43. C₆₁×#501	C₂²	semidirect
44. C₆₁×#501	C₂²	semidirect
45. C₆₁×#501	C₂²	semidirect
46. C₆₁×#501	C₂²	semidirect
47. C₆₁×#501	C₂²	semidirect
48. C₆₁×#500	C₂²	semidirect
49. C₆₁×#499	C₂²	semidirect
50. C₆₁×#479	C₂²	semidirect
51. C₆₁×#479	C₂²	semidirect
52. C₆₁×#479	C₂²	semidirect
56. C₆₁×#477	C₂²	semidirect
57. C₆₁×#477	C₂²	semidirect
60. C₆₁×#475	C₂²	semidirect
61. C₆₁×#475	C₂²	semidirect
64. C₆₁×#446	C₂²	semidirect
65. C₆₁×#446	C₂²	semidirect
89. C₂×SD₁₆×C₆₁	Q₈	semidirect
210. C₂×Q₈×C₆₁	C₂×Q₈	semidirect
227. SD₁₆×C₆₁	C₂×Q₈	semidirect
230. C₂×C₈×C₆₁	C₂×Q₈	semidirect
332. #61377	C₆₁	direct (N × H)
357. #3502	C₂×C₆₁	semidirect
359. #3388	C₂×C₆₁	semidirect
360. #3388	C₂×C₆₁	semidirect
361. #3386	C₂×C₆₁	semidirect
362. #3385	C₂×C₆₁	semidirect
363. #3164	C₂×C₆₁	semidirect
364. #3162	C₂×C₆₁	semidirect
365. #3082	C₂×C₆₁	semidirect
367. #3078	C₂×C₆₁	semidirect
369. #2961	C₂×C₆₁	semidirect
379. Q₈²	C₂²×C₆₁	semidirect
382. #557	C₂²×C₆₁	semidirect
383. #557	C₂²×C₆₁	semidirect
403. #501	C₂²×C₆₁	semidirect
404. #501	C₂²×C₆₁	semidirect
405. #501	C₂²×C₆₁	semidirect
406. #501	C₂²×C₆₁	semidirect
407. #501	C₂²×C₆₁	semidirect
408. #501	C₂²×C₆₁	semidirect
409. #500	C₂²×C₆₁	semidirect
410. #499	C₂²×C₆₁	semidirect
411. #479	C₂²×C₆₁	semidirect
412. #479	C₂²×C₆₁	semidirect
413. #479	C₂²×C₆₁	semidirect
417. #477	C₂²×C₆₁	semidirect
418. #477	C₂²×C₆₁	semidirect
421. #475	C₂²×C₆₁	semidirect
422. #475	C₂²×C₆₁	semidirect
425. #446	C₂²×C₆₁	semidirect
426. #446	C₂²×C₆₁	semidirect
446. C₆₁	#61377	direct (N × H)
451. C₂×SD₁₆	Q₈×C₆₁	semidirect
572. C₂×Q₈	C₂×Q₈×C₆₁	semidirect
589. SD₁₆	C₂×Q₈×C₆₁	semidirect
592. C₂×C₈	C₂×Q₈×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3502	2
C₆₁×#3501	2
C₆₁×#3388	2
C₆₁×#3386	2
C₆₁×#3385	2
C₆₁×#3164	2
C₆₁×#3162	2
C₆₁×#3082	2
C₆₁×#3081	2
C₆₁×#3078	2
C₆₁×#3077	2
C₆₁×#2961	2
C₆₁×#2949	2
C₂×C₆₁×#440	2
#61377	61

Subgroups — C61×#61377 #29564810

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61377 #29564810