Subgroups — C₆₁×#60948 #29564381

Order 15616.

1846 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3444	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3249	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3246	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3245	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3233	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3212	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3191	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3168	C₂	1	4	yes	maximal, complemented
9	C₆₁×#3107	C₂	1	4	yes	maximal, complemented
10	C₆₁×#3106	C₂	1	4	yes	maximal, complemented
11	C₂×C₆₁×#431	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#533	C₂²	1	2	yes	—
13	C₆₁×#533	C₂²	1	2	yes	—
14	C₆₁×#533	C₂²	1	2	yes	—
15	C₆₁×#532	C₂²	1	2	yes	—
16	C₆₁×#532	C₂²	1	2	yes	—
17	C₆₁×#532	C₂²	1	2	yes	—
18	C₆₁×#529	—	2	2	no	—
19	C₆₁×#529	—	2	2	no	—
20	C₆₁×#529	—	2	2	no	—
21	C₆₁×#529	—	2	2	no	—
22	C₆₁×#529	C₂²	1	4	yes	—
23	C₆₁×#529	C₂²	1	4	yes	—
24	C₆₁×#525	—	2	2	no	—
25	C₆₁×#525	—	2	2	no	—
26	C₆₁×#525	C₂²	1	4	yes	—
27	C₄×#41×C₆₁	—	2	2	no	—
28	C₄×#41×C₆₁	—	2	2	no	—
29	C₄×#41×C₆₁	C₂²	1	4	yes	—
30	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#499	C₂²	1	4	yes	complemented
32	C₆₁×#495	C₂²	1	4	yes	complemented
33	C₆₁×#488	C₂²	1	8	yes	complemented
34	C₆₁×#485	C₂²	1	8	yes	—
35	C₆₁×#482	C₂²	1	8	yes	—
36	C₆₁×#477	C₂²	1	4	yes	complemented
37	C₆₁×#476	C₂²	1	4	yes	complemented
38	C₆₁×#475	C₂²	1	4	yes	complemented
39	C₆₁×#474	C₂²	1	4	yes	complemented
40	C₆₁×#467	C₂²	1	4	yes	—
41	C₆₁×#466	C₂²	1	4	yes	—
42	C₆₁×#465	C₂²	1	8	yes	—
43	C₆₁×#462	C₂²	1	4	yes	complemented
44	C₆₁×#461	C₂²	1	4	yes	complemented
45	C₆₁×#460	C₂²	1	4	yes	complemented
46	C₆₁×#459	C₂²	1	4	yes	complemented
47	C₆₁×#452	C₂²	1	8	yes	—
48	C₆₁×#449	C₂²	1	8	yes	—
49	C₄×Q₁₆×C₆₁	C₂²	1	4	yes	complemented
50	C₄×SD₁₆×C₆₁	C₂²	1	8	yes	complemented
51	C₄×D₈×C₆₁	C₂²	1	4	yes	complemented
52	C₆₁×#431	C₂²	1	4	yes	—
53	C₆₁×#431	C₂²	1	4	yes	—
54	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
57	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
58	C₂×#41×C₆₁	—	2	2	no	—
59	C₂×#41×C₆₁	—	2	2	no	—
60	C₂×#41×C₆₁	C₂³	1	4	yes	—
61	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
64	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
65	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	—
66	C₂×D₈×C₆₁	C₂³	1	4	yes	—
67	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
68	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
69	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
70	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
71	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
72	#127×C₆₁	C₂³	1	2	yes	—
73	#126×C₆₁	—	2	4	no	—
74	#126×C₆₁	—	2	4	no	—
75	#125×C₆₁	—	2	2	no	—
76	#125×C₆₁	—	2	2	no	—
77	#125×C₆₁	C₂³	1	4	yes	—
78	#124×C₆₁	—	2	2	no	—
79	#124×C₆₁	—	2	2	no	—
80	#124×C₆₁	C₂³	1	4	yes	—
81	#123×C₆₁	—	2	4	no	—
82	#123×C₆₁	—	2	4	no	—
83	#123×C₆₁	—	2	4	no	—
84	C₂²⋊Q₈×C₆₁	—	2	2	no	—
85	C₂²⋊Q₈×C₆₁	—	2	2	no	—
86	C₂²⋊Q₈×C₆₁	—	2	2	no	—
87	C₂²⋊Q₈×C₆₁	—	2	2	no	—
88	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
89	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
90	#121×C₆₁	—	2	2	no	—
91	#121×C₆₁	—	2	2	no	—
92	#121×C₆₁	—	2	2	no	—
93	#121×C₆₁	—	2	2	no	—
94	#121×C₆₁	C₂³	1	4	yes	—
95	#121×C₆₁	C₂³	1	4	yes	—
96	#120×C₆₁	—	2	4	no	—
97	C₄×Q₈×C₆₁	—	2	2	no	—
98	C₄×Q₈×C₆₁	—	2	2	no	—
99	C₄×Q₈×C₆₁	—	2	2	no	—
100	C₄×Q₈×C₆₁	—	2	2	no	—
101	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
102	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
103	C₄×D₄×C₆₁	—	2	4	no	—
104	C₄×D₄×C₆₁	—	2	4	no	—
105	C₄×D₄×C₆₁	—	2	4	no	—
106	C₄×D₄×C₆₁	—	2	4	no	—
107	C₄×D₄×C₆₁	—	2	4	no	—
108	C₄×D₄×C₆₁	—	2	4	no	—
109	C₄×D₄×C₆₁	—	2	2	no	—
110	C₄×D₄×C₆₁	—	2	2	no	—
111	C₄×D₄×C₆₁	—	2	2	no	—
112	C₄×D₄×C₆₁	—	2	2	no	—
113	C₄×D₄×C₆₁	C₂³	1	4	yes	—
114	C₄×D₄×C₆₁	C₂³	1	4	yes	—
115	#117×C₆₁	—	2	2	no	—
116	#117×C₆₁	—	2	2	no	—
117	#117×C₆₁	—	2	4	no	—
118	#117×C₆₁	—	2	4	no	—
119	#117×C₆₁	—	2	4	no	—
120	#117×C₆₁	C₂³	1	4	yes	—
121	C₂×C₄²×C₆₁	—	2	4	no	—
122	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₆₁	D₄	1	2	yes	—
124	C₂×C₄²×C₆₁	D₄	1	2	yes	—
125	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
128	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
129	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
130	#107×C₆₁	C₂³	1	4	yes	—
131	#107×C₆₁	C₂³	1	4	yes	—
132	#106×C₆₁	C₂³	1	8	yes	—
133	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
134	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
135	#103×C₆₁	C₂³	1	8	yes	—
136	#103×C₆₁	C₂³	1	8	yes	—
137	#102×C₆₁	C₂³	1	8	yes	—
138	#102×C₆₁	C₂³	1	8	yes	—
139	C₂²⋊C₈×C₆₁	C₂³	1	8	yes	—
140	C₄×C₈×C₆₁	C₂³	1	4	yes	—
141	C₄×C₈×C₆₁	C₂³	1	4	yes	—
142	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
143	#41×C₆₁	—	4	4	no	—
144	#41×C₆₁	—	4	4	no	—
145	#41×C₆₁	—	4	8	no	—
146	#41×C₆₁	—	4	8	no	—
147	C₂×Q₈×C₆₁	—	2	2	no	—
148	C₂×Q₈×C₆₁	—	2	2	no	—
149	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
150	C₂×D₄×C₆₁	—	2	4	no	—
151	C₂×D₄×C₆₁	—	2	4	no	—
152	C₂×D₄×C₆₁	—	2	4	no	—
153	C₂×D₄×C₆₁	—	2	2	no	—
154	C₂×D₄×C₆₁	—	2	2	no	—
155	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₆₁	—	2	4	no	—
157	C₂²×C₄×C₆₁	—	2	4	no	—
158	C₂²×C₄×C₆₁	—	2	4	no	—
159	C₂²×C₄×C₆₁	—	2	4	no	—
160	C₂²×C₄×C₆₁	—	4	2	no	—
161	C₂²×C₄×C₆₁	—	4	1	no	—
162	C₂²×C₄×C₆₁	—	4	1	no	—
163	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
175	Q₁₆×C₆₁	—	4	4	no	—
176	SD₁₆×C₆₁	—	4	8	no	—
177	D₈×C₆₁	—	4	4	no	—
178	C₂×C₈×C₆₁	—	4	2	no	—
179	C₂×C₈×C₆₁	—	4	2	no	—
180	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
181	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
182	C₄⋊C₄×C₆₁	—	2	2	no	—
183	C₄⋊C₄×C₆₁	—	2	2	no	—
184	C₄⋊C₄×C₆₁	—	2	2	no	—
185	C₄⋊C₄×C₆₁	—	2	2	no	—
186	C₄⋊C₄×C₆₁	—	2	4	no	—
187	C₄⋊C₄×C₆₁	—	2	4	no	—
188	C₄⋊C₄×C₆₁	—	2	4	no	—
189	C₄⋊C₄×C₆₁	—	2	4	no	—
190	C₄⋊C₄×C₆₁	—	2	4	no	—
191	C₄⋊C₄×C₆₁	—	2	4	no	—
192	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
193	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
194	C₂²⋊C₄×C₆₁	—	2	4	no	—
195	C₂²⋊C₄×C₆₁	—	2	4	no	—
196	C₂²⋊C₄×C₆₁	—	2	4	no	—
197	C₂²⋊C₄×C₆₁	—	2	4	no	—
198	C₂²⋊C₄×C₆₁	—	2	4	no	—
199	C₂²⋊C₄×C₆₁	—	2	4	no	—
200	C₂²⋊C₄×C₆₁	—	2	4	no	—
201	C₂²⋊C₄×C₆₁	—	2	4	no	—
202	C₂²⋊C₄×C₆₁	—	2	4	no	—
203	C₄²×C₆₁	—	2	4	no	—
204	C₄²×C₆₁	—	2	4	no	—
205	C₄²×C₆₁	—	2	4	no	—
206	C₄²×C₆₁	C₂×D₄	1	2	yes	—
207	C₄²×C₆₁	C₂×D₄	1	2	yes	—
208	C₄²×C₆₁	C₂×D₄	1	2	yes	—
209	C₄²×C₆₁	C₂×D₄	1	2	yes	—
210	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₆₁	C₂×D₄	1	2	yes	—
212	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
214	C₄²×C₆₁	C₂⁴	1	2	yes	—
215	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
216	C₂³×C₆₁	—	2	2	no	—
217	C₂³×C₆₁	—	2	4	no	—
218	C₂³×C₆₁	—	4	1	no	—
219	C₂³×C₆₁	—	4	1	no	—
220	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
221	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
222	Q₈×C₆₁	—	2	4	no	—
223	Q₈×C₆₁	—	2	4	no	—
224	Q₈×C₆₁	—	4	4	no	—
225	Q₈×C₆₁	—	4	4	no	—
226	D₄×C₆₁	—	2	4	no	—
227	D₄×C₆₁	—	2	4	no	—
228	D₄×C₆₁	—	4	4	no	—
229	D₄×C₆₁	—	4	8	no	—
230	D₄×C₆₁	—	4	8	no	—
231	D₄×C₆₁	—	4	8	no	—
232	D₄×C₆₁	—	4	4	no	—
233	C₂×C₄×C₆₁	—	2	2	no	—
234	C₂×C₄×C₆₁	—	2	4	no	—
235	C₂×C₄×C₆₁	—	2	4	no	—
236	C₂×C₄×C₆₁	—	2	2	no	—
237	C₂×C₄×C₆₁	—	2	4	no	—
238	C₂×C₄×C₆₁	—	2	1	no	—
239	C₂×C₄×C₆₁	—	2	1	no	—
240	C₂×C₄×C₆₁	—	2	2	no	—
241	C₂×C₄×C₆₁	—	2	2	no	—
242	C₂×C₄×C₆₁	—	2	4	no	—
243	C₂×C₄×C₆₁	—	2	4	no	—
244	C₂×C₄×C₆₁	—	2	4	no	—
245	C₂×C₄×C₆₁	—	4	1	no	—
246	C₂×C₄×C₆₁	—	4	2	no	—
247	C₂×C₄×C₆₁	—	4	2	no	—
248	C₂×C₄×C₆₁	—	4	1	no	—
249	C₂×C₄×C₆₁	—	4	8	no	—
250	C₂×C₄×C₆₁	—	4	8	no	—
251	C₂×C₄×C₆₁	—	4	8	no	—
252	C₂×C₄×C₆₁	#135	1	4	yes	—
253	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
260	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
262	C₈×C₆₁	—	2	4	no	—
263	C₈×C₆₁	—	2	4	no	—
264	#60948	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂²×C₆₁	—	2	1	no	—
266	C₂²×C₆₁	—	2	1	no	—
267	C₂²×C₆₁	—	2	2	no	—
268	C₂²×C₆₁	—	2	2	no	—
269	C₂²×C₆₁	—	2	2	no	—
270	C₂²×C₆₁	—	4	4	no	—
271	C₂²×C₆₁	—	4	4	no	—
272	C₂²×C₆₁	—	4	4	no	—
273	C₂²×C₆₁	—	4	4	no	—
274	C₂²×C₆₁	C₂×#135	1	2	yes	—
275	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
276	C₄×C₆₁	—	2	2	no	—
277	C₄×C₆₁	—	2	1	no	—
278	C₄×C₆₁	—	2	1	no	—
279	C₄×C₆₁	—	2	1	no	—
280	C₄×C₆₁	—	2	1	no	—
281	C₄×C₆₁	—	2	2	no	—
282	C₄×C₆₁	—	4	4	no	—
283	C₄×C₆₁	—	4	4	no	—
284	C₄×C₆₁	—	4	4	no	—
285	C₄×C₆₁	C₂×#135	1	4	yes	—
286	C₄×C₆₁	#575	1	2	yes	—
287	C₄×C₆₁	#585	1	1	yes	characteristic
288	C₄×C₆₁	#585	1	1	yes	characteristic
289	#3444	C₂×C₆₁	1	2	yes	complemented
290	#3249	C₂×C₆₁	1	1	yes	characteristic, complemented
291	#3246	C₂×C₆₁	1	2	yes	complemented
292	#3245	C₂×C₆₁	1	1	yes	characteristic, complemented
293	#3233	C₂×C₆₁	1	4	yes	complemented
294	#3212	C₂×C₆₁	1	4	yes	complemented
295	#3191	C₂×C₆₁	1	4	yes	complemented
296	#3168	C₂×C₆₁	1	4	yes	complemented
297	#3107	C₂×C₆₁	1	4	yes	complemented
298	#3106	C₂×C₆₁	1	4	yes	complemented
299	C₂×#431	C₂×C₆₁	1	1	yes	characteristic, complemented
300	C₂×C₆₁	—	2	2	no	—
301	C₂×C₆₁	—	4	2	no	—
302	C₂×C₆₁	—	8	4	no	—
303	C₂×C₆₁	#3449	1	1	yes	characteristic
304	C₂×C₆₁	C₂²×#135	1	1	yes	characteristic
305	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
306	#533	C₂²×C₆₁	1	2	yes	—
307	#533	C₂²×C₆₁	1	2	yes	—
308	#533	C₂²×C₆₁	1	2	yes	—
309	#532	C₂²×C₆₁	1	2	yes	—
310	#532	C₂²×C₆₁	1	2	yes	—
311	#532	C₂²×C₆₁	1	2	yes	—
312	#529	—	2	2	no	—
313	#529	—	2	2	no	—
314	#529	—	2	2	no	—
315	#529	—	2	2	no	—
316	#529	C₂²×C₆₁	1	4	yes	—
317	#529	C₂²×C₆₁	1	4	yes	—
318	#525	—	2	2	no	—
319	#525	—	2	2	no	—
320	#525	C₂²×C₆₁	1	4	yes	—
321	C₄×#41	—	2	2	no	—
322	C₄×#41	—	2	2	no	—
323	C₄×#41	C₂²×C₆₁	1	4	yes	—
324	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
325	#499	C₂²×C₆₁	1	4	yes	complemented
326	#495	C₂²×C₆₁	1	4	yes	complemented
327	#488	C₂²×C₆₁	1	8	yes	complemented
328	#485	C₂²×C₆₁	1	8	yes	—
329	#482	C₂²×C₆₁	1	8	yes	—
330	#477	C₂²×C₆₁	1	4	yes	complemented
331	#476	C₂²×C₆₁	1	4	yes	complemented
332	#475	C₂²×C₆₁	1	4	yes	complemented
333	#474	C₂²×C₆₁	1	4	yes	complemented
334	#467	C₂²×C₆₁	1	4	yes	—
335	#466	C₂²×C₆₁	1	4	yes	—
336	#465	C₂²×C₆₁	1	8	yes	—
337	#462	C₂²×C₆₁	1	4	yes	complemented
338	#461	C₂²×C₆₁	1	4	yes	complemented
339	#460	C₂²×C₆₁	1	4	yes	complemented
340	#459	C₂²×C₆₁	1	4	yes	complemented
341	#452	C₂²×C₆₁	1	8	yes	—
342	#449	C₂²×C₆₁	1	8	yes	—
343	C₄×Q₁₆	C₂²×C₆₁	1	4	yes	complemented
344	C₄×SD₁₆	C₂²×C₆₁	1	8	yes	complemented
345	C₄×D₈	C₂²×C₆₁	1	4	yes	complemented
346	#431	C₂²×C₆₁	1	4	yes	—
347	#431	C₂²×C₆₁	1	4	yes	—
348	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
349	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
350	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
351	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
352	C₆₁	#60948	1	1	yes	characteristic, direct product factor, Sylow
353	C₂×#41	—	2	2	no	—
354	C₂×#41	—	2	2	no	—
355	C₂×#41	C₂³×C₆₁	1	4	yes	—
356	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
357	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
359	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
360	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
361	C₂×D₈	C₂³×C₆₁	1	4	yes	—
362	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
363	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
364	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
365	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
366	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
367	#127	C₂³×C₆₁	1	2	yes	—
368	#126	—	2	4	no	—
369	#126	—	2	4	no	—
370	#125	—	2	2	no	—
371	#125	—	2	2	no	—
372	#125	C₂³×C₆₁	1	4	yes	—
373	#124	—	2	2	no	—
374	#124	—	2	2	no	—
375	#124	C₂³×C₆₁	1	4	yes	—
376	#123	—	2	4	no	—
377	#123	—	2	4	no	—
378	#123	—	2	4	no	—
379	C₂²⋊Q₈	—	2	2	no	—
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	—	2	2	no	—
382	C₂²⋊Q₈	—	2	2	no	—
383	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
384	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
385	#121	—	2	2	no	—
386	#121	—	2	2	no	—
387	#121	—	2	2	no	—
388	#121	—	2	2	no	—
389	#121	C₂³×C₆₁	1	4	yes	—
390	#121	C₂³×C₆₁	1	4	yes	—
391	#120	—	2	4	no	—
392	C₄×Q₈	—	2	2	no	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	—	2	2	no	—
396	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
397	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
398	C₄×D₄	—	2	4	no	—
399	C₄×D₄	—	2	4	no	—
400	C₄×D₄	—	2	4	no	—
401	C₄×D₄	—	2	4	no	—
402	C₄×D₄	—	2	4	no	—
403	C₄×D₄	—	2	4	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	C₂³×C₆₁	1	4	yes	—
409	C₄×D₄	C₂³×C₆₁	1	4	yes	—
410	#117	—	2	2	no	—
411	#117	—	2	2	no	—
412	#117	—	2	4	no	—
413	#117	—	2	4	no	—
414	#117	—	2	4	no	—
415	#117	C₂³×C₆₁	1	4	yes	—
416	C₂×C₄²	—	2	4	no	—
417	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
418	C₂×C₄²	D₄×C₆₁	1	2	yes	—
419	C₂×C₄²	D₄×C₆₁	1	2	yes	—
420	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
421	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
422	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
424	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
425	#107	C₂³×C₆₁	1	4	yes	—
426	#107	C₂³×C₆₁	1	4	yes	—
427	#106	C₂³×C₆₁	1	8	yes	—
428	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
429	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
430	#103	C₂³×C₆₁	1	8	yes	—
431	#103	C₂³×C₆₁	1	8	yes	—
432	#102	C₂³×C₆₁	1	8	yes	—
433	#102	C₂³×C₆₁	1	8	yes	—
434	C₂²⋊C₈	C₂³×C₆₁	1	8	yes	—
435	C₄×C₈	C₂³×C₆₁	1	4	yes	—
436	C₄×C₈	C₂³×C₆₁	1	4	yes	—
437	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
438	#41	—	4	4	no	—
439	#41	—	4	4	no	—
440	#41	—	4	8	no	—
441	#41	—	4	8	no	—
442	C₂×Q₈	—	2	2	no	—
443	C₂×Q₈	—	2	2	no	—
444	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
459	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
461	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
462	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
465	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
467	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
469	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
470	Q₁₆	—	4	4	no	—
471	SD₁₆	—	4	8	no	—
472	D₈	—	4	4	no	—
473	C₂×C₈	—	4	2	no	—
474	C₂×C₈	—	4	2	no	—
475	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
476	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
488	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₄²	—	2	4	no	—
499	C₄²	—	2	4	no	—
500	C₄²	—	2	4	no	—
501	C₄²	C₂×D₄×C₆₁	1	2	yes	—
502	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
503	C₄²	C₂×D₄×C₆₁	1	2	yes	—
504	C₄²	C₂×D₄×C₆₁	1	2	yes	—
505	C₄²	C₂×D₄×C₆₁	1	2	yes	—
506	C₄²	C₂×D₄×C₆₁	1	2	yes	—
507	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
508	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
509	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
510	C₄²	C₂⁴×C₆₁	1	2	yes	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	4	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	1	no	—
515	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
516	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
517	Q₈	—	2	4	no	—
518	Q₈	—	2	4	no	—
519	Q₈	—	4	4	no	—
520	Q₈	—	4	4	no	—
521	D₄	—	2	4	no	—
522	D₄	—	2	4	no	—
523	D₄	—	4	4	no	—
524	D₄	—	4	8	no	—
525	D₄	—	4	8	no	—
526	D₄	—	4	8	no	—
527	D₄	—	4	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	4	8	no	—
546	C₂×C₄	—	4	8	no	—
547	C₂×C₄	#135×C₆₁	1	4	yes	—
548	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
549	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
553	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
554	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
555	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
556	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
557	C₈	—	2	4	no	—
558	C₈	—	2	4	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	4	no	—
568	C₂²	C₂×#135×C₆₁	1	2	yes	—
569	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	1	no	—
576	C₄	—	4	4	no	—
577	C₄	—	4	4	no	—
578	C₄	—	4	4	no	—
579	C₄	C₂×#135×C₆₁	1	4	yes	—
580	C₄	C₆₁×#575	1	2	yes	—
581	C₄	C₆₁×#585	1	1	yes	characteristic
582	C₄	C₆₁×#585	1	1	yes	characteristic
583	C₂	—	2	2	no	—
584	C₂	—	4	2	no	—
585	C₂	—	8	4	no	—
586	C₂	C₆₁×#3449	1	1	yes	characteristic
587	C₂	C₂²×#135×C₆₁	1	1	yes	characteristic
588	C₂	C₂×C₆₁×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
socle	C₂²×C₆₁	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3444	C₂	semidirect
2. C₆₁×#3249	C₂	semidirect
3. C₆₁×#3246	C₂	semidirect
4. C₆₁×#3245	C₂	semidirect
5. C₆₁×#3233	C₂	semidirect
6. C₆₁×#3212	C₂	semidirect
7. C₆₁×#3191	C₂	semidirect
8. C₆₁×#3168	C₂	semidirect
9. C₆₁×#3107	C₂	semidirect
10. C₆₁×#3106	C₂	semidirect
11. C₂×C₆₁×#431	C₂	semidirect
31. C₆₁×#499	C₂²	semidirect
32. C₆₁×#495	C₂²	semidirect
33. C₆₁×#488	C₂²	semidirect
36. C₆₁×#477	C₂²	semidirect
37. C₆₁×#476	C₂²	semidirect
38. C₆₁×#475	C₂²	semidirect
39. C₆₁×#474	C₂²	semidirect
43. C₆₁×#462	C₂²	semidirect
44. C₆₁×#461	C₂²	semidirect
45. C₆₁×#460	C₂²	semidirect
46. C₆₁×#459	C₂²	semidirect
49. C₄×Q₁₆×C₆₁	C₂²	semidirect
50. C₄×SD₁₆×C₆₁	C₂²	semidirect
51. C₄×D₈×C₆₁	C₂²	semidirect
264. #60948	C₆₁	direct (N × H)
289. #3444	C₂×C₆₁	semidirect
290. #3249	C₂×C₆₁	semidirect
291. #3246	C₂×C₆₁	semidirect
292. #3245	C₂×C₆₁	semidirect
293. #3233	C₂×C₆₁	semidirect
294. #3212	C₂×C₆₁	semidirect
295. #3191	C₂×C₆₁	semidirect
296. #3168	C₂×C₆₁	semidirect
297. #3107	C₂×C₆₁	semidirect
298. #3106	C₂×C₆₁	semidirect
299. C₂×#431	C₂×C₆₁	semidirect
325. #499	C₂²×C₆₁	semidirect
326. #495	C₂²×C₆₁	semidirect
327. #488	C₂²×C₆₁	semidirect
330. #477	C₂²×C₆₁	semidirect
331. #476	C₂²×C₆₁	semidirect
332. #475	C₂²×C₆₁	semidirect
333. #474	C₂²×C₆₁	semidirect
337. #462	C₂²×C₆₁	semidirect
338. #461	C₂²×C₆₁	semidirect
339. #460	C₂²×C₆₁	semidirect
340. #459	C₂²×C₆₁	semidirect
343. C₄×Q₁₆	C₂²×C₆₁	semidirect
344. C₄×SD₁₆	C₂²×C₆₁	semidirect
345. C₄×D₈	C₂²×C₆₁	semidirect
352. C₆₁	#60948	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×#3444	2
C₆₁×#3249	2
C₆₁×#3246	2
C₆₁×#3245	2
C₆₁×#3233	2
C₆₁×#3212	2
C₆₁×#3191	2
C₆₁×#3168	2
C₆₁×#3107	2
C₆₁×#3106	2
C₂×C₆₁×#431	2
#60948	61

Subgroups — C61×#60948 #29564381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60948 #29564381