Subgroups — C₆₁×#60879 #29564312

Order 15616.

1654 conjugacy classes of subgroups.

The subgroup lattice has 638 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×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3244	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3243	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3233	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3232	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3166	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3160	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3140	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₆₁×#488	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3097	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3096	C₂	1	2	yes	maximal
13	C₆₁×#3082	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3081	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2922	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×#554	—	2	4	no	—
20	C₆₁×#554	—	2	2	no	—
21	C₆₁×#551	—	2	4	no	—
22	C₆₁×#544	C₂²	1	2	yes	—
23	C₆₁×#544	C₂²	1	4	yes	complemented
24	C₆₁×#542	C₂²	1	4	yes	—
25	C₆₁×#536	C₂²	1	1	yes	characteristic
26	C₆₁×#535	C₂²	1	1	yes	characteristic
27	C₆₁×#533	C₂²	1	1	yes	characteristic
28	C₆₁×#533	C₂²	1	1	yes	characteristic
29	C₆₁×#533	C₂²	1	2	yes	complemented
30	C₆₁×#529	C₂²	1	4	yes	—
31	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#125×C₆₁	C₂²	1	2	yes	complemented
33	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#520	C₂²	1	2	yes	—
35	C₆₁×#519	C₂²	1	1	yes	characteristic
36	C₆₁×#518	C₂²	1	1	yes	characteristic
37	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
38	C₆₁×#501	C₂²	1	4	yes	complemented
39	C₆₁×#500	C₂²	1	2	yes	complemented
40	C₆₁×#499	C₂²	1	2	yes	complemented
41	C₆₁×#499	C₂²	1	2	yes	complemented
42	C₆₁×#499	C₂²	1	4	yes	complemented
43	C₆₁×#498	C₂²	1	2	yes	complemented
44	C₆₁×#489	C₂²	1	4	yes	—
45	C₆₁×#488	C₂²	1	4	yes	—
46	C₆₁×#488	C₂²	1	2	yes	—
47	C₆₁×#488	C₂²	1	2	yes	—
48	C₆₁×#488	C₂²	1	2	yes	—
49	C₆₁×#488	C₂²	1	2	yes	—
50	C₆₁×#485	C₂²	1	4	yes	complemented
51	C₆₁×#485	C₂²	1	4	yes	complemented
52	C₆₁×#484	C₂²	1	4	yes	complemented
53	C₆₁×#483	C₂²	1	4	yes	complemented
54	C₆₁×#482	C₂²	1	4	yes	—
55	C₆₁×#482	C₂²	1	4	yes	—
56	C₆₁×#481	C₂²	1	4	yes	—
57	C₆₁×#480	C₂²	1	4	yes	—
58	C₆₁×#479	C₂²	1	4	yes	complemented
59	C₆₁×#479	C₂²	1	4	yes	complemented
60	C₆₁×#478	C₂²	1	4	yes	—
61	C₆₁×#478	C₂²	1	4	yes	—
62	C₆₁×#477	C₂²	1	4	yes	complemented
63	C₆₁×#476	C₂²	1	4	yes	—
64	C₆₁×#475	C₂²	1	4	yes	complemented
65	C₆₁×#474	C₂²	1	4	yes	—
66	C₆₁×#433	C₂²	1	2	yes	complemented
67	C₆₁×#433	C₂²	1	2	yes	complemented
68	C₆₁×#431	C₂²	1	4	yes	complemented
69	C₆₁×#428	C₂²	1	2	yes	—
70	C₆₁×#428	C₂²	1	2	yes	—
71	C₆₁×#427	C₂²	1	2	yes	—
72	C₆₁×#427	C₂²	1	2	yes	—
73	C₆₁×#424	C₂²	1	2	yes	—
74	C₆₁×#419	C₂²	1	2	yes	—
75	C₆₁×#418	C₂²	1	2	yes	—
76	C₂×#103×C₆₁	C₂²	1	2	yes	—
77	C₂×#102×C₆₁	C₂²	1	2	yes	—
78	C₆₁×#408	C₂²	1	2	yes	—
79	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
80	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
81	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
85	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
86	C₄⋊Q₈×C₆₁	—	2	1	no	—
87	C₄⋊Q₈×C₆₁	—	2	2	no	—
88	C₄⋊Q₈×C₆₁	—	2	4	no	—
89	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
90	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
91	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
92	#127×C₆₁	—	2	1	no	—
93	#126×C₆₁	—	2	4	no	—
94	#126×C₆₁	—	2	4	no	—
95	#125×C₆₁	—	2	2	no	—
96	#125×C₆₁	—	2	4	no	—
97	#125×C₆₁	—	2	2	no	—
98	#125×C₆₁	—	2	4	no	—
99	#125×C₆₁	C₂³	1	1	yes	characteristic
100	#125×C₆₁	C₂³	1	1	yes	characteristic
101	#125×C₆₁	C₂³	1	2	yes	—
102	#125×C₆₁	C₂³	1	2	yes	—
103	#125×C₆₁	C₂³	1	4	yes	—
104	#125×C₆₁	C₂³	1	2	yes	—
105	#124×C₆₁	—	2	1	no	—
106	#124×C₆₁	—	2	1	no	—
107	#124×C₆₁	—	2	4	no	—
108	#124×C₆₁	—	2	2	no	—
109	#124×C₆₁	C₂³	1	2	yes	—
110	#124×C₆₁	C₂³	1	2	yes	—
111	#123×C₆₁	—	2	2	no	—
112	#123×C₆₁	—	2	4	no	—
113	#123×C₆₁	—	2	4	no	—
114	C₂²⋊Q₈×C₆₁	—	2	2	no	—
115	C₂²⋊Q₈×C₆₁	—	2	2	no	—
116	C₂²⋊Q₈×C₆₁	—	2	4	no	—
117	C₂²⋊Q₈×C₆₁	—	2	4	no	—
118	C₂²⋊Q₈×C₆₁	—	2	4	no	—
119	C₂²⋊Q₈×C₆₁	—	2	4	no	—
120	C₂²⋊Q₈×C₆₁	—	2	4	no	—
121	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
122	#121×C₆₁	C₂³	1	4	yes	—
123	#120×C₆₁	—	2	2	no	—
124	C₄×Q₈×C₆₁	—	2	2	no	—
125	C₄×Q₈×C₆₁	—	2	2	no	—
126	C₄×Q₈×C₆₁	—	2	2	no	—
127	C₄×Q₈×C₆₁	—	2	2	no	—
128	C₄×Q₈×C₆₁	—	2	4	no	—
129	C₄×Q₈×C₆₁	D₄	1	2	yes	—
130	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
131	C₄×D₄×C₆₁	—	2	4	no	—
132	C₄×D₄×C₆₁	—	2	2	no	—
133	C₄×D₄×C₆₁	—	2	4	no	—
134	C₄×D₄×C₆₁	—	2	2	no	—
135	C₄×D₄×C₆₁	D₄	1	4	yes	—
136	C₄×D₄×C₆₁	D₄	1	2	yes	—
137	C₄×D₄×C₆₁	C₂³	1	4	yes	—
138	#117×C₆₁	—	2	2	no	—
139	#117×C₆₁	—	2	4	no	—
140	#117×C₆₁	C₂³	1	1	yes	characteristic
141	#117×C₆₁	C₂³	1	1	yes	characteristic
142	#117×C₆₁	C₂³	1	2	yes	—
143	#117×C₆₁	C₂³	1	4	yes	—
144	#117×C₆₁	C₂³	1	2	yes	—
145	#117×C₆₁	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
147	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
148	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
151	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
152	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
154	#107×C₆₁	C₂³	1	2	yes	—
155	#107×C₆₁	C₂³	1	2	yes	—
156	#107×C₆₁	C₂³	1	2	yes	—
157	#107×C₆₁	C₂³	1	2	yes	—
158	#107×C₆₁	C₂³	1	4	yes	—
159	#107×C₆₁	C₂³	1	4	yes	—
160	#106×C₆₁	C₂³	1	2	yes	—
161	#106×C₆₁	C₂³	1	2	yes	—
162	#106×C₆₁	C₂³	1	2	yes	—
163	#106×C₆₁	C₂³	1	2	yes	—
164	#106×C₆₁	C₂³	1	4	yes	—
165	#106×C₆₁	C₂³	1	4	yes	—
166	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
167	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
168	#103×C₆₁	C₂³	1	4	yes	—
169	#103×C₆₁	C₂³	1	4	yes	—
170	#103×C₆₁	C₂³	1	4	yes	—
171	#103×C₆₁	C₂³	1	4	yes	—
172	#102×C₆₁	C₂³	1	4	yes	—
173	#102×C₆₁	C₂³	1	4	yes	—
174	#102×C₆₁	C₂³	1	4	yes	—
175	#102×C₆₁	C₂³	1	4	yes	—
176	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
177	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
178	#97×C₆₁	C₂³	1	2	yes	—
179	C₄×C₈×C₆₁	C₂³	1	2	yes	—
180	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
181	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
182	C₄×C₈×C₆₁	C₂³	1	2	yes	—
183	C₂⁴×C₆₁	—	2	1	no	—
184	#41×C₆₁	—	2	4	no	—
185	C₂×Q₈×C₆₁	—	2	1	no	—
186	C₂×Q₈×C₆₁	—	2	2	no	—
187	C₂×Q₈×C₆₁	—	2	4	no	—
188	C₂×Q₈×C₆₁	—	2	2	no	—
189	C₂×Q₈×C₆₁	—	2	4	no	—
190	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
191	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
192	C₂×D₄×C₆₁	—	2	4	no	—
193	C₂×D₄×C₆₁	—	2	1	no	—
194	C₂×D₄×C₆₁	—	2	4	no	—
195	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
196	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
197	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₆₁	—	2	1	no	—
199	C₂²×C₄×C₆₁	—	2	4	no	—
200	C₂²×C₄×C₆₁	—	2	2	no	—
201	C₂²×C₄×C₆₁	—	2	4	no	—
202	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
203	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
206	M₁₆×C₆₁	—	2	4	no	—
207	C₂×C₈×C₆₁	—	2	4	no	—
208	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
209	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
210	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
211	C₄⋊C₄×C₆₁	—	2	4	no	—
212	C₄⋊C₄×C₆₁	—	2	2	no	—
213	C₄⋊C₄×C₆₁	—	2	4	no	—
214	C₄⋊C₄×C₆₁	—	2	4	no	—
215	C₄⋊C₄×C₆₁	—	2	4	no	—
216	C₄⋊C₄×C₆₁	—	2	4	no	—
217	C₄⋊C₄×C₆₁	—	2	2	no	—
218	C₄⋊C₄×C₆₁	—	2	2	no	—
219	C₄⋊C₄×C₆₁	—	2	4	no	—
220	C₄⋊C₄×C₆₁	—	2	4	no	—
221	C₄⋊C₄×C₆₁	—	2	2	no	—
222	C₄⋊C₄×C₆₁	—	2	2	no	—
223	C₄⋊C₄×C₆₁	—	2	4	no	—
224	C₄⋊C₄×C₆₁	—	2	2	no	—
225	C₄⋊C₄×C₆₁	—	2	2	no	—
226	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
227	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
228	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
229	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
230	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
231	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
232	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
233	C₂²⋊C₄×C₆₁	—	2	1	no	—
234	C₂²⋊C₄×C₆₁	—	2	1	no	—
235	C₂²⋊C₄×C₆₁	—	2	4	no	—
236	C₂²⋊C₄×C₆₁	—	2	2	no	—
237	C₂²⋊C₄×C₆₁	—	2	4	no	—
238	C₂²⋊C₄×C₆₁	—	2	4	no	—
239	C₂²⋊C₄×C₆₁	—	2	4	no	—
240	C₂²⋊C₄×C₆₁	—	2	4	no	—
241	C₂²⋊C₄×C₆₁	—	2	4	no	—
242	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
243	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
244	C₄²×C₆₁	—	2	4	no	—
245	C₄²×C₆₁	—	2	1	no	—
246	C₄²×C₆₁	—	2	4	no	—
247	C₄²×C₆₁	—	2	2	no	—
248	C₄²×C₆₁	—	2	1	no	—
249	C₄²×C₆₁	C₂×D₄	1	4	yes	—
250	C₄²×C₆₁	C₂×D₄	1	2	yes	—
251	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
252	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
253	C₄²×C₆₁	C₂⁴	1	2	yes	—
254	C₂³×C₆₁	—	2	2	no	—
255	C₂³×C₆₁	—	4	2	no	—
256	C₂³×C₆₁	—	8	2	no	—
257	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
258	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
259	Q₈×C₆₁	—	2	2	no	—
260	Q₈×C₆₁	—	2	4	no	—
261	Q₈×C₆₁	—	4	2	no	—
262	Q₈×C₆₁	—	8	4	no	—
263	Q₈×C₆₁	—	8	2	no	—
264	Q₈×C₆₁	—	8	2	no	—
265	D₄×C₆₁	—	2	4	no	—
266	D₄×C₆₁	—	2	2	no	—
267	D₄×C₆₁	—	2	4	no	—
268	D₄×C₆₁	—	4	2	no	—
269	D₄×C₆₁	—	8	4	no	—
270	C₂×C₄×C₆₁	—	2	4	no	—
271	C₂×C₄×C₆₁	—	2	2	no	—
272	C₂×C₄×C₆₁	—	2	2	no	—
273	C₂×C₄×C₆₁	—	2	2	no	—
274	C₂×C₄×C₆₁	—	2	2	no	—
275	C₂×C₄×C₆₁	—	2	4	no	—
276	C₂×C₄×C₆₁	—	2	2	no	—
277	C₂×C₄×C₆₁	—	4	4	no	—
278	C₂×C₄×C₆₁	—	4	2	no	—
279	C₂×C₄×C₆₁	—	4	2	no	—
280	C₂×C₄×C₆₁	—	8	4	no	—
281	C₂×C₄×C₆₁	—	8	2	no	—
282	C₂×C₄×C₆₁	—	8	4	no	—
283	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
284	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
285	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
286	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
287	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₆₁	2₋¹⁺⁴	1	4	yes	—
289	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
290	C₈×C₆₁	—	2	2	no	—
291	C₈×C₆₁	—	2	2	no	—
292	C₈×C₆₁	—	2	4	no	—
293	#60879	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
294	C₂²×C₆₁	—	2	2	no	—
295	C₂²×C₆₁	—	2	4	no	—
296	C₂²×C₆₁	—	2	2	no	—
297	C₂²×C₆₁	—	4	4	no	—
298	C₂²×C₆₁	—	4	2	no	—
299	C₂²×C₆₁	—	16	2	no	—
300	C₂²×C₆₁	#536	1	2	yes	—
301	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
302	C₄×C₆₁	—	2	2	no	—
303	C₄×C₆₁	—	2	4	no	—
304	C₄×C₆₁	—	2	2	no	—
305	C₄×C₆₁	—	2	2	no	—
306	C₄×C₆₁	—	4	2	no	—
307	C₄×C₆₁	—	4	4	no	—
308	C₄×C₆₁	—	4	2	no	—
309	C₄×C₆₁	—	4	2	no	—
310	C₄×C₆₁	—	4	2	no	—
311	C₄×C₆₁	—	4	2	no	—
312	C₄×C₆₁	#536	1	2	yes	—
313	C₄×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
314	#3510	C₂×C₆₁	1	1	yes	characteristic
315	#3504	C₂×C₆₁	1	1	yes	characteristic, complemented
316	#3244	C₂×C₆₁	1	4	yes	complemented
317	#3243	C₂×C₆₁	1	4	yes	complemented
318	#3233	C₂×C₆₁	1	4	yes	complemented
319	#3232	C₂×C₆₁	1	4	yes	complemented
320	#3166	C₂×C₆₁	1	1	yes	characteristic, complemented
321	#3160	C₂×C₆₁	1	1	yes	characteristic, complemented
322	#3140	C₂×C₆₁	1	1	yes	characteristic, complemented
323	C₂×#488	C₂×C₆₁	1	1	yes	characteristic, complemented
324	#3097	C₂×C₆₁	1	2	yes	complemented
325	#3096	C₂×C₆₁	1	2	yes	—
326	#3082	C₂×C₆₁	1	2	yes	complemented
327	#3081	C₂×C₆₁	1	2	yes	complemented
328	#2922	C₂×C₆₁	1	1	yes	characteristic, complemented
329	C₂×C₆₁	—	2	2	no	—
330	C₂×C₆₁	—	4	2	no	—
331	C₂×C₆₁	—	8	2	no	—
332	C₂×C₆₁	C₂×#536	1	1	yes	characteristic
333	C₂×C₆₁	#3584	1	2	yes	—
334	#559	—	2	2	no	—
335	#557	—	2	2	no	—
336	#556	—	2	2	no	—
337	#554	—	2	4	no	—
338	#554	—	2	2	no	—
339	#551	—	2	4	no	—
340	#544	C₂²×C₆₁	1	2	yes	—
341	#544	C₂²×C₆₁	1	4	yes	complemented
342	#542	C₂²×C₆₁	1	4	yes	—
343	#536	C₂²×C₆₁	1	1	yes	characteristic
344	#535	C₂²×C₆₁	1	1	yes	characteristic
345	#533	C₂²×C₆₁	1	1	yes	characteristic
346	#533	C₂²×C₆₁	1	1	yes	characteristic
347	#533	C₂²×C₆₁	1	2	yes	complemented
348	#529	C₂²×C₆₁	1	4	yes	—
349	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
350	C₂×#125	C₂²×C₆₁	1	2	yes	complemented
351	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
352	#520	C₂²×C₆₁	1	2	yes	—
353	#519	C₂²×C₆₁	1	1	yes	characteristic
354	#518	C₂²×C₆₁	1	1	yes	characteristic
355	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
356	#501	C₂²×C₆₁	1	4	yes	complemented
357	#500	C₂²×C₆₁	1	2	yes	complemented
358	#499	C₂²×C₆₁	1	2	yes	complemented
359	#499	C₂²×C₆₁	1	2	yes	complemented
360	#499	C₂²×C₆₁	1	4	yes	complemented
361	#498	C₂²×C₆₁	1	2	yes	complemented
362	#489	C₂²×C₆₁	1	4	yes	—
363	#488	C₂²×C₆₁	1	4	yes	—
364	#488	C₂²×C₆₁	1	2	yes	—
365	#488	C₂²×C₆₁	1	2	yes	—
366	#488	C₂²×C₆₁	1	2	yes	—
367	#488	C₂²×C₆₁	1	2	yes	—
368	#485	C₂²×C₆₁	1	4	yes	complemented
369	#485	C₂²×C₆₁	1	4	yes	complemented
370	#484	C₂²×C₆₁	1	4	yes	complemented
371	#483	C₂²×C₆₁	1	4	yes	complemented
372	#482	C₂²×C₆₁	1	4	yes	—
373	#482	C₂²×C₆₁	1	4	yes	—
374	#481	C₂²×C₆₁	1	4	yes	—
375	#480	C₂²×C₆₁	1	4	yes	—
376	#479	C₂²×C₆₁	1	4	yes	complemented
377	#479	C₂²×C₆₁	1	4	yes	complemented
378	#478	C₂²×C₆₁	1	4	yes	—
379	#478	C₂²×C₆₁	1	4	yes	—
380	#477	C₂²×C₆₁	1	4	yes	complemented
381	#476	C₂²×C₆₁	1	4	yes	—
382	#475	C₂²×C₆₁	1	4	yes	complemented
383	#474	C₂²×C₆₁	1	4	yes	—
384	#433	C₂²×C₆₁	1	2	yes	complemented
385	#433	C₂²×C₆₁	1	2	yes	complemented
386	#431	C₂²×C₆₁	1	4	yes	complemented
387	#428	C₂²×C₆₁	1	2	yes	—
388	#428	C₂²×C₆₁	1	2	yes	—
389	#427	C₂²×C₆₁	1	2	yes	—
390	#427	C₂²×C₆₁	1	2	yes	—
391	#424	C₂²×C₆₁	1	2	yes	—
392	#419	C₂²×C₆₁	1	2	yes	—
393	#418	C₂²×C₆₁	1	2	yes	—
394	C₂×#103	C₂²×C₆₁	1	2	yes	—
395	C₂×#102	C₂²×C₆₁	1	2	yes	—
396	#408	C₂²×C₆₁	1	2	yes	—
397	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
398	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
399	C₆₁	#60879	1	1	yes	characteristic, direct product factor, Sylow
400	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
401	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
402	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
403	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
404	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
405	C₄⋊Q₈	—	2	1	no	—
406	C₄⋊Q₈	—	2	2	no	—
407	C₄⋊Q₈	—	2	4	no	—
408	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
409	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
410	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
411	#127	—	2	1	no	—
412	#126	—	2	4	no	—
413	#126	—	2	4	no	—
414	#125	—	2	2	no	—
415	#125	—	2	4	no	—
416	#125	—	2	2	no	—
417	#125	—	2	4	no	—
418	#125	C₂³×C₆₁	1	2	yes	—
419	#125	C₂³×C₆₁	1	2	yes	—
420	#125	C₂³×C₆₁	1	1	yes	characteristic
421	#125	C₂³×C₆₁	1	4	yes	—
422	#125	C₂³×C₆₁	1	2	yes	—
423	#125	C₂³×C₆₁	1	1	yes	characteristic
424	#124	—	2	1	no	—
425	#124	—	2	1	no	—
426	#124	—	2	4	no	—
427	#124	—	2	2	no	—
428	#124	C₂³×C₆₁	1	2	yes	—
429	#124	C₂³×C₆₁	1	2	yes	—
430	#123	—	2	2	no	—
431	#123	—	2	4	no	—
432	#123	—	2	4	no	—
433	C₂²⋊Q₈	—	2	2	no	—
434	C₂²⋊Q₈	—	2	2	no	—
435	C₂²⋊Q₈	—	2	4	no	—
436	C₂²⋊Q₈	—	2	4	no	—
437	C₂²⋊Q₈	—	2	4	no	—
438	C₂²⋊Q₈	—	2	4	no	—
439	C₂²⋊Q₈	—	2	4	no	—
440	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
441	#121	C₂³×C₆₁	1	4	yes	—
442	#120	—	2	2	no	—
443	C₄×Q₈	—	2	2	no	—
444	C₄×Q₈	—	2	2	no	—
445	C₄×Q₈	—	2	2	no	—
446	C₄×Q₈	—	2	2	no	—
447	C₄×Q₈	—	2	4	no	—
448	C₄×Q₈	D₄×C₆₁	1	2	yes	—
449	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
450	C₄×D₄	—	2	4	no	—
451	C₄×D₄	—	2	2	no	—
452	C₄×D₄	—	2	4	no	—
453	C₄×D₄	—	2	2	no	—
454	C₄×D₄	D₄×C₆₁	1	4	yes	—
455	C₄×D₄	D₄×C₆₁	1	2	yes	—
456	C₄×D₄	C₂³×C₆₁	1	4	yes	—
457	#117	—	2	2	no	—
458	#117	—	2	4	no	—
459	#117	C₂³×C₆₁	1	1	yes	characteristic
460	#117	C₂³×C₆₁	1	1	yes	characteristic
461	#117	C₂³×C₆₁	1	2	yes	—
462	#117	C₂³×C₆₁	1	4	yes	—
463	#117	C₂³×C₆₁	1	1	yes	characteristic
464	#117	C₂³×C₆₁	1	2	yes	—
465	C₂×C₄⋊C₄	—	2	2	no	—
466	C₂×C₄⋊C₄	—	2	4	no	—
467	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
469	C₂×C₂²⋊C₄	—	2	2	no	—
470	C₂×C₂²⋊C₄	—	2	2	no	—
471	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
473	#107	C₂³×C₆₁	1	2	yes	—
474	#107	C₂³×C₆₁	1	2	yes	—
475	#107	C₂³×C₆₁	1	2	yes	—
476	#107	C₂³×C₆₁	1	2	yes	—
477	#107	C₂³×C₆₁	1	4	yes	—
478	#107	C₂³×C₆₁	1	4	yes	—
479	#106	C₂³×C₆₁	1	2	yes	—
480	#106	C₂³×C₆₁	1	2	yes	—
481	#106	C₂³×C₆₁	1	2	yes	—
482	#106	C₂³×C₆₁	1	2	yes	—
483	#106	C₂³×C₆₁	1	4	yes	—
484	#106	C₂³×C₆₁	1	4	yes	—
485	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
486	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
487	#103	C₂³×C₆₁	1	4	yes	—
488	#103	C₂³×C₆₁	1	4	yes	—
489	#103	C₂³×C₆₁	1	4	yes	—
490	#103	C₂³×C₆₁	1	4	yes	—
491	#102	C₂³×C₆₁	1	4	yes	—
492	#102	C₂³×C₆₁	1	4	yes	—
493	#102	C₂³×C₆₁	1	4	yes	—
494	#102	C₂³×C₆₁	1	4	yes	—
495	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
496	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
497	#97	C₂³×C₆₁	1	2	yes	—
498	C₄×C₈	C₂³×C₆₁	1	2	yes	—
499	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
500	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
501	C₄×C₈	C₂³×C₆₁	1	2	yes	—
502	C₂⁴	—	2	1	no	—
503	#41	—	2	4	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	2	no	—
506	C₂×Q₈	—	2	4	no	—
507	C₂×Q₈	—	2	2	no	—
508	C₂×Q₈	—	2	4	no	—
509	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
510	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
511	C₂×D₄	—	2	4	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	4	no	—
514	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
515	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
516	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
522	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
523	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
525	M₁₆	—	2	4	no	—
526	C₂×C₈	—	2	4	no	—
527	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
528	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
529	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
530	C₄⋊C₄	—	2	4	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
546	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
547	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
548	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
549	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
550	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
551	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
552	C₂²⋊C₄	—	2	1	no	—
553	C₂²⋊C₄	—	2	1	no	—
554	C₂²⋊C₄	—	2	4	no	—
555	C₂²⋊C₄	—	2	2	no	—
556	C₂²⋊C₄	—	2	4	no	—
557	C₂²⋊C₄	—	2	4	no	—
558	C₂²⋊C₄	—	2	4	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	2	4	no	—
561	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
562	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
563	C₄²	—	2	4	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	4	no	—
566	C₄²	—	2	2	no	—
567	C₄²	—	2	1	no	—
568	C₄²	C₂×D₄×C₆₁	1	4	yes	—
569	C₄²	C₂×D₄×C₆₁	1	2	yes	—
570	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
571	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
572	C₄²	C₂⁴×C₆₁	1	2	yes	—
573	C₂³	—	2	2	no	—
574	C₂³	—	4	2	no	—
575	C₂³	—	8	2	no	—
576	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
577	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
578	Q₈	—	2	2	no	—
579	Q₈	—	2	4	no	—
580	Q₈	—	4	2	no	—
581	Q₈	—	8	4	no	—
582	Q₈	—	8	2	no	—
583	Q₈	—	8	2	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	2	no	—
586	D₄	—	2	4	no	—
587	D₄	—	4	2	no	—
588	D₄	—	8	4	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	8	4	no	—
600	C₂×C₄	—	8	2	no	—
601	C₂×C₄	—	8	4	no	—
602	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
603	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
604	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
605	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
606	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
607	C₂×C₄	2₋¹⁺⁴×C₆₁	1	4	yes	—
608	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
609	C₈	—	2	2	no	—
610	C₈	—	2	2	no	—
611	C₈	—	2	4	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	4	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	16	2	no	—
618	C₂²	C₆₁×#536	1	2	yes	—
619	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
620	C₄	—	2	2	no	—
621	C₄	—	2	4	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	4	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	2	no	—
630	C₄	C₆₁×#536	1	2	yes	—
631	C₄	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
632	C₂	—	2	2	no	—
633	C₂	—	4	2	no	—
634	C₂	—	8	2	no	—
635	C₂	C₂×C₆₁×#536	1	1	yes	characteristic
636	C₂	C₆₁×#3584	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×#3504	C₂	semidirect
3. C₆₁×#3244	C₂	semidirect
4. C₆₁×#3243	C₂	semidirect
5. C₆₁×#3233	C₂	semidirect
6. C₆₁×#3232	C₂	semidirect
7. C₆₁×#3166	C₂	semidirect
8. C₆₁×#3160	C₂	semidirect
9. C₆₁×#3140	C₂	semidirect
10. C₂×C₆₁×#488	C₂	semidirect
11. C₆₁×#3097	C₂	semidirect
13. C₆₁×#3082	C₂	semidirect
14. C₆₁×#3081	C₂	semidirect
15. C₆₁×#2922	C₂	semidirect
23. C₆₁×#544	C₂²	semidirect
29. C₆₁×#533	C₂²	semidirect
32. C₂×#125×C₆₁	C₂²	semidirect
38. C₆₁×#501	C₂²	semidirect
39. C₆₁×#500	C₂²	semidirect
40. C₆₁×#499	C₂²	semidirect
41. C₆₁×#499	C₂²	semidirect
42. C₆₁×#499	C₂²	semidirect
43. C₆₁×#498	C₂²	semidirect
50. C₆₁×#485	C₂²	semidirect
51. C₆₁×#485	C₂²	semidirect
52. C₆₁×#484	C₂²	semidirect
53. C₆₁×#483	C₂²	semidirect
58. C₆₁×#479	C₂²	semidirect
59. C₆₁×#479	C₂²	semidirect
62. C₆₁×#477	C₂²	semidirect
64. C₆₁×#475	C₂²	semidirect
66. C₆₁×#433	C₂²	semidirect
67. C₆₁×#433	C₂²	semidirect
68. C₆₁×#431	C₂²	semidirect
293. #60879	C₆₁	direct (N × H)
315. #3504	C₂×C₆₁	semidirect
316. #3244	C₂×C₆₁	semidirect
317. #3243	C₂×C₆₁	semidirect
318. #3233	C₂×C₆₁	semidirect
319. #3232	C₂×C₆₁	semidirect
320. #3166	C₂×C₆₁	semidirect
321. #3160	C₂×C₆₁	semidirect
322. #3140	C₂×C₆₁	semidirect
323. C₂×#488	C₂×C₆₁	semidirect
324. #3097	C₂×C₆₁	semidirect
326. #3082	C₂×C₆₁	semidirect
327. #3081	C₂×C₆₁	semidirect
328. #2922	C₂×C₆₁	semidirect
341. #544	C₂²×C₆₁	semidirect
347. #533	C₂²×C₆₁	semidirect
350. C₂×#125	C₂²×C₆₁	semidirect
356. #501	C₂²×C₆₁	semidirect
357. #500	C₂²×C₆₁	semidirect
358. #499	C₂²×C₆₁	semidirect
359. #499	C₂²×C₆₁	semidirect
360. #499	C₂²×C₆₁	semidirect
361. #498	C₂²×C₆₁	semidirect
368. #485	C₂²×C₆₁	semidirect
369. #485	C₂²×C₆₁	semidirect
370. #484	C₂²×C₆₁	semidirect
371. #483	C₂²×C₆₁	semidirect
376. #479	C₂²×C₆₁	semidirect
377. #479	C₂²×C₆₁	semidirect
380. #477	C₂²×C₆₁	semidirect
382. #475	C₂²×C₆₁	semidirect
384. #433	C₂²×C₆₁	semidirect
385. #433	C₂²×C₆₁	semidirect
386. #431	C₂²×C₆₁	semidirect
399. C₆₁	#60879	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×#3504	2
C₆₁×#3244	2
C₆₁×#3243	2
C₆₁×#3233	2
C₆₁×#3232	2
C₆₁×#3166	2
C₆₁×#3160	2
C₆₁×#3140	2
C₂×C₆₁×#488	2
C₆₁×#3097	2
C₆₁×#3096	2
C₆₁×#3082	2
C₆₁×#3081	2
C₆₁×#2922	2
#60879	61

Subgroups — C61×#60879 #29564312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60879 #29564312