Subgroups — C₆₁×#61915 #29565348

Order 15616.

1640 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3507	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3400	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3398	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3395	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3377	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3374	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3365	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3223	C₂	1	4	yes	maximal, complemented
10	C₆₁×#3216	C₂	1	1	yes	maximal, characteristic
11	C₆₁×#3210	C₂	1	1	yes	maximal, characteristic
12	C₆₁×#3120	C₂	1	4	yes	maximal, complemented
13	C₆₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#564	—	2	2	no	—
17	C₆₁×#559	C₂²	1	2	yes	—
18	C₆₁×#557	—	2	1	no	—
19	C₆₁×#557	—	2	1	no	—
20	C₆₁×#557	C₂²	1	2	yes	—
21	C₆₁×#557	C₂²	1	2	yes	—
22	C₆₁×#557	C₂²	1	2	yes	—
23	C₆₁×#557	C₂²	1	2	yes	—
24	C₆₁×#557	C₂²	1	2	yes	—
25	C₆₁×#556	—	2	1	no	—
26	C₆₁×#556	C₂²	1	4	yes	—
27	C₆₁×#554	—	2	1	no	—
28	C₆₁×#552	—	2	2	no	—
29	C₆₁×#541	—	2	2	no	—
30	C₆₁×#541	—	2	2	no	—
31	C₆₁×#541	C₂²	1	4	yes	—
32	C₆₁×#539	—	2	2	no	—
33	C₆₁×#536	C₂²	1	2	yes	—
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	C₆₁×#532	C₂²	1	1	yes	characteristic
38	C₆₁×#529	—	2	2	no	—
39	C₆₁×#520	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#497	C₂²	1	2	yes	—
42	C₆₁×#497	C₂²	1	4	yes	—
43	C₆₁×#494	C₂²	1	1	yes	characteristic
44	C₆₁×#494	C₂²	1	4	yes	—
45	C₆₁×#492	C₂²	1	1	yes	characteristic
46	C₆₁×#491	C₂²	1	4	yes	—
47	C₆₁×#489	C₂²	1	2	yes	—
48	C₆₁×#488	C₂²	1	4	yes	—
49	C₆₁×#487	C₂²	1	1	yes	characteristic
50	C₆₁×#486	C₂²	1	1	yes	characteristic
51	C₆₁×#484	C₂²	1	2	yes	—
52	C₆₁×#483	C₂²	1	2	yes	—
53	C₆₁×#479	C₂²	1	4	yes	—
54	C₆₁×#478	C₂²	1	4	yes	—
55	C₆₁×#477	C₂²	1	2	yes	—
56	C₆₁×#475	C₂²	1	2	yes	—
57	C₆₁×#464	C₂²	1	4	yes	—
58	C₆₁×#464	C₂²	1	4	yes	—
59	C₆₁×#464	C₂²	1	4	yes	—
60	C₆₁×#462	C₂²	1	2	yes	—
61	C₆₁×#462	C₂²	1	2	yes	—
62	C₆₁×#462	C₂²	1	2	yes	—
63	C₆₁×#462	C₂²	1	4	yes	—
64	C₆₁×#462	C₂²	1	4	yes	—
65	C₆₁×#462	C₂²	1	4	yes	—
66	C₆₁×#461	C₂²	1	4	yes	—
67	C₆₁×#460	C₂²	1	2	yes	—
68	C₆₁×#452	C₂²	1	4	yes	—
69	C₆₁×#452	C₂²	1	4	yes	—
70	C₆₁×#451	C₂²	1	2	yes	—
71	C₆₁×#451	C₂²	1	2	yes	—
72	C₆₁×#446	C₂²	1	2	yes	—
73	C₆₁×#446	C₂²	1	4	yes	—
74	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
75	C₆₁×#441	C₂²	1	4	yes	—
76	C₆₁×#441	C₂²	1	4	yes	—
77	C₆₁×#440	C₂²	1	4	yes	—
78	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
79	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
80	C₄×Q₁₆×C₆₁	C₂²	1	4	yes	—
81	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	—
82	C₆₁×#433	C₂²	1	4	yes	—
83	C₆₁×#432	C₂²	1	1	yes	characteristic
84	C₆₁×#431	C₂²	1	1	yes	characteristic
85	C₂×#41×C₆₁	C₂³	1	2	yes	—
86	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
87	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
88	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
89	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
90	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
91	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
92	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
93	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
94	C₄⋊Q₈×C₆₁	—	2	2	no	—
95	C₄⋊Q₈×C₆₁	—	2	2	no	—
96	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
97	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
98	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
99	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
102	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
103	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
104	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
105	#127×C₆₁	C₂³	1	1	yes	characteristic
106	#126×C₆₁	—	2	4	no	—
107	#126×C₆₁	—	2	4	no	—
108	#126×C₆₁	—	2	4	no	—
109	#126×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	—	2	4	no	—
114	#125×C₆₁	—	2	4	no	—
115	#125×C₆₁	—	2	4	no	—
116	#125×C₆₁	—	2	4	no	—
117	#125×C₆₁	—	2	4	no	—
118	#125×C₆₁	—	2	4	no	—
119	#125×C₆₁	—	2	2	no	—
120	#125×C₆₁	—	2	1	no	—
121	#125×C₆₁	—	2	1	no	—
122	#125×C₆₁	D₄	1	2	yes	—
123	#125×C₆₁	C₂³	1	4	yes	—
124	#124×C₆₁	—	2	2	no	—
125	#124×C₆₁	C₂³	1	2	yes	—
126	#124×C₆₁	C₂³	1	4	yes	—
127	#123×C₆₁	—	2	4	no	—
128	#123×C₆₁	—	2	4	no	—
129	C₂²⋊Q₈×C₆₁	—	2	4	no	—
130	C₂²⋊Q₈×C₆₁	—	2	1	no	—
131	C₂²⋊Q₈×C₆₁	—	2	1	no	—
132	C₂²⋊Q₈×C₆₁	—	2	2	no	—
133	C₂²⋊Q₈×C₆₁	—	2	2	no	—
134	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
135	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
136	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
137	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
138	#121×C₆₁	—	2	1	no	—
139	#121×C₆₁	—	2	1	no	—
140	C₄×Q₈×C₆₁	—	2	2	no	—
141	C₄×Q₈×C₆₁	—	2	2	no	—
142	C₄×Q₈×C₆₁	—	2	2	no	—
143	C₄×Q₈×C₆₁	—	2	2	no	—
144	C₄×Q₈×C₆₁	—	2	2	no	—
145	C₄×Q₈×C₆₁	—	2	1	no	—
146	C₄×Q₈×C₆₁	—	2	1	no	—
147	C₄×Q₈×C₆₁	—	2	1	no	—
148	C₄×Q₈×C₆₁	—	2	1	no	—
149	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
150	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
151	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
152	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
153	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
154	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
155	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
156	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
157	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
158	C₄×D₄×C₆₁	—	2	2	no	—
159	C₄×D₄×C₆₁	—	2	4	no	—
160	C₄×D₄×C₆₁	—	2	1	no	—
161	C₄×D₄×C₆₁	—	2	1	no	—
162	C₄×D₄×C₆₁	C₂³	1	4	yes	—
163	#117×C₆₁	—	2	1	no	—
164	#117×C₆₁	—	2	1	no	—
165	#117×C₆₁	—	2	2	no	—
166	#117×C₆₁	—	2	4	no	—
167	#117×C₆₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
169	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
170	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₆₁	—	2	1	no	—
172	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
173	#107×C₆₁	C₂³	1	2	yes	—
174	#107×C₆₁	C₂³	1	2	yes	—
175	#106×C₆₁	C₂³	1	4	yes	—
176	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
177	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
178	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
179	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
180	#103×C₆₁	C₂³	1	2	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	4	yes	—
186	#103×C₆₁	C₂³	1	4	yes	—
187	#103×C₆₁	C₂³	1	4	yes	—
188	#102×C₆₁	C₂³	1	4	yes	—
189	#102×C₆₁	C₂³	1	4	yes	—
190	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
192	#97×C₆₁	C₂³	1	2	yes	—
193	#97×C₆₁	C₂³	1	4	yes	—
194	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₆₁	C₂³	1	4	yes	—
197	#41×C₆₁	—	4	4	no	—
198	C₂×Q₈×C₆₁	—	2	1	no	—
199	C₂×Q₈×C₆₁	—	2	1	no	—
200	C₂×Q₈×C₆₁	—	2	1	no	—
201	C₂×Q₈×C₆₁	—	4	2	no	—
202	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
203	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
204	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
205	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
206	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
207	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
208	C₂×D₄×C₆₁	—	2	2	no	—
209	C₂×D₄×C₆₁	—	2	1	no	—
210	C₂×D₄×C₆₁	—	2	1	no	—
211	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₆₁	—	2	1	no	—
213	C₂²×C₄×C₆₁	—	2	1	no	—
214	C₂²×C₄×C₆₁	—	2	2	no	—
215	C₂²×C₄×C₆₁	—	2	4	no	—
216	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
219	Q₁₆×C₆₁	—	4	2	no	—
220	Q₁₆×C₆₁	—	4	4	no	—
221	Q₁₆×C₆₁	—	4	4	no	—
222	Q₁₆×C₆₁	—	4	2	no	—
223	Q₁₆×C₆₁	—	4	4	no	—
224	SD₁₆×C₆₁	—	4	4	no	—
225	SD₁₆×C₆₁	—	4	4	no	—
226	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
227	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
228	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
229	C₄⋊C₄×C₆₁	—	2	1	no	—
230	C₄⋊C₄×C₆₁	—	2	4	no	—
231	C₄⋊C₄×C₆₁	—	2	2	no	—
232	C₄⋊C₄×C₆₁	—	2	2	no	—
233	C₄⋊C₄×C₆₁	—	2	4	no	—
234	C₄⋊C₄×C₆₁	—	2	1	no	—
235	C₄⋊C₄×C₆₁	—	2	1	no	—
236	C₄⋊C₄×C₆₁	—	2	1	no	—
237	C₄⋊C₄×C₆₁	—	2	1	no	—
238	C₄⋊C₄×C₆₁	—	2	1	no	—
239	C₄⋊C₄×C₆₁	—	2	1	no	—
240	C₄⋊C₄×C₆₁	—	2	1	no	—
241	C₄⋊C₄×C₆₁	—	2	1	no	—
242	C₄⋊C₄×C₆₁	—	2	4	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	4	no	—
248	C₄⋊C₄×C₆₁	—	2	4	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	C₂×D₄	1	2	yes	—
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	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
262	C₂²⋊C₄×C₆₁	—	2	2	no	—
263	C₂²⋊C₄×C₆₁	—	2	2	no	—
264	C₂²⋊C₄×C₆₁	—	2	2	no	—
265	C₂²⋊C₄×C₆₁	—	2	4	no	—
266	C₂²⋊C₄×C₆₁	—	2	4	no	—
267	C₂²⋊C₄×C₆₁	—	2	2	no	—
268	C₂²⋊C₄×C₆₁	—	2	4	no	—
269	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
270	C₄²×C₆₁	—	2	2	no	—
271	C₄²×C₆₁	—	2	2	no	—
272	C₄²×C₆₁	—	2	4	no	—
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	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
280	C₄²×C₆₁	C₂⁴	1	4	yes	—
281	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
282	C₂³×C₆₁	—	2	2	no	—
283	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
284	Q₈×C₆₁	—	2	4	no	—
285	Q₈×C₆₁	—	2	2	no	—
286	Q₈×C₆₁	—	2	4	no	—
287	Q₈×C₆₁	—	2	2	no	—
288	Q₈×C₆₁	—	2	2	no	—
289	Q₈×C₆₁	—	2	2	no	—
290	Q₈×C₆₁	—	2	4	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	D₄×C₆₁	—	2	4	no	—
296	D₄×C₆₁	—	4	4	no	—
297	D₄×C₆₁	—	4	2	no	—
298	D₄×C₆₁	—	8	1	no	—
299	C₂×C₄×C₆₁	—	2	2	no	—
300	C₂×C₄×C₆₁	—	2	2	no	—
301	C₂×C₄×C₆₁	—	2	2	no	—
302	C₂×C₄×C₆₁	—	2	2	no	—
303	C₂×C₄×C₆₁	—	2	2	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	—	4	1	no	—
309	C₂×C₄×C₆₁	—	4	4	no	—
310	C₂×C₄×C₆₁	—	4	2	no	—
311	C₂×C₄×C₆₁	—	8	4	no	—
312	C₂×C₄×C₆₁	—	8	1	no	—
313	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
316	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
317	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
321	C₈×C₆₁	—	2	2	no	—
322	C₈×C₆₁	—	2	4	no	—
323	C₈×C₆₁	—	2	2	no	—
324	#61915	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
325	C₂²×C₆₁	—	2	1	no	—
326	C₂²×C₆₁	—	2	1	no	—
327	C₂²×C₆₁	—	2	1	no	—
328	C₂²×C₆₁	—	4	2	no	—
329	C₂²×C₆₁	—	4	2	no	—
330	C₂²×C₆₁	—	4	2	no	—
331	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
332	C₄×C₆₁	—	2	1	no	—
333	C₄×C₆₁	—	2	1	no	—
334	C₄×C₆₁	—	2	4	no	—
335	C₄×C₆₁	—	2	1	no	—
336	C₄×C₆₁	—	2	1	no	—
337	C₄×C₆₁	—	2	4	no	—
338	C₄×C₆₁	—	4	2	no	—
339	C₄×C₆₁	—	4	2	no	—
340	C₄×C₆₁	—	4	2	no	—
341	C₄×C₆₁	—	4	2	no	—
342	C₄×C₆₁	—	4	2	no	—
343	C₄×C₆₁	—	4	2	no	—
344	C₄×C₆₁	—	4	2	no	—
345	C₄×C₆₁	#578	1	2	yes	—
346	C₄×C₆₁	#585	1	2	yes	—
347	#3556	C₂×C₆₁	1	1	yes	characteristic, complemented
348	#3507	C₂×C₆₁	1	1	yes	characteristic
349	#3400	C₂×C₆₁	1	2	yes	complemented
350	#3398	C₂×C₆₁	1	4	yes	complemented
351	#3395	C₂×C₆₁	1	2	yes	complemented
352	#3377	C₂×C₆₁	1	4	yes	complemented
353	#3374	C₂×C₆₁	1	2	yes	complemented
354	#3365	C₂×C₆₁	1	2	yes	complemented
355	#3223	C₂×C₆₁	1	4	yes	complemented
356	#3216	C₂×C₆₁	1	1	yes	characteristic
357	#3210	C₂×C₆₁	1	1	yes	characteristic
358	#3120	C₂×C₆₁	1	4	yes	complemented
359	#3113	C₂×C₆₁	1	1	yes	characteristic, complemented
360	#3104	C₂×C₆₁	1	1	yes	characteristic, complemented
361	#2985	C₂×C₆₁	1	1	yes	characteristic, complemented
362	C₂×C₆₁	—	4	1	no	—
363	C₂×C₆₁	—	8	2	no	—
364	C₂×C₆₁	#3487	1	1	yes	characteristic
365	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
366	C₂×C₆₁	#3586	1	1	yes	characteristic
367	#564	—	2	2	no	—
368	#559	C₂²×C₆₁	1	2	yes	—
369	#557	—	2	1	no	—
370	#557	—	2	1	no	—
371	#557	C₂²×C₆₁	1	2	yes	—
372	#557	C₂²×C₆₁	1	2	yes	—
373	#557	C₂²×C₆₁	1	2	yes	—
374	#557	C₂²×C₆₁	1	2	yes	—
375	#557	C₂²×C₆₁	1	2	yes	—
376	#556	—	2	1	no	—
377	#556	C₂²×C₆₁	1	4	yes	—
378	#554	—	2	1	no	—
379	#552	—	2	2	no	—
380	#541	—	2	2	no	—
381	#541	—	2	2	no	—
382	#541	C₂²×C₆₁	1	4	yes	—
383	#539	—	2	2	no	—
384	#536	C₂²×C₆₁	1	2	yes	—
385	#533	C₂²×C₆₁	1	1	yes	characteristic
386	#533	C₂²×C₆₁	1	1	yes	characteristic
387	#533	C₂²×C₆₁	1	1	yes	characteristic
388	#532	C₂²×C₆₁	1	1	yes	characteristic
389	#529	—	2	2	no	—
390	#520	C₂²×C₆₁	1	2	yes	—
391	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
392	#497	C₂²×C₆₁	1	2	yes	—
393	#497	C₂²×C₆₁	1	4	yes	—
394	#494	C₂²×C₆₁	1	1	yes	characteristic
395	#494	C₂²×C₆₁	1	4	yes	—
396	#492	C₂²×C₆₁	1	1	yes	characteristic
397	#491	C₂²×C₆₁	1	4	yes	—
398	#489	C₂²×C₆₁	1	2	yes	—
399	#488	C₂²×C₆₁	1	4	yes	—
400	#487	C₂²×C₆₁	1	1	yes	characteristic
401	#486	C₂²×C₆₁	1	1	yes	characteristic
402	#484	C₂²×C₆₁	1	2	yes	—
403	#483	C₂²×C₆₁	1	2	yes	—
404	#479	C₂²×C₆₁	1	4	yes	—
405	#478	C₂²×C₆₁	1	4	yes	—
406	#477	C₂²×C₆₁	1	2	yes	—
407	#475	C₂²×C₆₁	1	2	yes	—
408	#464	C₂²×C₆₁	1	4	yes	—
409	#464	C₂²×C₆₁	1	4	yes	—
410	#464	C₂²×C₆₁	1	4	yes	—
411	#462	C₂²×C₆₁	1	2	yes	—
412	#462	C₂²×C₆₁	1	2	yes	—
413	#462	C₂²×C₆₁	1	2	yes	—
414	#462	C₂²×C₆₁	1	4	yes	—
415	#462	C₂²×C₆₁	1	4	yes	—
416	#462	C₂²×C₆₁	1	4	yes	—
417	#461	C₂²×C₆₁	1	4	yes	—
418	#460	C₂²×C₆₁	1	2	yes	—
419	#452	C₂²×C₆₁	1	4	yes	—
420	#452	C₂²×C₆₁	1	4	yes	—
421	#451	C₂²×C₆₁	1	2	yes	—
422	#451	C₂²×C₆₁	1	2	yes	—
423	#446	C₂²×C₆₁	1	2	yes	—
424	#446	C₂²×C₆₁	1	4	yes	—
425	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
426	#441	C₂²×C₆₁	1	4	yes	—
427	#441	C₂²×C₆₁	1	4	yes	—
428	#440	C₂²×C₆₁	1	4	yes	—
429	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
430	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
431	C₄×Q₁₆	C₂²×C₆₁	1	4	yes	—
432	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	—
433	#433	C₂²×C₆₁	1	4	yes	—
434	#432	C₂²×C₆₁	1	1	yes	characteristic
435	#431	C₂²×C₆₁	1	1	yes	characteristic
436	C₆₁	#61915	1	1	yes	characteristic, direct product factor, Sylow
437	C₂×#41	C₂³×C₆₁	1	2	yes	—
438	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
439	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
440	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
441	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
442	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
443	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
444	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
445	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
446	C₄⋊Q₈	—	2	2	no	—
447	C₄⋊Q₈	—	2	2	no	—
448	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
449	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
450	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
451	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
452	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
453	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
454	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
455	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
456	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
457	#127	C₂³×C₆₁	1	1	yes	characteristic
458	#126	—	2	4	no	—
459	#126	—	2	4	no	—
460	#126	—	2	4	no	—
461	#126	—	2	4	no	—
462	#125	—	2	2	no	—
463	#125	—	2	4	no	—
464	#125	—	2	2	no	—
465	#125	—	2	2	no	—
466	#125	—	2	4	no	—
467	#125	—	2	4	no	—
468	#125	—	2	4	no	—
469	#125	—	2	4	no	—
470	#125	—	2	4	no	—
471	#125	—	2	4	no	—
472	#125	—	2	1	no	—
473	#125	—	2	1	no	—
474	#125	D₄×C₆₁	1	2	yes	—
475	#125	C₂³×C₆₁	1	4	yes	—
476	#124	—	2	2	no	—
477	#124	C₂³×C₆₁	1	2	yes	—
478	#124	C₂³×C₆₁	1	4	yes	—
479	#123	—	2	4	no	—
480	#123	—	2	4	no	—
481	C₂²⋊Q₈	—	2	4	no	—
482	C₂²⋊Q₈	—	2	1	no	—
483	C₂²⋊Q₈	—	2	1	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
487	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
488	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
489	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
490	#121	—	2	1	no	—
491	#121	—	2	1	no	—
492	C₄×Q₈	—	2	2	no	—
493	C₄×Q₈	—	2	2	no	—
494	C₄×Q₈	—	2	2	no	—
495	C₄×Q₈	—	2	2	no	—
496	C₄×Q₈	—	2	2	no	—
497	C₄×Q₈	—	2	1	no	—
498	C₄×Q₈	—	2	1	no	—
499	C₄×Q₈	—	2	1	no	—
500	C₄×Q₈	—	2	1	no	—
501	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
502	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
503	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
504	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
505	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
506	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
507	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
508	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
509	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	4	no	—
512	C₄×D₄	—	2	1	no	—
513	C₄×D₄	—	2	1	no	—
514	C₄×D₄	C₂³×C₆₁	1	4	yes	—
515	#117	—	2	1	no	—
516	#117	—	2	1	no	—
517	#117	—	2	2	no	—
518	#117	—	2	4	no	—
519	#117	C₂³×C₆₁	1	2	yes	—
520	C₂×C₄⋊C₄	—	2	1	no	—
521	C₂×C₄⋊C₄	—	2	2	no	—
522	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
523	C₂×C₄²	—	2	1	no	—
524	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
525	#107	C₂³×C₆₁	1	2	yes	—
526	#107	C₂³×C₆₁	1	2	yes	—
527	#106	C₂³×C₆₁	1	4	yes	—
528	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
529	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
530	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
531	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
532	#103	C₂³×C₆₁	1	2	yes	—
533	#103	C₂³×C₆₁	1	4	yes	—
534	#103	C₂³×C₆₁	1	2	yes	—
535	#103	C₂³×C₆₁	1	2	yes	—
536	#103	C₂³×C₆₁	1	2	yes	—
537	#103	C₂³×C₆₁	1	4	yes	—
538	#103	C₂³×C₆₁	1	4	yes	—
539	#103	C₂³×C₆₁	1	4	yes	—
540	#102	C₂³×C₆₁	1	4	yes	—
541	#102	C₂³×C₆₁	1	4	yes	—
542	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
543	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
544	#97	C₂³×C₆₁	1	2	yes	—
545	#97	C₂³×C₆₁	1	4	yes	—
546	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
547	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
548	C₄×C₈	C₂³×C₆₁	1	4	yes	—
549	#41	—	4	4	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	4	2	no	—
554	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
555	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
556	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
557	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
558	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
559	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
569	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
570	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
571	Q₁₆	—	4	2	no	—
572	Q₁₆	—	4	4	no	—
573	Q₁₆	—	4	4	no	—
574	Q₁₆	—	4	2	no	—
575	Q₁₆	—	4	4	no	—
576	SD₁₆	—	4	4	no	—
577	SD₁₆	—	4	4	no	—
578	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
579	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
580	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
606	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
607	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
608	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
609	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
610	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
611	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
612	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
613	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
622	C₄²	—	2	2	no	—
623	C₄²	—	2	2	no	—
624	C₄²	—	2	4	no	—
625	C₄²	—	2	2	no	—
626	C₄²	—	2	2	no	—
627	C₄²	—	2	4	no	—
628	C₄²	—	2	4	no	—
629	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
630	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
631	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
632	C₄²	C₂⁴×C₆₁	1	4	yes	—
633	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
634	C₂³	—	2	2	no	—
635	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
636	Q₈	—	2	4	no	—
637	Q₈	—	2	2	no	—
638	Q₈	—	2	4	no	—
639	Q₈	—	2	2	no	—
640	Q₈	—	2	2	no	—
641	Q₈	—	2	2	no	—
642	Q₈	—	2	4	no	—
643	Q₈	—	4	2	no	—
644	Q₈	—	4	2	no	—
645	Q₈	—	4	2	no	—
646	Q₈	—	4	2	no	—
647	D₄	—	2	4	no	—
648	D₄	—	4	4	no	—
649	D₄	—	4	2	no	—
650	D₄	—	8	1	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	4	2	no	—
663	C₂×C₄	—	8	4	no	—
664	C₂×C₄	—	8	1	no	—
665	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
666	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
667	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
668	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
669	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
670	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
671	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
672	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
673	C₈	—	2	2	no	—
674	C₈	—	2	4	no	—
675	C₈	—	2	2	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	2	no	—
682	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
683	C₄	—	2	1	no	—
684	C₄	—	2	4	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	4	no	—
688	C₄	—	2	1	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	2	no	—
696	C₄	C₆₁×#578	1	2	yes	—
697	C₄	C₆₁×#585	1	2	yes	—
698	C₂	—	4	1	no	—
699	C₂	—	8	2	no	—
700	C₂	C₆₁×#3487	1	1	yes	characteristic
701	C₂	C₂×C₆₁×#578	1	1	yes	characteristic
702	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×#532	C₂²
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×#3556	C₂	semidirect
3. C₆₁×#3400	C₂	semidirect
4. C₆₁×#3398	C₂	semidirect
5. C₆₁×#3395	C₂	semidirect
6. C₆₁×#3377	C₂	semidirect
7. C₆₁×#3374	C₂	semidirect
8. C₆₁×#3365	C₂	semidirect
9. C₆₁×#3223	C₂	semidirect
12. C₆₁×#3120	C₂	semidirect
13. C₆₁×#3113	C₂	semidirect
14. C₆₁×#3104	C₂	semidirect
15. C₆₁×#2985	C₂	semidirect
324. #61915	C₆₁	direct (N × H)
347. #3556	C₂×C₆₁	semidirect
349. #3400	C₂×C₆₁	semidirect
350. #3398	C₂×C₆₁	semidirect
351. #3395	C₂×C₆₁	semidirect
352. #3377	C₂×C₆₁	semidirect
353. #3374	C₂×C₆₁	semidirect
354. #3365	C₂×C₆₁	semidirect
355. #3223	C₂×C₆₁	semidirect
358. #3120	C₂×C₆₁	semidirect
359. #3113	C₂×C₆₁	semidirect
360. #3104	C₂×C₆₁	semidirect
361. #2985	C₂×C₆₁	semidirect
436. C₆₁	#61915	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×#3556	2
C₆₁×#3507	2
C₆₁×#3400	2
C₆₁×#3398	2
C₆₁×#3395	2
C₆₁×#3377	2
C₆₁×#3374	2
C₆₁×#3365	2
C₆₁×#3223	2
C₆₁×#3216	2
C₆₁×#3210	2
C₆₁×#3120	2
C₆₁×#3113	2
C₆₁×#3104	2
C₆₁×#2985	2
#61915	61

Subgroups — C61×#61915 #29565348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61915 #29565348