Subgroups — C₆₁×#25690 #29529123

Order 15616.

1072 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3508	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3166	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3080	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2641	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2037	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1995	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1965	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1856	C₂	1	4	yes	maximal, complemented
9	C₆₁×#1759	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#559	—	2	2	no	—
11	C₆₁×#550	—	2	2	no	—
12	C₆₁×#546	—	2	4	no	—
13	C₆₁×#540	—	2	2	no	—
14	C₆₁×#535	C₂²	1	2	yes	—
15	C₆₁×#533	C₂²	1	1	yes	characteristic
16	C₆₁×#532	—	2	2	no	—
17	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#518	C₂²	1	2	yes	—
20	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
21	C₆₁×#501	—	2	2	no	—
22	C₆₁×#499	—	2	2	no	—
23	C₆₁×#479	—	2	2	no	—
24	C₆₁×#478	—	2	2	no	—
25	C₆₁×#428	C₂²	1	4	yes	—
26	C₆₁×#428	C₂²	1	2	yes	—
27	C₆₁×#423	C₂²	1	1	yes	characteristic
28	C₂×#104×C₆₁	C₂²	1	2	yes	—
29	C₆₁×#417	C₂²	1	2	yes	—
30	C₂×#100×C₆₁	C₂²	1	4	yes	—
31	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
32	C₆₁×#394	—	2	4	no	—
33	C₆₁×#390	C₂²	1	4	yes	—
34	C₆₁×#376	C₂²	1	1	yes	characteristic
35	C₆₁×#339	C₂²	1	2	yes	—
36	C₆₁×#339	C₂²	1	4	yes	—
37	C₂×#41×C₆₁	—	2	4	no	—
38	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₆₁	D₄	1	4	yes	—
40	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
41	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
42	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
43	C₄⋊Q₈×C₆₁	D₄	1	2	yes	—
44	#127×C₆₁	—	2	2	no	—
45	#127×C₆₁	—	2	1	no	—
46	#127×C₆₁	—	2	1	no	—
47	#127×C₆₁	—	2	2	no	—
48	#125×C₆₁	—	2	2	no	—
49	#125×C₆₁	—	2	1	no	—
50	#125×C₆₁	—	2	1	no	—
51	#125×C₆₁	D₄	1	2	yes	—
52	#124×C₆₁	—	2	4	no	—
53	#124×C₆₁	—	2	2	no	—
54	#123×C₆₁	—	2	8	no	—
55	C₂²⋊Q₈×C₆₁	—	2	2	no	—
56	#121×C₆₁	—	2	4	no	—
57	#121×C₆₁	—	2	8	no	—
58	#121×C₆₁	—	2	4	no	—
59	#120×C₆₁	—	2	4	no	—
60	C₄×Q₈×C₆₁	—	2	2	no	—
61	C₄×Q₈×C₆₁	D₄	1	2	yes	—
62	C₄×D₄×C₆₁	—	2	4	no	—
63	C₄×D₄×C₆₁	—	2	2	no	—
64	C₄×D₄×C₆₁	—	2	4	no	—
65	C₄×D₄×C₆₁	—	2	4	no	—
66	C₄×D₄×C₆₁	D₄	1	2	yes	—
67	#117×C₆₁	—	2	1	no	—
68	#117×C₆₁	C₂³	1	2	yes	—
69	#117×C₆₁	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
74	C₂×C₄²×C₆₁	—	2	1	no	—
75	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
76	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
77	#107×C₆₁	—	2	2	no	—
78	#107×C₆₁	—	2	4	no	—
79	#106×C₆₁	—	2	2	no	—
80	#106×C₆₁	—	2	4	no	—
81	C₄⋊C₈×C₆₁	—	2	2	no	—
82	#104×C₆₁	—	2	4	no	—
83	#103×C₆₁	—	2	2	no	—
84	#102×C₆₁	—	2	2	no	—
85	#100×C₆₁	—	2	8	no	—
86	#97×C₆₁	—	2	1	no	—
87	C₄×C₈×C₆₁	—	2	1	no	—
88	#95×C₆₁	—	2	2	no	—
89	C₂⁴×C₆₁	C₂×D₄	1	4	yes	—
90	#41×C₆₁	—	2	2	no	—
91	#41×C₆₁	—	2	2	no	—
92	#41×C₆₁	—	8	8	no	—
93	C₂×Q₈×C₆₁	—	2	2	no	—
94	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
95	C₂×D₄×C₆₁	—	2	1	no	—
96	C₂×D₄×C₆₁	—	2	8	no	—
97	C₂×D₄×C₆₁	—	2	4	no	—
98	C₂×D₄×C₆₁	—	2	4	no	—
99	C₂×D₄×C₆₁	—	2	2	no	—
100	C₂×D₄×C₆₁	—	2	2	no	—
101	C₂×D₄×C₆₁	—	2	4	no	—
102	C₂×D₄×C₆₁	—	2	4	no	—
103	C₂×D₄×C₆₁	—	8	4	no	—
104	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₆₁	—	2	8	no	—
106	C₂²×C₄×C₆₁	—	2	2	no	—
107	C₂²×C₄×C₆₁	—	2	1	no	—
108	C₂²×C₄×C₆₁	—	2	2	no	—
109	C₂²×C₄×C₆₁	—	2	2	no	—
110	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
112	M₁₆×C₆₁	—	2	2	no	—
113	M₁₆×C₆₁	—	2	4	no	—
114	M₁₆×C₆₁	#41	1	4	yes	complemented
115	C₂×C₈×C₆₁	—	2	2	no	—
116	C₂×C₈×C₆₁	—	2	2	no	—
117	C₄⋊C₄×C₆₁	—	2	2	no	—
118	C₄⋊C₄×C₆₁	—	2	2	no	—
119	C₄⋊C₄×C₆₁	—	2	4	no	—
120	C₄⋊C₄×C₆₁	—	2	2	no	—
121	C₄⋊C₄×C₆₁	—	2	2	no	—
122	C₄⋊C₄×C₆₁	—	4	2	no	—
123	C₄⋊C₄×C₆₁	—	4	2	no	—
124	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
125	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
126	C₂²⋊C₄×C₆₁	—	2	8	no	—
127	C₂²⋊C₄×C₆₁	—	2	8	no	—
128	C₂²⋊C₄×C₆₁	—	2	1	no	—
129	C₂²⋊C₄×C₆₁	—	2	2	no	—
130	C₂²⋊C₄×C₆₁	—	2	2	no	—
131	C₂²⋊C₄×C₆₁	—	8	8	no	—
132	C₄²×C₆₁	—	2	2	no	—
133	C₄²×C₆₁	—	2	1	no	—
134	C₄²×C₆₁	—	2	2	no	—
135	C₄²×C₆₁	—	2	2	no	—
136	C₄²×C₆₁	—	2	2	no	—
137	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₆₁	C₂×D₄	1	2	yes	—
140	C₂³×C₆₁	—	2	4	no	—
141	C₂³×C₆₁	—	2	1	no	—
142	C₂³×C₆₁	—	2	8	no	—
143	C₂³×C₆₁	—	4	8	no	—
144	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₆₁	—	2	1	no	—
146	Q₈×C₆₁	—	2	1	no	—
147	Q₈×C₆₁	—	4	4	no	—
148	D₄×C₆₁	—	2	1	no	—
149	D₄×C₆₁	—	2	1	no	—
150	D₄×C₆₁	—	4	8	no	—
151	D₄×C₆₁	—	4	2	no	—
152	D₄×C₆₁	—	4	2	no	—
153	D₄×C₆₁	—	4	2	no	—
154	D₄×C₆₁	—	4	4	no	—
155	D₄×C₆₁	—	8	4	no	—
156	D₄×C₆₁	—	8	8	no	—
157	C₂×C₄×C₆₁	—	2	1	no	—
158	C₂×C₄×C₆₁	—	2	2	no	—
159	C₂×C₄×C₆₁	—	2	4	no	—
160	C₂×C₄×C₆₁	—	4	2	no	—
161	C₂×C₄×C₆₁	—	4	4	no	—
162	C₂×C₄×C₆₁	—	4	2	no	—
163	C₂×C₄×C₆₁	—	4	4	no	—
164	C₂×C₄×C₆₁	—	4	4	no	—
165	C₂×C₄×C₆₁	—	4	2	no	—
166	C₂×C₄×C₆₁	—	4	2	no	—
167	C₂×C₄×C₆₁	—	8	8	no	—
168	C₂×C₄×C₆₁	#120	1	2	yes	—
169	C₂×C₄×C₆₁	#120	1	2	yes	—
170	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
173	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
174	C₈×C₆₁	—	2	4	no	—
175	C₈×C₆₁	—	4	2	no	—
176	#25690	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂²×C₆₁	—	2	2	no	—
178	C₂²×C₆₁	—	4	1	no	—
179	C₂²×C₆₁	—	4	4	no	—
180	C₂²×C₆₁	—	4	2	no	—
181	C₂²×C₆₁	—	4	8	no	—
182	C₂²×C₆₁	—	8	8	no	—
183	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
184	C₂²×C₆₁	#547	1	2	yes	—
185	C₄×C₆₁	—	2	2	no	—
186	C₄×C₆₁	—	2	2	no	—
187	C₄×C₆₁	—	4	1	no	—
188	C₄×C₆₁	—	4	2	no	—
189	C₄×C₆₁	—	4	4	no	—
190	C₄×C₆₁	—	8	2	no	—
191	C₄×C₆₁	—	8	2	no	—
192	C₄×C₆₁	#532	1	1	yes	characteristic
193	C₄×C₆₁	#536	1	1	yes	characteristic
194	C₄×C₆₁	#548	1	2	yes	—
195	#3508	C₂×C₆₁	1	1	yes	characteristic
196	#3166	C₂×C₆₁	1	1	yes	characteristic, complemented
197	#3080	C₂×C₆₁	1	1	yes	characteristic, complemented
198	#2641	C₂×C₆₁	1	1	yes	characteristic, complemented
199	#2037	C₂×C₆₁	1	4	yes	complemented
200	#1995	C₂×C₆₁	1	1	yes	characteristic, complemented
201	#1965	C₂×C₆₁	1	1	yes	characteristic, complemented
202	#1856	C₂×C₆₁	1	4	yes	complemented
203	#1759	C₂×C₆₁	1	1	yes	characteristic, complemented
204	C₂×C₆₁	—	2	2	no	—
205	C₂×C₆₁	—	8	1	no	—
206	C₂×C₆₁	—	8	4	no	—
207	C₂×C₆₁	#2432	1	1	yes	characteristic
208	C₂×C₆₁	#3019	1	2	yes	—
209	#559	—	2	2	no	—
210	#550	—	2	2	no	—
211	#546	—	2	4	no	—
212	#540	—	2	2	no	—
213	#535	C₂²×C₆₁	1	2	yes	—
214	#533	C₂²×C₆₁	1	1	yes	characteristic
215	#532	—	2	2	no	—
216	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
217	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
218	#518	C₂²×C₆₁	1	2	yes	—
219	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
220	#501	—	2	2	no	—
221	#499	—	2	2	no	—
222	#479	—	2	2	no	—
223	#478	—	2	2	no	—
224	#428	C₂²×C₆₁	1	2	yes	—
225	#428	C₂²×C₆₁	1	4	yes	—
226	#423	C₂²×C₆₁	1	1	yes	characteristic
227	C₂×#104	C₂²×C₆₁	1	2	yes	—
228	#417	C₂²×C₆₁	1	2	yes	—
229	C₂×#100	C₂²×C₆₁	1	4	yes	—
230	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
231	#394	—	2	4	no	—
232	#390	C₂²×C₆₁	1	4	yes	—
233	#376	C₂²×C₆₁	1	1	yes	characteristic
234	#339	C₂²×C₆₁	1	2	yes	—
235	#339	C₂²×C₆₁	1	4	yes	—
236	C₆₁	#25690	1	1	yes	characteristic, direct product factor, Sylow
237	C₂×#41	—	2	4	no	—
238	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
239	C₂²×D₄	D₄×C₆₁	1	4	yes	—
240	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
241	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
242	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
243	C₄⋊Q₈	D₄×C₆₁	1	2	yes	—
244	#127	—	2	2	no	—
245	#127	—	2	1	no	—
246	#127	—	2	1	no	—
247	#127	—	2	2	no	—
248	#125	—	2	2	no	—
249	#125	—	2	1	no	—
250	#125	—	2	1	no	—
251	#125	D₄×C₆₁	1	2	yes	—
252	#124	—	2	4	no	—
253	#124	—	2	2	no	—
254	#123	—	2	8	no	—
255	C₂²⋊Q₈	—	2	2	no	—
256	#121	—	2	4	no	—
257	#121	—	2	8	no	—
258	#121	—	2	4	no	—
259	#120	—	2	4	no	—
260	C₄×Q₈	—	2	2	no	—
261	C₄×Q₈	D₄×C₆₁	1	2	yes	—
262	C₄×D₄	—	2	4	no	—
263	C₄×D₄	—	2	2	no	—
264	C₄×D₄	—	2	4	no	—
265	C₄×D₄	—	2	4	no	—
266	C₄×D₄	D₄×C₆₁	1	2	yes	—
267	#117	—	2	1	no	—
268	#117	C₂³×C₆₁	1	1	yes	characteristic
269	#117	C₂³×C₆₁	1	2	yes	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	4	no	—
273	C₂×C₂²⋊C₄	—	2	8	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
276	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
277	#107	—	2	2	no	—
278	#107	—	2	4	no	—
279	#106	—	2	2	no	—
280	#106	—	2	4	no	—
281	C₄⋊C₈	—	2	2	no	—
282	#104	—	2	4	no	—
283	#103	—	2	2	no	—
284	#102	—	2	2	no	—
285	#100	—	2	8	no	—
286	#97	—	2	1	no	—
287	C₄×C₈	—	2	1	no	—
288	#95	—	2	2	no	—
289	C₂⁴	C₂×D₄×C₆₁	1	4	yes	—
290	#41	—	2	2	no	—
291	#41	—	2	2	no	—
292	#41	—	8	8	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	8	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	8	4	no	—
304	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
311	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
312	M₁₆	—	2	2	no	—
313	M₁₆	—	2	4	no	—
314	M₁₆	#41×C₆₁	1	4	yes	complemented
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
325	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
326	C₂²⋊C₄	—	2	8	no	—
327	C₂²⋊C₄	—	2	8	no	—
328	C₂²⋊C₄	—	2	1	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	8	8	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
338	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₆₁	1	2	yes	—
340	C₂³	—	2	4	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	8	no	—
343	C₂³	—	4	8	no	—
344	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
345	Q₈	—	2	1	no	—
346	Q₈	—	2	1	no	—
347	Q₈	—	4	4	no	—
348	D₄	—	2	1	no	—
349	D₄	—	2	1	no	—
350	D₄	—	4	8	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	4	no	—
355	D₄	—	8	4	no	—
356	D₄	—	8	8	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	8	8	no	—
368	C₂×C₄	#120×C₆₁	1	2	yes	—
369	C₂×C₄	#120×C₆₁	1	2	yes	—
370	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
373	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
374	C₈	—	2	4	no	—
375	C₈	—	4	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	8	no	—
381	C₂²	—	8	8	no	—
382	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
383	C₂²	C₆₁×#547	1	2	yes	—
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	1	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	4	no	—
389	C₄	—	8	2	no	—
390	C₄	—	8	2	no	—
391	C₄	C₆₁×#532	1	1	yes	characteristic
392	C₄	C₆₁×#536	1	1	yes	characteristic
393	C₄	C₆₁×#548	1	2	yes	—
394	C₂	—	2	2	no	—
395	C₂	—	8	4	no	—
396	C₂	—	8	1	no	—
397	C₂	C₆₁×#2432	1	1	yes	characteristic
398	C₂	C₆₁×#3019	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#3508	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#3166	C₂	semidirect
3. C₆₁×#3080	C₂	semidirect
4. C₆₁×#2641	C₂	semidirect
5. C₆₁×#2037	C₂	semidirect
6. C₆₁×#1995	C₂	semidirect
7. C₆₁×#1965	C₂	semidirect
8. C₆₁×#1856	C₂	semidirect
9. C₆₁×#1759	C₂	semidirect
114. M₁₆×C₆₁	#41	semidirect
176. #25690	C₆₁	direct (N × H)
196. #3166	C₂×C₆₁	semidirect
197. #3080	C₂×C₆₁	semidirect
198. #2641	C₂×C₆₁	semidirect
199. #2037	C₂×C₆₁	semidirect
200. #1995	C₂×C₆₁	semidirect
201. #1965	C₂×C₆₁	semidirect
202. #1856	C₂×C₆₁	semidirect
203. #1759	C₂×C₆₁	semidirect
236. C₆₁	#25690	direct (N × H)
314. M₁₆	#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×#3508	2
C₆₁×#3166	2
C₆₁×#3080	2
C₆₁×#2641	2
C₆₁×#2037	2
C₆₁×#1995	2
C₆₁×#1965	2
C₆₁×#1856	2
C₆₁×#1759	2
#25690	61

Subgroups — C61×#25690 #29529123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25690 #29529123