Subgroups — C₆₁×#33653 #29537086

Order 15616.

568 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3061	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2913	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2237	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2235	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2234	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2233	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2159	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₆₁×#367	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2113	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#537	—	2	1	no	—
15	C₆₁×#520	—	2	1	no	—
16	C₂×M₃₂×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#468	—	2	2	no	—
19	C₆₁×#467	C₂²	1	2	yes	—
20	C₆₁×#466	C₂²	1	2	yes	—
21	C₆₁×#428	—	2	1	no	—
22	C₆₁×#428	—	2	2	no	—
23	C₆₁×#427	C₂²	1	1	yes	characteristic
24	C₆₁×#427	C₂²	1	2	yes	—
25	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#107×C₆₁	C₂²	1	2	yes	—
28	C₆₁×#417	—	2	1	no	—
29	C₆₁×#367	C₂²	1	2	yes	—
30	C₆₁×#367	C₂²	1	2	yes	—
31	C₆₁×#367	C₂²	1	2	yes	—
32	C₆₁×#366	C₂²	1	2	yes	—
33	C₆₁×#358	C₂²	1	1	yes	characteristic
34	C₆₁×#358	C₂²	1	1	yes	characteristic
35	C₆₁×#358	C₂²	1	2	yes	—
36	C₆₁×#357	C₂²	1	1	yes	characteristic
37	C₆₁×#357	C₂²	1	1	yes	characteristic
38	C₆₁×#357	C₂²	1	2	yes	—
39	C₆₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
40	C₆₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₂×#41×C₆₁	—	2	1	no	—
42	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
43	#135×C₆₁	—	2	2	no	—
44	#135×C₆₁	—	2	2	no	—
45	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
46	C₂×SD₁₆×C₆₁	—	2	1	no	—
47	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
48	#131×C₆₁	—	2	2	no	—
49	#131×C₆₁	—	2	2	no	—
50	C₂×M₁₆×C₆₁	D₄	1	1	yes	characteristic
51	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
52	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
54	C₂²⋊Q₈×C₆₁	—	2	2	no	—
55	C₂²⋊Q₈×C₆₁	—	4	1	no	—
56	#121×C₆₁	—	2	2	no	—
57	#121×C₆₁	—	4	1	no	—
58	#121×C₆₁	—	4	2	no	—
59	C₄×Q₈×C₆₁	—	4	1	no	—
60	C₄×D₄×C₆₁	—	4	2	no	—
61	C₄×D₄×C₆₁	—	4	1	no	—
62	#117×C₆₁	—	2	2	no	—
63	#117×C₆₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
67	M₃₂×C₆₁	—	2	2	no	—
68	C₂×C₁₆×C₆₁	—	2	2	no	—
69	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
70	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
71	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
72	#107×C₆₁	—	2	2	no	—
73	#107×C₆₁	—	2	1	no	—
74	#107×C₆₁	—	2	1	no	—
75	#107×C₆₁	C₂³	1	1	yes	characteristic
76	#107×C₆₁	C₂³	1	1	yes	characteristic
77	#107×C₆₁	C₂³	1	2	yes	—
78	#107×C₆₁	C₂³	1	2	yes	—
79	#106×C₆₁	—	2	2	no	—
80	#106×C₆₁	—	2	1	no	—
81	#103×C₆₁	—	2	2	no	—
82	#102×C₆₁	—	2	2	no	—
83	#41×C₆₁	—	2	2	no	—
84	#41×C₆₁	—	2	2	no	—
85	#41×C₆₁	—	4	2	no	—
86	#41×C₆₁	—	4	2	no	—
87	C₂×Q₈×C₆₁	—	2	1	no	—
88	C₂×Q₈×C₆₁	D₈	1	1	yes	characteristic
89	C₂×D₄×C₆₁	—	2	1	no	—
90	C₂×D₄×C₆₁	—	4	1	no	—
91	C₂×D₄×C₆₁	—	4	2	no	—
92	C₂×D₄×C₆₁	D₈	1	2	yes	—
93	C₂×D₄×C₆₁	D₈	1	1	yes	characteristic
94	C₂²×C₄×C₆₁	—	4	2	no	—
95	C₂²×C₄×C₆₁	—	4	1	no	—
96	C₂²×C₄×C₆₁	—	4	1	no	—
97	C₂²×C₄×C₆₁	—	4	1	no	—
98	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
100	Q₁₆×C₆₁	—	2	1	no	—
101	Q₁₆×C₆₁	—	2	1	no	—
102	SD₁₆×C₆₁	—	4	2	no	—
103	D₈×C₆₁	—	2	1	no	—
104	D₈×C₆₁	—	2	1	no	—
105	M₁₆×C₆₁	—	2	2	no	—
106	M₁₆×C₆₁	—	2	4	no	—
107	C₂×C₈×C₆₁	—	2	2	no	—
108	C₂×C₈×C₆₁	—	2	2	no	—
109	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₆₁	#41	1	2	yes	—
112	C₂×C₈×C₆₁	#41	1	2	yes	—
113	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
114	C₄⋊C₄×C₆₁	—	2	2	no	—
115	C₄⋊C₄×C₆₁	—	2	1	no	—
116	C₄⋊C₄×C₆₁	—	2	2	no	—
117	C₄⋊C₄×C₆₁	—	2	1	no	—
118	C₄⋊C₄×C₆₁	—	4	2	no	—
119	C₄⋊C₄×C₆₁	—	4	1	no	—
120	C₄⋊C₄×C₆₁	—	4	1	no	—
121	C₄⋊C₄×C₆₁	—	4	2	no	—
122	C₂²⋊C₄×C₆₁	—	4	2	no	—
123	C₂²⋊C₄×C₆₁	—	4	1	no	—
124	C₂²⋊C₄×C₆₁	—	4	2	no	—
125	C₂²⋊C₄×C₆₁	—	4	2	no	—
126	C₄²×C₆₁	—	4	2	no	—
127	C₄²×C₆₁	—	4	1	no	—
128	C₁₆×C₆₁	—	2	1	no	—
129	C₁₆×C₆₁	—	2	1	no	—
130	C₁₆×C₆₁	—	2	2	no	—
131	C₂³×C₆₁	—	4	1	no	—
132	C₂³×C₆₁	C₂×D₈	1	2	yes	—
133	C₂³×C₆₁	C₂×D₈	1	1	yes	characteristic
134	Q₈×C₆₁	—	2	2	no	—
135	Q₈×C₆₁	—	4	1	no	—
136	Q₈×C₆₁	—	4	1	no	—
137	D₄×C₆₁	—	2	4	no	—
138	D₄×C₆₁	—	2	2	no	—
139	D₄×C₆₁	—	4	1	no	—
140	D₄×C₆₁	—	4	1	no	—
141	D₄×C₆₁	—	8	2	no	—
142	D₄×C₆₁	—	16	2	no	—
143	C₂×C₄×C₆₁	—	2	2	no	—
144	C₂×C₄×C₆₁	—	2	2	no	—
145	C₂×C₄×C₆₁	—	4	1	no	—
146	C₂×C₄×C₆₁	—	4	2	no	—
147	C₂×C₄×C₆₁	—	4	1	no	—
148	C₂×C₄×C₆₁	—	4	2	no	—
149	C₂×C₄×C₆₁	—	4	1	no	—
150	C₂×C₄×C₆₁	—	8	2	no	—
151	C₂×C₄×C₆₁	—	16	1	no	—
152	C₂×C₄×C₆₁	—	16	2	no	—
153	C₂×C₄×C₆₁	—	16	1	no	—
154	C₂×C₄×C₆₁	#123	1	2	yes	—
155	C₂×C₄×C₆₁	C₂×D₈	1	2	yes	—
156	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₆₁	#137	1	2	yes	—
158	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
159	C₈×C₆₁	—	2	2	no	—
160	C₈×C₆₁	#123	1	2	yes	—
161	C₈×C₆₁	C₂×#41	1	1	yes	characteristic
162	C₈×C₆₁	C₂×#41	1	1	yes	characteristic
163	#33653	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂²×C₆₁	—	2	1	no	—
165	C₂²×C₆₁	—	2	1	no	—
166	C₂²×C₆₁	—	2	2	no	—
167	C₂²×C₆₁	—	2	2	no	—
168	C₂²×C₆₁	—	2	2	no	—
169	C₂²×C₆₁	—	8	1	no	—
170	C₂²×C₆₁	—	8	1	no	—
171	C₂²×C₆₁	—	8	1	no	—
172	C₂²×C₆₁	#480	1	2	yes	—
173	C₂²×C₆₁	C₂²×D₈	1	1	yes	characteristic
174	C₄×C₆₁	—	2	2	no	—
175	C₄×C₆₁	—	8	1	no	—
176	C₄×C₆₁	—	8	1	no	—
177	C₄×C₆₁	—	8	2	no	—
178	C₄×C₆₁	—	8	1	no	—
179	C₄×C₆₁	—	8	2	no	—
180	C₄×C₆₁	#480	1	2	yes	—
181	C₄×C₆₁	C₂×#123	1	1	yes	characteristic
182	C₄×C₆₁	C₂×#137	1	1	yes	characteristic
183	#3061	C₂×C₆₁	1	1	yes	characteristic
184	#2913	C₂×C₆₁	1	1	yes	characteristic, complemented
185	#2237	C₂×C₆₁	1	2	yes	complemented
186	#2235	C₂×C₆₁	1	2	yes	complemented
187	#2234	C₂×C₆₁	1	2	yes	complemented
188	#2233	C₂×C₆₁	1	2	yes	complemented
189	#2159	C₂×C₆₁	1	1	yes	characteristic, complemented
190	C₂×#367	C₂×C₆₁	1	1	yes	characteristic, complemented
191	#2139	C₂×C₆₁	1	1	yes	characteristic, complemented
192	#2138	C₂×C₆₁	1	1	yes	characteristic, complemented
193	#2113	C₂×C₆₁	1	1	yes	characteristic, complemented
194	C₂×C₆₁	—	2	2	no	—
195	C₂×C₆₁	—	4	2	no	—
196	C₂×C₆₁	—	16	1	no	—
197	C₂×C₆₁	C₂×#480	1	1	yes	characteristic
198	C₂×C₆₁	#3416	1	1	yes	characteristic
199	C₂×C₆₁	#3416	1	1	yes	characteristic
200	C₂×#135	C₂²×C₆₁	1	1	yes	characteristic
201	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
202	#537	—	2	1	no	—
203	#520	—	2	1	no	—
204	C₂×M₃₂	C₂²×C₆₁	1	1	yes	characteristic
205	C₂²×C₁₆	C₂²×C₆₁	1	1	yes	characteristic
206	#468	—	2	2	no	—
207	#467	C₂²×C₆₁	1	2	yes	—
208	#466	C₂²×C₆₁	1	2	yes	—
209	#428	—	2	1	no	—
210	#428	—	2	2	no	—
211	#427	C₂²×C₆₁	1	1	yes	characteristic
212	#427	C₂²×C₆₁	1	2	yes	—
213	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
214	C₂×#107	C₂²×C₆₁	1	2	yes	—
215	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
216	#417	—	2	1	no	—
217	#367	C₂²×C₆₁	1	2	yes	—
218	#367	C₂²×C₆₁	1	2	yes	—
219	#367	C₂²×C₆₁	1	2	yes	—
220	#366	C₂²×C₆₁	1	2	yes	—
221	#358	C₂²×C₆₁	1	1	yes	characteristic
222	#358	C₂²×C₆₁	1	1	yes	characteristic
223	#358	C₂²×C₆₁	1	2	yes	—
224	#357	C₂²×C₆₁	1	1	yes	characteristic
225	#357	C₂²×C₆₁	1	1	yes	characteristic
226	#357	C₂²×C₆₁	1	2	yes	—
227	C₂²⋊C₁₆	C₂²×C₆₁	1	2	yes	—
228	C₂²⋊C₁₆	C₂²×C₆₁	1	2	yes	—
229	C₆₁	#33653	1	1	yes	characteristic, direct product factor, Sylow
230	C₂×#41	—	2	1	no	—
231	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
232	#135	—	2	2	no	—
233	#135	—	2	2	no	—
234	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
235	C₂×SD₁₆	—	2	1	no	—
236	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
237	#131	—	2	2	no	—
238	#131	—	2	2	no	—
239	C₂×M₁₆	D₄×C₆₁	1	1	yes	characteristic
240	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
241	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
242	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
243	C₂²⋊Q₈	—	2	2	no	—
244	C₂²⋊Q₈	—	4	1	no	—
245	#121	—	2	2	no	—
246	#121	—	4	1	no	—
247	#121	—	4	2	no	—
248	C₄×Q₈	—	4	1	no	—
249	C₄×D₄	—	4	2	no	—
250	C₄×D₄	—	4	1	no	—
251	#117	—	2	2	no	—
252	#117	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	M₃₂	—	2	2	no	—
257	C₂×C₁₆	—	2	2	no	—
258	C₂×C₁₆	C₂³×C₆₁	1	2	yes	—
259	C₂×C₁₆	C₂³×C₆₁	1	1	yes	characteristic
260	C₂×C₁₆	C₂³×C₆₁	1	1	yes	characteristic
261	#107	—	2	2	no	—
262	#107	—	2	1	no	—
263	#107	—	2	1	no	—
264	#107	C₂³×C₆₁	1	1	yes	characteristic
265	#107	C₂³×C₆₁	1	1	yes	characteristic
266	#107	C₂³×C₆₁	1	2	yes	—
267	#107	C₂³×C₆₁	1	2	yes	—
268	#106	—	2	2	no	—
269	#106	—	2	1	no	—
270	#103	—	2	2	no	—
271	#102	—	2	2	no	—
272	#41	—	2	2	no	—
273	#41	—	2	2	no	—
274	#41	—	4	2	no	—
275	#41	—	4	2	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	D₈×C₆₁	1	1	yes	characteristic
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	D₈×C₆₁	1	2	yes	—
282	C₂×D₄	D₈×C₆₁	1	1	yes	characteristic
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
288	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
289	Q₁₆	—	2	1	no	—
290	Q₁₆	—	2	1	no	—
291	SD₁₆	—	4	2	no	—
292	D₈	—	2	1	no	—
293	D₈	—	2	1	no	—
294	M₁₆	—	2	2	no	—
295	M₁₆	—	2	4	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
299	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
300	C₂×C₈	#41×C₆₁	1	2	yes	—
301	C₂×C₈	#41×C₆₁	1	2	yes	—
302	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	4	1	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₄²	—	4	2	no	—
316	C₄²	—	4	1	no	—
317	C₁₆	—	2	1	no	—
318	C₁₆	—	2	1	no	—
319	C₁₆	—	2	2	no	—
320	C₂³	—	4	1	no	—
321	C₂³	C₂×D₈×C₆₁	1	2	yes	—
322	C₂³	C₂×D₈×C₆₁	1	1	yes	characteristic
323	Q₈	—	2	2	no	—
324	Q₈	—	4	1	no	—
325	Q₈	—	4	1	no	—
326	D₄	—	2	4	no	—
327	D₄	—	2	2	no	—
328	D₄	—	4	1	no	—
329	D₄	—	4	1	no	—
330	D₄	—	8	2	no	—
331	D₄	—	16	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	8	2	no	—
340	C₂×C₄	—	16	1	no	—
341	C₂×C₄	—	16	2	no	—
342	C₂×C₄	—	16	1	no	—
343	C₂×C₄	#123×C₆₁	1	2	yes	—
344	C₂×C₄	C₂×D₈×C₆₁	1	2	yes	—
345	C₂×C₄	C₂×D₈×C₆₁	1	1	yes	characteristic
346	C₂×C₄	#137×C₆₁	1	2	yes	—
347	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
348	C₈	—	2	2	no	—
349	C₈	#123×C₆₁	1	2	yes	—
350	C₈	C₂×#41×C₆₁	1	1	yes	characteristic
351	C₈	C₂×#41×C₆₁	1	1	yes	characteristic
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	8	1	no	—
358	C₂²	—	8	1	no	—
359	C₂²	—	8	1	no	—
360	C₂²	C₆₁×#480	1	2	yes	—
361	C₂²	C₂²×D₈×C₆₁	1	1	yes	characteristic
362	C₄	—	2	2	no	—
363	C₄	—	8	1	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	2	no	—
366	C₄	—	8	1	no	—
367	C₄	—	8	2	no	—
368	C₄	C₆₁×#480	1	2	yes	—
369	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
370	C₄	C₂×#137×C₆₁	1	1	yes	characteristic
371	C₂	—	2	2	no	—
372	C₂	—	4	2	no	—
373	C₂	—	16	1	no	—
374	C₂	C₂×C₆₁×#480	1	1	yes	characteristic
375	C₂	C₆₁×#3416	1	1	yes	characteristic
376	C₂	C₆₁×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₆₁
prime radical	C₆₁×#3061	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×#41×C₆₁ ◁ C₂×#131×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#2913	C₂	semidirect
3. C₆₁×#2237	C₂	semidirect
4. C₆₁×#2235	C₂	semidirect
5. C₆₁×#2234	C₂	semidirect
6. C₆₁×#2233	C₂	semidirect
7. C₆₁×#2159	C₂	semidirect
8. C₂×C₆₁×#367	C₂	semidirect
9. C₆₁×#2139	C₂	semidirect
10. C₆₁×#2138	C₂	semidirect
11. C₆₁×#2113	C₂	semidirect
163. #33653	C₆₁	direct (N × H)
184. #2913	C₂×C₆₁	semidirect
185. #2237	C₂×C₆₁	semidirect
186. #2235	C₂×C₆₁	semidirect
187. #2234	C₂×C₆₁	semidirect
188. #2233	C₂×C₆₁	semidirect
189. #2159	C₂×C₆₁	semidirect
190. C₂×#367	C₂×C₆₁	semidirect
191. #2139	C₂×C₆₁	semidirect
192. #2138	C₂×C₆₁	semidirect
193. #2113	C₂×C₆₁	semidirect
229. C₆₁	#33653	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×#3061	2
C₆₁×#2913	2
C₆₁×#2237	2
C₆₁×#2235	2
C₆₁×#2234	2
C₆₁×#2233	2
C₆₁×#2159	2
C₂×C₆₁×#367	2
C₆₁×#2139	2
C₆₁×#2138	2
C₆₁×#2113	2
#33653	61

Subgroups — C61×#33653 #29537086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#33653 #29537086