Subgroups — C₆₁×#25591 #29529024

Order 15616.

1120 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3138	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3038	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2858	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2003	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1994	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1966	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1888	C₂	1	4	yes	maximal, complemented
9	C₄×#104×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
11	C₆₁×#557	—	2	2	no	—
12	C₆₁×#556	—	2	2	no	—
13	C₆₁×#552	—	2	4	no	—
14	C₆₁×#541	—	2	2	no	—
15	C₆₁×#536	C₂²	1	2	yes	—
16	C₆₁×#533	—	2	2	no	—
17	C₆₁×#533	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#124×C₆₁	C₂²	1	4	yes	—
21	C₆₁×#519	C₂²	1	2	yes	—
22	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
23	C₆₁×#490	—	2	2	no	—
24	C₆₁×#486	—	2	2	no	—
25	C₆₁×#460	—	2	2	no	—
26	C₆₁×#459	—	2	2	no	—
27	C₆₁×#423	C₂²	1	1	yes	characteristic
28	C₂×#104×C₆₁	C₂²	1	2	yes	—
29	C₆₁×#418	C₂²	1	2	yes	—
30	C₆₁×#418	C₂²	1	4	yes	—
31	C₂×#101×C₆₁	C₂²	1	4	yes	—
32	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
33	C₆₁×#390	—	2	4	no	—
34	C₄³×C₆₁	C₂²	1	1	yes	characteristic
35	C₆₁×#339	C₂²	1	2	yes	—
36	C₆₁×#339	C₂²	1	4	yes	—
37	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
38	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
39	C₂²×D₄×C₆₁	—	2	2	no	—
40	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
41	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
42	C₂×SD₁₆×C₆₁	—	2	2	no	—
43	C₂×D₈×C₆₁	—	2	2	no	—
44	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
45	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
46	C₄⋊Q₈×C₆₁	—	2	2	no	—
47	C₄⋊Q₈×C₆₁	—	2	1	no	—
48	C₄⋊Q₈×C₆₁	—	2	1	no	—
49	C₄⋊Q₈×C₆₁	—	2	2	no	—
50	C₄⋊Q₈×C₆₁	D₄	1	2	yes	—
51	#127×C₆₁	—	2	2	no	—
52	#127×C₆₁	—	2	1	no	—
53	#127×C₆₁	—	2	1	no	—
54	#126×C₆₁	—	2	8	no	—
55	#125×C₆₁	—	2	4	no	—
56	#125×C₆₁	—	2	8	no	—
57	#125×C₆₁	D₄	1	2	yes	—
58	#124×C₆₁	—	2	2	no	—
59	#124×C₆₁	—	2	8	no	—
60	#124×C₆₁	—	4	4	no	—
61	#123×C₆₁	—	2	4	no	—
62	C₂²⋊Q₈×C₆₁	—	2	4	no	—
63	C₂²⋊Q₈×C₆₁	—	2	2	no	—
64	C₂²⋊Q₈×C₆₁	—	2	4	no	—
65	C₄×Q₈×C₆₁	—	2	4	no	—
66	C₄×Q₈×C₆₁	—	2	4	no	—
67	C₄×Q₈×C₆₁	—	2	4	no	—
68	C₄×Q₈×C₆₁	—	2	2	no	—
69	C₄×Q₈×C₆₁	D₄	1	2	yes	—
70	C₄×D₄×C₆₁	—	2	2	no	—
71	C₄×D₄×C₆₁	D₄	1	2	yes	—
72	#117×C₆₁	—	2	4	no	—
73	#117×C₆₁	—	2	4	no	—
74	#117×C₆₁	—	2	1	no	—
75	#117×C₆₁	C₂³	1	2	yes	—
76	#117×C₆₁	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₆₁	D₄	1	4	yes	—
78	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
79	C₂×C₄²×C₆₁	—	2	1	no	—
80	C₂×C₄²×C₆₁	—	2	2	no	—
81	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
82	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₆₁	—	2	2	no	—
84	#104×C₆₁	—	2	4	no	—
85	#102×C₆₁	—	2	4	no	—
86	#102×C₆₁	—	2	8	no	—
87	#101×C₆₁	—	4	4	no	—
88	#97×C₆₁	—	2	1	no	—
89	C₄×C₈×C₆₁	—	2	1	no	—
90	C₂⁴×C₆₁	—	2	2	no	—
91	#41×C₆₁	—	2	2	no	—
92	#41×C₆₁	—	2	2	no	—
93	C₂×Q₈×C₆₁	—	2	2	no	—
94	C₂×Q₈×C₆₁	—	2	2	no	—
95	C₂×Q₈×C₆₁	—	2	2	no	—
96	C₂×Q₈×C₆₁	—	2	4	no	—
97	C₂×Q₈×C₆₁	—	2	4	no	—
98	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
99	C₂×D₄×C₆₁	—	2	1	no	—
100	C₂×D₄×C₆₁	—	2	2	no	—
101	C₂×D₄×C₆₁	—	2	2	no	—
102	C₂×D₄×C₆₁	—	2	4	no	—
103	C₂×D₄×C₆₁	—	2	4	no	—
104	C₂×D₄×C₆₁	—	4	8	no	—
105	C₂×D₄×C₆₁	—	4	2	no	—
106	C₂×D₄×C₆₁	—	4	2	no	—
107	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₁	—	2	2	no	—
109	C₂²×C₄×C₆₁	—	2	2	no	—
110	C₂²×C₄×C₆₁	—	2	1	no	—
111	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
114	SD₁₆×C₆₁	—	4	4	no	—
115	D₈×C₆₁	—	4	4	no	—
116	M₁₆×C₆₁	—	2	2	no	—
117	M₁₆×C₆₁	—	2	2	no	—
118	M₁₆×C₆₁	—	2	4	no	—
119	C₂×C₈×C₆₁	—	2	2	no	—
120	C₂×C₈×C₆₁	—	2	2	no	—
121	C₄⋊C₄×C₆₁	—	2	8	no	—
122	C₄⋊C₄×C₆₁	—	2	8	no	—
123	C₄⋊C₄×C₆₁	—	2	4	no	—
124	C₄⋊C₄×C₆₁	—	2	4	no	—
125	C₄⋊C₄×C₆₁	—	2	2	no	—
126	C₄⋊C₄×C₆₁	—	2	2	no	—
127	C₄⋊C₄×C₆₁	—	2	4	no	—
128	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
130	C₂²⋊C₄×C₆₁	—	2	8	no	—
131	C₂²⋊C₄×C₆₁	—	2	1	no	—
132	C₂²⋊C₄×C₆₁	—	2	2	no	—
133	C₂²⋊C₄×C₆₁	—	2	2	no	—
134	C₂²⋊C₄×C₆₁	—	4	16	no	—
135	C₄²×C₆₁	—	2	8	no	—
136	C₄²×C₆₁	—	2	2	no	—
137	C₄²×C₆₁	—	2	1	no	—
138	C₄²×C₆₁	—	2	2	no	—
139	C₄²×C₆₁	—	2	2	no	—
140	C₄²×C₆₁	—	4	4	no	—
141	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₆₁	C₂×D₄	1	2	yes	—
144	C₄²×C₆₁	#41	1	4	yes	—
145	C₂³×C₆₁	—	2	1	no	—
146	C₂³×C₆₁	—	4	8	no	—
147	C₂³×C₆₁	—	4	2	no	—
148	C₂³×C₆₁	—	4	4	no	—
149	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₆₁	—	2	1	no	—
151	Q₈×C₆₁	—	2	1	no	—
152	Q₈×C₆₁	—	4	2	no	—
153	Q₈×C₆₁	—	4	2	no	—
154	Q₈×C₆₁	—	4	4	no	—
155	Q₈×C₆₁	—	4	4	no	—
156	D₄×C₆₁	—	2	1	no	—
157	D₄×C₆₁	—	2	1	no	—
158	D₄×C₆₁	—	4	2	no	—
159	D₄×C₆₁	—	4	2	no	—
160	D₄×C₆₁	—	4	2	no	—
161	D₄×C₆₁	—	4	4	no	—
162	D₄×C₆₁	—	8	4	no	—
163	D₄×C₆₁	—	8	4	no	—
164	C₂×C₄×C₆₁	—	2	4	no	—
165	C₂×C₄×C₆₁	—	2	2	no	—
166	C₂×C₄×C₆₁	—	2	4	no	—
167	C₂×C₄×C₆₁	—	2	4	no	—
168	C₂×C₄×C₆₁	—	2	1	no	—
169	C₂×C₄×C₆₁	—	2	4	no	—
170	C₂×C₄×C₆₁	—	2	8	no	—
171	C₂×C₄×C₆₁	—	4	4	no	—
172	C₂×C₄×C₆₁	—	4	2	no	—
173	C₂×C₄×C₆₁	—	4	4	no	—
174	C₂×C₄×C₆₁	#120	1	2	yes	—
175	C₂×C₄×C₆₁	#120	1	2	yes	—
176	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
179	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
180	C₈×C₆₁	—	4	2	no	—
181	C₈×C₆₁	—	4	2	no	—
182	#25591	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂²×C₆₁	—	2	2	no	—
184	C₂²×C₆₁	—	4	1	no	—
185	C₂²×C₆₁	—	4	2	no	—
186	C₂²×C₆₁	—	8	8	no	—
187	C₂²×C₆₁	—	8	2	no	—
188	C₂²×C₆₁	—	8	4	no	—
189	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
190	C₂²×C₆₁	#546	1	2	yes	—
191	C₄×C₆₁	—	2	2	no	—
192	C₄×C₆₁	—	4	4	no	—
193	C₄×C₆₁	—	4	4	no	—
194	C₄×C₆₁	—	4	1	no	—
195	C₄×C₆₁	—	4	2	no	—
196	C₄×C₆₁	—	4	4	no	—
197	C₄×C₆₁	#454	1	4	yes	—
198	C₄×C₆₁	#532	1	1	yes	characteristic
199	C₄×C₆₁	#535	1	1	yes	characteristic
200	C₄×C₆₁	#550	1	2	yes	—
201	#3509	C₂×C₆₁	1	1	yes	characteristic, complemented
202	#3138	C₂×C₆₁	1	1	yes	characteristic, complemented
203	#3038	C₂×C₆₁	1	1	yes	characteristic
204	#2858	C₂×C₆₁	1	1	yes	characteristic, complemented
205	#2003	C₂×C₆₁	1	4	yes	complemented
206	#1994	C₂×C₆₁	1	1	yes	characteristic, complemented
207	#1966	C₂×C₆₁	1	1	yes	characteristic, complemented
208	#1888	C₂×C₆₁	1	4	yes	complemented
209	C₄×#104	C₂×C₆₁	1	1	yes	characteristic, complemented
210	C₂×C₆₁	—	2	2	no	—
211	C₂×C₆₁	—	8	1	no	—
212	C₂×C₆₁	—	16	2	no	—
213	C₂×C₆₁	#2431	1	1	yes	characteristic
214	C₂×C₆₁	C₂×#454	1	2	yes	—
215	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
216	#557	—	2	2	no	—
217	#556	—	2	2	no	—
218	#552	—	2	4	no	—
219	#541	—	2	2	no	—
220	#536	C₂²×C₆₁	1	2	yes	—
221	#533	—	2	2	no	—
222	#533	C₂²×C₆₁	1	1	yes	characteristic
223	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
224	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
225	C₂×#124	C₂²×C₆₁	1	4	yes	—
226	#519	C₂²×C₆₁	1	2	yes	—
227	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
228	#490	—	2	2	no	—
229	#486	—	2	2	no	—
230	#460	—	2	2	no	—
231	#459	—	2	2	no	—
232	#423	C₂²×C₆₁	1	1	yes	characteristic
233	C₂×#104	C₂²×C₆₁	1	2	yes	—
234	#418	C₂²×C₆₁	1	4	yes	—
235	#418	C₂²×C₆₁	1	2	yes	—
236	C₂×#101	C₂²×C₆₁	1	4	yes	—
237	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
238	#390	—	2	4	no	—
239	C₄³	C₂²×C₆₁	1	1	yes	characteristic
240	#339	C₂²×C₆₁	1	2	yes	—
241	#339	C₂²×C₆₁	1	4	yes	—
242	C₆₁	#25591	1	1	yes	characteristic, direct product factor, Sylow
243	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
244	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
245	C₂²×D₄	—	2	2	no	—
246	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
247	AGL(1,ℤ/8)	—	4	4	no	—
248	C₂×SD₁₆	—	2	2	no	—
249	C₂×D₈	—	2	2	no	—
250	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
251	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	D₄×C₆₁	1	2	yes	—
257	#127	—	2	2	no	—
258	#127	—	2	1	no	—
259	#127	—	2	1	no	—
260	#126	—	2	8	no	—
261	#125	—	2	4	no	—
262	#125	—	2	8	no	—
263	#125	D₄×C₆₁	1	2	yes	—
264	#124	—	2	2	no	—
265	#124	—	2	8	no	—
266	#124	—	4	4	no	—
267	#123	—	2	4	no	—
268	C₂²⋊Q₈	—	2	4	no	—
269	C₂²⋊Q₈	—	2	2	no	—
270	C₂²⋊Q₈	—	2	4	no	—
271	C₄×Q₈	—	2	4	no	—
272	C₄×Q₈	—	2	4	no	—
273	C₄×Q₈	—	2	4	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	D₄×C₆₁	1	2	yes	—
276	C₄×D₄	—	2	2	no	—
277	C₄×D₄	D₄×C₆₁	1	2	yes	—
278	#117	—	2	4	no	—
279	#117	—	2	4	no	—
280	#117	—	2	1	no	—
281	#117	C₂³×C₆₁	1	1	yes	characteristic
282	#117	C₂³×C₆₁	1	2	yes	—
283	C₂×C₄⋊C₄	D₄×C₆₁	1	4	yes	—
284	C₂×C₂²⋊C₄	—	2	8	no	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
288	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
289	C₄⋊C₈	—	2	2	no	—
290	#104	—	2	4	no	—
291	#102	—	2	4	no	—
292	#102	—	2	8	no	—
293	#101	—	4	4	no	—
294	#97	—	2	1	no	—
295	C₄×C₈	—	2	1	no	—
296	C₂⁴	—	2	2	no	—
297	#41	—	2	2	no	—
298	#41	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	4	8	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
318	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
319	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
320	SD₁₆	—	4	4	no	—
321	D₈	—	4	4	no	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	2	4	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
335	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
336	C₂²⋊C₄	—	2	8	no	—
337	C₂²⋊C₄	—	2	1	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	4	16	no	—
341	C₄²	—	2	8	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	4	4	no	—
347	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
348	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
349	C₄²	C₂×D₄×C₆₁	1	2	yes	—
350	C₄²	#41×C₆₁	1	4	yes	—
351	C₂³	—	2	1	no	—
352	C₂³	—	4	8	no	—
353	C₂³	—	4	4	no	—
354	C₂³	—	4	2	no	—
355	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
356	Q₈	—	2	1	no	—
357	Q₈	—	2	1	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	4	4	no	—
361	Q₈	—	4	4	no	—
362	D₄	—	2	1	no	—
363	D₄	—	2	1	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	4	no	—
368	D₄	—	8	4	no	—
369	D₄	—	8	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	#120×C₆₁	1	2	yes	—
381	C₂×C₄	#120×C₆₁	1	2	yes	—
382	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
383	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
384	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
385	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	8	8	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	4	no	—
394	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
395	C₂²	C₆₁×#546	1	2	yes	—
396	C₄	—	2	2	no	—
397	C₄	—	4	4	no	—
398	C₄	—	4	4	no	—
399	C₄	—	4	1	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	4	no	—
402	C₄	C₆₁×#454	1	4	yes	—
403	C₄	C₆₁×#532	1	1	yes	characteristic
404	C₄	C₆₁×#535	1	1	yes	characteristic
405	C₄	C₆₁×#550	1	2	yes	—
406	C₂	—	2	2	no	—
407	C₂	—	8	1	no	—
408	C₂	—	16	2	no	—
409	C₂	C₆₁×#2431	1	1	yes	characteristic
410	C₂	C₂×C₆₁×#454	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#3038	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
1. C₆₁×#3509	C₂	semidirect
2. C₆₁×#3138	C₂	semidirect
4. C₆₁×#2858	C₂	semidirect
5. C₆₁×#2003	C₂	semidirect
6. C₆₁×#1994	C₂	semidirect
7. C₆₁×#1966	C₂	semidirect
8. C₆₁×#1888	C₂	semidirect
9. C₄×#104×C₆₁	C₂	semidirect
182. #25591	C₆₁	direct (N × H)
201. #3509	C₂×C₆₁	semidirect
202. #3138	C₂×C₆₁	semidirect
204. #2858	C₂×C₆₁	semidirect
205. #2003	C₂×C₆₁	semidirect
206. #1994	C₂×C₆₁	semidirect
207. #1966	C₂×C₆₁	semidirect
208. #1888	C₂×C₆₁	semidirect
209. C₄×#104	C₂×C₆₁	semidirect
242. C₆₁	#25591	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×#3509	2
C₆₁×#3138	2
C₆₁×#3038	2
C₆₁×#2858	2
C₆₁×#2003	2
C₆₁×#1994	2
C₆₁×#1966	2
C₆₁×#1888	2
C₄×#104×C₆₁	2
#25591	61

Subgroups — C61×#25591 #29529024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25591 #29529024