Subgroups — C₆₁×#25740 #29529173

Order 15616.

1458 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3497	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3152	C₂	1	2	yes	maximal, complemented
3	C₂×C₆₁×#456	C₂	1	4	yes	maximal, complemented
4	C₆₁×#2546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2007	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1980	C₂	1	2	yes	maximal, complemented
7	C₄×#101×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	2	yes	—
9	C₂×#137×C₆₁	C₂²	1	8	yes	—
10	C₆₁×#550	—	2	2	no	—
11	D₄×Q₈×C₆₁	—	2	2	no	—
12	C₆₁×#548	—	2	4	no	—
13	C₆₁×#537	—	2	2	no	—
14	C₆₁×#537	C₂²	1	2	yes	—
15	C₆₁×#532	—	2	2	no	—
16	C₆₁×#532	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
18	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₆₁×#497	—	2	4	no	—
21	C₆₁×#494	—	2	2	no	—
22	C₆₁×#492	—	2	2	no	—
23	C₆₁×#456	—	2	16	no	—
24	C₂×#104×C₆₁	C₂²	1	8	yes	—
25	C₂×#101×C₆₁	C₂²	1	2	yes	—
26	C₄×M₁₆×C₆₁	C₂²	1	2	yes	—
27	C₆₁×#398	—	2	2	no	—
28	C₆₁×#391	C₂²	1	2	yes	—
29	C₆₁×#389	—	2	2	no	—
30	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#343	C₂²	1	2	yes	—
32	2₋¹⁺⁴×C₆₁	—	2	8	no	—
33	2₋¹⁺⁴×C₆₁	—	4	4	no	—
34	C₂×#41×C₆₁	—	2	4	no	—
35	C₂×#41×C₆₁	—	2	4	no	—
36	C₂×#41×C₆₁	C₂³	1	4	yes	—
37	C₂²×Q₈×C₆₁	—	2	4	no	—
38	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
39	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
40	#137×C₆₁	—	2	16	no	—
41	#137×C₆₁	—	4	8	no	—
42	C₂×Q₁₆×C₆₁	—	2	8	no	—
43	C₂×SD₁₆×C₆₁	—	2	8	no	—
44	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
45	C₄⋊Q₈×C₆₁	—	2	2	no	—
46	C₄⋊Q₈×C₆₁	—	2	8	no	—
47	C₄⋊Q₈×C₆₁	—	2	2	no	—
48	C₄⋊Q₈×C₆₁	—	2	2	no	—
49	C₄⋊Q₈×C₆₁	D₄	1	2	yes	—
50	#127×C₆₁	—	2	2	no	—
51	#127×C₆₁	D₄	1	2	yes	—
52	#124×C₆₁	—	2	4	no	—
53	#124×C₆₁	D₄	1	4	yes	—
54	C₂²⋊Q₈×C₆₁	—	2	8	no	—
55	C₂²⋊Q₈×C₆₁	—	2	4	no	—
56	#121×C₆₁	—	2	8	no	—
57	#121×C₆₁	—	2	4	no	—
58	#121×C₆₁	—	2	2	no	—
59	#121×C₆₁	—	2	4	no	—
60	#121×C₆₁	—	2	2	no	—
61	C₄×Q₈×C₆₁	—	2	2	no	—
62	C₄×Q₈×C₆₁	—	2	2	no	—
63	C₄×D₄×C₆₁	—	2	4	no	—
64	C₄×D₄×C₆₁	—	2	4	no	—
65	C₄×D₄×C₆₁	—	2	2	no	—
66	C₄×D₄×C₆₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
71	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₆₁	D₄	1	2	yes	—
74	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
75	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
76	#104×C₆₁	—	2	16	no	—
77	#101×C₆₁	D₄	1	8	yes	complemented
78	#97×C₆₁	—	2	2	no	—
79	C₄×C₈×C₆₁	—	2	2	no	—
80	#95×C₆₁	—	2	1	no	—
81	#95×C₆₁	—	2	4	no	—
82	#41×C₆₁	—	2	8	no	—
83	#41×C₆₁	—	2	8	no	—
84	#41×C₆₁	—	4	8	no	—
85	#41×C₆₁	—	4	16	no	—
86	#41×C₆₁	—	4	8	no	—
87	C₂×Q₈×C₆₁	—	2	4	no	—
88	C₂×Q₈×C₆₁	—	2	2	no	—
89	C₂×Q₈×C₆₁	—	2	2	no	—
90	C₂×Q₈×C₆₁	—	2	4	no	—
91	C₂×Q₈×C₆₁	—	2	4	no	—
92	C₂×Q₈×C₆₁	—	2	4	no	—
93	C₂×Q₈×C₆₁	—	4	16	no	—
94	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
95	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
96	C₂×D₄×C₆₁	—	2	4	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	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₆₁	—	2	8	no	—
103	C₂²×C₄×C₆₁	—	2	2	no	—
104	C₂²×C₄×C₆₁	—	2	4	no	—
105	C₂²×C₄×C₆₁	—	2	2	no	—
106	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
111	Q₁₆×C₆₁	—	4	16	no	—
112	SD₁₆×C₆₁	—	4	16	no	—
113	M₁₆×C₆₁	—	2	4	no	—
114	M₁₆×C₆₁	C₂×D₄	1	8	yes	—
115	C₂×C₈×C₆₁	—	2	4	no	—
116	C₄⋊C₄×C₆₁	—	2	4	no	—
117	C₄⋊C₄×C₆₁	—	2	4	no	—
118	C₄⋊C₄×C₆₁	—	2	4	no	—
119	C₄⋊C₄×C₆₁	—	2	2	no	—
120	C₄⋊C₄×C₆₁	—	2	2	no	—
121	C₄⋊C₄×C₆₁	—	2	2	no	—
122	C₄⋊C₄×C₆₁	—	4	1	no	—
123	C₄⋊C₄×C₆₁	—	4	2	no	—
124	C₄⋊C₄×C₆₁	—	4	1	no	—
125	C₄⋊C₄×C₆₁	—	4	8	no	—
126	C₂²⋊C₄×C₆₁	—	2	8	no	—
127	C₂²⋊C₄×C₆₁	—	2	4	no	—
128	C₂²⋊C₄×C₆₁	—	2	4	no	—
129	C₄²×C₆₁	—	2	2	no	—
130	C₄²×C₆₁	—	2	2	no	—
131	C₄²×C₆₁	—	2	4	no	—
132	C₄²×C₆₁	C₂×D₄	1	2	yes	—
133	C₄²×C₆₁	C₂×D₄	1	2	yes	—
134	C₂³×C₆₁	—	2	4	no	—
135	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₆₁	—	2	8	no	—
137	Q₈×C₆₁	—	2	8	no	—
138	Q₈×C₆₁	—	4	8	no	—
139	Q₈×C₆₁	—	4	8	no	—
140	D₄×C₆₁	—	2	8	no	—
141	D₄×C₆₁	—	4	8	no	—
142	D₄×C₆₁	—	4	4	no	—
143	D₄×C₆₁	—	4	4	no	—
144	D₄×C₆₁	—	4	4	no	—
145	D₄×C₆₁	—	8	2	no	—
146	D₄×C₆₁	—	8	4	no	—
147	C₂×C₄×C₆₁	—	2	2	no	—
148	C₂×C₄×C₆₁	—	2	2	no	—
149	C₂×C₄×C₆₁	—	2	2	no	—
150	C₂×C₄×C₆₁	—	2	4	no	—
151	C₂×C₄×C₆₁	—	2	2	no	—
152	C₂×C₄×C₆₁	—	2	4	no	—
153	C₂×C₄×C₆₁	—	4	1	no	—
154	C₂×C₄×C₆₁	—	4	16	no	—
155	C₂×C₄×C₆₁	—	4	2	no	—
156	C₂×C₄×C₆₁	—	4	2	no	—
157	C₂×C₄×C₆₁	—	4	8	no	—
158	C₂×C₄×C₆₁	—	4	2	no	—
159	C₂×C₄×C₆₁	—	4	2	no	—
160	C₂×C₄×C₆₁	—	4	2	no	—
161	C₂×C₄×C₆₁	—	4	2	no	—
162	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
163	C₂×C₄×C₆₁	#120	1	2	yes	—
164	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
165	C₂×C₄×C₆₁	#127	1	4	yes	—
166	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
167	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
168	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
169	C₈×C₆₁	—	2	8	no	—
170	#25740	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂²×C₆₁	—	2	1	no	—
172	C₂²×C₆₁	—	2	1	no	—
173	C₂²×C₆₁	—	4	4	no	—
174	C₂²×C₆₁	—	4	4	no	—
175	C₂²×C₆₁	—	4	4	no	—
176	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
177	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
178	C₂²×C₆₁	#535	1	1	yes	characteristic
179	C₄×C₆₁	—	2	4	no	—
180	C₄×C₆₁	—	2	1	no	—
181	C₄×C₆₁	—	2	2	no	—
182	C₄×C₆₁	—	4	4	no	—
183	C₄×C₆₁	—	4	4	no	—
184	C₄×C₆₁	—	4	2	no	—
185	C₄×C₆₁	—	8	2	no	—
186	C₄×C₆₁	#456	1	2	yes	complemented
187	C₄×C₆₁	D₄²	1	4	yes	—
188	#3497	C₂×C₆₁	1	1	yes	characteristic
189	#3152	C₂×C₆₁	1	2	yes	complemented
190	C₂×#456	C₂×C₆₁	1	4	yes	complemented
191	#2546	C₂×C₆₁	1	1	yes	characteristic, complemented
192	#2007	C₂×C₆₁	1	4	yes	complemented
193	#1980	C₂×C₆₁	1	2	yes	complemented
194	C₄×#101	C₂×C₆₁	1	1	yes	characteristic, complemented
195	C₂×C₆₁	—	2	1	no	—
196	C₂×C₆₁	—	2	1	no	—
197	C₂×C₆₁	—	8	4	no	—
198	C₂×C₆₁	#2433	1	1	yes	characteristic
199	C₂×C₆₁	C₂×#456	1	1	yes	characteristic
200	C₂×C₆₁	#3022	1	1	yes	characteristic
201	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	2	yes	—
202	C₂×#137	C₂²×C₆₁	1	8	yes	—
203	#550	—	2	2	no	—
204	D₄×Q₈	—	2	2	no	—
205	#548	—	2	4	no	—
206	#537	—	2	2	no	—
207	#537	C₂²×C₆₁	1	2	yes	—
208	#532	—	2	2	no	—
209	#532	C₂²×C₆₁	1	2	yes	—
210	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
211	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
212	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
213	#497	—	2	4	no	—
214	#494	—	2	2	no	—
215	#492	—	2	2	no	—
216	#456	—	2	16	no	—
217	C₂×#104	C₂²×C₆₁	1	8	yes	—
218	C₂×#101	C₂²×C₆₁	1	2	yes	—
219	C₄×M₁₆	C₂²×C₆₁	1	2	yes	—
220	#398	—	2	2	no	—
221	#391	C₂²×C₆₁	1	2	yes	—
222	#389	—	2	2	no	—
223	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
224	#343	C₂²×C₆₁	1	2	yes	—
225	C₆₁	#25740	1	1	yes	characteristic, direct product factor, Sylow
226	2₋¹⁺⁴	—	2	8	no	—
227	2₋¹⁺⁴	—	4	4	no	—
228	C₂×#41	—	2	4	no	—
229	C₂×#41	—	2	4	no	—
230	C₂×#41	C₂³×C₆₁	1	4	yes	—
231	C₂²×Q₈	—	2	4	no	—
232	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
233	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
234	#137	—	2	16	no	—
235	#137	—	4	8	no	—
236	C₂×Q₁₆	—	2	8	no	—
237	C₂×SD₁₆	—	2	8	no	—
238	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
239	C₄⋊Q₈	—	2	2	no	—
240	C₄⋊Q₈	—	2	8	no	—
241	C₄⋊Q₈	—	2	2	no	—
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	D₄×C₆₁	1	2	yes	—
244	#127	—	2	2	no	—
245	#127	D₄×C₆₁	1	2	yes	—
246	#124	—	2	4	no	—
247	#124	D₄×C₆₁	1	4	yes	—
248	C₂²⋊Q₈	—	2	8	no	—
249	C₂²⋊Q₈	—	2	4	no	—
250	#121	—	2	8	no	—
251	#121	—	2	4	no	—
252	#121	—	2	2	no	—
253	#121	—	2	4	no	—
254	#121	—	2	2	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×Q₈	—	2	2	no	—
257	C₄×D₄	—	2	4	no	—
258	C₄×D₄	—	2	4	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	4	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
267	C₂×C₄²	D₄×C₆₁	1	2	yes	—
268	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
269	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
270	#104	—	2	16	no	—
271	#101	D₄×C₆₁	1	8	yes	complemented
272	#97	—	2	2	no	—
273	C₄×C₈	—	2	2	no	—
274	#95	—	2	1	no	—
275	#95	—	2	4	no	—
276	#41	—	2	8	no	—
277	#41	—	2	8	no	—
278	#41	—	4	8	no	—
279	#41	—	4	16	no	—
280	#41	—	4	8	no	—
281	C₂×Q₈	—	2	4	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	4	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	4	no	—
287	C₂×Q₈	—	4	16	no	—
288	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
289	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
296	C₂²×C₄	—	2	8	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
304	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
305	Q₁₆	—	4	16	no	—
306	SD₁₆	—	4	16	no	—
307	M₁₆	—	2	4	no	—
308	M₁₆	C₂×D₄×C₆₁	1	8	yes	—
309	C₂×C₈	—	2	4	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	8	no	—
320	C₂²⋊C₄	—	2	8	no	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	4	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	4	no	—
326	C₄²	C₂×D₄×C₆₁	1	2	yes	—
327	C₄²	C₂×D₄×C₆₁	1	2	yes	—
328	C₂³	—	2	4	no	—
329	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
330	Q₈	—	2	8	no	—
331	Q₈	—	2	8	no	—
332	Q₈	—	4	8	no	—
333	Q₈	—	4	8	no	—
334	D₄	—	2	8	no	—
335	D₄	—	4	8	no	—
336	D₄	—	4	4	no	—
337	D₄	—	4	4	no	—
338	D₄	—	4	4	no	—
339	D₄	—	8	2	no	—
340	D₄	—	8	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	16	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	8	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
357	C₂×C₄	#120×C₆₁	1	2	yes	—
358	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
359	C₂×C₄	#127×C₆₁	1	4	yes	—
360	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
361	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
362	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
363	C₈	—	2	8	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	4	no	—
369	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
370	C₂²	C₂×#127×C₆₁	1	1	yes	characteristic
371	C₂²	C₆₁×#535	1	1	yes	characteristic
372	C₄	—	2	4	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	2	no	—
375	C₄	—	4	4	no	—
376	C₄	—	4	4	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	2	no	—
379	C₄	C₆₁×#456	1	2	yes	complemented
380	C₄	D₄²×C₆₁	1	4	yes	—
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	8	4	no	—
384	C₂	C₆₁×#2433	1	1	yes	characteristic
385	C₂	C₂×C₆₁×#456	1	1	yes	characteristic
386	C₂	C₆₁×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#3497	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×#3152	C₂	semidirect
3. C₂×C₆₁×#456	C₂	semidirect
4. C₆₁×#2546	C₂	semidirect
5. C₆₁×#2007	C₂	semidirect
6. C₆₁×#1980	C₂	semidirect
7. C₄×#101×C₆₁	C₂	semidirect
77. #101×C₆₁	D₄	semidirect
170. #25740	C₆₁	direct (N × H)
186. C₄×C₆₁	#456	semidirect
189. #3152	C₂×C₆₁	semidirect
190. C₂×#456	C₂×C₆₁	semidirect
191. #2546	C₂×C₆₁	semidirect
192. #2007	C₂×C₆₁	semidirect
193. #1980	C₂×C₆₁	semidirect
194. C₄×#101	C₂×C₆₁	semidirect
225. C₆₁	#25740	direct (N × H)
271. #101	D₄×C₆₁	semidirect
379. C₄	C₆₁×#456	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₁×#3497	2
C₆₁×#3152	2
C₂×C₆₁×#456	2
C₆₁×#2546	2
C₆₁×#2007	2
C₆₁×#1980	2
C₄×#101×C₆₁	2
#25740	61

Subgroups — C61×#25740 #29529173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25740 #29529173