Subgroups — C₆₁×#12980 #29516413

Order 15616.

470 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#443	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#350	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#350	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2113	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1376	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1374	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#135×C₆₁	C₄	1	1	yes	characteristic
9	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
10	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
11	C₆₁×#504	—	2	2	no	—
12	C₆₁×#504	—	2	2	no	—
13	C₂×M₃₂×C₆₁	—	2	1	no	—
14	C₂×M₃₂×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×M₃₂×C₆₁	C₂²	1	1	yes	characteristic
16	C₂²×C₁₆×C₆₁	—	2	1	no	—
17	C₂²×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#443	—	2	2	no	—
20	C₆₁×#443	—	2	2	no	—
21	C₂×#108×C₆₁	C₄	1	1	yes	characteristic
22	C₂×#104×C₆₁	C₄	1	1	yes	characteristic
23	C₂×#104×C₆₁	C₄	1	1	yes	characteristic
24	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₆₁×#350	—	2	2	no	—
26	C₆₁×#350	—	2	2	no	—
27	C₆₁×C₂²⋊C₁₆	—	2	1	no	—
28	C₆₁×C₂²⋊C₁₆	—	2	1	no	—
29	C₂×#41×C₆₁	C₂×C₄	1	1	yes	characteristic
30	C₂×#41×C₆₁	C₂×C₄	1	1	yes	characteristic
31	#135×C₆₁	—	2	2	no	—
32	#135×C₆₁	—	2	2	no	—
33	C₂×Q₁₆×C₆₁	C₈	1	1	yes	characteristic
34	C₂×SD₁₆×C₆₁	C₈	1	1	yes	characteristic
35	C₂×SD₁₆×C₆₁	C₈	1	1	yes	characteristic
36	C₂×D₈×C₆₁	C₈	1	1	yes	characteristic
37	#131×C₆₁	—	2	1	no	—
38	#131×C₆₁	—	2	1	no	—
39	#131×C₆₁	—	2	1	no	—
40	#131×C₆₁	—	2	1	no	—
41	#131×C₆₁	—	2	1	no	—
42	#131×C₆₁	—	2	1	no	—
43	#131×C₆₁	D₄	1	2	yes	—
44	#131×C₆₁	D₄	1	2	yes	—
45	C₂×M₁₆×C₆₁	—	2	1	no	—
46	C₂×M₁₆×C₆₁	—	2	1	no	—
47	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
48	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₆₁	—	2	1	no	—
50	C₂²×C₈×C₆₁	—	2	1	no	—
51	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
54	M₃₂×C₆₁	—	2	4	no	—
55	M₃₂×C₆₁	—	2	1	no	—
56	M₃₂×C₆₁	—	2	1	no	—
57	M₃₂×C₆₁	—	2	1	no	—
58	M₃₂×C₆₁	D₄	1	2	yes	—
59	C₂×C₁₆×C₆₁	—	2	4	no	—
60	C₂×C₁₆×C₆₁	—	2	1	no	—
61	C₂×C₁₆×C₆₁	—	2	1	no	—
62	C₂×C₁₆×C₆₁	—	2	1	no	—
63	C₂×C₁₆×C₆₁	—	2	1	no	—
64	C₂×C₁₆×C₆₁	—	2	1	no	—
65	C₂×C₁₆×C₆₁	—	2	1	no	—
66	C₂×C₁₆×C₆₁	—	2	1	no	—
67	C₂×C₁₆×C₆₁	D₄	1	1	yes	characteristic
68	C₂×C₁₆×C₆₁	D₄	1	1	yes	characteristic
69	#108×C₆₁	—	2	2	no	—
70	#104×C₆₁	—	2	2	no	—
71	#104×C₆₁	—	2	2	no	—
72	C₄×C₈×C₆₁	—	2	1	no	—
73	C₄×C₈×C₆₁	—	2	1	no	—
74	#41×C₆₁	—	2	1	no	—
75	#41×C₆₁	—	2	1	no	—
76	#41×C₆₁	—	2	1	no	—
77	#41×C₆₁	—	2	1	no	—
78	#41×C₆₁	—	2	1	no	—
79	#41×C₆₁	—	2	1	no	—
80	#41×C₆₁	C₂²⋊C₄	1	2	yes	—
81	#41×C₆₁	M₁₆	1	2	yes	—
82	C₂×Q₈×C₆₁	C₂×C₈	1	1	yes	characteristic
83	C₂×Q₈×C₆₁	C₂×C₈	1	1	yes	characteristic
84	C₂×D₄×C₆₁	—	2	1	no	—
85	C₂×D₄×C₆₁	—	2	1	no	—
86	C₂×D₄×C₆₁	C₂×C₈	1	1	yes	characteristic
87	C₂×D₄×C₆₁	C₂×C₈	1	1	yes	characteristic
88	C₂²×C₄×C₆₁	—	2	1	no	—
89	C₂²×C₄×C₆₁	—	2	1	no	—
90	C₂²×C₄×C₆₁	—	2	1	no	—
91	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
92	Q₁₆×C₆₁	—	2	2	no	—
93	SD₁₆×C₆₁	—	2	2	no	—
94	SD₁₆×C₆₁	—	2	2	no	—
95	D₈×C₆₁	—	2	2	no	—
96	M₁₆×C₆₁	—	2	1	no	—
97	M₁₆×C₆₁	—	2	2	no	—
98	M₁₆×C₆₁	—	2	2	no	—
99	M₁₆×C₆₁	—	2	1	no	—
100	M₁₆×C₆₁	—	2	1	no	—
101	M₁₆×C₆₁	—	4	1	no	—
102	M₁₆×C₆₁	—	4	1	no	—
103	M₁₆×C₆₁	C₂²⋊C₄	1	2	yes	—
104	C₂×C₈×C₆₁	—	2	1	no	—
105	C₂×C₈×C₆₁	—	2	1	no	—
106	C₂×C₈×C₆₁	—	2	1	no	—
107	C₂×C₈×C₆₁	—	2	2	no	—
108	C₂×C₈×C₆₁	—	2	2	no	—
109	C₂×C₈×C₆₁	—	2	1	no	—
110	C₂×C₈×C₆₁	—	4	1	no	—
111	C₂×C₈×C₆₁	—	4	1	no	—
112	C₂×C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
113	C₂×C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
114	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₆₁	#41	1	1	yes	characteristic
119	C₂×C₈×C₆₁	#41	1	1	yes	characteristic
120	C₄²×C₆₁	—	2	1	no	—
121	C₄²×C₆₁	—	2	1	no	—
122	C₁₆×C₆₁	—	2	1	no	—
123	C₁₆×C₆₁	—	2	2	no	—
124	C₁₆×C₆₁	—	2	1	no	—
125	C₁₆×C₆₁	—	4	1	no	—
126	C₁₆×C₆₁	—	4	1	no	—
127	C₂³×C₆₁	—	2	1	no	—
128	C₂³×C₆₁	—	2	1	no	—
129	C₂³×C₆₁	#131	1	1	yes	characteristic
130	Q₈×C₆₁	—	2	1	no	—
131	Q₈×C₆₁	—	2	1	no	—
132	Q₈×C₆₁	—	2	1	no	—
133	Q₈×C₆₁	C₂²⋊C₈	1	2	yes	—
134	D₄×C₆₁	—	2	2	no	—
135	D₄×C₆₁	—	2	2	no	—
136	D₄×C₆₁	—	2	1	no	—
137	D₄×C₆₁	—	2	1	no	—
138	D₄×C₆₁	—	2	1	no	—
139	D₄×C₆₁	—	4	1	no	—
140	D₄×C₆₁	—	4	1	no	—
141	D₄×C₆₁	C₂²⋊C₈	1	2	yes	—
142	C₂×C₄×C₆₁	—	2	1	no	—
143	C₂×C₄×C₆₁	—	2	2	no	—
144	C₂×C₄×C₆₁	—	2	2	no	—
145	C₂×C₄×C₆₁	—	2	2	no	—
146	C₂×C₄×C₆₁	—	2	1	no	—
147	C₂×C₄×C₆₁	—	4	1	no	—
148	C₂×C₄×C₆₁	—	4	1	no	—
149	C₂×C₄×C₆₁	—	4	1	no	—
150	C₂×C₄×C₆₁	—	4	1	no	—
151	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
155	C₂×C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
156	C₂×C₄×C₆₁	#131	1	1	yes	characteristic
157	C₈×C₆₁	—	2	2	no	—
158	C₈×C₆₁	—	2	1	no	—
159	C₈×C₆₁	—	2	1	no	—
160	C₈×C₆₁	—	4	1	no	—
161	C₈×C₆₁	#120	1	1	yes	characteristic
162	C₈×C₆₁	#121	1	1	yes	characteristic
163	C₈×C₆₁	#121	1	1	yes	characteristic
164	C₈×C₆₁	#123	1	1	yes	characteristic
165	#12980	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂²×C₆₁	—	2	1	no	—
167	C₂²×C₆₁	—	2	1	no	—
168	C₂²×C₆₁	—	2	2	no	—
169	C₂²×C₆₁	—	4	1	no	—
170	C₂²×C₆₁	—	4	1	no	—
171	C₂²×C₆₁	—	4	1	no	—
172	C₂²×C₆₁	—	4	1	no	—
173	C₂²×C₆₁	—	4	1	no	—
174	C₂²×C₆₁	#408	1	1	yes	characteristic
175	C₂²×C₆₁	C₈×D₄	1	1	yes	characteristic
176	C₂²×C₆₁	#435	1	1	yes	characteristic
177	C₄×C₆₁	—	2	2	no	—
178	C₄×C₆₁	—	4	2	no	—
179	C₄×C₆₁	—	4	1	no	—
180	C₄×C₆₁	#386	1	1	yes	characteristic
181	C₄×C₆₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
182	C₄×C₆₁	C₈×D₄	1	1	yes	characteristic
183	C₄×C₆₁	#435	1	1	yes	characteristic
184	C₂×#504	C₂×C₆₁	1	1	yes	characteristic, complemented
185	C₂×#443	C₂×C₆₁	1	1	yes	characteristic
186	C₂×#350	C₂×C₆₁	1	1	yes	characteristic, complemented
187	C₂×#350	C₂×C₆₁	1	1	yes	characteristic, complemented
188	#2113	C₂×C₆₁	1	1	yes	characteristic, complemented
189	#1376	C₂×C₆₁	1	1	yes	characteristic, complemented
190	#1374	C₂×C₆₁	1	1	yes	characteristic, complemented
191	C₂×C₆₁	—	2	1	no	—
192	C₂×C₆₁	—	2	1	no	—
193	C₂×C₆₁	—	4	2	no	—
194	C₂×C₆₁	—	8	1	no	—
195	C₂×C₆₁	#1869	1	1	yes	characteristic
196	C₂×C₆₁	#2170	1	1	yes	characteristic
197	C₂×C₆₁	#2171	1	1	yes	characteristic
198	C₂×#135	C₄×C₆₁	1	1	yes	characteristic
199	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
200	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
201	#504	—	2	2	no	—
202	#504	—	2	2	no	—
203	C₂×M₃₂	—	2	1	no	—
204	C₂×M₃₂	C₂²×C₆₁	1	1	yes	characteristic
205	C₂×M₃₂	C₂²×C₆₁	1	1	yes	characteristic
206	C₂²×C₁₆	—	2	1	no	—
207	C₂²×C₁₆	C₂²×C₆₁	1	1	yes	characteristic
208	C₂²×C₁₆	C₂²×C₆₁	1	1	yes	characteristic
209	#443	—	2	2	no	—
210	#443	—	2	2	no	—
211	C₂×#108	C₄×C₆₁	1	1	yes	characteristic
212	C₂×#104	C₄×C₆₁	1	1	yes	characteristic
213	C₂×#104	C₄×C₆₁	1	1	yes	characteristic
214	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
215	#350	—	2	2	no	—
216	#350	—	2	2	no	—
217	C₂²⋊C₁₆	—	2	1	no	—
218	C₂²⋊C₁₆	—	2	1	no	—
219	C₆₁	#12980	1	1	yes	characteristic, direct product factor, Sylow
220	C₂×#41	C₂×C₄×C₆₁	1	1	yes	characteristic
221	C₂×#41	C₂×C₄×C₆₁	1	1	yes	characteristic
222	#135	—	2	2	no	—
223	#135	—	2	2	no	—
224	C₂×Q₁₆	C₈×C₆₁	1	1	yes	characteristic
225	C₂×SD₁₆	C₈×C₆₁	1	1	yes	characteristic
226	C₂×SD₁₆	C₈×C₆₁	1	1	yes	characteristic
227	C₂×D₈	C₈×C₆₁	1	1	yes	characteristic
228	#131	—	2	1	no	—
229	#131	—	2	1	no	—
230	#131	—	2	1	no	—
231	#131	—	2	1	no	—
232	#131	—	2	1	no	—
233	#131	—	2	1	no	—
234	#131	D₄×C₆₁	1	2	yes	—
235	#131	D₄×C₆₁	1	2	yes	—
236	C₂×M₁₆	—	2	1	no	—
237	C₂×M₁₆	—	2	1	no	—
238	C₂×M₁₆	C₂×C₄×C₆₁	1	1	yes	characteristic
239	C₂×M₁₆	C₂×C₄×C₆₁	1	1	yes	characteristic
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	C₂×C₄×C₆₁	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
244	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
245	M₃₂	—	2	4	no	—
246	M₃₂	—	2	1	no	—
247	M₃₂	—	2	1	no	—
248	M₃₂	—	2	1	no	—
249	M₃₂	D₄×C₆₁	1	2	yes	—
250	C₂×C₁₆	—	2	4	no	—
251	C₂×C₁₆	—	2	1	no	—
252	C₂×C₁₆	—	2	1	no	—
253	C₂×C₁₆	—	2	1	no	—
254	C₂×C₁₆	—	2	1	no	—
255	C₂×C₁₆	—	2	1	no	—
256	C₂×C₁₆	—	2	1	no	—
257	C₂×C₁₆	—	2	1	no	—
258	C₂×C₁₆	D₄×C₆₁	1	1	yes	characteristic
259	C₂×C₁₆	D₄×C₆₁	1	1	yes	characteristic
260	#108	—	2	2	no	—
261	#104	—	2	2	no	—
262	#104	—	2	2	no	—
263	C₄×C₈	—	2	1	no	—
264	C₄×C₈	—	2	1	no	—
265	#41	—	2	1	no	—
266	#41	—	2	1	no	—
267	#41	—	2	1	no	—
268	#41	—	2	1	no	—
269	#41	—	2	1	no	—
270	#41	—	2	1	no	—
271	#41	C₂²⋊C₄×C₆₁	1	2	yes	—
272	#41	M₁₆×C₆₁	1	2	yes	—
273	C₂×Q₈	C₂×C₈×C₆₁	1	1	yes	characteristic
274	C₂×Q₈	C₂×C₈×C₆₁	1	1	yes	characteristic
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	C₂×C₈×C₆₁	1	1	yes	characteristic
278	C₂×D₄	C₂×C₈×C₆₁	1	1	yes	characteristic
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
283	Q₁₆	—	2	2	no	—
284	SD₁₆	—	2	2	no	—
285	SD₁₆	—	2	2	no	—
286	D₈	—	2	2	no	—
287	M₁₆	—	2	1	no	—
288	M₁₆	—	2	2	no	—
289	M₁₆	—	2	2	no	—
290	M₁₆	—	2	1	no	—
291	M₁₆	—	2	1	no	—
292	M₁₆	—	4	1	no	—
293	M₁₆	—	4	1	no	—
294	M₁₆	C₂²⋊C₄×C₆₁	1	2	yes	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	C₂×C₈×C₆₁	1	1	yes	characteristic
304	C₂×C₈	C₂×C₈×C₆₁	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
306	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
307	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
308	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
309	C₂×C₈	#41×C₆₁	1	1	yes	characteristic
310	C₂×C₈	#41×C₆₁	1	1	yes	characteristic
311	C₄²	—	2	1	no	—
312	C₄²	—	2	1	no	—
313	C₁₆	—	2	1	no	—
314	C₁₆	—	2	2	no	—
315	C₁₆	—	2	1	no	—
316	C₁₆	—	4	1	no	—
317	C₁₆	—	4	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	#131×C₆₁	1	1	yes	characteristic
321	Q₈	—	2	1	no	—
322	Q₈	—	2	1	no	—
323	Q₈	—	2	1	no	—
324	Q₈	C₂²⋊C₈×C₆₁	1	2	yes	—
325	D₄	—	2	2	no	—
326	D₄	—	2	2	no	—
327	D₄	—	2	1	no	—
328	D₄	—	2	1	no	—
329	D₄	—	2	1	no	—
330	D₄	—	4	1	no	—
331	D₄	—	4	1	no	—
332	D₄	C₂²⋊C₈×C₆₁	1	2	yes	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
343	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
344	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
345	C₂×C₄	C₂²×C₈×C₆₁	1	1	yes	characteristic
346	C₂×C₄	C₂×M₁₆×C₆₁	1	1	yes	characteristic
347	C₂×C₄	#131×C₆₁	1	1	yes	characteristic
348	C₈	—	2	2	no	—
349	C₈	—	2	1	no	—
350	C₈	—	2	1	no	—
351	C₈	—	4	1	no	—
352	C₈	#120×C₆₁	1	1	yes	characteristic
353	C₈	#121×C₆₁	1	1	yes	characteristic
354	C₈	#121×C₆₁	1	1	yes	characteristic
355	C₈	#123×C₆₁	1	1	yes	characteristic
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	4	1	no	—
364	C₂²	C₆₁×#408	1	1	yes	characteristic
365	C₂²	C₈×D₄×C₆₁	1	1	yes	characteristic
366	C₂²	C₆₁×#435	1	1	yes	characteristic
367	C₄	—	2	2	no	—
368	C₄	—	4	2	no	—
369	C₄	—	4	1	no	—
370	C₄	C₆₁×#386	1	1	yes	characteristic
371	C₄	C₂×C₂²⋊C₈×C₆₁	1	1	yes	characteristic
372	C₄	C₈×D₄×C₆₁	1	1	yes	characteristic
373	C₄	C₆₁×#435	1	1	yes	characteristic
374	C₂	—	2	1	no	—
375	C₂	—	2	1	no	—
376	C₂	—	4	2	no	—
377	C₂	—	8	1	no	—
378	C₂	C₆₁×#1869	1	1	yes	characteristic
379	C₂	C₆₁×#2170	1	1	yes	characteristic
380	C₂	C₆₁×#2171	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₆₁	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₆₁
Frattini, cosocle	C₂²×C₈	C₂³×C₆₁
socle	C₂²×C₆₁	C₈×D₄
prime radical	C₂×#135×C₆₁	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₆₁ ◁ C₂²×C₁₆×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#504	C₂	semidirect
3. C₂×C₆₁×#350	C₂	semidirect
4. C₂×C₆₁×#350	C₂	semidirect
5. C₆₁×#2113	C₂	semidirect
6. C₆₁×#1376	C₂	semidirect
7. C₆₁×#1374	C₂	semidirect
165. #12980	C₆₁	direct (N × H)
184. C₂×#504	C₂×C₆₁	semidirect
186. C₂×#350	C₂×C₆₁	semidirect
187. C₂×#350	C₂×C₆₁	semidirect
188. #2113	C₂×C₆₁	semidirect
189. #1376	C₂×C₆₁	semidirect
190. #1374	C₂×C₆₁	semidirect
219. C₆₁	#12980	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#504	2
C₂×C₆₁×#443	2
C₂×C₆₁×#350	2
C₆₁×#2113	2
C₆₁×#1376	2
C₆₁×#1374	2
#12980	61

Subgroups — C61×#12980 #29516413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#12980 #29516413