Subgroups — C₆₁×#19385 #29522818

Order 15616.

708 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3036	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2972	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1679	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1665	C₂	1	4	yes	maximal, complemented
7	C₆₁×#1570	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1540	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×AGL(1,ℤ/8)×C₆₁	—	2	1	no	—
11	C₆₁×#532	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#492	C₂²	1	2	yes	complemented
15	C₆₁×#487	C₂²	1	2	yes	complemented
16	C₆₁×#474	—	2	2	no	—
17	C₆₁×#474	C₂²	1	4	yes	—
18	C₆₁×#463	—	2	2	no	—
19	C₆₁×#461	—	2	2	no	—
20	C₆₁×#461	C₂²	1	2	yes	—
21	C₆₁×#459	C₂²	1	2	yes	—
22	C₆₁×#448	—	2	2	no	—
23	C₈×D₄×C₆₁	—	2	2	no	—
24	C₈×D₄×C₆₁	C₂²	1	4	yes	—
25	C₆₁×#431	C₂²	1	1	yes	characteristic
26	C₆₁×#431	C₂²	1	1	yes	characteristic
27	C₂×#107×C₆₁	—	2	1	no	—
28	C₆₁×#423	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#417	—	2	1	no	—
31	C₂×#102×C₆₁	—	2	1	no	—
32	C₂×C₂²⋊C₈×C₆₁	—	2	2	no	—
33	C₆₁×#334	C₂²	1	4	yes	complemented
34	C₆₁×#332	C₂²	1	2	yes	complemented
35	C₆₁×#332	C₂²	1	4	yes	complemented
36	C₆₁×#331	C₂²	1	2	yes	complemented
37	C₂×#41×C₆₁	—	2	1	no	—
38	C₂²×Q₈×C₆₁	—	2	1	no	—
39	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₆₁	—	2	1	no	—
41	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
42	C₂×SD₁₆×C₆₁	—	2	2	no	—
43	C₂×SD₁₆×C₆₁	—	2	4	no	—
44	C₂×D₈×C₆₁	—	2	2	no	—
45	C₂×M₁₆×C₆₁	—	2	1	no	—
46	C₂²×C₈×C₆₁	—	2	1	no	—
47	C₂²×C₈×C₆₁	—	2	4	no	—
48	C₄⋊Q₈×C₆₁	—	2	1	no	—
49	C₄⋊Q₈×C₆₁	—	2	1	no	—
50	C₄⋊Q₈×C₆₁	—	2	1	no	—
51	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
53	#127×C₆₁	C₂³	1	1	yes	characteristic
54	#124×C₆₁	—	2	1	no	—
55	#121×C₆₁	—	2	1	no	—
56	#121×C₆₁	—	2	1	no	—
57	C₄×D₄×C₆₁	—	2	1	no	—
58	C₄×D₄×C₆₁	—	2	1	no	—
59	C₄×D₄×C₆₁	—	2	1	no	—
60	C₄×D₄×C₆₁	—	2	1	no	—
61	C₄×D₄×C₆₁	D₄	1	2	yes	—
62	C₄×D₄×C₆₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
67	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
68	#107×C₆₁	—	2	4	no	—
69	C₄⋊C₈×C₆₁	—	2	1	no	—
70	C₄⋊C₈×C₆₁	—	2	1	no	—
71	C₄⋊C₈×C₆₁	D₄	1	2	yes	—
72	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
73	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
74	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
75	#103×C₆₁	—	2	4	no	—
76	#103×C₆₁	—	2	2	no	—
77	#102×C₆₁	—	2	4	no	—
78	#102×C₆₁	—	2	2	no	—
79	C₂²⋊C₈×C₆₁	—	2	1	no	—
80	C₂²⋊C₈×C₆₁	—	2	4	no	—
81	C₂²⋊C₈×C₆₁	D₄	1	2	yes	—
82	C₄×C₈×C₆₁	—	2	1	no	—
83	C₄×C₈×C₆₁	C₂³	1	2	yes	—
84	C₂⁴×C₆₁	—	2	1	no	—
85	#41×C₆₁	—	4	2	no	—
86	#41×C₆₁	—	4	2	no	—
87	C₂×Q₈×C₆₁	—	2	1	no	—
88	C₂×Q₈×C₆₁	—	2	2	no	—
89	C₂×Q₈×C₆₁	—	4	1	no	—
90	C₂×Q₈×C₆₁	—	8	2	no	—
91	C₂×D₄×C₆₁	—	2	1	no	—
92	C₂×D₄×C₆₁	—	2	2	no	—
93	C₂×D₄×C₆₁	—	2	1	no	—
94	C₂×D₄×C₆₁	—	2	1	no	—
95	C₂×D₄×C₆₁	—	2	1	no	—
96	C₂×D₄×C₆₁	—	4	1	no	—
97	C₂×D₄×C₆₁	SD₁₆	1	4	yes	complemented
98	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₆₁	—	2	1	no	—
100	C₂²×C₄×C₆₁	—	2	2	no	—
101	C₂²×C₄×C₆₁	—	2	2	no	—
102	C₂²×C₄×C₆₁	—	4	1	no	—
103	C₂²×C₄×C₆₁	—	4	1	no	—
104	C₂²×C₄×C₆₁	—	8	2	no	—
105	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
108	SD₁₆×C₆₁	—	4	4	no	—
109	SD₁₆×C₆₁	—	8	4	no	—
110	D₈×C₆₁	—	4	4	no	—
111	M₁₆×C₆₁	—	4	2	no	—
112	C₂×C₈×C₆₁	—	2	2	no	—
113	C₂×C₈×C₆₁	—	2	2	no	—
114	C₂×C₈×C₆₁	—	2	2	no	—
115	C₂×C₈×C₆₁	—	4	2	no	—
116	C₂×C₈×C₆₁	—	8	4	no	—
117	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
118	C₄⋊C₄×C₆₁	—	2	1	no	—
119	C₄⋊C₄×C₆₁	—	2	2	no	—
120	C₄⋊C₄×C₆₁	—	2	1	no	—
121	C₄⋊C₄×C₆₁	—	2	2	no	—
122	C₄⋊C₄×C₆₁	—	2	1	no	—
123	C₄⋊C₄×C₆₁	—	4	1	no	—
124	C₄⋊C₄×C₆₁	—	4	1	no	—
125	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
126	C₂²⋊C₄×C₆₁	—	2	2	no	—
127	C₂²⋊C₄×C₆₁	—	2	2	no	—
128	C₂²⋊C₄×C₆₁	—	4	1	no	—
129	C₂²⋊C₄×C₆₁	—	4	1	no	—
130	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₆₁	#41	1	1	yes	characteristic
133	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
134	C₂³×C₆₁	—	2	2	no	—
135	C₂³×C₆₁	—	2	4	no	—
136	C₂³×C₆₁	—	4	1	no	—
137	C₂³×C₆₁	—	8	1	no	—
138	C₂³×C₆₁	—	8	1	no	—
139	C₂³×C₆₁	#121	1	1	yes	characteristic
140	Q₈×C₆₁	—	4	1	no	—
141	Q₈×C₆₁	—	4	1	no	—
142	Q₈×C₆₁	—	4	4	no	—
143	Q₈×C₆₁	—	8	2	no	—
144	D₄×C₆₁	—	2	2	no	—
145	D₄×C₆₁	—	2	4	no	—
146	D₄×C₆₁	—	4	1	no	—
147	D₄×C₆₁	—	4	1	no	—
148	D₄×C₆₁	—	4	2	no	—
149	D₄×C₆₁	—	8	1	no	—
150	D₄×C₆₁	—	8	2	no	—
151	D₄×C₆₁	C₂×SD₁₆	1	4	yes	—
152	C₂×C₄×C₆₁	—	2	2	no	—
153	C₂×C₄×C₆₁	—	2	2	no	—
154	C₂×C₄×C₆₁	—	4	1	no	—
155	C₂×C₄×C₆₁	—	4	4	no	—
156	C₂×C₄×C₆₁	—	4	1	no	—
157	C₂×C₄×C₆₁	—	4	2	no	—
158	C₂×C₄×C₆₁	—	8	2	no	—
159	C₂×C₄×C₆₁	—	8	1	no	—
160	C₂×C₄×C₆₁	—	8	2	no	—
161	C₂×C₄×C₆₁	—	8	2	no	—
162	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
163	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
164	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
165	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
166	C₂×C₄×C₆₁	#135	1	2	yes	—
167	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
170	C₈×C₆₁	—	2	4	no	—
171	C₈×C₆₁	—	4	2	no	—
172	C₈×C₆₁	—	4	2	no	—
173	C₈×C₆₁	—	4	2	no	—
174	#19385	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂²×C₆₁	—	2	1	no	—
176	C₂²×C₆₁	—	2	1	no	—
177	C₂²×C₆₁	—	2	4	no	—
178	C₂²×C₆₁	—	4	2	no	—
179	C₂²×C₆₁	—	4	2	no	—
180	C₂²×C₆₁	—	8	4	no	—
181	C₂²×C₆₁	—	8	1	no	—
182	C₂²×C₆₁	—	8	1	no	—
183	C₂²×C₆₁	—	8	1	no	—
184	C₂²×C₆₁	#465	1	2	yes	—
185	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
186	C₄×C₆₁	—	2	1	no	—
187	C₄×C₆₁	—	2	1	no	—
188	C₄×C₆₁	—	2	1	no	—
189	C₄×C₆₁	—	4	2	no	—
190	C₄×C₆₁	—	8	2	no	—
191	C₄×C₆₁	—	8	1	no	—
192	C₄×C₆₁	#465	1	2	yes	—
193	C₄×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
194	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
195	C₄×C₆₁	#576	1	2	yes	—
196	#3206	C₂×C₆₁	1	1	yes	characteristic, complemented
197	C₂×#474	C₂×C₆₁	1	1	yes	characteristic, complemented
198	#3036	C₂×C₆₁	1	1	yes	characteristic
199	#2972	C₂×C₆₁	1	1	yes	characteristic, complemented
200	#1679	C₂×C₆₁	1	4	yes	complemented
201	#1665	C₂×C₆₁	1	4	yes	complemented
202	#1570	C₂×C₆₁	1	1	yes	characteristic, complemented
203	#1549	C₂×C₆₁	1	1	yes	characteristic, complemented
204	#1540	C₂×C₆₁	1	1	yes	characteristic, complemented
205	C₂×C₆₁	—	2	2	no	—
206	C₂×C₆₁	—	4	4	no	—
207	C₂×C₆₁	—	16	1	no	—
208	C₂×C₆₁	#3041	1	1	yes	characteristic
209	C₂×C₆₁	C₂×#465	1	1	yes	characteristic
210	C₂×C₆₁	#3069	1	1	yes	characteristic
211	C₂×AGL(1,ℤ/8)	—	2	1	no	—
212	#532	C₂²×C₆₁	1	1	yes	characteristic
213	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
214	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
215	#492	C₂²×C₆₁	1	2	yes	complemented
216	#487	C₂²×C₆₁	1	2	yes	complemented
217	#474	—	2	2	no	—
218	#474	C₂²×C₆₁	1	4	yes	—
219	#463	—	2	2	no	—
220	#461	—	2	2	no	—
221	#461	C₂²×C₆₁	1	2	yes	—
222	#459	C₂²×C₆₁	1	2	yes	—
223	#448	—	2	2	no	—
224	C₈×D₄	—	2	2	no	—
225	C₈×D₄	C₂²×C₆₁	1	4	yes	—
226	#431	C₂²×C₆₁	1	1	yes	characteristic
227	#431	C₂²×C₆₁	1	1	yes	characteristic
228	C₂×#107	—	2	1	no	—
229	#423	C₂²×C₆₁	1	1	yes	characteristic
230	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
231	#417	—	2	1	no	—
232	C₂×#102	—	2	1	no	—
233	C₂×C₂²⋊C₈	—	2	2	no	—
234	#334	C₂²×C₆₁	1	4	yes	complemented
235	#332	C₂²×C₆₁	1	2	yes	complemented
236	#332	C₂²×C₆₁	1	4	yes	complemented
237	#331	C₂²×C₆₁	1	2	yes	complemented
238	C₆₁	#19385	1	1	yes	characteristic, direct product factor, Sylow
239	C₂×#41	—	2	1	no	—
240	C₂²×Q₈	—	2	1	no	—
241	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
242	C₂³×C₄	—	2	1	no	—
243	AGL(1,ℤ/8)	—	4	4	no	—
244	C₂×SD₁₆	—	2	2	no	—
245	C₂×SD₁₆	—	2	4	no	—
246	C₂×D₈	—	2	2	no	—
247	C₂×M₁₆	—	2	1	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	—	2	4	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
254	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
255	#127	C₂³×C₆₁	1	1	yes	characteristic
256	#124	—	2	1	no	—
257	#121	—	2	1	no	—
258	#121	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	D₄×C₆₁	1	2	yes	—
264	C₄×D₄	C₂³×C₆₁	1	2	yes	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	—	2	1	no	—
269	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
270	#107	—	2	4	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	D₄×C₆₁	1	2	yes	—
274	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
275	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
276	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
277	#103	—	2	4	no	—
278	#103	—	2	2	no	—
279	#102	—	2	4	no	—
280	#102	—	2	2	no	—
281	C₂²⋊C₈	—	2	1	no	—
282	C₂²⋊C₈	—	2	4	no	—
283	C₂²⋊C₈	D₄×C₆₁	1	2	yes	—
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	C₂³×C₆₁	1	2	yes	—
286	C₂⁴	—	2	1	no	—
287	#41	—	4	2	no	—
288	#41	—	4	2	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	4	1	no	—
292	C₂×Q₈	—	8	2	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	SD₁₆×C₆₁	1	4	yes	complemented
300	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	8	2	no	—
307	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
309	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
310	SD₁₆	—	4	4	no	—
311	SD₁₆	—	8	4	no	—
312	D₈	—	4	4	no	—
313	M₁₆	—	4	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	4	2	no	—
318	C₂×C₈	—	8	4	no	—
319	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	4	1	no	—
331	C₂²⋊C₄	—	4	1	no	—
332	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
333	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
334	C₄²	#41×C₆₁	1	1	yes	characteristic
335	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
336	C₂³	—	2	2	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	8	1	no	—
340	C₂³	—	8	1	no	—
341	C₂³	#121×C₆₁	1	1	yes	characteristic
342	Q₈	—	4	1	no	—
343	Q₈	—	4	1	no	—
344	Q₈	—	4	4	no	—
345	Q₈	—	8	2	no	—
346	D₄	—	2	2	no	—
347	D₄	—	2	4	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	2	no	—
351	D₄	—	8	1	no	—
352	D₄	—	8	2	no	—
353	D₄	C₂×SD₁₆×C₆₁	1	4	yes	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	8	2	no	—
361	C₂×C₄	—	8	1	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
365	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
366	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
367	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
368	C₂×C₄	#135×C₆₁	1	2	yes	—
369	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
372	C₈	—	2	4	no	—
373	C₈	—	4	2	no	—
374	C₈	—	4	2	no	—
375	C₈	—	4	2	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	8	4	no	—
382	C₂²	—	8	1	no	—
383	C₂²	—	8	1	no	—
384	C₂²	—	8	1	no	—
385	C₂²	C₆₁×#465	1	2	yes	—
386	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	4	2	no	—
391	C₄	—	8	2	no	—
392	C₄	—	8	1	no	—
393	C₄	C₆₁×#465	1	2	yes	—
394	C₄	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
395	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
396	C₄	C₆₁×#576	1	2	yes	—
397	C₂	—	2	2	no	—
398	C₂	—	4	4	no	—
399	C₂	—	16	1	no	—
400	C₂	C₆₁×#3041	1	1	yes	characteristic
401	C₂	C₂×C₆₁×#465	1	1	yes	characteristic
402	C₂	C₆₁×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₆₁×#3036	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ 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×#3206	C₂	semidirect
2. C₂×C₆₁×#474	C₂	semidirect
4. C₆₁×#2972	C₂	semidirect
5. C₆₁×#1679	C₂	semidirect
6. C₆₁×#1665	C₂	semidirect
7. C₆₁×#1570	C₂	semidirect
8. C₆₁×#1549	C₂	semidirect
9. C₆₁×#1540	C₂	semidirect
14. C₆₁×#492	C₂²	semidirect
15. C₆₁×#487	C₂²	semidirect
33. C₆₁×#334	C₂²	semidirect
34. C₆₁×#332	C₂²	semidirect
35. C₆₁×#332	C₂²	semidirect
36. C₆₁×#331	C₂²	semidirect
97. C₂×D₄×C₆₁	SD₁₆	semidirect
174. #19385	C₆₁	direct (N × H)
196. #3206	C₂×C₆₁	semidirect
197. C₂×#474	C₂×C₆₁	semidirect
199. #2972	C₂×C₆₁	semidirect
200. #1679	C₂×C₆₁	semidirect
201. #1665	C₂×C₆₁	semidirect
202. #1570	C₂×C₆₁	semidirect
203. #1549	C₂×C₆₁	semidirect
204. #1540	C₂×C₆₁	semidirect
215. #492	C₂²×C₆₁	semidirect
216. #487	C₂²×C₆₁	semidirect
234. #334	C₂²×C₆₁	semidirect
235. #332	C₂²×C₆₁	semidirect
236. #332	C₂²×C₆₁	semidirect
237. #331	C₂²×C₆₁	semidirect
238. C₆₁	#19385	direct (N × H)
299. C₂×D₄	SD₁₆×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3206	2
C₂×C₆₁×#474	2
C₆₁×#3036	2
C₆₁×#2972	2
C₆₁×#1679	2
C₆₁×#1665	2
C₆₁×#1570	2
C₆₁×#1549	2
C₆₁×#1540	2
#19385	61

Subgroups — C61×#19385 #29522818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19385 #29522818