Subgroups — C₂×C₆₁×#2484 #29538240

Order 15616.

2918 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2484	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₆₁×#400	C₂	1	2	yes	maximal, complemented
5	C₂×C₆₁×#398	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#387	C₂	1	4	yes	maximal, complemented
7	C₂×C₆₁×#385	C₂	1	2	yes	maximal
8	C₂×C₆₁×#381	C₂	1	2	yes	maximal
9	C₂×C₆₁×#381	C₂	1	1	yes	maximal, characteristic
10	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#117×C₆₁	—	2	8	no	—
14	C₂×#117×C₆₁	C₂²	1	8	yes	—
15	C₂²×C₄⋊C₄×C₆₁	—	2	8	no	—
16	C₂²×C₄⋊C₄×C₆₁	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₆₁	C₂²	1	8	yes	—
22	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
24	C₂²×C₄²×C₆₁	C₂²	1	2	yes	—
25	C₆₁×#400	C₂²	1	16	yes	complemented
26	C₆₁×#398	C₂²	1	16	yes	complemented
27	C₆₁×#387	C₂²	1	32	yes	complemented
28	C₆₁×#385	C₂²	1	16	yes	—
29	C₆₁×#381	C₂²	1	8	yes	—
30	C₆₁×#381	C₂²	1	16	yes	—
31	C₂×#95×C₆₁	C₂²	1	2	yes	—
32	C₂×#95×C₆₁	C₂²	1	4	yes	—
33	C₂×#95×C₆₁	C₂²	1	4	yes	—
34	C₂×#95×C₆₁	C₂²	1	2	yes	—
35	C₂×#95×C₆₁	C₂²	1	4	yes	—
36	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₆₁	—	2	4	no	—
38	C₂³×C₄×C₆₁	—	2	8	no	—
39	C₂³×C₄×C₆₁	—	2	8	no	—
40	C₂³×C₄×C₆₁	—	2	4	no	—
41	C₂³×C₄×C₆₁	—	2	8	no	—
42	C₂³×C₄×C₆₁	D₄	1	8	yes	—
43	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
44	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
45	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
46	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
47	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
48	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
50	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
53	#117×C₆₁	—	2	32	no	—
54	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
55	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
56	C₂×C₄⋊C₄×C₆₁	—	2	32	no	—
57	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
58	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	16	no	—
60	C₂×C₄⋊C₄×C₆₁	C₂³	1	16	yes	—
61	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
62	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
64	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
65	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
66	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
67	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
68	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
69	C₂×C₄²×C₆₁	—	2	8	no	—
70	C₂×C₄²×C₆₁	C₂³	1	8	yes	—
71	#95×C₆₁	C₂³	1	8	yes	—
72	#95×C₆₁	C₂³	1	16	yes	—
73	#95×C₆₁	C₂³	1	16	yes	—
74	#95×C₆₁	C₂³	1	8	yes	—
75	#95×C₆₁	C₂³	1	16	yes	—
76	C₂⁴×C₆₁	—	2	4	no	—
77	C₂⁴×C₆₁	—	2	4	no	—
78	C₂⁴×C₆₁	C₂×D₄	1	4	yes	—
79	C₂⁴×C₆₁	#41	1	8	yes	—
80	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
81	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
82	C₂²×C₄×C₆₁	—	2	32	no	—
83	C₂²×C₄×C₆₁	—	2	32	no	—
84	C₂²×C₄×C₆₁	—	2	8	no	—
85	C₂²×C₄×C₆₁	—	2	4	no	—
86	C₂²×C₄×C₆₁	—	2	16	no	—
87	C₂²×C₄×C₆₁	—	2	4	no	—
88	C₂²×C₄×C₆₁	—	2	4	no	—
89	C₂²×C₄×C₆₁	—	2	4	no	—
90	C₂²×C₄×C₆₁	—	2	16	no	—
91	C₂²×C₄×C₆₁	—	2	4	no	—
92	C₂²×C₄×C₆₁	—	2	4	no	—
93	C₂²×C₄×C₆₁	—	2	8	no	—
94	C₂²×C₄×C₆₁	—	2	4	no	—
95	C₂²×C₄×C₆₁	—	2	8	no	—
96	C₂²×C₄×C₆₁	—	2	8	no	—
97	C₂²×C₄×C₆₁	—	2	8	no	—
98	C₂²×C₄×C₆₁	—	2	16	no	—
99	C₂²×C₄×C₆₁	—	2	8	no	—
100	C₂²×C₄×C₆₁	—	2	8	no	—
101	C₂²×C₄×C₆₁	—	2	8	no	—
102	C₂²×C₄×C₆₁	—	4	16	no	—
103	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₆₁	C₂×D₄	1	16	yes	—
106	C₂²×C₄×C₆₁	#41	1	8	yes	—
107	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
108	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
109	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
110	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
111	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
112	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
113	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
114	C₄⋊C₄×C₆₁	—	2	16	no	—
115	C₄⋊C₄×C₆₁	—	2	16	no	—
116	C₄⋊C₄×C₆₁	—	2	8	no	—
117	C₄⋊C₄×C₆₁	—	2	8	no	—
118	C₄⋊C₄×C₆₁	—	2	32	no	—
119	C₂²⋊C₄×C₆₁	—	2	16	no	—
120	C₂²⋊C₄×C₆₁	—	2	16	no	—
121	C₄²×C₆₁	—	2	16	no	—
122	C₂³×C₆₁	—	2	8	no	—
123	C₂³×C₆₁	—	2	8	no	—
124	C₂³×C₆₁	—	2	32	no	—
125	C₂³×C₆₁	—	2	4	no	—
126	C₂³×C₆₁	—	2	4	no	—
127	C₂³×C₆₁	#123	1	16	yes	—
128	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
129	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
130	C₂³×C₆₁	C₂×#41	1	8	yes	—
131	C₂³×C₆₁	C₂×#41	1	4	yes	—
132	C₂³×C₆₁	C₂×#41	1	4	yes	—
133	C₂³×C₆₁	2₋¹⁺⁴	1	4	yes	—
134	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
135	C₂×C₄×C₆₁	—	2	32	no	—
136	C₂×C₄×C₆₁	—	2	32	no	—
137	C₂×C₄×C₆₁	—	2	8	no	—
138	C₂×C₄×C₆₁	—	2	8	no	—
139	C₂×C₄×C₆₁	—	2	16	no	—
140	C₂×C₄×C₆₁	—	2	4	no	—
141	C₂×C₄×C₆₁	—	2	4	no	—
142	C₂×C₄×C₆₁	—	2	4	no	—
143	C₂×C₄×C₆₁	—	2	4	no	—
144	C₂×C₄×C₆₁	—	2	4	no	—
145	C₂×C₄×C₆₁	—	2	4	no	—
146	C₂×C₄×C₆₁	—	2	4	no	—
147	C₂×C₄×C₆₁	—	2	8	no	—
148	C₂×C₄×C₆₁	—	2	8	no	—
149	C₂×C₄×C₆₁	—	2	8	no	—
150	C₂×C₄×C₆₁	—	2	8	no	—
151	C₂×C₄×C₆₁	—	2	8	no	—
152	C₂×C₄×C₆₁	—	2	8	no	—
153	C₂×C₄×C₆₁	—	4	16	no	—
154	C₂×C₄×C₆₁	—	4	8	no	—
155	C₂×C₄×C₆₁	—	4	8	no	—
156	C₂×C₄×C₆₁	—	4	8	no	—
157	C₂×C₄×C₆₁	—	4	16	no	—
158	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
159	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
160	C₂×C₄×C₆₁	C₂×#41	1	8	yes	—
161	C₂×#2484	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂²×C₆₁	—	2	4	no	—
163	C₂²×C₆₁	—	2	4	no	—
164	C₂²×C₆₁	—	2	16	no	—
165	C₂²×C₆₁	—	2	32	no	—
166	C₂²×C₆₁	C₂×#123	1	8	yes	—
167	C₂²×C₆₁	C₂×#123	1	4	yes	—
168	C₂²×C₆₁	#525	1	4	yes	—
169	C₂²×C₆₁	#536	1	4	yes	—
170	C₂²×C₆₁	#552	1	16	yes	—
171	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
172	C₂²×C₆₁	C₂²×#41	1	2	yes	—
173	C₂²×C₆₁	C₂²×#41	1	2	yes	—
174	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
175	C₄×C₆₁	—	2	4	no	—
176	C₄×C₆₁	—	2	4	no	—
177	C₄×C₆₁	—	2	8	no	—
178	C₄×C₆₁	—	4	4	no	—
179	C₄×C₆₁	—	4	4	no	—
180	C₄×C₆₁	—	4	4	no	—
181	C₄×C₆₁	—	4	8	no	—
182	C₂²×#117	C₂×C₆₁	1	1	yes	characteristic
183	C₂³×C₄⋊C₄	C₂×C₆₁	1	1	yes	characteristic
184	#2484	C₂×C₆₁	1	16	yes	direct product factor
185	C₂×#400	C₂×C₆₁	1	2	yes	complemented
186	C₂×#398	C₂×C₆₁	1	2	yes	complemented
187	C₂×#387	C₂×C₆₁	1	4	yes	complemented
188	C₂×#385	C₂×C₆₁	1	2	yes	—
189	C₂×#381	C₂×C₆₁	1	2	yes	—
190	C₂×#381	C₂×C₆₁	1	1	yes	characteristic
191	C₂×C₆₁	—	2	8	no	—
192	C₂×C₆₁	#2484	1	8	yes	direct product factor
193	C₂×C₆₁	C₂²×#123	1	1	yes	characteristic
194	C₂×C₆₁	C₂×#525	1	1	yes	characteristic
195	C₂×C₆₁	C₂×#536	1	1	yes	characteristic
196	C₂×C₆₁	C₂×#552	1	4	yes	—
197	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
198	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
199	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
200	C₂×#117	—	2	8	no	—
201	C₂×#117	C₂²×C₆₁	1	8	yes	—
202	C₂²×C₄⋊C₄	—	2	8	no	—
203	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
204	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
205	C₂²×C₄⋊C₄	C₂²×C₆₁	1	4	yes	—
206	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
207	C₂²×C₄⋊C₄	C₂²×C₆₁	1	8	yes	—
208	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
209	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
210	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
211	C₂²×C₄²	C₂²×C₆₁	1	2	yes	—
212	#400	C₂²×C₆₁	1	16	yes	complemented
213	#398	C₂²×C₆₁	1	16	yes	complemented
214	#387	C₂²×C₆₁	1	32	yes	complemented
215	#385	C₂²×C₆₁	1	16	yes	—
216	#381	C₂²×C₆₁	1	8	yes	—
217	#381	C₂²×C₆₁	1	16	yes	—
218	C₂×#95	C₂²×C₆₁	1	2	yes	—
219	C₂×#95	C₂²×C₆₁	1	4	yes	—
220	C₂×#95	C₂²×C₆₁	1	4	yes	—
221	C₂×#95	C₂²×C₆₁	1	4	yes	—
222	C₂×#95	C₂²×C₆₁	1	2	yes	—
223	C₆₁	C₂×#2484	1	1	yes	characteristic, direct product factor, Sylow
224	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
225	C₂³×C₄	—	2	4	no	—
226	C₂³×C₄	—	2	8	no	—
227	C₂³×C₄	—	2	8	no	—
228	C₂³×C₄	—	2	4	no	—
229	C₂³×C₄	—	2	8	no	—
230	C₂³×C₄	D₄×C₆₁	1	8	yes	—
231	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
232	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
233	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
234	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
235	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
236	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
237	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
238	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
239	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
240	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
241	#117	—	2	32	no	—
242	C₂×C₄⋊C₄	—	2	8	no	—
243	C₂×C₄⋊C₄	—	2	8	no	—
244	C₂×C₄⋊C₄	—	2	32	no	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	—	2	16	no	—
248	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
249	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
250	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
251	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
252	C₂×C₄⋊C₄	C₂³×C₆₁	1	16	yes	—
253	C₂×C₂²⋊C₄	—	2	8	no	—
254	C₂×C₂²⋊C₄	—	2	8	no	—
255	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
256	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
257	C₂×C₄²	—	2	8	no	—
258	C₂×C₄²	C₂³×C₆₁	1	8	yes	—
259	#95	C₂³×C₆₁	1	8	yes	—
260	#95	C₂³×C₆₁	1	16	yes	—
261	#95	C₂³×C₆₁	1	16	yes	—
262	#95	C₂³×C₆₁	1	8	yes	—
263	#95	C₂³×C₆₁	1	16	yes	—
264	C₂⁴	—	2	4	no	—
265	C₂⁴	—	2	4	no	—
266	C₂⁴	C₂×D₄×C₆₁	1	4	yes	—
267	C₂⁴	#41×C₆₁	1	8	yes	—
268	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
269	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
270	C₂²×C₄	—	2	32	no	—
271	C₂²×C₄	—	2	32	no	—
272	C₂²×C₄	—	2	8	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	16	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	16	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	8	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	2	8	no	—
285	C₂²×C₄	—	2	8	no	—
286	C₂²×C₄	—	2	16	no	—
287	C₂²×C₄	—	2	8	no	—
288	C₂²×C₄	—	2	8	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	4	16	no	—
291	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
292	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
293	C₂²×C₄	C₂×D₄×C₆₁	1	16	yes	—
294	C₂²×C₄	#41×C₆₁	1	8	yes	—
295	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
296	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
297	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
298	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
299	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
300	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
301	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
302	C₄⋊C₄	—	2	16	no	—
303	C₄⋊C₄	—	2	16	no	—
304	C₄⋊C₄	—	2	8	no	—
305	C₄⋊C₄	—	2	8	no	—
306	C₄⋊C₄	—	2	32	no	—
307	C₂²⋊C₄	—	2	16	no	—
308	C₂²⋊C₄	—	2	16	no	—
309	C₄²	—	2	16	no	—
310	C₂³	—	2	8	no	—
311	C₂³	—	2	32	no	—
312	C₂³	—	2	4	no	—
313	C₂³	—	2	4	no	—
314	C₂³	—	2	8	no	—
315	C₂³	#123×C₆₁	1	16	yes	—
316	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
317	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
318	C₂³	C₂×#41×C₆₁	1	8	yes	—
319	C₂³	C₂×#41×C₆₁	1	4	yes	—
320	C₂³	C₂×#41×C₆₁	1	4	yes	—
321	C₂³	2₋¹⁺⁴×C₆₁	1	4	yes	—
322	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
323	C₂×C₄	—	2	32	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	32	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	16	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	8	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	4	8	no	—
342	C₂×C₄	—	4	16	no	—
343	C₂×C₄	—	4	16	no	—
344	C₂×C₄	—	4	8	no	—
345	C₂×C₄	—	4	8	no	—
346	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
347	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
348	C₂×C₄	C₂×#41×C₆₁	1	8	yes	—
349	C₂²	—	2	4	no	—
350	C₂²	—	2	4	no	—
351	C₂²	—	2	16	no	—
352	C₂²	—	2	32	no	—
353	C₂²	C₂×#123×C₆₁	1	8	yes	—
354	C₂²	C₂×#123×C₆₁	1	4	yes	—
355	C₂²	C₆₁×#525	1	4	yes	—
356	C₂²	C₆₁×#536	1	4	yes	—
357	C₂²	C₆₁×#552	1	16	yes	—
358	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
359	C₂²	C₂²×#41×C₆₁	1	2	yes	—
360	C₂²	C₂²×#41×C₆₁	1	2	yes	—
361	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
362	C₄	—	2	4	no	—
363	C₄	—	2	4	no	—
364	C₄	—	2	8	no	—
365	C₄	—	4	4	no	—
366	C₄	—	4	4	no	—
367	C₄	—	4	4	no	—
368	C₄	—	4	8	no	—
369	C₂	—	2	8	no	—
370	C₂	C₆₁×#2484	1	8	yes	direct product factor
371	C₂	C₂²×#123×C₆₁	1	1	yes	characteristic
372	C₂	C₂×C₆₁×#525	1	1	yes	characteristic
373	C₂	C₂×C₆₁×#536	1	1	yes	characteristic
374	C₂	C₂×C₆₁×#552	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₆₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
prime radical	C₂⁵×C₆₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₆₁×#2484	C₂	direct (N × H)
4. C₂×C₆₁×#400	C₂	semidirect
5. C₂×C₆₁×#398	C₂	semidirect
6. C₂×C₆₁×#387	C₂	semidirect
25. C₆₁×#400	C₂²	semidirect
26. C₆₁×#398	C₂²	semidirect
27. C₆₁×#387	C₂²	semidirect
161. C₂×#2484	C₆₁	direct (N × H)
184. #2484	C₂×C₆₁	direct (N × H)
185. C₂×#400	C₂×C₆₁	semidirect
186. C₂×#398	C₂×C₆₁	semidirect
187. C₂×#387	C₂×C₆₁	semidirect
192. C₂×C₆₁	#2484	direct (N × H)
212. #400	C₂²×C₆₁	semidirect
213. #398	C₂²×C₆₁	semidirect
214. #387	C₂²×C₆₁	semidirect
223. C₆₁	C₂×#2484	direct (N × H)
370. C₂	C₆₁×#2484	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#117×C₆₁	2
C₂³×C₄⋊C₄×C₆₁	2
C₆₁×#2484	2
C₂×C₆₁×#400	2
C₂×C₆₁×#398	2
C₂×C₆₁×#387	2
C₂×C₆₁×#385	2
C₂×C₆₁×#381	2
C₂×#2484	61

Subgroups — C2×C61×#2484 #29538240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#2484 #29538240