Subgroups — C₂×C₆₁×#1528 #29521073

Order 15616.

1050 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×#125×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#432	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1528	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₆₁×#330	C₂	1	4	yes	maximal, complemented
6	C₂²×M₁₆×C₆₁	—	2	1	no	—
7	C₂×#125×C₆₁	—	2	1	no	—
8	C₂×#125×C₆₁	—	2	2	no	—
9	C₂×#125×C₆₁	—	2	1	no	—
10	C₂×#125×C₆₁	—	2	2	no	—
11	C₂×#125×C₆₁	C₄	1	4	yes	—
12	C₂×#125×C₆₁	C₄	1	2	yes	—
13	C₂×#125×C₆₁	C₂²	1	2	yes	—
14	C₂×#125×C₆₁	C₂²	1	4	yes	—
15	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
19	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
20	C₆₁×#432	—	2	2	no	—
21	C₆₁×#432	C₂²	1	4	yes	—
22	C₂×C₄⋊C₈×C₆₁	—	2	1	no	—
23	C₂×C₂²⋊C₈×C₆₁	—	2	1	no	—
24	C₄×M₁₆×C₆₁	—	2	2	no	—
25	C₄×M₁₆×C₆₁	C₂²	1	4	yes	—
26	C₂×#97×C₆₁	C₂²	1	2	yes	—
27	C₂×#97×C₆₁	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₆₁	—	2	1	no	—
29	C₆₁×#330	C₂²	1	16	yes	complemented
30	C₂³×C₄×C₆₁	—	2	1	no	—
31	C₂³×C₄×C₆₁	—	2	1	no	—
32	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
35	C₂×M₁₆×C₆₁	—	2	8	no	—
36	C₂×M₁₆×C₆₁	—	2	4	no	—
37	C₂²×C₈×C₆₁	—	2	2	no	—
38	C₂²×C₈×C₆₁	—	2	2	no	—
39	#125×C₆₁	—	2	4	no	—
40	#125×C₆₁	—	2	4	no	—
41	#125×C₆₁	—	2	4	no	—
42	#125×C₆₁	—	2	4	no	—
43	#125×C₆₁	—	2	2	no	—
44	#125×C₆₁	—	2	2	no	—
45	#125×C₆₁	—	2	4	no	—
46	#125×C₆₁	C₂×C₄	1	4	yes	—
47	#125×C₆₁	C₂×C₄	1	8	yes	—
48	#125×C₆₁	C₂³	1	4	yes	—
49	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
50	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
58	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₆₁	D₄	1	2	yes	—
69	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₆₁	D₄	1	2	yes	—
71	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
73	C₄⋊C₈×C₆₁	—	2	4	no	—
74	C₂²⋊C₈×C₆₁	—	2	4	no	—
75	#97×C₆₁	—	2	2	no	—
76	#97×C₆₁	—	2	2	no	—
77	#97×C₆₁	C₂³	1	4	yes	—
78	#97×C₆₁	C₂³	1	4	yes	—
79	C₄×C₈×C₆₁	—	2	4	no	—
80	C₂⁴×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₆₁	—	2	4	no	—
82	C₂²×C₄×C₆₁	—	2	4	no	—
83	C₂²×C₄×C₆₁	—	2	4	no	—
84	C₂²×C₄×C₆₁	—	2	4	no	—
85	C₂²×C₄×C₆₁	—	2	2	no	—
86	C₂²×C₄×C₆₁	—	2	2	no	—
87	C₂²×C₄×C₆₁	—	4	2	no	—
88	C₂²×C₄×C₆₁	—	4	4	no	—
89	C₂²×C₄×C₆₁	—	4	4	no	—
90	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
95	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
102	M₁₆×C₆₁	—	2	16	no	—
103	C₂×C₈×C₆₁	—	2	8	no	—
104	C₂×C₈×C₆₁	—	2	4	no	—
105	C₂×C₈×C₆₁	—	2	4	no	—
106	C₂×C₈×C₆₁	—	4	4	no	—
107	C₄⋊C₄×C₆₁	—	2	4	no	—
108	C₄⋊C₄×C₆₁	—	2	8	no	—
109	C₄⋊C₄×C₆₁	—	2	8	no	—
110	C₄⋊C₄×C₆₁	—	2	4	no	—
111	C₄⋊C₄×C₆₁	—	2	2	no	—
112	C₄⋊C₄×C₆₁	—	2	2	no	—
113	C₄⋊C₄×C₆₁	—	2	4	no	—
114	C₄⋊C₄×C₆₁	—	2	4	no	—
115	C₄⋊C₄×C₆₁	—	2	4	no	—
116	C₄⋊C₄×C₆₁	—	2	4	no	—
117	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
118	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
119	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
120	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
121	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
122	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
124	C₄²×C₆₁	C₂×D₄	1	2	yes	—
125	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₆₁	C₂×D₄	1	2	yes	—
128	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
129	C₂³×C₆₁	—	2	2	no	—
130	C₂³×C₆₁	—	2	2	no	—
131	C₂³×C₆₁	#104	1	4	yes	—
132	C₂³×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
133	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₆₁	—	2	2	no	—
135	C₂×C₄×C₆₁	—	2	2	no	—
136	C₂×C₄×C₆₁	—	2	4	no	—
137	C₂×C₄×C₆₁	—	2	4	no	—
138	C₂×C₄×C₆₁	—	2	2	no	—
139	C₂×C₄×C₆₁	—	2	2	no	—
140	C₂×C₄×C₆₁	—	2	2	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	—	4	2	no	—
146	C₂×C₄×C₆₁	—	4	2	no	—
147	C₂×C₄×C₆₁	—	4	8	no	—
148	C₂×C₄×C₆₁	—	4	8	no	—
149	C₂×C₄×C₆₁	—	4	4	no	—
150	C₂×C₄×C₆₁	—	4	4	no	—
151	C₂×C₄×C₆₁	#101	1	4	yes	—
152	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
161	C₈×C₆₁	—	2	8	no	—
162	C₈×C₆₁	—	4	4	no	—
163	C₂×#1528	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂²×C₆₁	—	2	2	no	—
165	C₂²×C₆₁	—	2	2	no	—
166	C₂²×C₆₁	—	2	8	no	—
167	C₂²×C₆₁	C₂×#101	1	2	yes	—
168	C₂²×C₆₁	C₂×#104	1	4	yes	—
169	C₂²×C₆₁	C₂×#104	1	2	yes	—
170	C₂²×C₆₁	#421	1	2	yes	—
171	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
172	C₄×C₆₁	—	2	1	no	—
173	C₄×C₆₁	—	2	1	no	—
174	C₄×C₆₁	—	2	1	no	—
175	C₄×C₆₁	—	2	1	no	—
176	C₄×C₆₁	—	2	2	no	—
177	C₄×C₆₁	—	2	1	no	—
178	C₄×C₆₁	—	2	1	no	—
179	C₄×C₆₁	—	2	2	no	—
180	C₄×C₆₁	—	4	4	no	—
181	C₄×C₆₁	—	4	4	no	—
182	C₄×C₆₁	C₂×#101	1	4	yes	—
183	C₂²×#125	C₂×C₆₁	1	1	yes	characteristic
184	C₂×#432	C₂×C₆₁	1	1	yes	characteristic
185	C₂×C₄×M₁₆	C₂×C₆₁	1	1	yes	characteristic
186	#1528	C₂×C₆₁	1	8	yes	direct product factor
187	C₂×#330	C₂×C₆₁	1	4	yes	complemented
188	C₂×C₆₁	—	2	4	no	—
189	C₂×C₆₁	#1528	1	4	yes	direct product factor
190	C₂×C₆₁	C₂²×#101	1	1	yes	characteristic
191	C₂×C₆₁	C₂²×#104	1	1	yes	characteristic
192	C₂×C₆₁	C₂×#421	1	1	yes	characteristic
193	C₂²×M₁₆	—	2	1	no	—
194	C₂×#125	—	2	1	no	—
195	C₂×#125	—	2	2	no	—
196	C₂×#125	—	2	1	no	—
197	C₂×#125	—	2	2	no	—
198	C₂×#125	C₄×C₆₁	1	2	yes	—
199	C₂×#125	C₄×C₆₁	1	4	yes	—
200	C₂×#125	C₂²×C₆₁	1	2	yes	—
201	C₂×#125	C₂²×C₆₁	1	4	yes	—
202	C₂²×C₄⋊C₄	—	2	1	no	—
203	C₂²×C₄⋊C₄	—	2	1	no	—
204	C₂²×C₄⋊C₄	C₄×C₆₁	1	1	yes	characteristic
205	C₂²×C₄⋊C₄	C₄×C₆₁	1	1	yes	characteristic
206	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
207	#432	—	2	2	no	—
208	#432	C₂²×C₆₁	1	4	yes	—
209	C₂×C₄⋊C₈	—	2	1	no	—
210	C₂×C₂²⋊C₈	—	2	1	no	—
211	C₄×M₁₆	—	2	2	no	—
212	C₄×M₁₆	C₂²×C₆₁	1	4	yes	—
213	C₂×#97	C₂²×C₆₁	1	2	yes	—
214	C₂×#97	C₂²×C₆₁	1	2	yes	—
215	C₂×C₄×C₈	—	2	1	no	—
216	#330	C₂²×C₆₁	1	16	yes	complemented
217	C₆₁	C₂×#1528	1	1	yes	characteristic, direct product factor, Sylow
218	C₂³×C₄	—	2	1	no	—
219	C₂³×C₄	—	2	1	no	—
220	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
221	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
222	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
223	C₂×M₁₆	—	2	8	no	—
224	C₂×M₁₆	—	2	4	no	—
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	—	2	2	no	—
227	#125	—	2	4	no	—
228	#125	—	2	4	no	—
229	#125	—	2	4	no	—
230	#125	—	2	4	no	—
231	#125	—	2	2	no	—
232	#125	—	2	2	no	—
233	#125	—	2	4	no	—
234	#125	C₂×C₄×C₆₁	1	4	yes	—
235	#125	C₂×C₄×C₆₁	1	8	yes	—
236	#125	C₂³×C₆₁	1	4	yes	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	4	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	4	no	—
249	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
250	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
251	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	4	yes	—
252	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	4	yes	—
253	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
254	C₂×C₄²	C₂×C₄×C₆₁	1	2	yes	—
255	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
256	C₂×C₄²	D₄×C₆₁	1	2	yes	—
257	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
258	C₂×C₄²	D₄×C₆₁	1	2	yes	—
259	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
261	C₄⋊C₈	—	2	4	no	—
262	C₂²⋊C₈	—	2	4	no	—
263	#97	—	2	2	no	—
264	#97	—	2	2	no	—
265	#97	C₂³×C₆₁	1	4	yes	—
266	#97	C₂³×C₆₁	1	4	yes	—
267	C₄×C₈	—	2	4	no	—
268	C₂⁴	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
279	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
281	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
282	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
283	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
289	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
290	M₁₆	—	2	16	no	—
291	C₂×C₈	—	2	8	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	4	4	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	8	no	—
297	C₄⋊C₄	—	2	8	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
306	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
307	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
308	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
309	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
310	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
311	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
312	C₄²	C₂×D₄×C₆₁	1	2	yes	—
313	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
314	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
315	C₄²	C₂×D₄×C₆₁	1	2	yes	—
316	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
317	C₂³	—	2	2	no	—
318	C₂³	—	2	2	no	—
319	C₂³	#104×C₆₁	1	4	yes	—
320	C₂³	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
321	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	8	no	—
336	C₂×C₄	—	4	8	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	#101×C₆₁	1	4	yes	—
340	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
341	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
342	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
343	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
344	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
345	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
346	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
347	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
349	C₈	—	2	8	no	—
350	C₈	—	4	4	no	—
351	C₂²	—	2	8	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	C₂×#101×C₆₁	1	2	yes	—
355	C₂²	C₂×#104×C₆₁	1	4	yes	—
356	C₂²	C₂×#104×C₆₁	1	2	yes	—
357	C₂²	C₆₁×#421	1	2	yes	—
358	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	2	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	2	no	—
367	C₄	—	4	4	no	—
368	C₄	—	4	4	no	—
369	C₄	C₂×#101×C₆₁	1	4	yes	—
370	C₂	—	2	4	no	—
371	C₂	C₆₁×#1528	1	4	yes	direct product factor
372	C₂	C₂²×#101×C₆₁	1	1	yes	characteristic
373	C₂	C₂²×#104×C₆₁	1	1	yes	characteristic
374	C₂	C₂×C₆₁×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₂⁴×C₆₁	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₆₁×#1528	C₂	direct (N × H)
5. C₂×C₆₁×#330	C₂	semidirect
29. C₆₁×#330	C₂²	semidirect
163. C₂×#1528	C₆₁	direct (N × H)
186. #1528	C₂×C₆₁	direct (N × H)
187. C₂×#330	C₂×C₆₁	semidirect
189. C₂×C₆₁	#1528	direct (N × H)
216. #330	C₂²×C₆₁	semidirect
217. C₆₁	C₂×#1528	direct (N × H)
371. C₂	C₆₁×#1528	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×#125×C₆₁	2
C₂×C₆₁×#432	2
C₂×C₄×M₁₆×C₆₁	2
C₆₁×#1528	2
C₂×C₆₁×#330	2
C₂×#1528	61

Subgroups — C2×C61×#1528 #29521073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#1528 #29521073