Subgroups — C₆₁×#23703 #29527136

Order 15616.

932 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2324	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2076	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2067	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2054	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2033	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1999	C₂	1	1	yes	maximal, characteristic
10	C₄×#107×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1762	C₂	1	2	yes	maximal, complemented
12	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#121×C₆₁	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
15	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
16	C₄×D₈×C₆₁	—	2	4	no	—
17	C₆₁×#433	—	2	4	no	—
18	C₂×#107×C₆₁	C₂²	1	2	yes	—
19	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×#102×C₆₁	C₂²	1	2	yes	—
23	C₂×#102×C₆₁	C₂²	1	2	yes	—
24	C₂×#102×C₆₁	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₆₁×#390	—	2	2	no	—
30	C₆₁×#390	C₂²	1	2	yes	—
31	C₆₁×#389	C₂²	1	2	yes	—
32	C₆₁×#388	—	2	2	no	—
33	C₆₁×#386	—	2	2	no	—
34	C₆₁×#385	—	2	2	no	—
35	C₆₁×#380	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
37	C₆₁×#340	C₂²	1	2	yes	—
38	C₆₁×#340	C₂²	1	2	yes	—
39	C₆₁×#340	C₂²	1	1	yes	characteristic
40	C₆₁×#340	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₆₁	—	2	2	no	—
42	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₆₁	—	2	2	no	—
44	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
45	C₂×D₈×C₆₁	—	2	4	no	—
46	C₂×D₈×C₆₁	—	2	2	no	—
47	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
51	#121×C₆₁	—	2	4	no	—
52	#121×C₆₁	—	2	4	no	—
53	C₄×D₄×C₆₁	—	2	4	no	—
54	C₄×D₄×C₆₁	—	2	4	no	—
55	#117×C₆₁	—	2	2	no	—
56	#117×C₆₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₆₁	—	2	2	no	—
71	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
73	#107×C₆₁	—	2	2	no	—
74	#107×C₆₁	—	2	4	no	—
75	C₄⋊C₈×C₆₁	—	2	2	no	—
76	C₄⋊C₈×C₆₁	—	2	2	no	—
77	#102×C₆₁	—	2	4	no	—
78	#102×C₆₁	—	2	4	no	—
79	#102×C₆₁	—	2	4	no	—
80	C₂²⋊C₈×C₆₁	—	2	2	no	—
81	C₂²⋊C₈×C₆₁	—	2	2	no	—
82	#97×C₆₁	—	2	2	no	—
83	C₄×C₈×C₆₁	D₄	1	4	yes	complemented
84	#95×C₆₁	—	2	2	no	—
85	#95×C₆₁	—	2	2	no	—
86	#95×C₆₁	—	2	2	no	—
87	C₂⁴×C₆₁	—	2	2	no	—
88	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
89	C₂×D₄×C₆₁	—	2	8	no	—
90	C₂×D₄×C₆₁	—	2	2	no	—
91	C₂×D₄×C₆₁	—	2	2	no	—
92	C₂×D₄×C₆₁	—	2	2	no	—
93	C₂×D₄×C₆₁	—	2	2	no	—
94	C₂×D₄×C₆₁	—	2	2	no	—
95	C₂×D₄×C₆₁	—	8	2	no	—
96	C₂×D₄×C₆₁	—	8	2	no	—
97	C₂×D₄×C₆₁	#41	1	4	yes	—
98	C₂²×C₄×C₆₁	—	2	2	no	—
99	C₂²×C₄×C₆₁	—	2	1	no	—
100	C₂²×C₄×C₆₁	—	2	1	no	—
101	C₂²×C₄×C₆₁	—	2	2	no	—
102	C₂²×C₄×C₆₁	—	2	2	no	—
103	C₂²×C₄×C₆₁	—	2	2	no	—
104	C₂²×C₄×C₆₁	—	2	2	no	—
105	C₂²×C₄×C₆₁	—	4	4	no	—
106	C₂²×C₄×C₆₁	—	8	2	no	—
107	C₂²×C₄×C₆₁	—	8	2	no	—
108	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
114	D₈×C₆₁	—	2	8	no	—
115	C₂×C₈×C₆₁	—	2	2	no	—
116	C₂×C₈×C₆₁	—	2	2	no	—
117	C₂×C₈×C₆₁	—	2	1	no	—
118	C₂×C₈×C₆₁	—	2	1	no	—
119	C₂×C₈×C₆₁	—	2	2	no	—
120	C₂×C₈×C₆₁	—	2	2	no	—
121	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
123	C₄⋊C₄×C₆₁	—	2	2	no	—
124	C₄⋊C₄×C₆₁	—	2	2	no	—
125	C₄⋊C₄×C₆₁	—	2	2	no	—
126	C₄⋊C₄×C₆₁	—	2	2	no	—
127	C₄⋊C₄×C₆₁	—	2	2	no	—
128	C₄⋊C₄×C₆₁	—	2	2	no	—
129	C₄⋊C₄×C₆₁	—	2	2	no	—
130	C₄⋊C₄×C₆₁	—	8	2	no	—
131	C₄⋊C₄×C₆₁	#41	1	4	yes	—
132	C₂²⋊C₄×C₆₁	—	2	8	no	—
133	C₂²⋊C₄×C₆₁	—	2	2	no	—
134	C₂²⋊C₄×C₆₁	—	2	2	no	—
135	C₂²⋊C₄×C₆₁	—	4	4	no	—
136	C₂²⋊C₄×C₆₁	—	8	2	no	—
137	C₂²⋊C₄×C₆₁	—	8	2	no	—
138	C₂²⋊C₄×C₆₁	—	8	2	no	—
139	C₄²×C₆₁	—	2	1	no	—
140	C₄²×C₆₁	—	2	1	no	—
141	C₄²×C₆₁	—	8	2	no	—
142	C₄²×C₆₁	C₂×D₄	1	2	yes	—
143	C₄²×C₆₁	#41	1	2	yes	—
144	C₂³×C₆₁	—	2	1	no	—
145	C₂³×C₆₁	—	2	4	no	—
146	C₂³×C₆₁	—	2	2	no	—
147	C₂³×C₆₁	—	2	2	no	—
148	C₂³×C₆₁	—	2	1	no	—
149	C₂³×C₆₁	—	2	1	no	—
150	C₂³×C₆₁	—	4	2	no	—
151	C₂³×C₆₁	—	4	2	no	—
152	C₂³×C₆₁	—	4	2	no	—
153	C₂³×C₆₁	—	4	2	no	—
154	C₂³×C₆₁	—	4	2	no	—
155	C₂³×C₆₁	—	4	2	no	—
156	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
157	D₄×C₆₁	—	2	4	no	—
158	D₄×C₆₁	—	2	4	no	—
159	D₄×C₆₁	—	4	2	no	—
160	D₄×C₆₁	—	4	2	no	—
161	D₄×C₆₁	—	8	8	no	—
162	C₂×C₄×C₆₁	—	2	1	no	—
163	C₂×C₄×C₆₁	—	2	2	no	—
164	C₂×C₄×C₆₁	—	2	1	no	—
165	C₂×C₄×C₆₁	—	2	1	no	—
166	C₂×C₄×C₆₁	—	2	1	no	—
167	C₂×C₄×C₆₁	—	2	1	no	—
168	C₂×C₄×C₆₁	—	2	2	no	—
169	C₂×C₄×C₆₁	—	2	4	no	—
170	C₂×C₄×C₆₁	—	2	1	no	—
171	C₂×C₄×C₆₁	—	2	2	no	—
172	C₂×C₄×C₆₁	—	2	1	no	—
173	C₂×C₄×C₆₁	—	4	2	no	—
174	C₂×C₄×C₆₁	—	4	2	no	—
175	C₂×C₄×C₆₁	—	4	1	no	—
176	C₂×C₄×C₆₁	—	4	2	no	—
177	C₂×C₄×C₆₁	—	4	1	no	—
178	C₂×C₄×C₆₁	—	4	2	no	—
179	C₂×C₄×C₆₁	—	4	2	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	—	4	2	no	—
182	C₂×C₄×C₆₁	—	4	2	no	—
183	C₂×C₄×C₆₁	—	4	2	no	—
184	C₂×C₄×C₆₁	—	8	8	no	—
185	C₂×C₄×C₆₁	#121	1	2	yes	—
186	C₂×C₄×C₆₁	#121	1	2	yes	—
187	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
189	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
191	C₈×C₆₁	—	2	2	no	—
192	C₈×C₆₁	—	2	2	no	—
193	C₈×C₆₁	—	4	1	no	—
194	C₈×C₆₁	—	4	1	no	—
195	#23703	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂²×C₆₁	—	4	2	no	—
197	C₂²×C₆₁	—	4	4	no	—
198	C₂²×C₆₁	—	4	2	no	—
199	C₂²×C₆₁	—	4	4	no	—
200	C₂²×C₆₁	—	4	1	no	—
201	C₂²×C₆₁	—	4	4	no	—
202	C₂²×C₆₁	—	4	1	no	—
203	C₂²×C₆₁	—	4	1	no	—
204	C₂²×C₆₁	—	8	2	no	—
205	C₂²×C₆₁	—	8	2	no	—
206	C₂²×C₆₁	—	8	2	no	—
207	C₂²×C₆₁	—	8	2	no	—
208	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
209	C₂²×C₆₁	#525	1	2	yes	—
210	C₂²×C₆₁	#576	1	1	yes	characteristic
211	C₂²×C₆₁	#576	1	2	yes	—
212	C₂²×C₆₁	#578	1	1	yes	characteristic
213	C₄×C₆₁	—	2	2	no	—
214	C₄×C₆₁	—	2	2	no	—
215	C₄×C₆₁	—	4	4	no	—
216	C₄×C₆₁	—	4	1	no	—
217	C₄×C₆₁	—	4	1	no	—
218	C₄×C₆₁	—	4	1	no	—
219	C₄×C₆₁	—	8	2	no	—
220	C₄×C₆₁	—	8	2	no	—
221	C₄×C₆₁	#525	1	1	yes	characteristic
222	C₄×C₆₁	#529	1	2	yes	—
223	C₄×C₆₁	#532	1	1	yes	characteristic
224	C₂×C₄×D₈	C₂×C₆₁	1	1	yes	characteristic, complemented
225	C₂×#433	C₂×C₆₁	1	1	yes	characteristic, complemented
226	#2324	C₂×C₆₁	1	2	yes	complemented
227	#2087	C₂×C₆₁	1	1	yes	characteristic, complemented
228	#2076	C₂×C₆₁	1	1	yes	characteristic, complemented
229	#2067	C₂×C₆₁	1	2	yes	complemented
230	#2054	C₂×C₆₁	1	1	yes	characteristic, complemented
231	#2033	C₂×C₆₁	1	2	yes	complemented
232	#1999	C₂×C₆₁	1	1	yes	characteristic
233	C₄×#107	C₂×C₆₁	1	1	yes	characteristic, complemented
234	#1762	C₂×C₆₁	1	2	yes	complemented
235	C₂×C₆₁	—	8	1	no	—
236	C₂×C₆₁	—	8	4	no	—
237	C₂×C₆₁	#2392	1	1	yes	characteristic
238	C₂×C₆₁	#3058	1	1	yes	characteristic
239	C₂×C₆₁	#3061	1	1	yes	characteristic
240	C₂×C₆₁	#3122	1	2	yes	—
241	C₂×C₆₁	#3124	1	2	yes	—
242	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
243	C₂×#121	C₂²×C₆₁	1	2	yes	—
244	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
245	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
246	C₄×D₈	—	2	4	no	—
247	#433	—	2	4	no	—
248	C₂×#107	C₂²×C₆₁	1	2	yes	—
249	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
252	C₂×#102	C₂²×C₆₁	1	2	yes	—
253	C₂×#102	C₂²×C₆₁	1	2	yes	—
254	C₂×#102	C₂²×C₆₁	1	2	yes	—
255	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
256	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
257	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
258	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
259	#390	—	2	2	no	—
260	#390	C₂²×C₆₁	1	2	yes	—
261	#389	C₂²×C₆₁	1	2	yes	—
262	#388	—	2	2	no	—
263	#386	—	2	2	no	—
264	#385	—	2	2	no	—
265	#380	C₂²×C₆₁	1	2	yes	—
266	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
267	#340	C₂²×C₆₁	1	1	yes	characteristic
268	#340	C₂²×C₆₁	1	2	yes	—
269	#340	C₂²×C₆₁	1	1	yes	characteristic
270	#340	C₂²×C₆₁	1	2	yes	—
271	C₆₁	#23703	1	1	yes	characteristic, direct product factor, Sylow
272	C₂²×D₄	—	2	2	no	—
273	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
274	C₂³×C₄	—	2	2	no	—
275	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
276	C₂×D₈	—	2	4	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
282	#121	—	2	4	no	—
283	#121	—	2	4	no	—
284	C₄×D₄	—	2	4	no	—
285	C₄×D₄	—	2	4	no	—
286	#117	—	2	2	no	—
287	#117	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
290	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
304	#107	—	2	2	no	—
305	#107	—	2	4	no	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	2	2	no	—
308	#102	—	2	4	no	—
309	#102	—	2	4	no	—
310	#102	—	2	4	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	C₂²⋊C₈	—	2	2	no	—
313	#97	—	2	2	no	—
314	C₄×C₈	D₄×C₆₁	1	4	yes	complemented
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	C₂⁴	—	2	2	no	—
319	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
320	C₂×D₄	—	2	8	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	8	2	no	—
327	C₂×D₄	—	8	2	no	—
328	C₂×D₄	#41×C₆₁	1	4	yes	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	8	2	no	—
338	C₂²×C₄	—	8	2	no	—
339	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
344	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
345	D₈	—	2	8	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
353	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	8	2	no	—
362	C₄⋊C₄	#41×C₆₁	1	4	yes	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	2	2	no	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	4	4	no	—
367	C₂²⋊C₄	—	8	2	no	—
368	C₂²⋊C₄	—	8	2	no	—
369	C₂²⋊C₄	—	8	2	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	8	2	no	—
373	C₄²	C₂×D₄×C₆₁	1	2	yes	—
374	C₄²	#41×C₆₁	1	2	yes	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
388	D₄	—	2	4	no	—
389	D₄	—	2	4	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	8	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	8	8	no	—
416	C₂×C₄	#121×C₆₁	1	2	yes	—
417	C₂×C₄	#121×C₆₁	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
420	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
421	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
422	C₈	—	2	2	no	—
423	C₈	—	2	2	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	2	no	—
438	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
439	C₂²	C₆₁×#525	1	2	yes	—
440	C₂²	C₆₁×#576	1	2	yes	—
441	C₂²	C₆₁×#576	1	1	yes	characteristic
442	C₂²	C₆₁×#578	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	4	no	—
448	C₄	—	4	1	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	2	no	—
451	C₄	C₆₁×#525	1	1	yes	characteristic
452	C₄	C₆₁×#529	1	2	yes	—
453	C₄	C₆₁×#532	1	1	yes	characteristic
454	C₂	—	8	1	no	—
455	C₂	—	8	4	no	—
456	C₂	C₆₁×#2392	1	1	yes	characteristic
457	C₂	C₆₁×#3058	1	1	yes	characteristic
458	C₂	C₆₁×#3061	1	1	yes	characteristic
459	C₂	C₆₁×#3122	1	2	yes	—
460	C₂	C₆₁×#3124	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#1999	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×#117×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×D₈×C₆₁	C₂	semidirect
2. C₂×C₆₁×#433	C₂	semidirect
3. C₆₁×#2324	C₂	semidirect
4. C₆₁×#2087	C₂	semidirect
5. C₆₁×#2076	C₂	semidirect
6. C₆₁×#2067	C₂	semidirect
7. C₆₁×#2054	C₂	semidirect
8. C₆₁×#2033	C₂	semidirect
10. C₄×#107×C₆₁	C₂	semidirect
11. C₆₁×#1762	C₂	semidirect
83. C₄×C₈×C₆₁	D₄	semidirect
195. #23703	C₆₁	direct (N × H)
224. C₂×C₄×D₈	C₂×C₆₁	semidirect
225. C₂×#433	C₂×C₆₁	semidirect
226. #2324	C₂×C₆₁	semidirect
227. #2087	C₂×C₆₁	semidirect
228. #2076	C₂×C₆₁	semidirect
229. #2067	C₂×C₆₁	semidirect
230. #2054	C₂×C₆₁	semidirect
231. #2033	C₂×C₆₁	semidirect
233. C₄×#107	C₂×C₆₁	semidirect
234. #1762	C₂×C₆₁	semidirect
271. C₆₁	#23703	direct (N × H)
314. C₄×C₈	D₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₈×C₆₁	2
C₂×C₆₁×#433	2
C₆₁×#2324	2
C₆₁×#2087	2
C₆₁×#2076	2
C₆₁×#2067	2
C₆₁×#2054	2
C₆₁×#2033	2
C₆₁×#1999	2
C₄×#107×C₆₁	2
C₆₁×#1762	2
#23703	61

Subgroups — C61×#23703 #29527136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#23703 #29527136