Subgroups — C₆₁×#24693 #29528126

Order 15616.

828 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#474	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#442	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2563	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2357	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2073	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2054	C₂	1	2	yes	maximal
7	C₆₁×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1949	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1925	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1804	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
16	C₆₁×#474	—	2	4	no	—
17	C₆₁×#442	—	2	4	no	—
18	C₂×#107×C₆₁	C₂²	1	2	yes	—
19	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
22	C₂×#102×C₆₁	C₂²	1	2	yes	—
23	C₂×#102×C₆₁	C₂²	1	2	yes	—
24	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
27	C₆₁×#393	—	2	1	no	—
28	C₆₁×#393	—	2	1	no	—
29	C₆₁×#390	C₂²	1	2	yes	—
30	C₆₁×#390	C₂²	1	2	yes	—
31	C₆₁×#388	—	2	2	no	—
32	C₆₁×#382	C₂²	1	2	yes	—
33	C₆₁×#382	C₂²	1	1	yes	characteristic
34	C₆₁×#381	—	2	1	no	—
35	C₆₁×#380	—	2	2	no	—
36	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
39	C₆₁×#340	C₂²	1	2	yes	—
40	C₆₁×#340	C₂²	1	2	yes	—
41	C₆₁×#340	C₂²	1	2	yes	—
42	C₆₁×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₆₁	—	2	1	no	—
44	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₆₁	—	2	1	no	—
47	C₂³×C₄×C₆₁	—	2	1	no	—
48	C₂×D₈×C₆₁	—	2	2	no	—
49	C₂×D₈×C₆₁	—	2	2	no	—
50	C₂×D₈×C₆₁	—	2	2	no	—
51	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
54	C₄⋊Q₈×C₆₁	—	2	2	no	—
55	C₄⋊Q₈×C₆₁	—	2	2	no	—
56	C₄×D₄×C₆₁	—	2	2	no	—
57	C₄×D₄×C₆₁	—	2	2	no	—
58	C₄×D₄×C₆₁	—	2	2	no	—
59	C₄×D₄×C₆₁	D₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
72	C₂×C₄²×C₆₁	—	2	2	no	—
73	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
74	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
75	#107×C₆₁	—	2	4	no	—
76	#106×C₆₁	—	2	2	no	—
77	C₄⋊C₈×C₆₁	—	2	4	no	—
78	C₄⋊C₈×C₆₁	—	2	2	no	—
79	#102×C₆₁	—	2	2	no	—
80	#102×C₆₁	—	2	4	no	—
81	#102×C₆₁	—	2	4	no	—
82	#102×C₆₁	—	2	2	no	—
83	#97×C₆₁	—	2	2	no	—
84	#95×C₆₁	—	2	1	no	—
85	#95×C₆₁	—	2	2	no	—
86	#95×C₆₁	—	2	2	no	—
87	#95×C₆₁	—	2	2	no	—
88	#95×C₆₁	—	2	1	no	—
89	#95×C₆₁	D₄	1	1	yes	characteristic
90	#95×C₆₁	D₄	1	1	yes	characteristic
91	C₂⁴×C₆₁	—	2	1	no	—
92	C₂⁴×C₆₁	—	2	1	no	—
93	C₂×Q₈×C₆₁	—	4	2	no	—
94	C₂×Q₈×C₆₁	—	8	2	no	—
95	C₂×D₄×C₆₁	—	2	1	no	—
96	C₂×D₄×C₆₁	—	2	1	no	—
97	C₂×D₄×C₆₁	—	2	1	no	—
98	C₂×D₄×C₆₁	—	2	1	no	—
99	C₂×D₄×C₆₁	—	2	1	no	—
100	C₂×D₄×C₆₁	—	2	1	no	—
101	C₂×D₄×C₆₁	—	2	1	no	—
102	C₂×D₄×C₆₁	—	2	1	no	—
103	C₂×D₄×C₆₁	—	2	1	no	—
104	C₂×D₄×C₆₁	—	2	1	no	—
105	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₆₁	#41	1	2	yes	—
107	C₂²×C₄×C₆₁	—	2	1	no	—
108	C₂²×C₄×C₆₁	—	2	4	no	—
109	C₂²×C₄×C₆₁	—	2	1	no	—
110	C₂²×C₄×C₆₁	—	2	2	no	—
111	C₂²×C₄×C₆₁	—	2	2	no	—
112	C₂²×C₄×C₆₁	—	4	4	no	—
113	C₂²×C₄×C₆₁	—	4	2	no	—
114	C₂²×C₄×C₆₁	—	8	2	no	—
115	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
120	D₈×C₆₁	—	2	8	no	—
121	C₂×C₈×C₆₁	—	2	1	no	—
122	C₂×C₈×C₆₁	—	2	1	no	—
123	C₂×C₈×C₆₁	—	2	1	no	—
124	C₂×C₈×C₆₁	—	2	2	no	—
125	C₂×C₈×C₆₁	—	2	2	no	—
126	C₂×C₈×C₆₁	—	2	2	no	—
127	C₂×C₈×C₆₁	—	2	1	no	—
128	C₂×C₈×C₆₁	—	2	1	no	—
129	C₂×C₈×C₆₁	#41	1	2	yes	—
130	C₄⋊C₄×C₆₁	—	2	1	no	—
131	C₄⋊C₄×C₆₁	—	2	1	no	—
132	C₄⋊C₄×C₆₁	—	2	2	no	—
133	C₄⋊C₄×C₆₁	—	2	2	no	—
134	C₄⋊C₄×C₆₁	—	2	1	no	—
135	C₄⋊C₄×C₆₁	—	2	2	no	—
136	C₄⋊C₄×C₆₁	—	2	2	no	—
137	C₄⋊C₄×C₆₁	—	4	2	no	—
138	C₄⋊C₄×C₆₁	—	4	2	no	—
139	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
140	C₂²⋊C₄×C₆₁	—	2	4	no	—
141	C₂²⋊C₄×C₆₁	—	4	4	no	—
142	C₂²⋊C₄×C₆₁	—	4	2	no	—
143	C₂²⋊C₄×C₆₁	—	8	2	no	—
144	C₂²⋊C₄×C₆₁	—	8	2	no	—
145	C₂²⋊C₄×C₆₁	—	8	2	no	—
146	C₄²×C₆₁	—	2	2	no	—
147	C₄²×C₆₁	—	2	2	no	—
148	C₄²×C₆₁	—	8	2	no	—
149	C₄²×C₆₁	C₂×D₄	1	2	yes	—
150	C₄²×C₆₁	#41	1	2	yes	—
151	C₂³×C₆₁	—	2	2	no	—
152	C₂³×C₆₁	—	2	2	no	—
153	C₂³×C₆₁	—	4	1	no	—
154	C₂³×C₆₁	—	4	1	no	—
155	C₂³×C₆₁	—	4	1	no	—
156	C₂³×C₆₁	—	4	1	no	—
157	C₂³×C₆₁	—	4	2	no	—
158	C₂³×C₆₁	—	4	2	no	—
159	C₂³×C₆₁	—	4	2	no	—
160	C₂³×C₆₁	—	4	2	no	—
161	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₆₁	—	8	4	no	—
163	D₄×C₆₁	—	2	2	no	—
164	D₄×C₆₁	—	2	2	no	—
165	D₄×C₆₁	—	2	2	no	—
166	D₄×C₆₁	—	2	2	no	—
167	D₄×C₆₁	—	4	1	no	—
168	D₄×C₆₁	—	4	1	no	—
169	D₄×C₆₁	—	4	1	no	—
170	D₄×C₆₁	—	4	1	no	—
171	C₂×C₄×C₆₁	—	2	2	no	—
172	C₂×C₄×C₆₁	—	2	2	no	—
173	C₂×C₄×C₆₁	—	2	2	no	—
174	C₂×C₄×C₆₁	—	2	2	no	—
175	C₂×C₄×C₆₁	—	2	2	no	—
176	C₂×C₄×C₆₁	—	2	2	no	—
177	C₂×C₄×C₆₁	—	2	2	no	—
178	C₂×C₄×C₆₁	—	2	2	no	—
179	C₂×C₄×C₆₁	—	2	2	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	—	4	1	no	—
182	C₂×C₄×C₆₁	—	4	2	no	—
183	C₂×C₄×C₆₁	—	4	2	no	—
184	C₂×C₄×C₆₁	—	4	2	no	—
185	C₂×C₄×C₆₁	—	4	2	no	—
186	C₂×C₄×C₆₁	—	4	2	no	—
187	C₂×C₄×C₆₁	—	4	2	no	—
188	C₂×C₄×C₆₁	—	4	2	no	—
189	C₂×C₄×C₆₁	—	8	4	no	—
190	C₂×C₄×C₆₁	—	8	4	no	—
191	C₂×C₄×C₆₁	#121	1	2	yes	—
192	C₂×C₄×C₆₁	#121	1	2	yes	—
193	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
198	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
199	C₈×C₆₁	—	2	2	no	—
200	C₈×C₆₁	—	4	2	no	—
201	C₈×C₆₁	—	4	1	no	—
202	#24693	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂²×C₆₁	—	4	4	no	—
204	C₂²×C₆₁	—	4	2	no	—
205	C₂²×C₆₁	—	4	2	no	—
206	C₂²×C₆₁	—	4	2	no	—
207	C₂²×C₆₁	—	4	2	no	—
208	C₂²×C₆₁	—	8	2	no	—
209	C₂²×C₆₁	—	8	2	no	—
210	C₂²×C₆₁	—	8	2	no	—
211	C₂²×C₆₁	—	8	1	no	—
212	C₂²×C₆₁	—	8	1	no	—
213	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
214	C₂²×C₆₁	#547	1	1	yes	characteristic
215	C₂²×C₆₁	#548	1	1	yes	characteristic
216	C₂²×C₆₁	#575	1	2	yes	—
217	C₂²×C₆₁	#576	1	2	yes	—
218	C₄×C₆₁	—	2	2	no	—
219	C₄×C₆₁	—	2	2	no	—
220	C₄×C₆₁	—	4	2	no	—
221	C₄×C₆₁	—	4	2	no	—
222	C₄×C₆₁	—	4	2	no	—
223	C₄×C₆₁	—	8	2	no	—
224	C₄×C₆₁	—	8	1	no	—
225	C₄×C₆₁	—	8	2	no	—
226	C₄×C₆₁	#525	1	1	yes	characteristic
227	C₄×C₆₁	#536	1	1	yes	characteristic
228	C₄×C₆₁	#552	1	1	yes	characteristic
229	C₄×C₆₁	#556	1	1	yes	characteristic
230	C₂×#474	C₂×C₆₁	1	1	yes	characteristic, complemented
231	C₂×#442	C₂×C₆₁	1	1	yes	characteristic
232	#2563	C₂×C₆₁	1	1	yes	characteristic, complemented
233	#2357	C₂×C₆₁	1	1	yes	characteristic, complemented
234	#2073	C₂×C₆₁	1	2	yes	complemented
235	#2054	C₂×C₆₁	1	2	yes	—
236	#1993	C₂×C₆₁	1	1	yes	characteristic, complemented
237	#1949	C₂×C₆₁	1	2	yes	complemented
238	#1940	C₂×C₆₁	1	1	yes	characteristic, complemented
239	#1925	C₂×C₆₁	1	2	yes	complemented
240	#1804	C₂×C₆₁	1	1	yes	characteristic, complemented
241	C₂×C₆₁	—	8	2	no	—
242	C₂×C₆₁	—	8	2	no	—
243	C₂×C₆₁	#2415	1	1	yes	characteristic
244	C₂×C₆₁	#3040	1	1	yes	characteristic
245	C₂×C₆₁	#3041	1	1	yes	characteristic
246	C₂×C₆₁	#3347	1	2	yes	—
247	C₂×C₆₁	#3370	1	2	yes	—
248	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
249	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
250	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
251	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
252	#474	—	2	4	no	—
253	#442	—	2	4	no	—
254	C₂×#107	C₂²×C₆₁	1	2	yes	—
255	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
257	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
258	C₂×#102	C₂²×C₆₁	1	2	yes	—
259	C₂×#102	C₂²×C₆₁	1	2	yes	—
260	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
261	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
262	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
263	#393	—	2	1	no	—
264	#393	—	2	1	no	—
265	#390	C₂²×C₆₁	1	2	yes	—
266	#390	C₂²×C₆₁	1	2	yes	—
267	#388	—	2	2	no	—
268	#382	C₂²×C₆₁	1	2	yes	—
269	#382	C₂²×C₆₁	1	1	yes	characteristic
270	#381	—	2	1	no	—
271	#380	—	2	2	no	—
272	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
273	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
274	C₄×C₂²⋊C₄	—	2	1	no	—
275	#340	C₂²×C₆₁	1	2	yes	—
276	#340	C₂²×C₆₁	1	2	yes	—
277	#340	C₂²×C₆₁	1	2	yes	—
278	#336	C₂²×C₆₁	1	2	yes	—
279	C₆₁	#24693	1	1	yes	characteristic, direct product factor, Sylow
280	C₂²×Q₈	—	2	1	no	—
281	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
282	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
283	C₂³×C₄	—	2	1	no	—
284	C₂³×C₄	—	2	1	no	—
285	C₂×D₈	—	2	2	no	—
286	C₂×D₈	—	2	2	no	—
287	C₂×D₈	—	2	2	no	—
288	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
290	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
291	C₄⋊Q₈	—	2	2	no	—
292	C₄⋊Q₈	—	2	2	no	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	D₄×C₆₁	1	4	yes	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
311	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
312	#107	—	2	4	no	—
313	#106	—	2	2	no	—
314	C₄⋊C₈	—	2	4	no	—
315	C₄⋊C₈	—	2	2	no	—
316	#102	—	2	2	no	—
317	#102	—	2	4	no	—
318	#102	—	2	4	no	—
319	#102	—	2	2	no	—
320	#97	—	2	2	no	—
321	#95	—	2	1	no	—
322	#95	—	2	2	no	—
323	#95	—	2	2	no	—
324	#95	—	2	2	no	—
325	#95	—	2	1	no	—
326	#95	D₄×C₆₁	1	1	yes	characteristic
327	#95	D₄×C₆₁	1	1	yes	characteristic
328	C₂⁴	—	2	1	no	—
329	C₂⁴	—	2	1	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×Q₈	—	8	2	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
343	C₂×D₄	#41×C₆₁	1	2	yes	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	8	2	no	—
352	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
356	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
357	D₈	—	2	8	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	#41×C₆₁	1	2	yes	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	—	8	2	no	—
381	C₂²⋊C₄	—	8	2	no	—
382	C₂²⋊C₄	—	8	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	8	2	no	—
386	C₄²	C₂×D₄×C₆₁	1	2	yes	—
387	C₄²	#41×C₆₁	1	2	yes	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	1	no	—
398	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
399	Q₈	—	8	4	no	—
400	D₄	—	2	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	2	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	4	1	no	—
405	D₄	—	4	1	no	—
406	D₄	—	4	1	no	—
407	D₄	—	4	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	8	4	no	—
427	C₂×C₄	—	8	4	no	—
428	C₂×C₄	#121×C₆₁	1	2	yes	—
429	C₂×C₄	#121×C₆₁	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
431	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
432	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
434	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
435	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
436	C₈	—	2	2	no	—
437	C₈	—	4	1	no	—
438	C₈	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	8	1	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
450	C₂²	C₆₁×#547	1	1	yes	characteristic
451	C₂²	C₆₁×#548	1	1	yes	characteristic
452	C₂²	C₆₁×#575	1	2	yes	—
453	C₂²	C₆₁×#576	1	2	yes	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	8	1	no	—
460	C₄	—	8	2	no	—
461	C₄	—	8	2	no	—
462	C₄	C₆₁×#525	1	1	yes	characteristic
463	C₄	C₆₁×#536	1	1	yes	characteristic
464	C₄	C₆₁×#552	1	1	yes	characteristic
465	C₄	C₆₁×#556	1	1	yes	characteristic
466	C₂	—	8	2	no	—
467	C₂	—	8	2	no	—
468	C₂	C₆₁×#2415	1	1	yes	characteristic
469	C₂	C₆₁×#3040	1	1	yes	characteristic
470	C₂	C₆₁×#3041	1	1	yes	characteristic
471	C₂	C₆₁×#3347	1	2	yes	—
472	C₂	C₆₁×#3370	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×D₈×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₄×C₄⋊C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#474	C₂	semidirect
3. C₆₁×#2563	C₂	semidirect
4. C₆₁×#2357	C₂	semidirect
5. C₆₁×#2073	C₂	semidirect
7. C₆₁×#1993	C₂	semidirect
8. C₆₁×#1949	C₂	semidirect
9. C₆₁×#1940	C₂	semidirect
10. C₆₁×#1925	C₂	semidirect
11. C₆₁×#1804	C₂	semidirect
202. #24693	C₆₁	direct (N × H)
230. C₂×#474	C₂×C₆₁	semidirect
232. #2563	C₂×C₆₁	semidirect
233. #2357	C₂×C₆₁	semidirect
234. #2073	C₂×C₆₁	semidirect
236. #1993	C₂×C₆₁	semidirect
237. #1949	C₂×C₆₁	semidirect
238. #1940	C₂×C₆₁	semidirect
239. #1925	C₂×C₆₁	semidirect
240. #1804	C₂×C₆₁	semidirect
279. C₆₁	#24693	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×#474	2
C₂×C₆₁×#442	2
C₆₁×#2563	2
C₆₁×#2357	2
C₆₁×#2073	2
C₆₁×#2054	2
C₆₁×#1993	2
C₆₁×#1949	2
C₆₁×#1940	2
C₆₁×#1925	2
C₆₁×#1804	2
#24693	61

Subgroups — C61×#24693 #29528126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24693 #29528126