Subgroups — C₆₁×#24532 #29527965

Order 15616.

982 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#451	C₂	1	1	yes	maximal, characteristic
2	C₂²×#103×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2502	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₂²⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2072	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2056	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1892	C₂	1	1	yes	maximal, characteristic
8	C₆₁×#1878	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1850	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1824	C₂	1	1	yes	maximal, characteristic
11	C₆₁×#1803	C₂	1	2	yes	maximal, complemented
12	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#451	—	2	4	no	—
20	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
21	C₂×#103×C₆₁	—	2	4	no	—
22	C₂×#103×C₆₁	C₂²	1	2	yes	—
23	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#103×C₆₁	C₂²	1	2	yes	—
25	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₆₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₆₁×#398	—	2	2	no	—
29	C₆₁×#391	—	2	2	no	—
30	C₆₁×#391	C₂²	1	2	yes	—
31	C₆₁×#391	C₂²	1	2	yes	—
32	C₆₁×#385	—	2	1	no	—
33	C₆₁×#385	—	2	1	no	—
34	C₆₁×#384	C₂²	1	2	yes	—
35	C₆₁×#380	—	2	1	no	—
36	C₆₁×#380	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
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×Q₈×C₆₁	—	2	2	no	—
45	C₂²×Q₈×C₆₁	—	2	4	no	—
46	C₂²×Q₈×C₆₁	—	4	2	no	—
47	C₂²×Q₈×C₆₁	D₄	1	4	yes	—
48	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₆₁	—	2	1	no	—
52	C₂³×C₄×C₆₁	—	2	1	no	—
53	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
54	C₂×Q₁₆×C₆₁	—	2	2	no	—
55	C₂×Q₁₆×C₆₁	—	2	2	no	—
56	C₂×Q₁₆×C₆₁	—	2	4	no	—
57	C₂×Q₁₆×C₆₁	—	4	2	no	—
58	C₂²×C₈×C₆₁	—	2	2	no	—
59	C₂²×C₈×C₆₁	—	4	2	no	—
60	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
61	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²⋊Q₈×C₆₁	—	2	2	no	—
64	C₂²⋊Q₈×C₆₁	—	2	2	no	—
65	C₄×Q₈×C₆₁	—	2	4	no	—
66	C₄×Q₈×C₆₁	—	4	2	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
71	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
77	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₆₁	—	2	2	no	—
82	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
83	C₄⋊C₈×C₆₁	—	4	2	no	—
84	#103×C₆₁	—	2	4	no	—
85	#103×C₆₁	—	2	4	no	—
86	#103×C₆₁	—	2	2	no	—
87	#103×C₆₁	—	2	2	no	—
88	#103×C₆₁	—	4	2	no	—
89	C₂²⋊C₈×C₆₁	—	2	2	no	—
90	#95×C₆₁	—	2	2	no	—
91	#95×C₆₁	—	2	2	no	—
92	#95×C₆₁	—	2	1	no	—
93	#95×C₆₁	—	2	2	no	—
94	#95×C₆₁	—	2	2	no	—
95	#95×C₆₁	D₄	1	2	yes	—
96	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₆₁	—	2	4	no	—
98	C₂×Q₈×C₆₁	—	2	1	no	—
99	C₂×Q₈×C₆₁	—	2	1	no	—
100	C₂×Q₈×C₆₁	—	2	2	no	—
101	C₂×Q₈×C₆₁	—	2	8	no	—
102	C₂×Q₈×C₆₁	—	2	1	no	—
103	C₂×Q₈×C₆₁	—	2	2	no	—
104	C₂×Q₈×C₆₁	—	2	1	no	—
105	C₂×Q₈×C₆₁	—	2	2	no	—
106	C₂×Q₈×C₆₁	—	2	2	no	—
107	C₂×Q₈×C₆₁	—	2	2	no	—
108	C₂×Q₈×C₆₁	—	4	4	no	—
109	C₂×Q₈×C₆₁	—	4	4	no	—
110	C₂×Q₈×C₆₁	—	4	8	no	—
111	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
112	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
113	C₂×Q₈×C₆₁	#41	1	4	yes	—
114	C₂²×C₄×C₆₁	—	2	1	no	—
115	C₂²×C₄×C₆₁	—	2	2	no	—
116	C₂²×C₄×C₆₁	—	2	2	no	—
117	C₂²×C₄×C₆₁	—	2	4	no	—
118	C₂²×C₄×C₆₁	—	2	1	no	—
119	C₂²×C₄×C₆₁	—	2	1	no	—
120	C₂²×C₄×C₆₁	—	2	2	no	—
121	C₂²×C₄×C₆₁	—	2	2	no	—
122	C₂²×C₄×C₆₁	—	2	1	no	—
123	C₂²×C₄×C₆₁	—	4	4	no	—
124	C₂²×C₄×C₆₁	—	4	2	no	—
125	C₂²×C₄×C₆₁	—	8	2	no	—
126	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₆₁	#41	1	2	yes	—
131	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
132	Q₁₆×C₆₁	—	4	4	no	—
133	Q₁₆×C₆₁	—	4	4	no	—
134	C₂×C₈×C₆₁	—	2	1	no	—
135	C₂×C₈×C₆₁	—	2	1	no	—
136	C₂×C₈×C₆₁	—	2	2	no	—
137	C₂×C₈×C₆₁	—	2	2	no	—
138	C₂×C₈×C₆₁	—	2	2	no	—
139	C₂×C₈×C₆₁	—	2	2	no	—
140	C₂×C₈×C₆₁	—	2	2	no	—
141	C₂×C₈×C₆₁	—	4	4	no	—
142	C₄⋊C₄×C₆₁	—	2	2	no	—
143	C₄⋊C₄×C₆₁	—	2	1	no	—
144	C₄⋊C₄×C₆₁	—	2	2	no	—
145	C₄⋊C₄×C₆₁	—	2	2	no	—
146	C₄⋊C₄×C₆₁	—	2	1	no	—
147	C₄⋊C₄×C₆₁	—	2	2	no	—
148	C₄⋊C₄×C₆₁	—	4	4	no	—
149	C₄⋊C₄×C₆₁	—	4	2	no	—
150	C₄⋊C₄×C₆₁	—	4	2	no	—
151	C₄⋊C₄×C₆₁	—	8	2	no	—
152	C₄⋊C₄×C₆₁	—	8	2	no	—
153	C₂²⋊C₄×C₆₁	—	2	2	no	—
154	C₂²⋊C₄×C₆₁	—	4	2	no	—
155	C₂²⋊C₄×C₆₁	—	4	2	no	—
156	C₂²⋊C₄×C₆₁	Q₁₆	1	4	yes	complemented
157	C₄²×C₆₁	—	2	2	no	—
158	C₄²×C₆₁	—	2	2	no	—
159	C₄²×C₆₁	—	4	4	no	—
160	C₂³×C₆₁	—	2	2	no	—
161	C₂³×C₆₁	—	2	2	no	—
162	C₂³×C₆₁	#121	1	2	yes	—
163	C₂³×C₆₁	C₂×Q₁₆	1	2	yes	—
164	C₂³×C₆₁	#137	1	2	yes	—
165	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₆₁	—	2	2	no	—
167	Q₈×C₆₁	—	2	4	no	—
168	Q₈×C₆₁	—	2	2	no	—
169	Q₈×C₆₁	—	2	2	no	—
170	Q₈×C₆₁	—	4	8	no	—
171	Q₈×C₆₁	—	4	2	no	—
172	Q₈×C₆₁	—	4	1	no	—
173	Q₈×C₆₁	—	4	1	no	—
174	Q₈×C₆₁	—	4	2	no	—
175	Q₈×C₆₁	#123	1	4	yes	—
176	C₂×C₄×C₆₁	—	2	2	no	—
177	C₂×C₄×C₆₁	—	2	2	no	—
178	C₂×C₄×C₆₁	—	2	4	no	—
179	C₂×C₄×C₆₁	—	2	2	no	—
180	C₂×C₄×C₆₁	—	2	2	no	—
181	C₂×C₄×C₆₁	—	2	2	no	—
182	C₂×C₄×C₆₁	—	2	2	no	—
183	C₂×C₄×C₆₁	—	2	4	no	—
184	C₂×C₄×C₆₁	—	2	2	no	—
185	C₂×C₄×C₆₁	—	2	2	no	—
186	C₂×C₄×C₆₁	—	2	2	no	—
187	C₂×C₄×C₆₁	—	2	2	no	—
188	C₂×C₄×C₆₁	—	4	8	no	—
189	C₂×C₄×C₆₁	—	4	2	no	—
190	C₂×C₄×C₆₁	—	4	1	no	—
191	C₂×C₄×C₆₁	—	4	1	no	—
192	C₂×C₄×C₆₁	—	4	2	no	—
193	C₂×C₄×C₆₁	—	4	2	no	—
194	C₂×C₄×C₆₁	—	4	2	no	—
195	C₂×C₄×C₆₁	—	4	2	no	—
196	C₂×C₄×C₆₁	—	4	2	no	—
197	C₂×C₄×C₆₁	—	4	2	no	—
198	C₂×C₄×C₆₁	—	4	2	no	—
199	C₂×C₄×C₆₁	—	4	2	no	—
200	C₂×C₄×C₆₁	—	8	4	no	—
201	C₂×C₄×C₆₁	#121	1	2	yes	—
202	C₂×C₄×C₆₁	C₂×Q₁₆	1	4	yes	—
203	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
205	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
207	C₈×C₆₁	—	4	1	no	—
208	C₈×C₆₁	—	4	2	no	—
209	C₈×C₆₁	—	4	1	no	—
210	#24532	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂²×C₆₁	—	2	2	no	—
212	C₂²×C₆₁	—	2	2	no	—
213	C₂²×C₆₁	—	2	4	no	—
214	C₂²×C₆₁	—	2	4	no	—
215	C₂²×C₆₁	#462	1	4	yes	—
216	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
217	C₂²×C₆₁	#546	1	2	yes	—
218	C₂²×C₆₁	C₂²×Q₁₆	1	1	yes	characteristic
219	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
220	C₂²×C₆₁	#577	1	2	yes	—
221	C₄×C₆₁	—	2	2	no	—
222	C₄×C₆₁	—	2	4	no	—
223	C₄×C₆₁	—	2	4	no	—
224	C₄×C₆₁	—	4	2	no	—
225	C₄×C₆₁	—	4	2	no	—
226	C₄×C₆₁	—	8	1	no	—
227	C₄×C₆₁	—	8	1	no	—
228	C₄×C₆₁	—	8	2	no	—
229	C₄×C₆₁	—	8	2	no	—
230	C₄×C₆₁	C₂×#123	1	1	yes	characteristic
231	C₄×C₆₁	#534	1	1	yes	characteristic
232	C₄×C₆₁	#551	1	2	yes	—
233	C₂×#451	C₂×C₆₁	1	1	yes	characteristic
234	C₂²×#103	C₂×C₆₁	1	1	yes	characteristic
235	#2502	C₂×C₆₁	1	1	yes	characteristic
236	Q₈×C₂²⋊C₄	C₂×C₆₁	1	1	yes	characteristic
237	#2072	C₂×C₆₁	1	2	yes	complemented
238	#2056	C₂×C₆₁	1	2	yes	complemented
239	#1892	C₂×C₆₁	1	1	yes	characteristic
240	#1878	C₂×C₆₁	1	2	yes	complemented
241	#1850	C₂×C₆₁	1	1	yes	characteristic
242	#1824	C₂×C₆₁	1	1	yes	characteristic
243	#1803	C₂×C₆₁	1	2	yes	complemented
244	C₂×C₆₁	—	2	4	no	—
245	C₂×C₆₁	#2412	1	1	yes	characteristic
246	C₂×C₆₁	C₂×#462	1	1	yes	characteristic
247	C₂×C₆₁	#3043	1	1	yes	characteristic
248	C₂×C₆₁	#3299	1	2	yes	—
249	C₂×C₆₁	#3316	1	2	yes	—
250	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
251	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
252	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
253	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
254	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
255	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
256	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
257	#451	—	2	4	no	—
258	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
259	C₂×#103	—	2	4	no	—
260	C₂×#103	C₂²×C₆₁	1	2	yes	—
261	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
262	C₂×#103	C₂²×C₆₁	1	2	yes	—
263	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
264	C₂×#103	C₂²×C₆₁	1	2	yes	—
265	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
266	#398	—	2	2	no	—
267	#391	—	2	2	no	—
268	#391	C₂²×C₆₁	1	2	yes	—
269	#391	C₂²×C₆₁	1	2	yes	—
270	#385	—	2	1	no	—
271	#385	—	2	1	no	—
272	#384	C₂²×C₆₁	1	2	yes	—
273	#380	—	2	1	no	—
274	#380	C₂²×C₆₁	1	1	yes	characteristic
275	C₄×C₂²⋊C₄	—	2	1	no	—
276	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
277	#340	C₂²×C₆₁	1	2	yes	—
278	#340	C₂²×C₆₁	1	2	yes	—
279	#340	C₂²×C₆₁	1	2	yes	—
280	#336	C₂²×C₆₁	1	2	yes	—
281	C₆₁	#24532	1	1	yes	characteristic, direct product factor, Sylow
282	C₂²×Q₈	—	2	1	no	—
283	C₂²×Q₈	—	2	2	no	—
284	C₂²×Q₈	—	2	4	no	—
285	C₂²×Q₈	—	4	2	no	—
286	C₂²×Q₈	D₄×C₆₁	1	4	yes	—
287	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
288	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
289	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
290	C₂³×C₄	—	2	1	no	—
291	C₂³×C₄	—	2	1	no	—
292	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
293	C₂×Q₁₆	—	2	2	no	—
294	C₂×Q₁₆	—	2	2	no	—
295	C₂×Q₁₆	—	2	4	no	—
296	C₂×Q₁₆	—	4	2	no	—
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	4	2	no	—
299	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
300	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
302	C₂²⋊Q₈	—	2	2	no	—
303	C₂²⋊Q₈	—	2	2	no	—
304	C₄×Q₈	—	2	4	no	—
305	C₄×Q₈	—	4	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
319	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
322	C₄⋊C₈	—	4	2	no	—
323	#103	—	2	4	no	—
324	#103	—	2	4	no	—
325	#103	—	2	2	no	—
326	#103	—	2	2	no	—
327	#103	—	4	2	no	—
328	C₂²⋊C₈	—	2	2	no	—
329	#95	—	2	2	no	—
330	#95	—	2	2	no	—
331	#95	—	2	1	no	—
332	#95	—	2	2	no	—
333	#95	—	2	2	no	—
334	#95	D₄×C₆₁	1	2	yes	—
335	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	8	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	4	4	no	—
348	C₂×Q₈	—	4	4	no	—
349	C₂×Q₈	—	4	8	no	—
350	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
351	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
352	C₂×Q₈	#41×C₆₁	1	4	yes	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	4	4	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	8	2	no	—
365	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
369	C₂²×C₄	#41×C₆₁	1	2	yes	—
370	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
371	Q₁₆	—	4	4	no	—
372	Q₁₆	—	4	4	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	4	4	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	4	4	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	—	8	2	no	—
391	C₄⋊C₄	—	8	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₂²⋊C₄	Q₁₆×C₆₁	1	4	yes	complemented
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	4	4	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	#121×C₆₁	1	2	yes	—
402	C₂³	C₂×Q₁₆×C₆₁	1	2	yes	—
403	C₂³	#137×C₆₁	1	2	yes	—
404	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
405	Q₈	—	2	2	no	—
406	Q₈	—	2	4	no	—
407	Q₈	—	2	2	no	—
408	Q₈	—	2	2	no	—
409	Q₈	—	4	8	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	4	1	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	4	1	no	—
414	Q₈	#123×C₆₁	1	4	yes	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	4	8	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	8	4	no	—
440	C₂×C₄	#121×C₆₁	1	2	yes	—
441	C₂×C₄	C₂×Q₁₆×C₆₁	1	4	yes	—
442	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
443	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
444	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
445	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
446	C₈	—	4	2	no	—
447	C₈	—	4	1	no	—
448	C₈	—	4	1	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	2	2	no	—
453	C₂²	C₆₁×#462	1	4	yes	—
454	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
455	C₂²	C₆₁×#546	1	2	yes	—
456	C₂²	C₂²×Q₁₆×C₆₁	1	1	yes	characteristic
457	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
458	C₂²	C₆₁×#577	1	2	yes	—
459	C₄	—	2	4	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	4	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	8	1	no	—
465	C₄	—	8	2	no	—
466	C₄	—	8	2	no	—
467	C₄	—	8	1	no	—
468	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
469	C₄	C₆₁×#534	1	1	yes	characteristic
470	C₄	C₆₁×#551	1	2	yes	—
471	C₂	—	2	4	no	—
472	C₂	C₆₁×#2412	1	1	yes	characteristic
473	C₂	C₂×C₆₁×#462	1	1	yes	characteristic
474	C₂	C₆₁×#3043	1	1	yes	characteristic
475	C₂	C₆₁×#3299	1	2	yes	—
476	C₂	C₆₁×#3316	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
5. C₆₁×#2072	C₂	semidirect
6. C₆₁×#2056	C₂	semidirect
8. C₆₁×#1878	C₂	semidirect
11. C₆₁×#1803	C₂	semidirect
156. C₂²⋊C₄×C₆₁	Q₁₆	semidirect
210. #24532	C₆₁	direct (N × H)
237. #2072	C₂×C₆₁	semidirect
238. #2056	C₂×C₆₁	semidirect
240. #1878	C₂×C₆₁	semidirect
243. #1803	C₂×C₆₁	semidirect
281. C₆₁	#24532	direct (N × H)
395. C₂²⋊C₄	Q₁₆×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#451	2
C₂²×#103×C₆₁	2
C₆₁×#2502	2
Q₈×C₂²⋊C₄×C₆₁	2
C₆₁×#2072	2
C₆₁×#2056	2
C₆₁×#1892	2
C₆₁×#1878	2
C₆₁×#1850	2
C₆₁×#1824	2
C₆₁×#1803	2
#24532	61

Subgroups — C61×#24532 #29527965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24532 #29527965