Subgroups — C₆₁×#24783 #29528216

Order 15616.

984 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#470	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#435	C₂	1	1	yes	maximal, characteristic
4	C₂²×#106×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2417	C₂	1	2	yes	maximal
6	C₆₁×#2066	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2035	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1971	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1944	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1872	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1809	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
19	C₆₁×#470	—	2	4	no	—
20	C₆₁×#467	—	2	4	no	—
21	C₆₁×#435	—	2	4	no	—
22	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#106×C₆₁	—	2	4	no	—
24	C₂×#106×C₆₁	C₂²	1	2	yes	—
25	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#103×C₆₁	C₂²	1	2	yes	—
29	C₂×#103×C₆₁	C₂²	1	2	yes	—
30	C₂×#103×C₆₁	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#398	—	2	2	no	—
35	C₆₁×#396	—	2	2	no	—
36	C₆₁×#391	C₂²	1	2	yes	—
37	C₆₁×#389	C₂²	1	2	yes	—
38	C₆₁×#386	—	2	2	no	—
39	C₆₁×#380	—	2	2	no	—
40	C₆₁×#380	C₂²	1	2	yes	—
41	C₆₁×#340	C₂²	1	2	yes	—
42	C₆₁×#340	C₂²	1	2	yes	—
43	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
44	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₆₁	—	2	2	no	—
46	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
48	C₂×Q₁₆×C₆₁	—	2	2	no	—
49	C₂×Q₁₆×C₆₁	—	2	2	no	—
50	C₂×Q₁₆×C₆₁	—	2	2	no	—
51	C₂×M₁₆×C₆₁	—	2	2	no	—
52	C₂×M₁₆×C₆₁	—	2	2	no	—
53	C₂×M₁₆×C₆₁	—	2	2	no	—
54	C₂²×C₈×C₆₁	—	2	2	no	—
55	C₂²×C₈×C₆₁	—	2	2	no	—
56	C₂²×C₈×C₆₁	D₄	1	4	yes	—
57	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
61	C₂²⋊Q₈×C₆₁	—	2	4	no	—
62	C₂²⋊Q₈×C₆₁	—	2	4	no	—
63	C₂²⋊Q₈×C₆₁	—	2	4	no	—
64	C₂²⋊Q₈×C₆₁	—	4	2	no	—
65	C₄×D₄×C₆₁	—	2	2	no	—
66	C₄×D₄×C₆₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₆₁	—	4	2	no	—
73	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
77	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
83	#107×C₆₁	—	2	2	no	—
84	#106×C₆₁	—	2	2	no	—
85	#106×C₆₁	—	2	4	no	—
86	#106×C₆₁	D₄	1	4	yes	complemented
87	C₄⋊C₈×C₆₁	—	2	2	no	—
88	#103×C₆₁	—	2	4	no	—
89	#103×C₆₁	—	2	4	no	—
90	#103×C₆₁	—	4	2	no	—
91	C₂²⋊C₈×C₆₁	—	2	2	no	—
92	C₂²⋊C₈×C₆₁	—	2	2	no	—
93	#97×C₆₁	—	2	2	no	—
94	#95×C₆₁	—	2	2	no	—
95	#95×C₆₁	—	2	2	no	—
96	#95×C₆₁	—	2	2	no	—
97	#95×C₆₁	—	2	2	no	—
98	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
99	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₆₁	—	2	2	no	—
101	C₂×Q₈×C₆₁	—	2	2	no	—
102	C₂×Q₈×C₆₁	—	2	2	no	—
103	C₂×Q₈×C₆₁	—	2	2	no	—
104	C₂×Q₈×C₆₁	—	2	2	no	—
105	C₂×Q₈×C₆₁	—	2	2	no	—
106	C₂×D₄×C₆₁	—	2	2	no	—
107	C₂×D₄×C₆₁	—	2	4	no	—
108	C₂²×C₄×C₆₁	—	2	1	no	—
109	C₂²×C₄×C₆₁	—	2	1	no	—
110	C₂²×C₄×C₆₁	—	2	1	no	—
111	C₂²×C₄×C₆₁	—	2	1	no	—
112	C₂²×C₄×C₆₁	—	2	2	no	—
113	C₂²×C₄×C₆₁	—	2	1	no	—
114	C₂²×C₄×C₆₁	—	2	1	no	—
115	C₂²×C₄×C₆₁	—	2	1	no	—
116	C₂²×C₄×C₆₁	—	2	1	no	—
117	C₂²×C₄×C₆₁	—	2	1	no	—
118	C₂²×C₄×C₆₁	—	2	1	no	—
119	C₂²×C₄×C₆₁	—	2	2	no	—
120	C₂²×C₄×C₆₁	—	2	2	no	—
121	C₂²×C₄×C₆₁	—	2	2	no	—
122	C₂²×C₄×C₆₁	—	4	4	no	—
123	C₂²×C₄×C₆₁	—	4	4	no	—
124	C₂²×C₄×C₆₁	—	8	2	no	—
125	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
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	M₁₆×C₆₁	—	4	4	no	—
134	C₂×C₈×C₆₁	—	2	1	no	—
135	C₂×C₈×C₆₁	—	2	1	no	—
136	C₂×C₈×C₆₁	—	2	8	no	—
137	C₂×C₈×C₆₁	—	2	1	no	—
138	C₂×C₈×C₆₁	—	2	1	no	—
139	C₂×C₈×C₆₁	—	2	1	no	—
140	C₂×C₈×C₆₁	—	2	1	no	—
141	C₂×C₈×C₆₁	—	2	1	no	—
142	C₂×C₈×C₆₁	—	2	1	no	—
143	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₆₁	#41	1	2	yes	—
147	C₄⋊C₄×C₆₁	—	2	2	no	—
148	C₄⋊C₄×C₆₁	—	2	2	no	—
149	C₄⋊C₄×C₆₁	—	2	2	no	—
150	C₄⋊C₄×C₆₁	—	2	2	no	—
151	C₄⋊C₄×C₆₁	—	2	2	no	—
152	C₄⋊C₄×C₆₁	—	2	2	no	—
153	C₄⋊C₄×C₆₁	—	4	4	no	—
154	C₄⋊C₄×C₆₁	—	4	4	no	—
155	C₄⋊C₄×C₆₁	—	4	4	no	—
156	C₄⋊C₄×C₆₁	—	8	2	no	—
157	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
158	C₂²⋊C₄×C₆₁	—	2	2	no	—
159	C₂²⋊C₄×C₆₁	—	2	2	no	—
160	C₂²⋊C₄×C₆₁	—	4	4	no	—
161	C₂²⋊C₄×C₆₁	—	4	4	no	—
162	C₂²⋊C₄×C₆₁	—	8	2	no	—
163	C₄²×C₆₁	—	2	1	no	—
164	C₄²×C₆₁	—	2	1	no	—
165	C₂³×C₆₁	—	2	1	no	—
166	C₂³×C₆₁	—	2	1	no	—
167	C₂³×C₆₁	—	2	2	no	—
168	C₂³×C₆₁	—	2	1	no	—
169	C₂³×C₆₁	—	2	1	no	—
170	C₂³×C₆₁	—	2	1	no	—
171	C₂³×C₆₁	—	2	2	no	—
172	C₂³×C₆₁	—	2	2	no	—
173	C₂³×C₆₁	#121	1	2	yes	—
174	C₂³×C₆₁	#137	1	4	yes	—
175	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₆₁	—	4	2	no	—
177	Q₈×C₆₁	—	4	2	no	—
178	Q₈×C₆₁	—	4	2	no	—
179	Q₈×C₆₁	—	4	2	no	—
180	D₄×C₆₁	—	4	4	no	—
181	C₂×C₄×C₆₁	—	2	1	no	—
182	C₂×C₄×C₆₁	—	2	1	no	—
183	C₂×C₄×C₆₁	—	2	2	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	1	no	—
188	C₂×C₄×C₆₁	—	2	1	no	—
189	C₂×C₄×C₆₁	—	2	1	no	—
190	C₂×C₄×C₆₁	—	2	4	no	—
191	C₂×C₄×C₆₁	—	2	1	no	—
192	C₂×C₄×C₆₁	—	2	1	no	—
193	C₂×C₄×C₆₁	—	2	2	no	—
194	C₂×C₄×C₆₁	—	2	2	no	—
195	C₂×C₄×C₆₁	—	4	2	no	—
196	C₂×C₄×C₆₁	—	4	2	no	—
197	C₂×C₄×C₆₁	—	4	1	no	—
198	C₂×C₄×C₆₁	—	4	1	no	—
199	C₂×C₄×C₆₁	—	4	1	no	—
200	C₂×C₄×C₆₁	—	4	1	no	—
201	C₂×C₄×C₆₁	—	4	2	no	—
202	C₂×C₄×C₆₁	—	4	2	no	—
203	C₂×C₄×C₆₁	—	4	2	no	—
204	C₂×C₄×C₆₁	—	4	2	no	—
205	C₂×C₄×C₆₁	—	4	2	no	—
206	C₂×C₄×C₆₁	—	4	2	no	—
207	C₂×C₄×C₆₁	—	4	2	no	—
208	C₂×C₄×C₆₁	—	4	2	no	—
209	C₂×C₄×C₆₁	—	4	2	no	—
210	C₂×C₄×C₆₁	—	8	8	no	—
211	C₂×C₄×C₆₁	#121	1	2	yes	—
212	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
218	C₈×C₆₁	—	2	2	no	—
219	C₈×C₆₁	—	4	1	no	—
220	C₈×C₆₁	—	4	1	no	—
221	C₈×C₆₁	#121	1	4	yes	—
222	#24783	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂²×C₆₁	—	2	4	no	—
224	C₂²×C₆₁	—	2	2	no	—
225	C₂²×C₆₁	—	2	4	no	—
226	C₂²×C₆₁	—	2	2	no	—
227	C₂²×C₆₁	—	4	2	no	—
228	C₂²×C₆₁	—	4	1	no	—
229	C₂²×C₆₁	—	4	2	no	—
230	C₂²×C₆₁	—	4	1	no	—
231	C₂²×C₆₁	—	4	1	no	—
232	C₂²×C₆₁	#470	1	4	yes	complemented
233	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
234	C₂²×C₆₁	D₄²	1	1	yes	characteristic
235	C₂²×C₆₁	#547	1	1	yes	characteristic
236	C₂²×C₆₁	C₂×#137	1	2	yes	—
237	C₂²×C₆₁	#577	1	2	yes	—
238	C₄×C₆₁	—	2	2	no	—
239	C₄×C₆₁	—	4	1	no	—
240	C₄×C₆₁	—	4	4	no	—
241	C₄×C₆₁	—	4	1	no	—
242	C₄×C₆₁	—	4	1	no	—
243	C₄×C₆₁	—	8	2	no	—
244	C₄×C₆₁	—	8	2	no	—
245	C₄×C₆₁	—	8	2	no	—
246	C₄×C₆₁	C₂×#121	1	1	yes	characteristic
247	C₄×C₆₁	#537	1	1	yes	characteristic
248	C₄×C₆₁	#548	1	1	yes	characteristic
249	C₄×C₆₁	#553	1	1	yes	characteristic
250	C₂×#470	C₂×C₆₁	1	1	yes	characteristic, complemented
251	C₂×#467	C₂×C₆₁	1	1	yes	characteristic, complemented
252	C₂×#435	C₂×C₆₁	1	1	yes	characteristic
253	C₂²×#106	C₂×C₆₁	1	1	yes	characteristic, complemented
254	#2417	C₂×C₆₁	1	2	yes	—
255	#2066	C₂×C₆₁	1	2	yes	complemented
256	#2035	C₂×C₆₁	1	2	yes	complemented
257	#1971	C₂×C₆₁	1	1	yes	characteristic, complemented
258	#1944	C₂×C₆₁	1	1	yes	characteristic, complemented
259	#1872	C₂×C₆₁	1	2	yes	complemented
260	#1809	C₂×C₆₁	1	1	yes	characteristic, complemented
261	C₂×C₆₁	—	2	4	no	—
262	C₂×C₆₁	—	8	1	no	—
263	C₂×C₆₁	#2416	1	1	yes	characteristic
264	C₂×C₆₁	C₂×#470	1	1	yes	characteristic
265	C₂×C₆₁	#3060	1	1	yes	characteristic
266	C₂×C₆₁	#3266	1	2	yes	—
267	C₂×C₆₁	#3344	1	2	yes	—
268	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
269	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
270	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
271	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
272	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
273	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
275	#470	—	2	4	no	—
276	#467	—	2	4	no	—
277	#435	—	2	4	no	—
278	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
279	C₂×#106	—	2	4	no	—
280	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
281	C₂×#106	C₂²×C₆₁	1	2	yes	—
282	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
283	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
284	C₂×#103	C₂²×C₆₁	1	2	yes	—
285	C₂×#103	C₂²×C₆₁	1	2	yes	—
286	C₂×#103	C₂²×C₆₁	1	2	yes	—
287	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
288	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
289	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
290	#398	—	2	2	no	—
291	#396	—	2	2	no	—
292	#391	C₂²×C₆₁	1	2	yes	—
293	#389	C₂²×C₆₁	1	2	yes	—
294	#386	—	2	2	no	—
295	#380	—	2	2	no	—
296	#380	C₂²×C₆₁	1	2	yes	—
297	#340	C₂²×C₆₁	1	2	yes	—
298	#340	C₂²×C₆₁	1	2	yes	—
299	C₆₁	#24783	1	1	yes	characteristic, direct product factor, Sylow
300	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
301	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
302	C₂³×C₄	—	2	2	no	—
303	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
305	C₂×Q₁₆	—	2	2	no	—
306	C₂×Q₁₆	—	2	2	no	—
307	C₂×Q₁₆	—	2	2	no	—
308	C₂×M₁₆	—	2	2	no	—
309	C₂×M₁₆	—	2	2	no	—
310	C₂×M₁₆	—	2	2	no	—
311	C₂²×C₈	—	2	2	no	—
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	D₄×C₆₁	1	4	yes	—
314	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
318	C₂²⋊Q₈	—	2	4	no	—
319	C₂²⋊Q₈	—	2	4	no	—
320	C₂²⋊Q₈	—	2	4	no	—
321	C₂²⋊Q₈	—	4	2	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	4	no	—
325	C₂×C₄⋊C₄	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	4	2	no	—
330	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
332	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
340	#107	—	2	2	no	—
341	#106	—	2	2	no	—
342	#106	—	2	4	no	—
343	#106	D₄×C₆₁	1	4	yes	complemented
344	C₄⋊C₈	—	2	2	no	—
345	#103	—	2	4	no	—
346	#103	—	2	4	no	—
347	#103	—	4	2	no	—
348	C₂²⋊C₈	—	2	2	no	—
349	C₂²⋊C₈	—	2	2	no	—
350	#97	—	2	2	no	—
351	#95	—	2	2	no	—
352	#95	—	2	2	no	—
353	#95	—	2	2	no	—
354	#95	—	2	2	no	—
355	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
356	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	4	4	no	—
380	C₂²×C₄	—	4	4	no	—
381	C₂²×C₄	—	8	2	no	—
382	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
387	C₂²×C₄	#41×C₆₁	1	2	yes	—
388	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
389	Q₁₆	—	4	4	no	—
390	M₁₆	—	4	4	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	8	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
401	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
402	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
403	C₂×C₈	#41×C₆₁	1	2	yes	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	4	4	no	—
411	C₄⋊C₄	—	4	4	no	—
412	C₄⋊C₄	—	4	4	no	—
413	C₄⋊C₄	—	8	2	no	—
414	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂²⋊C₄	—	4	4	no	—
419	C₂²⋊C₄	—	8	2	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	1	no	—
426	C₂³	—	2	1	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	1	no	—
430	C₂³	#121×C₆₁	1	2	yes	—
431	C₂³	#137×C₆₁	1	4	yes	—
432	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
433	Q₈	—	4	2	no	—
434	Q₈	—	4	2	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	4	2	no	—
437	D₄	—	4	4	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	8	8	no	—
468	C₂×C₄	#121×C₆₁	1	2	yes	—
469	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
471	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
472	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
473	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
474	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
475	C₈	—	2	2	no	—
476	C₈	—	4	1	no	—
477	C₈	—	4	1	no	—
478	C₈	#121×C₆₁	1	4	yes	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	4	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	2	no	—
488	C₂²	C₆₁×#470	1	4	yes	complemented
489	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
490	C₂²	D₄²×C₆₁	1	1	yes	characteristic
491	C₂²	C₆₁×#547	1	1	yes	characteristic
492	C₂²	C₂×#137×C₆₁	1	2	yes	—
493	C₂²	C₆₁×#577	1	2	yes	—
494	C₄	—	2	2	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	4	no	—
499	C₄	—	8	2	no	—
500	C₄	—	8	2	no	—
501	C₄	—	8	2	no	—
502	C₄	C₂×#121×C₆₁	1	1	yes	characteristic
503	C₄	C₆₁×#537	1	1	yes	characteristic
504	C₄	C₆₁×#548	1	1	yes	characteristic
505	C₄	C₆₁×#553	1	1	yes	characteristic
506	C₂	—	2	4	no	—
507	C₂	—	8	1	no	—
508	C₂	C₆₁×#2416	1	1	yes	characteristic
509	C₂	C₂×C₆₁×#470	1	1	yes	characteristic
510	C₂	C₆₁×#3060	1	1	yes	characteristic
511	C₂	C₆₁×#3266	1	2	yes	—
512	C₂	C₆₁×#3344	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#470	C₂	semidirect
2. C₂×C₆₁×#467	C₂	semidirect
4. C₂²×#106×C₆₁	C₂	semidirect
6. C₆₁×#2066	C₂	semidirect
7. C₆₁×#2035	C₂	semidirect
8. C₆₁×#1971	C₂	semidirect
9. C₆₁×#1944	C₂	semidirect
10. C₆₁×#1872	C₂	semidirect
11. C₆₁×#1809	C₂	semidirect
86. #106×C₆₁	D₄	semidirect
222. #24783	C₆₁	direct (N × H)
232. C₂²×C₆₁	#470	semidirect
250. C₂×#470	C₂×C₆₁	semidirect
251. C₂×#467	C₂×C₆₁	semidirect
253. C₂²×#106	C₂×C₆₁	semidirect
255. #2066	C₂×C₆₁	semidirect
256. #2035	C₂×C₆₁	semidirect
257. #1971	C₂×C₆₁	semidirect
258. #1944	C₂×C₆₁	semidirect
259. #1872	C₂×C₆₁	semidirect
260. #1809	C₂×C₆₁	semidirect
299. C₆₁	#24783	direct (N × H)
343. #106	D₄×C₆₁	semidirect
488. C₂²	C₆₁×#470	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#470	2
C₂×C₆₁×#467	2
C₂×C₆₁×#435	2
C₂²×#106×C₆₁	2
C₆₁×#2417	2
C₆₁×#2066	2
C₆₁×#2035	2
C₆₁×#1971	2
C₆₁×#1944	2
C₆₁×#1872	2
C₆₁×#1809	2
#24783	61

Subgroups — C61×#24783 #29528216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24783 #29528216