Subgroups — C₆₁×#18752 #29522185

Order 15616.

1020 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3100	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1644	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1622	C₂	1	4	yes	maximal, complemented
7	C₆₁×#1548	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1486	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#137×C₆₁	—	2	1	no	—
11	C₆₁×#554	—	2	2	no	—
12	C₆₁×#554	—	2	2	no	—
13	C₆₁×#554	—	2	2	no	—
14	C₆₁×#554	C₂²	1	4	yes	—
15	C₆₁×#532	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#125×C₆₁	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
19	C₂×C₂²⋊Q₈×C₆₁	—	2	2	no	—
20	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₆₁	—	2	1	no	—
22	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
24	C₆₁×#492	C₂²	1	2	yes	complemented
25	C₆₁×#487	C₂²	1	2	yes	complemented
26	C₆₁×#480	—	2	1	no	—
27	C₆₁×#474	C₂²	1	2	yes	—
28	C₆₁×#464	—	2	2	no	—
29	C₆₁×#462	C₂²	1	2	yes	complemented
30	C₆₁×#461	—	2	2	no	—
31	C₆₁×#460	C₂²	1	2	yes	complemented
32	C₆₁×#459	C₂²	1	2	yes	—
33	C₆₁×#448	—	2	2	no	—
34	C₆₁×#447	—	2	1	no	—
35	C₄×D₈×C₆₁	—	2	2	no	—
36	C₆₁×#431	C₂²	1	1	yes	characteristic
37	C₆₁×#431	C₂²	1	1	yes	characteristic
38	C₆₁×#423	C₂²	1	1	yes	characteristic
39	C₆₁×#417	—	2	1	no	—
40	C₆₁×#333	C₂²	1	4	yes	complemented
41	C₆₁×Q₈⋊C₈	C₂²	1	4	yes	complemented
42	C₆₁×D₄⋊C₈	C₂²	1	4	yes	—
43	C₂×#41×C₆₁	—	2	1	no	—
44	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
45	C₂²×Q₈×C₆₁	D₄	1	2	yes	—
46	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₆₁	—	2	2	no	—
48	C₂³×C₄×C₆₁	—	2	1	no	—
49	#137×C₆₁	—	4	4	no	—
50	C₂×Q₁₆×C₆₁	—	2	2	no	—
51	C₂×SD₁₆×C₆₁	—	2	2	no	—
52	C₂×SD₁₆×C₆₁	—	2	4	no	—
53	C₂×D₈×C₆₁	—	2	2	no	—
54	C₂×M₁₆×C₆₁	—	2	1	no	—
55	C₄⋊Q₈×C₆₁	—	2	1	no	—
56	C₄⋊Q₈×C₆₁	—	2	1	no	—
57	C₄⋊Q₈×C₆₁	D₄	1	2	yes	—
58	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
60	#127×C₆₁	C₂³	1	1	yes	characteristic
61	#125×C₆₁	—	2	4	no	—
62	#125×C₆₁	—	2	4	no	—
63	#124×C₆₁	—	2	1	no	—
64	C₂²⋊Q₈×C₆₁	—	2	4	no	—
65	C₂²⋊Q₈×C₆₁	—	2	8	no	—
66	C₂²⋊Q₈×C₆₁	—	2	4	no	—
67	C₂²⋊Q₈×C₆₁	—	2	8	no	—
68	#121×C₆₁	—	2	1	no	—
69	#121×C₆₁	—	2	1	no	—
70	C₄×Q₈×C₆₁	—	2	1	no	—
71	C₄×Q₈×C₆₁	—	2	1	no	—
72	C₄×Q₈×C₆₁	D₄	1	2	yes	—
73	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
74	C₄×D₄×C₆₁	—	2	4	no	—
75	C₄×D₄×C₆₁	—	2	4	no	—
76	C₄×D₄×C₆₁	—	2	1	no	—
77	C₄×D₄×C₆₁	—	2	1	no	—
78	C₄×D₄×C₆₁	—	2	1	no	—
79	C₄×D₄×C₆₁	—	2	1	no	—
80	C₄×D₄×C₆₁	D₄	1	2	yes	—
81	C₄×D₄×C₆₁	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
83	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
84	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
85	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
86	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
87	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
88	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
89	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
93	C₂×C₄²×C₆₁	—	2	1	no	—
94	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
95	#107×C₆₁	—	2	2	no	—
96	C₄⋊C₈×C₆₁	—	2	1	no	—
97	C₄⋊C₈×C₆₁	—	2	1	no	—
98	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
99	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
100	#103×C₆₁	—	2	4	no	—
101	#103×C₆₁	—	2	2	no	—
102	#102×C₆₁	—	2	2	no	—
103	#102×C₆₁	—	2	2	no	—
104	#102×C₆₁	—	2	2	no	—
105	C₂²⋊C₈×C₆₁	—	2	1	no	—
106	C₂²⋊C₈×C₆₁	—	2	1	no	—
107	C₄×C₈×C₆₁	—	2	1	no	—
108	C₄×C₈×C₆₁	C₂³	1	2	yes	—
109	C₂⁴×C₆₁	—	2	1	no	—
110	#41×C₆₁	—	4	2	no	—
111	#41×C₆₁	—	4	2	no	—
112	C₂×Q₈×C₆₁	—	2	1	no	—
113	C₂×Q₈×C₆₁	—	2	2	no	—
114	C₂×Q₈×C₆₁	—	2	2	no	—
115	C₂×Q₈×C₆₁	—	2	2	no	—
116	C₂×Q₈×C₆₁	—	2	1	no	—
117	C₂×Q₈×C₆₁	—	8	2	no	—
118	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
119	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
120	C₂×D₄×C₆₁	—	2	4	no	—
121	C₂×D₄×C₆₁	—	2	1	no	—
122	C₂×D₄×C₆₁	—	2	1	no	—
123	C₂×D₄×C₆₁	—	2	1	no	—
124	C₂×D₄×C₆₁	—	2	1	no	—
125	C₂×D₄×C₆₁	—	4	1	no	—
126	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₆₁	—	2	1	no	—
128	C₂²×C₄×C₆₁	—	2	1	no	—
129	C₂²×C₄×C₆₁	—	2	1	no	—
130	C₂²×C₄×C₆₁	—	2	2	no	—
131	C₂²×C₄×C₆₁	—	2	8	no	—
132	C₂²×C₄×C₆₁	—	2	2	no	—
133	C₂²×C₄×C₆₁	—	2	2	no	—
134	C₂²×C₄×C₆₁	—	4	2	no	—
135	C₂²×C₄×C₆₁	—	4	2	no	—
136	C₂²×C₄×C₆₁	—	4	1	no	—
137	C₂²×C₄×C₆₁	—	8	4	no	—
138	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
141	Q₁₆×C₆₁	—	4	4	no	—
142	SD₁₆×C₆₁	—	4	4	no	—
143	SD₁₆×C₆₁	—	8	4	no	—
144	D₈×C₆₁	—	4	4	no	—
145	M₁₆×C₆₁	—	4	2	no	—
146	C₂×C₈×C₆₁	—	2	2	no	—
147	C₂×C₈×C₆₁	—	2	2	no	—
148	C₂×C₈×C₆₁	—	2	2	no	—
149	C₄⋊C₄×C₆₁	—	2	8	no	—
150	C₄⋊C₄×C₆₁	—	2	8	no	—
151	C₄⋊C₄×C₆₁	—	2	1	no	—
152	C₄⋊C₄×C₆₁	—	2	2	no	—
153	C₄⋊C₄×C₆₁	—	2	2	no	—
154	C₄⋊C₄×C₆₁	—	2	2	no	—
155	C₄⋊C₄×C₆₁	—	2	1	no	—
156	C₄⋊C₄×C₆₁	—	2	2	no	—
157	C₄⋊C₄×C₆₁	—	2	2	no	—
158	C₄⋊C₄×C₆₁	—	2	2	no	—
159	C₄⋊C₄×C₆₁	—	2	1	no	—
160	C₄⋊C₄×C₆₁	—	2	1	no	—
161	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
162	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
163	C₂²⋊C₄×C₆₁	—	2	8	no	—
164	C₂²⋊C₄×C₆₁	—	2	2	no	—
165	C₂²⋊C₄×C₆₁	—	2	2	no	—
166	C₂²⋊C₄×C₆₁	—	4	1	no	—
167	C₂²⋊C₄×C₆₁	—	4	1	no	—
168	C₄²×C₆₁	—	2	2	no	—
169	C₄²×C₆₁	—	2	2	no	—
170	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
174	C₂³×C₆₁	—	2	4	no	—
175	C₂³×C₆₁	—	2	2	no	—
176	C₂³×C₆₁	—	4	2	no	—
177	C₂³×C₆₁	—	4	2	no	—
178	C₂³×C₆₁	—	4	1	no	—
179	C₂³×C₆₁	#120	1	1	yes	characteristic
180	Q₈×C₆₁	—	2	2	no	—
181	Q₈×C₆₁	—	2	2	no	—
182	Q₈×C₆₁	—	4	4	no	—
183	Q₈×C₆₁	—	4	2	no	—
184	Q₈×C₆₁	—	4	1	no	—
185	Q₈×C₆₁	—	4	1	no	—
186	Q₈×C₆₁	—	8	2	no	—
187	D₄×C₆₁	—	2	4	no	—
188	D₄×C₆₁	—	2	2	no	—
189	D₄×C₆₁	—	4	2	no	—
190	D₄×C₆₁	—	4	1	no	—
191	D₄×C₆₁	—	4	1	no	—
192	D₄×C₆₁	—	4	2	no	—
193	D₄×C₆₁	—	8	2	no	—
194	D₄×C₆₁	#137	1	4	yes	complemented
195	C₂×C₄×C₆₁	—	2	2	no	—
196	C₂×C₄×C₆₁	—	2	2	no	—
197	C₂×C₄×C₆₁	—	2	2	no	—
198	C₂×C₄×C₆₁	—	2	2	no	—
199	C₂×C₄×C₆₁	—	2	4	no	—
200	C₂×C₄×C₆₁	—	4	1	no	—
201	C₂×C₄×C₆₁	—	4	2	no	—
202	C₂×C₄×C₆₁	—	4	4	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	4	no	—
208	C₂×C₄×C₆₁	—	4	1	no	—
209	C₂×C₄×C₆₁	—	8	8	no	—
210	C₂×C₄×C₆₁	—	8	2	no	—
211	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
212	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
213	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
214	C₂×C₄×C₆₁	#135	1	2	yes	—
215	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
216	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
219	C₈×C₆₁	—	4	2	no	—
220	C₈×C₆₁	—	4	2	no	—
221	C₈×C₆₁	—	4	2	no	—
222	#18752	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂²×C₆₁	—	2	1	no	—
224	C₂²×C₆₁	—	2	1	no	—
225	C₂²×C₆₁	—	2	4	no	—
226	C₂²×C₆₁	—	4	8	no	—
227	C₂²×C₆₁	—	4	2	no	—
228	C₂²×C₆₁	—	4	2	no	—
229	C₂²×C₆₁	—	8	1	no	—
230	C₂²×C₆₁	—	8	1	no	—
231	C₂²×C₆₁	—	8	1	no	—
232	C₂²×C₆₁	#449	1	2	yes	—
233	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
234	C₄×C₆₁	—	2	1	no	—
235	C₄×C₆₁	—	2	1	no	—
236	C₄×C₆₁	—	2	1	no	—
237	C₄×C₆₁	—	4	2	no	—
238	C₄×C₆₁	—	4	2	no	—
239	C₄×C₆₁	—	4	2	no	—
240	C₄×C₆₁	—	4	4	no	—
241	C₄×C₆₁	—	8	1	no	—
242	C₄×C₆₁	#449	1	2	yes	—
243	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
244	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₄×C₆₁	C₂×#137	1	2	yes	—
246	C₂×#554	C₂×C₆₁	1	1	yes	characteristic, complemented
247	#3206	C₂×C₆₁	1	1	yes	characteristic, complemented
248	#3100	C₂×C₆₁	1	1	yes	characteristic
249	#3037	C₂×C₆₁	1	1	yes	characteristic, complemented
250	#1644	C₂×C₆₁	1	4	yes	complemented
251	#1622	C₂×C₆₁	1	4	yes	complemented
252	#1548	C₂×C₆₁	1	1	yes	characteristic, complemented
253	#1486	C₂×C₆₁	1	1	yes	characteristic, complemented
254	#1479	C₂×C₆₁	1	1	yes	characteristic, complemented
255	C₂×C₆₁	—	2	2	no	—
256	C₂×C₆₁	—	4	4	no	—
257	C₂×C₆₁	—	16	1	no	—
258	C₂×C₆₁	C₂×#449	1	1	yes	characteristic
259	C₂×C₆₁	#3004	1	1	yes	characteristic
260	C₂×C₆₁	#3019	1	1	yes	characteristic
261	C₂×#137	—	2	1	no	—
262	#554	—	2	2	no	—
263	#554	—	2	2	no	—
264	#554	—	2	2	no	—
265	#554	C₂²×C₆₁	1	4	yes	—
266	#532	C₂²×C₆₁	1	1	yes	characteristic
267	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
268	C₂×#125	—	2	1	no	—
269	C₂×C₂²⋊Q₈	—	2	1	no	—
270	C₂×C₂²⋊Q₈	—	2	2	no	—
271	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
272	C₂×C₄×D₄	—	2	1	no	—
273	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	—	2	1	no	—
275	#492	C₂²×C₆₁	1	2	yes	complemented
276	#487	C₂²×C₆₁	1	2	yes	complemented
277	#480	—	2	1	no	—
278	#474	C₂²×C₆₁	1	2	yes	—
279	#464	—	2	2	no	—
280	#462	C₂²×C₆₁	1	2	yes	complemented
281	#461	—	2	2	no	—
282	#460	C₂²×C₆₁	1	2	yes	complemented
283	#459	C₂²×C₆₁	1	2	yes	—
284	#448	—	2	2	no	—
285	#447	—	2	1	no	—
286	C₄×D₈	—	2	2	no	—
287	#431	C₂²×C₆₁	1	1	yes	characteristic
288	#431	C₂²×C₆₁	1	1	yes	characteristic
289	#423	C₂²×C₆₁	1	1	yes	characteristic
290	#417	—	2	1	no	—
291	#333	C₂²×C₆₁	1	4	yes	complemented
292	Q₈⋊C₈	C₂²×C₆₁	1	4	yes	complemented
293	D₄⋊C₈	C₂²×C₆₁	1	4	yes	—
294	C₆₁	#18752	1	1	yes	characteristic, direct product factor, Sylow
295	C₂×#41	—	2	1	no	—
296	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
297	C₂²×Q₈	D₄×C₆₁	1	2	yes	—
298	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
299	C₂³×C₄	—	2	2	no	—
300	C₂³×C₄	—	2	1	no	—
301	#137	—	4	4	no	—
302	C₂×Q₁₆	—	2	2	no	—
303	C₂×SD₁₆	—	2	2	no	—
304	C₂×SD₁₆	—	2	4	no	—
305	C₂×D₈	—	2	2	no	—
306	C₂×M₁₆	—	2	1	no	—
307	C₄⋊Q₈	—	2	1	no	—
308	C₄⋊Q₈	—	2	1	no	—
309	C₄⋊Q₈	D₄×C₆₁	1	2	yes	—
310	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
311	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
312	#127	C₂³×C₆₁	1	1	yes	characteristic
313	#125	—	2	4	no	—
314	#125	—	2	4	no	—
315	#124	—	2	1	no	—
316	C₂²⋊Q₈	—	2	4	no	—
317	C₂²⋊Q₈	—	2	8	no	—
318	C₂²⋊Q₈	—	2	4	no	—
319	C₂²⋊Q₈	—	2	8	no	—
320	#121	—	2	1	no	—
321	#121	—	2	1	no	—
322	C₄×Q₈	—	2	1	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×Q₈	D₄×C₆₁	1	2	yes	—
325	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
326	C₄×D₄	—	2	4	no	—
327	C₄×D₄	—	2	4	no	—
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	2	1	no	—
330	C₄×D₄	—	2	1	no	—
331	C₄×D₄	—	2	1	no	—
332	C₄×D₄	D₄×C₆₁	1	2	yes	—
333	C₄×D₄	C₂³×C₆₁	1	2	yes	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	4	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	4	no	—
341	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
342	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	1	no	—
345	C₂×C₄²	—	2	1	no	—
346	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
347	#107	—	2	2	no	—
348	C₄⋊C₈	—	2	1	no	—
349	C₄⋊C₈	—	2	1	no	—
350	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
351	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
352	#103	—	2	4	no	—
353	#103	—	2	2	no	—
354	#102	—	2	2	no	—
355	#102	—	2	2	no	—
356	#102	—	2	2	no	—
357	C₂²⋊C₈	—	2	1	no	—
358	C₂²⋊C₈	—	2	1	no	—
359	C₄×C₈	—	2	1	no	—
360	C₄×C₈	C₂³×C₆₁	1	2	yes	—
361	C₂⁴	—	2	1	no	—
362	#41	—	4	2	no	—
363	#41	—	4	2	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	8	2	no	—
370	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
371	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	4	1	no	—
378	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	8	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	8	4	no	—
390	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
393	Q₁₆	—	4	4	no	—
394	SD₁₆	—	4	4	no	—
395	SD₁₆	—	8	4	no	—
396	D₈	—	4	4	no	—
397	M₁₆	—	4	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
414	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
415	C₂²⋊C₄	—	2	8	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	4	1	no	—
419	C₂²⋊C₄	—	4	1	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
423	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
424	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
425	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
426	C₂³	—	2	4	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	1	no	—
431	C₂³	#120×C₆₁	1	1	yes	characteristic
432	Q₈	—	2	2	no	—
433	Q₈	—	2	2	no	—
434	Q₈	—	4	4	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	4	1	no	—
437	Q₈	—	4	1	no	—
438	Q₈	—	8	2	no	—
439	D₄	—	2	4	no	—
440	D₄	—	2	2	no	—
441	D₄	—	4	2	no	—
442	D₄	—	4	1	no	—
443	D₄	—	4	1	no	—
444	D₄	—	4	2	no	—
445	D₄	—	8	2	no	—
446	D₄	#137×C₆₁	1	4	yes	complemented
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	8	8	no	—
462	C₂×C₄	—	8	2	no	—
463	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
464	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
465	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
466	C₂×C₄	#135×C₆₁	1	2	yes	—
467	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
468	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
471	C₈	—	4	2	no	—
472	C₈	—	4	2	no	—
473	C₈	—	4	2	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	4	8	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	8	1	no	—
481	C₂²	—	8	1	no	—
482	C₂²	—	8	1	no	—
483	C₂²	C₆₁×#449	1	2	yes	—
484	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	4	no	—
492	C₄	—	8	1	no	—
493	C₄	C₆₁×#449	1	2	yes	—
494	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
495	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
496	C₄	C₂×#137×C₆₁	1	2	yes	—
497	C₂	—	2	2	no	—
498	C₂	—	4	4	no	—
499	C₂	—	16	1	no	—
500	C₂	C₂×C₆₁×#449	1	1	yes	characteristic
501	C₂	C₆₁×#3004	1	1	yes	characteristic
502	C₂	C₆₁×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₆₁×#3100	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#554	C₂	semidirect
2. C₆₁×#3206	C₂	semidirect
4. C₆₁×#3037	C₂	semidirect
5. C₆₁×#1644	C₂	semidirect
6. C₆₁×#1622	C₂	semidirect
7. C₆₁×#1548	C₂	semidirect
8. C₆₁×#1486	C₂	semidirect
9. C₆₁×#1479	C₂	semidirect
24. C₆₁×#492	C₂²	semidirect
25. C₆₁×#487	C₂²	semidirect
29. C₆₁×#462	C₂²	semidirect
31. C₆₁×#460	C₂²	semidirect
40. C₆₁×#333	C₂²	semidirect
41. C₆₁×Q₈⋊C₈	C₂²	semidirect
194. D₄×C₆₁	#137	semidirect
222. #18752	C₆₁	direct (N × H)
246. C₂×#554	C₂×C₆₁	semidirect
247. #3206	C₂×C₆₁	semidirect
249. #3037	C₂×C₆₁	semidirect
250. #1644	C₂×C₆₁	semidirect
251. #1622	C₂×C₆₁	semidirect
252. #1548	C₂×C₆₁	semidirect
253. #1486	C₂×C₆₁	semidirect
254. #1479	C₂×C₆₁	semidirect
275. #492	C₂²×C₆₁	semidirect
276. #487	C₂²×C₆₁	semidirect
280. #462	C₂²×C₆₁	semidirect
282. #460	C₂²×C₆₁	semidirect
291. #333	C₂²×C₆₁	semidirect
292. Q₈⋊C₈	C₂²×C₆₁	semidirect
294. C₆₁	#18752	direct (N × H)
446. D₄	#137×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×#554	2
C₆₁×#3206	2
C₆₁×#3100	2
C₆₁×#3037	2
C₆₁×#1644	2
C₆₁×#1622	2
C₆₁×#1548	2
C₆₁×#1486	2
C₆₁×#1479	2
#18752	61

Subgroups — C61×#18752 #29522185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#18752 #29522185