Subgroups — C₆₁×#18675 #29522108

Order 15616.

1122 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3497	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1651	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1642	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1637	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1631	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1492	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₆₁	—	2	1	no	—
13	C₆₁×#550	—	2	1	no	—
14	C₆₁×#550	C₂²	1	2	yes	—
15	D₄×Q₈×C₆₁	—	2	1	no	—
16	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
17	C₆₁×#548	—	2	2	no	—
18	C₆₁×#548	—	2	2	no	—
19	C₆₁×#537	—	2	2	no	—
20	C₆₁×#537	—	2	1	no	—
21	C₆₁×#533	C₂²	1	1	yes	characteristic
22	C₆₁×#532	—	2	2	no	—
23	C₆₁×#532	C₂²	1	1	yes	characteristic
24	C₆₁×#532	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#498	C₂²	1	1	yes	characteristic
27	C₆₁×#492	C₂²	1	1	yes	characteristic
28	C₆₁×#487	C₂²	1	1	yes	characteristic
29	C₆₁×#486	C₂²	1	1	yes	characteristic
30	C₆₁×#479	—	2	2	no	—
31	C₆₁×#477	C₂²	1	2	yes	—
32	C₆₁×#476	C₂²	1	2	yes	—
33	C₆₁×#475	—	2	1	no	—
34	C₆₁×#475	C₂²	1	2	yes	—
35	C₆₁×#465	—	2	2	no	—
36	C₆₁×#465	—	2	2	no	—
37	C₆₁×#461	C₂²	1	2	yes	—
38	C₆₁×#460	—	2	1	no	—
39	C₄×SD₁₆×C₆₁	—	2	2	no	—
40	C₆₁×#428	—	2	1	no	—
41	C₆₁×#423	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
43	C₆₁×#419	—	2	1	no	—
44	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#332	C₂²	1	2	yes	—
46	C₆₁×#331	C₂²	1	2	yes	—
47	C₆₁×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₆₁×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₆₁×D₄⋊C₈	C₂²	1	2	yes	—
50	C₆₁×D₄⋊C₈	C₂²	1	2	yes	—
51	2₋¹⁺⁴×C₆₁	—	4	4	no	—
52	2₋¹⁺⁴×C₆₁	—	4	4	no	—
53	C₂×#41×C₆₁	—	2	4	no	—
54	C₂×#41×C₆₁	—	2	2	no	—
55	C₂×#41×C₆₁	—	2	2	no	—
56	C₂×#41×C₆₁	—	2	1	no	—
57	C₂×#41×C₆₁	—	2	1	no	—
58	C₂²×Q₈×C₆₁	—	2	2	no	—
59	C₂²×Q₈×C₆₁	—	2	2	no	—
60	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
61	C₂×SD₁₆×C₆₁	—	2	2	no	—
62	C₂×SD₁₆×C₆₁	—	2	2	no	—
63	C₂×M₁₆×C₆₁	—	2	1	no	—
64	C₂²×C₈×C₆₁	—	2	1	no	—
65	C₂²×C₈×C₆₁	—	2	1	no	—
66	C₄⋊Q₈×C₆₁	—	2	2	no	—
67	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
68	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
69	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
70	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
71	#127×C₆₁	—	2	2	no	—
72	#127×C₆₁	D₄	1	1	yes	characteristic
73	#127×C₆₁	C₂³	1	1	yes	characteristic
74	#125×C₆₁	—	2	1	no	—
75	#124×C₆₁	—	2	4	no	—
76	#124×C₆₁	—	2	1	no	—
77	#124×C₆₁	—	2	1	no	—
78	C₂²⋊Q₈×C₆₁	—	2	2	no	—
79	C₂²⋊Q₈×C₆₁	—	2	4	no	—
80	C₂²⋊Q₈×C₆₁	—	2	2	no	—
81	C₂²⋊Q₈×C₆₁	—	2	4	no	—
82	C₂²⋊Q₈×C₆₁	—	2	1	no	—
83	C₂²⋊Q₈×C₆₁	—	2	1	no	—
84	#121×C₆₁	—	2	4	no	—
85	#121×C₆₁	—	2	2	no	—
86	#121×C₆₁	—	2	4	no	—
87	#121×C₆₁	—	2	4	no	—
88	#121×C₆₁	—	2	1	no	—
89	#121×C₆₁	—	2	1	no	—
90	#121×C₆₁	—	2	2	no	—
91	#121×C₆₁	D₄	1	2	yes	—
92	#121×C₆₁	D₄	1	2	yes	—
93	C₄×Q₈×C₆₁	—	2	1	no	—
94	C₄×Q₈×C₆₁	—	2	1	no	—
95	C₄×Q₈×C₆₁	—	2	1	no	—
96	C₄×Q₈×C₆₁	—	2	1	no	—
97	C₄×Q₈×C₆₁	D₄	1	2	yes	—
98	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
99	C₄×D₄×C₆₁	—	2	4	no	—
100	C₄×D₄×C₆₁	—	2	2	no	—
101	C₄×D₄×C₆₁	—	2	2	no	—
102	C₄×D₄×C₆₁	—	2	1	no	—
103	C₄×D₄×C₆₁	—	2	1	no	—
104	C₄×D₄×C₆₁	D₄	1	2	yes	—
105	C₄×D₄×C₆₁	C₂³	1	2	yes	—
106	#117×C₆₁	—	2	1	no	—
107	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
108	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₆₁	—	2	1	no	—
110	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
111	#107×C₆₁	—	2	2	no	—
112	#106×C₆₁	—	2	2	no	—
113	#106×C₆₁	—	2	2	no	—
114	#106×C₆₁	—	2	2	no	—
115	C₄⋊C₈×C₆₁	—	2	1	no	—
116	C₄⋊C₈×C₆₁	—	2	1	no	—
117	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
118	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
119	#103×C₆₁	—	2	2	no	—
120	#103×C₆₁	—	2	2	no	—
121	#103×C₆₁	—	2	2	no	—
122	#103×C₆₁	—	2	2	no	—
123	#102×C₆₁	—	2	2	no	—
124	#102×C₆₁	—	2	2	no	—
125	C₄×C₈×C₆₁	—	2	1	no	—
126	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
127	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
128	#41×C₆₁	—	4	16	no	—
129	#41×C₆₁	—	4	4	no	—
130	#41×C₆₁	—	4	8	no	—
131	#41×C₆₁	—	4	4	no	—
132	#41×C₆₁	—	4	2	no	—
133	#41×C₆₁	—	4	2	no	—
134	#41×C₆₁	—	4	2	no	—
135	#41×C₆₁	—	4	2	no	—
136	C₂×Q₈×C₆₁	—	2	4	no	—
137	C₂×Q₈×C₆₁	—	2	1	no	—
138	C₂×Q₈×C₆₁	—	2	1	no	—
139	C₂×Q₈×C₆₁	—	2	2	no	—
140	C₂×Q₈×C₆₁	—	2	1	no	—
141	C₂×Q₈×C₆₁	—	2	1	no	—
142	C₂×Q₈×C₆₁	—	2	1	no	—
143	C₂×Q₈×C₆₁	—	4	4	no	—
144	C₂×Q₈×C₆₁	—	4	8	no	—
145	C₂×Q₈×C₆₁	—	4	4	no	—
146	C₂×Q₈×C₆₁	SD₁₆	1	4	yes	complemented
147	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
148	C₂×D₄×C₆₁	—	2	4	no	—
149	C₂×D₄×C₆₁	—	2	2	no	—
150	C₂×D₄×C₆₁	—	2	2	no	—
151	C₂×D₄×C₆₁	—	2	4	no	—
152	C₂×D₄×C₆₁	—	2	1	no	—
153	C₂×D₄×C₆₁	—	2	1	no	—
154	C₂×D₄×C₆₁	—	2	1	no	—
155	C₂×D₄×C₆₁	—	2	1	no	—
156	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
157	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₆₁	—	2	1	no	—
159	C₂²×C₄×C₆₁	—	2	4	no	—
160	C₂²×C₄×C₆₁	—	2	4	no	—
161	C₂²×C₄×C₆₁	—	2	1	no	—
162	C₂²×C₄×C₆₁	—	2	2	no	—
163	C₂²×C₄×C₆₁	—	2	2	no	—
164	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
167	SD₁₆×C₆₁	—	4	4	no	—
168	SD₁₆×C₆₁	—	8	2	no	—
169	M₁₆×C₆₁	—	4	2	no	—
170	C₂×C₈×C₆₁	—	2	1	no	—
171	C₂×C₈×C₆₁	—	2	1	no	—
172	C₂×C₈×C₆₁	—	2	2	no	—
173	C₂×C₈×C₆₁	—	2	2	no	—
174	C₂×C₈×C₆₁	—	4	2	no	—
175	C₂×C₈×C₆₁	—	8	1	no	—
176	C₄⋊C₄×C₆₁	—	2	4	no	—
177	C₄⋊C₄×C₆₁	—	2	2	no	—
178	C₄⋊C₄×C₆₁	—	2	1	no	—
179	C₄⋊C₄×C₆₁	—	2	1	no	—
180	C₄⋊C₄×C₆₁	—	2	2	no	—
181	C₄⋊C₄×C₆₁	—	2	1	no	—
182	C₄⋊C₄×C₆₁	—	2	1	no	—
183	C₄⋊C₄×C₆₁	—	2	1	no	—
184	C₄⋊C₄×C₆₁	—	2	1	no	—
185	C₄⋊C₄×C₆₁	—	2	1	no	—
186	C₄⋊C₄×C₆₁	—	4	1	no	—
187	C₄⋊C₄×C₆₁	—	4	1	no	—
188	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
189	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
190	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
191	C₂²⋊C₄×C₆₁	—	2	4	no	—
192	C₂²⋊C₄×C₆₁	—	2	4	no	—
193	C₂²⋊C₄×C₆₁	—	2	2	no	—
194	C₂²⋊C₄×C₆₁	—	2	2	no	—
195	C₂²⋊C₄×C₆₁	—	2	2	no	—
196	C₂²⋊C₄×C₆₁	—	2	2	no	—
197	C₂²⋊C₄×C₆₁	—	4	1	no	—
198	C₄²×C₆₁	—	2	2	no	—
199	C₄²×C₆₁	—	2	2	no	—
200	C₄²×C₆₁	—	4	1	no	—
201	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
205	C₂³×C₆₁	—	2	2	no	—
206	C₂³×C₆₁	—	2	2	no	—
207	C₂³×C₆₁	#120	1	1	yes	characteristic
208	Q₈×C₆₁	—	2	2	no	—
209	Q₈×C₆₁	—	2	4	no	—
210	Q₈×C₆₁	—	4	8	no	—
211	Q₈×C₆₁	—	4	2	no	—
212	Q₈×C₆₁	—	4	1	no	—
213	Q₈×C₆₁	—	4	1	no	—
214	Q₈×C₆₁	—	4	2	no	—
215	Q₈×C₆₁	—	4	1	no	—
216	Q₈×C₆₁	—	4	1	no	—
217	Q₈×C₆₁	C₂×SD₁₆	1	4	yes	—
218	D₄×C₆₁	—	2	2	no	—
219	D₄×C₆₁	—	2	2	no	—
220	D₄×C₆₁	—	4	2	no	—
221	D₄×C₆₁	—	4	8	no	—
222	D₄×C₆₁	—	4	4	no	—
223	D₄×C₆₁	—	4	4	no	—
224	D₄×C₆₁	—	4	1	no	—
225	D₄×C₆₁	—	4	1	no	—
226	D₄×C₆₁	—	4	1	no	—
227	D₄×C₆₁	—	4	1	no	—
228	D₄×C₆₁	—	4	2	no	—
229	D₄×C₆₁	—	8	1	no	—
230	D₄×C₆₁	—	8	4	no	—
231	C₂×C₄×C₆₁	—	2	2	no	—
232	C₂×C₄×C₆₁	—	2	4	no	—
233	C₂×C₄×C₆₁	—	2	1	no	—
234	C₂×C₄×C₆₁	—	2	1	no	—
235	C₂×C₄×C₆₁	—	2	2	no	—
236	C₂×C₄×C₆₁	—	2	2	no	—
237	C₂×C₄×C₆₁	—	2	2	no	—
238	C₂×C₄×C₆₁	—	4	1	no	—
239	C₂×C₄×C₆₁	—	4	8	no	—
240	C₂×C₄×C₆₁	—	4	8	no	—
241	C₂×C₄×C₆₁	—	4	2	no	—
242	C₂×C₄×C₆₁	—	4	2	no	—
243	C₂×C₄×C₆₁	—	4	4	no	—
244	C₂×C₄×C₆₁	—	4	1	no	—
245	C₂×C₄×C₆₁	—	4	1	no	—
246	C₂×C₄×C₆₁	—	8	1	no	—
247	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
248	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
249	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
250	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
251	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
252	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
255	C₈×C₆₁	—	2	2	no	—
256	C₈×C₆₁	—	4	1	no	—
257	C₈×C₆₁	—	4	2	no	—
258	C₈×C₆₁	—	4	2	no	—
259	#18675	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₂²×C₆₁	—	2	1	no	—
261	C₂²×C₆₁	—	2	1	no	—
262	C₂²×C₆₁	—	4	2	no	—
263	C₂²×C₆₁	—	4	2	no	—
264	C₂²×C₆₁	—	4	2	no	—
265	C₂²×C₆₁	—	4	2	no	—
266	C₂²×C₆₁	—	4	2	no	—
267	C₂²×C₆₁	—	4	2	no	—
268	C₂²×C₆₁	#450	1	2	yes	—
269	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
270	C₄×C₆₁	—	2	4	no	—
271	C₄×C₆₁	—	2	1	no	—
272	C₄×C₆₁	—	2	1	no	—
273	C₄×C₆₁	—	2	1	no	—
274	C₄×C₆₁	—	4	2	no	—
275	C₄×C₆₁	—	4	2	no	—
276	C₄×C₆₁	—	4	2	no	—
277	C₄×C₆₁	—	8	1	no	—
278	C₄×C₆₁	—	8	1	no	—
279	C₄×C₆₁	#450	1	2	yes	—
280	C₄×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
281	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
282	C₄×C₆₁	#577	1	1	yes	characteristic
283	C₄×C₆₁	#578	1	1	yes	characteristic
284	#3497	C₂×C₆₁	1	1	yes	characteristic
285	#3246	C₂×C₆₁	1	1	yes	characteristic, complemented
286	#3167	C₂×C₆₁	1	1	yes	characteristic, complemented
287	#3078	C₂×C₆₁	1	1	yes	characteristic, complemented
288	#1651	C₂×C₆₁	1	2	yes	complemented
289	#1642	C₂×C₆₁	1	2	yes	complemented
290	#1637	C₂×C₆₁	1	2	yes	complemented
291	#1631	C₂×C₆₁	1	2	yes	complemented
292	#1547	C₂×C₆₁	1	1	yes	characteristic, complemented
293	#1492	C₂×C₆₁	1	1	yes	characteristic, complemented
294	C₂×Q₈⋊C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
295	C₂×C₆₁	—	2	2	no	—
296	C₂×C₆₁	—	8	2	no	—
297	C₂×C₆₁	—	8	2	no	—
298	C₂×C₆₁	C₂×#450	1	1	yes	characteristic
299	C₂×C₆₁	#3013	1	1	yes	characteristic
300	C₂×C₆₁	#3018	1	1	yes	characteristic
301	C₂×2₋¹⁺⁴	—	2	1	no	—
302	#550	—	2	1	no	—
303	#550	C₂²×C₆₁	1	2	yes	—
304	D₄×Q₈	—	2	1	no	—
305	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
306	#548	—	2	2	no	—
307	#548	—	2	2	no	—
308	#537	—	2	2	no	—
309	#537	—	2	1	no	—
310	#533	C₂²×C₆₁	1	1	yes	characteristic
311	#532	—	2	2	no	—
312	#532	C₂²×C₆₁	1	1	yes	characteristic
313	#532	C₂²×C₆₁	1	1	yes	characteristic
314	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
315	#498	C₂²×C₆₁	1	1	yes	characteristic
316	#492	C₂²×C₆₁	1	1	yes	characteristic
317	#487	C₂²×C₆₁	1	1	yes	characteristic
318	#486	C₂²×C₆₁	1	1	yes	characteristic
319	#479	—	2	2	no	—
320	#477	C₂²×C₆₁	1	2	yes	—
321	#476	C₂²×C₆₁	1	2	yes	—
322	#475	—	2	1	no	—
323	#475	C₂²×C₆₁	1	2	yes	—
324	#465	—	2	2	no	—
325	#465	—	2	2	no	—
326	#461	C₂²×C₆₁	1	2	yes	—
327	#460	—	2	1	no	—
328	C₄×SD₁₆	—	2	2	no	—
329	#428	—	2	1	no	—
330	#423	C₂²×C₆₁	1	1	yes	characteristic
331	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
332	#419	—	2	1	no	—
333	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
334	#332	C₂²×C₆₁	1	2	yes	—
335	#331	C₂²×C₆₁	1	2	yes	—
336	Q₈⋊C₈	C₂²×C₆₁	1	2	yes	—
337	Q₈⋊C₈	C₂²×C₆₁	1	2	yes	—
338	D₄⋊C₈	C₂²×C₆₁	1	2	yes	—
339	D₄⋊C₈	C₂²×C₆₁	1	2	yes	—
340	C₆₁	#18675	1	1	yes	characteristic, direct product factor, Sylow
341	2₋¹⁺⁴	—	4	4	no	—
342	2₋¹⁺⁴	—	4	4	no	—
343	C₂×#41	—	2	4	no	—
344	C₂×#41	—	2	2	no	—
345	C₂×#41	—	2	2	no	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	—	2	1	no	—
348	C₂²×Q₈	—	2	2	no	—
349	C₂²×Q₈	—	2	2	no	—
350	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
351	C₂×SD₁₆	—	2	2	no	—
352	C₂×SD₁₆	—	2	2	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂²×C₈	—	2	1	no	—
355	C₂²×C₈	—	2	1	no	—
356	C₄⋊Q₈	—	2	2	no	—
357	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
358	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
359	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
360	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
361	#127	—	2	2	no	—
362	#127	D₄×C₆₁	1	1	yes	characteristic
363	#127	C₂³×C₆₁	1	1	yes	characteristic
364	#125	—	2	1	no	—
365	#124	—	2	4	no	—
366	#124	—	2	1	no	—
367	#124	—	2	1	no	—
368	C₂²⋊Q₈	—	2	2	no	—
369	C₂²⋊Q₈	—	2	4	no	—
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	—	2	4	no	—
372	C₂²⋊Q₈	—	2	1	no	—
373	C₂²⋊Q₈	—	2	1	no	—
374	#121	—	2	4	no	—
375	#121	—	2	2	no	—
376	#121	—	2	4	no	—
377	#121	—	2	4	no	—
378	#121	—	2	1	no	—
379	#121	—	2	1	no	—
380	#121	—	2	2	no	—
381	#121	D₄×C₆₁	1	2	yes	—
382	#121	D₄×C₆₁	1	2	yes	—
383	C₄×Q₈	—	2	1	no	—
384	C₄×Q₈	—	2	1	no	—
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	D₄×C₆₁	1	2	yes	—
388	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
389	C₄×D₄	—	2	4	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	D₄×C₆₁	1	2	yes	—
395	C₄×D₄	C₂³×C₆₁	1	2	yes	—
396	#117	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
401	#107	—	2	2	no	—
402	#106	—	2	2	no	—
403	#106	—	2	2	no	—
404	#106	—	2	2	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	—	2	1	no	—
407	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
408	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
409	#103	—	2	2	no	—
410	#103	—	2	2	no	—
411	#103	—	2	2	no	—
412	#103	—	2	2	no	—
413	#102	—	2	2	no	—
414	#102	—	2	2	no	—
415	C₄×C₈	—	2	1	no	—
416	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
417	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
418	#41	—	4	16	no	—
419	#41	—	4	4	no	—
420	#41	—	4	8	no	—
421	#41	—	4	4	no	—
422	#41	—	4	2	no	—
423	#41	—	4	2	no	—
424	#41	—	4	2	no	—
425	#41	—	4	2	no	—
426	C₂×Q₈	—	2	4	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	4	4	no	—
434	C₂×Q₈	—	4	8	no	—
435	C₂×Q₈	—	4	4	no	—
436	C₂×Q₈	SD₁₆×C₆₁	1	4	yes	complemented
437	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
447	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
457	SD₁₆	—	4	4	no	—
458	SD₁₆	—	8	2	no	—
459	M₁₆	—	4	2	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	4	2	no	—
465	C₂×C₈	—	8	1	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
479	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
480	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₄²	—	2	2	no	—
489	C₄²	—	2	2	no	—
490	C₄²	—	4	1	no	—
491	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
492	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
493	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
494	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
495	C₂³	—	2	2	no	—
496	C₂³	—	2	2	no	—
497	C₂³	#120×C₆₁	1	1	yes	characteristic
498	Q₈	—	2	2	no	—
499	Q₈	—	2	4	no	—
500	Q₈	—	4	8	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	4	1	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	2	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	Q₈	C₂×SD₁₆×C₆₁	1	4	yes	—
508	D₄	—	2	2	no	—
509	D₄	—	2	2	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	8	no	—
512	D₄	—	4	4	no	—
513	D₄	—	4	4	no	—
514	D₄	—	4	1	no	—
515	D₄	—	4	1	no	—
516	D₄	—	4	1	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	2	no	—
519	D₄	—	8	1	no	—
520	D₄	—	8	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	8	no	—
530	C₂×C₄	—	4	8	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	8	1	no	—
537	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
538	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
539	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
540	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
541	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
542	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
545	C₈	—	2	2	no	—
546	C₈	—	4	1	no	—
547	C₈	—	4	2	no	—
548	C₈	—	4	2	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	C₆₁×#450	1	2	yes	—
558	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
559	C₄	—	2	4	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	2	no	—
566	C₄	—	8	1	no	—
567	C₄	—	8	1	no	—
568	C₄	C₆₁×#450	1	2	yes	—
569	C₄	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
570	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
571	C₄	C₆₁×#577	1	1	yes	characteristic
572	C₄	C₆₁×#578	1	1	yes	characteristic
573	C₂	—	2	2	no	—
574	C₂	—	8	2	no	—
575	C₂	—	8	2	no	—
576	C₂	C₂×C₆₁×#450	1	1	yes	characteristic
577	C₂	C₆₁×#3013	1	1	yes	characteristic
578	C₂	C₆₁×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₆₁×#3497	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
2. C₆₁×#3246	C₂	semidirect
3. C₆₁×#3167	C₂	semidirect
4. C₆₁×#3078	C₂	semidirect
5. C₆₁×#1651	C₂	semidirect
6. C₆₁×#1642	C₂	semidirect
7. C₆₁×#1637	C₂	semidirect
8. C₆₁×#1631	C₂	semidirect
9. C₆₁×#1547	C₂	semidirect
10. C₆₁×#1492	C₂	semidirect
11. C₂×C₆₁×Q₈⋊C₈	C₂	semidirect
146. C₂×Q₈×C₆₁	SD₁₆	semidirect
259. #18675	C₆₁	direct (N × H)
285. #3246	C₂×C₆₁	semidirect
286. #3167	C₂×C₆₁	semidirect
287. #3078	C₂×C₆₁	semidirect
288. #1651	C₂×C₆₁	semidirect
289. #1642	C₂×C₆₁	semidirect
290. #1637	C₂×C₆₁	semidirect
291. #1631	C₂×C₆₁	semidirect
292. #1547	C₂×C₆₁	semidirect
293. #1492	C₂×C₆₁	semidirect
294. C₂×Q₈⋊C₈	C₂×C₆₁	semidirect
340. C₆₁	#18675	direct (N × H)
436. C₂×Q₈	SD₁₆×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3497	2
C₆₁×#3246	2
C₆₁×#3167	2
C₆₁×#3078	2
C₆₁×#1651	2
C₆₁×#1642	2
C₆₁×#1637	2
C₆₁×#1631	2
C₆₁×#1547	2
C₆₁×#1492	2
C₂×C₆₁×Q₈⋊C₈	2
#18675	61

Subgroups — C61×#18675 #29522108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#18675 #29522108