Subgroups — C₆₁×#61907 #29565340

Order 15616.

2092 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3399	C₂	1	6	yes	maximal, complemented
4	C₆₁×#3391	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3366	C₂	1	6	yes	maximal, complemented
6	C₆₁×#3362	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3217	C₂	1	3	yes	maximal, complemented
8	C₆₁×#3205	C₂	1	3	yes	maximal, complemented
9	C₆₁×#3109	C₂	1	3	yes	maximal, complemented
10	C₆₁×#3105	C₂	1	3	yes	maximal, complemented
11	C₆₁×#2984	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₆₁	—	2	1	no	—
13	C₆₁×#559	C₂²	1	3	yes	complemented
14	Q₈²×C₆₁	C₂²	1	1	yes	characteristic, complemented
15	C₆₁×#554	C₂²	1	3	yes	complemented
16	C₆₁×#550	—	2	3	no	—
17	C₆₁×#550	—	2	1	no	—
18	C₆₁×#550	C₂²	1	2	yes	—
19	C₆₁×#550	C₂²	1	6	yes	—
20	C₆₁×#550	C₂²	1	1	yes	characteristic, complemented
21	C₆₁×#548	—	2	1	no	—
22	C₆₁×#547	—	2	3	no	—
23	C₆₁×#542	—	2	3	no	—
24	C₆₁×#532	C₂²	1	3	yes	—
25	C₂×#127×C₆₁	C₂²	1	3	yes	—
26	C₆₁×#529	C₂²	1	3	yes	—
27	C₂×#121×C₆₁	—	2	3	no	—
28	C₆₁×#520	—	2	1	no	—
29	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₆₁	C₂²	1	3	yes	—
31	C₆₁×#496	C₂²	1	6	yes	complemented
32	C₆₁×#493	C₂²	1	6	yes	complemented
33	C₆₁×#490	C₂²	1	6	yes	complemented
34	C₆₁×#486	C₂²	1	6	yes	complemented
35	C₆₁×#484	C₂²	1	1	yes	characteristic
36	C₆₁×#481	C₂²	1	3	yes	—
37	C₆₁×#478	C₂²	1	6	yes	complemented
38	C₆₁×#476	C₂²	1	6	yes	complemented
39	C₆₁×#463	C₂²	1	6	yes	complemented
40	C₆₁×#460	C₂²	1	6	yes	complemented
41	C₆₁×#459	C₂²	1	6	yes	complemented
42	C₆₁×#459	C₂²	1	6	yes	complemented
43	C₆₁×#459	C₂²	1	12	yes	complemented
44	C₆₁×#450	C₂²	1	3	yes	—
45	C₆₁×#447	C₂²	1	3	yes	—
46	C₆₁×#447	C₂²	1	6	yes	—
47	C₆₁×#446	C₂²	1	6	yes	complemented
48	C₈×Q₈×C₆₁	C₂²	1	2	yes	complemented
49	C₆₁×#442	C₂²	1	12	yes	complemented
50	C₄×SD₁₆×C₆₁	C₂²	1	6	yes	complemented
51	C₄×D₈×C₆₁	C₂²	1	6	yes	complemented
52	C₆₁×#432	C₂²	1	3	yes	—
53	C₆₁×#431	C₂²	1	3	yes	—
54	C₂×#41×C₆₁	—	2	1	no	—
55	C₂×#41×C₆₁	—	2	6	no	—
56	C₂×#41×C₆₁	—	2	2	no	—
57	C₂×#41×C₆₁	—	2	3	no	—
58	C₂×#41×C₆₁	—	4	8	no	—
59	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₆₁	—	2	3	no	—
61	C₂²×D₄×C₆₁	—	2	3	no	—
62	C₂²×D₄×C₆₁	C₂³	1	3	yes	—
63	C₂³×C₄×C₆₁	—	2	3	no	—
64	C₂×SD₁₆×C₆₁	C₂³	1	6	yes	—
65	C₂×D₈×C₆₁	C₂³	1	6	yes	—
66	C₂×D₈×C₆₁	C₂³	1	12	yes	—
67	C₄⋊Q₈×C₆₁	—	2	3	no	—
68	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
69	#127×C₆₁	—	2	3	no	—
70	#127×C₆₁	—	2	3	no	—
71	#127×C₆₁	C₂³	1	6	yes	—
72	#127×C₆₁	C₂³	1	6	yes	—
73	#127×C₆₁	C₂³	1	3	yes	—
74	#126×C₆₁	—	2	3	no	—
75	#125×C₆₁	C₂³	1	3	yes	—
76	#124×C₆₁	—	2	3	no	—
77	#124×C₆₁	—	2	3	no	—
78	#124×C₆₁	C₂³	1	3	yes	—
79	#123×C₆₁	—	2	3	no	—
80	#123×C₆₁	—	2	6	no	—
81	C₂²⋊Q₈×C₆₁	—	2	3	no	—
82	C₂²⋊Q₈×C₆₁	—	2	6	no	—
83	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
84	#121×C₆₁	—	2	3	no	—
85	#121×C₆₁	—	2	3	no	—
86	#121×C₆₁	—	2	6	no	—
87	#121×C₆₁	—	2	6	no	—
88	#121×C₆₁	—	2	12	no	—
89	#121×C₆₁	C₂³	1	3	yes	—
90	C₄×Q₈×C₆₁	—	2	1	no	—
91	C₄×Q₈×C₆₁	D₄	1	3	yes	—
92	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
93	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
94	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
96	C₄×D₄×C₆₁	—	2	3	no	—
97	C₄×D₄×C₆₁	—	2	3	no	—
98	C₄×D₄×C₆₁	—	2	3	no	—
99	C₄×D₄×C₆₁	—	2	3	no	—
100	C₄×D₄×C₆₁	—	2	3	no	—
101	C₄×D₄×C₆₁	C₂³	1	6	yes	—
102	C₄×D₄×C₆₁	C₂³	1	6	yes	—
103	C₄×D₄×C₆₁	C₂³	1	6	yes	—
104	C₄×D₄×C₆₁	C₂³	1	3	yes	—
105	#117×C₆₁	—	2	3	no	—
106	C₂×C₄⋊C₄×C₆₁	—	2	3	no	—
107	C₂×C₄⋊C₄×C₆₁	D₄	1	3	yes	—
108	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₆₁	—	2	3	no	—
110	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
111	#107×C₆₁	C₂³	1	2	yes	—
112	#106×C₆₁	C₂³	1	6	yes	—
113	C₄⋊C₈×C₆₁	C₂³	1	6	yes	—
114	C₄⋊C₈×C₆₁	C₂³	1	6	yes	—
115	#103×C₆₁	C₂³	1	2	yes	—
116	#102×C₆₁	C₂³	1	6	yes	—
117	#102×C₆₁	C₂³	1	6	yes	—
118	#102×C₆₁	C₂³	1	6	yes	—
119	#102×C₆₁	C₂³	1	12	yes	—
120	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
121	C₂²⋊C₈×C₆₁	C₂³	1	3	yes	—
122	#97×C₆₁	C₂³	1	6	yes	—
123	C₄×C₈×C₆₁	C₂³	1	6	yes	—
124	C₂⁴×C₆₁	—	2	3	no	—
125	#41×C₆₁	—	4	24	no	—
126	#41×C₆₁	—	4	4	no	—
127	#41×C₆₁	—	4	8	no	—
128	#41×C₆₁	—	8	6	no	—
129	C₂×Q₈×C₆₁	—	2	4	no	—
130	C₂×Q₈×C₆₁	—	2	3	no	—
131	C₂×Q₈×C₆₁	C₂×D₄	1	3	yes	—
132	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
134	C₂×D₄×C₆₁	—	2	3	no	—
135	C₂×D₄×C₆₁	—	2	3	no	—
136	C₂×D₄×C₆₁	—	2	3	no	—
137	C₂×D₄×C₆₁	—	2	6	no	—
138	C₂×D₄×C₆₁	—	2	6	no	—
139	C₂×D₄×C₆₁	—	2	6	no	—
140	C₂×D₄×C₆₁	—	2	6	no	—
141	C₂×D₄×C₆₁	—	2	3	no	—
142	C₂×D₄×C₆₁	—	4	6	no	—
143	C₂×D₄×C₆₁	—	4	12	no	—
144	C₂×D₄×C₆₁	—	8	6	no	—
145	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
146	C₂×D₄×C₆₁	C₂⁴	1	3	yes	—
147	C₂²×C₄×C₆₁	—	2	1	no	—
148	C₂²×C₄×C₆₁	—	2	3	no	—
149	C₂²×C₄×C₆₁	—	2	6	no	—
150	C₂²×C₄×C₆₁	—	2	6	no	—
151	C₂²×C₄×C₆₁	—	2	6	no	—
152	C₂²×C₄×C₆₁	—	4	12	no	—
153	C₂²×C₄×C₆₁	C₂×D₄	1	3	yes	—
154	C₂²×C₄×C₆₁	C₂×D₄	1	3	yes	—
155	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
156	SD₁₆×C₆₁	—	4	6	no	—
157	D₈×C₆₁	—	4	6	no	—
158	D₈×C₆₁	—	4	12	no	—
159	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
160	C₂×C₈×C₆₁	C₂⁴	1	6	yes	—
161	C₄⋊C₄×C₆₁	—	2	3	no	—
162	C₄⋊C₄×C₆₁	—	2	3	no	—
163	C₄⋊C₄×C₆₁	—	2	1	no	—
164	C₄⋊C₄×C₆₁	—	2	1	no	—
165	C₄⋊C₄×C₆₁	—	2	3	no	—
166	C₄⋊C₄×C₆₁	—	2	3	no	—
167	C₄⋊C₄×C₆₁	C₂×D₄	1	3	yes	—
168	C₄⋊C₄×C₆₁	C₂×D₄	1	3	yes	—
169	C₄⋊C₄×C₆₁	C₂×D₄	1	6	yes	—
170	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
171	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
172	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
173	C₂²⋊C₄×C₆₁	—	2	1	no	—
174	C₂²⋊C₄×C₆₁	—	2	6	no	—
175	C₂²⋊C₄×C₆₁	—	2	6	no	—
176	C₂²⋊C₄×C₆₁	—	2	3	no	—
177	C₂²⋊C₄×C₆₁	—	2	3	no	—
178	C₂²⋊C₄×C₆₁	—	2	3	no	—
179	C₂²⋊C₄×C₆₁	—	2	3	no	—
180	C₂²⋊C₄×C₆₁	—	2	6	no	—
181	C₄²×C₆₁	—	2	3	no	—
182	C₄²×C₆₁	C₂×D₄	1	3	yes	—
183	C₄²×C₆₁	C₂×D₄	1	3	yes	—
184	C₄²×C₆₁	C₂⁴	1	3	yes	—
185	C₄²×C₆₁	C₂⁴	1	3	yes	—
186	C₂³×C₆₁	—	2	3	no	—
187	C₂³×C₆₁	—	2	6	no	—
188	C₂³×C₆₁	—	4	6	no	—
189	C₂³×C₆₁	—	4	6	no	—
190	C₂³×C₆₁	—	4	6	no	—
191	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
192	Q₈×C₆₁	—	2	6	no	—
193	Q₈×C₆₁	—	2	2	no	—
194	Q₈×C₆₁	—	8	3	no	—
195	Q₈×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
196	D₄×C₆₁	—	2	6	no	—
197	D₄×C₆₁	—	2	6	no	—
198	D₄×C₆₁	—	2	6	no	—
199	D₄×C₆₁	—	4	6	no	—
200	D₄×C₆₁	—	4	12	no	—
201	D₄×C₆₁	—	4	6	no	—
202	D₄×C₆₁	—	4	12	no	—
203	D₄×C₆₁	—	4	6	no	—
204	D₄×C₆₁	—	8	6	no	—
205	D₄×C₆₁	—	8	6	no	—
206	D₄×C₆₁	—	8	3	no	—
207	C₂×C₄×C₆₁	—	2	6	no	—
208	C₂×C₄×C₆₁	—	2	6	no	—
209	C₂×C₄×C₆₁	—	2	2	no	—
210	C₂×C₄×C₆₁	—	2	1	no	—
211	C₂×C₄×C₆₁	—	2	3	no	—
212	C₂×C₄×C₆₁	—	2	2	no	—
213	C₂×C₄×C₆₁	—	2	1	no	—
214	C₂×C₄×C₆₁	—	4	12	no	—
215	C₂×C₄×C₆₁	—	4	2	no	—
216	C₂×C₄×C₆₁	—	4	12	no	—
217	C₂×C₄×C₆₁	—	4	6	no	—
218	C₂×C₄×C₆₁	—	8	6	no	—
219	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
221	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
222	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
223	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
224	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
225	C₈×C₆₁	—	2	2	no	—
226	C₈×C₆₁	—	2	6	no	—
227	#61907	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂²×C₆₁	—	2	1	no	—
229	C₂²×C₆₁	—	2	1	no	—
230	C₂²×C₆₁	—	4	6	no	—
231	C₂²×C₆₁	—	4	3	no	—
232	C₂²×C₆₁	—	4	6	no	—
233	C₂²×C₆₁	—	4	3	no	—
234	C₂²×C₆₁	—	4	3	no	—
235	C₂²×C₆₁	—	4	6	no	—
236	C₂²×C₆₁	—	8	12	no	—
237	C₂²×C₆₁	#576	1	2	yes	—
238	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
239	C₄×C₆₁	—	2	1	no	—
240	C₄×C₆₁	—	2	3	no	—
241	C₄×C₆₁	—	2	3	no	—
242	C₄×C₆₁	—	2	3	no	—
243	C₄×C₆₁	—	4	1	no	—
244	C₄×C₆₁	—	4	1	no	—
245	C₄×C₆₁	—	4	2	no	—
246	C₄×C₆₁	—	4	3	no	—
247	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	6	yes	—
248	C₄×C₆₁	#585	1	2	yes	—
249	#3522	C₂×C₆₁	1	1	yes	characteristic, complemented
250	C₂×#550	C₂×C₆₁	1	1	yes	characteristic, complemented
251	#3399	C₂×C₆₁	1	6	yes	complemented
252	#3391	C₂×C₆₁	1	2	yes	complemented
253	#3366	C₂×C₆₁	1	6	yes	complemented
254	#3362	C₂×C₆₁	1	2	yes	complemented
255	#3217	C₂×C₆₁	1	3	yes	complemented
256	#3205	C₂×C₆₁	1	3	yes	complemented
257	#3109	C₂×C₆₁	1	3	yes	complemented
258	#3105	C₂×C₆₁	1	3	yes	complemented
259	#2984	C₂×C₆₁	1	1	yes	characteristic, complemented
260	C₂×C₆₁	—	2	2	no	—
261	C₂×C₆₁	—	8	3	no	—
262	C₂×C₆₁	—	8	6	no	—
263	C₂×C₆₁	#3487	1	1	yes	characteristic
264	C₂×C₆₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
265	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
266	C₂²×#41	—	2	1	no	—
267	#559	C₂²×C₆₁	1	3	yes	complemented
268	Q₈²	C₂²×C₆₁	1	1	yes	characteristic, complemented
269	#554	C₂²×C₆₁	1	3	yes	complemented
270	#550	—	2	1	no	—
271	#550	—	2	3	no	—
272	#550	C₂²×C₆₁	1	2	yes	—
273	#550	C₂²×C₆₁	1	6	yes	—
274	#550	C₂²×C₆₁	1	1	yes	characteristic, complemented
275	#548	—	2	1	no	—
276	#547	—	2	3	no	—
277	#542	—	2	3	no	—
278	#532	C₂²×C₆₁	1	3	yes	—
279	C₂×#127	C₂²×C₆₁	1	3	yes	—
280	#529	C₂²×C₆₁	1	3	yes	—
281	C₂×#121	—	2	3	no	—
282	#520	—	2	1	no	—
283	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
284	C₂×C₄×D₄	C₂²×C₆₁	1	3	yes	—
285	#496	C₂²×C₆₁	1	6	yes	complemented
286	#493	C₂²×C₆₁	1	6	yes	complemented
287	#490	C₂²×C₆₁	1	6	yes	complemented
288	#486	C₂²×C₆₁	1	6	yes	complemented
289	#484	C₂²×C₆₁	1	1	yes	characteristic
290	#481	C₂²×C₆₁	1	3	yes	—
291	#478	C₂²×C₆₁	1	6	yes	complemented
292	#476	C₂²×C₆₁	1	6	yes	complemented
293	#463	C₂²×C₆₁	1	6	yes	complemented
294	#460	C₂²×C₆₁	1	6	yes	complemented
295	#459	C₂²×C₆₁	1	6	yes	complemented
296	#459	C₂²×C₆₁	1	6	yes	complemented
297	#459	C₂²×C₆₁	1	12	yes	complemented
298	#450	C₂²×C₆₁	1	3	yes	—
299	#447	C₂²×C₆₁	1	3	yes	—
300	#447	C₂²×C₆₁	1	6	yes	—
301	#446	C₂²×C₆₁	1	6	yes	complemented
302	C₈×Q₈	C₂²×C₆₁	1	2	yes	complemented
303	#442	C₂²×C₆₁	1	12	yes	complemented
304	C₄×SD₁₆	C₂²×C₆₁	1	6	yes	complemented
305	C₄×D₈	C₂²×C₆₁	1	6	yes	complemented
306	#432	C₂²×C₆₁	1	3	yes	—
307	#431	C₂²×C₆₁	1	3	yes	—
308	C₆₁	#61907	1	1	yes	characteristic, direct product factor, Sylow
309	C₂×#41	—	2	1	no	—
310	C₂×#41	—	2	6	no	—
311	C₂×#41	—	2	2	no	—
312	C₂×#41	—	2	3	no	—
313	C₂×#41	—	4	8	no	—
314	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
315	C₂²×D₄	—	2	3	no	—
316	C₂²×D₄	—	2	3	no	—
317	C₂²×D₄	C₂³×C₆₁	1	3	yes	—
318	C₂³×C₄	—	2	3	no	—
319	C₂×SD₁₆	C₂³×C₆₁	1	6	yes	—
320	C₂×D₈	C₂³×C₆₁	1	6	yes	—
321	C₂×D₈	C₂³×C₆₁	1	12	yes	—
322	C₄⋊Q₈	—	2	3	no	—
323	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
324	#127	—	2	3	no	—
325	#127	—	2	3	no	—
326	#127	C₂³×C₆₁	1	6	yes	—
327	#127	C₂³×C₆₁	1	6	yes	—
328	#127	C₂³×C₆₁	1	3	yes	—
329	#126	—	2	3	no	—
330	#125	C₂³×C₆₁	1	3	yes	—
331	#124	—	2	3	no	—
332	#124	—	2	3	no	—
333	#124	C₂³×C₆₁	1	3	yes	—
334	#123	—	2	3	no	—
335	#123	—	2	6	no	—
336	C₂²⋊Q₈	—	2	3	no	—
337	C₂²⋊Q₈	—	2	6	no	—
338	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
339	#121	—	2	3	no	—
340	#121	—	2	6	no	—
341	#121	—	2	6	no	—
342	#121	—	2	12	no	—
343	#121	—	2	3	no	—
344	#121	C₂³×C₆₁	1	3	yes	—
345	C₄×Q₈	—	2	1	no	—
346	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
347	C₄×Q₈	D₄×C₆₁	1	3	yes	—
348	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
349	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
350	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
351	C₄×D₄	—	2	3	no	—
352	C₄×D₄	—	2	3	no	—
353	C₄×D₄	—	2	3	no	—
354	C₄×D₄	—	2	3	no	—
355	C₄×D₄	—	2	3	no	—
356	C₄×D₄	C₂³×C₆₁	1	6	yes	—
357	C₄×D₄	C₂³×C₆₁	1	6	yes	—
358	C₄×D₄	C₂³×C₆₁	1	3	yes	—
359	C₄×D₄	C₂³×C₆₁	1	6	yes	—
360	#117	—	2	3	no	—
361	C₂×C₄⋊C₄	—	2	3	no	—
362	C₂×C₄⋊C₄	D₄×C₆₁	1	3	yes	—
363	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	—	2	3	no	—
365	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
366	#107	C₂³×C₆₁	1	2	yes	—
367	#106	C₂³×C₆₁	1	6	yes	—
368	C₄⋊C₈	C₂³×C₆₁	1	6	yes	—
369	C₄⋊C₈	C₂³×C₆₁	1	6	yes	—
370	#103	C₂³×C₆₁	1	2	yes	—
371	#102	C₂³×C₆₁	1	6	yes	—
372	#102	C₂³×C₆₁	1	6	yes	—
373	#102	C₂³×C₆₁	1	6	yes	—
374	#102	C₂³×C₆₁	1	12	yes	—
375	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
376	C₂²⋊C₈	C₂³×C₆₁	1	3	yes	—
377	#97	C₂³×C₆₁	1	6	yes	—
378	C₄×C₈	C₂³×C₆₁	1	6	yes	—
379	C₂⁴	—	2	3	no	—
380	#41	—	4	24	no	—
381	#41	—	4	8	no	—
382	#41	—	4	4	no	—
383	#41	—	8	6	no	—
384	C₂×Q₈	—	2	4	no	—
385	C₂×Q₈	—	2	3	no	—
386	C₂×Q₈	C₂×D₄×C₆₁	1	3	yes	—
387	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
388	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
389	C₂×D₄	—	2	3	no	—
390	C₂×D₄	—	2	3	no	—
391	C₂×D₄	—	2	3	no	—
392	C₂×D₄	—	2	6	no	—
393	C₂×D₄	—	2	6	no	—
394	C₂×D₄	—	2	6	no	—
395	C₂×D₄	—	2	6	no	—
396	C₂×D₄	—	2	3	no	—
397	C₂×D₄	—	4	6	no	—
398	C₂×D₄	—	4	12	no	—
399	C₂×D₄	—	8	6	no	—
400	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
401	C₂×D₄	C₂⁴×C₆₁	1	3	yes	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	3	no	—
404	C₂²×C₄	—	2	6	no	—
405	C₂²×C₄	—	2	6	no	—
406	C₂²×C₄	—	2	6	no	—
407	C₂²×C₄	—	4	12	no	—
408	C₂²×C₄	C₂×D₄×C₆₁	1	3	yes	—
409	C₂²×C₄	C₂×D₄×C₆₁	1	3	yes	—
410	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
411	SD₁₆	—	4	6	no	—
412	D₈	—	4	6	no	—
413	D₈	—	4	12	no	—
414	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
415	C₂×C₈	C₂⁴×C₆₁	1	6	yes	—
416	C₄⋊C₄	—	2	3	no	—
417	C₄⋊C₄	—	2	3	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	3	no	—
421	C₄⋊C₄	—	2	3	no	—
422	C₄⋊C₄	C₂×D₄×C₆₁	1	3	yes	—
423	C₄⋊C₄	C₂×D₄×C₆₁	1	3	yes	—
424	C₄⋊C₄	C₂×D₄×C₆₁	1	6	yes	—
425	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
426	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
427	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	6	no	—
430	C₂²⋊C₄	—	2	6	no	—
431	C₂²⋊C₄	—	2	3	no	—
432	C₂²⋊C₄	—	2	3	no	—
433	C₂²⋊C₄	—	2	3	no	—
434	C₂²⋊C₄	—	2	3	no	—
435	C₂²⋊C₄	—	2	6	no	—
436	C₄²	—	2	3	no	—
437	C₄²	C₂×D₄×C₆₁	1	3	yes	—
438	C₄²	C₂×D₄×C₆₁	1	3	yes	—
439	C₄²	C₂⁴×C₆₁	1	3	yes	—
440	C₄²	C₂⁴×C₆₁	1	3	yes	—
441	C₂³	—	2	3	no	—
442	C₂³	—	2	6	no	—
443	C₂³	—	4	6	no	—
444	C₂³	—	4	6	no	—
445	C₂³	—	4	6	no	—
446	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
447	Q₈	—	2	6	no	—
448	Q₈	—	2	2	no	—
449	Q₈	—	8	3	no	—
450	Q₈	AGL(1,ℤ/8)×C₆₁	1	4	yes	—
451	D₄	—	2	6	no	—
452	D₄	—	2	6	no	—
453	D₄	—	2	6	no	—
454	D₄	—	4	6	no	—
455	D₄	—	4	12	no	—
456	D₄	—	4	6	no	—
457	D₄	—	4	12	no	—
458	D₄	—	4	6	no	—
459	D₄	—	8	6	no	—
460	D₄	—	8	6	no	—
461	D₄	—	8	3	no	—
462	C₂×C₄	—	2	6	no	—
463	C₂×C₄	—	2	6	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	3	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	4	12	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	12	no	—
472	C₂×C₄	—	4	6	no	—
473	C₂×C₄	—	8	6	no	—
474	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
476	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
477	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
478	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
479	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
480	C₈	—	2	2	no	—
481	C₈	—	2	6	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	4	6	no	—
485	C₂²	—	4	3	no	—
486	C₂²	—	4	3	no	—
487	C₂²	—	4	6	no	—
488	C₂²	—	4	6	no	—
489	C₂²	—	4	3	no	—
490	C₂²	—	8	12	no	—
491	C₂²	C₆₁×#576	1	2	yes	—
492	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
493	C₄	—	2	3	no	—
494	C₄	—	2	3	no	—
495	C₄	—	2	3	no	—
496	C₄	—	2	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	3	no	—
500	C₄	—	4	1	no	—
501	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	6	yes	—
502	C₄	C₆₁×#585	1	2	yes	—
503	C₂	—	2	2	no	—
504	C₂	—	8	6	no	—
505	C₂	—	8	3	no	—
506	C₂	C₆₁×#3487	1	1	yes	characteristic
507	C₂	C₂²×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
508	C₂	C₂×C₆₁×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄×Q₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3522	C₂	semidirect
2. C₂×C₆₁×#550	C₂	semidirect
3. C₆₁×#3399	C₂	semidirect
4. C₆₁×#3391	C₂	semidirect
5. C₆₁×#3366	C₂	semidirect
6. C₆₁×#3362	C₂	semidirect
7. C₆₁×#3217	C₂	semidirect
8. C₆₁×#3205	C₂	semidirect
9. C₆₁×#3109	C₂	semidirect
10. C₆₁×#3105	C₂	semidirect
11. C₆₁×#2984	C₂	semidirect
13. C₆₁×#559	C₂²	semidirect
14. Q₈²×C₆₁	C₂²	semidirect
15. C₆₁×#554	C₂²	semidirect
20. C₆₁×#550	C₂²	semidirect
31. C₆₁×#496	C₂²	semidirect
32. C₆₁×#493	C₂²	semidirect
33. C₆₁×#490	C₂²	semidirect
34. C₆₁×#486	C₂²	semidirect
37. C₆₁×#478	C₂²	semidirect
38. C₆₁×#476	C₂²	semidirect
39. C₆₁×#463	C₂²	semidirect
40. C₆₁×#460	C₂²	semidirect
41. C₆₁×#459	C₂²	semidirect
42. C₆₁×#459	C₂²	semidirect
43. C₆₁×#459	C₂²	semidirect
47. C₆₁×#446	C₂²	semidirect
48. C₈×Q₈×C₆₁	C₂²	semidirect
49. C₆₁×#442	C₂²	semidirect
50. C₄×SD₁₆×C₆₁	C₂²	semidirect
51. C₄×D₈×C₆₁	C₂²	semidirect
227. #61907	C₆₁	direct (N × H)
249. #3522	C₂×C₆₁	semidirect
250. C₂×#550	C₂×C₆₁	semidirect
251. #3399	C₂×C₆₁	semidirect
252. #3391	C₂×C₆₁	semidirect
253. #3366	C₂×C₆₁	semidirect
254. #3362	C₂×C₆₁	semidirect
255. #3217	C₂×C₆₁	semidirect
256. #3205	C₂×C₆₁	semidirect
257. #3109	C₂×C₆₁	semidirect
258. #3105	C₂×C₆₁	semidirect
259. #2984	C₂×C₆₁	semidirect
267. #559	C₂²×C₆₁	semidirect
268. Q₈²	C₂²×C₆₁	semidirect
269. #554	C₂²×C₆₁	semidirect
274. #550	C₂²×C₆₁	semidirect
285. #496	C₂²×C₆₁	semidirect
286. #493	C₂²×C₆₁	semidirect
287. #490	C₂²×C₆₁	semidirect
288. #486	C₂²×C₆₁	semidirect
291. #478	C₂²×C₆₁	semidirect
292. #476	C₂²×C₆₁	semidirect
293. #463	C₂²×C₆₁	semidirect
294. #460	C₂²×C₆₁	semidirect
295. #459	C₂²×C₆₁	semidirect
296. #459	C₂²×C₆₁	semidirect
297. #459	C₂²×C₆₁	semidirect
301. #446	C₂²×C₆₁	semidirect
302. C₈×Q₈	C₂²×C₆₁	semidirect
303. #442	C₂²×C₆₁	semidirect
304. C₄×SD₁₆	C₂²×C₆₁	semidirect
305. C₄×D₈	C₂²×C₆₁	semidirect
308. C₆₁	#61907	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#3522	2
C₂×C₆₁×#550	2
C₆₁×#3399	2
C₆₁×#3391	2
C₆₁×#3366	2
C₆₁×#3362	2
C₆₁×#3217	2
C₆₁×#3205	2
C₆₁×#3109	2
C₆₁×#3105	2
C₆₁×#2984	2
#61907	61

Subgroups — C61×#61907 #29565340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61907 #29565340