Subgroups — C₆₁×#24145 #29527578

Order 15616.

1038 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×AGL(1,ℤ/8)×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2547	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2038	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2003	C₂	1	2	yes	maximal
7	C₆₁×#1986	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1966	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1888	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1857	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1806	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
13	C₆₁×#557	—	2	1	no	—
14	C₆₁×#557	—	2	1	no	—
15	C₆₁×#556	—	2	1	no	—
16	C₆₁×#556	—	2	1	no	—
17	C₆₁×#552	—	2	2	no	—
18	C₆₁×#552	—	2	2	no	—
19	C₆₁×#541	—	2	2	no	—
20	C₆₁×#536	C₂²	1	2	yes	—
21	C₆₁×#533	—	2	1	no	—
22	C₆₁×#533	—	2	1	no	—
23	C₆₁×#533	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#124×C₆₁	C₂²	1	2	yes	—
26	C₆₁×#519	C₂²	1	2	yes	—
27	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
29	C₆₁×#478	—	2	2	no	—
30	C₆₁×#476	—	2	1	no	—
31	C₆₁×#474	—	2	1	no	—
32	C₆₁×#442	—	2	1	no	—
33	C₆₁×#440	—	2	1	no	—
34	C₄×SD₁₆×C₆₁	—	2	1	no	—
35	C₄×D₈×C₆₁	—	2	1	no	—
36	C₆₁×#428	C₂²	1	2	yes	—
37	C₆₁×#428	C₂²	1	1	yes	characteristic
38	C₆₁×#423	C₂²	1	1	yes	characteristic
39	C₂×#104×C₆₁	C₂²	1	2	yes	—
40	C₆₁×#418	C₂²	1	2	yes	—
41	C₆₁×#418	C₂²	1	1	yes	characteristic
42	C₆₁×#417	C₂²	1	1	yes	characteristic
43	C₂×#101×C₆₁	C₂²	1	2	yes	—
44	C₂×#101×C₆₁	C₂²	1	2	yes	—
45	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
46	C₆₁×#397	—	2	2	no	—
47	C₆₁×#391	C₂²	1	2	yes	—
48	C₆₁×#380	—	2	2	no	—
49	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
50	C₆₁×#339	C₂²	1	2	yes	—
51	C₆₁×#339	C₂²	1	2	yes	—
52	C₆₁×#339	C₂²	1	2	yes	—
53	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
55	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₆₁	—	2	1	no	—
57	AGL(1,ℤ/8)×C₆₁	—	2	2	no	—
58	AGL(1,ℤ/8)×C₆₁	—	2	2	no	—
59	C₂×SD₁₆×C₆₁	—	2	1	no	—
60	C₂×D₈×C₆₁	—	2	1	no	—
61	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
63	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₆₁	—	2	2	no	—
65	C₄⋊Q₈×C₆₁	—	2	1	no	—
66	C₄⋊Q₈×C₆₁	—	2	1	no	—
67	C₄⋊Q₈×C₆₁	—	2	1	no	—
68	C₄⋊Q₈×C₆₁	—	2	1	no	—
69	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
70	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
71	#126×C₆₁	—	2	4	no	—
72	#126×C₆₁	—	2	4	no	—
73	#125×C₆₁	—	2	2	no	—
74	#125×C₆₁	—	2	2	no	—
75	#125×C₆₁	—	2	4	no	—
76	#125×C₆₁	—	2	4	no	—
77	#125×C₆₁	D₄	1	2	yes	—
78	#124×C₆₁	—	2	2	no	—
79	#124×C₆₁	—	2	4	no	—
80	#124×C₆₁	—	4	2	no	—
81	#123×C₆₁	—	2	4	no	—
82	C₂²⋊Q₈×C₆₁	—	2	2	no	—
83	C₂²⋊Q₈×C₆₁	—	2	2	no	—
84	C₂²⋊Q₈×C₆₁	—	2	1	no	—
85	C₂²⋊Q₈×C₆₁	—	2	1	no	—
86	C₂²⋊Q₈×C₆₁	—	2	2	no	—
87	C₂²⋊Q₈×C₆₁	—	2	2	no	—
88	C₄×Q₈×C₆₁	—	2	2	no	—
89	C₄×Q₈×C₆₁	—	2	2	no	—
90	C₄×Q₈×C₆₁	—	2	2	no	—
91	C₄×Q₈×C₆₁	—	2	2	no	—
92	C₄×Q₈×C₆₁	—	2	2	no	—
93	C₄×Q₈×C₆₁	—	2	2	no	—
94	C₄×Q₈×C₆₁	—	2	1	no	—
95	C₄×Q₈×C₆₁	—	2	1	no	—
96	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
97	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
98	C₄×D₄×C₆₁	—	2	1	no	—
99	C₄×D₄×C₆₁	—	2	1	no	—
100	C₄×D₄×C₆₁	—	2	1	no	—
101	C₄×D₄×C₆₁	—	2	1	no	—
102	C₄×D₄×C₆₁	—	2	1	no	—
103	C₄×D₄×C₆₁	—	2	1	no	—
104	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
105	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
106	#117×C₆₁	—	2	2	no	—
107	#117×C₆₁	—	2	2	no	—
108	#117×C₆₁	—	2	4	no	—
109	#117×C₆₁	—	2	1	no	—
110	#117×C₆₁	C₂³	1	2	yes	—
111	#117×C₆₁	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
113	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
114	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
115	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
117	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
118	C₂×C₄²×C₆₁	—	2	1	no	—
119	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
120	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
121	#107×C₆₁	—	2	1	no	—
122	#107×C₆₁	—	2	2	no	—
123	#106×C₆₁	—	2	1	no	—
124	#106×C₆₁	—	2	2	no	—
125	C₄⋊C₈×C₆₁	—	2	1	no	—
126	C₄⋊C₈×C₆₁	—	2	1	no	—
127	#104×C₆₁	—	4	2	no	—
128	#103×C₆₁	—	2	1	no	—
129	#102×C₆₁	—	2	1	no	—
130	#102×C₆₁	—	2	1	no	—
131	#102×C₆₁	—	2	1	no	—
132	#102×C₆₁	—	2	2	no	—
133	#102×C₆₁	—	2	2	no	—
134	#101×C₆₁	—	2	4	no	—
135	#101×C₆₁	—	4	2	no	—
136	#97×C₆₁	—	2	1	no	—
137	C₄×C₈×C₆₁	—	2	1	no	—
138	#95×C₆₁	—	2	1	no	—
139	#95×C₆₁	—	2	4	no	—
140	C₂⁴×C₆₁	—	2	1	no	—
141	#41×C₆₁	—	2	1	no	—
142	#41×C₆₁	—	2	1	no	—
143	#41×C₆₁	—	2	1	no	—
144	#41×C₆₁	—	2	1	no	—
145	C₂×Q₈×C₆₁	—	2	1	no	—
146	C₂×Q₈×C₆₁	—	2	1	no	—
147	C₂×Q₈×C₆₁	—	2	2	no	—
148	C₂×Q₈×C₆₁	—	2	2	no	—
149	C₂×Q₈×C₆₁	—	2	2	no	—
150	C₂×Q₈×C₆₁	—	2	2	no	—
151	C₂×Q₈×C₆₁	—	2	2	no	—
152	C₂×Q₈×C₆₁	—	2	2	no	—
153	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₆₁	—	2	1	no	—
155	C₂×D₄×C₆₁	—	2	1	no	—
156	C₂×D₄×C₆₁	—	2	1	no	—
157	C₂×D₄×C₆₁	—	2	1	no	—
158	C₂×D₄×C₆₁	—	2	1	no	—
159	C₂×D₄×C₆₁	—	2	1	no	—
160	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
161	C₂×D₄×C₆₁	#41	1	2	yes	—
162	C₂²×C₄×C₆₁	—	2	1	no	—
163	C₂²×C₄×C₆₁	—	2	1	no	—
164	C₂²×C₄×C₆₁	—	2	1	no	—
165	C₂²×C₄×C₆₁	—	2	1	no	—
166	C₂²×C₄×C₆₁	—	2	2	no	—
167	C₂²×C₄×C₆₁	—	4	4	no	—
168	C₂²×C₄×C₆₁	—	4	1	no	—
169	C₂²×C₄×C₆₁	—	4	1	no	—
170	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
171	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
174	SD₁₆×C₆₁	—	2	4	no	—
175	D₈×C₆₁	—	2	4	no	—
176	M₁₆×C₆₁	—	2	1	no	—
177	M₁₆×C₆₁	—	2	2	no	—
178	M₁₆×C₆₁	—	2	1	no	—
179	M₁₆×C₆₁	—	2	2	no	—
180	M₁₆×C₆₁	—	2	1	no	—
181	M₁₆×C₆₁	#41	1	2	yes	—
182	C₂×C₈×C₆₁	—	2	1	no	—
183	C₂×C₈×C₆₁	—	2	1	no	—
184	C₂×C₈×C₆₁	—	2	2	no	—
185	C₄⋊C₄×C₆₁	—	2	4	no	—
186	C₄⋊C₄×C₆₁	—	2	4	no	—
187	C₄⋊C₄×C₆₁	—	2	4	no	—
188	C₄⋊C₄×C₆₁	—	2	4	no	—
189	C₄⋊C₄×C₆₁	—	2	2	no	—
190	C₄⋊C₄×C₆₁	—	2	2	no	—
191	C₄⋊C₄×C₆₁	—	2	2	no	—
192	C₄⋊C₄×C₆₁	—	2	2	no	—
193	C₄⋊C₄×C₆₁	—	2	1	no	—
194	C₄⋊C₄×C₆₁	—	2	1	no	—
195	C₄⋊C₄×C₆₁	—	2	1	no	—
196	C₄⋊C₄×C₆₁	—	2	1	no	—
197	C₄⋊C₄×C₆₁	—	2	2	no	—
198	C₄⋊C₄×C₆₁	—	2	2	no	—
199	C₄⋊C₄×C₆₁	—	2	1	no	—
200	C₄⋊C₄×C₆₁	—	2	1	no	—
201	C₄⋊C₄×C₆₁	—	4	2	no	—
202	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
203	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
204	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
205	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
206	C₂²⋊C₄×C₆₁	—	2	4	no	—
207	C₂²⋊C₄×C₆₁	—	2	4	no	—
208	C₂²⋊C₄×C₆₁	—	2	1	no	—
209	C₂²⋊C₄×C₆₁	—	2	2	no	—
210	C₂²⋊C₄×C₆₁	—	2	1	no	—
211	C₂²⋊C₄×C₆₁	—	2	1	no	—
212	C₂²⋊C₄×C₆₁	—	4	8	no	—
213	C₂²⋊C₄×C₆₁	—	4	1	no	—
214	C₂²⋊C₄×C₆₁	—	4	1	no	—
215	C₄²×C₆₁	—	2	4	no	—
216	C₄²×C₆₁	—	2	4	no	—
217	C₄²×C₆₁	—	2	1	no	—
218	C₄²×C₆₁	—	2	1	no	—
219	C₄²×C₆₁	—	2	1	no	—
220	C₄²×C₆₁	—	2	2	no	—
221	C₄²×C₆₁	—	2	2	no	—
222	C₄²×C₆₁	—	2	2	no	—
223	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
224	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
225	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
227	C₂³×C₆₁	—	2	1	no	—
228	C₂³×C₆₁	—	2	2	no	—
229	C₂³×C₆₁	—	4	2	no	—
230	C₂³×C₆₁	—	4	2	no	—
231	C₂³×C₆₁	—	4	1	no	—
232	C₂³×C₆₁	—	4	1	no	—
233	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₆₁	—	2	1	no	—
235	Q₈×C₆₁	—	2	1	no	—
236	Q₈×C₆₁	—	4	2	no	—
237	Q₈×C₆₁	—	4	2	no	—
238	Q₈×C₆₁	—	4	2	no	—
239	Q₈×C₆₁	—	4	2	no	—
240	Q₈×C₆₁	—	4	2	no	—
241	Q₈×C₆₁	—	4	2	no	—
242	D₄×C₆₁	—	2	1	no	—
243	D₄×C₆₁	—	2	2	no	—
244	D₄×C₆₁	—	2	1	no	—
245	D₄×C₆₁	—	2	2	no	—
246	D₄×C₆₁	—	4	1	no	—
247	D₄×C₆₁	—	4	1	no	—
248	D₄×C₆₁	—	4	1	no	—
249	D₄×C₆₁	—	4	1	no	—
250	C₂×C₄×C₆₁	—	2	2	no	—
251	C₂×C₄×C₆₁	—	2	1	no	—
252	C₂×C₄×C₆₁	—	2	1	no	—
253	C₂×C₄×C₆₁	—	2	2	no	—
254	C₂×C₄×C₆₁	—	2	2	no	—
255	C₂×C₄×C₆₁	—	2	4	no	—
256	C₂×C₄×C₆₁	—	2	1	no	—
257	C₂×C₄×C₆₁	—	2	4	no	—
258	C₂×C₄×C₆₁	—	2	4	no	—
259	C₂×C₄×C₆₁	—	4	1	no	—
260	C₂×C₄×C₆₁	—	4	2	no	—
261	C₂×C₄×C₆₁	—	4	1	no	—
262	C₂×C₄×C₆₁	—	4	1	no	—
263	C₂×C₄×C₆₁	—	4	2	no	—
264	C₂×C₄×C₆₁	—	4	2	no	—
265	C₂×C₄×C₆₁	—	4	2	no	—
266	C₂×C₄×C₆₁	—	4	2	no	—
267	C₂×C₄×C₆₁	—	4	1	no	—
268	C₂×C₄×C₆₁	—	4	2	no	—
269	C₂×C₄×C₆₁	—	8	2	no	—
270	C₂×C₄×C₆₁	—	8	2	no	—
271	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
272	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
273	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
274	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
275	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
279	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
280	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
281	C₈×C₆₁	—	2	2	no	—
282	C₈×C₆₁	—	4	1	no	—
283	C₈×C₆₁	—	4	2	no	—
284	#24145	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
285	C₂²×C₆₁	—	2	1	no	—
286	C₂²×C₆₁	—	2	1	no	—
287	C₂²×C₆₁	—	4	4	no	—
288	C₂²×C₆₁	—	4	1	no	—
289	C₂²×C₆₁	—	4	2	no	—
290	C₂²×C₆₁	—	4	1	no	—
291	C₂²×C₆₁	—	4	1	no	—
292	C₂²×C₆₁	—	8	2	no	—
293	C₂²×C₆₁	—	8	1	no	—
294	C₂²×C₆₁	—	8	1	no	—
295	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
296	C₂²×C₆₁	#546	1	1	yes	characteristic
297	C₂²×C₆₁	#547	1	1	yes	characteristic
298	C₄×C₆₁	—	2	1	no	—
299	C₄×C₆₁	—	2	1	no	—
300	C₄×C₆₁	—	2	1	no	—
301	C₄×C₆₁	—	4	4	no	—
302	C₄×C₆₁	—	4	1	no	—
303	C₄×C₆₁	—	4	1	no	—
304	C₄×C₆₁	—	4	2	no	—
305	C₄×C₆₁	—	4	1	no	—
306	C₄×C₆₁	—	4	2	no	—
307	C₄×C₆₁	—	8	2	no	—
308	C₄×C₆₁	—	8	1	no	—
309	C₄×C₆₁	#454	1	2	yes	—
310	C₄×C₆₁	#525	1	1	yes	characteristic
311	C₄×C₆₁	#537	1	1	yes	characteristic
312	C₄×C₆₁	#548	1	1	yes	characteristic
313	C₄×C₆₁	#550	1	1	yes	characteristic
314	#3509	C₂×C₆₁	1	1	yes	characteristic, complemented
315	#3077	C₂×C₆₁	1	1	yes	characteristic, complemented
316	C₄×AGL(1,ℤ/8)	C₂×C₆₁	1	1	yes	characteristic
317	#2547	C₂×C₆₁	1	1	yes	characteristic, complemented
318	#2038	C₂×C₆₁	1	2	yes	complemented
319	#2003	C₂×C₆₁	1	2	yes	—
320	#1986	C₂×C₆₁	1	1	yes	characteristic, complemented
321	#1966	C₂×C₆₁	1	1	yes	characteristic, complemented
322	#1888	C₂×C₆₁	1	2	yes	complemented
323	#1857	C₂×C₆₁	1	2	yes	complemented
324	#1806	C₂×C₆₁	1	1	yes	characteristic, complemented
325	C₂×C₆₁	—	2	1	no	—
326	C₂×C₆₁	—	2	1	no	—
327	C₂×C₆₁	—	8	1	no	—
328	C₂×C₆₁	—	8	2	no	—
329	C₂×C₆₁	#2407	1	1	yes	characteristic
330	C₂×C₆₁	C₂×#454	1	1	yes	characteristic
331	C₂×C₆₁	#3020	1	1	yes	characteristic
332	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
333	#557	—	2	1	no	—
334	#557	—	2	1	no	—
335	#556	—	2	1	no	—
336	#556	—	2	1	no	—
337	#552	—	2	2	no	—
338	#552	—	2	2	no	—
339	#541	—	2	2	no	—
340	#536	C₂²×C₆₁	1	2	yes	—
341	#533	—	2	1	no	—
342	#533	—	2	1	no	—
343	#533	C₂²×C₆₁	1	1	yes	characteristic
344	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
345	C₂×#124	C₂²×C₆₁	1	2	yes	—
346	#519	C₂²×C₆₁	1	2	yes	—
347	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
348	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
349	#478	—	2	2	no	—
350	#476	—	2	1	no	—
351	#474	—	2	1	no	—
352	#442	—	2	1	no	—
353	#440	—	2	1	no	—
354	C₄×SD₁₆	—	2	1	no	—
355	C₄×D₈	—	2	1	no	—
356	#428	C₂²×C₆₁	1	2	yes	—
357	#428	C₂²×C₆₁	1	1	yes	characteristic
358	#423	C₂²×C₆₁	1	1	yes	characteristic
359	C₂×#104	C₂²×C₆₁	1	2	yes	—
360	#418	C₂²×C₆₁	1	2	yes	—
361	#418	C₂²×C₆₁	1	1	yes	characteristic
362	#417	C₂²×C₆₁	1	1	yes	characteristic
363	C₂×#101	C₂²×C₆₁	1	2	yes	—
364	C₂×#101	C₂²×C₆₁	1	2	yes	—
365	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
366	#397	—	2	2	no	—
367	#391	C₂²×C₆₁	1	2	yes	—
368	#380	—	2	2	no	—
369	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
370	#339	C₂²×C₆₁	1	2	yes	—
371	#339	C₂²×C₆₁	1	2	yes	—
372	#339	C₂²×C₆₁	1	2	yes	—
373	C₆₁	#24145	1	1	yes	characteristic, direct product factor, Sylow
374	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
375	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
376	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
377	C₂³×C₄	—	2	1	no	—
378	AGL(1,ℤ/8)	—	2	2	no	—
379	AGL(1,ℤ/8)	—	2	2	no	—
380	C₂×SD₁₆	—	2	1	no	—
381	C₂×D₈	—	2	1	no	—
382	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
383	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
384	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
385	C₄⋊Q₈	—	2	2	no	—
386	C₄⋊Q₈	—	2	1	no	—
387	C₄⋊Q₈	—	2	1	no	—
388	C₄⋊Q₈	—	2	1	no	—
389	C₄⋊Q₈	—	2	1	no	—
390	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
391	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
392	#126	—	2	4	no	—
393	#126	—	2	4	no	—
394	#125	—	2	2	no	—
395	#125	—	2	2	no	—
396	#125	—	2	4	no	—
397	#125	—	2	4	no	—
398	#125	D₄×C₆₁	1	2	yes	—
399	#124	—	2	2	no	—
400	#124	—	2	4	no	—
401	#124	—	4	2	no	—
402	#123	—	2	4	no	—
403	C₂²⋊Q₈	—	2	2	no	—
404	C₂²⋊Q₈	—	2	2	no	—
405	C₂²⋊Q₈	—	2	1	no	—
406	C₂²⋊Q₈	—	2	1	no	—
407	C₂²⋊Q₈	—	2	2	no	—
408	C₂²⋊Q₈	—	2	2	no	—
409	C₄×Q₈	—	2	2	no	—
410	C₄×Q₈	—	2	2	no	—
411	C₄×Q₈	—	2	2	no	—
412	C₄×Q₈	—	2	2	no	—
413	C₄×Q₈	—	2	2	no	—
414	C₄×Q₈	—	2	2	no	—
415	C₄×Q₈	—	2	1	no	—
416	C₄×Q₈	—	2	1	no	—
417	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
418	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
419	C₄×D₄	—	2	1	no	—
420	C₄×D₄	—	2	1	no	—
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	—	2	1	no	—
423	C₄×D₄	—	2	1	no	—
424	C₄×D₄	—	2	1	no	—
425	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
426	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
427	#117	—	2	2	no	—
428	#117	—	2	2	no	—
429	#117	—	2	4	no	—
430	#117	—	2	1	no	—
431	#117	C₂³×C₆₁	1	1	yes	characteristic
432	#117	C₂³×C₆₁	1	2	yes	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
435	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
436	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	4	no	—
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
441	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
442	#107	—	2	1	no	—
443	#107	—	2	2	no	—
444	#106	—	2	1	no	—
445	#106	—	2	2	no	—
446	C₄⋊C₈	—	2	1	no	—
447	C₄⋊C₈	—	2	1	no	—
448	#104	—	4	2	no	—
449	#103	—	2	1	no	—
450	#102	—	2	1	no	—
451	#102	—	2	1	no	—
452	#102	—	2	1	no	—
453	#102	—	2	2	no	—
454	#102	—	2	2	no	—
455	#101	—	2	4	no	—
456	#101	—	4	2	no	—
457	#97	—	2	1	no	—
458	C₄×C₈	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	—	2	4	no	—
461	C₂⁴	—	2	1	no	—
462	#41	—	2	1	no	—
463	#41	—	2	1	no	—
464	#41	—	2	1	no	—
465	#41	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	2	no	—
469	C₂×Q₈	—	2	2	no	—
470	C₂×Q₈	—	2	2	no	—
471	C₂×Q₈	—	2	2	no	—
472	C₂×Q₈	—	2	2	no	—
473	C₂×Q₈	—	2	2	no	—
474	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
482	C₂×D₄	#41×C₆₁	1	2	yes	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	4	4	no	—
489	C₂²×C₄	—	4	1	no	—
490	C₂²×C₄	—	4	1	no	—
491	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
492	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
494	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
495	SD₁₆	—	2	4	no	—
496	D₈	—	2	4	no	—
497	M₁₆	—	2	1	no	—
498	M₁₆	—	2	2	no	—
499	M₁₆	—	2	1	no	—
500	M₁₆	—	2	2	no	—
501	M₁₆	—	2	1	no	—
502	M₁₆	#41×C₆₁	1	2	yes	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	2	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	—	2	4	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	4	2	no	—
523	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
524	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
525	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
526	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
527	C₂²⋊C₄	—	2	4	no	—
528	C₂²⋊C₄	—	2	4	no	—
529	C₂²⋊C₄	—	2	1	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	2	1	no	—
533	C₂²⋊C₄	—	4	8	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₂²⋊C₄	—	4	1	no	—
536	C₄²	—	2	4	no	—
537	C₄²	—	2	4	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	2	no	—
542	C₄²	—	2	2	no	—
543	C₄²	—	2	2	no	—
544	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
545	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
546	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
547	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
548	C₂³	—	2	2	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	4	2	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
555	Q₈	—	2	1	no	—
556	Q₈	—	2	1	no	—
557	Q₈	—	4	2	no	—
558	Q₈	—	4	2	no	—
559	Q₈	—	4	2	no	—
560	Q₈	—	4	2	no	—
561	Q₈	—	4	2	no	—
562	Q₈	—	4	2	no	—
563	D₄	—	2	1	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	1	no	—
566	D₄	—	2	2	no	—
567	D₄	—	4	1	no	—
568	D₄	—	4	1	no	—
569	D₄	—	4	1	no	—
570	D₄	—	4	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	8	2	no	—
591	C₂×C₄	—	8	2	no	—
592	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
593	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
594	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
595	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
596	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
597	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
598	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
599	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
600	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
601	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
602	C₈	—	2	2	no	—
603	C₈	—	4	1	no	—
604	C₈	—	4	2	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	4	4	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	8	2	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
616	C₂²	C₆₁×#546	1	1	yes	characteristic
617	C₂²	C₆₁×#547	1	1	yes	characteristic
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	4	4	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	2	no	—
627	C₄	—	8	2	no	—
628	C₄	—	8	1	no	—
629	C₄	C₆₁×#454	1	2	yes	—
630	C₄	C₆₁×#525	1	1	yes	characteristic
631	C₄	C₆₁×#537	1	1	yes	characteristic
632	C₄	C₆₁×#548	1	1	yes	characteristic
633	C₄	C₆₁×#550	1	1	yes	characteristic
634	C₂	—	2	1	no	—
635	C₂	—	2	1	no	—
636	C₂	—	8	2	no	—
637	C₂	—	8	1	no	—
638	C₂	C₆₁×#2407	1	1	yes	characteristic
639	C₂	C₂×C₆₁×#454	1	1	yes	characteristic
640	C₂	C₆₁×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×AGL(1,ℤ/8)×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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. C₆₁×#3509	C₂	semidirect
2. C₆₁×#3077	C₂	semidirect
4. C₆₁×#2547	C₂	semidirect
5. C₆₁×#2038	C₂	semidirect
7. C₆₁×#1986	C₂	semidirect
8. C₆₁×#1966	C₂	semidirect
9. C₆₁×#1888	C₂	semidirect
10. C₆₁×#1857	C₂	semidirect
11. C₆₁×#1806	C₂	semidirect
284. #24145	C₆₁	direct (N × H)
314. #3509	C₂×C₆₁	semidirect
315. #3077	C₂×C₆₁	semidirect
317. #2547	C₂×C₆₁	semidirect
318. #2038	C₂×C₆₁	semidirect
320. #1986	C₂×C₆₁	semidirect
321. #1966	C₂×C₆₁	semidirect
322. #1888	C₂×C₆₁	semidirect
323. #1857	C₂×C₆₁	semidirect
324. #1806	C₂×C₆₁	semidirect
373. C₆₁	#24145	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×#3509	2
C₆₁×#3077	2
C₄×AGL(1,ℤ/8)×C₆₁	2
C₆₁×#2547	2
C₆₁×#2038	2
C₆₁×#2003	2
C₆₁×#1986	2
C₆₁×#1966	2
C₆₁×#1888	2
C₆₁×#1857	2
C₆₁×#1806	2
#24145	61

Subgroups — C61×#24145 #29527578

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24145 #29527578