Subgroups — C₆₁×#29493 #29532926

Order 15616.

950 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2860	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#127×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2083	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2071	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2041	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2011	C₂	1	1	yes	maximal, characteristic
7	C₆₁×#1970	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1934	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1879	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1862	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1744	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₆₁	C₂²	1	2	yes	—
13	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×#126×C₆₁	—	2	1	no	—
15	C₂×C₄×D₄×C₆₁	—	2	1	no	—
16	C₂×C₄×D₄×C₆₁	—	2	1	no	—
17	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
18	C₂×#107×C₆₁	C₂²	1	2	yes	—
19	C₂×#102×C₆₁	C₂²	1	2	yes	—
20	C₂×#102×C₆₁	C₂²	1	2	yes	—
21	C₂×#102×C₆₁	C₂²	1	2	yes	—
22	C₂×#102×C₆₁	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
24	C₆₁×#390	—	2	1	no	—
25	C₆₁×#390	—	2	1	no	—
26	C₆₁×#390	C₂²	1	1	yes	characteristic
27	C₆₁×#390	C₂²	1	2	yes	—
28	C₆₁×#390	C₂²	1	1	yes	characteristic
29	C₆₁×#390	C₂²	1	1	yes	characteristic
30	C₆₁×#389	C₂²	1	1	yes	characteristic
31	C₆₁×#389	C₂²	1	1	yes	characteristic
32	C₆₁×#389	C₂²	1	1	yes	characteristic
33	C₆₁×#388	—	2	1	no	—
34	C₆₁×#388	—	2	1	no	—
35	C₆₁×#388	—	2	1	no	—
36	C₆₁×#384	C₂²	1	1	yes	characteristic
37	C₄³×C₆₁	C₂²	1	1	yes	characteristic
38	C₆₁×#340	C₂²	1	2	yes	—
39	C₆₁×#340	C₂²	1	2	yes	—
40	C₆₁×#336	C₂²	1	1	yes	characteristic
41	C₆₁×#336	C₂²	1	1	yes	characteristic
42	C₆₁×#336	C₂²	1	2	yes	—
43	C₂²×D₄×C₆₁	—	2	1	no	—
44	C₂²×D₄×C₆₁	—	2	1	no	—
45	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
47	C₂³×C₄×C₆₁	—	2	2	no	—
48	C₂×D₈×C₆₁	—	2	4	no	—
49	C₂×D₈×C₆₁	—	2	4	no	—
50	C₂×D₈×C₆₁	—	4	2	no	—
51	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
52	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
53	#127×C₆₁	—	2	4	no	—
54	#126×C₆₁	—	4	4	no	—
55	C₄×D₄×C₆₁	—	4	2	no	—
56	C₄×D₄×C₆₁	—	4	2	no	—
57	C₄×D₄×C₆₁	—	4	4	no	—
58	C₄×D₄×C₆₁	—	4	4	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
77	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
84	#107×C₆₁	—	4	2	no	—
85	#102×C₆₁	—	2	4	no	—
86	#102×C₆₁	—	2	4	no	—
87	#102×C₆₁	—	4	2	no	—
88	#102×C₆₁	—	4	2	no	—
89	C₄×C₈×C₆₁	—	2	4	no	—
90	#95×C₆₁	—	2	1	no	—
91	#95×C₆₁	—	2	1	no	—
92	#95×C₆₁	—	2	1	no	—
93	C₂⁴×C₆₁	—	2	2	no	—
94	C₂⁴×C₆₁	—	2	1	no	—
95	C₂×D₄×C₆₁	—	2	4	no	—
96	C₂×D₄×C₆₁	—	2	4	no	—
97	C₂×D₄×C₆₁	—	2	2	no	—
98	C₂×D₄×C₆₁	—	2	2	no	—
99	C₂×D₄×C₆₁	—	2	2	no	—
100	C₂×D₄×C₆₁	—	2	2	no	—
101	C₂×D₄×C₆₁	—	2	2	no	—
102	C₂×D₄×C₆₁	—	2	2	no	—
103	C₂×D₄×C₆₁	—	2	2	no	—
104	C₂×D₄×C₆₁	—	2	1	no	—
105	C₂×D₄×C₆₁	—	2	1	no	—
106	C₂×D₄×C₆₁	—	4	2	no	—
107	C₂×D₄×C₆₁	—	4	2	no	—
108	C₂×D₄×C₆₁	—	4	2	no	—
109	C₂×D₄×C₆₁	—	4	2	no	—
110	C₂×D₄×C₆₁	#41	1	4	yes	—
111	C₂²×C₄×C₆₁	—	2	1	no	—
112	C₂²×C₄×C₆₁	—	2	1	no	—
113	C₂²×C₄×C₆₁	—	2	1	no	—
114	C₂²×C₄×C₆₁	—	2	2	no	—
115	C₂²×C₄×C₆₁	—	4	4	no	—
116	C₂²×C₄×C₆₁	—	4	4	no	—
117	C₂²×C₄×C₆₁	—	4	4	no	—
118	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
125	D₈×C₆₁	—	4	8	no	—
126	C₂×C₈×C₆₁	—	2	2	no	—
127	C₂×C₈×C₆₁	—	2	2	no	—
128	C₂×C₈×C₆₁	—	2	2	no	—
129	C₂×C₈×C₆₁	—	2	2	no	—
130	C₂×C₈×C₆₁	—	2	2	no	—
131	C₂×C₈×C₆₁	#41	1	4	yes	—
132	C₄⋊C₄×C₆₁	—	2	2	no	—
133	C₄⋊C₄×C₆₁	—	2	2	no	—
134	C₄⋊C₄×C₆₁	—	2	1	no	—
135	C₄⋊C₄×C₆₁	—	2	2	no	—
136	C₄⋊C₄×C₆₁	—	2	1	no	—
137	C₄⋊C₄×C₆₁	—	2	2	no	—
138	C₄⋊C₄×C₆₁	—	4	2	no	—
139	C₄⋊C₄×C₆₁	—	4	2	no	—
140	C₄⋊C₄×C₆₁	—	4	2	no	—
141	C₄⋊C₄×C₆₁	—	4	2	no	—
142	C₄⋊C₄×C₆₁	—	4	2	no	—
143	C₂²⋊C₄×C₆₁	—	4	2	no	—
144	C₂²⋊C₄×C₆₁	—	4	4	no	—
145	C₂²⋊C₄×C₆₁	—	4	4	no	—
146	C₂²⋊C₄×C₆₁	—	4	2	no	—
147	C₂²⋊C₄×C₆₁	—	4	2	no	—
148	C₂²⋊C₄×C₆₁	—	4	2	no	—
149	C₂²⋊C₄×C₆₁	—	4	2	no	—
150	C₂²⋊C₄×C₆₁	—	4	2	no	—
151	C₂²⋊C₄×C₆₁	—	4	4	no	—
152	C₄²×C₆₁	—	2	2	no	—
153	C₄²×C₆₁	—	2	2	no	—
154	C₄²×C₆₁	—	2	2	no	—
155	C₄²×C₆₁	—	2	2	no	—
156	C₄²×C₆₁	—	2	1	no	—
157	C₄²×C₆₁	—	2	1	no	—
158	C₄²×C₆₁	—	4	1	no	—
159	C₄²×C₆₁	D₈	1	4	yes	complemented
160	C₂³×C₆₁	—	2	4	no	—
161	C₂³×C₆₁	—	4	2	no	—
162	C₂³×C₆₁	—	4	2	no	—
163	C₂³×C₆₁	—	4	2	no	—
164	C₂³×C₆₁	—	4	2	no	—
165	C₂³×C₆₁	—	4	2	no	—
166	C₂³×C₆₁	—	4	2	no	—
167	C₂³×C₆₁	—	4	1	no	—
168	C₂³×C₆₁	—	4	1	no	—
169	C₂³×C₆₁	—	4	1	no	—
170	C₂³×C₆₁	—	4	1	no	—
171	C₂³×C₆₁	—	4	1	no	—
172	C₂³×C₆₁	—	4	1	no	—
173	C₂³×C₆₁	—	4	1	no	—
174	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
175	D₄×C₆₁	—	2	4	no	—
176	D₄×C₆₁	—	2	4	no	—
177	D₄×C₆₁	—	4	8	no	—
178	D₄×C₆₁	—	4	8	no	—
179	D₄×C₆₁	—	4	2	no	—
180	D₄×C₆₁	—	4	2	no	—
181	D₄×C₆₁	—	4	2	no	—
182	D₄×C₆₁	—	4	2	no	—
183	C₂×C₄×C₆₁	—	2	1	no	—
184	C₂×C₄×C₆₁	—	2	1	no	—
185	C₂×C₄×C₆₁	—	2	1	no	—
186	C₂×C₄×C₆₁	—	2	1	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	1	no	—
191	C₂×C₄×C₆₁	—	2	1	no	—
192	C₂×C₄×C₆₁	—	2	1	no	—
193	C₂×C₄×C₆₁	—	2	1	no	—
194	C₂×C₄×C₆₁	—	2	1	no	—
195	C₂×C₄×C₆₁	—	2	1	no	—
196	C₂×C₄×C₆₁	—	4	1	no	—
197	C₂×C₄×C₆₁	—	4	1	no	—
198	C₂×C₄×C₆₁	—	4	2	no	—
199	C₂×C₄×C₆₁	—	4	1	no	—
200	C₂×C₄×C₆₁	—	4	1	no	—
201	C₂×C₄×C₆₁	—	4	1	no	—
202	C₂×C₄×C₆₁	—	4	1	no	—
203	C₂×C₄×C₆₁	—	4	2	no	—
204	C₂×C₄×C₆₁	—	4	1	no	—
205	C₂×C₄×C₆₁	—	4	2	no	—
206	C₂×C₄×C₆₁	—	4	1	no	—
207	C₂×C₄×C₆₁	—	4	1	no	—
208	C₂×C₄×C₆₁	—	8	8	no	—
209	C₂×C₄×C₆₁	C₂×D₈	1	2	yes	—
210	C₂×C₄×C₆₁	C₂×D₈	1	2	yes	—
211	C₂×C₄×C₆₁	C₂×D₈	1	2	yes	—
212	C₂×C₄×C₆₁	#135	1	2	yes	—
213	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
214	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
215	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
216	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
218	C₈×C₆₁	—	2	4	no	—
219	C₈×C₆₁	—	4	2	no	—
220	#29493	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂²×C₆₁	—	4	4	no	—
222	C₂²×C₆₁	—	4	4	no	—
223	C₂²×C₆₁	—	4	4	no	—
224	C₂²×C₆₁	—	8	2	no	—
225	C₂²×C₆₁	—	8	2	no	—
226	C₂²×C₆₁	—	8	2	no	—
227	C₂²×C₆₁	—	8	2	no	—
228	C₂²×C₆₁	—	8	1	no	—
229	C₂²×C₆₁	—	8	1	no	—
230	C₂²×C₆₁	—	8	1	no	—
231	C₂²×C₆₁	—	8	1	no	—
232	C₂²×C₆₁	—	8	1	no	—
233	C₂²×C₆₁	—	8	1	no	—
234	C₂²×C₆₁	—	8	1	no	—
235	C₂²×C₆₁	#525	1	1	yes	characteristic
236	C₂²×C₆₁	#532	1	1	yes	characteristic
237	C₂²×C₆₁	#535	1	1	yes	characteristic
238	C₂²×C₆₁	C₂²×D₈	1	1	yes	characteristic
239	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
240	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
241	C₂²×C₆₁	#575	1	1	yes	characteristic
242	C₄×C₆₁	—	2	2	no	—
243	C₄×C₆₁	—	2	2	no	—
244	C₄×C₆₁	—	2	2	no	—
245	C₄×C₆₁	—	2	2	no	—
246	C₄×C₆₁	—	2	2	no	—
247	C₄×C₆₁	—	4	1	no	—
248	C₄×C₆₁	—	8	1	no	—
249	C₄×C₆₁	—	8	1	no	—
250	C₄×C₆₁	—	8	1	no	—
251	C₄×C₆₁	—	8	2	no	—
252	C₄×C₆₁	#551	1	2	yes	—
253	C₄×C₆₁	#553	1	2	yes	—
254	#2860	C₂×C₆₁	1	1	yes	characteristic, complemented
255	C₄×#127	C₂×C₆₁	1	1	yes	characteristic, complemented
256	#2083	C₂×C₆₁	1	1	yes	characteristic, complemented
257	#2071	C₂×C₆₁	1	1	yes	characteristic, complemented
258	#2041	C₂×C₆₁	1	1	yes	characteristic, complemented
259	#2011	C₂×C₆₁	1	1	yes	characteristic
260	#1970	C₂×C₆₁	1	2	yes	complemented
261	#1934	C₂×C₆₁	1	2	yes	complemented
262	#1879	C₂×C₆₁	1	2	yes	complemented
263	#1862	C₂×C₆₁	1	2	yes	complemented
264	#1744	C₂×C₆₁	1	1	yes	characteristic, complemented
265	C₂×C₆₁	—	8	4	no	—
266	C₂×C₆₁	—	16	1	no	—
267	C₂×C₆₁	#2603	1	1	yes	characteristic
268	C₂×C₆₁	#3100	1	1	yes	characteristic
269	C₂×C₆₁	#3105	1	1	yes	characteristic
270	C₂×C₆₁	#3169	1	1	yes	characteristic
271	C₂×C₆₁	#3180	1	1	yes	characteristic
272	C₂×C₆₁	#3205	1	1	yes	characteristic
273	C₂×C₆₁	#3212	1	1	yes	characteristic
274	C₂²×D₈	C₂²×C₆₁	1	2	yes	—
275	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
276	C₂×#126	—	2	1	no	—
277	C₂×C₄×D₄	—	2	1	no	—
278	C₂×C₄×D₄	—	2	1	no	—
279	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
280	C₂×#107	C₂²×C₆₁	1	2	yes	—
281	C₂×#102	C₂²×C₆₁	1	2	yes	—
282	C₂×#102	C₂²×C₆₁	1	2	yes	—
283	C₂×#102	C₂²×C₆₁	1	2	yes	—
284	C₂×#102	C₂²×C₆₁	1	2	yes	—
285	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
286	#390	—	2	1	no	—
287	#390	—	2	1	no	—
288	#390	C₂²×C₆₁	1	2	yes	—
289	#390	C₂²×C₆₁	1	1	yes	characteristic
290	#390	C₂²×C₆₁	1	1	yes	characteristic
291	#390	C₂²×C₆₁	1	1	yes	characteristic
292	#389	C₂²×C₆₁	1	1	yes	characteristic
293	#389	C₂²×C₆₁	1	1	yes	characteristic
294	#389	C₂²×C₆₁	1	1	yes	characteristic
295	#388	—	2	1	no	—
296	#388	—	2	1	no	—
297	#388	—	2	1	no	—
298	#384	C₂²×C₆₁	1	1	yes	characteristic
299	C₄³	C₂²×C₆₁	1	1	yes	characteristic
300	#340	C₂²×C₆₁	1	2	yes	—
301	#340	C₂²×C₆₁	1	2	yes	—
302	#336	C₂²×C₆₁	1	1	yes	characteristic
303	#336	C₂²×C₆₁	1	1	yes	characteristic
304	#336	C₂²×C₆₁	1	2	yes	—
305	C₆₁	#29493	1	1	yes	characteristic, direct product factor, Sylow
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
309	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
310	C₂³×C₄	—	2	2	no	—
311	C₂×D₈	—	2	4	no	—
312	C₂×D₈	—	2	4	no	—
313	C₂×D₈	—	4	2	no	—
314	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
315	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
316	#127	—	2	4	no	—
317	#126	—	4	4	no	—
318	C₄×D₄	—	4	2	no	—
319	C₄×D₄	—	4	2	no	—
320	C₄×D₄	—	4	4	no	—
321	C₄×D₄	—	4	4	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
341	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
342	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
343	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
346	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
347	#107	—	4	2	no	—
348	#102	—	2	4	no	—
349	#102	—	2	4	no	—
350	#102	—	4	2	no	—
351	#102	—	4	2	no	—
352	C₄×C₈	—	2	4	no	—
353	#95	—	2	1	no	—
354	#95	—	2	1	no	—
355	#95	—	2	1	no	—
356	C₂⁴	—	2	2	no	—
357	C₂⁴	—	2	1	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	#41×C₆₁	1	4	yes	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	4	4	no	—
379	C₂²×C₄	—	4	4	no	—
380	C₂²×C₄	—	4	4	no	—
381	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
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	1	yes	characteristic
387	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
388	D₈	—	4	8	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	#41×C₆₁	1	4	yes	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₄⋊C₄	—	4	2	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₂²⋊C₄	—	4	4	no	—
407	C₂²⋊C₄	—	4	2	no	—
408	C₂²⋊C₄	—	4	4	no	—
409	C₂²⋊C₄	—	4	2	no	—
410	C₂²⋊C₄	—	4	2	no	—
411	C₂²⋊C₄	—	4	2	no	—
412	C₂²⋊C₄	—	4	2	no	—
413	C₂²⋊C₄	—	4	4	no	—
414	C₂²⋊C₄	—	4	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	4	1	no	—
422	C₄²	D₈×C₆₁	1	4	yes	complemented
423	C₂³	—	2	4	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
438	D₄	—	2	4	no	—
439	D₄	—	2	4	no	—
440	D₄	—	4	8	no	—
441	D₄	—	4	8	no	—
442	D₄	—	4	2	no	—
443	D₄	—	4	2	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	2	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	8	8	no	—
472	C₂×C₄	C₂×D₈×C₆₁	1	2	yes	—
473	C₂×C₄	C₂×D₈×C₆₁	1	2	yes	—
474	C₂×C₄	C₂×D₈×C₆₁	1	2	yes	—
475	C₂×C₄	#135×C₆₁	1	2	yes	—
476	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
477	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
478	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
479	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
480	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
481	C₈	—	2	4	no	—
482	C₈	—	4	2	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	8	2	no	—
487	C₂²	—	8	2	no	—
488	C₂²	—	8	2	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	1	no	—
491	C₂²	—	8	1	no	—
492	C₂²	—	8	1	no	—
493	C₂²	—	8	1	no	—
494	C₂²	—	8	1	no	—
495	C₂²	—	8	1	no	—
496	C₂²	—	8	1	no	—
497	C₂²	C₆₁×#525	1	1	yes	characteristic
498	C₂²	C₆₁×#532	1	1	yes	characteristic
499	C₂²	C₆₁×#535	1	1	yes	characteristic
500	C₂²	C₂²×D₈×C₆₁	1	1	yes	characteristic
501	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
502	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
503	C₂²	C₆₁×#575	1	1	yes	characteristic
504	C₄	—	2	2	no	—
505	C₄	—	2	2	no	—
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	4	1	no	—
510	C₄	—	8	1	no	—
511	C₄	—	8	1	no	—
512	C₄	—	8	1	no	—
513	C₄	—	8	2	no	—
514	C₄	C₆₁×#551	1	2	yes	—
515	C₄	C₆₁×#553	1	2	yes	—
516	C₂	—	8	4	no	—
517	C₂	—	16	1	no	—
518	C₂	C₆₁×#2603	1	1	yes	characteristic
519	C₂	C₆₁×#3100	1	1	yes	characteristic
520	C₂	C₆₁×#3105	1	1	yes	characteristic
521	C₂	C₆₁×#3169	1	1	yes	characteristic
522	C₂	C₆₁×#3180	1	1	yes	characteristic
523	C₂	C₆₁×#3205	1	1	yes	characteristic
524	C₂	C₆₁×#3212	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#2011	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₄³×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#2860	C₂	semidirect
2. C₄×#127×C₆₁	C₂	semidirect
3. C₆₁×#2083	C₂	semidirect
4. C₆₁×#2071	C₂	semidirect
5. C₆₁×#2041	C₂	semidirect
7. C₆₁×#1970	C₂	semidirect
8. C₆₁×#1934	C₂	semidirect
9. C₆₁×#1879	C₂	semidirect
10. C₆₁×#1862	C₂	semidirect
11. C₆₁×#1744	C₂	semidirect
159. C₄²×C₆₁	D₈	semidirect
220. #29493	C₆₁	direct (N × H)
254. #2860	C₂×C₆₁	semidirect
255. C₄×#127	C₂×C₆₁	semidirect
256. #2083	C₂×C₆₁	semidirect
257. #2071	C₂×C₆₁	semidirect
258. #2041	C₂×C₆₁	semidirect
260. #1970	C₂×C₆₁	semidirect
261. #1934	C₂×C₆₁	semidirect
262. #1879	C₂×C₆₁	semidirect
263. #1862	C₂×C₆₁	semidirect
264. #1744	C₂×C₆₁	semidirect
305. C₆₁	#29493	direct (N × H)
422. C₄²	D₈×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#2860	2
C₄×#127×C₆₁	2
C₆₁×#2083	2
C₆₁×#2071	2
C₆₁×#2041	2
C₆₁×#2011	2
C₆₁×#1970	2
C₆₁×#1934	2
C₆₁×#1879	2
C₆₁×#1862	2
C₆₁×#1744	2
#29493	61

Subgroups — C61×#29493 #29532926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#29493 #29532926