Subgroups — C₆₁×#29942 #29533375

Order 15616.

696 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2857	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2283	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2101	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2085	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2077	C₂	1	2	yes	maximal
6	C₆₁×#2075	C₂	1	2	yes	maximal
7	C₆₁×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1987	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1947	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1797	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
14	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#107×C₆₁	C₂²	1	2	yes	—
16	C₂×#106×C₆₁	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
20	C₆₁×#391	—	2	1	no	—
21	C₆₁×#389	—	2	1	no	—
22	C₆₁×#389	C₂²	1	2	yes	—
23	C₆₁×#384	C₂²	1	1	yes	characteristic
24	C₆₁×#383	—	2	1	no	—
25	C₆₁×#382	C₂²	1	1	yes	characteristic
26	C₆₁×#382	C₂²	1	1	yes	characteristic
27	C₆₁×#381	—	2	1	no	—
28	C₆₁×#380	—	2	1	no	—
29	C₆₁×#380	C₂²	1	1	yes	characteristic
30	C₆₁×#380	C₂²	1	1	yes	characteristic
31	C₆₁×#380	C₂²	1	2	yes	—
32	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
34	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
35	C₆₁×#376	—	2	1	no	—
36	C₆₁×#340	C₂²	1	2	yes	—
37	C₆₁×#340	C₂²	1	2	yes	—
38	C₆₁×#340	C₂²	1	2	yes	—
39	C₆₁×#340	C₂²	1	2	yes	—
40	C₆₁×#340	C₂²	1	2	yes	—
41	C₆₁×#340	C₂²	1	2	yes	—
42	C₆₁×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₆₁	—	2	1	no	—
44	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₆₁	—	2	2	no	—
50	C₄⋊Q₈×C₆₁	—	2	2	no	—
51	C₂²⋊Q₈×C₆₁	—	4	4	no	—
52	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
65	C₂×C₄²×C₆₁	—	2	2	no	—
66	C₂×C₄²×C₆₁	—	2	2	no	—
67	C₂×C₄²×C₆₁	—	2	1	no	—
68	C₂×C₄²×C₆₁	—	2	1	no	—
69	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
73	#107×C₆₁	—	4	2	no	—
74	#106×C₆₁	—	4	2	no	—
75	C₄⋊C₈×C₆₁	—	2	2	no	—
76	C₄⋊C₈×C₆₁	—	2	2	no	—
77	C₂²⋊C₈×C₆₁	—	4	2	no	—
78	#95×C₆₁	—	2	1	no	—
79	#95×C₆₁	—	2	1	no	—
80	#95×C₆₁	—	2	1	no	—
81	#95×C₆₁	—	2	1	no	—
82	#95×C₆₁	—	2	1	no	—
83	#95×C₆₁	—	2	1	no	—
84	#95×C₆₁	—	2	1	no	—
85	#95×C₆₁	—	2	1	no	—
86	#95×C₆₁	—	2	2	no	—
87	#95×C₆₁	—	2	2	no	—
88	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
89	C₂×Q₈×C₆₁	—	4	2	no	—
90	C₂×Q₈×C₆₁	—	4	2	no	—
91	C₂×Q₈×C₆₁	—	4	2	no	—
92	C₂²×C₄×C₆₁	—	2	2	no	—
93	C₂²×C₄×C₆₁	—	2	2	no	—
94	C₂²×C₄×C₆₁	—	2	2	no	—
95	C₂²×C₄×C₆₁	—	2	2	no	—
96	C₂²×C₄×C₆₁	—	2	2	no	—
97	C₂²×C₄×C₆₁	—	2	1	no	—
98	C₂²×C₄×C₆₁	—	2	1	no	—
99	C₂²×C₄×C₆₁	—	2	1	no	—
100	C₂²×C₄×C₆₁	—	2	1	no	—
101	C₂²×C₄×C₆₁	—	2	1	no	—
102	C₂²×C₄×C₆₁	—	2	1	no	—
103	C₂²×C₄×C₆₁	—	2	1	no	—
104	C₂²×C₄×C₆₁	—	2	1	no	—
105	C₂²×C₄×C₆₁	—	2	1	no	—
106	C₂²×C₄×C₆₁	—	2	1	no	—
107	C₂²×C₄×C₆₁	—	2	2	no	—
108	C₂²×C₄×C₆₁	—	2	2	no	—
109	C₂²×C₄×C₆₁	—	4	1	no	—
110	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₆₁	—	2	2	no	—
117	C₂×C₈×C₆₁	—	2	2	no	—
118	C₂×C₈×C₆₁	—	2	2	no	—
119	C₂×C₈×C₆₁	—	2	2	no	—
120	C₂×C₈×C₆₁	—	2	2	no	—
121	C₂×C₈×C₆₁	—	2	2	no	—
122	C₄⋊C₄×C₆₁	—	2	2	no	—
123	C₄⋊C₄×C₆₁	—	2	2	no	—
124	C₄⋊C₄×C₆₁	—	2	1	no	—
125	C₄⋊C₄×C₆₁	—	2	2	no	—
126	C₄⋊C₄×C₆₁	—	2	1	no	—
127	C₄⋊C₄×C₆₁	—	2	1	no	—
128	C₄⋊C₄×C₆₁	—	2	1	no	—
129	C₄⋊C₄×C₆₁	—	2	1	no	—
130	C₄⋊C₄×C₆₁	—	2	1	no	—
131	C₄⋊C₄×C₆₁	—	2	1	no	—
132	C₄⋊C₄×C₆₁	—	2	1	no	—
133	C₄⋊C₄×C₆₁	—	2	2	no	—
134	C₄⋊C₄×C₆₁	—	4	2	no	—
135	C₄⋊C₄×C₆₁	—	4	4	no	—
136	C₄⋊C₄×C₆₁	—	4	2	no	—
137	C₄⋊C₄×C₆₁	—	4	2	no	—
138	C₂²⋊C₄×C₆₁	—	4	2	no	—
139	C₂²⋊C₄×C₆₁	—	4	2	no	—
140	C₂²⋊C₄×C₆₁	—	4	4	no	—
141	C₄²×C₆₁	—	2	2	no	—
142	C₄²×C₆₁	—	2	2	no	—
143	C₄²×C₆₁	—	2	1	no	—
144	C₄²×C₆₁	—	2	1	no	—
145	C₄²×C₆₁	—	4	2	no	—
146	C₄²×C₆₁	—	4	2	no	—
147	C₄²×C₆₁	#41	1	2	yes	—
148	C₄²×C₆₁	#41	1	2	yes	—
149	C₂³×C₆₁	—	2	1	no	—
150	C₂³×C₆₁	—	2	1	no	—
151	C₂³×C₆₁	—	2	1	no	—
152	C₂³×C₆₁	—	2	1	no	—
153	C₂³×C₆₁	—	2	1	no	—
154	C₂³×C₆₁	—	2	1	no	—
155	C₂³×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
156	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₆₁	—	8	4	no	—
158	C₂×C₄×C₆₁	—	2	1	no	—
159	C₂×C₄×C₆₁	—	2	1	no	—
160	C₂×C₄×C₆₁	—	2	1	no	—
161	C₂×C₄×C₆₁	—	2	1	no	—
162	C₂×C₄×C₆₁	—	2	1	no	—
163	C₂×C₄×C₆₁	—	2	1	no	—
164	C₂×C₄×C₆₁	—	2	1	no	—
165	C₂×C₄×C₆₁	—	2	1	no	—
166	C₂×C₄×C₆₁	—	2	1	no	—
167	C₂×C₄×C₆₁	—	2	1	no	—
168	C₂×C₄×C₆₁	—	2	1	no	—
169	C₂×C₄×C₆₁	—	4	4	no	—
170	C₂×C₄×C₆₁	—	4	1	no	—
171	C₂×C₄×C₆₁	—	4	1	no	—
172	C₂×C₄×C₆₁	—	4	1	no	—
173	C₂×C₄×C₆₁	—	4	1	no	—
174	C₂×C₄×C₆₁	—	4	4	no	—
175	C₂×C₄×C₆₁	—	4	2	no	—
176	C₂×C₄×C₆₁	—	4	1	no	—
177	C₂×C₄×C₆₁	—	4	1	no	—
178	C₂×C₄×C₆₁	—	4	2	no	—
179	C₂×C₄×C₆₁	—	4	1	no	—
180	C₂×C₄×C₆₁	—	4	1	no	—
181	C₂×C₄×C₆₁	—	4	1	no	—
182	C₂×C₄×C₆₁	—	4	1	no	—
183	C₂×C₄×C₆₁	—	4	2	no	—
184	C₂×C₄×C₆₁	—	4	2	no	—
185	C₂×C₄×C₆₁	—	4	2	no	—
186	C₂×C₄×C₆₁	—	4	1	no	—
187	C₂×C₄×C₆₁	—	4	1	no	—
188	C₂×C₄×C₆₁	—	4	1	no	—
189	C₂×C₄×C₆₁	—	4	1	no	—
190	C₂×C₄×C₆₁	—	4	1	no	—
191	C₂×C₄×C₆₁	—	4	1	no	—
192	C₂×C₄×C₆₁	—	4	2	no	—
193	C₂×C₄×C₆₁	#123	1	2	yes	—
194	C₂×C₄×C₆₁	#123	1	2	yes	—
195	C₂×C₄×C₆₁	#135	1	2	yes	—
196	C₂×C₄×C₆₁	#137	1	2	yes	—
197	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
201	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
202	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
203	C₈×C₆₁	—	4	2	no	—
204	C₈×C₆₁	—	4	2	no	—
205	#29942	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂²×C₆₁	—	2	2	no	—
207	C₂²×C₆₁	—	2	2	no	—
208	C₂²×C₆₁	—	2	2	no	—
209	C₂²×C₆₁	—	4	1	no	—
210	C₂²×C₆₁	—	4	1	no	—
211	C₂²×C₆₁	—	4	1	no	—
212	C₂²×C₆₁	—	4	1	no	—
213	C₂²×C₆₁	C₂×#123	1	1	yes	characteristic
214	C₂²×C₆₁	#536	1	1	yes	characteristic
215	C₂²×C₆₁	#537	1	1	yes	characteristic
216	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
217	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
219	C₂²×C₆₁	#575	1	1	yes	characteristic
220	C₄×C₆₁	—	2	2	no	—
221	C₄×C₆₁	—	4	1	no	—
222	C₄×C₆₁	—	4	1	no	—
223	C₄×C₆₁	—	4	1	no	—
224	C₄×C₆₁	—	8	2	no	—
225	C₄×C₆₁	—	8	1	no	—
226	C₄×C₆₁	—	8	1	no	—
227	C₄×C₆₁	—	8	1	no	—
228	C₄×C₆₁	—	8	2	no	—
229	C₄×C₆₁	—	8	1	no	—
230	C₄×C₆₁	#485	1	4	yes	—
231	C₄×C₆₁	#541	1	1	yes	characteristic
232	C₄×C₆₁	#541	1	1	yes	characteristic
233	C₄×C₆₁	#542	1	1	yes	characteristic
234	C₄×C₆₁	#542	1	1	yes	characteristic
235	#2857	C₂×C₆₁	1	1	yes	characteristic
236	#2283	C₂×C₆₁	1	1	yes	characteristic
237	#2101	C₂×C₆₁	1	2	yes	complemented
238	#2085	C₂×C₆₁	1	2	yes	complemented
239	#2077	C₂×C₆₁	1	2	yes	—
240	#2075	C₂×C₆₁	1	2	yes	—
241	#1987	C₂×C₆₁	1	1	yes	characteristic, complemented
242	#1987	C₂×C₆₁	1	1	yes	characteristic, complemented
243	#1948	C₂×C₆₁	1	1	yes	characteristic, complemented
244	#1947	C₂×C₆₁	1	1	yes	characteristic, complemented
245	#1797	C₂×C₆₁	1	1	yes	characteristic
246	C₂×C₆₁	—	4	2	no	—
247	C₂×C₆₁	#2625	1	1	yes	characteristic
248	C₂×C₆₁	C₂×#485	1	1	yes	characteristic
249	C₂×C₆₁	#3094	1	1	yes	characteristic
250	C₂×C₆₁	#3233	1	1	yes	characteristic
251	C₂×C₆₁	#3238	1	1	yes	characteristic
252	C₂×C₆₁	#3247	1	1	yes	characteristic
253	C₂×C₆₁	#3252	1	1	yes	characteristic
254	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
255	C₂×C₂²⋊Q₈	—	2	1	no	—
256	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
257	C₂×#107	C₂²×C₆₁	1	2	yes	—
258	C₂×#106	C₂²×C₆₁	1	2	yes	—
259	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
260	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
261	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
262	#391	—	2	1	no	—
263	#389	—	2	1	no	—
264	#389	C₂²×C₆₁	1	2	yes	—
265	#384	C₂²×C₆₁	1	1	yes	characteristic
266	#383	—	2	1	no	—
267	#382	C₂²×C₆₁	1	1	yes	characteristic
268	#382	C₂²×C₆₁	1	1	yes	characteristic
269	#381	—	2	1	no	—
270	#380	—	2	1	no	—
271	#380	C₂²×C₆₁	1	1	yes	characteristic
272	#380	C₂²×C₆₁	1	2	yes	—
273	#380	C₂²×C₆₁	1	1	yes	characteristic
274	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
275	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
276	C₄×C₂²⋊C₄	—	2	1	no	—
277	#376	—	2	1	no	—
278	#340	C₂²×C₆₁	1	2	yes	—
279	#340	C₂²×C₆₁	1	2	yes	—
280	#340	C₂²×C₆₁	1	2	yes	—
281	#340	C₂²×C₆₁	1	2	yes	—
282	#340	C₂²×C₆₁	1	2	yes	—
283	#340	C₂²×C₆₁	1	2	yes	—
284	#336	C₂²×C₆₁	1	2	yes	—
285	C₆₁	#29942	1	1	yes	characteristic, direct product factor, Sylow
286	C₂²×Q₈	—	2	1	no	—
287	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
288	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
289	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
291	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
292	C₄⋊Q₈	—	2	2	no	—
293	C₄⋊Q₈	—	2	2	no	—
294	C₂²⋊Q₈	—	4	4	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	2	1	no	—
308	C₂×C₄²	—	2	2	no	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
313	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
316	#107	—	4	2	no	—
317	#106	—	4	2	no	—
318	C₄⋊C₈	—	2	2	no	—
319	C₄⋊C₈	—	2	2	no	—
320	C₂²⋊C₈	—	4	2	no	—
321	#95	—	2	1	no	—
322	#95	—	2	1	no	—
323	#95	—	2	1	no	—
324	#95	—	2	1	no	—
325	#95	—	2	1	no	—
326	#95	—	2	1	no	—
327	#95	—	2	1	no	—
328	#95	—	2	1	no	—
329	#95	—	2	2	no	—
330	#95	—	2	2	no	—
331	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	—	4	2	no	—
334	C₂×Q₈	—	4	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
358	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	4	2	no	—
389	C₄²	—	4	2	no	—
390	C₄²	#41×C₆₁	1	2	yes	—
391	C₄²	#41×C₆₁	1	2	yes	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
399	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
400	Q₈	—	8	4	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	#123×C₆₁	1	2	yes	—
437	C₂×C₄	#123×C₆₁	1	2	yes	—
438	C₂×C₄	#135×C₆₁	1	2	yes	—
439	C₂×C₄	#137×C₆₁	1	2	yes	—
440	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
441	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
442	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
443	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
444	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
445	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
446	C₈	—	4	2	no	—
447	C₈	—	4	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	C₂×#123×C₆₁	1	1	yes	characteristic
456	C₂²	C₆₁×#536	1	1	yes	characteristic
457	C₂²	C₆₁×#537	1	1	yes	characteristic
458	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
459	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
460	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
461	C₂²	C₆₁×#575	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	4	1	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	1	no	—
466	C₄	—	8	2	no	—
467	C₄	—	8	1	no	—
468	C₄	—	8	1	no	—
469	C₄	—	8	1	no	—
470	C₄	—	8	2	no	—
471	C₄	—	8	1	no	—
472	C₄	C₆₁×#485	1	4	yes	—
473	C₄	C₆₁×#541	1	1	yes	characteristic
474	C₄	C₆₁×#541	1	1	yes	characteristic
475	C₄	C₆₁×#542	1	1	yes	characteristic
476	C₄	C₆₁×#542	1	1	yes	characteristic
477	C₂	—	4	2	no	—
478	C₂	C₆₁×#2625	1	1	yes	characteristic
479	C₂	C₂×C₆₁×#485	1	1	yes	characteristic
480	C₂	C₆₁×#3094	1	1	yes	characteristic
481	C₂	C₆₁×#3233	1	1	yes	characteristic
482	C₂	C₆₁×#3238	1	1	yes	characteristic
483	C₂	C₆₁×#3247	1	1	yes	characteristic
484	C₂	C₆₁×#3252	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂⁴×C₆₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₆₁×#2101	C₂	semidirect
4. C₆₁×#2085	C₂	semidirect
7. C₆₁×#1987	C₂	semidirect
8. C₆₁×#1987	C₂	semidirect
9. C₆₁×#1948	C₂	semidirect
10. C₆₁×#1947	C₂	semidirect
205. #29942	C₆₁	direct (N × H)
237. #2101	C₂×C₆₁	semidirect
238. #2085	C₂×C₆₁	semidirect
241. #1987	C₂×C₆₁	semidirect
242. #1987	C₂×C₆₁	semidirect
243. #1948	C₂×C₆₁	semidirect
244. #1947	C₂×C₆₁	semidirect
285. C₆₁	#29942	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×#2857	2
C₆₁×#2283	2
C₆₁×#2101	2
C₆₁×#2085	2
C₆₁×#2077	2
C₆₁×#2075	2
C₆₁×#1987	2
C₆₁×#1948	2
C₆₁×#1947	2
C₆₁×#1797	2
#29942	61

Subgroups — C61×#29942 #29533375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#29942 #29533375