Subgroups — C₆₁×#36961 #29540394

Order 15616.

2442 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	C₂×C₆₁×#537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#126×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2854	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2723	C₂	1	8	yes	maximal, complemented
5	C₆₁×#2714	C₂	1	8	yes	maximal, complemented
6	C₆₁×#2617	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2539	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2504	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2406	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2404	C₂	1	2	yes	maximal, complemented
11	C₆₁×#2313	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₆₁	C₂²	1	2	yes	—
13	C₆₁×#537	—	2	8	no	—
14	C₂×#126×C₆₁	—	2	8	no	—
15	C₂×#126×C₆₁	C₂²	1	8	yes	—
16	C₂×#123×C₆₁	C₂²	1	4	yes	—
17	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	4	yes	complemented
18	C₂×#121×C₆₁	C₂²	1	2	yes	—
19	C₂×#121×C₆₁	C₂²	1	2	yes	—
20	C₂×#121×C₆₁	C₂²	1	4	yes	complemented
21	C₂×#120×C₆₁	C₂²	1	4	yes	—
22	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
29	C₆₁×#399	C₂²	1	4	yes	—
30	C₆₁×#397	C₂²	1	4	yes	—
31	C₆₁×#397	C₂²	1	8	yes	complemented
32	C₆₁×#395	C₂²	1	4	yes	complemented
33	C₆₁×#394	C₂²	1	8	yes	—
34	C₆₁×#394	C₂²	1	4	yes	complemented
35	C₆₁×#393	C₂²	1	4	yes	—
36	C₆₁×#392	C₂²	1	4	yes	—
37	C₆₁×#392	C₂²	1	4	yes	—
38	C₆₁×#392	C₂²	1	4	yes	—
39	C₆₁×#390	C₂²	1	8	yes	—
40	C₆₁×#390	C₂²	1	4	yes	complemented
41	C₆₁×#390	C₂²	1	4	yes	complemented
42	C₆₁×#389	C₂²	1	4	yes	complemented
43	C₆₁×#388	C₂²	1	8	yes	complemented
44	C₆₁×#387	C₂²	1	8	yes	complemented
45	C₆₁×#386	C₂²	1	4	yes	—
46	C₆₁×#386	C₂²	1	4	yes	—
47	C₆₁×#386	C₂²	1	8	yes	—
48	C₆₁×#385	C₂²	1	8	yes	complemented
49	C₆₁×#382	C₂²	1	4	yes	complemented
50	C₆₁×#381	C₂²	1	2	yes	—
51	C₆₁×#380	C₂²	1	2	yes	—
52	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
53	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
54	C₂×#41×C₆₁	—	2	8	no	—
55	C₂×#41×C₆₁	—	4	8	no	—
56	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
57	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
58	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
59	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
60	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
61	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
62	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
65	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
69	#126×C₆₁	—	2	32	no	—
70	#123×C₆₁	—	4	8	no	—
71	C₂²⋊Q₈×C₆₁	—	2	16	no	—
72	#121×C₆₁	—	2	8	no	—
73	#121×C₆₁	—	2	8	no	—
74	#121×C₆₁	—	2	16	no	—
75	#120×C₆₁	—	4	8	no	—
76	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
78	C₂×C₄⋊C₄×C₆₁	D₄	1	8	yes	complemented
79	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
82	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
85	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
96	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
97	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
98	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
99	C₂×C₄²×C₆₁	—	2	4	no	—
100	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
101	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
102	#95×C₆₁	C₂³	1	4	yes	—
103	#95×C₆₁	C₂³	1	4	yes	—
104	#95×C₆₁	C₂³	1	4	yes	—
105	#95×C₆₁	C₂³	1	4	yes	—
106	#95×C₆₁	C₂³	1	8	yes	—
107	#95×C₆₁	C₂³	1	8	yes	—
108	C₂⁴×C₆₁	—	2	2	no	—
109	C₂⁴×C₆₁	—	2	4	no	—
110	C₂⁴×C₆₁	—	4	2	no	—
111	C₂⁴×C₆₁	—	4	2	no	—
112	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
113	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
114	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
115	#41×C₆₁	—	4	32	no	—
116	C₂×Q₈×C₆₁	—	2	4	no	—
117	C₂×Q₈×C₆₁	—	4	4	no	—
118	C₂×D₄×C₆₁	—	2	8	no	—
119	C₂×D₄×C₆₁	—	2	8	no	—
120	C₂×D₄×C₆₁	—	2	8	no	—
121	C₂×D₄×C₆₁	—	2	4	no	—
122	C₂×D₄×C₆₁	—	2	4	no	—
123	C₂×D₄×C₆₁	—	2	4	no	—
124	C₂×D₄×C₆₁	—	4	4	no	—
125	C₂×D₄×C₆₁	—	4	8	no	—
126	C₂×D₄×C₆₁	—	4	4	no	—
127	C₂×D₄×C₆₁	—	4	4	no	—
128	C₂×D₄×C₆₁	—	4	8	no	—
129	C₂×D₄×C₆₁	—	4	8	no	—
130	C₂²×C₄×C₆₁	—	2	4	no	—
131	C₂²×C₄×C₆₁	—	2	2	no	—
132	C₂²×C₄×C₆₁	—	2	2	no	—
133	C₂²×C₄×C₆₁	—	2	2	no	—
134	C₂²×C₄×C₆₁	—	2	4	no	—
135	C₂²×C₄×C₆₁	—	2	8	no	—
136	C₂²×C₄×C₆₁	—	4	2	no	—
137	C₂²×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	C₂²×C₄×C₆₁	—	4	4	no	—
142	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
145	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
146	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
153	C₄⋊C₄×C₆₁	—	2	8	no	—
154	C₄⋊C₄×C₆₁	—	2	8	no	—
155	C₄⋊C₄×C₆₁	—	2	4	no	—
156	C₄⋊C₄×C₆₁	—	2	4	no	—
157	C₄⋊C₄×C₆₁	—	4	4	no	—
158	C₄⋊C₄×C₆₁	—	4	8	no	—
159	C₄⋊C₄×C₆₁	C₂×D₄	1	16	yes	—
160	C₂²⋊C₄×C₆₁	—	2	8	no	—
161	C₂²⋊C₄×C₆₁	—	2	8	no	—
162	C₂²⋊C₄×C₆₁	—	2	8	no	—
163	C₂²⋊C₄×C₆₁	—	2	8	no	—
164	C₂²⋊C₄×C₆₁	—	2	8	no	—
165	C₂²⋊C₄×C₆₁	—	2	8	no	—
166	C₂²⋊C₄×C₆₁	—	4	8	no	—
167	C₂²⋊C₄×C₆₁	—	4	8	no	—
168	C₂²⋊C₄×C₆₁	—	4	8	no	—
169	C₂²⋊C₄×C₆₁	—	4	8	no	—
170	C₄²×C₆₁	—	2	8	no	—
171	C₄²×C₆₁	—	4	4	no	—
172	C₂³×C₆₁	—	2	2	no	—
173	C₂³×C₆₁	—	2	2	no	—
174	C₂³×C₆₁	—	2	2	no	—
175	C₂³×C₆₁	—	2	4	no	—
176	C₂³×C₆₁	—	2	4	no	—
177	C₂³×C₆₁	—	2	4	no	—
178	C₂³×C₆₁	—	2	4	no	—
179	C₂³×C₆₁	—	2	8	no	—
180	C₂³×C₆₁	—	2	8	no	—
181	C₂³×C₆₁	—	2	4	no	—
182	C₂³×C₆₁	—	2	4	no	—
183	C₂³×C₆₁	—	4	4	no	—
184	C₂³×C₆₁	—	4	4	no	—
185	C₂³×C₆₁	—	4	4	no	—
186	C₂³×C₆₁	—	8	8	no	—
187	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
188	C₂³×C₆₁	H(5,𝔽₂)	1	4	yes	—
189	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
190	Q₈×C₆₁	—	4	8	no	—
191	D₄×C₆₁	—	4	8	no	—
192	D₄×C₆₁	—	4	16	no	—
193	D₄×C₆₁	—	8	4	no	—
194	D₄×C₆₁	—	8	4	no	—
195	D₄×C₆₁	—	8	16	no	—
196	C₂×C₄×C₆₁	—	2	8	no	—
197	C₂×C₄×C₆₁	—	2	4	no	—
198	C₂×C₄×C₆₁	—	2	4	no	—
199	C₂×C₄×C₆₁	—	2	4	no	—
200	C₂×C₄×C₆₁	—	2	2	no	—
201	C₂×C₄×C₆₁	—	2	2	no	—
202	C₂×C₄×C₆₁	—	2	2	no	—
203	C₂×C₄×C₆₁	—	2	4	no	—
204	C₂×C₄×C₆₁	—	2	8	no	—
205	C₂×C₄×C₆₁	—	2	4	no	—
206	C₂×C₄×C₆₁	—	2	4	no	—
207	C₂×C₄×C₆₁	—	2	4	no	—
208	C₂×C₄×C₆₁	—	2	8	no	—
209	C₂×C₄×C₆₁	—	2	4	no	—
210	C₂×C₄×C₆₁	—	2	4	no	—
211	C₂×C₄×C₆₁	—	2	8	no	—
212	C₂×C₄×C₆₁	—	4	4	no	—
213	C₂×C₄×C₆₁	—	4	4	no	—
214	C₂×C₄×C₆₁	—	4	16	no	—
215	C₂×C₄×C₆₁	—	4	4	no	—
216	C₂×C₄×C₆₁	—	4	4	no	—
217	C₂×C₄×C₆₁	—	4	4	no	—
218	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
219	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
220	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
221	#36961	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂²×C₆₁	—	2	2	no	—
223	C₂²×C₆₁	—	2	2	no	—
224	C₂²×C₆₁	—	2	8	no	—
225	C₂²×C₆₁	—	4	4	no	—
226	C₂²×C₆₁	—	4	2	no	—
227	C₂²×C₆₁	—	4	4	no	—
228	C₂²×C₆₁	—	4	2	no	—
229	C₂²×C₆₁	—	4	4	no	—
230	C₂²×C₆₁	—	4	2	no	—
231	C₂²×C₆₁	—	4	8	no	—
232	C₂²×C₆₁	—	4	8	no	—
233	C₂²×C₆₁	—	4	8	no	—
234	C₂²×C₆₁	—	8	8	no	—
235	C₂²×C₆₁	#535	1	4	yes	—
236	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
237	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
238	C₂²×C₆₁	#585	1	2	yes	—
239	C₂²×C₆₁	#585	1	2	yes	—
240	C₄×C₆₁	—	2	4	no	—
241	C₄×C₆₁	—	2	4	no	—
242	C₄×C₆₁	—	2	4	no	—
243	C₄×C₆₁	—	4	2	no	—
244	C₄×C₆₁	—	4	4	no	—
245	C₄×C₆₁	—	4	2	no	—
246	C₄×C₆₁	—	4	2	no	—
247	C₄×C₆₁	—	4	8	no	—
248	C₂×#537	C₂×C₆₁	1	1	yes	characteristic, complemented
249	C₂²×#126	C₂×C₆₁	1	1	yes	characteristic, complemented
250	#2854	C₂×C₆₁	1	2	yes	complemented
251	#2723	C₂×C₆₁	1	8	yes	complemented
252	#2714	C₂×C₆₁	1	8	yes	complemented
253	#2617	C₂×C₆₁	1	2	yes	complemented
254	#2539	C₂×C₆₁	1	2	yes	complemented
255	#2504	C₂×C₆₁	1	2	yes	complemented
256	#2406	C₂×C₆₁	1	2	yes	complemented
257	#2404	C₂×C₆₁	1	2	yes	complemented
258	#2313	C₂×C₆₁	1	1	yes	characteristic, complemented
259	C₂×C₆₁	—	2	4	no	—
260	C₂×C₆₁	—	8	4	no	—
261	C₂×C₆₁	—	8	2	no	—
262	C₂×C₆₁	C₂×#535	1	1	yes	characteristic
263	C₂×C₆₁	#3485	1	1	yes	characteristic
264	C₂×C₆₁	#3487	1	1	yes	characteristic
265	C₂×C₆₁	#3560	1	4	yes	—
266	C₂²×#41	C₂²×C₆₁	1	2	yes	—
267	#537	—	2	8	no	—
268	C₂×#126	—	2	8	no	—
269	C₂×#126	C₂²×C₆₁	1	8	yes	—
270	C₂×#123	C₂²×C₆₁	1	4	yes	—
271	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	4	yes	complemented
272	C₂×#121	C₂²×C₆₁	1	2	yes	—
273	C₂×#121	C₂²×C₆₁	1	2	yes	—
274	C₂×#121	C₂²×C₆₁	1	4	yes	complemented
275	C₂×#120	C₂²×C₆₁	1	4	yes	—
276	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
277	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
278	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
279	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
280	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
281	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
282	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
283	#399	C₂²×C₆₁	1	4	yes	—
284	#397	C₂²×C₆₁	1	4	yes	—
285	#397	C₂²×C₆₁	1	8	yes	complemented
286	#395	C₂²×C₆₁	1	4	yes	complemented
287	#394	C₂²×C₆₁	1	8	yes	—
288	#394	C₂²×C₆₁	1	4	yes	complemented
289	#393	C₂²×C₆₁	1	4	yes	—
290	#392	C₂²×C₆₁	1	4	yes	—
291	#392	C₂²×C₆₁	1	4	yes	—
292	#392	C₂²×C₆₁	1	4	yes	—
293	#390	C₂²×C₆₁	1	8	yes	—
294	#390	C₂²×C₆₁	1	4	yes	complemented
295	#390	C₂²×C₆₁	1	4	yes	complemented
296	#389	C₂²×C₆₁	1	4	yes	complemented
297	#388	C₂²×C₆₁	1	8	yes	complemented
298	#387	C₂²×C₆₁	1	8	yes	complemented
299	#386	C₂²×C₆₁	1	4	yes	—
300	#386	C₂²×C₆₁	1	4	yes	—
301	#386	C₂²×C₆₁	1	8	yes	—
302	#385	C₂²×C₆₁	1	8	yes	complemented
303	#382	C₂²×C₆₁	1	4	yes	complemented
304	#381	C₂²×C₆₁	1	2	yes	—
305	#380	C₂²×C₆₁	1	2	yes	—
306	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
307	C₆₁	#36961	1	1	yes	characteristic, direct product factor, Sylow
308	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
309	C₂×#41	—	2	8	no	—
310	C₂×#41	—	4	8	no	—
311	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
312	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
313	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
314	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
315	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
316	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
317	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
318	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
322	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
324	#126	—	2	32	no	—
325	#123	—	4	8	no	—
326	C₂²⋊Q₈	—	2	16	no	—
327	#121	—	2	8	no	—
328	#121	—	2	8	no	—
329	#121	—	2	16	no	—
330	#120	—	4	8	no	—
331	C₂×C₄⋊C₄	—	2	4	no	—
332	C₂×C₄⋊C₄	—	2	4	no	—
333	C₂×C₄⋊C₄	D₄×C₆₁	1	8	yes	complemented
334	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
335	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
336	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
339	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
340	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
341	C₂×C₂²⋊C₄	—	2	4	no	—
342	C₂×C₂²⋊C₄	—	2	4	no	—
343	C₂×C₂²⋊C₄	—	2	4	no	—
344	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
354	C₂×C₄²	—	2	4	no	—
355	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
356	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
357	#95	C₂³×C₆₁	1	4	yes	—
358	#95	C₂³×C₆₁	1	4	yes	—
359	#95	C₂³×C₆₁	1	4	yes	—
360	#95	C₂³×C₆₁	1	4	yes	—
361	#95	C₂³×C₆₁	1	8	yes	—
362	#95	C₂³×C₆₁	1	8	yes	—
363	C₂⁴	—	2	2	no	—
364	C₂⁴	—	2	4	no	—
365	C₂⁴	—	4	2	no	—
366	C₂⁴	—	4	2	no	—
367	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
368	C₂⁴	C₂⁴×C₆₁	1	4	yes	—
369	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
370	#41	—	4	32	no	—
371	C₂×Q₈	—	2	4	no	—
372	C₂×Q₈	—	4	4	no	—
373	C₂×D₄	—	2	8	no	—
374	C₂×D₄	—	2	8	no	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	—	4	8	no	—
381	C₂×D₄	—	4	4	no	—
382	C₂×D₄	—	4	4	no	—
383	C₂×D₄	—	4	8	no	—
384	C₂×D₄	—	4	8	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	8	no	—
391	C₂²×C₄	—	4	4	no	—
392	C₂²×C₄	—	4	4	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
398	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
399	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
400	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
401	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
403	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
404	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
405	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
406	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
407	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
408	C₄⋊C₄	—	2	8	no	—
409	C₄⋊C₄	—	2	8	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	4	8	no	—
413	C₄⋊C₄	—	4	4	no	—
414	C₄⋊C₄	C₂×D₄×C₆₁	1	16	yes	—
415	C₂²⋊C₄	—	2	8	no	—
416	C₂²⋊C₄	—	2	8	no	—
417	C₂²⋊C₄	—	2	8	no	—
418	C₂²⋊C₄	—	2	8	no	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	4	8	no	—
422	C₂²⋊C₄	—	4	8	no	—
423	C₂²⋊C₄	—	4	8	no	—
424	C₂²⋊C₄	—	4	8	no	—
425	C₄²	—	2	8	no	—
426	C₄²	—	4	4	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	4	no	—
431	C₂³	—	2	4	no	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	2	8	no	—
435	C₂³	—	2	8	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	4	4	no	—
439	C₂³	—	4	4	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	8	8	no	—
442	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
443	C₂³	H(5,𝔽₂)×C₆₁	1	4	yes	—
444	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
445	Q₈	—	4	8	no	—
446	D₄	—	4	8	no	—
447	D₄	—	4	16	no	—
448	D₄	—	8	4	no	—
449	D₄	—	8	4	no	—
450	D₄	—	8	16	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	8	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	8	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	—	4	16	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
474	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
475	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
476	C₂²	—	2	8	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	4	8	no	—
480	C₂²	—	4	8	no	—
481	C₂²	—	4	8	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	8	8	no	—
489	C₂²	C₆₁×#535	1	4	yes	—
490	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
491	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
492	C₂²	C₆₁×#585	1	2	yes	—
493	C₂²	C₆₁×#585	1	2	yes	—
494	C₄	—	2	4	no	—
495	C₄	—	2	4	no	—
496	C₄	—	2	4	no	—
497	C₄	—	4	8	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	4	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	2	no	—
502	C₂	—	2	4	no	—
503	C₂	—	8	2	no	—
504	C₂	—	8	4	no	—
505	C₂	C₂×C₆₁×#535	1	1	yes	characteristic
506	C₂	C₆₁×#3485	1	1	yes	characteristic
507	C₂	C₆₁×#3487	1	1	yes	characteristic
508	C₂	C₆₁×#3560	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#537	C₂	semidirect
2. C₂²×#126×C₆₁	C₂	semidirect
3. C₆₁×#2854	C₂	semidirect
4. C₆₁×#2723	C₂	semidirect
5. C₆₁×#2714	C₂	semidirect
6. C₆₁×#2617	C₂	semidirect
7. C₆₁×#2539	C₂	semidirect
8. C₆₁×#2504	C₂	semidirect
9. C₆₁×#2406	C₂	semidirect
10. C₆₁×#2404	C₂	semidirect
11. C₆₁×#2313	C₂	semidirect
17. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
20. C₂×#121×C₆₁	C₂²	semidirect
31. C₆₁×#397	C₂²	semidirect
32. C₆₁×#395	C₂²	semidirect
34. C₆₁×#394	C₂²	semidirect
40. C₆₁×#390	C₂²	semidirect
41. C₆₁×#390	C₂²	semidirect
42. C₆₁×#389	C₂²	semidirect
43. C₆₁×#388	C₂²	semidirect
44. C₆₁×#387	C₂²	semidirect
48. C₆₁×#385	C₂²	semidirect
49. C₆₁×#382	C₂²	semidirect
78. C₂×C₄⋊C₄×C₆₁	D₄	semidirect
221. #36961	C₆₁	direct (N × H)
248. C₂×#537	C₂×C₆₁	semidirect
249. C₂²×#126	C₂×C₆₁	semidirect
250. #2854	C₂×C₆₁	semidirect
251. #2723	C₂×C₆₁	semidirect
252. #2714	C₂×C₆₁	semidirect
253. #2617	C₂×C₆₁	semidirect
254. #2539	C₂×C₆₁	semidirect
255. #2504	C₂×C₆₁	semidirect
256. #2406	C₂×C₆₁	semidirect
257. #2404	C₂×C₆₁	semidirect
258. #2313	C₂×C₆₁	semidirect
271. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
274. C₂×#121	C₂²×C₆₁	semidirect
285. #397	C₂²×C₆₁	semidirect
286. #395	C₂²×C₆₁	semidirect
288. #394	C₂²×C₆₁	semidirect
294. #390	C₂²×C₆₁	semidirect
295. #390	C₂²×C₆₁	semidirect
296. #389	C₂²×C₆₁	semidirect
297. #388	C₂²×C₆₁	semidirect
298. #387	C₂²×C₆₁	semidirect
302. #385	C₂²×C₆₁	semidirect
303. #382	C₂²×C₆₁	semidirect
307. C₆₁	#36961	direct (N × H)
333. C₂×C₄⋊C₄	D₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#537	2
C₂²×#126×C₆₁	2
C₆₁×#2854	2
C₆₁×#2723	2
C₆₁×#2714	2
C₆₁×#2617	2
C₆₁×#2539	2
C₆₁×#2504	2
C₆₁×#2406	2
C₆₁×#2404	2
C₆₁×#2313	2
#36961	61

Subgroups — C61×#36961 #29540394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#36961 #29540394