Subgroups — C₆₁×#63002 #29566435

Order 15616.

11160 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×2₋¹⁺⁴×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3500	C₂	1	10	yes	maximal, complemented
4	C₆₁×#3497	C₂	1	5	yes	maximal, complemented
5	C₆₁×#3489	C₂	1	10	yes	maximal, complemented
6	C₆₁×#3488	C₂	1	10	yes	maximal, complemented
7	C₆₁×#3487	C₂	1	5	yes	maximal, complemented
8	C₆₁×#3486	C₂	1	5	yes	maximal, complemented
9	D₄×#41×C₆₁	C₂	1	10	yes	maximal, complemented
10	C₂×C₆₁×#548	C₂	1	5	yes	maximal, complemented
11	C₄×2₋¹⁺⁴×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#585	—	2	16	no	—
13	C₂×2₋¹⁺⁴×C₆₁	—	2	16	no	—
14	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	5	yes	complemented
16	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	10	yes	complemented
17	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	5	yes	complemented
18	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	10	yes	complemented
19	C₂²×#41×C₆₁	C₂²	1	10	yes	complemented
20	C₂²×#41×C₆₁	C₂²	1	5	yes	complemented
21	C₂²×#41×C₆₁	C₂²	1	10	yes	complemented
22	C₂³×Q₈×C₆₁	C₂²	1	5	yes	complemented
23	C₆₁×#550	C₂²	1	10	yes	complemented
24	C₆₁×#550	C₂²	1	20	yes	complemented
25	D₄×Q₈×C₆₁	C₂²	1	10	yes	complemented
26	D₄×Q₈×C₆₁	C₂²	1	20	yes	complemented
27	C₆₁×#548	C₂²	1	10	yes	complemented
28	C₆₁×#548	C₂²	1	20	yes	complemented
29	C₆₁×#548	C₂²	1	20	yes	complemented
30	C₆₁×#548	C₂²	1	20	yes	complemented
31	C₆₁×#548	C₂²	1	10	yes	complemented
32	C₆₁×#548	C₂²	1	20	yes	complemented
33	C₆₁×#547	C₂²	1	30	yes	complemented
34	C₆₁×#546	C₂²	1	10	yes	complemented
35	C₆₁×#546	C₂²	1	30	yes	complemented
36	C₆₁×#546	C₂²	1	60	yes	complemented
37	D₄²×C₆₁	C₂²	1	30	yes	complemented
38	C₆₁×#537	C₂²	1	30	yes	complemented
39	C₆₁×#536	C₂²	1	30	yes	complemented
40	C₆₁×#535	C₂²	1	30	yes	complemented
41	C₆₁×#532	C₂²	1	30	yes	complemented
42	C₂×#124×C₆₁	C₂²	1	15	yes	complemented
43	C₆₁×#525	C₂²	1	30	yes	complemented
44	C₆₁×#525	C₂²	1	30	yes	complemented
45	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	15	yes	complemented
46	C₂×#121×C₆₁	C₂²	1	15	yes	complemented
47	C₆₁×#520	C₂²	1	10	yes	complemented
48	C₆₁×#519	C₂²	1	5	yes	complemented
49	C₄×#41×C₆₁	C₂²	1	10	yes	complemented
50	C₂×C₄×Q₈×C₆₁	C₂²	1	5	yes	complemented
51	C₂×C₄×D₄×C₆₁	C₂²	1	15	yes	complemented
52	2₋¹⁺⁴×C₆₁	—	2	80	no	—
53	2₋¹⁺⁴×C₆₁	—	2	40	no	—
54	2₋¹⁺⁴×C₆₁	—	2	40	no	—
55	2₋¹⁺⁴×C₆₁	D₄	1	16	yes	complemented
56	H(5,𝔽₂)×C₆₁	—	2	80	no	—
57	C₂×#41×C₆₁	—	2	80	no	—
58	C₂×#41×C₆₁	—	2	80	no	—
59	C₂×#41×C₆₁	—	2	40	no	—
60	C₂×#41×C₆₁	C₂³	1	30	yes	—
61	C₂×#41×C₆₁	C₂³	1	30	yes	—
62	C₂×#41×C₆₁	C₂³	1	30	yes	—
63	C₂×#41×C₆₁	C₂³	1	10	yes	—
64	C₂×#41×C₆₁	C₂³	1	10	yes	—
65	C₂×#41×C₆₁	C₂³	1	20	yes	—
66	C₂×#41×C₆₁	C₂³	1	10	yes	—
67	C₂×#41×C₆₁	C₂³	1	10	yes	—
68	C₂²×Q₈×C₆₁	—	2	40	no	—
69	C₂²×Q₈×C₆₁	C₂³	1	15	yes	—
70	C₂²×Q₈×C₆₁	C₂³	1	10	yes	—
71	C₂²×Q₈×C₆₁	C₂³	1	20	yes	—
72	C₂²×Q₈×C₆₁	C₂³	1	10	yes	—
73	C₂²×Q₈×C₆₁	C₂³	1	5	yes	—
74	C₂²×D₄×C₆₁	C₂³	1	15	yes	—
75	C₂²×D₄×C₆₁	C₂³	1	10	yes	—
76	C₂²×D₄×C₆₁	C₂³	1	30	yes	—
77	C₂²×D₄×C₆₁	C₂³	1	15	yes	—
78	C₂³×C₄×C₆₁	C₂³	1	15	yes	—
79	C₂³×C₄×C₆₁	C₂³	1	15	yes	—
80	C₄⋊Q₈×C₆₁	C₂³	1	30	yes	—
81	#127×C₆₁	C₂³	1	30	yes	—
82	#124×C₆₁	C₂³	1	10	yes	—
83	#124×C₆₁	C₂³	1	30	yes	—
84	#124×C₆₁	C₂³	1	60	yes	—
85	#123×C₆₁	C₂³	1	60	yes	—
86	#123×C₆₁	C₂³	1	20	yes	—
87	C₂²⋊Q₈×C₆₁	C₂³	1	30	yes	—
88	C₂²⋊Q₈×C₆₁	C₂³	1	60	yes	—
89	C₂²⋊Q₈×C₆₁	C₂³	1	30	yes	—
90	C₂²⋊Q₈×C₆₁	C₂³	1	10	yes	—
91	C₂²⋊Q₈×C₆₁	C₂³	1	30	yes	—
92	#121×C₆₁	C₂³	1	20	yes	—
93	#121×C₆₁	C₂³	1	60	yes	—
94	#121×C₆₁	C₂³	1	30	yes	—
95	#121×C₆₁	C₂³	1	60	yes	—
96	#121×C₆₁	C₂³	1	30	yes	—
97	#121×C₆₁	C₂³	1	30	yes	—
98	#121×C₆₁	C₂³	1	10	yes	—
99	#120×C₆₁	C₂³	1	60	yes	—
100	#120×C₆₁	C₂³	1	20	yes	—
101	C₄×Q₈×C₆₁	C₂³	1	10	yes	—
102	C₄×Q₈×C₆₁	C₂³	1	20	yes	—
103	C₄×Q₈×C₆₁	C₂³	1	10	yes	—
104	C₄×D₄×C₆₁	C₂³	1	30	yes	—
105	C₄×D₄×C₆₁	C₂³	1	60	yes	—
106	C₄×D₄×C₆₁	C₂³	1	30	yes	—
107	C₄×D₄×C₆₁	C₂³	1	30	yes	—
108	C₄×D₄×C₆₁	C₂³	1	10	yes	—
109	C₄×D₄×C₆₁	C₂³	1	10	yes	—
110	C₄×D₄×C₆₁	C₂³	1	30	yes	—
111	#117×C₆₁	C₂³	1	30	yes	—
112	C₂×C₄⋊C₄×C₆₁	C₂³	1	15	yes	—
113	C₂×C₄⋊C₄×C₆₁	C₂³	1	15	yes	—
114	C₂×C₂²⋊C₄×C₆₁	C₂³	1	5	yes	—
115	C₂×C₂²⋊C₄×C₆₁	C₂³	1	15	yes	—
116	C₂×C₂²⋊C₄×C₆₁	C₂³	1	30	yes	—
117	C₂×C₄²×C₆₁	C₂³	1	15	yes	—
118	C₂⁴×C₆₁	C₂⁴	1	5	yes	—
119	C₂⁴×C₆₁	C₂⁴	1	15	yes	—
120	#41×C₆₁	—	2	40	no	—
121	#41×C₆₁	—	2	80	no	—
122	#41×C₆₁	—	2	40	no	—
123	#41×C₆₁	—	2	40	no	—
124	#41×C₆₁	—	2	120	no	—
125	#41×C₆₁	—	2	120	no	—
126	#41×C₆₁	—	2	120	no	—
127	#41×C₆₁	C₂×D₄	1	80	yes	complemented
128	C₂×Q₈×C₆₁	—	2	40	no	—
129	C₂×Q₈×C₆₁	—	2	80	no	—
130	C₂×Q₈×C₆₁	—	2	40	no	—
131	C₂×Q₈×C₆₁	—	2	60	no	—
132	C₂×Q₈×C₆₁	C₂×D₄	1	40	yes	complemented
133	C₂×Q₈×C₆₁	C₂⁴	1	30	yes	—
134	C₂×Q₈×C₆₁	C₂⁴	1	10	yes	—
135	C₂×Q₈×C₆₁	C₂⁴	1	10	yes	—
136	C₂×D₄×C₆₁	—	2	40	no	—
137	C₂×D₄×C₆₁	—	2	120	no	—
138	C₂×D₄×C₆₁	—	2	60	no	—
139	C₂×D₄×C₆₁	—	4	30	no	—
140	C₂×D₄×C₆₁	C₂⁴	1	10	yes	—
141	C₂×D₄×C₆₁	C₂⁴	1	20	yes	—
142	C₂×D₄×C₆₁	C₂⁴	1	20	yes	—
143	C₂×D₄×C₆₁	C₂⁴	1	30	yes	—
144	C₂×D₄×C₆₁	C₂⁴	1	10	yes	—
145	C₂×D₄×C₆₁	C₂⁴	1	20	yes	—
146	C₂×D₄×C₆₁	C₂⁴	1	30	yes	—
147	C₂×D₄×C₆₁	C₂⁴	1	10	yes	—
148	C₂²×C₄×C₆₁	—	2	60	no	—
149	C₂²×C₄×C₆₁	—	2	60	no	—
150	C₂²×C₄×C₆₁	C₂⁴	1	15	yes	—
151	C₂²×C₄×C₆₁	C₂⁴	1	5	yes	—
152	C₂²×C₄×C₆₁	C₂⁴	1	10	yes	—
153	C₂²×C₄×C₆₁	C₂⁴	1	30	yes	—
154	C₂²×C₄×C₆₁	C₂⁴	1	10	yes	—
155	C₂²×C₄×C₆₁	C₂⁴	1	30	yes	—
156	C₂²×C₄×C₆₁	C₂⁴	1	5	yes	—
157	C₂²×C₄×C₆₁	C₂⁴	1	15	yes	—
158	C₂²×C₄×C₆₁	C₂⁴	1	15	yes	—
159	C₄⋊C₄×C₆₁	C₂⁴	1	10	yes	—
160	C₄⋊C₄×C₆₁	C₂⁴	1	30	yes	—
161	C₄⋊C₄×C₆₁	C₂⁴	1	30	yes	—
162	C₄⋊C₄×C₆₁	C₂⁴	1	10	yes	—
163	C₄⋊C₄×C₆₁	C₂⁴	1	20	yes	—
164	C₂²⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
165	C₂²⋊C₄×C₆₁	C₂⁴	1	10	yes	—
166	C₂²⋊C₄×C₆₁	C₂⁴	1	60	yes	—
167	C₂²⋊C₄×C₆₁	C₂⁴	1	5	yes	—
168	C₂²⋊C₄×C₆₁	C₂⁴	1	5	yes	—
169	C₂²⋊C₄×C₆₁	C₂⁴	1	5	yes	—
170	C₂²⋊C₄×C₆₁	C₂⁴	1	30	yes	—
171	C₂²⋊C₄×C₆₁	C₂⁴	1	20	yes	—
172	C₂²⋊C₄×C₆₁	C₂⁴	1	20	yes	—
173	C₄²×C₆₁	C₂⁴	1	10	yes	—
174	C₄²×C₆₁	C₂⁴	1	30	yes	—
175	C₂³×C₆₁	—	2	10	no	—
176	C₂³×C₆₁	—	2	10	no	—
177	C₂³×C₆₁	—	2	30	no	—
178	C₂³×C₆₁	—	4	5	no	—
179	C₂³×C₆₁	—	4	15	no	—
180	C₂³×C₆₁	—	4	15	no	—
181	C₂³×C₆₁	C₂⁵	1	10	yes	—
182	C₂³×C₆₁	C₂⁵	1	5	yes	—
183	C₂³×C₆₁	C₂⁵	1	5	yes	—
184	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
185	Q₈×C₆₁	—	2	60	no	—
186	Q₈×C₆₁	—	2	20	no	—
187	Q₈×C₆₁	C₂²×D₄	1	40	yes	—
188	D₄×C₆₁	—	2	40	no	—
189	D₄×C₆₁	—	2	40	no	—
190	D₄×C₆₁	—	2	20	no	—
191	D₄×C₆₁	—	2	60	no	—
192	D₄×C₆₁	—	2	20	no	—
193	D₄×C₆₁	—	4	30	no	—
194	D₄×C₆₁	—	4	20	no	—
195	D₄×C₆₁	C₂²×D₄	1	40	yes	—
196	C₂×C₄×C₆₁	—	2	10	no	—
197	C₂×C₄×C₆₁	—	2	30	no	—
198	C₂×C₄×C₆₁	—	2	20	no	—
199	C₂×C₄×C₆₁	—	2	20	no	—
200	C₂×C₄×C₆₁	—	2	60	no	—
201	C₂×C₄×C₆₁	—	2	60	no	—
202	C₂×C₄×C₆₁	—	4	5	no	—
203	C₂×C₄×C₆₁	—	4	15	no	—
204	C₂×C₄×C₆₁	C₂²×D₄	1	60	yes	—
205	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
206	C₂×C₄×C₆₁	C₂⁵	1	5	yes	—
207	C₂×C₄×C₆₁	C₂⁵	1	10	yes	—
208	C₂×C₄×C₆₁	C₂⁵	1	10	yes	—
209	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
210	C₂×C₄×C₆₁	C₂⁵	1	5	yes	—
211	C₂×C₄×C₆₁	C₂⁵	1	10	yes	—
212	#63002	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂²×C₆₁	—	2	1	no	—
214	C₂²×C₆₁	—	2	5	no	—
215	C₂²×C₆₁	—	2	5	no	—
216	C₂²×C₆₁	—	2	1	no	—
217	C₂²×C₆₁	—	2	5	no	—
218	C₂²×C₆₁	—	2	10	no	—
219	C₂²×C₆₁	—	2	10	no	—
220	C₂²×C₆₁	—	2	5	no	—
221	C₂²×C₆₁	—	2	5	no	—
222	C₂²×C₆₁	—	2	10	no	—
223	C₂²×C₆₁	—	4	20	no	—
224	C₂²×C₆₁	—	8	30	no	—
225	C₂²×C₆₁	C₂³×D₄	1	10	yes	—
226	C₂²×C₆₁	#585	1	2	yes	complemented
227	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
228	C₄×C₆₁	—	2	1	no	—
229	C₄×C₆₁	—	2	5	no	—
230	C₄×C₆₁	—	2	10	no	—
231	C₄×C₆₁	—	2	10	no	—
232	C₄×C₆₁	—	2	1	no	—
233	C₄×C₆₁	—	2	5	no	—
234	C₄×C₆₁	C₂³×D₄	1	20	yes	—
235	C₂×#585	C₂×C₆₁	1	1	yes	characteristic, complemented
236	C₂²×2₋¹⁺⁴	C₂×C₆₁	1	1	yes	characteristic, complemented
237	#3500	C₂×C₆₁	1	10	yes	complemented
238	#3497	C₂×C₆₁	1	5	yes	complemented
239	#3489	C₂×C₆₁	1	10	yes	complemented
240	#3488	C₂×C₆₁	1	10	yes	complemented
241	#3487	C₂×C₆₁	1	5	yes	complemented
242	#3486	C₂×C₆₁	1	5	yes	complemented
243	D₄×#41	C₂×C₆₁	1	10	yes	complemented
244	C₂×#548	C₂×C₆₁	1	5	yes	complemented
245	C₄×2₋¹⁺⁴	C₂×C₆₁	1	1	yes	characteristic, complemented
246	C₂×C₆₁	—	2	2	no	—
247	C₂×C₆₁	—	2	10	no	—
248	C₂×C₆₁	—	4	5	no	—
249	C₂×C₆₁	—	4	10	no	—
250	C₂×C₆₁	C₂⁴×D₄	1	1	yes	characteristic
251	C₂×C₆₁	C₂×#585	1	1	yes	characteristic
252	C₂×C₆₁	2₋¹⁺⁶	1	1	yes	characteristic
253	#585	—	2	16	no	—
254	C₂×2₋¹⁺⁴	—	2	16	no	—
255	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	1	yes	characteristic
256	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	5	yes	complemented
257	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	10	yes	complemented
258	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	5	yes	complemented
259	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	10	yes	complemented
260	C₂²×#41	C₂²×C₆₁	1	10	yes	complemented
261	C₂²×#41	C₂²×C₆₁	1	5	yes	complemented
262	C₂²×#41	C₂²×C₆₁	1	10	yes	complemented
263	C₂³×Q₈	C₂²×C₆₁	1	5	yes	complemented
264	#550	C₂²×C₆₁	1	10	yes	complemented
265	#550	C₂²×C₆₁	1	20	yes	complemented
266	D₄×Q₈	C₂²×C₆₁	1	10	yes	complemented
267	D₄×Q₈	C₂²×C₆₁	1	20	yes	complemented
268	#548	C₂²×C₆₁	1	10	yes	complemented
269	#548	C₂²×C₆₁	1	20	yes	complemented
270	#548	C₂²×C₆₁	1	20	yes	complemented
271	#548	C₂²×C₆₁	1	20	yes	complemented
272	#548	C₂²×C₆₁	1	10	yes	complemented
273	#548	C₂²×C₆₁	1	20	yes	complemented
274	#547	C₂²×C₆₁	1	30	yes	complemented
275	#546	C₂²×C₆₁	1	10	yes	complemented
276	#546	C₂²×C₆₁	1	30	yes	complemented
277	#546	C₂²×C₆₁	1	60	yes	complemented
278	D₄²	C₂²×C₆₁	1	30	yes	complemented
279	#537	C₂²×C₆₁	1	30	yes	complemented
280	#536	C₂²×C₆₁	1	30	yes	complemented
281	#535	C₂²×C₆₁	1	30	yes	complemented
282	#532	C₂²×C₆₁	1	30	yes	complemented
283	C₂×#124	C₂²×C₆₁	1	15	yes	complemented
284	#525	C₂²×C₆₁	1	30	yes	complemented
285	#525	C₂²×C₆₁	1	30	yes	complemented
286	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	15	yes	complemented
287	C₂×#121	C₂²×C₆₁	1	15	yes	complemented
288	#520	C₂²×C₆₁	1	10	yes	complemented
289	#519	C₂²×C₆₁	1	5	yes	complemented
290	C₄×#41	C₂²×C₆₁	1	10	yes	complemented
291	C₂×C₄×Q₈	C₂²×C₆₁	1	5	yes	complemented
292	C₂×C₄×D₄	C₂²×C₆₁	1	15	yes	complemented
293	C₆₁	#63002	1	1	yes	characteristic, direct product factor, Sylow
294	2₋¹⁺⁴	—	2	80	no	—
295	2₋¹⁺⁴	—	2	40	no	—
296	2₋¹⁺⁴	—	2	40	no	—
297	2₋¹⁺⁴	D₄×C₆₁	1	16	yes	complemented
298	H(5,𝔽₂)	—	2	80	no	—
299	C₂×#41	—	2	80	no	—
300	C₂×#41	—	2	80	no	—
301	C₂×#41	—	2	40	no	—
302	C₂×#41	C₂³×C₆₁	1	30	yes	—
303	C₂×#41	C₂³×C₆₁	1	30	yes	—
304	C₂×#41	C₂³×C₆₁	1	30	yes	—
305	C₂×#41	C₂³×C₆₁	1	10	yes	—
306	C₂×#41	C₂³×C₆₁	1	10	yes	—
307	C₂×#41	C₂³×C₆₁	1	20	yes	—
308	C₂×#41	C₂³×C₆₁	1	10	yes	—
309	C₂×#41	C₂³×C₆₁	1	10	yes	—
310	C₂²×Q₈	—	2	40	no	—
311	C₂²×Q₈	C₂³×C₆₁	1	15	yes	—
312	C₂²×Q₈	C₂³×C₆₁	1	10	yes	—
313	C₂²×Q₈	C₂³×C₆₁	1	20	yes	—
314	C₂²×Q₈	C₂³×C₆₁	1	10	yes	—
315	C₂²×Q₈	C₂³×C₆₁	1	5	yes	—
316	C₂²×D₄	C₂³×C₆₁	1	15	yes	—
317	C₂²×D₄	C₂³×C₆₁	1	10	yes	—
318	C₂²×D₄	C₂³×C₆₁	1	30	yes	—
319	C₂²×D₄	C₂³×C₆₁	1	15	yes	—
320	C₂³×C₄	C₂³×C₆₁	1	15	yes	—
321	C₂³×C₄	C₂³×C₆₁	1	15	yes	—
322	C₄⋊Q₈	C₂³×C₆₁	1	30	yes	—
323	#127	C₂³×C₆₁	1	30	yes	—
324	#124	C₂³×C₆₁	1	30	yes	—
325	#124	C₂³×C₆₁	1	60	yes	—
326	#124	C₂³×C₆₁	1	10	yes	—
327	#123	C₂³×C₆₁	1	20	yes	—
328	#123	C₂³×C₆₁	1	60	yes	—
329	C₂²⋊Q₈	C₂³×C₆₁	1	30	yes	—
330	C₂²⋊Q₈	C₂³×C₆₁	1	60	yes	—
331	C₂²⋊Q₈	C₂³×C₆₁	1	10	yes	—
332	C₂²⋊Q₈	C₂³×C₆₁	1	30	yes	—
333	C₂²⋊Q₈	C₂³×C₆₁	1	30	yes	—
334	#121	C₂³×C₆₁	1	30	yes	—
335	#121	C₂³×C₆₁	1	60	yes	—
336	#121	C₂³×C₆₁	1	10	yes	—
337	#121	C₂³×C₆₁	1	30	yes	—
338	#121	C₂³×C₆₁	1	30	yes	—
339	#121	C₂³×C₆₁	1	20	yes	—
340	#121	C₂³×C₆₁	1	60	yes	—
341	#120	C₂³×C₆₁	1	20	yes	—
342	#120	C₂³×C₆₁	1	60	yes	—
343	C₄×Q₈	C₂³×C₆₁	1	10	yes	—
344	C₄×Q₈	C₂³×C₆₁	1	20	yes	—
345	C₄×Q₈	C₂³×C₆₁	1	10	yes	—
346	C₄×D₄	C₂³×C₆₁	1	10	yes	—
347	C₄×D₄	C₂³×C₆₁	1	30	yes	—
348	C₄×D₄	C₂³×C₆₁	1	30	yes	—
349	C₄×D₄	C₂³×C₆₁	1	30	yes	—
350	C₄×D₄	C₂³×C₆₁	1	10	yes	—
351	C₄×D₄	C₂³×C₆₁	1	30	yes	—
352	C₄×D₄	C₂³×C₆₁	1	60	yes	—
353	#117	C₂³×C₆₁	1	30	yes	—
354	C₂×C₄⋊C₄	C₂³×C₆₁	1	15	yes	—
355	C₂×C₄⋊C₄	C₂³×C₆₁	1	15	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₆₁	1	5	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₆₁	1	15	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₆₁	1	30	yes	—
359	C₂×C₄²	C₂³×C₆₁	1	15	yes	—
360	C₂⁴	C₂⁴×C₆₁	1	5	yes	—
361	C₂⁴	C₂⁴×C₆₁	1	15	yes	—
362	#41	—	2	40	no	—
363	#41	—	2	80	no	—
364	#41	—	2	40	no	—
365	#41	—	2	40	no	—
366	#41	—	2	120	no	—
367	#41	—	2	120	no	—
368	#41	—	2	120	no	—
369	#41	C₂×D₄×C₆₁	1	80	yes	complemented
370	C₂×Q₈	—	2	40	no	—
371	C₂×Q₈	—	2	80	no	—
372	C₂×Q₈	—	2	40	no	—
373	C₂×Q₈	—	2	60	no	—
374	C₂×Q₈	C₂×D₄×C₆₁	1	40	yes	complemented
375	C₂×Q₈	C₂⁴×C₆₁	1	30	yes	—
376	C₂×Q₈	C₂⁴×C₆₁	1	10	yes	—
377	C₂×Q₈	C₂⁴×C₆₁	1	10	yes	—
378	C₂×D₄	—	2	40	no	—
379	C₂×D₄	—	2	120	no	—
380	C₂×D₄	—	2	60	no	—
381	C₂×D₄	—	4	30	no	—
382	C₂×D₄	C₂⁴×C₆₁	1	10	yes	—
383	C₂×D₄	C₂⁴×C₆₁	1	20	yes	—
384	C₂×D₄	C₂⁴×C₆₁	1	20	yes	—
385	C₂×D₄	C₂⁴×C₆₁	1	30	yes	—
386	C₂×D₄	C₂⁴×C₆₁	1	10	yes	—
387	C₂×D₄	C₂⁴×C₆₁	1	20	yes	—
388	C₂×D₄	C₂⁴×C₆₁	1	30	yes	—
389	C₂×D₄	C₂⁴×C₆₁	1	10	yes	—
390	C₂²×C₄	—	2	60	no	—
391	C₂²×C₄	—	2	60	no	—
392	C₂²×C₄	C₂⁴×C₆₁	1	15	yes	—
393	C₂²×C₄	C₂⁴×C₆₁	1	5	yes	—
394	C₂²×C₄	C₂⁴×C₆₁	1	10	yes	—
395	C₂²×C₄	C₂⁴×C₆₁	1	30	yes	—
396	C₂²×C₄	C₂⁴×C₆₁	1	10	yes	—
397	C₂²×C₄	C₂⁴×C₆₁	1	30	yes	—
398	C₂²×C₄	C₂⁴×C₆₁	1	5	yes	—
399	C₂²×C₄	C₂⁴×C₆₁	1	15	yes	—
400	C₂²×C₄	C₂⁴×C₆₁	1	15	yes	—
401	C₄⋊C₄	C₂⁴×C₆₁	1	10	yes	—
402	C₄⋊C₄	C₂⁴×C₆₁	1	30	yes	—
403	C₄⋊C₄	C₂⁴×C₆₁	1	30	yes	—
404	C₄⋊C₄	C₂⁴×C₆₁	1	10	yes	—
405	C₄⋊C₄	C₂⁴×C₆₁	1	20	yes	—
406	C₂²⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
407	C₂²⋊C₄	C₂⁴×C₆₁	1	10	yes	—
408	C₂²⋊C₄	C₂⁴×C₆₁	1	60	yes	—
409	C₂²⋊C₄	C₂⁴×C₆₁	1	5	yes	—
410	C₂²⋊C₄	C₂⁴×C₆₁	1	5	yes	—
411	C₂²⋊C₄	C₂⁴×C₆₁	1	5	yes	—
412	C₂²⋊C₄	C₂⁴×C₆₁	1	30	yes	—
413	C₂²⋊C₄	C₂⁴×C₆₁	1	20	yes	—
414	C₂²⋊C₄	C₂⁴×C₆₁	1	20	yes	—
415	C₄²	C₂⁴×C₆₁	1	10	yes	—
416	C₄²	C₂⁴×C₆₁	1	30	yes	—
417	C₂³	—	2	10	no	—
418	C₂³	—	2	10	no	—
419	C₂³	—	2	30	no	—
420	C₂³	—	4	5	no	—
421	C₂³	—	4	15	no	—
422	C₂³	—	4	15	no	—
423	C₂³	C₂⁵×C₆₁	1	10	yes	—
424	C₂³	C₂⁵×C₆₁	1	5	yes	—
425	C₂³	C₂⁵×C₆₁	1	5	yes	—
426	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
427	Q₈	—	2	60	no	—
428	Q₈	—	2	20	no	—
429	Q₈	C₂²×D₄×C₆₁	1	40	yes	—
430	D₄	—	2	40	no	—
431	D₄	—	2	40	no	—
432	D₄	—	2	20	no	—
433	D₄	—	2	60	no	—
434	D₄	—	2	20	no	—
435	D₄	—	4	30	no	—
436	D₄	—	4	20	no	—
437	D₄	C₂²×D₄×C₆₁	1	40	yes	—
438	C₂×C₄	—	2	10	no	—
439	C₂×C₄	—	2	30	no	—
440	C₂×C₄	—	2	20	no	—
441	C₂×C₄	—	2	20	no	—
442	C₂×C₄	—	2	60	no	—
443	C₂×C₄	—	2	60	no	—
444	C₂×C₄	—	4	5	no	—
445	C₂×C₄	—	4	15	no	—
446	C₂×C₄	C₂²×D₄×C₆₁	1	60	yes	—
447	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
448	C₂×C₄	C₂⁵×C₆₁	1	5	yes	—
449	C₂×C₄	C₂⁵×C₆₁	1	10	yes	—
450	C₂×C₄	C₂⁵×C₆₁	1	10	yes	—
451	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
452	C₂×C₄	C₂⁵×C₆₁	1	5	yes	—
453	C₂×C₄	C₂⁵×C₆₁	1	10	yes	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	5	no	—
456	C₂²	—	2	5	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	5	no	—
459	C₂²	—	2	10	no	—
460	C₂²	—	2	10	no	—
461	C₂²	—	2	5	no	—
462	C₂²	—	2	5	no	—
463	C₂²	—	2	10	no	—
464	C₂²	—	4	20	no	—
465	C₂²	—	8	30	no	—
466	C₂²	C₂³×D₄×C₆₁	1	10	yes	—
467	C₂²	C₆₁×#585	1	2	yes	complemented
468	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	5	no	—
471	C₄	—	2	10	no	—
472	C₄	—	2	10	no	—
473	C₄	—	2	1	no	—
474	C₄	—	2	5	no	—
475	C₄	C₂³×D₄×C₆₁	1	20	yes	—
476	C₂	—	2	2	no	—
477	C₂	—	2	10	no	—
478	C₂	—	4	5	no	—
479	C₂	—	4	10	no	—
480	C₂	C₂⁴×D₄×C₆₁	1	1	yes	characteristic
481	C₂	C₂×C₆₁×#585	1	1	yes	characteristic
482	C₂	C₆₁×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#585	C₂	semidirect
2. C₂²×2₋¹⁺⁴×C₆₁	C₂	semidirect
3. C₆₁×#3500	C₂	semidirect
4. C₆₁×#3497	C₂	semidirect
5. C₆₁×#3489	C₂	semidirect
6. C₆₁×#3488	C₂	semidirect
7. C₆₁×#3487	C₂	semidirect
8. C₆₁×#3486	C₂	semidirect
9. D₄×#41×C₆₁	C₂	semidirect
10. C₂×C₆₁×#548	C₂	semidirect
11. C₄×2₋¹⁺⁴×C₆₁	C₂	semidirect
15. C₂×2₋¹⁺⁴×C₆₁	C₂²	semidirect
16. C₂×2₋¹⁺⁴×C₆₁	C₂²	semidirect
17. C₂×2₋¹⁺⁴×C₆₁	C₂²	semidirect
18. C₂×H(5,𝔽₂)×C₆₁	C₂²	semidirect
19. C₂²×#41×C₆₁	C₂²	semidirect
20. C₂²×#41×C₆₁	C₂²	semidirect
21. C₂²×#41×C₆₁	C₂²	semidirect
22. C₂³×Q₈×C₆₁	C₂²	semidirect
23. C₆₁×#550	C₂²	semidirect
24. C₆₁×#550	C₂²	semidirect
25. D₄×Q₈×C₆₁	C₂²	semidirect
26. D₄×Q₈×C₆₁	C₂²	semidirect
27. C₆₁×#548	C₂²	semidirect
28. C₆₁×#548	C₂²	semidirect
29. C₆₁×#548	C₂²	semidirect
30. C₆₁×#548	C₂²	semidirect
31. C₆₁×#548	C₂²	semidirect
32. C₆₁×#548	C₂²	semidirect
33. C₆₁×#547	C₂²	semidirect
34. C₆₁×#546	C₂²	semidirect
35. C₆₁×#546	C₂²	semidirect
36. C₆₁×#546	C₂²	semidirect
37. D₄²×C₆₁	C₂²	semidirect
38. C₆₁×#537	C₂²	semidirect
39. C₆₁×#536	C₂²	semidirect
40. C₆₁×#535	C₂²	semidirect
41. C₆₁×#532	C₂²	semidirect
42. C₂×#124×C₆₁	C₂²	semidirect
43. C₆₁×#525	C₂²	semidirect
44. C₆₁×#525	C₂²	semidirect
45. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
46. C₂×#121×C₆₁	C₂²	semidirect
47. C₆₁×#520	C₂²	semidirect
48. C₆₁×#519	C₂²	semidirect
49. C₄×#41×C₆₁	C₂²	semidirect
50. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
51. C₂×C₄×D₄×C₆₁	C₂²	semidirect
55. 2₋¹⁺⁴×C₆₁	D₄	semidirect
127. #41×C₆₁	C₂×D₄	semidirect
132. C₂×Q₈×C₆₁	C₂×D₄	semidirect
212. #63002	C₆₁	direct (N × H)
226. C₂²×C₆₁	#585	semidirect
235. C₂×#585	C₂×C₆₁	semidirect
236. C₂²×2₋¹⁺⁴	C₂×C₆₁	semidirect
237. #3500	C₂×C₆₁	semidirect
238. #3497	C₂×C₆₁	semidirect
239. #3489	C₂×C₆₁	semidirect
240. #3488	C₂×C₆₁	semidirect
241. #3487	C₂×C₆₁	semidirect
242. #3486	C₂×C₆₁	semidirect
243. D₄×#41	C₂×C₆₁	semidirect
244. C₂×#548	C₂×C₆₁	semidirect
245. C₄×2₋¹⁺⁴	C₂×C₆₁	semidirect
256. C₂×2₋¹⁺⁴	C₂²×C₆₁	semidirect
257. C₂×2₋¹⁺⁴	C₂²×C₆₁	semidirect
258. C₂×2₋¹⁺⁴	C₂²×C₆₁	semidirect
259. C₂×H(5,𝔽₂)	C₂²×C₆₁	semidirect
260. C₂²×#41	C₂²×C₆₁	semidirect
261. C₂²×#41	C₂²×C₆₁	semidirect
262. C₂²×#41	C₂²×C₆₁	semidirect
263. C₂³×Q₈	C₂²×C₆₁	semidirect
264. #550	C₂²×C₆₁	semidirect
265. #550	C₂²×C₆₁	semidirect
266. D₄×Q₈	C₂²×C₆₁	semidirect
267. D₄×Q₈	C₂²×C₆₁	semidirect
268. #548	C₂²×C₆₁	semidirect
269. #548	C₂²×C₆₁	semidirect
270. #548	C₂²×C₆₁	semidirect
271. #548	C₂²×C₆₁	semidirect
272. #548	C₂²×C₆₁	semidirect
273. #548	C₂²×C₆₁	semidirect
274. #547	C₂²×C₆₁	semidirect
275. #546	C₂²×C₆₁	semidirect
276. #546	C₂²×C₆₁	semidirect
277. #546	C₂²×C₆₁	semidirect
278. D₄²	C₂²×C₆₁	semidirect
279. #537	C₂²×C₆₁	semidirect
280. #536	C₂²×C₆₁	semidirect
281. #535	C₂²×C₆₁	semidirect
282. #532	C₂²×C₆₁	semidirect
283. C₂×#124	C₂²×C₆₁	semidirect
284. #525	C₂²×C₆₁	semidirect
285. #525	C₂²×C₆₁	semidirect
286. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
287. C₂×#121	C₂²×C₆₁	semidirect
288. #520	C₂²×C₆₁	semidirect
289. #519	C₂²×C₆₁	semidirect
290. C₄×#41	C₂²×C₆₁	semidirect
291. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
292. C₂×C₄×D₄	C₂²×C₆₁	semidirect
293. C₆₁	#63002	direct (N × H)
297. 2₋¹⁺⁴	D₄×C₆₁	semidirect
369. #41	C₂×D₄×C₆₁	semidirect
374. C₂×Q₈	C₂×D₄×C₆₁	semidirect
467. C₂²	C₆₁×#585	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#585	2
C₂²×2₋¹⁺⁴×C₆₁	2
C₆₁×#3500	2
C₆₁×#3497	2
C₆₁×#3489	2
C₆₁×#3488	2
C₆₁×#3487	2
C₆₁×#3486	2
D₄×#41×C₆₁	2
C₂×C₆₁×#548	2
C₄×2₋¹⁺⁴×C₆₁	2
#63002	61

Subgroups — C61×#63002 #29566435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#63002 #29566435