Subgroups — C₆₁×#36966 #29540399

Order 15616.

2406 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#124×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2855	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2700	C₂	1	8	yes	maximal, complemented
5	C₆₁×#2674	C₂	1	8	yes	maximal, complemented
6	C₆₁×#2626	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2561	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2483	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2434	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2405	C₂	1	2	yes	maximal
11	C₆₁×#2312	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#543	—	2	8	no	—
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	4	yes	complemented
16	C₂×#124×C₆₁	—	2	8	no	—
17	C₂×#124×C₆₁	C₂²	1	8	yes	—
18	C₂×#123×C₆₁	C₂²	1	4	yes	—
19	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	4	yes	complemented
22	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	4	yes	complemented
23	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
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	complemented
30	C₆₁×#397	C₂²	1	4	yes	complemented
31	C₆₁×#397	C₂²	1	8	yes	complemented
32	C₆₁×#396	C₂²	1	8	yes	complemented
33	C₆₁×#395	C₂²	1	8	yes	complemented
34	C₆₁×#394	C₂²	1	8	yes	—
35	C₆₁×#393	C₂²	1	4	yes	complemented
36	C₆₁×#393	C₂²	1	4	yes	complemented
37	C₆₁×#391	C₂²	1	4	yes	complemented
38	C₆₁×#391	C₂²	1	4	yes	complemented
39	C₆₁×#389	C₂²	1	4	yes	complemented
40	C₆₁×#388	C₂²	1	8	yes	complemented
41	C₆₁×#388	C₂²	1	8	yes	complemented
42	C₆₁×#387	C₂²	1	8	yes	complemented
43	C₆₁×#386	C₂²	1	4	yes	—
44	C₆₁×#385	C₂²	1	4	yes	—
45	C₆₁×#385	C₂²	1	4	yes	—
46	C₆₁×#385	C₂²	1	4	yes	complemented
47	C₆₁×#381	C₂²	1	4	yes	—
48	C₆₁×#381	C₂²	1	4	yes	complemented
49	C₆₁×#380	C₂²	1	2	yes	—
50	C₆₁×#379	C₂²	1	4	yes	—
51	C₆₁×#379	C₂²	1	2	yes	—
52	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
53	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
54	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₆₁	—	2	4	no	—
56	C₂²×Q₈×C₆₁	—	4	4	no	—
57	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
58	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
59	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
60	C₂²×D₄×C₆₁	—	2	4	no	—
61	C₂²×D₄×C₆₁	—	4	4	no	—
62	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
63	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
67	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
68	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
70	C₄⋊Q₈×C₆₁	—	4	8	no	—
71	#124×C₆₁	—	2	32	no	—
72	#123×C₆₁	—	4	8	no	—
73	C₂²⋊Q₈×C₆₁	—	2	8	no	—
74	C₂²⋊Q₈×C₆₁	—	2	8	no	—
75	C₂²⋊Q₈×C₆₁	—	2	16	no	—
76	C₂²⋊Q₈×C₆₁	—	2	16	no	—
77	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
78	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
83	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
84	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
85	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
86	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₆₁	D₄	1	8	yes	—
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	4	yes	—
96	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
98	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
99	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
100	C₂×C₄²×C₆₁	—	2	4	no	—
101	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
102	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
103	#95×C₆₁	C₂³	1	4	yes	—
104	#95×C₆₁	C₂³	1	4	yes	—
105	#95×C₆₁	C₂³	1	8	yes	—
106	#95×C₆₁	C₂³	1	8	yes	—
107	#95×C₆₁	C₂³	1	8	yes	—
108	#95×C₆₁	C₂³	1	8	yes	—
109	C₂⁴×C₆₁	—	2	4	no	—
110	C₂⁴×C₆₁	—	2	2	no	—
111	C₂⁴×C₆₁	—	2	4	no	—
112	C₂⁴×C₆₁	—	4	2	no	—
113	C₂⁴×C₆₁	—	4	2	no	—
114	C₂⁴×C₆₁	—	4	2	no	—
115	C₂⁴×C₆₁	—	4	2	no	—
116	C₂⁴×C₆₁	C₂×D₄	1	4	yes	—
117	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
118	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
119	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
120	C₂×Q₈×C₆₁	—	2	8	no	—
121	C₂×Q₈×C₆₁	—	2	4	no	—
122	C₂×Q₈×C₆₁	—	2	4	no	—
123	C₂×Q₈×C₆₁	—	2	8	no	—
124	C₂×Q₈×C₆₁	—	4	4	no	—
125	C₂×Q₈×C₆₁	—	4	4	no	—
126	C₂×Q₈×C₆₁	—	4	4	no	—
127	C₂×Q₈×C₆₁	—	4	16	no	—
128	C₂×D₄×C₆₁	—	2	8	no	—
129	C₂×D₄×C₆₁	—	2	8	no	—
130	C₂×D₄×C₆₁	—	4	4	no	—
131	C₂×D₄×C₆₁	—	4	16	no	—
132	C₂²×C₄×C₆₁	—	2	2	no	—
133	C₂²×C₄×C₆₁	—	2	4	no	—
134	C₂²×C₄×C₆₁	—	2	2	no	—
135	C₂²×C₄×C₆₁	—	2	2	no	—
136	C₂²×C₄×C₆₁	—	2	4	no	—
137	C₂²×C₄×C₆₁	—	2	4	no	—
138	C₂²×C₄×C₆₁	—	2	4	no	—
139	C₂²×C₄×C₆₁	—	4	2	no	—
140	C₂²×C₄×C₆₁	—	4	2	no	—
141	C₂²×C₄×C₆₁	—	4	2	no	—
142	C₂²×C₄×C₆₁	—	4	4	no	—
143	C₂²×C₄×C₆₁	—	4	4	no	—
144	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
145	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
148	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
154	C₄⋊C₄×C₆₁	—	2	8	no	—
155	C₄⋊C₄×C₆₁	—	2	4	no	—
156	C₄⋊C₄×C₆₁	—	2	8	no	—
157	C₄⋊C₄×C₆₁	—	2	4	no	—
158	C₄⋊C₄×C₆₁	—	2	16	no	—
159	C₄⋊C₄×C₆₁	—	4	4	no	—
160	C₄⋊C₄×C₆₁	—	4	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	—	2	8	no	—
167	C₂²⋊C₄×C₆₁	—	4	4	no	—
168	C₂²⋊C₄×C₆₁	—	4	8	no	—
169	C₂²⋊C₄×C₆₁	—	4	4	no	—
170	C₂²⋊C₄×C₆₁	—	4	8	no	—
171	C₂²⋊C₄×C₆₁	C₂×D₄	1	16	yes	—
172	C₄²×C₆₁	—	2	8	no	—
173	C₄²×C₆₁	—	4	4	no	—
174	C₂³×C₆₁	—	2	2	no	—
175	C₂³×C₆₁	—	2	2	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	2	no	—
181	C₂³×C₆₁	—	2	4	no	—
182	C₂³×C₆₁	—	2	4	no	—
183	C₂³×C₆₁	—	2	4	no	—
184	C₂³×C₆₁	—	4	4	no	—
185	C₂³×C₆₁	—	4	4	no	—
186	C₂³×C₆₁	—	4	4	no	—
187	C₂³×C₆₁	—	4	4	no	—
188	C₂³×C₆₁	—	4	4	no	—
189	C₂³×C₆₁	—	8	8	no	—
190	C₂³×C₆₁	—	8	8	no	—
191	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
192	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
193	C₂³×C₆₁	2₋¹⁺⁴	1	4	yes	—
194	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
195	Q₈×C₆₁	—	4	16	no	—
196	Q₈×C₆₁	—	8	4	no	—
197	Q₈×C₆₁	—	8	4	no	—
198	D₄×C₆₁	—	4	16	no	—
199	C₂×C₄×C₆₁	—	2	8	no	—
200	C₂×C₄×C₆₁	—	2	2	no	—
201	C₂×C₄×C₆₁	—	2	4	no	—
202	C₂×C₄×C₆₁	—	2	2	no	—
203	C₂×C₄×C₆₁	—	2	4	no	—
204	C₂×C₄×C₆₁	—	2	2	no	—
205	C₂×C₄×C₆₁	—	2	2	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	8	no	—
210	C₂×C₄×C₆₁	—	2	4	no	—
211	C₂×C₄×C₆₁	—	2	8	no	—
212	C₂×C₄×C₆₁	—	2	4	no	—
213	C₂×C₄×C₆₁	—	2	8	no	—
214	C₂×C₄×C₆₁	—	2	8	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	—	4	4	no	—
219	C₂×C₄×C₆₁	—	8	4	no	—
220	C₂×C₄×C₆₁	—	8	4	no	—
221	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
222	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
223	C₂×C₄×C₆₁	H(5,𝔽₂)	1	4	yes	—
224	#36966	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂²×C₆₁	—	2	2	no	—
226	C₂²×C₆₁	—	2	2	no	—
227	C₂²×C₆₁	—	2	8	no	—
228	C₂²×C₆₁	—	2	4	no	—
229	C₂²×C₆₁	—	2	4	no	—
230	C₂²×C₆₁	—	2	4	no	—
231	C₂²×C₆₁	—	4	8	no	—
232	C₂²×C₆₁	—	4	2	no	—
233	C₂²×C₆₁	—	4	2	no	—
234	C₂²×C₆₁	—	4	2	no	—
235	C₂²×C₆₁	—	4	8	no	—
236	C₂²×C₆₁	—	8	8	no	—
237	C₂²×C₆₁	—	8	8	no	—
238	C₂²×C₆₁	#536	1	4	yes	—
239	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
240	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
241	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
242	C₂²×C₆₁	#585	1	2	yes	—
243	C₄×C₆₁	—	2	4	no	—
244	C₄×C₆₁	—	2	4	no	—
245	C₄×C₆₁	—	2	4	no	—
246	C₄×C₆₁	—	4	2	no	—
247	C₄×C₆₁	—	4	2	no	—
248	C₄×C₆₁	—	4	4	no	—
249	C₄×C₆₁	—	4	4	no	—
250	C₄×C₆₁	—	4	8	no	—
251	C₂×#543	C₂×C₆₁	1	1	yes	characteristic, complemented
252	C₂²×#124	C₂×C₆₁	1	1	yes	characteristic
253	#2855	C₂×C₆₁	1	2	yes	complemented
254	#2700	C₂×C₆₁	1	8	yes	complemented
255	#2674	C₂×C₆₁	1	8	yes	complemented
256	#2626	C₂×C₆₁	1	2	yes	complemented
257	#2561	C₂×C₆₁	1	2	yes	complemented
258	#2483	C₂×C₆₁	1	2	yes	complemented
259	#2434	C₂×C₆₁	1	2	yes	complemented
260	#2405	C₂×C₆₁	1	2	yes	—
261	#2312	C₂×C₆₁	1	1	yes	characteristic, complemented
262	C₂×C₆₁	—	2	4	no	—
263	C₂×C₆₁	—	4	4	no	—
264	C₂×C₆₁	—	8	2	no	—
265	C₂×C₆₁	C₂×#536	1	1	yes	characteristic
266	C₂×C₆₁	#3484	1	1	yes	characteristic
267	C₂×C₆₁	#3485	1	1	yes	characteristic
268	C₂×C₆₁	#3561	1	4	yes	—
269	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
270	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
271	#543	—	2	8	no	—
272	C₂×C₄⋊Q₈	C₂²×C₆₁	1	4	yes	complemented
273	C₂×#124	—	2	8	no	—
274	C₂×#124	C₂²×C₆₁	1	8	yes	—
275	C₂×#123	C₂²×C₆₁	1	4	yes	—
276	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
277	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
278	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	4	yes	complemented
279	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	4	yes	complemented
280	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
281	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
282	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
283	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
284	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
285	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
286	#399	C₂²×C₆₁	1	4	yes	complemented
287	#397	C₂²×C₆₁	1	4	yes	complemented
288	#397	C₂²×C₆₁	1	8	yes	complemented
289	#396	C₂²×C₆₁	1	8	yes	complemented
290	#395	C₂²×C₆₁	1	8	yes	complemented
291	#394	C₂²×C₆₁	1	8	yes	—
292	#393	C₂²×C₆₁	1	4	yes	complemented
293	#393	C₂²×C₆₁	1	4	yes	complemented
294	#391	C₂²×C₆₁	1	4	yes	complemented
295	#391	C₂²×C₆₁	1	4	yes	complemented
296	#389	C₂²×C₆₁	1	4	yes	complemented
297	#388	C₂²×C₆₁	1	8	yes	complemented
298	#388	C₂²×C₆₁	1	8	yes	complemented
299	#387	C₂²×C₆₁	1	8	yes	complemented
300	#386	C₂²×C₆₁	1	4	yes	—
301	#385	C₂²×C₆₁	1	4	yes	—
302	#385	C₂²×C₆₁	1	4	yes	—
303	#385	C₂²×C₆₁	1	4	yes	complemented
304	#381	C₂²×C₆₁	1	4	yes	—
305	#381	C₂²×C₆₁	1	4	yes	complemented
306	#380	C₂²×C₆₁	1	2	yes	—
307	#379	C₂²×C₆₁	1	4	yes	—
308	#379	C₂²×C₆₁	1	2	yes	—
309	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
310	C₆₁	#36966	1	1	yes	characteristic, direct product factor, Sylow
311	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
312	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
313	C₂²×Q₈	—	2	4	no	—
314	C₂²×Q₈	—	4	4	no	—
315	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
316	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
317	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
318	C₂²×D₄	—	2	4	no	—
319	C₂²×D₄	—	4	4	no	—
320	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
321	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
325	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
326	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
327	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
328	C₄⋊Q₈	—	4	8	no	—
329	#124	—	2	32	no	—
330	#123	—	4	8	no	—
331	C₂²⋊Q₈	—	2	8	no	—
332	C₂²⋊Q₈	—	2	8	no	—
333	C₂²⋊Q₈	—	2	16	no	—
334	C₂²⋊Q₈	—	2	16	no	—
335	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
336	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
337	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
339	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
340	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
341	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
342	C₂×C₂²⋊C₄	—	2	4	no	—
343	C₂×C₂²⋊C₄	—	2	8	no	—
344	C₂×C₂²⋊C₄	—	2	4	no	—
345	C₂×C₂²⋊C₄	—	2	4	no	—
346	C₂×C₂²⋊C₄	D₄×C₆₁	1	8	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	4	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
358	C₂×C₄²	—	2	4	no	—
359	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
360	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
361	#95	C₂³×C₆₁	1	4	yes	—
362	#95	C₂³×C₆₁	1	4	yes	—
363	#95	C₂³×C₆₁	1	8	yes	—
364	#95	C₂³×C₆₁	1	8	yes	—
365	#95	C₂³×C₆₁	1	8	yes	—
366	#95	C₂³×C₆₁	1	8	yes	—
367	C₂⁴	—	2	4	no	—
368	C₂⁴	—	2	2	no	—
369	C₂⁴	—	2	4	no	—
370	C₂⁴	—	4	2	no	—
371	C₂⁴	—	4	2	no	—
372	C₂⁴	—	4	2	no	—
373	C₂⁴	—	4	2	no	—
374	C₂⁴	C₂×D₄×C₆₁	1	4	yes	—
375	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
376	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
377	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
378	C₂×Q₈	—	2	8	no	—
379	C₂×Q₈	—	2	4	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	—	2	8	no	—
382	C₂×Q₈	—	4	4	no	—
383	C₂×Q₈	—	4	4	no	—
384	C₂×Q₈	—	4	4	no	—
385	C₂×Q₈	—	4	16	no	—
386	C₂×D₄	—	2	8	no	—
387	C₂×D₄	—	2	8	no	—
388	C₂×D₄	—	4	4	no	—
389	C₂×D₄	—	4	16	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	4	4	no	—
401	C₂²×C₄	—	4	4	no	—
402	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
403	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
404	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
405	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
406	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
407	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
408	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
409	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
411	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
412	C₄⋊C₄	—	2	8	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	8	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	16	no	—
417	C₄⋊C₄	—	4	4	no	—
418	C₄⋊C₄	—	4	8	no	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	8	no	—
423	C₂²⋊C₄	—	2	8	no	—
424	C₂²⋊C₄	—	2	8	no	—
425	C₂²⋊C₄	—	4	4	no	—
426	C₂²⋊C₄	—	4	8	no	—
427	C₂²⋊C₄	—	4	4	no	—
428	C₂²⋊C₄	—	4	8	no	—
429	C₂²⋊C₄	C₂×D₄×C₆₁	1	16	yes	—
430	C₄²	—	2	8	no	—
431	C₄²	—	4	4	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	4	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	2	8	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	4	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	4	no	—
444	C₂³	—	4	4	no	—
445	C₂³	—	4	4	no	—
446	C₂³	—	4	4	no	—
447	C₂³	—	8	8	no	—
448	C₂³	—	8	8	no	—
449	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
450	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
451	C₂³	2₋¹⁺⁴×C₆₁	1	4	yes	—
452	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
453	Q₈	—	4	16	no	—
454	Q₈	—	8	4	no	—
455	Q₈	—	8	4	no	—
456	D₄	—	4	16	no	—
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	8	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	2	8	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	8	4	no	—
478	C₂×C₄	—	8	4	no	—
479	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
480	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
481	C₂×C₄	H(5,𝔽₂)×C₆₁	1	4	yes	—
482	C₂²	—	2	8	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	2	4	no	—
487	C₂²	—	2	4	no	—
488	C₂²	—	4	8	no	—
489	C₂²	—	4	8	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	8	8	no	—
494	C₂²	—	8	8	no	—
495	C₂²	C₆₁×#536	1	4	yes	—
496	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
497	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
498	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
499	C₂²	C₆₁×#585	1	2	yes	—
500	C₄	—	2	4	no	—
501	C₄	—	2	4	no	—
502	C₄	—	2	4	no	—
503	C₄	—	4	8	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	4	no	—
507	C₄	—	4	4	no	—
508	C₂	—	2	4	no	—
509	C₂	—	4	4	no	—
510	C₂	—	8	2	no	—
511	C₂	C₂×C₆₁×#536	1	1	yes	characteristic
512	C₂	C₆₁×#3484	1	1	yes	characteristic
513	C₂	C₆₁×#3485	1	1	yes	characteristic
514	C₂	C₆₁×#3561	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
prime radical	C₂³×D₄×C₆₁	C₂²
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×#543	C₂	semidirect
3. C₆₁×#2855	C₂	semidirect
4. C₆₁×#2700	C₂	semidirect
5. C₆₁×#2674	C₂	semidirect
6. C₆₁×#2626	C₂	semidirect
7. C₆₁×#2561	C₂	semidirect
8. C₆₁×#2483	C₂	semidirect
9. C₆₁×#2434	C₂	semidirect
11. C₆₁×#2312	C₂	semidirect
15. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
21. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
22. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
29. C₆₁×#399	C₂²	semidirect
30. C₆₁×#397	C₂²	semidirect
31. C₆₁×#397	C₂²	semidirect
32. C₆₁×#396	C₂²	semidirect
33. C₆₁×#395	C₂²	semidirect
35. C₆₁×#393	C₂²	semidirect
36. C₆₁×#393	C₂²	semidirect
37. C₆₁×#391	C₂²	semidirect
38. C₆₁×#391	C₂²	semidirect
39. C₆₁×#389	C₂²	semidirect
40. C₆₁×#388	C₂²	semidirect
41. C₆₁×#388	C₂²	semidirect
42. C₆₁×#387	C₂²	semidirect
46. C₆₁×#385	C₂²	semidirect
48. C₆₁×#381	C₂²	semidirect
224. #36966	C₆₁	direct (N × H)
251. C₂×#543	C₂×C₆₁	semidirect
253. #2855	C₂×C₆₁	semidirect
254. #2700	C₂×C₆₁	semidirect
255. #2674	C₂×C₆₁	semidirect
256. #2626	C₂×C₆₁	semidirect
257. #2561	C₂×C₆₁	semidirect
258. #2483	C₂×C₆₁	semidirect
259. #2434	C₂×C₆₁	semidirect
261. #2312	C₂×C₆₁	semidirect
272. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
278. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
279. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
286. #399	C₂²×C₆₁	semidirect
287. #397	C₂²×C₆₁	semidirect
288. #397	C₂²×C₆₁	semidirect
289. #396	C₂²×C₆₁	semidirect
290. #395	C₂²×C₆₁	semidirect
292. #393	C₂²×C₆₁	semidirect
293. #393	C₂²×C₆₁	semidirect
294. #391	C₂²×C₆₁	semidirect
295. #391	C₂²×C₆₁	semidirect
296. #389	C₂²×C₆₁	semidirect
297. #388	C₂²×C₆₁	semidirect
298. #388	C₂²×C₆₁	semidirect
299. #387	C₂²×C₆₁	semidirect
303. #385	C₂²×C₆₁	semidirect
305. #381	C₂²×C₆₁	semidirect
310. C₆₁	#36966	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#543	2
C₂²×#124×C₆₁	2
C₆₁×#2855	2
C₆₁×#2700	2
C₆₁×#2674	2
C₆₁×#2626	2
C₆₁×#2561	2
C₆₁×#2483	2
C₆₁×#2434	2
C₆₁×#2405	2
C₆₁×#2312	2
#36966	61

Subgroups — C61×#36966 #29540399

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#36966 #29540399