Subgroups — C₆₁×#36967 #29540400

Order 15616.

2926 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#534	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#124×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2854	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2710	C₂	1	8	yes	maximal, complemented
5	C₆₁×#2670	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×#2436	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2405	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2403	C₂	1	2	yes	maximal, complemented
11	C₆₁×#2312	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
13	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₆₁	C₂²	1	2	yes	—
15	C₆₁×#534	—	2	8	no	—
16	C₂×#124×C₆₁	—	2	8	no	—
17	C₂×#124×C₆₁	C₂²	1	8	yes	complemented
18	C₂×#124×C₆₁	C₂²	1	4	yes	complemented
19	C₂×#123×C₆₁	C₂²	1	4	yes	complemented
20	C₂×#123×C₆₁	C₂²	1	4	yes	complemented
21	C₂×#121×C₆₁	C₂²	1	2	yes	—
22	C₂×#121×C₆₁	C₂²	1	2	yes	—
23	C₂×#120×C₆₁	C₂²	1	4	yes	complemented
24	C₂×#120×C₆₁	C₂²	1	4	yes	complemented
25	C₂×#120×C₆₁	C₂²	1	4	yes	complemented
26	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic, complemented
31	C₆₁×#399	C₂²	1	4	yes	complemented
32	C₆₁×#397	C₂²	1	4	yes	complemented
33	C₆₁×#394	C₂²	1	8	yes	complemented
34	C₆₁×#394	C₂²	1	8	yes	complemented
35	C₆₁×#393	C₂²	1	8	yes	complemented
36	C₆₁×#392	C₂²	1	8	yes	—
37	C₆₁×#392	C₂²	1	4	yes	complemented
38	C₆₁×#392	C₂²	1	4	yes	complemented
39	C₆₁×#391	C₂²	1	4	yes	complemented
40	C₆₁×#390	C₂²	1	8	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×#388	C₂²	1	8	yes	complemented
45	C₆₁×#386	C₂²	1	4	yes	complemented
46	C₆₁×#386	C₂²	1	4	yes	complemented
47	C₆₁×#386	C₂²	1	4	yes	complemented
48	C₆₁×#385	C₂²	1	4	yes	complemented
49	C₆₁×#380	C₂²	1	2	yes	complemented
50	C₆₁×#379	C₂²	1	2	yes	—
51	C₆₁×#379	C₂²	1	4	yes	complemented
52	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
53	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
54	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
55	C₂⁵×C₆₁	C₂³	1	2	yes	—
56	C₂²×Q₈×C₆₁	—	2	4	no	—
57	C₂²×Q₈×C₆₁	—	4	4	no	—
58	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
59	C₂²×D₄×C₆₁	—	2	8	no	—
60	C₂²×D₄×C₆₁	—	2	4	no	—
61	C₂²×D₄×C₆₁	—	4	4	no	—
62	C₂²×D₄×C₆₁	—	4	8	no	—
63	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
64	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
65	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
66	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
67	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
68	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
69	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
72	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
75	#124×C₆₁	—	2	32	no	—
76	#124×C₆₁	—	4	8	no	—
77	#123×C₆₁	—	2	16	no	—
78	#123×C₆₁	—	4	8	no	—
79	#121×C₆₁	—	2	8	no	—
80	#121×C₆₁	—	2	8	no	—
81	#120×C₆₁	—	2	16	no	—
82	#120×C₆₁	—	4	8	no	—
83	#120×C₆₁	—	4	8	no	—
84	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
88	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
90	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
91	C₂×C₂²⋊C₄×C₆₁	D₄	1	8	yes	complemented
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	8	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	4	yes	—
98	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
102	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
103	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
104	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
105	C₂×C₄²×C₆₁	—	2	4	no	—
106	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
107	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
108	#95×C₆₁	C₂³	1	4	yes	—
109	#95×C₆₁	C₂³	1	4	yes	—
110	#95×C₆₁	C₂³	1	8	yes	—
111	#95×C₆₁	C₂³	1	8	yes	—
112	C₂⁴×C₆₁	—	2	4	no	—
113	C₂⁴×C₆₁	—	2	2	no	—
114	C₂⁴×C₆₁	—	2	4	no	—
115	C₂⁴×C₆₁	—	2	4	no	—
116	C₂⁴×C₆₁	—	4	2	no	—
117	C₂⁴×C₆₁	—	4	2	no	—
118	C₂⁴×C₆₁	—	4	4	no	—
119	C₂⁴×C₆₁	—	4	2	no	—
120	C₂⁴×C₆₁	—	4	2	no	—
121	C₂⁴×C₆₁	—	4	4	no	—
122	C₂⁴×C₆₁	—	4	4	no	—
123	C₂⁴×C₆₁	C₂×D₄	1	4	yes	—
124	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
125	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
126	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
127	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
128	C₂×Q₈×C₆₁	—	2	8	no	—
129	C₂×Q₈×C₆₁	—	2	8	no	—
130	C₂×Q₈×C₆₁	—	4	4	no	—
131	C₂×Q₈×C₆₁	—	4	16	no	—
132	C₂×D₄×C₆₁	—	2	8	no	—
133	C₂×D₄×C₆₁	—	2	8	no	—
134	C₂×D₄×C₆₁	—	2	8	no	—
135	C₂×D₄×C₆₁	—	2	8	no	—
136	C₂×D₄×C₆₁	—	2	8	no	—
137	C₂×D₄×C₆₁	—	2	4	no	—
138	C₂×D₄×C₆₁	—	2	4	no	—
139	C₂×D₄×C₆₁	—	2	8	no	—
140	C₂×D₄×C₆₁	—	4	4	no	—
141	C₂×D₄×C₆₁	—	4	4	no	—
142	C₂×D₄×C₆₁	—	4	4	no	—
143	C₂×D₄×C₆₁	—	4	16	no	—
144	C₂×D₄×C₆₁	—	4	8	no	—
145	C₂×D₄×C₆₁	—	4	8	no	—
146	C₂×D₄×C₆₁	—	4	4	no	—
147	C₂×D₄×C₆₁	—	4	4	no	—
148	C₂×D₄×C₆₁	—	4	8	no	—
149	C₂×D₄×C₆₁	—	4	32	no	—
150	C₂²×C₄×C₆₁	—	2	2	no	—
151	C₂²×C₄×C₆₁	—	2	4	no	—
152	C₂²×C₄×C₆₁	—	2	2	no	—
153	C₂²×C₄×C₆₁	—	2	2	no	—
154	C₂²×C₄×C₆₁	—	2	4	no	—
155	C₂²×C₄×C₆₁	—	2	4	no	—
156	C₂²×C₄×C₆₁	—	4	2	no	—
157	C₂²×C₄×C₆₁	—	4	4	no	—
158	C₂²×C₄×C₆₁	—	4	2	no	—
159	C₂²×C₄×C₆₁	—	4	2	no	—
160	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
163	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
169	C₄⋊C₄×C₆₁	—	2	4	no	—
170	C₄⋊C₄×C₆₁	—	2	4	no	—
171	C₄⋊C₄×C₆₁	—	4	4	no	—
172	C₄⋊C₄×C₆₁	—	4	8	no	—
173	C₂²⋊C₄×C₆₁	—	2	8	no	—
174	C₂²⋊C₄×C₆₁	—	2	8	no	—
175	C₂²⋊C₄×C₆₁	—	2	8	no	—
176	C₂²⋊C₄×C₆₁	—	2	8	no	—
177	C₂²⋊C₄×C₆₁	—	2	8	no	—
178	C₂²⋊C₄×C₆₁	—	2	8	no	—
179	C₂²⋊C₄×C₆₁	—	2	16	no	—
180	C₂²⋊C₄×C₆₁	—	4	4	no	—
181	C₂²⋊C₄×C₆₁	—	4	4	no	—
182	C₂²⋊C₄×C₆₁	—	4	8	no	—
183	C₂²⋊C₄×C₆₁	—	4	8	no	—
184	C₂²⋊C₄×C₆₁	—	4	8	no	—
185	C₂²⋊C₄×C₆₁	C₂×D₄	1	16	yes	—
186	C₄²×C₆₁	—	2	8	no	—
187	C₄²×C₆₁	—	4	4	no	—
188	C₂³×C₆₁	—	2	2	no	—
189	C₂³×C₆₁	—	2	2	no	—
190	C₂³×C₆₁	—	2	4	no	—
191	C₂³×C₆₁	—	2	4	no	—
192	C₂³×C₆₁	—	2	4	no	—
193	C₂³×C₆₁	—	2	8	no	—
194	C₂³×C₆₁	—	2	2	no	—
195	C₂³×C₆₁	—	2	4	no	—
196	C₂³×C₆₁	—	2	8	no	—
197	C₂³×C₆₁	—	2	4	no	—
198	C₂³×C₆₁	—	2	4	no	—
199	C₂³×C₆₁	—	2	4	no	—
200	C₂³×C₆₁	—	2	4	no	—
201	C₂³×C₆₁	—	2	8	no	—
202	C₂³×C₆₁	—	2	4	no	—
203	C₂³×C₆₁	—	4	4	no	—
204	C₂³×C₆₁	—	4	4	no	—
205	C₂³×C₆₁	—	4	4	no	—
206	C₂³×C₆₁	—	4	8	no	—
207	C₂³×C₆₁	—	4	4	no	—
208	C₂³×C₆₁	—	4	4	no	—
209	C₂³×C₆₁	—	8	8	no	—
210	C₂³×C₆₁	—	8	8	no	—
211	C₂³×C₆₁	—	8	4	no	—
212	C₂³×C₆₁	—	8	4	no	—
213	C₂³×C₆₁	—	8	16	no	—
214	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
215	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
216	C₂³×C₆₁	H(5,𝔽₂)	1	4	yes	—
217	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
218	Q₈×C₆₁	—	4	16	no	—
219	D₄×C₆₁	—	4	16	no	—
220	D₄×C₆₁	—	4	16	no	—
221	D₄×C₆₁	—	4	16	no	—
222	D₄×C₆₁	—	8	4	no	—
223	D₄×C₆₁	—	8	4	no	—
224	D₄×C₆₁	—	8	16	no	—
225	C₂×C₄×C₆₁	—	2	8	no	—
226	C₂×C₄×C₆₁	—	2	2	no	—
227	C₂×C₄×C₆₁	—	2	4	no	—
228	C₂×C₄×C₆₁	—	2	2	no	—
229	C₂×C₄×C₆₁	—	2	4	no	—
230	C₂×C₄×C₆₁	—	2	2	no	—
231	C₂×C₄×C₆₁	—	2	2	no	—
232	C₂×C₄×C₆₁	—	2	4	no	—
233	C₂×C₄×C₆₁	—	2	8	no	—
234	C₂×C₄×C₆₁	—	2	8	no	—
235	C₂×C₄×C₆₁	—	2	4	no	—
236	C₂×C₄×C₆₁	—	2	4	no	—
237	C₂×C₄×C₆₁	—	2	4	no	—
238	C₂×C₄×C₆₁	—	2	4	no	—
239	C₂×C₄×C₆₁	—	2	8	no	—
240	C₂×C₄×C₆₁	—	4	4	no	—
241	C₂×C₄×C₆₁	—	4	4	no	—
242	C₂×C₄×C₆₁	—	4	8	no	—
243	C₂×C₄×C₆₁	—	4	4	no	—
244	C₂×C₄×C₆₁	—	4	4	no	—
245	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
246	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₆₁	H(5,𝔽₂)	1	4	yes	—
248	#36967	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
249	C₂²×C₆₁	—	2	2	no	—
250	C₂²×C₆₁	—	2	2	no	—
251	C₂²×C₆₁	—	2	8	no	—
252	C₂²×C₆₁	—	2	4	no	—
253	C₂²×C₆₁	—	2	4	no	—
254	C₂²×C₆₁	—	2	4	no	—
255	C₂²×C₆₁	—	4	8	no	—
256	C₂²×C₆₁	—	4	4	no	—
257	C₂²×C₆₁	—	4	2	no	—
258	C₂²×C₆₁	—	4	2	no	—
259	C₂²×C₆₁	—	4	4	no	—
260	C₂²×C₆₁	—	4	4	no	—
261	C₂²×C₆₁	—	4	2	no	—
262	C₂²×C₆₁	—	4	8	no	—
263	C₂²×C₆₁	—	4	8	no	—
264	C₂²×C₆₁	—	4	8	no	—
265	C₂²×C₆₁	—	8	8	no	—
266	C₂²×C₆₁	—	8	8	no	—
267	C₂²×C₆₁	—	8	16	no	—
268	C₂²×C₆₁	#535	1	4	yes	—
269	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
270	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
271	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
272	C₂²×C₆₁	#585	1	2	yes	—
273	C₄×C₆₁	—	2	4	no	—
274	C₄×C₆₁	—	2	4	no	—
275	C₄×C₆₁	—	2	4	no	—
276	C₄×C₆₁	—	4	2	no	—
277	C₄×C₆₁	—	4	4	no	—
278	C₄×C₆₁	—	4	2	no	—
279	C₄×C₆₁	—	4	8	no	—
280	C₂×#534	C₂×C₆₁	1	1	yes	characteristic, complemented
281	C₂²×#124	C₂×C₆₁	1	1	yes	characteristic, complemented
282	#2854	C₂×C₆₁	1	2	yes	complemented
283	#2710	C₂×C₆₁	1	8	yes	complemented
284	#2670	C₂×C₆₁	1	8	yes	complemented
285	#2617	C₂×C₆₁	1	2	yes	complemented
286	#2539	C₂×C₆₁	1	2	yes	complemented
287	#2436	C₂×C₆₁	1	2	yes	complemented
288	#2405	C₂×C₆₁	1	2	yes	complemented
289	#2403	C₂×C₆₁	1	2	yes	complemented
290	#2312	C₂×C₆₁	1	1	yes	characteristic, complemented
291	C₂×C₆₁	—	2	4	no	—
292	C₂×C₆₁	—	4	4	no	—
293	C₂×C₆₁	—	8	4	no	—
294	C₂×C₆₁	—	8	2	no	—
295	C₂×C₆₁	C₂×#535	1	1	yes	characteristic
296	C₂×C₆₁	#3484	1	1	yes	characteristic
297	C₂×C₆₁	#3485	1	1	yes	characteristic
298	C₂×C₆₁	#3558	1	4	yes	—
299	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
300	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
301	C₂³×D₄	C₂²×C₆₁	1	2	yes	—
302	#534	—	2	8	no	—
303	C₂×#124	—	2	8	no	—
304	C₂×#124	C₂²×C₆₁	1	8	yes	complemented
305	C₂×#124	C₂²×C₆₁	1	4	yes	complemented
306	C₂×#123	C₂²×C₆₁	1	4	yes	complemented
307	C₂×#123	C₂²×C₆₁	1	4	yes	complemented
308	C₂×#121	C₂²×C₆₁	1	2	yes	—
309	C₂×#121	C₂²×C₆₁	1	2	yes	—
310	C₂×#120	C₂²×C₆₁	1	4	yes	complemented
311	C₂×#120	C₂²×C₆₁	1	4	yes	complemented
312	C₂×#120	C₂²×C₆₁	1	4	yes	complemented
313	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
314	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
315	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
316	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
317	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic, complemented
318	#399	C₂²×C₆₁	1	4	yes	complemented
319	#397	C₂²×C₆₁	1	4	yes	complemented
320	#394	C₂²×C₆₁	1	8	yes	complemented
321	#394	C₂²×C₆₁	1	8	yes	complemented
322	#393	C₂²×C₆₁	1	8	yes	complemented
323	#392	C₂²×C₆₁	1	8	yes	—
324	#392	C₂²×C₆₁	1	4	yes	complemented
325	#392	C₂²×C₆₁	1	4	yes	complemented
326	#391	C₂²×C₆₁	1	4	yes	complemented
327	#390	C₂²×C₆₁	1	4	yes	complemented
328	#390	C₂²×C₆₁	1	8	yes	complemented
329	#389	C₂²×C₆₁	1	4	yes	complemented
330	#388	C₂²×C₆₁	1	8	yes	complemented
331	#388	C₂²×C₆₁	1	8	yes	complemented
332	#386	C₂²×C₆₁	1	4	yes	complemented
333	#386	C₂²×C₆₁	1	4	yes	complemented
334	#386	C₂²×C₆₁	1	4	yes	complemented
335	#385	C₂²×C₆₁	1	4	yes	complemented
336	#380	C₂²×C₆₁	1	2	yes	complemented
337	#379	C₂²×C₆₁	1	2	yes	—
338	#379	C₂²×C₆₁	1	4	yes	complemented
339	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
340	C₆₁	#36967	1	1	yes	characteristic, direct product factor, Sylow
341	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
342	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
343	C₂⁵	C₂³×C₆₁	1	2	yes	—
344	C₂²×Q₈	—	2	4	no	—
345	C₂²×Q₈	—	4	4	no	—
346	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
347	C₂²×D₄	—	2	4	no	—
348	C₂²×D₄	—	2	8	no	—
349	C₂²×D₄	—	4	4	no	—
350	C₂²×D₄	—	4	8	no	—
351	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
352	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
353	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
354	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
355	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
356	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
357	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
360	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
361	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
362	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
363	#124	—	2	32	no	—
364	#124	—	4	8	no	—
365	#123	—	2	16	no	—
366	#123	—	4	8	no	—
367	#121	—	2	8	no	—
368	#121	—	2	8	no	—
369	#120	—	2	16	no	—
370	#120	—	4	8	no	—
371	#120	—	4	8	no	—
372	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
374	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
375	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
376	C₂×C₂²⋊C₄	—	2	4	no	—
377	C₂×C₂²⋊C₄	—	2	4	no	—
378	C₂×C₂²⋊C₄	—	2	4	no	—
379	C₂×C₂²⋊C₄	D₄×C₆₁	1	8	yes	complemented
380	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
393	C₂×C₄²	—	2	4	no	—
394	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
395	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
396	#95	C₂³×C₆₁	1	4	yes	—
397	#95	C₂³×C₆₁	1	4	yes	—
398	#95	C₂³×C₆₁	1	8	yes	—
399	#95	C₂³×C₆₁	1	8	yes	—
400	C₂⁴	—	2	4	no	—
401	C₂⁴	—	2	2	no	—
402	C₂⁴	—	2	4	no	—
403	C₂⁴	—	2	4	no	—
404	C₂⁴	—	4	2	no	—
405	C₂⁴	—	4	2	no	—
406	C₂⁴	—	4	4	no	—
407	C₂⁴	—	4	2	no	—
408	C₂⁴	—	4	2	no	—
409	C₂⁴	—	4	4	no	—
410	C₂⁴	—	4	4	no	—
411	C₂⁴	C₂×D₄×C₆₁	1	4	yes	—
412	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
413	C₂⁴	C₂⁴×C₆₁	1	4	yes	—
414	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
415	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
416	C₂×Q₈	—	2	8	no	—
417	C₂×Q₈	—	2	8	no	—
418	C₂×Q₈	—	4	4	no	—
419	C₂×Q₈	—	4	16	no	—
420	C₂×D₄	—	2	8	no	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	8	no	—
423	C₂×D₄	—	2	8	no	—
424	C₂×D₄	—	2	8	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	8	no	—
428	C₂×D₄	—	4	4	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	—	4	4	no	—
431	C₂×D₄	—	4	16	no	—
432	C₂×D₄	—	4	8	no	—
433	C₂×D₄	—	4	8	no	—
434	C₂×D₄	—	4	4	no	—
435	C₂×D₄	—	4	4	no	—
436	C₂×D₄	—	4	8	no	—
437	C₂×D₄	—	4	32	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	—	4	2	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
449	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
451	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
453	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
454	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
455	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	4	8	no	—
460	C₄⋊C₄	—	4	4	no	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	—	2	8	no	—
464	C₂²⋊C₄	—	2	8	no	—
465	C₂²⋊C₄	—	2	8	no	—
466	C₂²⋊C₄	—	2	8	no	—
467	C₂²⋊C₄	—	2	16	no	—
468	C₂²⋊C₄	—	4	4	no	—
469	C₂²⋊C₄	—	4	8	no	—
470	C₂²⋊C₄	—	4	8	no	—
471	C₂²⋊C₄	—	4	8	no	—
472	C₂²⋊C₄	—	4	4	no	—
473	C₂²⋊C₄	C₂×D₄×C₆₁	1	16	yes	—
474	C₄²	—	2	8	no	—
475	C₄²	—	4	4	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	2	8	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	8	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	2	4	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	8	no	—
491	C₂³	—	4	4	no	—
492	C₂³	—	4	4	no	—
493	C₂³	—	4	4	no	—
494	C₂³	—	4	8	no	—
495	C₂³	—	4	4	no	—
496	C₂³	—	4	4	no	—
497	C₂³	—	8	8	no	—
498	C₂³	—	8	8	no	—
499	C₂³	—	8	4	no	—
500	C₂³	—	8	4	no	—
501	C₂³	—	8	16	no	—
502	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
503	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
504	C₂³	H(5,𝔽₂)×C₆₁	1	4	yes	—
505	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
506	Q₈	—	4	16	no	—
507	D₄	—	4	16	no	—
508	D₄	—	4	16	no	—
509	D₄	—	4	16	no	—
510	D₄	—	8	4	no	—
511	D₄	—	8	4	no	—
512	D₄	—	8	16	no	—
513	C₂×C₄	—	2	8	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	2	8	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	8	no	—
528	C₂×C₄	—	4	4	no	—
529	C₂×C₄	—	4	4	no	—
530	C₂×C₄	—	4	8	no	—
531	C₂×C₄	—	4	4	no	—
532	C₂×C₄	—	4	4	no	—
533	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
534	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
535	C₂×C₄	H(5,𝔽₂)×C₆₁	1	4	yes	—
536	C₂²	—	2	8	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	2	4	no	—
541	C₂²	—	2	4	no	—
542	C₂²	—	4	8	no	—
543	C₂²	—	4	8	no	—
544	C₂²	—	4	8	no	—
545	C₂²	—	4	8	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	8	8	no	—
553	C₂²	—	8	8	no	—
554	C₂²	—	8	16	no	—
555	C₂²	C₆₁×#535	1	4	yes	—
556	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
557	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
558	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
559	C₂²	C₆₁×#585	1	2	yes	—
560	C₄	—	2	4	no	—
561	C₄	—	2	4	no	—
562	C₄	—	2	4	no	—
563	C₄	—	4	8	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	4	no	—
566	C₄	—	4	2	no	—
567	C₂	—	2	4	no	—
568	C₂	—	4	4	no	—
569	C₂	—	8	2	no	—
570	C₂	—	8	4	no	—
571	C₂	C₂×C₆₁×#535	1	1	yes	characteristic
572	C₂	C₆₁×#3484	1	1	yes	characteristic
573	C₂	C₆₁×#3485	1	1	yes	characteristic
574	C₂	C₆₁×#3558	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×#534	C₂	semidirect
2. C₂²×#124×C₆₁	C₂	semidirect
3. C₆₁×#2854	C₂	semidirect
4. C₆₁×#2710	C₂	semidirect
5. C₆₁×#2670	C₂	semidirect
6. C₆₁×#2617	C₂	semidirect
7. C₆₁×#2539	C₂	semidirect
8. C₆₁×#2436	C₂	semidirect
9. C₆₁×#2405	C₂	semidirect
10. C₆₁×#2403	C₂	semidirect
11. C₆₁×#2312	C₂	semidirect
12. C₂³×Q₈×C₆₁	C₂²	semidirect
17. C₂×#124×C₆₁	C₂²	semidirect
18. C₂×#124×C₆₁	C₂²	semidirect
19. C₂×#123×C₆₁	C₂²	semidirect
20. C₂×#123×C₆₁	C₂²	semidirect
23. C₂×#120×C₆₁	C₂²	semidirect
24. C₂×#120×C₆₁	C₂²	semidirect
25. C₂×#120×C₆₁	C₂²	semidirect
28. C₂²×C₂²⋊C₄×C₆₁	C₂²	semidirect
29. C₂²×C₂²⋊C₄×C₆₁	C₂²	semidirect
30. C₂²×C₄²×C₆₁	C₂²	semidirect
31. C₆₁×#399	C₂²	semidirect
32. C₆₁×#397	C₂²	semidirect
33. C₆₁×#394	C₂²	semidirect
34. C₆₁×#394	C₂²	semidirect
35. C₆₁×#393	C₂²	semidirect
37. C₆₁×#392	C₂²	semidirect
38. C₆₁×#392	C₂²	semidirect
39. C₆₁×#391	C₂²	semidirect
40. C₆₁×#390	C₂²	semidirect
41. C₆₁×#390	C₂²	semidirect
42. C₆₁×#389	C₂²	semidirect
43. C₆₁×#388	C₂²	semidirect
44. C₆₁×#388	C₂²	semidirect
45. C₆₁×#386	C₂²	semidirect
46. C₆₁×#386	C₂²	semidirect
47. C₆₁×#386	C₂²	semidirect
48. C₆₁×#385	C₂²	semidirect
49. C₆₁×#380	C₂²	semidirect
51. C₆₁×#379	C₂²	semidirect
52. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
91. C₂×C₂²⋊C₄×C₆₁	D₄	semidirect
248. #36967	C₆₁	direct (N × H)
280. C₂×#534	C₂×C₆₁	semidirect
281. C₂²×#124	C₂×C₆₁	semidirect
282. #2854	C₂×C₆₁	semidirect
283. #2710	C₂×C₆₁	semidirect
284. #2670	C₂×C₆₁	semidirect
285. #2617	C₂×C₆₁	semidirect
286. #2539	C₂×C₆₁	semidirect
287. #2436	C₂×C₆₁	semidirect
288. #2405	C₂×C₆₁	semidirect
289. #2403	C₂×C₆₁	semidirect
290. #2312	C₂×C₆₁	semidirect
299. C₂³×Q₈	C₂²×C₆₁	semidirect
304. C₂×#124	C₂²×C₆₁	semidirect
305. C₂×#124	C₂²×C₆₁	semidirect
306. C₂×#123	C₂²×C₆₁	semidirect
307. C₂×#123	C₂²×C₆₁	semidirect
310. C₂×#120	C₂²×C₆₁	semidirect
311. C₂×#120	C₂²×C₆₁	semidirect
312. C₂×#120	C₂²×C₆₁	semidirect
315. C₂²×C₂²⋊C₄	C₂²×C₆₁	semidirect
316. C₂²×C₂²⋊C₄	C₂²×C₆₁	semidirect
317. C₂²×C₄²	C₂²×C₆₁	semidirect
318. #399	C₂²×C₆₁	semidirect
319. #397	C₂²×C₆₁	semidirect
320. #394	C₂²×C₆₁	semidirect
321. #394	C₂²×C₆₁	semidirect
322. #393	C₂²×C₆₁	semidirect
324. #392	C₂²×C₆₁	semidirect
325. #392	C₂²×C₆₁	semidirect
326. #391	C₂²×C₆₁	semidirect
327. #390	C₂²×C₆₁	semidirect
328. #390	C₂²×C₆₁	semidirect
329. #389	C₂²×C₆₁	semidirect
330. #388	C₂²×C₆₁	semidirect
331. #388	C₂²×C₆₁	semidirect
332. #386	C₂²×C₆₁	semidirect
333. #386	C₂²×C₆₁	semidirect
334. #386	C₂²×C₆₁	semidirect
335. #385	C₂²×C₆₁	semidirect
336. #380	C₂²×C₆₁	semidirect
338. #379	C₂²×C₆₁	semidirect
339. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
340. C₆₁	#36967	direct (N × H)
379. C₂×C₂²⋊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×#534	2
C₂²×#124×C₆₁	2
C₆₁×#2854	2
C₆₁×#2710	2
C₆₁×#2670	2
C₆₁×#2617	2
C₆₁×#2539	2
C₆₁×#2436	2
C₆₁×#2405	2
C₆₁×#2403	2
C₆₁×#2312	2
#36967	61

Subgroups — C61×#36967 #29540400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#36967 #29540400