Subgroups — C₆₁×#24660 #29528093

Order 15616.

876 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#432	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2857	C₂	1	1	yes	maximal, characteristic
4	C₄×C₂²⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2035	C₂	1	2	yes	maximal
6	C₆₁×#2001	C₂	1	2	yes	maximal
7	C₆₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1971	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1935	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#462	—	2	4	no	—
19	C₆₁×#432	—	2	4	no	—
20	C₂×#106×C₆₁	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#103×C₆₁	C₂²	1	2	yes	—
24	C₂×#103×C₆₁	C₂²	1	2	yes	—
25	C₂×#103×C₆₁	C₂²	1	2	yes	—
26	C₂×#103×C₆₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
28	C₂×#97×C₆₁	C₂²	1	2	yes	—
29	C₆₁×#391	C₂²	1	1	yes	characteristic
30	C₆₁×#391	C₂²	1	2	yes	—
31	C₆₁×#389	—	2	1	no	—
32	C₆₁×#389	—	2	1	no	—
33	C₆₁×#389	C₂²	1	1	yes	characteristic
34	C₆₁×#387	—	2	1	no	—
35	C₆₁×#385	—	2	1	no	—
36	C₆₁×#384	C₂²	1	1	yes	characteristic
37	C₆₁×#380	—	2	1	no	—
38	C₆₁×#380	—	2	1	no	—
39	C₆₁×#380	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
41	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
42	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
43	C₆₁×#340	C₂²	1	2	yes	—
44	C₆₁×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
46	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
50	C₂×Q₁₆×C₆₁	—	2	4	no	—
51	C₂×Q₁₆×C₆₁	—	2	4	no	—
52	C₂×Q₁₆×C₆₁	—	4	2	no	—
53	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
54	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₆₁	—	2	2	no	—
56	C₄⋊Q₈×C₆₁	—	2	2	no	—
57	C₂²⋊Q₈×C₆₁	—	2	2	no	—
58	C₂²⋊Q₈×C₆₁	—	2	2	no	—
59	C₂²⋊Q₈×C₆₁	—	4	2	no	—
60	C₂²⋊Q₈×C₆₁	—	4	2	no	—
61	C₄×Q₈×C₆₁	—	2	2	no	—
62	C₄×Q₈×C₆₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
78	C₂×C₄²×C₆₁	—	2	2	no	—
79	C₂×C₄²×C₆₁	—	2	2	no	—
80	C₂×C₄²×C₆₁	—	2	1	no	—
81	C₂×C₄²×C₆₁	—	2	1	no	—
82	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
86	#106×C₆₁	—	4	2	no	—
87	C₄⋊C₈×C₆₁	—	2	2	no	—
88	C₄⋊C₈×C₆₁	D₄	1	4	yes	—
89	#103×C₆₁	—	2	4	no	—
90	#103×C₆₁	—	2	4	no	—
91	#103×C₆₁	—	4	2	no	—
92	#103×C₆₁	—	4	2	no	—
93	C₂²⋊C₈×C₆₁	—	2	4	no	—
94	#97×C₆₁	—	2	4	no	—
95	#95×C₆₁	—	2	1	no	—
96	#95×C₆₁	—	2	1	no	—
97	#95×C₆₁	—	2	1	no	—
98	#95×C₆₁	—	2	1	no	—
99	#95×C₆₁	—	2	1	no	—
100	#95×C₆₁	—	2	2	no	—
101	#95×C₆₁	—	2	2	no	—
102	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
103	C₂×Q₈×C₆₁	—	2	1	no	—
104	C₂×Q₈×C₆₁	—	2	1	no	—
105	C₂×Q₈×C₆₁	—	2	2	no	—
106	C₂×Q₈×C₆₁	—	2	1	no	—
107	C₂×Q₈×C₆₁	—	2	2	no	—
108	C₂×Q₈×C₆₁	—	2	2	no	—
109	C₂×Q₈×C₆₁	—	2	2	no	—
110	C₂×Q₈×C₆₁	—	2	1	no	—
111	C₂×Q₈×C₆₁	—	2	1	no	—
112	C₂×Q₈×C₆₁	—	2	2	no	—
113	C₂×Q₈×C₆₁	—	2	2	no	—
114	C₂×Q₈×C₆₁	#41	1	2	yes	—
115	C₂²×C₄×C₆₁	—	2	2	no	—
116	C₂²×C₄×C₆₁	—	2	1	no	—
117	C₂²×C₄×C₆₁	—	2	1	no	—
118	C₂²×C₄×C₆₁	—	2	2	no	—
119	C₂²×C₄×C₆₁	—	2	2	no	—
120	C₂²×C₄×C₆₁	—	2	2	no	—
121	C₂²×C₄×C₆₁	—	2	2	no	—
122	C₂²×C₄×C₆₁	—	2	1	no	—
123	C₂²×C₄×C₆₁	—	2	1	no	—
124	C₂²×C₄×C₆₁	—	2	1	no	—
125	C₂²×C₄×C₆₁	—	2	1	no	—
126	C₂²×C₄×C₆₁	—	2	1	no	—
127	C₂²×C₄×C₆₁	—	2	1	no	—
128	C₂²×C₄×C₆₁	—	2	1	no	—
129	C₂²×C₄×C₆₁	—	2	1	no	—
130	C₂²×C₄×C₆₁	—	2	2	no	—
131	C₂²×C₄×C₆₁	—	2	2	no	—
132	C₂²×C₄×C₆₁	—	4	1	no	—
133	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
139	Q₁₆×C₆₁	—	4	8	no	—
140	C₂×C₈×C₆₁	—	2	2	no	—
141	C₂×C₈×C₆₁	—	2	2	no	—
142	C₂×C₈×C₆₁	—	2	2	no	—
143	C₂×C₈×C₆₁	—	2	2	no	—
144	C₂×C₈×C₆₁	—	2	2	no	—
145	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
146	C₄⋊C₄×C₆₁	—	2	4	no	—
147	C₄⋊C₄×C₆₁	—	2	1	no	—
148	C₄⋊C₄×C₆₁	—	2	1	no	—
149	C₄⋊C₄×C₆₁	—	2	1	no	—
150	C₄⋊C₄×C₆₁	—	2	1	no	—
151	C₄⋊C₄×C₆₁	—	2	2	no	—
152	C₄⋊C₄×C₆₁	—	2	1	no	—
153	C₄⋊C₄×C₆₁	—	2	2	no	—
154	C₄⋊C₄×C₆₁	—	4	2	no	—
155	C₄⋊C₄×C₆₁	—	4	2	no	—
156	C₄⋊C₄×C₆₁	—	4	4	no	—
157	C₄⋊C₄×C₆₁	—	4	2	no	—
158	C₄⋊C₄×C₆₁	—	4	2	no	—
159	C₄⋊C₄×C₆₁	—	4	2	no	—
160	C₄⋊C₄×C₆₁	—	4	2	no	—
161	C₄⋊C₄×C₆₁	#41	1	2	yes	—
162	C₂²⋊C₄×C₆₁	—	2	4	no	—
163	C₂²⋊C₄×C₆₁	—	4	4	no	—
164	C₂²⋊C₄×C₆₁	—	4	2	no	—
165	C₄²×C₆₁	—	2	2	no	—
166	C₄²×C₆₁	—	2	2	no	—
167	C₄²×C₆₁	—	2	1	no	—
168	C₄²×C₆₁	—	2	1	no	—
169	C₄²×C₆₁	—	4	2	no	—
170	C₄²×C₆₁	—	4	2	no	—
171	C₄²×C₆₁	C₂×D₄	1	2	yes	—
172	C₄²×C₆₁	#41	1	2	yes	—
173	C₂³×C₆₁	—	2	1	no	—
174	C₂³×C₆₁	—	2	1	no	—
175	C₂³×C₆₁	—	2	1	no	—
176	C₂³×C₆₁	—	2	1	no	—
177	C₂³×C₆₁	—	2	1	no	—
178	C₂³×C₆₁	—	2	1	no	—
179	C₂³×C₆₁	#137	1	2	yes	—
180	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
181	Q₈×C₆₁	—	2	2	no	—
182	Q₈×C₆₁	—	2	2	no	—
183	Q₈×C₆₁	—	4	1	no	—
184	Q₈×C₆₁	—	4	1	no	—
185	Q₈×C₆₁	—	4	2	no	—
186	Q₈×C₆₁	—	4	2	no	—
187	Q₈×C₆₁	—	4	2	no	—
188	Q₈×C₆₁	—	4	2	no	—
189	C₂×C₄×C₆₁	—	2	1	no	—
190	C₂×C₄×C₆₁	—	2	1	no	—
191	C₂×C₄×C₆₁	—	2	1	no	—
192	C₂×C₄×C₆₁	—	2	1	no	—
193	C₂×C₄×C₆₁	—	2	1	no	—
194	C₂×C₄×C₆₁	—	2	2	no	—
195	C₂×C₄×C₆₁	—	2	2	no	—
196	C₂×C₄×C₆₁	—	2	1	no	—
197	C₂×C₄×C₆₁	—	2	1	no	—
198	C₂×C₄×C₆₁	—	2	1	no	—
199	C₂×C₄×C₆₁	—	2	1	no	—
200	C₂×C₄×C₆₁	—	2	1	no	—
201	C₂×C₄×C₆₁	—	2	1	no	—
202	C₂×C₄×C₆₁	—	4	4	no	—
203	C₂×C₄×C₆₁	—	4	1	no	—
204	C₂×C₄×C₆₁	—	4	1	no	—
205	C₂×C₄×C₆₁	—	4	1	no	—
206	C₂×C₄×C₆₁	—	4	1	no	—
207	C₂×C₄×C₆₁	—	4	1	no	—
208	C₂×C₄×C₆₁	—	4	1	no	—
209	C₂×C₄×C₆₁	—	4	1	no	—
210	C₂×C₄×C₆₁	—	4	1	no	—
211	C₂×C₄×C₆₁	—	4	4	no	—
212	C₂×C₄×C₆₁	—	4	1	no	—
213	C₂×C₄×C₆₁	—	4	2	no	—
214	C₂×C₄×C₆₁	—	4	2	no	—
215	C₂×C₄×C₆₁	—	4	2	no	—
216	C₂×C₄×C₆₁	—	4	2	no	—
217	C₂×C₄×C₆₁	—	4	1	no	—
218	C₂×C₄×C₆₁	—	4	1	no	—
219	C₂×C₄×C₆₁	—	4	1	no	—
220	C₂×C₄×C₆₁	—	4	1	no	—
221	C₂×C₄×C₆₁	—	4	2	no	—
222	C₂×C₄×C₆₁	—	4	2	no	—
223	C₂×C₄×C₆₁	—	4	1	no	—
224	C₂×C₄×C₆₁	#121	1	2	yes	—
225	C₂×C₄×C₆₁	#121	1	2	yes	—
226	C₂×C₄×C₆₁	#137	1	2	yes	—
227	C₂×C₄×C₆₁	#137	1	2	yes	—
228	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
234	C₈×C₆₁	—	2	4	no	—
235	C₈×C₆₁	—	4	2	no	—
236	#24660	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂²×C₆₁	—	2	2	no	—
238	C₂²×C₆₁	—	2	2	no	—
239	C₂²×C₆₁	—	2	2	no	—
240	C₂²×C₆₁	—	4	1	no	—
241	C₂²×C₆₁	—	4	1	no	—
242	C₂²×C₆₁	—	4	1	no	—
243	C₂²×C₆₁	—	4	1	no	—
244	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
245	C₂²×C₆₁	#525	1	1	yes	characteristic
246	C₂²×C₆₁	#535	1	1	yes	characteristic
247	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
248	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
249	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
250	C₂²×C₆₁	#575	1	1	yes	characteristic
251	C₄×C₆₁	—	2	2	no	—
252	C₄×C₆₁	—	4	2	no	—
253	C₄×C₆₁	—	4	1	no	—
254	C₄×C₆₁	—	4	2	no	—
255	C₄×C₆₁	—	4	1	no	—
256	C₄×C₆₁	—	4	1	no	—
257	C₄×C₆₁	—	8	2	no	—
258	C₄×C₆₁	—	8	2	no	—
259	C₄×C₆₁	—	8	1	no	—
260	C₄×C₆₁	—	8	1	no	—
261	C₄×C₆₁	#470	1	4	yes	—
262	C₄×C₆₁	#546	1	1	yes	characteristic
263	C₄×C₆₁	#550	1	1	yes	characteristic
264	C₄×C₆₁	#553	1	1	yes	characteristic
265	C₄×C₆₁	#555	1	1	yes	characteristic
266	C₂×#462	C₂×C₆₁	1	1	yes	characteristic, complemented
267	C₂×#432	C₂×C₆₁	1	1	yes	characteristic
268	#2857	C₂×C₆₁	1	1	yes	characteristic
269	C₄×C₂²⋊Q₈	C₂×C₆₁	1	1	yes	characteristic
270	#2035	C₂×C₆₁	1	2	yes	—
271	#2001	C₂×C₆₁	1	2	yes	—
272	#1981	C₂×C₆₁	1	1	yes	characteristic, complemented
273	#1971	C₂×C₆₁	1	2	yes	complemented
274	#1948	C₂×C₆₁	1	1	yes	characteristic, complemented
275	#1935	C₂×C₆₁	1	2	yes	complemented
276	#1803	C₂×C₆₁	1	1	yes	characteristic, complemented
277	C₂×C₆₁	—	4	2	no	—
278	C₂×C₆₁	#2414	1	1	yes	characteristic
279	C₂×C₆₁	C₂×#470	1	1	yes	characteristic
280	C₂×C₆₁	#3056	1	1	yes	characteristic
281	C₂×C₆₁	#3113	1	1	yes	characteristic
282	C₂×C₆₁	#3116	1	1	yes	characteristic
283	C₂×C₆₁	#3216	1	1	yes	characteristic
284	C₂×C₆₁	#3218	1	1	yes	characteristic
285	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
286	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
287	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
288	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
289	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
290	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
291	#462	—	2	4	no	—
292	#432	—	2	4	no	—
293	C₂×#106	C₂²×C₆₁	1	2	yes	—
294	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
295	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
296	C₂×#103	C₂²×C₆₁	1	2	yes	—
297	C₂×#103	C₂²×C₆₁	1	2	yes	—
298	C₂×#103	C₂²×C₆₁	1	2	yes	—
299	C₂×#103	C₂²×C₆₁	1	2	yes	—
300	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
301	C₂×#97	C₂²×C₆₁	1	2	yes	—
302	#391	C₂²×C₆₁	1	2	yes	—
303	#391	C₂²×C₆₁	1	1	yes	characteristic
304	#389	—	2	1	no	—
305	#389	—	2	1	no	—
306	#389	C₂²×C₆₁	1	1	yes	characteristic
307	#387	—	2	1	no	—
308	#385	—	2	1	no	—
309	#384	C₂²×C₆₁	1	1	yes	characteristic
310	#380	—	2	1	no	—
311	#380	—	2	1	no	—
312	#380	C₂²×C₆₁	1	1	yes	characteristic
313	C₄×C₄⋊C₄	—	2	1	no	—
314	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
315	C₄×C₂²⋊C₄	—	2	1	no	—
316	#340	C₂²×C₆₁	1	2	yes	—
317	#340	C₂²×C₆₁	1	2	yes	—
318	C₆₁	#24660	1	1	yes	characteristic, direct product factor, Sylow
319	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
320	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
321	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
322	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
324	C₂×Q₁₆	—	2	4	no	—
325	C₂×Q₁₆	—	2	4	no	—
326	C₂×Q₁₆	—	4	2	no	—
327	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
328	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
329	C₄⋊Q₈	—	2	2	no	—
330	C₄⋊Q₈	—	2	2	no	—
331	C₂²⋊Q₈	—	2	2	no	—
332	C₂²⋊Q₈	—	2	2	no	—
333	C₂²⋊Q₈	—	4	2	no	—
334	C₂²⋊Q₈	—	4	2	no	—
335	C₄×Q₈	—	2	2	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₄²	—	2	2	no	—
353	C₂×C₄²	—	2	2	no	—
354	C₂×C₄²	—	2	1	no	—
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
357	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
360	#106	—	4	2	no	—
361	C₄⋊C₈	—	2	2	no	—
362	C₄⋊C₈	D₄×C₆₁	1	4	yes	—
363	#103	—	2	4	no	—
364	#103	—	2	4	no	—
365	#103	—	4	2	no	—
366	#103	—	4	2	no	—
367	C₂²⋊C₈	—	2	4	no	—
368	#97	—	2	4	no	—
369	#95	—	2	1	no	—
370	#95	—	2	1	no	—
371	#95	—	2	1	no	—
372	#95	—	2	1	no	—
373	#95	—	2	1	no	—
374	#95	—	2	2	no	—
375	#95	—	2	2	no	—
376	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	#41×C₆₁	1	2	yes	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	4	1	no	—
407	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
412	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
413	Q₁₆	—	4	8	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	4	4	no	—
429	C₄⋊C₄	—	4	2	no	—
430	C₄⋊C₄	—	4	2	no	—
431	C₄⋊C₄	—	4	2	no	—
432	C₄⋊C₄	—	4	2	no	—
433	C₄⋊C₄	—	4	2	no	—
434	C₄⋊C₄	—	4	2	no	—
435	C₄⋊C₄	#41×C₆₁	1	2	yes	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₂²⋊C₄	—	4	4	no	—
438	C₂²⋊C₄	—	4	2	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	4	2	no	—
444	C₄²	—	4	2	no	—
445	C₄²	C₂×D₄×C₆₁	1	2	yes	—
446	C₄²	#41×C₆₁	1	2	yes	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	1	no	—
453	C₂³	#137×C₆₁	1	2	yes	—
454	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
455	Q₈	—	2	2	no	—
456	Q₈	—	2	2	no	—
457	Q₈	—	4	1	no	—
458	Q₈	—	4	1	no	—
459	Q₈	—	4	2	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	4	2	no	—
462	Q₈	—	4	2	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	4	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	#121×C₆₁	1	2	yes	—
499	C₂×C₄	#121×C₆₁	1	2	yes	—
500	C₂×C₄	#137×C₆₁	1	2	yes	—
501	C₂×C₄	#137×C₆₁	1	2	yes	—
502	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
503	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
504	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
505	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
506	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
507	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
508	C₈	—	2	4	no	—
509	C₈	—	4	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	1	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	4	1	no	—
517	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
518	C₂²	C₆₁×#525	1	1	yes	characteristic
519	C₂²	C₆₁×#535	1	1	yes	characteristic
520	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
521	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
522	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
523	C₂²	C₆₁×#575	1	1	yes	characteristic
524	C₄	—	2	2	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	2	no	—
530	C₄	—	8	1	no	—
531	C₄	—	8	2	no	—
532	C₄	—	8	2	no	—
533	C₄	—	8	1	no	—
534	C₄	C₆₁×#470	1	4	yes	—
535	C₄	C₆₁×#546	1	1	yes	characteristic
536	C₄	C₆₁×#550	1	1	yes	characteristic
537	C₄	C₆₁×#553	1	1	yes	characteristic
538	C₄	C₆₁×#555	1	1	yes	characteristic
539	C₂	—	4	2	no	—
540	C₂	C₆₁×#2414	1	1	yes	characteristic
541	C₂	C₂×C₆₁×#470	1	1	yes	characteristic
542	C₂	C₆₁×#3056	1	1	yes	characteristic
543	C₂	C₆₁×#3113	1	1	yes	characteristic
544	C₂	C₆₁×#3116	1	1	yes	characteristic
545	C₂	C₆₁×#3216	1	1	yes	characteristic
546	C₂	C₆₁×#3218	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
1. C₂×C₆₁×#462	C₂	semidirect
7. C₆₁×#1981	C₂	semidirect
8. C₆₁×#1971	C₂	semidirect
9. C₆₁×#1948	C₂	semidirect
10. C₆₁×#1935	C₂	semidirect
11. C₆₁×#1803	C₂	semidirect
236. #24660	C₆₁	direct (N × H)
266. C₂×#462	C₂×C₆₁	semidirect
272. #1981	C₂×C₆₁	semidirect
273. #1971	C₂×C₆₁	semidirect
274. #1948	C₂×C₆₁	semidirect
275. #1935	C₂×C₆₁	semidirect
276. #1803	C₂×C₆₁	semidirect
318. C₆₁	#24660	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×#462	2
C₂×C₆₁×#432	2
C₆₁×#2857	2
C₄×C₂²⋊Q₈×C₆₁	2
C₆₁×#2035	2
C₆₁×#2001	2
C₆₁×#1981	2
C₆₁×#1971	2
C₆₁×#1948	2
C₆₁×#1935	2
C₆₁×#1803	2
#24660	61

Subgroups — C61×#24660 #29528093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24660 #29528093