Subgroups — C₆₁×#26234 #29529667

Order 15616.

934 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#483	C₂	1	2	yes	maximal, complemented
2	C₆₁×#2542	C₂	1	1	yes	maximal, characteristic
3	D₄×C₄⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2035	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2035	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1954	C₂	1	1	yes	maximal, characteristic
9	C₆₁×#1948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1872	C₂	1	2	yes	maximal, complemented
11	C₄×#106×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
14	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₆₁	—	2	1	no	—
16	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
18	C₆₁×#483	—	2	8	no	—
19	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#106×C₆₁	C₂²	1	2	yes	—
21	C₂×#106×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×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#399	—	2	2	no	—
31	C₆₁×#390	—	2	1	no	—
32	C₆₁×#389	—	2	1	no	—
33	C₆₁×#385	—	2	2	no	—
34	C₆₁×#384	—	2	1	no	—
35	C₆₁×#384	C₂²	1	1	yes	characteristic
36	C₆₁×#380	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×#340	C₂²	1	1	yes	characteristic
40	C₆₁×#340	C₂²	1	1	yes	characteristic
41	C₆₁×#340	C₂²	1	2	yes	—
42	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
43	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₆₁	—	2	2	no	—
45	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
49	C₄⋊Q₈×C₆₁	—	2	2	no	—
50	C₄⋊Q₈×C₆₁	—	2	2	no	—
51	C₂²⋊Q₈×C₆₁	—	2	4	no	—
52	C₂²⋊Q₈×C₆₁	—	2	4	no	—
53	C₂²⋊Q₈×C₆₁	—	4	2	no	—
54	C₂²⋊Q₈×C₆₁	—	4	2	no	—
55	C₄×D₄×C₆₁	—	2	2	no	—
56	C₄×D₄×C₆₁	—	2	2	no	—
57	C₄×D₄×C₆₁	—	4	4	no	—
58	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₆₁	—	4	2	no	—
67	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
77	C₂×C₄²×C₆₁	—	2	1	no	—
78	C₂×C₄²×C₆₁	—	2	1	no	—
79	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
80	#106×C₆₁	—	2	4	no	—
81	#106×C₆₁	—	2	2	no	—
82	#106×C₆₁	D₄	1	4	yes	complemented
83	C₄⋊C₈×C₆₁	—	2	2	no	—
84	#103×C₆₁	—	2	4	no	—
85	#103×C₆₁	—	2	4	no	—
86	#103×C₆₁	—	4	2	no	—
87	#103×C₆₁	—	4	2	no	—
88	C₂²⋊C₈×C₆₁	—	2	4	no	—
89	C₂²⋊C₈×C₆₁	—	4	2	no	—
90	C₄×C₈×C₆₁	—	2	2	no	—
91	#95×C₆₁	—	2	1	no	—
92	#95×C₆₁	—	2	1	no	—
93	#95×C₆₁	—	2	2	no	—
94	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
95	C₂×Q₈×C₆₁	—	2	2	no	—
96	C₂×Q₈×C₆₁	—	2	2	no	—
97	C₂×Q₈×C₆₁	—	2	2	no	—
98	C₂×Q₈×C₆₁	—	2	2	no	—
99	C₂×Q₈×C₆₁	—	2	2	no	—
100	C₂×Q₈×C₆₁	—	2	2	no	—
101	C₂×D₄×C₆₁	—	2	2	no	—
102	C₂×D₄×C₆₁	—	2	2	no	—
103	C₂×D₄×C₆₁	SD₁₆	1	4	yes	—
104	C₂²×C₄×C₆₁	—	2	1	no	—
105	C₂²×C₄×C₆₁	—	2	1	no	—
106	C₂²×C₄×C₆₁	—	2	1	no	—
107	C₂²×C₄×C₆₁	—	2	2	no	—
108	C₂²×C₄×C₆₁	—	2	2	no	—
109	C₂²×C₄×C₆₁	—	2	2	no	—
110	C₂²×C₄×C₆₁	—	2	2	no	—
111	C₂²×C₄×C₆₁	—	2	2	no	—
112	C₂²×C₄×C₆₁	—	2	2	no	—
113	C₂²×C₄×C₆₁	—	2	1	no	—
114	C₂²×C₄×C₆₁	—	2	2	no	—
115	C₂²×C₄×C₆₁	—	2	2	no	—
116	C₂²×C₄×C₆₁	—	4	4	no	—
117	C₂²×C₄×C₆₁	—	4	4	no	—
118	C₂²×C₄×C₆₁	—	8	2	no	—
119	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
123	C₂×C₈×C₆₁	—	2	1	no	—
124	C₂×C₈×C₆₁	—	2	1	no	—
125	C₂×C₈×C₆₁	—	2	2	no	—
126	C₂×C₈×C₆₁	—	2	1	no	—
127	C₂×C₈×C₆₁	—	2	2	no	—
128	C₂×C₈×C₆₁	—	2	1	no	—
129	C₂×C₈×C₆₁	—	2	2	no	—
130	C₂×C₈×C₆₁	—	2	1	no	—
131	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₆₁	—	2	2	no	—
133	C₄⋊C₄×C₆₁	—	2	1	no	—
134	C₄⋊C₄×C₆₁	—	2	1	no	—
135	C₄⋊C₄×C₆₁	—	2	1	no	—
136	C₄⋊C₄×C₆₁	—	2	2	no	—
137	C₄⋊C₄×C₆₁	—	2	1	no	—
138	C₄⋊C₄×C₆₁	—	2	1	no	—
139	C₄⋊C₄×C₆₁	—	2	2	no	—
140	C₄⋊C₄×C₆₁	—	4	4	no	—
141	C₄⋊C₄×C₆₁	—	4	4	no	—
142	C₄⋊C₄×C₆₁	—	4	4	no	—
143	C₄⋊C₄×C₆₁	—	4	2	no	—
144	C₄⋊C₄×C₆₁	—	4	2	no	—
145	C₄⋊C₄×C₆₁	—	4	2	no	—
146	C₄⋊C₄×C₆₁	—	8	1	no	—
147	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
148	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
149	C₄⋊C₄×C₆₁	#41	1	2	yes	—
150	C₂²⋊C₄×C₆₁	—	2	4	no	—
151	C₂²⋊C₄×C₆₁	—	4	4	no	—
152	C₂²⋊C₄×C₆₁	—	4	4	no	—
153	C₂²⋊C₄×C₆₁	—	4	4	no	—
154	C₄²×C₆₁	—	4	2	no	—
155	C₄²×C₆₁	—	4	2	no	—
156	C₄²×C₆₁	#41	1	2	yes	—
157	C₄²×C₆₁	#41	1	2	yes	—
158	C₂³×C₆₁	—	2	2	no	—
159	C₂³×C₆₁	—	2	2	no	—
160	C₂³×C₆₁	—	2	2	no	—
161	C₂³×C₆₁	—	2	2	no	—
162	C₂³×C₆₁	—	2	2	no	—
163	C₂³×C₆₁	—	2	2	no	—
164	C₂³×C₆₁	C₂×SD₁₆	1	4	yes	—
165	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₆₁	—	4	2	no	—
167	Q₈×C₆₁	—	4	2	no	—
168	Q₈×C₆₁	—	4	2	no	—
169	Q₈×C₆₁	—	4	2	no	—
170	D₄×C₆₁	—	2	8	no	—
171	C₂×C₄×C₆₁	—	2	1	no	—
172	C₂×C₄×C₆₁	—	2	1	no	—
173	C₂×C₄×C₆₁	—	2	2	no	—
174	C₂×C₄×C₆₁	—	2	2	no	—
175	C₂×C₄×C₆₁	—	2	2	no	—
176	C₂×C₄×C₆₁	—	2	2	no	—
177	C₂×C₄×C₆₁	—	2	2	no	—
178	C₂×C₄×C₆₁	—	2	2	no	—
179	C₂×C₄×C₆₁	—	4	1	no	—
180	C₂×C₄×C₆₁	—	4	1	no	—
181	C₂×C₄×C₆₁	—	4	1	no	—
182	C₂×C₄×C₆₁	—	4	1	no	—
183	C₂×C₄×C₆₁	—	4	1	no	—
184	C₂×C₄×C₆₁	—	4	1	no	—
185	C₂×C₄×C₆₁	—	4	2	no	—
186	C₂×C₄×C₆₁	—	4	2	no	—
187	C₂×C₄×C₆₁	—	4	2	no	—
188	C₂×C₄×C₆₁	—	4	2	no	—
189	C₂×C₄×C₆₁	—	4	2	no	—
190	C₂×C₄×C₆₁	—	4	2	no	—
191	C₂×C₄×C₆₁	—	4	2	no	—
192	C₂×C₄×C₆₁	—	4	2	no	—
193	C₂×C₄×C₆₁	—	4	1	no	—
194	C₂×C₄×C₆₁	—	4	1	no	—
195	C₂×C₄×C₆₁	—	4	2	no	—
196	C₂×C₄×C₆₁	—	4	2	no	—
197	C₂×C₄×C₆₁	—	4	1	no	—
198	C₂×C₄×C₆₁	—	8	8	no	—
199	C₂×C₄×C₆₁	#123	1	2	yes	—
200	C₂×C₄×C₆₁	#123	1	2	yes	—
201	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
202	C₂×C₄×C₆₁	#137	1	2	yes	—
203	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
209	C₈×C₆₁	—	2	2	no	—
210	C₈×C₆₁	—	4	1	no	—
211	C₈×C₆₁	—	4	2	no	—
212	#26234	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂²×C₆₁	—	2	4	no	—
214	C₂²×C₆₁	—	2	4	no	—
215	C₂²×C₆₁	—	2	4	no	—
216	C₂²×C₆₁	—	4	2	no	—
217	C₂²×C₆₁	—	4	2	no	—
218	C₂²×C₆₁	—	4	2	no	—
219	C₂²×C₆₁	—	4	2	no	—
220	C₂²×C₆₁	C₂×#123	1	1	yes	characteristic
221	C₂²×C₆₁	D₄²	1	1	yes	characteristic
222	C₂²×C₆₁	#546	1	1	yes	characteristic
223	C₂²×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
224	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
225	C₂²×C₆₁	#577	1	1	yes	characteristic
226	C₂²×C₆₁	#578	1	1	yes	characteristic
227	C₄×C₆₁	—	2	2	no	—
228	C₄×C₆₁	—	4	2	no	—
229	C₄×C₆₁	—	4	2	no	—
230	C₄×C₆₁	—	4	2	no	—
231	C₄×C₆₁	—	4	2	no	—
232	C₄×C₆₁	—	8	2	no	—
233	C₄×C₆₁	—	8	2	no	—
234	C₄×C₆₁	—	8	1	no	—
235	C₄×C₆₁	#483	1	4	yes	complemented
236	C₄×C₆₁	#532	1	1	yes	characteristic
237	C₄×C₆₁	#540	1	1	yes	characteristic
238	C₄×C₆₁	#550	1	1	yes	characteristic
239	C₄×C₆₁	#559	1	1	yes	characteristic
240	C₂×#483	C₂×C₆₁	1	2	yes	complemented
241	#2542	C₂×C₆₁	1	1	yes	characteristic
242	D₄×C₄⋊C₄	C₂×C₆₁	1	1	yes	characteristic
243	#2035	C₂×C₆₁	1	2	yes	complemented
244	#2035	C₂×C₆₁	1	2	yes	complemented
245	#1981	C₂×C₆₁	1	1	yes	characteristic, complemented
246	#1956	C₂×C₆₁	1	1	yes	characteristic, complemented
247	#1954	C₂×C₆₁	1	1	yes	characteristic
248	#1948	C₂×C₆₁	1	1	yes	characteristic, complemented
249	#1872	C₂×C₆₁	1	2	yes	complemented
250	C₄×#106	C₂×C₆₁	1	1	yes	characteristic, complemented
251	C₂×C₆₁	—	4	4	no	—
252	C₂×C₆₁	#2445	1	1	yes	characteristic
253	C₂×C₆₁	C₂×#483	1	1	yes	characteristic
254	C₂×C₆₁	#3097	1	1	yes	characteristic
255	C₂×C₆₁	#3276	1	1	yes	characteristic
256	C₂×C₆₁	D₄×SD₁₆	1	1	yes	characteristic
257	C₂×C₆₁	#3298	1	1	yes	characteristic
258	C₂×C₆₁	#3331	1	1	yes	characteristic
259	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
260	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
261	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
262	C₂×C₄×D₄	—	2	1	no	—
263	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
265	#483	—	2	8	no	—
266	C₂×#106	C₂²×C₆₁	1	2	yes	—
267	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
268	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
270	C₂×#103	C₂²×C₆₁	1	2	yes	—
271	C₂×#103	C₂²×C₆₁	1	2	yes	—
272	C₂×#103	C₂²×C₆₁	1	2	yes	—
273	C₂×#103	C₂²×C₆₁	1	2	yes	—
274	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
275	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
276	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
277	#399	—	2	2	no	—
278	#390	—	2	1	no	—
279	#389	—	2	1	no	—
280	#385	—	2	2	no	—
281	#384	—	2	1	no	—
282	#384	C₂²×C₆₁	1	1	yes	characteristic
283	#380	C₂²×C₆₁	1	2	yes	—
284	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
285	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
286	#340	C₂²×C₆₁	1	1	yes	characteristic
287	#340	C₂²×C₆₁	1	2	yes	—
288	#340	C₂²×C₆₁	1	1	yes	characteristic
289	C₆₁	#26234	1	1	yes	characteristic, direct product factor, Sylow
290	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
291	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
292	C₂³×C₄	—	2	2	no	—
293	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
294	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
296	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
297	C₄⋊Q₈	—	2	2	no	—
298	C₄⋊Q₈	—	2	2	no	—
299	C₂²⋊Q₈	—	2	4	no	—
300	C₂²⋊Q₈	—	2	4	no	—
301	C₂²⋊Q₈	—	4	2	no	—
302	C₂²⋊Q₈	—	4	2	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	—	4	4	no	—
306	C₂×C₄⋊C₄	—	2	4	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	4	2	no	—
315	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
328	#106	—	2	4	no	—
329	#106	—	2	2	no	—
330	#106	D₄×C₆₁	1	4	yes	complemented
331	C₄⋊C₈	—	2	2	no	—
332	#103	—	2	4	no	—
333	#103	—	2	4	no	—
334	#103	—	4	2	no	—
335	#103	—	4	2	no	—
336	C₂²⋊C₈	—	2	4	no	—
337	C₂²⋊C₈	—	4	2	no	—
338	C₄×C₈	—	2	2	no	—
339	#95	—	2	1	no	—
340	#95	—	2	1	no	—
341	#95	—	2	2	no	—
342	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	SD₁₆×C₆₁	1	4	yes	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	4	4	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	—	8	2	no	—
367	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
370	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	4	4	no	—
389	C₄⋊C₄	—	4	4	no	—
390	C₄⋊C₄	—	4	4	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	—	8	1	no	—
395	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
396	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
397	C₄⋊C₄	#41×C₆₁	1	2	yes	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	—	4	4	no	—
401	C₂²⋊C₄	—	4	4	no	—
402	C₄²	—	4	2	no	—
403	C₄²	—	4	2	no	—
404	C₄²	#41×C₆₁	1	2	yes	—
405	C₄²	#41×C₆₁	1	2	yes	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	C₂×SD₁₆×C₆₁	1	4	yes	—
413	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	4	2	no	—
417	Q₈	—	4	2	no	—
418	D₄	—	2	8	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	8	8	no	—
447	C₂×C₄	#123×C₆₁	1	2	yes	—
448	C₂×C₄	#123×C₆₁	1	2	yes	—
449	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
450	C₂×C₄	#137×C₆₁	1	2	yes	—
451	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
455	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
456	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
457	C₈	—	2	2	no	—
458	C₈	—	4	1	no	—
459	C₈	—	4	2	no	—
460	C₂²	—	2	4	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	4	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	C₂×#123×C₆₁	1	1	yes	characteristic
468	C₂²	D₄²×C₆₁	1	1	yes	characteristic
469	C₂²	C₆₁×#546	1	1	yes	characteristic
470	C₂²	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
471	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
472	C₂²	C₆₁×#577	1	1	yes	characteristic
473	C₂²	C₆₁×#578	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	8	1	no	—
480	C₄	—	8	2	no	—
481	C₄	—	8	2	no	—
482	C₄	C₆₁×#483	1	4	yes	complemented
483	C₄	C₆₁×#532	1	1	yes	characteristic
484	C₄	C₆₁×#540	1	1	yes	characteristic
485	C₄	C₆₁×#550	1	1	yes	characteristic
486	C₄	C₆₁×#559	1	1	yes	characteristic
487	C₂	—	4	4	no	—
488	C₂	C₆₁×#2445	1	1	yes	characteristic
489	C₂	C₂×C₆₁×#483	1	1	yes	characteristic
490	C₂	C₆₁×#3097	1	1	yes	characteristic
491	C₂	C₆₁×#3276	1	1	yes	characteristic
492	C₂	D₄×SD₁₆×C₆₁	1	1	yes	characteristic
493	C₂	C₆₁×#3298	1	1	yes	characteristic
494	C₂	C₆₁×#3331	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×D₄×C₆₁	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄×D₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#483	C₂	semidirect
4. C₆₁×#2035	C₂	semidirect
5. C₆₁×#2035	C₂	semidirect
6. C₆₁×#1981	C₂	semidirect
7. C₆₁×#1956	C₂	semidirect
9. C₆₁×#1948	C₂	semidirect
10. C₆₁×#1872	C₂	semidirect
11. C₄×#106×C₆₁	C₂	semidirect
82. #106×C₆₁	D₄	semidirect
212. #26234	C₆₁	direct (N × H)
235. C₄×C₆₁	#483	semidirect
240. C₂×#483	C₂×C₆₁	semidirect
243. #2035	C₂×C₆₁	semidirect
244. #2035	C₂×C₆₁	semidirect
245. #1981	C₂×C₆₁	semidirect
246. #1956	C₂×C₆₁	semidirect
248. #1948	C₂×C₆₁	semidirect
249. #1872	C₂×C₆₁	semidirect
250. C₄×#106	C₂×C₆₁	semidirect
289. C₆₁	#26234	direct (N × H)
330. #106	D₄×C₆₁	semidirect
482. C₄	C₆₁×#483	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#483	2
C₆₁×#2542	2
D₄×C₄⋊C₄×C₆₁	2
C₆₁×#2035	2
C₆₁×#1981	2
C₆₁×#1956	2
C₆₁×#1954	2
C₆₁×#1948	2
C₆₁×#1872	2
C₄×#106×C₆₁	2
#26234	61

Subgroups — C61×#26234 #29529667

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#26234 #29529667