Subgroups — C₆₁×#21536 #29524969

Order 15616.

1066 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#469	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2324	C₂	1	2	yes	maximal, complemented
5	C₆₁×#1972	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1944	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1934	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1893	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1809	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#106×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1762	C₂	1	2	yes	maximal, complemented
12	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#121×C₆₁	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
17	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#469	C₄	1	8	yes	complemented
19	C₄×D₈×C₆₁	—	2	4	no	—
20	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#102×C₆₁	C₂²	1	2	yes	—
24	C₂×#102×C₆₁	C₂²	1	2	yes	—
25	C₂×#102×C₆₁	C₂²	1	2	yes	—
26	C₆₁×#405	—	2	4	no	—
27	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#390	—	2	2	no	—
32	C₆₁×#390	C₂²	1	2	yes	—
33	C₆₁×#389	C₂²	1	2	yes	—
34	C₆₁×#388	—	2	2	no	—
35	C₆₁×#386	—	2	2	no	—
36	C₆₁×#385	—	2	2	no	—
37	C₆₁×#380	C₂²	1	2	yes	—
38	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
39	C₆₁×#340	C₂²	1	2	yes	—
40	C₆₁×#340	C₂²	1	2	yes	—
41	C₆₁×#340	C₂²	1	2	yes	—
42	C₂²×D₄×C₆₁	—	2	2	no	—
43	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₆₁	—	2	2	no	—
45	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
46	C₂×D₈×C₆₁	—	2	2	no	—
47	C₂×D₈×C₆₁	—	2	2	no	—
48	C₂×D₈×C₆₁	C₂×C₄	1	4	yes	—
49	C₂×M₁₆×C₆₁	—	2	2	no	—
50	C₂×M₁₆×C₆₁	—	2	2	no	—
51	C₂×M₁₆×C₆₁	C₂×C₄	1	4	yes	complemented
52	C₂²×C₈×C₆₁	—	2	2	no	—
53	C₂²×C₈×C₆₁	—	2	2	no	—
54	C₂²×C₈×C₆₁	—	2	2	no	—
55	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
59	#121×C₆₁	—	2	4	no	—
60	#121×C₆₁	C₂×C₄	1	8	yes	complemented
61	C₄×D₄×C₆₁	—	2	4	no	—
62	C₄×D₄×C₆₁	—	2	4	no	—
63	#117×C₆₁	—	2	2	no	—
64	#117×C₆₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
71	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
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	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₆₁	—	2	2	no	—
79	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
81	#107×C₆₁	—	2	2	no	—
82	#106×C₆₁	—	2	2	no	—
83	#106×C₆₁	C₂×C₄	1	4	yes	complemented
84	#102×C₆₁	—	2	4	no	—
85	#102×C₆₁	—	2	4	no	—
86	#102×C₆₁	C₂×C₄	1	8	yes	complemented
87	#97×C₆₁	—	2	2	no	—
88	#97×C₆₁	—	2	2	no	—
89	C₄×C₈×C₆₁	—	2	2	no	—
90	C₄×C₈×C₆₁	D₄	1	4	yes	complemented
91	#95×C₆₁	—	2	2	no	—
92	#95×C₆₁	—	2	2	no	—
93	#95×C₆₁	—	2	2	no	—
94	C₂⁴×C₆₁	—	2	2	no	—
95	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
96	C₂×D₄×C₆₁	—	2	8	no	—
97	C₂×D₄×C₆₁	—	2	2	no	—
98	C₂×D₄×C₆₁	—	2	2	no	—
99	C₂×D₄×C₆₁	—	2	2	no	—
100	C₂×D₄×C₆₁	—	2	2	no	—
101	C₂×D₄×C₆₁	—	2	2	no	—
102	C₂×D₄×C₆₁	—	8	2	no	—
103	C₂×D₄×C₆₁	—	8	2	no	—
104	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₆₁	—	2	1	no	—
106	C₂²×C₄×C₆₁	—	2	1	no	—
107	C₂²×C₄×C₆₁	—	2	1	no	—
108	C₂²×C₄×C₆₁	—	2	1	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	—	4	4	no	—
113	C₂²×C₄×C₆₁	—	8	2	no	—
114	C₂²×C₄×C₆₁	—	8	2	no	—
115	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₆₁	#41	1	2	yes	—
122	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
123	D₈×C₆₁	—	2	8	no	—
124	M₁₆×C₆₁	—	2	8	no	—
125	C₂×C₈×C₆₁	—	2	8	no	—
126	C₂×C₈×C₆₁	—	2	1	no	—
127	C₂×C₈×C₆₁	—	2	1	no	—
128	C₂×C₈×C₆₁	—	2	1	no	—
129	C₂×C₈×C₆₁	—	2	1	no	—
130	C₂×C₈×C₆₁	—	2	1	no	—
131	C₂×C₈×C₆₁	—	2	1	no	—
132	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₆₁	#41	1	2	yes	—
137	C₂×C₈×C₆₁	#41	1	2	yes	—
138	C₄⋊C₄×C₆₁	—	2	2	no	—
139	C₄⋊C₄×C₆₁	—	2	2	no	—
140	C₄⋊C₄×C₆₁	—	2	2	no	—
141	C₄⋊C₄×C₆₁	—	2	2	no	—
142	C₄⋊C₄×C₆₁	—	2	2	no	—
143	C₄⋊C₄×C₆₁	—	2	2	no	—
144	C₄⋊C₄×C₆₁	—	2	2	no	—
145	C₄⋊C₄×C₆₁	—	8	2	no	—
146	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
147	C₂²⋊C₄×C₆₁	—	2	8	no	—
148	C₂²⋊C₄×C₆₁	—	2	2	no	—
149	C₂²⋊C₄×C₆₁	—	2	2	no	—
150	C₂²⋊C₄×C₆₁	—	4	4	no	—
151	C₂²⋊C₄×C₆₁	—	8	2	no	—
152	C₂²⋊C₄×C₆₁	—	8	2	no	—
153	C₂²⋊C₄×C₆₁	—	8	2	no	—
154	C₄²×C₆₁	—	2	1	no	—
155	C₄²×C₆₁	—	2	1	no	—
156	C₄²×C₆₁	—	8	2	no	—
157	C₄²×C₆₁	C₂×D₄	1	2	yes	—
158	C₄²×C₆₁	#41	1	2	yes	—
159	C₂³×C₆₁	—	2	1	no	—
160	C₂³×C₆₁	—	2	1	no	—
161	C₂³×C₆₁	—	2	2	no	—
162	C₂³×C₆₁	—	2	2	no	—
163	C₂³×C₆₁	—	2	4	no	—
164	C₂³×C₆₁	—	4	2	no	—
165	C₂³×C₆₁	—	4	2	no	—
166	C₂³×C₆₁	—	4	2	no	—
167	C₂³×C₆₁	—	4	2	no	—
168	C₂³×C₆₁	—	4	2	no	—
169	C₂³×C₆₁	—	4	2	no	—
170	C₂³×C₆₁	C₄×D₄	1	2	yes	—
171	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
172	D₄×C₆₁	—	2	4	no	—
173	D₄×C₆₁	—	2	4	no	—
174	D₄×C₆₁	—	4	2	no	—
175	D₄×C₆₁	—	4	2	no	—
176	D₄×C₆₁	—	8	8	no	—
177	C₂×C₄×C₆₁	—	2	1	no	—
178	C₂×C₄×C₆₁	—	2	1	no	—
179	C₂×C₄×C₆₁	—	2	2	no	—
180	C₂×C₄×C₆₁	—	2	2	no	—
181	C₂×C₄×C₆₁	—	2	2	no	—
182	C₂×C₄×C₆₁	—	2	2	no	—
183	C₂×C₄×C₆₁	—	2	2	no	—
184	C₂×C₄×C₆₁	—	2	2	no	—
185	C₂×C₄×C₆₁	—	2	4	no	—
186	C₂×C₄×C₆₁	—	2	1	no	—
187	C₂×C₄×C₆₁	—	2	1	no	—
188	C₂×C₄×C₆₁	—	2	2	no	—
189	C₂×C₄×C₆₁	—	2	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	2	no	—
194	C₂×C₄×C₆₁	—	4	2	no	—
195	C₂×C₄×C₆₁	—	4	2	no	—
196	C₂×C₄×C₆₁	—	4	2	no	—
197	C₂×C₄×C₆₁	—	4	2	no	—
198	C₂×C₄×C₆₁	—	8	8	no	—
199	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
200	C₂×C₄×C₆₁	#121	1	2	yes	—
201	C₂×C₄×C₆₁	#121	1	2	yes	—
202	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
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	C₂×#41	1	1	yes	characteristic
208	C₈×C₆₁	—	2	2	no	—
209	C₈×C₆₁	—	2	2	no	—
210	C₈×C₆₁	—	2	2	no	—
211	C₈×C₆₁	C₄×D₄	1	4	yes	—
212	#21536	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂²×C₆₁	—	2	4	no	—
214	C₂²×C₆₁	—	2	2	no	—
215	C₂²×C₆₁	—	4	2	no	—
216	C₂²×C₆₁	—	4	1	no	—
217	C₂²×C₆₁	—	4	1	no	—
218	C₂²×C₆₁	—	4	4	no	—
219	C₂²×C₆₁	—	4	4	no	—
220	C₂²×C₆₁	—	4	4	no	—
221	C₂²×C₆₁	—	8	2	no	—
222	C₂²×C₆₁	—	8	2	no	—
223	C₂²×C₆₁	—	8	2	no	—
224	C₂²×C₆₁	—	8	2	no	—
225	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
226	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
227	C₂²×C₆₁	#532	1	1	yes	characteristic
228	C₂²×C₆₁	#576	1	2	yes	—
229	C₂²×C₆₁	#577	1	2	yes	—
230	C₄×C₆₁	—	2	2	no	—
231	C₄×C₆₁	—	2	2	no	—
232	C₄×C₆₁	—	2	2	no	—
233	C₄×C₆₁	—	4	4	no	—
234	C₄×C₆₁	—	4	1	no	—
235	C₄×C₆₁	—	4	1	no	—
236	C₄×C₆₁	—	8	2	no	—
237	C₄×C₆₁	—	8	2	no	—
238	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
239	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
240	C₄×C₆₁	#525	1	1	yes	characteristic
241	C₄×C₆₁	#529	1	1	yes	characteristic
242	C₂×#469	C₂×C₆₁	1	1	yes	characteristic
243	C₂×C₄×D₈	C₂×C₆₁	1	1	yes	characteristic, complemented
244	C₂×#405	C₂×C₆₁	1	1	yes	characteristic, complemented
245	#2324	C₂×C₆₁	1	2	yes	complemented
246	#1972	C₂×C₆₁	1	1	yes	characteristic, complemented
247	#1944	C₂×C₆₁	1	1	yes	characteristic, complemented
248	#1934	C₂×C₆₁	1	2	yes	complemented
249	#1893	C₂×C₆₁	1	2	yes	complemented
250	#1809	C₂×C₆₁	1	1	yes	characteristic, complemented
251	C₄×#106	C₂×C₆₁	1	1	yes	characteristic, complemented
252	#1762	C₂×C₆₁	1	2	yes	complemented
253	C₂×C₆₁	—	4	2	no	—
254	C₂×C₆₁	—	8	4	no	—
255	C₂×C₆₁	C₄×#121	1	1	yes	characteristic
256	C₂×C₆₁	#2946	1	2	yes	—
257	C₂×C₆₁	#3058	1	1	yes	characteristic
258	C₂×C₆₁	#3060	1	1	yes	characteristic
259	C₂×C₆₁	#3179	1	2	yes	—
260	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
261	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
262	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
263	C₂×#121	C₂²×C₆₁	1	2	yes	—
264	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
265	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
266	#469	C₄×C₆₁	1	8	yes	complemented
267	C₄×D₈	—	2	4	no	—
268	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
269	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
270	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
271	C₂×#102	C₂²×C₆₁	1	2	yes	—
272	C₂×#102	C₂²×C₆₁	1	2	yes	—
273	C₂×#102	C₂²×C₆₁	1	2	yes	—
274	#405	—	2	4	no	—
275	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
276	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
277	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
278	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
279	#390	—	2	2	no	—
280	#390	C₂²×C₆₁	1	2	yes	—
281	#389	C₂²×C₆₁	1	2	yes	—
282	#388	—	2	2	no	—
283	#386	—	2	2	no	—
284	#385	—	2	2	no	—
285	#380	C₂²×C₆₁	1	2	yes	—
286	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
287	#340	C₂²×C₆₁	1	2	yes	—
288	#340	C₂²×C₆₁	1	2	yes	—
289	#340	C₂²×C₆₁	1	2	yes	—
290	C₆₁	#21536	1	1	yes	characteristic, direct product factor, Sylow
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
293	C₂³×C₄	—	2	2	no	—
294	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
295	C₂×D₈	—	2	2	no	—
296	C₂×D₈	—	2	2	no	—
297	C₂×D₈	C₂×C₄×C₆₁	1	4	yes	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	C₂×C₄×C₆₁	1	4	yes	complemented
301	C₂²×C₈	—	2	2	no	—
302	C₂²×C₈	—	2	2	no	—
303	C₂²×C₈	—	2	2	no	—
304	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
308	#121	—	2	4	no	—
309	#121	C₂×C₄×C₆₁	1	8	yes	complemented
310	C₄×D₄	—	2	4	no	—
311	C₄×D₄	—	2	4	no	—
312	#117	—	2	2	no	—
313	#117	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
316	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
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	—	2	2	no	—
325	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
327	C₂×C₄²	—	2	2	no	—
328	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
330	#107	—	2	2	no	—
331	#106	—	2	2	no	—
332	#106	C₂×C₄×C₆₁	1	4	yes	complemented
333	#102	—	2	4	no	—
334	#102	—	2	4	no	—
335	#102	C₂×C₄×C₆₁	1	8	yes	complemented
336	#97	—	2	2	no	—
337	#97	—	2	2	no	—
338	C₄×C₈	—	2	2	no	—
339	C₄×C₈	D₄×C₆₁	1	4	yes	complemented
340	#95	—	2	2	no	—
341	#95	—	2	2	no	—
342	#95	—	2	2	no	—
343	C₂⁴	—	2	2	no	—
344	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
345	C₂×D₄	—	2	8	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	8	2	no	—
352	C₂×D₄	—	8	2	no	—
353	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	4	4	no	—
362	C₂²×C₄	—	8	2	no	—
363	C₂²×C₄	—	8	2	no	—
364	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
370	C₂²×C₄	#41×C₆₁	1	2	yes	—
371	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
372	D₈	—	2	8	no	—
373	M₁₆	—	2	8	no	—
374	C₂×C₈	—	2	8	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
382	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
383	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
384	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
385	C₂×C₈	#41×C₆₁	1	2	yes	—
386	C₂×C₈	#41×C₆₁	1	2	yes	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	8	2	no	—
395	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
396	C₂²⋊C₄	—	2	8	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	—	8	2	no	—
401	C₂²⋊C₄	—	8	2	no	—
402	C₂²⋊C₄	—	8	2	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	8	2	no	—
406	C₄²	C₂×D₄×C₆₁	1	2	yes	—
407	C₄²	#41×C₆₁	1	2	yes	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	C₄×D₄×C₆₁	1	2	yes	—
420	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
421	D₄	—	2	4	no	—
422	D₄	—	2	4	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	8	8	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	8	8	no	—
448	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
449	C₂×C₄	#121×C₆₁	1	2	yes	—
450	C₂×C₄	#121×C₆₁	1	2	yes	—
451	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₄×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	C₂×#41×C₆₁	1	1	yes	characteristic
456	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
457	C₈	—	2	2	no	—
458	C₈	—	2	2	no	—
459	C₈	—	2	2	no	—
460	C₈	C₄×D₄×C₆₁	1	4	yes	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	4	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	8	2	no	—
471	C₂²	—	8	2	no	—
472	C₂²	—	8	2	no	—
473	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
474	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
475	C₂²	C₆₁×#532	1	1	yes	characteristic
476	C₂²	C₆₁×#576	1	2	yes	—
477	C₂²	C₆₁×#577	1	2	yes	—
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	—	4	1	no	—
482	C₄	—	4	1	no	—
483	C₄	—	4	4	no	—
484	C₄	—	8	2	no	—
485	C₄	—	8	2	no	—
486	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
487	C₄	C₄×#41×C₆₁	1	1	yes	characteristic
488	C₄	C₆₁×#525	1	1	yes	characteristic
489	C₄	C₆₁×#529	1	1	yes	characteristic
490	C₂	—	4	2	no	—
491	C₂	—	8	4	no	—
492	C₂	C₄×#121×C₆₁	1	1	yes	characteristic
493	C₂	C₆₁×#2946	1	2	yes	—
494	C₂	C₆₁×#3058	1	1	yes	characteristic
495	C₂	C₆₁×#3060	1	1	yes	characteristic
496	C₂	C₆₁×#3179	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×C₆₁×#469	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×#117×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₈×C₆₁	C₂	semidirect
3. C₂×C₆₁×#405	C₂	semidirect
4. C₆₁×#2324	C₂	semidirect
5. C₆₁×#1972	C₂	semidirect
6. C₆₁×#1944	C₂	semidirect
7. C₆₁×#1934	C₂	semidirect
8. C₆₁×#1893	C₂	semidirect
9. C₆₁×#1809	C₂	semidirect
10. C₄×#106×C₆₁	C₂	semidirect
11. C₆₁×#1762	C₂	semidirect
18. C₆₁×#469	C₄	semidirect
51. C₂×M₁₆×C₆₁	C₂×C₄	semidirect
60. #121×C₆₁	C₂×C₄	semidirect
83. #106×C₆₁	C₂×C₄	semidirect
86. #102×C₆₁	C₂×C₄	semidirect
90. C₄×C₈×C₆₁	D₄	semidirect
212. #21536	C₆₁	direct (N × H)
243. C₂×C₄×D₈	C₂×C₆₁	semidirect
244. C₂×#405	C₂×C₆₁	semidirect
245. #2324	C₂×C₆₁	semidirect
246. #1972	C₂×C₆₁	semidirect
247. #1944	C₂×C₆₁	semidirect
248. #1934	C₂×C₆₁	semidirect
249. #1893	C₂×C₆₁	semidirect
250. #1809	C₂×C₆₁	semidirect
251. C₄×#106	C₂×C₆₁	semidirect
252. #1762	C₂×C₆₁	semidirect
266. #469	C₄×C₆₁	semidirect
290. C₆₁	#21536	direct (N × H)
300. C₂×M₁₆	C₂×C₄×C₆₁	semidirect
309. #121	C₂×C₄×C₆₁	semidirect
332. #106	C₂×C₄×C₆₁	semidirect
335. #102	C₂×C₄×C₆₁	semidirect
339. C₄×C₈	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×#469	2
C₂×C₄×D₈×C₆₁	2
C₂×C₆₁×#405	2
C₆₁×#2324	2
C₆₁×#1972	2
C₆₁×#1944	2
C₆₁×#1934	2
C₆₁×#1893	2
C₆₁×#1809	2
C₄×#106×C₆₁	2
C₆₁×#1762	2
#21536	61

Subgroups — C61×#21536 #29524969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21536 #29524969