Subgroups — C₆₁×#24546 #29527979

Order 15616.

996 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#452	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#417	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2502	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2341	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2071	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2055	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1894	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1878	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1823	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1803	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#452	—	2	4	no	—
20	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
21	C₆₁×#417	—	2	4	no	—
22	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#103×C₆₁	C₂²	1	2	yes	—
24	C₂×#103×C₆₁	C₂²	1	2	yes	—
25	C₂×#102×C₆₁	C₂²	1	2	yes	—
26	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₆₁×#398	—	2	1	no	—
29	C₆₁×#398	—	2	1	no	—
30	C₆₁×#391	C₂²	1	2	yes	—
31	C₆₁×#390	—	2	2	no	—
32	C₆₁×#390	C₂²	1	2	yes	—
33	C₆₁×#385	—	2	2	no	—
34	C₆₁×#384	C₂²	1	2	yes	—
35	C₆₁×#380	—	2	1	no	—
36	C₆₁×#380	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×#340	C₂²	1	2	yes	—
40	C₆₁×#340	C₂²	1	2	yes	—
41	C₆₁×#340	C₂²	1	2	yes	—
42	C₆₁×#336	C₂²	1	2	yes	—
43	C₂×#41×C₆₁	—	2	2	no	—
44	C₂×#41×C₆₁	—	2	4	no	—
45	C₂×#41×C₆₁	—	4	2	no	—
46	C₂×#41×C₆₁	D₄	1	4	yes	—
47	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₆₁	—	2	1	no	—
50	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₆₁	—	2	1	no	—
52	C₂³×C₄×C₆₁	—	2	1	no	—
53	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
54	C₂×Q₁₆×C₆₁	—	2	2	no	—
55	C₂×Q₁₆×C₆₁	—	2	4	no	—
56	C₂×SD₁₆×C₆₁	—	2	2	no	—
57	C₂×SD₁₆×C₆₁	—	4	2	no	—
58	C₂×M₁₆×C₆₁	—	2	2	no	—
59	C₂×M₁₆×C₆₁	—	4	2	no	—
60	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
61	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²⋊Q₈×C₆₁	—	2	2	no	—
64	C₂²⋊Q₈×C₆₁	—	2	2	no	—
65	C₄×Q₈×C₆₁	—	2	4	no	—
66	C₄×Q₈×C₆₁	—	4	2	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
71	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
77	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
82	C₂×C₄²×C₆₁	—	2	2	no	—
83	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
84	C₄⋊C₈×C₆₁	—	4	2	no	—
85	#103×C₆₁	—	2	4	no	—
86	#103×C₆₁	—	2	2	no	—
87	#103×C₆₁	—	4	2	no	—
88	#102×C₆₁	—	2	4	no	—
89	#102×C₆₁	—	2	2	no	—
90	C₂²⋊C₈×C₆₁	—	2	2	no	—
91	#95×C₆₁	—	2	1	no	—
92	#95×C₆₁	—	2	2	no	—
93	#95×C₆₁	—	2	2	no	—
94	#95×C₆₁	D₄	1	1	yes	characteristic
95	#95×C₆₁	D₄	1	1	yes	characteristic
96	C₂⁴×C₆₁	—	2	1	no	—
97	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
98	#41×C₆₁	—	2	8	no	—
99	#41×C₆₁	—	4	4	no	—
100	#41×C₆₁	—	4	8	no	—
101	C₂×Q₈×C₆₁	—	2	1	no	—
102	C₂×Q₈×C₆₁	—	2	2	no	—
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	2	no	—
107	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
108	C₂×Q₈×C₆₁	#41	1	4	yes	—
109	C₂×D₄×C₆₁	—	2	4	no	—
110	C₂×D₄×C₆₁	—	2	2	no	—
111	C₂×D₄×C₆₁	—	2	1	no	—
112	C₂×D₄×C₆₁	—	2	2	no	—
113	C₂×D₄×C₆₁	—	4	4	no	—
114	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₆₁	—	2	1	no	—
116	C₂²×C₄×C₆₁	—	2	2	no	—
117	C₂²×C₄×C₆₁	—	2	2	no	—
118	C₂²×C₄×C₆₁	—	2	4	no	—
119	C₂²×C₄×C₆₁	—	2	1	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	—	4	4	no	—
124	C₂²×C₄×C₆₁	—	4	2	no	—
125	C₂²×C₄×C₆₁	—	8	1	no	—
126	C₂²×C₄×C₆₁	—	8	1	no	—
127	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₆₁	#41	1	2	yes	—
132	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
133	Q₁₆×C₆₁	—	4	4	no	—
134	SD₁₆×C₆₁	—	4	4	no	—
135	M₁₆×C₆₁	—	4	4	no	—
136	C₂×C₈×C₆₁	—	2	1	no	—
137	C₂×C₈×C₆₁	—	2	1	no	—
138	C₂×C₈×C₆₁	—	2	2	no	—
139	C₂×C₈×C₆₁	—	2	2	no	—
140	C₂×C₈×C₆₁	—	2	2	no	—
141	C₂×C₈×C₆₁	—	2	2	no	—
142	C₂×C₈×C₆₁	—	2	2	no	—
143	C₄⋊C₄×C₆₁	—	2	2	no	—
144	C₄⋊C₄×C₆₁	—	2	1	no	—
145	C₄⋊C₄×C₆₁	—	2	2	no	—
146	C₄⋊C₄×C₆₁	—	2	2	no	—
147	C₄⋊C₄×C₆₁	—	2	1	no	—
148	C₄⋊C₄×C₆₁	—	2	2	no	—
149	C₄⋊C₄×C₆₁	—	4	4	no	—
150	C₄⋊C₄×C₆₁	—	4	2	no	—
151	C₄⋊C₄×C₆₁	—	4	2	no	—
152	C₄⋊C₄×C₆₁	—	8	2	no	—
153	C₄⋊C₄×C₆₁	—	8	2	no	—
154	C₂²⋊C₄×C₆₁	—	2	4	no	—
155	C₂²⋊C₄×C₆₁	—	4	2	no	—
156	C₂²⋊C₄×C₆₁	—	4	4	no	—
157	C₂²⋊C₄×C₆₁	—	8	2	no	—
158	C₂²⋊C₄×C₆₁	—	8	1	no	—
159	C₄²×C₆₁	—	2	2	no	—
160	C₄²×C₆₁	—	2	2	no	—
161	C₄²×C₆₁	—	4	4	no	—
162	C₂³×C₆₁	—	2	2	no	—
163	C₂³×C₆₁	—	2	2	no	—
164	C₂³×C₆₁	—	2	1	no	—
165	C₂³×C₆₁	—	2	1	no	—
166	C₂³×C₆₁	—	2	2	no	—
167	C₂³×C₆₁	—	4	2	no	—
168	C₂³×C₆₁	—	4	2	no	—
169	C₂³×C₆₁	—	4	1	no	—
170	C₂³×C₆₁	—	4	1	no	—
171	C₂³×C₆₁	#121	1	2	yes	—
172	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₆₁	—	2	2	no	—
174	Q₈×C₆₁	—	2	4	no	—
175	Q₈×C₆₁	—	4	1	no	—
176	Q₈×C₆₁	—	4	1	no	—
177	Q₈×C₆₁	—	4	2	no	—
178	Q₈×C₆₁	#123	1	4	yes	—
179	D₄×C₆₁	—	2	2	no	—
180	D₄×C₆₁	—	2	2	no	—
181	D₄×C₆₁	—	4	8	no	—
182	D₄×C₆₁	—	4	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	2	no	—
187	C₂×C₄×C₆₁	—	2	2	no	—
188	C₂×C₄×C₆₁	—	2	2	no	—
189	C₂×C₄×C₆₁	—	2	2	no	—
190	C₂×C₄×C₆₁	—	2	4	no	—
191	C₂×C₄×C₆₁	—	2	2	no	—
192	C₂×C₄×C₆₁	—	2	2	no	—
193	C₂×C₄×C₆₁	—	2	2	no	—
194	C₂×C₄×C₆₁	—	4	8	no	—
195	C₂×C₄×C₆₁	—	4	1	no	—
196	C₂×C₄×C₆₁	—	4	1	no	—
197	C₂×C₄×C₆₁	—	4	2	no	—
198	C₂×C₄×C₆₁	—	4	2	no	—
199	C₂×C₄×C₆₁	—	4	2	no	—
200	C₂×C₄×C₆₁	—	4	2	no	—
201	C₂×C₄×C₆₁	—	4	2	no	—
202	C₂×C₄×C₆₁	—	4	1	no	—
203	C₂×C₄×C₆₁	—	4	2	no	—
204	C₂×C₄×C₆₁	—	4	1	no	—
205	C₂×C₄×C₆₁	—	4	2	no	—
206	C₂×C₄×C₆₁	—	8	4	no	—
207	C₂×C₄×C₆₁	#121	1	2	yes	—
208	C₂×C₄×C₆₁	#137	1	4	yes	—
209	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
211	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
213	C₈×C₆₁	—	4	1	no	—
214	C₈×C₆₁	—	4	2	no	—
215	C₈×C₆₁	—	4	1	no	—
216	#24546	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂²×C₆₁	—	2	2	no	—
218	C₂²×C₆₁	—	2	2	no	—
219	C₂²×C₆₁	—	2	2	no	—
220	C₂²×C₆₁	—	4	2	no	—
221	C₂²×C₆₁	—	4	2	no	—
222	C₂²×C₆₁	—	4	2	no	—
223	C₂²×C₆₁	—	4	2	no	—
224	C₂²×C₆₁	—	4	2	no	—
225	C₂²×C₆₁	—	8	2	no	—
226	C₂²×C₆₁	—	8	2	no	—
227	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
228	C₂²×C₆₁	#546	1	2	yes	—
229	C₂²×C₆₁	C₂×#137	1	2	yes	—
230	C₂²×C₆₁	#576	1	1	yes	characteristic
231	C₂²×C₆₁	#577	1	1	yes	characteristic
232	C₄×C₆₁	—	2	2	no	—
233	C₄×C₆₁	—	2	4	no	—
234	C₄×C₆₁	—	2	4	no	—
235	C₄×C₆₁	—	4	2	no	—
236	C₄×C₆₁	—	8	2	no	—
237	C₄×C₆₁	—	8	1	no	—
238	C₄×C₆₁	—	8	1	no	—
239	C₄×C₆₁	—	8	2	no	—
240	C₄×C₆₁	C₂×#123	1	1	yes	characteristic
241	C₄×C₆₁	#534	1	1	yes	characteristic
242	C₄×C₆₁	#551	1	2	yes	—
243	C₂×#452	C₂×C₆₁	1	1	yes	characteristic
244	C₂×#417	C₂×C₆₁	1	1	yes	characteristic
245	#2502	C₂×C₆₁	1	1	yes	characteristic, complemented
246	#2341	C₂×C₆₁	1	1	yes	characteristic
247	#2071	C₂×C₆₁	1	2	yes	complemented
248	#2055	C₂×C₆₁	1	2	yes	complemented
249	#1894	C₂×C₆₁	1	1	yes	characteristic, complemented
250	#1878	C₂×C₆₁	1	2	yes	complemented
251	#1851	C₂×C₆₁	1	1	yes	characteristic, complemented
252	#1823	C₂×C₆₁	1	1	yes	characteristic, complemented
253	#1803	C₂×C₆₁	1	2	yes	complemented
254	C₂×C₆₁	—	4	2	no	—
255	C₂×C₆₁	—	8	2	no	—
256	C₂×C₆₁	#2412	1	1	yes	characteristic
257	C₂×C₆₁	#3039	1	1	yes	characteristic
258	C₂×C₆₁	#3045	1	1	yes	characteristic
259	C₂×C₆₁	#3316	1	2	yes	—
260	C₂×C₆₁	#3333	1	2	yes	—
261	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
262	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
263	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
264	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
265	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
266	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
267	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
268	#452	—	2	4	no	—
269	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
270	#417	—	2	4	no	—
271	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
272	C₂×#103	C₂²×C₆₁	1	2	yes	—
273	C₂×#103	C₂²×C₆₁	1	2	yes	—
274	C₂×#102	C₂²×C₆₁	1	2	yes	—
275	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
276	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
277	#398	—	2	1	no	—
278	#398	—	2	1	no	—
279	#391	C₂²×C₆₁	1	2	yes	—
280	#390	—	2	2	no	—
281	#390	C₂²×C₆₁	1	2	yes	—
282	#385	—	2	2	no	—
283	#384	C₂²×C₆₁	1	2	yes	—
284	#380	—	2	1	no	—
285	#380	C₂²×C₆₁	1	1	yes	characteristic
286	C₄×C₂²⋊C₄	—	2	1	no	—
287	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
288	#340	C₂²×C₆₁	1	2	yes	—
289	#340	C₂²×C₆₁	1	2	yes	—
290	#340	C₂²×C₆₁	1	2	yes	—
291	#336	C₂²×C₆₁	1	2	yes	—
292	C₆₁	#24546	1	1	yes	characteristic, direct product factor, Sylow
293	C₂×#41	—	2	2	no	—
294	C₂×#41	—	2	4	no	—
295	C₂×#41	—	4	2	no	—
296	C₂×#41	D₄×C₆₁	1	4	yes	—
297	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
298	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
299	C₂²×D₄	—	2	1	no	—
300	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
301	C₂³×C₄	—	2	1	no	—
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
304	C₂×Q₁₆	—	2	2	no	—
305	C₂×Q₁₆	—	2	4	no	—
306	C₂×SD₁₆	—	2	2	no	—
307	C₂×SD₁₆	—	4	2	no	—
308	C₂×M₁₆	—	2	2	no	—
309	C₂×M₁₆	—	4	2	no	—
310	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
311	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
313	C₂²⋊Q₈	—	2	2	no	—
314	C₂²⋊Q₈	—	2	2	no	—
315	C₄×Q₈	—	2	4	no	—
316	C₄×Q₈	—	4	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
325	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
332	C₂×C₄²	—	2	2	no	—
333	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
334	C₄⋊C₈	—	4	2	no	—
335	#103	—	2	4	no	—
336	#103	—	2	2	no	—
337	#103	—	4	2	no	—
338	#102	—	2	4	no	—
339	#102	—	2	2	no	—
340	C₂²⋊C₈	—	2	2	no	—
341	#95	—	2	1	no	—
342	#95	—	2	2	no	—
343	#95	—	2	2	no	—
344	#95	D₄×C₆₁	1	1	yes	characteristic
345	#95	D₄×C₆₁	1	1	yes	characteristic
346	C₂⁴	—	2	1	no	—
347	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
348	#41	—	2	8	no	—
349	#41	—	4	4	no	—
350	#41	—	4	8	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
358	C₂×Q₈	#41×C₆₁	1	4	yes	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	4	4	no	—
364	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	8	1	no	—
376	C₂²×C₄	—	8	1	no	—
377	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
378	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
381	C₂²×C₄	#41×C₆₁	1	2	yes	—
382	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
383	Q₁₆	—	4	4	no	—
384	SD₁₆	—	4	4	no	—
385	M₁₆	—	4	4	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	4	4	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₄⋊C₄	—	8	2	no	—
403	C₄⋊C₄	—	8	2	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	4	2	no	—
406	C₂²⋊C₄	—	4	4	no	—
407	C₂²⋊C₄	—	8	2	no	—
408	C₂²⋊C₄	—	8	1	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	4	4	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	1	no	—
421	C₂³	#121×C₆₁	1	2	yes	—
422	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
423	Q₈	—	2	2	no	—
424	Q₈	—	2	4	no	—
425	Q₈	—	4	1	no	—
426	Q₈	—	4	2	no	—
427	Q₈	—	4	1	no	—
428	Q₈	#123×C₆₁	1	4	yes	—
429	D₄	—	2	2	no	—
430	D₄	—	2	2	no	—
431	D₄	—	4	8	no	—
432	D₄	—	4	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	8	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	8	4	no	—
457	C₂×C₄	#121×C₆₁	1	2	yes	—
458	C₂×C₄	#137×C₆₁	1	4	yes	—
459	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
460	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
461	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
462	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
463	C₈	—	4	2	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	1	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
477	C₂²	C₆₁×#546	1	2	yes	—
478	C₂²	C₂×#137×C₆₁	1	2	yes	—
479	C₂²	C₆₁×#576	1	1	yes	characteristic
480	C₂²	C₆₁×#577	1	1	yes	characteristic
481	C₄	—	2	4	no	—
482	C₄	—	2	2	no	—
483	C₄	—	2	4	no	—
484	C₄	—	4	2	no	—
485	C₄	—	8	1	no	—
486	C₄	—	8	2	no	—
487	C₄	—	8	2	no	—
488	C₄	—	8	1	no	—
489	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
490	C₄	C₆₁×#534	1	1	yes	characteristic
491	C₄	C₆₁×#551	1	2	yes	—
492	C₂	—	4	2	no	—
493	C₂	—	8	2	no	—
494	C₂	C₆₁×#2412	1	1	yes	characteristic
495	C₂	C₆₁×#3039	1	1	yes	characteristic
496	C₂	C₆₁×#3045	1	1	yes	characteristic
497	C₂	C₆₁×#3316	1	2	yes	—
498	C₂	C₆₁×#3333	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×#41×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₄×C₂²⋊C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₆₁×#2502	C₂	semidirect
5. C₆₁×#2071	C₂	semidirect
6. C₆₁×#2055	C₂	semidirect
7. C₆₁×#1894	C₂	semidirect
8. C₆₁×#1878	C₂	semidirect
9. C₆₁×#1851	C₂	semidirect
10. C₆₁×#1823	C₂	semidirect
11. C₆₁×#1803	C₂	semidirect
216. #24546	C₆₁	direct (N × H)
245. #2502	C₂×C₆₁	semidirect
247. #2071	C₂×C₆₁	semidirect
248. #2055	C₂×C₆₁	semidirect
249. #1894	C₂×C₆₁	semidirect
250. #1878	C₂×C₆₁	semidirect
251. #1851	C₂×C₆₁	semidirect
252. #1823	C₂×C₆₁	semidirect
253. #1803	C₂×C₆₁	semidirect
292. C₆₁	#24546	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×#452	2
C₂×C₆₁×#417	2
C₆₁×#2502	2
C₆₁×#2341	2
C₆₁×#2071	2
C₆₁×#2055	2
C₆₁×#1894	2
C₆₁×#1878	2
C₆₁×#1851	2
C₆₁×#1823	2
C₆₁×#1803	2
#24546	61

Subgroups — C61×#24546 #29527979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24546 #29527979