Subgroups — C₆₁×#24580 #29528013

Order 15616.

842 conjugacy classes of subgroups.

The subgroup lattice has 440 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	1	yes	maximal, characteristic
2	C₂²×#106×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2502	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2344	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2084	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2066	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1948	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1927	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1892	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1850	C₂	1	1	yes	maximal, characteristic
11	C₆₁×#1824	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×#117×C₆₁	—	2	1	no	—
15	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
17	C₆₁×#483	—	2	4	no	—
18	C₂×#106×C₆₁	—	2	4	no	—
19	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#106×C₆₁	C₂²	1	2	yes	—
22	C₂×#106×C₆₁	C₂²	1	2	yes	—
23	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
24	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₆₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₆₁×#398	—	2	2	no	—
29	C₆₁×#391	C₂²	1	2	yes	—
30	C₆₁×#389	C₂²	1	2	yes	—
31	C₆₁×#387	—	2	2	no	—
32	C₆₁×#385	—	2	1	no	—
33	C₆₁×#385	—	2	1	no	—
34	C₆₁×#384	C₂²	1	2	yes	—
35	C₆₁×#381	—	2	1	no	—
36	C₆₁×#380	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
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	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₆₁	—	2	1	no	—
45	C₂³×C₄×C₆₁	—	2	1	no	—
46	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₆₁	—	2	2	no	—
48	C₂²×C₈×C₆₁	—	2	4	no	—
49	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
52	C₂²⋊Q₈×C₆₁	—	2	2	no	—
53	C₂²⋊Q₈×C₆₁	—	2	2	no	—
54	#117×C₆₁	—	4	4	no	—
55	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₆₁	D₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₆₁	—	2	2	no	—
75	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
76	#106×C₆₁	—	2	4	no	—
77	#106×C₆₁	—	2	4	no	—
78	#106×C₆₁	—	2	2	no	—
79	#106×C₆₁	—	2	2	no	—
80	C₄⋊C₈×C₆₁	—	2	4	no	—
81	#103×C₆₁	—	2	4	no	—
82	#103×C₆₁	—	2	2	no	—
83	#103×C₆₁	—	2	2	no	—
84	C₂²⋊C₈×C₆₁	—	2	2	no	—
85	#95×C₆₁	—	2	2	no	—
86	#95×C₆₁	—	2	1	no	—
87	#95×C₆₁	—	2	2	no	—
88	#95×C₆₁	—	2	2	no	—
89	#95×C₆₁	—	2	2	no	—
90	#95×C₆₁	D₄	1	2	yes	—
91	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
92	C₂×Q₈×C₆₁	—	2	1	no	—
93	C₂×Q₈×C₆₁	—	2	2	no	—
94	C₂×Q₈×C₆₁	—	2	1	no	—
95	C₂×Q₈×C₆₁	—	2	2	no	—
96	C₂²×C₄×C₆₁	—	2	2	no	—
97	C₂²×C₄×C₆₁	—	2	2	no	—
98	C₂²×C₄×C₆₁	—	2	4	no	—
99	C₂²×C₄×C₆₁	—	2	1	no	—
100	C₂²×C₄×C₆₁	—	2	1	no	—
101	C₂²×C₄×C₆₁	—	2	1	no	—
102	C₂²×C₄×C₆₁	—	2	2	no	—
103	C₂²×C₄×C₆₁	—	2	2	no	—
104	C₂²×C₄×C₆₁	—	2	1	no	—
105	C₂²×C₄×C₆₁	—	4	2	no	—
106	C₂²×C₄×C₆₁	—	4	2	no	—
107	C₂²×C₄×C₆₁	—	4	2	no	—
108	C₂²×C₄×C₆₁	—	8	2	no	—
109	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₆₁	#41	1	2	yes	—
114	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
115	C₂×C₈×C₆₁	—	2	8	no	—
116	C₂×C₈×C₆₁	—	2	2	no	—
117	C₂×C₈×C₆₁	—	2	2	no	—
118	C₂×C₈×C₆₁	—	2	1	no	—
119	C₂×C₈×C₆₁	—	2	1	no	—
120	C₂×C₈×C₆₁	—	2	2	no	—
121	C₂×C₈×C₆₁	—	2	2	no	—
122	C₂×C₈×C₆₁	#41	1	4	yes	—
123	C₄⋊C₄×C₆₁	—	2	4	no	—
124	C₄⋊C₄×C₆₁	—	2	1	no	—
125	C₄⋊C₄×C₆₁	—	2	1	no	—
126	C₄⋊C₄×C₆₁	—	2	2	no	—
127	C₄⋊C₄×C₆₁	—	2	1	no	—
128	C₄⋊C₄×C₆₁	—	2	2	no	—
129	C₄⋊C₄×C₆₁	—	2	2	no	—
130	C₄⋊C₄×C₆₁	—	2	1	no	—
131	C₄⋊C₄×C₆₁	—	2	2	no	—
132	C₄⋊C₄×C₆₁	—	4	2	no	—
133	C₄⋊C₄×C₆₁	—	4	2	no	—
134	C₄⋊C₄×C₆₁	—	4	4	no	—
135	C₄⋊C₄×C₆₁	—	8	2	no	—
136	C₄⋊C₄×C₆₁	—	8	2	no	—
137	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
139	C₂²⋊C₄×C₆₁	—	2	2	no	—
140	C₂²⋊C₄×C₆₁	—	4	2	no	—
141	C₂²⋊C₄×C₆₁	—	4	2	no	—
142	C₂²⋊C₄×C₆₁	SD₁₆	1	4	yes	—
143	C₄²×C₆₁	—	2	2	no	—
144	C₄²×C₆₁	—	2	2	no	—
145	C₄²×C₆₁	—	4	4	no	—
146	C₂³×C₆₁	—	2	2	no	—
147	C₂³×C₆₁	—	2	2	no	—
148	C₂³×C₆₁	#121	1	2	yes	—
149	C₂³×C₆₁	C₂×SD₁₆	1	2	yes	—
150	C₂³×C₆₁	#137	1	2	yes	—
151	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₆₁	—	4	1	no	—
153	Q₈×C₆₁	—	4	1	no	—
154	Q₈×C₆₁	—	4	2	no	—
155	C₂×C₄×C₆₁	—	2	2	no	—
156	C₂×C₄×C₆₁	—	2	2	no	—
157	C₂×C₄×C₆₁	—	2	2	no	—
158	C₂×C₄×C₆₁	—	2	2	no	—
159	C₂×C₄×C₆₁	—	2	2	no	—
160	C₂×C₄×C₆₁	—	2	4	no	—
161	C₂×C₄×C₆₁	—	2	2	no	—
162	C₂×C₄×C₆₁	—	2	2	no	—
163	C₂×C₄×C₆₁	—	2	2	no	—
164	C₂×C₄×C₆₁	—	2	2	no	—
165	C₂×C₄×C₆₁	—	2	2	no	—
166	C₂×C₄×C₆₁	—	4	1	no	—
167	C₂×C₄×C₆₁	—	4	1	no	—
168	C₂×C₄×C₆₁	—	4	1	no	—
169	C₂×C₄×C₆₁	—	4	1	no	—
170	C₂×C₄×C₆₁	—	4	8	no	—
171	C₂×C₄×C₆₁	—	4	1	no	—
172	C₂×C₄×C₆₁	—	4	1	no	—
173	C₂×C₄×C₆₁	—	4	2	no	—
174	C₂×C₄×C₆₁	—	4	2	no	—
175	C₂×C₄×C₆₁	—	4	2	no	—
176	C₂×C₄×C₆₁	—	4	2	no	—
177	C₂×C₄×C₆₁	—	4	2	no	—
178	C₂×C₄×C₆₁	—	4	2	no	—
179	C₂×C₄×C₆₁	—	4	2	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	—	8	4	no	—
182	C₂×C₄×C₆₁	#121	1	2	yes	—
183	C₂×C₄×C₆₁	C₂×SD₁₆	1	4	yes	—
184	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
186	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
188	C₈×C₆₁	—	2	4	no	—
189	C₈×C₆₁	—	4	1	no	—
190	C₈×C₆₁	—	4	1	no	—
191	#24580	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂²×C₆₁	—	2	4	no	—
193	C₂²×C₆₁	—	2	4	no	—
194	C₂²×C₆₁	—	2	2	no	—
195	C₂²×C₆₁	—	2	2	no	—
196	C₂²×C₆₁	#461	1	4	yes	—
197	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
198	C₂²×C₆₁	#547	1	2	yes	—
199	C₂²×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
200	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
201	C₂²×C₆₁	#577	1	2	yes	—
202	C₄×C₆₁	—	2	4	no	—
203	C₄×C₆₁	—	2	2	no	—
204	C₄×C₆₁	—	4	2	no	—
205	C₄×C₆₁	—	4	2	no	—
206	C₄×C₆₁	—	4	2	no	—
207	C₄×C₆₁	—	8	2	no	—
208	C₄×C₆₁	—	8	1	no	—
209	C₄×C₆₁	—	8	1	no	—
210	C₄×C₆₁	—	8	2	no	—
211	C₄×C₆₁	#525	1	1	yes	characteristic
212	C₄×C₆₁	#536	1	1	yes	characteristic
213	C₄×C₆₁	#552	1	2	yes	—
214	C₂×#483	C₂×C₆₁	1	1	yes	characteristic
215	C₂²×#106	C₂×C₆₁	1	1	yes	characteristic
216	#2502	C₂×C₆₁	1	1	yes	characteristic
217	#2344	C₂×C₆₁	1	1	yes	characteristic
218	#2084	C₂×C₆₁	1	2	yes	complemented
219	#2066	C₂×C₆₁	1	2	yes	complemented
220	#1948	C₂×C₆₁	1	2	yes	complemented
221	#1927	C₂×C₆₁	1	2	yes	complemented
222	#1892	C₂×C₆₁	1	1	yes	characteristic
223	#1850	C₂×C₆₁	1	1	yes	characteristic
224	#1824	C₂×C₆₁	1	1	yes	characteristic
225	C₂×C₆₁	—	2	4	no	—
226	C₂×C₆₁	#2413	1	1	yes	characteristic
227	C₂×C₆₁	C₂×#461	1	1	yes	characteristic
228	C₂×C₆₁	#3043	1	1	yes	characteristic
229	C₂×C₆₁	#3335	1	2	yes	—
230	C₂×C₆₁	#3344	1	2	yes	—
231	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
232	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
233	C₂×#117	—	2	1	no	—
234	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
236	#483	—	2	4	no	—
237	C₂×#106	—	2	4	no	—
238	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
239	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
240	C₂×#106	C₂²×C₆₁	1	2	yes	—
241	C₂×#106	C₂²×C₆₁	1	2	yes	—
242	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
243	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
244	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
245	C₂×#103	C₂²×C₆₁	1	2	yes	—
246	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
247	#398	—	2	2	no	—
248	#391	C₂²×C₆₁	1	2	yes	—
249	#389	C₂²×C₆₁	1	2	yes	—
250	#387	—	2	2	no	—
251	#385	—	2	1	no	—
252	#385	—	2	1	no	—
253	#384	C₂²×C₆₁	1	2	yes	—
254	#381	—	2	1	no	—
255	#380	C₂²×C₆₁	1	1	yes	characteristic
256	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
257	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
258	#340	C₂²×C₆₁	1	2	yes	—
259	#340	C₂²×C₆₁	1	2	yes	—
260	#340	C₂²×C₆₁	1	2	yes	—
261	#336	C₂²×C₆₁	1	2	yes	—
262	C₆₁	#24580	1	1	yes	characteristic, direct product factor, Sylow
263	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
264	C₂³×C₄	—	2	1	no	—
265	C₂³×C₄	—	2	1	no	—
266	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	2	4	no	—
269	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
272	C₂²⋊Q₈	—	2	2	no	—
273	C₂²⋊Q₈	—	2	2	no	—
274	#117	—	4	4	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	D₄×C₆₁	1	4	yes	—
285	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
296	#106	—	2	4	no	—
297	#106	—	2	4	no	—
298	#106	—	2	2	no	—
299	#106	—	2	2	no	—
300	C₄⋊C₈	—	2	4	no	—
301	#103	—	2	4	no	—
302	#103	—	2	2	no	—
303	#103	—	2	2	no	—
304	C₂²⋊C₈	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	—	2	1	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	D₄×C₆₁	1	2	yes	—
311	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	8	2	no	—
329	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
333	C₂²×C₄	#41×C₆₁	1	2	yes	—
334	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
335	C₂×C₈	—	2	8	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	#41×C₆₁	1	4	yes	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	8	2	no	—
356	C₄⋊C₄	—	8	2	no	—
357	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
358	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	4	2	no	—
362	C₂²⋊C₄	SD₁₆×C₆₁	1	4	yes	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	4	4	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	2	no	—
368	C₂³	#121×C₆₁	1	2	yes	—
369	C₂³	C₂×SD₁₆×C₆₁	1	2	yes	—
370	C₂³	#137×C₆₁	1	2	yes	—
371	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
372	Q₈	—	4	1	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	8	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	8	4	no	—
402	C₂×C₄	#121×C₆₁	1	2	yes	—
403	C₂×C₄	C₂×SD₁₆×C₆₁	1	4	yes	—
404	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
406	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
407	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
408	C₈	—	2	4	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	1	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	2	no	—
415	C₂²	C₆₁×#461	1	4	yes	—
416	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
417	C₂²	C₆₁×#547	1	2	yes	—
418	C₂²	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
419	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
420	C₂²	C₆₁×#577	1	2	yes	—
421	C₄	—	2	4	no	—
422	C₄	—	2	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	8	1	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	2	no	—
429	C₄	—	8	1	no	—
430	C₄	C₆₁×#525	1	1	yes	characteristic
431	C₄	C₆₁×#536	1	1	yes	characteristic
432	C₄	C₆₁×#552	1	2	yes	—
433	C₂	—	2	4	no	—
434	C₂	C₆₁×#2413	1	1	yes	characteristic
435	C₂	C₂×C₆₁×#461	1	1	yes	characteristic
436	C₂	C₆₁×#3043	1	1	yes	characteristic
437	C₂	C₆₁×#3335	1	2	yes	—
438	C₂	C₆₁×#3344	1	2	yes	—

	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 ◁ C₄×C₂²⋊C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₆₁×#2084	C₂	semidirect
6. C₆₁×#2066	C₂	semidirect
7. C₆₁×#1948	C₂	semidirect
8. C₆₁×#1927	C₂	semidirect
191. #24580	C₆₁	direct (N × H)
218. #2084	C₂×C₆₁	semidirect
219. #2066	C₂×C₆₁	semidirect
220. #1948	C₂×C₆₁	semidirect
221. #1927	C₂×C₆₁	semidirect
262. C₆₁	#24580	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×#483	2
C₂²×#106×C₆₁	2
C₆₁×#2502	2
C₆₁×#2344	2
C₆₁×#2084	2
C₆₁×#2066	2
C₆₁×#1948	2
C₆₁×#1927	2
C₆₁×#1892	2
C₆₁×#1850	2
C₆₁×#1824	2
#24580	61

Subgroups — C61×#24580 #29528013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24580 #29528013