Subgroups — C₆₁×#25504 #29528937

Order 15616.

1108 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#470	C₂	1	2	yes	maximal
3	C₆₁×#2855	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2043	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2024	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2016	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1894	C₂	1	2	yes	maximal
9	C₆₁×#1878	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1865	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1728	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
14	C₆₁×#533	—	2	8	no	—
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#125×C₆₁	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
19	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
22	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
23	C₂×#117×C₆₁	—	2	1	no	—
24	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
25	C₆₁×#470	—	2	8	no	—
26	C₂×#106×C₆₁	C₂²	1	2	yes	—
27	C₂×#103×C₆₁	C₂²	1	2	yes	—
28	C₂×#103×C₆₁	C₂²	1	2	yes	—
29	C₂×#103×C₆₁	C₂²	1	2	yes	—
30	C₂×#103×C₆₁	C₂²	1	2	yes	—
31	C₆₁×#391	C₂²	1	1	yes	characteristic
32	C₆₁×#391	C₂²	1	1	yes	characteristic
33	C₆₁×#389	C₂²	1	1	yes	characteristic
34	C₆₁×#389	C₂²	1	1	yes	characteristic
35	C₆₁×#387	—	2	1	no	—
36	C₆₁×#387	—	2	1	no	—
37	C₆₁×#385	—	2	1	no	—
38	C₆₁×#381	—	2	1	no	—
39	C₆₁×#380	C₂²	1	1	yes	characteristic
40	C₆₁×#340	C₂²	1	2	yes	—
41	C₆₁×#340	C₂²	1	2	yes	—
42	C₆₁×#336	C₂²	1	1	yes	characteristic
43	C₆₁×#336	C₂²	1	1	yes	characteristic
44	C₆₁×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₆₁	—	2	1	no	—
46	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
48	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
51	C₂×Q₁₆×C₆₁	—	2	4	no	—
52	C₂×Q₁₆×C₆₁	—	2	4	no	—
53	C₂×Q₁₆×C₆₁	—	4	2	no	—
54	C₂×M₁₆×C₆₁	—	2	4	no	—
55	C₂×M₁₆×C₆₁	—	2	4	no	—
56	C₂×M₁₆×C₆₁	—	4	2	no	—
57	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
59	C₄⋊Q₈×C₆₁	—	2	4	no	—
60	C₄⋊Q₈×C₆₁	—	2	4	no	—
61	#125×C₆₁	—	2	8	no	—
62	C₂²⋊Q₈×C₆₁	—	2	8	no	—
63	C₂²⋊Q₈×C₆₁	—	2	4	no	—
64	C₂²⋊Q₈×C₆₁	—	2	4	no	—
65	C₂²⋊Q₈×C₆₁	D₄	1	8	yes	—
66	C₄×Q₈×C₆₁	—	2	8	no	—
67	C₄×Q₈×C₆₁	—	2	4	no	—
68	C₄×Q₈×C₆₁	—	2	4	no	—
69	#117×C₆₁	—	2	8	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
71	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
73	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
75	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
82	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
85	C₂×C₄²×C₆₁	—	2	4	no	—
86	C₂×C₄²×C₆₁	—	2	2	no	—
87	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
91	#106×C₆₁	—	2	4	no	—
92	#103×C₆₁	—	2	4	no	—
93	#103×C₆₁	—	2	4	no	—
94	#103×C₆₁	—	2	4	no	—
95	#103×C₆₁	—	4	2	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	1	no	—
101	#95×C₆₁	—	2	1	no	—
102	#95×C₆₁	—	2	1	no	—
103	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
104	C₂×Q₈×C₆₁	—	2	4	no	—
105	C₂×Q₈×C₆₁	—	2	2	no	—
106	C₂×Q₈×C₆₁	—	2	2	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	2	no	—
111	C₂×Q₈×C₆₁	—	2	1	no	—
112	C₂×Q₈×C₆₁	—	2	2	no	—
113	C₂×Q₈×C₆₁	—	2	1	no	—
114	C₂×Q₈×C₆₁	—	4	2	no	—
115	C₂×Q₈×C₆₁	—	4	2	no	—
116	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₆₁	—	2	2	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	1	no	—
122	C₂²×C₄×C₆₁	—	2	1	no	—
123	C₂²×C₄×C₆₁	—	2	2	no	—
124	C₂²×C₄×C₆₁	—	2	2	no	—
125	C₂²×C₄×C₆₁	—	2	2	no	—
126	C₂²×C₄×C₆₁	—	2	2	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	1	no	—
131	C₂²×C₄×C₆₁	—	4	1	no	—
132	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
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	M₁₆×C₆₁	—	4	8	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	—	2	2	no	—
146	C₂×C₈×C₆₁	#41	1	4	yes	—
147	C₄⋊C₄×C₆₁	—	2	4	no	—
148	C₄⋊C₄×C₆₁	—	2	4	no	—
149	C₄⋊C₄×C₆₁	—	2	8	no	—
150	C₄⋊C₄×C₆₁	—	2	4	no	—
151	C₄⋊C₄×C₆₁	—	2	8	no	—
152	C₄⋊C₄×C₆₁	—	2	2	no	—
153	C₄⋊C₄×C₆₁	—	2	2	no	—
154	C₄⋊C₄×C₆₁	—	2	2	no	—
155	C₄⋊C₄×C₆₁	—	2	1	no	—
156	C₄⋊C₄×C₆₁	—	2	1	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	C₂×D₄	1	4	yes	—
161	C₂²⋊C₄×C₆₁	—	2	8	no	—
162	C₂²⋊C₄×C₆₁	—	4	2	no	—
163	C₂²⋊C₄×C₆₁	—	4	2	no	—
164	C₄²×C₆₁	—	2	8	no	—
165	C₄²×C₆₁	—	2	2	no	—
166	C₄²×C₆₁	—	2	2	no	—
167	C₄²×C₆₁	—	2	2	no	—
168	C₄²×C₆₁	—	2	2	no	—
169	C₂³×C₆₁	—	2	1	no	—
170	C₂³×C₆₁	—	2	1	no	—
171	C₂³×C₆₁	—	2	1	no	—
172	C₂³×C₆₁	—	2	1	no	—
173	C₂³×C₆₁	—	2	1	no	—
174	C₂³×C₆₁	—	2	1	no	—
175	C₂³×C₆₁	#120	1	2	yes	—
176	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
177	Q₈×C₆₁	—	2	4	no	—
178	Q₈×C₆₁	—	2	4	no	—
179	Q₈×C₆₁	—	4	8	no	—
180	Q₈×C₆₁	—	4	2	no	—
181	Q₈×C₆₁	—	4	2	no	—
182	Q₈×C₆₁	—	4	2	no	—
183	Q₈×C₆₁	—	4	2	no	—
184	C₂×C₄×C₆₁	—	2	8	no	—
185	C₂×C₄×C₆₁	—	2	1	no	—
186	C₂×C₄×C₆₁	—	2	1	no	—
187	C₂×C₄×C₆₁	—	2	1	no	—
188	C₂×C₄×C₆₁	—	2	1	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	4	no	—
194	C₂×C₄×C₆₁	—	2	4	no	—
195	C₂×C₄×C₆₁	—	2	1	no	—
196	C₂×C₄×C₆₁	—	2	4	no	—
197	C₂×C₄×C₆₁	—	2	4	no	—
198	C₂×C₄×C₆₁	—	2	1	no	—
199	C₂×C₄×C₆₁	—	2	1	no	—
200	C₂×C₄×C₆₁	—	4	4	no	—
201	C₂×C₄×C₆₁	—	4	2	no	—
202	C₂×C₄×C₆₁	—	4	2	no	—
203	C₂×C₄×C₆₁	—	4	2	no	—
204	C₂×C₄×C₆₁	—	4	2	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	1	no	—
212	C₂×C₄×C₆₁	—	4	1	no	—
213	C₂×C₄×C₆₁	—	4	1	no	—
214	C₂×C₄×C₆₁	—	4	1	no	—
215	C₂×C₄×C₆₁	—	4	1	no	—
216	C₂×C₄×C₆₁	—	4	1	no	—
217	C₂×C₄×C₆₁	#120	1	2	yes	—
218	C₂×C₄×C₆₁	#137	1	2	yes	—
219	C₂×C₄×C₆₁	#137	1	2	yes	—
220	C₂×C₄×C₆₁	#137	1	2	yes	—
221	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
223	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
224	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
225	C₈×C₆₁	—	2	4	no	—
226	C₈×C₆₁	—	4	2	no	—
227	#25504	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂²×C₆₁	—	2	2	no	—
229	C₂²×C₆₁	—	2	2	no	—
230	C₂²×C₆₁	—	2	2	no	—
231	C₂²×C₆₁	—	4	1	no	—
232	C₂²×C₆₁	—	4	1	no	—
233	C₂²×C₆₁	—	4	1	no	—
234	C₂²×C₆₁	—	4	1	no	—
235	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
236	C₂²×C₆₁	#532	1	1	yes	characteristic
237	C₂²×C₆₁	#537	1	1	yes	characteristic
238	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
239	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
240	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
241	C₂²×C₆₁	#575	1	1	yes	characteristic
242	C₄×C₆₁	—	2	2	no	—
243	C₄×C₆₁	—	2	2	no	—
244	C₄×C₆₁	—	2	2	no	—
245	C₄×C₆₁	—	2	2	no	—
246	C₄×C₆₁	—	4	4	no	—
247	C₄×C₆₁	—	4	1	no	—
248	C₄×C₆₁	—	4	4	no	—
249	C₄×C₆₁	—	8	1	no	—
250	C₄×C₆₁	—	8	1	no	—
251	C₄×C₆₁	—	8	1	no	—
252	C₄×C₆₁	—	8	1	no	—
253	C₄×C₆₁	#546	1	2	yes	—
254	C₄×C₆₁	#547	1	2	yes	—
255	C₂×#533	C₂×C₆₁	1	1	yes	characteristic
256	C₂×#470	C₂×C₆₁	1	2	yes	—
257	#2855	C₂×C₆₁	1	1	yes	characteristic
258	#2058	C₂×C₆₁	1	1	yes	characteristic, complemented
259	#2043	C₂×C₆₁	1	1	yes	characteristic, complemented
260	#2024	C₂×C₆₁	1	1	yes	characteristic, complemented
261	#2016	C₂×C₆₁	1	1	yes	characteristic, complemented
262	#1894	C₂×C₆₁	1	2	yes	—
263	#1878	C₂×C₆₁	1	2	yes	complemented
264	#1865	C₂×C₆₁	1	2	yes	complemented
265	#1728	C₂×C₆₁	1	1	yes	characteristic
266	C₂×C₆₁	—	4	2	no	—
267	C₂×C₆₁	#2430	1	1	yes	characteristic
268	C₂×C₆₁	#3004	1	1	yes	characteristic
269	C₂×C₆₁	#3007	1	1	yes	characteristic
270	C₂×C₆₁	#3172	1	1	yes	characteristic
271	C₂×C₆₁	#3185	1	1	yes	characteristic
272	C₂×C₆₁	#3252	1	1	yes	characteristic
273	C₂×C₆₁	#3255	1	1	yes	characteristic
274	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
275	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
276	#533	—	2	8	no	—
277	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
278	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
279	C₂×#125	—	2	1	no	—
280	C₂×C₂²⋊Q₈	—	2	1	no	—
281	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
282	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
283	C₂×C₄×Q₈	—	2	1	no	—
284	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
285	C₂×#117	—	2	1	no	—
286	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
287	#470	—	2	8	no	—
288	C₂×#106	C₂²×C₆₁	1	2	yes	—
289	C₂×#103	C₂²×C₆₁	1	2	yes	—
290	C₂×#103	C₂²×C₆₁	1	2	yes	—
291	C₂×#103	C₂²×C₆₁	1	2	yes	—
292	C₂×#103	C₂²×C₆₁	1	2	yes	—
293	#391	C₂²×C₆₁	1	1	yes	characteristic
294	#391	C₂²×C₆₁	1	1	yes	characteristic
295	#389	C₂²×C₆₁	1	1	yes	characteristic
296	#389	C₂²×C₆₁	1	1	yes	characteristic
297	#387	—	2	1	no	—
298	#387	—	2	1	no	—
299	#385	—	2	1	no	—
300	#381	—	2	1	no	—
301	#380	C₂²×C₆₁	1	1	yes	characteristic
302	#340	C₂²×C₆₁	1	2	yes	—
303	#340	C₂²×C₆₁	1	2	yes	—
304	#336	C₂²×C₆₁	1	1	yes	characteristic
305	#336	C₂²×C₆₁	1	2	yes	—
306	#336	C₂²×C₆₁	1	1	yes	characteristic
307	C₆₁	#25504	1	1	yes	characteristic, direct product factor, Sylow
308	C₂²×Q₈	—	2	1	no	—
309	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
310	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
311	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
312	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
313	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
314	C₂×Q₁₆	—	2	4	no	—
315	C₂×Q₁₆	—	2	4	no	—
316	C₂×Q₁₆	—	4	2	no	—
317	C₂×M₁₆	—	2	4	no	—
318	C₂×M₁₆	—	2	4	no	—
319	C₂×M₁₆	—	4	2	no	—
320	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
321	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
322	C₄⋊Q₈	—	2	4	no	—
323	C₄⋊Q₈	—	2	4	no	—
324	#125	—	2	8	no	—
325	C₂²⋊Q₈	—	2	8	no	—
326	C₂²⋊Q₈	—	2	4	no	—
327	C₂²⋊Q₈	—	2	4	no	—
328	C₂²⋊Q₈	D₄×C₆₁	1	8	yes	—
329	C₄×Q₈	—	2	8	no	—
330	C₄×Q₈	—	2	4	no	—
331	C₄×Q₈	—	2	4	no	—
332	#117	—	2	8	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₄²	—	2	2	no	—
349	C₂×C₄²	—	2	4	no	—
350	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
351	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
354	#106	—	2	4	no	—
355	#103	—	2	4	no	—
356	#103	—	2	4	no	—
357	#103	—	2	4	no	—
358	#103	—	4	2	no	—
359	#95	—	2	1	no	—
360	#95	—	2	1	no	—
361	#95	—	2	1	no	—
362	#95	—	2	1	no	—
363	#95	—	2	1	no	—
364	#95	—	2	1	no	—
365	#95	—	2	1	no	—
366	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
367	C₂×Q₈	—	2	4	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	4	2	no	—
378	C₂×Q₈	—	4	2	no	—
379	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	4	1	no	—
395	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
398	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
401	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
402	Q₁₆	—	4	8	no	—
403	M₁₆	—	4	8	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	#41×C₆₁	1	4	yes	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	2	8	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	8	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	4	2	no	—
421	C₄⋊C₄	—	4	2	no	—
422	C₄⋊C₄	—	4	2	no	—
423	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
424	C₂²⋊C₄	—	2	8	no	—
425	C₂²⋊C₄	—	4	2	no	—
426	C₂²⋊C₄	—	4	2	no	—
427	C₄²	—	2	8	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	#120×C₆₁	1	2	yes	—
439	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
440	Q₈	—	2	4	no	—
441	Q₈	—	2	4	no	—
442	Q₈	—	4	8	no	—
443	Q₈	—	4	2	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	4	2	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	#120×C₆₁	1	2	yes	—
481	C₂×C₄	#137×C₆₁	1	2	yes	—
482	C₂×C₄	#137×C₆₁	1	2	yes	—
483	C₂×C₄	#137×C₆₁	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
485	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
486	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
487	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
488	C₈	—	2	4	no	—
489	C₈	—	4	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	1	no	—
497	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
498	C₂²	C₆₁×#532	1	1	yes	characteristic
499	C₂²	C₆₁×#537	1	1	yes	characteristic
500	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
501	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
502	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
503	C₂²	C₆₁×#575	1	1	yes	characteristic
504	C₄	—	2	2	no	—
505	C₄	—	2	2	no	—
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	1	no	—
510	C₄	—	4	4	no	—
511	C₄	—	8	1	no	—
512	C₄	—	8	1	no	—
513	C₄	—	8	1	no	—
514	C₄	—	8	1	no	—
515	C₄	C₆₁×#546	1	2	yes	—
516	C₄	C₆₁×#547	1	2	yes	—
517	C₂	—	4	2	no	—
518	C₂	C₆₁×#2430	1	1	yes	characteristic
519	C₂	C₆₁×#3004	1	1	yes	characteristic
520	C₂	C₆₁×#3007	1	1	yes	characteristic
521	C₂	C₆₁×#3172	1	1	yes	characteristic
522	C₂	C₆₁×#3185	1	1	yes	characteristic
523	C₂	C₆₁×#3252	1	1	yes	characteristic
524	C₂	C₆₁×#3255	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
4. C₆₁×#2058	C₂	semidirect
5. C₆₁×#2043	C₂	semidirect
6. C₆₁×#2024	C₂	semidirect
7. C₆₁×#2016	C₂	semidirect
9. C₆₁×#1878	C₂	semidirect
10. C₆₁×#1865	C₂	semidirect
227. #25504	C₆₁	direct (N × H)
258. #2058	C₂×C₆₁	semidirect
259. #2043	C₂×C₆₁	semidirect
260. #2024	C₂×C₆₁	semidirect
261. #2016	C₂×C₆₁	semidirect
263. #1878	C₂×C₆₁	semidirect
264. #1865	C₂×C₆₁	semidirect
307. C₆₁	#25504	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×#533	2
C₂×C₆₁×#470	2
C₆₁×#2855	2
C₆₁×#2058	2
C₆₁×#2043	2
C₆₁×#2024	2
C₆₁×#2016	2
C₆₁×#1894	2
C₆₁×#1878	2
C₆₁×#1865	2
C₆₁×#1728	2
#25504	61

Subgroups — C61×#25504 #29528937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25504 #29528937