Subgroups — C₆₁×#24501 #29527934

Order 15616.

1208 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#450	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#390	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2065	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2055	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1968	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1934	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1872	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1853	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1786	C₂	1	1	yes	maximal, characteristic
12	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
14	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₆₁	—	2	1	no	—
17	C₂²×C₂²⋊C₄×C₆₁	—	2	1	no	—
18	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#450	—	2	4	no	—
20	C₆₁×#431	—	2	4	no	—
21	C₂×#106×C₆₁	C₂²	1	2	yes	complemented
22	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	complemented
23	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
24	C₂×#102×C₆₁	C₂²	1	2	yes	—
25	C₂×#102×C₆₁	C₂²	1	2	yes	—
26	C₂×#102×C₆₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	complemented
30	C₆₁×#391	C₂²	1	1	yes	characteristic, complemented
31	C₆₁×#391	C₂²	1	1	yes	characteristic, complemented
32	C₆₁×#390	—	2	1	no	—
33	C₆₁×#390	—	2	1	no	—
34	C₆₁×#390	C₂²	1	2	yes	—
35	C₆₁×#390	C₂²	1	2	yes	—
36	C₆₁×#389	C₂²	1	1	yes	characteristic, complemented
37	C₆₁×#389	C₂²	1	1	yes	characteristic, complemented
38	C₆₁×#387	—	2	1	no	—
39	C₆₁×#387	—	2	1	no	—
40	C₆₁×#385	—	2	1	no	—
41	C₆₁×#381	—	2	1	no	—
42	C₆₁×#380	C₂²	1	1	yes	characteristic
43	C₆₁×#340	C₂²	1	2	yes	complemented
44	C₆₁×#340	C₂²	1	2	yes	complemented
45	C₂⁵×C₆₁	—	2	1	no	—
46	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₆₁	—	2	4	no	—
48	C₂²×D₄×C₆₁	—	2	1	no	—
49	C₂²×D₄×C₆₁	—	2	2	no	—
50	C₂²×D₄×C₆₁	—	2	2	no	—
51	C₂²×D₄×C₆₁	—	4	2	no	—
52	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
53	C₂³×C₄×C₆₁	—	2	1	no	—
54	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
57	C₂×SD₁₆×C₆₁	—	2	4	no	—
58	C₂×SD₁₆×C₆₁	—	2	4	no	—
59	C₂×SD₁₆×C₆₁	—	4	2	no	—
60	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
61	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
62	C₂²⋊Q₈×C₆₁	—	2	2	no	—
63	C₂²⋊Q₈×C₆₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₆₁	—	4	2	no	—
69	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₆₁	—	4	4	no	—
80	C₂×C₂²⋊C₄×C₆₁	—	4	4	no	—
81	C₂×C₄²×C₆₁	—	2	2	no	—
82	C₂×C₄²×C₆₁	—	2	2	no	—
83	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
87	#106×C₆₁	—	4	2	no	—
88	C₄⋊C₈×C₆₁	—	2	4	no	—
89	#103×C₆₁	—	4	2	no	—
90	#102×C₆₁	—	2	4	no	—
91	#102×C₆₁	—	2	4	no	—
92	#102×C₆₁	—	4	2	no	—
93	C₂²⋊C₈×C₆₁	—	2	2	no	—
94	C₂²⋊C₈×C₆₁	D₄	1	4	yes	—
95	C₄×C₈×C₆₁	—	2	4	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	—	2	4	no	—
104	C₂⁴×C₆₁	—	2	2	no	—
105	C₂⁴×C₆₁	—	4	2	no	—
106	C₂⁴×C₆₁	—	4	2	no	—
107	C₂⁴×C₆₁	—	4	2	no	—
108	C₂⁴×C₆₁	—	4	2	no	—
109	C₂⁴×C₆₁	—	4	2	no	—
110	C₂⁴×C₆₁	—	4	2	no	—
111	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂×Q₈×C₆₁	—	2	1	no	—
113	C₂×Q₈×C₆₁	—	2	1	no	—
114	C₂×Q₈×C₆₁	—	2	2	no	—
115	C₂×Q₈×C₆₁	—	2	2	no	—
116	C₂×D₄×C₆₁	—	2	4	no	—
117	C₂×D₄×C₆₁	—	2	2	no	—
118	C₂×D₄×C₆₁	—	2	2	no	—
119	C₂×D₄×C₆₁	—	2	2	no	—
120	C₂×D₄×C₆₁	—	2	2	no	—
121	C₂×D₄×C₆₁	—	2	2	no	—
122	C₂×D₄×C₆₁	—	4	8	no	—
123	C₂×D₄×C₆₁	—	4	8	no	—
124	C₂×D₄×C₆₁	—	4	2	no	—
125	C₂×D₄×C₆₁	—	4	2	no	—
126	C₂×D₄×C₆₁	#41	1	4	yes	—
127	C₂²×C₄×C₆₁	—	2	2	no	—
128	C₂²×C₄×C₆₁	—	2	2	no	—
129	C₂²×C₄×C₆₁	—	2	2	no	—
130	C₂²×C₄×C₆₁	—	2	2	no	—
131	C₂²×C₄×C₆₁	—	2	2	no	—
132	C₂²×C₄×C₆₁	—	2	2	no	—
133	C₂²×C₄×C₆₁	—	2	1	no	—
134	C₂²×C₄×C₆₁	—	2	1	no	—
135	C₂²×C₄×C₆₁	—	2	1	no	—
136	C₂²×C₄×C₆₁	—	2	1	no	—
137	C₂²×C₄×C₆₁	—	2	2	no	—
138	C₂²×C₄×C₆₁	—	4	1	no	—
139	C₂²×C₄×C₆₁	—	4	2	no	—
140	C₂²×C₄×C₆₁	—	4	2	no	—
141	C₂²×C₄×C₆₁	—	4	2	no	—
142	C₂²×C₄×C₆₁	SD₁₆	1	4	yes	complemented
143	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₆₁	#41	1	2	yes	—
150	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
151	SD₁₆×C₆₁	—	4	8	no	—
152	C₂×C₈×C₆₁	—	2	2	no	—
153	C₂×C₈×C₆₁	—	2	2	no	—
154	C₂×C₈×C₆₁	—	2	2	no	—
155	C₂×C₈×C₆₁	—	2	2	no	—
156	C₂×C₈×C₆₁	—	2	2	no	—
157	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
158	C₄⋊C₄×C₆₁	—	2	1	no	—
159	C₄⋊C₄×C₆₁	—	2	2	no	—
160	C₄⋊C₄×C₆₁	—	2	1	no	—
161	C₄⋊C₄×C₆₁	—	2	2	no	—
162	C₄⋊C₄×C₆₁	—	2	2	no	—
163	C₄⋊C₄×C₆₁	—	2	2	no	—
164	C₄⋊C₄×C₆₁	—	4	2	no	—
165	C₄⋊C₄×C₆₁	—	4	2	no	—
166	C₄⋊C₄×C₆₁	—	4	2	no	—
167	C₄⋊C₄×C₆₁	—	4	2	no	—
168	C₂²⋊C₄×C₆₁	—	4	4	no	—
169	C₂²⋊C₄×C₆₁	—	4	2	no	—
170	C₂²⋊C₄×C₆₁	—	4	2	no	—
171	C₂²⋊C₄×C₆₁	—	4	4	no	—
172	C₂²⋊C₄×C₆₁	—	4	4	no	—
173	C₂²⋊C₄×C₆₁	—	4	4	no	—
174	C₄²×C₆₁	—	2	2	no	—
175	C₄²×C₆₁	—	2	2	no	—
176	C₄²×C₆₁	—	2	1	no	—
177	C₄²×C₆₁	—	2	1	no	—
178	C₄²×C₆₁	—	2	1	no	—
179	C₄²×C₆₁	—	2	1	no	—
180	C₂³×C₆₁	—	2	1	no	—
181	C₂³×C₆₁	—	2	1	no	—
182	C₂³×C₆₁	—	2	1	no	—
183	C₂³×C₆₁	—	2	1	no	—
184	C₂³×C₆₁	—	2	4	no	—
185	C₂³×C₆₁	—	4	8	no	—
186	C₂³×C₆₁	—	4	8	no	—
187	C₂³×C₆₁	—	4	8	no	—
188	C₂³×C₆₁	—	4	2	no	—
189	C₂³×C₆₁	—	4	2	no	—
190	C₂³×C₆₁	—	4	2	no	—
191	C₂³×C₆₁	—	4	2	no	—
192	C₂³×C₆₁	—	4	2	no	—
193	C₂³×C₆₁	—	4	2	no	—
194	C₂³×C₆₁	—	8	4	no	—
195	C₂³×C₆₁	—	8	4	no	—
196	C₂³×C₆₁	—	8	4	no	—
197	C₂³×C₆₁	—	8	4	no	—
198	C₂³×C₆₁	#121	1	2	yes	—
199	C₂³×C₆₁	C₂×SD₁₆	1	2	yes	—
200	C₂³×C₆₁	#135	1	2	yes	—
201	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
202	Q₈×C₆₁	—	4	2	no	—
203	Q₈×C₆₁	—	4	2	no	—
204	D₄×C₆₁	—	2	4	no	—
205	D₄×C₆₁	—	2	4	no	—
206	D₄×C₆₁	—	4	8	no	—
207	D₄×C₆₁	—	4	2	no	—
208	D₄×C₆₁	—	4	2	no	—
209	C₂×C₄×C₆₁	—	2	1	no	—
210	C₂×C₄×C₆₁	—	2	1	no	—
211	C₂×C₄×C₆₁	—	2	1	no	—
212	C₂×C₄×C₆₁	—	2	1	no	—
213	C₂×C₄×C₆₁	—	2	1	no	—
214	C₂×C₄×C₆₁	—	2	1	no	—
215	C₂×C₄×C₆₁	—	2	1	no	—
216	C₂×C₄×C₆₁	—	2	1	no	—
217	C₂×C₄×C₆₁	—	2	8	no	—
218	C₂×C₄×C₆₁	—	2	4	no	—
219	C₂×C₄×C₆₁	—	2	4	no	—
220	C₂×C₄×C₆₁	—	2	1	no	—
221	C₂×C₄×C₆₁	—	2	1	no	—
222	C₂×C₄×C₆₁	—	2	1	no	—
223	C₂×C₄×C₆₁	—	4	4	no	—
224	C₂×C₄×C₆₁	—	4	1	no	—
225	C₂×C₄×C₆₁	—	4	1	no	—
226	C₂×C₄×C₆₁	—	4	1	no	—
227	C₂×C₄×C₆₁	—	4	1	no	—
228	C₂×C₄×C₆₁	—	4	2	no	—
229	C₂×C₄×C₆₁	—	4	1	no	—
230	C₂×C₄×C₆₁	—	4	1	no	—
231	C₂×C₄×C₆₁	—	4	2	no	—
232	C₂×C₄×C₆₁	—	4	1	no	—
233	C₂×C₄×C₆₁	—	4	1	no	—
234	C₂×C₄×C₆₁	—	4	2	no	—
235	C₂×C₄×C₆₁	—	4	1	no	—
236	C₂×C₄×C₆₁	—	4	1	no	—
237	C₂×C₄×C₆₁	—	4	1	no	—
238	C₂×C₄×C₆₁	—	4	1	no	—
239	C₂×C₄×C₆₁	—	8	4	no	—
240	C₂×C₄×C₆₁	#121	1	2	yes	—
241	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
242	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
243	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
244	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
246	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
248	C₈×C₆₁	—	2	4	no	—
249	C₈×C₆₁	—	4	2	no	—
250	#24501	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₂²×C₆₁	—	2	2	no	—
252	C₂²×C₆₁	—	2	2	no	—
253	C₂²×C₆₁	—	2	2	no	—
254	C₂²×C₆₁	—	2	2	no	—
255	C₂²×C₆₁	—	2	2	no	—
256	C₂²×C₆₁	—	2	2	no	—
257	C₂²×C₆₁	—	4	4	no	—
258	C₂²×C₆₁	—	4	4	no	—
259	C₂²×C₆₁	—	4	4	no	—
260	C₂²×C₆₁	—	8	16	no	—
261	C₂²×C₆₁	—	8	2	no	—
262	C₂²×C₆₁	—	8	2	no	—
263	C₂²×C₆₁	—	8	2	no	—
264	C₂²×C₆₁	—	8	2	no	—
265	C₂²×C₆₁	#465	1	4	yes	—
266	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
267	C₂²×C₆₁	#525	1	1	yes	characteristic
268	C₂²×C₆₁	#535	1	1	yes	characteristic
269	C₂²×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
270	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
271	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
272	C₂²×C₆₁	#575	1	1	yes	characteristic
273	C₄×C₆₁	—	2	2	no	—
274	C₄×C₆₁	—	2	2	no	—
275	C₄×C₆₁	—	2	2	no	—
276	C₄×C₆₁	—	2	2	no	—
277	C₄×C₆₁	—	4	1	no	—
278	C₄×C₆₁	—	8	1	no	—
279	C₄×C₆₁	—	8	1	no	—
280	C₄×C₆₁	—	8	2	no	—
281	C₄×C₆₁	—	8	1	no	—
282	C₄×C₆₁	—	8	1	no	—
283	C₄×C₆₁	#546	1	2	yes	—
284	C₄×C₆₁	#551	1	2	yes	—
285	C₂×#450	C₂×C₆₁	1	1	yes	characteristic
286	C₂×#431	C₂×C₆₁	1	1	yes	characteristic, complemented
287	#2855	C₂×C₆₁	1	1	yes	characteristic, complemented
288	C₂×#390	C₂×C₆₁	1	1	yes	characteristic
289	#2065	C₂×C₆₁	1	2	yes	complemented
290	#2055	C₂×C₆₁	1	2	yes	complemented
291	#1968	C₂×C₆₁	1	2	yes	complemented
292	#1934	C₂×C₆₁	1	2	yes	complemented
293	#1872	C₂×C₆₁	1	1	yes	characteristic, complemented
294	#1853	C₂×C₆₁	1	1	yes	characteristic, complemented
295	#1786	C₂×C₆₁	1	1	yes	characteristic
296	C₂×C₆₁	—	2	4	no	—
297	C₂×C₆₁	—	8	4	no	—
298	C₂×C₆₁	#2411	1	1	yes	characteristic
299	C₂×C₆₁	C₂×#465	1	1	yes	characteristic
300	C₂×C₆₁	#3055	1	1	yes	characteristic
301	C₂×C₆₁	#3101	1	1	yes	characteristic
302	C₂×C₆₁	#3105	1	1	yes	characteristic
303	C₂×C₆₁	#3208	1	1	yes	characteristic
304	C₂×C₆₁	#3211	1	1	yes	characteristic
305	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
306	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
307	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
308	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
309	C₂²×C₂²⋊C₄	—	2	1	no	—
310	C₂²×C₂²⋊C₄	—	2	1	no	—
311	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
312	#450	—	2	4	no	—
313	#431	—	2	4	no	—
314	C₂×#106	C₂²×C₆₁	1	2	yes	complemented
315	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	complemented
316	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
317	C₂×#102	C₂²×C₆₁	1	2	yes	—
318	C₂×#102	C₂²×C₆₁	1	2	yes	—
319	C₂×#102	C₂²×C₆₁	1	2	yes	—
320	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
321	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
322	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	complemented
323	#391	C₂²×C₆₁	1	1	yes	characteristic, complemented
324	#391	C₂²×C₆₁	1	1	yes	characteristic, complemented
325	#390	—	2	1	no	—
326	#390	—	2	1	no	—
327	#390	C₂²×C₆₁	1	2	yes	—
328	#390	C₂²×C₆₁	1	2	yes	—
329	#389	C₂²×C₆₁	1	1	yes	characteristic, complemented
330	#389	C₂²×C₆₁	1	1	yes	characteristic, complemented
331	#387	—	2	1	no	—
332	#387	—	2	1	no	—
333	#385	—	2	1	no	—
334	#381	—	2	1	no	—
335	#380	C₂²×C₆₁	1	1	yes	characteristic
336	#340	C₂²×C₆₁	1	2	yes	complemented
337	#340	C₂²×C₆₁	1	2	yes	complemented
338	C₆₁	#24501	1	1	yes	characteristic, direct product factor, Sylow
339	C₂⁵	—	2	1	no	—
340	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
341	C₂²×D₄	—	2	4	no	—
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	—	2	2	no	—
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	—	4	2	no	—
346	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
347	C₂³×C₄	—	2	1	no	—
348	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
349	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
350	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
351	C₂×SD₁₆	—	2	4	no	—
352	C₂×SD₁₆	—	2	4	no	—
353	C₂×SD₁₆	—	4	2	no	—
354	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
355	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	4	2	no	—
363	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	—	2	2	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	4	4	no	—
374	C₂×C₂²⋊C₄	—	4	4	no	—
375	C₂×C₄²	—	2	2	no	—
376	C₂×C₄²	—	2	2	no	—
377	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
378	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
381	#106	—	4	2	no	—
382	C₄⋊C₈	—	2	4	no	—
383	#103	—	4	2	no	—
384	#102	—	2	4	no	—
385	#102	—	2	4	no	—
386	#102	—	4	2	no	—
387	C₂²⋊C₈	—	2	2	no	—
388	C₂²⋊C₈	D₄×C₆₁	1	4	yes	—
389	C₄×C₈	—	2	4	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	#95	—	2	1	no	—
393	#95	—	2	1	no	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	C₂⁴	—	2	4	no	—
398	C₂⁴	—	2	2	no	—
399	C₂⁴	—	4	2	no	—
400	C₂⁴	—	4	2	no	—
401	C₂⁴	—	4	2	no	—
402	C₂⁴	—	4	2	no	—
403	C₂⁴	—	4	2	no	—
404	C₂⁴	—	4	2	no	—
405	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	4	8	no	—
417	C₂×D₄	—	4	8	no	—
418	C₂×D₄	—	4	2	no	—
419	C₂×D₄	—	4	2	no	—
420	C₂×D₄	#41×C₆₁	1	4	yes	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	4	1	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	—	4	2	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	SD₁₆×C₆₁	1	4	yes	complemented
437	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
440	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
443	C₂²×C₄	#41×C₆₁	1	2	yes	—
444	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
445	SD₁₆	—	4	8	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	—	4	2	no	—
460	C₄⋊C₄	—	4	2	no	—
461	C₄⋊C₄	—	4	2	no	—
462	C₂²⋊C₄	—	4	4	no	—
463	C₂²⋊C₄	—	4	2	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₂²⋊C₄	—	4	4	no	—
466	C₂²⋊C₄	—	4	4	no	—
467	C₂²⋊C₄	—	4	4	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₂³	—	2	1	no	—
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	4	8	no	—
480	C₂³	—	4	8	no	—
481	C₂³	—	4	8	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	8	4	no	—
489	C₂³	—	8	4	no	—
490	C₂³	—	8	4	no	—
491	C₂³	—	8	4	no	—
492	C₂³	#121×C₆₁	1	2	yes	—
493	C₂³	C₂×SD₁₆×C₆₁	1	2	yes	—
494	C₂³	#135×C₆₁	1	2	yes	—
495	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
496	Q₈	—	4	2	no	—
497	Q₈	—	4	2	no	—
498	D₄	—	2	4	no	—
499	D₄	—	2	4	no	—
500	D₄	—	4	8	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	8	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	8	4	no	—
534	C₂×C₄	#121×C₆₁	1	2	yes	—
535	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
536	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
537	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
538	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
539	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
540	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
541	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
542	C₈	—	2	4	no	—
543	C₈	—	4	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	4	no	—
553	C₂²	—	8	16	no	—
554	C₂²	—	8	2	no	—
555	C₂²	—	8	2	no	—
556	C₂²	—	8	2	no	—
557	C₂²	—	8	2	no	—
558	C₂²	C₆₁×#465	1	4	yes	—
559	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
560	C₂²	C₆₁×#525	1	1	yes	characteristic
561	C₂²	C₆₁×#535	1	1	yes	characteristic
562	C₂²	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
563	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
564	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
565	C₂²	C₆₁×#575	1	1	yes	characteristic
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	4	1	no	—
571	C₄	—	8	1	no	—
572	C₄	—	8	1	no	—
573	C₄	—	8	1	no	—
574	C₄	—	8	2	no	—
575	C₄	—	8	1	no	—
576	C₄	C₆₁×#546	1	2	yes	—
577	C₄	C₆₁×#551	1	2	yes	—
578	C₂	—	2	4	no	—
579	C₂	—	8	4	no	—
580	C₂	C₆₁×#2411	1	1	yes	characteristic
581	C₂	C₂×C₆₁×#465	1	1	yes	characteristic
582	C₂	C₆₁×#3055	1	1	yes	characteristic
583	C₂	C₆₁×#3101	1	1	yes	characteristic
584	C₂	C₆₁×#3105	1	1	yes	characteristic
585	C₂	C₆₁×#3208	1	1	yes	characteristic
586	C₂	C₆₁×#3211	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂³×D₄×C₆₁	C₂²
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
2. C₂×C₆₁×#431	C₂	semidirect
3. C₆₁×#2855	C₂	semidirect
5. C₆₁×#2065	C₂	semidirect
6. C₆₁×#2055	C₂	semidirect
7. C₆₁×#1968	C₂	semidirect
8. C₆₁×#1934	C₂	semidirect
9. C₆₁×#1872	C₂	semidirect
10. C₆₁×#1853	C₂	semidirect
21. C₂×#106×C₆₁	C₂²	semidirect
22. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
23. C₂×#103×C₆₁	C₂²	semidirect
29. C₂×C₄×C₈×C₆₁	C₂²	semidirect
30. C₆₁×#391	C₂²	semidirect
31. C₆₁×#391	C₂²	semidirect
36. C₆₁×#389	C₂²	semidirect
37. C₆₁×#389	C₂²	semidirect
43. C₆₁×#340	C₂²	semidirect
44. C₆₁×#340	C₂²	semidirect
142. C₂²×C₄×C₆₁	SD₁₆	semidirect
250. #24501	C₆₁	direct (N × H)
286. C₂×#431	C₂×C₆₁	semidirect
287. #2855	C₂×C₆₁	semidirect
289. #2065	C₂×C₆₁	semidirect
290. #2055	C₂×C₆₁	semidirect
291. #1968	C₂×C₆₁	semidirect
292. #1934	C₂×C₆₁	semidirect
293. #1872	C₂×C₆₁	semidirect
294. #1853	C₂×C₆₁	semidirect
314. C₂×#106	C₂²×C₆₁	semidirect
315. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
316. C₂×#103	C₂²×C₆₁	semidirect
322. C₂×C₄×C₈	C₂²×C₆₁	semidirect
323. #391	C₂²×C₆₁	semidirect
324. #391	C₂²×C₆₁	semidirect
329. #389	C₂²×C₆₁	semidirect
330. #389	C₂²×C₆₁	semidirect
336. #340	C₂²×C₆₁	semidirect
337. #340	C₂²×C₆₁	semidirect
338. C₆₁	#24501	direct (N × H)
436. C₂²×C₄	SD₁₆×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×#450	2
C₂×C₆₁×#431	2
C₆₁×#2855	2
C₂×C₆₁×#390	2
C₆₁×#2065	2
C₆₁×#2055	2
C₆₁×#1968	2
C₆₁×#1934	2
C₆₁×#1872	2
C₆₁×#1853	2
C₆₁×#1786	2
#24501	61

Subgroups — C61×#24501 #29527934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24501 #29527934