Subgroups — C₆₁×#24570 #29528003

Order 15616.

936 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3006	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#417	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2880	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2078	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2051	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1907	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1900	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1855	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1821	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1816	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#131×C₆₁	C₂²	1	2	yes	—
16	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#480	—	2	1	no	—
20	C₆₁×#480	—	2	1	no	—
21	C₆₁×#480	—	2	2	no	—
22	C₆₁×#449	—	2	1	no	—
23	C₆₁×#449	—	2	1	no	—
24	C₆₁×#448	—	2	1	no	—
25	C₆₁×#447	—	2	1	no	—
26	C₂×#108×C₆₁	C₂²	1	2	yes	complemented
27	C₂×#107×C₆₁	C₂²	1	2	yes	complemented
28	C₆₁×#417	—	2	1	no	—
29	C₆₁×#417	—	2	1	no	—
30	C₆₁×#417	C₂²	1	2	yes	—
31	C₆₁×#417	C₂²	1	1	yes	characteristic
32	C₆₁×#417	C₂²	1	2	yes	—
33	C₆₁×#417	C₂²	1	1	yes	characteristic
34	C₂×#103×C₆₁	—	2	1	no	—
35	C₂×#102×C₆₁	—	2	1	no	—
36	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
37	C₂×#100×C₆₁	C₂²	1	2	yes	complemented
38	C₆₁×#408	—	2	2	no	—
39	C₆₁×#408	C₂²	1	2	yes	—
40	C₆₁×#407	—	2	1	no	—
41	C₆₁×#407	C₂²	1	1	yes	characteristic
42	C₆₁×#407	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₈×C₆₁	—	2	1	no	—
44	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#343	C₂²	1	2	yes	complemented
46	C₆₁×#343	C₂²	1	2	yes	complemented
47	C₆₁×#343	C₂²	1	2	yes	complemented
48	C₆₁×#341	C₂²	1	2	yes	complemented
49	C₂×#41×C₆₁	—	2	1	no	—
50	C₂×#41×C₆₁	—	2	1	no	—
51	C₂×#41×C₆₁	—	2	4	no	—
52	C₂×#41×C₆₁	—	4	2	no	—
53	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
54	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
55	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
56	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
58	C₂²×D₄×C₆₁	—	2	1	no	—
59	C₂²×D₄×C₆₁	—	2	1	no	—
60	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₆₁	—	2	1	no	—
63	C₂³×C₄×C₆₁	—	2	1	no	—
64	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
65	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
66	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
67	C₂×SD₁₆×C₆₁	—	2	1	no	—
68	C₂×SD₁₆×C₆₁	—	2	1	no	—
69	C₂×D₈×C₆₁	—	2	1	no	—
70	C₂×D₈×C₆₁	—	2	1	no	—
71	#131×C₆₁	—	2	4	no	—
72	#131×C₆₁	—	4	2	no	—
73	C₂×M₁₆×C₆₁	—	2	1	no	—
74	C₂×M₁₆×C₆₁	—	2	2	no	—
75	C₂×M₁₆×C₆₁	—	4	2	no	—
76	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
77	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
78	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
79	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₆₁	—	2	1	no	—
81	C₂²×C₈×C₆₁	—	2	2	no	—
82	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
83	#121×C₆₁	—	2	1	no	—
84	#121×C₆₁	—	2	1	no	—
85	#121×C₆₁	—	2	1	no	—
86	#121×C₆₁	—	2	1	no	—
87	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
88	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
89	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
90	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
91	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
92	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
95	#108×C₆₁	—	4	2	no	—
96	#107×C₆₁	—	2	2	no	—
97	#107×C₆₁	—	2	2	no	—
98	#103×C₆₁	—	2	2	no	—
99	#103×C₆₁	—	2	2	no	—
100	#103×C₆₁	—	2	1	no	—
101	#103×C₆₁	—	2	1	no	—
102	#102×C₆₁	—	2	2	no	—
103	#102×C₆₁	—	2	2	no	—
104	#102×C₆₁	—	2	1	no	—
105	#102×C₆₁	—	2	1	no	—
106	#102×C₆₁	—	2	2	no	—
107	#102×C₆₁	—	2	2	no	—
108	#100×C₆₁	—	4	2	no	—
109	C₂²⋊C₈×C₆₁	—	2	1	no	—
110	C₂²⋊C₈×C₆₁	—	2	1	no	—
111	C₂²⋊C₈×C₆₁	—	2	1	no	—
112	C₂²⋊C₈×C₆₁	—	2	1	no	—
113	C₂²⋊C₈×C₆₁	—	2	2	no	—
114	C₂²⋊C₈×C₆₁	—	2	2	no	—
115	C₂²⋊C₈×C₆₁	D₄	1	1	yes	characteristic
116	C₂²⋊C₈×C₆₁	D₄	1	1	yes	characteristic
117	C₂²⋊C₈×C₆₁	D₄	1	2	yes	—
118	C₂⁴×C₆₁	—	2	1	no	—
119	C₂⁴×C₆₁	—	2	1	no	—
120	C₂⁴×C₆₁	#41	1	1	yes	characteristic
121	#41×C₆₁	—	2	2	no	—
122	#41×C₆₁	—	2	2	no	—
123	#41×C₆₁	—	2	2	no	—
124	#41×C₆₁	—	2	2	no	—
125	#41×C₆₁	—	2	2	no	—
126	#41×C₆₁	—	4	4	no	—
127	#41×C₆₁	—	4	1	no	—
128	#41×C₆₁	—	4	1	no	—
129	#41×C₆₁	—	4	4	no	—
130	#41×C₆₁	#41	1	4	yes	—
131	C₂×Q₈×C₆₁	—	2	1	no	—
132	C₂×Q₈×C₆₁	—	2	2	no	—
133	C₂×Q₈×C₆₁	—	4	1	no	—
134	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
135	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
136	C₂×D₄×C₆₁	—	2	1	no	—
137	C₂×D₄×C₆₁	—	2	2	no	—
138	C₂×D₄×C₆₁	—	2	1	no	—
139	C₂×D₄×C₆₁	—	2	1	no	—
140	C₂×D₄×C₆₁	—	2	1	no	—
141	C₂×D₄×C₆₁	—	2	1	no	—
142	C₂×D₄×C₆₁	—	2	1	no	—
143	C₂×D₄×C₆₁	—	2	1	no	—
144	C₂×D₄×C₆₁	—	2	2	no	—
145	C₂×D₄×C₆₁	—	2	2	no	—
146	C₂×D₄×C₆₁	—	4	1	no	—
147	C₂×D₄×C₆₁	—	4	4	no	—
148	C₂×D₄×C₆₁	—	4	1	no	—
149	C₂×D₄×C₆₁	—	4	1	no	—
150	C₂×D₄×C₆₁	—	8	2	no	—
151	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₆₁	—	2	1	no	—
154	C₂²×C₄×C₆₁	—	2	2	no	—
155	C₂²×C₄×C₆₁	—	2	2	no	—
156	C₂²×C₄×C₆₁	—	2	1	no	—
157	C₂²×C₄×C₆₁	—	2	1	no	—
158	C₂²×C₄×C₆₁	—	2	1	no	—
159	C₂²×C₄×C₆₁	—	2	1	no	—
160	C₂²×C₄×C₆₁	—	2	1	no	—
161	C₂²×C₄×C₆₁	—	2	2	no	—
162	C₂²×C₄×C₆₁	—	4	4	no	—
163	C₂²×C₄×C₆₁	—	4	1	no	—
164	C₂²×C₄×C₆₁	—	4	1	no	—
165	C₂²×C₄×C₆₁	—	8	2	no	—
166	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
171	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
172	SD₁₆×C₆₁	—	4	2	no	—
173	SD₁₆×C₆₁	—	4	2	no	—
174	D₈×C₆₁	—	4	2	no	—
175	D₈×C₆₁	—	4	2	no	—
176	M₁₆×C₆₁	—	2	2	no	—
177	M₁₆×C₆₁	—	2	2	no	—
178	M₁₆×C₆₁	—	2	2	no	—
179	M₁₆×C₆₁	—	2	2	no	—
180	M₁₆×C₆₁	—	2	2	no	—
181	M₁₆×C₆₁	—	2	2	no	—
182	M₁₆×C₆₁	—	4	4	no	—
183	M₁₆×C₆₁	—	4	2	no	—
184	C₂×C₈×C₆₁	—	2	2	no	—
185	C₂×C₈×C₆₁	—	2	2	no	—
186	C₂×C₈×C₆₁	—	2	2	no	—
187	C₂×C₈×C₆₁	—	2	1	no	—
188	C₂×C₈×C₆₁	—	2	1	no	—
189	C₂×C₈×C₆₁	—	2	2	no	—
190	C₂×C₈×C₆₁	—	4	4	no	—
191	C₂×C₈×C₆₁	—	4	2	no	—
192	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
193	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
194	C₄⋊C₄×C₆₁	—	2	2	no	—
195	C₄⋊C₄×C₆₁	—	2	1	no	—
196	C₄⋊C₄×C₆₁	—	2	2	no	—
197	C₄⋊C₄×C₆₁	—	2	1	no	—
198	C₄⋊C₄×C₆₁	—	4	1	no	—
199	C₄⋊C₄×C₆₁	—	4	1	no	—
200	C₂²⋊C₄×C₆₁	—	4	1	no	—
201	C₂²⋊C₄×C₆₁	—	4	1	no	—
202	C₂³×C₆₁	—	2	1	no	—
203	C₂³×C₆₁	—	2	2	no	—
204	C₂³×C₆₁	—	2	2	no	—
205	C₂³×C₆₁	—	2	1	no	—
206	C₂³×C₆₁	—	4	1	no	—
207	C₂³×C₆₁	—	4	2	no	—
208	C₂³×C₆₁	—	4	2	no	—
209	C₂³×C₆₁	—	4	1	no	—
210	C₂³×C₆₁	—	4	2	no	—
211	C₂³×C₆₁	—	8	1	no	—
212	C₂³×C₆₁	—	8	1	no	—
213	C₂³×C₆₁	—	8	1	no	—
214	C₂³×C₆₁	#121	1	1	yes	characteristic
215	C₂³×C₆₁	#121	1	1	yes	characteristic
216	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
217	Q₈×C₆₁	—	2	1	no	—
218	Q₈×C₆₁	—	2	1	no	—
219	Q₈×C₆₁	—	2	1	no	—
220	Q₈×C₆₁	—	4	2	no	—
221	Q₈×C₆₁	#123	1	2	yes	—
222	D₄×C₆₁	—	2	4	no	—
223	D₄×C₆₁	—	2	1	no	—
224	D₄×C₆₁	—	2	1	no	—
225	D₄×C₆₁	—	2	1	no	—
226	D₄×C₆₁	—	4	2	no	—
227	D₄×C₆₁	—	4	2	no	—
228	D₄×C₆₁	—	4	2	no	—
229	D₄×C₆₁	—	4	2	no	—
230	D₄×C₆₁	—	4	1	no	—
231	D₄×C₆₁	—	4	1	no	—
232	D₄×C₆₁	—	4	2	no	—
233	D₄×C₆₁	—	8	2	no	—
234	D₄×C₆₁	—	8	2	no	—
235	D₄×C₆₁	#123	1	2	yes	—
236	C₂×C₄×C₆₁	—	2	1	no	—
237	C₂×C₄×C₆₁	—	2	2	no	—
238	C₂×C₄×C₆₁	—	2	1	no	—
239	C₂×C₄×C₆₁	—	2	1	no	—
240	C₂×C₄×C₆₁	—	2	1	no	—
241	C₂×C₄×C₆₁	—	2	1	no	—
242	C₂×C₄×C₆₁	—	2	4	no	—
243	C₂×C₄×C₆₁	—	2	2	no	—
244	C₂×C₄×C₆₁	—	2	2	no	—
245	C₂×C₄×C₆₁	—	2	1	no	—
246	C₂×C₄×C₆₁	—	4	2	no	—
247	C₂×C₄×C₆₁	—	4	2	no	—
248	C₂×C₄×C₆₁	—	4	2	no	—
249	C₂×C₄×C₆₁	—	4	2	no	—
250	C₂×C₄×C₆₁	—	4	1	no	—
251	C₂×C₄×C₆₁	—	4	2	no	—
252	C₂×C₄×C₆₁	—	8	2	no	—
253	C₂×C₄×C₆₁	—	8	2	no	—
254	C₂×C₄×C₆₁	—	8	2	no	—
255	C₂×C₄×C₆₁	—	8	1	no	—
256	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
257	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
258	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
261	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
262	C₈×C₆₁	—	2	2	no	—
263	C₈×C₆₁	—	2	2	no	—
264	C₈×C₆₁	—	4	1	no	—
265	C₈×C₆₁	—	4	2	no	—
266	C₈×C₆₁	—	4	1	no	—
267	C₈×C₆₁	—	4	2	no	—
268	#24570	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂²×C₆₁	—	2	1	no	—
270	C₂²×C₆₁	—	2	1	no	—
271	C₂²×C₆₁	—	2	1	no	—
272	C₂²×C₆₁	—	2	1	no	—
273	C₂²×C₆₁	—	2	1	no	—
274	C₂²×C₆₁	—	2	2	no	—
275	C₂²×C₆₁	—	2	1	no	—
276	C₂²×C₆₁	—	2	1	no	—
277	C₂²×C₆₁	—	4	4	no	—
278	C₂²×C₆₁	—	4	1	no	—
279	C₂²×C₆₁	—	4	1	no	—
280	C₂²×C₆₁	—	4	1	no	—
281	C₂²×C₆₁	—	4	1	no	—
282	C₂²×C₆₁	—	4	1	no	—
283	C₂²×C₆₁	—	8	4	no	—
284	C₂²×C₆₁	—	8	1	no	—
285	C₂²×C₆₁	—	8	1	no	—
286	C₂²×C₆₁	—	8	1	no	—
287	C₂²×C₆₁	—	16	2	no	—
288	C₂²×C₆₁	#472	1	2	yes	—
289	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
290	C₂²×C₆₁	#551	1	2	yes	—
291	C₄×C₆₁	—	2	1	no	—
292	C₄×C₆₁	—	2	1	no	—
293	C₄×C₆₁	—	2	2	no	—
294	C₄×C₆₁	—	4	1	no	—
295	C₄×C₆₁	—	8	2	no	—
296	C₄×C₆₁	—	8	1	no	—
297	C₄×C₆₁	C₂×#123	1	1	yes	characteristic
298	C₄×C₆₁	#534	1	1	yes	characteristic
299	C₄×C₆₁	#546	1	2	yes	—
300	C₂×#480	C₂×C₆₁	1	1	yes	characteristic, complemented
301	#3006	C₂×C₆₁	1	1	yes	characteristic
302	C₂×#417	C₂×C₆₁	1	1	yes	characteristic, complemented
303	#2880	C₂×C₆₁	1	1	yes	characteristic, complemented
304	#2078	C₂×C₆₁	1	2	yes	complemented
305	#2051	C₂×C₆₁	1	2	yes	complemented
306	#1907	C₂×C₆₁	1	2	yes	complemented
307	#1900	C₂×C₆₁	1	1	yes	characteristic, complemented
308	#1855	C₂×C₆₁	1	1	yes	characteristic, complemented
309	#1821	C₂×C₆₁	1	1	yes	characteristic, complemented
310	#1816	C₂×C₆₁	1	2	yes	complemented
311	C₂×C₆₁	—	2	2	no	—
312	C₂×C₆₁	—	2	2	no	—
313	C₂×C₆₁	—	4	1	no	—
314	C₂×C₆₁	—	4	2	no	—
315	C₂×C₆₁	—	8	1	no	—
316	C₂×C₆₁	—	16	1	no	—
317	C₂×C₆₁	#2412	1	1	yes	characteristic
318	C₂×C₆₁	C₂×#472	1	1	yes	characteristic
319	C₂×C₆₁	#3069	1	1	yes	characteristic
320	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
321	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
322	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
323	C₂×#131	C₂²×C₆₁	1	2	yes	—
324	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
325	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
326	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
327	#480	—	2	1	no	—
328	#480	—	2	1	no	—
329	#480	—	2	2	no	—
330	#449	—	2	1	no	—
331	#449	—	2	1	no	—
332	#448	—	2	1	no	—
333	#447	—	2	1	no	—
334	C₂×#108	C₂²×C₆₁	1	2	yes	complemented
335	C₂×#107	C₂²×C₆₁	1	2	yes	complemented
336	#417	—	2	1	no	—
337	#417	—	2	1	no	—
338	#417	C₂²×C₆₁	1	2	yes	—
339	#417	C₂²×C₆₁	1	1	yes	characteristic
340	#417	C₂²×C₆₁	1	2	yes	—
341	#417	C₂²×C₆₁	1	1	yes	characteristic
342	C₂×#103	—	2	1	no	—
343	C₂×#102	—	2	1	no	—
344	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
345	C₂×#100	C₂²×C₆₁	1	2	yes	complemented
346	#408	—	2	2	no	—
347	#408	C₂²×C₆₁	1	2	yes	—
348	#407	—	2	1	no	—
349	#407	C₂²×C₆₁	1	1	yes	characteristic
350	#407	C₂²×C₆₁	1	1	yes	characteristic
351	C₂×C₂²⋊C₈	—	2	1	no	—
352	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
353	#343	C₂²×C₆₁	1	2	yes	complemented
354	#343	C₂²×C₆₁	1	2	yes	complemented
355	#343	C₂²×C₆₁	1	2	yes	complemented
356	#341	C₂²×C₆₁	1	2	yes	complemented
357	C₆₁	#24570	1	1	yes	characteristic, direct product factor, Sylow
358	C₂×#41	—	2	1	no	—
359	C₂×#41	—	2	1	no	—
360	C₂×#41	—	2	4	no	—
361	C₂×#41	—	4	2	no	—
362	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
363	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
364	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
365	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
366	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
367	C₂²×D₄	—	2	1	no	—
368	C₂²×D₄	—	2	1	no	—
369	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
370	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	—	2	1	no	—
373	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
374	AGL(1,ℤ/8)	—	2	4	no	—
375	AGL(1,ℤ/8)	—	4	2	no	—
376	C₂×SD₁₆	—	2	1	no	—
377	C₂×SD₁₆	—	2	1	no	—
378	C₂×D₈	—	2	1	no	—
379	C₂×D₈	—	2	1	no	—
380	#131	—	2	4	no	—
381	#131	—	4	2	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	2	no	—
384	C₂×M₁₆	—	4	2	no	—
385	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
386	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
387	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
388	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
389	C₂²×C₈	—	2	1	no	—
390	C₂²×C₈	—	2	2	no	—
391	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
392	#121	—	2	1	no	—
393	#121	—	2	1	no	—
394	#121	—	2	1	no	—
395	#121	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
402	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	#108	—	4	2	no	—
405	#107	—	2	2	no	—
406	#107	—	2	2	no	—
407	#103	—	2	2	no	—
408	#103	—	2	2	no	—
409	#103	—	2	1	no	—
410	#103	—	2	1	no	—
411	#102	—	2	2	no	—
412	#102	—	2	2	no	—
413	#102	—	2	1	no	—
414	#102	—	2	1	no	—
415	#102	—	2	2	no	—
416	#102	—	2	2	no	—
417	#100	—	4	2	no	—
418	C₂²⋊C₈	—	2	1	no	—
419	C₂²⋊C₈	—	2	1	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	C₂²⋊C₈	—	2	2	no	—
423	C₂²⋊C₈	—	2	2	no	—
424	C₂²⋊C₈	D₄×C₆₁	1	1	yes	characteristic
425	C₂²⋊C₈	D₄×C₆₁	1	1	yes	characteristic
426	C₂²⋊C₈	D₄×C₆₁	1	2	yes	—
427	C₂⁴	—	2	1	no	—
428	C₂⁴	—	2	1	no	—
429	C₂⁴	#41×C₆₁	1	1	yes	characteristic
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	2	2	no	—
435	#41	—	4	4	no	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	—	4	4	no	—
439	#41	#41×C₆₁	1	4	yes	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	4	1	no	—
443	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
444	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	—	4	4	no	—
457	C₂×D₄	—	4	1	no	—
458	C₂×D₄	—	4	1	no	—
459	C₂×D₄	—	8	2	no	—
460	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
461	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	4	4	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	4	1	no	—
474	C₂²×C₄	—	8	2	no	—
475	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
479	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
481	SD₁₆	—	4	2	no	—
482	SD₁₆	—	4	2	no	—
483	D₈	—	4	2	no	—
484	D₈	—	4	2	no	—
485	M₁₆	—	2	2	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	2	2	no	—
488	M₁₆	—	2	2	no	—
489	M₁₆	—	2	2	no	—
490	M₁₆	—	2	2	no	—
491	M₁₆	—	4	4	no	—
492	M₁₆	—	4	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	4	4	no	—
500	C₂×C₈	—	4	2	no	—
501	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
502	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	4	1	no	—
508	C₄⋊C₄	—	4	1	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	4	1	no	—
519	C₂³	—	4	2	no	—
520	C₂³	—	8	1	no	—
521	C₂³	—	8	1	no	—
522	C₂³	—	8	1	no	—
523	C₂³	#121×C₆₁	1	1	yes	characteristic
524	C₂³	#121×C₆₁	1	1	yes	characteristic
525	C₂³	C₂×#41×C₆₁	1	1	yes	characteristic
526	Q₈	—	2	1	no	—
527	Q₈	—	2	1	no	—
528	Q₈	—	2	1	no	—
529	Q₈	—	4	2	no	—
530	Q₈	#123×C₆₁	1	2	yes	—
531	D₄	—	2	4	no	—
532	D₄	—	2	1	no	—
533	D₄	—	2	1	no	—
534	D₄	—	2	1	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	2	no	—
541	D₄	—	4	1	no	—
542	D₄	—	8	2	no	—
543	D₄	—	8	2	no	—
544	D₄	#123×C₆₁	1	2	yes	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	8	2	no	—
562	C₂×C₄	—	8	2	no	—
563	C₂×C₄	—	8	2	no	—
564	C₂×C₄	—	8	1	no	—
565	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
566	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
569	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
570	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
571	C₈	—	2	2	no	—
572	C₈	—	2	2	no	—
573	C₈	—	4	2	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	2	no	—
576	C₈	—	4	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	8	4	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	16	2	no	—
596	C₂²	C₆₁×#472	1	2	yes	—
597	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
598	C₂²	C₆₁×#551	1	2	yes	—
599	C₄	—	2	1	no	—
600	C₄	—	2	1	no	—
601	C₄	—	2	2	no	—
602	C₄	—	4	1	no	—
603	C₄	—	8	2	no	—
604	C₄	—	8	1	no	—
605	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
606	C₄	C₆₁×#534	1	1	yes	characteristic
607	C₄	C₆₁×#546	1	2	yes	—
608	C₂	—	2	2	no	—
609	C₂	—	2	2	no	—
610	C₂	—	4	1	no	—
611	C₂	—	4	2	no	—
612	C₂	—	8	1	no	—
613	C₂	—	16	1	no	—
614	C₂	C₆₁×#2412	1	1	yes	characteristic
615	C₂	C₂×C₆₁×#472	1	1	yes	characteristic
616	C₂	C₆₁×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#3006	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂³×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#480	C₂	semidirect
3. C₂×C₆₁×#417	C₂	semidirect
4. C₆₁×#2880	C₂	semidirect
5. C₆₁×#2078	C₂	semidirect
6. C₆₁×#2051	C₂	semidirect
7. C₆₁×#1907	C₂	semidirect
8. C₆₁×#1900	C₂	semidirect
9. C₆₁×#1855	C₂	semidirect
10. C₆₁×#1821	C₂	semidirect
11. C₆₁×#1816	C₂	semidirect
26. C₂×#108×C₆₁	C₂²	semidirect
27. C₂×#107×C₆₁	C₂²	semidirect
36. C₂×#102×C₆₁	C₂²	semidirect
37. C₂×#100×C₆₁	C₂²	semidirect
45. C₆₁×#343	C₂²	semidirect
46. C₆₁×#343	C₂²	semidirect
47. C₆₁×#343	C₂²	semidirect
48. C₆₁×#341	C₂²	semidirect
268. #24570	C₆₁	direct (N × H)
300. C₂×#480	C₂×C₆₁	semidirect
302. C₂×#417	C₂×C₆₁	semidirect
303. #2880	C₂×C₆₁	semidirect
304. #2078	C₂×C₆₁	semidirect
305. #2051	C₂×C₆₁	semidirect
306. #1907	C₂×C₆₁	semidirect
307. #1900	C₂×C₆₁	semidirect
308. #1855	C₂×C₆₁	semidirect
309. #1821	C₂×C₆₁	semidirect
310. #1816	C₂×C₆₁	semidirect
334. C₂×#108	C₂²×C₆₁	semidirect
335. C₂×#107	C₂²×C₆₁	semidirect
344. C₂×#102	C₂²×C₆₁	semidirect
345. C₂×#100	C₂²×C₆₁	semidirect
353. #343	C₂²×C₆₁	semidirect
354. #343	C₂²×C₆₁	semidirect
355. #343	C₂²×C₆₁	semidirect
356. #341	C₂²×C₆₁	semidirect
357. C₆₁	#24570	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×#480	2
C₆₁×#3006	2
C₂×C₆₁×#417	2
C₆₁×#2880	2
C₆₁×#2078	2
C₆₁×#2051	2
C₆₁×#1907	2
C₆₁×#1900	2
C₆₁×#1855	2
C₆₁×#1821	2
C₆₁×#1816	2
#24570	61

Subgroups — C61×#24570 #29528003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24570 #29528003