Subgroups — C₆₁×#18756 #29522189

Order 15616.

1224 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1647	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1625	C₂	1	4	yes	maximal, complemented
7	C₆₁×#1546	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1486	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₆₁	—	2	1	no	—
11	C₂×AGL(1,ℤ/8)×C₆₁	—	2	1	no	—
12	C₆₁×#547	—	2	2	no	—
13	C₆₁×#547	—	2	2	no	—
14	C₆₁×#547	—	2	2	no	—
15	C₆₁×#547	C₂²	1	4	yes	—
16	C₆₁×#532	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×#123×C₆₁	—	2	2	no	—
19	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
20	C₂×#121×C₆₁	—	2	1	no	—
21	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
24	C₆₁×#500	C₂²	1	2	yes	complemented
25	C₆₁×#486	C₂²	1	2	yes	complemented
26	C₆₁×#480	—	2	1	no	—
27	C₆₁×#480	—	2	2	no	—
28	C₆₁×#474	—	2	2	no	—
29	C₆₁×#474	C₂²	1	2	yes	complemented
30	C₆₁×#463	—	2	2	no	—
31	C₆₁×#461	C₂²	1	2	yes	complemented
32	C₆₁×#459	C₂²	1	2	yes	complemented
33	C₆₁×#459	C₂²	1	2	yes	complemented
34	C₆₁×#447	—	2	1	no	—
35	C₄×D₈×C₆₁	—	2	2	no	—
36	C₆₁×#431	C₂²	1	1	yes	characteristic
37	C₆₁×#431	C₂²	1	1	yes	characteristic
38	C₆₁×#423	C₂²	1	1	yes	characteristic
39	C₆₁×#417	—	2	1	no	—
40	C₆₁×#332	C₂²	1	4	yes	complemented
41	C₆₁×D₄⋊C₈	C₂²	1	4	yes	complemented
42	C₆₁×D₄⋊C₈	C₂²	1	4	yes	complemented
43	C₂×#41×C₆₁	—	2	4	no	—
44	C₂×#41×C₆₁	—	2	4	no	—
45	C₂×#41×C₆₁	—	2	1	no	—
46	C₂×#41×C₆₁	—	4	4	no	—
47	C₂×#41×C₆₁	—	4	4	no	—
48	C₂²×Q₈×C₆₁	—	2	1	no	—
49	C₂²×D₄×C₆₁	—	2	2	no	—
50	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₆₁	—	2	2	no	—
53	C₂³×C₄×C₆₁	—	2	1	no	—
54	C₂³×C₄×C₆₁	—	2	1	no	—
55	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
56	C₂×SD₁₆×C₆₁	—	2	2	no	—
57	C₂×D₈×C₆₁	—	2	2	no	—
58	C₂×D₈×C₆₁	—	2	2	no	—
59	C₂×M₁₆×C₆₁	—	2	1	no	—
60	C₄⋊Q₈×C₆₁	—	2	1	no	—
61	C₄⋊Q₈×C₆₁	—	2	1	no	—
62	C₄⋊Q₈×C₆₁	D₄	1	2	yes	—
63	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
65	#127×C₆₁	C₂³	1	1	yes	characteristic
66	#124×C₆₁	—	2	1	no	—
67	#123×C₆₁	—	2	8	no	—
68	#123×C₆₁	—	2	8	no	—
69	C₂²⋊Q₈×C₆₁	—	2	4	no	—
70	C₂²⋊Q₈×C₆₁	—	2	4	no	—
71	#121×C₆₁	—	2	4	no	—
72	#121×C₆₁	—	2	4	no	—
73	#121×C₆₁	—	2	1	no	—
74	#121×C₆₁	—	2	1	no	—
75	C₄×D₄×C₆₁	—	2	1	no	—
76	C₄×D₄×C₆₁	—	2	1	no	—
77	C₄×D₄×C₆₁	—	2	1	no	—
78	C₄×D₄×C₆₁	—	2	1	no	—
79	C₄×D₄×C₆₁	—	2	1	no	—
80	C₄×D₄×C₆₁	—	2	1	no	—
81	C₄×D₄×C₆₁	D₄	1	2	yes	—
82	C₄×D₄×C₆₁	D₄	1	2	yes	—
83	C₄×D₄×C₆₁	C₂³	1	2	yes	—
84	C₄×D₄×C₆₁	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
86	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
87	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
88	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
89	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
90	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
95	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
96	#107×C₆₁	—	2	2	no	—
97	#107×C₆₁	—	2	4	no	—
98	C₄⋊C₈×C₆₁	—	2	1	no	—
99	C₄⋊C₈×C₆₁	—	2	1	no	—
100	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
101	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
102	#103×C₆₁	—	2	2	no	—
103	#102×C₆₁	—	2	2	no	—
104	#102×C₆₁	—	2	2	no	—
105	#102×C₆₁	—	2	2	no	—
106	#102×C₆₁	—	2	4	no	—
107	C₂²⋊C₈×C₆₁	—	2	1	no	—
108	C₂²⋊C₈×C₆₁	—	2	1	no	—
109	C₄×C₈×C₆₁	—	2	1	no	—
110	C₄×C₈×C₆₁	C₂³	1	2	yes	—
111	C₂⁴×C₆₁	—	2	1	no	—
112	C₂⁴×C₆₁	—	2	1	no	—
113	#41×C₆₁	—	4	8	no	—
114	#41×C₆₁	—	4	16	no	—
115	#41×C₆₁	—	4	8	no	—
116	#41×C₆₁	—	4	2	no	—
117	#41×C₆₁	—	4	2	no	—
118	C₂×Q₈×C₆₁	—	2	2	no	—
119	C₂×Q₈×C₆₁	—	2	2	no	—
120	C₂×Q₈×C₆₁	—	2	1	no	—
121	C₂×Q₈×C₆₁	—	4	2	no	—
122	C₂×Q₈×C₆₁	—	4	2	no	—
123	C₂×D₄×C₆₁	—	2	8	no	—
124	C₂×D₄×C₆₁	—	2	1	no	—
125	C₂×D₄×C₆₁	—	2	1	no	—
126	C₂×D₄×C₆₁	—	2	2	no	—
127	C₂×D₄×C₆₁	—	2	1	no	—
128	C₂×D₄×C₆₁	—	2	1	no	—
129	C₂×D₄×C₆₁	—	2	1	no	—
130	C₂×D₄×C₆₁	—	4	2	no	—
131	C₂×D₄×C₆₁	—	4	8	no	—
132	C₂×D₄×C₆₁	—	4	1	no	—
133	C₂×D₄×C₆₁	D₈	1	4	yes	complemented
134	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
135	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₆₁	—	2	8	no	—
137	C₂²×C₄×C₆₁	—	2	1	no	—
138	C₂²×C₄×C₆₁	—	2	1	no	—
139	C₂²×C₄×C₆₁	—	2	2	no	—
140	C₂²×C₄×C₆₁	—	2	2	no	—
141	C₂²×C₄×C₆₁	—	2	2	no	—
142	C₂²×C₄×C₆₁	—	2	2	no	—
143	C₂²×C₄×C₆₁	—	2	2	no	—
144	C₂²×C₄×C₆₁	—	4	4	no	—
145	C₂²×C₄×C₆₁	—	4	8	no	—
146	C₂²×C₄×C₆₁	—	4	2	no	—
147	C₂²×C₄×C₆₁	—	4	2	no	—
148	C₂²×C₄×C₆₁	—	4	1	no	—
149	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
152	SD₁₆×C₆₁	—	4	4	no	—
153	D₈×C₆₁	—	4	4	no	—
154	D₈×C₆₁	—	4	4	no	—
155	M₁₆×C₆₁	—	4	2	no	—
156	C₂×C₈×C₆₁	—	2	2	no	—
157	C₂×C₈×C₆₁	—	2	2	no	—
158	C₂×C₈×C₆₁	—	2	2	no	—
159	C₄⋊C₄×C₆₁	—	2	8	no	—
160	C₄⋊C₄×C₆₁	—	2	1	no	—
161	C₄⋊C₄×C₆₁	—	2	2	no	—
162	C₄⋊C₄×C₆₁	—	2	1	no	—
163	C₄⋊C₄×C₆₁	—	2	2	no	—
164	C₄⋊C₄×C₆₁	—	2	2	no	—
165	C₄⋊C₄×C₆₁	—	2	1	no	—
166	C₄⋊C₄×C₆₁	—	2	1	no	—
167	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
168	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
170	C₂²⋊C₄×C₆₁	—	2	8	no	—
171	C₂²⋊C₄×C₆₁	—	2	2	no	—
172	C₂²⋊C₄×C₆₁	—	2	2	no	—
173	C₂²⋊C₄×C₆₁	—	2	2	no	—
174	C₂²⋊C₄×C₆₁	—	2	2	no	—
175	C₂²⋊C₄×C₆₁	—	4	1	no	—
176	C₂²⋊C₄×C₆₁	—	4	1	no	—
177	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
181	C₂³×C₆₁	—	2	2	no	—
182	C₂³×C₆₁	—	2	4	no	—
183	C₂³×C₆₁	—	2	2	no	—
184	C₂³×C₆₁	—	4	2	no	—
185	C₂³×C₆₁	—	4	2	no	—
186	C₂³×C₆₁	—	4	2	no	—
187	C₂³×C₆₁	—	4	2	no	—
188	C₂³×C₆₁	—	4	2	no	—
189	C₂³×C₆₁	—	4	1	no	—
190	C₂³×C₆₁	#120	1	1	yes	characteristic
191	Q₈×C₆₁	—	4	2	no	—
192	Q₈×C₆₁	—	4	2	no	—
193	Q₈×C₆₁	—	4	4	no	—
194	Q₈×C₆₁	—	4	1	no	—
195	Q₈×C₆₁	—	4	1	no	—
196	D₄×C₆₁	—	2	2	no	—
197	D₄×C₆₁	—	2	2	no	—
198	D₄×C₆₁	—	2	2	no	—
199	D₄×C₆₁	—	2	4	no	—
200	D₄×C₆₁	—	4	2	no	—
201	D₄×C₆₁	—	4	2	no	—
202	D₄×C₆₁	—	4	16	no	—
203	D₄×C₆₁	—	4	1	no	—
204	D₄×C₆₁	—	4	1	no	—
205	D₄×C₆₁	—	4	2	no	—
206	D₄×C₆₁	—	8	2	no	—
207	D₄×C₆₁	C₂×D₈	1	4	yes	—
208	C₂×C₄×C₆₁	—	2	2	no	—
209	C₂×C₄×C₆₁	—	2	2	no	—
210	C₂×C₄×C₆₁	—	2	2	no	—
211	C₂×C₄×C₆₁	—	2	4	no	—
212	C₂×C₄×C₆₁	—	4	1	no	—
213	C₂×C₄×C₆₁	—	4	4	no	—
214	C₂×C₄×C₆₁	—	4	2	no	—
215	C₂×C₄×C₆₁	—	4	16	no	—
216	C₂×C₄×C₆₁	—	4	2	no	—
217	C₂×C₄×C₆₁	—	4	4	no	—
218	C₂×C₄×C₆₁	—	4	2	no	—
219	C₂×C₄×C₆₁	—	4	2	no	—
220	C₂×C₄×C₆₁	—	4	4	no	—
221	C₂×C₄×C₆₁	—	4	4	no	—
222	C₂×C₄×C₆₁	—	4	1	no	—
223	C₂×C₄×C₆₁	—	8	2	no	—
224	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
225	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
226	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
227	C₂×C₄×C₆₁	C₂×D₈	1	2	yes	—
228	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
229	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
232	C₈×C₆₁	—	4	2	no	—
233	C₈×C₆₁	—	4	2	no	—
234	C₈×C₆₁	—	4	2	no	—
235	#18756	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂²×C₆₁	—	2	1	no	—
237	C₂²×C₆₁	—	2	1	no	—
238	C₂²×C₆₁	—	2	4	no	—
239	C₂²×C₆₁	—	4	8	no	—
240	C₂²×C₆₁	—	4	2	no	—
241	C₂²×C₆₁	—	4	2	no	—
242	C₂²×C₆₁	—	4	2	no	—
243	C₂²×C₆₁	—	4	2	no	—
244	C₂²×C₆₁	—	4	2	no	—
245	C₂²×C₆₁	—	8	4	no	—
246	C₂²×C₆₁	—	8	1	no	—
247	C₂²×C₆₁	—	8	1	no	—
248	C₂²×C₆₁	—	8	1	no	—
249	C₂²×C₆₁	#447	1	2	yes	—
250	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
251	C₄×C₆₁	—	2	1	no	—
252	C₄×C₆₁	—	2	1	no	—
253	C₄×C₆₁	—	2	1	no	—
254	C₄×C₆₁	—	4	2	no	—
255	C₄×C₆₁	—	4	4	no	—
256	C₄×C₆₁	—	4	2	no	—
257	C₄×C₆₁	—	8	1	no	—
258	C₄×C₆₁	#447	1	2	yes	—
259	C₄×C₆₁	C₂²×D₈	1	1	yes	characteristic
260	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
261	C₄×C₆₁	#575	1	2	yes	—
262	C₂×#547	C₂×C₆₁	1	1	yes	characteristic, complemented
263	#3226	C₂×C₆₁	1	1	yes	characteristic, complemented
264	#3100	C₂×C₆₁	1	1	yes	characteristic, complemented
265	#3036	C₂×C₆₁	1	1	yes	characteristic, complemented
266	#1647	C₂×C₆₁	1	4	yes	complemented
267	#1625	C₂×C₆₁	1	4	yes	complemented
268	#1546	C₂×C₆₁	1	1	yes	characteristic, complemented
269	#1486	C₂×C₆₁	1	1	yes	characteristic, complemented
270	#1478	C₂×C₆₁	1	1	yes	characteristic, complemented
271	C₂×C₆₁	—	2	2	no	—
272	C₂×C₆₁	—	4	4	no	—
273	C₂×C₆₁	—	8	2	no	—
274	C₂×C₆₁	—	16	1	no	—
275	C₂×C₆₁	C₂×#447	1	1	yes	characteristic
276	C₂×C₆₁	#3005	1	1	yes	characteristic
277	C₂×C₆₁	#3020	1	1	yes	characteristic
278	C₂²×#41	—	2	1	no	—
279	C₂×AGL(1,ℤ/8)	—	2	1	no	—
280	#547	—	2	2	no	—
281	#547	—	2	2	no	—
282	#547	—	2	2	no	—
283	#547	C₂²×C₆₁	1	4	yes	—
284	#532	C₂²×C₆₁	1	1	yes	characteristic
285	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
286	C₂×#123	—	2	2	no	—
287	C₂×C₂²⋊Q₈	—	2	1	no	—
288	C₂×#121	—	2	1	no	—
289	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
290	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
291	C₂²×C₄⋊C₄	—	2	1	no	—
292	#500	C₂²×C₆₁	1	2	yes	complemented
293	#486	C₂²×C₆₁	1	2	yes	complemented
294	#480	—	2	1	no	—
295	#480	—	2	2	no	—
296	#474	—	2	2	no	—
297	#474	C₂²×C₆₁	1	2	yes	complemented
298	#463	—	2	2	no	—
299	#461	C₂²×C₆₁	1	2	yes	complemented
300	#459	C₂²×C₆₁	1	2	yes	complemented
301	#459	C₂²×C₆₁	1	2	yes	complemented
302	#447	—	2	1	no	—
303	C₄×D₈	—	2	2	no	—
304	#431	C₂²×C₆₁	1	1	yes	characteristic
305	#431	C₂²×C₆₁	1	1	yes	characteristic
306	#423	C₂²×C₆₁	1	1	yes	characteristic
307	#417	—	2	1	no	—
308	#332	C₂²×C₆₁	1	4	yes	complemented
309	D₄⋊C₈	C₂²×C₆₁	1	4	yes	complemented
310	D₄⋊C₈	C₂²×C₆₁	1	4	yes	complemented
311	C₆₁	#18756	1	1	yes	characteristic, direct product factor, Sylow
312	C₂×#41	—	2	4	no	—
313	C₂×#41	—	2	4	no	—
314	C₂×#41	—	2	1	no	—
315	C₂×#41	—	4	4	no	—
316	C₂×#41	—	4	4	no	—
317	C₂²×Q₈	—	2	1	no	—
318	C₂²×D₄	—	2	2	no	—
319	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
320	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
321	C₂³×C₄	—	2	2	no	—
322	C₂³×C₄	—	2	1	no	—
323	C₂³×C₄	—	2	1	no	—
324	AGL(1,ℤ/8)	—	4	4	no	—
325	C₂×SD₁₆	—	2	2	no	—
326	C₂×D₈	—	2	2	no	—
327	C₂×D₈	—	2	2	no	—
328	C₂×M₁₆	—	2	1	no	—
329	C₄⋊Q₈	—	2	1	no	—
330	C₄⋊Q₈	—	2	1	no	—
331	C₄⋊Q₈	D₄×C₆₁	1	2	yes	—
332	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
333	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
334	#127	C₂³×C₆₁	1	1	yes	characteristic
335	#124	—	2	1	no	—
336	#123	—	2	8	no	—
337	#123	—	2	8	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	—	2	4	no	—
340	#121	—	2	4	no	—
341	#121	—	2	4	no	—
342	#121	—	2	1	no	—
343	#121	—	2	1	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	—	2	1	no	—
348	C₄×D₄	—	2	1	no	—
349	C₄×D₄	—	2	1	no	—
350	C₄×D₄	D₄×C₆₁	1	2	yes	—
351	C₄×D₄	D₄×C₆₁	1	2	yes	—
352	C₄×D₄	C₂³×C₆₁	1	2	yes	—
353	C₄×D₄	C₂³×C₆₁	1	2	yes	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	4	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	4	no	—
358	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
359	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
360	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
365	#107	—	2	2	no	—
366	#107	—	2	4	no	—
367	C₄⋊C₈	—	2	1	no	—
368	C₄⋊C₈	—	2	1	no	—
369	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
370	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
371	#103	—	2	2	no	—
372	#102	—	2	2	no	—
373	#102	—	2	2	no	—
374	#102	—	2	2	no	—
375	#102	—	2	4	no	—
376	C₂²⋊C₈	—	2	1	no	—
377	C₂²⋊C₈	—	2	1	no	—
378	C₄×C₈	—	2	1	no	—
379	C₄×C₈	C₂³×C₆₁	1	2	yes	—
380	C₂⁴	—	2	1	no	—
381	C₂⁴	—	2	1	no	—
382	#41	—	4	8	no	—
383	#41	—	4	16	no	—
384	#41	—	4	8	no	—
385	#41	—	4	2	no	—
386	#41	—	4	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	4	2	no	—
391	C₂×Q₈	—	4	2	no	—
392	C₂×D₄	—	2	8	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	4	2	no	—
400	C₂×D₄	—	4	8	no	—
401	C₂×D₄	—	4	1	no	—
402	C₂×D₄	D₈×C₆₁	1	4	yes	complemented
403	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
404	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
405	C₂²×C₄	—	2	8	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	4	4	no	—
414	C₂²×C₄	—	4	8	no	—
415	C₂²×C₄	—	4	2	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	—	4	1	no	—
418	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
421	SD₁₆	—	4	4	no	—
422	D₈	—	4	4	no	—
423	D₈	—	4	4	no	—
424	M₁₆	—	4	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₄⋊C₄	—	2	8	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
437	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
438	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
439	C₂²⋊C₄	—	2	8	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	4	1	no	—
445	C₂²⋊C₄	—	4	1	no	—
446	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
447	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
448	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
449	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
450	C₂³	—	2	4	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	1	no	—
459	C₂³	#120×C₆₁	1	1	yes	characteristic
460	Q₈	—	4	2	no	—
461	Q₈	—	4	2	no	—
462	Q₈	—	4	4	no	—
463	Q₈	—	4	1	no	—
464	Q₈	—	4	1	no	—
465	D₄	—	2	2	no	—
466	D₄	—	2	2	no	—
467	D₄	—	2	2	no	—
468	D₄	—	2	4	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	16	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	2	no	—
475	D₄	—	8	2	no	—
476	D₄	C₂×D₈×C₆₁	1	4	yes	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	16	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	—	4	4	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	8	2	no	—
493	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
494	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
495	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
496	C₂×C₄	C₂×D₈×C₆₁	1	2	yes	—
497	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
498	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
500	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
501	C₈	—	4	2	no	—
502	C₈	—	4	2	no	—
503	C₈	—	4	2	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	4	no	—
507	C₂²	—	4	8	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	8	4	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	1	no	—
516	C₂²	—	8	1	no	—
517	C₂²	C₆₁×#447	1	2	yes	—
518	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	4	no	—
524	C₄	—	4	2	no	—
525	C₄	—	8	1	no	—
526	C₄	C₆₁×#447	1	2	yes	—
527	C₄	C₂²×D₈×C₆₁	1	1	yes	characteristic
528	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
529	C₄	C₆₁×#575	1	2	yes	—
530	C₂	—	2	2	no	—
531	C₂	—	4	4	no	—
532	C₂	—	8	2	no	—
533	C₂	—	16	1	no	—
534	C₂	C₂×C₆₁×#447	1	1	yes	characteristic
535	C₂	C₆₁×#3005	1	1	yes	characteristic
536	C₂	C₆₁×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#547	C₂	semidirect
2. C₆₁×#3226	C₂	semidirect
3. C₆₁×#3100	C₂	semidirect
4. C₆₁×#3036	C₂	semidirect
5. C₆₁×#1647	C₂	semidirect
6. C₆₁×#1625	C₂	semidirect
7. C₆₁×#1546	C₂	semidirect
8. C₆₁×#1486	C₂	semidirect
9. C₆₁×#1478	C₂	semidirect
24. C₆₁×#500	C₂²	semidirect
25. C₆₁×#486	C₂²	semidirect
29. C₆₁×#474	C₂²	semidirect
31. C₆₁×#461	C₂²	semidirect
32. C₆₁×#459	C₂²	semidirect
33. C₆₁×#459	C₂²	semidirect
40. C₆₁×#332	C₂²	semidirect
41. C₆₁×D₄⋊C₈	C₂²	semidirect
42. C₆₁×D₄⋊C₈	C₂²	semidirect
133. C₂×D₄×C₆₁	D₈	semidirect
235. #18756	C₆₁	direct (N × H)
262. C₂×#547	C₂×C₆₁	semidirect
263. #3226	C₂×C₆₁	semidirect
264. #3100	C₂×C₆₁	semidirect
265. #3036	C₂×C₆₁	semidirect
266. #1647	C₂×C₆₁	semidirect
267. #1625	C₂×C₆₁	semidirect
268. #1546	C₂×C₆₁	semidirect
269. #1486	C₂×C₆₁	semidirect
270. #1478	C₂×C₆₁	semidirect
292. #500	C₂²×C₆₁	semidirect
293. #486	C₂²×C₆₁	semidirect
297. #474	C₂²×C₆₁	semidirect
299. #461	C₂²×C₆₁	semidirect
300. #459	C₂²×C₆₁	semidirect
301. #459	C₂²×C₆₁	semidirect
308. #332	C₂²×C₆₁	semidirect
309. D₄⋊C₈	C₂²×C₆₁	semidirect
310. D₄⋊C₈	C₂²×C₆₁	semidirect
311. C₆₁	#18756	direct (N × H)
402. C₂×D₄	D₈×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×#547	2
C₆₁×#3226	2
C₆₁×#3100	2
C₆₁×#3036	2
C₆₁×#1647	2
C₆₁×#1625	2
C₆₁×#1546	2
C₆₁×#1486	2
C₆₁×#1478	2
#18756	61

Subgroups — C61×#18756 #29522189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#18756 #29522189