Subgroups — C₆₁×#18540 #29521973

Order 15616.

1146 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3165	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3110	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#1651	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1649	C₂	1	4	yes	maximal, complemented
7	C₆₁×#1556	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1491	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1490	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₆₁	—	2	1	no	—
11	D₄×Q₈×C₆₁	—	2	2	no	—
12	D₄×Q₈×C₆₁	—	2	2	no	—
13	D₄×Q₈×C₆₁	—	2	2	no	—
14	D₄×Q₈×C₆₁	C₂²	1	4	yes	—
15	C₆₁×#533	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
17	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
19	C₂×C₂²⋊Q₈×C₆₁	—	2	2	no	—
20	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₆₁	—	2	1	no	—
22	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₆₁×#501	—	2	2	no	—
24	C₆₁×#500	C₂²	1	2	yes	complemented
25	C₆₁×#498	C₂²	1	2	yes	complemented
26	C₆₁×#484	—	2	1	no	—
27	C₆₁×#483	—	2	1	no	—
28	C₆₁×#475	C₂²	1	2	yes	complemented
29	C₆₁×#474	C₂²	1	2	yes	—
30	C₆₁×#462	C₂²	1	2	yes	complemented
31	C₆₁×#461	C₂²	1	2	yes	—
32	C₆₁×#451	—	2	1	no	—
33	C₆₁×#450	—	2	1	no	—
34	C₆₁×#441	—	2	2	no	—
35	C₆₁×#440	—	2	2	no	—
36	C₆₁×#432	C₂²	1	1	yes	characteristic
37	C₆₁×#432	C₂²	1	1	yes	characteristic
38	C₆₁×#428	—	2	2	no	—
39	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#332	C₂²	1	4	yes	complemented
41	C₆₁×Q₈⋊C₈	C₂²	1	4	yes	complemented
42	C₆₁×D₄⋊C₈	C₂²	1	4	yes	—
43	C₂²×Q₈×C₆₁	—	2	2	no	—
44	C₂²×Q₈×C₆₁	—	2	4	no	—
45	C₂²×Q₈×C₆₁	—	2	4	no	—
46	C₂²×Q₈×C₆₁	—	2	1	no	—
47	C₂²×Q₈×C₆₁	—	4	8	no	—
48	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₆₁	—	2	2	no	—
51	C₂³×C₄×C₆₁	—	2	1	no	—
52	C₂×Q₁₆×C₆₁	—	2	2	no	—
53	C₂×SD₁₆×C₆₁	—	2	2	no	—
54	C₂×M₁₆×C₆₁	—	2	1	no	—
55	C₄⋊Q₈×C₆₁	—	2	4	no	—
56	C₄⋊Q₈×C₆₁	—	2	4	no	—
57	C₄⋊Q₈×C₆₁	—	2	1	no	—
58	C₄⋊Q₈×C₆₁	—	2	1	no	—
59	C₄⋊Q₈×C₆₁	D₄	1	2	yes	—
60	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
61	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
63	#125×C₆₁	—	2	1	no	—
64	C₂²⋊Q₈×C₆₁	—	2	4	no	—
65	C₂²⋊Q₈×C₆₁	—	2	8	no	—
66	C₂²⋊Q₈×C₆₁	—	2	4	no	—
67	C₂²⋊Q₈×C₆₁	—	2	8	no	—
68	C₂²⋊Q₈×C₆₁	—	2	1	no	—
69	C₂²⋊Q₈×C₆₁	—	2	1	no	—
70	C₄×Q₈×C₆₁	—	2	1	no	—
71	C₄×Q₈×C₆₁	—	2	1	no	—
72	C₄×Q₈×C₆₁	—	2	1	no	—
73	C₄×Q₈×C₆₁	—	2	1	no	—
74	C₄×Q₈×C₆₁	D₄	1	2	yes	—
75	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
76	C₄×D₄×C₆₁	—	2	4	no	—
77	C₄×D₄×C₆₁	—	2	4	no	—
78	C₄×D₄×C₆₁	—	2	1	no	—
79	C₄×D₄×C₆₁	—	2	1	no	—
80	C₄×D₄×C₆₁	D₄	1	2	yes	—
81	C₄×D₄×C₆₁	C₂³	1	2	yes	—
82	#117×C₆₁	—	2	1	no	—
83	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
84	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
85	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
86	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
88	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
91	C₂×C₄²×C₆₁	—	2	1	no	—
92	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
93	#107×C₆₁	—	2	4	no	—
94	#107×C₆₁	—	2	2	no	—
95	#106×C₆₁	—	2	4	no	—
96	#106×C₆₁	—	2	2	no	—
97	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
98	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
99	#103×C₆₁	—	2	2	no	—
100	#103×C₆₁	—	2	2	no	—
101	#103×C₆₁	—	2	2	no	—
102	#102×C₆₁	—	2	2	no	—
103	C₂²⋊C₈×C₆₁	—	2	1	no	—
104	C₂²⋊C₈×C₆₁	—	2	1	no	—
105	#97×C₆₁	—	2	1	no	—
106	#97×C₆₁	—	2	1	no	—
107	#97×C₆₁	—	2	1	no	—
108	C₄×C₈×C₆₁	C₂³	1	2	yes	—
109	C₂⁴×C₆₁	—	2	1	no	—
110	C₂×Q₈×C₆₁	—	2	4	no	—
111	C₂×Q₈×C₆₁	—	2	8	no	—
112	C₂×Q₈×C₆₁	—	2	1	no	—
113	C₂×Q₈×C₆₁	—	2	2	no	—
114	C₂×Q₈×C₆₁	—	2	2	no	—
115	C₂×Q₈×C₆₁	—	2	1	no	—
116	C₂×Q₈×C₆₁	—	2	1	no	—
117	C₂×Q₈×C₆₁	—	4	8	no	—
118	C₂×Q₈×C₆₁	—	4	4	no	—
119	C₂×Q₈×C₆₁	—	4	16	no	—
120	C₂×Q₈×C₆₁	—	4	8	no	—
121	C₂×Q₈×C₆₁	—	4	8	no	—
122	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₆₁	—	2	4	no	—
124	C₂×D₄×C₆₁	—	2	1	no	—
125	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₆₁	—	2	1	no	—
127	C₂²×C₄×C₆₁	—	2	8	no	—
128	C₂²×C₄×C₆₁	—	2	1	no	—
129	C₂²×C₄×C₆₁	—	2	2	no	—
130	C₂²×C₄×C₆₁	—	2	1	no	—
131	C₂²×C₄×C₆₁	—	2	2	no	—
132	C₂²×C₄×C₆₁	—	2	2	no	—
133	C₂²×C₄×C₆₁	—	4	8	no	—
134	C₂²×C₄×C₆₁	—	4	4	no	—
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	Q₁₆×C₆₁	—	4	4	no	—
139	SD₁₆×C₆₁	—	4	4	no	—
140	M₁₆×C₆₁	—	2	4	no	—
141	C₂×C₈×C₆₁	—	2	2	no	—
142	C₂×C₈×C₆₁	—	2	2	no	—
143	C₂×C₈×C₆₁	—	2	2	no	—
144	C₄⋊C₄×C₆₁	—	2	8	no	—
145	C₄⋊C₄×C₆₁	—	2	2	no	—
146	C₄⋊C₄×C₆₁	—	2	2	no	—
147	C₄⋊C₄×C₆₁	—	2	1	no	—
148	C₄⋊C₄×C₆₁	—	2	1	no	—
149	C₄⋊C₄×C₆₁	—	2	2	no	—
150	C₄⋊C₄×C₆₁	—	2	2	no	—
151	C₄⋊C₄×C₆₁	—	2	2	no	—
152	C₄⋊C₄×C₆₁	—	2	1	no	—
153	C₄⋊C₄×C₆₁	—	2	1	no	—
154	C₄⋊C₄×C₆₁	—	2	1	no	—
155	C₄⋊C₄×C₆₁	—	2	1	no	—
156	C₄⋊C₄×C₆₁	—	4	1	no	—
157	C₄⋊C₄×C₆₁	—	4	1	no	—
158	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
160	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
161	C₂²⋊C₄×C₆₁	—	2	8	no	—
162	C₂²⋊C₄×C₆₁	—	2	2	no	—
163	C₂²⋊C₄×C₆₁	—	2	2	no	—
164	C₂²⋊C₄×C₆₁	—	4	1	no	—
165	C₄²×C₆₁	—	2	2	no	—
166	C₄²×C₆₁	—	2	2	no	—
167	C₄²×C₆₁	—	4	1	no	—
168	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
172	C₂³×C₆₁	—	2	4	no	—
173	C₂³×C₆₁	—	2	2	no	—
174	C₂³×C₆₁	—	4	2	no	—
175	C₂³×C₆₁	—	4	2	no	—
176	C₂³×C₆₁	#120	1	1	yes	characteristic
177	Q₈×C₆₁	—	2	4	no	—
178	Q₈×C₆₁	—	2	2	no	—
179	Q₈×C₆₁	—	4	16	no	—
180	Q₈×C₆₁	—	4	4	no	—
181	Q₈×C₆₁	—	4	4	no	—
182	Q₈×C₆₁	—	4	2	no	—
183	Q₈×C₆₁	—	4	2	no	—
184	Q₈×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
185	D₄×C₆₁	—	2	4	no	—
186	D₄×C₆₁	—	2	2	no	—
187	D₄×C₆₁	#137	1	4	yes	—
188	C₂×C₄×C₆₁	—	2	4	no	—
189	C₂×C₄×C₆₁	—	2	2	no	—
190	C₂×C₄×C₆₁	—	2	2	no	—
191	C₂×C₄×C₆₁	—	2	2	no	—
192	C₂×C₄×C₆₁	—	2	2	no	—
193	C₂×C₄×C₆₁	—	2	2	no	—
194	C₂×C₄×C₆₁	—	2	4	no	—
195	C₂×C₄×C₆₁	—	2	2	no	—
196	C₂×C₄×C₆₁	—	4	16	no	—
197	C₂×C₄×C₆₁	—	4	4	no	—
198	C₂×C₄×C₆₁	—	4	4	no	—
199	C₂×C₄×C₆₁	—	4	2	no	—
200	C₂×C₄×C₆₁	—	4	2	no	—
201	C₂×C₄×C₆₁	—	4	4	no	—
202	C₂×C₄×C₆₁	—	4	1	no	—
203	C₂×C₄×C₆₁	—	4	1	no	—
204	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
205	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
206	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
207	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
210	C₈×C₆₁	—	2	4	no	—
211	C₈×C₆₁	—	4	2	no	—
212	C₈×C₆₁	—	4	2	no	—
213	#18540	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂²×C₆₁	—	2	1	no	—
215	C₂²×C₆₁	—	2	1	no	—
216	C₂²×C₆₁	—	2	4	no	—
217	C₂²×C₆₁	—	4	8	no	—
218	C₂²×C₆₁	—	4	2	no	—
219	C₂²×C₆₁	—	4	2	no	—
220	C₂²×C₆₁	#456	1	2	yes	—
221	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
222	C₄×C₆₁	—	2	4	no	—
223	C₄×C₆₁	—	2	1	no	—
224	C₄×C₆₁	—	2	1	no	—
225	C₄×C₆₁	—	2	1	no	—
226	C₄×C₆₁	—	2	1	no	—
227	C₄×C₆₁	—	4	4	no	—
228	C₄×C₆₁	—	4	2	no	—
229	C₄×C₆₁	—	4	2	no	—
230	C₄×C₆₁	—	8	1	no	—
231	C₄×C₆₁	—	8	1	no	—
232	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
233	C₄×C₆₁	C₂×#137	1	2	yes	—
234	C₂×D₄×Q₈	C₂×C₆₁	1	1	yes	characteristic
235	#3165	C₂×C₆₁	1	1	yes	characteristic, complemented
236	#3113	C₂×C₆₁	1	1	yes	characteristic, complemented
237	#3110	C₂×C₆₁	1	1	yes	characteristic
238	#1651	C₂×C₆₁	1	4	yes	complemented
239	#1649	C₂×C₆₁	1	4	yes	complemented
240	#1556	C₂×C₆₁	1	1	yes	characteristic, complemented
241	#1491	C₂×C₆₁	1	1	yes	characteristic, complemented
242	#1490	C₂×C₆₁	1	1	yes	characteristic
243	C₂×C₆₁	—	2	2	no	—
244	C₂×C₆₁	—	4	4	no	—
245	C₂×C₆₁	#3003	1	1	yes	characteristic
246	C₂×C₆₁	#3004	1	1	yes	characteristic
247	C₂×C₆₁	C₂×#456	1	1	yes	characteristic
248	C₂³×Q₈	—	2	1	no	—
249	D₄×Q₈	—	2	2	no	—
250	D₄×Q₈	—	2	2	no	—
251	D₄×Q₈	—	2	2	no	—
252	D₄×Q₈	C₂²×C₆₁	1	4	yes	—
253	#533	C₂²×C₆₁	1	1	yes	characteristic
254	C₂×C₄⋊Q₈	—	2	1	no	—
255	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
256	C₂×C₂²⋊Q₈	—	2	1	no	—
257	C₂×C₂²⋊Q₈	—	2	2	no	—
258	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
259	C₂×C₄×D₄	—	2	1	no	—
260	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
261	#501	—	2	2	no	—
262	#500	C₂²×C₆₁	1	2	yes	complemented
263	#498	C₂²×C₆₁	1	2	yes	complemented
264	#484	—	2	1	no	—
265	#483	—	2	1	no	—
266	#475	C₂²×C₆₁	1	2	yes	complemented
267	#474	C₂²×C₆₁	1	2	yes	—
268	#462	C₂²×C₆₁	1	2	yes	complemented
269	#461	C₂²×C₆₁	1	2	yes	—
270	#451	—	2	1	no	—
271	#450	—	2	1	no	—
272	#441	—	2	2	no	—
273	#440	—	2	2	no	—
274	#432	C₂²×C₆₁	1	1	yes	characteristic
275	#432	C₂²×C₆₁	1	1	yes	characteristic
276	#428	—	2	2	no	—
277	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
278	#332	C₂²×C₆₁	1	4	yes	complemented
279	Q₈⋊C₈	C₂²×C₆₁	1	4	yes	complemented
280	D₄⋊C₈	C₂²×C₆₁	1	4	yes	—
281	C₆₁	#18540	1	1	yes	characteristic, direct product factor, Sylow
282	C₂²×Q₈	—	2	2	no	—
283	C₂²×Q₈	—	2	4	no	—
284	C₂²×Q₈	—	2	4	no	—
285	C₂²×Q₈	—	2	1	no	—
286	C₂²×Q₈	—	4	8	no	—
287	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
288	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
289	C₂³×C₄	—	2	2	no	—
290	C₂³×C₄	—	2	1	no	—
291	C₂×Q₁₆	—	2	2	no	—
292	C₂×SD₁₆	—	2	2	no	—
293	C₂×M₁₆	—	2	1	no	—
294	C₄⋊Q₈	—	2	4	no	—
295	C₄⋊Q₈	—	2	4	no	—
296	C₄⋊Q₈	—	2	1	no	—
297	C₄⋊Q₈	—	2	1	no	—
298	C₄⋊Q₈	D₄×C₆₁	1	2	yes	—
299	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
300	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
301	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
302	#125	—	2	1	no	—
303	C₂²⋊Q₈	—	2	4	no	—
304	C₂²⋊Q₈	—	2	8	no	—
305	C₂²⋊Q₈	—	2	4	no	—
306	C₂²⋊Q₈	—	2	8	no	—
307	C₂²⋊Q₈	—	2	1	no	—
308	C₂²⋊Q₈	—	2	1	no	—
309	C₄×Q₈	—	2	1	no	—
310	C₄×Q₈	—	2	1	no	—
311	C₄×Q₈	—	2	1	no	—
312	C₄×Q₈	—	2	1	no	—
313	C₄×Q₈	D₄×C₆₁	1	2	yes	—
314	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
315	C₄×D₄	—	2	4	no	—
316	C₄×D₄	—	2	4	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	—	2	1	no	—
319	C₄×D₄	D₄×C₆₁	1	2	yes	—
320	C₄×D₄	C₂³×C₆₁	1	2	yes	—
321	#117	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
326	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
327	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
332	#107	—	2	4	no	—
333	#107	—	2	2	no	—
334	#106	—	2	4	no	—
335	#106	—	2	2	no	—
336	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
337	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
338	#103	—	2	2	no	—
339	#103	—	2	2	no	—
340	#103	—	2	2	no	—
341	#102	—	2	2	no	—
342	C₂²⋊C₈	—	2	1	no	—
343	C₂²⋊C₈	—	2	1	no	—
344	#97	—	2	1	no	—
345	#97	—	2	1	no	—
346	#97	—	2	1	no	—
347	C₄×C₈	C₂³×C₆₁	1	2	yes	—
348	C₂⁴	—	2	1	no	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	—	2	8	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	4	8	no	—
357	C₂×Q₈	—	4	4	no	—
358	C₂×Q₈	—	4	16	no	—
359	C₂×Q₈	—	4	8	no	—
360	C₂×Q₈	—	4	8	no	—
361	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	8	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	4	8	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
377	Q₁₆	—	4	4	no	—
378	SD₁₆	—	4	4	no	—
379	M₁₆	—	2	4	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	4	1	no	—
396	C₄⋊C₄	—	4	1	no	—
397	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
398	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
399	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
400	C₂²⋊C₄	—	2	8	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	4	1	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	4	1	no	—
407	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
408	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
409	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
410	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
411	C₂³	—	2	4	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	#120×C₆₁	1	1	yes	characteristic
416	Q₈	—	2	4	no	—
417	Q₈	—	2	2	no	—
418	Q₈	—	4	16	no	—
419	Q₈	—	4	4	no	—
420	Q₈	—	4	4	no	—
421	Q₈	—	4	2	no	—
422	Q₈	—	4	2	no	—
423	Q₈	AGL(1,ℤ/8)×C₆₁	1	4	yes	—
424	D₄	—	2	4	no	—
425	D₄	—	2	2	no	—
426	D₄	#137×C₆₁	1	4	yes	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	16	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
444	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
445	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
449	C₈	—	2	4	no	—
450	C₈	—	4	2	no	—
451	C₈	—	4	2	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	4	8	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	C₆₁×#456	1	2	yes	—
459	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
460	C₄	—	2	4	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	4	4	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	8	1	no	—
469	C₄	—	8	1	no	—
470	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
471	C₄	C₂×#137×C₆₁	1	2	yes	—
472	C₂	—	2	2	no	—
473	C₂	—	4	4	no	—
474	C₂	C₆₁×#3003	1	1	yes	characteristic
475	C₂	C₆₁×#3004	1	1	yes	characteristic
476	C₂	C₂×C₆₁×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₂²×D₄×C₆₁	D₄
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
2. C₆₁×#3165	C₂	semidirect
3. C₆₁×#3113	C₂	semidirect
5. C₆₁×#1651	C₂	semidirect
6. C₆₁×#1649	C₂	semidirect
7. C₆₁×#1556	C₂	semidirect
8. C₆₁×#1491	C₂	semidirect
24. C₆₁×#500	C₂²	semidirect
25. C₆₁×#498	C₂²	semidirect
28. C₆₁×#475	C₂²	semidirect
30. C₆₁×#462	C₂²	semidirect
40. C₆₁×#332	C₂²	semidirect
41. C₆₁×Q₈⋊C₈	C₂²	semidirect
213. #18540	C₆₁	direct (N × H)
235. #3165	C₂×C₆₁	semidirect
236. #3113	C₂×C₆₁	semidirect
238. #1651	C₂×C₆₁	semidirect
239. #1649	C₂×C₆₁	semidirect
240. #1556	C₂×C₆₁	semidirect
241. #1491	C₂×C₆₁	semidirect
262. #500	C₂²×C₆₁	semidirect
263. #498	C₂²×C₆₁	semidirect
266. #475	C₂²×C₆₁	semidirect
268. #462	C₂²×C₆₁	semidirect
278. #332	C₂²×C₆₁	semidirect
279. Q₈⋊C₈	C₂²×C₆₁	semidirect
281. C₆₁	#18540	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×D₄×Q₈×C₆₁	2
C₆₁×#3165	2
C₆₁×#3113	2
C₆₁×#3110	2
C₆₁×#1651	2
C₆₁×#1649	2
C₆₁×#1556	2
C₆₁×#1491	2
C₆₁×#1490	2
#18540	61

Subgroups — C61×#18540 #29521973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#18540 #29521973