Subgroups — C₆₁×#24571 #29528004

Order 15616.

910 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3007	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#417	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2880	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2079	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2052	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1908	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1901	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×#1815	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#137×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×#137×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×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#483	—	2	1	no	—
20	C₆₁×#483	—	2	1	no	—
21	C₆₁×#483	—	2	2	no	—
22	C₆₁×#452	—	2	1	no	—
23	C₆₁×#452	—	2	1	no	—
24	C₆₁×#451	—	2	1	no	—
25	C₆₁×#450	—	2	1	no	—
26	C₂×#108×C₆₁	C₂²	1	2	yes	complemented
27	C₂×#106×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×#103×C₆₁	C₂²	1	2	yes	complemented
36	C₂×#102×C₆₁	—	2	1	no	—
37	C₂×#101×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×Q₈×C₆₁	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₆₁	—	2	1	no	—
60	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₆₁	—	2	1	no	—
62	C₂³×C₄×C₆₁	—	2	1	no	—
63	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
64	#137×C₆₁	—	2	4	no	—
65	#137×C₆₁	—	4	2	no	—
66	C₂×Q₁₆×C₆₁	—	2	1	no	—
67	C₂×Q₁₆×C₆₁	—	2	1	no	—
68	C₂×SD₁₆×C₆₁	—	2	1	no	—
69	C₂×SD₁₆×C₆₁	—	2	1	no	—
70	#131×C₆₁	—	2	4	no	—
71	#131×C₆₁	—	4	2	no	—
72	C₂×M₁₆×C₆₁	—	2	1	no	—
73	C₂×M₁₆×C₆₁	—	2	2	no	—
74	C₂×M₁₆×C₆₁	—	4	2	no	—
75	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
76	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
77	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
78	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₆₁	—	2	1	no	—
80	C₂²×C₈×C₆₁	—	2	2	no	—
81	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
82	C₂²⋊Q₈×C₆₁	—	2	1	no	—
83	C₂²⋊Q₈×C₆₁	—	2	1	no	—
84	C₂²⋊Q₈×C₆₁	—	2	1	no	—
85	C₂²⋊Q₈×C₆₁	—	2	1	no	—
86	C₂×C₄⋊C₄×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	#106×C₆₁	—	2	2	no	—
97	#106×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	#103×C₆₁	—	2	2	no	—
103	#103×C₆₁	—	2	2	no	—
104	#102×C₆₁	—	2	2	no	—
105	#102×C₆₁	—	2	2	no	—
106	#102×C₆₁	—	2	1	no	—
107	#102×C₆₁	—	2	1	no	—
108	#101×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	#41	1	1	yes	characteristic
120	#41×C₆₁	—	2	2	no	—
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	—	4	4	no	—
126	#41×C₆₁	—	4	1	no	—
127	#41×C₆₁	—	4	1	no	—
128	#41×C₆₁	—	4	4	no	—
129	#41×C₆₁	#41	1	4	yes	—
130	C₂×Q₈×C₆₁	—	2	1	no	—
131	C₂×Q₈×C₆₁	—	2	2	no	—
132	C₂×Q₈×C₆₁	—	2	1	no	—
133	C₂×Q₈×C₆₁	—	2	1	no	—
134	C₂×Q₈×C₆₁	—	2	2	no	—
135	C₂×Q₈×C₆₁	—	2	2	no	—
136	C₂×Q₈×C₆₁	—	4	1	no	—
137	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
138	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
139	C₂×D₄×C₆₁	—	2	1	no	—
140	C₂×D₄×C₆₁	—	2	2	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	1	no	—
145	C₂×D₄×C₆₁	—	4	1	no	—
146	C₂×D₄×C₆₁	—	4	4	no	—
147	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
148	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₆₁	—	2	1	no	—
150	C₂²×C₄×C₆₁	—	2	2	no	—
151	C₂²×C₄×C₆₁	—	2	2	no	—
152	C₂²×C₄×C₆₁	—	2	1	no	—
153	C₂²×C₄×C₆₁	—	2	1	no	—
154	C₂²×C₄×C₆₁	—	2	1	no	—
155	C₂²×C₄×C₆₁	—	2	1	no	—
156	C₂²×C₄×C₆₁	—	2	1	no	—
157	C₂²×C₄×C₆₁	—	2	1	no	—
158	C₂²×C₄×C₆₁	—	2	2	no	—
159	C₂²×C₄×C₆₁	—	4	4	no	—
160	C₂²×C₄×C₆₁	—	4	1	no	—
161	C₂²×C₄×C₆₁	—	4	1	no	—
162	C₂²×C₄×C₆₁	—	8	2	no	—
163	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
168	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
169	Q₁₆×C₆₁	—	4	2	no	—
170	Q₁₆×C₆₁	—	4	2	no	—
171	SD₁₆×C₆₁	—	4	2	no	—
172	SD₁₆×C₆₁	—	4	2	no	—
173	M₁₆×C₆₁	—	2	2	no	—
174	M₁₆×C₆₁	—	2	2	no	—
175	M₁₆×C₆₁	—	2	2	no	—
176	M₁₆×C₆₁	—	2	2	no	—
177	M₁₆×C₆₁	—	2	2	no	—
178	M₁₆×C₆₁	—	2	2	no	—
179	M₁₆×C₆₁	—	4	4	no	—
180	M₁₆×C₆₁	—	4	2	no	—
181	C₂×C₈×C₆₁	—	2	2	no	—
182	C₂×C₈×C₆₁	—	2	2	no	—
183	C₂×C₈×C₆₁	—	2	2	no	—
184	C₂×C₈×C₆₁	—	2	1	no	—
185	C₂×C₈×C₆₁	—	2	1	no	—
186	C₂×C₈×C₆₁	—	2	2	no	—
187	C₂×C₈×C₆₁	—	4	4	no	—
188	C₂×C₈×C₆₁	—	4	2	no	—
189	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
191	C₄⋊C₄×C₆₁	—	2	2	no	—
192	C₄⋊C₄×C₆₁	—	2	1	no	—
193	C₄⋊C₄×C₆₁	—	2	2	no	—
194	C₄⋊C₄×C₆₁	—	2	1	no	—
195	C₄⋊C₄×C₆₁	—	4	1	no	—
196	C₄⋊C₄×C₆₁	—	4	1	no	—
197	C₄⋊C₄×C₆₁	—	4	1	no	—
198	C₄⋊C₄×C₆₁	—	4	1	no	—
199	C₂²⋊C₄×C₆₁	—	4	1	no	—
200	C₂²⋊C₄×C₆₁	—	4	1	no	—
201	C₂³×C₆₁	—	2	1	no	—
202	C₂³×C₆₁	—	2	2	no	—
203	C₂³×C₆₁	—	2	2	no	—
204	C₂³×C₆₁	—	2	1	no	—
205	C₂³×C₆₁	—	4	1	no	—
206	C₂³×C₆₁	—	4	2	no	—
207	C₂³×C₆₁	—	4	2	no	—
208	C₂³×C₆₁	—	8	1	no	—
209	C₂³×C₆₁	#121	1	1	yes	characteristic
210	C₂³×C₆₁	#121	1	1	yes	characteristic
211	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
212	Q₈×C₆₁	—	2	1	no	—
213	Q₈×C₆₁	—	2	1	no	—
214	Q₈×C₆₁	—	2	1	no	—
215	Q₈×C₆₁	—	4	2	no	—
216	Q₈×C₆₁	—	4	1	no	—
217	Q₈×C₆₁	—	4	1	no	—
218	Q₈×C₆₁	—	4	2	no	—
219	Q₈×C₆₁	#123	1	2	yes	—
220	D₄×C₆₁	—	2	4	no	—
221	D₄×C₆₁	—	2	1	no	—
222	D₄×C₆₁	—	2	1	no	—
223	D₄×C₆₁	—	2	1	no	—
224	D₄×C₆₁	—	4	2	no	—
225	D₄×C₆₁	—	4	2	no	—
226	D₄×C₆₁	—	4	2	no	—
227	D₄×C₆₁	—	4	2	no	—
228	D₄×C₆₁	#123	1	2	yes	—
229	C₂×C₄×C₆₁	—	2	1	no	—
230	C₂×C₄×C₆₁	—	2	2	no	—
231	C₂×C₄×C₆₁	—	2	1	no	—
232	C₂×C₄×C₆₁	—	2	1	no	—
233	C₂×C₄×C₆₁	—	2	1	no	—
234	C₂×C₄×C₆₁	—	2	1	no	—
235	C₂×C₄×C₆₁	—	2	4	no	—
236	C₂×C₄×C₆₁	—	2	2	no	—
237	C₂×C₄×C₆₁	—	2	2	no	—
238	C₂×C₄×C₆₁	—	2	1	no	—
239	C₂×C₄×C₆₁	—	4	2	no	—
240	C₂×C₄×C₆₁	—	4	2	no	—
241	C₂×C₄×C₆₁	—	4	2	no	—
242	C₂×C₄×C₆₁	—	4	2	no	—
243	C₂×C₄×C₆₁	—	4	1	no	—
244	C₂×C₄×C₆₁	—	4	1	no	—
245	C₂×C₄×C₆₁	—	4	2	no	—
246	C₂×C₄×C₆₁	—	4	2	no	—
247	C₂×C₄×C₆₁	—	8	2	no	—
248	C₂×C₄×C₆₁	—	8	2	no	—
249	C₂×C₄×C₆₁	—	8	1	no	—
250	C₂×C₄×C₆₁	—	8	2	no	—
251	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
252	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
253	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
256	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
257	C₈×C₆₁	—	2	2	no	—
258	C₈×C₆₁	—	2	2	no	—
259	C₈×C₆₁	—	4	1	no	—
260	C₈×C₆₁	—	4	2	no	—
261	C₈×C₆₁	—	4	1	no	—
262	C₈×C₆₁	—	4	2	no	—
263	#24571	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₂²×C₆₁	—	2	1	no	—
265	C₂²×C₆₁	—	2	1	no	—
266	C₂²×C₆₁	—	2	1	no	—
267	C₂²×C₆₁	—	2	1	no	—
268	C₂²×C₆₁	—	2	1	no	—
269	C₂²×C₆₁	—	2	2	no	—
270	C₂²×C₆₁	—	2	1	no	—
271	C₂²×C₆₁	—	2	1	no	—
272	C₂²×C₆₁	—	4	4	no	—
273	C₂²×C₆₁	—	4	1	no	—
274	C₂²×C₆₁	—	4	1	no	—
275	C₂²×C₆₁	—	4	1	no	—
276	C₂²×C₆₁	—	4	1	no	—
277	C₂²×C₆₁	—	4	1	no	—
278	C₂²×C₆₁	—	8	4	no	—
279	C₂²×C₆₁	#471	1	2	yes	—
280	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
281	C₂²×C₆₁	#551	1	2	yes	—
282	C₄×C₆₁	—	2	1	no	—
283	C₄×C₆₁	—	2	1	no	—
284	C₄×C₆₁	—	2	2	no	—
285	C₄×C₆₁	—	4	1	no	—
286	C₄×C₆₁	—	8	1	no	—
287	C₄×C₆₁	—	8	2	no	—
288	C₄×C₆₁	—	8	1	no	—
289	C₄×C₆₁	C₂×#123	1	1	yes	characteristic
290	C₄×C₆₁	#534	1	1	yes	characteristic
291	C₄×C₆₁	#546	1	2	yes	—
292	C₂×#483	C₂×C₆₁	1	1	yes	characteristic, complemented
293	#3007	C₂×C₆₁	1	1	yes	characteristic
294	C₂×#417	C₂×C₆₁	1	1	yes	characteristic
295	#2880	C₂×C₆₁	1	1	yes	characteristic
296	#2079	C₂×C₆₁	1	2	yes	complemented
297	#2052	C₂×C₆₁	1	2	yes	complemented
298	#1908	C₂×C₆₁	1	2	yes	complemented
299	#1901	C₂×C₆₁	1	1	yes	characteristic, complemented
300	#1855	C₂×C₆₁	1	1	yes	characteristic, complemented
301	#1821	C₂×C₆₁	1	1	yes	characteristic, complemented
302	#1815	C₂×C₆₁	1	2	yes	complemented
303	C₂×C₆₁	—	2	2	no	—
304	C₂×C₆₁	—	2	2	no	—
305	C₂×C₆₁	—	4	1	no	—
306	C₂×C₆₁	—	4	2	no	—
307	C₂×C₆₁	—	8	1	no	—
308	C₂×C₆₁	#2412	1	1	yes	characteristic
309	C₂×C₆₁	C₂×#471	1	1	yes	characteristic
310	C₂×C₆₁	#3069	1	1	yes	characteristic
311	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
312	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic
313	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic
314	C₂×#131	C₂²×C₆₁	1	2	yes	—
315	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
316	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
317	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
318	#483	—	2	1	no	—
319	#483	—	2	1	no	—
320	#483	—	2	2	no	—
321	#452	—	2	1	no	—
322	#452	—	2	1	no	—
323	#451	—	2	1	no	—
324	#450	—	2	1	no	—
325	C₂×#108	C₂²×C₆₁	1	2	yes	complemented
326	C₂×#106	C₂²×C₆₁	1	2	yes	complemented
327	#417	—	2	1	no	—
328	#417	—	2	1	no	—
329	#417	C₂²×C₆₁	1	2	yes	—
330	#417	C₂²×C₆₁	1	1	yes	characteristic
331	#417	C₂²×C₆₁	1	2	yes	—
332	#417	C₂²×C₆₁	1	1	yes	characteristic
333	C₂×#103	—	2	1	no	—
334	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
335	C₂×#102	—	2	1	no	—
336	C₂×#101	C₂²×C₆₁	1	2	yes	complemented
337	#408	—	2	2	no	—
338	#408	C₂²×C₆₁	1	2	yes	—
339	#407	—	2	1	no	—
340	#407	C₂²×C₆₁	1	1	yes	characteristic
341	#407	C₂²×C₆₁	1	1	yes	characteristic
342	C₂×C₂²⋊C₈	—	2	1	no	—
343	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
344	#343	C₂²×C₆₁	1	2	yes	complemented
345	#343	C₂²×C₆₁	1	2	yes	complemented
346	#343	C₂²×C₆₁	1	2	yes	complemented
347	#341	C₂²×C₆₁	1	2	yes	complemented
348	C₆₁	#24571	1	1	yes	characteristic, direct product factor, Sylow
349	C₂×#41	—	2	1	no	—
350	C₂×#41	—	2	1	no	—
351	C₂×#41	—	2	4	no	—
352	C₂×#41	—	4	2	no	—
353	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
354	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
355	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
356	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
357	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
358	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
359	C₂²×D₄	—	2	1	no	—
360	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
361	C₂³×C₄	—	2	1	no	—
362	C₂³×C₄	—	2	1	no	—
363	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
364	#137	—	2	4	no	—
365	#137	—	4	2	no	—
366	C₂×Q₁₆	—	2	1	no	—
367	C₂×Q₁₆	—	2	1	no	—
368	C₂×SD₁₆	—	2	1	no	—
369	C₂×SD₁₆	—	2	1	no	—
370	#131	—	2	4	no	—
371	#131	—	4	2	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	2	no	—
374	C₂×M₁₆	—	4	2	no	—
375	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
376	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
377	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
378	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	2	2	no	—
381	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
382	C₂²⋊Q₈	—	2	1	no	—
383	C₂²⋊Q₈	—	2	1	no	—
384	C₂²⋊Q₈	—	2	1	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
393	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	#108	—	4	2	no	—
396	#106	—	2	2	no	—
397	#106	—	2	2	no	—
398	#103	—	2	2	no	—
399	#103	—	2	2	no	—
400	#103	—	2	1	no	—
401	#103	—	2	1	no	—
402	#103	—	2	2	no	—
403	#103	—	2	2	no	—
404	#102	—	2	2	no	—
405	#102	—	2	2	no	—
406	#102	—	2	1	no	—
407	#102	—	2	1	no	—
408	#101	—	4	2	no	—
409	C₂²⋊C₈	—	2	1	no	—
410	C₂²⋊C₈	—	2	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	2	2	no	—
414	C₂²⋊C₈	—	2	2	no	—
415	C₂²⋊C₈	D₄×C₆₁	1	1	yes	characteristic
416	C₂²⋊C₈	D₄×C₆₁	1	1	yes	characteristic
417	C₂²⋊C₈	D₄×C₆₁	1	2	yes	—
418	C₂⁴	—	2	1	no	—
419	C₂⁴	#41×C₆₁	1	1	yes	characteristic
420	#41	—	2	2	no	—
421	#41	—	2	2	no	—
422	#41	—	2	2	no	—
423	#41	—	2	2	no	—
424	#41	—	2	2	no	—
425	#41	—	4	4	no	—
426	#41	—	4	1	no	—
427	#41	—	4	1	no	—
428	#41	—	4	4	no	—
429	#41	#41×C₆₁	1	4	yes	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	2	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	4	1	no	—
437	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
438	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	4	1	no	—
446	C₂×D₄	—	4	4	no	—
447	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
448	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	4	4	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	—	4	1	no	—
462	C₂²×C₄	—	8	2	no	—
463	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
467	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
469	Q₁₆	—	4	2	no	—
470	Q₁₆	—	4	2	no	—
471	SD₁₆	—	4	2	no	—
472	SD₁₆	—	4	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	2	no	—
475	M₁₆	—	2	2	no	—
476	M₁₆	—	2	2	no	—
477	M₁₆	—	2	2	no	—
478	M₁₆	—	2	2	no	—
479	M₁₆	—	4	4	no	—
480	M₁₆	—	4	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	2	no	—
487	C₂×C₈	—	4	4	no	—
488	C₂×C₈	—	4	2	no	—
489	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
490	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	4	1	no	—
496	C₄⋊C₄	—	4	1	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	2	1	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	4	1	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	8	1	no	—
509	C₂³	#121×C₆₁	1	1	yes	characteristic
510	C₂³	#121×C₆₁	1	1	yes	characteristic
511	C₂³	C₂×#41×C₆₁	1	1	yes	characteristic
512	Q₈	—	2	1	no	—
513	Q₈	—	2	1	no	—
514	Q₈	—	2	1	no	—
515	Q₈	—	4	2	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	4	2	no	—
518	Q₈	—	4	1	no	—
519	Q₈	#123×C₆₁	1	2	yes	—
520	D₄	—	2	4	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	#123×C₆₁	1	2	yes	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	8	2	no	—
548	C₂×C₄	—	8	2	no	—
549	C₂×C₄	—	8	1	no	—
550	C₂×C₄	—	8	2	no	—
551	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
552	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
553	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
555	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
556	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
557	C₈	—	2	2	no	—
558	C₈	—	2	2	no	—
559	C₈	—	4	2	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	2	no	—
562	C₈	—	4	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	8	4	no	—
578	C₂²	C₆₁×#471	1	2	yes	—
579	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
580	C₂²	C₆₁×#551	1	2	yes	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	2	no	—
584	C₄	—	4	1	no	—
585	C₄	—	8	2	no	—
586	C₄	—	8	1	no	—
587	C₄	—	8	1	no	—
588	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
589	C₄	C₆₁×#534	1	1	yes	characteristic
590	C₄	C₆₁×#546	1	2	yes	—
591	C₂	—	2	2	no	—
592	C₂	—	2	2	no	—
593	C₂	—	4	1	no	—
594	C₂	—	4	2	no	—
595	C₂	—	8	1	no	—
596	C₂	C₆₁×#2412	1	1	yes	characteristic
597	C₂	C₂×C₆₁×#471	1	1	yes	characteristic
598	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	C₂²×#41×C₆₁	C₂²
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×#483	C₂	semidirect
5. C₆₁×#2079	C₂	semidirect
6. C₆₁×#2052	C₂	semidirect
7. C₆₁×#1908	C₂	semidirect
8. C₆₁×#1901	C₂	semidirect
9. C₆₁×#1855	C₂	semidirect
10. C₆₁×#1821	C₂	semidirect
11. C₆₁×#1815	C₂	semidirect
26. C₂×#108×C₆₁	C₂²	semidirect
27. C₂×#106×C₆₁	C₂²	semidirect
35. C₂×#103×C₆₁	C₂²	semidirect
37. C₂×#101×C₆₁	C₂²	semidirect
45. C₆₁×#343	C₂²	semidirect
46. C₆₁×#343	C₂²	semidirect
47. C₆₁×#343	C₂²	semidirect
48. C₆₁×#341	C₂²	semidirect
263. #24571	C₆₁	direct (N × H)
292. C₂×#483	C₂×C₆₁	semidirect
296. #2079	C₂×C₆₁	semidirect
297. #2052	C₂×C₆₁	semidirect
298. #1908	C₂×C₆₁	semidirect
299. #1901	C₂×C₆₁	semidirect
300. #1855	C₂×C₆₁	semidirect
301. #1821	C₂×C₆₁	semidirect
302. #1815	C₂×C₆₁	semidirect
325. C₂×#108	C₂²×C₆₁	semidirect
326. C₂×#106	C₂²×C₆₁	semidirect
334. C₂×#103	C₂²×C₆₁	semidirect
336. C₂×#101	C₂²×C₆₁	semidirect
344. #343	C₂²×C₆₁	semidirect
345. #343	C₂²×C₆₁	semidirect
346. #343	C₂²×C₆₁	semidirect
347. #341	C₂²×C₆₁	semidirect
348. C₆₁	#24571	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×#483	2
C₆₁×#3007	2
C₂×C₆₁×#417	2
C₆₁×#2880	2
C₆₁×#2079	2
C₆₁×#2052	2
C₆₁×#1908	2
C₆₁×#1901	2
C₆₁×#1855	2
C₆₁×#1821	2
C₆₁×#1815	2
#24571	61

Subgroups — C61×#24571 #29528004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24571 #29528004