Subgroups — C₆₁×#24497 #29527930

Order 15616.

950 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#482	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#419	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2436	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2347	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2068	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2042	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1983	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1927	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1895	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×#124×C₆₁	C₂²	1	2	yes	—
15	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
17	C₆₁×#482	—	2	4	no	—
18	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
21	C₆₁×#419	—	2	4	no	—
22	C₂×#103×C₆₁	C₂²	1	2	yes	—
23	C₂×#103×C₆₁	C₂²	1	2	yes	—
24	C₂×#103×C₆₁	C₂²	1	2	yes	—
25	C₂×#103×C₆₁	C₂²	1	2	yes	—
26	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#102×C₆₁	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#393	—	2	1	no	—
31	C₆₁×#393	—	2	1	no	—
32	C₆₁×#391	C₂²	1	2	yes	—
33	C₆₁×#389	C₂²	1	2	yes	—
34	C₆₁×#388	—	2	2	no	—
35	C₆₁×#386	—	2	2	no	—
36	C₆₁×#383	—	2	1	no	—
37	C₆₁×#380	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
39	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
40	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#340	C₂²	1	2	yes	—
42	C₆₁×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₆₁	—	2	1	no	—
44	C₂²×Q₈×C₆₁	—	2	4	no	—
45	C₂²×Q₈×C₆₁	—	2	2	no	—
46	C₂²×Q₈×C₆₁	—	2	2	no	—
47	C₂²×Q₈×C₆₁	—	4	2	no	—
48	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
49	C₂²×D₄×C₆₁	—	2	1	no	—
50	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₆₁	—	2	1	no	—
52	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
53	C₂×M₁₆×C₆₁	—	2	2	no	—
54	C₂×M₁₆×C₆₁	—	4	2	no	—
55	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
58	#124×C₆₁	—	2	4	no	—
59	#124×C₆₁	—	4	2	no	—
60	#121×C₆₁	—	2	2	no	—
61	#121×C₆₁	—	2	2	no	—
62	#117×C₆₁	—	2	2	no	—
63	#117×C₆₁	D₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
75	C₂×C₄²×C₆₁	—	2	1	no	—
76	C₂×C₄²×C₆₁	—	2	2	no	—
77	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
78	#107×C₆₁	—	2	2	no	—
79	#106×C₆₁	—	2	2	no	—
80	C₄⋊C₈×C₆₁	—	4	2	no	—
81	#103×C₆₁	—	2	4	no	—
82	#103×C₆₁	—	2	4	no	—
83	#103×C₆₁	—	2	4	no	—
84	#103×C₆₁	—	4	2	no	—
85	#102×C₆₁	—	2	2	no	—
86	#102×C₆₁	—	2	2	no	—
87	#102×C₆₁	—	4	2	no	—
88	C₂²⋊C₈×C₆₁	—	2	2	no	—
89	#95×C₆₁	—	2	1	no	—
90	#95×C₆₁	—	2	2	no	—
91	#95×C₆₁	—	2	2	no	—
92	#95×C₆₁	—	2	2	no	—
93	#95×C₆₁	—	2	2	no	—
94	#95×C₆₁	D₄	1	1	yes	characteristic
95	#95×C₆₁	D₄	1	1	yes	characteristic
96	C₂⁴×C₆₁	—	2	1	no	—
97	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
98	C₂×Q₈×C₆₁	—	2	2	no	—
99	C₂×Q₈×C₆₁	—	2	8	no	—
100	C₂×Q₈×C₆₁	—	2	2	no	—
101	C₂×Q₈×C₆₁	—	2	2	no	—
102	C₂×Q₈×C₆₁	—	2	2	no	—
103	C₂×Q₈×C₆₁	—	2	2	no	—
104	C₂×Q₈×C₆₁	—	4	4	no	—
105	C₂×Q₈×C₆₁	—	4	8	no	—
106	C₂×Q₈×C₆₁	—	4	4	no	—
107	C₂×Q₈×C₆₁	—	4	2	no	—
108	C₂×Q₈×C₆₁	#41	1	4	yes	—
109	C₂×D₄×C₆₁	—	2	1	no	—
110	C₂×D₄×C₆₁	—	2	1	no	—
111	C₂×D₄×C₆₁	—	2	2	no	—
112	C₂×D₄×C₆₁	—	2	2	no	—
113	C₂×D₄×C₆₁	—	4	4	no	—
114	C₂×D₄×C₆₁	—	4	2	no	—
115	C₂²×C₄×C₆₁	—	2	2	no	—
116	C₂²×C₄×C₆₁	—	2	2	no	—
117	C₂²×C₄×C₆₁	—	2	1	no	—
118	C₂²×C₄×C₆₁	—	2	1	no	—
119	C₂²×C₄×C₆₁	—	2	2	no	—
120	C₂²×C₄×C₆₁	—	2	1	no	—
121	C₂²×C₄×C₆₁	—	2	2	no	—
122	C₂²×C₄×C₆₁	—	4	4	no	—
123	C₂²×C₄×C₆₁	—	4	2	no	—
124	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₆₁	#41	1	2	yes	—
129	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
130	M₁₆×C₆₁	—	4	4	no	—
131	C₂×C₈×C₆₁	—	2	1	no	—
132	C₂×C₈×C₆₁	—	2	1	no	—
133	C₂×C₈×C₆₁	—	2	2	no	—
134	C₂×C₈×C₆₁	—	2	2	no	—
135	C₂×C₈×C₆₁	—	2	2	no	—
136	C₂×C₈×C₆₁	—	2	2	no	—
137	C₂×C₈×C₆₁	—	2	2	no	—
138	C₄⋊C₄×C₆₁	—	2	1	no	—
139	C₄⋊C₄×C₆₁	—	2	1	no	—
140	C₄⋊C₄×C₆₁	—	2	1	no	—
141	C₄⋊C₄×C₆₁	—	2	2	no	—
142	C₄⋊C₄×C₆₁	—	2	1	no	—
143	C₄⋊C₄×C₆₁	—	2	2	no	—
144	C₄⋊C₄×C₆₁	—	4	4	no	—
145	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
146	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
147	C₂²⋊C₄×C₆₁	—	2	4	no	—
148	C₂²⋊C₄×C₆₁	—	4	2	no	—
149	C₂²⋊C₄×C₆₁	—	4	4	no	—
150	C₂²⋊C₄×C₆₁	—	4	4	no	—
151	C₂²⋊C₄×C₆₁	—	4	2	no	—
152	C₂²⋊C₄×C₆₁	—	8	1	no	—
153	C₄²×C₆₁	—	2	4	no	—
154	C₄²×C₆₁	—	2	2	no	—
155	C₄²×C₆₁	—	2	2	no	—
156	C₄²×C₆₁	—	8	2	no	—
157	C₂³×C₆₁	—	2	2	no	—
158	C₂³×C₆₁	—	2	2	no	—
159	C₂³×C₆₁	—	2	1	no	—
160	C₂³×C₆₁	—	2	1	no	—
161	C₂³×C₆₁	—	4	1	no	—
162	C₂³×C₆₁	—	4	2	no	—
163	C₂³×C₆₁	—	4	2	no	—
164	C₂³×C₆₁	—	4	1	no	—
165	C₂³×C₆₁	—	4	1	no	—
166	C₂³×C₆₁	#121	1	2	yes	—
167	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
168	Q₈×C₆₁	—	2	4	no	—
169	Q₈×C₆₁	—	2	4	no	—
170	Q₈×C₆₁	—	4	8	no	—
171	Q₈×C₆₁	—	4	2	no	—
172	Q₈×C₆₁	—	4	2	no	—
173	D₄×C₆₁	—	4	1	no	—
174	D₄×C₆₁	—	4	1	no	—
175	D₄×C₆₁	—	4	2	no	—
176	D₄×C₆₁	—	8	4	no	—
177	C₂×C₄×C₆₁	—	2	2	no	—
178	C₂×C₄×C₆₁	—	2	2	no	—
179	C₂×C₄×C₆₁	—	2	2	no	—
180	C₂×C₄×C₆₁	—	2	4	no	—
181	C₂×C₄×C₆₁	—	2	2	no	—
182	C₂×C₄×C₆₁	—	2	2	no	—
183	C₂×C₄×C₆₁	—	2	2	no	—
184	C₂×C₄×C₆₁	—	2	2	no	—
185	C₂×C₄×C₆₁	—	2	4	no	—
186	C₂×C₄×C₆₁	—	2	2	no	—
187	C₂×C₄×C₆₁	—	2	2	no	—
188	C₂×C₄×C₆₁	—	2	2	no	—
189	C₂×C₄×C₆₁	—	2	2	no	—
190	C₂×C₄×C₆₁	—	4	8	no	—
191	C₂×C₄×C₆₁	—	4	2	no	—
192	C₂×C₄×C₆₁	—	4	2	no	—
193	C₂×C₄×C₆₁	—	4	2	no	—
194	C₂×C₄×C₆₁	—	4	1	no	—
195	C₂×C₄×C₆₁	—	4	1	no	—
196	C₂×C₄×C₆₁	—	4	1	no	—
197	C₂×C₄×C₆₁	—	4	2	no	—
198	C₂×C₄×C₆₁	—	4	2	no	—
199	C₂×C₄×C₆₁	—	4	2	no	—
200	C₂×C₄×C₆₁	—	4	2	no	—
201	C₂×C₄×C₆₁	#121	1	2	yes	—
202	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
204	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
206	C₈×C₆₁	—	4	1	no	—
207	C₈×C₆₁	—	4	1	no	—
208	C₈×C₆₁	—	4	2	no	—
209	#24497	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂²×C₆₁	—	2	2	no	—
211	C₂²×C₆₁	—	2	2	no	—
212	C₂²×C₆₁	—	2	2	no	—
213	C₂²×C₆₁	—	4	2	no	—
214	C₂²×C₆₁	—	4	2	no	—
215	C₂²×C₆₁	—	8	1	no	—
216	C₂²×C₆₁	—	8	1	no	—
217	C₂²×C₆₁	—	8	1	no	—
218	C₂²×C₆₁	—	8	2	no	—
219	C₂²×C₆₁	—	8	2	no	—
220	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
221	C₂²×C₆₁	#546	1	2	yes	—
222	C₂²×C₆₁	#575	1	2	yes	—
223	C₂²×C₆₁	#577	1	1	yes	characteristic
224	C₂²×C₆₁	#578	1	1	yes	characteristic
225	C₄×C₆₁	—	2	2	no	—
226	C₄×C₆₁	—	4	4	no	—
227	C₄×C₆₁	—	4	2	no	—
228	C₄×C₆₁	—	4	2	no	—
229	C₄×C₆₁	—	4	2	no	—
230	C₄×C₆₁	—	4	2	no	—
231	C₄×C₆₁	—	8	1	no	—
232	C₄×C₆₁	—	8	2	no	—
233	C₄×C₆₁	#525	1	1	yes	characteristic
234	C₄×C₆₁	#535	1	1	yes	characteristic
235	C₄×C₆₁	#551	1	2	yes	—
236	C₂×#482	C₂×C₆₁	1	1	yes	characteristic
237	C₂×#419	C₂×C₆₁	1	1	yes	characteristic, complemented
238	#2436	C₂×C₆₁	1	1	yes	characteristic
239	#2347	C₂×C₆₁	1	1	yes	characteristic, complemented
240	#2068	C₂×C₆₁	1	2	yes	complemented
241	#2042	C₂×C₆₁	1	2	yes	complemented
242	#1983	C₂×C₆₁	1	2	yes	complemented
243	#1927	C₂×C₆₁	1	2	yes	complemented
244	#1895	C₂×C₆₁	1	1	yes	characteristic
245	#1851	C₂×C₆₁	1	1	yes	characteristic, complemented
246	#1787	C₂×C₆₁	1	1	yes	characteristic, complemented
247	C₂×C₆₁	—	4	2	no	—
248	C₂×C₆₁	—	16	1	no	—
249	C₂×C₆₁	#2411	1	1	yes	characteristic
250	C₂×C₆₁	#3040	1	1	yes	characteristic
251	C₂×C₆₁	#3046	1	1	yes	characteristic
252	C₂×C₆₁	#3313	1	2	yes	—
253	C₂×C₆₁	#3326	1	2	yes	—
254	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
255	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
256	C₂×#124	C₂²×C₆₁	1	2	yes	—
257	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
258	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
259	#482	—	2	4	no	—
260	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
261	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
263	#419	—	2	4	no	—
264	C₂×#103	C₂²×C₆₁	1	2	yes	—
265	C₂×#103	C₂²×C₆₁	1	2	yes	—
266	C₂×#103	C₂²×C₆₁	1	2	yes	—
267	C₂×#103	C₂²×C₆₁	1	2	yes	—
268	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
269	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
270	C₂×#102	C₂²×C₆₁	1	2	yes	—
271	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
272	#393	—	2	1	no	—
273	#393	—	2	1	no	—
274	#391	C₂²×C₆₁	1	2	yes	—
275	#389	C₂²×C₆₁	1	2	yes	—
276	#388	—	2	2	no	—
277	#386	—	2	2	no	—
278	#383	—	2	1	no	—
279	#380	C₂²×C₆₁	1	1	yes	characteristic
280	C₄×C₄⋊C₄	—	2	1	no	—
281	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
282	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
283	#340	C₂²×C₆₁	1	2	yes	—
284	#336	C₂²×C₆₁	1	2	yes	—
285	C₆₁	#24497	1	1	yes	characteristic, direct product factor, Sylow
286	C₂²×Q₈	—	2	1	no	—
287	C₂²×Q₈	—	2	4	no	—
288	C₂²×Q₈	—	2	2	no	—
289	C₂²×Q₈	—	2	2	no	—
290	C₂²×Q₈	—	4	2	no	—
291	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
294	C₂³×C₄	—	2	1	no	—
295	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	—	4	2	no	—
298	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
299	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
301	#124	—	2	4	no	—
302	#124	—	4	2	no	—
303	#121	—	2	2	no	—
304	#121	—	2	2	no	—
305	#117	—	2	2	no	—
306	#117	D₄×C₆₁	1	4	yes	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
321	#107	—	2	2	no	—
322	#106	—	2	2	no	—
323	C₄⋊C₈	—	4	2	no	—
324	#103	—	2	4	no	—
325	#103	—	2	4	no	—
326	#103	—	2	4	no	—
327	#103	—	4	2	no	—
328	#102	—	2	2	no	—
329	#102	—	2	2	no	—
330	#102	—	4	2	no	—
331	C₂²⋊C₈	—	2	2	no	—
332	#95	—	2	1	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	#95	—	2	2	no	—
337	#95	D₄×C₆₁	1	1	yes	characteristic
338	#95	D₄×C₆₁	1	1	yes	characteristic
339	C₂⁴	—	2	1	no	—
340	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	8	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	4	4	no	—
348	C₂×Q₈	—	4	8	no	—
349	C₂×Q₈	—	4	4	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	#41×C₆₁	1	4	yes	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	4	4	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
371	C₂²×C₄	#41×C₆₁	1	2	yes	—
372	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
373	M₁₆	—	4	4	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	4	4	no	—
388	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
389	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
390	C₂²⋊C₄	—	2	4	no	—
391	C₂²⋊C₄	—	4	2	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₂²⋊C₄	—	8	1	no	—
396	C₄²	—	2	4	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	8	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	#121×C₆₁	1	2	yes	—
410	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
411	Q₈	—	2	4	no	—
412	Q₈	—	2	4	no	—
413	Q₈	—	4	8	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	D₄	—	4	1	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	1	no	—
419	D₄	—	8	4	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	2	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	—	4	8	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	#121×C₆₁	1	2	yes	—
445	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
446	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
447	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
448	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
449	C₈	—	4	1	no	—
450	C₈	—	4	2	no	—
451	C₈	—	4	1	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	1	no	—
462	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
463	C₂²	C₆₁×#546	1	2	yes	—
464	C₂²	C₆₁×#575	1	2	yes	—
465	C₂²	C₆₁×#577	1	1	yes	characteristic
466	C₂²	C₆₁×#578	1	1	yes	characteristic
467	C₄	—	2	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	4	no	—
473	C₄	—	8	1	no	—
474	C₄	—	8	2	no	—
475	C₄	C₆₁×#525	1	1	yes	characteristic
476	C₄	C₆₁×#535	1	1	yes	characteristic
477	C₄	C₆₁×#551	1	2	yes	—
478	C₂	—	4	2	no	—
479	C₂	—	16	1	no	—
480	C₂	C₆₁×#2411	1	1	yes	characteristic
481	C₂	C₆₁×#3040	1	1	yes	characteristic
482	C₂	C₆₁×#3046	1	1	yes	characteristic
483	C₂	C₆₁×#3313	1	2	yes	—
484	C₂	C₆₁×#3326	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×#121×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₄×C₂²⋊C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#419	C₂	semidirect
4. C₆₁×#2347	C₂	semidirect
5. C₆₁×#2068	C₂	semidirect
6. C₆₁×#2042	C₂	semidirect
7. C₆₁×#1983	C₂	semidirect
8. C₆₁×#1927	C₂	semidirect
10. C₆₁×#1851	C₂	semidirect
11. C₆₁×#1787	C₂	semidirect
209. #24497	C₆₁	direct (N × H)
237. C₂×#419	C₂×C₆₁	semidirect
239. #2347	C₂×C₆₁	semidirect
240. #2068	C₂×C₆₁	semidirect
241. #2042	C₂×C₆₁	semidirect
242. #1983	C₂×C₆₁	semidirect
243. #1927	C₂×C₆₁	semidirect
245. #1851	C₂×C₆₁	semidirect
246. #1787	C₂×C₆₁	semidirect
285. C₆₁	#24497	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×#482	2
C₂×C₆₁×#419	2
C₆₁×#2436	2
C₆₁×#2347	2
C₆₁×#2068	2
C₆₁×#2042	2
C₆₁×#1983	2
C₆₁×#1927	2
C₆₁×#1895	2
C₆₁×#1851	2
C₆₁×#1787	2
#24497	61

Subgroups — C61×#24497 #29527930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24497 #29527930