Subgroups — C₆₁×#24543 #29527976

Order 15616.

980 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#452	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#417	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2503	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2341	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2073	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2055	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1894	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1878	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1824	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1805	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#452	—	2	4	no	—
20	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
21	C₆₁×#417	—	2	4	no	—
22	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#103×C₆₁	C₂²	1	2	yes	—
24	C₂×#103×C₆₁	C₂²	1	2	yes	—
25	C₂×#102×C₆₁	C₂²	1	2	yes	—
26	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₆₁×#400	—	2	1	no	—
29	C₆₁×#400	—	2	1	no	—
30	C₆₁×#391	C₂²	1	2	yes	—
31	C₆₁×#390	—	2	2	no	—
32	C₆₁×#390	C₂²	1	2	yes	—
33	C₆₁×#382	C₂²	1	2	yes	—
34	C₆₁×#381	—	2	2	no	—
35	C₆₁×#380	—	2	1	no	—
36	C₆₁×#380	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×#340	C₂²	1	2	yes	—
40	C₆₁×#340	C₂²	1	2	yes	—
41	C₆₁×#340	C₂²	1	2	yes	—
42	C₆₁×#336	C₂²	1	2	yes	—
43	C₂×#41×C₆₁	—	2	2	no	—
44	C₂×#41×C₆₁	—	2	4	no	—
45	C₂×#41×C₆₁	—	4	2	no	—
46	C₂×#41×C₆₁	D₄	1	4	yes	—
47	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
53	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
54	C₂×Q₁₆×C₆₁	—	2	2	no	—
55	C₂×Q₁₆×C₆₁	—	2	4	no	—
56	C₂×SD₁₆×C₆₁	—	2	2	no	—
57	C₂×SD₁₆×C₆₁	—	4	2	no	—
58	C₂×M₁₆×C₆₁	—	2	2	no	—
59	C₂×M₁₆×C₆₁	—	4	2	no	—
60	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
61	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²⋊Q₈×C₆₁	—	2	2	no	—
64	C₂²⋊Q₈×C₆₁	—	2	2	no	—
65	C₄×Q₈×C₆₁	—	2	4	no	—
66	C₄×Q₈×C₆₁	—	4	2	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
71	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
80	C₂×C₄²×C₆₁	—	2	2	no	—
81	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
82	C₄⋊C₈×C₆₁	—	4	2	no	—
83	#103×C₆₁	—	2	4	no	—
84	#103×C₆₁	—	2	2	no	—
85	#103×C₆₁	—	4	2	no	—
86	#102×C₆₁	—	2	4	no	—
87	#102×C₆₁	—	2	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	#41×C₆₁	—	2	8	no	—
99	#41×C₆₁	—	4	4	no	—
100	#41×C₆₁	—	4	8	no	—
101	C₂×Q₈×C₆₁	—	2	1	no	—
102	C₂×Q₈×C₆₁	—	2	2	no	—
103	C₂×Q₈×C₆₁	—	2	1	no	—
104	C₂×Q₈×C₆₁	—	2	1	no	—
105	C₂×Q₈×C₆₁	—	2	2	no	—
106	C₂×Q₈×C₆₁	—	2	2	no	—
107	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
108	C₂×Q₈×C₆₁	#41	1	4	yes	—
109	C₂×D₄×C₆₁	—	2	4	no	—
110	C₂×D₄×C₆₁	—	2	2	no	—
111	C₂×D₄×C₆₁	—	2	1	no	—
112	C₂×D₄×C₆₁	—	2	2	no	—
113	C₂×D₄×C₆₁	—	4	4	no	—
114	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₆₁	—	2	1	no	—
116	C₂²×C₄×C₆₁	—	2	2	no	—
117	C₂²×C₄×C₆₁	—	2	2	no	—
118	C₂²×C₄×C₆₁	—	2	4	no	—
119	C₂²×C₄×C₆₁	—	2	1	no	—
120	C₂²×C₄×C₆₁	—	2	1	no	—
121	C₂²×C₄×C₆₁	—	2	2	no	—
122	C₂²×C₄×C₆₁	—	2	2	no	—
123	C₂²×C₄×C₆₁	—	4	4	no	—
124	C₂²×C₄×C₆₁	—	4	4	no	—
125	C₂²×C₄×C₆₁	—	4	2	no	—
126	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₆₁	#41	1	2	yes	—
131	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
132	Q₁₆×C₆₁	—	4	4	no	—
133	SD₁₆×C₆₁	—	4	4	no	—
134	M₁₆×C₆₁	—	4	4	no	—
135	C₂×C₈×C₆₁	—	2	1	no	—
136	C₂×C₈×C₆₁	—	2	1	no	—
137	C₂×C₈×C₆₁	—	2	2	no	—
138	C₂×C₈×C₆₁	—	2	2	no	—
139	C₂×C₈×C₆₁	—	2	2	no	—
140	C₂×C₈×C₆₁	—	2	2	no	—
141	C₂×C₈×C₆₁	—	2	2	no	—
142	C₄⋊C₄×C₆₁	—	2	2	no	—
143	C₄⋊C₄×C₆₁	—	2	1	no	—
144	C₄⋊C₄×C₆₁	—	2	2	no	—
145	C₄⋊C₄×C₆₁	—	2	2	no	—
146	C₄⋊C₄×C₆₁	—	2	1	no	—
147	C₄⋊C₄×C₆₁	—	2	2	no	—
148	C₄⋊C₄×C₆₁	—	4	4	no	—
149	C₄⋊C₄×C₆₁	—	4	2	no	—
150	C₄⋊C₄×C₆₁	—	4	2	no	—
151	C₂²⋊C₄×C₆₁	—	4	2	no	—
152	C₂²⋊C₄×C₆₁	—	4	4	no	—
153	C₂²⋊C₄×C₆₁	—	4	2	no	—
154	C₂²⋊C₄×C₆₁	—	8	2	no	—
155	C₂²⋊C₄×C₆₁	—	8	1	no	—
156	C₄²×C₆₁	—	2	2	no	—
157	C₄²×C₆₁	—	2	2	no	—
158	C₄²×C₆₁	—	4	4	no	—
159	C₂³×C₆₁	—	2	2	no	—
160	C₂³×C₆₁	—	2	2	no	—
161	C₂³×C₆₁	—	2	1	no	—
162	C₂³×C₆₁	—	2	1	no	—
163	C₂³×C₆₁	—	2	2	no	—
164	C₂³×C₆₁	—	4	2	no	—
165	C₂³×C₆₁	—	4	2	no	—
166	C₂³×C₆₁	—	4	1	no	—
167	C₂³×C₆₁	—	4	1	no	—
168	C₂³×C₆₁	#121	1	2	yes	—
169	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₆₁	—	2	2	no	—
171	Q₈×C₆₁	—	2	4	no	—
172	Q₈×C₆₁	—	4	1	no	—
173	Q₈×C₆₁	—	4	1	no	—
174	Q₈×C₆₁	—	4	2	no	—
175	Q₈×C₆₁	#123	1	4	yes	—
176	D₄×C₆₁	—	2	2	no	—
177	D₄×C₆₁	—	2	2	no	—
178	D₄×C₆₁	—	4	8	no	—
179	D₄×C₆₁	—	4	2	no	—
180	C₂×C₄×C₆₁	—	2	2	no	—
181	C₂×C₄×C₆₁	—	2	4	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	—	2	2	no	—
191	C₂×C₄×C₆₁	—	2	2	no	—
192	C₂×C₄×C₆₁	—	4	8	no	—
193	C₂×C₄×C₆₁	—	4	1	no	—
194	C₂×C₄×C₆₁	—	4	1	no	—
195	C₂×C₄×C₆₁	—	4	2	no	—
196	C₂×C₄×C₆₁	—	4	2	no	—
197	C₂×C₄×C₆₁	—	4	2	no	—
198	C₂×C₄×C₆₁	—	4	2	no	—
199	C₂×C₄×C₆₁	—	4	4	no	—
200	C₂×C₄×C₆₁	—	4	2	no	—
201	C₂×C₄×C₆₁	—	4	1	no	—
202	C₂×C₄×C₆₁	—	4	1	no	—
203	C₂×C₄×C₆₁	—	8	4	no	—
204	C₂×C₄×C₆₁	#121	1	2	yes	—
205	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
207	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
209	C₈×C₆₁	—	4	1	no	—
210	C₈×C₆₁	—	4	2	no	—
211	C₈×C₆₁	—	4	1	no	—
212	#24543	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂²×C₆₁	—	2	2	no	—
214	C₂²×C₆₁	—	2	2	no	—
215	C₂²×C₆₁	—	2	2	no	—
216	C₂²×C₆₁	—	4	2	no	—
217	C₂²×C₆₁	—	4	2	no	—
218	C₂²×C₆₁	—	4	2	no	—
219	C₂²×C₆₁	—	4	2	no	—
220	C₂²×C₆₁	—	4	2	no	—
221	C₂²×C₆₁	—	8	2	no	—
222	C₂²×C₆₁	—	8	2	no	—
223	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
224	C₂²×C₆₁	#546	1	2	yes	—
225	C₂²×C₆₁	#575	1	2	yes	—
226	C₂²×C₆₁	#577	1	1	yes	characteristic
227	C₂²×C₆₁	#578	1	1	yes	characteristic
228	C₄×C₆₁	—	2	2	no	—
229	C₄×C₆₁	—	2	4	no	—
230	C₄×C₆₁	—	4	2	no	—
231	C₄×C₆₁	—	4	2	no	—
232	C₄×C₆₁	—	8	1	no	—
233	C₄×C₆₁	—	8	2	no	—
234	C₄×C₆₁	—	8	1	no	—
235	C₄×C₆₁	—	8	2	no	—
236	C₄×C₆₁	C₂×#123	1	1	yes	characteristic
237	C₄×C₆₁	#534	1	1	yes	characteristic
238	C₄×C₆₁	#551	1	2	yes	—
239	C₂×#452	C₂×C₆₁	1	1	yes	characteristic
240	C₂×#417	C₂×C₆₁	1	1	yes	characteristic
241	#2503	C₂×C₆₁	1	1	yes	characteristic, complemented
242	#2341	C₂×C₆₁	1	1	yes	characteristic
243	#2073	C₂×C₆₁	1	2	yes	complemented
244	#2055	C₂×C₆₁	1	2	yes	complemented
245	#1894	C₂×C₆₁	1	1	yes	characteristic, complemented
246	#1878	C₂×C₆₁	1	2	yes	complemented
247	#1851	C₂×C₆₁	1	1	yes	characteristic, complemented
248	#1824	C₂×C₆₁	1	1	yes	characteristic, complemented
249	#1805	C₂×C₆₁	1	2	yes	complemented
250	C₂×C₆₁	—	4	2	no	—
251	C₂×C₆₁	—	8	2	no	—
252	C₂×C₆₁	#2412	1	1	yes	characteristic
253	C₂×C₆₁	#3040	1	1	yes	characteristic
254	C₂×C₆₁	#3046	1	1	yes	characteristic
255	C₂×C₆₁	#3317	1	2	yes	—
256	C₂×C₆₁	#3327	1	2	yes	—
257	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
258	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
259	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
260	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
261	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
262	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
263	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
264	#452	—	2	4	no	—
265	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
266	#417	—	2	4	no	—
267	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
268	C₂×#103	C₂²×C₆₁	1	2	yes	—
269	C₂×#103	C₂²×C₆₁	1	2	yes	—
270	C₂×#102	C₂²×C₆₁	1	2	yes	—
271	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
272	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
273	#400	—	2	1	no	—
274	#400	—	2	1	no	—
275	#391	C₂²×C₆₁	1	2	yes	—
276	#390	—	2	2	no	—
277	#390	C₂²×C₆₁	1	2	yes	—
278	#382	C₂²×C₆₁	1	2	yes	—
279	#381	—	2	2	no	—
280	#380	—	2	1	no	—
281	#380	C₂²×C₆₁	1	1	yes	characteristic
282	C₄×C₂²⋊C₄	—	2	1	no	—
283	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
284	#340	C₂²×C₆₁	1	2	yes	—
285	#340	C₂²×C₆₁	1	2	yes	—
286	#340	C₂²×C₆₁	1	2	yes	—
287	#336	C₂²×C₆₁	1	2	yes	—
288	C₆₁	#24543	1	1	yes	characteristic, direct product factor, Sylow
289	C₂×#41	—	2	2	no	—
290	C₂×#41	—	2	4	no	—
291	C₂×#41	—	4	2	no	—
292	C₂×#41	D₄×C₆₁	1	4	yes	—
293	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
294	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
297	C₂³×C₄	—	2	1	no	—
298	C₂³×C₄	—	2	1	no	—
299	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
300	C₂×Q₁₆	—	2	2	no	—
301	C₂×Q₁₆	—	2	4	no	—
302	C₂×SD₁₆	—	2	2	no	—
303	C₂×SD₁₆	—	4	2	no	—
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	—	4	2	no	—
306	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
307	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
309	C₂²⋊Q₈	—	2	2	no	—
310	C₂²⋊Q₈	—	2	2	no	—
311	C₄×Q₈	—	2	4	no	—
312	C₄×Q₈	—	4	2	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
326	C₂×C₄²	—	2	2	no	—
327	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
328	C₄⋊C₈	—	4	2	no	—
329	#103	—	2	4	no	—
330	#103	—	2	2	no	—
331	#103	—	4	2	no	—
332	#102	—	2	4	no	—
333	#102	—	2	2	no	—
334	C₂²⋊C₈	—	2	2	no	—
335	#95	—	2	1	no	—
336	#95	—	2	2	no	—
337	#95	—	2	2	no	—
338	#95	—	2	2	no	—
339	#95	—	2	2	no	—
340	#95	D₄×C₆₁	1	1	yes	characteristic
341	#95	D₄×C₆₁	1	1	yes	characteristic
342	C₂⁴	—	2	1	no	—
343	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
344	#41	—	2	8	no	—
345	#41	—	4	4	no	—
346	#41	—	4	8	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
354	C₂×Q₈	#41×C₆₁	1	4	yes	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	4	4	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
376	C₂²×C₄	#41×C₆₁	1	2	yes	—
377	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
378	Q₁₆	—	4	4	no	—
379	SD₁₆	—	4	4	no	—
380	M₁₆	—	4	4	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	4	4	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	—	4	2	no	—
398	C₂²⋊C₄	—	4	4	no	—
399	C₂²⋊C₄	—	4	2	no	—
400	C₂²⋊C₄	—	8	2	no	—
401	C₂²⋊C₄	—	8	1	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	4	4	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	#121×C₆₁	1	2	yes	—
415	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
416	Q₈	—	2	2	no	—
417	Q₈	—	2	4	no	—
418	Q₈	—	4	1	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	4	1	no	—
421	Q₈	#123×C₆₁	1	4	yes	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	8	no	—
425	D₄	—	4	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	4	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	8	4	no	—
450	C₂×C₄	#121×C₆₁	1	2	yes	—
451	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
454	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
455	C₈	—	4	2	no	—
456	C₈	—	4	1	no	—
457	C₈	—	4	1	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	8	2	no	—
468	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
469	C₂²	C₆₁×#546	1	2	yes	—
470	C₂²	C₆₁×#575	1	2	yes	—
471	C₂²	C₆₁×#577	1	1	yes	characteristic
472	C₂²	C₆₁×#578	1	1	yes	characteristic
473	C₄	—	2	2	no	—
474	C₄	—	2	4	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	1	no	—
479	C₄	—	8	2	no	—
480	C₄	—	8	1	no	—
481	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
482	C₄	C₆₁×#534	1	1	yes	characteristic
483	C₄	C₆₁×#551	1	2	yes	—
484	C₂	—	4	2	no	—
485	C₂	—	8	2	no	—
486	C₂	C₆₁×#2412	1	1	yes	characteristic
487	C₂	C₆₁×#3040	1	1	yes	characteristic
488	C₂	C₆₁×#3046	1	1	yes	characteristic
489	C₂	C₆₁×#3317	1	2	yes	—
490	C₂	C₆₁×#3327	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×#41×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
3. C₆₁×#2503	C₂	semidirect
5. C₆₁×#2073	C₂	semidirect
6. C₆₁×#2055	C₂	semidirect
7. C₆₁×#1894	C₂	semidirect
8. C₆₁×#1878	C₂	semidirect
9. C₆₁×#1851	C₂	semidirect
10. C₆₁×#1824	C₂	semidirect
11. C₆₁×#1805	C₂	semidirect
212. #24543	C₆₁	direct (N × H)
241. #2503	C₂×C₆₁	semidirect
243. #2073	C₂×C₆₁	semidirect
244. #2055	C₂×C₆₁	semidirect
245. #1894	C₂×C₆₁	semidirect
246. #1878	C₂×C₆₁	semidirect
247. #1851	C₂×C₆₁	semidirect
248. #1824	C₂×C₆₁	semidirect
249. #1805	C₂×C₆₁	semidirect
288. C₆₁	#24543	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×#452	2
C₂×C₆₁×#417	2
C₆₁×#2503	2
C₆₁×#2341	2
C₆₁×#2073	2
C₆₁×#2055	2
C₆₁×#1894	2
C₆₁×#1878	2
C₆₁×#1851	2
C₆₁×#1824	2
C₆₁×#1805	2
#24543	61

Subgroups — C61×#24543 #29527976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24543 #29527976