Subgroups — C₆₁×#25313 #29528746

Order 15616.

712 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	C₆₁×#3139	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3077	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#461	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2064	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2046	C₂	1	2	yes	maximal
7	C₆₁×#1977	C₂	1	2	yes	maximal
8	C₆₁×#1966	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1930	C₂	1	2	yes	maximal, complemented
11	C₄×#100×C₆₁	C₂	1	1	yes	maximal, characteristic
12	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
13	C₆₁×#533	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
16	C₆₁×#491	—	2	2	no	—
17	C₆₁×#487	—	2	1	no	—
18	C₆₁×#487	—	2	1	no	—
19	C₆₁×#478	—	2	2	no	—
20	C₆₁×#476	—	2	1	no	—
21	C₆₁×#474	—	2	1	no	—
22	C₆₁×#461	—	2	1	no	—
23	C₆₁×#461	—	2	2	no	—
24	C₆₁×#461	—	2	1	no	—
25	C₆₁×#446	—	2	2	no	—
26	C₆₁×#446	—	2	1	no	—
27	C₈×Q₈×C₆₁	—	2	1	no	—
28	C₂×#108×C₆₁	C₂²	1	2	yes	—
29	C₆₁×#428	C₂²	1	2	yes	—
30	C₆₁×#424	C₂²	1	2	yes	—
31	C₆₁×#423	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₆₁×#419	C₂²	1	2	yes	—
34	C₆₁×#419	C₂²	1	2	yes	—
35	C₆₁×#418	C₂²	1	2	yes	—
36	C₂×#103×C₆₁	C₂²	1	2	yes	—
37	C₂×#101×C₆₁	C₂²	1	2	yes	—
38	C₂×#101×C₆₁	C₂²	1	2	yes	—
39	C₂×#100×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×#100×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#405	C₂²	1	2	yes	—
42	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
44	C₆₁×#343	C₂²	1	1	yes	characteristic
45	C₆₁×#343	C₂²	1	1	yes	characteristic
46	C₆₁×#341	C₂²	1	2	yes	—
47	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
48	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₆₁	—	2	1	no	—
50	C₂×SD₁₆×C₆₁	—	2	4	no	—
51	C₂×SD₁₆×C₆₁	—	2	2	no	—
52	C₂×SD₁₆×C₆₁	—	2	2	no	—
53	C₂×SD₁₆×C₆₁	—	4	2	no	—
54	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
55	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
56	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
60	C₄⋊Q₈×C₆₁	—	2	1	no	—
61	C₄⋊Q₈×C₆₁	—	2	1	no	—
62	C₄⋊Q₈×C₆₁	—	2	1	no	—
63	C₄⋊Q₈×C₆₁	—	2	1	no	—
64	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
65	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
66	#125×C₆₁	D₄	1	2	yes	—
67	C₂²⋊Q₈×C₆₁	—	2	1	no	—
68	C₂²⋊Q₈×C₆₁	—	2	1	no	—
69	C₄×Q₈×C₆₁	—	2	1	no	—
70	C₄×Q₈×C₆₁	—	2	1	no	—
71	C₄×D₄×C₆₁	—	2	1	no	—
72	C₄×D₄×C₆₁	—	2	1	no	—
73	C₄×D₄×C₆₁	—	2	1	no	—
74	C₄×D₄×C₆₁	—	2	1	no	—
75	#117×C₆₁	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
80	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
81	#108×C₆₁	—	4	2	no	—
82	#107×C₆₁	—	2	2	no	—
83	#106×C₆₁	—	2	2	no	—
84	C₄⋊C₈×C₆₁	—	2	2	no	—
85	C₄⋊C₈×C₆₁	—	2	2	no	—
86	C₄⋊C₈×C₆₁	—	2	1	no	—
87	C₄⋊C₈×C₆₁	—	2	1	no	—
88	C₄⋊C₈×C₆₁	D₄	1	1	yes	characteristic
89	C₄⋊C₈×C₆₁	D₄	1	1	yes	characteristic
90	C₄⋊C₈×C₆₁	D₄	1	2	yes	—
91	#103×C₆₁	—	2	2	no	—
92	#103×C₆₁	—	2	2	no	—
93	#103×C₆₁	—	2	2	no	—
94	#103×C₆₁	—	2	2	no	—
95	#103×C₆₁	—	2	2	no	—
96	#103×C₆₁	—	2	2	no	—
97	#102×C₆₁	—	2	2	no	—
98	#102×C₆₁	—	2	2	no	—
99	#101×C₆₁	—	2	4	no	—
100	#101×C₆₁	—	4	2	no	—
101	#100×C₆₁	—	2	2	no	—
102	#100×C₆₁	—	2	2	no	—
103	#97×C₆₁	—	2	2	no	—
104	#97×C₆₁	—	2	1	no	—
105	#97×C₆₁	—	2	1	no	—
106	C₄×C₈×C₆₁	—	2	2	no	—
107	C₄×C₈×C₆₁	—	2	1	no	—
108	C₄×C₈×C₆₁	—	2	1	no	—
109	C₂⁴×C₆₁	—	2	1	no	—
110	C₂×Q₈×C₆₁	—	2	1	no	—
111	C₂×Q₈×C₆₁	—	2	1	no	—
112	C₂×Q₈×C₆₁	—	2	2	no	—
113	C₂×Q₈×C₆₁	—	2	2	no	—
114	C₂×Q₈×C₆₁	—	2	2	no	—
115	C₂×Q₈×C₆₁	—	2	2	no	—
116	C₂×Q₈×C₆₁	—	2	2	no	—
117	C₂×Q₈×C₆₁	—	2	2	no	—
118	C₂×D₄×C₆₁	—	2	1	no	—
119	C₂×D₄×C₆₁	—	2	1	no	—
120	C₂×D₄×C₆₁	—	2	1	no	—
121	C₂×D₄×C₆₁	—	2	1	no	—
122	C₂×D₄×C₆₁	—	2	1	no	—
123	C₂×D₄×C₆₁	#41	1	2	yes	—
124	C₂²×C₄×C₆₁	—	2	2	no	—
125	C₂²×C₄×C₆₁	—	2	1	no	—
126	C₂²×C₄×C₆₁	—	4	1	no	—
127	C₂²×C₄×C₆₁	—	4	1	no	—
128	C₂²×C₄×C₆₁	—	8	2	no	—
129	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
130	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
131	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
132	SD₁₆×C₆₁	—	4	4	no	—
133	SD₁₆×C₆₁	—	4	4	no	—
134	M₁₆×C₆₁	—	2	1	no	—
135	M₁₆×C₆₁	—	2	1	no	—
136	M₁₆×C₆₁	—	2	1	no	—
137	M₁₆×C₆₁	—	2	1	no	—
138	M₁₆×C₆₁	—	2	2	no	—
139	M₁₆×C₆₁	—	2	1	no	—
140	M₁₆×C₆₁	—	2	2	no	—
141	M₁₆×C₆₁	—	2	1	no	—
142	M₁₆×C₆₁	—	2	1	no	—
143	M₁₆×C₆₁	#41	1	2	yes	—
144	C₂×C₈×C₆₁	—	2	1	no	—
145	C₂×C₈×C₆₁	—	2	2	no	—
146	C₂×C₈×C₆₁	—	2	2	no	—
147	C₂×C₈×C₆₁	—	2	1	no	—
148	C₂×C₈×C₆₁	—	2	1	no	—
149	C₂×C₈×C₆₁	—	2	1	no	—
150	C₂×C₈×C₆₁	—	2	2	no	—
151	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
153	C₄⋊C₄×C₆₁	—	2	2	no	—
154	C₄⋊C₄×C₆₁	—	2	2	no	—
155	C₄⋊C₄×C₆₁	—	2	1	no	—
156	C₄⋊C₄×C₆₁	—	2	1	no	—
157	C₄⋊C₄×C₆₁	—	2	1	no	—
158	C₄⋊C₄×C₆₁	—	2	1	no	—
159	C₄⋊C₄×C₆₁	—	4	1	no	—
160	C₄⋊C₄×C₆₁	—	4	1	no	—
161	C₄⋊C₄×C₆₁	—	4	1	no	—
162	C₄⋊C₄×C₆₁	—	4	1	no	—
163	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
165	C₂²⋊C₄×C₆₁	—	2	2	no	—
166	C₂²⋊C₄×C₆₁	—	4	1	no	—
167	C₂²⋊C₄×C₆₁	—	4	1	no	—
168	C₄²×C₆₁	—	2	2	no	—
169	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
173	C₂³×C₆₁	—	2	2	no	—
174	C₂³×C₆₁	—	4	1	no	—
175	C₂³×C₆₁	—	4	1	no	—
176	C₂³×C₆₁	—	8	1	no	—
177	C₂³×C₆₁	—	8	1	no	—
178	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
179	Q₈×C₆₁	—	4	2	no	—
180	Q₈×C₆₁	—	4	2	no	—
181	Q₈×C₆₁	—	4	2	no	—
182	Q₈×C₆₁	—	4	2	no	—
183	Q₈×C₆₁	—	4	2	no	—
184	Q₈×C₆₁	—	8	1	no	—
185	D₄×C₆₁	—	2	2	no	—
186	D₄×C₆₁	—	2	2	no	—
187	D₄×C₆₁	—	4	1	no	—
188	D₄×C₆₁	—	4	1	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	1	no	—
193	C₂×C₄×C₆₁	—	4	1	no	—
194	C₂×C₄×C₆₁	—	4	2	no	—
195	C₂×C₄×C₆₁	—	4	2	no	—
196	C₂×C₄×C₆₁	—	4	2	no	—
197	C₂×C₄×C₆₁	—	8	2	no	—
198	C₂×C₄×C₆₁	—	8	2	no	—
199	C₂×C₄×C₆₁	—	8	1	no	—
200	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
201	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
202	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
203	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
204	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
210	C₈×C₆₁	—	2	2	no	—
211	C₈×C₆₁	—	2	2	no	—
212	C₈×C₆₁	—	2	2	no	—
213	C₈×C₆₁	—	4	1	no	—
214	C₈×C₆₁	—	4	1	no	—
215	C₈×C₆₁	—	4	1	no	—
216	C₈×C₆₁	—	4	2	no	—
217	#25313	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂²×C₆₁	—	2	1	no	—
219	C₂²×C₆₁	—	2	1	no	—
220	C₂²×C₆₁	—	4	2	no	—
221	C₂²×C₆₁	—	8	2	no	—
222	C₂²×C₆₁	—	8	2	no	—
223	C₂²×C₆₁	—	8	1	no	—
224	C₂²×C₆₁	—	8	1	no	—
225	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
226	C₂²×C₆₁	#529	1	1	yes	characteristic
227	C₂²×C₆₁	#542	1	1	yes	characteristic
228	C₄×C₆₁	—	2	1	no	—
229	C₄×C₆₁	—	2	1	no	—
230	C₄×C₆₁	—	2	1	no	—
231	C₄×C₆₁	—	4	2	no	—
232	C₄×C₆₁	—	4	2	no	—
233	C₄×C₆₁	—	8	2	no	—
234	C₄×C₆₁	—	8	1	no	—
235	C₄×C₆₁	#471	1	2	yes	—
236	C₄×C₆₁	#546	1	1	yes	characteristic
237	C₄×C₆₁	#548	1	1	yes	characteristic
238	C₄×C₆₁	#548	1	1	yes	characteristic
239	C₄×C₆₁	#550	1	1	yes	characteristic
240	#3139	C₂×C₆₁	1	1	yes	characteristic, complemented
241	#3077	C₂×C₆₁	1	1	yes	characteristic
242	C₂×#461	C₂×C₆₁	1	1	yes	characteristic
243	#2962	C₂×C₆₁	1	1	yes	characteristic, complemented
244	#2064	C₂×C₆₁	1	2	yes	complemented
245	#2046	C₂×C₆₁	1	2	yes	—
246	#1977	C₂×C₆₁	1	2	yes	—
247	#1966	C₂×C₆₁	1	1	yes	characteristic, complemented
248	#1950	C₂×C₆₁	1	1	yes	characteristic, complemented
249	#1930	C₂×C₆₁	1	2	yes	complemented
250	C₄×#100	C₂×C₆₁	1	1	yes	characteristic
251	C₂×C₆₁	—	2	1	no	—
252	C₂×C₆₁	—	2	1	no	—
253	C₂×C₆₁	—	8	2	no	—
254	C₂×C₆₁	#2426	1	1	yes	characteristic
255	C₂×C₆₁	C₂×#471	1	1	yes	characteristic
256	C₂×C₆₁	#3069	1	1	yes	characteristic
257	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
258	#533	C₂²×C₆₁	1	1	yes	characteristic
259	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
260	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
261	#491	—	2	2	no	—
262	#487	—	2	1	no	—
263	#487	—	2	1	no	—
264	#478	—	2	2	no	—
265	#476	—	2	1	no	—
266	#474	—	2	1	no	—
267	#461	—	2	1	no	—
268	#461	—	2	2	no	—
269	#461	—	2	1	no	—
270	#446	—	2	2	no	—
271	#446	—	2	1	no	—
272	C₈×Q₈	—	2	1	no	—
273	C₂×#108	C₂²×C₆₁	1	2	yes	—
274	#428	C₂²×C₆₁	1	2	yes	—
275	#424	C₂²×C₆₁	1	2	yes	—
276	#423	C₂²×C₆₁	1	1	yes	characteristic
277	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
278	#419	C₂²×C₆₁	1	2	yes	—
279	#419	C₂²×C₆₁	1	2	yes	—
280	#418	C₂²×C₆₁	1	2	yes	—
281	C₂×#103	C₂²×C₆₁	1	2	yes	—
282	C₂×#101	C₂²×C₆₁	1	2	yes	—
283	C₂×#101	C₂²×C₆₁	1	2	yes	—
284	C₂×#100	C₂²×C₆₁	1	1	yes	characteristic
285	C₂×#100	C₂²×C₆₁	1	1	yes	characteristic
286	#405	C₂²×C₆₁	1	2	yes	—
287	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
288	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
289	#343	C₂²×C₆₁	1	1	yes	characteristic
290	#343	C₂²×C₆₁	1	1	yes	characteristic
291	#341	C₂²×C₆₁	1	2	yes	—
292	C₆₁	#25313	1	1	yes	characteristic, direct product factor, Sylow
293	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
294	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
295	C₂³×C₄	—	2	1	no	—
296	C₂×SD₁₆	—	2	4	no	—
297	C₂×SD₁₆	—	2	2	no	—
298	C₂×SD₁₆	—	2	2	no	—
299	C₂×SD₁₆	—	4	2	no	—
300	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
301	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
302	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
303	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
304	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
306	C₄⋊Q₈	—	2	1	no	—
307	C₄⋊Q₈	—	2	1	no	—
308	C₄⋊Q₈	—	2	1	no	—
309	C₄⋊Q₈	—	2	1	no	—
310	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
311	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
312	#125	D₄×C₆₁	1	2	yes	—
313	C₂²⋊Q₈	—	2	1	no	—
314	C₂²⋊Q₈	—	2	1	no	—
315	C₄×Q₈	—	2	1	no	—
316	C₄×Q₈	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	—	2	1	no	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	#117	C₂³×C₆₁	1	2	yes	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
327	#108	—	4	2	no	—
328	#107	—	2	2	no	—
329	#106	—	2	2	no	—
330	C₄⋊C₈	—	2	2	no	—
331	C₄⋊C₈	—	2	2	no	—
332	C₄⋊C₈	—	2	1	no	—
333	C₄⋊C₈	—	2	1	no	—
334	C₄⋊C₈	D₄×C₆₁	1	1	yes	characteristic
335	C₄⋊C₈	D₄×C₆₁	1	1	yes	characteristic
336	C₄⋊C₈	D₄×C₆₁	1	2	yes	—
337	#103	—	2	2	no	—
338	#103	—	2	2	no	—
339	#103	—	2	2	no	—
340	#103	—	2	2	no	—
341	#103	—	2	2	no	—
342	#103	—	2	2	no	—
343	#102	—	2	2	no	—
344	#102	—	2	2	no	—
345	#101	—	2	4	no	—
346	#101	—	4	2	no	—
347	#100	—	2	2	no	—
348	#100	—	2	2	no	—
349	#97	—	2	2	no	—
350	#97	—	2	1	no	—
351	#97	—	2	1	no	—
352	C₄×C₈	—	2	2	no	—
353	C₄×C₈	—	2	1	no	—
354	C₄×C₈	—	2	1	no	—
355	C₂⁴	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	#41×C₆₁	1	2	yes	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	4	1	no	—
373	C₂²×C₄	—	4	1	no	—
374	C₂²×C₄	—	8	2	no	—
375	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
376	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
378	SD₁₆	—	4	4	no	—
379	SD₁₆	—	4	4	no	—
380	M₁₆	—	2	1	no	—
381	M₁₆	—	2	1	no	—
382	M₁₆	—	2	1	no	—
383	M₁₆	—	2	1	no	—
384	M₁₆	—	2	2	no	—
385	M₁₆	—	2	1	no	—
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	1	no	—
388	M₁₆	—	2	1	no	—
389	M₁₆	#41×C₆₁	1	2	yes	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
398	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	4	1	no	—
406	C₄⋊C₄	—	4	1	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
410	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	4	1	no	—
413	C₂²⋊C₄	—	4	1	no	—
414	C₄²	—	2	2	no	—
415	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
416	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
417	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
418	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
419	C₂³	—	2	2	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	8	1	no	—
423	C₂³	—	8	1	no	—
424	C₂³	C₂×#41×C₆₁	1	1	yes	characteristic
425	Q₈	—	4	2	no	—
426	Q₈	—	4	2	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	4	2	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	8	1	no	—
431	D₄	—	2	2	no	—
432	D₄	—	2	2	no	—
433	D₄	—	4	1	no	—
434	D₄	—	4	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	8	2	no	—
444	C₂×C₄	—	8	2	no	—
445	C₂×C₄	—	8	1	no	—
446	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
447	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
448	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
449	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
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	1	yes	characteristic
454	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
455	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
456	C₈	—	2	2	no	—
457	C₈	—	2	2	no	—
458	C₈	—	2	2	no	—
459	C₈	—	4	1	no	—
460	C₈	—	4	1	no	—
461	C₈	—	4	1	no	—
462	C₈	—	4	2	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	8	2	no	—
468	C₂²	—	8	1	no	—
469	C₂²	—	8	1	no	—
470	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
471	C₂²	C₆₁×#529	1	1	yes	characteristic
472	C₂²	C₆₁×#542	1	1	yes	characteristic
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	8	1	no	—
479	C₄	—	8	2	no	—
480	C₄	C₆₁×#471	1	2	yes	—
481	C₄	C₆₁×#546	1	1	yes	characteristic
482	C₄	C₆₁×#548	1	1	yes	characteristic
483	C₄	C₆₁×#548	1	1	yes	characteristic
484	C₄	C₆₁×#550	1	1	yes	characteristic
485	C₂	—	2	1	no	—
486	C₂	—	2	1	no	—
487	C₂	—	8	2	no	—
488	C₂	C₆₁×#2426	1	1	yes	characteristic
489	C₂	C₂×C₆₁×#471	1	1	yes	characteristic
490	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×D₄×C₆₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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. C₆₁×#3139	C₂	semidirect
4. C₆₁×#2962	C₂	semidirect
5. C₆₁×#2064	C₂	semidirect
8. C₆₁×#1966	C₂	semidirect
9. C₆₁×#1950	C₂	semidirect
10. C₆₁×#1930	C₂	semidirect
217. #25313	C₆₁	direct (N × H)
240. #3139	C₂×C₆₁	semidirect
243. #2962	C₂×C₆₁	semidirect
244. #2064	C₂×C₆₁	semidirect
247. #1966	C₂×C₆₁	semidirect
248. #1950	C₂×C₆₁	semidirect
249. #1930	C₂×C₆₁	semidirect
292. C₆₁	#25313	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₁×#3139	2
C₆₁×#3077	2
C₂×C₆₁×#461	2
C₆₁×#2962	2
C₆₁×#2064	2
C₆₁×#2046	2
C₆₁×#1977	2
C₆₁×#1966	2
C₆₁×#1950	2
C₆₁×#1930	2
C₄×#100×C₆₁	2
#25313	61

Subgroups — C61×#25313 #29528746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25313 #29528746