Subgroups — C₆₁×#25594 #29529027

Order 15616.

1050 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3140	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3040	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2658	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2005	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2003	C₂	1	2	yes	maximal
7	C₆₁×#1995	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1966	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1888	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1886	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1759	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#557	—	2	2	no	—
15	C₆₁×#556	—	2	2	no	—
16	C₆₁×#552	—	2	4	no	—
17	C₆₁×#541	—	2	2	no	—
18	C₆₁×#536	C₂²	1	2	yes	—
19	C₆₁×#533	—	2	2	no	—
20	C₆₁×#533	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
22	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#124×C₆₁	C₂²	1	2	yes	—
24	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
25	C₆₁×#519	C₂²	1	2	yes	—
26	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
27	C₆₁×#489	—	2	2	no	—
28	C₆₁×#488	—	2	2	no	—
29	C₆₁×#464	—	2	2	no	—
30	C₆₁×#463	—	2	2	no	—
31	C₆₁×#423	C₂²	1	1	yes	characteristic
32	C₂×#104×C₆₁	C₂²	1	2	yes	—
33	C₆₁×#419	C₂²	1	1	yes	characteristic
34	C₆₁×#419	C₂²	1	2	yes	—
35	C₆₁×#418	C₂²	1	1	yes	characteristic
36	C₆₁×#418	C₂²	1	2	yes	—
37	C₂×#101×C₆₁	C₂²	1	2	yes	—
38	C₂×#101×C₆₁	C₂²	1	2	yes	—
39	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#399	—	2	4	no	—
41	C₆₁×#376	C₂²	1	1	yes	characteristic
42	C₆₁×#339	C₂²	1	2	yes	—
43	C₆₁×#339	C₂²	1	2	yes	—
44	C₆₁×#339	C₂²	1	2	yes	—
45	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
48	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
49	#137×C₆₁	—	4	2	no	—
50	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
51	C₂×Q₁₆×C₆₁	—	2	1	no	—
52	C₂×SD₁₆×C₆₁	—	2	1	no	—
53	C₂×SD₁₆×C₆₁	—	2	1	no	—
54	C₂×D₈×C₆₁	—	2	1	no	—
55	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₆₁	—	2	2	no	—
59	C₄⋊Q₈×C₆₁	—	2	1	no	—
60	C₄⋊Q₈×C₆₁	—	2	1	no	—
61	C₄⋊Q₈×C₆₁	—	2	2	no	—
62	C₄⋊Q₈×C₆₁	—	2	4	no	—
63	C₄⋊Q₈×C₆₁	—	4	2	no	—
64	C₄⋊Q₈×C₆₁	D₄	1	2	yes	—
65	#126×C₆₁	—	2	8	no	—
66	#125×C₆₁	—	2	4	no	—
67	#125×C₆₁	—	2	8	no	—
68	#125×C₆₁	D₄	1	2	yes	—
69	#124×C₆₁	—	2	2	no	—
70	#124×C₆₁	—	2	2	no	—
71	#124×C₆₁	—	2	1	no	—
72	#124×C₆₁	—	2	1	no	—
73	#124×C₆₁	—	2	4	no	—
74	#124×C₆₁	—	4	2	no	—
75	#123×C₆₁	—	2	4	no	—
76	C₂²⋊Q₈×C₆₁	—	2	4	no	—
77	C₂²⋊Q₈×C₆₁	—	2	2	no	—
78	C₂²⋊Q₈×C₆₁	—	2	4	no	—
79	C₄×Q₈×C₆₁	—	2	4	no	—
80	C₄×Q₈×C₆₁	—	2	4	no	—
81	C₄×Q₈×C₆₁	—	2	4	no	—
82	C₄×Q₈×C₆₁	—	2	2	no	—
83	C₄×Q₈×C₆₁	D₄	1	2	yes	—
84	C₄×D₄×C₆₁	—	2	2	no	—
85	C₄×D₄×C₆₁	D₄	1	2	yes	—
86	#117×C₆₁	—	2	4	no	—
87	#117×C₆₁	—	2	4	no	—
88	#117×C₆₁	—	2	1	no	—
89	#117×C₆₁	C₂³	1	2	yes	—
90	#117×C₆₁	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
92	C₂×C₄⋊C₄×C₆₁	D₄	1	4	yes	—
93	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
94	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
95	C₂×C₄²×C₆₁	—	2	1	no	—
96	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
97	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₆₁	—	2	2	no	—
99	#104×C₆₁	—	2	4	no	—
100	#103×C₆₁	—	2	2	no	—
101	#103×C₆₁	—	2	4	no	—
102	#102×C₆₁	—	2	2	no	—
103	#102×C₆₁	—	2	4	no	—
104	#101×C₆₁	—	4	2	no	—
105	#101×C₆₁	—	4	2	no	—
106	#97×C₆₁	—	2	1	no	—
107	C₄×C₈×C₆₁	—	2	1	no	—
108	#95×C₆₁	—	2	2	no	—
109	C₂⁴×C₆₁	—	2	1	no	—
110	#41×C₆₁	—	2	2	no	—
111	#41×C₆₁	—	2	2	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×Q₈×C₆₁	—	2	2	no	—
119	C₂×Q₈×C₆₁	—	2	1	no	—
120	C₂×Q₈×C₆₁	—	2	1	no	—
121	C₂×Q₈×C₆₁	—	2	2	no	—
122	C₂×Q₈×C₆₁	—	2	2	no	—
123	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
124	C₂×D₄×C₆₁	—	2	1	no	—
125	C₂×D₄×C₆₁	—	2	1	no	—
126	C₂×D₄×C₆₁	—	2	1	no	—
127	C₂×D₄×C₆₁	—	2	2	no	—
128	C₂×D₄×C₆₁	—	2	2	no	—
129	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₆₁	—	2	2	no	—
131	C₂²×C₄×C₆₁	—	2	2	no	—
132	C₂²×C₄×C₆₁	—	2	1	no	—
133	C₂²×C₄×C₆₁	—	2	1	no	—
134	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
137	Q₁₆×C₆₁	—	4	2	no	—
138	SD₁₆×C₆₁	—	4	2	no	—
139	SD₁₆×C₆₁	—	4	2	no	—
140	D₈×C₆₁	—	4	2	no	—
141	M₁₆×C₆₁	—	2	2	no	—
142	M₁₆×C₆₁	—	2	2	no	—
143	M₁₆×C₆₁	—	2	2	no	—
144	M₁₆×C₆₁	—	2	2	no	—
145	C₂×C₈×C₆₁	—	2	2	no	—
146	C₂×C₈×C₆₁	—	2	1	no	—
147	C₂×C₈×C₆₁	—	2	1	no	—
148	C₄⋊C₄×C₆₁	—	2	8	no	—
149	C₄⋊C₄×C₆₁	—	2	8	no	—
150	C₄⋊C₄×C₆₁	—	2	4	no	—
151	C₄⋊C₄×C₆₁	—	2	4	no	—
152	C₄⋊C₄×C₆₁	—	2	2	no	—
153	C₄⋊C₄×C₆₁	—	2	2	no	—
154	C₄⋊C₄×C₆₁	—	2	4	no	—
155	C₄⋊C₄×C₆₁	—	4	8	no	—
156	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
158	C₂²⋊C₄×C₆₁	—	2	8	no	—
159	C₂²⋊C₄×C₆₁	—	2	1	no	—
160	C₂²⋊C₄×C₆₁	—	2	2	no	—
161	C₂²⋊C₄×C₆₁	—	2	2	no	—
162	C₂²⋊C₄×C₆₁	—	4	8	no	—
163	C₂²⋊C₄×C₆₁	—	4	2	no	—
164	C₂²⋊C₄×C₆₁	—	4	2	no	—
165	C₄²×C₆₁	—	2	8	no	—
166	C₄²×C₆₁	—	2	2	no	—
167	C₄²×C₆₁	—	2	1	no	—
168	C₄²×C₆₁	—	2	2	no	—
169	C₄²×C₆₁	—	2	2	no	—
170	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₆₁	C₂×D₄	1	2	yes	—
173	C₄²×C₆₁	#41	1	4	yes	—
174	C₂³×C₆₁	—	2	1	no	—
175	C₂³×C₆₁	—	4	4	no	—
176	C₂³×C₆₁	—	4	1	no	—
177	C₂³×C₆₁	—	4	2	no	—
178	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₆₁	—	2	1	no	—
180	Q₈×C₆₁	—	2	1	no	—
181	Q₈×C₆₁	—	4	4	no	—
182	Q₈×C₆₁	—	4	2	no	—
183	Q₈×C₆₁	—	4	2	no	—
184	Q₈×C₆₁	—	4	2	no	—
185	Q₈×C₆₁	—	4	2	no	—
186	Q₈×C₆₁	—	4	1	no	—
187	Q₈×C₆₁	—	4	1	no	—
188	Q₈×C₆₁	—	4	2	no	—
189	D₄×C₆₁	—	2	1	no	—
190	D₄×C₆₁	—	2	1	no	—
191	D₄×C₆₁	—	4	2	no	—
192	D₄×C₆₁	—	4	1	no	—
193	D₄×C₆₁	—	4	1	no	—
194	D₄×C₆₁	—	4	2	no	—
195	C₂×C₄×C₆₁	—	2	2	no	—
196	C₂×C₄×C₆₁	—	2	4	no	—
197	C₂×C₄×C₆₁	—	2	4	no	—
198	C₂×C₄×C₆₁	—	2	1	no	—
199	C₂×C₄×C₆₁	—	2	4	no	—
200	C₂×C₄×C₆₁	—	2	4	no	—
201	C₂×C₄×C₆₁	—	2	4	no	—
202	C₂×C₄×C₆₁	—	4	2	no	—
203	C₂×C₄×C₆₁	—	4	4	no	—
204	C₂×C₄×C₆₁	—	4	4	no	—
205	C₂×C₄×C₆₁	—	4	2	no	—
206	C₂×C₄×C₆₁	—	4	1	no	—
207	C₂×C₄×C₆₁	—	4	2	no	—
208	C₂×C₄×C₆₁	#120	1	2	yes	—
209	C₂×C₄×C₆₁	#120	1	2	yes	—
210	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
213	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
214	C₈×C₆₁	—	4	1	no	—
215	C₈×C₆₁	—	4	1	no	—
216	C₈×C₆₁	—	4	2	no	—
217	#25594	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂²×C₆₁	—	2	2	no	—
219	C₂²×C₆₁	—	4	1	no	—
220	C₂²×C₆₁	—	4	2	no	—
221	C₂²×C₆₁	—	8	4	no	—
222	C₂²×C₆₁	—	8	1	no	—
223	C₂²×C₆₁	—	8	2	no	—
224	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
225	C₂²×C₆₁	#546	1	2	yes	—
226	C₄×C₆₁	—	2	2	no	—
227	C₄×C₆₁	—	2	2	no	—
228	C₄×C₆₁	—	4	4	no	—
229	C₄×C₆₁	—	4	4	no	—
230	C₄×C₆₁	—	4	1	no	—
231	C₄×C₆₁	—	4	2	no	—
232	C₄×C₆₁	—	4	4	no	—
233	C₄×C₆₁	—	8	1	no	—
234	C₄×C₆₁	#532	1	1	yes	characteristic
235	C₄×C₆₁	#535	1	1	yes	characteristic
236	C₄×C₆₁	#550	1	2	yes	—
237	#3509	C₂×C₆₁	1	1	yes	characteristic, complemented
238	#3140	C₂×C₆₁	1	1	yes	characteristic, complemented
239	#3040	C₂×C₆₁	1	1	yes	characteristic
240	#2658	C₂×C₆₁	1	1	yes	characteristic, complemented
241	#2005	C₂×C₆₁	1	2	yes	complemented
242	#2003	C₂×C₆₁	1	2	yes	—
243	#1995	C₂×C₆₁	1	1	yes	characteristic, complemented
244	#1966	C₂×C₆₁	1	1	yes	characteristic, complemented
245	#1888	C₂×C₆₁	1	2	yes	complemented
246	#1886	C₂×C₆₁	1	2	yes	complemented
247	#1759	C₂×C₆₁	1	1	yes	characteristic, complemented
248	C₂×C₆₁	—	2	2	no	—
249	C₂×C₆₁	—	8	1	no	—
250	C₂×C₆₁	—	16	1	no	—
251	C₂×C₆₁	#2431	1	1	yes	characteristic
252	C₂×C₆₁	#3020	1	2	yes	—
253	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic
254	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
255	#557	—	2	2	no	—
256	#556	—	2	2	no	—
257	#552	—	2	4	no	—
258	#541	—	2	2	no	—
259	#536	C₂²×C₆₁	1	2	yes	—
260	#533	—	2	2	no	—
261	#533	C₂²×C₆₁	1	1	yes	characteristic
262	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
263	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
264	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
265	C₂×#124	C₂²×C₆₁	1	2	yes	—
266	#519	C₂²×C₆₁	1	2	yes	—
267	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
268	#489	—	2	2	no	—
269	#488	—	2	2	no	—
270	#464	—	2	2	no	—
271	#463	—	2	2	no	—
272	#423	C₂²×C₆₁	1	1	yes	characteristic
273	C₂×#104	C₂²×C₆₁	1	2	yes	—
274	#419	C₂²×C₆₁	1	2	yes	—
275	#419	C₂²×C₆₁	1	1	yes	characteristic
276	#418	C₂²×C₆₁	1	2	yes	—
277	#418	C₂²×C₆₁	1	1	yes	characteristic
278	C₂×#101	C₂²×C₆₁	1	2	yes	—
279	C₂×#101	C₂²×C₆₁	1	2	yes	—
280	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
281	#399	—	2	4	no	—
282	#376	C₂²×C₆₁	1	1	yes	characteristic
283	#339	C₂²×C₆₁	1	2	yes	—
284	#339	C₂²×C₆₁	1	2	yes	—
285	#339	C₂²×C₆₁	1	2	yes	—
286	C₆₁	#25594	1	1	yes	characteristic, direct product factor, Sylow
287	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
288	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
289	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
290	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
291	#137	—	4	2	no	—
292	AGL(1,ℤ/8)	—	4	2	no	—
293	C₂×Q₁₆	—	2	1	no	—
294	C₂×SD₁₆	—	2	1	no	—
295	C₂×SD₁₆	—	2	1	no	—
296	C₂×D₈	—	2	1	no	—
297	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
298	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
299	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
300	C₄⋊Q₈	—	2	2	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	2	no	—
304	C₄⋊Q₈	—	2	4	no	—
305	C₄⋊Q₈	—	4	2	no	—
306	C₄⋊Q₈	D₄×C₆₁	1	2	yes	—
307	#126	—	2	8	no	—
308	#125	—	2	4	no	—
309	#125	—	2	8	no	—
310	#125	D₄×C₆₁	1	2	yes	—
311	#124	—	2	2	no	—
312	#124	—	2	2	no	—
313	#124	—	2	1	no	—
314	#124	—	2	1	no	—
315	#124	—	2	4	no	—
316	#124	—	4	2	no	—
317	#123	—	2	4	no	—
318	C₂²⋊Q₈	—	2	4	no	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	—	2	4	no	—
321	C₄×Q₈	—	2	4	no	—
322	C₄×Q₈	—	2	4	no	—
323	C₄×Q₈	—	2	4	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	D₄×C₆₁	1	2	yes	—
326	C₄×D₄	—	2	2	no	—
327	C₄×D₄	D₄×C₆₁	1	2	yes	—
328	#117	—	2	4	no	—
329	#117	—	2	4	no	—
330	#117	—	2	1	no	—
331	#117	C₂³×C₆₁	1	1	yes	characteristic
332	#117	C₂³×C₆₁	1	2	yes	—
333	C₂×C₄⋊C₄	—	2	4	no	—
334	C₂×C₄⋊C₄	D₄×C₆₁	1	4	yes	—
335	C₂×C₂²⋊C₄	—	2	4	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
339	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
340	C₄⋊C₈	—	2	2	no	—
341	#104	—	2	4	no	—
342	#103	—	2	2	no	—
343	#103	—	2	4	no	—
344	#102	—	2	2	no	—
345	#102	—	2	4	no	—
346	#101	—	4	2	no	—
347	#101	—	4	2	no	—
348	#97	—	2	1	no	—
349	C₄×C₈	—	2	1	no	—
350	#95	—	2	2	no	—
351	C₂⁴	—	2	1	no	—
352	#41	—	2	2	no	—
353	#41	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
377	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
379	Q₁₆	—	4	2	no	—
380	SD₁₆	—	4	2	no	—
381	SD₁₆	—	4	2	no	—
382	D₈	—	4	2	no	—
383	M₁₆	—	2	2	no	—
384	M₁₆	—	2	2	no	—
385	M₁₆	—	2	2	no	—
386	M₁₆	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₄⋊C₄	—	2	8	no	—
391	C₄⋊C₄	—	2	8	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	4	8	no	—
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	1	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	4	8	no	—
405	C₂²⋊C₄	—	4	2	no	—
406	C₂²⋊C₄	—	4	2	no	—
407	C₄²	—	2	8	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
413	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
414	C₄²	C₂×D₄×C₆₁	1	2	yes	—
415	C₄²	#41×C₆₁	1	4	yes	—
416	C₂³	—	2	1	no	—
417	C₂³	—	4	4	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	1	no	—
420	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
421	Q₈	—	2	1	no	—
422	Q₈	—	2	1	no	—
423	Q₈	—	4	4	no	—
424	Q₈	—	4	2	no	—
425	Q₈	—	4	2	no	—
426	Q₈	—	4	2	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	4	1	no	—
430	Q₈	—	4	2	no	—
431	D₄	—	2	1	no	—
432	D₄	—	2	1	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	1	no	—
435	D₄	—	4	1	no	—
436	D₄	—	4	2	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	#120×C₆₁	1	2	yes	—
451	C₂×C₄	#120×C₆₁	1	2	yes	—
452	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
455	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
456	C₈	—	4	1	no	—
457	C₈	—	4	1	no	—
458	C₈	—	4	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	8	4	no	—
463	C₂²	—	8	1	no	—
464	C₂²	—	8	2	no	—
465	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
466	C₂²	C₆₁×#546	1	2	yes	—
467	C₄	—	2	2	no	—
468	C₄	—	2	2	no	—
469	C₄	—	4	4	no	—
470	C₄	—	4	4	no	—
471	C₄	—	4	1	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	4	no	—
474	C₄	—	8	1	no	—
475	C₄	C₆₁×#532	1	1	yes	characteristic
476	C₄	C₆₁×#535	1	1	yes	characteristic
477	C₄	C₆₁×#550	1	2	yes	—
478	C₂	—	2	2	no	—
479	C₂	—	8	1	no	—
480	C₂	—	16	1	no	—
481	C₂	C₆₁×#2431	1	1	yes	characteristic
482	C₂	C₆₁×#3020	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×AGL(1,ℤ/8)×C₆₁	C₂²
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×#3509	C₂	semidirect
2. C₆₁×#3140	C₂	semidirect
4. C₆₁×#2658	C₂	semidirect
5. C₆₁×#2005	C₂	semidirect
7. C₆₁×#1995	C₂	semidirect
8. C₆₁×#1966	C₂	semidirect
9. C₆₁×#1888	C₂	semidirect
10. C₆₁×#1886	C₂	semidirect
11. C₆₁×#1759	C₂	semidirect
217. #25594	C₆₁	direct (N × H)
237. #3509	C₂×C₆₁	semidirect
238. #3140	C₂×C₆₁	semidirect
240. #2658	C₂×C₆₁	semidirect
241. #2005	C₂×C₆₁	semidirect
243. #1995	C₂×C₆₁	semidirect
244. #1966	C₂×C₆₁	semidirect
245. #1888	C₂×C₆₁	semidirect
246. #1886	C₂×C₆₁	semidirect
247. #1759	C₂×C₆₁	semidirect
286. C₆₁	#25594	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×#3509	2
C₆₁×#3140	2
C₆₁×#3040	2
C₆₁×#2658	2
C₆₁×#2005	2
C₆₁×#2003	2
C₆₁×#1995	2
C₆₁×#1966	2
C₆₁×#1888	2
C₆₁×#1886	2
C₆₁×#1759	2
#25594	61

Subgroups — C61×#25594 #29529027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25594 #29529027