Subgroups — C₆₁×#19962 #29523395

Order 15616.

692 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3399	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3287	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1712	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1688	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1668	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1667	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1621	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1620	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1591	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₆₁	—	2	1	no	—
13	C₆₁×#559	C₂²	1	2	yes	—
14	C₆₁×#550	C₂²	1	2	yes	—
15	C₆₁×#496	—	2	2	no	—
16	C₆₁×#495	—	2	1	no	—
17	C₆₁×#493	C₂²	1	1	yes	characteristic
18	C₆₁×#493	C₂²	1	1	yes	characteristic
19	C₆₁×#493	C₂²	1	2	yes	—
20	C₆₁×#493	C₂²	1	2	yes	—
21	C₆₁×#466	—	2	1	no	—
22	C₆₁×#463	—	2	2	no	—
23	C₆₁×#463	—	2	2	no	—
24	C₆₁×#460	C₂²	1	2	yes	—
25	C₆₁×#460	C₂²	1	2	yes	—
26	C₆₁×#460	C₂²	1	2	yes	—
27	C₆₁×#459	—	2	2	no	—
28	C₆₁×#459	C₂²	1	2	yes	—
29	C₆₁×#449	—	2	2	no	—
30	C₆₁×#446	C₂²	1	2	yes	—
31	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₆₁×#442	—	2	2	no	—
33	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
34	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
35	C₄×D₈×C₆₁	—	2	1	no	—
36	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×#335	C₂²	1	1	yes	characteristic
38	C₆₁×#334	C₂²	1	1	yes	characteristic
39	C₆₁×#331	C₂²	1	2	yes	—
40	C₆₁×#331	C₂²	1	2	yes	—
41	C₆₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₆₁×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₆₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₈²×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×#41×C₆₁	—	2	2	no	—
46	#135×C₆₁	—	4	4	no	—
47	C₂×Q₁₆×C₆₁	D₄	1	1	yes	characteristic
48	C₂×SD₁₆×C₆₁	—	2	2	no	—
49	C₂×SD₁₆×C₆₁	—	2	2	no	—
50	C₂×SD₁₆×C₆₁	—	2	2	no	—
51	C₂×SD₁₆×C₆₁	D₄	1	1	yes	characteristic
52	C₂×D₈×C₆₁	—	2	2	no	—
53	C₂×D₈×C₆₁	—	2	1	no	—
54	C₂×D₈×C₆₁	—	2	1	no	—
55	C₂×D₈×C₆₁	—	2	2	no	—
56	C₂×D₈×C₆₁	—	2	1	no	—
57	C₂×D₈×C₆₁	—	2	2	no	—
58	C₂×D₈×C₆₁	—	2	1	no	—
59	C₂×D₈×C₆₁	—	4	2	no	—
60	C₂²×C₈×C₆₁	—	2	1	no	—
61	#127×C₆₁	—	2	2	no	—
62	#127×C₆₁	C₂³	1	2	yes	—
63	#127×C₆₁	C₂³	1	2	yes	—
64	#124×C₆₁	—	2	2	no	—
65	#124×C₆₁	—	2	2	no	—
66	#123×C₆₁	—	4	2	no	—
67	#121×C₆₁	—	2	2	no	—
68	#121×C₆₁	—	4	2	no	—
69	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
70	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
71	C₄×D₄×C₆₁	—	2	2	no	—
72	C₄×D₄×C₆₁	—	2	2	no	—
73	C₄×D₄×C₆₁	—	2	2	no	—
74	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
75	#107×C₆₁	D₄	1	1	yes	characteristic
76	#106×C₆₁	D₄	1	1	yes	characteristic
77	C₄⋊C₈×C₆₁	—	2	1	no	—
78	C₄⋊C₈×C₆₁	—	2	2	no	—
79	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
82	#103×C₆₁	D₄	1	1	yes	characteristic
83	#103×C₆₁	D₄	1	2	yes	—
84	#102×C₆₁	—	2	2	no	—
85	#102×C₆₁	—	2	2	no	—
86	#102×C₆₁	—	2	2	no	—
87	#102×C₆₁	—	2	2	no	—
88	#102×C₆₁	D₄	1	1	yes	characteristic
89	C₂²⋊C₈×C₆₁	—	2	1	no	—
90	#97×C₆₁	—	2	2	no	—
91	C₄×C₈×C₆₁	—	2	1	no	—
92	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
95	#41×C₆₁	—	4	4	no	—
96	#41×C₆₁	—	8	2	no	—
97	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
98	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
99	C₂×D₄×C₆₁	—	2	2	no	—
100	C₂×D₄×C₆₁	—	2	2	no	—
101	C₂×D₄×C₆₁	—	2	2	no	—
102	C₂×D₄×C₆₁	—	2	2	no	—
103	C₂×D₄×C₆₁	—	2	2	no	—
104	C₂×D₄×C₆₁	—	2	2	no	—
105	C₂×D₄×C₆₁	—	4	2	no	—
106	C₂×D₄×C₆₁	—	4	2	no	—
107	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₁	—	2	1	no	—
109	C₂²×C₄×C₆₁	—	4	2	no	—
110	C₂²×C₄×C₆₁	—	4	2	no	—
111	Q₁₆×C₆₁	—	2	2	no	—
112	SD₁₆×C₆₁	—	2	2	no	—
113	SD₁₆×C₆₁	—	4	4	no	—
114	SD₁₆×C₆₁	—	8	2	no	—
115	SD₁₆×C₆₁	—	8	2	no	—
116	D₈×C₆₁	—	4	4	no	—
117	D₈×C₆₁	—	4	2	no	—
118	D₈×C₆₁	—	4	2	no	—
119	D₈×C₆₁	—	8	2	no	—
120	D₈×C₆₁	—	8	1	no	—
121	D₈×C₆₁	—	8	1	no	—
122	D₈×C₆₁	—	8	4	no	—
123	D₈×C₆₁	—	8	2	no	—
124	C₂×C₈×C₆₁	—	2	1	no	—
125	C₂×C₈×C₆₁	—	2	1	no	—
126	C₂×C₈×C₆₁	—	2	2	no	—
127	C₂×C₈×C₆₁	—	2	1	no	—
128	C₂×C₈×C₆₁	—	4	2	no	—
129	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₄⋊C₄×C₆₁	—	2	2	no	—
134	C₄⋊C₄×C₆₁	—	2	1	no	—
135	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
136	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
137	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
138	C₂²⋊C₄×C₆₁	—	2	1	no	—
139	C₂²⋊C₄×C₆₁	—	4	2	no	—
140	C₂²⋊C₄×C₆₁	—	4	2	no	—
141	C₂²⋊C₄×C₆₁	—	4	2	no	—
142	C₂²⋊C₄×C₆₁	—	4	2	no	—
143	C₄²×C₆₁	—	2	1	no	—
144	C₄²×C₆₁	—	2	2	no	—
145	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
146	C₂³×C₆₁	—	2	1	no	—
147	C₂³×C₆₁	—	4	2	no	—
148	C₂³×C₆₁	—	4	2	no	—
149	Q₈×C₆₁	—	2	1	no	—
150	Q₈×C₆₁	—	2	2	no	—
151	Q₈×C₆₁	—	2	1	no	—
152	Q₈×C₆₁	—	2	2	no	—
153	D₄×C₆₁	—	2	1	no	—
154	D₄×C₆₁	—	2	1	no	—
155	D₄×C₆₁	—	4	2	no	—
156	D₄×C₆₁	—	4	2	no	—
157	D₄×C₆₁	—	4	2	no	—
158	D₄×C₆₁	—	4	2	no	—
159	D₄×C₆₁	—	4	2	no	—
160	D₄×C₆₁	—	4	2	no	—
161	D₄×C₆₁	—	4	2	no	—
162	D₄×C₆₁	—	4	2	no	—
163	D₄×C₆₁	—	8	2	no	—
164	D₄×C₆₁	—	8	2	no	—
165	D₄×C₆₁	—	8	4	no	—
166	D₄×C₆₁	—	16	2	no	—
167	C₂×C₄×C₆₁	—	2	1	no	—
168	C₂×C₄×C₆₁	—	2	1	no	—
169	C₂×C₄×C₆₁	—	2	2	no	—
170	C₂×C₄×C₆₁	—	2	2	no	—
171	C₂×C₄×C₆₁	—	2	1	no	—
172	C₂×C₄×C₆₁	—	4	1	no	—
173	C₂×C₄×C₆₁	—	4	1	no	—
174	C₂×C₄×C₆₁	—	8	4	no	—
175	C₂×C₄×C₆₁	—	16	2	no	—
176	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
179	C₈×C₆₁	—	2	2	no	—
180	C₈×C₆₁	—	2	1	no	—
181	C₈×C₆₁	—	2	1	no	—
182	C₈×C₆₁	—	4	1	no	—
183	C₈×C₆₁	—	4	2	no	—
184	C₈×C₆₁	—	4	1	no	—
185	C₈×C₆₁	#135	1	2	yes	complemented
186	C₈×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
187	#19962	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂²×C₆₁	—	4	1	no	—
189	C₂²×C₆₁	—	4	1	no	—
190	C₂²×C₆₁	—	4	1	no	—
191	C₂²×C₆₁	—	8	2	no	—
192	C₂²×C₆₁	—	8	2	no	—
193	C₂²×C₆₁	—	8	2	no	—
194	C₂²×C₆₁	—	8	2	no	—
195	C₂²×C₆₁	—	8	2	no	—
196	C₂²×C₆₁	—	8	2	no	—
197	C₂²×C₆₁	D₄²	1	1	yes	characteristic
198	C₄×C₆₁	—	2	1	no	—
199	C₄×C₆₁	—	4	1	no	—
200	C₄×C₆₁	—	4	2	no	—
201	C₄×C₆₁	—	4	1	no	—
202	C₄×C₆₁	—	4	1	no	—
203	C₄×C₆₁	—	4	2	no	—
204	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
205	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
206	C₄×C₆₁	#576	1	1	yes	characteristic
207	C₄×C₆₁	#576	1	1	yes	characteristic
208	#3399	C₂×C₆₁	1	2	yes	complemented
209	#3396	C₂×C₆₁	1	1	yes	characteristic, complemented
210	#3287	C₂×C₆₁	1	1	yes	characteristic, complemented
211	#1712	C₂×C₆₁	1	1	yes	characteristic, complemented
212	#1688	C₂×C₆₁	1	2	yes	complemented
213	#1668	C₂×C₆₁	1	1	yes	characteristic, complemented
214	#1667	C₂×C₆₁	1	1	yes	characteristic, complemented
215	#1621	C₂×C₆₁	1	2	yes	complemented
216	#1620	C₂×C₆₁	1	2	yes	complemented
217	#1591	C₂×C₆₁	1	1	yes	characteristic, complemented
218	C₈×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
219	C₂×C₆₁	—	8	1	no	—
220	C₂×C₆₁	—	16	2	no	—
221	C₂×C₆₁	—	16	2	no	—
222	C₂×C₆₁	#3274	1	1	yes	characteristic
223	C₂×C₆₁	#3287	1	1	yes	characteristic
224	C₂×C₆₁	#3292	1	1	yes	characteristic
225	C₂×#135	—	2	1	no	—
226	#559	C₂²×C₆₁	1	2	yes	—
227	#550	C₂²×C₆₁	1	2	yes	—
228	#496	—	2	2	no	—
229	#495	—	2	1	no	—
230	#493	C₂²×C₆₁	1	1	yes	characteristic
231	#493	C₂²×C₆₁	1	2	yes	—
232	#493	C₂²×C₆₁	1	1	yes	characteristic
233	#493	C₂²×C₆₁	1	2	yes	—
234	#466	—	2	1	no	—
235	#463	—	2	2	no	—
236	#463	—	2	2	no	—
237	#460	C₂²×C₆₁	1	2	yes	—
238	#460	C₂²×C₆₁	1	2	yes	—
239	#460	C₂²×C₆₁	1	2	yes	—
240	#459	—	2	2	no	—
241	#459	C₂²×C₆₁	1	2	yes	—
242	#449	—	2	2	no	—
243	#446	C₂²×C₆₁	1	2	yes	—
244	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
245	#442	—	2	2	no	—
246	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
247	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
248	C₄×D₈	—	2	1	no	—
249	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
250	#335	C₂²×C₆₁	1	1	yes	characteristic
251	#334	C₂²×C₆₁	1	1	yes	characteristic
252	#331	C₂²×C₆₁	1	2	yes	—
253	#331	C₂²×C₆₁	1	2	yes	—
254	Q₈⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
255	Q₈⋊C₈	C₂²×C₆₁	1	2	yes	—
256	D₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
257	C₈²	C₂²×C₆₁	1	1	yes	characteristic
258	C₆₁	#19962	1	1	yes	characteristic, direct product factor, Sylow
259	C₂×#41	—	2	2	no	—
260	#135	—	4	4	no	—
261	C₂×Q₁₆	D₄×C₆₁	1	1	yes	characteristic
262	C₂×SD₁₆	—	2	2	no	—
263	C₂×SD₁₆	—	2	2	no	—
264	C₂×SD₁₆	—	2	2	no	—
265	C₂×SD₁₆	D₄×C₆₁	1	1	yes	characteristic
266	C₂×D₈	—	2	2	no	—
267	C₂×D₈	—	2	1	no	—
268	C₂×D₈	—	2	1	no	—
269	C₂×D₈	—	2	2	no	—
270	C₂×D₈	—	2	1	no	—
271	C₂×D₈	—	2	2	no	—
272	C₂×D₈	—	2	1	no	—
273	C₂×D₈	—	4	2	no	—
274	C₂²×C₈	—	2	1	no	—
275	#127	—	2	2	no	—
276	#127	C₂³×C₆₁	1	2	yes	—
277	#127	C₂³×C₆₁	1	2	yes	—
278	#124	—	2	2	no	—
279	#124	—	2	2	no	—
280	#123	—	4	2	no	—
281	#121	—	2	2	no	—
282	#121	—	4	2	no	—
283	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
284	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
285	C₄×D₄	—	2	2	no	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
289	#107	D₄×C₆₁	1	1	yes	characteristic
290	#106	D₄×C₆₁	1	1	yes	characteristic
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
294	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
295	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
296	#103	D₄×C₆₁	1	1	yes	characteristic
297	#103	D₄×C₆₁	1	2	yes	—
298	#102	—	2	2	no	—
299	#102	—	2	2	no	—
300	#102	—	2	2	no	—
301	#102	—	2	2	no	—
302	#102	D₄×C₆₁	1	1	yes	characteristic
303	C₂²⋊C₈	—	2	1	no	—
304	#97	—	2	2	no	—
305	C₄×C₈	—	2	1	no	—
306	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
307	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
308	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
309	#41	—	4	4	no	—
310	#41	—	8	2	no	—
311	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
312	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	4	2	no	—
325	Q₁₆	—	2	2	no	—
326	SD₁₆	—	2	2	no	—
327	SD₁₆	—	4	4	no	—
328	SD₁₆	—	8	2	no	—
329	SD₁₆	—	8	2	no	—
330	D₈	—	4	4	no	—
331	D₈	—	4	2	no	—
332	D₈	—	4	2	no	—
333	D₈	—	8	2	no	—
334	D₈	—	8	1	no	—
335	D₈	—	8	1	no	—
336	D₈	—	8	4	no	—
337	D₈	—	8	2	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
344	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
345	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
346	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
350	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
351	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	2	no	—
359	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
360	C₂³	—	2	1	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	Q₈	—	2	1	no	—
364	Q₈	—	2	2	no	—
365	Q₈	—	2	1	no	—
366	Q₈	—	2	2	no	—
367	D₄	—	2	1	no	—
368	D₄	—	2	1	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	8	2	no	—
378	D₄	—	8	2	no	—
379	D₄	—	8	4	no	—
380	D₄	—	16	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	8	4	no	—
389	C₂×C₄	—	16	2	no	—
390	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
392	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	2	no	—
398	C₈	—	4	1	no	—
399	C₈	#135×C₆₁	1	2	yes	complemented
400	C₈	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	2	no	—
409	C₂²	—	8	2	no	—
410	C₂²	D₄²×C₆₁	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	2	no	—
417	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
418	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
419	C₄	C₆₁×#576	1	1	yes	characteristic
420	C₄	C₆₁×#576	1	1	yes	characteristic
421	C₂	—	8	1	no	—
422	C₂	—	16	2	no	—
423	C₂	—	16	2	no	—
424	C₂	C₆₁×#3274	1	1	yes	characteristic
425	C₂	C₆₁×#3287	1	1	yes	characteristic
426	C₂	C₆₁×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3399	C₂	semidirect
2. C₆₁×#3396	C₂	semidirect
3. C₆₁×#3287	C₂	semidirect
4. C₆₁×#1712	C₂	semidirect
5. C₆₁×#1688	C₂	semidirect
6. C₆₁×#1668	C₂	semidirect
7. C₆₁×#1667	C₂	semidirect
8. C₆₁×#1621	C₂	semidirect
9. C₆₁×#1620	C₂	semidirect
10. C₆₁×#1591	C₂	semidirect
11. C₈×SD₁₆×C₆₁	C₂	semidirect
185. C₈×C₆₁	#135	semidirect
187. #19962	C₆₁	direct (N × H)
208. #3399	C₂×C₆₁	semidirect
209. #3396	C₂×C₆₁	semidirect
210. #3287	C₂×C₆₁	semidirect
211. #1712	C₂×C₆₁	semidirect
212. #1688	C₂×C₆₁	semidirect
213. #1668	C₂×C₆₁	semidirect
214. #1667	C₂×C₆₁	semidirect
215. #1621	C₂×C₆₁	semidirect
216. #1620	C₂×C₆₁	semidirect
217. #1591	C₂×C₆₁	semidirect
218. C₈×SD₁₆	C₂×C₆₁	semidirect
258. C₆₁	#19962	direct (N × H)
399. C₈	#135×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3399	2
C₆₁×#3396	2
C₆₁×#3287	2
C₆₁×#1712	2
C₆₁×#1688	2
C₆₁×#1668	2
C₆₁×#1667	2
C₆₁×#1621	2
C₆₁×#1620	2
C₆₁×#1591	2
C₈×SD₁₆×C₆₁	2
#19962	61

Subgroups — C61×#19962 #29523395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19962 #29523395