Subgroups — C₆₁×#33777 #29537210

Order 15616.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#495	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2249	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2242	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2211	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2210	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2188	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2187	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2185	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2184	C₂	1	1	yes	maximal, characteristic
11	C₆₁×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₆₁	—	2	1	no	—
14	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₆₁×#529	—	2	1	no	—
16	C₂×#124×C₆₁	—	2	1	no	—
17	C₂×Q₃₂×C₆₁	C₂²	1	2	yes	complemented
18	C₂×SD₃₂×C₆₁	C₂²	1	2	yes	—
19	C₂×SD₃₂×C₆₁	C₂²	1	2	yes	complemented
20	C₂×D₁₆×C₆₁	C₂²	1	2	yes	—
21	C₆₁×#499	C₂²	1	1	yes	characteristic, complemented
22	C₆₁×#495	—	2	1	no	—
23	C₆₁×#495	—	2	1	no	—
24	C₆₁×#495	C₂²	1	2	yes	—
25	C₆₁×#495	C₂²	1	2	yes	—
26	C₆₁×#495	C₂²	1	1	yes	characteristic, complemented
27	C₆₁×#488	—	2	1	no	—
28	C₆₁×#467	C₂²	1	1	yes	characteristic
29	C₆₁×#466	C₂²	1	1	yes	characteristic
30	C₆₁×#465	—	2	1	no	—
31	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
32	C₄×SD₁₆×C₆₁	—	2	1	no	—
33	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
35	C₆₁×C₄⋊C₁₆	C₂²	1	2	yes	complemented
36	C₆₁×#358	C₂²	1	2	yes	complemented
37	C₆₁×#358	C₂²	1	2	yes	complemented
38	C₆₁×#357	C₂²	1	2	yes	—
39	C₆₁×#357	C₂²	1	2	yes	—
40	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
41	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₄×C₁₆×C₆₁	C₂²	1	2	yes	complemented
43	C₂²×Q₈×C₆₁	—	2	1	no	—
44	C₂²×D₄×C₆₁	—	2	1	no	—
45	C₂×Q₁₆×C₆₁	—	2	1	no	—
46	C₂×Q₁₆×C₆₁	—	4	2	no	—
47	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
48	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
49	C₂×SD₁₆×C₆₁	—	2	2	no	—
50	C₂×SD₁₆×C₆₁	—	2	2	no	—
51	C₂×SD₁₆×C₆₁	—	2	1	no	—
52	C₂×SD₁₆×C₆₁	—	4	4	no	—
53	C₂×D₈×C₆₁	—	2	1	no	—
54	C₂×D₈×C₆₁	—	4	2	no	—
55	C₂×D₈×C₆₁	C₂³	1	2	yes	—
56	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
59	#126×C₆₁	—	4	1	no	—
60	#125×C₆₁	—	2	1	no	—
61	#124×C₆₁	—	2	1	no	—
62	#124×C₆₁	—	2	2	no	—
63	#124×C₆₁	—	2	2	no	—
64	#124×C₆₁	—	4	1	no	—
65	#124×C₆₁	—	4	1	no	—
66	#123×C₆₁	—	4	1	no	—
67	C₂²⋊Q₈×C₆₁	—	2	1	no	—
68	#121×C₆₁	—	2	1	no	—
69	C₄×Q₈×C₆₁	—	2	1	no	—
70	C₄×D₄×C₆₁	—	2	1	no	—
71	C₄×D₄×C₆₁	—	4	1	no	—
72	#117×C₆₁	—	4	1	no	—
73	C₂×C₂²⋊C₄×C₆₁	—	4	1	no	—
74	C₂×C₂²⋊C₄×C₆₁	—	4	1	no	—
75	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
76	Q₃₂×C₆₁	—	4	2	no	—
77	SD₃₂×C₆₁	—	4	2	no	—
78	SD₃₂×C₆₁	—	4	2	no	—
79	D₁₆×C₆₁	—	4	2	no	—
80	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
81	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
82	#107×C₆₁	C₂³	1	1	yes	characteristic
83	#107×C₆₁	C₂³	1	1	yes	characteristic
84	#106×C₆₁	—	2	1	no	—
85	#103×C₆₁	—	2	1	no	—
86	#103×C₆₁	—	2	1	no	—
87	#102×C₆₁	—	2	1	no	—
88	#102×C₆₁	—	2	1	no	—
89	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
90	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
91	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
93	C₂⁴×C₆₁	—	4	1	no	—
94	C₂×Q₈×C₆₁	—	2	1	no	—
95	C₂×Q₈×C₆₁	—	2	2	no	—
96	C₂×Q₈×C₆₁	—	4	2	no	—
97	C₂×Q₈×C₆₁	—	4	2	no	—
98	C₂×Q₈×C₆₁	—	4	1	no	—
99	C₂×D₄×C₆₁	—	2	1	no	—
100	C₂×D₄×C₆₁	—	2	2	no	—
101	C₂×D₄×C₆₁	—	4	2	no	—
102	C₂×D₄×C₆₁	—	4	2	no	—
103	C₂×D₄×C₆₁	—	4	1	no	—
104	C₂×D₄×C₆₁	—	4	1	no	—
105	C₂²×C₄×C₆₁	—	4	1	no	—
106	C₂²×C₄×C₆₁	—	4	1	no	—
107	C₂²×C₄×C₆₁	D₈	1	1	yes	characteristic
108	C₂²×C₄×C₆₁	D₈	1	1	yes	characteristic
109	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
110	Q₁₆×C₆₁	—	2	2	no	—
111	Q₁₆×C₆₁	—	2	2	no	—
112	Q₁₆×C₆₁	—	2	2	no	—
113	Q₁₆×C₆₁	—	4	2	no	—
114	SD₁₆×C₆₁	—	4	4	no	—
115	SD₁₆×C₆₁	—	4	2	no	—
116	SD₁₆×C₆₁	—	4	4	no	—
117	D₈×C₆₁	—	2	2	no	—
118	D₈×C₆₁	—	2	2	no	—
119	D₈×C₆₁	—	2	2	no	—
120	D₈×C₆₁	—	4	2	no	—
121	C₂×C₈×C₆₁	—	2	2	no	—
122	C₂×C₈×C₆₁	—	2	2	no	—
123	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
127	C₄⋊C₄×C₆₁	—	2	1	no	—
128	C₄⋊C₄×C₆₁	—	2	1	no	—
129	C₄⋊C₄×C₆₁	—	4	1	no	—
130	C₄⋊C₄×C₆₁	—	4	1	no	—
131	C₄⋊C₄×C₆₁	—	4	1	no	—
132	C₄⋊C₄×C₆₁	—	4	1	no	—
133	C₂²⋊C₄×C₆₁	—	4	1	no	—
134	C₂²⋊C₄×C₆₁	—	4	2	no	—
135	C₂²⋊C₄×C₆₁	—	4	2	no	—
136	C₂²⋊C₄×C₆₁	—	4	2	no	—
137	C₂²⋊C₄×C₆₁	—	4	2	no	—
138	C₂²⋊C₄×C₆₁	—	4	1	no	—
139	C₂²⋊C₄×C₆₁	—	4	1	no	—
140	C₂²⋊C₄×C₆₁	—	4	1	no	—
141	C₂²⋊C₄×C₆₁	—	4	1	no	—
142	C₄²×C₆₁	—	4	1	no	—
143	C₄²×C₆₁	D₈	1	1	yes	characteristic
144	C₄²×C₆₁	D₈	1	1	yes	characteristic
145	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
147	C₁₆×C₆₁	—	2	2	no	—
148	C₁₆×C₆₁	—	2	2	no	—
149	C₂³×C₆₁	—	4	1	no	—
150	C₂³×C₆₁	—	4	2	no	—
151	C₂³×C₆₁	—	8	2	no	—
152	C₂³×C₆₁	—	8	2	no	—
153	C₂³×C₆₁	—	8	2	no	—
154	C₂³×C₆₁	C₂×D₈	1	1	yes	characteristic
155	Q₈×C₆₁	—	4	2	no	—
156	Q₈×C₆₁	—	4	1	no	—
157	Q₈×C₆₁	—	4	2	no	—
158	Q₈×C₆₁	—	4	1	no	—
159	Q₈×C₆₁	—	8	2	no	—
160	D₄×C₆₁	—	4	2	no	—
161	D₄×C₆₁	—	4	1	no	—
162	D₄×C₆₁	—	4	2	no	—
163	D₄×C₆₁	—	4	1	no	—
164	D₄×C₆₁	—	8	2	no	—
165	D₄×C₆₁	—	8	2	no	—
166	C₂×C₄×C₆₁	—	2	2	no	—
167	C₂×C₄×C₆₁	—	2	1	no	—
168	C₂×C₄×C₆₁	—	2	1	no	—
169	C₂×C₄×C₆₁	—	4	1	no	—
170	C₂×C₄×C₆₁	—	4	1	no	—
171	C₂×C₄×C₆₁	—	4	1	no	—
172	C₂×C₄×C₆₁	—	4	2	no	—
173	C₂×C₄×C₆₁	—	4	1	no	—
174	C₂×C₄×C₆₁	—	8	2	no	—
175	C₂×C₄×C₆₁	—	8	2	no	—
176	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
177	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
178	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
182	C₈×C₆₁	—	2	1	no	—
183	C₈×C₆₁	—	2	1	no	—
184	C₈×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
185	C₈×C₆₁	H(5,𝔽₂)	1	2	yes	—
186	#33777	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂²×C₆₁	—	2	1	no	—
188	C₂²×C₆₁	—	2	1	no	—
189	C₂²×C₆₁	—	8	1	no	—
190	C₂²×C₆₁	—	8	2	no	—
191	C₂²×C₆₁	—	8	1	no	—
192	C₂²×C₆₁	—	8	2	no	—
193	C₂²×C₆₁	—	8	2	no	—
194	C₂²×C₆₁	—	8	1	no	—
195	C₂²×C₆₁	—	16	4	no	—
196	C₂²×C₆₁	#508	1	2	yes	—
197	C₂²×C₆₁	C₂²×D₈	1	1	yes	characteristic
198	C₄×C₆₁	—	2	1	no	—
199	C₄×C₆₁	—	2	1	no	—
200	C₄×C₆₁	—	2	1	no	—
201	C₄×C₆₁	—	2	1	no	—
202	C₄×C₆₁	—	2	1	no	—
203	C₄×C₆₁	—	8	1	no	—
204	C₄×C₆₁	—	8	1	no	—
205	C₄×C₆₁	—	8	2	no	—
206	C₄×C₆₁	—	8	1	no	—
207	C₄×C₆₁	#535	1	1	yes	characteristic
208	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
209	#3168	C₂×C₆₁	1	1	yes	characteristic, complemented
210	C₂×#495	C₂×C₆₁	1	1	yes	characteristic, complemented
211	#2249	C₂×C₆₁	1	2	yes	complemented
212	#2242	C₂×C₆₁	1	2	yes	complemented
213	#2211	C₂×C₆₁	1	2	yes	complemented
214	#2210	C₂×C₆₁	1	2	yes	complemented
215	#2188	C₂×C₆₁	1	1	yes	characteristic, complemented
216	#2187	C₂×C₆₁	1	1	yes	characteristic, complemented
217	#2185	C₂×C₆₁	1	1	yes	characteristic, complemented
218	#2184	C₂×C₆₁	1	1	yes	characteristic
219	#2162	C₂×C₆₁	1	1	yes	characteristic, complemented
220	C₂×C₆₁	—	2	2	no	—
221	C₂×C₆₁	—	16	1	no	—
222	C₂×C₆₁	—	16	2	no	—
223	C₂×C₆₁	#3205	1	1	yes	characteristic
224	C₂×C₆₁	C₂×#508	1	1	yes	characteristic
225	C₂×C₆₁	#3414	1	1	yes	characteristic
226	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
227	C₂²×SD₁₆	—	2	1	no	—
228	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
229	#529	—	2	1	no	—
230	C₂×#124	—	2	1	no	—
231	C₂×Q₃₂	C₂²×C₆₁	1	2	yes	complemented
232	C₂×SD₃₂	C₂²×C₆₁	1	2	yes	—
233	C₂×SD₃₂	C₂²×C₆₁	1	2	yes	complemented
234	C₂×D₁₆	C₂²×C₆₁	1	2	yes	—
235	#499	C₂²×C₆₁	1	1	yes	characteristic, complemented
236	#495	—	2	1	no	—
237	#495	—	2	1	no	—
238	#495	C₂²×C₆₁	1	2	yes	—
239	#495	C₂²×C₆₁	1	2	yes	—
240	#495	C₂²×C₆₁	1	1	yes	characteristic, complemented
241	#488	—	2	1	no	—
242	#467	C₂²×C₆₁	1	1	yes	characteristic
243	#466	C₂²×C₆₁	1	1	yes	characteristic
244	#465	—	2	1	no	—
245	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
246	C₄×SD₁₆	—	2	1	no	—
247	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
248	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
249	C₄⋊C₁₆	C₂²×C₆₁	1	2	yes	complemented
250	#358	C₂²×C₆₁	1	2	yes	complemented
251	#358	C₂²×C₆₁	1	2	yes	complemented
252	#357	C₂²×C₆₁	1	2	yes	—
253	#357	C₂²×C₆₁	1	2	yes	—
254	C₂²⋊C₁₆	C₂²×C₆₁	1	1	yes	characteristic
255	C₂²⋊C₁₆	C₂²×C₆₁	1	1	yes	characteristic
256	C₄×C₁₆	C₂²×C₆₁	1	2	yes	complemented
257	C₆₁	#33777	1	1	yes	characteristic, direct product factor, Sylow
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×D₄	—	2	1	no	—
260	C₂×Q₁₆	—	2	1	no	—
261	C₂×Q₁₆	—	4	2	no	—
262	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
263	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
264	C₂×SD₁₆	—	2	2	no	—
265	C₂×SD₁₆	—	2	2	no	—
266	C₂×SD₁₆	—	2	1	no	—
267	C₂×SD₁₆	—	4	4	no	—
268	C₂×D₈	—	2	1	no	—
269	C₂×D₈	—	4	2	no	—
270	C₂×D₈	C₂³×C₆₁	1	2	yes	—
271	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
272	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
274	#126	—	4	1	no	—
275	#125	—	2	1	no	—
276	#124	—	2	2	no	—
277	#124	—	2	2	no	—
278	#124	—	2	1	no	—
279	#124	—	4	1	no	—
280	#124	—	4	1	no	—
281	#123	—	4	1	no	—
282	C₂²⋊Q₈	—	2	1	no	—
283	#121	—	2	1	no	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	4	1	no	—
287	#117	—	4	1	no	—
288	C₂×C₂²⋊C₄	—	4	1	no	—
289	C₂×C₂²⋊C₄	—	4	1	no	—
290	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
291	Q₃₂	—	4	2	no	—
292	SD₃₂	—	4	2	no	—
293	SD₃₂	—	4	2	no	—
294	D₁₆	—	4	2	no	—
295	C₂×C₁₆	C₂³×C₆₁	1	2	yes	—
296	C₂×C₁₆	C₂³×C₆₁	1	2	yes	—
297	#107	C₂³×C₆₁	1	1	yes	characteristic
298	#107	C₂³×C₆₁	1	1	yes	characteristic
299	#106	—	2	1	no	—
300	#103	—	2	1	no	—
301	#103	—	2	1	no	—
302	#102	—	2	1	no	—
303	#102	—	2	1	no	—
304	C₄×C₈	D₄×C₆₁	1	1	yes	characteristic
305	C₄×C₈	D₄×C₆₁	1	1	yes	characteristic
306	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
307	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
308	C₂⁴	—	4	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	4	2	no	—
312	C₂×Q₈	—	4	2	no	—
313	C₂×Q₈	—	4	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	D₈×C₆₁	1	1	yes	characteristic
323	C₂²×C₄	D₈×C₆₁	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
325	Q₁₆	—	2	2	no	—
326	Q₁₆	—	2	2	no	—
327	Q₁₆	—	2	2	no	—
328	Q₁₆	—	4	2	no	—
329	SD₁₆	—	4	4	no	—
330	SD₁₆	—	4	2	no	—
331	SD₁₆	—	4	4	no	—
332	D₈	—	2	2	no	—
333	D₈	—	2	2	no	—
334	D₈	—	2	2	no	—
335	D₈	—	4	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
339	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
340	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
341	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	—	4	1	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₂²⋊C₄	—	4	2	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	4	1	no	—
356	C₂²⋊C₄	—	4	1	no	—
357	C₄²	—	4	1	no	—
358	C₄²	D₈×C₆₁	1	1	yes	characteristic
359	C₄²	D₈×C₆₁	1	1	yes	characteristic
360	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
361	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
362	C₁₆	—	2	2	no	—
363	C₁₆	—	2	2	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	8	2	no	—
367	C₂³	—	8	2	no	—
368	C₂³	—	8	2	no	—
369	C₂³	C₂×D₈×C₆₁	1	1	yes	characteristic
370	Q₈	—	4	2	no	—
371	Q₈	—	4	1	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	4	1	no	—
374	Q₈	—	8	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	1	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	1	no	—
379	D₄	—	8	2	no	—
380	D₄	—	8	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	—	8	2	no	—
391	C₂×C₄	C₂×D₈×C₆₁	1	1	yes	characteristic
392	C₂×C₄	C₂×D₈×C₆₁	1	1	yes	characteristic
393	C₂×C₄	C₂×D₈×C₆₁	1	1	yes	characteristic
394	C₂×C₄	C₂×D₈×C₆₁	1	1	yes	characteristic
395	C₂×C₄	C₂×D₈×C₆₁	1	1	yes	characteristic
396	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
397	C₈	—	2	1	no	—
398	C₈	—	2	1	no	—
399	C₈	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
400	C₈	H(5,𝔽₂)×C₆₁	1	2	yes	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	16	4	no	—
410	C₂²	C₆₁×#508	1	2	yes	—
411	C₂²	C₂²×D₈×C₆₁	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	8	1	no	—
418	C₄	—	8	1	no	—
419	C₄	—	8	2	no	—
420	C₄	—	8	1	no	—
421	C₄	C₆₁×#535	1	1	yes	characteristic
422	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
423	C₂	—	2	2	no	—
424	C₂	—	16	2	no	—
425	C₂	—	16	1	no	—
426	C₂	C₆₁×#3205	1	1	yes	characteristic
427	C₂	C₂×C₆₁×#508	1	1	yes	characteristic
428	C₂	C₆₁×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₆₁
prime radical	C₆₁×#2184	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ C₂×C₄×C₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3168	C₂	semidirect
2. C₂×C₆₁×#495	C₂	semidirect
3. C₆₁×#2249	C₂	semidirect
4. C₆₁×#2242	C₂	semidirect
5. C₆₁×#2211	C₂	semidirect
6. C₆₁×#2210	C₂	semidirect
7. C₆₁×#2188	C₂	semidirect
8. C₆₁×#2187	C₂	semidirect
9. C₆₁×#2185	C₂	semidirect
11. C₆₁×#2162	C₂	semidirect
17. C₂×Q₃₂×C₆₁	C₂²	semidirect
19. C₂×SD₃₂×C₆₁	C₂²	semidirect
21. C₆₁×#499	C₂²	semidirect
26. C₆₁×#495	C₂²	semidirect
31. C₄×Q₁₆×C₆₁	C₂²	semidirect
33. C₄×D₈×C₆₁	C₂²	semidirect
35. C₆₁×C₄⋊C₁₆	C₂²	semidirect
36. C₆₁×#358	C₂²	semidirect
37. C₆₁×#358	C₂²	semidirect
42. C₄×C₁₆×C₆₁	C₂²	semidirect
186. #33777	C₆₁	direct (N × H)
209. #3168	C₂×C₆₁	semidirect
210. C₂×#495	C₂×C₆₁	semidirect
211. #2249	C₂×C₆₁	semidirect
212. #2242	C₂×C₆₁	semidirect
213. #2211	C₂×C₆₁	semidirect
214. #2210	C₂×C₆₁	semidirect
215. #2188	C₂×C₆₁	semidirect
216. #2187	C₂×C₆₁	semidirect
217. #2185	C₂×C₆₁	semidirect
219. #2162	C₂×C₆₁	semidirect
231. C₂×Q₃₂	C₂²×C₆₁	semidirect
233. C₂×SD₃₂	C₂²×C₆₁	semidirect
235. #499	C₂²×C₆₁	semidirect
240. #495	C₂²×C₆₁	semidirect
245. C₄×Q₁₆	C₂²×C₆₁	semidirect
247. C₄×D₈	C₂²×C₆₁	semidirect
249. C₄⋊C₁₆	C₂²×C₆₁	semidirect
250. #358	C₂²×C₆₁	semidirect
251. #358	C₂²×C₆₁	semidirect
256. C₄×C₁₆	C₂²×C₆₁	semidirect
257. C₆₁	#33777	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×#3168	2
C₂×C₆₁×#495	2
C₆₁×#2249	2
C₆₁×#2242	2
C₆₁×#2211	2
C₆₁×#2210	2
C₆₁×#2188	2
C₆₁×#2187	2
C₆₁×#2185	2
C₆₁×#2184	2
C₆₁×#2162	2
#33777	61

Subgroups — C61×#33777 #29537210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#33777 #29537210