Subgroups — C₆₁×#60423 #29563856

Order 15616.

2890 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₆₁	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#518	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3042	C₂	1	8	yes	maximal, complemented
5	C₆₁×#3041	C₂	1	8	yes	maximal, complemented
6	C₆₁×#3036	C₂	1	8	yes	maximal, complemented
7	C₆₁×#2905	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2896	C₂	1	2	yes	maximal, complemented
9	C₂²×#41×C₆₁	C₂²	1	2	yes	—
10	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×AGL(1,ℤ/8)×C₆₁	—	2	16	no	—
12	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	8	yes	—
13	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	8	yes	complemented
14	C₂²×SD₁₆×C₆₁	C₂²	1	4	yes	complemented
15	C₂²×D₈×C₆₁	C₂²	1	4	yes	complemented
16	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
17	C₆₁×#537	—	2	2	no	—
18	C₆₁×#536	C₂²	1	4	yes	complemented
19	C₆₁×#535	C₂²	1	4	yes	complemented
20	C₆₁×#534	—	2	2	no	—
21	C₆₁×#532	C₂²	1	4	yes	complemented
22	C₆₁×#525	—	2	4	no	—
23	C₆₁×#518	—	2	4	no	—
24	C₆₁×#518	C₂²	1	8	yes	complemented
25	C₂×C₄×D₄×C₆₁	—	2	2	no	—
26	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	complemented
27	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₆₁	—	2	2	no	—
30	C₆₁×#463	C₂²	1	32	yes	complemented
31	C₆₁×#461	C₂²	1	16	yes	complemented
32	C₆₁×#459	C₂²	1	16	yes	complemented
33	C₆₁×#424	C₂²	1	8	yes	complemented
34	C₆₁×#423	C₂²	1	4	yes	complemented
35	C₆₁×#419	C₂²	1	4	yes	complemented
36	C₆₁×#418	C₂²	1	4	yes	complemented
37	C₆₁×#417	C₂²	1	8	yes	complemented
38	C₆₁×#416	C₂²	1	8	yes	complemented
39	C₂⁵×C₆₁	—	2	1	no	—
40	C₂×#41×C₆₁	—	2	2	no	—
41	C₂×#41×C₆₁	—	2	2	no	—
42	C₂×#41×C₆₁	—	2	8	no	—
43	C₂×#41×C₆₁	—	2	8	no	—
44	C₂×#41×C₆₁	C₂³	1	4	yes	—
45	C₂×#41×C₆₁	C₂³	1	4	yes	—
46	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
47	C₂²×D₄×C₆₁	—	2	2	no	—
48	C₂²×D₄×C₆₁	—	2	1	no	—
49	C₂²×D₄×C₆₁	—	2	2	no	—
50	C₂²×D₄×C₆₁	—	2	4	no	—
51	C₂²×D₄×C₆₁	D₄	1	8	yes	complemented
52	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
53	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
54	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
55	C₂³×C₄×C₆₁	—	2	2	no	—
56	C₂³×C₄×C₆₁	—	2	4	no	—
57	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
58	AGL(1,ℤ/8)×C₆₁	—	2	32	no	—
59	AGL(1,ℤ/8)×C₆₁	—	2	32	no	—
60	C₂×SD₁₆×C₆₁	—	2	16	no	—
61	C₂×SD₁₆×C₆₁	C₂³	1	16	yes	—
62	C₂×D₈×C₆₁	—	2	16	no	—
63	C₂×D₈×C₆₁	C₂³	1	16	yes	—
64	C₂×M₁₆×C₆₁	—	2	8	no	—
65	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
66	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
67	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
68	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	complemented
69	#127×C₆₁	C₂³	1	4	yes	complemented
70	#124×C₆₁	C₂³	1	8	yes	complemented
71	#123×C₆₁	—	2	8	no	—
72	C₂²⋊Q₈×C₆₁	—	2	8	no	—
73	#121×C₆₁	—	2	8	no	—
74	#121×C₆₁	—	2	8	no	—
75	#120×C₆₁	—	2	8	no	—
76	C₄×D₄×C₆₁	—	2	16	no	—
77	C₄×D₄×C₆₁	—	2	8	no	—
78	C₄×D₄×C₆₁	—	2	8	no	—
79	C₄×D₄×C₆₁	C₂³	1	16	yes	—
80	#117×C₆₁	—	2	2	no	—
81	#117×C₆₁	D₄	1	4	yes	—
82	#117×C₆₁	C₂³	1	4	yes	—
83	#117×C₆₁	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
85	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
86	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₆₁	—	2	16	no	—
89	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
90	C₂×C₄²×C₆₁	—	2	1	no	—
91	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
92	C₄⋊C₈×C₆₁	C₂³	1	16	yes	complemented
93	#103×C₆₁	C₂³	1	16	yes	complemented
94	#102×C₆₁	C₂³	1	16	yes	complemented
95	C₂⁴×C₆₁	—	2	2	no	—
96	C₂⁴×C₆₁	—	2	8	no	—
97	C₂⁴×C₆₁	—	2	4	no	—
98	C₂⁴×C₆₁	—	2	2	no	—
99	C₂⁴×C₆₁	—	8	4	no	—
100	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
101	#41×C₆₁	—	2	8	no	—
102	#41×C₆₁	—	2	8	no	—
103	#41×C₆₁	—	2	8	no	—
104	#41×C₆₁	—	2	8	no	—
105	#41×C₆₁	—	4	8	no	—
106	#41×C₆₁	—	4	8	no	—
107	C₂×Q₈×C₆₁	—	2	2	no	—
108	C₂×Q₈×C₆₁	—	2	4	no	—
109	C₂×Q₈×C₆₁	—	2	4	no	—
110	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
111	C₂×D₄×C₆₁	—	2	4	no	—
112	C₂×D₄×C₆₁	—	2	4	no	—
113	C₂×D₄×C₆₁	—	2	16	no	—
114	C₂×D₄×C₆₁	—	2	8	no	—
115	C₂×D₄×C₆₁	—	2	4	no	—
116	C₂×D₄×C₆₁	—	2	2	no	—
117	C₂×D₄×C₆₁	—	2	4	no	—
118	C₂×D₄×C₆₁	—	2	2	no	—
119	C₂×D₄×C₆₁	—	2	8	no	—
120	C₂×D₄×C₆₁	—	2	8	no	—
121	C₂×D₄×C₆₁	—	2	4	no	—
122	C₂×D₄×C₆₁	—	2	4	no	—
123	C₂×D₄×C₆₁	—	4	8	no	—
124	C₂×D₄×C₆₁	C₂×D₄	1	16	yes	—
125	C₂×D₄×C₆₁	C₂×D₄	1	8	yes	—
126	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
127	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₆₁	—	2	2	no	—
129	C₂²×C₄×C₆₁	—	2	2	no	—
130	C₂²×C₄×C₆₁	—	2	4	no	—
131	C₂²×C₄×C₆₁	—	2	4	no	—
132	C₂²×C₄×C₆₁	—	2	16	no	—
133	C₂²×C₄×C₆₁	—	4	8	no	—
134	C₂²×C₄×C₆₁	—	8	8	no	—
135	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₆₁	#41	1	4	yes	—
140	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
142	SD₁₆×C₆₁	—	2	32	no	—
143	D₈×C₆₁	—	2	32	no	—
144	M₁₆×C₆₁	—	2	8	no	—
145	M₁₆×C₆₁	—	2	8	no	—
146	C₂×C₈×C₆₁	—	2	8	no	—
147	C₂×C₈×C₆₁	C₂⁴	1	8	yes	—
148	C₄⋊C₄×C₆₁	—	2	2	no	—
149	C₄⋊C₄×C₆₁	—	2	8	no	—
150	C₄⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
151	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
152	C₂²⋊C₄×C₆₁	—	2	4	no	—
153	C₂²⋊C₄×C₆₁	—	2	16	no	—
154	C₂²⋊C₄×C₆₁	—	2	16	no	—
155	C₂²⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
156	C₄²×C₆₁	—	2	4	no	—
157	C₄²×C₆₁	C₂×D₄	1	4	yes	—
158	C₄²×C₆₁	C₂⁴	1	4	yes	—
159	C₂³×C₆₁	—	2	8	no	—
160	C₂³×C₆₁	—	2	4	no	—
161	C₂³×C₆₁	—	2	16	no	—
162	C₂³×C₆₁	—	2	4	no	—
163	C₂³×C₆₁	—	4	2	no	—
164	C₂³×C₆₁	—	4	8	no	—
165	C₂³×C₆₁	—	4	4	no	—
166	C₂³×C₆₁	—	8	4	no	—
167	C₂³×C₆₁	—	8	8	no	—
168	C₂³×C₆₁	—	8	16	no	—
169	C₂³×C₆₁	#121	1	4	yes	—
170	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
171	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₆₁	—	2	4	no	—
173	Q₈×C₆₁	—	2	4	no	—
174	Q₈×C₆₁	—	4	4	no	—
175	D₄×C₆₁	—	2	8	no	—
176	D₄×C₆₁	—	2	16	no	—
177	D₄×C₆₁	—	2	4	no	—
178	D₄×C₆₁	—	2	4	no	—
179	D₄×C₆₁	—	2	4	no	—
180	D₄×C₆₁	—	4	8	no	—
181	D₄×C₆₁	—	4	8	no	—
182	D₄×C₆₁	—	4	4	no	—
183	D₄×C₆₁	—	8	8	no	—
184	D₄×C₆₁	C₂²×D₄	1	8	yes	—
185	C₂×C₄×C₆₁	—	2	4	no	—
186	C₂×C₄×C₆₁	—	2	4	no	—
187	C₂×C₄×C₆₁	—	4	4	no	—
188	C₂×C₄×C₆₁	—	4	4	no	—
189	C₂×C₄×C₆₁	—	4	4	no	—
190	C₂×C₄×C₆₁	—	4	8	no	—
191	C₂×C₄×C₆₁	—	4	8	no	—
192	C₂×C₄×C₆₁	—	8	16	no	—
193	C₂×C₄×C₆₁	#121	1	8	yes	—
194	C₂×C₄×C₆₁	#121	1	4	yes	—
195	C₂×C₄×C₆₁	C₂²×D₄	1	8	yes	—
196	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
199	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
201	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
202	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
203	C₈×C₆₁	—	2	8	no	—
204	#60423	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂²×C₆₁	—	2	2	no	—
206	C₂²×C₆₁	—	2	4	no	—
207	C₂²×C₆₁	—	2	8	no	—
208	C₂²×C₆₁	—	4	4	no	—
209	C₂²×C₆₁	—	4	16	no	—
210	C₂²×C₆₁	—	4	8	no	—
211	C₂²×C₆₁	—	4	8	no	—
212	C₂²×C₆₁	—	4	4	no	—
213	C₂²×C₆₁	—	8	16	no	—
214	C₂²×C₆₁	—	8	8	no	—
215	C₂²×C₆₁	C₂×#121	1	4	yes	—
216	C₂²×C₆₁	C₂×#121	1	2	yes	—
217	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
218	C₄×C₆₁	—	2	8	no	—
219	C₄×C₆₁	—	4	4	no	—
220	C₄×C₆₁	—	4	4	no	—
221	C₄×C₆₁	C₂×#121	1	2	yes	—
222	C₄×C₆₁	C₂×#121	1	4	yes	—
223	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
224	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
225	C₂²×AGL(1,ℤ/8)	C₂×C₆₁	1	2	yes	complemented
226	#3449	C₂×C₆₁	1	1	yes	characteristic, complemented
227	C₂×#518	C₂×C₆₁	1	1	yes	characteristic, complemented
228	#3042	C₂×C₆₁	1	8	yes	complemented
229	#3041	C₂×C₆₁	1	8	yes	complemented
230	#3036	C₂×C₆₁	1	8	yes	complemented
231	#2905	C₂×C₆₁	1	1	yes	characteristic, complemented
232	#2896	C₂×C₆₁	1	2	yes	complemented
233	C₂×C₆₁	—	2	2	no	—
234	C₂×C₆₁	—	2	4	no	—
235	C₂×C₆₁	—	4	8	no	—
236	C₂×C₆₁	—	8	4	no	—
237	C₂×C₆₁	C₂²×#121	1	1	yes	characteristic
238	C₂×C₆₁	#3585	1	2	yes	—
239	C₂²×#41	C₂²×C₆₁	1	2	yes	—
240	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
241	C₂×AGL(1,ℤ/8)	—	2	16	no	—
242	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	8	yes	—
243	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	8	yes	complemented
244	C₂²×SD₁₆	C₂²×C₆₁	1	4	yes	complemented
245	C₂²×D₈	C₂²×C₆₁	1	4	yes	complemented
246	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
247	#537	—	2	2	no	—
248	#536	C₂²×C₆₁	1	4	yes	complemented
249	#535	C₂²×C₆₁	1	4	yes	complemented
250	#534	—	2	2	no	—
251	#532	C₂²×C₆₁	1	4	yes	complemented
252	#525	—	2	4	no	—
253	#518	—	2	4	no	—
254	#518	C₂²×C₆₁	1	8	yes	complemented
255	C₂×C₄×D₄	—	2	2	no	—
256	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	complemented
257	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
258	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
259	C₂²×C₂²⋊C₄	—	2	2	no	—
260	#463	C₂²×C₆₁	1	32	yes	complemented
261	#461	C₂²×C₆₁	1	16	yes	complemented
262	#459	C₂²×C₆₁	1	16	yes	complemented
263	#424	C₂²×C₆₁	1	8	yes	complemented
264	#423	C₂²×C₆₁	1	4	yes	complemented
265	#419	C₂²×C₆₁	1	4	yes	complemented
266	#418	C₂²×C₆₁	1	4	yes	complemented
267	#417	C₂²×C₆₁	1	8	yes	complemented
268	#416	C₂²×C₆₁	1	8	yes	complemented
269	C₆₁	#60423	1	1	yes	characteristic, direct product factor, Sylow
270	C₂⁵	—	2	1	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	—	2	8	no	—
274	C₂×#41	—	2	8	no	—
275	C₂×#41	C₂³×C₆₁	1	4	yes	—
276	C₂×#41	C₂³×C₆₁	1	4	yes	—
277	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
278	C₂²×D₄	—	2	2	no	—
279	C₂²×D₄	—	2	1	no	—
280	C₂²×D₄	—	2	2	no	—
281	C₂²×D₄	—	2	4	no	—
282	C₂²×D₄	D₄×C₆₁	1	8	yes	complemented
283	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
284	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
285	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
286	C₂³×C₄	—	2	2	no	—
287	C₂³×C₄	—	2	4	no	—
288	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
289	AGL(1,ℤ/8)	—	2	32	no	—
290	AGL(1,ℤ/8)	—	2	32	no	—
291	C₂×SD₁₆	—	2	16	no	—
292	C₂×SD₁₆	C₂³×C₆₁	1	16	yes	—
293	C₂×D₈	—	2	16	no	—
294	C₂×D₈	C₂³×C₆₁	1	16	yes	—
295	C₂×M₁₆	—	2	8	no	—
296	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
297	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
298	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
299	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	complemented
300	#127	C₂³×C₆₁	1	4	yes	complemented
301	#124	C₂³×C₆₁	1	8	yes	complemented
302	#123	—	2	8	no	—
303	C₂²⋊Q₈	—	2	8	no	—
304	#121	—	2	8	no	—
305	#121	—	2	8	no	—
306	#120	—	2	8	no	—
307	C₄×D₄	—	2	16	no	—
308	C₄×D₄	—	2	8	no	—
309	C₄×D₄	—	2	8	no	—
310	C₄×D₄	C₂³×C₆₁	1	16	yes	—
311	#117	—	2	2	no	—
312	#117	D₄×C₆₁	1	4	yes	—
313	#117	C₂³×C₆₁	1	4	yes	—
314	#117	C₂³×C₆₁	1	4	yes	—
315	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	4	no	—
319	C₂×C₂²⋊C₄	—	2	16	no	—
320	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
323	C₄⋊C₈	C₂³×C₆₁	1	16	yes	complemented
324	#103	C₂³×C₆₁	1	16	yes	complemented
325	#102	C₂³×C₆₁	1	16	yes	complemented
326	C₂⁴	—	2	2	no	—
327	C₂⁴	—	2	8	no	—
328	C₂⁴	—	2	4	no	—
329	C₂⁴	—	2	2	no	—
330	C₂⁴	—	8	4	no	—
331	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
332	#41	—	2	8	no	—
333	#41	—	2	8	no	—
334	#41	—	2	8	no	—
335	#41	—	2	8	no	—
336	#41	—	4	8	no	—
337	#41	—	4	8	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	16	no	—
345	C₂×D₄	—	2	8	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	8	no	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	4	8	no	—
355	C₂×D₄	C₂×D₄×C₆₁	1	16	yes	—
356	C₂×D₄	C₂×D₄×C₆₁	1	8	yes	—
357	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
358	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	16	no	—
364	C₂²×C₄	—	4	8	no	—
365	C₂²×C₄	—	8	8	no	—
366	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
367	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
370	C₂²×C₄	#41×C₆₁	1	4	yes	—
371	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
373	SD₁₆	—	2	32	no	—
374	D₈	—	2	32	no	—
375	M₁₆	—	2	8	no	—
376	M₁₆	—	2	8	no	—
377	C₂×C₈	—	2	8	no	—
378	C₂×C₈	C₂⁴×C₆₁	1	8	yes	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
382	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	2	16	no	—
385	C₂²⋊C₄	—	2	16	no	—
386	C₂²⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
387	C₄²	—	2	4	no	—
388	C₄²	C₂×D₄×C₆₁	1	4	yes	—
389	C₄²	C₂⁴×C₆₁	1	4	yes	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	8	no	—
392	C₂³	—	2	16	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	8	no	—
396	C₂³	—	4	4	no	—
397	C₂³	—	8	4	no	—
398	C₂³	—	8	8	no	—
399	C₂³	—	8	16	no	—
400	C₂³	#121×C₆₁	1	4	yes	—
401	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
402	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
403	Q₈	—	2	4	no	—
404	Q₈	—	2	4	no	—
405	Q₈	—	4	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	4	no	—
409	D₄	—	2	8	no	—
410	D₄	—	2	16	no	—
411	D₄	—	4	8	no	—
412	D₄	—	4	8	no	—
413	D₄	—	4	4	no	—
414	D₄	—	8	8	no	—
415	D₄	C₂²×D₄×C₆₁	1	8	yes	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	8	no	—
422	C₂×C₄	—	4	8	no	—
423	C₂×C₄	—	8	16	no	—
424	C₂×C₄	#121×C₆₁	1	8	yes	—
425	C₂×C₄	#121×C₆₁	1	4	yes	—
426	C₂×C₄	C₂²×D₄×C₆₁	1	8	yes	—
427	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
428	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
429	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
431	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
432	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
433	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
434	C₈	—	2	8	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	8	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	16	no	—
440	C₂²	—	4	8	no	—
441	C₂²	—	4	8	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	8	16	no	—
444	C₂²	—	8	8	no	—
445	C₂²	C₂×#121×C₆₁	1	4	yes	—
446	C₂²	C₂×#121×C₆₁	1	2	yes	—
447	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
448	C₄	—	2	8	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	4	no	—
451	C₄	C₂×#121×C₆₁	1	2	yes	—
452	C₄	C₂×#121×C₆₁	1	4	yes	—
453	C₄	C₂³×D₄×C₆₁	1	1	yes	characteristic
454	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
455	C₂	—	2	2	no	—
456	C₂	—	2	4	no	—
457	C₂	—	4	8	no	—
458	C₂	—	8	4	no	—
459	C₂	C₂²×#121×C₆₁	1	1	yes	characteristic
460	C₂	C₆₁×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×#117×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×AGL(1,ℤ/8)×C₆₁	C₂	semidirect
2. C₆₁×#3449	C₂	semidirect
3. C₂×C₆₁×#518	C₂	semidirect
4. C₆₁×#3042	C₂	semidirect
5. C₆₁×#3041	C₂	semidirect
6. C₆₁×#3036	C₂	semidirect
7. C₆₁×#2905	C₂	semidirect
8. C₆₁×#2896	C₂	semidirect
13. C₂×AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
14. C₂²×SD₁₆×C₆₁	C₂²	semidirect
15. C₂²×D₈×C₆₁	C₂²	semidirect
18. C₆₁×#536	C₂²	semidirect
19. C₆₁×#535	C₂²	semidirect
21. C₆₁×#532	C₂²	semidirect
24. C₆₁×#518	C₂²	semidirect
26. C₂×C₄×D₄×C₆₁	C₂²	semidirect
30. C₆₁×#463	C₂²	semidirect
31. C₆₁×#461	C₂²	semidirect
32. C₆₁×#459	C₂²	semidirect
33. C₆₁×#424	C₂²	semidirect
34. C₆₁×#423	C₂²	semidirect
35. C₆₁×#419	C₂²	semidirect
36. C₆₁×#418	C₂²	semidirect
37. C₆₁×#417	C₂²	semidirect
38. C₆₁×#416	C₂²	semidirect
51. C₂²×D₄×C₆₁	D₄	semidirect
68. C₄⋊Q₈×C₆₁	C₂³	semidirect
69. #127×C₆₁	C₂³	semidirect
70. #124×C₆₁	C₂³	semidirect
92. C₄⋊C₈×C₆₁	C₂³	semidirect
93. #103×C₆₁	C₂³	semidirect
94. #102×C₆₁	C₂³	semidirect
204. #60423	C₆₁	direct (N × H)
225. C₂²×AGL(1,ℤ/8)	C₂×C₆₁	semidirect
226. #3449	C₂×C₆₁	semidirect
227. C₂×#518	C₂×C₆₁	semidirect
228. #3042	C₂×C₆₁	semidirect
229. #3041	C₂×C₆₁	semidirect
230. #3036	C₂×C₆₁	semidirect
231. #2905	C₂×C₆₁	semidirect
232. #2896	C₂×C₆₁	semidirect
243. C₂×AGL(1,ℤ/8)	C₂²×C₆₁	semidirect
244. C₂²×SD₁₆	C₂²×C₆₁	semidirect
245. C₂²×D₈	C₂²×C₆₁	semidirect
248. #536	C₂²×C₆₁	semidirect
249. #535	C₂²×C₆₁	semidirect
251. #532	C₂²×C₆₁	semidirect
254. #518	C₂²×C₆₁	semidirect
256. C₂×C₄×D₄	C₂²×C₆₁	semidirect
260. #463	C₂²×C₆₁	semidirect
261. #461	C₂²×C₆₁	semidirect
262. #459	C₂²×C₆₁	semidirect
263. #424	C₂²×C₆₁	semidirect
264. #423	C₂²×C₆₁	semidirect
265. #419	C₂²×C₆₁	semidirect
266. #418	C₂²×C₆₁	semidirect
267. #417	C₂²×C₆₁	semidirect
268. #416	C₂²×C₆₁	semidirect
269. C₆₁	#60423	direct (N × H)
282. C₂²×D₄	D₄×C₆₁	semidirect
299. C₄⋊Q₈	C₂³×C₆₁	semidirect
300. #127	C₂³×C₆₁	semidirect
301. #124	C₂³×C₆₁	semidirect
323. C₄⋊C₈	C₂³×C₆₁	semidirect
324. #103	C₂³×C₆₁	semidirect
325. #102	C₂³×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₆₁	2
C₆₁×#3449	2
C₂×C₆₁×#518	2
C₆₁×#3042	2
C₆₁×#3041	2
C₆₁×#3036	2
C₆₁×#2905	2
C₆₁×#2896	2
#60423	61

Subgroups — C61×#60423 #29563856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60423 #29563856