Subgroups — C₅×#9611 #11932331

Order 1280.

382 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#1947	C₂	1	2	yes	maximal
2	C₅×#1844	C₂	1	1	yes	maximal, characteristic
3	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#334	C₂	1	1	yes	maximal, characteristic
5	C₅×#1296	C₂	1	2	yes	maximal
6	C₂×C₅×#107	—	2	2	no	—
7	C₂×C₅×#106	—	2	1	no	—
8	C₂×C₅×#106	—	2	1	no	—
9	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
10	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₅×C₈	—	2	1	no	—
12	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₅×#384	C₂²	1	2	yes	—
14	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₅×#340	—	2	2	no	—
16	C₅×#336	—	2	1	no	—
17	C₅×#334	C₄	1	4	yes	complemented
18	#9611	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₅×C₈	—	2	1	no	—
20	C₂²×C₅×C₈	—	2	2	no	—
21	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
22	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
23	C₂×C₅×C₄⋊C₄	—	2	2	no	—
24	C₂×C₅×C₄⋊C₄	—	2	2	no	—
25	C₂×C₅×C₄⋊C₄	—	2	2	no	—
26	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
27	C₂×C₄²×C₅	—	2	1	no	—
28	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
29	C₅×#107	—	4	4	no	—
30	C₅×#106	—	4	2	no	—
31	C₅×#106	—	4	2	no	—
32	C₅×C₄⋊C₈	—	2	2	no	—
33	C₅×C₄⋊C₈	—	2	1	no	—
34	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
35	C₅×C₄⋊C₈	Q₈	1	2	yes	—
36	C₄×C₅×C₈	—	4	2	no	—
37	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
38	C₄×C₅×C₈	Q₈	1	2	yes	—
39	C₅×#95	—	2	1	no	—
40	#1947	C₂×C₅	1	2	yes	—
41	#1844	C₂×C₅	1	1	yes	characteristic
42	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
43	C₂×#334	C₂×C₅	1	1	yes	characteristic
44	#1296	C₂×C₅	1	2	yes	—
45	C₂²×C₄×C₅	—	2	2	no	—
46	C₂²×C₄×C₅	—	4	2	no	—
47	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₅	#41	1	1	yes	characteristic
50	C₂×C₅×C₈	—	2	1	no	—
51	C₂×C₅×C₈	—	2	1	no	—
52	C₂×C₅×C₈	—	2	4	no	—
53	C₂×C₅×C₈	—	2	2	no	—
54	C₂×C₅×C₈	—	4	1	no	—
55	C₂×C₅×C₈	—	4	2	no	—
56	C₂×C₅×C₈	—	4	2	no	—
57	C₂×C₅×C₈	—	4	1	no	—
58	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
59	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
60	C₂×C₅×C₈	D₈	1	2	yes	—
61	C₂×C₅×C₈	Q₁₆	1	2	yes	—
62	C₅×C₄⋊C₄	—	2	2	no	—
63	C₅×C₄⋊C₄	—	4	2	no	—
64	C₅×C₄⋊C₄	—	4	2	no	—
65	C₅×C₄⋊C₄	—	4	2	no	—
66	C₅×C₄⋊C₄	—	4	2	no	—
67	C₅×C₄⋊C₄	—	8	2	no	—
68	C₅×C₄⋊C₄	SD₁₆	1	4	yes	—
69	C₄²×C₅	—	4	1	no	—
70	C₄²×C₅	—	4	1	no	—
71	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
72	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
73	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
74	C₄²×C₅	#41	1	1	yes	characteristic
75	C₂×#107	—	2	2	no	—
76	C₂×#106	—	2	1	no	—
77	C₂×#106	—	2	1	no	—
78	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
79	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
80	C₂×C₄×C₈	—	2	1	no	—
81	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
82	#384	C₂²×C₅	1	2	yes	—
83	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
84	#340	—	2	2	no	—
85	#336	—	2	1	no	—
86	#334	C₄×C₅	1	4	yes	complemented
87	C₂³×C₅	#121	1	1	yes	characteristic
88	C₂×C₄×C₅	—	2	2	no	—
89	C₂×C₄×C₅	—	2	4	no	—
90	C₂×C₄×C₅	—	4	2	no	—
91	C₂×C₄×C₅	—	4	2	no	—
92	C₂×C₄×C₅	—	8	2	no	—
93	C₂×C₄×C₅	—	8	2	no	—
94	C₂×C₄×C₅	—	8	2	no	—
95	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
97	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
98	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
99	C₂×C₄×C₅	#125	1	1	yes	characteristic
100	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
101	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
102	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
103	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
104	C₂×C₄×C₅	#135	1	2	yes	—
105	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
106	C₂×C₄×C₅	#137	1	1	yes	characteristic
107	C₅×C₈	—	2	2	no	—
108	C₅×C₈	—	4	4	no	—
109	C₅×C₈	—	4	2	no	—
110	C₅×C₈	#107	1	4	yes	complemented
111	C₂²×C₈	—	2	1	no	—
112	C₂²×C₈	—	2	2	no	—
113	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
114	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
115	C₂×C₄⋊C₄	—	2	2	no	—
116	C₂×C₄⋊C₄	—	2	2	no	—
117	C₂×C₄⋊C₄	—	2	2	no	—
118	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
119	C₂×C₄²	—	2	1	no	—
120	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
121	#107	—	4	4	no	—
122	#106	—	4	2	no	—
123	#106	—	4	2	no	—
124	C₄⋊C₈	—	2	2	no	—
125	C₄⋊C₈	—	2	1	no	—
126	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
127	C₄⋊C₈	C₅×Q₈	1	2	yes	—
128	C₄×C₈	—	4	2	no	—
129	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
130	C₄×C₈	C₅×Q₈	1	2	yes	—
131	#95	—	2	1	no	—
132	C₂²×C₅	#389	1	1	yes	characteristic
133	C₂²×C₅	#459	1	1	yes	characteristic
134	C₂²×C₅	#462	1	1	yes	characteristic
135	C₂²×C₅	#465	1	2	yes	—
136	C₂²×C₅	#471	1	2	yes	—
137	C₄×C₅	—	2	1	no	—
138	C₄×C₅	—	2	1	no	—
139	C₄×C₅	—	4	4	no	—
140	C₄×C₅	—	16	2	no	—
141	C₄×C₅	C₂×#107	1	1	yes	characteristic
142	C₄×C₅	#428	1	1	yes	characteristic
143	C₄×C₅	C₄×SD₁₆	1	2	yes	—
144	C₄×C₅	#474	1	1	yes	characteristic
145	C₄×C₅	#477	1	1	yes	characteristic
146	C₄×C₅	#498	1	1	yes	characteristic
147	C₄×C₅	#499	1	1	yes	characteristic
148	C₂²×C₄	—	2	2	no	—
149	C₂²×C₄	—	4	2	no	—
150	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
151	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
152	C₂²×C₄	C₅×#41	1	1	yes	characteristic
153	C₂×C₈	—	2	1	no	—
154	C₂×C₈	—	2	1	no	—
155	C₂×C₈	—	2	4	no	—
156	C₂×C₈	—	2	2	no	—
157	C₂×C₈	—	4	1	no	—
158	C₂×C₈	—	4	2	no	—
159	C₂×C₈	—	4	2	no	—
160	C₂×C₈	—	4	1	no	—
161	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
162	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
163	C₂×C₈	C₅×D₈	1	2	yes	—
164	C₂×C₈	C₅×Q₁₆	1	2	yes	—
165	C₄⋊C₄	—	2	2	no	—
166	C₄⋊C₄	—	4	2	no	—
167	C₄⋊C₄	—	4	2	no	—
168	C₄⋊C₄	—	4	2	no	—
169	C₄⋊C₄	—	4	2	no	—
170	C₄⋊C₄	—	8	2	no	—
171	C₄⋊C₄	C₅×SD₁₆	1	4	yes	—
172	C₄²	—	4	1	no	—
173	C₄²	—	4	1	no	—
174	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
175	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
176	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
177	C₄²	C₅×#41	1	1	yes	characteristic
178	C₂×C₅	#1665	1	2	yes	—
179	C₂×C₅	#1672	1	2	yes	—
180	C₂×C₅	#1941	1	1	yes	characteristic
181	C₂×C₅	#1947	1	1	yes	characteristic
182	C₂×C₅	#1951	1	1	yes	characteristic
183	C₂³	C₅×#121	1	1	yes	characteristic
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	—	8	2	no	—
189	C₂×C₄	—	8	2	no	—
190	C₂×C₄	—	8	2	no	—
191	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
192	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
193	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
194	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
195	C₂×C₄	C₅×#125	1	1	yes	characteristic
196	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
197	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
198	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
199	C₂×C₄	C₂×C₅×Q₁₆	1	1	yes	characteristic
200	C₂×C₄	C₅×#135	1	2	yes	—
201	C₂×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₂×C₄	C₅×#137	1	1	yes	characteristic
203	C₈	—	2	2	no	—
204	C₈	—	4	4	no	—
205	C₈	—	4	2	no	—
206	C₈	C₅×#107	1	4	yes	complemented
207	C₅	#9611	1	1	yes	characteristic, direct product factor, Sylow
208	C₂²	C₅×#389	1	1	yes	characteristic
209	C₂²	C₅×#459	1	1	yes	characteristic
210	C₂²	C₅×#462	1	1	yes	characteristic
211	C₂²	C₅×#465	1	2	yes	—
212	C₂²	C₅×#471	1	2	yes	—
213	C₄	—	2	1	no	—
214	C₄	—	2	1	no	—
215	C₄	—	4	4	no	—
216	C₄	—	16	2	no	—
217	C₄	C₂×C₅×#107	1	1	yes	characteristic
218	C₄	C₅×#428	1	1	yes	characteristic
219	C₄	C₄×C₅×SD₁₆	1	2	yes	—
220	C₄	C₅×#474	1	1	yes	characteristic
221	C₄	C₅×#477	1	1	yes	characteristic
222	C₄	C₅×#498	1	1	yes	characteristic
223	C₄	C₅×#499	1	1	yes	characteristic
224	C₂	C₅×#1665	1	2	yes	—
225	C₂	C₅×#1672	1	2	yes	—
226	C₂	C₅×#1941	1	1	yes	characteristic
227	C₂	C₅×#1947	1	1	yes	characteristic
228	C₂	C₅×#1951	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	#121
commutator	C₄²	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
17. C₅×#334	C₄	semidirect
18. #9611	C₅	direct (N × H)
86. #334	C₄×C₅	semidirect
110. C₅×C₈	#107	semidirect
206. C₈	C₅×#107	semidirect
207. C₅	#9611	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#1947	2
C₅×#1844	2
C₅×C₈×C₄⋊C₄	2
C₂×C₅×#334	2
C₅×#1296	2
#9611	5

Subgroups — C5×#9611 #11932331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#9611 #11932331