Subgroups — C₅×#8260 #11930980

Order 1280.

502 conjugacy classes of subgroups.

The subgroup lattice has 176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₄⋊C₈	C₂	1	2	yes	maximal
2	C₄²×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#322	C₂	1	2	yes	maximal
4	C₅×#1273	C₂	1	2	yes	maximal
5	C₂×C₅×C₄⋊C₈	C₄	1	4	yes	—
6	C₂×C₄×C₅×C₈	C₄	1	2	yes	—
7	C₂×C₄×C₅×C₈	C₄	1	2	yes	—
8	C₂×C₄×C₅×C₈	C₂²	1	4	yes	—
9	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₄³×C₅	C₂²	1	1	yes	characteristic
12	C₅×#336	C₄	1	4	yes	—
13	C₅×#322	—	2	4	no	—
14	#8260	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂²×C₅×C₈	C₂×C₄	1	8	yes	—
16	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
17	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
23	C₅×C₄⋊C₈	—	2	8	no	—
24	C₄×C₅×C₈	—	2	4	no	—
25	C₄×C₅×C₈	—	2	4	no	—
26	C₄×C₅×C₈	—	2	2	no	—
27	C₄×C₅×C₈	—	2	4	no	—
28	C₄×C₅×C₈	C₈	1	8	yes	complemented
29	C₄×C₅×C₈	D₄	1	2	yes	—
30	C₄×C₅×C₈	Q₈	1	2	yes	—
31	C₄×C₄⋊C₈	C₂×C₅	1	2	yes	—
32	C₄²×C₈	C₂×C₅	1	1	yes	characteristic
33	C₂×#322	C₂×C₅	1	2	yes	—
34	#1273	C₂×C₅	1	2	yes	—
35	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
36	C₂²×C₄×C₅	C₄²	1	2	yes	—
37	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
38	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
40	C₂×C₅×C₈	—	2	2	no	—
41	C₂×C₅×C₈	—	2	2	no	—
42	C₂×C₅×C₈	—	2	8	no	—
43	C₂×C₅×C₈	—	2	8	no	—
44	C₂×C₅×C₈	—	2	8	no	—
45	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
46	C₂×C₅×C₈	C₂×C₈	1	4	yes	—
47	C₂×C₅×C₈	C₂×C₈	1	4	yes	—
48	C₂×C₅×C₈	M₁₆	1	4	yes	—
49	C₄²×C₅	—	2	2	no	—
50	C₄²×C₅	—	2	4	no	—
51	C₄²×C₅	C₂×C₈	1	4	yes	—
52	C₄²×C₅	M₁₆	1	8	yes	—
53	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
54	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
55	C₄²×C₅	#41	1	2	yes	—
56	C₂×C₄⋊C₈	C₄×C₅	1	4	yes	—
57	C₂×C₄×C₈	C₄×C₅	1	2	yes	—
58	C₂×C₄×C₈	C₄×C₅	1	2	yes	—
59	C₂×C₄×C₈	C₂²×C₅	1	4	yes	—
60	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
61	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
62	C₄³	C₂²×C₅	1	1	yes	characteristic
63	#336	C₄×C₅	1	4	yes	—
64	#322	—	2	4	no	—
65	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
66	C₂×C₄×C₅	—	2	2	no	—
67	C₂×C₄×C₅	—	2	2	no	—
68	C₂×C₄×C₅	—	2	2	no	—
69	C₂×C₄×C₅	C₄×C₈	1	2	yes	—
70	C₂×C₄×C₅	C₄×C₈	1	2	yes	—
71	C₂×C₄×C₅	#97	1	4	yes	—
72	C₂×C₄×C₅	#97	1	4	yes	—
73	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
74	C₂×C₄×C₅	#117	1	1	yes	characteristic
75	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
76	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
77	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
78	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
79	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
80	C₂×C₄×C₅	#131	1	4	yes	—
81	C₅×C₈	—	2	4	no	—
82	C₅×C₈	—	4	8	no	—
83	C₅×C₈	C₄⋊C₈	1	8	yes	complemented
84	C₂²×C₈	C₂×C₄×C₅	1	8	yes	—
85	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
86	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
87	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
88	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
89	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
90	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
91	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
92	C₄⋊C₈	—	2	8	no	—
93	C₄×C₈	—	2	4	no	—
94	C₄×C₈	—	2	4	no	—
95	C₄×C₈	—	2	2	no	—
96	C₄×C₈	—	2	4	no	—
97	C₄×C₈	C₅×C₈	1	8	yes	complemented
98	C₄×C₈	C₅×D₄	1	2	yes	—
99	C₄×C₈	C₅×Q₈	1	2	yes	—
100	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
101	C₂²×C₅	C₂×C₄×C₈	1	1	yes	characteristic
102	C₂²×C₅	C₂×#97	1	2	yes	—
103	C₂²×C₅	C₄×M₁₆	1	1	yes	characteristic
104	C₂²×C₅	#405	1	2	yes	—
105	C₄×C₅	—	2	2	no	—
106	C₄×C₅	—	2	4	no	—
107	C₄×C₅	#322	1	4	yes	complemented
108	C₄×C₅	C₂×C₄⋊C₈	1	2	yes	—
109	C₄×C₅	#431	1	2	yes	—
110	C₄×C₅	#436	1	4	yes	—
111	C₄×C₅	#446	1	4	yes	—
112	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
113	C₂²×C₄	C₄²×C₅	1	2	yes	—
114	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
115	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
116	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	—	2	2	no	—
119	C₂×C₈	—	2	8	no	—
120	C₂×C₈	—	2	8	no	—
121	C₂×C₈	—	2	8	no	—
122	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
123	C₂×C₈	C₂×C₅×C₈	1	4	yes	—
124	C₂×C₈	C₂×C₅×C₈	1	4	yes	—
125	C₂×C₈	C₅×M₁₆	1	4	yes	—
126	C₄²	—	2	2	no	—
127	C₄²	—	2	4	no	—
128	C₄²	C₂×C₅×C₈	1	4	yes	—
129	C₄²	C₅×M₁₆	1	8	yes	—
130	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
131	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
132	C₄²	C₅×#41	1	2	yes	—
133	C₂×C₅	C₂×#322	1	1	yes	characteristic
134	C₂×C₅	#1450	1	1	yes	characteristic
135	C₂×C₅	#1451	1	2	yes	—
136	C₂×C₅	C₄×C₄⋊C₈	1	1	yes	characteristic
137	C₂×C₅	#1770	1	2	yes	—
138	C₂³	C₂×C₄²×C₅	1	1	yes	characteristic
139	C₂×C₄	—	2	2	no	—
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	C₄×C₅×C₈	1	2	yes	—
143	C₂×C₄	C₄×C₅×C₈	1	2	yes	—
144	C₂×C₄	C₅×#97	1	4	yes	—
145	C₂×C₄	C₅×#97	1	4	yes	—
146	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄	C₅×#117	1	1	yes	characteristic
148	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
149	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
150	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
151	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
152	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
153	C₂×C₄	C₅×#131	1	4	yes	—
154	C₈	—	2	4	no	—
155	C₈	—	4	8	no	—
156	C₈	C₅×C₄⋊C₈	1	8	yes	complemented
157	C₅	#8260	1	1	yes	characteristic, direct product factor, Sylow
158	C₂²	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
159	C₂²	C₂×C₄×C₅×C₈	1	1	yes	characteristic
160	C₂²	C₂×C₅×#97	1	2	yes	—
161	C₂²	C₄×C₅×M₁₆	1	1	yes	characteristic
162	C₂²	C₅×#405	1	2	yes	—
163	C₄	—	2	2	no	—
164	C₄	—	2	4	no	—
165	C₄	C₅×#322	1	4	yes	complemented
166	C₄	C₂×C₅×C₄⋊C₈	1	2	yes	—
167	C₄	C₅×#431	1	2	yes	—
168	C₄	C₅×#436	1	4	yes	—
169	C₄	C₅×#446	1	4	yes	—
170	C₂	C₂×C₅×#322	1	1	yes	characteristic
171	C₂	C₅×#1450	1	1	yes	characteristic
172	C₂	C₅×#1451	1	2	yes	—
173	C₂	C₄×C₅×C₄⋊C₈	1	1	yes	characteristic
174	C₂	C₅×#1770	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₅	C₂³
commutator	C₂²	C₂×C₄×C₅×C₈
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle, prime radical	C₂³×C₅	C₂×C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
14. #8260	C₅	direct (N × H)
28. C₄×C₅×C₈	C₈	semidirect
83. C₅×C₈	C₄⋊C₈	semidirect
97. C₄×C₈	C₅×C₈	semidirect
107. C₄×C₅	#322	semidirect
156. C₈	C₅×C₄⋊C₈	semidirect
157. C₅	#8260	direct (N × H)
165. C₄	C₅×#322	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×C₄⋊C₈	2
C₄²×C₅×C₈	2
C₂×C₅×#322	2
C₅×#1273	2
#8260	5

Subgroups — C5×#8260 #11930980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8260 #11930980