Subgroups — C₅×#13731 #11936451

Order 1280.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2252	C₂	1	2	yes	maximal
2	C₅×#1423	C₂	1	4	yes	maximal
3	C₄×C₅×C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₅×#500	—	2	2	no	—
5	C₂×C₅×C₃₂	C₂²	1	2	yes	—
6	C₅×#366	—	2	2	no	—
7	C₅×#366	C₂²	1	4	yes	—
8	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
9	#13731	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₅×C₄⋊Q₈	—	4	2	no	—
11	C₂×C₅×C₁₆	D₄	1	1	yes	characteristic
12	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
13	C₅×#107	—	2	4	no	—
14	C₅×#107	—	4	2	no	—
15	C₄×C₅×C₈	D₄	1	1	yes	characteristic
16	C₅×C₃₂	Q₈	1	4	yes	complemented
17	#2252	C₂×C₅	1	2	yes	—
18	#1423	C₂×C₅	1	4	yes	—
19	C₄×C₃₂	C₂×C₅	1	1	yes	characteristic
20	C₂×C₅×Q₈	—	8	2	no	—
21	C₂×C₅×C₈	D₈	1	1	yes	characteristic
22	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
23	C₅×C₄⋊C₄	—	4	4	no	—
24	C₅×C₄⋊C₄	—	8	2	no	—
25	C₄²×C₅	D₈	1	1	yes	characteristic
26	C₅×C₁₆	Q₁₆	1	2	yes	—
27	C₅×C₁₆	C₂×Q₈	1	2	yes	—
28	#500	—	2	2	no	—
29	C₂×C₃₂	C₂²×C₅	1	2	yes	—
30	#366	—	2	2	no	—
31	#366	C₂²×C₅	1	4	yes	—
32	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
33	C₅×Q₈	—	16	4	no	—
34	C₂×C₄×C₅	—	8	4	no	—
35	C₂×C₄×C₅	D₁₆	1	1	yes	characteristic
36	C₂×C₄×C₅	D₁₆	1	1	yes	characteristic
37	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
38	C₅×C₈	Q₃₂	1	2	yes	—
39	C₅×C₈	C₄⋊Q₈	1	1	yes	characteristic
40	C₅×C₈	C₂×Q₁₆	1	1	yes	characteristic
41	C₄⋊Q₈	—	4	2	no	—
42	C₂×C₁₆	C₅×D₄	1	1	yes	characteristic
43	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
44	#107	—	2	4	no	—
45	#107	—	4	2	no	—
46	C₄×C₈	C₅×D₄	1	1	yes	characteristic
47	C₃₂	C₅×Q₈	1	4	yes	complemented
48	C₂²×C₅	C₂×D₁₆	1	1	yes	characteristic
49	C₄×C₅	—	16	4	no	—
50	C₄×C₅	D₃₂	1	2	yes	—
51	C₄×C₅	Q₆₄	1	2	yes	—
52	C₄×C₅	#500	1	1	yes	characteristic
53	C₄×C₅	C₂×Q₃₂	1	1	yes	characteristic
54	C₂×Q₈	—	8	2	no	—
55	C₂×C₈	C₅×D₈	1	1	yes	characteristic
56	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
57	C₄⋊C₄	—	4	4	no	—
58	C₄⋊C₄	—	8	2	no	—
59	C₄²	C₅×D₈	1	1	yes	characteristic
60	C₁₆	C₅×Q₁₆	1	2	yes	—
61	C₁₆	C₂×C₅×Q₈	1	2	yes	—
62	C₂×C₅	#2252	1	1	yes	characteristic
63	C₂×C₅	C₂×D₃₂	1	1	yes	characteristic
64	C₂×C₅	C₂×Q₆₄	1	1	yes	characteristic
65	Q₈	—	16	4	no	—
66	C₂×C₄	—	8	4	no	—
67	C₂×C₄	C₅×D₁₆	1	1	yes	characteristic
68	C₂×C₄	C₅×D₁₆	1	1	yes	characteristic
69	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
70	C₈	C₅×Q₃₂	1	2	yes	—
71	C₈	C₅×C₄⋊Q₈	1	1	yes	characteristic
72	C₈	C₂×C₅×Q₁₆	1	1	yes	characteristic
73	C₅	#13731	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	C₂×C₅×D₁₆	1	1	yes	characteristic
75	C₄	—	16	4	no	—
76	C₄	C₅×D₃₂	1	2	yes	—
77	C₄	C₅×Q₆₄	1	2	yes	—
78	C₄	C₅×#500	1	1	yes	characteristic
79	C₄	C₂×C₅×Q₃₂	1	1	yes	characteristic
80	C₂	C₅×#2252	1	1	yes	characteristic
81	C₂	C₂×C₅×D₃₂	1	1	yes	characteristic
82	C₂	C₂×C₅×Q₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₅	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₅
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×C₈ ◁ C₄×C₅×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
9. #13731	C₅	direct (N × H)
16. C₅×C₃₂	Q₈	semidirect
47. C₃₂	C₅×Q₈	semidirect
73. C₅	#13731	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×#2252	2
C₅×#1423	2
C₄×C₅×C₃₂	2
#13731	5

Subgroups — C5×#13731 #11936451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13731 #11936451