Subgroups — C₅×#13733 #11936453

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×#1424	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	#13733	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	#1424	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	2	yes	—
36	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
37	C₅×C₈	Q₃₂	1	2	yes	—
38	C₅×C₈	C₄⋊Q₈	1	1	yes	characteristic
39	C₅×C₈	C₂×Q₁₆	1	1	yes	characteristic
40	C₄⋊Q₈	—	4	2	no	—
41	C₂×C₁₆	C₅×D₄	1	1	yes	characteristic
42	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
43	#107	—	2	4	no	—
44	#107	—	4	2	no	—
45	C₄×C₈	C₅×D₄	1	1	yes	characteristic
46	C₃₂	C₅×Q₈	1	4	yes	complemented
47	C₂²×C₅	C₂×D₁₆	1	1	yes	characteristic
48	C₄×C₅	—	16	4	no	—
49	C₄×C₅	SD₆₄	1	4	yes	—
50	C₄×C₅	#500	1	1	yes	characteristic
51	C₄×C₅	C₂×Q₃₂	1	1	yes	characteristic
52	C₂×Q₈	—	8	2	no	—
53	C₂×C₈	C₅×D₈	1	1	yes	characteristic
54	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
55	C₄⋊C₄	—	4	4	no	—
56	C₄⋊C₄	—	8	2	no	—
57	C₄²	C₅×D₈	1	1	yes	characteristic
58	C₁₆	C₅×Q₁₆	1	2	yes	—
59	C₁₆	C₂×C₅×Q₈	1	2	yes	—
60	C₂×C₅	#2252	1	1	yes	characteristic
61	C₂×C₅	C₂×SD₆₄	1	2	yes	—
62	Q₈	—	16	4	no	—
63	C₂×C₄	—	8	4	no	—
64	C₂×C₄	C₅×D₁₆	1	2	yes	—
65	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
66	C₈	C₅×Q₃₂	1	2	yes	—
67	C₈	C₅×C₄⋊Q₈	1	1	yes	characteristic
68	C₈	C₂×C₅×Q₁₆	1	1	yes	characteristic
69	C₅	#13733	1	1	yes	characteristic, direct product factor, Sylow
70	C₂²	C₂×C₅×D₁₆	1	1	yes	characteristic
71	C₄	—	16	4	no	—
72	C₄	C₅×SD₆₄	1	4	yes	—
73	C₄	C₅×#500	1	1	yes	characteristic
74	C₄	C₂×C₅×Q₃₂	1	1	yes	characteristic
75	C₂	C₅×#2252	1	1	yes	characteristic
76	C₂	C₂×C₅×SD₆₄	1	2	yes	—

	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. #13733	C₅	direct (N × H)
16. C₅×C₃₂	Q₈	semidirect
46. C₃₂	C₅×Q₈	semidirect
69. C₅	#13733	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×#1424	2
C₄×C₅×C₃₂	2
#13733	5

Subgroups — C5×#13733 #11936453

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13733 #11936453