Subgroups — C₅×#13732 #11936452

Order 1280.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2253	C₂	1	2	yes	maximal
2	C₅×#1424	C₂	1	2	yes	maximal
3	C₅×#1423	C₂	1	2	yes	maximal
4	C₄×C₅×C₃₂	C₂	1	1	yes	maximal, characteristic
5	C₅×#499	—	2	2	no	—
6	C₂×C₅×C₃₂	C₂²	1	1	yes	characteristic
7	C₂×C₅×C₃₂	C₂²	1	1	yes	characteristic
8	C₅×#367	—	2	2	no	—
9	C₅×#366	C₂²	1	4	yes	—
10	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
11	#13732	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₅×#125	—	4	2	no	—
13	C₂×C₅×C₁₆	D₄	1	1	yes	characteristic
14	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
15	C₅×#107	—	2	4	no	—
16	C₅×#106	—	4	2	no	—
17	C₄×C₅×C₈	D₄	1	1	yes	characteristic
18	C₅×C₃₂	Q₈	1	2	yes	—
19	C₅×C₃₂	Q₈	1	2	yes	—
20	#2253	C₂×C₅	1	2	yes	—
21	#1424	C₂×C₅	1	2	yes	—
22	#1423	C₂×C₅	1	2	yes	—
23	C₄×C₃₂	C₂×C₅	1	1	yes	characteristic
24	C₂×C₅×C₈	D₈	1	1	yes	characteristic
25	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
26	C₅×C₄⋊C₄	—	4	4	no	—
27	C₅×C₄⋊C₄	—	8	4	no	—
28	C₄²×C₅	D₈	1	1	yes	characteristic
29	C₅×C₁₆	Q₁₆	1	2	yes	—
30	C₅×C₁₆	C₂×Q₈	1	1	yes	characteristic
31	C₅×C₁₆	C₂×Q₈	1	1	yes	characteristic
32	#499	—	2	2	no	—
33	C₂×C₃₂	C₂²×C₅	1	1	yes	characteristic
34	C₂×C₃₂	C₂²×C₅	1	1	yes	characteristic
35	#367	—	2	2	no	—
36	#366	C₂²×C₅	1	4	yes	—
37	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
38	C₂×C₄×C₅	—	8	4	no	—
39	C₂×C₄×C₅	D₁₆	1	2	yes	—
40	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
41	C₅×C₈	Q₃₂	1	2	yes	—
42	C₅×C₈	C₄⋊Q₈	1	1	yes	characteristic
43	C₅×C₈	C₂×Q₁₆	1	1	yes	characteristic
44	#125	—	4	2	no	—
45	C₂×C₁₆	C₅×D₄	1	1	yes	characteristic
46	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
47	#107	—	2	4	no	—
48	#106	—	4	2	no	—
49	C₄×C₈	C₅×D₄	1	1	yes	characteristic
50	C₃₂	C₅×Q₈	1	2	yes	—
51	C₃₂	C₅×Q₈	1	2	yes	—
52	C₂²×C₅	C₂×D₁₆	1	1	yes	characteristic
53	C₄×C₅	—	2	2	no	—
54	C₄×C₅	—	16	4	no	—
55	C₄×C₅	#500	1	1	yes	characteristic
56	C₄×C₅	C₂×Q₃₂	1	1	yes	characteristic
57	C₂×C₈	C₅×D₈	1	1	yes	characteristic
58	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
59	C₄⋊C₄	—	4	4	no	—
60	C₄⋊C₄	—	8	4	no	—
61	C₄²	C₅×D₈	1	1	yes	characteristic
62	C₁₆	C₅×Q₁₆	1	2	yes	—
63	C₁₆	C₂×C₅×Q₈	1	1	yes	characteristic
64	C₁₆	C₂×C₅×Q₈	1	1	yes	characteristic
65	C₂×C₅	#2252	1	1	yes	characteristic
66	C₂×C₅	#2262	1	2	yes	—
67	C₂×C₄	—	8	4	no	—
68	C₂×C₄	C₅×D₁₆	1	2	yes	—
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	#13732	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	C₂×C₅×D₁₆	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	16	4	no	—
77	C₄	C₅×#500	1	1	yes	characteristic
78	C₄	C₂×C₅×Q₃₂	1	1	yes	characteristic
79	C₂	C₅×#2252	1	1	yes	characteristic
80	C₂	C₅×#2262	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
11. #13732	C₅	direct (N × H)
73. C₅	#13732	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×#2253	2
C₅×#1424	2
C₅×#1423	2
C₄×C₅×C₃₂	2
#13732	5

Subgroups — C5×#13732 #11936452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13732 #11936452