Subgroups — C₅×#63733 #13085561

Order 1440.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3787	C₂	1	1	yes	maximal, characteristic
2	C₅×#3712	C₂	1	2	yes	maximal
3	C₄×C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic
4	C₅×#622	C₄	1	2	yes	—
5	C₃×C₅×C₃⋊C₈	—	2	2	no	—
6	#63733	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×ΓL(1,𝔽₂₅)	—	6	2	no	—
8	C₂×C₅×C₃⋊D₃	Q₈	1	1	yes	characteristic
9	C₃²×C₄×C₅	D₄	1	1	yes	characteristic
10	C₅×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
11	C₅×#108	—	9	1	no	maximal, Hall
12	#3787	C₂×C₅	1	1	yes	characteristic
13	#3712	C₂×C₅	1	2	yes	—
14	C₄×C₅×D₃	—	6	2	no	—
15	C₃×C₅×C₈	—	6	2	no	—
16	C₅×C₃⋊C₈	—	2	2	no	—
17	C₂×C₃²×C₅	C₄⋊C₄	1	1	yes	characteristic
18	C₅×C₃⋊D₃	—	2	1	no	—
19	C₅×M₁₆	—	9	2	no	—
20	C₂×C₅×C₈	—	9	1	no	—
21	C₄×C₃⋊D₃	C₂²×C₅	1	1	yes	characteristic
22	#622	C₄×C₅	1	2	yes	—
23	C₃×C₃⋊C₈	—	2	2	no	—
24	C₂×C₅×D₃	—	6	2	no	—
25	C₃×C₄×C₅	—	2	2	no	—
26	C₅×Dic₃	—	6	2	no	—
27	ΓL(1,𝔽₂₅)	—	6	2	no	—
28	C₃²×C₅	#108	1	1	yes	characteristic, complemented, Hall
29	C₂×C₄×C₅	—	9	1	no	—
30	C₅×C₈	—	6	2	no	—
31	C₅×C₈	—	9	2	no	—
32	C₂×C₃⋊D₃	C₅×Q₈	1	1	yes	characteristic
33	C₃²×C₄	C₅×D₄	1	1	yes	characteristic
34	C₃⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
35	#108	—	9	1	no	Sylow
36	C₂×C₃×C₅	—	2	2	no	—
37	C₅×D₃	—	12	2	no	—
38	C₄×D₃	—	6	2	no	—
39	C₃×C₈	—	6	2	no	—
40	C₃⋊C₈	—	2	2	no	—
41	C₂²×C₅	—	9	1	no	—
42	C₄×C₅	—	9	1	no	—
43	C₄×C₅	GO⁺(4,𝔽₂)	1	1	yes	characteristic
44	C₂×C₃²	C₅×C₄⋊C₄	1	1	yes	characteristic
45	C₃⋊D₃	—	2	1	no	—
46	M₁₆	—	9	2	no	—
47	C₂×C₈	—	9	1	no	—
48	C₃×C₅	—	2	2	no	—
49	C₂×D₃	—	6	2	no	—
50	C₃×C₄	—	2	2	no	—
51	Dic₃	—	6	2	no	—
52	C₂×C₅	—	18	1	no	—
53	C₂×C₅	#3773	1	1	yes	characteristic
54	C₃²	C₅×#108	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₄	—	9	1	no	—
56	C₈	—	6	2	no	—
57	C₈	—	9	2	no	—
58	C₂×C₃	—	2	2	no	—
59	D₃	—	12	2	no	—
60	C₅	#63733	1	1	yes	characteristic, direct product factor, Sylow
61	C₂²	—	9	1	no	—
62	C₄	—	9	1	no	—
63	C₄	C₅×GO⁺(4,𝔽₂)	1	1	yes	characteristic
64	C₃	—	2	2	no	—
65	C₂	—	18	1	no	—
66	C₂	C₅×#3773	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₅	GO⁺(4,𝔽₂)
commutator	C₃⋊Dic₃	C₂×C₄×C₅
Frattini	C₄	C₅×GO⁺(4,𝔽₂)
Fitting	C₃²×C₄×C₅	D₄
socle	C₂×C₃²×C₅	C₄⋊C₄
prime radical	C₂×C₅×C₃⋊D₃	Q₈
cosocle	C₄×C₃⋊D₃	C₂²×C₅
hypocenter	C₃²	C₅×#108
LCS	G ▷ C₃⋊Dic₃ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄×C₅

Complements

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

N	H ≅ G/N	type
6. #63733	C₅	direct (N × H)
28. C₃²×C₅	#108	semidirect
54. C₃²	C₅×#108	semidirect
60. C₅	#63733	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×#3787	2
C₅×#3712	2
#63733	5
C₅×#108	9

Subgroups — C5×#63733 #13085561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#63733 #13085561