Subgroups — D₅×ΓL(1,𝔽₃₂)⋊C₉ #28358409

Order 13950.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×ΓL(1,𝔽₃₂)⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₅×ΓL(1,𝔽₃₂)	C₃	1	1	yes	maximal, characteristic
3	D₅×C₃₁⋊C₉	C₅	1	1	yes	maximal, characteristic, complemented
4	C₂×ΓL(1,𝔽₃₂)⋊C₉	—	5	1	no	maximal
5	C₃×C₅×ΓL(1,𝔽₃₂)	C₂×C₃	1	1	yes	characteristic
6	D₅×ΓL(1,𝔽₃₂)	C₉	1	1	yes	characteristic, complemented, Hall
7	C₅×C₃₁⋊C₉	C₂×C₅	1	1	yes	characteristic, complemented
8	ΓL(1,𝔽₃₂)⋊C₉	—	2	2	no	—
9	ΓL(1,𝔽₃₂)⋊C₉	D₅	1	1	yes	characteristic, direct product factor
10	C₃×D₅×C₃₁	C₃×C₅	1	1	yes	characteristic
11	C₂×C₃×ΓL(1,𝔽₃₂)	—	5	1	no	—
12	C₅×ΓL(1,𝔽₃₂)	C₂×C₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃₁⋊C₉	—	5	1	no	Hall
14	C₃×C₅×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic
15	C₃×ΓL(1,𝔽₃₂)	—	2	2	no	—
16	C₃×ΓL(1,𝔽₃₂)	C₃×D₅	1	1	yes	characteristic
17	C₅×C₉×D₅	—	31	1	no	maximal, Hall
18	D₅×C₃₁	C₅×C₉	1	1	yes	characteristic, complemented
19	C₂×ΓL(1,𝔽₃₂)	—	5	1	no	—
20	C₃₁⋊C₉	C₅×D₅	1	1	yes	characteristic, complemented, Hall
21	C₅²×C₉	—	31	1	no	Hall
22	C₂×C₃×C₃₁	—	5	1	no	—
23	C₅×C₃₁	C₂×C₅×C₉	1	1	yes	characteristic, complemented
24	ΓL(1,𝔽₃₂)	—	2	2	no	—
25	ΓL(1,𝔽₃₂)	C₉×D₅	1	1	yes	characteristic, complemented
26	C₃×C₅×D₅	—	31	1	no	—
27	C₃×C₃₁	C₃×C₅×D₅	1	1	yes	characteristic
28	C₂×C₅×C₉	—	155	1	no	—
29	C₉×D₅	—	31	1	no	—
30	C₃×C₅²	—	31	1	no	—
31	C₂×C₃₁	—	5	1	no	Hall
32	C₅×D₅	—	31	1	no	Hall
33	C₅×C₉	—	31	1	no	—
34	C₅×C₉	—	31	1	no	—
35	C₅×C₉	—	62	2	no	—
36	C₃₁	C₅×C₉×D₅	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃×C₅	—	155	1	no	—
38	C₃×D₅	(C₃₁⋊C₃)⋊C₅	1	1	yes	characteristic
39	C₅²	—	31	1	no	Sylow
40	C₂×C₉	—	155	1	no	Hall
41	C₃×C₅	—	31	1	no	—
42	C₃×C₅	—	62	2	no	—
43	C₃×C₅	C₂×(C₃₁⋊C₃)⋊C₅	1	1	yes	characteristic
44	C₂×C₅	—	155	1	no	—
45	D₅	ΓL(1,𝔽₃₂)⋊C₉	1	1	yes	characteristic, direct product factor
46	C₉	—	31	1	no	Sylow
47	C₂×C₃	—	5	1	no	—
48	C₅	—	31	1	no	—
49	C₅	—	62	2	no	—
50	C₅	C₂×ΓL(1,𝔽₃₂)⋊C₉	1	1	yes	characteristic, complemented
51	C₃	D₅×(C₃₁⋊C₃)⋊C₅	1	1	yes	characteristic
52	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₅×(C₃₁⋊C₃)⋊C₅
commutator, hypocenter	C₅×C₃₁	C₂×C₅×C₉
Fitting, socle, cosocle	C₃×C₅×C₃₁	C₂×C₃×C₅
prime radical	C₃×D₅×ΓL(1,𝔽₃₂)	C₃
LCS	G ▷ C₅×C₃₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₅×ΓL(1,𝔽₃₂)⋊C₉	C₂	semidirect
3. D₅×C₃₁⋊C₉	C₅	semidirect
6. D₅×ΓL(1,𝔽₃₂)	C₉	semidirect
7. C₅×C₃₁⋊C₉	C₂×C₅	semidirect
9. ΓL(1,𝔽₃₂)⋊C₉	D₅	direct (N × H)
12. C₅×ΓL(1,𝔽₃₂)	C₂×C₉	semidirect
18. D₅×C₃₁	C₅×C₉	semidirect
20. C₃₁⋊C₉	C₅×D₅	semidirect
23. C₅×C₃₁	C₂×C₅×C₉	semidirect
25. ΓL(1,𝔽₃₂)	C₉×D₅	semidirect
36. C₃₁	C₅×C₉×D₅	semidirect
45. D₅	ΓL(1,𝔽₃₂)⋊C₉	direct (N × H)
50. C₅	C₂×ΓL(1,𝔽₃₂)⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×ΓL(1,𝔽₃₂)⋊C₉	2
C₃×D₅×ΓL(1,𝔽₃₂)	3
D₅×C₃₁⋊C₉	5
C₂×ΓL(1,𝔽₃₂)⋊C₉	5
C₅×C₉×D₅	31

Subgroups — D5×ΓL(1,𝔽32)⋊C9 #28358409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×ΓL(1,𝔽₃₂)⋊C₉ #28358409