Subgroups — ΓL(1,𝔽₃₂)⋊(C₁₁⋊AGL(1,𝔽₅)) #46802089

Order 34100.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₁×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁×ΓL(1,𝔽₃₂)	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁⋊(C₃₁⋊AGL(1,𝔽₅))	C₅	1	1	yes	maximal, characteristic, complemented
4	ΓL(1,𝔽₃₂)⋊Dic₁₁	—	5	1	no	maximal
5	D₅×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic
6	C₂×C₁₁×ΓL(1,𝔽₃₂)	—	5	1	no	—
7	ΓL(1,𝔽₃₂)⋊AGL(1,𝔽₅)	—	11	1	no	maximal, Hall
8	C₅×C₁₁×C₃₁	C₄×C₅	1	1	yes	characteristic, complemented
9	C₁₁×ΓL(1,𝔽₃₂)	—	4	1	no	—
10	C₁₁×ΓL(1,𝔽₃₂)	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
11	D₅×ΓL(1,𝔽₃₂)	D₁₁	1	1	yes	characteristic
12	Dic₃₄₁	—	5	1	no	Hall
13	C₅×C₁₁⋊AGL(1,𝔽₅)	—	31	1	no	maximal, Hall
14	C₅×ΓL(1,𝔽₃₂)	Dic₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₁×C₃₁	—	5	1	no	—
16	C₃₁⋊AGL(1,𝔽₅)	—	11	1	no	—
17	Dic₃₁⋊C₅	—	55	1	no	—
18	C₅×D₅×C₁₁	—	31	1	no	—
19	C₁₁×C₃₁	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
20	D₅×C₃₁	C₅×D₁₁	1	1	yes	characteristic
21	C₂×ΓL(1,𝔽₃₂)	—	5	1	no	—
22	C₅²×C₁₁	—	31	1	no	Hall
23	C₁₁⋊AGL(1,𝔽₅)	—	31	1	no	—
24	C₅×Dic₁₁	—	155	1	no	—
25	C₅×C₃₁	C₅×Dic₁₁	1	1	yes	characteristic, complemented
26	ΓL(1,𝔽₃₂)	—	4	1	no	—
27	ΓL(1,𝔽₃₂)	C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
28	Dic₃₁	—	55	1	no	Hall
29	C₂×C₅×C₁₁	—	155	1	no	—
30	D₅×C₁₁	D₃₁⋊C₅	1	1	yes	characteristic
31	C₅×AGL(1,𝔽₅)	—	341	1	no	Hall
32	C₂×C₃₁	—	5	1	no	—
33	C₅×C₁₁	—	31	1	no	—
34	C₅×C₁₁	—	124	1	no	—
35	C₅×C₁₁	Dic₃₁⋊C₅	1	1	yes	characteristic, complemented
36	C₅×D₅	—	31	1	no	—
37	Dic₁₁	—	155	1	no	Hall
38	C₃₁	C₅×C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
39	C₅²	—	31	1	no	Sylow
40	C₂×C₁₁	—	5	1	no	—
41	AGL(1,𝔽₅)	—	341	1	no	—
42	C₄×C₅	—	1705	1	no	—
43	C₁₁	ΓL(1,𝔽₃₂)⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₅	—	155	1	no	—
45	D₅	ΓL(1,𝔽₃₂)⋊D₁₁	1	1	yes	characteristic
46	C₅	—	31	1	no	—
47	C₅	—	124	1	no	—
48	C₅	ΓL(1,𝔽₃₂)⋊Dic₁₁	1	1	yes	characteristic, complemented
49	C₄	—	1705	1	no	Sylow
50	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₁×C₃₁	C₄×C₅
prime radical	D₅×C₁₁×ΓL(1,𝔽₃₂)	C₂
cosocle	D₅×C₁₁×C₃₁	C₂×C₅
LCS	G ▷ C₅×C₁₁×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₁×ΓL(1,𝔽₃₂)	C₄	semidirect
3. C₁₁⋊(C₃₁⋊AGL(1,𝔽₅))	C₅	semidirect
8. C₅×C₁₁×C₃₁	C₄×C₅	semidirect
10. C₁₁×ΓL(1,𝔽₃₂)	AGL(1,𝔽₅)	semidirect
14. C₅×ΓL(1,𝔽₃₂)	Dic₁₁	semidirect
19. C₁₁×C₃₁	C₅×AGL(1,𝔽₅)	semidirect
25. C₅×C₃₁	C₅×Dic₁₁	semidirect
27. ΓL(1,𝔽₃₂)	C₁₁⋊AGL(1,𝔽₅)	semidirect
35. C₅×C₁₁	Dic₃₁⋊C₅	semidirect
38. C₃₁	C₅×C₁₁⋊AGL(1,𝔽₅)	semidirect
43. C₁₁	ΓL(1,𝔽₃₂)⋊AGL(1,𝔽₅)	semidirect
48. C₅	ΓL(1,𝔽₃₂)⋊Dic₁₁	semidirect

Maximal subgroups

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

subgroup	index
D₅×C₁₁×ΓL(1,𝔽₃₂)	2
C₁₁⋊(C₃₁⋊AGL(1,𝔽₅))	5
ΓL(1,𝔽₃₂)⋊Dic₁₁	5
ΓL(1,𝔽₃₂)⋊AGL(1,𝔽₅)	11
C₅×C₁₁⋊AGL(1,𝔽₅)	31

Subgroups — ΓL(1,𝔽32)⋊(C11⋊AGL(1,𝔽5)) #46802089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — ΓL(1,𝔽₃₂)⋊(C₁₁⋊AGL(1,𝔽₅)) #46802089