Subgroups — C₁₁×Dic₅×ΓL(1,𝔽₃₂) #46802015

Order 34100.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×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×Dic₅×C₃₁	C₅	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₁×ΓL(1,𝔽₃₂)	—	5	1	no	maximal
5	C₂×C₁₁×ΓL(1,𝔽₃₂)	—	2	2	no	—
6	C₂×C₁₁×ΓL(1,𝔽₃₂)	D₅	1	1	yes	characteristic
7	C₂×C₅×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic
8	Dic₅×ΓL(1,𝔽₃₂)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₁₁×C₃₁	C₄×C₅	1	1	yes	characteristic, complemented
10	C₁₁×ΓL(1,𝔽₃₂)	—	2	2	no	—
11	C₁₁×ΓL(1,𝔽₃₂)	Dic₅	1	1	yes	characteristic, direct product factor
12	C₂×C₅×ΓL(1,𝔽₃₂)	C₂×C₁₁	1	1	yes	characteristic
13	C₄×C₁₁×C₃₁	—	5	1	no	Hall
14	C₅×C₁₁×Dic₅	—	31	1	no	maximal, Hall
15	C₅×ΓL(1,𝔽₃₂)	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₁×C₃₁	C₅×D₅	1	1	yes	characteristic
17	Dic₅×C₃₁	C₅×C₁₁	1	1	yes	characteristic, complemented
18	C₄×ΓL(1,𝔽₃₂)	—	5	1	no	—
19	C₂×C₅²×C₁₁	—	31	1	no	—
20	C₁₁×C₃₁	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×C₃₁	C₂×C₅×C₁₁	1	1	yes	characteristic
22	C₂×ΓL(1,𝔽₃₂)	—	2	2	no	—
23	C₂×ΓL(1,𝔽₃₂)	D₅×C₁₁	1	1	yes	characteristic
24	C₅²×C₁₁	—	31	1	no	Hall
25	C₄×C₅×C₁₁	—	155	1	no	—
26	C₁₁×Dic₅	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor
27	C₅×C₃₁	C₄×C₅×C₁₁	1	1	yes	characteristic, complemented
28	ΓL(1,𝔽₃₂)	—	2	2	no	—
29	ΓL(1,𝔽₃₂)	C₁₁×Dic₅	1	1	yes	characteristic, direct product factor
30	C₄×C₃₁	—	5	1	no	Hall
31	C₂×C₅×C₁₁	—	31	1	no	—
32	C₂×C₅×C₁₁	—	62	2	no	—
33	C₂×C₅×C₁₁	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
34	C₅×Dic₅	—	31	1	no	Hall
35	C₂×C₃₁	C₅×D₅×C₁₁	1	1	yes	characteristic
36	C₅×C₁₁	—	31	1	no	—
37	C₅×C₁₁	—	62	2	no	—
38	C₅×C₁₁	C₄×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented
39	C₂×C₅²	—	31	1	no	—
40	C₄×C₁₁	—	5	1	no	Hall
41	C₃₁	C₅×C₁₁×Dic₅	1	1	yes	characteristic, complemented, Sylow
42	C₅²	—	31	1	no	Sylow
43	C₂×C₁₁	D₅×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
44	C₄×C₅	—	155	1	no	—
45	Dic₅	C₁₁×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor
46	C₁₁	Dic₅×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₅	—	31	1	no	—
48	C₂×C₅	—	62	2	no	—
49	C₂×C₅	C₂×C₁₁×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
50	C₅	—	31	1	no	—
51	C₅	—	62	2	no	—
52	C₅	C₄×C₁₁×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented
53	C₄	—	5	1	no	Sylow
54	C₂	D₅×C₁₁×ΓL(1,𝔽₃₂)	1	1	yes	characteristic

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

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×Dic₅×C₃₁	C₅	semidirect
8. Dic₅×ΓL(1,𝔽₃₂)	C₁₁	direct (N × H)
9. C₅×C₁₁×C₃₁	C₄×C₅	semidirect
11. C₁₁×ΓL(1,𝔽₃₂)	Dic₅	direct (N × H)
15. C₅×ΓL(1,𝔽₃₂)	C₄×C₁₁	semidirect
17. Dic₅×C₃₁	C₅×C₁₁	semidirect
20. C₁₁×C₃₁	C₅×Dic₅	semidirect
26. C₁₁×Dic₅	ΓL(1,𝔽₃₂)	direct (N × H)
27. C₅×C₃₁	C₄×C₅×C₁₁	semidirect
29. ΓL(1,𝔽₃₂)	C₁₁×Dic₅	direct (N × H)
38. C₅×C₁₁	C₄×ΓL(1,𝔽₃₂)	semidirect
41. C₃₁	C₅×C₁₁×Dic₅	semidirect
45. Dic₅	C₁₁×ΓL(1,𝔽₃₂)	direct (N × H)
46. C₁₁	Dic₅×ΓL(1,𝔽₃₂)	direct (N × H)
52. C₅	C₄×C₁₁×ΓL(1,𝔽₃₂)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₁₁×ΓL(1,𝔽₃₂)	2
C₁₁×Dic₅×C₃₁	5
C₄×C₁₁×ΓL(1,𝔽₃₂)	5
Dic₅×ΓL(1,𝔽₃₂)	11
C₅×C₁₁×Dic₅	31

Subgroups — C11×Dic5×ΓL(1,𝔽32) #46802015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×Dic₅×ΓL(1,𝔽₃₂) #46802015