Subgroups — C₅×#20291877 #46802005

Order 34100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#13133723	C₂	1	1	yes	maximal, characteristic
2	C₅×#13133723	C₄	1	1	yes	characteristic, complemented, Hall
3	#20291877	C₅	1	5	yes	maximal, direct product factor
4	C₅×C₃₁×Dic₁₁	C₅	1	1	yes	maximal, characteristic, complemented
5	C₂×#13133723	C₂×C₅	1	5	yes	—
6	C₂×C₅×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic
7	C₄×C₅×ΓL(1,𝔽₃₂)	—	11	1	no	maximal, Hall
8	C₅×C₁₁×C₃₁	C₄×C₅	1	1	yes	characteristic, complemented
9	#13133723	C₄×C₅	1	5	yes	complemented
10	C₂×C₅×ΓL(1,𝔽₃₂)	—	11	1	no	—
11	C₃₁×Dic₁₁	C₅²	1	1	yes	characteristic, complemented, Hall
12	C₅×Dic₁₁⋊C₅	—	31	1	no	maximal, Hall
13	C₅×ΓL(1,𝔽₃₂)	—	11	1	no	Hall
14	C₂×C₁₁×C₃₁	C₂×C₅²	1	1	yes	characteristic
15	C₄×C₅×C₃₁	—	11	1	no	—
16	C₄×ΓL(1,𝔽₃₂)	—	11	5	no	—
17	C₂×C₅×C₁₁⋊C₅	—	31	1	no	—
18	C₁₁×C₃₁	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×C₃₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic
20	C₂×ΓL(1,𝔽₃₂)	—	11	5	no	—
21	C₅×C₁₁⋊C₅	—	31	1	no	Hall
22	C₅×Dic₁₁	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented
23	Dic₁₁⋊C₅	—	31	5	no	—
24	C₅×C₃₁	Dic₁₁⋊C₅	1	1	yes	characteristic, complemented
25	ΓL(1,𝔽₃₂)	—	11	5	no	—
26	C₄×C₃₁	—	11	1	no	Hall
27	C₂×C₅×C₁₁	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
28	C₂×C₁₁⋊C₅	—	31	5	no	—
29	C₄×C₅²	—	341	1	no	Hall
30	C₂×C₃₁	C₅×AGL(1,𝔽₁₁)	1	1	yes	characteristic
31	C₅×C₁₁	C₄×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented
32	C₁₁⋊C₅	—	31	5	no	—
33	C₂×C₅²	—	341	1	no	—
34	Dic₁₁	C₅×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Hall
35	C₃₁	C₅×Dic₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
36	C₅²	—	341	1	no	Sylow
37	C₂×C₁₁	C₂×C₅×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
38	C₄×C₅	—	11	1	no	—
39	C₄×C₅	—	341	5	no	—
40	C₁₁	C₄×C₅×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	341	5	no	—
42	C₂×C₅	#16811778	1	1	yes	characteristic
43	C₅	—	341	5	no	—
44	C₅	#20291877	1	1	yes	characteristic, direct product factor
45	C₄	—	11	1	no	Sylow
46	C₂	C₅×#16811778	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	#16811778
commutator, hypocenter	C₁₁×C₃₁	C₄×C₅²
Frattini	C₂	C₅×#16811778
Fitting, socle	C₂×C₅×C₁₁×C₃₁	C₂×C₅
prime radical	C₂×C₅×#13133723	C₂
cosocle	C₂×C₁₁×C₃₁	C₂×C₅²
LCS	G ▷ C₁₁×C₃₁
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×#13133723	C₄	semidirect
3. #20291877	C₅	direct (N × H)
4. C₅×C₃₁×Dic₁₁	C₅	semidirect
8. C₅×C₁₁×C₃₁	C₄×C₅	semidirect
9. #13133723	C₄×C₅	semidirect
11. C₃₁×Dic₁₁	C₅²	semidirect
18. C₁₁×C₃₁	C₄×C₅²	semidirect
22. C₅×Dic₁₁	ΓL(1,𝔽₃₂)	semidirect
24. C₅×C₃₁	Dic₁₁⋊C₅	semidirect
31. C₅×C₁₁	C₄×ΓL(1,𝔽₃₂)	semidirect
34. Dic₁₁	C₅×ΓL(1,𝔽₃₂)	semidirect
35. C₃₁	C₅×Dic₁₁⋊C₅	semidirect
40. C₁₁	C₄×C₅×ΓL(1,𝔽₃₂)	semidirect
44. C₅	#20291877	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#13133723	2
#20291877	5
C₅×C₃₁×Dic₁₁	5
C₄×C₅×ΓL(1,𝔽₃₂)	11
C₅×Dic₁₁⋊C₅	31

Subgroups — C5×#20291877 #46802005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20291877 #46802005