Subgroups — #46802076

Order 34100.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#13133722	C₂	1	1	yes	maximal, characteristic
2	C₅×#13133722	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃₁×C₁₁⋊AGL(1,𝔽₅)	C₅	1	1	yes	maximal, characteristic, complemented
4	#20291878	—	5	1	no	maximal
5	D₅×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic
6	C₂×#13133722	—	5	1	no	—
7	AGL(1,𝔽₅)×ΓL(1,𝔽₃₂)	—	11	1	no	maximal, Hall
8	C₅×C₁₁×C₃₁	C₄×C₅	1	1	yes	characteristic, complemented
9	#13133722	—	4	1	no	—
10	#13133722	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
11	D₅×ΓL(1,𝔽₃₂)	—	11	1	no	—
12	C₃₁×Dic₁₁	—	5	1	no	Hall
13	(C₁₁⋊C₅)⋊AGL(1,𝔽₅)	—	31	1	no	maximal, Hall
14	C₅×ΓL(1,𝔽₃₂)	—	11	1	no	Hall
15	C₂×C₁₁×C₃₁	—	5	1	no	—
16	AGL(1,𝔽₅)×C₃₁	—	11	1	no	—
17	C₄×ΓL(1,𝔽₃₂)	—	55	1	no	—
18	D₅×C₁₁⋊C₅	—	31	1	no	—
19	C₁₁×C₃₁	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
20	D₅×C₃₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic
21	C₂×ΓL(1,𝔽₃₂)	—	55	1	no	—
22	C₅×C₁₁⋊C₅	—	31	1	no	Hall
23	C₁₁⋊AGL(1,𝔽₅)	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented
24	Dic₁₁⋊C₅	—	155	1	no	—
25	C₅×C₃₁	Dic₁₁⋊C₅	1	1	yes	characteristic, complemented
26	ΓL(1,𝔽₃₂)	—	11	1	no	—
27	ΓL(1,𝔽₃₂)	—	44	1	no	—
28	C₄×C₃₁	—	55	1	no	Hall
29	D₅×C₁₁	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
30	C₂×C₁₁⋊C₅	—	155	1	no	—
31	C₅×AGL(1,𝔽₅)	—	341	1	no	Hall
32	C₂×C₃₁	—	5	1	no	—
33	C₅×C₁₁	C₄×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented
34	C₁₁⋊C₅	—	31	1	no	—
35	C₁₁⋊C₅	—	124	1	no	—
36	C₅×D₅	—	341	1	no	—
37	Dic₁₁	—	5	1	no	Hall
38	C₃₁	(C₁₁⋊C₅)⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
39	C₅²	—	341	1	no	Sylow
40	C₂×C₁₁	—	5	1	no	—
41	AGL(1,𝔽₅)	—	11	1	no	—
42	C₄×C₅	—	1705	1	no	—
43	C₁₁	AGL(1,𝔽₅)×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₅	—	1705	1	no	—
45	D₅	#16811779	1	1	yes	characteristic
46	C₅	—	1364	1	no	—
47	C₅	—	341	1	no	—
48	C₅	#20291878	1	1	yes	characteristic, complemented
49	C₄	—	55	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×#13133722	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×#13133722	C₄	semidirect
3. C₃₁×C₁₁⋊AGL(1,𝔽₅)	C₅	semidirect
8. C₅×C₁₁×C₃₁	C₄×C₅	semidirect
10. #13133722	AGL(1,𝔽₅)	semidirect
19. C₁₁×C₃₁	C₅×AGL(1,𝔽₅)	semidirect
23. C₁₁⋊AGL(1,𝔽₅)	ΓL(1,𝔽₃₂)	semidirect
25. C₅×C₃₁	Dic₁₁⋊C₅	semidirect
33. C₅×C₁₁	C₄×ΓL(1,𝔽₃₂)	semidirect
38. C₃₁	(C₁₁⋊C₅)⋊AGL(1,𝔽₅)	semidirect
43. C₁₁	AGL(1,𝔽₅)×ΓL(1,𝔽₃₂)	semidirect
48. C₅	#20291878	semidirect

Maximal subgroups

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

subgroup	index
D₅×#13133722	2
C₃₁×C₁₁⋊AGL(1,𝔽₅)	5
#20291878	5
AGL(1,𝔽₅)×ΓL(1,𝔽₃₂)	11
(C₁₁⋊C₅)⋊AGL(1,𝔽₅)	31