Subgroups — #46776451

Order 33540.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊#16809813	C₂	1	1	yes	maximal, characteristic
2	C₄₃⋊#63121	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×#13131976	C₄	1	1	yes	characteristic, complemented, Hall
4	#20269447	—	5	1	no	maximal, Hall
5	C₄₃×D₆₅	C₂×C₃	1	1	yes	characteristic
6	#16809813	—	5	1	no	—
7	C₅×C₁₃×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	(C₄₃⋊C₃)⋊AGL(1,𝔽₅)	—	13	1	no	maximal, Hall
9	C₄₃⋊#261	—	5	1	no	Hall
10	#13131976	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	D₅×C₄₃⋊C₃	—	13	1	no	—
12	D₁₃×C₄₃	—	5	1	no	—
13	C₄₃⋊AGL(1,𝔽₅)	—	13	1	no	Hall
14	#63121⋊C₃	—	43	1	no	maximal, Hall
15	C₅×C₄₃⋊C₃	—	13	1	no	Hall
16	C₁₃×C₄₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
17	(C₄₃⋊C₃)⋊C₄	—	65	1	no	Hall
18	D₅×C₄₃	—	13	1	no	—
19	C₅⋊(D₁₃⋊C₃)	—	43	1	no	—
20	#63121	—	43	1	no	Hall
21	C₂×C₄₃⋊C₃	—	65	1	no	—
22	C₅×C₄₃	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Hall
23	C₅×C₁₃⋊C₃	—	43	1	no	Hall
24	Dic₄₃	—	65	1	no	Hall
25	AGL(1,𝔽₁₃)	—	215	1	no	Hall
26	D₆₅	D₄₃⋊C₃	1	1	yes	characteristic
27	C₄₃⋊C₃	—	13	1	no	Hall
28	C₂×C₄₃	—	65	1	no	—
29	D₁₃⋊C₃	—	215	1	no	—
30	C₅×C₁₃	(C₄₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Hall
31	C₃×AGL(1,𝔽₅)	—	559	1	no	Hall
32	#261	—	215	1	no	Hall
33	C₄₃	#63121⋊C₃	1	1	yes	characteristic, complemented, Sylow
34	C₁₃⋊C₃	—	43	1	no	Hall
35	C₃×D₅	—	559	1	no	—
36	D₁₃	—	5	1	no	—
37	AGL(1,𝔽₅)	—	559	1	no	Hall
38	C₃×C₅	—	559	1	no	Hall
39	C₁₃	(C₄₃⋊C₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	2795	1	no	Hall
41	D₅	—	13	1	no	—
42	C₂×C₃	—	2795	1	no	—
43	C₅	#20269447	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	2795	1	no	Sylow
45	C₃	—	559	1	no	Sylow
46	C₂	—	65	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₃×C₄₃	C₃×C₄
prime radical	C₅⋊#16809813	C₂
cosocle	C₄₃×D₆₅	C₂×C₃
LCS	G ▷ C₅×C₁₃×C₄₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₄₃⋊#63121	C₃	semidirect
3. C₅×#13131976	C₄	semidirect
7. C₅×C₁₃×C₄₃	C₃×C₄	semidirect
10. #13131976	AGL(1,𝔽₅)	semidirect
16. C₁₃×C₄₃	C₃×AGL(1,𝔽₅)	semidirect
22. C₅×C₄₃	AGL(1,𝔽₁₃)	semidirect
30. C₅×C₁₃	(C₄₃⋊C₃)⋊C₄	semidirect
33. C₄₃	#63121⋊C₃	semidirect
39. C₁₃	(C₄₃⋊C₃)⋊AGL(1,𝔽₅)	semidirect
43. C₅	#20269447	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊#16809813	2
C₄₃⋊#63121	3
#20269447	5
(C₄₃⋊C₃)⋊AGL(1,𝔽₅)	13
#63121⋊C₃	43