Subgroups — #24922524⋊C₃ #44544355

Order 31980.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊((C₁₃⋊C₃)⋊D₄₁)	C₂	1	1	yes	maximal, characteristic
2	#24922524	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₃⋊C₃×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	#14523821⋊C₃	—	5	1	no	maximal, Hall
5	D₂₆₆₅	C₂×C₃	1	1	yes	characteristic
6	(C₁₃⋊C₃)⋊D₄₁	—	5	1	no	—
7	C₅×C₁₃×C₄₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×#11717962	—	13	1	no	maximal, Hall
9	#14523821	—	5	1	no	Hall
10	C₁₃⋊C₃×C₄₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	C₃×D₂₀₅	—	13	1	no	—
12	D₅₃₃	—	5	1	no	—
13	#11717962	—	13	1	no	Hall
14	#63121⋊C₃	—	41	1	no	maximal, Hall
15	C₃×C₅×C₄₁	—	13	1	no	Hall
16	C₁₃×C₄₁	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
17	C₃×#4223	—	65	1	no	Hall
18	D₂₀₅	—	13	1	no	—
19	C₅⋊(D₁₃⋊C₃)	—	41	1	no	—
20	#63121	—	41	1	no	Hall
21	C₃×D₄₁	—	65	1	no	—
22	C₅×C₄₁	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Hall
23	C₅×C₁₃⋊C₃	#4223	1	1	yes	characteristic, complemented, Hall
24	#4223	—	65	1	no	Hall
25	AGL(1,𝔽₁₃)	—	205	1	no	Hall
26	D₆₅	—	41	1	no	—
27	C₃×C₄₁	—	13	1	no	Hall
28	D₄₁	—	65	1	no	—
29	D₁₃⋊C₃	—	205	1	no	—
30	C₅×C₁₃	C₃×#4223	1	1	yes	characteristic, complemented, Hall
31	C₃×AGL(1,𝔽₅)	—	533	1	no	Hall
32	#261	—	205	1	no	Hall
33	C₄₁	#63121⋊C₃	1	1	yes	characteristic, complemented, Sylow
34	C₁₃⋊C₃	#11717962	1	1	yes	characteristic, complemented, Hall
35	C₃×D₅	—	533	1	no	—
36	D₁₃	—	205	1	no	—
37	AGL(1,𝔽₅)	—	533	1	no	Hall
38	C₃×C₅	—	13	1	no	Hall
39	C₁₃	C₃×#11717962	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	2665	1	no	Hall
41	D₅	—	533	1	no	—
42	C₂×C₃	—	2665	1	no	—
43	C₅	#14523821⋊C₃	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	2665	1	no	Sylow
45	C₃	—	13	1	no	Sylow
46	C₂	—	2665	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₃×C₄₁	C₃×C₄
prime radical	C₅⋊((C₁₃⋊C₃)⋊D₄₁)	C₂
cosocle	D₂₆₆₅	C₂×C₃
LCS	G ▷ C₅×C₁₃×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. #24922524	C₃	semidirect
3. C₅×C₁₃⋊C₃×C₄₁	C₄	semidirect
7. C₅×C₁₃×C₄₁	C₃×C₄	semidirect
10. C₁₃⋊C₃×C₄₁	AGL(1,𝔽₅)	semidirect
16. C₁₃×C₄₁	C₃×AGL(1,𝔽₅)	semidirect
22. C₅×C₄₁	AGL(1,𝔽₁₃)	semidirect
23. C₅×C₁₃⋊C₃	#4223	semidirect
30. C₅×C₁₃	C₃×#4223	semidirect
33. C₄₁	#63121⋊C₃	semidirect
34. C₁₃⋊C₃	#11717962	semidirect
39. C₁₃	C₃×#11717962	semidirect
43. C₅	#14523821⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊((C₁₃⋊C₃)⋊D₄₁)	2
#24922524	3
#14523821⋊C₃	5
C₃×#11717962	13
#63121⋊C₃	41

Subgroups — #24922524⋊C3 #44544355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #24922524⋊C₃ #44544355