Subgroups — (C₄₃⋊C₃)⋊#1042 #27166408

Order 12900.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃⋊#1042	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₄₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	(C₄₃⋊C₃)⋊AGL(1,𝔽₅)	—	5	1	no	maximal
5	(C₄₃⋊C₃)⋊Dic₅	—	5	1	no	maximal
6	C₅×D₅×C₄₃	C₂×C₃	1	1	yes	characteristic
7	C₂×C₅×C₄₃⋊C₃	—	5	1	no	—
8	D₅×C₄₃⋊C₃	D₅	1	1	yes	characteristic
9	C₅²×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
10	C₄₃⋊AGL(1,𝔽₅)	—	5	1	no	—
11	Dic₂₁₅	—	5	1	no	—
12	C₅×C₄₃⋊C₃	—	4	1	no	—
13	C₅×C₄₃⋊C₃	Dic₅	1	1	yes	characteristic, complemented
14	C₅×C₄₃⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
15	(C₄₃⋊C₃)⋊C₄	—	25	1	no	Hall
16	C₂×C₅×C₄₃	—	5	1	no	—
17	D₅×C₄₃	C₃×D₅	1	1	yes	characteristic
18	C₃×#1042	—	43	1	no	maximal, Hall
19	C₂×C₄₃⋊C₃	—	5	1	no	—
20	C₅×C₄₃	—	4	1	no	—
21	C₅×C₄₃	C₃×Dic₅	1	1	yes	characteristic, complemented
22	C₅×C₄₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
23	Dic₄₃	—	25	1	no	Hall
24	C₃×C₅×D₅	—	43	1	no	—
25	C₄₃⋊C₃	#1042	1	1	yes	characteristic, complemented, Hall
26	#1042	—	43	1	no	Hall
27	C₂×C₄₃	—	5	1	no	—
28	C₃×C₅²	—	43	1	no	Hall
29	C₃×AGL(1,𝔽₅)	—	215	1	no	—
30	C₃×Dic₅	—	215	1	no	—
31	C₅×D₅	D₄₃⋊C₃	1	1	yes	characteristic
32	C₄₃	C₃×#1042	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃×C₅	—	215	1	no	—
34	C₃×D₅	—	43	1	no	—
35	C₅²	(C₄₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
36	AGL(1,𝔽₅)	—	215	1	no	—
37	Dic₅	—	215	1	no	—
38	C₃×C₅	—	43	1	no	—
39	C₃×C₅	—	43	1	no	—
40	C₃×C₅	—	172	1	no	—
41	C₃×C₄	—	1075	1	no	Hall
42	C₂×C₅	—	5	1	no	—
43	D₅	C₅⋊(D₄₃⋊C₃)	1	1	yes	characteristic
44	C₂×C₃	—	215	1	no	—
45	C₅	—	4	1	no	—
46	C₅	(C₄₃⋊C₃)⋊Dic₅	1	1	yes	characteristic, complemented
47	C₅	(C₄₃⋊C₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
48	C₄	—	1075	1	no	Sylow
49	C₃	—	43	1	no	Sylow
50	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₄₃	C₃×C₄
prime radical	C₅×D₅×C₄₃⋊C₃	C₂
cosocle	C₅×D₅×C₄₃	C₂×C₃
LCS	G ▷ C₅²×C₄₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₄₃⋊#1042	C₃	semidirect
3. C₅²×C₄₃⋊C₃	C₄	semidirect
9. C₅²×C₄₃	C₃×C₄	semidirect
13. C₅×C₄₃⋊C₃	Dic₅	semidirect
14. C₅×C₄₃⋊C₃	AGL(1,𝔽₅)	semidirect
21. C₅×C₄₃	C₃×Dic₅	semidirect
22. C₅×C₄₃	C₃×AGL(1,𝔽₅)	semidirect
25. C₄₃⋊C₃	#1042	semidirect
32. C₄₃	C₃×#1042	semidirect
35. C₅²	(C₄₃⋊C₃)⋊C₄	semidirect
46. C₅	(C₄₃⋊C₃)⋊Dic₅	semidirect
47. C₅	(C₄₃⋊C₃)⋊AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₅×C₄₃⋊C₃	2
C₄₃⋊#1042	3
(C₄₃⋊C₃)⋊AGL(1,𝔽₅)	5
(C₄₃⋊C₃)⋊Dic₅	5
C₃×#1042	43

Subgroups — (C43⋊C3)⋊#1042 #27166408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₄₃⋊C₃)⋊#1042 #27166408