Subgroups — (C₄₉⋊C₃)⋊#1043 #28412928

Order 14700.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₅×C₄₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄₉⋊#1043	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₄₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	(C₄₉⋊C₃)⋊AGL(1,𝔽₅)	—	5	6	no	maximal
5	C₄₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	ΓL(1,𝔽₈)⋊#1043	—	7	1	no	maximal
7	D₅×C₄₉⋊C₃	—	5	6	no	—
8	C₅²×C₄₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	ΓL(1,𝔽₈)×C₅⋊D₅	—	7	1	no	—
10	C₄₉⋊AGL(1,𝔽₅)	—	5	6	no	—
11	C₅×C₄₉⋊C₃	AGL(1,𝔽₅)	1	6	yes	complemented
12	C₇⋊#1043	—	7	1	no	—
13	(C₄₉⋊C₃)⋊C₄	—	25	1	no	Hall
14	C₅²×ΓL(1,𝔽₈)	—	7	1	no	—
15	D₅×C₄₉	—	5	6	no	—
16	ΓL(1,𝔽₈)⋊AGL(1,𝔽₅)	—	35	6	no	—
17	C₇×C₅⋊D₅	AGL(1,𝔽₇)	1	1	yes	characteristic
18	C₃×#1043	—	49	1	no	Hall
19	C₂×C₄₉⋊C₃	—	25	1	no	—
20	C₅×C₄₉	C₃×AGL(1,𝔽₅)	1	6	yes	complemented
21	D₅×ΓL(1,𝔽₈)	—	35	6	no	—
22	Dic₄₉	—	25	1	no	Hall
23	C₅²×C₇	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
24	C₃×C₅⋊D₅	—	49	1	no	—
25	C₄₉⋊C₃	#1043	1	1	yes	characteristic, complemented, Hall
26	C₇⋊AGL(1,𝔽₅)	—	35	6	no	—
27	C₅×ΓL(1,𝔽₈)	—	7	6	no	—
28	#1043	—	49	1	no	Hall
29	C₂×C₄₉	—	25	1	no	—
30	ΓL(1,𝔽₈)⋊C₄	—	175	1	no	—
31	C₃×C₅²	—	49	1	no	Hall
32	C₇×D₅	—	5	6	no	—
33	C₃×AGL(1,𝔽₅)	—	245	6	no	—
34	C₅⋊D₅	D₄₉⋊C₃	1	1	yes	characteristic
35	C₄₉	C₃×#1043	1	1	yes	characteristic, complemented, Sylow
36	C₂×ΓL(1,𝔽₈)	—	175	1	no	—
37	C₅×C₇	ΓL(1,𝔽₈)⋊AGL(1,𝔽₅)	1	6	yes	—
38	C₃×D₅	—	245	6	no	—
39	Dic₇	—	175	1	no	—
40	C₅²	(C₄₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
41	ΓL(1,𝔽₈)	—	7	1	no	—
42	AGL(1,𝔽₅)	—	245	6	no	—
43	C₃×C₅	—	49	6	no	—
44	C₂×C₇	—	25	1	no	—
45	C₃×C₄	—	1225	1	no	Hall
46	D₅	—	5	6	no	—
47	C₇	ΓL(1,𝔽₈)⋊#1043	1	1	yes	characteristic
48	C₂×C₃	—	1225	1	no	—
49	C₅	(C₄₉⋊C₃)⋊AGL(1,𝔽₅)	1	6	yes	complemented
50	C₄	—	1225	1	no	Sylow
51	C₃	—	49	1	no	Sylow
52	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅²×C₄₉	C₃×C₄
Frattini	C₇	ΓL(1,𝔽₈)⋊#1043
socle	C₅²×C₇	ΓL(1,𝔽₈)⋊C₄
prime radical	C₅⋊D₅×C₄₉⋊C₃	C₂
cosocle	C₄₉×C₅⋊D₅	C₂×C₃
LCS	G ▷ C₅²×C₄₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₄₉⋊#1043	C₃	semidirect
3. C₅²×C₄₉⋊C₃	C₄	semidirect
8. C₅²×C₄₉	C₃×C₄	semidirect
11. C₅×C₄₉⋊C₃	AGL(1,𝔽₅)	semidirect
20. C₅×C₄₉	C₃×AGL(1,𝔽₅)	semidirect
25. C₄₉⋊C₃	#1043	semidirect
35. C₄₉	C₃×#1043	semidirect
40. C₅²	(C₄₉⋊C₃)⋊C₄	semidirect
49. C₅	(C₄₉⋊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×C₄₉⋊C₃	2
C₄₉⋊#1043	3
(C₄₉⋊C₃)⋊AGL(1,𝔽₅)	5
ΓL(1,𝔽₈)⋊#1043	7

Subgroups — (C49⋊C3)⋊#1043 #28412928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₄₉⋊C₃)⋊#1043 #28412928