Subgroups — C₂×C₅⋊(D₂₉⋊C₄₉) #43249247

Order 28420.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊(D₂₉⋊C₄₉)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₂₉⋊C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₂₉⋊C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₂₉⋊C₄₉	—	5	1	no	maximal, Hall
5	C₂×C₇×D₁₄₅	C₇	1	1	yes	maximal, characteristic
6	C₂×C₂₉⋊C₄₉	D₅	1	1	yes	characteristic, complemented
7	D₂₉⋊C₄₉	—	5	2	no	—
8	C₇×D₁₄₅	C₂×C₇	1	2	yes	—
9	C₂×C₅×C₇×C₂₉	C₂×C₇	1	1	yes	characteristic
10	C₂₉⋊C₄₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₇×C₂₉	C₂²×C₇	1	1	yes	characteristic
12	C₂×D₅×C₄₉	—	29	1	no	maximal, Hall
13	C₂×C₇×D₂₉	—	5	1	no	—
14	C₂×D₁₄₅	C₄₉	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₄₉	—	29	1	no	—
16	D₅×C₄₉	—	29	2	no	—
17	C₂×C₇×C₂₉	C₇×D₅	1	1	yes	characteristic
18	C₇×D₂₉	—	5	2	no	—
19	C₂×C₅×C₂₉	C₂×C₄₉	1	1	yes	characteristic, complemented
20	D₁₄₅	C₂×C₄₉	1	2	yes	complemented
21	C₅×C₄₉	—	29	1	no	Hall
22	C₇×C₂₉	C₂×C₇×D₅	1	1	yes	characteristic
23	C₂²×C₄₉	—	145	1	no	Hall
24	C₅×C₂₉	C₂²×C₄₉	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇×D₅	—	203	1	no	—
26	C₂×D₂₉	—	5	1	no	Hall
27	C₂×C₄₉	—	29	1	no	—
28	C₂×C₄₉	—	145	2	no	—
29	C₂×C₅×C₇	D₂₉⋊C₇	1	1	yes	characteristic
30	C₇×D₅	—	203	2	no	—
31	C₂×C₂₉	D₅×C₄₉	1	1	yes	characteristic, complemented
32	D₂₉	—	5	2	no	—
33	C₄₉	—	29	1	no	Sylow
34	C₅×C₇	C₂×D₂₉⋊C₇	1	1	yes	characteristic
35	C₂₉	C₂×D₅×C₄₉	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₇	—	1015	1	no	—
37	C₂×D₅	—	203	1	no	Hall
38	C₂×C₇	—	1015	2	no	—
39	C₂×C₇	C₅⋊(D₂₉⋊C₇)	1	1	yes	characteristic
40	C₂×C₅	D₂₉⋊C₄₉	1	1	yes	characteristic, complemented
41	D₅	—	203	2	no	—
42	C₇	C₂×C₅⋊(D₂₉⋊C₇)	1	1	yes	characteristic
43	C₅	C₂×D₂₉⋊C₄₉	1	1	yes	characteristic, complemented, Sylow
44	C₂²	—	1015	1	no	Sylow
45	C₂	—	1015	2	no	—
46	C₂	C₅⋊(D₂₉⋊C₄₉)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	C₅⋊(D₂₉⋊C₇)
commutator, hypocenter	C₅×C₂₉	C₂²×C₄₉
Frattini	C₇	C₂×C₅⋊(D₂₉⋊C₇)
Fitting, socle	C₂×C₅×C₇×C₂₉	C₂×C₇
prime radical	C₂×C₇×D₁₄₅	C₇
cosocle	C₅×C₇×C₂₉	C₂²×C₇
LCS	G ▷ C₅×C₂₉
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₅⋊(D₂₉⋊C₄₉)	C₂	direct (N × H)
2. C₂×C₅×C₂₉⋊C₄₉	C₂	semidirect
3. C₅×C₂₉⋊C₄₉	C₂²	semidirect
6. C₂×C₂₉⋊C₄₉	D₅	semidirect
10. C₂₉⋊C₄₉	C₂×D₅	semidirect
14. C₂×D₁₄₅	C₄₉	semidirect
19. C₂×C₅×C₂₉	C₂×C₄₉	semidirect
20. D₁₄₅	C₂×C₄₉	semidirect
24. C₅×C₂₉	C₂²×C₄₉	semidirect
31. C₂×C₂₉	D₅×C₄₉	semidirect
35. C₂₉	C₂×D₅×C₄₉	semidirect
40. C₂×C₅	D₂₉⋊C₄₉	semidirect
43. C₅	C₂×D₂₉⋊C₄₉	semidirect
46. C₂	C₅⋊(D₂₉⋊C₄₉)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅⋊(D₂₉⋊C₄₉)	2
C₂×C₅×C₂₉⋊C₄₉	2
C₂×D₂₉⋊C₄₉	5
C₂×C₇×D₁₄₅	7
C₂×D₅×C₄₉	29

Subgroups — C2×C5⋊(D29⋊C49) #43249247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅⋊(D₂₉⋊C₄₉) #43249247