Subgroups — C₄₉×C₅⋊(D₁₃⋊C₃) #34062044

Order 19110.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃⋊C₃×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₉×D₆₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₉×D₁₃⋊C₃	—	5	1	no	maximal, Hall
4	C₅×C₁₃×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₇×C₅⋊(D₁₃⋊C₃)	C₇	1	1	yes	maximal, characteristic
6	C₁₃⋊C₃×C₄₉	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×D₅×C₄₉	—	13	1	no	maximal, Hall
8	C₅×C₇×C₁₃⋊C₃	C₂×C₇	1	1	yes	characteristic
9	D₁₃×C₄₉	—	5	1	no	Hall
10	C₇×D₆₅	C₃×C₇	1	1	yes	characteristic
11	C₃×C₅×C₄₉	—	13	1	no	Hall
12	C₁₃×C₄₉	C₃×D₅	1	1	yes	characteristic, complemented, Hall
13	C₇×D₁₃⋊C₃	—	5	1	no	—
14	D₅×C₄₉	—	13	1	no	Hall
15	C₅×C₇×C₁₃	C₂×C₃×C₇	1	1	yes	characteristic
16	C₅⋊(D₁₃⋊C₃)	C₄₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₄₉	—	65	1	no	Hall
18	C₇×C₁₃⋊C₃	C₇×D₅	1	1	yes	characteristic
19	C₅×C₄₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₃×C₇×D₅	—	13	1	no	—
21	C₅×C₁₃⋊C₃	C₂×C₄₉	1	1	yes	characteristic, complemented, Hall
22	C₇×D₁₃	—	5	1	no	—
23	C₃×C₄₉	—	13	1	no	Hall
24	D₆₅	C₃×C₄₉	1	1	yes	characteristic, complemented, Hall
25	C₃×C₅×C₇	—	13	1	no	—
26	C₂×C₄₉	—	65	1	no	Hall
27	C₇×C₁₃	C₃×C₇×D₅	1	1	yes	characteristic
28	D₁₃⋊C₃	—	5	1	no	Hall
29	C₇×D₅	—	13	1	no	—
30	C₅×C₁₃	C₂×C₃×C₄₉	1	1	yes	characteristic, complemented, Hall
31	C₄₉	C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₃×C₇	—	65	1	no	—
33	C₁₃⋊C₃	D₅×C₄₉	1	1	yes	characteristic, complemented, Hall
34	C₅×C₇	C₇×D₁₃⋊C₃	1	1	yes	characteristic
35	C₃×D₅	—	13	1	no	Hall
36	D₁₃	—	5	1	no	Hall
37	C₃×C₇	—	13	1	no	—
38	C₃×C₅	—	13	1	no	Hall
39	C₂×C₇	—	65	1	no	—
40	C₁₃	C₃×D₅×C₄₉	1	1	yes	characteristic, complemented, Sylow
41	D₅	—	13	1	no	Hall
42	C₇	C₇×C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic
43	C₂×C₃	—	65	1	no	Hall
44	C₅	C₄₉×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
45	C₃	—	13	1	no	Sylow
46	C₂	—	65	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₉	C₅⋊(D₁₃⋊C₃)
commutator, hypocenter	C₅×C₁₃	C₂×C₃×C₄₉
Frattini	C₇	C₇×C₅⋊(D₁₃⋊C₃)
Fitting	C₅×C₁₃×C₄₉	C₂×C₃
socle, cosocle	C₅×C₇×C₁₃	C₂×C₃×C₇
prime radical	C₇×C₅⋊(D₁₃⋊C₃)	C₇
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₄₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃⋊C₃×C₄₉	C₂	semidirect
2. C₄₉×D₆₅	C₃	semidirect
4. C₅×C₁₃×C₄₉	C₂×C₃	semidirect
6. C₁₃⋊C₃×C₄₉	D₅	semidirect
12. C₁₃×C₄₉	C₃×D₅	semidirect
16. C₅⋊(D₁₃⋊C₃)	C₄₉	direct (N × H)
19. C₅×C₄₉	D₁₃⋊C₃	semidirect
21. C₅×C₁₃⋊C₃	C₂×C₄₉	semidirect
24. D₆₅	C₃×C₄₉	semidirect
30. C₅×C₁₃	C₂×C₃×C₄₉	semidirect
31. C₄₉	C₅⋊(D₁₃⋊C₃)	direct (N × H)
33. C₁₃⋊C₃	D₅×C₄₉	semidirect
40. C₁₃	C₃×D₅×C₄₉	semidirect
44. C₅	C₄₉×D₁₃⋊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×C₄₉	2
C₄₉×D₆₅	3
C₄₉×D₁₃⋊C₃	5
C₇×C₅⋊(D₁₃⋊C₃)	7
C₃×D₅×C₄₉	13

Subgroups — C49×C5⋊(D13⋊C3) #34062044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₉×C₅⋊(D₁₃⋊C₃) #34062044