Subgroups — C₃×C₅×C₁₃×D₄₉ #34062014

Order 19110.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₃×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₃×D₄₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃×D₄₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₃×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₃×D₇	—	7	1	no	maximal
6	C₃×C₁₃×C₄₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×D₄₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₅×C₇×C₁₃	D₇	1	1	yes	characteristic
9	C₁₃×D₄₉	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
10	C₅×C₁₃×D₇	—	7	1	no	—
11	C₃×C₅×C₄₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₄₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₃×D₇	—	7	1	no	—
14	C₅×D₄₉	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₇×C₁₃	C₃×D₇	1	1	yes	characteristic
16	C₂×C₃×C₅×C₁₃	—	49	1	no	Hall
17	C₃×D₄₉	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₇×C₁₃	C₅×D₇	1	1	yes	characteristic
19	C₅×C₄₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
20	C₃×C₅×D₇	—	7	1	no	—
21	C₃×C₅×C₁₃	D₄₉	1	1	yes	characteristic, direct product factor, Hall
22	C₁₃×D₇	—	7	1	no	—
23	C₃×C₄₉	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₅×C₁₃	—	49	1	no	Hall
25	C₃×C₅×C₇	C₁₃×D₇	1	1	yes	characteristic
26	D₄₉	C₃×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
27	C₇×C₁₃	C₃×C₅×D₇	1	1	yes	characteristic
28	C₂×C₃×C₁₃	—	49	1	no	Hall
29	C₅×D₇	—	7	1	no	—
30	C₅×C₁₃	C₃×D₄₉	1	1	yes	characteristic, direct product factor, Hall
31	C₄₉	C₂×C₃×C₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
32	C₃×D₇	—	7	1	no	—
33	C₃×C₁₃	C₅×D₄₉	1	1	yes	characteristic, direct product factor, Hall
34	C₅×C₇	C₃×C₁₃×D₇	1	1	yes	characteristic
35	C₂×C₃×C₅	—	49	1	no	Hall
36	C₂×C₁₃	—	49	1	no	Hall
37	C₃×C₇	C₅×C₁₃×D₇	1	1	yes	characteristic
38	C₃×C₅	C₁₃×D₄₉	1	1	yes	characteristic, direct product factor, Hall
39	D₇	—	7	1	no	—
40	C₁₃	C₃×C₅×D₄₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	—	49	1	no	Hall
42	C₇	C₃×C₅×C₁₃×D₇	1	1	yes	characteristic
43	C₂×C₃	—	49	1	no	Hall
44	C₅	C₃×C₁₃×D₄₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×C₁₃×D₄₉	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₃	D₄₉
commutator, cosocle, hypocenter	C₄₉	C₂×C₃×C₅×C₁₃
Frattini	C₇	C₃×C₅×C₁₃×D₇
Fitting	C₃×C₅×C₁₃×C₄₉	C₂
socle	C₃×C₅×C₇×C₁₃	D₇
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₃×C₅×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₃×C₄₉	C₂	semidirect
2. C₅×C₁₃×D₄₉	C₃	direct (N × H)
3. C₃×C₁₃×D₄₉	C₅	direct (N × H)
4. C₅×C₁₃×C₄₉	C₂×C₃	semidirect
6. C₃×C₁₃×C₄₉	C₂×C₅	semidirect
7. C₃×C₅×D₄₉	C₁₃	direct (N × H)
9. C₁₃×D₄₉	C₃×C₅	direct (N × H)
11. C₃×C₅×C₄₉	C₂×C₁₃	semidirect
12. C₁₃×C₄₉	C₂×C₃×C₅	semidirect
14. C₅×D₄₉	C₃×C₁₃	direct (N × H)
17. C₃×D₄₉	C₅×C₁₃	direct (N × H)
19. C₅×C₄₉	C₂×C₃×C₁₃	semidirect
21. C₃×C₅×C₁₃	D₄₉	direct (N × H)
23. C₃×C₄₉	C₂×C₅×C₁₃	semidirect
26. D₄₉	C₃×C₅×C₁₃	direct (N × H)
30. C₅×C₁₃	C₃×D₄₉	direct (N × H)
31. C₄₉	C₂×C₃×C₅×C₁₃	semidirect
33. C₃×C₁₃	C₅×D₄₉	direct (N × H)
38. C₃×C₅	C₁₃×D₄₉	direct (N × H)
40. C₁₃	C₃×C₅×D₄₉	direct (N × H)
44. C₅	C₃×C₁₃×D₄₉	direct (N × H)
45. C₃	C₅×C₁₃×D₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₃×C₄₉	2
C₅×C₁₃×D₄₉	3
C₃×C₁₃×D₄₉	5
C₃×C₅×C₁₃×D₇	7
C₃×C₅×D₄₉	13

Subgroups — C3×C5×C13×D49 #34062014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₃×D₄₉ #34062014