Subgroups — D₅×C₁₃×#3861 #34062156

Order 19110.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×#3861	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₅×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₁₃×#3861	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	D₅×C₁₃×ΓL(1,𝔽₈)	—	7	8	no	maximal
6	C₁₃×#3861	D₅	1	1	yes	characteristic, direct product factor, Hall
7	D₅×#3861	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₃×ΓL(1,𝔽₈)	—	7	8	no	—
9	C₂×C₇²×C₁₃	—	5	1	no	Hall
10	C₇×D₅×C₁₃	ΓL(1,𝔽₈)	1	8	yes	complemented
11	C₅×#3861	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₇²×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₃×ΓL(1,𝔽₈)	—	35	8	no	—
14	C₇²×D₅	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
15	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
16	C₃×D₅×C₁₃	—	49	1	no	Hall
17	C₂×#3861	—	5	1	no	Hall
18	C₁₃×ΓL(1,𝔽₈)	—	7	8	no	—
19	C₅×C₇²	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
20	D₅×ΓL(1,𝔽₈)	—	7	8	no	—
21	C₃×C₅×C₁₃	—	49	1	no	Hall
22	C₂×C₇×C₁₃	—	5	8	no	—
23	#3861	D₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
24	D₅×C₁₃	#3861	1	1	yes	characteristic, direct product factor, Hall
25	C₅×ΓL(1,𝔽₈)	—	7	8	no	—
26	C₂×C₇²	—	5	1	no	Hall
27	C₇×C₁₃	D₅×ΓL(1,𝔽₈)	1	8	yes	complemented
28	C₂×C₃×C₁₃	—	245	1	no	Hall
29	C₇×D₅	C₁₃×ΓL(1,𝔽₈)	1	8	yes	complemented
30	C₅×C₁₃	C₂×#3861	1	1	yes	characteristic, complemented, Hall
31	C₇²	C₃×D₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
32	C₂×ΓL(1,𝔽₈)	—	35	8	no	—
33	C₃×C₁₃	—	49	1	no	Hall
34	C₅×C₇	C₂×C₁₃×ΓL(1,𝔽₈)	1	8	yes	complemented
35	C₃×D₅	—	49	1	no	Hall
36	C₂×C₁₃	—	5	1	no	Hall
37	ΓL(1,𝔽₈)	—	7	8	no	—
38	C₃×C₅	—	49	1	no	Hall
39	C₂×C₇	—	5	8	no	—
40	C₁₃	D₅×#3861	1	1	yes	characteristic, direct product factor, Sylow
41	D₅	C₁₃×#3861	1	1	yes	characteristic, direct product factor, Hall
42	C₇	D₅×C₁₃×ΓL(1,𝔽₈)	1	8	yes	complemented
43	C₂×C₃	—	245	1	no	Hall
44	C₅	C₂×C₁₃×#3861	1	1	yes	characteristic, complemented, Sylow
45	C₃	—	49	1	no	Sylow
46	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	D₅×#3861
commutator, cosocle, hypocenter	C₅×C₇²	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₅×C₇²
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×#3861	C₂	semidirect
2. C₇²×D₅×C₁₃	C₃	semidirect
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
6. C₁₃×#3861	D₅	direct (N × H)
7. D₅×#3861	C₁₃	direct (N × H)
10. C₇×D₅×C₁₃	ΓL(1,𝔽₈)	semidirect
11. C₅×#3861	C₂×C₁₃	semidirect
12. C₇²×C₁₃	C₃×D₅	semidirect
14. C₇²×D₅	C₃×C₁₃	semidirect
15. C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
19. C₅×C₇²	C₂×C₃×C₁₃	semidirect
23. #3861	D₅×C₁₃	direct (N × H)
24. D₅×C₁₃	#3861	direct (N × H)
27. C₇×C₁₃	D₅×ΓL(1,𝔽₈)	semidirect
29. C₇×D₅	C₁₃×ΓL(1,𝔽₈)	semidirect
30. C₅×C₁₃	C₂×#3861	semidirect
31. C₇²	C₃×D₅×C₁₃	semidirect
34. C₅×C₇	C₂×C₁₃×ΓL(1,𝔽₈)	semidirect
40. C₁₃	D₅×#3861	direct (N × H)
41. D₅	C₁₃×#3861	direct (N × H)
42. C₇	D₅×C₁₃×ΓL(1,𝔽₈)	semidirect
44. C₅	C₂×C₁₃×#3861	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₃×#3861	2
C₇²×D₅×C₁₃	3
C₂×C₁₃×#3861	5
D₅×C₁₃×ΓL(1,𝔽₈)	7
D₅×#3861	13

Subgroups — D5×C13×#3861 #34062156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₃×#3861 #34062156