Subgroups — C₅×C₁₃×#64424 #34062069

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	C₅×C₁₃×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×#64424	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×C₁₃×AGL(1,𝔽₇)	—	7	8	no	maximal
6	C₁₃×#3861	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×#64424	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₃×ΓL(1,𝔽₈)	—	7	8	no	—
9	C₁₃×C₇⋊D₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₅×C₁₃×D₇	—	7	8	no	—
11	C₅×#3861	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₇²×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
13	C₁₃×AGL(1,𝔽₇)	—	7	8	no	—
14	C₅×C₇⋊D₇	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
15	C₅×C₇×C₁₃	AGL(1,𝔽₇)	1	8	yes	complemented
16	C₂×C₃×C₅×C₁₃	—	49	1	no	Hall
17	#64424	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
18	C₁₃×ΓL(1,𝔽₈)	—	7	8	no	—
19	C₅×C₇²	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
20	C₅×AGL(1,𝔽₇)	—	7	8	no	—
21	C₃×C₅×C₁₃	—	49	1	no	Hall
22	C₁₃×D₇	—	7	8	no	—
23	#3861	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₅×C₁₃	—	49	1	no	Hall
25	C₅×ΓL(1,𝔽₈)	—	7	8	no	—
26	C₇⋊D₇	C₃×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
27	C₇×C₁₃	C₅×AGL(1,𝔽₇)	1	8	yes	complemented
28	C₂×C₃×C₁₃	—	49	1	no	Hall
29	C₅×D₇	—	7	8	no	—
30	C₅×C₁₃	#64424	1	1	yes	characteristic, direct product factor, Hall
31	C₇²	C₂×C₃×C₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
32	AGL(1,𝔽₇)	—	7	8	no	—
33	C₃×C₁₃	—	49	1	no	Hall
34	C₅×C₇	C₁₃×AGL(1,𝔽₇)	1	8	yes	complemented
35	C₂×C₃×C₅	—	49	1	no	Hall
36	C₂×C₁₃	—	49	1	no	Hall
37	ΓL(1,𝔽₈)	—	7	8	no	—
38	C₃×C₅	—	49	1	no	Hall
39	D₇	—	7	8	no	—
40	C₁₃	C₅×#64424	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	—	49	1	no	Hall
42	C₇	C₅×C₁₃×AGL(1,𝔽₇)	1	8	yes	complemented
43	C₂×C₃	—	49	1	no	Hall
44	C₅	C₁₃×#64424	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	49	1	no	Sylow
46	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₃	#64424
commutator, cosocle, hypocenter	C₇²	C₂×C₃×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₅×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×#3861	C₂	semidirect
2. C₅×C₁₃×C₇⋊D₇	C₃	semidirect
3. C₁₃×#64424	C₅	direct (N × H)
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
6. C₁₃×#3861	C₂×C₅	semidirect
7. C₅×#64424	C₁₃	direct (N × H)
9. C₁₃×C₇⋊D₇	C₃×C₅	semidirect
11. C₅×#3861	C₂×C₁₃	semidirect
12. C₇²×C₁₃	C₂×C₃×C₅	semidirect
14. C₅×C₇⋊D₇	C₃×C₁₃	semidirect
15. C₅×C₇×C₁₃	AGL(1,𝔽₇)	semidirect
17. #64424	C₅×C₁₃	direct (N × H)
19. C₅×C₇²	C₂×C₃×C₁₃	semidirect
23. #3861	C₂×C₅×C₁₃	semidirect
26. C₇⋊D₇	C₃×C₅×C₁₃	semidirect
27. C₇×C₁₃	C₅×AGL(1,𝔽₇)	semidirect
30. C₅×C₁₃	#64424	direct (N × H)
31. C₇²	C₂×C₃×C₅×C₁₃	semidirect
34. C₅×C₇	C₁₃×AGL(1,𝔽₇)	semidirect
40. C₁₃	C₅×#64424	direct (N × H)
42. C₇	C₅×C₁₃×AGL(1,𝔽₇)	semidirect
44. C₅	C₁₃×#64424	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×C₁₃×#3861	2
C₅×C₁₃×C₇⋊D₇	3
C₁₃×#64424	5
C₅×C₁₃×AGL(1,𝔽₇)	7
C₅×#64424	13

Subgroups — C5×C13×#64424 #34062069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₃×#64424 #34062069