Subgroups — C₁₃×C₅⋊#64425 #34062134

Order 19110.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×#3862	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×C₅⋊(C₇⋊D₇)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×#64425	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₃×C₅⋊AGL(1,𝔽₇)	—	7	2	no	maximal
6	C₁₃×#3862	D₅	1	1	yes	characteristic, complemented, Hall
7	C₅⋊#64425	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₃×ΓL(1,𝔽₈)	—	7	2	no	—
9	C₁₃×C₇⋊D₇	—	5	1	no	Hall
10	C₁₃×D₃₅	—	7	2	no	—
11	C₁₃×D₃₅	—	21	2	no	—
12	C₅×#3862	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₇²×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
14	C₁₃×AGL(1,𝔽₇)	—	35	2	no	—
15	C₅⋊(C₇⋊D₇)	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
16	C₅×C₇×C₁₃	—	3	2	no	—
17	C₅×C₇×C₁₃	AGL(1,𝔽₇)	1	2	yes	complemented
18	C₃×D₅×C₁₃	—	49	1	no	Hall
19	#64425	—	5	1	no	Hall
20	C₁₃×ΓL(1,𝔽₈)	—	7	2	no	—
21	C₅×C₇²	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
22	C₅⋊AGL(1,𝔽₇)	—	7	2	no	—
23	C₃×C₅×C₁₃	—	49	1	no	Hall
24	C₁₃×D₇	—	35	2	no	—
25	C₁₃×D₇	—	105	2	no	—
26	#3862	D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
27	D₅×C₁₃	—	49	1	no	Hall
28	C₅×ΓL(1,𝔽₈)	—	7	2	no	—
29	C₇⋊D₇	—	5	1	no	Hall
30	C₇×C₁₃	—	3	2	no	—
31	C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	1	2	yes	complemented
32	C₂×C₃×C₁₃	—	245	1	no	Hall
33	D₃₅	—	7	2	no	—
34	D₃₅	—	21	2	no	—
35	C₅×C₁₃	#64425	1	1	yes	characteristic, complemented, Hall
36	C₇²	C₃×D₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
37	AGL(1,𝔽₇)	—	35	2	no	—
38	C₃×C₁₃	—	49	1	no	Hall
39	C₅×C₇	—	3	2	no	—
40	C₅×C₇	C₁₃×AGL(1,𝔽₇)	1	2	yes	complemented
41	C₃×D₅	—	49	1	no	Hall
42	C₂×C₁₃	—	245	1	no	Hall
43	ΓL(1,𝔽₈)	—	7	2	no	—
44	C₃×C₅	—	49	1	no	Hall
45	D₇	—	35	2	no	—
46	D₇	—	105	2	no	—
47	C₁₃	C₅⋊#64425	1	1	yes	characteristic, direct product factor, Sylow
48	D₅	—	49	1	no	Hall
49	C₇	—	3	2	no	—
50	C₇	C₁₃×C₅⋊AGL(1,𝔽₇)	1	2	yes	complemented
51	C₂×C₃	—	245	1	no	Hall
52	C₅	C₁₃×#64425	1	1	yes	characteristic, complemented, Sylow
53	C₃	—	49	1	no	Sylow
54	C₂	—	245	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	C₅⋊#64425
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×#3862	C₂	semidirect
2. C₁₃×C₅⋊(C₇⋊D₇)	C₃	semidirect
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
6. C₁₃×#3862	D₅	semidirect
7. C₅⋊#64425	C₁₃	direct (N × H)
12. C₅×#3862	C₂×C₁₃	semidirect
13. C₇²×C₁₃	C₃×D₅	semidirect
15. C₅⋊(C₇⋊D₇)	C₃×C₁₃	semidirect
17. C₅×C₇×C₁₃	AGL(1,𝔽₇)	semidirect
21. C₅×C₇²	C₂×C₃×C₁₃	semidirect
26. #3862	D₅×C₁₃	semidirect
31. C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	semidirect
35. C₅×C₁₃	#64425	semidirect
36. C₇²	C₃×D₅×C₁₃	semidirect
40. C₅×C₇	C₁₃×AGL(1,𝔽₇)	semidirect
47. C₁₃	C₅⋊#64425	direct (N × H)
50. C₇	C₁₃×C₅⋊AGL(1,𝔽₇)	semidirect
52. C₅	C₁₃×#64425	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₃×#3862	2
C₁₃×C₅⋊(C₇⋊D₇)	3
C₁₃×#64425	5
C₁₃×C₅⋊AGL(1,𝔽₇)	7
C₅⋊#64425	13

Subgroups — C13×C5⋊#64425 #34062134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₅⋊#64425 #34062134