Subgroups — C₅×C₁₃×#64418 #34062110

Order 19110.

56 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	C₅×C₇×C₁₃×D₇	—	3	1	no	maximal, Hall
3	C₁₃×#64418	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇²×C₁₃	D₃	1	1	yes	characteristic, complemented, Hall
5	C₁₃×#3862	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×#64418	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₃×ΓL(1,𝔽₈)	—	14	1	no	—
8	C₇×C₁₃×D₇	—	3	1	no	Hall
9	C₂×C₅×C₇×C₁₃	—	21	1	no	—
10	C₅×C₁₃×D₇	—	3	1	no	—
11	C₅×#3862	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₇²×C₁₃	C₅×D₃	1	1	yes	characteristic, complemented, Hall
13	C₅×C₇×D₇	—	3	1	no	Hall
14	C₅×C₇×C₁₃	—	2	1	no	—
15	C₅×C₇×C₁₃	—	3	1	no	—
16	C₅×C₇×C₁₃	—	3	1	no	—
17	C₅×D₃×C₁₃	—	49	1	no	maximal, Hall
18	#64418	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
19	C₁₃×ΓL(1,𝔽₈)	—	14	1	no	—
20	C₅×C₇²	D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₁₃	—	49	1	no	Hall
22	C₂×C₇×C₁₃	—	21	1	no	—
23	C₁₃×D₇	—	3	1	no	—
24	#3862	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₅×C₁₃	—	21	1	no	Hall
26	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
27	C₇×D₇	—	3	1	no	Hall
28	C₇×C₁₃	—	2	1	no	—
29	C₇×C₁₃	—	3	1	no	—
30	C₇×C₁₃	—	3	1	no	—
31	D₃×C₁₃	—	49	1	no	Hall
32	C₂×C₅×C₇	—	21	1	no	—
33	C₅×D₇	—	3	1	no	—
34	C₅×C₁₃	#64418	1	1	yes	characteristic, direct product factor, Hall
35	C₇²	C₅×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
36	C₃×C₁₃	—	49	1	no	Hall
37	C₅×C₇	—	2	1	no	—
38	C₅×C₇	—	3	1	no	—
39	C₅×C₇	—	3	1	no	—
40	C₅×D₃	—	49	1	no	Hall
41	C₂×C₁₃	—	21	1	no	Hall
42	ΓL(1,𝔽₈)	—	14	1	no	—
43	C₃×C₅	—	49	1	no	Hall
44	C₂×C₇	—	21	1	no	—
45	D₇	—	3	1	no	—
46	C₁₃	C₅×#64418	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₅	—	21	1	no	Hall
48	C₇	—	2	1	no	—
49	C₇	—	3	1	no	—
50	C₇	—	3	1	no	—
51	D₃	—	49	1	no	Hall
52	C₅	C₁₃×#64418	1	1	yes	characteristic, direct product factor, Sylow
53	C₃	—	49	1	no	Sylow
54	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₃	#64418
commutator, cosocle, hypocenter	#3862	C₂×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₃	D₃
LCS	G ▷ #3862
UCS	C₁ ◁ C₅×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×#3862	C₂	semidirect
3. C₁₃×#64418	C₅	direct (N × H)
4. C₅×C₇²×C₁₃	D₃	semidirect
5. C₁₃×#3862	C₂×C₅	semidirect
6. C₅×#64418	C₁₃	direct (N × H)
11. C₅×#3862	C₂×C₁₃	semidirect
12. C₇²×C₁₃	C₅×D₃	semidirect
18. #64418	C₅×C₁₃	direct (N × H)
20. C₅×C₇²	D₃×C₁₃	semidirect
24. #3862	C₂×C₅×C₁₃	semidirect
34. C₅×C₁₃	#64418	direct (N × H)
35. C₇²	C₅×D₃×C₁₃	semidirect
46. C₁₃	C₅×#64418	direct (N × H)
52. C₅	C₁₃×#64418	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×#3862	2
C₅×C₇×C₁₃×D₇	3
C₁₃×#64418	5
C₅×#64418	13
C₅×D₃×C₁₃	49

Subgroups — C5×C13×#64418 #34062110

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₃×#64418 #34062110