Subgroups — D₅×C₁₃⋊#3862 #34062164

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	C₇²×D₅×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₁₃⋊#3862	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	D₅×#63271	—	7	1	no	maximal
6	D₅×#63270	—	7	1	no	maximal
7	C₁₃⋊#3862	D₅	1	1	yes	characteristic, direct product factor, Hall
8	D₅×#3862	—	13	1	no	maximal, Hall
9	C₅×#63270	—	7	1	no	—
10	C₅×#63271	—	7	1	no	—
11	C₂×C₇²×C₁₃	—	5	1	no	Hall
12	C₇×D₅×C₁₃	—	3	2	no	—
13	C₇×D₅×C₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	C₇×D₅×C₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
15	C₅×#3862	—	13	1	no	Hall
16	C₇²×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
17	C₂×#63271	—	35	1	no	—
18	C₂×#63270	—	35	1	no	—
19	C₇²×D₅	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₅×C₇×C₁₃	—	3	2	no	—
21	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
22	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
23	D₅×C₁₃⋊C₃	—	49	1	no	Hall
24	C₂×#3862	—	65	1	no	Hall
25	#63271	—	7	1	no	—
26	#63270	—	7	1	no	—
27	C₅×C₇²	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
28	D₅×ΓL(1,𝔽₈)	—	91	1	no	—
29	D₅×ΓL(1,𝔽₈)	—	91	1	no	—
30	C₅×C₁₃⋊C₃	—	49	1	no	Hall
31	C₂×C₇×C₁₃	—	5	1	no	—
32	C₂×C₇×C₁₃	—	5	1	no	—
33	C₂×C₇×C₁₃	—	15	2	no	—
34	#3862	—	13	1	no	Hall
35	D₅×C₁₃	#3862	1	1	yes	characteristic, complemented, Hall
36	C₅×ΓL(1,𝔽₈)	—	91	1	no	—
37	C₅×ΓL(1,𝔽₈)	—	91	1	no	—
38	C₂×C₇²	—	5	1	no	Hall
39	C₇×C₁₃	—	3	2	no	—
40	C₇×C₁₃	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
41	C₇×C₁₃	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
42	C₂×C₁₃⋊C₃	—	245	1	no	Hall
43	C₇×D₅	—	3	2	no	—
44	C₇×D₅	#63270	1	1	yes	characteristic, complemented
45	C₇×D₅	#63271	1	1	yes	characteristic, complemented
46	C₅×C₁₃	C₂×#3862	1	1	yes	characteristic, complemented, Hall
47	C₇²	D₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
48	C₂×ΓL(1,𝔽₈)	—	455	1	no	—
49	C₂×ΓL(1,𝔽₈)	—	455	1	no	—
50	C₁₃⋊C₃	—	49	1	no	Hall
51	C₅×C₇	—	3	2	no	—
52	C₅×C₇	C₂×#63270	1	1	yes	characteristic, complemented
53	C₅×C₇	C₂×#63271	1	1	yes	characteristic, complemented
54	C₃×D₅	—	637	1	no	Hall
55	C₂×C₁₃	—	5	1	no	Hall
56	ΓL(1,𝔽₈)	—	91	1	no	—
57	ΓL(1,𝔽₈)	—	91	1	no	—
58	C₃×C₅	—	637	1	no	Hall
59	C₂×C₇	—	5	1	no	—
60	C₂×C₇	—	5	1	no	—
61	C₂×C₇	—	15	2	no	—
62	C₁₃	D₅×#3862	1	1	yes	characteristic, complemented, Sylow
63	D₅	C₁₃⋊#3862	1	1	yes	characteristic, direct product factor, Hall
64	C₇	—	3	2	no	—
65	C₇	D₅×#63270	1	1	yes	characteristic, complemented
66	C₇	D₅×#63271	1	1	yes	characteristic, complemented
67	C₂×C₃	—	3185	1	no	Hall
68	C₅	C₂×C₁₃⋊#3862	1	1	yes	characteristic, complemented, Sylow
69	C₃	—	637	1	no	Sylow
70	C₂	—	5	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃⋊#3862	C₂	semidirect
2. C₇²×D₅×C₁₃	C₃	semidirect
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
7. C₁₃⋊#3862	D₅	direct (N × H)
13. C₇×D₅×C₁₃	ΓL(1,𝔽₈)	semidirect
14. C₇×D₅×C₁₃	ΓL(1,𝔽₈)	semidirect
16. C₇²×C₁₃	C₃×D₅	semidirect
19. C₇²×D₅	C₁₃⋊C₃	semidirect
21. C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
22. C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
27. C₅×C₇²	C₂×C₁₃⋊C₃	semidirect
35. D₅×C₁₃	#3862	semidirect
40. C₇×C₁₃	D₅×ΓL(1,𝔽₈)	semidirect
41. C₇×C₁₃	D₅×ΓL(1,𝔽₈)	semidirect
44. C₇×D₅	#63270	semidirect
45. C₇×D₅	#63271	semidirect
46. C₅×C₁₃	C₂×#3862	semidirect
47. C₇²	D₅×C₁₃⋊C₃	semidirect
52. C₅×C₇	C₂×#63270	semidirect
53. C₅×C₇	C₂×#63271	semidirect
62. C₁₃	D₅×#3862	semidirect
63. D₅	C₁₃⋊#3862	direct (N × H)
65. C₇	D₅×#63270	semidirect
66. C₇	D₅×#63271	semidirect
68. C₅	C₂×C₁₃⋊#3862	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
C₇²×D₅×C₁₃	3
C₂×C₁₃⋊#3862	5
D₅×#63271	7
D₅×#63270	7
D₅×#3862	13

Subgroups — D5×C13⋊#3862 #34062164

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₃⋊#3862 #34062164