Subgroups — C₅×#13095532⋊C₂ #29509552

Order 15540.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#13095538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#13095536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#13095532	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₇×D₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₅×#11715912	C₂²	1	1	yes	characteristic, complemented, Hall
6	#13095532⋊C₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₂₅₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×D₇×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₇×D₃₇	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₅×D₃₇⋊C₃	—	7	1	no	maximal, Hall
11	#13095538	C₂×C₅	1	1	yes	characteristic, complemented
12	#13095536	C₂×C₅	1	1	yes	characteristic, complemented
13	#13095532	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×C₇×C₃₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₃₇⋊C₃	—	7	1	no	—
16	C₅×D₃₇⋊C₃	—	7	1	no	—
17	C₅×D₃₇⋊C₃	—	7	1	no	—
18	D₇×D₃₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
19	#11715912	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×D₃₇	—	7	1	no	Hall
21	C₅×C₃₇⋊C₃	—	7	1	no	Hall
22	D₂₅₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
23	C₇×D₃₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
24	D₇×C₃₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
25	C₂×D₃₇⋊C₃	—	7	1	no	Hall
26	C₂×C₅×AGL(1,𝔽₇)	—	37	1	no	maximal, Hall
27	C₂×C₅×C₃₇	—	7	1	no	—
28	C₅×D₃₇	—	7	1	no	—
29	C₅×D₃₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
30	C₇×C₃₇	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
31	C₂×C₃₇⋊C₃	—	7	1	no	—
32	D₃₇⋊C₃	—	7	1	no	—
33	D₃₇⋊C₃	—	7	1	no	—
34	C₂×C₅×ΓL(1,𝔽₈)	—	37	1	no	—
35	C₅×AGL(1,𝔽₇)	—	37	1	no	—
36	C₅×AGL(1,𝔽₇)	—	37	1	no	—
37	C₅×C₃₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
38	C₂×D₃₇	—	7	1	no	Hall
39	C₂×C₅×D₇	—	37	1	no	Hall
40	C₃₇⋊C₃	—	7	1	no	Hall
41	C₅×ΓL(1,𝔽₈)	—	37	1	no	Hall
42	C₂×AGL(1,𝔽₇)	—	37	1	no	Hall
43	C₂×C₃₇	—	7	1	no	—
44	D₃₇	—	7	1	no	—
45	D₃₇	C₅×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
46	C₂×C₅×C₇	—	37	1	no	—
47	C₅×D₇	—	37	1	no	—
48	C₅×D₇	D₃₇⋊C₃	1	1	yes	characteristic, complemented
49	C₂²×C₃×C₅	—	259	1	no	Hall
50	C₂×ΓL(1,𝔽₈)	—	37	1	no	—
51	AGL(1,𝔽₇)	—	37	1	no	—
52	AGL(1,𝔽₇)	—	37	1	no	—
53	C₃₇	C₂×C₅×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
54	C₅×C₇	C₂×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
55	C₂×C₃×C₅	—	259	1	no	—
56	C₂×C₃×C₅	—	259	1	no	—
57	C₂×C₃×C₅	—	259	1	no	—
58	C₂×D₇	—	37	1	no	Hall
59	ΓL(1,𝔽₈)	—	37	1	no	Hall
60	C₂²×C₅	—	259	1	no	Hall
61	C₃×C₅	—	259	1	no	Hall
62	C₂×C₇	—	37	1	no	—
63	D₇	—	37	1	no	—
64	D₇	C₅×D₃₇⋊C₃	1	1	yes	characteristic, complemented
65	C₂²×C₃	—	259	1	no	Hall
66	C₂×C₅	—	259	1	no	—
67	C₂×C₅	—	7	1	no	—
68	C₂×C₅	—	37	1	no	—
69	C₇	C₂×C₅×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	259	1	no	—
71	C₂×C₃	—	259	1	no	—
72	C₂×C₃	—	259	1	no	—
73	C₅	#13095532⋊C₂	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	—	259	1	no	Sylow
75	C₃	—	259	1	no	Sylow
76	C₂	—	259	1	no	—
77	C₂	—	7	1	no	—
78	C₂	—	37	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#13095532⋊C₂
commutator, cosocle, hypocenter	C₇×C₃₇	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₃₇	C₂²×C₃
LCS	G ▷ C₇×C₃₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#13095538	C₂	semidirect
2. C₅×#13095536	C₂	semidirect
3. C₅×#13095532	C₂	semidirect
4. C₅×D₇×D₃₇	C₃	semidirect
5. C₅×#11715912	C₂²	semidirect
6. #13095532⋊C₂	C₅	direct (N × H)
7. C₅×D₂₅₉	C₂×C₃	semidirect
8. C₅×D₇×C₃₇	C₂×C₃	semidirect
9. C₅×C₇×D₃₇	C₂×C₃	semidirect
11. #13095538	C₂×C₅	semidirect
12. #13095536	C₂×C₅	semidirect
13. #13095532	C₂×C₅	semidirect
14. C₅×C₇×C₃₇	C₂²×C₃	semidirect
18. D₇×D₃₇	C₃×C₅	semidirect
19. #11715912	C₂²×C₅	semidirect
22. D₂₅₉	C₂×C₃×C₅	semidirect
23. C₇×D₃₇	C₂×C₃×C₅	semidirect
24. D₇×C₃₇	C₂×C₃×C₅	semidirect
29. C₅×D₃₇	AGL(1,𝔽₇)	semidirect
30. C₇×C₃₇	C₂²×C₃×C₅	semidirect
37. C₅×C₃₇	C₂×AGL(1,𝔽₇)	semidirect
45. D₃₇	C₅×AGL(1,𝔽₇)	semidirect
48. C₅×D₇	D₃₇⋊C₃	semidirect
53. C₃₇	C₂×C₅×AGL(1,𝔽₇)	semidirect
54. C₅×C₇	C₂×D₃₇⋊C₃	semidirect
64. D₇	C₅×D₃₇⋊C₃	semidirect
69. C₇	C₂×C₅×D₃₇⋊C₃	semidirect
73. C₅	#13095532⋊C₂	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×#13095538	2
C₅×#13095536	2
C₅×#13095532	2
C₅×D₇×D₃₇	3
#13095532⋊C₂	5
C₂×C₅×D₃₇⋊C₃	7
C₂×C₅×AGL(1,𝔽₇)	37

Subgroups — C5×#13095532⋊C2 #29509552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13095532⋊C₂ #29509552