Subgroups — C₂×C₅×#15690442 #44501371

Order 30660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15690442	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×#13095276	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₇×D₇₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×#13095276	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×#15690442	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₇×D₇₃	C₂×C₃	1	2	yes	complemented
7	C₂×C₅×C₇×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₅×D₇₃⋊C₃	—	7	1	no	maximal, Hall
9	#15690442	C₂×C₅	1	2	yes	direct product factor
10	C₂×#13095276	C₂×C₅	1	1	yes	characteristic, complemented
11	C₅×C₇×C₇₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₅×D₇₃⋊C₃	—	7	2	no	—
13	C₂×C₅×C₇₃⋊C₃	—	7	1	no	—
14	C₂×C₇×D₇₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
15	#13095276	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×D₇₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
17	C₅×C₇₃⋊C₃	—	7	1	no	Hall
18	C₂×C₇×C₇₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
19	C₇×D₇₃	C₂×C₃×C₅	1	2	yes	complemented
20	C₂×D₇₃⋊C₃	—	7	1	no	Hall
21	C₂×C₅×C₇₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
22	C₅×D₇₃	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
23	C₇×C₇₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
24	C₂×C₇₃⋊C₃	—	7	1	no	—
25	D₇₃⋊C₃	—	7	2	no	—
26	C₂²×C₅×ΓL(1,𝔽₈)	—	73	1	no	maximal, Hall
27	C₅×C₇₃	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
28	C₂×D₇₃	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
29	C₇₃⋊C₃	—	7	1	no	Hall
30	C₂×C₅×ΓL(1,𝔽₈)	—	73	2	no	—
31	C₂×C₅×ΓL(1,𝔽₈)	—	73	1	no	—
32	C₂×C₇₃	C₂×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
33	D₇₃	C₂×C₅×ΓL(1,𝔽₈)	1	2	yes	complemented
34	C₂²×C₅×C₇	—	73	1	no	Hall
35	C₅×ΓL(1,𝔽₈)	—	73	1	no	Hall
36	C₂²×ΓL(1,𝔽₈)	—	73	1	no	Hall
37	C₇₃	C₂²×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₅×C₇	—	73	2	no	—
39	C₂×C₅×C₇	D₇₃⋊C₃	1	1	yes	characteristic, complemented
40	C₂²×C₃×C₅	—	511	1	no	Hall
41	C₂×ΓL(1,𝔽₈)	—	73	2	no	—
42	C₂×ΓL(1,𝔽₈)	—	73	1	no	—
43	C₅×C₇	C₂×D₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×C₅	—	511	2	no	—
45	C₂×C₃×C₅	—	511	1	no	—
46	C₂²×C₇	—	73	1	no	Hall
47	ΓL(1,𝔽₈)	—	73	1	no	Hall
48	C₂²×C₅	—	73	1	no	Hall
49	C₃×C₅	—	511	1	no	Hall
50	C₂×C₇	—	73	2	no	—
51	C₂×C₇	C₅×D₇₃⋊C₃	1	1	yes	characteristic, complemented
52	C₂²×C₃	—	511	1	no	Hall
53	C₂×C₅	—	73	2	no	—
54	C₂×C₅	#15690442	1	1	yes	characteristic, direct product factor
55	C₇	C₂×C₅×D₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	—	511	2	no	—
57	C₂×C₃	—	511	1	no	—
58	C₅	C₂×#15690442	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	73	1	no	Sylow
60	C₃	—	511	1	no	Sylow
61	C₂	—	73	2	no	—
62	C₂	C₅×#15690442	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	#15690442
commutator, cosocle, hypocenter	C₇×C₇₃	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₇₃	C₂×C₃
LCS	G ▷ C₇×C₇₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#15690442	C₂	direct (N × H)
2. C₂×C₅×#13095276	C₂	semidirect
3. C₂×C₅×C₇×D₇₃	C₃	semidirect
4. C₅×#13095276	C₂²	semidirect
5. C₂×#15690442	C₅	direct (N × H)
6. C₅×C₇×D₇₃	C₂×C₃	semidirect
7. C₂×C₅×C₇×C₇₃	C₂×C₃	semidirect
9. #15690442	C₂×C₅	direct (N × H)
10. C₂×#13095276	C₂×C₅	semidirect
11. C₅×C₇×C₇₃	C₂²×C₃	semidirect
14. C₂×C₇×D₇₃	C₃×C₅	semidirect
15. #13095276	C₂²×C₅	semidirect
16. C₂×C₅×D₇₃	ΓL(1,𝔽₈)	semidirect
18. C₂×C₇×C₇₃	C₂×C₃×C₅	semidirect
19. C₇×D₇₃	C₂×C₃×C₅	semidirect
21. C₂×C₅×C₇₃	C₂×ΓL(1,𝔽₈)	semidirect
22. C₅×D₇₃	C₂×ΓL(1,𝔽₈)	semidirect
23. C₇×C₇₃	C₂²×C₃×C₅	semidirect
27. C₅×C₇₃	C₂²×ΓL(1,𝔽₈)	semidirect
28. C₂×D₇₃	C₅×ΓL(1,𝔽₈)	semidirect
32. C₂×C₇₃	C₂×C₅×ΓL(1,𝔽₈)	semidirect
33. D₇₃	C₂×C₅×ΓL(1,𝔽₈)	semidirect
37. C₇₃	C₂²×C₅×ΓL(1,𝔽₈)	semidirect
39. C₂×C₅×C₇	D₇₃⋊C₃	semidirect
43. C₅×C₇	C₂×D₇₃⋊C₃	semidirect
51. C₂×C₇	C₅×D₇₃⋊C₃	semidirect
54. C₂×C₅	#15690442	direct (N × H)
55. C₇	C₂×C₅×D₇₃⋊C₃	semidirect
58. C₅	C₂×#15690442	direct (N × H)
62. C₂	C₅×#15690442	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×#15690442	2
C₂×C₅×#13095276	2
C₂×C₅×C₇×D₇₃	3
C₂×#15690442	5
C₂×C₅×D₇₃⋊C₃	7
C₂²×C₅×ΓL(1,𝔽₈)	73

Subgroups — C2×C5×#15690442 #44501371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#15690442 #44501371