Subgroups — C₂×C₅×#15690445 #44501367

Order 30660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15690445	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×#13095275	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₇×C₇₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×#13095275	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×#15690445	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₇×C₇₃	C₂×C₃	1	2	yes	complemented
7	C₂×C₅×C₇×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂²×C₅×C₇₃⋊C₃	—	7	1	no	maximal, Hall
9	#15690445	C₂×C₅	1	2	yes	direct product factor
10	C₂×#13095275	C₂×C₅	1	1	yes	characteristic, complemented
11	C₅×C₇×C₇₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₇₃⋊C₃	—	7	2	no	—
13	C₂×C₅×C₇₃⋊C₃	—	7	1	no	—
14	C₂×D₇×C₇₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
15	#13095275	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₅×C₇₃	—	7	1	no	Hall
17	C₅×C₇₃⋊C₃	—	7	1	no	Hall
18	C₂×C₇×C₇₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
19	D₇×C₇₃	C₂×C₃×C₅	1	2	yes	complemented
20	C₂²×C₇₃⋊C₃	—	7	1	no	Hall
21	C₂×C₅×C₇₃	—	7	2	no	—
22	C₂×C₅×C₇₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
23	C₇×C₇₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
24	C₂×C₇₃⋊C₃	—	7	2	no	—
25	C₂×C₇₃⋊C₃	—	7	1	no	—
26	C₂×C₅×AGL(1,𝔽₇)	—	73	1	no	maximal, Hall
27	C₅×C₇₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₇₃	—	7	1	no	Hall
29	C₇₃⋊C₃	—	7	1	no	Hall
30	C₂×C₅×ΓL(1,𝔽₈)	—	73	1	no	—
31	C₅×AGL(1,𝔽₇)	—	73	2	no	—
32	C₂×C₇₃	—	7	2	no	—
33	C₂×C₇₃	C₅×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
34	C₂×C₅×D₇	C₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
35	C₅×ΓL(1,𝔽₈)	—	73	1	no	Hall
36	C₂×AGL(1,𝔽₇)	—	73	1	no	Hall
37	C₇₃	C₂×C₅×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₅×C₇	C₂×C₇₃⋊C₃	1	1	yes	characteristic, complemented
39	C₅×D₇	C₂×C₇₃⋊C₃	1	2	yes	complemented
40	C₂²×C₃×C₅	—	511	1	no	Hall
41	C₂×ΓL(1,𝔽₈)	—	73	1	no	—
42	AGL(1,𝔽₇)	—	73	2	no	—
43	C₅×C₇	C₂²×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×C₅	—	511	2	no	—
45	C₂×C₃×C₅	—	511	1	no	—
46	C₂×D₇	C₅×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
47	ΓL(1,𝔽₈)	—	73	1	no	Hall
48	C₂²×C₅	—	7	1	no	Hall
49	C₃×C₅	—	511	1	no	Hall
50	C₂×C₇	C₂×C₅×C₇₃⋊C₃	1	1	yes	characteristic, complemented
51	D₇	C₂×C₅×C₇₃⋊C₃	1	2	yes	complemented
52	C₂²×C₃	—	511	1	no	Hall
53	C₂×C₅	—	7	2	no	—
54	C₂×C₅	#15690445	1	1	yes	characteristic, direct product factor
55	C₇	C₂²×C₅×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	—	511	2	no	—
57	C₂×C₃	—	511	1	no	—
58	C₅	C₂×#15690445	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	7	1	no	Sylow
60	C₃	—	511	1	no	Sylow
61	C₂	—	7	2	no	—
62	C₂	C₅×#15690445	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	#15690445
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×#15690445	C₂	direct (N × H)
2. C₂×C₅×#13095275	C₂	semidirect
3. C₂×C₅×D₇×C₇₃	C₃	semidirect
4. C₅×#13095275	C₂²	semidirect
5. C₂×#15690445	C₅	direct (N × H)
6. C₅×D₇×C₇₃	C₂×C₃	semidirect
7. C₂×C₅×C₇×C₇₃	C₂×C₃	semidirect
9. #15690445	C₂×C₅	direct (N × H)
10. C₂×#13095275	C₂×C₅	semidirect
11. C₅×C₇×C₇₃	C₂²×C₃	semidirect
14. C₂×D₇×C₇₃	C₃×C₅	semidirect
15. #13095275	C₂²×C₅	semidirect
18. C₂×C₇×C₇₃	C₂×C₃×C₅	semidirect
19. D₇×C₇₃	C₂×C₃×C₅	semidirect
22. C₂×C₅×C₇₃	AGL(1,𝔽₇)	semidirect
23. C₇×C₇₃	C₂²×C₃×C₅	semidirect
27. C₅×C₇₃	C₂×AGL(1,𝔽₇)	semidirect
33. C₂×C₇₃	C₅×AGL(1,𝔽₇)	semidirect
34. C₂×C₅×D₇	C₇₃⋊C₃	semidirect
37. C₇₃	C₂×C₅×AGL(1,𝔽₇)	semidirect
38. C₂×C₅×C₇	C₂×C₇₃⋊C₃	semidirect
39. C₅×D₇	C₂×C₇₃⋊C₃	semidirect
43. C₅×C₇	C₂²×C₇₃⋊C₃	semidirect
46. C₂×D₇	C₅×C₇₃⋊C₃	semidirect
50. C₂×C₇	C₂×C₅×C₇₃⋊C₃	semidirect
51. D₇	C₂×C₅×C₇₃⋊C₃	semidirect
54. C₂×C₅	#15690445	direct (N × H)
55. C₇	C₂²×C₅×C₇₃⋊C₃	semidirect
58. C₅	C₂×#15690445	direct (N × H)
62. C₂	C₅×#15690445	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×#15690445	2
C₂×C₅×#13095275	2
C₂×C₅×D₇×C₇₃	3
C₂×#15690445	5
C₂²×C₅×C₇₃⋊C₃	7
C₂×C₅×AGL(1,𝔽₇)	73

Subgroups — C2×C5×#15690445 #44501367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#15690445 #44501367