Subgroups — C₃×C₆₇×#1043 #34117261

Order 20100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₅×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#1043	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×AGL(1,𝔽₅)×C₆₇	—	5	6	no	maximal
5	C₅⋊D₅×C₆₇	C₂×C₃	1	1	yes	characteristic
6	C₃×D₅×C₆₇	—	5	6	no	—
7	C₅²×C₆₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	AGL(1,𝔽₅)×C₆₇	—	5	6	no	—
9	C₃×C₅×C₆₇	AGL(1,𝔽₅)	1	6	yes	complemented
10	C₃×C₄×C₆₇	—	25	1	no	Hall
11	D₅×C₆₇	—	5	6	no	—
12	C₂×C₃×C₆₇	—	25	1	no	—
13	C₅×C₆₇	C₃×AGL(1,𝔽₅)	1	6	yes	complemented
14	C₃×#1043	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₄×C₆₇	—	25	1	no	Hall
16	C₃×C₆₇	#1043	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₅⋊D₅	C₂×C₆₇	1	1	yes	characteristic
18	C₂×C₆₇	—	25	1	no	—
19	#1043	C₃×C₆₇	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₅²	C₄×C₆₇	1	1	yes	characteristic, complemented, Hall
21	C₆₇	C₃×#1043	1	1	yes	characteristic, direct product factor, Sylow
22	C₃×AGL(1,𝔽₅)	—	5	6	no	—
23	C₅⋊D₅	C₂×C₃×C₆₇	1	1	yes	characteristic
24	C₃×D₅	—	5	6	no	—
25	C₅²	C₃×C₄×C₆₇	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	5	6	no	—
27	C₃×C₅	AGL(1,𝔽₅)×C₆₇	1	6	yes	complemented
28	C₃×C₄	—	25	1	no	Hall
29	D₅	—	5	6	no	—
30	C₂×C₃	—	25	1	no	—
31	C₅	C₃×AGL(1,𝔽₅)×C₆₇	1	6	yes	complemented
32	C₄	—	25	1	no	Sylow
33	C₃	C₆₇×#1043	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₆₇	#1043
commutator, hypocenter	C₅²	C₃×C₄×C₆₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₆₇	C₄
prime radical	C₃×C₅⋊D₅×C₆₇	C₂
cosocle	C₅⋊D₅	C₂×C₃×C₆₇
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₆₇

Complements

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

N	H ≅ G/N	type
2. C₆₇×#1043	C₃	direct (N × H)
3. C₃×C₅²×C₆₇	C₄	semidirect
7. C₅²×C₆₇	C₃×C₄	semidirect
9. C₃×C₅×C₆₇	AGL(1,𝔽₅)	semidirect
13. C₅×C₆₇	C₃×AGL(1,𝔽₅)	semidirect
14. C₃×#1043	C₆₇	direct (N × H)
16. C₃×C₆₇	#1043	direct (N × H)
19. #1043	C₃×C₆₇	direct (N × H)
20. C₃×C₅²	C₄×C₆₇	semidirect
21. C₆₇	C₃×#1043	direct (N × H)
25. C₅²	C₃×C₄×C₆₇	semidirect
27. C₃×C₅	AGL(1,𝔽₅)×C₆₇	semidirect
31. C₅	C₃×AGL(1,𝔽₅)×C₆₇	semidirect
33. C₃	C₆₇×#1043	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅⋊D₅×C₆₇	2
C₆₇×#1043	3
C₃×AGL(1,𝔽₅)×C₆₇	5
C₃×#1043	67

Subgroups — C3×C67×#1043 #34117261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₆₇×#1043 #34117261