Subgroups — C₂×C₅²×#3861 #20301310

Order 7350.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×#3861	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅²×C₇²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₅×#3861	C₅	1	6	yes	maximal, direct product factor
4	C₅²×C₇²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅²×ΓL(1,𝔽₈)	—	7	8	no	maximal
6	C₅×#3861	C₂×C₅	1	6	yes	direct product factor
7	C₅²×ΓL(1,𝔽₈)	—	7	8	no	—
8	C₂×C₅×C₇²	C₃×C₅	1	6	yes	complemented
9	C₂×C₅²×C₇	ΓL(1,𝔽₈)	1	8	yes	complemented
10	C₂×#3861	C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₅×C₇²	C₂×C₃×C₅	1	6	yes	complemented
12	C₂×C₅×ΓL(1,𝔽₈)	—	7	48	no	—
13	C₅²×C₇	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
14	C₂×C₃×C₅²	—	49	1	no	Hall
15	#3861	C₂×C₅²	1	1	yes	characteristic, direct product factor, Hall
16	C₅×ΓL(1,𝔽₈)	—	7	48	no	—
17	C₂×C₇²	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
18	C₃×C₅²	—	49	1	no	Hall
19	C₂×C₅×C₇	C₅×ΓL(1,𝔽₈)	1	48	yes	complemented
20	C₂×C₅²	#3861	1	1	yes	characteristic, direct product factor, Hall
21	C₇²	C₂×C₃×C₅²	1	1	yes	characteristic, complemented, Sylow
22	C₂×ΓL(1,𝔽₈)	—	7	8	no	—
23	C₅×C₇	C₂×C₅×ΓL(1,𝔽₈)	1	48	yes	complemented
24	C₂×C₃×C₅	—	49	6	no	—
25	C₅²	C₂×#3861	1	1	yes	characteristic, direct product factor, Sylow
26	ΓL(1,𝔽₈)	—	7	8	no	—
27	C₃×C₅	—	49	6	no	—
28	C₂×C₇	C₅²×ΓL(1,𝔽₈)	1	8	yes	complemented
29	C₂×C₅	C₅×#3861	1	6	yes	direct product factor
30	C₇	C₂×C₅²×ΓL(1,𝔽₈)	1	8	yes	complemented
31	C₂×C₃	—	49	1	no	Hall
32	C₅	C₂×C₅×#3861	1	6	yes	direct product factor
33	C₃	—	49	1	no	Sylow
34	C₂	C₅²×#3861	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₅²	#3861
commutator, hypocenter	C₇²	C₂×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₇²	C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₅²

Complements

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

N	H ≅ G/N	type
1. C₅²×#3861	C₂	direct (N × H)
2. C₂×C₅²×C₇²	C₃	semidirect
3. C₂×C₅×#3861	C₅	direct (N × H)
4. C₅²×C₇²	C₂×C₃	semidirect
6. C₅×#3861	C₂×C₅	direct (N × H)
8. C₂×C₅×C₇²	C₃×C₅	semidirect
9. C₂×C₅²×C₇	ΓL(1,𝔽₈)	semidirect
10. C₂×#3861	C₅²	direct (N × H)
11. C₅×C₇²	C₂×C₃×C₅	semidirect
13. C₅²×C₇	C₂×ΓL(1,𝔽₈)	semidirect
15. #3861	C₂×C₅²	direct (N × H)
17. C₂×C₇²	C₃×C₅²	semidirect
19. C₂×C₅×C₇	C₅×ΓL(1,𝔽₈)	semidirect
20. C₂×C₅²	#3861	direct (N × H)
21. C₇²	C₂×C₃×C₅²	semidirect
23. C₅×C₇	C₂×C₅×ΓL(1,𝔽₈)	semidirect
25. C₅²	C₂×#3861	direct (N × H)
28. C₂×C₇	C₅²×ΓL(1,𝔽₈)	semidirect
29. C₂×C₅	C₅×#3861	direct (N × H)
30. C₇	C₂×C₅²×ΓL(1,𝔽₈)	semidirect
32. C₅	C₂×C₅×#3861	direct (N × H)
34. C₂	C₅²×#3861	direct (N × H)

Subgroups — C2×C52×#3861 #20301310

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅²×#3861 #20301310