Subgroups — C₂×C₁₉×C₇⋊(C₅²⋊C₃) #34093096

Order 19950.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₇⋊(C₅²⋊C₃)	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅²×C₇×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉×C₅²⋊C₃	—	7	1	no	maximal, Hall
5	C₁₉×C₅²⋊C₃	—	7	1	no	Hall
6	C₂×C₅×C₇×C₁₉	—	3	2	no	—
7	C₂×C₇⋊(C₅²⋊C₃)	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅²×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₉×ΓL(1,𝔽₈)	—	25	1	no	maximal, Hall
10	C₅×C₇×C₁₉	—	3	2	no	—
11	C₇⋊(C₅²⋊C₃)	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Hall
12	C₅²×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
13	C₁₉×ΓL(1,𝔽₈)	—	25	1	no	Hall
14	C₂×C₅²×C₇	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
15	C₂×C₇×C₁₉	C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×C₁₉	—	3	2	no	—
17	C₅²×C₇	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅²⋊C₃	—	7	1	no	Hall
19	C₇×C₁₉	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₁₉	—	175	1	no	Hall
21	C₅×C₁₉	—	3	2	no	—
22	C₅²⋊C₃	—	7	1	no	Hall
23	C₂×C₅×C₇	—	3	2	no	—
24	C₃×C₁₉	—	175	1	no	Hall
25	C₂×C₅²	C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
26	C₂×ΓL(1,𝔽₈)	—	25	1	no	Hall
27	C₂×C₁₉	C₇⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor, Hall
28	C₅×C₇	—	3	2	no	—
29	C₅²	C₂×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
30	ΓL(1,𝔽₈)	—	25	1	no	Hall
31	C₁₉	C₂×C₇⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₇	C₁₉×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅	—	3	2	no	—
34	C₇	C₂×C₁₉×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃	—	175	1	no	Hall
36	C₅	—	3	2	no	—
37	C₃	—	175	1	no	Sylow
38	C₂	C₁₉×C₇⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₁₉	C₇⋊(C₅²⋊C₃)
commutator, cosocle, hypocenter	C₅²×C₇	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₇×C₁₉	C₃
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₂×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×C₇⋊(C₅²⋊C₃)	C₂	direct (N × H)
2. C₂×C₅²×C₇×C₁₉	C₃	semidirect
3. C₅²×C₇×C₁₉	C₂×C₃	semidirect
7. C₂×C₇⋊(C₅²⋊C₃)	C₁₉	direct (N × H)
8. C₂×C₅²×C₁₉	ΓL(1,𝔽₈)	semidirect
11. C₇⋊(C₅²⋊C₃)	C₂×C₁₉	direct (N × H)
12. C₅²×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
14. C₂×C₅²×C₇	C₃×C₁₉	semidirect
15. C₂×C₇×C₁₉	C₅²⋊C₃	semidirect
17. C₅²×C₇	C₂×C₃×C₁₉	semidirect
19. C₇×C₁₉	C₂×C₅²⋊C₃	semidirect
25. C₂×C₅²	C₁₉×ΓL(1,𝔽₈)	semidirect
27. C₂×C₁₉	C₇⋊(C₅²⋊C₃)	direct (N × H)
29. C₅²	C₂×C₁₉×ΓL(1,𝔽₈)	semidirect
31. C₁₉	C₂×C₇⋊(C₅²⋊C₃)	direct (N × H)
32. C₂×C₇	C₁₉×C₅²⋊C₃	semidirect
34. C₇	C₂×C₁₉×C₅²⋊C₃	semidirect
38. C₂	C₁₉×C₇⋊(C₅²⋊C₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×C₇⋊(C₅²⋊C₃)	2
C₂×C₅²×C₇×C₁₉	3
C₂×C₁₉×C₅²⋊C₃	7
C₂×C₇⋊(C₅²⋊C₃)	19
C₂×C₁₉×ΓL(1,𝔽₈)	25

Subgroups — C2×C19×C7⋊(C52⋊C3) #34093096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×C₇⋊(C₅²⋊C₃) #34093096