Subgroups — #34093086

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, complemented, Hall
2	C₅²×D₁₃₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	D₁₉×C₅²⋊C₃	—	7	1	no	maximal, Hall
5	C₁₉×C₅²⋊C₃	—	7	1	no	Hall
6	C₅×D₁₃₃	—	3	2	no	—
7	D₇⋊(C₅²⋊C₃)	—	19	1	no	maximal, Hall
8	C₅²×D₁₉	—	21	1	no	Hall
9	ΓL(1,𝔽₈)⋊D₁₉	—	25	1	no	maximal, Hall
10	C₅×C₇×C₁₉	—	3	2	no	—
11	C₇⋊(C₅²⋊C₃)	D₁₉	1	1	yes	characteristic, complemented, Hall
12	C₅²×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
13	C₁₉×ΓL(1,𝔽₈)	—	25	1	no	Hall
14	C₅²×D₇	—	19	1	no	Hall
15	D₁₃₃	C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
16	C₅×D₁₉	—	21	2	no	—
17	C₅²×C₇	C₃×D₁₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅²⋊C₃	—	133	1	no	Hall
19	C₇×C₁₉	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₃×D₁₉	—	175	1	no	Hall
21	C₅×C₁₉	—	3	2	no	—
22	C₅²⋊C₃	—	7	1	no	Hall
23	C₅×D₇	—	57	2	no	—
24	C₃×C₁₉	—	175	1	no	Hall
25	C₂×C₅²	—	399	1	no	Hall
26	AGL(1,𝔽₇)	—	475	1	no	Hall
27	D₁₉	—	21	1	no	Hall
28	C₅×C₇	—	3	2	no	—
29	C₅²	ΓL(1,𝔽₈)⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
30	ΓL(1,𝔽₈)	—	25	1	no	Hall
31	C₁₉	D₇⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented, Sylow
32	D₇	—	19	1	no	Hall
33	C₂×C₅	—	399	2	no	—
34	C₇	D₁₉×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃	—	3325	1	no	Hall
36	C₅	—	3	2	no	—
37	C₃	—	175	1	no	Sylow
38	C₂	—	399	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₁₉×C₇⋊(C₅²⋊C₃)	C₂	semidirect
2. C₅²×D₁₃₃	C₃	semidirect
3. C₅²×C₇×C₁₉	C₂×C₃	semidirect
11. C₇⋊(C₅²⋊C₃)	D₁₉	semidirect
12. C₅²×C₁₉	AGL(1,𝔽₇)	semidirect
15. D₁₃₃	C₅²⋊C₃	semidirect
17. C₅²×C₇	C₃×D₁₉	semidirect
19. C₇×C₁₉	C₂×C₅²⋊C₃	semidirect
29. C₅²	ΓL(1,𝔽₈)⋊D₁₉	semidirect
31. C₁₉	D₇⋊(C₅²⋊C₃)	semidirect
34. C₇	D₁₉×C₅²⋊C₃	semidirect

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
C₅²×D₁₃₃	3
D₁₉×C₅²⋊C₃	7
D₇⋊(C₅²⋊C₃)	19
ΓL(1,𝔽₈)⋊D₁₉	25