Subgroups — C₇×D₁₉⋊(C₅²⋊C₃) #34093079

Order 19950.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₉⋊(C₅²⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×C₇×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	D₁₉⋊(C₅²⋊C₃)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₉⋊(C₅²⋊C₃)	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₅×C₇×D₁₉	—	3	2	no	—
7	C₂×C₇×C₅²⋊C₃	—	19	1	no	maximal, Hall
8	C₅²×D₁₉	C₃×C₇	1	1	yes	characteristic, complemented, Hall
9	C₇×D₁₉⋊C₃	—	25	1	no	maximal, Hall
10	C₅×C₇×C₁₉	—	3	2	no	—
11	C₇×C₅²⋊C₃	—	19	1	no	Hall
12	C₅²×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
13	C₇×C₁₉⋊C₃	—	25	1	no	Hall
14	C₂×C₅²×C₇	—	19	1	no	Hall
15	C₇×D₁₉	C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
16	C₅×D₁₉	—	3	2	no	—
17	C₅²×C₇	D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅²⋊C₃	—	19	1	no	Hall
19	C₇×C₁₉	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
20	D₁₉⋊C₃	—	25	1	no	Hall
21	C₅×C₁₉	—	3	2	no	—
22	C₅²⋊C₃	—	19	1	no	Hall
23	C₂×C₅×C₇	—	57	2	no	—
24	C₁₉⋊C₃	—	25	1	no	Hall
25	C₂×C₅²	—	19	1	no	Hall
26	C₂×C₃×C₇	—	475	1	no	Hall
27	D₁₉	C₇×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
28	C₅×C₇	—	3	2	no	—
29	C₅²	C₇×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₃×C₇	—	475	1	no	Hall
31	C₁₉	C₂×C₇×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₇	—	19	1	no	Hall
33	C₂×C₅	—	57	2	no	—
34	C₇	D₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×C₃	—	475	1	no	Hall
36	C₅	—	3	2	no	—
37	C₃	—	475	1	no	Sylow
38	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₁₉⋊(C₅²⋊C₃)
commutator, cosocle, hypocenter	C₅²×C₁₉	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₉⋊(C₅²⋊C₃)	C₂	semidirect
2. C₅²×C₇×D₁₉	C₃	semidirect
3. C₅²×C₇×C₁₉	C₂×C₃	semidirect
4. D₁₉⋊(C₅²⋊C₃)	C₇	direct (N × H)
5. C₁₉⋊(C₅²⋊C₃)	C₂×C₇	semidirect
8. C₅²×D₁₉	C₃×C₇	semidirect
12. C₅²×C₁₉	C₂×C₃×C₇	semidirect
15. C₇×D₁₉	C₅²⋊C₃	semidirect
17. C₅²×C₇	D₁₉⋊C₃	semidirect
19. C₇×C₁₉	C₂×C₅²⋊C₃	semidirect
27. D₁₉	C₇×C₅²⋊C₃	semidirect
29. C₅²	C₇×D₁₉⋊C₃	semidirect
31. C₁₉	C₂×C₇×C₅²⋊C₃	semidirect
34. C₇	D₁₉⋊(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
C₇×C₁₉⋊(C₅²⋊C₃)	2
C₅²×C₇×D₁₉	3
D₁₉⋊(C₅²⋊C₃)	7
C₂×C₇×C₅²⋊C₃	19
C₇×D₁₉⋊C₃	25

Subgroups — C7×D19⋊(C52⋊C3) #34093079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₁₉⋊(C₅²⋊C₃) #34093079