Subgroups — C₇×C₅⋊(C₅⋊(D₁₉⋊C₃)) #34093039

Order 19950.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₅⋊D₉₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₅⋊(D₁₉⋊C₃)	—	5	6	no	maximal
4	C₅²×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅⋊(C₅⋊(D₁₉⋊C₃))	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₇×C₁₉⋊C₃	D₅	1	6	yes	complemented
7	C₅²×C₁₉⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×D₉₅	—	5	6	no	—
9	C₃×C₇×C₅⋊D₅	—	19	1	no	maximal, Hall
10	C₅⋊D₉₅	C₃×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×D₁₉⋊C₃	—	25	1	no	Hall
12	C₅×C₇×C₁₉	C₃×D₅	1	6	yes	complemented
13	C₅⋊(D₁₉⋊C₃)	—	5	6	no	—
14	C₃×C₅²×C₇	—	19	1	no	Hall
15	C₅²×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₁₉⋊C₃	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
17	C₇×C₅⋊D₅	—	19	1	no	Hall
18	C₅×C₁₉⋊C₃	C₇×D₅	1	6	yes	complemented
19	C₇×D₁₉	—	25	1	no	Hall
20	C₃×C₇×D₅	—	95	6	no	—
21	D₉₅	—	5	6	no	—
22	C₅²×C₇	D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅⋊D₅	—	19	1	no	Hall
24	C₇×C₁₉	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
25	D₁₉⋊C₃	—	25	1	no	Hall
26	C₃×C₅×C₇	—	19	6	no	—
27	C₅×C₁₉	C₃×C₇×D₅	1	6	yes	complemented
28	C₃×C₅²	—	19	1	no	Hall
29	C₇×D₅	—	95	6	no	—
30	C₁₉⋊C₃	C₇×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
31	C₅⋊D₅	—	19	1	no	Hall
32	C₂×C₃×C₇	—	475	1	no	Hall
33	D₁₉	—	25	1	no	Hall
34	C₅×C₇	C₅⋊(D₁₉⋊C₃)	1	6	yes	complemented
35	C₃×D₅	—	95	6	no	—
36	C₅²	C₇×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
37	C₃×C₇	—	19	1	no	Hall
38	C₁₉	C₃×C₇×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	—	19	6	no	—
40	C₂×C₇	—	475	1	no	Hall
41	D₅	—	95	6	no	—
42	C₇	C₅⋊(C₅⋊(D₁₉⋊C₃))	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	475	1	no	Hall
44	C₅	C₇×C₅⋊(D₁₉⋊C₃)	1	6	yes	complemented
45	C₃	—	19	1	no	Sylow
46	C₂	—	475	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₅⋊(C₅⋊(D₁₉⋊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. C₅²×C₇×C₁₉⋊C₃	C₂	semidirect
2. C₇×C₅⋊D₉₅	C₃	semidirect
4. C₅²×C₇×C₁₉	C₂×C₃	semidirect
5. C₅⋊(C₅⋊(D₁₉⋊C₃))	C₇	direct (N × H)
6. C₅×C₇×C₁₉⋊C₃	D₅	semidirect
7. C₅²×C₁₉⋊C₃	C₂×C₇	semidirect
10. C₅⋊D₉₅	C₃×C₇	semidirect
12. C₅×C₇×C₁₉	C₃×D₅	semidirect
15. C₅²×C₁₉	C₂×C₃×C₇	semidirect
16. C₇×C₁₉⋊C₃	C₅⋊D₅	semidirect
18. C₅×C₁₉⋊C₃	C₇×D₅	semidirect
22. C₅²×C₇	D₁₉⋊C₃	semidirect
24. C₇×C₁₉	C₃×C₅⋊D₅	semidirect
27. C₅×C₁₉	C₃×C₇×D₅	semidirect
30. C₁₉⋊C₃	C₇×C₅⋊D₅	semidirect
34. C₅×C₇	C₅⋊(D₁₉⋊C₃)	semidirect
36. C₅²	C₇×D₁₉⋊C₃	semidirect
38. C₁₉	C₃×C₇×C₅⋊D₅	semidirect
42. C₇	C₅⋊(C₅⋊(D₁₉⋊C₃))	direct (N × H)
44. C₅	C₇×C₅⋊(D₁₉⋊C₃)	semidirect

Maximal subgroups

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

subgroup	index
C₅²×C₇×C₁₉⋊C₃	2
C₇×C₅⋊D₉₅	3
C₇×C₅⋊(D₁₉⋊C₃)	5
C₅⋊(C₅⋊(D₁₉⋊C₃))	7
C₃×C₇×C₅⋊D₅	19

Subgroups — C7×C5⋊(C5⋊(D19⋊C3)) #34093039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₅⋊(C₅⋊(D₁₉⋊C₃)) #34093039