Subgroups — C₅²×(C₁₉⋊C₃)⋊D₇ #34093021

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	C₅²×D₁₃₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×(C₁₉⋊C₃)⋊D₇	C₅	1	6	yes	maximal, direct product factor
4	C₅²×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅²×D₁₉⋊C₃	—	7	1	no	maximal, Hall
6	C₅×C₇×C₁₉⋊C₃	C₂×C₅	1	6	yes	complemented
7	C₅²×C₁₉⋊C₃	D₇	1	1	yes	characteristic, complemented, Hall
8	C₅×D₁₃₃	C₃×C₅	1	6	yes	complemented
9	C₃×C₅²×D₇	—	19	1	no	maximal, Hall
10	C₅²×D₁₉	—	7	1	no	Hall
11	(C₁₉⋊C₃)⋊D₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₇×C₁₉	C₂×C₃×C₅	1	6	yes	complemented
13	C₅×D₁₉⋊C₃	—	7	6	no	—
14	C₃×C₅²×C₇	—	19	1	no	Hall
15	C₅²×C₁₉	C₃×D₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₁₉⋊C₃	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
17	C₅²×D₇	—	19	1	no	Hall
18	C₅×C₁₉⋊C₃	C₅×D₇	1	6	yes	complemented
19	D₁₃₃	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
20	C₃×C₅×D₇	—	19	6	no	—
21	C₅×D₁₉	—	7	6	no	—
22	C₅²×C₇	D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₅²	—	133	1	no	Hall
24	C₇×C₁₉	C₂×C₃×C₅²	1	1	yes	characteristic, complemented, Hall
25	D₁₉⋊C₃	—	7	1	no	Hall
26	C₃×C₅×C₇	—	19	6	no	—
27	C₅×C₁₉	C₃×C₅×D₇	1	6	yes	complemented
28	C₃×C₅²	—	19	1	no	Hall
29	C₅×D₇	—	19	6	no	—
30	C₁₉⋊C₃	C₅²×D₇	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅²	—	133	1	no	Hall
32	C₃×D₇	—	19	1	no	Hall
33	D₁₉	—	7	1	no	Hall
34	C₅×C₇	C₅×D₁₉⋊C₃	1	6	yes	complemented
35	C₂×C₃×C₅	—	133	6	no	—
36	C₅²	(C₁₉⋊C₃)⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
37	C₃×C₇	—	19	1	no	Hall
38	C₁₉	C₃×C₅²×D₇	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	—	19	6	no	—
40	D₇	—	19	1	no	Hall
41	C₂×C₅	—	133	6	no	—
42	C₇	C₅²×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	133	1	no	Hall
44	C₅	C₅×(C₁₉⋊C₃)⋊D₇	1	6	yes	direct product factor
45	C₃	—	19	1	no	Sylow
46	C₂	—	133	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²	(C₁₉⋊C₃)⋊D₇
commutator, cosocle, hypocenter	C₇×C₁₉	C₂×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₅²

Complements

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

N	H ≅ G/N	type
1. C₅²×C₇×C₁₉⋊C₃	C₂	semidirect
2. C₅²×D₁₃₃	C₃	semidirect
3. C₅×(C₁₉⋊C₃)⋊D₇	C₅	direct (N × H)
4. C₅²×C₇×C₁₉	C₂×C₃	semidirect
6. C₅×C₇×C₁₉⋊C₃	C₂×C₅	semidirect
7. C₅²×C₁₉⋊C₃	D₇	semidirect
8. C₅×D₁₃₃	C₃×C₅	semidirect
11. (C₁₉⋊C₃)⋊D₇	C₅²	direct (N × H)
12. C₅×C₇×C₁₉	C₂×C₃×C₅	semidirect
15. C₅²×C₁₉	C₃×D₇	semidirect
16. C₇×C₁₉⋊C₃	C₂×C₅²	semidirect
18. C₅×C₁₉⋊C₃	C₅×D₇	semidirect
19. D₁₃₃	C₃×C₅²	semidirect
22. C₅²×C₇	D₁₉⋊C₃	semidirect
24. C₇×C₁₉	C₂×C₃×C₅²	semidirect
27. C₅×C₁₉	C₃×C₅×D₇	semidirect
30. C₁₉⋊C₃	C₅²×D₇	semidirect
34. C₅×C₇	C₅×D₁₉⋊C₃	semidirect
36. C₅²	(C₁₉⋊C₃)⋊D₇	direct (N × H)
38. C₁₉	C₃×C₅²×D₇	semidirect
42. C₇	C₅²×D₁₉⋊C₃	semidirect
44. C₅	C₅×(C₁₉⋊C₃)⋊D₇	direct (N × H)

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
C₅²×D₁₃₃	3
C₅×(C₁₉⋊C₃)⋊D₇	5
C₅²×D₁₉⋊C₃	7
C₃×C₅²×D₇	19

Subgroups — C52×(C19⋊C3)⋊D7 #34093021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×(C₁₉⋊C₃)⋊D₇ #34093021