Subgroups — C₂×C₅²×C₁₇×D₁₉ #44568119

Order 32300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₇×D₁₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₁₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₁₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₁₇×D₁₉	C₅	1	6	yes	maximal, direct product factor
5	C₅×C₁₇×D₁₉	C₂×C₅	1	12	yes	direct product factor
6	C₂×C₅×C₁₇×C₁₉	C₂×C₅	1	6	yes	complemented
7	C₂×C₅²×D₁₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₅²×C₁₇	—	19	1	no	maximal, Hall
9	C₅×C₁₇×C₁₉	C₂²×C₅	1	6	yes	complemented
10	C₂×C₁₇×D₁₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅²×C₁₉	C₂×C₁₇	1	1	yes	characteristic, complemented
12	C₅²×D₁₉	C₂×C₁₇	1	2	yes	direct product factor
13	C₂×C₅²×C₁₇	—	19	2	no	—
14	C₂×C₅²×C₁₇	D₁₉	1	1	yes	characteristic, direct product factor
15	C₂×C₁₇×C₁₉	C₂×C₅²	1	1	yes	characteristic, complemented
16	C₁₇×D₁₉	C₂×C₅²	1	2	yes	direct product factor
17	C₅²×C₁₉	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
18	C₅²×C₁₇	C₂×D₁₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅×D₁₉	C₅×C₁₇	1	6	yes	direct product factor
20	C₂²×C₅×C₁₇	—	19	6	no	—
21	C₁₇×C₁₉	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
22	C₂×C₅×C₁₉	C₂×C₅×C₁₇	1	6	yes	complemented
23	C₅×D₁₉	C₂×C₅×C₁₇	1	12	yes	direct product factor
24	C₂×C₅×C₁₇	—	19	12	no	—
25	C₂×C₅×C₁₇	C₅×D₁₉	1	6	yes	direct product factor
26	C₂²×C₅²	—	19	1	no	Hall
27	C₅×C₁₉	C₂²×C₅×C₁₇	1	6	yes	complemented
28	C₅×C₁₇	C₂×C₅×D₁₉	1	6	yes	direct product factor
29	C₂×D₁₉	C₅²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
30	C₂²×C₁₇	—	19	1	no	Hall
31	C₂×C₅²	—	19	2	no	—
32	C₂×C₅²	C₁₇×D₁₉	1	1	yes	characteristic, direct product factor
33	C₂×C₁₉	C₂×C₅²×C₁₇	1	1	yes	characteristic, complemented
34	D₁₉	C₂×C₅²×C₁₇	1	2	yes	direct product factor
35	C₂×C₁₇	—	19	2	no	—
36	C₂×C₁₇	C₅²×D₁₉	1	1	yes	characteristic, direct product factor
37	C₅²	C₂×C₁₇×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
38	C₂²×C₅	—	19	6	no	—
39	C₁₉	C₂²×C₅²×C₁₇	1	1	yes	characteristic, complemented, Sylow
40	C₁₇	C₂×C₅²×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	—	19	12	no	—
42	C₂×C₅	C₅×C₁₇×D₁₉	1	6	yes	direct product factor
43	C₅	C₂×C₅×C₁₇×D₁₉	1	6	yes	direct product factor
44	C₂²	—	19	1	no	Sylow
45	C₂	—	19	2	no	—
46	C₂	C₅²×C₁₇×D₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅²×C₁₇	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂²×C₅²×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₇×C₁₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₅²×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅²×C₁₇×D₁₉	C₂	direct (N × H)
2. C₂×C₅²×C₁₇×C₁₉	C₂	semidirect
3. C₅²×C₁₇×C₁₉	C₂²	semidirect
4. C₂×C₅×C₁₇×D₁₉	C₅	direct (N × H)
5. C₅×C₁₇×D₁₉	C₂×C₅	direct (N × H)
6. C₂×C₅×C₁₇×C₁₉	C₂×C₅	semidirect
7. C₂×C₅²×D₁₉	C₁₇	direct (N × H)
9. C₅×C₁₇×C₁₉	C₂²×C₅	semidirect
10. C₂×C₁₇×D₁₉	C₅²	direct (N × H)
11. C₂×C₅²×C₁₉	C₂×C₁₇	semidirect
12. C₅²×D₁₉	C₂×C₁₇	direct (N × H)
14. C₂×C₅²×C₁₇	D₁₉	direct (N × H)
15. C₂×C₁₇×C₁₉	C₂×C₅²	semidirect
16. C₁₇×D₁₉	C₂×C₅²	direct (N × H)
17. C₅²×C₁₉	C₂²×C₁₇	semidirect
18. C₅²×C₁₇	C₂×D₁₉	direct (N × H)
19. C₂×C₅×D₁₉	C₅×C₁₇	direct (N × H)
21. C₁₇×C₁₉	C₂²×C₅²	semidirect
22. C₂×C₅×C₁₉	C₂×C₅×C₁₇	semidirect
23. C₅×D₁₉	C₂×C₅×C₁₇	direct (N × H)
25. C₂×C₅×C₁₇	C₅×D₁₉	direct (N × H)
27. C₅×C₁₉	C₂²×C₅×C₁₇	semidirect
28. C₅×C₁₇	C₂×C₅×D₁₉	direct (N × H)
29. C₂×D₁₉	C₅²×C₁₇	direct (N × H)
32. C₂×C₅²	C₁₇×D₁₉	direct (N × H)
33. C₂×C₁₉	C₂×C₅²×C₁₇	semidirect
34. D₁₉	C₂×C₅²×C₁₇	direct (N × H)
36. C₂×C₁₇	C₅²×D₁₉	direct (N × H)
37. C₅²	C₂×C₁₇×D₁₉	direct (N × H)
39. C₁₉	C₂²×C₅²×C₁₇	semidirect
40. C₁₇	C₂×C₅²×D₁₉	direct (N × H)
42. C₂×C₅	C₅×C₁₇×D₁₉	direct (N × H)
43. C₅	C₂×C₅×C₁₇×D₁₉	direct (N × H)
46. C₂	C₅²×C₁₇×D₁₉	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×C₁₇×D₁₉	2
C₂×C₅²×C₁₇×C₁₉	2
C₂×C₅×C₁₇×D₁₉	5
C₂×C₅²×D₁₉	17
C₂²×C₅²×C₁₇	19

Subgroups — C2×C52×C17×D19 #44568119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅²×C₁₇×D₁₉ #44568119