Subgroups — C₁₉×C₂₅×Dic₁₇ #44568014

Order 32300.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×C₁₉×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₁₉×C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅×C₁₉×Dic₁₇	C₅	1	1	yes	maximal, characteristic
4	C₂×C₅×C₁₇×C₁₉	C₂×C₅	1	1	yes	characteristic
5	C₄×C₁₉×C₂₅	—	17	1	no	maximal, Hall
6	C₂₅×Dic₁₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₇×C₁₉	C₄×C₅	1	1	yes	characteristic
8	C₁₉×Dic₁₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₁₉×C₂₅	D₁₇	1	1	yes	characteristic
10	C₂×C₁₇×C₂₅	C₂×C₁₉	1	1	yes	characteristic
11	C₂×C₁₇×C₁₉	C₂×C₂₅	1	1	yes	characteristic
12	C₁₉×C₂₅	Dic₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₁₇×C₂₅	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
14	C₄×C₅×C₁₉	—	17	1	no	—
15	C₅×Dic₁₇	C₅×C₁₉	1	1	yes	characteristic
16	C₁₇×C₁₉	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₁₉	C₅×D₁₇	1	1	yes	characteristic
18	C₂×C₅×C₁₇	C₂×C₅×C₁₉	1	1	yes	characteristic
19	C₄×C₂₅	—	17	1	no	Hall
20	C₅×C₁₉	C₅×Dic₁₇	1	1	yes	characteristic
21	C₅×C₁₇	C₄×C₅×C₁₉	1	1	yes	characteristic
22	C₄×C₁₉	—	17	1	no	Hall
23	Dic₁₇	C₁₉×C₂₅	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₂₅	C₁₉×D₁₇	1	1	yes	characteristic
25	C₂×C₁₉	C₂₅×D₁₇	1	1	yes	characteristic
26	C₂×C₁₇	C₂×C₁₉×C₂₅	1	1	yes	characteristic
27	C₂₅	C₁₉×Dic₁₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₄×C₅	—	17	1	no	—
29	C₁₉	C₂₅×Dic₁₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₁₇	C₄×C₁₉×C₂₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	C₅×C₁₉×D₁₇	1	1	yes	characteristic
32	C₅	C₅×C₁₉×Dic₁₇	1	1	yes	characteristic
33	C₄	—	17	1	no	Sylow
34	C₂	C₁₉×C₂₅×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₂₅	D₁₇
commutator, hypocenter	C₁₇	C₄×C₁₉×C₂₅
Frattini	C₂×C₅	C₅×C₁₉×D₁₇
Fitting	C₂×C₁₇×C₁₉×C₂₅	C₂
socle, prime radical	C₂×C₅×C₁₇×C₁₉	C₂×C₅
cosocle	C₂×C₅×C₁₇	C₂×C₅×C₁₉
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₁₉×C₂₅

Complements

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

N	H ≅ G/N	type
2. C₁₇×C₁₉×C₂₅	C₄	semidirect
6. C₂₅×Dic₁₇	C₁₉	direct (N × H)
8. C₁₉×Dic₁₇	C₂₅	direct (N × H)
12. C₁₉×C₂₅	Dic₁₇	direct (N × H)
13. C₁₇×C₂₅	C₄×C₁₉	semidirect
16. C₁₇×C₁₉	C₄×C₂₅	semidirect
23. Dic₁₇	C₁₉×C₂₅	direct (N × H)
27. C₂₅	C₁₉×Dic₁₇	direct (N × H)
29. C₁₉	C₂₅×Dic₁₇	direct (N × H)
30. C₁₇	C₄×C₁₉×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₇×C₁₉×C₂₅	2
C₅×C₁₉×Dic₁₇	5
C₄×C₁₉×C₂₅	17
C₂₅×Dic₁₇	19

Subgroups — C19×C25×Dic17 #44568014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₂₅×Dic₁₇ #44568014