Subgroups — Dic₅×C₉₇⋊C₉ #31775475

Order 17460.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₉₇⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₅×C₉₇	C₃	1	1	yes	maximal, characteristic
3	C₅×C₉₇⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄×C₉₇⋊C₉	—	5	1	no	maximal, Hall
5	C₂×C₃×C₅×C₉₇	C₂×C₃	1	1	yes	characteristic
6	Dic₅×C₉₇	C₉	1	1	yes	characteristic, complemented, Hall
7	C₂×C₉₇⋊C₉	D₅	1	1	yes	characteristic
8	C₃×C₅×C₉₇	C₃×C₄	1	1	yes	characteristic
9	C₃×C₄×C₉₇	—	5	1	no	—
10	C₂×C₅×C₉₇	C₂×C₉	1	1	yes	characteristic
11	C₉₇⋊C₉	Dic₅	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃×C₉₇	C₃×D₅	1	1	yes	characteristic
13	C₅×C₉₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
14	C₄×C₉₇	—	5	1	no	Hall
15	C₃×C₉₇	C₃×Dic₅	1	1	yes	characteristic
16	C₂×C₉₇	C₉×D₅	1	1	yes	characteristic
17	C₉×Dic₅	—	97	1	no	maximal, Hall
18	C₉₇	C₉×Dic₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅×C₉	—	97	1	no	—
20	C₃×Dic₅	C₉₇⋊C₃	1	1	yes	characteristic
21	C₅×C₉	—	97	1	no	Hall
22	C₄×C₉	—	485	1	no	Hall
23	C₂×C₃×C₅	C₂×C₉₇⋊C₃	1	1	yes	characteristic
24	Dic₅	C₉₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₉	—	97	1	no	—
26	C₃×C₅	C₄×C₉₇⋊C₃	1	1	yes	characteristic
27	C₃×C₄	—	5	1	no	—
28	C₂×C₅	C₂×C₉₇⋊C₉	1	1	yes	characteristic
29	C₉	—	97	1	no	Sylow
30	C₂×C₃	D₅×C₉₇⋊C₃	1	1	yes	characteristic
31	C₅	C₄×C₉₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	5	1	no	Sylow
33	C₃	Dic₅×C₉₇⋊C₃	1	1	yes	characteristic
34	C₂	D₅×C₉₇⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₅×C₉₇⋊C₃
commutator, hypocenter	C₅×C₉₇	C₄×C₉
Fitting, socle, prime radical, cosocle	C₂×C₃×C₅×C₉₇	C₂×C₃
LCS	G ▷ C₅×C₉₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
3. C₅×C₉₇⋊C₉	C₄	semidirect
6. Dic₅×C₉₇	C₉	semidirect
11. C₉₇⋊C₉	Dic₅	direct (N × H)
13. C₅×C₉₇	C₄×C₉	semidirect
18. C₉₇	C₉×Dic₅	semidirect
24. Dic₅	C₉₇⋊C₉	direct (N × H)
31. C₅	C₄×C₉₇⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₉₇⋊C₉	2
C₃×Dic₅×C₉₇	3
C₄×C₉₇⋊C₉	5
C₉×Dic₅	97

Subgroups — Dic5×C97⋊C9 #31775475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₅×C₉₇⋊C₉ #31775475