Subgroups — C₁₇×Dic₁₃⋊C₉ #22547331

Order 7956.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×C₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₇×Dic₁₃	C₃	1	1	yes	maximal, characteristic
3	C₁₇×C₁₃⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic
5	C₁₇×Dic₁₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃×C₁₇	C₃×C₄	1	1	yes	characteristic
7	C₄×C₉×C₁₇	—	13	1	no	maximal, Hall
8	Dic₁₃⋊C₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₁₃×C₁₇	C₂×C₉	1	1	yes	characteristic
10	C₂×C₉×C₁₇	—	13	1	no	—
11	C₂×C₁₃⋊C₉	C₂×C₁₇	1	1	yes	characteristic
12	C₁₃×C₁₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	C₃×C₄×C₁₇	—	13	1	no	—
14	C₃×Dic₁₃	C₃×C₁₇	1	1	yes	characteristic
15	C₉×C₁₇	—	13	1	no	Hall
16	C₁₃⋊C₉	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₇	D₁₃⋊C₃	1	1	yes	characteristic
18	C₂×C₃×C₁₃	C₂×C₃×C₁₇	1	1	yes	characteristic
19	C₄×C₁₇	—	13	1	no	Hall
20	Dic₁₃	C₉×C₁₇	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₇	Dic₁₃⋊C₃	1	1	yes	characteristic
22	C₃×C₁₃	C₃×C₄×C₁₇	1	1	yes	characteristic
23	C₄×C₉	—	13	1	no	Hall
24	C₂×C₁₇	D₁₃⋊C₉	1	1	yes	characteristic
25	C₂×C₁₃	C₂×C₉×C₁₇	1	1	yes	characteristic
26	C₂×C₉	—	13	1	no	—
27	C₁₇	Dic₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₁₃	C₄×C₉×C₁₇	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	13	1	no	—
30	C₉	—	13	1	no	Sylow
31	C₂×C₃	C₁₇×D₁₃⋊C₃	1	1	yes	characteristic
32	C₄	—	13	1	no	Sylow
33	C₃	C₁₇×Dic₁₃⋊C₃	1	1	yes	characteristic
34	C₂	C₁₇×D₁₃⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₇	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₄×C₉×C₁₇
Frattini	C₂×C₃	C₁₇×D₁₃⋊C₃
Fitting, socle	C₂×C₃×C₁₃×C₁₇	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₁₇

Complements

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

N	H ≅ G/N	type
3. C₁₇×C₁₃⋊C₉	C₄	semidirect
5. C₁₇×Dic₁₃	C₉	semidirect
8. Dic₁₃⋊C₉	C₁₇	direct (N × H)
12. C₁₃×C₁₇	C₄×C₉	semidirect
16. C₁₃⋊C₉	C₄×C₁₇	semidirect
20. Dic₁₃	C₉×C₁₇	semidirect
27. C₁₇	Dic₁₃⋊C₉	direct (N × H)
28. C₁₃	C₄×C₉×C₁₇	semidirect

Subgroups — C17×Dic13⋊C9 #22547331

Conjugacy classes of subgroups

Complements

Subgroups — C₁₇×Dic₁₃⋊C₉ #22547331