Subgroups — C₂×C₁₃×C₁₇×C₇⋊C₉ #42123786

Order 27846.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₇×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₇×C₁₃×C₁₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic
4	C₂×C₉×C₁₃×C₁₇	—	7	1	no	maximal, Hall
5	C₂×C₇×C₁₃×C₁₇	C₉	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₇×C₇⋊C₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₉×C₁₃×C₁₇	—	7	1	no	Hall
8	C₂×C₁₃×C₇⋊C₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₁₃×C₁₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₁₃×C₁₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₁₇×C₇⋊C₉	C₂×C₁₃	1	1	yes	characteristic, direct product factor, Hall
12	C₁₃×C₇⋊C₉	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₇×C₁₇	C₃×C₁₃	1	1	yes	characteristic
14	C₃×C₁₃×C₁₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₂×C₃×C₇×C₁₃	C₃×C₁₇	1	1	yes	characteristic
16	C₂×C₁₃×C₁₇	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₇×C₁₇	C₂×C₃×C₁₃	1	1	yes	characteristic
18	C₂×C₉×C₁₇	—	7	1	no	Hall
19	C₃×C₇×C₁₃	C₂×C₃×C₁₇	1	1	yes	characteristic
20	C₂×C₇×C₁₇	C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₉×C₁₃	—	7	1	no	Hall
22	C₁₃×C₁₇	C₂×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₇×C₁₃	C₉×C₁₇	1	1	yes	characteristic, complemented, Hall
24	C₉×C₁₇	—	7	1	no	Hall
25	C₂×C₇⋊C₉	C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
26	C₇×C₁₇	C₂×C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
27	C₉×C₁₃	—	7	1	no	Hall
28	C₂×C₃×C₁₇	C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
29	C₇×C₁₃	C₂×C₉×C₁₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₁₃	C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
31	C₇⋊C₉	C₂×C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₁₇	C₂×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
33	C₂×C₃×C₇	C₃×C₁₃×C₁₇	1	1	yes	characteristic
34	C₃×C₁₃	C₂×C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
35	C₂×C₁₇	C₁₃×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
36	C₂×C₁₃	C₁₇×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
37	C₃×C₇	C₂×C₃×C₁₃×C₁₇	1	1	yes	characteristic
38	C₂×C₉	—	7	1	no	Hall
39	C₁₇	C₂×C₁₃×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₇	C₉×C₁₃×C₁₇	1	1	yes	characteristic, complemented, Hall
41	C₁₃	C₂×C₁₇×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₉	—	7	1	no	Sylow
43	C₇	C₂×C₉×C₁₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃	C₁₃×C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
45	C₃	C₂×C₁₃×C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
46	C₂	C₁₃×C₁₇×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃×C₁₇	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₂×C₉×C₁₃×C₁₇
Frattini	C₃	C₂×C₁₃×C₁₇×ΓL(1,𝔽₈)
Fitting, socle, prime radical	C₂×C₃×C₇×C₁₃×C₁₇	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₃×C₁₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₁₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₇×C₇⋊C₉	C₂	direct (N × H)
5. C₂×C₇×C₁₃×C₁₇	C₉	semidirect
6. C₂×C₁₇×C₇⋊C₉	C₁₃	direct (N × H)
8. C₂×C₁₃×C₇⋊C₉	C₁₇	direct (N × H)
9. C₇×C₁₃×C₁₇	C₂×C₉	semidirect
11. C₁₇×C₇⋊C₉	C₂×C₁₃	direct (N × H)
12. C₁₃×C₇⋊C₉	C₂×C₁₇	direct (N × H)
16. C₂×C₁₃×C₁₇	C₇⋊C₉	direct (N × H)
20. C₂×C₇×C₁₇	C₉×C₁₃	semidirect
22. C₁₃×C₁₇	C₂×C₇⋊C₉	direct (N × H)
23. C₂×C₇×C₁₃	C₉×C₁₇	semidirect
25. C₂×C₇⋊C₉	C₁₃×C₁₇	direct (N × H)
26. C₇×C₁₇	C₂×C₉×C₁₃	semidirect
29. C₇×C₁₃	C₂×C₉×C₁₇	semidirect
31. C₇⋊C₉	C₂×C₁₃×C₁₇	direct (N × H)
35. C₂×C₁₇	C₁₃×C₇⋊C₉	direct (N × H)
36. C₂×C₁₃	C₁₇×C₇⋊C₉	direct (N × H)
39. C₁₇	C₂×C₁₃×C₇⋊C₉	direct (N × H)
40. C₂×C₇	C₉×C₁₃×C₁₇	semidirect
41. C₁₃	C₂×C₁₇×C₇⋊C₉	direct (N × H)
43. C₇	C₂×C₉×C₁₃×C₁₇	semidirect
46. C₂	C₁₃×C₁₇×C₇⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×C₁₇×C₇⋊C₉	2
C₂×C₃×C₇×C₁₃×C₁₇	3
C₂×C₉×C₁₃×C₁₇	7
C₂×C₁₇×C₇⋊C₉	13
C₂×C₁₃×C₇⋊C₉	17

Subgroups — C2×C13×C17×C7⋊C9 #42123786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×C₁₇×C₇⋊C₉ #42123786