Subgroups — C₉×C₁₃×D₇×C₁₇ #42123792

Order 27846.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₃×D₇×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	C₁₃×D₇×C₁₇	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×D₇×C₁₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₉×C₁₃×C₁₇	D₇	1	1	yes	characteristic, direct product factor, Hall
8	C₉×C₁₃×D₇	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	—	7	1	no	—
11	C₇×C₉×C₁₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₇×C₉×C₁₃	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
13	C₃×D₇×C₁₇	C₃×C₁₃	1	1	yes	characteristic
14	C₃×C₁₃×C₁₇	C₃×D₇	1	1	yes	characteristic
15	C₃×C₁₃×D₇	C₃×C₁₇	1	1	yes	characteristic
16	C₂×C₁₃×C₁₇	—	7	1	no	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	D₇×C₁₇	C₉×C₁₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₉×C₁₃	—	7	1	no	Hall
22	C₁₃×C₁₇	C₉×D₇	1	1	yes	characteristic, direct product factor, Hall
23	C₁₃×D₇	C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
24	C₉×C₁₇	C₁₃×D₇	1	1	yes	characteristic, direct product factor, Hall
25	C₉×D₇	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	D₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₃×C₁₇	—	7	1	no	—
29	C₇×C₁₃	C₂×C₉×C₁₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₁₃	—	7	1	no	—
31	C₇×C₉	C₂×C₁₃×C₁₇	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₇	C₃×C₁₃×D₇	1	1	yes	characteristic
33	C₃×D₇	C₃×C₁₃×C₁₇	1	1	yes	characteristic
34	C₃×C₁₃	C₃×D₇×C₁₇	1	1	yes	characteristic
35	C₂×C₁₇	—	7	1	no	Hall
36	C₂×C₁₃	—	7	1	no	Hall
37	C₃×C₇	C₂×C₃×C₁₃×C₁₇	1	1	yes	characteristic
38	C₂×C₉	—	7	1	no	Hall
39	C₁₇	C₉×C₁₃×D₇	1	1	yes	characteristic, direct product factor, Sylow
40	D₇	C₉×C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
41	C₁₃	C₉×D₇×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
42	C₉	C₁₃×D₇×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
43	C₇	C₂×C₉×C₁₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃	—	7	1	no	—
45	C₃	C₃×C₁₃×D₇×C₁₇	1	1	yes	characteristic
46	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉×C₁₃×C₁₇	D₇
commutator, hypocenter	C₇	C₂×C₉×C₁₃×C₁₇
Frattini	C₃	C₃×C₁₃×D₇×C₁₇
Fitting	C₇×C₉×C₁₃×C₁₇	C₂
socle	C₃×C₇×C₁₃×C₁₇	C₂×C₃
prime radical	C₃×C₁₃×D₇×C₁₇	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₃×C₁₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₉×C₁₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₉×C₁₃×C₁₇	C₂	semidirect
5. C₁₃×D₇×C₁₇	C₉	direct (N × H)
6. C₉×D₇×C₁₇	C₁₃	direct (N × H)
7. C₉×C₁₃×C₁₇	D₇	direct (N × H)
8. C₉×C₁₃×D₇	C₁₇	direct (N × H)
9. C₇×C₁₃×C₁₇	C₂×C₉	semidirect
11. C₇×C₉×C₁₇	C₂×C₁₃	semidirect
12. C₇×C₉×C₁₃	C₂×C₁₇	semidirect
20. D₇×C₁₇	C₉×C₁₃	direct (N × H)
22. C₁₃×C₁₇	C₉×D₇	direct (N × H)
23. C₁₃×D₇	C₉×C₁₇	direct (N × H)
24. C₉×C₁₇	C₁₃×D₇	direct (N × H)
25. C₉×D₇	C₁₃×C₁₇	direct (N × H)
26. C₇×C₁₇	C₂×C₉×C₁₃	semidirect
27. C₉×C₁₃	D₇×C₁₇	direct (N × H)
29. C₇×C₁₃	C₂×C₉×C₁₇	semidirect
31. C₇×C₉	C₂×C₁₃×C₁₇	semidirect
39. C₁₇	C₉×C₁₃×D₇	direct (N × H)
40. D₇	C₉×C₁₃×C₁₇	direct (N × H)
41. C₁₃	C₉×D₇×C₁₇	direct (N × H)
42. C₉	C₁₃×D₇×C₁₇	direct (N × H)
43. C₇	C₂×C₉×C₁₃×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₉×C₁₃×C₁₇	2
C₃×C₁₃×D₇×C₁₇	3
C₂×C₉×C₁₃×C₁₇	7
C₉×D₇×C₁₇	13
C₉×C₁₃×D₇	17

Subgroups — C9×C13×D7×C17 #42123792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₁₃×D₇×C₁₇ #42123792