Subgroups — C₂×C₇×C₁₇×C₁₃⋊C₉ #42123785

Order 27846.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₇×C₁₃⋊C₉	C₂	direct (N × H)
4. C₂×C₁₇×C₁₃⋊C₉	C₇	direct (N × H)
5. C₂×C₇×C₁₃×C₁₇	C₉	semidirect
7. C₁₇×C₁₃⋊C₉	C₂×C₇	direct (N × H)
8. C₂×C₇×C₁₃⋊C₉	C₁₇	direct (N × H)
9. C₇×C₁₃×C₁₇	C₂×C₉	semidirect
12. C₇×C₁₃⋊C₉	C₂×C₁₇	direct (N × H)
16. C₂×C₁₃×C₁₇	C₇×C₉	semidirect
20. C₂×C₇×C₁₇	C₁₃⋊C₉	direct (N × H)
21. C₂×C₁₃⋊C₉	C₇×C₁₇	direct (N × H)
22. C₁₃×C₁₇	C₂×C₇×C₉	semidirect
23. C₂×C₇×C₁₃	C₉×C₁₇	semidirect
26. C₇×C₁₇	C₂×C₁₃⋊C₉	direct (N × H)
27. C₁₃⋊C₉	C₂×C₇×C₁₇	direct (N × H)
29. C₇×C₁₃	C₂×C₉×C₁₇	semidirect
35. C₂×C₁₇	C₇×C₁₃⋊C₉	direct (N × H)
36. C₂×C₁₃	C₇×C₉×C₁₇	semidirect
39. C₁₇	C₂×C₇×C₁₃⋊C₉	direct (N × H)
40. C₂×C₇	C₁₇×C₁₃⋊C₉	direct (N × H)
41. C₁₃	C₂×C₇×C₉×C₁₇	semidirect
43. C₇	C₂×C₁₇×C₁₃⋊C₉	direct (N × H)
46. C₂	C₇×C₁₇×C₁₃⋊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
C₇×C₁₇×C₁₃⋊C₉	2
C₂×C₃×C₇×C₁₃×C₁₇	3
C₂×C₁₇×C₁₃⋊C₉	7
C₂×C₇×C₉×C₁₇	13
C₂×C₇×C₁₃⋊C₉	17

Subgroups — C2×C7×C17×C13⋊C9 #42123785

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₁₇×C₁₃⋊C₉ #42123785