Subgroups — C₅×C₇²×C₉×C₁₇ #49154151

Order 37485.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇²×C₁₇	C₃	1	1	yes	maximal, characteristic
2	C₇²×C₉×C₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₇×C₉×C₁₇	C₇	1	8	yes	maximal, direct product factor
4	C₅×C₇²×C₁₇	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₇²×C₁₇	C₃×C₅	1	1	yes	characteristic
6	C₅×C₇²×C₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₅×C₇×C₁₇	C₃×C₇	1	8	yes	—
8	C₇×C₉×C₁₇	C₅×C₇	1	8	yes	direct product factor
9	C₇²×C₁₇	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
10	C₅×C₉×C₁₇	C₇²	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₅×C₇²	C₃×C₁₇	1	1	yes	characteristic
12	C₅×C₇×C₁₇	C₇×C₉	1	8	yes	direct product factor
13	C₇²×C₉	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₇×C₁₇	C₃×C₅×C₇	1	8	yes	—
15	C₅×C₇×C₉	C₇×C₁₇	1	8	yes	direct product factor
16	C₃×C₅×C₁₇	C₃×C₇²	1	1	yes	characteristic
17	C₅×C₇²	C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
18	C₉×C₁₇	C₅×C₇²	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₇²	C₃×C₅×C₁₇	1	1	yes	characteristic
20	C₇×C₁₇	C₅×C₇×C₉	1	8	yes	direct product factor
21	C₃×C₅×C₇	C₃×C₇×C₁₇	1	8	yes	—
22	C₅×C₁₇	C₇²×C₉	1	1	yes	characteristic, direct product factor, Hall
23	C₇×C₉	C₅×C₇×C₁₇	1	8	yes	direct product factor
24	C₃×C₁₇	C₃×C₅×C₇²	1	1	yes	characteristic
25	C₇²	C₅×C₉×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₅×C₉	C₇²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
27	C₅×C₇	C₇×C₉×C₁₇	1	8	yes	direct product factor
28	C₃×C₇	C₃×C₅×C₇×C₁₇	1	8	yes	—
29	C₁₇	C₅×C₇²×C₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₃×C₅	C₃×C₇²×C₁₇	1	1	yes	characteristic
31	C₉	C₅×C₇²×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
32	C₇	C₅×C₇×C₉×C₁₇	1	8	yes	direct product factor
33	C₅	C₇²×C₉×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
34	C₃	C₃×C₅×C₇²×C₁₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₅×C₇²×C₁₇
socle, prime radical	C₃×C₅×C₇²×C₁₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇²×C₉×C₁₇	C₅	direct (N × H)
3. C₅×C₇×C₉×C₁₇	C₇	direct (N × H)
4. C₅×C₇²×C₁₇	C₉	direct (N × H)
6. C₅×C₇²×C₉	C₁₇	direct (N × H)
8. C₇×C₉×C₁₇	C₅×C₇	direct (N × H)
9. C₇²×C₁₇	C₅×C₉	direct (N × H)
10. C₅×C₉×C₁₇	C₇²	direct (N × H)
12. C₅×C₇×C₁₇	C₇×C₉	direct (N × H)
13. C₇²×C₉	C₅×C₁₇	direct (N × H)
15. C₅×C₇×C₉	C₇×C₁₇	direct (N × H)
17. C₅×C₇²	C₉×C₁₇	direct (N × H)
18. C₉×C₁₇	C₅×C₇²	direct (N × H)
20. C₇×C₁₇	C₅×C₇×C₉	direct (N × H)
22. C₅×C₁₇	C₇²×C₉	direct (N × H)
23. C₇×C₉	C₅×C₇×C₁₇	direct (N × H)
25. C₇²	C₅×C₉×C₁₇	direct (N × H)
26. C₅×C₉	C₇²×C₁₇	direct (N × H)
27. C₅×C₇	C₇×C₉×C₁₇	direct (N × H)
29. C₁₇	C₅×C₇²×C₉	direct (N × H)
31. C₉	C₅×C₇²×C₁₇	direct (N × H)
32. C₇	C₅×C₇×C₉×C₁₇	direct (N × H)
33. C₅	C₇²×C₉×C₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇²×C₁₇	3
C₇²×C₉×C₁₇	5
C₅×C₇×C₉×C₁₇	7
C₅×C₇²×C₉	17

Subgroups — C5×C72×C9×C17 #49154151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇²×C₉×C₁₇ #49154151