Subgroups — C₃³×C₅×C₉×C₁₇ #72198243

Order 20655.

1584 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₅×C₁₇	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₉×C₁₇	C₃	1	39	yes	maximal, direct product factor
3	C₃³×C₅×C₁₇	C₉	1	27	yes	direct product factor
4	C₃³×C₅×C₁₇	C₃²	1	13	yes	—
5	C₃×C₅×C₉×C₁₇	C₃²	1	117	yes	direct product factor
6	C₃³×C₉×C₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃⁴×C₁₇	C₃×C₅	1	1	yes	characteristic
8	C₃²×C₉×C₁₇	C₃×C₅	1	39	yes	direct product factor
9	C₃³×C₅×C₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃²×C₅×C₁₇	C₃×C₉	1	117	yes	direct product factor
11	C₃²×C₅×C₁₇	C₃³	1	13	yes	—
12	C₅×C₉×C₁₇	C₃³	1	27	yes	direct product factor
13	C₃³×C₁₇	C₅×C₉	1	27	yes	direct product factor
14	C₃³×C₁₇	C₃²×C₅	1	13	yes	—
15	C₃×C₉×C₁₇	C₃²×C₅	1	117	yes	direct product factor
16	C₃⁴×C₅	C₃×C₁₇	1	1	yes	characteristic
17	C₃²×C₅×C₉	C₃×C₁₇	1	39	yes	direct product factor
18	C₃×C₅×C₁₇	C₃²×C₉	1	39	yes	direct product factor
19	C₃×C₅×C₁₇	C₃⁴	1	1	yes	characteristic
20	C₃³×C₉	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₃²×C₁₇	C₃×C₅×C₉	1	117	yes	direct product factor
22	C₃²×C₁₇	C₃³×C₅	1	13	yes	—
23	C₉×C₁₇	C₃³×C₅	1	27	yes	direct product factor
24	C₃³×C₅	C₉×C₁₇	1	27	yes	direct product factor
25	C₃³×C₅	C₃²×C₁₇	1	13	yes	—
26	C₃×C₅×C₉	C₃²×C₁₇	1	117	yes	direct product factor
27	C₅×C₁₇	C₃³×C₉	1	1	yes	characteristic, direct product factor, Hall
28	C₃⁴	C₃×C₅×C₁₇	1	1	yes	characteristic
29	C₃²×C₉	C₃×C₅×C₁₇	1	39	yes	direct product factor
30	C₃×C₁₇	C₃²×C₅×C₉	1	39	yes	direct product factor
31	C₃×C₁₇	C₃⁴×C₅	1	1	yes	characteristic
32	C₃²×C₅	C₃×C₉×C₁₇	1	117	yes	direct product factor
33	C₃²×C₅	C₃³×C₁₇	1	13	yes	—
34	C₅×C₉	C₃³×C₁₇	1	27	yes	direct product factor
35	C₃³	C₅×C₉×C₁₇	1	27	yes	direct product factor
36	C₃³	C₃²×C₅×C₁₇	1	13	yes	—
37	C₃×C₉	C₃²×C₅×C₁₇	1	117	yes	direct product factor
38	C₁₇	C₃³×C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
39	C₃×C₅	C₃²×C₉×C₁₇	1	39	yes	direct product factor
40	C₃×C₅	C₃⁴×C₁₇	1	1	yes	characteristic
41	C₃²	C₃×C₅×C₉×C₁₇	1	117	yes	direct product factor
42	C₃²	C₃³×C₅×C₁₇	1	13	yes	—
43	C₉	C₃³×C₅×C₁₇	1	27	yes	direct product factor
44	C₅	C₃³×C₉×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₃²×C₅×C₉×C₁₇	1	39	yes	direct product factor
46	C₃	C₃⁴×C₅×C₁₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃⁴×C₅×C₁₇
socle, prime radical	C₃⁴×C₅×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. C₃²×C₅×C₉×C₁₇	C₃	direct (N × H)
3. C₃³×C₅×C₁₇	C₉	direct (N × H)
5. C₃×C₅×C₉×C₁₇	C₃²	direct (N × H)
6. C₃³×C₉×C₁₇	C₅	direct (N × H)
8. C₃²×C₉×C₁₇	C₃×C₅	direct (N × H)
9. C₃³×C₅×C₉	C₁₇	direct (N × H)
10. C₃²×C₅×C₁₇	C₃×C₉	direct (N × H)
12. C₅×C₉×C₁₇	C₃³	direct (N × H)
13. C₃³×C₁₇	C₅×C₉	direct (N × H)
15. C₃×C₉×C₁₇	C₃²×C₅	direct (N × H)
17. C₃²×C₅×C₉	C₃×C₁₇	direct (N × H)
18. C₃×C₅×C₁₇	C₃²×C₉	direct (N × H)
20. C₃³×C₉	C₅×C₁₇	direct (N × H)
21. C₃²×C₁₇	C₃×C₅×C₉	direct (N × H)
23. C₉×C₁₇	C₃³×C₅	direct (N × H)
24. C₃³×C₅	C₉×C₁₇	direct (N × H)
26. C₃×C₅×C₉	C₃²×C₁₇	direct (N × H)
27. C₅×C₁₇	C₃³×C₉	direct (N × H)
29. C₃²×C₉	C₃×C₅×C₁₇	direct (N × H)
30. C₃×C₁₇	C₃²×C₅×C₉	direct (N × H)
32. C₃²×C₅	C₃×C₉×C₁₇	direct (N × H)
34. C₅×C₉	C₃³×C₁₇	direct (N × H)
35. C₃³	C₅×C₉×C₁₇	direct (N × H)
37. C₃×C₉	C₃²×C₅×C₁₇	direct (N × H)
38. C₁₇	C₃³×C₅×C₉	direct (N × H)
39. C₃×C₅	C₃²×C₉×C₁₇	direct (N × H)
41. C₃²	C₃×C₅×C₉×C₁₇	direct (N × H)
43. C₉	C₃³×C₅×C₁₇	direct (N × H)
44. C₅	C₃³×C₉×C₁₇	direct (N × H)
45. C₃	C₃²×C₅×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
C₃⁴×C₅×C₁₇	3
C₃²×C₅×C₉×C₁₇	3
C₃³×C₉×C₁₇	5
C₃³×C₅×C₉	17

Subgroups — C33×C5×C9×C17 #72198243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₅×C₉×C₁₇ #72198243