Subgroups — C₂⁵×C₅×C₉×C₁₇ #72201754

Order 24480.

4488 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₅×C₉×C₁₇	C₂	1	31	yes	maximal, direct product factor
2	C₂⁵×C₃×C₅×C₁₇	C₃	1	1	yes	maximal, characteristic
3	C₂³×C₅×C₉×C₁₇	C₂²	1	155	yes	direct product factor
4	C₂⁵×C₉×C₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂⁴×C₃×C₅×C₁₇	C₂×C₃	1	31	yes	—
6	C₂⁵×C₅×C₁₇	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₂⁴×C₉×C₁₇	C₂×C₅	1	31	yes	direct product factor
8	C₂³×C₃×C₅×C₁₇	C₂²×C₃	1	155	yes	—
9	C₂²×C₅×C₉×C₁₇	C₂³	1	155	yes	direct product factor
10	C₂⁵×C₃×C₁₇	C₃×C₅	1	1	yes	characteristic
11	C₂×C₅×C₉×C₁₇	C₂⁴	1	31	yes	direct product factor
12	C₂⁵×C₅×C₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂⁴×C₅×C₁₇	C₂×C₉	1	31	yes	direct product factor
14	C₂³×C₉×C₁₇	C₂²×C₅	1	155	yes	direct product factor
15	C₂²×C₃×C₅×C₁₇	C₂³×C₃	1	155	yes	—
16	C₂⁴×C₃×C₁₇	C₂×C₃×C₅	1	31	yes	—
17	C₅×C₉×C₁₇	C₂⁵	1	1	yes	characteristic, direct product factor, Hall
18	C₂⁴×C₅×C₉	C₂×C₁₇	1	31	yes	direct product factor
19	C₂³×C₅×C₁₇	C₂²×C₉	1	155	yes	direct product factor
20	C₂²×C₉×C₁₇	C₂³×C₅	1	155	yes	direct product factor
21	C₂⁵×C₁₇	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₅×C₁₇	C₂⁴×C₃	1	31	yes	—
23	C₂⁵×C₃×C₅	C₃×C₁₇	1	1	yes	characteristic
24	C₂³×C₃×C₁₇	C₂²×C₃×C₅	1	155	yes	—
25	C₂³×C₅×C₉	C₂²×C₁₇	1	155	yes	direct product factor
26	C₂²×C₅×C₁₇	C₂³×C₉	1	155	yes	direct product factor
27	C₂×C₉×C₁₇	C₂⁴×C₅	1	31	yes	direct product factor
28	C₂⁵×C₉	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
29	C₂⁴×C₁₇	C₂×C₅×C₉	1	31	yes	direct product factor
30	C₃×C₅×C₁₇	C₂⁵×C₃	1	1	yes	characteristic
31	C₂⁴×C₃×C₅	C₂×C₃×C₁₇	1	31	yes	—
32	C₂²×C₃×C₁₇	C₂³×C₃×C₅	1	155	yes	—
33	C₂²×C₅×C₉	C₂³×C₁₇	1	155	yes	direct product factor
34	C₂×C₅×C₁₇	C₂⁴×C₉	1	31	yes	direct product factor
35	C₂⁵×C₅	C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
36	C₉×C₁₇	C₂⁵×C₅	1	1	yes	characteristic, direct product factor, Hall
37	C₂⁴×C₉	C₂×C₅×C₁₇	1	31	yes	direct product factor
38	C₂³×C₁₇	C₂²×C₅×C₉	1	155	yes	direct product factor
39	C₂³×C₃×C₅	C₂²×C₃×C₁₇	1	155	yes	—
40	C₂×C₃×C₁₇	C₂⁴×C₃×C₅	1	31	yes	—
41	C₂⁵×C₃	C₃×C₅×C₁₇	1	1	yes	characteristic
42	C₂×C₅×C₉	C₂⁴×C₁₇	1	31	yes	direct product factor
43	C₅×C₁₇	C₂⁵×C₉	1	1	yes	characteristic, direct product factor, Hall
44	C₂⁴×C₅	C₂×C₉×C₁₇	1	31	yes	direct product factor
45	C₂³×C₉	C₂²×C₅×C₁₇	1	155	yes	direct product factor
46	C₂²×C₁₇	C₂³×C₅×C₉	1	155	yes	direct product factor
47	C₂²×C₃×C₅	C₂³×C₃×C₁₇	1	155	yes	—
48	C₃×C₁₇	C₂⁵×C₃×C₅	1	1	yes	characteristic
49	C₂⁴×C₃	C₂×C₃×C₅×C₁₇	1	31	yes	—
50	C₅×C₉	C₂⁵×C₁₇	1	1	yes	characteristic, direct product factor, Hall
51	C₂³×C₅	C₂²×C₉×C₁₇	1	155	yes	direct product factor
52	C₂²×C₉	C₂³×C₅×C₁₇	1	155	yes	direct product factor
53	C₂×C₁₇	C₂⁴×C₅×C₉	1	31	yes	direct product factor
54	C₂⁵	C₅×C₉×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
55	C₂×C₃×C₅	C₂⁴×C₃×C₁₇	1	31	yes	—
56	C₂³×C₃	C₂²×C₃×C₅×C₁₇	1	155	yes	—
57	C₂²×C₅	C₂³×C₉×C₁₇	1	155	yes	direct product factor
58	C₂×C₉	C₂⁴×C₅×C₁₇	1	31	yes	direct product factor
59	C₁₇	C₂⁵×C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
60	C₂⁴	C₂×C₅×C₉×C₁₇	1	31	yes	direct product factor
61	C₃×C₅	C₂⁵×C₃×C₁₇	1	1	yes	characteristic
62	C₂²×C₃	C₂³×C₃×C₅×C₁₇	1	155	yes	—
63	C₂×C₅	C₂⁴×C₉×C₁₇	1	31	yes	direct product factor
64	C₉	C₂⁵×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
65	C₂³	C₂²×C₅×C₉×C₁₇	1	155	yes	direct product factor
66	C₂×C₃	C₂⁴×C₃×C₅×C₁₇	1	31	yes	—
67	C₅	C₂⁵×C₉×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
68	C₂²	C₂³×C₅×C₉×C₁₇	1	155	yes	direct product factor
69	C₃	C₂⁵×C₃×C₅×C₁₇	1	1	yes	characteristic
70	C₂	C₂⁴×C₅×C₉×C₁₇	1	31	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂⁵×C₃×C₅×C₁₇
socle, prime radical	C₂⁵×C₃×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
1. C₂⁴×C₅×C₉×C₁₇	C₂	direct (N × H)
3. C₂³×C₅×C₉×C₁₇	C₂²	direct (N × H)
4. C₂⁵×C₉×C₁₇	C₅	direct (N × H)
6. C₂⁵×C₅×C₁₇	C₉	direct (N × H)
7. C₂⁴×C₉×C₁₇	C₂×C₅	direct (N × H)
9. C₂²×C₅×C₉×C₁₇	C₂³	direct (N × H)
11. C₂×C₅×C₉×C₁₇	C₂⁴	direct (N × H)
12. C₂⁵×C₅×C₉	C₁₇	direct (N × H)
13. C₂⁴×C₅×C₁₇	C₂×C₉	direct (N × H)
14. C₂³×C₉×C₁₇	C₂²×C₅	direct (N × H)
17. C₅×C₉×C₁₇	C₂⁵	direct (N × H)
18. C₂⁴×C₅×C₉	C₂×C₁₇	direct (N × H)
19. C₂³×C₅×C₁₇	C₂²×C₉	direct (N × H)
20. C₂²×C₉×C₁₇	C₂³×C₅	direct (N × H)
21. C₂⁵×C₁₇	C₅×C₉	direct (N × H)
25. C₂³×C₅×C₉	C₂²×C₁₇	direct (N × H)
26. C₂²×C₅×C₁₇	C₂³×C₉	direct (N × H)
27. C₂×C₉×C₁₇	C₂⁴×C₅	direct (N × H)
28. C₂⁵×C₉	C₅×C₁₇	direct (N × H)
29. C₂⁴×C₁₇	C₂×C₅×C₉	direct (N × H)
33. C₂²×C₅×C₉	C₂³×C₁₇	direct (N × H)
34. C₂×C₅×C₁₇	C₂⁴×C₉	direct (N × H)
35. C₂⁵×C₅	C₉×C₁₇	direct (N × H)
36. C₉×C₁₇	C₂⁵×C₅	direct (N × H)
37. C₂⁴×C₉	C₂×C₅×C₁₇	direct (N × H)
38. C₂³×C₁₇	C₂²×C₅×C₉	direct (N × H)
42. C₂×C₅×C₉	C₂⁴×C₁₇	direct (N × H)
43. C₅×C₁₇	C₂⁵×C₉	direct (N × H)
44. C₂⁴×C₅	C₂×C₉×C₁₇	direct (N × H)
45. C₂³×C₉	C₂²×C₅×C₁₇	direct (N × H)
46. C₂²×C₁₇	C₂³×C₅×C₉	direct (N × H)
50. C₅×C₉	C₂⁵×C₁₇	direct (N × H)
51. C₂³×C₅	C₂²×C₉×C₁₇	direct (N × H)
52. C₂²×C₉	C₂³×C₅×C₁₇	direct (N × H)
53. C₂×C₁₇	C₂⁴×C₅×C₉	direct (N × H)
54. C₂⁵	C₅×C₉×C₁₇	direct (N × H)
57. C₂²×C₅	C₂³×C₉×C₁₇	direct (N × H)
58. C₂×C₉	C₂⁴×C₅×C₁₇	direct (N × H)
59. C₁₇	C₂⁵×C₅×C₉	direct (N × H)
60. C₂⁴	C₂×C₅×C₉×C₁₇	direct (N × H)
63. C₂×C₅	C₂⁴×C₉×C₁₇	direct (N × H)
64. C₉	C₂⁵×C₅×C₁₇	direct (N × H)
65. C₂³	C₂²×C₅×C₉×C₁₇	direct (N × H)
67. C₅	C₂⁵×C₉×C₁₇	direct (N × H)
68. C₂²	C₂³×C₅×C₉×C₁₇	direct (N × H)
70. C₂	C₂⁴×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
C₂⁴×C₅×C₉×C₁₇	2
C₂⁵×C₃×C₅×C₁₇	3
C₂⁵×C₉×C₁₇	5
C₂⁵×C₅×C₉	17

Subgroups — C25×C5×C9×C17 #72201754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₅×C₉×C₁₇ #72201754