Subgroups — C₂⁵×C₄×C₁₃×C₁₇ #72205285

Order 28288.

21104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄×C₁₃×C₁₇	C₂	1	62	yes	maximal, direct product factor
2	C₂⁶×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂⁵×C₁₃×C₁₇	C₄	1	32	yes	direct product factor
4	C₂⁵×C₁₃×C₁₇	C₂²	1	31	yes	—
5	C₂³×C₄×C₁₃×C₁₇	C₂²	1	620	yes	direct product factor
6	C₂⁴×C₁₃×C₁₇	C₂×C₄	1	496	yes	direct product factor
7	C₂⁴×C₁₃×C₁₇	C₂³	1	155	yes	—
8	C₂²×C₄×C₁₃×C₁₇	C₂³	1	1240	yes	direct product factor
9	C₂⁵×C₄×C₁₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂³×C₁₃×C₁₇	C₂²×C₄	1	1240	yes	direct product factor
11	C₂³×C₁₃×C₁₇	C₂⁴	1	155	yes	—
12	C₂×C₄×C₁₃×C₁₇	C₂⁴	1	496	yes	direct product factor
13	C₂⁵×C₄×C₁₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂⁶×C₁₇	C₂×C₁₃	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₇	C₂×C₁₃	1	62	yes	direct product factor
16	C₂²×C₁₃×C₁₇	C₂³×C₄	1	620	yes	direct product factor
17	C₂²×C₁₃×C₁₇	C₂⁵	1	31	yes	—
18	C₄×C₁₃×C₁₇	C₂⁵	1	32	yes	direct product factor
19	C₂⁶×C₁₃	C₂×C₁₇	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃	C₂×C₁₇	1	62	yes	direct product factor
21	C₂⁵×C₁₇	C₄×C₁₃	1	32	yes	direct product factor
22	C₂⁵×C₁₇	C₂²×C₁₃	1	31	yes	—
23	C₂³×C₄×C₁₇	C₂²×C₁₃	1	620	yes	direct product factor
24	C₂×C₁₃×C₁₇	C₂⁴×C₄	1	62	yes	direct product factor
25	C₂×C₁₃×C₁₇	C₂⁶	1	1	yes	characteristic
26	C₂⁵×C₁₃	C₄×C₁₇	1	32	yes	direct product factor
27	C₂⁵×C₁₃	C₂²×C₁₇	1	31	yes	—
28	C₂³×C₄×C₁₃	C₂²×C₁₇	1	620	yes	direct product factor
29	C₂⁴×C₁₇	C₂×C₄×C₁₃	1	496	yes	direct product factor
30	C₂⁴×C₁₇	C₂³×C₁₃	1	155	yes	—
31	C₂²×C₄×C₁₇	C₂³×C₁₃	1	1240	yes	direct product factor
32	C₁₃×C₁₇	C₂⁵×C₄	1	1	yes	characteristic, direct product factor, Hall
33	C₂⁴×C₁₃	C₂×C₄×C₁₇	1	496	yes	direct product factor
34	C₂⁴×C₁₃	C₂³×C₁₇	1	155	yes	—
35	C₂²×C₄×C₁₃	C₂³×C₁₇	1	1240	yes	direct product factor
36	C₂³×C₁₇	C₂²×C₄×C₁₃	1	1240	yes	direct product factor
37	C₂³×C₁₇	C₂⁴×C₁₃	1	155	yes	—
38	C₂×C₄×C₁₇	C₂⁴×C₁₃	1	496	yes	direct product factor
39	C₂⁵×C₄	C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
40	C₂³×C₁₃	C₂²×C₄×C₁₇	1	1240	yes	direct product factor
41	C₂³×C₁₃	C₂⁴×C₁₇	1	155	yes	—
42	C₂×C₄×C₁₃	C₂⁴×C₁₇	1	496	yes	direct product factor
43	C₂²×C₁₇	C₂³×C₄×C₁₃	1	620	yes	direct product factor
44	C₂²×C₁₇	C₂⁵×C₁₃	1	31	yes	—
45	C₄×C₁₇	C₂⁵×C₁₃	1	32	yes	direct product factor
46	C₂⁶	C₂×C₁₃×C₁₇	1	1	yes	characteristic
47	C₂⁴×C₄	C₂×C₁₃×C₁₇	1	62	yes	direct product factor
48	C₂²×C₁₃	C₂³×C₄×C₁₇	1	620	yes	direct product factor
49	C₂²×C₁₃	C₂⁵×C₁₇	1	31	yes	—
50	C₄×C₁₃	C₂⁵×C₁₇	1	32	yes	direct product factor
51	C₂×C₁₇	C₂⁴×C₄×C₁₃	1	62	yes	direct product factor
52	C₂×C₁₇	C₂⁶×C₁₃	1	1	yes	characteristic
53	C₂⁵	C₄×C₁₃×C₁₇	1	32	yes	direct product factor
54	C₂⁵	C₂²×C₁₃×C₁₇	1	31	yes	—
55	C₂³×C₄	C₂²×C₁₃×C₁₇	1	620	yes	direct product factor
56	C₂×C₁₃	C₂⁴×C₄×C₁₇	1	62	yes	direct product factor
57	C₂×C₁₃	C₂⁶×C₁₇	1	1	yes	characteristic
58	C₁₇	C₂⁵×C₄×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
59	C₂⁴	C₂×C₄×C₁₃×C₁₇	1	496	yes	direct product factor
60	C₂⁴	C₂³×C₁₃×C₁₇	1	155	yes	—
61	C₂²×C₄	C₂³×C₁₃×C₁₇	1	1240	yes	direct product factor
62	C₁₃	C₂⁵×C₄×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
63	C₂³	C₂²×C₄×C₁₃×C₁₇	1	1240	yes	direct product factor
64	C₂³	C₂⁴×C₁₃×C₁₇	1	155	yes	—
65	C₂×C₄	C₂⁴×C₁₃×C₁₇	1	496	yes	direct product factor
66	C₂²	C₂³×C₄×C₁₃×C₁₇	1	620	yes	direct product factor
67	C₂²	C₂⁵×C₁₃×C₁₇	1	31	yes	—
68	C₄	C₂⁵×C₁₃×C₁₇	1	32	yes	direct product factor
69	C₂	C₂⁶×C₁₃×C₁₇	1	1	yes	characteristic
70	C₂	C₂⁴×C₄×C₁₃×C₁₇	1	62	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁶×C₁₃×C₁₇
socle, prime radical	C₂⁶×C₁₃×C₁₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₄×C₁₃×C₁₇	C₂	direct (N × H)
3. C₂⁵×C₁₃×C₁₇	C₄	direct (N × H)
5. C₂³×C₄×C₁₃×C₁₇	C₂²	direct (N × H)
6. C₂⁴×C₁₃×C₁₇	C₂×C₄	direct (N × H)
8. C₂²×C₄×C₁₃×C₁₇	C₂³	direct (N × H)
9. C₂⁵×C₄×C₁₇	C₁₃	direct (N × H)
10. C₂³×C₁₃×C₁₇	C₂²×C₄	direct (N × H)
12. C₂×C₄×C₁₃×C₁₇	C₂⁴	direct (N × H)
13. C₂⁵×C₄×C₁₃	C₁₇	direct (N × H)
15. C₂⁴×C₄×C₁₇	C₂×C₁₃	direct (N × H)
16. C₂²×C₁₃×C₁₇	C₂³×C₄	direct (N × H)
18. C₄×C₁₃×C₁₇	C₂⁵	direct (N × H)
20. C₂⁴×C₄×C₁₃	C₂×C₁₇	direct (N × H)
21. C₂⁵×C₁₇	C₄×C₁₃	direct (N × H)
23. C₂³×C₄×C₁₇	C₂²×C₁₃	direct (N × H)
24. C₂×C₁₃×C₁₇	C₂⁴×C₄	direct (N × H)
26. C₂⁵×C₁₃	C₄×C₁₇	direct (N × H)
28. C₂³×C₄×C₁₃	C₂²×C₁₇	direct (N × H)
29. C₂⁴×C₁₇	C₂×C₄×C₁₃	direct (N × H)
31. C₂²×C₄×C₁₇	C₂³×C₁₃	direct (N × H)
32. C₁₃×C₁₇	C₂⁵×C₄	direct (N × H)
33. C₂⁴×C₁₃	C₂×C₄×C₁₇	direct (N × H)
35. C₂²×C₄×C₁₃	C₂³×C₁₇	direct (N × H)
36. C₂³×C₁₇	C₂²×C₄×C₁₃	direct (N × H)
38. C₂×C₄×C₁₇	C₂⁴×C₁₃	direct (N × H)
39. C₂⁵×C₄	C₁₃×C₁₇	direct (N × H)
40. C₂³×C₁₃	C₂²×C₄×C₁₇	direct (N × H)
42. C₂×C₄×C₁₃	C₂⁴×C₁₇	direct (N × H)
43. C₂²×C₁₇	C₂³×C₄×C₁₃	direct (N × H)
45. C₄×C₁₇	C₂⁵×C₁₃	direct (N × H)
47. C₂⁴×C₄	C₂×C₁₃×C₁₇	direct (N × H)
48. C₂²×C₁₃	C₂³×C₄×C₁₇	direct (N × H)
50. C₄×C₁₃	C₂⁵×C₁₇	direct (N × H)
51. C₂×C₁₇	C₂⁴×C₄×C₁₃	direct (N × H)
53. C₂⁵	C₄×C₁₃×C₁₇	direct (N × H)
55. C₂³×C₄	C₂²×C₁₃×C₁₇	direct (N × H)
56. C₂×C₁₃	C₂⁴×C₄×C₁₇	direct (N × H)
58. C₁₇	C₂⁵×C₄×C₁₃	direct (N × H)
59. C₂⁴	C₂×C₄×C₁₃×C₁₇	direct (N × H)
61. C₂²×C₄	C₂³×C₁₃×C₁₇	direct (N × H)
62. C₁₃	C₂⁵×C₄×C₁₇	direct (N × H)
63. C₂³	C₂²×C₄×C₁₃×C₁₇	direct (N × H)
65. C₂×C₄	C₂⁴×C₁₃×C₁₇	direct (N × H)
66. C₂²	C₂³×C₄×C₁₃×C₁₇	direct (N × H)
68. C₄	C₂⁵×C₁₃×C₁₇	direct (N × H)
70. C₂	C₂⁴×C₄×C₁₃×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×C₄×C₁₃×C₁₇	2
C₂⁶×C₁₃×C₁₇	2
C₂⁵×C₄×C₁₇	13
C₂⁵×C₄×C₁₃	17

Subgroups — C25×C4×C13×C17 #72205285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₄×C₁₃×C₁₇ #72205285