Subgroups — C₂⁴×C₄×C₁₃×C₂₉ #72201422

Order 24128.

2724 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₁₃×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄×C₁₃×C₂₉	C₂	1	30	yes	maximal, direct product factor
3	C₂⁴×C₁₃×C₂₉	C₄	1	16	yes	direct product factor
4	C₂⁴×C₁₃×C₂₉	C₂²	1	15	yes	—
5	C₂²×C₄×C₁₃×C₂₉	C₂²	1	140	yes	direct product factor
6	C₂³×C₁₃×C₂₉	C₂×C₄	1	120	yes	direct product factor
7	C₂³×C₁₃×C₂₉	C₂³	1	35	yes	—
8	C₂×C₄×C₁₃×C₂₉	C₂³	1	120	yes	direct product factor
9	C₂⁴×C₄×C₂₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₁₃×C₂₉	C₂²×C₄	1	140	yes	direct product factor
11	C₂²×C₁₃×C₂₉	C₂⁴	1	15	yes	—
12	C₄×C₁₃×C₂₉	C₂⁴	1	16	yes	direct product factor
13	C₂⁵×C₂₉	C₂×C₁₃	1	1	yes	characteristic
14	C₂³×C₄×C₂₉	C₂×C₁₃	1	30	yes	direct product factor
15	C₂⁴×C₄×C₁₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₁₃×C₂₉	C₂³×C₄	1	30	yes	direct product factor
17	C₂×C₁₃×C₂₉	C₂⁵	1	1	yes	characteristic
18	C₂⁴×C₂₉	C₄×C₁₃	1	16	yes	direct product factor
19	C₂⁴×C₂₉	C₂²×C₁₃	1	15	yes	—
20	C₂²×C₄×C₂₉	C₂²×C₁₃	1	140	yes	direct product factor
21	C₂⁵×C₁₃	C₂×C₂₉	1	1	yes	characteristic
22	C₂³×C₄×C₁₃	C₂×C₂₉	1	30	yes	direct product factor
23	C₁₃×C₂₉	C₂⁴×C₄	1	1	yes	characteristic, direct product factor, Hall
24	C₂³×C₂₉	C₂×C₄×C₁₃	1	120	yes	direct product factor
25	C₂³×C₂₉	C₂³×C₁₃	1	35	yes	—
26	C₂×C₄×C₂₉	C₂³×C₁₃	1	120	yes	direct product factor
27	C₂⁴×C₁₃	C₄×C₂₉	1	16	yes	direct product factor
28	C₂⁴×C₁₃	C₂²×C₂₉	1	15	yes	—
29	C₂²×C₄×C₁₃	C₂²×C₂₉	1	140	yes	direct product factor
30	C₂²×C₂₉	C₂²×C₄×C₁₃	1	140	yes	direct product factor
31	C₂²×C₂₉	C₂⁴×C₁₃	1	15	yes	—
32	C₄×C₂₉	C₂⁴×C₁₃	1	16	yes	direct product factor
33	C₂³×C₁₃	C₂×C₄×C₂₉	1	120	yes	direct product factor
34	C₂³×C₁₃	C₂³×C₂₉	1	35	yes	—
35	C₂×C₄×C₁₃	C₂³×C₂₉	1	120	yes	direct product factor
36	C₂⁴×C₄	C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₂₉	C₂³×C₄×C₁₃	1	30	yes	direct product factor
38	C₂×C₂₉	C₂⁵×C₁₃	1	1	yes	characteristic
39	C₂²×C₁₃	C₂²×C₄×C₂₉	1	140	yes	direct product factor
40	C₂²×C₁₃	C₂⁴×C₂₉	1	15	yes	—
41	C₄×C₁₃	C₂⁴×C₂₉	1	16	yes	direct product factor
42	C₂⁵	C₂×C₁₃×C₂₉	1	1	yes	characteristic
43	C₂³×C₄	C₂×C₁₃×C₂₉	1	30	yes	direct product factor
44	C₂₉	C₂⁴×C₄×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₂×C₁₃	C₂³×C₄×C₂₉	1	30	yes	direct product factor
46	C₂×C₁₃	C₂⁵×C₂₉	1	1	yes	characteristic
47	C₂⁴	C₄×C₁₃×C₂₉	1	16	yes	direct product factor
48	C₂⁴	C₂²×C₁₃×C₂₉	1	15	yes	—
49	C₂²×C₄	C₂²×C₁₃×C₂₉	1	140	yes	direct product factor
50	C₁₃	C₂⁴×C₄×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
51	C₂³	C₂×C₄×C₁₃×C₂₉	1	120	yes	direct product factor
52	C₂³	C₂³×C₁₃×C₂₉	1	35	yes	—
53	C₂×C₄	C₂³×C₁₃×C₂₉	1	120	yes	direct product factor
54	C₂²	C₂²×C₄×C₁₃×C₂₉	1	140	yes	direct product factor
55	C₂²	C₂⁴×C₁₃×C₂₉	1	15	yes	—
56	C₄	C₂⁴×C₁₃×C₂₉	1	16	yes	direct product factor
57	C₂	C₂³×C₄×C₁₃×C₂₉	1	30	yes	direct product factor
58	C₂	C₂⁵×C₁₃×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁵×C₁₃×C₂₉
socle, prime radical	C₂⁵×C₁₃×C₂₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄×C₁₃×C₂₉	C₂	direct (N × H)
3. C₂⁴×C₁₃×C₂₉	C₄	direct (N × H)
5. C₂²×C₄×C₁₃×C₂₉	C₂²	direct (N × H)
6. C₂³×C₁₃×C₂₉	C₂×C₄	direct (N × H)
8. C₂×C₄×C₁₃×C₂₉	C₂³	direct (N × H)
9. C₂⁴×C₄×C₂₉	C₁₃	direct (N × H)
10. C₂²×C₁₃×C₂₉	C₂²×C₄	direct (N × H)
12. C₄×C₁₃×C₂₉	C₂⁴	direct (N × H)
14. C₂³×C₄×C₂₉	C₂×C₁₃	direct (N × H)
15. C₂⁴×C₄×C₁₃	C₂₉	direct (N × H)
16. C₂×C₁₃×C₂₉	C₂³×C₄	direct (N × H)
18. C₂⁴×C₂₉	C₄×C₁₃	direct (N × H)
20. C₂²×C₄×C₂₉	C₂²×C₁₃	direct (N × H)
22. C₂³×C₄×C₁₃	C₂×C₂₉	direct (N × H)
23. C₁₃×C₂₉	C₂⁴×C₄	direct (N × H)
24. C₂³×C₂₉	C₂×C₄×C₁₃	direct (N × H)
26. C₂×C₄×C₂₉	C₂³×C₁₃	direct (N × H)
27. C₂⁴×C₁₃	C₄×C₂₉	direct (N × H)
29. C₂²×C₄×C₁₃	C₂²×C₂₉	direct (N × H)
30. C₂²×C₂₉	C₂²×C₄×C₁₃	direct (N × H)
32. C₄×C₂₉	C₂⁴×C₁₃	direct (N × H)
33. C₂³×C₁₃	C₂×C₄×C₂₉	direct (N × H)
35. C₂×C₄×C₁₃	C₂³×C₂₉	direct (N × H)
36. C₂⁴×C₄	C₁₃×C₂₉	direct (N × H)
37. C₂×C₂₉	C₂³×C₄×C₁₃	direct (N × H)
39. C₂²×C₁₃	C₂²×C₄×C₂₉	direct (N × H)
41. C₄×C₁₃	C₂⁴×C₂₉	direct (N × H)
43. C₂³×C₄	C₂×C₁₃×C₂₉	direct (N × H)
44. C₂₉	C₂⁴×C₄×C₁₃	direct (N × H)
45. C₂×C₁₃	C₂³×C₄×C₂₉	direct (N × H)
47. C₂⁴	C₄×C₁₃×C₂₉	direct (N × H)
49. C₂²×C₄	C₂²×C₁₃×C₂₉	direct (N × H)
50. C₁₃	C₂⁴×C₄×C₂₉	direct (N × H)
51. C₂³	C₂×C₄×C₁₃×C₂₉	direct (N × H)
53. C₂×C₄	C₂³×C₁₃×C₂₉	direct (N × H)
54. C₂²	C₂²×C₄×C₁₃×C₂₉	direct (N × H)
56. C₄	C₂⁴×C₁₃×C₂₉	direct (N × H)
57. C₂	C₂³×C₄×C₁₃×C₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₁₃×C₂₉	2
C₂³×C₄×C₁₃×C₂₉	2
C₂⁴×C₄×C₂₉	13
C₂⁴×C₄×C₁₃	29

Subgroups — C24×C4×C13×C29 #72201422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₄×C₁₃×C₂₉ #72201422