Subgroups — C₂×C₄³×C₇×C₂₉ #72203152

Order 25984.

2544 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×C₇×C₂₉	C₂	1	7	yes	maximal
2	C₄³×C₇×C₂₉	C₂	1	8	yes	maximal, direct product factor
3	C₂³×C₄×C₇×C₂₉	C₂²	1	7	yes	—
4	C₂×C₄²×C₇×C₂₉	C₄	1	56	yes	direct product factor
5	C₂×C₄²×C₇×C₂₉	C₂²	1	28	yes	—
6	C₂⁴×C₇×C₂₉	C₂³	1	1	yes	characteristic
7	C₂²×C₄×C₇×C₂₉	C₂×C₄	1	84	yes	—
8	C₂²×C₄×C₇×C₂₉	C₂³	1	14	yes	—
9	C₄²×C₇×C₂₉	C₂×C₄	1	112	yes	direct product factor
10	C₂×C₄³×C₂₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₄²×C₂₉	C₂×C₇	1	7	yes	—
12	C₄³×C₂₉	C₂×C₇	1	8	yes	direct product factor
13	C₂³×C₇×C₂₉	C₂²×C₄	1	14	yes	—
14	C₂³×C₇×C₂₉	C₂⁴	1	1	yes	characteristic
15	C₂×C₄×C₇×C₂₉	C₄²	1	112	yes	direct product factor
16	C₂×C₄×C₇×C₂₉	C₂²×C₄	1	84	yes	—
17	C₂³×C₄×C₂₉	C₂²×C₇	1	7	yes	—
18	C₂×C₄²×C₂₉	C₄×C₇	1	56	yes	direct product factor
19	C₂×C₄²×C₂₉	C₂²×C₇	1	28	yes	—
20	C₂×C₄³×C₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂²×C₇×C₂₉	C₂×C₄²	1	28	yes	—
22	C₂²×C₇×C₂₉	C₂³×C₄	1	7	yes	—
23	C₄×C₇×C₂₉	C₂×C₄²	1	56	yes	direct product factor
24	C₂⁴×C₂₉	C₂³×C₇	1	1	yes	characteristic
25	C₂²×C₄×C₂₉	C₂×C₄×C₇	1	84	yes	—
26	C₂²×C₄×C₂₉	C₂³×C₇	1	14	yes	—
27	C₄²×C₂₉	C₂×C₄×C₇	1	112	yes	direct product factor
28	C₂²×C₄²×C₇	C₂×C₂₉	1	7	yes	—
29	C₄³×C₇	C₂×C₂₉	1	8	yes	direct product factor
30	C₂×C₇×C₂₉	C₄³	1	8	yes	direct product factor
31	C₂×C₇×C₂₉	C₂²×C₄²	1	7	yes	—
32	C₂³×C₂₉	C₂²×C₄×C₇	1	14	yes	—
33	C₂³×C₂₉	C₂⁴×C₇	1	1	yes	characteristic
34	C₂×C₄×C₂₉	C₄²×C₇	1	112	yes	direct product factor
35	C₂×C₄×C₂₉	C₂²×C₄×C₇	1	84	yes	—
36	C₂³×C₄×C₇	C₂²×C₂₉	1	7	yes	—
37	C₂×C₄²×C₇	C₄×C₂₉	1	56	yes	direct product factor
38	C₂×C₄²×C₇	C₂²×C₂₉	1	28	yes	—
39	C₇×C₂₉	C₂×C₄³	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₄³	C₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²×C₂₉	C₂×C₄²×C₇	1	28	yes	—
42	C₂²×C₂₉	C₂³×C₄×C₇	1	7	yes	—
43	C₄×C₂₉	C₂×C₄²×C₇	1	56	yes	direct product factor
44	C₂⁴×C₇	C₂³×C₂₉	1	1	yes	characteristic
45	C₂²×C₄×C₇	C₂×C₄×C₂₉	1	84	yes	—
46	C₂²×C₄×C₇	C₂³×C₂₉	1	14	yes	—
47	C₄²×C₇	C₂×C₄×C₂₉	1	112	yes	direct product factor
48	C₂²×C₄²	C₂×C₇×C₂₉	1	7	yes	—
49	C₄³	C₂×C₇×C₂₉	1	8	yes	direct product factor
50	C₂×C₂₉	C₄³×C₇	1	8	yes	direct product factor
51	C₂×C₂₉	C₂²×C₄²×C₇	1	7	yes	—
52	C₂³×C₇	C₂²×C₄×C₂₉	1	14	yes	—
53	C₂³×C₇	C₂⁴×C₂₉	1	1	yes	characteristic
54	C₂×C₄×C₇	C₄²×C₂₉	1	112	yes	direct product factor
55	C₂×C₄×C₇	C₂²×C₄×C₂₉	1	84	yes	—
56	C₂³×C₄	C₂²×C₇×C₂₉	1	7	yes	—
57	C₂×C₄²	C₄×C₇×C₂₉	1	56	yes	direct product factor
58	C₂×C₄²	C₂²×C₇×C₂₉	1	28	yes	—
59	C₂₉	C₂×C₄³×C₇	1	1	yes	characteristic, direct product factor, Sylow
60	C₂²×C₇	C₂×C₄²×C₂₉	1	28	yes	—
61	C₂²×C₇	C₂³×C₄×C₂₉	1	7	yes	—
62	C₄×C₇	C₂×C₄²×C₂₉	1	56	yes	direct product factor
63	C₂⁴	C₂³×C₇×C₂₉	1	1	yes	characteristic
64	C₂²×C₄	C₂×C₄×C₇×C₂₉	1	84	yes	—
65	C₂²×C₄	C₂³×C₇×C₂₉	1	14	yes	—
66	C₄²	C₂×C₄×C₇×C₂₉	1	112	yes	direct product factor
67	C₂×C₇	C₄³×C₂₉	1	8	yes	direct product factor
68	C₂×C₇	C₂²×C₄²×C₂₉	1	7	yes	—
69	C₂³	C₂²×C₄×C₇×C₂₉	1	14	yes	—
70	C₂³	C₂⁴×C₇×C₂₉	1	1	yes	characteristic
71	C₂×C₄	C₄²×C₇×C₂₉	1	112	yes	direct product factor
72	C₂×C₄	C₂²×C₄×C₇×C₂₉	1	84	yes	—
73	C₇	C₂×C₄³×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	C₂×C₄²×C₇×C₂₉	1	28	yes	—
75	C₂²	C₂³×C₄×C₇×C₂₉	1	7	yes	—
76	C₄	C₂×C₄²×C₇×C₂₉	1	56	yes	direct product factor
77	C₂	C₄³×C₇×C₂₉	1	8	yes	direct product factor
78	C₂	C₂²×C₄²×C₇×C₂₉	1	7	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³	C₂⁴×C₇×C₂₉
socle, prime radical	C₂⁴×C₇×C₂₉	C₂³
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄³×C₇×C₂₉	C₂	direct (N × H)
4. C₂×C₄²×C₇×C₂₉	C₄	direct (N × H)
9. C₄²×C₇×C₂₉	C₂×C₄	direct (N × H)
10. C₂×C₄³×C₂₉	C₇	direct (N × H)
12. C₄³×C₂₉	C₂×C₇	direct (N × H)
15. C₂×C₄×C₇×C₂₉	C₄²	direct (N × H)
18. C₂×C₄²×C₂₉	C₄×C₇	direct (N × H)
20. C₂×C₄³×C₇	C₂₉	direct (N × H)
23. C₄×C₇×C₂₉	C₂×C₄²	direct (N × H)
27. C₄²×C₂₉	C₂×C₄×C₇	direct (N × H)
29. C₄³×C₇	C₂×C₂₉	direct (N × H)
30. C₂×C₇×C₂₉	C₄³	direct (N × H)
34. C₂×C₄×C₂₉	C₄²×C₇	direct (N × H)
37. C₂×C₄²×C₇	C₄×C₂₉	direct (N × H)
39. C₇×C₂₉	C₂×C₄³	direct (N × H)
40. C₂×C₄³	C₇×C₂₉	direct (N × H)
43. C₄×C₂₉	C₂×C₄²×C₇	direct (N × H)
47. C₄²×C₇	C₂×C₄×C₂₉	direct (N × H)
49. C₄³	C₂×C₇×C₂₉	direct (N × H)
50. C₂×C₂₉	C₄³×C₇	direct (N × H)
54. C₂×C₄×C₇	C₄²×C₂₉	direct (N × H)
57. C₂×C₄²	C₄×C₇×C₂₉	direct (N × H)
59. C₂₉	C₂×C₄³×C₇	direct (N × H)
62. C₄×C₇	C₂×C₄²×C₂₉	direct (N × H)
66. C₄²	C₂×C₄×C₇×C₂₉	direct (N × H)
67. C₂×C₇	C₄³×C₂₉	direct (N × H)
71. C₂×C₄	C₄²×C₇×C₂₉	direct (N × H)
73. C₇	C₂×C₄³×C₂₉	direct (N × H)
76. C₄	C₂×C₄²×C₇×C₂₉	direct (N × H)
77. C₂	C₄³×C₇×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
C₂²×C₄²×C₇×C₂₉	2
C₄³×C₇×C₂₉	2
C₂×C₄³×C₂₉	7
C₂×C₄³×C₇	29

Subgroups — C2×C43×C7×C29 #72203152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄³×C₇×C₂₉ #72203152