Subgroups — C₃³×C₄²×C₂₉ #72190873

Order 12528.

840 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₄×C₂₉	C₂	1	3	yes	maximal
2	C₃²×C₄²×C₂₉	C₃	1	13	yes	maximal, direct product factor
3	C₂²×C₃³×C₂₉	C₂²	1	1	yes	characteristic
4	C₃³×C₄×C₂₉	C₄	1	6	yes	direct product factor
5	C₂×C₃²×C₄×C₂₉	C₂×C₃	1	39	yes	—
6	C₂×C₃³×C₂₉	C₂×C₄	1	3	yes	—
7	C₃×C₄²×C₂₉	C₃²	1	13	yes	direct product factor
8	C₂²×C₃²×C₂₉	C₂²×C₃	1	13	yes	—
9	C₃²×C₄×C₂₉	C₃×C₄	1	78	yes	direct product factor
10	C₃³×C₂₉	C₄²	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₄×C₂₉	C₂×C₃²	1	39	yes	—
12	C₂×C₃²×C₂₉	C₂×C₃×C₄	1	39	yes	—
13	C₄²×C₂₉	C₃³	1	1	yes	characteristic, direct product factor, Hall
14	C₃³×C₄²	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂²×C₃×C₂₉	C₂²×C₃²	1	13	yes	—
16	C₃×C₄×C₂₉	C₃²×C₄	1	78	yes	direct product factor
17	C₃²×C₂₉	C₃×C₄²	1	13	yes	direct product factor
18	C₂×C₄×C₂₉	C₂×C₃³	1	3	yes	—
19	C₂×C₃³×C₄	C₂×C₂₉	1	3	yes	—
20	C₂×C₃×C₂₉	C₂×C₃²×C₄	1	39	yes	—
21	C₃²×C₄²	C₃×C₂₉	1	13	yes	direct product factor
22	C₂²×C₂₉	C₂²×C₃³	1	1	yes	characteristic
23	C₄×C₂₉	C₃³×C₄	1	6	yes	direct product factor
24	C₂²×C₃³	C₂²×C₂₉	1	1	yes	characteristic
25	C₃³×C₄	C₄×C₂₉	1	6	yes	direct product factor
26	C₃×C₂₉	C₃²×C₄²	1	13	yes	direct product factor
27	C₂×C₃²×C₄	C₂×C₃×C₂₉	1	39	yes	—
28	C₂×C₂₉	C₂×C₃³×C₄	1	3	yes	—
29	C₂×C₃³	C₂×C₄×C₂₉	1	3	yes	—
30	C₃×C₄²	C₃²×C₂₉	1	13	yes	direct product factor
31	C₂²×C₃²	C₂²×C₃×C₂₉	1	13	yes	—
32	C₃²×C₄	C₃×C₄×C₂₉	1	78	yes	direct product factor
33	C₂₉	C₃³×C₄²	1	1	yes	characteristic, direct product factor, Sylow
34	C₃³	C₄²×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×C₃×C₄	C₂×C₃²×C₂₉	1	39	yes	—
36	C₂×C₃²	C₂×C₃×C₄×C₂₉	1	39	yes	—
37	C₄²	C₃³×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
38	C₂²×C₃	C₂²×C₃²×C₂₉	1	13	yes	—
39	C₃×C₄	C₃²×C₄×C₂₉	1	78	yes	direct product factor
40	C₃²	C₃×C₄²×C₂₉	1	13	yes	direct product factor
41	C₂×C₄	C₂×C₃³×C₂₉	1	3	yes	—
42	C₂×C₃	C₂×C₃²×C₄×C₂₉	1	39	yes	—
43	C₂²	C₂²×C₃³×C₂₉	1	1	yes	characteristic
44	C₄	C₃³×C₄×C₂₉	1	6	yes	direct product factor
45	C₃	C₃²×C₄²×C₂₉	1	13	yes	direct product factor
46	C₂	C₂×C₃³×C₄×C₂₉	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₃³×C₂₉
socle, prime radical	C₂²×C₃³×C₂₉	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×C₄²×C₂₉	C₃	direct (N × H)
4. C₃³×C₄×C₂₉	C₄	direct (N × H)
7. C₃×C₄²×C₂₉	C₃²	direct (N × H)
9. C₃²×C₄×C₂₉	C₃×C₄	direct (N × H)
10. C₃³×C₂₉	C₄²	direct (N × H)
13. C₄²×C₂₉	C₃³	direct (N × H)
14. C₃³×C₄²	C₂₉	direct (N × H)
16. C₃×C₄×C₂₉	C₃²×C₄	direct (N × H)
17. C₃²×C₂₉	C₃×C₄²	direct (N × H)
21. C₃²×C₄²	C₃×C₂₉	direct (N × H)
23. C₄×C₂₉	C₃³×C₄	direct (N × H)
25. C₃³×C₄	C₄×C₂₉	direct (N × H)
26. C₃×C₂₉	C₃²×C₄²	direct (N × H)
30. C₃×C₄²	C₃²×C₂₉	direct (N × H)
32. C₃²×C₄	C₃×C₄×C₂₉	direct (N × H)
33. C₂₉	C₃³×C₄²	direct (N × H)
34. C₃³	C₄²×C₂₉	direct (N × H)
37. C₄²	C₃³×C₂₉	direct (N × H)
39. C₃×C₄	C₃²×C₄×C₂₉	direct (N × H)
40. C₃²	C₃×C₄²×C₂₉	direct (N × H)
44. C₄	C₃³×C₄×C₂₉	direct (N × H)
45. C₃	C₃²×C₄²×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
C₂×C₃³×C₄×C₂₉	2
C₃²×C₄²×C₂₉	3
C₃³×C₄²	29

Subgroups — C33×C42×C29 #72190873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₄²×C₂₉ #72190873