Subgroups — C₃×C₄⁴×C₂₉ #72199714

Order 22272.

7932 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄³×C₂₉	C₂	1	15	yes	maximal
2	C₂²×C₃×C₄²×C₂₉	C₂²	1	35	yes	—
3	C₃×C₄³×C₂₉	C₄	1	120	yes	direct product factor
4	C₂³×C₃×C₄×C₂₉	C₂³	1	15	yes	—
5	C₂×C₃×C₄²×C₂₉	C₂×C₄	1	420	yes	—
6	C₄⁴×C₂₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₄³×C₂₉	C₂×C₃	1	15	yes	—
8	C₂²×C₄²×C₂₉	C₂²×C₃	1	35	yes	—
9	C₄³×C₂₉	C₃×C₄	1	120	yes	direct product factor
10	C₂⁴×C₃×C₂₉	C₂⁴	1	1	yes	characteristic
11	C₂²×C₃×C₄×C₂₉	C₂²×C₄	1	210	yes	—
12	C₃×C₄²×C₂₉	C₄²	1	560	yes	direct product factor
13	C₂³×C₄×C₂₉	C₂³×C₃	1	15	yes	—
14	C₂×C₄²×C₂₉	C₂×C₃×C₄	1	420	yes	—
15	C₃×C₄⁴	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂³×C₃×C₂₉	C₂³×C₄	1	15	yes	—
17	C₂×C₃×C₄×C₂₉	C₂×C₄²	1	420	yes	—
18	C₂⁴×C₂₉	C₂⁴×C₃	1	1	yes	characteristic
19	C₂²×C₄×C₂₉	C₂²×C₃×C₄	1	210	yes	—
20	C₄²×C₂₉	C₃×C₄²	1	560	yes	direct product factor
21	C₂×C₃×C₄³	C₂×C₂₉	1	15	yes	—
22	C₂²×C₃×C₂₉	C₂²×C₄²	1	35	yes	—
23	C₃×C₄×C₂₉	C₄³	1	120	yes	direct product factor
24	C₄⁴	C₃×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂³×C₂₉	C₂³×C₃×C₄	1	15	yes	—
26	C₂×C₄×C₂₉	C₂×C₃×C₄²	1	420	yes	—
27	C₂²×C₃×C₄²	C₂²×C₂₉	1	35	yes	—
28	C₃×C₄³	C₄×C₂₉	1	120	yes	direct product factor
29	C₂×C₃×C₂₉	C₂×C₄³	1	15	yes	—
30	C₂×C₄³	C₂×C₃×C₂₉	1	15	yes	—
31	C₂²×C₂₉	C₂²×C₃×C₄²	1	35	yes	—
32	C₄×C₂₉	C₃×C₄³	1	120	yes	direct product factor
33	C₂³×C₃×C₄	C₂³×C₂₉	1	15	yes	—
34	C₂×C₃×C₄²	C₂×C₄×C₂₉	1	420	yes	—
35	C₃×C₂₉	C₄⁴	1	1	yes	characteristic, direct product factor, Hall
36	C₂²×C₄²	C₂²×C₃×C₂₉	1	35	yes	—
37	C₄³	C₃×C₄×C₂₉	1	120	yes	direct product factor
38	C₂×C₂₉	C₂×C₃×C₄³	1	15	yes	—
39	C₂⁴×C₃	C₂⁴×C₂₉	1	1	yes	characteristic
40	C₂²×C₃×C₄	C₂²×C₄×C₂₉	1	210	yes	—
41	C₃×C₄²	C₄²×C₂₉	1	560	yes	direct product factor
42	C₂³×C₄	C₂³×C₃×C₂₉	1	15	yes	—
43	C₂×C₄²	C₂×C₃×C₄×C₂₉	1	420	yes	—
44	C₂₉	C₃×C₄⁴	1	1	yes	characteristic, direct product factor, Sylow
45	C₂³×C₃	C₂³×C₄×C₂₉	1	15	yes	—
46	C₂×C₃×C₄	C₂×C₄²×C₂₉	1	420	yes	—
47	C₂⁴	C₂⁴×C₃×C₂₉	1	1	yes	characteristic
48	C₂²×C₄	C₂²×C₃×C₄×C₂₉	1	210	yes	—
49	C₄²	C₃×C₄²×C₂₉	1	560	yes	direct product factor
50	C₂²×C₃	C₂²×C₄²×C₂₉	1	35	yes	—
51	C₃×C₄	C₄³×C₂₉	1	120	yes	direct product factor
52	C₂³	C₂³×C₃×C₄×C₂₉	1	15	yes	—
53	C₂×C₄	C₂×C₃×C₄²×C₂₉	1	420	yes	—
54	C₂×C₃	C₂×C₄³×C₂₉	1	15	yes	—
55	C₂²	C₂²×C₃×C₄²×C₂₉	1	35	yes	—
56	C₄	C₃×C₄³×C₂₉	1	120	yes	direct product factor
57	C₃	C₄⁴×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
58	C₂	C₂×C₃×C₄³×C₂₉	1	15	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂⁴	C₂⁴×C₃×C₂₉
socle, prime radical	C₂⁴×C₃×C₂₉	C₂⁴
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₄³×C₂₉	C₄	direct (N × H)
6. C₄⁴×C₂₉	C₃	direct (N × H)
9. C₄³×C₂₉	C₃×C₄	direct (N × H)
12. C₃×C₄²×C₂₉	C₄²	direct (N × H)
15. C₃×C₄⁴	C₂₉	direct (N × H)
20. C₄²×C₂₉	C₃×C₄²	direct (N × H)
23. C₃×C₄×C₂₉	C₄³	direct (N × H)
24. C₄⁴	C₃×C₂₉	direct (N × H)
28. C₃×C₄³	C₄×C₂₉	direct (N × H)
32. C₄×C₂₉	C₃×C₄³	direct (N × H)
35. C₃×C₂₉	C₄⁴	direct (N × H)
37. C₄³	C₃×C₄×C₂₉	direct (N × H)
41. C₃×C₄²	C₄²×C₂₉	direct (N × H)
44. C₂₉	C₃×C₄⁴	direct (N × H)
49. C₄²	C₃×C₄²×C₂₉	direct (N × H)
51. C₃×C₄	C₄³×C₂₉	direct (N × H)
56. C₄	C₃×C₄³×C₂₉	direct (N × H)
57. C₃	C₄⁴×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×C₃×C₄³×C₂₉	2
C₄⁴×C₂₉	3
C₃×C₄⁴	29

Subgroups — C3×C44×C29 #72199714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄⁴×C₂₉ #72199714