Subgroups — C₂⁴×C₂₇×C₂₉ #72190876

Order 12528.

536 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂₇×C₂₉	C₂	1	15	yes	maximal, direct product factor
2	C₂⁴×C₉×C₂₉	C₃	1	1	yes	maximal, characteristic
3	C₂²×C₂₇×C₂₉	C₂²	1	35	yes	direct product factor
4	C₂³×C₉×C₂₉	C₂×C₃	1	15	yes	—
5	C₂×C₂₇×C₂₉	C₂³	1	15	yes	direct product factor
6	C₂⁴×C₃×C₂₉	C₉	1	1	yes	characteristic
7	C₂²×C₉×C₂₉	C₂²×C₃	1	35	yes	—
8	C₂₇×C₂₉	C₂⁴	1	1	yes	characteristic, direct product factor, Hall
9	C₂³×C₃×C₂₉	C₂×C₉	1	15	yes	—
10	C₂×C₉×C₂₉	C₂³×C₃	1	15	yes	—
11	C₂⁴×C₂₉	C₂₇	1	1	yes	characteristic, direct product factor, Hall
12	C₂⁴×C₂₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₂₉	C₂²×C₉	1	35	yes	—
14	C₉×C₂₉	C₂⁴×C₃	1	1	yes	characteristic
15	C₂³×C₂₉	C₂×C₂₇	1	15	yes	direct product factor
16	C₂³×C₂₇	C₂×C₂₉	1	15	yes	direct product factor
17	C₂×C₃×C₂₉	C₂³×C₉	1	15	yes	—
18	C₂⁴×C₉	C₃×C₂₉	1	1	yes	characteristic
19	C₂²×C₂₉	C₂²×C₂₇	1	35	yes	direct product factor
20	C₂²×C₂₇	C₂²×C₂₉	1	35	yes	direct product factor
21	C₃×C₂₉	C₂⁴×C₉	1	1	yes	characteristic
22	C₂³×C₉	C₂×C₃×C₂₉	1	15	yes	—
23	C₂×C₂₉	C₂³×C₂₇	1	15	yes	direct product factor
24	C₂×C₂₇	C₂³×C₂₉	1	15	yes	direct product factor
25	C₂⁴×C₃	C₉×C₂₉	1	1	yes	characteristic
26	C₂²×C₉	C₂²×C₃×C₂₉	1	35	yes	—
27	C₂₉	C₂⁴×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂₇	C₂⁴×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₂³×C₃	C₂×C₉×C₂₉	1	15	yes	—
30	C₂×C₉	C₂³×C₃×C₂₉	1	15	yes	—
31	C₂⁴	C₂₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
32	C₂²×C₃	C₂²×C₉×C₂₉	1	35	yes	—
33	C₉	C₂⁴×C₃×C₂₉	1	1	yes	characteristic
34	C₂³	C₂×C₂₇×C₂₉	1	15	yes	direct product factor
35	C₂×C₃	C₂³×C₉×C₂₉	1	15	yes	—
36	C₂²	C₂²×C₂₇×C₂₉	1	35	yes	direct product factor
37	C₃	C₂⁴×C₉×C₂₉	1	1	yes	characteristic
38	C₂	C₂³×C₂₇×C₂₉	1	15	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₂⁴×C₃×C₂₉
socle, prime radical	C₂⁴×C₃×C₂₉	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₂₇×C₂₉	C₂	direct (N × H)
3. C₂²×C₂₇×C₂₉	C₂²	direct (N × H)
5. C₂×C₂₇×C₂₉	C₂³	direct (N × H)
8. C₂₇×C₂₉	C₂⁴	direct (N × H)
11. C₂⁴×C₂₉	C₂₇	direct (N × H)
12. C₂⁴×C₂₇	C₂₉	direct (N × H)
15. C₂³×C₂₉	C₂×C₂₇	direct (N × H)
16. C₂³×C₂₇	C₂×C₂₉	direct (N × H)
19. C₂²×C₂₉	C₂²×C₂₇	direct (N × H)
20. C₂²×C₂₇	C₂²×C₂₉	direct (N × H)
23. C₂×C₂₉	C₂³×C₂₇	direct (N × H)
24. C₂×C₂₇	C₂³×C₂₉	direct (N × H)
27. C₂₉	C₂⁴×C₂₇	direct (N × H)
28. C₂₇	C₂⁴×C₂₉	direct (N × H)
31. C₂⁴	C₂₇×C₂₉	direct (N × H)
34. C₂³	C₂×C₂₇×C₂₉	direct (N × H)
36. C₂²	C₂²×C₂₇×C₂₉	direct (N × H)
38. C₂	C₂³×C₂₇×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
C₂³×C₂₇×C₂₉	2
C₂⁴×C₉×C₂₉	3
C₂⁴×C₂₇	29

Subgroups — C24×C27×C29 #72190876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₂₇×C₂₉ #72190876