Subgroups — C₂⁵×C₃⋊(C₃⋊D₃) #13181872

Order 1728.

79100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₃³	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₃⋊(C₃⋊D₃)	C₂	1	62	yes	maximal, direct product factor
3	C₂⁵×C₃⋊D₃	—	3	13	no	maximal
4	C₂⁴×C₃³	C₂²	1	31	yes	complemented
5	C₂³×C₃⋊(C₃⋊D₃)	C₂²	1	620	yes	direct product factor
6	C₂⁵×C₃²	D₃	1	13	yes	complemented
7	C₂⁴×C₃⋊D₃	—	3	806	no	—
8	C₂³×C₃³	C₂³	1	155	yes	complemented
9	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	1240	yes	direct product factor
10	C₂⁵×D₃	—	9	13	no	—
11	C₂⁴×C₃²	C₂×D₃	1	403	yes	complemented
12	C₂³×C₃⋊D₃	—	3	8060	no	—
13	C₂²×C₃³	C₂⁴	1	155	yes	complemented
14	C₂×C₃⋊(C₃⋊D₃)	C₂⁴	1	496	yes	direct product factor
15	C₂⁵×C₃	C₃⋊D₃	1	13	yes	complemented
16	C₂⁴×D₃	—	9	806	no	—
17	C₂³×C₃²	C₂²×D₃	1	2015	yes	complemented
18	C₂²×C₃⋊D₃	—	3	16120	no	—
19	C₂⁶	—	27	1	no	Sylow
20	C₂×C₃³	C₂⁵	1	31	yes	complemented
21	C₃⋊(C₃⋊D₃)	C₂⁵	1	32	yes	direct product factor
22	C₂⁴×C₃	C₂×C₃⋊D₃	1	403	yes	complemented
23	C₂³×D₃	—	9	8060	no	—
24	C₂²×C₃²	C₂³×D₃	1	2015	yes	complemented
25	C₂×C₃⋊D₃	—	3	6448	no	—
26	C₂⁵	—	27	62	no	—
27	C₂⁵	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor
28	C₃³	C₂⁶	1	1	yes	characteristic, complemented, Sylow
29	C₂³×C₃	C₂²×C₃⋊D₃	1	2015	yes	complemented
30	C₂²×D₃	—	9	16120	no	—
31	C₂×C₃²	C₂⁴×D₃	1	403	yes	complemented
32	C₃⋊D₃	—	3	416	no	—
33	C₂⁴	—	27	620	no	—
34	C₂⁴	C₂×C₃⋊(C₃⋊D₃)	1	31	yes	direct product factor
35	C₂²×C₃	C₂³×C₃⋊D₃	1	2015	yes	complemented
36	C₂×D₃	—	9	6448	no	—
37	C₃²	C₂⁵×D₃	1	13	yes	complemented
38	C₂³	—	27	1240	no	—
39	C₂³	C₂²×C₃⋊(C₃⋊D₃)	1	155	yes	direct product factor
40	C₂×C₃	C₂⁴×C₃⋊D₃	1	403	yes	complemented
41	D₃	—	9	416	no	—
42	C₂²	—	27	496	no	—
43	C₂²	C₂³×C₃⋊(C₃⋊D₃)	1	155	yes	direct product factor
44	C₃	C₂⁵×C₃⋊D₃	1	13	yes	complemented
45	C₂	—	27	32	no	—
46	C₂	C₂⁴×C₃⋊(C₃⋊D₃)	1	31	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁵	C₃⋊(C₃⋊D₃)
commutator, cosocle, hypocenter	C₃³	C₂⁶
Frattini	C₁	G
Fitting, socle	C₂⁵×C₃³	C₂
LCS	G ▷ C₃³
UCS	C₁ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₃³	C₂	semidirect
2. C₂⁴×C₃⋊(C₃⋊D₃)	C₂	direct (N × H)
4. C₂⁴×C₃³	C₂²	semidirect
5. C₂³×C₃⋊(C₃⋊D₃)	C₂²	direct (N × H)
6. C₂⁵×C₃²	D₃	semidirect
8. C₂³×C₃³	C₂³	semidirect
9. C₂²×C₃⋊(C₃⋊D₃)	C₂³	direct (N × H)
11. C₂⁴×C₃²	C₂×D₃	semidirect
13. C₂²×C₃³	C₂⁴	semidirect
14. C₂×C₃⋊(C₃⋊D₃)	C₂⁴	direct (N × H)
15. C₂⁵×C₃	C₃⋊D₃	semidirect
17. C₂³×C₃²	C₂²×D₃	semidirect
20. C₂×C₃³	C₂⁵	semidirect
21. C₃⋊(C₃⋊D₃)	C₂⁵	direct (N × H)
22. C₂⁴×C₃	C₂×C₃⋊D₃	semidirect
24. C₂²×C₃²	C₂³×D₃	semidirect
27. C₂⁵	C₃⋊(C₃⋊D₃)	direct (N × H)
28. C₃³	C₂⁶	semidirect
29. C₂³×C₃	C₂²×C₃⋊D₃	semidirect
31. C₂×C₃²	C₂⁴×D₃	semidirect
34. C₂⁴	C₂×C₃⋊(C₃⋊D₃)	direct (N × H)
35. C₂²×C₃	C₂³×C₃⋊D₃	semidirect
37. C₃²	C₂⁵×D₃	semidirect
39. C₂³	C₂²×C₃⋊(C₃⋊D₃)	direct (N × H)
40. C₂×C₃	C₂⁴×C₃⋊D₃	semidirect
43. C₂²	C₂³×C₃⋊(C₃⋊D₃)	direct (N × H)
44. C₃	C₂⁵×C₃⋊D₃	semidirect
46. C₂	C₂⁴×C₃⋊(C₃⋊D₃)	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×C₃³	2
C₂⁴×C₃⋊(C₃⋊D₃)	2
C₂⁵×C₃⋊D₃	3

Subgroups — C25×C3⋊(C3⋊D3) #13181872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₃⋊(C₃⋊D₃) #13181872