Subgroups — C₃×C₅²×D₉₃ #28358515

Order 13950.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×D₉₃	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₅²×D₃₁	—	3	1	no	maximal
4	C₃×C₅×D₉₃	C₅	1	6	yes	maximal, direct product factor
5	C₃×C₅²×C₃₁	—	2	1	no	—
6	C₃×C₅²×C₃₁	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅²×D₃₁	—	3	1	no	Hall
9	C₃²×C₅×C₃₁	C₂×C₅	1	6	yes	complemented
10	C₅×D₉₃	C₃×C₅	1	6	yes	direct product factor
11	C₃×C₅×D₃₁	—	3	6	no	—
12	C₅²×C₃₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×D₉₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₅×C₃₁	—	2	6	no	—
15	C₃×C₅×C₃₁	C₅×D₃	1	6	yes	complemented
16	C₃×C₅×C₃₁	C₂×C₃×C₅	1	6	yes	complemented
17	C₃×C₅²×D₃	—	31	1	no	maximal, Hall
18	C₅×D₃₁	—	3	6	no	—
19	C₃²×C₃₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₅²	D₃₁	1	1	yes	characteristic, complemented, Hall
21	D₉₃	C₃×C₅²	1	1	yes	characteristic, direct product factor
22	C₃×D₃₁	—	3	1	no	—
23	C₅×C₃₁	C₃×C₅×D₃	1	6	yes	complemented
24	C₂×C₃×C₅²	—	93	1	no	—
25	C₅²×D₃	—	31	1	no	—
26	C₃×C₃₁	—	2	1	no	—
27	C₃×C₃₁	C₅²×D₃	1	1	yes	characteristic, complemented
28	C₃×C₃₁	C₂×C₃×C₅²	1	1	yes	characteristic, complemented
29	C₃×C₅×D₃	—	31	6	no	—
30	C₃×C₅²	—	2	1	no	—
31	C₃×C₅²	C₃×D₃₁	1	1	yes	characteristic, complemented
32	C₃×C₅²	D₉₃	1	1	yes	characteristic, direct product factor
33	D₃₁	—	3	1	no	Hall
34	C₂×C₅²	—	93	1	no	Hall
35	C₃²×C₅	C₅×D₃₁	1	6	yes	complemented
36	C₃₁	C₃×C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃×C₅	—	93	6	no	—
38	C₅×D₃	—	31	6	no	—
39	C₅²	C₃×D₉₃	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×D₃	—	31	1	no	Hall
41	C₃×C₅	—	2	6	no	—
42	C₃×C₅	C₃×C₅×D₃₁	1	6	yes	complemented
43	C₃×C₅	C₅×D₉₃	1	6	yes	direct product factor
44	C₂×C₅	—	93	6	no	—
45	C₃²	C₅²×D₃₁	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	93	1	no	—
47	D₃	—	31	1	no	—
48	C₅	C₃×C₅×D₉₃	1	6	yes	direct product factor
49	C₃	—	2	1	no	—
50	C₃	C₃×C₅²×D₃₁	1	1	yes	characteristic, complemented
51	C₃	C₅²×D₉₃	1	1	yes	characteristic, direct product factor
52	C₂	—	93	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅²	D₉₃
commutator, cosocle, hypocenter	C₃×C₃₁	C₂×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₃₁	C₂
LCS	G ▷ C₃×C₃₁
UCS	C₁ ◁ C₃×C₅²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₃₁	C₂	semidirect
2. C₅²×D₉₃	C₃	direct (N × H)
4. C₃×C₅×D₉₃	C₅	direct (N × H)
6. C₃×C₅²×C₃₁	D₃	semidirect
7. C₃×C₅²×C₃₁	C₂×C₃	semidirect
9. C₃²×C₅×C₃₁	C₂×C₅	semidirect
10. C₅×D₉₃	C₃×C₅	direct (N × H)
12. C₅²×C₃₁	C₃×D₃	semidirect
13. C₃×D₉₃	C₅²	direct (N × H)
15. C₃×C₅×C₃₁	C₅×D₃	semidirect
16. C₃×C₅×C₃₁	C₂×C₃×C₅	semidirect
19. C₃²×C₃₁	C₂×C₅²	semidirect
20. C₃²×C₅²	D₃₁	semidirect
21. D₉₃	C₃×C₅²	direct (N × H)
23. C₅×C₃₁	C₃×C₅×D₃	semidirect
27. C₃×C₃₁	C₅²×D₃	semidirect
28. C₃×C₃₁	C₂×C₃×C₅²	semidirect
31. C₃×C₅²	C₃×D₃₁	semidirect
32. C₃×C₅²	D₉₃	direct (N × H)
35. C₃²×C₅	C₅×D₃₁	semidirect
36. C₃₁	C₃×C₅²×D₃	semidirect
39. C₅²	C₃×D₉₃	direct (N × H)
42. C₃×C₅	C₃×C₅×D₃₁	semidirect
43. C₃×C₅	C₅×D₉₃	direct (N × H)
45. C₃²	C₅²×D₃₁	semidirect
48. C₅	C₃×C₅×D₉₃	direct (N × H)
50. C₃	C₃×C₅²×D₃₁	semidirect
51. C₃	C₅²×D₉₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₅²×C₃₁	2
C₅²×D₉₃	3
C₃×C₅²×D₃₁	3
C₃×C₅×D₉₃	5
C₃×C₅²×D₃	31

Subgroups — C3×C52×D93 #28358515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅²×D₉₃ #28358515