Subgroups — C₃×D₁₃×D₉₃ #28408335

Order 14508.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₂₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₃×D₉₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₁₃×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₉₃	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×D₁₃×D₃₁	—	3	1	no	maximal
6	C₃²×C₁₃×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₁₂₀₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₃×D₉₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₄₀₃	—	3	1	no	—
10	C₃×D₁₃×C₃₁	—	2	1	no	—
11	C₃×D₁₃×C₃₁	D₃	1	1	yes	characteristic, complemented
12	C₃×D₁₃×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
13	C₃×C₁₃×D₃₁	—	3	1	no	—
14	D₁₃×D₃₁	—	3	1	no	Hall
15	C₃×C₁₃×C₃₁	—	2	1	no	—
16	C₃×C₁₃×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₃×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂×C₃×D₉₃	—	13	1	no	maximal, Hall
19	D₄₀₃	—	3	1	no	—
20	C₁₃×D₃₁	—	3	1	no	—
21	D₁₃×C₃₁	C₃×D₃	1	1	yes	characteristic, complemented
22	C₂×C₃²×C₃₁	—	13	1	no	—
23	C₃×D₉₃	—	13	1	no	—
24	C₃×D₉₃	D₁₃	1	1	yes	characteristic, direct product factor
25	C₃×D₃×D₁₃	—	31	1	no	maximal, Hall
26	C₁₃×C₃₁	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
27	C₂×D₉₃	—	13	1	no	—
28	C₂×C₃×D₃₁	—	39	1	no	—
29	C₃²×C₃₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
30	C₃×D₃₉	—	31	1	no	—
31	C₃×D₃×C₁₃	—	31	1	no	—
32	C₃²×D₁₃	D₃₁	1	1	yes	characteristic, complemented
33	C₂×C₃×C₃₁	—	13	1	no	—
34	C₂×C₃×C₃₁	—	13	1	no	—
35	C₂×C₃×C₃₁	—	26	1	no	—
36	D₉₃	—	13	1	no	—
37	D₉₃	C₃×D₁₃	1	1	yes	characteristic, direct product factor
38	C₃×D₃₁	—	3	1	no	—
39	C₃×D₃₁	—	39	1	no	—
40	C₂×C₃×D₁₃	—	93	1	no	—
41	D₃×D₁₃	—	31	1	no	—
42	C₂×D₃₁	—	39	1	no	Hall
43	C₃²×C₁₃	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
44	C₃×C₃₁	—	2	1	no	—
45	C₃×C₃₁	D₃×D₁₃	1	1	yes	characteristic, complemented
46	C₃×C₃₁	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
47	C₂×C₃×C₁₃	—	93	1	no	—
48	D₃₉	—	31	1	no	—
49	C₃×D₁₃	—	2	1	no	—
50	C₃×D₁₃	—	93	1	no	—
51	C₃×D₁₃	C₃×D₃₁	1	1	yes	characteristic, complemented
52	C₃×D₁₃	D₉₃	1	1	yes	characteristic, direct product factor
53	D₃×C₁₃	—	31	1	no	—
54	C₂×C₃₁	—	13	1	no	—
55	D₃₁	—	3	1	no	—
56	D₃₁	—	39	1	no	—
57	C₂×D₁₃	—	93	1	no	Hall
58	C₃×C₁₃	—	2	1	no	—
59	C₃×C₁₃	C₂×C₃×D₃₁	1	1	yes	characteristic, complemented
60	C₃×C₁₃	C₂×D₉₃	1	1	yes	characteristic, complemented
61	C₂×C₃×D₃	—	403	1	no	Hall
62	C₃₁	C₃×D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₁₃	—	93	1	no	—
64	D₁₃	—	93	1	no	—
65	D₁₃	C₃×D₉₃	1	1	yes	characteristic, direct product factor
66	C₂×C₃²	—	13	1	no	—
67	C₃×D₃	—	31	1	no	—
68	C₃×D₃	—	403	1	no	—
69	C₁₃	C₂×C₃×D₉₃	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₃	—	1209	1	no	—
71	C₂×D₃	—	403	1	no	—
72	C₃²	D₁₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	13	1	no	—
74	C₂×C₃	—	13	1	no	—
75	C₂×C₃	—	26	1	no	—
76	C₂×C₃	—	93	1	no	—
77	C₂×C₃	—	1209	1	no	—
78	D₃	—	31	1	no	—
79	D₃	—	403	1	no	—
80	C₂²	—	1209	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	C₃×D₁₃×D₃₁	1	1	yes	characteristic, complemented
83	C₃	D₁₃×D₉₃	1	1	yes	characteristic, direct product factor
84	C₂	—	13	1	no	—
85	C₂	—	93	1	no	—
86	C₂	—	1209	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₃×D₉₃
commutator, cosocle, hypocenter	C₃×C₁₃×C₃₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₃₁	C₂²
LCS	G ▷ C₃×C₁₃×C₃₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₂₀₉	C₂	semidirect
2. C₃×C₁₃×D₉₃	C₂	semidirect
3. C₃²×D₁₃×C₃₁	C₂	semidirect
4. D₁₃×D₉₃	C₃	direct (N × H)
6. C₃²×C₁₃×C₃₁	C₂²	semidirect
7. D₁₂₀₉	C₂×C₃	semidirect
8. C₁₃×D₉₃	C₂×C₃	semidirect
11. C₃×D₁₃×C₃₁	D₃	semidirect
12. C₃×D₁₃×C₃₁	C₂×C₃	semidirect
16. C₃×C₁₃×C₃₁	C₂×D₃	semidirect
17. C₃×C₁₃×C₃₁	C₂²×C₃	semidirect
21. D₁₃×C₃₁	C₃×D₃	semidirect
24. C₃×D₉₃	D₁₃	direct (N × H)
26. C₁₃×C₃₁	C₂×C₃×D₃	semidirect
29. C₃²×C₃₁	C₂×D₁₃	semidirect
32. C₃²×D₁₃	D₃₁	semidirect
37. D₉₃	C₃×D₁₃	direct (N × H)
43. C₃²×C₁₃	C₂×D₃₁	semidirect
45. C₃×C₃₁	D₃×D₁₃	semidirect
46. C₃×C₃₁	C₂×C₃×D₁₃	semidirect
51. C₃×D₁₃	C₃×D₃₁	semidirect
52. C₃×D₁₃	D₉₃	direct (N × H)
59. C₃×C₁₃	C₂×C₃×D₃₁	semidirect
60. C₃×C₁₃	C₂×D₉₃	semidirect
62. C₃₁	C₃×D₃×D₁₃	semidirect
65. D₁₃	C₃×D₉₃	direct (N × H)
69. C₁₃	C₂×C₃×D₉₃	semidirect
72. C₃²	D₁₃×D₃₁	semidirect
82. C₃	C₃×D₁₃×D₃₁	semidirect
83. C₃	D₁₃×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
C₃×D₁₂₀₉	2
C₃×C₁₃×D₉₃	2
C₃²×D₁₃×C₃₁	2
D₁₃×D₉₃	3
C₃×D₁₃×D₃₁	3
C₂×C₃×D₉₃	13
C₃×D₃×D₁₃	31

Subgroups — C3×D13×D93 #28408335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₃×D₉₃ #28408335