Subgroups — C₃×D₁₅×D₃₁ #19150144

Order 5580.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄₆₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₅×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₅×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₅×D₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×D₅×D₃₁	—	3	1	no	maximal
6	C₃²×C₅×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₃×D₃×D₃₁	—	5	1	no	maximal, Hall
8	D₄₆₅	C₂×C₃	1	1	yes	characteristic, complemented
9	D₁₅×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₁₅₅	—	3	1	no	—
11	C₃×D₅×C₃₁	—	3	1	no	—
12	C₃×C₅×D₃₁	—	2	1	no	—
13	C₃×C₅×D₃₁	D₃	1	1	yes	characteristic, complemented
14	C₃×C₅×D₃₁	C₂×C₃	1	1	yes	characteristic, complemented
15	D₅×D₃₁	—	3	1	no	Hall
16	C₃×D₉₃	—	5	1	no	—
17	C₃×D₃×C₃₁	—	5	1	no	—
18	C₃²×D₃₁	D₅	1	1	yes	characteristic, complemented
19	C₃×C₅×C₃₁	—	2	1	no	—
20	C₃×C₅×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented
21	C₃×C₅×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented
22	C₂×C₃×D₃₁	—	15	1	no	—
23	D₃×D₃₁	—	5	1	no	—
24	D₁₅₅	—	3	1	no	—
25	C₅×D₃₁	C₃×D₃	1	1	yes	characteristic, complemented
26	D₅×C₃₁	—	3	1	no	—
27	C₃²×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₃₁	—	15	1	no	—
29	D₉₃	—	5	1	no	—
30	C₃×D₃₁	—	2	1	no	—
31	C₃×D₃₁	—	15	1	no	—
32	C₃×D₃₁	C₃×D₅	1	1	yes	characteristic, complemented
33	C₃×D₃₁	D₁₅	1	1	yes	characteristic, direct product factor
34	D₃×C₃₁	—	5	1	no	—
35	C₂×C₃×D₁₅	—	31	1	no	maximal, Hall
36	C₅×C₃₁	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
37	C₂×D₃₁	—	15	1	no	Hall
38	C₃×C₃₁	—	2	1	no	—
39	C₃×C₃₁	C₂×C₃×D₅	1	1	yes	characteristic, complemented
40	C₃×C₃₁	C₂×D₁₅	1	1	yes	characteristic, complemented
41	C₂×C₃²×C₅	—	31	1	no	—
42	C₃×D₁₅	—	31	1	no	—
43	C₃×D₁₅	D₃₁	1	1	yes	characteristic, direct product factor
44	C₂×C₃₁	—	15	1	no	—
45	D₃₁	—	15	1	no	—
46	D₃₁	C₃×D₁₅	1	1	yes	characteristic, direct product factor
47	C₂×D₁₅	—	31	1	no	—
48	C₂×C₃×D₅	—	93	1	no	—
49	C₃²×C₅	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃×D₃	—	155	1	no	Hall
51	C₃₁	C₂×C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₃×C₅	—	31	1	no	—
53	C₂×C₃×C₅	—	31	1	no	—
54	C₂×C₃×C₅	—	62	1	no	—
55	D₁₅	—	31	1	no	—
56	D₁₅	C₃×D₃₁	1	1	yes	characteristic, direct product factor
57	C₃×D₅	—	3	1	no	—
58	C₃×D₅	—	93	1	no	—
59	C₂×D₅	—	93	1	no	Hall
60	C₂×C₃²	—	31	1	no	—
61	C₃×D₃	—	5	1	no	—
62	C₃×D₃	—	155	1	no	—
63	C₃×C₅	—	2	1	no	—
64	C₃×C₅	D₃×D₃₁	1	1	yes	characteristic, complemented
65	C₃×C₅	C₂×C₃×D₃₁	1	1	yes	characteristic, complemented
66	C₂²×C₃	—	465	1	no	—
67	C₂×D₃	—	155	1	no	—
68	C₂×C₅	—	31	1	no	—
69	D₅	—	3	1	no	—
70	D₅	—	93	1	no	—
71	C₃²	D₅×D₃₁	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	15	1	no	—
73	C₂×C₃	—	31	1	no	—
74	C₂×C₃	—	31	1	no	—
75	C₂×C₃	—	62	1	no	—
76	C₂×C₃	—	465	1	no	—
77	D₃	—	5	1	no	—
78	D₃	—	155	1	no	—
79	C₅	C₃×D₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	465	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	C₃×D₅×D₃₁	1	1	yes	characteristic, complemented
83	C₃	D₁₅×D₃₁	1	1	yes	characteristic, direct product factor
84	C₂	—	15	1	no	—
85	C₂	—	31	1	no	—
86	C₂	—	465	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₅×D₃₁
commutator, hypocenter	C₃×C₅×C₃₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₃₁	C₂²
LCS	G ▷ C₃×C₅×C₃₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₄₆₅	C₂	semidirect
2. C₃×D₁₅×C₃₁	C₂	semidirect
3. C₃²×C₅×D₃₁	C₂	semidirect
4. D₁₅×D₃₁	C₃	direct (N × H)
6. C₃²×C₅×C₃₁	C₂²	semidirect
8. D₄₆₅	C₂×C₃	semidirect
9. D₁₅×C₃₁	C₂×C₃	semidirect
13. C₃×C₅×D₃₁	D₃	semidirect
14. C₃×C₅×D₃₁	C₂×C₃	semidirect
18. C₃²×D₃₁	D₅	semidirect
20. C₃×C₅×C₃₁	C₂×D₃	semidirect
21. C₃×C₅×C₃₁	C₂²×C₃	semidirect
25. C₅×D₃₁	C₃×D₃	semidirect
27. C₃²×C₃₁	C₂×D₅	semidirect
32. C₃×D₃₁	C₃×D₅	semidirect
33. C₃×D₃₁	D₁₅	direct (N × H)
36. C₅×C₃₁	C₂×C₃×D₃	semidirect
39. C₃×C₃₁	C₂×C₃×D₅	semidirect
40. C₃×C₃₁	C₂×D₁₅	semidirect
43. C₃×D₁₅	D₃₁	direct (N × H)
46. D₃₁	C₃×D₁₅	direct (N × H)
49. C₃²×C₅	C₂×D₃₁	semidirect
51. C₃₁	C₂×C₃×D₁₅	semidirect
56. D₁₅	C₃×D₃₁	direct (N × H)
64. C₃×C₅	D₃×D₃₁	semidirect
65. C₃×C₅	C₂×C₃×D₃₁	semidirect
71. C₃²	D₅×D₃₁	semidirect
79. C₅	C₃×D₃×D₃₁	semidirect
82. C₃	C₃×D₅×D₃₁	semidirect
83. C₃	D₁₅×D₃₁	direct (N × H)

Subgroups — C3×D15×D31 #19150144

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₁₅×D₃₁ #19150144