Subgroups — D₃₁×C₃⋊D₁₅ #19150152

Order 5580.

120 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	C₃₁×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₅×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₅×D₃₁	—	3	4	no	maximal
5	C₃²×C₅×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃⋊D₃×D₃₁	—	5	1	no	maximal, Hall
7	D₄₆₅	—	3	4	no	—
8	D₁₅×C₃₁	—	3	4	no	—
9	C₃×C₅×D₃₁	D₃	1	4	yes	complemented
10	D₅×D₃₁	—	9	1	no	Hall
11	C₃⋊D₉₃	—	5	1	no	—
12	C₃⋊D₃×C₃₁	—	5	1	no	—
13	C₃²×D₃₁	D₅	1	1	yes	characteristic, complemented
14	C₃×C₅×C₃₁	C₂×D₃	1	4	yes	complemented
15	D₃×D₃₁	—	15	4	no	—
16	D₁₅₅	—	9	1	no	—
17	C₅×D₃₁	C₃⋊D₃	1	1	yes	characteristic, complemented
18	D₅×C₃₁	—	9	1	no	—
19	C₃²×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	D₉₃	—	15	4	no	—
21	C₃×D₃₁	D₁₅	1	4	yes	complemented
22	D₃×C₃₁	—	15	4	no	—
23	C₂×C₃⋊D₁₅	—	31	1	no	maximal, Hall
24	C₅×C₃₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
25	C₂×D₃₁	—	45	1	no	Hall
26	C₃×C₃₁	C₂×D₁₅	1	4	yes	complemented
27	C₂×C₃²×C₅	—	31	1	no	—
28	C₃⋊D₁₅	—	31	1	no	—
29	C₃⋊D₁₅	D₃₁	1	1	yes	characteristic, direct product factor
30	C₂×C₃₁	—	45	1	no	—
31	D₃₁	—	45	1	no	—
32	D₃₁	C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
33	C₂×D₁₅	—	93	4	no	—
34	C₃²×C₅	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃⋊D₃	—	155	1	no	Hall
36	C₃₁	C₂×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃×C₅	—	31	4	no	—
38	D₁₅	—	3	4	no	—
39	D₁₅	—	93	4	no	—
40	C₂×D₅	—	279	1	no	Hall
41	C₂×C₃²	—	31	1	no	—
42	C₃⋊D₃	—	5	1	no	—
43	C₃⋊D₃	—	155	1	no	—
44	C₃×C₅	D₃×D₃₁	1	4	yes	complemented
45	C₂×D₃	—	465	4	no	—
46	C₂×C₅	—	31	1	no	—
47	D₅	—	9	1	no	—
48	D₅	—	279	1	no	—
49	C₃²	D₅×D₃₁	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	31	4	no	—
51	D₃	—	15	4	no	—
52	D₃	—	465	4	no	—
53	C₅	C₃⋊D₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	1395	1	no	Sylow
55	C₃	D₁₅×D₃₁	1	4	yes	complemented
56	C₂	—	31	1	no	—
57	C₂	—	45	1	no	—
58	C₂	—	1395	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₄₆₅	C₂	semidirect
2. C₃₁×C₃⋊D₁₅	C₂	semidirect
3. C₃²×C₅×D₃₁	C₂	semidirect
5. C₃²×C₅×C₃₁	C₂²	semidirect
9. C₃×C₅×D₃₁	D₃	semidirect
13. C₃²×D₃₁	D₅	semidirect
14. C₃×C₅×C₃₁	C₂×D₃	semidirect
17. C₅×D₃₁	C₃⋊D₃	semidirect
19. C₃²×C₃₁	C₂×D₅	semidirect
21. C₃×D₃₁	D₁₅	semidirect
24. C₅×C₃₁	C₂×C₃⋊D₃	semidirect
26. C₃×C₃₁	C₂×D₁₅	semidirect
29. C₃⋊D₁₅	D₃₁	direct (N × H)
32. D₃₁	C₃⋊D₁₅	direct (N × H)
34. C₃²×C₅	C₂×D₃₁	semidirect
36. C₃₁	C₂×C₃⋊D₁₅	semidirect
44. C₃×C₅	D₃×D₃₁	semidirect
49. C₃²	D₅×D₃₁	semidirect
53. C₅	C₃⋊D₃×D₃₁	semidirect
55. C₃	D₁₅×D₃₁	semidirect

Subgroups — D31×C3⋊D15 #19150152

Conjugacy classes of subgroups

Complements

Subgroups — D₃₁×C₃⋊D₁₅ #19150152