Subgroups — D₉₃⋊D₁₅ #19150162

Order 5580.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₄₆₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₉₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₅⋊D₃₁	—	3	1	no	maximal
5	D₁₅×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	D₃	1	1	yes	characteristic, complemented
9	D₁₅×C₃₁	—	3	1	no	—
10	D₁₅×C₃₁	—	3	1	no	—
11	D₁₅×C₃₁	—	6	1	no	—
12	C₅×D₉₃	D₃	1	1	yes	characteristic, complemented
13	C₃×D₁₅₅	—	3	1	no	—
14	C₃×C₅×D₃₁	—	3	1	no	—
15	D₅×D₃₁	—	9	1	no	Hall
16	C₃⋊D₃×C₃₁	—	5	1	no	—
17	C₃×D₉₃	—	5	1	no	—
18	C₃×D₉₃	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	C₂×D₃	1	1	yes	characteristic, complemented
22	D₃×D₃₁	—	15	1	no	—
23	D₃×D₃₁	—	15	1	no	—
24	D₁₅₅	—	3	1	no	—
25	C₅×D₃₁	—	3	1	no	—
26	D₅×C₃₁	—	9	1	no	—
27	C₃²×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
28	D₉₃	—	5	1	no	—
29	D₉₃	D₁₅	1	1	yes	characteristic, complemented
30	C₃×D₃₁	—	3	1	no	—
31	C₃×D₃₁	—	15	1	no	—
32	D₃×C₃₁	—	15	1	no	—
33	D₃×C₃₁	—	15	1	no	—
34	D₃×C₃₁	—	30	1	no	—
35	D₃×D₁₅	—	31	1	no	maximal, Hall
36	C₅×C₃₁	D₃²	1	1	yes	characteristic, complemented, Hall
37	C₂×D₃₁	—	45	1	no	Hall
38	C₃×C₃₁	—	2	1	no	—
39	C₃×C₃₁	D₃×D₅	1	1	yes	characteristic, complemented
40	C₃×C₃₁	C₂×D₁₅	1	1	yes	characteristic, complemented
41	C₃⋊D₁₅	D₃₁	1	1	yes	characteristic, complemented
42	C₃×D₁₅	—	31	1	no	—
43	C₃×C₅×D₃	—	31	1	no	—
44	C₂×C₃₁	—	45	1	no	—
45	D₃₁	—	3	1	no	—
46	D₃₁	—	15	1	no	—
47	C₂×D₁₅	—	93	1	no	—
48	D₃×D₅	—	93	1	no	—
49	C₃²×C₅	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
50	D₃²	—	155	1	no	Hall
51	C₃₁	D₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₃×C₅	—	93	1	no	—
53	D₁₅	—	3	1	no	—
54	D₁₅	—	3	1	no	—
55	D₁₅	—	6	1	no	—
56	D₁₅	—	31	1	no	—
57	C₃×D₅	—	93	1	no	—
58	C₅×D₃	—	31	1	no	—
59	C₂×D₅	—	279	1	no	Hall
60	C₃⋊D₃	—	5	1	no	—
61	C₃×D₃	—	31	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	D₃×D₃₁	1	1	yes	characteristic, complemented
66	C₂×D₃	—	465	1	no	—
67	C₂×D₃	—	465	1	no	—
68	C₂×C₅	—	93	1	no	—
69	D₅	—	9	1	no	—
70	D₅	—	93	1	no	—
71	C₃²	D₅×D₃₁	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	93	1	no	—
73	C₂×C₃	—	465	1	no	—
74	D₃	—	15	1	no	—
75	D₃	—	15	1	no	—
76	D₃	—	30	1	no	—
77	D₃	—	31	1	no	—
78	D₃	—	155	1	no	—
79	C₅	(C₃⋊D₃)⋊D₃₁	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	1395	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₁₅×D₃₁	1	1	yes	characteristic, complemented
83	C₃	D₁₅⋊D₃₁	1	1	yes	characteristic, complemented
84	C₂	—	45	1	no	—
85	C₂	—	93	1	no	—
86	C₂	—	465	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. C₃₁×C₃⋊D₁₅	C₂	semidirect
2. C₃×D₄₆₅	C₂	semidirect
3. C₃×C₅×D₉₃	C₂	semidirect
6. C₃²×C₅×C₃₁	C₂²	semidirect
8. D₄₆₅	D₃	semidirect
12. C₅×D₉₃	D₃	semidirect
18. C₃×D₉₃	D₅	semidirect
20. C₃×C₅×C₃₁	C₂×D₃	semidirect
21. C₃×C₅×C₃₁	C₂×D₃	semidirect
27. C₃²×C₃₁	C₂×D₅	semidirect
29. D₉₃	D₁₅	semidirect
36. C₅×C₃₁	D₃²	semidirect
39. C₃×C₃₁	D₃×D₅	semidirect
40. C₃×C₃₁	C₂×D₁₅	semidirect
41. C₃⋊D₁₅	D₃₁	semidirect
49. C₃²×C₅	C₂×D₃₁	semidirect
51. C₃₁	D₃×D₁₅	semidirect
64. C₃×C₅	D₃×D₃₁	semidirect
65. C₃×C₅	D₃×D₃₁	semidirect
71. C₃²	D₅×D₃₁	semidirect
79. C₅	(C₃⋊D₃)⋊D₃₁	semidirect
82. C₃	D₁₅×D₃₁	semidirect
83. C₃	D₁₅⋊D₃₁	semidirect

Subgroups — D93⋊D15 #19150162

Conjugacy classes of subgroups

Complements

Subgroups — D₉₃⋊D₁₅ #19150162