Subgroups — D₅₇₃⋊D₁₅ #46806039

Order 34380.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₅₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₂₈₆₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₁₅×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₅⋊D₁₉₁	—	3	1	no	maximal
5	D₁₅×D₁₉₁	—	3	1	no	maximal
6	C₃²×C₅×C₁₉₁	C₂²	1	1	yes	characteristic, complemented, Hall
7	(C₃⋊D₃)⋊D₁₉₁	—	5	1	no	maximal, Hall
8	D₂₈₆₅	D₃	1	1	yes	characteristic, complemented
9	D₁₅×C₁₉₁	—	3	1	no	—
10	D₁₅×C₁₉₁	—	3	1	no	—
11	D₁₅×C₁₉₁	—	6	1	no	—
12	C₅×D₅₇₃	D₃	1	1	yes	characteristic, complemented
13	C₃×D₉₅₅	—	3	1	no	—
14	C₃×C₅×D₁₉₁	—	3	1	no	—
15	D₅×D₁₉₁	—	9	1	no	Hall
16	C₃⋊D₃×C₁₉₁	—	5	1	no	—
17	C₃×D₅₇₃	—	5	1	no	—
18	C₃×D₅₇₃	D₅	1	1	yes	characteristic, complemented
19	C₃×C₅×C₁₉₁	—	2	1	no	—
20	C₃×C₅×C₁₉₁	C₂×D₃	1	1	yes	characteristic, complemented
21	C₃×C₅×C₁₉₁	C₂×D₃	1	1	yes	characteristic, complemented
22	D₃×D₁₉₁	—	15	1	no	—
23	D₃×D₁₉₁	—	15	1	no	—
24	D₉₅₅	—	3	1	no	—
25	C₅×D₁₉₁	—	3	1	no	—
26	D₅×C₁₉₁	—	9	1	no	—
27	C₃²×C₁₉₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
28	D₅₇₃	—	5	1	no	—
29	D₅₇₃	D₁₅	1	1	yes	characteristic, complemented
30	C₃×D₁₉₁	—	3	1	no	—
31	C₃×D₁₉₁	—	15	1	no	—
32	D₃×C₁₉₁	—	15	1	no	—
33	D₃×C₁₉₁	—	15	1	no	—
34	D₃×C₁₉₁	—	30	1	no	—
35	C₅×C₁₉₁	D₃²	1	1	yes	characteristic, complemented, Hall
36	C₂×D₁₉₁	—	45	1	no	Hall
37	C₃×C₁₉₁	—	2	1	no	—
38	C₃×C₁₉₁	D₃×D₅	1	1	yes	characteristic, complemented
39	C₃×C₁₉₁	C₂×D₁₅	1	1	yes	characteristic, complemented
40	C₂×C₁₉₁	—	45	1	no	—
41	D₁₉₁	—	3	1	no	—
42	D₁₉₁	—	15	1	no	—
43	C₁₉₁	D₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
44	D₃×D₁₅	—	191	1	no	maximal, Hall
45	C₃⋊D₁₅	D₁₉₁	1	1	yes	characteristic, complemented
46	C₃×D₁₅	—	191	1	no	—
47	C₃×C₅×D₃	—	191	1	no	—
48	C₂×D₁₅	—	573	1	no	—
49	D₃×D₅	—	573	1	no	—
50	C₃²×C₅	C₂×D₁₉₁	1	1	yes	characteristic, complemented, Hall
51	D₃²	—	955	1	no	Hall
52	C₂×C₃×C₅	—	573	1	no	—
53	D₁₅	—	3	1	no	—
54	D₁₅	—	3	1	no	—
55	D₁₅	—	6	1	no	—
56	D₁₅	—	191	1	no	—
57	C₃×D₅	—	573	1	no	—
58	C₅×D₃	—	191	1	no	—
59	C₂×D₅	—	1719	1	no	Hall
60	C₃⋊D₃	—	5	1	no	—
61	C₃×D₃	—	955	1	no	—
62	C₃×D₃	—	191	1	no	—
63	C₃×C₅	—	2	1	no	—
64	C₃×C₅	D₃×D₁₉₁	1	1	yes	characteristic, complemented
65	C₃×C₅	D₃×D₁₉₁	1	1	yes	characteristic, complemented
66	C₂×D₃	—	2865	1	no	—
67	C₂×D₃	—	2865	1	no	—
68	C₂×C₅	—	573	1	no	—
69	D₅	—	9	1	no	—
70	D₅	—	573	1	no	—
71	C₃²	D₅×D₁₉₁	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	2865	1	no	—
73	C₂×C₃	—	573	1	no	—
74	D₃	—	15	1	no	—
75	D₃	—	15	1	no	—
76	D₃	—	30	1	no	—
77	D₃	—	955	1	no	—
78	D₃	—	191	1	no	—
79	C₅	(C₃⋊D₃)⋊D₁₉₁	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	8595	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₁₅×D₁₉₁	1	1	yes	characteristic, complemented
83	C₃	D₁₅⋊D₁₉₁	1	1	yes	characteristic, complemented
84	C₂	—	45	1	no	—
85	C₂	—	2865	1	no	—
86	C₂	—	573	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅×C₁₉₁	C₂²
LCS	G ▷ C₃²×C₅×C₁₉₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₅₇₃	C₂	semidirect
2. C₃×D₂₈₆₅	C₂	semidirect
3. C₃⋊D₁₅×C₁₉₁	C₂	semidirect
6. C₃²×C₅×C₁₉₁	C₂²	semidirect
8. D₂₈₆₅	D₃	semidirect
12. C₅×D₅₇₃	D₃	semidirect
18. C₃×D₅₇₃	D₅	semidirect
20. C₃×C₅×C₁₉₁	C₂×D₃	semidirect
21. C₃×C₅×C₁₉₁	C₂×D₃	semidirect
27. C₃²×C₁₉₁	C₂×D₅	semidirect
29. D₅₇₃	D₁₅	semidirect
35. C₅×C₁₉₁	D₃²	semidirect
38. C₃×C₁₉₁	D₃×D₅	semidirect
39. C₃×C₁₉₁	C₂×D₁₅	semidirect
43. C₁₉₁	D₃×D₁₅	semidirect
45. C₃⋊D₁₅	D₁₉₁	semidirect
50. C₃²×C₅	C₂×D₁₉₁	semidirect
64. C₃×C₅	D₃×D₁₉₁	semidirect
65. C₃×C₅	D₃×D₁₉₁	semidirect
71. C₃²	D₅×D₁₉₁	semidirect
79. C₅	(C₃⋊D₃)⋊D₁₉₁	semidirect
82. C₃	D₁₅×D₁₉₁	semidirect
83. C₃	D₁₅⋊D₁₉₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×D₅₇₃	2
C₃×D₂₈₆₅	2
C₃⋊D₁₅×C₁₉₁	2
D₁₅⋊D₁₉₁	3
D₁₅×D₁₉₁	3
(C₃⋊D₃)⋊D₁₉₁	5
D₃×D₁₅	191

Subgroups — D573⋊D15 #46806039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₇₃⋊D₁₅ #46806039