Subgroups — #30685609

Order 17100.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₈₅₅	C₂	1	2	yes	maximal, complemented
2	C₉×C₁₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152888	—	3	1	no	maximal
4	C₅²×C₉×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×D₁₇₁	—	5	2	no	maximal
6	C₅×D₂₈₅	—	3	2	no	—
7	C₃×C₁₉×C₅⋊D₅	D₃	1	1	yes	characteristic
8	(C₅⋊D₅)⋊D₁₉	—	9	1	no	Hall
9	D₈₅₅	D₅	1	2	yes	complemented
10	C₅×D₁₇₁	—	5	2	no	—
11	C₉×D₅×C₁₉	—	5	2	no	—
12	C₉×D₅×C₁₉	—	10	2	no	—
13	C₃×C₅²×C₁₉	C₂×D₃	1	1	yes	characteristic
14	D₅×D₅₇	—	15	2	no	—
15	C₁₉×C₅⋊D₅	D₉	1	1	yes	characteristic, complemented
16	C₅×D₉₅	—	9	2	no	—
17	D₄₅⋊D₅	—	19	1	no	maximal, Hall
18	C₅×C₉×C₁₉	—	2	2	no	—
19	C₅×C₉×C₁₉	C₂×D₅	1	2	yes	complemented
20	C₂×D₁₇₁	—	25	1	no	Hall
21	D₂₈₅	—	3	2	no	—
22	C₅×D₅₇	—	15	2	no	—
23	C₃×D₅×C₁₉	—	5	2	no	—
24	C₃×D₅×C₁₉	—	10	2	no	—
25	C₅²×C₁₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
26	C₅×D₄₅	—	19	2	no	—
27	C₉×C₅⋊D₅	D₁₉	1	1	yes	characteristic, complemented
28	D₅×D₁₉	—	45	2	no	—
29	C₂×C₉×C₁₉	—	25	1	no	—
30	D₁₇₁	—	5	2	no	—
31	D₁₅⋊D₅	—	57	1	no	—
32	C₃×C₅×C₁₉	—	2	2	no	—
33	C₃×C₅×C₁₉	D₃×D₅	1	2	yes	—
34	C₂×D₅₇	—	75	1	no	—
35	C₅²×C₉	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
36	D₉₅	—	9	2	no	—
37	C₅×D₁₉	—	45	2	no	—
38	D₅×C₁₉	—	5	2	no	—
39	D₅×C₁₉	—	10	2	no	—
40	D₅×D₉	—	95	2	no	—
41	C₉×C₁₉	D₅²	1	1	yes	characteristic, complemented, Hall
42	C₅×D₁₅	—	57	2	no	—
43	C₃×C₅⋊D₅	D₅₇	1	1	yes	characteristic
44	C₂×C₃×C₁₉	—	25	1	no	—
45	D₅₇	—	15	2	no	—
46	D₅²	—	171	1	no	Hall
47	C₅×C₁₉	—	2	2	no	—
48	C₅×C₁₉	D₅×D₉	1	2	yes	complemented
49	D₄₅	—	19	2	no	—
50	C₉×D₅	—	5	2	no	—
51	C₉×D₅	—	10	2	no	—
52	C₅×D₉	—	95	2	no	—
53	C₂×D₁₉	—	225	1	no	Hall
54	C₃×C₅²	C₂×D₅₇	1	1	yes	characteristic
55	D₃×D₅	—	285	2	no	—
56	C₃×C₁₉	D₁₅⋊D₅	1	1	yes	characteristic
57	C₅⋊D₅	D₁₇₁	1	1	yes	characteristic, complemented
58	C₅×D₅	—	171	2	no	—
59	C₅×C₉	—	2	2	no	—
60	C₅×C₉	D₅×D₁₉	1	2	yes	complemented
61	C₂×C₁₉	—	25	1	no	—
62	D₁₉	—	45	2	no	—
63	C₂×D₉	—	475	1	no	Hall
64	D₁₅	—	57	2	no	—
65	C₃×D₅	—	5	2	no	—
66	C₃×D₅	—	10	2	no	—
67	C₅×D₃	—	285	2	no	—
68	C₅²	C₂×D₁₇₁	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₅	—	855	2	no	—
70	C₁₉	D₄₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₉	—	25	1	no	—
72	D₉	—	95	2	no	—
73	C₃×C₅	—	2	2	no	—
74	C₃×C₅	D₅×D₅₇	1	2	yes	—
75	C₂×D₃	—	1425	1	no	—
76	C₂×C₅	—	855	2	no	—
77	D₅	—	5	2	no	—
78	D₅	—	10	2	no	—
79	D₅	—	171	2	no	—
80	C₉	(C₅⋊D₅)⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
81	C₂×C₃	—	25	1	no	—
82	D₃	—	285	2	no	—
83	C₅	—	2	2	no	—
84	C₅	D₅×D₁₇₁	1	2	yes	complemented
85	C₂²	—	4275	1	no	Sylow
86	C₃	#19152888	1	1	yes	characteristic
87	C₂	—	25	1	no	—
88	C₂	—	855	2	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅²×C₉×C₁₉	C₂²
Frattini	C₃	#19152888
socle	C₃×C₅²×C₁₉	C₂×D₃
LCS	G ▷ C₅²×C₉×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×D₈₅₅	C₂	semidirect
2. C₉×C₁₉×C₅⋊D₅	C₂	semidirect
4. C₅²×C₉×C₁₉	C₂²	semidirect
9. D₈₅₅	D₅	semidirect
15. C₁₉×C₅⋊D₅	D₉	semidirect
19. C₅×C₉×C₁₉	C₂×D₅	semidirect
25. C₅²×C₁₉	C₂×D₉	semidirect
27. C₉×C₅⋊D₅	D₁₉	semidirect
35. C₅²×C₉	C₂×D₁₉	semidirect
41. C₉×C₁₉	D₅²	semidirect
48. C₅×C₁₉	D₅×D₉	semidirect
57. C₅⋊D₅	D₁₇₁	semidirect
60. C₅×C₉	D₅×D₁₉	semidirect
68. C₅²	C₂×D₁₇₁	semidirect
70. C₁₉	D₄₅⋊D₅	semidirect
80. C₉	(C₅⋊D₅)⋊D₁₉	semidirect
84. C₅	D₅×D₁₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₈₅₅	2
C₉×C₁₉×C₅⋊D₅	2
#19152888	3
D₅×D₁₇₁	5
D₄₅⋊D₅	19