Subgroups — D₁₇₁⋊(C₅⋊D₅) #30685603

Order 17100.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅²×C₉×C₁₉	C₂²
Frattini	C₃	D₅₇⋊(C₅⋊D₅)
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. C₁₉×C₅⋊D₄₅	C₂	semidirect
2. C₅²×D₁₇₁	C₂	semidirect
3. C₉×C₅⋊D₉₅	C₂	semidirect
5. C₅²×C₉×C₁₉	C₂²	semidirect
12. C₅×D₁₇₁	D₅	semidirect
16. C₅⋊D₉₅	D₉	semidirect
20. C₅×C₉×C₁₉	C₂×D₅	semidirect
25. C₅²×C₁₉	C₂×D₉	semidirect
26. C₅⋊D₄₅	D₁₉	semidirect
30. D₁₇₁	C₅⋊D₅	semidirect
36. C₅²×C₉	C₂×D₁₉	semidirect
41. C₉×C₁₉	C₂×C₅⋊D₅	semidirect
49. C₅×C₁₉	D₅×D₉	semidirect
60. C₅×C₉	D₅×D₁₉	semidirect
68. C₅²	D₉×D₁₉	semidirect
70. C₁₉	D₉×C₅⋊D₅	semidirect
79. C₉	D₁₉×C₅⋊D₅	semidirect
83. C₅	D₄₅⋊D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×C₅⋊D₄₅	2
C₅²×D₁₇₁	2
C₉×C₅⋊D₉₅	2
D₅₇⋊(C₅⋊D₅)	3
D₄₅⋊D₁₉	5
D₉×C₅⋊D₅	19

Subgroups — D171⋊(C5⋊D5) #30685603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇₁⋊(C₅⋊D₅) #30685603