Subgroups — C₅⋊D₅×D₃₁⋊C₉ #42124499

Order 27900.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₅×C₃₁⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊(C₅⋊(D₃₁⋊C₉))	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×D₃₁⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅⋊D₅×D₃₁	C₃	1	1	yes	maximal, characteristic
5	C₅²×C₃₁⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₅×D₃₁⋊C₉	—	5	6	no	maximal
7	C₃×C₅⋊D₁₅₅	C₂×C₃	1	1	yes	characteristic
8	C₃×C₃₁×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
9	C₃×C₅²×D₃₁	C₂×C₃	1	1	yes	characteristic
10	C₅⋊D₅×D₃₁	C₉	1	1	yes	characteristic, complemented, Hall
11	C₅⋊(D₃₁⋊C₉)	—	5	6	no	—
12	D₅×C₃₁⋊C₉	—	5	6	no	—
13	C₅×D₃₁⋊C₉	D₅	1	6	yes	complemented
14	C₃×C₅²×C₃₁	C₂²×C₃	1	1	yes	characteristic
15	C₃×D₅×D₃₁	—	5	6	no	—
16	C₅⋊D₁₅₅	C₂×C₉	1	1	yes	characteristic, complemented
17	C₃₁×C₅⋊D₅	C₂×C₉	1	1	yes	characteristic, complemented
18	C₅²×D₃₁	C₂×C₉	1	1	yes	characteristic, complemented
19	C₅×C₃₁⋊C₉	C₂×D₅	1	6	yes	complemented
20	C₂×D₃₁⋊C₉	—	25	1	no	Hall
21	C₃×D₁₅₅	—	5	6	no	—
22	C₃×D₅×C₃₁	—	5	6	no	—
23	C₃×C₅×D₃₁	C₃×D₅	1	6	yes	—
24	C₂×C₉×C₅⋊D₅	—	31	1	no	maximal, Hall
25	C₅²×C₃₁	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
26	D₅×D₃₁	—	5	6	no	—
27	C₂×C₃₁⋊C₉	—	25	1	no	—
28	D₃₁⋊C₉	—	25	1	no	—
29	D₃₁⋊C₉	C₅⋊D₅	1	1	yes	characteristic, direct product factor
30	C₃×C₅×C₃₁	C₂×C₃×D₅	1	6	yes	—
31	C₂×C₅²×C₉	—	31	1	no	—
32	C₉×C₅⋊D₅	—	31	1	no	—
33	C₉×C₅⋊D₅	—	31	1	no	—
34	C₂×C₃×D₃₁	—	25	1	no	—
35	D₁₅₅	—	5	6	no	—
36	C₅×D₃₁	C₉×D₅	1	6	yes	complemented
37	D₅×C₃₁	—	5	6	no	—
38	C₂×C₃×C₅⋊D₅	—	31	1	no	—
39	C₃₁⋊C₉	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
40	C₅²×C₉	—	31	1	no	Hall
41	C₂×C₃×C₃₁	—	25	1	no	—
42	C₃×D₃₁	—	25	1	no	—
43	C₃×D₃₁	C₃×C₅⋊D₅	1	1	yes	characteristic
44	C₂×C₉×D₅	—	155	6	no	—
45	C₅×C₃₁	C₂×C₉×D₅	1	6	yes	complemented
46	C₂×C₃×C₅²	—	31	1	no	—
47	C₃×C₅⋊D₅	—	31	1	no	—
48	C₃×C₅⋊D₅	D₃₁⋊C₃	1	1	yes	characteristic
49	C₂×D₃₁	—	25	1	no	Hall
50	C₂×C₅⋊D₅	—	31	1	no	Hall
51	C₃×C₃₁	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic
52	C₂×C₅×C₉	—	31	6	no	—
53	C₉×D₅	—	155	6	no	—
54	C₉×D₅	—	155	6	no	—
55	C₃×C₅²	C₂×D₃₁⋊C₃	1	1	yes	characteristic
56	C₂×C₃₁	—	25	1	no	—
57	D₃₁	—	25	1	no	—
58	D₃₁	C₉×C₅⋊D₅	1	1	yes	characteristic, complemented
59	C₂×C₃×D₅	—	155	6	no	—
60	C₂×C₅²	—	31	1	no	—
61	C₅⋊D₅	—	31	1	no	—
62	C₅⋊D₅	D₃₁⋊C₉	1	1	yes	characteristic, direct product factor
63	C₅×C₉	—	31	6	no	—
64	C₂²×C₉	—	775	1	no	Hall
65	C₃₁	C₂×C₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃×C₅	—	31	6	no	—
67	C₃×D₅	—	5	6	no	—
68	C₃×D₅	—	155	6	no	—
69	C₅²	C₂×D₃₁⋊C₉	1	1	yes	characteristic, complemented, Sylow
70	C₂×D₅	—	155	6	no	—
71	C₂×C₉	—	775	1	no	—
72	C₂×C₉	—	775	1	no	—
73	C₂×C₉	—	31	1	no	—
74	C₃×C₅	D₅×D₃₁⋊C₃	1	6	yes	—
75	C₂²×C₃	—	775	1	no	—
76	C₂×C₅	—	31	6	no	—
77	D₅	—	5	6	no	—
78	D₅	—	155	6	no	—
79	C₉	—	31	1	no	Sylow
80	C₂×C₃	—	775	1	no	—
81	C₂×C₃	—	25	1	no	—
82	C₂×C₃	—	31	1	no	—
83	C₅	D₅×D₃₁⋊C₉	1	6	yes	complemented
84	C₂²	—	775	1	no	Sylow
85	C₃	C₅⋊D₅×D₃₁⋊C₃	1	1	yes	characteristic
86	C₂	—	775	1	no	—
87	C₂	—	25	1	no	—
88	C₂	—	31	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₅⋊D₅×D₃₁⋊C₃
commutator, hypocenter	C₅²×C₃₁	C₂²×C₉
Fitting, socle, cosocle	C₃×C₅²×C₃₁	C₂²×C₃
prime radical	C₃×C₅⋊D₅×D₃₁	C₃
LCS	G ▷ C₅²×C₃₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₅⋊D₅×C₃₁⋊C₉	C₂	semidirect
2. C₅⋊(C₅⋊(D₃₁⋊C₉))	C₂	semidirect
3. C₅²×D₃₁⋊C₉	C₂	semidirect
5. C₅²×C₃₁⋊C₉	C₂²	semidirect
10. C₅⋊D₅×D₃₁	C₉	semidirect
13. C₅×D₃₁⋊C₉	D₅	semidirect
16. C₅⋊D₁₅₅	C₂×C₉	semidirect
17. C₃₁×C₅⋊D₅	C₂×C₉	semidirect
18. C₅²×D₃₁	C₂×C₉	semidirect
19. C₅×C₃₁⋊C₉	C₂×D₅	semidirect
25. C₅²×C₃₁	C₂²×C₉	semidirect
29. D₃₁⋊C₉	C₅⋊D₅	direct (N × H)
36. C₅×D₃₁	C₉×D₅	semidirect
39. C₃₁⋊C₉	C₂×C₅⋊D₅	semidirect
45. C₅×C₃₁	C₂×C₉×D₅	semidirect
58. D₃₁	C₉×C₅⋊D₅	semidirect
62. C₅⋊D₅	D₃₁⋊C₉	direct (N × H)
65. C₃₁	C₂×C₉×C₅⋊D₅	semidirect
69. C₅²	C₂×D₃₁⋊C₉	semidirect
83. C₅	D₅×D₃₁⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊D₅×C₃₁⋊C₉	2
C₅⋊(C₅⋊(D₃₁⋊C₉))	2
C₅²×D₃₁⋊C₉	2
C₃×C₅⋊D₅×D₃₁	3
D₅×D₃₁⋊C₉	5
C₂×C₉×C₅⋊D₅	31

Subgroups — C5⋊D5×D31⋊C9 #42124499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊D₅×D₃₁⋊C₉ #42124499