Subgroups — C₅⋊D₅×#66526⋊C₂ #45686177

Order 33300.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₅×#66526	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊(C₅⋊(#66526⋊C₂))	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×#66526⋊C₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅⋊D₅×D₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
5	C₅²×#66526	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₅×#66526⋊C₂	—	5	6	no	maximal
7	C₅⋊D₅×C₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic
8	C₅⋊(C₅⋊(D₃₇⋊C₃))	C₂×C₃	1	1	yes	characteristic
9	C₅²×D₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic
10	C₅⋊D₅×D₃₇	C₉	1	1	yes	characteristic, complemented, Hall
11	D₅×#66526	—	5	6	no	—
12	C₅⋊(#66526⋊C₂)	—	5	6	no	—
13	C₅×#66526⋊C₂	D₅	1	6	yes	complemented
14	C₅²×C₃₇⋊C₃	C₂²×C₃	1	1	yes	characteristic
15	D₅×D₃₇⋊C₃	—	5	6	no	—
16	C₅⋊D₁₈₅	C₂×C₉	1	1	yes	characteristic, complemented
17	C₃₇×C₅⋊D₅	C₂×C₉	1	1	yes	characteristic, complemented
18	C₅²×D₃₇	C₂×C₉	1	1	yes	characteristic, complemented
19	C₅×#66526	C₂×D₅	1	6	yes	complemented
20	C₂×#66526⋊C₂	—	25	1	no	Hall
21	C₅⋊(D₃₇⋊C₃)	—	5	6	no	—
22	D₅×C₃₇⋊C₃	—	5	6	no	—
23	C₅×D₃₇⋊C₃	C₃×D₅	1	6	yes	—
24	C₅²×C₃₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
25	C₂×C₉×C₅⋊D₅	—	37	1	no	maximal, Hall
26	D₅×D₃₇	—	5	6	no	—
27	C₂×#66526	—	25	1	no	—
28	#66526⋊C₂	—	25	1	no	—
29	#66526⋊C₂	C₅⋊D₅	1	1	yes	characteristic, direct product factor
30	C₅×C₃₇⋊C₃	C₂×C₃×D₅	1	6	yes	—
31	C₂×C₅²×C₉	—	37	1	no	—
32	C₉×C₅⋊D₅	—	37	1	no	—
33	C₉×C₅⋊D₅	—	37	1	no	—
34	C₂×D₃₇⋊C₃	—	25	1	no	—
35	D₁₈₅	—	5	6	no	—
36	C₅×D₃₇	C₉×D₅	1	6	yes	complemented
37	D₅×C₃₇	—	5	6	no	—
38	#66526	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
39	C₂×C₃×C₅⋊D₅	—	37	1	no	—
40	C₅²×C₉	—	37	1	no	Hall
41	C₂×C₃₇⋊C₃	—	25	1	no	—
42	D₃₇⋊C₃	—	25	1	no	—
43	D₃₇⋊C₃	C₃×C₅⋊D₅	1	1	yes	characteristic
44	C₅×C₃₇	C₂×C₉×D₅	1	6	yes	complemented
45	C₂×C₉×D₅	—	185	6	no	—
46	C₂×C₃×C₅²	—	37	1	no	—
47	C₃×C₅⋊D₅	—	37	1	no	—
48	C₃×C₅⋊D₅	—	37	1	no	—
49	C₂×D₃₇	—	25	1	no	Hall
50	C₃₇⋊C₃	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic
51	C₂×C₅⋊D₅	—	37	1	no	Hall
52	C₂×C₅×C₉	—	37	6	no	—
53	C₉×D₅	—	185	6	no	—
54	C₉×D₅	—	185	6	no	—
55	C₃×C₅²	—	37	1	no	—
56	C₂×C₃₇	—	25	1	no	—
57	D₃₇	—	25	1	no	—
58	D₃₇	C₉×C₅⋊D₅	1	1	yes	characteristic, complemented
59	C₂×C₃×D₅	—	185	6	no	—
60	C₂×C₅²	—	37	1	no	—
61	C₅⋊D₅	—	37	1	no	—
62	C₅⋊D₅	#66526⋊C₂	1	1	yes	characteristic, direct product factor
63	C₅×C₉	—	37	6	no	—
64	C₃₇	C₂×C₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₉	—	925	1	no	Hall
66	C₂×C₃×C₅	—	37	6	no	—
67	C₃×D₅	—	185	6	no	—
68	C₃×D₅	—	185	6	no	—
69	C₅²	C₂×#66526⋊C₂	1	1	yes	characteristic, complemented, Sylow
70	C₂×D₅	—	185	6	no	—
71	C₂×C₉	—	37	1	no	—
72	C₂×C₉	—	925	1	no	—
73	C₂×C₉	—	925	1	no	—
74	C₃×C₅	—	37	6	no	—
75	C₂²×C₃	—	925	1	no	—
76	C₂×C₅	—	37	6	no	—
77	D₅	—	5	6	no	—
78	D₅	—	185	6	no	—
79	C₉	—	37	1	no	Sylow
80	C₂×C₃	—	37	1	no	—
81	C₂×C₃	—	925	1	no	—
82	C₂×C₃	—	925	1	no	—
83	C₅	D₅×#66526⋊C₂	1	6	yes	complemented
84	C₂²	—	925	1	no	Sylow
85	C₃	—	37	1	no	—
86	C₂	—	25	1	no	—
87	C₂	—	37	1	no	—
88	C₂	—	925	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₃₇	C₂²×C₉
prime radical	C₅⋊D₅×D₃₇⋊C₃	C₃
cosocle	C₅²×C₃₇⋊C₃	C₂²×C₃
LCS	G ▷ C₅²×C₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅⋊D₅×#66526	C₂	semidirect
2. C₅⋊(C₅⋊(#66526⋊C₂))	C₂	semidirect
3. C₅²×#66526⋊C₂	C₂	semidirect
5. C₅²×#66526	C₂²	semidirect
10. C₅⋊D₅×D₃₇	C₉	semidirect
13. C₅×#66526⋊C₂	D₅	semidirect
16. C₅⋊D₁₈₅	C₂×C₉	semidirect
17. C₃₇×C₅⋊D₅	C₂×C₉	semidirect
18. C₅²×D₃₇	C₂×C₉	semidirect
19. C₅×#66526	C₂×D₅	semidirect
24. C₅²×C₃₇	C₂²×C₉	semidirect
29. #66526⋊C₂	C₅⋊D₅	direct (N × H)
36. C₅×D₃₇	C₉×D₅	semidirect
38. #66526	C₂×C₅⋊D₅	semidirect
44. C₅×C₃₇	C₂×C₉×D₅	semidirect
58. D₃₇	C₉×C₅⋊D₅	semidirect
62. C₅⋊D₅	#66526⋊C₂	direct (N × H)
64. C₃₇	C₂×C₉×C₅⋊D₅	semidirect
69. C₅²	C₂×#66526⋊C₂	semidirect
83. C₅	D₅×#66526⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊D₅×#66526	2
C₅⋊(C₅⋊(#66526⋊C₂))	2
C₅²×#66526⋊C₂	2
C₅⋊D₅×D₃₇⋊C₃	3
D₅×#66526⋊C₂	5
C₂×C₉×C₅⋊D₅	37

Subgroups — C5⋊D5×#66526⋊C2 #45686177

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊D₅×#66526⋊C₂ #45686177