Subgroups — (C₅⋊(#66526⋊C₂))⋊D₅ #45686174

Order 33300.

144 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	2	yes	maximal, complemented
3	(C₅⋊(D₃₇⋊C₃))⋊D₅	C₃	1	1	yes	maximal, characteristic
4	C₅²×#66526	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×#66526⋊C₂	—	5	2	no	maximal
6	C₅⋊D₅×C₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic
7	C₅×C₅⋊(D₃₇⋊C₃)	C₂×C₃	1	2	yes	—
8	(C₅⋊D₅)⋊D₃₇	C₉	1	1	yes	characteristic, complemented, Hall
9	D₅×#66526	—	5	2	no	—
10	D₅×#66526	—	10	2	no	—
11	C₅⋊(#66526⋊C₂)	D₅	1	2	yes	complemented
12	C₅×#66526⋊C₂	—	5	2	no	—
13	C₅²×C₃₇⋊C₃	C₂²×C₃	1	1	yes	characteristic
14	D₅×D₃₇⋊C₃	—	5	2	no	—
15	C₃₇×C₅⋊D₅	C₂×C₉	1	1	yes	characteristic, complemented
16	C₅×D₁₈₅	C₂×C₉	1	2	yes	complemented
17	C₅×#66526	—	2	2	no	—
18	C₅×#66526	C₂×D₅	1	2	yes	complemented
19	C₂×#66526⋊C₂	—	25	1	no	Hall
20	C₅⋊(D₃₇⋊C₃)	C₃×D₅	1	2	yes	—
21	D₅×C₃₇⋊C₃	—	5	2	no	—
22	D₅×C₃₇⋊C₃	—	10	2	no	—
23	C₅×D₃₇⋊C₃	—	5	2	no	—
24	C₅²×C₃₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
25	C₉×D₅²	—	37	1	no	maximal, Hall
26	D₅×D₃₇	—	5	2	no	—
27	C₂×#66526	—	25	1	no	—
28	#66526⋊C₂	—	5	2	no	—
29	C₅×C₃₇⋊C₃	—	2	2	no	—
30	C₅×C₃₇⋊C₃	C₂×C₃×D₅	1	2	yes	—
31	C₉×C₅⋊D₅	—	37	1	no	—
32	C₅×C₉×D₅	—	37	2	no	—
33	C₂×D₃₇⋊C₃	—	25	1	no	—
34	D₁₈₅	C₉×D₅	1	2	yes	complemented
35	C₅×D₃₇	—	5	2	no	—
36	D₅×C₃₇	—	5	2	no	—
37	D₅×C₃₇	—	10	2	no	—
38	#66526	D₅²	1	1	yes	characteristic, complemented, Hall
39	C₃×D₅²	—	37	1	no	—
40	C₅²×C₉	—	37	1	no	Hall
41	C₂×C₃₇⋊C₃	—	25	1	no	—
42	D₃₇⋊C₃	—	5	2	no	—
43	C₅×C₃₇	—	2	2	no	—
44	C₅×C₃₇	C₂×C₉×D₅	1	2	yes	complemented
45	C₂×C₉×D₅	—	185	2	no	—
46	C₃×C₅⋊D₅	—	37	1	no	—
47	C₃×C₅×D₅	—	37	2	no	—
48	C₂×D₃₇	—	25	1	no	Hall
49	C₃₇⋊C₃	C₃×D₅²	1	1	yes	characteristic
50	D₅²	—	37	1	no	Hall
51	C₂×C₅×C₉	—	185	2	no	—
52	C₉×D₅	—	37	2	no	—
53	C₉×D₅	—	370	2	no	—
54	C₉×D₅	—	185	2	no	—
55	C₃×C₅²	—	37	1	no	—
56	C₂×C₃₇	—	25	1	no	—
57	D₃₇	—	5	2	no	—
58	C₂×C₃×D₅	—	185	2	no	—
59	C₅⋊D₅	#66526⋊C₂	1	1	yes	characteristic, complemented
60	C₅×D₅	—	37	2	no	—
61	C₅×C₉	—	37	2	no	—
62	C₅×C₉	—	74	2	no	—
63	C₃₇	C₉×D₅²	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₉	—	925	1	no	Hall
65	C₂×C₃×C₅	—	185	2	no	—
66	C₃×D₅	—	37	2	no	—
67	C₃×D₅	—	370	2	no	—
68	C₃×D₅	—	185	2	no	—
69	C₅²	C₂×#66526⋊C₂	1	1	yes	characteristic, complemented, Sylow
70	C₂×D₅	—	185	2	no	—
71	C₂×C₉	—	925	1	no	—
72	C₂×C₉	—	185	2	no	—
73	C₃×C₅	—	37	2	no	—
74	C₃×C₅	—	74	2	no	—
75	C₂²×C₃	—	925	1	no	—
76	C₂×C₅	—	185	2	no	—
77	D₅	—	5	2	no	—
78	D₅	—	10	2	no	—
79	D₅	—	37	2	no	—
80	C₉	—	37	1	no	Sylow
81	C₂×C₃	—	925	1	no	—
82	C₂×C₃	—	185	2	no	—
83	C₅	—	2	2	no	—
84	C₅	D₅×#66526⋊C₂	1	2	yes	complemented
85	C₂²	—	925	1	no	Sylow
86	C₃	—	37	1	no	—
87	C₂	—	25	1	no	—
88	C₂	—	185	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₃₇	C₂²×C₉
prime radical	(C₅⋊(D₃₇⋊C₃))⋊D₅	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
4. C₅²×#66526	C₂²	semidirect
8. (C₅⋊D₅)⋊D₃₇	C₉	semidirect
11. C₅⋊(#66526⋊C₂)	D₅	semidirect
15. C₃₇×C₅⋊D₅	C₂×C₉	semidirect
16. C₅×D₁₈₅	C₂×C₉	semidirect
18. C₅×#66526	C₂×D₅	semidirect
24. C₅²×C₃₇	C₂²×C₉	semidirect
34. D₁₈₅	C₉×D₅	semidirect
38. #66526	D₅²	semidirect
44. C₅×C₃₇	C₂×C₉×D₅	semidirect
59. C₅⋊D₅	#66526⋊C₂	semidirect
63. C₃₇	C₉×D₅²	semidirect
69. C₅²	C₂×#66526⋊C₂	semidirect
84. 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
(C₅⋊(D₃₇⋊C₃))⋊D₅	3
D₅×#66526⋊C₂	5
C₉×D₅²	37

Subgroups — (C5⋊(#66526⋊C2))⋊D5 #45686174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₅⋊(#66526⋊C₂))⋊D₅ #45686174