Subgroups — #30659271⋊C₂ #45686145

Order 33300.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30659275	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₅⋊D₅)⋊#66526	C₂	1	1	yes	maximal, characteristic, complemented
3	#30659271	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	C₅⋊D₅×C₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic
7	C₅⋊(C₅⋊(D₃₇⋊C₃))	C₂×C₃	1	1	yes	characteristic
8	C₅²×D₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic
9	C₅⋊D₅×D₃₇	C₉	1	1	yes	characteristic, complemented, Hall
10	C₅²×C₃₇⋊C₃	C₂²×C₃	1	1	yes	characteristic
11	D₅×D₃₇⋊C₃	—	15	2	no	—
12	C₅⋊D₁₈₅	C₂×C₉	1	1	yes	characteristic, complemented
13	C₃₇×C₅⋊D₅	C₂×C₉	1	1	yes	characteristic, complemented
14	C₅²×D₃₇	C₂×C₉	1	1	yes	characteristic, complemented
15	C₂×#66526⋊C₂	—	25	1	no	maximal, Hall
16	C₅⋊(D₃₇⋊C₃)	—	15	2	no	—
17	D₅×C₃₇⋊C₃	—	15	2	no	—
18	C₅×D₃₇⋊C₃	—	3	2	no	—
19	C₅²×C₃₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
20	C₂×(C₅⋊D₅)⋊C₉	—	37	1	no	maximal, Hall
21	D₅×D₃₇	—	15	2	no	—
22	C₂×#66526	—	25	1	no	—
23	#66526⋊C₂	—	25	1	no	—
24	#66526⋊C₂	—	25	1	no	—
25	C₅×C₃₇⋊C₃	—	3	2	no	—
26	C₂×C₅²⋊C₉	—	37	1	no	—
27	(C₅⋊D₅)⋊C₉	—	37	1	no	—
28	(C₅⋊D₅)⋊C₉	—	37	1	no	—
29	C₂×D₃₇⋊C₃	—	25	1	no	—
30	D₁₈₅	—	15	2	no	—
31	C₅×D₃₇	—	3	2	no	—
32	D₅×C₃₇	—	15	2	no	—
33	#66526	—	25	1	no	Hall
34	C₂×C₃×C₅⋊D₅	—	37	1	no	—
35	C₅²⋊C₉	—	37	1	no	Hall
36	C₂×C₃₇⋊C₃	—	25	1	no	—
37	D₃₇⋊C₃	—	25	1	no	—
38	D₃₇⋊C₃	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
39	C₅×C₃₇	—	3	2	no	—
40	C₂×C₃×C₅²	—	37	1	no	—
41	C₃×C₅⋊D₅	—	37	1	no	—
42	C₃×C₅⋊D₅	—	37	1	no	—
43	C₂×D₃₇	—	25	1	no	Hall
44	C₃₇⋊C₃	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
45	C₂×C₅⋊D₅	—	37	1	no	Hall
46	C₃×C₅²	—	37	1	no	—
47	C₂×C₃₇	—	25	1	no	—
48	D₃₇	—	25	1	no	—
49	D₃₇	(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, complemented
50	C₂×C₃×D₅	—	555	2	no	—
51	C₂×C₅²	—	37	1	no	—
52	C₅⋊D₅	—	37	1	no	—
53	C₅⋊D₅	#66526⋊C₂	1	1	yes	characteristic, complemented
54	C₃₇	C₂×(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₉	—	925	1	no	Hall
56	C₂×C₃×C₅	—	111	2	no	—
57	C₃×D₅	—	555	2	no	—
58	C₃×D₅	—	555	2	no	—
59	C₅²	C₂×#66526⋊C₂	1	1	yes	characteristic, complemented, Sylow
60	C₂×D₅	—	555	2	no	—
61	C₂×C₉	—	925	1	no	—
62	C₂×C₉	—	925	1	no	—
63	C₂×C₉	—	925	1	no	—
64	C₃×C₅	—	111	2	no	—
65	C₂²×C₃	—	925	1	no	—
66	C₂×C₅	—	111	2	no	—
67	D₅	—	15	2	no	—
68	D₅	—	555	2	no	—
69	C₉	—	925	1	no	Sylow
70	C₂×C₃	—	37	1	no	—
71	C₂×C₃	—	925	1	no	—
72	C₂×C₃	—	925	1	no	—
73	C₅	—	3	2	no	—
74	C₂²	—	925	1	no	Sylow
75	C₃	—	37	1	no	—
76	C₂	—	25	1	no	—
77	C₂	—	37	1	no	—
78	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. #30659275	C₂	semidirect
2. (C₅⋊D₅)⋊#66526	C₂	semidirect
3. #30659271	C₂	semidirect
5. C₅²⋊#66526	C₂²	semidirect
9. C₅⋊D₅×D₃₇	C₉	semidirect
12. C₅⋊D₁₈₅	C₂×C₉	semidirect
13. C₃₇×C₅⋊D₅	C₂×C₉	semidirect
14. C₅²×D₃₇	C₂×C₉	semidirect
19. C₅²×C₃₇	C₂²×C₉	semidirect
49. D₃₇	(C₅⋊D₅)⋊C₉	semidirect
53. C₅⋊D₅	#66526⋊C₂	semidirect
54. C₃₇	C₂×(C₅⋊D₅)⋊C₉	semidirect
59. C₅²	C₂×#66526⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
#30659275	2
(C₅⋊D₅)⋊#66526	2
#30659271	2
C₅⋊D₅×D₃₇⋊C₃	3
C₂×#66526⋊C₂	25
C₂×(C₅⋊D₅)⋊C₉	37

Subgroups — #30659271⋊C2 #45686145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #30659271⋊C₂ #45686145