Subgroups — #26012847⋊C₃ #45686149

Order 33300.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇⋊C₃×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#26012847	C₃	1	1	yes	maximal, characteristic, complemented
3	#16814882⋊C₃	—	3	1	no	maximal
4	C₅²⋊C₃×C₃₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	(C₅⋊D₅)⋊(C₃₇⋊C₃)	—	2	1	no	—
6	C₃₇×(C₅⋊D₅)⋊C₃	C₂×C₃	1	1	yes	characteristic
7	C₅⋊D₅×C₃₇⋊C₃	D₃	1	1	yes	characteristic
8	#16814882	—	3	1	no	Hall
9	C₅²⋊(C₃₇⋊C₃)	—	2	1	no	—
10	C₃₇×C₅²⋊C₃	C₃×C₄	1	1	yes	characteristic, complemented
11	C₅²×C₃₇⋊C₃	Dic₃	1	1	yes	characteristic, complemented
12	#10625193⋊C₃	—	15	2	no	—
13	C₃₇×C₅⋊D₅	C₃×D₃	1	1	yes	characteristic
14	C₃⋊(Dic₃₇⋊C₃)	—	25	1	no	maximal, Hall
15	D₅×C₃₇⋊C₃	—	15	2	no	—
16	C₅²×C₃₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
17	C₃×#64480	—	37	1	no	maximal, Hall
18	#10625193	—	15	2	no	—
19	C₂×C₃×C₃₇⋊C₃	—	25	1	no	—
20	C₅×C₃₇⋊C₃	—	3	2	no	—
21	C₃×(C₅⋊D₅)⋊C₃	—	37	1	no	—
22	Dic₁₁₁	—	25	1	no	—
23	Dic₃₇⋊C₃	—	75	1	no	—
24	D₅×C₃₇	—	15	2	no	—
25	C₃×C₃₇⋊C₃	—	25	1	no	Hall
26	C₃×#1044	—	111	1	no	—
27	#64480	—	37	1	no	—
28	C₃×C₅²⋊C₃	—	37	1	no	Hall
29	C₂×C₃×C₃₇	—	25	1	no	—
30	C₂×C₃₇⋊C₃	—	25	1	no	—
31	C₂×C₃₇⋊C₃	—	50	1	no	—
32	C₅×C₃₇	—	3	2	no	—
33	C₃×C₅⋊D₅	—	37	1	no	—
34	(C₅⋊D₅)⋊C₃	—	74	1	no	—
35	(C₅⋊D₅)⋊C₃	D₃₇⋊C₃	1	1	yes	characteristic
36	Dic₃₇	—	75	1	no	Hall
37	C₃×C₃₇	—	25	1	no	—
38	C₃₇⋊C₃	—	50	1	no	—
39	C₃₇⋊C₃	#64480	1	1	yes	characteristic, complemented
40	#1044	—	111	1	no	Hall
41	C₃×C₅²	—	37	1	no	—
42	C₅²⋊C₃	—	74	1	no	—
43	C₅²⋊C₃	Dic₃₇⋊C₃	1	1	yes	characteristic, complemented
44	C₂×C₃₇	—	25	1	no	—
45	C₃×AGL(1,𝔽₅)	—	555	2	no	—
46	C₅⋊D₅	C₃⋊(D₃₇⋊C₃)	1	1	yes	characteristic
47	C₃₇	C₃×#64480	1	1	yes	characteristic, complemented, Sylow
48	C₃×Dic₃	—	925	1	no	Hall
49	C₃×D₅	—	555	2	no	—
50	C₅²	C₃⋊(Dic₃₇⋊C₃)	1	1	yes	characteristic, complemented, Sylow
51	AGL(1,𝔽₅)	—	555	2	no	—
52	C₂×C₃²	—	925	1	no	—
53	C₃×C₅	—	111	2	no	—
54	C₃×C₄	—	2775	1	no	—
55	Dic₃	—	925	1	no	—
56	D₅	—	15	2	no	—
57	C₃²	—	925	1	no	Sylow
58	C₂×C₃	—	25	1	no	—
59	C₂×C₃	—	1850	1	no	—
60	C₂×C₃	—	925	1	no	—
61	C₅	—	3	2	no	—
62	C₄	—	2775	1	no	Sylow
63	C₃	—	25	1	no	—
64	C₃	—	37	1	no	—
65	C₃	—	1850	1	no	—
66	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₃₇×C₅²⋊C₃	C₃×C₄
Fitting, socle	C₅²×C₃₇	C₃×Dic₃
prime radical	C₃₇⋊C₃×(C₅⋊D₅)⋊C₃	C₂
cosocle	C₃₇×(C₅⋊D₅)⋊C₃	C₂×C₃
LCS	G ▷ C₃₇×C₅²⋊C₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. #26012847	C₃	semidirect
4. C₅²⋊C₃×C₃₇⋊C₃	C₄	semidirect
10. C₃₇×C₅²⋊C₃	C₃×C₄	semidirect
11. C₅²×C₃₇⋊C₃	Dic₃	semidirect
16. C₅²×C₃₇	C₃×Dic₃	semidirect
39. C₃₇⋊C₃	#64480	semidirect
43. C₅²⋊C₃	Dic₃₇⋊C₃	semidirect
47. C₃₇	C₃×#64480	semidirect
50. C₅²	C₃⋊(Dic₃₇⋊C₃)	semidirect

Maximal subgroups

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

subgroup	index
C₃₇⋊C₃×(C₅⋊D₅)⋊C₃	2
#26012847	3
#16814882⋊C₃	3
C₃⋊(Dic₃₇⋊C₃)	25
C₃×#64480	37

Subgroups — #26012847⋊C3 #45686149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #26012847⋊C₃ #45686149