Subgroups — C₃×#26012848 #45686202

Order 33300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃₇⋊(C₅²⋊C₃)	C₂	1	1	yes	maximal, characteristic
2	C₃×#16814887	C₃	1	1	yes	maximal, characteristic, complemented
3	#26012848	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₅²⋊(C₃₇⋊C₃)	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅²×D₃₇	C₂×C₃	1	1	yes	characteristic
6	D₃₇⋊(C₅²⋊C₃)	C₂×C₃	1	3	yes	—
7	#16814887	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₅²⋊(C₃₇⋊C₃)	C₃×C₄	1	3	yes	complemented
9	C₃×C₅²×C₃₇	C₃×C₄	1	1	yes	characteristic, complemented
10	C₃×#10625194	—	15	2	no	—
11	C₅²×D₃₇	C₂×C₃²	1	1	yes	characteristic
12	C₃×#3866⋊C₃	—	25	1	no	maximal, Hall
13	C₃×C₅×D₃₇	—	3	2	no	—
14	C₅²×C₃₇	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
15	C₃×#1039⋊C₃	—	37	1	no	maximal, Hall
16	#10625194	—	15	2	no	—
17	C₃×D₃₇⋊C₃	—	25	1	no	—
18	C₃×C₅×C₃₇	—	3	2	no	—
19	C₂×C₃×C₅²⋊C₃	—	37	1	no	—
20	C₃×#3866	—	25	1	no	—
21	#3866⋊C₃	—	25	3	no	—
22	C₅×D₃₇	—	3	2	no	—
23	C₃×C₃₇⋊C₃	—	25	1	no	Hall
24	C₃×#1039	—	37	1	no	—
25	#1039⋊C₃	—	37	3	no	—
26	C₃×C₅²⋊C₃	—	37	1	no	Hall
27	C₃×D₃₇	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
28	D₃₇⋊C₃	—	25	3	no	—
29	C₅×C₃₇	—	3	2	no	—
30	C₂×C₃×C₅²	—	37	1	no	—
31	C₂×C₅²⋊C₃	—	37	3	no	—
32	#3866	—	25	1	no	Hall
33	C₃×C₃₇	#1039⋊C₃	1	1	yes	characteristic, complemented
34	C₃₇⋊C₃	—	25	3	no	—
35	#1039	—	37	1	no	Hall
36	C₃×C₅²	#3866⋊C₃	1	1	yes	characteristic, complemented
37	C₅²⋊C₃	—	37	3	no	—
38	D₃₇	C₃×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
39	C₃×Dic₅	—	555	2	no	—
40	C₂×C₅²	—	37	1	no	—
41	C₃₇	C₃×#1039⋊C₃	1	1	yes	characteristic, complemented, Sylow
42	C₃²×C₄	—	925	1	no	Hall
43	C₂×C₃×C₅	—	111	2	no	—
44	C₅²	C₃×#3866⋊C₃	1	1	yes	characteristic, complemented, Sylow
45	Dic₅	—	555	2	no	—
46	C₂×C₃²	—	925	1	no	—
47	C₃×C₅	—	3	2	no	—
48	C₃×C₄	—	925	1	no	—
49	C₃×C₄	—	925	3	no	—
50	C₂×C₅	—	111	2	no	—
51	C₃²	—	925	1	no	Sylow
52	C₂×C₃	—	37	1	no	—
53	C₂×C₃	—	925	3	no	—
54	C₅	—	3	2	no	—
55	C₄	—	925	1	no	Sylow
56	C₃	—	925	3	no	—
57	C₃	#26012848	1	1	yes	characteristic, direct product factor
58	C₂	—	37	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#26012848
commutator, hypocenter	C₅²×C₃₇	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₃₇	C₃×C₄
prime radical	C₃×D₃₇⋊(C₅²⋊C₃)	C₂
cosocle	C₅²×D₃₇	C₂×C₃²
LCS	G ▷ C₅²×C₃₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃×#16814887	C₃	semidirect
3. #26012848	C₃	direct (N × H)
4. C₃×C₅²⋊(C₃₇⋊C₃)	C₄	semidirect
7. #16814887	C₃²	semidirect
8. C₅²⋊(C₃₇⋊C₃)	C₃×C₄	semidirect
9. C₃×C₅²×C₃₇	C₃×C₄	semidirect
14. C₅²×C₃₇	C₃²×C₄	semidirect
33. C₃×C₃₇	#1039⋊C₃	semidirect
36. C₃×C₅²	#3866⋊C₃	semidirect
41. C₃₇	C₃×#1039⋊C₃	semidirect
44. C₅²	C₃×#3866⋊C₃	semidirect
57. C₃	#26012848	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₃₇⋊(C₅²⋊C₃)	2
C₃×#16814887	3
#26012848	3
C₃×#3866⋊C₃	25
C₃×#1039⋊C₃	37

Subgroups — C3×#26012848 #45686202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#26012848 #45686202