Subgroups — C₃⋊#26012846 #45686266

Order 33300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#19149853	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#16814881	—	3	1	no	maximal
3	#26012846	—	3	3	no	maximal
4	C₃×C₃₇×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅⋊D₁₈₅	D₃	1	1	yes	characteristic
6	#19149853	D₃	1	3	yes	—
7	#16814881	—	9	1	no	Hall
8	C₃₇×C₅²⋊C₃	Dic₃	1	3	yes	complemented
9	C₃×C₅²×C₃₇	Dic₃	1	1	yes	characteristic, complemented
10	C₃⋊#10625192	—	15	1	no	—
11	C₃⋊#10625191	—	15	1	no	—
12	C₅⋊D₁₈₅	C₃⋊D₃	1	1	yes	characteristic
13	C₃⋊(C₃⋊#3866)	—	25	1	no	maximal, Hall
14	C₃×D₁₈₅	—	15	1	no	—
15	C₃×D₁₈₅	—	15	1	no	—
16	C₅²×C₃₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
17	C₃⋊#64480	—	37	1	no	maximal, Hall
18	#10625192	—	45	1	no	—
19	#10625191	—	45	1	no	—
20	C₃²×D₃₇	—	25	1	no	—
21	C₃×C₅×C₃₇	—	3	1	no	—
22	C₃×C₅×C₃₇	—	3	1	no	—
23	C₃×(C₅⋊D₅)⋊C₃	—	37	1	no	—
24	C₃⋊#3866	—	75	1	no	—
25	C₃⋊#3866	—	75	3	no	—
26	D₁₈₅	—	15	1	no	—
27	D₁₈₅	—	15	1	no	—
28	C₃²×C₃₇	—	25	1	no	Hall
29	C₃⋊#1044	—	111	1	no	—
30	#64480	—	111	3	no	—
31	C₃×C₅²⋊C₃	#3866	1	1	yes	characteristic, complemented, Hall
32	C₃×D₃₇	—	25	3	no	—
33	C₃×D₃₇	—	25	1	no	—
34	C₅×C₃₇	—	3	1	no	—
35	C₅×C₃₇	—	3	1	no	—
36	C₃×C₅⋊D₅	—	37	1	no	—
37	(C₅⋊D₅)⋊C₃	—	37	3	no	—
38	#3866	—	225	1	no	Hall
39	C₃×C₃₇	—	25	3	no	—
40	C₃×C₃₇	#64480	1	1	yes	characteristic, complemented
41	#1044	—	333	1	no	Hall
42	C₃×C₅²	C₃⋊#3866	1	1	yes	characteristic, complemented
43	C₅²⋊C₃	C₃⋊#3866	1	3	yes	complemented
44	D₃₇	—	25	1	no	—
45	ΓL(1,𝔽₁₆)	—	555	1	no	—
46	ΓL(1,𝔽₁₆)	—	555	1	no	—
47	C₅⋊D₅	—	37	1	no	—
48	C₃₇	C₃⋊#64480	1	1	yes	characteristic, complemented, Sylow
49	C₃⋊Dic₃	—	925	1	no	Hall
50	C₃×D₅	—	555	1	no	—
51	C₃×D₅	—	555	1	no	—
52	C₅²	C₃⋊(C₃⋊#3866)	1	1	yes	characteristic, complemented, Sylow
53	AGL(1,𝔽₅)	—	1665	1	no	—
54	AGL(1,𝔽₅)	—	1665	1	no	—
55	C₂×C₃²	—	925	1	no	—
56	C₃×C₅	—	3	1	no	—
57	C₃×C₅	—	3	1	no	—
58	Dic₃	—	2775	1	no	—
59	Dic₃	—	2775	3	no	—
60	D₅	—	555	1	no	—
61	D₅	—	555	1	no	—
62	C₃²	—	25	1	no	Sylow
63	C₂×C₃	—	925	3	no	—
64	C₂×C₃	—	925	1	no	—
65	C₅	—	3	1	no	—
66	C₅	—	3	1	no	—
67	C₄	—	8325	1	no	Sylow
68	C₃	—	25	3	no	—
69	C₃	#26012846	1	1	yes	characteristic, complemented
70	C₂	—	925	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₃×C₃₇×C₅²⋊C₃	C₄
Fitting, socle	C₃×C₅²×C₃₇	Dic₃
prime radical, cosocle	C₃×#19149853	C₂
LCS	G ▷ C₃×C₃₇×C₅²⋊C₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
4. C₃×C₃₇×C₅²⋊C₃	C₄	semidirect
8. C₃₇×C₅²⋊C₃	Dic₃	semidirect
9. C₃×C₅²×C₃₇	Dic₃	semidirect
16. C₅²×C₃₇	C₃⋊Dic₃	semidirect
31. C₃×C₅²⋊C₃	#3866	semidirect
40. C₃×C₃₇	#64480	semidirect
42. C₃×C₅²	C₃⋊#3866	semidirect
43. C₅²⋊C₃	C₃⋊#3866	semidirect
48. C₃₇	C₃⋊#64480	semidirect
52. C₅²	C₃⋊(C₃⋊#3866)	semidirect
69. C₃	#26012846	semidirect

Maximal subgroups

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

subgroup	index
C₃×#19149853	2
C₃⋊#16814881	3
#26012846	3
C₃⋊(C₃⋊#3866)	25
C₃⋊#64480	37

Subgroups — C3⋊#26012846 #45686266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#26012846 #45686266