Subgroups — C₃⋊(#3866⋊(C₅²⋊C₃)) #45686243

Order 33300.

80 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	C₅²×C₃⋊#3866	C₃	1	1	yes	maximal, characteristic, complemented
3	#3866⋊(C₅²⋊C₃)	—	3	1	no	maximal
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)	—	2	1	no	—
7	D₃₇⋊(C₅²⋊C₃)	D₃	1	1	yes	characteristic
8	C₅²×#3866	—	3	1	no	Hall
9	C₅²⋊(C₃₇⋊C₃)	—	2	1	no	—
10	C₅²⋊(C₃₇⋊C₃)	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₅²×C₃₇	C₃×C₄	1	1	yes	characteristic, complemented
12	C₅×C₃⋊#3866	—	3	2	no	—
13	C₅²×D₃₇	C₃×D₃	1	1	yes	characteristic
14	C₃⋊(#3866⋊C₃)	—	25	1	no	maximal, Hall
15	C₃×C₅×D₃₇	—	3	2	no	—
16	C₅²×C₃₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
17	Dic₃×C₅²⋊C₃	—	37	1	no	maximal, Hall
18	C₅×#3866	—	9	2	no	—
19	C₃×D₃₇⋊C₃	—	25	1	no	—
20	C₃×C₅×C₃₇	—	3	2	no	—
21	C₂×C₃×C₅²⋊C₃	—	37	1	no	—
22	C₃⋊#3866	C₅²⋊C₃	1	1	yes	characteristic, complemented
23	#3866⋊C₃	—	75	1	no	—
24	C₅×D₃₇	—	3	2	no	—
25	C₃×C₃₇⋊C₃	—	25	1	no	Hall
26	C₅²×Dic₃	—	37	1	no	—
27	C₄×C₅²⋊C₃	—	111	1	no	—
28	C₃×C₅²⋊C₃	—	37	1	no	Hall
29	C₃×D₃₇	C₂×C₅²⋊C₃	1	1	yes	characteristic
30	D₃₇⋊C₃	—	25	1	no	—
31	D₃₇⋊C₃	—	50	1	no	—
32	C₅×C₃₇	—	3	2	no	—
33	C₂×C₃×C₅²	—	37	1	no	—
34	C₂×C₅²⋊C₃	—	37	1	no	—
35	C₂×C₅²⋊C₃	—	74	1	no	—
36	#3866	—	3	1	no	Hall
37	C₃×C₃₇	C₄×C₅²⋊C₃	1	1	yes	characteristic, complemented
38	C₃₇⋊C₃	—	25	1	no	—
39	C₃₇⋊C₃	—	50	1	no	—
40	C₄×C₅²	—	111	1	no	Hall
41	C₃×C₅²	#3866⋊C₃	1	1	yes	characteristic, complemented
42	C₅²⋊C₃	—	37	1	no	—
43	C₅²⋊C₃	—	74	1	no	—
44	D₃₇	D₃×C₅²⋊C₃	1	1	yes	characteristic
45	C₅×Dic₃	—	111	2	no	—
46	C₂×C₅²	—	37	1	no	—
47	C₃₇	Dic₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
48	C₃×Dic₃	—	925	1	no	Hall
49	C₂×C₃×C₅	—	111	2	no	—
50	C₅²	C₃⋊(#3866⋊C₃)	1	1	yes	characteristic, complemented, Sylow
51	C₄×C₅	—	333	2	no	—
52	C₂×C₃²	—	925	1	no	—
53	C₃×C₅	—	3	2	no	—
54	C₃×C₄	—	2775	1	no	—
55	Dic₃	—	37	1	no	—
56	C₂×C₅	—	111	2	no	—
57	C₃²	—	925	1	no	Sylow
58	C₂×C₃	—	37	1	no	—
59	C₂×C₃	—	1850	1	no	—
60	C₂×C₃	—	925	1	no	—
61	C₅	—	3	2	no	—
62	C₄	—	111	1	no	Sylow
63	C₃	—	1850	1	no	—
64	C₃	—	925	1	no	—
65	C₃	#3866⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented
66	C₂	—	37	1	no	—

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

Complements

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

N	H ≅ G/N	type
2. C₅²×C₃⋊#3866	C₃	semidirect
4. C₃×C₅²⋊(C₃₇⋊C₃)	C₄	semidirect
10. C₅²⋊(C₃₇⋊C₃)	Dic₃	semidirect
11. C₃×C₅²×C₃₇	C₃×C₄	semidirect
16. C₅²×C₃₇	C₃×Dic₃	semidirect
22. C₃⋊#3866	C₅²⋊C₃	semidirect
37. C₃×C₃₇	C₄×C₅²⋊C₃	semidirect
41. C₃×C₅²	#3866⋊C₃	semidirect
47. C₃₇	Dic₃×C₅²⋊C₃	semidirect
50. C₅²	C₃⋊(#3866⋊C₃)	semidirect
65. C₃	#3866⋊(C₅²⋊C₃)	semidirect

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
C₅²×C₃⋊#3866	3
#3866⋊(C₅²⋊C₃)	3
C₃⋊(#3866⋊C₃)	25
Dic₃×C₅²⋊C₃	37

Subgroups — C3⋊(#3866⋊(C52⋊C3)) #45686243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(#3866⋊(C₅²⋊C₃)) #45686243