Subgroups — C₃⋊(Dic₃₇⋊(C₅²⋊C₃)) #45686116

Order 33300.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅²⋊(C₃₇⋊C₃)	C₂	1	1	yes	maximal, characteristic
2	C₅²×Dic₁₁₁	C₃	1	1	yes	maximal, characteristic, complemented
3	Dic₃₇⋊(C₅²⋊C₃)	—	3	1	no	maximal
4	C₃×C₅²⋊(C₃₇⋊C₃)	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅²⋊(C₃₇⋊C₃)	—	2	1	no	—
6	C₂×C₅²⋊(C₃₇⋊C₃)	D₃	1	1	yes	characteristic
7	C₂×C₃×C₅²×C₃₇	C₂×C₃	1	1	yes	characteristic
8	C₅²×Dic₃₇	—	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×Dic₁₁₁	—	3	2	no	—
13	C₂×C₅²×C₃₇	C₃×D₃	1	1	yes	characteristic
14	C₃⋊(Dic₃₇⋊C₃)	—	25	1	no	maximal, Hall
15	C₂×C₃×C₅×C₃₇	—	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×Dic₃₇	—	9	2	no	—
19	C₂×C₃×C₃₇⋊C₃	—	25	1	no	—
20	C₃×C₅×C₃₇	—	3	2	no	—
21	C₂×C₃×C₅²⋊C₃	—	37	1	no	—
22	Dic₁₁₁	C₅²⋊C₃	1	1	yes	characteristic, complemented
23	Dic₃₇⋊C₃	—	75	1	no	—
24	C₂×C₅×C₃₇	—	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	C₂×C₃×C₃₇	C₂×C₅²⋊C₃	1	1	yes	characteristic
30	C₂×C₃₇⋊C₃	—	25	1	no	—
31	C₂×C₃₇⋊C₃	—	50	1	no	—
32	C₅×C₃₇	—	3	2	no	—
33	C₂×C₃×C₅²	D₃₇⋊C₃	1	1	yes	characteristic
34	C₂×C₅²⋊C₃	—	37	1	no	—
35	C₂×C₅²⋊C₃	—	74	1	no	—
36	Dic₃₇	—	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	Dic₃₇⋊C₃	1	1	yes	characteristic, complemented
42	C₅²⋊C₃	—	37	1	no	—
43	C₅²⋊C₃	—	74	1	no	—
44	C₂×C₃₇	D₃×C₅²⋊C₃	1	1	yes	characteristic
45	C₅×Dic₃	—	111	2	no	—
46	C₂×C₅²	C₃⋊(D₃₇⋊C₃)	1	1	yes	characteristic
47	C₃₇	Dic₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
48	C₃×Dic₃	—	925	1	no	Hall
49	C₂×C₃×C₅	—	3	2	no	—
50	C₅²	C₃⋊(Dic₃₇⋊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	—	3	2	no	—
57	C₃²	—	925	1	no	Sylow
58	C₂×C₃	—	1850	1	no	—
59	C₂×C₃	—	925	1	no	—
60	C₂×C₃	D₃₇⋊(C₅²⋊C₃)	1	1	yes	characteristic
61	C₅	—	3	2	no	—
62	C₄	—	111	1	no	Sylow
63	C₃	—	1850	1	no	—
64	C₃	—	925	1	no	—
65	C₃	Dic₃₇⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented
66	C₂	C₃⋊(D₃₇⋊(C₅²⋊C₃))	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₅²×Dic₁₁₁	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. Dic₁₁₁	C₅²⋊C₃	semidirect
37. C₃×C₃₇	C₄×C₅²⋊C₃	semidirect
41. C₃×C₅²	Dic₃₇⋊C₃	semidirect
47. C₃₇	Dic₃×C₅²⋊C₃	semidirect
50. C₅²	C₃⋊(Dic₃₇⋊C₃)	semidirect
65. C₃	Dic₃₇⋊(C₅²⋊C₃)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅²⋊(C₃₇⋊C₃)	2
C₅²×Dic₁₁₁	3
Dic₃₇⋊(C₅²⋊C₃)	3
C₃⋊(Dic₃₇⋊C₃)	25
Dic₃×C₅²⋊C₃	37

Subgroups — C3⋊(Dic37⋊(C52⋊C3)) #45686116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(Dic₃₇⋊(C₅²⋊C₃)) #45686116