Subgroups — C₃⋊((Dic₁₈₁⋊C₃)⋊C₅) #45656404

Order 32580.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×(C₁₈₁⋊C₃)⋊C₅	C₂	1	1	yes	maximal, characteristic
2	(Dic₁₈₁⋊C₃)⋊C₅	—	3	1	no	maximal
3	C₃⋊(Dic₁₈₁⋊C₅)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×(C₁₈₁⋊C₃)⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃⋊(Dic₁₈₁⋊C₃)	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂×(C₁₈₁⋊C₃)⋊C₅	—	2	1	no	—
7	C₂×(C₁₈₁⋊C₃)⋊C₅	D₃	1	1	yes	characteristic
8	C₂×C₃×C₁₈₁⋊C₅	C₂×C₃	1	1	yes	characteristic
9	Dic₁₈₁⋊C₅	—	3	1	no	Hall
10	C₂×C₃×C₁₈₁⋊C₃	C₂×C₅	1	1	yes	characteristic
11	C₃×C₁₈₁⋊C₅	C₃×C₄	1	1	yes	characteristic, complemented
12	(C₁₈₁⋊C₃)⋊C₅	—	2	1	no	—
13	(C₁₈₁⋊C₃)⋊C₅	Dic₃	1	1	yes	characteristic, complemented
14	Dic₅₄₃	C₃×C₅	1	1	yes	characteristic, complemented
15	Dic₁₈₁⋊C₃	—	3	1	no	—
16	C₂×C₁₈₁⋊C₅	C₃×D₃	1	1	yes	characteristic
17	C₃×C₁₈₁⋊C₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₁₈₁	C₂×C₃×C₅	1	1	yes	characteristic
19	C₂×C₁₈₁⋊C₃	—	2	1	no	—
20	C₂×C₁₈₁⋊C₃	C₅×D₃	1	1	yes	characteristic
21	C₁₈₁⋊C₅	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
22	Dic₁₈₁	—	3	1	no	Hall
23	C₃×C₁₈₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented
24	C₁₈₁⋊C₃	—	2	1	no	—
25	C₁₈₁⋊C₃	C₅×Dic₃	1	1	yes	characteristic, complemented
26	C₂×C₁₈₁	C₃×C₅×D₃	1	1	yes	characteristic
27	C₁₈₁	C₃×C₅×Dic₃	1	1	yes	characteristic, complemented, Sylow
28	C₃×C₅×Dic₃	—	181	1	no	maximal, Hall
29	C₂×C₃²×C₅	—	181	1	no	—
30	C₃×C₄×C₅	—	543	1	no	—
31	C₅×Dic₃	—	181	1	no	—
32	C₃²×C₅	—	181	1	no	Hall
33	C₃×Dic₃	—	181	1	no	Hall
34	C₂×C₃×C₅	—	362	1	no	—
35	C₂×C₃×C₅	—	181	1	no	—
36	C₂×C₃×C₅	—	181	1	no	—
37	C₄×C₅	—	543	1	no	Hall
38	C₂×C₃²	—	181	1	no	—
39	C₃×C₅	—	362	1	no	—
40	C₃×C₅	—	181	1	no	—
41	C₃×C₅	—	181	1	no	—
42	C₃×C₄	—	543	1	no	—
43	Dic₃	—	181	1	no	—
44	C₂×C₅	—	181	1	no	—
45	C₃²	—	181	1	no	Sylow
46	C₂×C₃	—	362	1	no	—
47	C₂×C₃	—	181	1	no	—
48	C₂×C₃	(D₁₈₁⋊C₃)⋊C₅	1	1	yes	characteristic
49	C₅	—	181	1	no	Sylow
50	C₄	—	543	1	no	Sylow
51	C₃	—	362	1	no	—
52	C₃	—	181	1	no	—
53	C₃	(Dic₁₈₁⋊C₃)⋊C₅	1	1	yes	characteristic, complemented
54	C₂	C₃⋊((D₁₈₁⋊C₃)⋊C₅)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊((D₁₈₁⋊C₃)⋊C₅)
commutator, hypocenter	C₃×C₁₈₁	C₃×C₄×C₅
Fitting, socle, cosocle	C₂×C₃×C₁₈₁	C₂×C₃×C₅
prime radical	C₂×C₃×(C₁₈₁⋊C₃)⋊C₅	C₂
LCS	G ▷ C₃×C₁₈₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₃⋊(Dic₁₈₁⋊C₅)	C₃	semidirect
4. C₃×(C₁₈₁⋊C₃)⋊C₅	C₄	semidirect
5. C₃⋊(Dic₁₈₁⋊C₃)	C₅	semidirect
11. C₃×C₁₈₁⋊C₅	C₃×C₄	semidirect
13. (C₁₈₁⋊C₃)⋊C₅	Dic₃	semidirect
14. Dic₅₄₃	C₃×C₅	semidirect
17. C₃×C₁₈₁⋊C₃	C₄×C₅	semidirect
21. C₁₈₁⋊C₅	C₃×Dic₃	semidirect
23. C₃×C₁₈₁	C₃×C₄×C₅	semidirect
25. C₁₈₁⋊C₃	C₅×Dic₃	semidirect
27. C₁₈₁	C₃×C₅×Dic₃	semidirect
53. C₃	(Dic₁₈₁⋊C₃)⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×(C₁₈₁⋊C₃)⋊C₅	2
(Dic₁₈₁⋊C₃)⋊C₅	3
C₃⋊(Dic₁₈₁⋊C₅)	3
C₃⋊(Dic₁₈₁⋊C₃)	5
C₃×C₅×Dic₃	181

Subgroups — C3⋊((Dic181⋊C3)⋊C5) #45656404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊((Dic₁₈₁⋊C₃)⋊C₅) #45656404