Subgroups — C₅⋊(#14524212⋊C₃) #44570529

Order 32490.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉⋊C₃²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊#14524212	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅⋊#14524208	—	3	1	no	maximal
4	#14524212⋊C₃	—	5	1	no	maximal, Hall
5	C₅×#11762246	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅×#11762245	D₃	1	1	yes	characteristic, complemented
7	C₅×C₁₉×C₁₉⋊C₃	—	2	1	no	—
8	C₁₉×D₉₅	—	3	1	no	Hall
9	C₁₉⋊C₃²	D₅	1	1	yes	characteristic, complemented, Hall
10	#14524212	—	5	1	no	—
11	#14524208	—	15	1	no	—
12	C₅×C₁₉²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	#11762246	C₃×D₅	1	1	yes	characteristic, complemented
14	#11762245	D₁₅	1	1	yes	characteristic, complemented
15	C₁₉×C₁₉⋊C₃	—	2	1	no	—
16	C₃×C₅×C₁₉⋊C₃	—	38	1	no	—
17	C₁₉×D₁₉	—	15	1	no	Hall
18	C₅⋊(D₁₉⋊C₃)	—	57	1	no	—
19	D₅×C₁₉⋊C₃	—	57	1	no	—
20	C₁₉²	C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₅×C₁₉	—	38	1	no	—
22	C₅×C₁₉⋊C₃	—	2	1	no	—
23	C₅×C₁₉⋊C₃	—	38	1	no	—
24	C₅×C₁₉⋊C₃	—	38	1	no	—
25	C₅×C₁₉⋊C₃	—	57	1	no	—
26	C₅×C₁₉⋊C₃	—	57	1	no	—
27	C₅×C₁₉⋊C₃	—	114	2	no	—
28	D₉₅	—	3	1	no	—
29	D₅×C₁₉	—	57	1	no	—
30	C₃×C₁₉⋊C₃	—	38	1	no	—
31	C₂×C₁₉⋊C₃	—	285	1	no	—
32	D₁₉⋊C₃	—	285	1	no	—
33	C₅×C₁₉	—	2	1	no	—
34	C₅×C₁₉	—	3	1	no	—
35	C₅×C₁₉	—	3	1	no	—
36	C₅×C₁₉	—	6	2	no	—
37	C₃×D₁₅	—	361	1	no	maximal, Hall
38	C₃×C₁₉	—	38	1	no	—
39	C₁₉⋊C₃	—	2	1	no	—
40	C₁₉⋊C₃	—	38	1	no	—
41	C₁₉⋊C₃	—	38	1	no	—
42	C₁₉⋊C₃	—	57	1	no	—
43	C₁₉⋊C₃	—	57	1	no	—
44	C₁₉⋊C₃	—	114	2	no	—
45	C₃²×C₅	—	361	1	no	Hall
46	C₂×C₁₉	—	285	1	no	—
47	D₁₉	—	15	1	no	—
48	D₁₅	—	361	1	no	—
49	C₃×D₅	—	1083	1	no	—
50	C₁₉	—	2	1	no	—
51	C₁₉	—	3	1	no	—
52	C₁₉	—	3	1	no	—
53	C₁₉	—	6	2	no	—
54	C₃×D₃	—	1805	1	no	Hall
55	C₃×C₅	—	38	1	no	—
56	C₃×C₅	—	361	1	no	—
57	C₃×C₅	—	361	1	no	—
58	D₅	—	57	1	no	Hall
59	C₃²	—	361	1	no	Sylow
60	C₂×C₃	—	5415	1	no	—
61	D₃	—	1805	1	no	—
62	C₅	#14524212⋊C₃	1	1	yes	characteristic, complemented, Sylow
63	C₃	—	38	1	no	—
64	C₃	—	361	1	no	—
65	C₃	—	361	1	no	—
66	C₂	—	285	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₅×#11762246	C₂×C₃
Fitting, socle	C₅×C₁₉²	C₃×D₃
LCS	G ▷ C₅×#11762246
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₉⋊C₃²	C₂	semidirect
2. C₅⋊#14524212	C₃	semidirect
5. C₅×#11762246	C₂×C₃	semidirect
6. C₅×#11762245	D₃	semidirect
9. C₁₉⋊C₃²	D₅	semidirect
12. C₅×C₁₉²	C₃×D₃	semidirect
13. #11762246	C₃×D₅	semidirect
14. #11762245	D₁₅	semidirect
20. C₁₉²	C₃×D₁₅	semidirect
62. C₅	#14524212⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₉⋊C₃²	2
C₅⋊#14524212	3
C₅⋊#14524208	3
#14524212⋊C₃	5
C₃×D₁₅	361

Subgroups — C5⋊(#14524212⋊C3) #44570529

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊(#14524212⋊C₃) #44570529