Subgroups — D₅×#15692434 #44570548

Order 32490.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15692434	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×#11762245	C₃	1	1	yes	maximal, characteristic
3	C₂×#15692434	—	5	1	no	maximal, Hall
4	C₅×#11762245	C₂×C₃	1	1	yes	characteristic
5	D₅×C₁₉²	C₉	1	1	yes	characteristic, complemented, Hall
6	#15692434	D₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×#11762245	—	5	1	no	—
8	C₅×C₁₉²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	D₅×#4296	—	19	2	no	maximal
10	#11762245	C₃×D₅	1	1	yes	characteristic
11	C₅×#4296	—	19	2	no	—
12	C₂×C₁₉²	—	5	1	no	Hall
13	D₅×C₁₉⋊C₃	—	19	2	no	—
14	D₅×C₁₉⋊C₃	—	57	6	no	—
15	C₁₉²	C₉×D₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×#4296	—	95	2	no	—
17	C₅×C₁₉⋊C₃	—	19	2	no	—
18	C₅×C₁₉⋊C₃	—	57	6	no	—
19	D₅×C₁₉	—	3	6	no	—
20	D₅×C₁₉	#4296	1	2	yes	complemented
21	#4296	—	19	2	no	—
22	C₂×C₁₉⋊C₃	—	285	6	no	—
23	C₂×C₁₉⋊C₃	—	95	2	no	—
24	C₅×C₁₉	—	3	6	no	—
25	C₅×C₁₉	C₂×#4296	1	2	yes	complemented
26	C₉×D₅	—	361	1	no	Hall
27	C₁₉⋊C₃	—	19	2	no	—
28	C₁₉⋊C₃	—	57	6	no	—
29	C₅×C₉	—	361	1	no	Hall
30	C₂×C₁₉	—	5	2	no	—
31	C₂×C₁₉	—	15	6	no	—
32	C₃×D₅	—	361	1	no	—
33	C₁₉	—	3	6	no	—
34	C₁₉	D₅×#4296	1	2	yes	complemented
35	C₂×C₉	—	1805	1	no	Hall
36	C₃×C₅	—	361	1	no	—
37	D₅	#15692434	1	1	yes	characteristic, direct product factor, Hall
38	C₉	—	361	1	no	Sylow
39	C₂×C₃	—	1805	1	no	—
40	C₅	C₂×#15692434	1	1	yes	characteristic, complemented, Sylow
41	C₃	—	361	1	no	—
42	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₉²	C₂×C₉
prime radical	D₅×#11762245	C₃
cosocle	C₅×#11762245	C₂×C₃
LCS	G ▷ C₅×C₁₉²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×#15692434	C₂	semidirect
5. D₅×C₁₉²	C₉	semidirect
6. #15692434	D₅	direct (N × H)
8. C₅×C₁₉²	C₂×C₉	semidirect
15. C₁₉²	C₉×D₅	semidirect
20. D₅×C₁₉	#4296	semidirect
25. C₅×C₁₉	C₂×#4296	semidirect
34. C₁₉	D₅×#4296	semidirect
37. D₅	#15692434	direct (N × H)
40. C₅	C₂×#15692434	semidirect

Maximal subgroups

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

subgroup	index
C₅×#15692434	2
D₅×#11762245	3
C₂×#15692434	5
D₅×#4296	19

Subgroups — D5×#15692434 #44570548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#15692434 #44570548