Subgroups — Dic₅×#11762246 #36343142

Order 21660.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#11762246	C₂	1	1	yes	maximal, characteristic
2	C₁₉²×Dic₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×#11762246	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄×#11762246	—	5	1	no	maximal, Hall
5	C₂×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic
6	C₂×#11762246	D₅	1	1	yes	characteristic
7	C₅×C₁₉²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₄×C₁₉²	—	5	1	no	Hall
9	Dic₅×C₁₉⋊C₃	—	19	2	no	maximal
10	#11762246	Dic₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₉²	C₃×D₅	1	1	yes	characteristic
12	C₂×C₅×C₁₉⋊C₃	—	19	2	no	—
13	C₁₉×Dic₅	—	3	6	no	—
14	C₁₉×Dic₅	C₁₉⋊C₃	1	2	yes	complemented
15	C₁₉²	C₃×Dic₅	1	1	yes	characteristic, complemented, Sylow
16	C₅×C₁₉⋊C₃	—	19	2	no	—
17	C₄×C₁₉⋊C₃	—	95	2	no	—
18	C₂×C₅×C₁₉	—	3	6	no	—
19	C₂×C₅×C₁₉	C₂×C₁₉⋊C₃	1	2	yes	—
20	C₂×C₁₉⋊C₃	—	19	2	no	—
21	C₅×C₁₉	—	3	6	no	—
22	C₅×C₁₉	C₄×C₁₉⋊C₃	1	2	yes	complemented
23	C₄×C₁₉	—	5	2	no	—
24	C₄×C₁₉	—	15	6	no	—
25	C₃×Dic₅	—	361	1	no	Hall
26	C₁₉⋊C₃	—	19	2	no	—
27	C₂×C₁₉	—	3	6	no	—
28	C₂×C₁₉	D₅×C₁₉⋊C₃	1	2	yes	—
29	C₂×C₃×C₅	—	361	1	no	—
30	Dic₅	#11762246	1	1	yes	characteristic, direct product factor, Hall
31	C₁₉	—	3	6	no	—
32	C₁₉	Dic₅×C₁₉⋊C₃	1	2	yes	complemented
33	C₃×C₅	—	361	1	no	Hall
34	C₃×C₄	—	1805	1	no	Hall
35	C₂×C₅	C₂×#11762246	1	1	yes	characteristic
36	C₂×C₃	—	361	1	no	—
37	C₅	C₄×#11762246	1	1	yes	characteristic, complemented, Sylow
38	C₄	—	5	1	no	Sylow
39	C₃	—	361	1	no	Sylow
40	C₂	D₅×#11762246	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×#11762246
commutator, hypocenter	C₅×C₁₉²	C₃×C₄
Fitting, socle, cosocle	C₂×C₅×C₁₉²	C₂×C₃
prime radical	C₂×C₅×#11762246	C₂
LCS	G ▷ C₅×C₁₉²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₁₉²×Dic₅	C₃	semidirect
3. C₅×#11762246	C₄	semidirect
7. C₅×C₁₉²	C₃×C₄	semidirect
10. #11762246	Dic₅	direct (N × H)
14. C₁₉×Dic₅	C₁₉⋊C₃	semidirect
15. C₁₉²	C₃×Dic₅	semidirect
22. C₅×C₁₉	C₄×C₁₉⋊C₃	semidirect
30. Dic₅	#11762246	direct (N × H)
32. C₁₉	Dic₅×C₁₉⋊C₃	semidirect
37. C₅	C₄×#11762246	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#11762246	2
C₁₉²×Dic₅	3
C₄×#11762246	5
Dic₅×C₁₉⋊C₃	19

Subgroups — Dic5×#11762246 #36343142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₅×#11762246 #36343142