Subgroups — C₅⋊((C₁₉⋊C₃)⋊(D₁₉⋊C₃)) #44570541

Order 32490.

144 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⋊((C₁₉⋊C₃)⋊D₁₉)	C₃	1	2	yes	maximal, complemented
3	C₅⋊#14524207	C₃	1	1	yes	maximal, characteristic, complemented
4	C₅⋊#14524206	C₃	1	1	yes	maximal, characteristic, complemented
5	(C₁₉⋊C₃)⋊(D₁₉⋊C₃)	—	5	1	no	maximal, Hall
6	C₅×#11762246	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×#11762245	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	1	2	yes	complemented
9	C₅⋊(C₁₉⋊D₁₉)	C₃²	1	1	yes	characteristic, complemented, Hall
10	C₁₉⋊C₃²	D₅	1	1	yes	characteristic, complemented, Hall
11	(C₁₉⋊C₃)⋊D₁₉	—	5	2	no	—
12	#14524207	—	5	1	no	—
13	#14524206	—	5	1	no	—
14	C₅×C₁₉²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅⋊(D₁₉⋊C₃)	—	19	2	no	maximal
16	#11762246	C₃×D₅	1	1	yes	characteristic, complemented
17	#11762245	C₃×D₅	1	1	yes	characteristic, complemented
18	C₁₉×C₁₉⋊C₃	C₃×D₅	1	2	yes	complemented
19	C₃×C₅×C₁₉⋊C₃	—	19	2	no	—
20	C₁₉⋊D₁₉	—	5	1	no	Hall
21	C₃×D₉₅	—	19	2	no	—
22	C₅⋊(D₁₉⋊C₃)	—	19	2	no	—
23	C₅⋊(D₁₉⋊C₃)	—	19	2	no	—
24	C₅⋊(D₁₉⋊C₃)	—	19	2	no	—
25	C₅⋊(D₁₉⋊C₃)	—	57	6	no	—
26	C₁₉²	C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₁₉⋊C₃	—	95	2	no	—
28	C₃×C₅×C₁₉	—	19	2	no	—
29	C₅×C₁₉⋊C₃	—	19	2	no	—
30	C₅×C₁₉⋊C₃	—	19	2	no	—
31	C₅×C₁₉⋊C₃	—	57	6	no	—
32	C₅×C₁₉⋊C₃	D₁₉⋊C₃	1	2	yes	complemented
33	D₉₅	—	19	2	no	—
34	D₉₅	—	57	6	no	—
35	C₃×C₁₉⋊C₃	—	19	2	no	—
36	C₃×D₁₉	—	95	2	no	—
37	D₁₉⋊C₃	—	285	6	no	—
38	D₁₉⋊C₃	—	95	2	no	—
39	D₁₉⋊C₃	—	95	2	no	—
40	D₁₉⋊C₃	—	95	2	no	—
41	C₅×C₁₉	—	3	6	no	—
42	C₅×C₁₉	C₃×D₁₉⋊C₃	1	2	yes	complemented
43	C₃²×D₅	—	361	1	no	Hall
44	C₃×C₁₉	—	19	2	no	—
45	C₁₉⋊C₃	—	19	2	no	—
46	C₁₉⋊C₃	—	19	2	no	—
47	C₁₉⋊C₃	—	57	6	no	—
48	C₁₉⋊C₃	C₅⋊(D₁₉⋊C₃)	1	2	yes	complemented
49	C₃²×C₅	—	361	1	no	Hall
50	D₁₉	—	285	6	no	—
51	D₁₉	—	95	2	no	—
52	C₃×D₅	—	361	2	no	—
53	C₃×D₅	—	361	1	no	—
54	C₃×D₅	—	361	1	no	—
55	C₁₉	—	3	6	no	—
56	C₁₉	C₃×C₅⋊(D₁₉⋊C₃)	1	2	yes	complemented
57	C₂×C₃²	—	1805	1	no	Hall
58	C₃×C₅	—	19	2	no	—
59	C₃×C₅	—	361	1	no	—
60	C₃×C₅	—	361	1	no	—
61	D₅	—	361	1	no	Hall
62	C₃²	—	361	1	no	Sylow
63	C₂×C₃	—	1805	2	no	—
64	C₂×C₃	—	1805	1	no	—
65	C₂×C₃	—	1805	1	no	—
66	C₅	(C₁₉⋊C₃)⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
67	C₃	—	19	2	no	—
68	C₃	—	361	1	no	—
69	C₃	—	361	1	no	—
70	C₂	—	1805	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₉²	C₂×C₃²
LCS	G ▷ C₅×C₁₉²
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⋊((C₁₉⋊C₃)⋊D₁₉)	C₃	semidirect
3. C₅⋊#14524207	C₃	semidirect
4. C₅⋊#14524206	C₃	semidirect
6. C₅×#11762246	C₂×C₃	semidirect
7. C₅×#11762245	C₂×C₃	semidirect
8. C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	semidirect
9. C₅⋊(C₁₉⋊D₁₉)	C₃²	semidirect
10. C₁₉⋊C₃²	D₅	semidirect
14. C₅×C₁₉²	C₂×C₃²	semidirect
16. #11762246	C₃×D₅	semidirect
17. #11762245	C₃×D₅	semidirect
18. C₁₉×C₁₉⋊C₃	C₃×D₅	semidirect
26. C₁₉²	C₃²×D₅	semidirect
32. C₅×C₁₉⋊C₃	D₁₉⋊C₃	semidirect
42. C₅×C₁₉	C₃×D₁₉⋊C₃	semidirect
48. C₁₉⋊C₃	C₅⋊(D₁₉⋊C₃)	semidirect
56. C₁₉	C₃×C₅⋊(D₁₉⋊C₃)	semidirect
66. C₅	(C₁₉⋊C₃)⋊(D₁₉⋊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⋊((C₁₉⋊C₃)⋊D₁₉)	3
C₅⋊#14524207	3
C₅⋊#14524206	3
(C₁₉⋊C₃)⋊(D₁₉⋊C₃)	5
C₃×C₅⋊(D₁₉⋊C₃)	19

Subgroups — C5⋊((C19⋊C3)⋊(D19⋊C3)) #44570541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊((C₁₉⋊C₃)⋊(D₁₉⋊C₃)) #44570541