Subgroups — C₁₉⋊C₃×C₂²⋊(C₅²⋊C₃) #30685821

Order 17100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊(C₁₉⋊(C₅²⋊C₃))	C₃	1	2	yes	maximal, complemented
2	C₁₉×C₂²⋊(C₅²⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅²×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₉⋊C₃×C₅²⋊C₃	—	4	1	no	maximal, Hall
5	C₂×C₅²×C₁₉⋊C₃	—	3	1	no	—
6	C₂²×C₅²×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₁₉⋊(C₅²⋊C₃)	—	4	2	no	—
8	C₁₉×C₅²⋊C₃	—	4	1	no	—
9	C₅²×C₁₉⋊C₃	A₄	1	1	yes	characteristic, complemented
10	C₂²×C₅×C₁₉⋊C₃	—	3	2	no	—
11	C₂×C₅²×C₁₉	—	3	1	no	—
12	C₃×C₂²⋊(C₅²⋊C₃)	—	19	1	no	maximal, Hall
13	A₄×C₁₉⋊C₃	—	25	1	no	maximal, Hall
14	C₂×C₅×C₁₉⋊C₃	—	3	6	no	—
15	C₅²×C₁₉	C₃×A₄	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₅×C₁₉	—	3	2	no	—
17	C₂²×C₃×C₅²	—	19	1	no	—
18	C₂²⋊(C₅²⋊C₃)	—	19	2	no	—
19	C₂²⋊(C₅²⋊C₃)	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
20	C₅×C₁₉⋊C₃	—	3	2	no	—
21	C₂²⋊(C₁₉⋊C₃)	—	25	2	no	—
22	A₄×C₁₉	—	25	1	no	—
23	C₂²×C₁₉⋊C₃	C₅²⋊C₃	1	1	yes	characteristic, complemented
24	C₃×C₅²⋊C₃	—	76	1	no	Hall
25	C₂×C₅×C₁₉	—	3	6	no	—
26	C₃×C₁₉⋊C₃	—	100	1	no	Hall
27	C₂×C₃×C₅²	—	57	1	no	—
28	C₂×C₁₉⋊C₃	—	3	1	no	—
29	C₂²×C₅²	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
30	C₅×C₁₉	—	3	2	no	—
31	C₂²×C₁₉	C₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
32	C₃×C₅²	—	19	1	no	—
33	C₅²⋊C₃	—	4	1	no	—
34	C₅²⋊C₃	—	76	2	no	—
35	C₂²×C₃×C₅	—	57	2	no	—
36	C₃×C₁₉	—	100	1	no	—
37	C₁₉⋊C₃	—	100	2	no	—
38	C₁₉⋊C₃	C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor
39	C₂×C₅²	—	3	1	no	—
40	C₂×C₁₉	—	3	1	no	—
41	C₃×A₄	—	475	1	no	Hall
42	C₂×C₃×C₅	—	57	6	no	—
43	C₅²	A₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₅	—	3	2	no	—
45	C₁₉	C₃×C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented, Sylow
46	C₃×C₅	—	57	2	no	—
47	C₂²×C₃	—	19	1	no	—
48	A₄	—	25	1	no	—
49	A₄	—	475	2	no	—
50	C₂×C₅	—	3	6	no	—
51	C₃²	—	1900	1	no	Sylow
52	C₂×C₃	—	57	1	no	—
53	C₅	—	3	2	no	—
54	C₂²	C₁₉⋊C₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
55	C₃	—	19	1	no	—
56	C₃	—	100	1	no	—
57	C₃	—	1900	2	no	—
58	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₅²×C₁₉	C₃²
LCS	G ▷ C₂²×C₅²×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂²⋊(C₁₉⋊(C₅²⋊C₃))	C₃	semidirect
2. C₁₉×C₂²⋊(C₅²⋊C₃)	C₃	semidirect
3. C₂²×C₅²×C₁₉⋊C₃	C₃	semidirect
6. C₂²×C₅²×C₁₉	C₃²	semidirect
9. C₅²×C₁₉⋊C₃	A₄	semidirect
15. C₅²×C₁₉	C₃×A₄	semidirect
19. C₂²⋊(C₅²⋊C₃)	C₁₉⋊C₃	direct (N × H)
23. C₂²×C₁₉⋊C₃	C₅²⋊C₃	semidirect
29. C₂²×C₅²	C₃×C₁₉⋊C₃	semidirect
31. C₂²×C₁₉	C₃×C₅²⋊C₃	semidirect
38. C₁₉⋊C₃	C₂²⋊(C₅²⋊C₃)	direct (N × H)
43. C₅²	A₄×C₁₉⋊C₃	semidirect
45. C₁₉	C₃×C₂²⋊(C₅²⋊C₃)	semidirect
54. C₂²	C₁₉⋊C₃×C₅²⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²⋊(C₁₉⋊(C₅²⋊C₃))	3
C₁₉×C₂²⋊(C₅²⋊C₃)	3
C₂²×C₅²×C₁₉⋊C₃	3
C₁₉⋊C₃×C₅²⋊C₃	4
C₃×C₂²⋊(C₅²⋊C₃)	19
A₄×C₁₉⋊C₃	25

Subgroups — C19⋊C3×C22⋊(C52⋊C3) #30685821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉⋊C₃×C₂²⋊(C₅²⋊C₃) #30685821