Subgroups — (C₂²⋊(C₁₉⋊C₃))⋊(C₅²⋊C₃) #30685825

Order 17100.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊(C₁₉⋊(C₅²⋊C₃))	C₃	1	1	yes	maximal, characteristic, complemented
2	C₁₉×C₂²⋊(C₅²⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₂²⋊(C₁₉⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₉⋊(C₅²⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
5	C₁₉⋊C₃×C₅²⋊C₃	—	4	1	no	maximal, Hall
6	C₂×C₁₉⋊(C₅²⋊C₃)	—	3	1	no	—
7	C₂²×C₅²×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₁₉⋊(C₅²⋊C₃)	—	4	1	no	—
9	C₁₉⋊(C₅²⋊C₃)	A₄	1	1	yes	characteristic, complemented
10	C₁₉×C₅²⋊C₃	—	4	1	no	—
11	C₅²×C₁₉⋊C₃	—	4	1	no	—
12	C₅×C₂²⋊(C₁₉⋊C₃)	—	3	2	no	—
13	C₂×C₅²×C₁₉	—	3	1	no	—
14	A₄×C₅²⋊C₃	—	19	1	no	maximal, Hall
15	A₄×C₁₉⋊C₃	—	25	1	no	maximal, Hall
16	C₅²×C₁₉	C₃×A₄	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₅×C₁₉	—	3	2	no	—
18	C₂²⋊(C₅²⋊C₃)	—	19	1	no	—
19	C₂²⋊(C₅²⋊C₃)	C₁₉⋊C₃	1	1	yes	characteristic, complemented
20	C₅²×A₄	—	19	1	no	—
21	C₂²×C₅²⋊C₃	—	19	1	no	—
22	C₅×C₁₉⋊C₃	—	12	2	no	—
23	C₂²⋊(C₁₉⋊C₃)	—	25	1	no	—
24	C₂²⋊(C₁₉⋊C₃)	C₅²⋊C₃	1	1	yes	characteristic, complemented
25	A₄×C₁₉	—	25	1	no	—
26	C₂²×C₁₉⋊C₃	—	25	1	no	—
27	C₃×C₅²⋊C₃	—	76	1	no	Hall
28	C₂×C₅×C₁₉	—	9	2	no	—
29	C₃×C₁₉⋊C₃	—	100	1	no	Hall
30	C₂×C₅²⋊C₃	—	57	1	no	—
31	C₂×C₁₉⋊C₃	—	75	1	no	—
32	C₂²×C₅²	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
33	C₅×C₁₉	—	3	2	no	—
34	C₂²×C₁₉	C₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
35	C₃×C₅²	—	76	1	no	—
36	C₅²⋊C₃	—	4	1	no	—
37	C₅²⋊C₃	—	19	1	no	—
38	C₅²⋊C₃	—	76	1	no	—
39	C₅×A₄	—	57	2	no	—
40	C₃×C₁₉	—	100	1	no	—
41	C₁₉⋊C₃	—	4	1	no	—
42	C₁₉⋊C₃	—	25	1	no	—
43	C₁₉⋊C₃	—	100	1	no	—
44	C₂×C₅²	—	3	1	no	—
45	C₂×C₁₉	—	3	1	no	—
46	C₃×A₄	—	475	1	no	Hall
47	C₅²	A₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₅	—	3	2	no	—
49	C₁₉	A₄×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
50	C₃×C₅	—	228	2	no	—
51	C₂²×C₃	—	475	1	no	—
52	A₄	—	19	1	no	—
53	A₄	—	25	1	no	—
54	A₄	—	475	1	no	—
55	C₂×C₅	—	9	2	no	—
56	C₃²	—	1900	1	no	Sylow
57	C₂×C₃	—	1425	1	no	—
58	C₅	—	3	2	no	—
59	C₂²	C₁₉⋊C₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
60	C₃	—	76	1	no	—
61	C₃	—	100	1	no	—
62	C₃	—	1900	1	no	—
63	C₃	—	475	1	no	—
64	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. C₅²×C₂²⋊(C₁₉⋊C₃)	C₃	semidirect
4. C₂²×C₁₉⋊(C₅²⋊C₃)	C₃	semidirect
7. C₂²×C₅²×C₁₉	C₃²	semidirect
9. C₁₉⋊(C₅²⋊C₃)	A₄	semidirect
16. C₅²×C₁₉	C₃×A₄	semidirect
19. C₂²⋊(C₅²⋊C₃)	C₁₉⋊C₃	semidirect
24. C₂²⋊(C₁₉⋊C₃)	C₅²⋊C₃	semidirect
32. C₂²×C₅²	C₃×C₁₉⋊C₃	semidirect
34. C₂²×C₁₉	C₃×C₅²⋊C₃	semidirect
47. C₅²	A₄×C₁₉⋊C₃	semidirect
49. C₁₉	A₄×C₅²⋊C₃	semidirect
59. 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
C₅²×C₂²⋊(C₁₉⋊C₃)	3
C₂²×C₁₉⋊(C₅²⋊C₃)	3
C₁₉⋊C₃×C₅²⋊C₃	4
A₄×C₅²⋊C₃	19
A₄×C₁₉⋊C₃	25

Subgroups — (C22⋊(C19⋊C3))⋊(C52⋊C3) #30685825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂²⋊(C₁₉⋊C₃))⋊(C₅²⋊C₃) #30685825