Subgroups — C₅²×C₂²⋊#4296 #30685818

Order 17100.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₅²×#4296	—	4	1	no	maximal, Hall
3	C₅×C₂²⋊#4296	C₅	1	6	yes	maximal, direct product factor
4	C₂×C₅²×C₁₉⋊C₃	—	3	1	no	—
5	C₂²×C₅²×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
6	C₅²×C₁₉⋊C₃	A₄	1	1	yes	characteristic
7	C₂²×C₅×C₁₉⋊C₃	C₃×C₅	1	6	yes	—
8	C₂×C₅²×C₁₉	—	3	1	no	—
9	C₅²×C₂²⋊C₉	—	19	1	no	maximal, Hall
10	C₅×#4296	—	4	6	no	—
11	C₂²⋊#4296	C₅²	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₅×C₁₉⋊C₃	—	3	6	no	—
13	C₅²×C₁₉	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
14	C₂²×C₅×C₁₉	C₅×C₉	1	6	yes	complemented
15	C₂²×C₃×C₅²	—	19	1	no	—
16	C₅×C₁₉⋊C₃	C₅×A₄	1	6	yes	—
17	C₂²×C₁₉⋊C₃	C₃×C₅²	1	1	yes	characteristic
18	C₅²×C₉	—	76	1	no	Hall
19	C₂×C₅×C₁₉	—	3	6	no	—
20	C₅×C₂²⋊C₉	—	19	6	no	—
21	#4296	—	4	1	no	Hall
22	C₂×C₃×C₅²	—	57	1	no	—
23	C₂×C₁₉⋊C₃	—	3	1	no	—
24	C₂²×C₅²	#4296	1	1	yes	characteristic, complemented, Hall
25	C₅×C₁₉	C₅×C₂²⋊C₉	1	6	yes	complemented
26	C₂²×C₁₉	C₅²×C₉	1	1	yes	characteristic, complemented, Hall
27	C₃×C₅²	—	19	1	no	—
28	C₂²×C₃×C₅	—	19	6	no	—
29	C₁₉⋊C₃	C₅²×A₄	1	1	yes	characteristic
30	C₂×C₅²	—	3	1	no	—
31	C₅×C₉	—	76	6	no	—
32	C₂×C₁₉	—	3	1	no	—
33	C₂²⋊C₉	—	19	1	no	Hall
34	C₂×C₃×C₅	—	57	6	no	—
35	C₅²	C₂²⋊#4296	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²×C₅	C₅×#4296	1	6	yes	complemented
37	C₁₉	C₅²×C₂²⋊C₉	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₅	—	19	6	no	—
39	C₂²×C₃	—	19	1	no	—
40	C₂×C₅	—	3	6	no	—
41	C₉	—	76	1	no	Sylow
42	C₂×C₃	—	57	1	no	—
43	C₅	C₅×C₂²⋊#4296	1	6	yes	direct product factor
44	C₂²	C₅²×#4296	1	1	yes	characteristic, complemented, Sylow
45	C₃	—	19	1	no	—
46	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅²	C₂²⋊#4296
commutator, hypocenter	C₂²×C₁₉	C₅²×C₉
Frattini	C₁	G
Fitting, socle	C₂²×C₅²×C₁₉	C₉
prime radical	C₂²×C₅²×C₁₉⋊C₃	C₃
cosocle	C₂²×C₁₉⋊C₃	C₃×C₅²
LCS	G ▷ C₂²×C₁₉
UCS	C₁ ◁ C₅²

Complements

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

N	H ≅ G/N	type
3. C₅×C₂²⋊#4296	C₅	direct (N × H)
5. C₂²×C₅²×C₁₉	C₉	semidirect
11. C₂²⋊#4296	C₅²	direct (N × H)
13. C₅²×C₁₉	C₂²⋊C₉	semidirect
14. C₂²×C₅×C₁₉	C₅×C₉	semidirect
24. C₂²×C₅²	#4296	semidirect
25. C₅×C₁₉	C₅×C₂²⋊C₉	semidirect
26. C₂²×C₁₉	C₅²×C₉	semidirect
35. C₅²	C₂²⋊#4296	direct (N × H)
36. C₂²×C₅	C₅×#4296	semidirect
37. C₁₉	C₅²×C₂²⋊C₉	semidirect
43. C₅	C₅×C₂²⋊#4296	direct (N × H)
44. C₂²	C₅²×#4296	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅²×C₁₉⋊C₃	3
C₅²×#4296	4
C₅×C₂²⋊#4296	5
C₅²×C₂²⋊C₉	19

Subgroups — C52×C22⋊#4296 #30685818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₂²⋊#4296 #30685818