Subgroups — C₄×C₅²⋊#4296 #30685644

Order 17100.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²⋊#4296	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅²×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₅²⋊#4296	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₅²×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
5	C₄×C₅²×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
6	C₅²×C₁₉⋊C₃	C₃×C₄	1	1	yes	characteristic
7	C₄×C₅×C₁₉⋊C₃	—	3	2	no	—
8	C₂×C₅²×C₁₉	C₂×C₉	1	1	yes	characteristic
9	C₄×C₅²⋊C₉	—	19	1	no	maximal, Hall
10	C₄×#4296	—	25	1	no	maximal, Hall
11	C₂×C₅×C₁₉⋊C₃	—	3	2	no	—
12	C₅²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅²⋊C₉	—	19	1	no	—
14	C₄×C₅×C₁₉	—	3	2	no	—
15	C₂×#4296	—	25	1	no	—
16	C₃×C₄×C₅²	—	19	1	no	—
17	C₅×C₁₉⋊C₃	—	3	2	no	—
18	C₄×C₁₉⋊C₃	C₅²⋊C₃	1	1	yes	characteristic
19	C₅²⋊C₉	—	19	1	no	Hall
20	C₂×C₅×C₁₉	—	3	2	no	—
21	#4296	—	25	1	no	Hall
22	C₂×C₃×C₅²	—	19	1	no	—
23	C₂×C₁₉⋊C₃	C₂×C₅²⋊C₃	1	1	yes	characteristic
24	C₄×C₅²	#4296	1	1	yes	characteristic, complemented, Hall
25	C₅×C₁₉	—	3	2	no	—
26	C₄×C₁₉	C₅²⋊C₉	1	1	yes	characteristic, complemented, Hall
27	C₃×C₅²	—	19	1	no	—
28	C₃×C₄×C₅	—	57	2	no	—
29	C₁₉⋊C₃	C₄×C₅²⋊C₃	1	1	yes	characteristic
30	C₂×C₅²	C₂×#4296	1	1	yes	characteristic
31	C₂×C₁₉	C₂×C₅²⋊C₉	1	1	yes	characteristic
32	C₄×C₉	—	475	1	no	Hall
33	C₂×C₃×C₅	—	57	2	no	—
34	C₅²	C₄×#4296	1	1	yes	characteristic, complemented, Sylow
35	C₄×C₅	—	3	2	no	—
36	C₁₉	C₄×C₅²⋊C₉	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₉	—	475	1	no	—
38	C₃×C₅	—	57	2	no	—
39	C₃×C₄	—	19	1	no	—
40	C₂×C₅	—	3	2	no	—
41	C₉	—	475	1	no	Sylow
42	C₂×C₃	—	19	1	no	—
43	C₅	—	3	2	no	—
44	C₄	C₅²⋊#4296	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	19	1	no	—
46	C₂	C₂×C₅²⋊#4296	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	C₅²⋊#4296
commutator, hypocenter	C₅²×C₁₉	C₄×C₉
Frattini	C₂	C₂×C₅²⋊#4296
Fitting	C₄×C₅²×C₁₉	C₉
socle	C₂×C₅²×C₁₉	C₂×C₉
prime radical, cosocle	C₂×C₅²×C₁₉⋊C₃	C₂×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
3. C₅²⋊#4296	C₄	direct (N × H)
5. C₄×C₅²×C₁₉	C₉	semidirect
12. C₅²×C₁₉	C₄×C₉	semidirect
24. C₄×C₅²	#4296	semidirect
26. C₄×C₁₉	C₅²⋊C₉	semidirect
34. C₅²	C₄×#4296	semidirect
36. C₁₉	C₄×C₅²⋊C₉	semidirect
44. C₄	C₅²⋊#4296	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅²⋊#4296	2
C₄×C₅²×C₁₉⋊C₃	3
C₄×C₅²⋊C₉	19
C₄×#4296	25

Subgroups — C4×C52⋊#4296 #30685644

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅²⋊#4296 #30685644