Subgroups — C₂×(C₅⋊D₅)⋊#4296 #30685729

Order 17100.

100 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, complemented
2	(C₅⋊D₅)⋊#4296	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅⋊D₅×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₅²⋊#4296	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅²×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
6	C₅⋊D₅×C₁₉⋊C₃	C₂×C₃	1	2	yes	—
7	C₂×C₁₉×C₅⋊D₅	C₉	1	1	yes	characteristic, complemented, Hall
8	C₅²×C₁₉⋊C₃	C₂²×C₃	1	1	yes	characteristic
9	C₂×D₅×C₁₉⋊C₃	—	15	2	no	—
10	C₂×C₅²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
11	C₁₉×C₅⋊D₅	C₂×C₉	1	2	yes	complemented
12	C₂×(C₅⋊D₅)⋊C₉	—	19	1	no	maximal, Hall
13	C₂²×#4296	—	25	1	no	maximal, Hall
14	C₂×C₅×C₁₉⋊C₃	—	3	2	no	—
15	D₅×C₁₉⋊C₃	—	15	4	no	—
16	C₅²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅²⋊C₉	—	19	1	no	—
18	(C₅⋊D₅)⋊C₉	—	19	2	no	—
19	C₂×D₅×C₁₉	—	15	2	no	—
20	C₂×#4296	—	25	2	no	—
21	C₂×#4296	—	25	1	no	—
22	C₂×C₃×C₅⋊D₅	—	19	1	no	—
23	C₅×C₁₉⋊C₃	—	3	2	no	—
24	C₂²×C₁₉⋊C₃	—	25	1	no	—
25	C₅²⋊C₉	—	19	1	no	Hall
26	C₂×C₅×C₁₉	—	3	2	no	—
27	D₅×C₁₉	—	15	4	no	—
28	#4296	—	25	1	no	Hall
29	C₂×C₃×C₅²	—	19	1	no	—
30	C₃×C₅⋊D₅	—	19	2	no	—
31	C₂×C₁₉⋊C₃	—	75	2	no	—
32	C₂×C₁₉⋊C₃	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
33	C₂×C₅⋊D₅	#4296	1	1	yes	characteristic, complemented, Hall
34	C₅×C₁₉	—	3	2	no	—
35	C₂²×C₁₉	—	25	1	no	Hall
36	C₃×C₅²	—	19	1	no	—
37	C₂×C₃×D₅	—	285	2	no	—
38	C₁₉⋊C₃	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
39	C₂×C₅²	C₂×#4296	1	1	yes	characteristic, complemented
40	C₅⋊D₅	C₂×#4296	1	2	yes	complemented
41	C₂×C₁₉	—	75	2	no	—
42	C₂×C₁₉	(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, complemented
43	C₂²×C₉	—	475	1	no	Hall
44	C₂×C₃×C₅	—	57	2	no	—
45	C₃×D₅	—	285	4	no	—
46	C₅²	C₂²×#4296	1	1	yes	characteristic, complemented, Sylow
47	C₂×D₅	—	15	2	no	—
48	C₁₉	C₂×(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₉	—	475	1	no	—
50	C₂×C₉	—	475	2	no	—
51	C₃×C₅	—	57	2	no	—
52	C₂²×C₃	—	1425	1	no	—
53	C₂×C₅	—	3	2	no	—
54	D₅	—	15	4	no	—
55	C₉	—	475	1	no	Sylow
56	C₂×C₃	—	19	1	no	—
57	C₂×C₃	—	1425	2	no	—
58	C₅	—	3	2	no	—
59	C₂²	—	75	1	no	Sylow
60	C₃	—	19	1	no	—
61	C₂	—	75	2	no	—
62	C₂	(C₅⋊D₅)⋊#4296	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	(C₅⋊D₅)⋊#4296
commutator, hypocenter	C₅²×C₁₉	C₂²×C₉
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₉	C₂×C₉
prime radical	C₂×C₅⋊D₅×C₁₉⋊C₃	C₃
cosocle	C₅²×C₁₉⋊C₃	C₂²×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²⋊#4296	C₂	semidirect
2. (C₅⋊D₅)⋊#4296	C₂	direct (N × H)
4. C₅²⋊#4296	C₂²	semidirect
7. C₂×C₁₉×C₅⋊D₅	C₉	semidirect
10. C₂×C₅²×C₁₉	C₂×C₉	semidirect
11. C₁₉×C₅⋊D₅	C₂×C₉	semidirect
16. C₅²×C₁₉	C₂²×C₉	semidirect
33. C₂×C₅⋊D₅	#4296	semidirect
39. C₂×C₅²	C₂×#4296	semidirect
40. C₅⋊D₅	C₂×#4296	semidirect
42. C₂×C₁₉	(C₅⋊D₅)⋊C₉	semidirect
46. C₅²	C₂²×#4296	semidirect
48. C₁₉	C₂×(C₅⋊D₅)⋊C₉	semidirect
62. C₂	(C₅⋊D₅)⋊#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
(C₅⋊D₅)⋊#4296	2
C₂×C₅⋊D₅×C₁₉⋊C₃	3
C₂×(C₅⋊D₅)⋊C₉	19
C₂²×#4296	25

Subgroups — C2×(C5⋊D5)⋊#4296 #30685729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×(C₅⋊D₅)⋊#4296 #30685729