Subgroups — C₅×#4296⋊Dic₅ #30685631

Order 17100.

96 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	C₅×(C₁₉⋊C₃)⋊Dic₅	C₃	1	1	yes	maximal, characteristic
3	C₅²×#4296	C₄	1	1	yes	characteristic, complemented, Hall
4	#4296⋊Dic₅	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×#4296⋊C₄	—	5	1	no	maximal
6	C₂×C₅²×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
7	C₅×Dic₉₅	C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅×#4296	—	2	2	no	—
9	C₂×C₅×#4296	D₅	1	1	yes	characteristic
10	C₂×C₅×#4296	C₂×C₅	1	1	yes	characteristic
11	C₅²×C₁₉⋊C₃	C₃×C₄	1	1	yes	characteristic
12	(C₁₉⋊C₃)⋊Dic₅	C₃×C₅	1	1	yes	characteristic
13	C₅×(C₁₉⋊C₃)⋊C₄	—	5	1	no	—
14	C₂×C₅²×C₁₉	C₂×C₉	1	1	yes	characteristic
15	C₅×C₉×Dic₅	—	19	1	no	maximal, Hall
16	C₅×#4296	—	2	2	no	—
17	C₅×#4296	Dic₅	1	1	yes	characteristic, complemented
18	C₅×#4296	C₄×C₅	1	1	yes	characteristic, complemented
19	#4296⋊C₄	—	5	1	no	Hall
20	C₂×C₅×C₁₉⋊C₃	—	2	2	no	—
21	C₂×C₅×C₁₉⋊C₃	C₃×D₅	1	1	yes	characteristic
22	C₂×C₅×C₁₉⋊C₃	C₂×C₃×C₅	1	1	yes	characteristic
23	C₅²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
24	C₂×C₅²×C₉	—	19	1	no	—
25	Dic₉₅	C₅×C₉	1	1	yes	characteristic, complemented
26	C₅×Dic₁₉	—	5	1	no	—
27	C₂×#4296	C₅×D₅	1	1	yes	characteristic
28	C₃×C₅×Dic₅	—	19	1	no	—
29	C₅×C₁₉⋊C₃	—	2	2	no	—
30	C₅×C₁₉⋊C₃	C₃×Dic₅	1	1	yes	characteristic
31	C₅×C₁₉⋊C₃	C₃×C₄×C₅	1	1	yes	characteristic
32	(C₁₉⋊C₃)⋊C₄	—	5	1	no	—
33	C₅²×C₉	—	19	1	no	Hall
34	C₂×C₅×C₁₉	—	2	2	no	—
35	C₂×C₅×C₁₉	C₉×D₅	1	1	yes	characteristic
36	C₂×C₅×C₁₉	C₂×C₅×C₉	1	1	yes	characteristic
37	C₄×C₅×C₉	—	95	1	no	—
38	C₉×Dic₅	—	19	1	no	—
39	#4296	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
40	C₂×C₃×C₅²	—	19	1	no	—
41	C₂×C₁₉⋊C₃	C₃×C₅×D₅	1	1	yes	characteristic
42	C₅×Dic₅	—	171	1	no	Hall
43	C₅×C₁₉	—	2	2	no	—
44	C₅×C₁₉	C₉×Dic₅	1	1	yes	characteristic, complemented
45	C₅×C₁₉	C₄×C₅×C₉	1	1	yes	characteristic, complemented
46	C₂×C₅×C₉	—	19	1	no	—
47	C₂×C₅×C₉	—	19	1	no	—
48	C₂×C₅×C₉	—	38	2	no	—
49	Dic₁₉	—	5	1	no	Hall
50	C₃×C₅²	—	19	1	no	—
51	C₃×C₄×C₅	—	95	1	no	—
52	C₃×Dic₅	—	19	1	no	—
53	C₁₉⋊C₃	C₃×C₅×Dic₅	1	1	yes	characteristic
54	C₂×C₅²	AGL(1,𝔽₁₉)	1	1	yes	characteristic
55	C₅×C₉	—	19	1	no	—
56	C₅×C₉	—	19	1	no	—
57	C₅×C₉	—	38	2	no	—
58	C₂×C₁₉	C₅×C₉×D₅	1	1	yes	characteristic
59	C₄×C₉	—	95	1	no	Hall
60	C₂×C₃×C₅	—	19	1	no	—
61	C₂×C₃×C₅	—	19	1	no	—
62	C₂×C₃×C₅	—	38	2	no	—
63	C₅²	#4296⋊C₄	1	1	yes	characteristic, complemented, Sylow
64	C₄×C₅	—	855	1	no	—
65	Dic₅	—	171	1	no	—
66	C₁₉	C₅×C₉×Dic₅	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₉	—	19	1	no	—
68	C₃×C₅	—	19	1	no	—
69	C₃×C₅	—	19	1	no	—
70	C₃×C₅	—	38	2	no	—
71	C₃×C₄	—	95	1	no	—
72	C₂×C₅	—	2	2	no	—
73	C₂×C₅	C₅×AGL(1,𝔽₁₉)	1	1	yes	characteristic
74	C₂×C₅	C₅⋊AGL(1,𝔽₁₉)	1	1	yes	characteristic
75	C₉	—	19	1	no	Sylow
76	C₂×C₃	—	19	1	no	—
77	C₅	—	2	2	no	—
78	C₅	C₅×#4296⋊C₄	1	1	yes	characteristic, complemented
79	C₅	#4296⋊Dic₅	1	1	yes	characteristic, direct product factor
80	C₄	—	855	1	no	Sylow
81	C₃	—	19	1	no	—
82	C₂	C₅×C₅⋊AGL(1,𝔽₁₉)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	C₅⋊AGL(1,𝔽₁₉)
commutator, hypocenter	C₅×C₁₉	C₄×C₅×C₉
Frattini	C₂	C₅×C₅⋊AGL(1,𝔽₁₉)
Fitting, socle	C₂×C₅²×C₁₉	C₂×C₉
prime radical	C₂×C₅²×C₁₉⋊C₃	C₂×C₃
cosocle	C₂×C₅×C₁₉⋊C₃	C₂×C₃×C₅
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
3. C₅²×#4296	C₄	semidirect
4. #4296⋊Dic₅	C₅	direct (N × H)
7. C₅×Dic₉₅	C₉	semidirect
17. C₅×#4296	Dic₅	semidirect
18. C₅×#4296	C₄×C₅	semidirect
23. C₅²×C₁₉	C₄×C₉	semidirect
25. Dic₉₅	C₅×C₉	semidirect
39. #4296	C₅×Dic₅	semidirect
44. C₅×C₁₉	C₉×Dic₅	semidirect
45. C₅×C₁₉	C₄×C₅×C₉	semidirect
63. C₅²	#4296⋊C₄	semidirect
66. C₁₉	C₅×C₉×Dic₅	semidirect
78. C₅	C₅×#4296⋊C₄	semidirect
79. C₅	#4296⋊Dic₅	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×(C₁₉⋊C₃)⋊Dic₅	3
#4296⋊Dic₅	5
C₅×#4296⋊C₄	5
C₅×C₉×Dic₅	19

Subgroups — C5×#4296⋊Dic5 #30685631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#4296⋊Dic₅ #30685631