Subgroups — D₅²×#4296 #30685708

Order 17100.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₅×#4296	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₅×#4296	C₂	1	2	yes	maximal, complemented
3	D₅²×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₅²×#4296	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₅×#4296	—	5	2	no	maximal
6	C₅⋊D₅×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
7	C₅×D₅×C₁₉⋊C₃	C₂×C₃	1	2	yes	—
8	D₅²×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×#4296	—	5	2	no	—
10	D₅×#4296	—	5	2	no	—
11	D₅×#4296	—	10	2	no	—
12	D₅×#4296	D₅	1	2	yes	direct product factor
13	C₅²×C₁₉⋊C₃	C₂²×C₃	1	1	yes	characteristic
14	C₂×D₅×C₁₉⋊C₃	—	5	2	no	—
15	C₁₉×C₅⋊D₅	C₂×C₉	1	1	yes	characteristic, complemented
16	C₅×D₅×C₁₉	C₂×C₉	1	2	yes	complemented
17	C₉×D₅²	—	19	1	no	maximal, Hall
18	C₅×#4296	—	2	2	no	—
19	C₅×#4296	C₂×D₅	1	2	yes	complemented
20	C₂²×#4296	—	25	1	no	Hall
21	C₂×C₅×C₁₉⋊C₃	—	5	2	no	—
22	D₅×C₁₉⋊C₃	—	5	2	no	—
23	D₅×C₁₉⋊C₃	—	10	2	no	—
24	D₅×C₁₉⋊C₃	C₃×D₅	1	2	yes	—
25	C₅²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
26	C₉×C₅⋊D₅	—	19	1	no	—
27	C₅×C₉×D₅	—	19	2	no	—
28	C₂×D₅×C₁₉	—	5	2	no	—
29	C₂×#4296	—	5	2	no	—
30	C₂×#4296	—	25	1	no	—
31	C₃×D₅²	—	19	1	no	—
32	C₅×C₁₉⋊C₃	—	2	2	no	—
33	C₅×C₁₉⋊C₃	C₂×C₃×D₅	1	2	yes	—
34	C₂²×C₁₉⋊C₃	—	25	1	no	—
35	C₅²×C₉	—	19	1	no	Hall
36	C₂×C₅×C₁₉	—	5	2	no	—
37	D₅×C₁₉	—	5	2	no	—
38	D₅×C₁₉	—	10	2	no	—
39	D₅×C₁₉	C₉×D₅	1	2	yes	complemented
40	C₂×C₉×D₅	—	95	2	no	—
41	#4296	D₅²	1	1	yes	characteristic, direct product factor, Hall
42	C₃×C₅⋊D₅	—	19	1	no	—
43	C₃×C₅×D₅	—	19	2	no	—
44	C₂×C₁₉⋊C₃	—	5	2	no	—
45	C₂×C₁₉⋊C₃	—	25	1	no	—
46	D₅²	#4296	1	1	yes	characteristic, direct product factor, Hall
47	C₅×C₁₉	—	2	2	no	—
48	C₅×C₁₉	C₂×C₉×D₅	1	2	yes	complemented
49	C₂×C₅×C₉	—	95	2	no	—
50	C₉×D₅	—	19	2	no	—
51	C₉×D₅	—	95	2	no	—
52	C₉×D₅	—	190	2	no	—
53	C₂²×C₁₉	—	25	1	no	Hall
54	C₃×C₅²	—	19	1	no	—
55	C₂×C₃×D₅	—	95	2	no	—
56	C₁₉⋊C₃	C₃×D₅²	1	1	yes	characteristic
57	C₅⋊D₅	C₂×#4296	1	1	yes	characteristic, complemented
58	C₅×D₅	C₂×#4296	1	2	yes	complemented
59	C₅×C₉	—	19	2	no	—
60	C₅×C₉	—	38	2	no	—
61	C₂×C₁₉	—	5	2	no	—
62	C₂×C₁₉	—	25	1	no	—
63	C₂²×C₉	—	475	1	no	Hall
64	C₂×C₃×C₅	—	95	2	no	—
65	C₃×D₅	—	19	2	no	—
66	C₃×D₅	—	95	2	no	—
67	C₃×D₅	—	190	2	no	—
68	C₅²	C₂²×#4296	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₅	—	5	2	no	—
70	C₁₉	C₉×D₅²	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₉	—	95	2	no	—
72	C₂×C₉	—	475	1	no	—
73	C₃×C₅	—	19	2	no	—
74	C₃×C₅	—	38	2	no	—
75	C₂²×C₃	—	475	1	no	—
76	C₂×C₅	—	5	2	no	—
77	D₅	—	5	2	no	—
78	D₅	—	10	2	no	—
79	D₅	D₅×#4296	1	2	yes	direct product factor
80	C₉	—	19	1	no	Sylow
81	C₂×C₃	—	95	2	no	—
82	C₂×C₃	—	475	1	no	—
83	C₅	—	2	2	no	—
84	C₅	C₂×D₅×#4296	1	2	yes	complemented
85	C₂²	—	25	1	no	Sylow
86	C₃	—	19	1	no	—
87	C₂	—	5	2	no	—
88	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₁₉	C₂²×C₉
prime radical	D₅²×C₁₉⋊C₃	C₃
cosocle	C₅²×C₁₉⋊C₃	C₂²×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅⋊D₅×#4296	C₂	semidirect
2. C₅×D₅×#4296	C₂	semidirect
4. C₅²×#4296	C₂²	semidirect
8. D₅²×C₁₉	C₉	semidirect
12. D₅×#4296	D₅	direct (N × H)
15. C₁₉×C₅⋊D₅	C₂×C₉	semidirect
16. C₅×D₅×C₁₉	C₂×C₉	semidirect
19. C₅×#4296	C₂×D₅	semidirect
25. C₅²×C₁₉	C₂²×C₉	semidirect
39. D₅×C₁₉	C₉×D₅	semidirect
41. #4296	D₅²	direct (N × H)
46. D₅²	#4296	direct (N × H)
48. C₅×C₁₉	C₂×C₉×D₅	semidirect
57. C₅⋊D₅	C₂×#4296	semidirect
58. C₅×D₅	C₂×#4296	semidirect
68. C₅²	C₂²×#4296	semidirect
70. C₁₉	C₉×D₅²	semidirect
79. D₅	D₅×#4296	direct (N × H)
84. C₅	C₂×D₅×#4296	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊D₅×#4296	2
C₅×D₅×#4296	2
D₅²×C₁₉⋊C₃	3
C₂×D₅×#4296	5
C₉×D₅²	19

Subgroups — D52×#4296 #30685708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅²×#4296 #30685708