Finite Group Databasebeta

← D5×C3⋊D483 #44394648

Subgroups — D5×C3⋊D483 #44394648

Order 28980.

240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×D5×C23C211yesmaximal, characteristic, complemented
2C5×C3⋊D483C211yesmaximal, characteristic, complemented
3C3⋊D2415C211yesmaximal, characteristic, complemented
4D5×D483—34nomaximal
5C32×C5×C7×C23C2211yescharacteristic, complemented, Hall
6C2×C3⋊D483—51nomaximal, Hall
7D2415—34no—
8C5×D483—34no—
9C3×C7×D5×C23D314yescomplemented
10D5×C3⋊D69—71nomaximal, Hall
11D5×D161—91noHall
12C3⋊D483—51no—
13C3⋊D483D511yescharacteristic, direct product factor
14C2×C32×C7×C23—51no—
15C3×C5×C7×C23C2×D314yescomplemented
16C3⋊D345—71no—
17C5×C3⋊D69—71no—
18C32×D5×C23D711yescharacteristic, complemented
19C2×D483—154no—
20D805—91no—
21C7×D5×C23C3⋊D311yescharacteristic, complemented
22C5×D161—91no—
23C32×C7×C23C2×D511yescharacteristic, complemented, Hall
24D5×D69—214no—
25D5×C3⋊D21—231nomaximal, Hall
26C32×C5×C23C2×D711yescharacteristic, complemented, Hall
27C2×C3×C7×C23—54no—
28D483—34no—
29D483—154no—
30C2×C3⋊D69—351noHall
31C5×C7×C23C2×C3⋊D311yescharacteristic, complemented, Hall
32D345—214no—
33C5×D69—214no—
34C3×D5×C23D2114yescomplemented
35C2×D161—451noHall
36C3⋊D105—231no—
37C5×C3⋊D21—231no—
38C32×C7×D5D2311yescharacteristic, complemented
39C3×C7×C23D3×D514yescomplemented
40D5×D23—631noHall
41D5×D21—694no—
42C2×C32×C23—51no—
43C3⋊D69—71no—
44C3⋊D69—351no—
45C3×C5×C23C2×D2114yescomplemented
46C2×C7×C23—51no—
47D161—91no—
48D161—451no—
49C32×C5×C7C2×D2311yescharacteristic, complemented, Hall
50C2×D69—1054no—
51C2×C3⋊D21—1151noHall
52D115—631no—
53C5×D23—631no—
54D5×C23C3⋊D2111yescharacteristic, complemented
55D105—694no—
56C5×D21—694no—
57C3×C7×D5D6914yescomplemented
58C32×C23D5×D711yescharacteristic, complemented, Hall
59D5×C3⋊D3—1611noHall
60C7×C23D5×C3⋊D311yescharacteristic, complemented, Hall
61D5×D7—2071noHall
62C2×C3×C23—54no—
63D69—214no—
64D69—1054no—
65C2×C32×C7—51no—
66C3⋊D21—231no—
67C3⋊D21—1151no—
68C5×C23C2×C3⋊D2111yescharacteristic, complemented, Hall
69C3×C5×C7C2×D6914yescomplemented
70C2×D23—3151noHall
71C3⋊D15—1611no—
72C5×C3⋊D3—1611no—
73C32×D5D16111yescharacteristic, complemented
74C2×D21—3454no—
75D35—2071no—
76C5×D7—2071no—
77C7×D5C3⋊D6911yescharacteristic, complemented
78C3×C23D5×D2114yescomplemented
79C32×C7D5×D2311yescharacteristic, complemented, Hall
80D3×D5—4834no—
81C2×C23—51no—
82D23—3151no—
83D23—631no—
84C32×C5C2×D16111yescharacteristic, complemented, Hall
85C2×C3×C7—54no—
86D21—694no—
87D21—3454no—
88C2×C3⋊D3—8051noHall
89C5×C7C2×C3⋊D6911yescharacteristic, complemented, Hall
90D15—4834no—
91C3×D5D48314yescomplemented
92C5×D3—4834no—
93C2×D7—10351noHall
94C23D5×C3⋊D2111yescharacteristic, complemented, Sylow
95C3×C7D5×D6914yescomplemented
96C2×D5—14491noHall
97C2×C32—51no—
98C3⋊D3—8051no—
99C3⋊D3—1611no—
100C3×C5C2×D48314yescomplemented
101C2×C7—51no—
102D7—10351no—
103D7—2071no—
104C2×D3—24154no—
105C2×C5—14491no—
106D5—14491no—
107D5C3⋊D48311yescharacteristic, direct product factor
108C32D5×D16111yescharacteristic, complemented, Sylow
109C7D5×C3⋊D6911yescharacteristic, complemented, Sylow
110C2×C3—54no—
111D3—24154no—
112D3—4834no—
113C5C2×C3⋊D48311yescharacteristic, complemented, Sylow
114C22—72451noSylow
115C3D5×D48314yescomplemented
116C2—51no—
117C2—72451no—
118C2—14491no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C23C22
LCSG ▷ C32×C5×C7×C23
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C7×D5×C23C2semidirect
2. C5×C3⋊D483C2semidirect
3. C3⋊D2415C2semidirect
5. C32×C5×C7×C23C22semidirect
9. C3×C7×D5×C23D3semidirect
13. C3⋊D483D5direct (N × H)
15. C3×C5×C7×C23C2×D3semidirect
18. C32×D5×C23D7semidirect
21. C7×D5×C23C3⋊D3semidirect
23. C32×C7×C23C2×D5semidirect
26. C32×C5×C23C2×D7semidirect
31. C5×C7×C23C2×C3⋊D3semidirect
34. C3×D5×C23D21semidirect
38. C32×C7×D5D23semidirect
39. C3×C7×C23D3×D5semidirect
45. C3×C5×C23C2×D21semidirect
49. C32×C5×C7C2×D23semidirect
54. D5×C23C3⋊D21semidirect
57. C3×C7×D5D69semidirect
58. C32×C23D5×D7semidirect
60. C7×C23D5×C3⋊D3semidirect
68. C5×C23C2×C3⋊D21semidirect
69. C3×C5×C7C2×D69semidirect
73. C32×D5D161semidirect
77. C7×D5C3⋊D69semidirect
78. C3×C23D5×D21semidirect
79. C32×C7D5×D23semidirect
84. C32×C5C2×D161semidirect
89. C5×C7C2×C3⋊D69semidirect
91. C3×D5D483semidirect
94. C23D5×C3⋊D21semidirect
95. C3×C7D5×D69semidirect
100. C3×C5C2×D483semidirect
107. D5C3⋊D483direct (N × H)
108. C32D5×D161semidirect
109. C7D5×C3⋊D69semidirect
113. C5C2×C3⋊D483semidirect
115. C3D5×D483semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D5×C232
C5×C3⋊D4832
C3⋊D24152
D5×D4833
C2×C3⋊D4835
D5×C3⋊D697
D5×C3⋊D2123