Finite Group Databasebeta

← C3×C5×(C19⋊C3)⋊Dic5 #30685647

Subgroups — C3×C5×(C19⋊C3)⋊Dic5 #30685647

Order 17100.

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

normal subgroups only

This group has 192 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
1C2×C3×C52×C19⋊C3C211yesmaximal, characteristic
2C3×C5×Dic95C311yesmaximal, characteristic, complemented
3C5×(C19⋊C3)⋊Dic5C313yesmaximal, direct product factor
4C3×C52×C19⋊C3C411yescharacteristic, complemented, Hall
5C3×(C19⋊C3)⋊Dic5C511yesmaximal, characteristic, direct product factor
6C3×C5×(C19⋊C3)⋊C4—51nomaximal
7C2×C52×C19⋊C3C2×C313yes—
8C2×C3×C52×C19C2×C311yescharacteristic
9C5×Dic95C3211yescharacteristic, complemented, Hall
10C2×C3×C5×C19⋊C3—22no—
11C2×C3×C5×C19⋊C3D511yescharacteristic
12C2×C3×C5×C19⋊C3C2×C511yescharacteristic
13C3×C52×C19C3×C411yescharacteristic, complemented
14C52×C19⋊C3C3×C413yescomplemented
15C3×Dic95C3×C511yescharacteristic, complemented
16C3×C5×Dic19—51no—
17(C19⋊C3)⋊Dic5C3×C513yesdirect product factor
18C5×(C19⋊C3)⋊C4—53no—
19C2×C52×C19C2×C3211yescharacteristic
20C32×C5×Dic5—191nomaximal, Hall
21C3×C5×C19⋊C3—22no—
22C3×C5×C19⋊C3Dic511yescharacteristic, complemented
23C3×C5×C19⋊C3C4×C511yescharacteristic, complemented
24C3×(C19⋊C3)⋊C4—51noHall
25C2×C3×C5×C19—22no—
26C2×C3×C5×C19C3×D511yescharacteristic
27C2×C3×C5×C19C2×C3×C511yescharacteristic
28C2×C5×C19⋊C3—26no—
29C2×C5×C19⋊C3C3×D513yes—
30C2×C5×C19⋊C3C2×C3×C513yes—
31C52×C19C32×C411yescharacteristic, complemented, Hall
32C2×C32×C52—191no—
33Dic95C32×C511yescharacteristic, complemented
34C5×Dic19—51no—
35C2×C3×C19⋊C3C5×D511yescharacteristic
36C3×C5×Dic5—193no—
37C3×C5×Dic5—571no—
38C3×C5×C19—22no—
39C3×C5×C19C3×Dic511yescharacteristic, complemented
40C3×C5×C19C3×C4×C511yescharacteristic, complemented
41C5×C19⋊C3—26no—
42C5×C19⋊C3C3×Dic513yescomplemented
43C5×C19⋊C3C3×C4×C513yescomplemented
44C3×Dic19—51no—
45(C19⋊C3)⋊C4—53no—
46C32×C52—191noHall
47C2×C5×C19—22no—
48C2×C5×C19C32×D511yescharacteristic
49C2×C5×C19C2×C32×C511yescharacteristic
50C32×C4×C5—951no—
51C32×Dic5—191no—
52C3×C19⋊C3C5×Dic511yescharacteristic, complemented, Hall
53C2×C3×C52—193no—
54C2×C3×C52D19⋊C311yescharacteristic
55C2×C3×C19C3×C5×D511yescharacteristic
56C2×C19⋊C3C3×C5×D513yes—
57C5×Dic5—571noHall
58C5×C19—22no—
59C5×C19C32×Dic511yescharacteristic, complemented
60C5×C19C32×C4×C511yescharacteristic, complemented
61C2×C32×C5—191no—
62C2×C32×C5—191no—
63C2×C32×C5—382no—
64Dic19—51noHall
65C3×C52—193no—
66C3×C52(C19⋊C3)⋊C411yescharacteristic, complemented
67C3×C4×C5—2851no—
68C3×C4×C5—953no—
69C3×Dic5—193no—
70C3×Dic5—571no—
71C3×C19C3×C5×Dic511yescharacteristic, complemented
72C19⋊C3C3×C5×Dic513yescomplemented
73C2×C52C3×D19⋊C311yescharacteristic
74C32×C5—191no—
75C32×C5—191no—
76C32×C5—382no—
77C2×C19C32×C5×D511yescharacteristic
78C32×C4—951noHall
79C2×C3×C5—22no—
80C2×C3×C5—193no—
81C2×C3×C5—193no—
82C2×C3×C5—386no—
83C2×C3×C5C5×D19⋊C311yescharacteristic
84C2×C3×C5C5⋊(D19⋊C3)11yescharacteristic
85C52C3×(C19⋊C3)⋊C411yescharacteristic, complemented, Sylow
86C4×C5—2851no—
87Dic5—571no—
88C19C32×C5×Dic511yescharacteristic, complemented, Sylow
89C2×C32—191no—
90C3×C5—22no—
91C3×C5—193no—
92C3×C5—193no—
93C3×C5—386no—
94C3×C5C5×(C19⋊C3)⋊C411yescharacteristic, complemented
95C3×C5(C19⋊C3)⋊Dic511yescharacteristic, direct product factor
96C3×C4—2851no—
97C3×C4—953no—
98C2×C5—22no—
99C2×C5C3×C5×D19⋊C311yescharacteristic
100C2×C5C3×C5⋊(D19⋊C3)11yescharacteristic
101C32—191noSylow
102C2×C3—193no—
103C2×C3C5×C5⋊(D19⋊C3)11yescharacteristic
104C5—22no—
105C5C3×C5×(C19⋊C3)⋊C411yescharacteristic, complemented
106C5C3×(C19⋊C3)⋊Dic511yescharacteristic, direct product factor
107C4—2851noSylow
108C3—193no—
109C3C5×(C19⋊C3)⋊Dic511yescharacteristic, direct product factor
110C2C3×C5×C5⋊(D19⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C5C5⋊(D19⋊C3)
commutator, hypocenterC5×C19C32×C4×C5
FrattiniC2C3×C5×C5⋊(D19⋊C3)
Fitting, socleC2×C3×C52×C19C2×C3
prime radicalC2×C3×C52×C19⋊C3C2
cosocleC2×C5×C19C2×C32×C5
LCSG ▷ C5×C19
UCSC1 ◁ C2×C3×C5

Complements

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

NH ≅ G/Ntype
2. C3×C5×Dic95C3semidirect
3. C5×(C19⋊C3)⋊Dic5C3direct (N × H)
4. C3×C52×C19⋊C3C4semidirect
5. C3×(C19⋊C3)⋊Dic5C5direct (N × H)
9. C5×Dic95C32semidirect
13. C3×C52×C19C3×C4semidirect
14. C52×C19⋊C3C3×C4semidirect
15. C3×Dic95C3×C5semidirect
17. (C19⋊C3)⋊Dic5C3×C5direct (N × H)
22. C3×C5×C19⋊C3Dic5semidirect
23. C3×C5×C19⋊C3C4×C5semidirect
31. C52×C19C32×C4semidirect
33. Dic95C32×C5semidirect
39. C3×C5×C19C3×Dic5semidirect
40. C3×C5×C19C3×C4×C5semidirect
42. C5×C19⋊C3C3×Dic5semidirect
43. C5×C19⋊C3C3×C4×C5semidirect
52. C3×C19⋊C3C5×Dic5semidirect
59. C5×C19C32×Dic5semidirect
60. C5×C19C32×C4×C5semidirect
66. C3×C52(C19⋊C3)⋊C4semidirect
71. C3×C19C3×C5×Dic5semidirect
72. C19⋊C3C3×C5×Dic5semidirect
85. C52C3×(C19⋊C3)⋊C4semidirect
88. C19C32×C5×Dic5semidirect
94. C3×C5C5×(C19⋊C3)⋊C4semidirect
95. C3×C5(C19⋊C3)⋊Dic5direct (N × H)
105. C5C3×C5×(C19⋊C3)⋊C4semidirect
106. C5C3×(C19⋊C3)⋊Dic5direct (N × H)
109. C3C5×(C19⋊C3)⋊Dic5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C52×C19⋊C32
C3×C5×Dic953
C5×(C19⋊C3)⋊Dic53
C3×(C19⋊C3)⋊Dic55
C3×C5×(C19⋊C3)⋊C45
C32×C5×Dic519