Finite Group Databasebeta

← C3×(C5⋊(D19⋊C3))⋊D5 #30685745

Subgroups — C3×(C5⋊(D19⋊C3))⋊D5 #30685745

Order 17100.

288 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C3×C5⋊D5×C19⋊C3C211yesmaximal, characteristic, complemented
2C3×C5×C5⋊(D19⋊C3)C212yesmaximal, complemented
3C3×(C5⋊D5)⋊D19C311yesmaximal, characteristic, complemented
4(C5⋊(D19⋊C3))⋊D5C313yesmaximal, direct product factor
5C3×C52×C19⋊C3C2211yescharacteristic, complemented, Hall
6C3×D5×D19⋊C3—52nomaximal
7C3×C19×C5⋊D5C2×C311yescharacteristic, complemented
8C3×C5×D95C2×C312yescomplemented
9C5⋊D5×C19⋊C3C2×C313yescomplemented
10C5×C5⋊(D19⋊C3)C2×C316yescomplemented
11(C5⋊D5)⋊D19C3211yescharacteristic, complemented, Hall
12C3×C5⋊(D19⋊C3)D512yescomplemented
13C3×D5×C19⋊C3—52no—
14C3×D5×C19⋊C3—102no—
15C3×C5×D19⋊C3—52no—
16C3×C52×C19C22×C311yescharacteristic, complemented
17C52×C19⋊C3C22×C313yescomplemented
18C3×D5×D19—52no—
19D5×D19⋊C3—56no—
20C19×C5⋊D5C2×C3211yescharacteristic, complemented
21C5×D95C2×C3212yescomplemented
22C32×D52—191nomaximal, Hall
23C3×C5×C19⋊C3—22no—
24C3×C5×C19⋊C3C2×D512yescomplemented
25C2×C3×D19⋊C3—251noHall
26C3×D95C3×D512yescomplemented
27C3×D5×C19—52no—
28C3×D5×C19—102no—
29C3×C5×D19—52no—
30C5⋊(D19⋊C3)C3×D516yescomplemented
31D5×C19⋊C3—56no—
32D5×C19⋊C3—106no—
33C5×D19⋊C3—56no—
34C52×C19C22×C3211yescharacteristic, complemented, Hall
35C32×C5⋊D5—191no—
36C32×C5×D5—192no—
37D5×D19—52no—
38C2×C3×C19⋊C3—251no—
39C3×D19⋊C3—52no—
40C3×D52—193no—
41C3×D52—571no—
42C3×C5×C19—22no—
43C3×C5×C19C2×C3×D512yescomplemented
44C5×C19⋊C3—26no—
45C5×C19⋊C3C2×C3×D516yescomplemented
46C2×C3×D19—251no—
47C2×D19⋊C3—253no—
48C32×C52—191noHall
49D95C32×D512yescomplemented
50C5×D19—52no—
51D5×C19—52no—
52D5×C19—102no—
53C2×C32×D5—952no—
54C3×C19⋊C3D5211yescharacteristic, complemented, Hall
55C3×C5⋊D5—193no—
56C3×C5⋊D5D19⋊C311yescharacteristic, complemented
57C3×C5×D5—196no—
58C3×C5×D5—572no—
59C2×C3×C19—251no—
60C3×D19—52no—
61C2×C19⋊C3—253no—
62D19⋊C3—56no—
63D52—571noHall
64C5×C19—22no—
65C5×C19C2×C32×D512yescomplemented
66C2×C32×C5—952no—
67C32×D5—192no—
68C32×D5—952no—
69C32×D5—1902no—
70C2×D19—251noHall
71C3×C52—193no—
72C3×C52C2×D19⋊C311yescharacteristic, complemented
73C2×C3×D5—2852no—
74C2×C3×D5—956no—
75C3×C19C3×D5211yescharacteristic, complemented
76C19⋊C3C3×D5213yescomplemented
77C5⋊D5C3×D19⋊C311yescharacteristic, complemented
78C5×D5—572no—
79C32×C5—192no—
80C32×C5—382no—
81C2×C19—251no—
82D19—52no—
83C22×C32—4751noHall
84C2×C3×C5—2852no—
85C2×C3×C5—956no—
86C3×D5—52no—
87C3×D5—102no—
88C3×D5—196no—
89C3×D5—572no—
90C3×D5—956no—
91C3×D5—1906no—
92C52C2×C3×D19⋊C311yescharacteristic, complemented, Sylow
93C2×D5—2852no—
94C19C32×D5211yescharacteristic, complemented, Sylow
95C2×C32—952no—
96C2×C32—4751no—
97C3×C5—22no—
98C3×C5—196no—
99C3×C5—386no—
100C3×C5D5×D19⋊C312yescomplemented
101C22×C3—14251no—
102C22×C3—4753no—
103C2×C5—2852no—
104D5—52no—
105D5—102no—
106D5—572no—
107C32—191noSylow
108C2×C3—251no—
109C2×C3—2852no—
110C2×C3—956no—
111C2×C3—4753no—
112C5—22no—
113C5C3×D5×D19⋊C312yescomplemented
114C22—14251noSylow
115C3—193no—
116C3(C5⋊(D19⋊C3))⋊D511yescharacteristic, direct product factor
117C2—251no—
118C2—2852no—
subgroupG/H
center, hypercenterC3(C5⋊(D19⋊C3))⋊D5
commutator, cosocle, hypocenterC52×C19C22×C32
FrattiniC1G
Fitting, socleC3×C52×C19C22×C3
LCSG ▷ C52×C19
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C5⋊D5×C19⋊C3C2semidirect
2. C3×C5×C5⋊(D19⋊C3)C2semidirect
3. C3×(C5⋊D5)⋊D19C3semidirect
4. (C5⋊(D19⋊C3))⋊D5C3direct (N × H)
5. C3×C52×C19⋊C3C22semidirect
7. C3×C19×C5⋊D5C2×C3semidirect
8. C3×C5×D95C2×C3semidirect
9. C5⋊D5×C19⋊C3C2×C3semidirect
10. C5×C5⋊(D19⋊C3)C2×C3semidirect
11. (C5⋊D5)⋊D19C32semidirect
12. C3×C5⋊(D19⋊C3)D5semidirect
16. C3×C52×C19C22×C3semidirect
17. C52×C19⋊C3C22×C3semidirect
20. C19×C5⋊D5C2×C32semidirect
21. C5×D95C2×C32semidirect
24. C3×C5×C19⋊C3C2×D5semidirect
26. C3×D95C3×D5semidirect
30. C5⋊(D19⋊C3)C3×D5semidirect
34. C52×C19C22×C32semidirect
43. C3×C5×C19C2×C3×D5semidirect
45. C5×C19⋊C3C2×C3×D5semidirect
49. D95C32×D5semidirect
54. C3×C19⋊C3D52semidirect
56. C3×C5⋊D5D19⋊C3semidirect
65. C5×C19C2×C32×D5semidirect
72. C3×C52C2×D19⋊C3semidirect
75. C3×C19C3×D52semidirect
76. C19⋊C3C3×D52semidirect
77. C5⋊D5C3×D19⋊C3semidirect
92. C52C2×C3×D19⋊C3semidirect
94. C19C32×D52semidirect
100. C3×C5D5×D19⋊C3semidirect
113. C5C3×D5×D19⋊C3semidirect
116. C3(C5⋊(D19⋊C3))⋊D5direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5⋊D5×C19⋊C32
C3×C5×C5⋊(D19⋊C3)2
C3×(C5⋊D5)⋊D193
(C5⋊(D19⋊C3))⋊D53
C3×D5×D19⋊C35
C32×D5219