Finite Group Databasebeta

← C2×C5×D5×#4294 #30685561

Subgroups — C2×C5×D5×#4294 #30685561

Order 17100.

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

normal subgroups only

This group has 144 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
1C2×C52×#4294C211yesmaximal, characteristic, complemented
2C5×D5×#4294C212yesmaximal, direct product factor
3C2×C3×C5×D5×C19C311yesmaximal, characteristic
4C52×#4294C2211yescharacteristic, complemented, Hall
5C22×C5×#4294—51nomaximal
6C2×D5×#4294C511yesmaximal, characteristic, direct product factor
7C3×C5×D5×C19C2×C312yes—
8C2×C3×C52×C19C2×C311yescharacteristic
9C2×C5×D5×C19C911yescharacteristic, complemented, Hall
10C2×C5×#4294—22no—
11C2×C5×#4294—52no—
12C2×C5×#4294D511yescharacteristic, direct product factor
13C2×C5×#4294C2×C511yescharacteristic, complemented
14D5×#4294C2×C512yesdirect product factor
15C3×C52×C19C22×C311yescharacteristic
16C22×C3×C5×C19—51no—
17C2×C3×D5×C19C3×C511yescharacteristic
18C2×C52×C19C2×C911yescharacteristic, complemented
19C5×D5×C19C2×C912yescomplemented
20C2×C5×C9×D5—191nomaximal, Hall
21C5×#4294—22no—
22C5×#4294C2×D511yescharacteristic, direct product factor
23C5×#4294C22×C511yescharacteristic, complemented
24C22×#4294—51noHall
25C2×C3×C5×C19—22no—
26C2×C3×C5×C19—52no—
27C2×C3×C5×C19C3×D511yescharacteristic
28C2×C3×C5×C19C2×C3×C511yescharacteristic
29C3×D5×C19C2×C3×C512yes—
30C52×C19C22×C911yescharacteristic, complemented, Hall
31C2×C52×C9—191no—
32C5×C9×D5—192no—
33C22×C5×C19—51no—
34C2×D5×C19C5×C911yescharacteristic, complemented
35C2×#4294—52no—
36C2×#4294C5×D511yescharacteristic, direct product factor
37C2×C3×C5×D5C19⋊C311yescharacteristic
38C3×C5×C19—22no—
39C3×C5×C19C2×C3×D511yescharacteristic
40C3×C5×C19C22×C3×C511yescharacteristic
41C22×C3×C19—51no—
42C52×C9—191noHall
43C2×C5×C19—22no—
44C2×C5×C19—52no—
45C2×C5×C19C9×D511yescharacteristic, complemented
46C2×C5×C19C2×C5×C911yescharacteristic, complemented
47D5×C19C2×C5×C912yescomplemented
48C22×C5×C9—951no—
49C2×C9×D5—191no—
50#4294C2×C5×D511yescharacteristic, direct product factor, Hall
51C2×C3×C52C2×C19⋊C311yescharacteristic
52C3×C5×D5C2×C19⋊C312yes—
53C2×C3×C19—52no—
54C2×C3×C19C3×C5×D511yescharacteristic
55C2×C5×D5#429411yescharacteristic, direct product factor, Hall
56C5×C19—22no—
57C5×C19C2×C9×D511yescharacteristic, complemented
58C5×C19C22×C5×C911yescharacteristic, complemented
59C2×C5×C9—191no—
60C2×C5×C9—191no—
61C2×C5×C9—382no—
62C2×C5×C9—952no—
63C9×D5—192no—
64C22×C19—51noHall
65C3×C52C22×C19⋊C311yescharacteristic
66C22×C3×C5—51no—
67C2×C3×D5C5×C19⋊C311yescharacteristic
68C3×C19C2×C3×C5×D511yescharacteristic
69C2×C52C2×#429411yescharacteristic, complemented
70C5×D5C2×#429412yesdirect product factor
71C5×C9—191no—
72C5×C9—191no—
73C5×C9—382no—
74C2×C19—52no—
75C2×C19C5×C9×D511yescharacteristic, complemented
76C22×C9—951noHall
77C2×C3×C5—22no—
78C2×C3×C5—52no—
79C2×C3×C5D5×C19⋊C311yescharacteristic
80C2×C3×C5C2×C5×C19⋊C311yescharacteristic
81C3×D5C2×C5×C19⋊C312yes—
82C52C22×#429411yescharacteristic, complemented, Sylow
83C22×C5—51no—
84C2×D5C5×#429411yescharacteristic, direct product factor
85C19C2×C5×C9×D511yescharacteristic, complemented, Sylow
86C2×C9—191no—
87C2×C9—952no—
88C3×C5—22no—
89C3×C5C2×D5×C19⋊C311yescharacteristic
90C3×C5C22×C5×C19⋊C311yescharacteristic
91C22×C3—51no—
92C2×C5—22no—
93C2×C5—52no—
94C2×C5D5×#429411yescharacteristic, direct product factor
95C2×C5C2×C5×#429411yescharacteristic, complemented
96D5C2×C5×#429412yesdirect product factor
97C9—191noSylow
98C2×C3—52no—
99C2×C3C5×D5×C19⋊C311yescharacteristic
100C5—22no—
101C5C2×D5×#429411yescharacteristic, direct product factor
102C5C22×C5×#429411yescharacteristic, complemented
103C22—51noSylow
104C3C2×C5×D5×C19⋊C311yescharacteristic
105C2—52no—
106C2C5×D5×#429411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5D5×C19⋊C3
commutator, hypocenterC5×C19C22×C5×C9
FrattiniC3C2×C5×D5×C19⋊C3
Fitting, socleC2×C3×C52×C19C2×C3
prime radicalC2×C3×C5×D5×C19C3
cosocleC3×C5×C19C22×C3×C5
LCSG ▷ C5×C19
UCSC1 ◁ C2×C3×C5

Complements

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

NH ≅ G/Ntype
1. C2×C52×#4294C2semidirect
2. C5×D5×#4294C2direct (N × H)
4. C52×#4294C22semidirect
6. C2×D5×#4294C5direct (N × H)
9. C2×C5×D5×C19C9semidirect
12. C2×C5×#4294D5direct (N × H)
13. C2×C5×#4294C2×C5semidirect
14. D5×#4294C2×C5direct (N × H)
18. C2×C52×C19C2×C9semidirect
19. C5×D5×C19C2×C9semidirect
22. C5×#4294C2×D5direct (N × H)
23. C5×#4294C22×C5semidirect
30. C52×C19C22×C9semidirect
34. C2×D5×C19C5×C9semidirect
36. C2×#4294C5×D5direct (N × H)
45. C2×C5×C19C9×D5semidirect
46. C2×C5×C19C2×C5×C9semidirect
47. D5×C19C2×C5×C9semidirect
50. #4294C2×C5×D5direct (N × H)
55. C2×C5×D5#4294direct (N × H)
57. C5×C19C2×C9×D5semidirect
58. C5×C19C22×C5×C9semidirect
69. C2×C52C2×#4294semidirect
70. C5×D5C2×#4294direct (N × H)
75. C2×C19C5×C9×D5semidirect
82. C52C22×#4294semidirect
84. C2×D5C5×#4294direct (N × H)
85. C19C2×C5×C9×D5semidirect
94. C2×C5D5×#4294direct (N × H)
95. C2×C5C2×C5×#4294semidirect
96. D5C2×C5×#4294direct (N × H)
101. C5C2×D5×#4294direct (N × H)
102. C5C22×C5×#4294semidirect
106. C2C5×D5×#4294direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C52×#42942
C5×D5×#42942
C2×C3×C5×D5×C193
C22×C5×#42945
C2×D5×#42945
C2×C5×C9×D519