Finite Group Databasebeta

← C2×#11758794 #14522979

Subgroups — C2×#11758794 #14522979

Order 2000.

232 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 31 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×#92566C212yesmaximal, complemented
2C2×C5×#1044C211yesmaximal, characteristic, complemented
3#11758794C214yesmaximal, direct product factor
4C2×C5×C5⋊D5—22no—
5C2×C5×C5⋊D5C2211yescharacteristic
6#92566—22no—
7#92566C2214yescomplemented
8C5×#1044C2212yescomplemented
9C2×D52⋊C2—51nomaximal
10C2×C53D411yescharacteristic, complemented
11C5×C5⋊D5—24no—
12C5×C5⋊D5D411yescharacteristic, complemented
13C5×C5⋊D5C2311yescharacteristic
14C2×D52—52no—
15C2×D52—102no—
16C2×#1044D511yescharacteristic, complemented
17C2×C5×AGL(1,𝔽5)—101no—
18D52⋊C2—54no—
19C53C2×D411yescharacteristic, complemented, Sylow
20C2×C5⋊D5—22no—
21C2×C5⋊D5C2×D511yescharacteristic
22C2×C5×D5—101no—
23C2×C5×D5—102no—
24C2×C5×D5—102no—
25C2×C5×D5—102no—
26C2×C5×D5—204no—
27D52—54no—
28D52—104no—
29D52—104no—
30D52—102no—
31#1044C2×D512yescomplemented
32C5×AGL(1,𝔽5)—102no—
33C2×D20—251nomaximal
34C2×C52—22no—
35C2×C52—21no—
36C2×C52—44no—
37C2×C52—81no—
38C2×C52D2011yescharacteristic, complemented
39C5⋊D5—24no—
40C5⋊D5D2011yescharacteristic, complemented
41C5⋊D5C22×D511yescharacteristic
42C5×D5—101no—
43C5×D5—102no—
44C5×D5—102no—
45C5×D5—101no—
46C5×D5—104no—
47C5×D5—104no—
48C5×D5—208no—
49C22×D5—252no—
50C22×D5—502no—
51C2×AGL(1,𝔽5)—101no—
52C2×C4×C5—251no—
53D20—254no—
54C52—22no—
55C52—21no—
56C52—44no—
57C52—81no—
58C52C2×D2011yescharacteristic, complemented
59C22×C5—251no—
60C22×C5—502no—
61C2×D5—101no—
62C2×D5—102no—
63C2×D5—102no—
64C2×D5—102no—
65C2×D5—204no—
66C2×D5—254no—
67C2×D5—504no—
68C2×D5—502no—
69C2×D5—504no—
70AGL(1,𝔽5)—102no—
71C4×C5—252no—
72C2×D4—1251noSylow
73C2×C5—22no—
74C2×C5—21no—
75C2×C5—44no—
76C2×C5—81no—
77C2×C5—251no—
78C2×C5—251no—
79C2×C5—504no—
80C2×C5D52⋊C211yescharacteristic, complemented
81D5—102no—
82D5—101no—
83D5—101no—
84D5—102no—
85D5—104no—
86D5—104no—
87D5—208no—
88C23—1252no—
89D4—1254no—
90C2×C4—251no—
91C5—22no—
92C5—21no—
93C5—44no—
94C5—81no—
95C5C2×D52⋊C211yescharacteristic, complemented
96C22—251no—
97C22—502no—
98C22—1254no—
99C22—2502no—
100C4—252no—
101C2—251no—
102C2—251no—
103C2—504no—
104C2#1175879411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#11758794
commutator, cosocleC5×C5⋊D5C23
FrattiniC1G
Fitting, socleC2×C53D4
hypocenterC53C2×D4
LCSG ▷ C5×C5⋊D5 ▷ C53
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#92566C2semidirect
2. C2×C5×#1044C2semidirect
3. #11758794C2direct (N × H)
7. #92566C22semidirect
8. C5×#1044C22semidirect
10. C2×C53D4semidirect
12. C5×C5⋊D5D4semidirect
16. C2×#1044D5semidirect
19. C53C2×D4semidirect
31. #1044C2×D5semidirect
38. C2×C52D20semidirect
40. C5⋊D5D20semidirect
58. C52C2×D20semidirect
80. C2×C5D52⋊C2semidirect
95. C5C2×D52⋊C2semidirect
104. C2#11758794direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#925662
C2×C5×#10442
#117587942
C2×D52⋊C25
C2×D2025