Finite Group Databasebeta

← C23×D5×Dic5 #13107845

Subgroups — C23×D5×Dic5 #13107845

Order 1600.

2960 conjugacy classes of subgroups; only the 1240 normal subgroups are shown.

normal subgroups only

This group has 2960 conjugacy classes of subgroups — too many to draw. Only its 1240 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
1C24×C5×D5C211yesmaximal, characteristic
2C23×#1039C211yesmaximal, characteristic, complemented
3C23×C5×Dic5C211yesmaximal, characteristic, complemented
4C22×D5×Dic5C2128yesmaximal, direct product factor
5C24×C52C2211yescharacteristic
6C23×C5×D5C4116yescomplemented
7C23×C5×D5C22114yes—
8C22×#1039C22114yescomplemented
9C22×C5×Dic5C22114yescomplemented
10C2×D5×Dic5C221112yesdirect product factor
11C24×Dic5—51nomaximal
12C23×C4×D5—51nomaximal
13C23×C52C2×C418yescomplemented
14C23×C52C2317yes—
15C22×C5×D5C2×C41112yescomplemented
16C22×C5×D5C23128yes—
17C2×#1039C23128yescomplemented
18C2×C5×Dic5C23128yescomplemented
19D5×Dic5C23164yesdirect product factor
20C25×C5—51no—
21C24×D5D511yescharacteristic
22C23×C4×C5—51no—
23C23×Dic5—51no—
24C23×Dic5—51no—
25C23×Dic5—528no—
26C23×Dic5—102no—
27C23×Dic5D511yescharacteristic, direct product factor
28C22×C4×D5—528no—
29C22×C52C22×C4128yescomplemented
30C22×C52C2417yes—
31C2×C5×D5C22×C41112yescomplemented
32C2×C5×D5C2418yes—
33#1039C2418yescomplemented
34C5×Dic5C2418yescomplemented
35C24×C5—22no—
36C24×C5—516no—
37C24×C5—514no—
38C24×C5C2×D511yescharacteristic
39C24×C5C2×D511yescharacteristic
40C23×D5Dic5116yesdirect product factor
41C23×D5C2×D5114yes—
42C22×C4×C5—514no—
43C22×Dic5—514no—
44C22×Dic5—514no—
45C22×Dic5—5112no—
46C22×Dic5—1028no—
47C22×Dic5C2×D5114yesdirect product factor
48C2×C4×D5—5112no—
49C24×C4—251noSylow
50C2×C52C23×C4114yescomplemented
51C2×C52C2511yescharacteristic
52C5×D5C23×C4116yescomplemented
53C23×C5—216no—
54C23×C5—214no—
55C23×C5—5112no—
56C23×C5—528no—
57C23×C5C4×D518yescomplemented
58C23×C5C2×Dic518yescomplemented
59C23×C5C22×D517yes—
60C23×C5C22×D517yes—
61C22×D5C2×Dic51112yesdirect product factor
62C22×D5C22×D5128yes—
63C2×C4×C5—528no—
64C2×Dic5—528no—
65C2×Dic5—528no—
66C2×Dic5—564no—
67C2×Dic5—1056no—
68C2×Dic5C22×D5128yesdirect product factor
69C4×D5—564no—
70C25—51no—
71C23×C4—51no—
72C23×C4—2528no—
73C23×C4—251no—
74C52C24×C411yescharacteristic, complemented, Sylow
75C22×C5—256no—
76C22×C5—214no—
77C22×C5—5112no—
78C22×C5—58no—
79C22×C5C2×C4×D5128yescomplemented
80C22×C5C22×Dic5128yescomplemented
81C22×C5C23×D517yes—
82C22×C5C23×D517yes—
83C2×D5C22×Dic51112yesdirect product factor
84C2×D5C23×D518yes—
85C4×C5—58no—
86Dic5—58no—
87Dic5—58no—
88Dic5—1016no—
89Dic5C23×D518yesdirect product factor
90C24—516no—
91C24—514no—
92C24D5211yescharacteristic
93C22×C4—514no—
94C22×C4—25112no—
95C22×C4—2514no—
96C2×C5—228no—
97C2×C5—22no—
98C2×C5—516no—
99C2×C5C22×C4×D5114yescomplemented
100C2×C5C23×Dic5114yescomplemented
101C2×C5C24×D511yescharacteristic
102C2×C5C24×D511yescharacteristic
103D5C23×Dic5116yesdirect product factor
104C23—5112no—
105C23—528no—
106C23D5×Dic518yesdirect product factor
107C23C2×D5217yes—
108C2×C4—528no—
109C2×C4—2564no—
110C2×C4—2528no—
111C5—22no—
112C5C23×C4×D511yescharacteristic, complemented
113C5C24×Dic511yescharacteristic, complemented
114C22—5112no—
115C22—58no—
116C22C2×D5×Dic5128yesdirect product factor
117C22C22×D5217yes—
118C4—58no—
119C4—258no—
120C2—516no—
121C2C22×D5×Dic5114yesdirect product factor
122C2C23×D5211yescharacteristic
subgroupG/H
center, hypercenterC24D52
commutator, hypocenterC52C24×C4
FrattiniC2C23×D52
Fitting, socleC24×C52C22
prime radicalC24×C5×D5C2
cosocleC2×C52C25
LCSG ▷ C52
UCSC1 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C23×#1039C2semidirect
3. C23×C5×Dic5C2semidirect
4. C22×D5×Dic5C2direct (N × H)
6. C23×C5×D5C4semidirect
8. C22×#1039C22semidirect
9. C22×C5×Dic5C22semidirect
10. C2×D5×Dic5C22direct (N × H)
13. C23×C52C2×C4semidirect
15. C22×C5×D5C2×C4semidirect
17. C2×#1039C23semidirect
18. C2×C5×Dic5C23semidirect
19. D5×Dic5C23direct (N × H)
27. C23×Dic5D5direct (N × H)
29. C22×C52C22×C4semidirect
31. C2×C5×D5C22×C4semidirect
33. #1039C24semidirect
34. C5×Dic5C24semidirect
40. C23×D5Dic5direct (N × H)
47. C22×Dic5C2×D5direct (N × H)
50. C2×C52C23×C4semidirect
52. C5×D5C23×C4semidirect
57. C23×C5C4×D5semidirect
58. C23×C5C2×Dic5semidirect
61. C22×D5C2×Dic5direct (N × H)
68. C2×Dic5C22×D5direct (N × H)
74. C52C24×C4semidirect
79. C22×C5C2×C4×D5semidirect
80. C22×C5C22×Dic5semidirect
83. C2×D5C22×Dic5direct (N × H)
89. Dic5C23×D5direct (N × H)
99. C2×C5C22×C4×D5semidirect
100. C2×C5C23×Dic5semidirect
103. D5C23×Dic5direct (N × H)
106. C23D5×Dic5direct (N × H)
112. C5C23×C4×D5semidirect
113. C5C24×Dic5semidirect
116. C22C2×D5×Dic5direct (N × H)
121. C2C22×D5×Dic5direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C5×D52
C23×#10392
C23×C5×Dic52
C22×D5×Dic52
C24×Dic55
C23×C4×D55