Finite Group Databasebeta

← C5×#63783 #13086334

Subgroups — C5×#63783 #13086334

Order 1440.

168 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 32 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
1C5×#3830C211yesmaximal, characteristic
2C4×C5×#157C211yesmaximal, characteristic, complemented
3C5×#3788C211yesmaximal, characteristic, complemented
4C2×C5×#157—21no—
5C32×C5×D4C411yescharacteristic, complemented
6C5×#638—21no—
7C2×C5×C3⋊Dic3—21no—
8C4×C5×C3⋊D3C2211yescharacteristic
9C5×#634C411yescharacteristic, complemented
10C5×#622—21no—
11#63783C511yesmaximal, characteristic, direct product factor, Hall
12C5×#237—62no—
13C22×C32×C5—21no—
14C2×C5×C3⋊D3D411yescharacteristic
15C5×#157—22no—
16C32×C4×C5C2×C411yescharacteristic
17C5×C3⋊Dic3—21no—
18C5×C3⋊Dic3D411yescharacteristic
19C5×#104—91nomaximal, Hall
20#3830C2×C511yescharacteristic
21C4×#157C2×C511yescharacteristic, complemented
22#3788C2×C511yescharacteristic, complemented
23C3×C5×D4—22no—
24C5×#67—64no—
25C2×C5×Dic3—64no—
26C4×C5×D3—62no—
27C5×Dic6—62no—
28C2×C32×C5—41no—
29C2×C32×C5C22⋊C411yescharacteristic
30C5×C3⋊D3—21no—
31C5×#41—91no—
32C5×M16—91no—
33C42×C5—91no—
34C2×#157—21no—
35C32×D4C4×C511yescharacteristic, complemented
36#638—21no—
37C2×C3⋊Dic3—21no—
38C4×C3⋊D3C22×C511yescharacteristic
39#634C4×C511yescharacteristic, complemented
40#622—21no—
41C22×C3×C5—24no—
42C2×C5×D3—62no—
43C3×C4×C5—22no—
44C5×Dic3—62no—
45C5×Dic3—64no—
46#237—62no—
47C32×C5#10411yescharacteristic, complemented, Hall
48C5×Q8—91no—
49C5×D4—181no—
50C5×D4#15711yescharacteristic, complemented
51C2×C4×C5—91no—
52C2×C4×C5—181no—
53C2×C4×C5—181no—
54C5×C8—181no—
55C22×C32—21no—
56C2×C3⋊D3C5×D411yescharacteristic
57#157—22no—
58C32×C4C2×C4×C511yescharacteristic
59C3⋊Dic3—21no—
60C3⋊Dic3C5×D411yescharacteristic
61#104—91noSylow
62C2×C3×C5—22no—
63C2×C3×C5—44no—
64C5×D3—122no—
65C3×D4—22no—
66#67—64no—
67C2×Dic3—64no—
68C4×D3—62no—
69Dic6—62no—
70C22×C5—21no—
71C22×C5—91no—
72C4×C5—91no—
73C4×C5—182no—
74C4×C5—181no—
75C4×C5C2×#15711yescharacteristic
76C2×C32—41no—
77C2×C32C5×C22⋊C411yescharacteristic
78C3⋊D3—21no—
79#41—91no—
80M16—91no—
81C42—91no—
82C3×C5—22no—
83C22×C3—24no—
84C2×D3—62no—
85C3×C4—22no—
86Dic3—62no—
87Dic3—64no—
88C2×C5—41no—
89C2×C5—181no—
90C2×C5C22⋊#15711yescharacteristic
91C32C5×#10411yescharacteristic, complemented, Sylow
92Q8—91no—
93D4—181no—
94D4C5×#15711yescharacteristic, complemented
95C2×C4—91no—
96C2×C4—181no—
97C2×C4—181no—
98C8—181no—
99C2×C3—22no—
100C2×C3—44no—
101D3—122no—
102C5#6378311yescharacteristic, direct product factor, Sylow
103C22—21no—
104C22—91no—
105C4—91no—
106C4—182no—
107C4—181no—
108C4C2×C5×#15711yescharacteristic
109C3—22no—
110C2—41no—
111C2—181no—
112C2C5×C22⋊#15711yescharacteristic
subgroupG/H
centerC2×C5C22⋊#157
commutatorC32×C4C2×C4×C5
FrattiniC4C2×C5×#157
FittingC32×C5×D4C4
socleC2×C32×C5C22⋊C4
prime radicalC5×#3830C2
cosocleC4×C3⋊D3C22×C5
hypercenterC5×D4#157
hypocenterC32C5×#104
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×D4

Complements

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

NH ≅ G/Ntype
2. C4×C5×#157C2semidirect
3. C5×#3788C2semidirect
5. C32×C5×D4C4semidirect
9. C5×#634C4semidirect
11. #63783C5direct (N × H)
21. C4×#157C2×C5semidirect
22. #3788C2×C5semidirect
35. C32×D4C4×C5semidirect
39. #634C4×C5semidirect
47. C32×C5#104semidirect
50. C5×D4#157semidirect
91. C32C5×#104semidirect
94. D4C5×#157semidirect
102. C5#63783direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#38302
C4×C5×#1572
C5×#37882
#637835
C5×#1049