Finite Group Databasebeta

← C5×#63784 #13086337

Subgroups — C5×#63784 #13086337

Order 1440.

160 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 36 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×Q8×C3⋊D3C211yesmaximal, characteristic
2C5×C4⋊#157C211yesmaximal, characteristic
3C5×#3787C211yesmaximal, characteristic
4C2×C5×#157—21no—
5C32×C5×Q8C411yescharacteristic, complemented
6C4×C5×C3⋊D3—21no—
7C4×C5×C3⋊D3C2211yescharacteristic
8C5×#634—21no—
9C5×#634C411yescharacteristic, complemented
10C5×#622—21no—
11#63784C511yesmaximal, characteristic, direct product factor, Hall
12C5×D3×Q8—62no—
13C2×C5×C3⋊D3D411yescharacteristic
14C5×#157—41no—
15C32×C4×C5—21no—
16C32×C4×C5C2×C411yescharacteristic
17C5×C3⋊Dic3—21no—
18C5×C3⋊Dic3D411yescharacteristic
19C5×#103—91nomaximal, Hall
20Q8×C3⋊D3C2×C511yescharacteristic
21C4⋊#157C2×C511yescharacteristic
22#3787C2×C511yescharacteristic
23C3×C5×Q8—22no—
24C4×C5×D3—62no—
25C4×C5×D3—64no—
26C5×Dic6—62no—
27C5×Dic6—64no—
28C2×C32×C5C22⋊C411yescharacteristic
29C5×C3⋊D3SD1611yescharacteristic
30C5×C3⋊D3Q1611yescharacteristic
31C2×C5×Q8—91no—
32C2×C5×C8—91no—
33C5×C4⋊C4—91no—
34C2×#157—21no—
35C32×Q8C4×C511yescharacteristic, complemented
36C4×C3⋊D3—21no—
37C4×C3⋊D3C22×C511yescharacteristic
38#634—21no—
39#634C4×C511yescharacteristic, complemented
40#622—21no—
41C2×C5×D3—62no—
42C3×C4×C5—24no—
43C3×C4×C5—22no—
44C5×Dic3—62no—
45C5×Dic3—64no—
46D3×Q8—62no—
47C32×C5#10311yescharacteristic, complemented, Hall
48C5×Q8—91no—
49C5×Q8—181no—
50C5×Q8#15711yescharacteristic, complemented
51C2×C4×C5—91no—
52C2×C4×C5—181no—
53C2×C4×C5—181no—
54C5×C8—181no—
55C2×C3⋊D3C5×D411yescharacteristic
56#157—41no—
57C32×C4—21no—
58C32×C4C2×C4×C511yescharacteristic
59C3⋊Dic3—21no—
60C3⋊Dic3C5×D411yescharacteristic
61#103—91noSylow
62C2×C3×C5—22no—
63C5×D3—62no—
64C5×D3—62no—
65C3×Q8—22no—
66C4×D3—62no—
67C4×D3—64no—
68Dic6—62no—
69Dic6—64no—
70C22×C5—91no—
71C4×C5—21no—
72C4×C5—91no—
73C4×C5—181no—
74C4×C5—361no—
75C4×C5C2×#15711yescharacteristic
76C2×C32C5×C22⋊C411yescharacteristic
77C3⋊D3C5×SD1611yescharacteristic
78C3⋊D3C5×Q1611yescharacteristic
79C2×Q8—91no—
80C2×C8—91no—
81C4⋊C4—91no—
82C3×C5—22no—
83C2×D3—62no—
84C3×C4—24no—
85C3×C4—22no—
86Dic3—62no—
87Dic3—64no—
88C2×C5—91no—
89C2×C5—91no—
90C2×C5C22⋊#15711yescharacteristic
91C32C5×#10311yescharacteristic, complemented, Sylow
92Q8—91no—
93Q8—181no—
94Q8C5×#15711yescharacteristic, complemented
95C2×C4—91no—
96C2×C4—181no—
97C2×C4—181no—
98C8—181no—
99C2×C3—22no—
100D3—62no—
101D3—62no—
102C5#6378411yescharacteristic, direct product factor, Sylow
103C22—91no—
104C4—21no—
105C4—91no—
106C4—181no—
107C4—361no—
108C4C2×C5×#15711yescharacteristic
109C3—22no—
110C2—91no—
111C2—91no—
112C2C5×C22⋊#15711yescharacteristic
subgroupG/H
centerC2×C5C22⋊#157
commutatorC32×C4C2×C4×C5
FrattiniC4C2×C5×#157
FittingC32×C5×Q8C4
socleC2×C32×C5C22⋊C4
prime radicalC2×C5×C3⋊D3D4
cosocleC4×C3⋊D3C22×C5
hypercenterC5×Q8#157
hypocenterC32C5×#103
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×Q8

Complements

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

NH ≅ G/Ntype
5. C32×C5×Q8C4semidirect
9. C5×#634C4semidirect
11. #63784C5direct (N × H)
35. C32×Q8C4×C5semidirect
39. #634C4×C5semidirect
47. C32×C5#103semidirect
50. C5×Q8#157semidirect
91. C32C5×#103semidirect
94. Q8C5×#157semidirect
102. C5#63784direct (N × H)

Maximal subgroups

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

subgroupindex
C5×Q8×C3⋊D32
C5×C4⋊#1572
C5×#37872
#637845
C5×#1039