Finite Group Databasebeta

← D5×#338⋊C3 #14511549

Subgroups — D5×#338⋊C3 #14511549

Order 1920.

184 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 24 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×#338⋊C3C211yesmaximal, characteristic, complemented
2D5×#338C311yesmaximal, characteristic, complemented, Hall
3C4×D5×A4—41nomaximal
4C2×#338⋊C3—51nomaximal, Hall
5C2×D5×M16—31no—
6C5×#338C2×C311yescharacteristic, complemented
7#64780—31no—
8C2×D5×A4—41no—
9C4×C5×A4—41no—
10A4×Dic5—41no—
11#338⋊C3D511yescharacteristic, direct product factor
12C22×C4×D5A411yescharacteristic
13C2×C5×M16—31no—
14C2×#681—31no—
15D5×M16—62no—
16D5×M16—62no—
17C2×#676—32no—
18C2×C8×D5—32no—
19C2×#338—51noSylow
20C2×C5×A4—41no—
21D5×A4—42no—
22C3×C4×D5—161no—
23C2×C4×A4—201no—
24C23×D5SL(2,𝔽3)11yescharacteristic
25C22×C4×C5C2×A411yescharacteristic
26C22×Dic5SL(2,𝔽3)11yescharacteristic
27C2×C4×D5—31no—
28C2×C4×D5—31no—
29C2×C4×D5—31no—
30C2×C4×D5—31no—
31C5×M16—62no—
32C2×C5×C8—32no—
33#681—62no—
34C2×#168—32no—
35#676—64no—
36C8×D5—62no—
37C8×D5—62no—
38C22×M16—151no—
39#338—151no—
40#338C3×D511yescharacteristic, complemented
41C2×C3×D5—161no—
42C5×A4—41no—
43C3×C4×C5—161no—
44C3×Dic5—161no—
45C22×A4—201no—
46C4×A4—41no—
47C4×A4—201no—
48C23×C5C2×SL(2,𝔽3)11yescharacteristic
49C22×D5—31no—
50C22×D5—31no—
51C22×D5—42no—
52C2×C4×C5—31no—
53C2×C4×C5—31no—
54C2×Dic5—31no—
55C2×Dic5—31no—
56C4×D5—32no—
57C4×D5—31no—
58C4×D5—31no—
59C4×D5—31no—
60C4×D5C42⋊C311yescharacteristic
61C5×C8—62no—
62#168—62no—
63C23×C4—51no—
64C2×M16—31no—
65C2×M16—152no—
66C2×M16—151no—
67C2×M16—302no—
68C2×M16—302no—
69C22×C8—152no—
70C2×C3×C5—161no—
71C3×D5—162no—
72C2×A4—41no—
73C2×A4—202no—
74C2×C3×C4—801no—
75C22×C5—31no—
76C22×C5—41no—
77C2×D5—31no—
78C2×D5—62no—
79C2×D5—121no—
80C2×D5#95⋊C311yescharacteristic
81C4×C5—31no—
82C4×C5C2×C42⋊C311yescharacteristic
83Dic5—31no—
84Dic5#95⋊C311yescharacteristic
85C24—51no—
86C22×C4—51no—
87C22×C4—151no—
88C22×C4—151no—
89C22×C4—151no—
90C22×C4—151no—
91C22×C4D5×A411yescharacteristic
92M16—62no—
93M16—304no—
94M16—302no—
95C2×C8—32no—
96C2×C8—152no—
97C2×C8—302no—
98C2×C8—302no—
99C3×C5—161noHall
100C22×C3—801no—
101A4—41no—
102C3×C4—161no—
103C3×C4—801no—
104C2×C5—61no—
105C2×C5C2×#95⋊C311yescharacteristic
106D5—61no—
107D5#338⋊C312yesdirect product factor
108C23—151no—
109C23—151no—
110C23—202no—
111C23D5×SL(2,𝔽3)11yescharacteristic
112C2×C4—31no—
113C2×C4—31no—
114C2×C4—51no—
115C2×C4—151no—
116C2×C4—151no—
117C2×C4—152no—
118C2×C4—151no—
119C2×C4—151no—
120C2×C4—151no—
121C8—62no—
122C8—302no—
123C2×C3—161no—
124C2×C3—802no—
125C5C2×#338⋊C311yescharacteristic, complemented, Sylow
126C22—31no—
127C22—41no—
128C22—51no—
129C22—151no—
130C22—302no—
131C22—601no—
132C4—31no—
133C4—51no—
134C4—151no—
135C4D5×C42⋊C311yescharacteristic
136C3—161noSylow
137C2—52no—
138C2—61no—
139C2—301no—
140C2D5×#95⋊C311yescharacteristic
subgroupG/H
center, hypercenterC4D5×C42⋊C3
commutator, Fitting, cosocle, hypocenterC5×#338C2×C3
FrattiniC22×C4D5×A4
socleC2×C5C2×#95⋊C3
LCSG ▷ C5×#338
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C5×#338⋊C3C2semidirect
2. D5×#338C3semidirect
6. C5×#338C2×C3semidirect
11. #338⋊C3D5direct (N × H)
40. #338C3×D5semidirect
107. D5#338⋊C3direct (N × H)
125. C5C2×#338⋊C3semidirect

Maximal subgroups

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

subgroupindex
C5×#338⋊C32
D5×#3383
C4×D5×A44
C2×#338⋊C35