Finite Group Databasebeta

← C2×D5×S4 #92117

Subgroups — C2×D5×S4 #92117

Order 480.

262 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 35 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×D5×A4C211yesmaximal, characteristic, complemented
2C2×C5⋊S4C211yesmaximal, characteristic, complemented
3C2×C5×S4C211yesmaximal, characteristic, complemented
4D5×S4C214yesmaximal, direct product factor
5C2×D4×D5—31nomaximal, Hall
6C2×C5×A4C2211yescharacteristic, complemented
7C2×D3×D5—41nomaximal
8D5×A4C2212yescomplemented
9C5⋊S4C2212yescomplemented
10C5×S4C2212yescomplemented
11C22×S4—51nomaximal, Hall
12C23×D5—31no—
13C23×D5D311yescharacteristic, complemented
14C2×C5×D4—31no—
15C2×C22⋊D5—31no—
16C2×C22⋊D5—31no—
17D4×D5—34no—
18D4×D5—34no—
19C2×D20—31no—
20C2×C4×D5—31no—
21C2×D15—41no—
22C2×C5×D3—41no—
23C2×C3×D5—41no—
24C5×A4C2311yescharacteristic, complemented
25D3×D5—44no—
26C22×A4—51no—
27C2×S4—51no—
28C2×S4—54no—
29C2×S4D511yescharacteristic, direct product factor
30C23×C5—31no—
31C23×C5C2×D311yescharacteristic, complemented
32C22×D5—31no—
33C22×D5—31no—
34C22×D5—32no—
35C22×D5—31no—
36C22×D5—34no—
37C22×D5—61no—
38C22×D5—62no—
39C22×D5—61no—
40C22×D5C2×D312yescomplemented
41C5×D4—32no—
42C5×D4—32no—
43C2×C4×C5—31no—
44C22⋊D5—34no—
45C22⋊D5—32no—
46C22⋊D5—32no—
47C2×Dic5—31no—
48D20—34no—
49C4×D5—34no—
50C22×D4—151noSylow
51C2×C3×C5—41no—
52D15—42no—
53C3×D5—42no—
54C5×D3—42no—
55C22×D3—201no—
56C2×A4—52no—
57C2×A4C2×D511yescharacteristic, complemented
58S4—52no—
59S4C2×D512yesdirect product factor
60C22×C5—31no—
61C22×C5—31no—
62C22×C5—32no—
63C22×C5—61no—
64C22×C5—61no—
65C22×C5C22×D311yescharacteristic, complemented
66C2×D5—31no—
67C2×D5—32no—
68C2×D5—32no—
69C2×D5—32no—
70C2×D5—32no—
71C2×D5—61no—
72C2×D5—64no—
73C2×D5—61no—
74C2×D5—61no—
75C2×D5—64no—
76C2×D5S411yescharacteristic, direct product factor
77C4×C5—32no—
78Dic5—32no—
79C24—51no—
80C24—151no—
81C2×D4—31no—
82C2×D4—151no—
83C2×D4—154no—
84C2×D4—154no—
85C2×D4—151no—
86C2×D4—151no—
87C22×C4—151no—
88C3×C5—41noHall
89C22×C3—201no—
90C2×D3—41no—
91C2×D3—204no—
92C2×D3—201no—
93A4C22×D511yescharacteristic, complemented
94C2×C5—31no—
95C2×C5—31no—
96C2×C5—62no—
97C2×C5C2×S411yescharacteristic, complemented
98D5—32no—
99D5—62no—
100D5C2×S412yesdirect product factor
101C23—31no—
102C23—52no—
103C23—151no—
104C23—152no—
105C23—151no—
106C23—151no—
107C23—154no—
108C23—301no—
109C23—302no—
110C23—301no—
111C23D3×D511yescharacteristic, complemented
112D4—32no—
113D4—32no—
114D4—154no—
115D4—152no—
116D4—154no—
117D4—152no—
118C2×C4—31no—
119C2×C4—154no—
120C2×C4—151no—
121C2×C3—41no—
122C2×C3—202no—
123D3—42no—
124D3—202no—
125C5C22×S411yescharacteristic, complemented, Sylow
126C22—31no—
127C22—31no—
128C22—32no—
129C22—51no—
130C22—61no—
131C22—61no—
132C22—152no—
133C22—152no—
134C22—152no—
135C22—152no—
136C22—151no—
137C22—301no—
138C22—301no—
139C22—304no—
140C22—304no—
141C22—301no—
142C22C2×D3×D511yescharacteristic, complemented
143C4—32no—
144C4—152no—
145C3—41noSylow
146C2—31no—
147C2—31no—
148C2—52no—
149C2—62no—
150C2—152no—
151C2—302no—
152C2D5×S411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2D5×S4
commutator, cosocle, hypocenterC5×A4C23
FrattiniC1G
Fitting, socleC23×C5C2×D3
LCSG ▷ C5×A4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×D5×A4C2semidirect
2. C2×C5⋊S4C2semidirect
3. C2×C5×S4C2semidirect
4. D5×S4C2direct (N × H)
6. C2×C5×A4C22semidirect
8. D5×A4C22semidirect
9. C5⋊S4C22semidirect
10. C5×S4C22semidirect
13. C23×D5D3semidirect
24. C5×A4C23semidirect
29. C2×S4D5direct (N × H)
31. C23×C5C2×D3semidirect
40. C22×D5C2×D3semidirect
57. C2×A4C2×D5semidirect
59. S4C2×D5direct (N × H)
65. C22×C5C22×D3semidirect
76. C2×D5S4direct (N × H)
93. A4C22×D5semidirect
97. C2×C5C2×S4semidirect
100. D5C2×S4direct (N × H)
111. C23D3×D5semidirect
125. C5C22×S4semidirect
142. C22C2×D3×D5semidirect
152. C2D5×S4direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×A42
C2×C5⋊S42
C2×C5×S42
D5×S42
C2×D4×D53
C2×D3×D54
C22×S45