Finite Group Databasebeta

← C5×C4⋊(#126⋊C3) #14510943

Subgroups — C5×C4⋊(#126⋊C3) #14510943

Order 1920.

252 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 42 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×C5×#126⋊C3C212yesmaximal, complemented
2C4×C5×C42⋊C3C211yesmaximal, characteristic, complemented
3C5×#2860C311yesmaximal, characteristic, complemented, Hall
4C5×D4×A4—41nomaximal
5C5×#126⋊C3—22no—
6C2×C5×C42⋊C3C2211yescharacteristic
7C4⋊(#126⋊C3)C511yesmaximal, characteristic, direct product factor, Hall
8C2×C5×#126C2×C312yescomplemented
9C5×#390—31no—
10C5×#389—31no—
11C5×#388—32no—
12C43×C5C2×C311yescharacteristic, complemented
13C22×C5×A4—42no—
14C4×C5×A4—41no—
15C5×C42⋊C3D411yescharacteristic, complemented
16C2×#126⋊C3C2×C512yescomplemented
17C4×C42⋊C3C2×C511yescharacteristic, complemented
18C22×C5×D4A411yescharacteristic
19C5×#126—22no—
20C5×#126—62no—
21C2×C5×C4⋊C4—32no—
22C2×C5×C4⋊C4—31no—
23C2×C5×C22⋊C4—32no—
24C2×C5×C22⋊C4—32no—
25C2×C42×C5—31no—
26C2×C42×C5—31no—
27C2×C42×C5C22×C311yescharacteristic
28C5×#95—32no—
29#2860C3×C511yescharacteristic, complemented, Sylow
30C2×C5×A4—41no—
31C2×C5×A4—82no—
32C3×C5×D4—161no—
33D4×A4—41no—
34#126⋊C3—22no—
35C2×C42⋊C3C22×C511yescharacteristic
36C24×C5C2×A412yes—
37C2×C5×D4—61no—
38C2×C5×D4—61no—
39C22×C4×C5—31no—
40C22×C4×C5—31no—
41C22×C4×C5—32no—
42C22×C4×C5C2×A411yescharacteristic
43C5×C4⋊C4—62no—
44C5×C4⋊C4—62no—
45C5×C4⋊C4—61no—
46C5×C4⋊C4—61no—
47C5×C22⋊C4—62no—
48C5×C22⋊C4—62no—
49C5×C22⋊C4—64no—
50C42×C5—31no—
51C42×C5—61no—
52C42×C5—61no—
53C42×C5—62no—
54C42×C5C3×D411yescharacteristic, complemented
55C2×#126C2×C3×C512yescomplemented
56#390—31no—
57#389—31no—
58#388—32no—
59C43C2×C3×C511yescharacteristic, complemented
60C22×C3×C5—162no—
61C5×A4—41no—
62C3×C4×C5—161no—
63C22×A4—42no—
64C4×A4—41no—
65C42⋊C3C5×D411yescharacteristic, complemented
66C23×C5—22no—
67C23×C5—62no—
68C23×C5—62no—
69C23×C5C22×A411yescharacteristic
70C5×D4—41no—
71C5×D4—121no—
72C2×C4×C5—31no—
73C2×C4×C5—31no—
74C2×C4×C5—32no—
75C2×C4×C5—31no—
76C2×C4×C5—31no—
77C2×C4×C5—61no—
78C2×C4×C5—61no—
79C2×C4×C5—61no—
80C2×C4×C5—61no—
81C2×C4×C5—62no—
82C2×C4×C5—62no—
83C2×C4×C5—62no—
84C22×D4C5×A411yescharacteristic
85#126—22no—
86#126—62no—
87C2×C4⋊C4—32no—
88C2×C4⋊C4—31no—
89C2×C22⋊C4—32no—
90C2×C22⋊C4—32no—
91C2×C42—31no—
92C2×C42—31no—
93C2×C42C22×C3×C511yescharacteristic
94#95—32no—
95C2×C3×C5—161no—
96C2×C3×C5—322no—
97C2×A4—41no—
98C2×A4—82no—
99C3×D4—161no—
100C22×C5—31no—
101C22×C5—31no—
102C22×C5—42no—
103C22×C5—122no—
104C22×C5—122no—
105C22×C5D4×A411yescharacteristic
106C4×C5—31no—
107C4×C5—61no—
108C4×C5—61no—
109C4×C5—62no—
110C4×C5—122no—
111C4×C5#126⋊C311yescharacteristic, complemented
112C24C2×C5×A412yes—
113C2×D4—61no—
114C2×D4—61no—
115C22×C4—31no—
116C22×C4—31no—
117C22×C4—32no—
118C22×C4C2×C5×A411yescharacteristic
119C4⋊C4—62no—
120C4⋊C4—62no—
121C4⋊C4—61no—
122C4⋊C4—61no—
123C22⋊C4—62no—
124C22⋊C4—62no—
125C22⋊C4—64no—
126C42—31no—
127C42—61no—
128C42—61no—
129C42—62no—
130C42C3×C5×D411yescharacteristic, complemented
131C3×C5—161noHall
132C22×C3—162no—
133A4—41no—
134C3×C4—161no—
135C2×C5—31no—
136C2×C5—31no—
137C2×C5—82no—
138C2×C5C2×#126⋊C311yescharacteristic
139C23—22no—
140C23—62no—
141C23—62no—
142C23C22×C5×A411yescharacteristic
143D4—41no—
144D4—121no—
145C2×C4—31no—
146C2×C4—31no—
147C2×C4—32no—
148C2×C4—31no—
149C2×C4—31no—
150C2×C4—61no—
151C2×C4—61no—
152C2×C4—61no—
153C2×C4—61no—
154C2×C4—62no—
155C2×C4—62no—
156C2×C4—62no—
157C2×C3—161no—
158C2×C3—322no—
159C5C4⋊(#126⋊C3)11yescharacteristic, direct product factor, Sylow
160C22—31no—
161C22—31no—
162C22—42no—
163C22—122no—
164C22—122no—
165C22C5×D4×A411yescharacteristic
166C4—31no—
167C4—61no—
168C4—61no—
169C4—62no—
170C4—122no—
171C4C5×#126⋊C311yescharacteristic, complemented
172C3—161noSylow
173C2—31no—
174C2—31no—
175C2—82no—
176C2C2×C5×#126⋊C311yescharacteristic
subgroupG/H
centerC2×C5C2×#126⋊C3
commutator, cosocleC2×C42C22×C3×C5
FrattiniC23C22×C5×A4
FittingC5×#2860C3
socleC23×C5C22×A4
hypercenterC4×C5#126⋊C3
hypocenterC42C3×C5×D4
LCSG ▷ C2×C42 ▷ C42
UCSC1 ◁ C2×C5 ◁ C4×C5

Complements

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

NH ≅ G/Ntype
1. C2×C5×#126⋊C3C2semidirect
2. C4×C5×C42⋊C3C2semidirect
3. C5×#2860C3semidirect
7. C4⋊(#126⋊C3)C5direct (N × H)
8. C2×C5×#126C2×C3semidirect
12. C43×C5C2×C3semidirect
15. C5×C42⋊C3D4semidirect
16. C2×#126⋊C3C2×C5semidirect
17. C4×C42⋊C3C2×C5semidirect
29. #2860C3×C5semidirect
54. C42×C5C3×D4semidirect
55. C2×#126C2×C3×C5semidirect
59. C43C2×C3×C5semidirect
65. C42⋊C3C5×D4semidirect
111. C4×C5#126⋊C3semidirect
130. C42C3×C5×D4semidirect
159. C5C4⋊(#126⋊C3)direct (N × H)
171. C4C5×#126⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#126⋊C32
C4×C5×C42⋊C32
C5×#28603
C5×D4×A44
C4⋊(#126⋊C3)5