Finite Group Databasebeta

← C5×#2823⋊C3 #14510930

Subgroups — C5×#2823⋊C3 #14510930

Order 1920.

232 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 40 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
2C5×#384⋊C3C211yesmaximal, characteristic, complemented
3C5×#2823C311yesmaximal, characteristic, complemented, Hall
4C5×D4×A4—41nomaximal
5C5×#126⋊C3—22no—
6C2×C5×C42⋊C3C2211yescharacteristic
7#2823⋊C3C511yesmaximal, characteristic, direct product factor, Hall
8C2×C5×#126C2×C312yescomplemented
9C5×#398—31no—
10C5×#396—32no—
11C5×#394—31no—
12C5×#384C2×C311yescharacteristic, complemented
13C22×C5×A4—42no—
14C4×C5×A4—41no—
15C5×C42⋊C3D411yescharacteristic, complemented
16C2×#126⋊C3C2×C512yescomplemented
17#384⋊C3C2×C511yescharacteristic, complemented
18C22×C5×D4A411yescharacteristic
19C5×#126—22no—
20C5×#126—62no—
21C2×C5×C4⋊C4—32no—
22C2×C5×C4⋊C4—31no—
23C2×C5×C4⋊C4—31no—
24C2×C5×C4⋊C4—31no—
25C2×C5×C22⋊C4—32no—
26C2×C5×C22⋊C4—32no—
27C2×C42×C5C22×C311yescharacteristic
28C5×#95—31no—
29C5×#95—31no—
30#2823C3×C511yescharacteristic, complemented, Sylow
31C2×C5×A4—41no—
32C2×C5×A4—82no—
33C3×C5×D4—161no—
34D4×A4—41no—
35#126⋊C3—22no—
36C2×C42⋊C3C22×C511yescharacteristic
37C24×C5C2×A412yes—
38C2×C5×D4—121no—
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—121no—
46C5×C4⋊C4—121no—
47C5×C4⋊C4—121no—
48C5×C22⋊C4—62no—
49C5×C22⋊C4—62no—
50C5×C22⋊C4—122no—
51C42×C5—31no—
52C42×C5C3×D411yescharacteristic, complemented
53C2×#126C2×C3×C512yescomplemented
54#398—31no—
55#396—32no—
56#394—31no—
57#384C2×C3×C511yescharacteristic, complemented
58C22×C3×C5—162no—
59C5×A4—41no—
60C3×C4×C5—161no—
61C22×A4—42no—
62C4×A4—41no—
63C42⋊C3C5×D411yescharacteristic, complemented
64C23×C5—22no—
65C23×C5—62no—
66C23×C5—62no—
67C23×C5C22×A411yescharacteristic
68C5×D4—41no—
69C5×D4—121no—
70C2×C4×C5—31no—
71C2×C4×C5—31no—
72C2×C4×C5—61no—
73C2×C4×C5—61no—
74C2×C4×C5—61no—
75C2×C4×C5—62no—
76C2×C4×C5—62no—
77C2×C4×C5—61no—
78C2×C4×C5—62no—
79C2×C4×C5—62no—
80C22×D4C5×A411yescharacteristic
81#126—22no—
82#126—62no—
83C2×C4⋊C4—32no—
84C2×C4⋊C4—31no—
85C2×C4⋊C4—31no—
86C2×C4⋊C4—31no—
87C2×C22⋊C4—32no—
88C2×C22⋊C4—32no—
89C2×C42C22×C3×C511yescharacteristic
90#95—31no—
91#95—31no—
92C2×C3×C5—161no—
93C2×C3×C5—322no—
94C2×A4—41no—
95C2×A4—82no—
96C3×D4—161no—
97C22×C5—31no—
98C22×C5—31no—
99C22×C5—42no—
100C22×C5—122no—
101C22×C5—122no—
102C22×C5D4×A411yescharacteristic
103C4×C5—41no—
104C4×C5—61no—
105C4×C5—61no—
106C4×C5—122no—
107C4×C5—121no—
108C24C2×C5×A412yes—
109C2×D4—121no—
110C22×C4—31no—
111C22×C4—32no—
112C22×C4—31no—
113C22×C4C2×C5×A411yescharacteristic
114C4⋊C4—62no—
115C4⋊C4—62no—
116C4⋊C4—121no—
117C4⋊C4—121no—
118C4⋊C4—121no—
119C22⋊C4—62no—
120C22⋊C4—62no—
121C22⋊C4—122no—
122C42—31no—
123C42C3×C5×D411yescharacteristic, complemented
124C3×C5—161noHall
125C22×C3—162no—
126A4—41no—
127C3×C4—161no—
128C2×C5—31no—
129C2×C5—31no—
130C2×C5—82no—
131C2×C5#560⋊C311yescharacteristic
132C23—22no—
133C23—62no—
134C23—62no—
135C23C22×C5×A411yescharacteristic
136D4—41no—
137D4—121no—
138C2×C4—31no—
139C2×C4—31no—
140C2×C4—61no—
141C2×C4—61no—
142C2×C4—61no—
143C2×C4—62no—
144C2×C4—62no—
145C2×C4—61no—
146C2×C4—62no—
147C2×C4—62no—
148C2×C3—161no—
149C2×C3—322no—
150C5#2823⋊C311yescharacteristic, direct product factor, Sylow
151C22—31no—
152C22—31no—
153C22—42no—
154C22—122no—
155C22—122no—
156C22C5×D4×A411yescharacteristic
157C4—41no—
158C4—61no—
159C4—61no—
160C4—122no—
161C4—121no—
162C3—161noSylow
163C2—31no—
164C2—31no—
165C2—82no—
166C2C5×#560⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2×C5#560⋊C3
commutator, cosocleC2×C42C22×C3×C5
FrattiniC23C22×C5×A4
FittingC5×#2823C3
socleC23×C5C22×A4
hypocenterC42C3×C5×D4
LCSG ▷ C2×C42 ▷ C42
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
1. C2×C5×#126⋊C3C2semidirect
2. C5×#384⋊C3C2semidirect
3. C5×#2823C3semidirect
7. #2823⋊C3C5direct (N × H)
8. C2×C5×#126C2×C3semidirect
12. C5×#384C2×C3semidirect
15. C5×C42⋊C3D4semidirect
16. C2×#126⋊C3C2×C5semidirect
17. #384⋊C3C2×C5semidirect
30. #2823C3×C5semidirect
52. C42×C5C3×D4semidirect
53. C2×#126C2×C3×C5semidirect
57. #384C2×C3×C5semidirect
63. C42⋊C3C5×D4semidirect
123. C42C3×C5×D4semidirect
150. C5#2823⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#126⋊C32
C5×#384⋊C32
C5×#28233
C5×D4×A44
#2823⋊C35