Finite Group Databasebeta

← C2×C5×#383⋊C3 #14510893

Subgroups — C2×C5×#383⋊C3 #14510893

Order 1920.

288 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 58 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
1C22×C5×C42⋊C3C211yesmaximal, characteristic
2C5×#383⋊C3C212yesmaximal, direct product factor
3C2×C5×#383C311yesmaximal, characteristic, complemented, Hall
4C2×C4×C5×A4—41nomaximal
5C2×C5×C42⋊C3C412yescomplemented
6C2×C5×C42⋊C3C2211yescharacteristic
7C2×#383⋊C3C511yesmaximal, characteristic, direct product factor, Hall
8C22×C42×C5C2×C311yescharacteristic
9C5×#383—32no—
10C5×#383C2×C312yescomplemented
11C2×C5×#95—31no—
12C2×C5×#95—31no—
13C22×C5×A4—41no—
14C4×C5×A4—42no—
15C5×C42⋊C3C2×C411yescharacteristic, complemented
16C22×C42⋊C3C2×C511yescharacteristic
17#383⋊C3C2×C512yesdirect product factor
18C23×C4×C5—31no—
19C23×C4×C5—31no—
20C23×C4×C5A411yescharacteristic
21C2×C42×C5—31no—
22C2×C42×C5—32no—
23C2×C42×C5C3×C412yescomplemented
24C2×C42×C5C22×C311yescharacteristic
25C5×#95—32no—
26C5×#95—32no—
27C5×#95—32no—
28C5×#95—32no—
29C2×#383C3×C511yescharacteristic, complemented, Sylow
30C2×C5×A4—42no—
31C2×C5×A4—41no—
32C2×C3×C4×C5—161no—
33C2×C4×A4—41no—
34C2×C42⋊C3C4×C512yescomplemented
35C2×C42⋊C3C22×C511yescharacteristic
36C24×C5C2×A411yescharacteristic
37C22×C4×C5—32no—
38C22×C4×C5—32no—
39C22×C4×C5—31no—
40C22×C4×C5—31no—
41C22×C4×C5—32no—
42C22×C4×C5—61no—
43C22×C4×C5—62no—
44C22×C4×C5—61no—
45C22×C4×C5—61no—
46C22×C4×C5—64no—
47C22×C4×C5—61no—
48C22×C4×C5—61no—
49C22×C4×C5—61no—
50C22×C4×C5C2×A412yes—
51C42×C5—32no—
52C42×C5—31no—
53C42×C5—32no—
54C42×C5C2×C3×C411yescharacteristic, complemented
55C22×C42C2×C3×C511yescharacteristic
56#383—32no—
57#383C2×C3×C512yescomplemented
58C2×#95—31no—
59C2×#95—31no—
60C22×C3×C5—161no—
61C5×A4—41no—
62C3×C4×C5—162no—
63C22×A4—41no—
64C4×A4—42no—
65C42⋊C3C2×C4×C511yescharacteristic, complemented
66C23×C5—32no—
67C23×C5—31no—
68C23×C5—31no—
69C23×C5C4×A412yes—
70C23×C5C22×A411yescharacteristic
71C2×C4×C5—31no—
72C2×C4×C5—32no—
73C2×C4×C5—31no—
74C2×C4×C5—41no—
75C2×C4×C5—62no—
76C2×C4×C5—61no—
77C2×C4×C5—61no—
78C2×C4×C5—62no—
79C2×C4×C5—62no—
80C2×C4×C5—62no—
81C2×C4×C5—62no—
82C2×C4×C5—61no—
83C2×C4×C5—61no—
84C2×C4×C5—64no—
85C2×C4×C5—62no—
86C2×C4×C5—121no—
87C2×C4×C5—122no—
88C2×C4×C5—122no—
89C23×C4—31no—
90C23×C4—31no—
91C23×C4C5×A411yescharacteristic
92C2×C42—31no—
93C2×C42—32no—
94C2×C42C3×C4×C512yescomplemented
95C2×C42C22×C3×C511yescharacteristic
96#95—32no—
97#95—32no—
98#95—32no—
99#95—32no—
100C2×C3×C5—162no—
101C2×C3×C5—161no—
102C2×A4—42no—
103C2×A4—41no—
104C2×C3×C4—161no—
105C22×C5—31no—
106C22×C5—32no—
107C22×C5—32no—
108C22×C5—32no—
109C22×C5—32no—
110C22×C5—31no—
111C22×C5—31no—
112C22×C5#126⋊C311yescharacteristic
113C22×C5C2×C4×A411yescharacteristic
114C4×C5—42no—
115C4×C5—61no—
116C4×C5—62no—
117C4×C5—61no—
118C4×C5—122no—
119C24C2×C5×A411yescharacteristic
120C22×C4—32no—
121C22×C4—32no—
122C22×C4—31no—
123C22×C4—31no—
124C22×C4—32no—
125C22×C4—61no—
126C22×C4—62no—
127C22×C4—61no—
128C22×C4—61no—
129C22×C4—64no—
130C22×C4—61no—
131C22×C4—61no—
132C22×C4—61no—
133C22×C4C2×C5×A412yes—
134C42—32no—
135C42—31no—
136C42—32no—
137C42C2×C3×C4×C511yescharacteristic, complemented
138C3×C5—161noHall
139C22×C3—161no—
140A4—41no—
141C3×C4—162no—
142C2×C5—31no—
143C2×C5—31no—
144C2×C5—32no—
145C2×C5#383⋊C312yesdirect product factor
146C2×C5C2×#126⋊C311yescharacteristic
147C23—32no—
148C23—31no—
149C23—31no—
150C23C4×C5×A412yes—
151C23C22×C5×A411yescharacteristic
152C2×C4—31no—
153C2×C4—32no—
154C2×C4—31no—
155C2×C4—41no—
156C2×C4—62no—
157C2×C4—61no—
158C2×C4—61no—
159C2×C4—62no—
160C2×C4—62no—
161C2×C4—62no—
162C2×C4—62no—
163C2×C4—61no—
164C2×C4—61no—
165C2×C4—64no—
166C2×C4—62no—
167C2×C4—121no—
168C2×C4—122no—
169C2×C4—122no—
170C2×C3—162no—
171C2×C3—161no—
172C5C2×#383⋊C311yescharacteristic, direct product factor, Sylow
173C22—31no—
174C22—32no—
175C22—32no—
176C22—32no—
177C22—32no—
178C22—31no—
179C22—31no—
180C22C5×#126⋊C311yescharacteristic
181C22C2×C4×C5×A411yescharacteristic
182C4—42no—
183C4—61no—
184C4—62no—
185C4—61no—
186C4—122no—
187C3—161noSylow
188C2—31no—
189C2—31no—
190C2—32no—
191C2C5×#383⋊C312yesdirect product factor
192C2C2×C5×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC22×C5#126⋊C3
commutator, hypocenterC42C2×C3×C4×C5
FrattiniC23C22×C5×A4
FittingC2×C5×#383C3
socleC24×C5C2×A4
prime radicalC22×C5×C42⋊C3C2
cosocleC2×C42C22×C3×C5
LCSG ▷ C42
UCSC1 ◁ C22×C5

Complements

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

NH ≅ G/Ntype
2. C5×#383⋊C3C2direct (N × H)
3. C2×C5×#383C3semidirect
5. C2×C5×C42⋊C3C4semidirect
7. C2×#383⋊C3C5direct (N × H)
10. C5×#383C2×C3semidirect
15. C5×C42⋊C3C2×C4semidirect
17. #383⋊C3C2×C5direct (N × H)
23. C2×C42×C5C3×C4semidirect
29. C2×#383C3×C5semidirect
34. C2×C42⋊C3C4×C5semidirect
54. C42×C5C2×C3×C4semidirect
57. #383C2×C3×C5semidirect
65. C42⋊C3C2×C4×C5semidirect
94. C2×C42C3×C4×C5semidirect
137. C42C2×C3×C4×C5semidirect
145. C2×C5#383⋊C3direct (N × H)
172. C5C2×#383⋊C3direct (N × H)
191. C2C5×#383⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×C42⋊C32
C5×#383⋊C32
C2×C5×#3833
C2×C4×C5×A44
C2×#383⋊C35