Finite Group Databasebeta

← #14279443

Subgroups — #14279443

Order 1920.

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

normal subgroups only

This group has 240 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
1#11751174C211yesmaximal, characteristic
2C5×#4545C211yesmaximal, characteristic, complemented
3C3×#64765C211yesmaximal, characteristic, complemented
4#10598032—31nomaximal, Hall
5C3×C5×#127C2211yescharacteristic
6C2×#6715—21no—
7C2×#6715—21no—
8#91763C411yescharacteristic, complemented
9C4×C3⋊#168C411yescharacteristic, complemented
10C5×#834—21no—
11C3×#3966—21no—
12#67541—51nomaximal, Hall
13#65362—31no—
14C5×#353—31no—
15#64765D311yescharacteristic, complemented
16C2×C3×C5×D4—41no—
17C2×C3×C5×D4D411yescharacteristic
18C2×C3×C5×D4D411yescharacteristic
19C2×D60—21no—
20C2×D60—41no—
21C3×C42×C5C2×C411yescharacteristic
22#6715—42no—
23#6715—42no—
24C2×C3⋊#168—21no—
25C5×#217—41no—
26C3×C22⋊Dic5—41no—
27#5073—51no—
28C3×#353—51no—
29#4545D511yescharacteristic, complemented
30C5×#127C2×D311yescharacteristic
31C2×#686—61no—
32C2×#686—61no—
33#4020—31no—
34C5×#99—61no—
35#3966—21no—
36C4×#168—31no—
37#1408—151noSylow
38C23×C3×C5—21no—
39C23×C3×C5—21no—
40C22×D15—41no—
41C3×C5×D4—41no—
42C3×C5×D4—41no—
43C3×C5×D4—82no—
44C2×C3×C4×C5—21no—
45C2×C3×C4×C5C22⋊C411yescharacteristic
46D60—41no—
47D60—41no—
48D60—82no—
49C2×C5×Dic3—81no—
50C2×C3×Dic5—81no—
51C3⋊#168—22no—
52C3×#127C2×D511yescharacteristic
53C2×#213—101no—
54C2×#213—101no—
55#874—51no—
56C3×#99—101no—
57#834—21no—
58C4×C3⋊C8—51no—
59C2×C5×D4—41no—
60C2×C5×D4D1211yescharacteristic
61C2×C5×D4#6711yescharacteristic
62C2×D20—61no—
63C2×D20—121no—
64C5×C22⋊C4—121no—
65C42×C5C4×D311yescharacteristic
66C22⋊Dic5—41no—
67#686—122no—
68#686—122no—
69C2×#168—61no—
70#493—151no—
71#353—31no—
72#353—51no—
73C22×C3×C5—41no—
74C22×C3×C5—41no—
75C22×C3×C5—81no—
76C22×C3×C5—81no—
77C22×C3×C5#9911yescharacteristic
78C2×D15—82no—
79C2×D15—81no—
80C3×C4×C5—22no—
81C3×C4×C5—21no—
82C3×Dic5—161no—
83C5×Dic3—161no—
84C2×C3×D4—41no—
85C2×C3×D4D2011yescharacteristic
86C2×C3×D4C22⋊D511yescharacteristic
87C2×D12—101no—
88C2×D12—201no—
89C3×C22⋊C4—201no—
90C3×C42C4×D511yescharacteristic
91#217—41no—
92#213—202no—
93#213—202no—
94C2×C3⋊C8—101no—
95C23×C5—21no—
96C23×C5—21no—
97C22×D5—121no—
98C5×D4—41no—
99C5×D4—41no—
100C5×D4—82no—
101C2×C4×C5—21no—
102C2×C4×C5—241no—
103C2×C4×C5(C2×D3)⋊C411yescharacteristic
104C2×Dic5—81no—
105D20—121no—
106D20—121no—
107D20—242no—
108#168—62no—
109C2×D8—301no—
110C2×D8—301no—
111#127—151no—
112#127D3×D511yescharacteristic
113#99—61no—
114#99—101no—
115C4×C8—151no—
116C2×C3×C5—21no—
117C2×C3×C5—81no—
118C2×C3×C5—81no—
119C2×C3×C5#35311yescharacteristic
120D15—161no—
121C23×C3—21no—
122C23×C3—21no—
123C22×D3—201no—
124C3×D4—41no—
125C3×D4—41no—
126C3×D4—82no—
127C2×C3×C4—21no—
128C2×C3×C4—401no—
129C2×C3×C4#68511yescharacteristic
130C2×Dic3—81no—
131D12—201no—
132D12—201no—
133D12—402no—
134C3⋊C8—102no—
135C22×C5—41no—
136C22×C5—41no—
137C22×C5—81no—
138C22×C5—81no—
139C22×C5#80611yescharacteristic
140C2×D5—242no—
141C2×D5—241no—
142C4×C5—22no—
143C4×C5—21no—
144C4×C5—481no—
145Dic5—161no—
146C2×D4—41no—
147C2×D4—301no—
148C2×D4—601no—
149C2×D4#120211yescharacteristic
150C2×D4#120311yescharacteristic
151D8—602no—
152D8—602no—
153C2×C8—301no—
154C22⋊C4—121no—
155C22⋊C4—201no—
156C42#120011yescharacteristic
157C3×C5#140811yescharacteristic, complemented, Hall
158C22×C3—41no—
159C22×C3—41no—
160C22×C3—81no—
161C22×C3—81no—
162C22×C3#393811yescharacteristic
163C2×D3—402no—
164C2×D3—401no—
165C3×C4—22no—
166C3×C4—21no—
167C3×C4—801no—
168Dic3—161no—
169C2×C5—21no—
170C2×C5—81no—
171C2×C5—81no—
172C2×C5#447411yescharacteristic
173D5—481no—
174C23—21no—
175C23—21no—
176C23—601no—
177D4—41no—
178D4—41no—
179D4—82no—
180D4—601no—
181D4—601no—
182D4—1202no—
183C2×C4—21no—
184C2×C4—241no—
185C2×C4—401no—
186C2×C4#666711yescharacteristic
187C8—302no—
188C2×C3—21no—
189C2×C3—81no—
190C2×C3—81no—
191C2×C3#6469411yescharacteristic
192D3—801no—
193C5#6754111yescharacteristic, complemented, Sylow
194C22—41no—
195C22—41no—
196C22—81no—
197C22—81no—
198C22—1202no—
199C22—1201no—
200C22#9099711yescharacteristic
201C4—22no—
202C4—21no—
203C4—481no—
204C4—801no—
205C3#1059803211yescharacteristic, complemented, Sylow
206C2—21no—
207C2—81no—
208C2—81no—
209C2—2401no—
210C2#1174600811yescharacteristic
subgroupG/H
centerC2#11746008
commutatorC3×C42×C5C2×C4
Frattini, hypercenter#127D3×D5
Fitting, cosocleC3×C5×#127C22
socleC2×C3×C5#353
prime radical#11751174C2
hypocenterC3×C5#1408
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
2. C5×#4545C2semidirect
3. C3×#64765C2semidirect
8. #91763C4semidirect
9. C4×C3⋊#168C4semidirect
15. #64765D3semidirect
29. #4545D5semidirect
157. C3×C5#1408semidirect
193. C5#67541semidirect
205. C3#10598032semidirect

Maximal subgroups

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

subgroupindex
#117511742
C5×#45452
C3×#647652
#105980323
#675415