Finite Group Databasebeta

← #14298682

Subgroups — #14298682

Order 1920.

472 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 143 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#11756571C211yesmaximal, characteristic
2C2×C3×C5×#101C211yesmaximal, characteristic
3C2×#91120C211yesmaximal, characteristic
4#11746380C212yesmaximal
5#11746377C212yesmaximal
6#10600894—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C2×C3×C5×M16C2212yes—
9Q8×Dic15—22no—
10Q8×Dic15—22no—
11#91815C414yes—
12#91815C2211yescharacteristic
13#91815C2211yescharacteristic
14C2×#6710C2212yes—
15C3×C5×#101—22no—
16#91120—22no—
17#70101—51nomaximal, Hall
18#66146—31no—
19C2×C5×#101D311yescharacteristic
20C2×#3968—31no—
21#64779—32no—
22#64776—32no—
23C2×C3×C5×Q8—22no—
24C2×C3×C5×Q8—22no—
25C2×C3×C5×Q8D412yes—
26C2×C3×C5×Q8D412yes—
27C22×C3×C4×C5C2×C412yes—
28C22×C3×C4×C5C2311yescharacteristic
29C3×C5×M16—22no—
30C3×C5×M16—22no—
31C2×C3×C5×C8—22no—
32#6719C2×C412yes—
33#6719C2×C412yes—
34C4⋊Dic15—24no—
35C4⋊Dic15—21no—
36C4⋊Dic15—21no—
37C4×Dic15—24no—
38C4×Dic15—21no—
39C4×Dic15—21no—
40#6710—22no—
41#6710—22no—
42C2×C3⋊#168—22no—
43#5812—51no—
44C2×C3×#101D511yescharacteristic
45C2×#836—51no—
46#4559—52no—
47#4556—52no—
48C22×C5×Q8C2×D311yescharacteristic
49C2×C5×M16C2×D312yes—
50Q8×Dic5—62no—
51Q8×Dic5—62no—
52#4072—34no—
53#4072—31no—
54#4072—31no—
55C2×#681—32no—
56C5×#101—22no—
57#3968—62no—
58#1830—151noSylow
59C23×C3×C5C22×C411yescharacteristic
60C3×C5×Q8—24no—
61C3×C5×Q8—24no—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—22no—
64C2×C3×C4×C5C22⋊C414yes—
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×C3×C4×C5C2×D411yescharacteristic
67C2×C3×C4×C5#4112yes—
68C2×C3×C4×C5#4112yes—
69C2×Dic15—22no—
70C2×Dic15—22no—
71C3×C5×C8—42no—
72C3⋊#168—42no—
73C22×C3×Q8C2×D511yescharacteristic
74C2×C3×M16C2×D512yes—
75Q8×Dic3—102no—
76Q8×Dic3—102no—
77#926—54no—
78#926—51no—
79#926—51no—
80C2×#208—52no—
81C3×#101—22no—
82#836—102no—
83C2×C5×Q8—22no—
84C2×C5×Q8—22no—
85C2×C5×Q8D1212yes—
86C2×C5×Q8#6712yes—
87C22×C4×C5C4×D312yes—
88C22×C4×C5C22×D311yescharacteristic
89C5×M16—22no—
90C5×M16—22no—
91C2×C5×C8—22no—
92C22⋊Dic5—32no—
93C22⋊Dic5—32no—
94C4⋊Dic5—64no—
95C4⋊Dic5—61no—
96C4⋊Dic5—61no—
97C4×Dic5—64no—
98C4×Dic5—61no—
99C4×Dic5—61no—
100#681—62no—
101#681—62no—
102C2×#168—62no—
103#519—151no—
104C2×#101—151no—
105C2×#101D1511yescharacteristic
106#344—152no—
107#344—152no—
108C22×C3×C5—41no—
109C22×C3×C5C2×C22⋊C411yescharacteristic
110C22×C3×C5#11711yescharacteristic
111C22×C3×C5#11711yescharacteristic
112C3×C4×C5—24no—
113C3×C4×C5#12312yes—
114C3×C4×C5#12312yes—
115Dic15—42no—
116Dic15—42no—
117C2×C3×Q8—22no—
118C2×C3×Q8—22no—
119C2×C3×Q8D2012yes—
120C2×C3×Q8C22⋊D512yes—
121C22×C3×C4C4×D512yes—
122C22×C3×C4C22×D511yescharacteristic
123C3×M16—22no—
124C3×M16—22no—
125C2×C3×C8—22no—
126#217—52no—
127#217—52no—
128C4⋊Dic3—104no—
129C4⋊Dic3—101no—
130C4⋊Dic3—101no—
131C4×Dic3—104no—
132C4×Dic3—101no—
133C4×Dic3—101no—
134#208—102no—
135#208—102no—
136C2×C3⋊C8—102no—
137C23×C5C2×C4×D311yescharacteristic
138C5×Q8—24no—
139C5×Q8—24no—
140C2×C4×C5—22no—
141C2×C4×C5—22no—
142C2×C4×C5(C2×D3)⋊C414yes—
143C2×C4×C5C2×D1211yescharacteristic
144C2×C4×C5#23712yes—
145C2×C4×C5#23712yes—
146C2×C4×C5C2×#6711yescharacteristic
147C2×Dic5—62no—
148C2×Dic5—62no—
149C5×C8—42no—
150#168—122no—
151C22×Q8C2×D1511yescharacteristic
152C2×M16—152no—
153C2×M16C2×D1512yes—
154C4×Q8—302no—
155C4×Q8—302no—
156#117—154no—
157#117—151no—
158#117—151no—
159#101—22no—
160#101—302no—
161C2×C3×C5—21no—
162C2×C3×C5—21no—
163C2×C3×C5—21no—
164C2×C3×C5#38111yescharacteristic
165C23×C3C2×C4×D511yescharacteristic
166C3×Q8—24no—
167C3×Q8—24no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4#68514yes—
171C2×C3×C4C2×D2011yescharacteristic
172C2×C3×C4#71112yes—
173C2×C3×C4#71112yes—
174C2×C3×C4C2×C22⋊D511yescharacteristic
175C2×Dic3—102no—
176C2×Dic3—102no—
177C3×C8—42no—
178C3⋊C8—202no—
179C22×C5—41no—
180C22×C5#87711yescharacteristic
181C22×C5#87711yescharacteristic
182C22×C5C2×(C2×D3)⋊C411yescharacteristic
183C4×C5—24no—
184C4×C5#88612yes—
185C4×C5#93512yes—
186Dic5—122no—
187Dic5—122no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8D6012yes—
191C2×Q8#122012yes—
192C22×C4C4×D1512yes—
193C22×C4C22×D1511yescharacteristic
194M16—22no—
195M16—22no—
196M16—302no—
197M16—302no—
198C2×C8—22no—
199C2×C8—302no—
200C4⋊C4—304no—
201C4⋊C4—301no—
202C4⋊C4—301no—
203C22⋊C4—152no—
204C22⋊C4—152no—
205C42—304no—
206C42—301no—
207C42—301no—
208C3×C5#183011yescharacteristic, complemented, Hall
209C22×C3—41no—
210C22×C3#402311yescharacteristic
211C22×C3#402311yescharacteristic
212C22×C3C2×#68511yescharacteristic
213C3×C4—24no—
214C3×C4#403212yes—
215C3×C4#408112yes—
216Dic3—202no—
217Dic3—202no—
218C2×C5—21no—
219C2×C5—21no—
220C2×C5—21no—
221C2×C5#494311yescharacteristic
222C23C2×C4×D1511yescharacteristic
223Q8—24no—
224Q8—24no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—302no—
228C2×C4—302no—
229C2×C4#671414yes—
230C2×C4C2×D6011yescharacteristic
231C2×C4#681912yes—
232C2×C4#681912yes—
233C2×C4C2×#122011yescharacteristic
234C8—42no—
235C8—602no—
236C2×C3—21no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3#6523211yescharacteristic
240C5#7010111yescharacteristic, complemented, Sylow
241C22—41no—
242C22#9176611yescharacteristic
243C22#9176611yescharacteristic
244C22C2×#671411yescharacteristic
245C4—24no—
246C4—602no—
247C4—602no—
248C4#9177512yes—
249C4#9182412yes—
250C3#1060089411yescharacteristic, complemented, Sylow
251C2—21no—
252C2—21no—
253C2—21no—
254C2#1175104411yescharacteristic
subgroupG/H
centerC2#11751044
commutator, prime radicalC23×C3×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#101C2
socleC2×C3×C5#381
cosocleC22×C3×C4×C5C23
hypercenterC2×#101D15
hypocenterC3×C5#1830
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
208. C3×C5#1830semidirect
240. C5#70101semidirect
250. C3#10600894semidirect

Maximal subgroups

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

subgroupindex
#117565712
C2×C3×C5×#1012
C2×#911202
#117463802
#117463772
#106008943
#701015