Finite Group Databasebeta

← #14298419

Subgroups — #14298419

Order 1920.

544 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 110 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×#91357C211yesmaximal, characteristic
2#11752414C211yesmaximal, characteristic
3C3×#65755C211yesmaximal, characteristic
4#11746574C214yesmaximal, complemented
5#10604195—31nomaximal, Hall
6C22×C3×C4×D5C2211yescharacteristic
7C2×#6762C2212yes—
8C2×C3×#704C2212yes—
9C2×C4×Dic15C411yescharacteristic
10C2×C4×C5×Dic3C411yescharacteristic
11C2×#6668C2212yes—
12C2×#6665C412yes—
13#91357—22no—
14#91357—22no—
15#91232—22no—
16C3×#4003—22no—
17#69974—51nomaximal, Hall
18C2×#4018—31no—
19#65755—31no—
20#65755D311yescharacteristic
21#64919—34no—
22C23×C3×D5C2×C411yescharacteristic
23C22×C3×C4×C5C2×C411yescharacteristic
24C22×Dic15C2×C412yes—
25C22×C5×Dic3C2×C412yes—
26C22×C3×Dic5C2311yescharacteristic
27C2×C3×C4×D5—24no—
28C2×C3×C4×D5D412yes—
29C2×C3×C4×D5D412yes—
30#6762—24no—
31C2×C3⋊#170—22no—
32C3×#704—24no—
33C2×C3×#170—22no—
34C4×Dic15—22no—
35C4×C5×Dic3—22no—
36#6668—22no—
37#6668—22no—
38#6665—24no—
39C2×#926—51no—
40C3×#407—51no—
41#5207—51no—
42#4554—54no—
43C22×C4×D5C2×D311yescharacteristic
44C2×#704—32no—
45C2×#704C2×D312yes—
46C2×C42×C5—31no—
47C2×#685—32no—
48C2×#683—32no—
49C2×C4×Dic5—31no—
50#4018—62no—
51#4018—62no—
52#4003—22no—
53#4003—62no—
54#1822—151noSylow
55C23×C3×C5C22×C411yescharacteristic
56C22×C3×D5—22no—
57C22×C3×D5—42no—
58C22×C3×D5C22⋊C412yes—
59C2×C3×C4×C5—22no—
60C2×C3×C4×C5C22⋊C412yes—
61C2×Dic15—22no—
62C2×Dic15—42no—
63C2×C5×Dic3—22no—
64C2×C5×Dic3—42no—
65C2×C3×Dic5C2×D411yescharacteristic
66C2×C3×Dic5C2×D411yescharacteristic
67C2×C3×Dic5#4114yes—
68C3×C4×D5—24no—
69C3×C4×D5—24no—
70C3⋊#170—42no—
71C3×#170—42no—
72C23×C3×C4—51no—
73C2×C3×M16—52no—
74C2×#217—52no—
75#926—102no—
76#926—102no—
77C2×C4⋊Dic3—52no—
78C2×C4×Dic3—51no—
79C2×C4×Dic3AGL(1,𝔽5)11yescharacteristic
80C2×#208—52no—
81C3×C22⋊C8—102no—
82#830—102no—
83C23×D5C4×D311yescharacteristic
84C22×C4×C5—32no—
85C22×C4×C5C4×D311yescharacteristic
86C22×Dic5—32no—
87C22×Dic5C22×D311yescharacteristic
88C2×C4×D5—24no—
89C2×C4×D5D1212yes—
90C2×C4×D5#6712yes—
91#704—24no—
92#704—64no—
93C2×#170—22no—
94C2×#170—62no—
95C42×C5—62no—
96#685—64no—
97#683—62no—
98#683—62no—
99C4×Dic5—62no—
100C2×#117—151no—
101#407—51no—
102#407—151no—
103#343—154no—
104C22×C3×C5—22no—
105C22×C3×C5C2×C22⋊C411yescharacteristic
106C22×C3×C5#11712yes—
107C2×C3×D5—22no—
108C2×C3×D5—24no—
109C2×C3×D5—44no—
110C3×C4×C5—22no—
111Dic15—42no—
112C3×Dic5#12312yes—
113C3×Dic5#12312yes—
114C5×Dic3—42no—
115C24×C3—51no—
116C22×C3×C4—51no—
117C22×C3×C4—52no—
118C22×C3×C4—52no—
119C22×C3×C4—104no—
120C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
121C22×Dic3—52no—
122C22×Dic3C2×AGL(1,𝔽5)12yes—
123C3×M16—104no—
124C2×C3×C8—102no—
125#217—104no—
126C4⋊Dic3—102no—
127C4⋊Dic3—102no—
128C4×Dic3—22no—
129C4×Dic3—102no—
130#208—104no—
131C2×C3⋊C8—102no—
132C23×C5C2×C4×D311yescharacteristic
133C22×D5—22no—
134C22×D5—42no—
135C22×D5(C2×D3)⋊C412yes—
136C2×C4×C5—22no—
137C2×C4×C5—62no—
138C2×C4×C5—122no—
139C2×C4×C5(C2×D3)⋊C412yes—
140C2×Dic5—62no—
141C2×Dic5—122no—
142C2×Dic5C2×D1211yescharacteristic
143C2×Dic5#23714yes—
144C2×Dic5C2×#6711yescharacteristic
145C4×D5—24no—
146C4×D5—24no—
147#170—42no—
148#170—122no—
149C23×C4—51no—
150C2×M16—52no—
151C2×M16—152no—
152#117—302no—
153#117—302no—
154C2×C4⋊C4—152no—
155C2×C22⋊C4—152no—
156C2×C42—31no—
157C2×C42—151no—
158C22⋊C8—102no—
159C22⋊C8—302no—
160C2×C3×C5—22no—
161C2×C3×C5#38111yescharacteristic
162C2×C3×C5#41312yes—
163C3×D5—42no—
164C23×C3—52no—
165C23×C3—102no—
166C23×C3—202no—
167C23×C3C22×AGL(1,𝔽5)11yescharacteristic
168C2×C3×C4—22no—
169C2×C3×C4—54no—
170C2×C3×C4—51no—
171C2×C3×C4—51no—
172C2×C3×C4—104no—
173C2×C3×C4—104no—
174C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
175C2×Dic3—22no—
176C2×Dic3—42no—
177C2×Dic3—102no—
178C2×Dic3—202no—
179C3×C8—202no—
180C3⋊C8—202no—
181C22×C5—22no—
182C22×C5#87712yes—
183C22×C5C2×(C2×D3)⋊C411yescharacteristic
184C2×D5—24no—
185C2×D5—22no—
186C2×D5—44no—
187C4×C5—22no—
188C4×C5—122no—
189Dic5—122no—
190Dic5#88612yes—
191Dic5#93512yes—
192C24—51no—
193C22×C4—32no—
194C22×C4—51no—
195C22×C4—52no—
196C22×C4—52no—
197C22×C4—104no—
198C22×C4—152no—
199C22×C4D3×AGL(1,𝔽5)11yescharacteristic
200M16—104no—
201M16—304no—
202C2×C8—102no—
203C2×C8—302no—
204C4⋊C4—302no—
205C4⋊C4—302no—
206C22⋊C4—304no—
207C42—62no—
208C42—302no—
209C3×C5#182211yescharacteristic, complemented, Hall
210C22×C3—22no—
211C22×C3—104no—
212C22×C3—102no—
213C22×C3—204no—
214C22×C3#413012yes—
215C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
216C3×C4—22no—
217C3×C4—52no—
218C3×C4—52no—
219Dic3—42no—
220Dic3—202no—
221C2×C5—22no—
222C2×C5#494311yescharacteristic
223C2×C5#513212yes—
224D5—42no—
225C23—52no—
226C23—102no—
227C23—202no—
228C23C2×D3×AGL(1,𝔽5)11yescharacteristic
229C2×C4—22no—
230C2×C4—54no—
231C2×C4—51no—
232C2×C4—51no—
233C2×C4—62no—
234C2×C4—104no—
235C2×C4—104no—
236C2×C4—122no—
237C2×C4—302no—
238C2×C4—602no—
239C2×C4(C2×D3)⋊AGL(1,𝔽5)12yes—
240C8—202no—
241C8—602no—
242C2×C3—22no—
243C2×C3—202no—
244C2×C3#6576112yes—
245C2×C3#6576411yescharacteristic
246C5#6997411yescharacteristic, complemented, Sylow
247C22—22no—
248C22—102no—
249C22—104no—
250C22—204no—
251C22#9192312yes—
252C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
253C4—22no—
254C4—52no—
255C4—52no—
256C4—122no—
257C4—602no—
258C3#1060419511yescharacteristic, complemented, Sylow
259C2—22no—
260C2—202no—
261C2#1175181812yes—
262C2#1175198411yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1822
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #11746574C2semidirect
209. C3×C5#1822semidirect
246. C5#69974semidirect
258. C3#10604195semidirect

Maximal subgroups

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

subgroupindex
C2×#913572
#117524142
C3×#657552
#117465742
#106041953
#699745