Finite Group Databasebeta

← #14513749

Subgroups — #14513749

Order 1920.

542 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 65 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×#91956C211yesmaximal, characteristic
2C2×#91954C211yesmaximal, characteristic, complemented
3C4×C5×#41⋊C3C211yesmaximal, characteristic, complemented
4#11752114C214yesmaximal, complemented
5#10614258—31nomaximal, Hall
6C2×C5×#41⋊C3C2211yescharacteristic
7#91956—22no—
8#91954—22no—
9C2×C5⋊GL(2,𝔽3)C2212yes—
10C2×C5⋊#226C2212yescomplemented
11#91764—41nomaximal
12C4×C5×SL(2,𝔽3)C2212yescomplemented
13#85347—51nomaximal, Hall
14C4×C5×#41D311yescharacteristic, complemented
15C2×#4097—31no—
16C2×#4095—31no—
17C2×#4021—31no—
18#65317—34no—
19#65305—34no—
20#65293—31no—
21#65290—31no—
22#65213—31no—
23C2×D60—41no—
24C2×Dic30—41no—
25C5×#41⋊C3D412yes—
26C2×C5×SL(2,𝔽3)C2311yescharacteristic
27C5⋊GL(2,𝔽3)—22no—
28C5⋊#226—22no—
29C3×C42×C5—41no—
30#6714—44no—
31C2×#986—51no—
32C2×#984—51no—
33C4×#41⋊C3D511yescharacteristic, complemented
34#5395—54no—
35C2×C5×#41C2×D311yescharacteristic
36C22×D20—31no—
37C22×Dic10—31no—
38C4×C5×Q8C2×D312yes—
39C4×C5×D4—32no—
40C5×#117—31no—
41C2×C42×C5—31no—
42#4097—62no—
43#4097—62no—
44#4095—62no—
45#4095—62no—
46C2×#689—32no—
47C2×#688—32no—
48C2×#687—32no—
49C2×#686—32no—
50C2×#685—62no—
51C2×#681—31no—
52C2×#681—31no—
53#4021—34no—
54#4021—61no—
55#4021—61no—
56#3942—34no—
57#3941—34no—
58C4⋊#168—34no—
59#3040—151noSylow
60C22×D15—42no—
61C2×C3×C4×C5—41no—
62C2×C3×C4×C5—42no—
63C2×Dic15—42no—
64D60—82no—
65Dic30—82no—
66C5×SL(2,𝔽3)C2×D411yescharacteristic
67C2×#41⋊C3C2×D511yescharacteristic
68#986—102no—
69#984—102no—
70C2×GL(2,𝔽3)—52no—
71C2×#226—52no—
72#875—201no—
73C4×SL(2,𝔽3)C2×D512yescomplemented
74C23×D5—61no—
75C5×#41—32no—
76C5×#41D1212yes—
77C2×C5×Q8C22×D311yescharacteristic
78C2×C5×D4—31no—
79C22×C4×C5—31no—
80C22×C4×C5—32no—
81C22×Dic5—61no—
82C2×D20—32no—
83C2×D20—62no—
84C2×D20—62no—
85C2×D20—61no—
86C2×Dic10—32no—
87C2×Dic10—62no—
88C2×Dic10—62no—
89C2×Dic10—61no—
90C5×C4⋊C4—32no—
91C5×C22⋊C4—61no—
92C42×C5—31no—
93C42×C5—32no—
94C42×C5S411yescharacteristic
95#689—62no—
96#689—62no—
97#688—62no—
98#688—62no—
99#687—64no—
100#686—64no—
101#685—64no—
102#685—64no—
103#681—62no—
104#681—62no—
105C2×#168—32no—
106C2×#168—32no—
107C2×#137—151no—
108C2×AGL(1,ℤ/8)—151no—
109C2×#124—151no—
110C4×#41D1511yescharacteristic, complemented
111#464—154no—
112#463—154no—
113#423—151no—
114#419—151no—
115#418—151no—
116C22×C3×C5—41no—
117C2×D15—82no—
118C2×D15—84no—
119C3×C4×C5—42no—
120C3×C4×C5—82no—
121Dic15—82no—
122C2×D12—201no—
123C2×Dic6—201no—
124#41⋊C3D2012yes—
125C2×SL(2,𝔽3)C22×D511yescharacteristic
126GL(2,𝔽3)—102no—
127#226—102no—
128C3×C42—41no—
129(C2×D3)⋊C4—204no—
130C23×C5—31no—
131C22×D5—62no—
132C22×D5—122no—
133C22×D5—124no—
134C5×Q8—31no—
135C5×Q8C2×D1211yescharacteristic
136C5×D4—32no—
137C5×D4—61no—
138C2×C4×C5—31no—
139C2×C4×C5—32no—
140C2×C4×C5—32no—
141C2×C4×C5—32no—
142C2×C4×C5—122no—
143C2×C4×C5C2×S412yes—
144C2×C4×C5C2×S411yescharacteristic
145C2×Dic5—62no—
146C2×Dic5—122no—
147D20—62no—
148D20—62no—
149D20—122no—
150Dic10—62no—
151Dic10—62no—
152Dic10—122no—
153#168—62no—
154#168—62no—
155C2×#41C2×D1511yescharacteristic
156C22×Q8—151no—
157C22×D4—151no—
158#137—302no—
159#137—302no—
160AGL(1,ℤ/8)—302no—
161AGL(1,ℤ/8)—302no—
162C2×Q16—152no—
163C2×SD16—152no—
164C2×SD16—152no—
165C2×D8—152no—
166C2×M16—151no—
167C2×M16—151no—
168#124—154no—
169#124—301no—
170#124—301no—
171C4×Q8C2×D1512yes—
172C4×D4—32no—
173#117—31no—
174C2×C22⋊C4—302no—
175C2×C42—31no—
176C4⋊C8—154no—
177#103—154no—
178#102—154no—
179C2×C3×C5—41no—
180C2×C3×C5—42no—
181D15—162no—
182C22×D3—202no—
183C2×C3×C4—41no—
184C2×C3×C4—42no—
185C2×Dic3—202no—
186D12—402no—
187Dic6—402no—
188SL(2,𝔽3)C2×D2011yescharacteristic
189C22×C5—32no—
190C22×C5—62no—
191C22×C5C22×S411yescharacteristic
192C2×D5—122no—
193C2×D5—124no—
194C2×D5—244no—
195C4×C5—22no—
196C4×C5—31no—
197C4×C5—31no—
198C4×C5—62no—
199C4×C5C4⋊S412yes—
200Dic5—122no—
201C24—301no—
202#41—32no—
203#41D6012yes—
204C2×Q8—152no—
205C2×Q8—302no—
206C2×Q8—302no—
207C2×Q8—301no—
208C2×Q8C22×D1511yescharacteristic
209C2×D4—31no—
210C2×D4—152no—
211C2×D4—302no—
212C2×D4—302no—
213C2×D4—301no—
214C22×C4—31no—
215C22×C4—32no—
216C22×C4—301no—
217Q16—302no—
218Q16—302no—
219SD16—304no—
220SD16—302no—
221SD16—302no—
222D8—304no—
223M16—302no—
224M16—302no—
225C2×C8—152no—
226C2×C8—152no—
227C4⋊C4—32no—
228C22⋊C4—61no—
229C22⋊C4—304no—
230C22⋊C4—304no—
231C42—32no—
232C42—31no—
233C42C5⋊S411yescharacteristic
234C3×C5—41noHall
235C22×C3—41no—
236C2×D3—402no—
237C2×D3—404no—
238C3×C4—42no—
239C3×C4—82no—
240Dic3—402no—
241C2×C5—62no—
242C2×C5C2×C4⋊S411yescharacteristic
243C2×C5#592312yes—
244D5—242no—
245C23—31no—
246C23—302no—
247C23—602no—
248C23—604no—
249Q8—31no—
250Q8—302no—
251Q8—302no—
252Q8—602no—
253Q8C2×D6011yescharacteristic
254D4—32no—
255D4—61no—
256D4—302no—
257D4—302no—
258D4—602no—
259C2×C4—31no—
260C2×C4—32no—
261C2×C4—32no—
262C2×C4—32no—
263C2×C4—122no—
264C2×C4—302no—
265C2×C4—602no—
266C2×C4C2×C5⋊S412yes—
267C2×C4C2×C5⋊S411yescharacteristic
268C8—302no—
269C8—302no—
270C2×C3—41no—
271C2×C3—42no—
272D3—802no—
273C5#8534711yescharacteristic, complemented, Sylow
274C22—32no—
275C22—62no—
276C22—602no—
277C22—604no—
278C22—1204no—
279C22C22×C5⋊S411yescharacteristic
280C4—22no—
281C4—31no—
282C4—31no—
283C4—62no—
284C4—602no—
285C4C4⋊(C5⋊S4)12yes—
286C3—41noSylow
287C2—62no—
288C2—1202no—
289C2C2×C4⋊(C5⋊S4)11yescharacteristic
290C2#1175690712yes—
subgroupG/H
center, FrattiniC22C22×C5⋊S4
commutator, cosocleC2×C5×SL(2,𝔽3)C23
FittingC4×C5×#41D3
socleC22×C5C22×S4
prime radicalC2×#91956C2
hypercenterC42C5⋊S4
hypocenterC5×SL(2,𝔽3)C2×D4
LCSG ▷ C2×C5×SL(2,𝔽3) ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C2×#91954C2semidirect
3. C4×C5×#41⋊C3C2semidirect
4. #11752114C2semidirect
10. C2×C5⋊#226C22semidirect
12. C4×C5×SL(2,𝔽3)C22semidirect
14. C4×C5×#41D3semidirect
33. C4×#41⋊C3D5semidirect
73. C4×SL(2,𝔽3)C2×D5semidirect
110. C4×#41D15semidirect
273. C5#85347semidirect

Maximal subgroups

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

subgroupindex
C2×#919562
C2×#919542
C4×C5×#41⋊C32
#117521142
#106142583
#917644
#853475