Finite Group Databasebeta

← #14513440

Subgroups — #14513440

Order 1920.

542 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 59 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×C5×#984C211yesmaximal, characteristic, complemented
3Dic5×#41⋊C3C211yesmaximal, characteristic, complemented
4#11751604C214yesmaximal, complemented
5#10615699—31nomaximal, Hall
6C2×C5×#41⋊C3C2211yescharacteristic
7#91956—22no—
8C2×C5⋊GL(2,𝔽3)C2212yes—
9C5×#984—22no—
10C2×C5×#226C2212yescomplemented
11#91375—41nomaximal
12Dic5×SL(2,𝔽3)C2212yescomplemented
13#85347—51nomaximal, Hall
14C2×C5×#137—31no—
15#41×Dic5D311yescharacteristic, complemented
16C2×#4095—31no—
17C2×#4093—31no—
18#65514—31no—
19#65474—34no—
20#65454—34no—
21#65420—31no—
22#65407—31no—
23C2×D60—41no—
24C2×C5×Dic6—41no—
25C5×#41⋊C3D412yes—
26C2×C5×SL(2,𝔽3)C2311yescharacteristic
27C5⋊GL(2,𝔽3)—22no—
28C5×#226—22no—
29C3×C4×Dic5—41no—
30#6667—44no—
31C2×#986—51no—
32C2×#984D511yescharacteristic, complemented
33C4×#41⋊C3—51no—
34#5395—54no—
35C2×C5×#41C2×D311yescharacteristic
36C22×C5×Q8—31no—
37C22×D20—31no—
38C5×#137—62no—
39C5×#137—62no—
40C2×C5×Q16—32no—
41C2×C5×SD16—32no—
42C2×C5×M16—31no—
43#4095—62no—
44#4095—62no—
45#4093—34no—
46#4093—61no—
47#4093—61no—
48Q8×Dic5C2×D312yes—
49C2×#688—32no—
50D4×Dic5—32no—
51C2×#686—32no—
52C2×#685—62no—
53#4072—31no—
54C2×C4×Dic5—31no—
55C2×#681—31no—
56#3967—34no—
57#3953—34no—
58#3946—34no—
59#3040—151noSylow
60C22×D15—42no—
61C2×C3×C4×C5—41no—
62D60—82no—
63C2×C5×Dic3—42no—
64C5×Dic6—82no—
65C2×C3×Dic5—42no—
66C5×SL(2,𝔽3)C2×D411yescharacteristic
67C2×#41⋊C3C2×D511yescharacteristic
68#986—102no—
69#984—22no—
70C2×GL(2,𝔽3)—52no—
71C2×#226C2×D512yescomplemented
72#875—201no—
73C4×SL(2,𝔽3)—52no—
74C23×D5—61no—
75C5×#41—32no—
76C5×#41D1212yes—
77C2×C5×Q8—32no—
78C2×C5×Q8—62no—
79C2×C5×Q8—62no—
80C2×C5×Q8—61no—
81C2×C5×Q8C22×D311yescharacteristic
82C2×C5×D4—31no—
83C22×C4×C5—31no—
84C22×C4×C5—61no—
85C22×Dic5—32no—
86C2×D20—32no—
87C2×D20—62no—
88C2×D20—62no—
89C2×D20—61no—
90C5×Q16—62no—
91C5×Q16—62no—
92C5×SD16—64no—
93C5×M16—62no—
94C2×C5×C8—32no—
95C22⋊Dic5—61no—
96#688—62no—
97#688—62no—
98#686—64no—
99#685—64no—
100#685—64no—
101C4⋊Dic5—32no—
102C4×Dic5—31no—
103C4×Dic5—32no—
104C4×Dic5S411yescharacteristic
105#681—62no—
106C2×#168—32no—
107C2×#137—31no—
108C2×AGL(1,ℤ/8)—151no—
109C2×#124—151no—
110C4×#41—51no—
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×Dic5—82no—
121C5×Dic3—82no—
122C2×D12—201no—
123C2×Dic6—41no—
124#41⋊C3C22⋊D512yes—
125C2×SL(2,𝔽3)C22×D511yescharacteristic
126GL(2,𝔽3)—102no—
127#226—22no—
128C3×C42—201no—
129(C2×D3)⋊C4—204no—
130C23×C5—31no—
131C22×D5—62no—
132C22×D5—122no—
133C22×D5—124no—
134C5×Q8—31no—
135C5×Q8—62no—
136C5×Q8—62no—
137C5×Q8—122no—
138C5×Q8C2×D1211yescharacteristic
139C5×D4—32no—
140C5×D4—61no—
141C2×C4×C5—31no—
142C2×C4×C5—32no—
143C2×C4×C5—32no—
144C2×C4×C5—62no—
145C2×C4×C5—122no—
146C2×C4×C5C2×S411yescharacteristic
147C2×Dic5—32no—
148C2×Dic5—122no—
149C2×Dic5C2×S412yes—
150D20—62no—
151D20—62no—
152D20—122no—
153C5×C8—62no—
154#168—62no—
155C2×#41D3×D511yescharacteristic
156C22×Q8—31no—
157C22×D4—151no—
158#137—62no—
159#137—62no—
160AGL(1,ℤ/8)—302no—
161AGL(1,ℤ/8)—302no—
162C2×Q16—32no—
163C2×SD16—32no—
164C2×SD16—152no—
165C2×D8—152no—
166C2×M16—31no—
167C2×M16—151no—
168#124—154no—
169#124—301no—
170#124—301no—
171C4×Q8—52no—
172C4×D4—152no—
173#117—151no—
174C2×C22⋊C4—302no—
175C2×C42—151no—
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—202no—
185C2×Dic3—42no—
186D12—402no—
187Dic6—82no—
188SL(2,𝔽3)C2×C22⋊D511yescharacteristic
189C22×C5—32no—
190C22×C5—62no—
191C22×C5C22×S411yescharacteristic
192C2×D5—122no—
193C2×D5—124no—
194C2×D5—244no—
195C4×C5—31no—
196C4×C5—31no—
197C4×C5—122no—
198C4×C5C4⋊S412yes—
199Dic5—22no—
200Dic5—62no—
201C24—301no—
202#41—32no—
203#41#120312yes—
204C2×Q8—32no—
205C2×Q8—62no—
206C2×Q8—62no—
207C2×Q8—61no—
208C2×Q8C2×D3×D511yescharacteristic
209C2×D4—31no—
210C2×D4—152no—
211C2×D4—302no—
212C2×D4—302no—
213C2×D4—301no—
214C22×C4—31no—
215C22×C4—61no—
216C22×C4—152no—
217Q16—62no—
218Q16—62no—
219SD16—64no—
220SD16—302no—
221SD16—302no—
222D8—304no—
223M16—62no—
224M16—302no—
225C2×C8—32no—
226C2×C8—152no—
227C4⋊C4—152no—
228C22⋊C4—304no—
229C22⋊C4—304no—
230C22⋊C4—301no—
231C42—51no—
232C42—152no—
233C42—151no—
234C3×C5—41noHall
235C22×C3—41no—
236C2×D3—402no—
237C2×D3—404no—
238C3×C4—42no—
239C3×C4—402no—
240Dic3—82no—
241C2×C5—62no—
242C2×C5C2×C4⋊S411yescharacteristic
243C2×C5#592312yes—
244D5—242no—
245C23—31no—
246C23—302no—
247C23—602no—
248C23—604no—
249Q8—31no—
250Q8—62no—
251Q8—62no—
252Q8—122no—
253Q8C2×#120311yescharacteristic
254D4—32no—
255D4—61no—
256D4—302no—
257D4—302no—
258D4—602no—
259C2×C4—31no—
260C2×C4—32no—
261C2×C4—32no—
262C2×C4—52no—
263C2×C4—62no—
264C2×C4—122no—
265C2×C4—152no—
266C2×C4—602no—
267C2×C4D5×S411yescharacteristic
268C8—62no—
269C8—302no—
270C2×C3—42no—
271C2×C3—41no—
272D3—802no—
273C5#8534711yescharacteristic, complemented, Sylow
274C22—32no—
275C22—62no—
276C22—604no—
277C22—602no—
278C22—1204no—
279C22C2×D5×S411yescharacteristic
280C4—31no—
281C4—31no—
282C4—102no—
283C4—122no—
284C4—302no—
285C4#9190212yes—
286C3—41noSylow
287C2—62no—
288C2—1202no—
289C2#1175678212yes—
290C2C2×#9190211yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×S4
commutator, cosocleC2×C5×SL(2,𝔽3)C23
FittingC2×C5×#41C2×D3
socleC22×C5C22×S4
prime radicalC2×#91956C2
hypercenterC2×C4D5×S4
hypocenterC5×SL(2,𝔽3)C2×D4
LCSG ▷ C2×C5×SL(2,𝔽3) ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C5×#984C2semidirect
3. Dic5×#41⋊C3C2semidirect
4. #11751604C2semidirect
10. C2×C5×#226C22semidirect
12. Dic5×SL(2,𝔽3)C22semidirect
15. #41×Dic5D3semidirect
32. C2×#984D5semidirect
71. C2×#226C2×D5semidirect
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×C5×#9842
Dic5×#41⋊C32
#117516042
#106156993
#913754
#853475