Finite Group Databasebeta

← #14513747

Subgroups — #14513747

Order 1920.

480 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C4×C5×#41⋊C3C211yesmaximal, characteristic, complemented
2#11752146C212yesmaximal, complemented
3C4⋊(C5⋊GL(2,𝔽3))C211yesmaximal, characteristic, complemented
4C4×C5⋊GL(2,𝔽3)C212yesmaximal, complemented
5#11752110C211yesmaximal, characteristic, complemented
6#10614260—31nomaximal, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8C2×C5⋊GL(2,𝔽3)C2212yes—
9C4×D60—41nomaximal
10C4×C5×SL(2,𝔽3)C2211yescharacteristic
11C4×C5×SL(2,𝔽3)C2211yescharacteristic
12#91184C2212yes—
13#85345—51nomaximal, Hall
14C4×C5×#41D311yescharacteristic, complemented
15#65811—31no—
16#65527—32no—
17#65316—31no—
18C4×#688—32no—
19#65310—31no—
20#65304—31no—
21C4×#686—32no—
22#65297—31no—
23#65292—32no—
24#65214—31no—
25C2×D60—41no—
26C2×C4×D15—42no—
27C5×#41⋊C3—21no—
28C2×C5×SL(2,𝔽3)C2311yescharacteristic
29C5⋊GL(2,𝔽3)—22no—
30C3×C42×C5—41no—
31#6714—42no—
32C4⋊Dic15—41no—
33C4×#41⋊C3D511yescharacteristic, complemented
34#5427—52no—
35C4⋊GL(2,𝔽3)—51no—
36C4×GL(2,𝔽3)—52no—
37#5391—51no—
38C2×C5×#41C2×D311yescharacteristic
39C2×#709—61no—
40C4×C5×Q8C2×D311yescharacteristic
41C4×C5×Q8C2×D311yescharacteristic
42C4×C5×D4—31no—
43C4×C5×D4—31no—
44C5×#117—31no—
45C2×C42×C5—31no—
46C2×#688—32no—
47C2×#686—32no—
48#4076—32no—
49#4076—61no—
50#4021—61no—
51#4020—31no—
52C4×D20—32no—
53C4×D20—61no—
54#4015—31no—
55#3967—32no—
56#3964—32no—
57C22⋊#168—32no—
58#3941—32no—
59#3941—32no—
60#3940—32no—
61#3939—32no—
62C4⋊#168—31no—
63C4⋊#168—31no—
64C4×#168—32no—
65#3106—151noSylow
66C22×D15—42no—
67C2×C3×C4×C5—41no—
68C2×C3×C4×C5—41no—
69C2×C3×C4×C5—41no—
70C2×Dic15—42no—
71D60—44no—
72C4×D15—84no—
73C5×SL(2,𝔽3)#4111yescharacteristic, complemented
74C2×#41⋊C3C2×D511yescharacteristic
75C2×GL(2,𝔽3)—52no—
76C4×D12—201no—
77C4×SL(2,𝔽3)C2×D511yescharacteristic
78C4×SL(2,𝔽3)C2×D511yescharacteristic
79#859—52no—
80C5×#41—21no—
81C5×#41—61no—
82C2×C5×Q8C22×D311yescharacteristic
83C2×C5×D4—31no—
84C22×C4×C5—31no—
85C22×C4×C5—31no—
86C22×C4×C5—31no—
87C2×C22⋊D5—62no—
88#709—124no—
89C2×D20—32no—
90C2×D20—61no—
91C2×D20—61no—
92C2×C4×D5—62no—
93C2×Dic10—61no—
94C5×C4⋊C4—31no—
95C5×C4⋊C4—31no—
96C5×C22⋊C4—61no—
97C42×C5—31no—
98C42×C5—31no—
99C42×C5—31no—
100C42×C5S411yescharacteristic
101#688—62no—
102#688—62no—
103#686—64no—
104#685—62no—
105#685—62no—
106C4⋊Dic5—32no—
107C4⋊Dic5—61no—
108C2×#168—32no—
109C2×#168—32no—
110#532—151no—
111C4×#41D1511yescharacteristic, complemented
112#482—152no—
113#477—151no—
114#476—151no—
115#460—151no—
116#459—151no—
117#449—152no—
118C4×SD16—152no—
119C4×D8—152no—
120#431—151no—
121C22×C3×C5—41no—
122C2×D15—44no—
123C2×D15—82no—
124C2×D15—82no—
125C3×C4×C5—42no—
126C3×C4×C5—42no—
127C3×C4×C5—81no—
128Dic15—82no—
129C2×D12—201no—
130C2×C4×D3—202no—
131#41⋊C3—21no—
132C2×SL(2,𝔽3)C22×D511yescharacteristic
133GL(2,𝔽3)—102no—
134C3×C42—41no—
135(C2×D3)⋊C4—202no—
136C4⋊Dic3—201no—
137C23×C5—31no—
138C22×D5—62no—
139C5×Q8—31no—
140C5×Q8#23511yescharacteristic
141C5×D4—32no—
142C5×D4—61no—
143C2×C4×C5—31no—
144C2×C4×C5—31no—
145C2×C4×C5—31no—
146C2×C4×C5—61no—
147C2×C4×C5—61no—
148C2×C4×C5—62no—
149C2×C4×C5—62no—
150C2×C4×C5C2×S411yescharacteristic
151C2×C4×C5C2×S411yescharacteristic
152C2×C4×C5C2×S411yescharacteristic
153C22⋊D5—124no—
154C2×Dic5—62no—
155D20—62no—
156D20—62no—
157D20—122no—
158D20—122no—
159C4×D5—124no—
160Dic10—122no—
161#168—62no—
162#168—62no—
163C2×#41—301no—
164C2×#41C2×D1511yescharacteristic
165C2×SD16—152no—
166C2×D8—152no—
167C4⋊Q8—151no—
168#127—151no—
169#124—301no—
170#121—152no—
171#121—301no—
172C4×Q8C2×D1511yescharacteristic
173C4×Q8C2×D1511yescharacteristic
174C4×D4—31no—
175C4×D4—31no—
176C4×D4—152no—
177C4×D4—301no—
178#117—31no—
179C2×C42—31no—
180#107—152no—
181#106—152no—
182C4⋊C8—151no—
183C4⋊C8—151no—
184#103—152no—
185#102—152no—
186#102—152no—
187#102—152no—
188C22⋊C8—152no—
189C4×C8—152no—
190C2×C3×C5—41no—
191C2×C3×C5—41no—
192C2×C3×C5—41no—
193D15—84no—
194C22×D3—202no—
195C2×C3×C4—41no—
196C2×C3×C4—41no—
197C2×C3×C4—41no—
198C2×Dic3—202no—
199D12—204no—
200C4×D3—404no—
201SL(2,𝔽3)#70911yescharacteristic, complemented
202C22×C5—61no—
203C22×C5—61no—
204C22×C5—61no—
205C22×C5C22×S411yescharacteristic
206C2×D5—122no—
207C2×D5—122no—
208C2×D5—122no—
209C4×C5—21no—
210C4×C5—31no—
211C4×C5—31no—
212C4×C5—61no—
213C4×C5—61no—
214C4×C5#98512yes—
215C4×C5#98612yes—
216Dic5—122no—
217#41—21no—
218#41—61no—
219#41—604no—
220C2×Q8—301no—
221C2×Q8C22×D1511yescharacteristic
222C2×D4—31no—
223C2×D4—152no—
224C2×D4—301no—
225C2×D4—302no—
226C2×D4—301no—
227C22×C4—31no—
228C22×C4—31no—
229C22×C4—31no—
230C22×C4—302no—
231SD16—302no—
232SD16—302no—
233D8—304no—
234C2×C8—152no—
235C2×C8—152no—
236C4⋊C4—31no—
237C4⋊C4—31no—
238C4⋊C4—152no—
239C4⋊C4—301no—
240C22⋊C4—61no—
241C22⋊C4—302no—
242C22⋊C4—302no—
243C42—31no—
244C42—31no—
245C42—31no—
246C42C5⋊S411yescharacteristic
247C3×C5—41noHall
248C22×C3—41no—
249C2×D3—204no—
250C2×D3—402no—
251C2×D3—402no—
252C3×C4—42no—
253C3×C4—42no—
254C3×C4—81no—
255Dic3—402no—
256C2×C5—121no—
257C2×C5#591211yescharacteristic
258C2×C5C2×#98511yescharacteristic
259C2×C5C2×#98611yescharacteristic
260D5—242no—
261C23—31no—
262C23—302no—
263Q8—31no—
264Q8—602no—
265Q8#681711yescharacteristic
266D4—32no—
267D4—61no—
268D4—302no—
269D4—302no—
270D4—602no—
271D4—604no—
272D4—602no—
273C2×C4—31no—
274C2×C4—31no—
275C2×C4—31no—
276C2×C4—61no—
277C2×C4—61no—
278C2×C4—62no—
279C2×C4—62no—
280C2×C4—302no—
281C2×C4—604no—
282C2×C4C2×C5⋊S411yescharacteristic
283C2×C4C2×C5⋊S411yescharacteristic
284C2×C4C2×C5⋊S411yescharacteristic
285C8—302no—
286C8—302no—
287C2×C3—41no—
288C2×C3—41no—
289C2×C3—41no—
290D3—404no—
291C5#8534511yescharacteristic, complemented, Sylow
292C22—61no—
293C22—61no—
294C22—61no—
295C22—602no—
296C22—602no—
297C22—602no—
298C22C22×C5⋊S411yescharacteristic
299C4—21no—
300C4—31no—
301C4—31no—
302C4—61no—
303C4—61no—
304C4—602no—
305C4#9195512yes—
306C4#9195612yes—
307C3—41noSylow
308C2—121no—
309C2—1202no—
310C2#1175689611yescharacteristic
311C2C2×#9195511yescharacteristic
312C2C2×#9195611yescharacteristic
subgroupG/H
centerC2×C4C2×C5⋊S4
commutator, cosocleC2×C5×SL(2,𝔽3)C23
FrattiniC22C22×C5⋊S4
FittingC4×C5×#41D3
socleC22×C5C22×S4
hypercenterC42C5⋊S4
hypocenterC5×SL(2,𝔽3)#41
LCSG ▷ C2×C5×SL(2,𝔽3) ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×C5×#41⋊C3C2semidirect
2. #11752146C2semidirect
3. C4⋊(C5⋊GL(2,𝔽3))C2semidirect
4. C4×C5⋊GL(2,𝔽3)C2semidirect
5. #11752110C2semidirect
14. C4×C5×#41D3semidirect
33. C4×#41⋊C3D5semidirect
73. C5×SL(2,𝔽3)#41semidirect
111. C4×#41D15semidirect
201. SL(2,𝔽3)#709semidirect
291. C5#85345semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#41⋊C32
#117521462
C4⋊(C5⋊GL(2,𝔽3))2
C4×C5⋊GL(2,𝔽3)2
#117521102
#106142603
C4×D604
#853455