Finite Group Databasebeta

← #14513438

Subgroups — #14513438

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×#91954C211yesmaximal, characteristic, complemented
2C2×C5×#986C211yesmaximal, characteristic
3Dic5×#41⋊C3C211yesmaximal, characteristic, complemented
4#11751601C214yesmaximal, complemented
5#10615664—31nomaximal, Hall
6C2×C5×#41⋊C3C2211yescharacteristic
7#91954—22no—
8C2×C5⋊#226C2212yescomplemented
9C5×#986—22no—
10C2×C5×GL(2,𝔽3)C2212yes—
11#91373—41nomaximal
12Dic5×SL(2,𝔽3)C2212yescomplemented
13#85347—51nomaximal, Hall
14C2×C5×AGL(1,ℤ/8)—31no—
15#41×Dic5D311yescharacteristic, complemented
16C2×#4097—31no—
17C2×#4082—31no—
18#65504—31no—
19#65455—34no—
20#65442—34no—
21#65409—31no—
22#65407—31no—
23C2×Dic30—41no—
24C2×C5×D12—41no—
25C5×#41⋊C3D412yes—
26C2×C5×SL(2,𝔽3)C2311yescharacteristic
27C5⋊#226—22no—
28C5×GL(2,𝔽3)—22no—
29C3×C4×Dic5—41no—
30(C2×D3)⋊Dic5—44no—
31C2×#986D511yescharacteristic
32C2×#984—51no—
33C4×#41⋊C3—51no—
34#5395—54no—
35C2×C5×#41C2×D311yescharacteristic
36C22×C5×D4—31no—
37C22×Dic10—31no—
38C5×AGL(1,ℤ/8)—62no—
39C5×AGL(1,ℤ/8)—62no—
40C2×C5×SD16—32no—
41C2×C5×D8—32no—
42C2×C5×M16—31no—
43C2×C22⋊Dic5—62no—
44#4097—62no—
45#4097—62no—
46Q8×Dic5C2×D312yes—
47C2×#689—32no—
48#4082—34no—
49#4082—61no—
50#4082—61no—
51D4×Dic5—32no—
52C2×#687—32no—
53#4072—31no—
54C2×C4×Dic5—31no—
55C2×#681—31no—
56#3964—34no—
57#3948—34no—
58#3946—34no—
59#3040—151noSylow
60C22×C5×D3—42no—
61C2×C3×C4×C5—41no—
62C2×Dic15—42no—
63Dic30—82no—
64C5×D12—82no—
65C2×C3×Dic5—42no—
66C5×SL(2,𝔽3)C2×D411yescharacteristic
67C2×#41⋊C3C2×D511yescharacteristic
68#986—22no—
69#984—102no—
70C2×GL(2,𝔽3)C2×D512yes—
71C2×#226—52no—
72#875—201no—
73C4×SL(2,𝔽3)—52no—
74C24×C5—61no—
75C5×#41—32no—
76C5×#41D1212yes—
77C2×C5×Q8C22×D311yescharacteristic
78C2×C5×D4—31no—
79C2×C5×D4—32no—
80C2×C5×D4—62no—
81C2×C5×D4—62no—
82C2×C5×D4—61no—
83C22×C4×C5—31no—
84C22×Dic5—32no—
85C22×Dic5—61no—
86C2×Dic10—32no—
87C2×Dic10—62no—
88C2×Dic10—62no—
89C2×Dic10—61no—
90C5×SD16—62no—
91C5×SD16—62no—
92C5×D8—64no—
93C5×M16—62no—
94C2×C5×C8—32no—
95C22⋊Dic5—61no—
96C22⋊Dic5—64no—
97C22⋊Dic5—64no—
98#689—62no—
99#689—62no—
100#687—64no—
101C4⋊Dic5—32no—
102C4×Dic5—31no—
103C4×Dic5—32no—
104C4×Dic5S411yescharacteristic
105#681—62no—
106C2×#168—32no—
107C2×#137—151no—
108C2×AGL(1,ℤ/8)—31no—
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×C5×D3—82no—
118C2×C5×D3—84no—
119C3×C4×C5—42no—
120Dic15—82no—
121C3×Dic5—82no—
122C2×D12—41no—
123C2×Dic6—201no—
124#41⋊C3C22⋊D512yes—
125C2×SL(2,𝔽3)C22×D511yescharacteristic
126GL(2,𝔽3)—22no—
127#226—102no—
128C3×C42—201no—
129(C2×D3)⋊C4—204no—
130C23×C5—31no—
131C23×C5—62no—
132C23×C5—122no—
133C23×C5—124no—
134C5×Q8—31no—
135C5×Q8C2×D1211yescharacteristic
136C5×D4—32no—
137C5×D4—61no—
138C5×D4—62no—
139C5×D4—62no—
140C5×D4—122no—
141C2×C4×C5—31no—
142C2×C4×C5—32no—
143C2×C4×C5—32no—
144C2×C4×C5C2×S411yescharacteristic
145C2×Dic5—32no—
146C2×Dic5—62no—
147C2×Dic5—122no—
148C2×Dic5—122no—
149C2×Dic5C2×S412yes—
150Dic10—62no—
151Dic10—62no—
152Dic10—122no—
153C5×C8—62no—
154#168—62no—
155C2×#41D3×D511yescharacteristic
156C22×Q8—151no—
157C22×D4—31no—
158#137—302no—
159#137—302no—
160AGL(1,ℤ/8)—62no—
161AGL(1,ℤ/8)—62no—
162C2×Q16—152no—
163C2×SD16—32no—
164C2×SD16—152no—
165C2×D8—32no—
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—
181C5×D3—162no—
182C22×D3—42no—
183C2×C3×C4—41no—
184C2×C3×C4—202no—
185C2×Dic3—202no—
186D12—82no—
187Dic6—402no—
188SL(2,𝔽3)C2×C22⋊D511yescharacteristic
189C22×C5—32no—
190C22×C5—62no—
191C22×C5—122no—
192C22×C5—124no—
193C22×C5—244no—
194C22×C5C22×S411yescharacteristic
195C4×C5—31no—
196C4×C5—31no—
197C4×C5C4⋊S412yes—
198Dic5—22no—
199Dic5—62no—
200Dic5—122no—
201C24—61no—
202#41—32no—
203#41#120312yes—
204C2×Q8—152no—
205C2×Q8—302no—
206C2×Q8—302no—
207C2×Q8—301no—
208C2×Q8C2×D3×D511yescharacteristic
209C2×D4—31no—
210C2×D4—32no—
211C2×D4—62no—
212C2×D4—62no—
213C2×D4—61no—
214C22×C4—31no—
215C22×C4—152no—
216C22×C4—301no—
217Q16—302no—
218Q16—302no—
219SD16—62no—
220SD16—62no—
221SD16—304no—
222D8—64no—
223M16—62no—
224M16—302no—
225C2×C8—32no—
226C2×C8—152no—
227C4⋊C4—152no—
228C22⋊C4—304no—
229C22⋊C4—301no—
230C22⋊C4—304no—
231C42—51no—
232C42—152no—
233C42—151no—
234C3×C5—41noHall
235C22×C3—41no—
236C2×D3—82no—
237C2×D3—84no—
238C3×C4—42no—
239C3×C4—402no—
240Dic3—402no—
241C2×C5—62no—
242C2×C5—242no—
243C2×C5C2×C4⋊S411yescharacteristic
244C2×C5#592312yes—
245C23—31no—
246C23—62no—
247C23—122no—
248C23—124no—
249Q8—31no—
250Q8—302no—
251Q8—302no—
252Q8—602no—
253Q8C2×#120311yescharacteristic
254D4—32no—
255D4—61no—
256D4—62no—
257D4—62no—
258D4—122no—
259C2×C4—31no—
260C2×C4—32no—
261C2×C4—32no—
262C2×C4—52no—
263C2×C4—152no—
264C2×C4—302no—
265C2×C4—602no—
266C2×C4—602no—
267C2×C4D5×S411yescharacteristic
268C8—62no—
269C8—302no—
270C2×C3—42no—
271C2×C3—41no—
272D3—162no—
273C5#8534711yescharacteristic, complemented, Sylow
274C22—32no—
275C22—62no—
276C22—124no—
277C22—122no—
278C22—244no—
279C22C2×D5×S411yescharacteristic
280C4—31no—
281C4—31no—
282C4—102no—
283C4—302no—
284C4—602no—
285C4#9190212yes—
286C3—41noSylow
287C2—62no—
288C2—242no—
289C2#1175678112yes—
290C2C2×#9190211yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×S4
commutator, cosocleC2×C5×SL(2,𝔽3)C23
FittingC2×C5×#41C2×D3
socleC22×C5C22×S4
prime radicalC2×C5×#986C2
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
1. C2×#91954C2semidirect
3. Dic5×#41⋊C3C2semidirect
4. #11751601C2semidirect
8. C2×C5⋊#226C22semidirect
12. Dic5×SL(2,𝔽3)C22semidirect
15. #41×Dic5D3semidirect
273. C5#85347semidirect

Maximal subgroups

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

subgroupindex
C2×#919542
C2×C5×#9862
Dic5×#41⋊C32
#117516012
#106156643
#913734
#853475