Finite Group Databasebeta

← #14513752

Subgroups — #14513752

Order 1920.

514 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C22×C5⋊#226C211yesmaximal, characteristic
2C5×#519⋊C3C211yesmaximal, characteristic
3#11752139C211yesmaximal, characteristic
4#11752107C212yesmaximal, complemented
5C4×C5⋊#226C212yesmaximal, complemented
6#10614280—31nomaximal, Hall
7C22×C5×SL(2,𝔽3)C2211yescharacteristic
8C2×C5⋊#226C414yescomplemented
9C2×C5⋊#226C2211yescharacteristic
10C2×C5⋊#226C2211yescharacteristic
11#91766—41nomaximal
12C4×C5×SL(2,𝔽3)C2212yes—
13#91184C2212yes—
14#85350—51nomaximal, Hall
15C5×#519D311yescharacteristic
16C22×#689—31no—
17#65850—31no—
18#65514—31no—
19#65319—32no—
20#65319—32no—
21C4×#689—32no—
22C4×#689—32no—
23#65293—31no—
24#65287—31no—
25#65286—31no—
26C22×Dic15—41no—
27C2×C5×SL(2,𝔽3)C2×C412yes—
28C2×C5×SL(2,𝔽3)C2311yescharacteristic
29C5⋊#226C2×C412yes—
30C5⋊#226C2×C412yes—
31C3×C5×C22⋊C4—41no—
32#6719—41no—
33#6712—42no—
34C4×Dic15—42no—
35C22×#226—51no—
36#519⋊C3D511yescharacteristic
37#5420—51no—
38#5388—52no—
39C4×#226—52no—
40C22×C5×Q8C2×D311yescharacteristic
41C22×Dic10—31no—
42C4×C5×Q8—32no—
43C4×C5×Q8C2×D312yes—
44C5×#117—31no—
45C5×#117—31no—
46C2×#689—31no—
47C2×#689—31no—
48C2×#689—34no—
49C2×#689—34no—
50C2×#689—31no—
51C2×#689—31no—
52#4072—31no—
53C2×#681—31no—
54C22×#168—31no—
55#4033—62no—
56#4023—61no—
57#4023—61no—
58C4×Dic10—32no—
59C4×Dic10—32no—
60#3967—32no—
61#3967—32no—
62#3942—32no—
63#3942—32no—
64#3940—32no—
65#3939—32no—
66#3935—32no—
67C4×#168—32no—
68#2950—151noSylow
69C23×C3×C5—41no—
70C2×C3×C4×C5—42no—
71C2×Dic15—44no—
72C2×Dic15—41no—
73C2×Dic15—41no—
74C2×Dic15—42no—
75C5×SL(2,𝔽3)C22×C411yescharacteristic
76C22×SL(2,𝔽3)C2×D511yescharacteristic
77C2×#226—54no—
78C2×#226—51no—
79C2×#226—51no—
80#877—201no—
81C4×SL(2,𝔽3)C2×D512yes—
82#859—52no—
83C2×C5×Q8—31no—
84C2×C5×Q8—32no—
85C2×C5×Q8C4×D312yes—
86C2×C5×Q8C22×D311yescharacteristic
87C22×C4×C5—31no—
88C22×Dic5—61no—
89C2×Dic10—31no—
90C2×Dic10—31no—
91C2×Dic10—34no—
92C2×Dic10—62no—
93C2×Dic10—61no—
94C5×C4⋊C4—32no—
95C5×C4⋊C4—32no—
96C5×C22⋊C4—31no—
97C5×C22⋊C4S411yescharacteristic
98C42×C5—32no—
99C42×C5—61no—
100C22⋊Dic5—61no—
101#689—34no—
102#689—34no—
103#689—32no—
104#689—32no—
105#689—32no—
106#689—32no—
107C4⋊Dic5—32no—
108#683—62no—
109#683—62no—
110C4×Dic5—62no—
111C4×Dic5—61no—
112C4×Dic5—62no—
113#681—62no—
114C2×#168—31no—
115C2×#168—31no—
116C2×#168—34no—
117C2×#168—32no—
118C22×Q16—151no—
119#519—151no—
120#519D1511yescharacteristic
121#441—152no—
122#441—152no—
123C4×Q16—152no—
124C4×Q16—152no—
125#427—151no—
126#419—151no—
127#419—151no—
128#405—151no—
129C22×C3×C5—42no—
130C22×C3×C5—41no—
131C22×C3×C5—82no—
132C3×C4×C5—82no—
133Dic15—42no—
134Dic15—42no—
135Dic15—82no—
136C22×Dic3—201no—
137C2×SL(2,𝔽3)C4×D512yes—
138C2×SL(2,𝔽3)C22×D511yescharacteristic
139#226—52no—
140#226—52no—
141C3×C22⋊C4—41no—
142#217—201no—
143Dic3⋊C4—202no—
144C4×Dic3—202no—
145C23×C5C2×S411yescharacteristic
146C5×Q8—32no—
147C5×Q8—31no—
148C5×Q8—61no—
149C5×Q8C2×C4×D311yescharacteristic
150C2×C4×C5—32no—
151C2×C4×C5—32no—
152C2×C4×C5—31no—
153C2×C4×C5—31no—
154C2×C4×C5—32no—
155C2×C4×C5C2×S412yes—
156C2×Dic5—64no—
157C2×Dic5—61no—
158C2×Dic5—61no—
159C2×Dic5—62no—
160Dic10—32no—
161Dic10—32no—
162Dic10—61no—
163Dic10—61no—
164Dic10—64no—
165#168—32no—
166#168—32no—
167#168—62no—
168C22×Q8—151no—
169C22×Q8C2×D1511yescharacteristic
170C2×Q16—151no—
171C2×Q16—151no—
172C2×Q16—154no—
173C2×Q16—154no—
174C2×Q16—151no—
175C2×Q16—151no—
176C2×M16—151no—
177C22×C8—151no—
178C4×Q8—32no—
179C4×Q8—152no—
180C4×Q8—152no—
181C4×Q8—302no—
182C4×Q8C2×D1512yes—
183#117—31no—
184#117—31no—
185#117—151no—
186#117—301no—
187#117—301no—
188#107—152no—
189#106—152no—
190#103—152no—
191#103—152no—
192#103—152no—
193#103—152no—
194#97—152no—
195C4×C8—152no—
196C2×C3×C5—41no—
197C2×C3×C5—42no—
198C2×C3×C5—82no—
199C23×C3—41no—
200C2×C3×C4—42no—
201C2×Dic3—201no—
202C2×Dic3—201no—
203C2×Dic3—204no—
204C2×Dic3—202no—
205SL(2,𝔽3)C2×C4×D511yescharacteristic
206C22×C5—22no—
207C22×C5C4×S412yes—
208C22×C5C22×S411yescharacteristic
209C4×C5—22no—
210C4×C5—31no—
211C4×C5—31no—
212C4×C5—32no—
213C4×C5—62no—
214Dic5—62no—
215Dic5—62no—
216Dic5—122no—
217C2×Q8—31no—
218C2×Q8—32no—
219C2×Q8—151no—
220C2×Q8—151no—
221C2×Q8—154no—
222C2×Q8—301no—
223C2×Q8—302no—
224C2×Q8C4×D1512yes—
225C2×Q8C22×D1511yescharacteristic
226C22×C4—31no—
227C22×C4—301no—
228Q16—154no—
229Q16—154no—
230Q16—152no—
231Q16—152no—
232Q16—152no—
233Q16—152no—
234M16—302no—
235C2×C8—151no—
236C2×C8—151no—
237C2×C8—154no—
238C2×C8—152no—
239C4⋊C4—32no—
240C4⋊C4—32no—
241C4⋊C4—152no—
242C4⋊C4—302no—
243C4⋊C4—302no—
244C22⋊C4—31no—
245C22⋊C4—301no—
246C22⋊C4C5⋊S411yescharacteristic
247C42—32no—
248C42—61no—
249C42—301no—
250C42—302no—
251C42—302no—
252C3×C5—41noHall
253C22×C3—42no—
254C22×C3—41no—
255C22×C3—82no—
256C3×C4—82no—
257Dic3—202no—
258Dic3—202no—
259Dic3—402no—
260C2×C5—22no—
261C2×C5C2×C4×S411yescharacteristic
262C2×C5#592712yes—
263C23C2×C5⋊S411yescharacteristic
264Q8—32no—
265Q8—31no—
266Q8—61no—
267Q8—152no—
268Q8—152no—
269Q8—301no—
270Q8—301no—
271Q8—304no—
272Q8C2×C4×D1511yescharacteristic
273C2×C4—32no—
274C2×C4—32no—
275C2×C4—31no—
276C2×C4—31no—
277C2×C4—32no—
278C2×C4—304no—
279C2×C4—301no—
280C2×C4—301no—
281C2×C4—302no—
282C2×C4C2×C5⋊S412yes—
283C8—152no—
284C8—152no—
285C8—302no—
286C2×C3—41no—
287C2×C3—42no—
288C2×C3—82no—
289C5#8535011yescharacteristic, complemented, Sylow
290C22—22no—
291C22C4×C5⋊S412yes—
292C22C22×C5⋊S411yescharacteristic
293C4—22no—
294C4—31no—
295C4—31no—
296C4—32no—
297C4—62no—
298C4—302no—
299C4—302no—
300C4—602no—
301C3—41noSylow
302C2—22no—
303C2C2×C4×C5⋊S411yescharacteristic
304C2#1175691112yes—
subgroupG/H
center, FrattiniC22C22×C5⋊S4
commutator, hypocenterC5×SL(2,𝔽3)C22×C4
FittingC5×#519D3
socleC22×C5C22×S4
prime radicalC22×C5×SL(2,𝔽3)C22
cosocleC2×C5×SL(2,𝔽3)C23
hypercenterC22⋊C4C5⋊S4
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
4. #11752107C2semidirect
5. C4×C5⋊#226C2semidirect
8. C2×C5⋊#226C4semidirect
289. C5#85350semidirect

Maximal subgroups

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

subgroupindex
C22×C5⋊#2262
C5×#519⋊C32
#117521392
#117521072
C4×C5⋊#2262
#106142803
#917664
#853505