Finite Group Databasebeta

← #14513767

Subgroups — #14513767

Order 1920.

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

normal subgroups only

This group has 546 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
1C2×#91955C211yesmaximal, characteristic
2C5×#520⋊C3C211yesmaximal, characteristic, complemented
3#11752145C211yesmaximal, characteristic, complemented
4C4×C5⋊GL(2,𝔽3)C212yesmaximal, complemented
5#11752107C212yesmaximal, complemented
6#10614289—31nomaximal, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8#91955C414yescomplemented
9C2×C5⋊GL(2,𝔽3)C2211yescharacteristic
10C2×C5⋊#226C2211yescharacteristic
11C4⋊C4×D15—41nomaximal
12C4×C5×SL(2,𝔽3)C2212yes—
13#91184C2212yes—
14#85364—51nomaximal, Hall
15C5×#520D311yescharacteristic, complemented
16C2×#4096—31no—
17#65857—31no—
18#65521—31no—
19#65319—32no—
20C4×#688—32no—
21C4×#687—32no—
22#65303—32no—
23#65286—31no—
24#65255—31no—
25C2×#3940—31no—
26C2×C4×D15—41no—
27C2×C4×D15—42no—
28C5×#41⋊C3C2×C412yescomplemented
29C2×C5×SL(2,𝔽3)C2311yescharacteristic
30C5⋊GL(2,𝔽3)C2×C412yescomplemented
31C5⋊#226C2×C412yescomplemented
32C3×C5×C4⋊C4—41no—
33C4⋊Dic15—41no—
34#6712—42no—
35C2×#985—51no—
36#520⋊C3D511yescharacteristic, complemented
37#5426—51no—
38C4×GL(2,𝔽3)—52no—
39#5388—52no—
40C2×C5×#41C2×D311yescharacteristic
41C2×#709—31no—
42C4×C5×Q8C2×D312yes—
43C4×C5×D4—32no—
44C5×#117—31no—
45C2×C5×C4⋊C4—31no—
46#4096—34no—
47#4096—34no—
48C2×#689—31no—
49C2×#688—31no—
50C2×#687—31no—
51C2×#686—31no—
52C2×C4⋊Dic5—31no—
53C2×#681—31no—
54C22×#168—31no—
55#4038—61no—
56D5×C4⋊C4—61no—
57#4027—62no—
58C4×D20—32no—
59C4×Dic10—32no—
60#3967—32no—
61#3964—32no—
62#3942—32no—
63#3941—32no—
64#3940—32no—
65#3940—32no—
66#3935—32no—
67C4×#168—32no—
68#2952—151noSylow
69C22×D15—41no—
70C2×C3×C4×C5—41no—
71C2×C3×C4×C5—42no—
72C2×Dic15—41no—
73C2×Dic15—42no—
74C4×D15—44no—
75C4×D15—84no—
76C5×SL(2,𝔽3)C22×C411yescharacteristic
77C2×#41⋊C3C2×D511yescharacteristic
78#985—54no—
79C2×GL(2,𝔽3)—51no—
80C2×#226—51no—
81D3×C4⋊C4—201no—
82C4×SL(2,𝔽3)C2×D512yes—
83#859—52no—
84C5×#41—32no—
85C5×#41C4×D312yescomplemented
86C2×C5×Q8C22×D311yescharacteristic
87C2×C5×D4—31no—
88C22×C4×C5—31no—
89C22×C4×C5—61no—
90C2×C22⋊D5—61no—
91C22×Dic5—61no—
92#709—34no—
93#709—62no—
94C2×D20—31no—
95C2×C4×D5—61no—
96C2×C4×D5—62no—
97C2×Dic10—31no—
98C5×C4⋊C4—32no—
99C5×C4⋊C4—31no—
100C5×C4⋊C4S411yescharacteristic
101C5×C22⋊C4—32no—
102C42×C5—32no—
103#689—32no—
104#689—32no—
105#688—32no—
106#688—32no—
107#687—34no—
108#686—34no—
109#685—62no—
110C4⋊Dic5—32no—
111C4⋊Dic5—61no—
112#683—62no—
113C4×Dic5—62no—
114#681—62no—
115C2×#168—34no—
116C2×#168—31no—
117C2×#168—31no—
118C2×#168—32no—
119C2×#135—151no—
120#520—151no—
121#520D1511yescharacteristic, complemented
122#442—152no—
123#441—152no—
124C4×SD16—152no—
125C4×SD16—152no—
126C2×#106—151no—
127#417—151no—
128#417—151no—
129#405—151no—
130C22×C3×C5—41no—
131C2×D15—42no—
132C2×D15—42no—
133C2×D15—42no—
134C3×C4×C5—42no—
135C3×C4×C5—82no—
136Dic15—42no—
137Dic15—82no—
138C2×C4×D3—201no—
139C2×C4×D3—202no—
140#41⋊C3C4×D512yescomplemented
141C2×SL(2,𝔽3)C22×D511yescharacteristic
142GL(2,𝔽3)—52no—
143#226—52no—
144C3×C4⋊C4—41no—
145C4⋊Dic3—201no—
146Dic3⋊C4—202no—
147C23×C5—31no—
148C22×D5—61no—
149C5×Q8—31no—
150C5×Q8C2×C4×D311yescharacteristic
151C5×D4—32no—
152C5×D4—61no—
153C2×C4×C5—31no—
154C2×C4×C5—32no—
155C2×C4×C5—32no—
156C2×C4×C5—32no—
157C2×C4×C5—241no—
158C2×C4×C5C2×S412yes—
159C2×C4×C5C2×S411yescharacteristic
160C22⋊D5—64no—
161C2×Dic5—61no—
162C2×Dic5—62no—
163C2×Dic5—241no—
164D20—32no—
165D20—61no—
166C4×D5—64no—
167C4×D5—242no—
168Dic10—32no—
169Dic10—61no—
170#168—32no—
171#168—32no—
172#168—62no—
173C2×#41—151no—
174C2×#41C2×D1511yescharacteristic
175#135—154no—
176#135—154no—
177C2×Q16—151no—
178C2×SD16—151no—
179C2×SD16—151no—
180C2×D8—151no—
181C2×M16—151no—
182C22×C8—151no—
183C4×Q8—152no—
184C4×Q8C2×D1512yes—
185C4×D4—32no—
186C4×D4—152no—
187C4×D4—302no—
188#117—31no—
189#117—301no—
190C2×C4⋊C4—31no—
191C2×C4⋊C4—151no—
192C2×C4⋊C4—301no—
193#106—152no—
194#106—152no—
195#103—152no—
196#103—152no—
197#102—152no—
198#102—152no—
199#97—152no—
200C4×C8—152no—
201C2×C3×C5—41no—
202C2×C3×C5—41no—
203C2×C3×C5—41no—
204D15—44no—
205C22×D3—201no—
206C2×C3×C4—41no—
207C2×C3×C4—42no—
208C2×Dic3—201no—
209C2×Dic3—202no—
210C4×D3—204no—
211C4×D3—404no—
212SL(2,𝔽3)C2×C4×D511yescharacteristic
213C22×C5—32no—
214C22×C5—61no—
215C22×C5—61no—
216C22×C5C22×S411yescharacteristic
217C2×D5—62no—
218C2×D5—121no—
219C2×D5—121no—
220C4×C5—22no—
221C4×C5—31no—
222C4×C5—31no—
223C4×C5—62no—
224C4×C5C4×S412yes—
225Dic5—62no—
226Dic5—122no—
227#41—32no—
228#41—154no—
229#41—302no—
230#41C4×D1512yescomplemented
231C2×Q8—151no—
232C2×Q8C22×D1511yescharacteristic
233C2×D4—31no—
234C2×D4—151no—
235C2×D4—301no—
236C22×C4—31no—
237C22×C4—61no—
238C22×C4—301no—
239C22×C4—301no—
240C22×C4—302no—
241Q16—152no—
242Q16—152no—
243SD16—154no—
244SD16—152no—
245SD16—152no—
246D8—154no—
247M16—302no—
248C2×C8—151no—
249C2×C8—151no—
250C2×C8—154no—
251C2×C8—152no—
252C4⋊C4—32no—
253C4⋊C4—31no—
254C4⋊C4—152no—
255C4⋊C4—301no—
256C4⋊C4—302no—
257C4⋊C4C5⋊S411yescharacteristic
258C22⋊C4—32no—
259C22⋊C4—302no—
260C42—32no—
261C42—302no—
262C3×C5—41noHall
263C22×C3—41no—
264C2×D3—202no—
265C2×D3—202no—
266C2×D3—202no—
267C3×C4—42no—
268C3×C4—82no—
269Dic3—202no—
270Dic3—402no—
271C2×C5—62no—
272C2×C5C2×C4×S411yescharacteristic
273C2×C5#592411yescharacteristic
274C2×C5#592611yescharacteristic
275D5—122no—
276C23—31no—
277C23—301no—
278Q8—31no—
279Q8—152no—
280Q8—301no—
281Q8C2×C4×D1511yescharacteristic
282D4—32no—
283D4—61no—
284D4—152no—
285D4—301no—
286D4—304no—
287C2×C4—31no—
288C2×C4—32no—
289C2×C4—32no—
290C2×C4—32no—
291C2×C4—241no—
292C2×C4—301no—
293C2×C4—304no—
294C2×C4—302no—
295C2×C4—1202no—
296C2×C4—1201no—
297C2×C4C2×C5⋊S412yes—
298C2×C4C2×C5⋊S411yescharacteristic
299C8—152no—
300C8—152no—
301C8—302no—
302C2×C3—41no—
303C2×C3—41no—
304C2×C3—41no—
305D3—204no—
306C5#8536411yescharacteristic, complemented, Sylow
307C22—32no—
308C22—61no—
309C22—61no—
310C22—302no—
311C22—601no—
312C22—601no—
313C22C22×C5⋊S411yescharacteristic
314C4—22no—
315C4—31no—
316C4—31no—
317C4—62no—
318C4—302no—
319C4—602no—
320C4C4×C5⋊S412yes—
321C3—41noSylow
322C2—62no—
323C2—602no—
324C2C2×C4×C5⋊S411yescharacteristic
325C2#1175690811yescharacteristic
326C2#1175691011yescharacteristic
subgroupG/H
center, FrattiniC22C22×C5⋊S4
commutator, hypocenterC5×SL(2,𝔽3)C22×C4
FittingC5×#520D3
socleC22×C5C22×S4
prime radicalC2×#91955C2
cosocleC2×C5×SL(2,𝔽3)C23
hypercenterC4⋊C4C5⋊S4
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×#520⋊C3C2semidirect
3. #11752145C2semidirect
4. C4×C5⋊GL(2,𝔽3)C2semidirect
5. #11752107C2semidirect
8. #91955C4semidirect
15. C5×#520D3semidirect
28. C5×#41⋊C3C2×C4semidirect
30. C5⋊GL(2,𝔽3)C2×C4semidirect
31. C5⋊#226C2×C4semidirect
36. #520⋊C3D5semidirect
85. C5×#41C4×D3semidirect
121. #520D15semidirect
140. #41⋊C3C4×D5semidirect
230. #41C4×D15semidirect
306. C5#85364semidirect

Maximal subgroups

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

subgroupindex
C2×#919552
C5×#520⋊C32
#117521452
C4×C5⋊GL(2,𝔽3)2
#117521072
#106142893
C4⋊C4×D154
#853645