Finite Group Databasebeta

← #14513531

Subgroups — #14513531

Order 1920.

638 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 83 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×#4150⋊C3C211yesmaximal, characteristic
2#11752145C211yesmaximal, characteristic, complemented
3C5×#5424C211yesmaximal, characteristic, complemented
4D5×#859C212yesmaximal, complemented
5#11751605C212yesmaximal, complemented
6#10610563—31nomaximal, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8#4150⋊C3C414yescomplemented
9C2×D5×SL(2,𝔽3)C2212yes—
10Dic3×D20—41nomaximal
11#91184C2212yes—
12C5×#859C2211yescharacteristic
13C5×#859C2211yescharacteristic
14#85534—51nomaximal, Hall
15C2×#4150D311yescharacteristic
16C2×#4047—31no—
17#65857—31no—
18C5×#416—31no—
19#65521—31no—
20C2×#3948—31no—
21#65293—31no—
22#65091—32no—
23D5×#103—32no—
24#65061—32no—
25#65060—32no—
26C2×C3×D20—41no—
27C5×#41⋊C3C2×C412yescomplemented
28C2×C5×SL(2,𝔽3)C2311yescharacteristic
29C2×D5×Dic3—42no—
30D5×SL(2,𝔽3)C2×C414yescomplemented
31C4⋊Dic15—41no—
32C4×C5×Dic3—41no—
33#6665—42no—
34C2×2−1+4⋊C3—51no—
35#5426—51no—
36#5424D511yescharacteristic, complemented
37#5420—52no—
38C2×#859—52no—
39C2×C5×#41C2×D311yescharacteristic
40#4150—34no—
41#4150Dic314yescomplemented
42C2×Q8×D5C2×D312yes—
43C2×#711—32no—
44C2×#709—31no—
45C22×Dic10—31no—
46C22×C5×C8—31no—
47C5×#117—31no—
48C2×C4⋊Dic5—31no—
49C2×#681—31no—
50#4047—64no—
51C2×#676—32no—
52C2×C8×D5—32no—
53#4038—32no—
54D5×C4⋊C4—32no—
55#4027—62no—
56C4×D20—61no—
57C4×Dic10—61no—
58C5×#103—31no—
59C5×#103—31no—
60C5×#102—31no—
61C5×#102—31no—
62#3967—32no—
63#3964—32no—
64#3948—32no—
65#3948—32no—
66#3942—32no—
67#3942—32no—
68#2898—151noSylow
69C22×C3×D5—42no—
70C2×C3×C4×C5—41no—
71C2×Dic15—42no—
72C2×C5×Dic3—41no—
73C2×C5×Dic3—41no—
74C3×D20—44no—
75C5×SL(2,𝔽3)C22×C411yescharacteristic
76D5×Dic3—84no—
772−1+4⋊C3—54no—
78C2×#41⋊C3C2×D511yescharacteristic
79C22×SL(2,𝔽3)—52no—
80D4×Dic3—201no—
81#859—52no—
82#859C2×D511yescharacteristic
83#859C2×D511yescharacteristic
84C5×#41—32no—
85C5×#41C2×Dic312yescomplemented
86C2×C5×Q8C22×D311yescharacteristic
87C2×C5×D4—31no—
88C22×C4×C5—31no—
89C2×C22⋊D5—32no—
90C22×Dic5—61no—
91C22×Dic5—61no—
92Q8×D5—34no—
93Q8×D5C2×Dic314yescomplemented
94#711—38no—
95#711—64no—
96#709—34no—
97#709—34no—
98C2×D20S411yescharacteristic
99C2×C4×D5—32no—
100C2×C4×D5—62no—
101C2×Dic10—31no—
102C2×Dic10—34no—
103C2×Dic10—32no—
104C2×Dic10—62no—
105C2×C5×C8—31no—
106C2×C5×C8—31no—
107C2×C5×C8—62no—
108C5×C4⋊C4—31no—
109C5×C4⋊C4—31no—
110C5×C22⋊C4—61no—
111C42×C5—61no—
112#685—62no—
113C4⋊Dic5—32no—
114C4⋊Dic5—61no—
115#683—62no—
116C4×Dic5—62no—
117#681—62no—
118C2×#168—32no—
119#676—64no—
120C8×D5—64no—
121C2×2−1+4—51no—
122C2×#131—151no—
123#520—151no—
124#419—152no—
125#419—151no—
126#417—152no—
127#417—151no—
128#416—31no—
129#416—152no—
130C2×#103—152no—
131C2×#103—151no—
132C22×C3×C5—41no—
133C2×C3×D5—44no—
134C2×C3×D5—82no—
135C2×C3×D5—82no—
136C3×C4×C5—42no—
137Dic15—82no—
138C5×Dic3—42no—
139C5×Dic3—81no—
140C2×C3×D4—201no—
141C22×Dic3—202no—
142#41⋊C3C4×D512yescomplemented
143C2×SL(2,𝔽3)—54no—
144C2×SL(2,𝔽3)C22×D511yescharacteristic
145#217—202no—
146C4⋊Dic3—201no—
147C4×Dic3—41no—
148C23×C5—31no—
149C22×D5C2×S412yes—
150C5×Q8—31no—
151C5×Q8C22×Dic311yescharacteristic
152C5×D4—32no—
153C5×D4—61no—
154C2×C4×C5—31no—
155C2×C4×C5—32no—
156C2×C4×C5—32no—
157C2×C4×C5—61no—
158C2×C4×C5—61no—
159C2×C4×C5C2×S411yescharacteristic
160C22⋊D5—38no—
161C2×Dic5—32no—
162C2×Dic5—64no—
163C2×Dic5—62no—
164C2×Dic5—241no—
165D20SL(2,ℤ/4)14yes—
166C4×D5—34no—
167C4×D5—34no—
168C4×D5—242no—
169Dic10—34no—
170Dic10—34no—
171Dic10—62no—
172C5×C8—61no—
173C5×C8—61no—
174#168—62no—
1752−1+4—54no—
1762−1+4—154no—
177C2×#41—151no—
178C2×#41—152no—
179C2×#41D3×D511yescharacteristic
180C22×Q8—52no—
181C22×Q8—151no—
182#131—304no—
183C2×M16—152no—
184C2×M16—151no—
185C22×C8—31no—
186C22×C8—152no—
187C4×Q8—301no—
188C4×D4—301no—
189C4×D4—302no—
190#117—31no—
191#117—152no—
192C2×C4⋊C4—152no—
193C2×C4⋊C4—151no—
194#103—31no—
195#103—31no—
196#103—152no—
197#103—152no—
198#103—152no—
199#103—152no—
200#103—152no—
201#102—31no—
202#102—31no—
203#102—152no—
204C2×C3×C5—41no—
205C2×C3×C5—41no—
206C2×C3×C5—41no—
207C3×D5—84no—
208C23×C3—202no—
209C3×D4—204no—
210C2×C3×C4—41no—
211C2×Dic3—41no—
212C2×Dic3—41no—
213C2×Dic3—202no—
214C2×Dic3—404no—
215SL(2,𝔽3)C2×C4×D511yescharacteristic
216C22×C5—32no—
217C22×C5—61no—
218C22×C5—61no—
219C22×C5C22×S411yescharacteristic
220C2×D5—22no—
221C2×D5—22no—
222C2×D5C2×SL(2,ℤ/4)14yes—
223C4×C5—31no—
224C4×C5—31no—
225C4×C5—121no—
226C4×C5—121no—
227C4×C5C2×SL(2,ℤ/4)12yes—
228Dic5—34no—
229Dic5—122no—
230#41—32no—
231#41—154no—
232#41—154no—
233#41—158no—
234#41—304no—
235#41D5×Dic312yescomplemented
236C2×Q8—54no—
237C2×Q8—152no—
238C2×Q8—154no—
239C2×Q8—151no—
240C2×Q8—154no—
241C2×Q8—302no—
242C2×Q8C2×D3×D511yescharacteristic
243C2×D4—31no—
244C2×D4—51no—
245C2×D4—152no—
246C22×C4—31no—
247C22×C4—152no—
248C22×C4—302no—
249C22×C4—301no—
250C22×C4—301no—
251M16—304no—
252M16—302no—
253C2×C8—31no—
254C2×C8—31no—
255C2×C8—62no—
256C2×C8—152no—
257C2×C8—304no—
258C4⋊C4—31no—
259C4⋊C4—31no—
260C4⋊C4—152no—
261C4⋊C4—302no—
262C4⋊C4—301no—
263C22⋊C4—61no—
264C22⋊C4—302no—
265C42—61no—
266C42—302no—
267C3×C5—41noHall
268C22×C3—41no—
269C22×C3—204no—
270C22×C3—402no—
271C22×C3—402no—
272C3×C4—42no—
273Dic3—42no—
274Dic3—81no—
275Dic3—402no—
276C2×C5—62no—
277C2×C5#592611yescharacteristic
278C2×C5#592711yescharacteristic
279C2×C5C22×SL(2,ℤ/4)11yescharacteristic
280D5—24no—
281C23—31no—
282C23—52no—
283Q8—31no—
284Q8—154no—
285Q8—154no—
286Q8—302no—
287Q8C2×D5×Dic311yescharacteristic
288D4—32no—
289D4—54no—
290D4—61no—
291D4—158no—
292C2×C4—31no—
293C2×C4—32no—
294C2×C4—32no—
295C2×C4—61no—
296C2×C4—61no—
297C2×C4—154no—
298C2×C4—154no—
299C2×C4—152no—
300C2×C4—304no—
301C2×C4—302no—
302C2×C4—1202no—
303C2×C4—1201no—
304C2×C4D5×S411yescharacteristic
305C8—61no—
306C8—61no—
307C8—302no—
308C2×C3—41no—
309C2×C3—41no—
310C2×C3—41no—
311C2×C3—404no—
312C5#8553411yescharacteristic, complemented, Sylow
313C22—32no—
314C22—54no—
315C22—61no—
316C22—61no—
317C22—102no—
318C22—102no—
319C22C2×D5×S411yescharacteristic
320C4—31no—
321C4—31no—
322C4—121no—
323C4—121no—
324C4—154no—
325C4—602no—
326C4D5×SL(2,ℤ/4)12yes—
327C3—41noSylow
328C2—62no—
329C2—104no—
330C2#1175677811yescharacteristic
331C2#1175678511yescharacteristic
332C2C2×D5×SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×S4
commutator, hypocenterC5×SL(2,𝔽3)C22×C4
FittingC2×C5×#41C2×D3
socleC22×C5C22×S4
prime radicalC2×#4150⋊C3C2
cosocleC2×C5×SL(2,𝔽3)C23
hypercenterC2×C4D5×S4
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11752145C2semidirect
3. C5×#5424C2semidirect
4. D5×#859C2semidirect
5. #11751605C2semidirect
8. #4150⋊C3C4semidirect
27. C5×#41⋊C3C2×C4semidirect
30. D5×SL(2,𝔽3)C2×C4semidirect
36. #5424D5semidirect
41. #4150Dic3semidirect
85. C5×#41C2×Dic3semidirect
93. Q8×D5C2×Dic3semidirect
142. #41⋊C3C4×D5semidirect
235. #41D5×Dic3semidirect
312. C5#85534semidirect

Maximal subgroups

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

subgroupindex
C2×#4150⋊C32
#117521452
C5×#54242
D5×#8592
#117516052
#106105633
Dic3×D204
#855345