Finite Group Databasebeta

← #14316366

Subgroups — #14316366

Order 1920.

432 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C3×#66082C211yesmaximal, characteristic
2#11751238C211yesmaximal, characteristic, complemented
3#11747554C212yesmaximal, complemented
4C5×#4553C211yesmaximal, characteristic, complemented
5#11745910C212yesmaximal, complemented
6#10599914—31nomaximal, Hall
7C2×C3×#709—21no—
8C2×C3×C5×M16C2211yescharacteristic
9#91813—21no—
10C2×Dic60C2211yescharacteristic, complemented
11C3×#4055—22no—
12C3×#4054—22no—
13C3×#4050—21no—
14C3×#4050C2212yes—
15#91101C2211yescharacteristic, complemented
16#91100—21no—
17C5×#812C2212yescomplemented
18#90947—22no—
19#90942—22no—
20#72113—51nomaximal, Hall
21#66082D311yescharacteristic
22#65426—31no—
23#65198—32no—
24C5×#349—31no—
25#64738—32no—
26C22×C3×C4×C5D411yescharacteristic
27C2×Dic30—21no—
28C2×C3×C22⋊D5—41no—
29C3×#709—22no—
30C3×#709—22no—
31C3×#709—41no—
32C3×#709—41no—
33C2×C3×D20—21no—
34C2×C3×C4×D5—41no—
35C2×C3×Dic10—21no—
36C3×C5×M16—22no—
37C2×C3×C5×C8D411yescharacteristic
38C2×C3×C5×C8C2311yescharacteristic
39#6719—41no—
40C4⋊Dic15—21no—
41#6712—41no—
42Dic60—22no—
43C3×Dic20—21no—
44C3×Dic20D412yes—
45C3×D40—21no—
46C3×D40D412yes—
47C3×#677—22no—
48C3×#677—22no—
49C5×C3⋊C16—22no—
50C3×#575—51no—
51#5195—52no—
52#5137—51no—
53#4566—52no—
54#4553D511yescharacteristic, complemented
55C2×#709—21no—
56C2×C5×M16C2×D311yescharacteristic
57#4070—61no—
58#4055—22no—
59#4054—22no—
60C2×Dic20—31no—
61#4050—21no—
62#4050C2×D312yes—
63C5×M32—32no—
64#3949—31no—
65#3948—61no—
66Dic40—62no—
67#3932—62no—
68#2191—151noSylow
69C23×C3×C5D811yescharacteristic
70C22×C3×D5—41no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5D811yescharacteristic
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×Dic15—41no—
76C2×Dic15—41no—
77Dic30—41no—
78Dic30—41no—
79C3×C22⋊D5—42no—
80C3×C22⋊D5—42no—
81C2×C3×Dic5—41no—
82C3×D20—22no—
83C3×D20—41no—
84C3×C4×D5—42no—
85C3×C4×D5—42no—
86C3×Dic10—22no—
87C3×Dic10—41no—
88C3×C5×C8—21no—
89C3×C5×C8C2×D412yes—
90C2×C3×#41—101no—
91C3×#137—102no—
92C3×AGL(1,ℤ/8)—102no—
93C3×#135—52no—
94C3×#135—101no—
95C2×C3×M16C2×D511yescharacteristic
96#924—101no—
97C2×Dic12—51no—
98#829—102no—
99#827—102no—
100#817—51no—
101#816—101no—
102#812C2×D512yescomplemented
103C22×C4×C5#6711yescharacteristic
104C2×C22⋊D5—41no—
105#709—22no—
106#709—22no—
107#709—41no—
108#709—41no—
109C2×D20—21no—
110C2×C4×D5—41no—
111C2×Dic10—21no—
112C2×Dic10—61no—
113C5×M16—22no—
114C2×C5×C8#6711yescharacteristic
115C2×C5×C8C22×D311yescharacteristic
116C22⋊Dic5—121no—
117C4⋊Dic5—61no—
118#683—121no—
119Dic20—21no—
120Dic20—62no—
121Dic20#6712yes—
122D40—21no—
123D40#6712yes—
124#677—22no—
125#677—22no—
126C5×C16—62no—
127#575—51no—
128#510—152no—
129#470—151no—
130#360—152no—
131#349—31no—
132C22×C3×C5—21no—
133C22×C3×C5—41no—
134C22×C3×C5C2×D811yescharacteristic
135C2×C3×D5—42no—
136C2×C3×D5—82no—
137C3×C4×C5—21no—
138C3×C4×C5#12011yescharacteristic
139C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
140Dic15—81no—
141Dic15—81no—
142C3×Dic5—42no—
143C3×#41—102no—
144C3×#41—102no—
145C3×#41—201no—
146C3×#41—201no—
147C2×C3×Q8—101no—
148C2×C3×D4—101no—
149C2×C3×D4—201no—
150C22×C3×C4—201no—
151C22×C3×C4D2011yescharacteristic
152C2×Dic6—101no—
153C3×Q16—52no—
154C3×Q16—101no—
155C3×SD16—102no—
156C3×SD16—102no—
157C3×D8—52no—
158C3×D8—101no—
159C3×M16—22no—
160C2×C3×C8D2011yescharacteristic
161C2×C3×C8C22×D511yescharacteristic
162#217—201no—
163C4⋊Dic3—101no—
164Dic3⋊C4—201no—
165Dic12—102no—
166C3⋊C16—22no—
167C23×C5#21311yescharacteristic
168C22×D5—41no—
169C2×C4×C5—21no—
170C2×C4×C5—21no—
171C2×C4×C5#21311yescharacteristic
172C2×C4×C5C2×#6711yescharacteristic
173C22⋊D5—42no—
174C22⋊D5—42no—
175C2×Dic5—41no—
176C2×Dic5—121no—
177C2×Dic5—121no—
178D20—22no—
179D20—41no—
180C4×D5—42no—
181C4×D5—42no—
182Dic10—22no—
183Dic10—41no—
184Dic10—121no—
185Dic10—121no—
186C5×C8—21no—
187C5×C8C2×#6712yes—
188C2×#41—101no—
189#137—102no—
190AGL(1,ℤ/8)—102no—
191#135—52no—
192#135—101no—
193C2×Q16—151no—
194C2×M16D3×D511yescharacteristic
195C22⋊Q8—301no—
196Q32—302no—
197SD32—302no—
198M32—32no—
199#106—151no—
200#103—301no—
201C2×C3×C5—21no—
202C2×C3×C5—41no—
203C2×C3×C5#44711yescharacteristic
204C3×D5—82no—
205C23×C3—201no—
206C23×C3D4011yescharacteristic
207C3×Q8—102no—
208C3×Q8—201no—
209C3×D4—102no—
210C3×D4—201no—
211C3×D4—202no—
212C3×D4—202no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—202no—
216C2×C3×C4—201no—
217C2×C3×C4—202no—
218C2×C3×C4D4011yescharacteristic
219C2×C3×C4C2×D2011yescharacteristic
220C2×Dic3—201no—
221C2×Dic3—201no—
222Dic6—201no—
223Dic6—201no—
224C3×C8—21no—
225C3×C8D4×D512yes—
226C22×C5—21no—
227C22×C5—41no—
228C22×C5C2×#21311yescharacteristic
229C2×D5—42no—
230C2×D5—82no—
231C4×C5—21no—
232C4×C5#93211yescharacteristic
233C4×C5#95311yescharacteristic
234Dic5—42no—
235Dic5—241no—
236Dic5—241no—
237#41—102no—
238#41—102no—
239#41—201no—
240#41—201no—
241C2×Q8—101no—
242C2×Q8—301no—
243C2×D4—101no—
244C2×D4—201no—
245C22×C4—201no—
246C22×C4#120211yescharacteristic
247Q16—52no—
248Q16—101no—
249Q16—302no—
250SD16—102no—
251SD16—102no—
252D8—52no—
253D8—101no—
254M16—22no—
255C2×C8#120211yescharacteristic
256C2×C8C2×D3×D511yescharacteristic
257C4⋊C4—301no—
258C4⋊C4—601no—
259C22⋊C4—601no—
260C16—62no—
261C3×C5#219111yescharacteristic, complemented, Hall
262C22×C3—21no—
263C22×C3—41no—
264C22×C3—202no—
265C22×C3—402no—
266C22×C3C2×D4011yescharacteristic
267C3×C4—21no—
268C3×C4—202no—
269C3×C4#402811yescharacteristic
270C3×C4#405411yescharacteristic
271Dic3—401no—
272Dic3—401no—
273C2×C5—21no—
274C2×C5—41no—
275C2×C5#521711yescharacteristic
276D5—82no—
277C23—201no—
278C23#665311yescharacteristic
279Q8—102no—
280Q8—201no—
281Q8—601no—
282Q8—601no—
283D4—102no—
284D4—201no—
285D4—202no—
286D4—202no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—202no—
290C2×C4—201no—
291C2×C4—202no—
292C2×C4—601no—
293C2×C4—601no—
294C2×C4#665311yescharacteristic
295C2×C4C2×#120211yescharacteristic
296C8—21no—
297C8D5×#6712yes—
298C2×C3—21no—
299C2×C3—41no—
300C2×C3—402no—
301C2×C3#6502111yescharacteristic
302C5#7211311yescharacteristic, complemented, Sylow
303C22—21no—
304C22—41no—
305C22—202no—
306C22—402no—
307C22C2×#665311yescharacteristic
308C4—21no—
309C4—202no—
310C4—1201no—
311C4—1201no—
312C4#9131211yescharacteristic
313C4#9156411yescharacteristic
314C3#1059991411yescharacteristic, complemented, Sylow
315C2—21no—
316C2—41no—
317C2—402no—
318C2#1174851211yescharacteristic
subgroupG/H
centerC2#11748512
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#447
prime radicalC3×#66082C2
hypercenterC2×M16D3×D5
hypocenterC3×C5#2191
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11751238C2semidirect
3. #11747554C2semidirect
4. C5×#4553C2semidirect
5. #11745910C2semidirect
10. C2×Dic60C22semidirect
15. #91101C22semidirect
17. C5×#812C22semidirect
54. #4553D5semidirect
102. #812C2×D5semidirect
261. C3×C5#2191semidirect
302. C5#72113semidirect
314. C3#10599914semidirect

Maximal subgroups

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

subgroupindex
C3×#660822
#117512382
#117475542
C5×#45532
#117459102
#105999143
#721135