Finite Group Databasebeta

← #14316351

Subgroups — #14316351

Order 1920.

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

normal subgroups only

This group has 432 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
1#11756507C211yesmaximal, characteristic
2#11751238C211yesmaximal, characteristic, complemented
3#11751010C212yesmaximal, complemented
4C3×C5×#349C211yesmaximal, characteristic, complemented
5#11746339C212yesmaximal, complemented
6#10599914—31nomaximal, Hall
7C2×#6817—21no—
8C2×C3×C5×M16C2211yescharacteristic
9#91813—21no—
10#91798—22no—
11#91797—22no—
12C2×Dic60C2211yescharacteristic, complemented
13#91793—21no—
14#91793C2212yes—
15C3×C5×M32C2212yescomplemented
16#91101C2211yescharacteristic, complemented
17#91100—21no—
18Dic120—22no—
19#91084—22no—
20#69121—51nomaximal, Hall
21#66082—31no—
22#65426—31no—
23#65198—32no—
24C5×#349D311yescharacteristic, complemented
25#64738—32no—
26C22×C3×C4×C5D411yescharacteristic
27C2×#1220—41no—
28#6817—22no—
29#6817—22no—
30#6817—41no—
31#6817—41no—
32C2×D60—21no—
33C2×C4×D15—41no—
34C2×Dic30—21no—
35C2×Dic30—21no—
36C3×C5×M16—22no—
37C2×C3×C5×C8D411yescharacteristic
38C2×C3×C5×C8C2311yescharacteristic
39#6719—41no—
40C4⋊Dic15—21no—
41#6712—41no—
42Dic60—21no—
43Dic60—22no—
44Dic60D412yes—
45D120—21no—
46D120D412yes—
47#6706—22no—
48#6706—22no—
49C3×C5×C16—22no—
50#5748—51no—
51#5137—51no—
52#4909—52no—
53C3×#349D511yescharacteristic, complemented
54#4518—52no—
55C2×#709—61no—
56C2×C5×M16C2×D311yescharacteristic
57#4070—61no—
58#4055—62no—
59#4054—62no—
60C2×Dic20—31no—
61#4050—32no—
62#4050—61no—
63C5×M32C2×D312yescomplemented
64#3949—31no—
65#3948—61no—
66Dic40—62no—
67#3932—62no—
68#2191—151noSylow
69C23×C3×C5D811yescharacteristic
70C22×D15—41no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5D811yescharacteristic
74C2×C3×C4×C5C2×D411yescharacteristic
75#1220—42no—
76#1220—42no—
77C2×Dic15—41no—
78C2×Dic15—41no—
79C2×Dic15—41no—
80D60—22no—
81D60—41no—
82C4×D15—42no—
83C4×D15—42no—
84Dic30—22no—
85Dic30—41no—
86Dic30—41no—
87Dic30—41no—
88C3×C5×C8—21no—
89C3×C5×C8C2×D412yes—
90C2×#235—101no—
91C2×C3×M16C2×D511yescharacteristic
92#924—101no—
93#909—102no—
94#908—102no—
95C2×Dic12—51no—
96#904—52no—
97#904—101no—
98C3×M32C2×D512yescomplemented
99#817—51no—
100#816—101no—
101Dic24—102no—
102#800—102no—
103C22×C4×C5D1211yescharacteristic
104C2×C22⋊D5—121no—
105#709—62no—
106#709—62no—
107#709—121no—
108#709—121no—
109C2×D20—61no—
110C2×C4×D5—121no—
111C2×Dic10—61no—
112C2×Dic10—61no—
113C5×M16—22no—
114C2×C5×C8D1211yescharacteristic
115C2×C5×C8C22×D311yescharacteristic
116C22⋊Dic5—121no—
117C4⋊Dic5—61no—
118#683—121no—
119Dic20—32no—
120Dic20—61no—
121Dic20—62no—
122D40—32no—
123D40—61no—
124#677—62no—
125#677—62no—
126C5×C16—22no—
127#575—151no—
128#510—152no—
129#470—151no—
130#360—152no—
131#349D1511yescharacteristic, complemented
132C22×C3×C5—21no—
133C22×C3×C5—41no—
134C22×C3×C5C2×D811yescharacteristic
135C2×D15—42no—
136C2×D15—82no—
137C3×C4×C5—21no—
138C3×C4×C5#12011yescharacteristic
139C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
140Dic15—42no—
141Dic15—81no—
142Dic15—81no—
143C22×C3×C4D2011yescharacteristic
144C2×#67—201no—
145#235—102no—
146#235—102no—
147#235—201no—
148#235—201no—
149C2×D12—101no—
150C2×C4×D3—201no—
151C2×Dic6—101no—
152C2×Dic6—101no—
153C3×M16—22no—
154C2×C3×C8D2011yescharacteristic
155C2×C3×C8C22×D511yescharacteristic
156#217—201no—
157C4⋊Dic3—101no—
158Dic3⋊C4—201no—
159Dic12—52no—
160Dic12—101no—
161Dic12—102no—
162D24—52no—
163D24—101no—
164#204—102no—
165#204—102no—
166C3×C16—22no—
167C23×C5D2411yescharacteristic
168C22×D5—121no—
169C2×C4×C5—21no—
170C2×C4×C5—21no—
171C2×C4×C5D2411yescharacteristic
172C2×C4×C5C2×D1211yescharacteristic
173C22⋊D5—122no—
174C22⋊D5—122no—
175C2×Dic5—121no—
176C2×Dic5—121no—
177C2×Dic5—121no—
178D20—62no—
179D20—121no—
180C4×D5—122no—
181C4×D5—122no—
182Dic10—62no—
183Dic10—121no—
184Dic10—121no—
185Dic10—121no—
186C5×C8—21no—
187C5×C8D3×D412yes—
188C2×#41—301no—
189#137—302no—
190AGL(1,ℤ/8)—302no—
191#135—152no—
192#135—301no—
193C2×Q16—151no—
194C2×M16C2×D1511yescharacteristic
195C22⋊Q8—301no—
196Q32—302no—
197SD32—302no—
198M32C2×D1512yescomplemented
199#106—151no—
200#103—301no—
201C2×C3×C5—21no—
202C2×C3×C5—41no—
203C2×C3×C5#44711yescharacteristic
204D15—82no—
205C23×C3D4011yescharacteristic
206C22×D3—201no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4D4011yescharacteristic
210C2×C3×C4C2×D2011yescharacteristic
211#67—202no—
212#67—202no—
213C2×Dic3—201no—
214C2×Dic3—201no—
215C2×Dic3—201no—
216D12—102no—
217D12—201no—
218C4×D3—202no—
219C4×D3—202no—
220Dic6—102no—
221Dic6—201no—
222Dic6—201no—
223Dic6—201no—
224C3×C8—21no—
225C3×C8D4×D512yes—
226C22×C5—21no—
227C22×C5—41no—
228C22×C5C2×D2411yescharacteristic
229C2×D5—122no—
230C2×D5—242no—
231C4×C5—21no—
232C4×C5#88211yescharacteristic
233C4×C5#90811yescharacteristic
234Dic5—122no—
235Dic5—241no—
236Dic5—241no—
237#41—302no—
238#41—302no—
239#41—601no—
240#41—601no—
241C2×Q8—301no—
242C2×Q8—301no—
243C2×D4—301no—
244C2×D4—601no—
245C22×C4—601no—
246C22×C4D6011yescharacteristic
247Q16—152no—
248Q16—301no—
249Q16—302no—
250SD16—302no—
251SD16—302no—
252D8—152no—
253D8—301no—
254M16—22no—
255C2×C8D6011yescharacteristic
256C2×C8C22×D1511yescharacteristic
257C4⋊C4—301no—
258C4⋊C4—601no—
259C22⋊C4—601no—
260C16—22no—
261C3×C5#219111yescharacteristic, complemented, Hall
262C22×C3—21no—
263C22×C3—41no—
264C22×C3C2×D4011yescharacteristic
265C2×D3—202no—
266C2×D3—402no—
267C3×C4—21no—
268C3×C4#402811yescharacteristic
269C3×C4#405411yescharacteristic
270Dic3—202no—
271Dic3—401no—
272Dic3—401no—
273C2×C5—21no—
274C2×C5—41no—
275C2×C5#473211yescharacteristic
276D5—242no—
277C23—601no—
278C23D12011yescharacteristic
279Q8—302no—
280Q8—601no—
281Q8—601no—
282Q8—601no—
283D4—302no—
284D4—601no—
285D4—602no—
286D4—602no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—602no—
290C2×C4—601no—
291C2×C4—602no—
292C2×C4—601no—
293C2×C4—601no—
294C2×C4D12011yescharacteristic
295C2×C4C2×D6011yescharacteristic
296C8—21no—
297C8D4×D1512yes—
298C2×C3—21no—
299C2×C3—41no—
300C2×C3#6502111yescharacteristic
301D3—402no—
302C5#6912111yescharacteristic, complemented, Sylow
303C22—21no—
304C22—41no—
305C22—602no—
306C22—1202no—
307C22C2×D12011yescharacteristic
308C4—21no—
309C4—602no—
310C4—1201no—
311C4—1201no—
312C4#9177111yescharacteristic
313C4#9179711yescharacteristic
314C3#1059991411yescharacteristic, complemented, Sylow
315C2—21no—
316C2—41no—
317C2—1202no—
318C2#1175083311yescharacteristic
subgroupG/H
centerC2#11750833
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#349C2
socleC2×C3×C5#447
prime radical#11756507C2
hypercenter#349D15
hypocenterC3×C5#2191
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. #11751238C2semidirect
3. #11751010C2semidirect
4. C3×C5×#349C2semidirect
5. #11746339C2semidirect
12. C2×Dic60C22semidirect
15. C3×C5×M32C22semidirect
16. #91101C22semidirect
24. C5×#349D3semidirect
53. C3×#349D5semidirect
63. C5×M32C2×D3semidirect
98. C3×M32C2×D5semidirect
131. #349D15semidirect
198. M32C2×D15semidirect
261. C3×C5#2191semidirect
302. C5#69121semidirect
314. C3#10599914semidirect

Maximal subgroups

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

subgroupindex
#117565072
#117512382
#117510102
C3×C5×#3492
#117463392
#105999143
#691215