Finite Group Databasebeta

← #14316364

Subgroups — #14316364

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
1C5×#5748C211yesmaximal, characteristic
2#11751238C211yesmaximal, characteristic, complemented
3#11747563C212yesmaximal, complemented
4C3×#64773C211yesmaximal, characteristic, complemented
5#11745912C212yesmaximal, complemented
6#10602906—31nomaximal, Hall
7C2×C5×#235—21no—
8C2×C3×C5×M16C2211yescharacteristic
9#91813—21no—
10C2×Dic60C2211yescharacteristic, complemented
11C5×#909—22no—
12C5×#908—22no—
13C5×#904—21no—
14C5×#904C2212yes—
15#91101C2211yescharacteristic, complemented
16#91100—21no—
17C3×#3944C2212yescomplemented
18#90948—22no—
19#90944—22no—
20#69121—51nomaximal, Hall
21C5×#575—31no—
22#65484—32no—
23#65426—31no—
24#64786—32no—
25#64773D311yescharacteristic, complemented
26C22×C3×C4×C5D411yescharacteristic
27C2×Dic30—21no—
28C2×C5×#67—41no—
29C5×#235—22no—
30C5×#235—22no—
31C5×#235—41no—
32C5×#235—41no—
33C2×C5×D12—21no—
34C2×C4×C5×D3—41no—
35C2×C5×Dic6—21no—
36C3×C5×M16—22no—
37C2×C3×C5×C8D411yescharacteristic
38C2×C3×C5×C8C2311yescharacteristic
39#6719—41no—
40C4⋊Dic15—21no—
41#6712—41no—
42Dic60—22no—
43C5×Dic12—21no—
44C5×Dic12D412yes—
45C5×D24—21no—
46C5×D24D412yes—
47C5×#204—22no—
48C5×#204—22no—
49C3×#672—22no—
50#5748D511yescharacteristic
51#5137—51no—
52#4909—52no—
53C3×#349—51no—
54#4518—52no—
55C2×C5×#41—61no—
56C5×#137—62no—
57C5×AGL(1,ℤ/8)—62no—
58C5×#135—32no—
59C5×#135—61no—
60C2×C5×M16C2×D311yescharacteristic
61#4070—61no—
62C2×Dic20—31no—
63#3961—62no—
64#3959—62no—
65#3949—31no—
66#3948—61no—
67#3944C2×D312yescomplemented
68#2191—151noSylow
69C23×C3×C5D811yescharacteristic
70C22×C5×D3—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—
79C5×#67—42no—
80C5×#67—42no—
81C2×C5×Dic3—41no—
82C5×D12—22no—
83C5×D12—41no—
84C4×C5×D3—42no—
85C4×C5×D3—42no—
86C5×Dic6—22no—
87C5×Dic6—41no—
88C3×C5×C8—21no—
89C3×C5×C8C2×D412yes—
90C2×#235—21no—
91C2×C3×M16C2×D511yescharacteristic
92#924—101no—
93#909—22no—
94#908—22no—
95C2×Dic12—51no—
96#904—21no—
97#904C2×D512yes—
98C3×M32—52no—
99#817—51no—
100#816—101no—
101Dic24—102no—
102#800—102no—
103C5×#41—62no—
104C5×#41—62no—
105C5×#41—121no—
106C5×#41—121no—
107C2×C5×Q8—61no—
108C2×C5×D4—61no—
109C2×C5×D4—121no—
110C22×C4×C5—121no—
111C22×C4×C5D1211yescharacteristic
112C2×Dic10—61no—
113C5×Q16—32no—
114C5×Q16—61no—
115C5×SD16—62no—
116C5×SD16—62no—
117C5×D8—32no—
118C5×D8—61no—
119C5×M16—22no—
120C2×C5×C8D1211yescharacteristic
121C2×C5×C8C22×D311yescharacteristic
122C22⋊Dic5—121no—
123C4⋊Dic5—61no—
124#683—121no—
125Dic20—62no—
126#672—22no—
127#575—31no—
128#510—152no—
129#470—151no—
130#360—152no—
131#349—51no—
132C22×C3×C5—21no—
133C22×C3×C5—41no—
134C22×C3×C5C2×D811yescharacteristic
135C2×C5×D3—42no—
136C2×C5×D3—82no—
137C3×C4×C5—21no—
138C3×C4×C5#12011yescharacteristic
139C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
140Dic15—81no—
141Dic15—81no—
142C5×Dic3—42no—
143C22×C3×C4C22⋊D511yescharacteristic
144C2×#67—41no—
145#235—22no—
146#235—22no—
147#235—41no—
148#235—41no—
149C2×D12—21no—
150C2×C4×D3—41no—
151C2×Dic6—21no—
152C2×Dic6—101no—
153C3×M16—22no—
154C2×C3×C8C22⋊D511yescharacteristic
155C2×C3×C8C22×D511yescharacteristic
156#217—201no—
157C4⋊Dic3—101no—
158Dic3⋊C4—201no—
159Dic12—21no—
160Dic12—102no—
161Dic12C22⋊D512yes—
162D24—21no—
163D24C22⋊D512yes—
164#204—22no—
165#204—22no—
166C3×C16—102no—
167C23×C5—121no—
168C23×C5D2411yescharacteristic
169C5×Q8—62no—
170C5×Q8—121no—
171C5×D4—62no—
172C5×D4—121no—
173C5×D4—122no—
174C5×D4—122no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—122no—
178C2×C4×C5—121no—
179C2×C4×C5—122no—
180C2×C4×C5D2411yescharacteristic
181C2×C4×C5C2×D1211yescharacteristic
182C2×Dic5—121no—
183C2×Dic5—121no—
184Dic10—121no—
185Dic10—121no—
186C5×C8—21no—
187C5×C8D3×D412yes—
188C2×#41—61no—
189#137—62no—
190AGL(1,ℤ/8)—62no—
191#135—32no—
192#135—61no—
193C2×Q16—151no—
194C2×M16D3×D511yescharacteristic
195C22⋊Q8—301no—
196Q32—302no—
197SD32—302no—
198M32—52no—
199#106—151no—
200#103—301no—
201C2×C3×C5—21no—
202C2×C3×C5—41no—
203C2×C3×C5#44711yescharacteristic
204C5×D3—82no—
205C23×C3#68611yescharacteristic
206C22×D3—41no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4#68611yescharacteristic
210C2×C3×C4C2×C22⋊D511yescharacteristic
211#67—42no—
212#67—42no—
213C2×Dic3—41no—
214C2×Dic3—201no—
215C2×Dic3—201no—
216D12—22no—
217D12—41no—
218C4×D3—42no—
219C4×D3—42no—
220Dic6—22no—
221Dic6—41no—
222Dic6—201no—
223Dic6—201no—
224C3×C8—21no—
225C3×C8C2×C22⋊D512yes—
226C22×C5—21no—
227C22×C5—41no—
228C22×C5—122no—
229C22×C5—242no—
230C22×C5C2×D2411yescharacteristic
231C4×C5—21no—
232C4×C5—122no—
233C4×C5#88211yescharacteristic
234C4×C5#90811yescharacteristic
235Dic5—241no—
236Dic5—241no—
237#41—62no—
238#41—62no—
239#41—121no—
240#41—121no—
241C2×Q8—61no—
242C2×Q8—301no—
243C2×D4—61no—
244C2×D4—121no—
245C22×C4—121no—
246C22×C4#120311yescharacteristic
247Q16—32no—
248Q16—61no—
249Q16—302no—
250SD16—62no—
251SD16—62no—
252D8—32no—
253D8—61no—
254M16—22no—
255C2×C8#120311yescharacteristic
256C2×C8C2×D3×D511yescharacteristic
257C4⋊C4—301no—
258C4⋊C4—601no—
259C22⋊C4—601no—
260C16—102no—
261C3×C5#219111yescharacteristic, complemented, Hall
262C22×C3—21no—
263C22×C3—41no—
264C22×C3C2×#68611yescharacteristic
265C2×D3—42no—
266C2×D3—82no—
267C3×C4—21no—
268C3×C4#407811yescharacteristic
269C3×C4#409911yescharacteristic
270Dic3—42no—
271Dic3—401no—
272Dic3—401no—
273C2×C5—21no—
274C2×C5—41no—
275C2×C5—242no—
276C2×C5#473211yescharacteristic
277C23—121no—
278C23#665411yescharacteristic
279Q8—62no—
280Q8—121no—
281Q8—601no—
282Q8—601no—
283D4—62no—
284D4—121no—
285D4—122no—
286D4—122no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—122no—
290C2×C4—121no—
291C2×C4—122no—
292C2×C4—601no—
293C2×C4—601no—
294C2×C4#665411yescharacteristic
295C2×C4C2×#120311yescharacteristic
296C8—21no—
297C8D3×C22⋊D512yes—
298C2×C3—21no—
299C2×C3—41no—
300C2×C3#6550611yescharacteristic
301D3—82no—
302C5#6912111yescharacteristic, complemented, Sylow
303C22—21no—
304C22—41no—
305C22—122no—
306C22—242no—
307C22C2×#665411yescharacteristic
308C4—21no—
309C4—122no—
310C4—1201no—
311C4—1201no—
312C4#9130411yescharacteristic
313C4#9157011yescharacteristic
314C3#1060290611yescharacteristic, complemented, Sylow
315C2—21no—
316C2—41no—
317C2—242no—
318C2#1174852011yescharacteristic
subgroupG/H
centerC2#11748520
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#447
prime radicalC5×#5748C2
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. #11747563C2semidirect
4. C3×#64773C2semidirect
5. #11745912C2semidirect
10. C2×Dic60C22semidirect
15. #91101C22semidirect
17. C3×#3944C22semidirect
25. #64773D3semidirect
67. #3944C2×D3semidirect
261. C3×C5#2191semidirect
302. C5#69121semidirect
314. C3#10602906semidirect

Maximal subgroups

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

subgroupindex
C5×#57482
#117512382
#117475632
C3×#647732
#117459122
#106029063
#691215