Finite Group Databasebeta

← #14316312

Subgroups — #14316312

Order 1920.

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

normal subgroups only

This group has 452 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, complemented
2#11751236C211yesmaximal, characteristic, complemented
3#11751009C212yesmaximal, complemented
4C3×C5×#349C211yesmaximal, characteristic, complemented
5#11746339C212yesmaximal, complemented
6#10599913—31nomaximal, Hall
7C2×#6817—21no—
8C2×C3×C5×M16C2211yescharacteristic
9#91819—21no—
10#91798—22no—
11#91797—22no—
12#91793—21no—
13#91793C2212yes—
14C2×D120C2211yescharacteristic, complemented
15C3×C5×M32C2212yescomplemented
16#91105—21no—
17#91101C2211yescharacteristic, complemented
18#91084—22no—
19D240—22no—
20#69120—51nomaximal, Hall
21#66082—31no—
22#65424—31no—
23#65197—32no—
24C5×#349D311yescharacteristic, complemented
25#64738—32no—
26C22×C3×C4×C5D411yescharacteristic
27C2×#1220—41no—
28C2×#1220—41no—
29#6817—22no—
30#6817—22no—
31#6817—41no—
32#6817—41no—
33C2×D60—21no—
34C2×D60—21no—
35C2×C4×D15—41no—
36C2×Dic30—21no—
37C3×C5×M16—22no—
38C2×C3×C5×C8D411yescharacteristic
39C2×C3×C5×C8C2311yescharacteristic
40#6714—41no—
41C4⋊Dic15—21no—
42Dic60—21no—
43Dic60D412yescomplemented
44D120—21no—
45D120—22no—
46D120D412yescomplemented
47#6706—22no—
48#6706—22no—
49C3×C5×C16—22no—
50#5748—51no—
51#5135—51no—
52#4908—52no—
53C3×#349D511yescharacteristic, complemented
54#4518—52no—
55C2×#709—61no—
56C2×C5×M16C2×D311yescharacteristic
57#4076—61no—
58#4055—62no—
59#4054—62no—
60#4050—32no—
61#4050—61no—
62C2×D40—31no—
63C5×M32C2×D312yescomplemented
64#3953—61no—
65#3949—31no—
66#3932—62no—
67D80—62no—
68#2190—151noSylow
69C23×C3×C5D811yescharacteristic
70C22×D15—41no—
71C22×D15—41no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5D811yescharacteristic
75C2×C3×C4×C5C2×D411yescharacteristic
76#1220—42no—
77#1220—42no—
78#1220—82no—
79C2×Dic15—41no—
80C2×Dic15—41no—
81D60—22no—
82D60—41no—
83D60—41no—
84D60—41no—
85C4×D15—42no—
86C4×D15—42no—
87Dic30—22no—
88Dic30—41no—
89C3×C5×C8—21no—
90C3×C5×C8C2×D412yes—
91C2×#235—101no—
92C2×C3×M16C2×D511yescharacteristic
93#930—101no—
94#909—102no—
95#908—102no—
96#904—52no—
97#904—101no—
98C2×D24—51no—
99C3×M32C2×D512yescomplemented
100#821—101no—
101#817—51no—
102#800—102no—
103D48—102no—
104C22×C4×C5D1211yescharacteristic
105C2×C22⋊D5—121no—
106C2×C22⋊D5—121no—
107#709—62no—
108#709—62no—
109#709—121no—
110#709—121no—
111C2×D20—61no—
112C2×D20—61no—
113C2×C4×D5—121no—
114C2×Dic10—61no—
115C5×M16—22no—
116C2×C5×C8D1211yescharacteristic
117C2×C5×C8C22×D311yescharacteristic
118#685—121no—
119C4⋊Dic5—61no—
120Dic20—32no—
121Dic20—61no—
122D40—32no—
123D40—61no—
124D40—62no—
125#677—62no—
126#677—62no—
127C5×C16—22no—
128#575—151no—
129#509—152no—
130#469—151no—
131#360—152no—
132#349D1511yescharacteristic, complemented
133C22×C3×C5—21no—
134C22×C3×C5—41no—
135C22×C3×C5C2×D811yescharacteristic
136C2×D15—42no—
137C2×D15—82no—
138C2×D15—81no—
139C2×D15—81no—
140C2×D15—81no—
141C3×C4×C5—21no—
142C3×C4×C5#12011yescharacteristic
143C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
144Dic15—42no—
145Dic15—81no—
146C22×C3×C4D2011yescharacteristic
147C2×#67—201no—
148C2×#67—201no—
149#235—102no—
150#235—102no—
151#235—201no—
152#235—201no—
153C2×D12—101no—
154C2×D12—101no—
155C2×C4×D3—201no—
156C2×Dic6—101no—
157C3×M16—22no—
158C2×C3×C8D2011yescharacteristic
159C2×C3×C8C22×D511yescharacteristic
160(C2×D3)⋊C4—201no—
161C4⋊Dic3—101no—
162Dic12—52no—
163Dic12—101no—
164D24—52no—
165D24—101no—
166D24—102no—
167#204—102no—
168#204—102no—
169C3×C16—22no—
170C23×C5D2411yescharacteristic
171C22×D5—121no—
172C22×D5—121no—
173C2×C4×C5—21no—
174C2×C4×C5—21no—
175C2×C4×C5D2411yescharacteristic
176C2×C4×C5C2×D1211yescharacteristic
177C22⋊D5—122no—
178C22⋊D5—122no—
179C22⋊D5—242no—
180C2×Dic5—121no—
181C2×Dic5—121no—
182D20—62no—
183D20—121no—
184D20—121no—
185D20—121no—
186C4×D5—122no—
187C4×D5—122no—
188Dic10—62no—
189Dic10—121no—
190C5×C8—21no—
191C5×C8D3×D412yes—
192C2×#41—301no—
193#137—302no—
194AGL(1,ℤ/8)—302no—
195#135—152no—
196#135—301no—
197C2×D8—151no—
198C2×M16C2×D1511yescharacteristic
199#121—301no—
200SD32—302no—
201D16—302no—
202M32C2×D1512yescomplemented
203#106—151no—
204#102—301no—
205C2×C3×C5—21no—
206C2×C3×C5—41no—
207C2×C3×C5#44711yescharacteristic
208D15—82no—
209D15—161no—
210C23×C3D4011yescharacteristic
211C22×D3—201no—
212C22×D3—201no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4D4011yescharacteristic
216C2×C3×C4C2×D2011yescharacteristic
217#67—202no—
218#67—202no—
219#67—402no—
220C2×Dic3—201no—
221C2×Dic3—201no—
222D12—102no—
223D12—201no—
224D12—201no—
225D12—201no—
226C4×D3—202no—
227C4×D3—202no—
228Dic6—102no—
229Dic6—201no—
230C3×C8—21no—
231C3×C8D4×D512yes—
232C22×C5—21no—
233C22×C5—41no—
234C22×C5C2×D2411yescharacteristic
235C2×D5—122no—
236C2×D5—242no—
237C2×D5—241no—
238C2×D5—241no—
239C2×D5—241no—
240C4×C5—21no—
241C4×C5#88211yescharacteristic
242C4×C5#90811yescharacteristic
243Dic5—122no—
244Dic5—241no—
245#41—302no—
246#41—302no—
247#41—601no—
248#41—601no—
249C2×Q8—301no—
250C2×D4—301no—
251C2×D4—301no—
252C2×D4—601no—
253C2×D4—601no—
254C22×C4—601no—
255C22×C4D6011yescharacteristic
256Q16—152no—
257Q16—301no—
258SD16—302no—
259SD16—302no—
260D8—152no—
261D8—301no—
262D8—302no—
263M16—22no—
264C2×C8D6011yescharacteristic
265C2×C8C22×D1511yescharacteristic
266C4⋊C4—301no—
267C22⋊C4—601no—
268C16—22no—
269C3×C5#219011yescharacteristic, complemented, Hall
270C22×C3—21no—
271C22×C3—41no—
272C22×C3C2×D4011yescharacteristic
273C2×D3—202no—
274C2×D3—402no—
275C2×D3—401no—
276C2×D3—401no—
277C2×D3—401no—
278C3×C4—21no—
279C3×C4#402811yescharacteristic
280C3×C4#405411yescharacteristic
281Dic3—202no—
282Dic3—401no—
283C2×C5—21no—
284C2×C5—41no—
285C2×C5#473211yescharacteristic
286D5—242no—
287D5—481no—
288C23—601no—
289C23—601no—
290C23D12011yescharacteristic
291Q8—302no—
292Q8—601no—
293D4—302no—
294D4—601no—
295D4—602no—
296D4—602no—
297D4—601no—
298D4—601no—
299D4—1202no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—602no—
303C2×C4—601no—
304C2×C4—602no—
305C2×C4—601no—
306C2×C4D12011yescharacteristic
307C2×C4C2×D6011yescharacteristic
308C8—21no—
309C8D4×D1512yes—
310C2×C3—21no—
311C2×C3—41no—
312C2×C3#6502111yescharacteristic
313D3—402no—
314D3—801no—
315C5#6912011yescharacteristic, complemented, Sylow
316C22—21no—
317C22—41no—
318C22—602no—
319C22—1201no—
320C22—1201no—
321C22—1202no—
322C22—1201no—
323C22C2×D12011yescharacteristic
324C4—21no—
325C4—602no—
326C4—1201no—
327C4#9177111yescharacteristic
328C4#9179711yescharacteristic
329C3#1059991311yescharacteristic, complemented, Sylow
330C2—21no—
331C2—41no—
332C2—1202no—
333C2—2401no—
334C2#1175083311yescharacteristic
subgroupG/H
centerC2#11750833
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#349C2
socleC2×C3×C5#447
hypercenter#349D15
hypocenterC3×C5#2190
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
1. #11756507C2semidirect
2. #11751236C2semidirect
3. #11751009C2semidirect
4. C3×C5×#349C2semidirect
5. #11746339C2semidirect
14. C2×D120C22semidirect
15. C3×C5×M32C22semidirect
17. #91101C22semidirect
24. C5×#349D3semidirect
43. Dic60D4semidirect
46. D120D4semidirect
53. C3×#349D5semidirect
63. C5×M32C2×D3semidirect
99. C3×M32C2×D5semidirect
132. #349D15semidirect
202. M32C2×D15semidirect
269. C3×C5#2190semidirect
315. C5#69120semidirect
329. C3#10599913semidirect

Maximal subgroups

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

subgroupindex
#117565072
#117512362
#117510092
C3×C5×#3492
#117463392
#105999133
#691205