Finite Group Databasebeta

← #14438712

Subgroups — #14438712

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#125C211yesmaximal, characteristic, complemented
2#11752672C211yesmaximal, characteristic
3#11751170C211yesmaximal, characteristic, complemented
4C5×#5067C211yesmaximal, characteristic, complemented
5#11747498C214yesmaximal, complemented
6#11747142C214yesmaximal, complemented
7#11747003C211yesmaximal, characteristic, complemented
8#11746936C211yesmaximal, characteristic, complemented
9#11746905C211yesmaximal, characteristic, complemented
10#10613447—31nomaximal, Hall
11C2×#6772C2212yes—
12C3×C5×#125C2211yescharacteristic
13#91758C2211yescharacteristic
14C5×#874C2211yescharacteristic
15C3×D5×C4⋊C4—22no—
16C3×D5×C4⋊C4C2212yes—
17C3×#4036C2212yes—
18C3×#4035—22no—
19C3×C42×D5C2211yescharacteristic
20C3×#4016C2211yescharacteristic
21#91449—22no—
22Dic5×D12—22no—
23#91373C2212yes—
24C2×#6649C2212yes—
25#91094C2214yes—
26#91087C2211yescharacteristic
27C5×#809C2214yes—
28C5×#803C2211yescharacteristic
29#90974C2214yes—
30#90966C2214yes—
31Dic5×C3⋊C8C2212yes—
32#83012—51nomaximal, Hall
33#66050—31no—
34D5×#125D311yescharacteristic, complemented
35C5×#490—31no—
36#65360—31no—
37#65358—31no—
38#65060—34no—
39#65057—34no—
40#64996—31no—
41#64992—31no—
42C2×Dic30C2312yes—
43C2×C5×D12—22no—
44C2×C5×D12C2312yes—
45C2×C3×C4×D5—22no—
46C2×C3×C4×D5D412yes—
47C2×C3×C4×D5C2311yescharacteristic
48C2×#1201—22no—
49C2×D3×Dic5—22no—
50#6772—28no—
51C3×C5×C4⋊C4—22no—
52C3×C5×C4⋊C4C2312yes—
53C3×C42×C5C2311yescharacteristic
54C4⋊Dic15—22no—
55C2×C3⋊#168C2312yes—
56C2×C5×C3⋊C8C2312yes—
57C3×C4⋊Dic5—22no—
58C3×C4⋊Dic5C2312yes—
59C3×#683—22no—
60C3×#683—22no—
61C3×#683—22no—
62C3×C4×Dic5D412yes—
63C3×C4×Dic5C2311yescharacteristic
64(C2×D3)⋊Dic5—24no—
65#6649—24no—
66C2×C3×#125—51no—
67#5477—51no—
68#5069—51no—
69#5069—51no—
70#5068—54no—
71#5067—51no—
72#5067D511yescharacteristic, complemented
73#4966—54no—
74C4×#208—51no—
75C2×#711—32no—
76C5×#127—31no—
77C5×#125C2×D311yescharacteristic
78#4084—62no—
79#4082—32no—
80D4×Dic5—62no—
81C2×#676—32no—
82D5×C4⋊C4—22no—
83D5×C4⋊C4C2×D312yes—
84#4036C2×D312yes—
85#4035—22no—
86C42×D5C2×D311yescharacteristic
87#4016C2×D311yescharacteristic
88#4015—31no—
89C5×#102—34no—
90C5×#97—31no—
91#3964—34no—
92#3948—34no—
93C8×Dic5—32no—
94#3942—34no—
95#3935—31no—
96#3142—151noSylow
97C22×C5×D3—22no—
98C22×C3×D5C2×D411yescharacteristic
99C2×C3×C4×C5—22no—
100C2×C3×C4×C5C2×D412yes—
101C2×C3×C4×C5C2411yescharacteristic
102C2×Dic15—22no—
103Dic30—24no—
104C5×D12—24no—
105C5×D12—44no—
106C2×C3×Dic5—22no—
107C2×C3×Dic5C2×D412yes—
108C2×C3×Dic5C2×D411yescharacteristic
109C3×C4×D5—42no—
110C3×C4×D5—44no—
111C3×C4×D5#4114yes—
112#1201—44no—
113D3×Dic5—44no—
114C3⋊#168—22no—
115C5×C3⋊C8—22no—
116C2×#235—52no—
117C3×#125—52no—
118C3×#125—51no—
119C3×#125—102no—
120C3×#125C2×D511yescharacteristic
121C2×C3×C4⋊C4—52no—
122C2×C3×C4⋊C4—102no—
123C2×C3×C42—51no—
124#930—102no—
125C2×#208—52no—
126#875—52no—
127#874C2×D511yescharacteristic
128C4×D12—102no—
129#869—51no—
130#810—54no—
131#810—54no—
132#809—54no—
133#809C2×D514yes—
134#803—51no—
135#803C2×D511yescharacteristic
136C4×C3⋊C8—52no—
137C2×C5×D4—32no—
138C2×C5×D4—62no—
139C2×C22⋊D5—62no—
140C22×Dic5—62no—
141#711—68no—
142C2×C4×D5—22no—
143C2×C4×D5#6712yes—
144C2×C4×D5C22×D311yescharacteristic
145C2×Dic10—32no—
146C2×C5×C8—32no—
147C5×C4⋊C4—22no—
148C5×C4⋊C4C22×D312yes—
149C42×C5C22×D311yescharacteristic
150C22⋊Dic5—64no—
151C4⋊Dic5—22no—
152C4⋊Dic5—62no—
153C4⋊Dic5C22×D312yes—
154#683—22no—
155#683—22no—
156#683—22no—
157C4×Dic5#6712yes—
158C4×Dic5C22×D311yescharacteristic
159C2×#168—32no—
160#676—64no—
161#532—151no—
162C2×#125—51no—
163#491—151no—
164#491—151no—
165#490—31no—
166#490—151no—
167#488—154no—
168#417—154no—
169C4×M16—151no—
170C22×C3×C5C22×D411yescharacteristic
171C2×C5×D3—42no—
172C2×C5×D3—44no—
173C2×C3×D5—22no—
174C2×C3×D5#12412yes—
175C3×C4×C5—22no—
176C3×C4×C5—42no—
177C3×C4×C5C2×#4112yes—
178Dic15—42no—
179C3×Dic5—22no—
180C3×Dic5—42no—
181C3×Dic5#12412yes—
182C22×C3×C4—51no—
183C22×C3×C4—52no—
184C22×C3×C4—102no—
185C2×#67—102no—
186#235—108no—
187C2×D12—22no—
188C2×D12C22×D512yes—
189C2×C4×D3—102no—
190C2×Dic6—52no—
191C3×C4⋊C4—22no—
192C3×C4⋊C4—52no—
193C3×C4⋊C4—102no—
194C3×C4⋊C4—102no—
195C3×C4⋊C4—102no—
196C3×C4⋊C4—102no—
197C3×C4⋊C4C22×D512yes—
198C3×C42—52no—
199C3×C42—51no—
200C3×C42C22×D511yescharacteristic
201(C2×D3)⋊C4—104no—
202C4⋊Dic3—102no—
203#208—104no—
204C2×C3⋊C8—52no—
205C2×C3⋊C8C22×D512yes—
206C23×C5—62no—
207C22×D5C2×#6711yescharacteristic
208C5×D4—64no—
209C5×D4—124no—
210C2×C4×C5—22no—
211C2×C4×C5C2×#6712yes—
212C2×C4×C5C23×D311yescharacteristic
213C22⋊D5—124no—
214C2×Dic5—22no—
215C2×Dic5—62no—
216C2×Dic5—124no—
217C2×Dic5C2×#6712yes—
218C2×Dic5C2×#6711yescharacteristic
219C4×D5—42no—
220C4×D5—44no—
221C4×D5#23914yes—
222Dic10—64no—
223C5×C8—62no—
224#168—62no—
225C2×#41—152no—
226C2×M16—152no—
227C4⋊Q8—151no—
228#127—31no—
229#125—52no—
230#125—51no—
231#125—102no—
232#125D3×D511yescharacteristic
233#124—152no—
234#121—302no—
235C4×D4—302no—
236C2×C4⋊C4—52no—
237C2×C4⋊C4—102no—
238C2×C42—51no—
239#103—154no—
240#103—154no—
241#102—34no—
242#102—154no—
243#97—31no—
244#97—151no—
245C4×C8—152no—
246C2×C3×C5C2×#12411yescharacteristic
247C2×C3×C5#57512yes—
248C3×D5—22no—
249C5×D3—82no—
250C23×C3—51no—
251C22×D3—22no—
252C2×C3×C4—22no—
253C2×C3×C4—51no—
254C2×C3×C4—54no—
255C2×C3×C4—52no—
256C2×C3×C4—102no—
257C2×C3×C4—202no—
258C2×C3×C4—204no—
259C2×C3×C4D4×D512yes—
260C2×C3×C4C23×D511yescharacteristic
261#67—204no—
262C2×Dic3—102no—
263D12—24no—
264D12—44no—
265C4×D3—204no—
266Dic6—104no—
267C3⋊C8—22no—
268C3⋊C8—102no—
269C22×C5—122no—
270C22×C5—124no—
271C22×C5C22×#6711yescharacteristic
272C2×D5—22no—
273C2×D5#94712yes—
274C4×C5—22no—
275C4×C5—42no—
276C4×C5C2×#23912yes—
277Dic5—22no—
278Dic5—42no—
279Dic5—122no—
280Dic5#94712yes—
281#41—308no—
282C2×Q8—152no—
283C2×D4—32no—
284C2×D4—62no—
285C2×D4—302no—
286C22×C4—51no—
287C22×C4—52no—
288C22×C4—102no—
289C22×C4—302no—
290M16—304no—
291C2×C8—32no—
292C2×C8—152no—
293C4⋊C4—22no—
294C4⋊C4—52no—
295C4⋊C4—102no—
296C4⋊C4—102no—
297C4⋊C4—102no—
298C4⋊C4—102no—
299C4⋊C4—302no—
300C4⋊C4C2×D3×D512yes—
301C22⋊C4—304no—
302C42—52no—
303C42—51no—
304C42C2×D3×D511yescharacteristic
305C3×C5#314211yescharacteristic, complemented, Hall
306C22×C3—52no—
307C22×C3—102no—
308C22×C3C2×D4×D511yescharacteristic
309C2×D3—44no—
310C2×D3—42no—
311C3×C4—22no—
312C3×C4—42no—
313C3×C4—52no—
314C3×C4—102no—
315C3×C4—202no—
316C3×C4D5×#4112yes—
317Dic3—202no—
318C2×C5—242no—
319C2×C5C2×#94711yescharacteristic
320C2×C5#582212yes—
321D5—22no—
322C23—51no—
323C23—62no—
324Q8—304no—
325D4—64no—
326D4—124no—
327D4—604no—
328C2×C4—22no—
329C2×C4—51no—
330C2×C4—54no—
331C2×C4—52no—
332C2×C4—102no—
333C2×C4—202no—
334C2×C4—204no—
335C2×C4—302no—
336C2×C4—604no—
337C2×C4D5×#6712yes—
338C2×C4C22×D3×D511yescharacteristic
339C8—62no—
340C8—302no—
341C2×C3—102no—
342C2×C3D5×#12411yescharacteristic
343C2×C3#6610712yes—
344D3—82no—
345C5#8301211yescharacteristic, complemented, Sylow
346C22—52no—
347C22—102no—
348C22—122no—
349C22—124no—
350C22C2×D5×#6711yescharacteristic
351C4—22no—
352C4—42no—
353C4—52no—
354C4—102no—
355C4—202no—
356C4—602no—
357C4D5×#23912yes—
358C3#1061344711yescharacteristic, complemented, Sylow
359C2—102no—
360C2—242no—
361C2D5×#94711yescharacteristic
362C2#1175534312yes—
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C22×D4
prime radical#11752672C2
hypercenter#125D3×D5
hypocenterC3×C5#3142
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C3×D5×#125C2semidirect
3. #11751170C2semidirect
4. C5×#5067C2semidirect
5. #11747498C2semidirect
6. #11747142C2semidirect
7. #11747003C2semidirect
8. #11746936C2semidirect
9. #11746905C2semidirect
34. D5×#125D3semidirect
72. #5067D5semidirect
305. C3×C5#3142semidirect
345. C5#83012semidirect
358. C3#10613447semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1252
#117526722
#117511702
C5×#50672
#117474982
#117471422
#117470032
#117469362
#117469052
#106134473
#830125