Finite Group Databasebeta

← #14281069

Subgroups — #14281069

Order 1920.

632 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#91782C211yesmaximal, characteristic
2#11750827C212yesmaximal, complemented
3C3×C5×#324C211yesmaximal, characteristic, complemented
4#11746349C211yesmaximal, characteristic, complemented
5#11746289C212yesmaximal, complemented
6#10598938—31nomaximal, Hall
7C22×D60C411yescharacteristic
8C22×C4×D15C411yescharacteristic
9C22×C4×D15C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×#6714C411yescharacteristic
12C2×#6714C2211yescharacteristic
13C2×C4×Dic15C411yescharacteristic
14C2×#6705—22no—
15#91782—22no—
16#91782—22no—
17C3×C5×C22⋊C8C2212yes—
18#91114C2212yes—
19#91104—22no—
20#68145—51nomaximal, Hall
21C2×#4039—31no—
22#65015—32no—
23C5×#324D311yescharacteristic, complemented
24#64748—31no—
25#64688—32no—
26C23×D15C2×C411yescharacteristic
27C23×D15C2×C411yescharacteristic
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5C2311yescharacteristic
31C22×Dic15C2×C411yescharacteristic
32C22×Dic15C2×C411yescharacteristic
33C2×D60—22no—
34C2×D60—22no—
35C2×D60—22no—
36C2×C4×D15—21no—
37C2×C4×D15—21no—
38C2×C4×D15—42no—
39C2×C4×D15—42no—
40C2×C4×D15D412yes—
41C2×C4×D15D412yes—
42C2×C3×C5×C8—22no—
43C3×C5×C4⋊C4—22no—
44#6714—22no—
45#6714—22no—
46C4×Dic15—21no—
47C4×Dic15—21no—
48C2×C3⋊#168—22no—
49#6705—44no—
50C2×#893—51no—
51#4726—52no—
52C3×#324D511yescharacteristic, complemented
53#4528—51no—
54#4468—52no—
55C22×D20—31no—
56C22×C4×D5—31no—
57C22×C4×D5—31no—
58C2×C5×C4⋊C4C2×D311yescharacteristic
59C2×#685—31no—
60C2×#685—31no—
61C2×C4×Dic5—31no—
62C2×#676—62no—
63#4039—62no—
64#4039—62no—
65C5×C22⋊C8C2×D312yes—
66C22⋊#168—32no—
67#3952—62no—
68#1465—151noSylow
69C23×C3×C5C22×C411yescharacteristic
70C22×D15—21no—
71C22×D15—21no—
72C22×D15—21no—
73C22×D15—21no—
74C22×D15—41no—
75C22×D15—41no—
76C22×D15—41no—
77C22×D15—41no—
78C22×D15C22⋊C412yes—
79C22×D15M1612yescomplemented
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5M1612yescomplemented
86C2×C3×C4×C5C2×D412yes—
87C2×Dic15—22no—
88C2×Dic15—21no—
89C2×Dic15—41no—
90C2×Dic15C22⋊C411yescharacteristic
91C2×Dic15C22⋊C411yescharacteristic
92D60—28no—
93C4×D15—24no—
94C4×D15—42no—
95C4×D15—42no—
96C4×D15—42no—
97C3×C5×C8—42no—
98C3⋊#168—42no—
99C22×D12—51no—
100C22×C4×D3—51no—
101C22×C4×D3—51no—
102C2×C3×C4⋊C4C2×D511yescharacteristic
103C2×(C2×D3)⋊C4—51no—
104C2×(C2×D3)⋊C4—51no—
105C2×C4×Dic3—51no—
106C2×ΓL(1,𝔽25)—102no—
107#893—102no—
108#893—102no—
109C3×C22⋊C8C2×D512yes—
110#830—52no—
111(C2×D3)⋊C8—102no—
112C23×D5—31no—
113C23×D5—31no—
114C22×C4×C5C4×D311yescharacteristic
115C22×C4×C5C4×D311yescharacteristic
116C22×C4×C5C22×D311yescharacteristic
117C22×Dic5—31no—
118C22×Dic5—31no—
119C2×D20—62no—
120C2×D20—62no—
121C2×D20—62no—
122C2×C4×D5—32no—
123C2×C4×D5—32no—
124C2×C4×D5—61no—
125C2×C4×D5—61no—
126C2×C4×D5—122no—
127C2×C4×D5—122no—
128C2×C5×C8—22no—
129C5×C4⋊C4—22no—
130#685—62no—
131#685—62no—
132C4×Dic5—61no—
133C4×Dic5—61no—
134C2×#168—62no—
135#676—124no—
136C2×C4×D4—151no—
137#407—152no—
138#324—151no—
139#324D1511yescharacteristic, complemented
140#323—152no—
141C22×C3×C5—21no—
142C22×C3×C5—21no—
143C22×C3×C5C2×C22⋊C411yescharacteristic
144C22×C3×C5C2×M1611yescharacteristic
145C22×C3×C5C2×M1611yescharacteristic
146C2×D15—22no—
147C2×D15—22no—
148C2×D15—22no—
149C2×D15—22no—
150C2×D15—42no—
151C2×D15—42no—
152C2×D15—42no—
153C2×D15—41no—
154C2×D15—41no—
155C2×D15—42no—
156C3×C4×C5—22no—
157C3×C4×C5—22no—
158C3×C4×C5—41no—
159Dic15—21no—
160Dic15—41no—
161Dic15#9912yes—
162C23×D3—51no—
163C23×D3—51no—
164C22×C3×C4C4×D511yescharacteristic
165C22×C3×C4C4×D511yescharacteristic
166C22×C3×C4C22×D511yescharacteristic
167C22×Dic3—51no—
168C22×Dic3—51no—
169C2×D12—102no—
170C2×D12—102no—
171C2×D12—102no—
172C2×C4×D3—52no—
173C2×C4×D3—52no—
174C2×C4×D3—101no—
175C2×C4×D3—101no—
176C2×C4×D3—202no—
177C2×C4×D3—202no—
178C2×C3×C8—22no—
179C3×C4⋊C4—22no—
180(C2×D3)⋊C4—102no—
181(C2×D3)⋊C4—102no—
182C4×Dic3—101no—
183C4×Dic3—101no—
184C2×C3⋊C8—102no—
185ΓL(1,𝔽25)—204no—
186C23×C5C2×C4×D311yescharacteristic
187C22×D5—32no—
188C22×D5—32no—
189C22×D5—61no—
190C22×D5—61no—
191C22×D5—61no—
192C22×D5—61no—
193C22×D5—121no—
194C22×D5—121no—
195C22×D5—121no—
196C22×D5—121no—
197C2×C4×C5—21no—
198C2×C4×C5—21no—
199C2×C4×C5—21no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5ΓL(1,𝔽25)12yescomplemented
203C2×C4×C5D3×D412yes—
204C2×Dic5—31no—
205C2×Dic5—31no—
206C2×Dic5—62no—
207C2×Dic5—61no—
208C2×Dic5—121no—
209D20—68no—
210C4×D5—64no—
211C4×D5—122no—
212C4×D5—122no—
213C4×D5—122no—
214C5×C8—42no—
215#168—122no—
216C22×D4—151no—
217C23×C4—151no—
218C23×C4—151no—
219C2×M16—302no—
220C4×D4—302no—
221C4×D4—302no—
222C2×C4⋊C4C2×D1511yescharacteristic
223C2×C22⋊C4—151no—
224C2×C22⋊C4—151no—
225C2×C42—151no—
226C22⋊C8—152no—
227C22⋊C8—302no—
228C22⋊C8C2×D1512yes—
229C2×C3×C5—21no—
230C2×C3×C5—21no—
231C2×C3×C5#40711yescharacteristic
232C2×C3×C5C2×#9911yescharacteristic
233C2×C3×C5#41311yescharacteristic
234D15—42no—
235D15—42no—
236C23×C3C2×C4×D511yescharacteristic
237C22×D3—52no—
238C22×D3—52no—
239C22×D3—101no—
240C22×D3—101no—
241C22×D3—101no—
242C22×D3—101no—
243C22×D3—201no—
244C22×D3—201no—
245C22×D3—201no—
246C22×D3—201no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4#67612yescomplemented
253C2×C3×C4D4×D512yes—
254C2×Dic3—51no—
255C2×Dic3—51no—
256C2×Dic3—102no—
257C2×Dic3—101no—
258C2×Dic3—201no—
259D12—108no—
260C4×D3—104no—
261C4×D3—202no—
262C4×D3—202no—
263C4×D3—202no—
264C3×C8—42no—
265C3⋊C8—202no—
266C22×C5—21no—
267C22×C5—21no—
268C22×C5D3×C22⋊C411yescharacteristic
269C22×C5C2×ΓL(1,𝔽25)11yescharacteristic
270C22×C5D3×M1611yescharacteristic
271C2×D5—62no—
272C2×D5—62no—
273C2×D5—62no—
274C2×D5—62no—
275C2×D5—122no—
276C2×D5—122no—
277C2×D5—122no—
278C2×D5—121no—
279C2×D5—121no—
280C2×D5—122no—
281C4×C5—22no—
282C4×C5—22no—
283C4×C5—41no—
284Dic5—32no—
285Dic5—61no—
286Dic5—121no—
287C24—151no—
288C24—151no—
289C2×D4—302no—
290C2×D4—302no—
291C2×D4—302no—
292C22×C4—151no—
293C22×C4—152no—
294C22×C4—152no—
295C22×C4—151no—
296C22×C4—301no—
297C22×C4—301no—
298C22×C4—602no—
299C22×C4—602no—
300C22×C4C4×D1511yescharacteristic
301C22×C4C4×D1511yescharacteristic
302C22×C4C22×D1511yescharacteristic
303M16—604no—
304C2×C8—22no—
305C2×C8—302no—
306C4⋊C4—22no—
307C22⋊C4—302no—
308C22⋊C4—302no—
309C42—301no—
310C42—301no—
311C3×C5#146511yescharacteristic, complemented, Hall
312C22×C3—21no—
313C22×C3—21no—
314C22×C3D5×C22⋊C411yescharacteristic
315C22×C3C2×#67611yescharacteristic
316C22×C3D5×M1611yescharacteristic
317C2×D3—102no—
318C2×D3—102no—
319C2×D3—102no—
320C2×D3—102no—
321C2×D3—202no—
322C2×D3—202no—
323C2×D3—202no—
324C2×D3—201no—
325C2×D3—201no—
326C2×D3—202no—
327C3×C4—22no—
328C3×C4—22no—
329C3×C4—41no—
330Dic3—52no—
331Dic3—101no—
332Dic3—201no—
333C2×C5—21no—
334C2×C5—21no—
335C2×C5#472611yescharacteristic
336C2×C5D3×#9911yescharacteristic
337C2×C5#475111yescharacteristic
338D5—122no—
339D5—122no—
340C23—152no—
341C23—152no—
342C23—301no—
343C23—301no—
344C23—301no—
345C23—301no—
346C23—601no—
347C23—601no—
348C23—601no—
349C23—601no—
350C23C2×C4×D1511yescharacteristic
351D4—308no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—151no—
358C2×C4—151no—
359C2×C4—304no—
360C2×C4—302no—
361C2×C4—301no—
362C2×C4—602no—
363C2×C4—602no—
364C2×C4—602no—
365C2×C4—601no—
366C2×C4#670512yescomplemented
367C2×C4D4×D1512yes—
368C8—42no—
369C8—602no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3#6501511yescharacteristic
373C2×C3D5×#9911yescharacteristic
374C2×C3#6504011yescharacteristic
375D3—202no—
376D3—202no—
377C5#6814511yescharacteristic, complemented, Sylow
378C22—21no—
379C22—21no—
380C22—302no—
381C22—302no—
382C22—302no—
383C22—302no—
384C22—602no—
385C22—602no—
386C22—602no—
387C22—602no—
388C22—601no—
389C22—601no—
390C22C22⋊C4×D1511yescharacteristic
391C22C2×#670511yescharacteristic
392C22M16×D1511yescharacteristic
393C4—22no—
394C4—22no—
395C4—41no—
396C4—152no—
397C4—301no—
398C4—601no—
399C3#1059893811yescharacteristic, complemented, Sylow
400C2—21no—
401C2—21no—
402C2—602no—
403C2—602no—
404C2#1175082711yescharacteristic
405C2D15×#9911yescharacteristic
406C2#1175085211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#324C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D60C4
cosocleC22×C3×C4×C5C23
hypercenter#324D15
hypocenterC3×C5#1465
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #11750827C2semidirect
3. C3×C5×#324C2semidirect
4. #11746349C2semidirect
5. #11746289C2semidirect
23. C5×#324D3semidirect
52. C3×#324D5semidirect
79. C22×D15M16semidirect
85. C2×C3×C4×C5M16semidirect
139. #324D15semidirect
202. C2×C4×C5ΓL(1,𝔽25)semidirect
252. C2×C3×C4#676semidirect
311. C3×C5#1465semidirect
366. C2×C4#6705semidirect
377. C5#68145semidirect
399. C3#10598938semidirect

Maximal subgroups

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

subgroupindex
C2×#917822
#117508272
C3×C5×#3242
#117463492
#117462892
#105989383
#681455