Finite Group Databasebeta

← #14287722

Subgroups — #14287722

Order 1920.

632 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C3×C5×#543C211yesmaximal, characteristic, complemented
2#11751147C212yesmaximal, complemented
3#11751061C211yesmaximal, characteristic
4#11746359C212yesmaximal, complemented
5#11746346C211yesmaximal, characteristic, complemented
6#10602685—31nomaximal, Hall
7C22×#1220—21no—
8C22×D60C2211yescharacteristic
9C3×C5×C22⋊Q8—22no—
10C3×C5×C22⋊Q8—21no—
11C3×C5×C22⋊Q8—22no—
12C3×C5×C22⋊Q8C2212yes—
13C2×C3×C5×C22⋊C4—21no—
14C2×C3×C5×C22⋊C4C2211yescharacteristic
15C2×#6717—22no—
16C2×#6714—21no—
17#91115C2211yescharacteristic
18#91114C2212yes—
19#91093—22no—
20#71892—51nomaximal, Hall
21C5×#543D311yescharacteristic, complemented
22#65335—32no—
23#65249—31no—
24#64758—32no—
25#64745—31no—
26C24×C3×C5D411yescharacteristic
27C23×D15—21no—
28C2×C3×C5×Q8—21no—
29C2×C3×C5×Q8D412yescomplemented
30C22×C3×C4×C5—21no—
31C22×C3×C4×C5—21no—
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5C2311yescharacteristic
34C2×#1220—42no—
35C2×#1220—42no—
36C2×#1220—42no—
37C22×Dic15—21no—
38C2×D60—22no—
39C2×D60—42no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—22no—
42C3×C5×C4⋊C4—22no—
43C3×C5×C4⋊C4D412yescomplemented
44C3×C5×C22⋊C4—22no—
45C3×C5×C22⋊C4—22no—
46C3×C5×C22⋊C4—22no—
47#6717—44no—
48#6714—42no—
49C2×C3⋊#168—22no—
50C3×#543D511yescharacteristic, complemented
51#5046—52no—
52#4960—51no—
53#4538—52no—
54#4525—51no—
55C22×C22⋊D5—61no—
56C22×D20—31no—
57C5×C22⋊Q8—22no—
58C5×C22⋊Q8—21no—
59C5×C22⋊Q8—22no—
60C5×C22⋊Q8C2×D312yes—
61C2×C5×C22⋊C4—21no—
62C2×C5×C22⋊C4C2×D311yescharacteristic
63C2×#688—62no—
64C2×#685—61no—
65#3963—31no—
66C22⋊#168—32no—
67#3941—62no—
68#1596—151noSylow
69C23×C3×C5—21no—
70C23×C3×C5—21no—
71C23×C3×C5—41no—
72C23×C3×C5—41no—
73C23×C3×C5SD1612yescomplemented
74C23×C3×C5C2×D411yescharacteristic
75C22×D15—22no—
76C22×D15—41no—
77C22×D15—41no—
78C22×D15—41no—
79C22×D15—41no—
80C22×D15—41no—
81C22×D15—41no—
82C3×C5×Q8—42no—
83C3×C5×Q8—81no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—81no—
90C2×C3×C4×C5—81no—
91C2×C3×C4×C5C2×D412yes—
92#1220—48no—
93C2×Dic15—22no—
94C2×Dic15—41no—
95C2×Dic15—41no—
96D60—24no—
97D60—42no—
98C3⋊#168—42no—
99C22×#67—101no—
100C22×D12—51no—
101C3×C22⋊Q8—22no—
102C3×C22⋊Q8—21no—
103C3×C22⋊Q8—22no—
104C3×C22⋊Q8C2×D512yes—
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4C2×D511yescharacteristic
107C2×#215—102no—
108C2×(C2×D3)⋊C4—101no—
109C3⋊#95—51no—
110#830—52no—
111#809—102no—
112C24×C5#6711yescharacteristic
113C23×D5—61no—
114C2×C5×Q8—21no—
115C2×C5×Q8#6712yescomplemented
116C22×C4×C5—21no—
117C22×C4×C5—21no—
118C22×C4×C5#6711yescharacteristic
119C22×C4×C5C22×D311yescharacteristic
120C2×C22⋊D5—122no—
121C2×C22⋊D5—122no—
122C2×C22⋊D5—122no—
123C22×Dic5—61no—
124C2×D20—62no—
125C2×D20—122no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—22no—
128C5×C4⋊C4—22no—
129C5×C4⋊C4#6712yescomplemented
130C5×C22⋊C4—22no—
131C5×C22⋊C4—22no—
132C5×C22⋊C4—22no—
133#688—124no—
134#685—122no—
135C2×#168—62no—
136#543D1511yescharacteristic, complemented
137#450—152no—
138#392—151no—
139#328—152no—
140#323—151no—
141C22×C3×C5—21no—
142C22×C3×C5—21no—
143C22×C3×C5—22no—
144C22×C3×C5—42no—
145C22×C3×C5—41no—
146C22×C3×C5—41no—
147C22×C3×C5—81no—
148C22×C3×C5#12011yescharacteristic
149C22×C3×C5C2×SD1611yescharacteristic
150C22×C3×C5#13711yescharacteristic
151C2×D15—42no—
152C2×D15—42no—
153C2×D15—42no—
154C2×D15—81no—
155C2×D15—81no—
156C2×D15—81no—
157C2×D15—81no—
158C3×C4×C5—22no—
159C3×C4×C5—41no—
160C3×C4×C5—42no—
161C3×C4×C5—42no—
162Dic15—42no—
163C24×C3C22⋊D511yescharacteristic
164C23×D3—101no—
165C2×C3×Q8—21no—
166C2×C3×Q8C22⋊D512yescomplemented
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4C22⋊D511yescharacteristic
170C22×C3×C4C22×D511yescharacteristic
171C2×#67—202no—
172C2×#67—202no—
173C2×#67—202no—
174C22×Dic3—101no—
175C2×D12—102no—
176C2×D12—202no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—22no—
179C3×C4⋊C4—22no—
180C3×C4⋊C4C22⋊D512yescomplemented
181C3×C22⋊C4—22no—
182C3×C22⋊C4—22no—
183C3×C22⋊C4—22no—
184#215—204no—
185(C2×D3)⋊C4—202no—
186C2×C3⋊C8—102no—
187C23×C5—21no—
188C23×C5—21no—
189C23×C5—41no—
190C23×C5—41no—
191C23×C5#21512yescomplemented
192C23×C5C2×#6711yescharacteristic
193C22×D5—62no—
194C22×D5—121no—
195C22×D5—121no—
196C22×D5—121no—
197C22×D5—121no—
198C22×D5—121no—
199C22×D5—121no—
200C5×Q8—42no—
201C5×Q8—81no—
202C2×C4×C5—22no—
203C2×C4×C5—21no—
204C2×C4×C5—22no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—81no—
208C2×C4×C5—81no—
209C2×C4×C5C2×#6712yes—
210C22⋊D5—128no—
211C2×Dic5—62no—
212C2×Dic5—121no—
213C2×Dic5—121no—
214D20—64no—
215D20—122no—
216#168—122no—
217C22×D4—151no—
218C22×D4—301no—
219C2×SD16—302no—
220C22⋊Q8—22no—
221C22⋊Q8—21no—
222C22⋊Q8—22no—
223C22⋊Q8C2×D1512yes—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—301no—
226C2×C22⋊C4C2×D1511yescharacteristic
227#102—302no—
228C22⋊C8—152no—
229#95—151no—
230C2×C3×C5—21no—
231C2×C3×C5—21no—
232C2×C3×C5—42no—
233C2×C3×C5#44811yescharacteristic
234C2×C3×C5#45311yescharacteristic
235C2×C3×C5B(4,𝔽2)11yescharacteristic
236D15—82no—
237C23×C3—21no—
238C23×C3—21no—
239C23×C3—41no—
240C23×C3—41no—
241C23×C3#68812yescomplemented
242C23×C3C2×C22⋊D511yescharacteristic
243C22×D3—102no—
244C22×D3—201no—
245C22×D3—201no—
246C22×D3—201no—
247C22×D3—201no—
248C22×D3—201no—
249C22×D3—201no—
250C3×Q8—42no—
251C3×Q8—81no—
252C2×C3×C4—22no—
253C2×C3×C4—21no—
254C2×C3×C4—22no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—81no—
258C2×C3×C4—81no—
259C2×C3×C4C2×C22⋊D512yes—
260#67—208no—
261C2×Dic3—102no—
262C2×Dic3—201no—
263C2×Dic3—201no—
264D12—104no—
265D12—202no—
266C3⋊C8—202no—
267C22×C5—21no—
268C22×C5—21no—
269C22×C5—22no—
270C22×C5—42no—
271C22×C5—41no—
272C22×C5—41no—
273C22×C5—81no—
274C22×C5C2×#21511yescharacteristic
275C22×C5#94211yescharacteristic
276C22×C5#95311yescharacteristic
277C2×D5—122no—
278C2×D5—122no—
279C2×D5—122no—
280C2×D5—241no—
281C2×D5—241no—
282C2×D5—241no—
283C2×D5—241no—
284C4×C5—22no—
285C4×C5—41no—
286C4×C5—42no—
287C4×C5—42no—
288Dic5—122no—
289C24—301no—
290C24#122011yescharacteristic
291C2×Q8—21no—
292C2×Q8#122012yescomplemented
293C2×D4—302no—
294C2×D4—602no—
295C2×D4—602no—
296C2×D4—602no—
297C2×D4—602no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—301no—
301C22×C4#122011yescharacteristic
302C22×C4C22×D1511yescharacteristic
303SD16—604no—
304C2×C8—302no—
305C4⋊C4—21no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4#122012yescomplemented
309C22⋊C4—22no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—602no—
313C3×C5#159611yescharacteristic, complemented, Hall
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—22no—
317C22×C3—42no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—81no—
321C22×C3C2×#68811yescharacteristic
322C22×C3#408811yescharacteristic
323C22×C3#409911yescharacteristic
324C2×D3—202no—
325C2×D3—202no—
326C2×D3—202no—
327C2×D3—401no—
328C2×D3—401no—
329C2×D3—401no—
330C2×D3—401no—
331C3×C4—22no—
332C3×C4—41no—
333C3×C4—42no—
334C3×C4—42no—
335Dic3—202no—
336C2×C5—21no—
337C2×C5—21no—
338C2×C5—42no—
339C2×C5#522711yescharacteristic
340C2×C5#524111yescharacteristic
341C2×C5#524411yescharacteristic
342D5—242no—
343C23—21no—
344C23—21no—
345C23—41no—
346C23—41no—
347C23—302no—
348C23—601no—
349C23—601no—
350C23—601no—
351C23—601no—
352C23—601no—
353C23—601no—
354C23#671712yescomplemented
355C23C2×#122011yescharacteristic
356Q8—42no—
357Q8—81no—
358D4—304no—
359D4—602no—
360D4—608no—
361C2×C4—22no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—302no—
369C2×C4—601no—
370C2×C4—601no—
371C2×C4C2×#122012yes—
372C8—602no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—42no—
376C2×C3#6551611yescharacteristic
377C2×C3#6553011yescharacteristic
378C2×C3#6553311yescharacteristic
379D3—402no—
380C5#7189211yescharacteristic, complemented, Sylow
381C22—21no—
382C22—21no—
383C22—22no—
384C22—42no—
385C22—41no—
386C22—41no—
387C22—81no—
388C22—602no—
389C22—602no—
390C22—602no—
391C22—1201no—
392C22—1201no—
393C22—1201no—
394C22—1201no—
395C22C2×#671711yescharacteristic
396C22#9183111yescharacteristic
397C22#9184211yescharacteristic
398C4—22no—
399C4—41no—
400C4—42no—
401C4—42no—
402C4—602no—
403C3#1060268511yescharacteristic, complemented, Sylow
404C2—21no—
405C2—21no—
406C2—42no—
407C2—1202no—
408C2#1175132811yescharacteristic
409C2#1175134211yescharacteristic
410C2#1175134511yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#543C2
socleC22×C3×C5#120
prime radical#11751061C2
hypercenter#543D15
hypocenterC3×C5#1596
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #543

Complements

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

NH ≅ G/Ntype
1. C3×C5×#543C2semidirect
2. #11751147C2semidirect
4. #11746359C2semidirect
5. #11746346C2semidirect
21. C5×#543D3semidirect
29. C2×C3×C5×Q8D4semidirect
43. C3×C5×C4⋊C4D4semidirect
50. C3×#543D5semidirect
73. C23×C3×C5SD16semidirect
115. C2×C5×Q8#67semidirect
129. C5×C4⋊C4#67semidirect
136. #543D15semidirect
166. C2×C3×Q8C22⋊D5semidirect
180. C3×C4⋊C4C22⋊D5semidirect
191. C23×C5#215semidirect
241. C23×C3#688semidirect
292. C2×Q8#1220semidirect
308. C4⋊C4#1220semidirect
313. C3×C5#1596semidirect
354. C23#6717semidirect
380. C5#71892semidirect
403. C3#10602685semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5432
#117511472
#117510612
#117463592
#117463462
#106026853
#718925