Finite Group Databasebeta

← #14287998

Subgroups — #14287998

Order 1920.

512 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 85 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#11756393C211yesmaximal, characteristic
2C3×C5×#451C211yesmaximal, characteristic, complemented
3#11751332C211yesmaximal, characteristic
4#11751329C211yesmaximal, characteristic, complemented
5#11746359C211yesmaximal, characteristic, complemented
6#11746289C211yesmaximal, characteristic
7#11746288C211yesmaximal, characteristic, complemented
8#10601773—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C2×C3×C5×Q16—21no—
11C3×C5×C22⋊Q8C2211yescharacteristic
12#91835—21no—
13C2×#6718—21no—
14C2×#6714—21no—
15C2×#6714C2211yescharacteristic
16#91813C2211yescharacteristic
17#91786—21no—
18#91785—21no—
19#91785—21no—
20C22⋊C4×D15—21no—
21#91767—21no—
22C3×C5×#103—21no—
23C3×C5×C22⋊C8C2211yescharacteristic
24#91119—21no—
25#91115—21no—
26#91115C2211yescharacteristic
27#91114C2211yescharacteristic
28#70980—51nomaximal, Hall
29#65968—31no—
30C5×#451D311yescharacteristic, complemented
31#65520—31no—
32#65517—31no—
33#64758—31no—
34#64688—31no—
35#64687—31no—
36C23×D15D411yescharacteristic
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8—42no—
40C2×C3×C5×Q8D411yescharacteristic
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C22×Dic15—21no—
44C22×Dic15D411yescharacteristic
45C2×C4×D15—21no—
46C2×C4×D15—21no—
47C2×Dic30—21no—
48C2×Dic30D411yescharacteristic
49C3×C5×Q16—42no—
50C2×C3×C5×C8—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4D411yescharacteristic
53C3×C5×C22⋊C4—21no—
54#6719—21no—
55#6718—42no—
56#6714—21no—
57#6714—21no—
58#6714—21no—
59#6714—21no—
60#6714—42no—
61C4⋊Dic15—21no—
62C4⋊Dic15D411yescharacteristic
63#6712—21no—
64#6712—21no—
65#6712—21no—
66C2×C3⋊#168—21no—
67#5634—51no—
68C3×#451D511yescharacteristic, complemented
69#5231—51no—
70#5228—51no—
71#4538—51no—
72#4468—51no—
73#4467—51no—
74C22×C5×Q8C2×D311yescharacteristic
75C2×C5×Q16—21no—
76C5×C22⋊Q8C2×D311yescharacteristic
77#4092—61no—
78C2×#689—61no—
79C2×#685—31no—
80C2×#685—61no—
81#4070—31no—
82#4043—61no—
83#4042—61no—
84#4042—61no—
85D5×C22⋊C4—61no—
86#4024—61no—
87C5×#103—21no—
88C5×C22⋊C8C2×D311yescharacteristic
89#3967—61no—
90#3963—31no—
91#3963—61no—
92C22⋊#168—31no—
93#1602—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—21no—
96C22×D15—21no—
97C22×D15—41no—
98C22×D15—41no—
99C22×D15Q1612yescomplemented
100C3×C5×Q8—22no—
101C3×C5×Q8—22no—
102C3×C5×Q8—41no—
103C3×C5×Q8—41no—
104C3×C5×Q8—41no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×Dic15—21no—
114C2×Dic15—21no—
115C2×Dic15—21no—
116C2×Dic15—41no—
117C2×Dic15—41no—
118C2×Dic15—41no—
119C2×Dic15—41no—
120C4×D15—81no—
121C4×D15—81no—
122Dic30—41no—
123Dic30—81no—
124C3×C5×C8—41no—
125C3⋊#168—41no—
126C22×C3×Q8C2×D511yescharacteristic
127C2×C3×Q16—21no—
128C3×C22⋊Q8C2×D511yescharacteristic
129#946—101no—
130C2×#216—101no—
131C2×(C2×D3)⋊C4—51no—
132C2×(C2×D3)⋊C4—101no—
133#924—51no—
134#897—101no—
135#896—101no—
136#896—101no—
137D3×C22⋊C4—101no—
138#878—101no—
139C3×#103—21no—
140C3×C22⋊C8C2×D511yescharacteristic
141#835—101no—
142C3⋊#95—51no—
143C3⋊#95—101no—
144#830—51no—
145C23×D5—31no—
146C2×C5×Q8—21no—
147C2×C5×Q8—21no—
148C2×C5×Q8—42no—
149C2×C5×Q8#6711yescharacteristic
150C22×C4×C5—21no—
151C22×C4×C5C22×D311yescharacteristic
152C22×Dic5—31no—
153C22×Dic5—61no—
154C2×C4×D5—61no—
155C2×C4×D5—61no—
156C2×Dic10—31no—
157C2×Dic10—61no—
158C5×Q16—42no—
159C2×C5×C8—21no—
160C5×C4⋊C4—21no—
161C5×C4⋊C4#6711yescharacteristic
162C5×C22⋊C4—21no—
163C22⋊Dic5—61no—
164#689—122no—
165#685—61no—
166#685—61no—
167#685—61no—
168#685—61no—
169#685—122no—
170C4⋊Dic5—31no—
171C4⋊Dic5—61no—
172#683—61no—
173#683—61no—
174#683—61no—
175C2×#168—61no—
176#543—151no—
177#451—151no—
178#451D1511yescharacteristic, complemented
179#393—151no—
180#328—151no—
181#328—151no—
182#323—151no—
183C22×C3×C5—21no—
184C22×C3×C5—21no—
185C22×C3×C5#12011yescharacteristic
186C22×C3×C5C2×Q1611yescharacteristic
187C22×C3×C5#13711yescharacteristic
188C2×D15—22no—
189C2×D15—41no—
190C2×D15—41no—
191C2×D15—42no—
192C2×D15—81no—
193C3×C4×C5—21no—
194C3×C4×C5—21no—
195C3×C4×C5—41no—
196C3×C4×C5—41no—
197C3×C4×C5—42no—
198Dic15—41no—
199Dic15—41no—
200Dic15—41no—
201Dic15—81no—
202C23×D3—51no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—42no—
206C2×C3×Q8C22⋊D511yescharacteristic
207C22×C3×C4—21no—
208C22×C3×C4C22×D511yescharacteristic
209C22×Dic3—51no—
210C22×Dic3—101no—
211C2×C4×D3—101no—
212C2×C4×D3—101no—
213C2×Dic6—51no—
214C2×Dic6—101no—
215C3×Q16—42no—
216C2×C3×C8—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4C22⋊D511yescharacteristic
219C3×C22⋊C4—21no—
220#217—101no—
221#216—202no—
222(C2×D3)⋊C4—101no—
223(C2×D3)⋊C4—101no—
224(C2×D3)⋊C4—101no—
225(C2×D3)⋊C4—101no—
226(C2×D3)⋊C4—202no—
227C4⋊Dic3—51no—
228C4⋊Dic3—101no—
229Dic3⋊C4—101no—
230Dic3⋊C4—101no—
231Dic3⋊C4—101no—
232C2×C3⋊C8—101no—
233C23×C5D3×D411yescharacteristic
234C22×D5—32no—
235C22×D5—61no—
236C22×D5—61no—
237C22×D5—121no—
238C22×D5—121no—
239C5×Q8—22no—
240C5×Q8—22no—
241C5×Q8—41no—
242C5×Q8—41no—
243C5×Q8—41no—
244C2×C4×C5—22no—
245C2×C4×C5—21no—
246C2×C4×C5—21no—
247C2×C4×C5—41no—
248C2×C4×C5—41no—
249C2×C4×C5—41no—
250C2×C4×C5D3×D411yescharacteristic
251C2×C4×C5C2×#6711yescharacteristic
252C2×Dic5—61no—
253C2×Dic5—61no—
254C2×Dic5—61no—
255C2×Dic5—121no—
256C2×Dic5—121no—
257C2×Dic5—121no—
258C2×Dic5—121no—
259C4×D5—241no—
260C4×D5—241no—
261Dic10—121no—
262Dic10—241no—
263C5×C8—41no—
264#168—121no—
265C22×Q8C2×D1511yescharacteristic
266C2×Q16—21no—
267C2×Q16—301no—
268C22⋊Q8—151no—
269C22⋊Q8—301no—
270C22⋊Q8—301no—
271C22⋊Q8—301no—
272C22⋊Q8—301no—
273C22⋊Q8—301no—
274C22⋊Q8C2×D1511yescharacteristic
275C2×C22⋊C4—151no—
276C2×C22⋊C4—301no—
277C2×C22⋊C4—301no—
278#103—21no—
279#103—301no—
280C22⋊C8—151no—
281C22⋊C8C2×D1511yescharacteristic
282#95—151no—
283#95—301no—
284C2×C3×C5—21no—
285C2×C3×C5—21no—
286C2×C3×C5#45111yescharacteristic
287C2×C3×C5#45511yescharacteristic
288C2×C3×C5B(4,𝔽2)11yescharacteristic
289D15—42no—
290C23×C3D4×D511yescharacteristic
291C22×D3—52no—
292C22×D3—101no—
293C22×D3—101no—
294C22×D3—201no—
295C22×D3—201no—
296C3×Q8—22no—
297C3×Q8—22no—
298C3×Q8—41no—
299C3×Q8—41no—
300C3×Q8—41no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4D4×D511yescharacteristic
308C2×C3×C4C2×C22⋊D511yescharacteristic
309C2×Dic3—101no—
310C2×Dic3—101no—
311C2×Dic3—101no—
312C2×Dic3—201no—
313C2×Dic3—201no—
314C2×Dic3—201no—
315C2×Dic3—201no—
316C4×D3—401no—
317C4×D3—401no—
318Dic6—201no—
319Dic6—401no—
320C3×C8—41no—
321C3⋊C8—201no—
322C22×C5—21no—
323C22×C5—21no—
324C22×C5D3×Q1611yescharacteristic
325C22×C5#91811yescharacteristic
326C22×C5#93711yescharacteristic
327C2×D5—62no—
328C2×D5—121no—
329C2×D5—121no—
330C2×D5—122no—
331C2×D5—241no—
332C4×C5—21no—
333C4×C5—21no—
334C4×C5—41no—
335C4×C5—41no—
336C4×C5—42no—
337Dic5—121no—
338Dic5—121no—
339Dic5—121no—
340Dic5—241no—
341C24—151no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—42no—
345C2×Q8—151no—
346C2×Q8—301no—
347C2×Q8#122011yescharacteristic
348C22×C4—21no—
349C22×C4—151no—
350C22×C4—301no—
351C22×C4—301no—
352C22×C4—301no—
353C22×C4C22×D1511yescharacteristic
354Q16—42no—
355Q16—602no—
356C2×C8—21no—
357C2×C8—301no—
358C4⋊C4—21no—
359C4⋊C4—151no—
360C4⋊C4—301no—
361C4⋊C4—301no—
362C4⋊C4—301no—
363C4⋊C4—301no—
364C4⋊C4#122011yescharacteristic
365C22⋊C4—21no—
366C22⋊C4—301no—
367C22⋊C4—301no—
368C22⋊C4—301no—
369C22⋊C4—301no—
370C22⋊C4—301no—
371C22⋊C4—602no—
372C3×C5#160211yescharacteristic, complemented, Hall
373C22×C3—21no—
374C22×C3—21no—
375C22×C3D5×Q1611yescharacteristic
376C22×C3#406411yescharacteristic
377C22×C3#408311yescharacteristic
378C2×D3—102no—
379C2×D3—201no—
380C2×D3—201no—
381C2×D3—202no—
382C2×D3—401no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—41no—
386C3×C4—42no—
387C3×C4—41no—
388Dic3—201no—
389Dic3—201no—
390Dic3—201no—
391Dic3—401no—
392C2×C5—21no—
393C2×C5—21no—
394C2×C5#503211yescharacteristic
395C2×C5#518611yescharacteristic
396C2×C5#520211yescharacteristic
397D5—122no—
398C23—152no—
399C23—301no—
400C23—301no—
401C23—601no—
402C23—601no—
403C23D4×D1511yescharacteristic
404Q8—22no—
405Q8—22no—
406Q8—41no—
407Q8—41no—
408Q8—41no—
409Q8—601no—
410Q8—1201no—
411C2×C4—22no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—301no—
418C2×C4—301no—
419C2×C4—301no—
420C2×C4—601no—
421C2×C4—601no—
422C2×C4—601no—
423C2×C4—601no—
424C2×C4—1201no—
425C2×C4—1201no—
426C2×C4D4×D1511yescharacteristic
427C2×C4C2×#122011yescharacteristic
428C8—41no—
429C8—601no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3#6532111yescharacteristic
433C2×C3#6547511yescharacteristic
434C2×C3#6549111yescharacteristic
435D3—202no—
436C5#7098011yescharacteristic, complemented, Sylow
437C22—21no—
438C22—21no—
439C22—302no—
440C22—602no—
441C22—601no—
442C22—601no—
443C22—1201no—
444C22Q16×D1511yescharacteristic
445C22#9180711yescharacteristic
446C22#9182611yescharacteristic
447C4—21no—
448C4—21no—
449C4—41no—
450C4—42no—
451C4—41no—
452C4—601no—
453C4—601no—
454C4—601no—
455C4—1201no—
456C3#1060177311yescharacteristic, complemented, Sylow
457C2—21no—
458C2—21no—
459C2—602no—
460C2#1175113311yescharacteristic
461C2#1175128711yescharacteristic
462C2#1175130311yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#451C2
socleC22×C3×C5#120
prime radicalC23×D15D4
hypercenter#451D15
hypocenterC3×C5#1602
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C3×C5×#451C2semidirect
4. #11751329C2semidirect
5. #11746359C2semidirect
7. #11746288C2semidirect
30. C5×#451D3semidirect
68. C3×#451D5semidirect
99. C22×D15Q16semidirect
178. #451D15semidirect
372. C3×C5#1602semidirect
436. C5#70980semidirect
456. C3#10601773semidirect

Maximal subgroups

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

subgroupindex
#117563932
C3×C5×#4512
#117513322
#117513292
#117463592
#117462892
#117462882
#106017733
#709805