Finite Group Databasebeta

← #14287764

Subgroups — #14287764

Order 1920.

544 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 95 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×#539C211yesmaximal, characteristic, complemented
2#11751147C211yesmaximal, characteristic, complemented
3#11751137C211yesmaximal, characteristic
4#11751092C211yesmaximal, characteristic, complemented
5#11746359C211yesmaximal, characteristic, complemented
6#11746358C211yesmaximal, characteristic, complemented
7#11746349C211yesmaximal, characteristic, complemented
8#10602681—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C3×C5×#126—21no—
11C3×C5×#125—21no—
12C3×C5×#123—21no—
13C3×C5×#123—21no—
14C3×C5×C22⋊Q8—21no—
15C3×C5×C22⋊Q8C2211yescharacteristic
16C3×C5×#121C2211yescharacteristic
17C3×C4×C5×D4—21no—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×#6717—21no—
20C2×#6715—21no—
21C2×#6714—21no—
22C2×#6714—21no—
23#91115C2211yescharacteristic
24#91114C2211yescharacteristic
25#91114C2211yescharacteristic
26#91093—21no—
27#91093—21no—
28#71888—51nomaximal, Hall
29C5×#539D311yescharacteristic, complemented
30#65335—31no—
31#65325—31no—
32#65280—31no—
33#64758—31no—
34#64757—31no—
35#64748—31no—
36C23×D15—21no—
37C2×C3×C5×Q8D411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4D411yescharacteristic
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5D411yescharacteristic
42C22×C3×C4×C5D411yescharacteristic
43C22×C3×C4×C5C2311yescharacteristic
44C22×Dic15—21no—
45C2×D60—21no—
46C2×D60—21no—
47C2×D60—42no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4D411yescharacteristic
55C3×C5×C4⋊C4D411yescharacteristic
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C5×C22⋊C4—21no—
61C3×C42×C5—21no—
62#6717—42no—
63#6715—42no—
64#6714—42no—
65#6714—42no—
66C2×C3⋊#168—21no—
67C2×C3⋊#168—21no—
68C3×#539D511yescharacteristic, complemented
69#5046—51no—
70#5036—51no—
71#4991—51no—
72#4538—51no—
73#4537—51no—
74#4528—51no—
75C22×D20—31no—
76C5×#126—21no—
77C5×#125—21no—
78C5×#123—21no—
79C5×#123—21no—
80C5×C22⋊Q8—21no—
81C5×C22⋊Q8C2×D311yescharacteristic
82C5×#121C2×D311yescharacteristic
83C4×C5×D4—21no—
84C2×C5×C4⋊C4C2×D311yescharacteristic
85C2×#688—61no—
86C2×#686—61no—
87C2×#685—61no—
88C2×#685—61no—
89#3963—31no—
90C22⋊#168—31no—
91C22⋊#168—31no—
92#3941—61no—
93#3941—61no—
94#1597—151noSylow
95C23×C3×C5—21no—
96C23×C3×C5C2×D411yescharacteristic
97C22×D15—22no—
98C22×D15—41no—
99C22×D15—41no—
100C22×D15—41no—
101C22×D15—41no—
102C22×D15—41no—
103C22×D15—41no—
104C3×C5×Q8—41no—
105C3×C5×D4—41no—
106C3×C5×D4—41no—
107C3×C5×D4—41no—
108C2×C3×C4×C5—21no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5—81no—
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5C2×D411yescharacteristic
120C2×Dic15—41no—
121C2×Dic15—41no—
122C2×Dic15—41no—
123D60—22no—
124D60—22no—
125D60—41no—
126D60—41no—
127C3⋊#168—41no—
128C3⋊#168—41no—
129C22×D12—51no—
130C3×#126—21no—
131C3×#125—21no—
132C3×#123—21no—
133C3×#123—21no—
134C3×C22⋊Q8—21no—
135C3×C22⋊Q8C2×D511yescharacteristic
136C3×#121C2×D511yescharacteristic
137C3×C4×D4—21no—
138C2×C3×C4⋊C4C2×D511yescharacteristic
139C2×#215—101no—
140C2×#213—101no—
141C2×(C2×D3)⋊C4—101no—
142C2×(C2×D3)⋊C4—101no—
143C3⋊#95—51no—
144#830—51no—
145#830—51no—
146#809—101no—
147#809—101no—
148C23×D5—61no—
149C2×C5×Q8#6711yescharacteristic
150C2×C5×D4—21no—
151C2×C5×D4#6711yescharacteristic
152C22×C4×C5—21no—
153C22×C4×C5#6711yescharacteristic
154C22×C4×C5#6711yescharacteristic
155C22×C4×C5C22×D311yescharacteristic
156C22×Dic5—61no—
157C2×D20—61no—
158C2×D20—61no—
159C2×D20—122no—
160C5×C4⋊C4—21no—
161C5×C4⋊C4—21no—
162C5×C4⋊C4—21no—
163C5×C4⋊C4—21no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4#6711yescharacteristic
167C5×C4⋊C4#6711yescharacteristic
168C5×C22⋊C4—21no—
169C5×C22⋊C4—21no—
170C5×C22⋊C4—21no—
171C5×C22⋊C4—21no—
172C5×C22⋊C4—21no—
173C42×C5—21no—
174#688—122no—
175#686—122no—
176#685—122no—
177#685—122no—
178C2×#168—61no—
179C2×#168—61no—
180#539D1511yescharacteristic, complemented
181#450—151no—
182#447—151no—
183#394—151no—
184#328—151no—
185#327—151no—
186#324—151no—
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5—41no—
190C22×C3×C5—41no—
191C22×C3×C5—41no—
192C22×C3×C5#12011yescharacteristic
193C22×C3×C5#13511yescharacteristic
194C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
195C2×D15—42no—
196C2×D15—42no—
197C2×D15—42no—
198C2×D15—81no—
199C2×D15—81no—
200C2×D15—81no—
201C2×D15—81no—
202C3×C4×C5—21no—
203C3×C4×C5—21no—
204C3×C4×C5—41no—
205C3×C4×C5—41no—
206C3×C4×C5—41no—
207C3×C4×C5—41no—
208C3×C4×C5—41no—
209Dic15—81no—
210C23×D3—101no—
211C2×C3×Q8C22⋊D511yescharacteristic
212C2×C3×D4—21no—
213C2×C3×D4C22⋊D511yescharacteristic
214C22×C3×C4—21no—
215C22×C3×C4C22⋊D511yescharacteristic
216C22×C3×C4C22⋊D511yescharacteristic
217C22×C3×C4C22×D511yescharacteristic
218C22×Dic3—101no—
219C2×D12—101no—
220C2×D12—101no—
221C2×D12—202no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4C22⋊D511yescharacteristic
229C3×C4⋊C4C22⋊D511yescharacteristic
230C3×C22⋊C4—21no—
231C3×C22⋊C4—21no—
232C3×C22⋊C4—21no—
233C3×C22⋊C4—21no—
234C3×C22⋊C4—21no—
235C3×C42—21no—
236#215—202no—
237#213—202no—
238(C2×D3)⋊C4—202no—
239(C2×D3)⋊C4—202no—
240C2×C3⋊C8—101no—
241C2×C3⋊C8—101no—
242C23×C5—21no—
243C23×C5C2×#6711yescharacteristic
244C22×D5—62no—
245C22×D5—121no—
246C22×D5—121no—
247C22×D5—121no—
248C22×D5—121no—
249C22×D5—121no—
250C22×D5—121no—
251C5×Q8—41no—
252C5×D4—41no—
253C5×D4—41no—
254C5×D4—41no—
255C2×C4×C5—21no—
256C2×C4×C5—21no—
257C2×C4×C5—21no—
258C2×C4×C5—21no—
259C2×C4×C5—21no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—41no—
263C2×C4×C5—41no—
264C2×C4×C5—81no—
265C2×C4×C5C2×#6711yescharacteristic
266C2×C4×C5C2×#6711yescharacteristic
267C2×Dic5—121no—
268C2×Dic5—121no—
269C2×Dic5—121no—
270D20—62no—
271D20—62no—
272D20—121no—
273D20—121no—
274#168—121no—
275#168—121no—
276C22×D4—151no—
277C2×SD16—301no—
278C2×D8—301no—
279#126—21no—
280#125—21no—
281#123—21no—
282#123—21no—
283C22⋊Q8—21no—
284C22⋊Q8C2×D1511yescharacteristic
285#121C2×D1511yescharacteristic
286C4×D4—21no—
287C2×C4⋊C4C2×D1511yescharacteristic
288C2×C22⋊C4—301no—
289C2×C22⋊C4—301no—
290#102—301no—
291#102—301no—
292C22⋊C8—151no—
293C22⋊C8—151no—
294#95—151no—
295C2×C3×C5—21no—
296C2×C3×C5—21no—
297C2×C3×C5—81no—
298C2×C3×C5#44911yescharacteristic
299C2×C3×C5#45411yescharacteristic
300C2×C3×C5B(4,𝔽2)11yescharacteristic
301D15—82no—
302C23×C3—21no—
303C23×C3C2×C22⋊D511yescharacteristic
304C22×D3—102no—
305C22×D3—201no—
306C22×D3—201no—
307C22×D3—201no—
308C22×D3—201no—
309C22×D3—201no—
310C22×D3—201no—
311C3×Q8—41no—
312C3×D4—41no—
313C3×D4—41no—
314C3×D4—41no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—81no—
325C2×C3×C4C2×C22⋊D511yescharacteristic
326C2×C3×C4C2×C22⋊D511yescharacteristic
327C2×Dic3—201no—
328C2×Dic3—201no—
329C2×Dic3—201no—
330D12—102no—
331D12—102no—
332D12—201no—
333D12—201no—
334C3⋊C8—201no—
335C3⋊C8—201no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5—41no—
339C22×C5—41no—
340C22×C5—41no—
341C22×C5#94911yescharacteristic
342C22×C5#95011yescharacteristic
343C22×C5#95311yescharacteristic
344C2×D5—122no—
345C2×D5—122no—
346C2×D5—122no—
347C2×D5—241no—
348C2×D5—241no—
349C2×D5—241no—
350C2×D5—241no—
351C4×C5—21no—
352C4×C5—21no—
353C4×C5—41no—
354C4×C5—41no—
355C4×C5—41no—
356C4×C5—41no—
357C4×C5—41no—
358Dic5—241no—
359C24—301no—
360C2×Q8#122011yescharacteristic
361C2×D4—21no—
362C2×D4—301no—
363C2×D4—301no—
364C2×D4—602no—
365C2×D4#122011yescharacteristic
366C22×C4—21no—
367C22×C4—301no—
368C22×C4#122011yescharacteristic
369C22×C4#122011yescharacteristic
370C22×C4C22×D1511yescharacteristic
371SD16—602no—
372D8—602no—
373C2×C8—301no—
374C2×C8—301no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4#122011yescharacteristic
382C4⋊C4#122011yescharacteristic
383C22⋊C4—21no—
384C22⋊C4—21no—
385C22⋊C4—21no—
386C22⋊C4—21no—
387C22⋊C4—21no—
388C22⋊C4—602no—
389C22⋊C4—602no—
390C42—21no—
391C3×C5#159711yescharacteristic, complemented, Hall
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—41no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3#409511yescharacteristic
398C22×C3#409611yescharacteristic
399C22×C3#409911yescharacteristic
400C2×D3—202no—
401C2×D3—202no—
402C2×D3—202no—
403C2×D3—401no—
404C2×D3—401no—
405C2×D3—401no—
406C2×D3—401no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—41no—
410C3×C4—41no—
411C3×C4—41no—
412C3×C4—41no—
413C3×C4—41no—
414Dic3—401no—
415C2×C5—21no—
416C2×C5—21no—
417C2×C5—81no—
418C2×C5#523811yescharacteristic
419C2×C5#524411yescharacteristic
420C2×C5#524511yescharacteristic
421D5—242no—
422C23—21no—
423C23—302no—
424C23—601no—
425C23—601no—
426C23—601no—
427C23—601no—
428C23—601no—
429C23—601no—
430C23C2×#122011yescharacteristic
431Q8—41no—
432D4—41no—
433D4—41no—
434D4—41no—
435D4—302no—
436D4—302no—
437D4—601no—
438D4—601no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—81no—
449C2×C4—601no—
450C2×C4—601no—
451C2×C4—601no—
452C2×C4C2×#122011yescharacteristic
453C2×C4C2×#122011yescharacteristic
454C8—601no—
455C8—601no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—81no—
459C2×C3#6552711yescharacteristic
460C2×C3#6553311yescharacteristic
461C2×C3#6553411yescharacteristic
462D3—402no—
463C5#7188811yescharacteristic, complemented, Sylow
464C22—21no—
465C22—21no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—602no—
470C22—602no—
471C22—602no—
472C22—1201no—
473C22—1201no—
474C22—1201no—
475C22—1201no—
476C22#9183811yescharacteristic
477C22#9183911yescharacteristic
478C22#9184211yescharacteristic
479C4—21no—
480C4—21no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—1201no—
487C3#1060268111yescharacteristic, complemented, Sylow
488C2—21no—
489C2—21no—
490C2—81no—
491C2—1202no—
492C2#1175133911yescharacteristic
493C2#1175134511yescharacteristic
494C2#1175134611yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#539C2
socleC22×C3×C5#120
prime radical#11751137C2
hypercenter#539D15
hypocenterC3×C5#1597
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
1. C3×C5×#539C2semidirect
2. #11751147C2semidirect
4. #11751092C2semidirect
5. #11746359C2semidirect
6. #11746358C2semidirect
7. #11746349C2semidirect
29. C5×#539D3semidirect
68. C3×#539D5semidirect
180. #539D15semidirect
391. C3×C5#1597semidirect
463. C5#71888semidirect
487. C3#10602681semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5392
#117511472
#117511372
#117510922
#117463592
#117463582
#117463492
#106026813
#718885