Finite Group Databasebeta

← #14471823

Subgroups — #14471823

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756338C211yesmaximal, characteristic, complemented
2C5×#5585C211yesmaximal, characteristic, complemented
3C3×Q8×#168C211yesmaximal, characteristic, complemented
4C4×#6660C211yesmaximal, characteristic, complemented
5#11747046C212yesmaximal, complemented
6#11747045C211yesmaximal, characteristic
7C4×#6654C212yesmaximal, complemented
8#11746961C211yesmaximal, characteristic, complemented
9#11746907C212yesmaximal, complemented
10#11746906C211yesmaximal, characteristic, complemented
11#11746894C212yesmaximal, complemented
12#10615444—31nomaximal, Hall
13C3×C4×C5×Q8C2211yescharacteristic
14#91835—21no—
15#91785—22no—
16C4⋊C4×D15—21no—
17C4×D60C2212yes—
18C4×D60C2211yescharacteristic
19#91759C2212yes—
20#91758C2211yescharacteristic
21C5×#947—21no—
22C5×#894—22no—
23C5×#893—21no—
24C5×#875C2212yes—
25C5×#874C2211yescharacteristic
26C4×C5×D12C2212yes—
27C4×C5×Dic6C2211yescharacteristic
28C2×#6660C2211yescharacteristic
29C2×#6654C2212yes—
30C3×C4⋊#168C2212yes—
31C3×C4⋊#168C2211yescharacteristic
32C3×C4×#168C2211yescharacteristic
33C3×C4×#168C2212yes—
34#90988C2212yes—
35#90985C2211yescharacteristic
36#90973C2211yescharacteristic
37#90973C2212yes—
38#90969C2211yescharacteristic
39#90967C2212yes—
40#90967C2212yes—
41#90967C2212yes—
42#79927—51nomaximal, Hall
43C5×#559—31no—
44#65913—31no—
45#65361—31no—
46#65359—31no—
47#65346—32no—
48#65345—32no—
49C4×#688—31no—
50Q8×#168D311yescharacteristic, complemented
51#65310—31no—
52C4×#686—32no—
53#65298—32no—
54C2×C3×C5×Q8D411yescharacteristic
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×C4×D15—22no—
58C2×Dic30—21no—
59C2×C5×D12—21no—
60C2×C5×D12—21no—
61C2×C5×D12C2312yes—
62C2×C4×C5×D3—22no—
63C2×C5×Dic6C2311yescharacteristic
64C3×C5×C4⋊C4D411yescharacteristic
65C3×C5×C4⋊C4D412yes—
66C3×C42×C5C2311yescharacteristic
67C3×C42×C5C2312yes—
68#6714—21no—
69#6714—22no—
70C4⋊Dic15—21no—
71C4⋊Dic15C2311yescharacteristic
72C4⋊Dic15C2312yes—
73#6712—22no—
74#6712—22no—
75C5×(C2×D3)⋊C4—22no—
76C5×(C2×D3)⋊C4—22no—
77C5×(C2×D3)⋊C4—22no—
78C5×C4⋊Dic3C2311yescharacteristic
79C5×Dic3⋊C4—21no—
80C4×C5×Dic3—21no—
81C2×C3×#168C2311yescharacteristic
82C2×C3×#168C2311yescharacteristic
83C2×C3×#168C2312yes—
84#6660—22no—
85#6654—24no—
86#5585D511yescharacteristic, complemented
87#5579—51no—
88C3×C8×Q8—51no—
89#4850—51no—
90#4847—52no—
91#4844—52no—
92#4843—51no—
93#4697—52no—
94#4694—51no—
95C4×D24—52no—
96C4×#204—51no—
97C5×#127—31no—
98C5×#124—32no—
99C5×#124—61no—
100C5×#123—62no—
101C4×C5×Q8—31no—
102C4×C5×Q8C2×D311yescharacteristic
103C4×C5×D4—32no—
104C4×C5×D4—61no—
105#4092—61no—
106C2×#688—31no—
107C2×#686—32no—
108#4042—62no—
109D5×C4⋊C4—61no—
110C4×D20—32no—
111C4×D20—31no—
112#4016—32no—
113#4015—31no—
114#3967—32no—
115#3967—31no—
116#3964—32no—
117#3964—32no—
118#3964—32no—
119#3941—31no—
120#3940—31no—
121#3939—32no—
122C4⋊#168C2×D312yes—
123C4⋊#168C2×D311yescharacteristic
124C4×#168C2×D312yes—
125C4×#168C2×D311yescharacteristic
126#3361—151noSylow
127C22×D15—21no—
128C22×C5×D3—22no—
129C3×C5×Q8—22no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D412yes—
132C2×C3×C4×C5C2×D412yes—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—21no—
136C2×Dic15—22no—
137D60—21no—
138D60#4112yes—
139C4×D15—42no—
140C4×D15—82no—
141Dic30—81no—
142C2×C5×Dic3—21no—
143C2×C5×Dic3—21no—
144C5×D12—22no—
145C5×D12—22no—
146C5×D12—42no—
147C5×D12—81no—
148C4×C5×D3—82no—
149C5×Dic6—21no—
150C5×Dic6—21no—
151C3×#168—21no—
152C3×#168—22no—
153C3×#168—21no—
154C3×C4×Q8C2×D511yescharacteristic
155#947—21no—
156#946—101no—
157C2×D24—52no—
158C2×#204—51no—
159#896—102no—
160#894—22no—
161#893—21no—
162D3×C4⋊C4—101no—
163#875C2×D512yes—
164#874C2×D511yescharacteristic
165C4×D12—51no—
166C4×D12—52no—
167C4×D12C2×D512yes—
168#870—52no—
169#869—51no—
170C4×Dic6C2×D511yescharacteristic
171C3×C4⋊C8—51no—
172C3×C4⋊C8—52no—
173C3×C4×C8—51no—
174C3×C4×C8—52no—
175#821—52no—
176#821—52no—
177#821—52no—
178#821—51no—
179#818—52no—
180#817—51no—
181#816—51no—
182#816—52no—
183C2×C5×Q8—31no—
184C2×C5×Q8D1211yescharacteristic
185C2×C5×D4—32no—
186C2×C5×D4—61no—
187C2×C5×D4—61no—
188C22×C4×C5—62no—
189C2×D20—31no—
190C2×C4×D5—61no—
191C2×C4×D5—62no—
192C2×Dic10—61no—
193C5×C4⋊C4—31no—
194C5×C4⋊C4—61no—
195C5×C4⋊C4D1211yescharacteristic
196C5×C4⋊C4D1212yes—
197C5×C22⋊C4—62no—
198C5×C22⋊C4—62no—
199C5×C22⋊C4—62no—
200C42×C5—61no—
201C42×C5C22×D312yes—
202C42×C5C22×D311yescharacteristic
203#688—62no—
204#686—64no—
205#685—61no—
206#685—62no—
207C4⋊Dic5—32no—
208C4⋊Dic5—31no—
209C4⋊Dic5—61no—
210#683—62no—
211#683—62no—
212C2×#168C22×D311yescharacteristic
213C2×#168C22×D312yes—
214C2×#168C22×D311yescharacteristic
215#559—31no—
216#554—151no—
217#488—152no—
218#486—151no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—151no—
223C8×Q8—51no—
224C4×SD16—151no—
225C4×D8—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—22no—
228C2×D15—41no—
229C2×D15—41no—
230C2×C5×D3—42no—
231C2×C5×D3—42no—
232C2×C5×D3—42no—
233C3×C4×C5—22no—
234C3×C4×C5—22no—
235C3×C4×C5—21no—
236C3×C4×C5#13512yes—
237C3×C4×C5C2×#4111yescharacteristic
238C3×C4×C52−1+411yescharacteristic
239Dic15—41no—
240Dic15—42no—
241C5×Dic3—41no—
242C5×Dic3—41no—
243C2×C3×Q8C22⋊D511yescharacteristic
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—51no—
247C2×D12C22×D512yes—
248C2×C4×D3—22no—
249C2×C4×D3—101no—
250C2×C4×D3—102no—
251C2×Dic6—101no—
252C2×Dic6C22×D511yescharacteristic
253C2×C3×C8—52no—
254C2×C3×C8—51no—
255C2×C3×C8—51no—
256C3×C4⋊C4C22⋊D511yescharacteristic
257C3×C4⋊C4C22⋊D512yes—
258C3×C42C22×D511yescharacteristic
259C3×C42C22×D512yes—
260(C2×D3)⋊C4—22no—
261(C2×D3)⋊C4—22no—
262(C2×D3)⋊C4—22no—
263(C2×D3)⋊C4—101no—
264(C2×D3)⋊C4—102no—
265C4⋊Dic3—51no—
266C4⋊Dic3—52no—
267C4⋊Dic3—101no—
268C4⋊Dic3C22×D511yescharacteristic
269Dic3⋊C4—21no—
270Dic3⋊C4—102no—
271Dic3⋊C4—102no—
272C4×Dic3—21no—
273D24—104no—
274#204—102no—
275C23×C5—62no—
276C22×D5—61no—
277C5×Q8—22no—
278C5×Q8—61no—
279C5×Q8—61no—
280C5×D4—62no—
281C5×D4—62no—
282C5×D4—122no—
283C5×D4—241no—
284C2×C4×C5—61no—
285C2×C4×C5—61no—
286C2×C4×C5—242no—
287C2×C4×C5C2×D1212yes—
288C2×C4×C5C2×D1212yes—
289C2×C4×C5C2×D1211yescharacteristic
290C2×C4×C5C2×D1211yescharacteristic
291C2×C4×C5C23×D311yescharacteristic
292C2×Dic5—61no—
293C2×Dic5—62no—
294D20—32no—
295D20—61no—
296C4×D5—122no—
297C4×D5—242no—
298Dic10—241no—
299#168—21no—
300#168—22no—
301#168—21no—
302C2×SD16—151no—
303C2×D8—152no—
304C4⋊Q8—151no—
305#127—31no—
306#125—152no—
307#124—32no—
308#124—61no—
309#123—62no—
310C22⋊Q8—301no—
311C22⋊Q8—302no—
312C4×Q8—31no—
313C4×Q8D3×D511yescharacteristic
314C4×D4—32no—
315C4×D4—61no—
316C4×D4—152no—
317C4×D4—151no—
318C2×C4⋊C4—301no—
319#107—152no—
320#106—151no—
321C4⋊C8—51no—
322C4⋊C8—52no—
323#103—151no—
324#103—152no—
325#102—151no—
326#102—152no—
327#102—152no—
328#102—152no—
329C4×C8—52no—
330C4×C8—51no—
331C2×C3×C5#54811yescharacteristic
332C2×C3×C5C2×#13511yescharacteristic
333C2×C3×C5#57611yescharacteristic
334D15—42no—
335C5×D3—82no—
336C22×D3—22no—
337C22×D3—101no—
338C3×Q8—22no—
339C2×C3×C4C2×C22⋊D511yescharacteristic
340C2×C3×C4C2×C22⋊D512yes—
341C2×C3×C4C2×C22⋊D512yes—
342C2×C3×C4C2×C22⋊D511yescharacteristic
343C2×C3×C4C23×D511yescharacteristic
344C2×Dic3—21no—
345C2×Dic3—21no—
346C2×Dic3—101no—
347C2×Dic3—102no—
348D12—22no—
349D12—22no—
350D12—42no—
351D12—52no—
352D12—81no—
353D12—101no—
354C4×D3—82no—
355C4×D3—202no—
356C4×D3—402no—
357Dic6—21no—
358Dic6—21no—
359Dic6—401no—
360C3×C8—101no—
361C3×C8—102no—
362C3×C8—101no—
363C22×C5—122no—
364C22×C5—122no—
365C22×C5—122no—
366C22×C5C22×D1211yescharacteristic
367C2×D5—62no—
368C2×D5—121no—
369C2×D5—121no—
370C4×C5—22no—
371C4×C5—21no—
372C4×C5—22no—
373C4×C5—121no—
374C4×C5—121no—
375C4×C5#90412yes—
376C4×C5#100711yescharacteristic
377C4×C5D3×#4111yescharacteristic
378Dic5—121no—
379Dic5—122no—
380C2×Q8—31no—
381C2×Q8—301no—
382C2×Q8#120311yescharacteristic
383C2×D4—32no—
384C2×D4—61no—
385C2×D4—61no—
386C2×D4—151no—
387C22×C4—62no—
388C22×C4—301no—
389C22×C4—302no—
390SD16—302no—
391D8—304no—
392C2×C8—51no—
393C2×C8—51no—
394C2×C8—52no—
395C4⋊C4—31no—
396C4⋊C4—61no—
397C4⋊C4—151no—
398C4⋊C4—152no—
399C4⋊C4—302no—
400C4⋊C4—301no—
401C4⋊C4—302no—
402C4⋊C4#120311yescharacteristic
403C4⋊C4#120312yes—
404C22⋊C4—62no—
405C22⋊C4—62no—
406C22⋊C4—62no—
407C22⋊C4—301no—
408C22⋊C4—302no—
409C42—61no—
410C42C2×D3×D512yes—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3C22×C22⋊D511yescharacteristic
414C2×D3—42no—
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—102no—
418C2×D3—201no—
419C2×D3—201no—
420C3×C4—22no—
421C3×C4—21no—
422C3×C4—22no—
423C3×C4#409612yes—
424C3×C4D5×#4111yescharacteristic
425C3×C4#415011yescharacteristic
426Dic3—41no—
427Dic3—41no—
428Dic3—201no—
429Dic3—202no—
430C2×C5—242no—
431C2×C5#557611yescharacteristic
432C2×C5C2×#90411yescharacteristic
433C2×C5#575211yescharacteristic
434D5—122no—
435C23—62no—
436C23—301no—
437Q8—22no—
438Q8—61no—
439Q8—61no—
440Q8—1201no—
441D4—62no—
442D4—62no—
443D4—122no—
444D4—152no—
445D4—241no—
446D4—301no—
447C2×C4—61no—
448C2×C4—61no—
449C2×C4—242no—
450C2×C4—301no—
451C2×C4—302no—
452C2×C4—602no—
453C2×C4—1202no—
454C2×C4C2×#120312yes—
455C2×C4C2×#120312yes—
456C2×C4C2×#120311yescharacteristic
457C2×C4C2×#120311yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—101no—
460C8—102no—
461C8—101no—
462C2×C3C2×#409611yescharacteristic
463C2×C3#6616511yescharacteristic
464C2×C3#6616911yescharacteristic
465D3—82no—
466D3—202no—
467C5#7992711yescharacteristic, complemented, Sylow
468C22—122no—
469C22—122no—
470C22—122no—
471C22—302no—
472C22—601no—
473C22—601no—
474C22C22×#120311yescharacteristic
475C4—22no—
476C4—21no—
477C4—22no—
478C4—121no—
479C4—121no—
480C4—602no—
481C4—601no—
482C4#9130312yes—
483C4#9203011yescharacteristic
484C4#9203411yescharacteristic
485C3#1061544411yescharacteristic, complemented, Sylow
486C2—242no—
487C2—602no—
488C2C2×#9130311yescharacteristic
489C2#1175513411yescharacteristic
490C2#1175530511yescharacteristic
subgroupG/H
centerC22C22×#1203
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radical#11747045C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756338C2semidirect
2. C5×#5585C2semidirect
3. C3×Q8×#168C2semidirect
4. C4×#6660C2semidirect
5. #11747046C2semidirect
7. C4×#6654C2semidirect
8. #11746961C2semidirect
9. #11746907C2semidirect
10. #11746906C2semidirect
11. #11746894C2semidirect
50. Q8×#168D3semidirect
86. #5585D5semidirect
412. C3×C5#3361semidirect
467. C5#79927semidirect
485. C3#10615444semidirect

Maximal subgroups

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

subgroupindex
#117563382
C5×#55852
C3×Q8×#1682
C4×#66602
#117470462
#117470452
C4×#66542
#117469612
#117469072
#117469062
#117468942
#106154443
#799275