Finite Group Databasebeta

← #14471614

Subgroups — #14471614

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756491C211yesmaximal, characteristic, complemented
2#11756489C211yesmaximal, characteristic, complemented
3C3×C5×#487C211yesmaximal, characteristic, complemented
4#11751185C211yesmaximal, characteristic, complemented
5#11751184C211yesmaximal, characteristic, complemented
6#11750920C212yesmaximal
7#11750901C212yesmaximal, complemented
8#11750897C212yesmaximal, complemented
9#11750889C212yesmaximal, complemented
10C4×D120C211yesmaximal, characteristic
11C8×Dic30C211yesmaximal, characteristic, complemented
12#10613352—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14C3×C5×C4⋊Q8C2211yescharacteristic
15#91836C2212yes—
16#91835—22no—
17Q8×Dic15C2212yes—
18C2×#6717C2212yes—
19C2×D120C2211yescharacteristic
20#91787—22no—
21#91786—21no—
22#91786—21no—
23#91782C2212yes—
24#91781—21no—
25C4⋊C4×D15—21no—
26#91779C2212yes—
27C4×D60C2211yescharacteristic
28C4×D60C2211yescharacteristic
29C4×Dic30C2211yescharacteristic
30C3×C5×#103C2212yes—
31C3×C5×#103C2212yes—
32C3×C4×C5×C8C2211yescharacteristic
33#91119C2212yes—
34#91105C2211yescharacteristic
35#91105C2211yescharacteristic
36#91102C2211yescharacteristic
37#91098C2212yes—
38C8×Dic15C2212yes—
39#91093C2212yes—
40#91092C2212yes—
41C4⋊(C3⋊#168)C2211yescharacteristic
42#81621—51nomaximal, Hall
43#66066—31no—
44#66064—31no—
45C5×#487D311yescharacteristic, complemented
46#65373—31no—
47#65372—31no—
48#65108—32no—
49#65089—32no—
50#65085—32no—
51#65077—32no—
52C4×D40—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×Q8C2312yes—
56C2×D60C2311yescharacteristic
57C2×D60C2311yescharacteristic
58C2×C4×D15—21no—
59C2×C4×D15—21no—
60C2×C4×D15—22no—
61C2×Dic30D411yescharacteristic
62C2×C3×C5×C8C2311yescharacteristic
63C2×C3×C5×C8C2311yescharacteristic
64C3×C5×C4⋊C4—21no—
65C3×C5×C4⋊C4—21no—
66C3×C5×C4⋊C4—21no—
67C3×C5×C4⋊C4C2312yes—
68C3×C42×C5C2311yescharacteristic
69#6717—24no—
70#6714—21no—
71#6714—21no—
72#6714—22no—
73#6714—22no—
74#6714—22no—
75C4⋊Dic15—22no—
76C4⋊Dic15—22no—
77C4⋊Dic15D411yescharacteristic
78C4⋊Dic15C2311yescharacteristic
79C4⋊Dic15C2311yescharacteristic
80#6712—22no—
81#6712D412yes—
82C4×Dic15—22no—
83C4×Dic15C2312yes—
84C2×C3⋊#168C2312yes—
85D120—22no—
86#5732—51no—
87#5730—51no—
88C3×#487D511yescharacteristic, complemented
89#5084—51no—
90#5083—51no—
91#4819—52no—
92#4800—52no—
93#4796—52no—
94#4788—52no—
95C4×D24—51no—
96C8×Dic6—51no—
97C5×C4⋊Q8C2×D311yescharacteristic
98C5×C4⋊Q8C2×D311yescharacteristic
99#4093—32no—
100#4092—62no—
101Q8×Dic5—32no—
102C2×#688—32no—
103C2×D40—31no—
104#4044—62no—
105#4043—61no—
106#4043—61no—
107#4039—32no—
108#4038—61no—
109D5×C4⋊C4—61no—
110#4036—32no—
111C4×D20—31no—
112C4×D20—31no—
113C4×Dic10—31no—
114C5×#103C2×D312yes—
115C5×#103C2×D312yes—
116C4×C5×C8C2×D311yescharacteristic
117#3967—32no—
118#3953—31no—
119#3953—31no—
120#3950—31no—
121#3946—32no—
122C8×Dic5—32no—
123#3941—32no—
124#3940—32no—
125C4⋊#168—31no—
126#3360—151noSylow
127C22×D15—21no—
128C22×D15—21no—
129C3×C5×Q8—22no—
130C3×C5×Q8—22no—
131C3×C5×Q8—81no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2411yescharacteristic
137C2×Dic15—21no—
138C2×Dic15—21no—
139C2×Dic15C2×D412yes—
140C2×Dic15C2×D412yes—
141D60—21no—
142D60—21no—
143D60—21no—
144D60#4112yes—
145C4×D15—42no—
146C4×D15—42no—
147C4×D15—82no—
148Dic30—22no—
149C3×C5×C8—21no—
150C3×C5×C8—21no—
151C3⋊#168—22no—
152C3×C4⋊Q8C2×D511yescharacteristic
153C3×C4⋊Q8C2×D511yescharacteristic
154#947—52no—
155#946—102no—
156Q8×Dic3—52no—
157C2×#215—52no—
158C2×D24—51no—
159#898—102no—
160#897—101no—
161#897—101no—
162#893—52no—
163#892—101no—
164D3×C4⋊C4—101no—
165#890—52no—
166C4×D12—51no—
167C4×D12—51no—
168C4×Dic6—51no—
169C3×#103C2×D512yes—
170C3×#103C2×D512yes—
171C3×C4×C8C2×D511yescharacteristic
172#835—52no—
173#821—51no—
174#821—51no—
175#818—51no—
176Dic3⋊C8—52no—
177C8×Dic3—52no—
178#809—52no—
179#808—52no—
180C4⋊(C3⋊C8)—51no—
181C2×C5×Q8—21no—
182C2×C5×Q8C22×D312yes—
183C2×D20—31no—
184C2×D20—31no—
185C2×C4×D5—61no—
186C2×C4×D5—61no—
187C2×C4×D5—62no—
188C2×Dic10—31no—
189C2×C5×C8C22×D311yescharacteristic
190C2×C5×C8C22×D311yescharacteristic
191C5×C4⋊C4—21no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4C22×D312yes—
195C42×C5C22×D311yescharacteristic
196#688—64no—
197#685—62no—
198#685—62no—
199#685—62no—
200#685—61no—
201#685—61no—
202C4⋊Dic5—31no—
203C4⋊Dic5—31no—
204C4⋊Dic5—31no—
205C4⋊Dic5—62no—
206C4⋊Dic5—62no—
207#683—32no—
208#683—62no—
209C4×Dic5—32no—
210C4×Dic5—62no—
211C2×#168—32no—
212D40—62no—
213#556—151no—
214#554—151no—
215#488—152no—
216#487D1511yescharacteristic, complemented
217#479—152no—
218#476—151no—
219#463—152no—
220#461—151no—
221C8×Q8—151no—
222C4×SD16—152no—
223C4×D8—151no—
224C22×C3×C5C22×D411yescharacteristic
225C2×D15—22no—
226C2×D15—41no—
227C2×D15—41no—
228C2×D15—41no—
229C2×D15—41no—
230C2×D15—41no—
231C3×C4×C5—21no—
232C3×C4×C5—42no—
233C3×C4×C5—42no—
234C3×C4×C5#13512yes—
235C3×C4×C5C2×#4111yescharacteristic
236C3×C4×C52−1+411yescharacteristic
237Dic15—22no—
238Dic15—22no—
239Dic15—41no—
240Dic15—41no—
241C2×C3×Q8—21no—
242C2×C3×Q8C22×D512yes—
243C2×D12—51no—
244C2×D12—51no—
245C2×C4×D3—101no—
246C2×C4×D3—101no—
247C2×C4×D3—102no—
248C2×Dic6—51no—
249C2×C3×C8C22×D511yescharacteristic
250C2×C3×C8C22×D511yescharacteristic
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4C22×D512yes—
255C3×C42C22×D511yescharacteristic
256#215—104no—
257(C2×D3)⋊C4—102no—
258(C2×D3)⋊C4—102no—
259(C2×D3)⋊C4—102no—
260(C2×D3)⋊C4—101no—
261(C2×D3)⋊C4—101no—
262C4⋊Dic3—51no—
263C4⋊Dic3—51no—
264C4⋊Dic3—51no—
265C4⋊Dic3—102no—
266C4⋊Dic3—102no—
267Dic3⋊C4—52no—
268Dic3⋊C4—102no—
269C4×Dic3—52no—
270C4×Dic3—102no—
271C2×C3⋊C8—52no—
272D24—102no—
273C22×D5—61no—
274C22×D5—61no—
275C5×Q8—22no—
276C5×Q8—22no—
277C5×Q8—81no—
278C2×C4×C5—22no—
279C2×C4×C5—22no—
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5C23×D311yescharacteristic
283C2×Dic5—32no—
284C2×Dic5—32no—
285C2×Dic5—61no—
286C2×Dic5—61no—
287D20—32no—
288D20—61no—
289D20—61no—
290D20—61no—
291C4×D5—122no—
292C4×D5—122no—
293C4×D5—242no—
294Dic10—62no—
295C5×C8—21no—
296C5×C8—21no—
297#168—62no—
298C2×SD16—152no—
299C2×D8—151no—
300C4⋊Q8C2×D1511yescharacteristic
301C4⋊Q8C2×D1511yescharacteristic
302#126—302no—
303#125—152no—
304#124—152no—
305C22⋊Q8—301no—
306C22⋊Q8—301no—
307C22⋊Q8—302no—
308C4×Q8—151no—
309C4×Q8—152no—
310C4×D4—152no—
311C4×D4—151no—
312C4×D4—151no—
313#117—301no—
314C2×C4⋊C4—301no—
315#107—151no—
316#106—152no—
317C4⋊C8—152no—
318C4⋊C8—151no—
319#103—152no—
320#103C2×D1512yes—
321#103C2×D1512yes—
322#102—151no—
323#102—151no—
324#102—152no—
325C4×C8—152no—
326C4×C8C2×D1511yescharacteristic
327C2×C3×C5#54811yescharacteristic
328C2×C3×C5C2×#13511yescharacteristic
329C2×C3×C5#57711yescharacteristic
330D15—42no—
331D15—81no—
332C22×D3—101no—
333C22×D3—101no—
334C3×Q8—22no—
335C3×Q8—22no—
336C3×Q8—81no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4D4×D511yescharacteristic
341C2×C3×C4C23×D511yescharacteristic
342C2×Dic3—52no—
343C2×Dic3—52no—
344C2×Dic3—101no—
345C2×Dic3—101no—
346D12—52no—
347D12—101no—
348D12—101no—
349D12—101no—
350C4×D3—202no—
351C4×D3—202no—
352C4×D3—402no—
353Dic6—102no—
354C3×C8—21no—
355C3×C8—21no—
356C3⋊C8—102no—
357C22×C5C2×D3×D411yescharacteristic
358C2×D5—62no—
359C2×D5—121no—
360C2×D5—121no—
361C2×D5—121no—
362C2×D5—121no—
363C2×D5—121no—
364C4×C5—21no—
365C4×C5—42no—
366C4×C5—42no—
367C4×C5#91912yes—
368C4×C5D3×#4111yescharacteristic
369C4×C5#101011yescharacteristic
370Dic5—62no—
371Dic5—62no—
372Dic5—121no—
373Dic5—121no—
374C2×Q8—21no—
375C2×Q8—151no—
376C2×Q8C22×D1512yes—
377C2×D4—151no—
378C2×D4—151no—
379C22×C4—302no—
380C22×C4—301no—
381C22×C4—301no—
382SD16—304no—
383D8—302no—
384C2×C8—152no—
385C2×C8C22×D1511yescharacteristic
386C2×C8C22×D1511yescharacteristic
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—151no—
391C4⋊C4—152no—
392C4⋊C4—151no—
393C4⋊C4—151no—
394C4⋊C4—302no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4C22×D1512yes—
398C22⋊C4—302no—
399C22⋊C4—302no—
400C22⋊C4—302no—
401C22⋊C4—301no—
402C22⋊C4—301no—
403C42—152no—
404C42—302no—
405C42C22×D1511yescharacteristic
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3C2×D4×D511yescharacteristic
408C2×D3—102no—
409C2×D3—201no—
410C2×D3—201no—
411C2×D3—201no—
412C2×D3—201no—
413C2×D3—201no—
414C3×C4—21no—
415C3×C4—42no—
416C3×C4—42no—
417C3×C4#406512yes—
418C3×C4D5×#4111yescharacteristic
419C3×C4#415011yescharacteristic
420Dic3—102no—
421Dic3—102no—
422Dic3—201no—
423Dic3—201no—
424C2×C5#567711yescharacteristic
425C2×C5#576211yescharacteristic
426C2×C5C2×#91911yescharacteristic
427D5—122no—
428D5—241no—
429C23—301no—
430C23—301no—
431Q8—22no—
432Q8—22no—
433Q8—81no—
434Q8—302no—
435D4—152no—
436D4—301no—
437D4—301no—
438D4—301no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—152no—
442C2×C4—152no—
443C2×C4—301no—
444C2×C4—301no—
445C2×C4—602no—
446C2×C4—602no—
447C2×C4—1202no—
448C2×C4D4×D1511yescharacteristic
449C2×C4D4×D1511yescharacteristic
450C2×C4C23×D1511yescharacteristic
451C8—21no—
452C8—21no—
453C8—302no—
454C2×C3#6601111yescharacteristic
455C2×C3#6609611yescharacteristic
456C2×C3C2×#406511yescharacteristic
457D3—202no—
458D3—401no—
459C5#8162111yescharacteristic, complemented, Sylow
460C22—302no—
461C22—601no—
462C22—601no—
463C22—601no—
464C22—601no—
465C22—601no—
466C22C2×D4×D1511yescharacteristic
467C4—21no—
468C4—42no—
469C4—42no—
470C4—302no—
471C4—302no—
472C4—601no—
473C4—601no—
474C4#9180812yes—
475C4#41×D1511yescharacteristic
476C4#9210111yescharacteristic
477C3#1061335211yescharacteristic, complemented, Sylow
478C2—602no—
479C2—1201no—
480C2#1175643611yescharacteristic
481C2#1175652111yescharacteristic
482C2C2×#9180811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#487C2
socleC22×C3×C5C22×D4
prime radicalC2×D120C22
hypercenter#487D15
hypocenterC3×C5#3360
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #11756491C2semidirect
2. #11756489C2semidirect
3. C3×C5×#487C2semidirect
4. #11751185C2semidirect
5. #11751184C2semidirect
7. #11750901C2semidirect
8. #11750897C2semidirect
9. #11750889C2semidirect
11. C8×Dic30C2semidirect
45. C5×#487D3semidirect
88. C3×#487D5semidirect
216. #487D15semidirect
406. C3×C5#3360semidirect
459. C5#81621semidirect
477. C3#10613352semidirect

Maximal subgroups

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

subgroupindex
#117564912
#117564892
C3×C5×#4872
#117511852
#117511842
#117509202
#117509012
#117508972
#117508892
C4×D1202
C8×Dic302
#106133523
#816215