Finite Group Databasebeta

← #14471682

Subgroups — #14471682

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#11752645C211yesmaximal, characteristic, complemented
2#11752483C211yesmaximal, characteristic, complemented
3C4×D120C211yesmaximal, characteristic
4C5×C8×Dic6C211yesmaximal, characteristic, complemented
5C3×#64970C211yesmaximal, characteristic, complemented
6#11747988C212yesmaximal, complemented
7#11747863C212yesmaximal, complemented
8#11747830C212yesmaximal, complemented
9#11747798C212yesmaximal
10#11747085C211yesmaximal, characteristic, complemented
11#11746942C211yesmaximal, characteristic, complemented
12#10611657—31nomaximal, Hall
13C2×D120C2211yescharacteristic
14C4×D60C2211yescharacteristic
15C4×D60C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19#91437—21no—
20#91428C2212yes—
21#91411—22no—
22#91383—21no—
23#91383—21no—
24#91381C2212yes—
25#91374C2212yes—
26#91347—21no—
27#91345—22no—
28Dic3×Dic10C2212yes—
29C2×#6658C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91105C2211yescharacteristic
32#91105C2211yescharacteristic
33#91102C2211yescharacteristic
34C5×Dic3⋊C8C2212yes—
35C5×C8×Dic3C2212yes—
36C5×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×#3948C2212yes—
38C3×#3948C2212yes—
39#90987C2212yes—
40#90971C2212yes—
41#90968C2212yes—
42#81621—51nomaximal, Hall
43#65918—31no—
44#65913—31no—
45C5×C8×Q8—31no—
46#65133—32no—
47#65131—31no—
48#65130—31no—
49#65118—32no—
50#64986—32no—
51C4×D40—31no—
52C4×#677—32no—
53#64970D311yescharacteristic, complemented
54C2×D60C2311yescharacteristic
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×C4×D15—21no—
58C2×C5×Dic6D411yescharacteristic
59C2×C3×Dic10—21no—
60C2×C3×Dic10C2312yes—
61C2×#1200—22no—
62C2×C3×C5×C8C2311yescharacteristic
63C2×C3×C5×C8C2311yescharacteristic
64C3×C42×C5C2311yescharacteristic
65#6714—21no—
66#6714—21no—
67C4⋊Dic15C2311yescharacteristic
68C4⋊Dic15C2311yescharacteristic
69D120—22no—
70C5×C4⋊Dic3D411yescharacteristic
71C5×Dic3⋊C4D412yes—
72C4×C5×Dic3C2312yes—
73C2×C5×C3⋊C8C2312yes—
74C3×C4⋊Dic5—21no—
75C3×C4⋊Dic5—21no—
76C3×C4⋊Dic5—21no—
77C3×C4⋊Dic5C2312yes—
78#6669—22no—
79#6668—22no—
80#6668—22no—
81#6667—22no—
82#6667—22no—
83#6667—22no—
84Dic3×Dic5—22no—
85#6658—24no—
86#5732—51no—
87#5730—51no—
88C3×#487—51no—
89#5084—51no—
90#5083—51no—
91#4819—52no—
92#4800—52no—
93#4796—52no—
94#4788—52no—
95C4×D24—51no—
96C8×Dic6D511yescharacteristic, complemented
97C4×C5×Q8—31no—
98#4092—61no—
99#4092—61no—
100C2×D40—31no—
101C2×#677—32no—
102#4044—62no—
103#4042—62no—
104#4038—61no—
105D5×C4⋊C4—61no—
106#4021—32no—
107C4×D20—31no—
108C4×D20—31no—
109C4×D20—32no—
110#4016—32no—
111#4015C2×D311yescharacteristic
112#4015C2×D311yescharacteristic
113C4×Dic10—32no—
114C5×C4⋊C8—32no—
115C5×C4⋊C8—31no—
116C4×C5×C8—32no—
117C4×C5×C8C2×D311yescharacteristic
118#3953—31no—
119#3953—31no—
120#3953—32no—
121#3950—31no—
122#3949—32no—
123#3948—32no—
124#3948C2×D312yes—
125#3948C2×D312yes—
126#3360—151noSylow
127C22×D15—21no—
128C22×D15—21no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—21no—
133C2×Dic15—21no—
134D60—21no—
135D60—21no—
136D60—21no—
137D60#4112yes—
138C4×D15—42no—
139C4×D15—42no—
140C2×C5×Dic3C2×D412yes—
141C2×C5×Dic3C2×D412yes—
142C5×Dic6—22no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—22no—
145C3×Dic10—22no—
146C3×Dic10—22no—
147C3×Dic10—81no—
148#1200—82no—
149C3×C5×C8—21no—
150C3×C5×C8—21no—
151C5×C3⋊C8—22no—
152C3×C4⋊Q8—51no—
153C3×C4⋊Q8—51no—
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×Dic6C2×D511yescharacteristic
169C3×#103—52no—
170C3×#103—52no—
171C3×C4×C8C2×D511yescharacteristic
172#835—52no—
173#821—51no—
174#821—51no—
175#818—51no—
176Dic3⋊C8C2×D512yes—
177C8×Dic3C2×D512yes—
178#809—52no—
179#808—52no—
180C4⋊(C3⋊C8)C2×D511yescharacteristic
181C2×C5×Q8—31no—
182C2×D20—31no—
183C2×D20—31no—
184C2×C4×D5—61no—
185C2×C4×D5—61no—
186C2×C4×D5—62no—
187C2×Dic10—21no—
188C2×Dic10C22×D312yes—
189C2×C5×C8—32no—
190C2×C5×C8C22×D311yescharacteristic
191C2×C5×C8C22×D311yescharacteristic
192C5×C4⋊C4—32no—
193C5×C4⋊C4—31no—
194C42×C5—32no—
195C42×C5C22×D311yescharacteristic
196#685—62no—
197#685—62no—
198#685—62no—
199#685—61no—
200#685—61no—
201C4⋊Dic5—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5—21no—
204C4⋊Dic5—31no—
205C4⋊Dic5—31no—
206C4⋊Dic5C22×D312yes—
207#683—62no—
208#683—62no—
209#683—62no—
210C4×Dic5—62no—
211D40—62no—
212#677—64no—
213#556—151no—
214#554—151no—
215#488—152no—
216#487—51no—
217#479—152no—
218#476—151no—
219#463—152no—
220#461—151no—
221C8×Q8—31no—
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#13512yes—
233C3×C4×C5C2×#4111yescharacteristic
234C3×C4×C52−1+411yescharacteristic
235Dic15—41no—
236Dic15—41no—
237C3×Dic5—42no—
238C3×Dic5—42no—
239C5×Dic3—22no—
240C5×Dic3—22no—
241C2×C3×Q8—52no—
242C2×C3×Q8—101no—
243C2×D12—51no—
244C2×D12—51no—
245C2×C4×D3—101no—
246C2×C4×D3—101no—
247C2×C4×D3—102no—
248C2×Dic6D2011yescharacteristic
249C2×C3×C8C22×D511yescharacteristic
250C2×C3×C8C22×D511yescharacteristic
251C3×C4⋊C4—52no—
252C3×C4⋊C4—101no—
253C3×C4⋊C4—101no—
254C3×C4⋊C4—101no—
255C3×C42C22×D511yescharacteristic
256#215—104no—
257(C2×D3)⋊C4—101no—
258(C2×D3)⋊C4—101no—
259(C2×D3)⋊C4—102no—
260(C2×D3)⋊C4—102no—
261(C2×D3)⋊C4—102no—
262C4⋊Dic3—51no—
263C4⋊Dic3—51no—
264C4⋊Dic3—102no—
265C4⋊Dic3—102no—
266C4⋊Dic3D2011yescharacteristic
267Dic3⋊C4—102no—
268Dic3⋊C4D2012yes—
269C4×Dic3—102no—
270C4×Dic3C22×D512yes—
271C2×C3⋊C8C22×D512yes—
272D24—102no—
273C22×D5—61no—
274C22×D5—61no—
275C5×Q8—62no—
276C2×C4×C5—32no—
277C2×C4×C5—32no—
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5D3×D411yescharacteristic
280C2×C4×C5C23×D311yescharacteristic
281C2×Dic5—22no—
282C2×Dic5—22no—
283C2×Dic5—61no—
284C2×Dic5—61no—
285D20—32no—
286D20—61no—
287D20—61no—
288D20—61no—
289C4×D5—122no—
290C4×D5—122no—
291C4×D5—242no—
292Dic10—22no—
293Dic10—22no—
294Dic10—81no—
295C5×C8—21no—
296C5×C8—21no—
297C5×C8—62no—
298C2×SD16—152no—
299C2×D8—151no—
300C4⋊Q8—51no—
301C4⋊Q8—51no—
302#126—302no—
303#125—152no—
304#124—152no—
305C22⋊Q8—302no—
306C22⋊Q8—301no—
307C22⋊Q8—301no—
308C4×Q8—31no—
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—32no—
318C4⋊C8—31no—
319#103—52no—
320#103—52no—
321#103—152no—
322#102—152no—
323#102—151no—
324#102—151no—
325C4×C8—32no—
326C4×C8D3×D511yescharacteristic
327C2×C3×C5#54811yescharacteristic
328C2×C3×C5C2×#13511yescharacteristic
329C2×C3×C5#57711yescharacteristic
330D15—42no—
331D15—81no—
332C22×D3—101no—
333C22×D3—101no—
334C3×Q8—102no—
335C3×Q8—102no—
336C3×Q8—401no—
337C2×C3×C4—102no—
338C2×C3×C4—102no—
339C2×C3×C4C2×D2011yescharacteristic
340C2×C3×C4C2×D2011yescharacteristic
341C2×C3×C4C23×D511yescharacteristic
342C2×Dic3—101no—
343C2×Dic3—101no—
344C2×Dic3C2×D2012yes—
345C2×Dic3C2×D2012yes—
346D12—52no—
347D12—101no—
348D12—101no—
349D12—101no—
350C4×D3—202no—
351C4×D3—202no—
352C4×D3—402no—
353Dic6—22no—
354C3×C8—21no—
355C3×C8—21no—
356C3⋊C8—22no—
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—62no—
366C4×C5—62no—
367C4×C5#91912yes—
368C4×C5D3×#4111yescharacteristic
369C4×C5#101011yescharacteristic
370Dic5—42no—
371Dic5—42no—
372Dic5—121no—
373Dic5—121no—
374C2×Q8—31no—
375C2×Q8—52no—
376C2×Q8—101no—
377C2×D4—151no—
378C2×D4—151no—
379C22×C4—302no—
380C22×C4—301no—
381C22×C4—301no—
382SD16—304no—
383D8—302no—
384C2×C8—32no—
385C2×C8C2×D3×D511yescharacteristic
386C2×C8C2×D3×D511yescharacteristic
387C4⋊C4—31no—
388C4⋊C4—32no—
389C4⋊C4—52no—
390C4⋊C4—101no—
391C4⋊C4—101no—
392C4⋊C4—101no—
393C4⋊C4—151no—
394C4⋊C4—151no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—302no—
398C22⋊C4—302no—
399C22⋊C4—302no—
400C22⋊C4—302no—
401C22⋊C4—301no—
402C22⋊C4—301no—
403C42—32no—
404C42—302no—
405C42C2×D3×D511yescharacteristic
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3C22×D2011yescharacteristic
408C2×D3—102no—
409C2×D3—201no—
410C2×D3—201no—
411C2×D3—201no—
412C2×D3—201no—
413C2×D3—201no—
414C3×C4—21no—
415C3×C4—202no—
416C3×C4—202no—
417C3×C4#405012yes—
418C3×C4#414711yescharacteristic
419C3×C4D5×#4111yescharacteristic
420Dic3—22no—
421Dic3—22no—
422Dic3—201no—
423Dic3—201no—
424C2×C5#567711yescharacteristic
425C2×C5#576211yescharacteristic
426C2×C5C2×#91911yescharacteristic
427D5—122no—
428D5—241no—
429C23—301no—
430C23—301no—
431Q8—62no—
432Q8—102no—
433Q8—102no—
434Q8—401no—
435D4—152no—
436D4—301no—
437D4—301no—
438D4—301no—
439C2×C4—32no—
440C2×C4—32no—
441C2×C4—102no—
442C2×C4—102no—
443C2×C4—301no—
444C2×C4—301no—
445C2×C4—602no—
446C2×C4—602no—
447C2×C4—1202no—
448C2×C4D3×D2011yescharacteristic
449C2×C4D3×D2011yescharacteristic
450C2×C4C22×D3×D511yescharacteristic
451C8—21no—
452C8—21no—
453C8—62no—
454C2×C3#6591011yescharacteristic
455C2×C3C2×#405011yescharacteristic
456C2×C3#6608511yescharacteristic
457D3—202no—
458D3—401no—
459C5#8162111yescharacteristic, complemented, Sylow
460C22—302no—
461C22—601no—
462C22—601no—
463C22—601no—
464C22—601no—
465C22—601no—
466C22C2×D3×D2011yescharacteristic
467C4—21no—
468C4—62no—
469C4—62no—
470C4—202no—
471C4—202no—
472C4—601no—
473C4—601no—
474C4#9127512yes—
475C4#9200011yescharacteristic
476C4#9201611yescharacteristic
477C3#1061165711yescharacteristic, complemented, Sylow
478C2—602no—
479C2—1201no—
480C2#1175254611yescharacteristic
481C2#1175397011yescharacteristic
482C2C2×#9127511yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×D120C22
hypercenterC4×C8D3×D5
hypocenterC3×C5#3360
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #11752645C2semidirect
2. #11752483C2semidirect
4. C5×C8×Dic6C2semidirect
5. C3×#64970C2semidirect
6. #11747988C2semidirect
7. #11747863C2semidirect
8. #11747830C2semidirect
10. #11747085C2semidirect
11. #11746942C2semidirect
53. #64970D3semidirect
96. C8×Dic6D5semidirect
406. C3×C5#3360semidirect
459. C5#81621semidirect
477. C3#10611657semidirect

Maximal subgroups

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

subgroupindex
#117526452
#117524832
C4×D1202
C5×C8×Dic62
C3×#649702
#117479882
#117478632
#117478302
#117477982
#117470852
#117469422
#106116573
#816215