Finite Group Databasebeta

← #14471841

Subgroups — #14471841

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#11752645C211yesmaximal, characteristic, complemented
2#11752636C211yesmaximal, characteristic, complemented
3C4×#6706C211yesmaximal, characteristic, complemented
4C5×C8×Dic6C211yesmaximal, characteristic, complemented
5C3×#64983C211yesmaximal, characteristic, complemented
6#11747970C212yesmaximal, complemented
7#11747967C212yesmaximal, complemented
8#11747784C212yesmaximal, complemented
9#11747740C212yesmaximal, complemented
10#11747043C211yesmaximal, characteristic
11#11746917C211yesmaximal, characteristic, complemented
12#10611658—31nomaximal, Hall
13C2×#6706C2211yescharacteristic
14C4×D60C2211yescharacteristic
15C4×Dic30C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C3×#4020C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19#91437—21no—
20#91434—21no—
21#91428C2212yes—
22Dic3×D20C2212yes—
23#91411—22no—
24#91407—22no—
25#91383—21no—
26#91381C2212yes—
27#91368—21no—
28#91364C2212yes—
29C2×#6653C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91105C2211yescharacteristic
32#91101C2211yescharacteristic
33#91100C2211yescharacteristic
34C5×Dic3⋊C8C2212yes—
35C5×C8×Dic3C2212yes—
36C5×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×#3953C2212yes—
38C3×#3953C2212yes—
39#90990C2212yes—
40#90974C2212yes—
41#90965C2212yes—
42#81585—51nomaximal, Hall
43#65919—31no—
44#65913—31no—
45C5×C8×Q8—31no—
46#65139—31no—
47#65136—32no—
48#65133—32no—
49#65132—31no—
50#64986—32no—
51#64983D311yescharacteristic, complemented
52C4×D40—32no—
53C4×#677—31no—
54C2×D60C2311yescharacteristic
55C2×C4×D15—21no—
56C2×Dic30C2311yescharacteristic
57C2×C5×Dic6D411yescharacteristic
58C2×C3×D20—21no—
59C2×C3×D20—21no—
60C2×C3×D20C2312yes—
61C2×C3×Dic10—21no—
62C2×#1200—22no—
63C2×D5×Dic3—22no—
64C2×C3×C5×C8C2311yescharacteristic
65C2×C3×C5×C8C2311yescharacteristic
66C3×C42×C5C2311yescharacteristic
67#6714—21no—
68C4⋊Dic15C2311yescharacteristic
69C4⋊Dic15C2311yescharacteristic
70#6712—21no—
71C4×Dic15—21no—
72#6706—22no—
73C5×C4⋊Dic3D411yescharacteristic
74C5×Dic3⋊C4D412yes—
75C4×C5×Dic3C2312yes—
76C2×C5×C3⋊C8C2312yes—
77C3×C4⋊Dic5—21no—
78C3×C4⋊Dic5C2312yes—
79#6669—22no—
80#6668—22no—
81#6667—22no—
82#6665—22no—
83#6665—22no—
84#6665—22no—
85#6653—24no—
86#5730—51no—
87#5713—51no—
88C3×#486—51no—
89#5091—51no—
90#5072—51no—
91#4787—52no—
92#4768—52no—
93#4763—52no—
94#4756—52no—
95C4×#204—51no—
96C8×Dic6D511yescharacteristic, complemented
97C4×C5×Q8—31no—
98#4093—61no—
99#4092—61no—
100C2×D40—32no—
101C2×#677—31no—
102#4042—62no—
103#4040—62no—
104#4039—61no—
105D5×C4⋊C4—61no—
106#4021—32no—
107#4020C2×D311yescharacteristic
108C4×D20—32no—
109C4×D20—31no—
110C4×D20—32no—
111#4016—32no—
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C5×C4⋊C8—32no—
115C5×C4⋊C8—31no—
116C4×C5×C8—32no—
117C4×C5×C8C2×D311yescharacteristic
118#3953—32no—
119#3953—31no—
120#3953C2×D312yes—
121#3953C2×D312yes—
122#3950—32no—
123#3949—31no—
124#3948—31no—
125#3948—32no—
126#3361—151noSylow
127C22×D15—21no—
128C22×C3×D5—22no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—21no—
133C2×Dic15—21no—
134C2×Dic15—21no—
135D60—21no—
136D60#4112yes—
137C4×D15—42no—
138Dic30—21no—
139Dic30—21no—
140C2×C5×Dic3C2×D412yes—
141C2×C5×Dic3C2×D412yes—
142C5×Dic6—22no—
143C2×C3×Dic5—22no—
144C3×D20—22no—
145C3×D20—22no—
146C3×D20—42no—
147C3×D20—81no—
148C3×Dic10—81no—
149#1200—82no—
150D5×Dic3—82no—
151C3×C5×C8—21no—
152C3×C5×C8—21no—
153C5×C3⋊C8—22no—
154C3×C4⋊Q8—51no—
155C3×#127—51no—
156#946—102no—
157#936—52no—
158#936—101no—
159#935—102no—
160D4×Dic3—52no—
161D4×Dic3—101no—
162C2×#213—52no—
163C2×#204—51no—
164#897—101no—
165#893—52no—
166D3×C4⋊C4—101no—
167#890—52no—
168C4×D12—51no—
169C4×Dic6—51no—
170C4×Dic6C2×D511yescharacteristic
171C3×#102—52no—
172C3×#102—52no—
173C3×C4×C8C2×D511yescharacteristic
174#832—52no—
175#821—51no—
176#817—51no—
177#816—51no—
178Dic3⋊C8C2×D512yes—
179C8×Dic3C2×D512yes—
180#810—52no—
181#807—52no—
182C4⋊(C3⋊C8)C2×D511yescharacteristic
183C2×C5×Q8—31no—
184C2×D20—21no—
185C2×D20—21no—
186C2×D20—31no—
187C2×D20C22×D312yes—
188C2×C4×D5—61no—
189C2×C4×D5—62no—
190C2×C4×D5—62no—
191C2×Dic10—21no—
192C2×Dic10—31no—
193C2×C5×C8—32no—
194C2×C5×C8C22×D311yescharacteristic
195C2×C5×C8C22×D311yescharacteristic
196C5×C4⋊C4—32no—
197C5×C4⋊C4—31no—
198C42×C5—32no—
199C42×C5C22×D311yescharacteristic
200#685—62no—
201#685—62no—
202#685—62no—
203#685—62no—
204#685—61no—
205C4⋊Dic5—21no—
206C4⋊Dic5—31no—
207C4⋊Dic5—31no—
208C4⋊Dic5C22×D312yes—
209#683—62no—
210#683—62no—
211#683—61no—
212C4×Dic5—61no—
213D40—64no—
214#677—62no—
215#559—151no—
216#554—151no—
217#488—152no—
218#486—51no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—151no—
223C8×Q8—31no—
224C4×SD16—151no—
225C4×D8—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—22no—
228C2×D15—41no—
229C2×D15—41no—
230C2×C3×D5—42no—
231C2×C3×D5—42no—
232C2×C3×D5—42no—
233C3×C4×C5—21no—
234C3×C4×C5#13512yes—
235C3×C4×C5C2×#4111yescharacteristic
236C3×C4×C52−1+411yescharacteristic
237Dic15—41no—
238Dic15—41no—
239Dic15—41no—
240C3×Dic5—42no—
241C5×Dic3—22no—
242C5×Dic3—22no—
243C2×C3×Q8—101no—
244C2×C3×D4—52no—
245C2×C3×D4—101no—
246C2×C3×D4—101no—
247C22×Dic3—102no—
248C2×D12—51no—
249C2×C4×D3—101no—
250C2×C4×D3—102no—
251C2×Dic6—51no—
252C2×Dic6D2011yescharacteristic
253C2×C3×C8C22×D511yescharacteristic
254C2×C3×C8C22×D511yescharacteristic
255C3×C4⋊C4—52no—
256C3×C4⋊C4—101no—
257C3×C42C22×D511yescharacteristic
258#217—102no—
259#217—102no—
260#217—102no—
261#213—104no—
262(C2×D3)⋊C4—101no—
263(C2×D3)⋊C4—102no—
264C4⋊Dic3—51no—
265C4⋊Dic3—51no—
266C4⋊Dic3—102no—
267C4⋊Dic3D2011yescharacteristic
268Dic3⋊C4—101no—
269Dic3⋊C4—102no—
270Dic3⋊C4D2012yes—
271C4×Dic3—101no—
272C4×Dic3C22×D512yes—
273C2×C3⋊C8C22×D512yes—
274#204—102no—
275C22×D5—22no—
276C22×D5—61no—
277C5×Q8—62no—
278C2×C4×C5—32no—
279C2×C4×C5—32no—
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5C23×D311yescharacteristic
283C2×Dic5—22no—
284C2×Dic5—61no—
285C2×Dic5—61no—
286C2×Dic5—61no—
287D20—22no—
288D20—22no—
289D20—32no—
290D20—42no—
291D20—61no—
292D20—81no—
293C4×D5—122no—
294C4×D5—242no—
295C4×D5—242no—
296Dic10—61no—
297Dic10—61no—
298Dic10—81no—
299C5×C8—21no—
300C5×C8—21no—
301C5×C8—62no—
302C2×SD16—151no—
303C2×D8—152no—
304C4⋊Q8—51no—
305#127—51no—
306#125—152no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—302no—
311C22⋊Q8—301no—
312C4×Q8—31no—
313C4×Q8—151no—
314C4×D4—152no—
315C4×D4—152no—
316C4×D4—151no—
317C4×D4—301no—
318C2×C4⋊C4—301no—
319#107—152no—
320#106—151no—
321C4⋊C8—32no—
322C4⋊C8—31no—
323#103—152no—
324#103—151no—
325#102—52no—
326#102—52no—
327#102—152no—
328#102—151no—
329C4×C8—32no—
330C4×C8D3×D511yescharacteristic
331C2×C3×C5#54811yescharacteristic
332C2×C3×C5C2×#13511yescharacteristic
333C2×C3×C5#57611yescharacteristic
334D15—42no—
335C3×D5—82no—
336C23×C3—102no—
337C22×D3—101no—
338C3×Q8—401no—
339C3×D4—102no—
340C3×D4—102no—
341C3×D4—202no—
342C3×D4—401no—
343C2×C3×C4—102no—
344C2×C3×C4C2×D2011yescharacteristic
345C2×C3×C4C2×D2011yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—101no—
348C2×Dic3—101no—
349C2×Dic3—101no—
350C2×Dic3—402no—
351C2×Dic3C2×D2012yes—
352C2×Dic3C2×D2012yes—
353D12—52no—
354D12—101no—
355C4×D3—202no—
356C4×D3—402no—
357Dic6—22no—
358Dic6—101no—
359Dic6—101no—
360C3×C8—21no—
361C3×C8—21no—
362C3⋊C8—22no—
363C22×C5C2×D3×D411yescharacteristic
364C2×D5—42no—
365C2×D5—42no—
366C2×D5—42no—
367C2×D5—62no—
368C2×D5—121no—
369C2×D5—121no—
370C4×C5—21no—
371C4×C5—62no—
372C4×C5—62no—
373C4×C5#91612yes—
374C4×C5D3×#4111yescharacteristic
375C4×C5#101011yescharacteristic
376Dic5—42no—
377Dic5—121no—
378Dic5—121no—
379Dic5—121no—
380C2×Q8—31no—
381C2×Q8—101no—
382C2×Q8—151no—
383C2×D4—52no—
384C2×D4—101no—
385C2×D4—101no—
386C2×D4—151no—
387C22×C4—302no—
388C22×C4—302no—
389C22×C4—301no—
390SD16—302no—
391D8—304no—
392C2×C8—32no—
393C2×C8C2×D3×D511yescharacteristic
394C2×C8C2×D3×D511yescharacteristic
395C4⋊C4—31no—
396C4⋊C4—32no—
397C4⋊C4—52no—
398C4⋊C4—101no—
399C4⋊C4—151no—
400C4⋊C4—151no—
401C4⋊C4—302no—
402C4⋊C4—302no—
403C4⋊C4—301no—
404C22⋊C4—302no—
405C22⋊C4—302no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—301no—
409C42—32no—
410C42—301no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—202no—
414C22×C3—202no—
415C22×C3—202no—
416C22×C3C22×D2011yescharacteristic
417C2×D3—102no—
418C2×D3—201no—
419C2×D3—201no—
420C3×C4—21no—
421C3×C4—202no—
422C3×C4#405012yes—
423C3×C4#414711yescharacteristic
424C3×C4D5×#4111yescharacteristic
425Dic3—22no—
426Dic3—22no—
427Dic3—201no—
428Dic3—201no—
429Dic3—201no—
430C2×C5#567711yescharacteristic
431C2×C5#575711yescharacteristic
432C2×C5C2×#91611yescharacteristic
433D5—82no—
434D5—122no—
435C23—102no—
436C23—301no—
437Q8—62no—
438Q8—301no—
439Q8—301no—
440Q8—401no—
441D4—102no—
442D4—102no—
443D4—152no—
444D4—202no—
445D4—301no—
446D4—401no—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—102no—
450C2×C4—301no—
451C2×C4—301no—
452C2×C4—301no—
453C2×C4—602no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4D3×D2011yescharacteristic
457C2×C4D3×D2011yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—21no—
460C8—21no—
461C8—62no—
462C2×C3—402no—
463C2×C3#6591011yescharacteristic
464C2×C3C2×#405011yescharacteristic
465C2×C3#6608611yescharacteristic
466D3—202no—
467C5#8158511yescharacteristic, complemented, Sylow
468C22—202no—
469C22—202no—
470C22—202no—
471C22—302no—
472C22—601no—
473C22—601no—
474C22C2×D3×D2011yescharacteristic
475C4—21no—
476C4—62no—
477C4—62no—
478C4—202no—
479C4—601no—
480C4—601no—
481C4—601no—
482C4#9127212yes—
483C4#9200011yescharacteristic
484C4#9201611yescharacteristic
485C3#1061165811yescharacteristic, complemented, Sylow
486C2—402no—
487C2—602no—
488C2#1175254611yescharacteristic
489C2#1175397111yescharacteristic
490C2C2×#9127211yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radical#11747043C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#3361
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. #11752636C2semidirect
3. C4×#6706C2semidirect
4. C5×C8×Dic6C2semidirect
5. C3×#64983C2semidirect
6. #11747970C2semidirect
7. #11747967C2semidirect
8. #11747784C2semidirect
9. #11747740C2semidirect
11. #11746917C2semidirect
51. #64983D3semidirect
96. C8×Dic6D5semidirect
412. C3×C5#3361semidirect
467. C5#81585semidirect
485. C3#10611658semidirect

Maximal subgroups

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

subgroupindex
#117526452
#117526362
C4×#67062
C5×C8×Dic62
C3×#649832
#117479702
#117479672
#117477842
#117477402
#117470432
#117469172
#106116583
#815855