Finite Group Databasebeta

← #14471462

Subgroups — #14471462

Order 1920.

852 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65887C211yesmaximal, characteristic, complemented
2#11752539C211yesmaximal, characteristic, complemented
3C4×#6715C211yesmaximal, characteristic, complemented
4C5×#5007C211yesmaximal, characteristic, complemented
5#11749102C212yesmaximal, complemented
6#11748976C212yesmaximal, complemented
7#11747410C212yesmaximal, complemented
8#11747223C212yesmaximal, complemented
9#11747043C211yesmaximal, characteristic, complemented
10#11746895C211yesmaximal, characteristic, complemented
11#11746846C211yesmaximal, characteristic, complemented
12#10612723—31nomaximal, Hall
13C2×C3×#709—21no—
14C2×D15⋊Q8—21no—
15C3×C4×C5×D4C2211yescharacteristic
16C2×#6715C2211yescharacteristic
17C4×D60C2211yescharacteristic
18C5×#869C2211yescharacteristic
19C3×#4086C2212yes—
20C3×#4076—21no—
21C3×#4039C2212yes—
22C3×#4030—22no—
23C3×#4020C2211yescharacteristic
24C3×C4×Dic10C2211yescharacteristic
25#91468C2212yes—
26#91419—22no—
27#91418C2212yes—
28#91383—21no—
29C2×#6653C2212yes—
30#91116C2211yescharacteristic
31#91093C2211yescharacteristic
32#91091C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34C5×#832C2212yes—
35C5×#807C2212yes—
36C5×C4⋊(C3⋊C8)C2211yescharacteristic
37#90982C2212yes—
38#90965C2212yes—
39#90964C2212yes—
40#90964C2212yes—
41Dic5×C3⋊C8C2212yes—
42#83580—51nomaximal, Hall
43#66061—31no—
44#65887D311yescharacteristic, complemented
45C5×#474—31no—
46#65377—31no—
47C4×#686—31no—
48#65179—32no—
49#65161—32no—
50#65132—31no—
51#65119—31no—
52#65075—32no—
53#65049—32no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×D60C2311yescharacteristic
57C2×C4×D15—21no—
58C2×C5×Dic6—21no—
59C2×C3×C22⋊D5—22no—
60C2×C3×C22⋊D5—22no—
61C3×#709—44no—
62C2×C3×D20—21no—
63C2×C3×D20—21no—
64C2×C3×D20C2312yes—
65C2×C3×C4×D5—22no—
66C2×C3×Dic10D411yescharacteristic
67C2×#1204—22no—
68C2×#1200—22no—
69D15⋊Q8—44no—
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C22⋊C4—21no—
72C3×C42×C5C2311yescharacteristic
73#6715—22no—
74#6714—21no—
75C4⋊Dic15C2311yescharacteristic
76C2×C3⋊#168C2311yescharacteristic
77C2×C3⋊#168C2311yescharacteristic
78C5×C4⋊Dic3—21no—
79C5×C4⋊Dic3C2312yes—
80C2×C5×C3⋊C8C2312yes—
81C3×#685—22no—
82C3×C4⋊Dic5D411yescharacteristic
83C3×#683D412yes—
84C3×C4×Dic5C2312yes—
85#6668—22no—
86#6667—22no—
87#6653—24no—
88C3×#550—51no—
89Q8×D12—51no—
90#5072—52no—
91#5072—51no—
92#5070—51no—
93#5070—52no—
94Q8×C3⋊C8—51no—
95C4×#213—51no—
96C4×#213—52no—
97#5007—52no—
98#5007D511yescharacteristic, complemented
99C2×Q8×D5—61no—
100C2×#709—21no—
101C5×C4⋊Q8—31no—
102C4×C5×D4C2×D311yescharacteristic
103#4092—61no—
104#4086C2×D312yes—
105C2×#686—31no—
106#4076—21no—
107C2×D40—32no—
108#4042—62no—
109#4039—32no—
110#4039C2×D312yes—
111#4034—32no—
112#4030—22no—
113#4020C2×D311yescharacteristic
114C4×D20—31no—
115C4×Dic10C2×D311yescharacteristic
116C5×#107—32no—
117C5×C4⋊C8—31no—
118C5×#102—32no—
119#3964—31no—
120#3953—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3941—32no—
124#3941—32no—
125#3941—31no—
126#3939—31no—
127C4×#168—31no—
128#3358—151noSylow
129C23×C3×C5—21no—
130C22×D15—21no—
131C22×C3×D5—22no—
132C3×C5×D4—21no—
133C3×C5×D4—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—42no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2411yescharacteristic
139C2×Dic15—21no—
140D60—21no—
141D60#4112yescomplemented
142C4×D15—42no—
143C2×C5×Dic3—22no—
144C5×Dic6—42no—
145C3×C22⋊D5—44no—
146C3×C22⋊D5—82no—
147C2×C3×Dic5C2×D412yes—
148C2×C3×Dic5C2×D412yes—
149C3×D20—22no—
150C3×D20—22no—
151C3×D20—42no—
152C3×D20—81no—
153C3×C4×D5—44no—
154C3×Dic10D814yescomplemented
155#1204—44no—
156#1200—44no—
157C3⋊#168—21no—
158C3⋊#168—21no—
159C5×C3⋊C8—22no—
160C2×C3×#41—101no—
161C2×D3×Q8—101no—
162C3×#127—52no—
163C3×#127—51no—
164C3×#121—102no—
165C3×#121—101no—
166C3×C4×Q8—51no—
167C3×C4×D4—52no—
168C3×C4×D4C2×D511yescharacteristic
169C2×#213—51no—
170C2×#213—52no—
171#897—102no—
172#897—101no—
173C4×D12—51no—
174C4×D12—52no—
175#869—52no—
176#869C2×D511yescharacteristic
177#832—51no—
178#832—52no—
179#832—52no—
180#832—52no—
181#832C2×D512yes—
182#809—51no—
183#807—51no—
184#807C2×D512yes—
185C4⋊(C3⋊C8)—52no—
186C4⋊(C3⋊C8)C2×D511yescharacteristic
187C4×C3⋊C8—51no—
188C4×C3⋊C8—52no—
189C2×C5×Q8—61no—
190C2×C5×D4C22×D311yescharacteristic
191C22×C4×C5—21no—
192C2×C22⋊D5—22no—
193C2×C22⋊D5—22no—
194Q8×D5—124no—
195#709—44no—
196C2×D20—21no—
197C2×D20—21no—
198C2×D20—31no—
199C2×D20C22×D312yes—
200C2×C4×D5—22no—
201C2×C4×D5—61no—
202C2×C4×D5—62no—
203C2×Dic10—62no—
204C2×Dic10#6711yescharacteristic
205C2×C5×C8—32no—
206C5×C4⋊C4—32no—
207C5×C4⋊C4—61no—
208C5×C4⋊C4C22×D311yescharacteristic
209C5×C22⋊C4—21no—
210C42×C5C22×D311yescharacteristic
211#686—62no—
212#685—22no—
213#685—61no—
214#685—62no—
215C4⋊Dic5—31no—
216C4⋊Dic5#6711yescharacteristic
217#683—62no—
218#683#6712yes—
219C4×Dic5C22×D312yes—
220C2×#168—31no—
221C2×#168—31no—
222D40—64no—
223#550—51no—
224D4×Q8—151no—
225#486—152no—
226#486—151no—
227#474—31no—
228#474—152no—
229#459—152no—
230#459—151no—
231C8×Q8—151no—
232C4×D8—152no—
233C4×D8—151no—
234C22×C3×C5—41no—
235C22×C3×C5—41no—
236C22×C3×C5—41no—
237C22×C3×C5C22×D411yescharacteristic
238C2×D15—22no—
239C2×D15—41no—
240C2×D15—41no—
241C2×C3×D5—42no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C3×C4×C5—21no—
245C3×C4×C5—41no—
246C3×C4×C5C2×D812yes—
247C3×C4×C5C2×#4111yescharacteristic
248C3×C4×C52−1+411yescharacteristic
249Dic15—41no—
250C3×Dic5—22no—
251C3×Dic5C2×D814yes—
252C5×Dic3—42no—
253C3×#41—204no—
254C2×C3×Q8—51no—
255C2×C3×D4—52no—
256C2×C3×D4—102no—
257C2×C3×D4—102no—
258C2×C3×D4—101no—
259C2×C3×D4—101no—
260C2×C3×D4C22×D511yescharacteristic
261C22×C3×C4—21no—
262C22×C3×C4—102no—
263D3×Q8—204no—
264C2×D12—51no—
265C2×C4×D3—102no—
266C2×C4×D3—101no—
267C2×Dic6—21no—
268C2×Dic6—102no—
269C3×C4⋊C4—52no—
270C3×C4⋊C4—51no—
271C3×C4⋊C4C22×D511yescharacteristic
272C3×C22⋊C4—21no—
273C3×C22⋊C4—102no—
274C3×C42—52no—
275C3×C42C22×D511yescharacteristic
276#213—104no—
277#213—102no—
278(C2×D3)⋊C4—102no—
279(C2×D3)⋊C4—101no—
280C4⋊Dic3—21no—
281C4⋊Dic3—51no—
282C4⋊Dic3—102no—
283C4⋊Dic3C22×D512yes—
284C2×C3⋊C8—51no—
285C2×C3⋊C8—51no—
286C2×C3⋊C8C22×D512yes—
287C23×C5—21no—
288C22×D5—22no—
289C22×D5—61no—
290C5×Q8—122no—
291C5×D4—21no—
292C5×D4—21no—
293C2×C4×C5—21no—
294C2×C4×C5—42no—
295C2×C4×C5—62no—
296C2×C4×C5C2×#6711yescharacteristic
297C2×C4×C5C2×#6711yescharacteristic
298C2×C4×C5C23×D311yescharacteristic
299C22⋊D5—44no—
300C22⋊D5—82no—
301C2×Dic5—61no—
302C2×Dic5C2×#6712yes—
303C2×Dic5C2×#6712yes—
304D20—22no—
305D20—22no—
306D20—32no—
307D20—42no—
308D20—61no—
309D20—81no—
310C4×D5—44no—
311C4×D5—122no—
312C4×D5—124no—
313Dic10—124no—
314Dic10#21314yescomplemented
315C5×C8—62no—
316#168—61no—
317#168—61no—
318C2×#41—101no—
319C22×Q8—301no—
320C2×D8—152no—
321C2×D8—151no—
322C4⋊Q8—31no—
323C4⋊Q8—152no—
324#127—52no—
325#127—51no—
326C22⋊Q8—302no—
327C22⋊Q8—301no—
328#121—102no—
329#121—101no—
330C4×Q8—51no—
331C4×D4—52no—
332C4×D4—152no—
333C4×D4—151no—
334C4×D4D3×D511yescharacteristic
335#107—32no—
336#107—151no—
337C4⋊C8—31no—
338C4⋊C8—152no—
339#102—32no—
340#102—152no—
341#102—152no—
342#102—152no—
343#102—151no—
344#102—151no—
345C4×C8—152no—
346C4×C8—151no—
347C2×C3×C5—81no—
348C2×C3×C5#54811yescharacteristic
349C2×C3×C5C22×D811yescharacteristic
350C2×C3×C5#57711yescharacteristic
351D15—42no—
352C3×D5—82no—
353C23×C3—21no—
354C23×C3—102no—
355C22×D3—101no—
356C3×Q8—54no—
357C3×D4—21no—
358C3×D4—21no—
359C3×D4—102no—
360C3×D4—102no—
361C3×D4—204no—
362C3×D4—202no—
363C3×D4—401no—
364C3×D4—402no—
365C2×C3×C4—21no—
366C2×C3×C4—42no—
367C2×C3×C4—52no—
368C2×C3×C4—52no—
369C2×C3×C4—204no—
370C2×C3×C4D4×D511yescharacteristic
371C2×C3×C4D4×D511yescharacteristic
372C2×C3×C4C23×D511yescharacteristic
373C2×Dic3—22no—
374C2×Dic3—101no—
375D12—52no—
376D12—101no—
377C4×D3—204no—
378C4×D3—202no—
379Dic6—42no—
380Dic6—204no—
381C3⋊C8—22no—
382C3⋊C8—101no—
383C3⋊C8—101no—
384C22×C5—41no—
385C22×C5—41no—
386C22×C5—41no—
387C22×C5C22×#6711yescharacteristic
388C2×D5—42no—
389C2×D5—42no—
390C2×D5—42no—
391C2×D5—62no—
392C2×D5—121no—
393C2×D5—121no—
394C4×C5—21no—
395C4×C5—41no—
396C4×C5—122no—
397C4×C5C2×#21312yes—
398C4×C5D3×#4111yescharacteristic
399C4×C5#101011yescharacteristic
400Dic5—22no—
401Dic5—121no—
402Dic5C2×#21314yes—
403#41—204no—
404C2×Q8—51no—
405C2×Q8—61no—
406C2×Q8—302no—
407C2×Q8—604no—
408C2×D4—52no—
409C2×D4—102no—
410C2×D4—102no—
411C2×D4—101no—
412C2×D4—101no—
413C2×D4—151no—
414C2×D4C2×D3×D511yescharacteristic
415C22×C4—21no—
416C22×C4—102no—
417C22×C4—302no—
418C22×C4—301no—
419D8—304no—
420D8—302no—
421C2×C8—32no—
422C2×C8—151no—
423C2×C8—151no—
424C4⋊C4—32no—
425C4⋊C4—52no—
426C4⋊C4—51no—
427C4⋊C4—61no—
428C4⋊C4—151no—
429C4⋊C4—302no—
430C4⋊C4C2×D3×D511yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—102no—
433C22⋊C4—302no—
434C22⋊C4—301no—
435C42—52no—
436C42C2×D3×D511yescharacteristic
437C3×C5#335811yescharacteristic, complemented, Hall
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—202no—
442C22×C3—202no—
443C22×C3—202no—
444C22×C3C2×D4×D511yescharacteristic
445C2×D3—102no—
446C2×D3—201no—
447C2×D3—201no—
448C3×C4—21no—
449C3×C4—41no—
450C3×C4—54no—
451C3×C4—102no—
452C3×C4D5×D812yes—
453C3×C4#414711yescharacteristic
454C3×C4D5×#4111yescharacteristic
455Dic3—42no—
456Dic3—201no—
457C2×C5—81no—
458C2×C5C22×#21311yescharacteristic
459C2×C5#583111yescharacteristic
460C2×C5#583611yescharacteristic
461D5—82no—
462D5—122no—
463C23—21no—
464C23—102no—
465C23—301no—
466Q8—54no—
467Q8—122no—
468Q8—604no—
469D4—21no—
470D4—21no—
471D4—102no—
472D4—102no—
473D4—152no—
474D4—204no—
475D4—202no—
476D4—301no—
477D4—401no—
478D4—402no—
479C2×C4—21no—
480C2×C4—42no—
481C2×C4—52no—
482C2×C4—52no—
483C2×C4—62no—
484C2×C4—204no—
485C2×C4—301no—
486C2×C4—604no—
487C2×C4—602no—
488C2×C4D5×#6711yescharacteristic
489C2×C4D5×#6711yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—62no—
492C8—301no—
493C8—301no—
494C2×C3—81no—
495C2×C3—402no—
496C2×C3#6596711yescharacteristic
497C2×C3C2×D5×D811yescharacteristic
498C2×C3#6611211yescharacteristic
499D3—202no—
500C5#8358011yescharacteristic, complemented, Sylow
501C22—41no—
502C22—41no—
503C22—41no—
504C22—202no—
505C22—202no—
506C22—202no—
507C22—302no—
508C22—601no—
509C22—601no—
510C22C2×D5×#6711yescharacteristic
511C4—21no—
512C4—41no—
513C4—54no—
514C4—102no—
515C4—122no—
516C4—601no—
517C4D5×#21312yes—
518C4#9200011yescharacteristic
519C4#9201611yescharacteristic
520C3#1061272311yescharacteristic, complemented, Sylow
521C2—81no—
522C2—402no—
523C2—602no—
524C2#1175421511yescharacteristic
525C2C2×D5×#21311yescharacteristic
526C2#1175533511yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3358
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#65887C2semidirect
2. #11752539C2semidirect
3. C4×#6715C2semidirect
4. C5×#5007C2semidirect
5. #11749102C2semidirect
6. #11748976C2semidirect
7. #11747410C2semidirect
8. #11747223C2semidirect
9. #11747043C2semidirect
10. #11746895C2semidirect
11. #11746846C2semidirect
44. #65887D3semidirect
98. #5007D5semidirect
141. D60#41semidirect
154. C3×Dic10D8semidirect
314. Dic10#213semidirect
437. C3×C5#3358semidirect
500. C5#83580semidirect
520. C3#10612723semidirect

Maximal subgroups

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

subgroupindex
C3×#658872
#117525392
C4×#67152
C5×#50072
#117491022
#117489762
#117474102
#117472232
#117470432
#117468952
#117468462
#106127233
#835805