Finite Group Databasebeta

← #14471456

Subgroups — #14471456

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
1#11752539C211yesmaximal, characteristic, complemented
2#11752538C211yesmaximal, characteristic, complemented
3#11750944C211yesmaximal, characteristic, complemented
4C5×#4846C211yesmaximal, characteristic, complemented
5C3×#65119C211yesmaximal, characteristic, complemented
6#11747995C212yesmaximal, complemented
7#11747768C212yesmaximal, complemented
8#11747767C212yesmaximal, complemented
9#11747766C212yesmaximal, complemented
10C4×#6654C211yesmaximal, characteristic, complemented
11#11746912C211yesmaximal, characteristic, complemented
12#10612723—31nomaximal, Hall
13C2×D15⋊Q8—21no—
14C2×#6769—21no—
15C2×D120C2212yes—
16#91763C2211yescharacteristic
17C4×D60C2211yescharacteristic
18C4×C5×D12C2211yescharacteristic
19C5×#869C2211yescharacteristic
20C3×C4×Dic10C2211yescharacteristic
21#91468C2212yes—
22#91460—21no—
23#91451C2212yes—
24#91420—22no—
25#91419—22no—
26#91418C2212yes—
27#91418C2212yes—
28#91383—21no—
29C2×#6654C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91105C2212yes—
32C5×#821C2212yes—
33C5×#818C2212yes—
34C3×#3946C2212yes—
35C3×C8×Dic5C2212yes—
36C3×C4×#168C2211yescharacteristic
37#90988C2211yescharacteristic
38#90969C2212yes—
39#90969C2212yes—
40#90969C2211yescharacteristic
41#90967C2211yescharacteristic
42#79924—51nomaximal, Hall
43#66061—31no—
44#65887—31no—
45C5×#474—31no—
46#65377—31no—
47C4×#686—31no—
48#65179—32no—
49#65161—32no—
50#65132—31no—
51#65119D311yescharacteristic, complemented
52#65075—32no—
53#65049—32no—
54C2×D60—21no—
55C2×D60—21no—
56C2×D60C2312yes—
57C2×D60C2311yescharacteristic
58C2×C4×D15—21no—
59C2×C5×D12C2311yescharacteristic
60C2×C4×C5×D3—21no—
61C2×C5×Dic6—21no—
62C2×C3×Dic10D411yescharacteristic
63C2×#1204—22no—
64C2×#1203—22no—
65C2×#1203—22no—
66C2×#1200—22no—
67C2×#1200—22no—
68D15⋊Q8—44no—
69#6769—44no—
70C2×C3×C5×C8C2312yes—
71C3×C42×C5C2311yescharacteristic
72#6714—21no—
73C4⋊Dic15C2311yescharacteristic
74D120—24no—
75C5×(C2×D3)⋊C4—21no—
76C5×C4⋊Dic3—21no—
77C5×C4⋊Dic3C2312yes—
78C5×C4⋊Dic3C2311yescharacteristic
79C3×C4⋊Dic5D411yescharacteristic
80C3×#683D412yes—
81C3×C4×Dic5C2312yes—
82C2×C3×#168C2311yescharacteristic
83C2×C3×#168C2311yescharacteristic
84#6668—22no—
85#6667—22no—
86#6667—22no—
87#6654—22no—
88#5577—51no—
89Q8×D12—51no—
90C3×C8×Q8—51no—
91#4846—52no—
92#4846D511yescharacteristic, complemented
93#4843—51no—
94#4843—52no—
95#4694—51no—
96#4694—52no—
97C4×D24—51no—
98C4×D24—52no—
99C2×Q8×D5—61no—
100C2×#709—61no—
101C5×C4⋊Q8—31no—
102C4×C5×D4—31no—
103#4092—61no—
104#4086—32no—
105C2×#686—31no—
106#4076—61no—
107C2×D40—32no—
108#4042—62no—
109#4039—32no—
110#4039—32no—
111#4034—32no—
112#4030—62no—
113#4020—31no—
114C4×D20—31no—
115C4×Dic10C2×D311yescharacteristic
116C5×#107—32no—
117C5×C4⋊C8C2×D311yescharacteristic
118C5×#102—32no—
119#3964—31no—
120#3953—32no—
121#3946C2×D312yes—
122C8×Dic5C2×D312yes—
123#3941—31no—
124#3941—32no—
125#3941—32no—
126#3939—31no—
127C4×#168C2×D311yescharacteristic
128#3358—151noSylow
129C22×D15—21no—
130C22×D15—22no—
131C22×C5×D3—21no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—21no—
136D60—22no—
137D60—21no—
138D60—22no—
139D60—42no—
140D60—81no—
141D60#4112yescomplemented
142C4×D15—42no—
143C2×C5×Dic3—21no—
144C2×C5×Dic3—22no—
145C5×D12—21no—
146C5×D12—21no—
147C4×C5×D3—42no—
148C5×Dic6—42no—
149C2×C3×Dic5C2×D412yes—
150C2×C3×Dic5C2×D412yes—
151C3×Dic10D814yescomplemented
152#1204—44no—
153#1203—44no—
154#1203—82no—
155#1200—44no—
156#1200—44no—
157C3×C5×C8—22no—
158C3×#168—21no—
159C3×#168—21no—
160C2×#239—101no—
161C2×D3×Q8—101no—
162C3×C4×Q8—51no—
163C2×D24—51no—
164C2×D24—52no—
165#897—102no—
166#897—101no—
167#895—102no—
168#895—101no—
169#874—52no—
170#874—51no—
171C4×D12—51no—
172C4×D12—52no—
173C4×D12—52no—
174C4×D12C2×D511yescharacteristic
175#869—52no—
176#869C2×D511yescharacteristic
177C3×C4⋊C8—52no—
178C3×C4⋊C8C2×D511yescharacteristic
179C3×C4×C8—52no—
180C3×C4×C8—51no—
181#821—51no—
182#821—52no—
183#821—51no—
184#821—52no—
185#821—52no—
186#821C2×D512yes—
187#818—51no—
188#818C2×D512yes—
189C2×C5×Q8—61no—
190C2×C5×D4—31no—
191C22×C4×C5—61no—
192C2×C22⋊D5—62no—
193C2×C22⋊D5—62no—
194Q8×D5—124no—
195#709—124no—
196C2×D20—31no—
197C2×D20—32no—
198C2×D20—61no—
199C2×D20—61no—
200C2×C4×D5—61no—
201C2×C4×D5—62no—
202C2×C4×D5—62no—
203C2×Dic10—62no—
204C2×Dic10D1211yescharacteristic
205C2×C5×C8C22×D312yes—
206C5×C4⋊C4—31no—
207C5×C4⋊C4—32no—
208C5×C4⋊C4—61no—
209C5×C22⋊C4—61no—
210C42×C5C22×D311yescharacteristic
211#686—62no—
212#685—61no—
213#685—62no—
214#685—62no—
215C4⋊Dic5—31no—
216C4⋊Dic5D1211yescharacteristic
217#683—62no—
218#683D1212yes—
219C4×Dic5C22×D312yes—
220C2×#168C22×D311yescharacteristic
221C2×#168C22×D311yescharacteristic
222D40—64no—
223#550—151no—
224D4×Q8—151no—
225#486—152no—
226#486—151no—
227#474—31no—
228#474—152no—
229#459—152no—
230#459—151no—
231C8×Q8—51no—
232C4×D8—152no—
233C4×D8—151no—
234C22×C3×C5C22×D411yescharacteristic
235C2×D15—22no—
236C2×D15—41no—
237C2×D15—41no—
238C2×D15—42no—
239C2×D15—42no—
240C2×D15—42no—
241C2×C5×D3—41no—
242C2×C5×D3—41no—
243C2×C5×D3—41no—
244C3×C4×C5—21no—
245C3×C4×C5C2×D812yes—
246C3×C4×C5C2×#4111yescharacteristic
247C3×C4×C52−1+411yescharacteristic
248Dic15—41no—
249C3×Dic5—22no—
250C3×Dic5C2×D814yes—
251C5×Dic3—41no—
252C5×Dic3—42no—
253C2×C3×Q8—51no—
254#239—204no—
255D3×Q8—204no—
256C2×D12—51no—
257C2×D12—52no—
258C2×D12—102no—
259C2×D12—101no—
260C2×D12—102no—
261C2×D12—101no—
262C2×D12C22×D511yescharacteristic
263C2×C4×D3—21no—
264C2×C4×D3—102no—
265C2×C4×D3—102no—
266C2×C4×D3—101no—
267C2×Dic6—21no—
268C2×Dic6—102no—
269C2×C3×C8—51no—
270C2×C3×C8—51no—
271C2×C3×C8C22×D512yes—
272C3×C4⋊C4—52no—
273C3×C4⋊C4—51no—
274C3×C42—52no—
275C3×C42C22×D511yescharacteristic
276(C2×D3)⋊C4—21no—
277(C2×D3)⋊C4—102no—
278(C2×D3)⋊C4—102no—
279(C2×D3)⋊C4—101no—
280C4⋊Dic3—21no—
281C4⋊Dic3—51no—
282C4⋊Dic3—102no—
283C4⋊Dic3C22×D511yescharacteristic
284C4⋊Dic3C22×D512yes—
285D24—104no—
286D24—102no—
287C23×C5—61no—
288C22×D5—61no—
289C22×D5—62no—
290C5×Q8—122no—
291C5×D4—61no—
292C5×D4—61no—
293C2×C4×C5—62no—
294C2×C4×C5—61no—
295C2×C4×C5—122no—
296C2×C4×C5C2×D1211yescharacteristic
297C2×C4×C5C2×D1211yescharacteristic
298C2×C4×C5C23×D311yescharacteristic
299C22⋊D5—124no—
300C22⋊D5—242no—
301C2×Dic5—61no—
302C2×Dic5C2×D1212yes—
303C2×Dic5C2×D1212yes—
304D20—32no—
305D20—61no—
306D20—62no—
307D20—62no—
308D20—122no—
309D20—241no—
310C4×D5—122no—
311C4×D5—124no—
312C4×D5—124no—
313Dic10—124no—
314Dic10D2414yescomplemented
315C5×C8—22no—
316#168—21no—
317#168—21no—
318C2×#41—301no—
319C22×Q8—301no—
320C2×D8—151no—
321C2×D8—152no—
322C4⋊Q8—31no—
323C4⋊Q8—152no—
324#127—152no—
325#127—151no—
326C22⋊Q8—302no—
327C22⋊Q8—301no—
328#121—302no—
329#121—301no—
330C4×Q8—51no—
331C4×D4—31no—
332C4×D4—152no—
333C4×D4—152no—
334C4×D4—151no—
335#107—32no—
336#107—151no—
337C4⋊C8—52no—
338C4⋊C8D3×D511yescharacteristic
339#102—32no—
340#102—151no—
341#102—152no—
342#102—152no—
343#102—151no—
344#102—152no—
345C4×C8—52no—
346C4×C8—51no—
347C2×C3×C5#54811yescharacteristic
348C2×C3×C5C22×D811yescharacteristic
349C2×C3×C5#57711yescharacteristic
350D15—42no—
351D15—82no—
352C5×D3—81no—
353C22×D3—21no—
354C22×D3—101no—
355C22×D3—102no—
356C3×Q8—54no—
357C2×C3×C4—52no—
358C2×C3×C4—52no—
359C2×C3×C4D4×D511yescharacteristic
360C2×C3×C4D4×D511yescharacteristic
361C2×C3×C4C23×D511yescharacteristic
362C2×Dic3—22no—
363C2×Dic3—21no—
364C2×Dic3—101no—
365D12—21no—
366D12—21no—
367D12—52no—
368D12—101no—
369D12—102no—
370D12—102no—
371D12—204no—
372D12—202no—
373D12—401no—
374D12—402no—
375C4×D3—42no—
376C4×D3—204no—
377C4×D3—204no—
378C4×D3—202no—
379Dic6—42no—
380Dic6—204no—
381C3×C8—22no—
382C3×C8—101no—
383C3×C8—101no—
384C22×C5—121no—
385C22×C5—121no—
386C22×C5—121no—
387C22×C5C22×D1211yescharacteristic
388C2×D5—62no—
389C2×D5—121no—
390C2×D5—121no—
391C2×D5—122no—
392C2×D5—122no—
393C2×D5—122no—
394C4×C5—21no—
395C4×C5—122no—
396C4×C5—121no—
397C4×C5C2×D2412yes—
398C4×C5#100711yescharacteristic
399C4×C5D3×#4111yescharacteristic
400Dic5—22no—
401Dic5—121no—
402Dic5C2×D2414yes—
403#41—604no—
404C2×Q8—51no—
405C2×Q8—61no—
406C2×Q8—302no—
407C2×Q8—604no—
408C2×D4—31no—
409C2×D4—151no—
410C2×D4—152no—
411C2×D4—302no—
412C2×D4—302no—
413C2×D4—301no—
414C2×D4—301no—
415C22×C4—61no—
416C22×C4—302no—
417C22×C4—302no—
418C22×C4—301no—
419D8—304no—
420D8—302no—
421C2×C8—51no—
422C2×C8—51no—
423C2×C8C2×D3×D512yes—
424C4⋊C4—32no—
425C4⋊C4—31no—
426C4⋊C4—52no—
427C4⋊C4—51no—
428C4⋊C4—61no—
429C4⋊C4—151no—
430C4⋊C4—302no—
431C22⋊C4—61no—
432C22⋊C4—302no—
433C22⋊C4—302no—
434C22⋊C4—301no—
435C42—52no—
436C42C2×D3×D511yescharacteristic
437C3×C5#335811yescharacteristic, complemented, Hall
438C22×C3C2×D4×D511yescharacteristic
439C2×D3—41no—
440C2×D3—41no—
441C2×D3—41no—
442C2×D3—102no—
443C2×D3—201no—
444C2×D3—201no—
445C2×D3—202no—
446C2×D3—202no—
447C2×D3—202no—
448C3×C4—21no—
449C3×C4—54no—
450C3×C4—102no—
451C3×C4D5×D812yes—
452C3×C4#414711yescharacteristic
453C3×C4D5×#4111yescharacteristic
454Dic3—42no—
455Dic3—41no—
456Dic3—201no—
457C2×C5—241no—
458C2×C5#557611yescharacteristic
459C2×C5C22×D2411yescharacteristic
460C2×C5#575111yescharacteristic
461D5—122no—
462D5—242no—
463C23—61no—
464C23—301no—
465C23—302no—
466Q8—54no—
467Q8—122no—
468Q8—604no—
469D4—61no—
470D4—61no—
471D4—152no—
472D4—302no—
473D4—301no—
474D4—302no—
475D4—604no—
476D4—602no—
477D4—1201no—
478D4—1202no—
479C2×C4—52no—
480C2×C4—52no—
481C2×C4—61no—
482C2×C4—62no—
483C2×C4—122no—
484C2×C4—301no—
485C2×C4—604no—
486C2×C4—604no—
487C2×C4—602no—
488C2×C4D5×D1211yescharacteristic
489C2×C4D5×D1211yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—22no—
492C8—101no—
493C8—101no—
494C2×C3#6596711yescharacteristic
495C2×C3C2×D5×D811yescharacteristic
496C2×C3#6611211yescharacteristic
497D3—81no—
498D3—202no—
499D3—402no—
500C5#7992411yescharacteristic, complemented, Sylow
501C22—121no—
502C22—121no—
503C22—121no—
504C22—302no—
505C22—601no—
506C22—601no—
507C22—602no—
508C22—602no—
509C22—602no—
510C22C2×D5×D1211yescharacteristic
511C4—21no—
512C4—54no—
513C4—102no—
514C4—121no—
515C4—122no—
516C4—601no—
517C4D5×D2412yes—
518C4#9202411yescharacteristic
519C4#9202911yescharacteristic
520C3#1061272311yescharacteristic, complemented, Sylow
521C2—241no—
522C2—602no—
523C2—1202no—
524C2#1175334111yescharacteristic
525C2C2×D5×D2411yescharacteristic
526C2#1175402511yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3358
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. #11752539C2semidirect
2. #11752538C2semidirect
3. #11750944C2semidirect
4. C5×#4846C2semidirect
5. C3×#65119C2semidirect
6. #11747995C2semidirect
7. #11747768C2semidirect
8. #11747767C2semidirect
9. #11747766C2semidirect
10. C4×#6654C2semidirect
11. #11746912C2semidirect
51. #65119D3semidirect
92. #4846D5semidirect
141. D60#41semidirect
151. C3×Dic10D8semidirect
314. Dic10D24semidirect
437. C3×C5#3358semidirect
500. C5#79924semidirect
520. C3#10612723semidirect

Maximal subgroups

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

subgroupindex
#117525392
#117525382
#117509442
C5×#48462
C3×#651192
#117479952
#117477682
#117477672
#117477662
C4×#66542
#117469122
#106127233
#799245