Finite Group Databasebeta

← #14460275

Subgroups — #14460275

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756343C211yesmaximal, characteristic, complemented
2#11756336C211yesmaximal, characteristic
3C3×C4×C5×Q16C211yesmaximal, characteristic, complemented
4#11751288C212yesmaximal, complemented
5#11751128C211yesmaximal, characteristic, complemented
6#11751121C211yesmaximal, characteristic, complemented
7#11750986C212yesmaximal, complemented
8#11750908C212yesmaximal, complemented
9#11750905C212yesmaximal, complemented
10#11750795C211yesmaximal, characteristic, complemented
11C8×D60C211yesmaximal, characteristic, complemented
12#10611468—31nomaximal, Hall
13C2×#6821C2212yes—
14C2×C3×C5×Q16C2211yescharacteristic
15C3×C4×C5×Q8C2211yescharacteristic
16C3×C4×C5×Q8C2211yescharacteristic
17#91835C2212yes—
18C2×#6717C2212yes—
19C2×C8×D15C2212yes—
20#91787—22no—
21#91784—22no—
22#91784C2212yes—
23#91781C2212yes—
24#91764—21no—
25#91763—21no—
26#91763C2211yescharacteristic
27C4×D60—21no—
28C4×D60C2211yescharacteristic
29#91758C2211yescharacteristic
30C4×Dic30—21no—
31C3×C5×#107C2211yescharacteristic
32C3×C5×#103C2211yescharacteristic
33C3×C5×#103C2211yescharacteristic
34C3×C4×C5×C8C2211yescharacteristic
35#91119C2212yes—
36#91105C2212yes—
37#91105C2212yes—
38#91104C2212yes—
39#91093C2212yes—
40#91092C2212yes—
41C4⋊(C3⋊#168)C2211yescharacteristic
42#79737—51nomaximal, Hall
43#65918—31no—
44#65911—31no—
45C4×C5×Q16D311yescharacteristic, complemented
46#65476—32no—
47#65316—31no—
48#65309—31no—
49#65174—32no—
50#65096—32no—
51#65093—32no—
52#64983—31no—
53C8×D20—31no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×C3×C5×Q8C2311yescharacteristic
56#6821—24no—
57#6821—42no—
58C2×D60—22no—
59C2×D60—21no—
60C2×D60—22no—
61C2×D60—21no—
62C2×D60D411yescharacteristic
63C2×D60C2312yes—
64C2×C4×D15—22no—
65C2×C4×D15C2312yes—
66C2×Dic30—21no—
67C3×C5×Q16—22no—
68C2×C3×C5×C8C2311yescharacteristic
69C2×C3×C5×C8C2311yescharacteristic
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4—21no—
72C3×C5×C4⋊C4C2311yescharacteristic
73C3×C5×C4⋊C4C2311yescharacteristic
74C3×C42×C5—21no—
75C3×C42×C5—21no—
76C3×C42×C5C2311yescharacteristic
77#6717—42no—
78#6714—22no—
79#6714—22no—
80#6714—22no—
81#6714D412yes—
82C4⋊Dic15—21no—
83C4⋊Dic15D411yescharacteristic
84C4⋊Dic15C2312yes—
85#6712—22no—
86C4×Dic15—22no—
87C2×C3⋊#168C2312yes—
88C8×D15—42no—
89#5584—51no—
90#5577—51no—
91C3×C4×Q16D511yescharacteristic, complemented
92#5187—52no—
93#5027—51no—
94#5020—51no—
95#4885—52no—
96#4807—52no—
97#4804—52no—
98#4694—51no—
99C8×D12—51no—
100C2×#713—32no—
101C2×C5×Q16C2×D311yescharacteristic
102C4×C5×Q8C2×D311yescharacteristic
103C4×C5×Q8C2×D311yescharacteristic
104#4092—32no—
105C2×#688—32no—
106C2×C8×D5—32no—
107#4044—62no—
108#4041—32no—
109#4041—62no—
110#4038—32no—
111#4021—61no—
112#4020—31no—
113#4020—61no—
114C4×D20—31no—
115C4×D20—61no—
116#4015—31no—
117C4×Dic10—61no—
118C5×#107C2×D311yescharacteristic
119C5×#103C2×D311yescharacteristic
120C5×#103C2×D311yescharacteristic
121C4×C5×C8C2×D311yescharacteristic
122#3967—32no—
123#3953—32no—
124#3953—32no—
125#3952—32no—
126#3941—32no—
127#3940—32no—
128C4⋊#168—31no—
129#3304—151noSylow
130C22×D15—22no—
131C22×D15C2×D412yes—
132C3×C5×Q8—21no—
133C3×C5×Q8—21no—
134C3×C5×Q8—21no—
135C3×C5×Q8#4112yes—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2411yescharacteristic
143C2×Dic15—22no—
144C2×Dic15C2×D412yes—
145D60—22no—
146D60—22no—
147D60—22no—
148D60—44no—
149D60—42no—
150D60—81no—
151D60—82no—
152C4×D15—22no—
153C4×D15—22no—
154C4×D15—44no—
155Dic30—42no—
156C3×C5×C8—21no—
157C3×C5×C8—21no—
158C3⋊#168—22no—
159C2×#239—52no—
160C2×C3×Q16C2×D511yescharacteristic
161C3×C4×Q8C2×D511yescharacteristic
162C3×C4×Q8C2×D511yescharacteristic
163#946—52no—
164C2×#215—52no—
165C2×D3×C8—52no—
166#898—102no—
167#895—52no—
168#895—102no—
169#892—52no—
170#875—101no—
171#874—51no—
172#874—101no—
173C4×D12—51no—
174C4×D12—101no—
175#869—51no—
176C4×Dic6—101no—
177C3×#107C2×D511yescharacteristic
178C3×#103C2×D511yescharacteristic
179C3×#103C2×D511yescharacteristic
180C3×C4×C8C2×D511yescharacteristic
181#835—52no—
182#821—52no—
183#821—52no—
184(C2×D3)⋊C8—52no—
185#809—52no—
186#808—52no—
187C4⋊(C3⋊C8)—51no—
188C2×C5×Q8C22×D311yescharacteristic
189C2×C5×Q8C22×D311yescharacteristic
190#713—64no—
191#713—122no—
192C2×D20—31no—
193C2×D20—32no—
194C2×D20—62no—
195C2×D20—61no—
196C2×D20—62no—
197C2×D20—61no—
198C2×C4×D5—32no—
199C2×C4×D5—62no—
200C2×Dic10—61no—
201C5×Q16—22no—
202C2×C5×C8C22×D311yescharacteristic
203C2×C5×C8C22×D311yescharacteristic
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4C22×D311yescharacteristic
207C5×C4⋊C4C22×D311yescharacteristic
208C42×C5—21no—
209C42×C5—21no—
210C42×C5C22×D311yescharacteristic
211#688—122no—
212#685—32no—
213#685—62no—
214#685—62no—
215#685—62no—
216C4⋊Dic5—31no—
217C4⋊Dic5—32no—
218C4⋊Dic5—61no—
219#683—62no—
220C4×Dic5—62no—
221C2×#168—32no—
222C8×D5—122no—
223#556—151no—
224#550—151no—
225#486—151no—
226#482—152no—
227#475—151no—
228#465—152no—
229#460—151no—
230#452—152no—
231C4×Q16D1511yescharacteristic, complemented
232C8×D4—151no—
233#416—152no—
234C22×C3×C5C22×D411yescharacteristic
235C2×D15—22no—
236C2×D15—22no—
237C2×D15—22no—
238C2×D15—42no—
239C2×D15—42no—
240C2×D15—42no—
241C3×C4×C5—22no—
242C3×C4×C5—21no—
243C3×C4×C5—41no—
244C3×C4×C5—41no—
245C3×C4×C5—41no—
246C3×C4×C5#13512yes—
247C3×C4×C5C2×#4111yescharacteristic
248C3×C4×C5H(5,𝔽2)11yescharacteristic
249Dic15—22no—
250Dic15—42no—
251C2×C3×Q8C22×D511yescharacteristic
252C2×C3×Q8C22×D511yescharacteristic
253#239—104no—
254#239—202no—
255C2×D12—51no—
256C2×D12—52no—
257C2×D12—102no—
258C2×D12—101no—
259C2×D12—102no—
260C2×D12—101no—
261C2×C4×D3—52no—
262C2×C4×D3—102no—
263C2×Dic6—101no—
264C3×Q16—22no—
265C2×C3×C8C22×D511yescharacteristic
266C2×C3×C8C22×D511yescharacteristic
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4C22×D511yescharacteristic
270C3×C4⋊C4C22×D511yescharacteristic
271C3×C42—21no—
272C3×C42—21no—
273C3×C42C22×D511yescharacteristic
274#215—202no—
275(C2×D3)⋊C4—52no—
276(C2×D3)⋊C4—102no—
277(C2×D3)⋊C4—102no—
278(C2×D3)⋊C4—102no—
279C4⋊Dic3—51no—
280C4⋊Dic3—52no—
281C4⋊Dic3—101no—
282Dic3⋊C4—102no—
283C4×Dic3—102no—
284C2×C3⋊C8—52no—
285D3×C8—202no—
286C22×D5—32no—
287C22×D5—62no—
288C5×Q8—21no—
289C5×Q8—21no—
290C5×Q8—21no—
291C5×Q8#23512yes—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5D3×D411yescharacteristic
297C2×C4×C5D3×D411yescharacteristic
298C2×C4×C5C23×D311yescharacteristic
299C2×Dic5—32no—
300C2×Dic5—62no—
301D20—62no—
302D20—62no—
303D20—62no—
304D20—124no—
305D20—122no—
306D20—241no—
307D20—242no—
308C4×D5—62no—
309C4×D5—62no—
310C4×D5—124no—
311Dic10—122no—
312C5×C8—21no—
313C5×C8—21no—
314#168—62no—
315C2×#41—152no—
316C2×Q16C2×D1511yescharacteristic
317C2×SD16—152no—
318C22×C8—152no—
319C4⋊Q8—151no—
320#127—151no—
321#127—301no—
322#126—302no—
323#124—301no—
324C22⋊Q8—152no—
325#121—152no—
326#121—302no—
327C4×Q8—301no—
328C4×Q8C2×D1511yescharacteristic
329C4×Q8C2×D1511yescharacteristic
330C4×D4—151no—
331C4×D4—301no—
332#117—152no—
333#107C2×D1511yescharacteristic
334#106—152no—
335C4⋊C8—151no—
336#103—152no—
337#103C2×D1511yescharacteristic
338#103C2×D1511yescharacteristic
339#102—152no—
340#102—152no—
341#102—152no—
342C22⋊C8—152no—
343C4×C8C2×D1511yescharacteristic
344C2×C3×C5#54611yescharacteristic
345C2×C3×C5C2×#13511yescharacteristic
346C2×C3×C5#57711yescharacteristic
347D15—42no—
348D15—82no—
349C22×D3—52no—
350C22×D3—102no—
351C3×Q8—21no—
352C3×Q8—21no—
353C3×Q8—21no—
354C3×Q8#70912yes—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4D4×D511yescharacteristic
360C2×C3×C4D4×D511yescharacteristic
361C2×C3×C4C23×D511yescharacteristic
362C2×Dic3—52no—
363C2×Dic3—102no—
364D12—102no—
365D12—102no—
366D12—102no—
367D12—204no—
368D12—202no—
369D12—401no—
370D12—402no—
371C4×D3—102no—
372C4×D3—102no—
373C4×D3—204no—
374Dic6—202no—
375C3×C8—21no—
376C3×C8—21no—
377C3⋊C8—102no—
378C22×C5C2×D3×D411yescharacteristic
379C2×D5—62no—
380C2×D5—62no—
381C2×D5—62no—
382C2×D5—122no—
383C2×D5—122no—
384C2×D5—122no—
385C4×C5—21no—
386C4×C5—22no—
387C4×C5—41no—
388C4×C5—41no—
389C4×C5—41no—
390C4×C5#91912yes—
391C4×C5C2×#23511yescharacteristic
392C4×C5#100911yescharacteristic
393Dic5—62no—
394Dic5—122no—
395#41—304no—
396#41—602no—
397C2×Q8—301no—
398C2×Q8C22×D1511yescharacteristic
399C2×Q8C22×D1511yescharacteristic
400C2×D4—151no—
401C2×D4—152no—
402C2×D4—302no—
403C2×D4—302no—
404C2×D4—301no—
405C2×D4—301no—
406C22×C4—152no—
407C22×C4—302no—
408Q16—22no—
409SD16—602no—
410C2×C8—152no—
411C2×C8—602no—
412C2×C8C22×D1511yescharacteristic
413C2×C8C22×D1511yescharacteristic
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—151no—
417C4⋊C4—152no—
418C4⋊C4—302no—
419C4⋊C4—301no—
420C4⋊C4C22×D1511yescharacteristic
421C4⋊C4C22×D1511yescharacteristic
422C22⋊C4—152no—
423C22⋊C4—302no—
424C22⋊C4—302no—
425C22⋊C4—302no—
426C42—21no—
427C42—21no—
428C42—302no—
429C42C22×D1511yescharacteristic
430C3×C5#330411yescharacteristic, complemented, Hall
431C22×C3C2×D4×D511yescharacteristic
432C2×D3—102no—
433C2×D3—102no—
434C2×D3—102no—
435C2×D3—202no—
436C2×D3—202no—
437C2×D3—202no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—41no—
441C3×C4—41no—
442C3×C4—41no—
443C3×C4#406512yes—
444C3×C4C2×#70911yescharacteristic
445C3×C4#414911yescharacteristic
446Dic3—102no—
447Dic3—202no—
448C2×C5#555011yescharacteristic
449C2×C5C2×#91911yescharacteristic
450C2×C5#577011yescharacteristic
451D5—122no—
452D5—242no—
453C23—152no—
454C23—302no—
455Q8—21no—
456Q8—21no—
457Q8—21no—
458Q8—602no—
459Q8#681712yes—
460D4—302no—
461D4—302no—
462D4—302no—
463D4—604no—
464D4—602no—
465D4—1201no—
466D4—1202no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—152no—
472C2×C4—302no—
473C2×C4—302no—
474C2×C4—302no—
475C2×C4—604no—
476C2×C4D4×D1511yescharacteristic
477C2×C4D4×D1511yescharacteristic
478C2×C4C23×D1511yescharacteristic
479C8—21no—
480C8—21no—
481C8—302no—
482C2×C3#6588411yescharacteristic
483C2×C3C2×#406511yescharacteristic
484C2×C3#6610411yescharacteristic
485D3—202no—
486D3—402no—
487C5#7973711yescharacteristic, complemented, Sylow
488C22—302no—
489C22—302no—
490C22—302no—
491C22—602no—
492C22—602no—
493C22—602no—
494C22C2×D4×D1511yescharacteristic
495C4—22no—
496C4—21no—
497C4—41no—
498C4—41no—
499C4—41no—
500C4—302no—
501C4—602no—
502C4#9180812yes—
503C4C2×#681711yescharacteristic
504C4#9210011yescharacteristic
505C3#1061146811yescharacteristic, complemented, Sylow
506C2—602no—
507C2—1202no—
508C2#1175630911yescharacteristic
509C2C2×#9180811yescharacteristic
510C2#1175652911yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C4×C5×Q16C2
socleC22×C3×C5C22×D4
prime radical#11756336C2
hypercenterC4×Q16D15
hypocenterC3×C5#3304
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #11756343C2semidirect
3. C3×C4×C5×Q16C2semidirect
4. #11751288C2semidirect
5. #11751128C2semidirect
6. #11751121C2semidirect
7. #11750986C2semidirect
8. #11750908C2semidirect
9. #11750905C2semidirect
10. #11750795C2semidirect
11. C8×D60C2semidirect
45. C4×C5×Q16D3semidirect
91. C3×C4×Q16D5semidirect
231. C4×Q16D15semidirect
430. C3×C5#3304semidirect
487. C5#79737semidirect
505. C3#10611468semidirect

Maximal subgroups

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

subgroupindex
#117563432
#117563362
C3×C4×C5×Q162
#117512882
#117511282
#117511212
#117509862
#117509082
#117509052
#117507952
C8×D602
#106114683
#797375