Finite Group Databasebeta

← #14460107

Subgroups — #14460107

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756493C211yesmaximal, characteristic, complemented
2#11756485C211yesmaximal, characteristic, complemented
3C3×C5×#487C211yesmaximal, characteristic, complemented
4#11751185C211yesmaximal, characteristic, complemented
5#11751184C211yesmaximal, characteristic, complemented
6#11750915C212yesmaximal, complemented
7#11750911C212yesmaximal, complemented
8#11750908C212yesmaximal, complemented
9#11750905C212yesmaximal, complemented
10C4×D120C211yesmaximal, characteristic, complemented
11C8×D60C211yesmaximal, characteristic, complemented
12#10613346—31nomaximal, Hall
13C2×#6821C2212yes—
14C3×C5×C4⋊Q8C2211yescharacteristic
15C3×C5×C4⋊Q8C2211yescharacteristic
16#91836—22no—
17#91835C2212yes—
18C2×#6717C2212yes—
19C2×D120C2211yescharacteristic
20C2×C8×D15C2212yes—
21#91784—21no—
22#91784—21no—
23#91784C2212yes—
24#91783—22no—
25#91781—21no—
26#91781C2212yes—
27C4⋊C4×D15—21no—
28C4×D60C2211yescharacteristic
29C4×D60C2211yescharacteristic
30C4×D60C2211yescharacteristic
31C3×C5×#103C2212yes—
32C3×C5×#103C2212yes—
33C3×C4×C5×C8C2211yescharacteristic
34#91119C2212yes—
35#91105C2211yescharacteristic
36#91105C2211yescharacteristic
37#91104C2212yes—
38#91102C2211yescharacteristic
39#91093C2212yes—
40#91092C2212yes—
41C4⋊(C3⋊#168)C2211yescharacteristic
42#81615—51nomaximal, Hall
43#66068—31no—
44#66060—31no—
45C5×#487D311yescharacteristic, complemented
46#65373—31no—
47#65372—31no—
48#65103—32no—
49#65100—32no—
50#65096—32no—
51#65093—32no—
52C4×D40—31no—
53C8×D20—31no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×Q8C2312yes—
56#6821—24no—
57#6821—42no—
58C2×D60—22no—
59C2×D60—22no—
60C2×D60D411yescharacteristic
61C2×D60C2311yescharacteristic
62C2×D60C2311yescharacteristic
63C2×C4×D15—21no—
64C2×C4×D15—21no—
65C2×C4×D15—22no—
66C2×C4×D15C2312yes—
67C2×C3×C5×C8C2311yescharacteristic
68C2×C3×C5×C8C2311yescharacteristic
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4—21no—
72C3×C5×C4⋊C4C2312yes—
73C3×C42×C5C2311yescharacteristic
74#6717—42no—
75#6714—22no—
76#6714—22no—
77#6714—21no—
78#6714—21no—
79#6714—22no—
80#6714D412yes—
81C4⋊Dic15D411yescharacteristic
82C4⋊Dic15C2311yescharacteristic
83C4⋊Dic15C2311yescharacteristic
84#6712—22no—
85C4×Dic15—22no—
86C2×C3⋊#168C2312yes—
87D120—22no—
88C8×D15—42no—
89#5734—51no—
90#5726—51no—
91C3×#487D511yescharacteristic, complemented
92#5084—51no—
93#5083—51no—
94#4814—52no—
95#4810—52no—
96#4807—52no—
97#4804—52no—
98C4×D24—51no—
99C8×D12—51no—
100C2×#713—32no—
101C5×C4⋊Q8C2×D311yescharacteristic
102C5×C4⋊Q8C2×D311yescharacteristic
103#4093—62no—
104#4092—32no—
105C2×#688—32no—
106C2×D40—31no—
107C2×C8×D5—32no—
108#4041—32no—
109#4041—61no—
110#4041—61no—
111#4040—62no—
112#4038—32no—
113#4038—61no—
114D5×C4⋊C4—61no—
115C4×D20—31no—
116C4×D20—31no—
117C4×D20—31no—
118C5×#103C2×D312yes—
119C5×#103C2×D312yes—
120C4×C5×C8C2×D311yescharacteristic
121#3967—32no—
122#3953—31no—
123#3953—31no—
124#3952—32no—
125#3950—31no—
126#3941—32no—
127#3940—32no—
128C4⋊#168—31no—
129#3303—151noSylow
130C22×D15—21no—
131C22×D15—21no—
132C22×D15C2×D412yes—
133C3×C5×Q8—22no—
134C3×C5×Q8—22no—
135C3×C5×Q8—81no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2411yescharacteristic
141C2×Dic15—21no—
142C2×Dic15—21no—
143C2×Dic15C2×D412yes—
144D60—22no—
145D60—21no—
146D60—21no—
147D60—21no—
148D60—44no—
149D60—82no—
150D60#4112yes—
151C4×D15—22no—
152C4×D15—22no—
153C4×D15—44no—
154C4×D15—42no—
155C4×D15—42no—
156C3×C5×C8—21no—
157C3×C5×C8—21no—
158C3⋊#168—22no—
159C2×#239—52no—
160C3×C4⋊Q8C2×D511yescharacteristic
161C3×C4⋊Q8C2×D511yescharacteristic
162#947—102no—
163#946—52no—
164C2×#215—52no—
165C2×D24—51no—
166C2×D3×C8—52no—
167#895—52no—
168#895—101no—
169#895—101no—
170#894—102no—
171#892—52no—
172#892—101no—
173D3×C4⋊C4—101no—
174C4×D12—51no—
175C4×D12—51no—
176C4×D12—51no—
177C3×#103C2×D512yes—
178C3×#103C2×D512yes—
179C3×C4×C8C2×D511yescharacteristic
180#835—52no—
181#821—51no—
182#821—51no—
183(C2×D3)⋊C8—52no—
184#818—51no—
185#809—52no—
186#808—52no—
187C4⋊(C3⋊C8)—51no—
188C2×C5×Q8—21no—
189C2×C5×Q8C22×D312yes—
190#713—64no—
191#713—122no—
192C2×D20—31no—
193C2×D20—31no—
194C2×D20—31no—
195C2×D20—62no—
196C2×D20—62no—
197C2×C4×D5—32no—
198C2×C4×D5—62no—
199C2×C4×D5—61no—
200C2×C4×D5—61no—
201C2×C5×C8C22×D311yescharacteristic
202C2×C5×C8C22×D311yescharacteristic
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4C22×D312yes—
207C42×C5C22×D311yescharacteristic
208#688—122no—
209#685—32no—
210#685—62no—
211#685—62no—
212#685—62no—
213#685—61no—
214#685—61no—
215C4⋊Dic5—31no—
216C4⋊Dic5—31no—
217C4⋊Dic5—31no—
218#683—62no—
219C4×Dic5—62no—
220C2×#168—32no—
221D40—62no—
222C8×D5—122no—
223#555—151no—
224#547—151no—
225#487D1511yescharacteristic, complemented
226#485—152no—
227#476—151no—
228#465—152no—
229#461—151no—
230#449—152no—
231C4×D8—151no—
232C8×D4—151no—
233#416—152no—
234C22×C3×C5C22×D411yescharacteristic
235C2×D15—22no—
236C2×D15—22no—
237C2×D15—22no—
238C2×D15—22no—
239C2×D15—41no—
240C2×D15—41no—
241C2×D15—41no—
242C2×D15—41no—
243C2×D15—41no—
244C3×C4×C5—21no—
245C3×C4×C5—42no—
246C3×C4×C5—42no—
247C3×C4×C5#13512yes—
248C3×C4×C5C2×#4111yescharacteristic
249C3×C4×C5H(5,𝔽2)11yescharacteristic
250Dic15—22no—
251Dic15—41no—
252Dic15—41no—
253C2×C3×Q8—21no—
254C2×C3×Q8C22×D512yes—
255#239—104no—
256#239—202no—
257C2×D12—51no—
258C2×D12—51no—
259C2×D12—51no—
260C2×D12—102no—
261C2×D12—102no—
262C2×C4×D3—52no—
263C2×C4×D3—102no—
264C2×C4×D3—101no—
265C2×C4×D3—101no—
266C2×C3×C8C22×D511yescharacteristic
267C2×C3×C8C22×D511yescharacteristic
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4C22×D512yes—
272C3×C42C22×D511yescharacteristic
273#215—202no—
274(C2×D3)⋊C4—52no—
275(C2×D3)⋊C4—102no—
276(C2×D3)⋊C4—102no—
277(C2×D3)⋊C4—102no—
278(C2×D3)⋊C4—101no—
279(C2×D3)⋊C4—101no—
280C4⋊Dic3—51no—
281C4⋊Dic3—51no—
282C4⋊Dic3—51no—
283Dic3⋊C4—102no—
284C4×Dic3—102no—
285C2×C3⋊C8—52no—
286D24—102no—
287D3×C8—202no—
288C22×D5—32no—
289C22×D5—61no—
290C22×D5—61no—
291C5×Q8—22no—
292C5×Q8—22no—
293C5×Q8—81no—
294C2×C4×C5—22no—
295C2×C4×C5—22no—
296C2×C4×C5D3×D411yescharacteristic
297C2×C4×C5D3×D411yescharacteristic
298C2×C4×C5C23×D311yescharacteristic
299C2×Dic5—32no—
300C2×Dic5—61no—
301C2×Dic5—61no—
302D20—32no—
303D20—62no—
304D20—61no—
305D20—61no—
306D20—61no—
307D20—124no—
308D20—242no—
309C4×D5—62no—
310C4×D5—62no—
311C4×D5—124no—
312C4×D5—122no—
313C4×D5—122no—
314C5×C8—21no—
315C5×C8—21no—
316#168—62no—
317C2×#41—152no—
318C2×SD16—152no—
319C2×D8—151no—
320C22×C8—152no—
321C4⋊Q8C2×D1511yescharacteristic
322C4⋊Q8C2×D1511yescharacteristic
323#124—302no—
324#123—302no—
325C22⋊Q8—152no—
326#121—152no—
327#121—301no—
328#121—301no—
329C4×D4—151no—
330C4×D4—151no—
331C4×D4—151no—
332#117—152no—
333#117—301no—
334C2×C4⋊C4—301no—
335#107—151no—
336#106—152no—
337C4⋊C8—151no—
338#103—152no—
339#103C2×D1512yes—
340#103C2×D1512yes—
341#102—151no—
342#102—151no—
343#102—152no—
344C22⋊C8—152no—
345C4×C8C2×D1511yescharacteristic
346C2×C3×C5#54611yescharacteristic
347C2×C3×C5C2×#13511yescharacteristic
348C2×C3×C5#57711yescharacteristic
349D15—42no—
350D15—42no—
351D15—81no—
352C22×D3—52no—
353C22×D3—101no—
354C22×D3—101no—
355C3×Q8—22no—
356C3×Q8—22no—
357C3×Q8—81no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4D4×D511yescharacteristic
361C2×C3×C4D4×D511yescharacteristic
362C2×C3×C4C23×D511yescharacteristic
363C2×Dic3—52no—
364C2×Dic3—101no—
365C2×Dic3—101no—
366D12—52no—
367D12—101no—
368D12—101no—
369D12—101no—
370D12—102no—
371D12—204no—
372D12—402no—
373C4×D3—102no—
374C4×D3—102no—
375C4×D3—204no—
376C4×D3—202no—
377C4×D3—202no—
378C3×C8—21no—
379C3×C8—21no—
380C3⋊C8—102no—
381C22×C5C2×D3×D411yescharacteristic
382C2×D5—62no—
383C2×D5—62no—
384C2×D5—62no—
385C2×D5—62no—
386C2×D5—121no—
387C2×D5—121no—
388C2×D5—121no—
389C2×D5—121no—
390C2×D5—121no—
391C4×C5—21no—
392C4×C5—42no—
393C4×C5—42no—
394C4×C5#91912yes—
395C4×C5D3×#4111yescharacteristic
396C4×C5#100911yescharacteristic
397Dic5—62no—
398Dic5—121no—
399Dic5—121no—
400#41—304no—
401#41—602no—
402C2×Q8—21no—
403C2×Q8C22×D1512yes—
404C2×D4—151no—
405C2×D4—151no—
406C2×D4—151no—
407C2×D4—302no—
408C2×D4—302no—
409C22×C4—152no—
410C22×C4—302no—
411C22×C4—301no—
412C22×C4—301no—
413SD16—602no—
414D8—302no—
415C2×C8—152no—
416C2×C8—602no—
417C2×C8C22×D1511yescharacteristic
418C2×C8C22×D1511yescharacteristic
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—151no—
423C4⋊C4—151no—
424C4⋊C4—151no—
425C4⋊C4—302no—
426C4⋊C4C22×D1512yes—
427C22⋊C4—152no—
428C22⋊C4—302no—
429C22⋊C4—302no—
430C22⋊C4—302no—
431C22⋊C4—301no—
432C22⋊C4—301no—
433C42—302no—
434C42C22×D1511yescharacteristic
435C3×C5#330311yescharacteristic, complemented, Hall
436C22×C3C2×D4×D511yescharacteristic
437C2×D3—102no—
438C2×D3—102no—
439C2×D3—102no—
440C2×D3—102no—
441C2×D3—201no—
442C2×D3—201no—
443C2×D3—201no—
444C2×D3—201no—
445C2×D3—201no—
446C3×C4—21no—
447C3×C4—42no—
448C3×C4—42no—
449C3×C4#406512yes—
450C3×C4D5×#4111yescharacteristic
451C3×C4#414911yescharacteristic
452Dic3—102no—
453Dic3—201no—
454Dic3—201no—
455C2×C5#567611yescharacteristic
456C2×C5#576211yescharacteristic
457C2×C5C2×#91911yescharacteristic
458D5—122no—
459D5—122no—
460D5—241no—
461C23—152no—
462C23—301no—
463C23—301no—
464Q8—22no—
465Q8—22no—
466Q8—81no—
467D4—152no—
468D4—302no—
469D4—301no—
470D4—301no—
471D4—301no—
472D4—604no—
473D4—1202no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—152no—
477C2×C4—302no—
478C2×C4—302no—
479C2×C4—301no—
480C2×C4—301no—
481C2×C4—604no—
482C2×C4—602no—
483C2×C4—602no—
484C2×C4D4×D1511yescharacteristic
485C2×C4D4×D1511yescharacteristic
486C2×C4C23×D1511yescharacteristic
487C8—21no—
488C8—21no—
489C8—302no—
490C2×C3#6601011yescharacteristic
491C2×C3#6609611yescharacteristic
492C2×C3C2×#406511yescharacteristic
493D3—202no—
494D3—202no—
495D3—401no—
496C5#8161511yescharacteristic, complemented, Sylow
497C22—302no—
498C22—302no—
499C22—302no—
500C22—302no—
501C22—601no—
502C22—601no—
503C22—601no—
504C22—601no—
505C22—601no—
506C22C2×D4×D1511yescharacteristic
507C4—21no—
508C4—42no—
509C4—42no—
510C4—302no—
511C4—601no—
512C4—601no—
513C4#9180812yes—
514C4#41×D1511yescharacteristic
515C4#9210011yescharacteristic
516C3#1061334611yescharacteristic, complemented, Sylow
517C2—602no—
518C2—602no—
519C2—1201no—
520C2#1175643511yescharacteristic
521C2#1175652111yescharacteristic
522C2C2×#9180811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#487C2
socleC22×C3×C5C22×D4
hypercenter#487D15
hypocenterC3×C5#3303
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #11756493C2semidirect
2. #11756485C2semidirect
3. C3×C5×#487C2semidirect
4. #11751185C2semidirect
5. #11751184C2semidirect
6. #11750915C2semidirect
7. #11750911C2semidirect
8. #11750908C2semidirect
9. #11750905C2semidirect
10. C4×D120C2semidirect
11. C8×D60C2semidirect
45. C5×#487D3semidirect
91. C3×#487D5semidirect
225. #487D15semidirect
435. C3×C5#3303semidirect
496. C5#81615semidirect
516. C3#10613346semidirect

Maximal subgroups

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

subgroupindex
#117564932
#117564852
C3×C5×#4872
#117511852
#117511842
#117509152
#117509112
#117509082
#117509052
C4×D1202
C8×D602
#106133463
#816155