Finite Group Databasebeta

← #14460101

Subgroups — #14460101

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#11756314C211yesmaximal, characteristic, complemented
3C3×C5×#476C211yesmaximal, characteristic, complemented
4#11751194C211yesmaximal, characteristic, complemented
5C4×#6715C211yesmaximal, characteristic, complemented
6#11750969C212yesmaximal, complemented
7#11750965C212yesmaximal, complemented
8#11750942C211yesmaximal, characteristic, complemented
9#11750935C211yesmaximal, characteristic, complemented
10#11750882C212yesmaximal, complemented
11#11750873C212yesmaximal, complemented
12#10612807—31nomaximal, Hall
13C2×#6819C2212yes—
14C3×C5×C4⋊Q8C2211yescharacteristic
15C3×C4×C5×D4C2211yescharacteristic
16#91836—22no—
17C2×#6715C2211yescharacteristic
18#91819—21no—
19C2×C4⋊Dic15—21no—
20C2×#6706C2212yes—
21C2×C8×D15C2212yes—
22#91786C2212yes—
23#91784—21no—
24#91784C2212yes—
25#91781—21no—
26#91781C2212yes—
27#91775—22no—
28C4×D60C2211yescharacteristic
29C4×D60C2211yescharacteristic
30#91758C2211yescharacteristic
31C3×C5×#106C2212yes—
32C3×C5×C4⋊C8C2211yescharacteristic
33C3×C5×#102C2212yes—
34#91116C2211yescharacteristic
35#91104C2212yes—
36#91100C2212yes—
37#91094C2212yes—
38#91094C2212yes—
39#91093C2211yescharacteristic
40#91091C2211yescharacteristic
41C4×C3⋊#168C2211yescharacteristic
42#81076—51nomaximal, Hall
43#66068—31no—
44#65889—31no—
45C5×#476D311yescharacteristic, complemented
46#65382—31no—
47C4×#686—31no—
48#65156—32no—
49#65153—32no—
50#65130—31no—
51#65123—31no—
52#65070—32no—
53#65061—32no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C2×#1220—22no—
58C22×Dic15—22no—
59#6819—24no—
60#6819—42no—
61C2×D60—22no—
62C2×D60D411yescharacteristic
63C2×D60C2311yescharacteristic
64C2×C4×D15—21no—
65C2×C4×D15C2312yes—
66C2×Dic30C2312yes—
67C2×C3×C5×C8C2312yes—
68C3×C5×C4⋊C4—21no—
69C3×C5×C4⋊C4C2312yes—
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C22⋊C4—21no—
72C3×C42×C5C2311yescharacteristic
73#6715—22no—
74#6714—22no—
75#6714—22no—
76#6714—21no—
77#6714—22no—
78#6714D412yes—
79C4⋊Dic15—21no—
80C4⋊Dic15—21no—
81C4⋊Dic15—22no—
82C4⋊Dic15D411yescharacteristic
83C4⋊Dic15C2311yescharacteristic
84C4×Dic15—22no—
85C2×C3⋊#168C2311yescharacteristic
86C2×C3⋊#168C2311yescharacteristic
87#6706—42no—
88C8×D15—42no—
89#5734—51no—
90#5555—51no—
91C3×#476D511yescharacteristic, complemented
92#5093—51no—
93C4×#213—51no—
94#4868—52no—
95#4864—52no—
96#4841—51no—
97#4834—51no—
98#4781—52no—
99#4772—52no—
100C2×#711—32no—
101C5×C4⋊Q8C2×D311yescharacteristic
102C4×C5×D4C2×D311yescharacteristic
103#4093—62no—
104C2×#686—31no—
105#4076—61no—
106C2×C4⋊Dic5—61no—
107C2×#677—32no—
108C2×C8×D5—32no—
109#4043—32no—
110#4041—32no—
111#4041—61no—
112#4038—32no—
113#4038—61no—
114#4032—62no—
115C4×D20—31no—
116C4×D20—31no—
117#4015—31no—
118C5×#106C2×D312yes—
119C5×C4⋊C8C2×D311yescharacteristic
120C5×#102C2×D312yes—
121#3964—31no—
122#3952—32no—
123#3948—32no—
124#3942—32no—
125#3942—32no—
126#3941—31no—
127#3939—31no—
128C4×#168—31no—
129#3303—151noSylow
130C23×C3×C5—21no—
131C22×D15—21no—
132C22×D15C2×D412yes—
133C3×C5×Q8—81no—
134C3×C5×D4—21no—
135C3×C5×D4#4112yes—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—42no—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142#1220—44no—
143C2×Dic15—21no—
144C2×Dic15—22no—
145C2×Dic15—44no—
146C2×Dic15C2×D412yes—
147D60—22no—
148D60—21no—
149D60—21no—
150D60—82no—
151C4×D15—22no—
152C4×D15—22no—
153C4×D15—42no—
154Dic30—22no—
155Dic30—22no—
156C3×C5×C8—22no—
157C3⋊#168—21no—
158C3⋊#168—21no—
159C2×#237—52no—
160C3×C4⋊Q8C2×D511yescharacteristic
161C3×C4×D4C2×D511yescharacteristic
162#947—102no—
163C2×#213—51no—
164#930—101no—
165C2×C4⋊Dic3—101no—
166C2×#204—52no—
167C2×D3×C8—52no—
168#897—52no—
169#895—52no—
170#895—101no—
171#892—52no—
172#892—101no—
173#886—102no—
174C4×D12—51no—
175C4×D12—51no—
176#869—51no—
177C3×#106C2×D512yes—
178C3×C4⋊C8C2×D511yescharacteristic
179C3×#102C2×D512yes—
180#832—51no—
181(C2×D3)⋊C8—52no—
182#816—52no—
183#810—52no—
184#810—52no—
185#809—51no—
186#807—51no—
187C4×C3⋊C8—51no—
188C2×C5×Q8—21no—
189C2×C5×D4C22×D311yescharacteristic
190C22×C4×C5—21no—
191C2×C22⋊D5—62no—
192C22×Dic5—62no—
193#711—64no—
194#711—122no—
195C2×D20—31no—
196C2×D20—31no—
197C2×D20—62no—
198C2×C4×D5—32no—
199C2×C4×D5—61no—
200C2×Dic10—32no—
201C2×C5×C8C22×D312yes—
202C5×C4⋊C4—21no—
203C5×C4⋊C4C22×D311yescharacteristic
204C5×C4⋊C4C22×D312yes—
205C5×C22⋊C4—21no—
206C42×C5C22×D311yescharacteristic
207#686—62no—
208#685—32no—
209#685—62no—
210#685—62no—
211#685—62no—
212#685—61no—
213C4⋊Dic5—31no—
214C4⋊Dic5—31no—
215C4⋊Dic5—62no—
216C4⋊Dic5—61no—
217C4⋊Dic5—61no—
218C4×Dic5—62no—
219C2×#168—31no—
220C2×#168—31no—
221#677—122no—
222C8×D5—122no—
223#555—151no—
224#547—151no—
225#487—151no—
226#485—152no—
227#476D1511yescharacteristic, complemented
228#465—152no—
229#461—151no—
230#449—152no—
231C4×D8—151no—
232C8×D4—151no—
233#416—152no—
234C22×C3×C5—22no—
235C22×C3×C5—41no—
236C22×C3×C5—41no—
237C22×C3×C5C22×D411yescharacteristic
238C2×D15—22no—
239C2×D15—22no—
240C2×D15—22no—
241C2×D15—41no—
242C2×D15—41no—
243C2×D15—41no—
244C3×C4×C5—21no—
245C3×C4×C5—41no—
246C3×C4×C5—42no—
247C3×C4×C5#13512yes—
248C3×C4×C5C2×#4111yescharacteristic
249C3×C4×C5H(5,𝔽2)11yescharacteristic
250Dic15—22no—
251Dic15—42no—
252Dic15—41no—
253C2×C3×Q8—21no—
254C2×C3×D4C22×D511yescharacteristic
255C22×C3×C4—21no—
256C2×#67—102no—
257C22×Dic3—102no—
258#237—104no—
259#237—202no—
260C2×D12—51no—
261C2×D12—51no—
262C2×D12—102no—
263C2×C4×D3—52no—
264C2×C4×D3—101no—
265C2×Dic6—52no—
266C2×C3×C8C22×D512yes—
267C3×C4⋊C4—21no—
268C3×C4⋊C4C22×D511yescharacteristic
269C3×C4⋊C4C22×D512yes—
270C3×C22⋊C4—21no—
271C3×C42C22×D511yescharacteristic
272#213—102no—
273(C2×D3)⋊C4—52no—
274(C2×D3)⋊C4—102no—
275(C2×D3)⋊C4—102no—
276(C2×D3)⋊C4—102no—
277(C2×D3)⋊C4—101no—
278C4⋊Dic3—51no—
279C4⋊Dic3—51no—
280C4⋊Dic3—102no—
281C4⋊Dic3—101no—
282C4⋊Dic3—101no—
283C4×Dic3—102no—
284C2×C3⋊C8—51no—
285C2×C3⋊C8—51no—
286#204—202no—
287D3×C8—202no—
288C23×C5—21no—
289C22×D5—32no—
290C22×D5—61no—
291C5×Q8—81no—
292C5×D4—21no—
293C5×D4#23912yes—
294C2×C4×C5—22no—
295C2×C4×C5—21no—
296C2×C4×C5—42no—
297C2×C4×C5D3×D411yescharacteristic
298C2×C4×C5D3×D411yescharacteristic
299C2×C4×C5C23×D311yescharacteristic
300C22⋊D5—124no—
301C2×Dic5—32no—
302C2×Dic5—61no—
303C2×Dic5—62no—
304C2×Dic5—124no—
305D20—62no—
306D20—61no—
307D20—61no—
308D20—242no—
309C4×D5—62no—
310C4×D5—62no—
311C4×D5—122no—
312Dic10—62no—
313Dic10—62no—
314C5×C8—22no—
315#168—61no—
316#168—61no—
317C2×#41—152no—
318C2×SD16—152no—
319C2×D8—151no—
320C22×C8—152no—
321C4⋊Q8—151no—
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×D4C2×D1511yescharacteristic
332#117—152no—
333#117—301no—
334C2×C4⋊C4—301no—
335#107—151no—
336#106C2×D1512yes—
337C4⋊C8C2×D1511yescharacteristic
338#103—152no—
339#103—152no—
340#103—152no—
341#102—151no—
342#102—151no—
343#102C2×D1512yes—
344C22⋊C8—152no—
345C4×C8—151no—
346C2×C3×C5—42no—
347C2×C3×C5#54611yescharacteristic
348C2×C3×C5C2×#13511yescharacteristic
349C2×C3×C5#57711yescharacteristic
350D15—42no—
351D15—81no—
352C23×C3—21no—
353C22×D3—52no—
354C22×D3—101no—
355C3×Q8—81no—
356C3×D4—21no—
357C3×D4#71312yes—
358C2×C3×C4—22no—
359C2×C3×C4—21no—
360C2×C3×C4—42no—
361C2×C3×C4D4×D511yescharacteristic
362C2×C3×C4D4×D511yescharacteristic
363C2×C3×C4C23×D511yescharacteristic
364#67—204no—
365C2×Dic3—52no—
366C2×Dic3—101no—
367C2×Dic3—102no—
368C2×Dic3—204no—
369D12—101no—
370D12—101no—
371D12—102no—
372D12—402no—
373C4×D3—102no—
374C4×D3—102no—
375C4×D3—202no—
376Dic6—102no—
377Dic6—102no—
378C3×C8—22no—
379C3⋊C8—101no—
380C3⋊C8—101no—
381C22×C5—22no—
382C22×C5—41no—
383C22×C5—41no—
384C22×C5C2×D3×D411yescharacteristic
385C2×D5—62no—
386C2×D5—62no—
387C2×D5—62no—
388C2×D5—121no—
389C2×D5—121no—
390C2×D5—121no—
391C4×C5—21no—
392C4×C5—41no—
393C4×C5—42no—
394C4×C5#91612yes—
395C4×C5C2×#23911yescharacteristic
396C4×C5#100911yescharacteristic
397Dic5—62no—
398Dic5—121no—
399Dic5—122no—
400#41—304no—
401#41—602no—
402C2×Q8—21no—
403C2×Q8—152no—
404C2×D4—151no—
405C2×D4—151no—
406C2×D4—302no—
407C2×D4—302no—
408C2×D4C22×D1511yescharacteristic
409C22×C4—21no—
410C22×C4—152no—
411C22×C4—302no—
412C22×C4—301no—
413SD16—602no—
414D8—302no—
415C2×C8—151no—
416C2×C8—151no—
417C2×C8—602no—
418C2×C8C22×D1512yes—
419C4⋊C4—21no—
420C4⋊C4—151no—
421C4⋊C4—151no—
422C4⋊C4—302no—
423C4⋊C4—301no—
424C4⋊C4—301no—
425C4⋊C4C22×D1511yescharacteristic
426C4⋊C4C22×D1512yes—
427C22⋊C4—21no—
428C22⋊C4—152no—
429C22⋊C4—302no—
430C22⋊C4—302no—
431C22⋊C4—302no—
432C22⋊C4—301no—
433C42—302no—
434C42C22×D1511yescharacteristic
435C3×C5#330311yescharacteristic, complemented, Hall
436C22×C3—22no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3C2×D4×D511yescharacteristic
440C2×D3—102no—
441C2×D3—102no—
442C2×D3—102no—
443C2×D3—201no—
444C2×D3—201no—
445C2×D3—201no—
446C3×C4—21no—
447C3×C4—41no—
448C3×C4—42no—
449C3×C4#406212yes—
450C3×C4C2×#71311yescharacteristic
451C3×C4#414911yescharacteristic
452Dic3—102no—
453Dic3—201no—
454Dic3—202no—
455C2×C5—42no—
456C2×C5#563011yescharacteristic
457C2×C5C2×#91611yescharacteristic
458C2×C5#577511yescharacteristic
459D5—122no—
460D5—241no—
461C23—21no—
462C23—152no—
463C23—301no—
464Q8—81no—
465Q8—302no—
466Q8—302no—
467D4—21no—
468D4—302no—
469D4—301no—
470D4—301no—
471D4—604no—
472D4—1202no—
473D4#682112yes—
474C2×C4—22no—
475C2×C4—21no—
476C2×C4—42no—
477C2×C4—152no—
478C2×C4—302no—
479C2×C4—302no—
480C2×C4—301no—
481C2×C4—302no—
482C2×C4—604no—
483C2×C4—602no—
484C2×C4D4×D1511yescharacteristic
485C2×C4D4×D1511yescharacteristic
486C2×C4C23×D1511yescharacteristic
487C8—22no—
488C8—301no—
489C8—301no—
490C2×C3—42no—
491C2×C3#6596411yescharacteristic
492C2×C3C2×#406211yescharacteristic
493C2×C3#6610911yescharacteristic
494D3—202no—
495D3—401no—
496C5#8107611yescharacteristic, complemented, Sylow
497C22—22no—
498C22—41no—
499C22—41no—
500C22—302no—
501C22—302no—
502C22—302no—
503C22—601no—
504C22—601no—
505C22—601no—
506C22C2×D4×D1511yescharacteristic
507C4—21no—
508C4—41no—
509C4—42no—
510C4—302no—
511C4—602no—
512C4—601no—
513C4#9180512yes—
514C4C2×#682111yescharacteristic
515C4#9210011yescharacteristic
516C3#1061280711yescharacteristic, complemented, Sylow
517C2—42no—
518C2—602no—
519C2—1201no—
520C2#1175638911yescharacteristic
521C2C2×#9180511yescharacteristic
522C2#1175653411yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#476C2
socleC22×C3×C5C22×D4
hypercenter#476D15
hypocenterC3×C5#3303
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #11756493C2semidirect
2. #11756314C2semidirect
3. C3×C5×#476C2semidirect
4. #11751194C2semidirect
5. C4×#6715C2semidirect
6. #11750969C2semidirect
7. #11750965C2semidirect
8. #11750942C2semidirect
9. #11750935C2semidirect
10. #11750882C2semidirect
11. #11750873C2semidirect
45. C5×#476D3semidirect
91. C3×#476D5semidirect
227. #476D15semidirect
435. C3×C5#3303semidirect
496. C5#81076semidirect
516. C3#10612807semidirect

Maximal subgroups

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

subgroupindex
#117564932
#117563142
C3×C5×#4762
#117511942
C4×#67152
#117509692
#117509652
#117509422
#117509352
#117508822
#117508732
#106128073
#810765