Finite Group Databasebeta

← #14326790

Subgroups — #14326790

Order 1920.

1008 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91781C211yesmaximal, characteristic
2C3×C5×#389C211yesmaximal, characteristic, complemented
3#11751091C212yesmaximal
4#11751088C211yesmaximal, characteristic
5#11751085C211yesmaximal, characteristic, complemented
6#11751078C212yesmaximal, complemented
7C4⋊C4×Dic15C211yesmaximal, characteristic, complemented
8C4×#6714C211yesmaximal, characteristic
9C4×C4⋊Dic15C211yesmaximal, characteristic, complemented
10#11750771C212yesmaximal
11#11750749C212yesmaximal, complemented
12#10607710—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2212yes—
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C3×C42×C5C2211yescharacteristic
18C2×#6714C2211yescharacteristic
19C2×#6714C2211yescharacteristic
20C2×#6714C2212yes—
21C2×#6714C2212yes—
22C2×C4⋊Dic15C2211yescharacteristic
23C2×C4⋊Dic15C2212yes—
24C2×C4⋊Dic15C2211yescharacteristic
25C2×C4×Dic15C2212yes—
26C2×C4×Dic15C2212yes—
27C2×C4×Dic15C2211yescharacteristic
28C2×C4×Dic15C2212yes—
29#91781C418yescomplemented
30C3×C5×#95C2212yes—
31#91115C2211yescharacteristic
32#91115C2212yes—
33#91115C2212yes—
34#91115C2212yes—
35#91115C2212yes—
36#91115C2211yescharacteristic
37#75979—51nomaximal, Hall
38C2×#4038—31no—
39C5×#389D311yescharacteristic, complemented
40#65279—32no—
41#65276—31no—
42#65274—31no—
43#65266—32no—
44C4⋊C4×Dic5—31no—
45C4×#685—31no—
46C4×C4⋊Dic5—31no—
47#64959—32no—
48#64937—32no—
49C23×D15C2311yescharacteristic
50C22×C3×C4×C5C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2311yescharacteristic
57C22×Dic15C2312yes—
58C22×Dic15C2311yescharacteristic
59C22×Dic15C2311yescharacteristic
60C2×C4×D15—22no—
61C2×C4×D15—22no—
62C2×C4×D15C2×C414yes—
63C3×C5×C4⋊C4—22no—
64C3×C5×C4⋊C4—42no—
65C3×C5×C4⋊C4C2×C414yes—
66C3×C42×C5—22no—
67#6714—22no—
68#6714—22no—
69#6714—42no—
70#6714C2×C418yes—
71C4⋊Dic15—22no—
72C4⋊Dic15—42no—
73C4⋊Dic15C2×C414yes—
74C4×Dic15—24no—
75C4×Dic15—22no—
76C4×Dic15—24no—
77C4×Dic15C2×C418yes—
78C2×#892—51no—
79C3×#389D511yescharacteristic, complemented
80#4990—52no—
81#4987—51no—
82#4984—51no—
83#4977—52no—
84Dic3×C4⋊C4—51no—
85C4×(C2×D3)⋊C4—51no—
86C4×C4⋊Dic3—51no—
87#4670—52no—
88#4648—52no—
89C22×C4×D5—31no—
90C2×C5×C4⋊C4C2×D311yescharacteristic
91C2×C5×C4⋊C4C2×D312yes—
92C2×C5×C4⋊C4C2×D311yescharacteristic
93C2×C42×C5C2×D311yescharacteristic
94C2×#685—32no—
95C2×#685—31no—
96C2×#685—31no—
97C2×#685—32no—
98C2×C4⋊Dic5—31no—
99C2×C4⋊Dic5—31no—
100C2×C4⋊Dic5—32no—
101C2×C4×Dic5—32no—
102C2×C4×Dic5—32no—
103C2×C4×Dic5—32no—
104C2×C4×Dic5—31no—
105#4038—38no—
106C5×#95C2×D312yes—
107#3963—31no—
108#3963—32no—
109#3963—32no—
110#3963—32no—
111#3963—32no—
112#3963—31no—
113#2346—151noSylow
114C23×C3×C5C2411yescharacteristic
115C22×D15—21no—
116C22×D15—21no—
117C22×D15—21no—
118C22×D15—21no—
119C22×D15—21no—
120C22×D15—21no—
121C22×D15C22×C412yes—
122C2×C3×C4×C5—21no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—21no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—21no—
128C2×C3×C4×C5—21no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5C22×C414yes—
133C2×C3×C4×C5C22×C412yes—
134C2×C3×C4×C5#4112yes—
135C2×C3×C4×C5#4112yes—
136C2×C3×C4×C5#4112yes—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15—21no—
140C2×Dic15—21no—
141C2×Dic15—21no—
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—21no—
147C2×Dic15—21no—
148C2×Dic15—22no—
149C2×Dic15C22×C412yes—
150C2×Dic15C22×C414yes—
151C2×Dic15#4112yes—
152C4×D15—28no—
153C22×C4×D3—51no—
154C2×C3×C4⋊C4C2×D511yescharacteristic
155C2×C3×C4⋊C4C2×D512yes—
156C2×C3×C4⋊C4C2×D511yescharacteristic
157C2×C3×C42C2×D511yescharacteristic
158C2×(C2×D3)⋊C4—52no—
159C2×(C2×D3)⋊C4—51no—
160C2×(C2×D3)⋊C4—51no—
161C2×(C2×D3)⋊C4—52no—
162C2×C4⋊Dic3—51no—
163C2×C4⋊Dic3—51no—
164C2×C4⋊Dic3—52no—
165C2×C4×Dic3—52no—
166C2×C4×Dic3—52no—
167C2×C4×Dic3—52no—
168C2×C4×Dic3—51no—
169#892—58no—
170C3×#95C2×D512yes—
171C3⋊#95—51no—
172C3⋊#95—52no—
173C3⋊#95—52no—
174C3⋊#95—52no—
175C3⋊#95—52no—
176C3⋊#95—51no—
177C23×D5—31no—
178C22×C4×C5C22×D311yescharacteristic
179C22×C4×C5C22×D312yes—
180C22×C4×C5C22×D312yes—
181C22×C4×C5C22×D311yescharacteristic
182C22×C4×C5C22×D311yescharacteristic
183C22×Dic5—31no—
184C22×Dic5—31no—
185C22×Dic5—32no—
186C22×Dic5—31no—
187C22×Dic5—32no—
188C2×C4×D5—34no—
189C2×C4×D5—62no—
190C2×C4×D5—62no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—42no—
193C5×C4⋊C4C4×D314yes—
194C42×C5—22no—
195#685—38no—
196#685—62no—
197#685—62no—
198#685—122no—
199C4⋊Dic5—34no—
200C4⋊Dic5—62no—
201C4⋊Dic5—122no—
202C4×Dic5—38no—
203C4×Dic5—64no—
204C4×Dic5—64no—
205C4×Dic5—62no—
206C2×#117—151no—
207#389—151no—
208#389D1511yescharacteristic, complemented
209#388—152no—
210#388—152no—
211#382—152no—
212#380—151no—
213C4×C4⋊C4—151no—
214C4×C4⋊C4—151no—
215C4×C22⋊C4—151no—
216#376—152no—
217C22×C3×C5C23×C411yescharacteristic
218C22×C3×C5C2×#4111yescharacteristic
219C22×C3×C5C2×#4111yescharacteristic
220C22×C3×C5C2×#4111yescharacteristic
221C22×C3×C5C2×#4111yescharacteristic
222C22×C3×C5H(5,𝔽2)11yescharacteristic
223C22×C3×C52−1+411yescharacteristic
224C2×D15—22no—
225C2×D15—22no—
226C2×D15—22no—
227C2×D15—41no—
228C2×D15—41no—
229C2×D15—41no—
230C2×D15—41no—
231C3×C4×C5—24no—
232C3×C4×C5—22no—
233C3×C4×C5—42no—
234C3×C4×C5—41no—
235C3×C4×C5#11714yes—
236Dic15—22no—
237Dic15—24no—
238Dic15—22no—
239Dic15—42no—
240Dic15—41no—
241C23×D3—51no—
242C22×C3×C4C22×D511yescharacteristic
243C22×C3×C4C22×D512yes—
244C22×C3×C4C22×D512yes—
245C22×C3×C4C22×D511yescharacteristic
246C22×C3×C4C22×D511yescharacteristic
247C22×Dic3—51no—
248C22×Dic3—51no—
249C22×Dic3—52no—
250C22×Dic3—51no—
251C22×Dic3—52no—
252C2×C4×D3—54no—
253C2×C4×D3—102no—
254C2×C4×D3—102no—
255C3×C4⋊C4—22no—
256C3×C4⋊C4—42no—
257C3×C4⋊C4C4×D514yes—
258C3×C42—22no—
259(C2×D3)⋊C4—58no—
260(C2×D3)⋊C4—102no—
261(C2×D3)⋊C4—102no—
262(C2×D3)⋊C4—202no—
263C4⋊Dic3—54no—
264C4⋊Dic3—102no—
265C4⋊Dic3—202no—
266C4×Dic3—58no—
267C4×Dic3—104no—
268C4×Dic3—104no—
269C4×Dic3—102no—
270C23×C5C23×D311yescharacteristic
271C22×D5—32no—
272C22×D5—61no—
273C22×D5—61no—
274C22×D5—61no—
275C22×D5—61no—
276C22×D5—61no—
277C22×D5—61no—
278C2×C4×C5—21no—
279C2×C4×C5—22no—
280C2×C4×C5—21no—
281C2×C4×C5—22no—
282C2×C4×C5—21no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—21no—
286C2×C4×C5—22no—
287C2×C4×C5—21no—
288C2×C4×C5C2×C4×D314yes—
289C2×C4×C5C2×C4×D312yes—
290C2×C4×C5#23712yes—
291C2×C4×C5#23912yes—
292C2×C4×C5#23912yes—
293C2×Dic5—32no—
294C2×Dic5—34no—
295C2×Dic5—32no—
296C2×Dic5—61no—
297C2×Dic5—61no—
298C2×Dic5—62no—
299C2×Dic5—61no—
300C2×Dic5—62no—
301C2×Dic5—61no—
302C2×Dic5—61no—
303C2×Dic5—62no—
304C2×Dic5—62no—
305C2×Dic5—61no—
306C2×Dic5—62no—
307C2×Dic5—61no—
308C4×D5—68no—
309C23×C4—151no—
310#117—158no—
311C2×C4⋊C4—151no—
312C2×C4⋊C4—151no—
313C2×C4⋊C4—152no—
314C2×C4⋊C4C2×D1511yescharacteristic
315C2×C4⋊C4C2×D1512yes—
316C2×C4⋊C4C2×D1511yescharacteristic
317C2×C22⋊C4—152no—
318C2×C22⋊C4—151no—
319C2×C22⋊C4—151no—
320C2×C22⋊C4—152no—
321C2×C42—152no—
322C2×C42—152no—
323C2×C42—152no—
324C2×C42—151no—
325C2×C42C2×D1511yescharacteristic
326#95—151no—
327#95—152no—
328#95—152no—
329#95—151no—
330#95—152no—
331#95—152no—
332#95C2×D1512yes—
333C2×C3×C5C2×#11711yescharacteristic
334C2×C3×C5C4×#4111yescharacteristic
335C2×C3×C5#52011yescharacteristic
336C2×C3×C5#55211yescharacteristic
337C2×C3×C5#55211yescharacteristic
338C2×C3×C5#55511yescharacteristic
339C2×C3×C5#55511yescharacteristic
340D15—42no—
341C23×C3C23×D511yescharacteristic
342C22×D3—52no—
343C22×D3—101no—
344C22×D3—101no—
345C22×D3—101no—
346C22×D3—101no—
347C22×D3—101no—
348C22×D3—101no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—21no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4C2×C4×D514yes—
360C2×C3×C4C2×C4×D512yes—
361C2×C3×C4#71112yes—
362C2×C3×C4#71312yes—
363C2×C3×C4#71312yes—
364C2×Dic3—52no—
365C2×Dic3—54no—
366C2×Dic3—52no—
367C2×Dic3—101no—
368C2×Dic3—102no—
369C2×Dic3—101no—
370C2×Dic3—101no—
371C2×Dic3—102no—
372C2×Dic3—101no—
373C2×Dic3—101no—
374C2×Dic3—102no—
375C2×Dic3—101no—
376C2×Dic3—102no—
377C2×Dic3—102no—
378C2×Dic3—101no—
379C4×D3—108no—
380C22×C5C22×C4×D311yescharacteristic
381C22×C5C2×#23711yescharacteristic
382C22×C5#100411yescharacteristic
383C22×C5C2×#23911yescharacteristic
384C22×C5C2×#23911yescharacteristic
385C22×C5D3×#4111yescharacteristic
386C22×C5#101011yescharacteristic
387C2×D5—62no—
388C2×D5—62no—
389C2×D5—62no—
390C2×D5—121no—
391C2×D5—121no—
392C2×D5—121no—
393C2×D5—121no—
394C4×C5—22no—
395C4×C5—24no—
396C4×C5—41no—
397C4×C5—42no—
398C4×C5#89214yes—
399Dic5—62no—
400Dic5—62no—
401Dic5—64no—
402Dic5—121no—
403Dic5—122no—
404C24—151no—
405C22×C4—151no—
406C22×C4—151no—
407C22×C4—152no—
408C22×C4—154no—
409C22×C4—152no—
410C22×C4—151no—
411C22×C4—302no—
412C22×C4—302no—
413C22×C4C22×D1511yescharacteristic
414C22×C4C22×D1512yes—
415C22×C4C22×D1512yes—
416C22×C4C22×D1511yescharacteristic
417C22×C4C22×D1511yescharacteristic
418C4⋊C4—22no—
419C4⋊C4—42no—
420C4⋊C4—154no—
421C4⋊C4—302no—
422C4⋊C4—602no—
423C4⋊C4C4×D1514yes—
424C22⋊C4—158no—
425C22⋊C4—302no—
426C22⋊C4—302no—
427C22⋊C4—602no—
428C42—22no—
429C42—158no—
430C42—304no—
431C42—304no—
432C42—302no—
433C3×C5#234611yescharacteristic, complemented, Hall
434C22×C3C22×C4×D511yescharacteristic
435C22×C3C2×#71111yescharacteristic
436C22×C3#414411yescharacteristic
437C22×C3C2×#71311yescharacteristic
438C22×C3C2×#71311yescharacteristic
439C22×C3D5×#4111yescharacteristic
440C22×C3#415011yescharacteristic
441C2×D3—102no—
442C2×D3—102no—
443C2×D3—102no—
444C2×D3—201no—
445C2×D3—201no—
446C2×D3—201no—
447C2×D3—201no—
448C3×C4—24no—
449C3×C4—22no—
450C3×C4—41no—
451C3×C4—42no—
452C3×C4#403814yes—
453Dic3—102no—
454Dic3—104no—
455Dic3—102no—
456Dic3—201no—
457Dic3—202no—
458C2×C5C2×#89211yescharacteristic
459C2×C5#554611yescharacteristic
460C2×C5C4×#23911yescharacteristic
461C2×C5#561611yescharacteristic
462C2×C5#564211yescharacteristic
463C2×C5#569411yescharacteristic
464C2×C5#573411yescharacteristic
465D5—122no—
466C23—152no—
467C23—301no—
468C23—301no—
469C23—301no—
470C23—301no—
471C23—301no—
472C23—301no—
473C23C23×D1511yescharacteristic
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—152no—
485C2×C4—154no—
486C2×C4—152no—
487C2×C4—301no—
488C2×C4—302no—
489C2×C4—301no—
490C2×C4—301no—
491C2×C4—302no—
492C2×C4—301no—
493C2×C4—308no—
494C2×C4—302no—
495C2×C4—301no—
496C2×C4—302no—
497C2×C4—301no—
498C2×C4—301no—
499C2×C4—302no—
500C2×C4C2×C4×D1514yes—
501C2×C4C2×C4×D1512yes—
502C2×C4#681912yes—
503C2×C4#682112yes—
504C2×C4#682112yes—
505C2×C3C2×#403811yescharacteristic
506C2×C3#6588011yescharacteristic
507C2×C3C4×#71311yescharacteristic
508C2×C3#6595011yescharacteristic
509C2×C3#6597611yescharacteristic
510C2×C3#6602811yescharacteristic
511C2×C3#6606811yescharacteristic
512D3—202no—
513C5#7597911yescharacteristic, complemented, Sylow
514C22—302no—
515C22—302no—
516C22—302no—
517C22—601no—
518C22—601no—
519C22—601no—
520C22—601no—
521C22C22×C4×D1511yescharacteristic
522C22C2×#681911yescharacteristic
523C22#9209511yescharacteristic
524C22C2×#682111yescharacteristic
525C22C2×#682111yescharacteristic
526C22#41×D1511yescharacteristic
527C22#9210111yescharacteristic
528C4—24no—
529C4—22no—
530C4—41no—
531C4—42no—
532C4—304no—
533C4—302no—
534C4—302no—
535C4—602no—
536C4—601no—
537C4#9178114yes—
538C3#1060771011yescharacteristic, complemented, Sylow
539C2—602no—
540C2C2×#9178111yescharacteristic
541C2#1175630511yescharacteristic
542C2C4×#682111yescharacteristic
543C2#1175637511yescharacteristic
544C2#1175640111yescharacteristic
545C2#1175645311yescharacteristic
546C2#1175649311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#389C2
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenter#389D15
hypocenterC3×C5#2346
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. C3×C5×#389C2semidirect
5. #11751085C2semidirect
6. #11751078C2semidirect
7. C4⋊C4×Dic15C2semidirect
9. C4×C4⋊Dic15C2semidirect
11. #11750749C2semidirect
29. #91781C4semidirect
39. C5×#389D3semidirect
79. C3×#389D5semidirect
208. #389D15semidirect
433. C3×C5#2346semidirect
513. C5#75979semidirect
538. C3#10607710semidirect

Maximal subgroups

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

subgroupindex
C2×#917812
C3×C5×#3892
#117510912
#117510882
#117510852
#117510782
C4⋊C4×Dic152
C4×#67142
C4×C4⋊Dic152
#117507712
#117507492
#106077103
#759795