Finite Group Databasebeta

← #14326451

Subgroups — #14326451

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91371C211yesmaximal, characteristic
2#11750751C211yesmaximal, characteristic, complemented
3C5×#4664C211yesmaximal, characteristic
4C3×#64938C211yesmaximal, characteristic, complemented
5#11748892C212yesmaximal
6D3×#3963C211yesmaximal, characteristic
7Dic5×(C2×D3)⋊C4C212yesmaximal
8#11748814C212yesmaximal, complemented
9#11748665C212yesmaximal, complemented
10#11748653C211yesmaximal, characteristic, complemented
11#11748612C211yesmaximal, characteristic, complemented
12#10605790—31nomaximal, Hall
13C22×C4×C5×D3C2211yescharacteristic
14C22×D3×Dic5C2212yes—
15C2×#6712C2212yes—
16C2×C4×Dic15C2211yescharacteristic
17C2×C5×(C2×D3)⋊C4C2212yes—
18C2×C3×#683C2212yes—
19C2×C3×C4×Dic5C2212yes—
20C2×C3×C4×Dic5C2211yescharacteristic
21C2×Dic3⋊Dic5C2211yescharacteristic
22C2×Dic3⋊Dic5C2211yescharacteristic
23C2×(C2×D3)⋊Dic5C2211yescharacteristic
24C2×(C2×D3)⋊Dic5C2211yescharacteristic
25C2×Dic3×Dic5C2212yes—
26#91371C418yescomplemented
27C3×C5×#95C2211yescharacteristic
28#91115C2211yescharacteristic
29#91115C2212yes—
30C5×C3⋊#95C2211yescharacteristic
31C5×C3⋊#95C2212yes—
32C3×#3963C2211yescharacteristic
33#90994C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#73766—51nomaximal, Hall
38C2×#4072—31no—
39C5×#381—31no—
40C2×#3963—31no—
41#65235—32no—
42C22⋊C4×Dic5—32no—
43#64943—32no—
44#64942—32no—
45#64940—31no—
46#64939—31no—
47#64938D311yescharacteristic, complemented
48#64937—31no—
49C23×C5×D3C2311yescharacteristic
50C22×C3×C4×C5C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×Dic15C2312yes—
53C22×Dic15C2311yescharacteristic
54C22×Dic15C2311yescharacteristic
55C22×C5×Dic3C2312yes—
56C22×C5×Dic3C2311yescharacteristic
57C2×C4×C5×D3—24no—
58C2×C4×C5×D3C2×C414yes—
59C22×C3×Dic5C2311yescharacteristic
60C22×C3×Dic5C2311yescharacteristic
61C22×C3×Dic5C2312yes—
62C2×D3×Dic5—24no—
63C2×D3×Dic5—24no—
64C2×D3×Dic5—42no—
65#6712—42no—
66C4×Dic15C2×C414yescomplemented
67C5×(C2×D3)⋊C4—24no—
68C3×#683—24no—
69C3×C4×Dic5—42no—
70C3×C4×Dic5C2×C414yescomplemented
71Dic3⋊Dic5C2×C414yescomplemented
72Dic3⋊Dic5C2×C414yescomplemented
73(C2×D3)⋊Dic5C2×C414yes—
74(C2×D3)⋊Dic5C2×C414yes—
75Dic3×Dic5—24no—
76C2×#872—51no—
77C3×C4×C4⋊C4—51no—
78#4989—52no—
79#4978—52no—
80C4×(C2×D3)⋊C4—52no—
81#4937—51no—
82#4933—52no—
83#4664D511yescharacteristic
84D3×#95—51no—
85#4650—51no—
86#4648—51no—
87C23×C4×C5—31no—
88C23×Dic5—32no—
89C2×C5×C22⋊C4—32no—
90C2×C22⋊Dic5—31no—
91C2×C22⋊Dic5—31no—
92#4072—38no—
93C2×C4⋊Dic5—31no—
94C2×C4⋊Dic5—31no—
95C2×#683—32no—
96C2×#683C2×D312yes—
97C2×C4×Dic5—31no—
98C2×C4×Dic5—32no—
99C2×C4×Dic5C2×D312yes—
100C2×C4×Dic5C2×D311yescharacteristic
101C5×#95—31no—
102C5×#95—32no—
103C5×#95C2×D311yescharacteristic
104#3963—31no—
105#3963—32no—
106#3963—32no—
107#3963—32no—
108#3963—32no—
109#3963—32no—
110#3963C2×D311yescharacteristic
111#2343—151noSylow
112C23×C3×C5C2411yescharacteristic
113C22×C5×D3—22no—
114C22×C5×D3—21no—
115C22×C5×D3—21no—
116C22×C5×D3C22×C412yes—
117C22×C5×D3#4114yes—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5C22×C412yes—
123C2×Dic15—22no—
124C2×Dic15—21no—
125C2×Dic15—21no—
126C2×Dic15—22no—
127C2×Dic15—22no—
128C2×Dic15—22no—
129C2×Dic15C22×C412yes—
130C2×Dic15C22×C412yes—
131C2×C5×Dic3—22no—
132C2×C5×Dic3—22no—
133C2×C5×Dic3—22no—
134C2×C5×Dic3—22no—
135C2×C5×Dic3C22×C412yes—
136C4×C5×D3—28no—
137C2×C3×Dic5—22no—
138C2×C3×Dic5—22no—
139C2×C3×Dic5—21no—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—21no—
142C2×C3×Dic5C22×C412yes—
143C2×C3×Dic5C22×C412yes—
144C2×C3×Dic5#4114yes—
145D3×Dic5—48no—
146C22×C4×D3—52no—
147C22×C4×D3C2×D511yescharacteristic
148C2×C3×C4⋊C4—52no—
149C2×C3×C42—51no—
150C2×C3×C42—52no—
151C2×(C2×D3)⋊C4—51no—
152C2×(C2×D3)⋊C4—51no—
153C2×(C2×D3)⋊C4C2×D512yes—
154C2×Dic3⋊C4—51no—
155C2×Dic3⋊C4—51no—
156C2×Dic3⋊C4—52no—
157C2×C4×Dic3—51no—
158C2×C4×Dic3—52no—
159#872—58no—
160C3×#95—51no—
161C3×#95C2×D511yescharacteristic
162C3⋊#95—51no—
163C3⋊#95—52no—
164C3⋊#95—52no—
165C3⋊#95—52no—
166C3⋊#95—52no—
167C3⋊#95—52no—
168C3⋊#95C2×D511yescharacteristic
169C3⋊#95C2×D512yes—
170C24×C5—31no—
171C22×C4×C5—31no—
172C22×C4×C5—34no—
173C22×C4×C5—32no—
174C22×C4×C5—64no—
175C22×C4×C5C22×D312yes—
176C22×C4×C5C22×D311yescharacteristic
177C22×Dic5—31no—
178C22×Dic5—31no—
179C22×Dic5—32no—
180C22×Dic5—64no—
181C22×Dic5—64no—
182C22×Dic5—122no—
183C22×Dic5C22×D311yescharacteristic
184C22×Dic5C22×D311yescharacteristic
185C22×Dic5C22×D312yes—
186C5×C22⋊C4—64no—
187C22⋊Dic5—34no—
188C22⋊Dic5—34no—
189C4⋊Dic5—34no—
190C4⋊Dic5—34no—
191#683—24no—
192#683—122no—
193C4×Dic5—34no—
194C4×Dic5—42no—
195C4×Dic5—64no—
196C4×Dic5C4×D314yescomplemented
197C2×#117—151no—
198#387—152no—
199#387—152no—
200#385—152no—
201#383—151no—
202#382—151no—
203#381—31no—
204C4×C4⋊C4—51no—
205C4×C22⋊C4—152no—
206#376—151no—
207C2×#95—151no—
208C22×C3×C5C23×C411yescharacteristic
209C22×C3×C5C2×#4112yes—
210C22×C3×C5C2×#4112yes—
211C22×C3×C5H(5,𝔽2)11yescharacteristic
212C22×C3×C52−1+411yescharacteristic
213C2×C5×D3—22no—
214C2×C5×D3—22no—
215C2×C5×D3—24no—
216C2×C5×D3—24no—
217C2×C5×D3#11714yes—
218C3×C4×C5—22no—
219C3×C4×C5—42no—
220Dic15—22no—
221Dic15—22no—
222Dic15—42no—
223C3×Dic5—22no—
224C3×Dic5—22no—
225C3×Dic5—24no—
226C5×Dic3—22no—
227C5×Dic3—42no—
228C23×D3C22×D511yescharacteristic
229C22×C3×C4—52no—
230C22×C3×C4—51no—
231C22×C3×C4—51no—
232C22×C3×C4C22×D512yes—
233C22×C3×C4C22×D511yescharacteristic
234C22×Dic3—51no—
235C22×Dic3—51no—
236C22×Dic3—52no—
237C22×Dic3C22×D512yes—
238C22×Dic3C22×D511yescharacteristic
239C2×C4×D3—24no—
240C2×C4×D3—104no—
241C2×C4×D3—104no—
242C2×C4×D3—202no—
243C2×C4×D3C4×D514yes—
244C3×C4⋊C4—104no—
245C3×C42—54no—
246C3×C42—202no—
247(C2×D3)⋊C4—24no—
248(C2×D3)⋊C4—54no—
249(C2×D3)⋊C4—54no—
250Dic3⋊C4—54no—
251Dic3⋊C4—54no—
252Dic3⋊C4—202no—
253C4×Dic3—54no—
254C4×Dic3—104no—
255C23×C5—32no—
256C23×C5—34no—
257C23×C5—62no—
258C23×C5—61no—
259C23×C5—61no—
260C23×C5C23×D311yescharacteristic
261C2×C4×C5—22no—
262C2×C4×C5—22no—
263C2×C4×C5—22no—
264C2×C4×C5—22no—
265C2×C4×C5—32no—
266C2×C4×C5—68no—
267C2×C4×C5—62no—
268C2×C4×C5—62no—
269C2×C4×C5—62no—
270C2×C4×C5—62no—
271C2×C4×C5C2×C4×D312yes—
272C2×Dic5—22no—
273C2×Dic5—21no—
274C2×Dic5—22no—
275C2×Dic5—21no—
276C2×Dic5—22no—
277C2×Dic5—32no—
278C2×Dic5—32no—
279C2×Dic5—62no—
280C2×Dic5—61no—
281C2×Dic5—61no—
282C2×Dic5—62no—
283C2×Dic5—62no—
284C2×Dic5—62no—
285C2×Dic5—128no—
286C2×Dic5C2×C4×D312yes—
287C2×Dic5C2×C4×D312yes—
288C2×Dic5#23514yes—
289C23×C4—31no—
290C23×C4—152no—
291#117—158no—
292C2×C4⋊C4—52no—
293C2×C4⋊C4—151no—
294C2×C4⋊C4—151no—
295C2×C4⋊C4—152no—
296C2×C22⋊C4—32no—
297C2×C22⋊C4—151no—
298C2×C22⋊C4—151no—
299C2×C42—51no—
300C2×C42—52no—
301C2×C42—151no—
302C2×C42—152no—
303#95—31no—
304#95—32no—
305#95—51no—
306#95—152no—
307#95—152no—
308#95—152no—
309#95—152no—
310#95—151no—
311#95—152no—
312#95D3×D511yescharacteristic
313C2×C3×C5C2×#11711yescharacteristic
314C2×C3×C5C4×#4111yescharacteristic
315C2×C3×C5#52011yescharacteristic
316C2×C3×C5#55112yes—
317C2×C3×C5#55212yes—
318C5×D3—24no—
319C23×C3C23×D511yescharacteristic
320C22×D3—22no—
321C22×D3—21no—
322C22×D3—21no—
323C22×D3C2×C4×D512yes—
324C22×D3#71114yes—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—52no—
330C2×C3×C4—52no—
331C2×C3×C4—54no—
332C2×C3×C4—102no—
333C2×C3×C4—102no—
334C2×C3×C4—101no—
335C2×C3×C4—102no—
336C2×C3×C4—101no—
337C2×C3×C4C2×C4×D512yes—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—52no—
343C2×Dic3—52no—
344C2×Dic3—102no—
345C2×Dic3—101no—
346C2×Dic3—101no—
347C2×Dic3—102no—
348C2×Dic3—102no—
349C2×Dic3—102no—
350C2×Dic3C2×C4×D512yes—
351C4×D3—28no—
352C4×D3—208no—
353C22×C5—34no—
354C22×C5—62no—
355C22×C5—62no—
356C22×C5—64no—
357C22×C5—64no—
358C22×C5C22×C4×D311yescharacteristic
359C22×C5C2×#23512yes—
360C22×C5#100411yescharacteristic
361C22×C5#100711yescharacteristic
362C22×C5D3×#4112yes—
363C4×C5—22no—
364C4×C5—42no—
365C4×C5—62no—
366C4×C5—122no—
367Dic5—22no—
368Dic5—22no—
369Dic5—24no—
370Dic5—62no—
371Dic5—62no—
372Dic5—122no—
373C24—31no—
374C22×C4—31no—
375C22×C4—34no—
376C22×C4—32no—
377C22×C4—52no—
378C22×C4—51no—
379C22×C4—51no—
380C22×C4—64no—
381C22×C4—151no—
382C22×C4—151no—
383C22×C4—152no—
384C22×C4—304no—
385C22×C4—304no—
386C22×C4—602no—
387C22×C4C2×D3×D512yes—
388C22×C4C2×D3×D511yescharacteristic
389C4⋊C4—104no—
390C4⋊C4—154no—
391C4⋊C4—154no—
392C4⋊C4—602no—
393C22⋊C4—64no—
394C22⋊C4—154no—
395C22⋊C4—154no—
396C42—54no—
397C42—154no—
398C42—202no—
399C42—304no—
400C3×C5#234311yescharacteristic, complemented, Hall
401C22×C3C22×C4×D511yescharacteristic
402C22×C3C2×#71112yes—
403C22×C3D5×#4112yes—
404C22×C3#414911yescharacteristic
405C22×C3#415011yescharacteristic
406C2×D3—22no—
407C2×D3—22no—
408C2×D3—24no—
409C2×D3—24no—
410C2×D3#402314yes—
411C3×C4—22no—
412C3×C4—42no—
413C3×C4—102no—
414C3×C4—102no—
415C3×C4—104no—
416Dic3—22no—
417Dic3—42no—
418Dic3—102no—
419Dic3—102no—
420Dic3—202no—
421C2×C5—64no—
422C2×C5C4×#23511yescharacteristic
423C2×C5#550411yescharacteristic
424C2×C5D3×#11711yescharacteristic
425C2×C5#555612yes—
426C2×C5#558112yes—
427C23—32no—
428C23—34no—
429C23—62no—
430C23—61no—
431C23—61no—
432C23C22×D3×D511yescharacteristic
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—32no—
438C2×C4—52no—
439C2×C4—52no—
440C2×C4—54no—
441C2×C4—68no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4—62no—
445C2×C4—62no—
446C2×C4—102no—
447C2×C4—102no—
448C2×C4—101no—
449C2×C4—102no—
450C2×C4—101no—
451C2×C4—152no—
452C2×C4—152no—
453C2×C4—302no—
454C2×C4—301no—
455C2×C4—301no—
456C2×C4—302no—
457C2×C4—302no—
458C2×C4—302no—
459C2×C4—608no—
460C2×C4C4×D3×D512yes—
461C2×C3C2×#402311yescharacteristic
462C2×C3#6585611yescharacteristic
463C2×C3#6585711yescharacteristic
464C2×C3#6598412yes—
465C2×C3#6599212yes—
466D3—24no—
467C5#7376611yescharacteristic, complemented, Sylow
468C22—34no—
469C22—64no—
470C22—64no—
471C22—62no—
472C22—62no—
473C22C2×C4×D3×D511yescharacteristic
474C22D5×#23512yes—
475C22D3×#71112yes—
476C22#9202611yescharacteristic
477C22#9203011yescharacteristic
478C4—22no—
479C4—42no—
480C4—62no—
481C4—104no—
482C4—102no—
483C4—102no—
484C4—122no—
485C4—302no—
486C4—302no—
487C4—602no—
488C3#1060579011yescharacteristic, complemented, Sylow
489C2—64no—
490C2#1175266511yescharacteristic
491C2D3×#402311yescharacteristic
492C2#1175327912yes—
493C2#1175349312yes—
494C2#1175366811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenter#95D3×D5
hypocenterC3×C5#2343
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #11750751C2semidirect
4. C3×#64938C2semidirect
8. #11748814C2semidirect
9. #11748665C2semidirect
10. #11748653C2semidirect
11. #11748612C2semidirect
26. #91371C4semidirect
47. #64938D3semidirect
66. C4×Dic15C2×C4semidirect
70. C3×C4×Dic5C2×C4semidirect
71. Dic3⋊Dic5C2×C4semidirect
72. Dic3⋊Dic5C2×C4semidirect
196. C4×Dic5C4×D3semidirect
400. C3×C5#2343semidirect
467. C5#73766semidirect
488. C3#10605790semidirect

Maximal subgroups

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

subgroupindex
C2×#913712
#117507512
C5×#46642
C3×#649382
#117488922
D3×#39632
Dic5×(C2×D3)⋊C42
#117488142
#117486652
#117486532
#117486122
#106057903
#737665