Finite Group Databasebeta

← #14327543

Subgroups — #14327543

Order 1920.

1176 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×C4×D60C211yesmaximal, characteristic
2C5×#4937C211yesmaximal, characteristic, complemented
3C3×#65221C211yesmaximal, characteristic, complemented
4#11748904C212yesmaximal
5#11748888C211yesmaximal, characteristic, complemented
6#11748875C212yesmaximal, complemented
7#11748863C211yesmaximal, characteristic, complemented
8#11748829C212yesmaximal, complemented
9#11748688C212yesmaximal, complemented
10#11748670C211yesmaximal, characteristic, complemented
11#11748606C211yesmaximal, characteristic, complemented
12#10606028—31nomaximal, Hall
13C22×D60C2211yescharacteristic
14C22×C4×D15C2211yescharacteristic
15C22×C4×D15C2211yescharacteristic
16C22×#1200C2212yes—
17C2×C3×C42×C5C2211yescharacteristic
18C2×#6714C2211yescharacteristic
19C2×#6714C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C4×D60C418yescomplemented
22C2×C3×C4×Dic5C2212yes—
23C2×#6669C2212yes—
24C2×#6667C2212yes—
25C2×#6667C2212yes—
26C2×#6667C2212yes—
27C2×Dic3×Dic5C2212yes—
28C5×C3⋊#95C2212yes—
29C5×C3⋊#95C2211yescharacteristic
30C5×C3⋊#95C2212yes—
31C5×C3⋊#95C2211yescharacteristic
32C3×#3963C2211yescharacteristic
33C3×#3963C2212yes—
34C3×#3963C2211yescharacteristic
35#90994C2212yes—
36#90994C2212yes—
37#73417—51nomaximal, Hall
38C2×C4×D20—31no—
39C5×#383—31no—
40#65221D311yescharacteristic, complemented
41#64958—32no—
42#64956—31no—
43#64955—32no—
44#64955—31no—
45#64954—32no—
46#64953—31no—
47D5×#95—31no—
48#64942—32no—
49C23×D15C2311yescharacteristic
50C23×D15C2311yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C2×D60—22no—
57C2×D60—22no—
58C2×D60C2×C414yes—
59C2×C4×D15—42no—
60C2×C4×D15—42no—
61C2×C4×D15C2×C414yes—
62C2×C4×D15C2×C414yescomplemented
63C22×C5×Dic3C2312yes—
64C22×C5×Dic3C2312yes—
65C22×C3×Dic5C2312yes—
66C22×C3×Dic5C2312yes—
67C2×#1200—24no—
68C2×#1200—24no—
69C2×#1200—42no—
70C3×C42×C5C2×C414yescomplemented
71#6714C2×C414yes—
72#6714C2×C414yescomplemented
73C4⋊Dic15C2×C414yescomplemented
74C3×C4×Dic5—24no—
75#6669—42no—
76#6667—24no—
77#6667—24no—
78#6667—42no—
79Dic3×Dic5—42no—
80C2×C4×D12—51no—
81C3×#376—51no—
82#4940—52no—
83C4×(C2×D3)⋊C4—52no—
84#4937D511yescharacteristic, complemented
85#4667—51no—
86#4666—51no—
87#4665—52no—
88#4664—51no—
89D3×#95—51no—
90#4654—52no—
91C22×D20—31no—
92C22×C4×D5—31no—
93C22×C4×D5—31no—
94C22×C4×D5—32no—
95C2×C42×C5C2×D311yescharacteristic
96C2×#685—31no—
97C2×#685—31no—
98C2×#685—32no—
99C2×#685—32no—
100C2×#685—32no—
101C2×C4⋊Dic5—31no—
102C2×#683—32no—
103C2×C4×Dic5—32no—
104C2×C4×Dic5C2×D312yes—
105C4×D20—38no—
106C5×#95—32no—
107C5×#95—31no—
108C5×#95—31no—
109C5×#95—32no—
110#3963—32no—
111#3963—32no—
112#3963C2×D312yes—
113#3963C2×D311yescharacteristic
114#3963C2×D311yescharacteristic
115#2353—151noSylow
116C23×C3×C5C2411yescharacteristic
117C22×D15—22no—
118C22×D15—22no—
119C22×D15—22no—
120C22×D15—21no—
121C22×D15—21no—
122C22×D15—22no—
123C22×D15C22×C412yes—
124C22×D15C22×C412yes—
125C22×D15#4112yes—
126C22×D15#4112yes—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—21no—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C22×C412yes—
132C2×C3×C4×C5C22×C412yes—
133C2×C3×C4×C5C22×C412yes—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15C22×C412yes—
137C2×Dic15C22×C412yes—
138D60—28no—
139C4×D15—44no—
140C4×D15—44no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—22no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5#4114yes—
153#1200—48no—
154C22×D12—51no—
155C22×C4×D3—51no—
156C22×C4×D3—51no—
157C22×C4×D3—52no—
158C2×C3×C42—52no—
159C2×C3×C42C2×D511yescharacteristic
160C2×(C2×D3)⋊C4—51no—
161C2×(C2×D3)⋊C4—51no—
162C2×(C2×D3)⋊C4—52no—
163C2×(C2×D3)⋊C4—52no—
164C2×(C2×D3)⋊C4—52no—
165C2×C4⋊Dic3—51no—
166C2×Dic3⋊C4—52no—
167C2×C4×Dic3—52no—
168C4×D12—58no—
169C3×#95—52no—
170C3×#95—51no—
171C3×#95—51no—
172C3⋊#95—52no—
173C3⋊#95—52no—
174C3⋊#95C2×D512yes—
175C3⋊#95C2×D511yescharacteristic
176C3⋊#95C2×D511yescharacteristic
177C3⋊#95C2×D512yes—
178C23×D5—31no—
179C23×D5—31no—
180C22×C4×C5—32no—
181C22×C4×C5—32no—
182C22×C4×C5C22×D311yescharacteristic
183C22×C4×C5C22×D311yescharacteristic
184C22×C4×C5C22×D311yescharacteristic
185C22×Dic5—31no—
186C22×Dic5—31no—
187C22×Dic5C22×D312yes—
188C22×Dic5C22×D312yes—
189C2×D20—34no—
190C2×D20—62no—
191C2×D20—62no—
192C2×C4×D5—34no—
193C2×C4×D5—34no—
194C2×C4×D5—64no—
195C2×C4×D5—64no—
196C2×C4×D5—122no—
197C2×C4×D5—122no—
198C2×C4×D5—122no—
199C42×C5C4×D314yescomplemented
200#685—34no—
201#685—34no—
202#685—64no—
203#685—64no—
204#685—122no—
205C4⋊Dic5—34no—
206#683—122no—
207C4×Dic5—24no—
208C4×Dic5—122no—
209C2×C4×D4—151no—
210#388—152no—
211#387—152no—
212#386—152no—
213#383—31no—
214#381—151no—
215#380—151no—
216C4×C22⋊C4—151no—
217C4×C22⋊C4—152no—
218#376—51no—
219C2×#95—151no—
220C22×C3×C5C23×C411yescharacteristic
221C22×C3×C5C2×#4112yes—
222C22×C3×C5C2×#4111yescharacteristic
223C22×C3×C5C2×#4111yescharacteristic
224C22×C3×C5H(5,𝔽2)12yes—
225C2×D15—22no—
226C2×D15—22no—
227C2×D15—24no—
228C2×D15—24no—
229C2×D15—22no—
230C2×D15—22no—
231C2×D15—22no—
232C2×D15—42no—
233C2×D15—42no—
234C2×D15#11714yes—
235C3×C4×C5—22no—
236C3×C4×C5—22no—
237C3×C4×C5—22no—
238Dic15—22no—
239Dic15—22no—
240C3×Dic5—24no—
241C3×Dic5—42no—
242C5×Dic3—42no—
243C5×Dic3—42no—
244C23×D3—51no—
245C23×D3—51no—
246C22×C3×C4—52no—
247C22×C3×C4—52no—
248C22×C3×C4C22×D511yescharacteristic
249C22×C3×C4C22×D511yescharacteristic
250C22×C3×C4C22×D511yescharacteristic
251C22×Dic3—51no—
252C22×Dic3—51no—
253C22×Dic3C22×D512yes—
254C22×Dic3C22×D512yes—
255C2×D12—54no—
256C2×D12—102no—
257C2×D12—102no—
258C2×C4×D3—54no—
259C2×C4×D3—54no—
260C2×C4×D3—104no—
261C2×C4×D3—104no—
262C2×C4×D3—202no—
263C2×C4×D3—202no—
264C2×C4×D3—202no—
265C3×C42—104no—
266C3×C42C4×D514yescomplemented
267(C2×D3)⋊C4—54no—
268(C2×D3)⋊C4—54no—
269(C2×D3)⋊C4—104no—
270(C2×D3)⋊C4—104no—
271(C2×D3)⋊C4—202no—
272C4⋊Dic3—54no—
273Dic3⋊C4—202no—
274C4×Dic3—202no—
275C23×C5C23×D311yescharacteristic
276C22×D5—32no—
277C22×D5—32no—
278C22×D5—32no—
279C22×D5—32no—
280C22×D5—62no—
281C22×D5—62no—
282C22×D5—62no—
283C22×D5—61no—
284C22×D5—61no—
285C22×D5—62no—
286C2×C4×C5—22no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—22no—
290C2×C4×C5—62no—
291C2×C4×C5—62no—
292C2×C4×C5—62no—
293C2×C4×C5—62no—
294C2×C4×C5—62no—
295C2×C4×C5—62no—
296C2×C4×C5C2×C4×D312yes—
297C2×C4×C5C2×C4×D312yes—
298C2×C4×C5C2×C4×D312yes—
299C2×Dic5—22no—
300C2×Dic5—22no—
301C2×Dic5—22no—
302C2×Dic5—22no—
303C2×Dic5—22no—
304C2×Dic5—32no—
305C2×Dic5—32no—
306C2×Dic5—62no—
307C2×Dic5—62no—
308C2×Dic5#23514yes—
309D20—68no—
310C4×D5—128no—
311C4×D5—124no—
312C4×D5—124no—
313C22×D4—151no—
314C23×C4—152no—
315C23×C4—151no—
316C23×C4—151no—
317C4×D4—158no—
318C2×C4⋊C4—151no—
319C2×C4⋊C4—152no—
320C2×C22⋊C4—151no—
321C2×C22⋊C4—151no—
322C2×C22⋊C4—152no—
323C2×C22⋊C4—152no—
324C2×C22⋊C4—152no—
325C2×C42—52no—
326C2×C42—152no—
327C2×C42D3×D511yescharacteristic
328#95—31no—
329#95—31no—
330#95—32no—
331#95—32no—
332#95—51no—
333#95—51no—
334#95—52no—
335#95—152no—
336#95—152no—
337C2×C3×C5C2×#11711yescharacteristic
338C2×C3×C5C4×#4111yescharacteristic
339C2×C3×C5#51811yescharacteristic
340C2×C3×C5#55112yes—
341C2×C3×C5#55312yes—
342D15—24no—
343D15—42no—
344C23×C3C23×D511yescharacteristic
345C22×D3—52no—
346C22×D3—52no—
347C22×D3—52no—
348C22×D3—52no—
349C22×D3—102no—
350C22×D3—102no—
351C22×D3—102no—
352C22×D3—101no—
353C22×D3—101no—
354C22×D3—102no—
355C2×C3×C4—22no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—22no—
359C2×C3×C4—54no—
360C2×C3×C4—102no—
361C2×C3×C4—102no—
362C2×C3×C4—102no—
363C2×C3×C4—102no—
364C2×C3×C4—102no—
365C2×C3×C4C2×C4×D512yes—
366C2×C3×C4C2×C4×D512yes—
367C2×C3×C4C2×C4×D512yes—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—52no—
375C2×Dic3—52no—
376C2×Dic3—102no—
377C2×Dic3—102no—
378D12—108no—
379C4×D3—208no—
380C4×D3—204no—
381C4×D3—204no—
382C22×C5C22×C4×D311yescharacteristic
383C22×C5C2×#23512yes—
384C22×C5D3×#4111yescharacteristic
385C22×C5D3×#4111yescharacteristic
386C22×C5#100912yes—
387C2×D5—34no—
388C2×D5—62no—
389C2×D5—62no—
390C2×D5—64no—
391C2×D5—64no—
392C2×D5—62no—
393C2×D5—62no—
394C2×D5—62no—
395C2×D5—122no—
396C2×D5—122no—
397C4×C5—22no—
398C4×C5—22no—
399C4×C5—22no—
400C4×C5—122no—
401C4×C5—122no—
402Dic5—24no—
403Dic5—42no—
404Dic5—62no—
405Dic5—62no—
406C24—151no—
407C24—151no—
408C2×D4—154no—
409C2×D4—302no—
410C2×D4—302no—
411C22×C4—32no—
412C22×C4—32no—
413C22×C4—52no—
414C22×C4—52no—
415C22×C4—151no—
416C22×C4—151no—
417C22×C4—154no—
418C22×C4—154no—
419C22×C4—304no—
420C22×C4—304no—
421C22×C4—602no—
422C22×C4—602no—
423C22×C4—602no—
424C22×C4C2×D3×D511yescharacteristic
425C22×C4C2×D3×D511yescharacteristic
426C22×C4C2×D3×D511yescharacteristic
427C4⋊C4—154no—
428C4⋊C4—602no—
429C22⋊C4—154no—
430C22⋊C4—154no—
431C22⋊C4—304no—
432C22⋊C4—304no—
433C22⋊C4—602no—
434C42—104no—
435C42—602no—
436C42#120014yescomplemented
437C3×C5#235311yescharacteristic, complemented, Hall
438C22×C3C22×C4×D511yescharacteristic
439C22×C3D5×#4112yes—
440C22×C3D5×#4111yescharacteristic
441C22×C3D5×#4111yescharacteristic
442C22×C3#414912yes—
443C2×D3—54no—
444C2×D3—102no—
445C2×D3—102no—
446C2×D3—104no—
447C2×D3—104no—
448C2×D3—102no—
449C2×D3—102no—
450C2×D3—102no—
451C2×D3—202no—
452C2×D3—202no—
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—22no—
456C3×C4—104no—
457C3×C4—202no—
458Dic3—42no—
459Dic3—42no—
460Dic3—102no—
461Dic3—102no—
462C2×C5C4×#23511yescharacteristic
463C2×C5D3×#11711yescharacteristic
464C2×C5#552111yescharacteristic
465C2×C5#552712yes—
466C2×C5#553012yes—
467D5—64no—
468D5—122no—
469C23—152no—
470C23—152no—
471C23—152no—
472C23—152no—
473C23—302no—
474C23—302no—
475C23—302no—
476C23—301no—
477C23—301no—
478C23—302no—
479C23C22×D3×D511yescharacteristic
480D4—308no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—54no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—102no—
493C2×C4—102no—
494C2×C4—102no—
495C2×C4—102no—
496C2×C4—102no—
497C2×C4—152no—
498C2×C4—152no—
499C2×C4—302no—
500C2×C4—302no—
501C2×C4—604no—
502C2×C4—604no—
503C2×C4—608no—
504C2×C4C2×#120012yes—
505C2×C4C2×#120012yes—
506C2×C4C2×#120012yes—
507C2×C3D5×#11711yescharacteristic
508C2×C3#6585511yescharacteristic
509C2×C3#6585611yescharacteristic
510C2×C3#6603912yes—
511C2×C3#6604312yes—
512D3—104no—
513D3—202no—
514C5#7341711yescharacteristic, complemented, Sylow
515C22—154no—
516C22—302no—
517C22—304no—
518C22—302no—
519C22—304no—
520C22—302no—
521C22—302no—
522C22—302no—
523C22—602no—
524C22—602no—
525C22D5×#23512yes—
526C22#9201611yescharacteristic
527C22#9201611yescharacteristic
528C22#9201912yes—
529C22C22×#120011yescharacteristic
530C4—22no—
531C4—22no—
532C4—22no—
533C4—104no—
534C4—122no—
535C4—122no—
536C4—202no—
537C4—302no—
538C4—302no—
539C3#1060602811yescharacteristic, complemented, Sylow
540C2—304no—
541C2—602no—
542C2#1175269012yes—
543C2#1175276112yes—
544C2#1175441411yescharacteristic
545C2#1175446111yescharacteristic
546C2#1175451511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×D60C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2353
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C5×#4937C2semidirect
3. C3×#65221C2semidirect
5. #11748888C2semidirect
6. #11748875C2semidirect
7. #11748863C2semidirect
8. #11748829C2semidirect
9. #11748688C2semidirect
10. #11748670C2semidirect
11. #11748606C2semidirect
21. C4×D60C4semidirect
40. #65221D3semidirect
62. C2×C4×D15C2×C4semidirect
70. C3×C42×C5C2×C4semidirect
72. #6714C2×C4semidirect
73. C4⋊Dic15C2×C4semidirect
84. #4937D5semidirect
199. C42×C5C4×D3semidirect
266. C3×C42C4×D5semidirect
436. C42#1200semidirect
437. C3×C5#2353semidirect
514. C5#73417semidirect
539. C3#10606028semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D602
C5×#49372
C3×#652212
#117489042
#117488882
#117488752
#117488632
#117488292
#117486882
#117486702
#117486062
#106060283
#734175