Finite Group Databasebeta

← #14326418

Subgroups — #14326418

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×#91815C211yesmaximal, characteristic
2C3×C5×#381C211yesmaximal, characteristic
3C2×#91115C211yesmaximal, characteristic
4#11751047C212yesmaximal
5C22⋊C4×Dic15C212yesmaximal
6#11750755C212yesmaximal, complemented
7#11750754C212yesmaximal, complemented
8#11750752C211yesmaximal, characteristic, complemented
9#11750751C211yesmaximal, characteristic, complemented
10#11750750C211yesmaximal, characteristic, complemented
11#11750749C211yesmaximal, characteristic, complemented
12#10605790—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×Dic15C2212yes—
15C2×C3×C5×C22⋊C4C2212yes—
16C2×#6719C2211yescharacteristic
17C2×#6719C2211yescharacteristic
18#91815C418yescomplemented
19C2×C4⋊Dic15C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C2×#6712C2212yes—
22C2×#6712C2212yes—
23C2×C4×Dic15C2212yes—
24C2×C4×Dic15C2212yes—
25C2×C4×Dic15C2211yescharacteristic
26C2×C4×Dic15C2211yescharacteristic
27C3×C5×#95C2211yescharacteristic
28C3×C5×#95C2211yescharacteristic
29C3×C5×#95C2212yes—
30#91115C2211yescharacteristic
31#91115C2212yes—
32#91115C2211yescharacteristic
33#91115C2212yes—
34#91115C2212yes—
35#91115C2212yes—
36#91115C2212yes—
37#74059—51nomaximal, Hall
38C2×#4072—31no—
39C5×#381D311yescharacteristic
40C2×#3963—31no—
41#65235—32no—
42C22⋊C4×Dic5—32no—
43#64943—32no—
44#64942—32no—
45#64940—31no—
46#64939—31no—
47#64938—31no—
48#64937—31no—
49C24×C3×C5C2311yescharacteristic
50C22×C3×C4×C5—24no—
51C22×C3×C4×C5C2×C414yes—
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15—24no—
57C22×Dic15—24no—
58C22×Dic15—42no—
59C22×Dic15C2312yes—
60C22×Dic15C2311yescharacteristic
61C22×Dic15C2311yescharacteristic
62C22×Dic15C2311yescharacteristic
63C22×Dic15C2311yescharacteristic
64C22×Dic15C2312yes—
65C3×C5×C22⋊C4—24no—
66#6719C2×C414yes—
67#6719C2×C414yes—
68C4⋊Dic15C2×C414yescomplemented
69C4⋊Dic15C2×C414yescomplemented
70#6712—24no—
71#6712—42no—
72C4×Dic15—24no—
73C4×Dic15—42no—
74C4×Dic15C2×C414yescomplemented
75C4×Dic15C2×C414yescomplemented
76C2×#926—51no—
77C3×#381D511yescharacteristic
78C2×C3⋊#95—51no—
79#4946—52no—
80Dic3×C22⋊C4—52no—
81#4654—52no—
82#4653—52no—
83#4651—51no—
84#4650—51no—
85#4649—51no—
86#4648—51no—
87C23×C4×C5C2×D311yescharacteristic
88C23×Dic5—32no—
89C2×C5×C22⋊C4C2×D312yes—
90C2×C22⋊Dic5—31no—
91C2×C22⋊Dic5—31no—
92#4072—38no—
93C2×C4⋊Dic5—31no—
94C2×C4⋊Dic5—31no—
95C2×#683—32no—
96C2×#683—32no—
97C2×C4×Dic5—31no—
98C2×C4×Dic5—31no—
99C2×C4×Dic5—32no—
100C2×C4×Dic5—32no—
101C5×#95C2×D311yescharacteristic
102C5×#95C2×D311yescharacteristic
103C5×#95C2×D312yes—
104#3963—31no—
105#3963—32no—
106#3963—31no—
107#3963—32no—
108#3963—32no—
109#3963—32no—
110#3963—32no—
111#2343—151noSylow
112C23×C3×C5—22no—
113C23×C3×C5—21no—
114C23×C3×C5—21no—
115C23×C3×C5C22×C412yes—
116C23×C3×C5#4114yes—
117C23×C3×C5C2411yescharacteristic
118C2×C3×C4×C5—28no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5C22×C412yes—
128C2×C3×C4×C5C22×C412yes—
129C2×Dic15—22no—
130C2×Dic15—22no—
131C2×Dic15—22no—
132C2×Dic15—21no—
133C2×Dic15—22no—
134C2×Dic15—21no—
135C2×Dic15—21no—
136C2×Dic15—21no—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—48no—
141C2×Dic15C22×C412yes—
142C2×Dic15C22×C412yes—
143C2×Dic15C22×C412yes—
144C2×Dic15C22×C412yes—
145C2×Dic15#4114yes—
146C23×C3×C4C2×D511yescharacteristic
147C23×Dic3—52no—
148C2×C3×C22⋊C4C2×D512yes—
149C2×#217—51no—
150C2×#217—51no—
151#926—58no—
152C2×C4⋊Dic3—51no—
153C2×C4⋊Dic3—51no—
154C2×Dic3⋊C4—52no—
155C2×Dic3⋊C4—52no—
156C2×C4×Dic3—51no—
157C2×C4×Dic3—51no—
158C2×C4×Dic3—52no—
159C2×C4×Dic3—52no—
160C3×#95C2×D511yescharacteristic
161C3×#95C2×D511yescharacteristic
162C3×#95C2×D512yes—
163C3⋊#95—51no—
164C3⋊#95—52no—
165C3⋊#95—51no—
166C3⋊#95—52no—
167C3⋊#95—52no—
168C3⋊#95—52no—
169C3⋊#95—52no—
170C24×C5C22×D311yescharacteristic
171C22×C4×C5—24no—
172C22×C4×C5C4×D314yes—
173C22×C4×C5C22×D312yes—
174C22×C4×C5C22×D312yes—
175C22×C4×C5C22×D311yescharacteristic
176C22×C4×C5C22×D311yescharacteristic
177C22×Dic5—31no—
178C22×Dic5—31no—
179C22×Dic5—31no—
180C22×Dic5—31no—
181C22×Dic5—32no—
182C22×Dic5—32no—
183C22×Dic5—64no—
184C22×Dic5—64no—
185C22×Dic5—122no—
186C5×C22⋊C4—24no—
187C22⋊Dic5—34no—
188C22⋊Dic5—34no—
189C4⋊Dic5—34no—
190C4⋊Dic5—34no—
191#683—64no—
192#683—122no—
193C4×Dic5—34no—
194C4×Dic5—34no—
195C4×Dic5—64no—
196C4×Dic5—122no—
197C2×#117—151no—
198#387—152no—
199#387—152no—
200#385—152no—
201#383—151no—
202#382—151no—
203#381D1511yescharacteristic
204C4×C4⋊C4—151no—
205C4×C22⋊C4—152no—
206#376—151no—
207C2×#95—151no—
208C22×C3×C5—22no—
209C22×C3×C5—22no—
210C22×C3×C5—24no—
211C22×C3×C5—24no—
212C22×C3×C5#11714yes—
213C22×C3×C5C23×C411yescharacteristic
214C22×C3×C5C2×#4112yes—
215C22×C3×C5C2×#4112yes—
216C22×C3×C5H(5,𝔽2)11yescharacteristic
217C22×C3×C52−1+411yescharacteristic
218C3×C4×C5—22no—
219C3×C4×C5—22no—
220C3×C4×C5—42no—
221C3×C4×C5—42no—
222Dic15—22no—
223Dic15—22no—
224Dic15—22no—
225Dic15—22no—
226Dic15—24no—
227Dic15—42no—
228C24×C3C22×D511yescharacteristic
229C22×C3×C4—24no—
230C22×C3×C4C4×D514yes—
231C22×C3×C4C22×D512yes—
232C22×C3×C4C22×D512yes—
233C22×C3×C4C22×D511yescharacteristic
234C22×C3×C4C22×D511yescharacteristic
235C22×Dic3—52no—
236C22×Dic3—51no—
237C22×Dic3—51no—
238C22×Dic3—51no—
239C22×Dic3—51no—
240C22×Dic3—52no—
241C22×Dic3—104no—
242C22×Dic3—104no—
243C22×Dic3—202no—
244C3×C22⋊C4—24no—
245#217—54no—
246#217—54no—
247C4⋊Dic3—54no—
248C4⋊Dic3—54no—
249Dic3⋊C4—104no—
250Dic3⋊C4—202no—
251C4×Dic3—54no—
252C4×Dic3—54no—
253C4×Dic3—104no—
254C4×Dic3—202no—
255C23×C5—22no—
256C23×C5—21no—
257C23×C5—21no—
258C23×C5C2×C4×D312yes—
259C23×C5#23714yes—
260C23×C5C23×D311yescharacteristic
261C2×C4×C5—28no—
262C2×C4×C5—22no—
263C2×C4×C5—22no—
264C2×C4×C5—22no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5C2×C4×D312yes—
271C2×C4×C5C2×C4×D312yes—
272C2×Dic5—32no—
273C2×Dic5—32no—
274C2×Dic5—32no—
275C2×Dic5—32no—
276C2×Dic5—34no—
277C2×Dic5—62no—
278C2×Dic5—62no—
279C2×Dic5—62no—
280C2×Dic5—61no—
281C2×Dic5—62no—
282C2×Dic5—61no—
283C2×Dic5—61no—
284C2×Dic5—61no—
285C2×Dic5—62no—
286C2×Dic5—62no—
287C2×Dic5—62no—
288C2×Dic5—128no—
289C23×C4—152no—
290C23×C4C2×D1511yescharacteristic
291#117—158no—
292C2×C4⋊C4—151no—
293C2×C4⋊C4—151no—
294C2×C4⋊C4—152no—
295C2×C4⋊C4—152no—
296C2×C22⋊C4—151no—
297C2×C22⋊C4—151no—
298C2×C22⋊C4C2×D1512yes—
299C2×C42—151no—
300C2×C42—151no—
301C2×C42—152no—
302C2×C42—152no—
303#95—151no—
304#95—151no—
305#95—152no—
306#95—152no—
307#95—152no—
308#95—152no—
309#95—152no—
310#95C2×D1511yescharacteristic
311#95C2×D1511yescharacteristic
312#95C2×D1512yes—
313C2×C3×C5—24no—
314C2×C3×C5C2×#11711yescharacteristic
315C2×C3×C5C4×#4111yescharacteristic
316C2×C3×C5#52011yescharacteristic
317C2×C3×C5#55112yes—
318C2×C3×C5#55212yes—
319C23×C3—22no—
320C23×C3—21no—
321C23×C3—21no—
322C23×C3C2×C4×D512yes—
323C23×C3#71114yes—
324C23×C3C23×D511yescharacteristic
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—28no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4C2×C4×D512yes—
335C2×C3×C4C2×C4×D512yes—
336C2×Dic3—52no—
337C2×Dic3—52no—
338C2×Dic3—52no—
339C2×Dic3—52no—
340C2×Dic3—54no—
341C2×Dic3—102no—
342C2×Dic3—102no—
343C2×Dic3—102no—
344C2×Dic3—101no—
345C2×Dic3—102no—
346C2×Dic3—101no—
347C2×Dic3—101no—
348C2×Dic3—101no—
349C2×Dic3—102no—
350C2×Dic3—102no—
351C2×Dic3—102no—
352C2×Dic3—208no—
353C22×C5—24no—
354C22×C5—24no—
355C22×C5—22no—
356C22×C5—22no—
357C22×C5#87714yes—
358C22×C5C22×C4×D311yescharacteristic
359C22×C5C2×#23712yes—
360C22×C5D3×#4112yes—
361C22×C5#100911yescharacteristic
362C22×C5#101011yescharacteristic
363C4×C5—22no—
364C4×C5—22no—
365C4×C5—42no—
366C4×C5—42no—
367Dic5—64no—
368Dic5—62no—
369Dic5—62no—
370Dic5—62no—
371Dic5—62no—
372Dic5—122no—
373C24C22×D1511yescharacteristic
374C22×C4—24no—
375C22×C4—152no—
376C22×C4—151no—
377C22×C4—151no—
378C22×C4—151no—
379C22×C4—151no—
380C22×C4—152no—
381C22×C4—304no—
382C22×C4—304no—
383C22×C4—602no—
384C22×C4C4×D1514yes—
385C22×C4C22×D1512yes—
386C22×C4C22×D1512yes—
387C22×C4C22×D1511yescharacteristic
388C22×C4C22×D1511yescharacteristic
389C4⋊C4—154no—
390C4⋊C4—154no—
391C4⋊C4—304no—
392C4⋊C4—602no—
393C22⋊C4—24no—
394C22⋊C4—154no—
395C22⋊C4—154no—
396C42—154no—
397C42—154no—
398C42—304no—
399C42—602no—
400C3×C5#234311yescharacteristic, complemented, Hall
401C22×C3—22no—
402C22×C3—22no—
403C22×C3—24no—
404C22×C3—24no—
405C22×C3#402314yes—
406C22×C3C22×C4×D511yescharacteristic
407C22×C3C2×#71112yes—
408C22×C3D5×#4112yes—
409C22×C3#414911yescharacteristic
410C22×C3#415011yescharacteristic
411C3×C4—22no—
412C3×C4—22no—
413C3×C4—42no—
414C3×C4—42no—
415Dic3—102no—
416Dic3—102no—
417Dic3—102no—
418Dic3—102no—
419Dic3—104no—
420Dic3—202no—
421C2×C5—24no—
422C2×C5C2×#87711yescharacteristic
423C2×C5#552211yescharacteristic
424C2×C5#552311yescharacteristic
425C2×C5#565012yes—
426C2×C5#565812yes—
427C23—22no—
428C23—21no—
429C23—21no—
430C23C2×C4×D1512yes—
431C23#681914yes—
432C23C23×D1511yescharacteristic
433C2×C4—28no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—152no—
443C2×C4—152no—
444C2×C4—152no—
445C2×C4—152no—
446C2×C4—154no—
447C2×C4—302no—
448C2×C4—302no—
449C2×C4—302no—
450C2×C4—301no—
451C2×C4—302no—
452C2×C4—301no—
453C2×C4—301no—
454C2×C4—301no—
455C2×C4—302no—
456C2×C4—302no—
457C2×C4—302no—
458C2×C4—608no—
459C2×C4C2×C4×D1512yes—
460C2×C4C2×C4×D1512yes—
461C2×C3—24no—
462C2×C3C2×#402311yescharacteristic
463C2×C3#6585611yescharacteristic
464C2×C3#6585711yescharacteristic
465C2×C3#6598412yes—
466C2×C3#6599212yes—
467C5#7405911yescharacteristic, complemented, Sylow
468C22—24no—
469C22—24no—
470C22—22no—
471C22—22no—
472C22#9176614yes—
473C22C22×C4×D1511yescharacteristic
474C22C2×#681912yes—
475C22#41×D1512yes—
476C22#9210011yescharacteristic
477C22#9210111yescharacteristic
478C4—22no—
479C4—22no—
480C4—42no—
481C4—42no—
482C4—304no—
483C4—302no—
484C4—302no—
485C4—302no—
486C4—302no—
487C4—602no—
488C3#1060579011yescharacteristic, complemented, Sylow
489C2—24no—
490C2C2×#9176611yescharacteristic
491C2#1175628111yescharacteristic
492C2#1175628211yescharacteristic
493C2#1175640912yes—
494C2#1175641712yes—
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#381C2
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenter#381D15
hypocenterC3×C5#2343
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
6. #11750755C2semidirect
7. #11750754C2semidirect
8. #11750752C2semidirect
9. #11750751C2semidirect
10. #11750750C2semidirect
11. #11750749C2semidirect
18. #91815C4semidirect
68. C4⋊Dic15C2×C4semidirect
69. C4⋊Dic15C2×C4semidirect
74. C4×Dic15C2×C4semidirect
75. C4×Dic15C2×C4semidirect
400. C3×C5#2343semidirect
467. C5#74059semidirect
488. C3#10605790semidirect

Maximal subgroups

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

subgroupindex
C2×#918152
C3×C5×#3812
C2×#911152
#117510472
C22⋊C4×Dic152
#117507552
#117507542
#117507522
#117507512
#117507502
#117507492
#106057903
#740595