Finite Group Databasebeta

← #14326412

Subgroups — #14326412

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×C3×C5×#117C211yesmaximal, characteristic
2#11751312C211yesmaximal, characteristic
3C2×#91115C211yesmaximal, characteristic
4#11751081C212yesmaximal, complemented
5#11751081C212yesmaximal, complemented
6#11751051C212yesmaximal
7C22⋊C4×Dic15C212yesmaximal
8#11751038C211yesmaximal, characteristic, complemented
9#11751037C211yesmaximal, characteristic, complemented
10C4×C4⋊Dic15C211yesmaximal, characteristic, complemented
11#11751033C211yesmaximal, characteristic, complemented
12#10613968—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×Dic15C2212yes—
15C3×C5×#117C418yescomplemented
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C3×C5×C22⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4C2211yescharacteristic
20C2×C3×C42×C5C2211yescharacteristic
21C2×C3×C42×C5C2211yescharacteristic
22C2×#6719C2212yes—
23C2×C4⋊Dic15C2212yes—
24C2×C4⋊Dic15C2212yes—
25C2×C4×Dic15C2212yes—
26C2×C4×Dic15C2212yes—
27#91115C2211yescharacteristic
28#91115C2211yescharacteristic
29#91115C2212yes—
30#91115C2211yescharacteristic
31#91115C2211yescharacteristic
32#91115C2212yes—
33#91115C2212yes—
34#91115C2212yes—
35#91115C2212yes—
36#91115C2212yes—
37#82237—51nomaximal, Hall
38C2×C5×#117D311yescharacteristic
39#65500—31no—
40C2×#3963—31no—
41#65270—32no—
42#65270—32no—
43#65239—32no—
44C22⋊C4×Dic5—32no—
45#65226—31no—
46#65225—31no—
47C4×C4⋊Dic5—31no—
48#65221—31no—
49C24×C3×C5C2311yescharacteristic
50C22×C3×C4×C5—24no—
51C22×C3×C4×C5C2×C414yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×Dic15—24no—
59C22×Dic15—24no—
60C22×Dic15—42no—
61C22×Dic15C2312yes—
62C22×Dic15C2312yes—
63C22×Dic15C2312yes—
64C22×Dic15C2312yes—
65C3×C5×C4⋊C4C2×C414yescomplemented
66C3×C5×C4⋊C4C2×C414yescomplemented
67C3×C5×C22⋊C4C2×C414yes—
68C3×C5×C22⋊C4C2×C414yes—
69C3×C42×C5C2×C414yescomplemented
70C3×C42×C5C2×C414yescomplemented
71#6719—24no—
72C4⋊Dic15—24no—
73C4⋊Dic15—42no—
74C4×Dic15—24no—
75C4×Dic15—42no—
76C2×C3×#117D511yescharacteristic
77#5211—51no—
78C2×C3⋊#95—51no—
79#4980—52no—
80#4980—52no—
81#4950—52no—
82Dic3×C22⋊C4—52no—
83#4937—51no—
84#4936—51no—
85C4×C4⋊Dic3—51no—
86#4932—51no—
87C23×C4×C5C2×D311yescharacteristic
88C23×Dic5—32no—
89C5×#117Dic318yescomplemented
90C2×C5×C4⋊C4C2×D311yescharacteristic
91C2×C5×C4⋊C4C2×D311yescharacteristic
92C2×C5×C22⋊C4C2×D311yescharacteristic
93C2×C5×C22⋊C4C2×D311yescharacteristic
94C2×C42×C5C2×D311yescharacteristic
95C2×C42×C5C2×D311yescharacteristic
96C2×C22⋊Dic5—32no—
97C2×C4⋊Dic5—32no—
98C2×C4⋊Dic5—32no—
99C2×C4×Dic5—32no—
100C2×C4×Dic5—32no—
101#3963—31no—
102#3963—31no—
103#3963—32no—
104#3963—31no—
105#3963—31no—
106#3963—32no—
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—21no—
124C2×C3×C4×C5—21no—
125C2×C3×C4×C5—21no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5C22×C412yes—
128C2×C3×C4×C5C22×C412yes—
129C2×C3×C4×C5C22×C412yes—
130C2×C3×C4×C5C22×C412yes—
131C2×C3×C4×C5C22×C412yes—
132C2×C3×C4×C5C22×C412yes—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—48no—
145C2×Dic15#4114yes—
146C23×C3×C4C2×D511yescharacteristic
147C23×Dic3—52no—
148C3×#117Dic518yescomplemented
149C2×C3×C4⋊C4C2×D511yescharacteristic
150C2×C3×C4⋊C4C2×D511yescharacteristic
151C2×C3×C22⋊C4C2×D511yescharacteristic
152C2×C3×C22⋊C4C2×D511yescharacteristic
153C2×C3×C42C2×D511yescharacteristic
154C2×C3×C42C2×D511yescharacteristic
155C2×#217—52no—
156C2×C4⋊Dic3—52no—
157C2×C4⋊Dic3—52no—
158C2×C4×Dic3—52no—
159C2×C4×Dic3—52no—
160C3⋊#95—51no—
161C3⋊#95—51no—
162C3⋊#95—52no—
163C3⋊#95—51no—
164C3⋊#95—51no—
165C3⋊#95—52no—
166C3⋊#95—52no—
167C3⋊#95—52no—
168C3⋊#95—52no—
169C3⋊#95—52no—
170C24×C5C22×D311yescharacteristic
171C22×C4×C5—24no—
172C22×C4×C5C2×Dic314yes—
173C22×C4×C5C22×D311yescharacteristic
174C22×C4×C5C22×D311yescharacteristic
175C22×C4×C5C22×D311yescharacteristic
176C22×C4×C5C22×D311yescharacteristic
177C22×C4×C5C22×D311yescharacteristic
178C22×C4×C5C22×D311yescharacteristic
179C22×Dic5—32no—
180C22×Dic5—32no—
181C22×Dic5—32no—
182C22×Dic5—32no—
183C22×Dic5—64no—
184C22×Dic5—64no—
185C22×Dic5—122no—
186C5×C4⋊C4C2×Dic314yescomplemented
187C5×C4⋊C4C2×Dic314yescomplemented
188C5×C22⋊C4C2×Dic314yes—
189C5×C22⋊C4C2×Dic314yes—
190C42×C5C2×Dic314yescomplemented
191C42×C5C2×Dic314yescomplemented
192C22⋊Dic5—64no—
193C4⋊Dic5—64no—
194C4⋊Dic5—122no—
195C4×Dic5—64no—
196C4×Dic5—122no—
197C2×#117D1511yescharacteristic
198#387—152no—
199#387—152no—
200#385—152no—
201#383—151no—
202#382—151no—
203#381—151no—
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—22no—
221C3×C4×C5—22no—
222C3×C4×C5—22no—
223C3×C4×C5—22no—
224Dic15—24no—
225Dic15—42no—
226Dic15—42no—
227Dic15—42no—
228C24×C3C22×D511yescharacteristic
229C22×C3×C4—24no—
230C22×C3×C4C2×Dic514yes—
231C22×C3×C4C22×D511yescharacteristic
232C22×C3×C4C22×D511yescharacteristic
233C22×C3×C4C22×D511yescharacteristic
234C22×C3×C4C22×D511yescharacteristic
235C22×C3×C4C22×D511yescharacteristic
236C22×C3×C4C22×D511yescharacteristic
237C22×Dic3—52no—
238C22×Dic3—52no—
239C22×Dic3—52no—
240C22×Dic3—52no—
241C22×Dic3—104no—
242C22×Dic3—104no—
243C22×Dic3—202no—
244C3×C4⋊C4C2×Dic514yescomplemented
245C3×C4⋊C4C2×Dic514yescomplemented
246C3×C22⋊C4C2×Dic514yes—
247C3×C22⋊C4C2×Dic514yes—
248C3×C42C2×Dic514yescomplemented
249C3×C42C2×Dic514yescomplemented
250#217—104no—
251C4⋊Dic3—104no—
252C4⋊Dic3—202no—
253C4×Dic3—104no—
254C4×Dic3—202no—
255C23×C5—22no—
256C23×C5—21no—
257C23×C5—21no—
258C23×C5#23514yes—
259C23×C5C22×Dic312yes—
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—21no—
267C2×C4×C5—21no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5C22×Dic312yes—
271C2×C4×C5C22×Dic312yes—
272C2×C4×C5C22×Dic312yes—
273C2×C4×C5C22×Dic312yes—
274C2×C4×C5C22×Dic312yes—
275C2×C4×C5C22×Dic312yes—
276C2×Dic5—34no—
277C2×Dic5—62no—
278C2×Dic5—62no—
279C2×Dic5—62no—
280C2×Dic5—62no—
281C2×Dic5—62no—
282C2×Dic5—62no—
283C2×Dic5—62no—
284C2×Dic5—62no—
285C2×Dic5—62no—
286C2×Dic5—62no—
287C2×Dic5—62no—
288C2×Dic5—128no—
289C23×C4—152no—
290C23×C4C2×D1511yescharacteristic
291#117Dic1518yescomplemented
292C2×C4⋊C4—152no—
293C2×C4⋊C4—152no—
294C2×C4⋊C4C2×D1511yescharacteristic
295C2×C4⋊C4C2×D1511yescharacteristic
296C2×C22⋊C4—152no—
297C2×C22⋊C4C2×D1511yescharacteristic
298C2×C22⋊C4C2×D1511yescharacteristic
299C2×C42—152no—
300C2×C42—152no—
301C2×C42C2×D1511yescharacteristic
302C2×C42C2×D1511yescharacteristic
303#95—151no—
304#95—151no—
305#95—152no—
306#95—151no—
307#95—152no—
308#95—152no—
309#95—152no—
310#95—151no—
311#95—152no—
312#95—152no—
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×C3#70914yes—
323C23×C3C22×Dic512yes—
324C23×C3C23×D511yescharacteristic
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—28no—
334C2×C3×C4C22×Dic512yes—
335C2×C3×C4C22×Dic512yes—
336C2×C3×C4C22×Dic512yes—
337C2×C3×C4C22×Dic512yes—
338C2×C3×C4C22×Dic512yes—
339C2×C3×C4C22×Dic512yes—
340C2×Dic3—54no—
341C2×Dic3—102no—
342C2×Dic3—102no—
343C2×Dic3—102no—
344C2×Dic3—102no—
345C2×Dic3—102no—
346C2×Dic3—102no—
347C2×Dic3—102no—
348C2×Dic3—102no—
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#92614yes—
358C22×C5C2×#23512yes—
359C22×C5D3×#4112yes—
360C22×C5#100911yescharacteristic
361C22×C5#101011yescharacteristic
362C22×C5C23×Dic311yescharacteristic
363C4×C5—22no—
364C4×C5—22no—
365C4×C5—22no—
366C4×C5—22no—
367C4×C5—22no—
368C4×C5—22no—
369Dic5—64no—
370Dic5—122no—
371Dic5—122no—
372Dic5—122no—
373C24C22×D1511yescharacteristic
374C22×C4—24no—
375C22×C4—152no—
376C22×C4—152no—
377C22×C4—152no—
378C22×C4—152no—
379C22×C4—304no—
380C22×C4—304no—
381C22×C4—602no—
382C22×C4C2×Dic1514yes—
383C22×C4C22×D1511yescharacteristic
384C22×C4C22×D1511yescharacteristic
385C22×C4C22×D1511yescharacteristic
386C22×C4C22×D1511yescharacteristic
387C22×C4C22×D1511yescharacteristic
388C22×C4C22×D1511yescharacteristic
389C4⋊C4—304no—
390C4⋊C4—602no—
391C4⋊C4C2×Dic1514yescomplemented
392C4⋊C4C2×Dic1514yescomplemented
393C22⋊C4—304no—
394C22⋊C4C2×Dic1514yes—
395C22⋊C4C2×Dic1514yes—
396C42—304no—
397C42—602no—
398C42C2×Dic1514yescomplemented
399C42C2×Dic1514yescomplemented
400C3×C5#234311yescharacteristic, complemented, Hall
401C22×C3—24no—
402C22×C3—24no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3#407214yes—
406C22×C3C2×#70912yes—
407C22×C3D5×#4112yes—
408C22×C3#414911yescharacteristic
409C22×C3#415011yescharacteristic
410C22×C3C23×Dic511yescharacteristic
411C3×C4—22no—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—22no—
416C3×C4—22no—
417Dic3—104no—
418Dic3—202no—
419Dic3—202no—
420Dic3—202no—
421C2×C5—24no—
422C2×C5#552712yes—
423C2×C5#553112yes—
424C2×C5C2×#92611yescharacteristic
425C2×C5Dic3×#4111yescharacteristic
426C2×C5#582711yescharacteristic
427C23—22no—
428C23—21no—
429C23—21no—
430C23#681714yes—
431C23C22×Dic1512yes—
432C23C23×D1511yescharacteristic
433C2×C4—28no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—154no—
443C2×C4—302no—
444C2×C4—302no—
445C2×C4—302no—
446C2×C4—302no—
447C2×C4—302no—
448C2×C4—302no—
449C2×C4—302no—
450C2×C4—302no—
451C2×C4—302no—
452C2×C4—302no—
453C2×C4—302no—
454C2×C4—608no—
455C2×C4C22×Dic1512yes—
456C2×C4C22×Dic1512yes—
457C2×C4C22×Dic1512yes—
458C2×C4C22×Dic1512yes—
459C2×C4C22×Dic1512yes—
460C2×C4C22×Dic1512yes—
461C2×C3—24no—
462C2×C3#6586112yes—
463C2×C3#6586512yes—
464C2×C3C2×#407211yescharacteristic
465C2×C3#41×Dic511yescharacteristic
466C2×C3#6616111yescharacteristic
467C5#8223711yescharacteristic, complemented, Sylow
468C22—24no—
469C22—22no—
470C22—22no—
471C22—24no—
472C22#9181514yes—
473C22C2×#681712yes—
474C22#41×D1512yes—
475C22#9210011yescharacteristic
476C22#9210111yescharacteristic
477C22C23×Dic1511yescharacteristic
478C4—22no—
479C4—22no—
480C4—22no—
481C4—22no—
482C4—22no—
483C4—22no—
484C4—304no—
485C4—602no—
486C4—602no—
487C4—602no—
488C3#1061396811yescharacteristic, complemented, Sylow
489C2—24no—
490C2#1175628612yes—
491C2#1175629012yes—
492C2C2×#9181511yescharacteristic
493C2#41×Dic1511yescharacteristic
494C2#1175658611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×#117C2
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC2×#117D15
hypocenterC3×C5#2343
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
4. #11751081C2semidirect
5. #11751081C2semidirect
8. #11751038C2semidirect
9. #11751037C2semidirect
10. C4×C4⋊Dic15C2semidirect
11. #11751033C2semidirect
15. C3×C5×#117C4semidirect
65. C3×C5×C4⋊C4C2×C4semidirect
66. C3×C5×C4⋊C4C2×C4semidirect
69. C3×C42×C5C2×C4semidirect
70. C3×C42×C5C2×C4semidirect
89. C5×#117Dic3semidirect
148. C3×#117Dic5semidirect
186. C5×C4⋊C4C2×Dic3semidirect
187. C5×C4⋊C4C2×Dic3semidirect
190. C42×C5C2×Dic3semidirect
191. C42×C5C2×Dic3semidirect
244. C3×C4⋊C4C2×Dic5semidirect
245. C3×C4⋊C4C2×Dic5semidirect
248. C3×C42C2×Dic5semidirect
249. C3×C42C2×Dic5semidirect
291. #117Dic15semidirect
391. C4⋊C4C2×Dic15semidirect
392. C4⋊C4C2×Dic15semidirect
398. C42C2×Dic15semidirect
399. C42C2×Dic15semidirect
400. C3×C5#2343semidirect
467. C5#82237semidirect
488. C3#10613968semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1172
#117513122
C2×#911152
#117510812
#117510512
C22⋊C4×Dic152
#117510382
#117510372
C4×C4⋊Dic152
#117510332
#106139683
#822375