Finite Group Databasebeta

← #14320013

Subgroups — #14320013

Order 1920.

1248 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1200C211yesmaximal, characteristic
2D15×#95C211yesmaximal, characteristic
3C5×#4651C211yesmaximal, characteristic, complemented
4C3×#64940C211yesmaximal, characteristic, complemented
5#11748888C212yesmaximal
6#11748888C212yesmaximal
7#11748888C211yesmaximal, characteristic
8#11748647C212yesmaximal, complemented
9#11748646C212yesmaximal, complemented
10#11748618C211yesmaximal, characteristic, complemented
11#11748612C211yesmaximal, characteristic, complemented
12D5×#383—31nomaximal, Hall
13C22×C4×D15C2212yes—
14C22×C4×D15C2211yescharacteristic
15C22×#1200C2212yes—
16C22×#1200C2211yescharacteristic
17C22×#1200C2211yescharacteristic
18C2×C4×C5×Dic3C2211yescharacteristic
19C2×C3×C4×Dic5C2211yescharacteristic
20C2×Dic3×Dic5C2211yescharacteristic
21C2×Dic3×Dic5C2211yescharacteristic
22C4×#1200C418yescomplemented
23C3×C5×#95C2211yescharacteristic
24#91115C2211yescharacteristic
25#91115C2212yes—
26C5×C3⋊#95C2211yescharacteristic
27C5×C3⋊#95C2212yes—
28C5×C3⋊#95C2212yes—
29C3×#3963C2211yescharacteristic
30C3×#3963C2212yes—
31C3×#3963C2212yes—
32#90994C2212yes—
33#90994C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37D3×#383—51nomaximal, Hall
38C2×C42×D5—31no—
39C5×#383—31no—
40#65226—31no—
41D5×#95—31no—
42D5×#95—31no—
43D5×#95—32no—
44D5×#95—32no—
45#64940—31no—
46#64940—32no—
47#64940—32no—
48#64940D311yescharacteristic, complemented
49C23×D15C2311yescharacteristic
50C22×C3×C4×C5C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×Dic15C2312yes—
53C22×Dic15C2311yescharacteristic
54C2×C4×D15—24no—
55C2×C4×D15—24no—
56C2×C4×D15—24no—
57C2×C4×D15—24no—
58C2×C4×D15C2×C414yes—
59C22×C5×Dic3C2312yes—
60C22×C5×Dic3C2311yescharacteristic
61C22×C5×Dic3C2311yescharacteristic
62C22×C3×Dic5C2312yes—
63C22×C3×Dic5C2311yescharacteristic
64C22×C3×Dic5C2311yescharacteristic
65C2×#1200—22no—
66C2×#1200—24no—
67C2×#1200—22no—
68C2×#1200—24no—
69C2×#1200—24no—
70C2×#1200—24no—
71C2×#1200C2×C414yes—
72C2×#1200C2×C414yes—
73C4×C5×Dic3C2×C414yescomplemented
74C3×C4×Dic5C2×C414yescomplemented
75Dic3×Dic5C2×C414yescomplemented
76Dic3×Dic5C2×C414yescomplemented
77C2×C42×D3—51no—
78C3×#383—51no—
79#4937—51no—
80D3×#95—51no—
81D3×#95—51no—
82D3×#95—52no—
83D3×#95—52no—
84#4651—51no—
85#4651—52no—
86#4651—52no—
87#4651D511yescharacteristic, complemented
88C22×C4×D5—31no—
89C22×C4×D5—31no—
90C22×C4×D5—31no—
91C22×C4×D5—32no—
92C22×C4×D5—32no—
93C2×C42×C5—31no—
94C2×C4×Dic5—31no—
95C2×C4×Dic5—31no—
96C2×C4×Dic5C2×D311yescharacteristic
97C42×D5—38no—
98C5×#95—32no—
99C5×#95—32no—
100C5×#95—31no—
101C5×#95C2×D311yescharacteristic
102#3963—32no—
103#3963—31no—
104#3963—32no—
105#3963—32no—
106#3963—32no—
107#3963—32no—
108#3963—32no—
109#3963C2×D312yes—
110#3963C2×D312yes—
111#3963C2×D311yescharacteristic
112C2×#383—151noSylow
113C23×C3×C5C2411yescharacteristic
114C22×D15C22×C412yes—
115C22×D15#4112yes—
116C22×D15#4114yes—
117C22×D15#4112yes—
118C22×D15#4114yes—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5C22×C412yes—
124C2×Dic15—22no—
125C2×Dic15—22no—
126C2×Dic15—22no—
127C2×Dic15—22no—
128C2×Dic15C22×C412yes—
129C4×D15—28no—
130C4×D15—48no—
131C2×C5×Dic3—21no—
132C2×C5×Dic3—22no—
133C2×C5×Dic3—21no—
134C2×C5×Dic3—22no—
135C2×C5×Dic3—22no—
136C2×C5×Dic3—22no—
137C2×C5×Dic3C22×C412yes—
138C2×C5×Dic3C22×C412yes—
139C2×C3×Dic5—21no—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—21no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5C22×C412yes—
146C2×C3×Dic5C22×C412yes—
147#1200—28no—
148#1200—28no—
149#1200—48no—
150C22×C4×D3—51no—
151C22×C4×D3—51no—
152C22×C4×D3—51no—
153C22×C4×D3—52no—
154C22×C4×D3—52no—
155C2×C3×C42—51no—
156C2×C4×Dic3—51no—
157C2×C4×Dic3—51no—
158C2×C4×Dic3C2×D511yescharacteristic
159C42×D3—58no—
160C3×#95—52no—
161C3×#95—52no—
162C3×#95—51no—
163C3×#95C2×D511yescharacteristic
164C3⋊#95—52no—
165C3⋊#95—51no—
166C3⋊#95—52no—
167C3⋊#95—52no—
168C3⋊#95—52no—
169C3⋊#95—52no—
170C3⋊#95—52no—
171C3⋊#95C2×D512yes—
172C3⋊#95C2×D512yes—
173C3⋊#95C2×D511yescharacteristic
174C23×D5—31no—
175C22×C4×C5—31no—
176C22×C4×C5—31no—
177C22×C4×C5—32no—
178C22×C4×C5C22×D312yes—
179C22×C4×C5C22×D311yescharacteristic
180C22×Dic5—31no—
181C22×Dic5—32no—
182C22×Dic5C22×D312yes—
183C22×Dic5C22×D311yescharacteristic
184C22×Dic5C22×D311yescharacteristic
185C2×C4×D5—34no—
186C2×C4×D5—34no—
187C2×C4×D5—34no—
188C2×C4×D5—64no—
189C2×C4×D5—62no—
190C2×C4×D5—62no—
191C2×C4×D5—64no—
192C2×C4×D5—64no—
193C2×C4×D5—64no—
194C2×C4×D5—64no—
195C2×C4×D5—64no—
196C2×C4×D5—64no—
197C2×C4×D5—64no—
198C42×C5—34no—
199C4×Dic5—34no—
200C4×Dic5—34no—
201C4×Dic5C4×D314yescomplemented
202C22×C42—151no—
203#383—31no—
204#383—51no—
205#383—152no—
206#383—152no—
207#383—151no—
208#383—151no—
209C2×#95—152no—
210C2×#95—152no—
211C2×#95—151no—
212C2×#95—151no—
213C22×C3×C5C23×C411yescharacteristic
214C22×C3×C5C2×#4111yescharacteristic
215C22×C3×C5C2×#4112yes—
216C22×C3×C5C2×#4111yescharacteristic
217C22×C3×C5C2×#4112yes—
218C2×D15#11714yes—
219C2×D15#11714yes—
220C2×D15#11714yes—
221C2×D15#12618yes—
222C2×D15#12618yes—
223C3×C4×C5—22no—
224C3×C4×C5—42no—
225Dic15—22no—
226Dic15—42no—
227C3×Dic5—22no—
228C3×Dic5—22no—
229C3×Dic5—42no—
230C5×Dic3—22no—
231C5×Dic3—22no—
232C5×Dic3—42no—
233C23×D3—51no—
234C22×C3×C4—51no—
235C22×C3×C4—51no—
236C22×C3×C4—52no—
237C22×C3×C4C22×D512yes—
238C22×C3×C4C22×D511yescharacteristic
239C22×Dic3—51no—
240C22×Dic3—52no—
241C22×Dic3C22×D512yes—
242C22×Dic3C22×D511yescharacteristic
243C22×Dic3C22×D511yescharacteristic
244C2×C4×D3—54no—
245C2×C4×D3—54no—
246C2×C4×D3—54no—
247C2×C4×D3—104no—
248C2×C4×D3—102no—
249C2×C4×D3—102no—
250C2×C4×D3—104no—
251C2×C4×D3—104no—
252C2×C4×D3—104no—
253C2×C4×D3—104no—
254C2×C4×D3—104no—
255C2×C4×D3—104no—
256C2×C4×D3—104no—
257C3×C42—54no—
258C4×Dic3—54no—
259C4×Dic3—54no—
260C4×Dic3C4×D514yescomplemented
261C23×C5C23×D311yescharacteristic
262C22×D5—32no—
263C22×D5—34no—
264C22×D5—32no—
265C22×D5—34no—
266C22×D5—32no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—32no—
272C2×C4×C5—32no—
273C2×C4×C5—62no—
274C2×C4×C5—61no—
275C2×C4×C5—61no—
276C2×C4×C5—62no—
277C2×C4×C5—62no—
278C2×C4×C5—62no—
279C2×C4×C5C2×C4×D312yes—
280C2×Dic5—22no—
281C2×Dic5—21no—
282C2×Dic5—21no—
283C2×Dic5—22no—
284C2×Dic5—22no—
285C2×Dic5—22no—
286C2×Dic5—32no—
287C2×Dic5—62no—
288C2×Dic5—62no—
289C2×Dic5—62no—
290C2×Dic5—62no—
291C2×Dic5C2×C4×D312yes—
292C2×Dic5C2×C4×D312yes—
293C4×D5—68no—
294C4×D5—68no—
295C4×D5—68no—
296C4×D5—128no—
297C4×D5—128no—
298C23×C4—151no—
299C23×C4—151no—
300C23×C4—152no—
301C23×C4—151no—
302C23×C4—152no—
303C2×C42—31no—
304C2×C42—51no—
305C2×C42—158no—
306C2×C42—151no—
307C2×C42—151no—
308#95—32no—
309#95—32no—
310#95—31no—
311#95—52no—
312#95—52no—
313#95—51no—
314#95—152no—
315#95—152no—
316#95—152no—
317#95—152no—
318#95—152no—
319#95—152no—
320#95—151no—
321#95D3×D511yescharacteristic
322C2×C3×C5C2×#11711yescharacteristic
323C2×C3×C5C2×#11711yescharacteristic
324C2×C3×C5C2×#11711yescharacteristic
325C2×C3×C5C2×#12612yes—
326C2×C3×C5C2×#12612yes—
327D15#38318yescomplemented
328C23×C3C23×D511yescharacteristic
329C22×D3—52no—
330C22×D3—54no—
331C22×D3—52no—
332C22×D3—54no—
333C22×D3—52no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—52no—
339C2×C3×C4—52no—
340C2×C3×C4—102no—
341C2×C3×C4—101no—
342C2×C3×C4—101no—
343C2×C3×C4—102no—
344C2×C3×C4—102no—
345C2×C3×C4—102no—
346C2×C3×C4C2×C4×D512yes—
347C2×Dic3—22no—
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—52no—
354C2×Dic3—102no—
355C2×Dic3—102no—
356C2×Dic3—102no—
357C2×Dic3—102no—
358C2×Dic3C2×C4×D512yes—
359C2×Dic3C2×C4×D512yes—
360C4×D3—108no—
361C4×D3—108no—
362C4×D3—108no—
363C4×D3—208no—
364C4×D3—208no—
365C22×C5C22×C4×D311yescharacteristic
366C22×C5D3×#4112yes—
367C22×C5D3×#4111yescharacteristic
368C22×C5D3×#4112yes—
369C22×C5D3×#4111yescharacteristic
370C2×D5—38no—
371C2×D5—38no—
372C2×D5—34no—
373C2×D5—34no—
374C2×D5—34no—
375C4×C5—22no—
376C4×C5—42no—
377C4×C5—62no—
378C4×C5—62no—
379C4×C5—122no—
380Dic5—22no—
381Dic5—22no—
382Dic5—42no—
383Dic5—62no—
384Dic5—122no—
385C24—151no—
386C22×C4—31no—
387C22×C4—31no—
388C22×C4—32no—
389C22×C4—51no—
390C22×C4—51no—
391C22×C4—52no—
392C22×C4—154no—
393C22×C4—154no—
394C22×C4—151no—
395C22×C4—154no—
396C22×C4—152no—
397C22×C4—304no—
398C22×C4—304no—
399C22×C4—304no—
400C22×C4—304no—
401C22×C4—304no—
402C22×C4—302no—
403C22×C4—302no—
404C22×C4—304no—
405C22×C4—304no—
406C22×C4—304no—
407C22×C4C2×D3×D512yes—
408C22×C4C2×D3×D511yescharacteristic
409C42—34no—
410C42—54no—
411C42—154no—
412C42—154no—
413C3×C5C2×#38311yescharacteristic, complemented, Hall
414C22×C3C22×C4×D511yescharacteristic
415C22×C3D5×#4112yes—
416C22×C3D5×#4111yescharacteristic
417C22×C3D5×#4112yes—
418C22×C3D5×#4111yescharacteristic
419C2×D3—54no—
420C2×D3—54no—
421C2×D3—54no—
422C2×D3—58no—
423C2×D3—58no—
424C3×C4—22no—
425C3×C4—42no—
426C3×C4—102no—
427C3×C4—102no—
428C3×C4—202no—
429Dic3—22no—
430Dic3—22no—
431Dic3—42no—
432Dic3—102no—
433Dic3—202no—
434C2×C5D3×#11711yescharacteristic
435C2×C5D3×#11711yescharacteristic
436C2×C5D3×#11711yescharacteristic
437C2×C5D3×#12612yes—
438C2×C5D3×#12612yes—
439D5—38no—
440C23—152no—
441C23—154no—
442C23—152no—
443C23—154no—
444C23—152no—
445C23C22×D3×D511yescharacteristic
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—32no—
451C2×C4—32no—
452C2×C4—52no—
453C2×C4—52no—
454C2×C4—62no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—102no—
461C2×C4—101no—
462C2×C4—101no—
463C2×C4—102no—
464C2×C4—102no—
465C2×C4—102no—
466C2×C4—152no—
467C2×C4—308no—
468C2×C4—308no—
469C2×C4—308no—
470C2×C4—302no—
471C2×C4—302no—
472C2×C4—302no—
473C2×C4—302no—
474C2×C4—608no—
475C2×C4—608no—
476C2×C4C4×D3×D512yes—
477C2×C3D5×#11711yescharacteristic
478C2×C3D5×#11711yescharacteristic
479C2×C3D5×#11711yescharacteristic
480C2×C3D5×#12612yes—
481C2×C3D5×#12612yes—
482D3—58no—
483C5D3×#38311yescharacteristic, complemented, Sylow
484C22—154no—
485C22—158no—
486C22—154no—
487C22—154no—
488C22—158no—
489C22C2×C4×D3×D511yescharacteristic
490C22#9201612yes—
491C22#9202411yescharacteristic
492C22#9202412yes—
493C22#9203411yescharacteristic
494C4—22no—
495C4—42no—
496C4—62no—
497C4—62no—
498C4—102no—
499C4—102no—
500C4—122no—
501C4—202no—
502C4—302no—
503C4—602no—
504C3D5×#38311yescharacteristic, complemented, Sylow
505C2—158no—
506C2#1175272311yescharacteristic
507C2#1175282511yescharacteristic
508C2#1175301712yes—
509C2#1175383511yescharacteristic
510C2#1175393112yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenter#95D3×D5
hypocenterC3×C5C2×#383
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C5×#4651C2semidirect
4. C3×#64940C2semidirect
8. #11748647C2semidirect
9. #11748646C2semidirect
10. #11748618C2semidirect
11. #11748612C2semidirect
22. C4×#1200C4semidirect
48. #64940D3semidirect
73. C4×C5×Dic3C2×C4semidirect
74. C3×C4×Dic5C2×C4semidirect
75. Dic3×Dic5C2×C4semidirect
76. Dic3×Dic5C2×C4semidirect
87. #4651D5semidirect
201. C4×Dic5C4×D3semidirect
260. C4×Dic3C4×D5semidirect
327. D15#383semidirect
413. C3×C5C2×#383semidirect
483. C5D3×#383semidirect
504. C3D5×#383semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12002
D15×#952
C5×#46512
C3×#649402
#117488882
#117486472
#117486462
#117486182
#117486122
D5×#3833
D3×#3835