Finite Group Databasebeta

← #14319916

Subgroups — #14319916

Order 1920.

2176 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D15C211yesmaximal, characteristic
2C2×#91781C212yesmaximal, complemented
3C3×C5×#380C211yesmaximal, characteristic, complemented
4#11751313C211yesmaximal, characteristic, complemented
5#11751088C212yesmaximal, complemented
6#11751056C212yesmaximal
7C22⋊C4×Dic15C212yesmaximal, complemented
8#11750767C212yesmaximal, complemented
9#11750765C212yesmaximal, complemented
10#10605593—31nomaximal, Hall
11C24×D15C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C22×C4×D15—28no—
15C22×C4×D15C418yescomplemented
16C22×C4×D15C2211yescharacteristic
17C22×C4×D15C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2212yescomplemented
21C2×C3×C5×C22⋊C4C2212yes—
22C2×#6719C2212yes—
23C2×#6714C2214yes—
24C2×#6714C2214yes—
25C2×C4⋊Dic15C2212yescomplemented
26C2×C4×Dic15C2214yescomplemented
27#91781—28no—
28C3×C5×#95C2212yescomplemented
29#91115C2212yescomplemented
30#91115C2214yescomplemented
31#73862—51nomaximal, Hall
32C23×C4×D5—31no—
33C2×#4038—32no—
34C5×#380D311yescharacteristic, complemented
35#65501—31no—
36#65276—32no—
37#65244—32no—
38C22⋊C4×Dic5—32no—
39#64955—32no—
40#64953—32no—
41C24×C3×C5C2311yescharacteristic
42C23×D15—22no—
43C23×D15—22no—
44C23×D15—24no—
45C23×D15—24no—
46C23×D15C2×C414yes—
47C23×D15C2311yescharacteristic
48C23×D15C2311yescharacteristic
49C22×C3×C4×C5—24no—
50C22×C3×C4×C5C2×C414yes—
51C22×C3×C4×C5C2314yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15—24no—
55C22×Dic15C2×C414yes—
56C22×Dic15C2314yes—
57C22×Dic15C2311yescharacteristic
58C22×Dic15C2311yescharacteristic
59C2×C4×D15—24no—
60C2×C4×D15—24no—
61C2×C4×D15—24no—
62C2×C4×D15—232no—
63C2×C4×D15C2×C414yes—
64C2×C4×D15C2×C414yes—
65C2×C4×D15C2×C414yes—
66C2×C4×D15C2×C414yes—
67C2×C4×D15D418yes—
68C3×C5×C4⋊C4—24no—
69C3×C5×C22⋊C4—24no—
70#6719—24no—
71#6714—28no—
72#6714—28no—
73C4⋊Dic15—24no—
74C4×Dic15—28no—
75C23×C4×D3—51no—
76C2×#892—52no—
77C3×#380D511yescharacteristic, complemented
78#5212—51no—
79#4987—52no—
80#4955—52no—
81Dic3×C22⋊C4—52no—
82#4666—52no—
83#4664—52no—
84C24×D5—31no—
85C23×C4×C5C2×D311yescharacteristic
86C23×Dic5—31no—
87C22×C4×D5—31no—
88C22×C4×D5—38no—
89C22×C4×D5—31no—
90C22×C4×D5—31no—
91C22×C4×D5—31no—
92C22×C4×D5—68no—
93C2×C5×C4⋊C4C2×D312yescomplemented
94C2×C5×C22⋊C4C2×D312yes—
95C2×C22⋊Dic5—32no—
96C2×#685—34no—
97C2×#685—34no—
98C2×C4⋊Dic5—32no—
99C2×C4×Dic5—34no—
100#4038—68no—
101C5×#95C2×D312yescomplemented
102#3963—32no—
103#3963—34no—
104#2280—151noSylow
105C23×C3×C5—22no—
106C23×C3×C5—22no—
107C23×C3×C5C22×C412yes—
108C23×C3×C5#4112yes—
109C23×C3×C5#4112yes—
110C23×C3×C5C2411yescharacteristic
111C22×D15—216no—
112C22×D15—216no—
113C22×D15—28no—
114C22×D15—22no—
115C22×D15—21no—
116C22×D15—21no—
117C22×D15—22no—
118C22×D15—21no—
119C22×D15—21no—
120C22×D15—28no—
121C22×D15—28no—
122C22×D15C22×C412yes—
123C22×D15C22×C412yes—
124C22×D15C2×D414yes—
125C22×D15#4114yes—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—28no—
128C2×C3×C4×C5—24no—
129C2×C3×C4×C5—24no—
130C2×C3×C4×C5—24no—
131C2×C3×C4×C5C22×C412yes—
132C2×C3×C4×C5C22×C412yes—
133C2×C3×C4×C5C2×D414yes—
134C2×Dic15—22no—
135C2×Dic15—28no—
136C2×Dic15—24no—
137C2×Dic15—24no—
138C2×Dic15—24no—
139C2×Dic15C22×C412yes—
140C2×Dic15C22×C412yes—
141C2×Dic15C2×D414yes—
142C4×D15—28no—
143C4×D15—28no—
144C4×D15—28no—
145C4×D15C22⋊C4116yescomplemented
146C24×D3—51no—
147C23×C3×C4C2×D511yescharacteristic
148C23×Dic3—51no—
149C22×C4×D3—51no—
150C22×C4×D3—58no—
151C22×C4×D3—51no—
152C22×C4×D3—51no—
153C22×C4×D3—51no—
154C22×C4×D3—108no—
155C2×C3×C4⋊C4C2×D512yescomplemented
156C2×C3×C22⋊C4C2×D512yes—
157C2×#217—52no—
158C2×(C2×D3)⋊C4—54no—
159C2×(C2×D3)⋊C4—54no—
160C2×C4⋊Dic3—52no—
161C2×C4×Dic3—54no—
162#892—108no—
163C3×#95C2×D512yescomplemented
164C3⋊#95—52no—
165C3⋊#95—54no—
166C24×C5C22×D311yescharacteristic
167C23×D5—31no—
168C23×D5—31no—
169C23×D5—34no—
170C23×D5—64no—
171C23×D5—64no—
172C23×D5—62no—
173C23×D5—62no—
174C22×C4×C5—24no—
175C22×C4×C5C4×D314yes—
176C22×C4×C5C22×D314yes—
177C22×C4×C5C22×D311yescharacteristic
178C22×C4×C5C22×D311yescharacteristic
179C22×Dic5—31no—
180C22×Dic5—34no—
181C22×Dic5—31no—
182C22×Dic5—34no—
183C22×Dic5—64no—
184C2×C4×D5—34no—
185C2×C4×D5—38no—
186C2×C4×D5—34no—
187C2×C4×D5—34no—
188C2×C4×D5—34no—
189C2×C4×D5—632no—
190C2×C4×D5—64no—
191C2×C4×D5—64no—
192C2×C4×D5—64no—
193C5×C4⋊C4—24no—
194C5×C22⋊C4—24no—
195C22⋊Dic5—64no—
196#685—68no—
197#685—68no—
198C4⋊Dic5—64no—
199C4×Dic5—68no—
200C24×C4—151no—
201C2×#117—152no—
202#381—152no—
203#380—151no—
204#380—152no—
205#380D1511yescharacteristic, complemented
206#379—152no—
207C4×C22⋊C4—152no—
208C4×C22⋊C4—152no—
209C22×C3×C5—22no—
210C22×C3×C5—22no—
211C22×C3×C5—24no—
212C22×C3×C5—24no—
213C22×C3×C5#11714yescomplemented
214C22×C3×C5C23×C411yescharacteristic
215C22×C3×C5C22×D412yes—
216C22×C3×C5C2×#4111yescharacteristic
217C22×C3×C5C2×#4111yescharacteristic
218C22×C3×C5C2×#4112yes—
219C2×D15—232no—
220C2×D15—22no—
221C2×D15—22no—
222C2×D15—22no—
223C2×D15—22no—
224C2×D15—24no—
225C2×D15—24no—
226C2×D15—24no—
227C2×D15—24no—
228C2×D15C2×C22⋊C414yes—
229C2×D15#11714yescomplemented
230C3×C4×C5—22no—
231C3×C4×C5—44no—
232C3×C4×C5C2×C22⋊C414yes—
233Dic15—22no—
234Dic15—44no—
235Dic15C2×C22⋊C414yes—
236C24×C3C22×D511yescharacteristic
237C23×D3—51no—
238C23×D3—51no—
239C23×D3—54no—
240C23×D3—104no—
241C23×D3—104no—
242C23×D3—102no—
243C23×D3—102no—
244C22×C3×C4—24no—
245C22×C3×C4C4×D514yes—
246C22×C3×C4C22×D514yes—
247C22×C3×C4C22×D511yescharacteristic
248C22×C3×C4C22×D511yescharacteristic
249C22×Dic3—51no—
250C22×Dic3—54no—
251C22×Dic3—51no—
252C22×Dic3—54no—
253C22×Dic3—104no—
254C2×C4×D3—54no—
255C2×C4×D3—58no—
256C2×C4×D3—54no—
257C2×C4×D3—54no—
258C2×C4×D3—54no—
259C2×C4×D3—1032no—
260C2×C4×D3—104no—
261C2×C4×D3—104no—
262C2×C4×D3—104no—
263C3×C4⋊C4—24no—
264C3×C22⋊C4—24no—
265#217—104no—
266(C2×D3)⋊C4—108no—
267(C2×D3)⋊C4—108no—
268C4⋊Dic3—104no—
269C4×Dic3—108no—
270C23×C5—22no—
271C23×C5—22no—
272C23×C5C2×C4×D312yes—
273C23×C5#23712yes—
274C23×C5#23912yes—
275C23×C5C23×D311yescharacteristic
276C22×D5—32no—
277C22×D5—32no—
278C22×D5—34no—
279C22×D5—34no—
280C22×D5—68no—
281C22×D5—68no—
282C22×D5—616no—
283C22×D5—616no—
284C22×D5—68no—
285C22×D5—62no—
286C22×D5—61no—
287C22×D5—61no—
288C22×D5—61no—
289C22×D5—61no—
290C22×D5—62no—
291C2×C4×C5—22no—
292C2×C4×C5—28no—
293C2×C4×C5—24no—
294C2×C4×C5—24no—
295C2×C4×C5—24no—
296C2×C4×C5C2×C4×D312yes—
297C2×C4×C5C2×C4×D312yes—
298C2×C4×C5D3×D414yes—
299C2×Dic5—32no—
300C2×Dic5—34no—
301C2×Dic5—32no—
302C2×Dic5—68no—
303C2×Dic5—62no—
304C2×Dic5—64no—
305C2×Dic5—64no—
306C2×Dic5—64no—
307C4×D5—316no—
308C4×D5—68no—
309C4×D5—68no—
310C4×D5—68no—
311C25—151no—
312C23×C4—151no—
313C23×C4—151no—
314C23×C4—158no—
315C23×C4—151no—
316C23×C4—151no—
317C23×C4—151no—
318C23×C4—308no—
319C23×C4C2×D1511yescharacteristic
320#117—308no—
321C2×C4⋊C4—152no—
322C2×C4⋊C4C2×D1512yescomplemented
323C2×C22⋊C4—152no—
324C2×C22⋊C4—154no—
325C2×C22⋊C4—154no—
326C2×C22⋊C4C2×D1512yes—
327C2×C42—154no—
328#95—154no—
329#95—152no—
330#95C2×D1512yescomplemented
331C2×C3×C5—24no—
332C2×C3×C5C22×C22⋊C411yescharacteristic
333C2×C3×C5C2×#11711yescharacteristic
334C2×C3×C5C2×#11711yescharacteristic
335C2×C3×C5#52512yes—
336C2×C3×C5#52512yes—
337D15—24no—
338D15—24no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3C2×C4×D512yes—
342C23×C3#71112yes—
343C23×C3#71312yes—
344C23×C3C23×D511yescharacteristic
345C22×D3—52no—
346C22×D3—52no—
347C22×D3—54no—
348C22×D3—54no—
349C22×D3—108no—
350C22×D3—108no—
351C22×D3—1016no—
352C22×D3—1016no—
353C22×D3—102no—
354C22×D3—101no—
355C22×D3—101no—
356C22×D3—101no—
357C22×D3—101no—
358C22×D3—102no—
359C22×D3—108no—
360C2×C3×C4—22no—
361C2×C3×C4—28no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4C2×C4×D512yes—
366C2×C3×C4C2×C4×D512yes—
367C2×C3×C4D4×D514yes—
368C2×Dic3—52no—
369C2×Dic3—54no—
370C2×Dic3—52no—
371C2×Dic3—108no—
372C2×Dic3—102no—
373C2×Dic3—104no—
374C2×Dic3—104no—
375C2×Dic3—104no—
376C4×D3—516no—
377C4×D3—108no—
378C4×D3—108no—
379C4×D3—108no—
380C22×C5—22no—
381C22×C5—22no—
382C22×C5—24no—
383C22×C5—24no—
384C22×C5#89214yescomplemented
385C22×C5C22×C4×D311yescharacteristic
386C22×C5C2×D3×D412yes—
387C22×C5C2×#23711yescharacteristic
388C22×C5C2×#23911yescharacteristic
389C22×C5D3×#4112yes—
390C2×D5—34no—
391C2×D5—34no—
392C2×D5—632no—
393C2×D5—62no—
394C2×D5—62no—
395C2×D5—62no—
396C2×D5—62no—
397C2×D5—64no—
398C2×D5—64no—
399C2×D5—64no—
400C2×D5—64no—
401C4×C5—22no—
402C4×C5—44no—
403C4×C5D3×C22⋊C414yes—
404Dic5—34no—
405Dic5—62no—
406Dic5—124no—
407C24—151no—
408C24—151no—
409C24—154no—
410C24—304no—
411C24—304no—
412C24—302no—
413C24—302no—
414C24C22×D1511yescharacteristic
415C22×C4—24no—
416C22×C4—151no—
417C22×C4—154no—
418C22×C4—158no—
419C22×C4—154no—
420C22×C4—151no—
421C22×C4—154no—
422C22×C4—154no—
423C22×C4—154no—
424C22×C4—154no—
425C22×C4—304no—
426C22×C4—3032no—
427C22×C4—304no—
428C22×C4—304no—
429C22×C4—304no—
430C22×C4C4×D1514yes—
431C22×C4C22×D1514yes—
432C22×C4C22×D1511yescharacteristic
433C22×C4C22×D1511yescharacteristic
434C4⋊C4—24no—
435C4⋊C4—304no—
436C22⋊C4—24no—
437C22⋊C4—308no—
438C22⋊C4—308no—
439C22⋊C4—304no—
440C42—308no—
441C3×C5#228011yescharacteristic, complemented, Hall
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—24no—
445C22×C3—24no—
446C22×C3#403814yescomplemented
447C22×C3C22×C4×D511yescharacteristic
448C22×C3C2×D4×D512yes—
449C22×C3C2×#71111yescharacteristic
450C22×C3C2×#71311yescharacteristic
451C22×C3D5×#4112yes—
452C2×D3—54no—
453C2×D3—54no—
454C2×D3—1032no—
455C2×D3—102no—
456C2×D3—102no—
457C2×D3—102no—
458C2×D3—102no—
459C2×D3—104no—
460C2×D3—104no—
461C2×D3—104no—
462C2×D3—104no—
463C3×C4—22no—
464C3×C4—44no—
465C3×C4D5×C22⋊C414yes—
466Dic3—54no—
467Dic3—102no—
468Dic3—204no—
469C2×C5—24no—
470C2×C5C2×D3×C22⋊C411yescharacteristic
471C2×C5C2×#89211yescharacteristic
472C2×C5D3×#11711yescharacteristic
473C2×C5#560612yes—
474C2×C5#562712yes—
475D5—64no—
476D5—64no—
477C23—22no—
478C23—22no—
479C23—152no—
480C23—152no—
481C23—154no—
482C23—154no—
483C23—308no—
484C23—308no—
485C23—3016no—
486C23—3016no—
487C23—308no—
488C23—302no—
489C23—301no—
490C23—301no—
491C23—301no—
492C23—301no—
493C23—302no—
494C23C2×C4×D1512yes—
495C23#681912yes—
496C23#682112yes—
497C23C23×D1511yescharacteristic
498C2×C4—22no—
499C2×C4—28no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—152no—
504C2×C4—154no—
505C2×C4—1516no—
506C2×C4—152no—
507C2×C4—308no—
508C2×C4—308no—
509C2×C4—308no—
510C2×C4—302no—
511C2×C4—308no—
512C2×C4—304no—
513C2×C4—304no—
514C2×C4—304no—
515C2×C4C2×C4×D1512yes—
516C2×C4C2×C4×D1512yes—
517C2×C4D4×D1514yes—
518C2×C3—24no—
519C2×C3C2×D5×C22⋊C411yescharacteristic
520C2×C3C2×#403811yescharacteristic
521C2×C3D5×#11711yescharacteristic
522C2×C3#6594012yes—
523C2×C3#6596112yes—
524D3—104no—
525D3—104no—
526C5#7386211yescharacteristic, complemented, Sylow
527C22—24no—
528C22—24no—
529C22—22no—
530C22—22no—
531C22—154no—
532C22—154no—
533C22—3032no—
534C22—304no—
535C22—304no—
536C22—304no—
537C22—304no—
538C22—302no—
539C22—302no—
540C22—302no—
541C22—302no—
542C22#9178114yescomplemented
543C22C22×C4×D1511yescharacteristic
544C22C2×D4×D1512yes—
545C22C2×#681911yescharacteristic
546C22C2×#682111yescharacteristic
547C22#41×D1512yes—
548C4—22no—
549C4—44no—
550C4—154no—
551C4—302no—
552C4—604no—
553C4C22⋊C4×D1514yes—
554C3#1060559311yescharacteristic, complemented, Sylow
555C2—24no—
556C2—304no—
557C2—304no—
558C2C2×C22⋊C4×D1511yescharacteristic
559C2C2×#9178111yescharacteristic
560C2D15×#11711yescharacteristic
561C2#1175636512yes—
562C2#1175638612yes—
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#380C2
socle, cosocleC23×C3×C5C24
prime radicalC24×D15C22
hypercenter#380D15
hypocenterC3×C5#2280
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#91781C2semidirect
3. C3×C5×#380C2semidirect
4. #11751313C2semidirect
5. #11751088C2semidirect
7. C22⋊C4×Dic15C2semidirect
8. #11750767C2semidirect
9. #11750765C2semidirect
15. C22×C4×D15C4semidirect
20. C2×C3×C5×C4⋊C4C22semidirect
25. C2×C4⋊Dic15C22semidirect
26. C2×C4×Dic15C22semidirect
28. C3×C5×#95C22semidirect
29. #91115C22semidirect
30. #91115C22semidirect
34. C5×#380D3semidirect
77. C3×#380D5semidirect
93. C2×C5×C4⋊C4C2×D3semidirect
101. C5×#95C2×D3semidirect
145. C4×D15C22⋊C4semidirect
155. C2×C3×C4⋊C4C2×D5semidirect
163. C3×#95C2×D5semidirect
205. #380D15semidirect
213. C22×C3×C5#117semidirect
229. C2×D15#117semidirect
322. C2×C4⋊C4C2×D15semidirect
330. #95C2×D15semidirect
384. C22×C5#892semidirect
441. C3×C5#2280semidirect
446. C22×C3#4038semidirect
526. C5#73862semidirect
542. C22#91781semidirect
554. C3#10605593semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D152
C2×#917812
C3×C5×#3802
#117513132
#117510882
#117510562
C22⋊C4×Dic152
#117507672
#117507652
#106055933
#738625