Finite Group Databasebeta

← D15×#407 #14411623

Subgroups — D15×#407 #14411623

Order 1920.

2016 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D15C211yesmaximal, characteristic
2C2×M16×D15C212yesmaximal, complemented
3C3×C5×#407C211yesmaximal, characteristic, complemented
4#11751308C211yesmaximal, characteristic, complemented
5#11751227C212yesmaximal, complemented
6#11750827C214yesmaximal, complemented
7D15×C22⋊C8C214yesmaximal, complemented
8D5×#407—31nomaximal, Hall
9C24×D15C411yescharacteristic
10C23×C3×C4×C5C2211yescharacteristic
11C23×Dic15C411yescharacteristic
12C22×C4×D15—28no—
13C22×C4×D15C411yescharacteristic
14C22×C4×D15C411yescharacteristic
15C22×C4×D15C412yes—
16C22×C4×D15C412yes—
17C22×C4×D15C2211yescharacteristic
18C22×C4×D15C2212yes—
19C22×C4×D15C2212yes—
20C22×C4×D15C2211yescharacteristic
21C2×C3×C5×M16C2212yescomplemented
22C2×#6710C2212yescomplemented
23M16×D15—28no—
24C2×#6705C2214yescomplemented
25C2×C8×D15C2214yescomplemented
26C3×C5×C22⋊C8C2214yescomplemented
27#91114C2214yescomplemented
28#91104C2218yescomplemented
29D3×#407—51nomaximal, Hall
30C23×C4×D5—31no—
31C2×D5×M16—32no—
32C5×#407D311yescharacteristic, complemented
33#65496—31no—
34#65415—32no—
35#65015—34no—
36D5×C22⋊C8—34no—
37C24×C3×C5C2×C411yescharacteristic
38C23×D15—24no—
39C23×D15—28no—
40C23×D15C2×C411yescharacteristic
41C23×D15C2×C412yes—
42C23×D15C2×C411yescharacteristic
43C23×D15C2×C412yes—
44C22×C3×C4×C5—24no—
45C22×C3×C4×C5C2×C411yescharacteristic
46C22×C3×C4×C5C2×C412yes—
47C22×C3×C4×C5C2312yes—
48C22×C3×C4×C5C2311yescharacteristic
49C22×Dic15—24no—
50C22×Dic15C2×C411yescharacteristic
51C22×Dic15C2×C412yes—
52C22×Dic15C2×C412yes—
53C22×Dic15C2×C411yescharacteristic
54C2×C4×D15—24no—
55C2×C4×D15—24no—
56C2×C4×D15—24no—
57C2×C4×D15—28no—
58C2×C4×D15—28no—
59C2×C4×D15—28no—
60C2×C4×D15—28no—
61C2×C4×D15C2×C412yes—
62C2×C4×D15C2×C412yes—
63C2×C4×D15C2×C412yes—
64C2×C4×D15C2×C412yes—
65C2×C4×D15C2×C412yes—
66C2×C4×D15C2×C411yescharacteristic
67C2×C4×D15C2×C411yescharacteristic
68C2×C4×D15D418yes—
69C2×C4×D15C2312yes—
70C2×C4×D15C2311yescharacteristic
71C2×C4×D15C2311yescharacteristic
72C3×C5×M16—24no—
73C2×C3×C5×C8C2314yescomplemented
74#6710—24no—
75C2×C3⋊#168C2314yescomplemented
76#6705—28no—
77C8×D15—28no—
78C23×C4×D3—51no—
79C2×D3×M16—52no—
80C3×#407D511yescharacteristic, complemented
81#5207—51no—
82#5126—52no—
83#4726—54no—
84D3×C22⋊C8—54no—
85C24×D5—31no—
86C23×C4×C5C2×D311yescharacteristic
87C23×Dic5—31no—
88C22×C4×D5—31no—
89C22×C4×D5—32no—
90C22×C4×D5—32no—
91C22×C4×D5—31no—
92C22×C4×D5—31no—
93C22×C4×D5—31no—
94C22×C4×D5—32no—
95C22×C4×D5—32no—
96C22×C4×D5—68no—
97C2×C5×M16C2×D312yescomplemented
98C2×#681—32no—
99D5×M16—68no—
100C2×#676—34no—
101C2×C8×D5—34no—
102C5×C22⋊C8C2×D314yescomplemented
103C22⋊#168—34no—
104#3952—38no—
105C2×#407—151noSylow
106C23×C3×C5—22no—
107C23×C3×C5—24no—
108C23×C3×C5C22×C411yescharacteristic
109C23×C3×C5C22×C412yes—
110C22×D15—232no—
111C22×D15—22no—
112C22×D15—24no—
113C22×D15—24no—
114C22×D15—24no—
115C22×D15—24no—
116C22×D15—24no—
117C22×D15—24no—
118C22×D15—24no—
119C22×D15C22⋊C414yes—
120C22×D15M1618yescomplemented
121C22×D15C22×C411yescharacteristic
122C22×D15C22×C412yes—
123C22×D15C22×C411yescharacteristic
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—24no—
126C2×C3×C4×C5—24no—
127C2×C3×C4×C5C22×C412yes—
128C2×C3×C4×C5C22×C411yescharacteristic
129C2×C3×C4×C5C2×D414yes—
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15—22no—
132C2×Dic15—24no—
133C2×Dic15—24no—
134C2×Dic15C22⋊C414yes—
135C2×Dic15C22×C412yes—
136C2×Dic15C22×C411yescharacteristic
137C2×Dic15C22×C411yescharacteristic
138C4×D15—24no—
139C4×D15—24no—
140C4×D15—24no—
141C4×D15—24no—
142C4×D15—24no—
143C4×D15—24no—
144C4×D15C22⋊C414yes—
145C4×D15C22⋊C414yes—
146C4×D15C2×D414yes—
147C4×D15C2×D414yes—
148C3×C5×C8—24no—
149C3⋊#168—24no—
150C24×D3—51no—
151C23×C3×C4C2×D511yescharacteristic
152C23×Dic3—51no—
153C22×C4×D3—51no—
154C22×C4×D3—52no—
155C22×C4×D3—52no—
156C22×C4×D3—51no—
157C22×C4×D3—51no—
158C22×C4×D3—51no—
159C22×C4×D3—52no—
160C22×C4×D3—52no—
161C22×C4×D3—108no—
162C2×C3×M16C2×D512yescomplemented
163C2×#208—52no—
164D3×M16—108no—
165C2×ΓL(1,𝔽25)—54no—
166C2×D3×C8—54no—
167C3×C22⋊C8C2×D514yescomplemented
168#830—54no—
169(C2×D3)⋊C8—58no—
170C24×C5C4×D311yescharacteristic
171C23×D5—31no—
172C23×D5—32no—
173C23×D5—32no—
174C23×D5—31no—
175C23×D5—64no—
176C23×D5—68no—
177C22×C4×C5—24no—
178C22×C4×C5C4×D311yescharacteristic
179C22×C4×C5C4×D312yes—
180C22×C4×C5C22×D312yes—
181C22×C4×C5C22×D311yescharacteristic
182C22×Dic5—31no—
183C22×Dic5—32no—
184C22×Dic5—32no—
185C22×Dic5—31no—
186C22×Dic5—64no—
187C2×C4×D5—31no—
188C2×C4×D5—31no—
189C2×C4×D5—38no—
190C2×C4×D5—31no—
191C2×C4×D5—31no—
192C2×C4×D5—32no—
193C2×C4×D5—32no—
194C2×C4×D5—32no—
195C2×C4×D5—32no—
196C2×C4×D5—32no—
197C2×C4×D5—32no—
198C2×C4×D5—68no—
199C2×C4×D5—68no—
200C2×C4×D5—68no—
201C2×C4×D5—68no—
202C2×C4×D5—64no—
203C2×C4×D5—64no—
204C2×C4×D5—64no—
205C5×M16—24no—
206C2×C5×C8C22×D314yescomplemented
207#681—64no—
208C2×#168—34no—
209#676—68no—
210C8×D5—68no—
211C24×C4—151no—
212C22×M16—152no—
213#407—151no—
214#407—152no—
215#407—154no—
216#407D1511yescharacteristic, direct product factor
217C2×C22⋊C8—154no—
218C22×C3×C5—28no—
219C22×C3×C5—22no—
220C22×C3×C5—22no—
221C22×C3×C5—22no—
222C22×C3×C5C2×C22⋊C412yes—
223C22×C3×C5C2×M1614yescomplemented
224C22×C3×C5C23×C411yescharacteristic
225C2×D15—216no—
226C2×D15—28no—
227C2×D15—22no—
228C2×D15—22no—
229C2×D15—22no—
230C2×D15—28no—
231C2×D15—216no—
232C2×D15C2×C22⋊C412yes—
233C2×D15C2×C22⋊C412yes—
234C2×D15C2×M1614yes—
235C2×D15C2×M1614yescomplemented
236C3×C4×C5—22no—
237C3×C4×C5C2×C22⋊C412yes—
238C3×C4×C5C22×D412yes—
239Dic15—22no—
240Dic15C2×C22⋊C412yes—
241Dic15C2×C22⋊C412yes—
242C24×C3C4×D511yescharacteristic
243C23×D3—51no—
244C23×D3—52no—
245C23×D3—52no—
246C23×D3—51no—
247C23×D3—104no—
248C23×D3—108no—
249C22×C3×C4—24no—
250C22×C3×C4C4×D511yescharacteristic
251C22×C3×C4C4×D512yes—
252C22×C3×C4C22×D512yes—
253C22×C3×C4C22×D511yescharacteristic
254C22×Dic3—51no—
255C22×Dic3—52no—
256C22×Dic3—52no—
257C22×Dic3—51no—
258C22×Dic3—104no—
259C2×C4×D3—51no—
260C2×C4×D3—51no—
261C2×C4×D3—58no—
262C2×C4×D3—51no—
263C2×C4×D3—51no—
264C2×C4×D3—52no—
265C2×C4×D3—52no—
266C2×C4×D3—52no—
267C2×C4×D3—52no—
268C2×C4×D3—52no—
269C2×C4×D3—52no—
270C2×C4×D3—108no—
271C2×C4×D3—108no—
272C2×C4×D3—108no—
273C2×C4×D3—108no—
274C2×C4×D3—104no—
275C2×C4×D3—104no—
276C2×C4×D3—104no—
277C3×M16—24no—
278C2×C3×C8C22×D514yescomplemented
279#208—104no—
280C2×C3⋊C8—54no—
281ΓL(1,𝔽25)—108no—
282D3×C8—108no—
283C23×C5—22no—
284C23×C5—24no—
285C23×C5C2×C4×D311yescharacteristic
286C23×C5C2×C4×D312yes—
287C22×D5—31no—
288C22×D5—34no—
289C22×D5—38no—
290C22×D5—31no—
291C22×D5—32no—
292C22×D5—64no—
293C22×D5—64no—
294C22×D5—64no—
295C22×D5—64no—
296C22×D5—64no—
297C22×D5—64no—
298C22×D5—632no—
299C22×D5—62no—
300C22×D5—64no—
301C2×C4×C5—22no—
302C2×C4×C5—24no—
303C2×C4×C5—24no—
304C2×C4×C5C2×C4×D312yes—
305C2×C4×C5C2×C4×D311yescharacteristic
306C2×C4×C5D3×D414yes—
307C2×C4×C5C23×D311yescharacteristic
308C2×Dic5—34no—
309C2×Dic5—31no—
310C2×Dic5—31no—
311C2×Dic5—32no—
312C2×Dic5—64no—
313C2×Dic5—64no—
314C2×Dic5—62no—
315C4×D5—34no—
316C4×D5—34no—
317C4×D5—34no—
318C4×D5—34no—
319C4×D5—64no—
320C4×D5—64no—
321C4×D5—64no—
322C4×D5—64no—
323C4×D5—64no—
324C4×D5—64no—
325C5×C8—24no—
326#168—64no—
327C25—151no—
328C23×C4—151no—
329C23×C4—151no—
330C23×C4—151no—
331C23×C4—152no—
332C23×C4—152no—
333C23×C4—151no—
334C23×C4—152no—
335C23×C4—152no—
336C23×C4—151no—
337C23×C4—308no—
338C23×C4C2×D1511yescharacteristic
339C2×M16—152no—
340C2×M16—154no—
341C2×M16—308no—
342C2×M16C2×D1512yescomplemented
343C22×C8—154no—
344C22⋊C8—154no—
345C22⋊C8—158no—
346C22⋊C8C2×D1514yescomplemented
347C2×C3×C5—22no—
348C2×C3×C5—24no—
349C2×C3×C5C22×C22⋊C411yescharacteristic
350C2×C3×C5C22×M1612yes—
351D15—22no—
352D15—24no—
353D15#40714yesdirect product factor
354C23×C3—22no—
355C23×C3—24no—
356C23×C3C2×C4×D511yescharacteristic
357C23×C3C2×C4×D512yes—
358C22×D3—51no—
359C22×D3—51no—
360C22×D3—52no—
361C22×D3—54no—
362C22×D3—58no—
363C22×D3—104no—
364C22×D3—104no—
365C22×D3—104no—
366C22×D3—104no—
367C22×D3—104no—
368C22×D3—104no—
369C22×D3—1032no—
370C22×D3—102no—
371C22×D3—104no—
372C2×C3×C4—22no—
373C2×C3×C4—24no—
374C2×C3×C4—24no—
375C2×C3×C4C2×C4×D512yes—
376C2×C3×C4C2×C4×D511yescharacteristic
377C2×C3×C4D4×D514yes—
378C2×C3×C4C23×D511yescharacteristic
379C2×Dic3—51no—
380C2×Dic3—51no—
381C2×Dic3—54no—
382C2×Dic3—52no—
383C2×Dic3—104no—
384C2×Dic3—104no—
385C2×Dic3—102no—
386C4×D3—54no—
387C4×D3—54no—
388C4×D3—54no—
389C4×D3—54no—
390C4×D3—104no—
391C4×D3—104no—
392C4×D3—104no—
393C4×D3—104no—
394C4×D3—104no—
395C4×D3—104no—
396C3×C8—24no—
397C3⋊C8—104no—
398C22×C5—28no—
399C22×C5—22no—
400C22×C5—22no—
401C22×C5—22no—
402C22×C5D3×C22⋊C412yes—
403C22×C5D3×M1614yescomplemented
404C22×C5C22×C4×D311yescharacteristic
405C2×D5—32no—
406C2×D5—34no—
407C2×D5—32no—
408C2×D5—34no—
409C2×D5—68no—
410C2×D5—616no—
411C2×D5—68no—
412C2×D5—616no—
413C2×D5—62no—
414C2×D5—62no—
415C2×D5—62no—
416C4×C5—22no—
417C4×C5D3×C22⋊C412yes—
418C4×C5C2×D3×D412yes—
419Dic5—32no—
420Dic5—32no—
421Dic5—62no—
422C24—151no—
423C24—152no—
424C24—152no—
425C24—151no—
426C24—304no—
427C24—308no—
428C24C4×D1511yescharacteristic
429C22×C4—24no—
430C22×C4—151no—
431C22×C4—151no—
432C22×C4—151no—
433C22×C4—158no—
434C22×C4—151no—
435C22×C4—151no—
436C22×C4—152no—
437C22×C4—152no—
438C22×C4—151no—
439C22×C4—152no—
440C22×C4—152no—
441C22×C4—152no—
442C22×C4—152no—
443C22×C4—152no—
444C22×C4—152no—
445C22×C4—304no—
446C22×C4—308no—
447C22×C4—308no—
448C22×C4—308no—
449C22×C4—308no—
450C22×C4—304no—
451C22×C4—304no—
452C22×C4—304no—
453C22×C4C4×D1511yescharacteristic
454C22×C4C4×D1512yes—
455C22×C4C22×D1512yes—
456C22×C4C22×D1511yescharacteristic
457M16—24no—
458M16—308no—
459M16—304no—
460C2×C8—154no—
461C2×C8—308no—
462C2×C8C22×D1514yescomplemented
463C3×C5C2×#40711yescharacteristic, complemented, Hall
464C22×C3—28no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3D5×C22⋊C412yes—
469C22×C3D5×M1614yescomplemented
470C22×C3C22×C4×D511yescharacteristic
471C2×D3—52no—
472C2×D3—54no—
473C2×D3—52no—
474C2×D3—54no—
475C2×D3—108no—
476C2×D3—1016no—
477C2×D3—108no—
478C2×D3—1016no—
479C2×D3—102no—
480C2×D3—102no—
481C2×D3—102no—
482C3×C4—22no—
483C3×C4D5×C22⋊C412yes—
484C3×C4C2×D4×D512yes—
485Dic3—52no—
486Dic3—52no—
487Dic3—102no—
488C2×C5—22no—
489C2×C5—24no—
490C2×C5C2×D3×C22⋊C411yescharacteristic
491C2×C5C2×D3×M1612yes—
492D5—34no—
493D5—62no—
494D5—64no—
495C23—22no—
496C23—24no—
497C23—151no—
498C23—154no—
499C23—158no—
500C23—151no—
501C23—152no—
502C23—304no—
503C23—304no—
504C23—304no—
505C23—304no—
506C23—304no—
507C23—304no—
508C23—3032no—
509C23—302no—
510C23—304no—
511C23C2×C4×D1511yescharacteristic
512C23C2×C4×D1512yes—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—154no—
517C2×C4—151no—
518C2×C4—151no—
519C2×C4—154no—
520C2×C4—154no—
521C2×C4—154no—
522C2×C4—154no—
523C2×C4—152no—
524C2×C4—304no—
525C2×C4—304no—
526C2×C4—304no—
527C2×C4—304no—
528C2×C4—304no—
529C2×C4—304no—
530C2×C4—302no—
531C2×C4—304no—
532C2×C4—304no—
533C2×C4C2×C4×D1512yes—
534C2×C4C2×C4×D1511yescharacteristic
535C2×C4D4×D1514yes—
536C2×C4C23×D1511yescharacteristic
537C8—24no—
538C8—304no—
539C2×C3—22no—
540C2×C3—24no—
541C2×C3C2×D5×C22⋊C411yescharacteristic
542C2×C3C2×D5×M1612yes—
543D3—54no—
544D3—102no—
545D3—104no—
546C5D3×#40711yescharacteristic, complemented, Sylow
547C22—28no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—152no—
552C22—154no—
553C22—152no—
554C22—154no—
555C22—308no—
556C22—3016no—
557C22—308no—
558C22—3016no—
559C22—302no—
560C22—302no—
561C22—302no—
562C22C22⋊C4×D1512yes—
563C22M16×D1514yescomplemented
564C22C22×C4×D1511yescharacteristic
565C4—22no—
566C4—152no—
567C4—152no—
568C4—302no—
569C4C22⋊C4×D1512yes—
570C4C2×D4×D1512yes—
571C3D5×#40711yescharacteristic, complemented, Sylow
572C2—22no—
573C2—24no—
574C2—154no—
575C2—302no—
576C2—304no—
577C2C2×C22⋊C4×D1511yescharacteristic
578C2C2×M16×D1512yes—
subgroupG/H
center, FrattiniC2×C4C23×D15
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×#407C2
prime radicalC24×D15C4
cosocleC2×C3×C4×C5C24
hypercenter#407D15
hypocenterC3×C5C2×#407
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×M16×D15C2semidirect
3. C3×C5×#407C2semidirect
4. #11751308C2semidirect
5. #11751227C2semidirect
6. #11750827C2semidirect
7. D15×C22⋊C8C2semidirect
21. C2×C3×C5×M16C22semidirect
22. C2×#6710C22semidirect
24. C2×#6705C22semidirect
25. C2×C8×D15C22semidirect
26. C3×C5×C22⋊C8C22semidirect
27. #91114C22semidirect
28. #91104C22semidirect
32. C5×#407D3semidirect
73. C2×C3×C5×C8C23semidirect
75. C2×C3⋊#168C23semidirect
80. C3×#407D5semidirect
97. C2×C5×M16C2×D3semidirect
102. C5×C22⋊C8C2×D3semidirect
120. C22×D15M16semidirect
162. C2×C3×M16C2×D5semidirect
167. C3×C22⋊C8C2×D5semidirect
206. C2×C5×C8C22×D3semidirect
216. #407D15direct (N × H)
223. C22×C3×C5C2×M16semidirect
235. C2×D15C2×M16semidirect
278. C2×C3×C8C22×D5semidirect
342. C2×M16C2×D15semidirect
346. C22⋊C8C2×D15semidirect
353. D15#407direct (N × H)
403. C22×C5D3×M16semidirect
462. C2×C8C22×D15semidirect
463. C3×C5C2×#407semidirect
469. C22×C3D5×M16semidirect
546. C5D3×#407semidirect
563. C22M16×D15semidirect
571. C3D5×#407semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D152
C2×M16×D152
C3×C5×#4072
#117513082
#117512272
#117508272
D15×C22⋊C82
D5×#4073
D3×#4075