Finite Group Databasebeta

← D15×#484 #14431742

Subgroups — D15×#484 #14431742

Order 1920.

920 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D15×C22⋊Q8C211yesmaximal, characteristic
2C2×C4⋊C4×D15C211yesmaximal, characteristic
3C3×C5×#484C211yesmaximal, characteristic, complemented
4#11751145C211yesmaximal, characteristic, complemented
5#11751071C211yesmaximal, characteristic, complemented
6#11750985C212yesmaximal, complemented
7D15×#107C212yesmaximal, complemented
8#11750912C212yesmaximal, complemented
9D15×#103C212yesmaximal, complemented
10D15×C22⋊C8C211yesmaximal, characteristic
11#11750823C211yesmaximal, characteristic, complemented
12D5×#484—31nomaximal, Hall
13C2×Q8×D15C2211yescharacteristic
14C22×C4×D15—21no—
15C22×C4×D15C2211yescharacteristic
16C3×C5×C22⋊Q8C2211yescharacteristic
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18#91835C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20#91813C2211yescharacteristic
21C2×#6712—21no—
22C2×C8×D15C2212yes—
23#91786C2211yescharacteristic
24#91785—21no—
25C4⋊C4×D15—21no—
26C4⋊C4×D15—21no—
27C4⋊C4×D15—21no—
28C4⋊C4×D15C2212yes—
29C4⋊C4×D15C2211yescharacteristic
30C4⋊C4×D15C2212yes—
31C22⋊C4×D15—21no—
32#91767—21no—
33C3×C5×#107C2212yescomplemented
34C3×C5×#103C2212yescomplemented
35C3×C5×C22⋊C8C2211yescharacteristic
36#91119C2212yescomplemented
37#91114C2211yescharacteristic
38#91104C2212yes—
39#91102C2212yescomplemented
40#91100C2212yescomplemented
41#91094C2212yescomplemented
42#91091C2212yescomplemented
43#91091C2212yescomplemented
44D3×#484—51nomaximal, Hall
45D5×C22⋊Q8—31no—
46C2×D5×C4⋊C4—31no—
47C5×#484D311yescharacteristic, complemented
48#65333—31no—
49#65259—31no—
50#65173—32no—
51D5×#107—32no—
52#65098—32no—
53D5×#103—32no—
54D5×C22⋊C8—31no—
55#65011—31no—
56C23×D15D411yescharacteristic
57C2×C3×C5×Q8C2311yescharacteristic
58C22×C3×C4×C5—21no—
59C22×C3×C4×C5C2311yescharacteristic
60C22×Dic15—21no—
61C22×Dic15D411yescharacteristic
62Q8×D15—24no—
63C2×C4×D15—24no—
64C2×C4×D15—21no—
65C2×C4×D15—21no—
66C2×C4×D15—22no—
67C2×C4×D15—22no—
68C2×C4×D15—44no—
69C2×C4×D15D411yescharacteristic
70C2×C4×D15D411yescharacteristic
71C2×C4×D15C2311yescharacteristic
72C2×C4×D15C2311yescharacteristic
73C2×Dic30—21no—
74C2×Dic30C2311yescharacteristic
75C2×C3×C5×C8C2312yes—
76C3×C5×C4⋊C4—21no—
77C3×C5×C4⋊C4—21no—
78C3×C5×C4⋊C4C2312yes—
79C3×C5×C4⋊C4C2311yescharacteristic
80C3×C5×C22⋊C4—21no—
81#6719—21no—
82#6714—21no—
83#6714—21no—
84C4⋊Dic15—21no—
85C4⋊Dic15—21no—
86C4⋊Dic15C2312yes—
87C4⋊Dic15C2311yescharacteristic
88#6712—21no—
89#6712—21no—
90#6712—21no—
91#6712—22no—
92#6712—22no—
93C2×C3⋊#168C2312yes—
94C8×D15—24no—
95D3×C22⋊Q8—51no—
96C2×D3×C4⋊C4—51no—
97C3×#484D511yescharacteristic, complemented
98#5044—51no—
99#4970—51no—
100#4884—52no—
101D3×#107—52no—
102#4811—52no—
103D3×#103—52no—
104D3×C22⋊C8—51no—
105#4722—51no—
106C2×Q8×D5—31no—
107C22×C4×D5—31no—
108C22×C4×D5—61no—
109C5×C22⋊Q8C2×D311yescharacteristic
110C2×C5×C4⋊C4C2×D311yescharacteristic
111#4092—31no—
112C2×C4⋊Dic5—31no—
113#4070—31no—
114C2×#683—61no—
115C2×C8×D5—32no—
116#4043—31no—
117#4042—61no—
118D5×C4⋊C4—32no—
119D5×C4⋊C4—32no—
120D5×C4⋊C4—31no—
121D5×C4⋊C4—61no—
122D5×C4⋊C4—61no—
123D5×C4⋊C4—61no—
124D5×C22⋊C4—61no—
125#4024—61no—
126C5×#107C2×D312yescomplemented
127C5×#103C2×D312yescomplemented
128C5×C22⋊C8C2×D311yescharacteristic
129#3967—32no—
130C22⋊#168—31no—
131#3952—32no—
132#3950—32no—
133#3948—32no—
134#3942—32no—
135#3939—32no—
136#3939—32no—
137C2×#484—151noSylow
138C23×C3×C5C2×D411yescharacteristic
139C22×D15—22no—
140C22×D15—22no—
141C22×D15Q1614yes—
142C22×D15C2×D411yescharacteristic
143C22×D15C2×D411yescharacteristic
144C3×C5×Q8—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—42no—
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2411yescharacteristic
152C2×Dic15—22no—
153C2×Dic15—21no—
154C2×Dic15—22no—
155C2×Dic15—21no—
156C2×Dic15—42no—
157C2×Dic15C2×D411yescharacteristic
158C2×Dic15C2×D411yescharacteristic
159C4×D15—22no—
160C4×D15—22no—
161C4×D15—22no—
162C4×D15—44no—
163C4×D15—42no—
164C4×D15—42no—
165C4×D15—44no—
166C4×D15#4114yes—
167Dic30—22no—
168Dic30—42no—
169C3×C5×C8—22no—
170C3⋊#168—22no—
171C2×D3×Q8—51no—
172C22×C4×D3—51no—
173C22×C4×D3—101no—
174C3×C22⋊Q8C2×D511yescharacteristic
175C2×C3×C4⋊C4C2×D511yescharacteristic
176#946—51no—
177C2×C4⋊Dic3—51no—
178#924—51no—
179C2×Dic3⋊C4—101no—
180C2×D3×C8—52no—
181#897—51no—
182#896—101no—
183D3×C4⋊C4—51no—
184D3×C4⋊C4—52no—
185D3×C4⋊C4—52no—
186D3×C4⋊C4—101no—
187D3×C4⋊C4—101no—
188D3×C4⋊C4—101no—
189D3×C22⋊C4—101no—
190#878—101no—
191C3×#107C2×D512yescomplemented
192C3×#103C2×D512yescomplemented
193C3×C22⋊C8C2×D511yescharacteristic
194#835—52no—
195#830—51no—
196(C2×D3)⋊C8—52no—
197#818—52no—
198#816—52no—
199#810—52no—
200#807—52no—
201#807—52no—
202C23×D5—31no—
203C2×C5×Q8C22×D311yescharacteristic
204C22×C4×C5—21no—
205C22×C4×C5C22×D311yescharacteristic
206C22×Dic5—31no—
207C22×Dic5—61no—
208Q8×D5—64no—
209C2×C4×D5—31no—
210C2×C4×D5—31no—
211C2×C4×D5—31no—
212C2×C4×D5—31no—
213C2×C4×D5—64no—
214C2×C4×D5—62no—
215C2×C4×D5—62no—
216C2×C4×D5—61no—
217C2×C4×D5—61no—
218C2×C4×D5—124no—
219C2×Dic10—31no—
220C2×Dic10—61no—
221C2×C5×C8C22×D312yes—
222C5×C4⋊C4—21no—
223C5×C4⋊C4—21no—
224C5×C4⋊C4C22×D312yes—
225C5×C4⋊C4C22×D311yescharacteristic
226C5×C22⋊C4—21no—
227C22⋊Dic5—61no—
228#685—61no—
229#685—61no—
230C4⋊Dic5—31no—
231C4⋊Dic5—32no—
232C4⋊Dic5—61no—
233C4⋊Dic5—61no—
234#683—61no—
235#683—61no—
236#683—62no—
237#683—62no—
238#683—61no—
239C2×#168—32no—
240C8×D5—64no—
241C2×C22⋊Q8—151no—
242C22×C4⋊C4—151no—
243#484—151no—
244#484—151no—
245#484—152no—
246#484—152no—
247#484—151no—
248#484D1511yescharacteristic, direct product factor
249C2×#107—152no—
250C2×#103—152no—
251C2×C22⋊C8—151no—
252C22×C3×C5—21no—
253C22×C3×C5—21no—
254C22×C3×C5C2×Q1612yes—
255C22×C3×C5C22×D411yescharacteristic
256C2×D15—21no—
257C2×D15—21no—
258C2×D15—28no—
259C2×D15#12312yes—
260C2×D15C2×Q1612yes—
261C2×D15C2×Q1612yes—
262C2×D15AGL(1,ℤ/8)12yes—
263C3×C4×C5—21no—
264C3×C4×C5—41no—
265C3×C4×C5—42no—
266C3×C4×C5—41no—
267C3×C4×C5C2×#4112yes—
268Dic15—21no—
269Dic15—41no—
270Dic15—42no—
271Dic15—41no—
272Dic15#12312yes—
273C23×D3—51no—
274C2×C3×Q8C22×D511yescharacteristic
275C22×C3×C4—21no—
276C22×C3×C4C22×D511yescharacteristic
277C22×Dic3—51no—
278C22×Dic3—101no—
279D3×Q8—104no—
280C2×C4×D3—51no—
281C2×C4×D3—51no—
282C2×C4×D3—51no—
283C2×C4×D3—51no—
284C2×C4×D3—104no—
285C2×C4×D3—101no—
286C2×C4×D3—101no—
287C2×C4×D3—102no—
288C2×C4×D3—102no—
289C2×C4×D3—204no—
290C2×Dic6—51no—
291C2×Dic6—101no—
292C2×C3×C8C22×D512yes—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4C22×D511yescharacteristic
296C3×C4⋊C4C22×D512yes—
297C3×C22⋊C4—21no—
298#217—101no—
299(C2×D3)⋊C4—101no—
300(C2×D3)⋊C4—101no—
301C4⋊Dic3—51no—
302C4⋊Dic3—52no—
303C4⋊Dic3—101no—
304C4⋊Dic3—101no—
305Dic3⋊C4—101no—
306Dic3⋊C4—101no—
307Dic3⋊C4—102no—
308Dic3⋊C4—102no—
309Dic3⋊C4—101no—
310C2×C3⋊C8—52no—
311D3×C8—104no—
312C23×C5D3×D411yescharacteristic
313C22×D5—31no—
314C22×D5—34no—
315C22×D5—31no—
316C22×D5—62no—
317C22×D5—62no—
318C5×Q8—22no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—42no—
324C2×C4×C5D3×D411yescharacteristic
325C2×C4×C5C23×D311yescharacteristic
326C2×Dic5—31no—
327C2×Dic5—31no—
328C2×Dic5—62no—
329C2×Dic5—61no—
330C2×Dic5—62no—
331C2×Dic5—61no—
332C2×Dic5—122no—
333C4×D5—34no—
334C4×D5—62no—
335C4×D5—62no—
336C4×D5—62no—
337C4×D5—122no—
338C4×D5—124no—
339C4×D5—122no—
340C4×D5—124no—
341Dic10—62no—
342Dic10—122no—
343C5×C8—22no—
344#168—62no—
345C22×Q8—151no—
346C23×C4—151no—
347C23×C4—301no—
348C22×C8—152no—
349C22⋊Q8—151no—
350C22⋊Q8—151no—
351C22⋊Q8—151no—
352C22⋊Q8—301no—
353C22⋊Q8—301no—
354C22⋊Q8C2×D1511yescharacteristic
355C2×C4⋊C4—151no—
356C2×C4⋊C4—152no—
357C2×C4⋊C4—152no—
358C2×C4⋊C4—151no—
359C2×C4⋊C4—301no—
360C2×C4⋊C4—301no—
361C2×C4⋊C4—301no—
362C2×C4⋊C4—301no—
363C2×C4⋊C4C2×D1511yescharacteristic
364C2×C22⋊C4—301no—
365#107—152no—
366#107—152no—
367#107—152no—
368#107C2×D1512yescomplemented
369#103—152no—
370#103—152no—
371#103—152no—
372#103C2×D1512yescomplemented
373C22⋊C8—151no—
374C22⋊C8—152no—
375C22⋊C8C2×D1511yescharacteristic
376C2×C3×C5—22no—
377C2×C3×C5C2×#12311yescharacteristic
378C2×C3×C5C22×Q1611yescharacteristic
379C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
380D15—22no—
381D15#48414yesdirect product factor
382C23×C3D4×D511yescharacteristic
383C22×D3—51no—
384C22×D3—51no—
385C22×D3—54no—
386C22×D3—102no—
387C22×D3—102no—
388C3×Q8—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—42no—
394C2×C3×C4D4×D511yescharacteristic
395C2×C3×C4C23×D511yescharacteristic
396C2×Dic3—51no—
397C2×Dic3—51no—
398C2×Dic3—102no—
399C2×Dic3—101no—
400C2×Dic3—102no—
401C2×Dic3—101no—
402C2×Dic3—202no—
403C4×D3—54no—
404C4×D3—102no—
405C4×D3—102no—
406C4×D3—102no—
407C4×D3—202no—
408C4×D3—204no—
409C4×D3—202no—
410C4×D3—204no—
411Dic6—102no—
412Dic6—202no—
413C3×C8—22no—
414C3⋊C8—102no—
415C22×C5—21no—
416C22×C5—21no—
417C22×C5D3×Q1612yes—
418C22×C5C2×D3×D411yescharacteristic
419C2×D5—32no—
420C2×D5—32no—
421C2×D5—32no—
422C2×D5—32no—
423C2×D5—68no—
424C2×D5—61no—
425C2×D5—61no—
426C4×C5—21no—
427C4×C5—41no—
428C4×C5—42no—
429C4×C5—41no—
430C4×C5D3×#4112yes—
431Dic5—32no—
432Dic5—61no—
433Dic5—121no—
434Dic5—122no—
435Dic5—121no—
436C24—151no—
437C2×Q8—151no—
438C2×Q8—301no—
439C2×Q8—304no—
440C2×Q8C22×D1511yescharacteristic
441C22×C4—21no—
442C22×C4—151no—
443C22×C4—151no—
444C22×C4—151no—
445C22×C4—151no—
446C22×C4—151no—
447C22×C4—304no—
448C22×C4—301no—
449C22×C4—301no—
450C22×C4—302no—
451C22×C4—302no—
452C22×C4—301no—
453C22×C4—604no—
454C22×C4C22×D1511yescharacteristic
455C2×C8—152no—
456C2×C8—304no—
457C2×C8C22×D1512yes—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—152no—
461C4⋊C4—151no—
462C4⋊C4—302no—
463C4⋊C4—302no—
464C4⋊C4—301no—
465C4⋊C4—301no—
466C4⋊C4—301no—
467C4⋊C4—301no—
468C4⋊C4—301no—
469C4⋊C4C22×D1512yes—
470C4⋊C4C22×D1511yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—301no—
473C22⋊C4—301no—
474C22⋊C4—301no—
475C3×C5C2×#48411yescharacteristic, complemented, Hall
476C22×C3—21no—
477C22×C3—21no—
478C22×C3D5×Q1612yes—
479C22×C3C2×D4×D511yescharacteristic
480C2×D3—52no—
481C2×D3—52no—
482C2×D3—52no—
483C2×D3—52no—
484C2×D3—108no—
485C2×D3—101no—
486C2×D3—101no—
487C3×C4—21no—
488C3×C4—42no—
489C3×C4—41no—
490C3×C4—41no—
491C3×C4D5×#4112yes—
492Dic3—52no—
493Dic3—101no—
494Dic3—202no—
495Dic3—201no—
496Dic3—201no—
497C2×C5—22no—
498C2×C5D3×#12311yescharacteristic
499C2×C5C2×D3×Q1611yescharacteristic
500C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
501D5—34no—
502D5—62no—
503C23—151no—
504C23—154no—
505C23—151no—
506C23—302no—
507C23—302no—
508C23D4×D1511yescharacteristic
509Q8—22no—
510Q8—302no—
511Q8—602no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—42no—
517C2×C4—151no—
518C2×C4—154no—
519C2×C4—151no—
520C2×C4—302no—
521C2×C4—302no—
522C2×C4—302no—
523C2×C4—302no—
524C2×C4—301no—
525C2×C4—301no—
526C2×C4—302no—
527C2×C4—604no—
528C2×C4—602no—
529C2×C4—602no—
530C2×C4—604no—
531C2×C4—602no—
532C2×C4D4×D1511yescharacteristic
533C2×C4C23×D1511yescharacteristic
534C8—22no—
535C8—302no—
536C2×C3—22no—
537C2×C3D5×#12311yescharacteristic
538C2×C3C2×D5×Q1611yescharacteristic
539C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
540D3—54no—
541D3—102no—
542C5D3×#48411yescharacteristic, complemented, Sylow
543C22—21no—
544C22—21no—
545C22—152no—
546C22—152no—
547C22—152no—
548C22—152no—
549C22—308no—
550C22—301no—
551C22—301no—
552C22Q16×D1512yes—
553C22C2×D4×D1511yescharacteristic
554C4—21no—
555C4—41no—
556C4—42no—
557C4—41no—
558C4—152no—
559C4—301no—
560C4—601no—
561C4—602no—
562C4—601no—
563C4#41×D1512yes—
564C3D5×#48411yescharacteristic, complemented, Sylow
565C2—22no—
566C2—154no—
567C2—302no—
568C2D15×#12311yescharacteristic
569C2C2×Q16×D1511yescharacteristic
570C2D15×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#484C2
socleC22×C3×C5C22×D4
prime radicalC23×D15D4
hypercenter#484D15
hypocenterC3×C5C2×#484
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. C3×C5×#484C2semidirect
4. #11751145C2semidirect
5. #11751071C2semidirect
6. #11750985C2semidirect
7. D15×#107C2semidirect
8. #11750912C2semidirect
9. D15×#103C2semidirect
11. #11750823C2semidirect
33. C3×C5×#107C22semidirect
34. C3×C5×#103C22semidirect
36. #91119C22semidirect
39. #91102C22semidirect
40. #91100C22semidirect
41. #91094C22semidirect
42. #91091C22semidirect
43. #91091C22semidirect
47. C5×#484D3semidirect
97. C3×#484D5semidirect
126. C5×#107C2×D3semidirect
127. C5×#103C2×D3semidirect
191. C3×#107C2×D5semidirect
192. C3×#103C2×D5semidirect
248. #484D15direct (N × H)
368. #107C2×D15semidirect
372. #103C2×D15semidirect
381. D15#484direct (N × H)
475. C3×C5C2×#484semidirect
542. C5D3×#484semidirect
564. C3D5×#484semidirect

Maximal subgroups

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

subgroupindex
D15×C22⋊Q82
C2×C4⋊C4×D152
C3×C5×#4842
#117511452
#117510712
#117509852
D15×#1072
#117509122
D15×#1032
D15×C22⋊C82
#117508232
D5×#4843
D3×#4845