Finite Group Databasebeta

← D15×#470 #14428031

Subgroups — D15×#470 #14428031

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×D15C211yesmaximal, characteristic, complemented
2C2×M16×D15C211yesmaximal, characteristic
3D15×C22⋊Q8C212yesmaximal
4C3×C5×#470C211yesmaximal, characteristic, complemented
5#11751290C211yesmaximal, characteristic, complemented
6#11751238C211yesmaximal, characteristic, complemented
7#11751153C212yesmaximal, complemented
8#11750968C211yesmaximal, characteristic, complemented
9D15×#106C211yesmaximal, characteristic, complemented
10#11750917C212yesmaximal, complemented
11D15×#103C212yesmaximal, complemented
12D5×#470—31nomaximal, Hall
13C2×Q8×D15C2212yes—
14C22×C4×D15C2211yescharacteristic
15C2×C3×C5×Q16C2211yescharacteristic, complemented
16C2×C3×C5×M16C2211yescharacteristic
17C3×C5×C22⋊Q8C2212yes—
18#91835C2212yes—
19C2×#6718C2212yescomplemented
20#91813C2212yes—
21C2×#6710C2211yescharacteristic
22Q16×D15—24no—
23M16×D15—24no—
24C2×Dic60C2211yescharacteristic, complemented
25C2×#6705C2211yescharacteristic
26C2×#6705C2211yescharacteristic
27C2×C8×D15C2211yescharacteristic
28C2×C8×D15C2211yescharacteristic
29#91786C2212yes—
30#91785—22no—
31C4⋊C4×D15—22no—
32C4⋊C4×D15C2212yes—
33C22⋊C4×D15—22no—
34#91767—22no—
35C3×C5×#106C2211yescharacteristic, complemented
36C3×C5×#103C2212yescomplemented
37#91119C2212yescomplemented
38#91101C2211yescharacteristic, complemented
39#91100C2212yescomplemented
40#91094C2212yescomplemented
41#91092C2212yescomplemented
42D3×#470—51nomaximal, Hall
43C2×D5×Q16—31no—
44C2×D5×M16—31no—
45D5×C22⋊Q8—32no—
46C5×#470D311yescharacteristic, complemented
47#65478—31no—
48#65426—31no—
49#65341—32no—
50#65157—31no—
51D5×#106—31no—
52#65105—32no—
53D5×#103—32no—
54C23×D15D411yescharacteristic
55C2×C3×C5×Q8C2312yes—
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15D411yescharacteristic
58Q8×D15—24no—
59Q8×D15—24no—
60C2×C4×D15—22no—
61C2×C4×D15—22no—
62C2×C4×D15—22no—
63C2×C4×D15—22no—
64C2×C4×D15D411yescharacteristic
65C2×C4×D15D411yescharacteristic
66C2×C4×D15C2311yescharacteristic
67C2×C4×D15C2311yescharacteristic
68C2×Dic30—22no—
69C2×Dic30C2312yes—
70C3×C5×Q16—22no—
71C3×C5×M16—22no—
72C2×C3×C5×C8C2311yescharacteristic
73C2×C3×C5×C8C2311yescharacteristic
74C3×C5×C4⋊C4—22no—
75C3×C5×C4⋊C4C2312yes—
76C3×C5×C22⋊C4—22no—
77#6719—22no—
78#6718—24no—
79#6714—22no—
80#6714—22no—
81C4⋊Dic15—22no—
82C4⋊Dic15C2312yes—
83#6712—22no—
84#6712—22no—
85#6712—22no—
86#6710—22no—
87C2×C3⋊#168C2311yescharacteristic
88C2×C3⋊#168C2311yescharacteristic
89Dic60—22no—
90#6705—22no—
91#6705—22no—
92C8×D15—22no—
93C8×D15D414yes—
94C2×D3×Q16—51no—
95C2×D3×M16—51no—
96D3×C22⋊Q8—52no—
97C3×#470D511yescharacteristic, complemented
98#5189—51no—
99#5137—51no—
100#5052—52no—
101#4867—51no—
102D3×#106—51no—
103#4816—52no—
104D3×#103—52no—
105C2×Q8×D5—32no—
106C22×C4×D5—31no—
107C2×C5×Q16C2×D311yescharacteristic, complemented
108C2×C5×M16C2×D311yescharacteristic
109C5×C22⋊Q8C2×D312yes—
110#4092—32no—
111C2×#689—32no—
112#4070—32no—
113C2×#681—31no—
114D5×Q16—64no—
115D5×M16—64no—
116C2×Dic20—31no—
117C2×#676—31no—
118C2×#676—31no—
119C2×C8×D5—31no—
120C2×C8×D5—31no—
121#4043—32no—
122#4042—62no—
123D5×C4⋊C4—32no—
124D5×C4⋊C4—62no—
125D5×C22⋊C4—62no—
126#4024—62no—
127C5×#106C2×D311yescharacteristic, complemented
128C5×#103C2×D312yescomplemented
129#3967—32no—
130#3949—31no—
131#3948—32no—
132#3942—32no—
133#3940—32no—
134C2×#470—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—22no—
137C22×D15—24no—
138C22×D15C2×D411yescharacteristic
139C22×D15C2×D411yescharacteristic
140C3×C5×Q8—22no—
141C3×C5×Q8—22no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2411yescharacteristic
148C2×Dic15—22no—
149C2×Dic15—22no—
150C2×Dic15—22no—
151C2×Dic15C2×D411yescharacteristic
152C2×Dic15C2×D411yescharacteristic
153C4×D15—22no—
154C4×D15—21no—
155C4×D15—21no—
156C4×D15—22no—
157C4×D15—44no—
158C4×D15—44no—
159C4×D15C2×D412yes—
160C4×D15#4112yes—
161Dic30—22no—
162Dic30—22no—
163Dic30—44no—
164C3×C5×C8—21no—
165C3×C5×C8C2×D412yes—
166C3⋊#168—21no—
167C3⋊#168C2×D412yes—
168C2×D3×Q8—52no—
169C22×C4×D3—51no—
170C2×C3×Q16C2×D511yescharacteristic, complemented
171C2×C3×M16C2×D511yescharacteristic
172C3×C22⋊Q8C2×D512yes—
173#946—52no—
174C2×#216—52no—
175#924—52no—
176C2×#208—51no—
177D3×Q16—104no—
178D3×M16—104no—
179C2×Dic12—51no—
180C2×ΓL(1,𝔽25)—51no—
181C2×ΓL(1,𝔽25)—51no—
182C2×D3×C8—51no—
183C2×D3×C8—51no—
184#897—52no—
185#896—102no—
186D3×C4⋊C4—52no—
187D3×C4⋊C4—102no—
188D3×C22⋊C4—102no—
189#878—102no—
190C3×#106C2×D511yescharacteristic, complemented
191C3×#103C2×D512yescomplemented
192#835—52no—
193#817—51no—
194#816—52no—
195#810—52no—
196#808—52no—
197C23×D5—31no—
198C2×C5×Q8C22×D312yes—
199C22×C4×C5C22×D311yescharacteristic
200C22×Dic5—31no—
201Q8×D5—64no—
202Q8×D5—64no—
203C2×C4×D5—31no—
204C2×C4×D5—31no—
205C2×C4×D5—31no—
206C2×C4×D5—31no—
207C2×C4×D5—62no—
208C2×C4×D5—62no—
209C2×C4×D5—62no—
210C2×C4×D5—62no—
211C2×Dic10—32no—
212C2×Dic10—62no—
213C5×Q16—22no—
214C5×M16—22no—
215C2×C5×C8C22×D311yescharacteristic
216C2×C5×C8C22×D311yescharacteristic
217C5×C4⋊C4—22no—
218C5×C4⋊C4C22×D312yes—
219C5×C22⋊C4—22no—
220C22⋊Dic5—62no—
221#689—64no—
222#685—62no—
223#685—62no—
224C4⋊Dic5—32no—
225C4⋊Dic5—62no—
226#683—62no—
227#683—62no—
228#683—62no—
229#681—62no—
230C2×#168—31no—
231C2×#168—31no—
232Dic20—62no—
233#676—62no—
234#676—62no—
235C8×D5—34no—
236C8×D5—62no—
237C22×Q16—151no—
238C22×M16—151no—
239C2×C22⋊Q8—152no—
240#470—151no—
241#470—151no—
242#470—152no—
243#470—151no—
244#470—152no—
245#470D1511yescharacteristic, direct product factor
246C2×#106—151no—
247C2×#103—152no—
248C22×C3×C5—21no—
249C22×C3×C5—22no—
250C22×C3×C5C22×D411yescharacteristic
251C2×D15—21no—
252C2×D15—22no—
253C2×D15—44no—
254C2×D15#12112yes—
255C2×D15#13714yes—
256C3×C4×C5—21no—
257C3×C4×C5—42no—
258C3×C4×C5—42no—
259C3×C4×C5C22×D411yescharacteristic
260C3×C4×C5C2×#4111yescharacteristic
261Dic15—21no—
262Dic15—42no—
263Dic15—42no—
264Dic15#12112yes—
265C23×D3—51no—
266C2×C3×Q8C22×D512yes—
267C22×C3×C4C22×D511yescharacteristic
268C22×Dic3—51no—
269D3×Q8—104no—
270D3×Q8—104no—
271C2×C4×D3—51no—
272C2×C4×D3—51no—
273C2×C4×D3—51no—
274C2×C4×D3—51no—
275C2×C4×D3—102no—
276C2×C4×D3—102no—
277C2×C4×D3—102no—
278C2×C4×D3—102no—
279C2×Dic6—52no—
280C2×Dic6—102no—
281C3×Q16—22no—
282C3×M16—22no—
283C2×C3×C8C22×D511yescharacteristic
284C2×C3×C8C22×D511yescharacteristic
285C3×C4⋊C4—22no—
286C3×C4⋊C4C22×D512yes—
287C3×C22⋊C4—22no—
288#217—102no—
289#216—104no—
290(C2×D3)⋊C4—102no—
291(C2×D3)⋊C4—102no—
292C4⋊Dic3—52no—
293C4⋊Dic3—102no—
294Dic3⋊C4—102no—
295Dic3⋊C4—102no—
296Dic3⋊C4—102no—
297#208—102no—
298C2×C3⋊C8—51no—
299C2×C3⋊C8—51no—
300Dic12—102no—
301ΓL(1,𝔽25)—102no—
302ΓL(1,𝔽25)—102no—
303D3×C8—54no—
304D3×C8—102no—
305C23×C5D3×D411yescharacteristic
306C22×D5—31no—
307C22×D5—31no—
308C22×D5—62no—
309C22×D5—64no—
310C5×Q8—22no—
311C5×Q8—22no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5D3×D411yescharacteristic
317C2×C4×C5C23×D311yescharacteristic
318C2×Dic5—31no—
319C2×Dic5—31no—
320C2×Dic5—62no—
321C2×Dic5—62no—
322C2×Dic5—62no—
323C4×D5—32no—
324C4×D5—32no—
325C4×D5—62no—
326C4×D5—62no—
327C4×D5—61no—
328C4×D5—61no—
329C4×D5—124no—
330C4×D5—124no—
331Dic10—62no—
332Dic10—62no—
333Dic10—124no—
334C5×C8—21no—
335C5×C8D3×D412yes—
336#168—32no—
337#168—61no—
338C22×Q8—152no—
339C23×C4—151no—
340C2×Q16—152no—
341C2×Q16—151no—
342C2×Q16—304no—
343C2×Q16C2×D1511yescharacteristic, complemented
344C2×M16—151no—
345C2×M16—151no—
346C2×M16—151no—
347C2×M16—304no—
348C2×M16C2×D1511yescharacteristic
349C22×C8—151no—
350C22×C8—151no—
351C22⋊Q8—152no—
352C22⋊Q8—152no—
353C22⋊Q8—152no—
354C22⋊Q8—302no—
355C22⋊Q8—302no—
356C22⋊Q8C2×D1512yes—
357C2×C4⋊C4—152no—
358C2×C4⋊C4—302no—
359C2×C22⋊C4—302no—
360#106—151no—
361#106—152no—
362#106C2×D1511yescharacteristic, complemented
363#103—152no—
364#103—152no—
365#103—152no—
366#103C2×D1512yescomplemented
367C2×C3×C5—41no—
368C2×C3×C5C2×#12111yescharacteristic
369C2×C3×C5C2×#13712yes—
370D15—41no—
371D15#47014yesdirect product factor
372C23×C3D4×D511yescharacteristic
373C22×D3—51no—
374C22×D3—51no—
375C22×D3—102no—
376C22×D3—104no—
377C3×Q8—22no—
378C3×Q8—22no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4D4×D511yescharacteristic
384C2×C3×C4C23×D511yescharacteristic
385C2×Dic3—51no—
386C2×Dic3—51no—
387C2×Dic3—102no—
388C2×Dic3—102no—
389C2×Dic3—102no—
390C4×D3—52no—
391C4×D3—52no—
392C4×D3—102no—
393C4×D3—102no—
394C4×D3—101no—
395C4×D3—101no—
396C4×D3—204no—
397C4×D3—204no—
398Dic6—102no—
399Dic6—102no—
400Dic6—204no—
401C3×C8—21no—
402C3×C8D4×D512yes—
403C3⋊C8—52no—
404C3⋊C8—101no—
405C22×C5—22no—
406C22×C5—21no—
407C22×C5C2×D3×D411yescharacteristic
408C2×D5—34no—
409C2×D5—32no—
410C2×D5—62no—
411C2×D5—61no—
412C2×D5—124no—
413C4×C5—21no—
414C4×C5—42no—
415C4×C5—42no—
416C4×C5C2×D3×D411yescharacteristic
417C4×C5D3×#4111yescharacteristic
418Dic5—32no—
419Dic5—61no—
420Dic5—122no—
421Dic5—122no—
422C24—151no—
423C2×Q8—152no—
424C2×Q8—302no—
425C2×Q8—304no—
426C2×Q8—304no—
427C2×Q8C22×D1512yes—
428C22×C4—151no—
429C22×C4—151no—
430C22×C4—151no—
431C22×C4—151no—
432C22×C4—151no—
433C22×C4—302no—
434C22×C4—302no—
435C22×C4—302no—
436C22×C4—302no—
437C22×C4C22×D1511yescharacteristic
438Q16—22no—
439Q16—304no—
440Q16—302no—
441M16—22no—
442M16—302no—
443M16—302no—
444M16—302no—
445C2×C8—151no—
446C2×C8—154no—
447C2×C8—151no—
448C2×C8—302no—
449C2×C8C22×D1511yescharacteristic
450C2×C8C22×D1511yescharacteristic
451C4⋊C4—22no—
452C4⋊C4—152no—
453C4⋊C4—302no—
454C4⋊C4—302no—
455C4⋊C4—302no—
456C4⋊C4—302no—
457C4⋊C4C22×D1512yes—
458C22⋊C4—22no—
459C22⋊C4—302no—
460C22⋊C4—302no—
461C22⋊C4—302no—
462C3×C5C2×#47011yescharacteristic, complemented, Hall
463C22×C3—22no—
464C22×C3—21no—
465C22×C3C2×D4×D511yescharacteristic
466C2×D3—54no—
467C2×D3—52no—
468C2×D3—102no—
469C2×D3—101no—
470C2×D3—204no—
471C3×C4—21no—
472C3×C4—42no—
473C3×C4—42no—
474C3×C4C2×D4×D511yescharacteristic
475C3×C4D5×#4111yescharacteristic
476Dic3—52no—
477Dic3—101no—
478Dic3—202no—
479Dic3—202no—
480C2×C5—41no—
481C2×C5D3×#12111yescharacteristic
482C2×C5D3×#13712yes—
483D5—34no—
484D5—121no—
485C23—151no—
486C23—151no—
487C23—302no—
488C23—304no—
489C23D4×D1511yescharacteristic
490Q8—22no—
491Q8—22no—
492Q8—302no—
493Q8—302no—
494Q8—604no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—151no—
500C2×C4—152no—
501C2×C4—152no—
502C2×C4—151no—
503C2×C4—302no—
504C2×C4—302no—
505C2×C4—302no—
506C2×C4—301no—
507C2×C4—301no—
508C2×C4—302no—
509C2×C4—302no—
510C2×C4—604no—
511C2×C4—604no—
512C2×C4D4×D1511yescharacteristic
513C2×C4C23×D1511yescharacteristic
514C8—21no—
515C8—152no—
516C8—301no—
517C8D4×D1512yes—
518C2×C3—41no—
519C2×C3D5×#12111yescharacteristic
520C2×C3D5×#13712yes—
521D3—54no—
522D3—201no—
523C5D3×#47011yescharacteristic, complemented, Sylow
524C22—21no—
525C22—22no—
526C22—152no—
527C22—154no—
528C22—301no—
529C22—302no—
530C22—604no—
531C22C2×D4×D1511yescharacteristic
532C4—21no—
533C4—42no—
534C4—42no—
535C4—152no—
536C4—301no—
537C4—602no—
538C4—602no—
539C4C2×D4×D1511yescharacteristic
540C4#41×D1511yescharacteristic
541C3D5×#47011yescharacteristic, complemented, Sylow
542C2—41no—
543C2—154no—
544C2—601no—
545C2D15×#12111yescharacteristic
546C2D15×#13712yes—
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#470C2
socleC22×C3×C5C22×D4
prime radicalC23×D15D4
hypercenter#470D15
hypocenterC3×C5C2×#470
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D15C2semidirect
4. C3×C5×#470C2semidirect
5. #11751290C2semidirect
6. #11751238C2semidirect
7. #11751153C2semidirect
8. #11750968C2semidirect
9. D15×#106C2semidirect
10. #11750917C2semidirect
11. D15×#103C2semidirect
15. C2×C3×C5×Q16C22semidirect
19. C2×#6718C22semidirect
24. C2×Dic60C22semidirect
35. C3×C5×#106C22semidirect
36. C3×C5×#103C22semidirect
37. #91119C22semidirect
38. #91101C22semidirect
39. #91100C22semidirect
40. #91094C22semidirect
41. #91092C22semidirect
46. C5×#470D3semidirect
97. C3×#470D5semidirect
107. C2×C5×Q16C2×D3semidirect
127. C5×#106C2×D3semidirect
128. C5×#103C2×D3semidirect
170. C2×C3×Q16C2×D5semidirect
190. C3×#106C2×D5semidirect
191. C3×#103C2×D5semidirect
245. #470D15direct (N × H)
343. C2×Q16C2×D15semidirect
362. #106C2×D15semidirect
366. #103C2×D15semidirect
371. D15#470direct (N × H)
462. C3×C5C2×#470semidirect
523. C5D3×#470semidirect
541. C3D5×#470semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D152
C2×M16×D152
D15×C22⋊Q82
C3×C5×#4702
#117512902
#117512382
#117511532
#117509682
D15×#1062
#117509172
D15×#1032
D5×#4703
D3×#4705