Finite Group Databasebeta

← D15×#501 #14439890

Subgroups — D15×#501 #14439890

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D15×C4⋊Q8C211yesmaximal, characteristic
2D15×#125C211yesmaximal, characteristic
3C3×C5×#501C211yesmaximal, characteristic, complemented
4#11751182C211yesmaximal, characteristic, complemented
5#11751165C211yesmaximal, characteristic, complemented
6D15×#107C212yesmaximal
7#11750977C212yesmaximal, complemented
8D15×#106C212yesmaximal
9#11750957C212yesmaximal, complemented
10D15×#97C211yesmaximal, characteristic
11#11750803C211yesmaximal, characteristic, complemented
12D5×#501—31nomaximal, Hall
13C2×Q8×D15—21no—
14C3×C5×C4⋊Q8C2211yescharacteristic
15C3×C5×#125C2211yescharacteristic
16#91833—21no—
17C2×C8×D15C2212yes—
18C4⋊C4×D15—21no—
19C4⋊C4×D15—21no—
20C4⋊C4×D15—21no—
21C4⋊C4×D15C2211yescharacteristic
22C4⋊C4×D15C2212yes—
23C4⋊C4×D15C2211yescharacteristic
24#91779C2211yescharacteristic
25#91779C2211yescharacteristic
26#91778—21no—
27#91778—21no—
28#91777—21no—
29#91777C2212yes—
30C42×D15C2211yescharacteristic
31#91759C2211yescharacteristic
32#91758C2211yescharacteristic
33C3×C5×#107C2212yes—
34C3×C5×#106C2212yes—
35C3×C5×#97C2211yescharacteristic
36#91102C2212yes—
37#91101C2212yes—
38#91099C2212yes—
39#91092C2212yes—
40#91092C2212yes—
41#91091C2212yes—
42#91091C2212yes—
43#91087C2211yescharacteristic
44D3×#501—51nomaximal, Hall
45D5×C4⋊Q8—31no—
46D5×#125—31no—
47C5×#501D311yescharacteristic, complemented
48#65369—31no—
49#65354—31no—
50D5×#107—32no—
51#65165—32no—
52D5×#106—32no—
53#65145—32no—
54D5×#97—31no—
55#64991—31no—
56C2×C3×C5×Q8—21no—
57Q8×D15—44no—
58C2×C4×D15—21no—
59C2×C4×D15—21no—
60C2×C4×D15—22no—
61C2×C4×D15D411yescharacteristic
62C2×C4×D15D411yescharacteristic
63C2×C4×D15C2311yescharacteristic
64C2×Dic30—21no—
65C2×Dic30—22no—
66C2×C3×C5×C8C2312yes—
67C3×C5×C4⋊C4—21no—
68C3×C5×C4⋊C4—21no—
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4C2312yes—
71C3×C5×C4⋊C4C2311yescharacteristic
72C3×C5×C4⋊C4C2311yescharacteristic
73C3×C42×C5C2311yescharacteristic
74C4⋊Dic15—21no—
75C4⋊Dic15—21no—
76C4⋊Dic15—21no—
77C4⋊Dic15C2312yes—
78C4⋊Dic15C2311yescharacteristic
79C4⋊Dic15C2311yescharacteristic
80#6712—21no—
81#6712—21no—
82#6712—22no—
83#6712—22no—
84#6712—21no—
85#6712—21no—
86#6712—21no—
87#6712—21no—
88C4×Dic15D411yescharacteristic
89C4×Dic15D411yescharacteristic
90C4×Dic15C2311yescharacteristic
91C2×C3⋊#168C2312yes—
92C8×D15Q818yescomplemented
93D3×C4⋊Q8—51no—
94D3×#125—51no—
95C3×#501D511yescharacteristic, complemented
96#5081—51no—
97#5064—51no—
98D3×#107—52no—
99#4876—52no—
100D3×#106—52no—
101#4856—52no—
102D3×#97—51no—
103#4702—51no—
104C2×Q8×D5—61no—
105C5×C4⋊Q8C2×D311yescharacteristic
106C5×#125C2×D311yescharacteristic
107#4090—61no—
108C2×C8×D5—32no—
109D5×C4⋊C4—32no—
110D5×C4⋊C4—31no—
111D5×C4⋊C4—31no—
112D5×C4⋊C4—61no—
113D5×C4⋊C4—61no—
114D5×C4⋊C4—61no—
115#4036—31no—
116#4036—31no—
117#4035—61no—
118#4035—61no—
119#4034—32no—
120#4034—61no—
121C42×D5—31no—
122#4016—31no—
123#4015—31no—
124C5×#107C2×D312yes—
125C5×#106C2×D312yes—
126C5×#97C2×D311yescharacteristic
127#3950—32no—
128#3949—32no—
129#3947—32no—
130#3940—32no—
131#3940—32no—
132#3939—32no—
133#3939—32no—
134#3935—31no—
135C2×#501—151noSylow
136C22×D15C2×D411yescharacteristic
137C3×C5×Q8—42no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—21no—
145C2×Dic15—21no—
146C2×Dic15—22no—
147C2×Dic15C2×D411yescharacteristic
148C2×Dic15C2×D411yescharacteristic
149C2×Dic15C2×D411yescharacteristic
150C4×D15—22no—
151C4×D15—22no—
152C4×D15—42no—
153C4×D15—44no—
154C4×D15—42no—
155C4×D15C2×Q814yes—
156Dic30—44no—
157Dic30—42no—
158C3×C5×C8C2×Q814yescomplemented
159C3⋊#168C2×Q814yescomplemented
160C2×D3×Q8—101no—
161C3×C4⋊Q8C2×D511yescharacteristic
162C3×#125C2×D511yescharacteristic
163#944—101no—
164C2×D3×C8—52no—
165D3×C4⋊C4—51no—
166D3×C4⋊C4—52no—
167D3×C4⋊C4—51no—
168D3×C4⋊C4—101no—
169D3×C4⋊C4—101no—
170D3×C4⋊C4—101no—
171#890—51no—
172#890—51no—
173#889—101no—
174#889—101no—
175#888—52no—
176#888—101no—
177C42×D3—51no—
178#870—51no—
179#869—51no—
180C3×#107C2×D512yes—
181C3×#106C2×D512yes—
182C3×#97C2×D511yescharacteristic
183#818—52no—
184#817—52no—
185#815—52no—
186#808—52no—
187#808—52no—
188#807—52no—
189#807—52no—
190#803—51no—
191C2×C5×Q8—21no—
192Q8×D5—124no—
193C2×C4×D5—31no—
194C2×C4×D5—31no—
195C2×C4×D5—31no—
196C2×C4×D5—62no—
197C2×C4×D5—61no—
198C2×C4×D5—61no—
199C2×Dic10—62no—
200C2×Dic10—61no—
201C2×C5×C8C22×D312yes—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4C22×D311yescharacteristic
206C5×C4⋊C4C22×D311yescharacteristic
207C5×C4⋊C4C22×D312yes—
208C42×C5C22×D311yescharacteristic
209C4⋊Dic5—31no—
210C4⋊Dic5—32no—
211C4⋊Dic5—31no—
212C4⋊Dic5—61no—
213C4⋊Dic5—61no—
214C4⋊Dic5—61no—
215#683—62no—
216#683—62no—
217#683—61no—
218#683—61no—
219#683—61no—
220#683—61no—
221#683—61no—
222#683—61no—
223C4×Dic5—31no—
224C4×Dic5—31no—
225C4×Dic5—31no—
226C2×#168—32no—
227C8×D5—38no—
228C2×C4⋊Q8—151no—
229C2×#125—151no—
230#501—151no—
231#501—151no—
232#501—152no—
233#501—152no—
234#501—151no—
235#501D1511yescharacteristic, direct product factor
236C2×#107—152no—
237C2×#106—152no—
238C2×#97—151no—
239C22×C3×C5C22×D411yescharacteristic
240C2×D15C4⋊Q812yes—
241C2×D15AGL(1,ℤ/8)12yes—
242C2×D15#13712yes—
243C3×C4×C5—21no—
244C3×C4×C5—21no—
245C3×C4×C5—42no—
246C3×C4×C5—41no—
247C3×C4×C5—41no—
248C3×C4×C5C22×Q812yes—
249Dic15—21no—
250Dic15—21no—
251Dic15—42no—
252Dic15—41no—
253Dic15—41no—
254Dic15C4⋊Q812yes—
255C2×C3×Q8—21no—
256D3×Q8—204no—
257C2×C4×D3—51no—
258C2×C4×D3—51no—
259C2×C4×D3—51no—
260C2×C4×D3—101no—
261C2×C4×D3—101no—
262C2×C4×D3—102no—
263C2×Dic6—102no—
264C2×Dic6—101no—
265C2×C3×C8C22×D512yes—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4C22×D511yescharacteristic
270C3×C4⋊C4C22×D512yes—
271C3×C4⋊C4C22×D511yescharacteristic
272C3×C42C22×D511yescharacteristic
273C4⋊Dic3—51no—
274C4⋊Dic3—52no—
275C4⋊Dic3—51no—
276C4⋊Dic3—101no—
277C4⋊Dic3—101no—
278C4⋊Dic3—101no—
279Dic3⋊C4—102no—
280Dic3⋊C4—102no—
281Dic3⋊C4—101no—
282Dic3⋊C4—101no—
283Dic3⋊C4—101no—
284Dic3⋊C4—101no—
285Dic3⋊C4—101no—
286Dic3⋊C4—101no—
287C4×Dic3—51no—
288C4×Dic3—51no—
289C4×Dic3—51no—
290C2×C3⋊C8—52no—
291D3×C8—58no—
292C22×D5—31no—
293C5×Q8—42no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—22no—
297C2×C4×C5D3×D411yescharacteristic
298C2×C4×C5D3×D411yescharacteristic
299C2×C4×C5C23×D311yescharacteristic
300C2×Dic5—31no—
301C2×Dic5—31no—
302C2×Dic5—31no—
303C2×Dic5—61no—
304C2×Dic5—61no—
305C2×Dic5—62no—
306C4×D5—34no—
307C4×D5—62no—
308C4×D5—62no—
309C4×D5—122no—
310C4×D5—122no—
311C4×D5—124no—
312Dic10—124no—
313Dic10—122no—
314C5×C8D3×Q814yescomplemented
315#168—34no—
316C22×Q8—301no—
317C22×C8—152no—
318C4⋊Q8—152no—
319C4⋊Q8—151no—
320C4⋊Q8—301no—
321C4⋊Q8—301no—
322C4⋊Q8C2×D1511yescharacteristic
323#125—151no—
324#125—151no—
325#125—151no—
326#125—301no—
327#125—301no—
328#125C2×D1511yescharacteristic
329C2×C4⋊C4—151no—
330C2×C4⋊C4—151no—
331C2×C4⋊C4—152no—
332C2×C4⋊C4—301no—
333C2×C4⋊C4—301no—
334C2×C4⋊C4—301no—
335C2×C42—151no—
336#107—152no—
337#107—152no—
338#107—152no—
339#107C2×D1512yes—
340#106—152no—
341#106—152no—
342#106—152no—
343#106C2×D1512yes—
344#97—152no—
345#97—151no—
346#97C2×D1511yescharacteristic
347C2×C3×C5C2×C4⋊Q811yescharacteristic
348C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
349C2×C3×C5C2×#13711yescharacteristic
350D15#50114yesdirect product factor
351C22×D3—51no—
352C3×Q8—42no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—22no—
356C2×C3×C4D4×D511yescharacteristic
357C2×C3×C4D4×D511yescharacteristic
358C2×C3×C4C23×D511yescharacteristic
359C2×Dic3—51no—
360C2×Dic3—51no—
361C2×Dic3—51no—
362C2×Dic3—101no—
363C2×Dic3—101no—
364C2×Dic3—102no—
365C4×D3—54no—
366C4×D3—102no—
367C4×D3—102no—
368C4×D3—202no—
369C4×D3—202no—
370C4×D3—204no—
371Dic6—204no—
372Dic6—202no—
373C3×C8Q8×D514yescomplemented
374C3⋊C8—54no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—32no—
377C2×D5—32no—
378C2×D5—32no—
379C4×C5—21no—
380C4×C5—21no—
381C4×C5—42no—
382C4×C5—41no—
383C4×C5—41no—
384C4×C5C2×D3×Q812yes—
385Dic5—32no—
386Dic5—61no—
387Dic5—61no—
388Dic5—122no—
389Dic5—121no—
390Dic5—121no—
391C2×Q8—21no—
392C2×Q8—302no—
393C2×Q8—301no—
394C2×Q8—604no—
395C22×C4—151no—
396C22×C4—151no—
397C22×C4—151no—
398C22×C4—301no—
399C22×C4—301no—
400C22×C4—302no—
401C2×C8—152no—
402C2×C8—158no—
403C2×C8C22×D1512yes—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—151no—
408C4⋊C4—152no—
409C4⋊C4—151no—
410C4⋊C4—301no—
411C4⋊C4—301no—
412C4⋊C4—302no—
413C4⋊C4—301no—
414C4⋊C4—301no—
415C4⋊C4—301no—
416C4⋊C4—301no—
417C4⋊C4—302no—
418C4⋊C4—301no—
419C4⋊C4—301no—
420C4⋊C4—301no—
421C4⋊C4C22×D1511yescharacteristic
422C4⋊C4C22×D1512yes—
423C4⋊C4C22×D1511yescharacteristic
424C42—151no—
425C42—151no—
426C42—151no—
427C42C22×D1511yescharacteristic
428C3×C5C2×#50111yescharacteristic, complemented, Hall
429C22×C3C2×D4×D511yescharacteristic
430C2×D3—52no—
431C2×D3—52no—
432C2×D3—52no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—42no—
436C3×C4—41no—
437C3×C4—41no—
438C3×C4C2×Q8×D512yes—
439Dic3—52no—
440Dic3—101no—
441Dic3—101no—
442Dic3—202no—
443Dic3—201no—
444Dic3—201no—
445C2×C5D3×C4⋊Q811yescharacteristic
446C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
447C2×C5D3×#13711yescharacteristic
448D5—34no—
449C23—151no—
450Q8—42no—
451Q8—602no—
452Q8—604no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—22no—
456C2×C4—151no—
457C2×C4—154no—
458C2×C4—151no—
459C2×C4—151no—
460C2×C4—302no—
461C2×C4—302no—
462C2×C4—301no—
463C2×C4—301no—
464C2×C4—302no—
465C2×C4—604no—
466C2×C4—602no—
467C2×C4—602no—
468C2×C4D4×D1511yescharacteristic
469C2×C4D4×D1511yescharacteristic
470C2×C4C23×D1511yescharacteristic
471C8—154no—
472C8Q8×D1514yescomplemented
473C2×C3D5×C4⋊Q811yescharacteristic
474C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
475C2×C3D5×#13711yescharacteristic
476D3—54no—
477C5D3×#50111yescharacteristic, complemented, Sylow
478C22—152no—
479C22—152no—
480C22—152no—
481C22C2×D4×D1511yescharacteristic
482C4—21no—
483C4—21no—
484C4—42no—
485C4—41no—
486C4—41no—
487C4—152no—
488C4—301no—
489C4—301no—
490C4—602no—
491C4—601no—
492C4—601no—
493C4C2×Q8×D1512yes—
494C3D5×#50111yescharacteristic, complemented, Sylow
495C2—154no—
496C2D15×C4⋊Q811yescharacteristic
497C2D15×AGL(1,ℤ/8)11yescharacteristic
498C2D15×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#501C2
socleC22×C3×C5C22×D4
prime radicalC22×D15C2×D4
hypercenter#501D15
hypocenterC3×C5C2×#501
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. C3×C5×#501C2semidirect
4. #11751182C2semidirect
5. #11751165C2semidirect
7. #11750977C2semidirect
9. #11750957C2semidirect
11. #11750803C2semidirect
47. C5×#501D3semidirect
92. C8×D15Q8semidirect
95. C3×#501D5semidirect
158. C3×C5×C8C2×Q8semidirect
159. C3⋊#168C2×Q8semidirect
235. #501D15direct (N × H)
314. C5×C8D3×Q8semidirect
350. D15#501direct (N × H)
373. C3×C8Q8×D5semidirect
428. C3×C5C2×#501semidirect
472. C8Q8×D15semidirect
477. C5D3×#501semidirect
494. C3D5×#501semidirect

Maximal subgroups

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

subgroupindex
D15×C4⋊Q82
D15×#1252
C3×C5×#5012
#117511822
#117511652
D15×#1072
#117509772
D15×#1062
#117509572
D15×#972
#117508032
D5×#5013
D3×#5015