Finite Group Databasebeta

← D15×#391 #14320921

Subgroups — D15×#391 #14320921

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×D15C211yesmaximal, characteristic
2C2×C4⋊C4×D15C211yesmaximal, characteristic
3C2×C42×D15C211yesmaximal, characteristic
4C3×C5×#391C211yesmaximal, characteristic, complemented
5#11751330C211yesmaximal, characteristic, complemented
6#11751074C211yesmaximal, characteristic, complemented
7#11751030C211yesmaximal, characteristic, complemented
8D15×#95C214yesmaximal
9#11750747C214yesmaximal, complemented
10D5×#391—31nomaximal, Hall
11C22×C3×C5×Q8C2211yescharacteristic
12C2×Q8×D15—24no—
13C2×Q8×D15—24no—
14C2×Q8×D15C418yescomplemented
15C22×C4×D15C2212yes—
16C22×C4×D15C2212yes—
17C22×C4×D15C2212yes—
18C22×C4×D15C2211yescharacteristic
19C22×Dic30C2212yes—
20C22×Dic30C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C42×C5C2211yescharacteristic
23C2×C4⋊Dic15C2211yescharacteristic
24C2×#6712C2212yes—
25C2×C4×Dic15C2212yes—
26C2×C4×Dic15C2211yescharacteristic
27C4⋊C4×D15—24no—
28C42×D15—24no—
29C3×C5×#95C2214yes—
30#91115C2214yes—
31#91115C2214yes—
32#91115C2214yes—
33D3×#391—51nomaximal, Hall
34C22×Q8×D5—31no—
35C2×D5×C4⋊C4—31no—
36C2×C42×D5—31no—
37C5×#391D311yescharacteristic, complemented
38#65519—31no—
39#65263—31no—
40#65218—31no—
41D5×#95—34no—
42#64935—34no—
43C23×D15C2311yescharacteristic
44C2×C3×C5×Q8—22no—
45C2×C3×C5×Q8—22no—
46C2×C3×C5×Q8C2×C414yescomplemented
47C22×C3×C4×C5C2312yes—
48C22×C3×C4×C5C2312yes—
49C22×C3×C4×C5C2312yes—
50C22×C3×C4×C5C2311yescharacteristic
51C22×Dic15C2312yes—
52C22×Dic15C2312yes—
53C22×Dic15C2312yes—
54C22×Dic15C2311yescharacteristic
55Q8×D15—232no—
56C2×C4×D15—24no—
57C2×C4×D15—24no—
58C2×C4×D15—24no—
59C2×C4×D15—24no—
60C2×C4×D15—24no—
61C2×C4×D15—28no—
62C2×C4×D15C2×C418yes—
63C2×C4×D15C2×C414yes—
64C2×C4×D15D414yes—
65C2×C4×D15D414yes—
66C2×C4×D15Q818yescomplemented
67C2×Dic30—22no—
68C2×Dic30—22no—
69C2×Dic30—24no—
70C2×Dic30—24no—
71C2×Dic30C2×C414yescomplemented
72C2×Dic30C2×C418yescomplemented
73C3×C5×C4⋊C4—22no—
74C3×C42×C5—22no—
75C4⋊Dic15—22no—
76#6712—24no—
77C4×Dic15—22no—
78C4×Dic15—24no—
79C22×D3×Q8—51no—
80C2×D3×C4⋊C4—51no—
81C2×C42×D3—51no—
82C3×#391D511yescharacteristic, complemented
83#5229—51no—
84#4973—51no—
85#4929—51no—
86D3×#95—54no—
87#4646—54no—
88C22×C5×Q8C2×D311yescharacteristic
89C2×Q8×D5—38no—
90C2×Q8×D5—64no—
91C2×Q8×D5—64no—
92C22×C4×D5—31no—
93C22×C4×D5—32no—
94C22×C4×D5—32no—
95C22×C4×D5—32no—
96C22×Dic10—32no—
97C22×Dic10—31no—
98C2×C5×C4⋊C4C2×D311yescharacteristic
99C2×C42×C5C2×D311yescharacteristic
100C2×C4⋊Dic5—31no—
101C2×#683—32no—
102C2×C4×Dic5—32no—
103C2×C4×Dic5—31no—
104D5×C4⋊C4—64no—
105C42×D5—64no—
106C5×#95C2×D314yes—
107#3963—34no—
108#3963—34no—
109#3963—34no—
110C2×#391—151noSylow
111C23×C3×C5C2411yescharacteristic
112C22×D15C22×C412yes—
113C22×D15C2×D412yes—
114C22×D15C2×D412yes—
115C22×D15C2×Q814yes—
116C22×D15#4114yes—
117C3×C5×Q8—28no—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—24no—
124C2×C3×C4×C5C22×C414yes—
125C2×C3×C4×C5C22×C412yes—
126C2×C3×C4×C5C2×D412yes—
127C2×C3×C4×C5C2×D412yes—
128C2×C3×C4×C5C2×Q814yescomplemented
129C2×Dic15—22no—
130C2×Dic15—22no—
131C2×Dic15—22no—
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—24no—
135C2×Dic15C22×C414yes—
136C2×Dic15C22×C412yes—
137C2×Dic15C2×D412yes—
138C2×Dic15C2×D412yes—
139C2×Dic15C2×Q814yescomplemented
140C4×D15—216no—
141C4×D15—216no—
142C4×D15—48no—
143C4×D15C22⋊C4116yes—
144Dic30—28no—
145Dic30—216no—
146C22×C3×Q8C2×D511yescharacteristic
147C2×D3×Q8—58no—
148C2×D3×Q8—104no—
149C2×D3×Q8—104no—
150C22×C4×D3—51no—
151C22×C4×D3—52no—
152C22×C4×D3—52no—
153C22×C4×D3—52no—
154C22×Dic6—52no—
155C22×Dic6—51no—
156C2×C3×C4⋊C4C2×D511yescharacteristic
157C2×C3×C42C2×D511yescharacteristic
158C2×C4⋊Dic3—51no—
159C2×Dic3⋊C4—52no—
160C2×C4×Dic3—52no—
161C2×C4×Dic3—51no—
162D3×C4⋊C4—104no—
163C42×D3—104no—
164C3×#95C2×D514yes—
165C3⋊#95—54no—
166C3⋊#95—54no—
167C3⋊#95—54no—
168C23×D5—31no—
169C2×C5×Q8—22no—
170C2×C5×Q8—22no—
171C2×C5×Q8C4×D314yescomplemented
172C22×C4×C5C22×D312yes—
173C22×C4×C5C22×D312yes—
174C22×C4×C5C22×D312yes—
175C22×C4×C5C22×D311yescharacteristic
176C22×Dic5—31no—
177C22×Dic5—32no—
178C22×Dic5—32no—
179C22×Dic5—32no—
180Q8×D5—632no—
181C2×C4×D5—34no—
182C2×C4×D5—34no—
183C2×C4×D5—34no—
184C2×C4×D5—38no—
185C2×C4×D5—38no—
186C2×C4×D5—64no—
187C2×C4×D5—64no—
188C2×C4×D5—64no—
189C2×C4×D5—64no—
190C2×C4×D5—68no—
191C2×C4×D5—64no—
192C2×Dic10—38no—
193C2×Dic10—34no—
194C2×Dic10—64no—
195C2×Dic10—64no—
196C2×Dic10—62no—
197C2×Dic10—62no—
198C5×C4⋊C4—22no—
199C42×C5—22no—
200C4⋊Dic5—62no—
201#683—64no—
202C4×Dic5—64no—
203C4×Dic5—62no—
204C23×Q8—151no—
205C22×C4⋊C4—151no—
206C22×C42—151no—
207#391—151no—
208#391—151no—
209#391—151no—
210#391—154no—
211#391D1511yescharacteristic, direct product factor
212C2×#95—154no—
213C22×C3×C5C23×C411yescharacteristic
214C22×C3×C5C22×D411yescharacteristic
215C22×C3×C5C22×D411yescharacteristic
216C22×C3×C5C22×Q812yes—
217C22×C3×C5C2×#4112yes—
218C2×D15C2×C22⋊C414yes—
219C2×D15C4×Q818yes—
220C2×D15C22⋊Q818yes—
221C2×D15#12414yes—
222C2×D15C4⋊Q814yes—
223C3×C4×C5—24no—
224C3×C4×C5—24no—
225C3×C4×C5—42no—
226C3×C4×C5C2×C22⋊C414yes—
227Dic15—24no—
228Dic15—24no—
229Dic15—42no—
230Dic15C2×C22⋊C414yes—
231C23×D3—51no—
232C2×C3×Q8—22no—
233C2×C3×Q8—22no—
234C2×C3×Q8C4×D514yescomplemented
235C22×C3×C4C22×D512yes—
236C22×C3×C4C22×D512yes—
237C22×C3×C4C22×D512yes—
238C22×C3×C4C22×D511yescharacteristic
239C22×Dic3—51no—
240C22×Dic3—52no—
241C22×Dic3—52no—
242C22×Dic3—52no—
243D3×Q8—1032no—
244C2×C4×D3—54no—
245C2×C4×D3—54no—
246C2×C4×D3—54no—
247C2×C4×D3—58no—
248C2×C4×D3—58no—
249C2×C4×D3—104no—
250C2×C4×D3—104no—
251C2×C4×D3—104no—
252C2×C4×D3—104no—
253C2×C4×D3—104no—
254C2×C4×D3—108no—
255C2×Dic6—58no—
256C2×Dic6—54no—
257C2×Dic6—104no—
258C2×Dic6—104no—
259C2×Dic6—102no—
260C2×Dic6—102no—
261C3×C4⋊C4—22no—
262C3×C42—22no—
263C4⋊Dic3—102no—
264Dic3⋊C4—104no—
265C4×Dic3—104no—
266C4×Dic3—102no—
267C23×C5C23×D311yescharacteristic
268C22×D5—32no—
269C22×D5—32no—
270C22×D5—32no—
271C22×D5—34no—
272C22×D5—34no—
273C5×Q8—28no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—22no—
278C2×C4×C5—22no—
279C2×C4×C5—24no—
280C2×C4×C5C2×C4×D314yes—
281C2×C4×C5C2×C4×D312yes—
282C2×C4×C5D3×D412yes—
283C2×C4×C5D3×D412yes—
284C2×C4×C5D3×Q814yescomplemented
285C2×Dic5—32no—
286C2×Dic5—32no—
287C2×Dic5—32no—
288C2×Dic5—34no—
289C2×Dic5—34no—
290C2×Dic5—62no—
291C2×Dic5—62no—
292C2×Dic5—62no—
293C2×Dic5—62no—
294C2×Dic5—62no—
295C2×Dic5—64no—
296C4×D5—316no—
297C4×D5—616no—
298C4×D5—616no—
299C4×D5—128no—
300Dic10—616no—
301Dic10—68no—
302C22×Q8—158no—
303C22×Q8—152no—
304C22×Q8—151no—
305C22×Q8—304no—
306C22×Q8—304no—
307C22×Q8C2×D1511yescharacteristic
308C23×C4—151no—
309C23×C4—152no—
310C23×C4—152no—
311C23×C4—152no—
312C2×C4⋊C4—152no—
313C2×C4⋊C4—151no—
314C2×C4⋊C4—304no—
315C2×C4⋊C4C2×D1511yescharacteristic
316C2×C42—152no—
317C2×C42—151no—
318C2×C42—304no—
319C2×C42C2×D1511yescharacteristic
320#95—154no—
321#95—154no—
322#95—154no—
323#95C2×D1514yes—
324C2×C3×C5C22×C22⋊C411yescharacteristic
325C2×C3×C5C2×C4×Q812yes—
326C2×C3×C5C2×C22⋊Q812yes—
327C2×C3×C5C2×#12411yescharacteristic
328C2×C3×C5C2×C4⋊Q811yescharacteristic
329D15#39118yesdirect product factor
330C23×C3C23×D511yescharacteristic
331C22×D3—52no—
332C22×D3—52no—
333C22×D3—52no—
334C22×D3—54no—
335C22×D3—54no—
336C3×Q8—28no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—24no—
343C2×C3×C4C2×C4×D514yes—
344C2×C3×C4C2×C4×D512yes—
345C2×C3×C4D4×D512yes—
346C2×C3×C4D4×D512yes—
347C2×C3×C4Q8×D514yescomplemented
348C2×Dic3—52no—
349C2×Dic3—52no—
350C2×Dic3—52no—
351C2×Dic3—54no—
352C2×Dic3—54no—
353C2×Dic3—102no—
354C2×Dic3—102no—
355C2×Dic3—102no—
356C2×Dic3—102no—
357C2×Dic3—102no—
358C2×Dic3—104no—
359C4×D3—516no—
360C4×D3—1016no—
361C4×D3—1016no—
362C4×D3—208no—
363Dic6—1016no—
364Dic6—108no—
365C22×C5C22×C4×D311yescharacteristic
366C22×C5C2×D3×D411yescharacteristic
367C22×C5C2×D3×D411yescharacteristic
368C22×C5C2×D3×Q812yes—
369C22×C5D3×#4112yes—
370C2×D5—34no—
371C2×D5—34no—
372C2×D5—34no—
373C2×D5—38no—
374C2×D5—38no—
375C4×C5—24no—
376C4×C5—24no—
377C4×C5—42no—
378C4×C5D3×C22⋊C414yes—
379Dic5—34no—
380Dic5—64no—
381Dic5—64no—
382Dic5—122no—
383C24—151no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—158no—
387C2×Q8—154no—
388C2×Q8—304no—
389C2×Q8—304no—
390C2×Q8—3032no—
391C2×Q8—302no—
392C2×Q8—302no—
393C2×Q8C4×D1514yescomplemented
394C22×C4—151no—
395C22×C4—154no—
396C22×C4—154no—
397C22×C4—154no—
398C22×C4—152no—
399C22×C4—152no—
400C22×C4—158no—
401C22×C4—158no—
402C22×C4—152no—
403C22×C4—304no—
404C22×C4—304no—
405C22×C4—304no—
406C22×C4—304no—
407C22×C4—304no—
408C22×C4—308no—
409C22×C4C22×D1512yes—
410C22×C4C22×D1512yes—
411C22×C4C22×D1512yes—
412C22×C4C22×D1511yescharacteristic
413C4⋊C4—22no—
414C4⋊C4—304no—
415C4⋊C4—302no—
416C42—22no—
417C42—304no—
418C42—302no—
419C3×C5C2×#39111yescharacteristic, complemented, Hall
420C22×C3C22×C4×D511yescharacteristic
421C22×C3C2×D4×D511yescharacteristic
422C22×C3C2×D4×D511yescharacteristic
423C22×C3C2×Q8×D512yes—
424C22×C3D5×#4112yes—
425C2×D3—54no—
426C2×D3—54no—
427C2×D3—58no—
428C2×D3—58no—
429C2×D3—54no—
430C3×C4—24no—
431C3×C4—24no—
432C3×C4—42no—
433C3×C4D5×C22⋊C414yes—
434Dic3—54no—
435Dic3—104no—
436Dic3—104no—
437Dic3—202no—
438C2×C5C2×D3×C22⋊C411yescharacteristic
439C2×C5C4×D3×Q812yes—
440C2×C5D3×C22⋊Q812yes—
441C2×C5D3×#12411yescharacteristic
442C2×C5D3×C4⋊Q811yescharacteristic
443D5—38no—
444C23—152no—
445C23—152no—
446C23—152no—
447C23—154no—
448C23—154no—
449C23C23×D1511yescharacteristic
450Q8—28no—
451Q8—3016no—
452Q8—308no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—152no—
460C2×C4—152no—
461C2×C4—152no—
462C2×C4—1516no—
463C2×C4—154no—
464C2×C4—154no—
465C2×C4—3016no—
466C2×C4—3016no—
467C2×C4—302no—
468C2×C4—302no—
469C2×C4—302no—
470C2×C4—302no—
471C2×C4—302no—
472C2×C4—304no—
473C2×C4—608no—
474C2×C4C2×C4×D1514yes—
475C2×C4C2×C4×D1512yes—
476C2×C4D4×D1512yes—
477C2×C4D4×D1512yes—
478C2×C4Q8×D1514yescomplemented
479C2×C3C2×D5×C22⋊C411yescharacteristic
480C2×C3C4×Q8×D512yes—
481C2×C3D5×C22⋊Q812yes—
482C2×C3D5×#12411yescharacteristic
483C2×C3D5×C4⋊Q811yescharacteristic
484D3—58no—
485C5D3×#39111yescharacteristic, complemented, Sylow
486C22—158no—
487C22—158no—
488C22—154no—
489C22—154no—
490C22—154no—
491C22C22×C4×D1511yescharacteristic
492C22C2×D4×D1511yescharacteristic
493C22C2×D4×D1511yescharacteristic
494C22C2×Q8×D1512yes—
495C22#41×D1512yes—
496C4—24no—
497C4—24no—
498C4—42no—
499C4—154no—
500C4—304no—
501C4—304no—
502C4—602no—
503C4C22⋊C4×D1514yes—
504C3D5×#39111yescharacteristic, complemented, Sylow
505C2—158no—
506C2C2×C22⋊C4×D1511yescharacteristic
507C2C4×Q8×D1512yes—
508C2D15×C22⋊Q812yes—
509C2D15×#12411yescharacteristic
510C2D15×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#391C2
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenter#391D15
hypocenterC3×C5C2×#391
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
4. C3×C5×#391C2semidirect
5. #11751330C2semidirect
6. #11751074C2semidirect
7. #11751030C2semidirect
9. #11750747C2semidirect
14. C2×Q8×D15C4semidirect
37. C5×#391D3semidirect
46. C2×C3×C5×Q8C2×C4semidirect
66. C2×C4×D15Q8semidirect
71. C2×Dic30C2×C4semidirect
72. C2×Dic30C2×C4semidirect
82. C3×#391D5semidirect
128. C2×C3×C4×C5C2×Q8semidirect
139. C2×Dic15C2×Q8semidirect
171. C2×C5×Q8C4×D3semidirect
211. #391D15direct (N × H)
234. C2×C3×Q8C4×D5semidirect
284. C2×C4×C5D3×Q8semidirect
329. D15#391direct (N × H)
347. C2×C3×C4Q8×D5semidirect
393. C2×Q8C4×D15semidirect
419. C3×C5C2×#391semidirect
478. C2×C4Q8×D15semidirect
485. C5D3×#391semidirect
504. C3D5×#391semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D152
C2×C4⋊C4×D152
C2×C42×D152
C3×C5×#3912
#117513302
#117510742
#117510302
D15×#952
#117507472
D5×#3913
D3×#3915