Finite Group Databasebeta

← D15×#400 #14332024

Subgroups — D15×#400 #14332024

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D15C211yesmaximal, characteristic
2C2×C4⋊C4×D15C211yesmaximal, characteristic
3C3×C5×#400C211yesmaximal, characteristic, complemented
4#11751087C211yesmaximal, characteristic, complemented
5#11751086C211yesmaximal, characteristic, complemented
6D15×#95C211yesmaximal, characteristic
7D15×#95C212yesmaximal
8D15×#95C212yesmaximal
9#11750761C212yesmaximal, complemented
10#11750760C211yesmaximal, characteristic, complemented
11#11750759C212yesmaximal, complemented
12D5×#400—31nomaximal, Hall
13C22×C4×D15C2212yes—
14C22×C4×D15C2211yescharacteristic
15C22×C4×D15C2212yes—
16C22×C4×D15C2211yescharacteristic
17C22×C4×D15C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic
22C2×#6712C2211yescharacteristic
23C2×#6712C2212yes—
24C2×#6712C2211yescharacteristic
25C4⋊C4×D15—24no—
26C4⋊C4×D15—24no—
27C3×C5×#95C2212yes—
28C3×C5×#95C2211yescharacteristic
29C3×C5×#95C2212yes—
30#91115C2212yes—
31#91115C2212yes—
32#91115C2212yes—
33#91115C2212yes—
34#91115C2212yes—
35#91115C2212yes—
36#91115C2212yes—
37#91115C2211yescharacteristic
38D3×#400—51nomaximal, Hall
39C2×D5×C4⋊C4—31no—
40C2×D5×C4⋊C4—31no—
41C5×#400D311yescharacteristic, complemented
42#65275—31no—
43#65271—31no—
44D5×#95—31no—
45D5×#95—32no—
46D5×#95—32no—
47#64949—32no—
48#64948—31no—
49#64947—32no—
50C23×D15C2311yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15C2312yes—
57C22×Dic15C2311yescharacteristic
58C22×Dic15C2312yes—
59C22×Dic15C2311yescharacteristic
60C22×Dic15C2311yescharacteristic
61C2×C4×D15—22no—
62C2×C4×D15—22no—
63C2×C4×D15—24no—
64C2×C4×D15—22no—
65C2×C4×D15—24no—
66C2×C4×D15—24no—
67C2×C4×D15—28no—
68C2×C4×D15—24no—
69C2×C4×D15—24no—
70C2×C4×D15—24no—
71C2×C4×D15D414yes—
72C2×C4×D15Q814yes—
73C3×C5×C4⋊C4—22no—
74C3×C5×C4⋊C4—22no—
75C4⋊Dic15—22no—
76C4⋊Dic15—22no—
77#6712—22no—
78#6712—22no—
79#6712—24no—
80C2×D3×C4⋊C4—51no—
81C2×D3×C4⋊C4—51no—
82C3×#400D511yescharacteristic, complemented
83#4986—51no—
84#4985—51no—
85D3×#95—52no—
86D3×#95—51no—
87D3×#95—52no—
88#4660—52no—
89#4659—51no—
90#4658—52no—
91C22×C4×D5—31no—
92C22×C4×D5—31no—
93C22×C4×D5—32no—
94C22×C4×D5—31no—
95C22×C4×D5—32no—
96C2×C5×C4⋊C4C2×D311yescharacteristic
97C2×C5×C4⋊C4C2×D311yescharacteristic
98C2×C4⋊Dic5—31no—
99C2×C4⋊Dic5—31no—
100C2×#683—31no—
101C2×#683—32no—
102C2×#683—31no—
103D5×C4⋊C4—64no—
104D5×C4⋊C4—64no—
105C5×#95C2×D312yes—
106C5×#95C2×D311yescharacteristic
107C5×#95C2×D312yes—
108#3963—32no—
109#3963—32no—
110#3963—32no—
111#3963—32no—
112#3963—32no—
113#3963—32no—
114#3963—32no—
115#3963—31no—
116C2×#400—151noSylow
117C23×C3×C5C2411yescharacteristic
118C22×D15C2×D412yes—
119C22×D15C2×Q812yes—
120C22×D15#4112yes—
121C22×D15#4114yes—
122C22×D15#4114yes—
123C2×C3×C4×C5—21no—
124C2×C3×C4×C5—21no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—24no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5C2×D412yes—
134C2×C3×C4×C5C2×Q812yes—
135C2×Dic15—21no—
136C2×Dic15—21no—
137C2×Dic15—22no—
138C2×Dic15—21no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15—24no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15C2×D412yes—
146C2×Dic15C2×Q812yes—
147C4×D15—28no—
148C4×D15—28no—
149C4×D15—44no—
150C4×D15—48no—
151C4×D15—48no—
152C22×C4×D3—51no—
153C22×C4×D3—51no—
154C22×C4×D3—52no—
155C22×C4×D3—52no—
156C22×C4×D3—51no—
157C2×C3×C4⋊C4C2×D511yescharacteristic
158C2×C3×C4⋊C4C2×D511yescharacteristic
159C2×C4⋊Dic3—51no—
160C2×C4⋊Dic3—51no—
161C2×Dic3⋊C4—51no—
162C2×Dic3⋊C4—52no—
163C2×Dic3⋊C4—51no—
164D3×C4⋊C4—104no—
165D3×C4⋊C4—104no—
166C3×#95C2×D512yes—
167C3×#95C2×D511yescharacteristic
168C3×#95C2×D512yes—
169C3⋊#95—52no—
170C3⋊#95—52no—
171C3⋊#95—52no—
172C3⋊#95—52no—
173C3⋊#95—52no—
174C3⋊#95—52no—
175C3⋊#95—52no—
176C3⋊#95—51no—
177C23×D5—31no—
178C22×C4×C5C22×D312yes—
179C22×C4×C5C22×D311yescharacteristic
180C22×C4×C5C22×D312yes—
181C22×C4×C5C22×D311yescharacteristic
182C22×C4×C5C22×D311yescharacteristic
183C22×Dic5—31no—
184C22×Dic5—31no—
185C22×Dic5—32no—
186C22×Dic5—32no—
187C22×Dic5—31no—
188C2×C4×D5—34no—
189C2×C4×D5—34no—
190C2×C4×D5—64no—
191C2×C4×D5—62no—
192C2×C4×D5—62no—
193C2×C4×D5—64no—
194C2×C4×D5—68no—
195C2×C4×D5—64no—
196C2×C4×D5—64no—
197C2×C4×D5—64no—
198C2×C4×D5—62no—
199C2×C4×D5—64no—
200C5×C4⋊C4—22no—
201C5×C4⋊C4—22no—
202C4⋊Dic5—62no—
203C4⋊Dic5—62no—
204#683—62no—
205#683—64no—
206#683—62no—
207C22×C4⋊C4—151no—
208C22×C4⋊C4—151no—
209#400—151no—
210#400—151no—
211#400—152no—
212#400—151no—
213#400—152no—
214#400D1511yescharacteristic, direct product factor
215C2×#95—151no—
216C2×#95—152no—
217C2×#95—152no—
218C22×C3×C5C22×D411yescharacteristic
219C22×C3×C5C22×Q811yescharacteristic
220C22×C3×C5C2×#4111yescharacteristic
221C22×C3×C5C2×#4112yes—
222C22×C3×C5C2×#4112yes—
223C2×D15C22⋊Q814yes—
224C2×D15#12314yes—
225C2×D15#12414yes—
226C2×D15#12518yes—
227C2×D15#12618yes—
228C3×C4×C5—22no—
229C3×C4×C5—22no—
230C3×C4×C5—41no—
231C3×C4×C5—42no—
232C3×C4×C5—42no—
233Dic15—22no—
234Dic15—22no—
235Dic15—41no—
236Dic15—42no—
237Dic15—42no—
238C23×D3—51no—
239C22×C3×C4C22×D512yes—
240C22×C3×C4C22×D512yes—
241C22×C3×C4C22×D511yescharacteristic
242C22×C3×C4C22×D511yescharacteristic
243C22×C3×C4C22×D511yescharacteristic
244C22×Dic3—51no—
245C22×Dic3—51no—
246C22×Dic3—52no—
247C22×Dic3—52no—
248C22×Dic3—51no—
249C2×C4×D3—54no—
250C2×C4×D3—54no—
251C2×C4×D3—102no—
252C2×C4×D3—102no—
253C2×C4×D3—104no—
254C2×C4×D3—102no—
255C2×C4×D3—104no—
256C2×C4×D3—104no—
257C2×C4×D3—104no—
258C2×C4×D3—104no—
259C2×C4×D3—104no—
260C2×C4×D3—108no—
261C3×C4⋊C4—22no—
262C3×C4⋊C4—22no—
263C4⋊Dic3—102no—
264C4⋊Dic3—102no—
265Dic3⋊C4—102no—
266Dic3⋊C4—104no—
267Dic3⋊C4—102no—
268C23×C5C23×D311yescharacteristic
269C22×D5—32no—
270C22×D5—32no—
271C22×D5—34no—
272C22×D5—34no—
273C22×D5—32no—
274C2×C4×C5—21no—
275C2×C4×C5—22no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—22no—
279C2×C4×C5—22no—
280C2×C4×C5—24no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5D3×D412yes—
285C2×C4×C5D3×Q812yes—
286C2×Dic5—32no—
287C2×Dic5—32no—
288C2×Dic5—61no—
289C2×Dic5—62no—
290C2×Dic5—61no—
291C2×Dic5—61no—
292C2×Dic5—62no—
293C2×Dic5—62no—
294C2×Dic5—64no—
295C2×Dic5—62no—
296C2×Dic5—62no—
297C2×Dic5—62no—
298C4×D5—68no—
299C4×D5—68no—
300C4×D5—124no—
301C4×D5—128no—
302C4×D5—128no—
303C23×C4—151no—
304C23×C4—151no—
305C23×C4—151no—
306C23×C4—152no—
307C23×C4—152no—
308C2×C4⋊C4—151no—
309C2×C4⋊C4—152no—
310C2×C4⋊C4—151no—
311C2×C4⋊C4—151no—
312C2×C4⋊C4—151no—
313C2×C4⋊C4—304no—
314C2×C4⋊C4—304no—
315C2×C4⋊C4C2×D1511yescharacteristic
316C2×C4⋊C4C2×D1511yescharacteristic
317#95—152no—
318#95—152no—
319#95—152no—
320#95—151no—
321#95—152no—
322#95—152no—
323#95—152no—
324#95—152no—
325#95C2×D1511yescharacteristic
326#95C2×D1512yes—
327#95C2×D1512yes—
328C2×C3×C5C2×C22⋊Q811yescharacteristic
329C2×C3×C5C2×#12311yescharacteristic
330C2×C3×C5C2×#12411yescharacteristic
331C2×C3×C5C2×#12512yes—
332C2×C3×C5C2×#12612yes—
333D15#40018yesdirect product factor
334C23×C3C23×D511yescharacteristic
335C22×D3—52no—
336C22×D3—52no—
337C22×D3—52no—
338C22×D3—54no—
339C22×D3—54no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—24no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4D4×D512yes—
351C2×C3×C4Q8×D512yes—
352C2×Dic3—52no—
353C2×Dic3—52no—
354C2×Dic3—101no—
355C2×Dic3—101no—
356C2×Dic3—102no—
357C2×Dic3—101no—
358C2×Dic3—102no—
359C2×Dic3—102no—
360C2×Dic3—104no—
361C2×Dic3—102no—
362C2×Dic3—102no—
363C2×Dic3—102no—
364C4×D3—108no—
365C4×D3—108no—
366C4×D3—204no—
367C4×D3—208no—
368C4×D3—208no—
369C22×C5C2×D3×D411yescharacteristic
370C22×C5C2×D3×Q811yescharacteristic
371C22×C5D3×#4112yes—
372C22×C5D3×#4112yes—
373C22×C5D3×#4111yescharacteristic
374C2×D5—34no—
375C2×D5—34no—
376C2×D5—38no—
377C2×D5—38no—
378C2×D5—34no—
379C4×C5—22no—
380C4×C5—22no—
381C4×C5—41no—
382C4×C5—42no—
383C4×C5—42no—
384Dic5—62no—
385Dic5—62no—
386Dic5—121no—
387Dic5—122no—
388Dic5—122no—
389C24—151no—
390C22×C4—151no—
391C22×C4—151no—
392C22×C4—154no—
393C22×C4—154no—
394C22×C4—152no—
395C22×C4—151no—
396C22×C4—152no—
397C22×C4—302no—
398C22×C4—304no—
399C22×C4—302no—
400C22×C4—302no—
401C22×C4—304no—
402C22×C4—304no—
403C22×C4—308no—
404C22×C4—304no—
405C22×C4—304no—
406C22×C4—304no—
407C22×C4C22×D1512yes—
408C22×C4C22×D1511yescharacteristic
409C22×C4C22×D1512yes—
410C22×C4C22×D1511yescharacteristic
411C22×C4C22×D1511yescharacteristic
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—302no—
415C4⋊C4—304no—
416C4⋊C4—302no—
417C4⋊C4—302no—
418C4⋊C4—302no—
419C3×C5C2×#40011yescharacteristic, complemented, Hall
420C22×C3C2×D4×D511yescharacteristic
421C22×C3C2×Q8×D511yescharacteristic
422C22×C3D5×#4111yescharacteristic
423C22×C3D5×#4112yes—
424C22×C3D5×#4112yes—
425C2×D3—54no—
426C2×D3—54no—
427C2×D3—54no—
428C2×D3—58no—
429C2×D3—58no—
430C3×C4—22no—
431C3×C4—22no—
432C3×C4—41no—
433C3×C4—42no—
434C3×C4—42no—
435Dic3—102no—
436Dic3—102no—
437Dic3—201no—
438Dic3—202no—
439Dic3—202no—
440C2×C5D3×C22⋊Q811yescharacteristic
441C2×C5D3×#12311yescharacteristic
442C2×C5D3×#12411yescharacteristic
443C2×C5D3×#12512yes—
444C2×C5D3×#12612yes—
445D5—38no—
446C23—152no—
447C23—152no—
448C23—152no—
449C23—154no—
450C23—154no—
451C23C23×D1511yescharacteristic
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—21no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—152no—
463C2×C4—152no—
464C2×C4—308no—
465C2×C4—308no—
466C2×C4—301no—
467C2×C4—301no—
468C2×C4—302no—
469C2×C4—301no—
470C2×C4—302no—
471C2×C4—302no—
472C2×C4—304no—
473C2×C4—302no—
474C2×C4—302no—
475C2×C4—302no—
476C2×C4—604no—
477C2×C4—608no—
478C2×C4—608no—
479C2×C4D4×D1512yes—
480C2×C4Q8×D1512yes—
481C2×C3D5×C22⋊Q811yescharacteristic
482C2×C3D5×#12311yescharacteristic
483C2×C3D5×#12411yescharacteristic
484C2×C3D5×#12512yes—
485C2×C3D5×#12612yes—
486D3—58no—
487C5D3×#40011yescharacteristic, complemented, Sylow
488C22—154no—
489C22—154no—
490C22—154no—
491C22—158no—
492C22—158no—
493C22C2×D4×D1511yescharacteristic
494C22C2×Q8×D1511yescharacteristic
495C22#41×D1511yescharacteristic
496C22#41×D1512yes—
497C22#41×D1512yes—
498C4—22no—
499C4—22no—
500C4—41no—
501C4—42no—
502C4—42no—
503C4—302no—
504C4—302no—
505C4—601no—
506C4—602no—
507C4—602no—
508C3D5×#40011yescharacteristic, complemented, Sylow
509C2—158no—
510C2D15×C22⋊Q811yescharacteristic
511C2D15×#12311yescharacteristic
512C2D15×#12411yescharacteristic
513C2D15×#12512yes—
514C2D15×#12612yes—
subgroupG/H
center, FrattiniC23C23×D15
commutator, socle, cosocleC23×C3×C5C24
FittingC3×C5×#400C2
prime radicalC23×D15C23
hypercenter#400D15
hypocenterC3×C5C2×#400
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. C3×C5×#400C2semidirect
4. #11751087C2semidirect
5. #11751086C2semidirect
9. #11750761C2semidirect
10. #11750760C2semidirect
11. #11750759C2semidirect
41. C5×#400D3semidirect
82. C3×#400D5semidirect
214. #400D15direct (N × H)
333. D15#400direct (N × H)
419. C3×C5C2×#400semidirect
487. C5D3×#400semidirect
508. C3D5×#400semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D152
C3×C5×#4002
#117510872
#117510862
D15×#952
#117507612
#117507602
#117507592
D5×#4003
D3×#4005