Finite Group Databasebeta

← D5×#5031 #14426088

Subgroups — D5×#5031 #14426088

Order 1920.

960 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×Q8×D5C211yesmaximal, characteristic
2C2×D5×#216C212yesmaximal
3D5×#869C211yesmaximal, characteristic
4#11751132C211yesmaximal, characteristic, complemented
5C5×#5031C211yesmaximal, characteristic, complemented
6#11749350C212yesmaximal, complemented
7D5×#810C212yesmaximal
8#11747412C212yesmaximal, complemented
9#11747095C211yesmaximal, characteristic, complemented
10#11747094C211yesmaximal, characteristic, complemented
11D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic
12D5×#462—31nomaximal, Hall
13C2×C3×Q8×D5C2211yescharacteristic
14C2×D5×Dic6C2212yes—
15C3×C4×C5×Q8C2211yescharacteristic
16C2×#6718C2212yes—
17#91758C2211yescharacteristic
18C2×C5×#216C2212yes—
19C5×#869C2211yescharacteristic
20C3×Q8×Dic5C2211yescharacteristic
21C3×D5×C4⋊C4—21no—
22C3×D5×C4⋊C4C2211yescharacteristic
23C3×#4033—21no—
24C3×#4033C2211yescharacteristic
25C3×C42×D5—21no—
26C3×C42×D5C2211yescharacteristic
27C3×C4×Dic10—21no—
28C3×C4×Dic10C2211yescharacteristic
29D5×#216—28no—
30#91468—21no—
31#91468—21no—
32D5×C4⋊Dic3—21no—
33D5×C4⋊Dic3—21no—
34#91376C2212yes—
35C2×#6662C2212yes—
36C2×#6661C2212yes—
37C2×D5×C3⋊C8C2212yes—
38#91094C2212yes—
39C4⋊(C3⋊#168)C2211yescharacteristic
40C5×#810C2212yes—
41C5×C4⋊(C3⋊C8)C2211yescharacteristic
42#90982C2212yes—
43#90974C2212yes—
44#90972C2212yes—
45C2×#5031—51nomaximal, Hall
46C2×D5×Q16—32no—
47D5×C4⋊Q8—31no—
48C4×Q8×D5D311yescharacteristic
49C5×#462—31no—
50#65471—32no—
51#65379—31no—
52#65320—31no—
53#65138—31no—
54D5×C4⋊C8—31no—
55D5×#103—32no—
56#65082—32no—
57C2×C3×C5×Q8C2311yescharacteristic
58C2×Dic30C2312yes—
59C2×C5×Dic6C2312yes—
60C3×Q8×D5—22no—
61C3×Q8×D5D414yes—
62C2×C3×C4×D5—21no—
63C2×C3×C4×D5—21no—
64C2×C3×C4×D5D411yescharacteristic
65C2×C3×C4×D5D411yescharacteristic
66C2×C3×C4×D5C2311yescharacteristic
67C2×C3×Dic10—21no—
68C2×C3×Dic10C2311yescharacteristic
69C2×#1204—22no—
70C2×D5×Dic3—22no—
71D5×Dic6—24no—
72D5×Dic6—24no—
73C3×C5×C4⋊C4—21no—
74C3×C5×C4⋊C4C2311yescharacteristic
75C3×C42×C5—21no—
76C3×C42×C5C2311yescharacteristic
77#6718—24no—
78C4⋊Dic15—21no—
79C4⋊Dic15—21no—
80C2×C3⋊#168C2312yes—
81C5×#216—24no—
82C5×C4⋊Dic3—21no—
83C5×C4⋊Dic3—21no—
84C2×C5×C3⋊C8C2312yes—
85C3×C4⋊Dic5—21no—
86C3×C4⋊Dic5C2311yescharacteristic
87C3×#683—21no—
88C3×#683—21no—
89C3×#683—21no—
90C3×C4×Dic5—21no—
91C3×C4×Dic5—21no—
92C3×C4×Dic5—21no—
93C3×C4×Dic5D411yescharacteristic
94C3×C4×Dic5D411yescharacteristic
95C3×C4×Dic5C2311yescharacteristic
96#6668—22no—
97#6668—22no—
98#6662—24no—
99#6661—24no—
100D5×C3⋊C8—24no—
101C2×C3×C4×Q8—51no—
102C22×#216—52no—
103C2×#869—51no—
104#5031—51no—
105#5031—52no—
106#5031—51no—
107#5031—52no—
108#5031—51no—
109#5031D511yescharacteristic, direct product factor
110C2×#810—52no—
111C2×C4⋊(C3⋊C8)—51no—
112C2×Q8×D5—32no—
113C2×Q8×D5C2×D311yescharacteristic
114C2×C5×Q16—32no—
115C5×C4⋊Q8—31no—
116C4×C5×Q8C2×D311yescharacteristic
117Q8×Dic5C2×D311yescharacteristic
118#4090—32no—
119C2×#689—32no—
120C2×#689—32no—
121D5×Q16—68no—
122C2×Dic20—32no—
123C2×C8×D5—32no—
124D5×C4⋊C4—21no—
125D5×C4⋊C4—61no—
126D5×C4⋊C4—61no—
127D5×C4⋊C4C2×D311yescharacteristic
128#4034—61no—
129#4034—61no—
130#4033—21no—
131#4033C2×D311yescharacteristic
132C42×D5—21no—
133C42×D5C2×D311yescharacteristic
134#4015—31no—
135C4×Dic10—21no—
136C4×Dic10C2×D311yescharacteristic
137C5×C4⋊C8—31no—
138C5×#103—32no—
139#3967—32no—
140#3948—32no—
141#3946—32no—
142#3942—32no—
143C4⋊#168—31no—
144C2×#462—151noSylow
145C22×C3×D5C2×D411yescharacteristic
146C3×C5×Q8—21no—
147C3×C5×Q8C2×D412yes—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—21no—
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×C3×C4×C5C2411yescharacteristic
153C2×Dic15—22no—
154Dic30—22no—
155Dic30—22no—
156C2×C5×Dic3—22no—
157C5×Dic6—22no—
158C5×Dic6—22no—
159C2×C3×Dic5—21no—
160C2×C3×Dic5—21no—
161C2×C3×Dic5C2×D411yescharacteristic
162C2×C3×Dic5C2×D411yescharacteristic
163C2×C3×Dic5C2×D411yescharacteristic
164C3×C4×D5—24no—
165C3×C4×D5—22no—
166C3×C4×D5—42no—
167C3×C4×D5Q1614yescomplemented
168C3×C4×D5C2×D412yes—
169C3×C4×D5#4112yes—
170C3×Dic10—21no—
171C3×Dic10—24no—
172C3×Dic10C2×D412yes—
173#1204—44no—
174D5×Dic3—44no—
175C3⋊#168—22no—
176C5×C3⋊C8—22no—
177C22×C3×Q8—51no—
178C22×Dic6—52no—
179C3×C4×Q8—51no—
180C3×C4×Q8—51no—
181C3×C4×Q8—51no—
182C3×C4×Q8—101no—
183C3×C4×Q8—101no—
184C3×C4×Q8C2×D511yescharacteristic
185C2×C3×C4⋊C4—51no—
186C2×C3×C4⋊C4—101no—
187C2×C3×C42—51no—
188C2×C3×C42—101no—
189C2×#216—52no—
190C2×#216—52no—
191C2×#216—52no—
192C2×#216—108no—
193C2×#216C2×D512yes—
194C2×C4⋊Dic3—101no—
195C2×C4⋊Dic3—101no—
196C22×C3⋊C8—52no—
197#869—52no—
198#869—51no—
199#869—101no—
200#869—101no—
201#869C2×D511yescharacteristic
202#810—52no—
203#810—52no—
204#810—52no—
205#810C2×D512yes—
206C4⋊(C3⋊C8)—51no—
207C4⋊(C3⋊C8)—52no—
208C4⋊(C3⋊C8)C2×D511yescharacteristic
209C2×C5×Q8—32no—
210C2×C5×Q8C22×D311yescharacteristic
211Q8×D5—22no—
212Q8×D5—64no—
213Q8×D5—64no—
214Q8×D5D1214yes—
215C2×C4×D5—21no—
216C2×C4×D5—21no—
217C2×C4×D5—62no—
218C2×C4×D5#6711yescharacteristic
219C2×C4×D5#6711yescharacteristic
220C2×C4×D5C22×D311yescharacteristic
221C2×Dic10—21no—
222C2×Dic10—32no—
223C2×Dic10—62no—
224C2×Dic10C22×D311yescharacteristic
225C5×Q16—64no—
226C2×C5×C8—32no—
227C5×C4⋊C4—21no—
228C5×C4⋊C4—61no—
229C5×C4⋊C4—61no—
230C5×C4⋊C4C22×D311yescharacteristic
231C42×C5—21no—
232C42×C5C22×D311yescharacteristic
233#689—64no—
234#689—64no—
235C4⋊Dic5—21no—
236C4⋊Dic5—61no—
237C4⋊Dic5—61no—
238C4⋊Dic5C22×D311yescharacteristic
239#683—21no—
240#683—21no—
241#683—21no—
242#683—62no—
243#683—62no—
244C4×Dic5—21no—
245C4×Dic5—21no—
246C4×Dic5—21no—
247C4×Dic5#6711yescharacteristic
248C4×Dic5#6711yescharacteristic
249C4×Dic5C22×D311yescharacteristic
250C2×#168—32no—
251Dic20—64no—
252C8×D5—64no—
253C22×Q16—152no—
254C2×C4⋊Q8—151no—
255C2×C4×Q8—51no—
256#462—31no—
257#462—152no—
258#462—151no—
259#462—151no—
260#462—152no—
261#462—151no—
262C2×C4⋊C8—151no—
263C2×#103—152no—
264C22×C3×C5C22×D411yescharacteristic
265C2×C3×D5#12112yes—
266C2×C3×D5C2×Q1612yes—
267C2×C3×D5#13712yes—
268C3×C4×C5—22no—
269C3×C4×C5—21no—
270C3×C4×C5—41no—
271C3×C4×C5C2×Q1612yescomplemented
272C3×C4×C5C22×D411yescharacteristic
273C3×C4×C5C2×#4111yescharacteristic
274Dic15—42no—
275C3×Dic5—22no—
276C3×Dic5—21no—
277C3×Dic5—41no—
278C3×Dic5#12112yes—
279C3×Dic5C2×Q1612yescomplemented
280C5×Dic3—42no—
281C2×C3×Q8—54no—
282C2×C3×Q8—51no—
283C2×C3×Q8—101no—
284C2×C3×Q8—102no—
285C2×C3×Q8C22×D511yescharacteristic
286C22×C3×C4—51no—
287C22×C3×C4—51no—
288C22×C3×C4—51no—
289C22×C3×C4—101no—
290C22×C3×C4—101no—
291C22×Dic3—102no—
292C2×Dic6—52no—
293C2×Dic6—104no—
294C2×Dic6—104no—
295C2×Dic6—102no—
296C2×Dic6C22×D512yes—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—51no—
299C3×C4⋊C4—101no—
300C3×C4⋊C4—101no—
301C3×C4⋊C4—101no—
302C3×C4⋊C4—101no—
303C3×C4⋊C4C22×D511yescharacteristic
304C3×C42—21no—
305C3×C42—51no—
306C3×C42—51no—
307C3×C42—51no—
308C3×C42—101no—
309C3×C42—101no—
310C3×C42—101no—
311C3×C42C22×D511yescharacteristic
312#216—24no—
313#216—104no—
314#216—104no—
315#216—104no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3—102no—
319C4⋊Dic3—102no—
320C4⋊Dic3—101no—
321C4⋊Dic3—101no—
322C2×C3⋊C8—52no—
323C2×C3⋊C8—104no—
324C2×C3⋊C8C22×D512yes—
325C22×D5C2×#6711yescharacteristic
326C5×Q8—21no—
327C5×Q8—62no—
328C5×Q8—62no—
329C5×Q8C2×D1212yes—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—62no—
333C2×C4×C5C2×#6711yescharacteristic
334C2×C4×C5C2×#6711yescharacteristic
335C2×C4×C5C23×D311yescharacteristic
336C2×Dic5—21no—
337C2×Dic5—21no—
338C2×Dic5—62no—
339C2×Dic5C2×#6711yescharacteristic
340C2×Dic5C2×#6711yescharacteristic
341C2×Dic5C2×#6711yescharacteristic
342C4×D5—24no—
343C4×D5—22no—
344C4×D5—42no—
345C4×D5—124no—
346C4×D5#21614yescomplemented
347C4×D5C2×D1212yes—
348C4×D5#23512yes—
349Dic10—21no—
350Dic10—24no—
351Dic10—62no—
352Dic10—62no—
353Dic10—124no—
354Dic10C2×D1212yes—
355C5×C8—62no—
356#168—62no—
357C22×Q8—51no—
358C22×Q8—152no—
359C2×Q16—32no—
360C2×Q16—152no—
361C2×Q16—152no—
362C2×Q16—152no—
363C2×Q16—308no—
364C22×C8—152no—
365C4⋊Q8—31no—
366C4⋊Q8—152no—
367C4⋊Q8—151no—
368C4⋊Q8—301no—
369C4⋊Q8—301no—
370C4×Q8—51no—
371C4×Q8—51no—
372C4×Q8—51no—
373C4×Q8—101no—
374C4×Q8—101no—
375C4×Q8D3×D511yescharacteristic
376C2×C4⋊C4—51no—
377C2×C4⋊C4—101no—
378C2×C4⋊C4—301no—
379C2×C4⋊C4—301no—
380C2×C42—51no—
381C2×C42—101no—
382C4⋊C8—31no—
383C4⋊C8—152no—
384C4⋊C8—151no—
385#103—32no—
386#103—152no—
387#103—152no—
388#103—152no—
389C2×C3×C5C2×#12111yescharacteristic
390C2×C3×C5C22×Q1611yescharacteristic
391C2×C3×C5C2×#13711yescharacteristic
392C3×D5#46214yescomplemented
393C23×C3—51no—
394C3×Q8—21no—
395C3×Q8—52no—
396C3×Q8—104no—
397C3×Q8—101no—
398C3×Q8D4×D512yes—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—51no—
402C2×C3×C4—51no—
403C2×C3×C4—52no—
404C2×C3×C4—52no—
405C2×C3×C4—54no—
406C2×C3×C4—51no—
407C2×C3×C4—102no—
408C2×C3×C4—104no—
409C2×C3×C4—101no—
410C2×C3×C4—101no—
411C2×C3×C4—202no—
412C2×C3×C4D4×D511yescharacteristic
413C2×C3×C4D4×D511yescharacteristic
414C2×C3×C4C23×D511yescharacteristic
415C2×Dic3—22no—
416C2×Dic3—102no—
417C2×Dic3—204no—
418Dic6—22no—
419Dic6—22no—
420Dic6—102no—
421Dic6—102no—
422Dic6—204no—
423C3⋊C8—22no—
424C3⋊C8—102no—
425C22×C5C22×#6711yescharacteristic
426C2×D5#93012yes—
427C2×D5C2×#21612yes—
428C2×D5#95112yes—
429C4×C5—22no—
430C4×C5—21no—
431C4×C5—41no—
432C4×C5—122no—
433C4×C5C2×#21612yescomplemented
434C4×C5C22×D1211yescharacteristic
435C4×C5C2×#23511yescharacteristic
436Dic5—22no—
437Dic5—21no—
438Dic5—41no—
439Dic5—122no—
440Dic5#93012yes—
441Dic5C2×#21612yescomplemented
442C2×Q8—32no—
443C2×Q8—54no—
444C2×Q8—51no—
445C2×Q8—101no—
446C2×Q8—102no—
447C2×Q8—152no—
448C2×Q8—302no—
449C2×Q8—304no—
450C2×Q8—304no—
451C2×Q8C2×D3×D511yescharacteristic
452C22×C4—51no—
453C22×C4—51no—
454C22×C4—51no—
455C22×C4—101no—
456C22×C4—101no—
457C22×C4—302no—
458Q16—64no—
459Q16—304no—
460Q16—304no—
461Q16—304no—
462C2×C8—32no—
463C2×C8—152no—
464C2×C8—304no—
465C4⋊C4—21no—
466C4⋊C4—51no—
467C4⋊C4—61no—
468C4⋊C4—61no—
469C4⋊C4—101no—
470C4⋊C4—101no—
471C4⋊C4—101no—
472C4⋊C4—101no—
473C4⋊C4—302no—
474C4⋊C4—302no—
475C4⋊C4—301no—
476C4⋊C4—301no—
477C4⋊C4C2×D3×D511yescharacteristic
478C42—21no—
479C42—51no—
480C42—51no—
481C42—51no—
482C42—101no—
483C42—101no—
484C42—101no—
485C42C2×D3×D511yescharacteristic
486C3×C5C2×#46211yescharacteristic, complemented, Hall
487C22×C3—52no—
488C22×C3—52no—
489C22×C3—52no—
490C22×C3C2×D4×D511yescharacteristic
491C3×C4—21no—
492C3×C4—22no—
493C3×C4—41no—
494C3×C4—52no—
495C3×C4—52no—
496C3×C4—101no—
497C3×C4—102no—
498C3×C4—201no—
499C3×C4D5×Q1612yescomplemented
500C3×C4C2×D4×D511yescharacteristic
501C3×C4D5×#4111yescharacteristic
502Dic3—42no—
503Dic3—202no—
504C2×C5C2×#93011yescharacteristic
505C2×C5C22×#21611yescharacteristic
506C2×C5C2×#95111yescharacteristic
507D5#503114yesdirect product factor
508C23—51no—
509Q8—21no—
510Q8—52no—
511Q8—62no—
512Q8—62no—
513Q8—104no—
514Q8—101no—
515Q8—302no—
516Q8—302no—
517Q8—604no—
518Q8D5×D1212yes—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—51no—
522C2×C4—51no—
523C2×C4—52no—
524C2×C4—52no—
525C2×C4—54no—
526C2×C4—51no—
527C2×C4—62no—
528C2×C4—102no—
529C2×C4—104no—
530C2×C4—101no—
531C2×C4—101no—
532C2×C4—202no—
533C2×C4—302no—
534C2×C4—604no—
535C2×C4D5×#6711yescharacteristic
536C2×C4D5×#6711yescharacteristic
537C2×C4C22×D3×D511yescharacteristic
538C8—62no—
539C8—302no—
540C2×C3—54no—
541C2×C3D5×#12111yescharacteristic
542C2×C3C2×D5×Q1611yescharacteristic
543C2×C3D5×#13711yescharacteristic
544C5C2×#503111yescharacteristic, complemented, Sylow
545C22—52no—
546C22—52no—
547C22—52no—
548C22C2×D5×#6711yescharacteristic
549C4—21no—
550C4—22no—
551C4—41no—
552C4—52no—
553C4—52no—
554C4—101no—
555C4—102no—
556C4—122no—
557C4—201no—
558C4—602no—
559C4D5×#21612yescomplemented
560C4C2×D5×D1211yescharacteristic
561C4D5×#23511yescharacteristic
562C3D5×#46211yescharacteristic, complemented, Sylow
563C2—54no—
564C2D5×#93011yescharacteristic
565C2C2×D5×#21611yescharacteristic
566C2D5×#95111yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
hypercenterC4×Q8D3×D5
hypocenterC3×C5C2×#462
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
4. #11751132C2semidirect
5. C5×#5031C2semidirect
6. #11749350C2semidirect
8. #11747412C2semidirect
9. #11747095C2semidirect
10. #11747094C2semidirect
109. #5031D5direct (N × H)
167. C3×C4×D5Q16semidirect
271. C3×C4×C5C2×Q16semidirect
279. C3×Dic5C2×Q16semidirect
346. C4×D5#216semidirect
392. C3×D5#462semidirect
433. C4×C5C2×#216semidirect
441. Dic5C2×#216semidirect
486. C3×C5C2×#462semidirect
499. C3×C4D5×Q16semidirect
507. D5#5031direct (N × H)
544. C5C2×#5031semidirect
559. C4D5×#216semidirect
562. C3D5×#462semidirect

Maximal subgroups

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

subgroupindex
C3×C4×Q8×D52
C2×D5×#2162
D5×#8692
#117511322
C5×#50312
#117493502
D5×#8102
#117474122
#117470952
#117470942
D5×C4⋊(C3⋊C8)2
D5×#4623
C2×#50315