Finite Group Databasebeta

← D5×#5044 #14431758

Subgroups — D5×#5044 #14431758

Order 1920.

920 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×C22⋊Q8C211yesmaximal, characteristic
2C2×D5×C4⋊Dic3C211yesmaximal, characteristic
3#11751145C211yesmaximal, characteristic, complemented
4C5×#5044C211yesmaximal, characteristic, complemented
5#11749197C212yesmaximal, complemented
6D5×#835C212yesmaximal, complemented
7D5×#830C211yesmaximal, characteristic
8#11748461C211yesmaximal, characteristic, complemented
9#11748403C211yesmaximal, characteristic, complemented
10D5×#807C212yesmaximal, complemented
11#11747194C212yesmaximal, complemented
12D5×#484—31nomaximal, Hall
13C2×C3×Q8×D5C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×D5×Dic3—21no—
16C3×C5×C22⋊Q8C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C3×#4092C2211yescharacteristic
20C3×#4070C2211yescharacteristic
21C3×#4043C2211yescharacteristic
22C3×#4042—21no—
23C3×D5×C4⋊C4—21no—
24C3×D5×C4⋊C4C2211yescharacteristic
25C3×D5×C22⋊C4—21no—
26C3×#4024—21no—
27C2×#6668—21no—
28D5×C4⋊Dic3—21no—
29D5×C4⋊Dic3—21no—
30D5×C4⋊Dic3C2212yes—
31D5×C4⋊Dic3C2212yes—
32C2×D5×C3⋊C8C2212yes—
33#91119C2212yescomplemented
34#91114C2211yescharacteristic
35#91091C2212yescomplemented
36C5×#835C2212yescomplemented
37C5×#830C2211yescharacteristic
38C5×#807C2212yescomplemented
39#90990C2212yescomplemented
40#90989C2212yescomplemented
41#90971C2212yescomplemented
42#90970C2212yescomplemented
43#90955C2212yes—
44C2×#5044—51nomaximal, Hall
45D5×C22⋊Q8D311yescharacteristic
46C2×D5×C4⋊C4—31no—
47C5×#484—31no—
48#65333—31no—
49#65259—31no—
50#65173—32no—
51D5×#107—32no—
52#65098—32no—
53D5×#103—32no—
54D5×C22⋊C8—31no—
55#65011—31no—
56C23×C3×D5D411yescharacteristic
57C2×C3×C5×Q8C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15—21no—
60C22×C5×Dic3—21no—
61C22×C3×Dic5D411yescharacteristic
62C3×Q8×D5—24no—
63C2×C3×C4×D5—24no—
64C2×C3×C4×D5—21no—
65C2×C3×C4×D5—21no—
66C2×C3×C4×D5D411yescharacteristic
67C2×C3×C4×D5D411yescharacteristic
68C2×C3×C4×D5C2311yescharacteristic
69C2×C3×C4×D5C2311yescharacteristic
70C2×C3×Dic10—21no—
71C2×C3×Dic10C2311yescharacteristic
72C2×D5×Dic3—22no—
73C2×D5×Dic3—22no—
74C2×D5×Dic3—44no—
75C3×C5×C4⋊C4—21no—
76C3×C5×C4⋊C4C2311yescharacteristic
77C3×C5×C22⋊C4—21no—
78C4⋊Dic15—21no—
79C4⋊Dic15C2312yes—
80C2×C3⋊#168C2312yes—
81C5×C4⋊Dic3—21no—
82C5×C4⋊Dic3C2312yes—
83C2×C5×C3⋊C8C2312yes—
84C3×C22⋊Dic5—21no—
85C3×#685—21no—
86C3×#685—21no—
87C3×C4⋊Dic5—21no—
88C3×C4⋊Dic5C2311yescharacteristic
89C3×#683—21no—
90C3×#683—21no—
91C3×#683—21no—
92#6668—22no—
93#6668—22no—
94D5×C3⋊C8—24no—
95C2×C3×C22⋊Q8—51no—
96C22×C4⋊Dic3—51no—
97C2×#835—52no—
98C2×#830—51no—
99#5044—51no—
100#5044—51no—
101#5044—52no—
102#5044—51no—
103#5044—52no—
104#5044D511yescharacteristic, direct product factor
105C2×#807—52no—
106C2×Q8×D5C2×D311yescharacteristic
107C22×C4×D5—61no—
108C22×C4×D5C2×D311yescharacteristic
109C5×C22⋊Q8C2×D311yescharacteristic
110C2×C5×C4⋊C4—31no—
111#4092C2×D311yescharacteristic
112C2×C4⋊Dic5—31no—
113#4070C2×D311yescharacteristic
114C2×#683—61no—
115C2×C8×D5—32no—
116#4043C2×D311yescharacteristic
117#4042—21no—
118D5×C4⋊C4—21no—
119D5×C4⋊C4—32no—
120D5×C4⋊C4—32no—
121D5×C4⋊C4—61no—
122D5×C4⋊C4—61no—
123D5×C4⋊C4C2×D311yescharacteristic
124D5×C22⋊C4—21no—
125#4024—21no—
126C5×#107—32no—
127C5×#103—32no—
128C5×C22⋊C8—31no—
129#3967—32no—
130C22⋊#168—31no—
131#3952—32no—
132#3950—32no—
133#3948—32no—
134#3942—32no—
135#3939—32no—
136#3939—32no—
137C2×#484—151noSylow
138C23×C3×C5C2×D411yescharacteristic
139C22×C3×D5—22no—
140C22×C3×D5—22no—
141C22×C3×D5Q1614yes—
142C22×C3×D5C2×D411yescharacteristic
143C22×C3×D5C2×D411yescharacteristic
144C3×C5×Q8—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2411yescharacteristic
150C2×Dic15—22no—
151C2×Dic15—42no—
152C2×C5×Dic3—22no—
153C2×C5×Dic3—42no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5C2×D411yescharacteristic
158C2×C3×Dic5C2×D411yescharacteristic
159C3×C4×D5—22no—
160C3×C4×D5—22no—
161C3×C4×D5—22no—
162C3×C4×D5—42no—
163C3×C4×D5—42no—
164C3×C4×D5#4114yes—
165C3×Dic10—22no—
166C3×Dic10—42no—
167D5×Dic3—44no—
168D5×Dic3—44no—
169C3⋊#168—22no—
170C5×C3⋊C8—22no—
171C22×C3×Q8—51no—
172C23×C3×C4—51no—
173C23×Dic3—101no—
174C3×C22⋊Q8—51no—
175C3×C22⋊Q8—51no—
176C3×C22⋊Q8—51no—
177C3×C22⋊Q8—101no—
178C3×C22⋊Q8—101no—
179C3×C22⋊Q8C2×D511yescharacteristic
180C2×C3×C4⋊C4—51no—
181C2×C3×C4⋊C4—101no—
182C2×C3×C22⋊C4—101no—
183C2×C4⋊Dic3—51no—
184C2×C4⋊Dic3—52no—
185C2×C4⋊Dic3—52no—
186C2×C4⋊Dic3—101no—
187C2×C4⋊Dic3—101no—
188C2×C4⋊Dic3—101no—
189C2×C4⋊Dic3C2×D511yescharacteristic
190C22×C3⋊C8—52no—
191#835—52no—
192#835—52no—
193#835—52no—
194#835C2×D512yescomplemented
195#830—51no—
196#830—52no—
197#830C2×D511yescharacteristic
198#807—52no—
199#807—52no—
200#807—52no—
201#807C2×D512yescomplemented
202C23×D5#6711yescharacteristic
203C2×C5×Q8C22×D311yescharacteristic
204C22×C4×C5—61no—
205C22×C4×C5C22×D311yescharacteristic
206C22×Dic5—61no—
207C22×Dic5#6711yescharacteristic
208Q8×D5—24no—
209C2×C4×D5—24no—
210C2×C4×D5—21no—
211C2×C4×D5—21no—
212C2×C4×D5—62no—
213C2×C4×D5—62no—
214C2×C4×D5—124no—
215C2×C4×D5#6711yescharacteristic
216C2×C4×D5#6711yescharacteristic
217C2×C4×D5C22×D311yescharacteristic
218C2×C4×D5C22×D311yescharacteristic
219C2×Dic10—21no—
220C2×Dic10C22×D311yescharacteristic
221C2×C5×C8—32no—
222C5×C4⋊C4—21no—
223C5×C4⋊C4—32no—
224C5×C4⋊C4—61no—
225C5×C4⋊C4C22×D311yescharacteristic
226C5×C22⋊C4—21no—
227C22⋊Dic5—21no—
228#685—21no—
229#685—21no—
230C4⋊Dic5—21no—
231C4⋊Dic5—32no—
232C4⋊Dic5—61no—
233C4⋊Dic5C22×D311yescharacteristic
234#683—21no—
235#683—21no—
236#683—21no—
237#683—62no—
238#683—62no—
239C2×#168—32no—
240C8×D5—64no—
241C2×C22⋊Q8—51no—
242C22×C4⋊C4—151no—
243#484—31no—
244#484—151no—
245#484—152no—
246#484—152no—
247#484—151no—
248#484—151no—
249C2×#107—152no—
250C2×#103—152no—
251C2×C22⋊C8—151no—
252C22×C3×C5—21no—
253C22×C3×C5—21no—
254C22×C3×C5C2×Q1612yes—
255C22×C3×C5C22×D411yescharacteristic
256C2×C3×D5—21no—
257C2×C3×D5—21no—
258C2×C3×D5—28no—
259C2×C3×D5#12312yes—
260C2×C3×D5C2×Q1612yes—
261C2×C3×D5C2×Q1612yes—
262C2×C3×D5AGL(1,ℤ/8)12yes—
263C3×C4×C5—21no—
264C3×C4×C5—41no—
265C3×C4×C5—41no—
266C3×C4×C5C2×#4112yes—
267Dic15—42no—
268C3×Dic5—21no—
269C3×Dic5—41no—
270C3×Dic5—41no—
271C3×Dic5#12312yes—
272C5×Dic3—42no—
273C24×C3—51no—
274C2×C3×Q8—51no—
275C2×C3×Q8—101no—
276C2×C3×Q8—104no—
277C2×C3×Q8C22×D511yescharacteristic
278C22×C3×C4—51no—
279C22×C3×C4—51no—
280C22×C3×C4—51no—
281C22×C3×C4—51no—
282C22×C3×C4—51no—
283C22×C3×C4—104no—
284C22×C3×C4—101no—
285C22×C3×C4—101no—
286C22×C3×C4C22×D511yescharacteristic
287C22×Dic3—21no—
288C22×Dic3—102no—
289C22×Dic3—102no—
290C22×Dic3—101no—
291C22×Dic3—204no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—51no—
294C3×C4⋊C4—101no—
295C3×C4⋊C4—101no—
296C3×C4⋊C4—101no—
297C3×C4⋊C4—101no—
298C3×C4⋊C4C22×D511yescharacteristic
299C3×C22⋊C4—21no—
300C3×C22⋊C4—101no—
301C3×C22⋊C4—101no—
302C3×C22⋊C4—101no—
303C4⋊Dic3—21no—
304C4⋊Dic3—52no—
305C4⋊Dic3—102no—
306C4⋊Dic3—102no—
307C4⋊Dic3—101no—
308C4⋊Dic3C22×D512yes—
309C2×C3⋊C8—52no—
310C2×C3⋊C8—104no—
311C2×C3⋊C8C22×D512yes—
312C23×C5C2×#6711yescharacteristic
313C22×D5—22no—
314C22×D5—22no—
315C22×D5#21614yes—
316C22×D5C2×#6711yescharacteristic
317C22×D5C2×#6711yescharacteristic
318C5×Q8—22no—
319C2×C4×C5—22no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—62no—
323C2×C4×C5—122no—
324C2×C4×C5C2×#6711yescharacteristic
325C2×C4×C5C23×D311yescharacteristic
326C2×Dic5—22no—
327C2×Dic5—21no—
328C2×Dic5—21no—
329C2×Dic5—62no—
330C2×Dic5—122no—
331C2×Dic5C2×#6711yescharacteristic
332C2×Dic5C2×#6711yescharacteristic
333C4×D5—22no—
334C4×D5—22no—
335C4×D5—22no—
336C4×D5—42no—
337C4×D5—42no—
338C4×D5—124no—
339C4×D5—124no—
340C4×D5#23714yes—
341Dic10—22no—
342Dic10—42no—
343C5×C8—62no—
344#168—62no—
345C22×Q8—51no—
346C23×C4—51no—
347C23×C4—301no—
348C22×C8—152no—
349C22⋊Q8—51no—
350C22⋊Q8—51no—
351C22⋊Q8—51no—
352C22⋊Q8—101no—
353C22⋊Q8—101no—
354C22⋊Q8D3×D511yescharacteristic
355C2×C4⋊C4—31no—
356C2×C4⋊C4—51no—
357C2×C4⋊C4—101no—
358C2×C4⋊C4—152no—
359C2×C4⋊C4—152no—
360C2×C4⋊C4—151no—
361C2×C4⋊C4—301no—
362C2×C4⋊C4—301no—
363C2×C4⋊C4—301no—
364C2×C22⋊C4—101no—
365#107—32no—
366#107—152no—
367#107—152no—
368#107—152no—
369#103—32no—
370#103—152no—
371#103—152no—
372#103—152no—
373C22⋊C8—31no—
374C22⋊C8—152no—
375C22⋊C8—151no—
376C2×C3×C5—22no—
377C2×C3×C5C2×#12311yescharacteristic
378C2×C3×C5C22×Q1611yescharacteristic
379C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
380C3×D5—22no—
381C3×D5#48414yescomplemented
382C23×C3—51no—
383C23×C3—51no—
384C23×C3—54no—
385C23×C3—102no—
386C23×C3—102no—
387C23×C3D4×D511yescharacteristic
388C3×Q8—22no—
389C3×Q8—102no—
390C3×Q8—202no—
391C2×C3×C4—22no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—51no—
395C2×C3×C4—54no—
396C2×C3×C4—51no—
397C2×C3×C4—102no—
398C2×C3×C4—102no—
399C2×C3×C4—102no—
400C2×C3×C4—102no—
401C2×C3×C4—101no—
402C2×C3×C4—101no—
403C2×C3×C4—202no—
404C2×C3×C4—202no—
405C2×C3×C4D4×D511yescharacteristic
406C2×C3×C4C23×D511yescharacteristic
407C2×Dic3—22no—
408C2×Dic3—42no—
409C2×Dic3—102no—
410C2×Dic3—204no—
411C2×Dic3—204no—
412C2×Dic3—202no—
413C3⋊C8—22no—
414C3⋊C8—102no—
415C22×C5—21no—
416C22×C5—21no—
417C22×C5C2×#21612yes—
418C22×C5C22×#6711yescharacteristic
419C2×D5—21no—
420C2×D5—21no—
421C2×D5—28no—
422C2×D5#93512yes—
423C2×D5C2×#21612yes—
424C2×D5C2×#21612yes—
425C2×D5#94912yes—
426C4×C5—21no—
427C4×C5—41no—
428C4×C5—41no—
429C4×C5—122no—
430C4×C5C2×#23712yes—
431Dic5—21no—
432Dic5—41no—
433Dic5—41no—
434Dic5—122no—
435Dic5#93512yes—
436C24—51no—
437C2×Q8—51no—
438C2×Q8—101no—
439C2×Q8—104no—
440C2×Q8C2×D3×D511yescharacteristic
441C22×C4—51no—
442C22×C4—51no—
443C22×C4—51no—
444C22×C4—51no—
445C22×C4—51no—
446C22×C4—61no—
447C22×C4—104no—
448C22×C4—101no—
449C22×C4—101no—
450C22×C4—302no—
451C22×C4—302no—
452C22×C4—301no—
453C22×C4—604no—
454C22×C4C2×D3×D511yescharacteristic
455C2×C8—32no—
456C2×C8—152no—
457C2×C8—304no—
458C4⋊C4—21no—
459C4⋊C4—32no—
460C4⋊C4—51no—
461C4⋊C4—61no—
462C4⋊C4—101no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—101no—
466C4⋊C4—152no—
467C4⋊C4—302no—
468C4⋊C4—302no—
469C4⋊C4—301no—
470C4⋊C4C2×D3×D511yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—101no—
473C22⋊C4—101no—
474C22⋊C4—101no—
475C3×C5C2×#48411yescharacteristic, complemented, Hall
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—52no—
479C22×C3—52no—
480C22×C3—52no—
481C22×C3—52no—
482C22×C3—108no—
483C22×C3—101no—
484C22×C3—101no—
485C22×C3D5×Q1612yes—
486C22×C3C2×D4×D511yescharacteristic
487C3×C4—21no—
488C3×C4—41no—
489C3×C4—41no—
490C3×C4—52no—
491C3×C4—101no—
492C3×C4—201no—
493C3×C4—201no—
494C3×C4D5×#4112yes—
495Dic3—42no—
496Dic3—202no—
497C2×C5—22no—
498C2×C5C2×#93511yescharacteristic
499C2×C5C22×#21611yescharacteristic
500C2×C5C2×#94911yescharacteristic
501D5—22no—
502D5#504414yesdirect product factor
503C23—51no—
504C23—54no—
505C23—51no—
506C23—102no—
507C23—102no—
508C23D5×#6711yescharacteristic
509Q8—22no—
510Q8—102no—
511Q8—202no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—51no—
516C2×C4—54no—
517C2×C4—51no—
518C2×C4—62no—
519C2×C4—102no—
520C2×C4—102no—
521C2×C4—102no—
522C2×C4—102no—
523C2×C4—101no—
524C2×C4—101no—
525C2×C4—122no—
526C2×C4—202no—
527C2×C4—202no—
528C2×C4—302no—
529C2×C4—604no—
530C2×C4—604no—
531C2×C4—602no—
532C2×C4D5×#6711yescharacteristic
533C2×C4C22×D3×D511yescharacteristic
534C8—62no—
535C8—302no—
536C2×C3—22no—
537C2×C3—54no—
538C2×C3—102no—
539C2×C3D5×#12311yescharacteristic
540C2×C3C2×D5×Q1611yescharacteristic
541C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
542C5C2×#504411yescharacteristic, complemented, Sylow
543C22—21no—
544C22—21no—
545C22—52no—
546C22—52no—
547C22—52no—
548C22—52no—
549C22—108no—
550C22—101no—
551C22—101no—
552C22D5×#21612yes—
553C22C2×D5×#6711yescharacteristic
554C4—21no—
555C4—41no—
556C4—41no—
557C4—52no—
558C4—101no—
559C4—122no—
560C4—201no—
561C4—201no—
562C4—602no—
563C4D5×#23712yes—
564C3D5×#48411yescharacteristic, complemented, Sylow
565C2—22no—
566C2—54no—
567C2—102no—
568C2D5×#93511yescharacteristic
569C2C2×D5×#21611yescharacteristic
570C2D5×#94911yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC23×C3×D5D4
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5C2×#484
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #11751145C2semidirect
4. C5×#5044C2semidirect
5. #11749197C2semidirect
6. D5×#835C2semidirect
8. #11748461C2semidirect
9. #11748403C2semidirect
10. D5×#807C2semidirect
11. #11747194C2semidirect
33. #91119C22semidirect
35. #91091C22semidirect
36. C5×#835C22semidirect
38. C5×#807C22semidirect
39. #90990C22semidirect
40. #90989C22semidirect
41. #90971C22semidirect
42. #90970C22semidirect
104. #5044D5direct (N × H)
194. #835C2×D5semidirect
201. #807C2×D5semidirect
381. C3×D5#484semidirect
475. C3×C5C2×#484semidirect
502. D5#5044direct (N × H)
542. C5C2×#5044semidirect
564. C3D5×#484semidirect

Maximal subgroups

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

subgroupindex
C3×D5×C22⋊Q82
C2×D5×C4⋊Dic32
#117511452
C5×#50442
#117491972
D5×#8352
D5×#8302
#117484612
#117484032
D5×#8072
#117471942
D5×#4843
C2×#50445