Finite Group Databasebeta

← #12102415

Subgroups — #12102415

Order 1280.

862 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2319C211yesmaximal, characteristic
2C2×#65307C211yesmaximal, characteristic
3#10605114C211yesmaximal, characteristic, complemented
4C4×#3964C211yesmaximal, characteristic
5#10600453C211yesmaximal, characteristic
6#10600453C211yesmaximal, characteristic
7#10600430C211yesmaximal, characteristic
8#10600429C211yesmaximal, characteristic
9#10600425C211yesmaximal, characteristic, complemented
10#10600424C211yesmaximal, characteristic, complemented
11#10600396C211yesmaximal, characteristic, complemented
12#10600393C211yesmaximal, characteristic, complemented
13#10600274C211yesmaximal, characteristic, complemented
14C4×#3942C211yesmaximal, characteristic, complemented
15#10600228C211yesmaximal, characteristic, complemented
16C2×C4×C5×D4C2211yescharacteristic
17C22×#687C2211yescharacteristic
18C2×C4×Dic10C2211yescharacteristic
19C2×C4×Dic10C2211yescharacteristic
20C2×C4×Dic10C2211yescharacteristic
21C5×#390C2211yescharacteristic
22C5×#390C2211yescharacteristic
23C5×#389C2211yescharacteristic
24C5×#389C2211yescharacteristic
25C5×#388—21no—
26C5×#388—21no—
27C5×#381—21no—
28C5×#380—21no—
29C4×C5×C4⋊C4C2211yescharacteristic
30C5×#376C2211yescharacteristic
31C2×#3964C2211yescharacteristic
32C2×#3964C2211yescharacteristic
33C2×#3964C2211yescharacteristic
34#65307C418yescomplemented
35C2×#3942C2211yescharacteristic
36C2×#3942C2211yescharacteristic
37C2×#3942C2211yescharacteristic
38C2×#3940C2211yescharacteristic
39C2×#3939C2211yescharacteristic
40C2×#3939C2211yescharacteristic
41C4×C4⋊Dic5C2211yescharacteristic
42C4×C4⋊Dic5C2211yescharacteristic
43C4×C4⋊Dic5C2211yescharacteristic
44C2×#3935C2211yescharacteristic
45C2×C4×#168C2211yescharacteristic
46#64938—21no—
47#64938—21no—
48#64938—21no—
49#64937—21no—
50#64749C2211yescharacteristic
51#64749C2211yescharacteristic
52#64749C2211yescharacteristic
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64744C2211yescharacteristic
57#64744C2211yescharacteristic
58#64744C2211yescharacteristic
59#64744C2211yescharacteristic
60#21128—51nomaximal, Sylow
61C22×C5×D4C2311yescharacteristic
62C23×C4×C5—21no—
63C22×Dic10C2311yescharacteristic
64C4×C5×D4—22no—
65C4×C5×D4C2×C414yes—
66C2×C5×C4⋊C4—21no—
67C2×C5×C4⋊C4—21no—
68C2×C5×C4⋊C4C2311yescharacteristic
69C2×C5×C4⋊C4C2311yescharacteristic
70C2×C5×C4⋊C4C2311yescharacteristic
71C2×C5×C22⋊C4—21no—
72C2×C5×C22⋊C4—21no—
73C2×C5×C22⋊C4—21no—
74C2×C5×C22⋊C4—21no—
75C2×C5×C22⋊C4—21no—
76C2×C42×C5—21no—
77C2×C42×C5C2311yescharacteristic
78C2×C42×C5C2311yescharacteristic
79C2×C42×C5C2311yescharacteristic
80C2×#687—22no—
81C2×#687—22no—
82C2×#687C2×C414yes—
83C2×C4⋊Dic5C2311yescharacteristic
84C2×C4⋊Dic5C2311yescharacteristic
85C2×C4⋊Dic5C2311yescharacteristic
86C2×#683—21no—
87C2×#683—21no—
88C2×#683—21no—
89C2×C4×Dic5—21no—
90C2×C4×Dic5—21no—
91C2×C4×Dic5—21no—
92C2×C4×Dic5—21no—
93C2×C4×Dic5—21no—
94C2×C4×Dic5—21no—
95C22×#168C2311yescharacteristic
96C22×#168C2311yescharacteristic
97C22×#168C2311yescharacteristic
98C22×#168C2311yescharacteristic
99C4×Dic10—22no—
100C4×Dic10—22no—
101C4×Dic10—22no—
102C4×Dic10—22no—
103C4×Dic10—22no—
104C4×Dic10C2×C414yes—
105C5×#95—21no—
106C5×#95—21no—
107C5×#95—21no—
108C5×#95D411yescharacteristic
109C5×#95D411yescharacteristic
110C5×#95D411yescharacteristic
111C5×#95D411yescharacteristic
112#3964—22no—
113#3964—22no—
114#3964C2×C414yes—
115#3963—21no—
116#3963—21no—
117#3963—21no—
118#3942—22no—
119#3942—22no—
120#3942C2×C414yes—
121#3940—22no—
122#3939—22no—
123#3939C2×C414yes—
124#3935C2×C414yes—
125C4×#168—22no—
126C2×#440—51no—
127#2319D511yescharacteristic
128#2276—51no—
129#1926—51no—
130#1925—51no—
131#1921—51no—
132#1918—51no—
133#1880—51no—
134#1880—51no—
135#1865—51no—
136#1863—51no—
137#1776—51no—
138C4×#103—51no—
139C4×#102—51no—
140#1746—51no—
141C24×C5—21no—
142C2×C5×D4—21no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4C22×C412yes—
148C22×C4×C5—21no—
149C22×C4×C5—24no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—81no—
153C22×C4×C5—81no—
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2411yescharacteristic
161C22×Dic5—21no—
162C22×Dic5—21no—
163C22×Dic5—21no—
164C22×Dic5—21no—
165C2×Dic10—21no—
166C2×Dic10—21no—
167C2×Dic10—21no—
168C2×Dic10C22×C412yes—
169C2×Dic10#4112yes—
170C2×Dic10#4112yes—
171C5×C4⋊C4—21no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—81no—
177C5×C4⋊C4—81no—
178C5×C4⋊C4C22×C412yes—
179C5×C22⋊C4—24no—
180C5×C22⋊C4—81no—
181C5×C22⋊C4—81no—
182C5×C22⋊C4—81no—
183C5×C22⋊C4—81no—
184C42×C5—21no—
185C42×C5—21no—
186C42×C5—21no—
187C42×C5—21no—
188C42×C5—81no—
189C42×C5C22×C412yes—
190C42×C5#4112yes—
191#687—28no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—21no—
195C4⋊Dic5C22×C412yes—
196C4⋊Dic5#4112yes—
197C4⋊Dic5#4112yes—
198#683—24no—
199#683—24no—
200#683—24no—
201C4×Dic5—24no—
202C4×Dic5—24no—
203C4×Dic5—24no—
204C4×Dic5—81no—
205C4×Dic5—81no—
206C4×Dic5—81no—
207C2×#168—21no—
208C2×#168—21no—
209C2×#168—21no—
210C2×#168—21no—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168C22×C412yes—
218C2×#168C22×C412yes—
219C22×SD16—51no—
220C2×C4×Q8—51no—
221C2×C4×Q8—51no—
222C2×C4×Q8—51no—
223C2×C4×D4C2×D511yescharacteristic
224#440—58no—
225C2×#107—51no—
226C2×#107—51no—
227C2×#106—51no—
228C2×#103—51no—
229C2×#103—51no—
230C2×#103—51no—
231C2×#102—51no—
232C2×#102—51no—
233C2×#102—51no—
234C2×#97—51no—
235C2×C4×C8—51no—
236#390C2×D511yescharacteristic
237#390C2×D511yescharacteristic
238#389C2×D511yescharacteristic
239#389C2×D511yescharacteristic
240#388—21no—
241#388—21no—
242#381—21no—
243#380—21no—
244C4×C4⋊C4—51no—
245C4×C4⋊C4—51no—
246C4×C4⋊C4—51no—
247C4×C4⋊C4—101no—
248C4×C4⋊C4—101no—
249C4×C4⋊C4—101no—
250C4×C4⋊C4C2×D511yescharacteristic
251#376—101no—
252#376C2×D511yescharacteristic
253#340—51no—
254#340—51no—
255#340—51no—
256#340—51no—
257#340—51no—
258#340—51no—
259#336—51no—
260#336—51no—
261#336—51no—
262#336—51no—
263C23×C5—22no—
264C23×C5—41no—
265C23×C5—41no—
266C23×C5—41no—
267C23×C5—41no—
268C23×C5—41no—
269C23×C5—41no—
270C23×C5C22×D411yescharacteristic
271C5×D4—22no—
272C5×D4—22no—
273C5×D4—41no—
274C5×D4—41no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—22no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—84no—
301C2×C4×C5C4×D412yes—
302C2×C4×C5C4×D412yes—
303C2×C4×C5C23×C411yescharacteristic
304C2×C4×C5C2×#4111yescharacteristic
305C2×C4×C5C2×#4111yescharacteristic
306C2×C4×C5C2×#4111yescharacteristic
307C2×C4×C5C2×#4111yescharacteristic
308C2×C4×C5C2×#4111yescharacteristic
309C2×Dic5—22no—
310C2×Dic5—22no—
311C2×Dic5—22no—
312C2×Dic5—22no—
313C2×Dic5—22no—
314C2×Dic5—22no—
315C2×Dic5—41no—
316C2×Dic5—41no—
317C2×Dic5—41no—
318C2×Dic5—41no—
319C2×Dic5—41no—
320C2×Dic5—41no—
321Dic10—22no—
322Dic10—22no—
323Dic10—22no—
324Dic10#11714yes—
325#168—22no—
326#168—22no—
327#168—41no—
328#168—41no—
329C22×Q8—51no—
330C22×D4C22×D511yescharacteristic
331C23×C4—21no—
332C2×SD16—54no—
333C2×SD16—102no—
334C2×SD16—102no—
335C22×C8—51no—
336C22×C8—51no—
337C22×C8—51no—
338C22×C8—51no—
339C4×Q8—54no—
340C4×Q8—102no—
341C4×Q8—102no—
342C4×Q8—102no—
343C4×Q8—102no—
344C4×Q8—102no—
345C4×D4—22no—
346C4×D4C4×D514yes—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—51no—
350C2×C4⋊C4—51no—
351C2×C4⋊C4—51no—
352C2×C4⋊C4—101no—
353C2×C4⋊C4—101no—
354C2×C4⋊C4—101no—
355C2×C4⋊C4C22×D511yescharacteristic
356C2×C4⋊C4C22×D511yescharacteristic
357C2×C4⋊C4C22×D511yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C42—21no—
364C2×C42—101no—
365C2×C42—101no—
366C2×C42—101no—
367C2×C42—101no—
368C2×C42—101no—
369C2×C42—101no—
370C2×C42C22×D511yescharacteristic
371C2×C42C22×D511yescharacteristic
372C2×C42C22×D511yescharacteristic
373#107—54no—
374#107—102no—
375#106—102no—
376#103—54no—
377#103—102no—
378#103—102no—
379#102—54no—
380#102—102no—
381#102—102no—
382#97—54no—
383C4×C8—102no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—101no—
388#95—101no—
389#95—101no—
390#95C22⋊D511yescharacteristic
391#95C22⋊D511yescharacteristic
392#95C22⋊D511yescharacteristic
393#95C22⋊D511yescharacteristic
394C22×C5—42no—
395C22×C5—42no—
396C22×C5—42no—
397C22×C5—81no—
398C22×C5—81no—
399C22×C5—81no—
400C22×C5—81no—
401C22×C5C2×C4×D411yescharacteristic
402C22×C5#52511yescharacteristic
403C22×C5#52511yescharacteristic
404C22×C5#57611yescharacteristic
405C22×C5#57711yescharacteristic
406C22×C5#57711yescharacteristic
407C22×C5#57811yescharacteristic
408C4×C5—22no—
409C4×C5—22no—
410C4×C5—41no—
411C4×C5—41no—
412C4×C5—41no—
413C4×C5—41no—
414C4×C5—42no—
415C4×C5—81no—
416C4×C5—81no—
417C4×C5C2×#11711yescharacteristic
418C4×C5C4×#4111yescharacteristic
419C4×C5#52911yescharacteristic
420C4×C5#52911yescharacteristic
421Dic5—24no—
422Dic5—42no—
423Dic5—42no—
424Dic5—42no—
425C24—21no—
426C2×Q8—52no—
427C2×Q8—52no—
428C2×Q8—52no—
429C2×Q8—101no—
430C2×Q8—101no—
431C2×Q8—101no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4C2×C4×D512yes—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—81no—
443C22×C4—81no—
444C22×C4—101no—
445C22×C4—101no—
446C22×C4—101no—
447C22×C4—101no—
448C22×C4C2×C22⋊D511yescharacteristic
449C22×C4C2×C22⋊D511yescharacteristic
450C22×C4C2×C22⋊D511yescharacteristic
451C22×C4C2×C22⋊D511yescharacteristic
452C22×C4C2×C22⋊D511yescharacteristic
453C22×C4C2×C22⋊D511yescharacteristic
454C22×C4C23×D511yescharacteristic
455SD16—108no—
456C2×C8—52no—
457C2×C8—52no—
458C2×C8—101no—
459C2×C8—101no—
460C2×C8—101no—
461C2×C8—101no—
462C2×C8—101no—
463C2×C8—101no—
464C2×C8—101no—
465C2×C8—101no—
466C2×C8—101no—
467C2×C8—101no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—52no—
474C4⋊C4—52no—
475C4⋊C4—52no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4—104no—
479C4⋊C4—104no—
480C4⋊C4—101no—
481C4⋊C4—101no—
482C4⋊C4—101no—
483C4⋊C4—104no—
484C4⋊C4C2×C4×D512yes—
485C22⋊C4—24no—
486C22⋊C4—81no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C22⋊C4—81no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—81no—
495C42—104no—
496C42—104no—
497C42—104no—
498C42—401no—
499C42—401no—
500C42—401no—
501C42C2×C4×D512yes—
502C42#70912yes—
503C2×C5—82no—
504C2×C5#229011yescharacteristic
505C2×C5#294611yescharacteristic
506C2×C5#294711yescharacteristic
507C2×C5#311911yescharacteristic
508C2×C5#312111yescharacteristic
509C2×C5#312411yescharacteristic
510C2×C5#312611yescharacteristic
511C23—22no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23C22×C22⋊D511yescharacteristic
519Q8—54no—
520Q8—102no—
521Q8—102no—
522Q8—102no—
523D4—22no—
524D4—22no—
525D4—41no—
526D4—41no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—84no—
553C2×C4—102no—
554C2×C4—102no—
555C2×C4—102no—
556C2×C4—102no—
557C2×C4—102no—
558C2×C4—102no—
559C2×C4—201no—
560C2×C4—201no—
561C2×C4—201no—
562C2×C4—201no—
563C2×C4—201no—
564C2×C4—201no—
565C2×C4C4×C22⋊D512yes—
566C2×C4C4×C22⋊D512yes—
567C2×C4C22×C4×D511yescharacteristic
568C2×C4C2×#70911yescharacteristic
569C2×C4D5×#4111yescharacteristic
570C2×C4D5×#4111yescharacteristic
571C2×C4D5×#4111yescharacteristic
572C2×C4D5×#4111yescharacteristic
573C8—102no—
574C8—102no—
575C8—201no—
576C8—201no—
577C5#2112811yescharacteristic, complemented, Sylow
578C22—42no—
579C22—42no—
580C22—42no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22C2×C4×C22⋊D511yescharacteristic
586C22#6616211yescharacteristic
587C22#6616211yescharacteristic
588C22#6616911yescharacteristic
589C22#6617011yescharacteristic
590C22#6617011yescharacteristic
591C22#6617211yescharacteristic
592C4—22no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—42no—
599C4—81no—
600C4—81no—
601C4—104no—
602C4—202no—
603C4—202no—
604C4—202no—
605C4D5×#11711yescharacteristic
606C4#6585611yescharacteristic
607C4#6586211yescharacteristic
608C4#6586211yescharacteristic
609C2—82no—
610C2#1061399911yescharacteristic
611C2#1061426811yescharacteristic
612C2#1061430211yescharacteristic
613C2#1061516511yescharacteristic
614C2#1061517011yescharacteristic
615C2#1061519211yescharacteristic
616C2#1061519811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#2319C2
socleC23×C5C22×D4
prime radicalC22×C5×D4C23
cosocleC22×C4×C5C24
hypercenter#2319D5
hypocenterC5#21128
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
3. #10605114C2semidirect
9. #10600425C2semidirect
10. #10600424C2semidirect
11. #10600396C2semidirect
12. #10600393C2semidirect
13. #10600274C2semidirect
14. C4×#3942C2semidirect
15. #10600228C2semidirect
34. #65307C4semidirect
577. C5#21128semidirect

Maximal subgroups

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

subgroupindex
C5×#23192
C2×#653072
#106051142
C4×#39642
#106004532
#106004302
#106004292
#106004252
#106004242
#106003962
#106003932
#106002742
C4×#39422
#106002282
#211285