Finite Group Databasebeta

← #12030033

Subgroups — #12030033

Order 1280.

1326 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#388C211yesmaximal, characteristic
2C2×#65242C211yesmaximal, characteristic
3C2×#65217C211yesmaximal, characteristic, complemented
4#10602361C212yesmaximal, complemented
5#10602340C212yesmaximal
6#10602340C212yesmaximal
7#10602339C211yesmaximal, characteristic
8#10602327C211yesmaximal, characteristic, complemented
9#10600215C211yesmaximal, characteristic, complemented
10#10600213C211yesmaximal, characteristic, complemented
11#10600210C212yesmaximal, complemented
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C22⋊C4C2211yescharacteristic
14C22×C5×C22⋊C4C2211yescharacteristic
15C22×C5×C22⋊C4C2211yescharacteristic
16C22×C42×C5C2211yescharacteristic
17C22×C22⋊Dic5C2212yes—
18C22×C22⋊Dic5C2212yes—
19C22×C4⋊Dic5C2211yescharacteristic
20C22×C4⋊Dic5C2211yescharacteristic
21C22×#683C2212yes—
22C22×#683C2212yes—
23C5×#388—24no—
24C2×C5×#95C2211yescharacteristic
25C2×C5×#95C2211yescharacteristic
26C2×#3963C2212yes—
27C2×#3963C2211yescharacteristic
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2211yescharacteristic
36#65242C418yescomplemented
37#65217—24no—
38#14630—51nomaximal, Sylow
39C25×C5C2311yescharacteristic
40C23×C4×C5C2311yescharacteristic
41C23×C4×C5C2311yescharacteristic
42C23×C4×C5C2311yescharacteristic
43C23×C4×C5C2311yescharacteristic
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2311yescharacteristic
46C23×Dic5C2312yes—
47C23×Dic5C2312yes—
48C23×Dic5C2312yes—
49C23×Dic5C2312yes—
50C2×C5×C4⋊C4—22no—
51C2×C5×C4⋊C4—42no—
52C2×C5×C22⋊C4—22no—
53C2×C5×C22⋊C4—22no—
54C2×C5×C22⋊C4—22no—
55C2×C5×C22⋊C4—22no—
56C2×C5×C22⋊C4—42no—
57C2×C5×C22⋊C4—42no—
58C2×C5×C22⋊C4C2×C414yes—
59C2×C42×C5—42no—
60C2×C42×C5D414yes—
61C2×C22⋊Dic5—42no—
62C2×C22⋊Dic5—42no—
63C2×C22⋊Dic5—42no—
64C2×C22⋊Dic5—42no—
65C2×C22⋊Dic5—42no—
66C2×C22⋊Dic5C2×C418yes—
67C2×C4⋊Dic5—22no—
68C2×C4⋊Dic5—22no—
69C2×C4⋊Dic5—22no—
70C2×C4⋊Dic5—42no—
71C2×C4⋊Dic5C2×C414yes—
72C2×#683—24no—
73C2×#683—42no—
74C2×#683—42no—
75C2×#683—42no—
76C2×#683—42no—
77C2×#683—42no—
78C5×#95—22no—
79C5×#95—22no—
80#3963—24no—
81#3963—22no—
82#3963—42no—
83#3963—42no—
84#3963—42no—
85#3963—42no—
86#3963—42no—
87#3963—42no—
88#3963C2×C414yes—
89#3963C2×C418yes—
90C2×#397—51no—
91C2×#389—51no—
92C2×#388D511yescharacteristic
93#1445—51no—
94#1444—51no—
95#1444—52no—
96#1443—52no—
97#1439—51no—
98#1439—52no—
99#1439—52no—
100#1434—51no—
101C24×C5—21no—
102C24×C5—21no—
103C24×C5—21no—
104C24×C5—21no—
105C24×C5—21no—
106C24×C5—22no—
107C24×C5—22no—
108C24×C5—22no—
109C24×C5—22no—
110C24×C5—21no—
111C24×C5C22×C412yes—
112C24×C5C2411yescharacteristic
113C22×C4×C5—22no—
114C22×C4×C5—22no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—22no—
118C22×C4×C5—22no—
119C22×C4×C5—22no—
120C22×C4×C5—22no—
121C22×C4×C5—21no—
122C22×C4×C5—21no—
123C22×C4×C5—21no—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—21no—
127C22×C4×C5—21no—
128C22×C4×C5—21no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—21no—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5—22no—
136C22×C4×C5—21no—
137C22×C4×C5C22×C412yes—
138C22×C4×C5C22×C412yes—
139C22×C4×C5C2×D412yes—
140C22×C4×C5C2×D412yes—
141C22×C4×C5C2×D412yes—
142C22×C4×C5#4112yes—
143C22×Dic5—22no—
144C22×Dic5—22no—
145C22×Dic5—22no—
146C22×Dic5—22no—
147C22×Dic5—22no—
148C22×Dic5—22no—
149C22×Dic5—22no—
150C22×Dic5—22no—
151C22×Dic5—22no—
152C22×Dic5—22no—
153C22×Dic5—22no—
154C22×Dic5—22no—
155C22×Dic5—22no—
156C22×Dic5—22no—
157C22×Dic5—22no—
158C22×Dic5—22no—
159C22×Dic5—22no—
160C22×Dic5—22no—
161C22×Dic5—22no—
162C22×Dic5—22no—
163C22×Dic5—22no—
164C22×Dic5—22no—
165C22×Dic5—22no—
166C22×Dic5—22no—
167C22×Dic5—22no—
168C22×Dic5—22no—
169C22×Dic5C22×C414yes—
170C22×Dic5C22×C414yes—
171C5×C4⋊C4—44no—
172C5×C22⋊C4—28no—
173C5×C22⋊C4—44no—
174C5×C22⋊C4—44no—
175C42×C5—44no—
176C22⋊Dic5—48no—
177C22⋊Dic5—48no—
178C4⋊Dic5—28no—
179C4⋊Dic5—44no—
180#683—48no—
181#683—48no—
182C22×C4⋊C4—51no—
183C22×C4⋊C4—52no—
184C22×C4⋊C4—51no—
185C22×C4⋊C4—52no—
186C22×C4⋊C4C2×D511yescharacteristic
187C22×C22⋊C4—52no—
188C22×C22⋊C4—52no—
189C22×C22⋊C4C2×D511yescharacteristic
190C22×C22⋊C4C2×D511yescharacteristic
191C22×C22⋊C4C2×D511yescharacteristic
192C22×C42C2×D511yescharacteristic
193#397—58no—
194#389—104no—
195#388—24no—
196C2×#95—51no—
197C2×#95—52no—
198C2×#95—51no—
199C2×#95—52no—
200C2×#95—52no—
201C2×#95—52no—
202C2×#95—52no—
203C2×#95—52no—
204C2×#95—52no—
205C2×#95—52no—
206C2×#95C2×D511yescharacteristic
207C2×#95C2×D511yescharacteristic
208C23×C5—22no—
209C23×C5—22no—
210C23×C5—22no—
211C23×C5—24no—
212C23×C5—24no—
213C23×C5—41no—
214C23×C5—41no—
215C23×C5—41no—
216C23×C5—41no—
217C23×C5—41no—
218C23×C5—41no—
219C23×C5—42no—
220C23×C5—41no—
221C23×C5—41no—
222C23×C5—42no—
223C23×C5—42no—
224C23×C5—42no—
225C23×C5—42no—
226C23×C5—42no—
227C23×C5—42no—
228C23×C5—42no—
229C23×C5—42no—
230C23×C5—42no—
231C23×C5C23×C411yescharacteristic
232C23×C5C22×D411yescharacteristic
233C23×C5C2×#4111yescharacteristic
234C23×C5H(5,𝔽2)12yes—
235C23×C5H(5,𝔽2)12yes—
236C23×C5H(5,𝔽2)11yescharacteristic
237C23×C5H(5,𝔽2)11yescharacteristic
238C23×C5H(5,𝔽2)11yescharacteristic
239C23×C52−1+412yes—
240C23×C52−1+412yes—
241C23×C52−1+411yescharacteristic
242C2×C4×C5—24no—
243C2×C4×C5—22no—
244C2×C4×C5—22no—
245C2×C4×C5—24no—
246C2×C4×C5—22no—
247C2×C4×C5—24no—
248C2×C4×C5—22no—
249C2×C4×C5—22no—
250C2×C4×C5—22no—
251C2×C4×C5—22no—
252C2×C4×C5—22no—
253C2×C4×C5—22no—
254C2×C4×C5—41no—
255C2×C4×C5—41no—
256C2×C4×C5—42no—
257C2×C4×C5—42no—
258C2×C4×C5—42no—
259C2×C4×C5—42no—
260C2×C4×C5—42no—
261C2×C4×C5—41no—
262C2×C4×C5—41no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—41no—
266C2×C4×C5—41no—
267C2×C4×C5—42no—
268C2×C4×C5—42no—
269C2×C4×C5—42no—
270C2×C4×C5—42no—
271C2×C4×C5C4×D414yes—
272C2×Dic5—24no—
273C2×Dic5—24no—
274C2×Dic5—24no—
275C2×Dic5—24no—
276C2×Dic5—24no—
277C2×Dic5—24no—
278C2×Dic5—42no—
279C2×Dic5—42no—
280C2×Dic5—42no—
281C2×Dic5—42no—
282C2×Dic5—42no—
283C2×Dic5—42no—
284C2×Dic5—42no—
285C2×Dic5—42no—
286C2×Dic5—42no—
287C2×Dic5—42no—
288C2×Dic5—42no—
289C2×Dic5—42no—
290C2×Dic5—42no—
291C2×Dic5—42no—
292C2×Dic5—42no—
293C2×Dic5—42no—
294C2×Dic5—42no—
295C2×Dic5—42no—
296C2×Dic5—42no—
297C2×Dic5—42no—
298C2×Dic5—42no—
299C2×Dic5—42no—
300C25C22×D511yescharacteristic
301C23×C4—52no—
302C23×C4—52no—
303C23×C4—52no—
304C23×C4—52no—
305C23×C4C22×D511yescharacteristic
306C23×C4C22×D511yescharacteristic
307C23×C4C22×D511yescharacteristic
308C23×C4C22×D511yescharacteristic
309C23×C4C22×D511yescharacteristic
310C23×C4C22×D511yescharacteristic
311C2×C4⋊C4—22no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—54no—
314C2×C4⋊C4—102no—
315C2×C4⋊C4—102no—
316C2×C4⋊C4—104no—
317C2×C4⋊C4—102no—
318C2×C4⋊C4—202no—
319C2×C4⋊C4—202no—
320C2×C4⋊C4—202no—
321C2×C4⋊C4—202no—
322C2×C4⋊C4—202no—
323C2×C4⋊C4—202no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—58no—
331C2×C22⋊C4—202no—
332C2×C22⋊C4—202no—
333C2×C22⋊C4—202no—
334C2×C22⋊C4—202no—
335C2×C22⋊C4—202no—
336C2×C22⋊C4C4×D514yes—
337C2×C42—42no—
338C2×C42C22⋊D514yes—
339#95—22no—
340#95—22no—
341#95—54no—
342#95—58no—
343#95—102no—
344#95—104no—
345#95—202no—
346#95—202no—
347#95—202no—
348#95—202no—
349#95—202no—
350#95—202no—
351C22×C5—42no—
352C22×C5—42no—
353C22×C5—42no—
354C22×C5—44no—
355C22×C5—44no—
356C22×C5—81no—
357C22×C5—81no—
358C22×C5—82no—
359C22×C5—82no—
360C22×C5—81no—
361C22×C5—81no—
362C22×C5C2×C4×D411yescharacteristic
363C22×C5#51811yescharacteristic
364C22×C5#52011yescharacteristic
365C22×C5#52012yes—
366C22×C5#52012yes—
367C22×C5#53411yescharacteristic
368C22×C5#53511yescharacteristic
369C22×C5#53511yescharacteristic
370C22×C5#53611yescharacteristic
371C22×C5#53611yescharacteristic
372C22×C5#53711yescharacteristic
373C22×C5#53912yes—
374C22×C5#54011yescharacteristic
375C22×C5#54211yescharacteristic
376C22×C5#54212yes—
377C22×C5#56012yes—
378C22×C5#56012yes—
379C22×C5#56212yes—
380C22×C5#56212yes—
381C22×C5#56312yes—
382C22×C5#56312yes—
383C22×C5#56312yes—
384C22×C5#56312yes—
385C4×C5—24no—
386C4×C5—42no—
387C4×C5—42no—
388C4×C5—42no—
389C4×C5—81no—
390C4×C5—81no—
391Dic5—44no—
392Dic5—44no—
393Dic5—82no—
394Dic5—82no—
395C24—21no—
396C24—22no—
397C24—22no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—22no—
403C24—22no—
404C24—21no—
405C24C2×C4×D512yes—
406C24C23×D511yescharacteristic
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—54no—
432C22×C4—54no—
433C22×C4—102no—
434C22×C4—102no—
435C22×C4—102no—
436C22×C4—102no—
437C22×C4—102no—
438C22×C4—102no—
439C22×C4—102no—
440C22×C4—102no—
441C22×C4—102no—
442C22×C4—102no—
443C22×C4—102no—
444C22×C4—102no—
445C22×C4—102no—
446C22×C4—102no—
447C22×C4—102no—
448C22×C4—102no—
449C22×C4—102no—
450C22×C4—102no—
451C22×C4—102no—
452C22×C4—102no—
453C22×C4—102no—
454C22×C4—102no—
455C22×C4—102no—
456C22×C4—102no—
457C22×C4—102no—
458C22×C4—102no—
459C22×C4C2×C4×D512yes—
460C22×C4C2×C4×D512yes—
461C22×C4#70912yes—
462C22×C4C2×C22⋊D512yes—
463C22×C4C2×C22⋊D512yes—
464C22×C4C2×C22⋊D512yes—
465C4⋊C4—44no—
466C4⋊C4—108no—
467C4⋊C4—208no—
468C4⋊C4—204no—
469C4⋊C4—208no—
470C22⋊C4—28no—
471C22⋊C4—44no—
472C22⋊C4—44no—
473C22⋊C4—208no—
474C22⋊C4—208no—
475C42—44no—
476C2×C5—82no—
477C2×C5#232211yescharacteristic
478C2×C5#232411yescharacteristic
479C2×C5#232611yescharacteristic
480C2×C5#237612yes—
481C2×C5#238312yes—
482C2×C5#281411yescharacteristic
483C2×C5#281511yescharacteristic
484C2×C5#282011yescharacteristic
485C2×C5#282111yescharacteristic
486C2×C5#283712yes—
487C2×C5#283812yes—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—24no—
492C23—24no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23C22×C4×D511yescharacteristic
512C23C2×#70911yescharacteristic
513C23#414412yes—
514C23#414412yes—
515C23#414911yescharacteristic
516C23#414911yescharacteristic
517C23#414911yescharacteristic
518C23#415011yescharacteristic
519C23#415012yes—
520C23#415012yes—
521C23C22×C22⋊D511yescharacteristic
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—104no—
552C2×C4—104no—
553C2×C4—104no—
554C2×C4—104no—
555C2×C4—104no—
556C2×C4—104no—
557C2×C4—202no—
558C2×C4—202no—
559C2×C4—202no—
560C2×C4—202no—
561C2×C4—202no—
562C2×C4—202no—
563C2×C4—202no—
564C2×C4—202no—
565C2×C4—202no—
566C2×C4—202no—
567C2×C4—202no—
568C2×C4—202no—
569C2×C4—202no—
570C2×C4—202no—
571C2×C4—202no—
572C2×C4—202no—
573C2×C4—202no—
574C2×C4—202no—
575C2×C4—202no—
576C2×C4—202no—
577C2×C4—202no—
578C2×C4—202no—
579C2×C4C4×C22⋊D514yes—
580C5#1463011yescharacteristic, complemented, Sylow
581C22—42no—
582C22—42no—
583C22—44no—
584C22—44no—
585C22—42no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—82no—
590C22—82no—
591C22—81no—
592C22#6585511yescharacteristic
593C22#6585711yescharacteristic
594C22#6586811yescharacteristic
595C22#6586911yescharacteristic
596C22#6588012yes—
597C22#6588012yes—
598C22#6589512yes—
599C22#6589812yes—
600C22#6595412yes—
601C22#6595412yes—
602C22#6598512yes—
603C22#6600112yes—
604C22#6600612yes—
605C22#6601812yes—
606C22#6604612yes—
607C22#6604612yes—
608C22C2×C4×C22⋊D511yescharacteristic
609C22#6613811yescharacteristic
610C22#6613911yescharacteristic
611C22#6615911yescharacteristic
612C22#6615911yescharacteristic
613C22#6616411yescharacteristic
614C22#6616711yescharacteristic
615C4—24no—
616C4—42no—
617C4—42no—
618C4—42no—
619C4—81no—
620C4—81no—
621C4—204no—
622C4—204no—
623C4—402no—
624C4—402no—
625C2—82no—
626C2#1060722012yes—
627C2#1060722512yes—
628C2#1060754912yes—
629C2#1060755012yes—
630C2#1061396711yescharacteristic
631C2#1061405711yescharacteristic
632C2#1061405911yescharacteristic
633C2#1061445311yescharacteristic
634C2#1061462011yescharacteristic
635C2#1061472311yescharacteristic
636C2#1061483411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#388C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×#388D5
hypocenterC5#14630
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×#65217C2semidirect
4. #10602361C2semidirect
8. #10602327C2semidirect
9. #10600215C2semidirect
10. #10600213C2semidirect
11. #10600210C2semidirect
36. #65242C4semidirect
580. C5#14630semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3882
C2×#652422
C2×#652172
#106023612
#106023402
#106023392
#106023272
#106002152
#106002132
#106002102
#146305