Finite Group Databasebeta

← #12021765

Subgroups — #12021765

Order 1280.

1650 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4033C211yesmaximal, characteristic
2C2×#65263C211yesmaximal, characteristic
3C2×#65218C211yesmaximal, characteristic
4C5×C4⋊#95C211yesmaximal, characteristic
5#10602356C211yesmaximal, characteristic
6#10602356C211yesmaximal, characteristic
7C4×#3963C211yesmaximal, characteristic
8#10600214C212yesmaximal
9#10600214C212yesmaximal
10#10600196C212yesmaximal
11#10600194C212yesmaximal
12C23×Dic10C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C42×C5C2211yescharacteristic
16C22×C4⋊Dic5C2211yescharacteristic
17C22×#683C2212yes—
18C22×C4×Dic5C2211yescharacteristic
19C22×C4×Dic5C2212yes—
20C22×C4×Dic5C2211yescharacteristic
21C2×#4033—24no—
22C2×#4033—24no—
23C2×#4033C418yescomplemented
24C2×C5×#95C2212yes—
25C2×C5×#95C2212yes—
26C2×#3963C2211yescharacteristic
27C2×#3963C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2211yescharacteristic
34C2×#3963C2211yescharacteristic
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2211yescharacteristic
38#65263—24no—
39#65218—24no—
40#13931—51nomaximal, Sylow
41C23×C4×C5C2312yes—
42C23×C4×C5C2312yes—
43C23×C4×C5C2311yescharacteristic
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2311yescharacteristic
46C23×Dic5C2312yes—
47C23×Dic5C2311yescharacteristic
48C23×Dic5C2311yescharacteristic
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2312yes—
51C23×Dic5C2311yescharacteristic
52C22×Dic10—22no—
53C22×Dic10—22no—
54C22×Dic10—22no—
55C22×Dic10—22no—
56C22×Dic10C2×C414yes—
57C22×Dic10D414yes—
58C22×Dic10D414yes—
59C2×C5×C4⋊C4—22no—
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4—22no—
63C2×C5×C4⋊C4—22no—
64C2×C5×C4⋊C4C2×C414yes—
65C2×C42×C5—22no—
66C2×C42×C5—22no—
67C2×C42×C5—22no—
68C2×C4⋊Dic5—22no—
69C2×C4⋊Dic5—22no—
70C2×C4⋊Dic5—22no—
71C2×#683—24no—
72C2×#683—24no—
73C2×#683C2×C418yes—
74C2×C4×Dic5—22no—
75C2×C4×Dic5—22no—
76C2×C4×Dic5—24no—
77C2×C4×Dic5—24no—
78C2×C4×Dic5—22no—
79C2×C4×Dic5—22no—
80C2×C4×Dic5—22no—
81C2×C4×Dic5C2×C414yes—
82C2×C4×Dic5C2×C418yes—
83#4033—232no—
84C5×#95—24no—
85C5×#95—42no—
86#3963—22no—
87#3963—24no—
88#3963—24no—
89#3963—24no—
90#3963—24no—
91#3963—22no—
92#3963—22no—
93#3963—24no—
94#3963—24no—
95#3963—42no—
96#3963—42no—
97#3963Q814yescomplemented
98C22×C4×Q8—51no—
99C2×#391—51no—
100C2×#391—51no—
101#1445—52no—
102#1445—52no—
103C4⋊#95—51no—
104C4⋊#95—51no—
105C4⋊#95D511yescharacteristic
106#1434—52no—
107#1434—52no—
108C4×#95—51no—
109C24×C5C2411yescharacteristic
110C22×C4×C5—21no—
111C22×C4×C5—21no—
112C22×C4×C5—22no—
113C22×C4×C5—22no—
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—21no—
118C22×C4×C5—22no—
119C22×C4×C5—21no—
120C22×C4×C5—21no—
121C22×C4×C5—22no—
122C22×C4×C5—22no—
123C22×C4×C5—21no—
124C22×C4×C5—21no—
125C22×C4×C5—22no—
126C22×C4×C5—21no—
127C22×C4×C5—21no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
135C22×C4×C5C22×C414yes—
136C22×C4×C5C22×C412yes—
137C22×C4×C5C2×D412yes—
138C22×C4×C5C2×D412yes—
139C22×C4×C5C2×Q812yes—
140C22×C4×C5#4112yes—
141C22×C4×C5#4112yes—
142C22×C4×C5#4112yes—
143C22×C4×C5#4112yes—
144C22×C4×C5#4112yes—
145C22×Dic5—21no—
146C22×Dic5—21no—
147C22×Dic5—22no—
148C22×Dic5—22no—
149C22×Dic5—22no—
150C22×Dic5—22no—
151C22×Dic5—21no—
152C22×Dic5—21no—
153C22×Dic5—21no—
154C22×Dic5—21no—
155C22×Dic5—21no—
156C22×Dic5—21no—
157C22×Dic5—21no—
158C22×Dic5—21no—
159C22×Dic5—21no—
160C22×Dic5—21no—
161C22×Dic5—21no—
162C22×Dic5—21no—
163C22×Dic5—21no—
164C22×Dic5—21no—
165C22×Dic5—21no—
166C22×Dic5—21no—
167C22×Dic5—21no—
168C22×Dic5—21no—
169C22×Dic5—21no—
170C22×Dic5—21no—
171C22×Dic5—22no—
172C22×Dic5—22no—
173C22×Dic5—22no—
174C22×Dic5—22no—
175C22×Dic5—22no—
176C22×Dic5—22no—
177C22×Dic5—22no—
178C22×Dic5C22×C412yes—
179C22×Dic5C22×C414yes—
180C22×Dic5C22×C412yes—
181C22×Dic5C2×D414yes—
182C22×Dic5C2×D414yes—
183C22×Dic5C2×Q812yes—
184C22×Dic5C2×Q812yes—
185C22×Dic5#4112yes—
186C22×Dic5#4112yes—
187C2×Dic10—28no—
188C2×Dic10—28no—
189C2×Dic10—28no—
190C2×Dic10—28no—
191C2×Dic10—28no—
192C2×Dic10—28no—
193C2×Dic10C22⋊C4116yes—
194C5×C4⋊C4—28no—
195C5×C4⋊C4—44no—
196C42×C5—44no—
197C4⋊Dic5—44no—
198#683—216no—
199C4×Dic5—28no—
200C4×Dic5—216no—
201C4×Dic5—44no—
202C23×Q8—51no—
203C2×C4×Q8—58no—
204C2×C4×Q8—104no—
205C2×C4×Q8—104no—
206C22×C4⋊C4—52no—
207C22×C4⋊C4—51no—
208C22×C4⋊C4C2×D511yescharacteristic
209C22×C4⋊C4C2×D511yescharacteristic
210C22×C42—51no—
211C22×C42—52no—
212C22×C42—51no—
213C22×C42C2×D511yescharacteristic
214#391—104no—
215#391—104no—
216C2×#95—51no—
217C2×#95—51no—
218C2×#95—51no—
219C2×#95—51no—
220C2×#95—52no—
221C2×#95—52no—
222C2×#95—52no—
223C2×#95—52no—
224C2×#95—52no—
225C2×#95—52no—
226C2×#95—52no—
227C2×#95—52no—
228C2×#95C2×D512yes—
229C2×#95C2×D512yes—
230C23×C5C23×C411yescharacteristic
231C23×C5C22×D411yescharacteristic
232C23×C5C22×D411yescharacteristic
233C23×C5C22×Q811yescharacteristic
234C23×C5C2×#4111yescharacteristic
235C23×C5C2×#4111yescharacteristic
236C23×C5C2×#4111yescharacteristic
237C23×C5C2×#4111yescharacteristic
238C23×C5C2×#4111yescharacteristic
239C23×C5C2×#4111yescharacteristic
240C23×C5C2×#4111yescharacteristic
241C23×C5H(5,𝔽2)11yescharacteristic
242C23×C52−1+411yescharacteristic
243C23×C52−1+411yescharacteristic
244C23×C52−1+411yescharacteristic
245C2×C4×C5—24no—
246C2×C4×C5—24no—
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—41no—
257C2×C4×C5—41no—
258C2×C4×C5—42no—
259C2×C4×C5—41no—
260C2×C4×C5—42no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—41no—
266C2×C4×C5—42no—
267C2×C4×C5—42no—
268C2×C4×C5—42no—
269C2×C4×C5—42no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5—42no—
273C2×C4×C5C2×C22⋊C414yes—
274C2×C4×C5#11714yes—
275C2×C4×C5#11714yes—
276C2×C4×C5#12314yes—
277C2×C4×C5#12314yes—
278C2×C4×C5#12314yes—
279C2×C4×C5#12314yes—
280C2×Dic5—22no—
281C2×Dic5—24no—
282C2×Dic5—24no—
283C2×Dic5—22no—
284C2×Dic5—24no—
285C2×Dic5—24no—
286C2×Dic5—24no—
287C2×Dic5—24no—
288C2×Dic5—22no—
289C2×Dic5—22no—
290C2×Dic5—22no—
291C2×Dic5—22no—
292C2×Dic5—22no—
293C2×Dic5—22no—
294C2×Dic5—22no—
295C2×Dic5—22no—
296C2×Dic5—22no—
297C2×Dic5—22no—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—22no—
301C2×Dic5—41no—
302C2×Dic5—41no—
303C2×Dic5—41no—
304C2×Dic5—41no—
305C2×Dic5—41no—
306C2×Dic5—41no—
307C2×Dic5—41no—
308C2×Dic5—41no—
309C2×Dic5—41no—
310C2×Dic5—41no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313C2×Dic5—42no—
314C2×Dic5—42no—
315C2×Dic5—42no—
316C2×Dic5—42no—
317C2×Dic5—42no—
318C2×Dic5—42no—
319C2×Dic5—42no—
320C2×Dic5C2×C22⋊C418yes—
321C2×Dic5C4×Q814yes—
322Dic10—232no—
323C22×Q8—54no—
324C22×Q8—54no—
325C22×Q8—54no—
326C22×Q8—102no—
327C22×Q8—102no—
328C22×Q8—102no—
329C22×Q8—102no—
330C23×C4—52no—
331C23×C4—51no—
332C23×C4—51no—
333C23×C4—51no—
334C23×C4—51no—
335C23×C4—52no—
336C23×C4C22×D512yes—
337C23×C4C22×D512yes—
338C23×C4C22×D511yescharacteristic
339C23×C4C22×D511yescharacteristic
340C23×C4C22×D511yescharacteristic
341C4×Q8—1032no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—58no—
348C2×C4⋊C4—104no—
349C2×C4⋊C4—104no—
350C2×C4⋊C4—102no—
351C2×C4⋊C4—102no—
352C2×C4⋊C4—102no—
353C2×C4⋊C4C4×D514yes—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—58no—
358C2×C42—54no—
359C2×C42—104no—
360C2×C42—104no—
361C2×C42—102no—
362C2×C42—102no—
363C2×C42—102no—
364C2×C42—102no—
365C2×C42—102no—
366#95—24no—
367#95—42no—
368#95—54no—
369#95—102no—
370#95—102no—
371#95—104no—
372#95—104no—
373#95—104no—
374#95—104no—
375#95—104no—
376#95—104no—
377#95—102no—
378#95—202no—
379#95—202no—
380C22×C5C22×C22⋊C411yescharacteristic
381C22×C5C2×#11711yescharacteristic
382C22×C5C2×#11711yescharacteristic
383C22×C5C2×C4×Q811yescharacteristic
384C22×C5C4×#4111yescharacteristic
385C22×C5#51911yescharacteristic
386C22×C5#52011yescharacteristic
387C22×C5C2×#12311yescharacteristic
388C22×C5C2×#12311yescharacteristic
389C22×C5C2×#12311yescharacteristic
390C22×C5C2×#12311yescharacteristic
391C22×C5#52911yescharacteristic
392C22×C5#52911yescharacteristic
393C22×C5#53311yescharacteristic
394C22×C5#53311yescharacteristic
395C22×C5#54111yescharacteristic
396C22×C5#54111yescharacteristic
397C22×C5#54211yescharacteristic
398C22×C5#54211yescharacteristic
399C22×C5#54811yescharacteristic
400C22×C5#54811yescharacteristic
401C22×C5#54811yescharacteristic
402C22×C5#54811yescharacteristic
403C22×C5D4×Q811yescharacteristic
404C22×C5D4×Q811yescharacteristic
405C22×C5#55011yescharacteristic
406C22×C5#55011yescharacteristic
407C22×C5#55211yescharacteristic
408C22×C5#55211yescharacteristic
409C22×C5#55411yescharacteristic
410C22×C5#55611yescharacteristic
411C22×C5#55611yescharacteristic
412C22×C5#55611yescharacteristic
413C22×C5#55711yescharacteristic
414C22×C5#55911yescharacteristic
415C4×C5—44no—
416C4×C5—42no—
417C4×C5—42no—
418C4×C5—82no—
419C4×C5#38118yes—
420Dic5—24no—
421Dic5—28no—
422Dic5—42no—
423Dic5—42no—
424Dic5—42no—
425Dic5—82no—
426C24C23×D511yescharacteristic
427C2×Q8—516no—
428C2×Q8—108no—
429C2×Q8—108no—
430C2×Q8—108no—
431C2×Q8—108no—
432C2×Q8—108no—
433C2×Q8—108no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—52no—
460C22×C4—54no—
461C22×C4—54no—
462C22×C4—54no—
463C22×C4—52no—
464C22×C4—52no—
465C22×C4—52no—
466C22×C4—52no—
467C22×C4—52no—
468C22×C4—102no—
469C22×C4—102no—
470C22×C4—101no—
471C22×C4—101no—
472C22×C4—102no—
473C22×C4—102no—
474C22×C4—101no—
475C22×C4—101no—
476C22×C4—101no—
477C22×C4—101no—
478C22×C4—101no—
479C22×C4—101no—
480C22×C4—101no—
481C22×C4—101no—
482C22×C4—101no—
483C22×C4—101no—
484C22×C4—101no—
485C22×C4—101no—
486C22×C4—101no—
487C22×C4—101no—
488C22×C4—101no—
489C22×C4—101no—
490C22×C4—101no—
491C22×C4—101no—
492C22×C4—101no—
493C22×C4—101no—
494C22×C4—102no—
495C22×C4—102no—
496C22×C4—102no—
497C22×C4—102no—
498C22×C4—102no—
499C22×C4—102no—
500C22×C4—102no—
501C22×C4C2×C4×D514yes—
502C22×C4C2×C4×D512yes—
503C22×C4#70912yes—
504C22×C4#70912yes—
505C22×C4D4×D512yes—
506C22×C4D4×D512yes—
507C22×C4#71112yes—
508C22×C4#71112yes—
509C22×C4Q8×D512yes—
510C22×C4#71312yes—
511C4⋊C4—28no—
512C4⋊C4—44no—
513C4⋊C4—1016no—
514C4⋊C4—204no—
515C42—44no—
516C42—1016no—
517C42—108no—
518C42—204no—
519C2×C5C2×#38111yescharacteristic
520C2×C5#229511yescharacteristic
521C2×C5#232011yescharacteristic
522C2×C5Q8×C22⋊C411yescharacteristic
523C2×C5#234111yescharacteristic
524C2×C5#235511yescharacteristic
525C2×C5#235611yescharacteristic
526C2×C5#242111yescharacteristic
527C2×C5#242111yescharacteristic
528C2×C5#242311yescharacteristic
529C2×C5#242311yescharacteristic
530C2×C5#244611yescharacteristic
531C2×C5#244611yescharacteristic
532C2×C5#244811yescharacteristic
533C2×C5#244811yescharacteristic
534C23C22×C4×D511yescharacteristic
535C23C2×#70911yescharacteristic
536C23C2×#70911yescharacteristic
537C23C2×D4×D511yescharacteristic
538C23C2×D4×D511yescharacteristic
539C23C2×#71111yescharacteristic
540C23C2×#71111yescharacteristic
541C23#414411yescharacteristic
542C23C2×Q8×D511yescharacteristic
543C23C2×#71311yescharacteristic
544C23#414711yescharacteristic
545C23D5×#4111yescharacteristic
546C23D5×#4111yescharacteristic
547C23#415011yescharacteristic
548C23#415011yescharacteristic
549Q8—1032no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—58no—
579C2×C4—54no—
580C2×C4—102no—
581C2×C4—104no—
582C2×C4—102no—
583C2×C4—104no—
584C2×C4—104no—
585C2×C4—104no—
586C2×C4—104no—
587C2×C4—104no—
588C2×C4—102no—
589C2×C4—102no—
590C2×C4—102no—
591C2×C4—102no—
592C2×C4—102no—
593C2×C4—102no—
594C2×C4—102no—
595C2×C4—102no—
596C2×C4—102no—
597C2×C4—102no—
598C2×C4—102no—
599C2×C4—102no—
600C2×C4—102no—
601C2×C4—201no—
602C2×C4—201no—
603C2×C4—201no—
604C2×C4—201no—
605C2×C4—201no—
606C2×C4—201no—
607C2×C4—201no—
608C2×C4—201no—
609C2×C4—201no—
610C2×C4—201no—
611C2×C4—201no—
612C2×C4—201no—
613C2×C4—202no—
614C2×C4—202no—
615C2×C4—202no—
616C2×C4—202no—
617C2×C4—202no—
618C2×C4—202no—
619C2×C4—202no—
620C2×C4#401814yes—
621C2×C4D5×C22⋊C414yes—
622C2×C4#402914yes—
623C2×C4#402914yes—
624C2×C4#403814yes—
625C2×C4#404014yes—
626C2×C4#404014yes—
627C5#1393111yescharacteristic, complemented, Sylow
628C22C2×#401811yescharacteristic
629C22C2×D5×C22⋊C411yescharacteristic
630C22C2×#402911yescharacteristic
631C22C2×#402911yescharacteristic
632C22C2×#403811yescharacteristic
633C22C2×#404011yescharacteristic
634C22C2×#404011yescharacteristic
635C22#6584511yescharacteristic
636C22#6584711yescharacteristic
637C22#6586311yescharacteristic
638C22#6586711yescharacteristic
639C22C4×#71111yescharacteristic
640C22#6587611yescharacteristic
641C22#6588011yescharacteristic
642C22#6589311yescharacteristic
643C22#6590111yescharacteristic
644C22#6590211yescharacteristic
645C22C4×Q8×D511yescharacteristic
646C22#6590611yescharacteristic
647C22#6593211yescharacteristic
648C22#6593311yescharacteristic
649C22#6593411yescharacteristic
650C22#6593711yescharacteristic
651C22#6595611yescharacteristic
652C22#6595911yescharacteristic
653C22#6596611yescharacteristic
654C22#6596711yescharacteristic
655C22#6601111yescharacteristic
656C22#6601111yescharacteristic
657C22#6602511yescharacteristic
658C22#6603111yescharacteristic
659C22#6605211yescharacteristic
660C22#6606111yescharacteristic
661C22#6606211yescharacteristic
662C22#6606711yescharacteristic
663C4—42no—
664C4—42no—
665C4—44no—
666C4—82no—
667C4—108no—
668C4—104no—
669C4—202no—
670C4—202no—
671C4—202no—
672C4—402no—
673C4#6495318yes—
674C2C2×#6495311yescharacteristic
675C2#1060537211yescharacteristic
676C2#1060537511yescharacteristic
677C2#1060562311yescharacteristic
678C2#1060562511yescharacteristic
679C2#1060596311yescharacteristic
680C2#1060609411yescharacteristic
681C2#1060769311yescharacteristic
682C2#1060770111yescharacteristic
683C2#1060773611yescharacteristic
684C2#1060773811yescharacteristic
685C2#1060803211yescharacteristic
686C2#1060805211yescharacteristic
687C2#1060823511yescharacteristic
688C2#1060834511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C4⋊#95C2
socle, prime radical, cosocleC24×C5C24
hypercenterC4⋊#95D5
hypocenterC5#13931
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
23. C2×#4033C4semidirect
97. #3963Q8semidirect
627. C5#13931semidirect

Maximal subgroups

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

subgroupindex
C22×#40332
C2×#652632
C2×#652182
C5×C4⋊#952
#106023562
C4×#39632
#106002142
#106001962
#106001942
#139315