Finite Group Databasebeta

← #12106417

Subgroups — #12106417

Order 1280.

976 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×#65151C211yesmaximal, characteristic
2#10607696C211yesmaximal, characteristic
3C4×D5×C4⋊C4C211yesmaximal, characteristic
4C5×#1920C211yesmaximal, characteristic, complemented
5Dic5×#106C211yesmaximal, characteristic, complemented
6#10600395C211yesmaximal, characteristic, complemented
7#10600257C211yesmaximal, characteristic, complemented
8#10599671C211yesmaximal, characteristic
9#10599668C211yesmaximal, characteristic
10#10599664C211yesmaximal, characteristic
11#10599577C211yesmaximal, characteristic, complemented
12#10599574C211yesmaximal, characteristic, complemented
13#10599574C211yesmaximal, characteristic, complemented
14#10599420C211yesmaximal, characteristic, complemented
15#10599392C211yesmaximal, characteristic
16C2×#4043C2211yescharacteristic
17C2×D5×C4⋊C4C2211yescharacteristic
18C2×D5×C4⋊C4C2211yescharacteristic
19C2×#4033C2211yescharacteristic
20C2×C42×D5—21no—
21C2×C42×D5C2211yescharacteristic
22C2×C5×#106C2211yescharacteristic
23C5×#389C2211yescharacteristic
24C4×C5×C4⋊C4C2211yescharacteristic
25C2×#3952C2211yescharacteristic
26C2×#3952C2211yescharacteristic
27C2×#3949C2211yescharacteristic
28C2×#3948C2211yescharacteristic
29C2×#3948C2211yescharacteristic
30C2×C8×Dic5C2211yescharacteristic
31C2×C8×Dic5C2211yescharacteristic
32#65278—21no—
33#65276C2211yescharacteristic
34C4⋊C4×Dic5—21no—
35C4⋊C4×Dic5C2211yescharacteristic
36C4⋊C4×Dic5C2211yescharacteristic
37C4⋊C4×Dic5C2211yescharacteristic
38C2×#3942C2211yescharacteristic
39C2×#3942C2211yescharacteristic
40C2×#3940C2211yescharacteristic
41C2×#3940C2211yescharacteristic
42C4×C4⋊Dic5C2211yescharacteristic
43C4×#683—21no—
44#65218C2211yescharacteristic
45#65151C418yescomplemented
46#64955—21no—
47D5×#95—21no—
48#64943—21no—
49#64938—21no—
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#336C2211yescharacteristic
54#64771C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64744C2211yescharacteristic
60C4×#483—51nomaximal, Sylow
61C22×C4×D5—21no—
62C22×C4×D5—21no—
63C22×C4×D5D411yescharacteristic
64C22×C4×D5D411yescharacteristic
65C22×C4×D5C2311yescharacteristic
66C22×Dic10C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C2×C5×C4⋊C4—21no—
70C2×C5×C4⋊C4C2311yescharacteristic
71C2×C5×C4⋊C4C2311yescharacteristic
72C2×C5×C4⋊C4C2311yescharacteristic
73C2×C5×C4⋊C4C2311yescharacteristic
74C2×C42×C5—21no—
75C2×C42×C5C2311yescharacteristic
76C2×#685—21no—
77C2×#685—21no—
78C2×C4⋊Dic5—21no—
79C2×C4⋊Dic5C2311yescharacteristic
80C2×C4⋊Dic5C2311yescharacteristic
81C2×C4⋊Dic5C2311yescharacteristic
82C2×#683—21no—
83C2×#683—21no—
84C2×#683—21no—
85C2×C4×Dic5—21no—
86C2×C4×Dic5—21no—
87C2×C4×Dic5—21no—
88C2×C4×Dic5—21no—
89C2×C4×Dic5—21no—
90C2×C4×Dic5D411yescharacteristic
91C2×C4×Dic5D411yescharacteristic
92C2×C4×Dic5C2311yescharacteristic
93C22×#168C2311yescharacteristic
94C22×#168C2311yescharacteristic
95#4043—22no—
96#4043C2×C414yes—
97D5×C4⋊C4—22no—
98D5×C4⋊C4—22no—
99D5×C4⋊C4—22no—
100D5×C4⋊C4C2×C414yes—
101#4033—22no—
102#4033—22no—
103C42×D5—22no—
104C42×D5—22no—
105C42×D5—44no—
106C5×#106C2×C414yescomplemented
107C5×#95—21no—
108C5×#95—21no—
109#3963—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114#3963—21no—
115#3963—21no—
116#3952—22no—
117#3952C2×C414yes—
118#3949—22no—
119#3948—22no—
120#3948C2×C414yescomplemented
121C8×Dic5—22no—
122C8×Dic5—22no—
123#3942—22no—
124#3942C2×C414yescomplemented
125#3940—22no—
126#3940C2×C414yescomplemented
127C2×#483—51no—
128C4×C22⋊Q8—51no—
129C2×C4×C4⋊C4—51no—
130#1927—51no—
131#1927—51no—
132#1920—51no—
133#1920D511yescharacteristic, complemented
134#1872—51no—
135#1853—51no—
136#1823—51no—
137C4×#106—51no—
138C4×#106—51no—
139C4×#103—51no—
140C4×#103—51no—
141C4×C22⋊C8—51no—
142C23×D5C2×D411yescharacteristic
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5C2×D411yescharacteristic
148C22×C4×C5C2×D411yescharacteristic
149C22×C4×C5C2411yescharacteristic
150C22×Dic5—21no—
151C22×Dic5—21no—
152C22×Dic5—21no—
153C22×Dic5—21no—
154C22×Dic5C2×D411yescharacteristic
155C22×Dic5C2×D411yescharacteristic
156C22×Dic5C2×D411yescharacteristic
157C2×C4×D5—21no—
158C2×C4×D5—21no—
159C2×C4×D5—21no—
160C2×C4×D5—21no—
161C2×C4×D5—22no—
162C2×C4×D5—22no—
163C2×C4×D5—24no—
164C2×C4×D5—24no—
165C2×C4×D5—22no—
166C2×C4×D5—22no—
167C2×C4×D5—41no—
168C2×C4×D5—42no—
169C2×C4×D5—42no—
170C2×C4×D5—42no—
171C2×C4×D5—42no—
172C2×C4×D5SD1614yes—
173C2×C4×D5C22×C412yes—
174C2×C4×D5#4112yes—
175C2×Dic10—21no—
176C2×Dic10—21no—
177C2×Dic10—21no—
178C2×Dic10—21no—
179C2×Dic10—21no—
180C2×Dic10C22×C412yes—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8—21no—
186C2×C5×C8C22×C412yes—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—21no—
190C5×C4⋊C4—21no—
191C5×C4⋊C4—21no—
192C5×C4⋊C4—42no—
193C5×C4⋊C4C22×C412yes—
194C5×C4⋊C4C22×C412yes—
195C5×C4⋊C4#4112yes—
196C42×C5—21no—
197C42×C5—21no—
198C42×C5—42no—
199#685—24no—
200#685—42no—
201C4⋊Dic5—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5—24no—
204C4⋊Dic5—21no—
205C4⋊Dic5—21no—
206C4⋊Dic5C22×C412yes—
207C4⋊Dic5#4112yes—
208#683—24no—
209#683—24no—
210#683—42no—
211C4×Dic5—22no—
212C4×Dic5—22no—
213C4×Dic5—42no—
214C4×Dic5—42no—
215C4×Dic5—42no—
216C4×Dic5—42no—
217C4×Dic5—42no—
218C4×Dic5#4112yes—
219C4×Dic5#4112yes—
220C2×#168—21no—
221C2×#168—21no—
222C2×#168—21no—
223C2×#168—21no—
224C2×#168—21no—
225C2×#168C22×C412yes—
226C2×C22⋊Q8—51no—
227C2×C4×Q8—51no—
228C22×C4⋊C4—51no—
229C22×C4⋊C4—51no—
230C22×C42—51no—
231C22×C42—101no—
232#483—58no—
233C2×#106—51no—
234C2×#106—51no—
235C2×#106—51no—
236C2×#106C2×D511yescharacteristic
237C2×#103—51no—
238C2×#103—51no—
239C2×#103—51no—
240C2×#103—51no—
241C2×C22⋊C8—51no—
242C2×C22⋊C8—51no—
243C2×C4×C8—51no—
244C2×C4×C8—51no—
245#391—51no—
246#389C2×D511yescharacteristic
247#387—101no—
248#385—101no—
249#380—51no—
250C4×C4⋊C4—51no—
251C4×C4⋊C4—51no—
252C4×C4⋊C4—51no—
253C4×C4⋊C4—51no—
254C4×C4⋊C4—101no—
255C4×C4⋊C4—101no—
256C4×C4⋊C4—101no—
257C4×C4⋊C4C2×D511yescharacteristic
258C4×C22⋊C4—101no—
259C2×#95—101no—
260#340—51no—
261#340—51no—
262#340—51no—
263#340—51no—
264#340—51no—
265#340C2×D511yescharacteristic
266#340C2×D511yescharacteristic
267#340C2×D511yescharacteristic
268#336—51no—
269#336C2×D511yescharacteristic
270C23×C5C22×D411yescharacteristic
271C22×D5—21no—
272C22×D5—21no—
273C22×D5—21no—
274C22×D5—21no—
275C22×D5C4×D412yes—
276C22×D5C2×SD1612yes—
277C22×D5#13512yes—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—22no—
281C2×C4×C5—22no—
282C2×C4×C5—21no—
283C2×C4×C5—22no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—41no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5C2×SD1612yes—
296C2×C4×C5C23×C411yescharacteristic
297C2×C4×C5C2×#4111yescharacteristic
298C2×C4×C5C2×#4111yescharacteristic
299C2×C4×C5C2×#4111yescharacteristic
300C2×C4×C5C2×#4111yescharacteristic
301C2×C4×C5C2×#4111yescharacteristic
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—22no—
307C2×Dic5—22no—
308C2×Dic5—22no—
309C2×Dic5—41no—
310C2×Dic5—41no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313C2×Dic5—41no—
314C2×Dic5—41no—
315C2×Dic5—41no—
316C2×Dic5—41no—
317C2×Dic5—41no—
318C2×Dic5C4×D412yes—
319C2×Dic5#12312yes—
320C2×Dic5#12312yes—
321C2×Dic5C2×SD1612yes—
322C2×Dic5#13712yes—
323C4×D5—22no—
324C4×D5—22no—
325C4×D5—22no—
326C4×D5—22no—
327C4×D5—28no—
328C4×D5—44no—
329C4×D5—48no—
330C4×D5—48no—
331Dic10—22no—
332Dic10—22no—
333Dic10—41no—
334Dic10—41no—
335C5×C8—22no—
336C5×C8—41no—
337#168—22no—
338#168—41no—
339C22×Q8—51no—
340C23×C4—51no—
341C23×C4—51no—
342C23×C4—51no—
343C23×C4—101no—
344C23×C4—101no—
345C22×C8—51no—
346C22×C8—51no—
347C22×C8C22×D511yescharacteristic
348C22×C8C22×D511yescharacteristic
349C22⋊Q8—54no—
350C22⋊Q8—102no—
351C4×Q8—102no—
352C4×Q8—102no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—51no—
355C2×C4⋊C4—51no—
356C2×C4⋊C4—54no—
357C2×C4⋊C4—51no—
358C2×C4⋊C4—102no—
359C2×C4⋊C4—102no—
360C2×C4⋊C4—101no—
361C2×C4⋊C4—101no—
362C2×C4⋊C4—101no—
363C2×C4⋊C4—102no—
364C2×C4⋊C4—101no—
365C2×C4⋊C4C22×D511yescharacteristic
366C2×C4⋊C4C22×D511yescharacteristic
367C2×C4⋊C4C22×D511yescharacteristic
368C2×C4⋊C4C22×D511yescharacteristic
369C2×C22⋊C4—101no—
370C2×C22⋊C4—101no—
371C2×C42—21no—
372C2×C42—51no—
373C2×C42—51no—
374C2×C42—51no—
375C2×C42—102no—
376C2×C42—102no—
377C2×C42—101no—
378C2×C42—101no—
379C2×C42—101no—
380C2×C42—101no—
381C2×C42—101no—
382C2×C42—204no—
383C2×C42C22×D511yescharacteristic
384#106—54no—
385#106—102no—
386#106—102no—
387#106C4×D514yescomplemented
388#103—54no—
389#103—54no—
390#103—102no—
391#103—102no—
392C22⋊C8—54no—
393C22⋊C8—102no—
394C4×C8—102no—
395C4×C8—102no—
396#95—21no—
397#95—21no—
398#95—101no—
399#95—101no—
400#95—101no—
401#95—101no—
402#95—101no—
403#95—101no—
404#95—101no—
405C22×C5C2×C4×D411yescharacteristic
406C22×C5C2×#12311yescharacteristic
407C22×C5#52511yescharacteristic
408C22×C5C22×SD1611yescharacteristic
409C22×C5C2×#13511yescharacteristic
410C22×C5C2×#13711yescharacteristic
411C22×C5#57511yescharacteristic
412C2×D5—22no—
413C2×D5—22no—
414C2×D5—22no—
415C2×D5—22no—
416C2×D5—22no—
417C2×D5—22no—
418C2×D5C4×SD1614yes—
419C4×C5—22no—
420C4×C5—41no—
421C4×C5—42no—
422C4×C5—42no—
423C4×C5—42no—
424C4×C5—81no—
425C4×C5C4×#4111yescharacteristic
426C4×C5C4×#4111yescharacteristic
427C4×C5#52911yescharacteristic
428C4×C5#52911yescharacteristic
429Dic5—22no—
430Dic5—22no—
431Dic5—42no—
432Dic5—42no—
433Dic5—42no—
434Dic5—81no—
435Dic5#48314yescomplemented
436C24—51no—
437C2×Q8—52no—
438C2×Q8—101no—
439C2×Q8—101no—
440C2×Q8—101no—
441C2×Q8—101no—
442C2×Q8—101no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—51no—
448C22×C4—51no—
449C22×C4—51no—
450C22×C4—52no—
451C22×C4—52no—
452C22×C4—54no—
453C22×C4—102no—
454C22×C4—102no—
455C22×C4—102no—
456C22×C4—104no—
457C22×C4—102no—
458C22×C4—104no—
459C22×C4—101no—
460C22×C4—101no—
461C22×C4—101no—
462C22×C4—101no—
463C22×C4—101no—
464C22×C4—101no—
465C22×C4—101no—
466C22×C4—101no—
467C22×C4—201no—
468C22×C4—202no—
469C22×C4—202no—
470C22×C4—202no—
471C22×C4—202no—
472C22×C4D4×D511yescharacteristic
473C22×C4D4×D511yescharacteristic
474C22×C4C23×D511yescharacteristic
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—52no—
481C2×C8—101no—
482C2×C8—101no—
483C2×C8—101no—
484C2×C8—101no—
485C2×C8—101no—
486C2×C8C2×C4×D512yes—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C4⋊C4—52no—
494C4⋊C4—52no—
495C4⋊C4—104no—
496C4⋊C4—104no—
497C4⋊C4—104no—
498C4⋊C4—101no—
499C4⋊C4—101no—
500C4⋊C4—101no—
501C4⋊C4—101no—
502C4⋊C4—202no—
503C4⋊C4C2×C4×D512yes—
504C4⋊C4C2×C4×D512yes—
505C4⋊C4#71312yes—
506C22⋊C4—104no—
507C22⋊C4—202no—
508C42—21no—
509C42—21no—
510C42—42no—
511C42—52no—
512C42—52no—
513C42—102no—
514C42—102no—
515C42—202no—
516C42—202no—
517C42—202no—
518C42—202no—
519C42—202no—
520C2×C5C4×#12311yescharacteristic
521C2×C5C2×C4×SD1611yescharacteristic
522C2×C5C4×#13711yescharacteristic
523C2×C5C2×#48311yescharacteristic
524C2×C5#309111yescharacteristic
525C2×C5#310111yescharacteristic
526C2×C5#310811yescharacteristic
527D5—24no—
528C23—52no—
529C23—52no—
530C23—52no—
531C23—101no—
532C23—101no—
533C23—101no—
534C23—101no—
535C23C2×D4×D511yescharacteristic
536Q8—102no—
537Q8—102no—
538Q8—201no—
539Q8—201no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—52no—
558C2×C4—52no—
559C2×C4—52no—
560C2×C4—52no—
561C2×C4—52no—
562C2×C4—108no—
563C2×C4—101no—
564C2×C4—101no—
565C2×C4—101no—
566C2×C4—101no—
567C2×C4—102no—
568C2×C4—102no—
569C2×C4—102no—
570C2×C4—102no—
571C2×C4—102no—
572C2×C4—102no—
573C2×C4—102no—
574C2×C4—204no—
575C2×C4—208no—
576C2×C4—208no—
577C2×C4—201no—
578C2×C4—201no—
579C2×C4—201no—
580C2×C4—201no—
581C2×C4—201no—
582C2×C4—201no—
583C2×C4—201no—
584C2×C4—201no—
585C2×C4—201no—
586C2×C4D5×SD1612yes—
587C2×C4C22×C4×D511yescharacteristic
588C2×C4C2×#71311yescharacteristic
589C2×C4D5×#4111yescharacteristic
590C2×C4D5×#4111yescharacteristic
591C2×C4D5×#4111yescharacteristic
592C2×C4D5×#4111yescharacteristic
593C8—22no—
594C8—41no—
595C8—102no—
596C8—201no—
597C5C4×#48311yescharacteristic, complemented, Sylow
598C22—54no—
599C22—102no—
600C22—102no—
601C22—102no—
602C22—102no—
603C22—102no—
604C22—102no—
605C22C4×D4×D511yescharacteristic
606C22#6596111yescharacteristic
607C22D5×#12311yescharacteristic
608C22C2×D5×SD1611yescharacteristic
609C22D5×#13511yescharacteristic
610C22#6610711yescharacteristic
611C22D5×#13711yescharacteristic
612C4—22no—
613C4—42no—
614C4—42no—
615C4—41no—
616C4—42no—
617C4—54no—
618C4—81no—
619C4—102no—
620C4—102no—
621C4—202no—
622C4—202no—
623C4—202no—
624C4—401no—
625C4#6585611yescharacteristic
626C4C4×#71311yescharacteristic
627C4#6602511yescharacteristic
628C4#6604011yescharacteristic
629C2—104no—
630C2#1060667111yescharacteristic
631C2C4×D5×SD1611yescharacteristic
632C2#1061150511yescharacteristic
633C2#1061277511yescharacteristic
634C2#1061293611yescharacteristic
635C2#1061310211yescharacteristic
636C2D5×#48311yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1920C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1920D5
hypocenterC5C4×#483
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
4. C5×#1920C2semidirect
5. Dic5×#106C2semidirect
6. #10600395C2semidirect
7. #10600257C2semidirect
11. #10599577C2semidirect
12. #10599574C2semidirect
13. #10599574C2semidirect
14. #10599420C2semidirect
45. #65151C4semidirect
106. C5×#106C2×C4semidirect
120. #3948C2×C4semidirect
124. #3942C2×C4semidirect
126. #3940C2×C4semidirect
133. #1920D5semidirect
387. #106C4×D5semidirect
435. Dic5#483semidirect
597. C5C4×#483semidirect

Maximal subgroups

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

subgroupindex
C2×#651512
#106076962
C4×D5×C4⋊C42
C5×#19202
Dic5×#1062
#106003952
#106002572
#105996712
#105996682
#105996642
#105995772
#105995742
#105994202
#105993922
C4×#4835