Finite Group Databasebeta

← #12109476

Subgroups — #12109476

Order 1280.

750 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#4038C211yesmaximal, characteristic
2C5×#1917C211yesmaximal, characteristic, complemented
3#10601243C211yesmaximal, characteristic
4#10601238C211yesmaximal, characteristic, complemented
5#10600628C211yesmaximal, characteristic
6#10600602C211yesmaximal, characteristic, complemented
7#10600276C211yesmaximal, characteristic, complemented
8#10599455C211yesmaximal, characteristic
9#10599455C211yesmaximal, characteristic
10#10599451C211yesmaximal, characteristic
11#10599409C211yesmaximal, characteristic
12#10599406C211yesmaximal, characteristic, complemented
13#10599405C211yesmaximal, characteristic, complemented
14#10599398C211yesmaximal, characteristic, complemented
15#10599396C211yesmaximal, characteristic, complemented
16C2×#4038C411yescharacteristic
17C2×#4038C411yescharacteristic
18C2×C42×D5C2211yescharacteristic
19C2×C5×C4⋊C8C2211yescharacteristic
20C2×C5×#97C2211yescharacteristic
21C4×C5×C4⋊C4C2211yescharacteristic
22C2×#3952C2211yescharacteristic
23C2×#3952C2211yescharacteristic
24C2×#3952C2211yescharacteristic
25C2×#3952C2211yescharacteristic
26C2×#3947C2211yescharacteristic
27C2×#3947C2211yescharacteristic
28C2×#3946C2211yescharacteristic
29C2×#3946C2211yescharacteristic
30C2×#3946C2211yescharacteristic
31C2×#3946C2211yescharacteristic
32C2×#3946C2211yescharacteristic
33C2×#3946C2211yescharacteristic
34C4⋊C4×Dic5C411yescharacteristic
35C4⋊C4×Dic5C411yescharacteristic
36C4×#685C2211yescharacteristic
37C4×#685C2211yescharacteristic
38C4×C4⋊Dic5C2211yescharacteristic
39C42×Dic5C2211yescharacteristic
40C42×Dic5C2211yescharacteristic
41C2×C4⋊#168C2211yescharacteristic
42C2×#3935C2211yescharacteristic
43#64955C411yescharacteristic
44#64955C411yescharacteristic
45#64937C411yescharacteristic
46#64937C411yescharacteristic
47C5×#336C2211yescharacteristic
48C5×#336C2211yescharacteristic
49C5×#336C2211yescharacteristic
50C5×#336C2211yescharacteristic
51#64770C2211yescharacteristic
52#64770C2211yescharacteristic
53#64770C2211yescharacteristic
54#64770C2211yescharacteristic
55#64744C2211yescharacteristic
56#64744C2211yescharacteristic
57#64744C2211yescharacteristic
58#64744C2211yescharacteristic
59#21926—51nomaximal, Sylow
60C22×C4×D5C2×C411yescharacteristic
61C22×C4×D5C2×C411yescharacteristic
62C22×C4×D5C2311yescharacteristic
63C22×C5×C8C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C2×C5×C4⋊C4C2×C411yescharacteristic
68C2×C5×C4⋊C4C2×C411yescharacteristic
69C2×C42×C5C2311yescharacteristic
70C2×C42×C5C2311yescharacteristic
71C2×C42×C5C2311yescharacteristic
72C2×#685C2×C411yescharacteristic
73C2×#685C2×C411yescharacteristic
74C2×#685C2×C411yescharacteristic
75C2×#685C2×C411yescharacteristic
76C2×C4⋊Dic5C2×C411yescharacteristic
77C2×C4⋊Dic5C2×C411yescharacteristic
78C2×C4×Dic5C2×C411yescharacteristic
79C2×C4×Dic5C2×C411yescharacteristic
80C2×C4×Dic5C2×C411yescharacteristic
81C2×C4×Dic5C2×C411yescharacteristic
82C2×C4×Dic5C2×C411yescharacteristic
83C2×C4×Dic5C2×C411yescharacteristic
84C2×C4×Dic5C2×C411yescharacteristic
85C2×C4×Dic5C2×C411yescharacteristic
86C2×C4×Dic5C2×C411yescharacteristic
87C2×C4×Dic5C2×C411yescharacteristic
88C2×C4×Dic5C2311yescharacteristic
89C2×C4×Dic5C2311yescharacteristic
90C2×C4×Dic5C2311yescharacteristic
91C22×#168C2311yescharacteristic
92C22×#168C2311yescharacteristic
93C22×#168C2311yescharacteristic
94C22×#168C2311yescharacteristic
95#4038—24no—
96#4038—24no—
97C42×D5—22no—
98C42×D5—22no—
99C5×C4⋊C8—41no—
100C5×#97—41no—
101C5×#95C2×C411yescharacteristic
102C5×#95C2×C411yescharacteristic
103#3963C2×C411yescharacteristic
104#3963C2×C411yescharacteristic
105#3963C2×C411yescharacteristic
106#3963C2×C411yescharacteristic
107#3963C2×C411yescharacteristic
108#3963C2×C411yescharacteristic
109#3952—41no—
110#3952—41no—
111#3952—41no—
112#3952—41no—
113#3947—41no—
114#3947—41no—
115#3946—22no—
116#3946—22no—
117#3946—22no—
118#3946—22no—
119#3946—41no—
120#3946—41no—
121C4⋊#168—41no—
122#3935—41no—
123C4×#117—51no—
124#1924—51no—
125#1924—51no—
126#1924—51no—
127#1924—51no—
128#1917—51no—
129#1917—51no—
130#1917—51no—
131#1917D511yescharacteristic, complemented
132#1842—51no—
133#1831—51no—
134#1797—51no—
135#1797—51no—
136#1767—51no—
137#1767—51no—
138C23×D5C22×C411yescharacteristic
139C22×C4×C5C22×C411yescharacteristic
140C22×C4×C5C22×C411yescharacteristic
141C22×C4×C5C22×C411yescharacteristic
142C22×C4×C5C22×C411yescharacteristic
143C22×C4×C5C22×C411yescharacteristic
144C22×C4×C5C22×C411yescharacteristic
145C22×C4×C5C2411yescharacteristic
146C22×Dic5C22×C411yescharacteristic
147C22×Dic5C22×C411yescharacteristic
148C22×Dic5C22×C411yescharacteristic
149C22×Dic5C22×C411yescharacteristic
150C22×Dic5C22×C411yescharacteristic
151C22×Dic5C22×C411yescharacteristic
152C22×Dic5C22×C411yescharacteristic
153C2×C4×D5—22no—
154C2×C4×D5—22no—
155C2×C4×D5—21no—
156C2×C4×D5—21no—
157C2×C4×D5—21no—
158C2×C4×D5—21no—
159C2×C4×D5—21no—
160C2×C4×D5—21no—
161C2×C4×D5—22no—
162C2×C4×D5—41no—
163C2×C4×D5—41no—
164C2×C4×D5M1614yes—
165C2×C5×C8—21no—
166C2×C5×C8—21no—
167C2×C5×C8—21no—
168C2×C5×C8—21no—
169C2×C5×C8—21no—
170C2×C5×C8—21no—
171C2×C5×C8—21no—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C5×C4⋊C4—22no—
178C5×C4⋊C4—22no—
179C42×C5—21no—
180C42×C5—21no—
181C42×C5—21no—
182C42×C5—21no—
183C42×C5—21no—
184C42×C5—21no—
185#685—22no—
186#685—22no—
187#685—22no—
188#685—22no—
189C4⋊Dic5—22no—
190C4⋊Dic5—22no—
191C4×Dic5—21no—
192C4×Dic5—21no—
193C4×Dic5—21no—
194C4×Dic5—21no—
195C4×Dic5—22no—
196C4×Dic5—22no—
197C4×Dic5—22no—
198C4×Dic5—22no—
199C4×Dic5—22no—
200C4×Dic5—41no—
201C4×Dic5—41no—
202C4×Dic5—41no—
203C4×Dic5—41no—
204C4×Dic5M1614yes—
205C4×Dic5#4112yes—
206C4×Dic5#4112yes—
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×#168—21no—
218C2×#168—21no—
219C2×#117—51no—
220C2×#117—51no—
221C22×C42—51no—
222C2×C4⋊C8—51no—
223C2×C4⋊C8—51no—
224C2×C4⋊C8—51no—
225C2×C4⋊C8—51no—
226C2×C4⋊C8—51no—
227C2×C4⋊C8—51no—
228C2×C4⋊C8—51no—
229C2×C4⋊C8C2×D511yescharacteristic
230C2×C22⋊C8—51no—
231C2×C22⋊C8—51no—
232C2×C22⋊C8—51no—
233C2×C22⋊C8—51no—
234C2×#97—51no—
235C2×#97—51no—
236C2×#97—51no—
237C2×#97C2×D511yescharacteristic
238C4×C4⋊C4—51no—
239C4×C4⋊C4—51no—
240C4×C4⋊C4—51no—
241C4×C4⋊C4C2×D511yescharacteristic
242C4×C22⋊C4—51no—
243C4×C22⋊C4—51no—
244C4×C22⋊C4—51no—
245C4×C22⋊C4—51no—
246#376—51no—
247#376—51no—
248C43—51no—
249C43—51no—
250#336—51no—
251#336—51no—
252#336—51no—
253#336—51no—
254#336—51no—
255#336—51no—
256#336—51no—
257#336—51no—
258#336C2×D511yescharacteristic
259#336C2×D511yescharacteristic
260#336C2×D511yescharacteristic
261#336C2×D511yescharacteristic
262C23×C5C23×C411yescharacteristic
263C22×D5—21no—
264C22×D5—21no—
265C22×D5—21no—
266C22×D5—21no—
267C22×D5—21no—
268C22×D5—21no—
269C22×D5C2×M1612yes—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
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×C5C2×M1612yes—
287C2×C4×C5C2×M1612yes—
288C2×C4×C5C2×#4111yescharacteristic
289C2×C4×C5C2×#4111yescharacteristic
290C2×C4×C5H(5,𝔽2)11yescharacteristic
291C2×C4×C5H(5,𝔽2)11yescharacteristic
292C2×C4×C52−1+411yescharacteristic
293C2×C4×C52−1+411yescharacteristic
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—21no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—21no—
307C2×Dic5—21no—
308C2×Dic5—21no—
309C2×Dic5—21no—
310C2×Dic5#11712yes—
311C2×Dic5#11712yes—
312C2×Dic5C2×M1612yes—
313C2×Dic5C2×M1612yes—
314C2×Dic5C2×M1612yes—
315C4×D5—28no—
316C4×D5—44no—
317C4×D5—41no—
318C4×D5—41no—
319C4×D5—41no—
320C4×D5—41no—
321C5×C8—41no—
322C5×C8—41no—
323C5×C8—41no—
324C5×C8—41no—
325#168—41no—
326#168—41no—
327#168—41no—
328#168—41no—
329C23×C4—51no—
330C23×C4—51no—
331C23×C4—51no—
332C22×C8—51no—
333C22×C8—51no—
334C22×C8—51no—
335C22×C8—51no—
336C22×C8C22×D511yescharacteristic
337C22×C8C22×D511yescharacteristic
338C22×C8C22×D511yescharacteristic
339C22×C8C22×D511yescharacteristic
340#117—104no—
341#117—104no—
342C2×C4⋊C4—51no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4C4×D511yescharacteristic
345C2×C4⋊C4C4×D511yescharacteristic
346C2×C22⋊C4—51no—
347C2×C22⋊C4—51no—
348C2×C22⋊C4—51no—
349C2×C22⋊C4—51no—
350C2×C42—51no—
351C2×C42—51no—
352C2×C42—51no—
353C2×C42—51no—
354C2×C42—51no—
355C2×C42—51no—
356C2×C42—51no—
357C2×C42—51no—
358C2×C42—51no—
359C2×C42—51no—
360C2×C42—51no—
361C2×C42—51no—
362C2×C42—51no—
363C2×C42—102no—
364C2×C42—102no—
365C2×C42C22×D511yescharacteristic
366C2×C42C22×D511yescharacteristic
367C2×C42C22×D511yescharacteristic
368C4⋊C8—41no—
369C4⋊C8—102no—
370C4⋊C8—102no—
371C4⋊C8—102no—
372C4⋊C8—102no—
373C4⋊C8—201no—
374C4⋊C8—201no—
375C4⋊C8—201no—
376C22⋊C8—201no—
377C22⋊C8—201no—
378C22⋊C8—201no—
379C22⋊C8—201no—
380#97—41no—
381#97—201no—
382#97—201no—
383#97—201no—
384#95—51no—
385#95—51no—
386#95—51no—
387#95—51no—
388#95—51no—
389#95—51no—
390#95C4×D511yescharacteristic
391#95C4×D511yescharacteristic
392C22×C5C2×#11711yescharacteristic
393C22×C5#52011yescharacteristic
394C22×C5#52011yescharacteristic
395C22×C5C22×M1611yescharacteristic
396C22×C5C22×M1611yescharacteristic
397C22×C5#56811yescharacteristic
398C22×C5#56811yescharacteristic
399C2×D5—22no—
400C2×D5—22no—
401C2×D5—22no—
402C2×D5—41no—
403C2×D5—41no—
404C2×D5—41no—
405C2×D5—41no—
406C4×C5—22no—
407C4×C5—22no—
408C4×C5—41no—
409C4×C5—41no—
410C4×C5—41no—
411C4×C5—41no—
412C4×C5#54011yescharacteristic
413C4×C5#54111yescharacteristic
414C4×C5#54211yescharacteristic
415C4×C5#54211yescharacteristic
416Dic5—22no—
417Dic5—22no—
418Dic5—41no—
419Dic5—41no—
420Dic5—41no—
421Dic5—41no—
422Dic5#43214yes—
423C24—51no—
424C22×C4—51no—
425C22×C4—51no—
426C22×C4—51no—
427C22×C4—54no—
428C22×C4—51no—
429C22×C4—51no—
430C22×C4—51no—
431C22×C4—51no—
432C22×C4—102no—
433C22×C4—102no—
434C22×C4—102no—
435C22×C4—101no—
436C22×C4—101no—
437C22×C4—101no—
438C22×C4—101no—
439C22×C4—101no—
440C22×C4—101no—
441C22×C4—201no—
442C22×C4—201no—
443C22×C4C2×C4×D511yescharacteristic
444C22×C4C2×C4×D511yescharacteristic
445C22×C4C2×C4×D511yescharacteristic
446C22×C4C2×C4×D511yescharacteristic
447C22×C4C2×C4×D511yescharacteristic
448C22×C4C2×C4×D511yescharacteristic
449C22×C4C23×D511yescharacteristic
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—101no—
463C2×C8—101no—
464C2×C8—101no—
465C2×C8—101no—
466C2×C8—101no—
467C2×C8—101no—
468C2×C8—101no—
469C2×C8—101no—
470C2×C8—101no—
471C2×C8—101no—
472C2×C8—101no—
473C2×C8—101no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—102no—
477C4⋊C4—102no—
478C22⋊C4—102no—
479C22⋊C4—102no—
480C22⋊C4—102no—
481C22⋊C4—102no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—52no—
489C42—52no—
490C42—54no—
491C42—102no—
492C42—102no—
493C42—102no—
494C42—102no—
495C42—102no—
496C42—101no—
497C42—101no—
498C42—101no—
499C42—101no—
500C42—201no—
501C42—201no—
502C42—201no—
503C42—201no—
504C2×C5#231411yescharacteristic
505C2×C5C2×#43211yescharacteristic
506C2×C5#292111yescharacteristic
507C2×C5#298911yescharacteristic
508C2×C5#298911yescharacteristic
509C2×C5#298911yescharacteristic
510C2×C5#298911yescharacteristic
511D5—42no—
512C23—52no—
513C23—101no—
514C23—101no—
515C23—101no—
516C23—101no—
517C23—101no—
518C23—101no—
519C23C22×C4×D511yescharacteristic
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—52no—
537C2×C4—52no—
538C2×C4—52no—
539C2×C4—52no—
540C2×C4—52no—
541C2×C4—108no—
542C2×C4—101no—
543C2×C4—101no—
544C2×C4—101no—
545C2×C4—101no—
546C2×C4—101no—
547C2×C4—101no—
548C2×C4—101no—
549C2×C4—101no—
550C2×C4—101no—
551C2×C4—101no—
552C2×C4—101no—
553C2×C4—101no—
554C2×C4—101no—
555C2×C4—101no—
556C2×C4—101no—
557C2×C4—101no—
558C2×C4—204no—
559C2×C4—201no—
560C2×C4—201no—
561C2×C4—201no—
562C2×C4—201no—
563C2×C4D5×M1612yes—
564C2×C4D5×M1612yes—
565C2×C4#414411yescharacteristic
566C2×C4#414711yescharacteristic
567C2×C4D5×#4111yescharacteristic
568C2×C4D5×#4111yescharacteristic
569C2×C4#414911yescharacteristic
570C2×C4#415011yescharacteristic
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C8—201no—
576C8—201no—
577C8—201no—
578C8—201no—
579C5#2192611yescharacteristic, complemented, Sylow
580C22—102no—
581C22—102no—
582C22—102no—
583C22—201no—
584C22—201no—
585C22—201no—
586C22—201no—
587C22D5×#11711yescharacteristic
588C22#6588011yescharacteristic
589C22#6590811yescharacteristic
590C22C2×D5×M1611yescharacteristic
591C22C2×D5×M1611yescharacteristic
592C22#6608411yescharacteristic
593C22#6608411yescharacteristic
594C4—22no—
595C4—22no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—54no—
601C4—102no—
602C4—102no—
603C4—201no—
604C4—201no—
605C4—201no—
606C4—201no—
607C4#6597411yescharacteristic
608C4#6599711yescharacteristic
609C4#6603011yescharacteristic
610C4#6604411yescharacteristic
611C2—202no—
612C2#1060667511yescharacteristic
613C2D5×#43211yescharacteristic
614C2#1061110211yescharacteristic
615C2#1061119211yescharacteristic
616C2#1061125411yescharacteristic
617C2#1061167511yescharacteristic
618C2#1061167511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC5×#1917C2
prime radicalC23×D5C22×C4
cosocleC22×C4×C5C24
hypercenter#1917D5
hypocenterC5#21926
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
2. C5×#1917C2semidirect
4. #10601238C2semidirect
6. #10600602C2semidirect
7. #10600276C2semidirect
12. #10599406C2semidirect
13. #10599405C2semidirect
14. #10599398C2semidirect
15. #10599396C2semidirect
131. #1917D5semidirect
579. C5#21926semidirect

Maximal subgroups

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

subgroupindex
C4×#40382
C5×#19172
#106012432
#106012382
#106006282
#106006022
#106002762
#105994552
#105994512
#105994092
#105994062
#105994052
#105993982
#105993962
#219265