Finite Group Databasebeta

← #12109686

Subgroups — #12109686

Order 1280.

862 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊C8C211yesmaximal, characteristic
2#10605878C211yesmaximal, characteristic
3#10605484C211yesmaximal, characteristic
4C5×#1949C211yesmaximal, characteristic, complemented
5#10601423C211yesmaximal, characteristic
6#10601408C211yesmaximal, characteristic, complemented
7#10601370C211yesmaximal, characteristic
8#10601356C211yesmaximal, characteristic, complemented
9#10601248C211yesmaximal, characteristic, complemented
10#10600333C211yesmaximal, characteristic, complemented
11#10600261C211yesmaximal, characteristic, complemented
12#10599662C211yesmaximal, characteristic
13#10599661C211yesmaximal, characteristic
14#10599589C211yesmaximal, characteristic, complemented
15#10599588C211yesmaximal, characteristic, complemented
16C22×C8×D5C2211yescharacteristic
17C22×C8×D5C2211yescharacteristic
18C2×#4018—21no—
19C2×C42×D5C2211yescharacteristic
20C2×C5×#107C2211yescharacteristic
21C2×C5×#106C2211yescharacteristic
22C2×C5×C4⋊C8C2211yescharacteristic
23C5×#382C2211yescharacteristic
24C4×C5×C4⋊C4C2211yescharacteristic
25C2×#3950C2211yescharacteristic
26C2×#3949C2211yescharacteristic
27C2×#3946C2211yescharacteristic
28C2×#3946C2211yescharacteristic
29#65276C2211yescharacteristic
30#65276C2211yescharacteristic
31#65276C2211yescharacteristic
32#65276C2211yescharacteristic
33#65265C2211yescharacteristic
34#65265C2211yescharacteristic
35C4⋊C4×Dic5C2211yescharacteristic
36C4⋊C4×Dic5C2211yescharacteristic
37C2×#3940C2211yescharacteristic
38C2×#3940C2211yescharacteristic
39C2×#3939C2211yescharacteristic
40C2×#3939C2211yescharacteristic
41#65225C2211yescharacteristic
42C4×C4⋊Dic5C2211yescharacteristic
43C4×#683—21no—
44C2×C4⋊#168C2211yescharacteristic
45D5×C4⋊C8C418yescomplemented
46#64956—21no—
47#64955—21no—
48#64953—21no—
49#64940—21no—
50#64939—21no—
51#64937—21no—
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54#64771C2211yescharacteristic
55#64771C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#21962—51nomaximal, Sylow
61C22×C4×D5D411yescharacteristic
62C22×C4×D5D411yescharacteristic
63C22×C4×D5C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C2×C5×C4⋊C4C2311yescharacteristic
67C2×C5×C4⋊C4C2311yescharacteristic
68C2×C5×C4⋊C4C2311yescharacteristic
69C2×C5×C4⋊C4C2311yescharacteristic
70C2×C42×C5—21no—
71C2×C42×C5C2311yescharacteristic
72C2×#685—21no—
73C2×#685—21no—
74C2×#685—21no—
75C2×#685—21no—
76C2×C4⋊Dic5C2311yescharacteristic
77C2×C4⋊Dic5C2311yescharacteristic
78C2×C4⋊Dic5C2311yescharacteristic
79C2×C4⋊Dic5C2311yescharacteristic
80C2×#683—21no—
81C2×#683—21no—
82C2×#683—21no—
83C2×#683—21no—
84C2×C4×Dic5—21no—
85C2×C4×Dic5—21no—
86C2×C4×Dic5—21no—
87C2×C4×Dic5D411yescharacteristic
88C2×C4×Dic5D411yescharacteristic
89C2×C4×Dic5C2311yescharacteristic
90C22×#168C2311yescharacteristic
91C22×#168C2311yescharacteristic
92C2×C8×D5—41no—
93C2×C8×D5—41no—
94C2×C8×D5—41no—
95C2×C8×D5—41no—
96C2×C8×D5C2×C414yes—
97C2×C8×D5C2×C414yes—
98#4018—44no—
99C42×D5C2×C414yes—
100C42×D5Q814yes—
101C5×#107—41no—
102C5×#106—41no—
103C5×C4⋊C8C2×C414yes—
104C5×#95—21no—
105C5×#95—21no—
106C5×#95—21no—
107#3963—21no—
108#3963—21no—
109#3963—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114#3963—21no—
115#3963—21no—
116#3950—41no—
117#3949—41no—
118#3946C2×C414yes—
119#3946C2×C414yes—
120#3940—41no—
121#3940—41no—
122#3939—41no—
123#3939—41no—
124C4⋊#168C2×C414yes—
125C22×C4⋊C8—51no—
126#2285—51no—
127#2283—51no—
128#1949—51no—
129#1949—51no—
130#1949—51no—
131#1949D511yescharacteristic, complemented
132#1948—51no—
133#1948—51no—
134#1947—51no—
135#1947—51no—
136#1808—51no—
137#1808—51no—
138#1807—51no—
139#1807—51no—
140C23×D5C2×D411yescharacteristic
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5C2×D411yescharacteristic
146C22×C4×C5C2×D411yescharacteristic
147C22×C4×C5C2411yescharacteristic
148C22×Dic5—21no—
149C22×Dic5—21no—
150C22×Dic5—21no—
151C22×Dic5—21no—
152C22×Dic5C2×D411yescharacteristic
153C22×Dic5C2×D411yescharacteristic
154C22×Dic5C2×D411yescharacteristic
155C2×C4×D5—22no—
156C2×C4×D5—22no—
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×D5C4⋊C414yes—
164C2×C4×D5C4⋊C414yes—
165C2×C4×D5C22×C412yes—
166C2×C4×D5C2×Q812yes—
167C2×C5×C8—21no—
168C2×C5×C8—21no—
169C2×C5×C8—21no—
170C2×C5×C8—21no—
171C2×C5×C8C22×C412yes—
172C2×C5×C8C22×C412yes—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C42×C5—42no—
182C42×C5C22×C412yes—
183C42×C5C2×Q812yes—
184#685—42no—
185#685—42no—
186#685—42no—
187#685—42no—
188C4⋊Dic5—21no—
189C4⋊Dic5—21no—
190C4⋊Dic5—21no—
191C4⋊Dic5—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—21no—
195C4⋊Dic5—21no—
196#683—42no—
197#683—42no—
198#683—42no—
199#683—42no—
200C4×Dic5—42no—
201C4×Dic5—42no—
202C4×Dic5—42no—
203C4×Dic5C4⋊C414yes—
204C4×Dic5C4⋊C414yes—
205C4×Dic5C22×C412yes—
206C4×Dic5C2×Q812yes—
207C2×#168—21no—
208C2×#168—21no—
209C2×#168—21no—
210C2×#168—21no—
211C2×#168C22×C412yes—
212C2×#168C22×C412yes—
213C8×D5—44no—
214C8×D5—44no—
215C23×C8—51no—
216C23×C8—51no—
217C2×#117—101no—
218C22×C42—51no—
219C2×#107—51no—
220C2×#107—51no—
221C2×#107—51no—
222C2×#107C2×D511yescharacteristic
223C2×#106—51no—
224C2×#106—51no—
225C2×#106—51no—
226C2×#106C2×D511yescharacteristic
227C2×C4⋊C8—51no—
228C2×C4⋊C8—51no—
229C2×C4⋊C8—51no—
230C2×C4⋊C8—58no—
231C2×C4⋊C8C2×D511yescharacteristic
232#384—51no—
233#384—51no—
234#383—101no—
235#382—51no—
236#382—101no—
237#382C2×D511yescharacteristic
238#381—101no—
239#380—51no—
240#380—51no—
241#380—51no—
242#380—51no—
243#380—101no—
244C4×C4⋊C4—51no—
245C4×C4⋊C4—51no—
246C4×C4⋊C4—51no—
247C4×C4⋊C4—101no—
248C4×C4⋊C4C2×D511yescharacteristic
249C4×C22⋊C4—101no—
250#376—101no—
251#340—51no—
252#340—51no—
253#340—51no—
254#340—51no—
255#340—51no—
256#340—51no—
257#340C2×D511yescharacteristic
258#340C2×D511yescharacteristic
259C23×C5C22×D411yescharacteristic
260C22×D5—21no—
261C22×D5—21no—
262C22×D5—21no—
263C22×D5—21no—
264C22×D5C2×C4⋊C412yes—
265C22×D5AGL(1,ℤ/8)12yes—
266C22×D5#13712yes—
267C2×C4×C5—21no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—41no—
272C2×C4×C5—41no—
273C2×C4×C5—41no—
274C2×C4×C5—41no—
275C2×C4×C5—41no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5—41no—
279C2×C4×C5—41no—
280C2×C4×C5—41no—
281C2×C4×C5—41no—
282C2×C4×C5—41no—
283C2×C4×C5C2×C4⋊C412yes—
284C2×C4×C5C2×C4⋊C412yes—
285C2×C4×C5C23×C411yescharacteristic
286C2×C4×C5C22×Q811yescharacteristic
287C2×C4×C5H(5,𝔽2)11yescharacteristic
288C2×C4×C5H(5,𝔽2)11yescharacteristic
289C2×C4×C52−1+411yescharacteristic
290C2×C4×C52−1+411yescharacteristic
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—41no—
296C2×Dic5—41no—
297C2×Dic5—41no—
298C2×Dic5—41no—
299C2×Dic5—41no—
300C2×Dic5—41no—
301C2×Dic5—41no—
302C2×Dic5—41no—
303C2×Dic5—41no—
304C2×Dic5—41no—
305C2×Dic5—41no—
306C2×Dic5—41no—
307C2×Dic5C2×C4⋊C412yes—
308C2×Dic5C2×C4⋊C412yes—
309C2×Dic5C2×C4⋊C412yes—
310C2×Dic5#13512yes—
311C2×Dic5#13512yes—
312C4×D5—28no—
313C4×D5—22no—
314C4×D5—22no—
315C4×D5—22no—
316C4×D5—22no—
317C4×D5—28no—
318C5×C8—22no—
319C5×C8—22no—
320#168—22no—
321#168—22no—
322C23×C4—51no—
323C23×C4—51no—
324C23×C4—51no—
325C22×C8—51no—
326C22×C8—51no—
327C22×C8—54no—
328C22×C8—54no—
329C22×C8—201no—
330C22×C8—201no—
331C22×C8—201no—
332C22×C8—201no—
333C22×C8C22×D511yescharacteristic
334C22×C8C22×D511yescharacteristic
335#117—204no—
336C2×C4⋊C4—51no—
337C2×C4⋊C4—51no—
338C2×C4⋊C4—51no—
339C2×C4⋊C4—51no—
340C2×C4⋊C4—101no—
341C2×C4⋊C4—101no—
342C2×C4⋊C4—101no—
343C2×C4⋊C4—101no—
344C2×C4⋊C4C22×D511yescharacteristic
345C2×C4⋊C4C22×D511yescharacteristic
346C2×C4⋊C4C22×D511yescharacteristic
347C2×C4⋊C4C22×D511yescharacteristic
348C2×C22⋊C4—101no—
349C2×C22⋊C4—101no—
350C2×C22⋊C4—101no—
351C2×C22⋊C4—101no—
352C2×C42—21no—
353C2×C42—51no—
354C2×C42—51no—
355C2×C42—51no—
356C2×C42—54no—
357C2×C42—54no—
358C2×C42—101no—
359C2×C42—101no—
360C2×C42—101no—
361C2×C42C22×D511yescharacteristic
362#107—41no—
363#107—201no—
364#107—201no—
365#107—201no—
366#106—41no—
367#106—201no—
368#106—201no—
369#106—201no—
370C4⋊C8—54no—
371C4⋊C8—54no—
372C4⋊C8—54no—
373C4⋊C8C4×D514yes—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—101no—
378#95—101no—
379#95—101no—
380#95—101no—
381#95—101no—
382#95—101no—
383#95—101no—
384#95—101no—
385#95—101no—
386C22×C5C22×C4⋊C411yescharacteristic
387C22×C5#53711yescharacteristic
388C22×C5#53711yescharacteristic
389C22×C5C2×#13511yescharacteristic
390C22×C5C2×#13511yescharacteristic
391C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
392C22×C5C2×#13711yescharacteristic
393C2×D5—22no—
394C2×D5—22no—
395C2×D5—22no—
396C2×D5—22no—
397C2×D5—22no—
398C2×D5—22no—
399C2×D5#42814yes—
400C4×C5—22no—
401C4×C5—22no—
402C4×C5—81no—
403C4×C5—81no—
404C4×C5—81no—
405C4×C5—81no—
406C4×C5#51811yescharacteristic
407C4×C5#51911yescharacteristic
408C4×C5#54411yescharacteristic
409C4×C5#54411yescharacteristic
410Dic5—22no—
411Dic5—22no—
412Dic5—81no—
413Dic5—81no—
414Dic5—81no—
415Dic5—81no—
416Dic5#42714yes—
417C24—51no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—51no—
423C22×C4—51no—
424C22×C4—51no—
425C22×C4—52no—
426C22×C4—52no—
427C22×C4—54no—
428C22×C4—54no—
429C22×C4—102no—
430C22×C4—102no—
431C22×C4—102no—
432C22×C4—102no—
433C22×C4—101no—
434C22×C4—101no—
435C22×C4—101no—
436C22×C4—101no—
437C22×C4—101no—
438C22×C4—101no—
439C22×C4—101no—
440C22×C4—101no—
441C22×C4D4×D511yescharacteristic
442C22×C4D4×D511yescharacteristic
443C22×C4C23×D511yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—52no—
449C2×C8—52no—
450C2×C8—101no—
451C2×C8—101no—
452C2×C8—101no—
453C2×C8—101no—
454C2×C8—204no—
455C2×C8—204no—
456C2×C8C2×C4×D512yes—
457C2×C8C2×C4×D512yes—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—101no—
467C4⋊C4—101no—
468C4⋊C4—101no—
469C4⋊C4—101no—
470C4⋊C4—101no—
471C4⋊C4—101no—
472C4⋊C4—101no—
473C4⋊C4—101no—
474C4⋊C4—202no—
475C4⋊C4—202no—
476C4⋊C4—202no—
477C4⋊C4—202no—
478C22⋊C4—202no—
479C22⋊C4—202no—
480C22⋊C4—202no—
481C22⋊C4—202no—
482C42—42no—
483C42—52no—
484C42—52no—
485C42—54no—
486C42—54no—
487C42—202no—
488C42—202no—
489C42—202no—
490C42C2×C4×D512yes—
491C42Q8×D512yes—
492C2×C5#231611yescharacteristic
493C2×C5C2×#42711yescharacteristic
494C2×C5C2×#42811yescharacteristic
495C2×C5#324711yescharacteristic
496C2×C5#324711yescharacteristic
497C2×C5#324811yescharacteristic
498C2×C5#324811yescharacteristic
499D5—24no—
500C23—52no—
501C23—52no—
502C23—52no—
503C23—101no—
504C23—101no—
505C23—101no—
506C23—101no—
507C23C2×D4×D511yescharacteristic
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—52no—
525C2×C4—52no—
526C2×C4—52no—
527C2×C4—52no—
528C2×C4—52no—
529C2×C4—108no—
530C2×C4—108no—
531C2×C4—101no—
532C2×C4—101no—
533C2×C4—101no—
534C2×C4—101no—
535C2×C4—102no—
536C2×C4—102no—
537C2×C4—102no—
538C2×C4—102no—
539C2×C4—201no—
540C2×C4—201no—
541C2×C4—201no—
542C2×C4—201no—
543C2×C4—201no—
544C2×C4—201no—
545C2×C4—201no—
546C2×C4—201no—
547C2×C4—201no—
548C2×C4—201no—
549C2×C4—201no—
550C2×C4—201no—
551C2×C4D5×C4⋊C412yes—
552C2×C4D5×C4⋊C412yes—
553C2×C4C22×C4×D511yescharacteristic
554C2×C4#414411yescharacteristic
555C2×C4C2×Q8×D511yescharacteristic
556C2×C4#414711yescharacteristic
557C2×C4#414911yescharacteristic
558C2×C4#415011yescharacteristic
559C8—22no—
560C8—22no—
561C8—102no—
562C8—102no—
563C5#2196211yescharacteristic, complemented, Sylow
564C22—54no—
565C22—102no—
566C22—102no—
567C22—102no—
568C22—102no—
569C22—102no—
570C22—102no—
571C22C2×D5×C4⋊C411yescharacteristic
572C22#6594211yescharacteristic
573C22#6596311yescharacteristic
574C22D5×#13511yescharacteristic
575C22D5×#13511yescharacteristic
576C22D5×AGL(1,ℤ/8)11yescharacteristic
577C22D5×#13711yescharacteristic
578C4—22no—
579C4—22no—
580C4—54no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—102no—
586C4—102no—
587C4—401no—
588C4—401no—
589C4—401no—
590C4—401no—
591C4#6587911yescharacteristic
592C4#6590611yescharacteristic
593C4#6602311yescharacteristic
594C4#6606311yescharacteristic
595C2—104no—
596C2#1060792611yescharacteristic
597C2D5×#42711yescharacteristic
598C2D5×#42811yescharacteristic
599C2#1061224311yescharacteristic
600C2#1061230711yescharacteristic
601C2#1061287911yescharacteristic
602C2#1061294311yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1949C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1949D5
hypocenterC5#21962
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. C5×#1949C2semidirect
6. #10601408C2semidirect
8. #10601356C2semidirect
9. #10601248C2semidirect
10. #10600333C2semidirect
11. #10600261C2semidirect
14. #10599589C2semidirect
15. #10599588C2semidirect
45. D5×C4⋊C8C4semidirect
131. #1949D5semidirect
563. C5#21962semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊C82
#106058782
#106054842
C5×#19492
#106014232
#106014082
#106013702
#106013562
#106012482
#106003332
#106002612
#105996622
#105996612
#105995892
#105995882
#219625