Finite Group Databasebeta

← #12117003

Subgroups — #12117003

Order 1280.

810 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#107C211yesmaximal, characteristic
2#10607932C211yesmaximal, characteristic
3#10605499C211yesmaximal, characteristic
4C5×#1918C211yesmaximal, characteristic, complemented
5#10601402C211yesmaximal, characteristic, complemented
6#10600413C211yesmaximal, characteristic, complemented
7#10600274C211yesmaximal, characteristic, complemented
8#10599665C211yesmaximal, characteristic
9#10599665C211yesmaximal, characteristic
10#10599661C211yesmaximal, characteristic
11#10599653C211yesmaximal, characteristic, complemented
12#10599607C211yesmaximal, characteristic, complemented
13#10599579C211yesmaximal, characteristic, complemented
14#10599441C211yesmaximal, characteristic
15#10599414C211yesmaximal, characteristic, complemented
16C22×C8×D5C2211yescharacteristic
17C2×D5×C4⋊C4C2211yescharacteristic
18C2×D5×C4⋊C4C2211yescharacteristic
19C2×C5×#107C2211yescharacteristic
20C5×#389C2211yescharacteristic
21C4×C5×C4⋊C4C2211yescharacteristic
22C2×#3952C2211yescharacteristic
23C2×#3950C2211yescharacteristic
24C2×#3947C2211yescharacteristic
25#65276—21no—
26#65276C2211yescharacteristic
27#65276C2211yescharacteristic
28#65274C2211yescharacteristic
29#65267—21no—
30C4⋊C4×Dic5C2211yescharacteristic
31C4⋊C4×Dic5C2211yescharacteristic
32#65262C2211yescharacteristic
33C2×#3940C2211yescharacteristic
34C2×#3940C2211yescharacteristic
35C2×#3939C2211yescharacteristic
36C2×#3939C2211yescharacteristic
37C4×#685—21no—
38C4×#685C2211yescharacteristic
39C4×C4⋊Dic5C2211yescharacteristic
40#65222—21no—
41#65217C2211yescharacteristic
42C2×#3935C2211yescharacteristic
43D5×#107C418yescomplemented
44#64956—21no—
45#64955—21no—
46#64944—21no—
47#64941—21no—
48C5×#340C2211yescharacteristic
49C5×#340C2211yescharacteristic
50C5×#340C2211yescharacteristic
51C5×#336C2211yescharacteristic
52#64771C2211yescharacteristic
53#64771C2211yescharacteristic
54#64771C2211yescharacteristic
55#64770C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#22618—51nomaximal, Sylow
61C22×C4×D5—21no—
62C22×C4×D5—21no—
63C22×C4×D5C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C2×C5×C4⋊C4—21no—
67C2×C5×C4⋊C4C2311yescharacteristic
68C2×C5×C4⋊C4C2311yescharacteristic
69C2×C5×C4⋊C4C2311yescharacteristic
70C2×C5×C4⋊C4C2311yescharacteristic
71C2×C42×C5—21no—
72C2×C42×C5C2311yescharacteristic
73C2×#685—21no—
74C2×#685—21no—
75C2×#685D411yescharacteristic
76C2×#685D411yescharacteristic
77C2×C4⋊Dic5—21no—
78C2×C4⋊Dic5C2311yescharacteristic
79C2×C4⋊Dic5C2311yescharacteristic
80C2×C4⋊Dic5C2311yescharacteristic
81C2×C4⋊Dic5C2311yescharacteristic
82C2×#683—21no—
83C2×#683—21no—
84C2×#683—21no—
85C2×#683—21no—
86C2×C4×Dic5—21no—
87C2×C4×Dic5—21no—
88C2×C4×Dic5—21no—
89C2×C4×Dic5C2311yescharacteristic
90C22×#168C2311yescharacteristic
91C22×#168C2311yescharacteristic
92C2×C8×D5—22no—
93C2×C8×D5—22no—
94C2×C8×D5C2×C414yes—
95D5×C4⋊C4—22no—
96D5×C4⋊C4—22no—
97D5×C4⋊C4C2×C414yes—
98D5×C4⋊C4C2×C414yes—
99C5×#107C2×C414yes—
100C5×#95—21no—
101C5×#95—21no—
102#3963—21no—
103#3963—21no—
104#3963—21no—
105#3963—21no—
106#3963—21no—
107#3963—21no—
108#3963—21no—
109#3963—21no—
110#3963D411yescharacteristic
111#3963D411yescharacteristic
112#3952—22no—
113#3950C2×C414yes—
114#3947—22no—
115#3940—22no—
116#3940—22no—
117#3939C2×C414yes—
118#3939C2×C414yes—
119#3935—22no—
120C22×#107—51no—
121#2345—51no—
122#2345—51no—
123#1943—51no—
124#1943—51no—
125#1918—51no—
126#1918—51no—
127#1918—51no—
128#1918D511yescharacteristic, complemented
129#1824—51no—
130#1824—51no—
131#1807—51no—
132#1776—51no—
133#1776—51no—
134#1752—51no—
135C23×D5C2×D411yescharacteristic
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5C2×D411yescharacteristic
141C22×C4×C5C2×D411yescharacteristic
142C22×C4×C5C2411yescharacteristic
143C22×Dic5—21no—
144C22×Dic5—21no—
145C22×Dic5—21no—
146C22×Dic5—21no—
147C22×Dic5C2×D411yescharacteristic
148C22×Dic5C2×D411yescharacteristic
149C22×Dic5C2×D411yescharacteristic
150C2×C4×D5—21no—
151C2×C4×D5—21no—
152C2×C4×D5—21no—
153C2×C4×D5—21no—
154C2×C4×D5—24no—
155C2×C4×D5—24no—
156C2×C4×D5—81no—
157C2×C4×D5—81no—
158C2×C4×D5—81no—
159C2×C4×D5—81no—
160C2×C4×D5C22×C412yes—
161C2×C4×D5#4112yes—
162C2×C5×C8—21no—
163C2×C5×C8—21no—
164C2×C5×C8—21no—
165C2×C5×C8—21no—
166C2×C5×C8—21no—
167C2×C5×C8C22×C412yes—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—21no—
170C5×C4⋊C4—21no—
171C5×C4⋊C4—21no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—81no—
175C5×C4⋊C4C22×C412yes—
176C5×C4⋊C4C22×C412yes—
177C42×C5—21no—
178C42×C5—21no—
179C42×C5—81no—
180#685—22no—
181#685—22no—
182#685—42no—
183#685—42no—
184C4⋊Dic5—21no—
185C4⋊Dic5—21no—
186C4⋊Dic5—21no—
187C4⋊Dic5—21no—
188C4⋊Dic5—21no—
189C4⋊Dic5—21no—
190C4⋊Dic5—81no—
191C4⋊Dic5C22×C412yes—
192C4⋊Dic5C22×C412yes—
193#683—24no—
194#683—24no—
195#683—81no—
196#683—81no—
197C4×Dic5—21no—
198C4×Dic5—21no—
199C4×Dic5—81no—
200C4×Dic5—81no—
201C4×Dic5—81no—
202C2×#168—21no—
203C2×#168—21no—
204C2×#168—21no—
205C2×#168C22×C412yes—
206C2×#168#4112yes—
207C2×#168#4112yes—
208C8×D5—28no—
209C23×C8—51no—
210C22×C4⋊C4—51no—
211C22×C4⋊C4—51no—
212C2×#107—51no—
213C2×#107—51no—
214C2×#107—51no—
215C2×#107—58no—
216C2×#107C2×D511yescharacteristic
217C2×#106—51no—
218C2×#106—51no—
219C2×C22⋊C8—51no—
220C2×#97—51no—
221C2×#97—51no—
222#389—51no—
223#389—51no—
224#389—51no—
225#389C2×D511yescharacteristic
226#387—101no—
227#387—101no—
228#387—101no—
229#387—101no—
230#380—51no—
231#380—51no—
232#380—101no—
233#380—101no—
234C4×C4⋊C4—51no—
235C4×C4⋊C4—51no—
236C4×C4⋊C4—51no—
237C4×C4⋊C4C2×D511yescharacteristic
238C4×C22⋊C4—51no—
239C4×C22⋊C4—101no—
240C4×C22⋊C4—101no—
241#340—51no—
242#340—51no—
243#340—51no—
244#340—51no—
245#340—51no—
246#340—51no—
247#340—51no—
248#340C2×D511yescharacteristic
249#340C2×D511yescharacteristic
250#340C2×D511yescharacteristic
251#336—51no—
252#336C2×D511yescharacteristic
253C23×C5C22×D411yescharacteristic
254C22×D5—21no—
255C22×D5—21no—
256C22×D5—21no—
257C22×D5—21no—
258C22×D5C4×D412yes—
259C22×D5#13712yes—
260C22×D5#13712yes—
261C2×C4×C5—22no—
262C2×C4×C5—22no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—21no—
269C2×C4×C5—41no—
270C2×C4×C5—41no—
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×C5C23×C411yescharacteristic
280C2×C4×C5C2×#4111yescharacteristic
281C2×C4×C5C2×#4111yescharacteristic
282C2×C4×C5C2×#4111yescharacteristic
283C2×C4×C52−1+411yescharacteristic
284C2×C4×C52−1+411yescharacteristic
285C2×Dic5—21no—
286C2×Dic5—21no—
287C2×Dic5—22no—
288C2×Dic5—22no—
289C2×Dic5—21no—
290C2×Dic5—21no—
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×Dic5C4×D412yes—
306C4×D5—22no—
307C4×D5—22no—
308C4×D5—22no—
309C4×D5—22no—
310C4×D5—84no—
311C4×D5—84no—
312C5×C8—22no—
313C5×C8—41no—
314#168—41no—
315#168#11714yes—
316C23×C4—51no—
317C23×C4—101no—
318C23×C4—101no—
319C22×C8—51no—
320C22×C8—54no—
321C22×C8—51no—
322C22×C8—102no—
323C22×C8—102no—
324C22×C8C22×D511yescharacteristic
325C22×C8C22×D511yescharacteristic
326C2×C4⋊C4—21no—
327C2×C4⋊C4—51no—
328C2×C4⋊C4—51no—
329C2×C4⋊C4—54no—
330C2×C4⋊C4—54no—
331C2×C4⋊C4—51no—
332C2×C4⋊C4—51no—
333C2×C4⋊C4—102no—
334C2×C4⋊C4—102no—
335C2×C4⋊C4—101no—
336C2×C4⋊C4—101no—
337C2×C4⋊C4—101no—
338C2×C4⋊C4—101no—
339C2×C4⋊C4—101no—
340C2×C4⋊C4C22×D511yescharacteristic
341C2×C4⋊C4C22×D511yescharacteristic
342C2×C4⋊C4C22×D511yescharacteristic
343C2×C4⋊C4C22×D511yescharacteristic
344C2×C22⋊C4—51no—
345C2×C22⋊C4—51no—
346C2×C22⋊C4—101no—
347C2×C22⋊C4—101no—
348C2×C42—21no—
349C2×C42—51no—
350C2×C42—101no—
351C2×C42—101no—
352C2×C42—101no—
353C2×C42C22×D511yescharacteristic
354#107—54no—
355#107—54no—
356#107—54no—
357#107C4×D514yes—
358#106—102no—
359#106—102no—
360C22⋊C8—102no—
361#97—102no—
362#97—102no—
363#95—21no—
364#95—21no—
365#95—51no—
366#95—51no—
367#95—101no—
368#95—101no—
369#95—101no—
370#95—101no—
371#95—101no—
372#95—101no—
373#95—101no—
374#95—101no—
375C22×C5C2×C4×D411yescharacteristic
376C22×C5#54711yescharacteristic
377C22×C5#54711yescharacteristic
378C22×C5C2×#13711yescharacteristic
379C22×C5C2×#13711yescharacteristic
380C22×C5#57611yescharacteristic
381C22×C5#57611yescharacteristic
382C2×D5—22no—
383C2×D5—22no—
384C2×D5—22no—
385C2×D5—22no—
386C2×D5—22no—
387C2×D5—22no—
388C2×D5#44114yes—
389C4×C5—41no—
390C4×C5—41no—
391C4×C5—42no—
392C4×C5—42no—
393C4×C5—81no—
394C4×C5—81no—
395C4×C5C2×#11711yescharacteristic
396C4×C5#51911yescharacteristic
397C4×C5#55211yescharacteristic
398C4×C5#55211yescharacteristic
399Dic5—22no—
400Dic5—41no—
401Dic5—41no—
402Dic5—42no—
403Dic5—42no—
404Dic5—81no—
405Dic5—81no—
406C24—51no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—51no—
412C22×C4—52no—
413C22×C4—52no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—104no—
417C22×C4—104no—
418C22×C4—101no—
419C22×C4—101no—
420C22×C4—101no—
421C22×C4—101no—
422C22×C4—101no—
423C22×C4—101no—
424C22×C4—101no—
425C22×C4—101no—
426C22×C4—401no—
427C22×C4—401no—
428C22×C4—401no—
429C22×C4—401no—
430C22×C4D4×D511yescharacteristic
431C22×C4D4×D511yescharacteristic
432C22×C4C23×D511yescharacteristic
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—52no—
439C2×C8—52no—
440C2×C8—52no—
441C2×C8—108no—
442C2×C8—101no—
443C2×C8—101no—
444C2×C8—101no—
445C2×C8C2×C4×D512yes—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—52no—
453C4⋊C4—52no—
454C4⋊C4—81no—
455C4⋊C4—104no—
456C4⋊C4—104no—
457C4⋊C4—101no—
458C4⋊C4—101no—
459C4⋊C4—101no—
460C4⋊C4—101no—
461C4⋊C4—101no—
462C4⋊C4—101no—
463C4⋊C4—401no—
464C4⋊C4—401no—
465C4⋊C4—401no—
466C4⋊C4C2×C4×D512yes—
467C4⋊C4C2×C4×D512yes—
468C22⋊C4—102no—
469C22⋊C4—102no—
470C22⋊C4—202no—
471C22⋊C4—202no—
472C42—21no—
473C42—21no—
474C42—81no—
475C42—101no—
476C42—101no—
477C42—401no—
478C42—401no—
479C42—401no—
480C2×C5#234411yescharacteristic
481C2×C5C2×#44111yescharacteristic
482C2×C5#294811yescharacteristic
483C2×C5#334611yescharacteristic
484C2×C5#334611yescharacteristic
485C2×C5#334611yescharacteristic
486C2×C5#334611yescharacteristic
487D5—24no—
488C23—52no—
489C23—52no—
490C23—52no—
491C23—101no—
492C23—101no—
493C23—101no—
494C23—101no—
495C23C2×D4×D511yescharacteristic
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—52no—
515C2×C4—101no—
516C2×C4—101no—
517C2×C4—102no—
518C2×C4—102no—
519C2×C4—102no—
520C2×C4—102no—
521C2×C4—101no—
522C2×C4—101no—
523C2×C4—101no—
524C2×C4—101no—
525C2×C4—102no—
526C2×C4—102no—
527C2×C4—101no—
528C2×C4—101no—
529C2×C4—201no—
530C2×C4—201no—
531C2×C4—201no—
532C2×C4—201no—
533C2×C4—201no—
534C2×C4—201no—
535C2×C4—201no—
536C2×C4—201no—
537C2×C4—201no—
538C2×C4—201no—
539C2×C4—404no—
540C2×C4—404no—
541C2×C4C22×C4×D511yescharacteristic
542C2×C4#414711yescharacteristic
543C2×C4D5×#4111yescharacteristic
544C2×C4D5×#4111yescharacteristic
545C2×C4D5×#4111yescharacteristic
546C2×C4#415011yescharacteristic
547C8—22no—
548C8—41no—
549C8—54no—
550C8—201no—
551C5#2261811yescharacteristic, complemented, Sylow
552C22—54no—
553C22—102no—
554C22—102no—
555C22—102no—
556C22—102no—
557C22—102no—
558C22—102no—
559C22C4×D4×D511yescharacteristic
560C22#6596511yescharacteristic
561C22#6598911yescharacteristic
562C22#6609111yescharacteristic
563C22#6610311yescharacteristic
564C22D5×#13711yescharacteristic
565C22D5×#13711yescharacteristic
566C4—41no—
567C4—41no—
568C4—42no—
569C4—42no—
570C4—81no—
571C4—81no—
572C4—102no—
573C4—202no—
574C4—202no—
575C4—201no—
576C4—201no—
577C4—401no—
578C4—401no—
579C4D5×#11711yescharacteristic
580C4#6590611yescharacteristic
581C4#6602711yescharacteristic
582C4#6604211yescharacteristic
583C2—104no—
584C2#1060669211yescharacteristic
585C2#1061131911yescharacteristic
586C2D5×#44111yescharacteristic
587C2#1061271911yescharacteristic
588C2#1061298711yescharacteristic
589C2#1061302611yescharacteristic
590C2#1061326611yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1918C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1918D5
hypocenterC5#22618
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
4. C5×#1918C2semidirect
5. #10601402C2semidirect
6. #10600413C2semidirect
7. #10600274C2semidirect
11. #10599653C2semidirect
12. #10599607C2semidirect
13. #10599579C2semidirect
15. #10599414C2semidirect
43. D5×#107C4semidirect
128. #1918D5semidirect
551. C5#22618semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#1072
#106079322
#106054992
C5×#19182
#106014022
#106004132
#106002742
#105996652
#105996612
#105996532
#105996072
#105995792
#105994412
#105994142
#226185