Finite Group Databasebeta

← #12158403

Subgroups — #12158403

Order 1280.

708 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2354C211yesmaximal, characteristic
2#10605454C211yesmaximal, characteristic, complemented
3#10602402C211yesmaximal, characteristic
4#10602398C211yesmaximal, characteristic
5#10600448C211yesmaximal, characteristic
6#10600447C211yesmaximal, characteristic
7#10600446C211yesmaximal, characteristic
8#10600445C211yesmaximal, characteristic
9#10600371C211yesmaximal, characteristic, complemented
10#10600360C211yesmaximal, characteristic, complemented
11#10600278C211yesmaximal, characteristic, complemented
12#10600261C211yesmaximal, characteristic, complemented
13#10600259C211yesmaximal, characteristic, complemented
14#10600254C211yesmaximal, characteristic, complemented
15#10600253C211yesmaximal, characteristic, complemented
16C2×C4×C5×D4C2211yescharacteristic
17C2×C5×#117—21no—
18C5×#390C2211yescharacteristic
19C5×#390C2211yescharacteristic
20C5×#388—21no—
21C5×#388—21no—
22C5×#384C2211yescharacteristic
23C5×#380—21no—
24C4×C5×C4⋊C4C2211yescharacteristic
25C4×C5×C4⋊C4C2211yescharacteristic
26C4×C5×C4⋊C4C2211yescharacteristic
27C2×#3964C2211yescharacteristic
28C2×#3964C2211yescharacteristic
29C2×#3964C2211yescharacteristic
30C2×#3964C2211yescharacteristic
31#65275—21no—
32#65273—21no—
33C2×#3940C2211yescharacteristic
34C2×#3940C2211yescharacteristic
35C2×#3939C2211yescharacteristic
36C2×#3939C2211yescharacteristic
37C2×#3939C2211yescharacteristic
38C2×#3939C2211yescharacteristic
39#65225C2211yescharacteristic
40#65225C2211yescharacteristic
41#65224C2211yescharacteristic
42C4×C4⋊Dic5C2211yescharacteristic
43#65217C2211yescharacteristic
44#65217C2211yescharacteristic
45C2×C4⋊#168C2211yescharacteristic
46C2×C4⋊#168C2211yescharacteristic
47C2×C4⋊#168C2211yescharacteristic
48C2×#3935C2211yescharacteristic
49#64944—21no—
50#64943—21no—
51#64749C2211yescharacteristic
52#64749C2211yescharacteristic
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64744C2211yescharacteristic
58#64744C2211yescharacteristic
59#26098—51nomaximal, Sylow
60C22×C5×D4C2311yescharacteristic
61C23×C4×C5—21no—
62C4×C5×D4—22no—
63C4×C5×D4Q814yes—
64C5×#117—44no—
65C2×C5×C4⋊C4—21no—
66C2×C5×C4⋊C4—21no—
67C2×C5×C4⋊C4D411yescharacteristic
68C2×C5×C4⋊C4D411yescharacteristic
69C2×C5×C4⋊C4C2311yescharacteristic
70C2×C5×C4⋊C4C2311yescharacteristic
71C2×C5×C4⋊C4C2311yescharacteristic
72C2×C5×C22⋊C4—21no—
73C2×C5×C22⋊C4—21no—
74C2×C5×C22⋊C4—21no—
75C2×C5×C22⋊C4—21no—
76C2×C5×C22⋊C4—21no—
77C2×C42×C5—21no—
78C2×C42×C5—21no—
79C2×C42×C5C2311yescharacteristic
80C2×C42×C5C2311yescharacteristic
81C2×C42×C5C2311yescharacteristic
82C2×C4⋊Dic5—21no—
83C2×C4⋊Dic5—21no—
84C2×C4⋊Dic5C2311yescharacteristic
85C2×C4⋊Dic5C2311yescharacteristic
86C2×C4⋊Dic5C2311yescharacteristic
87C2×C4⋊Dic5C2311yescharacteristic
88C2×#683—21no—
89C2×#683—21no—
90C2×C4×Dic5—21no—
91C22×#168C2311yescharacteristic
92C22×#168C2311yescharacteristic
93C22×#168C2311yescharacteristic
94C22×#168C2311yescharacteristic
95C5×#95—21no—
96C5×#95—21no—
97C5×#95D411yescharacteristic
98C5×#95D411yescharacteristic
99#3964—22no—
100#3964—22no—
101#3964—41no—
102#3964—41no—
103#3963—21no—
104#3963—21no—
105#3963—21no—
106#3963—21no—
107#3963—21no—
108#3963—21no—
109#3963—21no—
110#3940—22no—
111#3940—41no—
112#3939—22no—
113#3939—41no—
114#3939—41no—
115#3939—41no—
116C4⋊#168—22no—
117C4⋊#168—22no—
118C4⋊#168—22no—
119#3935—22no—
120#2570—51no—
121#2354D511yescharacteristic
122#2093—51no—
123#2092—51no—
124#2067—51no—
125#2065—51no—
126#1949—51no—
127#1947—51no—
128#1947—51no—
129#1940—51no—
130#1921—51no—
131#1920—51no—
132#1847—51no—
133#1804—51no—
134#1762—51no—
135C24×C5—21no—
136C2×C5×D4—21no—
137C2×C5×D4—21no—
138C2×C5×D4—21no—
139C2×C5×D4—21no—
140C2×C5×D4—21no—
141C2×C5×D4C2×Q812yes—
142C22×C4×C5—21no—
143C22×C4×C5—24no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—42no—
147C22×C4×C5—42no—
148C22×C4×C5C2×D411yescharacteristic
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2411yescharacteristic
155C22×Dic5—21no—
156C22×Dic5—21no—
157C22×Dic5—21no—
158C22×Dic5—21no—
159C5×C4⋊C4—22no—
160C5×C4⋊C4—21no—
161C5×C4⋊C4—21no—
162C5×C4⋊C4—21no—
163C5×C4⋊C4—21no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—41no—
166C5×C4⋊C4—42no—
167C5×C4⋊C4—81no—
168C5×C4⋊C4C2×Q812yes—
169C5×C22⋊C4—24no—
170C5×C22⋊C4—42no—
171C5×C22⋊C4—42no—
172C5×C22⋊C4—81no—
173C5×C22⋊C4—81no—
174C42×C5—21no—
175C42×C5—21no—
176C42×C5—21no—
177C42×C5—21no—
178C42×C5—42no—
179C42×C5—42no—
180C42×C5C2×Q812yes—
181C42×C5#4112yes—
182C4⋊Dic5—21no—
183C4⋊Dic5—21no—
184C4⋊Dic5—21no—
185C4⋊Dic5—21no—
186C4⋊Dic5—21no—
187C4⋊Dic5—21no—
188C4⋊Dic5—21no—
189C4⋊Dic5—21no—
190C4⋊Dic5—42no—
191C4⋊Dic5—81no—
192#683—42no—
193#683—81no—
194C4×Dic5—81no—
195C2×#168—21no—
196C2×#168—21no—
197C2×#168—21no—
198C2×#168—21no—
199C2×#168—21no—
200C2×#168—21no—
201C2×#168—21no—
202C2×#168—21no—
203C2×#168—21no—
204C2×#168—21no—
205C2×#168#4112yes—
206C2×#168#4112yes—
207C2×C4×D4C2×D511yescharacteristic
208C2×#117—21no—
209C2×#107—51no—
210C2×#107—51no—
211C2×#107—51no—
212C2×#107—51no—
213C2×#106—51no—
214C2×#106—51no—
215C2×C4⋊C8—51no—
216C2×C4⋊C8—51no—
217C2×C4⋊C8—51no—
218C2×#102—51no—
219C2×#102—51no—
220C2×#102—51no—
221C2×#102—51no—
222C2×#97—51no—
223#400—101no—
224#398—101no—
225#390C2×D511yescharacteristic
226#390C2×D511yescharacteristic
227#389—51no—
228#389—51no—
229#388—21no—
230#388—21no—
231#387—101no—
232#387—101no—
233#384—51no—
234#384C2×D511yescharacteristic
235#382—51no—
236#382—51no—
237#380—21no—
238C4×C4⋊C4—51no—
239C4×C4⋊C4C2×D511yescharacteristic
240C4×C4⋊C4C2×D511yescharacteristic
241C4×C4⋊C4C2×D511yescharacteristic
242#340—51no—
243#340—51no—
244#340—51no—
245#340—51no—
246#340—51no—
247#340—51no—
248#336—51no—
249#336—51no—
250C23×C5—22no—
251C23×C5—41no—
252C23×C5—41no—
253C23×C5—41no—
254C23×C5—41no—
255C23×C5—41no—
256C23×C5—41no—
257C23×C5C22×D411yescharacteristic
258C5×D4—22no—
259C5×D4—22no—
260C5×D4—41no—
261C5×D4—41no—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—22no—
269C2×C4×C5—21no—
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—48no—
279C2×C4×C5—41no—
280C2×C4×C5—41no—
281C2×C4×C5—41no—
282C2×C4×C5—41no—
283C2×C4×C5—41no—
284C2×C4×C5—41no—
285C2×C4×C5—41no—
286C2×C4×C5—41no—
287C2×C4×C5C22⋊Q812yes—
288C2×C4×C5C22⋊Q812yes—
289C2×C4×C5AGL(1,ℤ/8)12yes—
290C2×C4×C5C22×Q811yescharacteristic
291C2×C4×C5C2×#4111yescharacteristic
292C2×C4×C5C2×#4111yescharacteristic
293C2×C4×C5C2×#4111yescharacteristic
294C2×C4×C5H(5,𝔽2)11yescharacteristic
295C2×C4×C52−1+411yescharacteristic
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×Dic5—41no—
308#168—22no—
309#168—22no—
310#168—41no—
311#168—41no—
312C22×D4C22×D511yescharacteristic
313C23×C4—21no—
314C22×C8—51no—
315C22×C8—51no—
316C22×C8—51no—
317C22×C8—51no—
318C4×D4—22no—
319C4×D4Dic1014yes—
320#117—44no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—51no—
324C2×C4⋊C4—51no—
325C2×C4⋊C4—51no—
326C2×C4⋊C4—51no—
327C2×C4⋊C4—101no—
328C2×C4⋊C4—101no—
329C2×C4⋊C4—101no—
330C2×C4⋊C4—101no—
331C2×C4⋊C4C22⋊D511yescharacteristic
332C2×C4⋊C4C22⋊D511yescharacteristic
333C2×C4⋊C4C22×D511yescharacteristic
334C2×C4⋊C4C22×D511yescharacteristic
335C2×C4⋊C4C22×D511yescharacteristic
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—101no—
344C2×C42C22×D511yescharacteristic
345C2×C42C22×D511yescharacteristic
346C2×C42C22×D511yescharacteristic
347#107—102no—
348#107—201no—
349#107—201no—
350#107—201no—
351#106—102no—
352#106—201no—
353C4⋊C8—102no—
354C4⋊C8—102no—
355C4⋊C8—102no—
356#102—102no—
357#102—102no—
358#102—201no—
359#102—201no—
360#97—102no—
361#95—21no—
362#95—21no—
363#95—101no—
364#95—101no—
365#95—101no—
366#95—101no—
367#95—101no—
368#95—101no—
369#95—101no—
370#95C22⋊D511yescharacteristic
371#95C22⋊D511yescharacteristic
372C22×C5—42no—
373C22×C5—42no—
374C22×C5—42no—
375C22×C5—81no—
376C22×C5—81no—
377C22×C5—81no—
378C22×C5—81no—
379C22×C5C2×C22⋊Q811yescharacteristic
380C22×C5#54711yescharacteristic
381C22×C5#55011yescharacteristic
382C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C5#57511yescharacteristic
384C22×C5#57611yescharacteristic
385C22×C5#57811yescharacteristic
386C4×C5—22no—
387C4×C5—22no—
388C4×C5—22no—
389C4×C5—42no—
390C4×C5—41no—
391C4×C5—41no—
392C4×C5—41no—
393C4×C5—81no—
394C4×C5—81no—
395C4×C5#53311yescharacteristic
396C4×C5#54411yescharacteristic
397C4×C5#55211yescharacteristic
398C4×C5#55311yescharacteristic
399Dic5—81no—
400Dic5—81no—
401Dic5—81no—
402Dic5—81no—
403C24—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4C2×Dic1012yes—
410C22×C4—21no—
411C22×C4—24no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—101no—
417C22×C4—101no—
418C22×C4—101no—
419C22×C4—101no—
420C22×C4C2×C22⋊D511yescharacteristic
421C22×C4C2×C22⋊D511yescharacteristic
422C22×C4C2×C22⋊D511yescharacteristic
423C22×C4C2×C22⋊D511yescharacteristic
424C22×C4C2×C22⋊D511yescharacteristic
425C22×C4C2×C22⋊D511yescharacteristic
426C22×C4C23×D511yescharacteristic
427C2×C8—52no—
428C2×C8—52no—
429C2×C8—101no—
430C2×C8—101no—
431C2×C8—101no—
432C2×C8—101no—
433C2×C8—101no—
434C2×C8—101no—
435C2×C8—101no—
436C2×C8—101no—
437C2×C8—101no—
438C2×C8—101no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—41no—
446C4⋊C4—42no—
447C4⋊C4—81no—
448C4⋊C4—101no—
449C4⋊C4—101no—
450C4⋊C4—101no—
451C4⋊C4—101no—
452C4⋊C4—101no—
453C4⋊C4—101no—
454C4⋊C4—101no—
455C4⋊C4—101no—
456C4⋊C4—202no—
457C4⋊C4—202no—
458C4⋊C4—401no—
459C4⋊C4—401no—
460C4⋊C4C2×Dic1012yes—
461C22⋊C4—24no—
462C22⋊C4—42no—
463C22⋊C4—42no—
464C22⋊C4—81no—
465C22⋊C4—81no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—42no—
471C42—42no—
472C42—401no—
473C42C2×Dic1012yes—
474C42#70912yes—
475C2×C5—82no—
476C2×C5#244111yescharacteristic
477C2×C5#307711yescharacteristic
478C2×C5#308311yescharacteristic
479C2×C5#334311yescharacteristic
480C2×C5#334711yescharacteristic
481C2×C5#339911yescharacteristic
482C2×C5#340211yescharacteristic
483C23—22no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23C22×C22⋊D511yescharacteristic
491D4—22no—
492D4—22no—
493D4—41no—
494D4—41no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—48no—
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—201no—
521C2×C4—201no—
522C2×C4—201no—
523C2×C4—201no—
524C2×C4—201no—
525C2×C4—201no—
526C2×C4—201no—
527C2×C4—201no—
528C2×C4—201no—
529C2×C4—201no—
530C2×C4—201no—
531C2×C4—201no—
532C2×C4#407012yes—
533C2×C4#407012yes—
534C2×C4#407812yes—
535C2×C4C22×Dic1011yescharacteristic
536C2×C4C2×#70911yescharacteristic
537C2×C4D5×#4111yescharacteristic
538C2×C4D5×#4111yescharacteristic
539C2×C4#414911yescharacteristic
540C2×C4#415011yescharacteristic
541C8—102no—
542C8—102no—
543C8—201no—
544C8—201no—
545C5#2609811yescharacteristic, complemented, Sylow
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C2×#407011yescharacteristic
554C22C2×#407811yescharacteristic
555C22#6615611yescharacteristic
556C22#6615811yescharacteristic
557C22#6616811yescharacteristic
558C22#6616911yescharacteristic
559C22#6617211yescharacteristic
560C4—22no—
561C4—22no—
562C4—22no—
563C4—42no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—401no—
570C4—401no—
571C4—401no—
572C4—401no—
573C4#6585111yescharacteristic
574C4#6585311yescharacteristic
575C4#6586311yescharacteristic
576C4#6586411yescharacteristic
577C2—82no—
578C2#1061398011yescharacteristic
579C2#1061402711yescharacteristic
580C2#1061429011yescharacteristic
581C2#1061524911yescharacteristic
582C2#1061532011yescharacteristic
583C2#1061537911yescharacteristic
584C2#1061541211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC5×#2354C2
socleC23×C5C22×D4
prime radicalC22×C5×D4C23
hypercenter#2354D5
hypocenterC5#26098
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #10605454C2semidirect
9. #10600371C2semidirect
10. #10600360C2semidirect
11. #10600278C2semidirect
12. #10600261C2semidirect
13. #10600259C2semidirect
14. #10600254C2semidirect
15. #10600253C2semidirect
545. C5#26098semidirect

Maximal subgroups

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

subgroupindex
C5×#23542
#106054542
#106024022
#106023982
#106004482
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