Finite Group Databasebeta

← #12002655

Subgroups — #12002655

Order 1280.

708 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2541C211yesmaximal, characteristic
2#10602557C211yesmaximal, characteristic, complemented
3C2×#64764C211yesmaximal, characteristic, complemented
4#10602397C211yesmaximal, characteristic, complemented
5C2×D4⋊#168C211yesmaximal, characteristic, complemented
6#10600259C211yesmaximal, characteristic, complemented
7#10598110C211yesmaximal, characteristic, complemented
8C2×C5×#127—21no—
9C2×C5×#127C2211yescharacteristic
10C2×C5×#121—21no—
11C2×C5×#121—21no—
12C2×C4×C5×D4C2211yescharacteristic
13C5×#392—22no—
14C5×#390—21no—
15C4×C5×C4⋊C4C2211yescharacteristic
16C2×#3964—22no—
17C2×#3964—21no—
18C2×#3939—21no—
19#65224C2211yescharacteristic
20C2×C4⋊#168C2211yescharacteristic
21C2×C4⋊#168C2211yescharacteristic
22C2×C4×#168C2211yescharacteristic
23#64764—22no—
24D4⋊#168—22no—
25#64749—21no—
26#64749—21no—
27#10408—51nomaximal, Sylow
28C22×C5×D4—22no—
29C22×C5×D4—22no—
30C22×C5×D4—21no—
31C22×C5×D4—21no—
32C22×C5×D4D411yescharacteristic
33C22×C5×D4D412yes—
34C23×C4×C5—21no—
35C5×#127—21no—
36C5×#127—21no—
37C5×#127—21no—
38C5×#127—21no—
39C5×#127—42no—
40C5×#127—42no—
41C5×#121—42no—
42C5×#121—42no—
43C5×#121—42no—
44C5×#121—42no—
45C4×C5×D4—21no—
46C4×C5×D4—21no—
47C4×C5×D4—21no—
48C4×C5×D4—21no—
49C2×C5×C4⋊C4D411yescharacteristic
50C2×C5×C4⋊C4D411yescharacteristic
51C2×C5×C4⋊C4D411yescharacteristic
52C2×C5×C22⋊C4—22no—
53C2×C5×C22⋊C4—22no—
54C2×C5×C22⋊C4—21no—
55C2×C42×C5—21no—
56C2×C42×C5C2311yescharacteristic
57C2×C4⋊Dic5—21no—
58C2×C4⋊Dic5—21no—
59C2×C4⋊Dic5—21no—
60C22×#168—21no—
61C22×#168—21no—
62C22×#168—21no—
63C5×#95—21no—
64#3964—44no—
65#3964—42no—
66#3939—42no—
67C4⋊#168—21no—
68C4⋊#168—21no—
69C4⋊#168—21no—
70C4⋊#168D412yescomplemented
71C4×#168—21no—
72C4×#168—21no—
73#2541D511yescharacteristic
74#1957—51no—
75#1947—51no—
76#1802—51no—
77C2×#331—51no—
78C2×D4⋊C8—51no—
79#1279—51no—
80C24×C5—21no—
81C24×C5—22no—
82C2×C5×D4—21no—
83C2×C5×D4—22no—
84C2×C5×D4—21no—
85C2×C5×D4—22no—
86C2×C5×D4—21no—
87C2×C5×D4—21no—
88C2×C5×D4—21no—
89C2×C5×D4—42no—
90C2×C5×D4—42no—
91C2×C5×D4—44no—
92C2×C5×D4—44no—
93C2×C5×D4—44no—
94C2×C5×D4—44no—
95C2×C5×D4—41no—
96C2×C5×D4—41no—
97C2×C5×D4—41no—
98C2×C5×D4—41no—
99C2×C5×D4—41no—
100C2×C5×D4—41no—
101C2×C5×D4—41no—
102C2×C5×D4—41no—
103C2×C5×D4—41no—
104C2×C5×D4—41no—
105C2×C5×D4—41no—
106C2×C5×D4—41no—
107C2×C5×D4—82no—
108C2×C5×D4—82no—
109C2×C5×D4D812yes—
110C22×C4×C5—21no—
111C22×C4×C5—21no—
112C22×C4×C5—21no—
113C22×C4×C5—41no—
114C22×C4×C5—41no—
115C22×C4×C5—41no—
116C22×C4×C5—41no—
117C22×C4×C5—41no—
118C22×C4×C5—41no—
119C22×C4×C5C2×D411yescharacteristic
120C22×C4×C5C2×D411yescharacteristic
121C22×C4×C5C2×D411yescharacteristic
122C22×Dic5—41no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4D812yes—
128C5×C4⋊C4SD1612yes—
129C5×C22⋊C4—44no—
130C5×C22⋊C4—44no—
131C5×C22⋊C4—41no—
132C5×C22⋊C4—41no—
133C42×C5—41no—
134C42×C5—41no—
135C42×C5C2×D411yescharacteristic
136C42×C5#4111yescharacteristic
137C42×C5#4111yescharacteristic
138C42×C5#4111yescharacteristic
139C4⋊Dic5—42no—
140C4⋊Dic5—41no—
141C4⋊Dic5—41no—
142C4⋊Dic5—41no—
143C4⋊Dic5—41no—
144C2×#168—22no—
145C2×#168—22no—
146C2×#168—41no—
147C2×#168—41no—
148C2×#168—41no—
149C2×#168—41no—
150C2×#168—41no—
151C2×#168—41no—
152C2×#168—41no—
153C2×#127—21no—
154C2×#127C2×D511yescharacteristic
155C2×#121—21no—
156C2×#121—21no—
157C2×C4×D4C2×D511yescharacteristic
158C2×#107—101no—
159C2×C4⋊C8—51no—
160C2×C4⋊C8—51no—
161C2×#102—101no—
162C2×#102—102no—
163C2×C4×C8—51no—
164#392—22no—
165#390—21no—
166#384—51no—
167C4×C4⋊C4C2×D511yescharacteristic
168#340—101no—
169#340—101no—
170#331—102no—
171D4⋊C8—102no—
172C23×C5—22no—
173C23×C5—41no—
174C23×C5—41no—
175C23×C5—41no—
176C23×C5—41no—
177C23×C5—41no—
178C23×C5—41no—
179C23×C5—42no—
180C23×C5—42no—
181C23×C5—42no—
182C23×C5—42no—
183C23×C5—42no—
184C23×C5—42no—
185C23×C5—42no—
186C23×C5#12011yescharacteristic
187C5×D4—22no—
188C5×D4—22no—
189C5×D4—44no—
190C5×D4—41no—
191C5×D4—41no—
192C5×D4—82no—
193C5×D4—88no—
194C5×D4—88no—
195C5×D4—81no—
196C5×D4—81no—
197C5×D4—81no—
198C5×D4—81no—
199C5×D4—81no—
200C5×D4—81no—
201C5×D4—81no—
202C5×D4—81no—
203C2×C4×C5—21no—
204C2×C4×C5—21no—
205C2×C4×C5—22no—
206C2×C4×C5—22no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5—41no—
213C2×C4×C5—41no—
214C2×C4×C5—81no—
215C2×C4×C5—81no—
216C2×C4×C5—81no—
217C2×C4×C5—81no—
218C2×C4×C5#12111yescharacteristic
219C2×C4×C5#12111yescharacteristic
220C2×C4×C5#12111yescharacteristic
221C2×C4×C5#12311yescharacteristic
222C2×C4×C5#12311yescharacteristic
223C2×C4×C5#12411yescharacteristic
224C2×C4×C5C2×D811yescharacteristic
225C2×C4×C5C2×D811yescharacteristic
226C2×C4×C5C2×SD1611yescharacteristic
227C2×C4×C5#13511yescharacteristic
228C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
229C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
230C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
231C2×C4×C5#13711yescharacteristic
232C2×Dic5—81no—
233C2×Dic5—81no—
234C2×Dic5—81no—
235#168—42no—
236#168—42no—
237#168—81no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—21no—
241C22×D4—21no—
242C22×D4C22⋊D511yescharacteristic
243C22×D4C22⋊D512yes—
244C23×C4—21no—
245C22×C8—101no—
246C22×C8—101no—
247C22×C8—101no—
248#127—21no—
249#127—21no—
250#127—21no—
251#127—21no—
252#127—42no—
253#127—42no—
254#121—42no—
255#121—42no—
256#121—42no—
257#121—42no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—21no—
262C2×C4⋊C4—101no—
263C2×C4⋊C4—101no—
264C2×C4⋊C4—101no—
265C2×C4⋊C4C22⋊D511yescharacteristic
266C2×C4⋊C4C22⋊D511yescharacteristic
267C2×C4⋊C4C22⋊D511yescharacteristic
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—21no—
271C2×C42—21no—
272C2×C42C22×D511yescharacteristic
273#107—202no—
274C4⋊C8—52no—
275C4⋊C8—101no—
276C4⋊C8—101no—
277C4⋊C8—101no—
278#102—204no—
279#102—202no—
280C4×C8—101no—
281C4×C8—101no—
282#95—21no—
283C22×C5—42no—
284C22×C5—42no—
285C22×C5—42no—
286C22×C5—81no—
287C22×C5—81no—
288C22×C5—81no—
289C22×C5—81no—
290C22×C5—82no—
291C22×C5—82no—
292C22×C5—82no—
293C22×C5—82no—
294C22×C5—82no—
295C22×C5—82no—
296C22×C5—82no—
297C22×C5#39411yescharacteristic
298C22×C5#44711yescharacteristic
299C22×C5#44711yescharacteristic
300C22×C5#45011yescharacteristic
301C22×C5#45211yescharacteristic
302C22×C5#45311yescharacteristic
303C22×C5#45511yescharacteristic
304C4×C5—21no—
305C4×C5—21no—
306C4×C5—42no—
307C4×C5—42no—
308C4×C5—81no—
309C4×C5#45911yescharacteristic
310C4×C5#46011yescharacteristic
311C4×C5#46611yescharacteristic
312C4×C5#46811yescharacteristic
313C4×C5#48011yescharacteristic
314C4×C5#48211yescharacteristic
315C4×C5#48611yescharacteristic
316C4×C5#49011yescharacteristic
317Dic5—161no—
318C24—21no—
319C24—22no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—22no—
325C2×D4—21no—
326C2×D4—22no—
327C2×D4—42no—
328C2×D4—42no—
329C2×D4—44no—
330C2×D4—44no—
331C2×D4—44no—
332C2×D4—44no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—82no—
346C2×D4—82no—
347C2×D4#68612yes—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—201no—
358C22×C4C2×C22⋊D511yescharacteristic
359C22×C4C2×C22⋊D511yescharacteristic
360C22×C4C2×C22⋊D511yescharacteristic
361C2×C8—102no—
362C2×C8—102no—
363C2×C8—201no—
364C2×C8—201no—
365C2×C8—201no—
366C2×C8—201no—
367C2×C8—201no—
368C2×C8—201no—
369C2×C8—201no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—202no—
375C4⋊C4—201no—
376C4⋊C4—201no—
377C4⋊C4—201no—
378C4⋊C4—201no—
379C4⋊C4#68612yes—
380C4⋊C4#68712yes—
381C22⋊C4—44no—
382C22⋊C4—44no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C42—41no—
386C42—41no—
387C42D4×D511yescharacteristic
388C42#71111yescharacteristic
389C42#71111yescharacteristic
390C42#71111yescharacteristic
391C2×C5—82no—
392C2×C5—162no—
393C2×C5#161911yescharacteristic
394C2×C5#163111yescharacteristic
395C2×C5#163911yescharacteristic
396C2×C5#164111yescharacteristic
397C2×C5#203311yescharacteristic
398C2×C5#203711yescharacteristic
399C2×C5#204111yescharacteristic
400C23—22no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23#409911yescharacteristic
415D4—22no—
416D4—22no—
417D4—44no—
418D4—41no—
419D4—41no—
420D4—82no—
421D4—88no—
422D4—88no—
423D4—81no—
424D4—81no—
425D4—81no—
426D4—81no—
427D4—81no—
428D4—81no—
429D4—81no—
430D4—81no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—401no—
447C2×C4—401no—
448C2×C4—401no—
449C2×C4C2×#68611yescharacteristic
450C2×C4C2×#68611yescharacteristic
451C2×C4#407811yescharacteristic
452C2×C4#407811yescharacteristic
453C2×C4#407811yescharacteristic
454C2×C4C2×#68711yescharacteristic
455C2×C4#408111yescharacteristic
456C2×C4#408111yescharacteristic
457C2×C4#408211yescharacteristic
458C2×C4#408411yescharacteristic
459C2×C4#408511yescharacteristic
460C2×C4#408511yescharacteristic
461C2×C4#409611yescharacteristic
462C2×C4#409711yescharacteristic
463C8—202no—
464C8—202no—
465C8—401no—
466C5#1040811yescharacteristic, complemented, Sylow
467C22—42no—
468C22—42no—
469C22—42no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22—82no—
478C22—82no—
479C22—82no—
480C22—82no—
481C22#6550611yescharacteristic
482C22#6550611yescharacteristic
483C22#6550711yescharacteristic
484C22#6551111yescharacteristic
485C22#6552811yescharacteristic
486C22#6553011yescharacteristic
487C22#6553111yescharacteristic
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—81no—
493C4—801no—
494C4#6532211yescharacteristic
495C4#6532411yescharacteristic
496C4#6532711yescharacteristic
497C4#6533111yescharacteristic
498C4#6535911yescharacteristic
499C4#6536011yescharacteristic
500C4#6536111yescharacteristic
501C4#6536411yescharacteristic
502C2—82no—
503C2—162no—
504C2#1060247211yescharacteristic
505C2#1060255511yescharacteristic
506C2#1060264511yescharacteristic
507C2#1060269911yescharacteristic
508C2#1060270111yescharacteristic
509C2#1060271211yescharacteristic
510C2#1060271311yescharacteristic
subgroupG/H
centerC23#4099
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
Fitting, prime radicalC5×#2541C2
socleC23×C5#120
hypercenter#2541D5
hypocenterC5#10408
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2541

Complements

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

NH ≅ G/Ntype
2. #10602557C2semidirect
3. C2×#64764C2semidirect
4. #10602397C2semidirect
5. C2×D4⋊#168C2semidirect
6. #10600259C2semidirect
7. #10598110C2semidirect
70. C4⋊#168D4semidirect
466. C5#10408semidirect

Maximal subgroups

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

subgroupindex
C5×#25412
#106025572
C2×#647642
#106023972
C2×D4⋊#1682
#106002592
#105981102
#104085