Finite Group Databasebeta

← #12002806

Subgroups — #12002806

Order 1280.

614 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2537C211yesmaximal, characteristic
2#10602397C211yesmaximal, characteristic, complemented
3#10602397C211yesmaximal, characteristic, complemented
4C2×D4⋊#168C211yesmaximal, characteristic, complemented
5C2×D4⋊#168C211yesmaximal, characteristic, complemented
6#10600367C211yesmaximal, characteristic, complemented
7#10598125C211yesmaximal, characteristic, complemented
8C2×C5×#121—21no—
9C2×C5×#121—21no—
10C2×C4×C5×D4C2211yescharacteristic
11C2×C4×C5×D4C2211yescharacteristic
12C5×#394—22no—
13C5×#384C2211yescharacteristic
14C5×#380—21no—
15C5×#380—21no—
16C2×#3964—21no—
17C2×#3964—21no—
18#65224C2211yescharacteristic
19C2×C4⋊#168C2211yescharacteristic
20C2×C4⋊#168C2211yescharacteristic
21C2×C4×#168C2211yescharacteristic
22D4⋊#168—22no—
23D4⋊#168—22no—
24#64749—21no—
25#64749—21no—
26#64749—22no—
27#10431—51nomaximal, Sylow
28C22×C5×D4—22no—
29C22×C5×D4D411yescharacteristic
30C22×C5×D4D411yescharacteristic
31C23×C4×C5—21no—
32C23×C4×C5—21no—
33C5×#121—42no—
34C5×#121—42no—
35C5×#121—42no—
36C5×#121—42no—
37C4×C5×D4—21no—
38C4×C5×D4—21no—
39C4×C5×D4—21no—
40C4×C5×D4—21no—
41C4×C5×D4—21no—
42C4×C5×D4—21no—
43C4×C5×D4—21no—
44C4×C5×D4—21no—
45C2×C5×C4⋊C4—21no—
46C2×C5×C4⋊C4—21no—
47C2×C5×C4⋊C4D411yescharacteristic
48C2×C5×C4⋊C4D411yescharacteristic
49C2×C5×C4⋊C4D412yes—
50C2×C5×C22⋊C4—22no—
51C2×C5×C22⋊C4—22no—
52C2×C5×C22⋊C4—21no—
53C2×C5×C22⋊C4—21no—
54C2×C42×C5C2311yescharacteristic
55C2×C4⋊Dic5—21no—
56C2×C4⋊Dic5—21no—
57C2×C4⋊Dic5—21no—
58C22×#168—21no—
59C22×#168—21no—
60C22×#168—21no—
61C5×#95—22no—
62#3964—42no—
63#3964—42no—
64C4⋊#168—21no—
65C4⋊#168—21no—
66C4⋊#168—21no—
67C4⋊#168—21no—
68C4×#168—21no—
69C4×#168D412yescomplemented
70#2537D511yescharacteristic
71#1834—51no—
72#1802—51no—
73#1802—51no—
74C2×D4⋊C8—51no—
75C2×D4⋊C8—51no—
76#1296—51no—
77C24×C5—21no—
78C24×C5—21no—
79C2×C5×D4—21no—
80C2×C5×D4—21no—
81C2×C5×D4—21no—
82C2×C5×D4—21no—
83C2×C5×D4—21no—
84C2×C5×D4—21no—
85C2×C5×D4—21no—
86C2×C5×D4—21no—
87C2×C5×D4—21no—
88C2×C5×D4—21no—
89C2×C5×D4—44no—
90C2×C5×D4—44no—
91C2×C5×D4—82no—
92C2×C5×D4D812yes—
93C2×C5×D4SD1612yes—
94C22×C4×C5—21no—
95C22×C4×C5—21no—
96C22×C4×C5—22no—
97C22×C4×C5—41no—
98C22×C4×C5—41no—
99C22×C4×C5—41no—
100C22×C4×C5—41no—
101C22×C4×C5—41no—
102C22×C4×C5—41no—
103C22×C4×C5—41no—
104C22×C4×C5—41no—
105C22×C4×C5—41no—
106C22×C4×C5—41no—
107C22×C4×C5—41no—
108C22×C4×C5—41no—
109C22×C4×C5C2×D411yescharacteristic
110C22×C4×C5C2×D411yescharacteristic
111C22×C4×C5C2×D411yescharacteristic
112C22×Dic5—41no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—42no—
118C5×C4⋊C4—41no—
119C5×C4⋊C4—41no—
120C5×C4⋊C4—41no—
121C5×C4⋊C4—41no—
122C5×C22⋊C4—44no—
123C5×C22⋊C4—44no—
124C5×C22⋊C4—41no—
125C5×C22⋊C4—41no—
126C5×C22⋊C4—41no—
127C5×C22⋊C4—41no—
128C42×C5C2×D411yescharacteristic
129C42×C5#4111yescharacteristic
130C42×C5#4111yescharacteristic
131C42×C5#4111yescharacteristic
132C4⋊Dic5—42no—
133C4⋊Dic5—41no—
134C4⋊Dic5—41no—
135C4⋊Dic5—41no—
136C4⋊Dic5—41no—
137C2×#168—22no—
138C2×#168—41no—
139C2×#168—41no—
140C2×#168—41no—
141C2×#168—41no—
142C2×#168—41no—
143C2×#168—41no—
144C2×#168—41no—
145C2×#168—41no—
146C2×#121—21no—
147C2×#121—21no—
148C2×C4×D4C2×D511yescharacteristic
149C2×C4×D4C2×D511yescharacteristic
150C2×C4⋊C8—51no—
151C2×C4⋊C8—51no—
152C2×#102—101no—
153C2×#102—101no—
154C2×C4×C8—51no—
155#394—22no—
156#384—51no—
157#384C2×D511yescharacteristic
158#380—21no—
159#380—21no—
160#340—101no—
161#340—101no—
162#340—102no—
163D4⋊C8—102no—
164D4⋊C8—102no—
165C23×C5—22no—
166C23×C5—22no—
167C23×C5—41no—
168C23×C5—41no—
169C23×C5—41no—
170C23×C5—41no—
171C23×C5—41no—
172C23×C5—41no—
173C23×C5—41no—
174C23×C5—41no—
175C23×C5—41no—
176C23×C5—41no—
177C23×C5—41no—
178C23×C5—41no—
179C23×C5#12011yescharacteristic
180C5×D4—22no—
181C5×D4—22no—
182C5×D4—22no—
183C5×D4—22no—
184C5×D4—41no—
185C5×D4—41no—
186C5×D4—41no—
187C5×D4—41no—
188C5×D4—88no—
189C2×C4×C5—21no—
190C2×C4×C5—21no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—42no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5—42no—
198C2×C4×C5—41no—
199C2×C4×C5—42no—
200C2×C4×C5—81no—
201C2×C4×C5—81no—
202C2×C4×C5—81no—
203C2×C4×C5—81no—
204C2×C4×C5—81no—
205C2×C4×C5—81no—
206C2×C4×C5—81no—
207C2×C4×C5—81no—
208C2×C4×C5#12111yescharacteristic
209C2×C4×C5#12111yescharacteristic
210C2×C4×C5#12111yescharacteristic
211C2×C4×C5#12311yescharacteristic
212C2×C4×C5#12311yescharacteristic
213C2×C4×C5#12411yescharacteristic
214C2×C4×C5C2×D811yescharacteristic
215C2×C4×C5C2×SD1611yescharacteristic
216C2×C4×C5#13511yescharacteristic
217C2×C4×C5#13511yescharacteristic
218C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
219C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
220C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
221C2×C4×C5#13711yescharacteristic
222C2×Dic5—81no—
223C2×Dic5—81no—
224C2×Dic5—81no—
225#168—42no—
226#168—81no—
227#168—81no—
228C22×D4—22no—
229C22×D4C22⋊D511yescharacteristic
230C22×D4C22⋊D511yescharacteristic
231C23×C4—21no—
232C23×C4—21no—
233C22×C8—101no—
234C22×C8—101no—
235C22×C8—101no—
236#121—42no—
237#121—42no—
238#121—42no—
239#121—42no—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4—21no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—21no—
247C4×D4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—101no—
251C2×C4⋊C4—101no—
252C2×C4⋊C4—101no—
253C2×C4⋊C4C22⋊D511yescharacteristic
254C2×C4⋊C4C22⋊D511yescharacteristic
255C2×C4⋊C4C22⋊D512yes—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C42C22×D511yescharacteristic
261C4⋊C8—101no—
262C4⋊C8—101no—
263C4⋊C8—101no—
264C4⋊C8—101no—
265#102—202no—
266#102—202no—
267C4×C8—52no—
268C4×C8—101no—
269#95—22no—
270C22×C5—42no—
271C22×C5—42no—
272C22×C5—42no—
273C22×C5—42no—
274C22×C5—42no—
275C22×C5—42no—
276C22×C5—81no—
277C22×C5—81no—
278C22×C5—81no—
279C22×C5—81no—
280C22×C5—81no—
281C22×C5—81no—
282C22×C5—81no—
283C22×C5—81no—
284C22×C5#39411yescharacteristic
285C22×C5#44711yescharacteristic
286C22×C5#44911yescharacteristic
287C22×C5#45011yescharacteristic
288C22×C5#45211yescharacteristic
289C22×C5#45411yescharacteristic
290C22×C5#45511yescharacteristic
291C4×C5—21no—
292C4×C5—21no—
293C4×C5—82no—
294C4×C5—81no—
295C4×C5—81no—
296C4×C5#46511yescharacteristic
297C4×C5#46611yescharacteristic
298C4×C5#46811yescharacteristic
299C4×C5#46911yescharacteristic
300C4×C5#48011yescharacteristic
301C4×C5#48111yescharacteristic
302C4×C5#48211yescharacteristic
303C4×C5#48211yescharacteristic
304Dic5—161no—
305C24—21no—
306C24—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—44no—
318C2×D4—44no—
319C2×D4—82no—
320C2×D4#68612yes—
321C2×D4#68712yes—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—201no—
338C22×C4C2×C22⋊D511yescharacteristic
339C22×C4C2×C22⋊D511yescharacteristic
340C22×C4C2×C22⋊D511yescharacteristic
341C2×C8—102no—
342C2×C8—201no—
343C2×C8—201no—
344C2×C8—201no—
345C2×C8—201no—
346C2×C8—201no—
347C2×C8—201no—
348C2×C8—201no—
349C2×C8—201no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—42no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—202no—
360C4⋊C4—201no—
361C4⋊C4—201no—
362C4⋊C4—201no—
363C4⋊C4—201no—
364C22⋊C4—44no—
365C22⋊C4—44no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C42D4×D511yescharacteristic
371C42#71111yescharacteristic
372C42#71111yescharacteristic
373C42#71111yescharacteristic
374C2×C5—82no—
375C2×C5—82no—
376C2×C5#162511yescharacteristic
377C2×C5#163511yescharacteristic
378C2×C5#163911yescharacteristic
379C2×C5#164611yescharacteristic
380C2×C5#203311yescharacteristic
381C2×C5#203411yescharacteristic
382C2×C5#204011yescharacteristic
383C23—22no—
384C23—22no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23#409911yescharacteristic
398D4—22no—
399D4—22no—
400D4—22no—
401D4—22no—
402D4—41no—
403D4—41no—
404D4—41no—
405D4—41no—
406D4—88no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—401no—
427C2×C4—401no—
428C2×C4—401no—
429C2×C4C2×#68611yescharacteristic
430C2×C4#407811yescharacteristic
431C2×C4#407811yescharacteristic
432C2×C4C2×#68711yescharacteristic
433C2×C4#408111yescharacteristic
434C2×C4#408111yescharacteristic
435C2×C4#408211yescharacteristic
436C2×C4#408411yescharacteristic
437C2×C4#408511yescharacteristic
438C2×C4#408511yescharacteristic
439C2×C4#409511yescharacteristic
440C2×C4#409611yescharacteristic
441C2×C4#409611yescharacteristic
442C2×C4#409711yescharacteristic
443C8—202no—
444C8—401no—
445C8—401no—
446C5#1043111yescharacteristic, complemented, Sylow
447C22—42no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22#6550611yescharacteristic
462C22#6550711yescharacteristic
463C22#6551111yescharacteristic
464C22#6552711yescharacteristic
465C22#6552811yescharacteristic
466C22#6553111yescharacteristic
467C22#6553411yescharacteristic
468C4—21no—
469C4—21no—
470C4—82no—
471C4—81no—
472C4—81no—
473C4—801no—
474C4#6532211yescharacteristic
475C4#6532311yescharacteristic
476C4#6532411yescharacteristic
477C4#6532411yescharacteristic
478C4#6532711yescharacteristic
479C4#6532811yescharacteristic
480C4#6533011yescharacteristic
481C4#6533111yescharacteristic
482C2—82no—
483C2—82no—
484C2#1060247211yescharacteristic
485C2#1060247311yescharacteristic
486C2#1060267011yescharacteristic
487C2#1060270111yescharacteristic
488C2#1060270311yescharacteristic
489C2#1060270411yescharacteristic
490C2#1060272211yescharacteristic
subgroupG/H
centerC23#4099
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
Fitting, prime radicalC5×#2537C2
socleC23×C5#120
hypercenter#2537D5
hypocenterC5#10431
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2537

Complements

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

NH ≅ G/Ntype
2. #10602397C2semidirect
3. #10602397C2semidirect
4. C2×D4⋊#168C2semidirect
5. C2×D4⋊#168C2semidirect
6. #10600367C2semidirect
7. #10598125C2semidirect
69. C4×#168D4semidirect
446. C5#10431semidirect

Maximal subgroups

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

subgroupindex
C5×#25372
#106023972
C2×D4⋊#1682
#106003672
#105981252
#104315