Finite Group Databasebeta

← #11995526

Subgroups — #11995526

Order 1280.

562 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65376C211yesmaximal, characteristic
2C2×#64977C211yesmaximal, characteristic
3C5×#1956C211yesmaximal, characteristic, complemented
4C2×#64767C211yesmaximal, characteristic, complemented
5#10600377C211yesmaximal, characteristic
6#10598145C211yesmaximal, characteristic, complemented
7#10598125C211yesmaximal, characteristic, complemented
8C2×C5×C4⋊Q8C2211yescharacteristic
9C22×#676—21no—
10C2×C4×D20C2211yescharacteristic
11C2×C5×#103—21no—
12C2×C5×#103—21no—
13C2×C4×C5×C8C2211yescharacteristic
14C5×#384C2211yescharacteristic
15C2×#3952—21no—
16#65376—22no—
17#65376C414yescomplemented
18C2×#3941—21no—
19C2×#3941—21no—
20C2×#3939—21no—
21C2×C4⋊#168C2211yescharacteristic
22C2×C4⋊#168C2211yescharacteristic
23C2×C4⋊#168C2211yescharacteristic
24#64977—22no—
25#64977—22no—
26#64767—22no—
27#64749—21no—
28#9227—51nomaximal, Sylow
29C22×C5×Q8—21no—
30C22×D20D411yescharacteristic
31C22×C4×D5—21no—
32C22×C5×C8D411yescharacteristic
33C22×C5×C8D411yescharacteristic
34C5×C4⋊Q8—21no—
35C5×C4⋊Q8—21no—
36C5×C4⋊Q8—21no—
37C5×C4⋊Q8C2×C412yes—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4—21no—
40C2×C5×C4⋊C4—21no—
41C2×C5×C4⋊C4—21no—
42C2×C5×C4⋊C4—21no—
43C2×C42×C5C2311yescharacteristic
44C2×#685—21no—
45C2×C4⋊Dic5D411yescharacteristic
46C22×#168—21no—
47C22×#168—21no—
48C22×#168—21no—
49C2×#676—24no—
50C2×#676—42no—
51C2×#676—42no—
52C4×D20—21no—
53C4×D20—21no—
54C4×D20C2×C412yes—
55C4×D20D412yes—
56C5×#103—42no—
57C5×#103—42no—
58C4×C5×C8—21no—
59C4×C5×C8—21no—
60#3952—24no—
61#3941—24no—
62#3941—42no—
63#3939—24no—
64C4⋊#168—21no—
65C4⋊#168—21no—
66C4⋊#168—21no—
67C4⋊#168—21no—
68C4⋊#168C2×C412yes—
69C4⋊#168D412yes—
70C2×#474—51no—
71C2×#436—51no—
72#1956D511yescharacteristic, complemented
73#1802—51no—
74C2×#332—51no—
75#1296—51no—
76#1277—51no—
77C23×D5—21no—
78C2×C5×Q8—22no—
79C2×C5×Q8—41no—
80C2×C5×Q8—41no—
81C2×C5×Q8—41no—
82C2×C5×Q8—41no—
83C2×C5×Q8—41no—
84C22×C4×C5—41no—
85C22×C4×C5—41no—
86C22×C4×C5C2×D411yescharacteristic
87C22×C4×C5C2×D411yescharacteristic
88C22×C4×C5#4111yescharacteristic
89C22×Dic5—21no—
90C2×D20—21no—
91C2×D20—21no—
92C2×D20—21no—
93C2×D20—21no—
94C2×D20—21no—
95C2×D20C22⋊C412yes—
96C2×C4×D5—22no—
97C2×C4×D5—22no—
98C2×C4×D5—41no—
99C2×C4×D5—41no—
100C2×C4×D5—41no—
101C2×C4×D5—41no—
102C2×C5×C8—21no—
103C2×C5×C8—21no—
104C2×C5×C8—21no—
105C2×C5×C8—21no—
106C2×C5×C8—21no—
107C2×C5×C8D812yes—
108C5×C4⋊C4—22no—
109C5×C4⋊C4—22no—
110C5×C4⋊C4—41no—
111C5×C4⋊C4—41no—
112C5×C4⋊C4—41no—
113C5×C4⋊C4—41no—
114C5×C4⋊C4—41no—
115C5×C4⋊C4—41no—
116C5×C4⋊C4—81no—
117C42×C5C22×C411yescharacteristic
118C42×C5C2×D411yescharacteristic
119C42×C5C2×D411yescharacteristic
120C42×C5#4111yescharacteristic
121#685—22no—
122#685—22no—
123C4⋊Dic5—21no—
124C4⋊Dic5C22⋊C412yes—
125C2×#168—22no—
126C2×#168—22no—
127C2×#168—41no—
128C2×#168—41no—
129C2×#168—41no—
130C2×#168—41no—
131C2×#168—41no—
132C2×#168—41no—
133C2×#168—41no—
134#676—48no—
135C22×M16—101no—
136C2×C4⋊Q8C2×D511yescharacteristic
137C2×C4×D4—51no—
138#474—54no—
139#474—102no—
140#436—102no—
141#436—102no—
142C2×#107—101no—
143C2×C4⋊C8—51no—
144C2×C4⋊C8—51no—
145C2×C4⋊C8—51no—
146C2×#103—21no—
147C2×#103—21no—
148C2×#102—101no—
149C2×#102—101no—
150C2×C22⋊C8—101no—
151C2×C4×C8C2×D511yescharacteristic
152#384C2×D511yescharacteristic
153#340—101no—
154#332—102no—
155C23×C5#12111yescharacteristic
156C22×D5—22no—
157C22×D5—41no—
158C22×D5—41no—
159C22×D5—41no—
160C22×D5—41no—
161C22×D5—41no—
162C22×D5—41no—
163C5×Q8—42no—
164C5×Q8—42no—
165C5×Q8—81no—
166C5×Q8—81no—
167C2×C4×C5—21no—
168C2×C4×C5—21no—
169C2×C4×C5—42no—
170C2×C4×C5—81no—
171C2×C4×C5—81no—
172C2×C4×C5—81no—
173C2×C4×C5—81no—
174C2×C4×C5—81no—
175C2×C4×C5C2×C22⋊C411yescharacteristic
176C2×C4×C5C4×D411yescharacteristic
177C2×C4×C5C4×D411yescharacteristic
178C2×C4×C5#12011yescharacteristic
179C2×C4×C5#12111yescharacteristic
180C2×C4×C5#12311yescharacteristic
181C2×C4×C5C2×D811yescharacteristic
182C2×C4×C5#13511yescharacteristic
183C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C5#13711yescharacteristic
187C2×C4×C5#13711yescharacteristic
188C2×C4×C5#13711yescharacteristic
189C2×Dic5—22no—
190C2×Dic5—41no—
191C2×Dic5—41no—
192D20—22no—
193D20—22no—
194D20—41no—
195D20—41no—
196C4×D5—42no—
197C4×D5—42no—
198C4×D5—42no—
199C4×D5—42no—
200C5×C8—22no—
201C5×C8—41no—
202#168—42no—
203#168—42no—
204#168—81no—
205C22×Q8—21no—
206C22×D4—51no—
207C23×C4—101no—
208C2×M16—104no—
209C2×M16—202no—
210C2×M16—202no—
211C22×C8—101no—
212C22×C8—101no—
213C22×C8—101no—
214C22×C8C22⋊D511yescharacteristic
215C22×C8C22⋊D511yescharacteristic
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8C4×D512yes—
220C4×D4—52no—
221C4×D4—52no—
222C4×D4—101no—
223C4×D4—101no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—51no—
230C2×C22⋊C4—101no—
231C2×C42C22×D511yescharacteristic
232#107—104no—
233C4⋊C8—52no—
234C4⋊C8—52no—
235C4⋊C8—101no—
236C4⋊C8—101no—
237C4⋊C8—101no—
238C4⋊C8—101no—
239#103—42no—
240#103—42no—
241#102—104no—
242#102—202no—
243C22⋊C8—104no—
244C4×C8—21no—
245C4×C8—21no—
246C22×C5#38611yescharacteristic
247C22×C5#45911yescharacteristic
248C22×C5#46311yescharacteristic
249C22×C5#46811yescharacteristic
250C22×C5#47011yescharacteristic
251C22×C5#47111yescharacteristic
252C22×C5#47311yescharacteristic
253C2×D5—42no—
254C2×D5—42no—
255C2×D5—42no—
256C2×D5—81no—
257C2×D5—81no—
258C2×D5—81no—
259C2×D5—81no—
260C4×C5—21no—
261C4×C5—21no—
262C4×C5—82no—
263C4×C5—161no—
264C4×C5#41711yescharacteristic
265C4×C5#41911yescharacteristic
266C4×C5C4×D811yescharacteristic
267C4×C5#44211yescharacteristic
268C4×C5#44711yescharacteristic
269C4×C5#44911yescharacteristic
270C4×C5#46811yescharacteristic
271C4×C5#47011yescharacteristic
272Dic5—42no—
273C24—101no—
274C2×Q8—22no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×D4—52no—
281C2×D4—101no—
282C2×D4—101no—
283C2×D4—101no—
284C2×D4—101no—
285C2×D4—101no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—101no—
289C22×C4—102no—
290C22×C4—102no—
291C22×C4—201no—
292C22×C4—201no—
293C22×C4—201no—
294C22×C4—201no—
295C22×C4D4×D511yescharacteristic
296C22×C4#71111yescharacteristic
297C22×C4C2×C22⋊D511yescharacteristic
298M16—208no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—102no—
305C2×C8—102no—
306C2×C8—201no—
307C2×C8—201no—
308C2×C8—201no—
309C2×C8—201no—
310C2×C8—201no—
311C2×C8—201no—
312C2×C8—201no—
313C2×C8#68612yes—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—52no—
323C4⋊C4—81no—
324C4⋊C4—101no—
325C22⋊C4—102no—
326C22⋊C4—102no—
327C42C2×C4×D511yescharacteristic
328C42#70911yescharacteristic
329C42D4×D511yescharacteristic
330C42D4×D511yescharacteristic
331C2×C5#168511yescharacteristic
332C2×C5#168911yescharacteristic
333C2×C5#169911yescharacteristic
334C2×C5#170311yescharacteristic
335C2×C5#187911yescharacteristic
336C2×C5#189411yescharacteristic
337C2×C5#190811yescharacteristic
338D5—82no—
339C23—102no—
340C23—201no—
341C23—201no—
342C23—201no—
343C23—201no—
344C23—201no—
345C23—201no—
346C23#408411yescharacteristic
347Q8—42no—
348Q8—42no—
349Q8—81no—
350Q8—81no—
351D4—102no—
352D4—102no—
353D4—201no—
354D4—201no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—102no—
364C2×C4—201no—
365C2×C4—201no—
366C2×C4—202no—
367C2×C4—202no—
368C2×C4—202no—
369C2×C4—202no—
370C2×C4D5×C22⋊C411yescharacteristic
371C2×C4#402711yescharacteristic
372C2×C4#402911yescharacteristic
373C2×C4#403011yescharacteristic
374C2×C4#406011yescharacteristic
375C2×C4#406111yescharacteristic
376C2×C4#406411yescharacteristic
377C2×C4#406411yescharacteristic
378C2×C4C4×C22⋊D511yescharacteristic
379C2×C4C2×#68611yescharacteristic
380C2×C4#407811yescharacteristic
381C2×C4#408311yescharacteristic
382C2×C4#409511yescharacteristic
383C2×C4#409611yescharacteristic
384C8—22no—
385C8—41no—
386C8—202no—
387C8—202no—
388C8—401no—
389C5#922711yescharacteristic, complemented, Sylow
390C22—202no—
391C22—202no—
392C22—202no—
393C22—401no—
394C22—401no—
395C22—401no—
396C22—401no—
397C22#6524511yescharacteristic
398C22#6534611yescharacteristic
399C22#6536111yescharacteristic
400C22#6546311yescharacteristic
401C22#6546611yescharacteristic
402C22#6547811yescharacteristic
403C22#6548111yescharacteristic
404C4—21no—
405C4—21no—
406C4—82no—
407C4—161no—
408C4—202no—
409C4#6509111yescharacteristic
410C4#6509211yescharacteristic
411C4#6510111yescharacteristic
412C4#6510511yescharacteristic
413C4C4×#68611yescharacteristic
414C4#6530311yescharacteristic
415C4#6532511yescharacteristic
416C4#6532611yescharacteristic
417C2—402no—
418C2#1060045011yescharacteristic
419C2#1060106411yescharacteristic
420C2#1060107911yescharacteristic
421C2#1060202711yescharacteristic
422C2#1060202811yescharacteristic
423C2#1060206111yescharacteristic
424C2#1060209911yescharacteristic
subgroupG/H
centerC23#4084
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1956C2
socleC23×C5#121
prime radicalC22×D20D4
cosocleC2×C42×C5C23
hypercenter#1956D5
hypocenterC5#9227
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
3. C5×#1956C2semidirect
4. C2×#64767C2semidirect
6. #10598145C2semidirect
7. #10598125C2semidirect
17. #65376C4semidirect
72. #1956D5semidirect
389. C5#9227semidirect

Maximal subgroups

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

subgroupindex
C2×#653762
C2×#649772
C5×#19562
C2×#647672
#106003772
#105981452
#105981252
#92275