Finite Group Databasebeta

← #11989606

Subgroups — #11989606

Order 1280.

584 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#431C211yesmaximal, characteristic
2#10610769C211yesmaximal, characteristic
3#10605483C211yesmaximal, characteristic
4C5×#1303C211yesmaximal, characteristic, complemented
5#10598237C211yesmaximal, characteristic, complemented
6#10598206C211yesmaximal, characteristic, complemented
7#10598111C211yesmaximal, characteristic, complemented
8C2×C42×D5C2211yescharacteristic
9C5×#431C2211yescharacteristic
10C5×#423C2211yescharacteristic
11C4×C5×C4⋊C4C2211yescharacteristic
12#65415—21no—
13M16×Dic5—21no—
14#65276—21no—
15#65266—21no—
16C4×#685—21no—
17C4×C4⋊Dic5C2211yescharacteristic
18#65221—21no—
19#65214C2211yescharacteristic
20#65213C2211yescharacteristic
21#65124—21no—
22#65124C412yescomplemented
23#65122—21no—
24#65122C412yescomplemented
25#65122C412yescomplemented
26D5×C4⋊C8C412yescomplemented
27D5×C22⋊C8—21no—
28#65007—21no—
29#64974—21no—
30C4×C8×D5—21no—
31#64953C412yes—
32#64940C412yes—
33#8096—51nomaximal, Sylow
34C22×C4×D5C2×C411yescharacteristic
35C22×C4×D5D411yescharacteristic
36C22×C4×D5D411yescharacteristic
37C2×C5×M16—21no—
38C2×C5×C4⋊C4—21no—
39C2×C42×C5—21no—
40C2×C42×C5C2311yescharacteristic
41C2×#685—22no—
42C2×C4⋊Dic5—21no—
43C2×C4×Dic5—21no—
44C2×C4×Dic5C2×C411yescharacteristic
45C2×C4×Dic5D411yescharacteristic
46C2×C4×Dic5D411yescharacteristic
47C2×#681—21no—
48C2×C8×D5—22no—
49C42×D5C2×C411yescharacteristic
50C42×D5C2×C411yescharacteristic
51C42×D5C2×C411yescharacteristic
52C42×D5C2×C411yescharacteristic
53C42×D5D411yescharacteristic
54C42×D5D411yescharacteristic
55C42×D5Q811yescharacteristic
56C42×D5Q811yescharacteristic
57C5×C4⋊C8—21no—
58C5×C4⋊C8C2×C412yes—
59C5×C4⋊C8C2×C412yes—
60C5×C22⋊C8—21no—
61C4×C5×C8—21no—
62C5×#95C2×C412yes—
63#3963—22no—
64#3963—22no—
65#3963—22no—
66#3963C2×C412yes—
67C22⋊#168—21no—
68#3952—22no—
69#3952—22no—
70#3952—22no—
71#3947—22no—
72#3946—22no—
73C8×Dic5—22no—
74C8×Dic5—22no—
75C4⋊#168—21no—
76C4⋊#168C2×C412yes—
77C4⋊#168C2×C412yes—
78C4×#168—21no—
79#2920—51no—
80C2×#431—51no—
81#2283—51no—
82#1303—51no—
83#1303—51no—
84#1303—51no—
85#1303D511yescharacteristic, complemented
86C23×D5C22⋊C411yescharacteristic
87C22×C4×C5—22no—
88C22×C4×C5C22×C411yescharacteristic
89C22×C4×C5C2×D411yescharacteristic
90C22×C4×C5C2×D411yescharacteristic
91C22×Dic5—22no—
92C22×Dic5C22⋊C411yescharacteristic
93C22×Dic5C22⋊C411yescharacteristic
94C22×Dic5C22⋊C411yescharacteristic
95C2×C4×D5—21no—
96C2×C4×D5—21no—
97C2×C4×D5—21no—
98C2×C4×D5—21no—
99C2×C4×D5—42no—
100C2×C4×D5—42no—
101C2×C4×D5C4211yescharacteristic
102C2×C4×D5C4211yescharacteristic
103C2×C4×D5C22⋊C411yescharacteristic
104C2×C4×D5C22⋊C411yescharacteristic
105C2×C4×D5C22⋊C411yescharacteristic
106C2×C4×D5C22⋊C411yescharacteristic
107C2×C4×D5C4⋊C411yescharacteristic
108C2×C4×D5C4⋊C411yescharacteristic
109C2×C4×D5C4⋊C411yescharacteristic
110C2×C4×D5C4⋊C411yescharacteristic
111C2×C4×D5C4⋊C411yescharacteristic
112C2×C4×D5C4⋊C411yescharacteristic
113C5×M16—41no—
114C5×M16—41no—
115C2×C5×C8—22no—
116C2×C5×C8—22no—
117C5×C4⋊C4—42no—
118C42×C5—41no—
119C42×C5—41no—
120C42×C5C22×C411yescharacteristic
121C42×C5C22×C411yescharacteristic
122C42×C5C2×D411yescharacteristic
123C42×C5C2×Q811yescharacteristic
124#685—44no—
125C4⋊Dic5—42no—
126C4×Dic5—41no—
127C4×Dic5—41no—
128C4×Dic5C4211yescharacteristic
129C4×Dic5C4211yescharacteristic
130C4×Dic5C22⋊C411yescharacteristic
131C4×Dic5C22⋊C411yescharacteristic
132C4×Dic5C22⋊C411yescharacteristic
133C4×Dic5C22⋊C411yescharacteristic
134C4×Dic5C4⋊C411yescharacteristic
135C4×Dic5C4⋊C411yescharacteristic
136C4×Dic5C4⋊C411yescharacteristic
137C4×Dic5C4⋊C411yescharacteristic
138C4×Dic5C4⋊C411yescharacteristic
139C4×Dic5C4⋊C411yescharacteristic
140#681—41no—
141#681—41no—
142C2×#168—22no—
143C2×#168—22no—
144C8×D5—44no—
145C22×C42—51no—
146#432—52no—
147#432—101no—
148#431—51no—
149#431—52no—
150#431—52no—
151#431—101no—
152#431—101no—
153#431—101no—
154#431C2×D511yescharacteristic
155#423—51no—
156#423C2×D511yescharacteristic
157C2×C4⋊C8—52no—
158#407—101no—
159C2×C22⋊C8—101no—
160C4×M16—101no—
161C2×C4×C8—101no—
162#383—52no—
163#382—101no—
164#381—52no—
165#380—101no—
166C4×C4⋊C4—51no—
167C4×C4⋊C4C2×D511yescharacteristic
168C4×C22⋊C4—101no—
169#376—101no—
170C23×C5C2×C22⋊C411yescharacteristic
171C22×D5—21no—
172C22×D5—21no—
173C22×D5—22no—
174C22×D5—41no—
175C22×D5#9511yescharacteristic
176C22×D5#9511yescharacteristic
177C2×C4×C5—22no—
178C2×C4×C5—41no—
179C2×C4×C5—42no—
180C2×C4×C5—42no—
181C2×C4×C5—42no—
182C2×C4×C5C2×C4211yescharacteristic
183C2×C4×C5C2×C22⋊C411yescharacteristic
184C2×C4×C5C2×C22⋊C411yescharacteristic
185C2×C4×C5C2×C4⋊C411yescharacteristic
186C2×C4×C5C2×C4⋊C411yescharacteristic
187C2×C4×C5C2×C4⋊C411yescharacteristic
188C2×C4×C5#13511yescharacteristic
189C2×C4×C5#13511yescharacteristic
190C2×C4×C5#13511yescharacteristic
191C2×C4×C5#13511yescharacteristic
192C2×Dic5—21no—
193C2×Dic5—21no—
194C2×Dic5—41no—
195C2×Dic5—41no—
196C2×Dic5—42no—
197C2×Dic5—42no—
198C2×Dic5—42no—
199C2×Dic5#9511yescharacteristic
200C2×Dic5#9511yescharacteristic
201C2×Dic5#9511yescharacteristic
202C2×Dic5#9511yescharacteristic
203C2×Dic5#9511yescharacteristic
204C2×Dic5#9511yescharacteristic
205C4×D5—22no—
206C4×D5—22no—
207C4×D5—21no—
208C4×D5—21no—
209C4×D5—21no—
210C4×D5—21no—
211C4×D5—22no—
212C4×D5—22no—
213C4×D5—21no—
214C4×D5—21no—
215C4×D5—21no—
216C4×D5—21no—
217C4×D5—41no—
218C4×D5—41no—
219C4×D5—41no—
220C4×D5—41no—
221C5×C8—42no—
222C5×C8—42no—
223#168—42no—
224#168—42no—
225C23×C4—51no—
226C23×C4—51no—
227C23×C4—51no—
228C2×M16—21no—
229C2×M16—101no—
230C22×C8—102no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—101no—
233C2×C22⋊C4—102no—
234C2×C42—21no—
235C2×C42—51no—
236C2×C42—51no—
237C2×C42—51no—
238C2×C42—51no—
239C2×C42—51no—
240C2×C42—51no—
241C2×C42—51no—
242C2×C42—51no—
243C2×C42—51no—
244C2×C42—51no—
245C2×C42—51no—
246C2×C42—101no—
247C2×C42C22×D511yescharacteristic
248C4⋊C8—21no—
249C4⋊C8—52no—
250C4⋊C8—52no—
251C4⋊C8—102no—
252C4⋊C8—101no—
253C4⋊C8C4×D512yes—
254C4⋊C8C4×D512yes—
255C22⋊C8—21no—
256C22⋊C8—102no—
257C22⋊C8—102no—
258C22⋊C8—102no—
259C22⋊C8—101no—
260#97—102no—
261C4×C8—21no—
262C4×C8—102no—
263C4×C8—102no—
264C4×C8—101no—
265#95—52no—
266#95—102no—
267#95—102no—
268#95—102no—
269#95C4×D512yes—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5C2×#9511yescharacteristic
273C22×C5#41611yescharacteristic
274C22×C5#41611yescharacteristic
275C2×D5—21no—
276C2×D5—21no—
277C2×D5—21no—
278C2×D5—21no—
279C2×D5—21no—
280C2×D5—42no—
281C2×D5—42no—
282C2×D5#34412yes—
283C4×C5—21no—
284C4×C5—21no—
285C4×C5—21no—
286C4×C5—82no—
287C4×C5#41611yescharacteristic
288C4×C5#41611yescharacteristic
289C4×C5#42112yes—
290C4×C5#42711yescharacteristic
291C4×C5#42711yescharacteristic
292Dic5—21no—
293Dic5—21no—
294Dic5—21no—
295Dic5—21no—
296Dic5—21no—
297Dic5—21no—
298Dic5—82no—
299C24—51no—
300C22×C4—22no—
301C22×C4—51no—
302C22×C4—51no—
303C22×C4—51no—
304C22×C4—51no—
305C22×C4—51no—
306C22×C4—51no—
307C22×C4—51no—
308C22×C4—51no—
309C22×C4—51no—
310C22×C4—51no—
311C22×C4—51no—
312C22×C4—51no—
313C22×C4—51no—
314C22×C4—51no—
315C22×C4—51no—
316C22×C4—101no—
317C22×C4—101no—
318C22×C4—101no—
319C22×C4—101no—
320C22×C4—102no—
321C22×C4—202no—
322C22×C4—202no—
323C22×C4C2×C4×D511yescharacteristic
324C22×C4D4×D511yescharacteristic
325C22×C4D4×D511yescharacteristic
326M16—41no—
327M16—41no—
328M16—201no—
329M16—201no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—102no—
333C2×C8—102no—
334C2×C8—204no—
335C4⋊C4—42no—
336C4⋊C4—202no—
337C22⋊C4—204no—
338C42—41no—
339C42—41no—
340C42—51no—
341C42—51no—
342C42—51no—
343C42—51no—
344C42—51no—
345C42—51no—
346C42—51no—
347C42—51no—
348C42—51no—
349C42—51no—
350C42—51no—
351C42—51no—
352C42—201no—
353C42—201no—
354C42C2×C4×D511yescharacteristic
355C42C2×C4×D511yescharacteristic
356C42D4×D511yescharacteristic
357C42Q8×D511yescharacteristic
358C2×C5—21no—
359C2×C5—21no—
360C2×C5#173311yescharacteristic
361C2×C5#173511yescharacteristic
362C2×C5C2×#34411yescharacteristic
363D5—22no—
364D5—41no—
365C23—51no—
366C23—51no—
367C23—102no—
368C23—101no—
369C23—101no—
370C23—201no—
371C23D5×C22⋊C411yescharacteristic
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—51no—
378C2×C4—51no—
379C2×C4—51no—
380C2×C4—51no—
381C2×C4—51no—
382C2×C4—51no—
383C2×C4—102no—
384C2×C4—102no—
385C2×C4—101no—
386C2×C4—101no—
387C2×C4—101no—
388C2×C4—101no—
389C2×C4—101no—
390C2×C4—101no—
391C2×C4—102no—
392C2×C4—102no—
393C2×C4—101no—
394C2×C4—101no—
395C2×C4—101no—
396C2×C4—101no—
397C2×C4—201no—
398C2×C4—201no—
399C2×C4—201no—
400C2×C4—201no—
401C2×C4—201no—
402C2×C4—201no—
403C2×C4—202no—
404C2×C4—202no—
405C2×C4—202no—
406C2×C4C42×D511yescharacteristic
407C2×C4D5×C22⋊C411yescharacteristic
408C2×C4D5×C22⋊C411yescharacteristic
409C2×C4D5×C4⋊C411yescharacteristic
410C2×C4D5×C4⋊C411yescharacteristic
411C2×C4D5×C4⋊C411yescharacteristic
412C2×C4#405811yescharacteristic
413C2×C4#406211yescharacteristic
414C2×C4#406211yescharacteristic
415C2×C4#406511yescharacteristic
416C8—42no—
417C8—42no—
418C8—202no—
419C8—202no—
420C5#809611yescharacteristic, complemented, Sylow
421C22—21no—
422C22—21no—
423C22—52no—
424C22—101no—
425C22—101no—
426C22—101no—
427C22—101no—
428C22—101no—
429C22—202no—
430C22—202no—
431C22D5×#9511yescharacteristic
432C22#6506111yescharacteristic
433C22#6509311yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—82no—
438C4—101no—
439C4—101no—
440C4—101no—
441C4—101no—
442C4—101no—
443C4—101no—
444C4—402no—
445C4#6506111yescharacteristic
446C4#6509311yescharacteristic
447C4#6511012yes—
448C4#6514911yescharacteristic
449C4#6516911yescharacteristic
450C2—21no—
451C2—21no—
452C2—102no—
453C2—201no—
454C2#1059954611yescharacteristic
455C2#1059965911yescharacteristic
456C2D5×#34411yescharacteristic
subgroupG/H
centerC2×C4D5×C22⋊C4
commutatorC2×C4×C5C2×C42
FrattiniC2×C42C22×D5
FittingC5×#1303C2
socleC22×C5C2×#95
prime radicalC23×D5C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1303D5
hypocenterC5#8096
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
4. C5×#1303C2semidirect
5. #10598237C2semidirect
6. #10598206C2semidirect
7. #10598111C2semidirect
22. #65124C4semidirect
24. #65122C4semidirect
25. #65122C4semidirect
26. D5×C4⋊C8C4semidirect
85. #1303D5semidirect
420. C5#8096semidirect

Maximal subgroups

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

subgroupindex
D5×#4312
#106107692
#106054832
C5×#13032
#105982372
#105982062
#105981112
#80965