Finite Group Databasebeta

← #11989683

Subgroups — #11989683

Order 1280.

522 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611062C211yesmaximal, characteristic
2D5×#432C211yesmaximal, characteristic
3#10610769C211yesmaximal, characteristic
4C5×#1307C211yesmaximal, characteristic, complemented
5#10598249C211yesmaximal, characteristic, complemented
6#10598249C211yesmaximal, characteristic, complemented
7#10598207C211yesmaximal, characteristic, complemented
8C2×C42×D5C2211yescharacteristic
9C5×#432C2211yescharacteristic
10C5×#432C2211yescharacteristic
11C5×#423C2211yescharacteristic
12#65415C412yes—
13M16×Dic5C412yes—
14#65215C2211yescharacteristic
15#65215C2211yescharacteristic
16#65213C2211yescharacteristic
17#65126—21no—
18#65124—21no—
19#65124—21no—
20#65124—21no—
21#65122—21no—
22#65122—21no—
23#65122—21no—
24D5×C4⋊C8—21no—
25#65015C412yes—
26D5×C22⋊C8C412yes—
27#65008C412yes—
28#65007C412yes—
29#64996—21no—
30#64994—21no—
31#64994—21no—
32D5×#97—21no—
33#8118—51nomaximal, Sylow
34C22×C4×D5C2×C411yescharacteristic
35C22×C4×D5C2×C411yescharacteristic
36C22×C4×D5C2×C411yescharacteristic
37C2×C5×M16C2×C412yes—
38C2×C42×C5C2311yescharacteristic
39C2×C4×Dic5C2×C411yescharacteristic
40C2×C4×Dic5C2×C411yescharacteristic
41C2×C4×Dic5C2×C411yescharacteristic
42C2×#681C2×C412yes—
43C2×#676—22no—
44C2×C8×D5—22no—
45C42×D5D411yescharacteristic
46C42×D5D411yescharacteristic
47C42×D5D411yescharacteristic
48C42×D5D411yescharacteristic
49C42×D5D411yescharacteristic
50C42×D5D411yescharacteristic
51C42×D5Q811yescharacteristic
52C42×D5Q811yescharacteristic
53C5×C4⋊C8—21no—
54C5×C4⋊C8—21no—
55C5×C4⋊C8—21no—
56C5×C4⋊C8—21no—
57C5×C22⋊C8C2×C412yes—
58C5×C22⋊C8C2×C412yes—
59C5×#97—21no—
60C5×#97—21no—
61C22⋊#168C2×C412yes—
62C22⋊#168C2×C412yes—
63#3952—22no—
64#3952—22no—
65#3952—22no—
66#3952—22no—
67#3947—22no—
68#3947—22no—
69#3946—22no—
70#3946—22no—
71C8×Dic5—22no—
72C8×Dic5—22no—
73C4⋊#168—21no—
74C4⋊#168—21no—
75C4⋊#168—21no—
76C4⋊#168—21no—
77#3935—21no—
78#3935—21no—
79#2920—51no—
80#2920—51no—
81C2×#432—51no—
82#1307—51no—
83#1307—51no—
84#1307—51no—
85#1307D511yescharacteristic, complemented
86C23×D5C4211yescharacteristic
87C22×C4×C5C22×C411yescharacteristic
88C22×C4×C5C22×C411yescharacteristic
89C22×C4×C5C22×C411yescharacteristic
90C22×Dic5C4211yescharacteristic
91C22×Dic5C4211yescharacteristic
92C22×Dic5C4211yescharacteristic
93C2×C4×D5—42no—
94C2×C4×D5—41no—
95C2×C4×D5—41no—
96C2×C4×D5—42no—
97C2×C4×D5C22⋊C411yescharacteristic
98C2×C4×D5C22⋊C411yescharacteristic
99C2×C4×D5C22⋊C411yescharacteristic
100C2×C4×D5C22⋊C411yescharacteristic
101C2×C4×D5C22⋊C411yescharacteristic
102C2×C4×D5C22⋊C411yescharacteristic
103C2×C4×D5C4⋊C411yescharacteristic
104C2×C4×D5C4⋊C411yescharacteristic
105C2×C4×D5C4⋊C411yescharacteristic
106C2×C4×D5C4⋊C411yescharacteristic
107C2×C4×D5C4⋊C411yescharacteristic
108C2×C4×D5C4⋊C411yescharacteristic
109C5×M16—42no—
110C2×C5×C8—22no—
111C2×C5×C8—22no—
112C2×C5×C8—22no—
113C42×C5C2×D411yescharacteristic
114C42×C5C2×D411yescharacteristic
115C42×C5C2×D411yescharacteristic
116C42×C5C2×Q811yescharacteristic
117C4×Dic5C22⋊C411yescharacteristic
118C4×Dic5C22⋊C411yescharacteristic
119C4×Dic5C22⋊C411yescharacteristic
120C4×Dic5C22⋊C411yescharacteristic
121C4×Dic5C22⋊C411yescharacteristic
122C4×Dic5C22⋊C411yescharacteristic
123C4×Dic5C4⋊C411yescharacteristic
124C4×Dic5C4⋊C411yescharacteristic
125C4×Dic5C4⋊C411yescharacteristic
126C4×Dic5C4⋊C411yescharacteristic
127C4×Dic5C4⋊C411yescharacteristic
128C4×Dic5C4⋊C411yescharacteristic
129#681—42no—
130C2×#168—22no—
131C2×#168—22no—
132C2×#168—22no—
133#676—44no—
134C8×D5—44no—
135C22×C42—51no—
136#432—51no—
137#432—51no—
138#432—52no—
139#432—101no—
140#432—101no—
141#432—101no—
142#432—101no—
143#432—101no—
144#432C2×D511yescharacteristic
145#432C2×D511yescharacteristic
146#431—52no—
147#431—101no—
148#431—101no—
149#431—101no—
150#423—51no—
151#423—101no—
152#423C2×D511yescharacteristic
153C2×C4⋊C8—101no—
154#407—52no—
155#407—52no—
156C2×C22⋊C8—52no—
157C4×M16—52no—
158C4×M16—101no—
159C2×#97—101no—
160C23×C5C2×C4211yescharacteristic
161C22×D5—22no—
162C22×D5—41no—
163C22×D5—41no—
164C22×D5#9511yescharacteristic
165C22×D5#9511yescharacteristic
166C2×C4×C5—21no—
167C2×C4×C5—21no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5C2×C22⋊C411yescharacteristic
171C2×C4×C5C2×C22⋊C411yescharacteristic
172C2×C4×C5C2×C22⋊C411yescharacteristic
173C2×C4×C5C2×C4⋊C411yescharacteristic
174C2×C4×C5C2×C4⋊C411yescharacteristic
175C2×C4×C5C2×C4⋊C411yescharacteristic
176C2×Dic5—22no—
177C2×Dic5—41no—
178C2×Dic5—41no—
179C2×Dic5#9511yescharacteristic
180C2×Dic5#9511yescharacteristic
181C2×Dic5#9511yescharacteristic
182C2×Dic5#9511yescharacteristic
183C2×Dic5#9511yescharacteristic
184C2×Dic5#9511yescharacteristic
185C4×D5—22no—
186C4×D5—22no—
187C4×D5—21no—
188C4×D5—21no—
189C4×D5—21no—
190C4×D5—21no—
191C4×D5—22no—
192C4×D5—22no—
193C4×D5—41no—
194C4×D5—41no—
195C4×D5—41no—
196C4×D5—41no—
197C4×D5—41no—
198C4×D5—41no—
199C5×C8—42no—
200C5×C8—42no—
201C5×C8—42no—
202#168—42no—
203#168—42no—
204#168—42no—
205C23×C4—51no—
206C23×C4—51no—
207C23×C4—51no—
208C2×M16—52no—
209C2×M16—102no—
210C2×M16C4×D512yes—
211C22×C8—102no—
212C2×C42—51no—
213C2×C42—51no—
214C2×C42—51no—
215C2×C42—51no—
216C2×C42—51no—
217C2×C42—51no—
218C2×C42—51no—
219C2×C42—51no—
220C2×C42—51no—
221C2×C42—51no—
222C2×C42—51no—
223C2×C42C22×D511yescharacteristic
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—102no—
229C4⋊C8—102no—
230C4⋊C8—101no—
231C4⋊C8—101no—
232C4⋊C8—101no—
233C4⋊C8—101no—
234C22⋊C8—52no—
235C22⋊C8—52no—
236C22⋊C8—102no—
237C22⋊C8—102no—
238C22⋊C8—102no—
239C22⋊C8—102no—
240C22⋊C8C4×D512yes—
241C22⋊C8C4×D512yes—
242#97—21no—
243#97—21no—
244#97—102no—
245#97—102no—
246#97—101no—
247#97—101no—
248C4×C8—102no—
249C4×C8—102no—
250C22×C5—21no—
251C22×C5—21no—
252C22×C5—21no—
253C22×C5C2×#9511yescharacteristic
254C2×D5—21no—
255C2×D5—21no—
256C2×D5—21no—
257C2×D5—21no—
258C2×D5—21no—
259C2×D5—44no—
260C2×D5#34412yes—
261C4×C5—21no—
262C4×C5—21no—
263C4×C5—21no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5#41311yescharacteristic
267C4×C5#41311yescharacteristic
268Dic5—21no—
269Dic5—21no—
270Dic5—21no—
271Dic5—21no—
272Dic5—21no—
273Dic5#34412yes—
274C24—51no—
275C22×C4—51no—
276C22×C4—51no—
277C22×C4—51no—
278C22×C4—51no—
279C22×C4—51no—
280C22×C4—51no—
281C22×C4—51no—
282C22×C4—51no—
283C22×C4—51no—
284C22×C4—51no—
285C22×C4—51no—
286C22×C4—51no—
287C22×C4—51no—
288C22×C4—51no—
289C22×C4—51no—
290C22×C4—201no—
291C22×C4—201no—
292C22×C4—202no—
293C22×C4—202no—
294C22×C4C2×C4×D511yescharacteristic
295C22×C4C2×C4×D511yescharacteristic
296C22×C4C2×C4×D511yescharacteristic
297M16—42no—
298M16—204no—
299M16—202no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—102no—
304C2×C8—102no—
305C2×C8—102no—
306C2×C8—204no—
307C42—51no—
308C42—51no—
309C42—51no—
310C42—51no—
311C42—51no—
312C42—51no—
313C42—51no—
314C42—51no—
315C42—51no—
316C42—51no—
317C42—51no—
318C42—51no—
319C42D4×D511yescharacteristic
320C42D4×D511yescharacteristic
321C42D4×D511yescharacteristic
322C42Q8×D511yescharacteristic
323C2×C5—41no—
324C2×C5#174211yescharacteristic
325C2×C5C2×#34411yescharacteristic
326C2×C5C2×#34411yescharacteristic
327D5—22no—
328D5—41no—
329C23—51no—
330C23—51no—
331C23—102no—
332C23—201no—
333C23—201no—
334C23C42×D511yescharacteristic
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—51no—
340C2×C4—51no—
341C2×C4—51no—
342C2×C4—51no—
343C2×C4—51no—
344C2×C4—51no—
345C2×C4—102no—
346C2×C4—102no—
347C2×C4—102no—
348C2×C4—102no—
349C2×C4—102no—
350C2×C4—101no—
351C2×C4—101no—
352C2×C4—101no—
353C2×C4—101no—
354C2×C4—201no—
355C2×C4—201no—
356C2×C4—201no—
357C2×C4—201no—
358C2×C4—201no—
359C2×C4—201no—
360C2×C4—201no—
361C2×C4—201no—
362C2×C4D5×C22⋊C411yescharacteristic
363C2×C4D5×C22⋊C411yescharacteristic
364C2×C4D5×C22⋊C411yescharacteristic
365C2×C4D5×C4⋊C411yescharacteristic
366C2×C4D5×C4⋊C411yescharacteristic
367C2×C4D5×C4⋊C411yescharacteristic
368C8—42no—
369C8—42no—
370C8—42no—
371C8—202no—
372C8—202no—
373C8—202no—
374C5#811811yescharacteristic, complemented, Sylow
375C22—21no—
376C22—21no—
377C22—21no—
378C22—52no—
379C22—101no—
380C22—101no—
381C22—101no—
382C22—101no—
383C22—101no—
384C22—204no—
385C22D5×#9511yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—52no—
392C4—101no—
393C4—101no—
394C4—101no—
395C4—101no—
396C4—101no—
397C4#6503411yescharacteristic
398C4#6504011yescharacteristic
399C2—41no—
400C2—102no—
401C2—201no—
402C2#1059978211yescharacteristic
403C2D5×#34411yescharacteristic
404C2D5×#34411yescharacteristic
subgroupG/H
centerC22D5×#95
commutatorC23×C5C2×C42
FrattiniC2×C42C22×D5
FittingC5×#1307C2
socleC22×C5C2×#95
prime radicalC23×D5C42
cosocleC2×C42×C5C23
hypercenter#1307D5
hypocenterC5#8118
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
4. C5×#1307C2semidirect
5. #10598249C2semidirect
6. #10598249C2semidirect
7. #10598207C2semidirect
85. #1307D5semidirect
374. C5#8118semidirect

Maximal subgroups

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

subgroupindex
#106110622
D5×#4322
#106107692
C5×#13072
#105982492
#105982072
#81185