Finite Group Databasebeta

← #11992272

Subgroups — #11992272

Order 1280.

456 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2929C211yesmaximal, characteristic
2#10602770C211yesmaximal, characteristic, complemented
3#10602763C211yesmaximal, characteristic, complemented
4#10602502C212yesmaximal
5#10598175C212yesmaximal, complemented
6C2×C5×#131C411yescharacteristic, complemented
7C23×C5×C8C2211yescharacteristic
8C5×#525C2211yescharacteristic
9C5×#435—21no—
10C5×#435—21no—
11C5×C8×D4—21no—
12C5×C8×D4—21no—
13C5×#424C411yescharacteristic, complemented
14C5×#408C411yescharacteristic, complemented
15C5×#407C2211yescharacteristic
16C5×#405C411yescharacteristic, complemented
17#65501C2212yes—
18#65496C2212yes—
19C2×#3951—21no—
20C2×#3949—21no—
21#64772—21no—
22#64771—21no—
23#64758—22no—
24#64757—22no—
25#8626—51nomaximal, Sylow
26C2×C5×#41C2×C411yescharacteristic
27C23×C4×C5C2311yescharacteristic
28C5×#131—42no—
29C2×C5×M16—21no—
30C2×C5×M16C2×C411yescharacteristic
31C2×C5×M16C2×C411yescharacteristic
32C22×C5×C8—21no—
33C22×C5×C8—42no—
34C22×C5×C8C2×C411yescharacteristic
35C22×C5×C8C2×C411yescharacteristic
36C22×C5×C8D411yescharacteristic
37C22×C5×C8D411yescharacteristic
38C22×C5×C8D411yescharacteristic
39C22×C5×C8D411yescharacteristic
40C5×#123—21no—
41C5×C22⋊Q8D411yescharacteristic
42C5×C22⋊Q8Q811yescharacteristic
43C5×#121D411yescharacteristic
44C5×#121Q811yescharacteristic
45C5×#120—21no—
46C4×C5×D4—21no—
47C4×C5×D4—21no—
48C5×#117C2×C411yescharacteristic
49C2×C22⋊Dic5—22no—
50C2×C4⋊Dic5—22no—
51C2×#681—22no—
52C5×C4⋊C8—21no—
53C5×C4⋊C8—21no—
54C5×C22⋊C8—21no—
55C5×C22⋊C8—21no—
56C5×C22⋊C8—21no—
57C5×C22⋊C8—21no—
58C5×#97—21no—
59C4×C5×C8—21no—
60#3963—22no—
61C22⋊#168—22no—
62C22⋊#168—22no—
63#3951—42no—
64#3949—42no—
65#2929D511yescharacteristic
66#1810—51no—
67#1807—51no—
68#1513—52no—
69#1305—52no—
70C24×C5#4111yescharacteristic
71C5×#41—41no—
72C5×#41—41no—
73C2×C5×Q8C4⋊C411yescharacteristic
74C2×C5×D4—21no—
75C2×C5×D4—21no—
76C2×C5×D4—21no—
77C2×C5×D4C4⋊C411yescharacteristic
78C22×C4×C5—21no—
79C22×C4×C5—41no—
80C22×C4×C5—41no—
81C22×C4×C5C22×C411yescharacteristic
82C22×C4×C5C2×D411yescharacteristic
83C22×C4×C5C2×D411yescharacteristic
84C22×C4×C5C2×D411yescharacteristic
85C22×C4×C5C2×Q811yescharacteristic
86C22×C4×C5#4111yescharacteristic
87C22×Dic5—42no—
88C5×M16—42no—
89C5×M16—41no—
90C5×M16—41no—
91C2×C5×C8—22no—
92C2×C5×C8—22no—
93C2×C5×C8—22no—
94C2×C5×C8—21no—
95C2×C5×C8—21no—
96C2×C5×C8—41no—
97C2×C5×C8—41no—
98C2×C5×C8—41no—
99C2×C5×C8—42no—
100C2×C5×C8C22⋊C411yescharacteristic
101C2×C5×C8C22⋊C411yescharacteristic
102C2×C5×C8C22⋊C411yescharacteristic
103C2×C5×C8C22⋊C411yescharacteristic
104C5×C4⋊C4—21no—
105C5×C4⋊C4—21no—
106C5×C4⋊C4C4⋊C411yescharacteristic
107C5×C4⋊C4C4⋊C411yescharacteristic
108C5×C22⋊C4—21no—
109C5×C22⋊C4—21no—
110C5×C22⋊C4—21no—
111C5×C22⋊C4—21no—
112C5×C22⋊C4—21no—
113C42×C5—21no—
114C22⋊Dic5—82no—
115C4⋊Dic5—42no—
116C4⋊Dic5—42no—
117#681—42no—
118#681—42no—
119C2×#168—42no—
120C2×#131Dic511yescharacteristic, complemented
121C23×C8C2×D511yescharacteristic
122#525C2×D511yescharacteristic
123#435—21no—
124#435—21no—
125C8×D4—21no—
126C8×D4—21no—
127C2×#108—101no—
128C2×#106—101no—
129#424Dic511yescharacteristic, complemented
130#408Dic511yescharacteristic, complemented
131#407—52no—
132#407C2×D511yescharacteristic
133#405Dic511yescharacteristic, complemented
134#380—52no—
135#341—101no—
136#340—101no—
137#328—102no—
138#327—102no—
139C23×C5—22no—
140C23×C5—21no—
141C23×C5—41no—
142C23×C5—41no—
143C23×C5#11711yescharacteristic
144C23×C5#12111yescharacteristic
145C23×C5C22⋊Q811yescharacteristic
146C5×Q8—41no—
147C5×D4—41no—
148C5×D4—42no—
149C5×D4—42no—
150C5×D4—42no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5C2×C22⋊C411yescharacteristic
166C2×C4×C5C2×C4⋊C411yescharacteristic
167C2×C4×C5#12111yescharacteristic
168C2×C4×C5C22⋊Q811yescharacteristic
169C2×Dic5—82no—
170C2×Dic5—82no—
171C2×Dic5—82no—
172C5×C8—21no—
173C5×C8—21no—
174C5×C8—21no—
175C5×C8—41no—
176C5×C8—41no—
177C5×C8#9912yes—
178#168—82no—
179C2×#41C2×Dic511yescharacteristic
180C23×C4C22×D511yescharacteristic
181#131—42no—
182C2×M16—21no—
183C2×M16—102no—
184C2×M16C2×Dic511yescharacteristic
185C2×M16C2×Dic511yescharacteristic
186C22×C8—21no—
187C22×C8—42no—
188C22×C8C2×Dic511yescharacteristic
189C22×C8C2×Dic511yescharacteristic
190C22×C8C22⋊D511yescharacteristic
191C22×C8C22⋊D511yescharacteristic
192C22×C8C22⋊D511yescharacteristic
193C22×C8C22⋊D511yescharacteristic
194#123—21no—
195C22⋊Q8Dic1011yescharacteristic
196C22⋊Q8D2011yescharacteristic
197#121Dic1011yescharacteristic
198#121D2011yescharacteristic
199#120—21no—
200C4×D4—21no—
201C4×D4—21no—
202#117C2×Dic511yescharacteristic
203C2×C4⋊C4—102no—
204C2×C22⋊C4—102no—
205#108—202no—
206#106—202no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C22⋊C8—21no—
210C22⋊C8—21no—
211C22⋊C8—21no—
212C22⋊C8—21no—
213C22⋊C8—102no—
214C22⋊C8—102no—
215#97—21no—
216C4×C8—21no—
217#95—102no—
218C22×C5—21no—
219C22×C5—21no—
220C22×C5—21no—
221C22×C5—21no—
222C22×C5—21no—
223C22×C5—21no—
224C22×C5—21no—
225C22×C5—21no—
226C22×C5—44no—
227C22×C5—41no—
228C22×C5—41no—
229C22×C5—41no—
230C22×C5#38011yescharacteristic
231C22×C5#47112yes—
232C4×C5—21no—
233C4×C5—21no—
234C4×C5—21no—
235C4×C5—41no—
236C4×C5—41no—
237C4×C5—41no—
238C4×C5C2×#9911yescharacteristic
239C4×C5#41011yescharacteristic
240Dic5—162no—
241C24#70911yescharacteristic
242#41—41no—
243#41—41no—
244C2×Q8C4⋊Dic511yescharacteristic
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C4⋊Dic511yescharacteristic
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—202no—
253C22×C4C2×Dic1011yescharacteristic
254C22×C4C2×D2011yescharacteristic
255C22×C4#70911yescharacteristic
256C22×C4C22×Dic511yescharacteristic
257C22×C4C2×C22⋊D511yescharacteristic
258C22×C4C2×C22⋊D511yescharacteristic
259M16—42no—
260M16—41no—
261M16—41no—
262M16—202no—
263M16—202no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—42no—
273C2×C8—202no—
274C2×C8C22⋊Dic511yescharacteristic
275C2×C8C22⋊Dic511yescharacteristic
276C2×C8C22⋊Dic511yescharacteristic
277C2×C8C22⋊Dic511yescharacteristic
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—202no—
281C4⋊C4—202no—
282C4⋊C4C4⋊Dic511yescharacteristic
283C4⋊C4C4⋊Dic511yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—402no—
290C42—21no—
291C2×C5—22no—
292C2×C5—41no—
293C2×C5—41no—
294C2×C5—81no—
295C2×C5#179911yescharacteristic
296C2×C5#181411yescharacteristic
297C2×C5#181511yescharacteristic
298C23—22no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23#407011yescharacteristic
303C23#407211yescharacteristic
304C23#407611yescharacteristic
305Q8—41no—
306D4—41no—
307D4—42no—
308D4—42no—
309D4—42no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—402no—
325C2×C4—402no—
326C2×C4—402no—
327C2×C4#407011yescharacteristic
328C2×C4C2×C4⋊Dic511yescharacteristic
329C2×C4#407611yescharacteristic
330C2×C4C2×C22⋊Dic511yescharacteristic
331C8—21no—
332C8—21no—
333C8—21no—
334C8—41no—
335C8—41no—
336C8—402no—
337C8#396612yes—
338C5#862611yescharacteristic, complemented, Sylow
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—44no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22#6543012yes—
352C22#6550111yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—802no—
360C4C2×#396611yescharacteristic
361C4#6552911yescharacteristic
362C2—22no—
363C2—41no—
364C2—41no—
365C2—81no—
366C2#1060241211yescharacteristic
367C2#1060280611yescharacteristic
368C2#1060280811yescharacteristic
subgroupG/H
centerC22#65501
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#2929C2
socleC22×C5#380
prime radicalC5×#525C22
cosocleC23×C4×C5C23
hypercenter#2929D5
hypocenterC5#8626
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2929

Complements

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

NH ≅ G/Ntype
2. #10602770C2semidirect
3. #10602763C2semidirect
5. #10598175C2semidirect
6. C2×C5×#131C4semidirect
13. C5×#424C4semidirect
14. C5×#408C4semidirect
16. C5×#405C4semidirect
120. C2×#131Dic5semidirect
129. #424Dic5semidirect
130. #408Dic5semidirect
133. #405Dic5semidirect
338. C5#8626semidirect

Maximal subgroups

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

subgroupindex
C5×#29292
#106027702
#106027632
#106025022
#105981752
#86265