Finite Group Databasebeta

← #11994330

Subgroups — #11994330

Order 1280.

812 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#399C211yesmaximal, characteristic
2#10613825C211yesmaximal, characteristic
3#10602347C212yesmaximal, complemented
4C2×#64745C211yesmaximal, characteristic
5#10598103C212yesmaximal, complemented
6C22×C5×C4⋊C4—21no—
7C22×C5×C4⋊C4C2211yescharacteristic
8C22×C5×C22⋊C4—21no—
9C22×C5×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic5—21no—
11C5×#399—22no—
12C5×#399C414yescomplemented
13C2×C5×#95C2211yescharacteristic
14#65501—21no—
15#65501C2212yes—
16C2×C22⋊#168C2212yes—
17#65239—24no—
18#64749—24no—
19#64745—22no—
20#9021—51nomaximal, Sylow
21C25×C5D411yescharacteristic
22C23×C4×C5—21no—
23C23×C4×C5—21no—
24C23×C4×C5D411yescharacteristic
25C23×C4×C5C2311yescharacteristic
26C23×Dic5—22no—
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4—24no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—44no—
32C2×C5×C4⋊C4C2×C412yescomplemented
33C2×C5×C22⋊C4—22no—
34C2×C5×C22⋊C4—22no—
35C2×C5×C22⋊C4—24no—
36C2×C5×C22⋊C4—44no—
37C2×C5×C22⋊C4C2×C412yes—
38C2×C5×C22⋊C4D412yes—
39C2×C22⋊Dic5—22no—
40C2×C22⋊Dic5—22no—
41C2×C22⋊Dic5—42no—
42C2×C22⋊Dic5—42no—
43C2×C4⋊Dic5—22no—
44C2×C4⋊Dic5D414yes—
45C22×#168—22no—
46C5×#95—21no—
47C5×#95C2×C412yescomplemented
48#3963—22no—
49#3963—22no—
50C22⋊#168—22no—
51C22⋊#168—22no—
52C2×#399D511yescharacteristic
53#2315—51no—
54#1824—52no—
55C2×#323—51no—
56#1294—52no—
57C24×C5—21no—
58C24×C5—21no—
59C24×C5—21no—
60C24×C5—21no—
61C24×C5—42no—
62C24×C5—42no—
63C24×C5C22⋊C412yes—
64C24×C5SD1612yes—
65C24×C5Q1612yes—
66C24×C5C2×D411yescharacteristic
67C22×C4×C5—24no—
68C22×C4×C5—22no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—22no—
72C22×C4×C5—42no—
73C22×C4×C5—42no—
74C22×C4×C5—41no—
75C22×C4×C5—41no—
76C22×C4×C5—42no—
77C22×C4×C5—42no—
78C22×C4×C5—42no—
79C22×C4×C5—41no—
80C22×C4×C5—41no—
81C22×C4×C5C22⋊C412yes—
82C22×C4×C5C22×C411yescharacteristic
83C22×C4×C5C2×D412yes—
84C22×C4×C5C2×D411yescharacteristic
85C22×C4×C5#4112yes—
86C22×Dic5—24no—
87C22×Dic5—44no—
88C22×Dic5—82no—
89C22×Dic5—82no—
90C5×C4⋊C4—24no—
91C5×C4⋊C4—48no—
92C5×C4⋊C4—42no—
93C5×C22⋊C4—24no—
94C5×C22⋊C4—24no—
95C5×C22⋊C4—48no—
96C22⋊Dic5—44no—
97C22⋊Dic5—42no—
98C22⋊Dic5—42no—
99C4⋊Dic5—44no—
100C4⋊Dic5—82no—
101C2×#168—44no—
102C2×#168—42no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4C2×D511yescharacteristic
105C22×C22⋊C4—21no—
106C22×C22⋊C4—101no—
107C22×C22⋊C4C2×D511yescharacteristic
108C2×C22⋊C8—52no—
109#399—22no—
110#399Dic514yescomplemented
111#385—104no—
112#380—52no—
113#380—101no—
114C2×#95C2×D511yescharacteristic
115#340—104no—
116#323—102no—
117C23×C5—22no—
118C23×C5—22no—
119C23×C5—22no—
120C23×C5—22no—
121C23×C5—22no—
122C23×C5—22no—
123C23×C5—22no—
124C23×C5—22no—
125C23×C5—42no—
126C23×C5—42no—
127C23×C5—44no—
128C23×C5—44no—
129C23×C5—42no—
130C23×C5—42no—
131C23×C5—82no—
132C23×C5—82no—
133C23×C5—81no—
134C23×C5—81no—
135C23×C5#10314yes—
136C23×C5C2×C22⋊C411yescharacteristic
137C23×C5#12011yescharacteristic
138C23×C5#12311yescharacteristic
139C23×C5C2×SD1611yescharacteristic
140C23×C5C2×Q1611yescharacteristic
141C23×C5AGL(1,ℤ/8)11yescharacteristic
142C23×C5#13711yescharacteristic
143C2×C4×C5—24no—
144C2×C4×C5—24no—
145C2×C4×C5—22no—
146C2×C4×C5—41no—
147C2×C4×C5—41no—
148C2×C4×C5—42no—
149C2×C4×C5—44no—
150C2×C4×C5—44no—
151C2×C4×C5—42no—
152C2×C4×C5—42no—
153C2×C4×C5—42no—
154C2×C4×C5—42no—
155C2×C4×C5—42no—
156C2×C4×C5—42no—
157C2×C4×C5—42no—
158C2×C4×C5—81no—
159C2×C4×C5—82no—
160C2×C4×C5—82no—
161C2×C4×C5C4×D412yes—
162C2×C4×C5#12112yes—
163C2×Dic5—44no—
164C2×Dic5—44no—
165C2×Dic5—44no—
166C2×Dic5—88no—
167#168—82no—
168C25C22⋊D511yescharacteristic
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—102no—
172C23×C4C22⋊D511yescharacteristic
173C23×C4C22×D511yescharacteristic
174C22×C8—102no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—44no—
180C2×C4⋊C4—54no—
181C2×C4⋊C4—102no—
182C2×C4⋊C4C2×Dic512yescomplemented
183C2×C22⋊C4—22no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—24no—
186C2×C22⋊C4—44no—
187C2×C22⋊C4—102no—
188C2×C22⋊C4—102no—
189C2×C22⋊C4—202no—
190C2×C22⋊C4—202no—
191C2×C22⋊C4C2×Dic512yes—
192C2×C22⋊C4C22⋊D512yes—
193C22⋊C8—102no—
194C22⋊C8—102no—
195#95—21no—
196#95—102no—
197#95—102no—
198#95C2×Dic512yescomplemented
199C22×C5—22no—
200C22×C5—22no—
201C22×C5—22no—
202C22×C5—22no—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5—21no—
206C22×C5—21no—
207C22×C5—24no—
208C22×C5—44no—
209C22×C5—44no—
210C22×C5—44no—
211C22×C5—42no—
212C22×C5—42no—
213C22×C5—82no—
214C22×C5—82no—
215C22×C5—82no—
216C22×C5#38611yescharacteristic
217C22×C5C2×#10311yescharacteristic
218C22×C5#41711yescharacteristic
219C22×C5#45011yescharacteristic
220C22×C5#45111yescharacteristic
221C22×C5#45312yes—
222C22×C5#45812yes—
223C22×C5#48311yescharacteristic
224C22×C5#48411yescharacteristic
225C4×C5—22no—
226C4×C5—22no—
227C4×C5—44no—
228C4×C5—42no—
229C4×C5—82no—
230Dic5—84no—
231C24—21no—
232C24—21no—
233C24—21no—
234C24—21no—
235C24—42no—
236C24—42no—
237C24#68812yes—
238C24#68912yes—
239C24C22⋊Dic512yes—
240C24C2×C22⋊D511yescharacteristic
241C22×C4—24no—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—104no—
256C22×C4—204no—
257C22×C4—402no—
258C22×C4—402no—
259C22×C4C22⋊Dic512yes—
260C22×C4D4×D512yes—
261C22×C4#71112yes—
262C22×C4C22×Dic511yescharacteristic
263C22×C4C2×C22⋊D511yescharacteristic
264C2×C8—204no—
265C2×C8—202no—
266C4⋊C4—24no—
267C4⋊C4—48no—
268C4⋊C4—42no—
269C4⋊C4—204no—
270C4⋊C4—402no—
271C22⋊C4—24no—
272C22⋊C4—24no—
273C22⋊C4—48no—
274C22⋊C4—204no—
275C22⋊C4—202no—
276C22⋊C4—202no—
277C2×C5—21no—
278C2×C5—21no—
279C2×C5—21no—
280C2×C5—21no—
281C2×C5—44no—
282C2×C5#161312yes—
283C2×C5#161412yes—
284C2×C5#187211yescharacteristic
285C2×C5#188711yescharacteristic
286C2×C5#189011yescharacteristic
287C23—22no—
288C23—22no—
289C23—22no—
290C23—22no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—42no—
296C23—44no—
297C23—44no—
298C23—42no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—82no—
303C23—81no—
304C23—82no—
305C23#396714yes—
306C23#408111yescharacteristic
307C23#408311yescharacteristic
308C23C2×#68811yescharacteristic
309C23C2×#68911yescharacteristic
310C23#409511yescharacteristic
311C23#409711yescharacteristic
312C23C2×C22⋊Dic511yescharacteristic
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—22no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—81no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—204no—
332C2×C4—204no—
333C2×C4—204no—
334C2×C4—408no—
335C2×C4D4×Dic512yes—
336C2×C4#408512yes—
337C8—402no—
338C5#902111yescharacteristic, complemented, Sylow
339C22—21no—
340C22—21no—
341C22—22no—
342C22—22no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—22no—
347C22—24no—
348C22—44no—
349C22—42no—
350C22—44no—
351C22—42no—
352C22—44no—
353C22—82no—
354C22—82no—
355C22—82no—
356C22#6533211yescharacteristic
357C22#6533311yescharacteristic
358C22#6533511yescharacteristic
359C22#6533911yescharacteristic
360C22#6534212yes—
361C22#6536612yes—
362C22#6550911yescharacteristic
363C22C2×#396711yescharacteristic
364C22#6552111yescharacteristic
365C4—22no—
366C4—22no—
367C4—44no—
368C4—42no—
369C4—82no—
370C4—404no—
371C2—21no—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—44no—
376C2#1060050712yes—
377C2#1060050912yes—
378C2#1060248511yescharacteristic
379C2#1060249711yescharacteristic
380C2#1060255611yescharacteristic
subgroupG/H
centerC23#4083
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#399C2
socleC23×C5#120
prime radicalC25×C5D4
cosocleC23×C4×C5C23
hypercenterC2×#399D5
hypocenterC5#9021
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
3. #10602347C2semidirect
5. #10598103C2semidirect
12. C5×#399C4semidirect
32. C2×C5×C4⋊C4C2×C4semidirect
47. C5×#95C2×C4semidirect
110. #399Dic5semidirect
182. C2×C4⋊C4C2×Dic5semidirect
198. #95C2×Dic5semidirect
338. C5#9021semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3992
#106138252
#106023472
C2×#647452
#105981032
#90215