Finite Group Databasebeta

← #11995055

Subgroups — #11995055

Order 1280.

946 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#380C211yesmaximal, characteristic
2#10615762C211yesmaximal, characteristic
3#10602919C211yesmaximal, characteristic
4C2×#64672C212yesmaximal, complemented
5#10598103C212yesmaximal, complemented
6C24×C4×C5C2211yescharacteristic
7C22×C5×C4⋊C4—21no—
8C22×C5×C22⋊C4—21no—
9C2×#4070C412yescomplemented
10C2×#4070C2211yescharacteristic
11C5×#380—24no—
12C2×C5×#95C2212yes—
13#65536—21no—
14#65501C412yescomplemented
15#65501C2211yescharacteristic
16#65499—22no—
17#65499—21no—
18C2×C22⋊#168—22no—
19C2×C22⋊#168C2212yes—
20#64672—24no—
21#9151—51nomaximal, Sylow
22C25×C5D411yescharacteristic
23C23×C4×C5—22no—
24C23×C4×C5—22no—
25C23×C4×C5—22no—
26C23×C4×C5—44no—
27C23×C4×C5C2×C412yes—
28C23×C4×C5D412yes—
29C23×C4×C5D411yescharacteristic
30C23×C4×C5C2311yescharacteristic
31C22×Dic10C2×C411yescharacteristic
32C2×C5×C4⋊C4—24no—
33C2×C5×C4⋊C4—44no—
34C2×C5×C22⋊C4—24no—
35C2×C5×C22⋊C4—42no—
36C2×C5×C22⋊C4—42no—
37C2×C22⋊Dic5—22no—
38C2×C22⋊Dic5—22no—
39C2×C22⋊Dic5—21no—
40C2×C22⋊Dic5—21no—
41C2×C4⋊Dic5C2×C411yescharacteristic
42C2×C4⋊Dic5C2×C412yes—
43#4070—22no—
44#4070—22no—
45#4070—44no—
46C2×#683—22no—
47C2×#683—21no—
48C22×#168—22no—
49C5×#95—22no—
50C5×#95D414yes—
51#3963—22no—
52#3963—21no—
53C22⋊#168—22no—
54C22⋊#168—22no—
55C22⋊#168—44no—
56#2848—51no—
57C2×#380D511yescharacteristic
58#1779—51no—
59C2×#328—52no—
60#1294—52no—
61C24×C5—21no—
62C24×C5—21no—
63C24×C5—21no—
64C24×C5—21no—
65C24×C5—42no—
66C24×C5—42no—
67C24×C5C22⋊C412yes—
68C24×C5SD1612yes—
69C24×C5Q1612yes—
70C24×C5C2×D411yescharacteristic
71C22×C4×C5—21no—
72C22×C4×C5—21no—
73C22×C4×C5—24no—
74C22×C4×C5—24no—
75C22×C4×C5—24no—
76C22×C4×C5—24no—
77C22×C4×C5—24no—
78C22×C4×C5—24no—
79C22×C4×C5—42no—
80C22×C4×C5—42no—
81C22×C4×C5—42no—
82C22×C4×C5—48no—
83C22×C4×C5—48no—
84C22×C4×C5—44no—
85C22×C4×C5—44no—
86C22×C4×C5—42no—
87C22×C4×C5—42no—
88C22×C4×C5C22⋊C412yes—
89C22×C4×C5C22×C411yescharacteristic
90C22×C4×C5C2×D411yescharacteristic
91C22×C4×C5C2×D412yes—
92C22×C4×C5#4112yes—
93C22×Dic5—21no—
94C22×Dic5—21no—
95C22×Dic5—22no—
96C2×Dic10—22no—
97C2×Dic10—42no—
98C5×C4⋊C4—48no—
99C5×C22⋊C4—48no—
100C22⋊Dic5—44no—
101C22⋊Dic5—44no—
102C22⋊Dic5—41no—
103C22⋊Dic5—41no—
104C22⋊Dic5—41no—
105C22⋊Dic5—41no—
106C4⋊Dic5—22no—
107C4⋊Dic5—42no—
108#683—44no—
109#683—42no—
110C2×#168—44no—
111C2×#168—42no—
112C24×C4C2×D511yescharacteristic
113C2×C22⋊Q8—51no—
114C2×C22⋊Q8—52no—
115C22×C4⋊C4—21no—
116C22×C22⋊C4—21no—
117C2×C22⋊C8—52no—
118C2×C22⋊C8—102no—
119#385—102no—
120#385—101no—
121#380—24no—
122#380—52no—
123#380—51no—
124#379—101no—
125C2×#95C2×D512yes—
126#328—104no—
127C23×C5—22no—
128C23×C5—22no—
129C23×C5—22no—
130C23×C5—22no—
131C23×C5—22no—
132C23×C5—22no—
133C23×C5—22no—
134C23×C5—22no—
135C23×C5—22no—
136C23×C5—22no—
137C23×C5—22no—
138C23×C5—22no—
139C23×C5—44no—
140C23×C5—44no—
141C23×C5—42no—
142C23×C5—42no—
143C23×C5—42no—
144C23×C5—42no—
145C23×C5—44no—
146C23×C5—44no—
147C23×C5#10314yes—
148C23×C5C2×C22⋊C411yescharacteristic
149C23×C5#12011yescharacteristic
150C23×C5#12311yescharacteristic
151C23×C5C2×SD1611yescharacteristic
152C23×C5C2×Q1611yescharacteristic
153C23×C5AGL(1,ℤ/8)11yescharacteristic
154C23×C5#13711yescharacteristic
155C2×C4×C5—24no—
156C2×C4×C5—24no—
157C2×C4×C5—22no—
158C2×C4×C5—22no—
159C2×C4×C5—22no—
160C2×C4×C5—22no—
161C2×C4×C5—42no—
162C2×C4×C5—42no—
163C2×C4×C5—48no—
164C2×C4×C5—48no—
165C2×C4×C5—44no—
166C2×C4×C5—44no—
167C2×C4×C5—44no—
168C2×C4×C5—84no—
169C2×C4×C5—84no—
170C2×C4×C5#9914yes—
171C2×C4×C5C4×D412yes—
172C2×C4×C5#12112yes—
173C2×Dic5—41no—
174C2×Dic5—41no—
175C2×Dic5—42no—
176C2×Dic5—42no—
177C2×Dic5—42no—
178C2×Dic5—42no—
179C2×Dic5—42no—
180Dic10—82no—
181#168—82no—
182C25C22⋊D511yescharacteristic
183C22×Q8—51no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—44no—
188C23×C4C4×D512yes—
189C23×C4D2012yes—
190C23×C4C22⋊D511yescharacteristic
191C23×C4C22×D511yescharacteristic
192C22×C8—102no—
193C22⋊Q8—102no—
194C22⋊Q8—102no—
195C22⋊Q8—204no—
196C2×C4⋊C4—24no—
197C2×C4⋊C4—44no—
198C2×C4⋊C4—51no—
199C2×C4⋊C4—52no—
200C2×C4⋊C4—102no—
201C2×C4⋊C4—101no—
202C2×C22⋊C4—24no—
203C2×C22⋊C4—42no—
204C2×C22⋊C4—42no—
205C2×C22⋊C4—102no—
206C2×C22⋊C4—102no—
207C2×C22⋊C4—101no—
208C2×C22⋊C4—101no—
209C22⋊C8—102no—
210C22⋊C8—102no—
211C22⋊C8—204no—
212#95—22no—
213#95—102no—
214#95—101no—
215#95C22⋊D514yes—
216C22×C5—21no—
217C22×C5—21no—
218C22×C5—21no—
219C22×C5—21no—
220C22×C5—22no—
221C22×C5—22no—
222C22×C5—22no—
223C22×C5—22no—
224C22×C5—24no—
225C22×C5—24no—
226C22×C5—24no—
227C22×C5—44no—
228C22×C5—44no—
229C22×C5—44no—
230C22×C5—44no—
231C22×C5—42no—
232C22×C5—42no—
233C22×C5—42no—
234C22×C5—42no—
235C22×C5#38611yescharacteristic
236C22×C5C2×#9912yes—
237C22×C5C2×#10311yescharacteristic
238C22×C5#41711yescharacteristic
239C22×C5#42112yes—
240C22×C5#45011yescharacteristic
241C22×C5#45111yescharacteristic
242C22×C5#48311yescharacteristic
243C22×C5#48411yescharacteristic
244C4×C5—22no—
245C4×C5—22no—
246C4×C5—24no—
247C4×C5—84no—
248Dic5—81no—
249Dic5—81no—
250Dic5—82no—
251C24—21no—
252C24—21no—
253C24—21no—
254C24—21no—
255C24—42no—
256C24—42no—
257C24#68512yes—
258C24#68712yes—
259C24#68912yes—
260C24C2×C22⋊D511yescharacteristic
261C2×Q8—102no—
262C2×Q8—202no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—48no—
275C22×C4—48no—
276C22×C4—44no—
277C22×C4—44no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—101no—
281C22×C4—102no—
282C22×C4—101no—
283C22×C4#68512yes—
284C22×C4C2×C4×D511yescharacteristic
285C22×C4C2×D2011yescharacteristic
286C22×C4#70912yes—
287C22×C4C2×C22⋊D512yes—
288C2×C8—204no—
289C2×C8—202no—
290C4⋊C4—48no—
291C4⋊C4—102no—
292C4⋊C4—202no—
293C4⋊C4—204no—
294C4⋊C4—202no—
295C22⋊C4—48no—
296C22⋊C4—204no—
297C22⋊C4—204no—
298C22⋊C4—201no—
299C22⋊C4—201no—
300C22⋊C4—201no—
301C22⋊C4—201no—
302C2×C5—21no—
303C2×C5—21no—
304C2×C5—21no—
305C2×C5—21no—
306C2×C5—44no—
307C2×C5#151312yes—
308C2×C5#152012yes—
309C2×C5#187211yescharacteristic
310C2×C5#189711yescharacteristic
311C2×C5#189811yescharacteristic
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—22no—
323C23—22no—
324C23—44no—
325C23—44no—
326C23—42no—
327C23—42no—
328C23—44no—
329C23—44no—
330C23—42no—
331C23—42no—
332C23#394214yes—
333C23C2×#68511yescharacteristic
334C23#407511yescharacteristic
335C23#407811yescharacteristic
336C23C2×#68711yescharacteristic
337C23#408811yescharacteristic
338C23C2×#68911yescharacteristic
339C23#409911yescharacteristic
340Q8—402no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—48no—
350C2×C4—48no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—84no—
355C2×C4—84no—
356C2×C4—202no—
357C2×C4—202no—
358C2×C4—202no—
359C2×C4—202no—
360C2×C4—201no—
361C2×C4—201no—
362C2×C4—202no—
363C2×C4#393814yes—
364C2×C4C4×C22⋊D512yes—
365C2×C4#407612yes—
366C8—402no—
367C5#915111yescharacteristic, complemented, Sylow
368C22—21no—
369C22—21no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—21no—
375C22—21no—
376C22—24no—
377C22—24no—
378C22—24no—
379C22—44no—
380C22—44no—
381C22—44no—
382C22—44no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22C2×#393812yes—
388C22#6525511yescharacteristic
389C22C2×#394211yescharacteristic
390C22#6525911yescharacteristic
391C22#6526011yescharacteristic
392C22#6529412yes—
393C22#6550211yescharacteristic
394C22#6550711yescharacteristic
395C22#6551711yescharacteristic
396C4—22no—
397C4—24no—
398C4—22no—
399C4—84no—
400C4—401no—
401C4—402no—
402C4—401no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2—21no—
407C2—44no—
408C2#1060030112yes—
409C2#1060030312yes—
410C2#1060233611yescharacteristic
411C2#1060235211yescharacteristic
412C2#1060238411yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#380C2
socleC23×C5C2×C22⋊C4
prime radicalC25×C5D4
cosocleC23×C4×C5C23
hypercenterC2×#380D5
hypocenterC5#9151
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C2×#64672C2semidirect
5. #10598103C2semidirect
9. C2×#4070C4semidirect
14. #65501C4semidirect
367. C5#9151semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3802
#106157622
#106029192
C2×#646722
#105981032
#91515