Finite Group Databasebeta

← #13017419

Subgroups — #13017419

Order 1280.

1050 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
1C22×C4×Dic10C211yesmaximal, characteristic
2#10604902C212yesmaximal
3C2×#64914C212yesmaximal
4C2×#64913C212yesmaximal
5C23×Dic10C411yescharacteristic
6C22×C42×C5C411yescharacteristic
7C22×C4⋊Dic5C2211yescharacteristic
8C22×#683C411yescharacteristic
9C22×#683C2211yescharacteristic
10C22×C4×Dic5C411yescharacteristic
11C22×C4×Dic5C2211yescharacteristic
12C2×C4×Dic10—24no—
13C2×C4×Dic10—24no—
14C2×C4×Dic10—24no—
15C2×C22⋊#170C2214yes—
16#64918—24no—
17#64914—24no—
18#64913—24no—
19#8303—51nomaximal, Sylow
20C23×C4×C5C2×C411yescharacteristic
21C23×C4×C5C2×C411yescharacteristic
22C23×C4×C5C2×C411yescharacteristic
23C23×Dic5C2×C411yescharacteristic
24C23×Dic5C2×C411yescharacteristic
25C23×Dic5C2×C411yescharacteristic
26C23×Dic5C2311yescharacteristic
27C22×Dic10—22no—
28C22×Dic10—22no—
29C22×Dic10—22no—
30C22×Dic10—22no—
31C22×Dic10—22no—
32C22×Dic10—22no—
33C22×Dic10C814yescomplemented
34C22×#170—24no—
35C2×C42×C5—22no—
36C2×C42×C5—22no—
37C2×C42×C5—22no—
38C2×C4⋊Dic5—22no—
39C2×C4⋊Dic5—22no—
40C2×C4⋊Dic5D414yes—
41C2×#683—22no—
42C2×#683—22no—
43C2×#683—22no—
44C2×#683—22no—
45C2×#683—22no—
46C2×#683D414yes—
47C2×C4×Dic5—22no—
48C2×C4×Dic5—22no—
49C2×C4×Dic5—22no—
50C2×C4×Dic5—22no—
51C2×C4×Dic5—22no—
52C2×C4×Dic5D414yes—
53C4×Dic10—232no—
54C22⋊#170—24no—
55C22⋊#170—24no—
56C22×C4×Q8—51no—
57#1817—52no—
58C2×#324—52no—
59C2×#324—52no—
60C24×C5C22×C411yescharacteristic
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—24no—
68C22×C4×C5—21no—
69C22×C4×C5—21no—
70C22×C4×C5—42no—
71C22×C4×C5C22⋊C412yes—
72C22×C4×C5C22⋊C412yes—
73C22×C4×C5C22⋊C412yes—
74C22×C4×C5C2×C812yes—
75C22×C4×C5M1612yes—
76C22×Dic5—21no—
77C22×Dic5—21no—
78C22×Dic5—21no—
79C22×Dic5—21no—
80C22×Dic5—21no—
81C22×Dic5—21no—
82C22×Dic5—21no—
83C22×Dic5—21no—
84C22×Dic5—21no—
85C22×Dic5—21no—
86C22×Dic5—42no—
87C22×Dic5—42no—
88C22×Dic5C22⋊C412yes—
89C22×Dic5C22⋊C412yes—
90C22×Dic5C22⋊C412yes—
91C22×Dic5C2×C812yes—
92C22×Dic5C2×C812yes—
93C22×Dic5M1612yes—
94C22×Dic5M1612yes—
95C22×Dic5C2×D412yes—
96C22×Dic5C2×D412yes—
97C22×Dic5C2×D412yes—
98C2×Dic10—28no—
99C2×Dic10—28no—
100C2×Dic10—28no—
101C2×Dic10—28no—
102C2×Dic10—28no—
103C2×Dic10—28no—
104C2×Dic10—28no—
105C2×#170—48no—
106C2×#170—44no—
107C42×C5—28no—
108C4⋊Dic5—28no—
109#683—28no—
110#683—28no—
111C4×Dic5—28no—
112C4×Dic5—28no—
113C23×Q8—51no—
114C2×C4×Q8—104no—
115C2×C4×Q8—104no—
116C2×C4×Q8—104no—
117C22×C4⋊C4—51no—
118C22×C4⋊C4—51no—
119C22×C4⋊C4—51no—
120C22×C42—51no—
121C22×C42—51no—
122C22×C42AGL(1,𝔽5)11yescharacteristic
123C2×C22⋊C8—54no—
124#336—104no—
125#324—104no—
126#324—104no—
127C23×C5—22no—
128C23×C5—22no—
129C23×C5C2×C22⋊C411yescharacteristic
130C23×C5C2×C22⋊C411yescharacteristic
131C23×C5C2×C22⋊C411yescharacteristic
132C23×C5C22×C811yescharacteristic
133C23×C5C2×M1611yescharacteristic
134C23×C5C2×M1611yescharacteristic
135C23×C5C2×M1611yescharacteristic
136C2×C4×C5—24no—
137C2×C4×C5—24no—
138C2×C4×C5—22no—
139C2×C4×C5—22no—
140C2×C4×C5—22no—
141C2×C4×C5—22no—
142C2×C4×C5—22no—
143C2×C4×C5—22no—
144C2×C4×C5—22no—
145C2×C4×C5—22no—
146C2×C4×C5—22no—
147C2×C4×C5—42no—
148C2×C4×C5—42no—
149C2×C4×C5—42no—
150C2×C4×C5C22⋊C814yes—
151C2×C4×C5#10114yes—
152C2×Dic5—22no—
153C2×Dic5—22no—
154C2×Dic5—22no—
155C2×Dic5—22no—
156C2×Dic5—22no—
157C2×Dic5—22no—
158C2×Dic5—22no—
159C2×Dic5—22no—
160C2×Dic5—22no—
161C2×Dic5—22no—
162C2×Dic5—22no—
163C2×Dic5—22no—
164C2×Dic5—24no—
165C2×Dic5—22no—
166C2×Dic5—42no—
167C2×Dic5—42no—
168C2×Dic5—42no—
169C2×Dic5—42no—
170C2×Dic5—42no—
171C2×Dic5C22⋊C814yes—
172C2×Dic5C22⋊C814yes—
173C2×Dic5#12014yes—
174Dic10—232no—
175#170—84no—
176C22×Q8—54no—
177C22×Q8—102no—
178C22×Q8—102no—
179C22×Q8—102no—
180C22×Q8—102no—
181C22×Q8—102no—
182C22×Q8—102no—
183C23×C4—51no—
184C23×C4—51no—
185C23×C4—51no—
186C23×C4—51no—
187C23×C4C2×AGL(1,𝔽5)11yescharacteristic
188C23×C4C2×AGL(1,𝔽5)11yescharacteristic
189C23×C4C2×AGL(1,𝔽5)11yescharacteristic
190C22×C8—104no—
191C4×Q8—1032no—
192C2×C4⋊C4—54no—
193C2×C4⋊C4—54no—
194C2×C4⋊C4—102no—
195C2×C4⋊C4—102no—
196C2×C4⋊C4—102no—
197C2×C4⋊C4—102no—
198C2×C4⋊C4—102no—
199C2×C4⋊C4—102no—
200C2×C4⋊C4—102no—
201C2×C42—22no—
202C2×C42—22no—
203C2×C42—22no—
204C2×C42—54no—
205C2×C42—102no—
206C2×C42—102no—
207C2×C42—102no—
208C2×C42—102no—
209C2×C42—102no—
210C22⋊C8—104no—
211C22⋊C8—104no—
212C22×C5—22no—
213C22×C5—22no—
214C22×C5—22no—
215C22×C5—22no—
216C22×C5—21no—
217C22×C5—21no—
218C22×C5—21no—
219C22×C5—21no—
220C22×C5#37911yescharacteristic
221C22×C5C2×C22⋊C811yescharacteristic
222C22×C5C2×C22⋊C811yescharacteristic
223C22×C5C2×C22⋊C811yescharacteristic
224C22×C5#40711yescharacteristic
225C22×C5#40711yescharacteristic
226C22×C5#40711yescharacteristic
227C22×C5#41012yes—
228C22×C5C2×#10112yes—
229C4×C5—24no—
230C4×C5—24no—
231C4×C5—42no—
232Dic5—24no—
233Dic5—24no—
234Dic5—24no—
235Dic5—42no—
236C24C22×AGL(1,𝔽5)11yescharacteristic
237C2×Q8—108no—
238C2×Q8—108no—
239C2×Q8—108no—
240C2×Q8—108no—
241C2×Q8—108no—
242C2×Q8—108no—
243C2×Q8—108no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—24no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—42no—
254C22×C4—52no—
255C22×C4—52no—
256C22×C4—52no—
257C22×C4—52no—
258C22×C4—52no—
259C22×C4—52no—
260C22×C4—52no—
261C22×C4—52no—
262C22×C4—52no—
263C22×C4—52no—
264C22×C4—101no—
265C22×C4—101no—
266C22×C4—101no—
267C22×C4—101no—
268C22×C4—101no—
269C22×C4—101no—
270C22×C4—101no—
271C22×C4—101no—
272C22×C4—101no—
273C22×C4—101no—
274C22×C4—202no—
275C22×C4—202no—
276C22×C4D5⋊C812yes—
277C22×C4#70012yes—
278C22×C4C22⋊AGL(1,𝔽5)12yes—
279C22×C4C22⋊AGL(1,𝔽5)12yes—
280C22×C4C22⋊AGL(1,𝔽5)12yes—
281C2×C8—204no—
282C2×C8—208no—
283C4⋊C4—108no—
284C4⋊C4—108no—
285C4⋊C4—108no—
286C42—28no—
287C42—108no—
288C42—108no—
289C2×C5—21no—
290C2×C5—21no—
291C2×C5—21no—
292C2×C5—21no—
293C2×C5#146112yes—
294C2×C5#146712yes—
295C2×C5#177911yescharacteristic
296C2×C5#178211yescharacteristic
297C2×C5#178411yescharacteristic
298C23—22no—
299C23—22no—
300C23C2×D5⋊C811yescharacteristic
301C23C2×#70011yescharacteristic
302C23D5⋊M1611yescharacteristic
303C23D5⋊M1611yescharacteristic
304C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
305C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
306C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
307Q8—1032no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—54no—
323C2×C4—54no—
324C2×C4—54no—
325C2×C4—102no—
326C2×C4—102no—
327C2×C4—104no—
328C2×C4—102no—
329C2×C4—102no—
330C2×C4—102no—
331C2×C4—102no—
332C2×C4—102no—
333C2×C4—102no—
334C2×C4—102no—
335C2×C4—102no—
336C2×C4—102no—
337C2×C4—102no—
338C2×C4—102no—
339C2×C4—202no—
340C2×C4—202no—
341C2×C4—202no—
342C2×C4—202no—
343C2×C4—202no—
344C2×C4#400314yes—
345C2×C4#400514yes—
346C8—404no—
347C5#830311yescharacteristic, complemented, Sylow
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22#6574512yes—
357C22C2×#400311yescharacteristic
358C22D5⋊(C22⋊C8)11yescharacteristic
359C22D5⋊(C22⋊C8)11yescharacteristic
360C22#6575511yescharacteristic
361C22#6575611yescharacteristic
362C22#6575611yescharacteristic
363C22C2×#400512yes—
364C22#6580011yescharacteristic
365C4—24no—
366C4—24no—
367C4—42no—
368C4—104no—
369C4—104no—
370C4—104no—
371C4—202no—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—21no—
376C2#1060416112yes—
377C2#1060416412yes—
378C2#1060489111yescharacteristic
379C2#1060489811yescharacteristic
380C2#1060490511yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC23×C5C22×C8
FrattiniC24C22×AGL(1,𝔽5)
FittingC22×C42×C5C4
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22×C4
cosocleC23×Dic5C23
hypercenterC22×C42AGL(1,𝔽5)
hypocenterC5#8303
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
33. C22×Dic10C8semidirect
347. C5#8303semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic102
#106049022
C2×#649142
C2×#649132
#83035