Finite Group Databasebeta

← #11995040

Subgroups — #11995040

Order 1280.

800 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
2#10613811C211yesmaximal, characteristic
3#10602324C211yesmaximal, characteristic, complemented
4C2×#64671C212yesmaximal
5#10598103C212yesmaximal, complemented
6C22×C5×C4⋊C4—21no—
7C22×C42×C5—21no—
8C22×C42×C5C2211yescharacteristic
9C2×#4076C2211yescharacteristic
10C2×#4075—21no—
11C4×C5×C4⋊C4—24no—
12C2×C5×#95C2212yes—
13#65502—21no—
14#65501C2211yescharacteristic
15C2×C22⋊#168C2212yes—
16#65229—22no—
17#65228C412yescomplemented
18#65217C412yescomplemented
19#64744—22no—
20#64671—24no—
21#9148—51nomaximal, Sylow
22C23×C4×C5—22no—
23C23×C4×C5D411yescharacteristic
24C23×C4×C5D411yescharacteristic
25C23×C4×C5C2311yescharacteristic
26C22×C22⋊D5—21no—
27C22×D20C2×C411yescharacteristic
28C2×C5×C4⋊C4—24no—
29C2×C5×C4⋊C4—28no—
30C2×C42×C5—22no—
31C2×C42×C5—22no—
32C2×C42×C5—24no—
33C2×C42×C5—42no—
34C2×C42×C5—42no—
35C2×C42×C5C2×C412yes—
36C2×C42×C5D412yes—
37C2×C22⋊Dic5—21no—
38#4076—22no—
39#4076—22no—
40#4075—42no—
41#4075—42no—
42C2×#685—22no—
43C2×#685—22no—
44C2×#685—21no—
45C2×C4⋊Dic5C2×C411yescharacteristic
46C2×C4⋊Dic5C2×C412yes—
47C2×#683—22no—
48C22×#168—22no—
49C5×#95—22no—
50C5×#95D414yes—
51#3963—22no—
52#3963—21no—
53C22⋊#168—22no—
54C22⋊#168—22no—
55#2854—51no—
56C2×C4×C4⋊C4D511yescharacteristic, complemented
57#1817—51no—
58C2×#327—52no—
59#1294—52no—
60C24×C5C2×D411yescharacteristic
61C23×D5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—24no—
69C22×C4×C5—28no—
70C22×C4×C5—24no—
71C22×C4×C5—42no—
72C22×C4×C5—44no—
73C22×C4×C5—42no—
74C22×C4×C5—42no—
75C22×C4×C5C22⋊C412yes—
76C22×C4×C5C22⋊C412yes—
77C22×C4×C5D812yes—
78C22×C4×C5SD1612yes—
79C22×C4×C5C22×C411yescharacteristic
80C22×C4×C5C2×D411yescharacteristic
81C22×C4×C5C2×D412yes—
82C22×C4×C5#4112yes—
83C2×C22⋊D5—41no—
84C2×C22⋊D5—41no—
85C2×C22⋊D5—41no—
86C2×C22⋊D5—41no—
87C2×C22⋊D5—41no—
88C2×C22⋊D5—41no—
89C22×Dic5—22no—
90C22×Dic5—21no—
91C2×D20—22no—
92C2×D20—42no—
93C5×C4⋊C4—216no—
94C42×C5—24no—
95C42×C5—24no—
96C42×C5—48no—
97C22⋊Dic5—41no—
98C22⋊Dic5—41no—
99#685—44no—
100#685—44no—
101#685—42no—
102C4⋊Dic5—22no—
103C4⋊Dic5—42no—
104#683—44no—
105C2×#168—44no—
106C2×#168—42no—
107C2×#123—101no—
108C2×#121—51no—
109C22×C4⋊C4—21no—
110C22×C42—21no—
111C22×C42C2×D511yescharacteristic
112C2×C22⋊C8—52no—
113#390—52no—
114#389—52no—
115#388—102no—
116#386—101no—
117#380—51no—
118C4×C4⋊C4—24no—
119C2×#95C2×D512yes—
120#336—102no—
121#327—104no—
122C23×C5—22no—
123C23×C5—22no—
124C23×C5C2×C22⋊C411yescharacteristic
125C23×C5#12011yescharacteristic
126C23×C5#12311yescharacteristic
127C23×C5C2×D811yescharacteristic
128C23×C5C2×SD1611yescharacteristic
129C23×C5AGL(1,ℤ/8)11yescharacteristic
130C23×C5#13711yescharacteristic
131C22×D5—41no—
132C22×D5—42no—
133C22×D5—41no—
134C22×D5—41no—
135C22×D5—42no—
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—22no—
148C2×C4×C5—28no—
149C2×C4×C5—42no—
150C2×C4×C5—42no—
151C2×C4×C5—44no—
152C2×C4×C5—48no—
153C2×C4×C5—48no—
154C2×C4×C5—44no—
155C2×C4×C5#10214yes—
156C2×C4×C5#10414yes—
157C2×C4×C5C4×D412yes—
158C2×C4×C5#12112yes—
159C22⋊D5—81no—
160C22⋊D5—81no—
161C22⋊D5—81no—
162C22⋊D5—81no—
163C2×Dic5—41no—
164C2×Dic5—42no—
165C2×Dic5—41no—
166C2×Dic5—42no—
167C2×Dic5—41no—
168C2×Dic5—42no—
169D20—82no—
170#168—82no—
171C22×D4—51no—
172C22×D4—101no—
173C23×C4—22no—
174C23×C4C22⋊D511yescharacteristic
175C23×C4C22⋊D511yescharacteristic
176C23×C4C22×D511yescharacteristic
177C22×C8—102no—
178#123—202no—
179#123—202no—
180#121—102no—
181#121—102no—
182C2×C4⋊C4—28no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—51no—
185C2×C4⋊C4—52no—
186C2×C4⋊C4—102no—
187C2×C22⋊C4—101no—
188C2×C22⋊C4—102no—
189C2×C22⋊C4—102no—
190C2×C22⋊C4—101no—
191C2×C42—22no—
192C2×C42—22no—
193C2×C42—24no—
194C2×C42—42no—
195C2×C42—42no—
196C2×C42C4×D512yes—
197C2×C42D2012yes—
198C22⋊C8—102no—
199C22⋊C8—102no—
200#95—22no—
201#95—102no—
202#95—101no—
203#95C22⋊D514yes—
204C22×C5—21no—
205C22×C5—21no—
206C22×C5—21no—
207C22×C5—21no—
208C22×C5—22no—
209C22×C5—22no—
210C22×C5—22no—
211C22×C5—22no—
212C22×C5#38611yescharacteristic
213C22×C5#41012yes—
214C22×C5C2×#10211yescharacteristic
215C22×C5#41711yescharacteristic
216C22×C5C2×#10412yes—
217C22×C5#44711yescharacteristic
218C22×C5#44811yescharacteristic
219C22×C5#48011yescharacteristic
220C22×C5#48111yescharacteristic
221C2×D5—81no—
222C2×D5—81no—
223C2×D5—81no—
224C2×D5—82no—
225C2×D5—82no—
226C4×C5—24no—
227C4×C5—24no—
228C4×C5—22no—
229C4×C5—22no—
230C4×C5—48no—
231Dic5—81no—
232Dic5—82no—
233C24—101no—
234C24C2×C22⋊D511yescharacteristic
235C2×D4—102no—
236C2×D4—202no—
237C2×D4—201no—
238C2×D4—201no—
239C2×D4—201no—
240C2×D4—201no—
241C2×D4—201no—
242C2×D4—201no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—24no—
250C22×C4—28no—
251C22×C4—24no—
252C22×C4—42no—
253C22×C4—44no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—102no—
257C22×C4—101no—
258C22×C4#68512yes—
259C22×C4#68512yes—
260C22×C4#68612yes—
261C22×C4#68812yes—
262C22×C4C2×C4×D511yescharacteristic
263C22×C4C2×D2011yescharacteristic
264C22×C4#70912yes—
265C22×C4C2×C22⋊D512yes—
266C2×C8—204no—
267C2×C8—202no—
268C4⋊C4—216no—
269C4⋊C4—102no—
270C4⋊C4—202no—
271C4⋊C4—204no—
272C22⋊C4—201no—
273C22⋊C4—201no—
274C22⋊C4—204no—
275C22⋊C4—204no—
276C22⋊C4—202no—
277C42—24no—
278C42—24no—
279C42—48no—
280C2×C5—21no—
281C2×C5—21no—
282C2×C5—21no—
283C2×C5—21no—
284C2×C5#150212yes—
285C2×C5#150912yes—
286C2×C5#187411yescharacteristic
287C2×C5#189611yescharacteristic
288C2×C5#189911yescharacteristic
289D5—161no—
290C23—22no—
291C23—22no—
292C23—202no—
293C23—202no—
294C23—201no—
295C23—201no—
296C23—201no—
297C23C2×#68511yescharacteristic
298C23#407511yescharacteristic
299C23C2×#68611yescharacteristic
300C23#407811yescharacteristic
301C23C2×#68811yescharacteristic
302C23#408811yescharacteristic
303C23#409911yescharacteristic
304D4—402no—
305D4—401no—
306D4—401no—
307D4—401no—
308D4—401no—
309C2×C4—24no—
310C2×C4—24no—
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—22no—
320C2×C4—22no—
321C2×C4—28no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—48no—
325C2×C4—48no—
326C2×C4—44no—
327C2×C4—44no—
328C2×C4—202no—
329C2×C4—202no—
330C2×C4—201no—
331C2×C4—202no—
332C2×C4—201no—
333C2×C4—201no—
334C2×C4#393714yes—
335C2×C4#394114yes—
336C2×C4C4×C22⋊D512yes—
337C2×C4#407612yes—
338C8—402no—
339C5#914811yescharacteristic, complemented, Sylow
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—402no—
349C22—402no—
350C22—401no—
351C22—401no—
352C22—401no—
353C22C2×#393712yes—
354C22C2×#394111yescharacteristic
355C22#6525511yescharacteristic
356C22#6525611yescharacteristic
357C22#6525711yescharacteristic
358C22#6529512yes—
359C22#6550211yescharacteristic
360C22#6550611yescharacteristic
361C22#6551611yescharacteristic
362C4—24no—
363C4—24no—
364C4—22no—
365C4—22no—
366C4—48no—
367C4—402no—
368C4—401no—
369C2—21no—
370C2—21no—
371C2—21no—
372C2—21no—
373C2—801no—
374C2#1060026212yes—
375C2#1060026312yes—
376C2#1060232511yescharacteristic
377C2#1060235311yescharacteristic
378C2#1060238811yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C4×C5×C4⋊C4C2
socleC23×C5C2×C22⋊C4
prime radicalC2×#4076C22
cosocleC23×C4×C5C23
hypercenterC2×C4×C4⋊C4D5
hypocenterC5#9148
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C5×C4⋊C4C2semidirect
3. #10602324C2semidirect
5. #10598103C2semidirect
17. #65228C4semidirect
18. #65217C4semidirect
56. C2×C4×C4⋊C4D5semidirect
339. C5#9148semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×C4⋊C42
#106138112
#106023242
C2×#646712
#105981032
#91485