Finite Group Databasebeta

← #11995046

Subgroups — #11995046

Order 1280.

756 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2854C211yesmaximal, characteristic
2C2×#65221C211yesmaximal, characteristic, complemented
3C2×#64757C212yesmaximal
4#10602324C211yesmaximal, characteristic, complemented
5#10598115C212yesmaximal, complemented
6C2×C5×#123—21no—
7C2×C5×#121C2211yescharacteristic
8C22×C42×C5C2211yescharacteristic
9C22×C4×Dic5—21no—
10C5×#390C412yescomplemented
11C5×#389C412yescomplemented
12C5×#388—22no—
13C5×#386—21no—
14C5×#380C2211yescharacteristic
15C2×#3963—21no—
16C2×#3963C2212yes—
17C2×C22⋊#168C2212yes—
18#65221—24no—
19#64757—24no—
20#64744—22no—
21#9149—51nomaximal, Sylow
22C22×C5×D4—21no—
23C22×C5×D4C2×C411yescharacteristic
24C23×C4×C5D411yescharacteristic
25C23×C4×C5D411yescharacteristic
26C23×C4×C5C2311yescharacteristic
27C23×Dic5—22no—
28C5×#123—44no—
29C5×#121—22no—
30C5×#121—22no—
31C2×C5×C4⋊C4—22no—
32C2×C5×C4⋊C4C2×C411yescharacteristic
33C2×C5×C4⋊C4C2×C412yes—
34C2×C5×C22⋊C4—21no—
35C2×C5×C22⋊C4—22no—
36C2×C5×C22⋊C4—22no—
37C2×C5×C22⋊C4—21no—
38C2×C42×C5—22no—
39C2×C42×C5—22no—
40C2×C42×C5C2×C412yes—
41C2×C42×C5D412yes—
42C2×C4×Dic5—28no—
43C2×C4×Dic5—24no—
44C22×#168—22no—
45C5×#95—22no—
46C5×#95—21no—
47#3963—24no—
48#3963—22no—
49#3963D414yes—
50C22⋊#168—22no—
51C22⋊#168—22no—
52#2854D511yescharacteristic
53C2×#376—51no—
54#1817—51no—
55C2×#327—52no—
56#1294—52no—
57C24×C5—21no—
58C24×C5C2×D411yescharacteristic
59C2×C5×D4—22no—
60C2×C5×D4—42no—
61C2×C5×D4—41no—
62C2×C5×D4—41no—
63C2×C5×D4—42no—
64C2×C5×D4—42no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—24no—
68C22×C4×C5—21no—
69C22×C4×C5—21no—
70C22×C4×C5—22no—
71C22×C4×C5—22no—
72C22×C4×C5—22no—
73C22×C4×C5—21no—
74C22×C4×C5—42no—
75C22×C4×C5C22⋊C412yes—
76C22×C4×C5C22⋊C412yes—
77C22×C4×C5C22×C411yescharacteristic
78C22×C4×C5C2×D412yes—
79C22×C4×C5C2×D411yescharacteristic
80C22×C4×C5#4112yes—
81C22×Dic5—28no—
82C22×Dic5—24no—
83C22×Dic5—44no—
84C22×Dic5—42no—
85C22×Dic5—42no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4—42no—
88C5×C4⋊C4—44no—
89C5×C22⋊C4—44no—
90C5×C22⋊C4—42no—
91C5×C22⋊C4—44no—
92C5×C22⋊C4—42no—
93C42×C5—24no—
94C42×C5—24no—
95C4×Dic5—216no—
96C2×#168—44no—
97C2×#168—42no—
98C2×#123—21no—
99C2×#121C2×D511yescharacteristic
100C22×C42—101no—
101C22×C42C2×D511yescharacteristic
102C2×C22⋊C8—52no—
103#390Dic512yescomplemented
104#389Dic512yescomplemented
105#388—22no—
106#386—21no—
107#380C2×D511yescharacteristic
108#376—104no—
109C2×#95—52no—
110C2×#95—101no—
111#336—102no—
112#327—104no—
113C23×C5—22no—
114C23×C5—22no—
115C23×C5—41no—
116C23×C5—42no—
117C23×C5—41no—
118C23×C5—41no—
119C23×C5—42no—
120C23×C5C2×C22⋊C411yescharacteristic
121C23×C5#12011yescharacteristic
122C23×C5#12311yescharacteristic
123C23×C5#13512yes—
124C23×C5AGL(1,ℤ/8)12yes—
125C5×D4—82no—
126C5×D4—82no—
127C5×D4—82no—
128C2×C4×C5—24no—
129C2×C4×C5—24no—
130C2×C4×C5—22no—
131C2×C4×C5—22no—
132C2×C4×C5—22no—
133C2×C4×C5—22no—
134C2×C4×C5—22no—
135C2×C4×C5—22no—
136C2×C4×C5—22no—
137C2×C4×C5—42no—
138C2×C4×C5—42no—
139C2×C4×C5—42no—
140C2×C4×C5—42no—
141C2×C4×C5—41no—
142C2×C4×C5—42no—
143C2×C4×C5—41no—
144C2×C4×C5—42no—
145C2×C4×C5—41no—
146C2×C4×C5—42no—
147C2×C4×C5#10414yes—
148C2×C4×C5C4×D412yes—
149C2×C4×C5#12112yes—
150C2×Dic5—28no—
151C2×Dic5—44no—
152C2×Dic5—48no—
153C2×Dic5—48no—
154C2×Dic5—44no—
155#168—82no—
156C22×D4—21no—
157C22×D4C2×Dic511yescharacteristic
158C23×C4—102no—
159C23×C4C22⋊D511yescharacteristic
160C23×C4C22⋊D511yescharacteristic
161C23×C4C22×D511yescharacteristic
162C22×C8—102no—
163#123—44no—
164#121—22no—
165#121—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4C2×Dic511yescharacteristic
168C2×C4⋊C4C2×Dic512yes—
169C2×C22⋊C4—21no—
170C2×C22⋊C4—22no—
171C2×C22⋊C4—22no—
172C2×C22⋊C4—21no—
173C2×C42—22no—
174C2×C42—22no—
175C2×C42—104no—
176C2×C42—108no—
177C2×C42C2×Dic512yes—
178C2×C42C22⋊D512yes—
179C22⋊C8—102no—
180C22⋊C8—102no—
181#95—22no—
182#95—21no—
183#95—54no—
184#95—104no—
185#95—102no—
186C22×C5—21no—
187C22×C5—21no—
188C22×C5—21no—
189C22×C5—21no—
190C22×C5—24no—
191C22×C5—24no—
192C22×C5—81no—
193C22×C5—81no—
194C22×C5—81no—
195C22×C5—82no—
196C22×C5—82no—
197C22×C5#38611yescharacteristic
198C22×C5#41012yes—
199C22×C5#41611yescharacteristic
200C22×C5#41811yescharacteristic
201C22×C5C2×#10412yes—
202C22×C5#44912yes—
203C22×C5#48212yes—
204C4×C5—24no—
205C4×C5—22no—
206C4×C5—22no—
207C4×C5—42no—
208C4×C5—81no—
209C4×C5—82no—
210Dic5—48no—
211C24—21no—
212C24C2×C22⋊D511yescharacteristic
213C2×D4—22no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—41no—
218C2×D4—41no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—24no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—21no—
228C22×C4—42no—
229C22×C4—108no—
230C22×C4—104no—
231C22×C4—204no—
232C22×C4—202no—
233C22×C4—202no—
234C22×C4C22⋊Dic512yes—
235C22×C4C22⋊Dic512yes—
236C22×C4D4×D512yes—
237C22×C4#71112yes—
238C22×C4C22×Dic511yescharacteristic
239C22×C4C2×C22⋊D511yescharacteristic
240C2×C8—204no—
241C2×C8—202no—
242C4⋊C4—22no—
243C4⋊C4—42no—
244C4⋊C4—44no—
245C22⋊C4—44no—
246C22⋊C4—42no—
247C22⋊C4—44no—
248C22⋊C4—42no—
249C42—24no—
250C42—24no—
251C42—1016no—
252C2×C5—22no—
253C2×C5—22no—
254C2×C5—161no—
255C2×C5#150012yes—
256C2×C5#150512yes—
257C2×C5#187511yescharacteristic
258C2×C5#189611yescharacteristic
259C2×C5#189911yescharacteristic
260C23—22no—
261C23—22no—
262C23—41no—
263C23—41no—
264C23—41no—
265C23—42no—
266C23—42no—
267C23#407812yes—
268C23#408111yescharacteristic
269C23#408311yescharacteristic
270C23#409612yes—
271C23C2×C22⋊Dic511yescharacteristic
272D4—82no—
273D4—82no—
274D4—82no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—108no—
295C2×C4—204no—
296C2×C4—208no—
297C2×C4—208no—
298C2×C4—204no—
299C2×C4#396914yes—
300C2×C4D4×Dic512yes—
301C2×C4#408512yes—
302C8—402no—
303C5#914911yescharacteristic, complemented, Sylow
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—24no—
309C22—24no—
310C22—81no—
311C22—81no—
312C22—82no—
313C22—82no—
314C22—81no—
315C22#6532412yes—
316C22#6532612yes—
317C22#6550411yescharacteristic
318C22#6550911yescharacteristic
319C22#6552211yescharacteristic
320C22C2×#396912yes—
321C22#6552912yes—
322C4—22no—
323C4—22no—
324C4—24no—
325C4—42no—
326C4—82no—
327C4—81no—
328C4—208no—
329C2—22no—
330C2—22no—
331C2—161no—
332C2#1060247111yescharacteristic
333C2#1060249811yescharacteristic
334C2#1060250411yescharacteristic
335C2#1060254712yes—
336C2#1060260512yes—
subgroupG/H
centerC23C2×C22⋊Dic5
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#2854C2
socleC23×C5C2×C22⋊C4
prime radicalC2×C5×#121C22
cosocleC23×C4×C5C23
hypercenter#2854D5
hypocenterC5#9149
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2854

Complements

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

NH ≅ G/Ntype
2. C2×#65221C2semidirect
4. #10602324C2semidirect
5. #10598115C2semidirect
10. C5×#390C4semidirect
11. C5×#389C4semidirect
103. #390Dic5semidirect
104. #389Dic5semidirect
303. C5#9149semidirect

Maximal subgroups

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

subgroupindex
C5×#28542
C2×#652212
C2×#647572
#106023242
#105981152
#91495