Finite Group Databasebeta

← #12009886

Subgroups — #12009886

Order 1280.

464 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 87 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
1#10614104C211yesmaximal, characteristic
2C4×C5×#100C211yesmaximal, characteristic
3#10602395C211yesmaximal, characteristic
4#10597986C214yesmaximal, complemented
5C2×C4×C5×D4C2211yescharacteristic
6C2×#4081—21no—
7C22×C4⋊Dic5C411yescharacteristic
8C2×C5×#100—21no—
9C4×C5×M16—21no—
10#65501—21no—
11#65501C411yescharacteristic
12#65496—21no—
13#65272C2212yes—
14#65242C412yes—
15#65232—21no—
16#65217—21no—
17C5×#343C2212yes—
18#64748C2212yes—
19#64745—21no—
20#11780—51nomaximal, Sylow
21C22×C5×D4D411yescharacteristic
22C23×C4×C5C2×C411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×Dic5—21no—
25C2×C5×M16—22no—
26C4×C5×D4—41no—
27C4×C5×D4—41no—
28C2×C5×C4⋊C4C2311yescharacteristic
29C2×C5×C22⋊C4C2×C411yescharacteristic
30C2×C5×C22⋊C4D411yescharacteristic
31C2×C42×C5D411yescharacteristic
32C2×C22⋊Dic5—21no—
33C2×C22⋊Dic5—22no—
34#4081—44no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—41no—
38C2×C4⋊Dic5—41no—
39C2×C4⋊Dic5C2×C412yes—
40C2×#683—22no—
41C2×#681—41no—
42C5×#100—24no—
43C5×#97—41no—
44C4×C5×C8—41no—
45#3963—22no—
46#3963—22no—
47#3963C2×C412yes—
48C22⋊#168—22no—
49C22⋊#168—41no—
50#2486—51no—
51C4×#100D511yescharacteristic
52#1465—51no—
53#1346—54no—
54C24×C5C22⋊C411yescharacteristic
55C24×C5C22⋊C411yescharacteristic
56C2×C5×D4—22no—
57C2×C5×D4—22no—
58C2×C5×D4—41no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—42no—
64C22×C4×C5—42no—
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22×C411yescharacteristic
68C22×C4×C5C2×D411yescharacteristic
69C22×C4×C5C2×D411yescharacteristic
70C22×Dic5—22no—
71C22×Dic5—22no—
72C22×Dic5—42no—
73C22×Dic5—42no—
74C22×Dic5—42no—
75C5×M16—24no—
76C5×M16—42no—
77C2×C5×C8—42no—
78C5×C4⋊C4—41no—
79C5×C22⋊C4—41no—
80C5×C22⋊C4—41no—
81C42×C5—21no—
82C42×C5—21no—
83C22⋊Dic5—42no—
84C22⋊Dic5—44no—
85C4⋊Dic5—42no—
86C4⋊Dic5—41no—
87C4⋊Dic5—41no—
88C4⋊Dic5—42no—
89#683—44no—
90#681—82no—
91C2×#168—42no—
92C2×#123—101no—
93C2×C4×D4C2×D511yescharacteristic
94C22×C4⋊C4—51no—
95C2×#100—21no—
96#407—101no—
97C4×M16—21no—
98#398—52no—
99#397—52no—
100#389—101no—
101#381—101no—
102#380—51no—
103#380—101no—
104#343C2×D512yes—
105#324—52no—
106#323—101no—
107C23×C5—21no—
108C23×C5—21no—
109C23×C5—21no—
110C23×C5—21no—
111C23×C5—21no—
112C23×C5—41no—
113C23×C5—41no—
114C23×C5—41no—
115C23×C5—41no—
116C23×C5#10412yes—
117C23×C5C2×C22⋊C411yescharacteristic
118C5×D4—44no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—22no—
122C2×C4×C5—21no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5—42no—
128C2×C4×C5—41no—
129C2×C4×C5—41no—
130C2×C4×C5—41no—
131C2×C4×C5—81no—
132C2×C4×C5#9911yescharacteristic
133C2×C4×C5#9911yescharacteristic
134C2×C4×C5AGL(1,ℤ/8)12yes—
135C2×Dic5—42no—
136C2×Dic5—42no—
137C2×Dic5—42no—
138C2×Dic5—42no—
139C2×Dic5—42no—
140C2×Dic5—42no—
141C2×Dic5—84no—
142C5×C8—44no—
143#168—82no—
144C22×D4C22⋊D511yescharacteristic
145C23×C4—101no—
146C23×C4C4×D511yescharacteristic
147C23×C4D2011yescharacteristic
148C2×M16—22no—
149C2×M16—201no—
150#123—204no—
151C4×D4—41no—
152C4×D4—41no—
153C2×C4⋊C4—52no—
154C2×C4⋊C4—101no—
155C2×C4⋊C4—101no—
156C2×C4⋊C4—102no—
157C2×C4⋊C4—201no—
158C2×C4⋊C4—201no—
159C2×C4⋊C4C22×D511yescharacteristic
160C2×C22⋊C4—101no—
161C2×C22⋊C4—102no—
162C2×C22⋊C4C4×D511yescharacteristic
163C2×C22⋊C4D2011yescharacteristic
164C2×C42C22⋊D511yescharacteristic
165#100—24no—
166C22⋊C8—102no—
167C22⋊C8—201no—
168#97—41no—
169C4×C8—41no—
170#95—52no—
171#95—102no—
172#95—102no—
173C22×C5—21no—
174C22×C5—21no—
175C22×C5—22no—
176C22×C5—42no—
177C22×C5—42no—
178C22×C5—42no—
179C22×C5—41no—
180C22×C5—41no—
181C22×C5—41no—
182C22×C5—41no—
183C22×C5—41no—
184C22×C5—81no—
185C22×C5C2×#9911yescharacteristic
186C22×C5#41811yescharacteristic
187C22×C5C2×#10411yescharacteristic
188C4×C5—21no—
189C4×C5—22no—
190C4×C5—41no—
191C4×C5—41no—
192C4×C5—41no—
193C4×C5#35212yes—
194Dic5—82no—
195Dic5—82no—
196C24#68511yescharacteristic
197C24#68511yescharacteristic
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—41no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—102no—
208C22×C4—102no—
209C22×C4—202no—
210C22×C4—202no—
211C22×C4—202no—
212C22×C4#68511yescharacteristic
213C22×C4#68511yescharacteristic
214C22×C4C2×C4×D511yescharacteristic
215C22×C4C2×D2011yescharacteristic
216C22×C4C2×C22⋊D511yescharacteristic
217M16—24no—
218M16—42no—
219M16—402no—
220C2×C8—42no—
221C2×C8—202no—
222C4⋊C4—41no—
223C4⋊C4—202no—
224C4⋊C4—202no—
225C4⋊C4—201no—
226C4⋊C4—201no—
227C4⋊C4—204no—
228C22⋊C4—41no—
229C22⋊C4—41no—
230C22⋊C4—202no—
231C22⋊C4—204no—
232C42—21no—
233C42—21no—
234C2×C5—21no—
235C2×C5—21no—
236C2×C5—42no—
237C2×C5—81no—
238C2×C5#150711yescharacteristic
239C2×C5C2×#35211yescharacteristic
240C2×C5#213511yescharacteristic
241C23—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—41no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23#393712yes—
251C23C2×#68511yescharacteristic
252D4—44no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—81no—
266C2×C4—202no—
267C2×C4—202no—
268C2×C4—202no—
269C2×C4—202no—
270C2×C4—202no—
271C2×C4—202no—
272C2×C4—404no—
273C2×C4#393811yescharacteristic
274C2×C4#393811yescharacteristic
275C2×C4#409512yes—
276C8—44no—
277C8—402no—
278C5#1178011yescharacteristic, complemented, Sylow
279C22—21no—
280C22—21no—
281C22—22no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—81no—
291C22C2×#393711yescharacteristic
292C22C2×#393811yescharacteristic
293C22#6529011yescharacteristic
294C4—22no—
295C4—21no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—402no—
300C4—402no—
301C4#6469612yes—
302C2—21no—
303C2—21no—
304C2—42no—
305C2—81no—
306C2#1060023711yescharacteristic
307C2C2×#6469611yescharacteristic
308C2#1060094311yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC4×C5×#100C2
socleC22×C5C2×#99
prime radicalC22×C5×D4D4
cosocleC2×C5×C4⋊C4C23
hypercenterC4×#100D5
hypocenterC5#11780
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
4. #10597986C2semidirect
278. C5#11780semidirect

Maximal subgroups

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

subgroupindex
#106141042
C4×C5×#1002
#106023952
#105979862
#117805