Finite Group Databasebeta

← #12009916

Subgroups — #12009916

Order 1280.

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

normal subgroups only

This group has 460 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#10614115C211yesmaximal, characteristic
2C4×C5×#99C211yesmaximal, characteristic
3#10602395C211yesmaximal, characteristic
4#10597981C214yesmaximal, complemented
5C2×C4×C5×D4C2211yescharacteristic
6C2×#4015C411yescharacteristic, complemented
7C2×C5×#99—21no—
8C4×C5×C22⋊C4—21no—
9#65510—21no—
10#65501—21no—
11#65501—21no—
12#65496—21no—
13#65266—21no—
14#65236C412yescomplemented
15#65236C2212yes—
16C4×C4⋊Dic5C411yescharacteristic, complemented
17C5×#342C2212yes—
18#64748—21no—
19#64745C2212yes—
20#11787—51nomaximal, Sylow
21C22×C5×D4D411yescharacteristic
22C23×C4×C5D411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C22×Dic10C2×C412yes—
25C4×C5×D4—41no—
26C4×C5×D4—41no—
27C2×C5×C4⋊C4D411yescharacteristic
28C2×C5×C22⋊C4—22no—
29C2×C5×C22⋊C4C2×C411yescharacteristic
30C2×C5×C22⋊C4C2311yescharacteristic
31C2×C42×C5—41no—
32C2×C42×C5C2×C411yescharacteristic
33C2×C22⋊Dic5—22no—
34C2×C22⋊Dic5—22no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—21no—
38C2×C4×Dic5—21no—
39C2×#681—41no—
40#4015—41no—
41#4015—41no—
42C5×#99—24no—
43C5×#95—41no—
44#3963—22no—
45#3963—22no—
46#3963C2×C412yes—
47C22⋊#168—22no—
48C22⋊#168—41no—
49#2563—51no—
50C4×#99D511yescharacteristic
51#1465—51no—
52#1351—54no—
53C24×C5C22⋊C411yescharacteristic
54C24×C5C2×D411yescharacteristic
55C2×C5×D4—22no—
56C2×C5×D4—22no—
57C2×C5×D4—41no—
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—42no—
63C22×C4×C5—42no—
64C22×C4×C5—42no—
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22×C411yescharacteristic
69C22×C4×C5C2×D411yescharacteristic
70C22×Dic5—22no—
71C22×Dic5—22no—
72C2×Dic10—42no—
73C2×Dic10—82no—
74C5×C4⋊C4—41no—
75C5×C22⋊C4—24no—
76C5×C22⋊C4—41no—
77C5×C22⋊C4—41no—
78C5×C22⋊C4—42no—
79C42×C5—21no—
80C42×C5—21no—
81C42×C5—82no—
82C22⋊Dic5—82no—
83C22⋊Dic5—82no—
84C4⋊Dic5—42no—
85C4⋊Dic5—42no—
86C4⋊Dic5—41no—
87C4⋊Dic5—41no—
88C4×Dic5—42no—
89#681—82no—
90C2×#168—42no—
91C2×C4⋊Q8—51no—
92C2×C4×D4C2×D511yescharacteristic
93C2×#99—21no—
94#407—101no—
95#393—52no—
96#393—52no—
97#390—101no—
98#382—101no—
99#380—101no—
100#380—101no—
101C4×C4⋊C4—51no—
102C4×C22⋊C4—21no—
103#342C2×D512yes—
104#324—101no—
105#323—52no—
106C23×C5—21no—
107C23×C5—21no—
108C23×C5—21no—
109C23×C5—21no—
110C23×C5—21no—
111C23×C5—41no—
112C23×C5—41no—
113C23×C5—41no—
114C23×C5—41no—
115C23×C5C2×C22⋊C411yescharacteristic
116C23×C5#13712yes—
117C5×D4—44no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—22no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—21no—
124C2×C4×C5—42no—
125C2×C4×C5—42no—
126C2×C4×C5—41no—
127C2×C4×C5—41no—
128C2×C4×C5—41no—
129C2×C4×C5—44no—
130C2×C4×C5—81no—
131C2×C4×C5—81no—
132C2×C4×C5—82no—
133C2×C4×C5—82no—
134C2×C4×C5#9911yescharacteristic
135C2×C4×C5#9911yescharacteristic
136C2×C4×C5#10412yes—
137C2×Dic5—42no—
138C2×Dic5—42no—
139C2×Dic5—42no—
140C2×Dic5—42no—
141C2×Dic5—42no—
142C2×Dic5—42no—
143Dic10—84no—
144#168—82no—
145C22×Q8—52no—
146C22×D4C22⋊D511yescharacteristic
147C23×C4D2011yescharacteristic
148C23×C4C22⋊D511yescharacteristic
149C2×M16—201no—
150C4⋊Q8—201no—
151C4⋊Q8—201no—
152C4×D4—41no—
153C4×D4—41no—
154C2×C4⋊C4—101no—
155C2×C4⋊C4—101no—
156C2×C4⋊C4—101no—
157C2×C4⋊C4D2011yescharacteristic
158C2×C22⋊C4—22no—
159C2×C22⋊C4—102no—
160C2×C22⋊C4—102no—
161C2×C22⋊C4C4×D511yescharacteristic
162C2×C22⋊C4C22×D511yescharacteristic
163C2×C42—41no—
164C2×C42—101no—
165C2×C42C4×D511yescharacteristic
166#99—24no—
167C22⋊C8—102no—
168C22⋊C8—201no—
169#95—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—41no—
179C22×C5—41no—
180C22×C5—41no—
181C22×C5—41no—
182C22×C5—41no—
183C22×C5—81no—
184C22×C5—81no—
185C22×C5C2×#9911yescharacteristic
186C22×C5#41911yescharacteristic
187C22×C5C2×#10411yescharacteristic
188C4×C5—21no—
189C4×C5—22no—
190C4×C5—41no—
191C4×C5—41no—
192C4×C5—41no—
193C4×C5—84no—
194C4×C5#35412yes—
195Dic5—82no—
196Dic5—82no—
197C24#68511yescharacteristic
198C24C2×C22⋊D511yescharacteristic
199C2×Q8—202no—
200C2×Q8—402no—
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—41no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—102no—
212C22×C4—102no—
213C22×C4#68511yescharacteristic
214C22×C4#68511yescharacteristic
215C22×C4#68511yescharacteristic
216C22×C4C2×C4×D511yescharacteristic
217C22×C4C2×D2011yescharacteristic
218M16—402no—
219C2×C8—202no—
220C4⋊C4—41no—
221C4⋊C4—202no—
222C4⋊C4—202no—
223C4⋊C4—201no—
224C4⋊C4—201no—
225C22⋊C4—24no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—42no—
229C22⋊C4—402no—
230C22⋊C4—402no—
231C42—21no—
232C42—21no—
233C42—82no—
234C42—202no—
235C2×C5—21no—
236C2×C5—21no—
237C2×C5—42no—
238C2×C5—81no—
239C2×C5#150811yescharacteristic
240C2×C5#212211yescharacteristic
241C2×C5C2×#35411yescharacteristic
242C23—21no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23C2×#68511yescharacteristic
252C23#409712yes—
253Q8—404no—
254D4—44no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—44no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—82no—
270C2×C4—82no—
271C2×C4—202no—
272C2×C4—202no—
273C2×C4—202no—
274C2×C4—202no—
275C2×C4—202no—
276C2×C4—202no—
277C2×C4#393712yes—
278C2×C4#393811yescharacteristic
279C2×C4#393811yescharacteristic
280C8—402no—
281C5#1178711yescharacteristic, complemented, Sylow
282C22—21no—
283C22—21no—
284C22—22no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22—81no—
294C22C2×#393711yescharacteristic
295C22C2×#393811yescharacteristic
296C22#6529311yescharacteristic
297C4—22no—
298C4—21no—
299C4—41no—
300C4—41no—
301C4—41no—
302C4—84no—
303C4—402no—
304C4—402no—
305C4#6469312yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—81no—
310C2#1060023811yescharacteristic
311C2C2×#6469311yescharacteristic
312C2#1060085011yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C22⋊C4C22×D5
FittingC4×C5×#99C2
socleC22×C5C2×#99
prime radicalC22×C5×D4D4
cosocleC2×C5×C22⋊C4C23
hypercenterC4×#99D5
hypocenterC5#11787
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
4. #10597981C2semidirect
6. C2×#4015C4semidirect
14. #65236C4semidirect
16. C4×C4⋊Dic5C4semidirect
281. C5#11787semidirect

Maximal subgroups

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

subgroupindex
#106141152
C4×C5×#992
#106023952
#105979812
#117875