Finite Group Databasebeta

← #12010033

Subgroups — #12010033

Order 1280.

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

normal subgroups only

This group has 434 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
1C2×#65275C211yesmaximal, characteristic
2C5×#1821C211yesmaximal, characteristic
3#10602345C211yesmaximal, characteristic
4#10597987C214yesmaximal, complemented
5C22×C5×C4⋊C4C2211yescharacteristic
6C22×C4⋊Dic5C411yescharacteristic
7C5×#407—21no—
8C2×#3963—21no—
9C2×#3963—21no—
10C2×#3963C411yescharacteristic
11#65496—21no—
12#65275—21no—
13#65275—21no—
14#65275C412yes—
15#65275C2212yes—
16C5×#343—21no—
17C5×#343C2212yes—
18#64748—21no—
19#64748C2212yes—
20#11814—51nomaximal, Sylow
21C23×C4×C5C2×C411yescharacteristic
22C23×C4×C5D411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×Dic5—21no—
25C23×Dic5—21no—
26C2×C5×M16—22no—
27C2×C5×C4⋊C4—41no—
28C2×C5×C4⋊C4—41no—
29C2×C5×C4⋊C4C2×C411yescharacteristic
30C2×C5×C4⋊C4D411yescharacteristic
31C2×C5×C4⋊C4D411yescharacteristic
32C2×C5×C4⋊C4C2311yescharacteristic
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5—41no—
35C2×C4⋊Dic5—41no—
36C2×C4⋊Dic5C2×C412yes—
37C2×#681—41no—
38C5×C22⋊C8—41no—
39C5×C22⋊C8—41no—
40#3963—22no—
41#3963—22no—
42#3963—21no—
43#3963—22no—
44#3963—22no—
45#3963C2×C412yes—
46C22⋊#168—22no—
47C22⋊#168—41no—
48C2×#400—51no—
49#1821D511yescharacteristic
50#1463—51no—
51#1353—54no—
52C24×C5C22⋊C411yescharacteristic
53C22×C4×C5—21no—
54C22×C4×C5—21no—
55C22×C4×C5—21no—
56C22×C4×C5—21no—
57C22×C4×C5—21no—
58C22×C4×C5—21no—
59C22×C4×C5—22no—
60C22×C4×C5—41no—
61C22×C4×C5—42no—
62C22×C4×C5—42no—
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22×C411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×C4×C5C2×D411yescharacteristic
69C22×Dic5—22no—
70C22×Dic5—22no—
71C22×Dic5—42no—
72C22×Dic5—42no—
73C22×Dic5—44no—
74C22×Dic5—42no—
75C22×Dic5—41no—
76C22×Dic5—41no—
77C5×M16—42no—
78C5×M16—42no—
79C2×C5×C8—42no—
80C5×C4⋊C4—41no—
81C5×C4⋊C4—41no—
82C5×C4⋊C4—41no—
83C5×C4⋊C4—41no—
84C4⋊Dic5—42no—
85C4⋊Dic5—42no—
86#681—82no—
87C2×#168—42no—
88C22×C4⋊C4—51no—
89C22×C4⋊C4C2×D511yescharacteristic
90#407—21no—
91#407—101no—
92#400—52no—
93#400—52no—
94#400—101no—
95#400—101no—
96C2×#95—51no—
97C2×#95—101no—
98C2×#95—101no—
99#343—21no—
100#343C2×D512yes—
101#324—52no—
102#324—101no—
103C23×C5—22no—
104C23×C5—22no—
105C23×C5—21no—
106C23×C5—21no—
107C23×C5#9911yescharacteristic
108C23×C5#9911yescharacteristic
109C23×C5C2×C22⋊C411yescharacteristic
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—42no—
120C2×C4×C5—42no—
121C2×C4×C5—42no—
122C2×C4×C5—42no—
123C2×C4×C5—42no—
124C2×C4×C5—41no—
125C2×C4×C5—41no—
126C2×C4×C5—41no—
127C2×C4×C5—41no—
128C2×C4×C5—81no—
129C2×C4×C5#13712yes—
130C2×Dic5—42no—
131C2×Dic5—42no—
132C2×Dic5—44no—
133C2×Dic5—42no—
134C2×Dic5—42no—
135C2×Dic5—84no—
136C2×Dic5—82no—
137C2×Dic5—82no—
138C5×C8—82no—
139#168—82no—
140C23×C4—101no—
141C23×C4—101no—
142C23×C4C4×D511yescharacteristic
143C23×C4D2011yescharacteristic
144C23×C4C22⋊D511yescharacteristic
145C2×M16—22no—
146C2×M16—201no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—52no—
150C2×C4⋊C4—101no—
151C2×C4⋊C4—201no—
152C2×C4⋊C4—201no—
153C2×C4⋊C4C4×D511yescharacteristic
154C2×C4⋊C4D2011yescharacteristic
155C2×C4⋊C4C22⋊D511yescharacteristic
156C2×C4⋊C4C22×D511yescharacteristic
157C22⋊C8—41no—
158C22⋊C8—41no—
159C22⋊C8—102no—
160C22⋊C8—201no—
161#95—52no—
162#95—101no—
163#95—102no—
164#95—102no—
165#95—102no—
166#95—102no—
167C22×C5—24no—
168C22×C5—24no—
169C22×C5—21no—
170C22×C5—21no—
171C22×C5—21no—
172C22×C5—21no—
173C22×C5—21no—
174C22×C5—21no—
175C22×C5#35212yes—
176C22×C5#35512yes—
177C22×C5C2×#9911yescharacteristic
178C22×C5#41911yescharacteristic
179C22×C5#42111yescharacteristic
180C4×C5—22no—
181C4×C5—41no—
182C4×C5—41no—
183C4×C5—41no—
184C4×C5—41no—
185C4×C5—41no—
186Dic5—82no—
187Dic5—82no—
188C24#68511yescharacteristic
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—41no—
197C22×C4—42no—
198C22×C4—42no—
199C22×C4—102no—
200C22×C4—102no—
201C22×C4—202no—
202C22×C4—202no—
203C22×C4—204no—
204C22×C4—202no—
205C22×C4—201no—
206C22×C4—201no—
207C22×C4#68511yescharacteristic
208C22×C4#68511yescharacteristic
209C22×C4#68511yescharacteristic
210C22×C4C2×C4×D511yescharacteristic
211C22×C4C2×D2011yescharacteristic
212C22×C4C2×C22⋊D511yescharacteristic
213M16—42no—
214M16—42no—
215M16—402no—
216C2×C8—42no—
217C2×C8—202no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—202no—
223C4⋊C4—202no—
224C2×C5—21no—
225C2×C5—22no—
226C2×C5—22no—
227C2×C5—21no—
228C2×C5#151111yescharacteristic
229C2×C5C2×#35211yescharacteristic
230C2×C5C2×#35511yescharacteristic
231C23—21no—
232C23—21no—
233C23—22no—
234C23—22no—
235C23#393811yescharacteristic
236C23#393811yescharacteristic
237C23C2×#68511yescharacteristic
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—81no—
257C2×C4—202no—
258C2×C4—202no—
259C2×C4—204no—
260C2×C4—202no—
261C2×C4—202no—
262C2×C4—404no—
263C2×C4—402no—
264C2×C4—402no—
265C2×C4#409712yes—
266C8—82no—
267C8—402no—
268C5#1181411yescharacteristic, complemented, Sylow
269C22—24no—
270C22—24no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22#6469612yes—
278C22#6469712yes—
279C22C2×#393811yescharacteristic
280C22#6529311yescharacteristic
281C22#6529411yescharacteristic
282C4—22no—
283C4—41no—
284C4—41no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—402no—
289C4—402no—
290C2—21no—
291C2—21no—
292C2—22no—
293C2—22no—
294C2#1060032611yescharacteristic
295C2C2×#6469611yescharacteristic
296C2C2×#6469711yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1821C2
socleC22×C5C2×#99
prime radicalC24×C5C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#1821D5
hypocenterC5#11814
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
4. #10597987C2semidirect
268. C5#11814semidirect

Maximal subgroups

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

subgroupindex
C2×#652752
C5×#18212
#106023452
#105979872
#118145