Finite Group Databasebeta

← #12010116

Subgroups — #12010116

Order 1280.

384 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 91 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×#2399C211yesmaximal, characteristic
2#10602430C211yesmaximal, characteristic
3#10602418C211yesmaximal, characteristic
4#10598141C212yesmaximal
5#10598139C212yesmaximal
6C2×C4×C5×Q8C411yescharacteristic
7C2×C4×C5×Q8C2211yescharacteristic
8C5×#398—21no—
9C5×#398C411yescharacteristic
10C5×#398C2211yescharacteristic
11C5×#395—21no—
12C5×#395C411yescharacteristic
13C5×#395C2211yescharacteristic
14C4×C5×C4⋊C4—21no—
15C4×C5×C4⋊C4—21no—
16C5×#376C411yescharacteristic
17C2×#3968—21no—
18#65215—21no—
19#65213—21no—
20#64750C2212yes—
21#64748—21no—
22#64748C2212yes—
23#11831—51nomaximal, Sylow
24C22×C5×Q8C2×C411yescharacteristic
25C22×C5×Q8D411yescharacteristic
26C4×C5×Q8—41no—
27C4×C5×Q8—41no—
28C4×C5×Q8—41no—
29C4×C5×Q8—41no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4C2×C411yescharacteristic
36C2×C5×C4⋊C4C2×C411yescharacteristic
37C2×C5×C4⋊C4D411yescharacteristic
38C2×C5×C4⋊C4C2311yescharacteristic
39C2×C42×C5—21no—
40C2×C42×C5—21no—
41C2×C42×C5C2×C411yescharacteristic
42C2×C42×C5D411yescharacteristic
43C2×C42×C5D411yescharacteristic
44C2×#681—22no—
45C5×#95—21no—
46C5×#95—21no—
47C5×#95—21no—
48C5×#95—21no—
49C5×#95—21no—
50C5×#95C2×C411yescharacteristic
51C5×#95C2×C411yescharacteristic
52#3968—42no—
53C22⋊#168—22no—
54C4⋊#168—41no—
55C4⋊#168—41no—
56C4⋊#168—41no—
57#3935—41no—
58#2399D511yescharacteristic
59#1801—51no—
60#1467—51no—
61#1354—52no—
62#1346—52no—
63C2×C5×Q8—21no—
64C2×C5×Q8—21no—
65C2×C5×Q8—41no—
66C2×C5×Q8—41no—
67C2×C5×Q8—42no—
68C2×C5×Q8—41no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—21no—
73C22×C4×C5C22⋊C411yescharacteristic
74C22×C4×C5C22⋊C411yescharacteristic
75C22×C4×C5C22⋊C411yescharacteristic
76C22×C4×C5C22⋊C411yescharacteristic
77C22×C4×C5C22×C411yescharacteristic
78C22×C4×C5C2×D411yescharacteristic
79C22×C4×C5C2×D411yescharacteristic
80C5×C4⋊C4—41no—
81C5×C4⋊C4—41no—
82C5×C4⋊C4—41no—
83C5×C4⋊C4—41no—
84C5×C4⋊C4—42no—
85C5×C4⋊C4—42no—
86C5×C4⋊C4—42no—
87C5×C4⋊C4—42no—
88C5×C4⋊C4—41no—
89C5×C4⋊C4—41no—
90C42×C5—24no—
91C42×C5—21no—
92C42×C5—21no—
93C42×C5—21no—
94C42×C5—21no—
95C42×C5—21no—
96C42×C5—21no—
97C42×C5—41no—
98C42×C5—41no—
99#681—42no—
100#681—42no—
101C2×#168—42no—
102C2×#168—42no—
103C2×C4×Q8Dic511yescharacteristic
104C2×C4×Q8C2×D511yescharacteristic
105#432—101no—
106#423—101no—
107C2×#101—101no—
108#398—21no—
109#398Dic511yescharacteristic
110#398C2×D511yescharacteristic
111#395—21no—
112#395Dic511yescharacteristic
113#395C2×D511yescharacteristic
114C4×C4⋊C4—21no—
115C4×C4⋊C4—21no—
116#376Dic511yescharacteristic
117#343—52no—
118#324—52no—
119#324—101no—
120C23×C5C2×C22⋊C411yescharacteristic
121C5×Q8—42no—
122C5×Q8—42no—
123C5×Q8—42no—
124C5×Q8—42no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—22no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—22no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—41no—
141C2×C4×C5—41no—
142C2×C4×C5—41no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5—41no—
147C2×C4×C5—41no—
148C2×C4×C5—41no—
149C2×C4×C5—41no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5#9911yescharacteristic
153C2×C4×C5#9911yescharacteristic
154C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C5#13711yescharacteristic
156#168—82no—
157#168—82no—
158C22×Q8C2×Dic511yescharacteristic
159C22×Q8C22⋊D511yescharacteristic
160C2×M16—102no—
161C4×Q8—41no—
162C4×Q8—41no—
163C4×Q8—41no—
164C4×Q8—41no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4C2×Dic511yescharacteristic
171C2×C4⋊C4C2×Dic511yescharacteristic
172C2×C4⋊C4C22⋊D511yescharacteristic
173C2×C4⋊C4C22×D511yescharacteristic
174C2×C42—21no—
175C2×C42—21no—
176C2×C42C2×Dic511yescharacteristic
177C2×C42C22⋊D511yescharacteristic
178C2×C42C22⋊D511yescharacteristic
179C4⋊C8—201no—
180C4⋊C8—201no—
181C4⋊C8—201no—
182#101—202no—
183C22⋊C8—102no—
184#97—201no—
185#95—21no—
186#95—21no—
187#95—21no—
188#95—21no—
189#95—21no—
190#95C2×Dic511yescharacteristic
191#95C2×Dic511yescharacteristic
192C22×C5—21no—
193C22×C5—21no—
194C22×C5C2×#9911yescharacteristic
195C22×C5#41711yescharacteristic
196C22×C5#42111yescharacteristic
197C4×C5—21no—
198C4×C5—21no—
199C4×C5—21no—
200C4×C5—42no—
201C4×C5—42no—
202C4×C5—41no—
203C4×C5—41no—
204C4×C5—42no—
205C4×C5—41no—
206C4×C5—41no—
207C4×C5—41no—
208C4×C5—81no—
209C4×C5#35612yes—
210C2×Q8—21no—
211C2×Q8—21no—
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8—42no—
215C2×Q8—41no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4C22⋊Dic511yescharacteristic
221C22×C4C22⋊Dic511yescharacteristic
222C22×C4C22⋊Dic511yescharacteristic
223C22×C4C22⋊Dic511yescharacteristic
224C22×C4C22×Dic511yescharacteristic
225C22×C4C2×C22⋊D511yescharacteristic
226C22×C4C2×C22⋊D511yescharacteristic
227M16—202no—
228M16—202no—
229C2×C8—202no—
230C2×C8—202no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C42—24no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—41no—
249C42—41no—
250C2×C5—21no—
251C2×C5—21no—
252C2×C5#151311yescharacteristic
253C2×C5#212011yescharacteristic
254C2×C5C2×#35611yescharacteristic
255C23C2×C22⋊Dic511yescharacteristic
256Q8—42no—
257Q8—42no—
258Q8—42no—
259Q8—42no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4#396611yescharacteristic
288C2×C4#396611yescharacteristic
289C2×C4#409511yescharacteristic
290C2×C4#409711yescharacteristic
291C8—402no—
292C8—402no—
293C5#1183111yescharacteristic, complemented, Sylow
294C22—21no—
295C22—21no—
296C22C2×#396611yescharacteristic
297C22#6552111yescharacteristic
298C22#6552511yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—42no—
303C4—42no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—42no—
308C4—41no—
309C4—41no—
310C4—81no—
311C4#6476812yes—
312C2—21no—
313C2—21no—
314C2#1060250211yescharacteristic
315C2#1060250911yescharacteristic
316C2C2×#6476811yescharacteristic
subgroupG/H
centerC22C2×#3966
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#2399C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#2399D5
hypocenterC5#11831
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2399

Complements

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

NH ≅ G/Ntype
293. C5#11831semidirect

Maximal subgroups

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

subgroupindex
C5×#23992
#106024302
#106024182
#105981412
#105981392
#118315