Finite Group Databasebeta

← #11997175

Subgroups — #11997175

Order 1280.

522 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 119 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×#2536C211yesmaximal, characteristic
2#10614167C211yesmaximal, characteristic, complemented
3#10602430C211yesmaximal, characteristic, complemented
4#10602391C212yesmaximal
5#10598122C212yesmaximal, complemented
6C2×C5×C22⋊Q8—21no—
7C2×C4×C5×Q8C2211yescharacteristic
8C2×C4×C5×D4C2211yescharacteristic
9C5×#398C412yes—
10C5×#394C412yes—
11C5×#388—22no—
12C5×#382C2211yescharacteristic
13C5×#380—21no—
14C2×#3968—21no—
15#65313—24no—
16#65215—22no—
17#65214C2212yes—
18#65213C2212yes—
19D4⋊#168—24no—
20#64750—21no—
21#9490—51nomaximal, Sylow
22C22×C5×Q8D411yescharacteristic
23C22×C5×D4C2×C411yescharacteristic
24C23×C4×C5—21no—
25C5×C22⋊Q8—44no—
26C4×C5×Q8—22no—
27C4×C5×Q8—22no—
28C4×C5×D4—22no—
29C4×C5×D4—22no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4C2×C411yescharacteristic
33C2×C5×C4⋊C4C2×C412yes—
34C2×C5×C4⋊C4D411yescharacteristic
35C2×C5×C22⋊C4—22no—
36C2×C5×C22⋊C4—22no—
37C2×C5×C22⋊C4—21no—
38C2×C42×C5D412yes—
39C2×C42×C5C2311yescharacteristic
40C2×#681—22no—
41C5×#95—22no—
42C5×#95—21no—
43C5×#95C2×C412yes—
44#3968—42no—
45C22⋊#168—22no—
46C4⋊#168—24no—
47C4⋊#168—22no—
48C4⋊#168—22no—
49C4⋊#168—22no—
50#3935—24no—
51C4×#168D414yes—
52#2983—51no—
53#2536D511yescharacteristic
54#1801—51no—
55#1486—52no—
56#1286—52no—
57C24×C5—21no—
58C2×C5×Q8—22no—
59C2×C5×Q8—22no—
60C2×C5×Q8—21no—
61C2×C5×Q8—21no—
62C2×C5×D4—22no—
63C2×C5×D4—42no—
64C22×C4×C5—22no—
65C22×C4×C5—21no—
66C22×C4×C5—42no—
67C22×C4×C5—42no—
68C22×C4×C5—41no—
69C22×C4×C5—41no—
70C22×C4×C5C22⋊C412yes—
71C22×C4×C5C22⋊C412yes—
72C22×C4×C5C22×C411yescharacteristic
73C22×C4×C5C2×D411yescharacteristic
74C22×C4×C5C2×D411yescharacteristic
75C5×C4⋊C4—24no—
76C5×C4⋊C4—22no—
77C5×C4⋊C4—22no—
78C5×C4⋊C4—44no—
79C5×C4⋊C4—42no—
80C5×C22⋊C4—44no—
81C5×C22⋊C4—44no—
82C5×C22⋊C4—41no—
83C5×C22⋊C4—41no—
84C42×C5—22no—
85C42×C5—22no—
86C42×C5C2×D412yes—
87C42×C5#4112yes—
88#681—42no—
89#681—42no—
90C2×#168—24no—
91C2×#168—42no—
92C2×C22⋊Q8—21no—
93C2×C4×Q8C2×D511yescharacteristic
94C2×C4×D4C2×D511yescharacteristic
95#446—104no—
96#432—102no—
97#431—52no—
98#423—52no—
99C2×#101—101no—
100#398Dic512yes—
101#394Dic512yes—
102#388—22no—
103#382C2×D511yescharacteristic
104#380—21no—
105#343—101no—
106D4⋊C8—104no—
107C23×C5—22no—
108C23×C5—41no—
109C23×C5—41no—
110C23×C5—41no—
111C23×C5—41no—
112C23×C5—41no—
113C23×C5—41no—
114C23×C5C2×C22⋊C411yescharacteristic
115C5×Q8—42no—
116C5×Q8—42no—
117C5×D4—24no—
118C5×D4—42no—
119C2×C4×C5—22no—
120C2×C4×C5—22no—
121C2×C4×C5—22no—
122C2×C4×C5—22no—
123C2×C4×C5—41no—
124C2×C4×C5—41no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5—42no—
128C2×C4×C5—41no—
129C2×C4×C5—41no—
130C2×C4×C5—42no—
131C2×C4×C5—41no—
132C2×C4×C5—82no—
133C2×C4×C5—82no—
134C2×C4×C5C4×D412yes—
135C2×C4×C5#12011yescharacteristic
136C2×C4×C5#12112yes—
137C2×C4×C5#12311yescharacteristic
138C2×C4×C5AGL(1,ℤ/8)12yes—
139C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C5#13711yescharacteristic
141#168—44no—
142#168—82no—
143C22×Q8C22⋊D511yescharacteristic
144C22×D4C2×Dic511yescharacteristic
145C23×C4—21no—
146C2×M16—102no—
147C22⋊Q8—44no—
148C4×Q8—22no—
149C4×Q8—22no—
150C4×D4—22no—
151C4×D4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4C2×Dic511yescharacteristic
155C2×C4⋊C4C2×Dic512yes—
156C2×C4⋊C4C22⋊D511yescharacteristic
157C2×C22⋊C4—22no—
158C2×C22⋊C4—22no—
159C2×C22⋊C4—21no—
160C2×C42C22⋊D512yes—
161C2×C42C22×D511yescharacteristic
162C4⋊C8—104no—
163C4⋊C8—102no—
164C4⋊C8—102no—
165C4⋊C8—102no—
166#101—202no—
167C22⋊C8—102no—
168#97—104no—
169C4×C8—54no—
170#95—22no—
171#95—21no—
172#95C2×Dic512yes—
173C22×C5—21no—
174C22×C5—21no—
175C22×C5—42no—
176C22×C5—42no—
177C22×C5—42no—
178C22×C5—81no—
179C22×C5—81no—
180C22×C5—81no—
181C22×C5—81no—
182C22×C5#38611yescharacteristic
183C22×C5#41711yescharacteristic
184C22×C5#41811yescharacteristic
185C4×C5—22no—
186C4×C5—21no—
187C4×C5—21no—
188C4×C5—42no—
189C4×C5—42no—
190C4×C5—82no—
191C4×C5—81no—
192C4×C5#46812yes—
193C4×C5#46912yes—
194C24—21no—
195C2×Q8—21no—
196C2×Q8—22no—
197C2×Q8—22no—
198C2×Q8—21no—
199C2×D4—22no—
200C2×D4—42no—
201C22×C4—22no—
202C22×C4—21no—
203C22×C4—41no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—41no—
207C22×C4C22⋊Dic512yes—
208C22×C4C22⋊Dic512yes—
209C22×C4C22×Dic511yescharacteristic
210C22×C4C2×C22⋊D511yescharacteristic
211C22×C4C2×C22⋊D511yescharacteristic
212M16—202no—
213M16—202no—
214C2×C8—104no—
215C2×C8—202no—
216C4⋊C4—24no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—44no—
220C4⋊C4—42no—
221C22⋊C4—44no—
222C22⋊C4—44no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C42—22no—
226C42—22no—
227C42D4×D512yes—
228C42#71112yes—
229C2×C5—21no—
230C2×C5—21no—
231C2×C5—82no—
232C2×C5#189111yescharacteristic
233C2×C5#189511yescharacteristic
234C2×C5#191211yescharacteristic
235C23—22no—
236C23—41no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23C2×C22⋊Dic511yescharacteristic
243Q8—42no—
244Q8—42no—
245D4—24no—
246D4—42no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—82no—
261C2×C4—82no—
262C2×C4#407812yes—
263C2×C4D4×Dic512yes—
264C2×C4#408111yescharacteristic
265C2×C4#408311yescharacteristic
266C2×C4#408512yes—
267C2×C4#409511yescharacteristic
268C2×C4#409711yescharacteristic
269C8—204no—
270C8—402no—
271C5#949011yescharacteristic, complemented, Sylow
272C22—21no—
273C22—21no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—81no—
278C22—81no—
279C22—81no—
280C22—81no—
281C22#6550411yescharacteristic
282C22#6550911yescharacteristic
283C22#6552111yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—42no—
288C4—42no—
289C4—82no—
290C4—81no—
291C4#6532812yes—
292C4#6533112yes—
293C2—21no—
294C2—21no—
295C2—82no—
296C2#1060247511yescharacteristic
297C2#1060250711yescharacteristic
298C2#1060265711yescharacteristic
subgroupG/H
centerC22#65509
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2536C2
socleC22×C5#386
prime radicalC22×C5×D4C2×C4
cosocleC2×C42×C5C23
hypercenter#2536D5
hypocenterC5#9490
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2536

Complements

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

NH ≅ G/Ntype
2. #10614167C2semidirect
3. #10602430C2semidirect
5. #10598122C2semidirect
271. C5#9490semidirect

Maximal subgroups

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

subgroupindex
C5×#25362
#106141672
#106024302
#106023912
#105981222
#94905