Finite Group Databasebeta

← #11997139

Subgroups — #11997139

Order 1280.

542 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 131 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×#2972C211yesmaximal, characteristic
2#10614119C211yesmaximal, characteristic
3#10602410C211yesmaximal, characteristic
4#10601563C212yesmaximal, complemented
5#10598229C212yesmaximal, complemented
6C2×C4×C5×D4C2211yescharacteristic
7C2×C4×Dic10C2211yescharacteristic
8C5×C8×D4—24no—
9C5×#431C2212yes—
10C2×C5×C22⋊C8—22no—
11#65510—21no—
12C2×#3965—21no—
13#65499—22no—
14#65262—21no—
15#65238C412yes—
16#65236C412yes—
17#65225C2211yescharacteristic
18#65213C2212yes—
19#64750—21no—
20#64676—24no—
21#9483—51nomaximal, Sylow
22C22×C5×D4D411yescharacteristic
23C23×C4×C5D412yes—
24C22×Dic10C2×C411yescharacteristic
25C22×C5×C8—24no—
26C4×C5×D4—22no—
27C4×C5×D4—22no—
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C5×C22⋊C4C2×C412yes—
30C2×C42×C5C2311yescharacteristic
31C2×C22⋊Dic5—22no—
32C2×C22⋊Dic5—22no—
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5C2×C411yescharacteristic
35C2×#683—21no—
36C2×#683—22no—
37C2×C4×Dic5—21no—
38C2×#681—22no—
39C4×Dic10—22no—
40C4×Dic10—22no—
41C5×C4⋊C8—22no—
42C5×C22⋊C8—24no—
43C5×C22⋊C8—22no—
44C4×C5×C8D414yes—
45#3965—42no—
46#3963—22no—
47#3963—21no—
48#3963C2×C412yes—
49C4⋊#168—22no—
50C4⋊#168—22no—
51#2972D511yescharacteristic
52#2580—51no—
53#1800—51no—
54#1487—52no—
55#1286—52no—
56C24×C5C22⋊C412yes—
57C2×C5×D4—22no—
58C2×C5×D4—22no—
59C2×C5×D4SD1612yes—
60C2×C5×D4Q1612yes—
61C22×C4×C5—22no—
62C22×C4×C5—22no—
63C22×C4×C5—82no—
64C22×C4×C5C22⋊C412yes—
65C22×C4×C5C22×C411yescharacteristic
66C22×C4×C5C2×D411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×Dic5—21no—
69C22×Dic5—22no—
70C22×Dic5—21no—
71C2×Dic10—22no—
72C2×Dic10—42no—
73C2×C5×C8—24no—
74C2×C5×C8—84no—
75C5×C4⋊C4—22no—
76C5×C22⋊C4—24no—
77C42×C5C2×D412yes—
78C42×C5#4112yes—
79C22⋊Dic5—44no—
80C22⋊Dic5—82no—
81C4⋊Dic5—22no—
82C4⋊Dic5—42no—
83#683—41no—
84#683—41no—
85#683—82no—
86C4×Dic5—42no—
87#681—42no—
88#681—42no—
89C2×#168—42no—
90C2×C4×Q8—51no—
91C2×C4×D4C2×D511yescharacteristic
92C8×D4—24no—
93#431C2×D512yes—
94#423—52no—
95C2×#100—101no—
96C2×C22⋊C8—22no—
97#399—52no—
98#393—52no—
99#390—101no—
100#389—101no—
101#385—102no—
102#382—51no—
103#343—101no—
104Q8⋊C8—104no—
105C23×C5—22no—
106C23×C5—22no—
107C23×C5—42no—
108C23×C5—42no—
109C23×C5#10314yes—
110C23×C5C2×C22⋊C411yescharacteristic
111C5×D4—24no—
112C5×D4—24no—
113C2×C4×C5—22no—
114C2×C4×C5—41no—
115C2×C4×C5—41no—
116C2×C4×C5—44no—
117C2×C4×C5—42no—
118C2×C4×C5—82no—
119C2×C4×C5C4×D412yes—
120C2×C4×C5#12011yescharacteristic
121C2×C4×C5#12112yes—
122C2×C4×C5#12311yescharacteristic
123C2×C4×C5C2×SD1611yescharacteristic
124C2×C4×C5C2×Q1611yescharacteristic
125C2×C4×C5#13512yes—
126C2×Dic5—22no—
127C2×Dic5—41no—
128C2×Dic5—41no—
129C2×Dic5—41no—
130C2×Dic5—42no—
131C2×Dic5—42no—
132C2×Dic5—41no—
133C2×Dic5—41no—
134C2×Dic5—42no—
135Dic10—24no—
136Dic10—42no—
137C5×C8—44no—
138#168—82no—
139C22×Q8—51no—
140C22×D4D2011yescharacteristic
141C23×C4C22⋊D512yes—
142C2×M16—102no—
143C22×C8—24no—
144C4×Q8—102no—
145C4×Q8—102no—
146C4×D4—22no—
147C4×D4—22no—
148C2×C4⋊C4—51no—
149C2×C4⋊C4—101no—
150C2×C4⋊C4—101no—
151C2×C4⋊C4—102no—
152C2×C4⋊C4D2011yescharacteristic
153C2×C22⋊C4—102no—
154C2×C22⋊C4—102no—
155C2×C22⋊C4C4×D512yes—
156C2×C42—101no—
157C2×C42C22×D511yescharacteristic
158C4⋊C8—22no—
159C4⋊C8—102no—
160C4⋊C8—102no—
161#100—202no—
162C22⋊C8—24no—
163C22⋊C8—22no—
164C4×C8C22⋊D514yes—
165#95—52no—
166#95—102no—
167#95—101no—
168C22×C5—21no—
169C22×C5—21no—
170C22×C5—24no—
171C22×C5—44no—
172C22×C5—42no—
173C22×C5—42no—
174C22×C5—82no—
175C22×C5#38611yescharacteristic
176C22×C5C2×#10311yescharacteristic
177C22×C5#41611yescharacteristic
178C4×C5—22no—
179C4×C5—21no—
180C4×C5—21no—
181C4×C5—42no—
182C4×C5#46512yes—
183C4×C5#46712yes—
184Dic5—42no—
185Dic5—82no—
186Dic5—81no—
187C24#68512yes—
188C2×Q8—102no—
189C2×Q8—202no—
190C2×D4—22no—
191C2×D4—22no—
192C2×D4#67712yes—
193C2×D4Dic2012yes—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—82no—
197C22×C4—101no—
198C22×C4—102no—
199C22×C4—101no—
200C22×C4#68512yes—
201C22×C4C2×C4×D511yescharacteristic
202C22×C4C2×D2011yescharacteristic
203C22×C4C2×C22⋊D511yescharacteristic
204M16—202no—
205M16—202no—
206C2×C8—24no—
207C2×C8—84no—
208C2×C8—202no—
209C4⋊C4—22no—
210C4⋊C4—102no—
211C4⋊C4—201no—
212C4⋊C4—202no—
213C4⋊C4—201no—
214C4⋊C4—402no—
215C22⋊C4—24no—
216C22⋊C4—204no—
217C22⋊C4—402no—
218C42—202no—
219C42#70912yes—
220C42C2×C22⋊D512yes—
221C2×C5—21no—
222C2×C5—21no—
223C2×C5—44no—
224C2×C5#189111yescharacteristic
225C2×C5#189211yescharacteristic
226C2×C5#191111yescharacteristic
227C23—22no—
228C23—22no—
229C23—42no—
230C23—42no—
231C23#394814yes—
232C23C2×#68511yescharacteristic
233Q8—104no—
234Q8—202no—
235D4—24no—
236D4—24no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—44no—
241C2×C4—42no—
242C2×C4—82no—
243C2×C4—102no—
244C2×C4—201no—
245C2×C4—201no—
246C2×C4—202no—
247C2×C4—201no—
248C2×C4—202no—
249C2×C4—201no—
250C2×C4—202no—
251C2×C4—201no—
252C2×C4C2×#67711yescharacteristic
253C2×C4#405012yes—
254C2×C4C2×Dic2011yescharacteristic
255C2×C4C4×C22⋊D512yes—
256C2×C4#407511yescharacteristic
257C2×C4#407612yes—
258C2×C4#409911yescharacteristic
259C8—44no—
260C8—402no—
261C5#948311yescharacteristic, complemented, Sylow
262C22—21no—
263C22—21no—
264C22—24no—
265C22—44no—
266C22—42no—
267C22—42no—
268C22—82no—
269C22C2×#394811yescharacteristic
270C22#6540211yescharacteristic
271C22#6550211yescharacteristic
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—202no—
277C4—402no—
278C4—401no—
279C4#6540312yes—
280C4#6540512yes—
281C2—21no—
282C2—21no—
283C2—44no—
284C2#1060244511yescharacteristic
285C2#1060276511yescharacteristic
286C2#1060282211yescharacteristic
subgroupG/H
centerC22#65502
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2972C2
socleC22×C5#386
prime radicalC22×C5×D4D4
cosocleC2×C42×C5C23
hypercenter#2972D5
hypocenterC5#9483
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2972

Complements

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

NH ≅ G/Ntype
4. #10601563C2semidirect
5. #10598229C2semidirect
261. C5#9483semidirect

Maximal subgroups

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

subgroupindex
C5×#29722
#106141192
#106024102
#106015632
#105982292
#94835