Finite Group Databasebeta

← #11997157

Subgroups — #11997157

Order 1280.

518 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 111 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#10614119C211yesmaximal, characteristic
2#10614035C211yesmaximal, characteristic
3C5×#1800C211yesmaximal, characteristic
4#10601293C212yesmaximal, complemented
5#10598204C212yesmaximal, complemented
6C2×C4×C5×D4C2211yescharacteristic
7C2×C4×Dic10C2211yescharacteristic
8C5×#423C2212yes—
9C2×C5×#100—21no—
10#65510—21no—
11#65499—22no—
12#65496—22no—
13#65301—24no—
14#65262—21no—
15#65238C412yes—
16#65236C412yes—
17#65225C2211yescharacteristic
18#65214C2212yes—
19C5×#343—21no—
20#64704—24no—
21#9487—51nomaximal, Sylow
22C22×C5×D4D411yescharacteristic
23C23×C4×C5D412yes—
24C22×Dic10C2×C411yescharacteristic
25C2×C5×M16—22no—
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—24no—
39C4×Dic10—22no—
40C4×Dic10—22no—
41C5×C4⋊C8—22no—
42C5×C4⋊C8—22no—
43C5×#100—42no—
44#3963—22no—
45#3963—21no—
46#3963C2×C412yes—
47C22⋊#168—24no—
48C22⋊#168—22no—
49C4⋊#168—22no—
50C4×#168D414yes—
51#2975—51no—
52#2580—51no—
53#1800D511yescharacteristic
54#1487—52no—
55#1286—52no—
56C24×C5C22⋊C412yes—
57C2×C5×D4—22no—
58C2×C5×D4—21no—
59C2×C5×D4—22no—
60C2×C5×D4—21no—
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—
73C5×M16—42no—
74C5×M16—42no—
75C2×C5×C8—42no—
76C5×C4⋊C4—22no—
77C5×C22⋊C4—24no—
78C42×C5C2×D412yes—
79C42×C5#4112yes—
80C22⋊Dic5—44no—
81C22⋊Dic5—82no—
82C4⋊Dic5—22no—
83C4⋊Dic5—41no—
84C4⋊Dic5—41no—
85#683—41no—
86#683—41no—
87#683—82no—
88C4×Dic5—42no—
89#681—84no—
90C2×#168—24no—
91C2×C4×Q8—51no—
92C2×C4×D4C2×D511yescharacteristic
93#436—104no—
94#431—52no—
95#423C2×D512yes—
96C2×#100—21no—
97#407—102no—
98#399—52no—
99#393—52no—
100#390—101no—
101#389—101no—
102#385—102no—
103#382—51no—
104#343—21no—
105Q8⋊C8—104no—
106C23×C5—22no—
107C23×C5—22no—
108C23×C5—22no—
109C23×C5—42no—
110C23×C5—42no—
111C23×C5C2×C22⋊C411yescharacteristic
112C5×D4—42no—
113C5×D4—42no—
114C2×C4×C5—22no—
115C2×C4×C5—41no—
116C2×C4×C5—41no—
117C2×C4×C5—44no—
118C2×C4×C5—42no—
119C2×C4×C5—82no—
120C2×C4×C5C4×D412yes—
121C2×C4×C5#12011yescharacteristic
122C2×C4×C5#12112yes—
123C2×C4×C5#12311yescharacteristic
124C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C5#13712yes—
126C2×C4×C5#13711yescharacteristic
127C2×Dic5—22no—
128C2×Dic5—41no—
129C2×Dic5—41no—
130C2×Dic5—41no—
131C2×Dic5—42no—
132C2×Dic5—42no—
133C2×Dic5—41no—
134C2×Dic5—41no—
135C2×Dic5—42no—
136Dic10—24no—
137Dic10—42no—
138C5×C8—82no—
139#168—44no—
140C22×Q8—51no—
141C22×D4C22⋊D511yescharacteristic
142C23×C4D2012yes—
143C2×M16—22no—
144C2×M16—104no—
145C4×Q8—102no—
146C4×Q8—102no—
147C4×D4—22no—
148C4×D4—22no—
149C2×C4⋊C4—51no—
150C2×C4⋊C4—101no—
151C2×C4⋊C4—101no—
152C2×C4⋊C4—102no—
153C2×C4⋊C4C22⋊D511yescharacteristic
154C2×C22⋊C4—102no—
155C2×C22⋊C4—102no—
156C2×C22⋊C4C4×D512yes—
157C2×C42—101no—
158C2×C42C22×D511yescharacteristic
159C4⋊C8—22no—
160C4⋊C8—22no—
161C4⋊C8—102no—
162#100—42no—
163C22⋊C8—104no—
164C22⋊C8—102no—
165C4×C8—54no—
166#95—52no—
167#95—102no—
168#95—101no—
169C22×C5—21no—
170C22×C5—21no—
171C22×C5—44no—
172C22×C5—42no—
173C22×C5—42no—
174C22×C5—42no—
175C22×C5—82no—
176C22×C5#38611yescharacteristic
177C22×C5#41711yescharacteristic
178C22×C5#41911yescharacteristic
179C4×C5—22no—
180C4×C5—21no—
181C4×C5—21no—
182C4×C5—42no—
183C4×C5#46812yes—
184C4×C5#47012yes—
185Dic5—42no—
186Dic5—82no—
187Dic5—81no—
188C24#68512yes—
189C2×Q8—102no—
190C2×Q8—202no—
191C2×D4—22no—
192C2×D4—21no—
193C2×D4—22no—
194C2×D4—21no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—82no—
198C22×C4—101no—
199C22×C4—102no—
200C22×C4—101no—
201C22×C4#68512yes—
202C22×C4C2×C4×D511yescharacteristic
203C22×C4C2×D2011yescharacteristic
204C22×C4C2×C22⋊D511yescharacteristic
205M16—42no—
206M16—42no—
207M16—404no—
208C2×C8—42no—
209C2×C8—104no—
210C4⋊C4—22no—
211C4⋊C4—102no—
212C4⋊C4—201no—
213C4⋊C4—201no—
214C4⋊C4—201no—
215C4⋊C4—201no—
216C4⋊C4—402no—
217C22⋊C4—24no—
218C22⋊C4—204no—
219C22⋊C4—402no—
220C42—202no—
221C42D4×D512yes—
222C42#71112yes—
223C2×C5—21no—
224C2×C5—21no—
225C2×C5—82no—
226C2×C5#189111yescharacteristic
227C2×C5#189411yescharacteristic
228C2×C5#191111yescharacteristic
229C23—22no—
230C23—22no—
231C23—22no—
232C23—42no—
233C23—42no—
234C23C2×#68511yescharacteristic
235Q8—104no—
236Q8—202no—
237D4—42no—
238D4—42no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—44no—
243C2×C4—42no—
244C2×C4—82no—
245C2×C4—102no—
246C2×C4—201no—
247C2×C4—201no—
248C2×C4—202no—
249C2×C4—201no—
250C2×C4—202no—
251C2×C4—201no—
252C2×C4—201no—
253C2×C4—202no—
254C2×C4#402712yes—
255C2×C4#402811yescharacteristic
256C2×C4#403211yescharacteristic
257C2×C4#407811yescharacteristic
258C2×C4#408512yes—
259C2×C4#408811yescharacteristic
260C2×C4#409712yes—
261C8—82no—
262C8—204no—
263C5#948711yescharacteristic, complemented, Sylow
264C22—21no—
265C22—21no—
266C22—44no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—82no—
271C22#6524711yescharacteristic
272C22#6525511yescharacteristic
273C22#6529311yescharacteristic
274C4—21no—
275C4—21no—
276C4—22no—
277C4—42no—
278C4—202no—
279C4—402no—
280C4—401no—
281C4#6533112yes—
282C4#6534112yes—
283C2—21no—
284C2—21no—
285C2—82no—
286C2#1060030911yescharacteristic
287C2#1060086411yescharacteristic
288C2#1060092911yescharacteristic
subgroupG/H
centerC22#65247
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1800C2
socleC22×C5#386
prime radicalC22×C5×D4D4
cosocleC2×C42×C5C23
hypercenter#1800D5
hypocenterC5#9487
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
4. #10601293C2semidirect
5. #10598204C2semidirect
263. C5#9487semidirect

Maximal subgroups

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

subgroupindex
#106141192
#106140352
C5×#18002
#106012932
#105982042
#94875