Finite Group Databasebeta

← #11999890

Subgroups — #11999890

Order 1280.

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

normal subgroups only

This group has 632 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
1C2×#65259C212yesmaximal
2#10605092C211yesmaximal, characteristic
3C5×#1445C211yesmaximal, characteristic
4C2×#64672C212yesmaximal
5#10598104C211yesmaximal, characteristic
6C22×C5×C4⋊C4C2211yescharacteristic
7C2×#4070C2212yes—
8C2×C5×#95—22no—
9C2×C5×#95C2211yescharacteristic
10C2×C5×#95C2211yescharacteristic
11#65501—22no—
12C2×C22⋊#168C2212yes—
13#65259—24no—
14#65259—24no—
15C2×#3942—22no—
16C2×#3939—22no—
17#64950—22no—
18#64945—22no—
19#64672—24no—
20#9972—51nomaximal, Sylow
21C23×C4×C5—21no—
22C23×C4×C5—21no—
23C23×C4×C5D412yes—
24C23×C4×C5C2311yescharacteristic
25C22×Dic10D412yes—
26C2×C5×C4⋊C4—22no—
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4D412yes—
30C2×C22⋊Dic5—22no—
31C2×C4⋊Dic5—22no—
32C2×C4⋊Dic5—22no—
33C2×C4⋊Dic5D412yes—
34#4070—22no—
35#4070—22no—
36#4070—22no—
37#4070—22no—
38C2×#683—22no—
39C22×#168—22no—
40C5×#95—22no—
41C5×#95—22no—
42C5×#95—44no—
43#3963—24no—
44C22⋊#168—22no—
45C22⋊#168D414yes—
46#3942—28no—
47#3939—28no—
48C2×#484—52no—
49#2659—51no—
50C2×#328—52no—
51#1445D511yescharacteristic
52#1280—51no—
53C24×C5C2×D411yescharacteristic
54C22×C4×C5—22no—
55C22×C4×C5—22no—
56C22×C4×C5—22no—
57C22×C4×C5—22no—
58C22×C4×C5—42no—
59C22×C4×C5—42no—
60C22×C4×C5—42no—
61C22×C4×C5—41no—
62C22×C4×C5—42no—
63C22×C4×C5—42no—
64C22×C4×C5—42no—
65C22×C4×C5—41no—
66C22×C4×C5—41no—
67C22×C4×C5—41no—
68C22×C4×C5—42no—
69C22×C4×C5Q1614yes—
70C22×C4×C5C2×D411yescharacteristic
71C22×C4×C5C2×D412yes—
72C22×C4×C5C2×D412yes—
73C22×C4×C5#4111yescharacteristic
74C22×Dic5—22no—
75C22×Dic5—22no—
76C2×Dic10—22no—
77C2×Dic10—22no—
78C2×Dic10—44no—
79C5×C4⋊C4—24no—
80C5×C4⋊C4—42no—
81C22⋊Dic5—42no—
82C22⋊Dic5—42no—
83C4⋊Dic5—22no—
84C4⋊Dic5—22no—
85C4⋊Dic5—82no—
86C4⋊Dic5—82no—
87#683—42no—
88#683—42no—
89C2×#168—24no—
90C2×#168—44no—
91C2×C22⋊Q8—52no—
92C22×C4⋊C4C2×D511yescharacteristic
93#484—104no—
94#484—104no—
95C2×#107—102no—
96C2×#103—102no—
97C2×C22⋊C8—52no—
98#398—102no—
99#395—102no—
100#380—102no—
101C2×#95—22no—
102C2×#95C2×D511yescharacteristic
103C2×#95C2×D511yescharacteristic
104#328—104no—
105C23×C5—21no—
106C23×C5—21no—
107C23×C5—22no—
108C23×C5#12011yescharacteristic
109C23×C5#12111yescharacteristic
110C23×C5#12711yescharacteristic
111C23×C5C2×Q1612yes—
112C23×C5#13712yes—
113C2×C4×C5—24no—
114C2×C4×C5—24no—
115C2×C4×C5—41no—
116C2×C4×C5—42no—
117C2×C4×C5—41no—
118C2×C4×C5—42no—
119C2×C4×C5—42no—
120C2×C4×C5—44no—
121C2×C4×C5—44no—
122C2×C4×C5—42no—
123C2×C4×C5—44no—
124C2×C4×C5—42no—
125C2×C4×C5—82no—
126C2×C4×C5—82no—
127C2×C4×C5—81no—
128C2×C4×C5—82no—
129C2×C4×C5—81no—
130C2×C4×C5—81no—
131C2×C4×C5—81no—
132C2×C4×C5#12012yes—
133C2×C4×C5#12112yes—
134C2×Dic5—42no—
135C2×Dic5—42no—
136C2×Dic5—42no—
137C2×Dic5—42no—
138C2×Dic5—44no—
139Dic10—44no—
140Dic10—82no—
141#168—44no—
142C22×Q8—52no—
143C23×C4—21no—
144C23×C4—21no—
145C23×C4C22⋊D512yes—
146C23×C4C22×D511yescharacteristic
147C22×C8—102no—
148C22⋊Q8—102no—
149C22⋊Q8—102no—
150C22⋊Q8—102no—
151C22⋊Q8—102no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—52no—
156C2×C4⋊C4—102no—
157C2×C4⋊C4—102no—
158C2×C4⋊C4—102no—
159C2×C4⋊C4D2012yes—
160C2×C22⋊C4—102no—
161#107—108no—
162#103—108no—
163C22⋊C8—54no—
164C22⋊C8—102no—
165#95—22no—
166#95—22no—
167#95—44no—
168#95—104no—
169C22×C5—22no—
170C22×C5—22no—
171C22×C5—22no—
172C22×C5—22no—
173C22×C5—21no—
174C22×C5—21no—
175C22×C5—21no—
176C22×C5—21no—
177C22×C5#39211yescharacteristic
178C22×C5#45112yes—
179C22×C5#45311yescharacteristic
180C22×C5#45411yescharacteristic
181C22×C5#45812yes—
182C22×C5#46212yes—
183C22×C5#49411yescharacteristic
184C22×C5#49711yescharacteristic
185C4×C5—22no—
186C4×C5—22no—
187C4×C5—44no—
188C4×C5—82no—
189C4×C5—82no—
190Dic5—82no—
191Dic5—82no—
192C24C2×C22⋊D511yescharacteristic
193C2×Q8—102no—
194C2×Q8—102no—
195C2×Q8—204no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—41no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—102no—
212C22×C4—102no—
213C22×C4#68914yes—
214C22×C4C2×D2011yescharacteristic
215C22×C4#70911yescharacteristic
216C22×C4D4×D512yes—
217C22×C4D4×D512yes—
218C2×C8—104no—
219C2×C8—204no—
220C4⋊C4—24no—
221C4⋊C4—42no—
222C4⋊C4—102no—
223C4⋊C4—102no—
224C4⋊C4—202no—
225C4⋊C4—202no—
226C4⋊C4—402no—
227C4⋊C4—402no—
228C22⋊C4—202no—
229C22⋊C4—202no—
230C2×C5—21no—
231C2×C5—22no—
232C2×C5—21no—
233C2×C5#161412yes—
234C2×C5#161712yes—
235C2×C5#200611yescharacteristic
236C2×C5#201611yescharacteristic
237C2×C5#202211yescharacteristic
238C23—22no—
239C23—21no—
240C23—21no—
241C23#407611yescharacteristic
242C23#408311yescharacteristic
243C23#408611yescharacteristic
244C23C2×#68912yes—
245C23#409712yes—
246Q8—204no—
247Q8—402no—
248C2×C4—24no—
249C2×C4—24no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—42no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—42no—
260C2×C4—82no—
261C2×C4—82no—
262C2×C4—81no—
263C2×C4—82no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—204no—
268C2×C4—202no—
269C2×C4—202no—
270C2×C4—202no—
271C2×C4—202no—
272C2×C4#402812yes—
273C2×C4#403012yes—
274C8—204no—
275C5#997211yescharacteristic, complemented, Sylow
276C22—21no—
277C22—21no—
278C22—22no—
279C22—22no—
280C22—22no—
281C22—22no—
282C22—21no—
283C22—21no—
284C22#6524911yescharacteristic
285C22#6532012yes—
286C22#6533912yes—
287C22#6534212yes—
288C22#6534911yescharacteristic
289C22#6535111yescharacteristic
290C22#6536611yescharacteristic
291C22#6538111yescharacteristic
292C4—22no—
293C4—22no—
294C4—44no—
295C4—82no—
296C4—82no—
297C4—402no—
298C4—402no—
299C2—21no—
300C2—22no—
301C2—21no—
302C2#1060033211yescharacteristic
303C2#1060045711yescharacteristic
304C2#1060048411yescharacteristic
305C2#1060050912yes—
306C2#1060051212yes—
subgroupG/H
centerC23#4083
commutator, cosocleC23×C4×C5C23
FrattiniC23×C4C22×D5
FittingC5×#1445C2
socleC23×C5#120
prime radicalC24×C5C2×D4
hypercenter#1445D5
hypocenterC5#9972
LCSG ▷ C23×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1445

Complements

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

NH ≅ G/Ntype
275. C5#9972semidirect

Maximal subgroups

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

subgroupindex
C2×#652592
#106050922
C5×#14452
C2×#646722
#105981042
#99725