Finite Group Databasebeta

← #11999893

Subgroups — #11999893

Order 1280.

632 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 121 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×#2659C211yesmaximal, characteristic
2C2×#65332C212yesmaximal
3C2×#64758C212yesmaximal
4#10600215C211yesmaximal, characteristic
5#10598104C211yesmaximal, characteristic
6C2×C5×C22⋊Q8C2212yes—
7C22×C4⋊Dic5C2211yescharacteristic
8C5×#398—22no—
9C5×#395—22no—
10C5×#380—22no—
11C2×C5×#95C2211yescharacteristic
12C2×#3967—22no—
13C2×#3963—22no—
14C2×#3963C2211yescharacteristic
15C2×C22⋊#168C2212yes—
16#65332—24no—
17#65332—24no—
18C2×#3940—22no—
19#64758—24no—
20#9973—51nomaximal, Sylow
21C22×C5×Q8D412yes—
22C23×C4×C5D412yes—
23C23×C4×C5C2311yescharacteristic
24C23×Dic5—21no—
25C23×Dic5—21no—
26C5×C22⋊Q8—22no—
27C5×C22⋊Q8—22no—
28C5×C22⋊Q8—22no—
29C5×C22⋊Q8—22no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—22no—
32C2×C5×C4⋊C4—22no—
33C2×C5×C4⋊C4D412yes—
34C2×C5×C22⋊C4—22no—
35C2×C4⋊Dic5—22no—
36C2×C4⋊Dic5—22no—
37C2×C4⋊Dic5—21no—
38C2×C4⋊Dic5D412yes—
39C22×#168—22no—
40C5×#95—24no—
41C5×#95—22no—
42#3967—28no—
43#3963—22no—
44#3963—44no—
45C22⋊#168—22no—
46C22⋊#168D414yes—
47#3940—28no—
48C2×#483—52no—
49#2659D511yescharacteristic
50C2×#328—52no—
51#1445—51no—
52#1280—51no—
53C24×C5C2×D411yescharacteristic
54C2×C5×Q8—22no—
55C2×C5×Q8—22no—
56C2×C5×Q8—44no—
57C22×C4×C5—22no—
58C22×C4×C5—22no—
59C22×C4×C5—22no—
60C22×C4×C5—22no—
61C22×C4×C5—42no—
62C22×C4×C5—42no—
63C22×C4×C5—42no—
64C22×C4×C5SD1614yes—
65C22×C4×C5C2×D411yescharacteristic
66C22×C4×C5C2×D412yes—
67C22×C4×C5C2×D412yes—
68C22×C4×C5#4111yescharacteristic
69C22×Dic5—22no—
70C22×Dic5—22no—
71C22×Dic5—41no—
72C22×Dic5—42no—
73C22×Dic5—41no—
74C22×Dic5—41no—
75C22×Dic5—41no—
76C22×Dic5—42no—
77C22×Dic5—42no—
78C22×Dic5—42no—
79C5×C4⋊C4—22no—
80C5×C4⋊C4—22no—
81C5×C4⋊C4—42no—
82C5×C4⋊C4—42no—
83C5×C4⋊C4—82no—
84C5×C4⋊C4—82no—
85C5×C22⋊C4—42no—
86C5×C22⋊C4—42no—
87C4⋊Dic5—24no—
88C4⋊Dic5—42no—
89C2×#168—24no—
90C2×#168—44no—
91C2×C22⋊Q8C2×D512yes—
92C22×C4⋊C4—51no—
93#483—104no—
94#483—104no—
95C2×#106—102no—
96C2×#103—102no—
97C2×C22⋊C8—52no—
98#398—22no—
99#395—22no—
100#380—22no—
101C2×#95—51no—
102C2×#95—102no—
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×SD1612yes—
112C23×C5#13712yes—
113C5×Q8—44no—
114C5×Q8—82no—
115C2×C4×C5—24no—
116C2×C4×C5—24no—
117C2×C4×C5—41no—
118C2×C4×C5—42no—
119C2×C4×C5—41no—
120C2×C4×C5—42no—
121C2×C4×C5—42no—
122C2×C4×C5—44no—
123C2×C4×C5—42no—
124C2×C4×C5—42no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5—44no—
128C2×C4×C5—82no—
129C2×C4×C5#12012yes—
130C2×C4×C5#12112yes—
131C2×Dic5—44no—
132C2×Dic5—42no—
133C2×Dic5—42no—
134C2×Dic5—44no—
135C2×Dic5—82no—
136C2×Dic5—81no—
137C2×Dic5—82no—
138C2×Dic5—81no—
139C2×Dic5—81no—
140C2×Dic5—81no—
141#168—44no—
142C22×Q8C22⋊D512yes—
143C23×C4—101no—
144C23×C4—101no—
145C23×C4C22⋊D512yes—
146C23×C4C22×D511yescharacteristic
147C22×C8—102no—
148C22⋊Q8—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C22⋊Q8—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—52no—
156C2×C4⋊C4—102no—
157C2×C4⋊C4—102no—
158C2×C4⋊C4—101no—
159C2×C4⋊C4C22⋊D512yes—
160C2×C22⋊C4—22no—
161#106—108no—
162#103—108no—
163C22⋊C8—54no—
164C22⋊C8—102no—
165#95—24no—
166#95—22no—
167#95—102no—
168#95—204no—
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#44812yes—
179C22×C5#45511yescharacteristic
180C22×C5#45611yescharacteristic
181C22×C5#45812yes—
182C22×C5#46112yes—
183C22×C5#49211yescharacteristic
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—22no—
194C2×Q8—22no—
195C2×Q8—44no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—102no—
204C22×C4—102no—
205C22×C4—201no—
206C22×C4—202no—
207C22×C4—201no—
208C22×C4—201no—
209C22×C4—201no—
210C22×C4—202no—
211C22×C4—202no—
212C22×C4—202no—
213C22×C4#68814yes—
214C22×C4D4×D511yescharacteristic
215C22×C4D4×D512yes—
216C22×C4#71111yescharacteristic
217C22×C4C2×C22⋊D512yes—
218C2×C8—104no—
219C2×C8—204no—
220C4⋊C4—22no—
221C4⋊C4—22no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—82no—
225C4⋊C4—82no—
226C4⋊C4—104no—
227C4⋊C4—202no—
228C22⋊C4—42no—
229C22⋊C4—42no—
230C2×C5—21no—
231C2×C5—22no—
232C2×C5—21no—
233C2×C5#160812yes—
234C2×C5#161112yes—
235C2×C5#200711yescharacteristic
236C2×C5#201311yescharacteristic
237C2×C5#202211yescharacteristic
238C23—21no—
239C23—22no—
240C23—21no—
241C23#408411yescharacteristic
242C23#408611yescharacteristic
243C23C2×#68812yes—
244C23#408812yes—
245C23#409911yescharacteristic
246Q8—44no—
247Q8—82no—
248C2×C4—24no—
249C2×C4—24no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—44no—
260C2×C4—42no—
261C2×C4—82no—
262C2×C4—202no—
263C2×C4—204no—
264C2×C4—204no—
265C2×C4—202no—
266C2×C4—401no—
267C2×C4—402no—
268C2×C4—401no—
269C2×C4—401no—
270C2×C4—401no—
271C2×C4—402no—
272C2×C4#408312yes—
273C2×C4#408512yes—
274C8—204no—
275C5#997311yescharacteristic, complemented, Sylow
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—22no—
284C22#6537212yes—
285C22#6537411yescharacteristic
286C22#6537511yescharacteristic
287C22#6551211yescharacteristic
288C22#6551612yes—
289C22#6553111yescharacteristic
290C22#6553212yes—
291C22#6553511yescharacteristic
292C4—22no—
293C4—22no—
294C4—44no—
295C4—82no—
296C4—82no—
297C4—402no—
298C4—402no—
299C2—21no—
300C2—22no—
301C2—21no—
302C2#1060258411yescharacteristic
303C2#1060264211yescharacteristic
304C2#1060267411yescharacteristic
305C2#1060268312yes—
306C2#1060269112yes—
subgroupG/H
centerC23#4099
commutator, cosocleC23×C4×C5C23
FrattiniC23×C4C22×D5
FittingC5×#2659C2
socleC23×C5#120
prime radicalC24×C5C2×D4
hypercenter#2659D5
hypocenterC5#9973
LCSG ▷ C23×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2659

Complements

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

NH ≅ G/Ntype
275. C5#9973semidirect

Maximal subgroups

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

subgroupindex
C5×#26592
C2×#653322
C2×#647582
#106002152
#105981042
#99735