Finite Group Databasebeta

← #12002297

Subgroups — #12002297

Order 1280.

500 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 109 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×#2646C211yesmaximal, characteristic
2#10600294C212yesmaximal
3#10600215C211yesmaximal, characteristic
4#10598115C212yesmaximal
5#10598104C211yesmaximal, characteristic
6C22×C4⋊Dic5C2211yescharacteristic
7C5×#400—22no—
8C5×#398—22no—
9C5×#385—22no—
10C5×#380C2212yes—
11C2×C5×#95C2211yescharacteristic
12C2×#3963—22no—
13C2×#3963C2211yescharacteristic
14C2×C22⋊#168C2212yes—
15#64749—22no—
16#64749—22no—
17#10346—51nomaximal, Sylow
18C23×C4×C5D412yes—
19C23×C4×C5C2311yescharacteristic
20C23×Dic5—21no—
21C23×Dic5—21no—
22C2×C5×C4⋊C4—22no—
23C2×C5×C4⋊C4—22no—
24C2×C5×C4⋊C4D412yes—
25C2×C5×C4⋊C4D412yes—
26C2×C5×C22⋊C4—22no—
27C2×C4⋊Dic5—22no—
28C2×C4⋊Dic5—22no—
29C2×C4⋊Dic5—21no—
30C2×C4⋊Dic5Q812yes—
31C22×#168—22no—
32C5×#95—22no—
33C5×#95—22no—
34C5×#95—22no—
35C5×#95—22no—
36#3963—22no—
37#3963—44no—
38C22⋊#168—22no—
39C22⋊#168—22no—
40#2646D511yescharacteristic
41#1823—52no—
42#1445—51no—
43#1294—52no—
44#1280—51no—
45C24×C5C2×D411yescharacteristic
46C22×C4×C5—22no—
47C22×C4×C5—22no—
48C22×C4×C5—22no—
49C22×C4×C5—22no—
50C22×C4×C5—22no—
51C22×C4×C5—42no—
52C22×C4×C5—42no—
53C22×C4×C5—42no—
54C22×C4×C5C2×D412yes—
55C22×C4×C5C2×Q811yescharacteristic
56C22×C4×C5#4112yes—
57C22×C4×C5#4111yescharacteristic
58C22×Dic5—22no—
59C22×Dic5—22no—
60C22×Dic5—41no—
61C22×Dic5—42no—
62C22×Dic5—41no—
63C22×Dic5—41no—
64C22×Dic5—41no—
65C22×Dic5—42no—
66C22×Dic5—42no—
67C22×Dic5—42no—
68C5×C4⋊C4—42no—
69C5×C4⋊C4—42no—
70C5×C4⋊C4—82no—
71C5×C4⋊C4—82no—
72C5×C22⋊C4—42no—
73C5×C22⋊C4—42no—
74C4⋊Dic5—24no—
75C4⋊Dic5—42no—
76C2×#168—42no—
77C2×#168—42no—
78C2×#168—42no—
79C22×C4⋊C4—51no—
80C2×C22⋊C8—52no—
81#400—22no—
82#398—22no—
83#385—22no—
84#380C2×D512yes—
85C2×#95—51no—
86C2×#95—102no—
87C2×#95C2×D511yescharacteristic
88#340—102no—
89#340—102no—
90C23×C5—21no—
91C23×C5—21no—
92C23×C5—22no—
93C23×C5#12011yescharacteristic
94C23×C5C22⋊Q811yescharacteristic
95C23×C5#12411yescharacteristic
96C23×C5#13512yes—
97C23×C5AGL(1,ℤ/8)12yes—
98C2×C4×C5—22no—
99C2×C4×C5—22no—
100C2×C4×C5—41no—
101C2×C4×C5—41no—
102C2×C4×C5—42no—
103C2×C4×C5—44no—
104C2×C4×C5—42no—
105C2×C4×C5—42no—
106C2×C4×C5—42no—
107C2×C4×C5—42no—
108C2×C4×C5—42no—
109C2×C4×C5—42no—
110C2×C4×C5—42no—
111C2×C4×C5—42no—
112C2×C4×C5—42no—
113C2×C4×C5—82no—
114C2×C4×C5C22⋊Q812yes—
115C2×C4×C5#12412yes—
116C2×Dic5—44no—
117C2×Dic5—42no—
118C2×Dic5—42no—
119C2×Dic5—44no—
120C2×Dic5—82no—
121C2×Dic5—81no—
122C2×Dic5—82no—
123C2×Dic5—81no—
124C2×Dic5—81no—
125C2×Dic5—81no—
126#168—82no—
127C23×C4—101no—
128C23×C4—101no—
129C23×C4C22⋊D512yes—
130C23×C4C22×D511yescharacteristic
131C22×C8—102no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—52no—
135C2×C4⋊C4—102no—
136C2×C4⋊C4—102no—
137C2×C4⋊C4—101no—
138C2×C4⋊C4C22⋊D512yes—
139C2×C4⋊C4C22⋊D512yes—
140C2×C22⋊C4—22no—
141C22⋊C8—102no—
142C22⋊C8—102no—
143#95—22no—
144#95—22no—
145#95—22no—
146#95—22no—
147#95—102no—
148#95—204no—
149C22×C5—22no—
150C22×C5—22no—
151C22×C5—22no—
152C22×C5—22no—
153C22×C5—21no—
154C22×C5—21no—
155C22×C5—21no—
156C22×C5—21no—
157C22×C5#39311yescharacteristic
158C22×C5#44912yes—
159C22×C5#45511yescharacteristic
160C22×C5#45611yescharacteristic
161C22×C5#45812yes—
162C22×C5#47812yes—
163C22×C5#48811yescharacteristic
164C22×C5#49011yescharacteristic
165C4×C5—22no—
166C4×C5—22no—
167C4×C5—82no—
168C4×C5—82no—
169C4×C5—82no—
170Dic5—82no—
171Dic5—82no—
172C24C2×C22⋊D511yescharacteristic
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—42no—
179C22×C4—42no—
180C22×C4—42no—
181C22×C4—102no—
182C22×C4—102no—
183C22×C4—201no—
184C22×C4—202no—
185C22×C4—202no—
186C22×C4—201no—
187C22×C4—201no—
188C22×C4—201no—
189C22×C4—202no—
190C22×C4—202no—
191C22×C4Q8×D511yescharacteristic
192C22×C4#71312yes—
193C22×C4#71311yescharacteristic
194C22×C4C2×C22⋊D512yes—
195C2×C8—202no—
196C2×C8—202no—
197C2×C8—202no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—82no—
201C4⋊C4—82no—
202C4⋊C4—104no—
203C4⋊C4—202no—
204C22⋊C4—42no—
205C22⋊C4—42no—
206C2×C5—21no—
207C2×C5—22no—
208C2×C5—21no—
209C2×C5#160912yes—
210C2×C5#161212yes—
211C2×C5#202511yescharacteristic
212C2×C5#202811yescharacteristic
213C2×C5#203011yescharacteristic
214C23—21no—
215C23—22no—
216C23—21no—
217C23#409211yescharacteristic
218C23#409311yescharacteristic
219C23#409512yes—
220C23#409612yes—
221C23#409911yescharacteristic
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—44no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—82no—
238C2×C4—204no—
239C2×C4—202no—
240C2×C4—204no—
241C2×C4—202no—
242C2×C4—402no—
243C2×C4—401no—
244C2×C4—401no—
245C2×C4—401no—
246C2×C4—401no—
247C2×C4—402no—
248C2×C4#409212yes—
249C2×C4#409312yes—
250C8—402no—
251C5#1034611yescharacteristic, complemented, Sylow
252C22—22no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22#6535512yes—
261C22#6535611yescharacteristic
262C22#6535711yescharacteristic
263C22#6552011yescharacteristic
264C22#6552712yes—
265C22#6553111yescharacteristic
266C22#6553212yes—
267C22#6553511yescharacteristic
268C4—22no—
269C4—22no—
270C4—82no—
271C4—82no—
272C4—82no—
273C4—402no—
274C4—402no—
275C2—21no—
276C2—22no—
277C2—21no—
278C2#1060253611yescharacteristic
279C2#1060267512yes—
280C2#1060267912yes—
281C2#1060268711yescharacteristic
282C2#1060269811yescharacteristic
subgroupG/H
centerC23#4099
commutator, cosocleC23×C4×C5C23
FrattiniC23×C4C22×D5
FittingC5×#2646C2
socleC23×C5#120
prime radicalC24×C5C2×D4
hypercenter#2646D5
hypocenterC5#10346
LCSG ▷ C23×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2646

Complements

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

NH ≅ G/Ntype
251. C5#10346semidirect

Maximal subgroups

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

subgroupindex
C5×#26462
#106002942
#106002152
#105981152
#105981042
#103465