Finite Group Databasebeta

← #12008713

Subgroups — #12008713

Order 1280.

418 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 87 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#10613965C211yesmaximal, characteristic
2C5×#1464C211yesmaximal, characteristic
3#10602365C211yesmaximal, characteristic
4#10597944C214yesmaximal, complemented
5C2×C5×#117C2211yescharacteristic
6C2×#4072C411yescharacteristic
7C22×C4⋊Dic5C411yescharacteristic
8C5×#432—21no—
9#65266C412yes—
10#65265C2212yes—
11#65235—21no—
12#65235—21no—
13#65217—21no—
14#65217—21no—
15#65215—21no—
16C5×#324C2212yes—
17C5×#323—21no—
18#64748C2212yes—
19#64745—21no—
20#11516—51nomaximal, Sylow
21C23×C4×C5C2×C411yescharacteristic
22C23×Dic5—21no—
23C5×#117—41no—
24C5×#117—41no—
25C2×C5×C4⋊C4C2×C411yescharacteristic
26C2×C5×C4⋊C4C2311yescharacteristic
27C2×C5×C22⋊C4D411yescharacteristic
28C2×C5×C22⋊C4D411yescharacteristic
29C2×C42×C5D411yescharacteristic
30C2×C42×C5D411yescharacteristic
31C2×C22⋊Dic5—21no—
32#4072—24no—
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5—41no—
36C2×C4⋊Dic5—41no—
37C2×C4⋊Dic5C2×C412yes—
38C2×#683—22no—
39C2×#683—22no—
40C2×C4×Dic5C2×C412yes—
41C5×C4⋊C8—41no—
42C5×C22⋊C8—22no—
43C5×#97—41no—
44#3963—22no—
45#3963—22no—
46C22⋊#168—22no—
47C4⋊#168—41no—
48#3935—41no—
49#2317—51no—
50#1464—51no—
51#1464D511yescharacteristic
52#1325—54no—
53C24×C5C22⋊C411yescharacteristic
54C22×C4×C5—22no—
55C22×C4×C5—21no—
56C22×C4×C5—21no—
57C22×C4×C5—22no—
58C22×C4×C5C22⋊C411yescharacteristic
59C22×C4×C5C22⋊C411yescharacteristic
60C22×C4×C5C22⋊C411yescharacteristic
61C22×C4×C5C22×C411yescharacteristic
62C22×C4×C5C2×D411yescharacteristic
63C22×C4×C5C2×D411yescharacteristic
64C22×Dic5—22no—
65C22×Dic5—22no—
66C22×Dic5—42no—
67C22×Dic5—82no—
68C2×C5×C8—42no—
69C5×C4⋊C4—41no—
70C5×C4⋊C4—41no—
71C5×C22⋊C4—41no—
72C5×C22⋊C4—41no—
73C42×C5—21no—
74C42×C5—21no—
75C42×C5—21no—
76C42×C5—21no—
77C22⋊Dic5—24no—
78C4⋊Dic5—24no—
79C4⋊Dic5—41no—
80C4⋊Dic5—41no—
81C4⋊Dic5—42no—
82#683—82no—
83#683—82no—
84C4×Dic5—22no—
85C4×Dic5M1614yes—
86C2×#168—42no—
87C2×#117—51no—
88C2×#117C2×D511yescharacteristic
89C22×C4⋊C4—51no—
90#432—21no—
91#432—101no—
92#389—101no—
93#389—101no—
94#385—101no—
95#385—101no—
96#384—52no—
97#382—52no—
98#324—52no—
99#324C2×D512yes—
100#323—21no—
101#323—101no—
102C23×C5—21no—
103C23×C5—21no—
104C23×C5—41no—
105C23×C5—41no—
106C23×C5#10112yes—
107C23×C5C2×C22⋊C411yescharacteristic
108C2×C4×C5—24no—
109C2×C4×C5—24no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—41no—
119C2×C4×C5—41no—
120C2×C4×C5—41no—
121C2×C4×C5—41no—
122C2×C4×C5#9911yescharacteristic
123C2×C4×C5#9911yescharacteristic
124C2×C4×C5C2×M1612yes—
125C2×Dic5—24no—
126C2×Dic5—42no—
127C2×Dic5—42no—
128C2×Dic5—42no—
129C2×Dic5—42no—
130C2×Dic5—42no—
131C2×Dic5—84no—
132C5×C8—82no—
133#168—82no—
134C23×C4—101no—
135C23×C4C4×D511yescharacteristic
136#117—41no—
137#117—41no—
138#117—104no—
139C2×C4⋊C4—52no—
140C2×C4⋊C4—101no—
141C2×C4⋊C4—101no—
142C2×C4⋊C4—102no—
143C2×C4⋊C4—102no—
144C2×C4⋊C4—201no—
145C2×C4⋊C4—201no—
146C2×C4⋊C4C4×D511yescharacteristic
147C2×C4⋊C4C22×D511yescharacteristic
148C2×C22⋊C4—101no—
149C2×C22⋊C4D2011yescharacteristic
150C2×C22⋊C4C22⋊D511yescharacteristic
151C2×C42—52no—
152C2×C42D2011yescharacteristic
153C2×C42C22⋊D511yescharacteristic
154C4⋊C8—41no—
155C4⋊C8—201no—
156C22⋊C8—22no—
157C22⋊C8—102no—
158#97—41no—
159#97—201no—
160#95—102no—
161#95—102no—
162C22×C5—21no—
163C22×C5—21no—
164C22×C5—22no—
165C22×C5—42no—
166C22×C5—42no—
167C22×C5—41no—
168C22×C5—41no—
169C22×C5#40711yescharacteristic
170C22×C5C2×#9911yescharacteristic
171C22×C5C2×#10111yescharacteristic
172C4×C5—21no—
173C4×C5—21no—
174C4×C5—22no—
175C4×C5—41no—
176C4×C5—41no—
177C4×C5—41no—
178C4×C5—41no—
179Dic5—44no—
180Dic5—82no—
181C24#68511yescharacteristic
182C22×C4—22no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—22no—
186C22×C4—102no—
187C22×C4—102no—
188C22×C4—202no—
189C22×C4—402no—
190C22×C4#68511yescharacteristic
191C22×C4#68511yescharacteristic
192C22×C4#68511yescharacteristic
193C22×C4C2×C4×D511yescharacteristic
194C22×C4C2×D2011yescharacteristic
195C22×C4C2×C22⋊D511yescharacteristic
196C2×C8—42no—
197C2×C8—202no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—104no—
201C4⋊C4—202no—
202C4⋊C4—201no—
203C4⋊C4—201no—
204C4⋊C4—402no—
205C4⋊C4—402no—
206C22⋊C4—41no—
207C22⋊C4—41no—
208C22⋊C4—104no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—54no—
214C42—102no—
215C2×C5—21no—
216C2×C5—21no—
217C2×C5—42no—
218C2×C5#146311yescharacteristic
219C2×C5#212811yescharacteristic
220C2×C5#213511yescharacteristic
221C23—21no—
222C23—21no—
223C23—41no—
224C23—41no—
225C23#395612yes—
226C23C2×#68511yescharacteristic
227C2×C4—24no—
228C2×C4—24no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—104no—
242C2×C4—202no—
243C2×C4—202no—
244C2×C4—202no—
245C2×C4—202no—
246C2×C4—202no—
247C2×C4—404no—
248C2×C4#393811yescharacteristic
249C2×C4#393811yescharacteristic
250C2×C4D5×M1612yes—
251C8—82no—
252C8—402no—
253C5#1151611yescharacteristic, complemented, Sylow
254C22—21no—
255C22—21no—
256C22—22no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22C2×#393811yescharacteristic
262C22#6541511yescharacteristic
263C22C2×#395611yescharacteristic
264C4—21no—
265C4—21no—
266C4—22no—
267C4—41no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—204no—
272C4—402no—
273C2—21no—
274C2—21no—
275C2—42no—
276C2#1060076411yescharacteristic
277C2#1060085411yescharacteristic
278C2#1060094311yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1464C2
socleC22×C5C2×#99
prime radicalC24×C5C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#1464D5
hypocenterC5#11516
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
4. #10597944C2semidirect
253. C5#11516semidirect

Maximal subgroups

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

subgroupindex
#106139652
C5×#14642
#106023652
#105979442
#115165