Finite Group Databasebeta

← #12008673

Subgroups — #12008673

Order 1280.

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

normal subgroups only

This group has 510 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#10613961C211yesmaximal, characteristic
2C5×#1464C211yesmaximal, characteristic
3#10602365C211yesmaximal, characteristic
4#10597936C214yesmaximal
5C23×Dic10C411yescharacteristic
6C2×C5×#117C2211yescharacteristic
7C2×#4072C411yescharacteristic
8C5×#432—21no—
9#65263—21no—
10#65263—21no—
11#65232C412yes—
12#65232C2212yes—
13#65218—21no—
14#65218—21no—
15#65215—21no—
16C5×#324—21no—
17C5×#323C2212yes—
18#64748—21no—
19#64745C2212yes—
20#11504—51nomaximal, Sylow
21C23×C4×C5C2×C411yescharacteristic
22C23×Dic5C2×C412yes—
23C22×Dic10—21no—
24C22×Dic10—21no—
25C22×Dic10—24no—
26C22×Dic10—41no—
27C22×Dic10—41no—
28C22×Dic10—42no—
29C5×#117—41no—
30C5×#117—41no—
31C2×C5×C4⋊C4D411yescharacteristic
32C2×C5×C4⋊C4D411yescharacteristic
33C2×C5×C22⋊C4C2×C411yescharacteristic
34C2×C5×C22⋊C4C2311yescharacteristic
35C2×C42×C5D411yescharacteristic
36C2×C42×C5D411yescharacteristic
37C2×C22⋊Dic5C2×C412yes—
38#4072—42no—
39C2×C4⋊Dic5—21no—
40C2×C4×Dic5—21no—
41C5×C4⋊C8—41no—
42C5×C22⋊C8—22no—
43C5×#97—41no—
44#3963—22no—
45#3963—22no—
46#3963—22no—
47#3963—22no—
48C22⋊#168—22no—
49C4⋊#168—41no—
50#3935—41no—
51#2310—51no—
52#1464—51no—
53#1464D511yescharacteristic
54#1317—54no—
55C24×C5C22×C411yescharacteristic
56C22×C4×C5—22no—
57C22×C4×C5—21no—
58C22×C4×C5—21no—
59C22×C4×C5—22no—
60C22×C4×C5C22⋊C411yescharacteristic
61C22×C4×C5C22⋊C411yescharacteristic
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5C2×D411yescharacteristic
65C22×C4×C5C2×D411yescharacteristic
66C22×Dic5—22no—
67C22×Dic5—22no—
68C22×Dic5—22no—
69C22×Dic5—42no—
70C22×Dic5—42no—
71C22×Dic5M1614yes—
72C2×Dic10—24no—
73C2×Dic10—24no—
74C2×Dic10—48no—
75C2×Dic10—48no—
76C2×Dic10—42no—
77C2×Dic10—42no—
78C2×Dic10—41no—
79C2×Dic10—41no—
80C2×Dic10—42no—
81C2×C5×C8—42no—
82C5×C4⋊C4—41no—
83C5×C4⋊C4—41no—
84C5×C22⋊C4—41no—
85C5×C22⋊C4—41no—
86C42×C5—21no—
87C42×C5—21no—
88C42×C5—21no—
89C42×C5—21no—
90C22⋊Dic5—42no—
91C4⋊Dic5—42no—
92C4×Dic5—42no—
93C2×#168—42no—
94C23×Q8—51no—
95C2×#117—51no—
96C2×#117C2×D511yescharacteristic
97#432—21no—
98#432—101no—
99#391—101no—
100#391—101no—
101#391—101no—
102#391—101no—
103#381—52no—
104#381—52no—
105#324—21no—
106#324—101no—
107#323—52no—
108#323C2×D512yes—
109C23×C5—21no—
110C23×C5—21no—
111C23×C5—41no—
112C23×C5—41no—
113C23×C5C2×C22⋊C411yescharacteristic
114C23×C5C2×M1612yes—
115C2×C4×C5—24no—
116C2×C4×C5—24no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—41no—
126C2×C4×C5—41no—
127C2×C4×C5—41no—
128C2×C4×C5—41no—
129C2×C4×C5#9911yescharacteristic
130C2×C4×C5#9911yescharacteristic
131C2×C4×C5#10012yes—
132C2×Dic5—24no—
133C2×Dic5—44no—
134C2×Dic5—42no—
135C2×Dic5—42no—
136C2×Dic5—44no—
137C2×Dic5—42no—
138C2×Dic5—42no—
139C2×Dic5—42no—
140Dic10—44no—
141Dic10—44no—
142Dic10—48no—
143C5×C8—82no—
144#168—82no—
145C22×Q8—104no—
146C22×Q8—101no—
147C22×Q8—101no—
148C22×Q8—201no—
149C22×Q8—201no—
150C22×Q8—202no—
151C23×C4—52no—
152C23×C4C4×D511yescharacteristic
153#117—41no—
154#117—41no—
155#117—202no—
156C2×C4⋊C4—101no—
157C2×C4⋊C4D2011yescharacteristic
158C2×C4⋊C4C22⋊D511yescharacteristic
159C2×C22⋊C4—52no—
160C2×C22⋊C4C4×D511yescharacteristic
161C2×C22⋊C4C22×D511yescharacteristic
162C2×C42—101no—
163C2×C42D2011yescharacteristic
164C2×C42C22⋊D511yescharacteristic
165C4⋊C8—41no—
166C4⋊C8—201no—
167C22⋊C8—22no—
168C22⋊C8—102no—
169#97—41no—
170#97—201no—
171#95—102no—
172#95—102no—
173#95—102no—
174#95—102no—
175C22×C5—21no—
176C22×C5—21no—
177C22×C5—22no—
178C22×C5—42no—
179C22×C5—42no—
180C22×C5—41no—
181C22×C5—41no—
182C22×C5#40711yescharacteristic
183C22×C5C2×#9911yescharacteristic
184C22×C5C2×#10011yescharacteristic
185C4×C5—21no—
186C4×C5—21no—
187C4×C5—22no—
188C4×C5—41no—
189C4×C5—41no—
190C4×C5—41no—
191C4×C5—41no—
192Dic5—44no—
193Dic5—82no—
194C24C2×C4×D511yescharacteristic
195C2×Q8—104no—
196C2×Q8—104no—
197C2×Q8—208no—
198C2×Q8—208no—
199C2×Q8—202no—
200C2×Q8—202no—
201C2×Q8—201no—
202C2×Q8—201no—
203C2×Q8—202no—
204C22×C4—22no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—54no—
209C22×C4—102no—
210C22×C4—102no—
211C22×C4—102no—
212C22×C4—202no—
213C22×C4—202no—
214C22×C4#68511yescharacteristic
215C22×C4#68511yescharacteristic
216C22×C4#68511yescharacteristic
217C22×C4#68511yescharacteristic
218C22×C4C2×D2011yescharacteristic
219C22×C4C2×C22⋊D511yescharacteristic
220C2×C8—42no—
221C2×C8—202no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—202no—
225C22⋊C4—41no—
226C22⋊C4—41no—
227C22⋊C4—202no—
228C42—21no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—202no—
233C2×C5—21no—
234C2×C5—21no—
235C2×C5—42no—
236C2×C5#146211yescharacteristic
237C2×C5#212311yescharacteristic
238C2×C5#212311yescharacteristic
239C23—21no—
240C23—21no—
241C23—41no—
242C23—41no—
243C23D5×M1612yes—
244C23C2×#68511yescharacteristic
245Q8—204no—
246Q8—204no—
247Q8—208no—
248C2×C4—24no—
249C2×C4—24no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—104no—
263C2×C4—204no—
264C2×C4—202no—
265C2×C4—202no—
266C2×C4—204no—
267C2×C4—202no—
268C2×C4—202no—
269C2×C4—202no—
270C2×C4#393811yescharacteristic
271C2×C4#393811yescharacteristic
272C2×C4#395512yes—
273C8—82no—
274C8—402no—
275C5#1150411yescharacteristic, complemented, Sylow
276C22—21no—
277C22—21no—
278C22—22no—
279C22—42no—
280C22—42no—
281C22—41no—
282C22—41no—
283C22C2×#393811yescharacteristic
284C22#6541511yescharacteristic
285C22C2×#395511yescharacteristic
286C4—21no—
287C4—21no—
288C4—22no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—204no—
294C4—402no—
295C2—21no—
296C2—21no—
297C2—42no—
298C2#1060076011yescharacteristic
299C2#1060085111yescharacteristic
300C2#1060094011yescharacteristic
subgroupG/H
centerC22C2×#3938
commutator, prime radicalC24×C5C22×C4
FrattiniC2×C22⋊C4C22×D5
FittingC5×#1464C2
socleC22×C5C2×#99
cosocleC2×C5×C22⋊C4C23
hypercenter#1464D5
hypocenterC5#11504
LCSG ▷ C24×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
275. C5#11504semidirect

Maximal subgroups

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

subgroupindex
#106139612
C5×#14642
#106023652
#105979362
#115045