Finite Group Databasebeta

← #11996697

Subgroups — #11996697

Order 1280.

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

normal subgroups only

This group has 466 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
1#10614974C211yesmaximal, characteristic
2#10610995C211yesmaximal, characteristic
3C5×#1548C211yesmaximal, characteristic
4#10602567C211yesmaximal, characteristic
5#10601321C211yesmaximal, characteristic
6#10598237C211yesmaximal, characteristic
7#10598206C211yesmaximal, characteristic
8C2×C5×C4⋊Q8C2211yescharacteristic
9C2×C4×Dic10C2211yescharacteristic
10C5×#431C2211yescharacteristic
11C5×#423C2211yescharacteristic
12#65518C414yes—
13C2×#3956—21no—
14#65265—21no—
15#65263—21no—
16#65262—22no—
17C4×C4⋊Dic5C2211yescharacteristic
18#65214C2211yescharacteristic
19#65213C2211yescharacteristic
20#65120—22no—
21#65008—22no—
22#64968—22no—
23C5×#333—22no—
24#64774—21no—
25#64766—22no—
26#9400—51nomaximal, Sylow
27C22×C5×Q8C2×C412yes—
28C22×Dic10D411yescharacteristic
29C2×C5×M16—21no—
30C5×C4⋊Q8—21no—
31C5×C4⋊Q8—21no—
32C5×C4⋊Q8—21no—
33C5×C4⋊Q8—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—21no—
36C2×C42×C5C2311yescharacteristic
37C2×C4⋊Dic5—21no—
38C2×C4⋊Dic5D411yescharacteristic
39C2×#683—24no—
40C2×#683C2×C412yes—
41C2×C4×Dic5—21no—
42C2×C4×Dic5D412yes—
43C2×#681—21no—
44C4×Dic10—21no—
45C4×Dic10—21no—
46C4×Dic10—21no—
47C4×Dic10—21no—
48C5×C4⋊C8—21no—
49C5×C4⋊C8—21no—
50C5×C4⋊C8D412yes—
51C5×C22⋊C8—21no—
52C4×C5×C8—21no—
53#3963—24no—
54#3963C2×C412yes—
55C22⋊#168—21no—
56#3956—42no—
57#3947—24no—
58#3946—24no—
59C4⋊#168—21no—
60C4⋊#168—21no—
61C4⋊#168D412yes—
62C4×#168—21no—
63#2983—51no—
64#2567—51no—
65#1801—51no—
66#1548—51no—
67#1548D511yescharacteristic
68#1303—51no—
69#1303—51no—
70C2×C5×Q8—22no—
71C2×C5×Q8—22no—
72C2×C5×Q8—82no—
73C22×C4×C5—22no—
74C22×C4×C5C22×C411yescharacteristic
75C22×C4×C5C2×D411yescharacteristic
76C22×C4×C5C2×D411yescharacteristic
77C22×Dic5—22no—
78C22×Dic5C22⋊C412yes—
79C22×Dic5C22⋊C412yes—
80C2×Dic10—21no—
81C2×Dic10—21no—
82C2×Dic10—21no—
83C2×Dic10—21no—
84C2×Dic10—21no—
85C2×Dic10—21no—
86C5×M16—41no—
87C5×M16—41no—
88C2×C5×C8—22no—
89C2×C5×C8—41no—
90C5×C4⋊C4—41no—
91C5×C4⋊C4—41no—
92C5×C4⋊C4—41no—
93C5×C4⋊C4—41no—
94C42×C5C2×D411yescharacteristic
95C42×C5C2×D411yescharacteristic
96C42×C5#4111yescharacteristic
97C42×C5#4111yescharacteristic
98C4⋊Dic5—24no—
99C4⋊Dic5—21no—
100C4⋊Dic5—21no—
101#683—22no—
102#683—22no—
103#683—84no—
104C4×Dic5—22no—
105C4×Dic5—22no—
106C4×Dic5—41no—
107C4×Dic5—41no—
108#681—41no—
109#681—41no—
110C2×#168—22no—
111C2×#168—41no—
112C2×C4⋊Q8C2×D511yescharacteristic
113C2×C4×Q8—51no—
114#446—102no—
115#446—102no—
116#432—102no—
117#431—51no—
118#431C2×D511yescharacteristic
119#423—51no—
120#423C2×D511yescharacteristic
121C2×#101—101no—
122#395—54no—
123#391—101no—
124#389—102no—
125#384—101no—
126C4×C4⋊C4—51no—
127#343—101no—
128#333—22no—
129#333—102no—
130C23×C5C2×C22⋊C411yescharacteristic
131C5×Q8—82no—
132C5×Q8—82no—
133C2×C4×C5—22no—
134C2×C4×C5—41no—
135C2×C4×C5—44no—
136C2×C4×C5—42no—
137C2×C4×C5C4×D411yescharacteristic
138C2×C4×C5C4×D411yescharacteristic
139C2×C4×C5#12011yescharacteristic
140C2×C4×C5#12111yescharacteristic
141C2×C4×C5#12111yescharacteristic
142C2×C4×C5#12311yescharacteristic
143C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C5#13711yescharacteristic
145C2×C4×C5#13711yescharacteristic
146C2×C4×C5#13711yescharacteristic
147C2×Dic5—24no—
148C2×Dic5—22no—
149C2×Dic5—22no—
150C2×Dic5—22no—
151C2×Dic5—22no—
152C2×Dic5—42no—
153C2×Dic5—42no—
154C2×Dic5—42no—
155Dic10—41no—
156Dic10—41no—
157Dic10—41no—
158Dic10—41no—
159C5×C8—42no—
160C5×C8—81no—
161#168—42no—
162#168—81no—
163C22×Q8—51no—
164C22×Q8C4×D512yes—
165C2×M16—21no—
166C2×M16—101no—
167C4⋊Q8—21no—
168C4⋊Q8—21no—
169C4⋊Q8—21no—
170C4⋊Q8—21no—
171C4×Q8—101no—
172C4×Q8—101no—
173C4×Q8—101no—
174C4×Q8—101no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—52no—
178C2×C4⋊C4—51no—
179C2×C4⋊C4—101no—
180C2×C4⋊C4—104no—
181C2×C42—52no—
182C2×C42—101no—
183C2×C42C22×D511yescharacteristic
184C4⋊C8—21no—
185C4⋊C8—21no—
186C4⋊C8—52no—
187C4⋊C8—104no—
188C4⋊C8—101no—
189C4⋊C8—101no—
190C4⋊C8C22⋊D512yes—
191#101—202no—
192C22⋊C8—21no—
193C22⋊C8—101no—
194#97—104no—
195C4×C8—21no—
196C4×C8—101no—
197#95—52no—
198#95—104no—
199C22×C5—21no—
200C22×C5—21no—
201C22×C5#38611yescharacteristic
202C22×C5#41711yescharacteristic
203C22×C5#41911yescharacteristic
204C4×C5—21no—
205C4×C5—21no—
206C4×C5—21no—
207C4×C5—82no—
208C4×C5#45612yes—
209C4×C5#46811yescharacteristic
210C4×C5#46811yescharacteristic
211C4×C5#47011yescharacteristic
212C4×C5#47011yescharacteristic
213Dic5—44no—
214Dic5—42no—
215Dic5—42no—
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—82no—
219C2×Q8—101no—
220C2×Q8—101no—
221C2×Q8—101no—
222C2×Q8—101no—
223C2×Q8—101no—
224C2×Q8—101no—
225C22×C4—22no—
226C22×C4—52no—
227C22×C4—52no—
228C22×C4—102no—
229C22×C4C2×C4×D511yescharacteristic
230C22×C4D4×D511yescharacteristic
231C22×C4D4×D511yescharacteristic
232M16—41no—
233M16—41no—
234M16—201no—
235M16—201no—
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—102no—
239C2×C8—201no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—104no—
245C4⋊C4—102no—
246C4⋊C4—101no—
247C4⋊C4—102no—
248C4⋊C4—101no—
249C4⋊C4—404no—
250C42—102no—
251C42—102no—
252C42—201no—
253C42—201no—
254C42#70911yescharacteristic
255C42D4×D511yescharacteristic
256C42#71111yescharacteristic
257C42C2×C22⋊D511yescharacteristic
258C2×C5—21no—
259C2×C5—21no—
260C2×C5#188611yescharacteristic
261C2×C5#189411yescharacteristic
262C2×C5#191411yescharacteristic
263C23D5×C22⋊C411yescharacteristic
264Q8—82no—
265Q8—82no—
266Q8—201no—
267Q8—201no—
268Q8—201no—
269Q8—201no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—44no—
273C2×C4—42no—
274C2×C4—104no—
275C2×C4—102no—
276C2×C4—102no—
277C2×C4—102no—
278C2×C4—102no—
279C2×C4—202no—
280C2×C4—202no—
281C2×C4—202no—
282C2×C4#402711yescharacteristic
283C2×C4#402911yescharacteristic
284C2×C4#403011yescharacteristic
285C2×C4#406011yescharacteristic
286C2×C4#406111yescharacteristic
287C2×C4#406411yescharacteristic
288C2×C4#406411yescharacteristic
289C2×C4C4×C22⋊D511yescharacteristic
290C2×C4#408311yescharacteristic
291C2×C4#408411yescharacteristic
292C8—42no—
293C8—81no—
294C8—202no—
295C8—401no—
296C5#940011yescharacteristic, complemented, Sylow
297C22—21no—
298C22—21no—
299C22#6509111yescharacteristic
300C22#6509211yescharacteristic
301C22#6524511yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—82no—
306C4—204no—
307C4—202no—
308C4—202no—
309C4#6510111yescharacteristic
310C4#6510511yescharacteristic
311C4#6546311yescharacteristic
312C4#6547811yescharacteristic
313C4#6549412yes—
314C2—21no—
315C2—21no—
316C2#1060088211yescharacteristic
317C2#1060106411yescharacteristic
318C2#1060113811yescharacteristic
subgroupG/H
centerC22#65245
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1548C2
socleC22×C5#386
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1548D5
hypocenterC5#9400
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
296. C5#9400semidirect

Maximal subgroups

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

subgroupindex
#106149742
#106109952
C5×#15482
#106025672
#106013212
#105982372
#105982062
#94005