Finite Group Databasebeta

← #11996889

Subgroups — #11996889

Order 1280.

400 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 97 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#10614938C211yesmaximal, characteristic
2#10610998C211yesmaximal, characteristic
3C5×#1548C211yesmaximal, characteristic
4#10602566C211yesmaximal, characteristic
5#10601304C211yesmaximal, characteristic
6#10598234C211yesmaximal, characteristic
7#10598201C211yesmaximal, characteristic
8C2×C5×C4⋊Q8C2211yescharacteristic
9#65804C2211yescharacteristic
10C5×#431C2211yescharacteristic
11C5×#423C2211yescharacteristic
12#65369C414yes—
13#65368—21no—
14#65367—21no—
15#65253—22no—
16#65214C2211yescharacteristic
17#65213C2211yescharacteristic
18C4×#681C2211yescharacteristic
19#65120—21no—
20#65119—21no—
21#65009—22no—
22#64968—21no—
23C8×Dic10—21no—
24C5×#333—21no—
25C5×#333—21no—
26#64767—21no—
27#64767—21no—
28#64706—21no—
29#64702—21no—
30#9434—51nomaximal, Sylow
31C22×C5×Q8—21no—
32C2×C5×M16—21no—
33C5×C4⋊Q8—21no—
34C5×C4⋊Q8—21no—
35C5×C4⋊Q8—21no—
36C5×C4⋊Q8C2×C412yes—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4—21no—
39C2×C42×C5C2311yescharacteristic
40#4072D412yes—
41#4070—21no—
42#4070—21no—
43C2×#681—21no—
44C2×#681—21no—
45#4016C2×C412yes—
46#4015D411yescharacteristic
47#4015D411yescharacteristic
48C4×Dic10—21no—
49C4×Dic10—21no—
50C5×C4⋊C8—21no—
51C5×C4⋊C8—21no—
52C5×C4⋊C8D411yescharacteristic
53C5×C4⋊C8D411yescharacteristic
54C5×C22⋊C8—21no—
55C4×C5×C8—21no—
56C22⋊#168—21no—
57#3947—22no—
58#3946—22no—
59#3946—22no—
60C8×Dic5—22no—
61#3940—24no—
62#3939—24no—
63C4⋊#168—21no—
64C4⋊#168—21no—
65C4⋊#168D411yescharacteristic
66C4⋊#168D411yescharacteristic
67#3935C2×C412yes—
68C4×#168—21no—
69C4×#168—21no—
70#3165—51no—
71#2986—51no—
72#1561—51no—
73#1548D511yescharacteristic
74#1546—51no—
75#1299—51no—
76#1299—51no—
77C2×C5×Q8—22no—
78C2×C5×Q8—41no—
79C2×C5×Q8—81no—
80C2×C5×Q8—81no—
81C22×C4×C5—41no—
82C22×C4×C5C2×D411yescharacteristic
83C22×C4×C5#4111yescharacteristic
84C22×C4×C5#4111yescharacteristic
85C2×Dic10—21no—
86C2×Dic10—21no—
87C5×M16—81no—
88C2×C5×C8—21no—
89C2×C5×C8—21no—
90C2×C5×C8—41no—
91C5×C4⋊C4—22no—
92C5×C4⋊C4—22no—
93C5×C4⋊C4—41no—
94C5×C4⋊C4—41no—
95C42×C5C22×C411yescharacteristic
96C42×C5C2×D411yescharacteristic
97C42×C5C2×D411yescharacteristic
98C42×C5C2×D411yescharacteristic
99C22⋊Dic5—22no—
100C4⋊Dic5—21no—
101C4⋊Dic5—21no—
102C4⋊Dic5C22⋊C412yes—
103C4⋊Dic5C22⋊C412yes—
104#683—22no—
105#683—22no—
106C4×Dic5—22no—
107#681—22no—
108#681—22no—
109#681—81no—
110C2×#168—22no—
111C2×#168—21no—
112C2×#168—21no—
113C2×#168—41no—
114#533—51no—
115C2×C4⋊Q8C2×D511yescharacteristic
116#501—54no—
117#500—101no—
118#498—101no—
119#446—101no—
120#446—101no—
121C8×Q8—101no—
122C8×Q8—101no—
123#433—102no—
124#431—51no—
125#431C2×D511yescharacteristic
126#428—102no—
127#423—51no—
128#423C2×D511yescharacteristic
129C4×M16—51no—
130#333—21no—
131#333—21no—
132#332—101no—
133#332—101no—
134#332—101no—
135#332—101no—
136C23×C5#12311yescharacteristic
137C5×Q8—82no—
138C5×Q8—81no—
139C5×Q8—81no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—42no—
147C2×C4×C5—82no—
148C2×C4×C5C2×C22⋊C411yescharacteristic
149C2×C4×C5C4×D411yescharacteristic
150C2×C4×C5C4×D411yescharacteristic
151C2×C4×C5#12011yescharacteristic
152C2×C4×C5#12111yescharacteristic
153C2×C4×C5#12111yescharacteristic
154C2×Dic5—22no—
155C2×Dic5—22no—
156Dic10—41no—
157Dic10—41no—
158Dic10—41no—
159Dic10—41no—
160C5×C8—41no—
161C5×C8—41no—
162C5×C8—81no—
163#168—24no—
164#168—41no—
165#168—41no—
166#168—81no—
167C22×Q8—21no—
168C2×M16—21no—
169C2×M16—101no—
170C2×M16—101no—
171C4⋊Q8—21no—
172C4⋊Q8—21no—
173C4⋊Q8—21no—
174C4⋊Q8—51no—
175C4⋊Q8—51no—
176C4⋊Q8C4×D512yes—
177#125—52no—
178C22⋊Q8—101no—
179C22⋊Q8—101no—
180C4×Q8—101no—
181C4×Q8—101no—
182#117—52no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C42C22×D511yescharacteristic
186#107—104no—
187#106—104no—
188C4⋊C8—21no—
189C4⋊C8—21no—
190C4⋊C8—51no—
191C4⋊C8—51no—
192C4⋊C8—102no—
193C4⋊C8—102no—
194C4⋊C8—101no—
195C4⋊C8—101no—
196C4⋊C8C22⋊D511yescharacteristic
197C4⋊C8C22⋊D511yescharacteristic
198C22⋊C8—21no—
199C22⋊C8—101no—
200#97—52no—
201#97—102no—
202C4×C8—21no—
203C4×C8—102no—
204C4×C8—101no—
205C4×C8—101no—
206C22×C5—21no—
207C22×C5—21no—
208C22×C5—21no—
209C22×C5#38611yescharacteristic
210C4×C5—21no—
211C4×C5—21no—
212C4×C5—21no—
213C4×C5—82no—
214C4×C5#45611yescharacteristic
215C4×C5#45611yescharacteristic
216C4×C5#47111yescharacteristic
217C4×C5#47111yescharacteristic
218C4×C5#47211yescharacteristic
219C4×C5#47311yescharacteristic
220Dic5—42no—
221Dic5—42no—
222C2×Q8—22no—
223C2×Q8—41no—
224C2×Q8—81no—
225C2×Q8—81no—
226C2×Q8—101no—
227C2×Q8—101no—
228C22×C4—41no—
229C22×C4#70911yescharacteristic
230C22×C4D4×D511yescharacteristic
231C22×C4#71111yescharacteristic
232M16—81no—
233M16—102no—
234M16—102no—
235M16—401no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—41no—
239C2×C8—102no—
240C2×C8—101no—
241C2×C8—101no—
242C2×C8—201no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—52no—
248C4⋊C4—52no—
249C4⋊C4—102no—
250C4⋊C4—101no—
251C4⋊C4—102no—
252C4⋊C4—101no—
253C22⋊C4—102no—
254C42—102no—
255C42C2×C4×D511yescharacteristic
256C42D4×D511yescharacteristic
257C42D4×D511yescharacteristic
258C42C2×C22⋊D511yescharacteristic
259C2×C5—41no—
260C2×C5#188611yescharacteristic
261C2×C5#190711yescharacteristic
262C2×C5#190811yescharacteristic
263C23#402911yescharacteristic
264Q8—82no—
265Q8—81no—
266Q8—81no—
267Q8—201no—
268Q8—201no—
269Q8—201no—
270Q8—201no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—82no—
279C2×C4—102no—
280C2×C4—102no—
281C2×C4D5×C22⋊C411yescharacteristic
282C2×C4#402711yescharacteristic
283C2×C4#403011yescharacteristic
284C2×C4C4×C22⋊D511yescharacteristic
285C2×C4#408311yescharacteristic
286C2×C4#408411yescharacteristic
287C8—41no—
288C8—41no—
289C8—81no—
290C8—104no—
291C8—201no—
292C8—201no—
293C8—401no—
294C5#943411yescharacteristic, complemented, Sylow
295C22—21no—
296C22—21no—
297C22—21no—
298C22#6524511yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—82no—
303C4—202no—
304C4—202no—
305C4#6503711yescharacteristic
306C4#6503811yescharacteristic
307C4#6546611yescharacteristic
308C4#6548111yescharacteristic
309C4#6549411yescharacteristic
310C4#6549411yescharacteristic
311C2—41no—
312C2#1060088111yescharacteristic
313C2#1060107911yescharacteristic
314C2#1060113811yescharacteristic
subgroupG/H
centerC22#65245
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1548C2
socleC22×C5#386
prime radicalC23×C5#123
cosocleC2×C42×C5C23
hypercenter#1548D5
hypocenterC5#9434
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
294. C5#9434semidirect

Maximal subgroups

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

subgroupindex
#106149382
#106109982
C5×#15482
#106025662
#106013042
#105982342
#105982012
#94345