Finite Group Databasebeta

← #11996719

Subgroups — #11996719

Order 1280.

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

normal subgroups only

This group has 450 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#10610995C211yesmaximal, characteristic
2#10605453C211yesmaximal, characteristic
3#10601573C211yesmaximal, characteristic
4#10601321C211yesmaximal, characteristic
5#10601301C211yesmaximal, characteristic
6C5×#1303C211yesmaximal, characteristic
7#10598111C211yesmaximal, characteristic
8C2×#4015C2211yescharacteristic
9C2×C4×Dic10C2211yescharacteristic
10C5×#431C2211yescharacteristic
11C5×#423C2211yescharacteristic
12C4×C5×C4⋊C4C2211yescharacteristic
13C2×#3956—21no—
14#65263—22no—
15#65225—21no—
16#65218—21no—
17#65214C2211yescharacteristic
18#65213C2211yescharacteristic
19#65120—22no—
20#65008—22no—
21#64968—22no—
22#64948C414yes—
23#64774—21no—
24#64706—22no—
25#64702—22no—
26#9404—51nomaximal, Sylow
27C22×Dic10—21no—
28C22×Dic10D411yescharacteristic
29C2×C5×M16—21no—
30C2×C5×C4⋊C4—21no—
31C2×C42×C5—21no—
32C2×C42×C5C2311yescharacteristic
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5C2×C412yes—
35C2×C4⋊Dic5D411yescharacteristic
36C2×#683C2×C412yes—
37C2×C4×Dic5D412yes—
38C2×#681—21no—
39#4015—21no—
40#4015—21no—
41#4015—21no—
42#4015—21no—
43C4×Dic10—21no—
44C4×Dic10—21no—
45C4×Dic10—21no—
46C4×Dic10—21no—
47C5×C4⋊C8—21no—
48C5×C4⋊C8—21no—
49C5×C4⋊C8D412yes—
50C5×C22⋊C8—21no—
51C4×C5×C8—21no—
52C5×#95C2×C412yes—
53#3963—24no—
54#3963—24no—
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#2568—51no—
65#1801—51no—
66#1549—51no—
67#1549—51no—
68#1303—51no—
69#1303D511yescharacteristic
70C22×C4×C5—22no—
71C22×C4×C5C22×C411yescharacteristic
72C22×C4×C5C2×D411yescharacteristic
73C22×C4×C5C2×D411yescharacteristic
74C22×Dic5—22no—
75C22×Dic5C22⋊C412yes—
76C22×Dic5C22⋊C412yes—
77C2×Dic10—21no—
78C2×Dic10—21no—
79C2×Dic10—21no—
80C2×Dic10—21no—
81C2×Dic10—21no—
82C2×Dic10—21no—
83C2×Dic10—44no—
84C2×Dic10—41no—
85C2×Dic10—41no—
86C5×M16—41no—
87C5×M16—41no—
88C2×C5×C8—22no—
89C2×C5×C8—41no—
90C5×C4⋊C4—42no—
91C42×C5—41no—
92C42×C5—41no—
93C42×C5C2×D411yescharacteristic
94C42×C5C2×D411yescharacteristic
95C42×C5#4111yescharacteristic
96C42×C5#4111yescharacteristic
97C4⋊Dic5—21no—
98C4⋊Dic5—21no—
99C4⋊Dic5—22no—
100C4⋊Dic5—22no—
101C4⋊Dic5—41no—
102C4⋊Dic5—41no—
103#683—22no—
104#683—22no—
105C4×Dic5—22no—
106C4×Dic5—22no—
107#681—41no—
108#681—41no—
109C2×#168—22no—
110C2×#168—41no—
111C2×C4⋊Q8—51no—
112C2×C4×Q8—51no—
113#446—102no—
114#446—102no—
115#432—102no—
116#431—51no—
117#431C2×D511yescharacteristic
118#423—51no—
119#423C2×D511yescharacteristic
120C2×#101—101no—
121#400—54no—
122#391—101no—
123#391—102no—
124#382—101no—
125C4×C4⋊C4C2×D511yescharacteristic
126#343—101no—
127#332—102no—
128#332—102no—
129C23×C5C2×C22⋊C411yescharacteristic
130C2×C4×C5—22no—
131C2×C4×C5—41no—
132C2×C4×C5—42no—
133C2×C4×C5—42no—
134C2×C4×C5—42no—
135C2×C4×C5C4×D411yescharacteristic
136C2×C4×C5C4×D411yescharacteristic
137C2×C4×C5#12011yescharacteristic
138C2×C4×C5#12111yescharacteristic
139C2×C4×C5#12111yescharacteristic
140C2×C4×C5#12311yescharacteristic
141C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C5#13711yescharacteristic
143C2×C4×C5#13711yescharacteristic
144C2×C4×C5#13711yescharacteristic
145C2×Dic5—22no—
146C2×Dic5—22no—
147C2×Dic5—22no—
148C2×Dic5—22no—
149C2×Dic5—42no—
150C2×Dic5—44no—
151C2×Dic5—42no—
152Dic10—41no—
153Dic10—41no—
154Dic10—41no—
155Dic10—41no—
156Dic10—82no—
157Dic10—82no—
158C5×C8—42no—
159C5×C8—81no—
160#168—42no—
161#168—81no—
162C22×Q8—51no—
163C22×Q8—101no—
164C2×M16—21no—
165C2×M16—101no—
166C4⋊Q8—101no—
167C4⋊Q8—101no—
168C4⋊Q8—101no—
169C4⋊Q8—101no—
170C4×Q8—101no—
171C4×Q8—101no—
172C4×Q8—101no—
173C4×Q8—101no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—52no—
176C2×C4⋊C4—51no—
177C2×C4⋊C4—52no—
178C2×C4⋊C4—101no—
179C2×C42—21no—
180C2×C42—52no—
181C2×C42C22×D511yescharacteristic
182C4⋊C8—21no—
183C4⋊C8—21no—
184C4⋊C8—52no—
185C4⋊C8—104no—
186C4⋊C8—101no—
187C4⋊C8—101no—
188C4⋊C8D2012yes—
189#101—202no—
190C22⋊C8—21no—
191C22⋊C8—101no—
192#97—104no—
193C4×C8—21no—
194C4×C8—101no—
195#95—104no—
196#95—104no—
197#95C4×D512yes—
198C22×C5—21no—
199C22×C5—21no—
200C22×C5#38611yescharacteristic
201C22×C5#41711yescharacteristic
202C22×C5#41911yescharacteristic
203C4×C5—21no—
204C4×C5—21no—
205C4×C5—21no—
206C4×C5—82no—
207C4×C5#45412yes—
208C4×C5#46811yescharacteristic
209C4×C5#46811yescharacteristic
210C4×C5#47011yescharacteristic
211C4×C5#47011yescharacteristic
212Dic5—42no—
213Dic5—42no—
214Dic5—82no—
215C2×Q8—101no—
216C2×Q8—101no—
217C2×Q8—101no—
218C2×Q8—101no—
219C2×Q8—101no—
220C2×Q8—101no—
221C2×Q8—204no—
222C2×Q8—201no—
223C2×Q8—201no—
224C22×C4—22no—
225C22×C4—52no—
226C22×C4—52no—
227C22×C4—102no—
228C22×C4C2×C4×D511yescharacteristic
229C22×C4D4×D511yescharacteristic
230C22×C4D4×D511yescharacteristic
231M16—41no—
232M16—41no—
233M16—201no—
234M16—201no—
235C2×C8—22no—
236C2×C8—41no—
237C2×C8—102no—
238C2×C8—201no—
239C4⋊C4—42no—
240C4⋊C4—102no—
241C4⋊C4—101no—
242C4⋊C4—102no—
243C4⋊C4—101no—
244C4⋊C4—102no—
245C4⋊C4—102no—
246C4⋊C4—201no—
247C4⋊C4—201no—
248C42—41no—
249C42—41no—
250C42—102no—
251C42—102no—
252C42C2×D2011yescharacteristic
253C42#70911yescharacteristic
254C42D4×D511yescharacteristic
255C42#71311yescharacteristic
256C2×C5—21no—
257C2×C5—21no—
258C2×C5#188811yescharacteristic
259C2×C5#189411yescharacteristic
260C2×C5#191511yescharacteristic
261C23D5×C22⋊C411yescharacteristic
262Q8—201no—
263Q8—201no—
264Q8—201no—
265Q8—201no—
266Q8—402no—
267Q8—402no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—102no—
274C2×C4—102no—
275C2×C4—102no—
276C2×C4—102no—
277C2×C4—202no—
278C2×C4—204no—
279C2×C4—202no—
280C2×C4C4×D2011yescharacteristic
281C2×C4#402811yescharacteristic
282C2×C4#403011yescharacteristic
283C2×C4#403911yescharacteristic
284C2×C4#404011yescharacteristic
285C2×C4#404111yescharacteristic
286C2×C4#405711yescharacteristic
287C2×C4#406111yescharacteristic
288C2×C4#406111yescharacteristic
289C2×C4#406411yescharacteristic
290C8—42no—
291C8—81no—
292C8—202no—
293C8—401no—
294C5#940411yescharacteristic, complemented, Sylow
295C22—21no—
296C22—21no—
297C22#6495411yescharacteristic
298C22#6506011yescharacteristic
299C22#6509111yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—82no—
304C4—202no—
305C4—202no—
306C4—402no—
307C4#6506911yescharacteristic
308C4#6510511yescharacteristic
309C4#6511612yes—
310C4#6515711yescharacteristic
311C4#6517511yescharacteristic
312C2—21no—
313C2—21no—
314C2#1059955911yescharacteristic
315C2#1059967711yescharacteristic
316C2#1059983411yescharacteristic
subgroupG/H
centerC22#64954
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1303C2
socleC22×C5#386
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1303D5
hypocenterC5#9404
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
294. C5#9404semidirect

Maximal subgroups

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

subgroupindex
#106109952
#106054532
#106015732
#106013212
#106013012
C5×#13032
#105981112
#94045