Finite Group Databasebeta

← #11991073

Subgroups — #11991073

Order 1280.

802 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C2×C5×#555C211yesmaximal, characteristic
2#10602568C212yesmaximal, complemented
3#10602410C211yesmaximal, characteristic, complemented
4#10602394C211yesmaximal, characteristic, complemented
5#10602391C212yesmaximal, complemented
6C5×#555—24no—
7C5×#555—24no—
8C2×C5×C4⋊Q8C2211yescharacteristic
9C2×C5×#124—22no—
10C2×C5×#121—21no—
11C2×C5×#121C412yes—
12C2×C4×C5×D4C2211yescharacteristic
13C2×C4×C5×D4C2211yescharacteristic
14C2×C5×#117—21no—
15C2×C5×#117C412yes—
16C2×#3965—21no—
17#65214C2212yes—
18#65213C2212yes—
19#64767—24no—
20D4⋊#168—24no—
21#64750—21no—
22#64745—22no—
23#8397—51nomaximal, Sylow
24C22×C5×Q8—21no—
25C22×C5×D4—22no—
26C22×C5×D4C2×C411yescharacteristic
27C22×C5×D4D411yescharacteristic
28C23×C4×C5—21no—
29C23×C4×C5C2×C412yes—
30C5×C4⋊Q8—22no—
31C5×C4⋊Q8D414yes—
32C5×#124—216no—
33C5×#121—28no—
34C5×#121—24no—
35C5×#121—24no—
36C4×C5×D4—22no—
37C4×C5×D4—22no—
38C4×C5×D4—22no—
39C4×C5×D4D414yes—
40C5×#117—28no—
41C5×#117—24no—
42C5×#117—24no—
43C2×C5×C4⋊C4—21no—
44C2×C5×C4⋊C4C2×C411yescharacteristic
45C2×C5×C4⋊C4C2×C412yes—
46C2×C5×C4⋊C4D411yescharacteristic
47C2×C5×C22⋊C4—22no—
48C2×C5×C22⋊C4—22no—
49C2×C5×C22⋊C4—21no—
50C2×C5×C22⋊C4D412yes—
51C2×C42×C5—22no—
52C2×C42×C5C2311yescharacteristic
53C2×#681—22no—
54#3965—42no—
55C22⋊#168—22no—
56C4⋊#168—22no—
57C4⋊#168—22no—
58C4⋊#168—22no—
59C4×#168—22no—
60C2×#555D511yescharacteristic
61#1800—51no—
62#1549—52no—
63#1486—52no—
64#1460—51no—
65C24×C5—21no—
66C24×C5C22⋊C412yes—
67C2×C5×Q8—24no—
68C2×C5×Q8—82no—
69C2×C5×D4—28no—
70C2×C5×D4—21no—
71C2×C5×D4—22no—
72C2×C5×D4—22no—
73C2×C5×D4—21no—
74C2×C5×D4—21no—
75C2×C5×D4—42no—
76C2×C5×D4—84no—
77C2×C5×D4C22⋊C412yes—
78C22×C4×C5—21no—
79C22×C4×C5—22no—
80C22×C4×C5—22no—
81C22×C4×C5—22no—
82C22×C4×C5—24no—
83C22×C4×C5—44no—
84C22×C4×C5—42no—
85C22×C4×C5—41no—
86C22×C4×C5—41no—
87C22×C4×C5C22⋊C412yes—
88C22×C4×C5C22×C411yescharacteristic
89C22×C4×C5C2×D411yescharacteristic
90C22×C4×C5C2×D411yescharacteristic
91C5×C4⋊C4—21no—
92C5×C4⋊C4—22no—
93C5×C4⋊C4—24no—
94C5×C4⋊C4—22no—
95C5×C4⋊C4C22⋊C412yes—
96C5×C4⋊C4C22⋊C414yes—
97C5×C22⋊C4—28no—
98C5×C22⋊C4—28no—
99C5×C22⋊C4—24no—
100C5×C22⋊C4—24no—
101C42×C5—28no—
102C42×C5C2×D412yes—
103C42×C5C2×D412yes—
104#681—42no—
105#681—42no—
106C2×#168—42no—
107C2×#168—42no—
108#555—24no—
109#555—24no—
110C2×C4⋊Q8C2×D511yescharacteristic
111C2×#124—22no—
112C2×#121—21no—
113C2×#121Dic512yes—
114C2×C4×D4C2×D511yescharacteristic
115C2×C4×D4C2×D511yescharacteristic
116C2×#117—21no—
117C2×#117Dic512yes—
118#431—52no—
119#423—52no—
120C2×#100—101no—
121#343—101no—
122#332—104no—
123D4⋊C8—104no—
124#323—102no—
125C23×C5—22no—
126C23×C5—22no—
127C23×C5—22no—
128C23×C5—22no—
129C23×C5—42no—
130C23×C5—42no—
131C23×C5—42no—
132C23×C5—42no—
133C23×C5—41no—
134C23×C5—41no—
135C23×C5C2×C22⋊C411yescharacteristic
136C5×Q8—84no—
137C5×D4—24no—
138C5×D4—42no—
139C5×D4—42no—
140C5×D4—42no—
141C5×D4—88no—
142C2×C4×C5—22no—
143C2×C4×C5—22no—
144C2×C4×C5—22no—
145C2×C4×C5—24no—
146C2×C4×C5—41no—
147C2×C4×C5—44no—
148C2×C4×C5—44no—
149C2×C4×C5—41no—
150C2×C4×C5—41no—
151C2×C4×C5—44no—
152C2×C4×C5—44no—
153C2×C4×C5—44no—
154C2×C4×C5—42no—
155C2×C4×C5C2×C22⋊C411yescharacteristic
156C2×C4×C5C2×C22⋊C411yescharacteristic
157C2×C4×C5#12012yes—
158C2×C4×C5#12012yes—
159C2×C4×C5#13512yes—
160C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C5#13711yescharacteristic
162#168—82no—
163#168—82no—
164C22×Q8—21no—
165C22×D4—22no—
166C22×D4C2×Dic511yescharacteristic
167C22×D4C22⋊D511yescharacteristic
168C23×C4—21no—
169C23×C4C2×Dic512yes—
170C2×M16—102no—
171C4⋊Q8—22no—
172C4⋊Q8C22⋊D514yes—
173#124—216no—
174#121—28no—
175#121—24no—
176#121—24no—
177C4×D4—22no—
178C4×D4—22no—
179C4×D4—22no—
180C4×D4C22⋊D514yes—
181#117—28no—
182#117—24no—
183#117—24no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4C2×Dic511yescharacteristic
186C2×C4⋊C4C2×Dic512yes—
187C2×C4⋊C4C22⋊D511yescharacteristic
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—21no—
191C2×C22⋊C4C22⋊D512yes—
192C2×C42—22no—
193C2×C42C22×D511yescharacteristic
194C4⋊C8—102no—
195C4⋊C8—102no—
196C4⋊C8—102no—
197#100—202no—
198C22⋊C8—102no—
199C4×C8—102no—
200C22×C5—21no—
201C22×C5—21no—
202C22×C5—42no—
203C22×C5—42no—
204C22×C5—42no—
205C22×C5—42no—
206C22×C5—42no—
207C22×C5—42no—
208C22×C5—82no—
209C22×C5—82no—
210C22×C5—82no—
211C22×C5—82no—
212C22×C5#37911yescharacteristic
213C22×C5#41611yescharacteristic
214C22×C5#41711yescharacteristic
215C4×C5—22no—
216C4×C5—21no—
217C4×C5—44no—
218C4×C5—42no—
219C4×C5—42no—
220C4×C5#41312yes—
221C4×C5#44912yes—
222C4×C5#45212yes—
223C24—21no—
224C24C22⋊Dic512yes—
225C2×Q8—24no—
226C2×Q8—82no—
227C2×D4—28no—
228C2×D4—22no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4—22no—
232C2×D4—21no—
233C2×D4—42no—
234C2×D4—84no—
235C2×D4C22⋊Dic512yes—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—24no—
241C22×C4—44no—
242C22×C4—42no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4C22⋊Dic512yes—
246C22×C4C22×Dic511yescharacteristic
247C22×C4C2×C22⋊D511yescharacteristic
248C22×C4C2×C22⋊D511yescharacteristic
249M16—202no—
250M16—202no—
251C2×C8—202no—
252C2×C8—202no—
253C4⋊C4—21no—
254C4⋊C4—22no—
255C4⋊C4—24no—
256C4⋊C4—22no—
257C4⋊C4C22⋊Dic512yes—
258C4⋊C4C22⋊Dic514yes—
259C22⋊C4—28no—
260C22⋊C4—28no—
261C22⋊C4—24no—
262C22⋊C4—24no—
263C42—28no—
264C42C2×C22⋊D512yes—
265C42C2×C22⋊D512yes—
266C2×C5—21no—
267C2×C5—21no—
268C2×C5—82no—
269C2×C5—82no—
270C2×C5#178511yescharacteristic
271C2×C5#178811yescharacteristic
272C2×C5#179511yescharacteristic
273C23—22no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—42no—
278C23—42no—
279C23—42no—
280C23—42no—
281C23—41no—
282C23—41no—
283C23C2×C22⋊Dic511yescharacteristic
284Q8—84no—
285D4—24no—
286D4—42no—
287D4—42no—
288D4—42no—
289D4—88no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—24no—
294C2×C4—41no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—42no—
303C2×C4#409511yescharacteristic
304C2×C4#409612yes—
305C2×C4#409711yescharacteristic
306C2×C4C2×C22⋊Dic511yescharacteristic
307C2×C4C2×C22⋊Dic511yescharacteristic
308C2×C4#409912yes—
309C2×C4#409912yes—
310C8—402no—
311C8—402no—
312C5#839711yescharacteristic, complemented, Sylow
313C22—21no—
314C22—21no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22—42no—
320C22—42no—
321C22—82no—
322C22—82no—
323C22—82no—
324C22—82no—
325C22#6552111yescharacteristic
326C22#6552211yescharacteristic
327C22#6553611yescharacteristic
328C4—21no—
329C4—22no—
330C4—42no—
331C4—42no—
332C4—44no—
333C4#6552612yes—
334C4#6552712yes—
335C4#6552812yes—
336C2—21no—
337C2—21no—
338C2—82no—
339C2—82no—
340C2#1060292811yescharacteristic
341C2#1060293011yescharacteristic
342C2#1060293411yescharacteristic
subgroupG/H
centerC22#65536
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
Fitting, prime radicalC2×C5×#555C2
socleC22×C5#379
cosocleC2×C42×C5C23
hypercenterC2×#555D5
hypocenterC5#8397
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
2. #10602568C2semidirect
3. #10602410C2semidirect
4. #10602394C2semidirect
5. #10602391C2semidirect
312. C5#8397semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#5552
#106025682
#106024102
#106023942
#106023912
#83975