Finite Group Databasebeta

← #11991053

Subgroups — #11991053

Order 1280.

998 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 998 conjugacy classes of subgroups — too many to draw. Only its 159 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×#547C211yesmaximal, characteristic
2#10602567C212yesmaximal, complemented
3#10602410C211yesmaximal, characteristic, complemented
4#10602394C211yesmaximal, characteristic, complemented
5#10602391C212yesmaximal, complemented
6C22×C5×#41C412yes—
7C5×#547—24no—
8C5×#547—24no—
9C2×C5×C4⋊Q8C2211yescharacteristic
10C2×C5×#123—22no—
11C2×C5×C22⋊Q8C412yes—
12C2×C5×#121—21no—
13C2×C4×C5×D4C2211yescharacteristic
14C2×C4×C5×D4C2211yescharacteristic
15C22×C5×C4⋊C4—21no—
16C2×#3965—21no—
17#65214C2212yes—
18#65213C2212yes—
19#64766—24no—
20D4⋊#168—24no—
21#64750—21no—
22#64745—22no—
23#8393—51nomaximal, Sylow
24C2×C5×#41—24no—
25C2×C5×#41—24no—
26C2×C5×#41—48no—
27C22×C5×Q8C2×C412yes—
28C22×C5×D4—22no—
29C22×C5×D4C2×C411yescharacteristic
30C22×C5×D4D411yescharacteristic
31C23×C4×C5—22no—
32C23×C4×C5—21no—
33C23×C4×C5C2×C412yes—
34C5×C4⋊Q8—22no—
35C5×C4⋊Q8D414yes—
36C5×#123—216no—
37C5×C22⋊Q8—24no—
38C5×C22⋊Q8—24no—
39C5×#121—28no—
40C4×C5×D4—22no—
41C4×C5×D4—22no—
42C4×C5×D4—22no—
43C4×C5×D4D414yes—
44C2×C5×C4⋊C4—28no—
45C2×C5×C4⋊C4—22no—
46C2×C5×C4⋊C4—21no—
47C2×C5×C4⋊C4—21no—
48C2×C5×C4⋊C4C2×C411yescharacteristic
49C2×C5×C4⋊C4D411yescharacteristic
50C2×C5×C22⋊C4—22no—
51C2×C5×C22⋊C4—21no—
52C2×C5×C22⋊C4D412yes—
53C2×C42×C5C2311yescharacteristic
54C2×#681—22no—
55#3965—42no—
56C22⋊#168—22no—
57C4⋊#168—22no—
58C4⋊#168—22no—
59C4⋊#168—22no—
60C4×#168—22no—
61C2×#547D511yescharacteristic
62#1800—51no—
63#1548—52no—
64#1486—52no—
65#1460—51no—
66C24×C5—21no—
67C24×C5C22⋊C412yes—
68C5×#41—416no—
69C5×#41—48no—
70C5×#41—48no—
71C2×C5×Q8—22no—
72C2×C5×Q8—44no—
73C2×C5×Q8C22⋊C414yes—
74C2×C5×D4—24no—
75C2×C5×D4—28no—
76C2×C5×D4—21no—
77C2×C5×D4—22no—
78C2×C5×D4—22no—
79C2×C5×D4—21no—
80C2×C5×D4—21no—
81C2×C5×D4—48no—
82C2×C5×D4C22⋊C412yes—
83C22×C4×C5—28no—
84C22×C4×C5—21no—
85C22×C4×C5—22no—
86C22×C4×C5—22no—
87C22×C4×C5—22no—
88C22×C4×C5—24no—
89C22×C4×C5—44no—
90C22×C4×C5—48no—
91C22×C4×C5—42no—
92C22×C4×C5—41no—
93C22×C4×C5—41no—
94C22×C4×C5C22⋊C412yes—
95C22×C4×C5C22×C411yescharacteristic
96C22×C4×C5C2×D411yescharacteristic
97C22×C4×C5C2×D411yescharacteristic
98C5×C4⋊C4—28no—
99C5×C4⋊C4—21no—
100C5×C4⋊C4—22no—
101C5×C4⋊C4—24no—
102C5×C4⋊C4—24no—
103C5×C4⋊C4C22⋊C412yes—
104C5×C22⋊C4—28no—
105C5×C22⋊C4—24no—
106C5×C22⋊C4—24no—
107C42×C5C2×D412yes—
108C42×C5C2×D412yes—
109#681—42no—
110#681—42no—
111C2×#168—42no—
112C2×#168—42no—
113C22×#41Dic512yes—
114#547—24no—
115#547—24no—
116C2×C4⋊Q8C2×D511yescharacteristic
117C2×#123—22no—
118C2×C22⋊Q8Dic512yes—
119C2×#121—21no—
120C2×C4×D4C2×D511yescharacteristic
121C2×C4×D4C2×D511yescharacteristic
122C22×C4⋊C4—21no—
123#431—52no—
124#423—52no—
125C2×#100—101no—
126#343—101no—
127#333—104no—
128D4⋊C8—104no—
129#323—102no—
130C23×C5—24no—
131C23×C5—22no—
132C23×C5—22no—
133C23×C5—22no—
134C23×C5—22no—
135C23×C5—42no—
136C23×C5—42no—
137C23×C5—42no—
138C23×C5—41no—
139C23×C5—41no—
140C23×C5C2×C22⋊C411yescharacteristic
141C5×Q8—44no—
142C5×Q8—44no—
143C5×D4—24no—
144C5×D4—22no—
145C5×D4—416no—
146C5×D4—42no—
147C5×D4—42no—
148C5×D4#10014yescomplemented
149C2×C4×C5—22no—
150C2×C4×C5—22no—
151C2×C4×C5—22no—
152C2×C4×C5—24no—
153C2×C4×C5—41no—
154C2×C4×C5—44no—
155C2×C4×C5—44no—
156C2×C4×C5—416no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—44no—
160C2×C4×C5—44no—
161C2×C4×C5—44no—
162C2×C4×C5—42no—
163C2×C4×C5C2×C22⋊C411yescharacteristic
164C2×C4×C5C2×C22⋊C411yescharacteristic
165C2×C4×C5#12012yes—
166C2×C4×C5#12012yes—
167C2×C4×C5#13512yes—
168C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C5#13711yescharacteristic
170#168—82no—
171#168—82no—
172C2×#41—24no—
173C2×#41—24no—
174C2×#41—48no—
175C22×Q8C2×Dic512yes—
176C22×D4—22no—
177C22×D4C2×Dic511yescharacteristic
178C22×D4C22⋊D511yescharacteristic
179C23×C4—22no—
180C23×C4—21no—
181C23×C4C2×Dic512yes—
182C2×M16—102no—
183C4⋊Q8—22no—
184C4⋊Q8C22⋊D514yes—
185#123—216no—
186C22⋊Q8—24no—
187C22⋊Q8—24no—
188#121—28no—
189C4×D4—22no—
190C4×D4—22no—
191C4×D4—22no—
192C4×D4C22⋊D514yes—
193C2×C4⋊C4—28no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4C2×Dic511yescharacteristic
198C2×C4⋊C4C22⋊D511yescharacteristic
199C2×C22⋊C4—22no—
200C2×C22⋊C4—21no—
201C2×C22⋊C4C22⋊D512yes—
202C2×C42C22×D511yescharacteristic
203C4⋊C8—102no—
204C4⋊C8—102no—
205C4⋊C8—102no—
206#100—202no—
207C22⋊C8—102no—
208C4×C8—102no—
209C22×C5—21no—
210C22×C5—21no—
211C22×C5—24no—
212C22×C5—44no—
213C22×C5—44no—
214C22×C5—42no—
215C22×C5—42no—
216C22×C5—42no—
217C22×C5—42no—
218C22×C5—42no—
219C22×C5—82no—
220C22×C5—82no—
221C22×C5#37911yescharacteristic
222C22×C5#41611yescharacteristic
223C22×C5#41711yescharacteristic
224C4×C5—22no—
225C4×C5—21no—
226C4×C5—42no—
227C4×C5—44no—
228C4×C5—42no—
229C4×C5C2×#10012yes—
230C4×C5#44912yes—
231C4×C5#45212yes—
232C24—21no—
233C24C22⋊Dic512yes—
234#41—416no—
235#41—48no—
236#41—48no—
237C2×Q8—22no—
238C2×Q8—44no—
239C2×Q8C22⋊Dic514yes—
240C2×D4—24no—
241C2×D4—28no—
242C2×D4—22no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—48no—
248C2×D4C22⋊Dic512yes—
249C22×C4—28no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—24no—
255C22×C4—44no—
256C22×C4—48no—
257C22×C4—42no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4C22⋊Dic512yes—
261C22×C4C22×Dic511yescharacteristic
262C22×C4C2×C22⋊D511yescharacteristic
263C22×C4C2×C22⋊D511yescharacteristic
264M16—202no—
265M16—202no—
266C2×C8—202no—
267C2×C8—202no—
268C4⋊C4—28no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4C22⋊Dic512yes—
274C22⋊C4—28no—
275C22⋊C4—24no—
276C22⋊C4—24no—
277C42C2×C22⋊D512yes—
278C42C2×C22⋊D512yes—
279C2×C5—21no—
280C2×C5—21no—
281C2×C5—44no—
282C2×C5—82no—
283C2×C5#178311yescharacteristic
284C2×C5#178811yescharacteristic
285C2×C5#179611yescharacteristic
286C23—24no—
287C23—22no—
288C23—22no—
289C23—22no—
290C23—22no—
291C23—42no—
292C23—42no—
293C23—42no—
294C23—41no—
295C23—41no—
296C23C2×C22⋊Dic511yescharacteristic
297Q8—44no—
298Q8—44no—
299D4—24no—
300D4—22no—
301D4—416no—
302D4—42no—
303D4—42no—
304D4#396514yescomplemented
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—24no—
309C2×C4—41no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4—416no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—42no—
319C2×C4#409511yescharacteristic
320C2×C4#409612yes—
321C2×C4#409711yescharacteristic
322C2×C4C2×C22⋊Dic511yescharacteristic
323C2×C4C2×C22⋊Dic511yescharacteristic
324C2×C4#409912yes—
325C2×C4#409912yes—
326C8—402no—
327C8—402no—
328C5#839311yescharacteristic, complemented, Sylow
329C22—21no—
330C22—21no—
331C22—24no—
332C22—44no—
333C22—44no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22—82no—
340C22—82no—
341C22#6552111yescharacteristic
342C22#6552211yescharacteristic
343C22#6553611yescharacteristic
344C4—21no—
345C4—22no—
346C4—42no—
347C4—44no—
348C4—42no—
349C4C2×#396512yes—
350C4#6552712yes—
351C4#6552812yes—
352C2—21no—
353C2—21no—
354C2—44no—
355C2—82no—
356C2#1060292211yescharacteristic
357C2#1060292811yescharacteristic
358C2#1060293711yescharacteristic
subgroupG/H
centerC22#65536
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
Fitting, prime radicalC2×C5×#547C2
socleC22×C5#379
cosocleC2×C42×C5C23
hypercenterC2×#547D5
hypocenterC5#8393
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
2. #10602567C2semidirect
3. #10602410C2semidirect
4. #10602394C2semidirect
5. #10602391C2semidirect
148. C5×D4#100semidirect
304. D4#3965semidirect
328. C5#8393semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#5472
#106025672
#106024102
#106023942
#106023912
#83935