Finite Group Databasebeta

← #12009831

Subgroups — #12009831

Order 1280.

462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C5×#2583C211yesmaximal, characteristic
2C2×#64750C211yesmaximal, characteristic
3#10602345C211yesmaximal, characteristic
4#10598141C212yesmaximal, complemented
5#10598139C212yesmaximal, complemented
6C2×C5×C22⋊Q8C411yescharacteristic
7C22×C5×C4⋊C4C2211yescharacteristic
8C22×#681—21no—
9C5×#398C411yescharacteristic
10C5×#398C2211yescharacteristic
11C5×#395C411yescharacteristic
12C5×#395C2211yescharacteristic
13C5×#389—21no—
14C5×#389—21no—
15C5×#385—21no—
16C5×#385—21no—
17C4×C5×C22⋊C4C411yescharacteristic
18#65496—21no—
19#64750—21no—
20#64750C2212yes—
21#64748—21no—
22#64748C2212yes—
23#11768—51nomaximal, Sylow
24C22×C5×Q8C2×C411yescharacteristic
25C23×C4×C5C2×C411yescharacteristic
26C23×C4×C5D411yescharacteristic
27C23×C4×C5D411yescharacteristic
28C5×C22⋊Q8—41no—
29C5×C22⋊Q8—41no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—41no—
36C2×C5×C4⋊C4—41no—
37C2×C5×C4⋊C4C2×C411yescharacteristic
38C2×C5×C4⋊C4C2×C411yescharacteristic
39C2×C5×C4⋊C4D411yescharacteristic
40C2×C5×C4⋊C4D411yescharacteristic
41C2×C5×C4⋊C4C2311yescharacteristic
42C2×C5×C22⋊C4—21no—
43C2×C5×C22⋊C4—21no—
44C2×C42×C5—21no—
45C2×#681—24no—
46C2×#681—22no—
47C2×#681—41no—
48C2×#681—42no—
49C2×#681—41no—
50C22×#168—41no—
51C5×#95—21no—
52C5×#95—21no—
53C5×#95—21no—
54C5×#95—21no—
55C5×#95C2×C411yescharacteristic
56C5×#95C2×C411yescharacteristic
57C22⋊#168—22no—
58C22⋊#168—41no—
59#2583D511yescharacteristic
60C2×#343—51no—
61#1463—51no—
62#1354—52no—
63#1346—52no—
64C24×C5C22⋊C411yescharacteristic
65C2×C5×Q8—41no—
66C2×C5×Q8—81no—
67C22×C4×C5—21no—
68C22×C4×C5—21no—
69C22×C4×C5—22no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—21no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5—21no—
76C22×C4×C5—21no—
77C22×C4×C5—21no—
78C22×C4×C5—21no—
79C22×C4×C5—21no—
80C22×C4×C5—81no—
81C22×C4×C5—81no—
82C22×C4×C5C22⋊C411yescharacteristic
83C22×C4×C5C22⋊C411yescharacteristic
84C22×C4×C5C22⋊C411yescharacteristic
85C22×C4×C5C22×C411yescharacteristic
86C22×C4×C5C2×D411yescharacteristic
87C22×C4×C5C2×D411yescharacteristic
88C5×C4⋊C4—41no—
89C5×C4⋊C4—41no—
90C5×C4⋊C4—41no—
91C5×C4⋊C4—41no—
92C5×C4⋊C4—41no—
93C5×C4⋊C4—42no—
94C5×C4⋊C4—42no—
95C5×C4⋊C4—41no—
96C5×C4⋊C4—41no—
97C5×C4⋊C4—81no—
98C5×C4⋊C4—81no—
99C5×C22⋊C4—24no—
100C5×C22⋊C4—41no—
101C5×C22⋊C4—41no—
102C42×C5—81no—
103#681—24no—
104#681—44no—
105#681—42no—
106#681—82no—
107C2×#168—44no—
108C2×#168—42no—
109C2×#168—42no—
110C22×M16—101no—
111C2×C22⋊Q8Dic511yescharacteristic
112C22×C4⋊C4C2×D511yescharacteristic
113#407—101no—
114#398Dic511yescharacteristic
115#398C2×D511yescharacteristic
116#395Dic511yescharacteristic
117#395C2×D511yescharacteristic
118#389—21no—
119#389—21no—
120#385—21no—
121#385—21no—
122C4×C22⋊C4Dic511yescharacteristic
123#343—52no—
124#343—101no—
125#324—52no—
126#324—101no—
127C23×C5—22no—
128C23×C5—21no—
129C23×C5—21no—
130C23×C5—41no—
131C23×C5#9911yescharacteristic
132C23×C5#9911yescharacteristic
133C23×C5C2×C22⋊C411yescharacteristic
134C5×Q8—82no—
135C2×C4×C5—22no—
136C2×C4×C5—22no—
137C2×C4×C5—22no—
138C2×C4×C5—22no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—22no—
144C2×C4×C5—22no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—42no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5—41no—
153C2×C4×C5—41no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5—41no—
164C2×C4×C5—81no—
165C2×C4×C5—81no—
166C2×C4×C5—81no—
167C2×C4×C5#10412yes—
168C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C5#13711yescharacteristic
170#168—44no—
171#168—82no—
172C22×Q8C2×Dic511yescharacteristic
173C23×C4C2×Dic511yescharacteristic
174C23×C4C22⋊D511yescharacteristic
175C23×C4C22⋊D511yescharacteristic
176C2×M16—104no—
177C2×M16—102no—
178C2×M16—201no—
179C2×M16—202no—
180C2×M16—201no—
181C22×C8—201no—
182C22⋊Q8—41no—
183C22⋊Q8—41no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4C2×Dic511yescharacteristic
192C2×C4⋊C4C2×Dic511yescharacteristic
193C2×C4⋊C4C22⋊D511yescharacteristic
194C2×C4⋊C4C22⋊D511yescharacteristic
195C2×C4⋊C4C22×D511yescharacteristic
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C42—21no—
199C22⋊C8—102no—
200C22⋊C8—201no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95C2×Dic511yescharacteristic
206#95C2×Dic511yescharacteristic
207C22×C5—21no—
208C22×C5—21no—
209C22×C5—21no—
210C22×C5—21no—
211C22×C5—21no—
212C22×C5—21no—
213C22×C5—21no—
214C22×C5—42no—
215C22×C5—42no—
216C22×C5#35612yes—
217C22×C5C2×#9911yescharacteristic
218C22×C5#41711yescharacteristic
219C22×C5C2×#10411yescharacteristic
220C4×C5—21no—
221C4×C5—22no—
222C4×C5—21no—
223C4×C5—42no—
224C4×C5—42no—
225C4×C5—41no—
226C4×C5—41no—
227C4×C5—41no—
228C4×C5—41no—
229C4×C5—81no—
230C4×C5—81no—
231C24C22⋊Dic511yescharacteristic
232C2×Q8—41no—
233C2×Q8—81no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—81no—
248C22×C4—81no—
249C22×C4C22⋊Dic511yescharacteristic
250C22×C4C22⋊Dic511yescharacteristic
251C22×C4C22⋊Dic511yescharacteristic
252C22×C4C22×Dic511yescharacteristic
253C22×C4C2×C22⋊D511yescharacteristic
254C22×C4C2×C22⋊D511yescharacteristic
255M16—104no—
256M16—204no—
257M16—202no—
258M16—402no—
259C2×C8—204no—
260C2×C8—202no—
261C2×C8—202no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—41no—
269C4⋊C4—42no—
270C4⋊C4—41no—
271C4⋊C4—81no—
272C4⋊C4—81no—
273C22⋊C4—24no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C42—81no—
277C2×C5—21no—
278C2×C5—21no—
279C2×C5—22no—
280C2×C5—41no—
281C2×C5#150411yescharacteristic
282C2×C5#212111yescharacteristic
283C2×C5C2×#35611yescharacteristic
284C23—22no—
285C23—21no—
286C23—21no—
287C23—41no—
288C23#396611yescharacteristic
289C23#396611yescharacteristic
290C23C2×C22⋊Dic511yescharacteristic
291Q8—82no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4#396912yes—
325C2×C4#409511yescharacteristic
326C2×C4#409711yescharacteristic
327C8—204no—
328C8—402no—
329C5#1176811yescharacteristic, complemented, Sylow
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—42no—
339C22#6476812yes—
340C22C2×#396611yescharacteristic
341C22#6552111yescharacteristic
342C22C2×#396911yescharacteristic
343C4—21no—
344C4—21no—
345C4—22no—
346C4—42no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—81no—
353C4—81no—
354C2—21no—
355C2—21no—
356C2—22no—
357C2—41no—
358C2#1060250111yescharacteristic
359C2C2×#6476811yescharacteristic
360C2#1060264011yescharacteristic
subgroupG/H
centerC22C2×#3966
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#2583C2
socleC22×C5C2×#99
prime radicalC24×C5C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#2583D5
hypocenterC5#11768
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2583

Complements

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

NH ≅ G/Ntype
4. #10598141C2semidirect
5. #10598139C2semidirect
329. C5#11768semidirect

Maximal subgroups

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

subgroupindex
C5×#25832
C2×#647502
#106023452
#105981412
#105981392
#117685