Finite Group Databasebeta

← #11996965

Subgroups — #11996965

Order 1280.

486 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 107 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×#2545C211yesmaximal, characteristic
2#10614167C211yesmaximal, characteristic, complemented
3#10602512C212yesmaximal
4#10602418C211yesmaximal, characteristic, complemented
5#10598112C212yesmaximal, complemented
6C2×C5×C4⋊Q8C411yescharacteristic
7C2×C5×#124C411yescharacteristic
8C2×C5×#124C2211yescharacteristic
9C2×C4×C5×Q8C2211yescharacteristic
10C5×#396—21no—
11C5×#396—21no—
12C5×#391C411yescharacteristic
13C5×#390C411yescharacteristic
14C5×#388—21no—
15C5×#388—21no—
16C4×C5×C4⋊C4C2211yescharacteristic
17#65313—24no—
18#65215—21no—
19#65215C2212yes—
20#65215C2212yes—
21#65214—21no—
22#64760—24no—
23#64748—21no—
24#64748—21no—
25#9448—51nomaximal, Sylow
26C22×C5×Q8C2×C411yescharacteristic
27C22×C5×Q8C2×C411yescharacteristic
28C22×C5×D4C2×C411yescharacteristic
29C5×C4⋊Q8—42no—
30C5×#124—22no—
31C5×#124—22no—
32C5×#124—42no—
33C4×C5×Q8—22no—
34C4×C5×Q8—22no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—21no—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4C2×C411yescharacteristic
39C2×C5×C4⋊C4D411yescharacteristic
40C2×C5×C4⋊C4D411yescharacteristic
41C2×C5×C22⋊C4—21no—
42C2×C5×C22⋊C4—21no—
43C2×C5×C22⋊C4—21no—
44C2×C5×C22⋊C4—21no—
45C2×C5×C22⋊C4—21no—
46C2×C5×C22⋊C4—21no—
47C2×C42×C5C2×C411yescharacteristic
48C2×C42×C5C2×C411yescharacteristic
49C2×C42×C5D411yescharacteristic
50C2×C42×C5D411yescharacteristic
51C2×C42×C5C2311yescharacteristic
52C5×#95—21no—
53C5×#95—21no—
54C5×#95—21no—
55C22⋊#168—22no—
56C22⋊#168—22no—
57C4⋊#168—22no—
58C4⋊#168—22no—
59C4⋊#168—22no—
60C4⋊#168—22no—
61#3935—22no—
62#3935—22no—
63#3935D414yes—
64C4×#168—22no—
65#2983—51no—
66#2545D511yescharacteristic
67#1533—52no—
68#1467—51no—
69#1285—52no—
70C24×C5—21no—
71C2×C5×Q8—22no—
72C2×C5×Q8—22no—
73C2×C5×Q8—22no—
74C2×C5×Q8—41no—
75C2×C5×Q8—41no—
76C2×C5×Q8—41no—
77C2×C5×D4—22no—
78C2×C5×D4—41no—
79C2×C5×D4—41no—
80C22×C4×C5—21no—
81C22×C4×C5—21no—
82C22×C4×C5—21no—
83C22×C4×C5C22⋊C411yescharacteristic
84C22×C4×C5C22⋊C411yescharacteristic
85C22×C4×C5C22⋊C411yescharacteristic
86C22×C4×C5C22⋊C411yescharacteristic
87C22×C4×C5C22×C411yescharacteristic
88C22×C4×C5C2×D411yescharacteristic
89C22×C4×C5C2×D411yescharacteristic
90C5×C4⋊C4—22no—
91C5×C4⋊C4—22no—
92C5×C4⋊C4—22no—
93C5×C4⋊C4—42no—
94C5×C4⋊C4—42no—
95C5×C4⋊C4—42no—
96C5×C22⋊C4—42no—
97C5×C22⋊C4—42no—
98C5×C22⋊C4—42no—
99C5×C22⋊C4—42no—
100C5×C22⋊C4—41no—
101C5×C22⋊C4—42no—
102C5×C22⋊C4—41no—
103C42×C5—21no—
104C42×C5—21no—
105C42×C5—21no—
106C42×C5—21no—
107C42×C5—41no—
108C42×C5—41no—
109C42×C5C2×D412yes—
110C42×C5#4112yes—
111C2×#168—24no—
112C2×#168—42no—
113C2×C4⋊Q8Dic511yescharacteristic
114C2×#124Dic511yescharacteristic
115C2×#124C2×D511yescharacteristic
116C2×C4×Q8C2×D511yescharacteristic
117#446—104no—
118#432—52no—
119#432—52no—
120#432—101no—
121#431—101no—
122#396—21no—
123#396—21no—
124#391Dic511yescharacteristic
125#390Dic511yescharacteristic
126#388—21no—
127#388—21no—
128C4×C4⋊C4C2×D511yescharacteristic
129#329—104no—
130#324—101no—
131#324—101no—
132C23×C5—41no—
133C23×C5—41no—
134C23×C5—41no—
135C23×C5—41no—
136C23×C5—41no—
137C23×C5—41no—
138C23×C5—41no—
139C23×C5C2×C22⋊C411yescharacteristic
140C5×Q8—44no—
141C5×Q8—82no—
142C5×D4—82no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—22no—
148C2×C4×C5—21no—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
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—41no—
165C2×C4×C5#10012yes—
166C2×C4×C5C4×D412yes—
167C2×C4×C5#12011yescharacteristic
168C2×C4×C5#12112yes—
169C2×C4×C5#12311yescharacteristic
170#168—44no—
171#168—82no—
172C22×Q8C2×Dic511yescharacteristic
173C22×Q8C2×Dic511yescharacteristic
174C22×D4C2×Dic511yescharacteristic
175C4⋊Q8—42no—
176#124—22no—
177#124—22no—
178#124—42no—
179C4×Q8—22no—
180C4×Q8—22no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4C2×Dic511yescharacteristic
185C2×C4⋊C4C22⋊D511yescharacteristic
186C2×C4⋊C4C22⋊D511yescharacteristic
187C2×C22⋊C4—21no—
188C2×C22⋊C4—21no—
189C2×C22⋊C4—21no—
190C2×C22⋊C4—21no—
191C2×C22⋊C4—21no—
192C2×C22⋊C4—21no—
193C2×C42C2×Dic511yescharacteristic
194C2×C42C2×Dic511yescharacteristic
195C2×C42C22⋊D511yescharacteristic
196C2×C42C22⋊D511yescharacteristic
197C2×C42C22×D511yescharacteristic
198C4⋊C8—102no—
199C4⋊C8—102no—
200C4⋊C8—102no—
201C4⋊C8—102no—
202C22⋊C8—102no—
203C22⋊C8—102no—
204#97—54no—
205#97—102no—
206#97—102no—
207C4×C8—102no—
208#95—21no—
209#95—21no—
210#95—21no—
211C22×C5—21no—
212C22×C5—21no—
213C22×C5—81no—
214C22×C5—81no—
215C22×C5—81no—
216C22×C5—81no—
217C22×C5—81no—
218C22×C5—81no—
219C22×C5—81no—
220C22×C5#38611yescharacteristic
221C22×C5C2×#10011yescharacteristic
222C22×C5#41311yescharacteristic
223C4×C5—22no—
224C4×C5—22no—
225C4×C5—22no—
226C4×C5—21no—
227C4×C5—21no—
228C4×C5—42no—
229C4×C5—41no—
230C4×C5—41no—
231C4×C5—41no—
232C4×C5—81no—
233C4×C5—81no—
234C24—21no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×D4—22no—
242C2×D4—41no—
243C2×D4—41no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4C22⋊Dic511yescharacteristic
248C22×C4C22⋊Dic511yescharacteristic
249C22×C4C22⋊Dic511yescharacteristic
250C22×C4C22⋊Dic511yescharacteristic
251C22×C4C22×Dic511yescharacteristic
252C22×C4C2×C22⋊D511yescharacteristic
253C22×C4C2×C22⋊D511yescharacteristic
254C2×C8—104no—
255C2×C8—202no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—42no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—41no—
274C42—41no—
275C42D4×D512yes—
276C42#71112yes—
277C2×C5—21no—
278C2×C5—21no—
279C2×C5—161no—
280C2×C5#188411yescharacteristic
281C2×C5#190011yescharacteristic
282C2×C5#191211yescharacteristic
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23C2×C22⋊Dic511yescharacteristic
291Q8—44no—
292Q8—82no—
293D4—82no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4#396512yes—
317C2×C4D4×Dic512yes—
318C2×C4#408111yescharacteristic
319C2×C4#408311yescharacteristic
320C2×C4#408512yes—
321C8—204no—
322C8—402no—
323C5#944811yescharacteristic, complemented, Sylow
324C22—21no—
325C22—21no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22C2×#396511yescharacteristic
334C22#6550911yescharacteristic
335C22#6552611yescharacteristic
336C4—22no—
337C4—21no—
338C4—21no—
339C4—22no—
340C4—22no—
341C4—42no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—81no—
346C4—81no—
347C2—21no—
348C2—21no—
349C2—161no—
350C2#1060247611yescharacteristic
351C2#1060261011yescharacteristic
352C2#1060265711yescharacteristic
subgroupG/H
centerC22#65509
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2545C2
socleC22×C5#386
prime radicalC22×C5×D4C2×C4
cosocleC2×C42×C5C23
hypercenter#2545D5
hypocenterC5#9448
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2545

Complements

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

NH ≅ G/Ntype
2. #10614167C2semidirect
4. #10602418C2semidirect
5. #10598112C2semidirect
323. C5#9448semidirect

Maximal subgroups

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

subgroupindex
C5×#25452
#106141672
#106025122
#106024182
#105981122
#94485