Finite Group Databasebeta

← #12003803

Subgroups — #12003803

Order 1280.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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#10605949C211yesmaximal, characteristic
2#10600609C211yesmaximal, characteristic
3#10600608C211yesmaximal, characteristic
4#10600341C211yesmaximal, characteristic
5C5×#1295C211yesmaximal, characteristic
6#10598150C211yesmaximal, characteristic
7#10598150C211yesmaximal, characteristic
8C2×C5×#97C2211yescharacteristic
9C2×C5×#97C2211yescharacteristic
10C5×#382C2211yescharacteristic
11C2×#3950—21no—
12C2×#3949—21no—
13#65275—21no—
14#65268—21no—
15#65225C2211yescharacteristic
16#65225C2211yescharacteristic
17#65224C2211yescharacteristic
18C2×#3935C2211yescharacteristic
19#64949—21no—
20#64949—21no—
21#64945—21no—
22#64945—21no—
23#64771—21no—
24#64771—21no—
25#64749—21no—
26#64749—21no—
27#10584—51nomaximal, Sylow
28C22×Dic10—21no—
29C22×C5×C8—21no—
30C22×C5×C8—21no—
31C2×C5×C4⋊C4D411yescharacteristic
32C2×C5×C4⋊C4D411yescharacteristic
33C2×C42×C5C2311yescharacteristic
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—21no—
38C2×C4⋊Dic5D411yescharacteristic
39C2×C4⋊Dic5D411yescharacteristic
40C2×C4⋊Dic5D411yescharacteristic
41C2×C4⋊Dic5D411yescharacteristic
42C2×#683—21no—
43C2×#683—21no—
44C22×#168—21no—
45C5×#97—21no—
46C5×#97—21no—
47C5×#97Q812yescomplemented
48C5×#97Q812yescomplemented
49C5×#95—21no—
50C5×#95—21no—
51#3963—21no—
52#3963—21no—
53#3963—21no—
54#3963—21no—
55#3963—21no—
56#3963—21no—
57#3963—21no—
58#3963—21no—
59#3950—42no—
60#3949—42no—
61#3935—21no—
62#3935Q812yescomplemented
63#2844—51no—
64#1847—51no—
65#1836—51no—
66#1836—51no—
67#1295—51no—
68#1295—51no—
69#1295D511yescharacteristic
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5C2×D411yescharacteristic
73C22×C4×C5C2×D411yescharacteristic
74C22×C4×C5C2×D411yescharacteristic
75C22×Dic5—21no—
76C22×Dic5—21no—
77C22×Dic5—21no—
78C22×Dic5—21no—
79C22×Dic5—41no—
80C2×Dic10—81no—
81C2×Dic10—81no—
82C2×Dic10—81no—
83C2×C5×C8—22no—
84C2×C5×C8—22no—
85C2×C5×C8—22no—
86C2×C5×C8—22no—
87C2×C5×C8—41no—
88C2×C5×C8—41no—
89C5×C4⋊C4—41no—
90C5×C4⋊C4—41no—
91C42×C5C2×Q811yescharacteristic
92C42×C5C2×Q811yescharacteristic
93C42×C5C2×Q811yescharacteristic
94C42×C5#4111yescharacteristic
95C4⋊Dic5—41no—
96C4⋊Dic5—41no—
97C4⋊Dic5—41no—
98C4⋊Dic5—41no—
99C4⋊Dic5—41no—
100C4⋊Dic5—41no—
101C4⋊Dic5—42no—
102C4⋊Dic5—42no—
103C4⋊Dic5—81no—
104#683—81no—
105#683—81no—
106C2×#168—22no—
107C2×#168—41no—
108C2×#168—41no—
109C2×#107—101no—
110C2×#106—101no—
111C2×#97—51no—
112C2×#97C2×D511yescharacteristic
113C2×#97C2×D511yescharacteristic
114#400—101no—
115#400—101no—
116#400—101no—
117#395—101no—
118#395—101no—
119#395—101no—
120#384—51no—
121#382—51no—
122#382—51no—
123#382C2×D511yescharacteristic
124#340—101no—
125#340—101no—
126#340—101no—
127#340—101no—
128C23×C5#12011yescharacteristic
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—41no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5—41no—
139C2×C4×C5—41no—
140C2×C4×C5—41no—
141C2×C4×C5C22⋊Q811yescharacteristic
142C2×C4×C5C22⋊Q811yescharacteristic
143C2×C4×C5C22⋊Q811yescharacteristic
144C2×C4×C5C4⋊Q811yescharacteristic
145C2×C4×C5C4⋊Q811yescharacteristic
146C2×C4×C5C4⋊Q811yescharacteristic
147C2×Dic5—41no—
148C2×Dic5—41no—
149C2×Dic5—41no—
150C2×Dic5—41no—
151C2×Dic5—41no—
152C2×Dic5—41no—
153C2×Dic5—41no—
154C2×Dic5—41no—
155C2×Dic5—41no—
156C2×Dic5—41no—
157C2×Dic5—41no—
158C2×Dic5—41no—
159C2×Dic5—81no—
160C2×Dic5—81no—
161C2×Dic5—81no—
162Dic10—84no—
163C5×C8—24no—
164C5×C8—42no—
165#168—42no—
166C22×Q8—101no—
167C22×C8—21no—
168C22×C8—21no—
169C22×C8—101no—
170C2×C4⋊C4—51no—
171C2×C4⋊C4—51no—
172C2×C4⋊C4—51no—
173C2×C4⋊C4—51no—
174C2×C4⋊C4—101no—
175C2×C4⋊C4—101no—
176C2×C4⋊C4—101no—
177C2×C4⋊C4—101no—
178C2×C4⋊C4—101no—
179C2×C4⋊C4—101no—
180C2×C4⋊C4D2011yescharacteristic
181C2×C4⋊C4D2011yescharacteristic
182C2×C42C22×D511yescharacteristic
183#107—202no—
184#106—202no—
185#97—21no—
186#97—21no—
187#97—52no—
188#97—101no—
189#97Dic1012yescomplemented
190#97Dic1012yescomplemented
191#95—21no—
192#95—21no—
193#95—101no—
194#95—101no—
195#95—101no—
196#95—101no—
197#95—101no—
198#95—101no—
199#95—101no—
200#95—101no—
201C22×C5#39511yescharacteristic
202C22×C5#45311yescharacteristic
203C22×C5#45411yescharacteristic
204C22×C5#45411yescharacteristic
205C22×C5#45511yescharacteristic
206C22×C5#45511yescharacteristic
207C22×C5#45611yescharacteristic
208C4×C5—21no—
209C4×C5—21no—
210C4×C5—21no—
211C4×C5—21no—
212C4×C5—21no—
213C4×C5—21no—
214C4×C5—81no—
215C4×C5—81no—
216Dic5—81no—
217Dic5—81no—
218Dic5—81no—
219Dic5—81no—
220Dic5—161no—
221C2×Q8—401no—
222C2×Q8—401no—
223C2×Q8—401no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—101no—
227C22×C4—101no—
228C22×C4—101no—
229C22×C4—101no—
230C22×C4—201no—
231C22×C4C2×D2011yescharacteristic
232C22×C4D4×D511yescharacteristic
233C22×C4D4×D511yescharacteristic
234C2×C8—22no—
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—22no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—102no—
241C2×C8—201no—
242C2×C8—201no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—201no—
246C4⋊C4—201no—
247C4⋊C4—201no—
248C4⋊C4—201no—
249C4⋊C4—201no—
250C4⋊C4—201no—
251C4⋊C4—202no—
252C4⋊C4—202no—
253C4⋊C4—401no—
254C4⋊C4—401no—
255C4⋊C4—401no—
256C42C2×Dic1011yescharacteristic
257C42C2×Dic1011yescharacteristic
258C42#71111yescharacteristic
259C42Q8×D511yescharacteristic
260C2×C5#165711yescharacteristic
261C2×C5#165911yescharacteristic
262C2×C5#166411yescharacteristic
263C2×C5#166411yescharacteristic
264C2×C5#206011yescharacteristic
265C2×C5#206111yescharacteristic
266C2×C5#206111yescharacteristic
267C23#402811yescharacteristic
268Q8—404no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—201no—
282C2×C4—201no—
283C2×C4—201no—
284C2×C4—201no—
285C2×C4—201no—
286C2×C4—201no—
287C2×C4—201no—
288C2×C4—201no—
289C2×C4—201no—
290C2×C4—201no—
291C2×C4—201no—
292C2×C4—201no—
293C2×C4—401no—
294C2×C4—401no—
295C2×C4—401no—
296C2×C4#401511yescharacteristic
297C2×C4#402411yescharacteristic
298C2×C4#402411yescharacteristic
299C2×C4#403411yescharacteristic
300C2×C4#403411yescharacteristic
301C2×C4#404311yescharacteristic
302C8—24no—
303C8—42no—
304C8—202no—
305C5#1058411yescharacteristic, complemented, Sylow
306C22#6494511yescharacteristic
307C22#6503511yescharacteristic
308C22#6504211yescharacteristic
309C22#6511111yescharacteristic
310C22#6511411yescharacteristic
311C22#6511511yescharacteristic
312C22#6511611yescharacteristic
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—81no—
320C4—81no—
321C4—401no—
322C4—401no—
323C4—401no—
324C4—401no—
325C4—801no—
326C2#1059914511yescharacteristic
327C2#1059915211yescharacteristic
328C2#1059916411yescharacteristic
329C2#1059917211yescharacteristic
330C2#1059952811yescharacteristic
331C2#1059952911yescharacteristic
332C2#1059977211yescharacteristic
subgroupG/H
centerC23#4028
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1295C2
socle, prime radicalC23×C5#120
hypercenter#1295D5
hypocenterC5#10584
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
47. C5×#97Q8semidirect
48. C5×#97Q8semidirect
62. #3935Q8semidirect
189. #97Dic10semidirect
190. #97Dic10semidirect
305. C5#10584semidirect

Maximal subgroups

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

subgroupindex
#106059492
#106006092
#106006082
#106003412
C5×#12952
#105981502
#105845