Finite Group Databasebeta

← #12003714

Subgroups — #12003714

Order 1280.

560 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 121 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#10605092C211yesmaximal, characteristic
2#10600720C212yesmaximal
3#10600208C211yesmaximal, characteristic
4C5×#1280C211yesmaximal, characteristic
5#10598166C212yesmaximal
6C22×C4⋊Dic5C2211yescharacteristic
7C2×#4070—21no—
8C2×C5×C22⋊C8C2212yes—
9C2×C5×#95C2211yescharacteristic
10#65501—21no—
11#65501C2212yes—
12C2×#3963—21no—
13C2×#3963—21no—
14C2×#3963C2211yescharacteristic
15C2×#3950—22no—
16#64950—22no—
17#64945—22no—
18#64771—22no—
19#10569—51nomaximal, Sylow
20C23×C4×C5D411yescharacteristic
21C23×C4×C5D411yescharacteristic
22C23×C4×C5C2311yescharacteristic
23C23×Dic5—21no—
24C23×Dic5—21no—
25C22×Dic10—21no—
26C22×C5×C8—22no—
27C2×C22⋊Dic5—22no—
28C2×C4⋊Dic5—22no—
29C2×C4⋊Dic5—21no—
30C2×C4⋊Dic5—21no—
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5—42no—
33C2×C4⋊Dic5D412yes—
34C2×C4⋊Dic5D412yes—
35#4070—42no—
36#4070—42no—
37C2×#683—22no—
38C5×C22⋊C8—22no—
39C5×C22⋊C8Q814yescomplemented
40C5×#95—22no—
41#3963—22no—
42#3963—22no—
43#3963—21no—
44#3963—42no—
45#3963—42no—
46#3963Q812yescomplemented
47#3950—44no—
48#2659—51no—
49#1852—52no—
50#1442—51no—
51#1294—52no—
52#1280D511yescharacteristic
53C24×C5C2×D411yescharacteristic
54C22×C4×C5—21no—
55C22×C4×C5—21no—
56C22×C4×C5—21no—
57C22×C4×C5—21no—
58C22×C4×C5—41no—
59C22×C4×C5—41no—
60C22×C4×C5—41no—
61C22×C4×C5—41no—
62C22×C4×C5—41no—
63C22×C4×C5—41no—
64C22×C4×C5D812yes—
65C22×C4×C5Q1612yes—
66C22×C4×C5C2×D412yes—
67C22×C4×C5C2×Q812yes—
68C22×C4×C5C2×Q811yescharacteristic
69C22×C4×C5#4111yescharacteristic
70C22×Dic5—22no—
71C22×Dic5—22no—
72C22×Dic5—22no—
73C22×Dic5—22no—
74C22×Dic5—41no—
75C22×Dic5—41no—
76C22×Dic5—41no—
77C22×Dic5—41no—
78C22×Dic5—41no—
79C22×Dic5—41no—
80C22×Dic5—41no—
81C22×Dic5—41no—
82C22×Dic5—41no—
83C22×Dic5—41no—
84C22×Dic5—41no—
85C22×Dic5—41no—
86C2×Dic10—42no—
87C2×Dic10—81no—
88C2×Dic10—81no—
89C2×C5×C8—24no—
90C2×C5×C8—42no—
91C2×C5×C8—42no—
92C22⋊Dic5—42no—
93C22⋊Dic5—42no—
94C4⋊Dic5—24no—
95C4⋊Dic5—42no—
96C4⋊Dic5—42no—
97C4⋊Dic5—42no—
98C4⋊Dic5—42no—
99C4⋊Dic5—81no—
100C4⋊Dic5—81no—
101#683—44no—
102C2×C22⋊Q8—101no—
103C22×C4⋊C4—51no—
104C2×#107—102no—
105C2×C22⋊C8C2×D512yes—
106#398—102no—
107#395—102no—
108#380—52no—
109#380—101no—
110C2×#95—51no—
111C2×#95—101no—
112C2×#95—101no—
113C2×#95C2×D511yescharacteristic
114#340—102no—
115C23×C5—21no—
116C23×C5—21no—
117C23×C5—21no—
118C23×C5—21no—
119C23×C5#12011yescharacteristic
120C23×C5C22⋊Q811yescharacteristic
121C23×C5C4⋊Q811yescharacteristic
122C23×C5C2×D811yescharacteristic
123C23×C5C2×Q1611yescharacteristic
124C23×C5AGL(1,ℤ/8)11yescharacteristic
125C23×C5#13711yescharacteristic
126C2×C4×C5—22no—
127C2×C4×C5—22no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—42no—
131C2×C4×C5—41no—
132C2×C4×C5—41no—
133C2×C4×C5—41no—
134C2×C4×C5—41no—
135C2×C4×C5—41no—
136C2×C4×C5—41no—
137C2×C4×C5—42no—
138C2×C4×C5—42no—
139C2×C4×C5—81no—
140C2×C4×C5—81no—
141C2×C4×C5C22⋊Q812yes—
142C2×C4×C5C4⋊Q812yes—
143C2×Dic5—42no—
144C2×Dic5—42no—
145C2×Dic5—42no—
146C2×Dic5—42no—
147C2×Dic5—42no—
148C2×Dic5—42no—
149C2×Dic5—42no—
150C2×Dic5—42no—
151C2×Dic5—42no—
152C2×Dic5—42no—
153C2×Dic5—42no—
154C2×Dic5—42no—
155C2×Dic5—81no—
156C2×Dic5—81no—
157C2×Dic5—81no—
158C2×Dic5—81no—
159C2×Dic5—81no—
160C2×Dic5—81no—
161C2×Dic5—81no—
162C2×Dic5—81no—
163Dic10—84no—
164C5×C8—44no—
165C22×Q8—101no—
166C23×C4—101no—
167C23×C4—101no—
168C23×C4D2011yescharacteristic
169C23×C4D2011yescharacteristic
170C23×C4C22×D511yescharacteristic
171C22×C8—22no—
172C22⋊Q8—202no—
173C22⋊Q8—202no—
174C2×C4⋊C4—52no—
175C2×C4⋊C4—52no—
176C2×C4⋊C4—102no—
177C2×C4⋊C4—102no—
178C2×C4⋊C4—101no—
179C2×C4⋊C4—101no—
180C2×C4⋊C4—101no—
181C2×C4⋊C4—202no—
182C2×C22⋊C4—102no—
183#107—204no—
184C22⋊C8—22no—
185C22⋊C8Dic1014yescomplemented
186#95—22no—
187#95—52no—
188#95—102no—
189#95—102no—
190#95—101no—
191#95—202no—
192#95—202no—
193C22×C5—21no—
194C22×C5—21no—
195C22×C5—21no—
196C22×C5—21no—
197C22×C5—21no—
198C22×C5—21no—
199C22×C5—21no—
200C22×C5—21no—
201C22×C5—21no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5#39511yescharacteristic
206C22×C5#44711yescharacteristic
207C22×C5#45111yescharacteristic
208C22×C5#45411yescharacteristic
209C22×C5#45511yescharacteristic
210C22×C5B(4,𝔽2)11yescharacteristic
211C22×C5#45811yescharacteristic
212C22×C5#47411yescharacteristic
213C22×C5#47711yescharacteristic
214C22×C5#50011yescharacteristic
215C22×C5#50111yescharacteristic
216C4×C5—22no—
217C4×C5—22no—
218C4×C5—42no—
219C4×C5—42no—
220Dic5—82no—
221Dic5—82no—
222Dic5—82no—
223Dic5—82no—
224C24C2×D2011yescharacteristic
225C2×Q8—202no—
226C2×Q8—401no—
227C2×Q8—401no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—102no—
239C22×C4—102no—
240C22×C4—102no—
241C22×C4—102no—
242C22×C4—201no—
243C22×C4—201no—
244C22×C4—201no—
245C22×C4—201no—
246C22×C4—201no—
247C22×C4—201no—
248C22×C4—201no—
249C22×C4—201no—
250C22×C4—201no—
251C22×C4—201no—
252C22×C4—201no—
253C22×C4—201no—
254C22×C4D4012yes—
255C22×C4Dic2012yes—
256C22×C4C2×Dic1012yes—
257C22×C4D4×D512yes—
258C22×C4#71111yescharacteristic
259C22×C4Q8×D511yescharacteristic
260C2×C8—24no—
261C2×C8—42no—
262C2×C8—42no—
263C4⋊C4—104no—
264C4⋊C4—202no—
265C4⋊C4—202no—
266C4⋊C4—202no—
267C4⋊C4—204no—
268C4⋊C4—202no—
269C4⋊C4—401no—
270C4⋊C4—401no—
271C22⋊C4—202no—
272C22⋊C4—202no—
273C2×C5—21no—
274C2×C5—21no—
275C2×C5—21no—
276C2×C5—21no—
277C2×C5#159811yescharacteristic
278C2×C5#160211yescharacteristic
279C2×C5#160711yescharacteristic
280C2×C5#161711yescharacteristic
281C2×C5#205711yescharacteristic
282C2×C5#206111yescharacteristic
283C2×C5#206211yescharacteristic
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23#401511yescharacteristic
289C23#402811yescharacteristic
290C23#404311yescharacteristic
291C23C2×D4011yescharacteristic
292C23C2×Dic2011yescharacteristic
293C23#405411yescharacteristic
294C23#405511yescharacteristic
295Q8—404no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—202no—
312C2×C4—202no—
313C2×C4—202no—
314C2×C4—202no—
315C2×C4—202no—
316C2×C4—202no—
317C2×C4—202no—
318C2×C4—202no—
319C2×C4—202no—
320C2×C4—202no—
321C2×C4—202no—
322C2×C4—202no—
323C2×C4—401no—
324C2×C4—401no—
325C2×C4—401no—
326C2×C4—401no—
327C2×C4—401no—
328C2×C4—401no—
329C2×C4—401no—
330C2×C4—401no—
331C2×C4#402412yes—
332C2×C4#403412yes—
333C8—44no—
334C5#1056911yescharacteristic, complemented, Sylow
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22#6494511yescharacteristic
348C22#6497111yescharacteristic
349C22#6499111yescharacteristic
350C22#6502111yescharacteristic
351C22#6502811yescharacteristic
352C22#6503011yescharacteristic
353C22#6503111yescharacteristic
354C22#6503511yescharacteristic
355C22#6504211yescharacteristic
356C22#6513511yescharacteristic
357C22#6513911yescharacteristic
358C4—22no—
359C4—22no—
360C4—42no—
361C4—42no—
362C4—402no—
363C4—402no—
364C4—402no—
365C4—402no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2#1059890311yescharacteristic
371C2#1059890811yescharacteristic
372C2#1059892411yescharacteristic
373C2#1059893411yescharacteristic
374C2#1059942511yescharacteristic
375C2#1059975111yescharacteristic
376C2#1059977211yescharacteristic
subgroupG/H
centerC23#4028
commutator, cosocleC23×C4×C5C23
FrattiniC23×C4C22×D5
FittingC5×#1280C2
socleC23×C5#120
prime radicalC24×C5C2×D4
hypercenter#1280D5
hypocenterC5#10569
LCSG ▷ C23×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
39. C5×C22⋊C8Q8semidirect
46. #3963Q8semidirect
185. C22⋊C8Dic10semidirect
334. C5#10569semidirect

Maximal subgroups

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

subgroupindex
#106050922
#106007202
#106002082
C5×#12802
#105981662
#105695