Finite Group Databasebeta

← #11993295

Subgroups — #11993295

Order 1280.

612 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10613887C211yesmaximal, characteristic
2C2×C5×#324C211yesmaximal, characteristic
3#10602358C211yesmaximal, characteristic
4#10600720C212yesmaximal
5#10598166C212yesmaximal
6C22×C5×C4⋊C4C2211yescharacteristic
7C2×#4072—21no—
8C22×C4⋊Dic5C2211yescharacteristic
9C2×C5×C22⋊C8C2212yes—
10#65501—21no—
11#65501C2212yes—
12C2×#3963—21no—
13C2×#3963—21no—
14C2×#3963C2211yescharacteristic
15C2×#3950—22no—
16#65274—22no—
17#65274—22no—
18C5×#324C414yescomplemented
19#64771—22no—
20#8856—51nomaximal, Sylow
21C23×C4×C5D411yescharacteristic
22C23×C4×C5D411yescharacteristic
23C23×C4×C5C2311yescharacteristic
24C23×Dic5—21no—
25C23×Dic5—21no—
26C22×C5×C8—22no—
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4C2×C412yes—
30C2×C5×C4⋊C4Q812yes—
31C2×C22⋊Dic5—22no—
32#4072—42no—
33#4072—42no—
34C2×C4⋊Dic5—22no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—21no—
38C2×C4⋊Dic5—21no—
39C2×C4⋊Dic5—42no—
40C2×C4⋊Dic5D412yes—
41C2×C4⋊Dic5D412yes—
42C2×C4×Dic5—22no—
43C5×C22⋊C8—22no—
44C5×C22⋊C8C2×C414yes—
45#3963—22no—
46#3963—22no—
47#3963—22no—
48#3963—42no—
49#3963—42no—
50#3950—44no—
51#2316—51no—
52#1852—52no—
53C2×#324D511yescharacteristic
54#1441—51no—
55#1294—52no—
56C24×C5C2×D411yescharacteristic
57C22×C4×C5—21no—
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—41no—
64C22×C4×C5—41no—
65C22×C4×C5—41no—
66C22×C4×C5—41no—
67C22×C4×C5C4⋊C412yes—
68C22×C4×C5C4⋊C412yes—
69C22×C4×C5D812yes—
70C22×C4×C5Q1612yes—
71C22×C4×C5C22×C411yescharacteristic
72C22×C4×C5C2×D412yes—
73C22×C4×C5C2×Q811yescharacteristic
74C22×C4×C5#4112yes—
75C22×Dic5—22no—
76C22×Dic5—22no—
77C22×Dic5—22no—
78C22×Dic5—22no—
79C22×Dic5—41no—
80C22×Dic5—41no—
81C22×Dic5—41no—
82C22×Dic5—41no—
83C22×Dic5—41no—
84C22×Dic5—41no—
85C22×Dic5—41no—
86C22×Dic5—41no—
87C22×Dic5—41no—
88C22×Dic5—41no—
89C22×Dic5—41no—
90C22×Dic5—41no—
91C2×C5×C8—24no—
92C2×C5×C8—42no—
93C2×C5×C8—42no—
94C5×C4⋊C4—24no—
95C5×C4⋊C4—24no—
96C22⋊Dic5—42no—
97C22⋊Dic5—42no—
98C4⋊Dic5—24no—
99C4⋊Dic5—42no—
100C4⋊Dic5—42no—
101C4⋊Dic5—42no—
102C4⋊Dic5—42no—
103C4⋊Dic5—42no—
104C4⋊Dic5—81no—
105C4⋊Dic5—81no—
106C4×Dic5—44no—
107C2×#117—101no—
108C22×C4⋊C4—51no—
109C22×C4⋊C4C2×D511yescharacteristic
110C2×#107—102no—
111C2×C22⋊C8C2×D512yes—
112#389—102no—
113#389—102no—
114#380—52no—
115#380—101no—
116C2×#95—51no—
117C2×#95—101no—
118C2×#95—101no—
119#340—102no—
120#324Dic514yescomplemented
121C23×C5—21no—
122C23×C5—21no—
123C23×C5—21no—
124C23×C5—21no—
125C23×C5C2×C4⋊C411yescharacteristic
126C23×C5#12011yescharacteristic
127C23×C5#12311yescharacteristic
128C23×C5C2×D811yescharacteristic
129C23×C5C2×Q1611yescharacteristic
130C23×C5AGL(1,ℤ/8)11yescharacteristic
131C23×C5#13711yescharacteristic
132C2×C4×C5—22no—
133C2×C4×C5—22no—
134C2×C4×C5—22no—
135C2×C4×C5—22no—
136C2×C4×C5—22no—
137C2×C4×C5—22no—
138C2×C4×C5—22no—
139C2×C4×C5—22no—
140C2×C4×C5—22no—
141C2×C4×C5—41no—
142C2×C4×C5—41no—
143C2×C4×C5—42no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5—42no—
147C2×C4×C5—81no—
148C2×C4×C5#10714yescomplemented
149C2×C4×C5C4×D412yes—
150C2×C4×C5C22⋊Q812yes—
151C2×Dic5—42no—
152C2×Dic5—42no—
153C2×Dic5—42no—
154C2×Dic5—42no—
155C2×Dic5—42no—
156C2×Dic5—42no—
157C2×Dic5—42no—
158C2×Dic5—42no—
159C2×Dic5—42no—
160C2×Dic5—42no—
161C2×Dic5—42no—
162C2×Dic5—42no—
163C2×Dic5—81no—
164C2×Dic5—81no—
165C2×Dic5—81no—
166C2×Dic5—81no—
167C2×Dic5—81no—
168C2×Dic5—81no—
169C2×Dic5—81no—
170C2×Dic5—81no—
171C5×C8—44no—
172C23×C4—101no—
173C23×C4—101no—
174C23×C4D2011yescharacteristic
175C23×C4D2011yescharacteristic
176C23×C4C22×D511yescharacteristic
177C22×C8—22no—
178#117—202no—
179#117—202no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—52no—
183C2×C4⋊C4—52no—
184C2×C4⋊C4—102no—
185C2×C4⋊C4—101no—
186C2×C4⋊C4—101no—
187C2×C4⋊C4—101no—
188C2×C4⋊C4—101no—
189C2×C4⋊C4—202no—
190C2×C4⋊C4Dic1012yes—
191C2×C4⋊C4C2×Dic512yes—
192C2×C22⋊C4—102no—
193C2×C42—102no—
194#107—204no—
195C22⋊C8—22no—
196C22⋊C8C2×Dic514yes—
197#95—102no—
198#95—102no—
199#95—102no—
200#95—202no—
201#95—202no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5—21no—
206C22×C5—21no—
207C22×C5—21no—
208C22×C5—21no—
209C22×C5—21no—
210C22×C5—21no—
211C22×C5—21no—
212C22×C5—21no—
213C22×C5—21no—
214C22×C5#38511yescharacteristic
215C22×C5C2×#10711yescharacteristic
216C22×C5#42811yescharacteristic
217C22×C5#44711yescharacteristic
218C22×C5#45111yescharacteristic
219C22×C5#45411yescharacteristic
220C22×C5#45611yescharacteristic
221C22×C5B(4,𝔽2)11yescharacteristic
222C22×C5#45811yescharacteristic
223C22×C5#48011yescharacteristic
224C22×C5#48411yescharacteristic
225C4×C5—24no—
226C4×C5—22no—
227C4×C5—22no—
228C4×C5—42no—
229Dic5—82no—
230Dic5—82no—
231Dic5—82no—
232Dic5—82no—
233C24C2×D2011yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—102no—
245C22×C4—102no—
246C22×C4—102no—
247C22×C4—102no—
248C22×C4—201no—
249C22×C4—201no—
250C22×C4—201no—
251C22×C4—201no—
252C22×C4—201no—
253C22×C4—201no—
254C22×C4—201no—
255C22×C4—201no—
256C22×C4—201no—
257C22×C4—201no—
258C22×C4—201no—
259C22×C4—201no—
260C22×C4D4012yes—
261C22×C4Dic2012yes—
262C22×C4C4⋊Dic512yes—
263C22×C4C4⋊Dic512yes—
264C22×C4C2×Dic1011yescharacteristic
265C22×C4D4×D512yes—
266C22×C4#71112yes—
267C22×C4C22×Dic511yescharacteristic
268C2×C8—24no—
269C2×C8—42no—
270C2×C8—42no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4—104no—
274C4⋊C4—202no—
275C4⋊C4—202no—
276C4⋊C4—202no—
277C4⋊C4—202no—
278C4⋊C4—202no—
279C4⋊C4—401no—
280C4⋊C4—401no—
281C22⋊C4—202no—
282C22⋊C4—202no—
283C42—204no—
284C2×C5—21no—
285C2×C5—21no—
286C2×C5—21no—
287C2×C5—21no—
288C2×C5#159811yescharacteristic
289C2×C5#160511yescharacteristic
290C2×C5#161011yescharacteristic
291C2×C5#161711yescharacteristic
292C2×C5#185211yescharacteristic
293C2×C5#185711yescharacteristic
294C2×C5#186711yescharacteristic
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23#402811yescharacteristic
300C23#403211yescharacteristic
301C23C2×D4011yescharacteristic
302C23C2×Dic2011yescharacteristic
303C23#405411yescharacteristic
304C23#405511yescharacteristic
305C23C2×C4⋊Dic511yescharacteristic
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—202no—
323C2×C4—202no—
324C2×C4—202no—
325C2×C4—202no—
326C2×C4—202no—
327C2×C4—202no—
328C2×C4—202no—
329C2×C4—202no—
330C2×C4—202no—
331C2×C4—202no—
332C2×C4—202no—
333C2×C4—202no—
334C2×C4—401no—
335C2×C4—401no—
336C2×C4—401no—
337C2×C4—401no—
338C2×C4—401no—
339C2×C4—401no—
340C2×C4—401no—
341C2×C4—401no—
342C2×C4#395014yescomplemented
343C2×C4#402412yes—
344C2×C4D4×Dic512yes—
345C8—44no—
346C5#885611yescharacteristic, complemented, Sylow
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22#6501111yescharacteristic
360C22#6502111yescharacteristic
361C22#6502511yescharacteristic
362C22#6502811yescharacteristic
363C22#6503011yescharacteristic
364C22#6503111yescharacteristic
365C22#6504111yescharacteristic
366C22#6504211yescharacteristic
367C22#6523911yescharacteristic
368C22C2×#395011yescharacteristic
369C22#6541011yescharacteristic
370C4—24no—
371C4—22no—
372C4—22no—
373C4—42no—
374C4—402no—
375C4—402no—
376C4—402no—
377C4—402no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—21no—
382C2#1059892411yescharacteristic
383C2#1059892811yescharacteristic
384C2#1059893211yescharacteristic
385C2#1059893411yescharacteristic
386C2#1060072011yescharacteristic
387C2#1060081411yescharacteristic
388C2#1060089511yescharacteristic
subgroupG/H
centerC23#4028
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#324C2
socleC23×C5#120
prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenterC2×#324D5
hypocenterC5#8856
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
18. C5×#324C4semidirect
120. #324Dic5semidirect
148. C2×C4×C5#107semidirect
342. C2×C4#3950semidirect
346. C5#8856semidirect

Maximal subgroups

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

subgroupindex
#106138872
C2×C5×#3242
#106023582
#106007202
#105981662
#88565