Finite Group Databasebeta

← #11993292

Subgroups — #11993292

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
2C5×#1441C211yesmaximal, characteristic
3#10602348C212yesmaximal
4C2×#64748C211yesmaximal, characteristic
5#10598103C212yesmaximal
6C22×C5×C4⋊C4C2211yescharacteristic
7C22×C5×C4⋊C4C2211yescharacteristic
8C2×#4072—21no—
9C2×C5×#95—21no—
10C2×C5×#95—21no—
11C2×C5×#95C2211yescharacteristic
12#65501—21no—
13#65501C2212yes—
14C2×C22⋊#168C2212yes—
15#65274—22no—
16#65274—22no—
17C2×#3939—22no—
18#64749—22no—
19#64748C414yescomplemented
20#8856—51nomaximal, Sylow
21C23×C4×C5—21no—
22C23×C4×C5—21no—
23C23×C4×C5D411yescharacteristic
24C23×C4×C5D411yescharacteristic
25C23×C4×C5C2311yescharacteristic
26C2×C5×C4⋊C4—22no—
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4—42no—
30C2×C5×C4⋊C4C2×C412yes—
31C2×C5×C4⋊C4Q812yes—
32C2×C22⋊Dic5—22no—
33#4072—42no—
34#4072—42no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—21no—
38C2×C4⋊Dic5—21no—
39C2×C4⋊Dic5D412yes—
40C2×C4⋊Dic5D412yes—
41C2×C4×Dic5—22no—
42C22×#168—22no—
43C5×#95—22no—
44C5×#95—42no—
45C5×#95—42no—
46#3963—22no—
47#3963—22no—
48C22⋊#168—22no—
49C22⋊#168C2×C414yes—
50#3939—44no—
51#2316—51no—
52#1852—52no—
53C2×#324—51no—
54#1441D511yescharacteristic
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—22no—
64C22×C4×C5—22no—
65C22×C4×C5—41no—
66C22×C4×C5—41no—
67C22×C4×C5—41no—
68C22×C4×C5—41no—
69C22×C4×C5—41no—
70C22×C4×C5—41no—
71C22×C4×C5—41no—
72C22×C4×C5—41no—
73C22×C4×C5—41no—
74C22×C4×C5—41no—
75C22×C4×C5—41no—
76C22×C4×C5—41no—
77C22×C4×C5—41no—
78C22×C4×C5—41no—
79C22×C4×C5—41no—
80C22×C4×C5—41no—
81C22×C4×C5C4⋊C412yes—
82C22×C4×C5C4⋊C412yes—
83C22×C4×C5D812yes—
84C22×C4×C5Q1612yes—
85C22×C4×C5C22×C411yescharacteristic
86C22×C4×C5C2×D412yes—
87C22×C4×C5C2×Q811yescharacteristic
88C22×C4×C5#4112yes—
89C22×Dic5—22no—
90C22×Dic5—22no—
91C5×C4⋊C4—24no—
92C5×C4⋊C4—24no—
93C5×C4⋊C4—24no—
94C5×C4⋊C4—42no—
95C22⋊Dic5—42no—
96C22⋊Dic5—42no—
97C4⋊Dic5—42no—
98C4⋊Dic5—42no—
99C4⋊Dic5—42no—
100C4⋊Dic5—42no—
101C4⋊Dic5—81no—
102C4⋊Dic5—81no—
103C4×Dic5—44no—
104C2×#168—24no—
105C2×#168—42no—
106C2×#168—42no—
107C2×#117—101no—
108C22×C4⋊C4C2×D511yescharacteristic
109C22×C4⋊C4C2×D511yescharacteristic
110C2×#107—102no—
111C2×C22⋊C8—52no—
112#389—102no—
113#389—102no—
114#380—52no—
115#380—101no—
116C2×#95—21no—
117C2×#95—21no—
118C2×#95C2×D511yescharacteristic
119#340—102no—
120#324—54no—
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—42no—
148C2×C4×C5—42no—
149C2×C4×C5—42no—
150C2×C4×C5—42no—
151C2×C4×C5—42no—
152C2×C4×C5—42no—
153C2×C4×C5—81no—
154C2×C4×C5—81no—
155C2×C4×C5—81no—
156C2×C4×C5—81no—
157C2×C4×C5—81no—
158C2×C4×C5—81no—
159C2×C4×C5—81no—
160C2×C4×C5—81no—
161C2×C4×C5—81no—
162C2×C4×C5#10714yescomplemented
163C2×C4×C5C4×D412yes—
164C2×C4×C5C22⋊Q812yes—
165C2×Dic5—42no—
166C2×Dic5—42no—
167C2×Dic5—42no—
168C2×Dic5—42no—
169C2×Dic5—42no—
170C2×Dic5—42no—
171#168—44no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4C22⋊D511yescharacteristic
175C23×C4C22⋊D511yescharacteristic
176C23×C4C22×D511yescharacteristic
177C22×C8—102no—
178#117—202no—
179#117—202no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—52no—
185C2×C4⋊C4—52no—
186C2×C4⋊C4—101no—
187C2×C4⋊C4—101no—
188C2×C4⋊C4—101no—
189C2×C4⋊C4—101no—
190C2×C4⋊C4Dic1012yes—
191C2×C4⋊C4C4×D512yes—
192C2×C22⋊C4—102no—
193C2×C42—102no—
194#107—204no—
195C22⋊C8—54no—
196C22⋊C8—102no—
197#95—22no—
198#95—42no—
199#95—42no—
200#95—102no—
201#95—102no—
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—
229C4×C5—82no—
230C4×C5—82no—
231Dic5—82no—
232Dic5—82no—
233C24C2×C22⋊D511yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—102no—
259C22×C4—102no—
260C22×C4#68312yes—
261C22×C4#68312yes—
262C22×C4#68612yes—
263C22×C4#68912yes—
264C22×C4C2×Dic1011yescharacteristic
265C22×C4C2×C4×D511yescharacteristic
266C22×C4D4×D512yes—
267C22×C4#71112yes—
268C2×C8—104no—
269C2×C8—202no—
270C2×C8—202no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4—24no—
274C4⋊C4—42no—
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—
299C23C2×#68311yescharacteristic
300C23C2×#68611yescharacteristic
301C23#408111yescharacteristic
302C23#408311yescharacteristic
303C23C2×#68911yescharacteristic
304C23#409511yescharacteristic
305C23#409711yescharacteristic
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—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—202no—
337C2×C4—202no—
338C2×C4—202no—
339C2×C4—202no—
340C2×C4—202no—
341C2×C4—202no—
342C2×C4#393914yescomplemented
343C2×C4#402412yes—
344C2×C4#402712yes—
345C8—204no—
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#6523511yescharacteristic
360C22C2×#393911yescharacteristic
361C22#6528411yescharacteristic
362C22#6532111yescharacteristic
363C22#6532211yescharacteristic
364C22#6532511yescharacteristic
365C22#6533311yescharacteristic
366C22#6533911yescharacteristic
367C22#6534211yescharacteristic
368C22#6535111yescharacteristic
369C22#6538411yescharacteristic
370C4—24no—
371C4—22no—
372C4—22no—
373C4—42no—
374C4—82no—
375C4—82no—
376C4—402no—
377C4—402no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—21no—
382C2#1060029711yescharacteristic
383C2#1060039011yescharacteristic
384C2#1060046511yescharacteristic
385C2#1060049611yescharacteristic
386C2#1060050011yescharacteristic
387C2#1060050511yescharacteristic
388C2#1060051211yescharacteristic
subgroupG/H
centerC23#4083
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#1441C2
socleC23×C5#120
prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenter#1441D5
hypocenterC5#8856
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1441

Complements

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

NH ≅ G/Ntype
19. #64748C4semidirect
162. C2×C4×C5#107semidirect
342. C2×C4#3939semidirect
346. C5#8856semidirect

Maximal subgroups

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

subgroupindex
#106138872
C5×#14412
#106023482
C2×#647482
#105981032
#88565