Finite Group Databasebeta

← #11993298

Subgroups — #11993298

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
1C5×#2316C211yesmaximal, characteristic
2#10602358C211yesmaximal, characteristic
3C2×#64748C211yesmaximal, characteristic
4#10600298C212yesmaximal
5#10598115C212yesmaximal
6C2×C5×#117—21no—
7C22×C5×C4⋊C4C2211yescharacteristic
8C22×C4⋊Dic5C2211yescharacteristic
9C5×#389—22no—
10C5×#389—22no—
11C5×#380—21no—
12C5×#380C2212yes—
13C2×#3963—21no—
14C2×#3963—21no—
15C2×#3963C2211yescharacteristic
16C2×C22⋊#168C2212yes—
17C2×#3940—22no—
18#64749—22no—
19#64748C414yescomplemented
20#8857—51nomaximal, Sylow
21C23×C4×C5D411yescharacteristic
22C23×C4×C5D411yescharacteristic
23C23×C4×C5C2311yescharacteristic
24C23×Dic5—21no—
25C23×Dic5—21no—
26C5×#117—42no—
27C5×#117—42no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4C2×C412yes—
35C2×C5×C4⋊C4D412yes—
36C2×C5×C4⋊C4D412yes—
37C2×C5×C4⋊C4Q812yes—
38C2×C5×C22⋊C4—22no—
39C2×C42×C5—22no—
40C2×C4⋊Dic5—22no—
41C2×C4⋊Dic5—42no—
42C22×#168—22no—
43C5×#95—22no—
44C5×#95—22no—
45#3963—22no—
46#3963—42no—
47#3963—42no—
48C22⋊#168—22no—
49C22⋊#168C2×C414yes—
50#3940—44no—
51#2316D511yescharacteristic
52#1853—52no—
53C2×#324—51no—
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—22no—
64C22×C4×C5—22no—
65C22×C4×C5—41no—
66C22×C4×C5—41no—
67C22×C4×C5—41no—
68C22×C4×C5—41no—
69C22×C4×C5C4⋊C412yes—
70C22×C4×C5C4⋊C412yes—
71C22×C4×C5SD1612yes—
72C22×C4×C5SD1612yes—
73C22×C4×C5C22×C411yescharacteristic
74C22×C4×C5C2×D412yes—
75C22×C4×C5C2×Q811yescharacteristic
76C22×C4×C5#4112yes—
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—
91C5×C4⋊C4—24no—
92C5×C4⋊C4—24no—
93C5×C4⋊C4—42no—
94C5×C4⋊C4—42no—
95C5×C4⋊C4—42no—
96C5×C4⋊C4—42no—
97C5×C4⋊C4—81no—
98C5×C4⋊C4—81no—
99C5×C22⋊C4—42no—
100C5×C22⋊C4—42no—
101C42×C5—44no—
102C4⋊Dic5—24no—
103C4⋊Dic5—42no—
104C2×#168—24no—
105C2×#168—42no—
106C2×#168—42no—
107C2×#117—21no—
108C22×C4⋊C4—51no—
109C22×C4⋊C4C2×D511yescharacteristic
110C2×#106—102no—
111C2×C22⋊C8—52no—
112#389—22no—
113#389—22no—
114#380—21no—
115#380C2×D512yes—
116C2×#95—51no—
117C2×#95—101no—
118C2×#95—101no—
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×SD1611yescharacteristic
129C23×C5C2×SD1611yescharacteristic
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#10614yescomplemented
155C2×C4×C5C4×D412yes—
156C2×C4×C5C22⋊Q812yes—
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—
171#168—44no—
172C23×C4—101no—
173C23×C4—101no—
174C23×C4C22⋊D511yescharacteristic
175C23×C4C22⋊D511yescharacteristic
176C23×C4C22×D511yescharacteristic
177C22×C8—102no—
178#117—42no—
179#117—42no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—102no—
187C2×C4⋊C4—202no—
188C2×C4⋊C4Dic1012yes—
189C2×C4⋊C4C4×D512yes—
190C2×C4⋊C4C22⋊D512yes—
191C2×C4⋊C4C22⋊D512yes—
192C2×C22⋊C4—22no—
193C2×C42—22no—
194#106—204no—
195C22⋊C8—54no—
196C22⋊C8—102no—
197#95—22no—
198#95—22no—
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×#10611yescharacteristic
216C22×C5#42811yescharacteristic
217C22×C5#44811yescharacteristic
218C22×C5#45011yescharacteristic
219C22×C5#45411yescharacteristic
220C22×C5#45611yescharacteristic
221C22×C5B(4,𝔽2)11yescharacteristic
222C22×C5#45811yescharacteristic
223C22×C5#48111yescharacteristic
224C22×C5#48311yescharacteristic
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—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×C4#68312yes—
261C22×C4#68312yes—
262C22×C4#68712yes—
263C22×C4#68812yes—
264C22×C4C2×Dic1011yescharacteristic
265C22×C4C2×C4×D511yescharacteristic
266C22×C4#70912yes—
267C22×C4C2×C22⋊D512yes—
268C2×C8—104no—
269C2×C8—202no—
270C2×C8—202no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—81no—
278C4⋊C4—81no—
279C4⋊C4—104no—
280C4⋊C4—202no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C42—44no—
284C2×C5—21no—
285C2×C5—21no—
286C2×C5—21no—
287C2×C5—21no—
288C2×C5#159911yescharacteristic
289C2×C5#160411yescharacteristic
290C2×C5#161111yescharacteristic
291C2×C5#161611yescharacteristic
292C2×C5#185311yescharacteristic
293C2×C5#185711yescharacteristic
294C2×C5#186711yescharacteristic
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23C2×#68311yescharacteristic
300C23#407511yescharacteristic
301C23#407811yescharacteristic
302C23C2×#68711yescharacteristic
303C23C2×#68811yescharacteristic
304C23#408811yescharacteristic
305C23#409911yescharacteristic
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—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#394014yescomplemented
343C2×C4#407012yes—
344C2×C4C4×C22⋊D512yes—
345C8—204no—
346C5#885711yescharacteristic, 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—
359C22C2×#394011yescharacteristic
360C22#6525311yescharacteristic
361C22#6525711yescharacteristic
362C22#6526011yescharacteristic
363C22#6549911yescharacteristic
364C22#6550711yescharacteristic
365C22#6551611yescharacteristic
366C22#6553211yescharacteristic
367C22#6553311yescharacteristic
368C22#6553411yescharacteristic
369C22#6553511yescharacteristic
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#1060234911yescharacteristic
383C2#1060245011yescharacteristic
384C2#1060245111yescharacteristic
385C2#1060266811yescharacteristic
386C2#1060267311yescharacteristic
387C2#1060269111yescharacteristic
388C2#1060269511yescharacteristic
subgroupG/H
centerC23#4099
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#2316C2
socleC23×C5#120
prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenter#2316D5
hypocenterC5#8857
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2316

Complements

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

NH ≅ G/Ntype
19. #64748C4semidirect
154. C2×C4×C5#106semidirect
342. C2×C4#3940semidirect
346. C5#8857semidirect

Maximal subgroups

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

subgroupindex
C5×#23162
#106023582
C2×#647482
#106002982
#105981152
#88575