Finite Group Databasebeta

← #11994707

Subgroups — #11994707

Order 1280.

604 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#387C211yesmaximal, characteristic
2C2×#65215C211yesmaximal, characteristic
3C2×#64748C212yesmaximal
4#10602324C211yesmaximal, characteristic
5#10598104C212yesmaximal
6C22×C5×C4⋊C4C411yescharacteristic
7C22×C5×C4⋊C4C2211yescharacteristic
8C22×C42×C5C2211yescharacteristic
9C5×#387—21no—
10C5×#387—21no—
11C5×#387—21no—
12C5×#387—21no—
13C2×C5×#95C411yescharacteristic
14C2×C5×#95C411yescharacteristic
15C2×C5×#95C411yescharacteristic
16C2×C5×#95C2211yescharacteristic
17C2×C22⋊#168C2212yes—
18C2×C22⋊#168C2212yes—
19#65215—24no—
20C2×C4⋊#168—21no—
21C2×#3935—21no—
22#64748—24no—
23#64744—21no—
24#64744—21no—
25#9086—51nomaximal, Sylow
26C23×C4×C5C2×C411yescharacteristic
27C23×C4×C5C2×C411yescharacteristic
28C23×C4×C5C2×C411yescharacteristic
29C23×C4×C5C2×C411yescharacteristic
30C23×C4×C5C2×C411yescharacteristic
31C23×C4×C5C2×C411yescharacteristic
32C23×C4×C5C2311yescharacteristic
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—22no—
36C2×C5×C4⋊C4—22no—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4—22no—
40C2×C5×C4⋊C4—22no—
41C2×C42×C5—22no—
42C2×C42×C5—22no—
43C2×C42×C5D411yescharacteristic
44C2×C42×C5D411yescharacteristic
45C2×C42×C5D411yescharacteristic
46C2×C42×C5D411yescharacteristic
47C22×#168—22no—
48C22×#168—22no—
49C5×#95—21no—
50C5×#95—21no—
51C5×#95—21no—
52C5×#95—21no—
53C5×#95—21no—
54C5×#95—21no—
55C5×#95—21no—
56C5×#95—21no—
57C22⋊#168—22no—
58C22⋊#168—22no—
59C22⋊#168—22no—
60C22⋊#168D414yes—
61C4⋊#168—24no—
62#3935—24no—
63C2×#432—51no—
64C2×#387D511yescharacteristic
65#1817—51no—
66C2×#324—52no—
67#1280—52no—
68C24×C5C22×C411yescharacteristic
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—22no—
72C22×C4×C5—22no—
73C22×C4×C5—22no—
74C22×C4×C5—21no—
75C22×C4×C5—21no—
76C22×C4×C5—21no—
77C22×C4×C5—21no—
78C22×C4×C5—22no—
79C22×C4×C5—22no—
80C22×C4×C5—22no—
81C22×C4×C5—21no—
82C22×C4×C5—21no—
83C22×C4×C5—22no—
84C22×C4×C5—22no—
85C22×C4×C5—41no—
86C22×C4×C5—41no—
87C22×C4×C5—41no—
88C22×C4×C5—41no—
89C22×C4×C5—41no—
90C22×C4×C5—41no—
91C22×C4×C5—41no—
92C22×C4×C5—41no—
93C22×C4×C5—41no—
94C22×C4×C5C22⋊C411yescharacteristic
95C22×C4×C5C22⋊C411yescharacteristic
96C22×C4×C5C22⋊C411yescharacteristic
97C22×C4×C5C22⋊C411yescharacteristic
98C22×C4×C5M1612yes—
99C22×C4×C5M1612yes—
100C22×C4×C5C2×D412yes—
101C22×C4×C5C2×D411yescharacteristic
102C22×C4×C5C2×D411yescharacteristic
103C22×C4×C5#4112yes—
104C5×C4⋊C4—24no—
105C5×C4⋊C4—24no—
106C5×C4⋊C4—41no—
107C5×C4⋊C4—42no—
108C5×C4⋊C4—41no—
109C42×C5—21no—
110C42×C5—21no—
111C42×C5—22no—
112C42×C5—22no—
113C42×C5—21no—
114C42×C5—21no—
115C2×#168—24no—
116C2×#168—42no—
117C2×#168—42no—
118C2×#168—42no—
119C2×#168—42no—
120C2×#168—42no—
121C22×C4⋊C4Dic511yescharacteristic
122C22×C4⋊C4C2×D511yescharacteristic
123C22×C42C2×D511yescharacteristic
124#432—104no—
125C2×C4⋊C8—101no—
126C2×C22⋊C8—52no—
127C2×C22⋊C8—52no—
128C2×#97—101no—
129#387—21no—
130#387—21no—
131#387—21no—
132#387—21no—
133C2×#95Dic511yescharacteristic
134C2×#95Dic511yescharacteristic
135C2×#95Dic511yescharacteristic
136C2×#95C2×D511yescharacteristic
137#336—101no—
138#336—101no—
139#324—104no—
140C23×C5—21no—
141C23×C5—21no—
142C23×C5—21no—
143C23×C5—21no—
144C23×C5C2×C22⋊C411yescharacteristic
145C23×C5C4×D412yes—
146C23×C5C2×M1611yescharacteristic
147C23×C5C2×M1611yescharacteristic
148C23×C5#13112yes—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
160C2×C4×C5—22no—
161C2×C4×C5—22no—
162C2×C4×C5—21no—
163C2×C4×C5—21no—
164C2×C4×C5—21no—
165C2×C4×C5—21no—
166C2×C4×C5—24no—
167C2×C4×C5—42no—
168C2×C4×C5—42no—
169C2×C4×C5—44no—
170C2×C4×C5—42no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—42no—
176C2×C4×C5—42no—
177C2×C4×C5—42no—
178C2×C4×C5—42no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—41no—
185C2×C4×C5—82no—
186C2×C4×C5—82no—
187C2×C4×C5#10112yes—
188C2×C4×C5#12011yescharacteristic
189C2×C4×C5#12112yes—
190C2×C4×C5#12311yescharacteristic
191#168—44no—
192#168—82no—
193C23×C4C2×Dic511yescharacteristic
194C23×C4C2×Dic511yescharacteristic
195C23×C4C2×Dic511yescharacteristic
196C23×C4C2×Dic511yescharacteristic
197C23×C4C2×Dic511yescharacteristic
198C23×C4C2×Dic511yescharacteristic
199C23×C4C22×D511yescharacteristic
200C22×C8—102no—
201C22×C8—102no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C42—22no—
211C2×C42—22no—
212C2×C42C22⋊D511yescharacteristic
213C2×C42C22⋊D511yescharacteristic
214C2×C42C22⋊D511yescharacteristic
215C2×C42C22⋊D511yescharacteristic
216C4⋊C8—104no—
217C22⋊C8—54no—
218C22⋊C8—102no—
219C22⋊C8—102no—
220C22⋊C8—102no—
221#97—104no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230C22×C5—22no—
231C22×C5—22no—
232C22×C5—21no—
233C22×C5—21no—
234C22×C5—21no—
235C22×C5—21no—
236C22×C5—22no—
237C22×C5—22no—
238C22×C5#38611yescharacteristic
239C22×C5#40711yescharacteristic
240C22×C5#40811yescharacteristic
241C22×C5#41011yescharacteristic
242C22×C5#41011yescharacteristic
243C22×C5C2×#10111yescharacteristic
244C22×C5#41311yescharacteristic
245C22×C5#43512yes—
246C22×C5#43612yes—
247C4×C5—21no—
248C4×C5—22no—
249C4×C5—21no—
250C4×C5—22no—
251C4×C5—41no—
252C4×C5—41no—
253C4×C5—42no—
254C4×C5—41no—
255C4×C5—42no—
256C4×C5—81no—
257C4×C5—81no—
258C24C22×Dic511yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4#68112yes—
285C22×C4#68112yes—
286C22×C4C22⋊Dic511yescharacteristic
287C22×C4C22⋊Dic511yescharacteristic
288C22×C4C22⋊Dic511yescharacteristic
289C22×C4C22⋊Dic511yescharacteristic
290C22×C4D4×D512yes—
291C22×C4#71112yes—
292C22×C4C2×C22⋊D511yescharacteristic
293C22×C4C2×C22⋊D511yescharacteristic
294C2×C8—104no—
295C2×C8—202no—
296C2×C8—202no—
297C2×C8—202no—
298C2×C8—202no—
299C2×C8—202no—
300C4⋊C4—24no—
301C4⋊C4—24no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—42no—
305C42—21no—
306C42—21no—
307C42—21no—
308C42—21no—
309C42—22no—
310C42—22no—
311C2×C5—22no—
312C2×C5—22no—
313C2×C5#146411yescharacteristic
314C2×C5#146711yescharacteristic
315C2×C5#147011yescharacteristic
316C2×C5#147311yescharacteristic
317C2×C5#187011yescharacteristic
318C2×C5#189911yescharacteristic
319C2×C5#190111yescharacteristic
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23C2×#68111yescharacteristic
325C23C2×#68111yescharacteristic
326C23D4×Dic512yes—
327C23#409412yes—
328C23C2×C22⋊Dic511yescharacteristic
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—24no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4#396812yes—
368C2×C4#408111yescharacteristic
369C2×C4#408311yescharacteristic
370C2×C4#408512yes—
371C8—204no—
372C8—402no—
373C5#908611yescharacteristic, complemented, Sylow
374C22—22no—
375C22—22no—
376C22—22no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—22no—
382C22#6530012yes—
383C22#6530112yes—
384C22#6549611yescharacteristic
385C22#6550911yescharacteristic
386C22C2×#396811yescharacteristic
387C22#6552311yescharacteristic
388C22#6552611yescharacteristic
389C22#6552911yescharacteristic
390C22#6552911yescharacteristic
391C4—21no—
392C4—22no—
393C4—21no—
394C4—22no—
395C4—42no—
396C4—42no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—81no—
401C4—81no—
402C2—22no—
403C2—22no—
404C2#1060236511yescharacteristic
405C2#1060240411yescharacteristic
406C2#1060241811yescharacteristic
407C2#1060249111yescharacteristic
408C2#1060249811yescharacteristic
409C2#1060253011yescharacteristic
410C2#1060253811yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic5
commutator, prime radicalC24×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#387C2
socleC23×C5C2×C22⋊C4
cosocleC23×C4×C5C23
hypercenterC2×#387D5
hypocenterC5#9086
LCSG ▷ C24×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
373. C5#9086semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3872
C2×#652152
C2×#647482
#106023242
#105981042
#90865