Finite Group Databasebeta

← #11991968

Subgroups — #11991968

Order 1280.

682 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64938C211yesmaximal, characteristic
2C2×#64689C212yesmaximal
3#10600701C212yesmaximal
4C5×#1280C211yesmaximal, characteristic
5#10598104C211yesmaximal, characteristic
6C22×#683C411yescharacteristic
7C22×#683C2211yescharacteristic
8C22×C4×Dic5C411yescharacteristic
9C22×C4×Dic5C411yescharacteristic
10C22×C4×Dic5C2211yescharacteristic
11C2×C5×C22⋊C8C2212yes—
12C2×C5×#95C2211yescharacteristic
13C2×#3963C411yescharacteristic
14C2×C22⋊#168C2212yes—
15C2×#3946—22no—
16#64938—22no—
17#64938—22no—
18#64770—22no—
19#64689—24no—
20#8560—51nomaximal, Sylow
21C23×C4×C5C2×C411yescharacteristic
22C23×C4×C5C2×C411yescharacteristic
23C23×C4×C5C2311yescharacteristic
24C23×Dic5C2×C411yescharacteristic
25C23×Dic5C2×C411yescharacteristic
26C23×Dic5C2×C411yescharacteristic
27C23×Dic5C2×C411yescharacteristic
28C22×C5×C8—22no—
29C2×#683—22no—
30C2×#683—22no—
31C2×#683—22no—
32C2×#683—22no—
33C2×#683C814yescomplemented
34C2×#683D412yes—
35C2×#683Q812yes—
36C2×C4×Dic5—22no—
37C2×C4×Dic5—21no—
38C2×C4×Dic5—21no—
39C2×C4×Dic5—22no—
40C2×C4×Dic5—21no—
41C2×C4×Dic5—21no—
42C2×C4×Dic5—42no—
43C2×C4×Dic5—42no—
44C2×C4×Dic5D412yes—
45C2×C4×Dic5D412yes—
46C22×#168—22no—
47C5×C22⋊C8—22no—
48C5×C22⋊C8—22no—
49C5×#95—22no—
50#3963—22no—
51C22⋊#168—22no—
52C22⋊#168—22no—
53#3946—44no—
54C2×C4×C4⋊C4—51no—
55#1797—52no—
56C2×#324—52no—
57#1280—51no—
58#1280D511yescharacteristic
59C24×C5C22×C411yescharacteristic
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—41no—
65C22×C4×C5—41no—
66C22×C4×C5—41no—
67C22×C4×C5—41no—
68C22×C4×C5—41no—
69C22×C4×C5—41no—
70C22×C4×C5C2×C812yes—
71C22×C4×C5M1612yes—
72C22×C4×C5C2×D412yes—
73C22×C4×C5C2×D411yescharacteristic
74C22×C4×C5C2×Q811yescharacteristic
75C22×C4×C5#4112yes—
76C22×Dic5—21no—
77C22×Dic5—21no—
78C22×Dic5—21no—
79C22×Dic5—21no—
80C22×Dic5—21no—
81C22×Dic5—21no—
82C22×Dic5—22no—
83C22×Dic5—22no—
84C22×Dic5—21no—
85C22×Dic5—21no—
86C22×Dic5—41no—
87C22×Dic5—41no—
88C22×Dic5—41no—
89C22×Dic5—41no—
90C22×Dic5C22⋊C412yes—
91C22×Dic5C22⋊C411yescharacteristic
92C22×Dic5C22⋊C411yescharacteristic
93C22×Dic5C4⋊C412yes—
94C22×Dic5C4⋊C412yes—
95C22×Dic5C2×C812yes—
96C22×Dic5C2×C812yes—
97C22×Dic5M1612yes—
98C22×Dic5M1612yes—
99C2×C5×C8—42no—
100C2×C5×C8—42no—
101C2×C5×C8—42no—
102#683—24no—
103#683—24no—
104#683—28no—
105C4×Dic5—24no—
106C4×Dic5—24no—
107C4×Dic5—24no—
108C4×Dic5—42no—
109C4×Dic5—42no—
110C4×Dic5—42no—
111C2×#168—42no—
112C2×#168—42no—
113C2×#168—42no—
114C22×C4⋊C4—51no—
115C22×C4⋊C4—51no—
116C22×C42—51no—
117C22×C42—51no—
118C22×C42—51no—
119C2×C4⋊C8—102no—
120C2×C22⋊C8—52no—
121C2×C22⋊C8C2×D512yes—
122C4×C4⋊C4—102no—
123C4×C4⋊C4—102no—
124C2×#95—51no—
125C2×#95C2×D511yescharacteristic
126#336—102no—
127#324—104no—
128C23×C5—21no—
129C23×C5—21no—
130C23×C5—21no—
131C23×C5—21no—
132C23×C5C2×C22⋊C411yescharacteristic
133C23×C5C2×C4⋊C411yescharacteristic
134C23×C5#11711yescharacteristic
135C23×C5C22×C811yescharacteristic
136C23×C5C2×M1611yescharacteristic
137C23×C5C2×M1611yescharacteristic
138C23×C5C2×M1611yescharacteristic
139C2×C4×C5—22no—
140C2×C4×C5—22no—
141C2×C4×C5—22no—
142C2×C4×C5—22no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—42no—
146C2×C4×C5—42no—
147C2×C4×C5—42no—
148C2×C4×C5—41no—
149C2×C4×C5—41no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5—42no—
153C2×C4×C5—42no—
154C2×C4×C5#12112yes—
155C2×C4×C5C22⋊Q812yes—
156C2×Dic5—24no—
157C2×Dic5—24no—
158C2×Dic5—22no—
159C2×Dic5—22no—
160C2×Dic5—21no—
161C2×Dic5—21no—
162C2×Dic5—22no—
163C2×Dic5—22no—
164C2×Dic5—21no—
165C2×Dic5—21no—
166C2×Dic5—22no—
167C2×Dic5—22no—
168C2×Dic5—22no—
169C2×Dic5—22no—
170C2×Dic5—22no—
171C2×Dic5—42no—
172C2×Dic5—42no—
173C2×Dic5—42no—
174C2×Dic5—41no—
175C2×Dic5—41no—
176C2×Dic5—42no—
177C2×Dic5C22⋊C814yes—
178C2×Dic5#9912yes—
179C2×Dic5#10112yes—
180C2×Dic5C4⋊C814yescomplemented
181C5×C8—82no—
182#168—82no—
183C23×C4—51no—
184C23×C4—51no—
185C23×C4—51no—
186C23×C4—51no—
187C23×C4C4×D511yescharacteristic
188C23×C4C4×D511yescharacteristic
189C23×C4C22×D511yescharacteristic
190C22×C8—22no—
191C22×C8—102no—
192C2×C4⋊C4—54no—
193C2×C4⋊C4—52no—
194C2×C4⋊C4—52no—
195C2×C4⋊C4—102no—
196C2×C4⋊C4—102no—
197C2×C4⋊C4—102no—
198C2×C4⋊C4—102no—
199C2×C42—52no—
200C2×C42—52no—
201C2×C42—101no—
202C2×C42—101no—
203C2×C42—102no—
204C2×C42—102no—
205C2×C42—101no—
206C2×C42—101no—
207C2×C42—202no—
208C2×C42—202no—
209C4⋊C8—204no—
210C22⋊C8—22no—
211C22⋊C8—22no—
212C22⋊C8—102no—
213C22⋊C8—102no—
214#95—22no—
215#95—102no—
216C22×C5—21no—
217C22×C5—21no—
218C22×C5—21no—
219C22×C5—21no—
220C22×C5—21no—
221C22×C5—21no—
222C22×C5—21no—
223C22×C5—21no—
224C22×C5—21no—
225C22×C5—21no—
226C22×C5—21no—
227C22×C5—21no—
228C22×C5#38011yescharacteristic
229C22×C5C2×C22⋊C811yescharacteristic
230C22×C5#40711yescharacteristic
231C22×C5C2×#9911yescharacteristic
232C22×C5#41011yescharacteristic
233C22×C5C2×#10111yescharacteristic
234C22×C5#41311yescharacteristic
235C22×C5C2×C4⋊C811yescharacteristic
236C22×C5#42311yescharacteristic
237C22×C5#43111yescharacteristic
238C22×C5#43211yescharacteristic
239C4×C5—22no—
240C4×C5—22no—
241C4×C5—42no—
242C4×C5—42no—
243Dic5—24no—
244Dic5—24no—
245Dic5—22no—
246Dic5—22no—
247Dic5—42no—
248C24C2×C4×D511yescharacteristic
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—52no—
260C22×C4—51no—
261C22×C4—51no—
262C22×C4—52no—
263C22×C4—52no—
264C22×C4—52no—
265C22×C4—52no—
266C22×C4—52no—
267C22×C4—52no—
268C22×C4—102no—
269C22×C4—102no—
270C22×C4—101no—
271C22×C4—101no—
272C22×C4—101no—
273C22×C4—101no—
274C22×C4—101no—
275C22×C4—101no—
276C22×C4—101no—
277C22×C4—101no—
278C22×C4—201no—
279C22×C4—201no—
280C22×C4—201no—
281C22×C4—201no—
282C22×C4C8×D512yes—
283C22×C4#67612yes—
284C22×C4#70912yes—
285C22×C4D4×D512yes—
286C22×C4D4×D511yescharacteristic
287C22×C4Q8×D511yescharacteristic
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—42no—
291C2×C8—202no—
292C2×C8—202no—
293C2×C8—202no—
294C4⋊C4—108no—
295C4⋊C4—104no—
296C4⋊C4—104no—
297C42—104no—
298C42—104no—
299C42—104no—
300C42—202no—
301C42—202no—
302C42—202no—
303C2×C5—21no—
304C2×C5—21no—
305C2×C5—21no—
306C2×C5—21no—
307C2×C5#145911yescharacteristic
308C2×C5#146111yescharacteristic
309C2×C5#146311yescharacteristic
310C2×C5#146411yescharacteristic
311C2×C5#179711yescharacteristic
312C2×C5#179911yescharacteristic
313C2×C5#180111yescharacteristic
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23#401811yescharacteristic
319C23D5×C22⋊C411yescharacteristic
320C23D5×C4⋊C411yescharacteristic
321C23C2×C8×D511yescharacteristic
322C23C2×#67611yescharacteristic
323C23D5×M1611yescharacteristic
324C23D5×M1611yescharacteristic
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—52no—
341C2×C4—52no—
342C2×C4—54no—
343C2×C4—54no—
344C2×C4—104no—
345C2×C4—104no—
346C2×C4—102no—
347C2×C4—101no—
348C2×C4—102no—
349C2×C4—101no—
350C2×C4—102no—
351C2×C4—102no—
352C2×C4—102no—
353C2×C4—102no—
354C2×C4—102no—
355C2×C4—101no—
356C2×C4—101no—
357C2×C4—102no—
358C2×C4—102no—
359C2×C4—202no—
360C2×C4—202no—
361C2×C4—202no—
362C2×C4—201no—
363C2×C4—201no—
364C2×C4—202no—
365C2×C4#403012yes—
366C2×C4#404212yes—
367C8—82no—
368C8—402no—
369C5#856011yescharacteristic, complemented, Sylow
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22#6495611yescharacteristic
383C22#6497411yescharacteristic
384C22#6499411yescharacteristic
385C22D5×C22⋊C811yescharacteristic
386C22#6501511yescharacteristic
387C22#6502911yescharacteristic
388C22D5×#9911yescharacteristic
389C22#6503411yescharacteristic
390C22D5×#10111yescharacteristic
391C22D5×C4⋊C811yescharacteristic
392C22#6512611yescharacteristic
393C4—22no—
394C4—22no—
395C4—42no—
396C4—42no—
397C4—104no—
398C4—102no—
399C4—102no—
400C4—104no—
401C4—202no—
402C2—21no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2#1059889511yescharacteristic
407C2#1059891211yescharacteristic
408C2#1059891811yescharacteristic
409C2#1059893711yescharacteristic
410C2#1059945511yescharacteristic
411C2#1059975211yescharacteristic
412C2#1059979011yescharacteristic
subgroupG/H
centerC23D5×C22⋊C4
commutatorC23×C5C22×C8
FrattiniC23×C4C22×D5
FittingC5×#1280C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22×C4
cosocleC23×C4×C5C23
hypercenter#1280D5
hypocenterC5#8560
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
33. C2×#683C8semidirect
180. C2×Dic5C4⋊C8semidirect
369. C5#8560semidirect

Maximal subgroups

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

subgroupindex
C2×#649382
C2×#646892
#106007012
C5×#12802
#105981042
#85605