Finite Group Databasebeta

← #11991967

Subgroups — #11991967

Order 1280.

682 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×Dic5C211yesmaximal, characteristic
2C2×C5×#324C211yesmaximal, characteristic
3C2×#64748C211yesmaximal, characteristic
4#10600701C212yesmaximal
5#10598165C212yesmaximal
6C22×C5×C4⋊C4C2211yescharacteristic
7C22×C4⋊Dic5C411yescharacteristic
8C22×C4×Dic5C411yescharacteristic
9C22×C4×Dic5C411yescharacteristic
10C22×C4×Dic5C2211yescharacteristic
11C2×C5×C22⋊C8C2212yes—
12C2×#3963C411yescharacteristic
13C2×#3963C2211yescharacteristic
14C2×C22⋊#168C2212yes—
15C2×#3946—22no—
16C4⋊C4×Dic5—22no—
17C4⋊C4×Dic5—22no—
18C5×#324—22no—
19#64770—22no—
20#64748—22no—
21#8560—51nomaximal, Sylow
22C23×C4×C5C2×C411yescharacteristic
23C23×C4×C5C2×C411yescharacteristic
24C23×C4×C5C2311yescharacteristic
25C23×Dic5C2×C411yescharacteristic
26C23×Dic5C2×C411yescharacteristic
27C23×Dic5C2×C411yescharacteristic
28C23×Dic5C2×C411yescharacteristic
29C22×C5×C8—22no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—22no—
32C2×C5×C4⋊C4D412yes—
33C2×C5×C4⋊C4Q812yes—
34C2×C4⋊Dic5—22no—
35C2×C4⋊Dic5—22no—
36C2×C4⋊Dic5C814yescomplemented
37C2×C4×Dic5—22no—
38C2×C4×Dic5—21no—
39C2×C4×Dic5—21no—
40C2×C4×Dic5—22no—
41C2×C4×Dic5—21no—
42C2×C4×Dic5—21no—
43C2×C4×Dic5—42no—
44C2×C4×Dic5—42no—
45C2×C4×Dic5D412yes—
46C2×C4×Dic5D412yes—
47C22×#168—22no—
48C5×C22⋊C8—22no—
49C5×C22⋊C8—22no—
50#3963—22no—
51#3963—22no—
52C22⋊#168—22no—
53C22⋊#168—22no—
54#3946—44no—
55C2×C4×C4⋊C4—51no—
56#1797—52no—
57C2×#324—51no—
58C2×#324D511yescharacteristic
59#1280—52no—
60C24×C5C22×C411yescharacteristic
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—41no—
68C22×C4×C5—41no—
69C22×C4×C5—41no—
70C22×C4×C5—41no—
71C22×C4×C5C4⋊C412yes—
72C22×C4×C5C4⋊C412yes—
73C22×C4×C5C2×C812yes—
74C22×C4×C5M1612yes—
75C22×C4×C5C2×D412yes—
76C22×C4×C5C2×D411yescharacteristic
77C22×C4×C5C2×Q811yescharacteristic
78C22×C4×C5#4112yes—
79C22×Dic5—21no—
80C22×Dic5—21no—
81C22×Dic5—22no—
82C22×Dic5—22no—
83C22×Dic5—21no—
84C22×Dic5—21no—
85C22×Dic5—21no—
86C22×Dic5—21no—
87C22×Dic5—41no—
88C22×Dic5—41no—
89C22×Dic5—41no—
90C22×Dic5—41no—
91C22×Dic5—41no—
92C22×Dic5—41no—
93C22×Dic5C22⋊C412yes—
94C22×Dic5C22⋊C411yescharacteristic
95C22×Dic5C22⋊C411yescharacteristic
96C22×Dic5C2×C812yes—
97C22×Dic5C2×C812yes—
98C22×Dic5M1612yes—
99C22×Dic5M1612yes—
100C2×C5×C8—42no—
101C2×C5×C8—42no—
102C2×C5×C8—42no—
103C5×C4⋊C4—24no—
104C5×C4⋊C4—24no—
105C4⋊Dic5—28no—
106C4×Dic5—24no—
107C4×Dic5—24no—
108C4×Dic5—24no—
109C4×Dic5—42no—
110C4×Dic5—42no—
111C4×Dic5—42no—
112C2×#168—42no—
113C2×#168—42no—
114C2×#168—42no—
115C22×C4⋊C4—51no—
116C22×C4⋊C4C2×D511yescharacteristic
117C22×C42—51no—
118C22×C42—51no—
119C22×C42—51no—
120C2×C4⋊C8—102no—
121C2×C22⋊C8—52no—
122C2×C22⋊C8C2×D512yes—
123C4×C4⋊C4—102no—
124C4×C4⋊C4—102no—
125C2×#95—51no—
126C2×#95—51no—
127#336—102no—
128#324—22no—
129#324—102no—
130C23×C5—21no—
131C23×C5—21no—
132C23×C5—21no—
133C23×C5—21no—
134C23×C5C2×C22⋊C411yescharacteristic
135C23×C5C2×C4⋊C411yescharacteristic
136C23×C5#11711yescharacteristic
137C23×C5C22×C811yescharacteristic
138C23×C5C2×M1611yescharacteristic
139C23×C5C2×M1611yescharacteristic
140C23×C5C2×M1611yescharacteristic
141C2×C4×C5—22no—
142C2×C4×C5—22no—
143C2×C4×C5—22no—
144C2×C4×C5—22no—
145C2×C4×C5—22no—
146C2×C4×C5—22no—
147C2×C4×C5—22no—
148C2×C4×C5—22no—
149C2×C4×C5—22no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5—42no—
153C2×C4×C5—42no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5—42no—
157C2×C4×C5C4⋊C814yescomplemented
158C2×C4×C5#12112yes—
159C2×C4×C5C22⋊Q812yes—
160C2×Dic5—24no—
161C2×Dic5—24no—
162C2×Dic5—21no—
163C2×Dic5—21no—
164C2×Dic5—22no—
165C2×Dic5—21no—
166C2×Dic5—21no—
167C2×Dic5—22no—
168C2×Dic5—22no—
169C2×Dic5—22no—
170C2×Dic5—42no—
171C2×Dic5—42no—
172C2×Dic5—42no—
173C2×Dic5—42no—
174C2×Dic5—41no—
175C2×Dic5—41no—
176C2×Dic5—41no—
177C2×Dic5—41no—
178C2×Dic5—42no—
179C2×Dic5—42no—
180C2×Dic5C22⋊C814yes—
181C2×Dic5#9912yes—
182C2×Dic5#10112yes—
183C5×C8—82no—
184#168—82no—
185C23×C4—51no—
186C23×C4—51no—
187C23×C4—51no—
188C23×C4—51no—
189C23×C4C4×D511yescharacteristic
190C23×C4C4×D511yescharacteristic
191C23×C4C22×D511yescharacteristic
192C22×C8—22no—
193C22×C8—102no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—54no—
197C2×C4⋊C4—102no—
198C2×C4⋊C4—102no—
199C2×C4⋊C4Dic1012yes—
200C2×C4⋊C4C22⋊D512yes—
201C2×C42—52no—
202C2×C42—52no—
203C2×C42—101no—
204C2×C42—101no—
205C2×C42—102no—
206C2×C42—102no—
207C2×C42—101no—
208C2×C42—101no—
209C2×C42—202no—
210C2×C42—202no—
211C4⋊C8—204no—
212C22⋊C8—22no—
213C22⋊C8—22no—
214C22⋊C8—102no—
215C22⋊C8—102no—
216#95—102no—
217#95—102no—
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—21no—
229C22×C5—21no—
230C22×C5#38011yescharacteristic
231C22×C5C2×C22⋊C811yescharacteristic
232C22×C5#40711yescharacteristic
233C22×C5C2×#9911yescharacteristic
234C22×C5#41011yescharacteristic
235C22×C5C2×#10111yescharacteristic
236C22×C5#41311yescharacteristic
237C22×C5C2×C4⋊C811yescharacteristic
238C22×C5#42311yescharacteristic
239C22×C5#43111yescharacteristic
240C22×C5#43211yescharacteristic
241C4×C5—24no—
242C4×C5—22no—
243C4×C5—22no—
244C4×C5—42no—
245Dic5—24no—
246Dic5—22no—
247Dic5—22no—
248Dic5—42no—
249Dic5—42no—
250C24C2×C4×D511yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—52no—
262C22×C4—51no—
263C22×C4—51no—
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—201no—
277C22×C4—201no—
278C22×C4—201no—
279C22×C4—201no—
280C22×C4—201no—
281C22×C4—201no—
282C22×C4C8×D512yes—
283C22×C4#67612yes—
284C22×C4#68312yes—
285C22×C4#68312yes—
286C22×C4C2×Dic1011yescharacteristic
287C22×C4D4×D512yes—
288C22×C4#71112yes—
289C22×C4C2×C22⋊D511yescharacteristic
290C2×C8—42no—
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—202no—
294C2×C8—202no—
295C2×C8—202no—
296C4⋊C4—24no—
297C4⋊C4—24no—
298C4⋊C4—108no—
299C42—104no—
300C42—104no—
301C42—104no—
302C42—202no—
303C42—202no—
304C42—202no—
305C2×C5—21no—
306C2×C5—21no—
307C2×C5—21no—
308C2×C5—21no—
309C2×C5#145911yescharacteristic
310C2×C5#146111yescharacteristic
311C2×C5#146311yescharacteristic
312C2×C5#146411yescharacteristic
313C2×C5#179711yescharacteristic
314C2×C5#179911yescharacteristic
315C2×C5#180111yescharacteristic
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23#402311yescharacteristic
321C23D5×C22⋊C411yescharacteristic
322C23C2×C8×D511yescharacteristic
323C23C2×#67611yescharacteristic
324C23D5×M1611yescharacteristic
325C23D5×M1611yescharacteristic
326C23C2×#68311yescharacteristic
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—52no—
344C2×C4—52no—
345C2×C4—54no—
346C2×C4—104no—
347C2×C4—104no—
348C2×C4—102no—
349C2×C4—101no—
350C2×C4—101no—
351C2×C4—102no—
352C2×C4—101no—
353C2×C4—101no—
354C2×C4—102no—
355C2×C4—102no—
356C2×C4—202no—
357C2×C4—202no—
358C2×C4—202no—
359C2×C4—202no—
360C2×C4—201no—
361C2×C4—201no—
362C2×C4—201no—
363C2×C4—201no—
364C2×C4—202no—
365C2×C4—202no—
366C2×C4#394614yescomplemented
367C2×C4#402412yes—
368C2×C4#408512yes—
369C8—82no—
370C8—402no—
371C5#856011yescharacteristic, complemented, Sylow
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22#6500711yescharacteristic
385C22#6500811yescharacteristic
386C22D5×C22⋊C811yescharacteristic
387C22#6501511yescharacteristic
388C22#6502911yescharacteristic
389C22D5×#9911yescharacteristic
390C22D5×#10111yescharacteristic
391C22#6504011yescharacteristic
392C22#6523111yescharacteristic
393C22C2×#394611yescharacteristic
394C22#6540711yescharacteristic
395C4—22no—
396C4—22no—
397C4—24no—
398C4—42no—
399C4—104no—
400C4—102no—
401C4—102no—
402C4—202no—
403C4—202no—
404C2—21no—
405C2—21no—
406C2—21no—
407C2—21no—
408C2#1059891811yescharacteristic
409C2#1059891911yescharacteristic
410C2#1059893611yescharacteristic
411C2#1059893711yescharacteristic
412C2#1060070111yescharacteristic
413C2#1060082111yescharacteristic
414C2#1060089011yescharacteristic
subgroupG/H
centerC23D5×C22⋊C4
commutatorC23×C5C22×C8
FrattiniC23×C4C22×D5
FittingC2×C5×#324C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22×C4
cosocleC23×C4×C5C23
hypercenterC2×#324D5
hypocenterC5#8560
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
36. C2×C4⋊Dic5C8semidirect
157. C2×C4×C5C4⋊C8semidirect
366. C2×C4#3946semidirect
371. C5#8560semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×Dic52
C2×C5×#3242
C2×#647482
#106007012
#105981652
#85605