Finite Group Databasebeta

← #12018455

Subgroups — #12018455

Order 1280.

498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65404C211yesmaximal, characteristic
2C5×#1808C211yesmaximal, characteristic, complemented
3C2×C22⋊#672C211yesmaximal, characteristic, complemented
4C2×#64711C211yesmaximal, characteristic, complemented
5C2×#64711C211yesmaximal, characteristic, complemented
6C2×#64709C211yesmaximal, characteristic, complemented
7#10598213C211yesmaximal, characteristic, complemented
8C23×C5×C8C2211yescharacteristic
9C2×#4076—21no—
10C22×D40C2211yescharacteristic
11C2×C5×#107C2211yescharacteristic
12C2×C5×#107C2211yescharacteristic
13C5×#380—21no—
14#65404—22no—
15#65404—22no—
16C2×#3953—21no—
17C2×#3950C2211yescharacteristic
18C22×#672C2211yescharacteristic
19C22×#672C2211yescharacteristic
20C5×#340—21no—
21C22⋊#672—22no—
22#64711—22no—
23#64711—22no—
24#64709—22no—
25#13380—51nomaximal, Sylow
26C23×C4×C5D411yescharacteristic
27C22×C22⋊D5—41no—
28C22×D20—21no—
29C22×C5×C8—21no—
30C22×C5×C8—21no—
31C22×C5×C8—21no—
32C22×C5×C8—21no—
33C22×C5×C8—21no—
34C22×C5×C8—21no—
35C22×C5×C8D411yescharacteristic
36C22×C5×C8C2311yescharacteristic
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4—21no—
39C2×C5×C22⋊C4—41no—
40#4076—24no—
41#4076—42no—
42C2×#685—41no—
43C2×C4⋊Dic5—21no—
44C2×D40—21no—
45C2×D40—21no—
46C2×D40—21no—
47C2×D40—21no—
48C2×D40—21no—
49C2×D40D412yes—
50C5×#107—21no—
51C5×#107—21no—
52C5×#107—21no—
53C5×#107—21no—
54C5×#95—41no—
55#3953—24no—
56#3950—21no—
57#3950D412yes—
58C2×#672—21no—
59C2×#672—21no—
60C2×#672—21no—
61C2×#672—21no—
62C2×#672—21no—
63C2×#672D412yescomplemented
64C2×#466—51no—
65C2×#366—51no—
66C2×#357—51no—
67C2×#357—51no—
68C2×C22⋊C16—51no—
69#1808D511yescharacteristic, complemented
70#1380—51no—
71C24×C5D811yescharacteristic
72C23×D5—41no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5—21no—
76C22×C4×C5—21no—
77C22×C4×C5—21no—
78C22×C4×C5—21no—
79C22×C4×C5—41no—
80C22×C4×C5—41no—
81C22×C4×C5D811yescharacteristic
82C22×C4×C5C2×D411yescharacteristic
83C2×C22⋊D5—44no—
84C2×C22⋊D5—82no—
85C2×C22⋊D5—82no—
86C22×Dic5—41no—
87C2×D20—22no—
88C2×D20—41no—
89C2×D20—41no—
90C2×D20—41no—
91C2×D20—41no—
92C2×D20—41no—
93C2×C5×C8—21no—
94C2×C5×C8—21no—
95C2×C5×C8—21no—
96C2×C5×C8—41no—
97C2×C5×C8—41no—
98C2×C5×C8—41no—
99C2×C5×C8—41no—
100C2×C5×C8C2×D411yescharacteristic
101C2×C5×C8C2×D411yescharacteristic
102C2×C5×C8C2×D411yescharacteristic
103C2×C5×C8#4111yescharacteristic
104C2×C5×C8#4111yescharacteristic
105C2×C5×C8#4111yescharacteristic
106C5×C4⋊C4—41no—
107C5×C4⋊C4—41no—
108C5×C4⋊C4—41no—
109C5×C4⋊C4—41no—
110C5×C22⋊C4—82no—
111#685—44no—
112C4⋊Dic5—22no—
113C4⋊Dic5—41no—
114D40—22no—
115D40—22no—
116D40—41no—
117D40—41no—
118#672—22no—
119#672—41no—
120C22×D8—51no—
121C23×C8C2×D511yescharacteristic
122C2×#121—101no—
123C22×C16—51no—
124C22×C16—51no—
125#466—102no—
126#466—102no—
127C2×#107—51no—
128C2×#107C2×D511yescharacteristic
129C2×#107C2×D511yescharacteristic
130C2×#102—101no—
131#380—21no—
132#366—102no—
133#357—102no—
134#357—102no—
135C22⋊C16—102no—
136#340—21no—
137C23×C5—21no—
138C23×C5—21no—
139C23×C5—21no—
140C23×C5—21no—
141C23×C5—21no—
142C23×C5—21no—
143C23×C5D1612yes—
144C23×C5C2×D811yescharacteristic
145C22×D5—42no—
146C22×D5—81no—
147C22×D5—81no—
148C22×D5—81no—
149C22×D5—81no—
150C22×D5—81no—
151C22×D5—81no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—81no—
160C2×C4×C5—81no—
161C2×C4×C5—81no—
162C2×C4×C5—81no—
163C2×C4×C5—81no—
164C2×C4×C5—81no—
165C2×C4×C5#12011yescharacteristic
166C2×C4×C5#12111yescharacteristic
167C2×C4×C5#12311yescharacteristic
168C2×C4×C5#13511yescharacteristic
169C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C5#13711yescharacteristic
171C22⋊D5—88no—
172C2×Dic5—42no—
173C2×Dic5—81no—
174C2×Dic5—81no—
175D20—42no—
176D20—42no—
177D20—81no—
178D20—81no—
179C5×C8—41no—
180C5×C8#12111yescharacteristic
181C5×C8#12111yescharacteristic
182C5×C8#12311yescharacteristic
183C5×C8#12411yescharacteristic
184C22×D4—101no—
185C22×D4—201no—
186C23×C4C22⋊D511yescharacteristic
187C2×D8—52no—
188C2×D8—101no—
189C2×D8—101no—
190C2×D8—101no—
191C2×D8—101no—
192C2×D8—101no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8C22⋊D511yescharacteristic
200C22×C8C22×D511yescharacteristic
201#121—104no—
202#121—202no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—101no—
206C2×C22⋊C4—41no—
207C2×C22⋊C4—201no—
208C2×C16—52no—
209C2×C16—101no—
210C2×C16—101no—
211C2×C16—101no—
212C2×C16—101no—
213C2×C16—101no—
214#107—21no—
215#107—21no—
216#107—21no—
217#107—21no—
218#107—52no—
219#107—101no—
220#102—104no—
221#95—41no—
222C22×C5—22no—
223C22×C5—22no—
224C22×C5—22no—
225C22×C5—41no—
226C22×C5—41no—
227C22×C5—41no—
228C22×C5—41no—
229C22×C5#44711yescharacteristic
230C22×C5#46611yescharacteristic
231C22×C5#48011yescharacteristic
232C22×C5C2×D1611yescharacteristic
233C22×C5#50811yescharacteristic
234C22×C5#50911yescharacteristic
235C22×C5#51011yescharacteristic
236C2×D5—82no—
237C2×D5—82no—
238C2×D5—82no—
239C2×D5—161no—
240C2×D5—161no—
241C2×D5—161no—
242C2×D5—161no—
243C4×C5—41no—
244C4×C5—161no—
245C4×C5—161no—
246C4×C5#39411yescharacteristic
247C4×C5#45211yescharacteristic
248C4×C5#46811yescharacteristic
249C4×C5#48211yescharacteristic
250Dic5—82no—
251C24—201no—
252C24#68611yescharacteristic
253C2×D4—102no—
254C2×D4—204no—
255C2×D4—201no—
256C2×D4—201no—
257C2×D4—201no—
258C2×D4—201no—
259C2×D4—201no—
260C2×D4—402no—
261C2×D4—402no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—201no—
271C22×C4#68611yescharacteristic
272C22×C4C2×C22⋊D511yescharacteristic
273D8—102no—
274D8—102no—
275D8—201no—
276D8—201no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8#70911yescharacteristic
285C2×C8#70911yescharacteristic
286C2×C8D4×D511yescharacteristic
287C2×C8D4×D511yescharacteristic
288C2×C8D4×D511yescharacteristic
289C2×C8#71111yescharacteristic
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—102no—
295C4⋊C4—201no—
296C22⋊C4—82no—
297C22⋊C4—204no—
298C16—102no—
299C16—201no—
300C2×C5—42no—
301C2×C5#203311yescharacteristic
302C2×C5#218411yescharacteristic
303C2×C5#218911yescharacteristic
304C2×C5#221511yescharacteristic
305C2×C5#222011yescharacteristic
306C2×C5#223211yescharacteristic
307C2×C5#223411yescharacteristic
308D5—162no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—202no—
316C23—401no—
317C23—401no—
318C23—401no—
319C23—401no—
320C23—401no—
321C23—401no—
322C23#395812yes—
323C23C2×#68611yescharacteristic
324D4—202no—
325D4—202no—
326D4—408no—
327D4—401no—
328D4—401no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—202no—
343C2×C4—401no—
344C2×C4—401no—
345C2×C4#407511yescharacteristic
346C2×C4#408311yescharacteristic
347C2×C4#408511yescharacteristic
348C2×C4#408811yescharacteristic
349C2×C4#409511yescharacteristic
350C2×C4#409611yescharacteristic
351C8—41no—
352C8#402911yescharacteristic
353C8#403011yescharacteristic
354C8#403011yescharacteristic
355C8#403111yescharacteristic
356C5#1338011yescharacteristic, complemented, Sylow
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—402no—
365C22—402no—
366C22—402no—
367C22—801no—
368C22—801no—
369C22—801no—
370C22—801no—
371C22#6525611yescharacteristic
372C22#6532511yescharacteristic
373C22#6532711yescharacteristic
374C22C2×#395811yescharacteristic
375C22#6546811yescharacteristic
376C22#6548211yescharacteristic
377C22#6548311yescharacteristic
378C4—41no—
379C4—161no—
380C4—161no—
381C4—402no—
382C4#6524811yescharacteristic
383C4#6529211yescharacteristic
384C4#6533611yescharacteristic
385C4#6533811yescharacteristic
386C2—42no—
387C2—802no—
388C2#1060031611yescharacteristic
389C2#1060139211yescharacteristic
390C2#1060144611yescharacteristic
391C2#1060186411yescharacteristic
392C2#1060186811yescharacteristic
393C2#1060187711yescharacteristic
394C2#1060187911yescharacteristic
subgroupG/H
centerC23C2×#686
commutator, cosocleC22×C5×C8C23
FrattiniC22×C8C22×D5
FittingC5×#1808C2
socleC23×C5C2×D8
prime radicalC2×#65404C2
hypercenter#1808D5
hypocenterC5#13380
LCSG ▷ C22×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ #1808

Complements

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

NH ≅ G/Ntype
2. C5×#1808C2semidirect
3. C2×C22⋊#672C2semidirect
4. C2×#64711C2semidirect
5. C2×#64711C2semidirect
6. C2×#64709C2semidirect
7. #10598213C2semidirect
63. C2×#672D4semidirect
69. #1808D5semidirect
356. C5#13380semidirect

Maximal subgroups

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

subgroupindex
C2×#654042
C5×#18082
C2×C22⋊#6722
C2×#647112
C2×#647092
#105982132
#133805