Finite Group Databasebeta

← #12254134

Subgroups — #12254134

Order 1280.

580 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#427C211yesmaximal, characteristic
2C2×#65405C211yesmaximal, characteristic
3#10602756C211yesmaximal, characteristic
4#10601448C214yesmaximal, complemented
5#10601447C212yesmaximal, complemented
6#10601442C212yesmaximal, complemented
7#10601396C212yesmaximal, complemented
8#10601395C212yesmaximal, complemented
9C23×C5×C8C2211yescharacteristic
10C2×C5×#117—21no—
11C2×#4070—21no—
12C22×Dic20C2211yescharacteristic
13C5×#427—21no—
14C5×#427—21no—
15C5×#427C2212yes—
16C5×#427C2212yes—
17C2×C5×#107C2211yescharacteristic
18C2×C5×#107C2211yescharacteristic
19C2×C5×#106—21no—
20#65405—21no—
21#65405—21no—
22#65405C2212yes—
23#65405C2212yes—
24C2×#3950C2211yescharacteristic
25C2×#3948—21no—
26C2×#3944C2212yes—
27C22⋊#672C2212yes—
28C22⋊#672C2212yes—
29#64712C2214yescomplemented
30#64712C2214yescomplemented
31#64710C2214yescomplemented
32#64709C2214yescomplemented
33#33649—51nomaximal, Sylow
34C23×C4×C5D411yescharacteristic
35C22×Dic10—21no—
36C22×C5×C8—24no—
37C22×C5×C8D411yescharacteristic
38C22×C5×C8D411yescharacteristic
39C22×C5×C8D411yescharacteristic
40C22×C5×C8C2311yescharacteristic
41C22×C5×C8C2311yescharacteristic
42C22×C5×C8C2311yescharacteristic
43C5×#117—22no—
44C5×#117—22no—
45C5×#117—41no—
46C5×#117—41no—
47C2×C5×C4⋊C4—21no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C22⋊C4—41no—
50C2×C42×C5—41no—
51C2×C22⋊Dic5—41no—
52C2×C4⋊Dic5—21no—
53#4070—22no—
54#4070—22no—
55#4070—41no—
56#4070—41no—
57C2×#683—41no—
58C2×Dic20—24no—
59C2×Dic20—21no—
60C2×Dic20C2312yes—
61C5×#107—21no—
62C5×#107—21no—
63C5×#107C2312yes—
64C5×#107C2312yes—
65C5×#106—22no—
66C5×#106—22no—
67#3950—21no—
68#3950C2312yes—
69#3948—22no—
70#3948—22no—
71#3944—24no—
72C2×#672C2314yes—
73C2×#467—51no—
74C2×#427D511yescharacteristic
75#2237—54no—
76#2236—52no—
77#2235—52no—
78#2159—52no—
79#2141—52no—
80#2112—51no—
81C24×C5D811yescharacteristic
82C22×C4×C5—22no—
83C22×C4×C5—22no—
84C22×C4×C5—41no—
85C22×C4×C5—41no—
86C22×C4×C5D811yescharacteristic
87C22×C4×C5D811yescharacteristic
88C22×C4×C5D811yescharacteristic
89C22×C4×C5C2×D411yescharacteristic
90C22×C4×C5C2×D411yescharacteristic
91C22×C4×C5C2×D411yescharacteristic
92C22×Dic5—41no—
93C22×Dic5—41no—
94C2×Dic10—22no—
95C2×Dic10—42no—
96C2×Dic10—42no—
97C2×Dic10—41no—
98C2×C5×C8—22no—
99C2×C5×C8—22no—
100C2×C5×C8—22no—
101C2×C5×C8—22no—
102C2×C5×C8—22no—
103C2×C5×C8C2×D411yescharacteristic
104C2×C5×C8C2×D411yescharacteristic
105C2×C5×C8C2×D411yescharacteristic
106C2×C5×C8#4114yes—
107C2×C5×C8C2411yescharacteristic
108C5×C4⋊C4—22no—
109C5×C4⋊C4—22no—
110C5×C4⋊C4—41no—
111C5×C4⋊C4—41no—
112C5×C22⋊C4—42no—
113C5×C22⋊C4—42no—
114C42×C5—42no—
115C42×C5—42no—
116C22⋊Dic5—42no—
117C22⋊Dic5—42no—
118C4⋊Dic5—22no—
119C4⋊Dic5—41no—
120#683—42no—
121#683—42no—
122Dic20—24no—
123Dic20—42no—
124#672—24no—
125C22×Q16—51no—
126C23×C8C2×D511yescharacteristic
127C2×C22⋊Q8—101no—
128C2×#117—21no—
129C2×M32—52no—
130#467—52no—
131#467—52no—
132#467—101no—
133#467—101no—
134#427—21no—
135#427—21no—
136#427C2×D512yes—
137#427C2×D512yes—
138C2×#107—51no—
139C2×#107C2×D511yescharacteristic
140C2×#107C2×D511yescharacteristic
141C2×#106—21no—
142C2×#103—101no—
143#367—54no—
144#366—54no—
145#358—54no—
146#358—54no—
147C22⋊C16—52no—
148C22⋊C16—52no—
149C23×C5—22no—
150C23×C5—22no—
151C23×C5—41no—
152C23×C5C2×D811yescharacteristic
153C23×C5C2×D811yescharacteristic
154C23×C5C2×D811yescharacteristic
155C2×C4×C5—22no—
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—42no—
163C2×C4×C5—42no—
164C2×C4×C5—82no—
165C2×C4×C5—82no—
166C2×C4×C5#12312yes—
167C2×C4×C5C2×D811yescharacteristic
168C2×C4×C5C2×D811yescharacteristic
169C2×C4×C5C2×D811yescharacteristic
170C2×C4×C5#13712yes—
171C2×C4×C5C22×D411yescharacteristic
172C2×Dic5—42no—
173C2×Dic5—42no—
174C2×Dic5—82no—
175C2×Dic5—82no—
176Dic10—42no—
177Dic10—42no—
178Dic10—82no—
179C5×C8—21no—
180C5×C8—21no—
181C5×C8#12312yes—
182C5×C8C2×#4112yes—
183C22×Q8—101no—
184C23×C4C22⋊D511yescharacteristic
185C2×Q16—52no—
186C2×Q16—104no—
187C2×Q16—101no—
188C22×C8—24no—
189C22×C8C22⋊D511yescharacteristic
190C22×C8C22⋊D511yescharacteristic
191C22×C8C22⋊D511yescharacteristic
192C22×C8C22×D511yescharacteristic
193C22×C8C22×D511yescharacteristic
194C22×C8C22×D511yescharacteristic
195C22⋊Q8—102no—
196C22⋊Q8—102no—
197C22⋊Q8—201no—
198C22⋊Q8—201no—
199#117—22no—
200#117—22no—
201#117—41no—
202#117—41no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—101no—
206C2×C4⋊C4—201no—
207C2×C22⋊C4—41no—
208C2×C22⋊C4—201no—
209C2×C42—41no—
210M32—104no—
211C2×C16—54no—
212#107—21no—
213#107—21no—
214#107—52no—
215#107—101no—
216#107C22×D512yes—
217#107C22×D512yes—
218#106—22no—
219#106—22no—
220#103—102no—
221#103—102no—
222C22×C5—21no—
223C22×C5—21no—
224C22×C5—21no—
225C22×C5—21no—
226C22×C5—21no—
227C22×C5—21no—
228C22×C5—21no—
229C22×C5—44no—
230C22×C5#48012yes—
231C22×C5#51012yes—
232C22×C5C22×D811yescharacteristic
233C4×C5—21no—
234C4×C5—21no—
235C4×C5—82no—
236C4×C5—82no—
237C4×C5#48012yes—
238C4×C5C2×#12311yescharacteristic
239C4×C5C2×#13711yescharacteristic
240Dic5—82no—
241Dic5—82no—
242C24#68611yescharacteristic
243C2×Q8—102no—
244C2×Q8—201no—
245C2×Q8—202no—
246C2×Q8—202no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—201no—
252C22×C4—201no—
253C22×C4#68611yescharacteristic
254C22×C4#68611yescharacteristic
255C22×C4#68611yescharacteristic
256C22×C4C2×C22⋊D511yescharacteristic
257C22×C4C2×C22⋊D511yescharacteristic
258C22×C4C2×C22⋊D511yescharacteristic
259Q16—104no—
260Q16—202no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8#70914yes—
267C2×C8C2×C22⋊D511yescharacteristic
268C2×C8C2×C22⋊D511yescharacteristic
269C2×C8C2×C22⋊D511yescharacteristic
270C2×C8C23×D511yescharacteristic
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—102no—
276C4⋊C4—201no—
277C4⋊C4—202no—
278C4⋊C4—202no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—202no—
282C22⋊C4—202no—
283C42—42no—
284C42—42no—
285C16—104no—
286C2×C5—22no—
287C2×C5—22no—
288C2×C5—41no—
289C2×C5C2×#48011yescharacteristic
290C2×C5C2×#51011yescharacteristic
291C2×C5#341411yescharacteristic
292C23—22no—
293C23—22no—
294C23—41no—
295C23C2×#68611yescharacteristic
296C23C2×#68611yescharacteristic
297C23C2×#68611yescharacteristic
298Q8—202no—
299Q8—202no—
300Q8—402no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—202no—
313C2×C4—202no—
314C2×C4—402no—
315C2×C4—402no—
316C2×C4#407512yes—
317C2×C4C2×#68611yescharacteristic
318C2×C4C2×#68611yescharacteristic
319C2×C4C2×#68611yescharacteristic
320C2×C4#408812yes—
321C2×C4C22×C22⋊D511yescharacteristic
322C8—21no—
323C8—21no—
324C8#407512yes—
325C8C2×#70912yes—
326C5#3364911yescharacteristic, complemented, Sylow
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—44no—
335C22#6525612yes—
336C22#6548412yes—
337C22C22×#68611yescharacteristic
338C4—21no—
339C4—21no—
340C4—82no—
341C4—82no—
342C4—402no—
343C4—402no—
344C4#6525612yes—
345C4C2×#407511yescharacteristic
346C4C2×#408811yescharacteristic
347C2—22no—
348C2—22no—
349C2—41no—
350C2C2×#6525611yescharacteristic
351C2#1061562511yescharacteristic
352C2C2×#6548411yescharacteristic
subgroupG/H
centerC22C22×#686
commutator, cosocleC2×C5×C8C24
FrattiniC2×C8C23×D5
FittingC2×C5×#427C2
socleC22×C5C22×D8
prime radicalC24×C5D8
hypercenterC2×#427D5
hypocenterC5#33649
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
4. #10601448C2semidirect
5. #10601447C2semidirect
6. #10601442C2semidirect
7. #10601396C2semidirect
8. #10601395C2semidirect
29. #64712C22semidirect
30. #64712C22semidirect
31. #64710C22semidirect
32. #64709C22semidirect
326. C5#33649semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4272
C2×#654052
#106027562
#106014482
#106014472
#106014422
#106013962
#106013952
#336495