Finite Group Databasebeta

← #12015315

Subgroups — #12015315

Order 1280.

434 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2929C211yesmaximal, characteristic
2#10602807C211yesmaximal, characteristic, complemented
3#10602805C211yesmaximal, characteristic, complemented
4#10602509C212yesmaximal
5#10598183C212yesmaximal, complemented
6C2×C5×#131C2211yescharacteristic
7C23×C5×C8C411yescharacteristic, complemented
8C5×#525C2211yescharacteristic
9C5×#435—21no—
10C5×#435—21no—
11C5×C8×D4—21no—
12C5×C8×D4—21no—
13C5×#424C411yescharacteristic, complemented
14C5×#408C2211yescharacteristic
15C5×#407C411yescharacteristic, complemented
16C5×#405C411yescharacteristic, complemented
17#65529C2212yes—
18#65526C2212yes—
19C2×#3951—21no—
20#65395—21no—
21#64780—21no—
22#64777—21no—
23#64759—22no—
24#64756—22no—
25#12805—51nomaximal, Sylow
26C2×C5×#41C2311yescharacteristic
27C23×C4×C5C2×C411yescharacteristic
28C5×#131—41no—
29C5×#131—41no—
30C2×C5×M16C2×C411yescharacteristic
31C2×C5×M16C2×C411yescharacteristic
32C2×C5×M16D411yescharacteristic
33C2×C5×M16D411yescharacteristic
34C22×C5×C8—21no—
35C22×C5×C8—21no—
36C22×C5×C8—41no—
37C22×C5×C8—41no—
38C22×C5×C8C2×C411yescharacteristic
39C22×C5×C8C2×C411yescharacteristic
40C22×C5×C8D411yescharacteristic
41C22×C5×C8D411yescharacteristic
42C5×#123D411yescharacteristic
43C5×#123Q811yescharacteristic
44C5×C22⋊Q8—21no—
45C5×#121—21no—
46C5×#120D411yescharacteristic
47C5×#120Q811yescharacteristic
48C4×C5×D4—21no—
49C4×C5×D4—21no—
50C5×#117C2×C411yescharacteristic
51#4072—22no—
52C2×#681—22no—
53C5×C4⋊C8—21no—
54C5×C4⋊C8—21no—
55C5×C22⋊C8—21no—
56C5×C22⋊C8—21no—
57C5×C22⋊C8—21no—
58C5×C22⋊C8—21no—
59C5×#97—21no—
60C4×C5×C8—21no—
61#3968—22no—
62#3966—22no—
63#3966—22no—
64#3965—22no—
65#3951—41no—
66#3951—41no—
67#3950—41no—
68#3949—41no—
69#2929D511yescharacteristic
70#2120—52no—
71#1813—51no—
72#1812—51no—
73#1395—52no—
74C24×C5C4⋊C411yescharacteristic
75C5×#41—41no—
76C5×#41—41no—
77C2×C5×Q8#4111yescharacteristic
78C2×C5×D4—21no—
79C2×C5×D4—21no—
80C2×C5×D4C2×D411yescharacteristic
81C2×C5×D4C2×Q811yescharacteristic
82C2×C5×D4#4111yescharacteristic
83C22×C4×C5—21no—
84C22×C4×C5—21no—
85C22×C4×C5—41no—
86C22×C4×C5—41no—
87C22×C4×C5C4⋊C411yescharacteristic
88C22×C4×C5C22×C411yescharacteristic
89C22×C4×C5C2×D411yescharacteristic
90C22×C4×C5C2×D411yescharacteristic
91C5×M16—41no—
92C5×M16—41no—
93C5×M16—41no—
94C5×M16—41no—
95C2×C5×C8—21no—
96C2×C5×C8—21no—
97C2×C5×C8—21no—
98C2×C5×C8—21no—
99C2×C5×C8—21no—
100C2×C5×C8—21no—
101C2×C5×C8—21no—
102C2×C5×C8—21no—
103C2×C5×C8—42no—
104C2×C5×C8—41no—
105C2×C5×C8—41no—
106C2×C5×C8—41no—
107C2×C5×C8C22⋊C411yescharacteristic
108C2×C5×C8C22⋊C411yescharacteristic
109C2×C5×C8C22⋊C411yescharacteristic
110C2×C5×C8C22⋊C411yescharacteristic
111C5×C4⋊C4—21no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—21no—
114C5×C22⋊C4—21no—
115C5×C22⋊C4—21no—
116C5×C22⋊C4—21no—
117C5×C22⋊C4—21no—
118C5×C22⋊C4C4⋊C411yescharacteristic
119C5×C22⋊C4C4⋊C411yescharacteristic
120C42×C5—21no—
121C22⋊Dic5—42no—
122C4⋊Dic5—42no—
123C4×Dic5—42no—
124#681—42no—
125#681—42no—
126C2×#168—42no—
127C2×#131C2×D511yescharacteristic
128C23×C8Dic511yescharacteristic, complemented
129#525C2×D511yescharacteristic
130#435—21no—
131#435—21no—
132C8×D4—21no—
133C8×D4—21no—
134C2×#108—101no—
135#427—101no—
136#424Dic511yescharacteristic, complemented
137#413—52no—
138#410—52no—
139#408C2×D511yescharacteristic
140#407Dic511yescharacteristic, complemented
141#405Dic511yescharacteristic, complemented
142#352—102no—
143AΣL(1,𝔽16)—102no—
144#338—101no—
145H(3,ℤ/4)—101no—
146C23×C5—21no—
147C23×C5—41no—
148C23×C5—42no—
149C23×C5C2×C4⋊C411yescharacteristic
150C23×C5#12111yescharacteristic
151C23×C5C22⋊Q811yescharacteristic
152C5×Q8—41no—
153C5×D4—41no—
154C5×D4—41no—
155C5×D4—41no—
156C5×D4—42no—
157C5×D4—42no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×C4×C5—21no—
163C2×C4×C5—21no—
164C2×C4×C5—21no—
165C2×C4×C5—21no—
166C2×C4×C5—21no—
167C2×C4×C5—42no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5C2×C22⋊C411yescharacteristic
172C2×C4×C5#11711yescharacteristic
173C2×C4×C5#12111yescharacteristic
174C2×C4×C5C22⋊Q811yescharacteristic
175C2×Dic5—82no—
176C5×C8—21no—
177C5×C8—21no—
178C5×C8—21no—
179C5×C8—41no—
180C5×C8—41no—
181C5×C8#9911yescharacteristic
182C5×C8#9911yescharacteristic
183#168—82no—
184C2×#41C22×D511yescharacteristic
185C23×C4C2×Dic511yescharacteristic
186#131—41no—
187#131—41no—
188C2×M16—102no—
189C2×M16C2×Dic511yescharacteristic
190C2×M16C2×Dic511yescharacteristic
191C2×M16C22⋊D511yescharacteristic
192C2×M16C22⋊D511yescharacteristic
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—41no—
196C22×C8—41no—
197C22×C8C2×Dic511yescharacteristic
198C22×C8C2×Dic511yescharacteristic
199C22×C8C22⋊D511yescharacteristic
200C22×C8C22⋊D511yescharacteristic
201#123Dic1011yescharacteristic
202#123D2011yescharacteristic
203C22⋊Q8—21no—
204#121—21no—
205#120Dic1011yescharacteristic
206#120D2011yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209#117—102no—
210#117C2×Dic511yescharacteristic
211#108—201no—
212#108—201no—
213#107—201no—
214#106—201no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217#101—102no—
218#100—102no—
219#99—102no—
220#99—102no—
221C22⋊C8—21no—
222C22⋊C8—21no—
223C22⋊C8—21no—
224C22⋊C8—21no—
225#97—21no—
226C4×C8—21no—
227C22×C5—22no—
228C22×C5—21no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5—41no—
232C22×C5—41no—
233C22×C5—41no—
234C22×C5—41no—
235C22×C5—42no—
236C22×C5—42no—
237C22×C5—41no—
238C22×C5#38011yescharacteristic
239C4×C5—21no—
240C4×C5—21no—
241C4×C5—21no—
242C4×C5—41no—
243C4×C5—41no—
244C4×C5—41no—
245C4×C5C2×#9911yescharacteristic
246C4×C5#41011yescharacteristic
247Dic5—162no—
248C24C4⋊Dic511yescharacteristic
249#41—41no—
250#41—41no—
251C2×Q8#70911yescharacteristic
252C2×D4—21no—
253C2×D4—21no—
254C2×D4C2×Dic1011yescharacteristic
255C2×D4C2×D2011yescharacteristic
256C2×D4#70911yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4C4⋊Dic511yescharacteristic
262C22×C4C22×Dic511yescharacteristic
263C22×C4C2×C22⋊D511yescharacteristic
264C22×C4C2×C22⋊D511yescharacteristic
265M16—41no—
266M16—41no—
267M16—41no—
268M16—41no—
269M16—202no—
270M16—202no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—42no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—202no—
284C2×C8C22⋊Dic511yescharacteristic
285C2×C8C22⋊Dic511yescharacteristic
286C2×C8C22⋊Dic511yescharacteristic
287C2×C8C22⋊Dic511yescharacteristic
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—202no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—202no—
297C22⋊C4C4⋊Dic511yescharacteristic
298C22⋊C4C4⋊Dic511yescharacteristic
299C42—21no—
300C42—202no—
301C2×C5—21no—
302C2×C5—41no—
303C2×C5—41no—
304C2×C5—42no—
305C2×C5—41no—
306C2×C5#179911yescharacteristic
307C23—21no—
308C23—41no—
309C23—42no—
310C23#407011yescharacteristic
311C23C2×C4⋊Dic511yescharacteristic
312C23#407611yescharacteristic
313Q8—41no—
314D4—41no—
315D4—41no—
316D4—41no—
317D4—42no—
318D4—42no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—402no—
333C2×C4#407011yescharacteristic
334C2×C4#407211yescharacteristic
335C2×C4#407611yescharacteristic
336C2×C4C2×C22⋊Dic511yescharacteristic
337C8—21no—
338C8—21no—
339C8—21no—
340C8—41no—
341C8—41no—
342C8—402no—
343C8#396611yescharacteristic
344C8#396611yescharacteristic
345C5#1280511yescharacteristic, complemented, Sylow
346C22—22no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—42no—
355C22—42no—
356C22—41no—
357C22#6550111yescharacteristic
358C4—21no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—802no—
365C4C2×#396611yescharacteristic
366C4#6552911yescharacteristic
367C2—21no—
368C2—41no—
369C2—42no—
370C2—41no—
371C2—41no—
372C2#1060241211yescharacteristic
subgroupG/H
centerC4#65529
commutatorC22×C4×C5C22×C4
FrattiniC2×#41C22×D5
FittingC5×#2929C2
socleC2×C5#1799
prime radicalC5×#525C22
cosocleC2×C5×#41C23
hypercenter#2929D5
hypocenterC5#12805
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C2×C8 ◁ C2×#131 ◁ #2929

Complements

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

NH ≅ G/Ntype
2. #10602807C2semidirect
3. #10602805C2semidirect
5. #10598183C2semidirect
7. C23×C5×C8C4semidirect
13. C5×#424C4semidirect
15. C5×#407C4semidirect
16. C5×#405C4semidirect
128. C23×C8Dic5semidirect
136. #424Dic5semidirect
140. #407Dic5semidirect
141. #405Dic5semidirect
345. C5#12805semidirect

Maximal subgroups

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

subgroupindex
C5×#29292
#106028072
#106028052
#106025092
#105981832
#128055