Finite Group Databasebeta

← #13031483

Subgroups — #13031483

Order 1280.

610 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10617190C212yesmaximal
2C8×#713C211yesmaximal, characteristic
3#10604017C214yesmaximal, complemented
4#10604015C212yesmaximal, complemented
5#10603821C212yesmaximal, complemented
6#10603819C211yesmaximal, characteristic, complemented
7#10603814C212yesmaximal, complemented
8D5⋊#335C211yesmaximal, characteristic, complemented
9C4×#713C2211yescharacteristic
10#65787—22no—
11#65706—24no—
12#65701—22no—
13#65683C2214yes—
14#65681C2212yes—
15#65680C2214yes—
16D5⋊(C4⋊C8)C2212yes—
17C5×C8×Q8C411yescharacteristic
18Q8×#168C411yescharacteristic
19#65123C411yescharacteristic
20#65123C412yes—
21#65122C2211yescharacteristic
22#65122C2212yes—
23C8×D20C411yescharacteristic
24C8×D20C412yes—
25C4×C8×D5C2211yescharacteristic
26C4×C8×D5C2212yes—
27#64884C2211yescharacteristic
28#64884C2211yescharacteristic
29#64884C2212yes—
30#64884C2212yes—
31#64883C2214yes—
32#64882C2212yes—
33#64881C2214yes—
34#17829—51nomaximal, Sylow
35C2×#713D411yescharacteristic
36C2×#700—22no—
37C2×D5⋊C8—22no—
38C4×C5×Q8C2×C411yescharacteristic
39Q8×Dic5Q811yescharacteristic
40C2×C8×D5C2×C411yescharacteristic
41C2×C8×D5C2×C412yes—
42C2×C8×D5C2×C411yescharacteristic
43C2×C8×D5C2×C412yes—
44#4039Q812yes—
45#4039Q811yescharacteristic
46#4038D411yescharacteristic
47#4038D412yes—
48C4×D20C2×C412yes—
49C4×D20C2×C411yescharacteristic
50C42×D5C2311yescharacteristic
51C42×D5C2312yes—
52#4004—22no—
53#4003—24no—
54#4003—24no—
55#4002—24no—
56C4⋊#170—22no—
57C4⋊#170C2312yes—
58C4⋊#170C2314yes—
59C4⋊#170C2312yes—
60C4×#170—24no—
61C5×C4⋊C8C2×C411yescharacteristic
62C5×C4⋊C8C2×C412yes—
63C4×C5×C8C2×C411yescharacteristic
64C4×C5×C8C2×C412yes—
65#3952C2×C412yes—
66#3952C2×C412yes—
67#3952C2×C412yes—
68C8×Dic5C2312yes—
69C8×Dic5C2311yescharacteristic
70C8×Dic5C2311yescharacteristic
71C4⋊#168C2×C411yescharacteristic
72C4⋊#168C2×C412yes—
73C4×#168C2×C411yescharacteristic
74C4×#168C2×C412yes—
75C8×#41—51no—
76#2925—52no—
77#1572—54no—
78#1570—52no—
79#1568—52no—
80#1567—51no—
81#1564—52no—
82C2×#335—51no—
83C2×C5×Q8C4⋊C411yescharacteristic
84#713—22no—
85#713—22no—
86C2×D20C4⋊C412yes—
87C2×D20C4⋊C411yescharacteristic
88C2×C4×D5C22×C412yes—
89C2×C4×D5C22×C411yescharacteristic
90C2×C4×D5C2×D412yes—
91C2×C4×D5C2×D411yescharacteristic
92C2×C4×D5C2×Q812yes—
93C2×C4×D5C2×Q811yescharacteristic
94C2×#170—22no—
95C2×#170—22no—
96C2×#170—24no—
97#700—44no—
98D5⋊C8—44no—
99C2×C5×C8C22×C412yes—
100C2×C5×C8C22×C411yescharacteristic
101C2×C5×C8C22×C411yescharacteristic
102C5×C4⋊C4C4⋊C412yes—
103C5×C4⋊C4C4⋊C411yescharacteristic
104C42×C5C22×C412yes—
105C42×C5C22×C411yescharacteristic
106#685C4⋊C412yes—
107#685C4⋊C412yes—
108#685C4⋊C412yes—
109C4⋊Dic5C4⋊C412yes—
110C4⋊Dic5C4⋊C411yescharacteristic
111C4×Dic5C2×D412yes—
112C4×Dic5C2×D411yescharacteristic
113C4×Dic5C2×Q812yes—
114C4×Dic5C2×Q811yescharacteristic
115C4×Dic5C2411yescharacteristic
116C2×#168C22×C412yes—
117C2×#168C22×C411yescharacteristic
118C2×#168C22×C411yescharacteristic
119C8×D5—22no—
120C8×D5—24no—
121C8×D5—41no—
122C8×D5—42no—
123C4×#41—51no—
124C8×Q8—51no—
125C8×Q8AGL(1,𝔽5)11yescharacteristic
126C8×D4—51no—
127C8×D4—52no—
128C8×D4—51no—
129C8×D4—52no—
130#433—104no—
131#432—54no—
132#431—51no—
133#431—52no—
134#431—54no—
135#423—52no—
136C2×C4⋊C8—52no—
137#408—102no—
138#405—102no—
139C2×C4×C8—51no—
140C2×C4×C8—52no—
141#335—51no—
142#335—51no—
143#335—52no—
144#335—52no—
145#335—52no—
146#334—54no—
147#334—54no—
148C22×D5C2×C4⋊C412yes—
149C22×D5C2×C4⋊C411yescharacteristic
150C5×Q8—22no—
151C2×C4×C5C2×C4⋊C412yes—
152C2×C4×C5C2×C4⋊C411yescharacteristic
153C2×C4×C5C2×C4⋊C412yes—
154C2×C4×C5C2×C4⋊C411yescharacteristic
155C2×C4×C5C23×C411yescharacteristic
156C2×Dic5C2×C4⋊C412yes—
157C2×Dic5C2×C4⋊C411yescharacteristic
158C2×Dic5C22×D411yescharacteristic
159C2×Dic5C22×Q811yescharacteristic
160D20—24no—
161D20—22no—
162C4×D5—21no—
163C4×D5—22no—
164C4×D5—21no—
165C4×D5—22no—
166C4×D5—22no—
167C4×D5—22no—
168C4×D5—41no—
169C4×D5—42no—
170C4×D5#13512yes—
171C4×D5#13512yes—
172#170—42no—
173#170—42no—
174#170—44no—
175C5×C8—22no—
176C5×C8—21no—
177C5×C8—21no—
178#168—22no—
179#168—21no—
180#168#13112yes—
181C2×#41—51no—
182C2×M16—102no—
183C22×C8—51no—
184C22×C8—52no—
185C22×C8—51no—
186C22×C8—52no—
187C22×C8—102no—
188C4×Q8—51no—
189C4×Q8C2×AGL(1,𝔽5)11yescharacteristic
190C4×D4—52no—
191C4×D4—51no—
192C4×D4—52no—
193C4×D4—51no—
194#117—51no—
195#117—52no—
196C2×C42—51no—
197C2×C42—52no—
198C4⋊C8—52no—
199C4⋊C8—52no—
200C4⋊C8—54no—
201C4⋊C8—51no—
202C4⋊C8—52no—
203C4⋊C8—102no—
204C4⋊C8—102no—
205C4⋊C8C2×AGL(1,𝔽5)11yescharacteristic
206C4⋊C8C2×AGL(1,𝔽5)12yes—
207C22⋊C8—52no—
208C22⋊C8—52no—
209C22⋊C8—52no—
210C22⋊C8—104no—
211C22⋊C8—104no—
212#97—104no—
213C4×C8—52no—
214C4×C8—51no—
215C4×C8—51no—
216C4×C8—51no—
217C4×C8—52no—
218C4×C8—104no—
219C4×C8C2×AGL(1,𝔽5)11yescharacteristic
220C4×C8C2×AGL(1,𝔽5)12yes—
221C22×C5C22×C4⋊C411yescharacteristic
222C2×D5—21no—
223C2×D5—21no—
224C2×D5—22no—
225C2×D5—22no—
226C2×D5—22no—
227C2×D5#42712yes—
228C4×C5—22no—
229C4×C5—21no—
230C4×C5—22no—
231C4×C5#42712yes—
232C4×C5C2×#13111yescharacteristic
233C4×C5#56811yescharacteristic
234Dic5—21no—
235Dic5—22no—
236Dic5—21no—
237Dic5C2×#13511yescharacteristic
238Dic5C2×#13511yescharacteristic
239#41—102no—
240#41—102no—
241C2×Q8C4⋊AGL(1,𝔽5)11yescharacteristic
242C2×D4—52no—
243C2×D4—51no—
244C22×C4—51no—
245C22×C4—52no—
246C22×C4—51no—
247C22×C4—52no—
248C22×C4—51no—
249C22×C4—52no—
250M16—204no—
251C2×C8—51no—
252C2×C8—52no—
253C2×C8—51no—
254C2×C8—102no—
255C2×C8—104no—
256C2×C8—102no—
257C2×C8—104no—
258C2×C8—102no—
259C2×C8—201no—
260C2×C8—202no—
261C2×C8—204no—
262C2×C8C22×AGL(1,𝔽5)11yescharacteristic
263C2×C8C22×AGL(1,𝔽5)12yes—
264C2×C8C22×AGL(1,𝔽5)11yescharacteristic
265C4⋊C4—52no—
266C4⋊C4—51no—
267C4⋊C4C4⋊AGL(1,𝔽5)12yes—
268C4⋊C4C4⋊AGL(1,𝔽5)11yescharacteristic
269C22⋊C4—52no—
270C22⋊C4—52no—
271C22⋊C4—52no—
272C42—52no—
273C42—51no—
274C42—52no—
275C42—51no—
276C42—51no—
277C42C22×AGL(1,𝔽5)12yes—
278C42C22×AGL(1,𝔽5)11yescharacteristic
279C2×C5#290611yescharacteristic
280C2×C5C2×#42711yescharacteristic
281C2×C5#291611yescharacteristic
282D5—22no—
283D5—42no—
284C23—51no—
285C23—52no—
286Q8—22no—
287D4—104no—
288D4—102no—
289C2×C4—51no—
290C2×C4—52no—
291C2×C4—52no—
292C2×C4—51no—
293C2×C4—52no—
294C2×C4—51no—
295C2×C4—102no—
296C2×C4—102no—
297C2×C4—101no—
298C2×C4—102no—
299C2×C4—101no—
300C2×C4—102no—
301C2×C4—201no—
302C2×C4—202no—
303C2×C4C2×C4⋊AGL(1,𝔽5)12yes—
304C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
305C2×C4C2×C4⋊AGL(1,𝔽5)12yes—
306C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
307C2×C4C23×AGL(1,𝔽5)11yescharacteristic
308C8—21no—
309C8—22no—
310C8—21no—
311C8—52no—
312C8—102no—
313C8—101no—
314C8—202no—
315C8—202no—
316C8—204no—
317C5#1782911yescharacteristic, complemented, Sylow
318C22—52no—
319C22—101no—
320C22—101no—
321C22—102no—
322C22—102no—
323C22—102no—
324C22C22×C4⋊AGL(1,𝔽5)11yescharacteristic
325C4—22no—
326C4—21no—
327C4—22no—
328C4—51no—
329C4—51no—
330C4—101no—
331C4—102no—
332C4—101no—
333C4#6572112yes—
334C4#6626011yescharacteristic
335C4D5⋊#13111yescharacteristic
336C2—102no—
337C2—202no—
338C2#1061718611yescharacteristic
339C2C2×#6572111yescharacteristic
340C2#1061741811yescharacteristic
subgroupG/H
centerC22C22×C4⋊AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×C8×Q8C4
socleC22×C5C22×C4⋊C4
prime radicalC2×#713D4
cosocleC4×Dic5C24
hypercenterC8×Q8AGL(1,𝔽5)
hypocenterC5#17829
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8

Complements

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

NH ≅ G/Ntype
3. #10604017C2semidirect
4. #10604015C2semidirect
5. #10603821C2semidirect
6. #10603819C2semidirect
7. #10603814C2semidirect
8. D5⋊#335C2semidirect
317. C5#17829semidirect

Maximal subgroups

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

subgroupindex
#106171902
C8×#7132
#106040172
#106040152
#106038212
#106038192
#106038142
D5⋊#3352
#178295