Finite Group Databasebeta

← #13025492

Subgroups — #13025492

Order 1280.

570 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5⋊#108C211yesmaximal, characteristic
2C2×D5⋊M32C211yesmaximal, characteristic
3C2×#65169C211yesmaximal, characteristic
4#10598620C214yesmaximal, complemented
5C2×D5⋊M16—21no—
6C22×C8×D5C2211yescharacteristic
7C2×#4038—21no—
8C2×#3998—21no—
9D5⋊#108—22no—
10D5⋊#108C414yescomplemented
11C2×#3996C2212yes—
12C2×#3995—21no—
13D5⋊M32—22no—
14D5⋊M32C414yescomplemented
15C2×#3990—21no—
16C2×D5⋊C16C2212yes—
17C2×C5×#107C411yescharacteristic
18C2×#3950C411yescharacteristic
19C2×#3940—21no—
20#65169—21no—
21#65169—21no—
22#65169C412yes—
23#65169C2212yes—
24#12561—51nomaximal, Sylow
25C22×C4×D5D411yescharacteristic
26C2×#704—41no—
27D5⋊M16—24no—
28D5⋊M16—42no—
29C2×#700—22no—
30C2×D5⋊C8—41no—
31C22×C5×C8C2×C411yescharacteristic
32C2×C5×C4⋊C4—21no—
33C2×#685—41no—
34C2×C4⋊Dic5—21no—
35C2×C4×Dic5—41no—
36C22×#168D411yescharacteristic
37C2×C8×D5C2×C411yescharacteristic
38C2×C8×D5C2×C412yes—
39C2×C8×D5C2×C412yes—
40C2×C8×D5D411yescharacteristic
41C2×C8×D5D411yescharacteristic
42C2×C8×D5D412yes—
43C2×C8×D5Q812yes—
44C2×C8×D5C2311yescharacteristic
45#4038—22no—
46#4038—22no—
47#4038—41no—
48#4038—41no—
49#3998—24no—
50C2×#674—22no—
51#3996—22no—
52#3996C2×C414yescomplemented
53#3995—24no—
54#3990—24no—
55D5⋊C16—22no—
56D5⋊C16C2×C414yescomplemented
57C5×#107—21no—
58C5×#107C2×C412yes—
59#3950—21no—
60#3950C2×C412yes—
61#3940—22no—
62#3940—22no—
63C22×M32—51no—
64C22×#108—51no—
65C2×#427—51no—
66#1382—54no—
67C23×D5SD1611yescharacteristic
68C22×C4×C5—41no—
69C22×C4×C5C22⋊C411yescharacteristic
70C22×Dic5—41no—
71C22×Dic5D811yescharacteristic
72C2×C4×D5C22⋊C411yescharacteristic
73C2×C4×D5C22⋊C412yes—
74C2×C4×D5C4⋊C412yes—
75C2×C4×D5D811yescharacteristic
76C2×C4×D5SD1612yes—
77C2×C4×D5SD1611yescharacteristic
78C2×C4×D5Q1612yes—
79C2×C4×D5C2×D411yescharacteristic
80#704—44no—
81C2×#170—42no—
82#700—24no—
83#700—42no—
84D5⋊C8—44no—
85C2×C5×C8C4212yes—
86C2×C5×C8C22⋊C411yescharacteristic
87C2×C5×C8C4⋊C412yes—
88C2×C5×C8C22×C411yescharacteristic
89C5×C4⋊C4—22no—
90C5×C4⋊C4—41no—
91#685—42no—
92#685—42no—
93C4⋊Dic5—22no—
94C4⋊Dic5—41no—
95C4×Dic5—42no—
96C4×Dic5—42no—
97C2×#168C22⋊C411yescharacteristic
98C2×#168C22⋊C412yes—
99C2×#168C4⋊C412yes—
100C2×#168C2×D411yescharacteristic
101C8×D5C4212yes—
102C8×D5C22⋊C412yes—
103C8×D5C22⋊C412yes—
104C8×D5C4⋊C412yes—
105C8×D5C4⋊C412yes—
106C8×D5C4⋊C412yes—
107C8×D5C22×C411yescharacteristic
108C8×D5C22×C411yescharacteristic
109C8×D5C2×D411yescharacteristic
110C8×D5C2×Q811yescharacteristic
111#674—24no—
112C22×M16—101no—
113C23×C8—51no—
114C2×#117—101no—
115C2×M32—54no—
116C2×M32—101no—
117C2×M32—102no—
118C2×M32—101no—
119C22×C16—52no—
120C2×#108—52no—
121C2×#108—54no—
122C2×#108—101no—
123C2×#108—102no—
124#427—52no—
125#427—52no—
126#427—101no—
127#427—101no—
128C2×#107—51no—
129C2×#107AGL(1,𝔽5)11yescharacteristic
130C2×#106—101no—
131C23×C5#10211yescharacteristic
132C22×D5—41no—
133C22×D5—41no—
134C22×D5#10211yescharacteristic
135C22×D5#10312yes—
136C22×D5#10612yes—
137C22×D5C2×SD1611yescharacteristic
138C2×C4×C5—42no—
139C2×C4×C5—82no—
140C2×C4×C5#9512yes—
141C2×C4×C5#10211yescharacteristic
142C2×C4×C5#10312yes—
143C2×C4×C5C2×C22⋊C411yescharacteristic
144C2×Dic5—42no—
145C2×Dic5—82no—
146C2×Dic5#10211yescharacteristic
147C2×Dic5#10212yes—
148C2×Dic5#10712yes—
149C2×Dic5C2×D811yescharacteristic
150C4×D5#9512yes—
151C4×D5#10212yes—
152C4×D5#10312yes—
153C4×D5#10312yes—
154C4×D5#10612yes—
155C4×D5#10712yes—
156C4×D5C2×C22⋊C411yescharacteristic
157C4×D5C2×C4⋊C411yescharacteristic
158C4×D5C2×SD1611yescharacteristic
159C4×D5C2×Q1611yescharacteristic
160#170—44no—
161C5×C8#9512yes—
162C5×C8C2×C4211yescharacteristic
163C5×C8C2×C4⋊C411yescharacteristic
164#168#9512yes—
165#168C2×C22⋊C411yescharacteristic
166#168C2×C4⋊C411yescharacteristic
167C23×C4—51no—
168C2×M16—102no—
169C2×M16—104no—
170C2×M16—202no—
171C2×M16—201no—
172C22×C8—51no—
173C22×C8—52no—
174C22×C8—52no—
175C22×C8—52no—
176C22×C8—52no—
177C22×C8—51no—
178C22×C8—51no—
179C22×C8—51no—
180C22×C8—51no—
181C22×C8—201no—
182C22×C8C2×AGL(1,𝔽5)11yescharacteristic
183#117—102no—
184#117—102no—
185#117—201no—
186#117—201no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—101no—
189C2×C22⋊C4—201no—
190C2×C42—201no—
191M32—104no—
192M32—104no—
193C2×C16—54no—
194C2×C16—102no—
195C2×C16—102no—
196#108—54no—
197#108—104no—
198#108—102no—
199#107—21no—
200#107—52no—
201#107—101no—
202#107C2×AGL(1,𝔽5)12yes—
203#106—102no—
204#106—102no—
205C22×C5—21no—
206C22×C5—21no—
207C22×C5#34012yes—
208C22×C5C2×#10211yescharacteristic
209C2×D5—21no—
210C2×D5—21no—
211C2×D5—21no—
212C2×D5—21no—
213C2×D5—42no—
214C2×D5—42no—
215C2×D5#34012yes—
216C2×D5C2×#10311yescharacteristic
217C2×D5C2×#10611yescharacteristic
218C4×C5—82no—
219C4×C5#34012yes—
220C4×C5C2×#9511yescharacteristic
221C4×C5C2×#10311yescharacteristic
222Dic5—82no—
223Dic5#34012yes—
224Dic5C2×#10211yescharacteristic
225Dic5C2×#10711yescharacteristic
226C24—51no—
227C22×C4—41no—
228C22×C4—51no—
229C22×C4—51no—
230C22×C4—51no—
231C22×C4—52no—
232C22×C4—52no—
233C22×C4—51no—
234C22×C4—51no—
235C22×C4—52no—
236C22×C4—52no—
237C22×C4—201no—
238C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
239M16—104no—
240M16—202no—
241M16—204no—
242C2×C8—51no—
243C2×C8—51no—
244C2×C8—52no—
245C2×C8—52no—
246C2×C8—51no—
247C2×C8—51no—
248C2×C8—52no—
249C2×C8—51no—
250C2×C8—52no—
251C2×C8—51no—
252C2×C8—52no—
253C2×C8—52no—
254C2×C8—52no—
255C2×C8—52no—
256C2×C8—204no—
257C2×C8—202no—
258C2×C8C4×AGL(1,𝔽5)12yes—
259C2×C8C4⋊AGL(1,𝔽5)12yes—
260C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
261C2×C8C22×AGL(1,𝔽5)11yescharacteristic
262C4⋊C4—22no—
263C4⋊C4—41no—
264C4⋊C4—102no—
265C4⋊C4—201no—
266C22⋊C4—202no—
267C22⋊C4—202no—
268C42—202no—
269C42—202no—
270C16—104no—
271C2×C5—22no—
272C2×C5C2×#34011yescharacteristic
273C2×C5#214311yescharacteristic
274C2×C5#214311yescharacteristic
275D5—22no—
276D5—21no—
277D5—21no—
278C23—51no—
279C23—51no—
280C23—52no—
281C23—52no—
282C23—201no—
283C23—201no—
284C23#400711yescharacteristic
285C2×C4—42no—
286C2×C4—52no—
287C2×C4—52no—
288C2×C4—51no—
289C2×C4—51no—
290C2×C4—52no—
291C2×C4—52no—
292C2×C4—52no—
293C2×C4—52no—
294C2×C4—51no—
295C2×C4—52no—
296C2×C4—51no—
297C2×C4—51no—
298C2×C4—52no—
299C2×C4—51no—
300C2×C4—82no—
301C2×C4—202no—
302C2×C4—402no—
303C2×C4(C2×AGL(1,𝔽5))⋊C412yes—
304C2×C4#400711yescharacteristic
305C2×C4#400912yes—
306C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
307C8—51no—
308C8—52no—
309C8—51no—
310C8—204no—
311C8(C2×AGL(1,𝔽5))⋊C412yes—
312C8C2×C4×AGL(1,𝔽5)11yescharacteristic
313C8C2×C4⋊AGL(1,𝔽5)11yescharacteristic
314C5#1256111yescharacteristic, complemented, Sylow
315C22—21no—
316C22—21no—
317C22—52no—
318C22—51no—
319C22—51no—
320C22—101no—
321C22—101no—
322C22—101no—
323C22—101no—
324C22—202no—
325C22—202no—
326C22#6487412yes—
327C22C2×#400711yescharacteristic
328C4—51no—
329C4—52no—
330C4—51no—
331C4—82no—
332C4—402no—
333C4#6487412yes—
334C4C2×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
335C4C2×#400911yescharacteristic
336C2—22no—
337C2—102no—
338C2—101no—
339C2—101no—
340C2C2×#6487411yescharacteristic
341C2#1060478811yescharacteristic
342C2#1060483411yescharacteristic
subgroupG/H
centerC22C2×#4007
commutatorC5×C8C2×C42
FrattiniC2×C8C22×AGL(1,𝔽5)
FittingC2×C5×#107C4
socleC22×C5C2×#102
prime radicalC23×D5SD16
cosocleC2×C8×D5C23
hypercenterC2×#107AGL(1,𝔽5)
hypocenterC5#12561
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
4. #10598620C2semidirect
10. D5⋊#108C4semidirect
14. D5⋊M32C4semidirect
52. #3996C2×C4semidirect
56. D5⋊C16C2×C4semidirect
314. C5#12561semidirect

Maximal subgroups

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

subgroupindex
C2×D5⋊#1082
C2×D5⋊M322
C2×#651692
#105986202
#125615