Finite Group Databasebeta

← #13033629

Subgroups — #13033629

Order 1280.

930 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65759C211yesmaximal, characteristic
2C2×#65757C211yesmaximal, characteristic
3C4×#4023C211yesmaximal, characteristic
4#10604224C214yesmaximal
5#10604175C212yesmaximal, complemented
6C4×#4002C212yesmaximal, complemented
7#10603778C214yesmaximal, complemented
8C22×C4×Dic5C2211yescharacteristic
9C2×#4023C2212yes—
10C2×C22⋊#170C2212yes—
11C2×C22⋊#170C2212yes—
12#65759C418yescomplemented
13#65757C418yescomplemented
14C2×#4004C2212yes—
15C2×#4002C2214yes—
16C2×#4002C2212yes—
17C2×#4002C2212yes—
18C2×C4⋊#170C2212yes—
19C2×C4×#170C2214yes—
20C4×C5×C22⋊C4C411yescharacteristic
21C4×C22⋊Dic5C411yescharacteristic
22C22⋊C4×Dic5C412yes—
23C4×#683C411yescharacteristic
24C4×#683C411yescharacteristic
25C42×Dic5C2211yescharacteristic
26C42×Dic5C2211yescharacteristic
27#64938C412yes—
28#64937C2212yes—
29#64918C2218yes—
30#20467—51nomaximal, Sylow
31C23×C4×C5C2×C411yescharacteristic
32C23×Dic5C2×C411yescharacteristic
33C23×Dic5C2311yescharacteristic
34C22×#170C2314yes—
35C22×#170C2314yes—
36C2×C5×C22⋊C4C2×C412yes—
37C2×C42×C5C2×C411yescharacteristic
38C2×C42×C5C2×C411yescharacteristic
39C2×C22⋊Dic5C2×C412yes—
40C2×#683C2×C412yes—
41C2×#683C2×C412yes—
42C2×C4×Dic5C2×C412yes—
43C2×C4×Dic5C2×C412yes—
44C2×C4×Dic5C2×C411yescharacteristic
45C2×C4×Dic5C2×C411yescharacteristic
46C2×C4×Dic5C2×C411yescharacteristic
47C2×C4×Dic5C2×C411yescharacteristic
48C2×C4×Dic5C2×C414yes—
49C2×C4×Dic5C2×C414yes—
50C2×C4×Dic5C2312yes—
51C2×C4×Dic5C2311yescharacteristic
52C2×C4×Dic5C2311yescharacteristic
53C2×C4×Dic5C2312yes—
54#4023—28no—
55C22⋊#170C2×C418yes—
56C22⋊#170C2×C418yes—
57#4004C2×C418yes—
58#4002—28no—
59#4002C2×C418yes—
60#4002C2×C418yes—
61C4⋊#170C2×C418yes—
62C4×#170—28no—
63C5×#95C2×C412yes—
64#3963C2×C412yes—
65#3963C2×C412yes—
66#3963C2×C412yes—
67C2×#432—51no—
68C2×#432—51no—
69C4×#117—51no—
70#1768—54no—
71#1750—54no—
72#1745—52no—
73C4×#97—52no—
74C24×C5C22×C411yescharacteristic
75C22×C4×C5—41no—
76C22×C4×C5—41no—
77C22×C4×C5C4214yes—
78C22×C4×C5C22×C412yes—
79C22×C4×C5C22×C411yescharacteristic
80C22×C4×C5C22×C411yescharacteristic
81C22×C4×C5C22×C412yes—
82C22×Dic5—24no—
83C22×Dic5—42no—
84C22×Dic5C4214yes—
85C22×Dic5C22×C412yes—
86C22×Dic5C22×C411yescharacteristic
87C22×Dic5C22×C411yescharacteristic
88C22×Dic5C22×C411yescharacteristic
89C22×Dic5C22×C412yes—
90C22×Dic5C22×C412yes—
91C22×Dic5C22×C412yes—
92C22×Dic5C2411yescharacteristic
93C2×#170—24no—
94C2×#170—24no—
95C2×#170—24no—
96C2×#170—24no—
97C2×#170C22×C418yes—
98C2×#170C22×C418yes—
99C5×C22⋊C4—24no—
100C42×C5—41no—
101C42×C5—41no—
102C22⋊Dic5—24no—
103#683—24no—
104#683—24no—
105C4×Dic5—24no—
106C4×Dic5—42no—
107C4×Dic5—42no—
108C4×Dic5—41no—
109C4×Dic5—41no—
110C4×Dic5C4214yes—
111C4×Dic5C4214yes—
112C4×Dic5C22×C412yes—
113C4×Dic5C22×C412yes—
114C4×Dic5C22×C412yes—
115C4×Dic5C22×C412yes—
116C4×Dic5#4118yes—
117C2×#117—52no—
118C22×C42—51no—
119#432—58no—
120#432—58no—
121C2×C4⋊C8—52no—
122C2×C4⋊C8—52no—
123C2×C22⋊C8—52no—
124C2×C22⋊C8—52no—
125C2×#97—52no—
126C2×#97—52no—
127C2×#97—54no—
128C2×C4×C8—54no—
129C4×C4⋊C4—51no—
130C4×C4⋊C4—51no—
131C4×C4⋊C4—52no—
132C4×C22⋊C4—51no—
133C4×C22⋊C4—52no—
134C4×C22⋊C4AGL(1,𝔽5)11yescharacteristic
135#376—52no—
136C43—51no—
137C43—51no—
138#336—58no—
139C23×C5—22no—
140C23×C5—22no—
141C23×C5—21no—
142C23×C5—21no—
143C23×C5C2×C4212yes—
144C23×C5C23×C411yescharacteristic
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—22no—
148C2×C4×C5—22no—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—22no—
152C2×C4×C5—22no—
153C2×C4×C5—22no—
154C2×C4×C5—44no—
155C2×C4×C5C2×C4212yes—
156C2×C4×C5C2×C4212yes—
157C2×C4×C5#11714yes—
158C2×Dic5—22no—
159C2×Dic5—22no—
160C2×Dic5—22no—
161C2×Dic5—22no—
162C2×Dic5—22no—
163C2×Dic5—24no—
164C2×Dic5—24no—
165C2×Dic5—22no—
166C2×Dic5—22no—
167C2×Dic5—22no—
168C2×Dic5—44no—
169C2×Dic5C2×C4212yes—
170C2×Dic5C2×C4212yes—
171C2×Dic5C2×C4212yes—
172C2×Dic5#11714yes—
173C2×Dic5C23×C411yescharacteristic
174C2×Dic5C23×C411yescharacteristic
175C2×Dic5C2×#4114yes—
176#170—28no—
177#170—28no—
178C23×C4—51no—
179C23×C4—51no—
180C23×C4C2×AGL(1,𝔽5)11yescharacteristic
181C22×C8—54no—
182C22×C8—54no—
183#117—108no—
184C2×C4⋊C4—52no—
185C2×C4⋊C4—52no—
186C2×C22⋊C4—52no—
187C2×C22⋊C4C2×AGL(1,𝔽5)12yes—
188C2×C42—54no—
189C2×C42—54no—
190C2×C42—52no—
191C2×C42—51no—
192C2×C42—51no—
193C2×C42—51no—
194C2×C42—51no—
195C2×C42—52no—
196C2×C42—51no—
197C2×C42—52no—
198C2×C42—52no—
199C2×C42—51no—
200C2×C42C2×AGL(1,𝔽5)11yescharacteristic
201C2×C42C2×AGL(1,𝔽5)11yescharacteristic
202C4⋊C8—58no—
203C4⋊C8—58no—
204C22⋊C8—58no—
205C22⋊C8—58no—
206#97—58no—
207#97—58no—
208#97—108no—
209C4×C8—108no—
210#95—52no—
211#95—52no—
212#95—52no—
213#95C2×AGL(1,𝔽5)12yes—
214C22×C5—22no—
215C22×C5—22no—
216C22×C5—22no—
217C22×C5—42no—
218C22×C5—42no—
219C22×C5C22×C4211yescharacteristic
220C22×C5C2×#11712yes—
221C22×C5#56811yescharacteristic
222C22×C5#56811yescharacteristic
223C22×C5#56812yes—
224C4×C5—22no—
225C4×C5—22no—
226C4×C5—24no—
227C4×C5—42no—
228Dic5—22no—
229Dic5—22no—
230Dic5—24no—
231Dic5—22no—
232Dic5—42no—
233Dic5C4×#4112yes—
234Dic5C4×#4112yes—
235C24C22×AGL(1,𝔽5)11yescharacteristic
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—51no—
239C22×C4—52no—
240C22×C4—52no—
241C22×C4—51no—
242C22×C4—52no—
243C22×C4—51no—
244C22×C4—51no—
245C22×C4—54no—
246C22×C4—52no—
247C22×C4—104no—
248C22×C4—202no—
249C22×C4C4×AGL(1,𝔽5)14yes—
250C22×C4C22×AGL(1,𝔽5)12yes—
251C22×C4C22×AGL(1,𝔽5)11yescharacteristic
252C22×C4C22×AGL(1,𝔽5)11yescharacteristic
253C22×C4C22×AGL(1,𝔽5)12yes—
254C2×C8—58no—
255C2×C8—58no—
256C2×C8—104no—
257C2×C8—104no—
258C2×C8—104no—
259C2×C8—104no—
260C4⋊C4—104no—
261C4⋊C4—104no—
262C22⋊C4—24no—
263C22⋊C4—104no—
264C42—41no—
265C42—41no—
266C42—52no—
267C42—52no—
268C42—52no—
269C42—52no—
270C42—54no—
271C42—54no—
272C42—58no—
273C42—104no—
274C42—201no—
275C42—201no—
276C42—202no—
277C42—202no—
278C2×C5—42no—
279C2×C5C4×#11711yescharacteristic
280C2×C5#287311yescharacteristic
281C2×C5#287311yescharacteristic
282C2×C5#292312yes—
283C2×C5#292312yes—
284C23—22no—
285C23—21no—
286C23—21no—
287C23—22no—
288C23C2×C4×AGL(1,𝔽5)12yes—
289C23C23×AGL(1,𝔽5)11yescharacteristic
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—44no—
300C2×C4—51no—
301C2×C4—51no—
302C2×C4—54no—
303C2×C4—52no—
304C2×C4—52no—
305C2×C4—52no—
306C2×C4—54no—
307C2×C4—104no—
308C2×C4—104no—
309C2×C4—102no—
310C2×C4—102no—
311C2×C4—102no—
312C2×C4—102no—
313C2×C4—102no—
314C2×C4—102no—
315C2×C4—102no—
316C2×C4—102no—
317C2×C4—204no—
318C2×C4C2×C4×AGL(1,𝔽5)12yes—
319C2×C4C2×C4×AGL(1,𝔽5)12yes—
320C2×C4#413014yes—
321C8—108no—
322C8—108no—
323C5#2046711yescharacteristic, complemented, Sylow
324C22—22no—
325C22—22no—
326C22—22no—
327C22—42no—
328C22—42no—
329C22C22×C4×AGL(1,𝔽5)11yescharacteristic
330C22C2×#413012yes—
331C22#6625611yescharacteristic
332C22#6625611yescharacteristic
333C22#6626412yes—
334C4—24no—
335C4—22no—
336C4—22no—
337C4—42no—
338C4—52no—
339C4—52no—
340C4—102no—
341C4—102no—
342C4—104no—
343C4—102no—
344C4—202no—
345C2—42no—
346C2C4×#413011yescharacteristic
347C2#1061705011yescharacteristic
348C2#1061710611yescharacteristic
349C2#1061714112yes—
350C2#1061714212yes—
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FittingC4×C5×C22⋊C4C4
socleC23×C5C23×C4
prime radicalC24×C5C22×C4
cosocleC22×Dic5C24
hypercenterC4×C22⋊C4AGL(1,𝔽5)
hypocenterC5#20467
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. #10604175C2semidirect
6. C4×#4002C2semidirect
7. #10603778C2semidirect
12. #65759C4semidirect
13. #65757C4semidirect
323. C5#20467semidirect

Maximal subgroups

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

subgroupindex
C2×#657592
C2×#657572
C4×#40232
#106042242
#106041752
C4×#40022
#106037782
#204675