Finite Group Databasebeta

← #13031634

Subgroups — #13031634

Order 1280.

714 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10617120C212yesmaximal, complemented
2#10610896C211yesmaximal, characteristic
3C2×#64882C211yesmaximal, characteristic, complemented
4#10604687C211yesmaximal, characteristic, complemented
5#10604360C212yesmaximal, complemented
6#10604060C212yesmaximal, complemented
7#10604059C212yesmaximal, complemented
8#10604040C214yesmaximal, complemented
9C2×#4050C411yescharacteristic
10#65856C2212yes—
11#65748C2211yescharacteristic
12#65748C2211yescharacteristic
13C2×C4⋊#170C2212yes—
14#65703C2214yes—
15#65702C2214yes—
16#65692—24no—
17#65680—22no—
18D5⋊(C4⋊C8)—22no—
19C5×#427C411yescharacteristic
20C2×C8×Dic5C2211yescharacteristic
21#65291C412yes—
22#65162C411yescharacteristic
23#65162C2211yescharacteristic
24#65161C411yescharacteristic
25#65161C2211yescharacteristic
26#65141C412yes—
27#65141C2212yes—
28#64882C2212yes—
29#64882C2212yes—
30#64879C2212yes—
31C8×#170C2212yes—
32#64872C2214yes—
33#64871C2214yes—
34#17857—51nomaximal, Sylow
35C2×#709C2×C412yes—
36C22×#170—22no—
37C2×D5⋊C8—24no—
38C22×C5×C8C2×C411yescharacteristic
39C5×#117C2×C412yes—
40C2×C4×Dic5C2311yescharacteristic
41C22×#168C2×C411yescharacteristic
42C2×Dic20C2×C411yescharacteristic
43#4050C818yescomplemented
44C2×D40C2×C411yescharacteristic
45C2×#677C2×C412yes—
46#4039C2×C412yes—
47#4039C2312yes—
48#4033C2×C412yes—
49#4033C2312yes—
50#4027—22no—
51#4027—22no—
52#4018—22no—
53C42×D5—22no—
54C22⋊#170—21no—
55C22⋊#170D412yes—
56#4004—24no—
57#4003—24no—
58C4⋊#170—22no—
59C4⋊#170—21no—
60C4⋊#170D411yescharacteristic
61C4⋊#170D411yescharacteristic
62C4⋊#170C2314yes—
63C4×#170—24no—
64C4×#170C2312yes—
65C4×#170C2312yes—
66C5×#107C2×C411yescharacteristic
67C5×#107C2×C411yescharacteristic
68C5×#106C2×C412yes—
69C8×Dic5C2×C411yescharacteristic
70C8×Dic5C2×C411yescharacteristic
71C8×Dic5C2311yescharacteristic
72C8×Dic5C2311yescharacteristic
73#3942C2×C412yes—
74#3942C2×C412yes—
75#3941C2×C412yes—
76#3941C2×C412yes—
77#2988—52no—
78C4×#135—51no—
79SD16⋊C8—54no—
80C8×Q16—52no—
81C8×D8—52no—
82C2×#335—51no—
83#1477—52no—
84#1450—51no—
85C22×C4×C5C22×C411yescharacteristic
86C2×C22⋊D5—22no—
87C22×Dic5C2×D411yescharacteristic
88C22×Dic5#4111yescharacteristic
89#709—24no—
90#709C2×C818yescomplemented
91C2×D20C22×C412yes—
92C2×C4×D5—22no—
93C2×C4×D5—22no—
94C2×C4×D5—22no—
95C2×Dic10C22×C412yes—
96C2×#170—24no—
97C2×#170—22no—
98C2×#170—82no—
99C2×#170C2×D412yes—
100C2×#170C2×D412yes—
101D5⋊C8—84no—
102C2×C5×C8C2×C814yescomplemented
103C2×C5×C8C22×C411yescharacteristic
104C2×C5×C8C22×C411yescharacteristic
105C5×C4⋊C4C22×C412yes—
106C5×C4⋊C4C22×C412yes—
107C5×C22⋊C4—22no—
108C42×C5—22no—
109#685—22no—
110#685—22no—
111#683—22no—
112#683—22no—
113C4×Dic5—22no—
114C4×Dic5—22no—
115C4×Dic5C22×C411yescharacteristic
116C4×Dic5C2×D411yescharacteristic
117C4×Dic5#4111yescharacteristic
118C4×Dic5C2411yescharacteristic
119C2×#168—22no—
120C2×#168C22×C411yescharacteristic
121C2×#168C22×C411yescharacteristic
122Dic20C2×C814yescomplemented
123D40C2×C814yescomplemented
124#677C2×C818yescomplemented
125C2×#135—51no—
126C4×#41—52no—
127C8×Q8—54no—
128C4×Q16—51no—
129C4×Q16—51no—
130C4×SD16—52no—
131C4×SD16—52no—
132C4×D8—51no—
133C4×D8—51no—
134C8×D4—54no—
135C8×D4—104no—
136#431—51no—
137#431—51no—
138#431—102no—
139#427AGL(1,𝔽5)11yescharacteristic
140C2×C4⋊C8—52no—
141C2×C4⋊C8—102no—
142#416—52no—
143C2×C4×C8—51no—
144#335—52no—
145#335—52no—
146Q8⋊C8—54no—
147D4⋊C8—54no—
148#322—52no—
149C82—52no—
150C23×C5C4×D411yescharacteristic
151C22×D5—22no—
152C2×C4×C5—22no—
153C2×C4×C5—22no—
154C2×C4×C5C4×D411yescharacteristic
155C2×C4×C5C22×C812yes—
156C2×C4×C5#13112yes—
157C2×C4×C5C23×C411yescharacteristic
158C22⋊D5—28no—
159C2×Dic5—22no—
160C2×Dic5—21no—
161C2×Dic5—21no—
162C2×Dic5—41no—
163C2×Dic5C4×D411yescharacteristic
164C2×Dic5C4×D411yescharacteristic
165C2×Dic5C22×D411yescharacteristic
166C2×Dic5C2×#4111yescharacteristic
167D20—22no—
168D20C22×C814yes—
169C4×D5—28no—
170C4×D5—42no—
171C4×D5—42no—
172C4×D5—82no—
173Dic10—22no—
174Dic10C22×C814yes—
175#170—22no—
176#170—22no—
177#170—42no—
178#170—44no—
179C5×C8C22×C812yes—
180C5×C8C22×C812yes—
181#168—21no—
182#168—21no—
183C2×#41—52no—
184#135—58no—
185C2×Q16—51no—
186C2×SD16—52no—
187C2×D8—51no—
188C22×C8—51no—
189C22×C8—104no—
190C22×C8—102no—
191C22×C8C2×AGL(1,𝔽5)11yescharacteristic
192C4×Q8—52no—
193C4×Q8—52no—
194C4×D4—52no—
195C4×D4—52no—
196C4×D4—102no—
197C4×D4—102no—
198#117—102no—
199#117C2×AGL(1,𝔽5)12yes—
200C2×C42—51no—
201C2×C42—102no—
202#107C2×AGL(1,𝔽5)11yescharacteristic
203#107C2×AGL(1,𝔽5)11yescharacteristic
204#106C2×AGL(1,𝔽5)12yes—
205C4⋊C8—51no—
206C4⋊C8—51no—
207C4⋊C8—54no—
208C4⋊C8—102no—
209C4⋊C8—101no—
210C4⋊C8—104no—
211#103—52no—
212#103—52no—
213#102—52no—
214#102—52no—
215C22⋊C8—52no—
216C22⋊C8—104no—
217C22⋊C8—101no—
218C4×C8—52no—
219C4×C8—51no—
220C4×C8—51no—
221C4×C8—51no—
222C4×C8—51no—
223C4×C8—52no—
224C4×C8—104no—
225C22×C5—21no—
226C22×C5—21no—
227C22×C5C8×D412yes—
228C22×C5C2×C4×D411yescharacteristic
229C2×D5—24no—
230C2×D5—42no—
231C2×D5—42no—
232C4×C5—42no—
233C4×C5—42no—
234C4×C5C8×D412yes—
235C4×C5C23×C811yescharacteristic
236C4×C5C2×#13111yescharacteristic
237Dic5—24no—
238Dic5—21no—
239Dic5—21no—
240Dic5—21no—
241Dic5#57611yescharacteristic
242Dic5#57811yescharacteristic
243#41—58no—
244#41—104no—
245C2×Q8—52no—
246C2×D4—52no—
247C2×D4—102no—
248C22×C4—51no—
249C22×C4—51no—
250C22×C4—102no—
251C22×C4—102no—
252C22×C4—102no—
253C22×C4C22×AGL(1,𝔽5)11yescharacteristic
254Q16—54no—
255SD16—58no—
256D8—54no—
257C2×C8—52no—
258C2×C8—52no—
259C2×C8—51no—
260C2×C8—51no—
261C2×C8—102no—
262C2×C8—102no—
263C2×C8—104no—
264C2×C8—404no—
265C2×C8—402no—
266C2×C8D5⋊C814yescomplemented
267C2×C8C22×AGL(1,𝔽5)11yescharacteristic
268C2×C8C22×AGL(1,𝔽5)11yescharacteristic
269C4⋊C4—102no—
270C4⋊C4—102no—
271C4⋊C4C22×AGL(1,𝔽5)12yes—
272C4⋊C4C22×AGL(1,𝔽5)12yes—
273C22⋊C4—22no—
274C22⋊C4—102no—
275C22⋊C4—102no—
276C42—22no—
277C42—51no—
278C42—51no—
279C42—51no—
280C42—51no—
281C42—102no—
282C42—102no—
283C2×C5—22no—
284C2×C5C2×C8×D411yescharacteristic
285C2×C5#295111yescharacteristic
286C2×C5#295711yescharacteristic
287D5—44no—
288C23—102no—
289C23D4×AGL(1,𝔽5)11yescharacteristic
290Q8—54no—
291Q8—102no—
292D4—54no—
293D4—108no—
294D4—102no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—51no—
298C2×C4—51no—
299C2×C4—51no—
300C2×C4—51no—
301C2×C4—101no—
302C2×C4—101no—
303C2×C4—102no—
304C2×C4—108no—
305C2×C4—202no—
306C2×C4—202no—
307C2×C4—201no—
308C2×C4—402no—
309C2×C4C2×D5⋊C812yes—
310C2×C4D4×AGL(1,𝔽5)11yescharacteristic
311C2×C4#413312yes—
312C2×C4C23×AGL(1,𝔽5)11yescharacteristic
313C8—102no—
314C8—102no—
315C8—101no—
316C8—101no—
317C8—204no—
318C8—202no—
319C8C2×D5⋊C812yes—
320C8C2×D5⋊C812yes—
321C5#1785711yescharacteristic, complemented, Sylow
322C22—21no—
323C22—21no—
324C22—104no—
325C22—202no—
326C22—202no—
327C22#6570212yes—
328C22C2×D4×AGL(1,𝔽5)11yescharacteristic
329C4—42no—
330C4—42no—
331C4—51no—
332C4—51no—
333C4—101no—
334C4—101no—
335C4—101no—
336C4—104no—
337C4#6570212yes—
338C4C22×D5⋊C811yescharacteristic
339C4C2×#413311yescharacteristic
340C2—22no—
341C2—204no—
342C2C2×#6570211yescharacteristic
343C2#1061744011yescharacteristic
344C2#1061744511yescharacteristic
subgroupG/H
centerC22C2×D4×AGL(1,𝔽5)
commutatorC4×C5C23×C8
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#427C4
socleC22×C5C2×C4×D4
prime radicalC2×#4050C4
cosocleC4×Dic5C24
hypercenter#427AGL(1,𝔽5)
hypocenterC5#17857
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
1. #10617120C2semidirect
3. C2×#64882C2semidirect
4. #10604687C2semidirect
5. #10604360C2semidirect
6. #10604060C2semidirect
7. #10604059C2semidirect
8. #10604040C2semidirect
43. #4050C8semidirect
90. #709C2×C8semidirect
102. C2×C5×C8C2×C8semidirect
122. Dic20C2×C8semidirect
123. D40C2×C8semidirect
124. #677C2×C8semidirect
266. C2×C8D5⋊C8semidirect
321. C5#17857semidirect

Maximal subgroups

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

subgroupindex
#106171202
#106108962
C2×#648822
#106046872
#106043602
#106040602
#106040592
#106040402
#178575