Finite Group Databasebeta

← #11996065

Subgroups — #11996065

Order 1280.

436 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10615098C211yesmaximal, characteristic
2#10610994C211yesmaximal, characteristic
3C5×#1481C211yesmaximal, characteristic
4#10602631C211yesmaximal, characteristic
5#10601279C211yesmaximal, characteristic
6#10598229C211yesmaximal, characteristic
7#10598198C211yesmaximal, characteristic
8C5×#533C2211yescharacteristic
9C2×C4×Dic10C2211yescharacteristic
10C5×#431C2211yescharacteristic
11C2×C5×C4⋊C8C2211yescharacteristic
12C2×#3948—21no—
13#65383C412yescomplemented
14#65380C412yescomplemented
15#65352—22no—
16#65293—21no—
17#65284—21no—
18#65225C2211yescharacteristic
19#65214C2211yescharacteristic
20#65213C2211yescharacteristic
21#65119—22no—
22#65007—22no—
23C8×Dic10—22no—
24C5×Q8⋊C8—22no—
25#64771—21no—
26#64758—22no—
27#9304—51nomaximal, Sylow
28C22×Dic10D411yescharacteristic
29C22×C5×C8—21no—
30C5×C4⋊Q8C2×C411yescharacteristic
31C5×C4⋊Q8C2×C411yescharacteristic
32C5×#125—21no—
33C5×C22⋊Q8—21no—
34C5×C22⋊Q8—21no—
35C4×C5×Q8—21no—
36C4×C5×Q8—21no—
37C5×#117—21no—
38C2×C42×C5C2311yescharacteristic
39C2×C4⋊Dic5—21no—
40C2×C4⋊Dic5D411yescharacteristic
41C2×#683—21no—
42C2×C4×Dic5—21no—
43C2×#681—21no—
44C4×Dic10—21no—
45C4×Dic10—21no—
46C4×Dic10C2×C412yes—
47C4×Dic10D412yes—
48C5×C4⋊C8—21no—
49C5×C4⋊C8—21no—
50C5×C4⋊C8—21no—
51C5×C22⋊C8—21no—
52C4×C5×C8D412yes—
53#3963—21no—
54#3963—21no—
55C22⋊#168D412yes—
56#3948—42no—
57#3946—24no—
58C8×Dic5—24no—
59#3942—22no—
60#3942—22no—
61#3940—22no—
62#3939—22no—
63C4⋊#168—21no—
64C4⋊#168—21no—
65C4⋊#168C2×C412yes—
66C4×#168—21no—
67#3078—51no—
68#2982—51no—
69#1805—51no—
70#1518—51no—
71#1481D511yescharacteristic
72#1301—51no—
73#1286—51no—
74C2×C5×Q8—21no—
75C2×C5×Q8—21no—
76C22×C4×C5C2×D411yescharacteristic
77C22×C4×C5C2×D411yescharacteristic
78C22×C4×C5#4111yescharacteristic
79C22×Dic5—21no—
80C22×Dic5—21no—
81C22×Dic5—41no—
82C2×Dic10—21no—
83C2×Dic10—21no—
84C2×Dic10—21no—
85C2×Dic10C22⋊C412yes—
86C2×Dic10SD1612yes—
87C2×Dic10Q1612yes—
88C2×C5×C8—22no—
89C2×C5×C8—41no—
90C2×C5×C8—41no—
91C2×C5×C8—41no—
92C5×C4⋊C4—21no—
93C5×C4⋊C4—21no—
94C5×C4⋊C4—21no—
95C5×C4⋊C4—21no—
96C5×C4⋊C4—41no—
97C5×C4⋊C4—41no—
98C5×C22⋊C4—41no—
99C42×C5—41no—
100C42×C5C22×C411yescharacteristic
101C42×C5C2×D411yescharacteristic
102C42×C5C2×D411yescharacteristic
103C42×C5#4111yescharacteristic
104C4⋊Dic5—21no—
105C4⋊Dic5—41no—
106C4⋊Dic5—41no—
107C4⋊Dic5C22⋊C412yes—
108#683—22no—
109#683—22no—
110C4×Dic5—22no—
111C4×Dic5—22no—
112#681—41no—
113#681—41no—
114C2×#168—22no—
115C2×#168—22no—
116#533C2×D511yescharacteristic
117C2×C4×Q8—51no—
118#479—102no—
119#477—52no—
120#475—52no—
121C8×Q8—102no—
122C8×Q8—102no—
123#431—51no—
124#431—102no—
125#431C2×D511yescharacteristic
126#428—101no—
127#423—51no—
128C2×C4⋊C8C2×D511yescharacteristic
129#419—101no—
130C2×#103—101no—
131#382—51no—
132#340—101no—
133#328—102no—
134Q8⋊C8—22no—
135C23×C5#12111yescharacteristic
136C5×Q8—42no—
137C5×Q8—81no—
138C2×C4×C5—41no—
139C2×C4×C5—41no—
140C2×C4×C5—41no—
141C2×C4×C5—41no—
142C2×C4×C5C2×C22⋊C411yescharacteristic
143C2×C4×C5C4×D411yescharacteristic
144C2×C4×C5C4×D411yescharacteristic
145C2×C4×C5#12011yescharacteristic
146C2×C4×C5#12111yescharacteristic
147C2×C4×C5#12311yescharacteristic
148C2×C4×C5C2×SD1611yescharacteristic
149C2×C4×C5C2×Q1611yescharacteristic
150C2×C4×C5#13511yescharacteristic
151C2×C4×C5#13511yescharacteristic
152C2×Dic5—22no—
153C2×Dic5—22no—
154C2×Dic5—22no—
155C2×Dic5—22no—
156C2×Dic5—81no—
157C2×Dic5—81no—
158C2×Dic5—81no—
159C2×Dic5—81no—
160Dic10—22no—
161Dic10—22no—
162Dic10—22no—
163Dic10#10314yes—
164C5×C8—42no—
165C5×C8—81no—
166#168—42no—
167#168—42no—
168C22×Q8—51no—
169C2×M16—101no—
170C22×C8—21no—
171C4⋊Q8C4×D511yescharacteristic
172C4⋊Q8C4×D511yescharacteristic
173#125—21no—
174C22⋊Q8—21no—
175C22⋊Q8—21no—
176C4×Q8—21no—
177C4×Q8—21no—
178C4×Q8—52no—
179C4×Q8—52no—
180C4×Q8—101no—
181C4×Q8—101no—
182#117—21no—
183C2×C4⋊C4—51no—
184C2×C4⋊C4—101no—
185C2×C4⋊C4—101no—
186C2×C42—101no—
187C2×C42C22×D511yescharacteristic
188#107—102no—
189#106—102no—
190C4⋊C8—21no—
191C4⋊C8—21no—
192C4⋊C8—21no—
193C4⋊C8—52no—
194C4⋊C8—104no—
195C4⋊C8—101no—
196C4⋊C8—101no—
197#103—102no—
198#103—102no—
199#103—202no—
200C22⋊C8—21no—
201C22⋊C8—52no—
202C4×C8—104no—
203C4×C8—101no—
204C4×C8C22⋊D512yes—
205#95—101no—
206#95—101no—
207C22×C5—21no—
208C22×C5—21no—
209C22×C5#38611yescharacteristic
210C22×C5#46511yescharacteristic
211C22×C5#46711yescharacteristic
212C4×C5—21no—
213C4×C5—21no—
214C4×C5—21no—
215C4×C5—21no—
216C4×C5—81no—
217C4×C5—81no—
218C4×C5C2×#10311yescharacteristic
219C4×C5#41611yescharacteristic
220C4×C5#46511yescharacteristic
221C4×C5#46711yescharacteristic
222Dic5—24no—
223Dic5—42no—
224Dic5—161no—
225C2×Q8—21no—
226C2×Q8—21no—
227C2×Q8—52no—
228C2×Q8—52no—
229C2×Q8—52no—
230C2×Q8—101no—
231C2×Q8—101no—
232C2×Q8—101no—
233C22×C4—101no—
234C22×C4—101no—
235C22×C4—201no—
236C22×C4#70911yescharacteristic
237C22×C4D4×D511yescharacteristic
238C22×C4D4×D511yescharacteristic
239M16—201no—
240M16—201no—
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—102no—
246C2×C8—102no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—52no—
254C4⋊C4—102no—
255C4⋊C4—102no—
256C4⋊C4—101no—
257C4⋊C4—201no—
258C4⋊C4—201no—
259C22⋊C4—41no—
260C42—41no—
261C42—102no—
262C42—102no—
263C42C2×C4×D511yescharacteristic
264C42D4×D511yescharacteristic
265C42#71111yescharacteristic
266C42C2×C22⋊D511yescharacteristic
267C2×C5—21no—
268C2×C5—21no—
269C2×C5#188111yescharacteristic
270C2×C5#189211yescharacteristic
271C2×C5#190511yescharacteristic
272C23#403011yescharacteristic
273Q8—42no—
274Q8—54no—
275Q8—81no—
276Q8—102no—
277Q8—102no—
278Q8—102no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—102no—
284C2×C4—102no—
285C2×C4—102no—
286C2×C4—102no—
287C2×C4—401no—
288C2×C4—401no—
289C2×C4—401no—
290C2×C4—401no—
291C2×C4D5×C22⋊C411yescharacteristic
292C2×C4#402711yescharacteristic
293C2×C4#402911yescharacteristic
294C2×C4D5×SD1611yescharacteristic
295C2×C4#406211yescharacteristic
296C2×C4D5×Q1611yescharacteristic
297C2×C4#406511yescharacteristic
298C2×C4C4×C22⋊D511yescharacteristic
299C2×C4#408311yescharacteristic
300C2×C4#408411yescharacteristic
301C8—42no—
302C8—81no—
303C8—202no—
304C8—202no—
305C5#930411yescharacteristic, complemented, Sylow
306C22—21no—
307C22—21no—
308C22#6509611yescharacteristic
309C22#6510211yescharacteristic
310C22#6524511yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—81no—
316C4—81no—
317C4—104no—
318C4—202no—
319C4—801no—
320C4D5×#10311yescharacteristic
321C4#6509311yescharacteristic
322C4#6546011yescharacteristic
323C4#6547711yescharacteristic
324C2—21no—
325C2—21no—
326C2#1060080511yescharacteristic
327C2#1060106311yescharacteristic
328C2#1060120311yescharacteristic
subgroupG/H
centerC22#65245
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1481C2
socleC22×C5#386
prime radicalC23×C5#121
cosocleC2×C42×C5C23
hypercenter#1481D5
hypocenterC5#9304
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
13. #65383C4semidirect
14. #65380C4semidirect
305. C5#9304semidirect

Maximal subgroups

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

subgroupindex
#106150982
#106109942
C5×#14812
#106026312
#106012792
#105982292
#105981982
#93045