Finite Group Databasebeta

← #11996088

Subgroups — #11996088

Order 1280.

416 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 111 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#10614167C211yesmaximal, characteristic
2#10614162C211yesmaximal, characteristic
3C5×#1805C211yesmaximal, characteristic
4#10601222C211yesmaximal, characteristic
5#10600339C211yesmaximal, characteristic
6#10598198C211yesmaximal, characteristic
7#10598122C211yesmaximal, characteristic
8C2×C4×C5×Q8C2211yescharacteristic
9#65804C2211yescharacteristic
10C2×C5×C4⋊C8C2211yescharacteristic
11C2×C5×#103—21no—
12C5×#382C2211yescharacteristic
13#65514—21no—
14#65313—22no—
15#65313—22no—
16#65311—22no—
17#65310C412yescomplemented
18#65309C412yescomplemented
19#65253—21no—
20#65215—22no—
21#65214C2211yescharacteristic
22#65214C2211yescharacteristic
23#65213C2211yescharacteristic
24C5×#340—21no—
25#64704—22no—
26#64672—22no—
27#9308—51nomaximal, Sylow
28C22×C5×Q8D411yescharacteristic
29C22×C5×C8—21no—
30C4×C5×Q8—21no—
31C4×C5×Q8—21no—
32C4×C5×Q8C2×C412yes—
33C4×C5×Q8D412yes—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4D411yescharacteristic
37C2×C42×C5—21no—
38C2×C42×C5C2311yescharacteristic
39#4072—21no—
40#4070—21no—
41#4070—21no—
42C2×#681—21no—
43#4016—21no—
44#4015C2×C411yescharacteristic
45#4015C2×C411yescharacteristic
46C4×Dic10—21no—
47C4×Dic10—21no—
48C5×C4⋊C8—21no—
49C5×C4⋊C8—21no—
50C5×#103—42no—
51C5×#95—21no—
52C5×#95—21no—
53#3967—22no—
54#3967—22no—
55C22⋊#168—21no—
56C22⋊#168D412yes—
57#3940—22no—
58#3939—22no—
59C4⋊#168—24no—
60C4⋊#168—21no—
61C4⋊#168—21no—
62C4⋊#168—21no—
63C4⋊#168C2×C412yes—
64#3935—24no—
65C4×#168—21no—
66C4×#168D412yes—
67#3078—51no—
68#2983—51no—
69#1805D511yescharacteristic
70#1518—51no—
71#1481—51no—
72#1301—51no—
73#1286—51no—
74C2×C5×Q8—21no—
75C2×C5×Q8—21no—
76C2×C5×Q8—21no—
77C2×C5×Q8—21no—
78C2×C5×Q8—21no—
79C2×C5×Q8C22⋊C412yes—
80C22×C4×C5—21no—
81C22×C4×C5—21no—
82C22×C4×C5—41no—
83C22×C4×C5C2×D411yescharacteristic
84C22×C4×C5C2×D411yescharacteristic
85C22×C4×C5#4111yescharacteristic
86C2×Dic10—21no—
87C2×Dic10—21no—
88C2×C5×C8—41no—
89C2×C5×C8—41no—
90C2×C5×C8—41no—
91C5×C4⋊C4—22no—
92C5×C4⋊C4—21no—
93C5×C4⋊C4—22no—
94C5×C4⋊C4—41no—
95C5×C4⋊C4—41no—
96C5×C4⋊C4C22⋊C412yes—
97C42×C5—22no—
98C42×C5—22no—
99C42×C5C22×C411yescharacteristic
100C42×C5C2×D411yescharacteristic
101C42×C5C2×D411yescharacteristic
102C42×C5#4111yescharacteristic
103C22⋊Dic5—41no—
104C4⋊Dic5—21no—
105C4⋊Dic5—21no—
106C4⋊Dic5—21no—
107C4⋊Dic5—21no—
108#683—41no—
109#683—41no—
110C4×Dic5—41no—
111#681—41no—
112#681—41no—
113C2×#168—22no—
114C2×#168—22no—
115C2×#168—22no—
116#533—51no—
117C2×C4×Q8C2×D511yescharacteristic
118#479—102no—
119#477—52no—
120#475—52no—
121#446—102no—
122#446—102no—
123#432—102no—
124#431—51no—
125#431—51no—
126#428—101no—
127#423—51no—
128C2×C4⋊C8C2×D511yescharacteristic
129#419—101no—
130C2×#103—21no—
131#382C2×D511yescharacteristic
132#340—21no—
133#328—102no—
134Q8⋊C8—102no—
135C23×C5#12111yescharacteristic
136C5×Q8—22no—
137C5×Q8—22no—
138C5×Q8—41no—
139C5×Q8—41no—
140C2×C4×C5—22no—
141C2×C4×C5—22no—
142C2×C4×C5—41no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5—81no—
147C2×C4×C5—81no—
148C2×C4×C5—81no—
149C2×C4×C5—81no—
150C2×C4×C5C2×C22⋊C411yescharacteristic
151C2×C4×C5C4×D411yescharacteristic
152C2×C4×C5C4×D411yescharacteristic
153C2×C4×C5#12011yescharacteristic
154C2×C4×C5#12111yescharacteristic
155C2×C4×C5#12311yescharacteristic
156C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C5#13711yescharacteristic
158C2×C4×C5#13711yescharacteristic
159C2×C4×C5#13711yescharacteristic
160C2×Dic5—41no—
161C2×Dic5—41no—
162Dic10—42no—
163Dic10—81no—
164C5×C8—81no—
165#168—42no—
166#168—42no—
167#168—42no—
168C22×Q8C22⋊D511yescharacteristic
169C2×M16—101no—
170C22×C8—21no—
171C4⋊Q8—51no—
172C4⋊Q8—51no—
173#125—101no—
174C22⋊Q8—101no—
175C22⋊Q8—101no—
176C4×Q8—21no—
177C4×Q8—21no—
178C4×Q8—101no—
179C4×Q8—101no—
180C4×Q8C4×D512yes—
181C4×Q8D2012yes—
182#117—101no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4C22⋊D511yescharacteristic
186C2×C42—21no—
187C2×C42C22×D511yescharacteristic
188#107—102no—
189#106—102no—
190C4⋊C8—21no—
191C4⋊C8—21no—
192C4⋊C8—52no—
193C4⋊C8—104no—
194C4⋊C8—101no—
195C4⋊C8—101no—
196C4⋊C8—101no—
197#103—42no—
198#103—102no—
199#103—102no—
200C22⋊C8—52no—
201C22⋊C8—101no—
202#97—104no—
203C4×C8—52no—
204C4×C8—101no—
205#95—21no—
206#95—21no—
207C22×C5—21no—
208C22×C5—21no—
209C22×C5#38611yescharacteristic
210C22×C5#46811yescharacteristic
211C22×C5#47011yescharacteristic
212C4×C5—21no—
213C4×C5—21no—
214C4×C5—21no—
215C4×C5—21no—
216C4×C5—42no—
217C4×C5—42no—
218C4×C5—161no—
219C4×C5#41711yescharacteristic
220C4×C5#41911yescharacteristic
221C4×C5#46811yescharacteristic
222C4×C5#47011yescharacteristic
223Dic5—81no—
224Dic5—81no—
225C2×Q8—21no—
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—101no—
231C2×Q8—101no—
232C2×Q8#68512yes—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—41no—
236C22×C4D4×D511yescharacteristic
237C22×C4#71111yescharacteristic
238C22×C4C2×C22⋊D511yescharacteristic
239M16—201no—
240M16—201no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—102no—
245C2×C8—102no—
246C2×C8—102no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—101no—
253C4⋊C4—101no—
254C4⋊C4—101no—
255C4⋊C4—101no—
256C4⋊C4—201no—
257C4⋊C4—201no—
258C4⋊C4#68512yes—
259C22⋊C4—201no—
260C42—22no—
261C42—22no—
262C42—201no—
263C42C2×C4×D511yescharacteristic
264C42C2×D2011yescharacteristic
265C42D4×D511yescharacteristic
266C42#71111yescharacteristic
267C2×C5—21no—
268C2×C5—21no—
269C2×C5#188111yescharacteristic
270C2×C5#189411yescharacteristic
271C2×C5#190511yescharacteristic
272C23#408511yescharacteristic
273Q8—22no—
274Q8—22no—
275Q8—41no—
276Q8—41no—
277Q8—202no—
278Q8—401no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—201no—
290C2×C4—201no—
291C2×C4#402711yescharacteristic
292C2×C4#402711yescharacteristic
293C2×C4#402811yescharacteristic
294C2×C4#403211yescharacteristic
295C2×C4C2×#68511yescharacteristic
296C2×C4#407811yescharacteristic
297C2×C4#408511yescharacteristic
298C2×C4#408811yescharacteristic
299C2×C4#409711yescharacteristic
300C2×C4#409711yescharacteristic
301C8—81no—
302C8—202no—
303C8—202no—
304C8—202no—
305C5#930811yescharacteristic, complemented, Sylow
306C22—21no—
307C22—21no—
308C22#6524711yescharacteristic
309C22#6533111yescharacteristic
310C22#6534111yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—42no—
316C4—42no—
317C4—161no—
318C4—401no—
319C4—401no—
320C4#6525511yescharacteristic
321C4#6529311yescharacteristic
322C4#6533111yescharacteristic
323C4#6534111yescharacteristic
324C2—21no—
325C2—21no—
326C2#1060030911yescharacteristic
327C2#1060108611yescharacteristic
328C2#1060112711yescharacteristic
subgroupG/H
centerC22#65247
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1805C2
socleC22×C5#386
prime radicalC23×C5#121
cosocleC2×C42×C5C23
hypercenter#1805D5
hypocenterC5#9308
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
17. #65310C4semidirect
18. #65309C4semidirect
305. C5#9308semidirect

Maximal subgroups

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

subgroupindex
#106141672
#106141622
C5×#18052
#106012222
#106003392
#105981982
#105981222
#93085