Finite Group Databasebeta

← #11996010

Subgroups — #11996010

Order 1280.

454 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 107 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#10615101C211yesmaximal, characteristic
2#10605885C211yesmaximal, characteristic
3C5×#1518C211yesmaximal, characteristic
4#10602633C211yesmaximal, characteristic
5#10601572C211yesmaximal, characteristic
6#10598228C211yesmaximal, characteristic
7#10598122C211yesmaximal, characteristic
8C5×#533C2211yescharacteristic
9C2×#4015C2211yescharacteristic
10C5×#431C2211yescharacteristic
11C5×#382C2211yescharacteristic
12#65382C412yescomplemented
13#65381C412yescomplemented
14#65339—22no—
15#65320—22no—
16C4⋊C4×Dic5—21no—
17#65262—21no—
18#65221C2211yescharacteristic
19#65214C2211yescharacteristic
20#65213C2211yescharacteristic
21#64942—22no—
22#64935—22no—
23C5×#328—22no—
24#64752—21no—
25#64752—21no—
26#64701—22no—
27#9297—51nomaximal, Sylow
28C22×Dic10D412yes—
29C5×C4⋊Q8C2×C411yescharacteristic
30C5×C4⋊Q8C2×C411yescharacteristic
31C5×#125—21no—
32C5×C22⋊Q8—21no—
33C5×C22⋊Q8—21no—
34C4×C5×Q8—21no—
35C4×C5×Q8—21no—
36C5×#117—21no—
37C2×C5×C4⋊C4—21no—
38C2×C42×C5C2311yescharacteristic
39C2×#689—24no—
40C2×C4⋊Dic5—21no—
41C2×C4⋊Dic5—21no—
42C2×#683—22no—
43C2×C4×Dic5—22no—
44C2×C4×Dic5D411yescharacteristic
45C2×C4×Dic5D411yescharacteristic
46C2×#681—21no—
47#4015—21no—
48#4015—21no—
49#4015C2×C412yes—
50#4015D412yes—
51C5×C4⋊C8—21no—
52C5×C22⋊C8—21no—
53C4×C5×C8—21no—
54C5×#95—21no—
55C5×#95D412yes—
56#3963—22no—
57#3963—22no—
58#3963—21no—
59#3963—21no—
60C22⋊#168—21no—
61#3942—24no—
62C4⋊#168—21no—
63C4⋊#168—21no—
64C4⋊#168—21no—
65C4×#168C2×C412yes—
66#3209—51no—
67#2331—51no—
68#1995—51no—
69#1548—51no—
70#1518D511yescharacteristic
71#1286—51no—
72#1274—51no—
73C2×C5×Q8—21no—
74C2×C5×Q8—21no—
75C22×C4×C5—22no—
76C22×C4×C5C2×D411yescharacteristic
77C22×C4×C5C2×D411yescharacteristic
78C22×C4×C5C2×D411yescharacteristic
79C22×Dic5—22no—
80C22×Dic5—21no—
81C22×Dic5—21no—
82C2×Dic10—22no—
83C2×Dic10—82no—
84C2×Dic10C22⋊C414yes—
85C2×C5×C8—41no—
86C5×C4⋊C4—21no—
87C5×C4⋊C4—21no—
88C5×C4⋊C4—21no—
89C5×C4⋊C4—21no—
90C5×C4⋊C4—41no—
91C5×C4⋊C4—41no—
92C5×C4⋊C4—41no—
93C5×C4⋊C4—41no—
94C5×C22⋊C4—41no—
95C42×C5—41no—
96C42×C5C22×C411yescharacteristic
97C42×C5C2×D411yescharacteristic
98C42×C5#4111yescharacteristic
99C42×C5#4111yescharacteristic
100#689—84no—
101C4⋊Dic5—22no—
102C4⋊Dic5—22no—
103C4⋊Dic5—22no—
104C4⋊Dic5—22no—
105#683—82no—
106C4×Dic5—21no—
107C4×Dic5—21no—
108C4×Dic5—21no—
109C4×Dic5—82no—
110C4×Dic5Q1612yescomplemented
111#681—41no—
112#681—41no—
113C2×#168—22no—
114C2×#168—41no—
115#533C2×D511yescharacteristic
116C2×C4⋊Q8—51no—
117#494—52no—
118#487—52no—
119#462—102no—
120#451—102no—
121#431—51no—
122#431C2×D511yescharacteristic
123#423—51no—
124#391—102no—
125#389—101no—
126#387—102no—
127#382C2×D511yescharacteristic
128C4×C4⋊C4—101no—
129#376—51no—
130#339—101no—
131#339—101no—
132#333—102no—
133#328—22no—
134C23×C5#12011yescharacteristic
135C5×Q8—42no—
136C5×Q8—81no—
137C2×C4×C5—41no—
138C2×C4×C5—41no—
139C2×C4×C5—42no—
140C2×C4×C5—42no—
141C2×C4×C5—41no—
142C2×C4×C5—41no—
143C2×C4×C5—42no—
144C2×C4×C5C2×C22⋊C411yescharacteristic
145C2×C4×C5C4×D411yescharacteristic
146C2×C4×C5C4×D411yescharacteristic
147C2×C4×C5#12111yescharacteristic
148C2×C4×C5#12111yescharacteristic
149C2×C4×C5#12311yescharacteristic
150C2×C4×C5C2×Q1611yescharacteristic
151C2×C4×C5#13511yescharacteristic
152C2×C4×C5#13711yescharacteristic
153C2×C4×C5#13711yescharacteristic
154C2×Dic5—24no—
155C2×Dic5—22no—
156C2×Dic5—41no—
157C2×Dic5—42no—
158C2×Dic5—42no—
159C2×Dic5—41no—
160C2×Dic5—41no—
161C2×Dic5—41no—
162C2×Dic5—41no—
163Dic10—44no—
164Dic10—82no—
165C5×C8—81no—
166#168—42no—
167#168—81no—
168C22×Q8—52no—
169C2×Q16—104no—
170C2×M16—101no—
171C4⋊Q8—52no—
172C4⋊Q8—52no—
173C4⋊Q8—101no—
174C4⋊Q8—101no—
175C4⋊Q8C4×D511yescharacteristic
176C4⋊Q8C4×D511yescharacteristic
177#125—21no—
178C22⋊Q8—21no—
179C22⋊Q8—21no—
180C4×Q8—21no—
181C4×Q8—21no—
182#117—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—101no—
185C2×C4⋊C4—101no—
186C2×C4⋊C4—102no—
187C2×C42—51no—
188C2×C42—51no—
189C2×C42—102no—
190C2×C42C22×D511yescharacteristic
191C4⋊C8—21no—
192C4⋊C8—101no—
193C4⋊C8—101no—
194C4⋊C8—101no—
195#103—104no—
196C22⋊C8—21no—
197C22⋊C8—101no—
198C4×C8—21no—
199C4×C8—52no—
200#95—21no—
201#95—102no—
202#95—102no—
203#95—101no—
204#95—101no—
205#95C22⋊D512yes—
206C22×C5—21no—
207C22×C5—21no—
208C22×C5#38611yescharacteristic
209C22×C5#45111yescharacteristic
210C22×C5#45211yescharacteristic
211C4×C5—21no—
212C4×C5—21no—
213C4×C5—21no—
214C4×C5—21no—
215C4×C5—82no—
216C4×C5—81no—
217C4×C5—81no—
218C4×C5C4×Q1611yescharacteristic
219C4×C5#44111yescharacteristic
220C4×C5#46211yescharacteristic
221C4×C5#46411yescharacteristic
222Dic5—42no—
223Dic5—44no—
224Dic5—81no—
225C2×Q8—21no—
226C2×Q8—21no—
227C2×Q8—54no—
228C2×Q8—102no—
229C2×Q8—402no—
230C22×C4—22no—
231C22×C4—101no—
232C22×C4—102no—
233C22×C4—101no—
234C22×C4D4×D511yescharacteristic
235C22×C4D4×D511yescharacteristic
236C22×C4C2×C22⋊D511yescharacteristic
237Q16—404no—
238M16—201no—
239M16—201no—
240C2×C8—41no—
241C2×C8—102no—
242C2×C8—201no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—102no—
252C4⋊C4—102no—
253C4⋊C4—102no—
254C4⋊C4—102no—
255C4⋊C4—402no—
256C22⋊C4—41no—
257C42—41no—
258C42—52no—
259C42—101no—
260C42—101no—
261C42—101no—
262C42—402no—
263C42C2×C4×D511yescharacteristic
264C42#70911yescharacteristic
265C42D4×D511yescharacteristic
266C42#71111yescharacteristic
267C2×C5—21no—
268C2×C5—21no—
269C2×C5#187811yescharacteristic
270C2×C5#190511yescharacteristic
271C2×C5#191111yescharacteristic
272C23#408311yescharacteristic
273Q8—42no—
274Q8—81no—
275Q8—204no—
276Q8—402no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—102no—
285C2×C4—104no—
286C2×C4—201no—
287C2×C4—202no—
288C2×C4—202no—
289C2×C4—201no—
290C2×C4—201no—
291C2×C4—201no—
292C2×C4—201no—
293C2×C4D5×C22⋊C411yescharacteristic
294C2×C4#402711yescharacteristic
295C2×C4#402911yescharacteristic
296C2×C4#403011yescharacteristic
297C2×C4#406111yescharacteristic
298C2×C4#406211yescharacteristic
299C2×C4D5×Q1611yescharacteristic
300C2×C4#406411yescharacteristic
301C2×C4C4×C22⋊D511yescharacteristic
302C2×C4#408411yescharacteristic
303C8—81no—
304C8—202no—
305C8—401no—
306C5#929711yescharacteristic, complemented, Sylow
307C22—21no—
308C22—21no—
309C22#6524511yescharacteristic
310C22#6546211yescharacteristic
311C22#6547511yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—82no—
317C4—81no—
318C4—81no—
319C4—202no—
320C4—204no—
321C4—401no—
322C4#6507811yescharacteristic
323C4#6507911yescharacteristic
324C4#6508211yescharacteristic
325C4#6508711yescharacteristic
326C2—21no—
327C2—21no—
328C2#1060084511yescharacteristic
329C2#1060107411yescharacteristic
330C2#1060120111yescharacteristic
subgroupG/H
centerC22#65245
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1518C2
socleC22×C5#386
prime radicalC23×C5#120
cosocleC2×C42×C5C23
hypercenter#1518D5
hypocenterC5#9297
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
12. #65382C4semidirect
13. #65381C4semidirect
110. C4×Dic5Q16semidirect
306. C5#9297semidirect

Maximal subgroups

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

subgroupindex
#106151012
#106058852
C5×#15182
#106026332
#106015722
#105982282
#105981222
#92975