Finite Group Databasebeta

← #11996053

Subgroups — #11996053

Order 1280.

488 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
1#10614032C211yesmaximal, characteristic
2#10614027C211yesmaximal, characteristic
3C5×#1804C211yesmaximal, characteristic
4#10601222C211yesmaximal, characteristic, complemented
5#10600339C211yesmaximal, characteristic, complemented
6#10598198C211yesmaximal, characteristic, complemented
7#10598122C211yesmaximal, characteristic, complemented
8C2×C4×C5×D4C2211yescharacteristic
9#65804C2211yescharacteristic
10C2×C5×C4⋊C8C2211yescharacteristic
11C2×C5×#102—21no—
12C5×#382C2211yescharacteristic
13#65504—21no—
14C2×C22⋊#168—22no—
15D4×#168—22no—
16D4×#168—22no—
17#65298—22no—
18#65297C412yescomplemented
19#65296C412yescomplemented
20#65253—21no—
21#65214C2211yescharacteristic
22#65214C2211yescharacteristic
23#65213C2211yescharacteristic
24C5×#340—21no—
25#64704—22no—
26#64672—22no—
27#9303—51nomaximal, Sylow
28C22×C5×D4D411yescharacteristic
29C23×C4×C5—21no—
30C22×C5×C8—21no—
31C4×C5×D4—21no—
32C4×C5×D4—21no—
33C4×C5×D4C2×C412yes—
34C4×C5×D4D412yes—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4D411yescharacteristic
37C2×C5×C22⋊C4—21no—
38C2×C42×C5C2311yescharacteristic
39#4072—21no—
40#4070—21no—
41#4070—21no—
42C2×#681—21no—
43C22×#168—24no—
44#4016—21no—
45#4015C2×C411yescharacteristic
46#4015C2×C411yescharacteristic
47C4×Dic10—21no—
48C4×Dic10—21no—
49C5×C4⋊C8—21no—
50C5×C4⋊C8—21no—
51C5×#102—42no—
52C5×#95—21no—
53C5×#95—21no—
54#3964—22no—
55#3964—22no—
56C22⋊#168—24no—
57C22⋊#168—21no—
58C22⋊#168D412yes—
59#3940—22no—
60#3939—22no—
61C4⋊#168—21no—
62C4⋊#168—21no—
63C4⋊#168—21no—
64C4⋊#168C2×C412yes—
65C4×#168—21no—
66C4×#168D412yes—
67#3077—51no—
68#2972—51no—
69#1804D511yescharacteristic
70#1518—51no—
71#1481—51no—
72#1301—51no—
73#1286—51no—
74C24×C5—21no—
75C2×C5×D4—21no—
76C2×C5×D4—21no—
77C2×C5×D4—21no—
78C2×C5×D4C22⋊C412yes—
79C2×C5×D4SD1612yes—
80C2×C5×D4Q1612yes—
81C22×C4×C5—21no—
82C22×C4×C5—22no—
83C22×C4×C5—22no—
84C22×C4×C5—41no—
85C22×C4×C5—82no—
86C22×C4×C5C2×D411yescharacteristic
87C22×C4×C5C2×D411yescharacteristic
88C22×C4×C5#4111yescharacteristic
89C2×Dic10—21no—
90C2×Dic10—21no—
91C2×C5×C8—41no—
92C2×C5×C8—41no—
93C2×C5×C8—41no—
94C5×C4⋊C4—21no—
95C5×C4⋊C4—41no—
96C5×C4⋊C4—41no—
97C5×C4⋊C4C22⋊C412yes—
98C5×C22⋊C4—22no—
99C5×C22⋊C4—22no—
100C42×C5C22×C411yescharacteristic
101C42×C5C2×D411yescharacteristic
102C42×C5C2×D411yescharacteristic
103C42×C5#4111yescharacteristic
104C22⋊Dic5—41no—
105C4⋊Dic5—21no—
106C4⋊Dic5—21no—
107C4⋊Dic5—21no—
108C4⋊Dic5—21no—
109#683—41no—
110#683—41no—
111C4×Dic5—41no—
112#681—41no—
113#681—41no—
114C2×#168—22no—
115C2×#168—22no—
116C2×#168—22no—
117C2×#168—84no—
118#533—51no—
119C2×C4×D4C2×D511yescharacteristic
120#478—102no—
121#476—52no—
122#474—52no—
123C8×D4—102no—
124C8×D4—102no—
125#431—51no—
126#431—51no—
127#428—101no—
128#423—51no—
129C2×C4⋊C8C2×D511yescharacteristic
130#418—101no—
131C2×#102—21no—
132C2×C22⋊C8—102no—
133#382C2×D511yescharacteristic
134#340—21no—
135#328—102no—
136Q8⋊C8—102no—
137C23×C5—22no—
138C23×C5—22no—
139C23×C5—22no—
140C23×C5—81no—
141C23×C5—81no—
142C23×C5#12111yescharacteristic
143C5×D4—22no—
144C5×D4—22no—
145C5×D4—22no—
146C5×D4#10314yes—
147C2×C4×C5—22no—
148C2×C4×C5—41no—
149C2×C4×C5—41no—
150C2×C4×C5—44no—
151C2×C4×C5—82no—
152C2×C4×C5—81no—
153C2×C4×C5—81no—
154C2×C4×C5—81no—
155C2×C4×C5—81no—
156C2×C4×C5C2×C22⋊C411yescharacteristic
157C2×C4×C5C4×D411yescharacteristic
158C2×C4×C5C4×D411yescharacteristic
159C2×C4×C5#12011yescharacteristic
160C2×C4×C5#12111yescharacteristic
161C2×C4×C5#12311yescharacteristic
162C2×C4×C5C2×SD1611yescharacteristic
163C2×C4×C5C2×Q1611yescharacteristic
164C2×C4×C5#13511yescharacteristic
165C2×C4×C5#13511yescharacteristic
166C2×Dic5—41no—
167C2×Dic5—41no—
168Dic10—42no—
169Dic10—81no—
170C5×C8—81no—
171#168—42no—
172#168—42no—
173#168—42no—
174C22×D4C22⋊D511yescharacteristic
175C23×C4—21no—
176C2×M16—101no—
177C22×C8—21no—
178C22×C8—104no—
179C4⋊Q8—51no—
180C4⋊Q8—51no—
181#125—101no—
182C22⋊Q8—101no—
183C22⋊Q8—101no—
184C4×Q8—101no—
185C4×Q8—101no—
186C4×D4—21no—
187C4×D4—21no—
188C4×D4C4×D512yes—
189C4×D4D2012yes—
190#117—101no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4C22⋊D511yescharacteristic
193C2×C22⋊C4—21no—
194C2×C42C22×D511yescharacteristic
195#107—102no—
196#106—102no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—52no—
200C4⋊C8—101no—
201C4⋊C8—101no—
202C4⋊C8—101no—
203#102—42no—
204#102—102no—
205#102—102no—
206C22⋊C8—52no—
207C22⋊C8—104no—
208C22⋊C8—101no—
209C4×C8—52no—
210C4×C8—101no—
211#95—21no—
212#95—21no—
213C22×C5—21no—
214C22×C5—21no—
215C22×C5—24no—
216C22×C5—42no—
217C22×C5—42no—
218C22×C5—82no—
219C22×C5—82no—
220C22×C5#38611yescharacteristic
221C22×C5#46511yescharacteristic
222C22×C5#46711yescharacteristic
223C4×C5—21no—
224C4×C5—21no—
225C4×C5—21no—
226C4×C5—21no—
227C4×C5—42no—
228C4×C5—161no—
229C4×C5C2×#10311yescharacteristic
230C4×C5#41611yescharacteristic
231C4×C5#46511yescharacteristic
232C4×C5#46711yescharacteristic
233Dic5—81no—
234Dic5—81no—
235C24—21no—
236C2×Q8—101no—
237C2×Q8—101no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4#68512yes—
242C2×D4#68712yes—
243C2×D4#68912yes—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—41no—
248C22×C4—82no—
249C22×C4D4×D511yescharacteristic
250C22×C4#71111yescharacteristic
251C22×C4C2×C22⋊D511yescharacteristic
252M16—201no—
253M16—201no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—102no—
258C2×C8—102no—
259C2×C8—102no—
260C2×C8—404no—
261C4⋊C4—21no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—101no—
265C4⋊C4—101no—
266C4⋊C4—101no—
267C4⋊C4—101no—
268C4⋊C4—201no—
269C4⋊C4—201no—
270C4⋊C4#68512yes—
271C22⋊C4—22no—
272C22⋊C4—22no—
273C22⋊C4—201no—
274C42—201no—
275C42C2×C4×D511yescharacteristic
276C42C2×D2011yescharacteristic
277C42D4×D511yescharacteristic
278C42#71111yescharacteristic
279C2×C5—21no—
280C2×C5—21no—
281C2×C5—44no—
282C2×C5#188111yescharacteristic
283C2×C5#189211yescharacteristic
284C2×C5#190411yescharacteristic
285C23—22no—
286C23—22no—
287C23—22no—
288C23—81no—
289C23—81no—
290C23#408511yescharacteristic
291Q8—202no—
292Q8—401no—
293D4—22no—
294D4—22no—
295D4—22no—
296D4#394214yes—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—44no—
301C2×C4—82no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—201no—
307C2×C4—201no—
308C2×C4#402711yescharacteristic
309C2×C4#402711yescharacteristic
310C2×C4#402811yescharacteristic
311C2×C4#403211yescharacteristic
312C2×C4C2×#68511yescharacteristic
313C2×C4C2×#68711yescharacteristic
314C2×C4#408511yescharacteristic
315C2×C4C2×#68911yescharacteristic
316C2×C4#409611yescharacteristic
317C2×C4#409611yescharacteristic
318C8—81no—
319C8—202no—
320C8—202no—
321C8—202no—
322C5#930311yescharacteristic, complemented, Sylow
323C22—21no—
324C22—21no—
325C22—24no—
326C22—42no—
327C22—42no—
328C22—82no—
329C22—82no—
330C22#6524711yescharacteristic
331C22#6533011yescharacteristic
332C22#6534011yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—42no—
338C4—161no—
339C4—401no—
340C4—401no—
341C4C2×#394211yescharacteristic
342C4#6529111yescharacteristic
343C4#6533011yescharacteristic
344C4#6534011yescharacteristic
345C2—21no—
346C2—21no—
347C2—44no—
348C2#1060030711yescharacteristic
349C2#1060108611yescharacteristic
350C2#1060110711yescharacteristic
subgroupG/H
centerC22#65247
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1804C2
socleC22×C5#386
prime radicalC22×C5×D4D4
cosocleC2×C42×C5C23
hypercenter#1804D5
hypocenterC5#9303
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
4. #10601222C2semidirect
5. #10600339C2semidirect
6. #10598198C2semidirect
7. #10598122C2semidirect
18. #65297C4semidirect
19. #65296C4semidirect
322. C5#9303semidirect

Maximal subgroups

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

subgroupindex
#106140322
#106140272
C5×#18042
#106012222
#106003392
#105981982
#105981222
#93035