Finite Group Databasebeta

← #11997697

Subgroups — #11997697

Order 1280.

386 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#1770C211yesmaximal, characteristic
2C2×#64706C211yesmaximal, characteristic
3#10600570C211yesmaximal, characteristic
4#10600279C211yesmaximal, characteristic
5#10600260C211yesmaximal, characteristic
6#10598193C211yesmaximal, characteristic
7#10598145C211yesmaximal, characteristic
8C2×#4015C2211yescharacteristic
9C2×C5×C4⋊C8C2211yescharacteristic
10C2×C5×#97—21no—
11C2×C4×C5×C8C2211yescharacteristic
12C4×C5×C4⋊C4C2211yescharacteristic
13C2×#3942—21no—
14C2×#3942—21no—
15C2×#3940—21no—
16#65224C2211yescharacteristic
17C2×C4⋊#168C2211yescharacteristic
18C2×C4⋊#168C2211yescharacteristic
19C5×#336—21no—
20#64771—21no—
21#64771—21no—
22#64749—21no—
23#64706C414yescomplemented
24#9573—51nomaximal, Sylow
25C22×Dic10—21no—
26C22×C5×C8—21no—
27C22×C5×C8D411yescharacteristic
28C22×C5×C8D411yescharacteristic
29C2×C5×C4⋊C4D411yescharacteristic
30C2×C5×C4⋊C4D411yescharacteristic
31C2×C42×C5—21no—
32C2×C42×C5C2311yescharacteristic
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—21no—
38C22×#168—21no—
39C22×#168—21no—
40#4015—21no—
41#4015—21no—
42#4015—21no—
43#4015C2×C412yes—
44C5×C4⋊C8—21no—
45C5×C4⋊C8C2×C412yes—
46C5×#97—42no—
47C4×C5×C8—21no—
48C4×C5×C8—21no—
49C5×#95—21no—
50#3942—42no—
51#3942—42no—
52#3940—42no—
53C4⋊#168—21no—
54C4⋊#168—21no—
55C4⋊#168—21no—
56C4⋊#168C2×C412yes—
57#1990—51no—
58#1981—51no—
59#1948—51no—
60#1770D511yescharacteristic
61C2×#332—51no—
62#1296—51no—
63#1277—51no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5C2×D411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×C4×C5#4111yescharacteristic
69C22×Dic5—41no—
70C22×Dic5—41no—
71C2×Dic10—22no—
72C2×Dic10—41no—
73C2×Dic10—41no—
74C2×Dic10—41no—
75C2×Dic10—41no—
76C2×Dic10—41no—
77C2×C5×C8—21no—
78C2×C5×C8—21no—
79C2×C5×C8—22no—
80C2×C5×C8—21no—
81C2×C5×C8—21no—
82C2×C5×C8—21no—
83C2×C5×C8—41no—
84C2×C5×C8—41no—
85C2×C5×C8SD1612yes—
86C5×C4⋊C4—21no—
87C5×C4⋊C4—21no—
88C5×C4⋊C4—21no—
89C5×C4⋊C4—21no—
90C42×C5—41no—
91C42×C5—41no—
92C42×C5C22×C411yescharacteristic
93C42×C5#4111yescharacteristic
94C42×C5#4111yescharacteristic
95C42×C5#4111yescharacteristic
96C4⋊Dic5—22no—
97C4⋊Dic5—22no—
98C4⋊Dic5—41no—
99C4⋊Dic5—41no—
100C4⋊Dic5—41no—
101C4⋊Dic5—41no—
102C4⋊Dic5—41no—
103C4⋊Dic5—41no—
104C4⋊Dic5—81no—
105C2×#168—22no—
106C2×#168—41no—
107C2×#168—41no—
108C2×#168—41no—
109C2×#168—41no—
110C2×#168—41no—
111C2×C4⋊Q8—51no—
112C2×#106—101no—
113C2×C4⋊C8—51no—
114C2×C4⋊C8—51no—
115C2×C4⋊C8C2×D511yescharacteristic
116C2×#103—101no—
117C2×#103—101no—
118C2×#97—21no—
119C2×C4×C8C2×D511yescharacteristic
120#384—51no—
121C4×C4⋊C4C2×D511yescharacteristic
122#340—101no—
123#340—101no—
124#340—101no—
125#336—21no—
126#332—54no—
127C23×C5#12111yescharacteristic
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—41no—
131C2×C4×C5—41no—
132C2×C4×C5—41no—
133C2×C4×C5—41no—
134C2×C4×C5—41no—
135C2×C4×C5—41no—
136C2×C4×C5#11711yescharacteristic
137C2×C4×C5C4×D411yescharacteristic
138C2×C4×C5C4×D411yescharacteristic
139C2×C4×C5#12311yescharacteristic
140C2×C4×C5#12411yescharacteristic
141C2×C4×C5#12611yescharacteristic
142C2×C4×C5C2×SD1611yescharacteristic
143C2×C4×C5#13511yescharacteristic
144C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C5#13711yescharacteristic
148C2×C4×C5#13711yescharacteristic
149C2×C4×C5#13711yescharacteristic
150C2×Dic5—42no—
151C2×Dic5—81no—
152C2×Dic5—81no—
153C2×Dic5—81no—
154C2×Dic5—81no—
155C2×Dic5—81no—
156Dic10—42no—
157Dic10—42no—
158Dic10—81no—
159Dic10—81no—
160C5×C8—22no—
161C5×C8—42no—
162C5×C8—41no—
163#168—42no—
164#168—81no—
165C22×Q8—101no—
166C22×C8—21no—
167C22×C8—101no—
168C22×C8—101no—
169C22×C8C22⋊D511yescharacteristic
170C22×C8C22⋊D511yescharacteristic
171C4⋊Q8—52no—
172C4⋊Q8—101no—
173C4⋊Q8—101no—
174C4⋊Q8—101no—
175C2×C4⋊C4—101no—
176C2×C4⋊C4—101no—
177C2×C4⋊C4—101no—
178C2×C4⋊C4—101no—
179C2×C4⋊C4—101no—
180C2×C4⋊C4D2011yescharacteristic
181C2×C4⋊C4D2011yescharacteristic
182C2×C42—21no—
183C2×C42C22×D511yescharacteristic
184#106—202no—
185C4⋊C8—21no—
186C4⋊C8—52no—
187C4⋊C8—101no—
188C4⋊C8—101no—
189C4⋊C8—101no—
190C4⋊C8C4×D512yes—
191#103—202no—
192#103—202no—
193#97—42no—
194C4×C8—21no—
195C4×C8—21no—
196#95—21no—
197C22×C5#38811yescharacteristic
198C22×C5#46111yescharacteristic
199C22×C5#46411yescharacteristic
200C22×C5#46811yescharacteristic
201C22×C5#46911yescharacteristic
202C22×C5#47111yescharacteristic
203C22×C5#47311yescharacteristic
204C4×C5—21no—
205C4×C5—21no—
206C4×C5—81no—
207C4×C5—81no—
208C4×C5C4×SD1611yescharacteristic
209C4×C5#44011yescharacteristic
210C4×C5#44111yescharacteristic
211C4×C5#44211yescharacteristic
212C4×C5#48311yescharacteristic
213C4×C5#48511yescharacteristic
214C4×C5#48911yescharacteristic
215C4×C5#49011yescharacteristic
216Dic5—82no—
217Dic5—161no—
218C2×Q8—102no—
219C2×Q8—201no—
220C2×Q8—201no—
221C2×Q8—201no—
222C2×Q8—201no—
223C2×Q8—201no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—201no—
227C22×C4—201no—
228C22×C4C2×D2011yescharacteristic
229C22×C4#70911yescharacteristic
230C22×C4C2×C22⋊D511yescharacteristic
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—22no—
236C2×C8—21no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—102no—
240C2×C8—201no—
241C2×C8—201no—
242C2×C8—201no—
243C2×C8—201no—
244C2×C8—201no—
245C2×C8#68712yes—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—102no—
251C4⋊C4—102no—
252C4⋊C4—201no—
253C4⋊C4—201no—
254C4⋊C4—201no—
255C4⋊C4—201no—
256C4⋊C4—201no—
257C4⋊C4—201no—
258C4⋊C4—401no—
259C42—41no—
260C42—41no—
261C42C2×C4×D511yescharacteristic
262C42#70911yescharacteristic
263C42#70911yescharacteristic
264C42#70911yescharacteristic
265C2×C5#169111yescharacteristic
266C2×C5#169311yescharacteristic
267C2×C5#170011yescharacteristic
268C2×C5#170211yescharacteristic
269C2×C5#192711yescharacteristic
270C2×C5#193011yescharacteristic
271C2×C5#193611yescharacteristic
272C23#407611yescharacteristic
273Q8—202no—
274Q8—202no—
275Q8—401no—
276Q8—401no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—202no—
286C2×C4—401no—
287C2×C4—401no—
288C2×C4—401no—
289C2×C4—401no—
290C2×C4—401no—
291C2×C4#401811yescharacteristic
292C2×C4C4×D2011yescharacteristic
293C2×C4#402111yescharacteristic
294C2×C4#402211yescharacteristic
295C2×C4#405411yescharacteristic
296C2×C4#405411yescharacteristic
297C2×C4#405411yescharacteristic
298C2×C4#405511yescharacteristic
299C2×C4C4×C22⋊D511yescharacteristic
300C2×C4#407511yescharacteristic
301C2×C4C2×#68711yescharacteristic
302C2×C4#408811yescharacteristic
303C2×C4#409611yescharacteristic
304C2×C4#409711yescharacteristic
305C8—22no—
306C8—41no—
307C8—42no—
308C8—202no—
309C8—401no—
310C5#957311yescharacteristic, complemented, Sylow
311C22#6522911yescharacteristic
312C22#6530811yescharacteristic
313C22#6531711yescharacteristic
314C22#6542311yescharacteristic
315C22#6542411yescharacteristic
316C22#6543011yescharacteristic
317C22#6543211yescharacteristic
318C4—21no—
319C4—21no—
320C4—81no—
321C4—81no—
322C4—402no—
323C4—801no—
324C4#6499911yescharacteristic
325C4#6500011yescharacteristic
326C4#6500211yescharacteristic
327C4#6500311yescharacteristic
328C4#6526011yescharacteristic
329C4#6528511yescharacteristic
330C4C4×#68711yescharacteristic
331C4#6531911yescharacteristic
332C2#1060025711yescharacteristic
333C2#1060061111yescharacteristic
334C2#1060068411yescharacteristic
335C2#1060166511yescharacteristic
336C2#1060166611yescharacteristic
337C2#1060175411yescharacteristic
338C2#1060175911yescharacteristic
subgroupG/H
centerC23#4076
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1770C2
socle, prime radicalC23×C5#121
cosocleC2×C42×C5C23
hypercenter#1770D5
hypocenterC5#9573
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1770

Complements

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

NH ≅ G/Ntype
23. #64706C4semidirect
310. C5#9573semidirect

Maximal subgroups

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

subgroupindex
C5×#17702
C2×#647062
#106005702
#106002792
#106002602
#105981932
#105981452
#95735