Finite Group Databasebeta

← #11999049

Subgroups — #11999049

Order 1280.

578 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
1C2×#65359C211yesmaximal, characteristic
2C5×#1957C211yesmaximal, characteristic
3#10602557C211yesmaximal, characteristic
4#10600570C211yesmaximal, characteristic, complemented
5C2×C8×#168C211yesmaximal, characteristic, complemented
6#10600372C211yesmaximal, characteristic, complemented
7#10600367C211yesmaximal, characteristic, complemented
8C2×C5×#127C2211yescharacteristic
9C2×#4015C2211yescharacteristic
10C2×C5×#102—22no—
11C2×C4×C5×C8C2211yescharacteristic
12C5×#384C2211yescharacteristic
13C2×#3964—22no—
14C2×#3964—22no—
15#65359—22no—
16#65359C414yescomplemented
17C2×#3942—22no—
18#65224C2211yescharacteristic
19C2×C4×#168C2211yescharacteristic
20C2×C4×#168C2211yescharacteristic
21#64771—22no—
22#64749—22no—
23C8×#168—22no—
24#9822—51nomaximal, Sylow
25C22×C5×D4—21no—
26C22×C5×D4—21no—
27C22×C5×D4—21no—
28C22×Dic10—21no—
29C22×C5×C8D412yes—
30C5×#127—21no—
31C5×#127—21no—
32C5×#127—21no—
33C5×#127C2×C412yes—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—21no—
37C2×C42×C5C2311yescharacteristic
38C2×C4⋊Dic5—21no—
39C2×C4⋊Dic5—21no—
40C2×C4⋊Dic5—21no—
41C2×C4⋊Dic5—21no—
42C2×C4⋊Dic5—21no—
43C22×#168D412yes—
44C22×#168D412yes—
45#4015—21no—
46#4015—21no—
47#4015—21no—
48#4015C2×C412yes—
49C5×#102—44no—
50C4×C5×C8—21no—
51C4×C5×C8—21no—
52#3964—28no—
53#3964—44no—
54#3942—44no—
55C4×#168—21no—
56C4×#168—21no—
57C4×#168C2×C412yes—
58C4×#168D412yes—
59C2×#486—51no—
60#1990—51no—
61#1957—51no—
62#1957D511yescharacteristic
63#1956—51no—
64#1834—51no—
65C2×C82—51no—
66C24×C5—41no—
67C2×C5×D4—22no—
68C2×C5×D4—22no—
69C2×C5×D4—22no—
70C2×C5×D4—41no—
71C2×C5×D4—41no—
72C2×C5×D4—41no—
73C2×C5×D4—42no—
74C2×C5×D4—42no—
75C2×C5×D4—42no—
76C2×C5×D4—42no—
77C2×C5×D4—42no—
78C2×C5×D4—42no—
79C22×C4×C5—41no—
80C22×C4×C5C2×D411yescharacteristic
81C22×C4×C5C2×D411yescharacteristic
82C22×C4×C5C2×D411yescharacteristic
83C22×Dic5—41no—
84C22×Dic5—41no—
85C2×Dic10—22no—
86C2×Dic10—42no—
87C2×Dic10—42no—
88C2×Dic10—41no—
89C2×C5×C8—22no—
90C2×C5×C8—22no—
91C2×C5×C8SD1614yes—
92C5×C4⋊C4—42no—
93C5×C4⋊C4—42no—
94C5×C4⋊C4—42no—
95C42×C5C22×C411yescharacteristic
96C42×C5C2×D411yescharacteristic
97C42×C5#4111yescharacteristic
98C42×C5#4111yescharacteristic
99C4⋊Dic5—22no—
100C4⋊Dic5—22no—
101C4⋊Dic5—41no—
102C4⋊Dic5—41no—
103C4⋊Dic5—42no—
104C4⋊Dic5—42no—
105C4⋊Dic5—42no—
106C2×#168—22no—
107C2×#168—22no—
108C2×#168—22no—
109C2×#168—22no—
110C2×#168C22⋊C414yes—
111C2×#168D814yes—
112C2×C4⋊Q8—51no—
113C2×#127C2×D511yescharacteristic
114#486—54no—
115#486—102no—
116C2×#103—102no—
117C2×#102—22no—
118C2×#102—102no—
119C2×#102—102no—
120C2×C4×C8—51no—
121C2×C4×C8—51no—
122C2×C4×C8C2×D511yescharacteristic
123#384—51no—
124#384C2×D511yescharacteristic
125#340—102no—
126#340—102no—
127C82—102no—
128C23×C5—42no—
129C23×C5—81no—
130C23×C5—81no—
131C23×C5—81no—
132C23×C5—81no—
133C23×C5—81no—
134C23×C5—81no—
135C23×C5#12711yescharacteristic
136C5×D4—44no—
137C5×D4—44no—
138C5×D4—44no—
139C5×D4—82no—
140C5×D4—82no—
141C5×D4—82no—
142C2×C4×C5—81no—
143C2×C4×C5—81no—
144C2×C4×C5—81no—
145C2×C4×C5C2×C22⋊C411yescharacteristic
146C2×C4×C5C4×D411yescharacteristic
147C2×C4×C5C4×D411yescharacteristic
148C2×C4×C5#12111yescharacteristic
149C2×C4×C5#12111yescharacteristic
150C2×C4×C5#12411yescharacteristic
151C2×C4×C5C2×D812yes—
152C2×C4×C5C2×SD1612yes—
153C2×C4×C5#13512yes—
154C2×C4×C5#13512yes—
155C2×C4×C5#13512yes—
156C2×C4×C5#13512yes—
157C2×Dic5—42no—
158C2×Dic5—81no—
159C2×Dic5—81no—
160C2×Dic5—81no—
161C2×Dic5—81no—
162C2×Dic5—81no—
163Dic10—44no—
164Dic10—82no—
165C5×C8—24no—
166#168—24no—
167#168—24no—
168C22×Q8—101no—
169C22×D4—21no—
170C22×D4—21no—
171C22×D4—21no—
172C22×C8—52no—
173C22×C8—52no—
174C22×C8C22⋊D512yes—
175C4⋊Q8—52no—
176C4⋊Q8—101no—
177C4⋊Q8—101no—
178C4⋊Q8—101no—
179#127—21no—
180#127—21no—
181#127—21no—
182#127C4×D512yes—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—101no—
187C2×C4⋊C4—101no—
188C2×C4⋊C4—101no—
189C2×C4⋊C4—101no—
190C2×C4⋊C4—101no—
191C2×C42C22×D511yescharacteristic
192#103—204no—
193#102—44no—
194#102—108no—
195#102—204no—
196C4×C8—21no—
197C4×C8—21no—
198C4×C8—52no—
199C4×C8—52no—
200C4×C8—101no—
201C4×C8—101no—
202C22×C5—82no—
203C22×C5—82no—
204C22×C5—82no—
205C22×C5—161no—
206C22×C5—161no—
207C22×C5—161no—
208C22×C5—161no—
209C22×C5#39011yescharacteristic
210C22×C5#49211yescharacteristic
211C22×C5#49311yescharacteristic
212C22×C5#49511yescharacteristic
213C22×C5#49511yescharacteristic
214C22×C5#49511yescharacteristic
215C22×C5#49511yescharacteristic
216C4×C5—161no—
217C4×C5#41612yes—
218C4×C5C4×D812yes—
219C4×C5C4×SD1612yes—
220C4×C5#46512yes—
221C4×C5#46612yes—
222C4×C5#48812yes—
223Dic5—82no—
224Dic5—161no—
225C24—41no—
226C2×Q8—102no—
227C2×Q8—201no—
228C2×Q8—202no—
229C2×Q8—202no—
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—22no—
233C2×D4—42no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4—42no—
237C2×D4—42no—
238C2×D4—42no—
239C2×D4—42no—
240C2×D4—42no—
241C2×D4—41no—
242C22×C4—41no—
243C22×C4—201no—
244C22×C4—201no—
245C22×C4D4×D511yescharacteristic
246C22×C4D4×D511yescharacteristic
247C22×C4C2×C22⋊D511yescharacteristic
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—54no—
251C2×C8—54no—
252C2×C8—102no—
253C2×C8—102no—
254C2×C8—102no—
255C2×C8—102no—
256C2×C8#68714yes—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—102no—
261C4⋊C4—102no—
262C4⋊C4—201no—
263C4⋊C4—201no—
264C4⋊C4—202no—
265C4⋊C4—202no—
266C4⋊C4—202no—
267C42C2×C4×D511yescharacteristic
268C42#70911yescharacteristic
269C42D4×D511yescharacteristic
270C42#71111yescharacteristic
271C2×C5—162no—
272C2×C5#170611yescharacteristic
273C2×C5#170811yescharacteristic
274C2×C5#170911yescharacteristic
275C2×C5#171111yescharacteristic
276C2×C5#195811yescharacteristic
277C2×C5#196811yescharacteristic
278C2×C5#197011yescharacteristic
279C23—42no—
280C23—81no—
281C23—81no—
282C23—81no—
283C23—81no—
284C23—81no—
285C23—81no—
286C23#408611yescharacteristic
287Q8—204no—
288Q8—402no—
289D4—44no—
290D4—44no—
291D4—44no—
292D4—82no—
293D4—82no—
294D4—82no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—202no—
299C2×C4—401no—
300C2×C4—401no—
301C2×C4—401no—
302C2×C4—401no—
303C2×C4—401no—
304C2×C4D5×C22⋊C411yescharacteristic
305C2×C4#402711yescharacteristic
306C2×C4#403011yescharacteristic
307C2×C4#403111yescharacteristic
308C2×C4D5×D812yes—
309C2×C4#405812yes—
310C2×C4#406212yes—
311C2×C4#406212yes—
312C2×C4C4×C22⋊D511yescharacteristic
313C2×C4C2×#68712yes—
314C2×C4#408511yescharacteristic
315C2×C4#409612yes—
316C8—24no—
317C8—104no—
318C8—104no—
319C5#982211yescharacteristic, complemented, Sylow
320C22—82no—
321C22—82no—
322C22—82no—
323C22—161no—
324C22—161no—
325C22—161no—
326C22—161no—
327C22#6524611yescharacteristic
328C22#6534811yescharacteristic
329C22#6536511yescharacteristic
330C22#6544011yescharacteristic
331C22#6544411yescharacteristic
332C22#6545711yescharacteristic
333C22#6545711yescharacteristic
334C4—161no—
335C4—402no—
336C4—801no—
337C4#6504512yes—
338C4#6505712yes—
339C4#6506112yes—
340C4#6506412yes—
341C4C4×#68712yes—
342C4#6533012yes—
343C2—162no—
344C2#1060043911yescharacteristic
345C2#1060095111yescharacteristic
346C2#1060098311yescharacteristic
347C2#1060197511yescharacteristic
348C2#1060197611yescharacteristic
349C2#1060204911yescharacteristic
350C2#1060206711yescharacteristic
subgroupG/H
centerC23#4086
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1957C2
socleC23×C5#127
prime radicalC2×C5×#127C22
cosocleC2×C42×C5C23
hypercenter#1957D5
hypocenterC5#9822
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
4. #10600570C2semidirect
5. C2×C8×#168C2semidirect
6. #10600372C2semidirect
7. #10600367C2semidirect
16. #65359C4semidirect
319. C5#9822semidirect

Maximal subgroups

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

subgroupindex
C2×#653592
C5×#19572
#106025572
#106005702
C2×C8×#1682
#106003722
#106003672
#98225