Finite Group Databasebeta

← #11992602

Subgroups — #11992602

Order 1280.

384 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10614857C211yesmaximal, characteristic
2C5×#1509C211yesmaximal, characteristic
3#10602548C211yesmaximal, characteristic
4#10601587C211yesmaximal, characteristic, complemented
5C4×#3940C211yesmaximal, characteristic, complemented
6#10598240C211yesmaximal, characteristic, complemented
7#10598112C211yesmaximal, characteristic, complemented
8C5×#529C2211yescharacteristic
9C5×#432C2211yescharacteristic
10C4×C5×C4⋊C4C2211yescharacteristic
11#65313C411yescharacteristic, complemented
12Q8×#168C411yescharacteristic, complemented
13#65301C411yescharacteristic, complemented
14#65300—21no—
15D4×#168—21no—
16D4×#168C411yescharacteristic, complemented
17#65289—21no—
18#65286—21no—
19C2×#3940—21no—
20C4×C4⋊Dic5C2211yescharacteristic
21#65215C2211yescharacteristic
22#65215C2211yescharacteristic
23C2×C4×#168C2211yescharacteristic
24C5×#328—21no—
25C5×#327—21no—
26#64758—21no—
27#64757—21no—
28#64749—21no—
29#64700—21no—
30#64699—21no—
31#8694—51nomaximal, Sylow
32C5×#126—21no—
33C5×#125Q811yescharacteristic
34C5×#124Q811yescharacteristic
35C5×#123—21no—
36C5×C22⋊Q8D411yescharacteristic
37C5×#121D411yescharacteristic
38C4×C5×Q8C2×C411yescharacteristic
39C4×C5×D4—21no—
40C4×C5×D4C2×C411yescharacteristic
41C5×#117—21no—
42C2×C5×C4⋊C4—21no—
43C2×C42×C5—21no—
44C2×C42×C5C2311yescharacteristic
45C2×C4⋊Dic5—21no—
46C2×C4×Dic5—21no—
47C2×#681—21no—
48C22×#168—21no—
49C22×#168D411yescharacteristic
50C22×#168D411yescharacteristic
51C5×C4⋊C8—21no—
52C5×C22⋊C8—21no—
53C5×#97—21no—
54C5×#95—21no—
55#3963—21no—
56C22⋊#168—21no—
57C22⋊#168—21no—
58C22⋊#168—21no—
59C22⋊#168—21no—
60#3940—24no—
61C4⋊#168—21no—
62C4⋊#168—21no—
63C4⋊#168—21no—
64C4⋊#168C2×C411yescharacteristic
65C4⋊#168C2×C411yescharacteristic
66#3935—21no—
67#3935—21no—
68#3935—21no—
69C4×#168—21no—
70C4×#168C2×C411yescharacteristic
71C4×#168C2×C411yescharacteristic
72C4×#168D411yescharacteristic
73C4×#168D411yescharacteristic
74#2966—51no—
75C4×#106—51no—
76#1568—51no—
77#1509—51no—
78#1509D511yescharacteristic
79#1285—51no—
80#1285—51no—
81C2×C5×Q8C4⋊C411yescharacteristic
82C2×C5×D4—21no—
83C2×C5×D4C4⋊C411yescharacteristic
84C22×C4×C5—21no—
85C22×C4×C5—41no—
86C22×C4×C5C2×D411yescharacteristic
87C22×C4×C5C2×D411yescharacteristic
88C22×C4×C5#4111yescharacteristic
89C22×Dic5—41no—
90C2×C5×C8—41no—
91C5×C4⋊C4—21no—
92C5×C4⋊C4—21no—
93C5×C4⋊C4—21no—
94C5×C4⋊C4—21no—
95C5×C4⋊C4—22no—
96C5×C4⋊C4—41no—
97C5×C4⋊C4C4⋊C411yescharacteristic
98C5×C4⋊C4C4⋊C411yescharacteristic
99C5×C22⋊C4—21no—
100C5×C22⋊C4—21no—
101C5×C22⋊C4—21no—
102C5×C22⋊C4—21no—
103C5×C22⋊C4—21no—
104C42×C5—21no—
105C42×C5—81no—
106C42×C5C22×C411yescharacteristic
107C42×C5C2×D411yescharacteristic
108C42×C5C2×Q811yescharacteristic
109C42×C5#4111yescharacteristic
110C4⋊Dic5—22no—
111C4⋊Dic5—41no—
112C4×Dic5—81no—
113#681—42no—
114C2×#168—22no—
115C2×#168—21no—
116C2×#168—21no—
117C2×#168—41no—
118C2×#168—42no—
119C2×#168—41no—
120C2×#168C22⋊C411yescharacteristic
121C2×#168C22⋊C411yescharacteristic
122C2×#168C22⋊C411yescharacteristic
123C2×#168C22⋊C411yescharacteristic
124#529C2×D511yescharacteristic
125#446—51no—
126C8×Q8—51no—
127#436—51no—
128#435—101no—
129C8×D4—51no—
130C8×D4—101no—
131#433—101no—
132#432—51no—
133#432—51no—
134#432C2×D511yescharacteristic
135C2×#106—101no—
136#405—101no—
137C2×C4×C8—51no—
138C4×C4⋊C4—51no—
139C4×C4⋊C4C2×D511yescharacteristic
140#340—101no—
141#335—101no—
142#334—101no—
143#328—21no—
144#328—101no—
145#327—21no—
146#327—101no—
147C23×C5—21no—
148C23×C5#12111yescharacteristic
149C5×Q8—41no—
150C5×D4—41no—
151C5×D4—41no—
152C5×D4—41no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5—42no—
164C2×C4×C5—81no—
165C2×C4×C5—81no—
166C2×C4×C5C2×C22⋊C411yescharacteristic
167C2×C4×C5C2×C4⋊C411yescharacteristic
168C2×C4×C5#11711yescharacteristic
169C2×C4×C5#12111yescharacteristic
170C2×C4×C5C22⋊Q811yescharacteristic
171C2×C4×C5C22⋊Q811yescharacteristic
172C2×Dic5—42no—
173C2×Dic5—81no—
174C2×Dic5—81no—
175C5×C8—81no—
176#168—21no—
177#168—21no—
178#168—21no—
179#168—41no—
180#168—41no—
181#168—81no—
182#168#10412yes—
183C2×M16—101no—
184C22×C8—51no—
185C22×C8—51no—
186C22×C8—101no—
187#126—21no—
188#125Dic1011yescharacteristic
189#124Dic1011yescharacteristic
190#123—21no—
191C22⋊Q8C22⋊D511yescharacteristic
192#121C22⋊D511yescharacteristic
193C4×Q8C4×D511yescharacteristic
194C4×D4—21no—
195C4×D4C4×D511yescharacteristic
196#117—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—101no—
199C2×C42—21no—
200C2×C42—101no—
201C2×C42C22×D511yescharacteristic
202#106—104no—
203C4⋊C8—21no—
204C4⋊C8—51no—
205C4⋊C8—51no—
206C4⋊C8—101no—
207C4⋊C8—101no—
208C4⋊C8—101no—
209C22⋊C8—21no—
210C22⋊C8—101no—
211C22⋊C8—101no—
212C22⋊C8—101no—
213C22⋊C8—101no—
214#97—21no—
215#97—101no—
216#97—101no—
217#97—101no—
218C4×C8—51no—
219C4×C8—51no—
220C4×C8—51no—
221C4×C8—51no—
222C4×C8—101no—
223#95—21no—
224#95—101no—
225C22×C5—21no—
226C22×C5—21no—
227C22×C5—41no—
228C22×C5—41no—
229C22×C5—41no—
230C22×C5#38011yescharacteristic
231C22×C5#47111yescharacteristic
232C22×C5#47111yescharacteristic
233C4×C5—21no—
234C4×C5—21no—
235C4×C5—21no—
236C4×C5—21no—
237C4×C5—21no—
238C4×C5—41no—
239C4×C5—41no—
240C4×C5—41no—
241C4×C5—82no—
242C4×C5C2×#10411yescharacteristic
243C4×C5#42111yescharacteristic
244Dic5—82no—
245C2×Q8#68311yescharacteristic
246C2×D4—21no—
247C2×D4#68311yescharacteristic
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—201no—
251C22×C4D4×D511yescharacteristic
252C22×C4#71111yescharacteristic
253C22×C4C2×C22⋊D511yescharacteristic
254M16—202no—
255C2×C8—41no—
256C2×C8—51no—
257C2×C8—51no—
258C2×C8—51no—
259C2×C8—51no—
260C2×C8—102no—
261C2×C8—101no—
262C2×C8—101no—
263C2×C8—202no—
264C2×C8—201no—
265C2×C8—201no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—41no—
272C4⋊C4—102no—
273C4⋊C4—201no—
274C4⋊C4#68311yescharacteristic
275C4⋊C4#68311yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C42—21no—
282C42—81no—
283C42—401no—
284C42C2×Dic1011yescharacteristic
285C42C2×C4×D511yescharacteristic
286C42D4×D511yescharacteristic
287C42#71111yescharacteristic
288C2×C5—21no—
289C2×C5—21no—
290C2×C5—81no—
291C2×C5#180611yescharacteristic
292C2×C5#181211yescharacteristic
293C2×C5#181511yescharacteristic
294C23—21no—
295C23#408511yescharacteristic
296Q8—41no—
297D4—41no—
298D4—41no—
299D4—41no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—202no—
314C2×C4—401no—
315C2×C4—401no—
316C2×C4#402311yescharacteristic
317C2×C4#402411yescharacteristic
318C2×C4#402411yescharacteristic
319C2×C4D5×C22⋊C411yescharacteristic
320C2×C4C2×#68311yescharacteristic
321C2×C4#408511yescharacteristic
322C8—52no—
323C8—81no—
324C8—101no—
325C8—101no—
326C8—101no—
327C8—201no—
328C8—201no—
329C8—401no—
330C5#869411yescharacteristic, complemented, Sylow
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22#6523111yescharacteristic
337C22#6548911yescharacteristic
338C22#6549211yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—82no—
348C4—402no—
349C4D5×#10411yescharacteristic
350C4#6511011yescharacteristic
351C2—21no—
352C2—21no—
353C2—81no—
354C2#1060083411yescharacteristic
355C2#1060109211yescharacteristic
356C2#1060114811yescharacteristic
subgroupG/H
centerC22#65231
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1509C2
socleC22×C5#380
prime radicalC5×#121D4
cosocleC2×C42×C5C23
hypercenter#1509D5
hypocenterC5#8694
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1509

Complements

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

NH ≅ G/Ntype
4. #10601587C2semidirect
5. C4×#3940C2semidirect
6. #10598240C2semidirect
7. #10598112C2semidirect
11. #65313C4semidirect
12. Q8×#168C4semidirect
13. #65301C4semidirect
16. D4×#168C4semidirect
330. C5#8694semidirect

Maximal subgroups

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

subgroupindex
#106148572
C5×#15092
#106025482
#106015872
C4×#39402
#105982402
#105981122
#86945