Finite Group Databasebeta

← #12016193

Subgroups — #12016193

Order 1280.

508 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×C16C211yesmaximal, characteristic, complemented
2#10610284C211yesmaximal, characteristic
3C2×#64735C211yesmaximal, characteristic, complemented
4#10602224C211yesmaximal, characteristic, complemented
5C2×#64728C211yesmaximal, characteristic, complemented
6C5×#1379C211yesmaximal, characteristic, complemented
7#10598162C211yesmaximal, characteristic, complemented
8C2×#4047C2211yescharacteristic
9C22×C8×D5C2211yescharacteristic
10#65858C411yescharacteristic
11C2×C5×M32C2211yescharacteristic
12C22×C5×C16C2211yescharacteristic
13C5×#405C2211yescharacteristic
14#65418C411yescharacteristic
15#65415C411yescharacteristic
16C2×#3944C2211yescharacteristic
17C22×#672C2211yescharacteristic
18#65288C411yescharacteristic
19C2×D5×C16—22no—
20C2×D5×C16—22no—
21C2×D5×C16—22no—
22#64995—22no—
23C8×D20—22no—
24#64735—22no—
25#64728—22no—
26#64727—22no—
27#12983—51nomaximal, Sylow
28C2×#709C2×C411yescharacteristic
29C22×C4×D5C2×C411yescharacteristic
30C2×C5×M16C2×C411yescharacteristic
31C22×C5×C8C2311yescharacteristic
32C5×#117C2×C411yescharacteristic
33C2×#681C2×C411yescharacteristic
34C22×#168C2×C411yescharacteristic
35#4047—21no—
36#4047—21no—
37#4047—21no—
38#4047—21no—
39C2×#676—21no—
40C2×C8×D5—21no—
41C2×C8×D5—21no—
42C2×C8×D5—21no—
43C2×C8×D5—21no—
44C2×C8×D5—21no—
45C2×C8×D5D412yes—
46C2×C8×D5D412yes—
47#4043C812yes—
48#4041C812yes—
49#4032—21no—
50#4028—21no—
51C4×D20—22no—
52C5×M32—21no—
53C5×M32—21no—
54C2×C5×C16—21no—
55C2×C5×C16—21no—
56C2×C5×C16—21no—
57C2×C5×C16D412yescomplemented
58C5×#97—21no—
59C4×C5×C8—21no—
60#3952—22no—
61#3952—22no—
62#3944—21no—
63#3944—21no—
64C2×#672—21no—
65C2×#672—21no—
66C2×#672—21no—
67C2×#672D412yescomplemented
68C4⋊#168—22no—
69D5×C16—28no—
70C23×C16—51no—
71#2929—51no—
72C2×#350—51no—
73C2×#350—51no—
74#2112—51no—
75#1379—51no—
76#1379D511yescharacteristic, complemented
77C23×D5M1611yescharacteristic
78C22×C4×C5C22×C411yescharacteristic
79C2×C22⋊D5—21no—
80C22×Dic5M1611yescharacteristic
81#709—21no—
82#709—21no—
83#709—21no—
84#709—21no—
85C2×D20—22no—
86C2×D20C2×C811yescharacteristic
87C2×C4×D5—21no—
88C2×C4×D5—21no—
89C2×C4×D5—21no—
90C2×C4×D5—21no—
91C2×C4×D5—21no—
92C2×C4×D5C22⋊C412yes—
93C2×C4×D5C2×C812yes—
94C2×Dic10C2×C811yescharacteristic
95C5×M16—21no—
96C5×M16—21no—
97C2×C5×C8—21no—
98C2×C5×C8C2×D411yescharacteristic
99C2×C5×C8C2×D411yescharacteristic
100C2×C5×C8C2×D411yescharacteristic
101C2×C5×C8C2×D411yescharacteristic
102C2×C5×C8#4111yescharacteristic
103C2×C5×C8#4111yescharacteristic
104C5×C4⋊C4C2×C812yes—
105C5×C22⋊C4—21no—
106C42×C5—21no—
107#685—22no—
108#685—22no—
109C4⋊Dic5—22no—
110#681—21no—
111#681—21no—
112C2×#168—21no—
113C2×#168—21no—
114C2×#168—21no—
115C2×#168C22⋊C412yes—
116#676—41no—
117#676—41no—
118C8×D5—22no—
119C8×D5—22no—
120C8×D5—22no—
121C8×D5—22no—
122C8×D5—41no—
123C8×D5—41no—
124C5×C16—22no—
125C5×C16—41no—
126#672—22no—
127#672—41no—
128C2×#131—51no—
129C23×C8—51no—
130#525—51no—
131C2×M32—51no—
132C2×M32C2×D511yescharacteristic
133C22×C16—51no—
134C22×C16—102no—
135C22×C16—102no—
136C22×C16—102no—
137C22×C16C2×D511yescharacteristic
138#435—102no—
139C8×D4—102no—
140#424—51no—
141#408—51no—
142#407—51no—
143#405C2×D511yescharacteristic
144#350—102no—
145#350—102no—
146C22⋊C16—102no—
147C23×C5C2×M1611yescharacteristic
148C22×D5—21no—
149C22×D5—21no—
150C22×D5—24no—
151C22×D5—21no—
152C22×D5C22⋊C812yes—
153C2×C4×C5—22no—
154C2×C4×C5C2×C22⋊C411yescharacteristic
155C2×C4×C5C4×D411yescharacteristic
156C2×C4×C5C4×D411yescharacteristic
157C2×C4×C5C22×C811yescharacteristic
158C2×C4×C5#13111yescharacteristic
159C2×C4×C5#13111yescharacteristic
160C22⋊D5—41no—
161C22⋊D5—41no—
162C2×Dic5—21no—
163C2×Dic5—21no—
164C2×Dic5—21no—
165C2×Dic5C22⋊C812yes—
166D20—21no—
167D20—21no—
168D20—44no—
169C4×D5—22no—
170C4×D5—22no—
171C4×D5—22no—
172C4×D5—22no—
173C4×D5—41no—
174C4×D5—41no—
175Dic10—21no—
176Dic10—21no—
177C5×C8—41no—
178C5×C8#12011yescharacteristic
179C5×C8#12111yescharacteristic
180C5×C8#12111yescharacteristic
181C5×C8#12311yescharacteristic
182#168—22no—
183#168—41no—
184C2×#41—51no—
185C23×C4—51no—
186#131—101no—
187#131—101no—
188#131—101no—
189#131—101no—
190C2×M16—51no—
191C2×M16—101no—
192C2×M16C4×D511yescharacteristic
193C22×C8—51no—
194C22×C8—52no—
195C22×C8—52no—
196C22×C8—101no—
197C22×C8—101no—
198C22×C8—101no—
199C22×C8—101no—
200C22×C8—101no—
201C22×C8C22×D511yescharacteristic
202#123—101no—
203C22⋊Q8—52no—
204#121—52no—
205#120—101no—
206C4×D4—102no—
207#117C4×D511yescharacteristic
208M32—21no—
209M32—21no—
210M32—101no—
211M32—101no—
212C2×C16—21no—
213C2×C16—21no—
214C2×C16—21no—
215C2×C16—52no—
216C2×C16—108no—
217C2×C16—101no—
218C2×C16—101no—
219C2×C16—101no—
220C2×C16D2012yescomplemented
221C4⋊C8—102no—
222C22⋊C8—102no—
223C22⋊C8—102no—
224#97—21no—
225C4×C8—21no—
226C22×C5—22no—
227C22×C5C2×C22⋊C811yescharacteristic
228C22×C5#43511yescharacteristic
229C22×C5#43511yescharacteristic
230C2×D5—24no—
231C2×D5—24no—
232C2×D5—22no—
233C2×D5—22no—
234C2×D5—42no—
235C2×D5—41no—
236C2×D5#35014yescomplemented
237C4×C5—42no—
238C4×C5#38611yescharacteristic
239C4×C5#40811yescharacteristic
240C4×C5C8×D411yescharacteristic
241C4×C5C8×D411yescharacteristic
242Dic5—22no—
243Dic5—41no—
244C24—51no—
245#41—101no—
246#41—101no—
247#41—101no—
248#41—101no—
249C2×Q8—51no—
250C2×D4—51no—
251C2×D4—102no—
252C2×D4—101no—
253C22×C4—51no—
254C22×C4—52no—
255C22×C4—52no—
256C22×C4—101no—
257C22×C4—101no—
258C22×C4—101no—
259C22×C4—101no—
260C22×C4—101no—
261C22×C4C2×C4×D511yescharacteristic
262M16—21no—
263M16—21no—
264M16—101no—
265M16—101no—
266M16—201no—
267M16—201no—
268C2×C8—21no—
269C2×C8—52no—
270C2×C8—101no—
271C2×C8—101no—
272C2×C8—102no—
273C2×C8—102no—
274C2×C8—102no—
275C2×C8—102no—
276C2×C8—101no—
277C2×C8—201no—
278C2×C8—201no—
279C2×C8C2×D2011yescharacteristic
280C2×C8#70911yescharacteristic
281C2×C8D4×D511yescharacteristic
282C2×C8D4×D511yescharacteristic
283C2×C8D4×D511yescharacteristic
284C2×C8#71311yescharacteristic
285C4⋊C4—102no—
286C4⋊C4C8×D512yes—
287C22⋊C4—21no—
288C22⋊C4—102no—
289C22⋊C4—102no—
290C42—21no—
291C16—22no—
292C16—41no—
293C16—102no—
294C16—201no—
295C2×C5—21no—
296C2×C5—21no—
297C2×C5#186911yescharacteristic
298C2×C5C2×#35012yes—
299D5—24no—
300D5—81no—
301C23—52no—
302C23—104no—
303C23—101no—
304C23—101no—
305C23—101no—
306C23D5×M1611yescharacteristic
307Q8—101no—
308Q8—101no—
309D4—101no—
310D4—101no—
311D4—204no—
312D4—201no—
313D4—201no—
314C2×C4—22no—
315C2×C4—52no—
316C2×C4—101no—
317C2×C4—101no—
318C2×C4—102no—
319C2×C4—102no—
320C2×C4—102no—
321C2×C4—102no—
322C2×C4—101no—
323C2×C4—201no—
324C2×C4—201no—
325C2×C4C4×D2011yescharacteristic
326C2×C4D5×C22⋊C411yescharacteristic
327C2×C4#403911yescharacteristic
328C2×C4C2×C8×D511yescharacteristic
329C2×C4#404711yescharacteristic
330C2×C4#405311yescharacteristic
331C8—41no—
332C8—102no—
333C8—201no—
334C8#402811yescharacteristic
335C8#403011yescharacteristic
336C8#404011yescharacteristic
337C8#404111yescharacteristic
338C5#1298311yescharacteristic, complemented, Sylow
339C22—22no—
340C22—54no—
341C22—104no—
342C22—104no—
343C22—102no—
344C22—102no—
345C22—201no—
346C22—202no—
347C22#6499511yescharacteristic
348C22D5×C22⋊C811yescharacteristic
349C22#6512511yescharacteristic
350C4—42no—
351C4—102no—
352C4—201no—
353C4#6495411yescharacteristic
354C4C8×D2011yescharacteristic
355C4#6501611yescharacteristic
356C4#6512311yescharacteristic
357C2—21no—
358C2—21no—
359C2—104no—
360C2—401no—
361C2#1059946111yescharacteristic
362C2D5×#35012yes—
subgroupG/H
centerC2×C8D4×D5
commutatorC2×C4×C5C22×C8
FrattiniC22×C8C22×D5
FittingC5×#1379C2
socleC22×C5C2×C22⋊C8
prime radical#65858C4
cosocleC22×C5×C8C23
hypercenter#1379D5
hypocenterC5#12983
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ #1379

Complements

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

NH ≅ G/Ntype
1. C22×D5×C16C2semidirect
3. C2×#64735C2semidirect
4. #10602224C2semidirect
5. C2×#64728C2semidirect
6. C5×#1379C2semidirect
7. #10598162C2semidirect
57. C2×C5×C16D4semidirect
67. C2×#672D4semidirect
76. #1379D5semidirect
220. C2×C16D20semidirect
236. C2×D5#350semidirect
338. C5#12983semidirect

Maximal subgroups

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

subgroupindex
C22×D5×C162
#106102842
C2×#647352
#106022242
C2×#647282
C5×#13792
#105981622
#129835