Finite Group Databasebeta

← #12017477

Subgroups — #12017477

Order 1280.

438 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65433C211yesmaximal, characteristic
2C5×#2113C211yesmaximal, characteristic, complemented
3C2×#64781C211yesmaximal, characteristic, complemented
4C2×#64735C211yesmaximal, characteristic, complemented
5C2×#64731C211yesmaximal, characteristic, complemented
6#10602202C211yesmaximal, characteristic, complemented
7C2×C16×Dic5C211yesmaximal, characteristic, complemented
8C2×C5×#131C2211yescharacteristic
9C2×#4096C411yescharacteristic
10C2×#4047C2211yescharacteristic
11C2×C5×M32C2211yescharacteristic
12C22×C5×C16C2211yescharacteristic
13C2×#3969C411yescharacteristic
14#65433—22no—
15#65433—22no—
16C2×#3957C411yescharacteristic
17C2×#3954C411yescharacteristic
18C2×C8×Dic5C2211yescharacteristic
19C2×#3944C2211yescharacteristic
20C22×#672C2211yescharacteristic
21C5×C22⋊C16—22no—
22#64781—22no—
23#64735—22no—
24#64731—22no—
25#64727—22no—
26C16×Dic5—22no—
27#13195—51nomaximal, Sylow
28C2×C5×#41C2×C411yescharacteristic
29C2×#709C2×C411yescharacteristic
30C5×#131—21no—
31C5×#131—21no—
32C5×#131—21no—
33C5×#131—21no—
34C2×C5×M16—21no—
35C2×C5×M16C2×C411yescharacteristic
36C22×C5×C8—21no—
37C22×C5×C8C2311yescharacteristic
38#4096—22no—
39#4096—22no—
40C2×#689C811yescharacteristic
41C2×#688C811yescharacteristic
42C2×#687C811yescharacteristic
43C2×#686C811yescharacteristic
44C2×C4×Dic5C2×C411yescharacteristic
45C2×#681C2×C411yescharacteristic
46C22×#168C2×C411yescharacteristic
47#4047—21no—
48#4047—21no—
49#4047—21no—
50#4047—21no—
51C2×#676—21no—
52C2×C8×D5—21no—
53C5×M32—21no—
54C5×M32—21no—
55C2×C5×C16—21no—
56C2×C5×C16—21no—
57C2×C5×C16—21no—
58C2×C5×C16D412yes—
59#3969—22no—
60#3957—22no—
61#3954—22no—
62C8×Dic5D412yes—
63C8×Dic5D412yes—
64#3944—21no—
65#3944—21no—
66C2×#672—21no—
67C2×#672—21no—
68C2×#672—21no—
69C2×#672D412yes—
70C2×#443—51no—
71C2×#364—51no—
72C2×#350—51no—
73C2×#350—51no—
74#2113—51no—
75#2113D511yescharacteristic, complemented
76C2×C4×C16—51no—
77C5×#41—21no—
78C5×#41—21no—
79C5×#41—21no—
80C5×#41—21no—
81C2×C5×Q8C2×C811yescharacteristic
82C2×C5×D4—21no—
83C2×C5×D4C2×C811yescharacteristic
84C22×C4×C5—21no—
85C22×C4×C5C22×C411yescharacteristic
86C2×C22⋊D5—21no—
87C22×Dic5—21no—
88#709—21no—
89#709—21no—
90#709—21no—
91#709—21no—
92C2×D20C2×C811yescharacteristic
93C2×C4×D5—21no—
94C2×Dic10C2×C811yescharacteristic
95C5×M16—21no—
96C5×M16—21no—
97C5×M16—41no—
98C5×M16—41no—
99C2×C5×C8—21no—
100C2×C5×C8—41no—
101C2×C5×C8—41no—
102C2×C5×C8C2×D411yescharacteristic
103C2×C5×C8C2×D411yescharacteristic
104C2×C5×C8C2×D411yescharacteristic
105C2×C5×C8C2×D411yescharacteristic
106C2×C5×C8#4111yescharacteristic
107C2×C5×C8#4111yescharacteristic
108#689—22no—
109#688—22no—
110#687—22no—
111#686—22no—
112C4×Dic5—21no—
113C4×Dic5C22⋊C412yes—
114#681—21no—
115#681—21no—
116C2×#168—21no—
117C2×#168C22⋊C412yes—
118C2×#168C2×C811yescharacteristic
119C2×#168C2×C811yescharacteristic
120C2×#168M1612yes—
121#676—41no—
122#676—41no—
123C8×D5—41no—
124C8×D5—41no—
125C5×C16—22no—
126C5×C16—41no—
127#672—22no—
128#672—41no—
129C2×#135—51no—
130C2×#131—51no—
131C2×#131C2×D511yescharacteristic
132C2×M32—51no—
133C2×M32C2×D511yescharacteristic
134C22×C16—51no—
135C22×C16C2×D511yescharacteristic
136#443—102no—
137#443—102no—
138C2×#108—51no—
139C2×#104—51no—
140C2×#104—51no—
141C2×C4×C8—51no—
142#364—102no—
143#350—102no—
144#350—102no—
145C22⋊C16—22no—
146C22⋊C16—102no—
147C4×C16—102no—
148C23×C5—21no—
149C23×C5#13111yescharacteristic
150C22×D5—21no—
151C5×Q8—21no—
152C5×Q8—21no—
153C5×D4—21no—
154C5×D4—21no—
155C5×D4—41no—
156C5×D4—41no—
157C2×C4×C5—21no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5C2×C22⋊C411yescharacteristic
161C2×C4×C5C4×D411yescharacteristic
162C2×C4×C5C4×D411yescharacteristic
163C2×C4×C5C22×C811yescharacteristic
164C2×C4×C5C2×M1611yescharacteristic
165C2×C4×C5#13111yescharacteristic
166C22⋊D5—41no—
167C22⋊D5—41no—
168C2×Dic5—24no—
169C2×Dic5—22no—
170C2×Dic5—21no—
171D20—21no—
172D20—21no—
173C4×D5—41no—
174C4×D5—41no—
175Dic10—21no—
176Dic10—21no—
177C5×C8—41no—
178C5×C8#12111yescharacteristic
179C5×C8#12111yescharacteristic
180C5×C8#12411yescharacteristic
181C5×C8#12711yescharacteristic
182#168—41no—
183#168C22⋊C812yes—
184#168C22⋊C812yes—
185C2×#41—51no—
186C2×#41C4×D511yescharacteristic
187#135—102no—
188#135—102no—
189C2×Q16—51no—
190C2×SD16—51no—
191C2×SD16—51no—
192C2×D8—51no—
193#131—21no—
194#131—21no—
195#131—21no—
196#131—21no—
197#131—101no—
198#131—101no—
199#131—101no—
200#131—101no—
201C2×M16—21no—
202C2×M16—51no—
203C2×M16—101no—
204C2×M16C4×D511yescharacteristic
205C22×C8—21no—
206C22×C8—51no—
207C22×C8—101no—
208C22×C8C22×D511yescharacteristic
209C2×C42—51no—
210M32—21no—
211M32—21no—
212M32—101no—
213M32—101no—
214C2×C16—21no—
215C2×C16—21no—
216C2×C16—21no—
217C2×C16—52no—
218C2×C16—101no—
219C2×C16—101no—
220C2×C16—101no—
221C2×C16C22⋊D512yes—
222#108—102no—
223#104—102no—
224#104—102no—
225C4×C8—52no—
226C4×C8—52no—
227C22×C5—22no—
228C22×C5—42no—
229C22×C5—41no—
230C22×C5#40811yescharacteristic
231C22×C5C8×D411yescharacteristic
232C22×C5#43611yescharacteristic
233C2×D5—42no—
234C2×D5—41no—
235C4×C5—41no—
236C4×C5#39011yescharacteristic
237C4×C5C2×C22⋊C811yescharacteristic
238C4×C5C8×D411yescharacteristic
239C4×C5#43611yescharacteristic
240Dic5—24no—
241Dic5—41no—
242#41—21no—
243#41—21no—
244#41—21no—
245#41—21no—
246#41—101no—
247#41—101no—
248#41—101no—
249#41—101no—
250C2×Q8—51no—
251C2×Q8C8×D511yescharacteristic
252C2×D4—21no—
253C2×D4—51no—
254C2×D4—101no—
255C2×D4C8×D511yescharacteristic
256C22×C4—21no—
257C22×C4—101no—
258C22×C4—101no—
259C22×C4C2×C4×D511yescharacteristic
260Q16—102no—
261SD16—102no—
262SD16—102no—
263D8—102no—
264M16—21no—
265M16—21no—
266M16—41no—
267M16—41no—
268M16—101no—
269M16—101no—
270M16—201no—
271M16—201no—
272C2×C8—21no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—52no—
276C2×C8—51no—
277C2×C8—51no—
278C2×C8—52no—
279C2×C8—101no—
280C2×C8—201no—
281C2×C8—201no—
282C2×C8#70911yescharacteristic
283C2×C8D4×D511yescharacteristic
284C2×C8D4×D511yescharacteristic
285C2×C8D4×D511yescharacteristic
286C2×C8#71111yescharacteristic
287C2×C8C2×C22⋊D511yescharacteristic
288C42—52no—
289C42—101no—
290C16—22no—
291C16—41no—
292C16—102no—
293C16—201no—
294C2×C5—21no—
295C2×C5—21no—
296C2×C5—81no—
297C2×C5#195411yescharacteristic
298C2×C5#217012yes—
299D5—81no—
300C23—21no—
301C23—101no—
302C23#404711yescharacteristic
303Q8—21no—
304Q8—21no—
305Q8—101no—
306Q8—101no—
307D4—21no—
308D4—21no—
309D4—41no—
310D4—41no—
311D4—101no—
312D4—101no—
313D4—201no—
314D4—201no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—104no—
319C2×C4—102no—
320C2×C4—101no—
321C2×C4—201no—
322C2×C4—201no—
323C2×C4D5×C22⋊C411yescharacteristic
324C2×C4#402711yescharacteristic
325C2×C4C2×C8×D511yescharacteristic
326C2×C4D5×M1611yescharacteristic
327C2×C4#405311yescharacteristic
328C2×C4C4×C22⋊D511yescharacteristic
329C8—41no—
330C8—52no—
331C8—52no—
332C8—201no—
333C8#403011yescharacteristic
334C8#403111yescharacteristic
335C8#408511yescharacteristic
336C8#408611yescharacteristic
337C5#1319511yescharacteristic, complemented, Sylow
338C22—22no—
339C22—41no—
340C22—42no—
341C22—201no—
342C22—202no—
343C22#6501611yescharacteristic
344C22#6501811yescharacteristic
345C22C8×C22⋊D511yescharacteristic
346C4—41no—
347C4—104no—
348C4—201no—
349C4D5×C22⋊C811yescharacteristic
350C4#6501411yescharacteristic
351C4#6524611yescharacteristic
352C4#6541711yescharacteristic
353C2—21no—
354C2—21no—
355C2—81no—
356C2—401no—
357C2#1060070911yescharacteristic
358C2#1060224512yes—
subgroupG/H
centerC2×C8C2×C22⋊D5
commutatorC2×C4×C5C22×C8
FrattiniC22×C8C22×D5
FittingC5×#2113C2
socleC22×C5C8×D4
prime radicalC2×#4096C4
cosocleC22×C5×C8C23
hypercenter#2113D5
hypocenterC5#13195
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C8 ◁ C22×C16 ◁ #2113

Complements

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

NH ≅ G/Ntype
2. C5×#2113C2semidirect
3. C2×#64781C2semidirect
4. C2×#64735C2semidirect
5. C2×#64731C2semidirect
6. #10602202C2semidirect
7. C2×C16×Dic5C2semidirect
75. #2113D5semidirect
337. C5#13195semidirect

Maximal subgroups

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

subgroupindex
C2×#654332
C5×#21132
C2×#647812
C2×#647352
C2×#647312
#106022022
C2×C16×Dic52
#131955