Finite Group Databasebeta

← #12017708

Subgroups — #12017708

Order 1280.

418 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
1C2×#65483C211yesmaximal, characteristic
2C5×#1974C211yesmaximal, characteristic, complemented
3C2×#64787C211yesmaximal, characteristic, complemented
4C2×#64717C211yesmaximal, characteristic, complemented
5C2×#64713C211yesmaximal, characteristic, complemented
6#10600588C211yesmaximal, characteristic, complemented
7C2×#64681C211yesmaximal, characteristic, complemented
8C2×C5×#135C2211yescharacteristic
9C2×#4050C2211yescharacteristic
10C2×C5×#108C2211yescharacteristic
11C2×C5×#104—21no—
12C5×#408—21no—
13C2×C4×C5×C8C2211yescharacteristic
14#65483—22no—
15#65483—22no—
16C2×#3961C411yescharacteristic, complemented
17C2×#3960C411yescharacteristic, complemented
18C2×#3959C411yescharacteristic, complemented
19C2×#3958C411yescharacteristic, complemented
20#65399—21no—
21C2×#3951C2211yescharacteristic
22C22×#672C2211yescharacteristic
23C22×#672C2211yescharacteristic
24C2×#3937—21no—
25#64787—22no—
26#64717—22no—
27#64713—22no—
28#64681—22no—
29#13242—51nomaximal, Sylow
30C2×C5×#41—21no—
31C2×#709—21no—
32C5×#135—21no—
33C5×#135—21no—
34C5×#135—21no—
35C5×#135—21no—
36C2×C5×Q16C2×C411yescharacteristic
37C2×C5×SD16—21no—
38C2×C5×D8C2×C411yescharacteristic
39C2×C5×M16—21no—
40C22×C5×C8D411yescharacteristic
41C22×C5×C8C2311yescharacteristic
42C2×C42×C5D411yescharacteristic
43C2×#681—21no—
44C2×Dic20C2×C411yescharacteristic
45#4050—21no—
46#4050—21no—
47#4050—21no—
48#4050—21no—
49C2×D40C2×C411yescharacteristic
50C2×#677—21no—
51C5×#108—21no—
52C5×#108—21no—
53C5×#104—42no—
54C5×C22⋊C8—42no—
55C4×C5×C8—21no—
56C4×C5×C8—21no—
57#3961—22no—
58#3960—22no—
59#3959—22no—
60#3958—22no—
61#3952—42no—
62#3951—21no—
63#3951—21no—
64C2×#672—21no—
65C2×#672—21no—
66C2×#672C2×C411yescharacteristic
67C2×#672C2×C411yescharacteristic
68C2×#672D412yes—
69C2×#672D412yes—
70C2×#672D412yes—
71#3937—42no—
72C2×#508—51no—
73C2×#368—51no—
74C2×#359—51no—
75C2×#359—51no—
76C2×#346—51no—
77#1974—51no—
78#1974D511yescharacteristic, complemented
79C5×#41—41no—
80C5×#41—41no—
81C5×#41—41no—
82C5×#41—41no—
83C2×C5×Q8—21no—
84C2×C5×D4—21no—
85C2×C5×D4—41no—
86C22×C4×C5—21no—
87C22×C4×C5—41no—
88C22×C4×C5C2×D411yescharacteristic
89C2×C22⋊D5—41no—
90#709—41no—
91#709—41no—
92#709—41no—
93#709—41no—
94C2×D20—21no—
95C2×C4×D5—41no—
96C2×Dic10—21no—
97C5×Q16—21no—
98C5×Q16—21no—
99C5×SD16—41no—
100C5×SD16—41no—
101C5×D8—21no—
102C5×D8—21no—
103C5×M16—41no—
104C5×M16—41no—
105C2×C5×C8—21no—
106C2×C5×C8—21no—
107C2×C5×C8—41no—
108C2×C5×C8D812yes—
109C2×C5×C8C22×C411yescharacteristic
110C2×C5×C8C2×D411yescharacteristic
111C2×C5×C8C2×D411yescharacteristic
112C2×C5×C8C2×D411yescharacteristic
113C2×C5×C8#4111yescharacteristic
114C2×C5×C8#4111yescharacteristic
115C42×C5—21no—
116C42×C5D812yes—
117#681—41no—
118#681—41no—
119C2×#168—41no—
120Dic20—21no—
121Dic20—21no—
122D40—21no—
123D40—21no—
124#677—41no—
125#677—41no—
126#672—22no—
127#672C22⋊C412yes—
128#672C22⋊C412yes—
129C2×#135—51no—
130C2×#135C2×D511yescharacteristic
131#508—102no—
132#508—102no—
133C2×Q32—51no—
134C2×SD32—51no—
135C2×SD32—51no—
136C2×D16—51no—
137C22×C16—51no—
138C22×C16—51no—
139C2×#108—51no—
140C2×#108C2×D511yescharacteristic
141C2×#104—21no—
142C2×#104—101no—
143#408—21no—
144#408—101no—
145C2×C4×C8C2×D511yescharacteristic
146#368—102no—
147#359—102no—
148#359—102no—
149#346—102no—
150C23×C5—41no—
151C23×C5#13511yescharacteristic
152C22×D5—41no—
153C5×Q8—41no—
154C5×Q8—41no—
155C5×D4—41no—
156C5×D4—41no—
157C5×D4—81no—
158C5×D4—81no—
159C2×C4×C5—22no—
160C2×C4×C5—42no—
161C2×C4×C5—41no—
162C2×C4×C5—81no—
163C2×C4×C5—81no—
164C2×C4×C5C4×D411yescharacteristic
165C2×C4×C5#12111yescharacteristic
166C2×C4×C5#12711yescharacteristic
167C2×C4×C5C2×D811yescharacteristic
168C2×C4×C5C2×D811yescharacteristic
169C2×C4×C5#13511yescharacteristic
170C22⋊D5—81no—
171C22⋊D5—81no—
172C2×Dic5—41no—
173D20—41no—
174D20—41no—
175C4×D5—81no—
176C4×D5—81no—
177Dic10—41no—
178Dic10—41no—
179C5×C8—22no—
180C5×C8—81no—
181C5×C8C2×C22⋊C411yescharacteristic
182C5×C8C4×D411yescharacteristic
183C5×C8#12111yescharacteristic
184C5×C8#12411yescharacteristic
185#168—81no—
186C2×#41—21no—
187C2×#41—101no—
188#135—21no—
189#135—21no—
190#135—21no—
191#135—21no—
192#135—101no—
193#135—101no—
194#135—101no—
195#135—101no—
196C2×Q16—51no—
197C2×Q16C4×D511yescharacteristic
198C2×SD16—21no—
199C2×SD16—101no—
200C2×D8—51no—
201C2×D8C4×D511yescharacteristic
202C2×M16—21no—
203C2×M16—101no—
204C22×C8C22⋊D511yescharacteristic
205C22×C8C22×D511yescharacteristic
206C2×C42C22⋊D511yescharacteristic
207Q32—102no—
208SD32—102no—
209SD32—102no—
210D16—102no—
211C2×C16—51no—
212C2×C16—51no—
213C2×C16—52no—
214C2×C16—52no—
215C2×C16—52no—
216C2×C16—101no—
217C2×C16—101no—
218#108—21no—
219#108—21no—
220#108—101no—
221#108—101no—
222#104—42no—
223#104—202no—
224C22⋊C8—42no—
225C22⋊C8—202no—
226C4×C8—21no—
227C4×C8—21no—
228C22×C5—22no—
229C22×C5—82no—
230C22×C5—81no—
231C22×C5C4×D811yescharacteristic
232C22×C5#46611yescharacteristic
233C22×C5#49511yescharacteristic
234C2×D5—82no—
235C2×D5—81no—
236C4×C5—42no—
237C4×C5—81no—
238C4×C5#39011yescharacteristic
239C4×C5C4×D811yescharacteristic
240C4×C5#46611yescharacteristic
241C4×C5#49311yescharacteristic
242Dic5—81no—
243#41—41no—
244#41—41no—
245#41—41no—
246#41—41no—
247#41—201no—
248#41—201no—
249#41—201no—
250#41—201no—
251C2×Q8—21no—
252C2×Q8—101no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4—101no—
256C2×D4—201no—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—201no—
260C22×C4C2×C22⋊D511yescharacteristic
261Q16—21no—
262Q16—21no—
263Q16—101no—
264Q16—101no—
265SD16—41no—
266SD16—41no—
267SD16—201no—
268SD16—201no—
269D8—21no—
270D8—21no—
271D8—101no—
272D8—101no—
273M16—41no—
274M16—41no—
275M16—201no—
276M16—201no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—41no—
280C2×C8—201no—
281C2×C8#68612yes—
282C2×C8C2×C4×D511yescharacteristic
283C2×C8#70911yescharacteristic
284C2×C8D4×D511yescharacteristic
285C2×C8D4×D511yescharacteristic
286C2×C8D4×D511yescharacteristic
287C2×C8#71111yescharacteristic
288C42—21no—
289C42#68612yes—
290C16—52no—
291C16—52no—
292C16—102no—
293C2×C5—21no—
294C2×C5—21no—
295C2×C5—161no—
296C2×C5#197011yescharacteristic
297C2×C5#217912yes—
298D5—161no—
299C23—41no—
300C23—201no—
301C23#409611yescharacteristic
302Q8—41no—
303Q8—41no—
304Q8—201no—
305Q8—201no—
306D4—41no—
307D4—41no—
308D4—81no—
309D4—81no—
310D4—201no—
311D4—201no—
312D4—401no—
313D4—401no—
314C2×C4—22no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—201no—
320C2×C4—401no—
321C2×C4—401no—
322C2×C4C4×C22⋊D511yescharacteristic
323C2×C4C2×#68611yescharacteristic
324C2×C4C2×#68611yescharacteristic
325C2×C4#408511yescharacteristic
326C2×C4#408611yescharacteristic
327C2×C4#409611yescharacteristic
328C8—22no—
329C8—81no—
330C8—401no—
331C8D5×C22⋊C411yescharacteristic
332C8#402711yescharacteristic
333C8#403011yescharacteristic
334C8#403111yescharacteristic
335C5#1324211yescharacteristic, complemented, Sylow
336C22—22no—
337C22—82no—
338C22—81no—
339C22—402no—
340C22—401no—
341C22C4×#68611yescharacteristic
342C22#6532711yescharacteristic
343C22#6534811yescharacteristic
344C4—42no—
345C4—81no—
346C4—401no—
347C4#6524611yescharacteristic
348C4C4×#68611yescharacteristic
349C4#6532711yescharacteristic
350C4#6536211yescharacteristic
351C2—21no—
352C2—21no—
353C2—161no—
354C2—801no—
355C2#1060044011yescharacteristic
356C2#1060171512yes—
subgroupG/H
centerC2×C4C2×#686
commutatorC2×C5×C8C22×C4
FrattiniC22×C8C22×D5
FittingC5×#1974C2
socleC22×C5C4×D8
prime radicalC2×#65483C2
cosocleC22×C5×C8C23
hypercenter#1974D5
hypocenterC5#13242
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8 ◁ #1974

Complements

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

NH ≅ G/Ntype
2. C5×#1974C2semidirect
3. C2×#64787C2semidirect
4. C2×#64717C2semidirect
5. C2×#64713C2semidirect
6. #10600588C2semidirect
7. C2×#64681C2semidirect
16. C2×#3961C4semidirect
17. C2×#3960C4semidirect
18. C2×#3959C4semidirect
19. C2×#3958C4semidirect
78. #1974D5semidirect
335. C5#13242semidirect

Maximal subgroups

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

subgroupindex
C2×#654832
C5×#19742
C2×#647872
C2×#647172
C2×#647132
#106005882
C2×#646812
#132425