Finite Group Databasebeta

← #11995712

Subgroups — #11995712

Order 1280.

534 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×Q8×M16C211yesmaximal, characteristic, complemented
2C2×#65316C211yesmaximal, characteristic
3#10602415C211yesmaximal, characteristic, complemented
4#10601295C211yesmaximal, characteristic
5#10600669C211yesmaximal, characteristic
6#10598202C211yesmaximal, characteristic, complemented
7#10598159C211yesmaximal, characteristic, complemented
8C2×C4×C5×Q8C2211yescharacteristic
9C22×#688C412yes—
10C2×#4020C2211yescharacteristic
11C5×#446—22no—
12C5×#446—21no—
13C5×C8×Q8—21no—
14C5×#423—21no—
15C5×#423C2211yescharacteristic
16C4×C5×M16—21no—
17C4×C5×M16C2211yescharacteristic
18C2×#3955—21no—
19C2×#3955—21no—
20#65316—21no—
21#65316—21no—
22#65316—21no—
23#65316—21no—
24C2×#3941C412yes—
25#65214C2211yescharacteristic
26#65213C2211yescharacteristic
27C2×C4⋊#168C2211yescharacteristic
28Q8⋊#168—21no—
29Q8⋊#168—21no—
30#64705—22no—
31#9254—51nomaximal, Sylow
32C22×C5×Q8C2×C411yescharacteristic
33C22×D20—21no—
34C22×D20—21no—
35C22×D20C2×C412yes—
36C2×C5×M16—21no—
37C2×C5×M16D411yescharacteristic
38C2×C5×M16D411yescharacteristic
39C4×C5×Q8—21no—
40C4×C5×Q8—21no—
41C4×C5×Q8D411yescharacteristic
42C4×C5×Q8D411yescharacteristic
43C4×C5×Q8D411yescharacteristic
44C4×C5×Q8D411yescharacteristic
45C2×C5×C4⋊C4—21no—
46C2×C5×C4⋊C4C2×C411yescharacteristic
47C2×C42×C5—21no—
48C2×C42×C5C2311yescharacteristic
49C2×#688—22no—
50C2×#688—22no—
51C2×#688—44no—
52C2×#681—21no—
53C22×#168C2×C412yes—
54#4020—21no—
55#4020—21no—
56#4020—21no—
57#4020—21no—
58C5×C4⋊C8—22no—
59C5×C4⋊C8—22no—
60C5×C4⋊C8—21no—
61C5×C4⋊C8D412yes—
62C5×#97—22no—
63C5×#97—21no—
64C4×C5×C8—22no—
65C4×C5×C8—21no—
66C22⋊#168—21no—
67#3955—42no—
68#3955—42no—
69#3941—22no—
70#3941—22no—
71C4⋊#168—21no—
72C4⋊#168—21no—
73C4⋊#168—21no—
74C4⋊#168—21no—
75C4⋊#168—21no—
76C4×#168—21no—
77C2×#460—51no—
78Q8×M16D511yescharacteristic, complemented
79#1965—51no—
80#1545—51no—
81#1487—51no—
82#1292—51no—
83#1283—51no—
84C23×D5—22no—
85C2×C5×Q8—21no—
86C2×C5×Q8—22no—
87C2×C5×Q8—41no—
88C2×C5×Q8C22⋊C411yescharacteristic
89C2×C5×Q8C22⋊C411yescharacteristic
90C22×C4×C5—21no—
91C22×C4×C5—21no—
92C22×C4×C5C22×C411yescharacteristic
93C22×C4×C5C2×D411yescharacteristic
94C22×C4×C5#4111yescharacteristic
95C2×D20—22no—
96C2×D20—22no—
97C2×D20—42no—
98C2×D20—42no—
99C2×D20—41no—
100C2×D20—41no—
101C2×D20—41no—
102C2×D20—41no—
103C2×D20—41no—
104C2×D20—41no—
105C2×D20—41no—
106C2×D20—41no—
107C2×D20—82no—
108C5×M16—21no—
109C5×M16—21no—
110C5×M16—21no—
111C5×M16—41no—
112C5×M16—41no—
113C5×M16SD1612yescomplemented
114C2×C5×C8—21no—
115C2×C5×C8—22no—
116C2×C5×C8—21no—
117C5×C4⋊C4—21no—
118C5×C4⋊C4—21no—
119C5×C4⋊C4—21no—
120C5×C4⋊C4—21no—
121C5×C4⋊C4—21no—
122C5×C4⋊C4C22⋊C411yescharacteristic
123C5×C4⋊C4C22⋊C411yescharacteristic
124C42×C5—21no—
125C42×C5—21no—
126C42×C5—21no—
127C42×C5—21no—
128C42×C5C2×D411yescharacteristic
129C42×C5C2×D411yescharacteristic
130C42×C5C2×D411yescharacteristic
131C42×C5#4111yescharacteristic
132#688—44no—
133#688—44no—
134#681—41no—
135#681—41no—
136C2×#168—22no—
137C2×#168—42no—
138C2×#168—41no—
139C2×#168—41no—
140C22×SD16—52no—
141C2×#127—51no—
142C2×C4×Q8C2×D511yescharacteristic
143#460—101no—
144#460—101no—
145#460—101no—
146#460—101no—
147#446—21no—
148#446—22no—
149C8×Q8—21no—
150#431—51no—
151#423—21no—
152#423—51no—
153#423C2×D511yescharacteristic
154C2×C4⋊C8—51no—
155C2×#102—52no—
156C2×#100—101no—
157C2×#100—101no—
158C4×M16—21no—
159C4×M16C2×D511yescharacteristic
160#331—102no—
161Q8⋊C8—101no—
162Q8⋊C8—101no—
163C23×C5C4×D411yescharacteristic
164C22×D5—42no—
165C22×D5—42no—
166C22×D5—42no—
167C22×D5—82no—
168C22×D5—82no—
169C5×Q8—21no—
170C5×Q8—21no—
171C5×Q8—21no—
172C5×Q8—42no—
173C5×Q8#10012yescomplemented
174C2×C4×C5—21no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—21no—
178C2×C4×C5—21no—
179C2×C4×C5—21no—
180C2×C4×C5—41no—
181C2×C4×C5—42no—
182C2×C4×C5—81no—
183C2×C4×C5C2×C22⋊C411yescharacteristic
184C2×C4×C5C4×D411yescharacteristic
185C2×C4×C5#12011yescharacteristic
186C2×C4×C5#12111yescharacteristic
187C2×C4×C5#12111yescharacteristic
188C2×C4×C5#12311yescharacteristic
189C2×C4×C5C2×SD1611yescharacteristic
190C2×C4×C5#13511yescharacteristic
191C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C5#13711yescharacteristic
193D20—42no—
194D20—42no—
195D20—82no—
196D20—82no—
197D20—82no—
198D20—81no—
199D20—81no—
200D20—81no—
201D20—81no—
202C5×C8—22no—
203C5×C8—41no—
204C5×C8—42no—
205#168—42no—
206#168—81no—
207#168—81no—
208C22×Q8C4×D511yescharacteristic
209C22×D4—52no—
210C22×D4—101no—
211C22×D4—101no—
212C2×SD16—102no—
213C2×SD16—102no—
214C2×SD16—204no—
215C2×M16—21no—
216C2×M16—101no—
217C2×M16C22⋊D511yescharacteristic
218C2×M16C22⋊D511yescharacteristic
219C22×C8—52no—
220#127—101no—
221#127—101no—
222#127—101no—
223#127—101no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8D2011yescharacteristic
227C4×Q8D2011yescharacteristic
228C4×Q8C22⋊D511yescharacteristic
229C4×Q8C22⋊D511yescharacteristic
230C2×C4⋊C4—21no—
231C2×C4⋊C4C4×D511yescharacteristic
232C2×C42—21no—
233C2×C42C22×D511yescharacteristic
234C4⋊C8—22no—
235C4⋊C8—22no—
236C4⋊C8—21no—
237C4⋊C8—101no—
238C4⋊C8—101no—
239C4⋊C8—101no—
240C4⋊C8—101no—
241C4⋊C8—101no—
242C4⋊C8C22⋊D512yes—
243#102—102no—
244#102—102no—
245#100—202no—
246#100—202no—
247C22⋊C8—101no—
248#97—22no—
249#97—21no—
250C4×C8—22no—
251C4×C8—21no—
252C4×C8—101no—
253C22×C5—21no—
254C22×C5—21no—
255C22×C5#38611yescharacteristic
256C22×C5C4×SD1611yescharacteristic
257C22×C5#44011yescharacteristic
258C2×D5—82no—
259C2×D5—82no—
260C2×D5—82no—
261C2×D5—162no—
262C2×D5—162no—
263C4×C5—21no—
264C4×C5—22no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—41no—
268C4×C5—41no—
269C4×C5—41no—
270C4×C5C2×#10011yescharacteristic
271C4×C5#41311yescharacteristic
272C4×C5#44811yescharacteristic
273C4×C5#44911yescharacteristic
274C4×C5#46011yescharacteristic
275C4×C5#46411yescharacteristic
276C24—102no—
277C2×Q8—21no—
278C2×Q8—22no—
279C2×Q8—41no—
280C2×Q8#68511yescharacteristic
281C2×Q8#68511yescharacteristic
282C2×D4—102no—
283C2×D4—102no—
284C2×D4—202no—
285C2×D4—202no—
286C2×D4—201no—
287C2×D4—201no—
288C2×D4—201no—
289C2×D4—201no—
290C2×D4—201no—
291C2×D4—201no—
292C2×D4—201no—
293C2×D4—201no—
294C2×D4—402no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4C2×C4×D511yescharacteristic
298C22×C4#70911yescharacteristic
299C22×C4C2×C22⋊D511yescharacteristic
300SD16—204no—
301SD16—204no—
302M16—21no—
303M16—21no—
304M16—21no—
305M16—41no—
306M16—41no—
307M16—201no—
308M16—201no—
309M16#68812yescomplemented
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—102no—
314C2×C8—202no—
315C2×C8—201no—
316C2×C8—201no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4#68511yescharacteristic
323C4⋊C4#68511yescharacteristic
324C42—21no—
325C42—21no—
326C42—21no—
327C42—21no—
328C42C2×D2011yescharacteristic
329C42#70911yescharacteristic
330C42C2×C22⋊D511yescharacteristic
331C42C2×C22⋊D511yescharacteristic
332C2×C5—21no—
333C2×C5—21no—
334C2×C5#188011yescharacteristic
335C2×C5#190011yescharacteristic
336C2×C5#190311yescharacteristic
337D5—162no—
338C23—202no—
339C23—202no—
340C23—202no—
341C23—402no—
342C23—402no—
343C23C4×C22⋊D511yescharacteristic
344Q8—21no—
345Q8—21no—
346Q8—21no—
347Q8—42no—
348Q8#395512yescomplemented
349D4—202no—
350D4—202no—
351D4—402no—
352D4—402no—
353D4—402no—
354D4—401no—
355D4—401no—
356D4—401no—
357D4—401no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—81no—
367C2×C4C2×#68511yescharacteristic
368C2×C4C4×C22⋊D511yescharacteristic
369C2×C4#407511yescharacteristic
370C2×C4#407611yescharacteristic
371C2×C4#407611yescharacteristic
372C2×C4C2×#68811yescharacteristic
373C2×C4#408811yescharacteristic
374C2×C4#409511yescharacteristic
375C2×C4#409611yescharacteristic
376C2×C4#409911yescharacteristic
377C8—22no—
378C8—41no—
379C8—42no—
380C8—202no—
381C8—401no—
382C8—401no—
383C5#925411yescharacteristic, complemented, Sylow
384C22—21no—
385C22—21no—
386C22—402no—
387C22—402no—
388C22—402no—
389C22—802no—
390C22—802no—
391C22C4×#68811yescharacteristic
392C22#6531511yescharacteristic
393C22#6550211yescharacteristic
394C4—21no—
395C4—22no—
396C4—21no—
397C4—21no—
398C4—41no—
399C4—41no—
400C4—41no—
401C4#6531611yescharacteristic
402C4#6531711yescharacteristic
403C4C2×#395511yescharacteristic
404C4#6542111yescharacteristic
405C4#6551611yescharacteristic
406C4#6552711yescharacteristic
407C2—21no—
408C2—21no—
409C2—802no—
410C2#1060242611yescharacteristic
411C2#1060279511yescharacteristic
412C2#1060281611yescharacteristic
subgroupG/H
centerC22#65502
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×Q8×M16C2
socleC22×C5#386
prime radicalC2×#4020C22
cosocleC2×C42×C5C23
hypercenterQ8×M16D5
hypocenterC5#9254
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
1. C5×Q8×M16C2semidirect
3. #10602415C2semidirect
6. #10598202C2semidirect
7. #10598159C2semidirect
78. Q8×M16D5semidirect
113. C5×M16SD16semidirect
173. C5×Q8#100semidirect
309. M16#688semidirect
348. Q8#3955semidirect
383. C5#9254semidirect

Maximal subgroups

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

subgroupindex
C5×Q8×M162
C2×#653162
#106024152
#106012952
#106006692
#105982022
#105981592
#92545