Finite Group Databasebeta

← #11993252

Subgroups — #11993252

Order 1280.

516 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64977C211yesmaximal, characteristic
2C5×#1939C211yesmaximal, characteristic, complemented
3C2×#64703C211yesmaximal, characteristic
4C2×#64700C211yesmaximal, characteristic, complemented
5C4×#3941C211yesmaximal, characteristic
6#10598144C211yesmaximal, characteristic, complemented
7#10598110C211yesmaximal, characteristic, complemented
8C22×#676—21no—
9C2×C4×D20C2211yescharacteristic
10C2×C5×C4⋊C8—21no—
11C2×C5×C4⋊C8C2211yescharacteristic
12C2×C4×C5×C8C2211yescharacteristic
13C4×C5×C4⋊C4C2211yescharacteristic
14C2×#3952—21no—
15C2×#3941C411yescharacteristic
16C2×#3941C411yescharacteristic
17C2×C4⋊#168C2211yescharacteristic
18C2×C4×#168C2211yescharacteristic
19C2×C4×#168C2211yescharacteristic
20#64977—22no—
21#64977—22no—
22C5×#336—21no—
23#64749C411yescharacteristic
24#64749C411yescharacteristic
25#64703—22no—
26#64700—22no—
27#8849—51nomaximal, Sylow
28C22×D20C2×C411yescharacteristic
29C22×C4×D5—21no—
30C22×C5×C8—21no—
31C22×C5×C8D411yescharacteristic
32C22×C5×C8D411yescharacteristic
33C2×C5×C4⋊C4C2×C411yescharacteristic
34C2×C5×C4⋊C4C2×C411yescharacteristic
35C2×C42×C5—21no—
36C2×C42×C5C2311yescharacteristic
37C2×#685—21no—
38C2×C4⋊Dic5C2×C411yescharacteristic
39C22×#168—21no—
40C22×#168—21no—
41C22×#168C2×C411yescharacteristic
42C22×#168C2×C411yescharacteristic
43C2×#676—24no—
44C2×#676—42no—
45C2×#676—42no—
46C4×D20—21no—
47C4×D20—21no—
48C4×D20D412yes—
49C4×D20Q812yes—
50C5×C4⋊C8—21no—
51C5×C4⋊C8—21no—
52C5×C4⋊C8—42no—
53C4×C5×C8—21no—
54C4×C5×C8—21no—
55C5×#95—21no—
56#3952—24no—
57#3941—22no—
58#3941—22no—
59C4⋊#168—21no—
60C4⋊#168D412yes—
61C4×#168—21no—
62C4×#168—21no—
63C4×#168—21no—
64C4×#168—21no—
65C2×#436—51no—
66#1939D511yescharacteristic, complemented
67C4×#102—51no—
68C2×#334—51no—
69C2×D4⋊C8—51no—
70#1279—51no—
71#1273—51no—
72C23×D5—21no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5C22×C411yescharacteristic
76C22×C4×C5C2×D411yescharacteristic
77C22×C4×C5#4111yescharacteristic
78C22×Dic5—21no—
79C2×D20—21no—
80C2×D20—21no—
81C2×D20—21no—
82C2×D20—21no—
83C2×D20—21no—
84C2×D20C4⋊C412yes—
85C2×C4×D5—22no—
86C2×C4×D5—22no—
87C2×C4×D5—41no—
88C2×C4×D5—41no—
89C2×C4×D5—41no—
90C2×C4×D5—41no—
91C2×C5×C8—21no—
92C2×C5×C8—21no—
93C2×C5×C8—21no—
94C2×C5×C8—21no—
95C2×C5×C8—21no—
96C2×C5×C8—41no—
97C2×C5×C8—41no—
98C2×C5×C8—41no—
99C2×C5×C8SD1612yes—
100C5×C4⋊C4—21no—
101C5×C4⋊C4—21no—
102C5×C4⋊C4—21no—
103C5×C4⋊C4M1612yescomplemented
104C42×C5—41no—
105C42×C5—41no—
106C42×C5C2×D411yescharacteristic
107C42×C5C2×D411yescharacteristic
108C42×C5C2×Q811yescharacteristic
109C42×C5#4111yescharacteristic
110#685—22no—
111#685—22no—
112C4⋊Dic5—21no—
113C4⋊Dic5C4⋊C412yes—
114C2×#168—21no—
115C2×#168—21no—
116C2×#168—22no—
117C2×#168—21no—
118C2×#168—22no—
119C2×#168—21no—
120C2×#168—21no—
121C2×#168—41no—
122C2×#168—41no—
123C2×#168—41no—
124C2×#168—41no—
125C2×#168M1612yescomplemented
126#676—48no—
127C22×M16—101no—
128C2×C4×D4—51no—
129#436—102no—
130#436—102no—
131C2×C4⋊C8—21no—
132C2×C4⋊C8—51no—
133C2×C4⋊C8C2×D511yescharacteristic
134C2×#102—51no—
135C2×#102—51no—
136C2×C22⋊C8—101no—
137C2×C4×C8—51no—
138C2×C4×C8—51no—
139C2×C4×C8C2×D511yescharacteristic
140C4×C4⋊C4C2×D511yescharacteristic
141#340—51no—
142#340—51no—
143#336—21no—
144#334—102no—
145D4⋊C8—102no—
146C23×C5C4×D411yescharacteristic
147C22×D5—22no—
148C22×D5—41no—
149C22×D5—41no—
150C22×D5—41no—
151C22×D5—41no—
152C22×D5—41no—
153C22×D5—41no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—22no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5C2×C4⋊C411yescharacteristic
163C2×C4×C5C4×D411yescharacteristic
164C2×C4×C5#12011yescharacteristic
165C2×C4×C5C22⋊Q811yescharacteristic
166C2×C4×C5C22⋊Q811yescharacteristic
167C2×C4×C5#12311yescharacteristic
168C2×C4×C5C2×M1611yescharacteristic
169C2×C4×C5C2×M1611yescharacteristic
170C2×C4×C5#13111yescharacteristic
171C2×C4×C5#13111yescharacteristic
172C2×C4×C5C2×SD1611yescharacteristic
173C2×C4×C5#13511yescharacteristic
174C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
176C2×Dic5—22no—
177C2×Dic5—41no—
178C2×Dic5—41no—
179D20—22no—
180D20—22no—
181D20—41no—
182D20—41no—
183C4×D5—42no—
184C4×D5—42no—
185C4×D5—42no—
186C4×D5—42no—
187C5×C8—22no—
188C5×C8—41no—
189C5×C8—81no—
190#168—22no—
191#168—42no—
192#168—41no—
193#168—42no—
194C22×D4—51no—
195C23×C4—101no—
196C2×M16—104no—
197C2×M16—202no—
198C2×M16—202no—
199C22×C8—21no—
200C22×C8—51no—
201C22×C8—51no—
202C22×C8—101no—
203C22×C8—101no—
204C22×C8C22⋊D511yescharacteristic
205C22×C8C22⋊D511yescharacteristic
206C4×D4—52no—
207C4×D4—52no—
208C4×D4—101no—
209C4×D4—101no—
210C2×C4⋊C4—51no—
211C2×C4⋊C4C4×D511yescharacteristic
212C2×C4⋊C4C4×D511yescharacteristic
213C2×C22⋊C4—101no—
214C2×C42—21no—
215C2×C42C22×D511yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—42no—
219C4⋊C8—52no—
220C4⋊C8—101no—
221#102—102no—
222#102—102no—
223C22⋊C8—104no—
224C4×C8—21no—
225C4×C8—21no—
226C4×C8—101no—
227C4×C8—101no—
228C4×C8—101no—
229C4×C8—101no—
230#95—21no—
231C22×C5#38511yescharacteristic
232C22×C5#43511yescharacteristic
233C22×C5#43611yescharacteristic
234C22×C5C4×SD1611yescharacteristic
235C22×C5#44211yescharacteristic
236C22×C5#44311yescharacteristic
237C22×C5#44411yescharacteristic
238C2×D5—42no—
239C2×D5—42no—
240C2×D5—42no—
241C2×D5—81no—
242C2×D5—81no—
243C2×D5—81no—
244C2×D5—81no—
245C4×C5—21no—
246C4×C5—21no—
247C4×C5—42no—
248C4×C5—81no—
249C4×C5#42311yescharacteristic
250C4×C5#42411yescharacteristic
251C4×C5#43511yescharacteristic
252C4×C5#43611yescharacteristic
253C4×C5#44911yescharacteristic
254C4×C5#45011yescharacteristic
255C4×C5#47611yescharacteristic
256C4×C5#47811yescharacteristic
257Dic5—42no—
258C24—101no—
259C2×D4—52no—
260C2×D4—101no—
261C2×D4—101no—
262C2×D4—101no—
263C2×D4—101no—
264C2×D4—101no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—101no—
268C22×C4—102no—
269C22×C4—102no—
270C22×C4—201no—
271C22×C4—201no—
272C22×C4—201no—
273C22×C4—201no—
274C22×C4C2×C4×D511yescharacteristic
275C22×C4#70911yescharacteristic
276C22×C4C2×C22⋊D511yescharacteristic
277M16—208no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—52no—
287C2×C8—101no—
288C2×C8—101no—
289C2×C8—102no—
290C2×C8—101no—
291C2×C8—101no—
292C2×C8—101no—
293C2×C8—102no—
294C2×C8—201no—
295C2×C8—201no—
296C2×C8—201no—
297C2×C8—201no—
298C2×C8#68812yes—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—52no—
303C4⋊C4—101no—
304C4⋊C4#67612yescomplemented
305C22⋊C4—102no—
306C22⋊C4—102no—
307C42—41no—
308C42—41no—
309C42D4×D511yescharacteristic
310C42D4×D511yescharacteristic
311C42Q8×D511yescharacteristic
312C42#71311yescharacteristic
313C2×C5#158311yescharacteristic
314C2×C5#158611yescharacteristic
315C2×C5#159011yescharacteristic
316C2×C5#159411yescharacteristic
317C2×C5#185111yescharacteristic
318C2×C5#186411yescharacteristic
319C2×C5#186611yescharacteristic
320D5—82no—
321C23—102no—
322C23—201no—
323C23—201no—
324C23—201no—
325C23—201no—
326C23—201no—
327C23—201no—
328C23C4×C22⋊D511yescharacteristic
329D4—102no—
330D4—102no—
331D4—201no—
332D4—201no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—102no—
342C2×C4—201no—
343C2×C4—201no—
344C2×C4—202no—
345C2×C4—202no—
346C2×C4—202no—
347C2×C4—202no—
348C2×C4D5×C4⋊C411yescharacteristic
349C2×C4#403911yescharacteristic
350C2×C4#404011yescharacteristic
351C2×C4#404211yescharacteristic
352C2×C4C2×#67611yescharacteristic
353C2×C4#404711yescharacteristic
354C2×C4D5×M1611yescharacteristic
355C2×C4#405311yescharacteristic
356C2×C4#407811yescharacteristic
357C2×C4#408311yescharacteristic
358C2×C4C2×#68811yescharacteristic
359C2×C4#409211yescharacteristic
360C2×C4#409511yescharacteristic
361C2×C4#409611yescharacteristic
362C8—22no—
363C8—41no—
364C8—81no—
365C8—102no—
366C8—202no—
367C8—202no—
368C8—201no—
369C5#884911yescharacteristic, complemented, Sylow
370C22—202no—
371C22—202no—
372C22—202no—
373C22—401no—
374C22—401no—
375C22—401no—
376C22—401no—
377C22#6527811yescharacteristic
378C22#6530311yescharacteristic
379C22C4×#68811yescharacteristic
380C22#6540011yescharacteristic
381C22#6541711yescharacteristic
382C22#6543311yescharacteristic
383C22#6543411yescharacteristic
384C4—21no—
385C4—21no—
386C4—42no—
387C4—81no—
388C4—202no—
389C4#6512511yescharacteristic
390C4#6512611yescharacteristic
391C4#6512711yescharacteristic
392C4#6512811yescharacteristic
393C4#6532611yescharacteristic
394C4#6533511yescharacteristic
395C4#6535511yescharacteristic
396C4#6537311yescharacteristic
397C2—402no—
398C2#1060041911yescharacteristic
399C2#1060127111yescharacteristic
400C2#1060133811yescharacteristic
401C2#1060163711yescharacteristic
402C2#1060165411yescharacteristic
403C2#1060172611yescharacteristic
404C2#1060174311yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D5
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1939C2
socleC23×C5C4×D4
prime radicalC22×D20C2×C4
cosocleC2×C42×C5C23
hypercenter#1939D5
hypocenterC5#8849
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1939

Complements

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

NH ≅ G/Ntype
2. C5×#1939C2semidirect
4. C2×#64700C2semidirect
6. #10598144C2semidirect
7. #10598110C2semidirect
66. #1939D5semidirect
103. C5×C4⋊C4M16semidirect
125. C2×#168M16semidirect
304. C4⋊C4#676semidirect
369. C5#8849semidirect

Maximal subgroups

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

subgroupindex
C2×#649772
C5×#19392
C2×#647032
C2×#647002
C4×#39412
#105981442
#105981102
#88495