Finite Group Databasebeta

← #11992178

Subgroups — #11992178

Order 1280.

462 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#4053C211yesmaximal, characteristic
2#10601548C211yesmaximal, characteristic
3#10601538C211yesmaximal, characteristic, complemented
4#10601218C211yesmaximal, characteristic
5C2×#64699C211yesmaximal, characteristic, complemented
6C5×#1283C211yesmaximal, characteristic, complemented
7#10598159C211yesmaximal, characteristic, complemented
8C2×#4053C411yescharacteristic
9C2×#4053C411yescharacteristic
10C4×#709C2211yescharacteristic
11C5×#431C2211yescharacteristic
12C2×C5×C4⋊C8C2211yescharacteristic
13C4×C5×M16C2211yescharacteristic
14#65411C411yescharacteristic
15#65411C411yescharacteristic
16#65214C2211yescharacteristic
17C2×C4⋊#168C2211yescharacteristic
18C2×C4×#168C2211yescharacteristic
19#64997—21no—
20#64997—21no—
21C4×#676—21no—
22C4×C8×D5—21no—
23#64704—21no—
24#64703—21no—
25#64700—21no—
26#64699—21no—
27#64699—21no—
28#64699—21no—
29#64679—21no—
30#64676—21no—
31#8605—51nomaximal, Sylow
32C2×#709C2×C411yescharacteristic
33C2×C5×M16C2×C411yescharacteristic
34C2×C5×M16C2×C411yescharacteristic
35C22×C5×C8—21no—
36C2×C42×C5C2311yescharacteristic
37C4×C22⋊D5—21no—
38C4×C22⋊D5—21no—
39#4072C2×C411yescharacteristic
40C22×#168—21no—
41C22×#168C2×C411yescharacteristic
42C22×#168C2×C411yescharacteristic
43#4053—22no—
44#4053—22no—
45#4053—22no—
46#4053C814yescomplemented
47C2×#676—21no—
48C2×#676—21no—
49C2×C8×D5—21no—
50C2×C8×D5—21no—
51C4×D20D411yescharacteristic
52C4×D20Q811yescharacteristic
53#4018—21no—
54C42×D5—21no—
55C4×Dic10D411yescharacteristic
56C4×Dic10Q811yescharacteristic
57C5×C4⋊C8—21no—
58C5×C4⋊C8—21no—
59C5×C4⋊C8—21no—
60C5×C22⋊C8—21no—
61C5×#97—21no—
62C4×C5×C8—21no—
63C4×C5×C8—21no—
64C22⋊#168—21no—
65#3947—21no—
66#3947—21no—
67C8×Dic5—21no—
68C8×Dic5—21no—
69C4⋊#168—21no—
70C4⋊#168—21no—
71C4⋊#168—21no—
72C4×#168—21no—
73C4×#168D411yescharacteristic
74C4×#168D411yescharacteristic
75C4×#168D411yescharacteristic
76C4×#168D411yescharacteristic
77C4×#131—51no—
78#1564—51no—
79C2×#335—51no—
80#1477—51no—
81#1477—51no—
82#1283—51no—
83#1283D511yescharacteristic, complemented
84C22×C4×C5C22×C411yescharacteristic
85C22×C4×C5#4111yescharacteristic
86C22×C4×C5#4111yescharacteristic
87C2×C22⋊D5—21no—
88#709—21no—
89#709—21no—
90#709C2×C812yes—
91#709M1612yes—
92C2×D20C4⋊C411yescharacteristic
93C2×C4×D5—21no—
94C2×C4×D5—21no—
95C2×C4×D5—21no—
96C2×Dic10C4⋊C411yescharacteristic
97C5×M16—21no—
98C5×M16—21no—
99C5×M16C2×C812yes—
100C5×M16M1612yes—
101C2×C5×C8—21no—
102C2×C5×C8—21no—
103C2×C5×C8—41no—
104C2×C5×C8—41no—
105C2×C5×C8—81no—
106C42×C5C2×D411yescharacteristic
107C42×C5C2×D411yescharacteristic
108C42×C5C2×D411yescharacteristic
109C42×C5C2×Q811yescharacteristic
110C22⋊Dic5—21no—
111#685—21no—
112#685—21no—
113C4⋊Dic5C4⋊C411yescharacteristic
114C4⋊Dic5C4⋊C411yescharacteristic
115#683—21no—
116#683—21no—
117C4×Dic5—21no—
118C4×Dic5—21no—
119C4×Dic5—21no—
120C2×#168—21no—
121C2×#168—21no—
122C2×#168—41no—
123C2×#168—41no—
124C2×#168—81no—
125C2×#168C22⋊C411yescharacteristic
126C2×#168C22⋊C411yescharacteristic
127C2×#168C22⋊C411yescharacteristic
128C2×#168C22⋊C411yescharacteristic
129C2×#168C2×C812yes—
130C2×#168M1612yes—
131#676—24no—
132#676—24no—
133C8×D5—24no—
134C8×D5—24no—
135C2×#131—51no—
136C2×#131—51no—
137C4×#41—51no—
138#431—51no—
139#431C2×D511yescharacteristic
140C2×C4⋊C8—51no—
141C2×C4⋊C8C2×D511yescharacteristic
142#405—51no—
143#405—51no—
144#405—101no—
145#405—101no—
146C4×M16—101no—
147C4×M16C2×D511yescharacteristic
148C2×C4×C8—51no—
149C2×C4×C8—101no—
150#335—101no—
151#335—101no—
152#335—101no—
153#334—101no—
154Q8⋊C8—101no—
155Q8⋊C8—101no—
156D4⋊C8—101no—
157D4⋊C8—101no—
158C23×C5#11711yescharacteristic
159C22×D5—21no—
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×C4×C5—41no—
163C2×C4×C5C2×C22⋊C411yescharacteristic
164C2×C4×C5C2×C4⋊C411yescharacteristic
165C2×C4×C5#12111yescharacteristic
166C2×C4×C5#12111yescharacteristic
167C2×C4×C5C22⋊Q811yescharacteristic
168C2×C4×C5C22⋊Q811yescharacteristic
169C2×C4×C5C22×C811yescharacteristic
170C2×C4×C5C2×M1611yescharacteristic
171C2×C4×C5C2×M1611yescharacteristic
172C2×C4×C5C2×M1611yescharacteristic
173C22⋊D5—22no—
174C22⋊D5—22no—
175C2×Dic5—21no—
176C2×Dic5—21no—
177C2×Dic5—21no—
178D20—21no—
179D20C4⋊C812yes—
180C4×D5—22no—
181C4×D5—22no—
182C4×D5—42no—
183C4×D5—41no—
184C4×D5—41no—
185Dic10—21no—
186Dic10C4⋊C812yes—
187C5×C8—22no—
188C5×C8—22no—
189C5×C8—81no—
190C5×C8—81no—
191#168—21no—
192#168—21no—
193#168—81no—
194#168—81no—
195#168C22⋊C812yes—
196#168C22⋊C812yes—
197C2×#41—51no—
198#131—54no—
199#131—102no—
200#131—102no—
201#131—102no—
202C2×M16—101no—
203C2×M16—101no—
204C2×M16C4×D511yescharacteristic
205C2×M16C4×D511yescharacteristic
206C22×C8—21no—
207C22×C8—51no—
208C22×C8—51no—
209C22×C8—101no—
210C22×C8—101no—
211C22×C8—101no—
212C4×Q8—51no—
213C4×Q8—51no—
214C4×D4—51no—
215C4×D4—51no—
216C4×D4—101no—
217C4×D4—101no—
218#117—51no—
219#117—101no—
220C2×C42—101no—
221C2×C42C22×D511yescharacteristic
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—101no—
226C4⋊C8—101no—
227C4⋊C8—101no—
228C22⋊C8—21no—
229C22⋊C8—101no—
230#97—21no—
231#97—101no—
232#97—101no—
233C4×C8—21no—
234C4×C8—21no—
235C4×C8—51no—
236C4×C8—51no—
237C4×C8—51no—
238C4×C8—51no—
239C4×C8—101no—
240C4×C8—101no—
241C4×C8—101no—
242C22×C5—21no—
243C22×C5—21no—
244C22×C5#38011yescharacteristic
245C22×C5#43111yescharacteristic
246C22×C5#43211yescharacteristic
247C2×D5—22no—
248C2×D5—41no—
249C2×D5—41no—
250C4×C5—21no—
251C4×C5—21no—
252C4×C5—21no—
253C4×C5C2×C22⋊C811yescharacteristic
254C4×C5#40711yescharacteristic
255C4×C5C2×C4⋊C811yescharacteristic
256C4×C5#42311yescharacteristic
257C4×C5#47211yescharacteristic
258C4×C5#47311yescharacteristic
259Dic5—22no—
260Dic5—41no—
261Dic5—41no—
262#41—52no—
263#41—52no—
264#41—101no—
265#41—101no—
266C2×Q8—51no—
267C2×D4—51no—
268C2×D4—101no—
269C22×C4—101no—
270C22×C4—101no—
271C22×C4—101no—
272C22×C4C2×C4×D511yescharacteristic
273C22×C4#70911yescharacteristic
274C22×C4#70911yescharacteristic
275M16—21no—
276M16—21no—
277M16—104no—
278M16—104no—
279M16C8×D512yes—
280M16#67612yes—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—51no—
286C2×C8—51no—
287C2×C8—52no—
288C2×C8—52no—
289C2×C8—51no—
290C2×C8—51no—
291C2×C8—81no—
292C2×C8—104no—
293C2×C8—104no—
294C2×C8—101no—
295C2×C8—101no—
296C2×C8—201no—
297C2×C8—201no—
298C2×C8—401no—
299C4⋊C4—51no—
300C4⋊C4—51no—
301C4⋊C4—101no—
302C4⋊C4—101no—
303C22⋊C4—101no—
304C22⋊C4—101no—
305C22⋊C4—101no—
306C42—101no—
307C42—101no—
308C42—101no—
309C42D4×D511yescharacteristic
310C42D4×D511yescharacteristic
311C42D4×D511yescharacteristic
312C42Q8×D511yescharacteristic
313C2×C5—21no—
314C2×C5—21no—
315C2×C5#179711yescharacteristic
316C2×C5#181411yescharacteristic
317C2×C5#181611yescharacteristic
318D5—42no—
319C23—101no—
320C23#401811yescharacteristic
321Q8—52no—
322Q8—101no—
323D4—52no—
324D4—102no—
325D4—102no—
326D4—101no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—101no—
331C2×C4—102no—
332C2×C4—102no—
333C2×C4—101no—
334C2×C4—101no—
335C2×C4—202no—
336C2×C4—201no—
337C2×C4—201no—
338C2×C4D5×C22⋊C411yescharacteristic
339C2×C4#403011yescharacteristic
340C2×C4#403011yescharacteristic
341C2×C4D5×C4⋊C411yescharacteristic
342C2×C4#404211yescharacteristic
343C2×C4#404211yescharacteristic
344C2×C4C2×C8×D511yescharacteristic
345C2×C4C2×#67611yescharacteristic
346C2×C4D5×M1611yescharacteristic
347C2×C4D5×M1611yescharacteristic
348C8—22no—
349C8—22no—
350C8—52no—
351C8—52no—
352C8—81no—
353C8—81no—
354C8—101no—
355C8—101no—
356C8—401no—
357C8—401no—
358C5#860511yescharacteristic, complemented, Sylow
359C22—21no—
360C22—21no—
361C22—102no—
362C22—201no—
363C22—201no—
364C22#6495611yescharacteristic
365C22#6497411yescharacteristic
366C22#6499411yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—102no—
371C4—201no—
372C4—201no—
373C4D5×C22⋊C811yescharacteristic
374C4#6501511yescharacteristic
375C4#6503811yescharacteristic
376C4#6504411yescharacteristic
377C4D5×C4⋊C811yescharacteristic
378C4#6512611yescharacteristic
379C2—21no—
380C2—21no—
381C2—202no—
382C2#1059945511yescharacteristic
383C2#1059979411yescharacteristic
384C2#1059982511yescharacteristic
subgroupG/H
centerC2×C4#4030
commutatorC2×C4×C5C22×C8
FrattiniC2×C42C22×D5
FittingC5×#1283C2
socleC22×C5#380
prime radicalC2×#709C2×C4
cosocleC2×C42×C5C23
hypercenter#1283D5
hypocenterC5#8605
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
3. #10601538C2semidirect
5. C2×#64699C2semidirect
6. C5×#1283C2semidirect
7. #10598159C2semidirect
46. #4053C8semidirect
83. #1283D5semidirect
358. C5#8605semidirect

Maximal subgroups

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

subgroupindex
C4×#40532
#106015482
#106015382
#106012182
C2×#646992
C5×#12832
#105981592
#86055