Finite Group Databasebeta

← #12016669

Subgroups — #12016669

Order 1280.

558 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65446C211yesmaximal, characteristic
2C22×#3930C211yesmaximal, characteristic, complemented
3C2×C5×#357C211yesmaximal, characteristic, complemented
4C2×#64782C211yesmaximal, characteristic, complemented
5#10601423C211yesmaximal, characteristic, complemented
6#10598297C211yesmaximal, characteristic, complemented
7#10598213C211yesmaximal, characteristic, complemented
8C22×C5×D8C2211yescharacteristic
9C2×#4084—21no—
10C22×C8×D5C2211yescharacteristic
11C22×C5×C16C2211yescharacteristic
12C2×C5×#107C2211yescharacteristic
13C2×#3964—21no—
14#65446—22no—
15#65446C414yescomplemented
16C2×#3950C2211yescharacteristic
17C2×#3950C2211yescharacteristic
18C22×#672C2211yescharacteristic
19#65276—21no—
20C2×#3930—22no—
21C2×#3930—22no—
22C2×#3930—22no—
23C5×#357—22no—
24#64782—22no—
25#64749—21no—
26#13061—51nomaximal, Sylow
27C22×C5×D4—21no—
28C22×C22⋊D5—41no—
29C22×C4×D5D411yescharacteristic
30C2×C5×D8—21no—
31C2×C5×D8—21no—
32C2×C5×D8—21no—
33C2×C5×D8—21no—
34C2×C5×D8—21no—
35C2×C5×D8C2×C412yes—
36C22×C5×C8C2311yescharacteristic
37C2×C5×C4⋊C4—21no—
38C2×C22⋊Dic5—41no—
39#4084—24no—
40#4084—42no—
41C2×#685—41no—
42C2×C4⋊Dic5—21no—
43C2×C4⋊Dic5—21no—
44C22×#168D411yescharacteristic
45C2×C8×D5—21no—
46C2×C8×D5—21no—
47C2×C8×D5—21no—
48C2×C8×D5—21no—
49C2×C8×D5C2×C412yes—
50C2×C8×D5D412yes—
51C2×C5×C16—21no—
52C2×C5×C16—21no—
53C2×C5×C16D412yescomplemented
54C5×#107—21no—
55C5×#107—21no—
56#3964—24no—
57#3963—41no—
58#3950—21no—
59#3950—21no—
60#3950—21no—
61#3950C2×C412yes—
62C2×#672—21no—
63C2×#672—21no—
64C2×#672D412yescomplemented
65#3930—28no—
66C22×M32—51no—
67C2×#466—51no—
68C2×#357—51no—
69C2×#357D511yescharacteristic, complemented
70#1808—51no—
71#1380—51no—
72#1380—51no—
73C24×C5—41no—
74C23×D5D811yescharacteristic
75C2×C5×D4—22no—
76C2×C5×D4—41no—
77C2×C5×D4—41no—
78C2×C5×D4—41no—
79C2×C5×D4—41no—
80C2×C5×D4—41no—
81C22×C4×C5—41no—
82C22×C4×C5C2×D411yescharacteristic
83C2×C22⋊D5—44no—
84C2×C22⋊D5—82no—
85C2×C22⋊D5—82no—
86C22×Dic5—41no—
87C22×Dic5—41no—
88C22×Dic5D811yescharacteristic
89C2×C4×D5—21no—
90C2×C4×D5—21no—
91C2×C4×D5—21no—
92C2×C4×D5—21no—
93C2×C4×D5C22⋊C412yes—
94C2×C4×D5SD1612yes—
95C5×D8—22no—
96C5×D8—22no—
97C5×D8—41no—
98C5×D8—41no—
99C2×C5×C8C22×C411yescharacteristic
100C2×C5×C8C2×D411yescharacteristic
101C2×C5×C8C2×D411yescharacteristic
102C2×C5×C8C2×D411yescharacteristic
103C2×C5×C8#4111yescharacteristic
104C2×C5×C8#4111yescharacteristic
105C5×C4⋊C4—41no—
106C5×C4⋊C4—41no—
107C22⋊Dic5—44no—
108#685—82no—
109C4⋊Dic5—22no—
110C4⋊Dic5—41no—
111C4⋊Dic5—41no—
112C4⋊Dic5—41no—
113C2×#168—21no—
114C2×#168—21no—
115C2×#168C22⋊C412yes—
116C8×D5—22no—
117C8×D5—22no—
118C8×D5—22no—
119C8×D5—22no—
120C5×C16—22no—
121#672—22no—
122C22×D8C2×D511yescharacteristic
123C23×C8—51no—
124C2×#121—101no—
125C2×M32—102no—
126C2×M32—102no—
127C2×M32—102no—
128C22×C16—51no—
129C22×C16C2×D511yescharacteristic
130#466—54no—
131#466—102no—
132C2×#107—51no—
133C2×#107—51no—
134C2×#107C2×D511yescharacteristic
135C2×#102—101no—
136#380—101no—
137#357—22no—
138#357—102no—
139#340—101no—
140C23×C5—42no—
141C23×C5—81no—
142C23×C5—81no—
143C23×C5—81no—
144C23×C5—81no—
145C23×C5—81no—
146C23×C5—81no—
147C23×C5C2×D811yescharacteristic
148C22×D5—21no—
149C22×D5—21no—
150C22×D5—21no—
151C22×D5—21no—
152C22×D5—21no—
153C22×D5—21no—
154C22×D5#10212yes—
155C5×D4—42no—
156C5×D4—42no—
157C5×D4—81no—
158C5×D4—81no—
159C2×C4×C5—81no—
160C2×C4×C5—81no—
161C2×C4×C5—81no—
162C2×C4×C5C2×C22⋊C411yescharacteristic
163C2×C4×C5#12111yescharacteristic
164C2×C4×C5#12111yescharacteristic
165C2×C4×C5C2×SD1611yescharacteristic
166C2×C4×C5#13511yescharacteristic
167C2×C4×C5#13511yescharacteristic
168C22⋊D5—88no—
169C2×Dic5—21no—
170C2×Dic5—21no—
171C2×Dic5—42no—
172C2×Dic5—81no—
173C2×Dic5—81no—
174C2×Dic5—81no—
175C2×Dic5—81no—
176C2×Dic5—81no—
177C2×Dic5#10212yes—
178C4×D5—22no—
179C4×D5—22no—
180C4×D5—22no—
181C4×D5—22no—
182C5×C8C4×D411yescharacteristic
183C5×C8C4×D411yescharacteristic
184C5×C8#12011yescharacteristic
185C5×C8#12311yescharacteristic
186#168—22no—
187C22×D4—21no—
188C22×D4—201no—
189C23×C4—51no—
190C2×D8—21no—
191C2×D8—21no—
192C2×D8—21no—
193C2×D8—21no—
194C2×D8—21no—
195C2×D8C4×D512yes—
196C22×C8—51no—
197C22×C8—52no—
198C22×C8—52no—
199C22×C8—101no—
200C22×C8—101no—
201C22×C8—101no—
202C22×C8—101no—
203C22×C8C22×D511yescharacteristic
204#121—104no—
205#121—202no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—101no—
208C2×C4⋊C4—101no—
209C2×C22⋊C4—201no—
210C2×C22⋊C4—201no—
211M32—108no—
212C2×C16—21no—
213C2×C16—21no—
214C2×C16—52no—
215C2×C16—101no—
216C2×C16—101no—
217C2×C16C22⋊D512yescomplemented
218#107—21no—
219#107—21no—
220#107—52no—
221#107—101no—
222#107—101no—
223#107—101no—
224#102—104no—
225#95—201no—
226C22×C5—82no—
227C22×C5—82no—
228C22×C5—82no—
229C22×C5—161no—
230C22×C5—161no—
231C22×C5—161no—
232C22×C5—161no—
233C22×C5C2×#10211yescharacteristic
234C22×C5#46611yescharacteristic
235C22×C5#46611yescharacteristic
236C22×C5#50911yescharacteristic
237C22×C5#50911yescharacteristic
238C22×C5#50911yescharacteristic
239C22×C5#51011yescharacteristic
240C2×D5—22no—
241C2×D5—22no—
242C2×D5—22no—
243C2×D5—41no—
244C2×D5—41no—
245C2×D5—41no—
246C2×D5—41no—
247C4×C5—161no—
248C4×C5#38611yescharacteristic
249C4×C5#41611yescharacteristic
250C4×C5#46511yescharacteristic
251C4×C5#46511yescharacteristic
252Dic5—22no—
253Dic5—82no—
254Dic5—161no—
255C24—41no—
256C24—51no—
257C2×D4—22no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—204no—
264C2×D4—402no—
265C2×D4—402no—
266C22×C4—41no—
267C22×C4—51no—
268C22×C4—52no—
269C22×C4—52no—
270C22×C4—101no—
271C22×C4—101no—
272C22×C4—101no—
273C22×C4—101no—
274C22×C4—201no—
275C22×C4—201no—
276C22×C4D4×D511yescharacteristic
277D8—22no—
278D8—22no—
279D8—41no—
280D8—41no—
281C2×C8—52no—
282C2×C8—101no—
283C2×C8—101no—
284C2×C8—102no—
285C2×C8—102no—
286C2×C8—102no—
287C2×C8—102no—
288C2×C8C2×C4×D511yescharacteristic
289C2×C8#70911yescharacteristic
290C2×C8D4×D511yescharacteristic
291C2×C8D4×D511yescharacteristic
292C2×C8#71111yescharacteristic
293C2×C8C2×C22⋊D511yescharacteristic
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—102no—
297C4⋊C4—201no—
298C4⋊C4—201no—
299C4⋊C4—201no—
300C22⋊C4—204no—
301C22⋊C4—402no—
302C16—22no—
303C16—102no—
304C2×C5—162no—
305C2×C5#189311yescharacteristic
306C2×C5#213911yescharacteristic
307C2×C5#214011yescharacteristic
308C2×C5#221811yescharacteristic
309C2×C5#221811yescharacteristic
310C2×C5#222011yescharacteristic
311C2×C5#222011yescharacteristic
312D5—42no—
313C23—42no—
314C23—52no—
315C23—81no—
316C23—81no—
317C23—81no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—101no—
322C23—101no—
323C23—101no—
324C23—101no—
325C23—101no—
326C23—101no—
327C23D5×D811yescharacteristic
328D4—42no—
329D4—42no—
330D4—81no—
331D4—81no—
332D4—408no—
333C2×C4—52no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—101no—
338C2×C4—101no—
339C2×C4—102no—
340C2×C4—102no—
341C2×C4—102no—
342C2×C4—102no—
343C2×C4—202no—
344C2×C4—401no—
345C2×C4—401no—
346C2×C4—401no—
347C2×C4—401no—
348C2×C4—401no—
349C2×C4D5×C22⋊C411yescharacteristic
350C2×C4#403011yescharacteristic
351C2×C4#405811yescharacteristic
352C2×C4D5×SD1611yescharacteristic
353C2×C4#406211yescharacteristic
354C2×C4#408411yescharacteristic
355C8—102no—
356C8#402711yescharacteristic
357C8#402911yescharacteristic
358C8C4×C22⋊D511yescharacteristic
359C8#408311yescharacteristic
360C5#1306111yescharacteristic, complemented, Sylow
361C22—82no—
362C22—82no—
363C22—82no—
364C22—102no—
365C22—102no—
366C22—102no—
367C22—161no—
368C22—161no—
369C22—161no—
370C22—161no—
371C22—201no—
372C22—201no—
373C22—201no—
374C22—201no—
375C22D5×#10211yescharacteristic
376C22#6506411yescharacteristic
377C22#6520011yescharacteristic
378C22#6520011yescharacteristic
379C22#6520311yescharacteristic
380C22#6520411yescharacteristic
381C22#6544611yescharacteristic
382C4—102no—
383C4—161no—
384C4—402no—
385C4—801no—
386C4#6506111yescharacteristic
387C4#6506711yescharacteristic
388C4#6524511yescharacteristic
389C4#6546011yescharacteristic
390C2—162no—
391C2—202no—
392C2#1059998211yescharacteristic
393C2#1059998311yescharacteristic
394C2#1059999011yescharacteristic
395C2#1059999111yescharacteristic
396C2#1060099511yescharacteristic
397C2#1060226311yescharacteristic
398C2#1060228111yescharacteristic
subgroupG/H
centerC23D5×D8
commutatorC2×C5×C8C22×C4
FrattiniC22×C8C22×D5
FittingC2×C5×#357C2
socleC23×C5C2×D8
prime radicalC2×#65446C2
cosocleC22×C5×C8C23
hypercenterC2×#357D5
hypocenterC5#13061
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C22×#3930C2semidirect
3. C2×C5×#357C2semidirect
4. C2×#64782C2semidirect
5. #10601423C2semidirect
6. #10598297C2semidirect
7. #10598213C2semidirect
15. #65446C4semidirect
53. C2×C5×C16D4semidirect
64. C2×#672D4semidirect
69. C2×#357D5semidirect
217. C2×C16C22⋊D5semidirect
360. C5#13061semidirect

Maximal subgroups

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

subgroupindex
C2×#654462
C22×#39302
C2×C5×#3572
C2×#647822
#106014232
#105982972
#105982132
#130615