Finite Group Databasebeta

← #12018362

Subgroups — #12018362

Order 1280.

450 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65163C211yesmaximal, characteristic, complemented
2C2×C5×#357C211yesmaximal, characteristic
3#10602831C211yesmaximal, characteristic
4C2×#64782C211yesmaximal, characteristic
5#10598297C211yesmaximal, characteristic, complemented
6#10598295C211yesmaximal, characteristic, complemented
7#10598213C211yesmaximal, characteristic, complemented
8C22×C5×D8C2211yescharacteristic
9C2×#4034—21no—
10C22×C5×C16C2211yescharacteristic
11C2×C5×#107C2211yescharacteristic
12#65510—21no—
13C2×#3964—21no—
14C2×#3950C2211yescharacteristic
15C2×#3950C2211yescharacteristic
16C2×C8×Dic5C2211yescharacteristic
17C22×#672C2211yescharacteristic
18C2×#3939—21no—
19#65163—22no—
20#65163—22no—
21C5×#357—22no—
22#64782—22no—
23#13363—51nomaximal, Sylow
24C22×C5×D4—21no—
25C22×Dic10—41no—
26C2×C5×D8—21no—
27C2×C5×D8—21no—
28C2×C5×D8—21no—
29C2×C5×D8—21no—
30C2×C5×D8—21no—
31C2×C5×D8Q812yescomplemented
32C22×C5×C8C2311yescharacteristic
33C2×C5×C4⋊C4—21no—
34C2×C22⋊Dic5—41no—
35C2×C22⋊Dic5—41no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—21no—
38C2×#683—41no—
39C2×C4×Dic5D411yescharacteristic
40C22×#168D411yescharacteristic
41#4034—24no—
42#4034—42no—
43C2×C5×C16—21no—
44C2×C5×C16—21no—
45C2×C5×C16—21no—
46C5×#107—21no—
47C5×#107D412yes—
48#3964—42no—
49#3950—21no—
50#3950—21no—
51#3950—21no—
52#3950D412yes—
53C8×Dic5—21no—
54C8×Dic5—21no—
55C2×#672—21no—
56C2×#672—21no—
57C2×#672—21no—
58#3939—24no—
59C2×#500—51no—
60C2×#357—51no—
61C2×#357D511yescharacteristic
62#1970—51no—
63#1380—51no—
64#1380—51no—
65#1374—51no—
66C24×C5—41no—
67C2×C5×D4—22no—
68C2×C5×D4—41no—
69C2×C5×D4—41no—
70C2×C5×D4—41no—
71C2×C5×D4—41no—
72C2×C5×D4—41no—
73C22×C4×C5—41no—
74C22×C4×C5C2×D411yescharacteristic
75C22×Dic5—41no—
76C22×Dic5—41no—
77C22×Dic5D811yescharacteristic
78C22×Dic5D811yescharacteristic
79C2×Dic10—44no—
80C2×Dic10—82no—
81C2×Dic10—82no—
82C5×D8—22no—
83C5×D8—22no—
84C5×D8—41no—
85C5×D8—41no—
86C2×C5×C8C2×D411yescharacteristic
87C2×C5×C8C2×D411yescharacteristic
88C2×C5×C8C2×Q811yescharacteristic
89C2×C5×C8#4111yescharacteristic
90C2×C5×C8#4111yescharacteristic
91C2×C5×C8#4111yescharacteristic
92C5×C4⋊C4—22no—
93C5×C4⋊C4—41no—
94C22⋊Dic5—82no—
95C22⋊Dic5—82no—
96C4⋊Dic5—22no—
97C4⋊Dic5—41no—
98C4⋊Dic5—41no—
99C4⋊Dic5—41no—
100#683—44no—
101C4×Dic5—21no—
102C4×Dic5—21no—
103C2×#168—21no—
104C2×#168—21no—
105C2×#168SD1612yes—
106C5×C16—41no—
107#672—41no—
108C22×D8C2×D511yescharacteristic
109C2×C4⋊Q8—101no—
110C22×C16—51no—
111C22×C16C2×D511yescharacteristic
112#500—102no—
113#500—102no—
114C2×#107—51no—
115C2×#107—51no—
116C2×#107—101no—
117C2×#107C2×D511yescharacteristic
118C2×#102—101no—
119C2×C4×C8—51no—
120#390—101no—
121#357—22no—
122#357—102no—
123C23×C5—42no—
124C23×C5—81no—
125C23×C5—81no—
126C23×C5—81no—
127C23×C5—81no—
128C23×C5—81no—
129C23×C5—81no—
130C23×C5C2×D811yescharacteristic
131C5×D4—42no—
132C5×D4—42no—
133C5×D4—81no—
134C5×D4—81no—
135C2×C4×C5—42no—
136C2×C4×C5—81no—
137C2×C4×C5—81no—
138C2×C4×C5#12011yescharacteristic
139C2×C4×C5C22⋊Q811yescharacteristic
140C2×C4×C5#12411yescharacteristic
141C2×C4×C5C2×SD1611yescharacteristic
142C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C5#13711yescharacteristic
144C2×Dic5—21no—
145C2×Dic5—21no—
146C2×Dic5—21no—
147C2×Dic5—21no—
148C2×Dic5—42no—
149C2×Dic5—81no—
150C2×Dic5—81no—
151C2×Dic5—81no—
152C2×Dic5—81no—
153C2×Dic5—81no—
154C2×Dic5D1612yes—
155C2×Dic5SD3212yes—
156Dic10—88no—
157C5×C8C22⋊Q811yescharacteristic
158C5×C8C22⋊Q811yescharacteristic
159C5×C8#12411yescharacteristic
160C5×C8#12411yescharacteristic
161#168—22no—
162C22×Q8—201no—
163C22×D4—21no—
164C2×D8—21no—
165C2×D8—21no—
166C2×D8—21no—
167C2×D8—21no—
168C2×D8—21no—
169C2×D8Dic1012yescomplemented
170C22×C8—51no—
171C22×C8C22×D511yescharacteristic
172C4⋊Q8—104no—
173C4⋊Q8—202no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—101no—
176C2×C4⋊C4—101no—
177C2×C4⋊C4—201no—
178C2×C22⋊C4—201no—
179C2×C22⋊C4—201no—
180C2×C42—51no—
181C2×C16—21no—
182C2×C16—21no—
183C2×C16—21no—
184C2×C16—101no—
185C2×C16—101no—
186C2×C16—101no—
187#107—21no—
188#107—52no—
189#107—104no—
190#107—101no—
191#107—101no—
192#107—101no—
193#107C22⋊D512yes—
194#102—202no—
195C4×C8—101no—
196C4×C8—101no—
197C22×C5—82no—
198C22×C5—82no—
199C22×C5—82no—
200C22×C5—161no—
201C22×C5—161no—
202C22×C5—161no—
203C22×C5—161no—
204C22×C5#44711yescharacteristic
205C22×C5#47411yescharacteristic
206C22×C5#48611yescharacteristic
207C22×C5C2×D1611yescharacteristic
208C22×C5C2×SD3211yescharacteristic
209C22×C5#50911yescharacteristic
210C22×C5#51011yescharacteristic
211C4×C5—82no—
212C4×C5#39311yescharacteristic
213C4×C5#44811yescharacteristic
214C4×C5#47611yescharacteristic
215C4×C5#48911yescharacteristic
216Dic5—22no—
217Dic5—22no—
218Dic5—82no—
219Dic5—161no—
220C24—41no—
221C2×Q8—204no—
222C2×Q8—402no—
223C2×Q8—402no—
224C2×D4—22no—
225C2×D4—41no—
226C2×D4—41no—
227C2×D4—41no—
228C2×D4—41no—
229C2×D4—41no—
230C22×C4—41no—
231C22×C4—51no—
232C22×C4—51no—
233C22×C4—201no—
234C22×C4—201no—
235C22×C4D4×D511yescharacteristic
236D8—22no—
237D8—22no—
238D8—41no—
239D8—41no—
240C2×C8—52no—
241C2×C8—101no—
242C2×C8—101no—
243C2×C8C2×Dic1011yescharacteristic
244C2×C8#70911yescharacteristic
245C2×C8D4×D511yescharacteristic
246C2×C8#71111yescharacteristic
247C2×C8#71111yescharacteristic
248C2×C8C2×C22⋊D511yescharacteristic
249C4⋊C4—22no—
250C4⋊C4—41no—
251C4⋊C4—102no—
252C4⋊C4—204no—
253C4⋊C4—201no—
254C4⋊C4—201no—
255C4⋊C4—201no—
256C22⋊C4—402no—
257C22⋊C4—402no—
258C42—101no—
259C42—101no—
260C16—41no—
261C16—201no—
262C2×C5—162no—
263C2×C5#202311yescharacteristic
264C2×C5#218411yescharacteristic
265C2×C5#218511yescharacteristic
266C2×C5#222411yescharacteristic
267C2×C5#222611yescharacteristic
268C2×C5#224011yescharacteristic
269C2×C5#224311yescharacteristic
270C23—42no—
271C23—81no—
272C23—81no—
273C23—81no—
274C23—81no—
275C23—81no—
276C23—81no—
277C23D5×D811yescharacteristic
278Q8—408no—
279D4—42no—
280D4—42no—
281D4—81no—
282D4—81no—
283C2×C4—42no—
284C2×C4—52no—
285C2×C4—52no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—101no—
289C2×C4—101no—
290C2×C4—101no—
291C2×C4—101no—
292C2×C4—202no—
293C2×C4—401no—
294C2×C4—401no—
295C2×C4—401no—
296C2×C4—401no—
297C2×C4—401no—
298C2×C4#402411yescharacteristic
299C2×C4#403111yescharacteristic
300C2×C4#405711yescharacteristic
301C2×C4D5×SD1611yescharacteristic
302C2×C4#406111yescharacteristic
303C2×C4#408311yescharacteristic
304C8—102no—
305C8#402411yescharacteristic
306C8#403111yescharacteristic
307C8#407011yescharacteristic
308C8#408211yescharacteristic
309C5#1336311yescharacteristic, complemented, Sylow
310C22—82no—
311C22—82no—
312C22—82no—
313C22—161no—
314C22—161no—
315C22—161no—
316C22—161no—
317C22#6504811yescharacteristic
318C22#6504911yescharacteristic
319C22D5×D1611yescharacteristic
320C22#6520011yescharacteristic
321C22D5×SD3211yescharacteristic
322C22#6520411yescharacteristic
323C22#6544511yescharacteristic
324C4—82no—
325C4—102no—
326C4—102no—
327C4—402no—
328C4—801no—
329C4#6505011yescharacteristic
330C4#6505411yescharacteristic
331C4#6523611yescharacteristic
332C4#6545911yescharacteristic
333C2—162no—
334C2#1059997111yescharacteristic
335C2#1059997211yescharacteristic
336C2#1059997611yescharacteristic
337C2#1059997811yescharacteristic
338C2#1060095611yescharacteristic
339C2#1060226011yescharacteristic
340C2#1060227611yescharacteristic
subgroupG/H
centerC23D5×D8
commutator, cosocleC22×C5×C8C23
FrattiniC22×C8C22×D5
FittingC2×C5×#357C2
socleC23×C5C2×D8
prime radicalC22×C5×D8C22
hypercenterC2×#357D5
hypocenterC5#13363
LCSG ▷ C22×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
1. C2×#65163C2semidirect
5. #10598297C2semidirect
6. #10598295C2semidirect
7. #10598213C2semidirect
31. C2×C5×D8Q8semidirect
169. C2×D8Dic10semidirect
309. C5#13363semidirect

Maximal subgroups

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

subgroupindex
C2×#651632
C2×C5×#3572
#106028312
C2×#647822
#105982972
#105982952
#105982132
#133635