Finite Group Databasebeta

← #11988465

Subgroups — #11988465

Order 1280.

366 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2805C211yesmaximal, characteristic
2#10600478C211yesmaximal, characteristic
3#10600401C211yesmaximal, characteristic
4#10600400C211yesmaximal, characteristic
5#10598133C211yesmaximal, characteristic
6#10598129C211yesmaximal, characteristic
7#10598129C211yesmaximal, characteristic
8C5×#400—21no—
9C5×#400—21no—
10C5×#395—21no—
11C5×#391C2211yescharacteristic
12C5×#389—21no—
13C5×#389C2211yescharacteristic
14C5×#389C2211yescharacteristic
15C5×#387—21no—
16C5×#387—21no—
17C2×#3967—21no—
18C2×#3940—21no—
19C2×#3940—21no—
20C2×#3939—21no—
21#65224C2211yescharacteristic
22#64749—21no—
23#64749—21no—
24#64744C2211yescharacteristic
25#64744C2211yescharacteristic
26#64744C2211yescharacteristic
27#7807—51nomaximal, Sylow
28C22×C5×Q8D411yescharacteristic
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4D411yescharacteristic
34C2×C5×C4⋊C4D411yescharacteristic
35C2×C5×C4⋊C4D411yescharacteristic
36C2×C5×C4⋊C4D411yescharacteristic
37C2×C5×C4⋊C4D411yescharacteristic
38C2×C42×C5—21no—
39C2×C42×C5C2311yescharacteristic
40C2×C4⋊Dic5—21no—
41C2×C4⋊Dic5—21no—
42C2×C4⋊Dic5—21no—
43C22×#168—21no—
44C22×#168—21no—
45C22×#168—21no—
46C5×#95—21no—
47C5×#95—21no—
48C5×#95—21no—
49C5×#95—21no—
50C5×#95—21no—
51C5×#95—21no—
52C5×#95—21no—
53C5×#95—21no—
54C5×#95—21no—
55#3967—42no—
56#3940—42no—
57#3940—42no—
58#3939—42no—
59#2805D511yescharacteristic
60#2096—51no—
61#2084—51no—
62#2083—51no—
63#1272—51no—
64#1271—51no—
65#1271—51no—
66C2×C5×Q8—21no—
67C2×C5×Q8—21no—
68C2×C5×Q8—41no—
69C2×C5×Q8—41no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—21no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5—21no—
76C22×C4×C5C2×D411yescharacteristic
77C22×C4×C5C2×D411yescharacteristic
78C22×C4×C5C2×D411yescharacteristic
79C22×Dic5—41no—
80C5×C4⋊C4—21no—
81C5×C4⋊C4—21no—
82C5×C4⋊C4—21no—
83C5×C4⋊C4—41no—
84C5×C4⋊C4—41no—
85C5×C4⋊C4—41no—
86C5×C4⋊C4—41no—
87C5×C4⋊C4—41no—
88C5×C4⋊C4—41no—
89C5×C4⋊C4—41no—
90C5×C4⋊C4—81no—
91C5×C4⋊C4—81no—
92C5×C4⋊C4SD1612yes—
93C42×C5—41no—
94C42×C5—81no—
95C4⋊Dic5—41no—
96C4⋊Dic5—41no—
97C4⋊Dic5—41no—
98C4⋊Dic5—41no—
99C4⋊Dic5—41no—
100C4⋊Dic5—41no—
101C2×#168—22no—
102C2×#168—22no—
103C2×#168—22no—
104C2×#168—41no—
105C2×#168—41no—
106C2×#168—41no—
107C2×#168—41no—
108C2×#168—41no—
109C2×#168—41no—
110C2×#107—101no—
111C2×#106—101no—
112C2×#106—101no—
113C2×#103—101no—
114#400—21no—
115#400—21no—
116#395—21no—
117#391C2×D511yescharacteristic
118#389—21no—
119#389C2×D511yescharacteristic
120#389C2×D511yescharacteristic
121#387—21no—
122#387—21no—
123#384—51no—
124#340—101no—
125#340—101no—
126#336—51no—
127#336—51no—
128#336—51no—
129C23×C5#12011yescharacteristic
130C5×Q8—42no—
131C5×Q8—81no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—22no—
139C2×C4×C5—41no—
140C2×C4×C5—41no—
141C2×C4×C5—41no—
142C2×C4×C5—41no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5—41no—
147C2×C4×C5—41no—
148C2×C4×C5—41no—
149C2×C4×C5—41no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5—41no—
153C2×C4×C5—41no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5C2×SD1611yescharacteristic
157C2×C4×C5#13511yescharacteristic
158C2×C4×C5#13511yescharacteristic
159C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C5#13711yescharacteristic
161C2×C4×C5#13711yescharacteristic
162C2×Dic5—81no—
163C2×Dic5—81no—
164C2×Dic5—81no—
165#168—42no—
166#168—42no—
167#168—42no—
168C22×Q8C22⋊D511yescharacteristic
169C22×C8—101no—
170C22×C8—101no—
171C22×C8—101no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—101no—
177C2×C4⋊C4—101no—
178C2×C4⋊C4—101no—
179C2×C4⋊C4C22⋊D511yescharacteristic
180C2×C4⋊C4C22⋊D511yescharacteristic
181C2×C4⋊C4C22⋊D511yescharacteristic
182C2×C4⋊C4C22⋊D511yescharacteristic
183C2×C4⋊C4C22⋊D511yescharacteristic
184C2×C42—21no—
185C2×C42C22×D511yescharacteristic
186#107—202no—
187#106—202no—
188#106—202no—
189#103—202no—
190#95—21no—
191#95—21no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199C22×C5#44811yescharacteristic
200C22×C5#44911yescharacteristic
201C22×C5#45211yescharacteristic
202C22×C5#45311yescharacteristic
203C22×C5#45611yescharacteristic
204C22×C5#45611yescharacteristic
205C22×C5#45811yescharacteristic
206C4×C5—21no—
207C4×C5—21no—
208C4×C5—21no—
209C4×C5—21no—
210C4×C5—21no—
211C4×C5—21no—
212C4×C5—42no—
213C4×C5—81no—
214C4×C5—81no—
215C4×C5—81no—
216C4×C5—81no—
217C4×C5—81no—
218Dic5—161no—
219C2×Q8—21no—
220C2×Q8—21no—
221C2×Q8—41no—
222C2×Q8—41no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—201no—
230C22×C4C2×C22⋊D511yescharacteristic
231C22×C4C2×C22⋊D511yescharacteristic
232C22×C4C2×C22⋊D511yescharacteristic
233C2×C8—102no—
234C2×C8—102no—
235C2×C8—102no—
236C2×C8—201no—
237C2×C8—201no—
238C2×C8—201no—
239C2×C8—201no—
240C2×C8—201no—
241C2×C8—201no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—81no—
253C4⋊C4—81no—
254C4⋊C4—201no—
255C4⋊C4—201no—
256C4⋊C4—201no—
257C4⋊C4—201no—
258C4⋊C4—201no—
259C4⋊C4—201no—
260C4⋊C4#68812yes—
261C42—41no—
262C42—81no—
263C2×C5#160911yescharacteristic
264C2×C5#161111yescharacteristic
265C2×C5#161811yescharacteristic
266C2×C5#162211yescharacteristic
267C2×C5#165011yescharacteristic
268C2×C5#165311yescharacteristic
269C2×C5#166011yescharacteristic
270C23#409911yescharacteristic
271Q8—42no—
272Q8—81no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—401no—
298C2×C4—401no—
299C2×C4—401no—
300C2×C4C2×#68811yescharacteristic
301C2×C4#408811yescharacteristic
302C2×C4#409511yescharacteristic
303C2×C4#409611yescharacteristic
304C2×C4#409611yescharacteristic
305C2×C4#409711yescharacteristic
306C8—202no—
307C8—202no—
308C8—202no—
309C5#780711yescharacteristic, complemented, Sylow
310C22#6551611yescharacteristic
311C22#6552711yescharacteristic
312C22#6552811yescharacteristic
313C22#6553011yescharacteristic
314C22#6553211yescharacteristic
315C22#6553511yescharacteristic
316C22#6553511yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—42no—
324C4—81no—
325C4—81no—
326C4—81no—
327C4—81no—
328C4—81no—
329C4—801no—
330C2#1060267611yescharacteristic
331C2#1060267911yescharacteristic
332C2#1060269111yescharacteristic
333C2#1060271611yescharacteristic
334C2#1060272611yescharacteristic
335C2#1060273111yescharacteristic
336C2#1060274911yescharacteristic
subgroupG/H
centerC23#4099
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#2805C2
socle, prime radicalC23×C5#120
hypercenter#2805D5
hypocenterC5#7807
LCSG ▷ C2×C42×C5 ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2805

Complements

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

NH ≅ G/Ntype
309. C5#7807semidirect

Maximal subgroups

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

subgroupindex
C5×#28052
#106004782
#106004012
#106004002
#105981332
#105981292
#78075