Finite Group Databasebeta

← #12004077

Subgroups — #12004077

Order 1280.

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

normal subgroups only

This group has 292 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
1#10601569C211yesmaximal, characteristic
2#10601308C211yesmaximal, characteristic
3#10601239C211yesmaximal, characteristic
4#10601230C211yesmaximal, characteristic
5C5×#1301C211yesmaximal, characteristic
6#10598228C211yesmaximal, characteristic
7#10598205C211yesmaximal, characteristic
8#65804C2211yescharacteristic
9C5×#431C2211yescharacteristic
10C5×#423C2211yescharacteristic
11C2×C5×C4⋊C8C2211yescharacteristic
12C2×#3946—21no—
13C2×#3946—21no—
14#65221C2211yescharacteristic
15#65214C2211yescharacteristic
16C2×C4⋊#168C2211yescharacteristic
17#64775—21no—
18#64775—21no—
19#64706—21no—
20#64702—21no—
21#64701—21no—
22#64701—21no—
23#10628—51nomaximal, Sylow
24C2×C5×M16—21no—
25C22×C5×C8—21no—
26C2×C42×C5C2311yescharacteristic
27#4072—21no—
28#4070—21no—
29#4070—21no—
30C2×C4×Dic5D411yescharacteristic
31C2×C4×Dic5D411yescharacteristic
32C22×#168—21no—
33#4016—21no—
34#4015D411yescharacteristic
35#4015D411yescharacteristic
36C4×Dic10—21no—
37C4×Dic10—21no—
38C5×C4⋊C8—21no—
39C5×C4⋊C8—21no—
40C5×C4⋊C8—21no—
41C5×C4⋊C8—21no—
42C5×C4⋊C8—21no—
43C5×C22⋊C8—21no—
44C4×C5×C8—21no—
45#3963—21no—
46#3963—21no—
47C22⋊#168—21no—
48#3946—42no—
49#3946—42no—
50C4⋊#168—21no—
51C4⋊#168—21no—
52C4⋊#168—21no—
53C4×#168—21no—
54#1995—51no—
55#1843—51no—
56#1542—51no—
57#1542—51no—
58#1301—51no—
59#1301D511yescharacteristic
60#1274—51no—
61C22×C4×C5C2×D411yescharacteristic
62C22×C4×C5#4111yescharacteristic
63C22×C4×C5#4111yescharacteristic
64C22×Dic5—21no—
65C22×Dic5—21no—
66C2×Dic10—21no—
67C2×Dic10—21no—
68C5×M16—41no—
69C5×M16—41no—
70C2×C5×C8—41no—
71C2×C5×C8—41no—
72C2×C5×C8—41no—
73C2×C5×C8—41no—
74C2×C5×C8—41no—
75C42×C5C2×D411yescharacteristic
76C42×C5#4111yescharacteristic
77C42×C5#4111yescharacteristic
78C42×C5#4111yescharacteristic
79C22⋊Dic5—41no—
80C4⋊Dic5—21no—
81C4⋊Dic5—21no—
82C4⋊Dic5—21no—
83C4⋊Dic5—21no—
84#683—41no—
85#683—41no—
86C4×Dic5—21no—
87C4×Dic5—21no—
88C4×Dic5—41no—
89C4×Dic5SD1612yes—
90C4×Dic5Q1612yes—
91C2×#168—41no—
92C2×#168—41no—
93C2×#168—41no—
94C2×#168—41no—
95#533—51no—
96#431—51no—
97#431C2×D511yescharacteristic
98#423C2×D511yescharacteristic
99C2×C4⋊C8—51no—
100C2×C4⋊C8—101no—
101C2×C4⋊C8—101no—
102C2×C4⋊C8C2×D511yescharacteristic
103#376—51no—
104#339—101no—
105#339—101no—
106#333—101no—
107#333—101no—
108#332—101no—
109#332—101no—
110C23×C5#12311yescharacteristic
111C2×C4×C5—41no—
112C2×C4×C5—41no—
113C2×C4×C5#12111yescharacteristic
114C2×C4×C5#12311yescharacteristic
115C2×C4×C5#12311yescharacteristic
116C2×C4×C5#12411yescharacteristic
117C2×C4×C5#12611yescharacteristic
118C2×C4×C5#12611yescharacteristic
119C2×C4×C5C2×SD1611yescharacteristic
120C2×C4×C5C2×Q1611yescharacteristic
121C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C5#13711yescharacteristic
123C2×Dic5—22no—
124C2×Dic5—22no—
125C2×Dic5—41no—
126C2×Dic5—41no—
127C2×Dic5—41no—
128C2×Dic5—41no—
129C2×Dic5—41no—
130C2×Dic5—41no—
131Dic10—81no—
132Dic10—81no—
133C5×C8—81no—
134C5×C8—81no—
135C5×C8—81no—
136#168—81no—
137#168—81no—
138C2×M16—21no—
139C22×C8—21no—
140C22×C8—101no—
141C4⋊Q8—51no—
142C4⋊Q8—51no—
143#125—101no—
144C22⋊Q8—101no—
145C22⋊Q8—101no—
146C4×Q8—101no—
147C4×Q8—101no—
148#117—101no—
149C2×C42—51no—
150C2×C42—51no—
151C2×C42C22×D511yescharacteristic
152C4⋊C8—21no—
153C4⋊C8—21no—
154C4⋊C8—21no—
155C4⋊C8—21no—
156C4⋊C8—21no—
157C4⋊C8—101no—
158C4⋊C8—101no—
159C4⋊C8—101no—
160C4⋊C8—202no—
161C4⋊C8—202no—
162C22⋊C8—21no—
163C22⋊C8—101no—
164C4×C8—21no—
165C4×C8—101no—
166#95—101no—
167#95—101no—
168C22×C5—21no—
169C22×C5—21no—
170C22×C5#39711yescharacteristic
171C22×C5#48311yescharacteristic
172C22×C5#48411yescharacteristic
173C4×C5—21no—
174C4×C5—21no—
175C4×C5—21no—
176C4×C5—21no—
177C4×C5#46011yescharacteristic
178C4×C5#46211yescharacteristic
179C4×C5#48711yescharacteristic
180C4×C5#48911yescharacteristic
181Dic5—42no—
182Dic5—42no—
183Dic5—81no—
184Dic5—81no—
185C2×Q8—101no—
186C2×Q8—101no—
187C22×C4—101no—
188C22×C4—101no—
189C22×C4#70911yescharacteristic
190C22×C4D4×D511yescharacteristic
191C22×C4#71311yescharacteristic
192M16—41no—
193M16—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—201no—
200C2×C8—201no—
201C2×C8—201no—
202C2×C8—201no—
203C4⋊C4—101no—
204C4⋊C4—101no—
205C4⋊C4—101no—
206C4⋊C4—101no—
207C4⋊C4—201no—
208C4⋊C4—201no—
209C22⋊C4—201no—
210C42—52no—
211C42—52no—
212C42—101no—
213C42—101no—
214C42—201no—
215C42#70911yescharacteristic
216C42#70911yescharacteristic
217C42D4×D511yescharacteristic
218C42#71111yescharacteristic
219C2×C5—21no—
220C2×C5—21no—
221C2×C5#207211yescharacteristic
222C2×C5#208011yescharacteristic
223C2×C5#208011yescharacteristic
224C23#404011yescharacteristic
225Q8—401no—
226Q8—401no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—102no—
230C2×C4—102no—
231C2×C4—201no—
232C2×C4—201no—
233C2×C4—201no—
234C2×C4—201no—
235C2×C4—201no—
236C2×C4—201no—
237C2×C4#402211yescharacteristic
238C2×C4#402911yescharacteristic
239C2×C4#403011yescharacteristic
240C2×C4#403111yescharacteristic
241C2×C4#404011yescharacteristic
242C2×C4#404411yescharacteristic
243C2×C4#405711yescharacteristic
244C2×C4D5×SD1611yescharacteristic
245C2×C4#406111yescharacteristic
246C2×C4D5×Q1611yescharacteristic
247C8—81no—
248C8—81no—
249C8—81no—
250C8—401no—
251C8—401no—
252C5#1062811yescharacteristic, complemented, Sylow
253C22—21no—
254C22—21no—
255C22#6496411yescharacteristic
256C22#6515111yescharacteristic
257C22#6517311yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—21no—
262C4—202no—
263C4—202no—
264C4—401no—
265C4—401no—
266C4#6505111yescharacteristic
267C4#6505411yescharacteristic
268C4#6508111yescharacteristic
269C4#6508211yescharacteristic
270C2—21no—
271C2—21no—
272C2#1059970711yescharacteristic
273C2#1059972811yescharacteristic
274C2#1059983611yescharacteristic
subgroupG/H
centerC2×C4#4031
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1301C2
socleC22×C5#397
prime radicalC23×C5#123
hypercenter#1301D5
hypocenterC5#10628
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
252. C5#10628semidirect

Maximal subgroups

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

subgroupindex
#106015692
#106013082
#106012392
#106012302
C5×#13012
#105982282
#105982052
#106285