Finite Group Databasebeta

← #11987079

Subgroups — #11987079

Order 1280.

272 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×C5×#356C211yesmaximal, characteristic
2C2×#64768C211yesmaximal, characteristic
3#10602578C211yesmaximal, characteristic
4C2×C5×C4⋊Q8C2211yescharacteristic
5C2×C5×#101—21no—
6C2×#3968—21no—
7C2×#3967—21no—
8C2×#3967—21no—
9#65224C411yescharacteristic
10C2×C4×#168C411yescharacteristic
11C5×#356—21no—
12C5×#356C412yescomplemented
13#64768—21no—
14#64768C412yescomplemented
15#7499—51nomaximal, Sylow
16C22×C5×Q8D411yescharacteristic
17C22×C5×Q8D411yescharacteristic
18C2×C5×M16—41no—
19C5×C4⋊Q8—41no—
20C5×C4⋊Q8C2×C411yescharacteristic
21C5×C4⋊Q8C2×C411yescharacteristic
22C5×C4⋊Q8D411yescharacteristic
23C5×C4⋊Q8Q811yescharacteristic
24C2×C5×C4⋊C4—41no—
25C2×C42×C5C2×C411yescharacteristic
26C2×C4⋊Dic5—21no—
27C2×C4⋊Dic5—41no—
28C2×#681—41no—
29C22×#168—21no—
30C5×#101—22no—
31C5×#101—41no—
32#3968—22no—
33#3968—41no—
34#3967—42no—
35#3967—42no—
36C4×#168—41no—
37C2×#356—51no—
38C2×#356D511yescharacteristic
39#1956—51no—
40C2×C5×Q8—21no—
41C2×C5×Q8—21no—
42C2×C5×Q8—41no—
43C2×C5×Q8—41no—
44C2×C5×Q8—41no—
45C2×C5×Q8—41no—
46C2×C5×Q8C22⋊C411yescharacteristic
47C2×C5×Q8C22⋊C411yescharacteristic
48C2×C5×Q8C4⋊C411yescharacteristic
49C2×C5×Q8C4⋊C411yescharacteristic
50C22×C4×C5—21no—
51C22×C4×C5—21no—
52C22×C4×C5—21no—
53C22×C4×C5C22⋊C411yescharacteristic
54C22×Dic5—41no—
55C5×M16—42no—
56C5×M16—81no—
57C2×C5×C8—81no—
58C5×C4⋊C4—41no—
59C5×C4⋊C4—41no—
60C5×C4⋊C4—41no—
61C5×C4⋊C4—41no—
62C42×C5—21no—
63C42×C5C4211yescharacteristic
64C42×C5C4⋊C411yescharacteristic
65C4⋊Dic5—41no—
66C4⋊Dic5—41no—
67C4⋊Dic5—82no—
68#681—42no—
69#681—81no—
70C2×#168—22no—
71C2×#168—41no—
72C2×#168—41no—
73C2×#168—81no—
74C2×C4⋊Q8C2×D511yescharacteristic
75C2×#103—101no—
76C2×#103—101no—
77C2×#101—21no—
78C2×#101—101no—
79C2×C4×C8—51no—
80#384—51no—
81#356—21no—
82#356—52no—
83#356—101no—
84#356Dic512yescomplemented
85C23×C5#9911yescharacteristic
86C5×Q8—41no—
87C5×Q8—41no—
88C5×Q8—41no—
89C5×Q8—41no—
90C5×Q8—81no—
91C5×Q8—81no—
92C2×C4×C5—22no—
93C2×C4×C5—22no—
94C2×C4×C5—21no—
95C2×C4×C5—21no—
96C2×C4×C5—21no—
97C2×C4×C5—21no—
98C2×C4×C5—21no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—21no—
102C2×C4×C5—41no—
103C2×C4×C5—41no—
104C2×C4×C5—41no—
105C2×C4×C5—41no—
106C2×C4×C5#9511yescharacteristic
107C2×C4×C5#9911yescharacteristic
108C2×Dic5—82no—
109C2×Dic5—81no—
110C5×C8—82no—
111#168—42no—
112#168—82no—
113C22×Q8D2011yescharacteristic
114C22×Q8C22⋊D511yescharacteristic
115C2×M16—41no—
116C2×M16—201no—
117C22×C8—101no—
118C4⋊Q8—41no—
119C4⋊Q8Dic1011yescharacteristic
120C4⋊Q8C4×D511yescharacteristic
121C4⋊Q8C2×Dic511yescharacteristic
122C4⋊Q8C22⋊D511yescharacteristic
123C2×C4⋊C4—41no—
124C2×C4⋊C4—101no—
125C2×C4⋊C4—201no—
126C2×C42C4×D511yescharacteristic
127#103—202no—
128#103—202no—
129#101—22no—
130#101—41no—
131#101—102no—
132#101—201no—
133C4×C8—201no—
134C22×C5—21no—
135C22×C5—21no—
136C22×C5#34211yescharacteristic
137C22×C5#35311yescharacteristic
138C22×C5#35411yescharacteristic
139C4×C5—22no—
140C4×C5—22no—
141C4×C5—21no—
142C4×C5—21no—
143C4×C5—41no—
144C4×C5—41no—
145C4×C5—41no—
146C4×C5—41no—
147Dic5—161no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×Q8—41no—
153C2×Q8—41no—
154C2×Q8#68311yescharacteristic
155C2×Q8C4⋊Dic511yescharacteristic
156C2×Q8#68511yescharacteristic
157C2×Q8C22⋊Dic511yescharacteristic
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—201no—
162C22×C4#68511yescharacteristic
163M16—42no—
164M16—81no—
165M16—202no—
166M16—401no—
167C2×C8—81no—
168C2×C8—102no—
169C2×C8—201no—
170C2×C8—201no—
171C2×C8—401no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—201no—
177C4⋊C4—201no—
178C4⋊C4—402no—
179C42—21no—
180C42C4×Dic511yescharacteristic
181C42#68311yescharacteristic
182C2×C5—21no—
183C2×C5—21no—
184C2×C5#139311yescharacteristic
185C2×C5#141011yescharacteristic
186C2×C5#141111yescharacteristic
187C23#393811yescharacteristic
188Q8—41no—
189Q8—41no—
190Q8—41no—
191Q8—41no—
192Q8—81no—
193Q8—81no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—402no—
209C2×C4—401no—
210C2×C4#393811yescharacteristic
211C2×C4#396311yescharacteristic
212C8—82no—
213C8—202no—
214C8—402no—
215C5#749911yescharacteristic, complemented, Sylow
216C22—21no—
217C22—21no—
218C22#6469311yescharacteristic
219C22#6469411yescharacteristic
220C22#6474711yescharacteristic
221C4—22no—
222C4—22no—
223C4—21no—
224C4—21no—
225C4—41no—
226C4—41no—
227C4—41no—
228C4—41no—
229C4—801no—
230C2—21no—
231C2—21no—
232C2#1059804311yescharacteristic
233C2#1059804411yescharacteristic
234C2#1059818611yescharacteristic
subgroupG/H
centerC22#64694
commutatorC42×C5C42
FrattiniC2×C4⋊Q8C2×D5
FittingC2×C5×#356C2
socleC22×C5#353
prime radicalC23×C5#99
cosocleC2×C5×C4⋊Q8C22
hypercenterC2×#356D5
hypocenterC5#7499
LCSG ▷ C42×C5 ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
12. C5×#356C4semidirect
14. #64768C4semidirect
84. #356Dic5semidirect
215. C5#7499semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3562
C2×#647682
#106025782
#74995