Finite Group Databasebeta

← #11987093

Subgroups — #11987093

Order 1280.

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

normal subgroups only

This group has 260 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#10602579C211yesmaximal, characteristic
4C2×C5×C4⋊Q8C2211yescharacteristic
5C2×C5×#101—21no—
6C2×#3968—21no—
7C2×#3967—21no—
8C2×#3967—21no—
9#65225C411yescharacteristic
10C2×#3935C411yescharacteristic
11C5×#356—21no—
12C5×#356C412yescomplemented
13#64768—21no—
14#64768C412yescomplemented
15#7505—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×#681—41no—
28C22×#168—21no—
29C5×#101—22no—
30C5×#101—41no—
31#3968—22no—
32#3968—41no—
33#3967—42no—
34#3967—42no—
35#3963—41no—
36#3935—41no—
37C2×#356—51no—
38C2×#356D511yescharacteristic
39#1960—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—
67#681—42no—
68#681—81no—
69C2×#168—22no—
70C2×#168—41no—
71C2×#168—41no—
72C2×#168—81no—
73C2×C4⋊Q8C2×D511yescharacteristic
74C2×#103—101no—
75C2×#103—101no—
76C2×#101—21no—
77C2×#101—101no—
78C2×#97—51no—
79#382—51no—
80#356—21no—
81#356—52no—
82#356—101no—
83#356Dic512yescomplemented
84C23×C5#9911yescharacteristic
85C5×Q8—41no—
86C5×Q8—41no—
87C5×Q8—41no—
88C5×Q8—41no—
89C5×Q8—81no—
90C5×Q8—81no—
91C2×C4×C5—21no—
92C2×C4×C5—21no—
93C2×C4×C5—21no—
94C2×C4×C5—21no—
95C2×C4×C5—21no—
96C2×C4×C5—21no—
97C2×C4×C5—21no—
98C2×C4×C5—21no—
99C2×C4×C5—42no—
100C2×C4×C5—41no—
101C2×C4×C5—41no—
102C2×C4×C5—41no—
103C2×C4×C5—41no—
104C2×C4×C5#9511yescharacteristic
105C2×C4×C5#9911yescharacteristic
106C2×Dic5—82no—
107C2×Dic5—81no—
108C5×C8—82no—
109#168—42no—
110#168—82no—
111C22×Q8D2011yescharacteristic
112C22×Q8C22⋊D511yescharacteristic
113C2×M16—41no—
114C2×M16—201no—
115C22×C8—101no—
116C4⋊Q8—41no—
117C4⋊Q8Dic1011yescharacteristic
118C4⋊Q8C4×D511yescharacteristic
119C4⋊Q8C2×Dic511yescharacteristic
120C4⋊Q8C22⋊D511yescharacteristic
121C2×C4⋊C4—41no—
122C2×C4⋊C4—101no—
123C2×C42C4×D511yescharacteristic
124#103—202no—
125#103—202no—
126#101—22no—
127#101—41no—
128#101—102no—
129#101—201no—
130#97—201no—
131#95—201no—
132C22×C5—22no—
133C22×C5#34211yescharacteristic
134C22×C5#35311yescharacteristic
135C22×C5#35411yescharacteristic
136C4×C5—21no—
137C4×C5—21no—
138C4×C5—41no—
139C4×C5—41no—
140C4×C5—41no—
141C4×C5—41no—
142C4×C5—41no—
143C4×C5—41no—
144Dic5—161no—
145C2×Q8—21no—
146C2×Q8—21no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8#68311yescharacteristic
152C2×Q8C4⋊Dic511yescharacteristic
153C2×Q8#68511yescharacteristic
154C2×Q8C22⋊Dic511yescharacteristic
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—201no—
159C22×C4#68511yescharacteristic
160M16—42no—
161M16—81no—
162M16—202no—
163M16—401no—
164C2×C8—81no—
165C2×C8—102no—
166C2×C8—201no—
167C2×C8—201no—
168C2×C8—401no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—201no—
174C4⋊C4—201no—
175C42—21no—
176C42C4×Dic511yescharacteristic
177C42#68311yescharacteristic
178C2×C5—21no—
179C2×C5—21no—
180C2×C5#139311yescharacteristic
181C2×C5#141312yes—
182C23#393811yescharacteristic
183Q8—41no—
184Q8—41no—
185Q8—41no—
186Q8—41no—
187Q8—81no—
188Q8—81no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—42no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—402no—
203C2×C4—401no—
204C2×C4#393811yescharacteristic
205C2×C4#396311yescharacteristic
206C8—82no—
207C8—202no—
208C8—402no—
209C5#750511yescharacteristic, complemented, Sylow
210C22—22no—
211C22#6469311yescharacteristic
212C22#6469411yescharacteristic
213C22#6474711yescharacteristic
214C4—21no—
215C4—21no—
216C4—41no—
217C4—41no—
218C4—41no—
219C4—41no—
220C4—41no—
221C4—41no—
222C4—801no—
223C2—21no—
224C2—21no—
225C2#1059804212yes—
226C2#1059818611yescharacteristic
subgroupG/H
centerC22#64693
commutatorC42×C5C42
FrattiniC2×C4⋊Q8C2×D5
FittingC2×C5×#356C2
socleC22×C5#354
prime radicalC23×C5#99
cosocleC2×C5×C4⋊Q8C22
hypercenterC2×#356D5
hypocenterC5#7505
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
83. #356Dic5semidirect
209. C5#7505semidirect

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
#106025792
#75055