Finite Group Databasebeta

← #11987056

Subgroups — #11987056

Order 1280.

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

normal subgroups only

This group has 276 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
2#10602577C211yesmaximal, characteristic
3C2×#64766C211yesmaximal, characteristic
4C2×C5×C4⋊Q8C2211yescharacteristic
5#66146C411yescharacteristic
6C2×C5×#101—21no—
7C2×#3968C411yescharacteristic
8#65514—21no—
9C2×C4⋊#168—21no—
10C5×#356—21no—
11C5×#356C412yescomplemented
12#64766—21no—
13#64766C412yescomplemented
14#64743—21no—
15#7491—51nomaximal, Sylow
16C22×C5×Q8C2×C411yescharacteristic
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×C5D411yescharacteristic
26Q8×Dic5—42no—
27#4072—21no—
28#4072—41no—
29C2×#681—21no—
30C22×#168—41no—
31C5×#101—22no—
32C5×#101—41no—
33#3968—41no—
34#3967—42no—
35C4⋊#168—22no—
36C4⋊#168—41no—
37C2×#356D511yescharacteristic
38#1886—51no—
39C2×#333—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×Q8C4211yescharacteristic
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
54C5×M16—42no—
55C5×M16—81no—
56C2×C5×C8—81no—
57C5×C4⋊C4—41no—
58C5×C4⋊C4—41no—
59C5×C4⋊C4—41no—
60C5×C4⋊C4—41no—
61C42×C5—21no—
62C42×C5C22⋊C411yescharacteristic
63C42×C5C4⋊C411yescharacteristic
64C22⋊Dic5—41no—
65C4⋊Dic5—22no—
66C4⋊Dic5—42no—
67C4×Dic5—41no—
68C4×Dic5—42no—
69#681—41no—
70#681—41no—
71C2×#168—42no—
72C2×#168—41no—
73C2×#168—82no—
74C2×C4⋊Q8C2×D511yescharacteristic
75#519—51no—
76C2×C4⋊C8—101no—
77#419—101no—
78C2×#101—21no—
79C2×#101—51no—
80#356—21no—
81#356Dic512yescomplemented
82#339—101no—
83#333—52no—
84#333—101no—
85C23×C5#9911yescharacteristic
86C5×Q8—41no—
87C5×Q8—41no—
88C5×Q8—41no—
89C5×Q8—41no—
90C5×Q8—42no—
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—42no—
109C5×C8—82no—
110#168—82no—
111#168—81no—
112C22×Q8C4×D511yescharacteristic
113C22×Q8C22⋊D511yescharacteristic
114C2×M16—41no—
115C2×M16—101no—
116C22×C8—201no—
117C4⋊Q8—41no—
118C4⋊Q8Dic1011yescharacteristic
119C4⋊Q8C4×D511yescharacteristic
120C4⋊Q8C2×Dic511yescharacteristic
121C4⋊Q8C22⋊D511yescharacteristic
122C4×Q8—202no—
123#117—101no—
124#117—201no—
125C2×C4⋊C4—41no—
126C2×C42D2011yescharacteristic
127C4⋊C8—102no—
128C4⋊C8—201no—
129#103—202no—
130#101—22no—
131#101—41no—
132#101—201no—
133C22×C5—22no—
134C22×C5#34211yescharacteristic
135C22×C5AΣL(1,𝔽16)11yescharacteristic
136C22×C5#35211yescharacteristic
137C4×C5—21no—
138C4×C5—22no—
139C4×C5—21no—
140C4×C5—21no—
141C4×C5—21no—
142C4×C5—41no—
143C4×C5—41no—
144C4×C5—41no—
145C4×C5—41no—
146Dic5—82no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×Q8—41no—
153C2×Q8C4×Dic511yescharacteristic
154C2×Q8#68311yescharacteristic
155C2×Q8#68311yescharacteristic
156C2×Q8C22⋊Dic511yescharacteristic
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4#68511yescharacteristic
161M16—42no—
162M16—81no—
163M16—201no—
164M16—201no—
165C2×C8—81no—
166C2×C8—201no—
167C2×C8—202no—
168C2×C8—402no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—102no—
174C4⋊C4—202no—
175C22⋊C4—201no—
176C42—21no—
177C42—201no—
178C42—202no—
179C42C4⋊Dic511yescharacteristic
180C42#68511yescharacteristic
181C2×C5—21no—
182C2×C5—21no—
183C2×C5#139011yescharacteristic
184C2×C5#140512yes—
185C23#393811yescharacteristic
186Q8—41no—
187Q8—41no—
188Q8—41no—
189Q8—41no—
190Q8—42no—
191Q8—81no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—202no—
207C2×C4#393811yescharacteristic
208C2×C4#396311yescharacteristic
209C8—82no—
210C8—402no—
211C8—401no—
212C5#749111yescharacteristic, complemented, Sylow
213C22—22no—
214C22#6469111yescharacteristic
215C22#6469211yescharacteristic
216C22#6474711yescharacteristic
217C4—21no—
218C4—22no—
219C4—21no—
220C4—21no—
221C4—21no—
222C4—41no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—402no—
227C2—21no—
228C2—21no—
229C2#1059804112yes—
230C2#1059818511yescharacteristic
subgroupG/H
centerC22#64691
commutatorC2×C5×Q8C42
FrattiniC2×C4⋊Q8C2×D5
FittingC2×C5×#356C2
socleC22×C5AΣL(1,𝔽16)
prime radicalC23×C5#99
cosocleC2×C5×C4⋊Q8C22
hypercenterC2×#356D5
hypocenterC5#7491
LCSG ▷ C2×C5×Q8 ▷ 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
11. C5×#356C4semidirect
13. #64766C4semidirect
81. #356Dic5semidirect
212. C5#7491semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3562
#106025772
C2×#647662
#74915