Finite Group Databasebeta

← #13014778

Subgroups — #13014778

Order 1280.

440 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 118 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
1Dic5×C4⋊Q8C211yesmaximal, characteristic
2#10604188C212yesmaximal
3#10598828C214yesmaximal
4C2×C5×C4⋊Q8C411yescharacteristic
5C2×Q8×Dic5C412yes—
6#65519C2212yes—
7#65274—22no—
8C4⋊C4×Dic5—22no—
9#65224C411yescharacteristic
10C42×Dic5C2211yescharacteristic
11#64918—22no—
12#64918—22no—
13#64918C2214yes—
14#7605—51nomaximal, Sylow
15C22×C5×Q8C2×C412yes—
16C22×#170—24no—
17C5×C4⋊Q8—22no—
18C5×C4⋊Q8C814yescomplemented
19C2×C5×C4⋊C4—22no—
20C2×C42×C5C2×C411yescharacteristic
21Q8×Dic5—44no—
22C2×C4⋊Dic5—22no—
23C2×C4⋊Dic5—22no—
24C2×C4⋊Dic5C2×C412yes—
25C2×C4×Dic5—22no—
26C2×C4×Dic5C2×C411yescharacteristic
27C2×C4×Dic5D412yes—
28C2×C4×Dic5D412yes—
29C2×C4×Dic5C2311yescharacteristic
30#3963—24no—
31C4×C4⋊Q8—51no—
32#1839—52no—
33#1272—54no—
34C2×C5×Q8—22no—
35C2×C5×Q8—42no—
36C2×C5×Q8—42no—
37C2×C5×Q8C2×C814yes—
38C22×C4×C5—22no—
39C22×C4×C5C22⋊C412yes—
40C22×C4×C5C22×C411yescharacteristic
41C22×Dic5—22no—
42C22×Dic5C22⋊C411yescharacteristic
43C22×Dic5C22⋊C411yescharacteristic
44C22×Dic5C2×D412yes—
45C2×#170—44no—
46C2×#170—44no—
47C2×#170—44no—
48C5×C4⋊C4—28no—
49C42×C5C2×C812yes—
50C42×C5M1612yes—
51C4⋊Dic5—44no—
52C4⋊Dic5—44no—
53C4⋊Dic5—42no—
54C4×Dic5—22no—
55C4×Dic5—24no—
56C4×Dic5—42no—
57C4×Dic5—41no—
58C4×Dic5—44no—
59C2×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
60C2×C4×Q8—52no—
61#391—52no—
62#389—102no—
63#384—51no—
64C4×C4⋊C4—102no—
65C43—51no—
66#336—54no—
67#336—102no—
68#336—102no—
69C23×C5C2×C22⋊C411yescharacteristic
70C5×Q8—44no—
71C5×Q8—44no—
72C2×C4×C5—21no—
73C2×C4×C5—21no—
74C2×C4×C5—22no—
75C2×C4×C5—22no—
76C2×C4×C5—24no—
77C2×C4×C5—42no—
78C2×C4×C5—42no—
79C2×C4×C5C22⋊C814yes—
80C2×C4×C5C22×C811yescharacteristic
81C2×C4×C5C2×M1611yescharacteristic
82C2×Dic5—22no—
83C2×Dic5—22no—
84C2×Dic5—22no—
85C2×Dic5—21no—
86C2×Dic5—22no—
87C2×Dic5—42no—
88C2×Dic5—44no—
89C2×Dic5#10012yes—
90C2×Dic5#13714yes—
91#170—84no—
92C22×Q8C2×AGL(1,𝔽5)12yes—
93C22×C8—104no—
94C4⋊Q8—22no—
95C4⋊Q8#17014yescomplemented
96C4×Q8—204no—
97C2×C4⋊C4—22no—
98C2×C4⋊C4—52no—
99C2×C4⋊C4—102no—
100C2×C4⋊C4—102no—
101C2×C42—52no—
102C2×C42—51no—
103C2×C42—52no—
104C2×C42—51no—
105C2×C42—102no—
106C2×C42C2×AGL(1,𝔽5)11yescharacteristic
107#95—104no—
108C22×C5C2×C22⋊C811yescharacteristic
109C22×C5#41011yescharacteristic
110C22×C5C2×#10011yescharacteristic
111C22×C5#41912yes—
112C22×C5#42112yes—
113C4×C5—21no—
114C4×C5—21no—
115C4×C5—24no—
116C4×C5—44no—
117Dic5—22no—
118Dic5—24no—
119Dic5—41no—
120Dic5—82no—
121C2×Q8—22no—
122C2×Q8—42no—
123C2×Q8—42no—
124C2×Q8C2×#17014yes—
125C22×C4—22no—
126C22×C4—52no—
127C22×C4—51no—
128C22×C4—51no—
129C22×C4—102no—
130C22×C4C22⋊AGL(1,𝔽5)12yes—
131C22×C4C22×AGL(1,𝔽5)11yescharacteristic
132C2×C8—204no—
133C2×C8—204no—
134C2×C8—204no—
135C4⋊C4—28no—
136C4⋊C4—202no—
137C4⋊C4—204no—
138C4⋊C4—204no—
139C42—102no—
140C42—104no—
141C42—201no—
142C42—202no—
143C42—204no—
144C42C2×#17012yes—
145C42#70412yes—
146C2×C5#146011yescharacteristic
147C2×C5#147912yes—
148C2×C5#151512yes—
149C2×C5#153611yescharacteristic
150C2×C5#155811yescharacteristic
151C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
152Q8—44no—
153Q8—44no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—52no—
162C2×C4—54no—
163C2×C4—102no—
164C2×C4—102no—
165C2×C4—102no—
166C2×C4—101no—
167C2×C4—102no—
168C2×C4—202no—
169C2×C4—204no—
170C2×C4C22⋊#17014yes—
171C2×C4C22×#17011yescharacteristic
172C2×C4C2×#70411yescharacteristic
173C8—404no—
174C5#760511yescharacteristic, complemented, Sylow
175C22#6577111yescharacteristic
176C22D5⋊#10011yescharacteristic
177C22#6578212yes—
178C22#6578412yes—
179C22C2×C22⋊#17011yescharacteristic
180C4—21no—
181C4—21no—
182C4—24no—
183C4—44no—
184C4—104no—
185C4—102no—
186C4—201no—
187C4—402no—
188C2#1060462912yes—
189C2#1060463811yescharacteristic
190C2#1060466211yescharacteristic
191C2#1060493211yescharacteristic
192C2#1060496712yes—
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×C4⋊Q8C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×C4⋊Q8AGL(1,𝔽5)
hypocenterC5#7605
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
18. C5×C4⋊Q8C8semidirect
95. C4⋊Q8#170semidirect
174. C5#7605semidirect

Maximal subgroups

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

subgroupindex
Dic5×C4⋊Q82
#106041882
#105988282
#76055