Finite Group Databasebeta

← #13021445

Subgroups — #13021445

Order 1280.

434 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 124 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×#125C211yesmaximal, characteristic
2#10604187C211yesmaximal, characteristic
3#10604174C211yesmaximal, characteristic
4#10598721C214yesmaximal
5C2×C5×#125C411yescharacteristic
6C2×C4⋊#170C2212yes—
7C2×C4×#170C2212yes—
8#65274C412yes—
9#65270—22no—
10C4⋊C4×Dic5—22no—
11C4⋊C4×Dic5C2212yes—
12#65225C411yescharacteristic
13C42×Dic5C2211yescharacteristic
14#64918—22no—
15#64918—22no—
16#9875—51nomaximal, Sylow
17C22×#170—22no—
18C22×#170—22no—
19C5×#125—24no—
20C2×C5×C4⋊C4—22no—
21C2×C5×C4⋊C4C2×C412yes—
22C2×C42×C5C2×C411yescharacteristic
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
30C4⋊#170—24no—
31C4×#170—22no—
32C4×#170Q814yes—
33#3963—22no—
34#3963—22no—
35#3963—22no—
36C4×#125—51no—
37#1831—51no—
38#1744—51no—
39#1279—54no—
40C22×C4×C5—22no—
41C22×C4×C5C22⋊C412yes—
42C22×C4×C5C22×C411yescharacteristic
43C22×Dic5—22no—
44C22×Dic5C22⋊C412yes—
45C22×Dic5C2×D411yescharacteristic
46C22×Dic5C2×D411yescharacteristic
47C2×#170—24no—
48C2×#170—44no—
49C2×#170—42no—
50C2×#170—44no—
51C5×C4⋊C4—28no—
52C5×C4⋊C4—22no—
53C5×C4⋊C4M1614yes—
54C42×C5—22no—
55C4⋊Dic5—24no—
56C4⋊Dic5—44no—
57C4×Dic5—22no—
58C4×Dic5—24no—
59C4×Dic5—42no—
60C4×Dic5—44no—
61C4×Dic5C2×Q812yes—
62C4×Dic5#4112yes—
63C2×#125AGL(1,𝔽5)11yescharacteristic
64C2×C4⋊C8—52no—
65C2×C4×C8—52no—
66#389—52no—
67#387—102no—
68#382—51no—
69C4×C4⋊C4—52no—
70C4×C4⋊C4—102no—
71C43—51no—
72#336—102no—
73#336—102no—
74C23×C5C2×C22⋊C411yescharacteristic
75C2×C4×C5—22no—
76C2×C4×C5—24no—
77C2×C4×C5—22no—
78C2×C4×C5—22no—
79C2×C4×C5—42no—
80C2×C4×C5—42no—
81C2×C4×C5C4×Q812yes—
82C2×C4×C5C2×M1612yes—
83C2×C4×C5#13112yes—
84C2×Dic5—22no—
85C2×Dic5—22no—
86C2×Dic5—22no—
87C2×Dic5—22no—
88C2×Dic5—42no—
89C2×Dic5—42no—
90C2×Dic5—42no—
91C2×Dic5C22⋊Q812yes—
92C2×Dic5#12411yescharacteristic
93C2×Dic5C4⋊Q811yescharacteristic
94C2×Dic5#13514yes—
95#170—44no—
96#170—82no—
97C22×C8—102no—
98C22×C8—102no—
99#125—24no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—52no—
102C2×C4⋊C4—102no—
103C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
104C2×C42—51no—
105C2×C42—52no—
106C2×C42—51no—
107C2×C42—52no—
108C2×C42—102no—
109C2×C42C2×AGL(1,𝔽5)11yescharacteristic
110C4⋊C8—104no—
111C4×C8—54no—
112C4×C8—102no—
113#95—102no—
114#95—102no—
115#95—102no—
116C22×C5#39111yescharacteristic
117C22×C5#40711yescharacteristic
118C22×C5#40811yescharacteristic
119C22×C5#41612yes—
120C22×C5#42112yes—
121C4×C5—42no—
122C4×C5—44no—
123C4×C5#44614yes—
124Dic5—22no—
125Dic5—42no—
126Dic5—82no—
127Dic5#48812yes—
128Dic5#49912yes—
129C22×C4—22no—
130C22×C4—51no—
131C22×C4—51no—
132C22×C4—52no—
133C22×C4—102no—
134C22×C4C22⋊AGL(1,𝔽5)12yes—
135C22×C4C22×AGL(1,𝔽5)11yescharacteristic
136C2×C8—104no—
137C2×C8—204no—
138C2×C8—202no—
139C2×C8—204no—
140C4⋊C4—28no—
141C4⋊C4—22no—
142C4⋊C4—104no—
143C4⋊C4—204no—
144C4⋊C4#70414yes—
145C42—22no—
146C42—52no—
147C42—52no—
148C42—104no—
149C42—102no—
150C42—202no—
151C42—204no—
152C2×C5#148212yes—
153C2×C5#148812yes—
154C2×C5#198511yescharacteristic
155C2×C5#199111yescharacteristic
156C2×C5#199511yescharacteristic
157C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—24no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—54no—
165C2×C4—51no—
166C2×C4—51no—
167C2×C4—52no—
168C2×C4—102no—
169C2×C4—102no—
170C2×C4—102no—
171C2×C4—102no—
172C2×C4—202no—
173C2×C4—202no—
174C2×C4—202no—
175C2×C4#413312yes—
176C2×C4Q8×AGL(1,𝔽5)12yes—
177C2×C4C2×#70412yes—
178C8—204no—
179C8—402no—
180C5#987511yescharacteristic, complemented, Sylow
181C22#6578711yescharacteristic
182C22(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
183C22#6579412yes—
184C22#6579512yes—
185C22#6579811yescharacteristic
186C4—42no—
187C4—44no—
188C4—52no—
189C4—52no—
190C4—102no—
191C4—202no—
192C4—402no—
193C4#6578814yes—
194C2#1060458012yes—
195C2#1060458811yescharacteristic
196C2#1060459011yescharacteristic
197C2#1060498511yescharacteristic
198C2#1060500212yes—
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×#125C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×#125AGL(1,𝔽5)
hypocenterC5#9875
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
180. C5#9875semidirect

Maximal subgroups

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

subgroupindex
Dic5×#1252
#106041872
#106041742
#105987212
#98755