Finite Group Databasebeta

← #13017496

Subgroups — #13017496

Order 1280.

684 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 108 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×#66065C211yesmaximal, characteristic
2#10604967C214yesmaximal, complemented
3#10604159C212yesmaximal
4C2×C5×C4⋊Q8C411yescharacteristic
5C2×#4092C412yes—
6C2×Q8×Dic5C2212yes—
7#66065—28no—
8C2×#4044—22no—
9C2×#4035—22no—
10C2×#4018C2211yescharacteristic
11C2×#4016C411yescharacteristic
12#65748C2214yes—
13Q8⋊#170—28no—
14#64915—22no—
15#64914—22no—
16#8327—51nomaximal, Sylow
17C22×C5×Q8C2×C412yes—
18C22×C4×D5C2×C411yescharacteristic
19C5×C4⋊Q8—24no—
20C2×C5×C4⋊C4—22no—
21C2×C42×C5C2×C411yescharacteristic
22#4092—24no—
23#4092—24no—
24Q8×Dic5—24no—
25Q8×Dic5D418yes—
26C2×#685—22no—
27C2×#685D412yes—
28C2×C4⋊Dic5—22no—
29C2×C4⋊Dic5C2×C412yes—
30C2×#683—22no—
31C2×#683—22no—
32C2×#683D412yes—
33C2×C4×Dic5—22no—
34C2×C4×Dic5C2311yescharacteristic
35#4044—216no—
36#4035—216no—
37#4018—24no—
38#4016—24no—
39C22⋊#170—24no—
40C4⋊#170—24no—
41C4×#170—24no—
42C2×#541—51no—
43#1479—54no—
44#1458—52no—
45C23×D5C22⋊C411yescharacteristic
46C2×C5×Q8—22no—
47C2×C5×Q8—28no—
48C2×C5×Q8C22⋊C414yes—
49C22×C4×C5—22no—
50C22×C4×C5C22⋊C412yes—
51C22×C4×C5C22×C411yescharacteristic
52C22×Dic5—22no—
53C22×Dic5C22⋊C411yescharacteristic
54C22×Dic5C2×D412yes—
55C2×C4×D5—22no—
56C2×C4×D5—24no—
57C2×#170—44no—
58C5×C4⋊C4—28no—
59C42×C5—22no—
60#685—28no—
61#685—24no—
62C4⋊Dic5—22no—
63C4⋊Dic5—28no—
64C4⋊Dic5C22⋊C414yes—
65#683—28no—
66#683—28no—
67#683—24no—
68C4×Dic5—28no—
69C4×Dic5C2×D414yes—
70#541—108no—
71C2×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
72C2×#126—102no—
73C2×#125—51no—
74C2×#125—102no—
75C2×C22⋊Q8—52no—
76C2×C4×Q8—52no—
77C2×#117—51no—
78#431—54no—
79Q8⋊C8—108no—
80#324—102no—
81#323—102no—
82C23×C5C2×C22⋊C411yescharacteristic
83C22×D5—21no—
84C22×D5—22no—
85C22×D5—42no—
86C5×Q8—28no—
87C5×Q8—44no—
88C2×C4×C5—24no—
89C2×C4×C5—22no—
90C2×C4×C5—44no—
91C2×C4×C5—42no—
92C2×C4×C5C2×C22⋊C412yes—
93C2×C4×C5#13114yes—
94C2×Dic5—24no—
95C2×Dic5—21no—
96C2×Dic5—22no—
97C2×Dic5—42no—
98C2×Dic5—44no—
99C2×Dic5#12014yes—
100C4×D5—44no—
101#170—84no—
102C22×Q8C2×AGL(1,𝔽5)12yes—
103C23×C4—51no—
104C4⋊Q8—24no—
105#126—1016no—
106#125—104no—
107#125—1016no—
108C22⋊Q8—104no—
109C22⋊Q8—104no—
110C4×Q8—58no—
111C4×Q8—104no—
112#117—104no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—52no—
115C2×C4⋊C4—52no—
116C2×C4⋊C4—102no—
117C2×C4⋊C4—102no—
118C2×C4⋊C4—102no—
119C2×C22⋊C4—52no—
120C2×C22⋊C4—102no—
121C2×C42—51no—
122C2×C42—102no—
123C2×C42C2×AGL(1,𝔽5)11yescharacteristic
124C4⋊C8—104no—
125C22⋊C8—104no—
126C4×C8—104no—
127C22×C5—22no—
128C22×C5#37911yescharacteristic
129C22×C5#40812yes—
130C2×D5—42no—
131C2×D5—41no—
132C2×D5—82no—
133C4×C5—42no—
134C4×C5—44no—
135C4×C5#40814yes—
136Dic5—24no—
137Dic5—44no—
138Dic5—41no—
139C24—51no—
140C2×Q8—22no—
141C2×Q8—28no—
142C2×Q8C22⋊AGL(1,𝔽5)14yes—
143C22×C4—22no—
144C22×C4—52no—
145C22×C4—51no—
146C22×C4—102no—
147C22×C4—104no—
148C22×C4—102no—
149C22×C4C22⋊AGL(1,𝔽5)12yes—
150C22×C4C22×AGL(1,𝔽5)11yescharacteristic
151C2×C8—204no—
152C4⋊C4—28no—
153C4⋊C4—54no—
154C4⋊C4—104no—
155C4⋊C4—108no—
156C4⋊C4—108no—
157C4⋊C4—108no—
158C4⋊C4—102no—
159C22⋊C4—104no—
160C22⋊C4—108no—
161C42—22no—
162C42—54no—
163C42—108no—
164C2×C5—22no—
165C2×C5#178011yescharacteristic
166C2×C5#179612yes—
167D5—81no—
168C23—101no—
169C23—102no—
170C23—202no—
171C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
172Q8—28no—
173Q8—44no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—44no—
177C2×C4—42no—
178C2×C4—54no—
179C2×C4—104no—
180C2×C4—101no—
181C2×C4—102no—
182C2×C4—202no—
183C2×C4—204no—
184C2×C4—204no—
185C2×C4#413114yes—
186C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
187C8—404no—
188C5#832711yescharacteristic, complemented, Sylow
189C22—22no—
190C22—201no—
191C22—202no—
192C22—402no—
193C22#6577612yes—
194C22#6580011yescharacteristic
195C4—44no—
196C4—42no—
197C4—104no—
198C4—201no—
199C4—204no—
200C4#6577514yes—
201C2—22no—
202C2—401no—
203C2#1060494511yescharacteristic
204C2#1060497412yes—
subgroupG/H
centerC22#65800
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×C4⋊Q8C4
socleC22×C5#379
prime radicalC23×D5C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×C4⋊Q8AGL(1,𝔽5)
hypocenterC5#8327
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10604967C2semidirect
188. C5#8327semidirect

Maximal subgroups

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

subgroupindex
C2×#660652
#106049672
#106041592
#83275