Finite Group Databasebeta

← #11996830

Subgroups — #11996830

Order 1280.

436 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 95 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
1#10615067C211yesmaximal, characteristic
2#10615064C211yesmaximal, characteristic, complemented
3C5×#1537C211yesmaximal, characteristic, complemented
4#10601611C212yesmaximal
5#10598245C212yesmaximal, complemented
6C5×#533C2211yescharacteristic
7C2×#4020C2211yescharacteristic
8C5×#432C2212yes—
9#65377C414yes—
10#65356—22no—
11#65313—24no—
12#65290—22no—
13#65289—22no—
14#65215C2212yes—
15C4×#681C2211yescharacteristic
16C5×#330—22no—
17#64705—24no—
18#9424—51nomaximal, Sylow
19C22×D20—21no—
20C22×D20—22no—
21C5×C4⋊Q8C2×C412yes—
22C5×#125D412yes—
23C5×C22⋊Q8—22no—
24C4×C5×Q8—22no—
25C5×#117D412yes—
26C2×C42×C5C2311yescharacteristic
27C2×#681—21no—
28#4020—21no—
29#4020—22no—
30#4020C2×C412yes—
31C5×C4⋊C8—22no—
32C5×C22⋊C8—22no—
33C5×#97—22no—
34C22⋊#168—22no—
35#3941—28no—
36C4⋊#168—24no—
37C4⋊#168D414yes—
38#3935—22no—
39#3935—22no—
40#3935—21no—
41C4×#168—22no—
42C4×#168C2×C412yes—
43#3138—51no—
44#2987—51no—
45#1555—52no—
46#1537D511yescharacteristic, complemented
47#1291—52no—
48C23×D5—41no—
49C2×C5×Q8—22no—
50C22×C4×C5C2×D411yescharacteristic
51C22×C4×C5#4112yes—
52C2×D20—22no—
53C2×D20—24no—
54C2×D20—44no—
55C2×D20—41no—
56C2×D20—42no—
57C2×D20—84no—
58C2×C5×C8—42no—
59C5×C4⋊C4—22no—
60C5×C4⋊C4—24no—
61C5×C4⋊C4C22⋊C414yes—
62C5×C22⋊C4—22no—
63C42×C5—22no—
64C42×C5C22×C411yescharacteristic
65C42×C5C2×D412yes—
66C42×C5C2×D411yescharacteristic
67#681—42no—
68C2×#168—22no—
69C2×#168—24no—
70#533C2×D511yescharacteristic
71C2×#127—51no—
72#490—102no—
73#486—54no—
74#446—104no—
75#433—102no—
76#432—52no—
77#432C2×D512yes—
78#418—102no—
79C4×M16—51no—
80#331—104no—
81#330—22no—
82C23×C5#12311yescharacteristic
83C22×D5—42no—
84C22×D5—82no—
85C22×D5—84no—
86C5×Q8—82no—
87C2×C4×C5—22no—
88C2×C4×C5—24no—
89C2×C4×C5—42no—
90C2×C4×C5C2×C22⋊C411yescharacteristic
91C2×C4×C5C4×D412yes—
92C2×C4×C5#12011yescharacteristic
93C2×C4×C5#12112yes—
94D20—44no—
95D20—84no—
96D20—84no—
97D20—82no—
98C5×C8—82no—
99#168—42no—
100#168—44no—
101C22×D4—101no—
102C22×D4—102no—
103C2×M16—101no—
104C4⋊Q8C4×D512yes—
105#127—52no—
106#127—102no—
107#127—101no—
108#125C22⋊D512yes—
109C22⋊Q8—22no—
110C4×Q8—22no—
111#117D2012yes—
112C2×C42C22×D511yescharacteristic
113C4⋊C8—22no—
114C4⋊C8—54no—
115C4⋊C8—104no—
116#102—108no—
117C22⋊C8—22no—
118C22⋊C8—102no—
119#97—22no—
120#97—102no—
121#97—102no—
122#97—101no—
123C4×C8—52no—
124C4×C8—102no—
125C22×C5—21no—
126C22×C5—22no—
127C22×C5#38611yescharacteristic
128C2×D5—82no—
129C2×D5—84no—
130C2×D5—164no—
131C4×C5—21no—
132C4×C5—22no—
133C4×C5—22no—
134C4×C5—44no—
135C4×C5#45412yes—
136C24—201no—
137C2×Q8—22no—
138C2×D4—104no—
139C2×D4—102no—
140C2×D4—204no—
141C2×D4—201no—
142C2×D4—202no—
143C2×D4—404no—
144C22×C4C2×D2011yescharacteristic
145C22×C4#71112yes—
146M16—202no—
147C2×C8—42no—
148C2×C8—104no—
149C2×C8—102no—
150C4⋊C4—22no—
151C4⋊C4—24no—
152C4⋊C4#68514yes—
153C22⋊C4—22no—
154C42—22no—
155C42C2×C4×D511yescharacteristic
156C42D4×D512yes—
157C42C2×C22⋊D511yescharacteristic
158C2×C5—41no—
159C2×C5#188811yescharacteristic
160C2×C5#190312yes—
161D5—162no—
162C23—202no—
163C23—402no—
164C23—404no—
165C23#403211yescharacteristic
166Q8—82no—
167D4—204no—
168D4—404no—
169D4—404no—
170D4—402no—
171C2×C4—22no—
172C2×C4—24no—
173C2×C4—42no—
174C2×C4#402712yes—
175C2×C4#402811yescharacteristic
176C2×C4C2×#68511yescharacteristic
177C2×C4#408512yes—
178C8—82no—
179C8—202no—
180C8—204no—
181C5#942411yescharacteristic, complemented, Sylow
182C22—21no—
183C22—22no—
184C22—402no—
185C22—404no—
186C22—804no—
187C22#6524711yescharacteristic
188C4—21no—
189C4—22no—
190C4—22no—
191C4—44no—
192C4#6504212yes—
193C2—41no—
194C2—802no—
195C2#1060089711yescharacteristic
196C2#1060119312yes—
subgroupG/H
centerC22#65247
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1537C2
socleC22×C5#386
prime radicalC2×#4020C22
cosocleC2×C42×C5C23
hypercenter#1537D5
hypocenterC5#9424
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1537

Complements

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

NH ≅ G/Ntype
2. #10615064C2semidirect
3. C5×#1537C2semidirect
5. #10598245C2semidirect
46. #1537D5semidirect
181. C5#9424semidirect

Maximal subgroups

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

subgroupindex
#106150672
#106150642
C5×#15372
#106016112
#105982452
#94245