Finite Group Databasebeta

← #12003497

Subgroups — #12003497

Order 1280.

358 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 81 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#10610800C211yesmaximal, characteristic
2#10601311C211yesmaximal, characteristic
3#10601304C212yesmaximal
4#10601294C212yesmaximal
5C5×#1309C211yesmaximal, characteristic
6#65804C2212yes—
7C5×#423C2212yes—
8C5×#423C2211yescharacteristic
9#65426—22no—
10C2×#3954—22no—
11#65213C2211yescharacteristic
12C2×C4×#168C2211yescharacteristic
13#65140—22no—
14#65138—22no—
15#64706—22no—
16#64704—24no—
17#64702—22no—
18#10534—51nomaximal, Sylow
19C2×C5×M16—22no—
20C2×C5×M16D412yes—
21C2×C42×C5C2311yescharacteristic
22#4072—22no—
23#4070—22no—
24#4070—22no—
25C2×#681—21no—
26C22×#168—21no—
27C2×Dic20—22no—
28#4016—22no—
29#4015D412yes—
30#4015D412yes—
31C4×Dic10—22no—
32C4×Dic10—22no—
33C5×C4⋊C8—22no—
34C5×C4⋊C8—22no—
35C5×C4⋊C8—22no—
36#3954—44no—
37#3949—22no—
38#3948—24no—
39C4⋊#168—22no—
40C4×#168—21no—
41C4×#168D412yes—
42#3255—51no—
43#1848—51no—
44#1561—52no—
45#1493—52no—
46#1309D511yescharacteristic
47C22×C4×C5C2×D411yescharacteristic
48C22×C4×C5#4112yes—
49C2×Dic10—22no—
50C2×Dic10—22no—
51C5×M16—42no—
52C5×M16—82no—
53C2×C5×C8—22no—
54C2×C5×C8—42no—
55C42×C5C2×D412yes—
56C42×C5C2×D411yescharacteristic
57C42×C5#4111yescharacteristic
58C22⋊Dic5—42no—
59C4⋊Dic5—22no—
60C4⋊Dic5—22no—
61C4⋊Dic5—22no—
62C4⋊Dic5—22no—
63#683—42no—
64#683—42no—
65C4×Dic5—42no—
66#681—42no—
67C2×#168—22no—
68C2×#168—22no—
69C2×#168—22no—
70C2×#168—41no—
71Dic20—82no—
72#533—52no—
73#475—102no—
74#470—102no—
75#462—102no—
76C2×#108—102no—
77#423—51no—
78#423C2×D512yes—
79#423C2×D511yescharacteristic
80C2×C4×C8—51no—
81#332—102no—
82#332—102no—
83Q8⋊C8—104no—
84C23×C5#12411yescharacteristic
85C2×C4×C5—21no—
86C2×C4×C5—21no—
87C2×C4×C5—22no—
88C2×C4×C5—22no—
89C2×C4×C5#12011yescharacteristic
90C2×C4×C5#12112yes—
91C2×C4×C5#12111yescharacteristic
92C2×C4×C5#12312yes—
93C2×Dic5—42no—
94C2×Dic5—42no—
95Dic10—42no—
96Dic10—42no—
97Dic10—42no—
98Dic10—42no—
99C5×C8—42no—
100C5×C8—82no—
101#168—24no—
102#168—81no—
103C2×Q16—102no—
104C2×M16—22no—
105C2×M16—101no—
106C2×M16D2012yes—
107C22×C8—101no—
108C4⋊Q8—52no—
109C4⋊Q8—52no—
110#125—102no—
111C22⋊Q8—102no—
112C22⋊Q8—102no—
113C4×Q8—102no—
114C4×Q8—102no—
115#117—102no—
116C2×C42C22×D511yescharacteristic
117#108—204no—
118#106—102no—
119C4⋊C8—22no—
120C4⋊C8—22no—
121C4⋊C8—22no—
122C4⋊C8—102no—
123#103—104no—
124C4×C8—52no—
125C4×C8—101no—
126C22×C5—22no—
127C22×C5—21no—
128C22×C5#39411yescharacteristic
129C4×C5—22no—
130C4×C5—21no—
131C4×C5#45311yescharacteristic
132C4×C5#45611yescharacteristic
133C4×C5#47112yes—
134C4×C5#47312yes—
135Dic5—82no—
136Dic5—82no—
137C2×Q8—102no—
138C2×Q8—102no—
139C22×C4C2×D2011yescharacteristic
140C22×C4#70912yes—
141Q16—402no—
142M16—42no—
143M16—82no—
144M16—202no—
145C2×C8—22no—
146C2×C8—42no—
147C2×C8—102no—
148C2×C8—102no—
149C2×C8—102no—
150C2×C8—201no—
151C4⋊C4—102no—
152C4⋊C4—102no—
153C4⋊C4—102no—
154C4⋊C4—102no—
155C4⋊C4—202no—
156C4⋊C4—202no—
157C22⋊C4—202no—
158C42—202no—
159C42D4×D512yes—
160C42D4×D511yescharacteristic
161C42#71311yescharacteristic
162C2×C5—41no—
163C2×C5#203911yescharacteristic
164C2×C5#205212yes—
165C23#402111yescharacteristic
166Q8—202no—
167Q8—202no—
168Q8—202no—
169Q8—202no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—202no—
175C2×C4—202no—
176C2×C4#402811yescharacteristic
177C2×C4#403012yes—
178C2×C4#404012yes—
179C2×C4#404111yescharacteristic
180C8—42no—
181C8—82no—
182C8—104no—
183C8—401no—
184C5#1053411yescharacteristic, complemented, Sylow
185C22—21no—
186C22—22no—
187C22#6496111yescharacteristic
188C4—21no—
189C4—22no—
190C4—402no—
191C4—402no—
192C4#6503611yescharacteristic
193C4#6503712yes—
194C4#6504111yescharacteristic
195C4#6504412yes—
196C2—41no—
197C2#1059976911yescharacteristic
198C2#1059978012yes—
subgroupG/H
centerC22#64961
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1309C2
socleC22×C5#394
prime radicalC23×C5#124
hypercenter#1309D5
hypocenterC5#10534
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1309

Complements

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

NH ≅ G/Ntype
184. C5#10534semidirect

Maximal subgroups

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

subgroupindex
#106108002
#106013112
#106013042
#106012942
C5×#13092
#105345