Finite Group Databasebeta

← #12000635

Subgroups — #12000635

Order 1280.

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

normal subgroups only

This group has 500 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
1C2×#65369C212yesmaximal
2#10605948C211yesmaximal, characteristic
3C5×#1960C211yesmaximal, characteristic
4C2×#64685C212yesmaximal
5#10598121C211yesmaximal, characteristic
6C2×C5×C4⋊Q8C2211yescharacteristic
7C2×#4016C2212yes—
8C2×C5×#103—22no—
9C2×C5×#97C2211yescharacteristic
10C5×#382C2211yescharacteristic
11#65369—24no—
12#65369—24no—
13#65272—22no—
14C2×#3940—22no—
15C2×#3939—22no—
16C2×#3935C2212yes—
17#64950—22no—
18#64948—22no—
19#64685—24no—
20#10087—51nomaximal, Sylow
21C22×C5×Q8—21no—
22C22×C5×C8—21no—
23C5×C4⋊Q8—22no—
24C5×C4⋊Q8—21no—
25C5×C4⋊Q8D412yes—
26C2×C5×C4⋊C4—22no—
27C2×C5×C4⋊C4D412yes—
28C2×C42×C5C2311yescharacteristic
29C2×C4⋊Dic5—22no—
30C2×C4⋊Dic5D412yes—
31C2×C4⋊Dic5D412yes—
32C2×#683—22no—
33C2×#683—22no—
34C22×#168—22no—
35#4016—22no—
36#4016—22no—
37#4016—22no—
38#4016—22no—
39C5×#103—44no—
40C5×#97—22no—
41C5×#95—22no—
42#3963—22no—
43#3963—24no—
44#3940—28no—
45#3939—28no—
46#3935—22no—
47#3935D414yes—
48C2×#501—52no—
49#2822—51no—
50#1960D511yescharacteristic
51C2×#330—52no—
52#1295—51no—
53C2×C5×Q8—22no—
54C2×C5×Q8—42no—
55C2×C5×Q8—42no—
56C2×C5×Q8—41no—
57C22×C4×C5—22no—
58C22×C4×C5—41no—
59C22×C4×C5C2×D412yes—
60C22×C4×C5C2×D411yescharacteristic
61C22×Dic5—22no—
62C22×Dic5—22no—
63C2×C5×C8—22no—
64C2×C5×C8—41no—
65C2×C5×C8—41no—
66C5×C4⋊C4—24no—
67C5×C4⋊C4—42no—
68C5×C4⋊C4—42no—
69C42×C5C2×D411yescharacteristic
70C42×C5C2×D412yes—
71C42×C5#4111yescharacteristic
72C4⋊Dic5—22no—
73C4⋊Dic5—22no—
74C4⋊Dic5—22no—
75C4⋊Dic5—22no—
76C4⋊Dic5—82no—
77#683—42no—
78#683—42no—
79#683—42no—
80#683—42no—
81C2×#168—28no—
82C2×#168—24no—
83C2×C4⋊Q8C2×D511yescharacteristic
84C2×#125—52no—
85#501—104no—
86#501—104no—
87C2×#107—102no—
88C2×#106—102no—
89C2×#103—22no—
90C2×#97—52no—
91C2×#97C2×D511yescharacteristic
92#400—102no—
93#398—102no—
94#398—102no—
95#382C2×D511yescharacteristic
96#330—104no—
97C23×C5#12011yescharacteristic
98C5×Q8—44no—
99C5×Q8—82no—
100C2×C4×C5—21no—
101C2×C4×C5—21no—
102C2×C4×C5—24no—
103C2×C4×C5—42no—
104C2×C4×C5—42no—
105C2×C4×C5—44no—
106C2×C4×C5—81no—
107C2×C4×C5—81no—
108C2×C4×C5#12012yes—
109C2×C4×C5#12112yes—
110C2×C4×C5#12111yescharacteristic
111C2×C4×C5#12711yescharacteristic
112C2×Dic5—42no—
113C2×Dic5—42no—
114C2×Dic5—42no—
115C2×Dic5—42no—
116C2×Dic5—44no—
117C5×C8—42no—
118#168—28no—
119C22×Q8—21no—
120C22×C8—21no—
121C22×C8—102no—
122C4⋊Q8—21no—
123C4⋊Q8—22no—
124C4⋊Q8D2012yes—
125#125—102no—
126#125—102no—
127#125—102no—
128#125—102no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—52no—
131C2×C4⋊C4—52no—
132C2×C4⋊C4—102no—
133C2×C4⋊C4—102no—
134C2×C4⋊C4—102no—
135C2×C4⋊C4C22⋊D512yes—
136C2×C42C22×D511yescharacteristic
137#107—108no—
138#106—108no—
139#103—44no—
140#97—22no—
141#97—54no—
142#97—102no—
143#95—22no—
144#95—104no—
145#95—102no—
146C22×C5#39211yescharacteristic
147C22×C5#45311yescharacteristic
148C22×C5#45411yescharacteristic
149C22×C5#45614yes—
150C4×C5—22no—
151C4×C5—22no—
152C4×C5—21no—
153C4×C5—21no—
154C4×C5—82no—
155C4×C5—82no—
156Dic5—82no—
157Dic5—82no—
158C2×Q8—22no—
159C2×Q8—42no—
160C2×Q8—42no—
161C2×Q8—41no—
162C22×C4—22no—
163C22×C4—41no—
164C22×C4—102no—
165C22×C4—102no—
166C22×C4D4×D512yes—
167C22×C4C2×C22⋊D511yescharacteristic
168C2×C8—22no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—108no—
172C2×C8—104no—
173C4⋊C4—24no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—102no—
177C4⋊C4—102no—
178C4⋊C4—102no—
179C4⋊C4—102no—
180C4⋊C4—202no—
181C4⋊C4—202no—
182C4⋊C4—202no—
183C4⋊C4—202no—
184C4⋊C4—402no—
185C42C2×D2011yescharacteristic
186C42#70911yescharacteristic
187C42D4×D512yes—
188C2×C5#166012yes—
189C2×C5#166312yes—
190C2×C5#200512yes—
191C2×C5#200611yescharacteristic
192C23#408311yescharacteristic
193Q8—44no—
194Q8—82no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—24no—
198C2×C4—42no—
199C2×C4—44no—
200C2×C4—42no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—202no—
204C2×C4—202no—
205C2×C4—204no—
206C2×C4—202no—
207C2×C4—202no—
208C2×C4#402812yes—
209C2×C4#403012yes—
210C2×C4#407611yescharacteristic
211C2×C4#408611yescharacteristic
212C8—42no—
213C8—108no—
214C5#1008711yescharacteristic, complemented, Sylow
215C22#6524911yescharacteristic
216C22#6535111yescharacteristic
217C22#6536611yescharacteristic
218C22#6549414yes—
219C4—21no—
220C4—21no—
221C4—22no—
222C4—22no—
223C4—82no—
224C4—82no—
225C4—402no—
226C4—402no—
227C2#1060045711yescharacteristic
228C2#1060113912yes—
229C2#1060204512yes—
230C2#1060212312yes—
subgroupG/H
centerC23#4083
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1960C2
socle, prime radicalC23×C5#120
hypercenter#1960D5
hypocenterC5#10087
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
214. C5#10087semidirect

Maximal subgroups

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

subgroupindex
C2×#653692
#106059482
C5×#19602
C2×#646852
#105981212
#100875