Finite Group Databasebeta

← #12001591

Subgroups — #12001591

Order 1280.

466 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 103 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#10614954C212yesmaximal
2#10610210C211yesmaximal, characteristic
3C5×#1960C211yesmaximal, characteristic
4#10600339C212yesmaximal
5#10598152C211yesmaximal, characteristic
6C2×C5×C4⋊Q8C2211yescharacteristic
7#65804C2212yes—
8C2×C5×#103—22no—
9C2×C5×#97C2211yescharacteristic
10C5×#382C2211yescharacteristic
11#65395—22no—
12#65383—24no—
13#65382—22no—
14#65368—22no—
15#65260—24no—
16#65214C2212yes—
17#64991—22no—
18#64991—22no—
19#64672—24no—
20#10227—51nomaximal, Sylow
21C22×C5×Q8—21no—
22C22×C5×C8D412yes—
23C5×C4⋊Q8—22no—
24C5×C4⋊Q8—21no—
25C5×C4⋊Q8D412yes—
26C2×C5×C4⋊C4—22no—
27C2×C5×C4⋊C4—21no—
28C2×C42×C5C2311yescharacteristic
29#4072—22no—
30#4070—22no—
31#4070—22no—
32#4016—22no—
33#4015D412yes—
34#4015D412yes—
35C4×Dic10—22no—
36C4×Dic10—22no—
37C5×#103—44no—
38C5×#97—22no—
39C5×#95—22no—
40C22⋊#168D414yes—
41#3950—24no—
42#3949—22no—
43#3949—22no—
44#3942—28no—
45#3940—28no—
46C4⋊#168—22no—
47C4×#168—22no—
48#3229—52no—
49#3162—51no—
50#1960D511yescharacteristic
51#1518—52no—
52#1281—51no—
53C2×C5×Q8—22no—
54C2×C5×Q8—41no—
55C2×C5×Q8—42no—
56C2×C5×Q8—42no—
57C22×C4×C5—41no—
58C22×C4×C5—41no—
59C22×C4×C5C2×D412yes—
60C22×C4×C5C2×D411yescharacteristic
61C2×Dic10—22no—
62C2×Dic10—22no—
63C2×C5×C8—22no—
64C2×C5×C8—22no—
65C2×C5×C8SD1614yes—
66C5×C4⋊C4—24no—
67C5×C4⋊C4—42no—
68C5×C4⋊C4—42no—
69C42×C5C2×D411yescharacteristic
70C42×C5C2×D412yes—
71C42×C5#4111yescharacteristic
72C22⋊Dic5—42no—
73C4⋊Dic5—22no—
74C4⋊Dic5—22no—
75C4⋊Dic5—22no—
76C4⋊Dic5—22no—
77#683—42no—
78#683—42no—
79C4×Dic5—42no—
80C2×#168—24no—
81#533—52no—
82C2×C4⋊Q8C2×D511yescharacteristic
83#501—102no—
84#501—102no—
85#498—102no—
86#487—102no—
87#483—104no—
88#475—104no—
89#431—52no—
90#427—102no—
91C2×#103—22no—
92C2×#97C2×D511yescharacteristic
93#382C2×D511yescharacteristic
94#328—104no—
95C23×C5#12711yescharacteristic
96C5×Q8—44no—
97C5×Q8—82no—
98C2×C4×C5—42no—
99C2×C4×C5—42no—
100C2×C4×C5—81no—
101C2×C4×C5—81no—
102C2×C4×C5—82no—
103C2×C4×C5—81no—
104C2×C4×C5#12012yes—
105C2×C4×C5#12011yescharacteristic
106C2×C4×C5#12112yes—
107C2×C4×C5#12111yescharacteristic
108C2×C4×C5C2×SD1612yes—
109C2×C4×C5#13712yes—
110C2×Dic5—42no—
111C2×Dic5—42no—
112Dic10—44no—
113Dic10—82no—
114C5×C8—24no—
115#168—44no—
116C22×Q8—21no—
117C22×C8C22⋊D512yes—
118C4⋊Q8—21no—
119C4⋊Q8—22no—
120C4⋊Q8—52no—
121C4⋊Q8—52no—
122C4⋊Q8D2012yes—
123#125—102no—
124C22⋊Q8—102no—
125C22⋊Q8—102no—
126C4×Q8—102no—
127C4×Q8—102no—
128#117—102no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—21no—
131C2×C42C22×D511yescharacteristic
132#107—104no—
133#106—108no—
134#106—102no—
135#106—102no—
136C4⋊C8—102no—
137#103—44no—
138#103—108no—
139C22⋊C8—54no—
140#97—22no—
141C4×C8—102no—
142#95—22no—
143C22×C5—22no—
144C22×C5#39211yescharacteristic
145C22×C5#49211yescharacteristic
146C22×C5#49711yescharacteristic
147C4×C5—22no—
148C4×C5—22no—
149C4×C5—82no—
150C4×C5—161no—
151C4×C5#44812yes—
152C4×C5#46112yes—
153Dic5—82no—
154Dic5—82no—
155C2×Q8—22no—
156C2×Q8—41no—
157C2×Q8—42no—
158C2×Q8—42no—
159C2×Q8—102no—
160C2×Q8—102no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4D4×D512yes—
164C22×C4C2×C22⋊D511yescharacteristic
165C2×C8—22no—
166C2×C8—22no—
167C2×C8—104no—
168C2×C8#68714yes—
169C4⋊C4—24no—
170C4⋊C4—42no—
171C4⋊C4—42no—
172C4⋊C4—102no—
173C4⋊C4—102no—
174C4⋊C4—102no—
175C4⋊C4—102no—
176C4⋊C4—202no—
177C4⋊C4—202no—
178C22⋊C4—202no—
179C42—202no—
180C42C2×D2011yescharacteristic
181C42#70911yescharacteristic
182C42D4×D512yes—
183C2×C5—21no—
184C2×C5—21no—
185C2×C5#200912yes—
186C2×C5#201311yescharacteristic
187C23#408611yescharacteristic
188Q8—44no—
189Q8—82no—
190Q8—204no—
191Q8—402no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—81no—
195C2×C4—81no—
196C2×C4—82no—
197C2×C4—81no—
198C2×C4—202no—
199C2×C4—202no—
200C2×C4#402812yes—
201C2×C4#403012yes—
202C2×C4#407611yescharacteristic
203C2×C4C2×#68712yes—
204C2×C4#408311yescharacteristic
205C2×C4#409712yes—
206C8—24no—
207C8—204no—
208C5#1022711yescharacteristic, complemented, Sylow
209C22—22no—
210C22#6524911yescharacteristic
211C22#6534911yescharacteristic
212C22#6536511yescharacteristic
213C4—22no—
214C4—22no—
215C4—82no—
216C4—161no—
217C4—402no—
218C4—402no—
219C4#6530812yes—
220C4#6532912yes—
221C2—21no—
222C2—21no—
223C2#1060045411yescharacteristic
224C2#1060114412yes—
subgroupG/H
centerC22#65249
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1960C2
socleC22×C5#392
prime radicalC23×C5#127
hypercenter#1960D5
hypocenterC5#10227
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
208. C5#10227semidirect

Maximal subgroups

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

subgroupindex
#106149542
#106102102
C5×#19602
#106003392
#105981522
#102275