Finite Group Databasebeta

← #12001592

Subgroups — #12001592

Order 1280.

466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C5×#3162C211yesmaximal, characteristic
2#10615054C212yesmaximal
3#10602631C212yesmaximal
4#10600615C211yesmaximal, characteristic
5#10598152C211yesmaximal, characteristic
6C5×#533C2212yes—
7C2×#4015C2211yescharacteristic
8C5×#501—22no—
9C5×#501—22no—
10C5×#427—22no—
11C2×C5×#97C2211yescharacteristic
12C2×#3948—22no—
13#65370—22no—
14#65368—22no—
15#65332—24no—
16#65309—24no—
17#65225C2211yescharacteristic
18#65214C2212yes—
19#64758—24no—
20#10227—51nomaximal, Sylow
21C22×Dic10—21no—
22C22×C5×C8D412yes—
23C5×C4⋊Q8D412yes—
24C5×C4⋊Q8D412yes—
25C5×#125—22no—
26C5×C22⋊Q8—22no—
27C5×C22⋊Q8—22no—
28C4×C5×Q8—22no—
29C4×C5×Q8—22no—
30C5×#117—22no—
31C2×C42×C5C2311yescharacteristic
32C2×C4⋊Dic5—22no—
33C2×C4⋊Dic5—21no—
34#4015—22no—
35#4015—21no—
36#4015D412yes—
37C5×#107—24no—
38C5×#106—22no—
39C5×#106—22no—
40C5×#97—22no—
41#3967—28no—
42#3963—22no—
43C22⋊#168D414yes—
44#3948—44no—
45#3940—28no—
46C4⋊#168—22no—
47C4×#168—22no—
48#3229—52no—
49#3162D511yescharacteristic
50#1960—51no—
51#1518—52no—
52#1281—51no—
53C2×C5×Q8—22no—
54C2×C5×Q8—22no—
55C22×C4×C5C2×D412yes—
56C22×C4×C5C2×D411yescharacteristic
57C22×Dic5—41no—
58C22×Dic5—41no—
59C2×Dic10—22no—
60C2×Dic10—42no—
61C2×Dic10—42no—
62C2×Dic10—41no—
63C2×C5×C8—22no—
64C2×C5×C8—22no—
65C2×C5×C8SD1614yes—
66C5×C4⋊C4—22no—
67C5×C4⋊C4—22no—
68C5×C4⋊C4—22no—
69C5×C4⋊C4—22no—
70C5×C4⋊C4—42no—
71C5×C4⋊C4—42no—
72C5×C22⋊C4—42no—
73C42×C5—42no—
74C42×C5C2×D411yescharacteristic
75C42×C5C2×D412yes—
76C42×C5#4111yescharacteristic
77C4⋊Dic5—24no—
78C4⋊Dic5—42no—
79C4⋊Dic5—42no—
80C2×#168—24no—
81#533C2×D512yes—
82C2×C4⋊Q8—51no—
83#501—22no—
84#501—22no—
85#498—102no—
86#487—102no—
87#483—104no—
88#475—104no—
89#431—52no—
90#427—22no—
91C2×#103—102no—
92C2×#97C2×D511yescharacteristic
93#382—51no—
94#328—104no—
95C23×C5#12711yescharacteristic
96C5×Q8—44no—
97C5×Q8—82no—
98C2×C4×C5—42no—
99C2×C4×C5—42no—
100C2×C4×C5—42no—
101C2×C4×C5#12011yescharacteristic
102C2×C4×C5#12012yes—
103C2×C4×C5#12111yescharacteristic
104C2×C4×C5#12112yes—
105C2×C4×C5C2×SD1612yes—
106C2×C4×C5#13712yes—
107C2×Dic5—42no—
108C2×Dic5—81no—
109C2×Dic5—81no—
110C2×Dic5—82no—
111C2×Dic5—81no—
112Dic10—44no—
113Dic10—82no—
114C5×C8—24no—
115#168—44no—
116C22×Q8—101no—
117C22×C8C22⋊D512yes—
118C4⋊Q8—52no—
119C4⋊Q8—101no—
120C4⋊Q8—102no—
121C4⋊Q8C22⋊D512yes—
122C4⋊Q8C22⋊D512yes—
123#125—22no—
124C22⋊Q8—22no—
125C22⋊Q8—22no—
126C4×Q8—22no—
127C4×Q8—22no—
128#117—22no—
129C2×C4⋊C4—102no—
130C2×C4⋊C4—101no—
131C2×C42C22×D511yescharacteristic
132#107—24no—
133#106—22no—
134#106—22no—
135#106—108no—
136C4⋊C8—102no—
137#103—108no—
138#103—204no—
139C22⋊C8—54no—
140#97—22no—
141C4×C8—102no—
142#95—102no—
143C22×C5—22no—
144C22×C5#39211yescharacteristic
145C22×C5#49211yescharacteristic
146C22×C5#49711yescharacteristic
147C4×C5—22no—
148C4×C5—22no—
149C4×C5—82no—
150C4×C5—82no—
151C4×C5#44812yes—
152C4×C5#46112yes—
153Dic5—82no—
154Dic5—161no—
155C2×Q8—22no—
156C2×Q8—22no—
157C2×Q8—102no—
158C2×Q8—201no—
159C2×Q8—202no—
160C2×Q8—202no—
161C22×C4—201no—
162C22×C4—201no—
163C22×C4D4×D512yes—
164C22×C4C2×C22⋊D511yescharacteristic
165C2×C8—22no—
166C2×C8—22no—
167C2×C8—104no—
168C2×C8#68814yes—
169C4⋊C4—22no—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—42no—
174C4⋊C4—42no—
175C4⋊C4—104no—
176C4⋊C4—202no—
177C4⋊C4—202no—
178C22⋊C4—42no—
179C42—42no—
180C42D4×D511yescharacteristic
181C42#71111yescharacteristic
182C42C2×C22⋊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—42no—
195C2×C4—202no—
196C2×C4—401no—
197C2×C4—401no—
198C2×C4—402no—
199C2×C4—401no—
200C2×C4#408312yes—
201C2×C4#408411yescharacteristic
202C2×C4#408512yes—
203C2×C4C2×#68812yes—
204C2×C4#408812yes—
205C2×C4#409911yescharacteristic
206C8—24no—
207C8—204no—
208C5#1022711yescharacteristic, complemented, Sylow
209C22—22no—
210C22#6537411yescharacteristic
211C22#6537511yescharacteristic
212C22#6551211yescharacteristic
213C4—22no—
214C4—22no—
215C4—82no—
216C4—82no—
217C4—402no—
218C4—801no—
219C4#6537212yes—
220C4#6551612yes—
221C2—21no—
222C2—21no—
223C2#1060258411yescharacteristic
224C2#1060291312yes—
subgroupG/H
centerC22#65512
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#3162C2
socleC22×C5#392
prime radicalC23×C5#127
hypercenter#3162D5
hypocenterC5#10227
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3162

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
C5×#31622
#106150542
#106026312
#106006152
#105981522
#102275