Finite Group Databasebeta

← #12002799

Subgroups — #12002799

Order 1280.

402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 91 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#10605948C211yesmaximal, characteristic
2C5×#1847C211yesmaximal, characteristic
3C2×#64685C212yesmaximal
4#10600376C212yesmaximal
5#10598121C211yesmaximal, characteristic
6C2×#4016C2212yes—
7C2×C5×#107—21no—
8C2×C5×#106—21no—
9C2×C5×#97C2211yescharacteristic
10C5×#384C2211yescharacteristic
11C5×#382C2211yescharacteristic
12#65272—21no—
13#65272—21no—
14C2×#3935C2212yes—
15#64950—22no—
16#64948—22no—
17#64749—22no—
18#64749—22no—
19#64685—24no—
20#10429—51nomaximal, Sylow
21C22×C5×C8—21no—
22C2×C5×C4⋊C4—21no—
23C2×C5×C4⋊C4—22no—
24C2×C5×C4⋊C4D411yescharacteristic
25C2×C5×C4⋊C4D411yescharacteristic
26C2×C42×C5C2311yescharacteristic
27C2×C4⋊Dic5—21no—
28C2×C4⋊Dic5—21no—
29C2×C4⋊Dic5D412yes—
30C2×C4⋊Dic5D412yes—
31C2×#683—22no—
32C2×#683—22no—
33C22×#168—22no—
34#4016—22no—
35#4016—22no—
36#4016—22no—
37#4016—22no—
38C5×#107—42no—
39C5×#106—42no—
40C5×#97—21no—
41C5×#97D412yes—
42C5×#95—22no—
43#3963—21no—
44#3963—21no—
45#3963—22no—
46#3963—22no—
47#3935—22no—
48#3935—22no—
49#2822—51no—
50#1992—52no—
51#1847D511yescharacteristic
52C2×#330—52no—
53#1295—51no—
54C22×C4×C5—21no—
55C22×C4×C5—21no—
56C22×C4×C5—41no—
57C22×C4×C5C2×D412yes—
58C22×C4×C5C2×D411yescharacteristic
59C22×Dic5—22no—
60C22×Dic5—22no—
61C2×C5×C8—22no—
62C2×C5×C8—22no—
63C2×C5×C8—22no—
64C5×C4⋊C4—41no—
65C5×C4⋊C4—41no—
66C5×C4⋊C4—44no—
67C5×C4⋊C4—41no—
68C5×C4⋊C4—41no—
69C42×C5C2×D411yescharacteristic
70C42×C5#4111yescharacteristic
71C42×C5#4112yes—
72C4⋊Dic5—22no—
73C4⋊Dic5—22no—
74C4⋊Dic5—22no—
75C4⋊Dic5—22no—
76C4⋊Dic5—81no—
77C4⋊Dic5—81no—
78#683—42no—
79#683—42no—
80#683—42no—
81#683—42no—
82C2×#168—24no—
83C2×#168—42no—
84C2×#168—42no—
85C2×#125—52no—
86C2×#107—21no—
87C2×#106—21no—
88C2×#97—52no—
89C2×#97C2×D511yescharacteristic
90#400—102no—
91#398—102no—
92#398—101no—
93#398—101no—
94#384C2×D511yescharacteristic
95#382C2×D511yescharacteristic
96#340—102no—
97#340—102no—
98#330—104no—
99C23×C5#12011yescharacteristic
100C2×C4×C5—21no—
101C2×C4×C5—22no—
102C2×C4×C5—22no—
103C2×C4×C5—21no—
104C2×C4×C5—41no—
105C2×C4×C5—41no—
106C2×C4×C5—42no—
107C2×C4×C5—42no—
108C2×C4×C5—81no—
109C2×C4×C5—82no—
110C2×C4×C5#12112yes—
111C2×C4×C5#12111yescharacteristic
112C2×C4×C5#12312yes—
113C2×C4×C5#12411yescharacteristic
114C2×Dic5—42no—
115C2×Dic5—42no—
116C2×Dic5—42no—
117C2×Dic5—42no—
118C2×Dic5—42no—
119C2×Dic5—42no—
120C5×C8—24no—
121#168—44no—
122C22×C8—21no—
123C22×C8—102no—
124#125—102no—
125#125—102no—
126#125—102no—
127#125—102no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—52no—
131C2×C4⋊C4—52no—
132C2×C4⋊C4—102no—
133C2×C4⋊C4—102no—
134C2×C4⋊C4—101no—
135C2×C4⋊C4—101no—
136C2×C4⋊C4C22⋊D511yescharacteristic
137C2×C4⋊C4C22⋊D511yescharacteristic
138C2×C42C22×D511yescharacteristic
139#107—42no—
140#106—42no—
141#97—21no—
142#97—102no—
143#97—102no—
144#97D2012yes—
145#95—22no—
146#95—102no—
147#95—102no—
148#95—101no—
149#95—101no—
150C22×C5#39411yescharacteristic
151C22×C5#45311yescharacteristic
152C22×C5#45412yes—
153C22×C5#45611yescharacteristic
154C22×C5#45612yes—
155C4×C5—22no—
156C4×C5—22no—
157C4×C5—21no—
158C4×C5—21no—
159C4×C5—81no—
160C4×C5—81no—
161C4×C5—161no—
162Dic5—82no—
163Dic5—82no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—41no—
167C22×C4—102no—
168C22×C4—102no—
169C22×C4D4×D512yes—
170C22×C4C2×C22⋊D511yescharacteristic
171C2×C8—22no—
172C2×C8—22no—
173C2×C8—22no—
174C2×C8—104no—
175C2×C8—202no—
176C2×C8—202no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—44no—
182C4⋊C4—102no—
183C4⋊C4—102no—
184C4⋊C4—102no—
185C4⋊C4—102no—
186C4⋊C4—202no—
187C4⋊C4—202no—
188C4⋊C4—202no—
189C4⋊C4—202no—
190C4⋊C4—401no—
191C4⋊C4—401no—
192C42C2×D2011yescharacteristic
193C42#70911yescharacteristic
194C42#71312yes—
195C2×C5#165711yescharacteristic
196C2×C5#166011yescharacteristic
197C2×C5#166312yes—
198C2×C5#203812yes—
199C2×C5#203911yescharacteristic
200C23#408311yescharacteristic
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—81no—
210C2×C4—82no—
211C2×C4—202no—
212C2×C4—202no—
213C2×C4—202no—
214C2×C4—202no—
215C2×C4—202no—
216C2×C4—202no—
217C2×C4#404012yes—
218C2×C4#404112yes—
219C2×C4#407611yescharacteristic
220C2×C4#409311yescharacteristic
221C8—24no—
222C8—204no—
223C5#1042911yescharacteristic, complemented, Sylow
224C22#6528011yescharacteristic
225C22#6536611yescharacteristic
226C22#6538411yescharacteristic
227C22#6549012yes—
228C22#6549412yes—
229C4—21no—
230C4—21no—
231C4—22no—
232C4—22no—
233C4—81no—
234C4—81no—
235C4—161no—
236C4—402no—
237C4—402no—
238C2#1060038611yescharacteristic
239C2#1060147112yes—
240C2#1060212111yescharacteristic
241C2#1060212311yescharacteristic
242C2#1060218612yes—
subgroupG/H
centerC23#4083
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1847C2
socle, prime radicalC23×C5#120
hypercenter#1847D5
hypocenterC5#10429
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
223. C5#10429semidirect

Maximal subgroups

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

subgroupindex
#106059482
C5×#18472
C2×#646852
#106003762
#105981212
#104295