Finite Group Databasebeta

← #12002796

Subgroups — #12002796

Order 1280.

402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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×#2822C211yesmaximal, characteristic
2#10602534C212yesmaximal
3C2×#64763C212yesmaximal
4#10600343C211yesmaximal, characteristic
5#10598121C211yesmaximal, characteristic
6C2×C5×#125C2212yes—
7C5×#400—22no—
8C5×#398—21no—
9C5×#398—21no—
10C5×#398—22no—
11C5×#382C2211yescharacteristic
12C2×#3940—21no—
13C2×#3939—21no—
14#65224C2211yescharacteristic
15C2×#3935C2212yes—
16C2×#3935C2211yescharacteristic
17#64763—24no—
18#64749—22no—
19#64749—22no—
20#10429—51nomaximal, Sylow
21C5×#125—22no—
22C5×#125—22no—
23C5×#125—22no—
24C5×#125—22no—
25C2×C5×C4⋊C4—22no—
26C2×C5×C4⋊C4—22no—
27C2×C5×C4⋊C4—21no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4D412yes—
30C2×C5×C4⋊C4D412yes—
31C2×C5×C4⋊C4D411yescharacteristic
32C2×C5×C4⋊C4D411yescharacteristic
33C2×C42×C5C2311yescharacteristic
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5—22no—
36C22×#168—21no—
37C22×#168—22no—
38C5×#95—22no—
39C5×#95—22no—
40C5×#95—21no—
41C5×#95—21no—
42C5×#95—22no—
43#3940—42no—
44#3939—42no—
45#3935—21no—
46#3935—22no—
47#3935—22no—
48#3935D412yes—
49#2822D511yescharacteristic
50#1992—52no—
51#1847—51no—
52C2×#330—52no—
53#1295—51no—
54C22×C4×C5—22no—
55C22×C4×C5—22no—
56C22×C4×C5—21no—
57C22×C4×C5—21no—
58C22×C4×C5C2×D412yes—
59C22×C4×C5C2×D411yescharacteristic
60C22×Dic5—41no—
61C5×C4⋊C4—22no—
62C5×C4⋊C4—22no—
63C5×C4⋊C4—22no—
64C5×C4⋊C4—22no—
65C5×C4⋊C4—41no—
66C5×C4⋊C4—41no—
67C5×C4⋊C4—42no—
68C5×C4⋊C4—42no—
69C5×C4⋊C4—42no—
70C5×C4⋊C4—42no—
71C5×C4⋊C4—81no—
72C5×C4⋊C4—81no—
73C42×C5C2×D411yescharacteristic
74C42×C5#4111yescharacteristic
75C42×C5#4112yes—
76C4⋊Dic5—41no—
77C4⋊Dic5—41no—
78C4⋊Dic5—44no—
79C2×#168—22no—
80C2×#168—22no—
81C2×#168—22no—
82C2×#168—24no—
83C2×#168—42no—
84C2×#168—42no—
85C2×#125C2×D512yes—
86C2×#107—101no—
87C2×#106—101no—
88C2×#97—51no—
89C2×#97—52no—
90#400—22no—
91#398—21no—
92#398—21no—
93#398—22no—
94#384—51no—
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—42no—
105C2×C4×C5—42no—
106C2×C4×C5—41no—
107C2×C4×C5—41no—
108C2×C4×C5—42no—
109C2×C4×C5—42no—
110C2×C4×C5—42no—
111C2×C4×C5—42no—
112C2×C4×C5—42no—
113C2×C4×C5—42no—
114C2×C4×C5#12111yescharacteristic
115C2×C4×C5#12112yes—
116C2×C4×C5#12312yes—
117C2×C4×C5#12411yescharacteristic
118C2×Dic5—81no—
119C2×Dic5—82no—
120#168—24no—
121#168—44no—
122C22×C8—101no—
123C22×C8—102no—
124#125—22no—
125#125—22no—
126#125—22no—
127#125—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—102no—
133C2×C4⋊C4—101no—
134C2×C4⋊C4C22⋊D512yes—
135C2×C4⋊C4C22⋊D512yes—
136C2×C4⋊C4C22⋊D511yescharacteristic
137C2×C4⋊C4C22⋊D511yescharacteristic
138C2×C42C22×D511yescharacteristic
139#107—202no—
140#106—202no—
141#97—52no—
142#97—102no—
143#97—101no—
144#97—102no—
145#95—22no—
146#95—22no—
147#95—21no—
148#95—21no—
149#95—22no—
150C22×C5#39411yescharacteristic
151C22×C5#45311yescharacteristic
152C22×C5#45412yes—
153C22×C5#45612yes—
154C22×C5#45611yescharacteristic
155C4×C5—22no—
156C4×C5—22no—
157C4×C5—21no—
158C4×C5—21no—
159C4×C5—81no—
160C4×C5—81no—
161C4×C5—82no—
162C4×C5—82no—
163Dic5—161no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—201no—
169C22×C4C2×C22⋊D512yes—
170C22×C4C2×C22⋊D511yescharacteristic
171C2×C8—102no—
172C2×C8—102no—
173C2×C8—102no—
174C2×C8—104no—
175C2×C8—202no—
176C2×C8—202no—
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—81no—
188C4⋊C4—81no—
189C4⋊C4—201no—
190C4⋊C4—201no—
191C4⋊C4—204no—
192C42D4×D511yescharacteristic
193C42#71111yescharacteristic
194C42#71112yes—
195C2×C5#165711yescharacteristic
196C2×C5#166011yescharacteristic
197C2×C5#166312yes—
198C2×C5#203812yes—
199C2×C5#203911yescharacteristic
200C23#409911yescharacteristic
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—401no—
216C2×C4—402no—
217C2×C4#408112yes—
218C2×C4#408211yescharacteristic
219C2×C4#408411yescharacteristic
220C2×C4#408512yes—
221C8—104no—
222C8—204no—
223C5#1042911yescharacteristic, complemented, Sylow
224C22#6551111yescharacteristic
225C22#6553011yescharacteristic
226C22#6553412yes—
227C22#6553511yescharacteristic
228C22#6553512yes—
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—82no—
234C4—82no—
235C4—81no—
236C4—81no—
237C4—801no—
238C2#1060265612yes—
239C2#1060266911yescharacteristic
240C2#1060274811yescharacteristic
241C2#1060274911yescharacteristic
242C2#1060275412yes—
subgroupG/H
centerC23#4099
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#2822C2
socle, prime radicalC23×C5#120
hypercenter#2822D5
hypocenterC5#10429
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

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
C5×#28222
#106025342
C2×#647632
#106003432
#105981212
#104295