Finite Group Databasebeta

← #12003751

Subgroups — #12003751

Order 1280.

406 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 129 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×#2571C211yesmaximal, characteristic
2#10600370C211yesmaximal, characteristic
3#10600260C212yesmaximal
4#10598125C211yesmaximal, characteristic
5#10598110C212yesmaximal
6C5×#400—22no—
7C5×#389—22no—
8C5×#384C2211yescharacteristic
9C5×#382—22no—
10C4×C5×C4⋊C4C2212yes—
11C2×#3940—22no—
12C2×#3939—22no—
13#65224C2211yescharacteristic
14C2×C4⋊#168C2212yes—
15C2×C4×#168C2211yescharacteristic
16#64749—22no—
17#10576—51nomaximal, Sylow
18C2×C5×C4⋊C4—22no—
19C2×C5×C4⋊C4—22no—
20C2×C5×C4⋊C4D412yes—
21C2×C5×C4⋊C4D412yes—
22C2×C5×C4⋊C4D412yes—
23C2×C42×C5—22no—
24C2×C42×C5C2311yescharacteristic
25C2×C4⋊Dic5—21no—
26C2×C4⋊Dic5—22no—
27C22×#168—21no—
28C22×#168—22no—
29C5×#95—22no—
30C5×#95—24no—
31C5×#95—22no—
32#3940—44no—
33#3939—44no—
34C4⋊#168—22no—
35C4⋊#168Q814yes—
36C4×#168—21no—
37C4×#168Q812yes—
38#2571D511yescharacteristic
39#1948—52no—
40#1845—51no—
41#1296—51no—
42#1279—52no—
43C22×C4×C5—22no—
44C22×C4×C5—22no—
45C22×C4×C5—22no—
46C22×C4×C5C2×D411yescharacteristic
47C22×C4×C5C2×D412yes—
48C22×Dic5—41no—
49C5×C4⋊C4—22no—
50C5×C4⋊C4—22no—
51C5×C4⋊C4—22no—
52C5×C4⋊C4—22no—
53C5×C4⋊C4—42no—
54C5×C4⋊C4—42no—
55C5×C4⋊C4—42no—
56C5×C4⋊C4—82no—
57C42×C5—42no—
58C42×C5—42no—
59C42×C5C2×Q811yescharacteristic
60C42×C5C2×Q812yes—
61C42×C5#4111yescharacteristic
62C4⋊Dic5—42no—
63C4⋊Dic5—42no—
64C4⋊Dic5—42no—
65C2×#168—22no—
66C2×#168—22no—
67C2×#168—22no—
68C2×#168—24no—
69C2×#168—42no—
70C2×#168—42no—
71C2×#107—102no—
72C2×#106—102no—
73C2×C4⋊C8—52no—
74C2×C4×C8—51no—
75#400—22no—
76#389—22no—
77#384—51no—
78#384C2×D511yescharacteristic
79#382—22no—
80C4×C4⋊C4C2×D512yes—
81#340—102no—
82C23×C5#12011yescharacteristic
83C2×C4×C5—21no—
84C2×C4×C5—21no—
85C2×C4×C5—42no—
86C2×C4×C5—44no—
87C2×C4×C5—42no—
88C2×C4×C5—42no—
89C2×C4×C5—42no—
90C2×C4×C5—42no—
91C2×C4×C5—42no—
92C2×C4×C5—42no—
93C2×C4×C5C22⋊Q811yescharacteristic
94C2×C4×C5C22⋊Q812yes—
95C2×C4×C5C4⋊Q811yescharacteristic
96C2×C4×C5C4⋊Q812yes—
97C2×C4×C5#13512yes—
98C2×C4×C5#13512yes—
99C2×C4×C5AGL(1,ℤ/8)12yes—
100C2×C4×C5#13712yes—
101C2×Dic5—82no—
102C2×Dic5—81no—
103#168—24no—
104#168—44no—
105C22×C8—101no—
106C22×C8—102no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4—102no—
110C2×C4⋊C4—101no—
111C2×C4⋊C4C22⋊D512yes—
112C2×C4⋊C4C22⋊D512yes—
113C2×C4⋊C4C22⋊D512yes—
114C2×C42—22no—
115C2×C42C22×D511yescharacteristic
116#107—204no—
117#106—204no—
118C4⋊C8—54no—
119C4⋊C8—102no—
120C4×C8—52no—
121C4×C8—101no—
122#95—22no—
123#95—24no—
124#95—22no—
125C22×C5#39511yescharacteristic
126C22×C5#44912yes—
127C22×C5#45212yes—
128C22×C5#45311yescharacteristic
129C22×C5#45611yescharacteristic
130C4×C5—21no—
131C4×C5—21no—
132C4×C5—82no—
133C4×C5—82no—
134C4×C5—82no—
135C4×C5#47812yes—
136C4×C5#47912yes—
137C4×C5#49912yes—
138C4×C5#50112yes—
139Dic5—161no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—201no—
144C22×C4C2×C22⋊D511yescharacteristic
145C22×C4C2×C22⋊D512yes—
146C2×C8—102no—
147C2×C8—102no—
148C2×C8—102no—
149C2×C8—104no—
150C2×C8—202no—
151C2×C8—202no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—42no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C4⋊C4—82no—
160C4⋊C4—202no—
161C4⋊C4—202no—
162C4⋊C4—202no—
163C42—42no—
164C42—42no—
165C42Q8×D511yescharacteristic
166C42Q8×D512yes—
167C42#71311yescharacteristic
168C2×C5#162011yescharacteristic
169C2×C5#163411yescharacteristic
170C2×C5#165012yes—
171C2×C5#205912yes—
172C2×C5#206011yescharacteristic
173C23#409911yescharacteristic
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—42no—
177C2×C4—44no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—402no—
185C2×C4—401no—
186C2×C4#409011yescharacteristic
187C2×C4#409012yes—
188C2×C4#409211yescharacteristic
189C2×C4#409212yes—
190C2×C4#409512yes—
191C2×C4#409612yes—
192C2×C4#409612yes—
193C2×C4#409712yes—
194C8—104no—
195C8—204no—
196C5#1057611yescharacteristic, complemented, Sylow
197C22#6551811yescharacteristic
198C22#6552712yes—
199C22#6552812yes—
200C22#6553011yescharacteristic
201C22#6553511yescharacteristic
202C4—21no—
203C4—21no—
204C4—82no—
205C4—82no—
206C4—82no—
207C4—801no—
208C4#6535212yes—
209C4#6535312yes—
210C4#6535412yes—
211C4#6535512yes—
212C2#1060253212yes—
213C2#1060269311yescharacteristic
214C2#1060272111yescharacteristic
215C2#1060272612yes—
216C2#1060273611yescharacteristic
subgroupG/H
centerC23#4099
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#2571C2
socle, prime radicalC23×C5#120
hypercenter#2571D5
hypocenterC5#10576
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2571

Complements

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

NH ≅ G/Ntype
196. C5#10576semidirect

Maximal subgroups

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

subgroupindex
C5×#25712
#106003702
#106002602
#105981252
#105981102
#105765