Finite Group Databasebeta

← #12003804

Subgroups — #12003804

Order 1280.

382 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 97 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×#2845C211yesmaximal, characteristic
2#10600343C212yesmaximal
3#10600341C211yesmaximal, characteristic
4#10598121C211yesmaximal, characteristic
5#10598121C212yesmaximal
6C5×#398—22no—
7C5×#398—22no—
8C5×#398—22no—
9C5×#382C2211yescharacteristic
10C5×#382C2212yes—
11C2×#3940—22no—
12C2×#3939—22no—
13#65224C2211yescharacteristic
14C2×#3935C2211yescharacteristic
15C2×#3935C2212yes—
16#64749—22no—
17#10585—51nomaximal, Sylow
18C2×C5×C4⋊C4—22no—
19C2×C5×C4⋊C4—22no—
20C2×C5×C4⋊C4—22no—
21C2×C5×C4⋊C4D412yes—
22C2×C5×C4⋊C4D412yes—
23C2×C5×C4⋊C4D412yes—
24C2×C42×C5C2311yescharacteristic
25C2×C4⋊Dic5—22no—
26C2×C4⋊Dic5—21no—
27C22×#168—22no—
28C22×#168—21no—
29C5×#95—22no—
30C5×#95—22no—
31C5×#95—22no—
32C5×#95—22no—
33#3940—44no—
34#3939—44no—
35#3935—22no—
36#3935—21no—
37#3935Q814yes—
38#3935Q812yes—
39#2845D511yescharacteristic
40#1847—52no—
41#1836—51no—
42#1295—51no—
43#1295—52no—
44C22×C4×C5—22no—
45C22×C4×C5—22no—
46C22×C4×C5—22no—
47C22×C4×C5C2×D412yes—
48C22×C4×C5C2×D411yescharacteristic
49C22×Dic5—41no—
50C5×C4⋊C4—42no—
51C5×C4⋊C4—42no—
52C5×C4⋊C4—42no—
53C5×C4⋊C4—82no—
54C5×C4⋊C4—82no—
55C5×C4⋊C4—82no—
56C42×C5C2×Q812yes—
57C42×C5C2×Q811yescharacteristic
58C42×C5#4111yescharacteristic
59C4⋊Dic5—42no—
60C4⋊Dic5—42no—
61C4⋊Dic5—42no—
62C2×#168—24no—
63C2×#168—24no—
64C2×#168—24no—
65C2×#168—22no—
66C2×#168—41no—
67C2×#168—41no—
68C2×#107—102no—
69C2×#106—102no—
70C2×#97—51no—
71C2×#97—52no—
72#398—22no—
73#398—22no—
74#398—22no—
75#384—51no—
76#382C2×D511yescharacteristic
77#382C2×D512yes—
78#340—102no—
79C23×C5#12011yescharacteristic
80C2×C4×C5—22no—
81C2×C4×C5—21no—
82C2×C4×C5—21no—
83C2×C4×C5—22no—
84C2×C4×C5—42no—
85C2×C4×C5—42no—
86C2×C4×C5—42no—
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⋊Q812yes—
94C2×C4×C5C22⋊Q811yescharacteristic
95C2×C4×C5C4⋊Q812yes—
96C2×C4×C5C4⋊Q811yescharacteristic
97C2×Dic5—82no—
98C2×Dic5—81no—
99#168—28no—
100#168—42no—
101C22×C8—102no—
102C22×C8—101no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—101no—
107C2×C4⋊C4—102no—
108C2×C4⋊C4C22⋊D512yes—
109C2×C4⋊C4C22⋊D512yes—
110C2×C4⋊C4C22⋊D512yes—
111C2×C42C22×D511yescharacteristic
112#107—204no—
113#106—204no—
114#97—54no—
115#97—52no—
116#97—102no—
117#97—101no—
118#95—22no—
119#95—22no—
120#95—22no—
121#95—22no—
122C22×C5#39511yescharacteristic
123C22×C5#45312yes—
124C22×C5#45411yescharacteristic
125C22×C5#45511yescharacteristic
126C22×C5#45612yes—
127C4×C5—22no—
128C4×C5—22no—
129C4×C5—21no—
130C4×C5—21no—
131C4×C5—82no—
132C4×C5—82no—
133C4×C5—82no—
134Dic5—161no—
135C22×C4—22no—
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—201no—
139C22×C4C2×C22⋊D512yes—
140C22×C4C2×C22⋊D511yescharacteristic
141C2×C8—104no—
142C2×C8—104no—
143C2×C8—104no—
144C2×C8—102no—
145C2×C8—201no—
146C2×C8—201no—
147C4⋊C4—42no—
148C4⋊C4—42no—
149C4⋊C4—42no—
150C4⋊C4—82no—
151C4⋊C4—82no—
152C4⋊C4—82no—
153C4⋊C4—202no—
154C4⋊C4—202no—
155C4⋊C4—202no—
156C42Q8×D511yescharacteristic
157C42Q8×D512yes—
158C42#71311yescharacteristic
159C2×C5#165611yescharacteristic
160C2×C5#166112yes—
161C2×C5#166311yescharacteristic
162C2×C5#206012yes—
163C2×C5#206111yescharacteristic
164C23#409911yescharacteristic
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—402no—
179C2×C4—401no—
180C2×C4#409012yes—
181C2×C4#409011yescharacteristic
182C2×C4#409212yes—
183C2×C4#409211yescharacteristic
184C8—108no—
185C8—202no—
186C5#1058511yescharacteristic, complemented, Sylow
187C22#6551811yescharacteristic
188C22#6553012yes—
189C22#6553111yescharacteristic
190C22#6553411yescharacteristic
191C22#6553512yes—
192C4—22no—
193C4—22no—
194C4—21no—
195C4—21no—
196C4—82no—
197C4—82no—
198C4—82no—
199C4—801no—
200C2#1060269312yes—
201C2#1060269411yescharacteristic
202C2#1060274511yescharacteristic
203C2#1060274612yes—
204C2#1060275411yescharacteristic
subgroupG/H
centerC23#4099
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#2845C2
socle, prime radicalC23×C5#120
hypercenter#2845D5
hypocenterC5#10585
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2845

Complements

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

NH ≅ G/Ntype
186. C5#10585semidirect

Maximal subgroups

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

subgroupindex
C5×#28452
#106003432
#106003412
#105981212
#105855