Finite Group Databasebeta

← #12003811

Subgroups — #12003811

Order 1280.

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

normal subgroups only

This group has 350 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
1#10605950C211yesmaximal, characteristic
2#10600608C212yesmaximal
3#10600341C211yesmaximal, characteristic
4C5×#1295C211yesmaximal, characteristic
5#10598150C212yesmaximal
6C2×C5×#97C2212yes—
7C5×#382C2211yescharacteristic
8#65273—22no—
9#65225C2212yes—
10#65224C2211yescharacteristic
11C2×#3935C2211yescharacteristic
12#64950—22no—
13#64946—22no—
14#64771—22no—
15#64771—22no—
16#64749—22no—
17#10586—51nomaximal, Sylow
18C22×C5×C8—22no—
19C2×C5×C4⋊C4D412yes—
20C2×C42×C5C2311yescharacteristic
21C2×C4⋊Dic5—22no—
22C2×C4⋊Dic5—21no—
23C2×C4⋊Dic5—22no—
24C2×C4⋊Dic5D412yes—
25C2×C4⋊Dic5D412yes—
26C2×#683—22no—
27C2×#683—22no—
28C22×#168—21no—
29C5×#97—22no—
30C5×#97Q814yes—
31C5×#95—22no—
32#3963—22no—
33#3963—22no—
34#3963—22no—
35#3935—21no—
36#3935Q812yes—
37#2845—51no—
38#1836—52no—
39#1836—51no—
40#1295—52no—
41#1295D511yescharacteristic
42C22×C4×C5—22no—
43C22×C4×C5C2×D411yescharacteristic
44C22×C4×C5C2×D412yes—
45C22×Dic5—22no—
46C22×Dic5—22no—
47C22×Dic5—41no—
48C2×C5×C8—24no—
49C2×C5×C8—42no—
50C2×C5×C8—42no—
51C5×C4⋊C4—42no—
52C42×C5C2×Q812yes—
53C42×C5C2×Q811yescharacteristic
54C42×C5#4111yescharacteristic
55C4⋊Dic5—42no—
56C4⋊Dic5—42no—
57C4⋊Dic5—42no—
58C4⋊Dic5—44no—
59C4⋊Dic5—82no—
60#683—82no—
61#683—82no—
62C2×#168—22no—
63C2×#168—41no—
64C2×#168—41no—
65C2×#97—51no—
66C2×#97C2×D512yes—
67#398—102no—
68#398—102no—
69#398—102no—
70#384—51no—
71#382—52no—
72#382C2×D511yescharacteristic
73#340—102no—
74#340—102no—
75#340—102no—
76C23×C5#12011yescharacteristic
77C2×C4×C5—21no—
78C2×C4×C5—22no—
79C2×C4×C5—21no—
80C2×C4×C5—22no—
81C2×C4×C5—42no—
82C2×C4×C5—42no—
83C2×C4×C5—42no—
84C2×C4×C5C22⋊Q812yes—
85C2×C4×C5C22⋊Q811yescharacteristic
86C2×C4×C5C4⋊Q811yescharacteristic
87C2×C4×C5C4⋊Q812yes—
88C2×Dic5—42no—
89C2×Dic5—42no—
90C2×Dic5—42no—
91C2×Dic5—42no—
92C2×Dic5—42no—
93C2×Dic5—42no—
94C2×Dic5—81no—
95C2×Dic5—82no—
96C5×C8—44no—
97#168—42no—
98C22×C8—22no—
99C22×C8—101no—
100C2×C4⋊C4—52no—
101C2×C4⋊C4—52no—
102C2×C4⋊C4—101no—
103C2×C4⋊C4—102no—
104C2×C4⋊C4—102no—
105C2×C4⋊C4—102no—
106C2×C4⋊C4—102no—
107C2×C4⋊C4D2012yes—
108C2×C42C22×D511yescharacteristic
109#97—22no—
110#97—52no—
111#97—101no—
112#97Dic1014yes—
113#95—22no—
114#95—102no—
115#95—102no—
116#95—102no—
117C22×C5#39511yescharacteristic
118C22×C5#45411yescharacteristic
119C22×C5#45412yes—
120C22×C5#45511yescharacteristic
121C22×C5#45512yes—
122C4×C5—21no—
123C4×C5—22no—
124C4×C5—21no—
125C4×C5—22no—
126C4×C5—82no—
127Dic5—82no—
128Dic5—82no—
129Dic5—161no—
130C22×C4—22no—
131C22×C4—102no—
132C22×C4—102no—
133C22×C4—201no—
134C22×C4C2×D2011yescharacteristic
135C22×C4D4×D512yes—
136C2×C8—24no—
137C2×C8—42no—
138C2×C8—42no—
139C2×C8—102no—
140C2×C8—201no—
141C2×C8—201no—
142C4⋊C4—42no—
143C4⋊C4—202no—
144C4⋊C4—202no—
145C4⋊C4—202no—
146C4⋊C4—204no—
147C4⋊C4—402no—
148C4⋊C4—402no—
149C4⋊C4—402no—
150C42C2×Dic1012yes—
151C42#71111yescharacteristic
152C42Q8×D511yescharacteristic
153C2×C5#165811yescharacteristic
154C2×C5#166212yes—
155C2×C5#166211yescharacteristic
156C2×C5#206111yescharacteristic
157C2×C5#206112yes—
158C23#402811yescharacteristic
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—202no—
167C2×C4—202no—
168C2×C4—202no—
169C2×C4—202no—
170C2×C4—202no—
171C2×C4—202no—
172C2×C4—401no—
173C2×C4—402no—
174C2×C4#401511yescharacteristic
175C2×C4#402412yes—
176C2×C4#403412yes—
177C2×C4#404311yescharacteristic
178C8—44no—
179C8—202no—
180C5#1058611yescharacteristic, complemented, Sylow
181C22#6494511yescharacteristic
182C22#6503511yescharacteristic
183C22#6504211yescharacteristic
184C22#6511412yes—
185C22#6511612yes—
186C4—21no—
187C4—21no—
188C4—22no—
189C4—22no—
190C4—82no—
191C4—402no—
192C4—402no—
193C4—801no—
194C2#1059915112yes—
195C2#1059916711yescharacteristic
196C2#1059916811yescharacteristic
197C2#1059952912yes—
198C2#1059977211yescharacteristic
subgroupG/H
centerC23#4028
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1295C2
socle, prime radicalC23×C5#120
hypercenter#1295D5
hypocenterC5#10586
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
180. C5#10586semidirect

Maximal subgroups

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

subgroupindex
#106059502
#106006082
#106003412
C5×#12952
#105981502
#105865