Finite Group Databasebeta

← #12008648

Subgroups — #12008648

Order 1280.

288 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 87 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#10610807C211yesmaximal, characteristic
2#10599886C212yesmaximal
3C5×#1323C211yesmaximal, characteristic
4#10598209C211yesmaximal, characteristic
5#10598016C212yesmaximal
6#65851C411yescharacteristic
7C5×#424C2211yescharacteristic
8#65411C411yescharacteristic
9#65407C411yescharacteristic
10#65391C2211yescharacteristic
11C2×C8×Dic5C2211yescharacteristic
12#65286C411yescharacteristic
13#65119—22no—
14#65117—22no—
15C5×C22⋊C16C2212yes—
16C22⋊#672C2212yes—
17#64722—22no—
18#64721—22no—
19#11497—51nomaximal, Sylow
20C2×C5×M16C2×C411yescharacteristic
21C22×C5×C8C2311yescharacteristic
22C5×#117C2×C411yescharacteristic
23#4072C2×C411yescharacteristic
24C2×C4×Dic5C2×C411yescharacteristic
25C2×#681C2×C411yescharacteristic
26C22×#168C2×C411yescharacteristic
27#4036C812yes—
28#4034C812yes—
29#4024—22no—
30C4×Dic10—22no—
31C2×C5×C16—22no—
32C5×C4⋊C8—22no—
33#3947—21no—
34#3946—22no—
35#3946—22no—
36C8×Dic5—21no—
37C8×Dic5D412yes—
38C8×Dic5D412yes—
39C2×#672—22no—
40#3935—21no—
41C4×#168—21no—
42#2960—51no—
43#2163—52no—
44#1323—51no—
45#1323—52no—
46#1323D511yescharacteristic
47C22×C4×C5C22×C411yescharacteristic
48C22×Dic5M1612yes—
49C2×Dic10—22no—
50C5×M16—41no—
51C2×C5×C8—21no—
52C2×C5×C8—41no—
53C2×C5×C8C2×D412yes—
54C5×C4⋊C4C2×C812yes—
55C5×C22⋊C4—21no—
56C42×C5—21no—
57C22⋊Dic5—21no—
58C4⋊Dic5—22no—
59C4⋊Dic5C2×C812yes—
60#683—22no—
61#683—22no—
62C4×Dic5—21no—
63C4×Dic5C22⋊C412yes—
64C4×Dic5C2×C811yescharacteristic
65C4×Dic5C2×C811yescharacteristic
66#681—41no—
67C2×#168—22no—
68C2×#168—21no—
69C2×#168C22⋊C411yescharacteristic
70C2×#168C22⋊C411yescharacteristic
71C5×C16—42no—
72#672—42no—
73#533—51no—
74#446—102no—
75C8×Q8—102no—
76#424—51no—
77#424C2×D511yescharacteristic
78#423—51no—
79#405—51no—
80#405—51no—
81C2×C4×C8—51no—
82C4⋊C16—102no—
83C22⋊C16—52no—
84C22⋊C16C2×D512yes—
85#346—102no—
86C23×C5C2×M1611yescharacteristic
87C2×C4×C5—21no—
88C2×C4×C5—21no—
89C2×C4×C5—22no—
90C2×C4×C5C2×C22⋊C411yescharacteristic
91C2×C4×C5C22×C811yescharacteristic
92C2×Dic5—22no—
93C2×Dic5—42no—
94C2×Dic5C22⋊C812yes—
95C2×Dic5C22⋊C812yes—
96Dic10—44no—
97C5×C8—22no—
98C5×C8—41no—
99#168—21no—
100#168—41no—
101#168#10112yes—
102C2×M16—51no—
103C2×M16C4×D511yescharacteristic
104C22×C8—51no—
105C22×C8C22×D511yescharacteristic
106C4⋊Q8—52no—
107#125—52no—
108C22⋊Q8—102no—
109C4×Q8—102no—
110#117—51no—
111#117C4×D511yescharacteristic
112C2×C42—51no—
113C2×C16—22no—
114C2×C16—102no—
115C4⋊C8—22no—
116C4⋊C8—102no—
117C4⋊C8—102no—
118#97—101no—
119#97—101no—
120C4×C8—52no—
121C4×C8—52no—
122C4×C8—101no—
123C4×C8—101no—
124C22×C5—22no—
125C22×C5—21no—
126C22×C5C2×C22⋊C811yescharacteristic
127C4×C5—21no—
128C4×C5—42no—
129C4×C5#41011yescharacteristic
130C4×C5C2×#10111yescharacteristic
131Dic5—22no—
132Dic5—22no—
133Dic5—42no—
134C2×Q8—102no—
135C22×C4—52no—
136C22×C4C2×C4×D511yescharacteristic
137M16—41no—
138M16—201no—
139C2×C8—21no—
140C2×C8—41no—
141C2×C8—51no—
142C2×C8—51no—
143C2×C8—102no—
144C2×C8—101no—
145C2×C8D4×D512yes—
146C4⋊C4—52no—
147C4⋊C4—102no—
148C4⋊C4—102no—
149C4⋊C4—102no—
150C4⋊C4C8×D512yes—
151C22⋊C4—21no—
152C22⋊C4—101no—
153C42—21no—
154C42—52no—
155C42—51no—
156C42—51no—
157C42—101no—
158C16—42no—
159C16—202no—
160C2×C5—41no—
161C2×C5#146111yescharacteristic
162C2×C5#211712yes—
163C23D5×M1611yescharacteristic
164Q8—204no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—52no—
169C2×C4—52no—
170C2×C4—102no—
171C2×C4—202no—
172C2×C4D5×C22⋊C411yescharacteristic
173C2×C4C2×C8×D511yescharacteristic
174C8—22no—
175C8—41no—
176C8—52no—
177C8—101no—
178C8—201no—
179C5#1149711yescharacteristic, complemented, Sylow
180C22—21no—
181C22—22no—
182C22D5×C22⋊C811yescharacteristic
183C4—21no—
184C4—42no—
185C4—102no—
186C4—102no—
187C4—202no—
188C4#6502911yescharacteristic
189C4D5×#10111yescharacteristic
190C2—41no—
191C2#1059891811yescharacteristic
192C2#1059991812yes—
subgroupG/H
centerC2×C4D5×C22⋊C4
commutatorC2×C4×C5C22×C8
FrattiniC22×C8C22×D5
FittingC5×#1323C2
socleC22×C5C2×C22⋊C8
prime radicalC23×C5C2×M16
cosocleC22×C5×C8C23
hypercenter#1323D5
hypocenterC5#11497
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
179. C5#11497semidirect

Maximal subgroups

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

subgroupindex
#106108072
#105998862
C5×#13232
#105982092
#105980162
#114975