Finite Group Databasebeta

← #11996678

Subgroups — #11996678

Order 1280.

470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 131 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#10614210C211yesmaximal, characteristic
2#10614166C211yesmaximal, characteristic
3C5×#1801C211yesmaximal, characteristic
4#10601301C212yesmaximal
5#10598206C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×#4015C2211yescharacteristic
8C5×#423C2212yes—
9C2×C5×#101—21no—
10#65519—21no—
11Q8×#168—24no—
12#65275C414yes—
13#65266—21no—
14C4×C4⋊Dic5C2211yescharacteristic
15#65218—22no—
16#65214—22no—
17#65214C2212yes—
18C5×#343—21no—
19#64706—24no—
20#9396—51nomaximal, Sylow
21C22×C5×Q8D411yescharacteristic
22C22×Dic10—21no—
23C2×C5×M16—22no—
24C4×C5×Q8—22no—
25C4×C5×Q8—22no—
26C2×C5×C4⋊C4C2×C412yes—
27C2×C5×C4⋊C4D411yescharacteristic
28C2×C42×C5D412yes—
29C2×C42×C5C2311yescharacteristic
30C2×C4⋊Dic5—21no—
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5C2×C412yes—
33C2×C4×Dic5—21no—
34#4015—22no—
35#4015—22no—
36C5×C4⋊C8—22no—
37C5×C4⋊C8—22no—
38C5×#101—42no—
39#3963—24no—
40#3963—24no—
41#3963C2×C412yes—
42C22⋊#168—22no—
43C4⋊#168—24no—
44C4⋊#168D414yes—
45C4×#168—24no—
46C4×#168—22no—
47#2982—51no—
48#2568—51no—
49#1801D511yescharacteristic
50#1549—52no—
51#1303—52no—
52C2×C5×Q8—22no—
53C2×C5×Q8—22no—
54C2×C5×Q8SD1612yes—
55C2×C5×Q8Q1612yes—
56C22×C4×C5C22⋊C412yes—
57C22×C4×C5C22⋊C412yes—
58C22×C4×C5C22×C411yescharacteristic
59C22×C4×C5C2×D411yescharacteristic
60C22×C4×C5C2×D411yescharacteristic
61C22×Dic5—22no—
62C22×Dic5—22no—
63C2×Dic10—44no—
64C2×Dic10—41no—
65C2×Dic10—41no—
66C5×M16—42no—
67C5×M16—42no—
68C2×C5×C8—42no—
69C5×C4⋊C4—24no—
70C5×C4⋊C4—22no—
71C42×C5—22no—
72C42×C5—22no—
73C42×C5C2×D412yes—
74C42×C5#4112yes—
75C4⋊Dic5—24no—
76C4⋊Dic5—42no—
77C4⋊Dic5—42no—
78C4×Dic5—42no—
79C2×#168—24no—
80C2×C4⋊Q8—51no—
81C2×C4×Q8C2×D511yescharacteristic
82C8×Q8—104no—
83#431—52no—
84#431—102no—
85#423C2×D512yes—
86C2×#101—21no—
87#400—54no—
88#391—101no—
89#391—102no—
90#382—101no—
91C4×C4⋊C4—51no—
92#343—21no—
93#332—104no—
94C23×C5C2×C22⋊C411yescharacteristic
95C5×Q8—24no—
96C5×Q8—24no—
97C2×C4×C5—22no—
98C2×C4×C5—22no—
99C2×C4×C5—22no—
100C2×C4×C5—22no—
101C2×C4×C5—41no—
102C2×C4×C5—42no—
103C2×C4×C5#10314yes—
104C2×C4×C5C4×D412yes—
105C2×C4×C5#12011yescharacteristic
106C2×C4×C5#12112yes—
107C2×C4×C5#12311yescharacteristic
108C2×C4×C5C2×SD1611yescharacteristic
109C2×C4×C5C2×Q1611yescharacteristic
110C2×C4×C5#13512yes—
111C2×Dic5—42no—
112C2×Dic5—44no—
113C2×Dic5—42no—
114C2×Dic5—42no—
115C2×Dic5—42no—
116Dic10—82no—
117Dic10—82no—
118C5×C8—82no—
119#168—44no—
120C22×Q8—101no—
121C22×Q8C22⋊D511yescharacteristic
122C2×M16—22no—
123C4⋊Q8—102no—
124C4⋊Q8—102no—
125C4×Q8—22no—
126C4×Q8—22no—
127C2×C4⋊C4—52no—
128C2×C4⋊C4—101no—
129C2×C4⋊C4—101no—
130C2×C4⋊C4C4×D512yes—
131C2×C4⋊C4C22⋊D511yescharacteristic
132C2×C42—101no—
133C2×C42D2012yes—
134C2×C42C22×D511yescharacteristic
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8—54no—
138C4⋊C8—104no—
139#101—42no—
140C22⋊C8—102no—
141C4×C8—104no—
142C4×C8—102no—
143#95—52no—
144#95—104no—
145#95—104no—
146C22×C5—21no—
147C22×C5—21no—
148C22×C5#38611yescharacteristic
149C22×C5C2×#10311yescharacteristic
150C22×C5#41611yescharacteristic
151C4×C5—21no—
152C4×C5—24no—
153C4×C5—22no—
154C4×C5—42no—
155C4×C5#45412yes—
156C4×C5#46512yes—
157C4×C5#46712yes—
158Dic5—82no—
159Dic5—82no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—204no—
163C2×Q8—201no—
164C2×Q8—201no—
165C2×Q8#68712yes—
166C2×Q8#68912yes—
167C22×C4—102no—
168C22×C4—102no—
169C22×C4#68512yes—
170C22×C4#68512yes—
171C22×C4C2×C4×D511yescharacteristic
172C22×C4C2×D2011yescharacteristic
173C22×C4C2×C22⋊D511yescharacteristic
174M16—42no—
175M16—42no—
176C2×C8—42no—
177C2×C8—104no—
178C4⋊C4—24no—
179C4⋊C4—22no—
180C4⋊C4—104no—
181C4⋊C4—202no—
182C4⋊C4—202no—
183C42—22no—
184C42—22no—
185C42—202no—
186C42D4×D512yes—
187C42#71112yes—
188C2×C5—21no—
189C2×C5—21no—
190C2×C5#188811yescharacteristic
191C2×C5#189211yescharacteristic
192C2×C5#191511yescharacteristic
193C23C2×#68511yescharacteristic
194Q8—24no—
195Q8—24no—
196Q8—402no—
197Q8—402no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—42no—
204C2×C4—202no—
205C2×C4—204no—
206C2×C4—202no—
207C2×C4—202no—
208C2×C4—202no—
209C2×C4#394214yes—
210C2×C4#402712yes—
211C2×C4#402811yescharacteristic
212C2×C4#403211yescharacteristic
213C2×C4C2×#68711yescharacteristic
214C2×C4#408512yes—
215C2×C4C2×#68911yescharacteristic
216C2×C4#409612yes—
217C8—82no—
218C8—204no—
219C5#939611yescharacteristic, complemented, Sylow
220C22—21no—
221C22—21no—
222C22#6524711yescharacteristic
223C22C2×#394211yescharacteristic
224C22#6529111yescharacteristic
225C4—24no—
226C4—21no—
227C4—22no—
228C4—42no—
229C4—402no—
230C4—402no—
231C4#6504212yes—
232C4#6533012yes—
233C4#6534012yes—
234C2—21no—
235C2—21no—
236C2#1060030711yescharacteristic
237C2#1060089711yescharacteristic
238C2#1060093111yescharacteristic
subgroupG/H
centerC22#65247
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1801C2
socleC22×C5#386
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1801D5
hypocenterC5#9396
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
219. C5#9396semidirect

Maximal subgroups

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

subgroupindex
#106142102
#106141662
C5×#18012
#106013012
#105982062
#93965