Finite Group Databasebeta

← #11993769

Subgroups — #11993769

Order 1280.

476 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 147 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#10614961C211yesmaximal, characteristic
2C5×#1956C211yesmaximal, characteristic
3C2×#64766C211yesmaximal, characteristic
4#10600360C212yesmaximal
5#10598146C212yesmaximal
6C2×C5×C4⋊Q8C2211yescharacteristic
7C2×C5×#103—22no—
8C2×C4×C5×C8C2211yescharacteristic
9C5×#384C2211yescharacteristic
10#65519—22no—
11#65274—22no—
12C4⋊C4×Dic5—22no—
13C2×#3939—22no—
14C4×C4⋊Dic5C2212yes—
15C2×C4⋊#168C2212yes—
16#64766C414yescomplemented
17#64749—22no—
18#8929—51nomaximal, Sylow
19C22×C5×Q8D412yes—
20C22×C5×C8—21no—
21C5×C4⋊Q8—22no—
22C5×C4⋊Q8C2×C412yes—
23C5×C4⋊Q8Q812yes—
24C2×C5×C4⋊C4—22no—
25C2×C5×C4⋊C4—21no—
26C2×C5×C4⋊C4—22no—
27C2×C42×C5C2311yescharacteristic
28C2×C4⋊Dic5—22no—
29C2×C4⋊Dic5D412yes—
30C2×C4⋊Dic5D412yes—
31C2×C4×Dic5—22no—
32C2×C4×Dic5—22no—
33C22×#168—22no—
34C5×#103—44no—
35C4×C5×C8—22no—
36#3963—24no—
37#3963—22no—
38#3939—44no—
39C4⋊#168—22no—
40C4⋊#168C2×C414yes—
41#2369—51no—
42#1956D511yescharacteristic
43#1947—52no—
44C2×#333—51no—
45#1279—52no—
46C2×C5×Q8—22no—
47C2×C5×Q8—42no—
48C2×C5×Q8—42no—
49C2×C5×Q8C4⋊C414yes—
50C22×C4×C5—22no—
51C22×C4×C5—41no—
52C22×C4×C5C2×D412yes—
53C22×C4×C5C2×D411yescharacteristic
54C22×Dic5—22no—
55C22×Dic5—22no—
56C2×C5×C8—22no—
57C2×C5×C8—41no—
58C2×C5×C8—41no—
59C5×C4⋊C4—24no—
60C5×C4⋊C4—24no—
61C5×C4⋊C4—42no—
62C5×C4⋊C4—42no—
63C5×C4⋊C4—42no—
64C42×C5C22×C411yescharacteristic
65C42×C5C2×Q811yescharacteristic
66C42×C5#4112yes—
67C4⋊Dic5—22no—
68C4⋊Dic5—22no—
69C4⋊Dic5—22no—
70C4⋊Dic5—82no—
71C4⋊Dic5Q1614yes—
72C4×Dic5—42no—
73C4×Dic5—42no—
74C4×Dic5—82no—
75C2×#168—24no—
76C2×#168—42no—
77C2×#168—42no—
78C2×C4⋊Q8C2×D511yescharacteristic
79C2×#107—102no—
80C2×C4⋊C8—52no—
81C2×#103—22no—
82C2×C4×C8C2×D511yescharacteristic
83#391—102no—
84#389—102no—
85#384C2×D511yescharacteristic
86C4×C4⋊C4—52no—
87C4×C4⋊C4—102no—
88#340—102no—
89#333—54no—
90C23×C5#12011yescharacteristic
91C5×Q8—44no—
92C5×Q8—82no—
93C2×C4×C5—21no—
94C2×C4×C5—21no—
95C2×C4×C5—24no—
96C2×C4×C5—42no—
97C2×C4×C5—42no—
98C2×C4×C5—82no—
99C2×C4×C5—81no—
100C2×C4×C5C2×C4⋊C411yescharacteristic
101C2×C4×C5C4×D412yes—
102C2×C4×C5C22⋊Q812yes—
103C2×C4×C5#12311yescharacteristic
104C2×C4×C5C2×Q1612yes—
105C2×C4×C5#13512yes—
106C2×C4×C5AGL(1,ℤ/8)12yes—
107C2×C4×C5#13712yes—
108C2×Dic5—24no—
109C2×Dic5—42no—
110C2×Dic5—42no—
111C2×Dic5—42no—
112C2×Dic5—42no—
113C2×Dic5—42no—
114C5×C8—42no—
115#168—44no—
116C22×Q8C22⋊D512yes—
117C22×C8—21no—
118C22×C8—102no—
119C4⋊Q8—22no—
120C4⋊Q8Dic1012yes—
121C4⋊Q8C4×D512yes—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—52no—
126C2×C4⋊C4—52no—
127C2×C4⋊C4—102no—
128C2×C42—102no—
129C2×C42—102no—
130C2×C42C22×D511yescharacteristic
131#107—204no—
132C4⋊C8—54no—
133C4⋊C8—102no—
134#103—44no—
135C4×C8—22no—
136#95—104no—
137#95—102no—
138C22×C5#38511yescharacteristic
139C22×C5#44912yes—
140C22×C5#45112yes—
141C22×C5#45311yescharacteristic
142C22×C5#45511yescharacteristic
143C4×C5—21no—
144C4×C5—21no—
145C4×C5—44no—
146C4×C5—161no—
147C4×C5C4×Q1612yes—
148C4×C5#44012yes—
149C4×C5#47712yes—
150C4×C5#47912yes—
151Dic5—44no—
152Dic5—82no—
153C2×Q8—22no—
154C2×Q8—42no—
155C2×Q8—42no—
156C2×Q8#68314yes—
157C22×C4—22no—
158C22×C4—41no—
159C22×C4—102no—
160C22×C4—102no—
161C22×C4D4×D512yes—
162C22×C4C2×C22⋊D511yescharacteristic
163C2×C8—22no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—104no—
167C2×C8—202no—
168C2×C8—202no—
169C4⋊C4—24no—
170C4⋊C4—24no—
171C4⋊C4—42no—
172C4⋊C4—42no—
173C4⋊C4—42no—
174C4⋊C4—54no—
175C4⋊C4—102no—
176C4⋊C4—102no—
177C4⋊C4—102no—
178C4⋊C4—402no—
179C42—202no—
180C42—202no—
181C42—402no—
182C42C2×Dic1011yescharacteristic
183C42C2×C4×D511yescharacteristic
184C42#71112yes—
185C2×C5#162411yescharacteristic
186C2×C5#163311yescharacteristic
187C2×C5#164412yes—
188C2×C5#185611yescharacteristic
189C2×C5#186312yes—
190C23#408311yescharacteristic
191Q8—44no—
192Q8—82no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—24no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—81no—
199C2×C4—82no—
200C2×C4—104no—
201C2×C4—202no—
202C2×C4—202no—
203C2×C4—202no—
204C2×C4—202no—
205C2×C4—202no—
206C2×C4#402412yes—
207C2×C4#402712yes—
208C2×C4#406012yes—
209C2×C4#406212yes—
210C2×C4D5×Q1612yes—
211C2×C4#406412yes—
212C2×C4C2×#68311yescharacteristic
213C2×C4#408111yescharacteristic
214C8—42no—
215C8—204no—
216C5#892911yescharacteristic, complemented, Sylow
217C22#6523511yescharacteristic
218C22#6535011yescharacteristic
219C22#6536611yescharacteristic
220C22#6546112yes—
221C22#6547512yes—
222C4—21no—
223C4—21no—
224C4—44no—
225C4—161no—
226C4—204no—
227C4—402no—
228C4#6507912yes—
229C4#6508312yes—
230C4#6508812yes—
231C4#6510612yes—
232C2#1060043511yescharacteristic
233C2#1060102812yes—
234C2#1060203112yes—
235C2#1060205811yescharacteristic
236C2#1060210011yescharacteristic
subgroupG/H
centerC23#4083
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1956C2
socle, prime radicalC23×C5#120
cosocleC2×C42×C5C23
hypercenter#1956D5
hypocenterC5#8929
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
16. #64766C4semidirect
216. C5#8929semidirect

Maximal subgroups

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

subgroupindex
#106149612
C5×#19562
C2×#647662
#106003602
#105981462
#89295