Finite Group Databasebeta

← #12002373

Subgroups — #12002373

Order 1280.

400 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 91 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#10605949C211yesmaximal, characteristic
2C5×#1960C211yesmaximal, characteristic
3#10602581C212yesmaximal
4#10598150C212yesmaximal
5#10598121C211yesmaximal, characteristic
6C2×C5×C4⋊Q8C2211yescharacteristic
7C2×C5×#103—21no—
8C2×C5×#103—21no—
9C2×C5×#97C2211yescharacteristic
10C5×#382C2211yescharacteristic
11#65275—21no—
12#65268—21no—
13#65225C2212yes—
14C2×#3935C2212yes—
15#64949—22no—
16#64945—22no—
17#64749—22no—
18#64749—22no—
19#10359—51nomaximal, Sylow
20C22×C5×Q8—21no—
21C22×Dic10—21no—
22C22×C5×C8—21no—
23C5×C4⋊Q8—22no—
24C5×C4⋊Q8—21no—
25C5×C4⋊Q8Q812yescomplemented
26C2×C5×C4⋊C4—22no—
27C2×C5×C4⋊C4D411yescharacteristic
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C42×C5C2311yescharacteristic
30C2×C4⋊Dic5—21no—
31C2×C4⋊Dic5D412yes—
32C2×C4⋊Dic5D412yes—
33C2×#683—22no—
34C22×#168—22no—
35C5×#103—42no—
36C5×#103—42no—
37C5×#97—22no—
38C5×#95—22no—
39#3963—22no—
40#3963—21no—
41#3963—21no—
42#3963—22no—
43#3963—22no—
44#3935—22no—
45#3935—22no—
46#2844—51no—
47#1993—52no—
48#1960D511yescharacteristic
49#1295—52no—
50#1295—51no—
51C2×C5×Q8—22no—
52C2×C5×Q8—41no—
53C2×C5×Q8—41no—
54C2×C5×Q8—41no—
55C2×C5×Q8—41no—
56C2×C5×Q8—41no—
57C22×C4×C5—21no—
58C22×C4×C5—21no—
59C22×C4×C5—41no—
60C22×C4×C5C2×D412yes—
61C22×C4×C5C2×D411yescharacteristic
62C22×Dic5—22no—
63C22×Dic5—22no—
64C2×Dic10—81no—
65C2×Dic10—82no—
66C2×C5×C8—22no—
67C2×C5×C8—41no—
68C2×C5×C8—41no—
69C5×C4⋊C4—24no—
70C5×C4⋊C4—41no—
71C5×C4⋊C4—41no—
72C5×C4⋊C4—42no—
73C42×C5C2×Q811yescharacteristic
74C42×C5#4111yescharacteristic
75C42×C5#4112yes—
76C4⋊Dic5—42no—
77C4⋊Dic5—42no—
78C4⋊Dic5—81no—
79#683—82no—
80C2×#168—24no—
81C2×#168—42no—
82C2×#168—42no—
83C2×C4⋊Q8C2×D511yescharacteristic
84C2×#103—21no—
85C2×#103—21no—
86C2×#97—52no—
87C2×#97C2×D511yescharacteristic
88#400—102no—
89#400—101no—
90#395—102no—
91#395—101no—
92#382—52no—
93#382C2×D511yescharacteristic
94#340—102no—
95#340—102no—
96C23×C5#12011yescharacteristic
97C5×Q8—42no—
98C5×Q8—42no—
99C5×Q8—81no—
100C5×Q8—81no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—22no—
104C2×C4×C5—22no—
105C2×C4×C5—42no—
106C2×C4×C5—41no—
107C2×C4×C5—41no—
108C2×C4×C5—42no—
109C2×C4×C5—42no—
110C2×C4×C5—81no—
111C2×C4×C5—81no—
112C2×C4×C5C22⋊Q812yes—
113C2×C4×C5C22⋊Q811yescharacteristic
114C2×C4×C5#12412yes—
115C2×C4×C5#12411yescharacteristic
116C2×Dic5—42no—
117C2×Dic5—42no—
118C2×Dic5—42no—
119C2×Dic5—42no—
120C2×Dic5—42no—
121C2×Dic5—42no—
122Dic10—84no—
123C5×C8—42no—
124#168—44no—
125C22×Q8—21no—
126C22×Q8—101no—
127C22×C8—21no—
128C22×C8—102no—
129C4⋊Q8—21no—
130C4⋊Q8—22no—
131C4⋊Q8Dic1012yescomplemented
132C2×C4⋊C4—22no—
133C2×C4⋊C4—52no—
134C2×C4⋊C4—52no—
135C2×C4⋊C4—102no—
136C2×C4⋊C4—101no—
137C2×C4⋊C4C22⋊D511yescharacteristic
138C2×C4⋊C4C22⋊D511yescharacteristic
139C2×C42C22×D511yescharacteristic
140#103—42no—
141#103—42no—
142#97—22no—
143#97—102no—
144#97—102no—
145#95—22no—
146#95—102no—
147#95—101no—
148#95—101no—
149#95—102no—
150#95—102no—
151C22×C5#39311yescharacteristic
152C22×C5#45311yescharacteristic
153C22×C5#45411yescharacteristic
154C22×C5#45512yes—
155C22×C5#45612yes—
156C4×C5—21no—
157C4×C5—21no—
158C4×C5—22no—
159C4×C5—22no—
160C4×C5—81no—
161C4×C5—81no—
162C4×C5—82no—
163Dic5—82no—
164Dic5—82no—
165C2×Q8—22no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—41no—
169C2×Q8—41no—
170C2×Q8—41no—
171C2×Q8—401no—
172C2×Q8—402no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—41no—
176C22×C4—102no—
177C22×C4—102no—
178C22×C4D4×D512yes—
179C22×C4C2×C22⋊D511yescharacteristic
180C2×C8—22no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—104no—
184C2×C8—202no—
185C2×C8—202no—
186C4⋊C4—24no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—202no—
191C4⋊C4—202no—
192C4⋊C4—402no—
193C4⋊C4—401no—
194C42C2×Dic1011yescharacteristic
195C42#70911yescharacteristic
196C42#71112yes—
197C2×C5#165911yescharacteristic
198C2×C5#166011yescharacteristic
199C2×C5#166412yes—
200C2×C5#202711yescharacteristic
201C2×C5#202812yes—
202C23#408311yescharacteristic
203Q8—42no—
204Q8—42no—
205Q8—81no—
206Q8—81no—
207Q8—404no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—81no—
218C2×C4—81no—
219C2×C4—202no—
220C2×C4—202no—
221C2×C4—202no—
222C2×C4—202no—
223C2×C4—202no—
224C2×C4—202no—
225C2×C4#402412yes—
226C2×C4#403112yes—
227C2×C4#407011yescharacteristic
228C2×C4#408211yescharacteristic
229C8—42no—
230C8—204no—
231C5#1035911yescharacteristic, complemented, Sylow
232C22#6523611yescharacteristic
233C22#6535111yescharacteristic
234C22#6536611yescharacteristic
235C22#6549112yes—
236C22#6549412yes—
237C4—22no—
238C4—22no—
239C4—21no—
240C4—21no—
241C4—81no—
242C4—81no—
243C4—82no—
244C4—402no—
245C4—402no—
246C2#1060043611yescharacteristic
247C2#1060112612yes—
248C2#1060204612yes—
249C2#1060212211yescharacteristic
250C2#1060212311yescharacteristic
subgroupG/H
centerC23#4083
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1960C2
socle, prime radicalC23×C5#120
hypercenter#1960D5
hypocenterC5#10359
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
25. C5×C4⋊Q8Q8semidirect
131. C4⋊Q8Dic10semidirect
231. C5#10359semidirect

Maximal subgroups

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

subgroupindex
#106059492
C5×#19602
#106025812
#105981502
#105981212
#103595