Finite Group Databasebeta

← #11992751

Subgroups — #11992751

Order 1280.

404 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 99 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#10605032C211yesmaximal, characteristic
2#10601575C212yesmaximal
3C5×#1276C211yesmaximal, characteristic, complemented
4#10598228C212yesmaximal, complemented
5#10598102C211yesmaximal, characteristic, complemented
6C2×#4018C2211yescharacteristic
7C5×#431C2212yes—
8C43×C5C2211yescharacteristic
9#65229—22no—
10C4×#685C412yes—
11#65222—22no—
12#65221C2211yescharacteristic
13C4×#683C412yes—
14#65214C2212yes—
15#64689—22no—
16#64688—22no—
17#8732—51nomaximal, Sylow
18C22×C4×D5C2×C411yescharacteristic
19C2×C42×C5—22no—
20C2×C42×C5C2×C412yes—
21C2×C42×C5C2311yescharacteristic
22C2×#685—22no—
23C2×#685D412yes—
24C2×#683—22no—
25C2×#683D412yes—
26C2×C4×Dic5C2×C412yes—
27C2×C4×Dic5C2×C411yescharacteristic
28#4018—22no—
29#4018—21no—
30#4018—21no—
31C5×C4⋊C8—22no—
32C5×C22⋊C8—22no—
33C4×C5×C8—22no—
34#3963—22no—
35#3963—22no—
36#3963—22no—
37C22⋊#168—22no—
38C4⋊#168—22no—
39C4×#168—22no—
40#2298—51no—
41#1458—52no—
42#1276—51no—
43#1276D511yescharacteristic, complemented
44#1274—52no—
45C23×D5C22⋊C411yescharacteristic
46C22×C4×C5—22no—
47C22×C4×C5C22×C411yescharacteristic
48C22×C4×C5C2×D412yes—
49C22×Dic5—22no—
50C22×Dic5C22⋊C411yescharacteristic
51C22×Dic5C22⋊C412yes—
52C2×C4×D5—21no—
53C2×C4×D5—21no—
54C2×C4×D5—22no—
55C2×C4×D5—22no—
56C2×C5×C8—42no—
57C42×C5—22no—
58C42×C5—22no—
59C42×C5—44no—
60C42×C5#4112yes—
61C42×C5#4111yescharacteristic
62C42×C5#4111yescharacteristic
63#685—22no—
64#685—22no—
65#685—44no—
66#683—22no—
67#683—22no—
68#683—44no—
69C4×Dic5—21no—
70C4×Dic5—21no—
71C4×Dic5—22no—
72C4×Dic5—22no—
73C2×#168—42no—
74C2×#117—51no—
75#431—52no—
76#431C2×D512yes—
77#388—102no—
78#387—102no—
79C4×C4⋊C4—52no—
80C4×C22⋊C4—52no—
81#376—51no—
82C43C2×D511yescharacteristic
83#324—102no—
84#323—102no—
85C23×C5C2×C22⋊C411yescharacteristic
86C22×D5—21no—
87C22×D5—22no—
88C22×D5—42no—
89C2×C4×C5—24no—
90C2×C4×C5—42no—
91C2×C4×C5—42no—
92C2×C4×C5—42no—
93C2×C4×C5#11711yescharacteristic
94C2×C4×C5#11711yescharacteristic
95C2×C4×C5#12312yes—
96C2×C4×C5#12312yes—
97C2×C4×C5#13112yes—
98C2×C4×C5#13112yes—
99C2×Dic5—22no—
100C2×Dic5—21no—
101C2×Dic5—22no—
102C2×Dic5—42no—
103C2×Dic5—42no—
104C2×Dic5—42no—
105C2×Dic5—42no—
106C4×D5—42no—
107C4×D5—41no—
108C4×D5—41no—
109C5×C8—82no—
110#168—82no—
111C23×C4—51no—
112#117—102no—
113#117—101no—
114#117—101no—
115C2×C4⋊C4—52no—
116C2×C4⋊C4—102no—
117C2×C22⋊C4—52no—
118C2×C22⋊C4—102no—
119C2×C42—22no—
120C2×C42—51no—
121C2×C42—52no—
122C2×C42C4×D512yes—
123C2×C42C22×D511yescharacteristic
124C4⋊C8—22no—
125C4⋊C8—102no—
126C22⋊C8—22no—
127C22⋊C8—102no—
128C4×C8—22no—
129C4×C8—102no—
130#95—102no—
131#95—102no—
132#95—102no—
133C22×C5—22no—
134C22×C5#38111yescharacteristic
135C22×C5#40812yes—
136C2×D5—41no—
137C2×D5—42no—
138C2×D5—82no—
139C4×C5—22no—
140C4×C5—22no—
141C4×C5—44no—
142C4×C5#43312yes—
143C4×C5#43311yescharacteristic
144C4×C5#43311yescharacteristic
145Dic5—41no—
146Dic5—42no—
147Dic5—82no—
148C24—51no—
149C22×C4—22no—
150C22×C4—51no—
151C22×C4—52no—
152C22×C4—101no—
153C22×C4—101no—
154C22×C4—102no—
155C22×C4—102no—
156C22×C4—102no—
157C22×C4C2×C4×D511yescharacteristic
158C22×C4D4×D512yes—
159C2×C8—42no—
160C2×C8—202no—
161C4⋊C4—102no—
162C4⋊C4—102no—
163C4⋊C4—204no—
164C22⋊C4—102no—
165C22⋊C4—102no—
166C22⋊C4—204no—
167C42—22no—
168C42—22no—
169C42—44no—
170C42—101no—
171C42—101no—
172C42—102no—
173C42—102no—
174C42#70912yes—
175C42#71111yescharacteristic
176C42#71311yescharacteristic
177C2×C5—22no—
178C2×C5#181811yescharacteristic
179C2×C5#182712yes—
180D5—81no—
181C23—101no—
182C23—102no—
183C23—202no—
184C23D5×C22⋊C411yescharacteristic
185C2×C4—24no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—102no—
190C2×C4—101no—
191C2×C4—102no—
192C2×C4—202no—
193C2×C4—201no—
194C2×C4—201no—
195C2×C4—202no—
196C2×C4—202no—
197C2×C4—202no—
198C2×C4—202no—
199C2×C4#401811yescharacteristic
200C2×C4#402912yes—
201C2×C4#403811yescharacteristic
202C2×C4#404012yes—
203C2×C4#404712yes—
204C2×C4#405312yes—
205C8—82no—
206C8—402no—
207C5#873211yescharacteristic, complemented, Sylow
208C22—22no—
209C22—201no—
210C22—202no—
211C22—402no—
212C22#6495311yescharacteristic
213C22#6501612yes—
214C4—22no—
215C4—22no—
216C4—44no—
217C4—201no—
218C4—202no—
219C4—402no—
220C4#6497911yescharacteristic
221C4#6499811yescharacteristic
222C4#6512912yes—
223C2—22no—
224C2—401no—
225C2#1059945811yescharacteristic
226C2#1059953012yes—
subgroupG/H
centerC2×C4#4038
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1276C2
socleC22×C5#381
prime radicalC23×D5C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1276D5
hypocenterC5#8732
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
3. C5×#1276C2semidirect
4. #10598228C2semidirect
5. #10598102C2semidirect
43. #1276D5semidirect
207. C5#8732semidirect

Maximal subgroups

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

subgroupindex
#106050322
#106015752
C5×#12762
#105982282
#105981022
#87325