Finite Group Databasebeta

← #12003581

Subgroups — #12003581

Order 1280.

364 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 97 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#10610210C211yesmaximal, characteristic
2#10601585C212yesmaximal
3#10601569C212yesmaximal
4#10600629C211yesmaximal, characteristic
5C5×#1275C211yesmaximal, characteristic
6#65804C2212yes—
7C5×#431C2212yes—
8C2×C5×#97C2211yescharacteristic
9#65395—21no—
10#65395—21no—
11C2×#3946—21no—
12C4×C4⋊Dic5C2211yescharacteristic
13C2×C4⋊#168C2211yescharacteristic
14#64991—22no—
15#64991—22no—
16#64770—21no—
17#64702—22no—
18#64701—22no—
19#64687—22no—
20#64687—22no—
21#10548—51nomaximal, Sylow
22C22×C5×C8D411yescharacteristic
23C22×C5×C8D411yescharacteristic
24C2×C42×C5C2311yescharacteristic
25#4072—22no—
26C2×C4⋊Dic5—21no—
27#4070—22no—
28#4070—22no—
29C2×C4×Dic5—21no—
30C22×#168—21no—
31#4016—22no—
32#4015D412yes—
33#4015D412yes—
34C4×Dic10—22no—
35C4×Dic10—22no—
36C5×C4⋊C8—22no—
37C5×C22⋊C8—22no—
38C5×#97—22no—
39C4×C5×C8—22no—
40#3963D411yescharacteristic
41#3963D411yescharacteristic
42#3950—21no—
43#3950—21no—
44#3950—21no—
45#3950—21no—
46#3949—22no—
47#3949—22no—
48#3946—42no—
49C4⋊#168—22no—
50#3162—51no—
51#1940—51no—
52#1542—52no—
53#1503—52no—
54#1275D511yescharacteristic
55C22×C4×C5C2×D411yescharacteristic
56C22×C4×C5C2×D411yescharacteristic
57C22×C4×C5#4111yescharacteristic
58C22×Dic5—21no—
59C22×Dic5—21no—
60C2×Dic10—22no—
61C2×Dic10—22no—
62C2×C5×C8—21no—
63C2×C5×C8—21no—
64C2×C5×C8—21no—
65C2×C5×C8—21no—
66C2×C5×C8—42no—
67C2×C5×C8SD1612yes—
68C2×C5×C8Q1612yes—
69C42×C5C2×D412yes—
70C42×C5#4112yes—
71C22⋊Dic5—42no—
72C4⋊Dic5—22no—
73C4⋊Dic5—22no—
74C4⋊Dic5—22no—
75C4⋊Dic5—22no—
76C4⋊Dic5—42no—
77#683—42no—
78#683—42no—
79C4×Dic5—42no—
80C4×Dic5—41no—
81C4×Dic5—41no—
82C2×#168—41no—
83C2×#168—41no—
84C2×#168—41no—
85#533—52no—
86#501—102no—
87#501—102no—
88#431C2×D512yes—
89#427—101no—
90#427—101no—
91C2×C4⋊C8—51no—
92C2×C4⋊C8—101no—
93C2×#97C2×D511yescharacteristic
94C4×C4⋊C4—51no—
95#336—101no—
96#333—102no—
97#332—102no—
98#328—102no—
99#328—102no—
100C23×C5#12111yescharacteristic
101C2×C4×C5—41no—
102C2×C4×C5—41no—
103C2×C4×C5#12011yescharacteristic
104C2×C4×C5#12112yes—
105C2×C4×C5#12312yes—
106C2×C4×C5#12411yescharacteristic
107C2×C4×C5C2×SD1611yescharacteristic
108C2×C4×C5C2×Q1611yescharacteristic
109C2×C4×C5#13711yescharacteristic
110C2×C4×C5#13711yescharacteristic
111C2×Dic5—22no—
112C2×Dic5—41no—
113C2×Dic5—41no—
114C2×Dic5—41no—
115C2×Dic5—41no—
116C2×Dic5—42no—
117C2×Dic5—42no—
118C2×Dic5—41no—
119Dic10—82no—
120Dic10—82no—
121C5×C8—22no—
122C5×C8—22no—
123C5×C8—82no—
124#168—81no—
125C22×C8—101no—
126C22×C8D2011yescharacteristic
127C22×C8D2011yescharacteristic
128C4⋊Q8—52no—
129C4⋊Q8—52no—
130#125—102no—
131C22⋊Q8—102no—
132C22⋊Q8—102no—
133C4×Q8—102no—
134C4×Q8—102no—
135#117—102no—
136C2×C4⋊C4—101no—
137C2×C42—101no—
138C2×C42C22×D511yescharacteristic
139#107—101no—
140#107—101no—
141#107—101no—
142#107—101no—
143#106—102no—
144#106—102no—
145C4⋊C8—22no—
146C4⋊C8—102no—
147C4⋊C8—202no—
148C22⋊C8—22no—
149#97—22no—
150C4×C8—22no—
151#95—51no—
152#95—51no—
153C22×C5—21no—
154C22×C5—21no—
155C22×C5#39411yescharacteristic
156C22×C5#46111yescharacteristic
157C22×C5#46211yescharacteristic
158C4×C5—22no—
159C4×C5—22no—
160C4×C5#44811yescharacteristic
161C4×C5#45111yescharacteristic
162C4×C5#48711yescharacteristic
163C4×C5#49111yescharacteristic
164Dic5—42no—
165Dic5—81no—
166Dic5—82no—
167Dic5—82no—
168C2×Q8—102no—
169C2×Q8—102no—
170C22×C4—101no—
171C22×C4—101no—
172C22×C4C2×D2011yescharacteristic
173C22×C4D4×D511yescharacteristic
174C22×C4#71311yescharacteristic
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—42no—
180C2×C8—201no—
181C2×C8—201no—
182C2×C8—201no—
183C2×C8#67712yes—
184C2×C8Dic2012yes—
185C4⋊C4—102no—
186C4⋊C4—102no—
187C4⋊C4—102no—
188C4⋊C4—102no—
189C4⋊C4—202no—
190C4⋊C4—202no—
191C4⋊C4—202no—
192C22⋊C4—202no—
193C42—202no—
194C42—201no—
195C42—201no—
196C42#70912yes—
197C42D4×D512yes—
198C2×C5—21no—
199C2×C5—21no—
200C2×C5#204311yescharacteristic
201C2×C5#205011yescharacteristic
202C2×C5#205311yescharacteristic
203C23#404111yescharacteristic
204Q8—402no—
205Q8—402no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—102no—
209C2×C4—201no—
210C2×C4—201no—
211C2×C4—201no—
212C2×C4—201no—
213C2×C4—201no—
214C2×C4—202no—
215C2×C4—202no—
216C2×C4#402111yescharacteristic
217C2×C4#402811yescharacteristic
218C2×C4#403012yes—
219C2×C4#404012yes—
220C2×C4C2×#67711yescharacteristic
221C2×C4C2×Dic2011yescharacteristic
222C2×C4#405511yescharacteristic
223C2×C4#405511yescharacteristic
224C8—22no—
225C8—22no—
226C8—82no—
227C8—401no—
228C5#1054811yescharacteristic, complemented, Sylow
229C22—21no—
230C22—21no—
231C22#6496111yescharacteristic
232C22#6513011yescharacteristic
233C22#6513811yescharacteristic
234C4—22no—
235C4—22no—
236C4—202no—
237C4—401no—
238C4—402no—
239C4—402no—
240C4#6497011yescharacteristic
241C4#6499211yescharacteristic
242C4#6502711yescharacteristic
243C4#6502811yescharacteristic
244C2—21no—
245C2—21no—
246C2#1059942411yescharacteristic
247C2#1059949111yescharacteristic
248C2#1059951211yescharacteristic
subgroupG/H
centerC2×C4#4021
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1275C2
socleC22×C5#394
prime radicalC23×C5#121
hypercenter#1275D5
hypocenterC5#10548
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
228. C5#10548semidirect

Maximal subgroups

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

subgroupindex
#106102102
#106015852
#106015692
#106006292
C5×#12752
#105485