Finite Group Databasebeta

← #12001656

Subgroups — #12001656

Order 1280.

560 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#65139C212yesmaximal
2#10606074C211yesmaximal, characteristic
3C2×#64704C212yesmaximal
4#10600372C211yesmaximal, characteristic
5C5×#1296C211yesmaximal, characteristic
6C2×#4015C2211yescharacteristic
7C2×C4×Dic10C2212yes—
8C2×C5×C4⋊C8C2212yes—
9C5×#384C2211yescharacteristic
10C2×#3950—22no—
11C2×#3948—22no—
12#65274—22no—
13#65272—22no—
14#65263—22no—
15C2×#3942—22no—
16C2×C4×#168C2211yescharacteristic
17#65139—24no—
18#65139—24no—
19#64704—24no—
20#10237—51nomaximal, Sylow
21C22×Dic10—21no—
22C22×Dic10D412yes—
23C22×C5×C8—22no—
24C2×C5×C4⋊C4—22no—
25C2×C5×C4⋊C4D412yes—
26C2×C42×C5C2311yescharacteristic
27C2×C4⋊Dic5—22no—
28C2×C4⋊Dic5—22no—
29C2×C4⋊Dic5D412yes—
30C2×#683—22no—
31C2×C4×Dic5—22no—
32C22×#168—21no—
33#4015—22no—
34#4015—21no—
35#4015D412yes—
36C4×Dic10—22no—
37C4×Dic10—22no—
38C4×Dic10—22no—
39C4×Dic10—22no—
40C5×C4⋊C8—22no—
41C5×C4⋊C8D414yes—
42#3963—22no—
43#3963—24no—
44#3950—28no—
45#3948—28no—
46#3942—44no—
47C4×#168—22no—
48C2×#477—52no—
49#2582—51no—
50#1956—51no—
51C2×Q8⋊C8—52no—
52#1296D511yescharacteristic
53C22×C4×C5—22no—
54C22×C4×C5C2×D411yescharacteristic
55C22×C4×C5C2×D412yes—
56C22×Dic5—22no—
57C22×Dic5—22no—
58C22×Dic5—41no—
59C2×Dic10—22no—
60C2×Dic10—22no—
61C2×Dic10—22no—
62C2×Dic10—22no—
63C2×Dic10—22no—
64C2×Dic10—22no—
65C2×Dic10—42no—
66C2×Dic10—42no—
67C2×Dic10—41no—
68C2×Dic10Q1614yes—
69C2×C5×C8—24no—
70C2×C5×C8—42no—
71C2×C5×C8—42no—
72C5×C4⋊C4—42no—
73C5×C4⋊C4—42no—
74C5×C4⋊C4—42no—
75C42×C5C2×D412yes—
76C42×C5C2×D411yescharacteristic
77C42×C5#4111yescharacteristic
78C4⋊Dic5—24no—
79C4⋊Dic5—22no—
80C4⋊Dic5—22no—
81C4⋊Dic5—42no—
82C4⋊Dic5—82no—
83#683—42no—
84#683—42no—
85C4×Dic5—42no—
86C4×Dic5—42no—
87C2×#168—22no—
88C2×#168—41no—
89C2×#168—41no—
90C2×C4⋊Q8—51no—
91C2×C4×Q8—52no—
92#477—104no—
93#477—104no—
94C2×#107—102no—
95C2×C4⋊C8C2×D512yes—
96C2×#103—102no—
97C2×#103—102no—
98C2×C4×C8—51no—
99#398—102no—
100#391—102no—
101#389—102no—
102#384C2×D511yescharacteristic
103Q8⋊C8—104no—
104C23×C5#12011yescharacteristic
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—44no—
108C2×C4×C5—42no—
109C2×C4×C5#12012yes—
110C2×C4×C5#12111yescharacteristic
111C2×C4×C5#12112yes—
112C2×C4×C5#12711yescharacteristic
113C2×C4×C5C2×Q1612yes—
114C2×C4×C5#13512yes—
115C2×C4×C5#13712yes—
116C2×C4×C5#13712yes—
117C2×Dic5—24no—
118C2×Dic5—42no—
119C2×Dic5—42no—
120C2×Dic5—42no—
121C2×Dic5—42no—
122C2×Dic5—42no—
123C2×Dic5—42no—
124C2×Dic5—81no—
125C2×Dic5—81no—
126Dic10—24no—
127Dic10—24no—
128Dic10—42no—
129Dic10—42no—
130Dic10—44no—
131Dic10—82no—
132C5×C8—44no—
133#168—42no—
134C22×Q8—52no—
135C22×Q8—101no—
136C22×C8—22no—
137C22×C8—101no—
138C4⋊Q8—52no—
139C4⋊Q8—102no—
140C4⋊Q8—101no—
141C4×Q8—102no—
142C4×Q8—102no—
143C4×Q8—102no—
144C4×Q8—102no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—52no—
147C2×C4⋊C4—102no—
148C2×C4⋊C4—102no—
149C2×C4⋊C4—102no—
150C2×C4⋊C4D2012yes—
151C2×C42—102no—
152C2×C42C22×D511yescharacteristic
153#107—108no—
154C4⋊C8—22no—
155C4⋊C8D2014yes—
156#103—108no—
157#103—204no—
158C4×C8—102no—
159#95—104no—
160#95—102no—
161C22×C5#39211yescharacteristic
162C22×C5#45112yes—
163C22×C5#45212yes—
164C22×C5#45311yescharacteristic
165C22×C5#45411yescharacteristic
166C4×C5—21no—
167C4×C5—21no—
168C4×C5—82no—
169C4×C5#45112yes—
170C4×C5#45212yes—
171C4×C5#46712yes—
172C4×C5#47012yes—
173Dic5—44no—
174Dic5—82no—
175Dic5—82no—
176C2×Q8—54no—
177C2×Q8—102no—
178C2×Q8—102no—
179C2×Q8—102no—
180C2×Q8—102no—
181C2×Q8—102no—
182C2×Q8—102no—
183C2×Q8—202no—
184C2×Q8—202no—
185C2×Q8—201no—
186C22×C4—22no—
187C22×C4—102no—
188C22×C4—102no—
189C22×C4—201no—
190C22×C4C2×D2011yescharacteristic
191C22×C4D4×D512yes—
192C2×C8—24no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—102no—
196C2×C8—201no—
197C2×C8—201no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—104no—
202C4⋊C4—102no—
203C4⋊C4—102no—
204C4⋊C4—202no—
205C4⋊C4—202no—
206C4⋊C4—202no—
207C4⋊C4—402no—
208C42—202no—
209C42—202no—
210C42C2×D2012yes—
211C42D4×D511yescharacteristic
212C42#71311yescharacteristic
213C2×C5#163011yescharacteristic
214C2×C5#163311yescharacteristic
215C2×C5#163612yes—
216C2×C5#200112yes—
217C2×C5#200611yescharacteristic
218C23#402811yescharacteristic
219Q8—104no—
220Q8—104no—
221Q8—204no—
222Q8—202no—
223Q8—202no—
224Q8—402no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—104no—
230C2×C4—202no—
231C2×C4—202no—
232C2×C4—202no—
233C2×C4—202no—
234C2×C4—202no—
235C2×C4—202no—
236C2×C4—401no—
237C2×C4—401no—
238C2×C4#402011yescharacteristic
239C2×C4#402812yes—
240C2×C4#404111yescharacteristic
241C2×C4#404112yes—
242C2×C4#405812yes—
243C2×C4#406112yes—
244C2×C4#406112yes—
245C2×C4D5×Q1612yes—
246C8—44no—
247C8—202no—
248C5#1023711yescharacteristic, complemented, Sylow
249C22#6496011yescharacteristic
250C22#6503611yescharacteristic
251C22#6504211yescharacteristic
252C22#6507212yes—
253C22#6509712yes—
254C4—21no—
255C4—21no—
256C4—82no—
257C4—204no—
258C4—402no—
259C4—402no—
260C4#6507212yes—
261C4#6509712yes—
262C4#6515712yes—
263C4#6517612yes—
264C2#1059919711yescharacteristic
265C2#1059925112yes—
266C2#1059929811yescharacteristic
267C2#1059968112yes—
268C2#1059980111yescharacteristic
subgroupG/H
centerC23#4028
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1296C2
socle, prime radicalC23×C5#120
hypercenter#1296D5
hypocenterC5#10237
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
248. C5#10237semidirect

Maximal subgroups

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

subgroupindex
C2×#651392
#106060742
C2×#647042
#106003722
C5×#12962
#102375