Finite Group Databasebeta

← #12001653

Subgroups — #12001653

Order 1280.

560 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 131 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×#65380C212yesmaximal
2#10606074C211yesmaximal, characteristic
3C5×#1956C211yesmaximal, characteristic
4C2×#64676C212yesmaximal
5#10598125C211yesmaximal, characteristic
6C2×C5×C4⋊Q8C2211yescharacteristic
7C2×C4×Dic10C2212yes—
8C2×C5×#103—22no—
9C2×C4×C5×C8C2211yescharacteristic
10C5×#384C2211yescharacteristic
11#65380—24no—
12#65380—24no—
13#65274—22no—
14#65272—22no—
15#65263—22no—
16C2×#3942—22no—
17C2×#3939—22no—
18C2×C4⋊#168C2212yes—
19#64676—24no—
20#10237—51nomaximal, Sylow
21C22×C5×Q8—21no—
22C22×Dic10D412yes—
23C22×C5×C8—21no—
24C5×C4⋊Q8—22no—
25C5×C4⋊Q8—21no—
26C5×C4⋊Q8D412yes—
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4D412yes—
30C2×C42×C5C2311yescharacteristic
31C2×C4⋊Dic5—22no—
32C2×C4⋊Dic5D412yes—
33C2×#683—22no—
34C2×C4×Dic5—22no—
35C22×#168—22no—
36C4×Dic10—22no—
37C4×Dic10—22no—
38C4×Dic10—22no—
39C4×Dic10—22no—
40C5×#103—44no—
41C4×C5×C8—22no—
42#3963—22no—
43#3963—24no—
44#3942—28no—
45#3939—28no—
46C4⋊#168—22no—
47C4⋊#168D414yes—
48C2×#477—52no—
49#2582—51no—
50#1956D511yescharacteristic
51C2×Q8⋊C8—52no—
52#1296—51no—
53C2×C5×Q8—22no—
54C2×C5×Q8—42no—
55C2×C5×Q8—42no—
56C2×C5×Q8—41no—
57C22×C4×C5—22no—
58C22×C4×C5—41no—
59C22×C4×C5C2×D412yes—
60C22×C4×C5C2×D411yescharacteristic
61C22×Dic5—22no—
62C22×Dic5—22no—
63C2×Dic10—22no—
64C2×Dic10—22no—
65C2×Dic10—22no—
66C2×Dic10—22no—
67C2×Dic10—22no—
68C2×Dic10Q1614yes—
69C2×C5×C8—22no—
70C2×C5×C8—41no—
71C2×C5×C8—41no—
72C5×C4⋊C4—24no—
73C5×C4⋊C4—42no—
74C5×C4⋊C4—42no—
75C5×C4⋊C4—42no—
76C5×C4⋊C4—42no—
77C42×C5C2×D411yescharacteristic
78C42×C5C2×D412yes—
79C42×C5#4111yescharacteristic
80C4⋊Dic5—22no—
81C4⋊Dic5—22no—
82C4⋊Dic5—82no—
83#683—42no—
84#683—42no—
85C4×Dic5—42no—
86C4×Dic5—42no—
87C2×#168—24no—
88C2×#168—42no—
89C2×#168—42no—
90C2×C4⋊Q8C2×D511yescharacteristic
91C2×C4×Q8—52no—
92#477—104no—
93#477—104no—
94C2×#107—102no—
95C2×C4⋊C8—52no—
96C2×#103—22no—
97C2×#103—102no—
98C2×C4×C8C2×D511yescharacteristic
99#398—102no—
100#391—102no—
101#389—102no—
102#384C2×D511yescharacteristic
103Q8⋊C8—104no—
104C23×C5#12011yescharacteristic
105C5×Q8—44no—
106C5×Q8—82no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—42no—
110C2×C4×C5—44no—
111C2×C4×C5—42no—
112C2×C4×C5—81no—
113C2×C4×C5—81no—
114C2×C4×C5#12012yes—
115C2×C4×C5#12112yes—
116C2×C4×C5#12111yescharacteristic
117C2×C4×C5#12711yescharacteristic
118C2×C4×C5C2×Q1612yes—
119C2×C4×C5#13512yes—
120C2×C4×C5#13712yes—
121C2×C4×C5#13712yes—
122C2×Dic5—24no—
123C2×Dic5—42no—
124C2×Dic5—42no—
125C2×Dic5—42no—
126C2×Dic5—42no—
127C2×Dic5—42no—
128Dic10—24no—
129Dic10—24no—
130Dic10—42no—
131Dic10—42no—
132C5×C8—42no—
133#168—44no—
134C22×Q8—21no—
135C22×Q8—52no—
136C22×C8—21no—
137C22×C8—102no—
138C4⋊Q8—21no—
139C4⋊Q8—22no—
140C4⋊Q8D2012yes—
141C4×Q8—102no—
142C4×Q8—102no—
143C4×Q8—102no—
144C4×Q8—102no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—52no—
148C2×C4⋊C4—102no—
149C2×C4⋊C4—102no—
150C2×C4⋊C4C22⋊D512yes—
151C2×C42—102no—
152C2×C42C22×D511yescharacteristic
153#107—108no—
154C4⋊C8—54no—
155C4⋊C8—102no—
156#103—44no—
157#103—108no—
158C4×C8—22no—
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—82no—
170C4×C5#45112yes—
171C4×C5#45212yes—
172C4×C5#46712yes—
173C4×C5#47012yes—
174Dic5—44no—
175Dic5—82no—
176C2×Q8—22no—
177C2×Q8—42no—
178C2×Q8—42no—
179C2×Q8—41no—
180C2×Q8—54no—
181C2×Q8—102no—
182C2×Q8—102no—
183C2×Q8—102no—
184C2×Q8—102no—
185C2×Q8—102no—
186C22×C4—22no—
187C22×C4—41no—
188C22×C4—102no—
189C22×C4—102no—
190C22×C4D4×D512yes—
191C22×C4C2×C22⋊D511yescharacteristic
192C2×C8—22no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—104no—
196C2×C8—202no—
197C2×C8—202no—
198C4⋊C4—24no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—102no—
204C4⋊C4—102no—
205C4⋊C4—202no—
206C4⋊C4—202no—
207C4⋊C4—402no—
208C42—202no—
209C42—202no—
210C42C2×D2011yescharacteristic
211C42#70911yescharacteristic
212C42D4×D512yes—
213C2×C5#163011yescharacteristic
214C2×C5#163311yescharacteristic
215C2×C5#163612yes—
216C2×C5#200112yes—
217C2×C5#200611yescharacteristic
218C23#408311yescharacteristic
219Q8—44no—
220Q8—82no—
221Q8—104no—
222Q8—104no—
223Q8—202no—
224Q8—202no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—104no—
233C2×C4—202no—
234C2×C4—202no—
235C2×C4—202no—
236C2×C4—202no—
237C2×C4—202no—
238C2×C4#402812yes—
239C2×C4#403012yes—
240C2×C4#406112yes—
241C2×C4#406212yes—
242C2×C4D5×Q1612yes—
243C2×C4#406412yes—
244C2×C4#407611yescharacteristic
245C2×C4#408611yescharacteristic
246C8—42no—
247C8—204no—
248C5#1023711yescharacteristic, complemented, Sylow
249C22#6524911yescharacteristic
250C22#6535111yescharacteristic
251C22#6536611yescharacteristic
252C22#6546212yes—
253C22#6547512yes—
254C4—21no—
255C4—21no—
256C4—82no—
257C4—82no—
258C4—204no—
259C4—402no—
260C4#6509712yes—
261C4#6509912yes—
262C4#6510212yes—
263C4#6510512yes—
264C2#1060045711yescharacteristic
265C2#1060106612yes—
266C2#1060202912yes—
267C2#1060206311yescharacteristic
268C2#1060210011yescharacteristic
subgroupG/H
centerC23#4083
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1956C2
socle, prime radicalC23×C5#120
hypercenter#1956D5
hypocenterC5#10237
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

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×#653802
#106060742
C5×#19562
C2×#646762
#105981252
#102375