Finite Group Databasebeta

← #12001654

Subgroups — #12001654

Order 1280.

560 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C5×#2582C211yesmaximal, characteristic
2C2×#65310C212yesmaximal
3C2×Q8⋊#168C212yesmaximal
4#10600372C211yesmaximal, characteristic
5#10598125C211yesmaximal, characteristic
6C2×C4×C5×Q8C2212yes—
7C2×#4015C2211yescharacteristic
8C5×#398—22no—
9C5×#391—22no—
10C5×#389—22no—
11C5×#384C2211yescharacteristic
12C2×#3967—22no—
13#65310—24no—
14#65310—24no—
15C2×#3942—22no—
16C2×#3939—22no—
17C2×C4⋊#168C2212yes—
18C2×C4×#168C2211yescharacteristic
19Q8⋊#168—24no—
20#10237—51nomaximal, Sylow
21C22×C5×Q8D412yes—
22C22×Dic10—21no—
23C4×C5×Q8—22no—
24C4×C5×Q8—22no—
25C4×C5×Q8—22no—
26C4×C5×Q8—22no—
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4D412yes—
31C2×C5×C4⋊C4D412yes—
32C2×C42×C5—22no—
33C2×C42×C5C2311yescharacteristic
34C2×C4⋊Dic5—22no—
35C22×#168—21no—
36C22×#168—22no—
37#4015—22no—
38#4015—21no—
39#4015D412yes—
40C5×#95—24no—
41C5×#95—22no—
42#3967—28no—
43#3942—44no—
44#3939—28no—
45C4⋊#168—22no—
46C4⋊#168D414yes—
47C4×#168—22no—
48C2×#477—52no—
49#2582D511yescharacteristic
50#1956—51no—
51C2×Q8⋊C8—52no—
52#1296—51no—
53C2×C5×Q8—22no—
54C2×C5×Q8—22no—
55C2×C5×Q8—22no—
56C2×C5×Q8—22no—
57C2×C5×Q8—22no—
58C2×C5×Q8Q1614yes—
59C22×C4×C5—22no—
60C22×C4×C5—22no—
61C22×C4×C5—22no—
62C22×C4×C5C2×D411yescharacteristic
63C22×C4×C5C2×D412yes—
64C22×Dic5—41no—
65C2×Dic10—22no—
66C2×Dic10—42no—
67C2×Dic10—42no—
68C2×Dic10—41no—
69C5×C4⋊C4—22no—
70C5×C4⋊C4—22no—
71C5×C4⋊C4—42no—
72C5×C4⋊C4—42no—
73C5×C4⋊C4—42no—
74C5×C4⋊C4—42no—
75C5×C4⋊C4—42no—
76C5×C4⋊C4—82no—
77C42×C5—42no—
78C42×C5—42no—
79C42×C5C2×D411yescharacteristic
80C42×C5C2×D412yes—
81C42×C5#4111yescharacteristic
82C4⋊Dic5—24no—
83C4⋊Dic5—42no—
84C2×#168—22no—
85C2×#168—24no—
86C2×#168—41no—
87C2×#168—41no—
88C2×#168—42no—
89C2×#168—42no—
90C2×C4⋊Q8—51no—
91C2×C4×Q8C2×D512yes—
92#477—104no—
93#477—104no—
94C2×#107—102no—
95C2×C4⋊C8—52no—
96C2×#103—102no—
97C2×#103—102no—
98C2×C4×C8—51no—
99#398—22no—
100#391—22no—
101#389—22no—
102#384C2×D511yescharacteristic
103Q8⋊C8—104no—
104C23×C5#12011yescharacteristic
105C5×Q8—24no—
106C5×Q8—24no—
107C5×Q8—42no—
108C5×Q8—42no—
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—24no—
112C2×C4×C5—42no—
113C2×C4×C5—42no—
114C2×C4×C5—42no—
115C2×C4×C5—44no—
116C2×C4×C5—42no—
117C2×C4×C5—42no—
118C2×C4×C5—42no—
119C2×C4×C5#12012yes—
120C2×C4×C5#12111yescharacteristic
121C2×C4×C5#12112yes—
122C2×C4×C5#12711yescharacteristic
123C2×C4×C5C2×Q1612yes—
124C2×C4×C5#13512yes—
125C2×C4×C5#13712yes—
126C2×C4×C5#13712yes—
127C2×Dic5—42no—
128C2×Dic5—81no—
129C2×Dic5—81no—
130Dic10—44no—
131Dic10—82no—
132#168—42no—
133#168—44no—
134C22×Q8—101no—
135C22×Q8C22⋊D512yes—
136C22×C8—101no—
137C22×C8—102no—
138C4⋊Q8—52no—
139C4⋊Q8—102no—
140C4⋊Q8—101no—
141C4×Q8—22no—
142C4×Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—102no—
149C2×C4⋊C4C22⋊D512yes—
150C2×C4⋊C4C22⋊D512yes—
151C2×C42—22no—
152C2×C42C22×D511yescharacteristic
153#107—108no—
154C4⋊C8—54no—
155C4⋊C8—102no—
156#103—108no—
157#103—204no—
158C4×C8—102no—
159#95—24no—
160#95—22no—
161C22×C5#39211yescharacteristic
162C22×C5#45112yes—
163C22×C5#45212yes—
164C22×C5#45311yescharacteristic
165C22×C5#45411yescharacteristic
166C4×C5—21no—
167C4×C5—21no—
168C4×C5—44no—
169C4×C5—82no—
170C4×C5—82no—
171C4×C5#45112yes—
172C4×C5#45212yes—
173C4×C5#46712yes—
174C4×C5#47012yes—
175Dic5—82no—
176C2×Q8—22no—
177C2×Q8—22no—
178C2×Q8—22no—
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—102no—
182C2×Q8—202no—
183C2×Q8—202no—
184C2×Q8—201no—
185C2×Q8#68914yes—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—201no—
190C22×C4C2×C22⋊D511yescharacteristic
191C22×C4C2×C22⋊D512yes—
192C2×C8—102no—
193C2×C8—104no—
194C2×C8—201no—
195C2×C8—202no—
196C2×C8—201no—
197C2×C8—202no—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—82no—
206C4⋊C4—104no—
207C4⋊C4—202no—
208C42—42no—
209C42—42no—
210C42D4×D511yescharacteristic
211C42D4×D512yes—
212C42#71111yescharacteristic
213C2×C5#163011yescharacteristic
214C2×C5#163311yescharacteristic
215C2×C5#163612yes—
216C2×C5#200112yes—
217C2×C5#200611yescharacteristic
218C23#409911yescharacteristic
219Q8—24no—
220Q8—24no—
221Q8—42no—
222Q8—42no—
223Q8—204no—
224Q8—402no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—24no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—44no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—202no—
236C2×C4—401no—
237C2×C4—401no—
238C2×C4#408312yes—
239C2×C4#408411yescharacteristic
240C2×C4#408512yes—
241C2×C4#408611yescharacteristic
242C2×C4#408812yes—
243C2×C4C2×#68912yes—
244C2×C4#409612yes—
245C2×C4#409712yes—
246C8—202no—
247C8—204no—
248C5#1023711yescharacteristic, complemented, Sylow
249C22#6551211yescharacteristic
250C22#6551712yes—
251C22#6552812yes—
252C22#6553011yescharacteristic
253C22#6553411yescharacteristic
254C4—21no—
255C4—21no—
256C4—44no—
257C4—82no—
258C4—82no—
259C4—402no—
260C4#6533612yes—
261C4#6533912yes—
262C4#6534012yes—
263C4#6534112yes—
264C2#1060249312yes—
265C2#1060267211yescharacteristic
266C2#1060272912yes—
267C2#1060273311yescharacteristic
268C2#1060273711yescharacteristic
subgroupG/H
centerC23#4099
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#2582C2
socle, prime radicalC23×C5#120
hypercenter#2582D5
hypocenterC5#10237
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2582

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
C5×#25822
C2×#653102
C2×Q8⋊#1682
#106003722
#105981252
#102375