Finite Group Databasebeta

← #12017626

Subgroups — #12017626

Order 1280.

472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 107 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#10614206C211yesmaximal, characteristic
2C4×C5×#101C211yesmaximal, characteristic
3#10602430C211yesmaximal, characteristic
4C2×#64698C214yesmaximal
5C2×C4×C5×Q8C2211yescharacteristic
6C2×#4090C2212yes—
7C2×#4015C411yescharacteristic
8C2×C5×#101C2212yes—
9C4×C5×M16—21no—
10C2×#3968C2212yes—
11#65272—21no—
12#65272—21no—
13#65263C412yes—
14C4×C4⋊Dic5C411yescharacteristic
15#65217—21no—
16#65217—21no—
17#65213—21no—
18C5×#343—21no—
19#64750—21no—
20#64698—28no—
21#13227—51nomaximal, Sylow
22C22×C5×Q8C2311yescharacteristic
23C22×Dic10C2×C412yes—
24C2×C5×M16—22no—
25C4×C5×Q8—41no—
26C4×C5×Q8—41no—
27C2×C5×C4⋊C4C2×C411yescharacteristic
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C5×C4⋊C4D411yescharacteristic
30C2×C42×C5C2×C411yescharacteristic
31C2×C42×C5D411yescharacteristic
32C2×C42×C5D411yescharacteristic
33#4090—24no—
34#4090—24no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—21no—
38C2×#683—22no—
39C2×#683—22no—
40C2×C4×Dic5C2×C412yes—
41C2×#681—22no—
42#4015—41no—
43#4015—41no—
44C5×#101—22no—
45C5×#101D414yes—
46C5×#97—41no—
47C4×C5×C8—41no—
48#3968—24no—
49#3963—22no—
50#3963—22no—
51#3963—21no—
52C4⋊#168—41no—
53C4⋊#168—41no—
54#2546—51no—
55C2×#356—54no—
56#1801—51no—
57C4×#101D511yescharacteristic
58C2×C5×Q8—41no—
59C2×C5×Q8—41no—
60C2×C5×Q8C2×D412yes—
61C2×C5×Q8#4112yes—
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22×C411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×C4×C5C2×D411yescharacteristic
69C22×Dic5—22no—
70C22×Dic5—22no—
71C2×Dic10—24no—
72C2×Dic10—42no—
73C2×Dic10—42no—
74C5×M16—24no—
75C5×M16—42no—
76C2×C5×C8—42no—
77C5×C4⋊C4—41no—
78C5×C4⋊C4—41no—
79C5×C4⋊C4—41no—
80C42×C5—21no—
81C42×C5—21no—
82C42×C5—21no—
83C42×C5—21no—
84C42×C5—21no—
85C42×C5—21no—
86C4⋊Dic5—24no—
87C4⋊Dic5—42no—
88C4⋊Dic5—41no—
89C4⋊Dic5—41no—
90#683—44no—
91#683—42no—
92#683—42no—
93C4×Dic5—24no—
94#681—42no—
95#681—42no—
96C2×#168—42no—
97C2×C4⋊Q8—52no—
98C2×C4⋊Q8—51no—
99C2×C4×Q8C2×D511yescharacteristic
100#423—101no—
101C2×#101—52no—
102C2×#101C2×D512yes—
103C4×M16—21no—
104#398—101no—
105#398—101no—
106#391—52no—
107#389—101no—
108#389—101no—
109C4×C4⋊C4—51no—
110#356—108no—
111#343—21no—
112#343—101no—
113C23×C5C2×C22⋊C411yescharacteristic
114C5×Q8—42no—
115C5×Q8—42no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—22no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—41no—
127C2×C4×C5—41no—
128C2×C4×C5—41no—
129C2×C4×C5#9911yescharacteristic
130C2×C4×C5#9911yescharacteristic
131C2×C4×C5C4×D412yes—
132C2×C4×C5#12112yes—
133C2×C4×C5#12411yescharacteristic
134C2×C4×C5#12711yescharacteristic
135C2×Dic5—24no—
136C2×Dic5—42no—
137C2×Dic5—42no—
138C2×Dic5—42no—
139C2×Dic5—42no—
140C2×Dic5—42no—
141Dic10—84no—
142C5×C8—44no—
143#168—82no—
144C22×Q8—52no—
145C22×Q8C22×D511yescharacteristic
146C2×M16—22no—
147C2×M16—102no—
148C4⋊Q8—104no—
149C4⋊Q8—104no—
150C4⋊Q8—201no—
151C4⋊Q8—201no—
152C4×Q8—41no—
153C4×Q8—41no—
154C2×C4⋊C4—101no—
155C2×C4⋊C4—101no—
156C2×C4⋊C4—101no—
157C2×C4⋊C4—102no—
158C2×C4⋊C4—102no—
159C2×C4⋊C4C4×D511yescharacteristic
160C2×C4⋊C4D2011yescharacteristic
161C2×C4⋊C4C22⋊D511yescharacteristic
162C2×C42—52no—
163C2×C42C4×D511yescharacteristic
164C2×C42D2011yescharacteristic
165C2×C42C22⋊D511yescharacteristic
166C4⋊C8—201no—
167C4⋊C8—201no—
168#101—22no—
169#101—104no—
170#101D2014yes—
171#97—41no—
172C4×C8—41no—
173#95—101no—
174#95—102no—
175#95—102no—
176C22×C5—21no—
177C22×C5—21no—
178C22×C5#39011yescharacteristic
179C22×C5C2×#9911yescharacteristic
180C22×C5#41011yescharacteristic
181C4×C5—21no—
182C4×C5—21no—
183C4×C5—22no—
184C4×C5—22no—
185C4×C5—21no—
186C4×C5—41no—
187C4×C5—41no—
188C4×C5—41no—
189C4×C5#35612yescomplemented
190Dic5—44no—
191Dic5—82no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8—104no—
195C2×Q8—202no—
196C2×Q8—202no—
197C2×Q8C2×D2012yes—
198C2×Q8#70912yes—
199C22×C4—102no—
200C22×C4—102no—
201C22×C4#68511yescharacteristic
202C22×C4#68511yescharacteristic
203C22×C4#68511yescharacteristic
204C22×C4#68511yescharacteristic
205C22×C4C2×C4×D511yescharacteristic
206C22×C4C2×D2011yescharacteristic
207C22×C4C2×C22⋊D511yescharacteristic
208M16—24no—
209M16—42no—
210M16—202no—
211M16—202no—
212C2×C8—42no—
213C2×C8—202no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—104no—
218C4⋊C4—202no—
219C4⋊C4—201no—
220C4⋊C4—201no—
221C4⋊C4—202no—
222C4⋊C4—202no—
223C4⋊C4—204no—
224C42—21no—
225C42—21no—
226C42—21no—
227C42—21no—
228C42—21no—
229C42—21no—
230C42—104no—
231C2×C5—21no—
232C2×C5—21no—
233C2×C5#196411yescharacteristic
234C2×C5C2×#35611yescharacteristic
235C2×C5#213511yescharacteristic
236C23C2×#68511yescharacteristic
237Q8—42no—
238Q8—42no—
239Q8—404no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—104no—
254C2×C4—202no—
255C2×C4—202no—
256C2×C4—202no—
257C2×C4—202no—
258C2×C4—202no—
259C2×C4#393811yescharacteristic
260C2×C4#393811yescharacteristic
261C2×C4C4×D2012yes—
262C2×C4#402011yescharacteristic
263C2×C4#402111yescharacteristic
264C2×C4#407612yes—
265C8—44no—
266C8—402no—
267C5#1322711yescharacteristic, complemented, Sylow
268C22—21no—
269C22—21no—
270C22#6522811yescharacteristic
271C22C2×#393811yescharacteristic
272C22#6529511yescharacteristic
273C4—22no—
274C4—21no—
275C4—22no—
276C4—21no—
277C4—21no—
278C4—41no—
279C4—41no—
280C4—41no—
281C4—204no—
282C4—402no—
283C4#6469812yescomplemented
284C2—21no—
285C2—21no—
286C2#1060024911yescharacteristic
287C2C2×#6469811yescharacteristic
288C2#1060094311yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC22×Q8C22×D5
FittingC4×C5×#101C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC22×C5×Q8C23
hypercenterC4×#101D5
hypocenterC5#13227
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
189. C4×C5#356semidirect
267. C5#13227semidirect
283. C4#64698semidirect

Maximal subgroups

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

subgroupindex
#106142062
C4×C5×#1012
#106024302
C2×#646982
#132275