Finite Group Databasebeta

← #11991046

Subgroups — #11991046

Order 1280.

706 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 143 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×#65904C211yesmaximal, characteristic
2C5×#1461C211yesmaximal, characteristic
3#10602430C211yesmaximal, characteristic
4#10601572C212yesmaximal
5#10601563C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×Q8×Dic5—21no—
8#65904—24no—
9#65904—24no—
10C2×#4036—21no—
11C2×#4036—22no—
12C2×#4015C412yes—
13C2×#4015C2211yescharacteristic
14C2×C4×Dic10C412yes—
15C2×C4×Dic10C2211yescharacteristic
16C5×#431C2212yes—
17C2×#3968—21no—
18#65213C2212yes—
19C5×#324—22no—
20#64750—21no—
21#64701—24no—
22#64676—24no—
23#8392—51nomaximal, Sylow
24C22×C5×Q8D411yescharacteristic
25C22×Dic10C2×C412yes—
26C22×Dic10C2×C411yescharacteristic
27C4×C5×Q8—22no—
28C4×C5×Q8—22no—
29C2×C5×C4⋊C4D411yescharacteristic
30C2×C5×C4⋊C4D412yes—
31C2×C42×C5C2×C412yes—
32C2×C42×C5C2311yescharacteristic
33Q8×Dic5—28no—
34C2×C4⋊Dic5—22no—
35C2×C4⋊Dic5—22no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—21no—
38C2×C4⋊Dic5C2×C411yescharacteristic
39C2×#683—22no—
40C2×#683—21no—
41C2×C4×Dic5—22no—
42C2×C4×Dic5—21no—
43C2×#681—22no—
44#4036—216no—
45#4036—28no—
46#4015—24no—
47#4015—24no—
48#4015—22no—
49#4015D414yes—
50C4×Dic10—24no—
51C4×Dic10—22no—
52C4×Dic10—24no—
53C4×Dic10D414yes—
54C5×C4⋊C8—22no—
55C5×C22⋊C8—22no—
56C4×C5×C8—22no—
57#3968—42no—
58C4⋊#168—22no—
59C4⋊#168—22no—
60C2×#557—51no—
61#1801—51no—
62#1548—52no—
63#1487—52no—
64#1461D511yescharacteristic
65C2×C5×Q8—22no—
66C2×C5×Q8—22no—
67C2×C5×Q8SD1612yes—
68C2×C5×Q8Q1612yes—
69C22×C4×C5C22⋊C412yes—
70C22×C4×C5C22⋊C412yes—
71C22×C4×C5C22×C411yescharacteristic
72C22×C4×C5C2×D411yescharacteristic
73C22×C4×C5C2×D411yescharacteristic
74C22×Dic5—22no—
75C22×Dic5—21no—
76C22×Dic5—21no—
77C2×Dic10—21no—
78C2×Dic10—22no—
79C2×Dic10—42no—
80C2×Dic10—44no—
81C2×Dic10C22⋊C412yes—
82C2×Dic10C22⋊C414yes—
83C2×C5×C8—42no—
84C5×C4⋊C4—22no—
85C5×C4⋊C4—24no—
86C42×C5—22no—
87C42×C5—22no—
88C42×C5C2×D412yes—
89C42×C5C2×D412yes—
90C4⋊Dic5—28no—
91C4⋊Dic5—28no—
92C4⋊Dic5—21no—
93C4⋊Dic5—24no—
94C4⋊Dic5—24no—
95C4⋊Dic5C22⋊C412yes—
96#683—28no—
97#683—24no—
98C4×Dic5—28no—
99C4×Dic5—24no—
100#681—42no—
101#681—42no—
102C2×#168—42no—
103#557—104no—
104#557—104no—
105C2×C4⋊Q8—52no—
106C2×C4⋊Q8—51no—
107C2×#125—101no—
108C2×#125—102no—
109C2×C4×Q8—52no—
110C2×C4×Q8—51no—
111C2×C4×Q8—101no—
112C2×C4×Q8C2×D511yescharacteristic
113#431C2×D512yes—
114#423—52no—
115C2×#101—101no—
116#343—101no—
117#333—104no—
118Q8⋊C8—104no—
119#324—22no—
120C23×C5C2×C22⋊C411yescharacteristic
121C5×Q8—24no—
122C5×Q8—24no—
123C2×C4×C5—22no—
124C2×C4×C5—22no—
125C2×C4×C5—22no—
126C2×C4×C5—22no—
127C2×C4×C5—41no—
128C2×C4×C5—42no—
129C2×C4×C5#10314yes—
130C2×C4×C5C2×C22⋊C411yescharacteristic
131C2×C4×C5C2×C22⋊C411yescharacteristic
132C2×C4×C5#12012yes—
133C2×C4×C5#12012yes—
134C2×C4×C5C2×SD1611yescharacteristic
135C2×C4×C5C2×Q1611yescharacteristic
136C2×C4×C5#13712yes—
137C2×Dic5—22no—
138C2×Dic5—22no—
139C2×Dic5—24no—
140C2×Dic5—42no—
141C2×Dic5—44no—
142C2×Dic5—42no—
143Dic10—24no—
144Dic10—42no—
145Dic10—44no—
146Dic10—44no—
147C5×C8—82no—
148#168—82no—
149C22×Q8—51no—
150C22×Q8—52no—
151C22×Q8D2011yescharacteristic
152C2×M16—102no—
153C4⋊Q8—54no—
154C4⋊Q8—104no—
155C4⋊Q8—104no—
156C4⋊Q8—102no—
157#125—1016no—
158#125—108no—
159C4×Q8—22no—
160C4×Q8—22no—
161C4×Q8—54no—
162C4×Q8—104no—
163C4×Q8—104no—
164C4×Q8—108no—
165C4×Q8—102no—
166C2×C4⋊C4—51no—
167C2×C4⋊C4—102no—
168C2×C4⋊C4—102no—
169C2×C4⋊C4—102no—
170C2×C4⋊C4—101no—
171C2×C4⋊C4—101no—
172C2×C4⋊C4—101no—
173C2×C4⋊C4D2011yescharacteristic
174C2×C4⋊C4C22⋊D512yes—
175C2×C42—102no—
176C2×C42—101no—
177C2×C42C4×D512yes—
178C2×C42C22×D511yescharacteristic
179C4⋊C8—22no—
180C4⋊C8—102no—
181C4⋊C8—102no—
182#101—202no—
183C22⋊C8—22no—
184C4×C8—22no—
185C22×C5—21no—
186C22×C5—21no—
187C22×C5#37911yescharacteristic
188C22×C5C2×#10311yescharacteristic
189C22×C5#41911yescharacteristic
190C4×C5—22no—
191C4×C5—21no—
192C4×C5—24no—
193C4×C5—42no—
194C4×C5#41312yes—
195C4×C5#44812yes—
196C4×C5#45112yes—
197Dic5—42no—
198Dic5—42no—
199Dic5—44no—
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—52no—
203C2×Q8—54no—
204C2×Q8—101no—
205C2×Q8—102no—
206C2×Q8—202no—
207C2×Q8—204no—
208C2×Q8#67712yes—
209C2×Q8Dic2012yes—
210C22×C4—101no—
211C22×C4—102no—
212C22×C4—101no—
213C22×C4#68512yes—
214C22×C4#68512yes—
215C22×C4C2×C4×D511yescharacteristic
216C22×C4C2×D2011yescharacteristic
217C22×C4C2×C22⋊D511yescharacteristic
218M16—202no—
219M16—202no—
220C2×C8—42no—
221C2×C8—202no—
222C4⋊C4—22no—
223C4⋊C4—24no—
224C4⋊C4—52no—
225C4⋊C4—108no—
226C4⋊C4—108no—
227C4⋊C4—108no—
228C4⋊C4—101no—
229C4⋊C4—104no—
230C4⋊C4—104no—
231C4⋊C4—104no—
232C42—22no—
233C42—22no—
234C42—108no—
235C42—104no—
236C42D4×D512yes—
237C42D4×D512yes—
238C2×C5—21no—
239C2×C5—21no—
240C2×C5#178511yescharacteristic
241C2×C5#178711yescharacteristic
242C2×C5#179611yescharacteristic
243C23C2×#68511yescharacteristic
244Q8—24no—
245Q8—24no—
246Q8—104no—
247Q8—204no—
248Q8—202no—
249Q8—204no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—102no—
257C2×C4—102no—
258C2×C4—104no—
259C2×C4—202no—
260C2×C4—204no—
261C2×C4—202no—
262C2×C4#394814yes—
263C2×C4D5×C22⋊C411yescharacteristic
264C2×C4D5×C22⋊C411yescharacteristic
265C2×C4#402812yes—
266C2×C4C2×#67711yescharacteristic
267C2×C4C2×Dic2011yescharacteristic
268C2×C4#405512yes—
269C2×C4#408312yes—
270C8—82no—
271C8—402no—
272C5#839211yescharacteristic, complemented, Sylow
273C22—21no—
274C22—21no—
275C22#6524411yescharacteristic
276C22C2×#394811yescharacteristic
277C22#6540911yescharacteristic
278C4—24no—
279C4—22no—
280C4—21no—
281C4—42no—
282C4—202no—
283C4—202no—
284C4—204no—
285C4#6502712yes—
286C4#6502812yes—
287C4#6504012yes—
288C2—21no—
289C2—21no—
290C2#1060075611yescharacteristic
291C2#1060084411yescharacteristic
292C2#1060090711yescharacteristic
subgroupG/H
centerC22#65244
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1461C2
socleC22×C5#379
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1461D5
hypocenterC5#8392
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
272. C5#8392semidirect

Maximal subgroups

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

subgroupindex
C2×#659042
C5×#14612
#106024302
#106015722
#106015632
#83925