Finite Group Databasebeta

← #11991066

Subgroups — #11991066

Order 1280.

738 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 147 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×Q8×Dic10C211yesmaximal, characteristic
2C5×#1461C211yesmaximal, characteristic
3#10602430C211yesmaximal, characteristic
4#10601573C212yesmaximal
5#10601563C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×Q8×Dic5—21no—
8Q8×Dic10—24no—
9Q8×Dic10—24no—
10C2×#4034—21no—
11C2×#4034—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#64702—24no—
22#64676—24no—
23#8396—51nomaximal, Sylow
24C22×C5×Q8D411yescharacteristic
25C22×Dic10—22no—
26C22×Dic10—21no—
27C22×Dic10C2×C411yescharacteristic
28C4×C5×Q8—22no—
29C4×C5×Q8—22no—
30C2×C5×C4⋊C4D411yescharacteristic
31C2×C5×C4⋊C4D412yes—
32C2×C42×C5C2×C412yes—
33C2×C42×C5C2311yescharacteristic
34Q8×Dic5—28no—
35C2×C4⋊Dic5—22no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5C2×C412yes—
38C2×C4⋊Dic5C2×C411yescharacteristic
39C2×#683—22no—
40C2×#683—21no—
41C2×C4×Dic5—22no—
42C2×C4×Dic5—21no—
43C2×#681—22no—
44#4034—216no—
45#4034—28no—
46#4015—22no—
47#4015—24no—
48#4015—24no—
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×Q82—51no—
61#1801—51no—
62#1549—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—21no—
75C22×Dic5—21no—
76C22×Dic5—22no—
77C2×Dic10—21no—
78C2×Dic10—24no—
79C2×Dic10—28no—
80C2×Dic10—24no—
81C2×Dic10—82no—
82C2×Dic10—84no—
83C2×Dic10C22⋊C412yes—
84C2×C5×C8—42no—
85C5×C4⋊C4—22no—
86C5×C4⋊C4—24no—
87C42×C5—22no—
88C42×C5—22no—
89C42×C5C2×D412yes—
90C42×C5C2×D412yes—
91C4⋊Dic5—28no—
92C4⋊Dic5—21no—
93C4⋊Dic5—22no—
94C4⋊Dic5—24no—
95C4⋊Dic5C22⋊C414yes—
96C4⋊Dic5C22⋊C412yes—
97#683—28no—
98#683—24no—
99C4×Dic5—28no—
100C4×Dic5—24no—
101#681—42no—
102#681—42no—
103C2×#168—42no—
104Q82—104no—
105Q82—104no—
106C2×C4⋊Q8—52no—
107C2×C4⋊Q8—51no—
108C2×C4⋊Q8—101no—
109C2×C4⋊Q8—102no—
110C2×C4×Q8—52no—
111C2×C4×Q8—51no—
112C2×C4×Q8—101no—
113C2×C4×Q8C2×D511yescharacteristic
114#431C2×D512yes—
115#423—52no—
116C2×#101—101no—
117#343—101no—
118#332—104no—
119Q8⋊C8—104no—
120#324—22no—
121C23×C5C2×C22⋊C411yescharacteristic
122C5×Q8—24no—
123C5×Q8—24no—
124C2×C4×C5—22no—
125C2×C4×C5—22no—
126C2×C4×C5—22no—
127C2×C4×C5—22no—
128C2×C4×C5—41no—
129C2×C4×C5—42no—
130C2×C4×C5#10314yes—
131C2×C4×C5C2×C22⋊C411yescharacteristic
132C2×C4×C5C2×C22⋊C411yescharacteristic
133C2×C4×C5#12012yes—
134C2×C4×C5#12012yes—
135C2×C4×C5C2×SD1611yescharacteristic
136C2×C4×C5C2×Q1611yescharacteristic
137C2×C4×C5#13712yes—
138C2×Dic5—24no—
139C2×Dic5—22no—
140C2×Dic5—24no—
141C2×Dic5—22no—
142C2×Dic5—44no—
143C2×Dic5—42no—
144Dic10—24no—
145Dic10—22no—
146Dic10—84no—
147Dic10—88no—
148Dic10#10114yescomplemented
149C5×C8—82no—
150#168—82no—
151C22×Q8—51no—
152C22×Q8—102no—
153C22×Q8—101no—
154C22×Q8D2011yescharacteristic
155C2×M16—102no—
156C4⋊Q8—54no—
157C4⋊Q8—104no—
158C4⋊Q8—104no—
159C4⋊Q8—1016no—
160C4⋊Q8—108no—
161C4⋊Q8—102no—
162C4×Q8—22no—
163C4×Q8—22no—
164C4×Q8—54no—
165C4×Q8—104no—
166C4×Q8—104no—
167C4×Q8—108no—
168C4×Q8—102no—
169C2×C4⋊C4—51no—
170C2×C4⋊C4—52no—
171C2×C4⋊C4—102no—
172C2×C4⋊C4—102no—
173C2×C4⋊C4—101no—
174C2×C4⋊C4—101no—
175C2×C4⋊C4D2011yescharacteristic
176C2×C4⋊C4C22⋊D512yes—
177C2×C42—102no—
178C2×C42—101no—
179C2×C42C4×D512yes—
180C2×C42C22×D511yescharacteristic
181C4⋊C8—22no—
182C4⋊C8—102no—
183C4⋊C8—102no—
184#101—202no—
185C22⋊C8—22no—
186C4×C8—22no—
187C22×C5—21no—
188C22×C5—21no—
189C22×C5#37911yescharacteristic
190C22×C5C2×#10311yescharacteristic
191C22×C5#41911yescharacteristic
192C4×C5—22no—
193C4×C5—21no—
194C4×C5—24no—
195C4×C5—42no—
196C4×C5C2×#10112yes—
197C4×C5#44812yes—
198C4×C5#45112yes—
199Dic5—24no—
200Dic5—44no—
201Dic5—42no—
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—52no—
205C2×Q8—104no—
206C2×Q8—108no—
207C2×Q8—101no—
208C2×Q8—104no—
209C2×Q8—402no—
210C2×Q8—404no—
211C2×Q8#67712yes—
212C2×Q8Dic2012yes—
213C22×C4—101no—
214C22×C4—102no—
215C22×C4—101no—
216C22×C4#68512yes—
217C22×C4#68512yes—
218C22×C4C2×C4×D511yescharacteristic
219C22×C4C2×D2011yescharacteristic
220C22×C4C2×C22⋊D511yescharacteristic
221M16—202no—
222M16—202no—
223C2×C8—42no—
224C2×C8—202no—
225C4⋊C4—22no—
226C4⋊C4—24no—
227C4⋊C4—52no—
228C4⋊C4—54no—
229C4⋊C4—108no—
230C4⋊C4—108no—
231C4⋊C4—101no—
232C4⋊C4—102no—
233C4⋊C4—104no—
234C4⋊C4—104no—
235C42—22no—
236C42—22no—
237C42—108no—
238C42—104no—
239C42D4×D512yes—
240C42D4×D512yes—
241C2×C5—21no—
242C2×C5—21no—
243C2×C5#178411yescharacteristic
244C2×C5#178711yescharacteristic
245C2×C5#179511yescharacteristic
246C23C2×#68511yescharacteristic
247Q8—24no—
248Q8—24no—
249Q8—54no—
250Q8—104no—
251Q8—102no—
252Q8—404no—
253Q8—408no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—104no—
261C2×C4—102no—
262C2×C4—104no—
263C2×C4—102no—
264C2×C4—204no—
265C2×C4—202no—
266C2×C4#394814yes—
267C2×C4D5×C22⋊C411yescharacteristic
268C2×C4D5×C22⋊C411yescharacteristic
269C2×C4#402812yes—
270C2×C4C2×#67711yescharacteristic
271C2×C4C2×Dic2011yescharacteristic
272C2×C4#405512yes—
273C2×C4#408312yes—
274C8—82no—
275C8—402no—
276C5#839611yescharacteristic, complemented, Sylow
277C22—21no—
278C22—21no—
279C22#6524411yescharacteristic
280C22C2×#394811yescharacteristic
281C22#6540911yescharacteristic
282C4—24no—
283C4—22no—
284C4—21no—
285C4—42no—
286C4—104no—
287C4—204no—
288C4—202no—
289C4#6502712yes—
290C4#6502812yes—
291C4D5×#10112yes—
292C2—21no—
293C2—21no—
294C2#1060075611yescharacteristic
295C2#1060084111yescharacteristic
296C2#1060090611yescharacteristic
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#8396
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
148. Dic10#101semidirect
276. C5#8396semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic102
C5×#14612
#106024302
#106015732
#106015632
#83965