Finite Group Databasebeta

← #13014775

Subgroups — #13014775

Order 1280.

440 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 118 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
1Dic5×C4⋊Q8C211yesmaximal, characteristic
2#10604188C211yesmaximal, characteristic
3#10604188C211yesmaximal, characteristic
4#10598713C214yesmaximal
5C2×C5×C4⋊Q8C411yescharacteristic
6C2×Q8×Dic5—21no—
7#65519—21no—
8#65274—21no—
9#65274C2212yes—
10C4⋊C4×Dic5—21no—
11C4⋊C4×Dic5C412yes—
12#65224C411yescharacteristic
13C42×Dic5C2211yescharacteristic
14#64918—21no—
15#64918—21no—
16#64918—21no—
17#64918—21no—
18#64918C2212yes—
19#64918C2212yes—
20#7604—51nomaximal, Sylow
21C22×C5×Q8—21no—
22C22×#170—22no—
23C22×#170—22no—
24C5×C4⋊Q8—22no—
25C5×C4⋊Q8C814yescomplemented
26C2×C5×C4⋊C4—21no—
27C2×C5×C4⋊C4C2×C412yes—
28C2×C42×C5C2×C411yescharacteristic
29Q8×Dic5—44no—
30C2×C4⋊Dic5—21no—
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5—22no—
33C2×C4⋊Dic5C2×C412yes—
34C2×C4×Dic5—22no—
35C2×C4×Dic5C2×C411yescharacteristic
36C2×C4×Dic5D411yescharacteristic
37C2×C4×Dic5D411yescharacteristic
38C2×C4×Dic5D411yescharacteristic
39C2×C4×Dic5D411yescharacteristic
40C2×C4×Dic5C2311yescharacteristic
41#3963—22no—
42#3963—22no—
43C4×C4⋊Q8—51no—
44#1839—51no—
45#1839—51no—
46#1271—54no—
47C2×C5×Q8—24no—
48C2×C5×Q8—42no—
49C2×C5×Q8—42no—
50C22×C4×C5—22no—
51C22×C4×C5C22⋊C411yescharacteristic
52C22×C4×C5C22⋊C411yescharacteristic
53C22×C4×C5C22×C411yescharacteristic
54C22×Dic5—22no—
55C22×Dic5C22⋊C411yescharacteristic
56C22×Dic5C22⋊C411yescharacteristic
57C22×Dic5C2×D411yescharacteristic
58C22×Dic5C2×D411yescharacteristic
59C2×#170—42no—
60C2×#170—42no—
61C2×#170—42no—
62C2×#170—42no—
63C2×#170—42no—
64C2×#170—42no—
65C5×C4⋊C4—24no—
66C5×C4⋊C4—22no—
67C5×C4⋊C4C2×C814yes—
68C42×C5C2×C812yes—
69C42×C5M1612yes—
70C4⋊Dic5—42no—
71C4⋊Dic5—42no—
72C4⋊Dic5—44no—
73C4⋊Dic5—42no—
74C4×Dic5—22no—
75C4×Dic5—22no—
76C4×Dic5—22no—
77C4×Dic5—41no—
78C4×Dic5—41no—
79C4×Dic5—41no—
80C4×Dic5—44no—
81C2×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
82C2×C4×Q8—101no—
83#391—101no—
84#389—52no—
85#389—101no—
86#384—51no—
87C4×C4⋊C4—52no—
88C4×C4⋊C4—101no—
89C43—51no—
90#336—52no—
91#336—52no—
92#336—101no—
93#336—101no—
94#336—101no—
95#336—101no—
96C23×C5C2×C22⋊C411yescharacteristic
97C5×Q8—48no—
98C2×C4×C5—21no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—21no—
104C2×C4×C5—24no—
105C2×C4×C5—42no—
106C2×C4×C5—42no—
107C2×C4×C5C22⋊C812yes—
108C2×C4×C5C22⋊C812yes—
109C2×C4×C5C22×C811yescharacteristic
110C2×C4×C5C2×M1611yescharacteristic
111C2×Dic5—21no—
112C2×Dic5—21no—
113C2×Dic5—21no—
114C2×Dic5—21no—
115C2×Dic5—21no—
116C2×Dic5—21no—
117C2×Dic5—21no—
118C2×Dic5—21no—
119C2×Dic5—21no—
120C2×Dic5—42no—
121C2×Dic5—42no—
122C2×Dic5—42no—
123C2×Dic5#10112yes—
124C2×Dic5AGL(1,ℤ/8)12yes—
125C2×Dic5#13712yes—
126#170—82no—
127#170—82no—
128C22×Q8—21no—
129C22×C8—102no—
130C22×C8—102no—
131C4⋊Q8—22no—
132C4⋊Q8#17014yescomplemented
133C4×Q8—204no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—52no—
136C2×C4⋊C4—102no—
137C2×C4⋊C4—101no—
138C2×C4⋊C4—101no—
139C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
140C2×C42—51no—
141C2×C42—51no—
142C2×C42—51no—
143C2×C42—51no—
144C2×C42—51no—
145C2×C42—51no—
146C2×C42—102no—
147C2×C42C2×AGL(1,𝔽5)11yescharacteristic
148#95—102no—
149#95—102no—
150C22×C5C2×C22⋊C811yescharacteristic
151C22×C5#41011yescharacteristic
152C22×C5C2×#10111yescharacteristic
153C22×C5#41811yescharacteristic
154C22×C5#41911yescharacteristic
155C22×C5#42111yescharacteristic
156C22×C5#42111yescharacteristic
157C4×C5—21no—
158C4×C5—21no—
159C4×C5—22no—
160C4×C5—22no—
161C4×C5—44no—
162Dic5—22no—
163Dic5—22no—
164Dic5—22no—
165Dic5—41no—
166Dic5—82no—
167C2×Q8—24no—
168C2×Q8—42no—
169C2×Q8—42no—
170C22×C4—22no—
171C22×C4—51no—
172C22×C4—51no—
173C22×C4—51no—
174C22×C4—51no—
175C22×C4—102no—
176C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
177C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
178C22×C4C22×AGL(1,𝔽5)11yescharacteristic
179C2×C8—202no—
180C2×C8—202no—
181C2×C8—202no—
182C2×C8—202no—
183C2×C8—202no—
184C2×C8—202no—
185C4⋊C4—22no—
186C4⋊C4—24no—
187C4⋊C4—202no—
188C4⋊C4—202no—
189C4⋊C4—202no—
190C4⋊C4—204no—
191C4⋊C4C2×#17014yes—
192C42—102no—
193C42—102no—
194C42—102no—
195C42—201no—
196C42—201no—
197C42—201no—
198C42—204no—
199C42C2×#17012yes—
200C42#70412yes—
201C2×C5#146111yescharacteristic
202C2×C5#147811yescharacteristic
203C2×C5#147911yescharacteristic
204C2×C5#151411yescharacteristic
205C2×C5#151511yescharacteristic
206C2×C5#153711yescharacteristic
207C2×C5#155611yescharacteristic
208C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
209Q8—48no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—24no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—52no—
220C2×C4—52no—
221C2×C4—52no—
222C2×C4—101no—
223C2×C4—101no—
224C2×C4—101no—
225C2×C4—101no—
226C2×C4—101no—
227C2×C4—101no—
228C2×C4—101no—
229C2×C4—101no—
230C2×C4—101no—
231C2×C4—202no—
232C2×C4—202no—
233C2×C4—202no—
234C2×C4C22⋊#17012yes—
235C2×C4C22⋊#17012yes—
236C2×C4C22×#17011yescharacteristic
237C2×C4C2×#70411yescharacteristic
238C8—402no—
239C8—402no—
240C5#760411yescharacteristic, complemented, Sylow
241C22#6576711yescharacteristic
242C22#6576911yescharacteristic
243C22#6578211yescharacteristic
244C22#6578411yescharacteristic
245C22#6578511yescharacteristic
246C22D5⋊#10111yescharacteristic
247C22C2×C22⋊#17011yescharacteristic
248C4—22no—
249C4—22no—
250C4—21no—
251C4—21no—
252C4—44no—
253C4—102no—
254C4—102no—
255C4—102no—
256C4—201no—
257C4—402no—
258C2#1060462711yescharacteristic
259C2#1060462811yescharacteristic
260C2#1060463911yescharacteristic
261C2#1060466111yescharacteristic
262C2#1060492211yescharacteristic
263C2#1060496711yescharacteristic
264C2#1060497611yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×C4⋊Q8C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×C4⋊Q8AGL(1,𝔽5)
hypocenterC5#7604
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
25. C5×C4⋊Q8C8semidirect
132. C4⋊Q8#170semidirect
240. C5#7604semidirect

Maximal subgroups

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

subgroupindex
Dic5×C4⋊Q82
#106041882
#105987132
#76045