Finite Group Databasebeta

← #13014730

Subgroups — #13014730

Order 1280.

478 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 140 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#10604185C211yesmaximal, characteristic
3#10604173C211yesmaximal, characteristic
4#10598713C214yesmaximal
5C2×C5×C4⋊Q8C411yescharacteristic
6C2×Q8×Dic5—21no—
7C2×C4⋊#170—21no—
8C2×C4×#170—21no—
9#65519—21no—
10#65274—21no—
11#65274C2212yes—
12C4⋊C4×Dic5—21no—
13C4⋊C4×Dic5C412yes—
14#65224C411yescharacteristic
15C42×Dic5C2211yescharacteristic
16#64918—21no—
17#64918—21no—
18#64918C2212yes—
19#64918C2212yes—
20#7591—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
41C4⋊#170—42no—
42C4×#170—24no—
43#3963—22no—
44#3963—22no—
45C4×C4⋊Q8—51no—
46#1831—51no—
47#1744—51no—
48#1271—54no—
49C2×C5×Q8—24no—
50C2×C5×Q8—42no—
51C2×C5×Q8—42no—
52C22×C4×C5—22no—
53C22×C4×C5C22⋊C411yescharacteristic
54C22×C4×C5C22⋊C411yescharacteristic
55C22×C4×C5C22×C411yescharacteristic
56C22×Dic5—22no—
57C22×Dic5C22⋊C411yescharacteristic
58C22×Dic5C22⋊C411yescharacteristic
59C22×Dic5C2×D411yescharacteristic
60C22×Dic5C2×D411yescharacteristic
61C2×#170—24no—
62C2×#170—42no—
63C2×#170—42no—
64C2×#170—42no—
65C2×#170—42no—
66C2×#170—42no—
67C5×C4⋊C4—24no—
68C5×C4⋊C4—22no—
69C5×C4⋊C4C2×C814yes—
70C42×C5C2×C812yes—
71C42×C5M1612yes—
72C4⋊Dic5—42no—
73C4⋊Dic5—42no—
74C4⋊Dic5—44no—
75C4⋊Dic5—42no—
76C4×Dic5—22no—
77C4×Dic5—22no—
78C4×Dic5—22no—
79C4×Dic5—41no—
80C4×Dic5—41no—
81C4×Dic5—44no—
82C4×Dic5SD1612yes—
83C4×Dic5Q1612yes—
84C2×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
85C2×C4×Q8—101no—
86C2×C4⋊C8—101no—
87C2×C4×C8—101no—
88#391—101no—
89#389—52no—
90#389—101no—
91#384—51no—
92C4×C4⋊C4—52no—
93C4×C4⋊C4—101no—
94C43—51no—
95#336—52no—
96#336—52no—
97#336—101no—
98#336—101no—
99C23×C5C2×C22⋊C411yescharacteristic
100C5×Q8—48no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5—24no—
106C2×C4×C5—42no—
107C2×C4×C5—42no—
108C2×C4×C5C22⋊C812yes—
109C2×C4×C5C22⋊C812yes—
110C2×C4×C5#10312yes—
111C2×C4×C5#10412yes—
112C2×C4×C5C22×C811yescharacteristic
113C2×C4×C5C2×M1611yescharacteristic
114C2×Dic5—21no—
115C2×Dic5—21no—
116C2×Dic5—21no—
117C2×Dic5—21no—
118C2×Dic5—21no—
119C2×Dic5—21no—
120C2×Dic5—21no—
121C2×Dic5—21no—
122C2×Dic5—42no—
123C2×Dic5—42no—
124C2×Dic5—42no—
125C2×Dic5#10112yes—
126C2×Dic5#10312yes—
127C2×Dic5C2×SD1611yescharacteristic
128C2×Dic5C2×Q1611yescharacteristic
129C2×Dic5AGL(1,ℤ/8)12yes—
130#170—44no—
131#170—82no—
132C22×Q8—21no—
133C22×C8—102no—
134C22×C8—102no—
135C4⋊Q8—22no—
136C4⋊Q8#17014yescomplemented
137C4×Q8—204no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—52no—
140C2×C4⋊C4—102no—
141C2×C4⋊C4—101no—
142C2×C4⋊C4—101no—
143C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
144C2×C42—51no—
145C2×C42—51no—
146C2×C42—51no—
147C2×C42—51no—
148C2×C42—51no—
149C2×C42—51no—
150C2×C42—102no—
151C2×C42C2×AGL(1,𝔽5)11yescharacteristic
152C4⋊C8—202no—
153C4×C8—104no—
154#95—102no—
155#95—102no—
156C22×C5C2×C22⋊C811yescharacteristic
157C22×C5#41011yescharacteristic
158C22×C5C2×#10111yescharacteristic
159C22×C5C2×#10311yescharacteristic
160C22×C5#41811yescharacteristic
161C22×C5C2×#10411yescharacteristic
162C22×C5#42111yescharacteristic
163C4×C5—21no—
164C4×C5—21no—
165C4×C5—22no—
166C4×C5—44no—
167C4×C5Q8⋊C814yes—
168Dic5—22no—
169Dic5—22no—
170Dic5—21no—
171Dic5—21no—
172Dic5—22no—
173Dic5—82no—
174C2×Q8—24no—
175C2×Q8—42no—
176C2×Q8—42no—
177C22×C4—22no—
178C22×C4—51no—
179C22×C4—51no—
180C22×C4—51no—
181C22×C4—51no—
182C22×C4—102no—
183C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
184C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
185C22×C4C22×AGL(1,𝔽5)11yescharacteristic
186C2×C8—104no—
187C2×C8—202no—
188C2×C8—202no—
189C2×C8—202no—
190C2×C8—202no—
191C2×C8—202no—
192C4⋊C4—22no—
193C4⋊C4—24no—
194C4⋊C4—202no—
195C4⋊C4—202no—
196C4⋊C4—204no—
197C4⋊C4—202no—
198C4⋊C4C2×#17014yes—
199C42—52no—
200C42—52no—
201C42—102no—
202C42—102no—
203C42—102no—
204C42—201no—
205C42—201no—
206C42—204no—
207C42C2×#17012yes—
208C42#70412yes—
209C2×C5#146111yescharacteristic
210C2×C5C2×Q8⋊C811yescharacteristic
211C2×C5#147811yescharacteristic
212C2×C5#150511yescharacteristic
213C2×C5#151811yescharacteristic
214C2×C5#153111yescharacteristic
215C2×C5#154911yescharacteristic
216C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
217Q8—48no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—24no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—52no—
226C2×C4—51no—
227C2×C4—52no—
228C2×C4—51no—
229C2×C4—52no—
230C2×C4—101no—
231C2×C4—101no—
232C2×C4—101no—
233C2×C4—101no—
234C2×C4—101no—
235C2×C4—101no—
236C2×C4—101no—
237C2×C4—101no—
238C2×C4—202no—
239C2×C4—202no—
240C2×C4—202no—
241C2×C4#400912yes—
242C2×C4#401012yes—
243C2×C4C22⋊#17012yes—
244C2×C4C22⋊#17012yes—
245C2×C4C22×#17011yescharacteristic
246C2×C4C2×#70411yescharacteristic
247C8—204no—
248C8—402no—
249C5#759111yescharacteristic, complemented, Sylow
250C22#6576711yescharacteristic
251C22#6576911yescharacteristic
252C22C2×#400911yescharacteristic
253C22C2×#401011yescharacteristic
254C22#6578511yescharacteristic
255C22D5⋊#10111yescharacteristic
256C22C2×C22⋊#17011yescharacteristic
257C4—22no—
258C4—21no—
259C4—21no—
260C4—44no—
261C4—102no—
262C4—101no—
263C4—101no—
264C4—102no—
265C4—102no—
266C4—402no—
267C4Q8⋊#17014yes—
268C2#1060462411yescharacteristic
269C2#1060463111yescharacteristic
270C2#1060463711yescharacteristic
271C2#1060466011yescharacteristic
272C2#1060492211yescharacteristic
273C2C2×Q8⋊#17011yescharacteristic
274C2#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#7591
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
136. C4⋊Q8#170semidirect
249. C5#7591semidirect

Maximal subgroups

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

subgroupindex
Dic5×C4⋊Q82
#106041852
#106041732
#105987132
#75915