Finite Group Databasebeta

← #13014646

Subgroups — #13014646

Order 1280.

528 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C4×#4093C211yesmaximal, characteristic
2#10604174C212yesmaximal, complemented
3#10598828C212yesmaximal, complemented
4#10598712C212yesmaximal
5C2×C4×C5×Q8C411yescharacteristic
6C2×#4093C411yescharacteristic
7C2×C4×D20C411yescharacteristic
8C2×C4×#170—22no—
9#65519C2211yescharacteristic
10#65279—22no—
11#65277C2211yescharacteristic
12#65266C411yescharacteristic
13C4×#685—22no—
14C42×Dic5C2211yescharacteristic
15#64918—22no—
16#64918C2214yes—
17#7567—51nomaximal, Sylow
18C22×C5×Q8C2×C411yescharacteristic
19C22×D20C2×C411yescharacteristic
20C22×C4×D5—21no—
21C22×#170—24no—
22C4×C5×Q8—42no—
23C2×C5×C4⋊C4—21no—
24C2×C5×C4⋊C4C2×C411yescharacteristic
25C2×C42×C5—21no—
26C2×C42×C5C2×C411yescharacteristic
27#4093—22no—
28#4093C814yescomplemented
29C2×#685—22no—
30C2×#685—21no—
31C2×#685—22no—
32C2×C4⋊Dic5C2×C411yescharacteristic
33C2×C4×Dic5C2×C411yescharacteristic
34C2×C4×Dic5D412yes—
35C2×C4×Dic5D412yes—
36C2×C4×Dic5C2311yescharacteristic
37C4×D20—42no—
38C4×#170—28no—
39#3963—22no—
40#3963—22no—
41C4×#124—51no—
42#1744—52no—
43#1272—52no—
44#1270—52no—
45C23×D5—21no—
46C2×C5×Q8—21no—
47C2×C5×Q8—41no—
48C2×C5×Q8—41no—
49C2×C5×Q8C2×C812yes—
50C22×C4×C5—21no—
51C22×C4×C5—21no—
52C22×C4×C5C22⋊C411yescharacteristic
53C22×C4×C5C22⋊C411yescharacteristic
54C22×C4×C5C22×C411yescharacteristic
55C22×Dic5—21no—
56C22×Dic5C22⋊C412yes—
57C22×Dic5C2×D412yes—
58C2×D20—21no—
59C2×D20—41no—
60C2×D20—41no—
61C2×D20C2×C812yes—
62C2×C4×D5—42no—
63C2×C4×D5—44no—
64C2×#170—28no—
65C2×#170—44no—
66C2×#170—44no—
67C5×C4⋊C4—41no—
68C5×C4⋊C4—42no—
69C42×C5—22no—
70C42×C5—42no—
71#685—28no—
72#685—42no—
73#685—44no—
74C4⋊Dic5—41no—
75C4×Dic5—24no—
76C4×Dic5—24no—
77C4×Dic5—41no—
78C4×Dic5C2×C812yes—
79C4×Dic5M1612yes—
80C2×#124—51no—
81C2×C4×Q8AGL(1,𝔽5)11yescharacteristic
82C2×C4×D4—51no—
83C2×C4×C8—102no—
84#391—51no—
85#390—51no—
86#388—102no—
87#382—51no—
88C4×C22⋊C4—102no—
89C43—51no—
90#336—54no—
91#336—102no—
92C23×C5C2×C22⋊C411yescharacteristic
93C22×D5—22no—
94C22×D5—41no—
95C22×D5—41no—
96C22×D5—42no—
97C22×D5—42no—
98C5×Q8—42no—
99C5×Q8—42no—
100C2×C4×C5—21no—
101C2×C4×C5—21no—
102C2×C4×C5—22no—
103C2×C4×C5—21no—
104C2×C4×C5—22no—
105C2×C4×C5—41no—
106C2×C4×C5—41no—
107C2×C4×C5—41no—
108C2×C4×C5—42no—
109C2×C4×C5#10012yes—
110C2×C4×C5#10414yes—
111C2×C4×C5C22×C811yescharacteristic
112C2×C4×C5C2×M1611yescharacteristic
113C2×Dic5—22no—
114C2×Dic5—22no—
115C2×Dic5—22no—
116C2×Dic5—22no—
117C2×Dic5—41no—
118C2×Dic5—42no—
119C2×Dic5C22⋊C814yes—
120C2×Dic5#13514yes—
121D20—42no—
122D20—42no—
123C4×D5—84no—
124#170—48no—
125C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
126C22×D4—51no—
127C23×C4—101no—
128C22×C8—104no—
129#124—54no—
130#124—102no—
131C4×Q8—42no—
132C4×D4—202no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—51no—
135C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
136C2×C22⋊C4—102no—
137C2×C22⋊C4—102no—
138C2×C22⋊C4—101no—
139C2×C42—21no—
140C2×C42—51no—
141C2×C42—52no—
142C2×C42—52no—
143C2×C42—51no—
144C2×C42C2×AGL(1,𝔽5)11yescharacteristic
145C4×C8—108no—
146#95—102no—
147#95—102no—
148C22×C5C2×C22⋊C811yescharacteristic
149C22×C5#41011yescharacteristic
150C22×C5C2×#10011yescharacteristic
151C22×C5#41612yes—
152C22×C5C2×#10412yes—
153C2×D5—42no—
154C2×D5—44no—
155C2×D5—81no—
156C2×D5—82no—
157C2×D5—81no—
158C4×C5—21no—
159C4×C5—21no—
160C4×C5—41no—
161C4×C5—42no—
162C4×C5—81no—
163C4×C5#32914yes—
164Dic5—24no—
165Dic5—24no—
166Dic5—81no—
167C24—101no—
168C2×Q8—21no—
169C2×Q8—41no—
170C2×Q8—41no—
171C2×Q8D5⋊C812yes—
172C2×D4—52no—
173C2×D4—101no—
174C2×D4—201no—
175C2×D4—201no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—52no—
179C22×C4—52no—
180C22×C4—101no—
181C22×C4—204no—
182C22×C4—202no—
183C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
184C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
185C22×C4C22×AGL(1,𝔽5)11yescharacteristic
186C2×C8—108no—
187C2×C8—204no—
188C2×C8—204no—
189C4⋊C4—41no—
190C4⋊C4—42no—
191C4⋊C4—201no—
192C22⋊C4—108no—
193C22⋊C4—202no—
194C22⋊C4—204no—
195C42—22no—
196C42—42no—
197C42—52no—
198C42—52no—
199C42—104no—
200C42—104no—
201C42—201no—
202C2×C5#146011yescharacteristic
203C2×C5#147612yes—
204C2×C5#150012yes—
205C2×C5C2×#32911yescharacteristic
206C2×C5#154311yescharacteristic
207D5—82no—
208C23—102no—
209C23—202no—
210C23—201no—
211C23—201no—
212C23—202no—
213C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
214Q8—42no—
215Q8—42no—
216D4—202no—
217D4—202no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—54no—
228C2×C4—54no—
229C2×C4—102no—
230C2×C4—102no—
231C2×C4—102no—
232C2×C4—102no—
233C2×C4—201no—
234C2×C4—202no—
235C2×C4—404no—
236C2×C4#401014yes—
237C2×C4#401312yes—
238C2×C4C2×D5⋊C811yescharacteristic
239C2×C4D5⋊M1611yescharacteristic
240C8—208no—
241C5#756711yescharacteristic, complemented, Sylow
242C22—202no—
243C22—204no—
244C22—402no—
245C22—401no—
246C22—401no—
247C22#6574511yescharacteristic
248C22D5⋊(C22⋊C8)11yescharacteristic
249C22C2×#401012yes—
250C22#6579412yes—
251C22C2×#401311yescharacteristic
252C4—21no—
253C4—21no—
254C4—42no—
255C4—41no—
256C4—81no—
257C4—104no—
258C4—104no—
259C4—401no—
260C4#6492714yes—
261C2—402no—
262C2#1060442312yes—
263C2#1060443612yes—
264C2#1060487911yescharacteristic
265C2C2×#6492711yescharacteristic
266C2#1060500411yescharacteristic
subgroupG/H
centerC22×C4C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×Q8C4
socleC23×C5C2×C22⋊C4
prime radicalC22×D20C2×C4
cosocleC2×C4×Dic5C23
hypercenterC2×C4×Q8AGL(1,𝔽5)
hypocenterC5#7567
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #10604174C2semidirect
3. #10598828C2semidirect
28. #4093C8semidirect
241. C5#7567semidirect

Maximal subgroups

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

subgroupindex
C4×#40932
#106041742
#105988282
#105987122
#75675