Finite Group Databasebeta

← #13014657

Subgroups — #13014657

Order 1280.

516 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 146 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×#4090C211yesmaximal, characteristic
2C4×#4004C212yesmaximal
3#10598828C212yesmaximal
4#10598715C212yesmaximal
5C2×C4×C5×Q8C411yescharacteristic
6C2×#4090C411yescharacteristic
7C2×C4×Dic10C411yescharacteristic
8C2×#4004—22no—
9C2×C4×#170—22no—
10#65519C2211yescharacteristic
11#65265C411yescharacteristic
12#65263C2211yescharacteristic
13#65261—22no—
14C4×#683—22no—
15C42×Dic5C2211yescharacteristic
16#64918C2214yes—
17#7571—51nomaximal, Sylow
18C22×C5×Q8C2×C411yescharacteristic
19C22×Dic10C2×C411yescharacteristic
20C22×#170—24no—
21C4×C5×Q8—42no—
22C2×C5×C4⋊C4—21no—
23C2×C5×C4⋊C4C2×C411yescharacteristic
24C2×C42×C5—21no—
25C2×C42×C5C2×C411yescharacteristic
26#4090—22no—
27#4090C814yescomplemented
28C2×C4⋊Dic5C2×C411yescharacteristic
29C2×#683—22no—
30C2×#683—21no—
31C2×#683—22no—
32C2×C4×Dic5—21no—
33C2×C4×Dic5C2×C411yescharacteristic
34C2×C4×Dic5D412yes—
35C2×C4×Dic5D412yes—
36C2×C4×Dic5C2311yescharacteristic
37C4×Dic10—42no—
38#4004—28no—
39C4×#170—44no—
40#3963—22no—
41#3963—22no—
42C4×C4⋊Q8—51no—
43C4×C4⋊C8—52no—
44#1272—52no—
45#1272—52no—
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×Dic5—21no—
57C22×Dic5C22⋊C412yes—
58C22×Dic5C2×D412yes—
59C2×Dic10—21no—
60C2×Dic10—41no—
61C2×Dic10—41no—
62C2×Dic10C2×C812yes—
63C2×#170—28no—
64C2×#170—44no—
65C2×#170—44no—
66C5×C4⋊C4—41no—
67C5×C4⋊C4—42no—
68C42×C5—22no—
69C42×C5—42no—
70C4⋊Dic5—41no—
71#683—28no—
72#683—42no—
73#683—44no—
74C4×Dic5—24no—
75C4×Dic5—41no—
76C4×Dic5—42no—
77C4×Dic5C2×C812yes—
78C4×Dic5M1612yes—
79C4×Dic5SD1614yes—
80C4×Dic5Q1614yes—
81C2×C4⋊Q8—51no—
82C2×C4×Q8—51no—
83C2×C4×Q8AGL(1,𝔽5)11yescharacteristic
84C2×C4⋊C8—102no—
85C2×C4×C8—102no—
86#391—51no—
87#391—51no—
88#389—102no—
89#384—51no—
90C4×C4⋊C4—102no—
91C43—51no—
92#336—54no—
93C23×C5C2×C22⋊C411yescharacteristic
94C5×Q8—42no—
95C5×Q8—42no—
96C2×C4×C5—21no—
97C2×C4×C5—21no—
98C2×C4×C5—22no—
99C2×C4×C5—21no—
100C2×C4×C5—22no—
101C2×C4×C5—41no—
102C2×C4×C5—41no—
103C2×C4×C5—41no—
104C2×C4×C5—42no—
105C2×C4×C5#10012yes—
106C2×C4×C5#10314yes—
107C2×C4×C5C22×C811yescharacteristic
108C2×C4×C5C2×M1611yescharacteristic
109C2×Dic5—22no—
110C2×Dic5—22no—
111C2×Dic5—22no—
112C2×Dic5—41no—
113C2×Dic5—41no—
114C2×Dic5—41no—
115C2×Dic5—42no—
116C2×Dic5C22⋊C814yes—
117C2×Dic5#10314yes—
118C2×Dic5#10414yes—
119C2×Dic5C2×SD1612yes—
120C2×Dic5C2×Q1612yes—
121Dic10—42no—
122Dic10—42no—
123#170—48no—
124C22×Q8—51no—
125C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
126C22×C8—104no—
127C4⋊Q8—54no—
128C4⋊Q8—102no—
129C4×Q8—42no—
130C4×Q8—202no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—51no—
133C2×C4⋊C4—102no—
134C2×C4⋊C4—102no—
135C2×C4⋊C4—101no—
136C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
137C2×C42—21no—
138C2×C42—52no—
139C2×C42—51no—
140C2×C42—52no—
141C2×C42—51no—
142C2×C42—101no—
143C2×C42C2×AGL(1,𝔽5)11yescharacteristic
144C4⋊C8—108no—
145C4×C8—204no—
146#95—102no—
147#95—102no—
148C22×C5C2×C22⋊C811yescharacteristic
149C22×C5#41011yescharacteristic
150C22×C5C2×#10011yescharacteristic
151C22×C5C2×#10312yes—
152C22×C5C2×#10412yes—
153C4×C5—21no—
154C4×C5—21no—
155C4×C5—42no—
156C4×C5—41no—
157C4×C5—81no—
158C4×C5#33314yes—
159Dic5—22no—
160Dic5—22no—
161Dic5—42no—
162Dic5—81no—
163Dic5Q8⋊C818yes—
164C2×Q8—21no—
165C2×Q8—41no—
166C2×Q8—41no—
167C2×Q8—52no—
168C2×Q8—101no—
169C2×Q8—201no—
170C2×Q8—201no—
171C2×Q8D5⋊C812yes—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—52no—
175C22×C4—52no—
176C22×C4—101no—
177C22×C4—101no—
178C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
179C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
180C22×C4C22×AGL(1,𝔽5)11yescharacteristic
181C2×C8—108no—
182C2×C8—204no—
183C2×C8—204no—
184C4⋊C4—41no—
185C4⋊C4—42no—
186C4⋊C4—108no—
187C4⋊C4—201no—
188C4⋊C4—202no—
189C4⋊C4—204no—
190C42—22no—
191C42—42no—
192C42—52no—
193C42—52no—
194C42—54no—
195C42—54no—
196C42—104no—
197C42—201no—
198C42—202no—
199C2×C5#146011yescharacteristic
200C2×C5C2×Q8⋊C812yes—
201C2×C5#150312yes—
202C2×C5#152511yescharacteristic
203C2×C5C2×#33311yescharacteristic
204C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
205Q8—42no—
206Q8—42no—
207Q8—202no—
208Q8—202no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—54no—
219C2×C4—54no—
220C2×C4—54no—
221C2×C4—52no—
222C2×C4—52no—
223C2×C4—102no—
224C2×C4—102no—
225C2×C4—102no—
226C2×C4—201no—
227C2×C4—201no—
228C2×C4—202no—
229C2×C4—201no—
230C2×C4#400914yes—
231C2×C4#401312yes—
232C2×C4C2×D5⋊C811yescharacteristic
233C2×C4D5⋊M1611yescharacteristic
234C8—208no—
235C5#757111yescharacteristic, complemented, Sylow
236C22#6574511yescharacteristic
237C22D5⋊(C22⋊C8)11yescharacteristic
238C22C2×#400912yes—
239C22D5⋊#10412yes—
240C22C2×#401311yescharacteristic
241C4—21no—
242C4—21no—
243C4—42no—
244C4—41no—
245C4—58no—
246C4—81no—
247C4—102no—
248C4—102no—
249C4—202no—
250C4—401no—
251C4#6493114yes—
252C2#1060442412yes—
253C2D5⋊(Q8⋊C8)12yes—
254C2#1060487911yescharacteristic
255C2C2×#6493111yescharacteristic
256C2#1060499311yescharacteristic
subgroupG/H
centerC22×C4C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×Q8C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×C4×Q8AGL(1,𝔽5)
hypocenterC5#7571
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
27. #4090C8semidirect
235. C5#7571semidirect

Maximal subgroups

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

subgroupindex
C4×#40902
C4×#40042
#105988282
#105987152
#75715