Finite Group Databasebeta

← C2×#10604662 #13031112

Subgroups — C2×#10604662 #13031112

Order 1280.

1182 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 248 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×D5×C4⋊Q8C211yesmaximal, characteristic
2C2×#65684C212yesmaximal
3C2×#64931C214yesmaximal, complemented
4#10604662C218yesmaximal, direct product factor
5C22×Q8×D5C412yes—
6C2×C5×C4⋊Q8C411yescharacteristic
7C2×#4090C2212yes—
8D5×C4⋊Q8—24no—
9D5×C4⋊Q8C414yes—
10D5×C4⋊Q8C2214yes—
11C2×D5×C4⋊C4—22no—
12C2×#4034—22no—
13C2×C42×D5C2211yescharacteristic
14C2×#4015C411yescharacteristic
15C2×#4004C2214yes—
16C2×#4003—22no—
17C2×#4002—22no—
18#65684—24no—
19#65684C2218yes—
20#64931C22116yescomplemented
21C2×#1558—51nomaximal, Sylow
22C22×C5×Q8C2×C412yes—
23C2×Q8×D5—24no—
24C2×Q8×D5—48no—
25C2×Q8×D5C2×C418yes—
26C22×C4×D5—22no—
27C22×C4×D5C2×C411yescharacteristic
28C22×C4×D5D412yes—
29C22×Dic10—22no—
30C22×Dic10C2×C412yes—
31C22×#170—24no—
32C5×C4⋊Q8—22no—
33C5×C4⋊Q8C2×C414yes—
34C2×C5×C4⋊C4—22no—
35C2×C42×C5C2×C411yescharacteristic
36#4090—24no—
37#4090C2×C414yes—
38#4090C2314yes—
39C2×C4⋊Dic5—22no—
40C2×#683—24no—
41C2×C4×Dic5D412yes—
42C2×C4×Dic5C2311yescharacteristic
43D5×C4⋊C4—28no—
44D5×C4⋊C4—28no—
45#4034—28no—
46#4034—28no—
47C42×D5C2×C412yes—
48C42×D5D414yes—
49C42×D5C2312yes—
50#4015—22no—
51#4015C2×C414yes—
52#4004—24no—
53#4004C2318yes—
54#4003—28no—
55#4002—28no—
56C22×C4⋊Q8—51no—
57C2×#432—52no—
58#1558—58no—
59C2×#333—54no—
60C23×D5C22⋊C411yescharacteristic
61C2×C5×Q8—22no—
62C2×C5×Q8—44no—
63C2×C5×Q8C22×C414yes—
64C22×C4×C5—22no—
65C22×C4×C5C22⋊C412yes—
66C22×C4×C5C22×C411yescharacteristic
67C22×Dic5—22no—
68C22×Dic5C22⋊C411yescharacteristic
69C22×Dic5C2×D412yes—
70Q8×D5—416no—
71Q8×D5—416no—
72C2×C4×D5—24no—
73C2×C4×D5—28no—
74C2×C4×D5—28no—
75C2×C4×D5—48no—
76C2×C4×D5C22⋊C412yes—
77C2×C4×D5C22⋊C414yes—
78C2×C4×D5C22×C412yes—
79C2×C4×D5C2×D414yes—
80C2×Dic10—22no—
81C2×Dic10—28no—
82C2×Dic10—48no—
83C2×Dic10—44no—
84C2×Dic10C22×C414yes—
85C2×#170—28no—
86C2×#170—48no—
87C5×C4⋊C4—28no—
88C42×C5C22⋊C412yes—
89C42×C5C22×C412yes—
90C4⋊Dic5—28no—
91#683—28no—
92#683—28no—
93C4×Dic5C22⋊C414yes—
94C4×Dic5C22×C411yescharacteristic
95C4×Dic5C2×D414yes—
96C4×Dic5C2×D412yes—
97C4×Dic5C2411yescharacteristic
98C23×Q8—52no—
99C2×C4⋊Q8—52no—
100C2×C4⋊Q8—54no—
101C2×C4⋊Q8—54no—
102C2×C4⋊Q8—51no—
103C2×C4⋊Q8—102no—
104C2×C4⋊Q8—104no—
105C2×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
106C22×C4⋊C4—102no—
107C22×C42—51no—
108#432—58no—
109#432—104no—
110C2×C4⋊C8—54no—
111C2×C22⋊C8—102no—
112C2×#97—102no—
113#333—516no—
114C23×C5C2×C22⋊C411yescharacteristic
115C22×D5—24no—
116C22×D5#10014yes—
117C22×D5C2×C22⋊C412yes—
118C5×Q8—44no—
119C5×Q8—44no—
120C2×C4×C5—22no—
121C2×C4×C5—24no—
122C2×C4×C5—24no—
123C2×C4×C5—44no—
124C2×C4×C5C2×C22⋊C414yes—
125C2×C4×C5C2×C22⋊C411yescharacteristic
126C2×C4×C5C23×C411yescharacteristic
127C2×Dic5—22no—
128C2×Dic5—24no—
129C2×Dic5—44no—
130C2×Dic5C2×C22⋊C412yes—
131C2×Dic5C2×C22⋊C412yes—
132C2×Dic5#13718yes—
133C2×Dic5C22×D412yes—
134C4×D5—24no—
135C4×D5—24no—
136C4×D5—28no—
137C4×D5—28no—
138C4×D5—416no—
139Dic10—416no—
140Dic10—44no—
141Dic10—44no—
142#170—48no—
143C22×Q8—58no—
144C22×Q8—52no—
145C22×Q8—102no—
146C22×Q8—104no—
147C22×Q8—208no—
148C22×Q8C2×AGL(1,𝔽5)12yes—
149C23×C4—52no—
150C23×C4—51no—
151C23×C4—102no—
152C22×C8—104no—
153C4⋊Q8—22no—
154C4⋊Q8—54no—
155C4⋊Q8—54no—
156C4⋊Q8—54no—
157C4⋊Q8—108no—
158C4⋊Q8—108no—
159C4⋊Q8—104no—
160C4⋊Q8—102no—
161C4⋊Q8C2×AGL(1,𝔽5)14yes—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—108no—
164C2×C4⋊C4—108no—
165C2×C4⋊C4—104no—
166C2×C4⋊C4—102no—
167C2×C42—52no—
168C2×C42—51no—
169C2×C42—54no—
170C2×C42—52no—
171C2×C42—52no—
172C2×C42C2×AGL(1,𝔽5)11yescharacteristic
173C4⋊C8—58no—
174C4⋊C8—104no—
175C22⋊C8—108no—
176#97—108no—
177C22×C5C2×#10012yes—
178C22×C5#41914yes—
179C22×C5C22×C22⋊C411yescharacteristic
180C2×D5—28no—
181C2×D5—24no—
182C2×D5C2×#10014yes—
183C4×C5—21no—
184C4×C5—21no—
185C4×C5—24no—
186C4×C5—44no—
187Dic5—22no—
188Dic5—44no—
189Dic5#41914yes—
190Dic5C2×#13714yes—
191C24—51no—
192C2×Q8—22no—
193C2×Q8—44no—
194C2×Q8—54no—
195C2×Q8—108no—
196C2×Q8—102no—
197C2×Q8—204no—
198C2×Q8—208no—
199C2×Q8—2016no—
200C2×Q8—2016no—
201C2×Q8C22×AGL(1,𝔽5)14yes—
202C22×C4—22no—
203C22×C4—52no—
204C22×C4—51no—
205C22×C4—54no—
206C22×C4—54no—
207C22×C4—52no—
208C22×C4—52no—
209C22×C4—108no—
210C22×C4—104no—
211C22×C4—108no—
212C22×C4—102no—
213C22×C4—208no—
214C22×C4C22⋊AGL(1,𝔽5)12yes—
215C22×C4C22×AGL(1,𝔽5)11yescharacteristic
216C2×C8—108no—
217C2×C8—208no—
218C4⋊C4—28no—
219C4⋊C4—108no—
220C4⋊C4—108no—
221C4⋊C4—108no—
222C42—54no—
223C42—52no—
224C42—54no—
225C42—51no—
226C42—51no—
227C42C22⋊AGL(1,𝔽5)12yes—
228C42C22×AGL(1,𝔽5)12yes—
229C2×C5#155814yescomplemented
230C2×C5C22×#10011yescharacteristic
231C2×C5C2×#41912yes—
232D5—24no—
233C23—52no—
234C23—54no—
235C23—104no—
236C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
237Q8—44no—
238Q8—44no—
239Q8—204no—
240Q8—204no—
241Q8—2016no—
242C2×C4—22no—
243C2×C4—24no—
244C2×C4—24no—
245C2×C4—44no—
246C2×C4—52no—
247C2×C4—52no—
248C2×C4—58no—
249C2×C4—52no—
250C2×C4—108no—
251C2×C4—108no—
252C2×C4—104no—
253C2×C4—104no—
254C2×C4—102no—
255C2×C4—104no—
256C2×C4—2016no—
257C2×C4—204no—
258C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
259C2×C4C2×C22⋊AGL(1,𝔽5)14yes—
260C2×C4C23×AGL(1,𝔽5)11yescharacteristic
261C8—208no—
262C5C2×#155811yescharacteristic, complemented, Sylow
263C22—54no—
264C22—108no—
265C22—104no—
266C22D5⋊#10012yes—
267C22#6578214yes—
268C22C22×C22⋊AGL(1,𝔽5)11yescharacteristic
269C4—21no—
270C4—21no—
271C4—24no—
272C4—44no—
273C4—54no—
274C4—54no—
275C4—102no—
276C4—204no—
277C2—104no—
278C2#1060466214yesdirect product factor
279C2C2×D5⋊#10011yescharacteristic
280C2C2×#6578212yes—
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×C4⋊Q8C4
socleC23×C5C2×C22⋊C4
prime radicalC23×D5C22⋊C4
cosocleC4×Dic5C24
hypercenterC2×C4⋊Q8AGL(1,𝔽5)
hypocenterC5C2×#1558
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
3. C2×#64931C2semidirect
4. #10604662C2direct (N × H)
20. #64931C22semidirect
229. C2×C5#1558semidirect
262. C5C2×#1558semidirect
278. C2#10604662direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊Q82
C2×#656842
C2×#649312
#106046622
C2×#15585