Finite Group Databasebeta

← C2×#10601430 #12128134

Subgroups — C2×#10601430 #12128134

Order 1280.

1270 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#107C211yesmaximal, characteristic, complemented
2C22×#3952C211yesmaximal, characteristic
3C2×#65276C212yesmaximal
4C2×#64771C211yesmaximal, characteristic, complemented
5C2×#64749C212yesmaximal, complemented
6#10601430C218yesmaximal, direct product factor
7C23×C4×D5C2211yescharacteristic
8C23×C5×C8C2211yescharacteristic
9C22×C5×C4⋊C4C2212yes—
10C22×#685—22no—
11C22×C4⋊Dic5C2212yes—
12C23×#168C2211yescharacteristic
13C2×C5×#107—24no—
14C2×C5×#107C2214yescomplemented
15C2×#3963—22no—
16C2×#3952—24no—
17C2×#3952C2214yes—
18#65276—24no—
19#65276C2218yes—
20#64771C2214yescomplemented
21#64749C2218yescomplemented
22C2×#2076—51nomaximal, Sylow
23C24×D5D411yescharacteristic
24C23×C4×C5—22no—
25C23×C4×C5C2311yescharacteristic
26C23×Dic5—22no—
27C23×Dic5D411yescharacteristic
28C22×C4×D5—22no—
29C22×C4×D5—24no—
30C22×C4×D5—22no—
31C22×C4×D5—24no—
32C22×C4×D5D412yes—
33C22×C4×D5C2312yes—
34C22×C5×C8—24no—
35C22×C5×C8D414yes—
36C22×C5×C8C2312yes—
37C2×C5×C4⋊C4—24no—
38C2×C5×C4⋊C4—24no—
39C2×C5×C4⋊C4—22no—
40C2×C5×C4⋊C4C2314yes—
41C2×#685—28no—
42C2×#685—48no—
43C2×C4⋊Dic5—24no—
44C2×C4⋊Dic5—24no—
45C2×C4⋊Dic5—22no—
46C2×C4⋊Dic5C2314yes—
47C22×#168—22no—
48C22×#168—24no—
49C22×#168C2312yes—
50C5×#107—28no—
51#3963—28no—
52#3952—28no—
53C22×#107D511yescharacteristic, complemented
54C22×C22⋊C8—51no—
55C2×#380—52no—
56#2076—58no—
57C2×#340—51no—
58C2×#340—52no—
59C24×C5C2×D411yescharacteristic
60C23×D5—22no—
61C23×D5—24no—
62C23×D5—22no—
63C23×D5—24no—
64C23×D5Q1614yes—
65C23×D5C2×D412yes—
66C22×C4×C5—24no—
67C22×C4×C5—44no—
68C22×C4×C5—44no—
69C22×C4×C5—44no—
70C22×C4×C5C2×D411yescharacteristic
71C22×C4×C5C2×D412yes—
72C22×C4×C5#4114yes—
73C22×C4×C5#4112yes—
74C22×C4×C5#4114yes—
75C22×C4×C5C2411yescharacteristic
76C22×Dic5—22no—
77C22×Dic5—24no—
78C22×Dic5—24no—
79C22×Dic5—44no—
80C22×Dic5—44no—
81C22×Dic5—44no—
82C22×Dic5C2×D412yes—
83C2×C4×D5—24no—
84C2×C4×D5—28no—
85C2×C4×D5—22no—
86C2×C4×D5—24no—
87C2×C4×D5—22no—
88C2×C4×D5—24no—
89C2×C4×D5—44no—
90C2×C4×D5—44no—
91C2×C4×D5—48no—
92C2×C5×C8—28no—
93C2×C5×C8—24no—
94C2×C5×C8C2×D414yes—
95C5×C4⋊C4—24no—
96C5×C4⋊C4—24no—
97C5×C4⋊C4—44no—
98#685—416no—
99C4⋊Dic5—24no—
100C4⋊Dic5—24no—
101C4⋊Dic5—44no—
102C2×#168—22no—
103C2×#168—24no—
104C2×#168—44no—
105C24×C4—51no—
106C23×C8—51no—
107C23×C8C2×D511yescharacteristic
108C22×C4⋊C4—52no—
109C22×C4⋊C4C2×D512yes—
110C22×C22⋊C4—102no—
111C2×#107—24no—
112C2×#107C2×D514yescomplemented
113C2×C22⋊C8—54no—
114C2×C22⋊C8—104no—
115#380—58no—
116#380—104no—
117C2×#95—102no—
118#340—54no—
119#340—58no—
120C23×C5#12112yes—
121C23×C5#12314yes—
122C23×C5C2×Q1612yes—
123C23×C5#13512yes—
124C23×C5AGL(1,ℤ/8)14yes—
125C23×C5C22×D411yescharacteristic
126C22×D5—22no—
127C22×D5—24no—
128C22×D5—22no—
129C22×D5—24no—
130C22×D5—28no—
131C22×D5—216no—
132C22×D5—44no—
133C22×D5—44no—
134C22×D5—48no—
135C22×D5C2×Q1614yes—
136C2×C4×C5—44no—
137C2×C4×C5—44no—
138C2×C4×C5—44no—
139C2×C4×C5—88no—
140C2×C4×C5#12112yes—
141C2×C4×C5#12314yes—
142C2×C4×C5#12314yes—
143C2×C4×C5#12414yes—
144C2×C4×C5#12618yes—
145C2×C4×C5C22×D411yescharacteristic
146C2×C4×C5C2×#4112yes—
147C2×C4×C5C2×#4111yescharacteristic
148C2×C4×C5C2×#4112yes—
149C2×Dic5—22no—
150C2×Dic5—24no—
151C2×Dic5—44no—
152C2×Dic5—44no—
153C2×Dic5—44no—
154C2×Dic5—44no—
155C2×Dic5—88no—
156C4×D5—42no—
157C4×D5—42no—
158C4×D5—44no—
159C4×D5—48no—
160C5×C8—24no—
161#168—42no—
162C25—51no—
163C23×C4—22no—
164C23×C4—51no—
165C23×C4—52no—
166C23×C4—52no—
167C23×C4—104no—
168C23×C4—102no—
169C23×C4—104no—
170C23×C4—102no—
171C23×C4—102no—
172C23×C4C22×D511yescharacteristic
173C22×C8—24no—
174C22×C8—52no—
175C22×C8—104no—
176C22×C8—102no—
177C22×C8C22⋊D514yes—
178C22×C8C22×D512yes—
179C2×C4⋊C4—24no—
180C2×C4⋊C4—24no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—54no—
183C2×C4⋊C4—104no—
184C2×C4⋊C4—104no—
185C2×C4⋊C4—102no—
186C2×C4⋊C4C22×D514yes—
187C2×C22⋊C4—108no—
188C2×C22⋊C4—208no—
189#107—28no—
190C22⋊C8—108no—
191#95—108no—
192C22×C5#39714yes—
193C22×C5#46714yes—
194C22×C5#46914yes—
195C22×C5#48218yes—
196C22×C5#48418yes—
197C22×C5C2×#12111yescharacteristic
198C22×C5C2×#12312yes—
199C22×C5C22×Q1611yescharacteristic
200C22×C5C2×#13511yescharacteristic
201C22×C5C2×AGL(1,ℤ/8)12yes—
202C2×D5—28no—
203C2×D5—24no—
204C2×D5—44no—
205C2×D5—416no—
206C2×D5—42no—
207C2×D5—42no—
208C4×C5—84no—
209C4×C5#39714yes—
210C4×C5C2×#12311yescharacteristic
211C4×C5C2×#12411yescharacteristic
212C4×C5C2×#12612yes—
213Dic5—42no—
214Dic5—84no—
215C24—52no—
216C24—54no—
217C24—104no—
218C24—104no—
219C24—102no—
220C24—102no—
221C24D4×D511yescharacteristic
222C22×C4—24no—
223C22×C4—44no—
224C22×C4—44no—
225C22×C4—44no—
226C22×C4—52no—
227C22×C4—104no—
228C22×C4—102no—
229C22×C4—104no—
230C22×C4—102no—
231C22×C4—104no—
232C22×C4—102no—
233C22×C4—108no—
234C22×C4—104no—
235C22×C4—104no—
236C22×C4—208no—
237C22×C4—204no—
238C22×C4—204no—
239C22×C4—204no—
240C22×C4—204no—
241C22×C4—204no—
242C22×C4#70914yes—
243C22×C4D4×D511yescharacteristic
244C22×C4#71112yes—
245C22×C4#71314yes—
246C22×C4C2×C22⋊D512yes—
247C22×C4C23×D511yescharacteristic
248C2×C8—24no—
249C2×C8—28no—
250C2×C8—104no—
251C2×C8—102no—
252C2×C8—204no—
253C2×C8C2×C22⋊D514yes—
254C4⋊C4—24no—
255C4⋊C4—24no—
256C4⋊C4—44no—
257C4⋊C4—104no—
258C4⋊C4—104no—
259C4⋊C4—204no—
260C22⋊C4—2016no—
261C2×C5#207618yescomplemented
262C2×C5C2×#39711yescharacteristic
263C2×C5C2×#46711yescharacteristic
264C2×C5C2×#46911yescharacteristic
265C2×C5C2×#48212yes—
266C2×C5C2×#48412yes—
267D5—44no—
268C23—54no—
269C23—104no—
270C23—104no—
271C23—102no—
272C23—102no—
273C23—1016no—
274C23—108no—
275C23—204no—
276C23—208no—
277C23—204no—
278C23#404014yes—
279C23#405714yes—
280C23D5×Q1612yes—
281C23#406512yes—
282C23#408412yes—
283C23C2×D4×D511yescharacteristic
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—88no—
288C2×C4—104no—
289C2×C4—102no—
290C2×C4—204no—
291C2×C4—208no—
292C2×C4—204no—
293C2×C4—202no—
294C2×C4—202no—
295C2×C4—204no—
296C2×C4—204no—
297C2×C4—204no—
298C2×C4—408no—
299C2×C4#404014yes—
300C2×C4#404418yes—
301C2×C4#407514yes—
302C2×C4#408412yes—
303C2×C4#409314yes—
304C2×C4C2×#70912yes—
305C2×C4C2×#71111yescharacteristic
306C2×C4C2×#71312yes—
307C2×C4C22×C22⋊D511yescharacteristic
308C8—24no—
309C8—202no—
310C5C2×#207611yescharacteristic, complemented, Sylow
311C22—104no—
312C22—108no—
313C22—202no—
314C22—202no—
315C22—204no—
316C22—2016no—
317C22#6517318yes—
318C22#6517418yes—
319C22#6528214yes—
320C22#6544814yes—
321C22#6547714yes—
322C22C2×#404012yes—
323C22C2×#405712yes—
324C22C2×D5×Q1611yescharacteristic
325C22C2×#406511yescharacteristic
326C22C2×#408411yescharacteristic
327C4—84no—
328C4—202no—
329C4—404no—
330C4#6528214yes—
331C4C2×#404412yes—
332C4C2×#407511yescharacteristic
333C4C2×#409311yescharacteristic
334C2—204no—
335C2#1060143018yesdirect product factor
336C2C2×#6517412yes—
337C2C2×#6517312yes—
338C2C2×#6528211yescharacteristic
339C2C2×#6544811yescharacteristic
340C2C2×#6547711yescharacteristic
subgroupG/H
centerC24D4×D5
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC22×C5×#107C2
socleC24×C5C2×D4
prime radicalC24×D5D4
hypercenterC22×#107D5
hypocenterC5C2×#2076
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
1. C22×C5×#107C2semidirect
4. C2×#64771C2semidirect
5. C2×#64749C2semidirect
6. #10601430C2direct (N × H)
14. C2×C5×#107C22semidirect
20. #64771C22semidirect
21. #64749C22semidirect
53. C22×#107D5semidirect
112. C2×#107C2×D5semidirect
261. C2×C5#2076semidirect
310. C5C2×#2076semidirect
335. C2#10601430direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1072
C22×#39522
C2×#652762
C2×#647712
C2×#647492
#106014302
C2×#20765