Finite Group Databasebeta

← C2×#10610841 #12968921

Subgroups — C2×#10610841 #12968921

Order 1280.

1854 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65834C212yesmaximal
2C22×C5×#106C211yesmaximal, characteristic
3C2×#65395C211yesmaximal, characteristic
4C2×#65390C211yesmaximal, characteristic
5C2×#65253C212yesmaximal
6#10610841C2116yesmaximal, direct product factor
7C2×#65145C214yesmaximal, complemented
8C2×#65147C212yesmaximal, complemented
9C2×#65144C212yesmaximal, complemented
10C23×C5×C8C2211yescharacteristic
11C22×C5×C4⋊C4C2212yes—
12C2×#4072C2212yes—
13C2×#4072C2211yescharacteristic
14C2×#4070—24no—
15C22×#681C2211yescharacteristic
16#65834—28no—
17#65834C22116yes—
18C2×#4036—22no—
19C2×#4036C2214yes—
20C2×#4034—22no—
21C2×#4034C2214yes—
22C2×C5×#106C2212yes—
23C2×C5×#106C2212yes—
24C2×C5×#106C2218yes—
25#65395C2218yes—
26C2×#3950C2212yes—
27C2×#3949C2211yescharacteristic
28C2×#3949C2211yescharacteristic
29#65390C2218yes—
30C2×#3947C2212yes—
31C2×C8×Dic5C2212yes—
32#65253C22116yes—
33C2×#3940C2214yes—
34C2×#3939C2214yes—
35#65147C22116yescomplemented
36#65145C22132yescomplemented
37#65144C22116yescomplemented
38C2×#3163—51nomaximal, Sylow
39C23×C4×C5—22no—
40C23×C4×C5C2311yescharacteristic
41C22×Dic10—24no—
42C22×C5×C8Q818yescomplemented
43C22×C5×C8C2311yescharacteristic
44C22×C5×C8C2311yescharacteristic
45C22×C5×C8C2314yes—
46C2×C5×C4⋊C4—22no—
47C2×C5×C4⋊C4—24no—
48C2×C5×C4⋊C4C2314yes—
49C2×C5×C4⋊C4C2318yes—
50C2×C22⋊Dic5—22no—
51C2×C22⋊Dic5D412yes—
52#4072—24no—
53#4072D414yes—
54#4072C2318yes—
55#4072C2314yes—
56C2×C4⋊Dic5—24no—
57C2×C4⋊Dic5D412yes—
58C2×C4⋊Dic5C2312yes—
59C2×C4⋊Dic5C2312yes—
60#4070—232no—
61C2×#683—24no—
62C2×#683—24no—
63C2×C4×Dic5—22no—
64C2×C4×Dic5C2312yes—
65C2×#681Q818yescomplemented
66C2×#681C2314yes—
67C22×#168C2312yes—
68#4036—216no—
69#4036—28no—
70#4036C23116yes—
71#4034—216no—
72#4034—28no—
73#4034C23116yes—
74C5×#106C2318yes—
75C5×#106C2318yes—
76#3950C2318yes—
77#3949C2314yes—
78#3949C2314yes—
79#3947C2318yes—
80C8×Dic5C2318yes—
81#3940C23116yes—
82#3939C23116yes—
83C2×#544—52no—
84#3163—516no—
85C2×#501—54no—
86C2×#499—52no—
87C2×#498—52no—
88C2×#428—52no—
89C2×#427—51no—
90C22×#106D511yescharacteristic
91C2×#405—51no—
92C24×C5C2×D411yescharacteristic
93C22×C4×C5—24no—
94C22×C4×C5—28no—
95C22×C4×C5—84no—
96C22×C4×C5C2×D411yescharacteristic
97C22×C4×C5C2×D412yes—
98C22×C4×C5C2×Q814yes—
99C22×C4×C5C2×Q814yes—
100C22×C4×C5C2411yescharacteristic
101C22×C4×C5C2412yes—
102C22×Dic5—22no—
103C22×Dic5—22no—
104C22×Dic5C2×D414yes—
105C2×Dic10—216no—
106C2×Dic10—88no—
107C2×C5×C8C2×Q814yes—
108C2×C5×C8C2×Q814yes—
109C2×C5×C8C2×Q8116yescomplemented
110C2×C5×C8C2412yes—
111C2×C5×C8C2412yes—
112C5×C4⋊C4—28no—
113C5×C4⋊C4—24no—
114C5×C4⋊C4C2418yes—
115C22⋊Dic5—28no—
116C22⋊Dic5C2×D418yes—
117C4⋊Dic5—22no—
118C4⋊Dic5—22no—
119C4⋊Dic5—216no—
120C4⋊Dic5C2×D418yes—
121C4⋊Dic5C2414yes—
122C4⋊Dic5C2414yes—
123#683—216no—
124#683—216no—
125C4×Dic5—28no—
126C4×Dic5C2×D414yes—
127C4×Dic5C2414yes—
128#681C2×Q8116yescomplemented
129C2×#168C2×Q818yes—
130C2×#168C2414yes—
131C22×M16—51no—
132C23×C8C2×D511yescharacteristic
133#544—516no—
134#544—108no—
135C2×C4⋊Q8—54no—
136C2×C4⋊Q8—102no—
137C2×#125—54no—
138C2×#125—102no—
139C2×C22⋊Q8—104no—
140C2×#117—51no—
141C2×#117—52no—
142C22×C4⋊C4C2×D512yes—
143#501—532no—
144#499—516no—
145#498—516no—
146#428—516no—
147#427—58no—
148C2×#107—52no—
149C2×#107—54no—
150C2×#106—51no—
151C2×#106—51no—
152C2×#106—54no—
153C2×#106C2×D512yes—
154C2×#106C2×D512yes—
155C2×#106C2×D518yes—
156#405—58no—
157C2×#97—52no—
158C2×C4×C8—52no—
159C23×C5—24no—
160C23×C5C4⋊Q814yes—
161C23×C5C22×D412yes—
162C23×C5C22×D411yescharacteristic
163C2×C4×C5—28no—
164C2×C4×C5—48no—
165C2×C4×C5—88no—
166C2×C4×C5C4⋊Q818yes—
167C2×C4×C5C4⋊Q814yes—
168C2×C4×C5C22×D412yes—
169C2×C4×C5C22×D411yescharacteristic
170C2×C4×C5C22×Q812yes—
171C2×C4×C5C22×Q814yes—
172C2×C4×C5C22×Q812yes—
173C2×C4×C5C22×Q814yes—
174C2×C4×C5C2511yescharacteristic
175C2×Dic5—28no—
176C2×Dic5—24no—
177C2×Dic5—24no—
178C2×Dic5—44no—
179C2×Dic5—44no—
180C2×Dic5C22×D418yes—
181Dic10—816no—
182C5×C8C22×Q814yes—
183C5×C8C22×Q814yes—
184#168C22×Q818yes—
185C22×Q8—104no—
186C23×C4—22no—
187C23×C4C22×D511yescharacteristic
188C2×M16—58no—
189C2×M16—54no—
190C22×C8—52no—
191C22×C8Dic1018yescomplemented
192C22×C8C22×D511yescharacteristic
193C22×C8C22×D511yescharacteristic
194C22×C8C22×D514yes—
195C4⋊Q8—516no—
196C4⋊Q8—108no—
197C4⋊Q8—1016no—
198#125—516no—
199#125—108no—
200#125—1016no—
201C22⋊Q8—1032no—
202#117—54no—
203#117—54no—
204#117—58no—
205#117—104no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—24no—
208C2×C4⋊C4—52no—
209C2×C4⋊C4—52no—
210C2×C4⋊C4—52no—
211C2×C4⋊C4—104no—
212C2×C4⋊C4—104no—
213C2×C4⋊C4—104no—
214C2×C4⋊C4C22×D514yes—
215C2×C4⋊C4C22×D518yes—
216C2×C22⋊C4—52no—
217C2×C22⋊C4—102no—
218C2×C42—52no—
219C2×C42—102no—
220#107—58no—
221#107—516no—
222#106—54no—
223#106—54no—
224#106—516no—
225#106C22×D518yes—
226#106C22×D518yes—
227#97—58no—
228C4×C8—58no—
229C22×C5—28no—
230C22×C5—24no—
231C22×C5C2×C4⋊Q814yes—
232C22×C5C2×C4⋊Q812yes—
233C22×C5#57714yes—
234C22×C5C23×D411yescharacteristic
235C4×C5—48no—
236C4×C5C2×C4⋊Q814yes—
237C4×C5C2×C4⋊Q812yes—
238C4×C5C23×Q811yescharacteristic
239C4×C5C23×Q811yescharacteristic
240Dic5—28no—
241Dic5—44no—
242Dic5—44no—
243C24D4×D511yescharacteristic
244C2×Q8—1016no—
245C2×Q8—408no—
246C22×C4—24no—
247C22×C4—28no—
248C22×C4—54no—
249C22×C4—84no—
250C22×C4—102no—
251C22×C4—102no—
252C22×C4C2×Dic1014yes—
253C22×C4D4×D512yes—
254C22×C4D4×D511yescharacteristic
255C22×C4Q8×D514yes—
256C22×C4C23×D512yes—
257C22×C4C23×D511yescharacteristic
258M16—516no—
259C2×C8—58no—
260C2×C8—54no—
261C2×C8C2×Dic1014yes—
262C2×C8C2×Dic1014yes—
263C2×C8C2×Dic10116yescomplemented
264C2×C8C23×D512yes—
265C2×C8C23×D512yes—
266C4⋊C4—24no—
267C4⋊C4—28no—
268C4⋊C4—58no—
269C4⋊C4—54no—
270C4⋊C4—54no—
271C4⋊C4—1016no—
272C4⋊C4—1016no—
273C4⋊C4—1016no—
274C4⋊C4—102no—
275C4⋊C4—102no—
276C4⋊C4C23×D518yes—
277C22⋊C4—58no—
278C22⋊C4—108no—
279C42—54no—
280C42—54no—
281C42—108no—
282C2×C5—24no—
283C2×C5#316314yescomplemented
284C2×C5C22×C4⋊Q811yescharacteristic
285C2×C5C2×#57712yes—
286C23—24no—
287C23#403414yes—
288C23C2×D4×D512yes—
289C23C2×D4×D511yescharacteristic
290Q8—4016no—
291C2×C4—28no—
292C2×C4—48no—
293C2×C4—58no—
294C2×C4—88no—
295C2×C4—108no—
296C2×C4—104no—
297C2×C4—104no—
298C2×C4—204no—
299C2×C4—204no—
300C2×C4#403418yes—
301C2×C4#403414yes—
302C2×C4C22×Dic1012yes—
303C2×C4C22×Dic1014yes—
304C2×C4C2×D4×D511yescharacteristic
305C2×C4C2×D4×D512yes—
306C2×C4C2×Q8×D512yes—
307C2×C4C2×Q8×D514yes—
308C2×C4C24×D511yescharacteristic
309C8—58no—
310C8C22×Dic1014yes—
311C8C22×Dic1014yes—
312C5C2×#316311yescharacteristic, complemented, Sylow
313C22—28no—
314C22—24no—
315C22C2×#403414yes—
316C22C2×#403412yes—
317C22#6609614yes—
318C22C22×D4×D511yescharacteristic
319C4—48no—
320C4—108no—
321C4—204no—
322C4—204no—
323C4C2×#403412yes—
324C4C2×#403414yes—
325C4C23×Dic1011yescharacteristic
326C4C22×Q8×D511yescharacteristic
327C2—24no—
328C2#1061084114yesdirect product factor
329C2C22×#403411yescharacteristic
330C2C2×#6609612yes—
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC22×C5×#106C2
socleC23×C5C22×D4
prime radicalC24×C5C2×D4
hypercenterC22×#106D5
hypocenterC5C2×#3163
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
6. #10610841C2direct (N × H)
7. C2×#65145C2semidirect
8. C2×#65147C2semidirect
9. C2×#65144C2semidirect
35. #65147C22semidirect
36. #65145C22semidirect
37. #65144C22semidirect
42. C22×C5×C8Q8semidirect
65. C2×#681Q8semidirect
109. C2×C5×C8C2×Q8semidirect
128. #681C2×Q8semidirect
191. C22×C8Dic10semidirect
263. C2×C8C2×Dic10semidirect
283. C2×C5#3163semidirect
312. C5C2×#3163semidirect
328. C2#10610841direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658342
C22×C5×#1062
C2×#653952
C2×#653902
C2×#652532
#106108412
C2×#651452
C2×#651472
C2×#651442
C2×#31635