Finite Group Databasebeta

← C4×#65680 #13033607

Subgroups — C4×#65680 #13033607

Order 1280.

1318 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×#65680C212yesmaximal
2C43×D5C211yesmaximal, characteristic
3C4×C4⋊#170C214yesmaximal, complemented
4C4×#4003C214yesmaximal
5#10604174C212yesmaximal, complemented
6C42×#170C212yesmaximal, complemented
7C2×C42×D5C411yescharacteristic
8C2×C42×D5C411yescharacteristic
9C2×C42×D5C412yes—
10C2×C42×D5C2212yes—
11C2×C42×D5C2211yescharacteristic
12C2×#4003C2214yes—
13C2×C4⋊#170C2214yes—
14C2×C4×#170C2218yes—
15C2×C4×#170C2214yes—
16#65680C4116yesdirect product factor
17C43×C5C411yescharacteristic
18C42×Dic5C412yes—
19C42×Dic5C411yescharacteristic
20C42×Dic5C2211yescharacteristic
21C42×Dic5C2211yescharacteristic
22C42×Dic5C2212yes—
23#64918C2218yes—
24C4×#431—51nomaximal, Sylow
25C22×C4×D5C2×C411yescharacteristic
26C22×C4×D5C2×C412yes—
27C22×C4×D5C2×C412yes—
28C22×C4×D5C2×C411yescharacteristic
29C22×C4×D5C2311yescharacteristic
30C22×#170C2318yes—
31C2×C42×C5C2×C411yescharacteristic
32C2×C42×C5C2×C412yes—
33C2×C42×C5C2×C411yescharacteristic
34C2×C42×C5C2×C412yes—
35C2×C42×C5C2×C411yescharacteristic
36C2×C4×Dic5C2×C412yes—
37C2×C4×Dic5C2×C411yescharacteristic
38C2×C4×Dic5C2×C412yes—
39C2×C4×Dic5C2×C412yes—
40C2×C4×Dic5C2×C411yescharacteristic
41C2×C4×Dic5C2×C412yes—
42C2×C4×Dic5C2×C412yes—
43C2×C4×Dic5C2×C412yes—
44C2×C4×Dic5C2×C411yescharacteristic
45C2×C4×Dic5C2312yes—
46C2×C4×Dic5C2311yescharacteristic
47C2×C4×Dic5C2311yescharacteristic
48C2×C4×Dic5C2312yes—
49C42×D5—24no—
50C42×D5—24no—
51C42×D5—28no—
52C42×D5C8116yescomplemented
53C42×D5C2×C418yes—
54#4003C2×C4116yes—
55C4⋊#170C2×C4116yescomplemented
56C4×#170—216no—
57C4×#170C2×C4116yescomplemented
58C2×#431—52no—
59C2×C43—51no—
60C4×C4⋊C8—54no—
61C4×C22⋊C8—54no—
62#1744—52no—
63C42×C8—52no—
64C23×D5C22×C411yescharacteristic
65C22×C4×C5C22×C411yescharacteristic
66C22×C4×C5C22×C412yes—
67C22×C4×C5C22×C411yescharacteristic
68C22×C4×C5C22×C411yescharacteristic
69C22×C4×C5C22×C412yes—
70C22×Dic5C22×C411yescharacteristic
71C22×Dic5C22×C412yes—
72C22×Dic5C22×C411yescharacteristic
73C22×Dic5C22×C412yes—
74C22×Dic5C2411yescharacteristic
75C2×C4×D5—24no—
76C2×C4×D5—22no—
77C2×C4×D5—24no—
78C2×C4×D5—22no—
79C2×C4×D5—24no—
80C2×C4×D5—24no—
81C2×C4×D5—24no—
82C2×C4×D5C4214yes—
83C2×C4×D5C4214yes—
84C2×C4×D5C2×C818yes—
85C2×C4×D5C2×C818yes—
86C2×C4×D5C2×C818yes—
87C2×C4×D5C22×C414yes—
88C2×#170—216no—
89C2×#170C22×C4116yes—
90C42×C5—24no—
91C42×C5—22no—
92C42×C5C4214yes—
93C42×C5C2×C818yes—
94C42×C5M1614yes—
95C4×Dic5—22no—
96C4×Dic5—24no—
97C4×Dic5—24no—
98C4×Dic5—24no—
99C4×Dic5—24no—
100C4×Dic5C4214yes—
101C4×Dic5C2×C818yes—
102C4×Dic5C2×C818yes—
103C4×Dic5C2×C818yes—
104C4×Dic5M1614yes—
105C4×Dic5C22×C414yes—
106C4×Dic5C22×C414yes—
107C4×Dic5#4118yes—
108C22×C42—52no—
109C22×C42—51no—
110C22×C42—51no—
111C22×C42—52no—
112C22×C42—51no—
113#431—516no—
114C2×C4⋊C8—54no—
115C2×C22⋊C8—54no—
116C2×C4×C8—54no—
117C2×C4×C8—58no—
118C43—52no—
119C43—51no—
120C43—51no—
121C43—52no—
122C43—51no—
123C43AGL(1,𝔽5)11yescharacteristic
124#336—58no—
125C23×C5C23×C411yescharacteristic
126C22×D5—22no—
127C22×D5—21no—
128C22×D5—21no—
129C22×D5C2×C4212yes—
130C22×D5C22×C814yes—
131C2×C4×C5—22no—
132C2×C4×C5—22no—
133C2×C4×C5—22no—
134C2×C4×C5C2×C4212yes—
135C2×C4×C5C2×C4212yes—
136C2×C4×C5C2×C4212yes—
137C2×C4×C5#11714yes—
138C2×C4×C5C22×C814yes—
139C2×C4×C5C22×C814yes—
140C2×C4×C5C22×C814yes—
141C2×C4×C5C2×M1612yes—
142C2×C4×C5C2×M1614yes—
143C2×C4×C5C2×M1612yes—
144C2×Dic5—22no—
145C2×Dic5—21no—
146C2×Dic5—22no—
147C2×Dic5—21no—
148C2×Dic5C2×C4212yes—
149C2×Dic5C2×C4212yes—
150C2×Dic5#11714yes—
151C2×Dic5C22×C814yes—
152C2×Dic5C22×C814yes—
153C2×Dic5C22×C814yes—
154C2×Dic5C2×M1614yes—
155C2×Dic5C23×C412yes—
156C2×Dic5C2×#4114yes—
157C4×D5—28no—
158C4×D5—216no—
159C4×D5—28no—
160C4×D5—216no—
161C4×D5C4×C8116yescomplemented
162#170—216no—
163C23×C4—51no—
164C23×C4—52no—
165C23×C4—52no—
166C23×C4—51no—
167C23×C4—51no—
168C22×C8—58no—
169C2×C42—51no—
170C2×C42—52no—
171C2×C42—51no—
172C2×C42—52no—
173C2×C42—52no—
174C2×C42—52no—
175C2×C42—51no—
176C2×C42—51no—
177C2×C42—516no—
178C2×C42—58no—
179C2×C42—52no—
180C2×C42—52no—
181C2×C42—52no—
182C2×C42—52no—
183C2×C42—51no—
184C2×C42—104no—
185C2×C42—108no—
186C2×C42—104no—
187C2×C42C2×AGL(1,𝔽5)11yescharacteristic
188C2×C42C2×AGL(1,𝔽5)12yes—
189C2×C42C2×AGL(1,𝔽5)12yes—
190C2×C42C2×AGL(1,𝔽5)11yescharacteristic
191C2×C42C2×AGL(1,𝔽5)11yescharacteristic
192C4⋊C8—516no—
193C22⋊C8—516no—
194C4×C8—516no—
195C4×C8—1016no—
196C22×C5C22×C4211yescharacteristic
197C22×C5C2×#11712yes—
198C22×C5C23×C812yes—
199C22×C5C22×M1611yescharacteristic
200C22×C5C22×M1611yescharacteristic
201C2×D5—22no—
202C2×D5—24no—
203C2×D5—24no—
204C2×D5—22no—
205C2×D5C2×C4×C814yes—
206C4×C5—24no—
207C4×C5—22no—
208C4×C5C2×C4×C814yes—
209C4×C5C4×M1614yes—
210C4×C5#43118yescomplemented
211Dic5—22no—
212Dic5—24no—
213Dic5C2×C4×C814yes—
214Dic5#43118yescomplemented
215Dic5C4×#4114yes—
216C24—51no—
217C22×C4—51no—
218C22×C4—51no—
219C22×C4—52no—
220C22×C4—58no—
221C22×C4—54no—
222C22×C4—52no—
223C22×C4—51no—
224C22×C4—58no—
225C22×C4—58no—
226C22×C4—54no—
227C22×C4—54no—
228C22×C4—104no—
229C22×C4—104no—
230C22×C4—104no—
231C22×C4—102no—
232C22×C4—104no—
233C22×C4—102no—
234C22×C4—104no—
235C22×C4C22×AGL(1,𝔽5)12yes—
236C22×C4C22×AGL(1,𝔽5)11yescharacteristic
237C22×C4C22×AGL(1,𝔽5)11yescharacteristic
238C22×C4C22×AGL(1,𝔽5)12yes—
239C22×C4C22×AGL(1,𝔽5)11yescharacteristic
240C2×C8—516no—
241C2×C8—1016no—
242C42—22no—
243C42—24no—
244C42—58no—
245C42—58no—
246C42—58no—
247C42—54no—
248C42—54no—
249C42—54no—
250C42—54no—
251C42—58no—
252C42—104no—
253C42—104no—
254C42—104no—
255C42—102no—
256C42—104no—
257C42D5⋊C818yes—
258C42#70014yes—
259C42C4×AGL(1,𝔽5)14yes—
260C2×C5C4×#11711yescharacteristic
261C2×C5C22×C4×C811yescharacteristic
262C2×C5C2×C4×M1611yescharacteristic
263C2×C5C2×#43112yes—
264C2×C5C2×#43112yes—
265D5—24no—
266C23—54no—
267C23—52no—
268C23—101no—
269C23—101no—
270C23—102no—
271C23C23×AGL(1,𝔽5)11yescharacteristic
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—54no—
276C2×C4—54no—
277C2×C4—54no—
278C2×C4—52no—
279C2×C4—52no—
280C2×C4—54no—
281C2×C4—54no—
282C2×C4—516no—
283C2×C4—54no—
284C2×C4—52no—
285C2×C4—1016no—
286C2×C4—108no—
287C2×C4—101no—
288C2×C4—102no—
289C2×C4—101no—
290C2×C4—102no—
291C2×C4—108no—
292C2×C4—1016no—
293C2×C4C2×D5⋊C814yes—
294C2×C4C2×D5⋊C814yes—
295C2×C4C2×D5⋊C814yes—
296C2×C4C2×#70012yes—
297C2×C4C2×#70014yes—
298C2×C4D5⋊M1612yes—
299C2×C4C2×C4×AGL(1,𝔽5)12yes—
300C2×C4C2×C4×AGL(1,𝔽5)12yes—
301C2×C4C2×C4×AGL(1,𝔽5)12yes—
302C2×C4#413014yes—
303C8—1016no—
304C5C4×#43111yescharacteristic, complemented, Sylow
305C22—54no—
306C22—102no—
307C22—104no—
308C22—104no—
309C22—102no—
310C22C22×D5⋊C812yes—
311C22C22×#70011yescharacteristic
312C22C2×D5⋊M1611yescharacteristic
313C22C22×C4×AGL(1,𝔽5)11yescharacteristic
314C22C2×#413012yes—
315C4—24no—
316C4—22no—
317C4—54no—
318C4—58no—
319C4—54no—
320C4—102no—
321C4—104no—
322C4C4×D5⋊C814yes—
323C4C4×#70014yes—
324C4#6568018yesdirect product factor
325C2—104no—
326C2C2×C4×D5⋊C811yescharacteristic
327C2C2×C4×#70011yescharacteristic
328C2C2×#6568012yes—
329C2D5⋊#43112yes—
330C2C4×#413011yescharacteristic
subgroupG/H
centerC2×C42C2×AGL(1,𝔽5)
commutatorC2×C5C22×C4×C8
FrattiniC23C23×AGL(1,𝔽5)
FittingC43×C5C4
socleC23×C5C23×C4
prime radicalC23×D5C22×C4
cosocleC22×Dic5C24
hypercenterC43AGL(1,𝔽5)
hypocenterC5C4×#431
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
3. C4×C4⋊#170C2semidirect
5. #10604174C2semidirect
6. C42×#170C2semidirect
16. #65680C4direct (N × H)
52. C42×D5C8semidirect
55. C4⋊#170C2×C4semidirect
57. C4×#170C2×C4semidirect
161. C4×D5C4×C8semidirect
210. C4×C5#431semidirect
214. Dic5#431semidirect
304. C5C4×#431semidirect
324. C4#65680direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#656802
C43×D52
C4×C4⋊#1702
C4×#40032
#106041742
C42×#1702
C4×#4315