Finite Group Databasebeta

← C4×#65748 #13033604

Subgroups — C4×#65748 #13033604

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×#65748C212yesmaximal
2C2×C42×Dic5C211yesmaximal, characteristic
3C4×C22⋊#170C214yesmaximal
4C4×C4⋊#170C214yesmaximal, complemented
5#10604173C212yesmaximal, complemented
6C42×#170C212yesmaximal, complemented
7C22×C42×C5C411yescharacteristic
8C22×C4×Dic5C412yes—
9C22×C4×Dic5C411yescharacteristic
10C22×C4×Dic5C2212yes—
11C22×C4×Dic5C2211yescharacteristic
12C2×C22⋊#170C2214yes—
13#65748C4116yesdirect product factor
14C2×C4⋊#170C2214yes—
15C2×C4×#170C2218yes—
16C2×C4×#170C2214yes—
17C42×Dic5C411yescharacteristic
18C42×Dic5C412yes—
19C42×Dic5C411yescharacteristic
20C42×Dic5C2211yescharacteristic
21C42×Dic5C2211yescharacteristic
22C42×Dic5C2212yes—
23#64918C2218yes—
24C4×#431—51nomaximal, Sylow
25C23×C4×C5C2×C412yes—
26C23×C4×C5C2×C411yescharacteristic
27C23×Dic5C2×C411yescharacteristic
28C23×Dic5C2×C412yes—
29C23×Dic5C2311yescharacteristic
30C22×#170C2318yes—
31C2×C42×C5C818yescomplemented
32C2×C42×C5C2×C411yescharacteristic
33C2×C42×C5C2×C412yes—
34C2×C42×C5C2×C411yescharacteristic
35C2×C4×Dic5—28no—
36C2×C4×Dic5—28no—
37C2×C4×Dic5C818yescomplemented
38C2×C4×Dic5C2×C412yes—
39C2×C4×Dic5C2×C412yes—
40C2×C4×Dic5C2×C412yes—
41C2×C4×Dic5C2×C412yes—
42C2×C4×Dic5C2×C412yes—
43C2×C4×Dic5C2×C411yescharacteristic
44C2×C4×Dic5C2×C411yescharacteristic
45C2×C4×Dic5C2×C418yes—
46C2×C4×Dic5C2×C411yescharacteristic
47C2×C4×Dic5C2×C412yes—
48C2×C4×Dic5C2×C411yescharacteristic
49C2×C4×Dic5C2×C412yes—
50C2×C4×Dic5C2312yes—
51C2×C4×Dic5C2311yescharacteristic
52C2×C4×Dic5C2311yescharacteristic
53C2×C4×Dic5C2312yes—
54C22⋊#170C2×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—
64C24×C5C22×C411yescharacteristic
65C22×C4×C5—24no—
66C22×C4×C5—24no—
67C22×C4×C5C4214yes—
68C22×C4×C5C2×C814yes—
69C22×C4×C5C2×C818yes—
70C22×C4×C5C2×C814yes—
71C22×C4×C5C22×C412yes—
72C22×C4×C5C22×C411yescharacteristic
73C22×C4×C5C22×C411yescharacteristic
74C22×C4×C5C22×C412yes—
75C22×Dic5—24no—
76C22×Dic5—24no—
77C22×Dic5—24no—
78C22×Dic5—24no—
79C22×Dic5C4214yes—
80C22×Dic5C2×C818yes—
81C22×Dic5C22×C411yescharacteristic
82C22×Dic5C22×C411yescharacteristic
83C22×Dic5C22×C414yes—
84C22×Dic5C22×C412yes—
85C22×Dic5C22×C411yescharacteristic
86C22×Dic5C22×C412yes—
87C22×Dic5C2411yescharacteristic
88C2×#170—216no—
89C2×#170C22×C4116yes—
90C42×C5C2×C814yes—
91C42×C5C2×C818yes—
92C42×C5C2×C814yes—
93C4×Dic5—24no—
94C4×Dic5—24no—
95C4×Dic5—24no—
96C4×Dic5—24no—
97C4×Dic5—24no—
98C4×Dic5—24no—
99C4×Dic5C4214yes—
100C4×Dic5C4214yes—
101C4×Dic5C2×C814yes—
102C4×Dic5C2×C818yes—
103C4×Dic5C2×C814yes—
104C4×Dic5M1618yes—
105C4×Dic5C22×C414yes—
106C4×Dic5C22×C414yes—
107C4×Dic5#4118yes—
108C22×C42—51no—
109C22×C42—51no—
110C22×C42—52no—
111C22×C42—52no—
112C22×C42AGL(1,𝔽5)11yescharacteristic
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—
123C43—51no—
124#336—58no—
125C23×C5—22no—
126C23×C5—22no—
127C23×C5C2×C4212yes—
128C23×C5C22×C812yes—
129C23×C5C22×C812yes—
130C23×C5C23×C411yescharacteristic
131C2×C4×C5—22no—
132C2×C4×C5—22no—
133C2×C4×C5—216no—
134C2×C4×C5C4×C8116yescomplemented
135C2×C4×C5C2×C4212yes—
136C2×C4×C5C2×C4212yes—
137C2×C4×C5#11714yes—
138C2×C4×C5C22×C812yes—
139C2×C4×C5C22×C812yes—
140C2×C4×C5C22×C814yes—
141C2×C4×C5C22×C812yes—
142C2×C4×C5C22×C812yes—
143C2×C4×C5C22×C814yes—
144C2×C4×C5C2×M1614yes—
145C2×Dic5—22no—
146C2×Dic5—22no—
147C2×Dic5—22no—
148C2×Dic5—22no—
149C2×Dic5—28no—
150C2×Dic5—28no—
151C2×Dic5—216no—
152C2×Dic5C2×C4212yes—
153C2×Dic5C2×C4212yes—
154C2×Dic5C2×C4212yes—
155C2×Dic5#11714yes—
156C2×Dic5C22×C814yes—
157C2×Dic5C22×C814yes—
158C2×Dic5C2×M1614yes—
159C2×Dic5C2×M1614yes—
160C2×Dic5C23×C412yes—
161C2×Dic5C2×#4114yes—
162#170—216no—
163C23×C4—52no—
164C23×C4—51no—
165C23×C4—51no—
166C23×C4C2×AGL(1,𝔽5)12yes—
167C23×C4C2×AGL(1,𝔽5)11yescharacteristic
168C22×C8—58no—
169C2×C42—58no—
170C2×C42—58no—
171C2×C42—51no—
172C2×C42—52no—
173C2×C42—51no—
174C2×C42—51no—
175C2×C42—52no—
176C2×C42—51no—
177C2×C42—52no—
178C2×C42—51no—
179C2×C42—51no—
180C2×C42—52no—
181C2×C42—52no—
182C2×C42—52no—
183C2×C42—52no—
184C2×C42—52no—
185C2×C42—52no—
186C2×C42—108no—
187C2×C42—108no—
188C2×C42#17018yescomplemented
189C2×C42C2×AGL(1,𝔽5)11yescharacteristic
190C2×C42C2×AGL(1,𝔽5)12yes—
191C2×C42C2×AGL(1,𝔽5)11yescharacteristic
192C4⋊C8—516no—
193C22⋊C8—516no—
194C4×C8—516no—
195C4×C8—1016no—
196C22×C5—22no—
197C22×C5—24no—
198C22×C5—24no—
199C22×C5—22no—
200C22×C5C2×C4×C814yes—
201C22×C5C22×C4211yescharacteristic
202C22×C5C2×#11712yes—
203C22×C5C23×C811yescharacteristic
204C22×C5C23×C811yescharacteristic
205C22×C5C22×M1612yes—
206C4×C5—24no—
207C4×C5C2×C4×C814yes—
208C4×C5C2×C4×C814yes—
209C4×C5#43118yescomplemented
210Dic5—22no—
211Dic5—24no—
212Dic5—22no—
213Dic5C4×M1614yes—
214Dic5#43118yescomplemented
215Dic5C4×#4114yes—
216C24C22×AGL(1,𝔽5)11yescharacteristic
217C22×C4—24no—
218C22×C4—24no—
219C22×C4—51no—
220C22×C4—52no—
221C22×C4—51no—
222C22×C4—58no—
223C22×C4—54no—
224C22×C4—54no—
225C22×C4—52no—
226C22×C4—51no—
227C22×C4—51no—
228C22×C4—104no—
229C22×C4—104no—
230C22×C4—104no—
231C22×C4—104no—
232C22×C4D5⋊C814yes—
233C22×C4C4×AGL(1,𝔽5)14yes—
234C22×C4C2×#17018yes—
235C22×C4C2×#17014yes—
236C22×C4C22×AGL(1,𝔽5)12yes—
237C22×C4C22×AGL(1,𝔽5)11yescharacteristic
238C22×C4C22×AGL(1,𝔽5)11yescharacteristic
239C22×C4C22×AGL(1,𝔽5)12yes—
240C2×C8—516no—
241C2×C8—1016no—
242C42—54no—
243C42—58no—
244C42—54no—
245C42—58no—
246C42—54no—
247C42—54no—
248C42—54no—
249C42—54no—
250C42—58no—
251C42—104no—
252C42—104no—
253C42—104no—
254C42—104no—
255C42—104no—
256C42—104no—
257C42C2×#17014yes—
258C42C2×#17018yes—
259C42C2×#17014yes—
260C2×C5—24no—
261C2×C5C4×#11711yescharacteristic
262C2×C5C22×C4×C811yescharacteristic
263C2×C5C2×C4×M1611yescharacteristic
264C2×C5C2×#43112yes—
265C2×C5C2×#43112yes—
266C23—22no—
267C23—22no—
268C23C2×D5⋊C812yes—
269C23C2×C4×AGL(1,𝔽5)12yes—
270C23C22×#17012yes—
271C23C23×AGL(1,𝔽5)11yescharacteristic
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—216no—
275C2×C4—54no—
276C2×C4—54no—
277C2×C4—54no—
278C2×C4—52no—
279C2×C4—52no—
280C2×C4—54no—
281C2×C4—54no—
282C2×C4—54no—
283C2×C4—52no—
284C2×C4—52no—
285C2×C4—108no—
286C2×C4—1016no—
287C2×C4—108no—
288C2×C4—102no—
289C2×C4—102no—
290C2×C4—102no—
291C2×C4—102no—
292C2×C4C4×#170116yescomplemented
293C2×C4C2×D5⋊C812yes—
294C2×C4C2×D5⋊C812yes—
295C2×C4D5⋊M1614yes—
296C2×C4C2×C4×AGL(1,𝔽5)12yes—
297C2×C4C2×C4×AGL(1,𝔽5)12yes—
298C2×C4#413014yes—
299C2×C4C22×#17014yes—
300C2×C4C22×#17012yes—
301C2×C4C22×#17012yes—
302C2×C4C22×#17014yes—
303C8—1016no—
304C5C4×#43111yescharacteristic, complemented, Sylow
305C22—24no—
306C22—22no—
307C22—24no—
308C22—22no—
309C22C2×C4×#17014yes—
310C22C22×D5⋊C811yescharacteristic
311C22C2×D5⋊M1612yes—
312C22C22×C4×AGL(1,𝔽5)11yescharacteristic
313C22C2×#413012yes—
314C22C23×#17011yescharacteristic
315C4—24no—
316C4—54no—
317C4—58no—
318C4—54no—
319C4—102no—
320C4—104no—
321C4—102no—
322C4C2×C4×#17014yes—
323C4C2×C4×#17014yes—
324C4#6574818yesdirect product factor
325C2—24no—
326C2C4×D5⋊M1611yescharacteristic
327C2D5⋊#43112yes—
328C2C4×#413011yescharacteristic
329C2C22×C4×#17011yescharacteristic
330C2C2×#6574812yes—
subgroupG/H
centerC2×C42C2×AGL(1,𝔽5)
commutatorC2×C5C22×C4×C8
FrattiniC23C23×AGL(1,𝔽5)
FittingC22×C42×C5C4
socleC23×C5C23×C4
prime radicalC24×C5C22×C4
cosocleC22×Dic5C24
hypercenterC22×C42AGL(1,𝔽5)
hypocenterC5C4×#431
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C42 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
4. C4×C4⋊#170C2semidirect
5. #10604173C2semidirect
6. C42×#170C2semidirect
13. #65748C4direct (N × H)
31. C2×C42×C5C8semidirect
37. C2×C4×Dic5C8semidirect
55. C4⋊#170C2×C4semidirect
57. C4×#170C2×C4semidirect
134. C2×C4×C5C4×C8semidirect
188. C2×C42#170semidirect
209. C4×C5#431semidirect
214. Dic5#431semidirect
292. C2×C4C4×#170semidirect
304. C5C4×#431semidirect
324. C4#65748direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#657482
C2×C42×Dic52
C4×C22⋊#1702
C4×C4⋊#1702
#106041732
C42×#1702
C4×#4315