Finite Group Databasebeta

← C5×#17632 #11940352

Subgroups — C5×#17632 #11940352

Order 1280.

874 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3502C211yesmaximal, characteristic
2C5×#2983C211yesmaximal, characteristic
3C5×#2356C211yesmaximal, characteristic
4C5×#1518C212yesmaximal
5C5×#1515C214yesmaximal
6C5×#1506C214yesmaximal
7C5×#1503C212yesmaximal
8C5×Q82C414yescomplemented
9C5×#557—24no—
10C5×#557C414yescomplemented
11C5×#544—21no—
12C5×#544—22no—
13C5×#533C2212yes—
14C5×#533C2214yes—
15C5×#519—21no—
16C2×C4×C5×Q8C2211yescharacteristic
17C5×#446—24no—
18C5×#432C2214yes—
19C5×#431C2212yes—
20C5×#391—21no—
21C5×#387—22no—
22C5×#383C2212yes—
23C5×#382C2211yescharacteristic
24C4×C5×C4⋊C4—21no—
25C4×C5×C4⋊C4C2211yescharacteristic
26C5×#376C2212yes—
27C5×#328C2214yes—
28C5×#328C2214yes—
29C5×#328C2218yes—
30#17632C511yesmaximal, characteristic, direct product factor, Sylow
31C22×C5×Q8D411yescharacteristic
32C5×C4⋊Q8—28no—
33C5×C4⋊Q8—24no—
34C5×C4⋊Q8C2×C412yes—
35C5×C4⋊Q8C2×C414yes—
36C5×C4⋊Q8C2×C412yes—
37C5×C4⋊Q8C2×C414yes—
38C5×#125—28no—
39C5×#125—24no—
40C5×#125—22no—
41C5×#125—24no—
42C5×C22⋊Q8—24no—
43C5×C22⋊Q8—22no—
44C5×C22⋊Q8C2314yes—
45C4×C5×Q8—24no—
46C4×C5×Q8—24no—
47C4×C5×Q8—22no—
48C4×C5×Q8—24no—
49C4×C5×Q8C2×C414yes—
50C4×C5×Q8C2×C418yes—
51C4×C5×Q8C2×C414yes—
52C4×C5×Q8D414yes—
53C5×#117—24no—
54C5×#117—22no—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4—21no—
57C2×C5×C4⋊C4D411yescharacteristic
58C2×C5×C4⋊C4D412yes—
59C2×C42×C5—22no—
60C2×C42×C5—21no—
61C2×C42×C5C2312yes—
62C2×C42×C5C2311yescharacteristic
63C5×C4⋊C8—22no—
64C5×C4⋊C8—24no—
65C5×C22⋊C8C2314yes—
66C5×#97—24no—
67C4×C5×C8—22no—
68C5×#95—22no—
69C5×#95—22no—
70C5×#95—21no—
71C5×#95—22no—
72C5×#95C2311yescharacteristic
73C5×#95C2312yes—
74C5×#95C2311yescharacteristic
75#3502C2×C511yescharacteristic
76#2983C2×C511yescharacteristic
77#2356C2×C511yescharacteristic
78#1518C2×C512yes—
79#1515C2×C514yes—
80#1506C2×C514yes—
81#1503C2×C512yes—
82C2×C5×Q8—22no—
83C2×C5×Q8—24no—
84C2×C5×Q8—22no—
85C2×C5×Q8—22no—
86C2×C5×Q8C22⋊C414yes—
87C2×C5×Q8C22×C414yes—
88C22×C4×C5—21no—
89C22×C4×C5—22no—
90C22×C4×C5—21no—
91C22×C4×C5C2×D412yes—
92C22×C4×C5C2×D412yes—
93C22×C4×C5C2×D411yescharacteristic
94C22×C4×C5C2×D411yescharacteristic
95C22×C4×C5C2411yescharacteristic
96C2×C5×C8—24no—
97C5×C4⋊C4—24no—
98C5×C4⋊C4—22no—
99C5×C4⋊C4—24no—
100C5×C4⋊C4—22no—
101C5×C4⋊C4—22no—
102C5×C4⋊C4—24no—
103C5×C4⋊C4—24no—
104C5×C4⋊C4—28no—
105C5×C4⋊C4—24no—
106C5×C4⋊C4—42no—
107C5×C4⋊C4—42no—
108C5×C4⋊C4C22⋊C418yes—
109C5×C4⋊C4C22⋊C414yes—
110C5×C4⋊C4C22×C414yes—
111C5×C22⋊C4—24no—
112C42×C5—28no—
113C42×C5—24no—
114C42×C5—44no—
115C42×C5—42no—
116C42×C5C22×C414yes—
117C42×C5C22×C412yes—
118C42×C5C2×D412yes—
119C42×C5C2×D414yes—
120Q82C4×C514yescomplemented
121#557—24no—
122#557C4×C514yescomplemented
123#544—21no—
124#544—22no—
125#533C22×C512yes—
126#533C22×C514yes—
127#519—21no—
128C2×C4×Q8C22×C511yescharacteristic
129#446—24no—
130#432C22×C514yes—
131#431C22×C512yes—
132#391—21no—
133#387—22no—
134#383C22×C512yes—
135#382C22×C511yescharacteristic
136C4×C4⋊C4—21no—
137C4×C4⋊C4C22×C511yescharacteristic
138#376C22×C512yes—
139#328C22×C514yes—
140#328C22×C514yes—
141#328C22×C518yes—
142C23×C5C22×D411yescharacteristic
143C5×Q8—28no—
144C5×Q8—44no—
145C5×Q8—84no—
146C5×Q8—82no—
147C2×C4×C5—22no—
148C2×C4×C5—22no—
149C2×C4×C5—22no—
150C2×C4×C5—24no—
151C2×C4×C5—24no—
152C2×C4×C5—42no—
153C2×C4×C5—41no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—42no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—42no—
161C2×C4×C5—41no—
162C2×C4×C5—42no—
163C2×C4×C5C2×C22⋊C414yes—
164C2×C4×C5C2×C22⋊C412yes—
165C2×C4×C5C2×C22⋊C414yes—
166C2×C4×C5C2×C22⋊C412yes—
167C2×C4×C5#13712yes—
168C2×C4×C5#13712yes—
169C2×C4×C5C23×C411yescharacteristic
170C2×C4×C5C22×D411yescharacteristic
171C5×C8—44no—
172C22×Q8C5×D411yescharacteristic
173C4⋊Q8—28no—
174C4⋊Q8—24no—
175C4⋊Q8C2×C4×C512yes—
176C4⋊Q8C2×C4×C514yes—
177C4⋊Q8C2×C4×C512yes—
178C4⋊Q8C2×C4×C514yes—
179#125—28no—
180#125—24no—
181#125—22no—
182#125—24no—
183C22⋊Q8—24no—
184C22⋊Q8—22no—
185C22⋊Q8C23×C514yes—
186C4×Q8—24no—
187C4×Q8—24no—
188C4×Q8—22no—
189C4×Q8—24no—
190C4×Q8C2×C4×C514yes—
191C4×Q8C2×C4×C518yes—
192C4×Q8C2×C4×C514yes—
193C4×Q8C5×D414yes—
194#117—24no—
195#117—22no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C5×D411yescharacteristic
199C2×C4⋊C4C5×D412yes—
200C2×C42—22no—
201C2×C42—21no—
202C2×C42C23×C512yes—
203C2×C42C23×C511yescharacteristic
204C4⋊C8—22no—
205C4⋊C8—24no—
206C22⋊C8C23×C514yes—
207#97—24no—
208C4×C8—22no—
209#95—22no—
210#95—22no—
211#95—21no—
212#95—22no—
213#95C23×C511yescharacteristic
214#95C23×C512yes—
215#95C23×C511yescharacteristic
216C22×C5—21no—
217C22×C5—21no—
218C22×C5C22×C22⋊C411yescharacteristic
219C22×C5C2×#13711yescharacteristic
220C22×C5C2×#13711yescharacteristic
221C4×C5—21no—
222C4×C5—21no—
223C4×C5—24no—
224C4×C5—24no—
225C4×C5—22no—
226C4×C5—42no—
227C4×C5—44no—
228C4×C5—44no—
229C4×C5—81no—
230C4×C5—82no—
231C4×C5#41914yes—
232C2×Q8—22no—
233C2×Q8—24no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8C5×C22⋊C414yes—
237C2×Q8C22×C4×C514yes—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4C2×C5×D412yes—
242C22×C4C2×C5×D412yes—
243C22×C4C2×C5×D411yescharacteristic
244C22×C4C2×C5×D411yescharacteristic
245C22×C4C24×C511yescharacteristic
246C2×C8—24no—
247C4⋊C4—24no—
248C4⋊C4—22no—
249C4⋊C4—24no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—24no—
253C4⋊C4—24no—
254C4⋊C4—28no—
255C4⋊C4—24no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4C5×C22⋊C418yes—
259C4⋊C4C5×C22⋊C414yes—
260C4⋊C4C22×C4×C514yes—
261C22⋊C4—24no—
262C42—28no—
263C42—24no—
264C42—44no—
265C42—42no—
266C42C22×C4×C514yes—
267C42C22×C4×C512yes—
268C42C2×C5×D412yes—
269C42C2×C5×D414yes—
270C2×C5—21no—
271C2×C5—21no—
272C2×C5#288411yescharacteristic
273C2×C5C2×#41911yescharacteristic
274C2×C5#290111yescharacteristic
275C23C22×C5×D411yescharacteristic
276Q8—28no—
277Q8—44no—
278Q8—84no—
279Q8—82no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4C2×C5×C22⋊C414yes—
297C2×C4C2×C5×C22⋊C412yes—
298C2×C4C2×C5×C22⋊C414yes—
299C2×C4C2×C5×C22⋊C412yes—
300C2×C4C5×#13712yes—
301C2×C4C5×#13712yes—
302C2×C4C23×C4×C511yescharacteristic
303C2×C4C22×C5×D411yescharacteristic
304C8—44no—
305C5#1763211yescharacteristic, direct product factor, Sylow
306C22—21no—
307C22—21no—
308C22C22×C5×C22⋊C411yescharacteristic
309C22C2×C5×#13711yescharacteristic
310C22C2×C5×#13711yescharacteristic
311C4—21no—
312C4—21no—
313C4—24no—
314C4—24no—
315C4—22no—
316C4—42no—
317C4—44no—
318C4—44no—
319C4—81no—
320C4—82no—
321C4C5×#41914yes—
322C2—21no—
323C2—21no—
324C2C5×#288411yescharacteristic
325C2C2×C5×#41911yescharacteristic
326C2C5×#290111yescharacteristic
subgroupG/H
center, socleC22×C5C22×C22⋊C4
commutatorC2×C4C23×C4×C5
Frattini, cosocleC22×C4C24×C5
prime radicalC23×C5C22×D4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C4×C5×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
8. C5×Q82C4semidirect
10. C5×#557C4semidirect
30. #17632C5direct (N × H)
120. Q82C4×C5semidirect
122. #557C4×C5semidirect
305. C5#17632direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35022
C5×#29832
C5×#23562
C5×#15182
C5×#15152
C5×#15062
C5×#15032
#176325