Finite Group Databasebeta

← C5×#12803 #11935523

Subgroups — C5×#12803 #11935523

Order 1280.

480 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2326C211yesmaximal, characteristic
2C2×C5×#355C212yesmaximal
3C5×#1801C212yesmaximal, complemented
4C5×#1394C212yesmaximal, complemented
5C2×C5×#124C2211yescharacteristic
6C2×C4×C5×Q8C2211yescharacteristic
7C2×C4×C5×D4C411yescharacteristic
8C5×#423—22no—
9C2×C5×#101C2214yes—
10C5×#391C2211yescharacteristic
11C5×#390C411yescharacteristic
12C5×#388—22no—
13C5×#385—22no—
14C5×#384C411yescharacteristic
15C5×#376C411yescharacteristic
16C5×#355—24no—
17C5×#343—22no—
18#12803C511yesmaximal, characteristic, direct product factor, Sylow
19C22×C5×Q8C2311yescharacteristic
20C22×C5×D4C2×C411yescharacteristic
21C23×C4×C5—21no—
22C2×C5×M16—24no—
23C5×#124—22no—
24C5×#124D412yes—
25C5×#124Q812yes—
26C4×C5×Q8—42no—
27C4×C5×D4—42no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4C2×C411yescharacteristic
30C2×C5×C4⋊C4C2×C411yescharacteristic
31C2×C5×C4⋊C4D412yes—
32C2×C5×C22⋊C4—22no—
33C2×C5×C22⋊C4—21no—
34C2×C5×C22⋊C4—22no—
35C2×C42×C5C2×C411yescharacteristic
36C2×C42×C5C2×C411yescharacteristic
37C2×C42×C5C2×C411yescharacteristic
38C2×C42×C5D412yes—
39C5×C4⋊C8—44no—
40C5×#101—24no—
41C5×#101—24no—
42C5×#95—21no—
43C5×#95—21no—
44C5×#95—22no—
45#2326C2×C511yescharacteristic
46C2×#355C2×C512yes—
47#1801C2×C512yescomplemented
48#1394C2×C512yescomplemented
49C24×C5—21no—
50C2×C5×Q8—41no—
51C2×C5×Q8—41no—
52C2×C5×Q8C2×D411yescharacteristic
53C2×C5×Q8C2×Q811yescharacteristic
54C2×C5×Q8#4112yes—
55C2×C5×D4—21no—
56C2×C5×D4—41no—
57C2×C5×D4—41no—
58C2×C5×D4C4⋊C412yes—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—42no—
63C22×C4×C5—82no—
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22⋊C412yes—
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22×C411yescharacteristic
68C22×C4×C5C2×D412yes—
69C5×M16—44no—
70C5×M16—44no—
71C2×C5×C8—44no—
72C5×C4⋊C4—41no—
73C5×C4⋊C4—42no—
74C5×C4⋊C4—41no—
75C5×C4⋊C4—82no—
76C5×C22⋊C4—24no—
77C5×C22⋊C4—24no—
78C5×C22⋊C4—42no—
79C5×C22⋊C4—82no—
80C42×C5—22no—
81C42×C5—24no—
82C42×C5—21no—
83C42×C5—41no—
84C42×C5C4⋊C412yes—
85C2×#124C22×C511yescharacteristic
86C2×C4×Q8C22×C511yescharacteristic
87C2×C4×D4C4×C511yescharacteristic
88#423—22no—
89C2×#101C22×C514yes—
90#391C22×C511yescharacteristic
91#390C4×C511yescharacteristic
92#388—22no—
93#385—22no—
94#384C4×C511yescharacteristic
95#376C4×C511yescharacteristic
96#355—24no—
97#343—22no—
98C23×C5—22no—
99C23×C5—42no—
100C23×C5—42no—
101C23×C5—41no—
102C23×C5—41no—
103C23×C5C2×C22⋊C411yescharacteristic
104C5×Q8—41no—
105C5×Q8—41no—
106C5×Q8—42no—
107C5×D4—42no—
108C5×D4—42no—
109C2×C4×C5—21no—
110C2×C4×C5—22no—
111C2×C4×C5—21no—
112C2×C4×C5—22no—
113C2×C4×C5—22no—
114C2×C4×C5—21no—
115C2×C4×C5—22no—
116C2×C4×C5—41no—
117C2×C4×C5—41no—
118C2×C4×C5—41no—
119C2×C4×C5—42no—
120C2×C4×C5—41no—
121C2×C4×C5—41no—
122C2×C4×C5—42no—
123C2×C4×C5—41no—
124C2×C4×C5—41no—
125C2×C4×C5—41no—
126C2×C4×C5—84no—
127C2×C4×C5#9912yes—
128C2×C4×C5C2×C4⋊C411yescharacteristic
129C2×C4×C5#11711yescharacteristic
130C2×C4×C5#12112yes—
131C2×C4×C5C22⋊Q812yes—
132C5×C8—84no—
133C22×Q8C23×C511yescharacteristic
134C22×D4C2×C4×C511yescharacteristic
135C23×C4—21no—
136C2×M16—24no—
137#124—22no—
138#124C5×D412yes—
139#124C5×Q812yes—
140C4×Q8—42no—
141C4×D4—42no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4C2×C4×C511yescharacteristic
144C2×C4⋊C4C2×C4×C511yescharacteristic
145C2×C4⋊C4C5×D412yes—
146C2×C22⋊C4—22no—
147C2×C22⋊C4—21no—
148C2×C22⋊C4—22no—
149C2×C42C2×C4×C511yescharacteristic
150C2×C42C2×C4×C511yescharacteristic
151C2×C42C2×C4×C511yescharacteristic
152C2×C42C5×D412yes—
153C4⋊C8—44no—
154#101—24no—
155#101—24no—
156#95—21no—
157#95—21no—
158#95—22no—
159C22×C5—21no—
160C22×C5—21no—
161C22×C5—44no—
162C22×C5—42no—
163C22×C5—82no—
164C22×C5—81no—
165C22×C5—81no—
166C22×C5#38011yescharacteristic
167C22×C5C2×#9911yescharacteristic
168C22×C5#41011yescharacteristic
169C4×C5—22no—
170C4×C5—21no—
171C4×C5—21no—
172C4×C5—22no—
173C4×C5—22no—
174C4×C5—42no—
175C4×C5—42no—
176C4×C5—41no—
177C4×C5—81no—
178C4×C5—81no—
179C24—21no—
180C2×Q8—41no—
181C2×Q8—41no—
182C2×Q8C2×C5×D411yescharacteristic
183C2×Q8C2×C5×Q811yescharacteristic
184C2×Q8C5×#4112yes—
185C2×D4—21no—
186C2×D4—41no—
187C2×D4—41no—
188C2×D4C5×C4⋊C412yes—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—42no—
193C22×C4—82no—
194C22×C4C5×C22⋊C411yescharacteristic
195C22×C4C5×C22⋊C412yes—
196C22×C4C5×C22⋊C411yescharacteristic
197C22×C4C22×C4×C511yescharacteristic
198C22×C4C2×C5×D412yes—
199M16—44no—
200M16—44no—
201C2×C8—44no—
202C4⋊C4—41no—
203C4⋊C4—42no—
204C4⋊C4—41no—
205C4⋊C4—82no—
206C22⋊C4—24no—
207C22⋊C4—24no—
208C22⋊C4—42no—
209C22⋊C4—82no—
210C42—21no—
211C42—24no—
212C42—22no—
213C42—41no—
214C42C5×C4⋊C412yes—
215C2×C5—21no—
216C2×C5—21no—
217C2×C5—82no—
218C2×C5#179911yescharacteristic
219C2×C5#213311yescharacteristic
220C2×C5#213411yescharacteristic
221C23—22no—
222C23—42no—
223C23—42no—
224C23—41no—
225C23—41no—
226C23C2×C5×C22⋊C411yescharacteristic
227Q8—41no—
228Q8—41no—
229Q8—42no—
230D4—42no—
231D4—42no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—84no—
250C2×C4C5×#9912yes—
251C2×C4C2×C5×C4⋊C411yescharacteristic
252C2×C4C5×#11711yescharacteristic
253C2×C4C5×#12112yes—
254C2×C4C5×C22⋊Q812yes—
255C8—84no—
256C5#1280311yescharacteristic, direct product factor, Sylow
257C22—21no—
258C22—21no—
259C22—44no—
260C22—42no—
261C22—82no—
262C22—81no—
263C22—81no—
264C22C5×#38011yescharacteristic
265C22C2×C5×#9911yescharacteristic
266C22C5×#41011yescharacteristic
267C4—22no—
268C4—21no—
269C4—21no—
270C4—22no—
271C4—22no—
272C4—42no—
273C4—41no—
274C4—42no—
275C4—81no—
276C4—81no—
277C2—21no—
278C2—21no—
279C2—82no—
280C2C5×#179911yescharacteristic
281C2C5×#213311yescharacteristic
282C2C5×#213411yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC22×Q8C23×C5
prime radicalC22×C5×D4C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1801C2semidirect
4. C5×#1394C2semidirect
18. #12803C5direct (N × H)
47. #1801C2×C5semidirect
48. #1394C2×C5semidirect
256. C5#12803direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#23262
C2×C5×#3552
C5×#18012
C5×#13942
#128035