Finite Group Databasebeta

← C5×#12802 #11935522

Subgroups — C5×#12802 #11935522

Order 1280.

468 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 134 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
1C4×C5×C4⋊Q8C211yesmaximal, characteristic
2C2×C5×#356C212yesmaximal
3C5×#1801C212yesmaximal
4C5×#1394C212yesmaximal
5C2×C5×C4⋊Q8C2211yescharacteristic
6C2×C4×C5×Q8C411yescharacteristic
7C2×C4×C5×Q8C2211yescharacteristic
8C5×#423—22no—
9C2×C5×#101C2214yes—
10C5×#391C411yescharacteristic
11C5×#391C2211yescharacteristic
12C5×#389—22no—
13C5×#384C411yescharacteristic
14C4×C5×C4⋊C4—22no—
15C43×C5C411yescharacteristic
16C5×#356—24no—
17C5×#343—22no—
18#12802C511yesmaximal, characteristic, direct product factor, Sylow
19C22×C5×Q8C2×C411yescharacteristic
20C22×C5×Q8C2311yescharacteristic
21C2×C5×M16—24no—
22C5×C4⋊Q8—22no—
23C5×C4⋊Q8D412yes—
24C5×C4⋊Q8Q812yes—
25C4×C5×Q8—41no—
26C4×C5×Q8—41no—
27C4×C5×Q8—41no—
28C4×C5×Q8—41no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4C2×C411yescharacteristic
33C2×C5×C4⋊C4C2×C411yescharacteristic
34C2×C5×C4⋊C4D412yes—
35C2×C42×C5—21no—
36C2×C42×C5—21no—
37C2×C42×C5—21no—
38C2×C42×C5C2×C411yescharacteristic
39C2×C42×C5C2×C411yescharacteristic
40C2×C42×C5C2×C411yescharacteristic
41C2×C42×C5D412yes—
42C5×C4⋊C8—42no—
43C5×C4⋊C8—42no—
44C5×#101—24no—
45C5×#101—24no—
46C5×#95—22no—
47C5×#95—22no—
48C4×C4⋊Q8C2×C511yescharacteristic
49C2×#356C2×C512yes—
50#1801C2×C512yes—
51#1394C2×C512yes—
52C2×C5×Q8—21no—
53C2×C5×Q8—41no—
54C2×C5×Q8—41no—
55C2×C5×Q8—41no—
56C2×C5×Q8—41no—
57C2×C5×Q8C4⋊C412yes—
58C2×C5×Q8C2×D411yescharacteristic
59C2×C5×Q8C2×Q811yescharacteristic
60C2×C5×Q8#4112yes—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—21no—
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22⋊C412yes—
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22×C411yescharacteristic
69C22×C4×C5C2×D412yes—
70C5×M16—44no—
71C5×M16—44no—
72C2×C5×C8—44no—
73C5×C4⋊C4—24no—
74C5×C4⋊C4—24no—
75C5×C4⋊C4—41no—
76C5×C4⋊C4—42no—
77C5×C4⋊C4—41no—
78C5×C4⋊C4—44no—
79C5×C4⋊C4—42no—
80C42×C5—24no—
81C42×C5—21no—
82C42×C5—21no—
83C42×C5—22no—
84C42×C5—22no—
85C42×C5—21no—
86C42×C5—41no—
87C42×C5—42no—
88C42×C5—41no—
89C42×C5—41no—
90C42×C5C4⋊C412yes—
91C2×C4⋊Q8C22×C511yescharacteristic
92C2×C4×Q8C4×C511yescharacteristic
93C2×C4×Q8C22×C511yescharacteristic
94#423—22no—
95C2×#101C22×C514yes—
96#391C4×C511yescharacteristic
97#391C22×C511yescharacteristic
98#389—22no—
99#384C4×C511yescharacteristic
100C4×C4⋊C4—22no—
101C43C4×C511yescharacteristic
102#356—24no—
103#343—22no—
104C23×C5C2×C22⋊C411yescharacteristic
105C5×Q8—41no—
106C5×Q8—41no—
107C5×Q8—42no—
108C5×Q8—42no—
109C5×Q8—42no—
110C2×C4×C5—22no—
111C2×C4×C5—22no—
112C2×C4×C5—22no—
113C2×C4×C5—21no—
114C2×C4×C5—22no—
115C2×C4×C5—21no—
116C2×C4×C5—22no—
117C2×C4×C5—22no—
118C2×C4×C5—22no—
119C2×C4×C5—22no—
120C2×C4×C5—21no—
121C2×C4×C5—22no—
122C2×C4×C5—41no—
123C2×C4×C5—41no—
124C2×C4×C5—41no—
125C2×C4×C5—41no—
126C2×C4×C5—41no—
127C2×C4×C5—42no—
128C2×C4×C5—42no—
129C2×C4×C5—41no—
130C2×C4×C5#9911yescharacteristic
131C2×C4×C5#9911yescharacteristic
132C2×C4×C5C2×C4⋊C411yescharacteristic
133C2×C4×C5#11711yescharacteristic
134C2×C4×C5#12112yes—
135C2×C4×C5C22⋊Q812yes—
136C5×C8—84no—
137C22×Q8C2×C4×C511yescharacteristic
138C22×Q8C23×C511yescharacteristic
139C2×M16—24no—
140C4⋊Q8—22no—
141C4⋊Q8C5×D412yes—
142C4⋊Q8C5×Q812yes—
143C4×Q8—41no—
144C4×Q8—41no—
145C4×Q8—41no—
146C4×Q8—41no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4C2×C4×C511yescharacteristic
151C2×C4⋊C4C2×C4×C511yescharacteristic
152C2×C4⋊C4C5×D412yes—
153C2×C42—21no—
154C2×C42—21no—
155C2×C42—21no—
156C2×C42C2×C4×C511yescharacteristic
157C2×C42C2×C4×C511yescharacteristic
158C2×C42C2×C4×C511yescharacteristic
159C2×C42C5×D412yes—
160C4⋊C8—42no—
161C4⋊C8—42no—
162#101—24no—
163#101—24no—
164#95—22no—
165#95—22no—
166C22×C5—21no—
167C22×C5—21no—
168C22×C5#38011yescharacteristic
169C22×C5C2×#9911yescharacteristic
170C22×C5#41011yescharacteristic
171C4×C5—24no—
172C4×C5—22no—
173C4×C5—21no—
174C4×C5—21no—
175C4×C5—22no—
176C4×C5—21no—
177C4×C5—42no—
178C4×C5—42no—
179C4×C5—41no—
180C4×C5—42no—
181C4×C5—81no—
182C4×C5#35612yescomplemented
183C2×Q8—21no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8C5×C4⋊C412yes—
189C2×Q8C2×C5×D411yescharacteristic
190C2×Q8C2×C5×Q811yescharacteristic
191C2×Q8C5×#4112yes—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4C5×C22⋊C411yescharacteristic
197C22×C4C5×C22⋊C412yes—
198C22×C4C5×C22⋊C411yescharacteristic
199C22×C4C22×C4×C511yescharacteristic
200C22×C4C2×C5×D412yes—
201M16—44no—
202M16—44no—
203C2×C8—44no—
204C4⋊C4—24no—
205C4⋊C4—24no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—42no—
210C4⋊C4—44no—
211C42—24no—
212C42—21no—
213C42—22no—
214C42—22no—
215C42—21no—
216C42—21no—
217C42—41no—
218C42—42no—
219C42—41no—
220C42—41no—
221C42C5×C4⋊C412yes—
222C2×C5—21no—
223C2×C5—21no—
224C2×C5#179911yescharacteristic
225C2×C5C2×#35611yescharacteristic
226C2×C5#213211yescharacteristic
227C23C2×C5×C22⋊C411yescharacteristic
228Q8—41no—
229Q8—41no—
230Q8—42no—
231Q8—42no—
232Q8—42no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4C5×#9911yescharacteristic
254C2×C4C5×#9911yescharacteristic
255C2×C4C2×C5×C4⋊C411yescharacteristic
256C2×C4C5×#11711yescharacteristic
257C2×C4C5×#12112yes—
258C2×C4C5×C22⋊Q812yes—
259C8—84no—
260C5#1280211yescharacteristic, direct product factor, Sylow
261C22—21no—
262C22—21no—
263C22C5×#38011yescharacteristic
264C22C2×C5×#9911yescharacteristic
265C22C5×#41011yescharacteristic
266C4—24no—
267C4—22no—
268C4—21no—
269C4—21no—
270C4—22no—
271C4—21no—
272C4—42no—
273C4—42no—
274C4—41no—
275C4—42no—
276C4—81no—
277C4C5×#35612yescomplemented
278C2—21no—
279C2—21no—
280C2C5×#179911yescharacteristic
281C2C2×C5×#35611yescharacteristic
282C2C5×#213211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC22×Q8C23×C5
prime radicalC23×C5C2×C22⋊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
18. #12802C5direct (N × H)
182. C4×C5#356semidirect
260. C5#12802direct (N × H)
277. C4C5×#356semidirect

Maximal subgroups

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

subgroupindex
C4×C5×C4⋊Q82
C2×C5×#3562
C5×#18012
C5×#13942
#128025