Finite Group Databasebeta

← C5×#12112 #11934832

Subgroups — C5×#12112 #11934832

Order 1280.

390 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 74 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×#3202C211yesmaximal, characteristic
2C5×#2188C212yesmaximal, complemented
3C5×#2020C211yesmaximal, characteristic
4C5×#1350C212yesmaximal, complemented
5C5×#1315C211yesmaximal, characteristic
6C2×C5×#137—21no—
7C22×C5×Q16C2211yescharacteristic
8C5×#536—21no—
9C2×C5×Q32—22no—
10C5×#485—22no—
11C5×#470—21no—
12C5×#467C2212yes—
13C5×#451—22no—
14C2×C5×#101—21no—
15C5×#408C2211yescharacteristic
16C5×#358—22no—
17C5×C22⋊C16C2212yes—
18C5×#341C2211yescharacteristic
19#12112C511yesmaximal, characteristic, direct product factor, Sylow
20C2×C5×#41D411yescharacteristic
21C22×C5×Q8—21no—
22C22×C5×Q8—21no—
23C5×#137—42no—
24C5×#137—42no—
25C2×C5×Q16—21no—
26C2×C5×Q16—22no—
27C2×C5×Q16—42no—
28C2×C5×Q16—41no—
29C2×C5×Q16D412yes—
30C2×C5×SD16—41no—
31C2×C5×M16—21no—
32C2×C5×M16D411yescharacteristic
33C22×C5×C8C2311yescharacteristic
34C5×C4⋊Q8—41no—
35C5×#124—41no—
36C5×#123—41no—
37C5×#123—41no—
38C5×C22⋊Q8—22no—
39C5×C22⋊Q8—22no—
40C5×#117—21no—
41C5×Q32—44no—
42C2×C5×C16—22no—
43C5×#107D412yes—
44C5×#106—21no—
45C5×#103—22no—
46C5×#103—22no—
47C5×#101—42no—
48C5×C22⋊C8—22no—
49#3202C2×C511yescharacteristic
50#2188C2×C512yescomplemented
51#2020C2×C511yescharacteristic
52#1350C2×C512yescomplemented
53#1315C2×C511yescharacteristic
54C5×#41—41no—
55C5×#41—41no—
56C2×C5×Q8—22no—
57C2×C5×Q8—22no—
58C2×C5×Q8—41no—
59C2×C5×Q8—41no—
60C2×C5×Q8—41no—
61C2×C5×Q8—41no—
62C2×C5×Q8—41no—
63C2×C5×Q8—41no—
64C2×C5×Q8—81no—
65C2×C5×Q8—81no—
66C2×C5×Q8D811yescharacteristic
67C2×C5×D4—21no—
68C2×C5×D4D811yescharacteristic
69C22×C4×C5—21no—
70C22×C4×C5—41no—
71C22×C4×C5—41no—
72C22×C4×C5C2×D411yescharacteristic
73C5×Q16—24no—
74C5×Q16—42no—
75C5×Q16—42no—
76C5×Q16—44no—
77C5×Q16—81no—
78C5×SD16—44no—
79C5×M16—22no—
80C5×M16—41no—
81C5×M16—41no—
82C2×C5×C8—21no—
83C2×C5×C8—41no—
84C2×C5×C8—41no—
85C2×C5×C8C2×D412yes—
86C5×C4⋊C4—22no—
87C5×C4⋊C4—42no—
88C5×C4⋊C4—42no—
89C5×C22⋊C4—41no—
90C5×C22⋊C4—42no—
91C5×C22⋊C4—42no—
92C42×C5—41no—
93C5×C16—42no—
94C2×#137—21no—
95C22×Q16C22×C511yescharacteristic
96#536—21no—
97C2×Q32—22no—
98#485—22no—
99#470—21no—
100#467C22×C512yes—
101#451—22no—
102C2×#101—21no—
103#408C22×C511yescharacteristic
104#358—22no—
105C22⋊C16C22×C512yes—
106#341C22×C511yescharacteristic
107C23×C5—21no—
108C23×C5AGL(1,ℤ/8)11yescharacteristic
109C5×Q8—41no—
110C5×Q8—42no—
111C5×Q8—42no—
112C5×Q8—42no—
113C5×Q8—42no—
114C5×Q8—81no—
115C5×Q8—82no—
116C5×Q8—81no—
117C5×D4—41no—
118C5×D4—81no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—41no—
123C2×C4×C5—41no—
124C2×C4×C5—42no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5—81no—
128C2×C4×C5—82no—
129C2×C4×C5—81no—
130C2×C4×C5#12011yescharacteristic
131C2×C4×C5C2×D811yescharacteristic
132C5×C8—22no—
133C5×C8—42no—
134C5×C8—41no—
135C2×#41C5×D411yescharacteristic
136C22×Q8—21no—
137C22×Q8—21no—
138#137—42no—
139#137—42no—
140C2×Q16—21no—
141C2×Q16—22no—
142C2×Q16—42no—
143C2×Q16—41no—
144C2×Q16C5×D412yes—
145C2×SD16—41no—
146C2×M16—21no—
147C2×M16C5×D411yescharacteristic
148C22×C8C23×C511yescharacteristic
149C4⋊Q8—41no—
150#124—41no—
151#123—41no—
152#123—41no—
153C22⋊Q8—22no—
154C22⋊Q8—22no—
155#117—21no—
156Q32—44no—
157C2×C16—22no—
158#107C5×D412yes—
159#106—21no—
160#103—22no—
161#103—22no—
162#101—42no—
163C22⋊C8—22no—
164C22×C5—21no—
165C22×C5—22no—
166C22×C5—41no—
167C22×C5—42no—
168C22×C5#44711yescharacteristic
169C4×C5—21no—
170C4×C5—41no—
171C4×C5—82no—
172C4×C5—82no—
173C4×C5—82no—
174C4×C5#45311yescharacteristic
175C4×C5B(4,𝔽2)11yescharacteristic
176#41—41no—
177#41—41no—
178C2×Q8—22no—
179C2×Q8—22no—
180C2×Q8—41no—
181C2×Q8—41no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—81no—
187C2×Q8—81no—
188C2×Q8C5×D811yescharacteristic
189C2×D4—21no—
190C2×D4C5×D811yescharacteristic
191C22×C4—21no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4C2×C5×D411yescharacteristic
195Q16—24no—
196Q16—42no—
197Q16—42no—
198Q16—44no—
199Q16—81no—
200SD16—44no—
201M16—22no—
202M16—41no—
203M16—41no—
204C2×C8—21no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8C2×C5×D412yes—
208C4⋊C4—22no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C22⋊C4—41no—
212C22⋊C4—42no—
213C22⋊C4—42no—
214C42—41no—
215C16—42no—
216C2×C5—41no—
217C2×C5—81no—
218C2×C5#159511yescharacteristic
219C2×C5#219512yes—
220C23—21no—
221C23C5×AGL(1,ℤ/8)11yescharacteristic
222Q8—41no—
223Q8—42no—
224Q8—42no—
225Q8—42no—
226Q8—42no—
227Q8—81no—
228Q8—82no—
229Q8—81no—
230D4—41no—
231D4—81no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—81no—
241C2×C4—82no—
242C2×C4—81no—
243C2×C4C5×#12011yescharacteristic
244C2×C4C2×C5×D811yescharacteristic
245C8—22no—
246C8—42no—
247C8—41no—
248C5#1211211yescharacteristic, direct product factor, Sylow
249C22—21no—
250C22—22no—
251C22—41no—
252C22—42no—
253C22C5×#44711yescharacteristic
254C4—21no—
255C4—41no—
256C4—82no—
257C4—82no—
258C4—82no—
259C4C5×#45311yescharacteristic
260C4C5×B(4,𝔽2)11yescharacteristic
261C2—41no—
262C2—81no—
263C2C5×#159511yescharacteristic
264C2C5×#219512yes—
subgroupG/H
center, socleC22×C5#447
commutator, Frattini, cosocleC22×C8C23×C5
prime radicalC2×C5×#41D4
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#408 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2188C2semidirect
4. C5×#1350C2semidirect
19. #12112C5direct (N × H)
50. #2188C2×C5semidirect
52. #1350C2×C5semidirect
248. C5#12112direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32022
C5×#21882
C5×#20202
C5×#13502
C5×#13152
#121125