Finite Group Databasebeta

← C5×#12282 #11935002

Subgroups — C5×#12282 #11935002

Order 1280.

344 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 82 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×#3189C211yesmaximal, characteristic
2C5×#2236C212yesmaximal, complemented
3C5×#2076C211yesmaximal, characteristic
4C5×#1348C212yesmaximal, complemented
5C5×#1314C211yesmaximal, characteristic
6C2×C5×C22⋊Q8—21no—
7C5×#484—22no—
8C5×#467—21no—
9C5×#467C2212yes—
10C5×#451—22no—
11C2×C5×#107C2211yescharacteristic
12C2×C5×C22⋊C8C2211yescharacteristic
13C5×#380—21no—
14C5×#366—22no—
15C5×#358—22no—
16C5×C22⋊C16C2212yes—
17C5×#340—21no—
18C5×#340C2211yescharacteristic
19#12282C511yesmaximal, characteristic, direct product factor, Sylow
20C22×C5×Q8—21no—
21C23×C4×C5D411yescharacteristic
22C2×C5×Q16—21no—
23C2×C5×Q16D412yes—
24C22×C5×C8D411yescharacteristic
25C22×C5×C8C2311yescharacteristic
26C5×C22⋊Q8—22no—
27C5×C22⋊Q8—22no—
28C5×C22⋊Q8—41no—
29C5×C22⋊Q8—41no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—41no—
34C2×C5×C22⋊C4—41no—
35C2×C5×C22⋊C4—41no—
36C2×C5×C16—22no—
37C5×#107—21no—
38C5×#107—22no—
39C5×#107D412yes—
40C5×#103—22no—
41C5×#103—22no—
42C5×C22⋊C8—22no—
43C5×#95—41no—
44#3189C2×C511yescharacteristic
45#2236C2×C512yescomplemented
46#2076C2×C511yescharacteristic
47#1348C2×C512yescomplemented
48#1314C2×C511yescharacteristic
49C24×C5D811yescharacteristic
50C2×C5×Q8—22no—
51C2×C5×Q8—41no—
52C2×C5×Q8—81no—
53C2×C5×Q8—81no—
54C22×C4×C5—21no—
55C22×C4×C5—21no—
56C22×C4×C5—41no—
57C22×C4×C5—41no—
58C22×C4×C5—41no—
59C22×C4×C5—41no—
60C22×C4×C5—41no—
61C22×C4×C5—41no—
62C22×C4×C5D811yescharacteristic
63C22×C4×C5C2×D411yescharacteristic
64C5×Q16—42no—
65C5×Q16—81no—
66C2×C5×C8—21no—
67C2×C5×C8—41no—
68C2×C5×C8—41no—
69C2×C5×C8C2×D412yes—
70C5×C4⋊C4—22no—
71C5×C4⋊C4—41no—
72C5×C4⋊C4—42no—
73C5×C4⋊C4—41no—
74C5×C4⋊C4—41no—
75C5×C4⋊C4—42no—
76C5×C4⋊C4—41no—
77C5×C4⋊C4—41no—
78C5×C22⋊C4—42no—
79C5×C22⋊C4—42no—
80C5×C22⋊C4—82no—
81C5×C16—42no—
82C2×C22⋊Q8—21no—
83#484—22no—
84#467—21no—
85#467C22×C512yes—
86#451—22no—
87C2×#107C22×C511yescharacteristic
88C2×C22⋊C8C22×C511yescharacteristic
89#380—21no—
90#366—22no—
91#358—22no—
92C22⋊C16C22×C512yes—
93#340—21no—
94#340C22×C511yescharacteristic
95C23×C5—21no—
96C23×C5—21no—
97C23×C5—41no—
98C23×C5—41no—
99C23×C5Q3212yes—
100C23×C5C2×D811yescharacteristic
101C5×Q8—42no—
102C5×Q8—42no—
103C5×Q8—82no—
104C2×C4×C5—21no—
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—41no—
108C2×C4×C5—41no—
109C2×C4×C5—41no—
110C2×C4×C5—42no—
111C2×C4×C5—42no—
112C2×C4×C5—81no—
113C2×C4×C5—82no—
114C2×C4×C5—82no—
115C2×C4×C5—81no—
116C2×C4×C5—81no—
117C2×C4×C5—81no—
118C2×C4×C5—81no—
119C2×C4×C5—81no—
120C2×C4×C5—81no—
121C2×C4×C5#12011yescharacteristic
122C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
123C5×C8—22no—
124C5×C8—41no—
125C22×Q8—21no—
126C23×C4C5×D411yescharacteristic
127C2×Q16—21no—
128C2×Q16C5×D412yes—
129C22×C8C5×D411yescharacteristic
130C22×C8C23×C511yescharacteristic
131C22⋊Q8—22no—
132C22⋊Q8—22no—
133C22⋊Q8—41no—
134C22⋊Q8—41no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—41no—
139C2×C22⋊C4—41no—
140C2×C22⋊C4—41no—
141C2×C16—22no—
142#107—21no—
143#107—22no—
144#107C5×D412yes—
145#103—22no—
146#103—22no—
147C22⋊C8—22no—
148#95—41no—
149C22×C5—21no—
150C22×C5—21no—
151C22×C5—22no—
152C22×C5—42no—
153C22×C5—41no—
154C22×C5—41no—
155C22×C5—81no—
156C22×C5#44711yescharacteristic
157C22×C5C2×Q3211yescharacteristic
158C22×C5#51011yescharacteristic
159C4×C5—21no—
160C4×C5—41no—
161C4×C5—82no—
162C4×C5—82no—
163C4×C5—161no—
164C4×C5—161no—
165C4×C5#45511yescharacteristic
166C4×C5#45811yescharacteristic
167C24C5×D811yescharacteristic
168C2×Q8—22no—
169C2×Q8—41no—
170C2×Q8—81no—
171C2×Q8—81no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4C5×D811yescharacteristic
181C22×C4C2×C5×D411yescharacteristic
182Q16—42no—
183Q16—81no—
184C2×C8—21no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8C2×C5×D412yes—
188C4⋊C4—22no—
189C4⋊C4—41no—
190C4⋊C4—42no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C22⋊C4—42no—
197C22⋊C4—42no—
198C22⋊C4—82no—
199C16—42no—
200C2×C5—21no—
201C2×C5—21no—
202C2×C5—42no—
203C2×C5#160711yescharacteristic
204C2×C5#218811yescharacteristic
205C2×C5#219011yescharacteristic
206C23—21no—
207C23—21no—
208C23—41no—
209C23—41no—
210C23C5×Q3212yes—
211C23C2×C5×D811yescharacteristic
212Q8—42no—
213Q8—42no—
214Q8—82no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—81no—
224C2×C4—82no—
225C2×C4—82no—
226C2×C4—81no—
227C2×C4—81no—
228C2×C4—81no—
229C2×C4—81no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4C5×#12011yescharacteristic
233C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
234C8—22no—
235C8—41no—
236C5#1228211yescharacteristic, direct product factor, Sylow
237C22—21no—
238C22—21no—
239C22—22no—
240C22—42no—
241C22—41no—
242C22—41no—
243C22—81no—
244C22C5×#44711yescharacteristic
245C22C2×C5×Q3211yescharacteristic
246C22C5×#51011yescharacteristic
247C4—21no—
248C4—41no—
249C4—82no—
250C4—82no—
251C4—161no—
252C4—161no—
253C4C5×#45511yescharacteristic
254C4C5×#45811yescharacteristic
255C2—21no—
256C2—21no—
257C2—42no—
258C2C5×#160711yescharacteristic
259C2C5×#218811yescharacteristic
260C2C5×#219011yescharacteristic
subgroupG/H
center, socleC22×C5#447
commutator, Frattini, cosocleC22×C8C23×C5
prime radicalC24×C5D8
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×C22⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2236C2semidirect
4. C5×#1348C2semidirect
19. #12282C5direct (N × H)
45. #2236C2×C5semidirect
47. #1348C2×C5semidirect
236. C5#12282direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#31892
C5×#22362
C5×#20762
C5×#13482
C5×#13142
#122825