Finite Group Databasebeta

← C5×#7819 #11930539

Subgroups — C5×#7819 #11930539

Order 1280.

434 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2724C211yesmaximal, characteristic
2C5×#2093C211yesmaximal, characteristic
3C5×#2084C212yesmaximal, complemented
4C5×#1271C212yesmaximal, complemented
5C5×#1270C211yesmaximal, characteristic
6C2×C5×#123—21no—
7C2×C5×#107—21no—
8C2×C5×#106—22no—
9C2×C5×#102—21no—
10C5×#398—21no—
11C5×#397—22no—
12C5×#390C2211yescharacteristic
13C5×#389C2212yes—
14C5×#385—22no—
15C5×#384C2211yescharacteristic
16C5×#340—22no—
17C5×#336C2212yes—
18C5×#336C2211yescharacteristic
19#7819C511yesmaximal, characteristic, direct product factor, Sylow
20C22×C5×D4D411yescharacteristic
21C23×C4×C5—21no—
22C22×C5×C8—22no—
23C22×C5×C8—21no—
24C5×#123—42no—
25C5×#123—42no—
26C2×C5×C4⋊C4—22no—
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4D412yes—
31C2×C5×C4⋊C4D412yes—
32C2×C5×C4⋊C4D411yescharacteristic
33C2×C5×C22⋊C4—22no—
34C2×C5×C22⋊C4—21no—
35C2×C5×C22⋊C4—22no—
36C2×C42×C5C2311yescharacteristic
37C5×#107—42no—
38C5×#106—44no—
39C5×#102—42no—
40C5×#95—22no—
41C5×#95—21no—
42C5×#95—22no—
43#2724C2×C511yescharacteristic
44#2093C2×C511yescharacteristic
45#2084C2×C512yescomplemented
46#1271C2×C512yescomplemented
47#1270C2×C511yescharacteristic
48C24×C5—21no—
49C2×C5×D4—21no—
50C2×C5×D4—41no—
51C2×C5×D4—41no—
52C2×C5×D4SD1612yes—
53C22×C4×C5—21no—
54C22×C4×C5—22no—
55C22×C4×C5—22no—
56C22×C4×C5—42no—
57C22×C4×C5—41no—
58C22×C4×C5—81no—
59C22×C4×C5—81no—
60C22×C4×C5C2×D411yescharacteristic
61C22×C4×C5C2×D412yes—
62C2×C5×C8—24no—
63C2×C5×C8—22no—
64C2×C5×C8—42no—
65C2×C5×C8—41no—
66C2×C5×C8—41no—
67C2×C5×C8—42no—
68C5×C4⋊C4—22no—
69C5×C4⋊C4—22no—
70C5×C4⋊C4—42no—
71C5×C4⋊C4—41no—
72C5×C4⋊C4—41no—
73C5×C4⋊C4—41no—
74C5×C4⋊C4—42no—
75C5×C4⋊C4—42no—
76C5×C4⋊C4—42no—
77C5×C4⋊C4—42no—
78C5×C4⋊C4—81no—
79C5×C22⋊C4—42no—
80C5×C22⋊C4—44no—
81C5×C22⋊C4—42no—
82C5×C22⋊C4—42no—
83C42×C5—41no—
84C2×#123—21no—
85C2×#107—21no—
86C2×#106—22no—
87C2×#102—21no—
88#398—21no—
89#397—22no—
90#390C22×C511yescharacteristic
91#389C22×C512yes—
92#385—22no—
93#384C22×C511yescharacteristic
94#340—22no—
95#336C22×C512yes—
96#336C22×C511yescharacteristic
97C23×C5—22no—
98C23×C5—42no—
99C23×C5—41no—
100C23×C5—42no—
101C23×C5—41no—
102C23×C5#12011yescharacteristic
103C5×D4—42no—
104C5×D4—81no—
105C2×C4×C5—21no—
106C2×C4×C5—22no—
107C2×C4×C5—22no—
108C2×C4×C5—21no—
109C2×C4×C5—42no—
110C2×C4×C5—42no—
111C2×C4×C5—42no—
112C2×C4×C5—42no—
113C2×C4×C5—41no—
114C2×C4×C5—42no—
115C2×C4×C5—42no—
116C2×C4×C5—42no—
117C2×C4×C5—84no—
118C2×C4×C5—82no—
119C2×C4×C5—81no—
120C2×C4×C5C2×SD1611yescharacteristic
121C2×C4×C5#13512yes—
122C2×C4×C5AGL(1,ℤ/8)12yes—
123C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
124C5×C8—44no—
125C5×C8—42no—
126C22×D4C5×D411yescharacteristic
127C23×C4—21no—
128C22×C8—22no—
129C22×C8—21no—
130#123—42no—
131#123—42no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4C5×D412yes—
137C2×C4⋊C4C5×D412yes—
138C2×C4⋊C4C5×D411yescharacteristic
139C2×C22⋊C4—22no—
140C2×C22⋊C4—21no—
141C2×C22⋊C4—22no—
142C2×C42C23×C511yescharacteristic
143#107—42no—
144#106—44no—
145#102—42no—
146#95—22no—
147#95—21no—
148#95—22no—
149C22×C5—42no—
150C22×C5—44no—
151C22×C5—82no—
152C22×C5—81no—
153C22×C5—81no—
154C22×C5#44912yes—
155C22×C5#45011yescharacteristic
156C22×C5#45311yescharacteristic
157C22×C5#45612yes—
158C22×C5#45811yescharacteristic
159C4×C5—22no—
160C4×C5—22no—
161C4×C5—21no—
162C4×C5—21no—
163C4×C5—82no—
164C4×C5—81no—
165C4×C5—82no—
166C4×C5—161no—
167C24—21no—
168C2×D4—21no—
169C2×D4—41no—
170C2×D4—41no—
171C2×D4C5×SD1612yes—
172C22×C4—21no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—42no—
176C22×C4—41no—
177C22×C4—81no—
178C22×C4—81no—
179C22×C4C2×C5×D411yescharacteristic
180C22×C4C2×C5×D412yes—
181C2×C8—22no—
182C2×C8—24no—
183C2×C8—42no—
184C2×C8—41no—
185C2×C8—42no—
186C2×C8—41no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—41no—
190C4⋊C4—42no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—81no—
198C22⋊C4—42no—
199C22⋊C4—44no—
200C22⋊C4—42no—
201C22⋊C4—42no—
202C42—41no—
203C2×C5—82no—
204C2×C5#160912yes—
205C2×C5#161311yescharacteristic
206C2×C5#162011yescharacteristic
207C2×C5#165412yes—
208C2×C5#166011yescharacteristic
209C23—22no—
210C23—42no—
211C23—41no—
212C23—42no—
213C23—41no—
214C23C5×#12011yescharacteristic
215D4—42no—
216D4—81no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—84no—
230C2×C4—82no—
231C2×C4—81no—
232C2×C4C2×C5×SD1611yescharacteristic
233C2×C4C5×#13512yes—
234C2×C4C5×AGL(1,ℤ/8)12yes—
235C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
236C8—44no—
237C8—42no—
238C5#781911yescharacteristic, direct product factor, Sylow
239C22—42no—
240C22—44no—
241C22—82no—
242C22—81no—
243C22—81no—
244C22C5×#44912yes—
245C22C5×#45011yescharacteristic
246C22C5×#45311yescharacteristic
247C22C5×#45612yes—
248C22C5×#45811yescharacteristic
249C4—22no—
250C4—22no—
251C4—21no—
252C4—21no—
253C4—82no—
254C4—81no—
255C4—82no—
256C4—161no—
257C2—82no—
258C2C5×#160912yes—
259C2C5×#161311yescharacteristic
260C2C5×#162011yescharacteristic
261C2C5×#165412yes—
262C2C5×#166011yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC22×C5×D4D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#2084C2semidirect
4. C5×#1271C2semidirect
19. #7819C5direct (N × H)
45. #2084C2×C5semidirect
46. #1271C2×C5semidirect
238. C5#7819direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#27242
C5×#20932
C5×#20842
C5×#12712
C5×#12702
#78195