Finite Group Databasebeta

← C5×#10437 #11933157

Subgroups — C5×#10437 #11933157

Order 1280.

478 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 146 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×#2582C211yesmaximal, characteristic
2C5×#1844C211yesmaximal, characteristic
3C5×#1803C212yesmaximal
4C2×C5×Q8⋊C8C212yesmaximal
5C5×#1296C211yesmaximal, characteristic
6C2×C4×C5×Q8C2212yes—
7C2×C5×#106—22no—
8C2×C5×C4⋊C8C2212yes—
9C2×C5×#103—22no—
10C2×C4×C5×C8C2211yescharacteristic
11C5×#398—22no—
12C5×#391—22no—
13C5×#389—22no—
14C5×#384C2211yescharacteristic
15C5×#384C2211yescharacteristic
16C5×#340—22no—
17C5×Q8⋊C8—24no—
18#10437C511yesmaximal, characteristic, direct product factor, Sylow
19C22×C5×Q8D412yes—
20C22×C5×C8—21no—
21C22×C5×C8—22no—
22C4×C5×Q8—22no—
23C4×C5×Q8—22no—
24C4×C5×Q8—22no—
25C4×C5×Q8—22no—
26C2×C5×C4⋊C4—22no—
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4D412yes—
32C2×C5×C4⋊C4D412yes—
33C2×C42×C5—22no—
34C2×C42×C5C2311yescharacteristic
35C5×#106—44no—
36C5×C4⋊C8—22no—
37C5×C4⋊C8—22no—
38C5×#103—44no—
39C4×C5×C8—21no—
40C4×C5×C8D412yes—
41C5×#95—24no—
42C5×#95—22no—
43#2582C2×C511yescharacteristic
44#1844C2×C511yescharacteristic
45#1803C2×C512yes—
46C2×Q8⋊C8C2×C512yes—
47#1296C2×C511yescharacteristic
48C2×C5×Q8—22no—
49C2×C5×Q8—22no—
50C2×C5×Q8—22no—
51C2×C5×Q8—22no—
52C2×C5×Q8—22no—
53C2×C5×Q8SD1614yes—
54C22×C4×C5—22no—
55C22×C4×C5—22no—
56C22×C4×C5—22no—
57C22×C4×C5—41no—
58C22×C4×C5C2×D411yescharacteristic
59C22×C4×C5C2×D412yes—
60C2×C5×C8—22no—
61C2×C5×C8—22no—
62C2×C5×C8—22no—
63C2×C5×C8—42no—
64C2×C5×C8—42no—
65C2×C5×C8—42no—
66C5×C4⋊C4—22no—
67C5×C4⋊C4—22no—
68C5×C4⋊C4—42no—
69C5×C4⋊C4—42no—
70C5×C4⋊C4—42no—
71C5×C4⋊C4—42no—
72C5×C4⋊C4—42no—
73C5×C4⋊C4—42no—
74C5×C4⋊C4—42no—
75C5×C4⋊C4—42no—
76C5×C4⋊C4—82no—
77C42×C5—42no—
78C42×C5—42no—
79C42×C5C2×D411yescharacteristic
80C42×C5#4111yescharacteristic
81C42×C5#4112yes—
82C2×C4×Q8C22×C512yes—
83C2×#106—22no—
84C2×C4⋊C8C22×C512yes—
85C2×#103—22no—
86C2×C4×C8C22×C511yescharacteristic
87#398—22no—
88#391—22no—
89#389—22no—
90#384C22×C511yescharacteristic
91#384C22×C511yescharacteristic
92#340—22no—
93Q8⋊C8—24no—
94C23×C5#12011yescharacteristic
95C5×Q8—24no—
96C5×Q8—24no—
97C5×Q8—42no—
98C5×Q8—42no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—24no—
102C2×C4×C5—42no—
103C2×C4×C5—42no—
104C2×C4×C5—42no—
105C2×C4×C5—44no—
106C2×C4×C5—42no—
107C2×C4×C5—42no—
108C2×C4×C5—42no—
109C2×C4×C5—82no—
110C2×C4×C5—81no—
111C2×C4×C5#12111yescharacteristic
112C2×C4×C5#12112yes—
113C2×C4×C5#12312yes—
114C2×C4×C5#12411yescharacteristic
115C2×C4×C5C2×SD1612yes—
116C2×C4×C5#13512yes—
117C2×C4×C5#13712yes—
118C2×C4×C5#13712yes—
119C5×C8—24no—
120C5×C8—82no—
121C22×Q8C5×D412yes—
122C22×C8—21no—
123C22×C8—22no—
124C4×Q8—22no—
125C4×Q8—22no—
126C4×Q8—22no—
127C4×Q8—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4C5×D412yes—
134C2×C4⋊C4C5×D412yes—
135C2×C42—22no—
136C2×C42C23×C511yescharacteristic
137#106—44no—
138C4⋊C8—22no—
139C4⋊C8—22no—
140#103—44no—
141C4×C8—21no—
142C4×C8C5×D412yes—
143#95—24no—
144#95—22no—
145C22×C5#39411yescharacteristic
146C22×C5#44812yes—
147C22×C5#45212yes—
148C22×C5#45311yescharacteristic
149C22×C5#45611yescharacteristic
150C4×C5—21no—
151C4×C5—21no—
152C4×C5—44no—
153C4×C5—82no—
154C4×C5—82no—
155C4×C5—161no—
156C4×C5#46512yes—
157C4×C5#47012yes—
158C4×C5#48312yes—
159C4×C5#48512yes—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—22no—
163C2×Q8—22no—
164C2×Q8—22no—
165C2×Q8C5×SD1614yes—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—41no—
170C22×C4C2×C5×D411yescharacteristic
171C22×C4C2×C5×D412yes—
172C2×C8—22no—
173C2×C8—22no—
174C2×C8—22no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—42no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—82no—
189C42—42no—
190C42—42no—
191C42C2×C5×D411yescharacteristic
192C42C5×#4111yescharacteristic
193C42C5×#4112yes—
194C2×C5#162311yescharacteristic
195C2×C5#163011yescharacteristic
196C2×C5#165312yes—
197C2×C5#203512yes—
198C2×C5#203911yescharacteristic
199C23C5×#12011yescharacteristic
200Q8—24no—
201Q8—24no—
202Q8—42no—
203Q8—42no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—24no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—44no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—82no—
215C2×C4—81no—
216C2×C4C5×#12111yescharacteristic
217C2×C4C5×#12112yes—
218C2×C4C5×#12312yes—
219C2×C4C5×#12411yescharacteristic
220C2×C4C2×C5×SD1612yes—
221C2×C4C5×#13512yes—
222C2×C4C5×#13712yes—
223C2×C4C5×#13712yes—
224C8—24no—
225C8—82no—
226C5#1043711yescharacteristic, direct product factor, Sylow
227C22C5×#39411yescharacteristic
228C22C5×#44812yes—
229C22C5×#45212yes—
230C22C5×#45311yescharacteristic
231C22C5×#45611yescharacteristic
232C4—21no—
233C4—21no—
234C4—44no—
235C4—82no—
236C4—82no—
237C4—161no—
238C4C5×#46512yes—
239C4C5×#47012yes—
240C4C5×#48312yes—
241C4C5×#48512yes—
242C2C5×#162311yescharacteristic
243C2C5×#163011yescharacteristic
244C2C5×#165312yes—
245C2C5×#203512yes—
246C2C5×#203911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C5#120
commutator, Frattini, cosocleC2×C42C23×C5
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
18. #10437C5direct (N × H)
226. C5#10437direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25822
C5×#18442
C5×#18032
C2×C5×Q8⋊C82
C5×#12962
#104375