Finite Group Databasebeta

← C5×#10389 #11933109

Subgroups — C5×#10389 #11933109

Order 1280.

406 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2608C211yesmaximal, characteristic
2C5×#1826C212yesmaximal
3C5×#1820C211yesmaximal, characteristic
4C5×#1306C211yesmaximal, characteristic
5C5×#1284C212yesmaximal
6C2×C5×#117C2211yescharacteristic
7C5×#407C2212yes—
8C5×#396—22no—
9C5×#389—22no—
10C5×#387—22no—
11C5×#381C2211yescharacteristic
12C5×#381C2211yescharacteristic
13C4×C5×C22⋊C4C2212yes—
14C5×#342—22no—
15C5×#339—22no—
16C5×#339—22no—
17#10389C511yesmaximal, characteristic, direct product factor, Sylow
18C23×C4×C5C2311yescharacteristic
19C2×C5×M16—22no—
20C5×#117—22no—
21C5×#117—22no—
22C2×C5×C4⋊C4—22no—
23C2×C5×C4⋊C4—22no—
24C2×C5×C4⋊C4—22no—
25C2×C5×C4⋊C4Q812yes—
26C2×C5×C22⋊C4—22no—
27C2×C5×C22⋊C4—21no—
28C2×C5×C22⋊C4—21no—
29C2×C5×C22⋊C4D412yes—
30C2×C42×C5—21no—
31C2×C42×C5D412yes—
32C2×C42×C5D412yes—
33C5×C22⋊C8—22no—
34C5×C22⋊C8—22no—
35C5×#95—22no—
36C5×#95—22no—
37C5×#95—22no—
38C5×#95—22no—
39#2608C2×C511yescharacteristic
40#1826C2×C512yes—
41#1820C2×C511yescharacteristic
42#1306C2×C511yescharacteristic
43#1284C2×C512yes—
44C24×C5C2×D411yescharacteristic
45C22×C4×C5—22no—
46C22×C4×C5—22no—
47C22×C4×C5—22no—
48C22×C4×C5—22no—
49C22×C4×C5—42no—
50C22×C4×C5—41no—
51C22×C4×C5C2×D412yes—
52C22×C4×C5C2×Q811yescharacteristic
53C22×C4×C5#4112yes—
54C22×C4×C5#4111yescharacteristic
55C5×M16—42no—
56C5×M16—42no—
57C2×C5×C8—42no—
58C5×C4⋊C4—24no—
59C5×C4⋊C4—44no—
60C5×C4⋊C4—44no—
61C5×C4⋊C4—82no—
62C5×C22⋊C4—44no—
63C5×C22⋊C4—41no—
64C5×C22⋊C4—41no—
65C5×C22⋊C4—42no—
66C5×C22⋊C4—42no—
67C42×C5—42no—
68C42×C5—42no—
69C42×C5—42no—
70C2×#117C22×C511yescharacteristic
71#407C22×C512yes—
72#396—22no—
73#389—22no—
74#387—22no—
75#381C22×C511yescharacteristic
76#381C22×C511yescharacteristic
77C4×C22⋊C4C22×C512yes—
78#342—22no—
79#339—22no—
80#339—22no—
81C23×C5—22no—
82C23×C5—42no—
83C23×C5#12011yescharacteristic
84C23×C5C22⋊Q811yescharacteristic
85C23×C5#12411yescharacteristic
86C2×C4×C5—22no—
87C2×C4×C5—22no—
88C2×C4×C5—24no—
89C2×C4×C5—41no—
90C2×C4×C5—41no—
91C2×C4×C5—42no—
92C2×C4×C5—42no—
93C2×C4×C5—42no—
94C2×C4×C5—42no—
95C2×C4×C5—42no—
96C2×C4×C5—42no—
97C2×C4×C5—42no—
98C2×C4×C5—42no—
99C2×C4×C5—42no—
100C2×C4×C5—42no—
101C2×C4×C5—82no—
102C2×C4×C5—81no—
103C2×C4×C5—82no—
104C2×C4×C5C22⋊Q812yes—
105C2×C4×C5#12412yes—
106C5×C8—82no—
107C23×C4C23×C511yescharacteristic
108C2×M16—22no—
109#117—22no—
110#117—22no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4C5×Q812yes—
115C2×C22⋊C4—21no—
116C2×C22⋊C4—22no—
117C2×C22⋊C4—21no—
118C2×C22⋊C4C5×D412yes—
119C2×C42—21no—
120C2×C42C5×D412yes—
121C2×C42C5×D412yes—
122C22⋊C8—22no—
123C22⋊C8—22no—
124#95—22no—
125#95—22no—
126#95—22no—
127#95—22no—
128C22×C5—22no—
129C22×C5—21no—
130C22×C5—21no—
131C22×C5—22no—
132C22×C5—22no—
133C22×C5—82no—
134C22×C5#39311yescharacteristic
135C22×C5#45812yes—
136C4×C5—22no—
137C4×C5—22no—
138C4×C5—44no—
139C4×C5—82no—
140C4×C5—82no—
141C4×C5—82no—
142C4×C5—161no—
143C24C2×C5×D411yescharacteristic
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—42no—
149C22×C4—41no—
150C22×C4C2×C5×D412yes—
151C22×C4C2×C5×Q811yescharacteristic
152C22×C4C5×#4112yes—
153C22×C4C5×#4111yescharacteristic
154M16—42no—
155M16—42no—
156C2×C8—42no—
157C4⋊C4—24no—
158C4⋊C4—44no—
159C4⋊C4—44no—
160C4⋊C4—82no—
161C22⋊C4—44no—
162C22⋊C4—41no—
163C22⋊C4—41no—
164C22⋊C4—42no—
165C22⋊C4—42no—
166C42—42no—
167C42—42no—
168C42—42no—
169C2×C5—22no—
170C2×C5—41no—
171C2×C5—41no—
172C2×C5#203011yescharacteristic
173C2×C5#203112yes—
174C23—22no—
175C23—42no—
176C23C5×#12011yescharacteristic
177C23C5×C22⋊Q811yescharacteristic
178C23C5×#12411yescharacteristic
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—82no—
195C2×C4—81no—
196C2×C4—82no—
197C2×C4C5×C22⋊Q812yes—
198C2×C4C5×#12412yes—
199C8—82no—
200C5#1038911yescharacteristic, direct product factor, Sylow
201C22—22no—
202C22—21no—
203C22—21no—
204C22—22no—
205C22—22no—
206C22—82no—
207C22C5×#39311yescharacteristic
208C22C5×#45812yes—
209C4—22no—
210C4—22no—
211C4—44no—
212C4—82no—
213C4—82no—
214C4—82no—
215C4—161no—
216C2—22no—
217C2—41no—
218C2—41no—
219C2C5×#203011yescharacteristic
220C2C5×#203112yes—
subgroupG/H
center, socleC22×C5#393
commutator, Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
17. #10389C5direct (N × H)
200. C5#10389direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#26082
C5×#18262
C5×#18202
C5×#13062
C5×#12842
#103895