Finite Group Databasebeta

← C5×#10393 #11933113

Subgroups — C5×#10393 #11933113

Order 1280.

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

normal subgroups only

This group has 526 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×#2842C211yesmaximal, characteristic
2C5×#1819C211yesmaximal, characteristic
3C5×#1819C212yesmaximal
4C5×#1304C211yesmaximal, characteristic
5C5×#1304C212yesmaximal
6C22×C5×C22⋊C4C2211yescharacteristic
7C5×#399—22no—
8C5×#396—24no—
9C5×#379C2212yes—
10C5×#379C2211yescharacteristic
11C5×#379C2211yescharacteristic
12C5×#379C2212yes—
13C5×#342—24no—
14C5×#342—22no—
15#10393C511yesmaximal, characteristic, direct product factor, Sylow
16C25×C5C2311yescharacteristic
17C23×C4×C5Q812yes—
18C2×C5×C4⋊C4—24no—
19C2×C5×C4⋊C4—22no—
20C2×C5×C22⋊C4—22no—
21C2×C5×C22⋊C4—21no—
22C2×C5×C22⋊C4—21no—
23C2×C5×C22⋊C4—22no—
24C2×C5×C22⋊C4—22no—
25C2×C5×C22⋊C4—21no—
26C2×C5×C22⋊C4—22no—
27C2×C5×C22⋊C4—22no—
28C2×C5×C22⋊C4—22no—
29C2×C5×C22⋊C4—22no—
30C2×C5×C22⋊C4—22no—
31C2×C5×C22⋊C4—22no—
32C2×C5×C22⋊C4D414yes—
33C2×C5×C22⋊C4D412yes—
34C5×#95—22no—
35#2842C2×C511yescharacteristic
36#1819C2×C512yes—
37#1819C2×C511yescharacteristic
38#1304C2×C511yescharacteristic
39#1304C2×C512yes—
40C24×C5—42no—
41C24×C5—82no—
42C24×C5C2×D412yes—
43C24×C5C2×D411yescharacteristic
44C24×C5C2×Q811yescharacteristic
45C24×C5#4112yes—
46C24×C5#4111yescharacteristic
47C22×C4×C5—22no—
48C22×C4×C5—24no—
49C22×C4×C5—22no—
50C22×C4×C5—22no—
51C22×C4×C5—22no—
52C22×C4×C5—42no—
53C22×C4×C5—41no—
54C22×C4×C5—82no—
55C5×C4⋊C4—84no—
56C5×C4⋊C4—82no—
57C5×C22⋊C4—41no—
58C5×C22⋊C4—42no—
59C5×C22⋊C4—41no—
60C5×C22⋊C4—44no—
61C5×C22⋊C4—42no—
62C5×C22⋊C4—44no—
63C5×C22⋊C4—42no—
64C5×C22⋊C4—82no—
65C5×C22⋊C4—82no—
66C5×C22⋊C4—82no—
67C5×C22⋊C4—82no—
68C5×C22⋊C4—82no—
69C5×C22⋊C4—82no—
70C22×C22⋊C4C22×C511yescharacteristic
71#399—22no—
72#396—24no—
73#379C22×C512yes—
74#379C22×C511yescharacteristic
75#379C22×C511yescharacteristic
76#379C22×C512yes—
77#342—24no—
78#342—22no—
79C23×C5—24no—
80C23×C5—22no—
81C23×C5—42no—
82C23×C5—41no—
83C23×C5—42no—
84C23×C5—42no—
85C23×C5—42no—
86C23×C5—42no—
87C23×C5—42no—
88C23×C5—42no—
89C23×C5—41no—
90C23×C5—42no—
91C23×C5—88no—
92C23×C5#12011yescharacteristic
93C23×C5C22⋊Q812yes—
94C23×C5C22⋊Q811yescharacteristic
95C23×C5#12412yes—
96C23×C5#12411yescharacteristic
97C2×C4×C5—44no—
98C2×C4×C5—44no—
99C2×C4×C5—44no—
100C2×C4×C5—42no—
101C2×C4×C5—44no—
102C2×C4×C5—42no—
103C2×C4×C5—82no—
104C2×C4×C5—82no—
105C2×C4×C5—82no—
106C2×C4×C5—82no—
107C2×C4×C5—81no—
108C2×C4×C5—82no—
109C2×C4×C5—82no—
110C2×C4×C5—82no—
111C25C23×C511yescharacteristic
112C23×C4C5×Q812yes—
113C2×C4⋊C4—24no—
114C2×C4⋊C4—22no—
115C2×C22⋊C4—22no—
116C2×C22⋊C4—21no—
117C2×C22⋊C4—21no—
118C2×C22⋊C4—22no—
119C2×C22⋊C4—22no—
120C2×C22⋊C4—21no—
121C2×C22⋊C4—22no—
122C2×C22⋊C4—22no—
123C2×C22⋊C4—22no—
124C2×C22⋊C4—22no—
125C2×C22⋊C4—22no—
126C2×C22⋊C4—22no—
127C2×C22⋊C4C5×D414yes—
128C2×C22⋊C4C5×D412yes—
129#95—22no—
130C22×C5—22no—
131C22×C5—22no—
132C22×C5—21no—
133C22×C5—22no—
134C22×C5—21no—
135C22×C5—22no—
136C22×C5—22no—
137C22×C5—22no—
138C22×C5—22no—
139C22×C5—22no—
140C22×C5—22no—
141C22×C5—44no—
142C22×C5—84no—
143C22×C5—82no—
144C22×C5—82no—
145C22×C5—84no—
146C22×C5#39311yescharacteristic
147C22×C5#45812yes—
148C4×C5—82no—
149C4×C5—84no—
150C4×C5—82no—
151C4×C5—162no—
152C4×C5—161no—
153C24—42no—
154C24—82no—
155C24C2×C5×D412yes—
156C24C2×C5×D411yescharacteristic
157C24C2×C5×Q811yescharacteristic
158C24C5×#4112yes—
159C24C5×#4111yescharacteristic
160C22×C4—22no—
161C22×C4—24no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—42no—
166C22×C4—41no—
167C22×C4—82no—
168C4⋊C4—84no—
169C4⋊C4—82no—
170C22⋊C4—41no—
171C22⋊C4—42no—
172C22⋊C4—41no—
173C22⋊C4—44no—
174C22⋊C4—42no—
175C22⋊C4—44no—
176C22⋊C4—42no—
177C22⋊C4—82no—
178C22⋊C4—82no—
179C22⋊C4—82no—
180C22⋊C4—82no—
181C22⋊C4—82no—
182C22⋊C4—82no—
183C2×C5—22no—
184C2×C5—42no—
185C2×C5—41no—
186C2×C5—42no—
187C2×C5—41no—
188C2×C5#203011yescharacteristic
189C2×C5#203212yes—
190C23—24no—
191C23—22no—
192C23—42no—
193C23—41no—
194C23—42no—
195C23—42no—
196C23—42no—
197C23—42no—
198C23—42no—
199C23—42no—
200C23—41no—
201C23—42no—
202C23—88no—
203C23C5×#12011yescharacteristic
204C23C5×C22⋊Q812yes—
205C23C5×C22⋊Q811yescharacteristic
206C23C5×#12412yes—
207C23C5×#12411yescharacteristic
208C2×C4—44no—
209C2×C4—44no—
210C2×C4—44no—
211C2×C4—42no—
212C2×C4—44no—
213C2×C4—42no—
214C2×C4—82no—
215C2×C4—82no—
216C2×C4—82no—
217C2×C4—82no—
218C2×C4—81no—
219C2×C4—82no—
220C2×C4—82no—
221C2×C4—82no—
222C5#1039311yescharacteristic, direct product factor, Sylow
223C22—22no—
224C22—22no—
225C22—21no—
226C22—22no—
227C22—21no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—44no—
235C22—84no—
236C22—82no—
237C22—82no—
238C22—84no—
239C22C5×#39311yescharacteristic
240C22C5×#45812yes—
241C4—82no—
242C4—84no—
243C4—82no—
244C4—162no—
245C4—161no—
246C2—22no—
247C2—42no—
248C2—41no—
249C2—42no—
250C2—41no—
251C2C5×#203011yescharacteristic
252C2C5×#203212yes—
subgroupG/H
center, socleC22×C5#393
commutator, Frattini, cosocleC25C23×C5
prime radicalC25×C5C23
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C25×C5 ◁ G

Complements

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

NH ≅ G/Ntype
15. #10393C5direct (N × H)
222. C5#10393direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#28422
C5×#18192
C5×#13042
#103935