Finite Group Databasebeta

← C5×#10523 #11933243

Subgroups — C5×#10523 #11933243

Order 1280.

382 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 114 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×#3249C211yesmaximal, characteristic
2C5×#1994C212yesmaximal
3C5×#1831C211yesmaximal, characteristic
4C5×#1550C212yesmaximal
5C5×#1292C211yesmaximal, characteristic
6C5×#533C2212yes—
7C5×#477—22no—
8C5×#467—22no—
9C5×#462—22no—
10C5×#423C2212yes—
11C2×C5×C4⋊C8C2211yescharacteristic
12C2×C5×C4⋊C8C2211yescharacteristic
13C43×C5C2211yescharacteristic
14C5×#339—22no—
15C5×#339—22no—
16C5×#336—22no—
17C5×#333—22no—
18C5×#332—22no—
19#10523C511yesmaximal, characteristic, direct product factor, Sylow
20C2×C5×Q16—22no—
21C2×C5×M16—22no—
22C22×C5×C8—21no—
23C22×C5×C8D412yes—
24C5×C4⋊Q8D412yes—
25C5×C4⋊Q8D412yes—
26C5×#125—22no—
27C5×C22⋊Q8—22no—
28C5×C22⋊Q8—22no—
29C4×C5×Q8—22no—
30C4×C5×Q8—22no—
31C5×#117—22no—
32C2×C42×C5—21no—
33C2×C42×C5—21no—
34C2×C42×C5D411yescharacteristic
35C2×C42×C5D411yescharacteristic
36C2×C42×C5C2311yescharacteristic
37C5×#107—22no—
38C5×C4⋊C8—22no—
39C5×C4⋊C8—22no—
40C5×C4⋊C8—22no—
41C5×C4⋊C8—22no—
42C5×#103—24no—
43#3249C2×C511yescharacteristic
44#1994C2×C512yes—
45#1831C2×C511yescharacteristic
46#1550C2×C512yes—
47#1292C2×C511yescharacteristic
48C2×C5×Q8—22no—
49C2×C5×Q8—22no—
50C22×C4×C5—21no—
51C22×C4×C5—21no—
52C22×C4×C5C2×D411yescharacteristic
53C22×C4×C5C2×D411yescharacteristic
54C22×C4×C5#4111yescharacteristic
55C5×Q16—82no—
56C5×M16—42no—
57C5×M16—42no—
58C2×C5×C8—22no—
59C2×C5×C8—42no—
60C2×C5×C8—42no—
61C2×C5×C8—41no—
62C2×C5×C8—42no—
63C5×C4⋊C4—22no—
64C5×C4⋊C4—22no—
65C5×C4⋊C4—22no—
66C5×C4⋊C4—22no—
67C5×C4⋊C4—42no—
68C5×C4⋊C4—42no—
69C5×C22⋊C4—42no—
70C42×C5—21no—
71C42×C5—22no—
72C42×C5—41no—
73C42×C5—41no—
74C42×C5—42no—
75C42×C5—42no—
76C42×C5Q1612yescomplemented
77C42×C5C2×D412yes—
78C42×C5#4112yes—
79#533C22×C512yes—
80#477—22no—
81#467—22no—
82#462—22no—
83#423C22×C512yes—
84C2×C4⋊C8C22×C511yescharacteristic
85C2×C4⋊C8C22×C511yescharacteristic
86C43C22×C511yescharacteristic
87#339—22no—
88#339—22no—
89#336—22no—
90#333—22no—
91#332—22no—
92C23×C5#12111yescharacteristic
93C5×Q8—42no—
94C5×Q8—42no—
95C5×Q8—82no—
96C2×C4×C5—21no—
97C2×C4×C5—21no—
98C2×C4×C5—22no—
99C2×C4×C5—22no—
100C2×C4×C5—41no—
101C2×C4×C5—41no—
102C2×C4×C5—41no—
103C2×C4×C5—41no—
104C2×C4×C5—41no—
105C2×C4×C5—42no—
106C2×C4×C5—42no—
107C2×C4×C5#12011yescharacteristic
108C2×C4×C5#12112yes—
109C2×C4×C5#12312yes—
110C2×C4×C5#12411yescharacteristic
111C2×C4×C5C2×Q1611yescharacteristic
112C2×C4×C5#13511yescharacteristic
113C2×C4×C5#13712yes—
114C5×C8—42no—
115C5×C8—81no—
116C5×C8—82no—
117C2×Q16—22no—
118C2×M16—22no—
119C22×C8—21no—
120C22×C8C5×D412yes—
121C4⋊Q8C5×D412yes—
122C4⋊Q8C5×D412yes—
123#125—22no—
124C22⋊Q8—22no—
125C22⋊Q8—22no—
126C4×Q8—22no—
127C4×Q8—22no—
128#117—22no—
129C2×C42—21no—
130C2×C42—21no—
131C2×C42C5×D411yescharacteristic
132C2×C42C5×D411yescharacteristic
133C2×C42C23×C511yescharacteristic
134#107—22no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8—22no—
138C4⋊C8—22no—
139#103—24no—
140C22×C5—21no—
141C22×C5—21no—
142C22×C5#39411yescharacteristic
143C22×C5#46711yescharacteristic
144C22×C5#47011yescharacteristic
145C4×C5—22no—
146C4×C5—21no—
147C4×C5—42no—
148C4×C5—42no—
149C4×C5—82no—
150C4×C5—82no—
151C4×C5#45411yescharacteristic
152C4×C5#45511yescharacteristic
153C4×C5#46212yes—
154C4×C5#46412yes—
155C2×Q8—22no—
156C2×Q8—22no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4C2×C5×D411yescharacteristic
160C22×C4C2×C5×D411yescharacteristic
161C22×C4C5×#4111yescharacteristic
162Q16—82no—
163M16—42no—
164M16—42no—
165C2×C8—22no—
166C2×C8—42no—
167C2×C8—42no—
168C2×C8—41no—
169C2×C8—42no—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C22⋊C4—42no—
177C42—21no—
178C42—22no—
179C42—41no—
180C42—41no—
181C42—42no—
182C42—42no—
183C42C5×Q1612yescomplemented
184C42C2×C5×D412yes—
185C42C5×#4112yes—
186C2×C5—21no—
187C2×C5—21no—
188C2×C5#204011yescharacteristic
189C2×C5#205011yescharacteristic
190C2×C5#205611yescharacteristic
191C23C5×#12111yescharacteristic
192Q8—42no—
193Q8—42no—
194Q8—82no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4C5×#12011yescharacteristic
207C2×C4C5×#12112yes—
208C2×C4C5×#12312yes—
209C2×C4C5×#12411yescharacteristic
210C2×C4C2×C5×Q1611yescharacteristic
211C2×C4C5×#13511yescharacteristic
212C2×C4C5×#13712yes—
213C8—42no—
214C8—81no—
215C8—82no—
216C5#1052311yescharacteristic, direct product factor, Sylow
217C22—21no—
218C22—21no—
219C22C5×#39411yescharacteristic
220C22C5×#46711yescharacteristic
221C22C5×#47011yescharacteristic
222C4—21no—
223C4—22no—
224C4—42no—
225C4—42no—
226C4—82no—
227C4—82no—
228C4C5×#45411yescharacteristic
229C4C5×#45511yescharacteristic
230C4C5×#46212yes—
231C4C5×#46412yes—
232C2—21no—
233C2—21no—
234C2C5×#204011yescharacteristic
235C2C5×#205011yescharacteristic
236C2C5×#205611yescharacteristic
subgroupG/H
center, socleC22×C5#394
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC23×C5#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
19. #10523C5direct (N × H)
76. C42×C5Q16semidirect
183. C42C5×Q16semidirect
216. C5#10523direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32492
C5×#19942
C5×#18312
C5×#15502
C5×#12922
#105235