Finite Group Databasebeta

← C5×#18551 #11941271

Subgroups — C5×#18551 #11941271

Order 1280.

918 conjugacy classes of subgroups; only the 246 normal subgroups are shown.

normal subgroups only

This group has 918 conjugacy classes of subgroups — too many to draw. Only its 246 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
1C2×C5×Q82C211yesmaximal, characteristic
2C5×#3139C211yesmaximal, characteristic
3C5×#3113C212yesmaximal
4C5×#1645C218yesmaximal, complemented
5C5×#1558C211yesmaximal, characteristic
6C5×#1491C212yesmaximal
7C5×Q82—22no—
8C5×Q82—24no—
9C5×Q82C2214yes—
10C5×#533C2211yescharacteristic
11C2×C5×C4⋊Q8—22no—
12C2×C5×C4⋊Q8—22no—
13C2×C5×C4⋊Q8C2211yescharacteristic
14C2×C4×C5×Q8—22no—
15C2×C4×C5×Q8C2212yes—
16C5×#491—22no—
17C5×#487C2214yes—
18C5×#483—22no—
19C5×#475C2214yes—
20C5×#462C2214yes—
21C5×#451—22no—
22C5×#441—24no—
23C5×#432C2212yes—
24C5×#419—22no—
25C4×C5×M16C2211yescharacteristic
26C5×#333C2214yes—
27C5×Q8⋊C8C2218yes—
28#18551C511yesmaximal, characteristic, direct product factor, Sylow
29C22×C5×Q8—22no—
30C22×C5×Q8D412yes—
31C22×C5×Q8D412yes—
32C2×C5×Q16—24no—
33C2×C5×M16—21no—
34C5×C4⋊Q8—28no—
35C5×C4⋊Q8—28no—
36C5×C4⋊Q8—28no—
37C5×C4⋊Q8—28no—
38C5×C4⋊Q8—22no—
39C5×C4⋊Q8D412yes—
40C5×C4⋊Q8C2312yes—
41C5×C4⋊Q8C2312yes—
42C5×#125—21no—
43C5×C22⋊Q8—22no—
44C4×C5×Q8—28no—
45C4×C5×Q8—28no—
46C4×C5×Q8—22no—
47C4×C5×Q8—22no—
48C4×C5×Q8—22no—
49C4×C5×Q8D414yes—
50C4×C5×Q8C2314yes—
51C5×#117—21no—
52C2×C5×C4⋊C4—24no—
53C2×C5×C4⋊C4—22no—
54C2×C5×C4⋊C4—22no—
55C2×C5×C4⋊C4D412yes—
56C2×C42×C5—22no—
57C2×C42×C5—22no—
58C2×C42×C5C2311yescharacteristic
59C5×#106—24no—
60C5×C4⋊C8C2314yes—
61C5×#103—28no—
62C5×#103—24no—
63C5×#103—24no—
64C5×C22⋊C8—22no—
65C5×#97—21no—
66C5×#97—22no—
67C4×C5×C8C2312yes—
68C2×Q82C2×C511yescharacteristic
69#3139C2×C511yescharacteristic
70#3113C2×C512yes—
71#1645C2×C518yescomplemented
72#1558C2×C511yescharacteristic
73#1491C2×C512yes—
74C2×C5×Q8—28no—
75C2×C5×Q8—28no—
76C2×C5×Q8—22no—
77C2×C5×Q8—22no—
78C2×C5×Q8—22no—
79C2×C5×Q8—44no—
80C2×C5×Q8—84no—
81C2×C5×Q8C2×D414yes—
82C2×C5×Q8C2×D414yes—
83C22×C4×C5—22no—
84C22×C4×C5—22no—
85C22×C4×C5—22no—
86C22×C4×C5C2×D412yes—
87C22×C4×C5C2×D411yescharacteristic
88C5×Q16—48no—
89C5×M16—42no—
90C2×C5×C8—22no—
91C2×C5×C8—24no—
92C5×C4⋊C4—216no—
93C5×C4⋊C4—24no—
94C5×C4⋊C4—24no—
95C5×C4⋊C4—22no—
96C5×C4⋊C4—24no—
97C5×C4⋊C4—24no—
98C5×C4⋊C4—22no—
99C5×C4⋊C4—22no—
100C5×C4⋊C4—42no—
101C5×C4⋊C4C2×D414yes—
102C5×C22⋊C4—41no—
103C42×C5—28no—
104C42×C5—24no—
105C42×C5—24no—
106C42×C5—41no—
107C42×C5C2×D412yes—
108C42×C5C2×D411yescharacteristic
109C42×C5C2411yescharacteristic
110Q82—22no—
111Q82—24no—
112Q82C22×C514yes—
113#533C22×C511yescharacteristic
114C2×C4⋊Q8—22no—
115C2×C4⋊Q8—22no—
116C2×C4⋊Q8C22×C511yescharacteristic
117C2×C4×Q8—22no—
118C2×C4×Q8C22×C512yes—
119#491—22no—
120#487C22×C514yes—
121#483—22no—
122#475C22×C514yes—
123#462C22×C514yes—
124#451—22no—
125#441—24no—
126#432C22×C512yes—
127#419—22no—
128C4×M16C22×C511yescharacteristic
129#333C22×C514yes—
130Q8⋊C8C22×C518yes—
131C23×C5#12011yescharacteristic
132C5×Q8—28no—
133C5×Q8—24no—
134C5×Q8—44no—
135C5×Q8—44no—
136C5×Q8—82no—
137C5×Q8—88no—
138C5×Q8#13718yes—
139C2×C4×C5—28no—
140C2×C4×C5—24no—
141C2×C4×C5—22no—
142C2×C4×C5—24no—
143C2×C4×C5—24no—
144C2×C4×C5—24no—
145C2×C4×C5—44no—
146C2×C4×C5—44no—
147C2×C4×C5—42no—
148C2×C4×C5#12012yes—
149C2×C4×C5#12011yescharacteristic
150C2×C4×C5C22×D411yescharacteristic
151C2×C4×C5C22×D412yes—
152C5×C8—42no—
153C5×C8—44no—
154C22×Q8—22no—
155C22×Q8C5×D412yes—
156C22×Q8C5×D412yes—
157C2×Q16—24no—
158C2×M16—21no—
159C4⋊Q8—28no—
160C4⋊Q8—28no—
161C4⋊Q8—28no—
162C4⋊Q8—28no—
163C4⋊Q8—22no—
164C4⋊Q8C5×D412yes—
165C4⋊Q8C23×C512yes—
166C4⋊Q8C23×C512yes—
167#125—21no—
168C22⋊Q8—22no—
169C4×Q8—28no—
170C4×Q8—28no—
171C4×Q8—22no—
172C4×Q8—22no—
173C4×Q8—22no—
174C4×Q8C5×D414yes—
175C4×Q8C23×C514yes—
176#117—21no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4C5×D412yes—
181C2×C42—22no—
182C2×C42—22no—
183C2×C42C23×C511yescharacteristic
184#106—24no—
185C4⋊C8C23×C514yes—
186#103—28no—
187#103—24no—
188#103—24no—
189C22⋊C8—22no—
190#97—21no—
191#97—22no—
192C4×C8C23×C512yes—
193C22×C5—22no—
194C22×C5#45512yes—
195C22×C5C2×#12011yescharacteristic
196C4×C5—28no—
197C4×C5—22no—
198C4×C5—21no—
199C4×C5—21no—
200C4×C5—44no—
201C4×C5—44no—
202C4×C5—82no—
203C4×C5C2×#13714yes—
204C2×Q8—28no—
205C2×Q8—28no—
206C2×Q8—22no—
207C2×Q8—22no—
208C2×Q8—22no—
209C2×Q8—44no—
210C2×Q8—84no—
211C2×Q8C2×C5×D414yes—
212C2×Q8C2×C5×D414yes—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4C2×C5×D412yes—
217C22×C4C2×C5×D411yescharacteristic
218Q16—48no—
219M16—42no—
220C2×C8—22no—
221C2×C8—24no—
222C4⋊C4—216no—
223C4⋊C4—24no—
224C4⋊C4—24no—
225C4⋊C4—22no—
226C4⋊C4—24no—
227C4⋊C4—24no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—42no—
231C4⋊C4C2×C5×D414yes—
232C22⋊C4—41no—
233C42—28no—
234C42—24no—
235C42—24no—
236C42—41no—
237C42C2×C5×D412yes—
238C42C2×C5×D411yescharacteristic
239C42C24×C511yescharacteristic
240C2×C5—22no—
241C2×C5#300412yes—
242C2×C5C2×#45511yescharacteristic
243C23C5×#12011yescharacteristic
244Q8—28no—
245Q8—24no—
246Q8—44no—
247Q8—44no—
248Q8—82no—
249Q8—88no—
250Q8C5×#13718yes—
251C2×C4—28no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—24no—
255C2×C4—24no—
256C2×C4—24no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—42no—
260C2×C4C5×#12012yes—
261C2×C4C5×#12011yescharacteristic
262C2×C4C22×C5×D411yescharacteristic
263C2×C4C22×C5×D412yes—
264C8—42no—
265C8—44no—
266C5#1855111yescharacteristic, direct product factor, Sylow
267C22—22no—
268C22C5×#45512yes—
269C22C2×C5×#12011yescharacteristic
270C4—28no—
271C4—22no—
272C4—21no—
273C4—21no—
274C4—44no—
275C4—44no—
276C4—82no—
277C4C2×C5×#13714yes—
278C2—22no—
279C2C5×#300412yes—
280C2C2×C5×#45511yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC23×C5#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1645C2semidirect
28. #18551C5direct (N × H)
71. #1645C2×C5semidirect
266. C5#18551direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×Q822
C5×#31392
C5×#31132
C5×#16452
C5×#15582
C5×#14912
#185515