Finite Group Databasebeta

← C5×#68956 #14309002

Subgroups — C5×#68956 #14309002

Order 1920.

580 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 134 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×#5483C211yesmaximal, characteristic
2C5×#4943C211yesmaximal, characteristic
3C5×#4943C212yesmaximal
4C3×C5×#342C211yesmaximal, characteristic
5C5×#4527C212yesmaximal
6C5×#2030—31nomaximal, Hall
7C23×C5×Dic3C2211yescharacteristic
8C2×C3×C5×C22⋊C4C2212yes—
9C2×C3×C5×C22⋊C4C2211yescharacteristic
10C2×C5×#217C2211yescharacteristic
11C2×C5×#217C2212yes—
12C5×#924—22no—
13C5×#878—24no—
14C5×C3⋊#95—22no—
15C5×C3⋊#95—24no—
16#68956C511yesmaximal, characteristic, direct product factor, Hall
17C5×#543—31no—
18C5×#381—32no—
19C5×#381—31no—
20C5×#342—32no—
21C5×#342D311yescharacteristic
22C24×C3×C5C2311yescharacteristic
23C22×C3×C4×C5—22no—
24C22×C3×C4×C5D412yes—
25C22×C5×Dic3—21no—
26C22×C5×Dic3—22no—
27C22×C5×Dic3—22no—
28C22×C5×Dic3—21no—
29C22×C5×Dic3—21no—
30C22×C5×Dic3D414yes—
31C22×C5×Dic3Q812yescomplemented
32C2×C5×Dic6—22no—
33C3×C5×C22⋊C4—22no—
34C3×C5×C22⋊C4—22no—
35C3×C5×C22⋊C4—22no—
36C5×#217—22no—
37C5×#217—22no—
38C5×#217—22no—
39C5×C4⋊Dic3—22no—
40C5×Dic3⋊C4—24no—
41#5483C2×C511yescharacteristic
42#4943C2×C511yescharacteristic
43#4943C2×C512yes—
44C3×#342C2×C511yescharacteristic
45#4527C2×C512yes—
46C23×C4×C5—31no—
47C5×C22⋊Q8—64no—
48C5×C22⋊Q8—62no—
49C2×C5×C22⋊C4—32no—
50C2×C5×C22⋊C4—31no—
51C2×C5×C22⋊C4C2×D312yes—
52C2×C5×C22⋊C4C2×D311yescharacteristic
53C5×#95—64no—
54C5×#95—62no—
55#2030—31noSylow
56C23×C3×C5—42no—
57C23×C3×C5C2×D411yescharacteristic
58C23×C3×C5C2×D412yes—
59C23×C3×C5C2×Q811yescharacteristic
60C23×C3×C5#4112yes—
61C23×C3×C5#4111yescharacteristic
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—42no—
64C2×C3×C4×C5—44no—
65C2×C3×C4×C5—42no—
66C2×C5×Dic3—24no—
67C2×C5×Dic3—24no—
68C2×C5×Dic3—22no—
69C2×C5×Dic3—41no—
70C2×C5×Dic3—41no—
71C2×C5×Dic3—42no—
72C2×C5×Dic3—44no—
73C2×C5×Dic3—42no—
74C2×C5×Dic3—41no—
75C5×Dic6—82no—
76C23×Dic3C22×C511yescharacteristic
77C2×C3×C22⋊C4C22×C512yes—
78C2×C3×C22⋊C4C22×C511yescharacteristic
79C2×#217C22×C511yescharacteristic
80C2×#217C22×C512yes—
81#924—22no—
82#878—24no—
83C3⋊#95—22no—
84C3⋊#95—24no—
85C24×C5C22×D311yescharacteristic
86C2×C5×Q8—62no—
87C22×C4×C5—22no—
88C22×C4×C5—32no—
89C22×C4×C5—34no—
90C22×C4×C5—61no—
91C22×C4×C5—62no—
92C22×C4×C5—62no—
93C22×C4×C5—61no—
94C22×C4×C5—61no—
95C22×C4×C5D1212yes—
96C5×C4⋊C4—64no—
97C5×C4⋊C4—62no—
98C5×C22⋊C4—22no—
99C5×C22⋊C4—22no—
100C5×C22⋊C4—22no—
101C5×C22⋊C4—62no—
102C5×C22⋊C4—62no—
103C5×C22⋊C4—62no—
104#543—31no—
105#381—32no—
106#381—31no—
107#342—32no—
108#342C5×D311yescharacteristic
109C22×C3×C5—22no—
110C22×C3×C5—24no—
111C22×C3×C5—41no—
112C22×C3×C5—42no—
113C22×C3×C5—41no—
114C22×C3×C5#12011yescharacteristic
115C22×C3×C5C22⋊Q812yes—
116C22×C3×C5C22⋊Q811yescharacteristic
117C22×C3×C5#12411yescharacteristic
118C22×C3×C5#12412yes—
119C3×C4×C5—42no—
120C3×C4×C5—82no—
121C5×Dic3—42no—
122C5×Dic3—44no—
123C5×Dic3—81no—
124C24×C3C23×C511yescharacteristic
125C22×C3×C4—22no—
126C22×C3×C4C5×D412yes—
127C22×Dic3—21no—
128C22×Dic3—22no—
129C22×Dic3—22no—
130C22×Dic3—21no—
131C22×Dic3—21no—
132C22×Dic3C5×D414yes—
133C22×Dic3C5×Q812yescomplemented
134C2×Dic6—22no—
135C3×C22⋊C4—22no—
136C3×C22⋊C4—22no—
137C3×C22⋊C4—22no—
138#217—22no—
139#217—22no—
140#217—22no—
141C4⋊Dic3—22no—
142Dic3⋊C4—24no—
143C23×C5—42no—
144C23×C5C2×D1211yescharacteristic
145C23×C5#23512yes—
146C23×C5D3×D412yes—
147C23×C5#23711yescharacteristic
148C23×C5D3×Q811yescharacteristic
149C5×Q8—242no—
150C2×C4×C5—22no—
151C2×C4×C5—42no—
152C2×C4×C5—44no—
153C2×C4×C5—42no—
154C2×C4×C5—64no—
155C2×C4×C5—64no—
156C2×C4×C5—62no—
157C2×C4×C5—121no—
158C2×C4×C5—121no—
159C2×C4×C5—122no—
160C2×C4×C5—124no—
161C2×C4×C5—122no—
162C2×C4×C5—121no—
163C23×C4—31no—
164C22⋊Q8—64no—
165C22⋊Q8—62no—
166C2×C22⋊C4—32no—
167C2×C22⋊C4—31no—
168C2×C22⋊C4C2×C5×D312yes—
169C2×C22⋊C4C2×C5×D311yescharacteristic
170#95—64no—
171#95—62no—
172C2×C3×C5—21no—
173C2×C3×C5—22no—
174C2×C3×C5—22no—
175C2×C3×C5—21no—
176C2×C3×C5#39311yescharacteristic
177C2×C3×C5#45812yes—
178C23×C3—42no—
179C23×C3C2×C5×D411yescharacteristic
180C23×C3C2×C5×D412yes—
181C23×C3C2×C5×Q811yescharacteristic
182C23×C3C5×#4112yes—
183C23×C3C5×#4111yescharacteristic
184C2×C3×C4—22no—
185C2×C3×C4—42no—
186C2×C3×C4—44no—
187C2×C3×C4—42no—
188C2×Dic3—24no—
189C2×Dic3—24no—
190C2×Dic3—22no—
191C2×Dic3—41no—
192C2×Dic3—41no—
193C2×Dic3—42no—
194C2×Dic3—44no—
195C2×Dic3—42no—
196C2×Dic3—41no—
197Dic6—82no—
198C22×C5—22no—
199C22×C5—24no—
200C22×C5—42no—
201C22×C5—41no—
202C22×C5—41no—
203C22×C5#87511yescharacteristic
204C22×C5#88211yescharacteristic
205C22×C5#88512yes—
206C22×C5#89612yes—
207C22×C5#89711yescharacteristic
208C4×C5—42no—
209C4×C5—82no—
210C4×C5—122no—
211C4×C5—124no—
212C4×C5—241no—
213C24C22×C5×D311yescharacteristic
214C2×Q8—62no—
215C22×C4—22no—
216C22×C4—32no—
217C22×C4—34no—
218C22×C4—61no—
219C22×C4—62no—
220C22×C4—62no—
221C22×C4—61no—
222C22×C4—61no—
223C22×C4C5×D1212yes—
224C4⋊C4—64no—
225C4⋊C4—62no—
226C22⋊C4—22no—
227C22⋊C4—22no—
228C22⋊C4—22no—
229C22⋊C4—62no—
230C22⋊C4—62no—
231C22⋊C4—62no—
232C3×C5#203011yescharacteristic, complemented, Hall
233C22×C3—22no—
234C22×C3—24no—
235C22×C3—41no—
236C22×C3—42no—
237C22×C3—41no—
238C22×C3C5×#12011yescharacteristic
239C22×C3C5×C22⋊Q812yes—
240C22×C3C5×C22⋊Q811yescharacteristic
241C22×C3C5×#12411yescharacteristic
242C22×C3C5×#12412yes—
243C3×C4—42no—
244C3×C4—82no—
245Dic3—42no—
246Dic3—44no—
247Dic3—81no—
248C2×C5—22no—
249C2×C5—21no—
250C2×C5—22no—
251C2×C5—21no—
252C2×C5#467311yescharacteristic
253C2×C5#474212yes—
254C23—42no—
255C23C2×C5×D1211yescharacteristic
256C23C5×#23512yes—
257C23C5×D3×D412yes—
258C23C5×#23711yescharacteristic
259C23C5×D3×Q811yescharacteristic
260Q8—242no—
261C2×C4—22no—
262C2×C4—42no—
263C2×C4—44no—
264C2×C4—42no—
265C2×C4—64no—
266C2×C4—64no—
267C2×C4—62no—
268C2×C4—121no—
269C2×C4—121no—
270C2×C4—122no—
271C2×C4—124no—
272C2×C4—122no—
273C2×C4—121no—
274C2×C3—21no—
275C2×C3—22no—
276C2×C3—22no—
277C2×C3—21no—
278C2×C3C5×#39311yescharacteristic
279C2×C3C5×#45812yes—
280C5#6895611yescharacteristic, direct product factor, Sylow
281C22—22no—
282C22—24no—
283C22—42no—
284C22—41no—
285C22—41no—
286C22C5×#87511yescharacteristic
287C22C5×#88211yescharacteristic
288C22C5×#88512yes—
289C22C5×#89612yes—
290C22C5×#89711yescharacteristic
291C4—42no—
292C4—82no—
293C4—122no—
294C4—124no—
295C4—241no—
296C3C5×#203011yescharacteristic, complemented, Sylow
297C2—22no—
298C2—21no—
299C2—22no—
300C2—21no—
301C2C5×#467311yescharacteristic
302C2C5×#474212yes—
subgroupG/H
centerC22×C5#882
commutator, cosocleC24×C3C23×C5
FrattiniC24C22×C5×D3
FittingC3×C5×#342C2
socleC22×C3×C5#120
prime radicalC24×C3×C5C23
hypercenterC5×#342D3
hypocenterC3C5×#2030
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C24×C5 ◁ C5×#342

Complements

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

NH ≅ G/Ntype
16. #68956C5direct (N × H)
31. C22×C5×Dic3Q8semidirect
133. C22×Dic3C5×Q8semidirect
232. C3×C5#2030semidirect
280. C5#68956direct (N × H)
296. C3C5×#2030semidirect

Maximal subgroups

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

subgroupindex
C5×#54832
C5×#49432
C3×C5×#3422
C5×#45272
C5×#20303
#689565