Finite Group Databasebeta

← C2×C5⋊#5930 #14514623

Subgroups — C2×C5⋊#5930 #14514623

Order 1920.

536 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 39 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×C22⋊SL(2,𝔽3)C211yesmaximal, characteristic
2C5⋊#5930C212yesmaximal, direct product factor
3C2×#65517—31nomaximal, Hall
4C5×C22⋊SL(2,𝔽3)C2211yescharacteristic
5C2×A4⋊Dic5—41nomaximal
6C2×C5⋊#226—42nomaximal
7C2×#5930—51nomaximal, Hall
8C23×C5×Q8D311yescharacteristic
9C22×#689—32no—
10C2×#4070—31no—
11#65517—32no—
12#65517—34no—
13#65517—32no—
14C2×#3967—32no—
15C2×C22⋊#168—31no—
16C22×C5×A4—41no—
17C2×C5×SL(2,𝔽3)—42no—
18C2×C5×SL(2,𝔽3)—81no—
19A4⋊Dic5—42no—
20C5⋊#226—44no—
21C2×C22⋊SL(2,𝔽3)D511yescharacteristic
22#5930—52no—
23C22×C5×Q8—31no—
24C22×C5×Q8—32no—
25C22×C5×Q8—32no—
26C22×C5×Q8—61no—
27C22×C5×Q8—61no—
28C22×C5×Q8C2×D311yescharacteristic
29C23×C4×C5—31no—
30C22×Dic10—31no—
31C2×C22⋊Dic5—61no—
32C2×#689—34no—
33C2×#689—34no—
34C2×#689—62no—
35C2×#689—62no—
36C2×#689—62no—
37C2×#689—62no—
38C2×C4⋊Dic5—31no—
39#4070—32no—
40#4070—32no—
41#4070—61no—
42#4070—61no—
43C2×#683—61no—
44C22×#168—32no—
45#3967—34no—
46#3967—34no—
47C22⋊#168—32no—
48C22⋊#168—32no—
49C2×#451—151noSylow
50C2×C5×A4—42no—
51C2×C5×A4—41no—
52C2×Dic15—161no—
53C5×SL(2,𝔽3)—42no—
54C5×SL(2,𝔽3)—81no—
55C22⋊SL(2,𝔽3)C2×D511yescharacteristic
56C2×SL(2,ℤ/4)—201no—
57C2×#226—202no—
58C24×C5S411yescharacteristic
59C2×C5×Q8—21no—
60C2×C5×Q8—32no—
61C2×C5×Q8—32no—
62C2×C5×Q8—32no—
63C2×C5×Q8—32no—
64C2×C5×Q8—32no—
65C2×C5×Q8—61no—
66C2×C5×Q8—61no—
67C2×C5×Q8—62no—
68C2×C5×Q8—62no—
69C2×C5×Q8—62no—
70C2×C5×Q8—61no—
71C2×C5×Q8—61no—
72C2×C5×Q8—61no—
73C2×C5×Q8—62no—
74C2×C5×Q8S412yes—
75C22×C4×C5—31no—
76C22×C4×C5—31no—
77C22×C4×C5—31no—
78C22×C4×C5—31no—
79C22×C4×C5—31no—
80C22×C4×C5—31no—
81C22×C4×C5—62no—
82C22×C4×C5—62no—
83C22×Dic5—61no—
84C22×Dic5—61no—
85C2×Dic10—32no—
86C2×Dic10—62no—
87C2×Dic10—62no—
88C2×Dic10—61no—
89C22⋊Dic5—62no—
90C22⋊Dic5—62no—
91#689—64no—
92#689—64no—
93#689—64no—
94#689—64no—
95C4⋊Dic5—32no—
96C4⋊Dic5—61no—
97#683—62no—
98#683—62no—
99C2×#168—34no—
100C2×#168—62no—
101C2×#168—62no—
102C23×Q8D1511yescharacteristic
103C22×Q16—152no—
104C2×C22⋊Q8—151no—
105#451—152no—
106#451—154no—
107#451—152no—
108C2×#103—152no—
109C2×C22⋊C8—151no—
110C22×C3×C5—161no—
111C5×A4—41no—
112Dic15—162no—
113C22×A4—41no—
114C2×SL(2,𝔽3)—42no—
115C2×SL(2,𝔽3)—81no—
116SL(2,ℤ/4)—202no—
117#226—204no—
118C23×C5—31no—
119C23×C5—31no—
120C23×C5—32no—
121C23×C5#22612yescomplemented
122C23×C5C2×S411yescharacteristic
123C5×Q8—21no—
124C5×Q8—32no—
125C5×Q8—32no—
126C5×Q8—32no—
127C5×Q8—61no—
128C5×Q8—62no—
129C5×Q8—61no—
130C5×Q8—62no—
131C5×Q8—61no—
132C5×Q8C2×S412yes—
133C2×C4×C5—31no—
134C2×C4×C5—32no—
135C2×C4×C5—31no—
136C2×C4×C5—32no—
137C2×C4×C5—31no—
138C2×C4×C5—31no—
139C2×C4×C5—62no—
140C2×C4×C5—62no—
141C2×C4×C5—62no—
142C2×C4×C5—62no—
143C2×C4×C5—61no—
144C2×C4×C5—61no—
145C2×Dic5—62no—
146C2×Dic5—62no—
147C2×Dic5—121no—
148C2×Dic5—122no—
149C2×Dic5—121no—
150Dic10—64no—
151Dic10—122no—
152#168—64no—
153C22×Q8—31no—
154C22×Q8—32no—
155C22×Q8—32no—
156C22×Q8—61no—
157C22×Q8—61no—
158C22×Q8—151no—
159C22×Q8C2×D1511yescharacteristic
160C23×C4—31no—
161C2×Q16—154no—
162C2×Q16—154no—
163C2×Q16—302no—
164C2×Q16—302no—
165C2×Q16—302no—
166C2×Q16—302no—
167C22×C8—152no—
168C22⋊Q8—152no—
169C22⋊Q8—152no—
170C22⋊Q8—301no—
171C22⋊Q8—301no—
172C2×C4⋊C4—151no—
173C2×C4⋊C4—301no—
174C2×C22⋊C4—301no—
175#103—154no—
176#103—154no—
177C22⋊C8—152no—
178C22⋊C8—152no—
179C2×C3×C5—162no—
180C2×C3×C5—161no—
181C2×A4—42no—
182C2×A4—41no—
183C2×Dic3—801no—
184SL(2,𝔽3)—42no—
185SL(2,𝔽3)—81no—
186C22×C5—32no—
187C22×C5—31no—
188C22×C5—32no—
189C22×C5—32no—
190C22×C5—31no—
191C22×C5—31no—
192C22×C5—61no—
193C22×C5C2×#22611yescharacteristic, complemented
194C22×C5#102011yescharacteristic
195C4×C5—32no—
196C4×C5—32no—
197C4×C5—61no—
198C4×C5—61no—
199Dic5—122no—
200Dic5—122no—
201C24C5⋊S411yescharacteristic
202C2×Q8—21no—
203C2×Q8—32no—
204C2×Q8—32no—
205C2×Q8—32no—
206C2×Q8—32no—
207C2×Q8—32no—
208C2×Q8—61no—
209C2×Q8—61no—
210C2×Q8—62no—
211C2×Q8—62no—
212C2×Q8—62no—
213C2×Q8—61no—
214C2×Q8—61no—
215C2×Q8—61no—
216C2×Q8—62no—
217C2×Q8—152no—
218C2×Q8—301no—
219C2×Q8—302no—
220C2×Q8—302no—
221C2×Q8C5⋊S412yes—
222C22×C4—31no—
223C22×C4—31no—
224C22×C4—31no—
225C22×C4—31no—
226C22×C4—31no—
227C22×C4—31no—
228C22×C4—62no—
229C22×C4—62no—
230C22×C4—301no—
231C22×C4—301no—
232Q16—304no—
233Q16—304no—
234Q16—304no—
235Q16—304no—
236C2×C8—154no—
237C2×C8—302no—
238C2×C8—302no—
239C4⋊C4—152no—
240C4⋊C4—301no—
241C4⋊C4—302no—
242C4⋊C4—302no—
243C22⋊C4—302no—
244C22⋊C4—302no—
245C3×C5—161noHall
246C22×C3—161no—
247A4—41no—
248Dic3—802no—
249C2×C5—31no—
250C2×C5—31no—
251C2×C5—32no—
252C2×C5#593012yescomplemented
253C2×C5C2×#102011yescharacteristic
254C23—31no—
255C23—31no—
256C23—32no—
257C23C5⋊#22612yescomplemented
258C23C2×C5⋊S411yescharacteristic
259Q8—21no—
260Q8—32no—
261Q8—32no—
262Q8—32no—
263Q8—61no—
264Q8—62no—
265Q8—61no—
266Q8—62no—
267Q8—61no—
268Q8—304no—
269Q8—602no—
270Q8C2×C5⋊S412yes—
271C2×C4—31no—
272C2×C4—31no—
273C2×C4—32no—
274C2×C4—32no—
275C2×C4—31no—
276C2×C4—31no—
277C2×C4—62no—
278C2×C4—62no—
279C2×C4—62no—
280C2×C4—62no—
281C2×C4—61no—
282C2×C4—61no—
283C2×C4—302no—
284C2×C4—302no—
285C2×C4—601no—
286C2×C4—602no—
287C2×C4—601no—
288C8—304no—
289C2×C3—162no—
290C2×C3—161no—
291C5C2×#593011yescharacteristic, complemented, Sylow
292C22—32no—
293C22—31no—
294C22—32no—
295C22—32no—
296C22—31no—
297C22—31no—
298C22—61no—
299C22C2×C5⋊#22611yescharacteristic, complemented
300C22C5⋊#102011yescharacteristic
301C4—32no—
302C4—32no—
303C4—61no—
304C4—61no—
305C4—602no—
306C4—602no—
307C3—161noSylow
308C2—31no—
309C2—31no—
310C2—32no—
311C2C5⋊#593012yesdirect product factor
312C2C2×C5⋊#102011yescharacteristic
subgroupG/H
center, hypercenterC22C5⋊#1020
commutator, cosocle, hypocenterC5×C22⋊SL(2,𝔽3)C22
FrattiniC2C2×C5⋊#1020
FittingC23×C5×Q8D3
socleC24×C5S4
prime radicalC2×C5×C22⋊SL(2,𝔽3)C2
LCSG ▷ C5×C22⋊SL(2,𝔽3)
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C5⋊#5930C2direct (N × H)
121. C23×C5#226semidirect
193. C22×C5C2×#226semidirect
252. C2×C5#5930semidirect
257. C23C5⋊#226semidirect
291. C5C2×#5930semidirect
299. C22C2×C5⋊#226semidirect
311. C2C5⋊#5930direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×C22⋊SL(2,𝔽3)2
C5⋊#59302
C2×#655173
C2×A4⋊Dic54
C2×C5⋊#2264
C2×#59305