Finite Group Databasebeta

← #10614916⋊C3 #14512255

Subgroups — #10614916⋊C3 #14512255

Order 1920.

504 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 32 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×#127⋊C3C211yesmaximal, characteristic, complemented
2C2×C5⋊(#127⋊C3)C211yesmaximal, characteristic, complemented
3Dic5×C42⋊C3C211yesmaximal, characteristic, complemented
4#10614916C311yesmaximal, characteristic, complemented, Hall
5A4×C22⋊D5—41nomaximal
6C5×#127⋊C3—21no—
7C2×C5×C42⋊C3C2211yescharacteristic
8C5⋊(#127⋊C3)—21no—
9C4⋊(#127⋊C3)—51nomaximal, Hall
10C2×C5×#127C2×C311yescharacteristic, complemented
11C2×#4086—31no—
12C2×#4086—31no—
13C2×#4086—31no—
14C2×#4086—31no—
15C2×#4020C2×C311yescharacteristic, complemented
16C42×Dic5C2×C311yescharacteristic, complemented
17C22×C5×A4—41no—
18C2×D5×A4—41no—
19A4×Dic5—41no—
20C5×C42⋊C3D411yescharacteristic, complemented
21C2×#127⋊C3—51no—
22C2×#127⋊C3D511yescharacteristic, complemented
23C4×C42⋊C3—51no—
24C22×C5×D4—31no—
25C22×C5×D4—31no—
26C22×C22⋊D5—32no—
27C22×C22⋊D5—31no—
28C22×C22⋊D5—31no—
29C22×C22⋊D5—31no—
30C22×C22⋊D5A411yescharacteristic
31C22×D20—31no—
32C22×D20—31no—
33C5×#127—21no—
34C5×#127—61no—
35C2×C42×C5C22×C311yescharacteristic
36#4086—62no—
37#4086—64no—
38#4086—64no—
39#4086—62no—
40#4086—62no—
41#4086—62no—
42C2×C4×Dic5—31no—
43C2×C4×Dic5—31no—
44#4020—21no—
45#4020—61no—
46#2867—51noSylow
47C2×C5×A4—41no—
48C2×C5×A4—81no—
49D5×A4—81no—
50C3×C22⋊D5—161no—
51D4×A4—201no—
52#127⋊C3—21no—
53#127⋊C3—101no—
54C2×C42⋊C3C2×D511yescharacteristic
55C24×C5—31no—
56C24×C5C2×A411yescharacteristic
57C23×D5—31no—
58C23×D5C2×A411yescharacteristic
59C2×C5×D4—61no—
60C2×C5×D4—61no—
61C2×C5×D4—61no—
62C2×C5×D4—61no—
63C2×C5×D4—62no—
64C2×C5×D4—62no—
65C2×C5×D4—62no—
66C2×C5×D4—62no—
67C22×C4×C5—31no—
68C2×C22⋊D5—61no—
69C2×C22⋊D5—62no—
70C2×C22⋊D5—62no—
71C2×C22⋊D5—64no—
72C2×C22⋊D5—64no—
73C2×C22⋊D5—64no—
74C2×C22⋊D5—64no—
75C2×C22⋊D5—64no—
76C2×C22⋊D5—61no—
77C2×C22⋊D5—62no—
78C2×C22⋊D5—62no—
79C2×C22⋊D5—61no—
80C2×C22⋊D5—61no—
81C22×Dic5—31no—
82C22×Dic5C2×A411yescharacteristic
83C2×D20—61no—
84C2×D20—61no—
85C2×D20—61no—
86C2×D20—61no—
87C2×D20—62no—
88C2×D20—62no—
89C2×D20—62no—
90C2×D20—62no—
91C42×C5—31no—
92C42×C5C3×D411yescharacteristic, complemented
93C4×Dic5—34no—
94C4×Dic5—32no—
95C4×Dic5—32no—
96C2×#127—51no—
97C2×#127—151no—
98C2×#127—151no—
99C2×#127—151no—
100C2×#127—151no—
101C2×#127C3×D511yescharacteristic, complemented
102C43—51no—
103C22×C3×C5—161no—
104C2×C3×D5—161no—
105C5×A4—41no—
106C3×Dic5—161no—
107C22×A4—41no—
108C22×A4—201no—
109C4×A4—201no—
110C42⋊C3C22⋊D511yescharacteristic, complemented
111C23×C5—21no—
112C23×C5—61no—
113C23×C5—61no—
114C23×C5—61no—
115C23×C5—62no—
116C23×C5—61no—
117C23×C5—62no—
118C23×C5—61no—
119C23×C5C22×A411yescharacteristic
120C22×D5—21no—
121C22×D5—61no—
122C22×D5—62no—
123C22×D5—61no—
124C22×D5—61no—
125C22×D5—62no—
126C22×D5—61no—
127C22×D5—61no—
128C5×D4—122no—
129C5×D4—122no—
130C5×D4—122no—
131C5×D4—122no—
132C2×C4×C5—32no—
133C2×C4×C5—32no—
134C2×C4×C5—31no—
135C2×C4×C5—31no—
136C22⋊D5—41no—
137C22⋊D5—121no—
138C22⋊D5—124no—
139C22⋊D5—124no—
140C22⋊D5—128no—
141C22⋊D5—121no—
142C22⋊D5—122no—
143C22⋊D5—121no—
144C2×Dic5—34no—
145C2×Dic5—32no—
146C2×Dic5—31no—
147C2×Dic5—31no—
148D20—122no—
149D20—122no—
150D20—122no—
151D20—122no—
152C22×D4—31no—
153C22×D4—31no—
154C22×D4—51no—
155C22×D4—151no—
156C22×D4—151no—
157C22×D4—151no—
158C22×D4—151no—
159C22×D4—152no—
160C22×D4—151no—
161#127—21no—
162#127—61no—
163#127—101no—
164#127—301no—
165#127—302no—
166#127—302no—
167#127—304no—
168#127—304no—
169#127—302no—
170#127—302no—
171C2×C42—151no—
172C2×C42—151no—
173C2×C42C2×C3×D511yescharacteristic
174C2×C3×C5—161no—
175C2×C3×C5—321no—
176C3×D5—321no—
177C2×A4—41no—
178C2×A4—81no—
179C2×A4—401no—
180C3×D4—801no—
181C22×C5—31no—
182C22×C5—31no—
183C22×C5—41no—
184C22×C5—121no—
185C22×C5—121no—
186C22×C5—121no—
187C22×C5—122no—
188C22×C5—121no—
189C22×C5—122no—
190C22×C5—121no—
191C22×C5D4×A411yescharacteristic
192C2×D5—41no—
193C2×D5—121no—
194C2×D5—121no—
195C2×D5—121no—
196C2×D5—122no—
197C2×D5—121no—
198C2×D5—122no—
199C2×D5—121no—
200C4×C5—32no—
201C4×C5—32no—
202Dic5—34no—
203Dic5—31no—
204Dic5#127⋊C311yescharacteristic, complemented
205C24—31no—
206C24—51no—
207C24—151no—
208C24D5×A411yescharacteristic
209C2×D4—61no—
210C2×D4—61no—
211C2×D4—61no—
212C2×D4—61no—
213C2×D4—62no—
214C2×D4—62no—
215C2×D4—62no—
216C2×D4—62no—
217C2×D4—301no—
218C2×D4—301no—
219C2×D4—301no—
220C2×D4—301no—
221C2×D4—302no—
222C2×D4—302no—
223C2×D4—302no—
224C2×D4—302no—
225C2×D4—301no—
226C2×D4—301no—
227C2×D4—302no—
228C2×D4—302no—
229C2×D4—304no—
230C2×D4—302no—
231C2×D4—304no—
232C2×D4—304no—
233C2×D4—304no—
234C2×D4—304no—
235C2×D4—302no—
236C2×D4—301no—
237C2×D4—301no—
238C22×C4—31no—
239C22×C4—51no—
240C22×C4—151no—
241C42—31no—
242C42—152no—
243C42—154no—
244C42—152no—
245C42C3×C22⋊D511yescharacteristic, complemented
246C3×C5—161noHall
247C22×C3—161no—
248C22×C3—801no—
249A4—41no—
250C3×C4—801no—
251C2×C5—31no—
252C2×C5—31no—
253C2×C5—81no—
254C2×C5—241no—
255C2×C5C2×#127⋊C311yescharacteristic
256D5—81no—
257D5—241no—
258C23—21no—
259C23—61no—
260C23—61no—
261C23—61no—
262C23—62no—
263C23—61no—
264C23—62no—
265C23—61no—
266C23—101no—
267C23—301no—
268C23—301no—
269C23—301no—
270C23—302no—
271C23—301no—
272C23—302no—
273C23—301no—
274C23C2×D5×A411yescharacteristic
275D4—122no—
276D4—122no—
277D4—122no—
278D4—122no—
279D4—201no—
280D4—602no—
281D4—602no—
282D4—602no—
283D4—602no—
284D4—601no—
285D4—601no—
286D4—604no—
287D4—604no—
288D4—608no—
289D4—601no—
290D4—602no—
291C2×C4—32no—
292C2×C4—32no—
293C2×C4—31no—
294C2×C4—31no—
295C2×C4—151no—
296C2×C4—154no—
297C2×C4—152no—
298C2×C4—151no—
299C2×C3—161no—
300C2×C3—321no—
301C2×C3—1601no—
302C5C4⋊(#127⋊C3)11yescharacteristic, complemented, Sylow
303C22—31no—
304C22—31no—
305C22—41no—
306C22—121no—
307C22—121no—
308C22—121no—
309C22—122no—
310C22—121no—
311C22—122no—
312C22—121no—
313C22—201no—
314C22—601no—
315C22—601no—
316C22—601no—
317C22—602no—
318C22—601no—
319C22—602no—
320C22—601no—
321C22A4×C22⋊D511yescharacteristic
322C4—32no—
323C4—32no—
324C4—51no—
325C4—154no—
326C4—151no—
327C3—161noSylow
328C2—31no—
329C2—31no—
330C2—81no—
331C2—241no—
332C2—401no—
333C2—1201no—
334C2D5×#127⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D5×#127⋊C3
commutator, cosocleC2×C42×C5C22×C3
FrattiniC23C2×D5×A4
FittingC2×C5×#127C2×C3
socleC23×C5C22×A4
hypocenterC42×C5C3×D4
LCSG ▷ C2×C42×C5 ▷ C42×C5
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C5×#127⋊C3C2semidirect
2. C2×C5⋊(#127⋊C3)C2semidirect
3. Dic5×C42⋊C3C2semidirect
4. #10614916C3semidirect
10. C2×C5×#127C2×C3semidirect
15. C2×#4020C2×C3semidirect
16. C42×Dic5C2×C3semidirect
20. C5×C42⋊C3D4semidirect
22. C2×#127⋊C3D5semidirect
92. C42×C5C3×D4semidirect
101. C2×#127C3×D5semidirect
110. C42⋊C3C22⋊D5semidirect
204. Dic5#127⋊C3semidirect
245. C42C3×C22⋊D5semidirect
302. C5C4⋊(#127⋊C3)semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#127⋊C32
C2×C5⋊(#127⋊C3)2
Dic5×C42⋊C32
#106149163
A4×C22⋊D54
C4⋊(#127⋊C3)5