Finite Group Databasebeta

← C5×#2856⋊C3 #14510942

Subgroups — C5×#2856⋊C3 #14510942

Order 1920.

388 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 42 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
2C22×C5×C42⋊C3C211yesmaximal, characteristic, complemented
3C5×#384⋊C3C211yesmaximal, characteristic, complemented
4C5×#2856C311yesmaximal, characteristic, complemented, Hall
5C5×D4×A4—41nomaximal
6C5×#127⋊C3—21no—
7C2×C5×C42⋊C3—21no—
8C2×C5×C42⋊C3C2211yescharacteristic
9#2856⋊C3C511yesmaximal, characteristic, direct product factor, Hall
10C2×C5×#127C2×C311yescharacteristic, complemented
11C2×C5×#121—31no—
12C2×C5×#121—31no—
13C22×C42×C5C2×C311yescharacteristic, complemented
14C5×#390—31no—
15C5×#390—31no—
16C5×#384C2×C311yescharacteristic, complemented
17C22×C5×A4—41no—
18C22×C5×A4—41no—
19C4×C5×A4—41no—
20C5×C42⋊C3D411yescharacteristic, complemented
21C2×#127⋊C3C2×C511yescharacteristic, complemented
22C22×C42⋊C3C2×C511yescharacteristic, complemented
23#384⋊C3C2×C511yescharacteristic, complemented
24C22×C5×D4—31no—
25C22×C5×D4—31no—
26C22×C5×D4—31no—
27C22×C5×D4A411yescharacteristic
28C23×C4×C5—31no—
29C5×#127—21no—
30C5×#127—61no—
31C5×#121—62no—
32C5×#121—62no—
33C5×#121—62no—
34C5×#121—62no—
35C2×C5×C4⋊C4—31no—
36C2×C5×C4⋊C4—31no—
37C2×C5×C22⋊C4—32no—
38C2×C5×C22⋊C4—31no—
39C2×C5×C22⋊C4—31no—
40C2×C42×C5—21no—
41C2×C42×C5—31no—
42C2×C42×C5—61no—
43C2×C42×C5C22×C311yescharacteristic
44#2856C3×C511yescharacteristic, complemented, Sylow
45C2×C5×A4—41no—
46C2×C5×A4—81no—
47C2×C5×A4—81no—
48C3×C5×D4—161no—
49D4×A4—41no—
50#127⋊C3—21no—
51C2×C42⋊C3—21no—
52C2×C42⋊C3C22×C511yescharacteristic
53C24×C5—31no—
54C24×C5C2×A411yescharacteristic
55C24×C5C2×A411yescharacteristic
56C2×C5×D4—61no—
57C2×C5×D4—61no—
58C2×C5×D4—61no—
59C2×C5×D4—61no—
60C2×C5×D4—62no—
61C2×C5×D4—62no—
62C2×C5×D4—62no—
63C2×C5×D4—62no—
64C2×C5×D4—61no—
65C2×C5×D4—62no—
66C2×C5×D4—61no—
67C2×C5×D4—61no—
68C2×C5×D4—62no—
69C2×C5×D4—61no—
70C22×C4×C5—31no—
71C22×C4×C5—32no—
72C22×C4×C5—32no—
73C22×C4×C5—31no—
74C22×C4×C5—31no—
75C22×C4×C5—61no—
76C22×C4×C5—61no—
77C22×C4×C5—62no—
78C22×C4×C5C2×A411yescharacteristic
79C5×C4⋊C4—62no—
80C5×C4⋊C4—62no—
81C5×C22⋊C4—62no—
82C5×C22⋊C4—62no—
83C5×C22⋊C4—64no—
84C42×C5—31no—
85C42×C5—61no—
86C42×C5—61no—
87C42×C5C3×D411yescharacteristic, complemented
88C2×#127C2×C3×C511yescharacteristic, complemented
89C2×#121—31no—
90C2×#121—31no—
91C22×C42C2×C3×C511yescharacteristic, complemented
92#390—31no—
93#390—31no—
94#384C2×C3×C511yescharacteristic, complemented
95C22×C3×C5—161no—
96C22×C3×C5—161no—
97C5×A4—41no—
98C3×C4×C5—161no—
99C22×A4—41no—
100C22×A4—41no—
101C4×A4—41no—
102C42⋊C3C5×D411yescharacteristic, complemented
103C23×C5—21no—
104C23×C5—21no—
105C23×C5—31no—
106C23×C5—31no—
107C23×C5—61no—
108C23×C5—61no—
109C23×C5—61no—
110C23×C5—61no—
111C23×C5—62no—
112C23×C5—61no—
113C23×C5—62no—
114C23×C5—61no—
115C23×C5C22×A411yescharacteristic
116C5×D4—41no—
117C5×D4—122no—
118C5×D4—122no—
119C5×D4—122no—
120C5×D4—122no—
121C5×D4—121no—
122C5×D4—121no—
123C5×D4—122no—
124C5×D4—121no—
125C2×C4×C5—32no—
126C2×C4×C5—32no—
127C2×C4×C5—31no—
128C2×C4×C5—31no—
129C2×C4×C5—32no—
130C2×C4×C5—62no—
131C2×C4×C5—62no—
132C2×C4×C5—62no—
133C2×C4×C5—62no—
134C2×C4×C5—61no—
135C2×C4×C5—61no—
136C2×C4×C5—61no—
137C2×C4×C5—61no—
138C2×C4×C5—62no—
139C22×D4—31no—
140C22×D4—31no—
141C22×D4—31no—
142C22×D4C5×A411yescharacteristic
143C23×C4—31no—
144#127—21no—
145#127—61no—
146#121—62no—
147#121—62no—
148#121—62no—
149#121—62no—
150C2×C4⋊C4—31no—
151C2×C4⋊C4—31no—
152C2×C22⋊C4—32no—
153C2×C22⋊C4—31no—
154C2×C22⋊C4—31no—
155C2×C42—21no—
156C2×C42—31no—
157C2×C42—61no—
158C2×C42C22×C3×C511yescharacteristic
159C2×C3×C5—161no—
160C2×C3×C5—321no—
161C2×C3×C5—321no—
162C2×A4—41no—
163C2×A4—81no—
164C2×A4—81no—
165C3×D4—161no—
166C22×C5—31no—
167C22×C5—31no—
168C22×C5—31no—
169C22×C5—41no—
170C22×C5—61no—
171C22×C5—61no—
172C22×C5—61no—
173C22×C5—61no—
174C22×C5—121no—
175C22×C5—121no—
176C22×C5—121no—
177C22×C5—122no—
178C22×C5—121no—
179C22×C5—122no—
180C22×C5—121no—
181C22×C5#127⋊C311yescharacteristic, complemented
182C22×C5D4×A411yescharacteristic
183C4×C5—32no—
184C4×C5—32no—
185C4×C5—41no—
186C4×C5—62no—
187C4×C5—121no—
188C24—31no—
189C24C2×C5×A411yescharacteristic
190C24C2×C5×A411yescharacteristic
191C2×D4—61no—
192C2×D4—61no—
193C2×D4—61no—
194C2×D4—61no—
195C2×D4—62no—
196C2×D4—62no—
197C2×D4—62no—
198C2×D4—62no—
199C2×D4—61no—
200C2×D4—62no—
201C2×D4—61no—
202C2×D4—61no—
203C2×D4—62no—
204C2×D4—61no—
205C22×C4—31no—
206C22×C4—32no—
207C22×C4—32no—
208C22×C4—31no—
209C22×C4—31no—
210C22×C4—61no—
211C22×C4—61no—
212C22×C4—62no—
213C22×C4C2×C5×A411yescharacteristic
214C4⋊C4—62no—
215C4⋊C4—62no—
216C22⋊C4—62no—
217C22⋊C4—62no—
218C22⋊C4—64no—
219C42—31no—
220C42—61no—
221C42—61no—
222C42C3×C5×D411yescharacteristic, complemented
223C3×C5—161noHall
224C22×C3—161no—
225C22×C3—161no—
226A4—41no—
227C3×C4—161no—
228C2×C5—21no—
229C2×C5—31no—
230C2×C5—31no—
231C2×C5—61no—
232C2×C5—81no—
233C2×C5—241no—
234C2×C5C2×#127⋊C311yescharacteristic
235C23—21no—
236C23—21no—
237C23—31no—
238C23—31no—
239C23—61no—
240C23—61no—
241C23—61no—
242C23—61no—
243C23—62no—
244C23—61no—
245C23—62no—
246C23—61no—
247C23C22×C5×A411yescharacteristic
248D4—41no—
249D4—122no—
250D4—122no—
251D4—122no—
252D4—122no—
253D4—121no—
254D4—121no—
255D4—122no—
256D4—121no—
257C2×C4—32no—
258C2×C4—32no—
259C2×C4—31no—
260C2×C4—31no—
261C2×C4—32no—
262C2×C4—62no—
263C2×C4—62no—
264C2×C4—62no—
265C2×C4—62no—
266C2×C4—61no—
267C2×C4—61no—
268C2×C4—61no—
269C2×C4—61no—
270C2×C4—62no—
271C2×C3—161no—
272C2×C3—321no—
273C2×C3—321no—
274C5#2856⋊C311yescharacteristic, direct product factor, Sylow
275C22—31no—
276C22—31no—
277C22—31no—
278C22—41no—
279C22—61no—
280C22—61no—
281C22—61no—
282C22—61no—
283C22—121no—
284C22—121no—
285C22—121no—
286C22—122no—
287C22—121no—
288C22—122no—
289C22—121no—
290C22C5×#127⋊C311yescharacteristic, complemented
291C22C5×D4×A411yescharacteristic
292C4—32no—
293C4—32no—
294C4—41no—
295C4—62no—
296C4—121no—
297C3—161noSylow
298C2—21no—
299C2—31no—
300C2—31no—
301C2—61no—
302C2—81no—
303C2—241no—
304C2C2×C5×#127⋊C311yescharacteristic
subgroupG/H
centerC2×C5C2×#127⋊C3
commutator, cosocleC2×C42C22×C3×C5
FrattiniC23C22×C5×A4
FittingC5×#2856C3
socleC23×C5C22×A4
hypercenterC22×C5#127⋊C3
hypocenterC42C3×C5×D4
LCSG ▷ C2×C42 ▷ C42
UCSC1 ◁ C2×C5 ◁ C22×C5

Complements

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

NH ≅ G/Ntype
1. C2×C5×#127⋊C3C2semidirect
2. C22×C5×C42⋊C3C2semidirect
3. C5×#384⋊C3C2semidirect
4. C5×#2856C3semidirect
9. #2856⋊C3C5direct (N × H)
10. C2×C5×#127C2×C3semidirect
13. C22×C42×C5C2×C3semidirect
16. C5×#384C2×C3semidirect
20. C5×C42⋊C3D4semidirect
21. C2×#127⋊C3C2×C5semidirect
22. C22×C42⋊C3C2×C5semidirect
23. #384⋊C3C2×C5semidirect
44. #2856C3×C5semidirect
87. C42×C5C3×D4semidirect
88. C2×#127C2×C3×C5semidirect
91. C22×C42C2×C3×C5semidirect
94. #384C2×C3×C5semidirect
102. C42⋊C3C5×D4semidirect
181. C22×C5#127⋊C3semidirect
222. C42C3×C5×D4semidirect
274. C5#2856⋊C3direct (N × H)
290. C22C5×#127⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#127⋊C32
C22×C5×C42⋊C32
C5×#384⋊C32
C5×#28563
C5×D4×A44
#2856⋊C35