Finite Group Databasebeta

← D5×#519⋊C3 #14514044

Subgroups — D5×#519⋊C3 #14514044

Order 1920.

806 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C22×D5×SL(2,𝔽3)C211yesmaximal, characteristic
2C5×#519⋊C3C211yesmaximal, characteristic, complemented
3#66146⋊C3C211yesmaximal, characteristic, complemented
4#65906⋊C3C212yesmaximal, complemented
5C4×D5×SL(2,𝔽3)C212yesmaximal, complemented
6D5×#519C311yesmaximal, characteristic, complemented, Hall
7C22×C5×SL(2,𝔽3)C2211yescharacteristic
8C2×D5×SL(2,𝔽3)C414yescomplemented
9C2×D5×SL(2,𝔽3)C2211yescharacteristic
10C2×D5×SL(2,𝔽3)C2211yescharacteristic
11C3×D5×C22⋊C4—41nomaximal
12C4×C5×SL(2,𝔽3)C2212yescomplemented
13Dic5×SL(2,𝔽3)C2212yescomplemented
14C2×#519⋊C3—51nomaximal, Hall
15C22×Q8×D5C2×C311yescharacteristic
16C5×#519C2×C311yescharacteristic, complemented
17#66146C2×C311yescharacteristic, complemented
18#65906—32no—
19#65906C2×C312yescomplemented
20C4×Q8×D5—32no—
21C4×Q8×D5C2×C312yescomplemented
22D5×#117—31no—
23D5×#117—31no—
24#65850—31no—
25#65850—31no—
26C23×C3×D5—41no—
27C2×C3×C4×D5—42no—
28C2×C5×SL(2,𝔽3)C2×C412yescomplemented
29C2×C5×SL(2,𝔽3)C2311yescharacteristic
30D5×SL(2,𝔽3)C2×C412yes—
31D5×SL(2,𝔽3)C2×C412yescomplemented
32C3×C5×C22⋊C4—41no—
33C3×C22⋊Dic5—41no—
34C3×#685—42no—
35C23×SL(2,𝔽3)—51no—
36#519⋊C3—51no—
37#519⋊C3—52no—
38#519⋊C3D511yescharacteristic, direct product factor
39C2×C4×SL(2,𝔽3)—52no—
40C22×C5×Q8C22×C311yescharacteristic
41C2×Q8×D5—31no—
42C2×Q8×D5—31no—
43C2×Q8×D5—34no—
44C2×Q8×D5C3×C414yescomplemented
45C2×Q8×D5C22×C311yescharacteristic
46C2×Q8×D5C22×C311yescharacteristic
47C22×C4×D5—31no—
48C22×Dic10—31no—
49C4×C5×Q8—32no—
50C4×C5×Q8C22×C312yescomplemented
51C5×#117—31no—
52C5×#117—31no—
53Q8×Dic5—32no—
54Q8×Dic5C22×C312yescomplemented
55#4072—31no—
56#4072—31no—
57#4038—32no—
58#4038—32no—
59D5×C4⋊C4—32no—
60D5×C4⋊C4—32no—
61#4033—34no—
62#4033—32no—
63#4033—32no—
64D5×C22⋊C4—31no—
65D5×C22⋊C4A411yescharacteristic
66#4023—32no—
67#4023—31no—
68#4023—31no—
69#4018—32no—
70#4018—32no—
71C42×D5—32no—
72C42×D5—32no—
73C4×Dic10—34no—
74C4×Dic10—32no—
75C4×Dic10—32no—
76C2×#519—51noSylow
77C23×C3×C5—41no—
78C22×C3×D5—41no—
79C22×C3×D5—44no—
80C22×C3×D5—41no—
81C22×C3×D5—84no—
82C2×C3×C4×C5—42no—
83C2×C3×Dic5—42no—
84C3×C4×D5—84no—
85C5×SL(2,𝔽3)C22×C411yescharacteristic
86C22×SL(2,𝔽3)—54no—
87C22×SL(2,𝔽3)—51no—
88C22×SL(2,𝔽3)—51no—
89C22×SL(2,𝔽3)C2×D511yescharacteristic
90C2×C3×C22⋊C4—201no—
91C4×SL(2,𝔽3)—52no—
92C4×SL(2,𝔽3)C2×D512yescomplemented
93C23×D5C2×A411yescharacteristic
94C2×C5×Q8—31no—
95C2×C5×Q8—32no—
96C2×C5×Q8C2×C3×C412yescomplemented
97C2×C5×Q8C23×C311yescharacteristic
98C22×C4×C5—31no—
99C22×Dic5—31no—
100Q8×D5—34no—
101Q8×D5—34no—
102Q8×D5—34no—
103Q8×D5—34no—
104Q8×D5—32no—
105Q8×D5—32no—
106Q8×D5C2×C3×C412yes—
107Q8×D5C2×C3×C412yescomplemented
108C2×C4×D5—34no—
109C2×C4×D5—34no—
110C2×C4×D5—31no—
111C2×C4×D5—31no—
112C2×C4×D5—31no—
113C2×C4×D5—31no—
114C2×C4×D5—32no—
115C2×C4×D5C2×A412yes—
116C2×Dic10—34no—
117C2×Dic10—32no—
118C2×Dic10—34no—
119C2×Dic10—31no—
120C2×Dic10—31no—
121C5×C4⋊C4—32no—
122C5×C4⋊C4—32no—
123C5×C22⋊C4—31no—
124C5×C22⋊C4C2×A411yescharacteristic
125C42×C5—32no—
126C42×C5—32no—
127C22⋊Dic5—31no—
128C22⋊Dic5C2×A411yescharacteristic
129#685—32no—
130#685C2×A412yes—
131C4⋊Dic5—32no—
132C4⋊Dic5—32no—
133#683—34no—
134#683—32no—
135#683—32no—
136C4×Dic5—34no—
137C4×Dic5—32no—
138C4×Dic5—32no—
139C4×Dic5—32no—
140C4×Dic5—32no—
141C23×Q8—51no—
142#519—51no—
143#519—52no—
144#519—151no—
145#519—151no—
146#519—152no—
147#519C3×D511yescharacteristic, complemented
148C2×C4×Q8—52no—
149C2×C4×Q8—152no—
150C2×#117—151no—
151C2×#117—151no—
152C22×C3×C5—42no—
153C22×C3×C5—41no—
154C22×C3×C5—82no—
155C2×C3×D5—42no—
156C2×C3×D5—42no—
157C2×C3×D5—44no—
158C2×C3×D5—88no—
159C2×C3×D5—82no—
160C3×C4×C5—82no—
161C3×Dic5—82no—
162C24×C3—201no—
163C22×C3×C4—202no—
164C2×SL(2,𝔽3)—52no—
165C2×SL(2,𝔽3)—52no—
166C2×SL(2,𝔽3)C4×D512yescomplemented
167C2×SL(2,𝔽3)C22×D511yescharacteristic
168C3×C22⋊C4—41no—
169C3×C22⋊C4—202no—
170C3×C22⋊C4—201no—
171C23×C5C22×A411yescharacteristic
172C22×D5—24no—
173C22×D5C4×A414yes—
174C22×D5C22×A411yescharacteristic
175C22×D5C22×A411yescharacteristic
176C5×Q8—32no—
177C5×Q8—31no—
178C5×Q8—32no—
179C5×Q8C22×C3×C411yescharacteristic
180C2×C4×C5—32no—
181C2×C4×C5—32no—
182C2×C4×C5—31no—
183C2×C4×C5—31no—
184C2×C4×C5—32no—
185C2×C4×C5C22×A412yes—
186C2×Dic5—34no—
187C2×Dic5—31no—
188C2×Dic5—31no—
189C2×Dic5—32no—
190C2×Dic5C22×A412yes—
191C4×D5—24no—
192C4×D5—32no—
193C4×D5—34no—
194C4×D5—32no—
195C4×D5—34no—
196C4×D5—32no—
197C4×D5—32no—
198C4×D5—64no—
199Dic10—32no—
200Dic10—32no—
201Dic10—38no—
202Dic10—32no—
203Dic10—32no—
204C22×Q8—54no—
205C22×Q8—51no—
206C22×Q8—51no—
207C22×Q8—151no—
208C22×Q8—151no—
209C22×Q8—151no—
210C22×Q8—154no—
211C22×Q8C2×C3×D511yescharacteristic
212C23×C4—151no—
213C4×Q8—32no—
214C4×Q8—52no—
215C4×Q8—154no—
216C4×Q8—152no—
217C4×Q8—152no—
218C4×Q8—154no—
219C4×Q8—152no—
220C4×Q8—152no—
221C4×Q8—152no—
222C4×Q8C2×C3×D512yescomplemented
223#117—31no—
224#117—31no—
225#117—152no—
226#117—152no—
227#117—151no—
228#117—152no—
229#117—152no—
230#117—151no—
231#117—151no—
232#117—152no—
233#117—151no—
234C2×C4⋊C4—152no—
235C2×C4⋊C4—152no—
236C2×C22⋊C4—51no—
237C2×C22⋊C4—151no—
238C2×C42—152no—
239C2×C42—152no—
240C2×C3×C5—41no—
241C2×C3×C5—42no—
242C2×C3×C5—82no—
243C3×D5—44no—
244C3×D5—82no—
245C23×C3—41no—
246C23×C3—201no—
247C23×C3—201no—
248C23×C3—204no—
249C23×C3—404no—
250C2×C3×C4—42no—
251C2×C3×C4—202no—
252C2×C3×C4—404no—
253SL(2,𝔽3)C2×C4×D511yescharacteristic
254C22×C5—22no—
255C22×C5C2×C4×A412yes—
256C22×C5C23×A411yescharacteristic
257C2×D5—22no—
258C2×D5—28no—
259C2×D5C2×C4×A412yes—
260C2×D5C2×C4×A412yes—
261C2×D52−1+4⋊C314yes—
262C4×C5—22no—
263C4×C5—31no—
264C4×C5—32no—
265C4×C5—31no—
266C4×C5—62no—
267Dic5—22no—
268Dic5—32no—
269Dic5—32no—
270Dic5—62no—
271C24—51no—
272C2×Q8—31no—
273C2×Q8—32no—
274C2×Q8—52no—
275C2×Q8—52no—
276C2×Q8—152no—
277C2×Q8—154no—
278C2×Q8—151no—
279C2×Q8—151no—
280C2×Q8—154no—
281C2×Q8—154no—
282C2×Q8—154no—
283C2×Q8—154no—
284C2×Q8—154no—
285C2×Q8—152no—
286C2×Q8—152no—
287C2×Q8C3×C4×D512yescomplemented
288C2×Q8C22×C3×D511yescharacteristic
289C22×C4—31no—
290C22×C4—52no—
291C22×C4—151no—
292C22×C4—151no—
293C22×C4—151no—
294C22×C4—151no—
295C22×C4—154no—
296C22×C4—154no—
297C22×C4—152no—
298C22×C4—151no—
299C4⋊C4—32no—
300C4⋊C4—32no—
301C4⋊C4—152no—
302C4⋊C4—152no—
303C4⋊C4—152no—
304C4⋊C4—154no—
305C4⋊C4—152no—
306C22⋊C4—31no—
307C22⋊C4—51no—
308C22⋊C4—52no—
309C22⋊C4—152no—
310C22⋊C4—151no—
311C22⋊C4D5×A411yescharacteristic
312C42—32no—
313C42—32no—
314C42—152no—
315C42—152no—
316C42—152no—
317C42—154no—
318C42—152no—
319C3×C5—41noHall
320C22×C3—42no—
321C22×C3—41no—
322C22×C3—82no—
323C22×C3—204no—
324C22×C3—202no—
325C22×C3—202no—
326C22×C3—402no—
327C22×C3—408no—
328C3×C4—82no—
329C3×C4—402no—
330C2×C5—22no—
331C2×C5C22×C4×A411yescharacteristic
332C2×C5C2×2−1+4⋊C312yes—
333D5—22no—
334D5#519⋊C314yesdirect product factor
335C23—51no—
336C23—54no—
337C23—51no—
338C23—104no—
339C23C2×D5×A411yescharacteristic
340Q8—32no—
341Q8—31no—
342Q8—32no—
343Q8—152no—
344Q8—152no—
345Q8—158no—
346Q8—152no—
347Q8—152no—
348Q8C2×C3×C4×D511yescharacteristic
349C2×C4—32no—
350C2×C4—32no—
351C2×C4—31no—
352C2×C4—31no—
353C2×C4—32no—
354C2×C4—52no—
355C2×C4—104no—
356C2×C4—152no—
357C2×C4—152no—
358C2×C4—152no—
359C2×C4—154no—
360C2×C4—152no—
361C2×C4—154no—
362C2×C4—154no—
363C2×C4—151no—
364C2×C4—151no—
365C2×C4—152no—
366C2×C4—304no—
367C2×C4C2×D5×A412yes—
368C2×C3—41no—
369C2×C3—42no—
370C2×C3—82no—
371C2×C3—204no—
372C2×C3—402no—
373C5C2×#519⋊C311yescharacteristic, complemented, Sylow
374C22—22no—
375C22—52no—
376C22—54no—
377C22—52no—
378C22—108no—
379C22—102no—
380C22C4×D5×A412yes—
381C22C22×D5×A411yescharacteristic
382C4—22no—
383C4—31no—
384C4—32no—
385C4—31no—
386C4—62no—
387C4—102no—
388C4—152no—
389C4—152no—
390C4—302no—
391C3—41noSylow
392C2—22no—
393C2—54no—
394C2—102no—
395C2C2×C4×D5×A411yescharacteristic
396C2D5×2−1+4⋊C312yes—
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, hypocenterC5×Q8C22×C3×C4
FittingC5×#519C2×C3
socleC22×C5C23×A4
prime radicalC22×D5×SL(2,𝔽3)C2
cosocleC2×C5×Q8C23×C3
hypercenterC22⋊C4D5×A4
LCSG ▷ C5×Q8
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×#519⋊C3C2semidirect
3. #66146⋊C3C2semidirect
4. #65906⋊C3C2semidirect
5. C4×D5×SL(2,𝔽3)C2semidirect
6. D5×#519C3semidirect
8. C2×D5×SL(2,𝔽3)C4semidirect
12. C4×C5×SL(2,𝔽3)C22semidirect
13. Dic5×SL(2,𝔽3)C22semidirect
16. C5×#519C2×C3semidirect
17. #66146C2×C3semidirect
19. #65906C2×C3semidirect
21. C4×Q8×D5C2×C3semidirect
28. C2×C5×SL(2,𝔽3)C2×C4semidirect
31. D5×SL(2,𝔽3)C2×C4semidirect
38. #519⋊C3D5direct (N × H)
44. C2×Q8×D5C3×C4semidirect
50. C4×C5×Q8C22×C3semidirect
54. Q8×Dic5C22×C3semidirect
92. C4×SL(2,𝔽3)C2×D5semidirect
96. C2×C5×Q8C2×C3×C4semidirect
107. Q8×D5C2×C3×C4semidirect
147. #519C3×D5semidirect
166. C2×SL(2,𝔽3)C4×D5semidirect
222. C4×Q8C2×C3×D5semidirect
287. C2×Q8C3×C4×D5semidirect
334. D5#519⋊C3direct (N × H)
373. C5C2×#519⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×D5×SL(2,𝔽3)2
C5×#519⋊C32
#66146⋊C32
#65906⋊C32
C4×D5×SL(2,𝔽3)2
D5×#5193
C3×D5×C22⋊C44
C2×#519⋊C35