Finite Group Databasebeta

← #14297548

Subgroups — #14297548

Order 1920.

760 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 112 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×#91442C211yesmaximal, characteristic
2#11752028C212yesmaximal, complemented
3C2×#91172C212yesmaximal
4#11746788C211yesmaximal, characteristic, complemented
5C3×#64917C211yesmaximal, characteristic, complemented
6#10604217—31nomaximal, Hall
7C22×#1201C2211yescharacteristic
8C22×D3×Dic5C411yescharacteristic, complemented
9C22×D5×Dic3C2211yescharacteristic
10C2×#6763C2212yes—
11C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
12C2×Dic3⋊AGL(1,𝔽5)—22no—
13C2×C4×Dic15C411yescharacteristic, complemented
14C2×C5×(C2×D3)⋊C4C411yescharacteristic, complemented
15C2×C3×#685C2211yescharacteristic
16C2×#6669C411yescharacteristic, complemented
17#91442—22no—
18#91442—22no—
19#91172—24no—
20(C2×AGL(1,𝔽5))⋊Dic3—22no—
21#68959—51nomaximal, Hall
22C2×#4027—31no—
23C2×#4011—32no—
24#65765—32no—
25#64917—31no—
26#64917D311yescharacteristic, complemented
27C23×C5×D3C2×C411yescharacteristic
28C23×C3×D5C2311yescharacteristic
29C22×ΓL(1,𝔽16)—22no—
30C22×C3×AGL(1,𝔽5)—22no—
31C22×C3×C4×C5C2×C411yescharacteristic
32C22×Dic15C2×C411yescharacteristic
33C22×Dic15C2×C411yescharacteristic
34C22×C5×Dic3C2×C411yescharacteristic
35C22×C3×Dic5C2×C411yescharacteristic
36C2×#1201—22no—
37C2×#1201—22no—
38C2×#1201D412yes—
39C2×#1201Q812yes—
40C2×D3×Dic5—21no—
41C2×D3×Dic5—21no—
42C2×D3×Dic5—42no—
43C2×D5×Dic3—42no—
44C2×D5×Dic3D412yes—
45C2×D5×Dic3D412yes—
46#6763—22no—
47#6763—22no—
48C3×C22⋊AGL(1,𝔽5)—22no—
49C3×C22⋊AGL(1,𝔽5)—22no—
50Dic3⋊AGL(1,𝔽5)—44no—
51C4×Dic15—21no—
52C4×Dic15—21no—
53C5×(C2×D3)⋊C4—22no—
54C3×#685—22no—
55#6669—22no—
56C2×#67⋊C4—51no—
57C2×#806—52no—
58#4942—52no—
59C3×#342—51no—
60#4526—51no—
61C22×C22⋊D5—31no—
62C23×Dic5—31no—
63C22×C4×D5—31no—
64C2×C22⋊AGL(1,𝔽5)—32no—
65C2×C22⋊AGL(1,𝔽5)C2×D312yes—
66C2×C4⋊AGL(1,𝔽5)—62no—
67C2×C5×C22⋊C4—31no—
68C2×#685C2×D311yescharacteristic
69C2×#683—31no—
70C2×C4×Dic5—31no—
71#4027—62no—
72#4027—62no—
73#4011—64no—
74(C2×AGL(1,𝔽5))⋊C4—62no—
75#1799—151noSylow
76C23×C3×C5C22×C411yescharacteristic
77C22×C5×D3—21no—
78C22×C5×D3—21no—
79C22×C5×D3—41no—
80C22×C5×D3—41no—
81C22×C5×D3C4⋊C412yescomplemented
82C22×C3×D5—41no—
83C22×C3×D5—41no—
84C22×C3×D5C2×D412yes—
85C22×C3×D5C2×D411yescharacteristic
86C22×C3×D5C2×Q811yescharacteristic
87C22×C3×D5#4112yes—
88C2×ΓL(1,𝔽16)—42no—
89C2×ΓL(1,𝔽16)—42no—
90C2×ΓL(1,𝔽16)—42no—
91C2×C3×AGL(1,𝔽5)—42no—
92C2×C3×AGL(1,𝔽5)—42no—
93C2×C3×AGL(1,𝔽5)—42no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—41no—
96C2×Dic15—21no—
97C2×Dic15—21no—
98C2×Dic15—22no—
99C2×Dic15C22⋊C411yescharacteristic
100C2×Dic15C22⋊C411yescharacteristic
101C2×Dic15C4⋊C412yescomplemented
102C2×C5×Dic3—41no—
103C2×C5×Dic3C22⋊C412yes—
104C2×C3×Dic5—21no—
105C2×C3×Dic5—41no—
106#1201—24no—
107#1201—24no—
108D3×Dic5—42no—
109D3×Dic5—42no—
110D5×Dic3—24no—
111D5×Dic3—42no—
112C22×#67—51no—
113C23×Dic3—51no—
114C22×C4×D3—51no—
115C2×C3×C22⋊C4—51no—
116C2×C3×C22⋊C4—52no—
117C2×#217—52no—
118C2×(C2×D3)⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
119C2×Dic3⋊C4—51no—
120C2×Dic3⋊C4—102no—
121C2×C4×Dic3—51no—
122#67⋊C4—102no—
123#67⋊C4—102no—
124C3⋊#95—102no—
125#806—104no—
126C24×C5—31no—
127C23×D5C22×D311yescharacteristic
128C22×AGL(1,𝔽5)—22no—
129C22×AGL(1,𝔽5)—62no—
130C22×C4×C5—31no—
131C22×C4×C5C4×D311yescharacteristic
132C2×C22⋊D5—32no—
133C2×C22⋊D5—32no—
134C2×C22⋊D5—62no—
135C2×C22⋊D5—62no—
136C22×Dic5—31no—
137C22×Dic5—31no—
138C22×Dic5—61no—
139C22×Dic5—61no—
140C22×Dic5—122no—
141C22×Dic5C4×D311yescharacteristic
142C2×C4×D5—32no—
143C2×C4×D5—32no—
144C2×C4×D5—122no—
145C22⋊AGL(1,𝔽5)—22no—
146C22⋊AGL(1,𝔽5)—22no—
147C22⋊AGL(1,𝔽5)—62no—
148C22⋊AGL(1,𝔽5)—62no—
149C4⋊AGL(1,𝔽5)—124no—
150C5×C22⋊C4—62no—
151#685—22no—
152#683—62no—
153C4×Dic5—61no—
154C4×Dic5—61no—
155C2×C4×D4—151no—
156C2×#99—152no—
157#380—152no—
158#342—51no—
159#342—151no—
160C22×C3×C5—21no—
161C22×C3×C5—21no—
162C22×C3×C5C2×C22⋊C411yescharacteristic
163C22×C3×C5C2×C4⋊C411yescharacteristic
164C22×C3×C5#11711yescharacteristic
165C2×C5×D3—22no—
166C2×C5×D3—42no—
167C2×C5×D3—41no—
168C2×C5×D3—41no—
169C2×C5×D3—42no—
170C2×C3×D5—22no—
171C2×C3×D5—22no—
172C2×C3×D5—41no—
173C2×C3×D5—41no—
174C2×C3×D5—42no—
175C2×C3×D5#12112yes—
176C2×C3×D5C22⋊Q812yes—
177ΓL(1,𝔽16)—82no—
178C3×AGL(1,𝔽5)—82no—
179C3×C4×C5—41no—
180Dic15—22no—
181Dic15—21no—
182Dic15#9912yescomplemented
183C3×Dic5—41no—
184C5×Dic3—22no—
185C24×C3—51no—
186C23×D3C2×AGL(1,𝔽5)11yescharacteristic
187C22×C3×C4—51no—
188C22×C3×C4—102no—
189C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
190C2×#67—52no—
191C2×#67—52no—
192C2×#67—102no—
193C2×#67—102no—
194C22×Dic3—51no—
195C22×Dic3—51no—
196C22×Dic3—52no—
197C22×Dic3—52no—
198C22×Dic3—102no—
199C22×Dic3—202no—
200C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
201C2×C4×D3—101no—
202C2×C4×D3—101no—
203C2×C4×D3—202no—
204C3×C22⋊C4—102no—
205C3×C22⋊C4—102no—
206C3×C22⋊C4—102no—
207#217—102no—
208#217—102no—
209(C2×D3)⋊C4—22no—
210Dic3⋊C4—102no—
211Dic3⋊C4—204no—
212C4×Dic3—101no—
213C4×Dic3—101no—
214C23×C5—32no—
215C23×C5—61no—
216C23×C5—61no—
217C23×C5—121no—
218C23×C5—121no—
219C23×C5C2×C4×D311yescharacteristic
220C22×D5—41no—
221C22×D5—41no—
222C22×D5#23512yes—
223C22×D5D3×D412yes—
224C22×D5D3×D411yescharacteristic
225C22×D5D3×Q811yescharacteristic
226C2×AGL(1,𝔽5)—42no—
227C2×AGL(1,𝔽5)—42no—
228C2×AGL(1,𝔽5)—42no—
229C2×AGL(1,𝔽5)—122no—
230C2×AGL(1,𝔽5)—122no—
231C2×AGL(1,𝔽5)—122no—
232C2×C4×C5—21no—
233C2×C4×C5—32no—
234C2×C4×C5—41no—
235C2×C4×C5—121no—
236C22⋊D5—64no—
237C22⋊D5—64no—
238C2×Dic5—21no—
239C2×Dic5—31no—
240C2×Dic5—31no—
241C2×Dic5—32no—
242C2×Dic5—41no—
243C2×Dic5—62no—
244C2×Dic5—61no—
245C2×Dic5—61no—
246C2×Dic5—122no—
247C2×Dic5—122no—
248C4×D5—64no—
249C4×D5—122no—
250C22×D4—151no—
251C23×C4—151no—
252C23×C4—151no—
253C4×D4—302no—
254C4×D4—302no—
255C2×C4⋊C4—151no—
256C2×C4⋊C4—302no—
257C2×C22⋊C4—31no—
258C2×C22⋊C4—51no—
259C2×C22⋊C4—52no—
260C2×C22⋊C4—152no—
261C2×C42—151no—
262#99—304no—
263#95—302no—
264C2×C3×C5—21no—
265C2×C3×C5—21no—
266C2×C3×C5#38011yescharacteristic
267C2×C3×C5C2×#9911yescharacteristic
268C2×C3×C5#41011yescharacteristic
269C3×D5—22no—
270C3×D5—22no—
271C5×D3—42no—
272C23×C3—52no—
273C23×C3—51no—
274C23×C3—51no—
275C23×C3—52no—
276C23×C3—201no—
277C23×C3—201no—
278C23×C3C22×AGL(1,𝔽5)11yescharacteristic
279C22×D3—21no—
280C22×D3—21no—
281C22×D3—41no—
282C22×D3—41no—
283C22×D3C4⋊AGL(1,𝔽5)12yescomplemented
284C2×C3×C4—21no—
285C2×C3×C4—41no—
286C2×C3×C4—101no—
287C2×C3×C4—201no—
288C2×C3×C4—202no—
289C2×C3×C4—202no—
290C2×C3×C4—202no—
291#67—104no—
292#67—104no—
293C2×Dic3—41no—
294C2×Dic3—51no—
295C2×Dic3—52no—
296C2×Dic3—51no—
297C2×Dic3—104no—
298C2×Dic3—102no—
299C2×Dic3—101no—
300C2×Dic3—101no—
301C2×Dic3—202no—
302C2×Dic3—202no—
303C2×Dic3—202no—
304C2×Dic3—202no—
305C2×Dic3C22⋊AGL(1,𝔽5)12yes—
306C4×D3—202no—
307C4×D3—202no—
308C22×C5—21no—
309C22×C5—21no—
310C22×C5—62no—
311C22×C5—122no—
312C22×C5—122no—
313C22×C5—121no—
314C22×C5—121no—
315C22×C5#87211yescharacteristic
316C22×C5D3×C22⋊C411yescharacteristic
317C22×C5D3×C4⋊C411yescharacteristic
318C2×D5—22no—
319C2×D5—22no—
320C2×D5—42no—
321C2×D5—41no—
322C2×D5—41no—
323C2×D5#88412yes—
324C2×D5#89612yes—
325AGL(1,𝔽5)—82no—
326AGL(1,𝔽5)—242no—
327C4×C5—41no—
328C4×C5—62no—
329Dic5—32no—
330Dic5—41no—
331Dic5—62no—
332Dic5—61no—
333C24—31no—
334C24—51no—
335C2×D4—152no—
336C2×D4—152no—
337C2×D4—302no—
338C2×D4—302no—
339C22×C4—31no—
340C22×C4—51no—
341C22×C4—102no—
342C22×C4—152no—
343C22×C4—152no—
344C22×C4—151no—
345C22×C4—151no—
346C22×C4—301no—
347C22×C4—301no—
348C22×C4—302no—
349C22×C4—602no—
350C22×C4—602no—
351C22×C4D3×AGL(1,𝔽5)11yescharacteristic
352C4⋊C4—302no—
353C4⋊C4—604no—
354C22⋊C4—62no—
355C22⋊C4—102no—
356C22⋊C4—102no—
357C22⋊C4—102no—
358C22⋊C4—302no—
359C22⋊C4—302no—
360C42—301no—
361C42—301no—
362C3×C5#179911yescharacteristic, complemented, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—52no—
366C22×C3—52no—
367C22×C3—102no—
368C22×C3—102no—
369C22×C3—201no—
370C22×C3—201no—
371C22×C3—202no—
372C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
373C22×C3#413011yescharacteristic
374C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
375C2×D3—22no—
376C2×D3—42no—
377C2×D3—41no—
378C2×D3—41no—
379C2×D3—42no—
380C3×C4—41no—
381C3×C4—201no—
382C3×C4—402no—
383Dic3—22no—
384Dic3—52no—
385Dic3—102no—
386Dic3—101no—
387Dic3—402no—
388C2×C5—21no—
389C2×C5—21no—
390C2×C5—122no—
391C2×C5#466711yescharacteristic
392C2×C5#474011yescharacteristic
393C2×C5D3×#9911yescharacteristic
394D5—22no—
395D5—22no—
396C23—32no—
397C23—52no—
398C23—52no—
399C23—51no—
400C23—51no—
401C23—61no—
402C23—61no—
403C23—121no—
404C23—121no—
405C23—201no—
406C23—201no—
407C23C2×D3×AGL(1,𝔽5)11yescharacteristic
408D4—304no—
409D4—304no—
410C2×C4—21no—
411C2×C4—32no—
412C2×C4—41no—
413C2×C4—101no—
414C2×C4—121no—
415C2×C4—151no—
416C2×C4—152no—
417C2×C4—151no—
418C2×C4—201no—
419C2×C4—202no—
420C2×C4—202no—
421C2×C4—202no—
422C2×C4—304no—
423C2×C4—302no—
424C2×C4—301no—
425C2×C4—301no—
426C2×C4—602no—
427C2×C4—602no—
428C2×C4—602no—
429C2×C4—602no—
430C2×C4—602no—
431C2×C4—602no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—102no—
435C2×C3—102no—
436C2×C3#6576511yescharacteristic
437C2×C3D5⋊#9911yescharacteristic
438C2×C3#6577111yescharacteristic
439D3—42no—
440C5#6895911yescharacteristic, complemented, Sylow
441C22—21no—
442C22—21no—
443C22—52no—
444C22—52no—
445C22—62no—
446C22—102no—
447C22—102no—
448C22—122no—
449C22—122no—
450C22—121no—
451C22—121no—
452C22—202no—
453C22—201no—
454C22—201no—
455C22#9190911yescharacteristic
456C22D3×C4⋊AGL(1,𝔽5)11yescharacteristic
457C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
458C4—41no—
459C4—62no—
460C4—152no—
461C4—201no—
462C4—301no—
463C4—302no—
464C4—402no—
465C4—1202no—
466C3#1060421711yescharacteristic, complemented, Sylow
467C2—21no—
468C2—21no—
469C2—102no—
470C2—102no—
471C2—122no—
472C2#1175185211yescharacteristic
473C2#1175185411yescharacteristic
474C2#1175203111yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#1201C22
cosocleC23×C3×D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1799
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752028C2semidirect
4. #11746788C2semidirect
5. C3×#64917C2semidirect
8. C22×D3×Dic5C4semidirect
13. C2×C4×Dic15C4semidirect
14. C2×C5×(C2×D3)⋊C4C4semidirect
16. C2×#6669C4semidirect
26. #64917D3semidirect
81. C22×C5×D3C4⋊C4semidirect
101. C2×Dic15C4⋊C4semidirect
118. C2×(C2×D3)⋊C4AGL(1,𝔽5)semidirect
182. Dic15#99semidirect
283. C22×D3C4⋊AGL(1,𝔽5)semidirect
362. C3×C5#1799semidirect
440. C5#68959semidirect
466. C3#10604217semidirect

Maximal subgroups

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

subgroupindex
C2×#914422
#117520282
C2×#911722
#117467882
C3×#649172
#106042173
#689595