Finite Group Databasebeta

← #14297546

Subgroups — #14297546

Order 1920.

760 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 124 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×Dic3×D20C211yesmaximal, characteristic
2C2×#91228C211yesmaximal, characteristic
3C2×C3×#3999C211yesmaximal, characteristic
4#11752028C212yesmaximal, complemented
5#11746573C212yesmaximal, complemented
6#10604167—31nomaximal, Hall
7C22×C3×D20C2211yescharacteristic
8C22×D5×Dic3C411yescharacteristic, complemented
9C22×D5×Dic3C2211yescharacteristic
10C2×#6763C2212yes—
11C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
12C2×Dic3⋊AGL(1,𝔽5)—22no—
13C2×C4⋊Dic15C411yescharacteristic, complemented
14C2×C4×C5×Dic3C411yescharacteristic, complemented
15C2×#6665C411yescharacteristic, complemented
16C2×#6665C2211yescharacteristic
17Dic3×D20—22no—
18Dic3×D20—22no—
19#91228—22no—
20C3×#3999—22no—
21(C2×AGL(1,𝔽5))⋊Dic3—22no—
22#70028—51nomaximal, Hall
23C2×C4×D20—31no—
24#65765—32no—
25C2×#3999—31no—
26C2×#3999D311yescharacteristic
27#64917—32no—
28C23×C3×D5C2×C411yescharacteristic
29C23×C3×D5C2311yescharacteristic
30C22×ΓL(1,𝔽16)—22no—
31C22×C3×AGL(1,𝔽5)—22no—
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×Dic15C2×C411yescharacteristic
34C22×Dic15C2×C411yescharacteristic
35C22×C5×Dic3C2×C411yescharacteristic
36C22×C5×Dic3C2×C411yescharacteristic
37C2×C3×D20—22no—
38C2×C3×D20—22no—
39C2×C3×D20D412yes—
40C2×C3×D20Q812yes—
41C2×D5×Dic3—21no—
42C2×D5×Dic3—21no—
43C2×D5×Dic3—42no—
44C2×D5×Dic3—42no—
45C2×D5×Dic3D412yes—
46C2×D5×Dic3D412yes—
47#6763—22no—
48#6763—22no—
49C3×C22⋊AGL(1,𝔽5)—22no—
50C3×C22⋊AGL(1,𝔽5)—22no—
51Dic3⋊AGL(1,𝔽5)—44no—
52C4⋊Dic15—22no—
53C4×C5×Dic3—21no—
54C4×C5×Dic3—21no—
55#6665—22no—
56#6665—22no—
57C2×D4×Dic3—51no—
58C2×C3×#99—51no—
59C2×#834—51no—
60#4942—52no—
61#4527—52no—
62C22×D20C2×D311yescharacteristic
63C22×C4×D5—31no—
64C22×C4×D5—31no—
65C2×C22⋊AGL(1,𝔽5)—32no—
66C2×C22⋊AGL(1,𝔽5)C2×D312yes—
67C2×C4⋊AGL(1,𝔽5)—62no—
68C2×C42×C5—31no—
69C2×#685—31no—
70C2×#685—31no—
71C2×C4⋊Dic5—31no—
72C4×D20—62no—
73C4×D20—62no—
74(C2×AGL(1,𝔽5))⋊C4—62no—
75#3999—22no—
76#3999—62no—
77#1799—151noSylow
78C23×C3×C5C22×C411yescharacteristic
79C22×C3×D5—21no—
80C22×C3×D5—21no—
81C22×C3×D5—41no—
82C22×C3×D5—41no—
83C22×C3×D5—41no—
84C22×C3×D5—41no—
85C22×C3×D5C4⋊C412yescomplemented
86C22×C3×D5C2×D412yes—
87C22×C3×D5C2×D411yescharacteristic
88C22×C3×D5C2×Q811yescharacteristic
89C22×C3×D5#4112yes—
90C2×ΓL(1,𝔽16)—42no—
91C2×ΓL(1,𝔽16)—42no—
92C2×ΓL(1,𝔽16)—42no—
93C2×C3×AGL(1,𝔽5)—42no—
94C2×C3×AGL(1,𝔽5)—42no—
95C2×C3×AGL(1,𝔽5)—42no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5C4⋊C412yescomplemented
99C2×Dic15—21no—
100C2×Dic15—41no—
101C2×Dic15—41no—
102C2×Dic15C22⋊C412yes—
103C2×C5×Dic3—22no—
104C2×C5×Dic3—21no—
105C2×C5×Dic3—41no—
106C2×C5×Dic3C22⋊C411yescharacteristic
107C2×C5×Dic3C22⋊C411yescharacteristic
108C3×D20—24no—
109C3×D20—24no—
110D5×Dic3—24no—
111D5×Dic3—42no—
112D5×Dic3—42no—
113D5×Dic3—42no—
114C22×C3×D4—51no—
115C23×Dic3—51no—
116C23×Dic3—51no—
117C2×C3×C22⋊C4—52no—
118C2×#217—51no—
119C2×#217—51no—
120C2×#217—52no—
121D4×Dic3—102no—
122D4×Dic3—102no—
123C2×C4⋊Dic3—51no—
124C2×Dic3⋊C4—102no—
125C2×C4×Dic3AGL(1,𝔽5)11yescharacteristic, complemented
126C3×#99—102no—
127#834—102no—
128C3⋊#95—102no—
129C23×D5C4×D311yescharacteristic
130C23×D5C22×D311yescharacteristic
131C22×AGL(1,𝔽5)—22no—
132C22×AGL(1,𝔽5)—62no—
133C22×C4×C5—31no—
134C22×C4×C5—31no—
135C22×C4×C5C4×D311yescharacteristic
136C22×Dic5—31no—
137C22×Dic5—31no—
138C2×D20—22no—
139C2×D20—22no—
140C2×D20Dic612yes—
141C2×D20#6712yes—
142C2×C4×D5—32no—
143C2×C4×D5—32no—
144C2×C4×D5—61no—
145C2×C4×D5—61no—
146C2×C4×D5—122no—
147C2×C4×D5—122no—
148C22⋊AGL(1,𝔽5)—22no—
149C22⋊AGL(1,𝔽5)—22no—
150C22⋊AGL(1,𝔽5)—62no—
151C22⋊AGL(1,𝔽5)—62no—
152C4⋊AGL(1,𝔽5)—124no—
153C42×C5—61no—
154C42×C5—61no—
155#685—62no—
156#685—62no—
157C4⋊Dic5—62no—
158C2×C4×D4—151no—
159C2×#99—51no—
160C2×#99—151no—
161#380—152no—
162#342—152no—
163C22×C3×C5—21no—
164C22×C3×C5—21no—
165C22×C3×C5C2×C22⋊C411yescharacteristic
166C22×C3×C5C2×C4⋊C411yescharacteristic
167C22×C3×C5#11711yescharacteristic
168C2×C3×D5—22no—
169C2×C3×D5—22no—
170C2×C3×D5—22no—
171C2×C3×D5—41no—
172C2×C3×D5—41no—
173C2×C3×D5—42no—
174C2×C3×D5—42no—
175C2×C3×D5—41no—
176C2×C3×D5—41no—
177C2×C3×D5—42no—
178C2×C3×D5#12112yes—
179C2×C3×D5C22⋊Q812yes—
180ΓL(1,𝔽16)—82no—
181C3×AGL(1,𝔽5)—82no—
182C3×C4×C5—22no—
183Dic15—22no—
184Dic15—41no—
185C5×Dic3—21no—
186C5×Dic3—41no—
187C5×Dic3#9912yescomplemented
188C24×C3—51no—
189C24×C3—51no—
190C2×C3×D4—52no—
191C2×C3×D4—52no—
192C2×C3×D4—102no—
193C2×C3×D4—102no—
194C22×C3×C4—102no—
195C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
196C22×Dic3—51no—
197C22×Dic3—52no—
198C22×Dic3—52no—
199C22×Dic3—51no—
200C22×Dic3—101no—
201C22×Dic3—101no—
202C22×Dic3—102no—
203C22×Dic3—202no—
204C22×Dic3—202no—
205C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
206C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
207C3×C22⋊C4—102no—
208C3×C22⋊C4—102no—
209#217—102no—
210#217—102no—
211#217—102no—
212#217—102no—
213C4⋊Dic3—102no—
214Dic3⋊C4—204no—
215C4×Dic3—21no—
216C4×Dic3—21no—
217C23×C5C2×C4×D311yescharacteristic
218C22×D5—21no—
219C22×D5—21no—
220C22×D5—41no—
221C22×D5—41no—
222C22×D5—41no—
223C22×D5—41no—
224C22×D5Dic3⋊C412yescomplemented
225C22×D5C2×Dic611yescharacteristic
226C22×D5D3×D412yes—
227C22×D5#23712yes—
228C22×D5C2×#6711yescharacteristic
229C2×AGL(1,𝔽5)—42no—
230C2×AGL(1,𝔽5)—42no—
231C2×AGL(1,𝔽5)—42no—
232C2×AGL(1,𝔽5)—122no—
233C2×AGL(1,𝔽5)—122no—
234C2×AGL(1,𝔽5)—122no—
235C2×C4×C5—21no—
236C2×C4×C5—21no—
237C2×C4×C5—31no—
238C2×C4×C5—31no—
239C2×C4×C5—62no—
240C2×C4×C5—61no—
241C2×C4×C5—121no—
242C2×C4×C5Dic3⋊C412yescomplemented
243C2×Dic5—32no—
244C2×Dic5—61no—
245C2×Dic5—121no—
246C2×Dic5—121no—
247D20—24no—
248D20—24no—
249C4×D5—64no—
250C4×D5—122no—
251C4×D5—122no—
252C4×D5—122no—
253C22×D4—51no—
254C23×C4—151no—
255C23×C4—151no—
256C4×D4—302no—
257C4×D4—302no—
258C2×C4⋊C4—151no—
259C2×C4⋊C4—302no—
260C2×C22⋊C4—52no—
261C2×C22⋊C4—151no—
262C2×C22⋊C4—151no—
263C2×C22⋊C4—152no—
264C2×C42—31no—
265#99—102no—
266#99—302no—
267#95—302no—
268C2×C3×C5—21no—
269C2×C3×C5—21no—
270C2×C3×C5#38011yescharacteristic
271C2×C3×C5C2×#9911yescharacteristic
272C2×C3×C5#41011yescharacteristic
273C3×D5—22no—
274C3×D5—22no—
275C3×D5—42no—
276C23×C3—52no—
277C23×C3—51no—
278C23×C3—51no—
279C23×C3—52no—
280C23×C3—52no—
281C23×C3—101no—
282C23×C3—101no—
283C23×C3—201no—
284C23×C3—201no—
285C23×C3—201no—
286C23×C3—201no—
287C23×C3C22×AGL(1,𝔽5)11yescharacteristic
288C3×D4—104no—
289C3×D4—104no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—202no—
293C2×C3×C4—202no—
294C2×C3×C4—202no—
295C2×C3×C4C4⋊AGL(1,𝔽5)12yescomplemented
296C2×Dic3—22no—
297C2×Dic3—21no—
298C2×Dic3—41no—
299C2×Dic3—52no—
300C2×Dic3—104no—
301C2×Dic3—101no—
302C2×Dic3—202no—
303C2×Dic3—202no—
304C2×Dic3—201no—
305C2×Dic3—202no—
306C2×Dic3—201no—
307C2×Dic3—202no—
308C2×Dic3—202no—
309C2×Dic3—202no—
310C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
311C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
312C22×C5—21no—
313C22×C5—21no—
314C22×C5#87711yescharacteristic
315C22×C5D3×C22⋊C411yescharacteristic
316C22×C5C2×Dic3⋊C411yescharacteristic
317C2×D5—22no—
318C2×D5—22no—
319C2×D5—22no—
320C2×D5—41no—
321C2×D5—42no—
322C2×D5—41no—
323C2×D5—42no—
324C2×D5—41no—
325C2×D5—41no—
326C2×D5—42no—
327C2×D5#87812yes—
328C2×D5#93912yes—
329AGL(1,𝔽5)—82no—
330AGL(1,𝔽5)—242no—
331C4×C5—22no—
332C4×C5—32no—
333C4×C5—61no—
334C4×C5—121no—
335Dic5—62no—
336Dic5—121no—
337C24—51no—
338C24—51no—
339C2×D4—52no—
340C2×D4—52no—
341C2×D4—102no—
342C2×D4—102no—
343C22×C4—31no—
344C22×C4—31no—
345C22×C4—102no—
346C22×C4—152no—
347C22×C4—152no—
348C22×C4—151no—
349C22×C4—151no—
350C22×C4—301no—
351C22×C4—301no—
352C22×C4—302no—
353C22×C4—602no—
354C22×C4—602no—
355C22×C4D3×AGL(1,𝔽5)11yescharacteristic
356C4⋊C4—302no—
357C4⋊C4—604no—
358C22⋊C4—102no—
359C22⋊C4—102no—
360C22⋊C4—302no—
361C22⋊C4—302no—
362C22⋊C4—302no—
363C22⋊C4—302no—
364C42—61no—
365C42—61no—
366C3×C5#179911yescharacteristic, complemented, Hall
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—52no—
370C22×C3—52no—
371C22×C3—102no—
372C22×C3—102no—
373C22×C3—102no—
374C22×C3—201no—
375C22×C3—201no—
376C22×C3—202no—
377C22×C3—202no—
378C22×C3—202no—
379C22×C3—201no—
380C22×C3—201no—
381C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
382C22×C3#413011yescharacteristic
383C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
384C3×C4—22no—
385C3×C4—402no—
386Dic3—21no—
387Dic3—41no—
388Dic3—102no—
389Dic3—201no—
390Dic3—402no—
391Dic3#399912yescomplemented
392C2×C5—21no—
393C2×C5—21no—
394C2×C5#474011yescharacteristic
395C2×C5D3×#9911yescharacteristic
396C2×C5#494211yescharacteristic
397D5—22no—
398D5—22no—
399D5—42no—
400C23—52no—
401C23—52no—
402C23—51no—
403C23—51no—
404C23—52no—
405C23—101no—
406C23—101no—
407C23—201no—
408C23—201no—
409C23—201no—
410C23—201no—
411C23C2×D3×AGL(1,𝔽5)11yescharacteristic
412D4—104no—
413D4—104no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—31no—
417C2×C4—31no—
418C2×C4—62no—
419C2×C4—61no—
420C2×C4—121no—
421C2×C4—152no—
422C2×C4—202no—
423C2×C4—202no—
424C2×C4—202no—
425C2×C4—304no—
426C2×C4—301no—
427C2×C4—602no—
428C2×C4—602no—
429C2×C4—602no—
430C2×C4—601no—
431C2×C4—601no—
432C2×C4—602no—
433C2×C4—602no—
434C2×C4—602no—
435C2×C4Dic3⋊AGL(1,𝔽5)12yescomplemented
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—102no—
439C2×C3—102no—
440C2×C3—202no—
441C2×C3C2×#399911yescharacteristic
442C2×C3#6574511yescharacteristic
443C2×C3#6576511yescharacteristic
444C5#7002811yescharacteristic, complemented, Sylow
445C22—21no—
446C22—21no—
447C22—52no—
448C22—52no—
449C22—102no—
450C22—102no—
451C22—102no—
452C22—202no—
453C22—201no—
454C22—201no—
455C22—202no—
456C22—202no—
457C22—201no—
458C22—201no—
459C22#9192311yescharacteristic
460C22C2×Dic3⋊AGL(1,𝔽5)11yescharacteristic
461C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
462C4—22no—
463C4—32no—
464C4—61no—
465C4—121no—
466C4—302no—
467C4—402no—
468C4—601no—
469C4—1202no—
470C3#1060416711yescharacteristic, complemented, Sylow
471C2—21no—
472C2—21no—
473C2—102no—
474C2—102no—
475C2—202no—
476C2D3×#399911yescharacteristic
477C2#1175186211yescharacteristic
478C2#1175202811yescharacteristic
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×C3×D20C22
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
4. #11752028C2semidirect
5. #11746573C2semidirect
8. C22×D5×Dic3C4semidirect
13. C2×C4⋊Dic15C4semidirect
14. C2×C4×C5×Dic3C4semidirect
15. C2×#6665C4semidirect
85. C22×C3×D5C4⋊C4semidirect
98. C2×C3×C4×C5C4⋊C4semidirect
125. C2×C4×Dic3AGL(1,𝔽5)semidirect
187. C5×Dic3#99semidirect
224. C22×D5Dic3⋊C4semidirect
242. C2×C4×C5Dic3⋊C4semidirect
295. C2×C3×C4C4⋊AGL(1,𝔽5)semidirect
366. C3×C5#1799semidirect
391. Dic3#3999semidirect
435. C2×C4Dic3⋊AGL(1,𝔽5)semidirect
444. C5#70028semidirect
470. C3#10604167semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×D202
C2×#912282
C2×C3×#39992
#117520282
#117465732
#106041673
#700285