Finite Group Databasebeta

← #14313159

Subgroups — #14313159

Order 1920.

528 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C5×#5586C211yesmaximal, characteristic
2#11749173C211yesmaximal, characteristic, complemented
3#11749126C211yesmaximal, characteristic, complemented
4#11746357C211yesmaximal, characteristic, complemented
5C3×#64756C211yesmaximal, characteristic, complemented
6#11746003C211yesmaximal, characteristic, complemented
7#11746002C211yesmaximal, characteristic, complemented
8#10602509—31nomaximal, Hall
9C23×C5×Dic3C411yescharacteristic, complemented
10C2×C5×#237C2211yescharacteristic
11C3×C5×#120C2211yescharacteristic
12C5×#953C411yescharacteristic, complemented
13C5×#939—21no—
14C5×#935C2211yescharacteristic
15C5×D4×Dic3—21no—
16C5×#886C411yescharacteristic, complemented
17C5×#67⋊C4—21no—
18C5×#878—21no—
19C5×#877C411yescharacteristic, complemented
20#91529—21no—
21D3×#681—21no—
22#91118C2211yescharacteristic
23#91117C2211yescharacteristic
24C3×#3966C2211yescharacteristic
25C3×#3965C2211yescharacteristic
26#90996—21no—
27#90962—21no—
28#69136—51nomaximal, Hall
29C5×#525—31no—
30#65529—31no—
31#65526—31no—
32#64759—31no—
33#64759—31no—
34#64756—31no—
35#64756D311yescharacteristic, complemented
36C24×C3×C5C2×C411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4C2311yescharacteristic
39C2×C5×#67—21no—
40C2×C5×#67C2×C411yescharacteristic
41C2×C5×#67D411yescharacteristic
42C22×C5×Dic3—21no—
43C22×C5×Dic3—21no—
44C22×C5×Dic3—41no—
45C22×C5×Dic3—41no—
46C22×C5×Dic3C2×C411yescharacteristic
47C22×C5×Dic3C2×C411yescharacteristic
48C22×C5×Dic3D411yescharacteristic
49C5×#237—41no—
50C5×#237—41no—
51C2×C4×C5×D3D411yescharacteristic
52C2×C5×Dic6D411yescharacteristic
53C3×C5×C22⋊C4—21no—
54C3×C5×C22⋊C4C2×C411yescharacteristic
55#6719—21no—
56#6710—21no—
57C5×#217—21no—
58C5×#217—21no—
59C5×#217C2×C411yescharacteristic
60C5×(C2×D3)⋊C4—21no—
61C5×C4⋊Dic3—21no—
62C5×Dic3⋊C4—21no—
63C5×Dic3⋊C4—21no—
64C4×C5×Dic3—21no—
65C3×C22⋊Dic5—21no—
66C3×#681—21no—
67Dic3⋊Dic5—41no—
68Dic3×Dic5—41no—
69#6650—41no—
70D3×#168—41no—
71#5586D511yescharacteristic
72#4745—51no—
73#4740—51no—
74C3×AΣL(1,𝔽16)—51no—
75#4536—51no—
76#4476—51no—
77#4472—51no—
78C2×C5×#41—31no—
79C23×C4×C5—31no—
80C5×#123—31no—
81C5×#123—31no—
82C5×C22⋊Q8—61no—
83C5×#121—61no—
84C5×#120—31no—
85C5×#120C2×D311yescharacteristic
86C4×C5×D4—61no—
87C4×C5×D4—61no—
88C5×#117—31no—
89#4072—61no—
90C2×#681—61no—
91#3968—61no—
92#3966—31no—
93#3966—61no—
94#3966C2×D311yescharacteristic
95#3965—31no—
96#3965C2×D311yescharacteristic
97#2120—151noSylow
98C23×C3×C5—21no—
99C23×C3×C5—41no—
100C23×C3×C5—42no—
101C23×C3×C5C22×C411yescharacteristic
102C23×C3×C5C2×D411yescharacteristic
103C22×C5×D3C22⋊C411yescharacteristic
104C3×C5×D4—41no—
105C3×C5×D4—42no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×Dic15—41no—
109C5×#67—41no—
110C5×#67—41no—
111C5×#67—42no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—21no—
117C2×C5×Dic3—21no—
118C2×C5×Dic3—42no—
119C2×C5×Dic3—41no—
120C2×C5×Dic3—41no—
121C2×C5×Dic3—41no—
122C2×C5×Dic3C22⋊C411yescharacteristic
123C2×C5×Dic3C22⋊C411yescharacteristic
124C2×C5×Dic3C22⋊C411yescharacteristic
125C4×C5×D3—21no—
126C4×C5×D3—21no—
127C5×Dic6—41no—
128C2×C3×Dic5—41no—
129C3⋊#168—41no—
130C3×#168—41no—
131C23×Dic3Dic511yescharacteristic, complemented
132C2×#237C2×D511yescharacteristic
133C3×#120C2×D511yescharacteristic
134#953Dic511yescharacteristic, complemented
135#939—21no—
136#935C2×D511yescharacteristic
137D4×Dic3—21no—
138D3×M16—101no—
139#886Dic511yescharacteristic, complemented
140#67⋊C4—21no—
141#878—21no—
142#877—101no—
143#877Dic511yescharacteristic, complemented
144C3×#100—51no—
145C3×#99—51no—
146#834—51no—
147#833—51no—
148#824—101no—
149#806—101no—
150C24×C5C4×D311yescharacteristic
151C5×#41—121no—
152C5×#41—121no—
153C2×C5×Q8—31no—
154C2×C5×D4—21no—
155C2×C5×D4—31no—
156C2×C5×D4—31no—
157C2×C5×D4—61no—
158C2×C5×D4C22×D311yescharacteristic
159C22×C4×C5—31no—
160C22×C4×C5—31no—
161C22×C4×C5—31no—
162C22×C4×C5—31no—
163C22×C4×C5—61no—
164C22×C4×C5—61no—
165C22×C4×C5—121no—
166C22×C4×C5—121no—
167C5×C4⋊C4—61no—
168C5×C4⋊C4—61no—
169C5×C4⋊C4—61no—
170C5×C22⋊C4—21no—
171C5×C22⋊C4—31no—
172C5×C22⋊C4—61no—
173C5×C22⋊C4—61no—
174C5×C22⋊C4—61no—
175C5×C22⋊C4C4×D311yescharacteristic
176C42×C5—61no—
177C22⋊Dic5—21no—
178C22⋊Dic5—61no—
179C4⋊Dic5—121no—
180C4×Dic5—121no—
181#681—21no—
182#681—61no—
183#681—121no—
184C2×#168—121no—
185#525—31no—
186#413—151no—
187#410—151no—
188#352—151no—
189#352—151no—
190AΣL(1,𝔽16)—51no—
191AΣL(1,𝔽16)—151no—
192C22×C3×C5—22no—
193C22×C3×C5—21no—
194C22×C3×C5—21no—
195C22×C3×C5—41no—
196C22×C3×C5—41no—
197C22×C3×C5—41no—
198C22×C3×C5—42no—
199C22×C3×C5—42no—
200C22×C3×C5—41no—
201C22×C3×C5C2×C22⋊C411yescharacteristic
202C2×C5×D3—21no—
203C2×C5×D3—41no—
204C3×C4×C5—21no—
205C3×C4×C5—41no—
206Dic15—81no—
207C3×Dic5—81no—
208C5×Dic3—21no—
209C5×Dic3—21no—
210C5×Dic3—41no—
211C5×Dic3—41no—
212C5×Dic3#9911yescharacteristic
213C5×Dic3#9911yescharacteristic
214C24×C3C2×Dic511yescharacteristic
215C2×C3×D4—21no—
216C2×C3×D4C22×D511yescharacteristic
217C2×#67—21no—
218C2×#67C2×Dic511yescharacteristic
219C2×#67C22⋊D511yescharacteristic
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—41no—
223C22×Dic3—41no—
224C22×Dic3C2×Dic511yescharacteristic
225C22×Dic3C2×Dic511yescharacteristic
226C22×Dic3C22⋊D511yescharacteristic
227#237—41no—
228#237—41no—
229C2×C4×D3C22⋊D511yescharacteristic
230C2×Dic6C22⋊D511yescharacteristic
231C3×M16—101no—
232C3×C22⋊C4—21no—
233C3×C22⋊C4—101no—
234C3×C22⋊C4C2×Dic511yescharacteristic
235#217—21no—
236#217—21no—
237#217—101no—
238#217C2×Dic511yescharacteristic
239(C2×D3)⋊C4—21no—
240C4⋊Dic3—21no—
241Dic3⋊C4—21no—
242Dic3⋊C4—21no—
243Dic3⋊C4—201no—
244C4×Dic3—21no—
245C4×Dic3—201no—
246#208—101no—
247ΓL(1,𝔽25)—201no—
248D3×C8—201no—
249C23×C5—21no—
250C23×C5—31no—
251C23×C5—41no—
252C23×C5—42no—
253C23×C5C2×C4×D311yescharacteristic
254C23×C5D3×D411yescharacteristic
255C5×Q8—121no—
256C5×D4—41no—
257C5×D4—42no—
258C5×D4—121no—
259C5×D4—121no—
260C5×D4—122no—
261C2×C4×C5—21no—
262C2×C4×C5—31no—
263C2×C4×C5—31no—
264C2×C4×C5—31no—
265C2×C4×C5—61no—
266C2×C4×C5—61no—
267C2×C4×C5—61no—
268C2×C4×C5—61no—
269C2×C4×C5—61no—
270C2×C4×C5—61no—
271C2×C4×C5—61no—
272C2×C4×C5—61no—
273C2×C4×C5—121no—
274C2×C4×C5—121no—
275C2×C4×C5—122no—
276C2×C4×C5—121no—
277C2×C4×C5D3×D411yescharacteristic
278C2×Dic5—41no—
279C2×Dic5—121no—
280#168—41no—
281#168—121no—
282C2×#41—31no—
283C23×C4—31no—
284C2×M16—301no—
285#123—31no—
286#123—31no—
287C22⋊Q8—61no—
288#121—61no—
289#120—31no—
290#120D3×D511yescharacteristic
291C4×D4—61no—
292C4×D4—61no—
293#117—31no—
294#117—301no—
295#101—301no—
296#100—51no—
297#100—151no—
298#99—51no—
299#99—151no—
300#99—301no—
301C2×C3×C5—21no—
302C2×C3×C5—41no—
303C2×C3×C5—42no—
304C2×C3×C5—41no—
305C2×C3×C5C2×#9911yescharacteristic
306C5×D3—41no—
307C23×C3—21no—
308C23×C3—41no—
309C23×C3—42no—
310C23×C3C22×Dic511yescharacteristic
311C23×C3C2×C22⋊D511yescharacteristic
312C22×D3C22⋊Dic511yescharacteristic
313C3×D4—41no—
314C3×D4—42no—
315C2×C3×C4—21no—
316C2×C3×C4—201no—
317C2×C3×C4C2×C22⋊D511yescharacteristic
318#67—41no—
319#67—41no—
320#67—42no—
321C2×Dic3—21no—
322C2×Dic3—21no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—21no—
326C2×Dic3—21no—
327C2×Dic3—42no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—201no—
332C2×Dic3C22⋊Dic511yescharacteristic
333C2×Dic3C22⋊Dic511yescharacteristic
334C2×Dic3C22⋊Dic511yescharacteristic
335C4×D3—21no—
336C4×D3—21no—
337Dic6—41no—
338C3×C8—201no—
339C3⋊C8—201no—
340C22×C5—22no—
341C22×C5—21no—
342C22×C5—21no—
343C22×C5—41no—
344C22×C5—41no—
345C22×C5—41no—
346C22×C5—42no—
347C22×C5—42no—
348C22×C5—41no—
349C22×C5—61no—
350C22×C5—121no—
351C22×C5D3×C22⋊C411yescharacteristic
352C4×C5—21no—
353C4×C5—31no—
354C4×C5—31no—
355C4×C5—41no—
356C4×C5—61no—
357C4×C5—61no—
358C4×C5—121no—
359C4×C5—121no—
360Dic5—81no—
361Dic5—241no—
362C24D3×Dic511yescharacteristic
363#41—121no—
364#41—121no—
365C2×Q8—31no—
366C2×D4—21no—
367C2×D4—31no—
368C2×D4—31no—
369C2×D4—61no—
370C2×D4C2×D3×D511yescharacteristic
371C22×C4—31no—
372C22×C4—31no—
373C22×C4—31no—
374C22×C4—31no—
375C22×C4—61no—
376C22×C4—61no—
377C22×C4—121no—
378C22×C4—121no—
379M16—101no—
380M16—301no—
381M16—601no—
382C2×C8—601no—
383C4⋊C4—61no—
384C4⋊C4—61no—
385C4⋊C4—61no—
386C4⋊C4—601no—
387C22⋊C4—21no—
388C22⋊C4—31no—
389C22⋊C4—61no—
390C22⋊C4—61no—
391C22⋊C4—61no—
392C22⋊C4—101no—
393C22⋊C4—301no—
394C22⋊C4D3×Dic511yescharacteristic
395C42—61no—
396C42—601no—
397C3×C5#212011yescharacteristic, complemented, Hall
398C22×C3—22no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—41no—
407C22×C3C2×C22⋊Dic511yescharacteristic
408C2×D3—21no—
409C2×D3—41no—
410C3×C4—21no—
411C3×C4—41no—
412C3×C4—401no—
413Dic3—21no—
414Dic3—21no—
415Dic3—41no—
416Dic3—41no—
417Dic3—401no—
418Dic3#396611yescharacteristic
419Dic3#396611yescharacteristic
420C2×C5—21no—
421C2×C5—41no—
422C2×C5—42no—
423C2×C5—41no—
424C2×C5—121no—
425C2×C5D3×#9911yescharacteristic
426C23—21no—
427C23—31no—
428C23—41no—
429C23—42no—
430C23C2×D3×Dic511yescharacteristic
431C23D3×C22⋊D511yescharacteristic
432Q8—121no—
433D4—41no—
434D4—42no—
435D4—121no—
436D4—121no—
437D4—122no—
438C2×C4—21no—
439C2×C4—31no—
440C2×C4—31no—
441C2×C4—31no—
442C2×C4—61no—
443C2×C4—61no—
444C2×C4—61no—
445C2×C4—61no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—61no—
449C2×C4—61no—
450C2×C4—121no—
451C2×C4—121no—
452C2×C4—122no—
453C2×C4—121no—
454C2×C4—201no—
455C2×C4—601no—
456C2×C4D3×C22⋊D511yescharacteristic
457C8—201no—
458C8—601no—
459C2×C3—21no—
460C2×C3—41no—
461C2×C3—42no—
462C2×C3—41no—
463C2×C3C2×#396611yescharacteristic
464D3—41no—
465C5#6913611yescharacteristic, complemented, Sylow
466C22—22no—
467C22—21no—
468C22—21no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—42no—
473C22—42no—
474C22—41no—
475C22—61no—
476C22—121no—
477C22D3×C22⋊Dic511yescharacteristic
478C4—21no—
479C4—31no—
480C4—31no—
481C4—41no—
482C4—61no—
483C4—61no—
484C4—121no—
485C4—121no—
486C4—401no—
487C4—1201no—
488C3#1060250911yescharacteristic, complemented, Sylow
489C2—21no—
490C2—41no—
491C2—42no—
492C2—41no—
493C2—121no—
494C2D3×#396611yescharacteristic
subgroupG/H
centerC2D3×#3966
commutatorC23×C3×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC3×C5×#120C22
socleC2×C3×C5C2×#99
prime radicalC5×#5586C2
cosocleC2×C3×C5×D4C23
hypercenter#120D3×D5
hypocenterC3×C5#2120
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #120

Complements

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

NH ≅ G/Ntype
2. #11749173C2semidirect
3. #11749126C2semidirect
4. #11746357C2semidirect
5. C3×#64756C2semidirect
6. #11746003C2semidirect
7. #11746002C2semidirect
9. C23×C5×Dic3C4semidirect
12. C5×#953C4semidirect
16. C5×#886C4semidirect
19. C5×#877C4semidirect
35. #64756D3semidirect
131. C23×Dic3Dic5semidirect
134. #953Dic5semidirect
139. #886Dic5semidirect
143. #877Dic5semidirect
397. C3×C5#2120semidirect
465. C5#69136semidirect
488. C3#10602509semidirect

Maximal subgroups

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

subgroupindex
C5×#55862
#117491732
#117491262
#117463572
C3×#647562
#117460032
#117460022
#106025093
#691365