Finite Group Databasebeta

← #14313157

Subgroups — #14313157

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
1C3×#65920C211yesmaximal, characteristic
2#11749172C211yesmaximal, characteristic, complemented
3#11749123C211yesmaximal, characteristic, complemented
4#11746357C211yesmaximal, characteristic, complemented
5C5×#4536C211yesmaximal, characteristic, complemented
6#11746001C211yesmaximal, characteristic, complemented
7#11746000C211yesmaximal, characteristic, complemented
8#10599929—31nomaximal, Hall
9C23×C3×Dic5C411yescharacteristic, complemented
10C2×C3×#711C2211yescharacteristic
11C3×C5×#120C2211yescharacteristic
12C3×#4099C411yescharacteristic, complemented
13C3×#4085—21no—
14C3×#4081C2211yescharacteristic
15C3×D4×Dic5—21no—
16C3×#4032C411yescharacteristic, complemented
17C3×#4027—21no—
18C3×#4024—21no—
19C3×#4023C411yescharacteristic, complemented
20#91528—21no—
21D5×#208—21no—
22#91118C2211yescharacteristic
23#91117C2211yescharacteristic
24C5×#834C2211yescharacteristic
25C5×#833C2211yescharacteristic
26#90995—21no—
27#90961—21no—
28#71716—51nomaximal, Hall
29#65920D311yescharacteristic
30#65034—31no—
31#65029—31no—
32C5×AΣL(1,𝔽16)—31no—
33#64756—31no—
34#64696—31no—
35#64692—31no—
36C24×C3×C5C2×C411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4C2311yescharacteristic
39C2×C3×C22⋊D5—21no—
40C2×C3×C22⋊D5C2×C411yescharacteristic
41C2×C3×C22⋊D5D411yescharacteristic
42C22×C3×Dic5—21no—
43C22×C3×Dic5—21no—
44C22×C3×Dic5—41no—
45C22×C3×Dic5—41no—
46C22×C3×Dic5C2×C411yescharacteristic
47C22×C3×Dic5C2×C411yescharacteristic
48C22×C3×Dic5D411yescharacteristic
49C3×#711—41no—
50C3×#711—41no—
51C2×C3×C4×D5D411yescharacteristic
52C2×C3×Dic10D411yescharacteristic
53C3×C5×C22⋊C4—21no—
54C3×C5×C22⋊C4C2×C411yescharacteristic
55#6719—21no—
56#6710—21no—
57C5×#217—21no—
58C5×#208—21no—
59C3×C22⋊Dic5—21no—
60C3×C22⋊Dic5—21no—
61C3×C22⋊Dic5C2×C411yescharacteristic
62C3×#685—21no—
63C3×C4⋊Dic5—21no—
64C3×#683—21no—
65C3×#683—21no—
66C3×C4×Dic5—21no—
67#6668—41no—
68Dic3×Dic5—41no—
69#6649—41no—
70D5×C3⋊C8—41no—
71C3×#525—51no—
72#5240—51no—
73#5237—51no—
74#4539—51no—
75#4539—51no—
76#4536—51no—
77#4536D511yescharacteristic, complemented
78C23×Dic5Dic311yescharacteristic, complemented
79C2×#711C2×D311yescharacteristic
80C5×#120C2×D311yescharacteristic
81#4099Dic311yescharacteristic, complemented
82#4085—21no—
83#4081C2×D311yescharacteristic
84D4×Dic5—21no—
85D5×M16—61no—
86#4032Dic311yescharacteristic, complemented
87#4027—21no—
88#4024—21no—
89#4023—61no—
90#4023Dic311yescharacteristic, complemented
91C5×#100—31no—
92C5×#99—31no—
93#3966—31no—
94#3965—31no—
95#3956—61no—
96#3938—61no—
97#2120—151noSylow
98C23×C3×C5—21no—
99C23×C3×C5—41no—
100C23×C3×C5—42no—
101C23×C3×C5C22×C411yescharacteristic
102C23×C3×C5C2×D411yescharacteristic
103C22×C3×D5C22⋊C411yescharacteristic
104C3×C5×D4—41no—
105C3×C5×D4—42no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×Dic15—41no—
109C2×C5×Dic3—41no—
110C3×C22⋊D5—41no—
111C3×C22⋊D5—41no—
112C3×C22⋊D5—42no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5—21no—
118C2×C3×Dic5—21no—
119C2×C3×Dic5—42no—
120C2×C3×Dic5—41no—
121C2×C3×Dic5—41no—
122C2×C3×Dic5—41no—
123C2×C3×Dic5C22⋊C411yescharacteristic
124C2×C3×Dic5C22⋊C411yescharacteristic
125C2×C3×Dic5C22⋊C411yescharacteristic
126C3×C4×D5—21no—
127C3×C4×D5—21no—
128C3×Dic10—41no—
129C3⋊#168—41no—
130C5×C3⋊C8—41no—
131C2×C3×#41—51no—
132C23×C3×C4—51no—
133C3×#123—51no—
134C3×#123—51no—
135C3×C22⋊Q8—101no—
136C3×#121—101no—
137C3×#120—51no—
138C3×#120C2×D511yescharacteristic
139C3×C4×D4—101no—
140C3×C4×D4—101no—
141C3×#117—51no—
142#926—101no—
143C2×#208—101no—
144#836—101no—
145#834—51no—
146#834—101no—
147#834C2×D511yescharacteristic
148#833—51no—
149#833C2×D511yescharacteristic
150C24×C5C2×Dic311yescharacteristic
151C2×C5×D4—21no—
152C2×C5×D4C22×D311yescharacteristic
153C2×C22⋊D5—21no—
154C2×C22⋊D5C2×Dic311yescharacteristic
155C2×C22⋊D5#6711yescharacteristic
156C22×Dic5—21no—
157C22×Dic5—21no—
158C22×Dic5—41no—
159C22×Dic5—41no—
160C22×Dic5C2×Dic311yescharacteristic
161C22×Dic5C2×Dic311yescharacteristic
162C22×Dic5#6711yescharacteristic
163#711—41no—
164#711—41no—
165C2×C4×D5#6711yescharacteristic
166C2×Dic10#6711yescharacteristic
167C5×M16—61no—
168C5×C22⋊C4—21no—
169C5×C22⋊C4—61no—
170C5×C22⋊C4C2×Dic311yescharacteristic
171C22⋊Dic5—21no—
172C22⋊Dic5—21no—
173C22⋊Dic5—61no—
174C22⋊Dic5C2×Dic311yescharacteristic
175#685—21no—
176C4⋊Dic5—21no—
177#683—21no—
178#683—21no—
179#683—121no—
180C4×Dic5—21no—
181C4×Dic5—121no—
182#681—61no—
183#676—121no—
184C8×D5—121no—
185#525—51no—
186#413—151no—
187#410—151no—
188#352—151no—
189#352—151no—
190AΣL(1,𝔽16)—31no—
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×C3×D5—21no—
203C2×C3×D5—41no—
204C3×C4×C5—21no—
205C3×C4×C5—41no—
206Dic15—81no—
207C3×Dic5—21no—
208C3×Dic5—21no—
209C3×Dic5—41no—
210C3×Dic5—41no—
211C3×Dic5#9911yescharacteristic
212C3×Dic5#9911yescharacteristic
213C5×Dic3—81no—
214C24×C3C4×D511yescharacteristic
215C3×#41—201no—
216C3×#41—201no—
217C2×C3×Q8—51no—
218C2×C3×D4—21no—
219C2×C3×D4—51no—
220C2×C3×D4—51no—
221C2×C3×D4—101no—
222C2×C3×D4C22×D511yescharacteristic
223C22×C3×C4—51no—
224C22×C3×C4—51no—
225C22×C3×C4—51no—
226C22×C3×C4—51no—
227C22×C3×C4—101no—
228C22×C3×C4—101no—
229C22×C3×C4—201no—
230C22×C3×C4—201no—
231C3×C4⋊C4—101no—
232C3×C4⋊C4—101no—
233C3×C4⋊C4—101no—
234C3×C22⋊C4—21no—
235C3×C22⋊C4—51no—
236C3×C22⋊C4—101no—
237C3×C22⋊C4—101no—
238C3×C22⋊C4—101no—
239C3×C22⋊C4C4×D511yescharacteristic
240C3×C42—101no—
241#217—21no—
242#217—101no—
243C4⋊Dic3—201no—
244C4×Dic3—201no—
245#208—21no—
246#208—101no—
247#208—201no—
248C2×C3⋊C8—201no—
249C23×C5—21no—
250C23×C5—41no—
251C23×C5—42no—
252C23×C5C22×Dic311yescharacteristic
253C23×C5C2×#6711yescharacteristic
254C22×D5#21711yescharacteristic
255C5×D4—41no—
256C5×D4—42no—
257C2×C4×C5—21no—
258C2×C4×C5—121no—
259C2×C4×C5C2×#6711yescharacteristic
260C22⋊D5—41no—
261C22⋊D5—41no—
262C22⋊D5—42no—
263C2×Dic5—21no—
264C2×Dic5—21no—
265C2×Dic5—21no—
266C2×Dic5—21no—
267C2×Dic5—21no—
268C2×Dic5—21no—
269C2×Dic5—42no—
270C2×Dic5—41no—
271C2×Dic5—41no—
272C2×Dic5—41no—
273C2×Dic5—121no—
274C2×Dic5#21711yescharacteristic
275C2×Dic5#21711yescharacteristic
276C2×Dic5#21711yescharacteristic
277C4×D5—21no—
278C4×D5—21no—
279Dic10—41no—
280C5×C8—121no—
281#168—121no—
282C2×#41—51no—
283C23×C4—51no—
284C2×M16—301no—
285#123—51no—
286#123—51no—
287C22⋊Q8—101no—
288#121—101no—
289#120—51no—
290#120D3×D511yescharacteristic
291C4×D4—101no—
292C4×D4—101no—
293#117—51no—
294#117—301no—
295#101—301no—
296#100—31no—
297#100—151no—
298#99—31no—
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
306C3×D5—41no—
307C23×C3—21no—
308C23×C3—41no—
309C23×C3—42no—
310C23×C3—51no—
311C23×C3C2×C4×D511yescharacteristic
312C23×C3D4×D511yescharacteristic
313C3×Q8—201no—
314C3×D4—41no—
315C3×D4—42no—
316C3×D4—201no—
317C3×D4—201no—
318C3×D4—202no—
319C2×C3×C4—21no—
320C2×C3×C4—51no—
321C2×C3×C4—51no—
322C2×C3×C4—51no—
323C2×C3×C4—101no—
324C2×C3×C4—101no—
325C2×C3×C4—101no—
326C2×C3×C4—101no—
327C2×C3×C4—101no—
328C2×C3×C4—101no—
329C2×C3×C4—101no—
330C2×C3×C4—101no—
331C2×C3×C4—201no—
332C2×C3×C4—201no—
333C2×C3×C4—202no—
334C2×C3×C4—201no—
335C2×C3×C4D4×D511yescharacteristic
336C2×Dic3—41no—
337C2×Dic3—201no—
338C3⋊C8—41no—
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×C5C2×#21711yescharacteristic
350C2×D5—21no—
351C2×D5—41no—
352C4×C5—21no—
353C4×C5—41no—
354C4×C5—241no—
355Dic5—21no—
356Dic5—21no—
357Dic5—41no—
358Dic5—41no—
359Dic5—241no—
360Dic5#83411yescharacteristic
361Dic5#83411yescharacteristic
362C24D5×Dic311yescharacteristic
363#41—201no—
364#41—201no—
365C2×Q8—51no—
366C2×D4—21no—
367C2×D4—51no—
368C2×D4—51no—
369C2×D4—101no—
370C2×D4C2×D3×D511yescharacteristic
371C22×C4—51no—
372C22×C4—51no—
373C22×C4—51no—
374C22×C4—51no—
375C22×C4—101no—
376C22×C4—101no—
377C22×C4—201no—
378C22×C4—201no—
379M16—61no—
380M16—301no—
381M16—601no—
382C2×C8—601no—
383C4⋊C4—101no—
384C4⋊C4—101no—
385C4⋊C4—101no—
386C4⋊C4—601no—
387C22⋊C4—21no—
388C22⋊C4—51no—
389C22⋊C4—61no—
390C22⋊C4—101no—
391C22⋊C4—101no—
392C22⋊C4—101no—
393C22⋊C4—301no—
394C22⋊C4D5×Dic311yescharacteristic
395C42—101no—
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×C3—101no—
408C22×C3—201no—
409C22×C3D5×C22⋊C411yescharacteristic
410C3×C4—21no—
411C3×C4—41no—
412C3×C4—51no—
413C3×C4—51no—
414C3×C4—101no—
415C3×C4—101no—
416C3×C4—201no—
417C3×C4—201no—
418Dic3—81no—
419Dic3—401no—
420C2×C5—21no—
421C2×C5—41no—
422C2×C5—42no—
423C2×C5—41no—
424C2×C5C2×#83411yescharacteristic
425D5—41no—
426C23—21no—
427C23—41no—
428C23—42no—
429C23—51no—
430C23C2×D5×Dic311yescharacteristic
431C23D5×#6711yescharacteristic
432Q8—201no—
433D4—41no—
434D4—42no—
435D4—201no—
436D4—201no—
437D4—202no—
438C2×C4—21no—
439C2×C4—51no—
440C2×C4—51no—
441C2×C4—51no—
442C2×C4—101no—
443C2×C4—101no—
444C2×C4—101no—
445C2×C4—101no—
446C2×C4—101no—
447C2×C4—101no—
448C2×C4—101no—
449C2×C4—101no—
450C2×C4—121no—
451C2×C4—201no—
452C2×C4—201no—
453C2×C4—202no—
454C2×C4—201no—
455C2×C4—601no—
456C2×C4D5×#6711yescharacteristic
457C8—121no—
458C8—601no—
459C2×C3—21no—
460C2×C3—41no—
461C2×C3—42no—
462C2×C3—41no—
463C2×C3—201no—
464C2×C3D5×#9911yescharacteristic
465C5#7171611yescharacteristic, complemented, Sylow
466C22—22no—
467C22—21no—
468C22—21no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—42no—
473C22—42no—
474C22—41no—
475C22—101no—
476C22—201no—
477C22D5×#21711yescharacteristic
478C4—21no—
479C4—41no—
480C4—51no—
481C4—51no—
482C4—101no—
483C4—101no—
484C4—201no—
485C4—201no—
486C4—241no—
487C4—1201no—
488C3#1059992911yescharacteristic, complemented, Sylow
489C2—21no—
490C2—41no—
491C2—42no—
492C2—41no—
493C2—201no—
494C2D5×#83411yescharacteristic
subgroupG/H
centerC2D5×#834
commutatorC23×C3×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC3×C5×#120C22
socleC2×C3×C5C2×#99
prime radicalC3×#65920C2
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. #11749172C2semidirect
3. #11749123C2semidirect
4. #11746357C2semidirect
5. C5×#4536C2semidirect
6. #11746001C2semidirect
7. #11746000C2semidirect
9. C23×C3×Dic5C4semidirect
12. C3×#4099C4semidirect
16. C3×#4032C4semidirect
19. C3×#4023C4semidirect
77. #4536D5semidirect
78. C23×Dic5Dic3semidirect
81. #4099Dic3semidirect
86. #4032Dic3semidirect
90. #4023Dic3semidirect
397. C3×C5#2120semidirect
465. C5#71716semidirect
488. C3#10599929semidirect

Maximal subgroups

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

subgroupindex
C3×#659202
#117491722
#117491232
#117463572
C5×#45362
#117460012
#117460002
#105999293
#717165