Finite Group Databasebeta

← #14313318

Subgroups — #14313318

Order 1920.

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

normal subgroups only

This group has 468 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×#65982C211yesmaximal, characteristic
2#11749172C211yesmaximal, characteristic
3#11749123C211yesmaximal, characteristic
4#11746360C211yesmaximal, characteristic, complemented
5C5×#4539C211yesmaximal, characteristic, complemented
6#11746001C211yesmaximal, characteristic, complemented
7#11746000C211yesmaximal, characteristic, complemented
8#10599938—31nomaximal, Hall
9C2×C3×#711C2211yescharacteristic
10C22×C3×Dic10C411yescharacteristic, complemented
11C3×C5×#123C2211yescharacteristic
12C3×#4081C2211yescharacteristic
13C3×#4075C411yescharacteristic, complemented
14C3×#4042—21no—
15C3×#4034—21no—
16C3×#4032C411yescharacteristic, complemented
17C3×#4031—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#71870—51nomaximal, Hall
29#65982D311yescharacteristic
30#65034—31no—
31#65029—31no—
32C5×#352—31no—
33#64759—31no—
34#64696—31no—
35#64692—31no—
36C2×C3×C5×D4C2311yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C2×C3×C22⋊D5C2×C411yescharacteristic
39C2×C3×C22⋊D5D411yescharacteristic
40C22×C3×Dic5C2×C411yescharacteristic
41C22×C3×Dic5C2×C411yescharacteristic
42C22×C3×Dic5D411yescharacteristic
43C3×#711—41no—
44C3×#711—41no—
45C2×C3×C4×D5D411yescharacteristic
46C2×C3×Dic10—21no—
47C2×C3×Dic10—21no—
48C2×C3×Dic10—41no—
49C2×C3×Dic10—41no—
50C2×C3×Dic10D411yescharacteristic
51C3×C5×C4⋊C4—21no—
52C3×C5×C22⋊C4—21no—
53C3×C5×C22⋊C4C2×C411yescharacteristic
54#6719—21no—
55#6710—21no—
56C5×#217—21no—
57C5×#208—21no—
58C3×C22⋊Dic5—21no—
59C3×C22⋊Dic5C2×C411yescharacteristic
60C3×#685—21no—
61C3×#685—21no—
62C3×C4⋊Dic5—21no—
63C3×#683—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×#536—51no—
72#5240—51no—
73#5237—51no—
74#4539—51no—
75#4539—51no—
76#4539—51no—
77#4539D511yescharacteristic, complemented
78C2×#711C2×D311yescharacteristic
79C22×Dic10Dic311yescharacteristic, complemented
80C5×#123C2×D311yescharacteristic
81#4081C2×D311yescharacteristic
82#4075Dic311yescharacteristic, complemented
83D5×M16—61no—
84#4042—21no—
85#4034—21no—
86#4032Dic311yescharacteristic, complemented
87#4031—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#2123—151noSylow
98C23×C3×C5C22×C411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C22×C3×D5C22⋊C411yescharacteristic
101C3×C5×D4—41no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×Dic15—41no—
107C2×C5×Dic3—41no—
108C3×C22⋊D5—41no—
109C3×C22⋊D5—41no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—21no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5C22⋊C411yescharacteristic
118C2×C3×Dic5C22⋊C411yescharacteristic
119C2×C3×Dic5C22⋊C411yescharacteristic
120C3×C4×D5—21no—
121C3×C4×D5—21no—
122C3×Dic10—41no—
123C3×Dic10—42no—
124C3×Dic10—41no—
125C3×Dic10—41no—
126C3⋊#168—41no—
127C5×C3⋊C8—41no—
128C2×C3×#41—51no—
129C22×C3×Q8—51no—
130C3×C4⋊Q8—101no—
131C3×#124—101no—
132C3×#123—51no—
133C3×#123—51no—
134C3×#123—51no—
135C3×#123C2×D511yescharacteristic
136C3×C22⋊Q8—101no—
137C3×C22⋊Q8—101no—
138C3×#117—51no—
139#926—101no—
140C2×#208—101no—
141#836—101no—
142#834—51no—
143#834—101no—
144#834C2×D511yescharacteristic
145#833—51no—
146#833C2×D511yescharacteristic
147C2×C5×D4C22×D311yescharacteristic
148C22×C4×C5C2×Dic311yescharacteristic
149C2×C22⋊D5C2×Dic311yescharacteristic
150C2×C22⋊D5#6711yescharacteristic
151C22×Dic5C2×Dic311yescharacteristic
152C22×Dic5C2×Dic311yescharacteristic
153C22×Dic5#6711yescharacteristic
154#711—41no—
155#711—41no—
156C2×C4×D5#6711yescharacteristic
157C2×Dic10—21no—
158C2×Dic10—21no—
159C2×Dic10—41no—
160C2×Dic10—41no—
161C2×Dic10#6711yescharacteristic
162C5×M16—61no—
163C5×C4⋊C4—21no—
164C5×C22⋊C4—21no—
165C5×C22⋊C4—61no—
166C5×C22⋊C4C2×Dic311yescharacteristic
167C22⋊Dic5—21no—
168C22⋊Dic5—61no—
169C22⋊Dic5C2×Dic311yescharacteristic
170#685—21no—
171#685—21no—
172C4⋊Dic5—21no—
173#683—21no—
174#683—21no—
175#683—21no—
176#683—121no—
177C4×Dic5—21no—
178C4×Dic5—121no—
179#681—61no—
180#676—121no—
181C8×D5—121no—
182#536—51no—
183#413—151no—
184#410—151no—
185#352—31no—
186#352—151no—
187#352—151no—
188#352—151no—
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5—41no—
192C22×C3×C5—41no—
193C22×C3×C5C2×C22⋊C411yescharacteristic
194C2×C3×D5—21no—
195C2×C3×D5—41no—
196C3×C4×C5—21no—
197C3×C4×C5—41no—
198C3×C4×C5—41no—
199Dic15—81no—
200C3×Dic5—21no—
201C3×Dic5—21no—
202C3×Dic5—41no—
203C3×Dic5—41no—
204C3×Dic5#9911yescharacteristic
205C3×Dic5#9911yescharacteristic
206C5×Dic3—81no—
207C3×#41—201no—
208C3×#41—201no—
209C2×C3×Q8—51no—
210C2×C3×Q8—101no—
211C2×C3×Q8—101no—
212C2×C3×Q8—201no—
213C2×C3×Q8—201no—
214C2×C3×D4—51no—
215C2×C3×D4—51no—
216C2×C3×D4C22×D511yescharacteristic
217C22×C3×C4—51no—
218C22×C3×C4—51no—
219C22×C3×C4—51no—
220C22×C3×C4—51no—
221C22×C3×C4C4×D511yescharacteristic
222C3×C4⋊C4—21no—
223C3×C4⋊C4—101no—
224C3×C4⋊C4—101no—
225C3×C4⋊C4—101no—
226C3×C4⋊C4—101no—
227C3×C22⋊C4—21no—
228C3×C22⋊C4—51no—
229C3×C22⋊C4—101no—
230C3×C22⋊C4—101no—
231C3×C22⋊C4—101no—
232C3×C22⋊C4C4×D511yescharacteristic
233C3×C42—101no—
234#217—21no—
235#217—101no—
236C4⋊Dic3—201no—
237C4×Dic3—201no—
238#208—21no—
239#208—101no—
240#208—201no—
241C2×C3⋊C8—201no—
242C23×C5C22×Dic311yescharacteristic
243C23×C5C2×#6711yescharacteristic
244C22×D5#21711yescharacteristic
245C5×D4—41no—
246C2×C4×C5—21no—
247C2×C4×C5—21no—
248C2×C4×C5—41no—
249C2×C4×C5—121no—
250C2×C4×C5C2×#6711yescharacteristic
251C22⋊D5—41no—
252C22⋊D5—41no—
253C2×Dic5—21no—
254C2×Dic5—21no—
255C2×Dic5—21no—
256C2×Dic5—21no—
257C2×Dic5—21no—
258C2×Dic5—21no—
259C2×Dic5—41no—
260C2×Dic5—121no—
261C2×Dic5#21711yescharacteristic
262C2×Dic5#21711yescharacteristic
263C2×Dic5#21711yescharacteristic
264C4×D5—21no—
265C4×D5—21no—
266Dic10—41no—
267Dic10—42no—
268Dic10—41no—
269Dic10—41no—
270C5×C8—121no—
271#168—121no—
272C2×#41—51no—
273C22×Q8—51no—
274C2×M16—301no—
275C4⋊Q8—101no—
276#124—101no—
277#123—51no—
278#123—51no—
279#123—51no—
280#123D3×D511yescharacteristic
281C22⋊Q8—101no—
282C22⋊Q8—101no—
283#117—51no—
284#117—301no—
285#101—301no—
286#100—31no—
287#100—151no—
288#99—31no—
289#99—151no—
290#99—301no—
291C2×C3×C5—21no—
292C2×C3×C5—41no—
293C2×C3×C5—41no—
294C2×C3×C5C2×#9911yescharacteristic
295C3×D5—41no—
296C23×C3—51no—
297C23×C3C2×C4×D511yescharacteristic
298C23×C3D4×D511yescharacteristic
299C3×Q8—201no—
300C3×Q8—201no—
301C3×Q8—201no—
302C3×Q8—202no—
303C3×D4—41no—
304C3×D4—201no—
305C3×D4—201no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—41no—
309C2×C3×C4—51no—
310C2×C3×C4—51no—
311C2×C3×C4—51no—
312C2×C3×C4—101no—
313C2×C3×C4—101no—
314C2×C3×C4—101no—
315C2×C3×C4—101no—
316C2×C3×C4—101no—
317C2×C3×C4—101no—
318C2×C3×C4—101no—
319C2×C3×C4—101no—
320C2×C3×C4—201no—
321C2×C3×C4D4×D511yescharacteristic
322C2×Dic3—41no—
323C2×Dic3—201no—
324C3⋊C8—41no—
325C3⋊C8—201no—
326C22×C5—21no—
327C22×C5—21no—
328C22×C5—41no—
329C22×C5—41no—
330C22×C5C2×#21711yescharacteristic
331C2×D5—21no—
332C2×D5—41no—
333C4×C5—21no—
334C4×C5—41no—
335C4×C5—41no—
336C4×C5—241no—
337Dic5—21no—
338Dic5—21no—
339Dic5—41no—
340Dic5—41no—
341Dic5—241no—
342Dic5#83411yescharacteristic
343Dic5#83411yescharacteristic
344#41—201no—
345#41—201no—
346C2×Q8—51no—
347C2×Q8—101no—
348C2×Q8—101no—
349C2×Q8—201no—
350C2×Q8—201no—
351C2×D4—51no—
352C2×D4—51no—
353C2×D4C2×D3×D511yescharacteristic
354C22×C4—51no—
355C22×C4—51no—
356C22×C4—51no—
357C22×C4—51no—
358C22×C4D5×Dic311yescharacteristic
359M16—61no—
360M16—301no—
361M16—601no—
362C2×C8—601no—
363C4⋊C4—21no—
364C4⋊C4—101no—
365C4⋊C4—101no—
366C4⋊C4—101no—
367C4⋊C4—101no—
368C4⋊C4—601no—
369C22⋊C4—21no—
370C22⋊C4—51no—
371C22⋊C4—61no—
372C22⋊C4—101no—
373C22⋊C4—101no—
374C22⋊C4—101no—
375C22⋊C4—301no—
376C22⋊C4D5×Dic311yescharacteristic
377C42—101no—
378C42—601no—
379C3×C5#212311yescharacteristic, complemented, Hall
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3—101no—
385C22×C3—201no—
386C22×C3D5×C22⋊C411yescharacteristic
387C3×C4—21no—
388C3×C4—41no—
389C3×C4—41no—
390C3×C4—51no—
391C3×C4—51no—
392C3×C4—101no—
393C3×C4—101no—
394C3×C4—201no—
395C3×C4—201no—
396Dic3—81no—
397Dic3—401no—
398C2×C5—21no—
399C2×C5—41no—
400C2×C5—41no—
401C2×C5C2×#83411yescharacteristic
402D5—41no—
403C23—51no—
404C23C2×D5×Dic311yescharacteristic
405C23D5×#6711yescharacteristic
406Q8—201no—
407Q8—201no—
408Q8—201no—
409Q8—202no—
410D4—41no—
411D4—201no—
412D4—201no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—41no—
416C2×C4—51no—
417C2×C4—51no—
418C2×C4—51no—
419C2×C4—101no—
420C2×C4—101no—
421C2×C4—101no—
422C2×C4—101no—
423C2×C4—101no—
424C2×C4—101no—
425C2×C4—101no—
426C2×C4—101no—
427C2×C4—121no—
428C2×C4—201no—
429C2×C4—601no—
430C2×C4D5×#6711yescharacteristic
431C8—121no—
432C8—601no—
433C2×C3—21no—
434C2×C3—41no—
435C2×C3—41no—
436C2×C3—201no—
437C2×C3D5×#9911yescharacteristic
438C5#7187011yescharacteristic, complemented, Sylow
439C22—21no—
440C22—21no—
441C22—41no—
442C22—41no—
443C22—101no—
444C22—201no—
445C22D5×#21711yescharacteristic
446C4—21no—
447C4—41no—
448C4—41no—
449C4—51no—
450C4—51no—
451C4—101no—
452C4—101no—
453C4—201no—
454C4—201no—
455C4—241no—
456C4—1201no—
457C3#1059993811yescharacteristic, complemented, Sylow
458C2—21no—
459C2—41no—
460C2—41no—
461C2—201no—
462C2D5×#83411yescharacteristic
subgroupG/H
centerC2D5×#834
commutatorC23×C3×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC3×C5×#123C22
socleC2×C3×C5C2×#99
prime radicalC2×C3×#711C22
cosocleC2×C3×C5×D4C23
hypercenter#123D3×D5
hypocenterC3×C5#2123
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
4. #11746360C2semidirect
5. C5×#4539C2semidirect
6. #11746001C2semidirect
7. #11746000C2semidirect
10. C22×C3×Dic10C4semidirect
13. C3×#4075C4semidirect
16. C3×#4032C4semidirect
19. C3×#4023C4semidirect
77. #4539D5semidirect
79. C22×Dic10Dic3semidirect
82. #4075Dic3semidirect
86. #4032Dic3semidirect
90. #4023Dic3semidirect
379. C3×C5#2123semidirect
438. C5#71870semidirect
457. C3#10599938semidirect

Maximal subgroups

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

subgroupindex
C3×#659822
#117491722
#117491232
#117463602
C5×#45392
#117460012
#117460002
#105999383
#718705