Finite Group Databasebeta

← #14288315

Subgroups — #14288315

Order 1920.

456 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 80 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
1#11754484C211yesmaximal, characteristic
2#11750775C211yesmaximal, characteristic
3#11748447C211yesmaximal, characteristic, complemented
4#11748445C211yesmaximal, characteristic, complemented
5C5×#4452C211yesmaximal, characteristic, complemented
6C3×#64672C211yesmaximal, characteristic, complemented
7#11745950C211yesmaximal, characteristic
8#10599113—31nomaximal, Hall
9C2×#6714—21no—
10C2×#6714C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C5×#924C2211yescharacteristic
13C3×#4070C2211yescharacteristic
14#91576—21no—
15#91561—21no—
16#91429—21no—
17#91424—21no—
18#91419—21no—
19#91411—21no—
20C3×C5×#95C2211yescharacteristic
21#91115—21no—
22C5×#830C2211yescharacteristic
23C3×C22⋊#168C2211yescharacteristic
24#90987—21no—
25#90985—21no—
26#90973—21no—
27#90971—21no—
28#68320—51nomaximal, Hall
29#65968—31no—
30#65332—31no—
31#65010—31no—
32#64963—31no—
33C5×#328—31no—
34#64688—31no—
35#64672D311yescharacteristic, complemented
36C23×D15D411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×Dic15D411yescharacteristic
41C2×C5×Dic6D411yescharacteristic
42C2×C3×Dic10D411yescharacteristic
43C2×#1204—21no—
44C2×#1200—21no—
45C2×#1200—21no—
46#6714—21no—
47#6714—21no—
48#6714—42no—
49C4⋊Dic15—21no—
50C4⋊Dic15—21no—
51C5×#217—21no—
52C5×C4⋊Dic3D411yescharacteristic
53C5×Dic3⋊C4—21no—
54C2×C5×C3⋊C8—21no—
55C3×C22⋊Dic5—21no—
56C3×C4⋊Dic5D411yescharacteristic
57C3×#683—21no—
58C2×C3×#168—21no—
59Dic3⋊Dic5—21no—
60#6669—21no—
61#6668—21no—
62#6667—21no—
63#6667—21no—
64#5634—51no—
65#5043—51no—
66#4721—51no—
67#4674—51no—
68C3×#328—51no—
69#4468—51no—
70#4452D511yescharacteristic, complemented
71C5×C22⋊Q8—31no—
72#4092—61no—
73C2×#685—31no—
74C2×#685—61no—
75C2×C4⋊Dic5—31no—
76#4070C2×D311yescharacteristic
77#4043—61no—
78#4042—61no—
79#4042—61no—
80D5×C22⋊C4—61no—
81#4024—61no—
82C5×C22⋊C8—31no—
83C5×#95C2×D311yescharacteristic
84#3967—61no—
85#3963—61no—
86C22⋊#168C2×D311yescharacteristic
87#3949—61no—
88#3948—61no—
89#3940—61no—
90#1608—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×D15—21no—
93C22×D15—21no—
94C22×D15—41no—
95C22×D15—41no—
96C22×D15SD1612yes—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×Dic15—21no—
104C2×Dic15—41no—
105C2×Dic15—41no—
106C2×Dic15—41no—
107C2×Dic15—41no—
108C2×C5×Dic3—21no—
109C2×C5×Dic3—21no—
110C5×Dic6—41no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—21no—
113C3×Dic10—41no—
114#1204—81no—
115#1200—81no—
116#1200—81no—
117C3×#168—41no—
118C5×C3⋊C8—41no—
119C3×C22⋊Q8—51no—
120#946—101no—
121C2×(C2×D3)⋊C4—51no—
122C2×(C2×D3)⋊C4—101no—
123C2×C4⋊Dic3—51no—
124#924C2×D511yescharacteristic
125#897—101no—
126#896—101no—
127#896—101no—
128D3×C22⋊C4—101no—
129#878—101no—
130C3×C22⋊C8—51no—
131C3×#95C2×D511yescharacteristic
132#835—101no—
133C3⋊#95—101no—
134#830C2×D511yescharacteristic
135#817—101no—
136#816—101no—
137#808—101no—
138C23×D5—31no—
139C2×C5×Q8—31no—
140C22×C4×C5—21no—
141C22×C4×C5C22×D311yescharacteristic
142C22×Dic5—31no—
143C22×Dic5—61no—
144C2×C4×D5—61no—
145C2×C4×D5—61no—
146C2×Dic10—61no—
147C2×Dic10D1211yescharacteristic
148C2×C5×C8—61no—
149C5×C4⋊C4—31no—
150C5×C4⋊C4—61no—
151C5×C22⋊C4—61no—
152C22⋊Dic5—21no—
153#685—61no—
154#685—61no—
155#685—61no—
156#685—61no—
157#685—122no—
158C4⋊Dic5—61no—
159C4⋊Dic5—61no—
160C4⋊Dic5—61no—
161C4⋊Dic5D1211yescharacteristic
162#683—21no—
163#683—61no—
164#683—61no—
165C2×#168—21no—
166#543—151no—
167#483—151no—
168#483—151no—
169#397—151no—
170#328—31no—
171#328—51no—
172#323—151no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5#12011yescharacteristic
176C22×C3×C5C2×SD1611yescharacteristic
177C22×C3×C5#13711yescharacteristic
178C2×D15—22no—
179C2×D15—41no—
180C2×D15—41no—
181C2×D15—42no—
182C2×D15—81no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5—81no—
186Dic15—41no—
187Dic15—81no—
188C3×Dic5—41no—
189C3×Dic5—41no—
190C5×Dic3—41no—
191C5×Dic3—41no—
192C23×D3—51no—
193C2×C3×Q8—51no—
194C22×C3×C4—21no—
195C22×C3×C4C22×D511yescharacteristic
196C22×Dic3—51no—
197C22×Dic3—101no—
198C2×C4×D3—101no—
199C2×C4×D3—101no—
200C2×Dic6—101no—
201C2×Dic6D2011yescharacteristic
202C2×C3×C8—101no—
203C3×C4⋊C4—51no—
204C3×C4⋊C4—101no—
205C3×C22⋊C4—101no—
206#217—21no—
207(C2×D3)⋊C4—101no—
208(C2×D3)⋊C4—101no—
209(C2×D3)⋊C4—101no—
210(C2×D3)⋊C4—101no—
211(C2×D3)⋊C4—202no—
212C4⋊Dic3—101no—
213C4⋊Dic3—101no—
214C4⋊Dic3—101no—
215C4⋊Dic3D2011yescharacteristic
216Dic3⋊C4—21no—
217Dic3⋊C4—101no—
218Dic3⋊C4—101no—
219C2×C3⋊C8—21no—
220C23×C5D3×D411yescharacteristic
221C22×D5—32no—
222C22×D5—61no—
223C22×D5—61no—
224C22×D5—121no—
225C22×D5—121no—
226C5×Q8—121no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5—41no—
231C2×C4×C5—61no—
232C2×C4×C5—61no—
233C2×C4×C5C2×D1211yescharacteristic
234C2×C4×C5D3×D411yescharacteristic
235C2×Dic5—21no—
236C2×Dic5—21no—
237C2×Dic5—61no—
238C2×Dic5—121no—
239C2×Dic5—121no—
240C2×Dic5—121no—
241C2×Dic5—121no—
242C4×D5—241no—
243C4×D5—241no—
244Dic10—41no—
245Dic10—241no—
246C5×C8—121no—
247#168—41no—
248C22⋊Q8—31no—
249C22⋊Q8—51no—
250C22⋊Q8—301no—
251C22⋊Q8—301no—
252C22⋊Q8—301no—
253C22⋊Q8—301no—
254C22⋊Q8—301no—
255C2×C4⋊C4—151no—
256C2×C22⋊C4—151no—
257C2×C22⋊C4—301no—
258C2×C22⋊C4—301no—
259#106—301no—
260#106—301no—
261#103—301no—
262#103—301no—
263C22⋊C8—31no—
264C22⋊C8—51no—
265#95—301no—
266#95D3×D511yescharacteristic
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#44811yescharacteristic
270C2×C3×C5#45511yescharacteristic
271C2×C3×C5#45811yescharacteristic
272D15—42no—
273C23×C3D4×D511yescharacteristic
274C22×D3—52no—
275C22×D3—101no—
276C22×D3—101no—
277C22×D3—201no—
278C22×D3—201no—
279C3×Q8—201no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—101no—
285C2×C3×C4—101no—
286C2×C3×C4C2×D2011yescharacteristic
287C2×C3×C4D4×D511yescharacteristic
288C2×Dic3—21no—
289C2×Dic3—21no—
290C2×Dic3—101no—
291C2×Dic3—201no—
292C2×Dic3—201no—
293C2×Dic3—201no—
294C2×Dic3—201no—
295C4×D3—401no—
296C4×D3—401no—
297Dic6—41no—
298Dic6—401no—
299C3×C8—201no—
300C3⋊C8—41no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5#88211yescharacteristic
304C22×C5D3×SD1611yescharacteristic
305C22×C5#91811yescharacteristic
306C2×D5—62no—
307C2×D5—121no—
308C2×D5—121no—
309C2×D5—122no—
310C2×D5—241no—
311C4×C5—21no—
312C4×C5—21no—
313C4×C5—81no—
314C4×C5—121no—
315C4×C5—121no—
316Dic5—41no—
317Dic5—41no—
318Dic5—121no—
319Dic5—241no—
320C24—151no—
321C2×Q8—31no—
322C2×Q8—51no—
323C2×Q8—301no—
324C22×C4—21no—
325C22×C4—151no—
326C22×C4—301no—
327C22×C4—301no—
328C22×C4—301no—
329C22×C4C2×D3×D511yescharacteristic
330C2×C8—61no—
331C2×C8—101no—
332C4⋊C4—31no—
333C4⋊C4—51no—
334C4⋊C4—61no—
335C4⋊C4—101no—
336C4⋊C4—301no—
337C4⋊C4—301no—
338C4⋊C4—301no—
339C4⋊C4—301no—
340C4⋊C4—301no—
341C22⋊C4—61no—
342C22⋊C4—101no—
343C22⋊C4—301no—
344C22⋊C4—301no—
345C22⋊C4—301no—
346C22⋊C4—301no—
347C22⋊C4—602no—
348C3×C5#160811yescharacteristic, complemented, Hall
349C22×C3—21no—
350C22×C3—21no—
351C22×C3#402811yescharacteristic
352C22×C3D5×SD1611yescharacteristic
353C22×C3#406411yescharacteristic
354C2×D3—102no—
355C2×D3—201no—
356C2×D3—201no—
357C2×D3—202no—
358C2×D3—401no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—81no—
362C3×C4—201no—
363C3×C4—201no—
364Dic3—41no—
365Dic3—41no—
366Dic3—201no—
367Dic3—401no—
368C2×C5—21no—
369C2×C5—21no—
370C2×C5#474211yescharacteristic
371C2×C5#480611yescharacteristic
372C2×C5#482511yescharacteristic
373D5—122no—
374C23—152no—
375C23—301no—
376C23—301no—
377C23—601no—
378C23—601no—
379C23#679011yescharacteristic
380Q8—121no—
381Q8—201no—
382Q8—1201no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—61no—
388C2×C4—61no—
389C2×C4—101no—
390C2×C4—101no—
391C2×C4—301no—
392C2×C4—601no—
393C2×C4—601no—
394C2×C4—601no—
395C2×C4—601no—
396C2×C4—1201no—
397C2×C4—1201no—
398C2×C4D5×D1211yescharacteristic
399C2×C4D3×D2011yescharacteristic
400C8—121no—
401C8—201no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3#6503111yescharacteristic
405C2×C3#6509511yescharacteristic
406C2×C3#6511411yescharacteristic
407D3—202no—
408C5#6832011yescharacteristic, complemented, Sylow
409C22—21no—
410C22—21no—
411C22—302no—
412C22—602no—
413C22—601no—
414C22—601no—
415C22—1201no—
416C22#9147611yescharacteristic
417C22#9148711yescharacteristic
418C22#9151211yescharacteristic
419C4—21no—
420C4—21no—
421C4—81no—
422C4—121no—
423C4—121no—
424C4—201no—
425C4—201no—
426C4—601no—
427C4—1201no—
428C3#1059911311yescharacteristic, complemented, Sylow
429C2—21no—
430C2—21no—
431C2—602no—
432C2#1174711911yescharacteristic
433C2#1174713611yescharacteristic
434C2#1174749711yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5#120
prime radicalC23×D15D4
hypercenter#95D3×D5
hypocenterC3×C5#1608
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
3. #11748447C2semidirect
4. #11748445C2semidirect
5. C5×#4452C2semidirect
6. C3×#64672C2semidirect
35. #64672D3semidirect
70. #4452D5semidirect
348. C3×C5#1608semidirect
408. C5#68320semidirect
428. C3#10599113semidirect

Maximal subgroups

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

subgroupindex
#117544842
#117507752
#117484472
#117484452
C5×#44522
C3×#646722
#117459502
#105991133
#683205