Finite Group Databasebeta

← #14288293

Subgroups — #14288293

Order 1920.

456 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 82 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#11754468C211yesmaximal, characteristic
2#11751072C211yesmaximal, characteristic, complemented
3C5×#4971C211yesmaximal, characteristic, complemented
4C3×#65282C211yesmaximal, characteristic
5#11745964C211yesmaximal, characteristic, complemented
6#11745962C211yesmaximal, characteristic, complemented
7#11745948C211yesmaximal, characteristic
8#10601965—31nomaximal, Hall
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10#91813C2211yescharacteristic
11C5×#924C2211yescharacteristic
12C2×C3×#685—21no—
13C2×C3×#685C2211yescharacteristic
14#91574—21no—
15D5×#217—21no—
16#91431—21no—
17#91430—21no—
18#91422—21no—
19#91421—21no—
20#91114C2211yescharacteristic
21#91094—21no—
22#91092—21no—
23C5×#830C2211yescharacteristic
24C5×#810—21no—
25C5×#808—21no—
26C3×#3963—21no—
27C3×#3963C2211yescharacteristic
28#69710—51nomaximal, Hall
29#65968—31no—
30C5×#483—31no—
31#65282D311yescharacteristic
32#65260—31no—
33#64758—31no—
34#64688—31no—
35#64687—31no—
36C23×C3×D5D411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×Dic30D411yescharacteristic
40C2×C5×Dic6D411yescharacteristic
41C22×C3×Dic5—21no—
42C22×C3×Dic5D411yescharacteristic
43C2×#1204—21no—
44C2×D5×Dic3—21no—
45C2×D5×Dic3—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48#6719—21no—
49C4⋊Dic15D411yescharacteristic
50#6712—21no—
51C2×C3⋊#168—21no—
52C5×#217—21no—
53C5×C4⋊Dic3D411yescharacteristic
54C5×Dic3⋊C4—21no—
55C2×C5×C3⋊C8—21no—
56C3×#685—21no—
57C3×#685—21no—
58C3×#685—42no—
59Dic3⋊Dic5—21no—
60#6669—21no—
61#6668—21no—
62#6665—21no—
63#6665—21no—
64#5483—51no—
65C3×#397—51no—
66#4971—51no—
67#4971D511yescharacteristic, complemented
68#4525—51no—
69#4452—51no—
70#4452—51no—
71C5×C22⋊Q8—31no—
72C2×C5×C4⋊C4C2×D311yescharacteristic
73#4092—61no—
74C2×#685—21no—
75C2×#685C2×D311yescharacteristic
76#4070—31no—
77#4043—61no—
78#4042—61no—
79#4042—61no—
80D5×C22⋊C4—61no—
81#4024—61no—
82C5×#106—61no—
83C5×#103—61no—
84C5×C22⋊C8—31no—
85#3963—21no—
86#3963C2×D311yescharacteristic
87C22⋊#168—31no—
88#3942—61no—
89#3940—61no—
90#1608—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×C3×D5—21no—
93C22×C3×D5—21no—
94C22×C3×D5—41no—
95C22×C3×D5—41no—
96C22×C3×D5SD1612yes—
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—21no—
105Dic30—41no—
106C2×C5×Dic3—21no—
107C2×C5×Dic3—21no—
108C5×Dic6—41no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—41no—
111C2×C3×Dic5—41no—
112C2×C3×Dic5—41no—
113C2×C3×Dic5—41no—
114#1204—81no—
115D5×Dic3—81no—
116D5×Dic3—81no—
117C3⋊#168—41no—
118C5×C3⋊C8—41no—
119C2×C3×C4⋊C4C2×D511yescharacteristic
120C2×C3×C22⋊C4—51no—
121C2×C3×C22⋊C4—101no—
122C2×#217—101no—
123#924—51no—
124#924—101no—
125#924C2×D511yescharacteristic
126#878—101no—
127#878—101no—
128#878—101no—
129#878—101no—
130C3×#95—51no—
131C3×#95—101no—
132#830—51no—
133#830C2×D511yescharacteristic
134#810—21no—
135#810—101no—
136#808—21no—
137#808—101no—
138C23×D5#6711yescharacteristic
139C2×C5×Q8—31no—
140C22×C4×C5—21no—
141C22×C4×C5C22×D311yescharacteristic
142C22×Dic5—21no—
143C22×Dic5#6711yescharacteristic
144C2×C4×D5—61no—
145C2×C4×D5—61no—
146C2×Dic10—31no—
147C2×Dic10—61no—
148C2×C5×C8—61no—
149C5×C4⋊C4—21no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4—31no—
152C5×C4⋊C4—61no—
153C5×C22⋊C4—61no—
154C22⋊Dic5—61no—
155#685—21no—
156#685—21no—
157#685—42no—
158#685—61no—
159#685—61no—
160C4⋊Dic5—31no—
161C4⋊Dic5—61no—
162#683—61no—
163#683—61no—
164#683—61no—
165C2×#168—61no—
166#543—151no—
167#483—31no—
168#483—151no—
169#397—51no—
170#328—151no—
171#328—151no—
172#323—151no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5#12011yescharacteristic
176C22×C3×C5C2×SD1611yescharacteristic
177C22×C3×C5#13711yescharacteristic
178C2×C3×D5—22no—
179C2×C3×D5—41no—
180C2×C3×D5—41no—
181C2×C3×D5—42no—
182C2×C3×D5—81no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5—81no—
186Dic15—41no—
187Dic15—41no—
188C3×Dic5—41no—
189C3×Dic5—81no—
190C5×Dic3—41no—
191C5×Dic3—41no—
192C24×C3—51no—
193C22×C3×C4—21no—
194C22×C3×C4—51no—
195C22×C3×C4—101no—
196C22×C3×C4C22×D511yescharacteristic
197C22×Dic3—101no—
198C22×Dic3—101no—
199C2×Dic6—51no—
200C2×Dic6—101no—
201C2×Dic6C22⋊D511yescharacteristic
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C22⋊C4—101no—
205C3×C22⋊C4—101no—
206C3×C22⋊C4—202no—
207#217—21no—
208#217—101no—
209#217—101no—
210#217—101no—
211C4⋊Dic3—51no—
212C4⋊Dic3—101no—
213C4⋊Dic3C22⋊D511yescharacteristic
214Dic3⋊C4—21no—
215Dic3⋊C4—101no—
216Dic3⋊C4—101no—
217Dic3⋊C4—101no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—101no—
220C23×C5C2×#6711yescharacteristic
221C22×D5—21no—
222C22×D5—21no—
223C22×D5—41no—
224C22×D5—41no—
225C22×D5#21412yes—
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×C5D3×D411yescharacteristic
234C2×C4×C5D3×D411yescharacteristic
235C2×Dic5—21no—
236C2×Dic5—41no—
237C2×Dic5—41no—
238C2×Dic5—41no—
239C2×Dic5—41no—
240C2×Dic5—61no—
241C2×Dic5—61no—
242C4×D5—241no—
243C4×D5—241no—
244Dic10—121no—
245Dic10—241no—
246C5×C8—121no—
247#168—121no—
248C22⋊Q8—31no—
249C22⋊Q8—151no—
250C22⋊Q8—301no—
251C22⋊Q8—301no—
252C22⋊Q8—301no—
253C22⋊Q8—301no—
254C22⋊Q8—301no—
255C2×C4⋊C4D3×D511yescharacteristic
256C2×C22⋊C4—51no—
257C2×C22⋊C4—101no—
258C2×C22⋊C4—301no—
259#106—61no—
260#106—301no—
261#103—61no—
262#103—301no—
263C22⋊C8—31no—
264C22⋊C8—151no—
265#95—51no—
266#95—101no—
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#44811yescharacteristic
270C2×C3×C5#45511yescharacteristic
271C2×C3×C5#45811yescharacteristic
272C3×D5—42no—
273C23×C3—52no—
274C23×C3—101no—
275C23×C3—101no—
276C23×C3—201no—
277C23×C3—201no—
278C23×C3D4×D511yescharacteristic
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—101no—
284C2×C3×C4—201no—
285C2×C3×C4—201no—
286C2×C3×C4—201no—
287C2×C3×C4—201no—
288C2×C3×C4D4×D511yescharacteristic
289C2×C3×C4C2×C22⋊D511yescharacteristic
290C2×Dic3—21no—
291C2×Dic3—21no—
292C2×Dic3—101no—
293C2×Dic3—101no—
294C2×Dic3—401no—
295C2×Dic3—401no—
296Dic6—41no—
297Dic6—201no—
298Dic6—401no—
299C3⋊C8—41no—
300C3⋊C8—201no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5C2×#21411yescharacteristic
304C22×C5#93711yescharacteristic
305C22×C5#95111yescharacteristic
306C2×D5—22no—
307C2×D5—41no—
308C2×D5—41no—
309C2×D5—42no—
310C2×D5—81no—
311C4×C5—21no—
312C4×C5—21no—
313C4×C5—81no—
314C4×C5—121no—
315C4×C5—121no—
316Dic5—41no—
317Dic5—81no—
318Dic5—121no—
319Dic5—121no—
320C24—51no—
321C2×Q8—31no—
322C2×Q8—151no—
323C2×Q8—301no—
324C22×C4—21no—
325C22×C4—51no—
326C22×C4—101no—
327C22×C4—301no—
328C22×C4—301no—
329C22×C4C2×D3×D511yescharacteristic
330C2×C8—61no—
331C2×C8—301no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—31no—
335C4⋊C4—61no—
336C4⋊C4—151no—
337C4⋊C4—301no—
338C4⋊C4—301no—
339C4⋊C4—301no—
340C4⋊C4—301no—
341C22⋊C4—61no—
342C22⋊C4—101no—
343C22⋊C4—101no—
344C22⋊C4—202no—
345C22⋊C4—301no—
346C22⋊C4—301no—
347C22⋊C4—301no—
348C3×C5#160811yescharacteristic, complemented, Hall
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—102no—
352C22×C3—202no—
353C22×C3—201no—
354C22×C3—201no—
355C22×C3—401no—
356C22×C3D5×SD1611yescharacteristic
357C22×C3#406111yescharacteristic
358C22×C3#408311yescharacteristic
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—81no—
362C3×C4—201no—
363C3×C4—401no—
364Dic3—41no—
365Dic3—41no—
366Dic3—201no—
367Dic3—201no—
368C2×C5—21no—
369C2×C5—21no—
370C2×C5#504011yescharacteristic
371C2×C5#505311yescharacteristic
372C2×C5#506111yescharacteristic
373D5—42no—
374C23—52no—
375C23—101no—
376C23—101no—
377C23—201no—
378C23—201no—
379C23D5×#6711yescharacteristic
380Q8—121no—
381Q8—601no—
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—201no—
391C2×C4—201no—
392C2×C4—201no—
393C2×C4—201no—
394C2×C4—301no—
395C2×C4—301no—
396C2×C4—1201no—
397C2×C4—1201no—
398C2×C4D3×C22⋊D511yescharacteristic
399C2×C4#679011yescharacteristic
400C8—121no—
401C8—601no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—202no—
405C2×C3#6534211yescharacteristic
406C2×C3#6545911yescharacteristic
407C2×C3#6549111yescharacteristic
408C5#6971011yescharacteristic, complemented, Sylow
409C22—21no—
410C22—21no—
411C22—102no—
412C22—202no—
413C22—201no—
414C22—201no—
415C22—401no—
416C22D5×#21411yescharacteristic
417C22#9148411yescharacteristic
418C22#9157711yescharacteristic
419C4—21no—
420C4—21no—
421C4—81no—
422C4—121no—
423C4—121no—
424C4—201no—
425C4—401no—
426C4—601no—
427C4—601no—
428C3#1060196511yescharacteristic, complemented, Sylow
429C2—21no—
430C2—21no—
431C2—202no—
432C2#1174893911yescharacteristic
433C2#1174915411yescharacteristic
434C2#1174940911yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC23×C3×D5D4
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1608
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11751072C2semidirect
3. C5×#4971C2semidirect
5. #11745964C2semidirect
6. #11745962C2semidirect
67. #4971D5semidirect
348. C3×C5#1608semidirect
408. C5#69710semidirect
428. C3#10601965semidirect

Maximal subgroups

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

subgroupindex
#117544682
#117510722
C5×#49712
C3×#652822
#117459642
#117459622
#117459482
#106019653
#697105