Finite Group Databasebeta

← #14288342

Subgroups — #14288342

Order 1920.

432 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 78 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#11754471C211yesmaximal, characteristic
2#11751084C211yesmaximal, characteristic, complemented
3C5×#4971C211yesmaximal, characteristic, complemented
4C3×#65256C211yesmaximal, characteristic
5#11745963C211yesmaximal, characteristic, complemented
6#11745955C211yesmaximal, characteristic
7#11745953C211yesmaximal, characteristic, complemented
8#10601967—31nomaximal, Hall
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10C2×#6712—21no—
11C2×#6712C2211yescharacteristic
12C5×#924C2211yescharacteristic
13C3×#4076C2211yescharacteristic
14#91559—21no—
15#91537—21no—
16#91421—21no—
17#91407—21no—
18#91361—21no—
19#91346—21no—
20#91115—21no—
21#91115C2211yescharacteristic
22C5×#830C2211yescharacteristic
23C5×#810—21no—
24C5×#808—21no—
25C3×C22⋊#168C2211yescharacteristic
26C3×#3941—21no—
27C3×#3939—21no—
28#71166—51nomaximal, Hall
29#65979—31no—
30C5×#483—31no—
31#65269—31no—
32#65256D311yescharacteristic
33#64758—31no—
34#64690—31no—
35#64689—31no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×Dic15D411yescharacteristic
40C22×Dic15D411yescharacteristic
41C2×C5×Dic6D411yescharacteristic
42C2×C3×C22⋊D5—21no—
43C2×C3×D20D411yescharacteristic
44C2×D5×Dic3—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47#6712—21no—
48#6712—21no—
49#6712—42no—
50C5×#217—21no—
51C5×C4⋊Dic3D411yescharacteristic
52C5×Dic3⋊C4—21no—
53C2×C5×C3⋊C8—21no—
54C3×#685—21no—
55C3×C4⋊Dic5D411yescharacteristic
56C2×C3×#168—21no—
57Dic3⋊Dic5—21no—
58Dic3⋊Dic5—21no—
59#6668—21no—
60#6665—21no—
61#6665—21no—
62#6665—21no—
63Dic3×Dic5—21no—
64#5602—51no—
65C3×#480—51no—
66#4983—51no—
67#4971D511yescharacteristic, complemented
68#4537—51no—
69#4469—51no—
70#4467—51no—
71C5×C22⋊Q8—31no—
72C2×C5×C4⋊C4C2×D311yescharacteristic
73#4092—61no—
74#4076C2×D311yescharacteristic
75C2×#683—31no—
76C2×#683—61no—
77#4044—61no—
78#4040—61no—
79#4036—61no—
80#4032—61no—
81#4027—61no—
82C5×#106—61no—
83C5×#103—61no—
84C5×C22⋊C8—31no—
85#3963—31no—
86#3963—61no—
87C22⋊#168C2×D311yescharacteristic
88#3941—21no—
89#3939—21no—
90#1609—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×C3×D5—21no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×Dic15—22no—
100C2×Dic15—21no—
101C2×Dic15—21no—
102C2×Dic15—21no—
103C2×Dic15—21no—
104C2×Dic15—41no—
105C2×Dic15—41no—
106C2×Dic15—41no—
107C2×C5×Dic3—21no—
108C2×C5×Dic3—21no—
109C5×Dic6—41no—
110C3×C22⋊D5—41no—
111C3×C22⋊D5—41no—
112C2×C3×Dic5—21no—
113C3×D20—41no—
114D5×Dic3—81no—
115C3×#168—41no—
116C5×C3⋊C8—41no—
117C3×#121—51no—
118C2×C3×C4⋊C4C2×D511yescharacteristic
119#935—101no—
120#935—101no—
121D4×Dic3—101no—
122#924C2×D511yescharacteristic
123C2×Dic3⋊C4—51no—
124C2×Dic3⋊C4—101no—
125#889—101no—
126#879—101no—
127#878—101no—
128C3×#107—101no—
129C3×#102—101no—
130C3×C22⋊C8—51no—
131C3⋊#95—51no—
132C3⋊#95—101no—
133#830C2×D511yescharacteristic
134#810—21no—
135#808—21no—
136C2×C5×Q8—31no—
137C22×C4×C5—21no—
138C22×C4×C5C22×D311yescharacteristic
139C2×C22⋊D5—21no—
140C22×Dic5—31no—
141C22×Dic5—31no—
142C22×Dic5—61no—
143C2×D20#6711yescharacteristic
144C2×C4×D5—61no—
145C2×C5×C8—61no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4—21no—
148C5×C4⋊C4—31no—
149C5×C4⋊C4—61no—
150C5×C22⋊C4—61no—
151#685—21no—
152#685—61no—
153#685—61no—
154#685—61no—
155C4⋊Dic5—61no—
156C4⋊Dic5—61no—
157C4⋊Dic5#6711yescharacteristic
158#683—61no—
159#683—61no—
160#683—61no—
161#683—122no—
162C4×Dic5—61no—
163C2×#168—21no—
164#539—151no—
165#483—31no—
166#480—51no—
167#398—151no—
168#328—151no—
169#327—151no—
170#324—151no—
171C22×C3×C5—21no—
172C22×C3×C5—21no—
173C22×C3×C5#12011yescharacteristic
174C22×C3×C5#13511yescharacteristic
175C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
176C2×C3×D5—41no—
177C2×C3×D5—41no—
178C2×C3×D5—41no—
179C3×C4×C5—21no—
180C3×C4×C5—21no—
181C3×C4×C5—81no—
182Dic15—42no—
183Dic15—41no—
184Dic15—41no—
185C3×Dic5—41no—
186C5×Dic3—41no—
187C5×Dic3—41no—
188C2×C3×D4—51no—
189C2×C3×D4—101no—
190C22×C3×C4—21no—
191C22×C3×C4C22×D511yescharacteristic
192C22×Dic3—51no—
193C22×Dic3—51no—
194C22×Dic3—101no—
195C22×Dic3—101no—
196C2×Dic6C22⋊D511yescharacteristic
197C2×C3×C8—101no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—51no—
201C3×C22⋊C4—101no—
202#217—21no—
203#217—101no—
204#217—101no—
205#217—101no—
206C4⋊Dic3—101no—
207C4⋊Dic3C22⋊D511yescharacteristic
208Dic3⋊C4—21no—
209Dic3⋊C4—101no—
210Dic3⋊C4—101no—
211Dic3⋊C4—101no—
212Dic3⋊C4—101no—
213Dic3⋊C4—202no—
214C4×Dic3—101no—
215C2×C3⋊C8—21no—
216C23×C5D3×D411yescharacteristic
217C22×D5—21no—
218C5×Q8—121no—
219C2×C4×C5—41no—
220C2×C4×C5—41no—
221C2×C4×C5—41no—
222C2×C4×C5—41no—
223C2×C4×C5—61no—
224C2×C4×C5—61no—
225C2×C4×C5D3×D411yescharacteristic
226C2×C4×C5C2×#6711yescharacteristic
227C22⋊D5—41no—
228C22⋊D5—41no—
229C2×Dic5—21no—
230C2×Dic5—62no—
231C2×Dic5—61no—
232C2×Dic5—61no—
233C2×Dic5—61no—
234C2×Dic5—61no—
235C2×Dic5—121no—
236C2×Dic5—121no—
237C2×Dic5—121no—
238D20—41no—
239C4×D5—241no—
240C5×C8—121no—
241#168—41no—
242#126—301no—
243#125—301no—
244#123—301no—
245#123—301no—
246C22⋊Q8—31no—
247C22⋊Q8—301no—
248#121—51no—
249C4×D4—301no—
250C2×C4⋊C4—151no—
251C2×C4⋊C4—301no—
252C2×C4⋊C4D3×D511yescharacteristic
253#107—101no—
254#106—61no—
255#103—61no—
256#102—101no—
257C22⋊C8—31no—
258C22⋊C8—51no—
259#95—151no—
260#95—301no—
261C2×C3×C5—21no—
262C2×C3×C5—21no—
263C2×C3×C5#44911yescharacteristic
264C2×C3×C5#45611yescharacteristic
265C2×C3×C5#45811yescharacteristic
266C3×D5—81no—
267C23×C3—101no—
268C23×C3D4×D511yescharacteristic
269C3×D4—201no—
270C3×D4—201no—
271C3×D4—201no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—101no—
277C2×C3×C4D4×D511yescharacteristic
278C2×C3×C4C2×C22⋊D511yescharacteristic
279C2×Dic3—21no—
280C2×Dic3—21no—
281C2×Dic3—102no—
282C2×Dic3—101no—
283C2×Dic3—101no—
284C2×Dic3—101no—
285C2×Dic3—101no—
286C2×Dic3—201no—
287C2×Dic3—201no—
288C2×Dic3—201no—
289C2×Dic3—401no—
290Dic6—41no—
291C3×C8—201no—
292C3⋊C8—41no—
293C22×C5—21no—
294C22×C5—21no—
295C22×C5#91111yescharacteristic
296C22×C5#91211yescharacteristic
297C22×C5#93711yescharacteristic
298C2×D5—41no—
299C2×D5—41no—
300C2×D5—41no—
301C4×C5—21no—
302C4×C5—21no—
303C4×C5—81no—
304C4×C5—121no—
305C4×C5—121no—
306Dic5—41no—
307Dic5—122no—
308Dic5—121no—
309Dic5—121no—
310C2×Q8—31no—
311C2×D4—51no—
312C2×D4—101no—
313C22×C4—21no—
314C22×C4—151no—
315C22×C4—151no—
316C22×C4—301no—
317C22×C4—301no—
318C22×C4C2×D3×D511yescharacteristic
319C2×C8—61no—
320C2×C8—101no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—31no—
324C4⋊C4—51no—
325C4⋊C4—61no—
326C4⋊C4—301no—
327C4⋊C4—301no—
328C4⋊C4—301no—
329C4⋊C4—301no—
330C4⋊C4—301no—
331C4⋊C4—602no—
332C22⋊C4—61no—
333C22⋊C4—101no—
334C22⋊C4—301no—
335C22⋊C4—301no—
336C22⋊C4—301no—
337C42—301no—
338C3×C5#160911yescharacteristic, complemented, Hall
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—201no—
342C22×C3—201no—
343C22×C3—201no—
344C22×C3#406011yescharacteristic
345C22×C3#406211yescharacteristic
346C22×C3#408311yescharacteristic
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—81no—
350C3×C4—201no—
351Dic3—41no—
352Dic3—41no—
353Dic3—202no—
354Dic3—201no—
355Dic3—201no—
356C2×C5—21no—
357C2×C5—21no—
358C2×C5#505311yescharacteristic
359C2×C5#515811yescharacteristic
360C2×C5#520511yescharacteristic
361D5—81no—
362C23—101no—
363C23#679011yescharacteristic
364Q8—121no—
365D4—201no—
366D4—201no—
367D4—201no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—61no—
373C2×C4—61no—
374C2×C4—101no—
375C2×C4—302no—
376C2×C4—301no—
377C2×C4—301no—
378C2×C4—301no—
379C2×C4—301no—
380C2×C4—601no—
381C2×C4—601no—
382C2×C4—601no—
383C2×C4—1201no—
384C2×C4D5×#6711yescharacteristic
385C2×C4D3×C22⋊D511yescharacteristic
386C8—121no—
387C8—201no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—401no—
391C2×C3#6534211yescharacteristic
392C2×C3#6546111yescharacteristic
393C2×C3#6549411yescharacteristic
394C5#7116611yescharacteristic, complemented, Sylow
395C22—21no—
396C22—21no—
397C22—201no—
398C22—201no—
399C22—201no—
400C22#9149711yescharacteristic
401C22#9149811yescharacteristic
402C22#9157711yescharacteristic
403C4—21no—
404C4—21no—
405C4—81no—
406C4—121no—
407C4—121no—
408C4—201no—
409C4—602no—
410C4—601no—
411C4—601no—
412C3#1060196711yescharacteristic, complemented, Sylow
413C2—21no—
414C2—21no—
415C2—401no—
416C2#1174893911yescharacteristic
417C2#1174915811yescharacteristic
418C2#1174941211yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC3×#4076C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1609
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. #11751084C2semidirect
3. C5×#4971C2semidirect
5. #11745963C2semidirect
7. #11745953C2semidirect
67. #4971D5semidirect
338. C3×C5#1609semidirect
394. C5#71166semidirect
412. C3#10601967semidirect

Maximal subgroups

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

subgroupindex
#117544712
#117510842
C5×#49712
C3×#652562
#117459632
#117459552
#117459532
#106019673
#711665