Finite Group Databasebeta

← #14288040

Subgroups — #14288040

Order 1920.

488 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 83 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#11756274C211yesmaximal, characteristic
2C3×C5×#395C211yesmaximal, characteristic, complemented
3#11751329C211yesmaximal, characteristic, complemented
4#11751328C211yesmaximal, characteristic
5#11746349C211yesmaximal, characteristic, complemented
6#11746273C211yesmaximal, characteristic, complemented
7#11746272C211yesmaximal, characteristic
8#10600498—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C2×C3×C5×C4⋊C4—21no—
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×#6718—21no—
13C2×#6717—21no—
14#91819C2211yescharacteristic
15#91818—21no—
16C4×#1220—21no—
17#91813C2211yescharacteristic
18#91787—21no—
19#91785—21no—
20#91783—21no—
21#91778—21no—
22C3×C5×#95—21no—
23C3×C5×#95C2211yescharacteristic
24#91119—21no—
25#91119—21no—
26#91114C2211yescharacteristic
27#91114C2211yescharacteristic
28#69705—51nomaximal, Hall
29#65849—31no—
30C5×#395D311yescharacteristic, complemented
31#65517—31no—
32#65516—31no—
33#64748—31no—
34#64672—31no—
35#64671—31no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—42no—
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5D411yescharacteristic
42C22×C3×C4×C5D411yescharacteristic
43C22×C3×C4×C5C2311yescharacteristic
44C2×#1220—21no—
45C2×D60D411yescharacteristic
46C2×C4×D15—21no—
47C2×Dic30D411yescharacteristic
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—42no—
51#6719—21no—
52#6718—42no—
53#6717—42no—
54#6714—21no—
55#6714—21no—
56#6714—21no—
57#6714—21no—
58C4⋊Dic15D411yescharacteristic
59C4⋊Dic15D411yescharacteristic
60#6712—21no—
61#6712—21no—
62#6712—21no—
63#6712—21no—
64C4×Dic15—21no—
65C2×C3⋊#168—21no—
66C2×C3⋊#168—21no—
67#5515—51no—
68C3×#395D511yescharacteristic, complemented
69#5228—51no—
70#5227—51no—
71#4528—51no—
72#4452—51no—
73#4451—51no—
74C22×C5×Q8C2×D311yescharacteristic
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4C2×D311yescharacteristic
77C2×#689—61no—
78C2×#688—61no—
79#4076—31no—
80#4075—61no—
81C4×C22⋊D5—61no—
82#4070—31no—
83#4044—61no—
84#4042—61no—
85#4040—61no—
86#4035—61no—
87C5×#95—21no—
88C5×#95C2×D311yescharacteristic
89#3967—61no—
90#3967—61no—
91C22⋊#168—31no—
92C22⋊#168—31no—
93#1603—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—21no—
96C3×C5×Q8—22no—
97C3×C5×Q8—22no—
98C3×C5×Q8—41no—
99C3×C5×Q8—41no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—22no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114#1220—41no—
115#1220—41no—
116C2×Dic15—21no—
117C2×Dic15—21no—
118C2×Dic15—21no—
119D60—41no—
120C4×D15—81no—
121Dic30—41no—
122C3⋊#168—41no—
123C3⋊#168—41no—
124C22×C3×Q8C2×D511yescharacteristic
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4C2×D511yescharacteristic
127C2×#216—101no—
128C2×#215—101no—
129#930—51no—
130#929—101no—
131C4×#67—101no—
132#924—51no—
133#898—101no—
134#896—101no—
135#894—101no—
136#889—101no—
137C3×#95—21no—
138C3×#95C2×D511yescharacteristic
139#835—101no—
140#835—101no—
141#830—51no—
142#830—51no—
143C2×C5×Q8—21no—
144C2×C5×Q8—21no—
145C2×C5×Q8—42no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5#6711yescharacteristic
149C22×C4×C5#6711yescharacteristic
150C22×C4×C5C22×D311yescharacteristic
151C2×C22⋊D5—61no—
152C2×D20—31no—
153C2×C4×D5—61no—
154C2×Dic10—31no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4—21no—
157C5×C4⋊C4—42no—
158C22⋊Dic5—61no—
159#689—122no—
160#688—122no—
161#685—61no—
162#685—61no—
163#685—61no—
164#685—61no—
165C4⋊Dic5—31no—
166C4⋊Dic5—31no—
167#683—61no—
168#683—61no—
169#683—61no—
170#683—61no—
171C4×Dic5—61no—
172C2×#168—61no—
173C2×#168—61no—
174#539—151no—
175#451—151no—
176#448—151no—
177#395D1511yescharacteristic, complemented
178#328—151no—
179#327—151no—
180#324—151no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5#12011yescharacteristic
184C22×C3×C5#13511yescharacteristic
185C22×C3×C5#13711yescharacteristic
186C2×D15—41no—
187C2×D15—41no—
188C2×D15—41no—
189C3×C4×C5—21no—
190C3×C4×C5—21no—
191C3×C4×C5—42no—
192C3×C4×C5—41no—
193C3×C4×C5—41no—
194C3×C4×C5—42no—
195Dic15—41no—
196Dic15—41no—
197Dic15—41no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—42no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4C22⋊D511yescharacteristic
204C22×C3×C4C22⋊D511yescharacteristic
205C22×C3×C4C22×D511yescharacteristic
206C2×#67—101no—
207C2×D12—51no—
208C2×C4×D3—101no—
209C2×Dic6—51no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—42no—
213#217—101no—
214#216—202no—
215#215—202no—
216(C2×D3)⋊C4—101no—
217(C2×D3)⋊C4—101no—
218(C2×D3)⋊C4—101no—
219(C2×D3)⋊C4—101no—
220C4⋊Dic3—51no—
221C4⋊Dic3—51no—
222Dic3⋊C4—101no—
223Dic3⋊C4—101no—
224Dic3⋊C4—101no—
225Dic3⋊C4—101no—
226C4×Dic3—101no—
227C2×C3⋊C8—101no—
228C2×C3⋊C8—101no—
229C23×C5C2×#6711yescharacteristic
230C22×D5—61no—
231C5×Q8—22no—
232C5×Q8—22no—
233C5×Q8—41no—
234C5×Q8—41no—
235C2×C4×C5—22no—
236C2×C4×C5—22no—
237C2×C4×C5—21no—
238C2×C4×C5—21no—
239C2×C4×C5—21no—
240C2×C4×C5—21no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5—41no—
245C2×C4×C5—41no—
246C2×C4×C5—41no—
247C2×C4×C5D3×D411yescharacteristic
248C2×C4×C5D3×D411yescharacteristic
249C22⋊D5—121no—
250C22⋊D5—121no—
251C2×Dic5—61no—
252C2×Dic5—61no—
253C2×Dic5—61no—
254D20—121no—
255C4×D5—241no—
256Dic10—121no—
257#168—121no—
258#168—121no—
259C22×Q8C2×D1511yescharacteristic
260C2×Q16—301no—
261C2×SD16—301no—
262#126—301no—
263#125—301no—
264#123—301no—
265#123—301no—
266C22⋊Q8—151no—
267C22⋊Q8—301no—
268#121—151no—
269C4×D4—301no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4C2×D1511yescharacteristic
272#103—301no—
273#103—301no—
274C22⋊C8—151no—
275C22⋊C8—151no—
276#95—21no—
277#95C2×D1511yescharacteristic
278C2×C3×C5—21no—
279C2×C3×C5—21no—
280C2×C3×C5#45211yescharacteristic
281C2×C3×C5#45611yescharacteristic
282C2×C3×C5B(4,𝔽2)11yescharacteristic
283D15—81no—
284C23×C3C2×C22⋊D511yescharacteristic
285C22×D3—101no—
286C3×Q8—22no—
287C3×Q8—22no—
288C3×Q8—41no—
289C3×Q8—41no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4D4×D511yescharacteristic
303C2×C3×C4D4×D511yescharacteristic
304#67—201no—
305#67—201no—
306C2×Dic3—101no—
307C2×Dic3—101no—
308C2×Dic3—101no—
309D12—201no—
310C4×D3—401no—
311Dic6—201no—
312C3⋊C8—201no—
313C3⋊C8—201no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5#93711yescharacteristic
317C22×C5#94211yescharacteristic
318C22×C5#95011yescharacteristic
319C2×D5—121no—
320C2×D5—121no—
321C2×D5—121no—
322C4×C5—21no—
323C4×C5—21no—
324C4×C5—42no—
325C4×C5—41no—
326C4×C5—42no—
327C4×C5—41no—
328Dic5—121no—
329Dic5—121no—
330Dic5—121no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—42no—
334C2×Q8—151no—
335C2×D4—151no—
336C2×D4—301no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—301no—
340C22×C4#122011yescharacteristic
341C22×C4#122011yescharacteristic
342C22×C4C22×D1511yescharacteristic
343Q16—602no—
344SD16—602no—
345C2×C8—301no—
346C2×C8—301no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—42no—
350C4⋊C4—151no—
351C4⋊C4—151no—
352C4⋊C4—301no—
353C4⋊C4—301no—
354C4⋊C4—301no—
355C4⋊C4—301no—
356C22⋊C4—301no—
357C22⋊C4—301no—
358C22⋊C4—301no—
359C22⋊C4—301no—
360C22⋊C4—301no—
361C42—301no—
362C3×C5#160311yescharacteristic, complemented, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3#408311yescharacteristic
366C22×C3#408811yescharacteristic
367C22×C3#409611yescharacteristic
368C2×D3—201no—
369C2×D3—201no—
370C2×D3—201no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—42no—
374C3×C4—41no—
375C3×C4—42no—
376C3×C4—41no—
377Dic3—201no—
378Dic3—201no—
379Dic3—201no—
380C2×C5—21no—
381C2×C5—21no—
382C2×C5#503211yescharacteristic
383C2×C5#504711yescharacteristic
384C2×C5#509511yescharacteristic
385D5—241no—
386C23—301no—
387C23C2×#122011yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—41no—
391Q8—41no—
392Q8—601no—
393D4—601no—
394D4—601no—
395D4—601no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—301no—
409C2×C4—301no—
410C2×C4—301no—
411C2×C4—1201no—
412C2×C4D4×D1511yescharacteristic
413C2×C4D4×D1511yescharacteristic
414C8—601no—
415C8—601no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3#6532111yescharacteristic
419C2×C3#6533611yescharacteristic
420C2×C3#6538411yescharacteristic
421D3—401no—
422C5#6970511yescharacteristic, complemented, Sylow
423C22—21no—
424C22—21no—
425C22—601no—
426C22—601no—
427C22—601no—
428C22#9182611yescharacteristic
429C22#9183111yescharacteristic
430C22#9183911yescharacteristic
431C4—21no—
432C4—21no—
433C4—42no—
434C4—42no—
435C4—41no—
436C4—41no—
437C4—601no—
438C4—601no—
439C4—601no—
440C3#1060049811yescharacteristic, complemented, Sylow
441C2—21no—
442C2—21no—
443C2—1201no—
444C2#1175113311yescharacteristic
445C2#1175114811yescharacteristic
446C2#1175119611yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#395C2
socleC22×C3×C5#120
prime radical#91819C22
hypercenter#395D15
hypocenterC3×C5#1603
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C3×C5×#395C2semidirect
3. #11751329C2semidirect
5. #11746349C2semidirect
6. #11746273C2semidirect
30. C5×#395D3semidirect
68. C3×#395D5semidirect
177. #395D15semidirect
362. C3×C5#1603semidirect
422. C5#69705semidirect
440. C3#10600498semidirect

Maximal subgroups

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

subgroupindex
#117562742
C3×C5×#3952
#117513292
#117513282
#117463492
#117462732
#117462722
#106004983
#697055