Finite Group Databasebeta

← #14288058

Subgroups — #14288058

Order 1920.

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

normal subgroups only

This group has 488 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#11754470C211yesmaximal, characteristic
2#11751329C211yesmaximal, characteristic, complemented
3C5×#5230C211yesmaximal, characteristic, complemented
4C3×#65516C211yesmaximal, characteristic
5#11745965C211yesmaximal, characteristic, complemented
6#11745954C211yesmaximal, characteristic
7#11745952C211yesmaximal, characteristic, complemented
8#10600498—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C2×#6718—21no—
11#91813C2211yescharacteristic
12C2×C5×Dic3⋊C4—21no—
13C2×C5×Dic3⋊C4C2211yescharacteristic
14C2×C3×#688—21no—
15C3×#4076C2211yescharacteristic
16Dic3×C22⋊D5—21no—
17#91536—21no—
18#91431—21no—
19#91407—21no—
20#91362—21no—
21#91339—21no—
22#91119—21no—
23#91114C2211yescharacteristic
24C5×C3⋊#95—21no—
25C5×C3⋊#95C2211yescharacteristic
26C3×#3967—21no—
27C3×C22⋊#168C2211yescharacteristic
28#70974—51nomaximal, Hall
29#65849—31no—
30C5×#395—31no—
31#65517—31no—
32#65516D311yescharacteristic
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×C5C2311yescharacteristic
41C2×Dic30D411yescharacteristic
42C22×C5×Dic3—21no—
43C22×C5×Dic3D411yescharacteristic
44C22×C5×Dic3D411yescharacteristic
45C2×C3×C22⋊D5—21no—
46C2×C3×D20D411yescharacteristic
47C2×D5×Dic3—21no—
48#6719—21no—
49#6718—42no—
50C4⋊Dic15D411yescharacteristic
51#6712—21no—
52C2×C3⋊#168—21no—
53C5×Dic3⋊C4—21no—
54C5×Dic3⋊C4—21no—
55C5×Dic3⋊C4—42no—
56C3×#688—42no—
57C3×#685—21no—
58C3×C4⋊Dic5D411yescharacteristic
59C2×C3×#168—21no—
60#6669—21no—
61#6669—21no—
62#6668—21no—
63#6665—21no—
64#6665—21no—
65#6665—21no—
66Dic3×Dic5—21no—
67#5602—51no—
68C3×#448—51no—
69#5230D511yescharacteristic, complemented
70#5228—51no—
71#4537—51no—
72#4469—51no—
73#4467—51no—
74C22×C5×Q8C2×D311yescharacteristic
75C2×C5×C4⋊C4—31no—
76C2×C5×C4⋊C4—61no—
77C2×#689—61no—
78C2×#688—21no—
79#4076C2×D311yescharacteristic
80#4075—61no—
81C4×C22⋊D5—61no—
82#4070—31no—
83#4044—61no—
84#4042—61no—
85#4040—61no—
86#4035—61no—
87C5×#95—31no—
88C5×#95—61no—
89#3967—21no—
90#3967—61no—
91C22⋊#168—31no—
92C22⋊#168C2×D311yescharacteristic
93#1603—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C3×D5—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—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×Dic15—21no—
107C2×Dic15—21no—
108Dic30—41no—
109C2×C5×Dic3—22no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—41no—
115C2×C5×Dic3—41no—
116C2×C5×Dic3—41no—
117C3×C22⋊D5—41no—
118C3×C22⋊D5—41no—
119C2×C3×Dic5—21no—
120C3×D20—41no—
121D5×Dic3—81no—
122C3⋊#168—41no—
123C3×#168—41no—
124C22×C3×Q8C2×D511yescharacteristic
125C2×C3×SD16—101no—
126C3×#121—51no—
127C2×#216—101no—
128#935—101no—
129#935—101no—
130D4×Dic3—101no—
131#924—51no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4C2×D511yescharacteristic
134#889—101no—
135#879—101no—
136#878—101no—
137C3×#103—101no—
138C3×C22⋊C8—51no—
139#835—101no—
140C3⋊#95—21no—
141C3⋊#95C2×D511yescharacteristic
142#830—51no—
143C2×C5×Q8—21no—
144C2×C5×Q8—21no—
145C2×C5×Q8—42no—
146C22×C4×C5—21no—
147C22×C4×C5—31no—
148C22×C4×C5—31no—
149C22×C4×C5—61no—
150C22×C4×C5C22×D311yescharacteristic
151C2×C22⋊D5—21no—
152C2×D20#6711yescharacteristic
153C2×C4×D5—61no—
154C2×Dic10—31no—
155C5×C4⋊C4—61no—
156C5×C4⋊C4—61no—
157C5×C4⋊C4—122no—
158C22⋊Dic5—61no—
159#689—122no—
160#688—42no—
161#685—21no—
162#685—61no—
163#685—61no—
164#685—61no—
165C4⋊Dic5—31no—
166C4⋊Dic5#6711yescharacteristic
167#683—61no—
168#683—61no—
169#683—61no—
170#683—61no—
171C4×Dic5—61no—
172C2×#168—21no—
173C2×#168—61no—
174#539—151no—
175#451—151no—
176#448—51no—
177#395—31no—
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×C3×D5—41no—
187C2×C3×D5—41no—
188C2×C3×D5—41no—
189C3×C4×C5—21no—
190C3×C4×C5—21no—
191C3×C4×C5—42no—
192Dic15—41no—
193Dic15—41no—
194C3×Dic5—41no—
195C5×Dic3—42no—
196C5×Dic3—41no—
197C5×Dic3—41no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—42no—
201C2×C3×D4—51no—
202C2×C3×D4—101no—
203C22×C3×C4—21no—
204C22×C3×C4C22×D511yescharacteristic
205C22×Dic3—21no—
206C22×Dic3—101no—
207C22×Dic3C22⋊D511yescharacteristic
208C22×Dic3C22⋊D511yescharacteristic
209C2×Dic6—51no—
210C3×SD16—202no—
211C2×C3×C8—101no—
212C3×C4⋊C4—51no—
213C3×C22⋊C4—101no—
214#217—101no—
215#217—101no—
216#217—101no—
217#217—101no—
218#216—202no—
219C4⋊Dic3—51no—
220C4⋊Dic3—101no—
221Dic3⋊C4—21no—
222Dic3⋊C4—21no—
223Dic3⋊C4—42no—
224Dic3⋊C4—101no—
225Dic3⋊C4—101no—
226Dic3⋊C4—101no—
227C4×Dic3—101no—
228C2×C3⋊C8—101no—
229C23×C5D3×D411yescharacteristic
230C22×D5—21no—
231C5×Q8—22no—
232C5×Q8—22no—
233C5×Q8—41no—
234C5×Q8—41no—
235C2×C4×C5—22no—
236C2×C4×C5—41no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5—62no—
240C2×C4×C5—61no—
241C2×C4×C5—61no—
242C2×C4×C5—61no—
243C2×C4×C5—61no—
244C2×C4×C5—121no—
245C2×C4×C5—121no—
246C2×C4×C5—121no—
247C2×C4×C5D3×D411yescharacteristic
248C2×C4×C5C2×#6711yescharacteristic
249C22⋊D5—41no—
250C22⋊D5—41no—
251C2×Dic5—21no—
252C2×Dic5—61no—
253C2×Dic5—61no—
254D20—41no—
255C4×D5—241no—
256Dic10—121no—
257#168—41no—
258#168—121no—
259C22×Q8D3×D511yescharacteristic
260C2×Q16—301no—
261C2×SD16—101no—
262#126—301no—
263#125—301no—
264#123—301no—
265#123—301no—
266C22⋊Q8—151no—
267C22⋊Q8—301no—
268#121—51no—
269C4×D4—301no—
270C2×C4⋊C4—31no—
271C2×C4⋊C4—61no—
272#103—101no—
273#103—301no—
274C22⋊C8—51no—
275C22⋊C8—151no—
276#95—31no—
277#95—61no—
278C2×C3×C5—21no—
279C2×C3×C5—21no—
280C2×C3×C5#45211yescharacteristic
281C2×C3×C5#45611yescharacteristic
282C2×C3×C5B(4,𝔽2)11yescharacteristic
283C3×D5—81no—
284C23×C3—101no—
285C23×C3C2×C22⋊D511yescharacteristic
286C3×Q8—22no—
287C3×Q8—22no—
288C3×Q8—41no—
289C3×Q8—41no—
290C3×D4—201no—
291C3×D4—201no—
292C3×D4—201no—
293C2×C3×C4—22no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—101no—
298C2×C3×C4D4×D511yescharacteristic
299C2×C3×C4D4×D511yescharacteristic
300C2×Dic3—22no—
301C2×Dic3—21no—
302C2×Dic3—21no—
303C2×Dic3—21no—
304C2×Dic3—21no—
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—41no—
308C2×Dic3—101no—
309C2×Dic3—101no—
310C2×Dic3—401no—
311Dic6—201no—
312C3×C8—201no—
313C3⋊C8—201no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5#91511yescharacteristic
317C22×C5#91611yescharacteristic
318C22×C5#93711yescharacteristic
319C2×D5—41no—
320C2×D5—41no—
321C2×D5—41no—
322C4×C5—21no—
323C4×C5—21no—
324C4×C5—42no—
325C4×C5—122no—
326C4×C5—121no—
327C4×C5—121no—
328Dic5—41no—
329Dic5—121no—
330Dic5—121no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—42no—
334C2×Q8—151no—
335C2×D4—51no—
336C2×D4—101no—
337C22×C4—21no—
338C22×C4—31no—
339C22×C4—31no—
340C22×C4—61no—
341C22×C4—301no—
342C22×C4C2×D3×D511yescharacteristic
343Q16—602no—
344SD16—202no—
345C2×C8—101no—
346C2×C8—301no—
347C4⋊C4—51no—
348C4⋊C4—61no—
349C4⋊C4—61no—
350C4⋊C4—122no—
351C4⋊C4—151no—
352C4⋊C4—301no—
353C4⋊C4—301no—
354C4⋊C4—301no—
355C4⋊C4—301no—
356C22⋊C4—101no—
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—201no—
366C22×C3—201no—
367C22×C3—201no—
368C22×C3#408311yescharacteristic
369C22×C3#408811yescharacteristic
370C22×C3#409611yescharacteristic
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—42no—
374C3×C4—201no—
375Dic3—42no—
376Dic3—41no—
377Dic3—41no—
378Dic3—201no—
379Dic3—201no—
380C2×C5—21no—
381C2×C5—21no—
382C2×C5#503211yescharacteristic
383C2×C5#517311yescharacteristic
384C2×C5#520511yescharacteristic
385D5—81no—
386C23—101no—
387C23D3×C22⋊D511yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—41no—
391Q8—41no—
392Q8—601no—
393D4—201no—
394D4—201no—
395D4—201no—
396C2×C4—22no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—62no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—101no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—121no—
409C2×C4—301no—
410C2×C4—301no—
411C2×C4—1201no—
412C2×C4D5×#6711yescharacteristic
413C2×C4#679011yescharacteristic
414C8—201no—
415C8—601no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—401no—
419C2×C3#6532111yescharacteristic
420C2×C3#6533611yescharacteristic
421C2×C3#6538411yescharacteristic
422C5#7097411yescharacteristic, complemented, Sylow
423C22—21no—
424C22—21no—
425C22—201no—
426C22—201no—
427C22—201no—
428C22#9151711yescharacteristic
429C22#9151811yescharacteristic
430C22#9157711yescharacteristic
431C4—21no—
432C4—21no—
433C4—42no—
434C4—122no—
435C4—121no—
436C4—121no—
437C4—201no—
438C4—601no—
439C4—601no—
440C3#1060049811yescharacteristic, complemented, Sylow
441C2—21no—
442C2—21no—
443C2—401no—
444C2#1174940311yescharacteristic
445C2#1174941311yescharacteristic
446C2#1174952511yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5#120
prime radicalC3×#4076C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5#1603
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #11751329C2semidirect
3. C5×#5230C2semidirect
5. #11745965C2semidirect
7. #11745952C2semidirect
69. #5230D5semidirect
362. C3×C5#1603semidirect
422. C5#70974semidirect
440. C3#10600498semidirect

Maximal subgroups

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

subgroupindex
#117544702
#117513292
C5×#52302
C3×#655162
#117459652
#117459542
#117459522
#106004983
#709745