Finite Group Databasebeta

← #14288093

Subgroups — #14288093

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#11754479C211yesmaximal, characteristic
2C3×#65028C211yesmaximal, characteristic, complemented
3#11748828C211yesmaximal, characteristic, complemented
4#11748529C211yesmaximal, characteristic
5#11746290C211yesmaximal, characteristic, complemented
6C5×#4470C211yesmaximal, characteristic
7#11745961C211yesmaximal, characteristic, complemented
8#10599087—31nomaximal, Hall
9C22×C3×Dic10C2211yescharacteristic
10C2×#6712C2211yescharacteristic
11C5×#930C2211yescharacteristic
12C3×#4070C2211yescharacteristic
13C2×C3×Dic20—21no—
14#67⋊Dic5—21no—
15C2×Dic3⋊Dic5—21no—
16#91543—21no—
17#91423—21no—
18#91410—21no—
19#91341—21no—
20#91335—21no—
21C2×#6656—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23#91114C2211yescharacteristic
24C5×C3⋊#95C2211yescharacteristic
25C3×#3948—21no—
26#90994—21no—
27#90970—21no—
28#70982—51nomaximal, Hall
29#65936—31no—
30#65329—31no—
31#65028D311yescharacteristic, complemented
32#64945—31no—
33C5×#327—31no—
34#64689—31no—
35#64672—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15D411yescharacteristic
38C22×Dic15D411yescharacteristic
39C2×C5×#67—21no—
40C22×C5×Dic3—21no—
41C2×C5×D12D411yescharacteristic
42C22×C3×Dic5—21no—
43C2×C3×Dic10—21no—
44C2×C3×Dic10—21no—
45C2×C3×Dic10—42no—
46C2×C3×Dic10D411yescharacteristic
47C2×D3×Dic5—21no—
48C2×C3×C5×C8—21no—
49#6712—21no—
50#6712—21no—
51C2×C3⋊#168—21no—
52C5×(C2×D3)⋊C4—21no—
53C5×C4⋊Dic3D411yescharacteristic
54C3×C22⋊Dic5—21no—
55C3×C4⋊Dic5D411yescharacteristic
56C3×#683—21no—
57C3×Dic20—42no—
58Dic3⋊Dic5—21no—
59Dic3⋊Dic5—42no—
60#6668—21no—
61#6668—21no—
62(C2×D3)⋊Dic5—21no—
63(C2×D3)⋊Dic5—21no—
64(C2×D3)⋊Dic5—21no—
65Dic3×Dic5—21no—
66#6656—42no—
67#5645—51no—
68C3×#451—51no—
69#5230—51no—
70#5227—51no—
71#4538—51no—
72#4470D511yescharacteristic
73#4469—51no—
74C22×Dic10C2×D311yescharacteristic
75C5×#121—31no—
76#4081—61no—
77#4081—61no—
78D4×Dic5—61no—
79C2×#687—61no—
80C2×C4⋊Dic5—61no—
81#4070C2×D311yescharacteristic
82C2×#683—31no—
83C2×Dic20—21no—
84#4035—61no—
85#4025—61no—
86#4024—61no—
87C5×C22⋊C8C2×D311yescharacteristic
88C5×#95—31no—
89#3963—61no—
90C22⋊#168—31no—
91#3948—21no—
92#3942—61no—
93#1603—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C5×D3—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×Dic15—21no—
100C2×Dic15—21no—
101C2×Dic15—21no—
102C2×Dic15—21no—
103C2×Dic15—41no—
104C5×#67—41no—
105C5×#67—41no—
106C2×C5×Dic3—22no—
107C2×C5×Dic3—21no—
108C2×C5×Dic3—41no—
109C2×C5×Dic3—41no—
110C5×D12—41no—
111C2×C3×Dic5—22no—
112C2×C3×Dic5—21no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—41no—
115C2×C3×Dic5—41no—
116C3×Dic10—22no—
117C3×Dic10—22no—
118C3×Dic10—41no—
119C3×Dic10—41no—
120C3×Dic10—41no—
121D3×Dic5—81no—
122C3×C5×C8—41no—
123C3⋊#168—41no—
124C22×C3×Q8—51no—
125C2×C3×Q16—101no—
126C3×C22⋊Q8—51no—
127#946—101no—
128C2×#215—101no—
129#930C2×D511yescharacteristic
130C2×Dic3⋊C4—51no—
131C2×Dic3⋊C4—101no—
132#898—101no—
133#894—101no—
134#890—101no—
135#886—101no—
136#67⋊C4—101no—
137C3×#103—101no—
138C3×C22⋊C8C2×D511yescharacteristic
139#835—101no—
140C3⋊#95—101no—
141C3⋊#95C2×D511yescharacteristic
142#830—51no—
143C2×C5×D4—31no—
144C2×C5×D4—61no—
145C22×C4×C5—61no—
146C22×C4×C5C22×D311yescharacteristic
147C22×Dic5—21no—
148C22×Dic5—31no—
149C22×Dic5—31no—
150C22×Dic5—61no—
151C2×Dic10—21no—
152C2×Dic10—21no—
153C2×Dic10—42no—
154C2×Dic10#6711yescharacteristic
155C2×C5×C8—21no—
156C5×C4⋊C4—31no—
157C5×C22⋊C4—61no—
158C22⋊Dic5—21no—
159C22⋊Dic5—61no—
160C22⋊Dic5—61no—
161C22⋊Dic5—61no—
162#687—122no—
163C4⋊Dic5—61no—
164C4⋊Dic5—122no—
165C4⋊Dic5#6711yescharacteristic
166#683—21no—
167#683—61no—
168#683—61no—
169#683—61no—
170#683—61no—
171C4×Dic5—61no—
172C2×#168—61no—
173Dic20—42no—
174#539—151no—
175#451—51no—
176#448—151no—
177#395—151no—
178#328—151no—
179#327—31no—
180#324—151no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5#12011yescharacteristic
184C22×C3×C5#13511yescharacteristic
185C22×C3×C5#13711yescharacteristic
186C2×C5×D3—41no—
187C2×C5×D3—41no—
188C2×C5×D3—41no—
189C3×C4×C5—21no—
190C3×C4×C5—21no—
191Dic15—41no—
192Dic15—41no—
193C3×Dic5—41no—
194C3×Dic5—41no—
195C3×Dic5—42no—
196C5×Dic3—42no—
197C5×Dic3—41no—
198C2×C3×Q8—51no—
199C2×C3×Q8—101no—
200C2×C3×Q8—101no—
201C2×C3×Q8—202no—
202C22×C3×C4—101no—
203C22×C3×C4C22×D511yescharacteristic
204C2×#67—21no—
205C22×Dic3—21no—
206C22×Dic3—51no—
207C22×Dic3—51no—
208C2×D12D2011yescharacteristic
209C2×C4×D3—101no—
210C3×Q16—202no—
211C2×C3×C8—21no—
212C3×C4⋊C4—51no—
213C3×C4⋊C4—101no—
214C3×C22⋊C4—101no—
215#215—202no—
216(C2×D3)⋊C4—21no—
217(C2×D3)⋊C4—101no—
218(C2×D3)⋊C4—101no—
219(C2×D3)⋊C4—101no—
220C4⋊Dic3—101no—
221C4⋊Dic3—101no—
222C4⋊Dic3D2011yescharacteristic
223Dic3⋊C4—101no—
224Dic3⋊C4—101no—
225Dic3⋊C4—101no—
226Dic3⋊C4—202no—
227C4×Dic3—101no—
228C2×C3⋊C8—101no—
229C23×C5—61no—
230C23×C5D3×D411yescharacteristic
231C5×D4—121no—
232C5×D4—121no—
233C5×D4—121no—
234C2×C4×C5—41no—
235C2×C4×C5—62no—
236C2×C4×C5—61no—
237C2×C4×C5—121no—
238C2×C4×C5—121no—
239C2×C4×C5D3×D411yescharacteristic
240C2×C4×C5C2×#6711yescharacteristic
241C2×Dic5—22no—
242C2×Dic5—21no—
243C2×Dic5—21no—
244C2×Dic5—41no—
245C2×Dic5—41no—
246C2×Dic5—61no—
247C2×Dic5—61no—
248C2×Dic5—61no—
249C2×Dic5—61no—
250C2×Dic5—121no—
251C2×Dic5—241no—
252Dic10—22no—
253Dic10—22no—
254Dic10—41no—
255Dic10—41no—
256Dic10—41no—
257C5×C8—41no—
258#168—121no—
259C22×Q8—51no—
260C2×Q16—101no—
261C2×SD16—301no—
262#126—301no—
263#125—301no—
264#123—301no—
265#123—301no—
266C22⋊Q8—51no—
267C22⋊Q8—301no—
268#121—31no—
269C4×D4—301no—
270C2×C4⋊C4—151no—
271C2×C4⋊C4—301no—
272#103—101no—
273#103—301no—
274C22⋊C8—151no—
275C22⋊C8D3×D511yescharacteristic
276#95—31no—
277#95—301no—
278C2×C3×C5—21no—
279C2×C3×C5—21no—
280C2×C3×C5#45211yescharacteristic
281C2×C3×C5#45611yescharacteristic
282C2×C3×C5B(4,𝔽2)11yescharacteristic
283C5×D3—81no—
284C23×C3D4×D511yescharacteristic
285C22×D3—21no—
286C3×Q8—102no—
287C3×Q8—102no—
288C3×Q8—201no—
289C3×Q8—201no—
290C3×Q8—201no—
291C2×C3×C4—41no—
292C2×C3×C4—102no—
293C2×C3×C4—101no—
294C2×C3×C4—101no—
295C2×C3×C4—201no—
296C2×C3×C4—201no—
297C2×C3×C4C2×D2011yescharacteristic
298C2×C3×C4D4×D511yescharacteristic
299#67—41no—
300#67—41no—
301C2×Dic3—22no—
302C2×Dic3—21no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C2×Dic3—101no—
306C2×Dic3—101no—
307C2×Dic3—101no—
308C2×Dic3—101no—
309C2×Dic3—201no—
310D12—41no—
311C4×D3—401no—
312C3×C8—41no—
313C3⋊C8—201no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5—121no—
317C22×C5—121no—
318C22×C5—121no—
319C22×C5#91811yescharacteristic
320C22×C5#91911yescharacteristic
321C22×C5#93711yescharacteristic
322C4×C5—21no—
323C4×C5—21no—
324C4×C5—122no—
325C4×C5—121no—
326Dic5—41no—
327Dic5—42no—
328Dic5—41no—
329Dic5—121no—
330Dic5—121no—
331C2×Q8—51no—
332C2×Q8—101no—
333C2×Q8—101no—
334C2×Q8—202no—
335C2×D4—31no—
336C2×D4—61no—
337C22×C4—61no—
338C22×C4—101no—
339C22×C4—151no—
340C22×C4—151no—
341C22×C4—301no—
342C22×C4C2×D3×D511yescharacteristic
343Q16—202no—
344SD16—602no—
345C2×C8—21no—
346C2×C8—301no—
347C4⋊C4—31no—
348C4⋊C4—51no—
349C4⋊C4—101no—
350C4⋊C4—301no—
351C4⋊C4—301no—
352C4⋊C4—301no—
353C4⋊C4—301no—
354C4⋊C4—301no—
355C4⋊C4—602no—
356C22⋊C4—61no—
357C22⋊C4—101no—
358C22⋊C4—301no—
359C22⋊C4—301no—
360C22⋊C4—301no—
361C42—301no—
362C3×C5#160311yescharacteristic, complemented, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3#402811yescharacteristic
366C22×C3#405811yescharacteristic
367C22×C3#406111yescharacteristic
368C2×D3—41no—
369C2×D3—41no—
370C2×D3—41no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—201no—
374C3×C4—202no—
375C3×C4—201no—
376Dic3—42no—
377Dic3—41no—
378Dic3—201no—
379Dic3—201no—
380C2×C5—21no—
381C2×C5—21no—
382C2×C5—241no—
383C2×C5#503211yescharacteristic
384C2×C5#518711yescharacteristic
385C2×C5#520511yescharacteristic
386C23—61no—
387C23#677711yescharacteristic
388Q8—102no—
389Q8—102no—
390Q8—201no—
391Q8—201no—
392Q8—201no—
393D4—121no—
394D4—121no—
395D4—121no—
396C2×C4—41no—
397C2×C4—62no—
398C2×C4—61no—
399C2×C4—102no—
400C2×C4—101no—
401C2×C4—101no—
402C2×C4—121no—
403C2×C4—121no—
404C2×C4—201no—
405C2×C4—201no—
406C2×C4—301no—
407C2×C4—301no—
408C2×C4—301no—
409C2×C4—301no—
410C2×C4—601no—
411C2×C4—1201no—
412C2×C4D3×D2011yescharacteristic
413C2×C4D5×#6711yescharacteristic
414C8—41no—
415C8—601no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3#6503011yescharacteristic
419C2×C3#6507211yescharacteristic
420C2×C3#6511511yescharacteristic
421D3—81no—
422C5#7098211yescharacteristic, complemented, Sylow
423C22—21no—
424C22—21no—
425C22—121no—
426C22—121no—
427C22—121no—
428C22#9127911yescharacteristic
429C22#9128011yescharacteristic
430C22#9147411yescharacteristic
431C4—21no—
432C4—21no—
433C4—122no—
434C4—121no—
435C4—202no—
436C4—201no—
437C4—201no—
438C4—601no—
439C4—601no—
440C3#1059908711yescharacteristic, complemented, Sylow
441C2—21no—
442C2—21no—
443C2—241no—
444C2#1174713211yescharacteristic
445C2#1174815111yescharacteristic
446C2#1174825211yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5#120
prime radicalC5×#930C22
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1603
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#65028C2semidirect
3. #11748828C2semidirect
5. #11746290C2semidirect
7. #11745961C2semidirect
31. #65028D3semidirect
362. C3×C5#1603semidirect
422. C5#70982semidirect
440. C3#10599087semidirect

Maximal subgroups

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

subgroupindex
#117544792
C3×#650282
#117488282
#117485292
#117462902
C5×#44702
#117459612
#105990873
#709825