Finite Group Databasebeta

← #14288046

Subgroups — #14288046

Order 1920.

488 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C3×C5×#539C211yesmaximal, characteristic
2#11751151C211yesmaximal, characteristic, complemented
3#11751141C211yesmaximal, characteristic
4#11751080C211yesmaximal, characteristic, complemented
5#11746359C211yesmaximal, characteristic, complemented
6#11746358C211yesmaximal, characteristic
7#11746349C211yesmaximal, characteristic, complemented
8#10602682—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C3×C5×#126—21no—
11C3×C5×#125—21no—
12C3×C5×#123—21no—
13C3×C5×#123—21no—
14C3×C5×C22⋊Q8—21no—
15C3×C5×C22⋊Q8C2211yescharacteristic
16C3×C5×#121C2211yescharacteristic
17C3×C4×C5×D4—21no—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×#6718—21no—
20C2×#6716—21no—
21C2×#6712—21no—
22#91115—21no—
23#91115C2211yescharacteristic
24#91114C2211yescharacteristic
25#91114C2211yescharacteristic
26#91094—21no—
27#91094—21no—
28#71889—51nomaximal, Hall
29C5×#539D311yescharacteristic
30#65339—31no—
31#65329—31no—
32#65268—31no—
33#64758—31no—
34#64757—31no—
35#64748—31no—
36C2×C3×C5×Q8D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4D411yescharacteristic
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5D411yescharacteristic
41C22×C3×C4×C5D411yescharacteristic
42C22×C3×C4×C5C2311yescharacteristic
43C22×Dic15—21no—
44C22×Dic15—21no—
45C2×Dic30—21no—
46C2×Dic30—21no—
47C2×Dic30—42no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4D411yescharacteristic
55C3×C5×C4⋊C4D411yescharacteristic
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C5×C22⋊C4—21no—
61C3×C42×C5—21no—
62#6718—42no—
63#6716—42no—
64#6712—42no—
65C2×C3⋊#168—21no—
66C2×C3⋊#168—21no—
67C3×#539D511yescharacteristic
68#5050—51no—
69#5040—51no—
70#4979—51no—
71#4538—51no—
72#4537—51no—
73#4528—51no—
74C22×Dic10—31no—
75C5×#126—21no—
76C5×#125—21no—
77C5×#123—21no—
78C5×#123—21no—
79C5×C22⋊Q8—21no—
80C5×C22⋊Q8C2×D311yescharacteristic
81C5×#121C2×D311yescharacteristic
82C4×C5×D4—21no—
83C2×C5×C4⋊C4C2×D311yescharacteristic
84C2×#689—61no—
85C2×#687—61no—
86C2×#683—61no—
87#3963—31no—
88#3963—61no—
89C22⋊#168—31no—
90C22⋊#168—31no—
91#3942—61no—
92#3942—61no—
93#1603—151noSylow
94C23×C3×C5—21no—
95C23×C3×C5C2×D411yescharacteristic
96C3×C5×Q8—41no—
97C3×C5×D4—41no—
98C3×C5×D4—41no—
99C3×C5×D4—41no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—81no—
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×Dic15—22no—
113C2×Dic15—22no—
114C2×Dic15—41no—
115C2×Dic15—41no—
116C2×Dic15—41no—
117C2×Dic15—41no—
118Dic30—22no—
119Dic30—22no—
120Dic30—41no—
121Dic30—41no—
122C3⋊#168—41no—
123C3⋊#168—41no—
124C22×Dic6—51no—
125C3×#126—21no—
126C3×#125—21no—
127C3×#123—21no—
128C3×#123—21no—
129C3×C22⋊Q8—21no—
130C3×C22⋊Q8C2×D511yescharacteristic
131C3×#121C2×D511yescharacteristic
132C3×C4×D4—21no—
133C2×C3×C4⋊C4C2×D511yescharacteristic
134C2×#216—101no—
135C2×#214—101no—
136C2×Dic3⋊C4—101no—
137C3⋊#95—51no—
138C3⋊#95—101no—
139#830—51no—
140#830—51no—
141#810—101no—
142#810—101no—
143C2×C5×Q8#6711yescharacteristic
144C2×C5×D4—21no—
145C2×C5×D4#6711yescharacteristic
146C22×C4×C5—21no—
147C22×C4×C5#6711yescharacteristic
148C22×C4×C5#6711yescharacteristic
149C22×C4×C5C22×D311yescharacteristic
150C22×Dic5—61no—
151C22×Dic5—61no—
152C2×Dic10—61no—
153C2×Dic10—61no—
154C2×Dic10—122no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4—21no—
157C5×C4⋊C4—21no—
158C5×C4⋊C4—21no—
159C5×C4⋊C4—21no—
160C5×C4⋊C4—21no—
161C5×C4⋊C4#6711yescharacteristic
162C5×C4⋊C4#6711yescharacteristic
163C5×C22⋊C4—21no—
164C5×C22⋊C4—21no—
165C5×C22⋊C4—21no—
166C5×C22⋊C4—21no—
167C5×C22⋊C4—21no—
168C42×C5—21no—
169#689—122no—
170#687—122no—
171#683—122no—
172C2×#168—61no—
173C2×#168—61no—
174#539D1511yescharacteristic
175#451—151no—
176#448—151no—
177#395—151no—
178#328—151no—
179#327—151no—
180#324—151no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5—41no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5#12011yescharacteristic
187C22×C3×C5#13511yescharacteristic
188C22×C3×C5#13711yescharacteristic
189C3×C4×C5—21no—
190C3×C4×C5—21no—
191C3×C4×C5—41no—
192C3×C4×C5—41no—
193C3×C4×C5—41no—
194C3×C4×C5—41no—
195C3×C4×C5—41no—
196Dic15—42no—
197Dic15—42no—
198C2×C3×Q8C22⋊D511yescharacteristic
199C2×C3×D4—21no—
200C2×C3×D4C22⋊D511yescharacteristic
201C22×C3×C4—21no—
202C22×C3×C4C22⋊D511yescharacteristic
203C22×C3×C4C22⋊D511yescharacteristic
204C22×C3×C4C22×D511yescharacteristic
205C22×Dic3—101no—
206C22×Dic3—101no—
207C2×Dic6—101no—
208C2×Dic6—101no—
209C2×Dic6—202no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4C22⋊D511yescharacteristic
217C3×C4⋊C4C22⋊D511yescharacteristic
218C3×C22⋊C4—21no—
219C3×C22⋊C4—21no—
220C3×C22⋊C4—21no—
221C3×C22⋊C4—21no—
222C3×C22⋊C4—21no—
223C3×C42—21no—
224#216—202no—
225#214—202no—
226Dic3⋊C4—202no—
227C2×C3⋊C8—101no—
228C2×C3⋊C8—101no—
229C23×C5—21no—
230C23×C5C2×#6711yescharacteristic
231C5×Q8—41no—
232C5×D4—41no—
233C5×D4—41no—
234C5×D4—41no—
235C2×C4×C5—21no—
236C2×C4×C5—21no—
237C2×C4×C5—21no—
238C2×C4×C5—21no—
239C2×C4×C5—21no—
240C2×C4×C5—21no—
241C2×C4×C5—21no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5—81no—
245C2×C4×C5C2×#6711yescharacteristic
246C2×C4×C5C2×#6711yescharacteristic
247C2×Dic5—62no—
248C2×Dic5—62no—
249C2×Dic5—121no—
250C2×Dic5—121no—
251C2×Dic5—121no—
252C2×Dic5—121no—
253Dic10—62no—
254Dic10—62no—
255Dic10—121no—
256Dic10—121no—
257#168—121no—
258#168—121no—
259C22×Q8—151no—
260C2×Q16—301no—
261C2×SD16—301no—
262#126—21no—
263#125—21no—
264#123—21no—
265#123—21no—
266C22⋊Q8—21no—
267C22⋊Q8C2×D1511yescharacteristic
268#121C2×D1511yescharacteristic
269C4×D4—21no—
270C2×C4⋊C4—301no—
271C2×C4⋊C4C2×D1511yescharacteristic
272#103—301no—
273#103—301no—
274C22⋊C8—151no—
275C22⋊C8—151no—
276#95—151no—
277#95—301no—
278C2×C3×C5—21no—
279C2×C3×C5—21no—
280C2×C3×C5—81no—
281C2×C3×C5#45211yescharacteristic
282C2×C3×C5#45611yescharacteristic
283C2×C3×C5B(4,𝔽2)11yescharacteristic
284C23×C3—21no—
285C23×C3C2×C22⋊D511yescharacteristic
286C3×Q8—41no—
287C3×D4—41no—
288C3×D4—41no—
289C3×D4—41no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—81no—
300C2×C3×C4C2×C22⋊D511yescharacteristic
301C2×C3×C4C2×C22⋊D511yescharacteristic
302C2×Dic3—102no—
303C2×Dic3—102no—
304C2×Dic3—201no—
305C2×Dic3—201no—
306C2×Dic3—201no—
307C2×Dic3—201no—
308Dic6—102no—
309Dic6—102no—
310Dic6—201no—
311Dic6—201no—
312C3⋊C8—201no—
313C3⋊C8—201no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5—41no—
317C22×C5—41no—
318C22×C5—41no—
319C22×C5#95011yescharacteristic
320C22×C5#95111yescharacteristic
321C22×C5#95311yescharacteristic
322C4×C5—21no—
323C4×C5—21no—
324C4×C5—41no—
325C4×C5—41no—
326C4×C5—41no—
327C4×C5—41no—
328C4×C5—41no—
329Dic5—122no—
330Dic5—122no—
331C2×Q8—301no—
332C2×Q8—301no—
333C2×Q8—602no—
334C2×Q8#122011yescharacteristic
335C2×D4—21no—
336C2×D4#122011yescharacteristic
337C22×C4—21no—
338C22×C4—301no—
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—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—602no—
354C4⋊C4#122011yescharacteristic
355C4⋊C4#122011yescharacteristic
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—21no—
360C22⋊C4—21no—
361C42—21no—
362C3×C5#160311yescharacteristic, complemented, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3#409611yescharacteristic
369C22×C3#409711yescharacteristic
370C22×C3#409911yescharacteristic
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—41no—
374C3×C4—41no—
375C3×C4—41no—
376C3×C4—41no—
377C3×C4—41no—
378Dic3—202no—
379Dic3—202no—
380C2×C5—21no—
381C2×C5—21no—
382C2×C5—81no—
383C2×C5#523911yescharacteristic
384C2×C5#524411yescharacteristic
385C2×C5#524611yescharacteristic
386C23—21no—
387C23C2×#122011yescharacteristic
388Q8—41no—
389Q8—302no—
390Q8—302no—
391Q8—601no—
392Q8—601no—
393D4—41no—
394D4—41no—
395D4—41no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—81no—
406C2×C4—302no—
407C2×C4—302no—
408C2×C4—601no—
409C2×C4—601no—
410C2×C4—601no—
411C2×C4—601no—
412C2×C4C2×#122011yescharacteristic
413C2×C4C2×#122011yescharacteristic
414C8—601no—
415C8—601no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—81no—
419C2×C3#6552811yescharacteristic
420C2×C3#6553311yescharacteristic
421C2×C3#6553511yescharacteristic
422C5#7188911yescharacteristic, complemented, Sylow
423C22—21no—
424C22—21no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22#9183911yescharacteristic
429C22#9184011yescharacteristic
430C22#9184211yescharacteristic
431C4—21no—
432C4—21no—
433C4—41no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—41no—
438C4—602no—
439C4—602no—
440C3#1060268211yescharacteristic, complemented, Sylow
441C2—21no—
442C2—21no—
443C2—81no—
444C2#1175134011yescharacteristic
445C2#1175134511yescharacteristic
446C2#1175134711yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#539C2
socleC22×C3×C5#120
prime radicalC3×C5×#121C22
hypercenter#539D15
hypocenterC3×C5#1603
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
2. #11751151C2semidirect
4. #11751080C2semidirect
5. #11746359C2semidirect
7. #11746349C2semidirect
362. C3×C5#1603semidirect
422. C5#71889semidirect
440. C3#10602682semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5392
#117511512
#117511412
#117510802
#117463592
#117463582
#117463492
#106026823
#718895