Finite Group Databasebeta

← #14288187

Subgroups — #14288187

Order 1920.

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

normal subgroups only

This group has 520 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×#538C211yesmaximal, characteristic
2#11751151C211yesmaximal, characteristic, complemented
3#11751141C211yesmaximal, characteristic, complemented
4#11751048C211yesmaximal, characteristic, complemented
5#11746359C211yesmaximal, characteristic, complemented
6#11746358C211yesmaximal, characteristic, complemented
7#11746346C211yesmaximal, characteristic, complemented
8#10602678—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C3×C5×#126—21no—
11C3×C5×#124—21no—
12C3×C5×#123—21no—
13C3×C5×C22⋊Q8C2211yescharacteristic
14C3×C5×#121—21no—
15C3×C5×#121C2211yescharacteristic
16C3×C5×#120—21no—
17C3×C4×C5×D4—21no—
18C2×C3×C5×C22⋊C4C2211yescharacteristic
19C2×#6719—21no—
20C2×#6718—21no—
21C2×#6716—21no—
22#91115—21no—
23#91115C2211yescharacteristic
24#91114C2211yescharacteristic
25#91114C2211yescharacteristic
26#91094—21no—
27#91094—21no—
28#71885—51nomaximal, Hall
29C5×#538D311yescharacteristic
30#65339—31no—
31#65329—31no—
32#65236—31no—
33#64758—31no—
34#64757—31no—
35#64745—31no—
36C24×C3×C5D411yescharacteristic
37C2×C3×C5×Q8D411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4D411yescharacteristic
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5D411yescharacteristic
44C22×C3×C4×C5C2311yescharacteristic
45C22×Dic15—21no—
46C22×Dic15—21no—
47C2×Dic30—21no—
48C2×Dic30—21no—
49C2×Dic30—42no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4D411yescharacteristic
53C3×C5×C4⋊C4D411yescharacteristic
54C3×C5×C22⋊C4—21no—
55C3×C5×C22⋊C4—21no—
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#6719—42no—
63#6718—42no—
64#6716—42no—
65C2×C3⋊#168—21no—
66C2×C3⋊#168—21no—
67C3×#538D511yescharacteristic
68#5050—51no—
69#5040—51no—
70#4947—51no—
71#4538—51no—
72#4537—51no—
73#4525—51no—
74C22×Dic10—31no—
75C5×#126—21no—
76C5×#124—21no—
77C5×#123—21no—
78C5×C22⋊Q8C2×D311yescharacteristic
79C5×#121—21no—
80C5×#121C2×D311yescharacteristic
81C5×#120—21no—
82C4×C5×D4—21no—
83C2×C5×C22⋊C4C2×D311yescharacteristic
84C2×C22⋊Dic5—61no—
85C2×#689—61no—
86C2×#687—61no—
87#3963—31no—
88#3963—61no—
89C22⋊#168—31no—
90C22⋊#168—31no—
91#3942—61no—
92#3942—61no—
93#1606—151noSylow
94C23×C3×C5—21no—
95C23×C3×C5—21no—
96C23×C3×C5—21no—
97C23×C3×C5—21no—
98C23×C3×C5—41no—
99C23×C3×C5—41no—
100C23×C3×C5C2×D411yescharacteristic
101C3×C5×Q8—41no—
102C3×C5×D4—41no—
103C3×C5×D4—41no—
104C3×C5×D4—41no—
105C3×C5×D4—81no—
106C3×C5×D4—81no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—21no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—81no—
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×Dic15—22no—
117C2×Dic15—41no—
118C2×Dic15—41no—
119C2×Dic15—41no—
120C2×Dic15—41no—
121C2×Dic15—41no—
122Dic30—22no—
123Dic30—22no—
124Dic30—41no—
125Dic30—41no—
126C3⋊#168—41no—
127C3⋊#168—41no—
128C22×Dic6—51no—
129C3×#126—21no—
130C3×#124—21no—
131C3×#123—21no—
132C3×C22⋊Q8C2×D511yescharacteristic
133C3×#121—21no—
134C3×#121C2×D511yescharacteristic
135C3×#120—21no—
136C3×C4×D4—21no—
137C2×C3×C22⋊C4C2×D511yescharacteristic
138C2×#217—101no—
139C2×#216—101no—
140C2×#214—101no—
141C3⋊#95—51no—
142C3⋊#95—101no—
143#830—51no—
144#830—51no—
145#810—101no—
146#810—101no—
147C24×C5#6711yescharacteristic
148C2×C5×Q8#6711yescharacteristic
149C2×C5×D4—21no—
150C2×C5×D4—21no—
151C2×C5×D4—21no—
152C2×C5×D4#6711yescharacteristic
153C22×C4×C5—21no—
154C22×C4×C5#6711yescharacteristic
155C22×C4×C5C22×D311yescharacteristic
156C22×Dic5—61no—
157C22×Dic5—61no—
158C2×Dic10—61no—
159C2×Dic10—61no—
160C2×Dic10—122no—
161C5×C4⋊C4—21no—
162C5×C4⋊C4—21no—
163C5×C4⋊C4#6711yescharacteristic
164C5×C4⋊C4#6711yescharacteristic
165C5×C22⋊C4—21no—
166C5×C22⋊C4—21no—
167C5×C22⋊C4—21no—
168C5×C22⋊C4—21no—
169C5×C22⋊C4—21no—
170C5×C22⋊C4—21no—
171C5×C22⋊C4—21no—
172C42×C5—21no—
173C22⋊Dic5—122no—
174#689—122no—
175#687—122no—
176C2×#168—61no—
177C2×#168—61no—
178#538D1511yescharacteristic
179#451—151no—
180#448—151no—
181#393—151no—
182#328—151no—
183#327—151no—
184#323—151no—
185C22×C3×C5—21no—
186C22×C3×C5—21no—
187C22×C3×C5—42no—
188C22×C3×C5—41no—
189C22×C3×C5—41no—
190C22×C3×C5—41no—
191C22×C3×C5—41no—
192C22×C3×C5—41no—
193C22×C3×C5—41no—
194C22×C3×C5—81no—
195C22×C3×C5#12011yescharacteristic
196C22×C3×C5#13511yescharacteristic
197C22×C3×C5#13711yescharacteristic
198C3×C4×C5—21no—
199C3×C4×C5—21no—
200C3×C4×C5—41no—
201C3×C4×C5—41no—
202C3×C4×C5—41no—
203C3×C4×C5—41no—
204Dic15—42no—
205Dic15—81no—
206C24×C3C22⋊D511yescharacteristic
207C2×C3×Q8C22⋊D511yescharacteristic
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4C22⋊D511yescharacteristic
212C22×C3×C4—21no—
213C22×C3×C4C22⋊D511yescharacteristic
214C22×C3×C4C22×D511yescharacteristic
215C22×Dic3—101no—
216C22×Dic3—101no—
217C2×Dic6—101no—
218C2×Dic6—101no—
219C2×Dic6—202no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4C22⋊D511yescharacteristic
223C3×C4⋊C4C22⋊D511yescharacteristic
224C3×C22⋊C4—21no—
225C3×C22⋊C4—21no—
226C3×C22⋊C4—21no—
227C3×C22⋊C4—21no—
228C3×C22⋊C4—21no—
229C3×C22⋊C4—21no—
230C3×C22⋊C4—21no—
231C3×C42—21no—
232#217—202no—
233#216—202no—
234#214—202no—
235C2×C3⋊C8—101no—
236C2×C3⋊C8—101no—
237C23×C5—21no—
238C23×C5—21no—
239C23×C5—21no—
240C23×C5—21no—
241C23×C5—41no—
242C23×C5—41no—
243C23×C5C2×#6711yescharacteristic
244C5×Q8—41no—
245C5×D4—41no—
246C5×D4—41no—
247C5×D4—41no—
248C5×D4—81no—
249C5×D4—81no—
250C2×C4×C5—21no—
251C2×C4×C5—21no—
252C2×C4×C5—21no—
253C2×C4×C5—21no—
254C2×C4×C5—41no—
255C2×C4×C5—41no—
256C2×C4×C5—81no—
257C2×C4×C5C2×#6711yescharacteristic
258C2×C4×C5C2×#6711yescharacteristic
259C2×Dic5—62no—
260C2×Dic5—121no—
261C2×Dic5—121no—
262C2×Dic5—121no—
263C2×Dic5—121no—
264C2×Dic5—121no—
265Dic10—62no—
266Dic10—62no—
267Dic10—121no—
268Dic10—121no—
269#168—121no—
270#168—121no—
271C22×Q8—151no—
272C2×Q16—301no—
273C2×SD16—301no—
274#126—21no—
275#124—21no—
276#123—21no—
277C22⋊Q8C2×D1511yescharacteristic
278#121—21no—
279#121C2×D1511yescharacteristic
280#120—21no—
281C4×D4—21no—
282C2×C22⋊C4—301no—
283C2×C22⋊C4C2×D1511yescharacteristic
284#103—301no—
285#103—301no—
286C22⋊C8—151no—
287C22⋊C8—151no—
288#95—151no—
289#95—301no—
290C2×C3×C5—21no—
291C2×C3×C5—21no—
292C2×C3×C5—81no—
293C2×C3×C5—81no—
294C2×C3×C5#45211yescharacteristic
295C2×C3×C5#45511yescharacteristic
296C2×C3×C5B(4,𝔽2)11yescharacteristic
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—41no—
302C23×C3—41no—
303C23×C3C2×C22⋊D511yescharacteristic
304C3×Q8—41no—
305C3×D4—41no—
306C3×D4—41no—
307C3×D4—41no—
308C3×D4—81no—
309C3×D4—81no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—81no—
317C2×C3×C4C2×C22⋊D511yescharacteristic
318C2×C3×C4C2×C22⋊D511yescharacteristic
319C2×Dic3—102no—
320C2×Dic3—201no—
321C2×Dic3—201no—
322C2×Dic3—201no—
323C2×Dic3—201no—
324C2×Dic3—201no—
325Dic6—102no—
326Dic6—102no—
327Dic6—201no—
328Dic6—201no—
329C3⋊C8—201no—
330C3⋊C8—201no—
331C22×C5—21no—
332C22×C5—21no—
333C22×C5—42no—
334C22×C5—41no—
335C22×C5—41no—
336C22×C5—41no—
337C22×C5—41no—
338C22×C5—41no—
339C22×C5—41no—
340C22×C5—81no—
341C22×C5#95011yescharacteristic
342C22×C5#95111yescharacteristic
343C22×C5#95311yescharacteristic
344C4×C5—21no—
345C4×C5—21no—
346C4×C5—41no—
347C4×C5—41no—
348C4×C5—41no—
349C4×C5—41no—
350Dic5—122no—
351Dic5—241no—
352C24#122011yescharacteristic
353C2×Q8—301no—
354C2×Q8—301no—
355C2×Q8—602no—
356C2×Q8#122011yescharacteristic
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4#122011yescharacteristic
361C22×C4—21no—
362C22×C4—301no—
363C22×C4—301no—
364C22×C4#122011yescharacteristic
365C22×C4C22×D1511yescharacteristic
366Q16—602no—
367SD16—602no—
368C2×C8—301no—
369C2×C8—301no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4#122011yescharacteristic
373C4⋊C4#122011yescharacteristic
374C22⋊C4—21no—
375C22⋊C4—21no—
376C22⋊C4—21no—
377C22⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—21no—
381C22⋊C4—602no—
382C42—21no—
383C3×C5#160611yescharacteristic, complemented, Hall
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—42no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—81no—
394C22×C3#409611yescharacteristic
395C22×C3#409711yescharacteristic
396C22×C3#409911yescharacteristic
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—41no—
400C3×C4—41no—
401C3×C4—41no—
402C3×C4—41no—
403Dic3—202no—
404Dic3—401no—
405C2×C5—21no—
406C2×C5—21no—
407C2×C5—81no—
408C2×C5—81no—
409C2×C5#523911yescharacteristic
410C2×C5#524211yescharacteristic
411C2×C5#524411yescharacteristic
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—41no—
417C23—41no—
418C23C2×#122011yescharacteristic
419Q8—41no—
420Q8—302no—
421Q8—302no—
422Q8—601no—
423Q8—601no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—81no—
428D4—81no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—81no—
436C2×C4—302no—
437C2×C4—601no—
438C2×C4—601no—
439C2×C4—601no—
440C2×C4—601no—
441C2×C4—601no—
442C2×C4C2×#122011yescharacteristic
443C2×C4C2×#122011yescharacteristic
444C8—601no—
445C8—601no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—81no—
449C2×C3—81no—
450C2×C3#6552811yescharacteristic
451C2×C3#6553111yescharacteristic
452C2×C3#6553311yescharacteristic
453C5#7188511yescharacteristic, complemented, Sylow
454C22—21no—
455C22—21no—
456C22—42no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—81no—
464C22#9183911yescharacteristic
465C22#9184011yescharacteristic
466C22#9184211yescharacteristic
467C4—21no—
468C4—21no—
469C4—41no—
470C4—41no—
471C4—41no—
472C4—41no—
473C4—602no—
474C4—1201no—
475C3#1060267811yescharacteristic, complemented, Sylow
476C2—21no—
477C2—21no—
478C2—81no—
479C2—81no—
480C2#1175134011yescharacteristic
481C2#1175134311yescharacteristic
482C2#1175134511yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
Fitting, prime radicalC3×C5×#538C2
socleC22×C3×C5#120
hypercenter#538D15
hypocenterC3×C5#1606
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #538

Complements

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

NH ≅ G/Ntype
2. #11751151C2semidirect
3. #11751141C2semidirect
4. #11751048C2semidirect
5. #11746359C2semidirect
6. #11746358C2semidirect
7. #11746346C2semidirect
383. C3×C5#1606semidirect
453. C5#71885semidirect
475. C3#10602678semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5382
#117511512
#117511412
#117510482
#117463592
#117463582
#117463462
#106026783
#718855