Finite Group Databasebeta

← #14304710

Subgroups — #14304710

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#390C211yesmaximal, characteristic
2C2×#91116C211yesmaximal, characteristic
3C2×#91116C211yesmaximal, characteristic
4#11751029C211yesmaximal, characteristic, complemented
5C2×#91087C211yesmaximal, characteristic, complemented
6#11746350C211yesmaximal, characteristic, complemented
7#11746350C211yesmaximal, characteristic, complemented
8#10600438—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×C3×C5×C22⋊C4—21no—
12C2×C3×C5×C22⋊C4—21no—
13C2×C3×C42×C5C2211yescharacteristic
14C2×C4⋊Dic15C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C2×#6712—21no—
17C22×C3⋊#168C2211yescharacteristic
18C22×C3⋊#168C2211yescharacteristic
19#91116—22no—
20#91116C414yescomplemented
21#91115—21no—
22#91087—22no—
23#69645—51nomaximal, Hall
24C5×#390D311yescharacteristic
25C2×#3964—31no—
26C2×#3964—31no—
27#65217—31no—
28C2×#3935—31no—
29#64749—31no—
30#64749—31no—
31C24×C3×C5—21no—
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4C2×C412yes—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5D411yescharacteristic
40C22×C3×C4×C5D411yescharacteristic
41C22×C3×C4×C5C2311yescharacteristic
42C22×Dic15—21no—
43C22×Dic15—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C22⋊C4—42no—
47C3×C5×C22⋊C4—42no—
48C3×C42×C5—21no—
49C3×C42×C5—21no—
50C4⋊Dic15—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15—21no—
53C4⋊Dic15C2×C412yes—
54#6712—42no—
55C2×C3⋊#168—21no—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59C2×C3⋊#168C2×C412yes—
60C2×C3⋊#168D412yes—
61C3×#390D511yescharacteristic
62C2×#832—51no—
63C2×#832—51no—
64#4928—51no—
65C2×#803—51no—
66#4529—51no—
67#4529—51no—
68C22×C5×D4C2×D311yescharacteristic
69C2×C5×C4⋊C4C2×D311yescharacteristic
70C2×C5×C22⋊C4—21no—
71C2×C5×C22⋊C4—21no—
72C2×C42×C5C2×D311yescharacteristic
73C2×C4⋊Dic5—31no—
74C2×C4⋊Dic5—31no—
75C2×#683—61no—
76C22×#168—31no—
77C22×#168—31no—
78#3964—34no—
79#3964—62no—
80#3963—61no—
81#3935—62no—
82#1936—151noSylow
83C23×C3×C5—22no—
84C23×C3×C5—41no—
85C23×C3×C5—41no—
86C23×C3×C5—41no—
87C23×C3×C5—41no—
88C23×C3×C5—41no—
89C23×C3×C5—41no—
90C23×C3×C5C2×D411yescharacteristic
91C3×C5×D4—22no—
92C3×C5×D4—22no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5C22×C411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×Dic15—22no—
111C2×Dic15—41no—
112C2×Dic15—41no—
113C2×Dic15—41no—
114C2×Dic15—41no—
115C2×Dic15—41no—
116C3⋊#168—22no—
117C3⋊#168—22no—
118C22×C3×D4C2×D511yescharacteristic
119C2×C3×C4⋊C4C2×D511yescharacteristic
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C42C2×D511yescharacteristic
123C2×C4⋊Dic3—51no—
124C2×C4⋊Dic3—51no—
125C2×Dic3⋊C4—101no—
126C22×C3⋊C8—51no—
127C22×C3⋊C8—51no—
128#832—54no—
129#832—102no—
130C3⋊#95—101no—
131#803—102no—
132C24×C5—21no—
133C2×C5×D4—21no—
134C2×C5×D4—21no—
135C2×C5×D4—21no—
136C2×C5×D4—21no—
137C2×C5×D4—21no—
138C2×C5×D4C4×D312yes—
139C22×C4×C5—21no—
140C22×C4×C5#6711yescharacteristic
141C22×C4×C5#6711yescharacteristic
142C22×C4×C5C22×D311yescharacteristic
143C22×Dic5—61no—
144C22×Dic5—61no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4—21no—
147C5×C22⋊C4—42no—
148C5×C22⋊C4—42no—
149C42×C5—21no—
150C42×C5—21no—
151C4⋊Dic5—32no—
152C4⋊Dic5—61no—
153C4⋊Dic5—61no—
154C4⋊Dic5—61no—
155#683—122no—
156C2×#168—32no—
157C2×#168—32no—
158C2×#168—61no—
159C2×#168—61no—
160C2×#168—61no—
161C2×#168—61no—
162C2×#102—151no—
163C2×#102—151no—
164C2×#97—151no—
165#390D1511yescharacteristic
166#389—151no—
167#340—151no—
168#340—151no—
169C22×C3×C5—42no—
170C22×C3×C5—42no—
171C22×C3×C5—42no—
172C22×C3×C5—81no—
173C22×C3×C5—81no—
174C22×C3×C5—81no—
175C22×C3×C5—81no—
176C22×C3×C5C4×D411yescharacteristic
177C22×C3×C5#12111yescharacteristic
178C22×C3×C5#12411yescharacteristic
179C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
180C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
181C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
182C22×C3×C5#13711yescharacteristic
183C3×C4×C5—41no—
184C3×C4×C5—41no—
185C3×C4×C5—81no—
186C3×C4×C5#11711yescharacteristic
187C3×C4×C5C4×D411yescharacteristic
188C3×C4×C5#12311yescharacteristic
189C3×C4×C5#12611yescharacteristic
190Dic15—42no—
191Dic15—81no—
192C24×C3—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4C4×D512yes—
199C22×C3×C4—21no—
200C22×C3×C4C22⋊D511yescharacteristic
201C22×C3×C4C22⋊D511yescharacteristic
202C22×C3×C4C22×D511yescharacteristic
203C22×Dic3—101no—
204C22×Dic3—101no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—21no—
207C3×C22⋊C4—42no—
208C3×C22⋊C4—42no—
209C3×C42—21no—
210C3×C42—21no—
211C4⋊Dic3—52no—
212C4⋊Dic3—101no—
213C4⋊Dic3—101no—
214C4⋊Dic3—101no—
215Dic3⋊C4—202no—
216C2×C3⋊C8—52no—
217C2×C3⋊C8—52no—
218C2×C3⋊C8—101no—
219C2×C3⋊C8—101no—
220C2×C3⋊C8—101no—
221C2×C3⋊C8—101no—
222C23×C5—22no—
223C23×C5—41no—
224C23×C5—41no—
225C23×C5—41no—
226C23×C5—41no—
227C23×C5—41no—
228C23×C5—41no—
229C23×C5C2×#6711yescharacteristic
230C5×D4—22no—
231C5×D4—22no—
232C5×D4—41no—
233C5×D4—41no—
234C2×C4×C5—21no—
235C2×C4×C5—21no—
236C2×C4×C5—21no—
237C2×C4×C5—21no—
238C2×C4×C5—21no—
239C2×C4×C5—21no—
240C2×C4×C5—41no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5C2×C4×D311yescharacteristic
244C2×C4×C5#23511yescharacteristic
245C2×C4×C5D3×D411yescharacteristic
246C2×C4×C5#23711yescharacteristic
247C2×C4×C5#23711yescharacteristic
248C2×C4×C5#23711yescharacteristic
249C2×Dic5—62no—
250C2×Dic5—121no—
251C2×Dic5—121no—
252C2×Dic5—121no—
253C2×Dic5—121no—
254C2×Dic5—121no—
255#168—62no—
256#168—62no—
257C22×D4C2×D1511yescharacteristic
258C22×C8—151no—
259C22×C8—151no—
260C2×C4⋊C4—151no—
261C2×C4⋊C4—151no—
262C2×C4⋊C4—301no—
263C2×C4⋊C4C2×D1511yescharacteristic
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C42C2×D1511yescharacteristic
267#102—154no—
268#102—302no—
269#97—302no—
270#95—301no—
271C2×C3×C5—82no—
272C2×C3×C5#38811yescharacteristic
273C2×C3×C5#44011yescharacteristic
274C2×C3×C5#44211yescharacteristic
275C2×C3×C5#46811yescharacteristic
276C2×C3×C5#46911yescharacteristic
277C2×C3×C5#48911yescharacteristic
278C2×C3×C5#49011yescharacteristic
279C23×C3—22no—
280C23×C3—41no—
281C23×C3—41no—
282C23×C3—41no—
283C23×C3—41no—
284C23×C3—41no—
285C23×C3—41no—
286C23×C3C2×C22⋊D511yescharacteristic
287C3×D4—22no—
288C3×D4—22no—
289C3×D4—41no—
290C3×D4—41no—
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—41no—
300C2×C3×C4C2×C4×D511yescharacteristic
301C2×C3×C4#70911yescharacteristic
302C2×C3×C4D4×D511yescharacteristic
303C2×C3×C4#71111yescharacteristic
304C2×C3×C4#71111yescharacteristic
305C2×C3×C4#71111yescharacteristic
306C2×Dic3—102no—
307C2×Dic3—201no—
308C2×Dic3—201no—
309C2×Dic3—201no—
310C2×Dic3—201no—
311C2×Dic3—201no—
312C3⋊C8—102no—
313C3⋊C8—102no—
314C22×C5—42no—
315C22×C5—42no—
316C22×C5—42no—
317C22×C5—81no—
318C22×C5—81no—
319C22×C5—81no—
320C22×C5—81no—
321C22×C5C4×#6711yescharacteristic
322C22×C5#93211yescharacteristic
323C22×C5#93211yescharacteristic
324C22×C5#93611yescharacteristic
325C22×C5#93911yescharacteristic
326C22×C5#94911yescharacteristic
327C22×C5#95111yescharacteristic
328C4×C5—41no—
329C4×C5—41no—
330C4×C5—81no—
331C4×C5#87711yescharacteristic
332C4×C5#87911yescharacteristic
333C4×C5#67⋊C411yescharacteristic
334C4×C5#88311yescharacteristic
335Dic5—122no—
336Dic5—241no—
337C24—21no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4C4×D1512yes—
344C22×C4—21no—
345C22×C4—301no—
346C22×C4—301no—
347C22×C4#122011yescharacteristic
348C22×C4#122011yescharacteristic
349C22×C4C22×D1511yescharacteristic
350C2×C8—152no—
351C2×C8—152no—
352C2×C8—301no—
353C2×C8—301no—
354C2×C8—301no—
355C2×C8—301no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—152no—
359C4⋊C4—301no—
360C4⋊C4—301no—
361C4⋊C4—301no—
362C4⋊C4—602no—
363C22⋊C4—42no—
364C22⋊C4—42no—
365C42—21no—
366C42—21no—
367C3×C5#193611yescharacteristic, complemented, Hall
368C22×C3—42no—
369C22×C3—42no—
370C22×C3—42no—
371C22×C3—81no—
372C22×C3—81no—
373C22×C3—81no—
374C22×C3—81no—
375C22×C3C4×C22⋊D511yescharacteristic
376C22×C3#407811yescharacteristic
377C22×C3#407811yescharacteristic
378C22×C3#408211yescharacteristic
379C22×C3#408511yescharacteristic
380C22×C3#409511yescharacteristic
381C22×C3#409711yescharacteristic
382C3×C4—41no—
383C3×C4—41no—
384C3×C4—81no—
385C3×C4#402311yescharacteristic
386C3×C4#402511yescharacteristic
387C3×C4#402711yescharacteristic
388C3×C4#402911yescharacteristic
389Dic3—202no—
390Dic3—401no—
391C2×C5—82no—
392C2×C5#494511yescharacteristic
393C2×C5#501411yescharacteristic
394C2×C5#501811yescharacteristic
395C2×C5#503911yescharacteristic
396C2×C5#504211yescharacteristic
397C2×C5#505511yescharacteristic
398C2×C5#507111yescharacteristic
399C23—22no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23C2×#122011yescharacteristic
407D4—22no—
408D4—22no—
409D4—41no—
410D4—41no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—302no—
421C2×C4—601no—
422C2×C4—601no—
423C2×C4—601no—
424C2×C4—601no—
425C2×C4—601no—
426C2×C4C2×C4×D1511yescharacteristic
427C2×C4#681711yescharacteristic
428C2×C4D4×D1511yescharacteristic
429C2×C4#681911yescharacteristic
430C2×C4#681911yescharacteristic
431C2×C4#681911yescharacteristic
432C8—302no—
433C8—302no—
434C2×C3—82no—
435C2×C3#6523411yescharacteristic
436C2×C3#6530311yescharacteristic
437C2×C3#6530711yescharacteristic
438C2×C3#6532811yescharacteristic
439C2×C3#6533111yescharacteristic
440C2×C3#6534411yescharacteristic
441C2×C3#6536011yescharacteristic
442C5#6964511yescharacteristic, complemented, Sylow
443C22—42no—
444C22—42no—
445C22—42no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22C4×#122011yescharacteristic
451C22#9182111yescharacteristic
452C22#9182111yescharacteristic
453C22#9182511yescharacteristic
454C22#9182811yescharacteristic
455C22#9183811yescharacteristic
456C22#9184011yescharacteristic
457C4—41no—
458C4—41no—
459C4—81no—
460C4—602no—
461C4—1201no—
462C4#9176611yescharacteristic
463C4#9176811yescharacteristic
464C4#9177011yescharacteristic
465C4#9177211yescharacteristic
466C3#1060043811yescharacteristic, complemented, Sylow
467C2—82no—
468C2#1175104611yescharacteristic
469C2#1175111511yescharacteristic
470C2#1175111911yescharacteristic
471C2#1175114011yescharacteristic
472C2#1175114311yescharacteristic
473C2#1175115611yescharacteristic
474C2#1175117211yescharacteristic
subgroupG/H
centerC23C2×#1220
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#390C2
socleC23×C3×C5C2×D4
prime radicalC22×C3×C5×D4C22
cosocleC22×C3×C4×C5C23
hypercenter#390D15
hypocenterC3×C5#1936
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
4. #11751029C2semidirect
5. C2×#91087C2semidirect
6. #11746350C2semidirect
7. #11746350C2semidirect
20. #91116C4semidirect
367. C3×C5#1936semidirect
442. C5#69645semidirect
466. C3#10600438semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#3902
C2×#911162
#117510292
C2×#910872
#117463502
#106004383
#696455