Finite Group Databasebeta

← C3×#10602678 #14288186

Subgroups — C3×#10602678 #14288186

Order 1920.

520 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#538C211yesmaximal, characteristic
2C3×#65339C211yesmaximal, characteristic, complemented
3C3×#65329C211yesmaximal, characteristic, complemented
4C3×#65236C211yesmaximal, characteristic, complemented
5C3×#64758C211yesmaximal, characteristic, complemented
6C3×#64757C211yesmaximal, characteristic, complemented
7C3×#64745C211yesmaximal, characteristic, complemented
8#10602678C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×Dic10C2211yescharacteristic
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×C3×C22⋊Dic5—21no—
20C2×C3×#689—21no—
21C2×C3×#687—21no—
22C3×#3963—21no—
23C3×#3963C2211yescharacteristic
24C3×C22⋊#168C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26C3×#3942—21no—
27C3×#3942—21no—
28C3×#1606—51nomaximal, Hall
29C5×#538C2×C311yescharacteristic
30#65339C2×C311yescharacteristic, complemented
31#65329C2×C311yescharacteristic, complemented
32#65236C2×C311yescharacteristic, complemented
33#64758C2×C311yescharacteristic, complemented
34#64757C2×C311yescharacteristic, complemented
35#64745C2×C311yescharacteristic, complemented
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×C3×Dic5—21no—
46C22×C3×Dic5—21no—
47C2×C3×Dic10—21no—
48C2×C3×Dic10—21no—
49C2×C3×Dic10—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—
62C3×C22⋊Dic5—42no—
63C3×#689—42no—
64C3×#687—42no—
65C2×C3×#168—21no—
66C2×C3×#168—21no—
67C3×#538D511yescharacteristic
68C3×#451—51no—
69C3×#448—51no—
70C3×#393—51no—
71C3×#328—51no—
72C3×#327—51no—
73C3×#323—51no—
74C22×Dic10C22×C311yescharacteristic
75C5×#126—21no—
76C5×#124—21no—
77C5×#123—21no—
78C5×C22⋊Q8C22×C311yescharacteristic
79C5×#121—21no—
80C5×#121C22×C311yescharacteristic
81C5×#120—21no—
82C4×C5×D4—21no—
83C2×C5×C22⋊C4C22×C311yescharacteristic
84C2×C22⋊Dic5—21no—
85C2×#689—21no—
86C2×#687—21no—
87#3963—21no—
88#3963C22×C311yescharacteristic
89C22⋊#168C22×C311yescharacteristic
90C22⋊#168C22×C311yescharacteristic
91#3942—21no—
92#3942—21no—
93#1606—51noSylow
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×C3×Dic5—22no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—41no—
119C2×C3×Dic5—41no—
120C2×C3×Dic5—41no—
121C2×C3×Dic5—41no—
122C3×Dic10—22no—
123C3×Dic10—22no—
124C3×Dic10—41no—
125C3×Dic10—41no—
126C3×#168—41no—
127C3×#168—41no—
128C22×C3×Q8—51no—
129C2×C3×Q16—101no—
130C2×C3×SD16—101no—
131C3×#126—21no—
132C3×#124—21no—
133C3×#123—21no—
134C3×C22⋊Q8C2×D511yescharacteristic
135C3×#121—21no—
136C3×#121C2×D511yescharacteristic
137C3×#120—21no—
138C3×C4×D4—21no—
139C2×C3×C22⋊C4—101no—
140C2×C3×C22⋊C4C2×D511yescharacteristic
141C3×#103—101no—
142C3×#103—101no—
143C3×C22⋊C8—51no—
144C3×C22⋊C8—51no—
145C3×#95—51no—
146C3×#95—101no—
147C24×C5C3×D411yescharacteristic
148C2×C5×Q8C3×D411yescharacteristic
149C2×C5×D4—21no—
150C2×C5×D4—21no—
151C2×C5×D4—21no—
152C2×C5×D4C3×D411yescharacteristic
153C22×C4×C5—21no—
154C22×C4×C5C3×D411yescharacteristic
155C22×C4×C5C23×C311yescharacteristic
156C22×Dic5—21no—
157C22×Dic5—21no—
158C2×Dic10—21no—
159C2×Dic10—21no—
160C2×Dic10—42no—
161C5×C4⋊C4—21no—
162C5×C4⋊C4—21no—
163C5×C4⋊C4C3×D411yescharacteristic
164C5×C4⋊C4C3×D411yescharacteristic
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—42no—
174#689—42no—
175#687—42no—
176C2×#168—21no—
177C2×#168—21no—
178#538C3×D511yescharacteristic
179#451—51no—
180#448—51no—
181#393—51no—
182#328—51no—
183#327—51no—
184#323—51no—
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—
204C3×Dic5—42no—
205C3×Dic5—81no—
206C24×C3C22⋊D511yescharacteristic
207C2×C3×Q8—101no—
208C2×C3×Q8—101no—
209C2×C3×Q8—202no—
210C2×C3×Q8C22⋊D511yescharacteristic
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4C22⋊D511yescharacteristic
215C22×C3×C4—21no—
216C22×C3×C4—101no—
217C22×C3×C4—101no—
218C22×C3×C4C22⋊D511yescharacteristic
219C22×C3×C4C22×D511yescharacteristic
220C3×Q16—202no—
221C3×SD16—202no—
222C2×C3×C8—101no—
223C2×C3×C8—101no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4C22⋊D511yescharacteristic
227C3×C4⋊C4C22⋊D511yescharacteristic
228C3×C22⋊C4—21no—
229C3×C22⋊C4—21no—
230C3×C22⋊C4—21no—
231C3×C22⋊C4—21no—
232C3×C22⋊C4—21no—
233C3×C22⋊C4—21no—
234C3×C22⋊C4—21no—
235C3×C22⋊C4—202no—
236C3×C42—21no—
237C23×C5—21no—
238C23×C5—21no—
239C23×C5—21no—
240C23×C5—21no—
241C23×C5—41no—
242C23×C5—41no—
243C23×C5C2×C3×D411yescharacteristic
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×C3×D411yescharacteristic
258C2×C4×C5C2×C3×D411yescharacteristic
259C2×Dic5—22no—
260C2×Dic5—41no—
261C2×Dic5—41no—
262C2×Dic5—41no—
263C2×Dic5—41no—
264C2×Dic5—41no—
265Dic10—22no—
266Dic10—22no—
267Dic10—41no—
268Dic10—41no—
269#168—41no—
270#168—41no—
271C22×Q8—51no—
272C2×Q16—101no—
273C2×SD16—101no—
274#126—21no—
275#124—21no—
276#123—21no—
277C22⋊Q8C2×C3×D511yescharacteristic
278#121—21no—
279#121C2×C3×D511yescharacteristic
280#120—21no—
281C4×D4—21no—
282C2×C22⋊C4—101no—
283C2×C22⋊C4C2×C3×D511yescharacteristic
284#103—101no—
285#103—101no—
286C22⋊C8—51no—
287C22⋊C8—51no—
288#95—51no—
289#95—101no—
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×Q8—102no—
306C3×Q8—102no—
307C3×Q8—201no—
308C3×Q8—201no—
309C3×D4—41no—
310C3×D4—41no—
311C3×D4—41no—
312C3×D4—81no—
313C3×D4—81no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—81no—
321C2×C3×C4—102no—
322C2×C3×C4—201no—
323C2×C3×C4—201no—
324C2×C3×C4—201no—
325C2×C3×C4—201no—
326C2×C3×C4—201no—
327C2×C3×C4C2×C22⋊D511yescharacteristic
328C2×C3×C4C2×C22⋊D511yescharacteristic
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×C5C3×#12011yescharacteristic
342C22×C5C3×#13511yescharacteristic
343C22×C5C3×#13711yescharacteristic
344C4×C5—21no—
345C4×C5—21no—
346C4×C5—41no—
347C4×C5—41no—
348C4×C5—41no—
349C4×C5—41no—
350Dic5—42no—
351Dic5—81no—
352C24C3×C22⋊D511yescharacteristic
353C2×Q8—101no—
354C2×Q8—101no—
355C2×Q8—202no—
356C2×Q8C3×C22⋊D511yescharacteristic
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4C3×C22⋊D511yescharacteristic
361C22×C4—21no—
362C22×C4—101no—
363C22×C4—101no—
364C22×C4C3×C22⋊D511yescharacteristic
365C22×C4C22×C3×D511yescharacteristic
366Q16—202no—
367SD16—202no—
368C2×C8—101no—
369C2×C8—101no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4C3×C22⋊D511yescharacteristic
373C4⋊C4C3×C22⋊D511yescharacteristic
374C22⋊C4—21no—
375C22⋊C4—21no—
376C22⋊C4—21no—
377C22⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—21no—
381C22⋊C4—202no—
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—
403C3×C4—202no—
404C3×C4—401no—
405C2×C5—21no—
406C2×C5—21no—
407C2×C5—81no—
408C2×C5—81no—
409C2×C5C3×#45211yescharacteristic
410C2×C5C3×#45511yescharacteristic
411C2×C5C3×B(4,𝔽2)11yescharacteristic
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—41no—
417C23—41no—
418C23C2×C3×C22⋊D511yescharacteristic
419Q8—41no—
420Q8—102no—
421Q8—102no—
422Q8—201no—
423Q8—201no—
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—102no—
437C2×C4—201no—
438C2×C4—201no—
439C2×C4—201no—
440C2×C4—201no—
441C2×C4—201no—
442C2×C4C2×C3×C22⋊D511yescharacteristic
443C2×C4C2×C3×C22⋊D511yescharacteristic
444C8—201no—
445C8—201no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—81no—
449C2×C3—81no—
450C2×C3#6552811yescharacteristic
451C2×C3#6553111yescharacteristic
452C2×C3#6553311yescharacteristic
453C5C3×#160611yescharacteristic, complemented, Sylow
454C22—21no—
455C22—21no—
456C22—42no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—81no—
464C22C3×#409611yescharacteristic
465C22C3×#409711yescharacteristic
466C22C3×#409911yescharacteristic
467C4—21no—
468C4—21no—
469C4—41no—
470C4—41no—
471C4—41no—
472C4—41no—
473C4—202no—
474C4—401no—
475C3#1060267811yescharacteristic, direct product factor, Sylow
476C2—21no—
477C2—21no—
478C2—81no—
479C2—81no—
480C2C3×#6552811yescharacteristic
481C2C3×#6553111yescharacteristic
482C2C3×#6553311yescharacteristic
subgroupG/H
centerC22×C3#4099
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
Fitting, prime radicalC3×C5×#538C2
socleC22×C3×C5#120
hypercenterC3×#538D5
hypocenterC5C3×#1606
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#538

Complements

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

NH ≅ G/Ntype
2. C3×#65339C2semidirect
3. C3×#65329C2semidirect
4. C3×#65236C2semidirect
5. C3×#64758C2semidirect
6. C3×#64757C2semidirect
7. C3×#64745C2semidirect
8. #10602678C3direct (N × H)
30. #65339C2×C3semidirect
31. #65329C2×C3semidirect
32. #65236C2×C3semidirect
33. #64758C2×C3semidirect
34. #64757C2×C3semidirect
35. #64745C2×C3semidirect
383. C3×C5#1606semidirect
453. C5C3×#1606semidirect
475. C3#10602678direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5382
C3×#653392
C3×#653292
C3×#652362
C3×#647582
C3×#647572
C3×#647452
#106026783
C3×#16065