Finite Group Databasebeta

← C3×#10601772 #14287856

Subgroups — C3×#10601772 #14287856

Order 1920.

532 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×#65957C211yesmaximal, characteristic, complemented
2C3×C5×#450C211yesmaximal, characteristic
3C3×#65511C211yesmaximal, characteristic
4C3×#65507C211yesmaximal, characteristic
5C3×#64758C211yesmaximal, characteristic, complemented
6C3×#64689C211yesmaximal, characteristic, complemented
7C3×#64687C211yesmaximal, characteristic, complemented
8#10601772C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C2×C3×C5×SD16—21no—
11C3×C5×C22⋊Q8C2211yescharacteristic
12C2×C3×C22⋊Dic5—21no—
13C2×C3×C22⋊Dic5—21no—
14C3×#4090—21no—
15C2×C3×#687—21no—
16C3×#4070C2211yescharacteristic
17C2×C3×#683C2211yescharacteristic
18C3×#4035—21no—
19C3×#4035—21no—
20C3×#4034—21no—
21C3×#4024—21no—
22C3×#4023—21no—
23C3×C5×#102—21no—
24C3×C5×C22⋊C8C2211yescharacteristic
25C3×#3964—21no—
26C3×#3963C2211yescharacteristic
27C3×C22⋊#168C2211yescharacteristic
28C3×#1599—51nomaximal, Hall
29#65957C2×C311yescharacteristic, complemented
30C5×#450C2×C311yescharacteristic
31#65511C2×C311yescharacteristic
32#65507C2×C311yescharacteristic
33#64758C2×C311yescharacteristic, complemented
34#64689C2×C311yescharacteristic, complemented
35#64687C2×C311yescharacteristic, complemented
36C24×C3×C5—21no—
37C2×C3×C5×Q8D411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—42no—
41C22×C3×C4×C5C2311yescharacteristic
42C22×C3×Dic5—21no—
43C22×C3×Dic5D411yescharacteristic
44C22×C3×Dic5D411yescharacteristic
45C2×C3×Dic10—21no—
46C2×C3×Dic10D411yescharacteristic
47C3×C5×SD16—42no—
48C2×C3×C5×C8—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4D411yescharacteristic
51C3×C5×C22⋊C4—21no—
52C3×C22⋊Dic5—21no—
53C3×C22⋊Dic5—42no—
54C3×C22⋊Dic5—42no—
55C3×#687—42no—
56C3×C4⋊Dic5—21no—
57C3×C4⋊Dic5D411yescharacteristic
58C3×#683—21no—
59C3×#683—21no—
60C3×#683—21no—
61C3×#683—21no—
62C3×#683—21no—
63C3×#683—21no—
64C3×#683—21no—
65C3×C4×Dic5—21no—
66C3×C4×Dic5—21no—
67C2×C3×#168—21no—
68C3×#544—51no—
69C3×#450—51no—
70C3×#450D511yescharacteristic
71C3×#394—51no—
72C3×#328—51no—
73C3×#328—51no—
74C3×#324—51no—
75C22×C5×D4C22×C311yescharacteristic
76C2×C5×SD16—21no—
77C5×C22⋊Q8C22×C311yescharacteristic
78C2×C22⋊Dic5—21no—
79C2×C22⋊Dic5—21no—
80#4090—21no—
81C2×#687—21no—
82#4070C22×C311yescharacteristic
83C2×#683C22×C311yescharacteristic
84#4035—21no—
85#4035—21no—
86#4034—21no—
87#4024—21no—
88#4023—21no—
89C5×#102—21no—
90C5×C22⋊C8C22×C311yescharacteristic
91#3964—21no—
92#3963C22×C311yescharacteristic
93C22⋊#168C22×C311yescharacteristic
94#1599—51noSylow
95C23×C3×C5—22no—
96C23×C3×C5—41no—
97C23×C3×C5—41no—
98C23×C3×C5—41no—
99C23×C3×C5—41no—
100C23×C3×C5—41no—
101C23×C3×C5—41no—
102C23×C3×C5C2×D411yescharacteristic
103C3×C5×Q8—41no—
104C3×C5×D4—22no—
105C3×C5×D4—22no—
106C3×C5×D4—41no—
107C3×C5×D4—41no—
108C2×C3×C4×C5—21no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5—21no—
118C2×C3×Dic5—41no—
119C2×C3×Dic5—41no—
120C2×C3×Dic5—41no—
121C2×C3×Dic5—41no—
122C2×C3×Dic5SD1612yescomplemented
123C3×Dic10—41no—
124C3×Dic10—81no—
125C3×C5×C8—41no—
126C3×#168—41no—
127C22×C3×D4C2×D511yescharacteristic
128C2×C3×SD16—21no—
129C2×C3×SD16—101no—
130C3×C4⋊Q8—101no—
131C3×C4⋊Q8—101no—
132C3×#125—101no—
133C3×#125—101no—
134C3×C22⋊Q8—51no—
135C3×C22⋊Q8—101no—
136C3×C22⋊Q8C2×D511yescharacteristic
137C3×#117—101no—
138C2×C3×C4⋊C4—51no—
139C2×C3×C22⋊C4—101no—
140C2×C3×C22⋊C4—101no—
141C3×#102—21no—
142C3×#102—101no—
143C3×C22⋊C8—51no—
144C3×C22⋊C8C2×D511yescharacteristic
145C3×#95—51no—
146C24×C5—21no—
147C2×C5×Q8C3×D411yescharacteristic
148C2×C5×D4—21no—
149C2×C5×D4—21no—
150C2×C5×D4—42no—
151C22×C4×C5C23×C311yescharacteristic
152C22×Dic5—21no—
153C22×Dic5C3×D411yescharacteristic
154C22×Dic5C3×D411yescharacteristic
155C2×Dic10—21no—
156C2×Dic10C3×D411yescharacteristic
157C5×SD16—42no—
158C2×C5×C8—21no—
159C5×C4⋊C4—21no—
160C5×C4⋊C4C3×D411yescharacteristic
161C5×C22⋊C4—21no—
162C22⋊Dic5—21no—
163C22⋊Dic5—42no—
164C22⋊Dic5—42no—
165#687—42no—
166C4⋊Dic5—21no—
167C4⋊Dic5C3×D411yescharacteristic
168#683—21no—
169#683—21no—
170#683—21no—
171#683—21no—
172#683—21no—
173#683—21no—
174#683—21no—
175C4×Dic5—21no—
176C4×Dic5—21no—
177C2×#168—21no—
178#544—51no—
179#450—51no—
180#450C3×D511yescharacteristic
181#394—51no—
182#328—51no—
183#328—51no—
184#324—51no—
185C22×C3×C5—21no—
186C22×C3×C5—21no—
187C22×C3×C5—42no—
188C22×C3×C5—42no—
189C22×C3×C5—42no—
190C22×C3×C5—81no—
191C22×C3×C5—81no—
192C22×C3×C5—81no—
193C22×C3×C5—81no—
194C22×C3×C5#12011yescharacteristic
195C22×C3×C5C2×SD1611yescharacteristic
196C22×C3×C5#13711yescharacteristic
197C3×C4×C5—21no—
198C3×C4×C5—21no—
199C3×C4×C5—41no—
200C3×C4×C5—41no—
201C3×Dic5—22no—
202C3×Dic5—41no—
203C3×Dic5—41no—
204C3×Dic5—41no—
205C3×Dic5—81no—
206C24×C3—21no—
207C2×C3×Q8—51no—
208C2×C3×Q8—101no—
209C2×C3×Q8C22⋊D511yescharacteristic
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—42no—
213C22×C3×C4—51no—
214C22×C3×C4—51no—
215C22×C3×C4—101no—
216C22×C3×C4C22×D511yescharacteristic
217C3×SD16—42no—
218C3×SD16—202no—
219C2×C3×C8—21no—
220C2×C3×C8—101no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—51no—
223C3×C4⋊C4—101no—
224C3×C4⋊C4—101no—
225C3×C4⋊C4—101no—
226C3×C4⋊C4—101no—
227C3×C4⋊C4—101no—
228C3×C4⋊C4—101no—
229C3×C4⋊C4—101no—
230C3×C4⋊C4—101no—
231C3×C4⋊C4C22⋊D511yescharacteristic
232C3×C22⋊C4—21no—
233C3×C22⋊C4—101no—
234C3×C22⋊C4—202no—
235C3×C22⋊C4—202no—
236C3×C42—101no—
237C3×C42—101no—
238C23×C5—22no—
239C23×C5—41no—
240C23×C5—41no—
241C23×C5—41no—
242C23×C5—41no—
243C23×C5—41no—
244C23×C5—41no—
245C23×C5C2×C3×D411yescharacteristic
246C5×Q8—41no—
247C5×D4—22no—
248C5×D4—22no—
249C5×D4—41no—
250C5×D4—41no—
251C2×C4×C5—21no—
252C2×C4×C5—21no—
253C2×C4×C5—41no—
254C2×C4×C5C2×C3×D411yescharacteristic
255C2×C4×C5C2×C3×D411yescharacteristic
256C2×Dic5—21no—
257C2×Dic5—21no—
258C2×Dic5—21no—
259C2×Dic5—21no—
260C2×Dic5—21no—
261C2×Dic5—41no—
262C2×Dic5—41no—
263C2×Dic5—41no—
264C2×Dic5—41no—
265C2×Dic5C3×SD1612yescomplemented
266Dic10—41no—
267Dic10—81no—
268C5×C8—41no—
269#168—41no—
270C22×D4C2×C3×D511yescharacteristic
271C2×SD16—21no—
272C2×SD16—101no—
273C4⋊Q8—101no—
274C4⋊Q8—101no—
275#125—101no—
276#125—101no—
277C22⋊Q8—51no—
278C22⋊Q8—101no—
279C22⋊Q8C2×C3×D511yescharacteristic
280#117—101no—
281C2×C4⋊C4—51no—
282C2×C22⋊C4—101no—
283C2×C22⋊C4—101no—
284#102—21no—
285#102—101no—
286C22⋊C8—51no—
287C22⋊C8C2×C3×D511yescharacteristic
288#95—51no—
289C2×C3×C5—21no—
290C2×C3×C5—21no—
291C2×C3×C5—82no—
292C2×C3×C5#44811yescharacteristic
293C2×C3×C5#45411yescharacteristic
294C2×C3×C5B(4,𝔽2)11yescharacteristic
295C23×C3—22no—
296C23×C3—41no—
297C23×C3—41no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—41no—
302C23×C3D4×D511yescharacteristic
303C3×Q8—41no—
304C3×Q8—201no—
305C3×Q8—401no—
306C3×D4—22no—
307C3×D4—22no—
308C3×D4—41no—
309C3×D4—41no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—41no—
313C2×C3×C4—52no—
314C2×C3×C4—101no—
315C2×C3×C4—101no—
316C2×C3×C4—101no—
317C2×C3×C4—101no—
318C2×C3×C4—101no—
319C2×C3×C4—201no—
320C2×C3×C4—201no—
321C2×C3×C4—201no—
322C2×C3×C4—201no—
323C2×C3×C4D4×D511yescharacteristic
324C2×C3×C4C2×C22⋊D511yescharacteristic
325C3×C8—41no—
326C3×C8—201no—
327C22×C5—21no—
328C22×C5—21no—
329C22×C5—42no—
330C22×C5—42no—
331C22×C5—42no—
332C22×C5—81no—
333C22×C5—81no—
334C22×C5—81no—
335C22×C5—81no—
336C22×C5C3×#12011yescharacteristic
337C22×C5C2×C3×SD1611yescharacteristic
338C22×C5C3×#13711yescharacteristic
339C4×C5—21no—
340C4×C5—21no—
341C4×C5—41no—
342C4×C5—41no—
343Dic5—22no—
344Dic5—41no—
345Dic5—41no—
346Dic5—41no—
347Dic5—81no—
348C24—21no—
349C2×Q8—51no—
350C2×Q8—101no—
351C2×Q8C3×C22⋊D511yescharacteristic
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—42no—
355C22×C4—51no—
356C22×C4—51no—
357C22×C4—101no—
358C22×C4C22×C3×D511yescharacteristic
359SD16—42no—
360SD16—202no—
361C2×C8—21no—
362C2×C8—101no—
363C4⋊C4—21no—
364C4⋊C4—51no—
365C4⋊C4—101no—
366C4⋊C4—101no—
367C4⋊C4—101no—
368C4⋊C4—101no—
369C4⋊C4—101no—
370C4⋊C4—101no—
371C4⋊C4—101no—
372C4⋊C4—101no—
373C4⋊C4C3×C22⋊D511yescharacteristic
374C22⋊C4—21no—
375C22⋊C4—101no—
376C22⋊C4—202no—
377C22⋊C4—202no—
378C42—101no—
379C42—101no—
380C3×C5#159911yescharacteristic, complemented, Hall
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—42no—
384C22×C3—42no—
385C22×C3—42no—
386C22×C3—81no—
387C22×C3—81no—
388C22×C3—81no—
389C22×C3—81no—
390C22×C3D5×SD1611yescharacteristic
391C22×C3#406111yescharacteristic
392C22×C3#408311yescharacteristic
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—41no—
396C3×C4—41no—
397C3×C4—102no—
398C3×C4—201no—
399C3×C4—201no—
400C3×C4—201no—
401C3×C4—401no—
402C2×C5—21no—
403C2×C5—21no—
404C2×C5—82no—
405C2×C5C3×#44811yescharacteristic
406C2×C5C3×#45411yescharacteristic
407C2×C5C3×B(4,𝔽2)11yescharacteristic
408C23—22no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23C3×D4×D511yescharacteristic
416Q8—41no—
417Q8—201no—
418Q8—401no—
419D4—22no—
420D4—22no—
421D4—41no—
422D4—41no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—41no—
426C2×C4—52no—
427C2×C4—101no—
428C2×C4—101no—
429C2×C4—101no—
430C2×C4—101no—
431C2×C4—101no—
432C2×C4—201no—
433C2×C4—201no—
434C2×C4—201no—
435C2×C4—201no—
436C2×C4C3×D4×D511yescharacteristic
437C2×C4C2×C3×C22⋊D511yescharacteristic
438C8—41no—
439C8—201no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—82no—
443C2×C3#6532111yescharacteristic
444C2×C3#6545911yescharacteristic
445C2×C3#6549011yescharacteristic
446C5C3×#159911yescharacteristic, complemented, Sylow
447C22—21no—
448C22—21no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22C3×D5×SD1611yescharacteristic
457C22C3×#406111yescharacteristic
458C22C3×#408311yescharacteristic
459C4—21no—
460C4—21no—
461C4—41no—
462C4—41no—
463C4—102no—
464C4—201no—
465C4—201no—
466C4—201no—
467C4—401no—
468C3#1060177211yescharacteristic, direct product factor, Sylow
469C2—21no—
470C2—21no—
471C2—82no—
472C2C3×#6532111yescharacteristic
473C2C3×#6545911yescharacteristic
474C2C3×#6549011yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#450C2
socleC22×C3×C5#120
prime radicalC22×C3×C5×D4C22
hypercenterC3×#450D5
hypocenterC5C3×#1599
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#450

Complements

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

NH ≅ G/Ntype
1. C3×#65957C2semidirect
5. C3×#64758C2semidirect
6. C3×#64689C2semidirect
7. C3×#64687C2semidirect
8. #10601772C3direct (N × H)
29. #65957C2×C3semidirect
33. #64758C2×C3semidirect
34. #64689C2×C3semidirect
35. #64687C2×C3semidirect
122. C2×C3×Dic5SD16semidirect
265. C2×Dic5C3×SD16semidirect
380. C3×C5#1599semidirect
446. C5C3×#1599semidirect
468. C3#10601772direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659572
C3×C5×#4502
C3×#655112
C3×#655072
C3×#647582
C3×#646892
C3×#646872
#106017723
C3×#15995