Finite Group Databasebeta

← C3×#10599938 #14313298

Subgroups — C3×#10599938 #14313298

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65982C211yesmaximal, characteristic
2C3×#65034C211yesmaximal, characteristic
3C3×#65029C211yesmaximal, characteristic
4C3×C5×#352C211yesmaximal, characteristic, complemented
5C3×#64759C211yesmaximal, characteristic, complemented
6C3×#64696C211yesmaximal, characteristic, complemented
7C3×#64692C211yesmaximal, characteristic, complemented
8#10599938C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#711C2211yescharacteristic
10C22×C3×Dic10C411yescharacteristic, complemented
11C3×C5×#123C2211yescharacteristic
12C3×#4081C2211yescharacteristic
13C3×#4075C411yescharacteristic, complemented
14C3×D5×M16—21no—
15C3×#4042—21no—
16C3×#4034—21no—
17C3×#4032C411yescharacteristic, complemented
18C3×#4031—21no—
19C3×#4024—21no—
20C3×#4023—21no—
21C3×#4023C411yescharacteristic, complemented
22C3×C5×#100C2211yescharacteristic
23C3×C5×#99C2211yescharacteristic
24C3×#3966C2211yescharacteristic
25C3×#3965C2211yescharacteristic
26C3×#3956—21no—
27C3×#3938—21no—
28C3×#2123—51nomaximal, Hall
29#65982C2×C311yescharacteristic
30#65034C2×C311yescharacteristic
31#65029C2×C311yescharacteristic
32C5×#352C2×C311yescharacteristic, complemented
33#64759C2×C311yescharacteristic, complemented
34#64696C2×C311yescharacteristic, complemented
35#64692C2×C311yescharacteristic, complemented
36C2×C3×C5×D4C2311yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C2×C3×C22⋊D5C2×C411yescharacteristic
39C2×C3×C22⋊D5D411yescharacteristic
40C22×C3×Dic5C2×C411yescharacteristic
41C22×C3×Dic5C2×C411yescharacteristic
42C22×C3×Dic5D411yescharacteristic
43C3×#711—41no—
44C3×#711—41no—
45C2×C3×C4×D5D411yescharacteristic
46C2×C3×Dic10—21no—
47C2×C3×Dic10—21no—
48C2×C3×Dic10—41no—
49C2×C3×Dic10—41no—
50C2×C3×Dic10D411yescharacteristic
51C3×C5×M16—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C22⋊C4—21no—
54C3×C5×C22⋊C4—21no—
55C3×C5×C22⋊C4C2×C411yescharacteristic
56C3×C22⋊Dic5—21no—
57C3×C22⋊Dic5—21no—
58C3×C22⋊Dic5C2×C411yescharacteristic
59C3×#685—21no—
60C3×#685—21no—
61C3×C4⋊Dic5—21no—
62C3×#683—21no—
63C3×#683—21no—
64C3×#683—21no—
65C3×#683—41no—
66C3×C4×Dic5—21no—
67C3×C4×Dic5—41no—
68C3×#681—21no—
69C3×#676—41no—
70C3×C8×D5—41no—
71C3×#536—51no—
72C3×#413—51no—
73C3×#410—51no—
74C3×#352—51no—
75C3×#352—51no—
76C3×#352—51no—
77C3×#352D511yescharacteristic, complemented
78C2×#711C22×C311yescharacteristic
79C22×Dic10C3×C411yescharacteristic, complemented
80C5×#123C22×C311yescharacteristic
81#4081C22×C311yescharacteristic
82#4075C3×C411yescharacteristic, complemented
83D5×M16—21no—
84#4042—21no—
85#4034—21no—
86#4032C3×C411yescharacteristic, complemented
87#4031—21no—
88#4024—21no—
89#4023—21no—
90#4023C3×C411yescharacteristic, complemented
91C5×#100C22×C311yescharacteristic
92C5×#99C22×C311yescharacteristic
93#3966C22×C311yescharacteristic
94#3965C22×C311yescharacteristic
95#3956—21no—
96#3938—21no—
97#2123—51noSylow
98C23×C3×C5C22×C411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C22×C3×D5C22⋊C411yescharacteristic
101C3×C5×D4—41no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5C2×D411yescharacteristic
107C3×C22⋊D5—41no—
108C3×C22⋊D5—41no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—21no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5C22⋊C411yescharacteristic
118C2×C3×Dic5C22⋊C411yescharacteristic
119C2×C3×Dic5C22⋊C411yescharacteristic
120C3×C4×D5—21no—
121C3×C4×D5—21no—
122C3×Dic10—41no—
123C3×Dic10—42no—
124C3×Dic10—41no—
125C3×Dic10—41no—
126C3×C5×C8—41no—
127C3×#168—41no—
128C2×C3×#41—51no—
129C22×C3×Q8—51no—
130C2×C3×M16—101no—
131C3×C4⋊Q8—101no—
132C3×#124—101no—
133C3×#123—51no—
134C3×#123—51no—
135C3×#123—51no—
136C3×#123C2×D511yescharacteristic
137C3×C22⋊Q8—101no—
138C3×C22⋊Q8—101no—
139C3×#117—51no—
140C3×#117—101no—
141C3×#101—101no—
142C3×#100—51no—
143C3×#100C2×D511yescharacteristic
144C3×#99—51no—
145C3×#99—101no—
146C3×#99C2×D511yescharacteristic
147C2×C5×D4C23×C311yescharacteristic
148C22×C4×C5C2×C3×C411yescharacteristic
149C2×C22⋊D5C2×C3×C411yescharacteristic
150C2×C22⋊D5C3×D411yescharacteristic
151C22×Dic5C2×C3×C411yescharacteristic
152C22×Dic5C2×C3×C411yescharacteristic
153C22×Dic5C3×D411yescharacteristic
154#711—41no—
155#711—41no—
156C2×C4×D5C3×D411yescharacteristic
157C2×Dic10—21no—
158C2×Dic10—21no—
159C2×Dic10—41no—
160C2×Dic10—41no—
161C2×Dic10C3×D411yescharacteristic
162C5×M16—21no—
163C5×C4⋊C4—21no—
164C5×C22⋊C4—21no—
165C5×C22⋊C4—21no—
166C5×C22⋊C4C2×C3×C411yescharacteristic
167C22⋊Dic5—21no—
168C22⋊Dic5—21no—
169C22⋊Dic5C2×C3×C411yescharacteristic
170#685—21no—
171#685—21no—
172C4⋊Dic5—21no—
173#683—21no—
174#683—21no—
175#683—21no—
176#683—41no—
177C4×Dic5—21no—
178C4×Dic5—41no—
179#681—21no—
180#676—41no—
181C8×D5—41no—
182#536—51no—
183#413—51no—
184#410—51no—
185#352—51no—
186#352—51no—
187#352—51no—
188#352C3×D511yescharacteristic, complemented
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5—41no—
192C22×C3×C5—41no—
193C22×C3×C5C2×C22⋊C411yescharacteristic
194C2×C3×D5—21no—
195C2×C3×D5—41no—
196C3×C4×C5—21no—
197C3×C4×C5—41no—
198C3×C4×C5—41no—
199C3×C4×C5—81no—
200C3×Dic5—21no—
201C3×Dic5—21no—
202C3×Dic5—41no—
203C3×Dic5—41no—
204C3×Dic5—81no—
205C3×Dic5#9911yescharacteristic
206C3×Dic5#9911yescharacteristic
207C3×#41—201no—
208C3×#41—201no—
209C2×C3×Q8—51no—
210C2×C3×Q8—101no—
211C2×C3×Q8—101no—
212C2×C3×Q8—201no—
213C2×C3×Q8—201no—
214C2×C3×D4—51no—
215C2×C3×D4—51no—
216C2×C3×D4C22×D511yescharacteristic
217C22×C3×C4—51no—
218C22×C3×C4—51no—
219C22×C3×C4—51no—
220C22×C3×C4—51no—
221C22×C3×C4C4×D511yescharacteristic
222C3×M16—21no—
223C3×M16—101no—
224C3×M16—201no—
225C2×C3×C8—201no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—101no—
228C3×C4⋊C4—101no—
229C3×C4⋊C4—101no—
230C3×C4⋊C4—101no—
231C3×C4⋊C4—201no—
232C3×C22⋊C4—21no—
233C3×C22⋊C4—21no—
234C3×C22⋊C4—51no—
235C3×C22⋊C4—101no—
236C3×C22⋊C4—101no—
237C3×C22⋊C4—101no—
238C3×C22⋊C4—101no—
239C3×C22⋊C4C4×D511yescharacteristic
240C3×C42—101no—
241C3×C42—201no—
242C23×C5C22×C3×C411yescharacteristic
243C23×C5C2×C3×D411yescharacteristic
244C22×D5C3×C22⋊C411yescharacteristic
245C5×D4—41no—
246C2×C4×C5—21no—
247C2×C4×C5—21no—
248C2×C4×C5—41no—
249C2×C4×C5—41no—
250C2×C4×C5C2×C3×D411yescharacteristic
251C22⋊D5—41no—
252C22⋊D5—41no—
253C2×Dic5—21no—
254C2×Dic5—21no—
255C2×Dic5—21no—
256C2×Dic5—21no—
257C2×Dic5—21no—
258C2×Dic5—21no—
259C2×Dic5—41no—
260C2×Dic5—41no—
261C2×Dic5C3×C22⋊C411yescharacteristic
262C2×Dic5C3×C22⋊C411yescharacteristic
263C2×Dic5C3×C22⋊C411yescharacteristic
264C4×D5—21no—
265C4×D5—21no—
266Dic10—41no—
267Dic10—42no—
268Dic10—41no—
269Dic10—41no—
270C5×C8—41no—
271#168—41no—
272C2×#41—51no—
273C22×Q8—51no—
274C2×M16—101no—
275C4⋊Q8—101no—
276#124—101no—
277#123—51no—
278#123—51no—
279#123—51no—
280#123C2×C3×D511yescharacteristic
281C22⋊Q8—101no—
282C22⋊Q8—101no—
283#117—51no—
284#117—101no—
285#101—101no—
286#100—51no—
287#100C2×C3×D511yescharacteristic
288#99—51no—
289#99—101no—
290#99C2×C3×D511yescharacteristic
291C2×C3×C5—21no—
292C2×C3×C5—41no—
293C2×C3×C5—41no—
294C2×C3×C5C2×#9911yescharacteristic
295C3×D5—41no—
296C23×C3—51no—
297C23×C3C2×C4×D511yescharacteristic
298C23×C3D4×D511yescharacteristic
299C3×Q8—201no—
300C3×Q8—201no—
301C3×Q8—201no—
302C3×Q8—202no—
303C3×D4—41no—
304C3×D4—201no—
305C3×D4—201no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—51no—
311C2×C3×C4—51no—
312C2×C3×C4—51no—
313C2×C3×C4—101no—
314C2×C3×C4—101no—
315C2×C3×C4—101no—
316C2×C3×C4—101no—
317C2×C3×C4—101no—
318C2×C3×C4—101no—
319C2×C3×C4—101no—
320C2×C3×C4—101no—
321C2×C3×C4—201no—
322C2×C3×C4—201no—
323C2×C3×C4D4×D511yescharacteristic
324C3×C8—41no—
325C3×C8—201no—
326C22×C5—21no—
327C22×C5—21no—
328C22×C5—41no—
329C22×C5—41no—
330C22×C5C2×C3×C22⋊C411yescharacteristic
331C2×D5—21no—
332C2×D5—41no—
333C4×C5—21no—
334C4×C5—41no—
335C4×C5—41no—
336C4×C5—81no—
337Dic5—21no—
338Dic5—21no—
339Dic5—41no—
340Dic5—41no—
341Dic5—81no—
342Dic5C3×#9911yescharacteristic
343Dic5C3×#9911yescharacteristic
344#41—201no—
345#41—201no—
346C2×Q8—51no—
347C2×Q8—101no—
348C2×Q8—101no—
349C2×Q8—201no—
350C2×Q8—201no—
351C2×D4—51no—
352C2×D4—51no—
353C2×D4C22×C3×D511yescharacteristic
354C22×C4—51no—
355C22×C4—51no—
356C22×C4—51no—
357C22×C4—51no—
358C22×C4C3×C4×D511yescharacteristic
359M16—21no—
360M16—101no—
361M16—201no—
362C2×C8—201no—
363C4⋊C4—21no—
364C4⋊C4—101no—
365C4⋊C4—101no—
366C4⋊C4—101no—
367C4⋊C4—101no—
368C4⋊C4—201no—
369C22⋊C4—21no—
370C22⋊C4—21no—
371C22⋊C4—51no—
372C22⋊C4—101no—
373C22⋊C4—101no—
374C22⋊C4—101no—
375C22⋊C4—101no—
376C22⋊C4C3×C4×D511yescharacteristic
377C42—101no—
378C42—201no—
379C3×C5#212311yescharacteristic, complemented, Hall
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3—101no—
385C22×C3—201no—
386C22×C3D5×C22⋊C411yescharacteristic
387C3×C4—21no—
388C3×C4—41no—
389C3×C4—41no—
390C3×C4—51no—
391C3×C4—51no—
392C3×C4—81no—
393C3×C4—101no—
394C3×C4—101no—
395C3×C4—201no—
396C3×C4—201no—
397C3×C4—401no—
398C2×C5—21no—
399C2×C5—41no—
400C2×C5—41no—
401C2×C5C2×C3×#9911yescharacteristic
402D5—41no—
403C23—51no—
404C23C2×C3×C4×D511yescharacteristic
405C23C3×D4×D511yescharacteristic
406Q8—201no—
407Q8—201no—
408Q8—201no—
409Q8—202no—
410D4—41no—
411D4—201no—
412D4—201no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—51no—
418C2×C4—51no—
419C2×C4—51no—
420C2×C4—101no—
421C2×C4—101no—
422C2×C4—101no—
423C2×C4—101no—
424C2×C4—101no—
425C2×C4—101no—
426C2×C4—101no—
427C2×C4—101no—
428C2×C4—201no—
429C2×C4—201no—
430C2×C4C3×D4×D511yescharacteristic
431C8—41no—
432C8—201no—
433C2×C3—21no—
434C2×C3—41no—
435C2×C3—41no—
436C2×C3—201no—
437C2×C3D5×#9911yescharacteristic
438C5C3×#212311yescharacteristic, complemented, Sylow
439C22—21no—
440C22—21no—
441C22—41no—
442C22—41no—
443C22—101no—
444C22—201no—
445C22C3×D5×C22⋊C411yescharacteristic
446C4—21no—
447C4—41no—
448C4—41no—
449C4—51no—
450C4—51no—
451C4—81no—
452C4—101no—
453C4—101no—
454C4—201no—
455C4—201no—
456C4—401no—
457C3#1059993811yescharacteristic, direct product factor, Sylow
458C2—21no—
459C2—41no—
460C2—41no—
461C2—201no—
462C2C3×D5×#9911yescharacteristic
subgroupG/H
centerC2×C3D5×#99
commutatorC23×C5C22×C3×C4
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#352C2
socleC2×C3×C5C2×#99
prime radicalC2×C3×#711C22
cosocleC2×C5×D4C23×C3
hypercenterC3×#352D5
hypocenterC5C3×#2123
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#352

Complements

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

NH ≅ G/Ntype
4. C3×C5×#352C2semidirect
5. C3×#64759C2semidirect
6. C3×#64696C2semidirect
7. C3×#64692C2semidirect
8. #10599938C3direct (N × H)
10. C22×C3×Dic10C4semidirect
13. C3×#4075C4semidirect
17. C3×#4032C4semidirect
21. C3×#4023C4semidirect
32. C5×#352C2×C3semidirect
33. #64759C2×C3semidirect
34. #64696C2×C3semidirect
35. #64692C2×C3semidirect
77. C3×#352D5semidirect
79. C22×Dic10C3×C4semidirect
82. #4075C3×C4semidirect
86. #4032C3×C4semidirect
90. #4023C3×C4semidirect
188. #352C3×D5semidirect
379. C3×C5#2123semidirect
438. C5C3×#2123semidirect
457. C3#10599938direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659822
C3×#650342
C3×#650292
C3×C5×#3522
C3×#647592
C3×#646962
C3×#646922
#105999383
C3×#21235