Finite Group Databasebeta

← C3×#10618482 #14481805

Subgroups — C3×#10618482 #14481805

Order 1920.

1992 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#544C211yesmaximal, characteristic, complemented
2C3×#66063C214yesmaximal, complemented
3C3×#66062C214yesmaximal, complemented
4C3×#66023C214yesmaximal, complemented
5C3×#66022C214yesmaximal, complemented
6C3×#65968C214yesmaximal
7C3×#65956C214yesmaximal, complemented
8C3×D5×#117C212yesmaximal
9C3×#65853C212yesmaximal, complemented
10C2×C3×#4038C211yesmaximal, characteristic
11C3×#65834C211yesmaximal, characteristic, complemented
12#10618482C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C3×C5×C4⋊Q8C2214yescomplemented
15C3×C5×#125C2214yescomplemented
16C3×C5×C22⋊Q8C2214yes—
17C3×C5×#117C2212yes—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C3×#4092C2218yes—
20C3×Q8×Dic5C2214yescomplemented
21C3×#4090C2214yescomplemented
22C2×C3×#685C2212yes—
23C3×#4072C2212yes—
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C3×#4070C2214yes—
26C2×C3×C4×Dic5C2212yes—
27C3×#4043C2218yes—
28C3×#4042C2218yes—
29C3×#4042C2218yes—
30C3×#4038C2212yes—
31C3×#4038C2212yes—
32C3×#4038C2214yes—
33C3×#4038C2214yes—
34C3×D5×C4⋊C4C2212yes—
35C3×D5×C4⋊C4C2212yes—
36C3×#4036C2214yescomplemented
37C3×#4036C2214yescomplemented
38C3×#4035C2218yescomplemented
39C3×#4034C2214yescomplemented
40C3×#4034C2214yescomplemented
41C3×#4034C2214yescomplemented
42C3×#4033C2214yescomplemented
43C3×#4033C2218yescomplemented
44C3×D5×C22⋊C4C2214yes—
45C3×#4024C2218yes—
46C3×#4023C2214yes—
47C3×#4018C2214yes—
48C3×C42×D5C2214yes—
49C3×#4016C2214yescomplemented
50C3×#4015C2214yescomplemented
51C3×#3458—51nomaximal, Hall
52C5×#544C2×C311yescharacteristic, complemented
53#66063C2×C314yescomplemented
54#66062C2×C314yescomplemented
55#66023C2×C314yescomplemented
56#66022C2×C314yescomplemented
57#65968C2×C314yes—
58#65956C2×C314yescomplemented
59D5×#117C2×C312yes—
60#65853C2×C312yescomplemented
61C2×#4038C2×C311yescharacteristic
62#65834C2×C311yescharacteristic, complemented
63C23×C3×D5C2311yescharacteristic
64C2×C3×C5×Q8C2314yes—
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×Dic5C2312yes—
68C22×C3×Dic5C2311yescharacteristic
69C2×C3×C4×D5Q818yescomplemented
70C2×C3×C4×D5C2314yes—
71C2×C3×C4×D5C2314yes—
72C2×C3×C4×D5C2312yes—
73C2×C3×C4×D5C2312yes—
74C2×C3×Dic10C2314yes—
75C2×C3×Dic10C2318yes—
76C3×C5×C4⋊C4C2314yes—
77C3×C5×C4⋊C4C2312yes—
78C3×C5×C4⋊C4C2312yes—
79C3×C5×C4⋊C4C2314yes—
80C3×C5×C4⋊C4C2318yes—
81C3×C5×C22⋊C4C2314yes—
82C3×C42×C5C2314yes—
83C3×C22⋊Dic5C2314yes—
84C3×#685C2314yes—
85C3×#685C2318yes—
86C3×#685C2314yes—
87C3×C4⋊Dic5C2318yes—
88C3×C4⋊Dic5C2314yes—
89C3×C4⋊Dic5C2312yes—
90C3×C4⋊Dic5C2314yes—
91C3×C4⋊Dic5C2312yes—
92C3×#683C2314yes—
93C3×#683C2318yes—
94C3×#683C2318yes—
95C3×#683C2318yes—
96C3×#683C2314yes—
97C3×C4×Dic5C2314yes—
98C3×C4×Dic5C2314yes—
99C3×C4×Dic5C2314yes—
100C3×C4×Dic5C2314yes—
101C3×C4×Dic5C2314yes—
102C3×#544—54no—
103C3×#544—54no—
104C3×#544—52no—
105C3×#544—51no—
106C3×#544D511yescharacteristic, complemented
107C3×#543—54no—
108C3×#533—54no—
109C3×#533—54no—
110C3×#533—54no—
111C2×C3×#117—52no—
112C2×C3×#117—51no—
113C22×C4×D5C22×C311yescharacteristic
114C5×C4⋊Q8C22×C314yescomplemented
115C5×#125C22×C314yescomplemented
116C5×C22⋊Q8C22×C314yes—
117C5×#117C22×C312yes—
118C2×C5×C4⋊C4C22×C311yescharacteristic
119#4092C22×C318yes—
120Q8×Dic5C22×C314yescomplemented
121#4090C22×C314yescomplemented
122C2×#685C22×C312yes—
123#4072C22×C312yes—
124C2×C4⋊Dic5C22×C311yescharacteristic
125#4070C22×C314yes—
126C2×C4×Dic5C22×C312yes—
127#4043C22×C318yes—
128#4042C22×C318yes—
129#4042C22×C318yes—
130#4038C22×C312yes—
131#4038C22×C314yes—
132#4038C22×C314yes—
133#4038C22×C312yes—
134D5×C4⋊C4C22×C312yes—
135D5×C4⋊C4C22×C312yes—
136#4036C22×C314yescomplemented
137#4036C22×C314yescomplemented
138#4035C22×C318yescomplemented
139#4034C22×C314yescomplemented
140#4034C22×C314yescomplemented
141#4034C22×C314yescomplemented
142#4033C22×C318yescomplemented
143#4033C22×C314yescomplemented
144D5×C22⋊C4C22×C314yes—
145#4024C22×C318yes—
146#4023C22×C314yes—
147#4018C22×C314yes—
148C42×D5C22×C314yes—
149#4016C22×C314yescomplemented
150#4015C22×C314yescomplemented
151#3458—51noSylow
152C23×C3×C5C2411yescharacteristic
153C22×C3×D5—41no—
154C22×C3×D5—41no—
155C22×C3×D5C2×Q814yes—
156C22×C3×D5C2412yes—
157C3×C5×Q8—44no—
158C2×C3×C4×C5—42no—
159C2×C3×C4×C5C2×Q814yes—
160C2×C3×C4×C5C2414yes—
161C2×C3×C4×C5C2414yes—
162C2×C3×C4×C5C2414yes—
163C2×C3×C4×C5C2412yes—
164C2×C3×Dic5—42no—
165C2×C3×Dic5C2×Q814yes—
166C2×C3×Dic5C2414yes—
167C2×C3×Dic5C2414yes—
168C2×C3×Dic5C2414yes—
169C2×C3×Dic5C2411yescharacteristic
170C2×C3×Dic5C2411yescharacteristic
171C3×C4×D5—44no—
172C3×C4×D5—44no—
173C3×C4×D5C2×Q818yes—
174C3×C4×D5C2×Q818yes—
175C3×Dic10—44no—
176C3×Dic10—48no—
177C23×C3×C4—51no—
178C3×C4⋊Q8—54no—
179C3×C4⋊Q8—54no—
180C3×C4⋊Q8—54no—
181C3×C4⋊Q8—54no—
182C3×C4⋊Q8—54no—
183C3×C4⋊Q8C2×D514yescomplemented
184C3×#125—58no—
185C3×#125—54no—
186C3×#125—54no—
187C3×#125—54no—
188C3×#125C2×D514yescomplemented
189C3×C22⋊Q8—58no—
190C3×C22⋊Q8—54no—
191C3×C22⋊Q8—58no—
192C3×C22⋊Q8—58no—
193C3×C22⋊Q8—58no—
194C3×C22⋊Q8—58no—
195C3×C22⋊Q8C2×D514yes—
196C3×C4×Q8—54no—
197C3×C4×Q8—58no—
198C3×C4×Q8—54no—
199C3×#117—52no—
200C3×#117—52no—
201C3×#117—52no—
202C3×#117—54no—
203C3×#117—54no—
204C3×#117—54no—
205C3×#117—54no—
206C3×#117C2×D512yes—
207C2×C3×C4⋊C4—51no—
208C2×C3×C4⋊C4—52no—
209C2×C3×C4⋊C4—52no—
210C2×C3×C4⋊C4C2×D511yescharacteristic
211C2×C3×C22⋊C4—52no—
212C2×C3×C22⋊C4—54no—
213C2×C3×C42—52no—
214C2×C3×C42—54no—
215C23×D5C23×C311yescharacteristic
216C2×C5×Q8C23×C314yes—
217C22×C4×C5C23×C312yes—
218C22×C4×C5C23×C311yescharacteristic
219C22×Dic5C23×C312yes—
220C22×Dic5C23×C311yescharacteristic
221C2×C4×D5C3×Q818yescomplemented
222C2×C4×D5C23×C314yes—
223C2×C4×D5C23×C314yes—
224C2×C4×D5C23×C312yes—
225C2×C4×D5C23×C312yes—
226C2×Dic10C23×C318yes—
227C2×Dic10C23×C314yes—
228C5×C4⋊C4C23×C314yes—
229C5×C4⋊C4C23×C312yes—
230C5×C4⋊C4C23×C312yes—
231C5×C4⋊C4C23×C314yes—
232C5×C4⋊C4C23×C318yes—
233C5×C22⋊C4C23×C314yes—
234C42×C5C23×C314yes—
235C22⋊Dic5C23×C314yes—
236#685C23×C314yes—
237#685C23×C314yes—
238#685C23×C318yes—
239C4⋊Dic5C23×C312yes—
240C4⋊Dic5C23×C314yes—
241C4⋊Dic5C23×C318yes—
242C4⋊Dic5C23×C312yes—
243C4⋊Dic5C23×C314yes—
244#683C23×C318yes—
245#683C23×C318yes—
246#683C23×C314yes—
247#683C23×C314yes—
248#683C23×C318yes—
249C4×Dic5C23×C314yes—
250C4×Dic5C23×C314yes—
251C4×Dic5C23×C314yes—
252C4×Dic5C23×C314yes—
253C4×Dic5C23×C314yes—
254#544—54no—
255#544—54no—
256#544—52no—
257#544—51no—
258#544C3×D511yescharacteristic, complemented
259#543—54no—
260#533—54no—
261#533—54no—
262#533—54no—
263C2×#117—52no—
264C2×#117—51no—
265C22×C3×C5—21no—
266C22×C3×C5—21no—
267C22×C3×C5C22×Q812yes—
268C22×C3×C5C2511yescharacteristic
269C2×C3×D5—22no—
270C2×C3×D5—22no—
271C2×C3×D5—44no—
272C2×C3×D5C22×Q814yes—
273C3×C4×C5—24no—
274C3×C4×C5—24no—
275C3×C4×C5—24no—
276C3×C4×C5C22×Q814yes—
277C3×Dic5—24no—
278C3×Dic5—24no—
279C3×Dic5—24no—
280C3×Dic5C22×Q812yes—
281C3×Dic5C22×Q812yes—
282C24×C3—51no—
283C2×C3×Q8—54no—
284C2×C3×Q8—58no—
285C2×C3×Q8C22×D514yes—
286C22×C3×C4—51no—
287C22×C3×C4—58no—
288C22×C3×C4—52no—
289C22×C3×C4—52no—
290C22×C3×C4—52no—
291C22×C3×C4—54no—
292C22×C3×C4—54no—
293C22×C3×C4C22×D512yes—
294C22×C3×C4C22×D511yescharacteristic
295C3×C4⋊C4—54no—
296C3×C4⋊C4—54no—
297C3×C4⋊C4—58no—
298C3×C4⋊C4—58no—
299C3×C4⋊C4—58no—
300C3×C4⋊C4—52no—
301C3×C4⋊C4—54no—
302C3×C4⋊C4—52no—
303C3×C4⋊C4—54no—
304C3×C4⋊C4—58no—
305C3×C4⋊C4C22×D512yes—
306C3×C4⋊C4C22×D512yes—
307C3×C4⋊C4C22×D514yes—
308C3×C4⋊C4C22×D518yes—
309C3×C4⋊C4C22×D514yes—
310C3×C22⋊C4—54no—
311C3×C22⋊C4—58no—
312C3×C22⋊C4—54no—
313C3×C22⋊C4—54no—
314C3×C22⋊C4C22×D514yes—
315C3×C42—54no—
316C3×C42—54no—
317C3×C42—54no—
318C3×C42—54no—
319C3×C42—54no—
320C3×C42C22×D514yes—
321C23×C5C24×C311yescharacteristic
322C22×D5—41no—
323C22×D5—41no—
324C22×D5C2×C3×Q814yes—
325C22×D5C24×C312yes—
326C5×Q8—44no—
327C2×C4×C5—42no—
328C2×C4×C5C2×C3×Q814yes—
329C2×C4×C5C24×C314yes—
330C2×C4×C5C24×C314yes—
331C2×C4×C5C24×C314yes—
332C2×C4×C5C24×C312yes—
333C2×Dic5—42no—
334C2×Dic5C2×C3×Q814yes—
335C2×Dic5C24×C314yes—
336C2×Dic5C24×C314yes—
337C2×Dic5C24×C314yes—
338C2×Dic5C24×C311yescharacteristic
339C2×Dic5C24×C311yescharacteristic
340C4×D5—44no—
341C4×D5—44no—
342C4×D5C2×C3×Q818yes—
343C4×D5C2×C3×Q818yes—
344Dic10—44no—
345Dic10—48no—
346C23×C4—51no—
347C4⋊Q8—54no—
348C4⋊Q8—54no—
349C4⋊Q8—54no—
350C4⋊Q8—54no—
351C4⋊Q8—54no—
352C4⋊Q8C2×C3×D514yescomplemented
353#125—58no—
354#125—54no—
355#125—54no—
356#125—54no—
357#125C2×C3×D514yescomplemented
358C22⋊Q8—58no—
359C22⋊Q8—54no—
360C22⋊Q8—58no—
361C22⋊Q8—58no—
362C22⋊Q8—58no—
363C22⋊Q8—58no—
364C22⋊Q8C2×C3×D514yes—
365C4×Q8—54no—
366C4×Q8—58no—
367C4×Q8—54no—
368#117—52no—
369#117—52no—
370#117—52no—
371#117—54no—
372#117—54no—
373#117—54no—
374#117—54no—
375#117C2×C3×D512yes—
376C2×C4⋊C4—51no—
377C2×C4⋊C4—52no—
378C2×C4⋊C4—52no—
379C2×C4⋊C4C2×C3×D511yescharacteristic
380C2×C22⋊C4—52no—
381C2×C22⋊C4—54no—
382C2×C42—52no—
383C2×C42—54no—
384C2×C3×C5—22no—
385C2×C3×C5C23×Q811yescharacteristic
386C2×C3×C5#58511yescharacteristic
387C2×C3×C5#58511yescharacteristic
388C3×D5—24no—
389C23×C3—52no—
390C23×C3—54no—
391C23×C3—201no—
392C23×C3—201no—
393C23×C3C23×D511yescharacteristic
394C3×Q8—44no—
395C3×Q8—204no—
396C3×Q8—208no—
397C2×C3×C4—42no—
398C2×C3×C4—54no—
399C2×C3×C4—51no—
400C2×C3×C4—51no—
401C2×C3×C4—58no—
402C2×C3×C4—58no—
403C2×C3×C4—54no—
404C2×C3×C4—54no—
405C2×C3×C4—54no—
406C2×C3×C4—204no—
407C2×C3×C4—204no—
408C2×C3×C4—202no—
409C2×C3×C4Q8×D514yes—
410C2×C3×C4C23×D514yes—
411C2×C3×C4C23×D514yes—
412C2×C3×C4C23×D514yes—
413C2×C3×C4C23×D512yes—
414C22×C5—21no—
415C22×C5—21no—
416C22×C5C22×C3×Q812yes—
417C22×C5C25×C311yescharacteristic
418C2×D5—22no—
419C2×D5—22no—
420C2×D5—44no—
421C2×D5C22×C3×Q814yes—
422C4×C5—24no—
423C4×C5—24no—
424C4×C5—24no—
425C4×C5C22×C3×Q814yes—
426Dic5—24no—
427Dic5—24no—
428Dic5—24no—
429Dic5C22×C3×Q812yes—
430Dic5C22×C3×Q812yes—
431C24—51no—
432C2×Q8—54no—
433C2×Q8—58no—
434C2×Q8C22×C3×D514yes—
435C22×C4—51no—
436C22×C4—58no—
437C22×C4—52no—
438C22×C4—52no—
439C22×C4—52no—
440C22×C4—54no—
441C22×C4—54no—
442C22×C4C22×C3×D512yes—
443C22×C4C22×C3×D511yescharacteristic
444C4⋊C4—54no—
445C4⋊C4—54no—
446C4⋊C4—54no—
447C4⋊C4—52no—
448C4⋊C4—52no—
449C4⋊C4—58no—
450C4⋊C4—58no—
451C4⋊C4—58no—
452C4⋊C4—54no—
453C4⋊C4—58no—
454C4⋊C4C22×C3×D512yes—
455C4⋊C4C22×C3×D512yes—
456C4⋊C4C22×C3×D514yes—
457C4⋊C4C22×C3×D518yes—
458C4⋊C4C22×C3×D514yes—
459C22⋊C4—54no—
460C22⋊C4—58no—
461C22⋊C4—54no—
462C22⋊C4—54no—
463C22⋊C4C22×C3×D514yes—
464C42—54no—
465C42—54no—
466C42—54no—
467C42—54no—
468C42—54no—
469C42C22×C3×D514yes—
470C3×C5#345811yescharacteristic, complemented, Hall
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—54no—
474C22×C3—102no—
475C22×C3—102no—
476C22×C3—204no—
477C22×C3C2×Q8×D512yes—
478C22×C3C24×D511yescharacteristic
479C3×C4—24no—
480C3×C4—24no—
481C3×C4—24no—
482C3×C4—52no—
483C3×C4—52no—
484C3×C4—104no—
485C3×C4—104no—
486C3×C4—104no—
487C3×C4C2×Q8×D514yes—
488C2×C5—22no—
489C2×C5C23×C3×Q811yescharacteristic
490C2×C5C3×#58511yescharacteristic
491C2×C5C3×#58511yescharacteristic
492D5—24no—
493C23—52no—
494C23—54no—
495C23—201no—
496C23—201no—
497C23C23×C3×D511yescharacteristic
498Q8—44no—
499Q8—204no—
500Q8—208no—
501C2×C4—42no—
502C2×C4—54no—
503C2×C4—51no—
504C2×C4—51no—
505C2×C4—58no—
506C2×C4—58no—
507C2×C4—54no—
508C2×C4—54no—
509C2×C4—54no—
510C2×C4—204no—
511C2×C4—204no—
512C2×C4—202no—
513C2×C4C3×Q8×D514yes—
514C2×C4C23×C3×D514yes—
515C2×C4C23×C3×D514yes—
516C2×C4C23×C3×D514yes—
517C2×C4C23×C3×D512yes—
518C2×C3—22no—
519C2×C3—104no—
520C2×C3C22×Q8×D511yescharacteristic
521C2×C3#6628511yescharacteristic
522C2×C3#6628711yescharacteristic
523C5C3×#345811yescharacteristic, complemented, Sylow
524C22—21no—
525C22—21no—
526C22—54no—
527C22—102no—
528C22—102no—
529C22—204no—
530C22C2×C3×Q8×D512yes—
531C22C24×C3×D511yescharacteristic
532C4—24no—
533C4—24no—
534C4—24no—
535C4—52no—
536C4—52no—
537C4—104no—
538C4—104no—
539C4—104no—
540C4C2×C3×Q8×D514yes—
541C3#1061848211yescharacteristic, direct product factor, Sylow
542C2—22no—
543C2—104no—
544C2C22×C3×Q8×D511yescharacteristic
545C2C3×#6628511yescharacteristic
546C2C3×#6628711yescharacteristic
subgroupG/H
centerC22×C3C24×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC3×C5×#544C2
socleC22×C3×C5C25
prime radicalC23×C3×D5C23
hypercenterC3×#544D5
hypocenterC5C3×#3458
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#544

Complements

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

NH ≅ G/Ntype
1. C3×C5×#544C2semidirect
2. C3×#66063C2semidirect
3. C3×#66062C2semidirect
4. C3×#66023C2semidirect
5. C3×#66022C2semidirect
7. C3×#65956C2semidirect
9. C3×#65853C2semidirect
11. C3×#65834C2semidirect
12. #10618482C3direct (N × H)
14. C3×C5×C4⋊Q8C22semidirect
15. C3×C5×#125C22semidirect
20. C3×Q8×Dic5C22semidirect
21. C3×#4090C22semidirect
36. C3×#4036C22semidirect
37. C3×#4036C22semidirect
38. C3×#4035C22semidirect
39. C3×#4034C22semidirect
40. C3×#4034C22semidirect
41. C3×#4034C22semidirect
42. C3×#4033C22semidirect
43. C3×#4033C22semidirect
49. C3×#4016C22semidirect
50. C3×#4015C22semidirect
52. C5×#544C2×C3semidirect
53. #66063C2×C3semidirect
54. #66062C2×C3semidirect
55. #66023C2×C3semidirect
56. #66022C2×C3semidirect
58. #65956C2×C3semidirect
60. #65853C2×C3semidirect
62. #65834C2×C3semidirect
69. C2×C3×C4×D5Q8semidirect
106. C3×#544D5semidirect
114. C5×C4⋊Q8C22×C3semidirect
115. C5×#125C22×C3semidirect
120. Q8×Dic5C22×C3semidirect
121. #4090C22×C3semidirect
136. #4036C22×C3semidirect
137. #4036C22×C3semidirect
138. #4035C22×C3semidirect
139. #4034C22×C3semidirect
140. #4034C22×C3semidirect
141. #4034C22×C3semidirect
142. #4033C22×C3semidirect
143. #4033C22×C3semidirect
149. #4016C22×C3semidirect
150. #4015C22×C3semidirect
183. C3×C4⋊Q8C2×D5semidirect
188. C3×#125C2×D5semidirect
221. C2×C4×D5C3×Q8semidirect
258. #544C3×D5semidirect
352. C4⋊Q8C2×C3×D5semidirect
357. #125C2×C3×D5semidirect
470. C3×C5#3458semidirect
523. C5C3×#3458semidirect
541. C3#10618482direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5442
C3×#660632
C3×#660622
C3×#660232
C3×#660222
C3×#659682
C3×#659562
C3×D5×#1172
C3×#658532
C2×C3×#40382
C3×#658342
#106184823
C3×#34585