Finite Group Databasebeta

← Dic3×#4076 #14321478

Subgroups — Dic3×#4076 #14321478

Order 1920.

1648 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#4076C211yesmaximal, characteristic
3C2×Dic3×C22⋊D5C212yesmaximal, complemented
4C2×Dic3×D20C211yesmaximal, characteristic, complemented
5#11751313C211yesmaximal, characteristic, complemented
6#11749495C212yesmaximal, complemented
7Dic3×#685C212yesmaximal, complemented
8#11748857C211yesmaximal, characteristic, complemented
9#11748785C211yesmaximal, characteristic, complemented
10#11748770C212yesmaximal, complemented
11Dic3×C4⋊Dic5C211yesmaximal, characteristic, complemented
12C4×#4076—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C22×C3×C22⋊D5C2212yes—
17C22×C3×D20C2211yescharacteristic
18C22×D5×Dic3C2212yes—
19C2×#6719C2212yes—
20C2×C4⋊Dic15C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4×C5×Dic3—24no—
23C2×C4×C5×Dic3C2211yescharacteristic
24C2×C4×C5×Dic3C2211yescharacteristic
25C2×C4×C5×Dic3C2211yescharacteristic
26C2×C4×C5×Dic3C2211yescharacteristic
27C3×#4076C418yescomplemented
28C2×C3×#685C2212yes—
29C2×C3×C4⋊Dic5C2211yescharacteristic
30Dic3×C22⋊D5—28no—
31C2×#6668C2212yes—
32C2×#6665C2212yes—
33C2×#6665C2212yes—
34C2×#6665C2212yes—
35C2×Dic3×Dic5C2212yes—
36Dic3×D20—24no—
37#91115C2212yes—
38#90994C2212yes—
39#90994C2212yes—
40Dic3×#121—51nomaximal, Hall
41C22×C42×C5—31no—
42C2×#4076D311yescharacteristic
43C2×C4×C22⋊D5—32no—
44C2×C4×D20—31no—
45#65502—32no—
46#65501—31no—
47#65229—32no—
48#65228—31no—
49C4×#685—32no—
50C4×C4⋊Dic5—31no—
51#65217—31no—
52C24×C3×C5C2311yescharacteristic
53C23×C3×D5C2312yes—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5—22no—
56C22×C3×C4×C5C2×C414yescomplemented
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15C2312yes—
60C22×Dic15C2312yes—
61C22×C5×Dic3—22no—
62C22×C5×Dic3—22no—
63C22×C5×Dic3—22no—
64C22×C5×Dic3—22no—
65C22×C5×Dic3—22no—
66C22×C5×Dic3D414yescomplemented
67C22×C5×Dic3C2311yescharacteristic
68C22×C5×Dic3C2311yescharacteristic
69C22×C5×Dic3C2311yescharacteristic
70C22×C5×Dic3C2311yescharacteristic
71C2×C3×C22⋊D5—24no—
72C2×C3×C22⋊D5—24no—
73C2×C3×C22⋊D5C2×C418yescomplemented
74C22×C3×Dic5C2312yes—
75C2×C3×D20—22no—
76C2×C3×D20—22no—
77C2×C3×D20C2×C414yescomplemented
78C2×D5×Dic3—24no—
79C2×D5×Dic3—24no—
80C2×D5×Dic3—24no—
81#6719—24no—
82C4⋊Dic15—22no—
83C4⋊Dic15—22no—
84C4×C5×Dic3—22no—
85C4×C5×Dic3—22no—
86C4×C5×Dic3—22no—
87C4×C5×Dic3D414yescomplemented
88C3×#685C2×C418yescomplemented
89C3×C4⋊Dic5C2×C414yescomplemented
90#6668—24no—
91#6665—24no—
92#6665—24no—
93#6665—24no—
94Dic3×Dic5—24no—
95C2×C3×#121—51no—
96C2×D4×Dic3—52no—
97C2×D4×Dic3—51no—
98C22×C4×Dic3D511yescharacteristic, complemented
99#5221—51no—
100#5220—52no—
101#5212—51no—
102#4984—51no—
103Dic3×C4⋊C4—51no—
104#4951—52no—
105Dic3×C22⋊C4—52no—
106C23×C4×C5—31no—
107C23×C4×C5—31no—
108C23×C4×C5C2×D311yescharacteristic
109C22×C22⋊D5C2×D312yes—
110C22×D20C2×D311yescharacteristic
111C22×C4×D5—32no—
112C2×C42×C5—31no—
113C2×C42×C5—31no—
114C2×C42×C5—31no—
115C2×C42×C5—31no—
116C2×C42×C5—64no—
117C2×C22⋊Dic5—32no—
118#4076Dic318yesdirect product factor
119C4×C22⋊D5—68no—
120C2×#685—32no—
121C2×#685—32no—
122C2×#685—32no—
123C2×#685C2×D312yes—
124C2×C4⋊Dic5—31no—
125C2×C4⋊Dic5—31no—
126C2×C4⋊Dic5C2×D311yescharacteristic
127C2×#683—32no—
128C2×C4×Dic5—32no—
129C4×D20—64no—
130#3963—32no—
131#3963—32no—
132#3963—32no—
133C4×#121—151noSylow
134C23×C3×C5—21no—
135C23×C3×C5—21no—
136C23×C3×C5—21no—
137C23×C3×C5—21no—
138C23×C3×C5C22×C412yes—
139C23×C3×C5C2×D412yes—
140C23×C3×C5#4112yes—
141C23×C3×C5C2411yescharacteristic
142C22×C3×D5—22no—
143C22×C3×D5—22no—
144C22×C3×D5—22no—
145C22×C3×D5—22no—
146C22×C3×D5—22no—
147C22×C3×D5—22no—
148C22×C3×D5C22×C414yes—
149C2×C3×C4×C5—21no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—28no—
152C2×C3×C4×C5C22×C412yes—
153C2×C3×C4×C5C22×C412yes—
154C2×C3×C4×C5C2×D412yes—
155C2×C3×C4×C5#4112yes—
156C2×Dic15—22no—
157C2×Dic15—22no—
158C2×Dic15—22no—
159C2×Dic15—22no—
160C2×Dic15—22no—
161C2×Dic15—22no—
162C2×C5×Dic3—28no—
163C2×C5×Dic3—21no—
164C2×C5×Dic3—21no—
165C2×C5×Dic3—21no—
166C2×C5×Dic3—21no—
167C2×C5×Dic3—21no—
168C2×C5×Dic3—21no—
169C2×C5×Dic3—28no—
170C2×C5×Dic3C2×D412yes—
171C2×C5×Dic3C2×D412yes—
172C2×C5×Dic3C2×D412yes—
173C2×C5×Dic3C2×D412yes—
174C2×C5×Dic3#4112yes—
175C2×C5×Dic3#4112yes—
176C3×C22⋊D5—216no—
177C2×C3×Dic5—22no—
178C2×C3×Dic5—22no—
179C2×C3×Dic5C22×C414yes—
180C3×D20—28no—
181D5×Dic3—48no—
182C22×C3×D4—52no—
183C22×C3×D4—51no—
184C23×C3×C4C2×D511yescharacteristic
185C23×Dic3—52no—
186C23×Dic3C2×D511yescharacteristic
187C23×Dic3C2×D511yescharacteristic
188C3×#121—58no—
189C2×C3×C4⋊C4—51no—
190C2×C3×C22⋊C4—52no—
191C2×#217—52no—
192C2×#217—52no—
193C2×#217—52no—
194C2×#217—52no—
195D4×Dic3—108no—
196D4×Dic3—104no—
197C2×C4⋊Dic3—51no—
198C2×C4⋊Dic3—51no—
199C2×C4⋊Dic3—52no—
200C2×C4×Dic3—24no—
201C2×C4×Dic3—52no—
202C2×C4×Dic3C2×D511yescharacteristic
203C2×C4×Dic3C2×D511yescharacteristic
204C2×C4×Dic3C2×D511yescharacteristic
205C2×C4×Dic3C2×D511yescharacteristic
206C3⋊#95—52no—
207C3⋊#95—52no—
208C3⋊#95—52no—
209C24×C5C22×D311yescharacteristic
210C23×D5C22×D312yes—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—31no—
214C22×C4×C5—34no—
215C22×C4×C5—31no—
216C22×C4×C5—31no—
217C22×C4×C5—31no—
218C22×C4×C5—62no—
219C22×C4×C5—62no—
220C22×C4×C5—62no—
221C22×C4×C5—62no—
222C22×C4×C5—62no—
223C22×C4×C5C2×Dic314yescomplemented
224C22×C4×C5C22×D311yescharacteristic
225C22×C4×C5C22×D311yescharacteristic
226C2×C22⋊D5—24no—
227C2×C22⋊D5—24no—
228C2×C22⋊D5C2×Dic318yescomplemented
229C22×Dic5—32no—
230C22×Dic5—32no—
231C22×Dic5C22×D312yes—
232C2×D20—22no—
233C2×D20—22no—
234C2×D20C2×Dic314yescomplemented
235C2×C4×D5—64no—
236C2×C4×D5—64no—
237C2×C4×D5—64no—
238C42×C5—34no—
239C42×C5—62no—
240C42×C5—62no—
241C42×C5—62no—
242C22⋊Dic5—64no—
243#685—64no—
244#685—64no—
245#685—64no—
246#685C2×Dic318yescomplemented
247C4⋊Dic5—62no—
248C4⋊Dic5—62no—
249C4⋊Dic5C2×Dic314yescomplemented
250#683—64no—
251C4×Dic5—64no—
252C2×#121—51no—
253C2×C4×D4—151no—
254C2×C4×D4—152no—
255C22×C42—31no—
256#390—151no—
257#389—151no—
258#388—152no—
259#386—152no—
260#380—151no—
261C4×C4⋊C4—151no—
262C4×C22⋊C4—152no—
263C22×C3×C5—22no—
264C22×C3×C5—22no—
265C22×C3×C5—22no—
266C22×C3×C5—22no—
267C22×C3×C5—22no—
268C22×C3×C5—22no—
269C22×C3×C5C4×D414yescomplemented
270C22×C3×C5C23×C411yescharacteristic
271C22×C3×C5C22×D411yescharacteristic
272C22×C3×C5C22×D411yescharacteristic
273C22×C3×C5C2×#4111yescharacteristic
274C22×C3×C5C2×#4111yescharacteristic
275C22×C3×C5C2×#4111yescharacteristic
276C22×C3×C5C2×#4111yescharacteristic
277C2×C3×D5—24no—
278C2×C3×D5—24no—
279C2×C3×D5—24no—
280C2×C3×D5—42no—
281C2×C3×D5—42no—
282C2×C3×D5—42no—
283C2×C3×D5—42no—
284C3×C4×C5—22no—
285C3×C4×C5C4×D414yescomplemented
286Dic15—42no—
287Dic15—42no—
288C3×Dic5—24no—
289C5×Dic3—22no—
290C5×Dic3—22no—
291C5×Dic3—22no—
292C5×Dic3#12114yescomplemented
293C24×C3—52no—
294C24×C3C22×D511yescharacteristic
295C2×C3×D4—58no—
296C2×C3×D4—54no—
297C2×C3×D4—104no—
298C2×C3×D4—104no—
299C2×C3×D4—102no—
300C2×C3×D4—102no—
301C22×C3×C4—22no—
302C22×C3×C4—22no—
303C22×C3×C4—52no—
304C22×C3×C4C4×D514yescomplemented
305C22×C3×C4C22×D511yescharacteristic
306C22×C3×C4C22×D511yescharacteristic
307C22×Dic3—22no—
308C22×Dic3—22no—
309C22×Dic3—22no—
310C22×Dic3—22no—
311C22×Dic3—22no—
312C22×Dic3—52no—
313C22×Dic3—52no—
314C22×Dic3—104no—
315C22×Dic3—104no—
316C22×Dic3—104no—
317C22×Dic3D2014yescomplemented
318C22×Dic3C22×D511yescharacteristic
319C22×Dic3C22×D511yescharacteristic
320C22×Dic3C22×D511yescharacteristic
321C22×Dic3C22×D511yescharacteristic
322C3×C4⋊C4—54no—
323C3×C22⋊C4—58no—
324#217—104no—
325#217—104no—
326#217—104no—
327#217—104no—
328C4⋊Dic3—102no—
329C4⋊Dic3—102no—
330C4⋊Dic3—104no—
331C4×Dic3—22no—
332C4×Dic3—22no—
333C4×Dic3—22no—
334C4×Dic3—104no—
335C4×Dic3C22⋊D514yescomplemented
336C23×C5—21no—
337C23×C5—21no—
338C23×C5—21no—
339C23×C5—21no—
340C23×C5D3×D412yes—
341C23×C5#23712yes—
342C23×C5C22×Dic312yes—
343C23×C5C23×D311yescharacteristic
344C22×D5—22no—
345C22×D5—22no—
346C22×D5—22no—
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5C22×Dic314yes—
351C2×C4×C5—21no—
352C2×C4×C5—21no—
353C2×C4×C5—28no—
354C2×C4×C5—32no—
355C2×C4×C5—32no—
356C2×C4×C5—32no—
357C2×C4×C5—32no—
358C2×C4×C5—32no—
359C2×C4×C5—32no—
360C2×C4×C5—68no—
361C2×C4×C5—68no—
362C2×C4×C5—61no—
363C2×C4×C5—61no—
364C2×C4×C5—61no—
365C2×C4×C5—61no—
366C2×C4×C5—61no—
367C2×C4×C5—61no—
368C2×C4×C5D3×D412yes—
369C2×C4×C5#23712yes—
370C2×C4×C5C22×Dic312yes—
371C2×C4×C5C22×Dic312yes—
372C22⋊D5—216no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—62no—
376C2×Dic5—62no—
377C2×Dic5—62no—
378C2×Dic5—62no—
379C2×Dic5—62no—
380C2×Dic5—62no—
381C2×Dic5C22×Dic314yes—
382D20—28no—
383C4×D5—128no—
384C22×D4—52no—
385C22×D4—51no—
386C23×C4—31no—
387C23×C4—31no—
388C23×C4—152no—
389C23×C4D3×D511yescharacteristic
390#121—58no—
391C4×D4—304no—
392C4×D4—308no—
393C2×C4⋊C4—51no—
394C2×C4⋊C4—152no—
395C2×C4⋊C4—151no—
396C2×C4⋊C4—151no—
397C2×C22⋊C4—52no—
398C2×C22⋊C4—152no—
399C2×C22⋊C4—152no—
400C2×C22⋊C4—152no—
401C2×C22⋊C4—152no—
402C2×C42—31no—
403C2×C42—31no—
404C2×C42—31no—
405C2×C42—31no—
406C2×C42—64no—
407C2×C42—152no—
408#95—152no—
409#95—152no—
410#95—152no—
411C2×C3×C5—24no—
412C2×C3×C5C2×C4×D411yescharacteristic
413C2×C3×C5C2×C4×D411yescharacteristic
414C2×C3×C5C4×#4111yescharacteristic
415C2×C3×C5C2×#12111yescharacteristic
416C2×C3×C5#52511yescharacteristic
417C2×C3×C5#52911yescharacteristic
418C2×C3×C5#53211yescharacteristic
419C3×D5—44no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—54no—
425C23×C3—102no—
426C23×C3—102no—
427C23×C3—102no—
428C23×C3—102no—
429C23×C3—102no—
430C23×C3—102no—
431C23×C3C2×C4×D512yes—
432C23×C3C2×D2012yes—
433C23×C3#70912yes—
434C23×C3C23×D511yescharacteristic
435C3×D4—1016no—
436C3×D4—108no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—28no—
440C2×C3×C4—54no—
441C2×C3×C4—102no—
442C2×C3×C4—102no—
443C2×C3×C4C2×C4×D512yes—
444C2×C3×C4C2×C4×D512yes—
445C2×C3×C4#70912yes—
446C2×C3×C4C2×C22⋊D512yes—
447C2×Dic3—28no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—28no—
455C2×Dic3—102no—
456C2×Dic3—102no—
457C2×Dic3—102no—
458C2×Dic3—102no—
459C2×Dic3—102no—
460C2×Dic3—102no—
461C2×Dic3—208no—
462C2×Dic3C2×D2012yes—
463C2×Dic3C2×D2012yes—
464C2×Dic3#70912yes—
465C2×Dic3#70912yes—
466C2×Dic3C2×C22⋊D512yes—
467C2×Dic3C2×C22⋊D512yes—
468C22×C5—22no—
469C22×C5—22no—
470C22×C5—22no—
471C22×C5—22no—
472C22×C5—22no—
473C22×C5—22no—
474C22×C5D4×Dic314yescomplemented
475C22×C5C2×D3×D411yescharacteristic
476C22×C5C2×D3×D411yescharacteristic
477C22×C5C2×#23711yescharacteristic
478C22×C5C2×#23711yescharacteristic
479C22×C5D3×#4111yescharacteristic
480C22×C5D3×#4111yescharacteristic
481C22×C5C23×Dic311yescharacteristic
482C2×D5—24no—
483C2×D5—24no—
484C2×D5—24no—
485C2×D5—42no—
486C2×D5—42no—
487C2×D5—42no—
488C2×D5—42no—
489C4×C5—22no—
490C4×C5—34no—
491C4×C5—62no—
492C4×C5—62no—
493C4×C5—62no—
494C4×C5D4×Dic314yescomplemented
495Dic5—24no—
496Dic5—122no—
497Dic5—122no—
498C24—52no—
499C24C2×D3×D511yescharacteristic
500C2×D4—58no—
501C2×D4—54no—
502C2×D4—104no—
503C2×D4—104no—
504C2×D4—102no—
505C2×D4—102no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—31no—
509C22×C4—34no—
510C22×C4—31no—
511C22×C4—31no—
512C22×C4—31no—
513C22×C4—52no—
514C22×C4—62no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—152no—
520C22×C4—152no—
521C22×C4—304no—
522C22×C4—304no—
523C22×C4—304no—
524C22×C4D5×Dic314yescomplemented
525C22×C4C2×D3×D511yescharacteristic
526C22×C4C2×D3×D511yescharacteristic
527C4⋊C4—54no—
528C4⋊C4—304no—
529C4⋊C4—302no—
530C4⋊C4—302no—
531C22⋊C4—58no—
532C22⋊C4—304no—
533C22⋊C4—304no—
534C22⋊C4—304no—
535C22⋊C4—304no—
536C42—34no—
537C42—62no—
538C42—62no—
539C42—62no—
540C42—304no—
541C3×C5C4×#12111yescharacteristic, complemented, Hall
542C22×C3—22no—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—104no—
549C22×C3—104no—
550C22×C3—104no—
551C22×C3—202no—
552C22×C3—202no—
553C22×C3—202no—
554C22×C3—202no—
555C22×C3C4×D2014yescomplemented
556C22×C3C22×C4×D511yescharacteristic
557C22×C3C22×D2011yescharacteristic
558C22×C3C2×#70911yescharacteristic
559C22×C3C2×#70911yescharacteristic
560C22×C3C2×#70911yescharacteristic
561C22×C3C2×#70911yescharacteristic
562C22×C3C22×C22⋊D511yescharacteristic
563C3×C4—22no—
564C3×C4—104no—
565C3×C4C4×C22⋊D514yescomplemented
566Dic3—22no—
567Dic3—22no—
568Dic3—22no—
569Dic3—202no—
570Dic3—202no—
571Dic3#407614yesdirect product factor
572C2×C5—24no—
573C2×C5#559611yescharacteristic
574C2×C5#560011yescharacteristic
575C2×C5D3×#12111yescharacteristic
576C2×C5#560611yescharacteristic
577C2×C5C2×D4×Dic311yescharacteristic
578C2×C5C2×D4×Dic311yescharacteristic
579C2×C5Dic3×#4111yescharacteristic
580D5—44no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—54no—
586C23—102no—
587C23—102no—
588C23—102no—
589C23—102no—
590C23—102no—
591C23—102no—
592C23#676512yes—
593C23D3×D2012yes—
594C23C2×D5×Dic312yes—
595C23C22×D3×D511yescharacteristic
596D4—1016no—
597D4—108no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—28no—
601C2×C4—32no—
602C2×C4—32no—
603C2×C4—32no—
604C2×C4—32no—
605C2×C4—32no—
606C2×C4—32no—
607C2×C4—54no—
608C2×C4—68no—
609C2×C4—68no—
610C2×C4—61no—
611C2×C4—61no—
612C2×C4—61no—
613C2×C4—61no—
614C2×C4—61no—
615C2×C4—61no—
616C2×C4—102no—
617C2×C4—102no—
618C2×C4—302no—
619C2×C4—302no—
620C2×C4—302no—
621C2×C4—302no—
622C2×C4—302no—
623C2×C4—302no—
624C2×C4—608no—
625C2×C4C2×D5×Dic312yes—
626C2×C4C2×D5×Dic312yes—
627C2×C4#677912yes—
628C2×C4D3×C22⋊D512yes—
629C2×C3—24no—
630C2×C3—204no—
631C2×C3C2×C4×D2011yescharacteristic
632C2×C3C4×#70911yescharacteristic
633C2×C3#6581111yescharacteristic
634C2×C3#6581311yescharacteristic
635C2×C3C2×C4×C22⋊D511yescharacteristic
636C2×C3C2×#407611yescharacteristic
637C2×C3#6612511yescharacteristic
638C5Dic3×#12111yescharacteristic, complemented, Sylow
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—104no—
646C22—104no—
647C22—104no—
648C22—202no—
649C22—202no—
650C22—202no—
651C22—202no—
652C22Dic3×D2014yescomplemented
653C22C2×#676511yescharacteristic
654C22C2×D3×D2011yescharacteristic
655C22D3×#70911yescharacteristic
656C22D3×#70911yescharacteristic
657C22C22×D5×Dic311yescharacteristic
658C22C2×#677911yescharacteristic
659C22C2×D3×C22⋊D511yescharacteristic
660C4—22no—
661C4—34no—
662C4—62no—
663C4—62no—
664C4—62no—
665C4—104no—
666C4—602no—
667C4—602no—
668C4Dic3×C22⋊D514yescomplemented
669C3C4×#407611yescharacteristic, complemented, Sylow
670C2—24no—
671C2—204no—
672C2#1175434111yescharacteristic
673C2C2×Dic3×D2011yescharacteristic
674C2#1175435611yescharacteristic
675C2Dic3×#70911yescharacteristic
676C2#1175442211yescharacteristic
677C2D3×#407611yescharacteristic
678C2C2×Dic3×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C3×#4076C2
hypercenterC23×C4D3×D5
hypocenterC3×C5C4×#121
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C5×Dic3C2semidirect
3. C2×Dic3×C22⋊D5C2semidirect
4. C2×Dic3×D20C2semidirect
5. #11751313C2semidirect
6. #11749495C2semidirect
7. Dic3×#685C2semidirect
8. #11748857C2semidirect
9. #11748785C2semidirect
10. #11748770C2semidirect
11. Dic3×C4⋊Dic5C2semidirect
27. C3×#4076C4semidirect
56. C22×C3×C4×C5C2×C4semidirect
66. C22×C5×Dic3D4semidirect
73. C2×C3×C22⋊D5C2×C4semidirect
77. C2×C3×D20C2×C4semidirect
87. C4×C5×Dic3D4semidirect
88. C3×#685C2×C4semidirect
89. C3×C4⋊Dic5C2×C4semidirect
98. C22×C4×Dic3D5semidirect
118. #4076Dic3direct (N × H)
223. C22×C4×C5C2×Dic3semidirect
228. C2×C22⋊D5C2×Dic3semidirect
234. C2×D20C2×Dic3semidirect
246. #685C2×Dic3semidirect
249. C4⋊Dic5C2×Dic3semidirect
269. C22×C3×C5C4×D4semidirect
285. C3×C4×C5C4×D4semidirect
292. C5×Dic3#121semidirect
304. C22×C3×C4C4×D5semidirect
317. C22×Dic3D20semidirect
335. C4×Dic3C22⋊D5semidirect
474. C22×C5D4×Dic3semidirect
494. C4×C5D4×Dic3semidirect
524. C22×C4D5×Dic3semidirect
541. C3×C5C4×#121semidirect
555. C22×C3C4×D20semidirect
565. C3×C4C4×C22⋊D5semidirect
571. Dic3#4076direct (N × H)
638. C5Dic3×#121semidirect
652. C22Dic3×D20semidirect
668. C4Dic3×C22⋊D5semidirect
669. C3C4×#4076semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C5×Dic32
C2×C3×#40762
C2×Dic3×C22⋊D52
C2×Dic3×D202
#117513132
#117494952
Dic3×#6852
#117488572
#117487852
#117487702
Dic3×C4⋊Dic52
C4×#40763
Dic3×#1215