Finite Group Databasebeta

← C3×#10605502 #14327349

Subgroups — C3×#10605502 #14327349

Order 1920.

1320 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4038C211yesmaximal, characteristic, complemented
2C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×C4×D20C211yesmaximal, characteristic
4C3×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
5C3×#65276C211yesmaximal, characteristic, complemented
6C3×#65276C211yesmaximal, characteristic, complemented
7C3×#65229C212yesmaximal, complemented
8C3×C4×#685C212yesmaximal, complemented
9C3×#65225C211yesmaximal, characteristic, complemented
10C3×#64954C212yesmaximal
11C3×#64942C212yesmaximal, complemented
12#10605502C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×D20C2211yescharacteristic
14C22×C3×C4×D5C2212yes—
15C22×C3×C4×D5C2211yescharacteristic
16C22×C3×C4×D5C2211yescharacteristic
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C42×C5C2212yes—
20C2×C3×C42×C5C2211yescharacteristic
21C2×C3×#685C2212yes—
22C2×C3×#685C2212yes—
23C2×C3×#685C2212yes—
24C2×C3×#685C2211yescharacteristic
25C2×C3×#685C2211yescharacteristic
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×#683C2212yes—
30C2×C3×C4×Dic5C2212yes—
31C3×#4038—24no—
32C3×D5×C4⋊C4—24no—
33C3×C4×D20C418yescomplemented
34C3×C5×#95C2212yes—
35C3×#3963C2212yes—
36C3×#3963C2212yes—
37C3×#3963C2212yes—
38C3×#3963C2212yes—
39C3×#2352—51nomaximal, Hall
40C2×#4038C2×C311yescharacteristic, complemented
41C2×D5×C4⋊C4C2×C311yescharacteristic, complemented
42C2×C4×D20C2×C311yescharacteristic
43C4×C5×C4⋊C4C2×C311yescharacteristic, complemented
44#65276C2×C311yescharacteristic, complemented
45#65276C2×C311yescharacteristic, complemented
46#65229C2×C312yescomplemented
47C4×#685C2×C312yescomplemented
48#65225C2×C311yescharacteristic, complemented
49#64954C2×C312yes—
50#64942C2×C312yescomplemented
51C23×C3×D5C2311yescharacteristic
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2312yes—
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×Dic5C2312yes—
59C22×C3×Dic5C2312yes—
60C22×C3×Dic5C2311yescharacteristic
61C22×C3×Dic5C2311yescharacteristic
62C2×C3×D20—22no—
63C2×C3×D20—22no—
64C2×C3×D20C2×C414yes—
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5—22no—
67C2×C3×C4×D5—22no—
68C2×C3×C4×D5—22no—
69C2×C3×C4×D5—24no—
70C2×C3×C4×D5—24no—
71C2×C3×C4×D5—42no—
72C2×C3×C4×D5C2×C414yes—
73C2×C3×C4×D5C2×C414yescomplemented
74C3×C5×C4⋊C4—22no—
75C3×C5×C4⋊C4D414yescomplemented
76C3×C42×C5—42no—
77C3×C42×C5C2×C414yescomplemented
78C3×#685—24no—
79C3×#685—24no—
80C3×#685—42no—
81C3×#685C2×C414yes—
82C3×#685C2×C414yescomplemented
83C3×C4⋊Dic5—22no—
84C3×C4⋊Dic5—22no—
85C3×C4⋊Dic5C2×C414yescomplemented
86C3×#683—24no—
87C3×C4×Dic5—24no—
88C2×C3×C4×D4—51no—
89C2×C3×#117—51no—
90C22×C3×C4⋊C4—51no—
91C3×#388—52no—
92C3×#387—52no—
93C3×#386—52no—
94C3×#382—51no—
95C3×#380—51no—
96C3×#380—51no—
97C3×C4×C4⋊C4D511yescharacteristic, complemented
98C3×C4×C22⋊C4—52no—
99C22×D20C22×C311yescharacteristic
100C22×C4×D5C22×C312yes—
101C22×C4×D5C22×C311yescharacteristic
102C22×C4×D5C22×C311yescharacteristic
103C2×C5×C4⋊C4C22×C311yescharacteristic
104C2×C5×C4⋊C4C22×C311yescharacteristic
105C2×C42×C5C22×C312yes—
106C2×C42×C5C22×C311yescharacteristic
107C2×#685C22×C312yes—
108C2×#685C22×C312yes—
109C2×#685C22×C312yes—
110C2×#685C22×C311yescharacteristic
111C2×#685C22×C311yescharacteristic
112C2×C4⋊Dic5C22×C311yescharacteristic
113C2×C4⋊Dic5C22×C311yescharacteristic
114C2×C4⋊Dic5C22×C311yescharacteristic
115C2×#683C22×C312yes—
116C2×C4×Dic5C22×C312yes—
117#4038—24no—
118D5×C4⋊C4—24no—
119C4×D20C3×C418yescomplemented
120C5×#95C22×C312yes—
121#3963C22×C312yes—
122#3963C22×C312yes—
123#3963C22×C312yes—
124#3963C22×C312yes—
125#2352—51noSylow
126C23×C3×C5C2411yescharacteristic
127C22×C3×D5—21no—
128C22×C3×D5—21no—
129C22×C3×D5—21no—
130C22×C3×D5—21no—
131C22×C3×D5—21no—
132C22×C3×D5—21no—
133C22×C3×D5—21no—
134C22×C3×D5—21no—
135C22×C3×D5—21no—
136C22×C3×D5—21no—
137C22×C3×D5C22×C412yes—
138C22×C3×D5C22×C412yes—
139C22×C3×D5#4112yes—
140C22×C3×D5#4112yes—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5C22×C412yes—
151C2×C3×C4×C5C22×C412yes—
152C2×C3×C4×C5C22×C412yes—
153C2×C3×C4×C5C2×D414yes—
154C2×C3×C4×C5C2×D412yes—
155C2×C3×C4×C5#4112yes—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—21no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—21no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—22no—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5C22×C412yes—
167C2×C3×Dic5C22×C412yes—
168C3×D20—28no—
169C3×C4×D5—28no—
170C3×C4×D5—28no—
171C3×C4×D5—48no—
172C22×C3×D4—51no—
173C23×C3×C4—51no—
174C23×C3×C4—51no—
175C23×C3×C4—52no—
176C3×C4×D4—58no—
177C3×#117—104no—
178C2×C3×C4⋊C4—51no—
179C2×C3×C4⋊C4—51no—
180C2×C3×C4⋊C4—51no—
181C2×C3×C4⋊C4—52no—
182C2×C3×C4⋊C4—104no—
183C2×C3×C4⋊C4C2×D511yescharacteristic
184C2×C3×C4⋊C4C2×D511yescharacteristic
185C2×C3×C22⋊C4—51no—
186C2×C3×C22⋊C4—51no—
187C2×C3×C22⋊C4—52no—
188C2×C3×C22⋊C4—52no—
189C2×C3×C22⋊C4—52no—
190C2×C3×C42—52no—
191C2×C3×C42C2×D512yes—
192C2×C3×C42C2×D511yescharacteristic
193C3×#95—52no—
194C3×#95—52no—
195C3×#95—52no—
196C3×#95—52no—
197C3×#95C2×D512yes—
198C23×D5C23×C311yescharacteristic
199C23×D5C23×C311yescharacteristic
200C22×C4×C5C23×C312yes—
201C22×C4×C5C23×C311yescharacteristic
202C22×C4×C5C23×C311yescharacteristic
203C22×C4×C5C23×C312yes—
204C22×C4×C5C23×C311yescharacteristic
205C22×Dic5C23×C312yes—
206C22×Dic5C23×C312yes—
207C22×Dic5C23×C311yescharacteristic
208C22×Dic5C23×C311yescharacteristic
209C2×D20—22no—
210C2×D20—22no—
211C2×D20C2×C3×C414yes—
212C2×C4×D5—22no—
213C2×C4×D5—22no—
214C2×C4×D5—22no—
215C2×C4×D5—22no—
216C2×C4×D5—24no—
217C2×C4×D5—24no—
218C2×C4×D5—42no—
219C2×C4×D5C2×C3×C414yes—
220C2×C4×D5C2×C3×C414yescomplemented
221C5×C4⋊C4—22no—
222C5×C4⋊C4C3×D414yescomplemented
223C42×C5—42no—
224C42×C5C2×C3×C414yescomplemented
225#685—24no—
226#685—24no—
227#685—42no—
228#685C2×C3×C414yes—
229#685C2×C3×C414yescomplemented
230C4⋊Dic5—22no—
231C4⋊Dic5—22no—
232C4⋊Dic5C2×C3×C414yescomplemented
233#683—24no—
234C4×Dic5—24no—
235C2×C4×D4—51no—
236C2×#117—51no—
237C22×C4⋊C4—51no—
238#388—52no—
239#387—52no—
240#386—52no—
241#382—51no—
242#380—51no—
243#380—51no—
244C4×C4⋊C4C3×D511yescharacteristic, complemented
245C4×C22⋊C4—52no—
246C22×C3×C5C23×C411yescharacteristic
247C22×C3×C5C22×D411yescharacteristic
248C22×C3×C5C2×#4111yescharacteristic
249C22×C3×C5C2×#4111yescharacteristic
250C22×C3×C5C2×#4111yescharacteristic
251C22×C3×C5H(5,𝔽2)11yescharacteristic
252C22×C3×C52−1+411yescharacteristic
253C2×C3×D5—22no—
254C2×C3×D5—22no—
255C2×C3×D5—22no—
256C2×C3×D5—22no—
257C2×C3×D5—22no—
258C2×C3×D5—22no—
259C2×C3×D5—22no—
260C2×C3×D5—22no—
261C2×C3×D5—22no—
262C2×C3×D5—41no—
263C2×C3×D5—41no—
264C2×C3×D5—41no—
265C2×C3×D5—41no—
266C2×C3×D5#11714yescomplemented
267C3×C4×C5—22no—
268C3×C4×C5—22no—
269C3×C4×C5—24no—
270C3×C4×C5—42no—
271C3×C4×C5C4×D414yes—
272C3×Dic5—22no—
273C3×Dic5—22no—
274C3×Dic5—42no—
275C3×Dic5—42no—
276C24×C3—51no—
277C24×C3—51no—
278C2×C3×D4—54no—
279C2×C3×D4—102no—
280C2×C3×D4—102no—
281C22×C3×C4—51no—
282C22×C3×C4—51no—
283C22×C3×C4—54no—
284C22×C3×C4—54no—
285C22×C3×C4—52no—
286C22×C3×C4—52no—
287C22×C3×C4—104no—
288C22×C3×C4—102no—
289C22×C3×C4—102no—
290C22×C3×C4—102no—
291C22×C3×C4—102no—
292C22×C3×C4—104no—
293C22×C3×C4—202no—
294C22×C3×C4C22×D512yes—
295C22×C3×C4C22×D511yescharacteristic
296C22×C3×C4C22×D511yescharacteristic
297C22×C3×C4C22×D512yes—
298C22×C3×C4C22×D511yescharacteristic
299C3×C4⋊C4—22no—
300C3×C4⋊C4—54no—
301C3×C4⋊C4—104no—
302C3×C4⋊C4—102no—
303C3×C4⋊C4—102no—
304C3×C4⋊C4D2014yescomplemented
305C3×C22⋊C4—54no—
306C3×C22⋊C4—54no—
307C3×C22⋊C4—104no—
308C3×C22⋊C4—104no—
309C3×C22⋊C4—202no—
310C3×C42—42no—
311C3×C42—104no—
312C3×C42C4×D514yescomplemented
313C23×C5C24×C311yescharacteristic
314C22×D5—21no—
315C22×D5—21no—
316C22×D5—21no—
317C22×D5—21no—
318C22×D5—21no—
319C22×D5—21no—
320C22×D5—21no—
321C22×D5—21no—
322C22×D5—21no—
323C22×D5—21no—
324C22×D5C22×C3×C412yes—
325C22×D5C22×C3×C412yes—
326C22×D5C3×#4112yes—
327C22×D5C3×#4112yes—
328C2×C4×C5—22no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—22no—
333C2×C4×C5—21no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5C22×C3×C412yes—
338C2×C4×C5C22×C3×C412yes—
339C2×C4×C5C22×C3×C412yes—
340C2×C4×C5C2×C3×D414yes—
341C2×C4×C5C2×C3×D412yes—
342C2×C4×C5C3×#4112yes—
343C2×Dic5—21no—
344C2×Dic5—21no—
345C2×Dic5—21no—
346C2×Dic5—21no—
347C2×Dic5—22no—
348C2×Dic5—22no—
349C2×Dic5—22no—
350C2×Dic5—22no—
351C2×Dic5—22no—
352C2×Dic5—22no—
353C2×Dic5C22×C3×C412yes—
354C2×Dic5C22×C3×C412yes—
355D20—28no—
356C4×D5—28no—
357C4×D5—28no—
358C4×D5—48no—
359C22×D4—51no—
360C23×C4—51no—
361C23×C4—51no—
362C23×C4—52no—
363C4×D4—58no—
364#117—104no—
365C2×C4⋊C4—51no—
366C2×C4⋊C4—51no—
367C2×C4⋊C4—52no—
368C2×C4⋊C4—51no—
369C2×C4⋊C4—104no—
370C2×C4⋊C4C2×C3×D511yescharacteristic
371C2×C4⋊C4C2×C3×D511yescharacteristic
372C2×C22⋊C4—51no—
373C2×C22⋊C4—51no—
374C2×C22⋊C4—52no—
375C2×C22⋊C4—52no—
376C2×C22⋊C4—52no—
377C2×C42—52no—
378C2×C42C2×C3×D512yes—
379C2×C42C2×C3×D511yescharacteristic
380#95—52no—
381#95—52no—
382#95—52no—
383#95—52no—
384#95C2×C3×D512yes—
385C2×C3×C5C2×#11711yescharacteristic
386C2×C3×C5C2×C4×D411yescharacteristic
387C2×C3×C5#52011yescharacteristic
388C2×C3×C5#54611yescharacteristic
389C2×C3×C5#54811yescharacteristic
390C2×C3×C5#55211yescharacteristic
391C2×C3×C5#55311yescharacteristic
392C3×D5—24no—
393C3×D5—42no—
394C23×C3—52no—
395C23×C3—52no—
396C23×C3—52no—
397C23×C3—52no—
398C23×C3—101no—
399C23×C3—101no—
400C23×C3—101no—
401C23×C3—101no—
402C23×C3—101no—
403C23×C3—101no—
404C23×C3—101no—
405C23×C3—101no—
406C23×C3—101no—
407C23×C3—101no—
408C23×C3C23×D511yescharacteristic
409C3×D4—108no—
410C2×C3×C4—21no—
411C2×C3×C4—22no—
412C2×C3×C4—21no—
413C2×C3×C4—22no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—52no—
420C2×C3×C4—52no—
421C2×C3×C4—101no—
422C2×C3×C4—101no—
423C2×C3×C4—101no—
424C2×C3×C4—101no—
425C2×C3×C4—108no—
426C2×C3×C4—108no—
427C2×C3×C4—102no—
428C2×C3×C4—102no—
429C2×C3×C4—102no—
430C2×C3×C4—102no—
431C2×C3×C4—102no—
432C2×C3×C4—102no—
433C2×C3×C4—208no—
434C2×C3×C4C2×C4×D512yes—
435C2×C3×C4C2×C4×D512yes—
436C2×C3×C4C2×C4×D512yes—
437C2×C3×C4C2×D2014yes—
438C2×C3×C4C2×D2012yes—
439C2×C3×C4#70912yes—
440C22×C5C23×C3×C411yescharacteristic
441C22×C5C22×C3×D411yescharacteristic
442C22×C5C2×C3×#4111yescharacteristic
443C22×C5C2×C3×#4111yescharacteristic
444C22×C5C2×C3×#4111yescharacteristic
445C22×C5C3×H(5,𝔽2)11yescharacteristic
446C22×C5C3×2−1+411yescharacteristic
447C2×D5—22no—
448C2×D5—22no—
449C2×D5—22no—
450C2×D5—22no—
451C2×D5—22no—
452C2×D5—22no—
453C2×D5—22no—
454C2×D5—22no—
455C2×D5—22no—
456C2×D5—41no—
457C2×D5—41no—
458C2×D5—41no—
459C2×D5—41no—
460C2×D5C3×#11714yescomplemented
461C4×C5—22no—
462C4×C5—22no—
463C4×C5—24no—
464C4×C5—42no—
465C4×C5C3×C4×D414yes—
466Dic5—22no—
467Dic5—22no—
468Dic5—42no—
469Dic5—42no—
470C24—51no—
471C24—51no—
472C2×D4—54no—
473C2×D4—102no—
474C2×D4—102no—
475C22×C4—51no—
476C22×C4—51no—
477C22×C4—54no—
478C22×C4—54no—
479C22×C4—52no—
480C22×C4—52no—
481C22×C4—104no—
482C22×C4—102no—
483C22×C4—102no—
484C22×C4—102no—
485C22×C4—102no—
486C22×C4—104no—
487C22×C4—202no—
488C22×C4C22×C3×D512yes—
489C22×C4C22×C3×D511yescharacteristic
490C22×C4C22×C3×D511yescharacteristic
491C22×C4C22×C3×D512yes—
492C22×C4C22×C3×D511yescharacteristic
493C4⋊C4—22no—
494C4⋊C4—54no—
495C4⋊C4—104no—
496C4⋊C4—102no—
497C4⋊C4—102no—
498C4⋊C4C3×D2014yescomplemented
499C22⋊C4—54no—
500C22⋊C4—54no—
501C22⋊C4—104no—
502C22⋊C4—104no—
503C22⋊C4—202no—
504C42—42no—
505C42—104no—
506C42C3×C4×D514yescomplemented
507C3×C5#235211yescharacteristic, complemented, Hall
508C22×C3—54no—
509C22×C3—102no—
510C22×C3—102no—
511C22×C3—102no—
512C22×C3—102no—
513C22×C3—102no—
514C22×C3—102no—
515C22×C3—102no—
516C22×C3—102no—
517C22×C3—102no—
518C22×C3—201no—
519C22×C3—201no—
520C22×C3—201no—
521C22×C3—201no—
522C22×C3C22×C4×D511yescharacteristic
523C22×C3C22×D2011yescharacteristic
524C22×C3C2×#70911yescharacteristic
525C22×C3#414411yescharacteristic
526C22×C3#414711yescharacteristic
527C22×C3D5×#4111yescharacteristic
528C22×C3D5×#4111yescharacteristic
529C3×C4—22no—
530C3×C4—22no—
531C3×C4—24no—
532C3×C4—42no—
533C3×C4—102no—
534C3×C4—102no—
535C3×C4—202no—
536C3×C4—202no—
537C3×C4C4×D2014yes—
538C2×C5C2×C3×#11711yescharacteristic
539C2×C5C2×C3×C4×D411yescharacteristic
540C2×C5C3×#52011yescharacteristic
541C2×C5C3×#54611yescharacteristic
542C2×C5C3×#54811yescharacteristic
543C2×C5C3×#55211yescharacteristic
544C2×C5C3×#55311yescharacteristic
545D5—24no—
546D5—42no—
547C23—52no—
548C23—52no—
549C23—52no—
550C23—52no—
551C23—101no—
552C23—101no—
553C23—101no—
554C23—101no—
555C23—101no—
556C23—101no—
557C23—101no—
558C23—101no—
559C23—101no—
560C23—101no—
561C23C23×C3×D511yescharacteristic
562D4—108no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—52no—
573C2×C4—52no—
574C2×C4—101no—
575C2×C4—101no—
576C2×C4—101no—
577C2×C4—101no—
578C2×C4—108no—
579C2×C4—108no—
580C2×C4—102no—
581C2×C4—102no—
582C2×C4—102no—
583C2×C4—102no—
584C2×C4—102no—
585C2×C4—102no—
586C2×C4—208no—
587C2×C4C2×C3×C4×D512yes—
588C2×C4C2×C3×C4×D512yes—
589C2×C4C2×C3×C4×D512yes—
590C2×C4C2×C3×D2014yes—
591C2×C4C2×C3×D2012yes—
592C2×C4C3×#70912yes—
593C2×C3—104no—
594C2×C3—202no—
595C2×C3C2×C4×D2011yescharacteristic
596C2×C3#6583811yescharacteristic
597C2×C3D5×#11711yescharacteristic
598C2×C3#6588811yescharacteristic
599C2×C3#6589211yescharacteristic
600C2×C3#6591011yescharacteristic
601C2×C3#6591511yescharacteristic
602C5C3×#235211yescharacteristic, complemented, Sylow
603C22—54no—
604C22—102no—
605C22—102no—
606C22—102no—
607C22—102no—
608C22—102no—
609C22—102no—
610C22—102no—
611C22—102no—
612C22—102no—
613C22—201no—
614C22—201no—
615C22—201no—
616C22—201no—
617C22C22×C3×C4×D511yescharacteristic
618C22C22×C3×D2011yescharacteristic
619C22C2×C3×#70911yescharacteristic
620C22C3×#414411yescharacteristic
621C22C3×#414711yescharacteristic
622C22C3×D5×#4111yescharacteristic
623C22C3×D5×#4111yescharacteristic
624C4—22no—
625C4—24no—
626C4—22no—
627C4—42no—
628C4—102no—
629C4—102no—
630C4—202no—
631C4—202no—
632C4C3×C4×D2014yes—
633C3#1060550211yescharacteristic, direct product factor, Sylow
634C2—104no—
635C2—202no—
636C2C2×C3×C4×D2011yescharacteristic
637C2C3×#6583811yescharacteristic
638C2C3×D5×#11711yescharacteristic
639C2C3×#6588811yescharacteristic
640C2C3×#6589211yescharacteristic
641C2C3×#6591011yescharacteristic
642C2C3×#6591511yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C4⋊C4C2
socleC23×C3×C5C24
prime radicalC22×C3×D20C22
cosocleC23×C5C24×C3
hypercenterC3×C4×C4⋊C4D5
hypocenterC5C3×#2352
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4038C2semidirect
2. C2×C3×D5×C4⋊C4C2semidirect
4. C3×C4×C5×C4⋊C4C2semidirect
5. C3×#65276C2semidirect
6. C3×#65276C2semidirect
7. C3×#65229C2semidirect
8. C3×C4×#685C2semidirect
9. C3×#65225C2semidirect
11. C3×#64942C2semidirect
12. #10605502C3direct (N × H)
33. C3×C4×D20C4semidirect
40. C2×#4038C2×C3semidirect
41. C2×D5×C4⋊C4C2×C3semidirect
43. C4×C5×C4⋊C4C2×C3semidirect
44. #65276C2×C3semidirect
45. #65276C2×C3semidirect
46. #65229C2×C3semidirect
47. C4×#685C2×C3semidirect
48. #65225C2×C3semidirect
50. #64942C2×C3semidirect
73. C2×C3×C4×D5C2×C4semidirect
75. C3×C5×C4⋊C4D4semidirect
77. C3×C42×C5C2×C4semidirect
82. C3×#685C2×C4semidirect
85. C3×C4⋊Dic5C2×C4semidirect
97. C3×C4×C4⋊C4D5semidirect
119. C4×D20C3×C4semidirect
220. C2×C4×D5C2×C3×C4semidirect
222. C5×C4⋊C4C3×D4semidirect
224. C42×C5C2×C3×C4semidirect
229. #685C2×C3×C4semidirect
232. C4⋊Dic5C2×C3×C4semidirect
244. C4×C4⋊C4C3×D5semidirect
266. C2×C3×D5#117semidirect
304. C3×C4⋊C4D20semidirect
312. C3×C42C4×D5semidirect
460. C2×D5C3×#117semidirect
498. C4⋊C4C3×D20semidirect
506. C42C3×C4×D5semidirect
507. C3×C5#2352semidirect
602. C5C3×#2352semidirect
633. C3#10605502direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40382
C2×C3×D5×C4⋊C42
C2×C3×C4×D202
C3×C4×C5×C4⋊C42
C3×#652762
C3×#652292
C3×C4×#6852
C3×#652252
C3×#649542
C3×#649422
#106055023
C3×#23525