Finite Group Databasebeta

← C4×#91819 #14321433

Subgroups — C4×#91819 #14321433

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×C3×C42×C5C211yesmaximal, characteristic, complemented
2C2×#91819C211yesmaximal, characteristic
3C2×C4×#1220C212yesmaximal, complemented
4C2×C4×D60C211yesmaximal, characteristic, complemented
5#11751314C212yesmaximal, complemented
6#11751313C211yesmaximal, characteristic, complemented
7#11751041C212yesmaximal, complemented
8#11751040C211yesmaximal, characteristic, complemented
9C4×#6714C212yesmaximal, complemented
10C4×C4⋊Dic15C211yesmaximal, characteristic, complemented
11#11751029C211yesmaximal, characteristic, complemented
12C4×#4076—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C22×#1220C2212yes—
17C22×D60C2211yescharacteristic
18C22×C4×D15C2212yes—
19C2×C3×C42×C5—24no—
20C2×C3×C42×C5C2211yescharacteristic
21C2×C3×C42×C5C2211yescharacteristic
22C2×C3×C42×C5C2211yescharacteristic
23C2×C3×C42×C5C2211yescharacteristic
24C2×#6719C2212yes—
25#91819C418yesdirect product factor
26C4×#1220—28no—
27C2×#6714C2212yes—
28C2×#6714C2212yes—
29C2×#6714C2212yes—
30C2×#6714C2212yes—
31C2×C4⋊Dic15C2211yescharacteristic
32C2×C4⋊Dic15C2211yescharacteristic
33C2×C4⋊Dic15C2211yescharacteristic
34C2×#6712C2212yes—
35C2×C4×Dic15C2212yes—
36C4×D60—24no—
37#91115C2212yes—
38#91115C2212yes—
39#91115C2212yes—
40C4×#930—51nomaximal, Hall
41C22×C42×C5D311yescharacteristic, complemented
42C2×#4076—31no—
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×D15C2312yes—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5—22no—
56C22×C3×C4×C5—22no—
57C22×C3×C4×C5—22no—
58C22×C3×C4×C5—22no—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5C2×C414yescomplemented
62C22×C3×C4×C5D414yescomplemented
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2311yescharacteristic
68C22×C3×C4×C5C2311yescharacteristic
69C2×#1220—24no—
70C2×#1220—24no—
71C2×#1220C2×C418yescomplemented
72C22×Dic15C2312yes—
73C22×Dic15C2312yes—
74C22×Dic15C2312yes—
75C2×D60—22no—
76C2×D60—22no—
77C2×D60C2×C414yescomplemented
78C2×C4×D15—24no—
79C2×C4×D15—24no—
80C2×C4×D15—24no—
81C3×C42×C5—22no—
82C3×C42×C5—22no—
83C3×C42×C5—22no—
84C3×C42×C5D414yescomplemented
85#6719—24no—
86#6714—24no—
87#6714—24no—
88#6714—24no—
89#6714C2×C418yescomplemented
90C4⋊Dic15—22no—
91C4⋊Dic15—22no—
92C4⋊Dic15C2×C414yescomplemented
93#6712—24no—
94C4×Dic15—24no—
95C22×C3×C42D511yescharacteristic, complemented
96C2×#930—51no—
97C2×C4×#67—52no—
98C2×C4×D12—51no—
99#5213—52no—
100#5212—51no—
101#4940—52no—
102#4939—51no—
103C4×(C2×D3)⋊C4—52no—
104C4×C4⋊Dic3—51no—
105#4928—51no—
106C23×C4×C5C2×D311yescharacteristic
107C23×C4×C5C2×D311yescharacteristic
108C23×C4×C5C2×D311yescharacteristic
109C22×C22⋊D5—32no—
110C22×D20—31no—
111C22×C4×D5—32no—
112C2×C42×C5—24no—
113C2×C42×C5C2×D311yescharacteristic
114C2×C42×C5C2×D311yescharacteristic
115C2×C42×C5C2×D311yescharacteristic
116C2×C42×C5C2×D311yescharacteristic
117C2×C22⋊Dic5—32no—
118#4076—38no—
119C4×C22⋊D5—68no—
120C2×#685—32no—
121C2×#685—32no—
122C2×#685—32no—
123C2×#685—32no—
124C2×C4⋊Dic5—31no—
125C2×C4⋊Dic5—31no—
126C2×C4⋊Dic5—31no—
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×D15—22no—
143C22×D15—22no—
144C22×D15—22no—
145C22×D15—22no—
146C22×D15—22no—
147C22×D15—22no—
148C22×D15C22×C414yes—
149C2×C3×C4×C5—28no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—21no—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—21no—
157C2×C3×C4×C5—21no—
158C2×C3×C4×C5—28no—
159C2×C3×C4×C5—28no—
160C2×C3×C4×C5C22×C412yes—
161C2×C3×C4×C5C22×C412yes—
162C2×C3×C4×C5C2×D412yes—
163C2×C3×C4×C5C2×D412yes—
164C2×C3×C4×C5C2×D412yes—
165C2×C3×C4×C5C2×D412yes—
166C2×C3×C4×C5C2×D412yes—
167C2×C3×C4×C5#4112yes—
168C2×C3×C4×C5#4112yes—
169C2×C3×C4×C5#4112yes—
170#1220—216no—
171C2×Dic15—22no—
172C2×Dic15—22no—
173C2×Dic15—22no—
174C2×Dic15—22no—
175C2×Dic15—22no—
176C2×Dic15—22no—
177C2×Dic15—22no—
178C2×Dic15—22no—
179C2×Dic15C22×C414yes—
180D60—28no—
181C4×D15—48no—
182C23×C3×C4C2×D511yescharacteristic
183C23×C3×C4C2×D511yescharacteristic
184C23×C3×C4C2×D511yescharacteristic
185C22×#67—52no—
186C22×D12—51no—
187C22×C4×D3—52no—
188C2×C3×C42—24no—
189C2×C3×C42C2×D511yescharacteristic
190C2×C3×C42C2×D511yescharacteristic
191C2×C3×C42C2×D511yescharacteristic
192C2×C3×C42C2×D511yescharacteristic
193C2×#217—52no—
194#930—58no—
195C4×#67—108no—
196C2×(C2×D3)⋊C4—52no—
197C2×(C2×D3)⋊C4—52no—
198C2×(C2×D3)⋊C4—52no—
199C2×(C2×D3)⋊C4—52no—
200C2×C4⋊Dic3—51no—
201C2×C4⋊Dic3—51no—
202C2×C4⋊Dic3—51no—
203C2×Dic3⋊C4—52no—
204C2×C4×Dic3—52no—
205C4×D12—104no—
206C3⋊#95—52no—
207C3⋊#95—52no—
208C3⋊#95—52no—
209C24×C5C22×D311yescharacteristic
210C23×D5—32no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5C4×D314yescomplemented
219C22×C4×C5D1214yescomplemented
220C22×C4×C5C22×D311yescharacteristic
221C22×C4×C5C22×D311yescharacteristic
222C22×C4×C5C22×D311yescharacteristic
223C22×C4×C5C22×D311yescharacteristic
224C22×C4×C5C22×D311yescharacteristic
225C22×C4×C5C22×D311yescharacteristic
226C2×C22⋊D5—38no—
227C2×C22⋊D5—64no—
228C2×C22⋊D5—64no—
229C22×Dic5—32no—
230C22×Dic5—32no—
231C22×Dic5—32no—
232C2×D20—34no—
233C2×D20—62no—
234C2×D20—62no—
235C2×C4×D5—64no—
236C2×C4×D5—64no—
237C2×C4×D5—64no—
238C42×C5—22no—
239C42×C5—22no—
240C42×C5—22no—
241C42×C5#6714yescomplemented
242C22⋊Dic5—64no—
243#685—38no—
244#685—64no—
245#685—64no—
246#685—64no—
247C4⋊Dic5—34no—
248C4⋊Dic5—62no—
249C4⋊Dic5—62no—
250#683—64no—
251C4×Dic5—64no—
252C2×#121—151no—
253C2×C4×D4—152no—
254C2×C4×D4—151no—
255C22×C42D1511yescharacteristic, complemented
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×D15—24no—
278C2×D15—24no—
279C2×D15—24no—
280C2×D15—42no—
281C2×D15—42no—
282C2×D15—42no—
283C2×D15—42no—
284C3×C4×C5—22no—
285C3×C4×C5—22no—
286C3×C4×C5—22no—
287C3×C4×C5—22no—
288C3×C4×C5C4×D414yescomplemented
289C3×C4×C5#12114yescomplemented
290Dic15—24no—
291Dic15—42no—
292Dic15—42no—
293C24×C3C22×D511yescharacteristic
294C23×D3—52no—
295C22×C3×C4—22no—
296C22×C3×C4—22no—
297C22×C3×C4—22no—
298C22×C3×C4—22no—
299C22×C3×C4—22no—
300C22×C3×C4—22no—
301C22×C3×C4—22no—
302C22×C3×C4C4×D514yescomplemented
303C22×C3×C4D2014yescomplemented
304C22×C3×C4C22×D511yescharacteristic
305C22×C3×C4C22×D511yescharacteristic
306C22×C3×C4C22×D511yescharacteristic
307C22×C3×C4C22×D511yescharacteristic
308C22×C3×C4C22×D511yescharacteristic
309C22×C3×C4C22×D511yescharacteristic
310C2×#67—58no—
311C2×#67—104no—
312C2×#67—104no—
313C22×Dic3—52no—
314C22×Dic3—52no—
315C22×Dic3—52no—
316C2×D12—54no—
317C2×D12—102no—
318C2×D12—102no—
319C2×C4×D3—104no—
320C2×C4×D3—104no—
321C2×C4×D3—104no—
322C3×C42—22no—
323C3×C42—22no—
324C3×C42—22no—
325C3×C42C22⋊D514yescomplemented
326#217—104no—
327(C2×D3)⋊C4—58no—
328(C2×D3)⋊C4—104no—
329(C2×D3)⋊C4—104no—
330(C2×D3)⋊C4—104no—
331C4⋊Dic3—54no—
332C4⋊Dic3—102no—
333C4⋊Dic3—102no—
334Dic3⋊C4—104no—
335C4×Dic3—104no—
336C23×C5—21no—
337C23×C5—21no—
338C23×C5—21no—
339C23×C5—21no—
340C23×C5C2×C4×D312yes—
341C23×C5C2×D1212yes—
342C23×C5#23512yes—
343C23×C5C23×D311yescharacteristic
344C22×D5—34no—
345C22×D5—62no—
346C22×D5—62no—
347C22×D5—62no—
348C22×D5—62no—
349C22×D5—62no—
350C22×D5—62no—
351C2×C4×C5—28no—
352C2×C4×C5—21no—
353C2×C4×C5—21no—
354C2×C4×C5—21no—
355C2×C4×C5—21no—
356C2×C4×C5—21no—
357C2×C4×C5—21no—
358C2×C4×C5—21no—
359C2×C4×C5—21no—
360C2×C4×C5—28no—
361C2×C4×C5—28no—
362C2×C4×C5C2×C4×D312yes—
363C2×C4×C5C2×C4×D312yes—
364C2×C4×C5C2×D1212yes—
365C2×C4×C5C2×D1212yes—
366C2×C4×C5#23512yes—
367C2×C4×C5#23512yes—
368C2×C4×C5#23512yes—
369C2×C4×C5C2×#6712yes—
370C2×C4×C5C2×#6712yes—
371C2×C4×C5C2×#6712yes—
372C22⋊D5—616no—
373C2×Dic5—34no—
374C2×Dic5—62no—
375C2×Dic5—62no—
376C2×Dic5—62no—
377C2×Dic5—62no—
378C2×Dic5—62no—
379C2×Dic5—62no—
380C2×Dic5—62no—
381C2×Dic5—62no—
382D20—68no—
383C4×D5—128no—
384C22×D4—152no—
385C22×D4—151no—
386C23×C4—152no—
387C23×C4C2×D1511yescharacteristic
388C23×C4C2×D1511yescharacteristic
389C23×C4C2×D1511yescharacteristic
390#121—158no—
391C4×D4—308no—
392C4×D4—304no—
393C2×C4⋊C4—151no—
394C2×C4⋊C4—151no—
395C2×C4⋊C4—152no—
396C2×C4⋊C4—151no—
397C2×C22⋊C4—152no—
398C2×C22⋊C4—152no—
399C2×C22⋊C4—152no—
400C2×C22⋊C4—152no—
401C2×C22⋊C4—152no—
402C2×C42—24no—
403C2×C42—152no—
404C2×C42C2×D1511yescharacteristic
405C2×C42C2×D1511yescharacteristic
406C2×C42C2×D1511yescharacteristic
407C2×C42C2×D1511yescharacteristic
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
419D15—44no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3C2×C4×D512yes—
425C23×C3C2×D2012yes—
426C23×C3#70912yes—
427C23×C3C23×D511yescharacteristic
428C22×D3—54no—
429C22×D3—102no—
430C22×D3—102no—
431C22×D3—102no—
432C22×D3—102no—
433C22×D3—102no—
434C22×D3—102no—
435C2×C3×C4—28no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—28no—
445C2×C3×C4—28no—
446C2×C3×C4C2×C4×D512yes—
447C2×C3×C4C2×C4×D512yes—
448C2×C3×C4C2×D2012yes—
449C2×C3×C4C2×D2012yes—
450C2×C3×C4#70912yes—
451C2×C3×C4#70912yes—
452C2×C3×C4#70912yes—
453C2×C3×C4C2×C22⋊D512yes—
454C2×C3×C4C2×C22⋊D512yes—
455C2×C3×C4C2×C22⋊D512yes—
456#67—1016no—
457C2×Dic3—54no—
458C2×Dic3—102no—
459C2×Dic3—102no—
460C2×Dic3—102no—
461C2×Dic3—102no—
462C2×Dic3—102no—
463C2×Dic3—102no—
464C2×Dic3—102no—
465C2×Dic3—102no—
466D12—108no—
467C4×D3—208no—
468C22×C5—22no—
469C22×C5—22no—
470C22×C5—22no—
471C22×C5—22no—
472C22×C5—22no—
473C22×C5—22no—
474C22×C5C4×D1214yescomplemented
475C22×C5C22×C4×D311yescharacteristic
476C22×C5C22×D1211yescharacteristic
477C22×C5C2×#23511yescharacteristic
478C22×C5C2×#23511yescharacteristic
479C22×C5C2×#23511yescharacteristic
480C22×C5C2×#23511yescharacteristic
481C22×C5C22×#6711yescharacteristic
482C2×D5—64no—
483C2×D5—64no—
484C2×D5—64no—
485C2×D5—122no—
486C2×D5—122no—
487C2×D5—122no—
488C2×D5—122no—
489C4×C5—22no—
490C4×C5—22no—
491C4×C5—22no—
492C4×C5—22no—
493C4×C5C4×#6714yescomplemented
494C4×C5#93014yescomplemented
495Dic5—64no—
496Dic5—122no—
497Dic5—122no—
498C24—152no—
499C24C22×D1511yescharacteristic
500C2×D4—158no—
501C2×D4—154no—
502C2×D4—304no—
503C2×D4—304no—
504C2×D4—302no—
505C2×D4—302no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—152no—
514C22×C4—152no—
515C22×C4—152no—
516C22×C4—304no—
517C22×C4—304no—
518C22×C4—304no—
519C22×C4C4×D1514yescomplemented
520C22×C4D6014yescomplemented
521C22×C4C22×D1511yescharacteristic
522C22×C4C22×D1511yescharacteristic
523C22×C4C22×D1511yescharacteristic
524C22×C4C22×D1511yescharacteristic
525C22×C4C22×D1511yescharacteristic
526C22×C4C22×D1511yescharacteristic
527C4⋊C4—154no—
528C4⋊C4—304no—
529C4⋊C4—302no—
530C4⋊C4—302no—
531C22⋊C4—158no—
532C22⋊C4—304no—
533C22⋊C4—304no—
534C22⋊C4—304no—
535C22⋊C4—304no—
536C42—22no—
537C42—22no—
538C42—22no—
539C42—304no—
540C42#122014yescomplemented
541C3×C5C4×#12111yescharacteristic, complemented, Hall
542C22×C3—22no—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3C4×D2014yescomplemented
549C22×C3C22×C4×D511yescharacteristic
550C22×C3C22×D2011yescharacteristic
551C22×C3C2×#70911yescharacteristic
552C22×C3C2×#70911yescharacteristic
553C22×C3C2×#70911yescharacteristic
554C22×C3C2×#70911yescharacteristic
555C22×C3C22×C22⋊D511yescharacteristic
556C2×D3—104no—
557C2×D3—104no—
558C2×D3—104no—
559C2×D3—202no—
560C2×D3—202no—
561C2×D3—202no—
562C2×D3—202no—
563C3×C4—22no—
564C3×C4—22no—
565C3×C4—22no—
566C3×C4—22no—
567C3×C4C4×C22⋊D514yescomplemented
568C3×C4#407614yescomplemented
569Dic3—104no—
570Dic3—202no—
571Dic3—202no—
572C2×C5—24no—
573C2×C5C2×C4×D1211yescharacteristic
574C2×C5C4×#23511yescharacteristic
575C2×C5#547711yescharacteristic
576C2×C5#547911yescharacteristic
577C2×C5C2×C4×#6711yescharacteristic
578C2×C5C2×#93011yescharacteristic
579C2×C5#579111yescharacteristic
580D5—124no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—154no—
586C23—302no—
587C23—302no—
588C23—302no—
589C23—302no—
590C23—302no—
591C23—302no—
592C23C2×C4×D1512yes—
593C23C2×D6012yes—
594C23#681712yes—
595C23C23×D1511yescharacteristic
596D4—3016no—
597D4—308no—
598C2×C4—28no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—28no—
608C2×C4—28no—
609C2×C4—154no—
610C2×C4—302no—
611C2×C4—302no—
612C2×C4—302no—
613C2×C4—302no—
614C2×C4—302no—
615C2×C4—302no—
616C2×C4—302no—
617C2×C4—302no—
618C2×C4—608no—
619C2×C4C2×C4×D1512yes—
620C2×C4C2×C4×D1512yes—
621C2×C4C2×D6012yes—
622C2×C4C2×D6012yes—
623C2×C4#681712yes—
624C2×C4#681712yes—
625C2×C4#681712yes—
626C2×C4C2×#122012yes—
627C2×C4C2×#122012yes—
628C2×C4C2×#122012yes—
629C2×C3—24no—
630C2×C3C2×C4×D2011yescharacteristic
631C2×C3C4×#70911yescharacteristic
632C2×C3#6581111yescharacteristic
633C2×C3#6581311yescharacteristic
634C2×C3C2×C4×C22⋊D511yescharacteristic
635C2×C3C2×#407611yescharacteristic
636C2×C3#6612511yescharacteristic
637D3—204no—
638C5C4×#93011yescharacteristic, complemented, Sylow
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—304no—
646C22—304no—
647C22—304no—
648C22—602no—
649C22—602no—
650C22—602no—
651C22—602no—
652C22C4×D6014yescomplemented
653C22C22×C4×D1511yescharacteristic
654C22C22×D6011yescharacteristic
655C22C2×#681711yescharacteristic
656C22C2×#681711yescharacteristic
657C22C2×#681711yescharacteristic
658C22C2×#681711yescharacteristic
659C22C22×#122011yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—304no—
665C4—602no—
666C4—602no—
667C4C4×#122014yescomplemented
668C4#9181914yesdirect product factor
669C3C4×#407611yescharacteristic, complemented, Sylow
670C2—24no—
671C2—604no—
672C2C2×C4×D6011yescharacteristic
673C2C4×#681711yescharacteristic
674C2#1175623611yescharacteristic
675C2#1175623811yescharacteristic
676C2C2×C4×#122011yescharacteristic
677C2C2×#9181911yescharacteristic
678C2#1175655011yescharacteristic
subgroupG/H
centerC22×C4C22×D15
commutatorC22×C3×C5C23×C4
FrattiniC23C23×D15
FittingC22×C3×C42×C5C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91819C2
hypercenterC22×C42D15
hypocenterC3×C5C4×#121
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. C22×C3×C42×C5C2semidirect
3. C2×C4×#1220C2semidirect
4. C2×C4×D60C2semidirect
5. #11751314C2semidirect
6. #11751313C2semidirect
7. #11751041C2semidirect
8. #11751040C2semidirect
9. C4×#6714C2semidirect
10. C4×C4⋊Dic15C2semidirect
11. #11751029C2semidirect
25. #91819C4direct (N × H)
41. C22×C42×C5D3semidirect
61. C22×C3×C4×C5C2×C4semidirect
62. C22×C3×C4×C5D4semidirect
71. C2×#1220C2×C4semidirect
77. C2×D60C2×C4semidirect
84. C3×C42×C5D4semidirect
89. #6714C2×C4semidirect
92. C4⋊Dic15C2×C4semidirect
95. C22×C3×C42D5semidirect
218. C22×C4×C5C4×D3semidirect
219. C22×C4×C5D12semidirect
241. C42×C5#67semidirect
255. C22×C42D15semidirect
269. C22×C3×C5C4×D4semidirect
288. C3×C4×C5C4×D4semidirect
289. C3×C4×C5#121semidirect
302. C22×C3×C4C4×D5semidirect
303. C22×C3×C4D20semidirect
325. C3×C42C22⋊D5semidirect
474. C22×C5C4×D12semidirect
493. C4×C5C4×#67semidirect
494. C4×C5#930semidirect
519. C22×C4C4×D15semidirect
520. C22×C4D60semidirect
540. C42#1220semidirect
541. C3×C5C4×#121semidirect
548. C22×C3C4×D20semidirect
567. C3×C4C4×C22⋊D5semidirect
568. C3×C4#4076semidirect
638. C5C4×#930semidirect
652. C22C4×D60semidirect
667. C4C4×#1220semidirect
668. C4#91819direct (N × H)
669. C3C4×#4076semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C42×C52
C2×#918192
C2×C4×#12202
C2×C4×D602
#117513142
#117513132
#117510412
#117510402
C4×#67142
C4×C4⋊Dic152
#117510292
C4×#40763
C4×#9305