Finite Group Databasebeta

← C4×#91449 #14321496

Subgroups — C4×#91449 #14321496

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
1C2×C4×C5×D12C211yesmaximal, characteristic, complemented
2C2×C3×C42×D5C211yesmaximal, characteristic, complemented
3C2×#91449C211yesmaximal, characteristic
4C2×C4×#1201C212yesmaximal, complemented
5C4×C4⋊Dic15C211yesmaximal, characteristic, complemented
6#11748905C212yesmaximal, complemented
7#11748841C211yesmaximal, characteristic, complemented
8#11748764C211yesmaximal, characteristic, complemented
9#11748759C211yesmaximal, characteristic, complemented
10#11748714C212yesmaximal, complemented
11C4×(C2×D3)⋊Dic5C212yesmaximal, complemented
12C4×#4084—31nomaximal, Hall
13C22×C5×D12C2211yescharacteristic
14C22×C4×C5×D3C2212yes—
15C22×C3×C4×D5C2211yescharacteristic
16C22×C3×C4×D5C2211yescharacteristic
17C22×C3×C4×D5C2211yescharacteristic
18C22×#1201C2212yes—
19C2×C3×C42×C5C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4×Dic15C2212yes—
23C2×C5×(C2×D3)⋊C4C2212yes—
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C4×C5×D12—24no—
26C2×C3×C4×Dic5C2211yescharacteristic
27C2×C3×C4×Dic5C2211yescharacteristic
28C2×C3×C4×Dic5C2211yescharacteristic
29C3×C42×D5—24no—
30C2×#6669C2212yes—
31C2×(C2×D3)⋊Dic5C2212yes—
32C2×(C2×D3)⋊Dic5C2212yes—
33C2×(C2×D3)⋊Dic5C2212yes—
34C2×#6665C2212yes—
35#91449C418yesdirect product factor
36C4×#1201—28no—
37#91115C2212yes—
38#90994C2212yes—
39#90994C2212yes—
40C4×#930—51nomaximal, Hall
41C2×C4×C5×D4—31no—
42C2×#4084—31no—
43C2×C4×C22⋊D5—32no—
44C2×C42×D5D311yescharacteristic, complemented
45#65510—31no—
46C4×C22⋊Dic5—32no—
47#65276—31no—
48#65262—31no—
49#65245—32no—
50#65233—32no—
51C4×C4⋊Dic5—31no—
52C23×C5×D3C2312yes—
53C23×C3×D5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15C2312yes—
58C22×Dic15C2312yes—
59C22×C5×Dic3C2312yes—
60C2×C5×D12—22no—
61C2×C5×D12—22no—
62C2×C5×D12C2×C414yescomplemented
63C2×C4×C5×D3—24no—
64C2×C4×C5×D3—24no—
65C2×C4×C5×D3—24no—
66C22×C3×Dic5C2311yescharacteristic
67C22×C3×Dic5C2311yescharacteristic
68C22×C3×Dic5C2311yescharacteristic
69C2×C3×C4×D5—22no—
70C2×C3×C4×D5—22no—
71C2×C3×C4×D5—22no—
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5—22no—
75C2×C3×C4×D5—22no—
76C2×C3×C4×D5C2×C414yescomplemented
77C2×C3×C4×D5D414yescomplemented
78C2×#1201—24no—
79C2×#1201—24no—
80C2×#1201C2×C418yescomplemented
81C3×C42×C5D414yescomplemented
82C4⋊Dic15—22no—
83C4⋊Dic15C2×C414yescomplemented
84C4×Dic15—24no—
85C5×(C2×D3)⋊C4—24no—
86C5×C4⋊Dic3—22no—
87C3×C4×Dic5—22no—
88C3×C4×Dic5—22no—
89C3×C4×Dic5—22no—
90#6669—24no—
91(C2×D3)⋊Dic5—24no—
92(C2×D3)⋊Dic5—24no—
93(C2×D3)⋊Dic5C2×C418yescomplemented
94#6665—24no—
95C22×C3×C42—51no—
96C2×#930—51no—
97C2×C4×#67—52no—
98C2×C4×D12D511yescharacteristic, complemented
99#5213—52no—
100#5212—51no—
101#4940—52no—
102#4939—51no—
103C4×(C2×D3)⋊C4—52no—
104C4×C4⋊Dic3—51no—
105#4928—51no—
106C22×C5×D4—31no—
107C23×C4×C5—32no—
108C22×C22⋊D5—32no—
109C22×C4×D5C2×D311yescharacteristic
110C22×C4×D5C2×D311yescharacteristic
111C22×C4×D5C2×D311yescharacteristic
112C4×C5×D4—64no—
113C2×C5×C4⋊C4—31no—
114C2×C5×C22⋊C4—32no—
115C2×C42×C5C2×D311yescharacteristic
116C2×C22⋊Dic5—32no—
117C2×C22⋊Dic5—32no—
118C2×C22⋊Dic5—32no—
119#4084—38no—
120C4×C22⋊D5—68no—
121C2×#685—32no—
122C2×C4⋊Dic5—31no—
123C2×C4⋊Dic5—31no—
124C2×#683—32no—
125C2×C4×Dic5—32no—
126C2×C4×Dic5C2×D311yescharacteristic
127C2×C4×Dic5C2×D311yescharacteristic
128C2×C4×Dic5C2×D311yescharacteristic
129C42×D5—24no—
130#3963—32no—
131#3963—32no—
132#3963—32no—
133C4×#121—151noSylow
134C23×C3×C5C2411yescharacteristic
135C22×C5×D3—22no—
136C22×C5×D3—22no—
137C22×C5×D3—22no—
138C22×C5×D3—22no—
139C22×C5×D3—22no—
140C22×C5×D3—22no—
141C22×C5×D3C22×C414yes—
142C22×C3×D5—21no—
143C22×C3×D5—21no—
144C22×C3×D5—21no—
145C22×C3×D5—21no—
146C22×C3×D5C22×C412yes—
147C22×C3×D5C2×D412yes—
148C22×C3×D5#4112yes—
149C2×C3×C4×C5—21no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5C22×C412yes—
152C2×C3×C4×C5C2×D412yes—
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5C2×D412yes—
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5#4112yes—
157C2×C3×C4×C5#4112yes—
158C2×Dic15—22no—
159C2×Dic15—22no—
160C2×Dic15—22no—
161C2×Dic15—22no—
162C2×Dic15—22no—
163C2×Dic15C22×C414yes—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—22no—
166C2×C5×Dic3—22no—
167C5×D12—28no—
168C4×C5×D3—48no—
169C2×C3×Dic5—21no—
170C2×C3×Dic5—21no—
171C2×C3×Dic5—21no—
172C2×C3×Dic5—21no—
173C2×C3×Dic5—21no—
174C2×C3×Dic5—21no—
175C2×C3×Dic5C22×C412yes—
176C2×C3×Dic5C2×D412yes—
177C2×C3×Dic5#4112yes—
178C3×C4×D5—28no—
179C3×C4×D5—28no—
180C3×C4×D5—28no—
181#1201—216no—
182C23×C3×C4—51no—
183C23×C3×C4—51no—
184C23×C3×C4—51no—
185C22×#67—52no—
186C22×D12C2×D511yescharacteristic
187C22×C4×D3C2×D512yes—
188C2×C3×C42—51no—
189C2×C3×C42—51no—
190C2×C3×C42—51no—
191C2×C3×C42—104no—
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)⋊C4C2×D512yes—
200C2×C4⋊Dic3—51no—
201C2×C4⋊Dic3—51no—
202C2×C4⋊Dic3C2×D511yescharacteristic
203C2×Dic3⋊C4—52no—
204C2×C4×Dic3—52no—
205C4×D12—24no—
206C3⋊#95—52no—
207C3⋊#95—52no—
208C3⋊#95—52no—
209C24×C5—32no—
210C23×D5C22×D311yescharacteristic
211C2×C5×D4—34no—
212C2×C5×D4—62no—
213C2×C5×D4—62no—
214C22×C4×C5—32no—
215C22×C4×C5—64no—
216C22×C4×C5—64no—
217C22×C4×C5—64no—
218C22×C4×C5C22×D311yescharacteristic
219C22×C4×C5C22×D311yescharacteristic
220C22×C4×C5C22×D311yescharacteristic
221C2×C22⋊D5—38no—
222C2×C22⋊D5—64no—
223C2×C22⋊D5—64no—
224C22×Dic5—32no—
225C22×Dic5—32no—
226C22×Dic5C22×D311yescharacteristic
227C22×Dic5C22×D311yescharacteristic
228C22×Dic5C22×D311yescharacteristic
229C2×C4×D5—22no—
230C2×C4×D5—22no—
231C2×C4×D5—22no—
232C2×C4×D5—22no—
233C2×C4×D5—22no—
234C2×C4×D5—22no—
235C2×C4×D5—22no—
236C2×C4×D5C4×D314yescomplemented
237C2×C4×D5D1214yescomplemented
238C5×C4⋊C4—62no—
239C5×C22⋊C4—64no—
240C42×C5#6714yescomplemented
241C22⋊Dic5—38no—
242C22⋊Dic5—64no—
243C22⋊Dic5—64no—
244#685—64no—
245C4⋊Dic5—34no—
246C4⋊Dic5—62no—
247#683—64no—
248C4×Dic5—22no—
249C4×Dic5—22no—
250C4×Dic5—22no—
251C4×Dic5—64no—
252C2×#121—151no—
253C2×C4×D4—31no—
254C2×C4×D4—152no—
255C22×C42—51no—
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×C5C23×C411yescharacteristic
264C22×C3×C5C22×D411yescharacteristic
265C22×C3×C5C22×D411yescharacteristic
266C22×C3×C5C2×#4111yescharacteristic
267C22×C3×C5C2×#4111yescharacteristic
268C22×C3×C5C2×#4111yescharacteristic
269C22×C3×C5C2×#4111yescharacteristic
270C2×C5×D3—24no—
271C2×C5×D3—24no—
272C2×C5×D3—24no—
273C2×C5×D3—42no—
274C2×C5×D3—42no—
275C2×C5×D3—42no—
276C2×C5×D3—42no—
277C2×C3×D5—22no—
278C2×C3×D5—22no—
279C2×C3×D5—22no—
280C2×C3×D5—22no—
281C2×C3×D5—22no—
282C2×C3×D5—22no—
283C2×C3×D5C4×D414yescomplemented
284C3×C4×C5—22no—
285C3×C4×C5C4×D414yescomplemented
286C3×C4×C5#12114yescomplemented
287Dic15—24no—
288Dic15—42no—
289C3×Dic5—22no—
290C3×Dic5—22no—
291C3×Dic5—22no—
292C5×Dic3—42no—
293C24×C3—51no—
294C23×D3C22×D512yes—
295C22×C3×C4—51no—
296C22×C3×C4—51no—
297C22×C3×C4—51no—
298C22×C3×C4—54no—
299C22×C3×C4—54no—
300C22×C3×C4—102no—
301C22×C3×C4—102no—
302C22×C3×C4—102no—
303C22×C3×C4—102no—
304C22×C3×C4—102no—
305C22×C3×C4—102no—
306C22×C3×C4—102no—
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×Dic3C22×D512yes—
316C2×D12—22no—
317C2×D12—22no—
318C2×D12C4×D514yescomplemented
319C2×C4×D3—24no—
320C2×C4×D3—24no—
321C2×C4×D3—24no—
322C3×C42—102no—
323C3×C42—102no—
324C3×C42—102no—
325C3×C42C22⋊D514yescomplemented
326#217—104no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—58no—
329(C2×D3)⋊C4—104no—
330(C2×D3)⋊C4—104no—
331C4⋊Dic3—22no—
332C4⋊Dic3—54no—
333C4⋊Dic3—102no—
334Dic3⋊C4—104no—
335C4×Dic3—104no—
336C23×C5—34no—
337C23×C5—62no—
338C23×C5—62no—
339C23×C5—62no—
340C23×C5—62no—
341C23×C5—62no—
342C23×C5—62no—
343C23×C5C23×D311yescharacteristic
344C22×D5—21no—
345C22×D5—21no—
346C22×D5—21no—
347C22×D5—21no—
348C22×D5C2×C4×D312yes—
349C22×D5C2×D1212yes—
350C22×D5#23512yes—
351C5×D4—68no—
352C2×C4×C5—21no—
353C2×C4×C5—21no—
354C2×C4×C5—62no—
355C2×C4×C5—62no—
356C2×C4×C5—62no—
357C2×C4×C5—128no—
358C2×C4×C5C2×C4×D312yes—
359C2×C4×C5C2×D1212yes—
360C2×C4×C5#23512yes—
361C2×C4×C5#23512yes—
362C2×C4×C5C2×#6712yes—
363C2×C4×C5C2×#6712yes—
364C2×C4×C5C2×#6712yes—
365C22⋊D5—616no—
366C2×Dic5—21no—
367C2×Dic5—21no—
368C2×Dic5—21no—
369C2×Dic5—21no—
370C2×Dic5—21no—
371C2×Dic5—21no—
372C2×Dic5—34no—
373C2×Dic5—62no—
374C2×Dic5—62no—
375C2×Dic5—62no—
376C2×Dic5—62no—
377C2×Dic5—62no—
378C2×Dic5C2×C4×D312yes—
379C2×Dic5C2×D1212yes—
380C2×Dic5#23512yes—
381C4×D5—28no—
382C4×D5—28no—
383C4×D5—28no—
384C22×D4—31no—
385C22×D4—152no—
386C23×C4—32no—
387C23×C4—51no—
388C23×C4—51no—
389C23×C4—51no—
390#121—158no—
391C4×D4—64no—
392C4×D4—308no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—151no—
395C2×C4⋊C4—152no—
396C2×C4⋊C4—151no—
397C2×C22⋊C4—32no—
398C2×C22⋊C4—152no—
399C2×C22⋊C4—152no—
400C2×C22⋊C4—152no—
401C2×C22⋊C4—152no—
402C2×C42—51no—
403C2×C42—51no—
404C2×C42—51no—
405C2×C42—104no—
406C2×C42—152no—
407C2×C42D3×D511yescharacteristic
408#95—152no—
409#95—152no—
410#95—152no—
411C2×C3×C5C2×C4×D411yescharacteristic
412C2×C3×C5C2×C4×D411yescharacteristic
413C2×C3×C5C4×#4111yescharacteristic
414C2×C3×C5C2×#12111yescharacteristic
415C2×C3×C5#52511yescharacteristic
416C2×C3×C5#52911yescharacteristic
417C2×C3×C5#53211yescharacteristic
418C3×D5—24no—
419C5×D3—44no—
420C23×C3—52no—
421C23×C3—52no—
422C23×C3—52no—
423C23×C3—101no—
424C23×C3—101no—
425C23×C3—101no—
426C23×C3—101no—
427C23×C3C23×D511yescharacteristic
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—22no—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—22no—
434C22×D3C2×C4×D514yes—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—52no—
438C2×C3×C4—52no—
439C2×C3×C4—52no—
440C2×C3×C4—108no—
441C2×C3×C4—101no—
442C2×C3×C4—101no—
443C2×C3×C4—101no—
444C2×C3×C4—101no—
445C2×C3×C4—101no—
446C2×C3×C4—101no—
447C2×C3×C4—108no—
448C2×C3×C4—108no—
449C2×C3×C4C2×C4×D512yes—
450C2×C3×C4#70912yes—
451C2×C3×C4D4×D512yes—
452C2×C3×C4#71112yes—
453C2×C3×C4C2×C22⋊D512yes—
454C2×C3×C4C2×C22⋊D512yes—
455C2×C3×C4C2×C22⋊D512yes—
456#67—1016no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—54no—
461C2×Dic3—102no—
462C2×Dic3—102no—
463C2×Dic3—102no—
464C2×Dic3—102no—
465C2×Dic3—102no—
466D12—28no—
467C4×D3—48no—
468C22×C5—64no—
469C22×C5—64no—
470C22×C5—64no—
471C22×C5—122no—
472C22×C5—122no—
473C22×C5—122no—
474C22×C5—122no—
475C22×C5C22×C4×D311yescharacteristic
476C22×C5C22×D1211yescharacteristic
477C22×C5C2×#23511yescharacteristic
478C22×C5C2×#23511yescharacteristic
479C22×C5C2×#23511yescharacteristic
480C22×C5C2×#23511yescharacteristic
481C22×C5C22×#6711yescharacteristic
482C2×D5—22no—
483C2×D5—22no—
484C2×D5—22no—
485C2×D5—22no—
486C2×D5—22no—
487C2×D5—22no—
488C2×D5C4×D1214yescomplemented
489C4×C5—22no—
490C4×C5—122no—
491C4×C5C4×#6714yescomplemented
492C4×C5#93014yescomplemented
493Dic5—22no—
494Dic5—22no—
495Dic5—22no—
496Dic5—64no—
497Dic5—122no—
498C24—32no—
499C24—51no—
500C2×D4—34no—
501C2×D4—62no—
502C2×D4—62no—
503C2×D4—158no—
504C2×D4—304no—
505C2×D4—304no—
506C22×C4—32no—
507C22×C4—51no—
508C22×C4—51no—
509C22×C4—51no—
510C22×C4—54no—
511C22×C4—54no—
512C22×C4—64no—
513C22×C4—64no—
514C22×C4—64no—
515C22×C4—102no—
516C22×C4—102no—
517C22×C4—102no—
518C22×C4—102no—
519C22×C4—102no—
520C22×C4—102no—
521C22×C4—102no—
522C22×C4—152no—
523C22×C4—152no—
524C22×C4C2×D3×D511yescharacteristic
525C22×C4C2×D3×D511yescharacteristic
526C22×C4C2×D3×D511yescharacteristic
527C4⋊C4—62no—
528C4⋊C4—154no—
529C4⋊C4—304no—
530C4⋊C4—302no—
531C22⋊C4—64no—
532C22⋊C4—158no—
533C22⋊C4—304no—
534C22⋊C4—304no—
535C22⋊C4—304no—
536C42—102no—
537C42—102no—
538C42—102no—
539C42—304no—
540C42#120114yescomplemented
541C3×C5C4×#12111yescharacteristic, complemented, Hall
542C22×C3—54no—
543C22×C3—102no—
544C22×C3—102no—
545C22×C3—102no—
546C22×C3—102no—
547C22×C3—102no—
548C22×C3—102no—
549C22×C3C22×C4×D511yescharacteristic
550C22×C3C2×#70911yescharacteristic
551C22×C3C2×D4×D511yescharacteristic
552C22×C3C2×#71111yescharacteristic
553C22×C3D5×#4111yescharacteristic
554C22×C3D5×#4111yescharacteristic
555C22×C3C22×C22⋊D511yescharacteristic
556C2×D3—24no—
557C2×D3—24no—
558C2×D3—24no—
559C2×D3—42no—
560C2×D3—42no—
561C2×D3—42no—
562C2×D3—42no—
563C3×C4—22no—
564C3×C4—102no—
565C3×C4—102no—
566C3×C4—102no—
567C3×C4C4×C22⋊D514yescomplemented
568C3×C4#408414yescomplemented
569Dic3—42no—
570Dic3—104no—
571Dic3—202no—
572C2×C5—124no—
573C2×C5C2×C4×D1211yescharacteristic
574C2×C5C4×#23511yescharacteristic
575C2×C5#547711yescharacteristic
576C2×C5#547911yescharacteristic
577C2×C5C2×C4×#6711yescharacteristic
578C2×C5C2×#93011yescharacteristic
579C2×C5#579111yescharacteristic
580D5—24no—
581C23—34no—
582C23—52no—
583C23—52no—
584C23—52no—
585C23—62no—
586C23—62no—
587C23—62no—
588C23—62no—
589C23—62no—
590C23—62no—
591C23—101no—
592C23—101no—
593C23—101no—
594C23—101no—
595C23C22×D3×D511yescharacteristic
596D4—68no—
597D4—3016no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—52no—
601C2×C4—52no—
602C2×C4—52no—
603C2×C4—62no—
604C2×C4—62no—
605C2×C4—62no—
606C2×C4—108no—
607C2×C4—101no—
608C2×C4—101no—
609C2×C4—101no—
610C2×C4—101no—
611C2×C4—101no—
612C2×C4—101no—
613C2×C4—108no—
614C2×C4—108no—
615C2×C4—128no—
616C2×C4—154no—
617C2×C4—302no—
618C2×C4—302no—
619C2×C4—302no—
620C2×C4—302no—
621C2×C4—302no—
622C2×C4#677112yes—
623C2×C4#677212yes—
624C2×C4C4×D3×D512yes—
625C2×C4D5×D1212yes—
626C2×C4C2×#120112yes—
627C2×C4C2×#120112yes—
628C2×C4C2×#120112yes—
629C2×C3—104no—
630C2×C3C4×#71111yescharacteristic
631C2×C3C4×D4×D511yescharacteristic
632C2×C3#6588211yescharacteristic
633C2×C3#6589111yescharacteristic
634C2×C3C2×C4×C22⋊D511yescharacteristic
635C2×C3C2×#408411yescharacteristic
636C2×C3#6616211yescharacteristic
637D3—44no—
638C5C4×#93011yescharacteristic, complemented, Sylow
639C22—54no—
640C22—64no—
641C22—64no—
642C22—64no—
643C22—102no—
644C22—102no—
645C22—102no—
646C22—102no—
647C22—102no—
648C22—102no—
649C22—122no—
650C22—122no—
651C22—122no—
652C22—122no—
653C22C2×#677111yescharacteristic
654C22C2×#677211yescharacteristic
655C22C2×C4×D3×D511yescharacteristic
656C22C2×D5×D1211yescharacteristic
657C22D5×#23511yescharacteristic
658C22D5×#23511yescharacteristic
659C22C22×#120111yescharacteristic
660C4—22no—
661C4—102no—
662C4—102no—
663C4—102no—
664C4—122no—
665C4—304no—
666C4—602no—
667C4C4×#120114yescomplemented
668C4#9144914yesdirect product factor
669C3C4×#408411yescharacteristic, complemented, Sylow
670C2—104no—
671C2—124no—
672C2C4×#677211yescharacteristic
673C2#1175267111yescharacteristic
674C2#1175268211yescharacteristic
675C2C4×D5×D1211yescharacteristic
676C2C2×C4×#120111yescharacteristic
677C2C2×#9144911yescharacteristic
678C2#1175456311yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91449C2
hypercenterC2×C42D3×D5
hypocenterC3×C5C4×#121
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×C5×D12C2semidirect
2. C2×C3×C42×D5C2semidirect
4. C2×C4×#1201C2semidirect
5. C4×C4⋊Dic15C2semidirect
6. #11748905C2semidirect
7. #11748841C2semidirect
8. #11748764C2semidirect
9. #11748759C2semidirect
10. #11748714C2semidirect
11. C4×(C2×D3)⋊Dic5C2semidirect
35. #91449C4direct (N × H)
44. C2×C42×D5D3semidirect
62. C2×C5×D12C2×C4semidirect
76. C2×C3×C4×D5C2×C4semidirect
77. C2×C3×C4×D5D4semidirect
80. C2×#1201C2×C4semidirect
81. C3×C42×C5D4semidirect
83. C4⋊Dic15C2×C4semidirect
93. (C2×D3)⋊Dic5C2×C4semidirect
98. C2×C4×D12D5semidirect
236. C2×C4×D5C4×D3semidirect
237. C2×C4×D5D12semidirect
240. C42×C5#67semidirect
283. C2×C3×D5C4×D4semidirect
285. C3×C4×C5C4×D4semidirect
286. C3×C4×C5#121semidirect
318. C2×D12C4×D5semidirect
325. C3×C42C22⋊D5semidirect
488. C2×D5C4×D12semidirect
491. C4×C5C4×#67semidirect
492. C4×C5#930semidirect
540. C42#1201semidirect
541. C3×C5C4×#121semidirect
567. C3×C4C4×C22⋊D5semidirect
568. C3×C4#4084semidirect
638. C5C4×#930semidirect
667. C4C4×#1201semidirect
668. C4#91449direct (N × H)
669. C3C4×#4084semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×D122
C2×C3×C42×D52
C2×#914492
C2×C4×#12012
C4×C4⋊Dic152
#117489052
#117488412
#117487642
#117487592
#117487142
C4×(C2×D3)⋊Dic52
C4×#40843
C4×#9305