Finite Group Databasebeta

← C2×#11756422 #14481087

Subgroups — C2×#11756422 #14481087

Order 1920.

2520 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#123C211yesmaximal, characteristic, complemented
2C2×#91829C211yesmaximal, characteristic, complemented
3C2×#91828C211yesmaximal, characteristic, complemented
4C2×#91819C211yesmaximal, characteristic, complemented
5C2×C4×#1220C211yesmaximal, characteristic, complemented
6#11756422C2116yesmaximal, direct product factor
7C2×#91784C211yesmaximal, characteristic, complemented
8C2×#91783C211yesmaximal, characteristic, complemented
9C2×#91781C211yesmaximal, characteristic, complemented
10C2×#91778C211yesmaximal, characteristic, complemented
11C2×#91775C211yesmaximal, characteristic, complemented
12C2×#91773C211yesmaximal, characteristic, complemented
13C2×#91773C211yesmaximal, characteristic, complemented
14C2×#91773C211yesmaximal, characteristic, complemented
15C2×#91772C211yesmaximal, characteristic, complemented
16C2×#91770C211yesmaximal, characteristic, complemented
17C2×#65997—31nomaximal, Hall
18C22×C3×C5×D4C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic
22C22×#1220C2211yescharacteristic
23C22×#1220C2211yescharacteristic
24C22×#1220C2211yescharacteristic
25C22×#1220C2211yescharacteristic
26C23×Dic15C2211yescharacteristic
27C22×D60C2211yescharacteristic
28C22×D60C2211yescharacteristic
29C22×D60C2211yescharacteristic
30C22×C4×D15C2211yescharacteristic
31C22×C4×D15C2211yescharacteristic
32C22×C4×D15C2211yescharacteristic
33C3×C5×#123C2218yescomplemented
34C2×C3×C5×C4⋊C4C2211yescharacteristic
35C2×C3×C5×C4⋊C4C2211yescharacteristic
36C2×C3×C5×C22⋊C4C2211yescharacteristic
37C2×C3×C5×C22⋊C4C2211yescharacteristic
38C2×C3×C5×C22⋊C4C2211yescharacteristic
39C2×#6719C2211yescharacteristic
40#91829C2218yescomplemented
41#91828C2218yescomplemented
42#91819C2218yescomplemented
43C4×#1220C2218yescomplemented
44C2×#6714C2211yescharacteristic
45C2×#6714C2211yescharacteristic
46C2×#6714C2211yescharacteristic
47C2×#6714C2211yescharacteristic
48C2×#6714C2211yescharacteristic
49C2×#6714C2211yescharacteristic
50C2×C4⋊Dic15C2211yescharacteristic
51C2×C4⋊Dic15C2211yescharacteristic
52C2×#6712C2211yescharacteristic
53C2×#6712C2211yescharacteristic
54C2×#6712C2211yescharacteristic
55C2×#6712C2211yescharacteristic
56C2×C4×Dic15C2211yescharacteristic
57C2×C4×Dic15C2211yescharacteristic
58#91784C2218yescomplemented
59#91783C2218yescomplemented
60#91781C2218yescomplemented
61#91778C2218yescomplemented
62#91775C2218yescomplemented
63#91773C2218yescomplemented
64#91773C2218yescomplemented
65#91773C2218yescomplemented
66#91772C2218yescomplemented
67#91770C2218yescomplemented
68C2×#5663—51nomaximal, Hall
69C2×C5×#123D311yescharacteristic, complemented
70C2×#4086—31no—
71C2×#4085—31no—
72C2×#4076—31no—
73C2×C4×C22⋊D5—31no—
74#65997—316no—
75C2×#4041—31no—
76C2×#4040—31no—
77C2×#4038—31no—
78C2×#4035—31no—
79C2×#4032—31no—
80C2×#4030—31no—
81C2×#4030—31no—
82C2×#4030—31no—
83C2×#4029—31no—
84C2×#4027—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C2×C3×C5×D4—42no—
91C2×C3×C5×D4C2314yes—
92C22×C3×C4×C5—42no—
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2314yes—
99C2×#1220—24no—
100C2×#1220—24no—
101C2×#1220—42no—
102C2×#1220—42no—
103C2×#1220—42no—
104C2×#1220—42no—
105C2×#1220C2314yes—
106C2×#1220C2314yes—
107C2×#1220C2314yes—
108C2×#1220C2314yes—
109C2×#1220C2314yes—
110C2×#1220C2314yes—
111C22×Dic15—42no—
112C22×Dic15C2311yescharacteristic
113C22×Dic15C2311yescharacteristic
114C22×Dic15C2311yescharacteristic
115C22×Dic15C2311yescharacteristic
116C22×Dic15C2314yes—
117C22×Dic15C2311yescharacteristic
118C2×D60—42no—
119C2×D60—42no—
120C2×D60—42no—
121C2×D60C2314yes—
122C2×D60C2314yes—
123C2×D60C2314yes—
124C2×C4×D15—24no—
125C2×C4×D15—42no—
126C2×C4×D15—42no—
127C2×C4×D15C2314yes—
128C2×C4×D15C2314yes—
129C2×C4×D15C2314yes—
130C3×C5×C4⋊C4C2314yes—
131C3×C5×C4⋊C4C2314yes—
132C3×C5×C22⋊C4C2314yes—
133C3×C5×C22⋊C4C2314yes—
134C3×C5×C22⋊C4C2314yes—
135#6719C2314yes—
136#6714C2314yes—
137#6714C2314yes—
138#6714C2314yes—
139#6714C2314yes—
140#6714C2314yes—
141#6714C2314yes—
142C4⋊Dic15C2314yes—
143C4⋊Dic15C2314yes—
144#6712C2314yes—
145#6712C2314yes—
146#6712C2314yes—
147#6712C2314yes—
148C4×Dic15C2314yes—
149C4×Dic15C2314yes—
150C2×C3×#123D511yescharacteristic, complemented
151C2×#940—51no—
152C2×#939—51no—
153C2×#930—51no—
154C2×C4×#67—51no—
155#5663—516no—
156C2×#895—51no—
157C2×#894—51no—
158C2×#892—51no—
159C2×#889—51no—
160C2×#886—51no—
161C2×#884—51no—
162C2×#884—51no—
163C2×#884—51no—
164C2×#883—51no—
165C2×#67⋊C4—51no—
166C22×C5×D4C2×D311yescharacteristic
167C23×C4×C5C2×D311yescharacteristic
168C22×C22⋊D5—31no—
169C22×C22⋊D5—31no—
170C22×C22⋊D5—31no—
171C22×C22⋊D5—31no—
172C22×C22⋊D5—31no—
173C22×C22⋊D5—31no—
174C23×Dic5—31no—
175C22×D20—31no—
176C22×D20—31no—
177C22×D20—31no—
178C22×C4×D5—31no—
179C22×C4×D5—31no—
180C22×C4×D5—31no—
181C5×#123C2×D318yescomplemented
182C2×C5×C4⋊C4C2×D311yescharacteristic
183C2×C5×C4⋊C4C2×D311yescharacteristic
184C2×C5×C22⋊C4C2×D311yescharacteristic
185C2×C5×C22⋊C4C2×D311yescharacteristic
186C2×C5×C22⋊C4C2×D311yescharacteristic
187C2×C22⋊Dic5—31no—
188#4086—38no—
189#4085—38no—
190#4076—38no—
191C4×C22⋊D5—38no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685—31no—
198C2×C4⋊Dic5—31no—
199C2×C4⋊Dic5—31no—
200C2×#683—31no—
201C2×#683—31no—
202C2×#683—31no—
203C2×#683—31no—
204C2×C4×Dic5—31no—
205C2×C4×Dic5—31no—
206#4041—38no—
207#4040—38no—
208#4038—38no—
209#4035—38no—
210#4032—38no—
211#4030—38no—
212#4030—38no—
213#4030—38no—
214#4029—38no—
215#4027—38no—
216C2×#540—151noSylow
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5—22no—
220C23×C3×C5—22no—
221C23×C3×C5—22no—
222C23×C3×C5—22no—
223C23×C3×C5C2412yes—
224C23×C3×C5C2412yes—
225C23×C3×C5C2411yescharacteristic
226C22×D15—22no—
227C22×D15—22no—
228C22×D15—22no—
229C22×D15—22no—
230C22×D15—22no—
231C22×D15—22no—
232C22×D15—22no—
233C22×D15—22no—
234C22×D15—22no—
235C22×D15C2412yes—
236C22×D15C2412yes—
237C22×D15C2412yes—
238C3×C5×D4—44no—
239C2×C3×C4×C5—22no—
240C2×C3×C4×C5—22no—
241C2×C3×C4×C5—22no—
242C2×C3×C4×C5—22no—
243C2×C3×C4×C5—22no—
244C2×C3×C4×C5—44no—
245C2×C3×C4×C5C2412yes—
246C2×C3×C4×C5C2412yes—
247C2×C3×C4×C5C2412yes—
248C2×C3×C4×C5C2412yes—
249C2×C3×C4×C5C2412yes—
250#1220—28no—
251#1220—28no—
252#1220—44no—
253#1220—44no—
254#1220—44no—
255#1220—44no—
256C2×Dic15—22no—
257C2×Dic15—22no—
258C2×Dic15—22no—
259C2×Dic15—22no—
260C2×Dic15—44no—
261C2×Dic15#4114yes—
262C2×Dic15C2412yes—
263C2×Dic15C2412yes—
264C2×Dic15C2412yes—
265C2×Dic15C2412yes—
266C2×Dic15C2412yes—
267D60—44no—
268D60—44no—
269D60—44no—
270C4×D15—28no—
271C4×D15—44no—
272C4×D15—44no—
273C22×C3×D4C2×D511yescharacteristic
274C23×C3×C4C2×D511yescharacteristic
275C22×#67—51no—
276C22×#67—51no—
277C22×#67—51no—
278C22×#67—51no—
279C22×#67—51no—
280C22×#67—51no—
281C23×Dic3—51no—
282C22×D12—51no—
283C22×D12—51no—
284C22×D12—51no—
285C22×C4×D3—51no—
286C22×C4×D3—51no—
287C22×C4×D3—51no—
288C3×#123C2×D518yescomplemented
289C2×C3×C4⋊C4C2×D511yescharacteristic
290C2×C3×C4⋊C4C2×D511yescharacteristic
291C2×C3×C22⋊C4C2×D511yescharacteristic
292C2×C3×C22⋊C4C2×D511yescharacteristic
293C2×C3×C22⋊C4C2×D511yescharacteristic
294C2×#217—51no—
295#940—58no—
296#939—58no—
297#930—58no—
298C4×#67—58no—
299C2×(C2×D3)⋊C4—51no—
300C2×(C2×D3)⋊C4—51no—
301C2×(C2×D3)⋊C4—51no—
302C2×(C2×D3)⋊C4—51no—
303C2×(C2×D3)⋊C4—51no—
304C2×(C2×D3)⋊C4—51no—
305C2×C4⋊Dic3—51no—
306C2×C4⋊Dic3—51no—
307C2×Dic3⋊C4—51no—
308C2×Dic3⋊C4—51no—
309C2×Dic3⋊C4—51no—
310C2×Dic3⋊C4—51no—
311C2×C4×Dic3—51no—
312C2×C4×Dic3—51no—
313#895—58no—
314#894—58no—
315#892—58no—
316#889—58no—
317#886—58no—
318#884—58no—
319#884—58no—
320#884—58no—
321#883—58no—
322#67⋊C4—58no—
323C24×C5C22×D311yescharacteristic
324C24×C5C22×D311yescharacteristic
325C23×D5—31no—
326C23×D5—31no—
327C23×D5—31no—
328C2×C5×D4—42no—
329C2×C5×D4C22×D314yes—
330C22×C4×C5—42no—
331C22×C4×C5C22×D311yescharacteristic
332C22×C4×C5C22×D311yescharacteristic
333C22×C4×C5C22×D311yescharacteristic
334C22×C4×C5C22×D311yescharacteristic
335C22×C4×C5C22×D311yescharacteristic
336C22×C4×C5C22×D314yes—
337C2×C22⋊D5—34no—
338C2×C22⋊D5—34no—
339C2×C22⋊D5—34no—
340C2×C22⋊D5—34no—
341C2×C22⋊D5—34no—
342C2×C22⋊D5—34no—
343C2×C22⋊D5—64no—
344C2×C22⋊D5—64no—
345C2×C22⋊D5—122no—
346C2×C22⋊D5—122no—
347C2×C22⋊D5—122no—
348C2×C22⋊D5—122no—
349C22×Dic5—31no—
350C22×Dic5—31no—
351C22×Dic5—31no—
352C22×Dic5—31no—
353C22×Dic5—31no—
354C22×Dic5—34no—
355C22×Dic5—122no—
356C2×D20—34no—
357C2×D20—34no—
358C2×D20—34no—
359C2×D20—122no—
360C2×D20—122no—
361C2×D20—122no—
362C2×C4×D5—34no—
363C2×C4×D5—34no—
364C2×C4×D5—34no—
365C2×C4×D5—64no—
366C2×C4×D5—122no—
367C2×C4×D5—122no—
368C5×C4⋊C4C22×D314yes—
369C5×C4⋊C4C22×D314yes—
370C5×C22⋊C4C22×D314yes—
371C5×C22⋊C4C22×D314yes—
372C5×C22⋊C4C22×D314yes—
373C22⋊Dic5—34no—
374#685—34no—
375#685—34no—
376#685—34no—
377#685—34no—
378#685—34no—
379#685—34no—
380C4⋊Dic5—34no—
381C4⋊Dic5—34no—
382#683—34no—
383#683—34no—
384#683—34no—
385#683—34no—
386C4×Dic5—34no—
387C4×Dic5—34no—
388#540—1516no—
389C2×#127—151no—
390C2×#125—151no—
391C2×#123—151no—
392C2×#123—151no—
393C2×#123—151no—
394C2×#123D1511yescharacteristic, complemented
395C2×#121—151no—
396C2×#121—151no—
397C2×#121—151no—
398C2×#121—151no—
399C2×#121—151no—
400C2×#121—151no—
401C2×C4×D4—151no—
402C2×C4×D4—151no—
403C2×#117—151no—
404C22×C3×C5—22no—
405C22×C3×C5—22no—
406C22×C3×C5—22no—
407C22×C3×C5—22no—
408C22×C3×C5—22no—
409C22×C3×C5—22no—
410C22×C3×C5—44no—
411C22×C3×C5—44no—
412C22×C3×C5C2×#4112yes—
413C22×C3×C5H(5,𝔽2)12yes—
414C22×C3×C5H(5,𝔽2)12yes—
415C22×C3×C5C2511yescharacteristic
416C2×D15—22no—
417C2×D15—22no—
418C2×D15—22no—
419C2×D15—22no—
420C2×D15—22no—
421C2×D15—22no—
422C2×D15—22no—
423C2×D15—22no—
424C2×D15—22no—
425C2×D15—44no—
426C2×D15—44no—
427C2×D15—44no—
428C3×C4×C5—22no—
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431C3×C4×C5—22no—
432C3×C4×C5—22no—
433Dic15—22no—
434Dic15—22no—
435Dic15—22no—
436Dic15—22no—
437Dic15C2×#4114yes—
438C24×C3C22×D511yescharacteristic
439C24×C3C22×D511yescharacteristic
440C23×D3—51no—
441C23×D3—51no—
442C23×D3—51no—
443C2×C3×D4—42no—
444C2×C3×D4C22×D514yes—
445C22×C3×C4—42no—
446C22×C3×C4C22×D511yescharacteristic
447C22×C3×C4C22×D511yescharacteristic
448C22×C3×C4C22×D511yescharacteristic
449C22×C3×C4C22×D511yescharacteristic
450C22×C3×C4C22×D511yescharacteristic
451C22×C3×C4C22×D514yes—
452C2×#67—54no—
453C2×#67—54no—
454C2×#67—54no—
455C2×#67—54no—
456C2×#67—54no—
457C2×#67—54no—
458C2×#67—104no—
459C2×#67—104no—
460C2×#67—202no—
461C2×#67—202no—
462C2×#67—202no—
463C2×#67—202no—
464C22×Dic3—51no—
465C22×Dic3—51no—
466C22×Dic3—51no—
467C22×Dic3—51no—
468C22×Dic3—51no—
469C22×Dic3—54no—
470C22×Dic3—202no—
471C2×D12—54no—
472C2×D12—54no—
473C2×D12—54no—
474C2×D12—202no—
475C2×D12—202no—
476C2×D12—202no—
477C2×C4×D3—54no—
478C2×C4×D3—54no—
479C2×C4×D3—54no—
480C2×C4×D3—104no—
481C2×C4×D3—202no—
482C2×C4×D3—202no—
483C3×C4⋊C4C22×D514yes—
484C3×C4⋊C4C22×D514yes—
485C3×C22⋊C4C22×D514yes—
486C3×C22⋊C4C22×D514yes—
487C3×C22⋊C4C22×D514yes—
488#217—54no—
489(C2×D3)⋊C4—54no—
490(C2×D3)⋊C4—54no—
491(C2×D3)⋊C4—54no—
492(C2×D3)⋊C4—54no—
493(C2×D3)⋊C4—54no—
494(C2×D3)⋊C4—54no—
495C4⋊Dic3—54no—
496C4⋊Dic3—54no—
497Dic3⋊C4—54no—
498Dic3⋊C4—54no—
499Dic3⋊C4—54no—
500Dic3⋊C4—54no—
501C4×Dic3—54no—
502C4×Dic3—54no—
503C23×C5—22no—
504C23×C5—22no—
505C23×C5—22no—
506C23×C5—22no—
507C23×C5—22no—
508C23×C5—22no—
509C23×C5C23×D312yes—
510C23×C5C23×D312yes—
511C23×C5C23×D311yescharacteristic
512C22×D5—32no—
513C22×D5—32no—
514C22×D5—32no—
515C22×D5—62no—
516C22×D5—62no—
517C22×D5—62no—
518C22×D5—62no—
519C22×D5—62no—
520C22×D5—62no—
521C22×D5—62no—
522C22×D5—62no—
523C22×D5—62no—
524C5×D4—44no—
525C2×C4×C5—22no—
526C2×C4×C5—22no—
527C2×C4×C5—22no—
528C2×C4×C5—22no—
529C2×C4×C5—22no—
530C2×C4×C5—44no—
531C2×C4×C5C23×D312yes—
532C2×C4×C5C23×D312yes—
533C2×C4×C5C23×D312yes—
534C2×C4×C5C23×D312yes—
535C2×C4×C5C23×D312yes—
536C22⋊D5—68no—
537C22⋊D5—68no—
538C22⋊D5—124no—
539C22⋊D5—124no—
540C22⋊D5—124no—
541C22⋊D5—124no—
542C2×Dic5—34no—
543C2×Dic5—32no—
544C2×Dic5—32no—
545C2×Dic5—32no—
546C2×Dic5—32no—
547C2×Dic5—32no—
548C2×Dic5—62no—
549C2×Dic5—62no—
550C2×Dic5—62no—
551C2×Dic5—62no—
552C2×Dic5—124no—
553D20—124no—
554D20—124no—
555D20—124no—
556C4×D5—68no—
557C4×D5—124no—
558C4×D5—124no—
559C22×D4—151no—
560C22×D4—151no—
561C22×D4—151no—
562C22×D4—151no—
563C22×D4—151no—
564C22×D4—151no—
565C22×D4—151no—
566C22×D4—151no—
567C22×D4—151no—
568C22×D4C2×D1511yescharacteristic
569C23×C4—151no—
570C23×C4—151no—
571C23×C4—151no—
572C23×C4—151no—
573C23×C4C2×D1511yescharacteristic
574#127—158no—
575#125—158no—
576#123—158no—
577#123—158no—
578#123—158no—
579#123C2×D1518yescomplemented
580#121—158no—
581#121—158no—
582#121—158no—
583#121—158no—
584#121—158no—
585#121—158no—
586C4×D4—158no—
587C4×D4—158no—
588#117—158no—
589C2×C4⋊C4—151no—
590C2×C4⋊C4—151no—
591C2×C4⋊C4—151no—
592C2×C4⋊C4—151no—
593C2×C4⋊C4—151no—
594C2×C4⋊C4—151no—
595C2×C4⋊C4C2×D1511yescharacteristic
596C2×C4⋊C4C2×D1511yescharacteristic
597C2×C22⋊C4—151no—
598C2×C22⋊C4—151no—
599C2×C22⋊C4—151no—
600C2×C22⋊C4—151no—
601C2×C22⋊C4—151no—
602C2×C22⋊C4—151no—
603C2×C22⋊C4—151no—
604C2×C22⋊C4C2×D1511yescharacteristic
605C2×C22⋊C4C2×D1511yescharacteristic
606C2×C22⋊C4C2×D1511yescharacteristic
607C2×C42—151no—
608C2×C42—151no—
609C2×C3×C5—42no—
610C2×C3×C5—42no—
611C2×C3×C5#54014yescomplemented
612C2×C3×C5C22×#4111yescharacteristic
613C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
614C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
615D15—42no—
616D15—42no—
617D15—42no—
618C23×C3—22no—
619C23×C3—22no—
620C23×C3—22no—
621C23×C3—22no—
622C23×C3—22no—
623C23×C3—22no—
624C23×C3C23×D512yes—
625C23×C3C23×D512yes—
626C23×C3C23×D511yescharacteristic
627C22×D3—52no—
628C22×D3—52no—
629C22×D3—52no—
630C22×D3—102no—
631C22×D3—102no—
632C22×D3—102no—
633C22×D3—102no—
634C22×D3—102no—
635C22×D3—102no—
636C22×D3—102no—
637C22×D3—102no—
638C22×D3—102no—
639C3×D4—44no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—44no—
646C2×C3×C4C23×D512yes—
647C2×C3×C4C23×D512yes—
648C2×C3×C4C23×D512yes—
649C2×C3×C4C23×D512yes—
650C2×C3×C4C23×D512yes—
651#67—108no—
652#67—108no—
653#67—204no—
654#67—204no—
655#67—204no—
656#67—204no—
657C2×Dic3—54no—
658C2×Dic3—52no—
659C2×Dic3—52no—
660C2×Dic3—52no—
661C2×Dic3—52no—
662C2×Dic3—52no—
663C2×Dic3—102no—
664C2×Dic3—102no—
665C2×Dic3—102no—
666C2×Dic3—102no—
667C2×Dic3—204no—
668D12—204no—
669D12—204no—
670D12—204no—
671C4×D3—108no—
672C4×D3—204no—
673C4×D3—204no—
674C22×C5—22no—
675C22×C5—22no—
676C22×C5—22no—
677C22×C5—22no—
678C22×C5—22no—
679C22×C5—22no—
680C22×C5—44no—
681C22×C5—44no—
682C22×C5#100412yes—
683C22×C5D3×#4112yes—
684C22×C5#100912yes—
685C22×C5C24×D311yescharacteristic
686C2×D5—62no—
687C2×D5—62no—
688C2×D5—62no—
689C2×D5—62no—
690C2×D5—62no—
691C2×D5—62no—
692C2×D5—62no—
693C2×D5—62no—
694C2×D5—62no—
695C2×D5—124no—
696C2×D5—124no—
697C2×D5—124no—
698C4×C5—22no—
699C4×C5—22no—
700C4×C5—22no—
701C4×C5—22no—
702C4×C5—22no—
703Dic5—34no—
704Dic5—62no—
705Dic5—62no—
706Dic5—62no—
707Dic5—62no—
708C24—151no—
709C24—151no—
710C24—151no—
711C24C22×D1511yescharacteristic
712C24C22×D1511yescharacteristic
713C2×D4—42no—
714C2×D4—154no—
715C2×D4—154no—
716C2×D4—154no—
717C2×D4—154no—
718C2×D4—154no—
719C2×D4—154no—
720C2×D4—154no—
721C2×D4—154no—
722C2×D4—154no—
723C2×D4—304no—
724C2×D4—304no—
725C2×D4—602no—
726C2×D4—602no—
727C2×D4—602no—
728C2×D4—602no—
729C2×D4—602no—
730C2×D4—602no—
731C2×D4—602no—
732C2×D4C22×D1514yes—
733C22×C4—42no—
734C22×C4—151no—
735C22×C4—151no—
736C22×C4—151no—
737C22×C4—151no—
738C22×C4—151no—
739C22×C4—154no—
740C22×C4—154no—
741C22×C4—154no—
742C22×C4—154no—
743C22×C4—304no—
744C22×C4—602no—
745C22×C4—602no—
746C22×C4—602no—
747C22×C4C22×D1511yescharacteristic
748C22×C4C22×D1511yescharacteristic
749C22×C4C22×D1511yescharacteristic
750C22×C4C22×D1511yescharacteristic
751C22×C4C22×D1511yescharacteristic
752C22×C4C22×D1514yes—
753C4⋊C4—154no—
754C4⋊C4—154no—
755C4⋊C4—154no—
756C4⋊C4—154no—
757C4⋊C4—154no—
758C4⋊C4—154no—
759C4⋊C4C22×D1514yes—
760C4⋊C4C22×D1514yes—
761C22⋊C4—154no—
762C22⋊C4—154no—
763C22⋊C4—154no—
764C22⋊C4—154no—
765C22⋊C4—154no—
766C22⋊C4—154no—
767C22⋊C4—154no—
768C22⋊C4C22×D1514yes—
769C22⋊C4C22×D1514yes—
770C22⋊C4C22×D1514yes—
771C42—154no—
772C42—154no—
773C3×C5C2×#54011yescharacteristic, complemented, Hall
774C22×C3—22no—
775C22×C3—22no—
776C22×C3—22no—
777C22×C3—22no—
778C22×C3—22no—
779C22×C3—22no—
780C22×C3—44no—
781C22×C3—44no—
782C22×C3#414412yes—
783C22×C3D5×#4112yes—
784C22×C3#414912yes—
785C22×C3C24×D511yescharacteristic
786C2×D3—102no—
787C2×D3—102no—
788C2×D3—102no—
789C2×D3—102no—
790C2×D3—102no—
791C2×D3—102no—
792C2×D3—102no—
793C2×D3—102no—
794C2×D3—102no—
795C2×D3—204no—
796C2×D3—204no—
797C2×D3—204no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—22no—
802C3×C4—22no—
803Dic3—54no—
804Dic3—102no—
805Dic3—102no—
806Dic3—102no—
807Dic3—102no—
808C2×C5—42no—
809C2×C5—42no—
810C2×C5#566314yescomplemented
811C2×C5C2×#100411yescharacteristic
812C2×C5C2×D3×#4111yescharacteristic
813C2×C5C2×#100911yescharacteristic
814D5—122no—
815D5—122no—
816D5—122no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—152no—
824C23—152no—
825C23—152no—
826C23—302no—
827C23—302no—
828C23—302no—
829C23—302no—
830C23—302no—
831C23—302no—
832C23—302no—
833C23—302no—
834C23—302no—
835C23C23×D1512yes—
836C23C23×D1512yes—
837C23C23×D1511yescharacteristic
838D4—44no—
839D4—308no—
840D4—308no—
841D4—604no—
842D4—604no—
843D4—604no—
844D4—604no—
845D4—604no—
846D4—604no—
847D4—604no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—44no—
854C2×C4—154no—
855C2×C4—152no—
856C2×C4—152no—
857C2×C4—152no—
858C2×C4—152no—
859C2×C4—152no—
860C2×C4—308no—
861C2×C4—302no—
862C2×C4—302no—
863C2×C4—302no—
864C2×C4—302no—
865C2×C4—604no—
866C2×C4—604no—
867C2×C4—604no—
868C2×C4C23×D1512yes—
869C2×C4C23×D1512yes—
870C2×C4C23×D1512yes—
871C2×C4C23×D1512yes—
872C2×C4C23×D1512yes—
873C2×C3—42no—
874C2×C3—42no—
875C2×C3#6599714yescomplemented
876C2×C3C2×#414411yescharacteristic
877C2×C3C2×D5×#4111yescharacteristic
878C2×C3C2×#414911yescharacteristic
879D3—202no—
880D3—202no—
881D3—202no—
882C5C2×#566311yescharacteristic, complemented, Sylow
883C22—22no—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—44no—
890C22—44no—
891C22—302no—
892C22—302no—
893C22—302no—
894C22—302no—
895C22—302no—
896C22—302no—
897C22—302no—
898C22—302no—
899C22—302no—
900C22—604no—
901C22—604no—
902C22—604no—
903C22#9209512yes—
904C22#41×D1512yes—
905C22#9210012yes—
906C22C24×D1511yescharacteristic
907C4—22no—
908C4—22no—
909C4—22no—
910C4—22no—
911C4—22no—
912C4—154no—
913C4—302no—
914C4—302no—
915C4—302no—
916C4—302no—
917C3C2×#6599711yescharacteristic, complemented, Sylow
918C2—42no—
919C2—42no—
920C2—602no—
921C2—602no—
922C2—602no—
923C2#1175642214yesdirect product factor
924C2C2×#9209511yescharacteristic
925C2C2×#41×D1511yescharacteristic
926C2C2×#9210011yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#123C2
socleC23×C3×C5C24
hypercenterC2×#123D15
hypocenterC3×C5C2×#540
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#123C2semidirect
2. C2×#91829C2semidirect
3. C2×#91828C2semidirect
4. C2×#91819C2semidirect
5. C2×C4×#1220C2semidirect
6. #11756422C2direct (N × H)
7. C2×#91784C2semidirect
8. C2×#91783C2semidirect
9. C2×#91781C2semidirect
10. C2×#91778C2semidirect
11. C2×#91775C2semidirect
12. C2×#91773C2semidirect
13. C2×#91773C2semidirect
14. C2×#91773C2semidirect
15. C2×#91772C2semidirect
16. C2×#91770C2semidirect
33. C3×C5×#123C22semidirect
40. #91829C22semidirect
41. #91828C22semidirect
42. #91819C22semidirect
43. C4×#1220C22semidirect
58. #91784C22semidirect
59. #91783C22semidirect
60. #91781C22semidirect
61. #91778C22semidirect
62. #91775C22semidirect
63. #91773C22semidirect
64. #91773C22semidirect
65. #91773C22semidirect
66. #91772C22semidirect
67. #91770C22semidirect
69. C2×C5×#123D3semidirect
150. C2×C3×#123D5semidirect
181. C5×#123C2×D3semidirect
288. C3×#123C2×D5semidirect
394. C2×#123D15semidirect
579. #123C2×D15semidirect
611. C2×C3×C5#540semidirect
773. C3×C5C2×#540semidirect
810. C2×C5#5663semidirect
875. C2×C3#65997semidirect
882. C5C2×#5663semidirect
917. C3C2×#65997semidirect
923. C2#11756422direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1232
C2×#918292
C2×#918282
C2×#918192
C2×C4×#12202
#117564222
C2×#917842
C2×#917832
C2×#917812
C2×#917782
C2×#917752
C2×#917732
C2×#917722
C2×#917702
C2×#659973
C2×#56635