Finite Group Databasebeta

← C2×#11756435 #14482495

Subgroups — C2×#11756435 #14482495

Order 1920.

3800 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6821C211yesmaximal, characteristic, complemented
2C22×D4×D15C211yesmaximal, characteristic, complemented
3C2×C3×C5×#124C211yesmaximal, characteristic, complemented
4C2×#91835C211yesmaximal, characteristic, complemented
5C2×#91827C211yesmaximal, characteristic, complemented
6#11756435C2116yesmaximal, direct product factor
7C2×#91773C212yesmaximal, complemented
8C2×#91772C212yesmaximal, complemented
9C2×#91771C212yesmaximal, complemented
10C2×C22⋊C4×D15C212yesmaximal, complemented
11C2×C4×D60C211yesmaximal, characteristic, complemented
12C2×C4×D60C211yesmaximal, characteristic, complemented
13C2×#66010—31nomaximal, Hall
14C24×D15C2212yes—
15C22×C3×C5×Q8C2211yescharacteristic, complemented
16C22×C3×C5×D4C2211yescharacteristic
17C22×#1220C2212yes—
18C22×#1220C2212yescomplemented
19C2×#6821—28no—
20C2×#6821C2218yescomplemented
21C2×D4×D15—28no—
22C2×D4×D15C2218yescomplemented
23C22×D60C2211yescharacteristic
24C22×D60C2211yescharacteristic
25C22×D60C2212yescomplemented
26C22×C4×D15C2211yescharacteristic
27C22×C4×D15C2211yescharacteristic, complemented
28C22×C4×D15C2212yescomplemented
29C22×C4×D15C2212yescomplemented
30C3×C5×#124C2218yescomplemented
31C2×C3×C5×C22⋊C4C2212yescomplemented
32C2×C3×C5×C22⋊C4C2212yescomplemented
33C2×C3×C42×C5C2211yescharacteristic, complemented
34C2×#6719C2212yescomplemented
35#91835C2218yescomplemented
36#91827C2218yescomplemented
37C2×#6714C2212yes—
38C2×#6714C2211yescharacteristic
39C2×#6714C2212yescomplemented
40C2×#6714C2211yescharacteristic, complemented
41C2×C4⋊Dic15C2211yescharacteristic, complemented
42C2×C4⋊Dic15C2211yescharacteristic, complemented
43C2×#6712C2212yescomplemented
44#91773C22116yescomplemented
45#91772C22116yescomplemented
46#91771C22116yescomplemented
47C22⋊C4×D15C22116yescomplemented
48C4×D60C2218yescomplemented
49C4×D60C2218yescomplemented
50C2×#5676—51nomaximal, Hall
51C22×#713—31no—
52C22×D4×D5—31no—
53C2×C5×#124D311yescharacteristic, complemented
54C2×#4092—31no—
55C2×#4084—31no—
56#66010—316no—
57C2×#4030—32no—
58C2×#4029—32no—
59C2×#4028—32no—
60C2×D5×C22⋊C4—32no—
61C2×C4×D20—31no—
62C2×C4×D20—31no—
63C24×C3×C5C2312yes—
64C23×D15—28no—
65C23×D15—28no—
66C23×D15—44no—
67C23×D15C2311yescharacteristic
68C23×D15C2318yes—
69C23×D15C2312yes—
70C23×D15C2311yescharacteristic
71C2×C3×C5×Q8—24no—
72C2×C3×C5×Q8C2314yescomplemented
73C2×C3×C5×D4—24no—
74C2×C3×C5×D4C2314yes—
75C22×C3×C4×C5C2312yes—
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C2×#1220—28no—
80C2×#1220—44no—
81C2×#1220C2318yes—
82C2×#1220C2318yescomplemented
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2312yes—
85C22×Dic15C2311yescharacteristic
86#6821—232no—
87D4×D15—232no—
88C2×D60—28no—
89C2×D60—24no—
90C2×D60D418yescomplemented
91C2×D60C2314yes—
92C2×D60C2314yes—
93C2×D60C2318yescomplemented
94C2×C4×D15—28no—
95C2×C4×D15—24no—
96C2×C4×D15—24no—
97C2×C4×D15—44no—
98C2×C4×D15C2314yes—
99C2×C4×D15C2314yescomplemented
100C2×C4×D15C2318yescomplemented
101C2×C4×D15C2318yescomplemented
102C3×C5×C22⋊C4C2318yescomplemented
103C3×C5×C22⋊C4C2318yescomplemented
104C3×C42×C5C2314yescomplemented
105#6719C2318yescomplemented
106#6714C2314yes—
107#6714C2318yes—
108#6714C2318yescomplemented
109#6714C2314yescomplemented
110C4⋊Dic15C2314yescomplemented
111C4⋊Dic15C2314yescomplemented
112#6712C2318yescomplemented
113C22×#239—51no—
114C22×D3×D4—51no—
115C2×C3×#124D511yescharacteristic, complemented
116C2×#946—51no—
117C2×#938—51no—
118#5676—516no—
119C2×#884—52no—
120C2×#883—52no—
121C2×#882—52no—
122C2×D3×C22⋊C4—52no—
123C2×C4×D12—51no—
124C2×C4×D12—51no—
125C24×D5—32no—
126C22×C5×Q8C2×D311yescharacteristic, complemented
127C22×C5×D4C2×D311yescharacteristic
128C22×C22⋊D5—32no—
129C22×C22⋊D5—32no—
130C2×#713—38no—
131C2×#713—68no—
132C2×D4×D5—38no—
133C2×D4×D5—68no—
134C22×D20—31no—
135C22×D20—31no—
136C22×D20—32no—
137C22×C4×D5—31no—
138C22×C4×D5—31no—
139C22×C4×D5—32no—
140C22×C4×D5—32no—
141C5×#124C2×D318yescomplemented
142C2×C5×C22⋊C4C2×D312yescomplemented
143C2×C5×C22⋊C4C2×D312yescomplemented
144C2×C42×C5C2×D311yescharacteristic, complemented
145C2×C22⋊Dic5—32no—
146#4092—38no—
147#4084—38no—
148C2×#685—31no—
149C2×#685—32no—
150C2×#685—31no—
151C2×#685—32no—
152C2×C4⋊Dic5—31no—
153C2×C4⋊Dic5—31no—
154C2×#683—32no—
155#4030—316no—
156#4029—316no—
157#4028—316no—
158D5×C22⋊C4—316no—
159C4×D20—38no—
160C4×D20—38no—
161C2×#546—151noSylow
162C23×C3×C5—24no—
163C23×C3×C5—24no—
164C23×C3×C5—24no—
165C23×C3×C5C2414yes—
166C23×C3×C5C2411yescharacteristic
167C22×D15—22no—
168C22×D15—24no—
169C22×D15—24no—
170C22×D15—22no—
171C22×D15—22no—
172C22×D15—22no—
173C22×D15—22no—
174C22×D15—216no—
175C22×D15—216no—
176C22×D15—48no—
177C22×D15—432no—
178C22×D15C2×D418yes—
179C22×D15#4114yescomplemented
180C22×D15C2412yes—
181C22×D15C2414yes—
182C22×D15C2412yes—
183C3×C5×Q8—28no—
184C3×C5×D4—28no—
185C2×C3×C4×C5—24no—
186C2×C3×C4×C5—22no—
187C2×C3×C4×C5—22no—
188C2×C3×C4×C5C2×D414yes—
189C2×C3×C4×C5C2414yes—
190C2×C3×C4×C5C2412yes—
191C2×C3×C4×C5C2412yes—
192C2×C3×C4×C5C2412yes—
193#1220—216no—
194#1220—48no—
195C2×Dic15—22no—
196C2×Dic15—22no—
197C2×Dic15—24no—
198C2×Dic15C2412yes—
199C2×Dic15C2414yes—
200C2×Dic15C2412yes—
201D60—216no—
202D60—28no—
203D60C2×D4116yescomplemented
204C4×D15—216no—
205C4×D15—28no—
206C4×D15—28no—
207C4×D15—48no—
208C24×D3—52no—
209C22×C3×Q8C2×D511yescharacteristic, complemented
210C22×C3×D4C2×D511yescharacteristic
211C22×#67—52no—
212C22×#67—52no—
213C2×#239—58no—
214C2×#239—108no—
215C2×D3×D4—58no—
216C2×D3×D4—108no—
217C22×D12—51no—
218C22×D12—52no—
219C22×D12—51no—
220C22×C4×D3—51no—
221C22×C4×D3—51no—
222C22×C4×D3—52no—
223C22×C4×D3—52no—
224C3×#124C2×D518yescomplemented
225C2×C3×C22⋊C4C2×D512yescomplemented
226C2×C3×C22⋊C4C2×D512yescomplemented
227C2×C3×C42C2×D511yescharacteristic, complemented
228C2×#217—52no—
229#946—58no—
230#938—58no—
231C2×(C2×D3)⋊C4—51no—
232C2×(C2×D3)⋊C4—52no—
233C2×(C2×D3)⋊C4—51no—
234C2×(C2×D3)⋊C4—52no—
235C2×C4⋊Dic3—51no—
236C2×C4⋊Dic3—51no—
237C2×Dic3⋊C4—52no—
238#884—516no—
239#883—516no—
240#882—516no—
241D3×C22⋊C4—516no—
242C4×D12—58no—
243C4×D12—58no—
244C24×C5C22×D312yes—
245C23×D5—32no—
246C23×D5—31no—
247C23×D5—31no—
248C23×D5—38no—
249C23×D5—68no—
250C23×D5—68no—
251C23×D5—124no—
252C2×C5×Q8—24no—
253C2×C5×Q8C22×D314yescomplemented
254C2×C5×D4—24no—
255C2×C5×D4C22×D314yes—
256C22×C4×C5C22×D311yescharacteristic
257C22×C4×C5C22×D311yescharacteristic
258C22×C4×C5C22×D312yes—
259C22×C4×C5C22×D311yescharacteristic
260C2×C22⋊D5—38no—
261C2×C22⋊D5—38no—
262C2×C22⋊D5—68no—
263C2×C22⋊D5—124no—
264C22×Dic5—31no—
265C22×Dic5—32no—
266C22×Dic5—31no—
267#713—632no—
268D4×D5—632no—
269C2×D20—38no—
270C2×D20—34no—
271C2×D20—38no—
272C2×D20—34no—
273C2×D20—68no—
274C2×D20—64no—
275C2×C4×D5—34no—
276C2×C4×D5—34no—
277C2×C4×D5—38no—
278C2×C4×D5—38no—
279C2×C4×D5—68no—
280C2×C4×D5—64no—
281C2×C4×D5—64no—
282C2×C4×D5—124no—
283C5×C22⋊C4C22×D318yescomplemented
284C5×C22⋊C4C22×D318yescomplemented
285C42×C5C22×D314yescomplemented
286C22⋊Dic5—38no—
287#685—34no—
288#685—38no—
289#685—38no—
290#685—34no—
291C4⋊Dic5—34no—
292C4⋊Dic5—34no—
293#683—38no—
294C22×#41—151no—
295C23×D4—151no—
296#546—1516no—
297C2×#124D1511yescharacteristic, complemented
298C2×#123—152no—
299C2×C22⋊Q8—151no—
300C2×#121—151no—
301C2×#121—152no—
302C2×#120—152no—
303C2×C4×D4—151no—
304C2×C4×D4—151no—
305C22×C22⋊C4—152no—
306C22×C3×C5—24no—
307C22×C3×C5—24no—
308C22×C3×C5—24no—
309C22×C3×C5—48no—
310C22×C3×C5C22×D412yes—
311C22×C3×C5C2×#4112yes—
312C22×C3×C5H(5,𝔽2)12yes—
313C22×C3×C5C2511yescharacteristic
314C2×D15—28no—
315C2×D15—216no—
316C2×D15—22no—
317C2×D15—24no—
318C2×D15—24no—
319C2×D15—22no—
320C2×D15—22no—
321C2×D15—22no—
322C2×D15—22no—
323C2×D15—432no—
324C2×D15—44no—
325C2×D15C22×D418yes—
326C2×D15C2×#4114yescomplemented
327C3×C4×C5—24no—
328C3×C4×C5—22no—
329C3×C4×C5—22no—
330C3×C4×C5C22×D414yes—
331Dic15—22no—
332Dic15—22no—
333Dic15—24no—
334C24×C3C22×D512yes—
335C23×D3—51no—
336C23×D3—52no—
337C23×D3—51no—
338C23×D3—58no—
339C23×D3—108no—
340C23×D3—108no—
341C23×D3—204no—
342C2×C3×Q8—24no—
343C2×C3×Q8C22×D514yescomplemented
344C2×C3×D4—24no—
345C2×C3×D4C22×D514yes—
346C22×C3×C4C22×D512yes—
347C22×C3×C4C22×D511yescharacteristic
348C22×C3×C4C22×D511yescharacteristic
349C22×C3×C4C22×D511yescharacteristic
350C2×#67—58no—
351C2×#67—58no—
352C2×#67—108no—
353C2×#67—204no—
354C22×Dic3—51no—
355C22×Dic3—52no—
356C22×Dic3—51no—
357#239—1032no—
358D3×D4—1032no—
359C2×D12—58no—
360C2×D12—54no—
361C2×D12—54no—
362C2×D12—58no—
363C2×D12—104no—
364C2×D12—108no—
365C2×C4×D3—54no—
366C2×C4×D3—54no—
367C2×C4×D3—58no—
368C2×C4×D3—58no—
369C2×C4×D3—108no—
370C2×C4×D3—104no—
371C2×C4×D3—104no—
372C2×C4×D3—204no—
373C3×C22⋊C4C22×D518yescomplemented
374C3×C22⋊C4C22×D518yescomplemented
375C3×C42C22×D514yescomplemented
376#217—58no—
377(C2×D3)⋊C4—54no—
378(C2×D3)⋊C4—58no—
379(C2×D3)⋊C4—58no—
380(C2×D3)⋊C4—54no—
381C4⋊Dic3—54no—
382C4⋊Dic3—54no—
383Dic3⋊C4—58no—
384C23×C5—24no—
385C23×C5—24no—
386C23×C5—24no—
387C23×C5C23×D314yes—
388C23×C5C23×D311yescharacteristic
389C22×D5—38no—
390C22×D5—34no—
391C22×D5—32no—
392C22×D5—34no—
393C22×D5—32no—
394C22×D5—616no—
395C22×D5—616no—
396C22×D5—62no—
397C22×D5—64no—
398C22×D5—64no—
399C22×D5—62no—
400C22×D5—62no—
401C22×D5—62no—
402C22×D5—62no—
403C22×D5—128no—
404C22×D5—1232no—
405C5×Q8—28no—
406C5×D4—28no—
407C2×C4×C5—24no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5D3×D414yes—
411C2×C4×C5C23×D314yes—
412C2×C4×C5C23×D312yes—
413C2×C4×C5C23×D312yes—
414C2×C4×C5C23×D312yes—
415C22⋊D5—616no—
416C22⋊D5—128no—
417C2×Dic5—32no—
418C2×Dic5—34no—
419C2×Dic5—32no—
420C2×Dic5—62no—
421C2×Dic5—62no—
422C2×Dic5—64no—
423D20—316no—
424D20—68no—
425D20—616no—
426C4×D5—616no—
427C4×D5—68no—
428C4×D5—68no—
429C4×D5—128no—
430C25—152no—
431C2×#41—158no—
432C2×#41—308no—
433C22×Q8C2×D1511yescharacteristic, complemented
434C22×D4—152no—
435C22×D4—152no—
436C22×D4—158no—
437C22×D4—151no—
438C22×D4—151no—
439C22×D4—152no—
440C22×D4—308no—
441C22×D4C2×D1511yescharacteristic
442C23×C4—152no—
443C23×C4—151no—
444C23×C4—151no—
445C23×C4—152no—
446#124C2×D1518yescomplemented
447#123—1516no—
448C22⋊Q8—158no—
449#121—158no—
450#121—1516no—
451#120—1516no—
452C4×D4—158no—
453C4×D4—158no—
454C2×C4⋊C4—151no—
455C2×C4⋊C4—151no—
456C2×C4⋊C4—152no—
457C2×C22⋊C4—152no—
458C2×C22⋊C4—151no—
459C2×C22⋊C4—152no—
460C2×C22⋊C4—152no—
461C2×C22⋊C4—151no—
462C2×C22⋊C4—1516no—
463C2×C22⋊C4C2×D1512yescomplemented
464C2×C22⋊C4C2×D1512yescomplemented
465C2×C42C2×D1511yescharacteristic, complemented
466C2×C3×C5—44no—
467C2×C3×C5#54614yescomplemented
468C2×C3×C5C23×D411yescharacteristic
469C2×C3×C5C22×#4111yescharacteristic
470C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
471D15—24no—
472D15—28no—
473D15—42no—
474C23×C3—24no—
475C23×C3—24no—
476C23×C3—24no—
477C23×C3C23×D514yes—
478C23×C3C23×D511yescharacteristic
479C22×D3—58no—
480C22×D3—54no—
481C22×D3—52no—
482C22×D3—54no—
483C22×D3—52no—
484C22×D3—1016no—
485C22×D3—1016no—
486C22×D3—102no—
487C22×D3—104no—
488C22×D3—104no—
489C22×D3—102no—
490C22×D3—102no—
491C22×D3—102no—
492C22×D3—102no—
493C22×D3—208no—
494C22×D3—2032no—
495C3×Q8—28no—
496C3×D4—28no—
497C2×C3×C4—24no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4D4×D514yes—
501C2×C3×C4C23×D514yes—
502C2×C3×C4C23×D512yes—
503C2×C3×C4C23×D512yes—
504C2×C3×C4C23×D512yes—
505#67—1016no—
506#67—208no—
507C2×Dic3—52no—
508C2×Dic3—54no—
509C2×Dic3—52no—
510C2×Dic3—102no—
511C2×Dic3—102no—
512C2×Dic3—104no—
513D12—516no—
514D12—108no—
515D12—1016no—
516C4×D3—1016no—
517C4×D3—108no—
518C4×D3—108no—
519C4×D3—208no—
520C22×C5—24no—
521C22×C5—24no—
522C22×C5—24no—
523C22×C5—48no—
524C22×C5C2×D3×D412yes—
525C22×C5D3×#4112yes—
526C22×C5#100912yes—
527C22×C5C24×D311yescharacteristic
528C2×D5—38no—
529C2×D5—34no—
530C2×D5—616no—
531C2×D5—68no—
532C2×D5—62no—
533C2×D5—64no—
534C2×D5—64no—
535C2×D5—62no—
536C2×D5—62no—
537C2×D5—62no—
538C2×D5—62no—
539C2×D5—1232no—
540C2×D5—124no—
541C4×C5—24no—
542C4×C5—22no—
543C4×C5—22no—
544C4×C5C2×D3×D414yes—
545Dic5—62no—
546Dic5—62no—
547Dic5—64no—
548C24—151no—
549C24—152no—
550C24—151no—
551C24—158no—
552C24—308no—
553C24—308no—
554C24—604no—
555C24C22×D1512yes—
556#41—3032no—
557C2×Q8—24no—
558C2×Q8C22×D1514yescomplemented
559C2×D4—24no—
560C2×D4—158no—
561C2×D4—158no—
562C2×D4—158no—
563C2×D4—154no—
564C2×D4—154no—
565C2×D4—158no—
566C2×D4—308no—
567C2×D4—304no—
568C2×D4—3032no—
569C2×D4—308no—
570C2×D4—604no—
571C2×D4C22×D1514yes—
572C22×C4—152no—
573C22×C4—151no—
574C22×C4—151no—
575C22×C4—158no—
576C22×C4—154no—
577C22×C4—154no—
578C22×C4—158no—
579C22×C4—308no—
580C22×C4—304no—
581C22×C4—304no—
582C22×C4—604no—
583C22×C4C22×D1511yescharacteristic
584C22×C4C22×D1511yescharacteristic
585C22×C4C22×D1512yes—
586C22×C4C22×D1511yescharacteristic
587C4⋊C4—154no—
588C4⋊C4—154no—
589C4⋊C4—158no—
590C22⋊C4—158no—
591C22⋊C4—154no—
592C22⋊C4—158no—
593C22⋊C4—158no—
594C22⋊C4—154no—
595C22⋊C4C22×D1518yescomplemented
596C22⋊C4C22×D1518yescomplemented
597C42C22×D1514yescomplemented
598C3×C5C2×#54611yescharacteristic, complemented, Hall
599C22×C3—24no—
600C22×C3—24no—
601C22×C3—24no—
602C22×C3—48no—
603C22×C3C2×D4×D512yes—
604C22×C3D5×#4112yes—
605C22×C3#414912yes—
606C22×C3C24×D511yescharacteristic
607C2×D3—58no—
608C2×D3—54no—
609C2×D3—1016no—
610C2×D3—108no—
611C2×D3—102no—
612C2×D3—104no—
613C2×D3—104no—
614C2×D3—102no—
615C2×D3—102no—
616C2×D3—102no—
617C2×D3—102no—
618C2×D3—2032no—
619C2×D3—204no—
620C3×C4—24no—
621C3×C4—22no—
622C3×C4—22no—
623C3×C4C2×D4×D514yes—
624Dic3—102no—
625Dic3—102no—
626Dic3—104no—
627C2×C5—44no—
628C2×C5#567614yescomplemented
629C2×C5C22×D3×D411yescharacteristic
630C2×C5C2×D3×#4111yescharacteristic
631C2×C5C2×#100911yescharacteristic
632D5—64no—
633D5—68no—
634D5—122no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—158no—
639C23—154no—
640C23—152no—
641C23—154no—
642C23—152no—
643C23—3016no—
644C23—3016no—
645C23—302no—
646C23—304no—
647C23—304no—
648C23—302no—
649C23—302no—
650C23—302no—
651C23—302no—
652C23—608no—
653C23—6032no—
654C23C23×D1514yes—
655C23C23×D1511yescharacteristic
656Q8—28no—
657D4—28no—
658D4—1516no—
659D4—3016no—
660D4—308no—
661D4—3016no—
662D4—608no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—154no—
667C2×C4—152no—
668C2×C4—152no—
669C2×C4—3016no—
670C2×C4—302no—
671C2×C4—302no—
672C2×C4—304no—
673C2×C4—308no—
674C2×C4—308no—
675C2×C4—608no—
676C2×C4D4×D1514yes—
677C2×C4C23×D1512yes—
678C2×C4C23×D1512yes—
679C2×C4C23×D1514yes—
680C2×C4C23×D1512yes—
681C2×C3—44no—
682C2×C3#6601014yescomplemented
683C2×C3C22×D4×D511yescharacteristic
684C2×C3C2×D5×#4111yescharacteristic
685C2×C3C2×#414911yescharacteristic
686D3—104no—
687D3—108no—
688D3—202no—
689C5C2×#567611yescharacteristic, complemented, Sylow
690C22—24no—
691C22—24no—
692C22—24no—
693C22—48no—
694C22—158no—
695C22—154no—
696C22—302no—
697C22—304no—
698C22—304no—
699C22—302no—
700C22—308no—
701C22—3016no—
702C22—302no—
703C22—302no—
704C22—302no—
705C22—6032no—
706C22—604no—
707C22C2×D4×D1512yes—
708C22#41×D1512yes—
709C22#9210012yes—
710C22C24×D1511yescharacteristic
711C4—24no—
712C4—22no—
713C4—22no—
714C4—302no—
715C4—302no—
716C4—304no—
717C4C2×D4×D1514yes—
718C3C2×#6601011yescharacteristic, complemented, Sylow
719C2—44no—
720C2—304no—
721C2—308no—
722C2—602no—
723C2#1175643514yesdirect product factor
724C2C22×D4×D1511yescharacteristic
725C2C2×#41×D1511yescharacteristic
726C2C2×#9210011yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#124C2
socleC23×C3×C5C24
hypercenterC2×#124D15
hypocenterC3×C5C2×#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C22×#6821C2semidirect
2. C22×D4×D15C2semidirect
3. C2×C3×C5×#124C2semidirect
4. C2×#91835C2semidirect
5. C2×#91827C2semidirect
6. #11756435C2direct (N × H)
7. C2×#91773C2semidirect
8. C2×#91772C2semidirect
9. C2×#91771C2semidirect
10. C2×C22⋊C4×D15C2semidirect
11. C2×C4×D60C2semidirect
12. C2×C4×D60C2semidirect
15. C22×C3×C5×Q8C22semidirect
18. C22×#1220C22semidirect
20. C2×#6821C22semidirect
22. C2×D4×D15C22semidirect
25. C22×D60C22semidirect
27. C22×C4×D15C22semidirect
28. C22×C4×D15C22semidirect
29. C22×C4×D15C22semidirect
30. C3×C5×#124C22semidirect
31. C2×C3×C5×C22⋊C4C22semidirect
32. C2×C3×C5×C22⋊C4C22semidirect
33. C2×C3×C42×C5C22semidirect
34. C2×#6719C22semidirect
35. #91835C22semidirect
36. #91827C22semidirect
39. C2×#6714C22semidirect
40. C2×#6714C22semidirect
41. C2×C4⋊Dic15C22semidirect
42. C2×C4⋊Dic15C22semidirect
43. C2×#6712C22semidirect
44. #91773C22semidirect
45. #91772C22semidirect
46. #91771C22semidirect
47. C22⋊C4×D15C22semidirect
48. C4×D60C22semidirect
49. C4×D60C22semidirect
53. C2×C5×#124D3semidirect
72. C2×C3×C5×Q8C23semidirect
82. C2×#1220C23semidirect
90. C2×D60D4semidirect
93. C2×D60C23semidirect
99. C2×C4×D15C23semidirect
100. C2×C4×D15C23semidirect
101. C2×C4×D15C23semidirect
102. C3×C5×C22⋊C4C23semidirect
103. C3×C5×C22⋊C4C23semidirect
104. C3×C42×C5C23semidirect
105. #6719C23semidirect
108. #6714C23semidirect
109. #6714C23semidirect
110. C4⋊Dic15C23semidirect
111. C4⋊Dic15C23semidirect
112. #6712C23semidirect
115. C2×C3×#124D5semidirect
126. C22×C5×Q8C2×D3semidirect
141. C5×#124C2×D3semidirect
142. C2×C5×C22⋊C4C2×D3semidirect
143. C2×C5×C22⋊C4C2×D3semidirect
144. C2×C42×C5C2×D3semidirect
179. C22×D15#41semidirect
203. D60C2×D4semidirect
209. C22×C3×Q8C2×D5semidirect
224. C3×#124C2×D5semidirect
225. C2×C3×C22⋊C4C2×D5semidirect
226. C2×C3×C22⋊C4C2×D5semidirect
227. C2×C3×C42C2×D5semidirect
253. C2×C5×Q8C22×D3semidirect
283. C5×C22⋊C4C22×D3semidirect
284. C5×C22⋊C4C22×D3semidirect
285. C42×C5C22×D3semidirect
297. C2×#124D15semidirect
326. C2×D15C2×#41semidirect
343. C2×C3×Q8C22×D5semidirect
373. C3×C22⋊C4C22×D5semidirect
374. C3×C22⋊C4C22×D5semidirect
375. C3×C42C22×D5semidirect
433. C22×Q8C2×D15semidirect
446. #124C2×D15semidirect
463. C2×C22⋊C4C2×D15semidirect
464. C2×C22⋊C4C2×D15semidirect
465. C2×C42C2×D15semidirect
467. C2×C3×C5#546semidirect
558. C2×Q8C22×D15semidirect
595. C22⋊C4C22×D15semidirect
596. C22⋊C4C22×D15semidirect
597. C42C22×D15semidirect
598. C3×C5C2×#546semidirect
628. C2×C5#5676semidirect
682. C2×C3#66010semidirect
689. C5C2×#5676semidirect
718. C3C2×#66010semidirect
723. C2#11756435direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68212
C22×D4×D152
C2×C3×C5×#1242
C2×#918352
C2×#918272
#117564352
C2×#917732
C2×#917722
C2×#917712
C2×C22⋊C4×D152
C2×C4×D602
C2×#660103
C2×#56765