Finite Group Databasebeta

← C2×#11753275 #14480352

Subgroups — C2×#11753275 #14480352

Order 1920.

3968 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6790C211yesmaximal, characteristic, complemented
2C23×#1202C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D15C211yesmaximal, characteristic, complemented
4C2×C5×#886C211yesmaximal, characteristic, complemented
5C2×C3×#4028C211yesmaximal, characteristic, complemented
6C2×#91563C211yesmaximal, characteristic, complemented
7C2×#91536C211yesmaximal, characteristic, complemented
8C2×#91474C212yesmaximal, complemented
9C2×#91465C212yesmaximal, complemented
10C2×#91461C212yesmaximal, complemented
11C2×#91356C212yesmaximal, complemented
12#11753275C2116yesmaximal, direct product factor
13C2×#65987—31nomaximal, Hall
14C24×D15C2211yescharacteristic
15C24×C3×D5C2211yescharacteristic, complemented
16C23×D3×D5C2211yescharacteristic, complemented
17C22×C4×D15C2212yescomplemented
18C22×C5×#67C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic, complemented
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×D20C2212yescomplemented
22C2×#6790—28no—
23C2×#6790C2218yescomplemented
24C22×#1203C2211yescharacteristic, complemented
25C22×#1202—28no—
26C22×#1202C2212yes—
27C22×#1202C2218yescomplemented
28C22×#1202C2212yescomplemented
29C22×#1202C2211yescharacteristic, complemented
30C22×#1201C2212yescomplemented
31C22×#1200C2211yescharacteristic, complemented
32C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
33C2×#6719C2211yescharacteristic, complemented
34C2×#6714C2212yescomplemented
35C22⋊C4×D15C2218yescomplemented
36C2×C5×(C2×D3)⋊C4C2212yescomplemented
37C2×C5×C4⋊Dic3C2212yescomplemented
38C5×#886C2218yescomplemented
39C2×C3×#685C2212yescomplemented
40C3×#4028C2218yescomplemented
41#91563C2218yescomplemented
42C2×#6669C2212yescomplemented
43#91536C2218yescomplemented
44C2×#6665C2212yescomplemented
45C2×#6665C2212yescomplemented
46#91474C22116yescomplemented
47#91465C22116yescomplemented
48#91461C22116yescomplemented
49#91356C22116yescomplemented
50C2×#5589—51nomaximal, Hall
51C22×D4×D5—31no—
52C23×D20—31no—
53C2×C5×#123—31no—
54C2×#4083—31no—
55C2×#4075—31no—
56#65987—316no—
57C2×#4041—32no—
58C2×#4040—32no—
59C2×#4030—32no—
60C2×#4028—32no—
61C2×#4028D311yescharacteristic, complemented
62C2×D5×C22⋊C4—31no—
63C24×C3×C5C2311yescharacteristic
64C23×D15—44no—
65C23×D15D418yescomplemented
66C23×D15C2311yescharacteristic
67C23×D15C2311yescharacteristic
68C23×D15C2314yes—
69C23×C5×D3C2311yescharacteristic
70C23×C3×D5—24no—
71C23×C3×D5—44no—
72C23×C3×D5C2312yes—
73C23×C3×D5C2311yescharacteristic
74C23×C3×D5C2314yescomplemented
75C22×D3×D5—24no—
76C22×D3×D5—44no—
77C22×D3×D5C2314yescomplemented
78C22×C3×C4×C5C2312yes—
79C22×Dic15C2312yes—
80C2×C4×D15—44no—
81C2×C4×D15C2318yescomplemented
82C2×C5×#67—24no—
83C2×C5×#67C2314yes—
84C22×C5×Dic3—24no—
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2312yes—
87C22×C5×Dic3C2314yescomplemented
88C2×C3×C22⋊D5—24no—
89C2×C3×C22⋊D5C2314yes—
90C22×C3×Dic5C2311yescharacteristic
91C2×C3×D20—44no—
92C2×C3×D20C2318yescomplemented
93#6790—232no—
94C2×#1203—24no—
95C2×#1203C2314yescomplemented
96C2×#1202—28no—
97C2×#1202—28no—
98C2×#1202—24no—
99C2×#1202—232no—
100C2×#1202C2318yes—
101C2×#1202C2318yescomplemented
102C2×#1202C2314yescomplemented
103C2×#1201—44no—
104C2×#1201C2318yescomplemented
105C2×#1200—24no—
106C2×#1200C2314yescomplemented
107C3×C5×C22⋊C4C2314yescomplemented
108#6719C2314yescomplemented
109#6714C2318yescomplemented
110C5×(C2×D3)⋊C4C2318yescomplemented
111C5×C4⋊Dic3C2318yescomplemented
112C3×#685C2318yescomplemented
113#6669C2318yescomplemented
114#6665C2318yescomplemented
115#6665C2318yescomplemented
116C23×#67—51no—
117C22×D3×D4—51no—
118C2×C3×#120—51no—
119C2×#953—51no—
120C2×#938—52no—
121C2×#937—52no—
122C2×#935—51no—
123#5589—516no—
124C2×#886D511yescharacteristic, complemented
125C2×#884—52no—
126C2×#883—52no—
127C2×D3×C22⋊C4—51no—
128C24×D5—31no—
129C24×D5—31no—
130C24×D5C2×D311yescharacteristic, complemented
131C22×C5×D4—31no—
132C23×C4×C5—31no—
133C22×C22⋊D5—32no—
134C22×C22⋊D5—31no—
135C22×C22⋊D5C2×D311yescharacteristic
136C2×D4×D5—38no—
137C2×D4×D5—68no—
138C22×D20—32no—
139C22×D20—32no—
140C22×D20—31no—
141C22×D20—38no—
142C22×D20—68no—
143C22×D20C2×D312yescomplemented
144C22×C4×D5—31no—
145C22×C4×D5—32no—
146C5×#123—38no—
147C2×C5×C4⋊C4—32no—
148C2×C5×C22⋊C4—32no—
149C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
150C2×C22⋊Dic5—31no—
151#4083—38no—
152#4075—38no—
153C2×#685—32no—
154C2×#685—32no—
155C2×#685—32no—
156C2×#685C2×D312yescomplemented
157C2×#683—32no—
158#4041—316no—
159#4040—316no—
160#4030—316no—
161#4028—316no—
162#4028C2×D318yescomplemented
163D5×C22⋊C4—38no—
164C2×#534—151noSylow
165C23×C3×C5—24no—
166C23×C3×C5C2×D414yes—
167C23×C3×C5C2412yes—
168C23×C3×C5C2411yescharacteristic
169C22×D15—24no—
170C22×D15—24no—
171C22×D15—416no—
172C22×D15—48no—
173C22×D15C2×D414yes—
174C22×D15C2×D414yes—
175C22×D15C2×D4116yescomplemented
176C22×D15C2412yes—
177C22×D15C2412yes—
178C22×C5×D3—22no—
179C22×C5×D3—24no—
180C22×C5×D3C2412yes—
181C22×C3×D5—24no—
182C22×C3×D5—28no—
183C22×C3×D5—22no—
184C22×C3×D5—24no—
185C22×C3×D5—24no—
186C22×C3×D5—24no—
187C22×C3×D5—48no—
188C22×C3×D5—416no—
189C22×C3×D5C2412yes—
190C22×C3×D5C2414yes—
191C2×D3×D5—28no—
192C2×D3×D5—48no—
193C2×D3×D5—416no—
194C2×C3×C4×C5—24no—
195C2×C3×C4×C5C2414yes—
196C2×Dic15—24no—
197C2×Dic15C2414yes—
198C4×D15—48no—
199C5×#67—28no—
200C2×C5×Dic3—22no—
201C2×C5×Dic3—24no—
202C2×C5×Dic3—28no—
203C2×C5×Dic3C2412yes—
204C2×C5×Dic3C2414yes—
205C3×C22⋊D5—28no—
206C2×C3×Dic5—22no—
207C2×C3×Dic5C2412yes—
208C3×D20—48no—
209#1203—28no—
210#1202—216no—
211#1202—216no—
212#1202—28no—
213#1201—48no—
214#1200—28no—
215C25×C3—51no—
216C24×D3—51no—
217C24×D3—51no—
218C22×C3×D4—51no—
219C22×C3×D4—52no—
220C22×#67—52no—
221C22×#67—51no—
222C22×#67—52no—
223C22×#67—52no—
224C22×#67—58no—
225C22×#67—108no—
226C22×#67C2×D511yescharacteristic
227C23×Dic3C2×D511yescharacteristic, complemented
228C2×D3×D4—58no—
229C2×D3×D4—108no—
230C22×D12—51no—
231C22×C4×D3—51no—
232C22×C4×D3—52no—
233C3×#120—58no—
234C2×C3×C22⋊C4—52no—
235C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
236#953—58no—
237C2×#217—51no—
238C2×#217—52no—
239C2×#217—52no—
240#938—516no—
241#937—516no—
242#935—58no—
243C2×(C2×D3)⋊C4—52no—
244C2×(C2×D3)⋊C4C2×D512yescomplemented
245C2×C4⋊Dic3C2×D512yescomplemented
246C2×Dic3⋊C4—52no—
247#886C2×D518yescomplemented
248#884—516no—
249#883—516no—
250D3×C22⋊C4—58no—
251C24×C5—31no—
252C24×C5C22×D311yescharacteristic
253C23×D5—24no—
254C23×D5—31no—
255C23×D5—31no—
256C23×D5—38no—
257C23×D5—34no—
258C23×D5—34no—
259C23×D5—44no—
260C23×D5—64no—
261C23×D5—124no—
262C23×D5—124no—
263C23×D5C22×D312yes—
264C23×D5C22×D311yescharacteristic
265C23×D5C22×D314yescomplemented
266C2×C5×D4—34no—
267C2×C5×D4—64no—
268C22×C4×C5—32no—
269C22×C4×C5—31no—
270C22×C4×C5—34no—
271C22×C4×C5—64no—
272C22×C4×C5C22×D312yes—
273C2×C22⋊D5—24no—
274C2×C22⋊D5—38no—
275C2×C22⋊D5—34no—
276C2×C22⋊D5—64no—
277C2×C22⋊D5—124no—
278C2×C22⋊D5C22×D314yes—
279C22×Dic5—32no—
280C22×Dic5C22×D311yescharacteristic
281D4×D5—632no—
282C2×D20—38no—
283C2×D20—38no—
284C2×D20—34no—
285C2×D20—44no—
286C2×D20—68no—
287C2×D20—68no—
288C2×D20—632no—
289C2×D20—64no—
290C2×D20C22×D318yescomplemented
291C2×C4×D5—34no—
292C2×C4×D5—38no—
293C2×C4×D5—64no—
294C2×C4×D5—124no—
295C5×C4⋊C4—38no—
296C5×C22⋊C4—38no—
297C5×C22⋊C4C22×D314yescomplemented
298C22⋊Dic5—34no—
299#685—38no—
300#685—38no—
301#685—38no—
302#685C22×D318yescomplemented
303#683—38no—
304C23×D4—151no—
305C23×D4—151no—
306#534—1516no—
307C2×#123—31no—
308C2×#123—152no—
309C2×#123—151no—
310C2×#121—152no—
311C2×#121—152no—
312C2×#120—51no—
313C2×#120—152no—
314C2×#120—151no—
315C22×C22⋊C4—151no—
316C22×C3×C5—28no—
317C22×C3×C5—24no—
318C22×C3×C5C22×D414yes—
319C22×C3×C5C22×D412yes—
320C22×C3×C5H(5,𝔽2)14yes—
321C22×C3×C5C2511yescharacteristic
322C2×D15—28no—
323C2×D15—28no—
324C2×D15—24no—
325C2×D15—24no—
326C2×D15—416no—
327C2×D15C22×D414yes—
328C2×D15C22×D414yes—
329C2×C5×D3—22no—
330C2×C5×D3—24no—
331C2×C5×D3—44no—
332C2×C3×D5—24no—
333C2×C3×D5—22no—
334C2×C3×D5—24no—
335C2×C3×D5—24no—
336C2×C3×D5—24no—
337C2×C3×D5—416no—
338C2×C3×D5—44no—
339C2×C3×D5—48no—
340D3×D5—416no—
341C3×C4×C5—24no—
342Dic15—24no—
343C3×Dic5—22no—
344C5×Dic3—22no—
345C5×Dic3—24no—
346C24×C3—52no—
347C24×C3—51no—
348C24×C3—54no—
349C24×C3—104no—
350C24×C3—204no—
351C24×C3C22×D511yescharacteristic
352C23×D3—51no—
353C23×D3—51no—
354C23×D3—58no—
355C23×D3—54no—
356C23×D3—54no—
357C23×D3—104no—
358C23×D3—204no—
359C23×D3—204no—
360C23×D3C22×D511yescharacteristic
361C2×C3×D4—54no—
362C2×C3×D4—58no—
363C2×C3×D4—104no—
364C2×C3×D4—204no—
365C22×C3×C4—51no—
366C22×C3×C4C22×D512yes—
367C2×#67—24no—
368C2×#67—58no—
369C2×#67—58no—
370C2×#67—58no—
371C2×#67—54no—
372C2×#67—104no—
373C2×#67—108no—
374C2×#67—108no—
375C2×#67—1032no—
376C2×#67—204no—
377C2×#67C22×D514yes—
378C22×Dic3—24no—
379C22×Dic3—52no—
380C22×Dic3C22×D512yes—
381C22×Dic3C22×D511yescharacteristic
382C22×Dic3C22×D514yescomplemented
383D3×D4—1032no—
384C2×D12—54no—
385C2×D12—104no—
386C2×C4×D3—54no—
387C2×C4×D3—58no—
388C2×C4×D3—104no—
389C2×C4×D3—204no—
390C3×C22⋊C4—58no—
391C3×C22⋊C4C22×D514yescomplemented
392#217—54no—
393#217—58no—
394#217—58no—
395(C2×D3)⋊C4—58no—
396(C2×D3)⋊C4C22×D518yescomplemented
397C4⋊Dic3C22×D518yescomplemented
398Dic3⋊C4—58no—
399C23×C5—24no—
400C23×C5—32no—
401C23×C5—62no—
402C23×C5—64no—
403C23×C5D3×D414yes—
404C23×C5C23×D312yes—
405C23×C5C23×D311yescharacteristic
406C22×D5—24no—
407C22×D5—28no—
408C22×D5—22no—
409C22×D5—24no—
410C22×D5—24no—
411C22×D5—24no—
412C22×D5—34no—
413C22×D5—34no—
414C22×D5—32no—
415C22×D5—32no—
416C22×D5—316no—
417C22×D5—48no—
418C22×D5—416no—
419C22×D5—68no—
420C22×D5—64no—
421C22×D5—64no—
422C22×D5—128no—
423C22×D5—1216no—
424C22×D5—128no—
425C22×D5—1216no—
426C22×D5C23×D312yes—
427C22×D5C23×D314yes—
428C5×D4—68no—
429C2×C4×C5—24no—
430C2×C4×C5—34no—
431C2×C4×C5—32no—
432C2×C4×C5—62no—
433C2×C4×C5—68no—
434C2×C4×C5—64no—
435C2×C4×C5C23×D314yes—
436C22⋊D5—28no—
437C22⋊D5—68no—
438C22⋊D5—128no—
439C2×Dic5—22no—
440C2×Dic5—34no—
441C2×Dic5—64no—
442C2×Dic5C23×D312yes—
443D20—48no—
444D20—616no—
445D20—616no—
446D20—68no—
447C4×D5—68no—
448C4×D5—128no—
449C25—51no—
450C25—151no—
451C25—151no—
452C22×D4—31no—
453C22×D4—51no—
454C22×D4—52no—
455C22×D4—152no—
456C22×D4—152no—
457C22×D4—151no—
458C22×D4—158no—
459C22×D4—151no—
460C22×D4—158no—
461C22×D4—152no—
462C22×D4—308no—
463C22×D4—308no—
464C23×C4—31no—
465C23×C4—151no—
466C23×C4—152no—
467#123—38no—
468#123—1516no—
469#123—158no—
470#121—1516no—
471#121—1516no—
472#120—58no—
473#120—1516no—
474#120—158no—
475C2×C4⋊C4—32no—
476C2×C4⋊C4—152no—
477C2×C22⋊C4—32no—
478C2×C22⋊C4—52no—
479C2×C22⋊C4—152no—
480C2×C22⋊C4—152no—
481C2×C22⋊C4—151no—
482C2×C22⋊C4—152no—
483C2×C22⋊C4—158no—
484C2×C22⋊C4D3×D511yescharacteristic, complemented
485C2×C3×C5—24no—
486C2×C3×C5#53414yescomplemented
487C2×C3×C5C23×D411yescharacteristic
488C2×C3×C5C2×H(5,𝔽2)12yes—
489D15—24no—
490D15—24no—
491C3×D5—42no—
492C3×D5—44no—
493C5×D3—42no—
494C23×C3—24no—
495C23×C3—52no—
496C23×C3—54no—
497C23×C3—108no—
498C23×C3—104no—
499C23×C3—102no—
500C23×C3—104no—
501C23×C3—104no—
502C23×C3—104no—
503C23×C3—208no—
504C23×C3—2016no—
505C23×C3D4×D514yes—
506C23×C3C23×D512yes—
507C23×C3C23×D511yescharacteristic
508C22×D3—22no—
509C22×D3—24no—
510C22×D3—54no—
511C22×D3—54no—
512C22×D3—52no—
513C22×D3—52no—
514C22×D3—516no—
515C22×D3—108no—
516C22×D3—104no—
517C22×D3—104no—
518C22×D3—208no—
519C22×D3—2016no—
520C22×D3—2016no—
521C22×D3—208no—
522C22×D3C23×D512yes—
523C3×D4—108no—
524C3×D4—208no—
525C2×C3×C4—24no—
526C2×C3×C4—52no—
527C2×C3×C4—102no—
528C2×C3×C4C23×D514yes—
529#67—28no—
530#67—108no—
531#67—1016no—
532#67—1016no—
533#67—208no—
534C2×Dic3—22no—
535C2×Dic3—24no—
536C2×Dic3—28no—
537C2×Dic3—54no—
538C2×Dic3—104no—
539C2×Dic3C23×D514yes—
540C2×Dic3C23×D512yes—
541D12—108no—
542C4×D3—108no—
543C4×D3—208no—
544C22×C5—24no—
545C22×C5—28no—
546C22×C5—62no—
547C22×C5—64no—
548C22×C5—124no—
549C22×C5C2×D3×D414yes—
550C22×C5C2×D3×D412yes—
551C22×C5#100414yes—
552C22×C5C24×D311yescharacteristic
553C2×D5—24no—
554C2×D5—22no—
555C2×D5—24no—
556C2×D5—24no—
557C2×D5—24no—
558C2×D5—34no—
559C2×D5—34no—
560C2×D5—416no—
561C2×D5—48no—
562C2×D5—44no—
563C2×D5—64no—
564C2×D5—64no—
565C2×D5—68no—
566C2×D5—68no—
567C2×D5—1216no—
568C2×D5—1216no—
569C4×C5—24no—
570C4×C5—62no—
571C4×C5—64no—
572Dic5—22no—
573Dic5—64no—
574C24—31no—
575C24—52no—
576C24—51no—
577C24—54no—
578C24—104no—
579C24—154no—
580C24—151no—
581C24—151no—
582C24—158no—
583C24—154no—
584C24—204no—
585C24—304no—
586C24—604no—
587C24—604no—
588C24C2×D3×D511yescharacteristic
589C2×D4—34no—
590C2×D4—54no—
591C2×D4—58no—
592C2×D4—64no—
593C2×D4—104no—
594C2×D4—158no—
595C2×D4—158no—
596C2×D4—154no—
597C2×D4—154no—
598C2×D4—158no—
599C2×D4—204no—
600C2×D4—308no—
601C2×D4—308no—
602C2×D4—3032no—
603C2×D4—304no—
604C2×D4—304no—
605C2×D4—3032no—
606C2×D4—604no—
607C22×C4—34no—
608C22×C4—32no—
609C22×C4—31no—
610C22×C4—51no—
611C22×C4—64no—
612C22×C4—154no—
613C22×C4—152no—
614C22×C4—158no—
615C22×C4—304no—
616C22×C4—604no—
617C22×C4C2×D3×D512yes—
618C4⋊C4—38no—
619C4⋊C4—158no—
620C22⋊C4—38no—
621C22⋊C4—58no—
622C22⋊C4—158no—
623C22⋊C4—158no—
624C22⋊C4—154no—
625C22⋊C4—158no—
626C22⋊C4C2×D3×D514yescomplemented
627C3×C5C2×#53411yescharacteristic, complemented, Hall
628C22×C3—28no—
629C22×C3—24no—
630C22×C3—104no—
631C22×C3—102no—
632C22×C3—104no—
633C22×C3—104no—
634C22×C3—104no—
635C22×C3—2016no—
636C22×C3—204no—
637C22×C3—208no—
638C22×C3C2×D4×D514yes—
639C22×C3C2×D4×D512yes—
640C22×C3#414914yes—
641C22×C3C24×D511yescharacteristic
642C2×D3—22no—
643C2×D3—24no—
644C2×D3—44no—
645C2×D3—54no—
646C2×D3—54no—
647C2×D3—108no—
648C2×D3—108no—
649C2×D3—104no—
650C2×D3—104no—
651C2×D3—2016no—
652C2×D3—2016no—
653C3×C4—24no—
654C3×C4—102no—
655Dic3—22no—
656Dic3—24no—
657Dic3—104no—
658C2×C5—24no—
659C2×C5—122no—
660C2×C5#558914yescomplemented
661C2×C5C22×D3×D411yescharacteristic
662C2×C5C2×#100412yes—
663D5—44no—
664D5—42no—
665D5—64no—
666D5—64no—
667C23—24no—
668C23—32no—
669C23—54no—
670C23—52no—
671C23—62no—
672C23—64no—
673C23—102no—
674C23—108no—
675C23—104no—
676C23—104no—
677C23—104no—
678C23—104no—
679C23—154no—
680C23—154no—
681C23—152no—
682C23—152no—
683C23—1516no—
684C23—208no—
685C23—2016no—
686C23—308no—
687C23—304no—
688C23—304no—
689C23—6016no—
690C23—608no—
691C23—608no—
692C23—6016no—
693C23#677714yes—
694C23C22×D3×D512yes—
695C23C22×D3×D511yescharacteristic
696D4—68no—
697D4—108no—
698D4—208no—
699D4—3016no—
700D4—3016no—
701D4—308no—
702D4—308no—
703D4—608no—
704C2×C4—24no—
705C2×C4—34no—
706C2×C4—32no—
707C2×C4—52no—
708C2×C4—68no—
709C2×C4—64no—
710C2×C4—62no—
711C2×C4—102no—
712C2×C4—154no—
713C2×C4—308no—
714C2×C4—304no—
715C2×C4—608no—
716C2×C4C22×D3×D514yes—
717C2×C3—24no—
718C2×C3—202no—
719C2×C3—204no—
720C2×C3#6598714yescomplemented
721C2×C3C22×D4×D511yescharacteristic
722C2×C3C2×#414912yes—
723D3—42no—
724D3—104no—
725D3—104no—
726C5C2×#558911yescharacteristic, complemented, Sylow
727C22—28no—
728C22—24no—
729C22—62no—
730C22—64no—
731C22—102no—
732C22—104no—
733C22—104no—
734C22—104no—
735C22—104no—
736C22—124no—
737C22—154no—
738C22—154no—
739C22—2016no—
740C22—208no—
741C22—204no—
742C22—308no—
743C22—308no—
744C22—304no—
745C22—304no—
746C22—6016no—
747C22—6016no—
748C22C2×#677714yes—
749C22C2×#677712yes—
750C22#9202614yes—
751C22C23×D3×D511yescharacteristic
752C4—24no—
753C4—64no—
754C4—62no—
755C4—102no—
756C4—304no—
757C3C2×#6598711yescharacteristic, complemented, Sylow
758C2—24no—
759C2—122no—
760C2—204no—
761C2—202no—
762C2—304no—
763C2—304no—
764C2#1175327514yesdirect product factor
765C2C22×#677711yescharacteristic
766C2C2×#9202612yes—
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#534
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6790C2semidirect
2. C23×#1202C2semidirect
3. C2×C22⋊C4×D15C2semidirect
4. C2×C5×#886C2semidirect
5. C2×C3×#4028C2semidirect
6. C2×#91563C2semidirect
7. C2×#91536C2semidirect
8. C2×#91474C2semidirect
9. C2×#91465C2semidirect
10. C2×#91461C2semidirect
11. C2×#91356C2semidirect
12. #11753275C2direct (N × H)
15. C24×C3×D5C22semidirect
16. C23×D3×D5C22semidirect
17. C22×C4×D15C22semidirect
19. C23×C5×Dic3C22semidirect
21. C22×C3×D20C22semidirect
23. C2×#6790C22semidirect
24. C22×#1203C22semidirect
27. C22×#1202C22semidirect
28. C22×#1202C22semidirect
29. C22×#1202C22semidirect
30. C22×#1201C22semidirect
31. C22×#1200C22semidirect
32. C2×C3×C5×C22⋊C4C22semidirect
33. C2×#6719C22semidirect
34. C2×#6714C22semidirect
35. C22⋊C4×D15C22semidirect
36. C2×C5×(C2×D3)⋊C4C22semidirect
37. C2×C5×C4⋊Dic3C22semidirect
38. C5×#886C22semidirect
39. C2×C3×#685C22semidirect
40. C3×#4028C22semidirect
41. #91563C22semidirect
42. C2×#6669C22semidirect
43. #91536C22semidirect
44. C2×#6665C22semidirect
45. C2×#6665C22semidirect
46. #91474C22semidirect
47. #91465C22semidirect
48. #91461C22semidirect
49. #91356C22semidirect
61. C2×#4028D3semidirect
65. C23×D15D4semidirect
74. C23×C3×D5C23semidirect
77. C22×D3×D5C23semidirect
81. C2×C4×D15C23semidirect
87. C22×C5×Dic3C23semidirect
92. C2×C3×D20C23semidirect
95. C2×#1203C23semidirect
101. C2×#1202C23semidirect
102. C2×#1202C23semidirect
104. C2×#1201C23semidirect
106. C2×#1200C23semidirect
107. C3×C5×C22⋊C4C23semidirect
108. #6719C23semidirect
109. #6714C23semidirect
110. C5×(C2×D3)⋊C4C23semidirect
111. C5×C4⋊Dic3C23semidirect
112. C3×#685C23semidirect
113. #6669C23semidirect
114. #6665C23semidirect
115. #6665C23semidirect
124. C2×#886D5semidirect
130. C24×D5C2×D3semidirect
143. C22×D20C2×D3semidirect
149. C2×C5×C22⋊C4C2×D3semidirect
156. C2×#685C2×D3semidirect
162. #4028C2×D3semidirect
175. C22×D15C2×D4semidirect
227. C23×Dic3C2×D5semidirect
235. C2×C3×C22⋊C4C2×D5semidirect
244. C2×(C2×D3)⋊C4C2×D5semidirect
245. C2×C4⋊Dic3C2×D5semidirect
247. #886C2×D5semidirect
265. C23×D5C22×D3semidirect
290. C2×D20C22×D3semidirect
297. C5×C22⋊C4C22×D3semidirect
302. #685C22×D3semidirect
382. C22×Dic3C22×D5semidirect
391. C3×C22⋊C4C22×D5semidirect
396. (C2×D3)⋊C4C22×D5semidirect
397. C4⋊Dic3C22×D5semidirect
484. C2×C22⋊C4D3×D5semidirect
486. C2×C3×C5#534semidirect
626. C22⋊C4C2×D3×D5semidirect
627. C3×C5C2×#534semidirect
660. C2×C5#5589semidirect
720. C2×C3#65987semidirect
726. C5C2×#5589semidirect
757. C3C2×#65987semidirect
764. C2#11753275direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67902
C23×#12022
C2×C22⋊C4×D152
C2×C5×#8862
C2×C3×#40282
C2×#915632
C2×#915362
C2×#914742
C2×#914652
C2×#914612
C2×#913562
#117532752
C2×#659873
C2×#55895