Finite Group Databasebeta

← C2×#11753882 #14480457

Subgroups — C2×#11753882 #14480457

Order 1920.

3792 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D20C211yesmaximal, characteristic, complemented
2C22×#6771C211yesmaximal, characteristic, complemented
3C2×#91784C211yesmaximal, characteristic, complemented
4C2×C5×#892C211yesmaximal, characteristic, complemented
5C2×C3×#4041C211yesmaximal, characteristic, complemented
6C2×#91476C212yesmaximal, complemented
7C2×#91474C212yesmaximal, complemented
8C2×#91465C211yesmaximal, characteristic, complemented
9C2×#91458C212yesmaximal, complemented
10C2×#91450C211yesmaximal, characteristic, complemented
11C2×#91353C212yesmaximal, complemented
12#11753882C2116yesmaximal, direct product factor
13C2×#65859—31nomaximal, Hall
14C23×D3×D5C2212yes—
15C22×D60C2211yescharacteristic
16C22×D60C2212yescomplemented
17C22×C4×D15C2211yescharacteristic, complemented
18C22×C4×C5×D3C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C22×C3×D20C2212yescomplemented
21C22×C3×C4×D5C2211yescharacteristic, complemented
22C22×#1204C2211yescharacteristic, complemented
23C22×#1203C2211yescharacteristic
24C22×#1202C2212yes—
25C22×#1202C2211yescharacteristic, complemented
26C22×#1202C2212yescomplemented
27C22×#1202C2212yescomplemented
28C22×#1201C2211yescharacteristic
29C2×D3×D20—28no—
30C2×D3×D20C2218yescomplemented
31C2×#6771—28no—
32C2×#6771C2218yescomplemented
33C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
34C2×#6714C2212yescomplemented
35#91784C2218yescomplemented
36C2×C5×(C2×D3)⋊C4C2212yes—
37C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
38C2×C4×C5×Dic3C2212yescomplemented
39C5×#892C2218yescomplemented
40C2×C3×#685C2212yescomplemented
41C3×#4041C2218yescomplemented
42C2×#6667C2212yescomplemented
43C2×#6665C2212yescomplemented
44#91476C22116yescomplemented
45#91474C22116yescomplemented
46#91465C2218yescomplemented
47#91458C22116yescomplemented
48#91450C2218yescomplemented
49#91353C22116yescomplemented
50C2×#5607—51nomaximal, Hall
51C22×#709—31no—
52C23×D20—31no—
53C2×C5×#117—31no—
54#65859—316no—
55C2×#4041—31no—
56C2×#4041—31no—
57C2×#4041—31no—
58C2×#4041D311yescharacteristic, complemented
59C2×#4028—32no—
60C2×#4028—32no—
61C2×#4021—32no—
62C2×#4020—32no—
63C23×D15C2312yes—
64C23×D15C2311yescharacteristic
65C23×C5×D3C2311yescharacteristic
66C23×C3×D5C2311yescharacteristic
67C23×C3×D5C2312yes—
68C22×D3×D5—28no—
69C22×D3×D5—44no—
70C22×D3×D5—44no—
71C22×D3×D5C2318yes—
72C22×C3×C4×C5C2312yes—
73C22×C3×C4×C5C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C2×D60—24no—
76C2×D60—44no—
77C2×D60C2314yes—
78C2×D60C2318yescomplemented
79C2×C4×D15—24no—
80C2×C4×D15C2314yescomplemented
81C22×C5×Dic3C2312yes—
82C22×C5×Dic3C2311yescharacteristic
83C2×C4×C5×D3D418yescomplemented
84C2×C4×C5×D3C2314yes—
85C22×C3×Dic5C2311yescharacteristic
86C2×C3×D20—24no—
87C2×C3×D20—44no—
88C2×C3×D20C2314yes—
89C2×C3×D20C2318yescomplemented
90C2×C3×C4×D5—24no—
91C2×C3×C4×D5C2314yescomplemented
92C2×#1204—24no—
93C2×#1204C2314yescomplemented
94C2×#1203—24no—
95C2×#1203C2314yes—
96C2×#1202—24no—
97C2×#1202—28no—
98C2×#1202—44no—
99C2×#1202—44no—
100C2×#1202C2318yes—
101C2×#1202C2314yescomplemented
102C2×#1202C2318yescomplemented
103C2×#1202C2318yescomplemented
104C2×#1201—24no—
105C2×#1201C2314yes—
106D3×D20—232no—
107#6771—232no—
108C3×C5×C4⋊C4C2314yescomplemented
109#6714C2318yescomplemented
110C5×(C2×D3)⋊C4C2318yes—
111C5×C4⋊Dic3C2314yescomplemented
112C4×C5×Dic3C2318yescomplemented
113C3×#685C2318yescomplemented
114#6667C2318yescomplemented
115#6665C2318yescomplemented
116C22×D3×D4—51no—
117C22×#235—51no—
118C2×C3×#121—51no—
119C2×#940—52no—
120C2×#938—51no—
121C2×#937—52no—
122C2×#930—51no—
123#5607—516no—
124C2×#895—51no—
125C2×#892D511yescharacteristic, complemented
126C2×#885—52no—
127C2×#882—52no—
128C24×D5—32no—
129C23×C4×C5—31no—
130C22×C22⋊D5—31no—
131C22×C22⋊D5—31no—
132C2×#709—38no—
133C2×#709—68no—
134C22×D20—31no—
135C22×D20—32no—
136C22×D20—31no—
137C22×D20—32no—
138C22×D20—32no—
139C22×D20—32no—
140C22×D20—38no—
141C22×D20—68no—
142C22×D20C2×D311yescharacteristic
143C22×D20C2×D312yescomplemented
144C22×C4×D5—31no—
145C22×C4×D5C2×D311yescharacteristic, complemented
146C22×Dic10—31no—
147C5×#117—38no—
148C2×C5×C4⋊C4—31no—
149C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
150C2×C5×C22⋊C4—32no—
151C2×C42×C5—32no—
152C2×#685—32no—
153C2×#685—32no—
154C2×#685—32no—
155C2×#685C2×D312yescomplemented
156#4041—38no—
157#4041—38no—
158#4041—38no—
159#4041C2×D318yescomplemented
160#4028—316no—
161#4028—316no—
162#4021—316no—
163#4020—316no—
164C2×#535—151noSylow
165C23×C3×C5C2411yescharacteristic
166C22×D15—22no—
167C22×D15—24no—
168C22×D15—22no—
169C22×D15—24no—
170C22×D15—22no—
171C22×D15—24no—
172C22×D15C2414yes—
173C22×D15C2412yes—
174C22×C5×D3—22no—
175C22×C5×D3—22no—
176C22×C5×D3C2×D414yes—
177C22×C5×D3C2412yes—
178C22×C3×D5—22no—
179C22×C3×D5—24no—
180C22×C3×D5—22no—
181C22×C3×D5—24no—
182C22×C3×D5—22no—
183C22×C3×D5—24no—
184C22×C3×D5C2414yes—
185C22×C3×D5C2412yes—
186C2×D3×D5—216no—
187C2×D3×D5—48no—
188C2×D3×D5—48no—
189C2×D3×D5—432no—
190C2×C3×C4×C5—24no—
191C2×C3×C4×C5C2×D414yes—
192C2×C3×C4×C5C2414yes—
193C2×C3×C4×C5C2412yes—
194C2×Dic15—22no—
195C2×Dic15C2412yes—
196D60—28no—
197D60—48no—
198C4×D15—28no—
199C2×C5×Dic3—24no—
200C2×C5×Dic3C2×D414yes—
201C2×C5×Dic3C2414yes—
202C2×C5×Dic3C2412yes—
203C4×C5×D3C2×D4116yescomplemented
204C2×C3×Dic5—22no—
205C2×C3×Dic5C2412yes—
206C3×D20—28no—
207C3×D20—48no—
208C3×C4×D5—28no—
209#1204—28no—
210#1203—28no—
211#1202—28no—
212#1202—216no—
213#1202—48no—
214#1202—48no—
215#1201—28no—
216C24×D3—52no—
217C22×C3×D4—51no—
218C22×C3×D4—52no—
219C23×C3×C4—51no—
220C22×#67—51no—
221C22×#67—51no—
222C22×#67—52no—
223C22×#67—52no—
224C22×#67—52no—
225C2×D3×D4—58no—
226C2×D3×D4—108no—
227C2×#235—58no—
228C2×#235—108no—
229C22×D12—51no—
230C22×D12—51no—
231C22×D12—52no—
232C22×C4×D3—51no—
233C22×C4×D3C2×D511yescharacteristic
234C22×Dic6—51no—
235C3×#121—58no—
236C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
237C2×C3×C22⋊C4—52no—
238C2×#217—52no—
239#940—516no—
240#938—58no—
241#937—516no—
242#930—58no—
243C2×(C2×D3)⋊C4—52no—
244C2×(C2×D3)⋊C4—52no—
245C2×(C2×D3)⋊C4C2×D512yes—
246C2×C4⋊Dic3C2×D511yescharacteristic, complemented
247C2×C4×Dic3C2×D512yescomplemented
248#895—58no—
249#892C2×D518yescomplemented
250#885—516no—
251#882—516no—
252C24×C5—31no—
253C23×D5—31no—
254C23×D5—32no—
255C23×D5—38no—
256C23×D5—68no—
257C23×D5—124no—
258C23×D5—124no—
259C23×D5C22×D311yescharacteristic
260C23×D5C22×D312yes—
261C22×C4×C5—31no—
262C22×C4×C5—38no—
263C22×C4×C5—34no—
264C22×C4×C5—32no—
265C22×C4×C5C22×D312yes—
266C22×C4×C5C22×D311yescharacteristic
267C2×C22⋊D5—34no—
268C2×C22⋊D5—34no—
269C2×C22⋊D5—64no—
270C2×C22⋊D5—64no—
271C22×Dic5—31no—
272C22×Dic5C22×D311yescharacteristic
273#709—632no—
274C2×D20—24no—
275C2×D20—38no—
276C2×D20—34no—
277C2×D20—34no—
278C2×D20—38no—
279C2×D20—38no—
280C2×D20—38no—
281C2×D20—44no—
282C2×D20—632no—
283C2×D20—68no—
284C2×D20—64no—
285C2×D20—64no—
286C2×D20—124no—
287C2×D20—124no—
288C2×D20—124no—
289C2×D20C22×D314yes—
290C2×D20C22×D318yescomplemented
291C2×C4×D5—24no—
292C2×C4×D5—34no—
293C2×C4×D5—64no—
294C2×C4×D5C22×D314yescomplemented
295C2×Dic10—34no—
296C2×Dic10—64no—
297C5×C4⋊C4—34no—
298C5×C4⋊C4C22×D314yescomplemented
299C5×C22⋊C4—38no—
300C42×C5—38no—
301#685—38no—
302#685—38no—
303#685—38no—
304#685C22×D318yescomplemented
305C22×#41—151no—
306C23×D4—151no—
307#535—1516no—
308C2×#127—152no—
309C2×#124—152no—
310C2×#121—51no—
311C2×#121—151no—
312C2×#121—151no—
313C2×#121—151no—
314C2×#120—152no—
315C2×#120—152no—
316C2×#117—31no—
317C22×C3×C5C22×D412yes—
318C22×C3×C5H(5,𝔽2)12yes—
319C22×C3×C5H(5,𝔽2)12yes—
320C22×C3×C5C2511yescharacteristic
321C2×D15—22no—
322C2×D15—24no—
323C2×D15—22no—
324C2×D15—24no—
325C2×D15—22no—
326C2×D15—24no—
327C2×D15—48no—
328C2×D15—44no—
329C2×C5×D3—28no—
330C2×C5×D3—22no—
331C2×C5×D3—22no—
332C2×C5×D3C22×D414yes—
333C2×C3×D5—22no—
334C2×C3×D5—24no—
335C2×C3×D5—22no—
336C2×C3×D5—24no—
337C2×C3×D5—22no—
338C2×C3×D5—24no—
339C2×C3×D5—48no—
340C2×C3×D5—44no—
341D3×D5—432no—
342C3×C4×C5—24no—
343C3×C4×C5C22×D414yes—
344Dic15—22no—
345C3×Dic5—22no—
346C5×Dic3—24no—
347C5×Dic3C22×D414yes—
348C24×C3—52no—
349C24×C3—51no—
350C23×D3—52no—
351C23×D3—51no—
352C23×D3—58no—
353C23×D3—108no—
354C23×D3—204no—
355C23×D3—204no—
356C23×D3C22×D511yescharacteristic
357C2×C3×D4—54no—
358C2×C3×D4—58no—
359C2×C3×D4—104no—
360C2×C3×D4—204no—
361C22×C3×C4—51no—
362C22×C3×C4—54no—
363C22×C3×C4—104no—
364C22×C3×C4C22×D512yes—
365C22×C3×C4C22×D511yescharacteristic
366C2×#67—54no—
367C2×#67—58no—
368C2×#67—54no—
369C2×#67—58no—
370C2×#67—58no—
371C2×#67—104no—
372C2×#67—104no—
373C2×#67—108no—
374C2×#67—204no—
375C2×#67—204no—
376C22×Dic3—51no—
377C22×Dic3C22×D512yes—
378C22×Dic3C22×D511yescharacteristic
379D3×D4—1032no—
380#235—1032no—
381C2×D12—54no—
382C2×D12—54no—
383C2×D12—58no—
384C2×D12—104no—
385C2×D12—104no—
386C2×D12—204no—
387C2×C4×D3—54no—
388C2×C4×D3—104no—
389C2×C4×D3D2018yescomplemented
390C2×C4×D3C22×D514yes—
391C2×Dic6—54no—
392C2×Dic6—104no—
393C3×C4⋊C4C22×D514yescomplemented
394C3×C22⋊C4—58no—
395#217—58no—
396(C2×D3)⋊C4—58no—
397(C2×D3)⋊C4—58no—
398(C2×D3)⋊C4C22×D518yes—
399C4⋊Dic3C22×D514yescomplemented
400C4×Dic3C22×D518yescomplemented
401C23×C5—34no—
402C23×C5—32no—
403C23×C5—62no—
404C23×C5—62no—
405C23×C5C23×D311yescharacteristic
406C22×D5—22no—
407C22×D5—24no—
408C22×D5—22no—
409C22×D5—24no—
410C22×D5—22no—
411C22×D5—24no—
412C22×D5—34no—
413C22×D5—32no—
414C22×D5—616no—
415C22×D5—62no—
416C22×D5—64no—
417C22×D5—62no—
418C22×D5—64no—
419C22×D5—62no—
420C22×D5—64no—
421C22×D5—128no—
422C22×D5—128no—
423C22×D5—1232no—
424C22×D5C23×D314yes—
425C22×D5C23×D312yes—
426C2×C4×C5—24no—
427C2×C4×C5—34no—
428C2×C4×C5—32no—
429C2×C4×C5—316no—
430C2×C4×C5—34no—
431C2×C4×C5—64no—
432C2×C4×C5D3×D414yes—
433C2×C4×C5C23×D314yes—
434C2×C4×C5C23×D312yes—
435C22⋊D5—68no—
436C22⋊D5—68no—
437C2×Dic5—22no—
438C2×Dic5—32no—
439C2×Dic5—62no—
440C2×Dic5C23×D312yes—
441D20—28no—
442D20—48no—
443D20—616no—
444D20—68no—
445D20—68no—
446D20—128no—
447D20—128no—
448D20—128no—
449C4×D5—28no—
450C4×D5—68no—
451Dic10—68no—
452C25—152no—
453C2×#41—158no—
454C2×#41—308no—
455C22×Q8—151no—
456C22×D4—51no—
457C22×D4—52no—
458C22×D4—158no—
459C22×D4—152no—
460C22×D4—151no—
461C22×D4—152no—
462C22×D4—152no—
463C22×D4—151no—
464C22×D4—151no—
465C22×D4—151no—
466C22×D4—152no—
467C22×D4—308no—
468C23×C4—31no—
469C23×C4—51no—
470C23×C4—151no—
471#127—1516no—
472#124—1516no—
473#121—58no—
474#121—158no—
475#121—158no—
476#121—158no—
477#120—1516no—
478#120—1516no—
479#117—38no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4D3×D511yescharacteristic, complemented
482C2×C22⋊C4—32no—
483C2×C22⋊C4—52no—
484C2×C22⋊C4—152no—
485C2×C22⋊C4—152no—
486C2×C22⋊C4—152no—
487C2×C42—32no—
488C2×C3×C5#53514yescomplemented
489C2×C3×C5C23×D411yescharacteristic
490C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
491C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
492D15—44no—
493D15—42no—
494C3×D5—44no—
495C3×D5—42no—
496C5×D3—24no—
497C23×C3—54no—
498C23×C3—52no—
499C23×C3—102no—
500C23×C3—104no—
501C23×C3—102no—
502C23×C3—104no—
503C23×C3—102no—
504C23×C3—104no—
505C23×C3C23×D511yescharacteristic
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—54no—
509C22×D3—52no—
510C22×D3—102no—
511C22×D3—104no—
512C22×D3—102no—
513C22×D3—104no—
514C22×D3—102no—
515C22×D3—104no—
516C22×D3—1016no—
517C22×D3—208no—
518C22×D3—208no—
519C22×D3—2032no—
520C22×D3C2×D2014yes—
521C22×D3C23×D512yes—
522C3×D4—108no—
523C3×D4—208no—
524C2×C3×C4—24no—
525C2×C3×C4—52no—
526C2×C3×C4—102no—
527C2×C3×C4—108no—
528C2×C3×C4C2×D2014yes—
529C2×C3×C4C23×D514yes—
530C2×C3×C4C23×D512yes—
531#67—108no—
532#67—108no—
533#67—1016no—
534#67—208no—
535#67—208no—
536C2×Dic3—24no—
537C2×Dic3—52no—
538C2×Dic3—102no—
539C2×Dic3C2×D2014yes—
540C2×Dic3C23×D514yes—
541C2×Dic3C23×D512yes—
542D12—108no—
543D12—108no—
544D12—208no—
545C4×D3—108no—
546C4×D3C2×D20116yescomplemented
547Dic6—108no—
548C22×C5—34no—
549C22×C5—62no—
550C22×C5—62no—
551C22×C5—68no—
552C22×C5C2×D3×D412yes—
553C22×C5#100412yes—
554C22×C5#100912yes—
555C22×C5C24×D311yescharacteristic
556C2×D5—22no—
557C2×D5—24no—
558C2×D5—22no—
559C2×D5—24no—
560C2×D5—22no—
561C2×D5—24no—
562C2×D5—44no—
563C2×D5—48no—
564C2×D5—62no—
565C2×D5—64no—
566C2×D5—62no—
567C2×D5—64no—
568C2×D5—62no—
569C2×D5—64no—
570C2×D5—1232no—
571C2×D5—124no—
572C2×D5—128no—
573C4×C5—24no—
574C4×C5—34no—
575C4×C5—64no—
576C4×C5C2×D3×D414yes—
577Dic5—22no—
578Dic5—62no—
579C24—31no—
580C24—52no—
581C24—51no—
582C24—158no—
583C24—152no—
584C24—151no—
585C24—308no—
586C24—604no—
587C24—604no—
588#41—3032no—
589C2×Q8—154no—
590C2×Q8—304no—
591C2×D4—54no—
592C2×D4—58no—
593C2×D4—104no—
594C2×D4—158no—
595C2×D4—154no—
596C2×D4—158no—
597C2×D4—158no—
598C2×D4—154no—
599C2×D4—154no—
600C2×D4—154no—
601C2×D4—158no—
602C2×D4—204no—
603C2×D4—3032no—
604C2×D4—308no—
605C2×D4—304no—
606C2×D4—304no—
607C2×D4—304no—
608C2×D4—304no—
609C2×D4—604no—
610C2×D4—604no—
611C2×D4—604no—
612C22×C4—31no—
613C22×C4—38no—
614C22×C4—34no—
615C22×C4—32no—
616C22×C4—51no—
617C22×C4—54no—
618C22×C4—104no—
619C22×C4—151no—
620C22×C4—154no—
621C22×C4—304no—
622C22×C4C2×D3×D512yes—
623C22×C4C2×D3×D511yescharacteristic
624C4⋊C4—34no—
625C4⋊C4C2×D3×D514yescomplemented
626C22⋊C4—38no—
627C22⋊C4—58no—
628C22⋊C4—158no—
629C22⋊C4—158no—
630C22⋊C4—158no—
631C42—38no—
632C3×C5C2×#53511yescharacteristic, complemented, Hall
633C22×C3—102no—
634C22×C3—104no—
635C22×C3—102no—
636C22×C3—104no—
637C22×C3—102no—
638C22×C3—104no—
639C22×C3—208no—
640C22×C3—204no—
641C22×C3C22×D2012yes—
642C22×C3#414912yes—
643C22×C3#414912yes—
644C22×C3C24×D511yescharacteristic
645C2×D3—28no—
646C2×D3—22no—
647C2×D3—22no—
648C2×D3—102no—
649C2×D3—104no—
650C2×D3—102no—
651C2×D3—104no—
652C2×D3—102no—
653C2×D3—104no—
654C2×D3—2032no—
655C2×D3—204no—
656C2×D3—208no—
657C2×D3C22×D2014yes—
658C3×C4—24no—
659C3×C4—102no—
660C3×C4C22×D2014yes—
661Dic3—24no—
662Dic3—102no—
663Dic3C22×D2014yes—
664C2×C5—64no—
665C2×C5#560714yescomplemented
666C2×C5C22×D3×D411yescharacteristic
667C2×C5C2×#100411yescharacteristic
668C2×C5C2×#100911yescharacteristic
669D5—44no—
670D5—42no—
671D5—124no—
672D5—122no—
673C23—34no—
674C23—32no—
675C23—54no—
676C23—52no—
677C23—62no—
678C23—62no—
679C23—102no—
680C23—104no—
681C23—102no—
682C23—104no—
683C23—102no—
684C23—104no—
685C23—154no—
686C23—152no—
687C23—3016no—
688C23—302no—
689C23—304no—
690C23—302no—
691C23—304no—
692C23—302no—
693C23—304no—
694C23—608no—
695C23—608no—
696C23—6032no—
697C23C22×D3×D511yescharacteristic
698Q8—308no—
699D4—108no—
700D4—208no—
701D4—3016no—
702D4—308no—
703D4—308no—
704D4—308no—
705D4—308no—
706D4—608no—
707D4—608no—
708D4—608no—
709C2×C4—24no—
710C2×C4—34no—
711C2×C4—32no—
712C2×C4—316no—
713C2×C4—34no—
714C2×C4—52no—
715C2×C4—64no—
716C2×C4—102no—
717C2×C4—108no—
718C2×C4—152no—
719C2×C4—302no—
720C2×C4—308no—
721C2×C4D3×D2014yes—
722C2×C4C22×D3×D514yes—
723C2×C4C22×D3×D512yes—
724C2×C3—204no—
725C2×C3—202no—
726C2×C3#6585914yescomplemented
727C2×C3C23×D2011yescharacteristic
728C2×C3C2×#414911yescharacteristic
729C2×C3C2×#414911yescharacteristic
730D3—24no—
731D3—204no—
732D3—202no—
733C5C2×#560711yescharacteristic, complemented, Sylow
734C22—34no—
735C22—68no—
736C22—62no—
737C22—62no—
738C22—102no—
739C22—104no—
740C22—102no—
741C22—104no—
742C22—102no—
743C22—104no—
744C22—208no—
745C22—204no—
746C22—302no—
747C22—304no—
748C22—302no—
749C22—304no—
750C22—302no—
751C22—304no—
752C22—6032no—
753C22—608no—
754C22—604no—
755C22C2×D3×D2012yes—
756C22#9202612yes—
757C22#9203512yes—
758C22C23×D3×D511yescharacteristic
759C4—24no—
760C4—34no—
761C4—64no—
762C4—102no—
763C4—302no—
764C4C2×D3×D2014yes—
765C3C2×#6585911yescharacteristic, complemented, Sylow
766C2—64no—
767C2—204no—
768C2—202no—
769C2—604no—
770C2—602no—
771C2#1175388214yesdirect product factor
772C2C22×D3×D2011yescharacteristic
773C2C2×#9202611yescharacteristic
774C2C2×#9203511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#535
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×D20C2semidirect
2. C22×#6771C2semidirect
3. C2×#91784C2semidirect
4. C2×C5×#892C2semidirect
5. C2×C3×#4041C2semidirect
6. C2×#91476C2semidirect
7. C2×#91474C2semidirect
8. C2×#91465C2semidirect
9. C2×#91458C2semidirect
10. C2×#91450C2semidirect
11. C2×#91353C2semidirect
12. #11753882C2direct (N × H)
16. C22×D60C22semidirect
17. C22×C4×D15C22semidirect
20. C22×C3×D20C22semidirect
21. C22×C3×C4×D5C22semidirect
22. C22×#1204C22semidirect
25. C22×#1202C22semidirect
26. C22×#1202C22semidirect
27. C22×#1202C22semidirect
30. C2×D3×D20C22semidirect
32. C2×#6771C22semidirect
33. C2×C3×C5×C4⋊C4C22semidirect
34. C2×#6714C22semidirect
35. #91784C22semidirect
37. C2×C5×C4⋊Dic3C22semidirect
38. C2×C4×C5×Dic3C22semidirect
39. C5×#892C22semidirect
40. C2×C3×#685C22semidirect
41. C3×#4041C22semidirect
42. C2×#6667C22semidirect
43. C2×#6665C22semidirect
44. #91476C22semidirect
45. #91474C22semidirect
46. #91465C22semidirect
47. #91458C22semidirect
48. #91450C22semidirect
49. #91353C22semidirect
58. C2×#4041D3semidirect
78. C2×D60C23semidirect
80. C2×C4×D15C23semidirect
83. C2×C4×C5×D3D4semidirect
89. C2×C3×D20C23semidirect
91. C2×C3×C4×D5C23semidirect
93. C2×#1204C23semidirect
101. C2×#1202C23semidirect
102. C2×#1202C23semidirect
103. C2×#1202C23semidirect
108. C3×C5×C4⋊C4C23semidirect
109. #6714C23semidirect
111. C5×C4⋊Dic3C23semidirect
112. C4×C5×Dic3C23semidirect
113. C3×#685C23semidirect
114. #6667C23semidirect
115. #6665C23semidirect
125. C2×#892D5semidirect
143. C22×D20C2×D3semidirect
145. C22×C4×D5C2×D3semidirect
149. C2×C5×C4⋊C4C2×D3semidirect
155. C2×#685C2×D3semidirect
159. #4041C2×D3semidirect
203. C4×C5×D3C2×D4semidirect
236. C2×C3×C4⋊C4C2×D5semidirect
246. C2×C4⋊Dic3C2×D5semidirect
247. C2×C4×Dic3C2×D5semidirect
249. #892C2×D5semidirect
290. C2×D20C22×D3semidirect
294. C2×C4×D5C22×D3semidirect
298. C5×C4⋊C4C22×D3semidirect
304. #685C22×D3semidirect
389. C2×C4×D3D20semidirect
393. C3×C4⋊C4C22×D5semidirect
399. C4⋊Dic3C22×D5semidirect
400. C4×Dic3C22×D5semidirect
481. C2×C4⋊C4D3×D5semidirect
488. C2×C3×C5#535semidirect
546. C4×D3C2×D20semidirect
625. C4⋊C4C2×D3×D5semidirect
632. C3×C5C2×#535semidirect
665. C2×C5#5607semidirect
726. C2×C3#65859semidirect
733. C5C2×#5607semidirect
765. C3C2×#65859semidirect
771. C2#11753882direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D202
C22×#67712
C2×#917842
C2×C5×#8922
C2×C3×#40412
C2×#914762
C2×#914742
C2×#914652
C2×#914582
C2×#914502
C2×#913532
#117538822
C2×#658593
C2×#56075