Finite Group Databasebeta

← #14325985

Subgroups — #14325985

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D15C211yesmaximal, characteristic
2C2×#91561C212yesmaximal, complemented
3C2×#91428C211yesmaximal, characteristic, complemented
4C2×#91418C211yesmaximal, characteristic, complemented
5C5×#5221C211yesmaximal, characteristic, complemented
6C3×#65510C211yesmaximal, characteristic, complemented
7#11749520C212yesmaximal, complemented
8#11749520C212yesmaximal, complemented
9#11749502C212yesmaximal, complemented
10#11748799C211yesmaximal, characteristic, complemented
11C4×#6667C211yesmaximal, characteristic, complemented
12#10608162—31nomaximal, Hall
13C24×D15C2212yes—
14C22×C3×C5×D4C2211yescharacteristic
15C22×#1220C2212yes—
16C2×D4×D15—24no—
17C2×D4×D15—24no—
18C2×D4×D15C418yescomplemented
19C22×D60C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C22×#1200C2212yescomplemented
22C22×#1200C2212yescomplemented
23C2×C5×#217C2212yescomplemented
24C2×C5×#217C2212yescomplemented
25C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
26C2×C4×C5×Dic3C2211yescharacteristic, complemented
27C2×C3×C22⋊Dic5C2212yescomplemented
28C2×C3×C22⋊Dic5C2212yescomplemented
29C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
30C2×C3×C4×Dic5C2211yescharacteristic, complemented
31#91561—28no—
32C2×#6667C2211yescharacteristic
33C2×#6667C2212yes—
34C2×#6667C2211yescharacteristic
35C2×#6667C2212yescomplemented
36C2×#6667C2212yescomplemented
37#91428—24no—
38#91418—24no—
39#90994C2211yescharacteristic, complemented
40#90994C2211yescharacteristic, complemented
41#90994C2212yescomplemented
42#76431—51nomaximal, Hall
43C22×D4×D5—31no—
44C2×#4039—31no—
45C2×D5×C22⋊C4—32no—
46C2×C4×D20—31no—
47C5×#390—31no—
48#65510D311yescharacteristic, complemented
49#65276—31no—
50#65245—32no—
51#65245—32no—
52#65244—32no—
53C4×#685—31no—
54C24×C3×C5C2312yes—
55C23×D15—24no—
56C23×D15—24no—
57C23×D15—24no—
58C23×D15—24no—
59C23×D15—42no—
60C23×D15—42no—
61C23×D15C2×C418yescomplemented
62C23×D15C2312yes—
63C23×D15C2311yescharacteristic
64C2×C3×C5×D4—22no—
65C2×C3×C5×D4—22no—
66C2×C3×C5×D4C2×C414yescomplemented
67C22×C3×C4×C5C2311yescharacteristic
68C2×#1220—24no—
69C2×#1220—24no—
70C2×#1220C2×C418yescomplemented
71C22×Dic15C2311yescharacteristic
72D4×D15—232no—
73C2×D60C2×C414yes—
74C2×D60D414yes—
75C2×D60D414yes—
76C2×C4×D15—22no—
77C2×C4×D15—22no—
78C2×C4×D15C2×C414yescomplemented
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2312yes—
81C22×C5×Dic3C2311yescharacteristic
82C22×C3×Dic5C2312yes—
83C22×C3×Dic5C2311yescharacteristic
84C22×C3×Dic5C2311yescharacteristic
85C2×#1200—24no—
86C2×#1200—24no—
87C2×#1200—24no—
88C2×#1200—24no—
89C2×#1200—42no—
90C2×#1200—42no—
91C5×#217—24no—
92C5×#217—42no—
93C5×C4⋊Dic3—22no—
94C4×C5×Dic3—22no—
95C3×C22⋊Dic5—24no—
96C3×C22⋊Dic5—42no—
97C3×C4⋊Dic5—22no—
98C3×C4×Dic5—22no—
99#6667—24no—
100#6667—24no—
101#6667—24no—
102#6667—22no—
103#6667D414yescomplemented
104C22×D3×D4—51no—
105C2×#893—51no—
106C2×D3×C22⋊C4—52no—
107C2×C4×D12—51no—
108C3×#390—51no—
109#5221D511yescharacteristic, complemented
110#4987—51no—
111#4956—52no—
112#4956—52no—
113#4955—52no—
114C4×(C2×D3)⋊C4—51no—
115C24×D5—32no—
116C22×C5×D4C2×D311yescharacteristic
117C22×C22⋊D5—32no—
118C2×D4×D5—38no—
119C2×D4×D5—64no—
120C2×D4×D5—64no—
121C22×D20—31no—
122C22×C4×D5—31no—
123C22×C4×D5—32no—
124C22×C4×D5—32no—
125C2×C5×C4⋊C4—31no—
126C2×C5×C22⋊C4—32no—
127C2×C5×C22⋊C4—32no—
128C2×C42×C5—31no—
129C2×C22⋊Dic5C2×D312yescomplemented
130C2×C22⋊Dic5C2×D312yescomplemented
131C2×#685—31no—
132C2×#685—32no—
133C2×#685—32no—
134C2×#685—32no—
135C2×#685—31no—
136C2×C4⋊Dic5C2×D311yescharacteristic, complemented
137C2×C4×Dic5C2×D311yescharacteristic, complemented
138#4039—64no—
139D5×C22⋊C4—68no—
140C4×D20—64no—
141#3963—31no—
142#3963—31no—
143#3963—32no—
144D4×C22⋊C4—151noSylow
145C23×C3×C5—22no—
146C23×C3×C5—22no—
147C23×C3×C5—22no—
148C23×C3×C5—22no—
149C23×C3×C5—22no—
150C23×C3×C5—22no—
151C23×C3×C5C22×C414yes—
152C23×C3×C5C2411yescharacteristic
153C22×D15—22no—
154C22×D15—21no—
155C22×D15—21no—
156C22×D15—22no—
157C22×D15—22no—
158C22×D15—22no—
159C22×D15—21no—
160C22×D15—21no—
161C22×D15—216no—
162C22×D15—216no—
163C22×D15—48no—
164C22×D15—48no—
165C22×D15—48no—
166C22×D15—48no—
167C22×D15—48no—
168C22×D15C22×C414yes—
169C22×D15C22×C412yes—
170C22×D15C2×D414yes—
171C22×D15C2×D414yes—
172C22×D15C2×D412yes—
173C22×D15#4112yes—
174C3×C5×D4—28no—
175C2×C3×C4×C5C22×C412yes—
176C2×C3×C4×C5C2×D412yes—
177C2×C3×C4×C5C2×D412yes—
178#1220—216no—
179C2×Dic15—21no—
180C2×Dic15—21no—
181C2×Dic15C22×C412yes—
182D60C22⋊C4116yescomplemented
183C4×D15—28no—
184C2×C5×Dic3—21no—
185C2×C5×Dic3—21no—
186C2×C5×Dic3—21no—
187C2×C5×Dic3—22no—
188C2×C5×Dic3—22no—
189C2×C5×Dic3—21no—
190C2×C5×Dic3—21no—
191C2×C5×Dic3—22no—
192C2×C5×Dic3C2×D412yescomplemented
193C2×C3×Dic5—21no—
194C2×C3×Dic5—21no—
195C2×C3×Dic5—21no—
196C2×C3×Dic5—22no—
197C2×C3×Dic5—22no—
198C2×C3×Dic5—21no—
199C2×C3×Dic5—21no—
200C2×C3×Dic5—22no—
201C2×C3×Dic5C2×D412yescomplemented
202#1200—48no—
203#1200—48no—
204C24×D3—52no—
205C22×C3×D4C2×D511yescharacteristic
206C22×#67—52no—
207C2×D3×D4—58no—
208C2×D3×D4—104no—
209C2×D3×D4—104no—
210C22×D12—51no—
211C22×C4×D3—51no—
212C22×C4×D3—52no—
213C22×C4×D3—52no—
214C2×C3×C4⋊C4—51no—
215C2×C3×C22⋊C4—52no—
216C2×C3×C22⋊C4—52no—
217C2×C3×C42—51no—
218C2×#217C2×D512yescomplemented
219C2×#217C2×D512yescomplemented
220C2×(C2×D3)⋊C4—51no—
221C2×(C2×D3)⋊C4—51no—
222C2×(C2×D3)⋊C4—52no—
223C2×(C2×D3)⋊C4—52no—
224C2×(C2×D3)⋊C4—52no—
225C2×C4⋊Dic3C2×D511yescharacteristic, complemented
226C2×C4×Dic3C2×D511yescharacteristic, complemented
227#893—104no—
228D3×C22⋊C4—108no—
229C4×D12—104no—
230C3⋊#95—51no—
231C3⋊#95—51no—
232C3⋊#95—52no—
233C24×C5C22×D312yes—
234C23×D5—32no—
235C23×D5—31no—
236C23×D5—38no—
237C23×D5—64no—
238C23×D5—64no—
239C23×D5—64no—
240C23×D5—64no—
241C23×D5—122no—
242C23×D5—122no—
243C2×C5×D4—22no—
244C2×C5×D4—22no—
245C2×C5×D4C4×D314yescomplemented
246C22×C4×C5—31no—
247C22×C4×C5—31no—
248C22×C4×C5—32no—
249C22×C4×C5C22×D311yescharacteristic
250C2×C22⋊D5—38no—
251C2×C22⋊D5—64no—
252C2×C22⋊D5—64no—
253C22×Dic5—31no—
254C22×Dic5C22×D312yes—
255C22×Dic5C22×D311yescharacteristic
256C22×Dic5C22×D311yescharacteristic
257D4×D5—632no—
258C2×D20—34no—
259C2×D20—34no—
260C2×D20—34no—
261C2×C4×D5—34no—
262C2×C4×D5—62no—
263C2×C4×D5—62no—
264C2×C4×D5—64no—
265C2×C4×D5—64no—
266C2×C4×D5—64no—
267C2×C4×D5—64no—
268C2×C4×D5—122no—
269C2×C4×D5—122no—
270C5×C4⋊C4—62no—
271C5×C22⋊C4—64no—
272C5×C22⋊C4—122no—
273C42×C5—62no—
274C22⋊Dic5—24no—
275C22⋊Dic5—42no—
276#685—34no—
277#685—64no—
278#685—64no—
279#685—64no—
280#685—62no—
281C4⋊Dic5—22no—
282C4×Dic5—22no—
283C23×D4—151no—
284C2×C4×D4—151no—
285C2×C4×D4—151no—
286C22×C22⋊C4—152no—
287#390—31no—
288#390—51no—
289#386—152no—
290#386—152no—
291#380—151no—
292#379—152no—
293C4×C22⋊C4—151no—
294C22×C3×C5—24no—
295C22×C3×C5—24no—
296C22×C3×C5—24no—
297C22×C3×C5—42no—
298C22×C3×C5—42no—
299C22×C3×C5—42no—
300C22×C3×C5—42no—
301C22×C3×C5C23×C411yescharacteristic
302C22×C3×C5C22×D411yescharacteristic
303C22×C3×C5C22×D411yescharacteristic
304C22×C3×C5C22×D411yescharacteristic
305C22×C3×C5C2×#4111yescharacteristic
306C22×C3×C5H(5,𝔽2)11yescharacteristic
307C22×C3×C5H(5,𝔽2)11yescharacteristic
308C2×D15—22no—
309C2×D15—24no—
310C2×D15—22no—
311C2×D15—24no—
312C2×D15—24no—
313C2×D15—24no—
314C2×D15—22no—
315C2×D15—22no—
316C2×D15—22no—
317C2×D15—22no—
318C2×D15—24no—
319C2×D15—24no—
320C2×D15—432no—
321C2×D15C2×C22⋊C418yescomplemented
322C2×D15C4×D414yescomplemented
323C3×C4×C5C2×C22⋊C414yescomplemented
324Dic15—22no—
325C3×Dic5—22no—
326C3×Dic5—42no—
327C3×Dic5—41no—
328C5×Dic3—22no—
329C5×Dic3—42no—
330C5×Dic3—41no—
331C24×C3C22×D512yes—
332C23×D3—51no—
333C23×D3—52no—
334C23×D3—58no—
335C23×D3—104no—
336C23×D3—104no—
337C23×D3—104no—
338C23×D3—104no—
339C23×D3—202no—
340C23×D3—202no—
341C2×C3×D4—22no—
342C2×C3×D4—22no—
343C2×C3×D4C4×D514yescomplemented
344C22×C3×C4—51no—
345C22×C3×C4—51no—
346C22×C3×C4—52no—
347C22×C3×C4C22×D511yescharacteristic
348C2×#67—58no—
349C2×#67—104no—
350C2×#67—104no—
351C22×Dic3—51no—
352C22×Dic3C22×D511yescharacteristic
353C22×Dic3C22×D512yes—
354C22×Dic3C22×D511yescharacteristic
355D3×D4—1032no—
356C2×D12—54no—
357C2×D12—54no—
358C2×D12—54no—
359C2×C4×D3—54no—
360C2×C4×D3—102no—
361C2×C4×D3—102no—
362C2×C4×D3—104no—
363C2×C4×D3—104no—
364C2×C4×D3—104no—
365C2×C4×D3—104no—
366C2×C4×D3—202no—
367C2×C4×D3—202no—
368C3×C4⋊C4—102no—
369C3×C22⋊C4—104no—
370C3×C22⋊C4—202no—
371C3×C42—102no—
372#217—24no—
373#217—42no—
374(C2×D3)⋊C4—54no—
375(C2×D3)⋊C4—104no—
376(C2×D3)⋊C4—104no—
377(C2×D3)⋊C4—104no—
378(C2×D3)⋊C4—102no—
379C4⋊Dic3—22no—
380C4×Dic3—22no—
381C23×C5—22no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—22no—
385C23×C5—22no—
386C23×C5—22no—
387C23×C5C2×C4×D314yes—
388C23×C5C23×D311yescharacteristic
389C22×D5—32no—
390C22×D5—34no—
391C22×D5—32no—
392C22×D5—34no—
393C22×D5—34no—
394C22×D5—32no—
395C22×D5—616no—
396C22×D5—616no—
397C22×D5—62no—
398C22×D5—61no—
399C22×D5—61no—
400C22×D5—62no—
401C22×D5—61no—
402C22×D5—62no—
403C22×D5—62no—
404C22×D5—61no—
405C22×D5—128no—
406C22×D5—128no—
407C22×D5—128no—
408C22×D5—128no—
409C22×D5—128no—
410C5×D4—28no—
411C2×C4×C5—32no—
412C2×C4×C5—61no—
413C2×C4×C5—61no—
414C2×C4×C5—61no—
415C2×C4×C5—62no—
416C2×C4×C5—62no—
417C2×C4×C5—61no—
418C2×C4×C5—61no—
419C2×C4×C5—62no—
420C2×C4×C5C2×C4×D312yes—
421C2×C4×C5D3×D412yes—
422C2×C4×C5D3×D412yes—
423C22⋊D5—616no—
424C2×Dic5—21no—
425C2×Dic5—21no—
426C2×Dic5—21no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—21no—
430C2×Dic5—22no—
431C2×Dic5—21no—
432C2×Dic5—32no—
433C2×Dic5—61no—
434C2×Dic5—61no—
435C2×Dic5D3×D412yescomplemented
436D20—316no—
437C4×D5—68no—
438C4×D5—128no—
439C4×D5—128no—
440C25—152no—
441C22×D4—152no—
442C22×D4—158no—
443C22×D4—151no—
444C22×D4—304no—
445C22×D4—304no—
446C22×D4D3×D511yescharacteristic
447C23×C4—152no—
448C23×C4—152no—
449C23×C4—151no—
450C4×D4—304no—
451C4×D4—304no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—51no—
454C2×C22⋊C4—32no—
455C2×C22⋊C4—32no—
456C2×C22⋊C4—52no—
457C2×C22⋊C4—52no—
458C2×C22⋊C4—151no—
459C2×C22⋊C4—152no—
460C2×C22⋊C4—152no—
461C2×C22⋊C4—152no—
462C2×C22⋊C4—151no—
463C2×C22⋊C4—308no—
464C2×C42—31no—
465C2×C42—51no—
466#95—151no—
467#95—151no—
468#95—152no—
469C2×C3×C5—44no—
470C2×C3×C5C22×C22⋊C411yescharacteristic
471C2×C3×C5C2×C4×D411yescharacteristic
472C2×C3×C5#51811yescharacteristic
473C2×C3×C5D4211yescharacteristic
474C2×C3×C5D4211yescharacteristic
475C2×C3×C5#54611yescharacteristic
476C2×C3×C5#54611yescharacteristic
477D15—24no—
478D15—28no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3C2×C4×D514yes—
486C23×C3C23×D511yescharacteristic
487C22×D3—52no—
488C22×D3—54no—
489C22×D3—52no—
490C22×D3—54no—
491C22×D3—54no—
492C22×D3—52no—
493C22×D3—1016no—
494C22×D3—1016no—
495C22×D3—102no—
496C22×D3—101no—
497C22×D3—101no—
498C22×D3—102no—
499C22×D3—101no—
500C22×D3—102no—
501C22×D3—102no—
502C22×D3—101no—
503C22×D3—208no—
504C22×D3—208no—
505C22×D3—208no—
506C22×D3—208no—
507C22×D3—208no—
508C3×D4—28no—
509C2×C3×C4—52no—
510C2×C3×C4—101no—
511C2×C3×C4—101no—
512C2×C3×C4—101no—
513C2×C3×C4—102no—
514C2×C3×C4—102no—
515C2×C3×C4—101no—
516C2×C3×C4—101no—
517C2×C3×C4—102no—
518C2×C3×C4C2×C4×D512yes—
519C2×C3×C4D4×D512yes—
520C2×C3×C4D4×D512yes—
521#67—1016no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—21no—
528C2×Dic3—22no—
529C2×Dic3—21no—
530C2×Dic3—52no—
531C2×Dic3—101no—
532C2×Dic3—101no—
533C2×Dic3D4×D512yescomplemented
534D12—516no—
535C4×D3—108no—
536C4×D3—208no—
537C4×D3—208no—
538C22×C5—24no—
539C22×C5—24no—
540C22×C5—24no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5—42no—
545C22×C5C22×C4×D311yescharacteristic
546C22×C5C2×D3×D411yescharacteristic
547C22×C5C2×D3×D411yescharacteristic
548C22×C5C2×D3×D411yescharacteristic
549C22×C5#100411yescharacteristic
550C22×C5D3×#4111yescharacteristic
551C22×C5#100911yescharacteristic
552C2×D5—38no—
553C2×D5—34no—
554C2×D5—64no—
555C2×D5—62no—
556C2×D5—64no—
557C2×D5—62no—
558C2×D5—62no—
559C2×D5—64no—
560C2×D5—64no—
561C2×D5—62no—
562C2×D5—64no—
563C2×D5—62no—
564C2×D5—64no—
565C2×D5—62no—
566C2×D5—1232no—
567C4×C5—62no—
568C4×C5—121no—
569C4×C5—122no—
570C4×C5D3×C22⋊C414yescomplemented
571Dic5—22no—
572Dic5—42no—
573Dic5—41no—
574Dic5—62no—
575C24—151no—
576C24—152no—
577C24—158no—
578C24—304no—
579C24—304no—
580C24—304no—
581C24—304no—
582C24—602no—
583C24—602no—
584C24C2×D3×D512yes—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—158no—
588C2×D4—154no—
589C2×D4—154no—
590C2×D4—154no—
591C2×D4—3032no—
592C2×D4—304no—
593C2×D4—304no—
594C2×D4#120014yescomplemented
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—32no—
598C22×C4—51no—
599C22×C4—51no—
600C22×C4—52no—
601C22×C4—151no—
602C22×C4—154no—
603C22×C4—304no—
604C22×C4—304no—
605C22×C4—304no—
606C22×C4—304no—
607C22×C4—302no—
608C22×C4—302no—
609C22×C4—602no—
610C22×C4—602no—
611C22×C4C2×D3×D511yescharacteristic
612C4⋊C4—62no—
613C4⋊C4—102no—
614C22⋊C4—64no—
615C22⋊C4—104no—
616C22⋊C4—122no—
617C22⋊C4—154no—
618C22⋊C4—202no—
619C22⋊C4—304no—
620C22⋊C4—304no—
621C22⋊C4—304no—
622C22⋊C4—302no—
623C42—62no—
624C42—102no—
625C3×C5D4×C22⋊C411yescharacteristic, complemented, Hall
626C22×C3—24no—
627C22×C3—24no—
628C22×C3—24no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3C22×C4×D511yescharacteristic
634C22×C3C2×D4×D511yescharacteristic
635C22×C3C2×D4×D511yescharacteristic
636C22×C3C2×D4×D511yescharacteristic
637C22×C3#414411yescharacteristic
638C22×C3D5×#4111yescharacteristic
639C22×C3#414911yescharacteristic
640C2×D3—58no—
641C2×D3—54no—
642C2×D3—104no—
643C2×D3—102no—
644C2×D3—102no—
645C2×D3—104no—
646C2×D3—104no—
647C2×D3—102no—
648C2×D3—104no—
649C2×D3—102no—
650C2×D3—104no—
651C2×D3—102no—
652C2×D3—104no—
653C2×D3—102no—
654C2×D3—2032no—
655C3×C4—102no—
656C3×C4—202no—
657C3×C4—201no—
658C3×C4D5×C22⋊C414yescomplemented
659Dic3—22no—
660Dic3—42no—
661Dic3—41no—
662Dic3—102no—
663C2×C5—44no—
664C2×C5C2×D3×C22⋊C411yescharacteristic
665C2×C5C4×D3×D411yescharacteristic
666C2×C5#554511yescharacteristic
667C2×C5#560911yescharacteristic
668C2×C5#561211yescharacteristic
669C2×C5#567611yescharacteristic
670C2×C5#571711yescharacteristic
671D5—64no—
672D5—68no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—152no—
680C23—152no—
681C23—152no—
682C23—154no—
683C23—154no—
684C23—154no—
685C23—3016no—
686C23—3016no—
687C23—302no—
688C23—302no—
689C23—302no—
690C23—301no—
691C23—302no—
692C23—301no—
693C23—301no—
694C23—301no—
695C23—608no—
696C23—608no—
697C23—608no—
698C23—608no—
699C23—608no—
700C23C2×#120014yes—
701C23C22×D3×D511yescharacteristic
702D4—28no—
703D4—1516no—
704D4—3016no—
705C2×C4—32no—
706C2×C4—52no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—62no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—62no—
713C2×C4—61no—
714C2×C4—62no—
715C2×C4—101no—
716C2×C4—101no—
717C2×C4—102no—
718C2×C4—101no—
719C2×C4—101no—
720C2×C4—102no—
721C2×C4—101no—
722C2×C4—102no—
723C2×C4—152no—
724C2×C4—301no—
725C2×C4—301no—
726C2×C4—308no—
727C2×C4—608no—
728C2×C4—608no—
729C2×C4C2×#120012yes—
730C2×C4#679012yes—
731C2×C4#679012yes—
732C2×C3—44no—
733C2×C3C2×D5×C22⋊C411yescharacteristic
734C2×C3C4×D4×D511yescharacteristic
735C2×C3#6587911yescharacteristic
736C2×C3#6594311yescharacteristic
737C2×C3#6594611yescharacteristic
738C2×C3#6601011yescharacteristic
739C2×C3#6605111yescharacteristic
740D3—104no—
741D3—108no—
742C5#7643111yescharacteristic, complemented, Sylow
743C22—24no—
744C22—24no—
745C22—24no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—154no—
751C22—158no—
752C22—304no—
753C22—304no—
754C22—302no—
755C22—304no—
756C22—302no—
757C22—302no—
758C22—302no—
759C22—304no—
760C22—302no—
761C22—304no—
762C22—302no—
763C22—304no—
764C22—6032no—
765C22D3×D4×D511yescharacteristic
766C22#9202411yescharacteristic
767C22#9202611yescharacteristic
768C22#9202711yescharacteristic
769C22C22×#120011yescharacteristic
770C22C2×#679011yescharacteristic
771C22C2×#679011yescharacteristic
772C4—62no—
773C4—102no—
774C4—122no—
775C4—121no—
776C4—202no—
777C4—201no—
778C4—302no—
779C4#9156114yescomplemented
780C3#1060816211yescharacteristic, complemented, Sylow
781C2—44no—
782C2—304no—
783C2—308no—
784C2D4×#120011yescharacteristic
785C2#1175492211yescharacteristic
786C2#1175495811yescharacteristic
787C2#1175495911yescharacteristic
788C2#1175504411yescharacteristic
789C2#1175505911yescharacteristic
790C2C2×#9156111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×D4×D15C2
hypercenterC22×D4D3×D5
hypocenterC3×C5D4×C22⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91561C2semidirect
3. C2×#91428C2semidirect
4. C2×#91418C2semidirect
5. C5×#5221C2semidirect
6. C3×#65510C2semidirect
7. #11749520C2semidirect
8. #11749520C2semidirect
9. #11749502C2semidirect
10. #11748799C2semidirect
11. C4×#6667C2semidirect
18. C2×D4×D15C4semidirect
21. C22×#1200C22semidirect
22. C22×#1200C22semidirect
23. C2×C5×#217C22semidirect
24. C2×C5×#217C22semidirect
25. C2×C5×C4⋊Dic3C22semidirect
26. C2×C4×C5×Dic3C22semidirect
27. C2×C3×C22⋊Dic5C22semidirect
28. C2×C3×C22⋊Dic5C22semidirect
29. C2×C3×C4⋊Dic5C22semidirect
30. C2×C3×C4×Dic5C22semidirect
35. C2×#6667C22semidirect
36. C2×#6667C22semidirect
39. #90994C22semidirect
40. #90994C22semidirect
41. #90994C22semidirect
48. #65510D3semidirect
61. C23×D15C2×C4semidirect
66. C2×C3×C5×D4C2×C4semidirect
70. C2×#1220C2×C4semidirect
78. C2×C4×D15C2×C4semidirect
103. #6667D4semidirect
109. #5221D5semidirect
129. C2×C22⋊Dic5C2×D3semidirect
130. C2×C22⋊Dic5C2×D3semidirect
136. C2×C4⋊Dic5C2×D3semidirect
137. C2×C4×Dic5C2×D3semidirect
182. D60C22⋊C4semidirect
192. C2×C5×Dic3C2×D4semidirect
201. C2×C3×Dic5C2×D4semidirect
218. C2×#217C2×D5semidirect
219. C2×#217C2×D5semidirect
225. C2×C4⋊Dic3C2×D5semidirect
226. C2×C4×Dic3C2×D5semidirect
245. C2×C5×D4C4×D3semidirect
321. C2×D15C2×C22⋊C4semidirect
322. C2×D15C4×D4semidirect
323. C3×C4×C5C2×C22⋊C4semidirect
343. C2×C3×D4C4×D5semidirect
435. C2×Dic5D3×D4semidirect
533. C2×Dic3D4×D5semidirect
570. C4×C5D3×C22⋊C4semidirect
594. C2×D4#1200semidirect
625. C3×C5D4×C22⋊C4semidirect
658. C3×C4D5×C22⋊C4semidirect
742. C5#76431semidirect
779. C4#91561semidirect
780. C3#10608162semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D152
C2×#915612
C2×#914282
C2×#914182
C5×#52212
C3×#655102
#117495202
#117495022
#117487992
C4×#66672
#106081623
#764315