Finite Group Databasebeta

← #14322551

Subgroups — #14322551

Order 1920.

1760 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#709C211yesmaximal, characteristic
2C2×D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#91358C211yesmaximal, characteristic, complemented
4#11751313C211yesmaximal, characteristic, complemented
5C5×#5212C211yesmaximal, characteristic, complemented
6#11749518C212yesmaximal, complemented
7#11749489C212yesmaximal, complemented
8#11748896C212yesmaximal, complemented
9#11748759C211yesmaximal, characteristic, complemented
10#11748759C211yesmaximal, characteristic, complemented
11#11748672C212yesmaximal, complemented
12#10605734—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5C2211yescharacteristic
15C22×C3×C22⋊D5C2211yescharacteristic
16C2×C3×#709—24no—
17C2×C3×#709—24no—
18C2×C3×#709C418yescomplemented
19C22×C3×D20C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×C3×Dic10C2211yescharacteristic
23C22×D5×Dic3C2212yes—
24C2×#6719C2212yes—
25C2×C4⋊Dic15C2211yescharacteristic
26C2×C4⋊Dic15C2211yescharacteristic
27C2×C5×#217C2212yes—
28C2×C5×C4⋊Dic3C2211yescharacteristic
29C2×C5×C4⋊Dic3C2211yescharacteristic
30C2×#6668C2212yes—
31C2×#6665C2212yes—
32C2×#6665C2212yes—
33C2×#6665C2212yes—
34C2×Dic3×Dic5C2212yes—
35D5×C4⋊Dic3—24no—
36#91358—24no—
37#91115C2212yes—
38C5×C3⋊#95C2212yes—
39#90994C2212yes—
40#90994C2212yes—
41#84087—51nomaximal, Hall
42C22×#709D311yescharacteristic
43C2×#4038—31no—
44C2×D5×C4⋊C4—31no—
45C5×#380—31no—
46#65501—31no—
47#65276—31no—
48#65276—31no—
49#65246—32no—
50#65245—32no—
51#64954—32no—
52#64935—32no—
53C24×C3×C5C2311yescharacteristic
54C23×C3×D5C2311yescharacteristic
55C23×C3×D5C2311yescharacteristic
56C22×C3×C4×C5—22no—
57C22×C3×C4×C5—22no—
58C22×C3×C4×C5C2×C414yescomplemented
59C22×C3×C4×C5C2311yescharacteristic
60C22×C3×C4×C5C2311yescharacteristic
61C22×Dic15C2312yes—
62C22×Dic15C2312yes—
63C22×C5×Dic3C2312yes—
64C22×C5×Dic3C2312yes—
65C2×C3×C22⋊D5—22no—
66C2×C3×C22⋊D5—22no—
67C2×C3×C22⋊D5—22no—
68C2×C3×C22⋊D5—22no—
69C2×C3×C22⋊D5C2×C414yes—
70C2×C3×C22⋊D5C2×C414yescomplemented
71C22×C3×Dic5C2311yescharacteristic
72C22×C3×Dic5C2311yescharacteristic
73C3×#709—232no—
74C2×C3×D20—22no—
75C2×C3×D20—22no—
76C2×C3×D20C2×C414yes—
77C2×C3×C4×D5—22no—
78C2×C3×C4×D5—22no—
79C2×C3×C4×D5C2×C414yes—
80C2×C3×C4×D5C2×C414yescomplemented
81C2×C3×C4×D5D414yes—
82C2×C3×C4×D5D414yes—
83C2×C3×Dic10—22no—
84C2×C3×Dic10—22no—
85C2×C3×Dic10C2×C414yescomplemented
86C2×D5×Dic3—24no—
87C2×D5×Dic3—42no—
88C2×D5×Dic3—42no—
89#6719—42no—
90C4⋊Dic15—22no—
91C4⋊Dic15—22no—
92C5×#217—42no—
93C5×C4⋊Dic3—22no—
94C5×C4⋊Dic3—22no—
95#6668—24no—
96#6665—24no—
97#6665—42no—
98#6665—42no—
99Dic3×Dic5—24no—
100C22×C3×#41—51no—
101C2×#926—51no—
102C22×C4⋊Dic3—51no—
103#5229—52no—
104#5221—52no—
105#5220—52no—
106#5220—52no—
107#5212—51no—
108#5212—51no—
109#5212—51no—
110#5212D511yescharacteristic, complemented
111C23×C4×C5C2×D311yescharacteristic
112C22×C22⋊D5C2×D311yescharacteristic
113C22×C22⋊D5C2×D311yescharacteristic
114C2×#709—24no—
115C2×#709—24no—
116C2×#709Dic318yescomplemented
117C22×D20C2×D311yescharacteristic
118C22×C4×D5—32no—
119C22×C4×D5C2×D311yescharacteristic
120C22×C4×D5C2×D311yescharacteristic
121C22×Dic10C2×D311yescharacteristic
122C2×C5×C4⋊C4—31no—
123C2×C5×C4⋊C4—31no—
124C2×C5×C22⋊C4—32no—
125C2×C22⋊Dic5—32no—
126C2×#685—32no—
127C2×#685—32no—
128C2×#685—32no—
129C2×C4⋊Dic5—31no—
130C2×C4⋊Dic5—31no—
131C2×#683—32no—
132C2×C4×Dic5—32no—
133#4038—64no—
134D5×C4⋊C4—64no—
135C5×#95—32no—
136#3963—32no—
137#3963—32no—
138#3963—32no—
139#2311—151noSylow
140C23×C3×C5—21no—
141C23×C3×C5—21no—
142C23×C3×C5—21no—
143C23×C3×C5—21no—
144C23×C3×C5—21no—
145C23×C3×C5—21no—
146C23×C3×C5C22×C412yes—
147C23×C3×C5C2411yescharacteristic
148C22×C3×D5—21no—
149C22×C3×D5—21no—
150C22×C3×D5—21no—
151C22×C3×D5—21no—
152C22×C3×D5—21no—
153C22×C3×D5—21no—
154C22×C3×D5—21no—
155C22×C3×D5—21no—
156C22×C3×D5—21no—
157C22×C3×D5—21no—
158C22×C3×D5C22×C412yes—
159C22×C3×D5C22×C412yes—
160C22×C3×D5C2×D412yes—
161C22×C3×D5C2×D412yes—
162C2×C3×C4×C5—21no—
163C2×C3×C4×C5—21no—
164C2×C3×C4×C5—28no—
165C2×C3×C4×C5C22×C412yes—
166C2×C3×C4×C5C22×C412yes—
167C2×C3×C4×C5C2×D412yes—
168C2×C3×C4×C5C2×D412yes—
169C2×Dic15—22no—
170C2×Dic15—22no—
171C2×Dic15—22no—
172C2×Dic15—22no—
173C2×Dic15—22no—
174C2×Dic15—22no—
175C2×C5×Dic3—22no—
176C2×C5×Dic3—22no—
177C2×C5×Dic3—22no—
178C2×C5×Dic3—22no—
179C2×C5×Dic3—22no—
180C2×C5×Dic3—22no—
181C3×C22⋊D5—28no—
182C3×C22⋊D5—28no—
183C2×C3×Dic5—21no—
184C2×C3×Dic5—21no—
185C2×C3×Dic5C22×C412yes—
186C2×C3×Dic5C22×C412yes—
187C2×C3×Dic5C2×D412yes—
188C2×C3×Dic5C2×D412yes—
189C3×D20—28no—
190C3×C4×D5—28no—
191C3×C4×D5C22⋊C4116yescomplemented
192C3×Dic10—28no—
193D5×Dic3—48no—
194C2×C3×#41—58no—
195C2×C3×#41—104no—
196C2×C3×#41—104no—
197C22×C3×Q8—51no—
198C22×C3×D4—51no—
199C22×C3×D4—51no—
200C22×C3×D4—51no—
201C23×C3×C4—51no—
202C23×C3×C4—51no—
203C23×C3×C4C2×D511yescharacteristic
204C23×Dic3—52no—
205C2×#217—52no—
206C2×#217—52no—
207C2×#217—52no—
208C2×#217—52no—
209C2×#217C2×D512yes—
210#926—104no—
211C2×C4⋊Dic3—51no—
212C2×C4⋊Dic3—51no—
213C2×C4⋊Dic3—52no—
214C2×C4⋊Dic3—104no—
215C2×C4⋊Dic3C2×D511yescharacteristic
216C2×C4⋊Dic3C2×D511yescharacteristic
217C2×C4×Dic3—52no—
218C3⋊#95—52no—
219C3⋊#95—52no—
220C3⋊#95—52no—
221C3⋊#95C2×D512yes—
222C24×C5C22×D311yescharacteristic
223C23×D5C22×D311yescharacteristic
224C23×D5C22×D311yescharacteristic
225C22×C4×C5—22no—
226C22×C4×C5—22no—
227C22×C4×C5—32no—
228C22×C4×C5—32no—
229C22×C4×C5C2×Dic314yescomplemented
230C22×C4×C5C22×D311yescharacteristic
231C22×C4×C5C22×D311yescharacteristic
232C2×C22⋊D5—22no—
233C2×C22⋊D5—22no—
234C2×C22⋊D5—22no—
235C2×C22⋊D5—22no—
236C2×C22⋊D5C2×Dic314yes—
237C2×C22⋊D5C2×Dic314yescomplemented
238C22×Dic5—32no—
239C22×Dic5—32no—
240C22×Dic5C22×D311yescharacteristic
241C22×Dic5C22×D311yescharacteristic
242#709—232no—
243C2×D20—22no—
244C2×D20—22no—
245C2×D20C2×Dic314yes—
246C2×C4×D5—22no—
247C2×C4×D5—22no—
248C2×C4×D5—64no—
249C2×C4×D5—122no—
250C2×C4×D5—122no—
251C2×C4×D5C2×Dic314yes—
252C2×C4×D5C2×Dic314yescomplemented
253C2×C4×D5#6714yes—
254C2×C4×D5#6714yes—
255C2×Dic10—22no—
256C2×Dic10—22no—
257C2×Dic10C2×Dic314yescomplemented
258C5×C4⋊C4—62no—
259C5×C4⋊C4—62no—
260C5×C22⋊C4—122no—
261C22⋊Dic5—122no—
262#685—64no—
263#685—122no—
264#685—122no—
265C4⋊Dic5—62no—
266C4⋊Dic5—62no—
267#683—64no—
268C4×Dic5—64no—
269C22×#41—51no—
270C2×#117—151no—
271C22×C4⋊C4—151no—
272#391—152no—
273#390—152no—
274#386—152no—
275#386—152no—
276#380—31no—
277#380—151no—
278#380—151no—
279#380—151no—
280C22×C3×C5—22no—
281C22×C3×C5—22no—
282C22×C3×C5—22no—
283C22×C3×C5—41no—
284C22×C3×C5—41no—
285C22×C3×C5—41no—
286C22×C3×C5—41no—
287C22×C3×C5C23×C411yescharacteristic
288C22×C3×C5C22×D411yescharacteristic
289C22×C3×C5C22×D411yescharacteristic
290C22×C3×C5H(5,𝔽2)11yescharacteristic
291C22×C3×C5H(5,𝔽2)11yescharacteristic
292C22×C3×C52−1+411yescharacteristic
293C22×C3×C52−1+411yescharacteristic
294C2×C3×D5—22no—
295C2×C3×D5—22no—
296C2×C3×D5—22no—
297C2×C3×D5—22no—
298C2×C3×D5—22no—
299C2×C3×D5—22no—
300C2×C3×D5—22no—
301C2×C3×D5—22no—
302C2×C3×D5—22no—
303C2×C3×D5—41no—
304C2×C3×D5—41no—
305C2×C3×D5—41no—
306C2×C3×D5—41no—
307C2×C3×D5C2×C22⋊C414yes—
308C3×C4×C5—22no—
309C3×C4×C5C2×C22⋊C414yes—
310Dic15—42no—
311Dic15—42no—
312C3×Dic5—22no—
313C3×Dic5C2×C22⋊C414yes—
314C5×Dic3—42no—
315C5×Dic3—42no—
316C24×C3—51no—
317C24×C3—51no—
318C24×C3C22×D511yescharacteristic
319C3×#41—1032no—
320C2×C3×Q8—54no—
321C2×C3×Q8—102no—
322C2×C3×Q8—102no—
323C2×C3×D4—54no—
324C2×C3×D4—54no—
325C2×C3×D4—54no—
326C2×C3×D4—102no—
327C2×C3×D4—102no—
328C2×C3×D4—102no—
329C2×C3×D4—102no—
330C2×C3×D4—102no—
331C2×C3×D4—102no—
332C22×C3×C4—22no—
333C22×C3×C4—22no—
334C22×C3×C4—51no—
335C22×C3×C4—54no—
336C22×C3×C4—54no—
337C22×C3×C4—54no—
338C22×C3×C4—51no—
339C22×C3×C4—54no—
340C22×C3×C4—102no—
341C22×C3×C4—102no—
342C22×C3×C4C4×D514yescomplemented
343C22×C3×C4C22×D511yescharacteristic
344C22×C3×C4C22×D511yescharacteristic
345C22×Dic3—52no—
346C22×Dic3—52no—
347C22×Dic3—104no—
348C22×Dic3—202no—
349C22×Dic3—202no—
350C22×Dic3C22×D512yes—
351C22×Dic3C22×D512yes—
352#217—42no—
353#217—104no—
354#217—202no—
355#217—202no—
356#217—202no—
357C4⋊Dic3—22no—
358C4⋊Dic3—22no—
359C4⋊Dic3—104no—
360C4⋊Dic3—102no—
361C4⋊Dic3—102no—
362C4×Dic3—104no—
363C23×C5—21no—
364C23×C5—21no—
365C23×C5—21no—
366C23×C5—21no—
367C23×C5—21no—
368C23×C5—21no—
369C23×C5C22×Dic312yes—
370C23×C5C23×D311yescharacteristic
371C22×D5—21no—
372C22×D5—21no—
373C22×D5—21no—
374C22×D5—21no—
375C22×D5—21no—
376C22×D5—21no—
377C22×D5—21no—
378C22×D5—21no—
379C22×D5—21no—
380C22×D5—21no—
381C22×D5C22×Dic312yes—
382C22×D5C22×Dic312yes—
383C22×D5C2×#6712yes—
384C22×D5C2×#6712yes—
385C2×C4×C5—21no—
386C2×C4×C5—21no—
387C2×C4×C5—28no—
388C2×C4×C5—62no—
389C2×C4×C5—62no—
390C2×C4×C5—62no—
391C2×C4×C5—62no—
392C2×C4×C5—62no—
393C2×C4×C5—62no—
394C2×C4×C5C22×Dic312yes—
395C2×C4×C5C22×Dic312yes—
396C2×C4×C5C2×#6712yes—
397C2×C4×C5C2×#6712yes—
398C22⋊D5—28no—
399C22⋊D5—28no—
400C2×Dic5—21no—
401C2×Dic5—21no—
402C2×Dic5—62no—
403C2×Dic5—62no—
404C2×Dic5—62no—
405C2×Dic5—62no—
406C2×Dic5—62no—
407C2×Dic5—62no—
408C2×Dic5C22×Dic312yes—
409C2×Dic5C22×Dic312yes—
410C2×Dic5C2×#6712yes—
411C2×Dic5C2×#6712yes—
412D20—28no—
413C4×D5—28no—
414C4×D5—128no—
415C4×D5#217116yescomplemented
416Dic10—28no—
417C2×#41—58no—
418C2×#41—104no—
419C2×#41—104no—
420C22×Q8—51no—
421C22×D4—51no—
422C22×D4—51no—
423C22×D4—51no—
424C23×C4—51no—
425C23×C4—51no—
426C23×C4—152no—
427C23×C4D3×D511yescharacteristic
428#117—304no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—152no—
432C2×C4⋊C4—151no—
433C2×C4⋊C4—151no—
434C2×C4⋊C4—304no—
435C2×C22⋊C4—32no—
436C2×C22⋊C4—152no—
437C2×C22⋊C4—152no—
438C2×C22⋊C4—152no—
439C2×C22⋊C4—152no—
440C2×C42—152no—
441#95—32no—
442#95—152no—
443#95—152no—
444#95—152no—
445C2×C3×C5—42no—
446C2×C3×C5C22×C22⋊C411yescharacteristic
447C2×C3×C5#52011yescharacteristic
448C2×C3×C5#52011yescharacteristic
449C2×C3×C5#53511yescharacteristic
450C2×C3×C5#53611yescharacteristic
451C2×C3×C5#53711yescharacteristic
452C2×C3×C5#53711yescharacteristic
453C3×D5—24no—
454C3×D5—42no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—52no—
462C23×C3—52no—
463C23×C3—52no—
464C23×C3—52no—
465C23×C3—101no—
466C23×C3—101no—
467C23×C3—101no—
468C23×C3—101no—
469C23×C3—101no—
470C23×C3—101no—
471C23×C3—101no—
472C23×C3—101no—
473C23×C3—101no—
474C23×C3—101no—
475C23×C3C2×C4×D512yes—
476C23×C3C23×D511yescharacteristic
477C3×Q8—108no—
478C3×D4—108no—
479C3×D4—108no—
480C3×D4—108no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—28no—
484C2×C3×C4—52no—
485C2×C3×C4—52no—
486C2×C3×C4—52no—
487C2×C3×C4—516no—
488C2×C3×C4—52no—
489C2×C3×C4—101no—
490C2×C3×C4—101no—
491C2×C3×C4—108no—
492C2×C3×C4C2×C4×D512yes—
493C2×C3×C4C2×C4×D512yes—
494C2×C3×C4D4×D512yes—
495C2×C3×C4D4×D512yes—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—102no—
503C2×Dic3—102no—
504C2×Dic3—102no—
505C2×Dic3—102no—
506C2×Dic3—102no—
507C2×Dic3—102no—
508C2×Dic3—208no—
509C22×C5—22no—
510C22×C5—22no—
511C22×C5—22no—
512C22×C5—41no—
513C22×C5—41no—
514C22×C5—41no—
515C22×C5—41no—
516C22×C5#100911yescharacteristic
517C22×C5#100911yescharacteristic
518C22×C5#101011yescharacteristic
519C22×C5#101011yescharacteristic
520C22×C5C23×Dic311yescharacteristic
521C22×C5C22×#6711yescharacteristic
522C22×C5C22×#6711yescharacteristic
523C2×D5—22no—
524C2×D5—22no—
525C2×D5—22no—
526C2×D5—22no—
527C2×D5—22no—
528C2×D5—22no—
529C2×D5—22no—
530C2×D5—22no—
531C2×D5—22no—
532C2×D5—41no—
533C2×D5—41no—
534C2×D5—41no—
535C2×D5—41no—
536C2×D5C2×#21714yes—
537C4×C5—22no—
538C4×C5—122no—
539C4×C5—122no—
540C4×C5C2×#21714yes—
541Dic5—22no—
542Dic5—122no—
543Dic5—122no—
544Dic5C2×#21714yes—
545C24—51no—
546C24—51no—
547C24C2×D3×D511yescharacteristic
548#41—1032no—
549C2×Q8—54no—
550C2×Q8—102no—
551C2×Q8—102no—
552C2×D4—54no—
553C2×D4—54no—
554C2×D4—54no—
555C2×D4—102no—
556C2×D4—102no—
557C2×D4—102no—
558C2×D4—102no—
559C2×D4—102no—
560C2×D4—102no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—32no—
564C22×C4—32no—
565C22×C4—51no—
566C22×C4—54no—
567C22×C4—54no—
568C22×C4—54no—
569C22×C4—51no—
570C22×C4—54no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—152no—
574C22×C4—152no—
575C22×C4—304no—
576C22×C4—602no—
577C22×C4—602no—
578C22×C4D5×Dic314yescomplemented
579C22×C4C2×D3×D511yescharacteristic
580C22×C4C2×D3×D511yescharacteristic
581C4⋊C4—62no—
582C4⋊C4—62no—
583C4⋊C4—304no—
584C4⋊C4—302no—
585C4⋊C4—302no—
586C22⋊C4—122no—
587C22⋊C4—304no—
588C22⋊C4—602no—
589C22⋊C4—602no—
590C22⋊C4—602no—
591C42—304no—
592C3×C5#231111yescharacteristic, complemented, Hall
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—54no—
601C22×C3—102no—
602C22×C3—102no—
603C22×C3—102no—
604C22×C3—102no—
605C22×C3—102no—
606C22×C3—102no—
607C22×C3—102no—
608C22×C3—102no—
609C22×C3—102no—
610C22×C3—201no—
611C22×C3—201no—
612C22×C3—201no—
613C22×C3—201no—
614C22×C3C22×C4×D511yescharacteristic
615C22×C3C2×D4×D511yescharacteristic
616C22×C3C2×D4×D511yescharacteristic
617C22×C3#414411yescharacteristic
618C22×C3#414711yescharacteristic
619C22×C3#414911yescharacteristic
620C22×C3#415011yescharacteristic
621C3×C4—22no—
622C3×C4—54no—
623C3×C4—102no—
624C3×C4D5×C22⋊C414yes—
625Dic3—42no—
626Dic3—42no—
627Dic3—202no—
628Dic3—202no—
629C2×C5—42no—
630C2×C5#582511yescharacteristic
631C2×C5#582711yescharacteristic
632C2×C5#582711yescharacteristic
633C2×C5#583011yescharacteristic
634C2×C5#583311yescharacteristic
635C2×C5#583311yescharacteristic
636C2×C5C22×#21711yescharacteristic
637D5—24no—
638D5—42no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—52no—
646C23—52no—
647C23—52no—
648C23—52no—
649C23—101no—
650C23—101no—
651C23—101no—
652C23—101no—
653C23—101no—
654C23—101no—
655C23—101no—
656C23—101no—
657C23—101no—
658C23—101no—
659C23C2×D5×Dic312yes—
660C23C22×D3×D511yescharacteristic
661Q8—108no—
662D4—108no—
663D4—108no—
664D4—108no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—28no—
668C2×C4—52no—
669C2×C4—52no—
670C2×C4—52no—
671C2×C4—516no—
672C2×C4—52no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—101no—
680C2×C4—101no—
681C2×C4—108no—
682C2×C4—302no—
683C2×C4—302no—
684C2×C4—302no—
685C2×C4—302no—
686C2×C4—302no—
687C2×C4—302no—
688C2×C4—608no—
689C2×C4C2×D5×Dic312yes—
690C2×C4C2×D5×Dic312yes—
691C2×C4D5×#6712yes—
692C2×C4D5×#6712yes—
693C2×C3—42no—
694C2×C3—104no—
695C2×C3—202no—
696C2×C3C2×D5×C22⋊C411yescharacteristic
697C2×C3#6583811yescharacteristic
698C2×C3#6585711yescharacteristic
699C2×C3#6594111yescharacteristic
700C2×C3#6594211yescharacteristic
701C2×C3#6596211yescharacteristic
702C2×C3#6596311yescharacteristic
703C5#8408711yescharacteristic, complemented, Sylow
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—54no—
712C22—102no—
713C22—102no—
714C22—102no—
715C22—102no—
716C22—102no—
717C22—102no—
718C22—102no—
719C22—102no—
720C22—102no—
721C22—201no—
722C22—201no—
723C22—201no—
724C22—201no—
725C22#9200011yescharacteristic
726C22#9200111yescharacteristic
727C22#9201811yescharacteristic
728C22#9201911yescharacteristic
729C22C22×D5×Dic311yescharacteristic
730C22C2×D5×#6711yescharacteristic
731C22C2×D5×#6711yescharacteristic
732C4—22no—
733C4—54no—
734C4—102no—
735C4—122no—
736C4—122no—
737C4—602no—
738C4—602no—
739C4D5×#21714yes—
740C3#1060573411yescharacteristic, complemented, Sylow
741C2—42no—
742C2—104no—
743C2—202no—
744C2#1175430311yescharacteristic
745C2#1175431211yescharacteristic
746C2#1175431411yescharacteristic
747C2#1175449911yescharacteristic
748C2#1175450911yescharacteristic
749C2#1175463511yescharacteristic
750C2C2×D5×#21711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×#709C2
hypercenterC23×C4D3×D5
hypocenterC3×C5#2311
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×D5×C4⋊Dic3C2semidirect
3. C2×#91358C2semidirect
4. #11751313C2semidirect
5. C5×#5212C2semidirect
6. #11749518C2semidirect
7. #11749489C2semidirect
8. #11748896C2semidirect
9. #11748759C2semidirect
10. #11748759C2semidirect
11. #11748672C2semidirect
18. C2×C3×#709C4semidirect
58. C22×C3×C4×C5C2×C4semidirect
70. C2×C3×C22⋊D5C2×C4semidirect
80. C2×C3×C4×D5C2×C4semidirect
85. C2×C3×Dic10C2×C4semidirect
110. #5212D5semidirect
116. C2×#709Dic3semidirect
191. C3×C4×D5C22⋊C4semidirect
229. C22×C4×C5C2×Dic3semidirect
237. C2×C22⋊D5C2×Dic3semidirect
252. C2×C4×D5C2×Dic3semidirect
257. C2×Dic10C2×Dic3semidirect
342. C22×C3×C4C4×D5semidirect
415. C4×D5#217semidirect
578. C22×C4D5×Dic3semidirect
592. C3×C5#2311semidirect
703. C5#84087semidirect
740. C3#10605734semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#7092
C2×D5×C4⋊Dic32
C2×#913582
#117513132
C5×#52122
#117495182
#117494892
#117488962
#117487592
#117486722
#106057343
#840875