Finite Group Databasebeta

← #14322739

Subgroups — #14322739

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4023C211yesmaximal, characteristic
2#11751052C211yesmaximal, characteristic
3C5×#4951C211yesmaximal, characteristic
4#11749506C211yesmaximal, characteristic
5#11749506C211yesmaximal, characteristic
6#11749486C211yesmaximal, characteristic
7#11749485C211yesmaximal, characteristic
8#11748834C211yesmaximal, characteristic, complemented
9C4×#6668C211yesmaximal, characteristic, complemented
10#11748691C211yesmaximal, characteristic, complemented
11#11748690C211yesmaximal, characteristic, complemented
12#11748638C211yesmaximal, characteristic, complemented
13#11748601C211yesmaximal, characteristic, complemented
14#11748590C211yesmaximal, characteristic, complemented
15#11748580C211yesmaximal, characteristic, complemented
16#10607187—31nomaximal, Hall
17C23×C3×Dic5C2211yescharacteristic
18C2×C3×C5×C22⋊C4C2211yescharacteristic
19C2×#6719C2211yescharacteristic
20C2×#6719C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C5×#217C2211yescharacteristic
24C2×C5×#217C2211yescharacteristic
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C2×C4×C5×Dic3C2211yescharacteristic
27C2×C3×C22⋊Dic5C2211yescharacteristic
28C2×C3×#683C2211yescharacteristic
29C2×C3×#683C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31C2×C3×C4×Dic5C2211yescharacteristic
32C3×#4023C418yescomplemented
33C2×#6668C2211yescharacteristic
34C2×#6668C2211yescharacteristic
35C2×#6668C2211yescharacteristic
36C2×#6668C2211yescharacteristic
37C2×#6668C2211yescharacteristic
38C2×#6668C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40C2×Dic3×Dic5C2211yescharacteristic
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43C5×C3⋊#95C2211yescharacteristic
44C5×C3⋊#95C2211yescharacteristic
45#90994C2211yescharacteristic
46#90994C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#82231—51nomaximal, Hall
54C2×#4023D311yescharacteristic
55C5×#388—31no—
56#65267—31no—
57#65265—31no—
58#65240—31no—
59#65234—31no—
60#65233—31no—
61#65231—31no—
62#65231—31no—
63#65222—31no—
64C4×#683—31no—
65#64944—31no—
66#64941—31no—
67#64939—31no—
68#64938—31no—
69C24×C3×C5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×Dic15C2311yescharacteristic
73C22×Dic15C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×C5×Dic3C2311yescharacteristic
77C22×C5×Dic3C2311yescharacteristic
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C3×Dic5—22no—
81C22×C3×Dic5—22no—
82C22×C3×Dic5C2×C414yes—
83C22×C3×Dic5C2311yescharacteristic
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C3×C5×C22⋊C4C2×C414yes—
88#6719—41no—
89#6719—41no—
90C4⋊Dic15—41no—
91C4×Dic15—41no—
92C5×#217—41no—
93C5×#217—41no—
94C5×C4⋊Dic3—41no—
95C4×C5×Dic3—41no—
96C3×C22⋊Dic5C2×C414yes—
97C3×#683C2×C414yes—
98C3×#683C2×C414yes—
99C3×C4×Dic5C2×C414yes—
100C3×C4×Dic5C2×C414yes—
101#6668—22no—
102#6668—22no—
103#6668—22no—
104#6668—22no—
105#6668—41no—
106#6668—41no—
107Dic3×Dic5—41no—
108Dic3×Dic5—41no—
109C2×C3×#117—51no—
110#5212—51no—
111#5212—51no—
112#4980—51no—
113#4980—51no—
114#4980—51no—
115#4980—51no—
116#4951—51no—
117#4951—51no—
118#4951—51no—
119#4951D511yescharacteristic
120#4936—51no—
121#4935—51no—
122C4×C4⋊Dic3—51no—
123C4×C4⋊Dic3—51no—
124C23×Dic5C2×D311yescharacteristic
125C2×C5×C4⋊C4—31no—
126C2×C5×C22⋊C4—31no—
127C2×C5×C22⋊C4—31no—
128C2×C5×C22⋊C4C2×D311yescharacteristic
129C2×C42×C5—31no—
130C2×C22⋊Dic5—31no—
131C2×C22⋊Dic5—31no—
132C2×C22⋊Dic5C2×D311yescharacteristic
133C2×C4⋊Dic5—31no—
134C2×#683—31no—
135C2×#683—31no—
136C2×#683—31no—
137C2×#683—31no—
138C2×#683—31no—
139C2×#683—31no—
140C2×#683C2×D311yescharacteristic
141C2×#683C2×D311yescharacteristic
142C2×C4×Dic5—31no—
143C2×C4×Dic5—31no—
144C2×C4×Dic5—31no—
145C2×C4×Dic5C2×D311yescharacteristic
146C2×C4×Dic5C2×D311yescharacteristic
147#4023Dic318yescomplemented
148C5×#95—31no—
149C5×#95—31no—
150#3963—31no—
151#3963—31no—
152#3963—31no—
153#3963—31no—
154#3963—31no—
155#3963—31no—
156#3963—31no—
157#3963—31no—
158#3963—31no—
159#3963—31no—
160#2314—151noSylow
161C23×C3×C5—21no—
162C23×C3×C5—21no—
163C23×C3×C5—21no—
164C23×C3×C5—21no—
165C23×C3×C5—21no—
166C23×C3×C5—21no—
167C23×C3×C5C22×C412yes—
168C23×C3×C5C2411yescharacteristic
169C2×C3×C4×C5—21no—
170C2×C3×C4×C5—21no—
171C2×C3×C4×C5—21no—
172C2×C3×C4×C5—21no—
173C2×C3×C4×C5C22×C412yes—
174C2×C3×C4×C5C22×C412yes—
175C2×Dic15—21no—
176C2×Dic15—21no—
177C2×Dic15—21no—
178C2×Dic15—21no—
179C2×Dic15—21no—
180C2×Dic15—21no—
181C2×Dic15—21no—
182C2×Dic15—21no—
183C2×Dic15—21no—
184C2×Dic15—21no—
185C2×Dic15—21no—
186C2×Dic15—21no—
187C2×C5×Dic3—21no—
188C2×C5×Dic3—21no—
189C2×C5×Dic3—21no—
190C2×C5×Dic3—21no—
191C2×C5×Dic3—21no—
192C2×C5×Dic3—21no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3—21no—
199C2×C3×Dic5—21no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—28no—
206C2×C3×Dic5C22×C412yes—
207C2×C3×Dic5C22×C412yes—
208C2×C3×Dic5C22×C412yes—
209C2×C3×Dic5C22×C412yes—
210C2×C3×Dic5#4112yes—
211C2×C3×Dic5#4112yes—
212C23×C3×C4—51no—
213C3×#117—58no—
214C2×C3×C4⋊C4—51no—
215C2×C3×C4⋊C4—51no—
216C2×C3×C22⋊C4—51no—
217C2×C3×C22⋊C4C2×D511yescharacteristic
218C2×C3×C42—51no—
219C2×C3×C42—51no—
220C2×#217—51no—
221C2×#217—51no—
222C2×#217C2×D511yescharacteristic
223C2×#217C2×D511yescharacteristic
224C2×C4⋊Dic3—51no—
225C2×C4⋊Dic3—51no—
226C2×C4⋊Dic3—51no—
227C2×C4⋊Dic3—51no—
228C2×C4⋊Dic3—51no—
229C2×C4⋊Dic3—51no—
230C2×C4⋊Dic3—51no—
231C2×C4⋊Dic3C2×D511yescharacteristic
232C2×C4×Dic3—51no—
233C2×C4×Dic3—51no—
234C2×C4×Dic3—51no—
235C2×C4×Dic3C2×D511yescharacteristic
236C3⋊#95—51no—
237C3⋊#95—51no—
238C3⋊#95—51no—
239C3⋊#95—51no—
240C3⋊#95—51no—
241C3⋊#95—51no—
242C3⋊#95—51no—
243C3⋊#95—51no—
244C3⋊#95—51no—
245C3⋊#95—51no—
246C3⋊#95C2×D511yescharacteristic
247C3⋊#95C2×D511yescharacteristic
248C24×C5C22×D311yescharacteristic
249C22×C4×C5—31no—
250C22×C4×C5—31no—
251C22×C4×C5—31no—
252C22×C4×C5—31no—
253C22×C4×C5C22×D311yescharacteristic
254C22×C4×C5C22×D311yescharacteristic
255C22×Dic5—22no—
256C22×Dic5—22no—
257C22×Dic5—31no—
258C22×Dic5—31no—
259C22×Dic5—31no—
260C22×Dic5—31no—
261C22×Dic5C2×Dic314yes—
262C22×Dic5C22×D311yescharacteristic
263C22×Dic5C22×D311yescharacteristic
264C22×Dic5C22×D311yescharacteristic
265C22×Dic5C22×D311yescharacteristic
266C5×C4⋊C4—121no—
267C5×C22⋊C4—121no—
268C5×C22⋊C4—121no—
269C5×C22⋊C4C2×Dic314yes—
270C42×C5—121no—
271C22⋊Dic5—121no—
272C22⋊Dic5—121no—
273C22⋊Dic5C2×Dic314yes—
274C4⋊Dic5—121no—
275#683—62no—
276#683—62no—
277#683—62no—
278#683—62no—
279#683—121no—
280#683—121no—
281#683C2×Dic314yes—
282#683C2×Dic314yes—
283C4×Dic5—121no—
284C4×Dic5—121no—
285C4×Dic5—121no—
286C4×Dic5C2×Dic314yes—
287C4×Dic5C2×Dic314yes—
288C2×#117—51no—
289#388—31no—
290#388—151no—
291#388—151no—
292#388—151no—
293#387—151no—
294#387—151no—
295#387—151no—
296#387—151no—
297#384—151no—
298#382—151no—
299#380—151no—
300#380—151no—
301C4×C4⋊C4—151no—
302C4×C4⋊C4—151no—
303C22×C3×C5—22no—
304C22×C3×C5—22no—
305C22×C3×C5—22no—
306C22×C3×C5—41no—
307C22×C3×C5—41no—
308C22×C3×C5—41no—
309C22×C3×C5—41no—
310C22×C3×C5C23×C411yescharacteristic
311C22×C3×C5C2×#4111yescharacteristic
312C22×C3×C5C2×#4111yescharacteristic
313C22×C3×C5H(5,𝔽2)11yescharacteristic
314C22×C3×C5H(5,𝔽2)11yescharacteristic
315C22×C3×C52−1+411yescharacteristic
316C22×C3×C52−1+411yescharacteristic
317C3×C4×C5—22no—
318C3×C4×C5—22no—
319Dic15—41no—
320Dic15—41no—
321Dic15—41no—
322Dic15—41no—
323C3×Dic5—22no—
324C3×Dic5—22no—
325C3×Dic5—22no—
326C3×Dic5#11714yes—
327C5×Dic3—41no—
328C5×Dic3—41no—
329C5×Dic3—41no—
330C5×Dic3—41no—
331C24×C3C22×D511yescharacteristic
332C22×C3×C4—51no—
333C22×C3×C4—54no—
334C22×C3×C4—51no—
335C22×C3×C4—51no—
336C22×C3×C4—51no—
337C22×C3×C4—102no—
338C22×C3×C4—102no—
339C22×C3×C4C22×D511yescharacteristic
340C22×C3×C4C22×D511yescharacteristic
341C22×Dic3—51no—
342C22×Dic3—51no—
343C22×Dic3—51no—
344C22×Dic3—51no—
345C22×Dic3C22×D511yescharacteristic
346C22×Dic3C22×D511yescharacteristic
347C22×Dic3C22×D511yescharacteristic
348C22×Dic3C22×D511yescharacteristic
349C3×C4⋊C4—54no—
350C3×C4⋊C4—54no—
351C3×C22⋊C4—54no—
352C3×C22⋊C4C4×D514yes—
353C3×C42—54no—
354C3×C42—54no—
355#217—41no—
356#217—41no—
357#217—201no—
358#217—201no—
359C4⋊Dic3—41no—
360C4⋊Dic3—102no—
361C4⋊Dic3—102no—
362C4⋊Dic3—102no—
363C4⋊Dic3—102no—
364C4⋊Dic3—201no—
365C4⋊Dic3—201no—
366C4⋊Dic3—201no—
367C4×Dic3—41no—
368C4×Dic3—201no—
369C4×Dic3—201no—
370C4×Dic3—201no—
371C23×C5—21no—
372C23×C5—21no—
373C23×C5—21no—
374C23×C5—21no—
375C23×C5—21no—
376C23×C5—21no—
377C23×C5C22×Dic312yes—
378C23×C5C23×D311yescharacteristic
379C2×C4×C5—21no—
380C2×C4×C5—21no—
381C2×C4×C5—21no—
382C2×C4×C5—21no—
383C2×C4×C5—61no—
384C2×C4×C5—61no—
385C2×C4×C5—61no—
386C2×C4×C5—61no—
387C2×C4×C5—61no—
388C2×C4×C5—61no—
389C2×C4×C5—61no—
390C2×C4×C5—61no—
391C2×C4×C5—61no—
392C2×C4×C5—61no—
393C2×C4×C5—61no—
394C2×C4×C5—61no—
395C2×C4×C5C22×Dic312yes—
396C2×C4×C5C22×Dic312yes—
397C2×Dic5—21no—
398C2×Dic5—21no—
399C2×Dic5—21no—
400C2×Dic5—21no—
401C2×Dic5—21no—
402C2×Dic5—21no—
403C2×Dic5—28no—
404C2×Dic5—61no—
405C2×Dic5—61no—
406C2×Dic5—61no—
407C2×Dic5—61no—
408C2×Dic5—61no—
409C2×Dic5—61no—
410C2×Dic5—61no—
411C2×Dic5—61no—
412C2×Dic5—61no—
413C2×Dic5—61no—
414C2×Dic5—61no—
415C2×Dic5—61no—
416C2×Dic5#23512yes—
417C2×Dic5#23512yes—
418C2×Dic5C22×Dic312yes—
419C2×Dic5C22×Dic312yes—
420C2×Dic5C22×Dic312yes—
421C2×Dic5C22×Dic312yes—
422C23×C4—51no—
423#117—58no—
424C2×C4⋊C4—31no—
425C2×C4⋊C4—51no—
426C2×C4⋊C4—51no—
427C2×C4⋊C4—151no—
428C2×C4⋊C4—151no—
429C2×C4⋊C4—151no—
430C2×C4⋊C4—151no—
431C2×C4⋊C4—151no—
432C2×C4⋊C4—151no—
433C2×C4⋊C4—151no—
434C2×C22⋊C4—31no—
435C2×C22⋊C4—31no—
436C2×C22⋊C4—51no—
437C2×C22⋊C4—151no—
438C2×C22⋊C4—151no—
439C2×C22⋊C4D3×D511yescharacteristic
440C2×C42—31no—
441C2×C42—51no—
442C2×C42—51no—
443C2×C42—151no—
444C2×C42—151no—
445C2×C42—151no—
446#95—31no—
447#95—31no—
448#95—151no—
449#95—151no—
450#95—151no—
451#95—151no—
452#95—151no—
453#95—151no—
454#95—151no—
455#95—151no—
456#95—151no—
457#95—151no—
458C2×C3×C5—42no—
459C2×C3×C5C2×#11711yescharacteristic
460C2×C3×C5#52011yescharacteristic
461C2×C3×C5#52011yescharacteristic
462C2×C3×C5#54011yescharacteristic
463C2×C3×C5#54111yescharacteristic
464C2×C3×C5#54211yescharacteristic
465C2×C3×C5#54211yescharacteristic
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3C2×C4×D512yes—
473C23×C3C23×D511yescharacteristic
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—52no—
479C2×C3×C4—52no—
480C2×C3×C4—52no—
481C2×C3×C4—52no—
482C2×C3×C4—52no—
483C2×C3×C4—52no—
484C2×C3×C4—108no—
485C2×C3×C4—101no—
486C2×C3×C4—101no—
487C2×C3×C4—101no—
488C2×C3×C4—101no—
489C2×C3×C4—101no—
490C2×C3×C4—101no—
491C2×C3×C4C2×C4×D512yes—
492C2×C3×C4C2×C4×D512yes—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—101no—
506C2×Dic3—101no—
507C2×Dic3—101no—
508C2×Dic3—101no—
509C2×Dic3—101no—
510C2×Dic3—101no—
511C2×Dic3—101no—
512C2×Dic3—101no—
513C2×Dic3—101no—
514C2×Dic3—101no—
515C2×Dic3—101no—
516C2×Dic3—101no—
517C22×C5—22no—
518C22×C5—22no—
519C22×C5—22no—
520C22×C5—41no—
521C22×C5—41no—
522C22×C5—41no—
523C22×C5—41no—
524C22×C5C2×#23511yescharacteristic
525C22×C5C2×#23511yescharacteristic
526C22×C5#100911yescharacteristic
527C22×C5#100911yescharacteristic
528C22×C5#101011yescharacteristic
529C22×C5#101011yescharacteristic
530C22×C5C23×Dic311yescharacteristic
531C4×C5—22no—
532C4×C5—22no—
533C4×C5—121no—
534C4×C5—121no—
535C4×C5—121no—
536C4×C5—121no—
537Dic5—22no—
538Dic5—22no—
539Dic5—22no—
540Dic5—121no—
541Dic5—121no—
542Dic5—121no—
543Dic5—121no—
544Dic5#92614yes—
545C24C2×D3×D511yescharacteristic
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—51no—
551C22×C4—54no—
552C22×C4—51no—
553C22×C4—51no—
554C22×C4—51no—
555C22×C4—102no—
556C22×C4—102no—
557C22×C4—151no—
558C22×C4—151no—
559C22×C4—151no—
560C22×C4—151no—
561C22×C4C2×D3×D511yescharacteristic
562C22×C4C2×D3×D511yescharacteristic
563C4⋊C4—54no—
564C4⋊C4—54no—
565C4⋊C4—121no—
566C4⋊C4—302no—
567C4⋊C4—302no—
568C4⋊C4—302no—
569C4⋊C4—302no—
570C4⋊C4—601no—
571C4⋊C4—601no—
572C4⋊C4—601no—
573C22⋊C4—54no—
574C22⋊C4—121no—
575C22⋊C4—121no—
576C22⋊C4—601no—
577C22⋊C4—601no—
578C22⋊C4D5×Dic314yes—
579C42—54no—
580C42—54no—
581C42—121no—
582C42—601no—
583C42—601no—
584C42—601no—
585C3×C5#231411yescharacteristic, complemented, Hall
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3C22×C4×D511yescharacteristic
594C22×C3#414411yescharacteristic
595C22×C3#414411yescharacteristic
596C22×C3D5×#4111yescharacteristic
597C22×C3D5×#4111yescharacteristic
598C22×C3#415011yescharacteristic
599C22×C3#415011yescharacteristic
600C3×C4—22no—
601C3×C4—22no—
602C3×C4—54no—
603C3×C4—102no—
604C3×C4—102no—
605C3×C4—102no—
606Dic3—41no—
607Dic3—41no—
608Dic3—41no—
609Dic3—41no—
610Dic3—201no—
611Dic3—201no—
612Dic3—201no—
613Dic3—201no—
614C2×C5—42no—
615C2×C5#551811yescharacteristic
616C2×C5#553411yescharacteristic
617C2×C5#553411yescharacteristic
618C2×C5#553511yescharacteristic
619C2×C5C2×#92611yescharacteristic
620C2×C5#582711yescharacteristic
621C2×C5#582711yescharacteristic
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23C2×D5×Dic312yes—
629C23C22×D3×D511yescharacteristic
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—52no—
635C2×C4—52no—
636C2×C4—52no—
637C2×C4—52no—
638C2×C4—52no—
639C2×C4—52no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—108no—
653C2×C4—101no—
654C2×C4—101no—
655C2×C4—101no—
656C2×C4—101no—
657C2×C4—101no—
658C2×C4—101no—
659C2×C4—301no—
660C2×C4—301no—
661C2×C4—301no—
662C2×C4—301no—
663C2×C4—301no—
664C2×C4—301no—
665C2×C4—301no—
666C2×C4—301no—
667C2×C4—301no—
668C2×C4—301no—
669C2×C4—301no—
670C2×C4—301no—
671C2×C4C2×D5×Dic312yes—
672C2×C4C2×D5×Dic312yes—
673C2×C3—42no—
674C2×C3D5×#11711yescharacteristic
675C2×C3#6588011yescharacteristic
676C2×C3#6588011yescharacteristic
677C2×C3#6594911yescharacteristic
678C2×C3#6599611yescharacteristic
679C2×C3#6600311yescharacteristic
680C2×C3#6603511yescharacteristic
681C5#8223111yescharacteristic, complemented, Sylow
682C22—22no—
683C22—22no—
684C22—22no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22D5×#23511yescharacteristic
690C22D5×#23511yescharacteristic
691C22#9202011yescharacteristic
692C22#9202011yescharacteristic
693C22#9202711yescharacteristic
694C22#9202711yescharacteristic
695C22C22×D5×Dic311yescharacteristic
696C4—22no—
697C4—22no—
698C4—54no—
699C4—102no—
700C4—102no—
701C4—102no—
702C4—121no—
703C4—121no—
704C4—121no—
705C4—121no—
706C4—601no—
707C4—601no—
708C4—601no—
709C4—601no—
710C3#1060718711yescharacteristic, complemented, Sylow
711C2—42no—
712C2#1175309611yescharacteristic
713C2#1175309711yescharacteristic
714C2#1175309811yescharacteristic
715C2#1175319011yescharacteristic
716C2D5×#92611yescharacteristic
717C2#1175492311yescharacteristic
718C2#1175492311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2314
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
8. #11748834C2semidirect
9. C4×#6668C2semidirect
10. #11748691C2semidirect
11. #11748690C2semidirect
12. #11748638C2semidirect
13. #11748601C2semidirect
14. #11748590C2semidirect
15. #11748580C2semidirect
32. C3×#4023C4semidirect
147. #4023Dic3semidirect
585. C3×C5#2314semidirect
681. C5#82231semidirect
710. C3#10607187semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40232
#117510522
C5×#49512
#117495062
#117494862
#117494852
#117488342
C4×#66682
#117486912
#117486902
#117486382
#117486012
#117485902
#117485802
#106071873
#822315