Finite Group Databasebeta

← #14331068

Subgroups — #14331068

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4043C211yesmaximal, characteristic
2#11751081C211yesmaximal, characteristic, complemented
3C5×#4980C211yesmaximal, characteristic, complemented
4#11748865C211yesmaximal, characteristic, complemented
5#11748857C211yesmaximal, characteristic, complemented
6#11748791C211yesmaximal, characteristic
7#11748772C211yesmaximal, characteristic
8#11748771C211yesmaximal, characteristic
9#11748770C211yesmaximal, characteristic
10#11748738C211yesmaximal, characteristic
11#11748737C211yesmaximal, characteristic
12#11748698C211yesmaximal, characteristic, complemented
13#11748697C211yesmaximal, characteristic, complemented
14#11748672C211yesmaximal, characteristic, complemented
15#11748672C211yesmaximal, characteristic, complemented
16#10607045—31nomaximal, Hall
17C22×C3×C4×D5C2211yescharacteristic
18C22×C3×Dic10C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C2×C4×Dic15C2211yescharacteristic
22C2×C5×C4⋊Dic3C2211yescharacteristic
23C2×C4×C5×Dic3C2211yescharacteristic
24C2×C3×#685C2211yescharacteristic
25C2×C3×#685C2211yescharacteristic
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C3×#4043C418yescomplemented
29C2×#6668C2211yescharacteristic
30C2×#6668C2211yescharacteristic
31C2×#6668C2211yescharacteristic
32C2×#6668C2211yescharacteristic
33C2×#6665C2211yescharacteristic
34C2×#6665C2211yescharacteristic
35C2×#6665C2211yescharacteristic
36C2×#6665C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39#91115C2211yescharacteristic
40#91115C2211yescharacteristic
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43C5×C3⋊#95C2211yescharacteristic
44C5×C3⋊#95C2211yescharacteristic
45C5×C3⋊#95C2211yescharacteristic
46C5×C3⋊#95C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#82750—51nomaximal, Hall
54C2×#4043D311yescharacteristic
55C5×#387—31no—
56#65279—31no—
57#65270—31no—
58#65262—31no—
59#65229—31no—
60#65217—31no—
61#64959—31no—
62#64958—31no—
63#64956—31no—
64#64953—31no—
65#64943—31no—
66#64942—31no—
67#64935—31no—
68#64935—31no—
69C23×C3×D5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×Dic15C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×C5×Dic3C2311yescharacteristic
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C22×C3×Dic5C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C2×C3×C4×D5—41no—
85C2×C3×C4×D5—41no—
86C2×C3×C4×D5C2×C414yes—
87C2×C3×Dic10—41no—
88C2×C3×Dic10—41no—
89C2×C3×Dic10C2×C414yes—
90C3×C5×C4⋊C4C2×C414yes—
91C4⋊Dic15—41no—
92C4×Dic15—41no—
93C5×C4⋊Dic3—41no—
94C4×C5×Dic3—41no—
95C3×#685C2×C414yes—
96C3×#685C2×C414yes—
97C3×C4⋊Dic5C2×C414yes—
98C3×C4⋊Dic5C2×C414yes—
99#6668—41no—
100#6668—41no—
101#6668—41no—
102#6668—41no—
103#6665—41no—
104#6665—41no—
105#6665—41no—
106#6665—41no—
107Dic3×Dic5—41no—
108Dic3×Dic5—41no—
109C2×C3×C22⋊Q8—51no—
110#5229—51no—
111#5229—51no—
112#5212—51no—
113#5211—51no—
114#4984—51no—
115#4984—51no—
116#4980—51no—
117#4980—51no—
118#4980—51no—
119#4980D511yescharacteristic, complemented
120#4951—51no—
121#4951—51no—
122#4951—51no—
123#4951—51no—
124C22×C4×D5C2×D311yescharacteristic
125C22×Dic10C2×D311yescharacteristic
126C2×C5×C4⋊C4—31no—
127C2×C5×C4⋊C4C2×D311yescharacteristic
128C2×C42×C5—31no—
129C2×#685—31no—
130C2×#685—31no—
131C2×#685—31no—
132C2×#685—31no—
133C2×#685C2×D311yescharacteristic
134C2×#685C2×D311yescharacteristic
135C2×C4⋊Dic5—31no—
136C2×C4⋊Dic5C2×D311yescharacteristic
137C2×C4⋊Dic5C2×D311yescharacteristic
138C2×#683—31no—
139C2×#683—31no—
140C2×#683—31no—
141C2×#683—31no—
142C2×C4×Dic5—31no—
143C2×C4×Dic5—31no—
144C2×C4×Dic5—31no—
145#4043Dic318yescomplemented
146C5×#95—31no—
147C5×#95—31no—
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#2378—151noSylow
161C23×C3×C5C2411yescharacteristic
162C22×C3×D5—21no—
163C22×C3×D5—21no—
164C22×C3×D5—21no—
165C22×C3×D5—21no—
166C22×C3×D5—21no—
167C22×C3×D5—21no—
168C22×C3×D5C22×C412yes—
169C2×C3×C4×C5—21no—
170C2×C3×C4×C5—21no—
171C2×C3×C4×C5—21no—
172C2×C3×C4×C5—21no—
173C2×C3×C4×C5—21no—
174C2×C3×C4×C5—21no—
175C2×C3×C4×C5C22×C412yes—
176C2×C3×C4×C5C22×C412yes—
177C2×C3×C4×C5C22×C412yes—
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×Dic15—21no—
188C2×Dic15—21no—
189C2×Dic15—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×C5×Dic3—21no—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—21no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5C22×C412yes—
209C2×C3×Dic5C22×C412yes—
210C2×C3×Dic5C22×C412yes—
211C3×C4×D5—44no—
212C3×Dic10—44no—
213C22×C3×Q8—51no—
214C23×C3×C4—51no—
215C3×C22⋊Q8—58no—
216C2×C3×C4⋊C4—51no—
217C2×C3×C4⋊C4—51no—
218C2×C3×C4⋊C4C2×D511yescharacteristic
219C2×C3×C22⋊C4—51no—
220C2×C3×C22⋊C4—51no—
221C2×#217—51no—
222C2×#217—51no—
223C2×#217—51no—
224C2×#217—51no—
225C2×C4⋊Dic3—51no—
226C2×C4⋊Dic3—51no—
227C2×C4⋊Dic3—51no—
228C2×C4⋊Dic3—51no—
229C2×C4⋊Dic3—51no—
230C2×C4⋊Dic3C2×D511yescharacteristic
231C2×C4×Dic3—51no—
232C2×C4×Dic3—51no—
233C2×C4×Dic3—51no—
234C2×C4×Dic3C2×D511yescharacteristic
235C3⋊#95—51no—
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⋊#95C2×D511yescharacteristic
246C3⋊#95C2×D511yescharacteristic
247C3⋊#95C2×D511yescharacteristic
248C3⋊#95C2×D511yescharacteristic
249C23×D5C22×D311yescharacteristic
250C22×C4×C5—31no—
251C22×C4×C5—31no—
252C22×C4×C5—31no—
253C22×C4×C5—31no—
254C22×C4×C5C22×D311yescharacteristic
255C22×C4×C5C22×D311yescharacteristic
256C22×C4×C5C22×D311yescharacteristic
257C22×Dic5—31no—
258C22×Dic5—31no—
259C22×Dic5—31no—
260C22×Dic5—31no—
261C22×Dic5C22×D311yescharacteristic
262C22×Dic5C22×D311yescharacteristic
263C22×Dic5C22×D311yescharacteristic
264C2×C4×D5—41no—
265C2×C4×D5—41no—
266C2×C4×D5C2×Dic314yes—
267C2×Dic10—41no—
268C2×Dic10—41no—
269C2×Dic10C2×Dic314yes—
270C5×C4⋊C4—121no—
271C5×C4⋊C4C2×Dic314yes—
272C42×C5—121no—
273#685—121no—
274#685—121no—
275#685—121no—
276#685—121no—
277#685C2×Dic314yes—
278#685C2×Dic314yes—
279C4⋊Dic5—121no—
280C4⋊Dic5C2×Dic314yes—
281C4⋊Dic5C2×Dic314yes—
282#683—121no—
283#683—121no—
284#683—121no—
285#683—121no—
286C4×Dic5—121no—
287C4×Dic5—121no—
288C4×Dic5—121no—
289C2×C22⋊Q8—51no—
290#391—151no—
291#391—151no—
292#389—151no—
293#389—151no—
294#388—151no—
295#388—151no—
296#388—151no—
297#388—151no—
298#387—31no—
299#387—151no—
300#387—151no—
301#387—151no—
302#381—151no—
303#380—151no—
304C22×C3×C5C23×C411yescharacteristic
305C22×C3×C5H(5,𝔽2)11yescharacteristic
306C22×C3×C5H(5,𝔽2)11yescharacteristic
307C22×C3×C5H(5,𝔽2)11yescharacteristic
308C22×C3×C52−1+411yescharacteristic
309C22×C3×C52−1+411yescharacteristic
310C22×C3×C52−1+411yescharacteristic
311C2×C3×D5—22no—
312C2×C3×D5—22no—
313C2×C3×D5—22no—
314C2×C3×D5—41no—
315C2×C3×D5—41no—
316C2×C3×D5—41no—
317C2×C3×D5—41no—
318C3×C4×C5—22no—
319C3×C4×C5—22no—
320C3×C4×C5—22no—
321Dic15—41no—
322Dic15—41no—
323Dic15—41no—
324Dic15—41no—
325C3×Dic5—22no—
326C3×Dic5—22no—
327C3×Dic5—22no—
328C5×Dic3—41no—
329C5×Dic3—41no—
330C5×Dic3—41no—
331C5×Dic3—41no—
332C24×C3—51no—
333C2×C3×Q8—54no—
334C2×C3×Q8—201no—
335C2×C3×Q8—201no—
336C22×C3×C4—51no—
337C22×C3×C4—51no—
338C22×C3×C4—51no—
339C22×C3×C4—54no—
340C22×C3×C4—201no—
341C22×C3×C4—201no—
342C22×C3×C4C22×D511yescharacteristic
343C22×C3×C4C22×D511yescharacteristic
344C22×C3×C4C22×D511yescharacteristic
345C22×Dic3—51no—
346C22×Dic3—51no—
347C22×Dic3—51no—
348C22×Dic3—51no—
349C22×Dic3C22×D511yescharacteristic
350C22×Dic3C22×D511yescharacteristic
351C22×Dic3C22×D511yescharacteristic
352C22×Dic3C22×D511yescharacteristic
353C3×C4⋊C4—54no—
354C3×C4⋊C4—54no—
355C3×C4⋊C4C4×D514yes—
356C3×C22⋊C4—54no—
357C3×C22⋊C4—54no—
358#217—201no—
359#217—201no—
360#217—201no—
361#217—201no—
362C4⋊Dic3—41no—
363C4⋊Dic3—201no—
364C4⋊Dic3—201no—
365C4⋊Dic3—201no—
366C4⋊Dic3—201no—
367C4⋊Dic3—201no—
368C4×Dic3—41no—
369C4×Dic3—201no—
370C4×Dic3—201no—
371C4×Dic3—201no—
372C23×C5C23×D311yescharacteristic
373C22×D5—21no—
374C22×D5—21no—
375C22×D5—21no—
376C22×D5—21no—
377C22×D5—21no—
378C22×D5—21no—
379C22×D5C22×Dic312yes—
380C2×C4×C5—21no—
381C2×C4×C5—21no—
382C2×C4×C5—21no—
383C2×C4×C5—21no—
384C2×C4×C5—21no—
385C2×C4×C5—21no—
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×C5—61no—
396C2×C4×C5—61no—
397C2×C4×C5—61no—
398C2×C4×C5C22×Dic312yes—
399C2×C4×C5C22×Dic312yes—
400C2×C4×C5C22×Dic312yes—
401C2×Dic5—21no—
402C2×Dic5—21no—
403C2×Dic5—21no—
404C2×Dic5—21no—
405C2×Dic5—21no—
406C2×Dic5—21no—
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—61no—
417C2×Dic5—61no—
418C2×Dic5—61no—
419C2×Dic5C22×Dic312yes—
420C2×Dic5C22×Dic312yes—
421C2×Dic5C22×Dic312yes—
422C4×D5—44no—
423Dic10—44no—
424C22×Q8—51no—
425C23×C4—51no—
426C22⋊Q8—58no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—51no—
429C2×C4⋊C4—51no—
430C2×C4⋊C4—151no—
431C2×C4⋊C4—151no—
432C2×C4⋊C4—151no—
433C2×C4⋊C4—151no—
434C2×C4⋊C4—151no—
435C2×C4⋊C4D3×D511yescharacteristic
436C2×C22⋊C4—51no—
437C2×C22⋊C4—51no—
438C2×C22⋊C4—151no—
439C2×C22⋊C4—151no—
440C2×C22⋊C4—151no—
441C2×C22⋊C4—151no—
442C2×C42—31no—
443C2×C42—151no—
444C2×C42—151no—
445C2×C42—151no—
446#95—31no—
447#95—31no—
448#95—31no—
449#95—31no—
450#95—151no—
451#95—151no—
452#95—151no—
453#95—151no—
454#95—151no—
455#95—151no—
456#95—151no—
457#95—151no—
458#95—151no—
459#95—151no—
460C2×C3×C5#51811yescharacteristic
461C2×C3×C5#51911yescharacteristic
462C2×C3×C5#52011yescharacteristic
463C2×C3×C5#56211yescharacteristic
464C2×C3×C5#56211yescharacteristic
465C2×C3×C5#56311yescharacteristic
466C2×C3×C5#56311yescharacteristic
467C3×D5—42no—
468C23×C3—52no—
469C23×C3—101no—
470C23×C3—101no—
471C23×C3—101no—
472C23×C3—101no—
473C23×C3—101no—
474C23×C3—101no—
475C23×C3C23×D511yescharacteristic
476C3×Q8—204no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—52no—
484C2×C3×C4—52no—
485C2×C3×C4—52no—
486C2×C3×C4—101no—
487C2×C3×C4—101no—
488C2×C3×C4—101no—
489C2×C3×C4—101no—
490C2×C3×C4—101no—
491C2×C3×C4—101no—
492C2×C3×C4—204no—
493C2×C3×C4C2×C4×D512yes—
494C2×C3×C4C2×C4×D512yes—
495C2×C3×C4C2×C4×D512yes—
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—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
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—
517C2×Dic3—101no—
518C2×Dic3—101no—
519C2×Dic3—101no—
520C22×C5#100411yescharacteristic
521C22×C5#100411yescharacteristic
522C22×C5#100711yescharacteristic
523C22×C5#100711yescharacteristic
524C22×C5#100911yescharacteristic
525C22×C5#101011yescharacteristic
526C22×C5C23×Dic311yescharacteristic
527C2×D5—22no—
528C2×D5—22no—
529C2×D5—22no—
530C2×D5—41no—
531C2×D5—41no—
532C2×D5—41no—
533C2×D5—41no—
534C4×C5—22no—
535C4×C5—22no—
536C4×C5—22no—
537C4×C5—121no—
538C4×C5—121no—
539C4×C5—121no—
540C4×C5—121no—
541Dic5—22no—
542Dic5—22no—
543Dic5—22no—
544Dic5—121no—
545Dic5—121no—
546Dic5—121no—
547Dic5—121no—
548C24—51no—
549C2×Q8—54no—
550C2×Q8—201no—
551C2×Q8—201no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—51no—
557C22×C4—51no—
558C22×C4—51no—
559C22×C4—54no—
560C22×C4—151no—
561C22×C4—151no—
562C22×C4—151no—
563C22×C4—151no—
564C22×C4—201no—
565C22×C4—201no—
566C22×C4C2×D3×D511yescharacteristic
567C22×C4C2×D3×D511yescharacteristic
568C22×C4C2×D3×D511yescharacteristic
569C4⋊C4—54no—
570C4⋊C4—54no—
571C4⋊C4—121no—
572C4⋊C4—601no—
573C4⋊C4—601no—
574C4⋊C4—601no—
575C4⋊C4—601no—
576C4⋊C4—601no—
577C4⋊C4D5×Dic314yes—
578C22⋊C4—54no—
579C22⋊C4—54no—
580C22⋊C4—601no—
581C22⋊C4—601no—
582C22⋊C4—601no—
583C22⋊C4—601no—
584C42—121no—
585C42—601no—
586C42—601no—
587C42—601no—
588C3×C5#237811yescharacteristic, complemented, Hall
589C22×C3—102no—
590C22×C3—102no—
591C22×C3—102no—
592C22×C3—201no—
593C22×C3—201no—
594C22×C3—201no—
595C22×C3—201no—
596C22×C3C22×C4×D511yescharacteristic
597C22×C3#414411yescharacteristic
598C22×C3#414711yescharacteristic
599C22×C3#414911yescharacteristic
600C22×C3#414911yescharacteristic
601C22×C3#415011yescharacteristic
602C22×C3#415011yescharacteristic
603C3×C4—22no—
604C3×C4—22no—
605C3×C4—22no—
606C3×C4—102no—
607C3×C4—102no—
608C3×C4—102no—
609Dic3—41no—
610Dic3—41no—
611Dic3—41no—
612Dic3—41no—
613Dic3—201no—
614Dic3—201no—
615Dic3—201no—
616Dic3—201no—
617C2×C5#564611yescharacteristic
618C2×C5#564611yescharacteristic
619C2×C5#564711yescharacteristic
620C2×C5#564711yescharacteristic
621C2×C5#579811yescharacteristic
622C2×C5#581211yescharacteristic
623C2×C5#582711yescharacteristic
624D5—42no—
625C23—52no—
626C23—101no—
627C23—101no—
628C23—101no—
629C23—101no—
630C23—101no—
631C23—101no—
632C23C22×D3×D511yescharacteristic
633Q8—204no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—52no—
641C2×C4—52no—
642C2×C4—52no—
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—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—101no—
656C2×C4—101no—
657C2×C4—101no—
658C2×C4—101no—
659C2×C4—101no—
660C2×C4—101no—
661C2×C4—204no—
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×C4—301no—
672C2×C4—301no—
673C2×C4—301no—
674C2×C4C2×D5×Dic312yes—
675C2×C4C2×D5×Dic312yes—
676C2×C4C2×D5×Dic312yes—
677C2×C3—202no—
678C2×C3#6585511yescharacteristic
679C2×C3#6588011yescharacteristic
680C2×C3#6590611yescharacteristic
681C2×C3#6598111yescharacteristic
682C2×C3#6600111yescharacteristic
683C2×C3#6603311yescharacteristic
684C2×C3#6604611yescharacteristic
685C5#8275011yescharacteristic, complemented, Sylow
686C22—102no—
687C22—102no—
688C22—102no—
689C22—201no—
690C22—201no—
691C22—201no—
692C22—201no—
693C22#9201711yescharacteristic
694C22#9201711yescharacteristic
695C22#9202011yescharacteristic
696C22#9202711yescharacteristic
697C22#9202911yescharacteristic
698C22#9203011yescharacteristic
699C22C22×D5×Dic311yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—102no—
704C4—102no—
705C4—102no—
706C4—121no—
707C4—121no—
708C4—121no—
709C4—121no—
710C4—601no—
711C4—601no—
712C4—601no—
713C4—601no—
714C3#1060704511yescharacteristic, complemented, Sylow
715C2—202no—
716C2#1175380911yescharacteristic
717C2#1175381011yescharacteristic
718C2#1175381111yescharacteristic
719C2#1175381211yescharacteristic
720C2#1175448811yescharacteristic
721C2#1175492311yescharacteristic
722C2#1175514011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2378
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
2. #11751081C2semidirect
3. C5×#4980C2semidirect
4. #11748865C2semidirect
5. #11748857C2semidirect
12. #11748698C2semidirect
13. #11748697C2semidirect
14. #11748672C2semidirect
15. #11748672C2semidirect
28. C3×#4043C4semidirect
119. #4980D5semidirect
145. #4043Dic3semidirect
588. C3×C5#2378semidirect
685. C5#82750semidirect
714. C3#10607045semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40432
#117510812
C5×#49802
#117488652
#117488572
#117487912
#117487722
#117487712
#117487702
#117487382
#117487372
#117486982
#117486972
#117486722
#106070453
#827505