Finite Group Databasebeta

← #14326432

Subgroups — #14326432

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91398C211yesmaximal, characteristic
2#11751034C211yesmaximal, characteristic, complemented
3C4×C5×(C2×D3)⋊C4C211yesmaximal, characteristic
4C3×#65221C211yesmaximal, characteristic, complemented
5#11748893C211yesmaximal, characteristic
6#11748880C211yesmaximal, characteristic
7D3×#3963C211yesmaximal, characteristic
8Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic
9#11748824C211yesmaximal, characteristic, complemented
10#11748808C211yesmaximal, characteristic, complemented
11#11748722C211yesmaximal, characteristic
12#11748649C211yesmaximal, characteristic, complemented
13#11748646C211yesmaximal, characteristic, complemented
14#11748645C211yesmaximal, characteristic, complemented
15#11748580C211yesmaximal, characteristic, complemented
16#10605186—31nomaximal, Hall
17C22×C4×C5×D3C2211yescharacteristic
18C22×D3×Dic5C2211yescharacteristic
19C22×D3×Dic5C2211yescharacteristic
20C2×C3×C42×C5C2211yescharacteristic
21C2×#6712C2211yescharacteristic
22C2×#6712C2211yescharacteristic
23C2×C5×(C2×D3)⋊C4C2211yescharacteristic
24C2×C5×(C2×D3)⋊C4C2211yescharacteristic
25C2×C4×C5×Dic3C2211yescharacteristic
26C2×C3×C4×Dic5C2211yescharacteristic
27C2×C3×C4×Dic5C2211yescharacteristic
28C2×#6669C2211yescharacteristic
29C2×#6669C2211yescharacteristic
30C2×#6668C2211yescharacteristic
31C2×#6668C2211yescharacteristic
32C2×(C2×D3)⋊Dic5C2211yescharacteristic
33C2×(C2×D3)⋊Dic5C2211yescharacteristic
34C2×Dic3×Dic5C2211yescharacteristic
35C2×Dic3×Dic5C2211yescharacteristic
36#91398C418yescomplemented
37#91115C2211yescharacteristic
38#91115C2211yescharacteristic
39#91115C2211yescharacteristic
40#91115C2211yescharacteristic
41C5×C3⋊#95C2211yescharacteristic
42C5×C3⋊#95C2211yescharacteristic
43C3×#3963C2211yescharacteristic
44C3×#3963C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#73416—51nomaximal, Hall
54C2×#4023—31no—
55C4×C5×C22⋊C4—31no—
56#65499—31no—
57C2×#3963—31no—
58#65235—31no—
59#65232—31no—
60C22⋊C4×Dic5—31no—
61#65222—31no—
62#65222—31no—
63#65221D311yescharacteristic, complemented
64C4×#683—31no—
65#64941—31no—
66#64941—31no—
67#64940—31no—
68#64939—31no—
69C23×C5×D3C2311yescharacteristic
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
80C2×C4×C5×D3—22no—
81C2×C4×C5×D3—22no—
82C2×C4×C5×D3—41no—
83C22×C3×Dic5C2311yescharacteristic
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C2×D3×Dic5—22no—
88C2×D3×Dic5—22no—
89C2×D3×Dic5—22no—
90C2×D3×Dic5—22no—
91C2×D3×Dic5—41no—
92C2×D3×Dic5C2×C414yes—
93C3×C42×C5—22no—
94#6712—22no—
95#6712C2×C414yescomplemented
96C5×(C2×D3)⋊C4—22no—
97C5×(C2×D3)⋊C4C2×C414yes—
98C4×C5×Dic3—41no—
99C3×C4×Dic5—22no—
100C3×C4×Dic5C2×C414yescomplemented
101#6669—22no—
102#6669C2×C414yescomplemented
103#6668—41no—
104#6668—41no—
105(C2×D3)⋊Dic5—22no—
106(C2×D3)⋊Dic5C2×C414yes—
107Dic3×Dic5—41no—
108Dic3×Dic5C2×C414yescomplemented
109C2×#872—51no—
110C3×#376—51no—
111C4×(C2×D3)⋊C4—51no—
112C4×(C2×D3)⋊C4D511yescharacteristic
113#4936—51no—
114#4933—51no—
115#4933—51no—
116#4668—51no—
117#4668—51no—
118#4664—51no—
119D3×#95—51no—
120#4655—51no—
121#4655—51no—
122#4651—51no—
123#4649—51no—
124C23×C4×C5—31no—
125C23×Dic5—31no—
126C23×Dic5—31no—
127C2×C5×C22⋊C4—31no—
128C2×C5×C22⋊C4—31no—
129C2×C42×C5—31no—
130C2×C42×C5C2×D311yescharacteristic
131C2×C22⋊Dic5—31no—
132C2×C22⋊Dic5—31no—
133C2×#683—31no—
134C2×#683—31no—
135C2×#683—31no—
136C2×#683—31no—
137C2×#683—31no—
138C2×#683—31no—
139C2×C4×Dic5—31no—
140C2×C4×Dic5—31no—
141C2×C4×Dic5C2×D311yescharacteristic
142C2×C4×Dic5C2×D311yescharacteristic
143#4023—38no—
144C5×#95—31no—
145C5×#95—31no—
146#3963—31no—
147#3963—31no—
148#3963—31no—
149#3963—31no—
150#3963—31no—
151#3963—31no—
152#3963—31no—
153#3963—31no—
154#3963—31no—
155#3963—31no—
156#3963C2×D311yescharacteristic
157#3963C2×D311yescharacteristic
158#3963C2×D311yescharacteristic
159#3963C2×D311yescharacteristic
160#2343—151noSylow
161C23×C3×C5C2411yescharacteristic
162C22×C5×D3—21no—
163C22×C5×D3—21no—
164C22×C5×D3—21no—
165C22×C5×D3—21no—
166C22×C5×D3C22×C412yes—
167C22×C5×D3#4112yes—
168C22×C5×D3#4112yes—
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×C5—21no—
176C2×C3×C4×C5C22×C412yes—
177C2×C3×C4×C5#4112yes—
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×Dic15C22×C412yes—
189C2×Dic15C22×C412yes—
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×Dic3C22×C412yes—
199C4×C5×D3—44no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—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×Dic5—21no—
209C2×C3×Dic5C22×C412yes—
210C2×C3×Dic5C22×C412yes—
211C2×C3×Dic5#4112yes—
212D3×Dic5—28no—
213D3×Dic5—44no—
214C22×C4×D3—51no—
215C22×C4×D3—51no—
216C22×C4×D3C2×D511yescharacteristic
217C2×C3×C42—51no—
218C2×C3×C42—51no—
219C2×C3×C42C2×D511yescharacteristic
220C2×(C2×D3)⋊C4—51no—
221C2×(C2×D3)⋊C4—51no—
222C2×(C2×D3)⋊C4C2×D511yescharacteristic
223C2×(C2×D3)⋊C4C2×D511yescharacteristic
224C2×C4⋊Dic3—51no—
225C2×C4⋊Dic3—51no—
226C2×Dic3⋊C4—51no—
227C2×Dic3⋊C4—51no—
228C2×Dic3⋊C4—51no—
229C2×Dic3⋊C4—51no—
230C2×C4×Dic3—51no—
231C2×C4×Dic3—51no—
232C2×C4×Dic3C2×D511yescharacteristic
233#872—58no—
234C3×#95—51no—
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⋊#95—51no—
246C3⋊#95—51no—
247C3⋊#95—51no—
248C3⋊#95C2×D511yescharacteristic
249C3⋊#95C2×D511yescharacteristic
250C24×C5—31no—
251C22×C4×C5—31no—
252C22×C4×C5—31no—
253C22×C4×C5—31no—
254C22×C4×C5—62no—
255C22×C4×C5—62no—
256C22×C4×C5—121no—
257C22×C4×C5C22×D311yescharacteristic
258C22×C4×C5C22×D311yescharacteristic
259C22×C4×C5C22×D311yescharacteristic
260C22×Dic5—31no—
261C22×Dic5—31no—
262C22×Dic5—34no—
263C22×Dic5—31no—
264C22×Dic5—31no—
265C22×Dic5—62no—
266C22×Dic5—62no—
267C22×Dic5—62no—
268C22×Dic5—62no—
269C22×Dic5—121no—
270C22×Dic5C22×D311yescharacteristic
271C22×Dic5C22×D311yescharacteristic
272C22×Dic5C22×D311yescharacteristic
273C22×Dic5C22×D311yescharacteristic
274C5×C22⋊C4—34no—
275C5×C22⋊C4—62no—
276C42×C5—22no—
277C42×C5—121no—
278C22⋊Dic5—34no—
279C22⋊Dic5—62no—
280#683—34no—
281#683—34no—
282#683—62no—
283#683—62no—
284#683—121no—
285#683—121no—
286C4×Dic5—22no—
287C4×Dic5—34no—
288C4×Dic5—121no—
289C4×Dic5C4×D314yescomplemented
290C2×#117—151no—
291#387—151no—
292#387—151no—
293#387—151no—
294#387—151no—
295#385—151no—
296#385—151no—
297#383—151no—
298#382—151no—
299#381—151no—
300C4×C4⋊C4—151no—
301C4×C22⋊C4—31no—
302C4×C22⋊C4—151no—
303#376—51no—
304C2×#95—151no—
305C22×C3×C5C23×C411yescharacteristic
306C22×C3×C5C2×#4111yescharacteristic
307C22×C3×C5C2×#4111yescharacteristic
308C22×C3×C5C2×#4111yescharacteristic
309C22×C3×C5C2×#4111yescharacteristic
310C22×C3×C5H(5,𝔽2)11yescharacteristic
311C22×C3×C52−1+411yescharacteristic
312C2×C5×D3—22no—
313C2×C5×D3—22no—
314C2×C5×D3—22no—
315C2×C5×D3—22no—
316C2×C5×D3—22no—
317C2×C5×D3—22no—
318C2×C5×D3#11714yes—
319C3×C4×C5—22no—
320C3×C4×C5—22no—
321C3×C4×C5—41no—
322Dic15—22no—
323Dic15—22no—
324Dic15—41no—
325Dic15—41no—
326C3×Dic5—22no—
327C3×Dic5—22no—
328C3×Dic5—22no—
329C3×Dic5—41no—
330C5×Dic3—22no—
331C5×Dic3—41no—
332C5×Dic3—41no—
333C23×D3C22×D511yescharacteristic
334C22×C3×C4—51no—
335C22×C3×C4—51no—
336C22×C3×C4—51no—
337C22×C3×C4—51no—
338C22×C3×C4C22×D511yescharacteristic
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
348C2×C4×D3—22no—
349C2×C4×D3—22no—
350C2×C4×D3—41no—
351C2×C4×D3—54no—
352C2×C4×D3—102no—
353C2×C4×D3—102no—
354C2×C4×D3—102no—
355C2×C4×D3—102no—
356C2×C4×D3—201no—
357C3×C42—22no—
358C3×C42—54no—
359C3×C42—102no—
360(C2×D3)⋊C4—22no—
361(C2×D3)⋊C4—54no—
362(C2×D3)⋊C4—102no—
363(C2×D3)⋊C4C4×D514yes—
364C4⋊Dic3—201no—
365C4⋊Dic3—201no—
366Dic3⋊C4—54no—
367Dic3⋊C4—54no—
368Dic3⋊C4—102no—
369Dic3⋊C4—102no—
370C4×Dic3—41no—
371C4×Dic3—54no—
372C4×Dic3—201no—
373C23×C5—32no—
374C23×C5—32no—
375C23×C5—32no—
376C23×C5—61no—
377C23×C5—61no—
378C23×C5—61no—
379C23×C5—61no—
380C23×C5C23×D311yescharacteristic
381C2×C4×C5—21no—
382C2×C4×C5—21no—
383C2×C4×C5—21no—
384C2×C4×C5—21no—
385C2×C4×C5—21no—
386C2×C4×C5—21no—
387C2×C4×C5—21no—
388C2×C4×C5—32no—
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—124no—
398C2×C4×C5C2×C4×D312yes—
399C2×C4×C5#23512yes—
400C2×Dic5—21no—
401C2×Dic5—21no—
402C2×Dic5—21no—
403C2×Dic5—21no—
404C2×Dic5—21no—
405C2×Dic5—21no—
406C2×Dic5—21no—
407C2×Dic5—21no—
408C2×Dic5—21no—
409C2×Dic5—32no—
410C2×Dic5—32no—
411C2×Dic5—68no—
412C2×Dic5—61no—
413C2×Dic5—61no—
414C2×Dic5—61no—
415C2×Dic5—61no—
416C2×Dic5—61no—
417C2×Dic5—61no—
418C2×Dic5—61no—
419C2×Dic5—61no—
420C2×Dic5—61no—
421C2×Dic5—61no—
422C2×Dic5—124no—
423C2×Dic5C2×C4×D312yes—
424C2×Dic5C2×C4×D312yes—
425C2×Dic5#23512yes—
426C23×C4—31no—
427C23×C4—151no—
428C23×C4—151no—
429#117—158no—
430C2×C4⋊C4—151no—
431C2×C4⋊C4—151no—
432C2×C4⋊C4—151no—
433C2×C4⋊C4—151no—
434C2×C4⋊C4—151no—
435C2×C4⋊C4—151no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—151no—
439C2×C22⋊C4—151no—
440C2×C42—31no—
441C2×C42—51no—
442C2×C42—51no—
443C2×C42—151no—
444C2×C42—151no—
445C2×C42D3×D511yescharacteristic
446#95—31no—
447#95—31no—
448#95—51no—
449#95—51no—
450#95—51no—
451#95—51no—
452#95—151no—
453#95—151no—
454#95—151no—
455#95—151no—
456#95—151no—
457#95—151no—
458#95—151no—
459#95—151no—
460#95—151no—
461#95—151no—
462C2×C3×C5C2×#11711yescharacteristic
463C2×C3×C5C4×#4111yescharacteristic
464C2×C3×C5#52011yescharacteristic
465C2×C3×C5#55111yescharacteristic
466C2×C3×C5#55111yescharacteristic
467C2×C3×C5#55211yescharacteristic
468C2×C3×C5#55211yescharacteristic
469C5×D3—24no—
470C23×C3C23×D511yescharacteristic
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3C2×C4×D512yes—
476C22×D3#70912yes—
477C22×D3#70912yes—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—52no—
486C2×C3×C4—52no—
487C2×C3×C4—52no—
488C2×C3×C4—101no—
489C2×C3×C4—101no—
490C2×C3×C4—101no—
491C2×C3×C4—101no—
492C2×C3×C4—101no—
493C2×C3×C4—101no—
494C2×C3×C4—101no—
495C2×C3×C4—101no—
496C2×C3×C4—101no—
497C2×C3×C4C2×C4×D512yes—
498C2×C3×C4#71112yes—
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—52no—
508C2×Dic3—52no—
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×Dic3C2×C4×D512yes—
520C4×D3—44no—
521C4×D3—108no—
522C4×D3—204no—
523C22×C5—34no—
524C22×C5—62no—
525C22×C5—62no—
526C22×C5—62no—
527C22×C5—62no—
528C22×C5—62no—
529C22×C5—62no—
530C22×C5C22×C4×D311yescharacteristic
531C22×C5C2×#23511yescharacteristic
532C22×C5C2×#23511yescharacteristic
533C22×C5D3×#4111yescharacteristic
534C22×C5D3×#4111yescharacteristic
535C22×C5#100911yescharacteristic
536C22×C5#101011yescharacteristic
537C4×C5—22no—
538C4×C5—22no—
539C4×C5—41no—
540C4×C5—62no—
541C4×C5—121no—
542C4×C5—121no—
543Dic5—22no—
544Dic5—22no—
545Dic5—22no—
546Dic5—41no—
547Dic5—62no—
548Dic5—62no—
549Dic5—121no—
550Dic5—121no—
551C24—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—51no—
556C22×C4—51no—
557C22×C4—51no—
558C22×C4—51no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—121no—
562C22×C4—154no—
563C22×C4—151no—
564C22×C4—151no—
565C22×C4—151no—
566C22×C4—151no—
567C22×C4—302no—
568C22×C4—302no—
569C22×C4—302no—
570C22×C4—302no—
571C22×C4—601no—
572C22×C4C2×D3×D511yescharacteristic
573C22×C4C2×D3×D511yescharacteristic
574C22×C4C2×D3×D511yescharacteristic
575C4⋊C4—154no—
576C4⋊C4—154no—
577C4⋊C4—302no—
578C4⋊C4—302no—
579C4⋊C4—601no—
580C4⋊C4—601no—
581C22⋊C4—34no—
582C22⋊C4—62no—
583C22⋊C4—154no—
584C22⋊C4—302no—
585C42—22no—
586C42—54no—
587C42—102no—
588C42—121no—
589C42—154no—
590C42—601no—
591C3×C5#234311yescharacteristic, complemented, Hall
592C22×C3C22×C4×D511yescharacteristic
593C22×C3C2×#70911yescharacteristic
594C22×C3C2×#70911yescharacteristic
595C22×C3C2×#71111yescharacteristic
596C22×C3#414411yescharacteristic
597C22×C3D5×#4111yescharacteristic
598C22×C3#415011yescharacteristic
599C2×D3—22no—
600C2×D3—22no—
601C2×D3—22no—
602C2×D3—22no—
603C2×D3—22no—
604C2×D3—22no—
605C2×D3#401814yes—
606C3×C4—22no—
607C3×C4—22no—
608C3×C4—41no—
609C3×C4—102no—
610C3×C4—102no—
611C3×C4—102no—
612C3×C4—201no—
613Dic3—22no—
614Dic3—41no—
615Dic3—41no—
616Dic3—102no—
617Dic3—102no—
618Dic3—201no—
619Dic3—201no—
620C2×C5—64no—
621C2×C5C4×#23511yescharacteristic
622C2×C5D3×#11711yescharacteristic
623C2×C5#552311yescharacteristic
624C2×C5#552711yescharacteristic
625C2×C5#552711yescharacteristic
626C2×C5#552911yescharacteristic
627C2×C5#552911yescharacteristic
628C23—32no—
629C23—32no—
630C23—32no—
631C23—61no—
632C23—61no—
633C23—61no—
634C23—61no—
635C23C22×D3×D511yescharacteristic
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—32no—
644C2×C4—52no—
645C2×C4—52no—
646C2×C4—52no—
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—101no—
662C2×C4—101no—
663C2×C4—101no—
664C2×C4—124no—
665C2×C4—152no—
666C2×C4—152no—
667C2×C4—308no—
668C2×C4—301no—
669C2×C4—301no—
670C2×C4—301no—
671C2×C4—301no—
672C2×C4—301no—
673C2×C4—301no—
674C2×C4—301no—
675C2×C4—301no—
676C2×C4—301no—
677C2×C4—301no—
678C2×C4—604no—
679C2×C4C4×D3×D512yes—
680C2×C4#678212yes—
681C2×C3C2×#401811yescharacteristic
682C2×C3#6582911yescharacteristic
683C2×C3#6586511yescharacteristic
684C2×C3C4×#71111yescharacteristic
685C2×C3#6587511yescharacteristic
686C2×C3#6588011yescharacteristic
687C2×C3#6589011yescharacteristic
688D3—24no—
689C5#7341611yescharacteristic, complemented, Sylow
690C22—34no—
691C22—62no—
692C22—62no—
693C22—62no—
694C22—62no—
695C22—62no—
696C22—62no—
697C22#9200111yescharacteristic
698C22C2×C4×D3×D511yescharacteristic
699C22D5×#23511yescharacteristic
700C22D3×#70911yescharacteristic
701C22D3×#70911yescharacteristic
702C22#9201811yescharacteristic
703C22C2×#678211yescharacteristic
704C4—22no—
705C4—22no—
706C4—41no—
707C4—62no—
708C4—102no—
709C4—102no—
710C4—102no—
711C4—121no—
712C4—121no—
713C4—201no—
714C4—302no—
715C4—302no—
716C4—601no—
717C4—601no—
718C3#1060518611yescharacteristic, complemented, Sylow
719C2—64no—
720C2#1175266911yescharacteristic
721C2#1175268611yescharacteristic
722C2D3×#401811yescharacteristic
723C2#1175275811yescharacteristic
724C2C4×#678211yescharacteristic
725C2#1175443111yescharacteristic
726C2#1175443211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#2343
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11751034C2semidirect
4. C3×#65221C2semidirect
9. #11748824C2semidirect
10. #11748808C2semidirect
12. #11748649C2semidirect
13. #11748646C2semidirect
14. #11748645C2semidirect
15. #11748580C2semidirect
36. #91398C4semidirect
63. #65221D3semidirect
95. #6712C2×C4semidirect
100. C3×C4×Dic5C2×C4semidirect
102. #6669C2×C4semidirect
108. Dic3×Dic5C2×C4semidirect
289. C4×Dic5C4×D3semidirect
591. C3×C5#2343semidirect
689. C5#73416semidirect
718. C3#10605186semidirect

Maximal subgroups

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

subgroupindex
C2×#913982
#117510342
C4×C5×(C2×D3)⋊C42
C3×#652212
#117488932
#117488802
D3×#39632
Dic5×(C2×D3)⋊C42
#117488242
#117488082
#117487222
#117486492
#117486462
#117486452
#117485802
#106051863
#734165