Finite Group Databasebeta

← #14322721

Subgroups — #14322721

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×#91398C211yesmaximal, characteristic
2#11750753C211yesmaximal, characteristic, complemented
3C5×#4669C211yesmaximal, characteristic
4C3×#64938C211yesmaximal, characteristic, complemented
5#11748874C211yesmaximal, characteristic
6#11748874C211yesmaximal, characteristic
7#11748847C211yesmaximal, characteristic, complemented
8#11748815C211yesmaximal, characteristic, complemented
9#11748813C211yesmaximal, characteristic, complemented
10C4×#6668C211yesmaximal, characteristic, complemented
11#11748794C211yesmaximal, characteristic
12#11748715C211yesmaximal, characteristic
13#11748714C211yesmaximal, characteristic
14#11748642C211yesmaximal, characteristic, complemented
15#11748641C211yesmaximal, characteristic, complemented
16#10607187—31nomaximal, Hall
17C22×D3×Dic5C2211yescharacteristic
18C2×#6712C2211yescharacteristic
19C2×#6712C2211yescharacteristic
20C2×C4×Dic15C2211yescharacteristic
21C2×C5×(C2×D3)⋊C4C2211yescharacteristic
22C2×C5×(C2×D3)⋊C4C2211yescharacteristic
23C2×C5×(C2×D3)⋊C4C2211yescharacteristic
24C2×C5×Dic3⋊C4C2211yescharacteristic
25C2×C4×C5×Dic3C2211yescharacteristic
26C2×C3×#683C2211yescharacteristic
27C2×C3×#683C2211yescharacteristic
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31C2×Dic3⋊Dic5C2211yescharacteristic
32C2×#6669C2211yescharacteristic
33C2×#6669C2211yescharacteristic
34C2×#6668C2211yescharacteristic
35C2×#6668C2211yescharacteristic
36C2×(C2×D3)⋊Dic5C2211yescharacteristic
37C2×(C2×D3)⋊Dic5C2211yescharacteristic
38C2×(C2×D3)⋊Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40#91398C418yescomplemented
41C3×C5×#95C2211yescharacteristic
42#91115C2211yescharacteristic
43#91115C2211yescharacteristic
44#91115C2211yescharacteristic
45C5×C3⋊#95C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#73760—51nomaximal, Hall
54C2×#4023—31no—
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#64938D311yescharacteristic, complemented
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
80C22×C3×Dic5C2311yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C22×C3×Dic5C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C2×D3×Dic5—22no—
85C2×D3×Dic5—22no—
86C2×D3×Dic5C2×C414yes—
87#6712—41no—
88#6712C2×C414yes—
89C4×Dic15—41no—
90C5×(C2×D3)⋊C4—41no—
91C5×(C2×D3)⋊C4—41no—
92C5×(C2×D3)⋊C4C2×C414yes—
93C5×Dic3⋊C4—41no—
94C4×C5×Dic3—41no—
95C3×#683—22no—
96C3×#683—22no—
97C3×C4×Dic5—41no—
98C3×C4×Dic5—41no—
99C3×C4×Dic5C2×C414yes—
100Dic3⋊Dic5—41no—
101#6669—41no—
102#6669C2×C414yes—
103#6668—22no—
104#6668—22no—
105(C2×D3)⋊Dic5—41no—
106(C2×D3)⋊Dic5—41no—
107(C2×D3)⋊Dic5C2×C414yes—
108Dic3×Dic5C2×C414yes—
109C2×#872—51no—
110C3×C4×C4⋊C4—51no—
111#4987—51no—
112#4987—51no—
113#4977—51no—
114#4975—51no—
115#4940—51no—
116#4940—51no—
117C4×C4⋊Dic3—51no—
118#4933—51no—
119#4933—51no—
120#4669—51no—
121#4669D511yescharacteristic
122#4652—51no—
123#4652—51no—
124C23×Dic5—31no—
125C2×C5×C4⋊C4—31no—
126C2×C5×C22⋊C4—31no—
127C2×C5×C22⋊C4—31no—
128C2×C5×C22⋊C4—31no—
129C2×C42×C5—31no—
130C2×C22⋊Dic5—31no—
131C2×C22⋊Dic5—31no—
132C2×C22⋊Dic5—31no—
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×Dic5C2×D311yescharacteristic
145C2×C4×Dic5C2×D311yescharacteristic
146C2×C4×Dic5C2×D311yescharacteristic
147#4023—38no—
148C5×#95—31no—
149C5×#95C2×D311yescharacteristic
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#3963C2×D311yescharacteristic
160#2314—151noSylow
161C23×C3×C5C2411yescharacteristic
162C22×C5×D3—21no—
163C22×C5×D3—21no—
164C22×C5×D3—21no—
165C22×C5×D3—21no—
166C22×C5×D3—21no—
167C22×C5×D3—21no—
168C22×C5×D3C22×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×C5—21no—
176C2×C3×C4×C5—21no—
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×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—
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—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5C22×C412yes—
208C2×C3×Dic5C22×C412yes—
209C2×C3×Dic5#4112yes—
210C2×C3×Dic5#4112yes—
211D3×Dic5—28no—
212C22×C4×D3—51no—
213C2×C3×C4⋊C4—51no—
214C2×C3×C4⋊C4—51no—
215C2×C3×C42—51no—
216C2×C3×C42—51no—
217C2×C3×C42—51no—
218C2×(C2×D3)⋊C4—51no—
219C2×(C2×D3)⋊C4—51no—
220C2×(C2×D3)⋊C4—51no—
221C2×(C2×D3)⋊C4C2×D511yescharacteristic
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×Dic3⋊C4—51no—
231C2×Dic3⋊C4C2×D511yescharacteristic
232C2×C4×Dic3—51no—
233C2×C4×Dic3—51no—
234C2×C4×Dic3C2×D511yescharacteristic
235#872—58no—
236C3×#95—51no—
237C3×#95C2×D511yescharacteristic
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⋊#95C2×D511yescharacteristic
248C24×C5—31no—
249C22×C4×C5—31no—
250C22×C4×C5—31no—
251C22×C4×C5—31no—
252C22×C4×C5C22×D311yescharacteristic
253C22×C4×C5C22×D311yescharacteristic
254C22×C4×C5C22×D311yescharacteristic
255C22×Dic5—31no—
256C22×Dic5—31no—
257C22×Dic5—34no—
258C22×Dic5—31no—
259C22×Dic5—31no—
260C22×Dic5—62no—
261C22×Dic5—62no—
262C22×Dic5C22×D311yescharacteristic
263C22×Dic5C22×D311yescharacteristic
264C22×Dic5C22×D311yescharacteristic
265C22×Dic5C22×D311yescharacteristic
266C5×C4⋊C4—121no—
267C5×C22⋊C4—34no—
268C5×C22⋊C4—121no—
269C5×C22⋊C4—121no—
270C42×C5—121no—
271C22⋊Dic5—34no—
272C22⋊Dic5—121no—
273C22⋊Dic5—121no—
274C4⋊Dic5—121no—
275#683—22no—
276#683—22no—
277#683—34no—
278#683—34no—
279#683—62no—
280#683—62no—
281#683—121no—
282#683—121no—
283C4×Dic5—34no—
284C4×Dic5—41no—
285C4×Dic5—41no—
286C4×Dic5—121no—
287C4×Dic5C4×D314yes—
288C2×#117—151no—
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—51no—
302C4×C4⋊C4—151no—
303C22×C3×C5C23×C411yescharacteristic
304C22×C3×C5C2×#4111yescharacteristic
305C22×C3×C5C2×#4111yescharacteristic
306C22×C3×C5H(5,𝔽2)11yescharacteristic
307C22×C3×C5H(5,𝔽2)11yescharacteristic
308C22×C3×C52−1+411yescharacteristic
309C22×C3×C52−1+411yescharacteristic
310C2×C5×D3—22no—
311C2×C5×D3—22no—
312C2×C5×D3—22no—
313C2×C5×D3—41no—
314C2×C5×D3—41no—
315C2×C5×D3—41no—
316C2×C5×D3—41no—
317C3×C4×C5—22no—
318C3×C4×C5—41no—
319C3×C4×C5—41no—
320Dic15—22no—
321Dic15—22no—
322Dic15—41no—
323Dic15—41no—
324C3×Dic5—22no—
325C3×Dic5—41no—
326C3×Dic5—41no—
327C3×Dic5#11714yes—
328C5×Dic3—22no—
329C5×Dic3—41no—
330C5×Dic3—41no—
331C23×D3C22×D511yescharacteristic
332C22×C3×C4—51no—
333C22×C3×C4—51no—
334C22×C3×C4—51no—
335C22×C3×C4—51no—
336C22×C3×C4C22×D511yescharacteristic
337C22×C3×C4C22×D511yescharacteristic
338C22×C3×C4C22×D511yescharacteristic
339C22×Dic3—51no—
340C22×Dic3—51no—
341C22×Dic3—51no—
342C22×Dic3—51no—
343C22×Dic3C22×D511yescharacteristic
344C22×Dic3C22×D511yescharacteristic
345C22×Dic3C22×D511yescharacteristic
346C2×C4×D3—54no—
347C2×C4×D3—102no—
348C2×C4×D3—102no—
349C3×C4⋊C4—102no—
350C3×C4⋊C4—102no—
351C3×C42—54no—
352C3×C42—201no—
353C3×C42—201no—
354(C2×D3)⋊C4—41no—
355(C2×D3)⋊C4—41no—
356(C2×D3)⋊C4—54no—
357(C2×D3)⋊C4—201no—
358(C2×D3)⋊C4—201no—
359(C2×D3)⋊C4C4×D514yes—
360C4⋊Dic3—102no—
361C4⋊Dic3—102no—
362Dic3⋊C4—41no—
363Dic3⋊C4—54no—
364Dic3⋊C4—54no—
365Dic3⋊C4—201no—
366Dic3⋊C4—201no—
367Dic3⋊C4—201no—
368C4×Dic3—41no—
369C4×Dic3—54no—
370C4×Dic3—201no—
371C23×C5—32no—
372C23×C5—61no—
373C23×C5—61no—
374C23×C5—61no—
375C23×C5—61no—
376C23×C5—61no—
377C23×C5—61no—
378C23×C5C23×D311yescharacteristic
379C2×C4×C5—21no—
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—21no—
387C2×C4×C5—32no—
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×C5C2×C4×D312yes—
397C2×Dic5—21no—
398C2×Dic5—21no—
399C2×Dic5—21no—
400C2×Dic5—21no—
401C2×Dic5—21no—
402C2×Dic5—21no—
403C2×Dic5—21no—
404C2×Dic5—21no—
405C2×Dic5—32no—
406C2×Dic5—32no—
407C2×Dic5—61no—
408C2×Dic5—61no—
409C2×Dic5—61no—
410C2×Dic5—61no—
411C2×Dic5—68no—
412C2×Dic5—61no—
413C2×Dic5—61no—
414C2×Dic5—61no—
415C2×Dic5—61no—
416C2×Dic5—61no—
417C2×Dic5—61no—
418C2×Dic5C2×C4×D312yes—
419C2×Dic5C2×C4×D312yes—
420C2×Dic5#23512yes—
421C2×Dic5#23512yes—
422C23×C4—151no—
423#117—158no—
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—31no—
437C2×C22⋊C4—151no—
438C2×C22⋊C4—151no—
439C2×C22⋊C4—151no—
440C2×C42—31no—
441C2×C42—51no—
442C2×C42—51no—
443C2×C42—51no—
444C2×C42—151no—
445C2×C42—151no—
446#95—31no—
447#95—51no—
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#95D3×D511yescharacteristic
458C2×C3×C5C2×#11711yescharacteristic
459C2×C3×C5#52011yescharacteristic
460C2×C3×C5#52011yescharacteristic
461C2×C3×C5#54011yescharacteristic
462C2×C3×C5#54111yescharacteristic
463C2×C3×C5#54211yescharacteristic
464C2×C3×C5#54211yescharacteristic
465C5×D3—42no—
466C23×C3C23×D511yescharacteristic
467C22×D3—21no—
468C22×D3—21no—
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3C2×C4×D512yes—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—52no—
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—101no—
493C2×C3×C4—101no—
494C2×C3×C4C2×C4×D512yes—
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—52no—
504C2×Dic3—52no—
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×Dic3C2×C4×D512yes—
516C4×D3—108no—
517C22×C5—62no—
518C22×C5—62no—
519C22×C5—62no—
520C22×C5—121no—
521C22×C5—121no—
522C22×C5—121no—
523C22×C5—121no—
524C22×C5C22×C4×D311yescharacteristic
525C22×C5C2×#23511yescharacteristic
526C22×C5C2×#23511yescharacteristic
527C22×C5#100411yescharacteristic
528C22×C5#100711yescharacteristic
529C22×C5#100911yescharacteristic
530C22×C5#101011yescharacteristic
531C4×C5—22no—
532C4×C5—41no—
533C4×C5—41no—
534C4×C5—62no—
535C4×C5—121no—
536C4×C5—121no—
537Dic5—22no—
538Dic5—41no—
539Dic5—41no—
540Dic5—62no—
541Dic5—62no—
542Dic5—121no—
543Dic5—121no—
544Dic5#87214yes—
545C24—31no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—51no—
550C22×C4—51no—
551C22×C4—51no—
552C22×C4—51no—
553C22×C4—154no—
554C22×C4—151no—
555C22×C4—151no—
556C22×C4—151no—
557C22×C4—151no—
558C22×C4—302no—
559C22×C4—302no—
560C22×C4C2×D3×D511yescharacteristic
561C22×C4C2×D3×D511yescharacteristic
562C22×C4C2×D3×D511yescharacteristic
563C4⋊C4—102no—
564C4⋊C4—102no—
565C4⋊C4—121no—
566C4⋊C4—154no—
567C4⋊C4—154no—
568C4⋊C4—302no—
569C4⋊C4—302no—
570C4⋊C4—601no—
571C4⋊C4—601no—
572C4⋊C4—601no—
573C22⋊C4—34no—
574C22⋊C4—121no—
575C22⋊C4—121no—
576C22⋊C4—154no—
577C22⋊C4—601no—
578C22⋊C4—601no—
579C42—54no—
580C42—121no—
581C42—154no—
582C42—201no—
583C42—201no—
584C42—601no—
585C3×C5#231411yescharacteristic, complemented, Hall
586C22×C3C22×C4×D511yescharacteristic
587C22×C3#414411yescharacteristic
588C22×C3#414411yescharacteristic
589C22×C3D5×#4111yescharacteristic
590C22×C3D5×#4111yescharacteristic
591C22×C3#415011yescharacteristic
592C22×C3#415011yescharacteristic
593C2×D3—22no—
594C2×D3—22no—
595C2×D3—22no—
596C2×D3—41no—
597C2×D3—41no—
598C2×D3—41no—
599C2×D3—41no—
600C3×C4—22no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—54no—
604C3×C4—102no—
605C3×C4—201no—
606C3×C4—201no—
607Dic3—22no—
608Dic3—41no—
609Dic3—41no—
610Dic3—102no—
611Dic3—102no—
612Dic3—201no—
613Dic3—201no—
614C2×C5—122no—
615C2×C5C2×#87211yescharacteristic
616C2×C5#550411yescharacteristic
617C2×C5#552311yescharacteristic
618C2×C5#556111yescharacteristic
619C2×C5#556211yescharacteristic
620C2×C5#558211yescharacteristic
621C2×C5#558311yescharacteristic
622C23—32no—
623C23—61no—
624C23—61no—
625C23—61no—
626C23—61no—
627C23—61no—
628C23—61no—
629C23C22×D3×D511yescharacteristic
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—32no—
639C2×C4—52no—
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—101no—
652C2×C4—101no—
653C2×C4—101no—
654C2×C4—101no—
655C2×C4—101no—
656C2×C4—101no—
657C2×C4—101no—
658C2×C4—101no—
659C2×C4—152no—
660C2×C4—152no—
661C2×C4—308no—
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×C4C4×D3×D512yes—
673C2×C3D5×#11711yescharacteristic
674C2×C3#6588011yescharacteristic
675C2×C3#6588011yescharacteristic
676C2×C3#6594911yescharacteristic
677C2×C3#6599611yescharacteristic
678C2×C3#6600311yescharacteristic
679C2×C3#6603511yescharacteristic
680D3—42no—
681C5#7376011yescharacteristic, complemented, Sylow
682C22—62no—
683C22—62no—
684C22—62no—
685C22—121no—
686C22—121no—
687C22—121no—
688C22—121no—
689C22C2×C4×D3×D511yescharacteristic
690C22D5×#23511yescharacteristic
691C22D5×#23511yescharacteristic
692C22#9202011yescharacteristic
693C22#9202511yescharacteristic
694C22#9202711yescharacteristic
695C22#9203011yescharacteristic
696C4—22no—
697C4—41no—
698C4—41no—
699C4—54no—
700C4—62no—
701C4—102no—
702C4—121no—
703C4—121no—
704C4—201no—
705C4—201no—
706C4—302no—
707C4—302no—
708C4—601no—
709C4—601no—
710C3#1060718711yescharacteristic, complemented, Sylow
711C2—122no—
712C2D5×#87211yescharacteristic
713C2#1175282411yescharacteristic
714C2#1175289811yescharacteristic
715C2#1175289911yescharacteristic
716C2#1175334311yescharacteristic
717C2#1175349211yescharacteristic
718C2#1175367111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenter#95D3×D5
hypocenterC3×C5#2314
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #11750753C2semidirect
4. C3×#64938C2semidirect
7. #11748847C2semidirect
8. #11748815C2semidirect
9. #11748813C2semidirect
10. C4×#6668C2semidirect
14. #11748642C2semidirect
15. #11748641C2semidirect
40. #91398C4semidirect
68. #64938D3semidirect
585. C3×C5#2314semidirect
681. C5#73760semidirect
710. C3#10607187semidirect

Maximal subgroups

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

subgroupindex
C2×#913982
#117507532
C5×#46692
C3×#649382
#117488742
#117488472
#117488152
#117488132
C4×#66682
#117487942
#117487152
#117487142
#117486422
#117486412
#106071873
#737605