Finite Group Databasebeta

← #14331049

Subgroups — #14331049

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×#91369C211yesmaximal, characteristic
2#11750755C211yesmaximal, characteristic, complemented
3C5×#4667C211yesmaximal, characteristic
4C3×#64935C211yesmaximal, characteristic, complemented
5#11748818C211yesmaximal, characteristic, complemented
6#11748813C211yesmaximal, characteristic, complemented
7#11748777C211yesmaximal, characteristic
8#11748724C211yesmaximal, characteristic
9#11748721C211yesmaximal, characteristic
10#11748718C211yesmaximal, characteristic
11#11748715C211yesmaximal, characteristic
12#11748689C211yesmaximal, characteristic, complemented
13#11748672C211yesmaximal, characteristic, complemented
14#11748662C211yesmaximal, characteristic, complemented
15#11748633C211yesmaximal, characteristic, complemented
16#10605617—31nomaximal, Hall
17C22×C4×C5×D3C2211yescharacteristic
18C22×C3×Dic10C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20C2×#6712C2211yescharacteristic
21C2×C4×Dic15C2211yescharacteristic
22C2×C5×(C2×D3)⋊C4C2211yescharacteristic
23C2×C5×(C2×D3)⋊C4C2211yescharacteristic
24C2×C5×Dic3⋊C4C2211yescharacteristic
25C2×C5×Dic3⋊C4C2211yescharacteristic
26C2×C3×#683C2211yescharacteristic
27C2×C3×C4×Dic5C2211yescharacteristic
28C2×#6669C2211yescharacteristic
29C2×#6669C2211yescharacteristic
30C2×#6669C2211yescharacteristic
31C2×#6668C2211yescharacteristic
32C2×(C2×D3)⋊Dic5C2211yescharacteristic
33C2×(C2×D3)⋊Dic5C2211yescharacteristic
34C2×(C2×D3)⋊Dic5C2211yescharacteristic
35C2×(C2×D3)⋊Dic5C2211yescharacteristic
36C2×Dic3×Dic5C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38#91369C418yescomplemented
39C3×C5×#95C2211yescharacteristic
40#91115C2211yescharacteristic
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43C5×C3⋊#95C2211yescharacteristic
44C3×#3963C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#76617—51nomaximal, Hall
54C2×#4070—31no—
55C5×#380—31no—
56#65500—31no—
57#65267—31no—
58#65267—31no—
59#65261—31no—
60#65261—31no—
61#65234—31no—
62#65234—31no—
63#65233—31no—
64#65233—31no—
65#64943—31no—
66#64943—31no—
67#64935—31no—
68#64935D311yescharacteristic, 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
80C2×C4×C5×D3—41no—
81C2×C4×C5×D3—41no—
82C2×C4×C5×D3C2×C414yes—
83C22×C3×Dic5C2311yescharacteristic
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C2×C3×Dic10—41no—
88C2×C3×Dic10—41no—
89C2×C3×Dic10C2×C414yes—
90C4⋊Dic15C2×C414yes—
91#6712—41no—
92C4×Dic15—41no—
93C5×(C2×D3)⋊C4—41no—
94C5×(C2×D3)⋊C4—41no—
95C5×Dic3⋊C4—41no—
96C5×Dic3⋊C4—41no—
97C3×#683—41no—
98C3×C4×Dic5—41no—
99#6669—41no—
100#6669C2×C414yes—
101#6669C2×C414yes—
102#6668—41no—
103(C2×D3)⋊Dic5—41no—
104(C2×D3)⋊Dic5—41no—
105(C2×D3)⋊Dic5C2×C414yes—
106(C2×D3)⋊Dic5C2×C414yes—
107Dic3×Dic5—41no—
108Dic3×Dic5—41no—
109C2×#946—51no—
110C3×#391—51no—
111#5229—51no—
112#4990—51no—
113#4976—51no—
114#4940—51no—
115#4933—51no—
116#4670—51no—
117#4669—51no—
118#4667D511yescharacteristic
119#4664—51no—
120#4654—51no—
121#4653—51no—
122#4652—51no—
123#4647—51no—
124C23×C4×C5—31no—
125C22×Dic10C2×D311yescharacteristic
126C2×C5×C4⋊C4—31no—
127C2×C5×C4⋊C4—31no—
128C2×C5×C22⋊C4—31no—
129C2×C5×C22⋊C4—31no—
130C2×C22⋊Dic5—31no—
131C2×C22⋊Dic5—31no—
132C2×C22⋊Dic5—31no—
133C2×C22⋊Dic5—31no—
134C2×C4⋊Dic5—31no—
135#4070—38no—
136C2×#683—31no—
137C2×#683—31no—
138C2×#683—31no—
139C2×#683—31no—
140C2×#683—31no—
141C2×#683C2×D311yescharacteristic
142C2×C4×Dic5—31no—
143C2×C4×Dic5—31no—
144C2×C4×Dic5—31no—
145C2×C4×Dic5C2×D311yescharacteristic
146C5×#95—31no—
147C5×#95C2×D311yescharacteristic
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#3963—31no—
157#3963C2×D311yescharacteristic
158#3963C2×D311yescharacteristic
159#3963C2×D311yescharacteristic
160#2378—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—
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×Dic5—21no—
210C2×C3×Dic5C22×C412yes—
211C2×C3×Dic5C22×C412yes—
212C3×Dic10—44no—
213C22×C3×Q8—51no—
214C22×C4×D3C2×D511yescharacteristic
215C2×C3×C4⋊C4—51no—
216C2×C3×C42—51no—
217#946—58no—
218C2×(C2×D3)⋊C4—51no—
219C2×(C2×D3)⋊C4—51no—
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×Dic3⋊C4C2×D511yescharacteristic
231C2×Dic3⋊C4C2×D511yescharacteristic
232C2×C4×Dic3—51no—
233C2×C4×Dic3—51no—
234C2×C4×Dic3—51no—
235C3×#95—51no—
236C3×#95—51no—
237C3×#95—51no—
238C3×#95C2×D511yescharacteristic
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
249C24×C5—31no—
250C22×C4×C5—31no—
251C22×C4×C5—34no—
252C22×C4×C5—31no—
253C22×C4×C5—31no—
254C22×C4×C5—121no—
255C22×C4×C5—121no—
256C22×C4×C5C22×D311yescharacteristic
257C22×C4×C5C22×D311yescharacteristic
258C22×C4×C5C22×D311yescharacteristic
259C22×Dic5—31no—
260C22×Dic5—31no—
261C22×Dic5—31no—
262C22×Dic5—31no—
263C22×Dic5C22×D311yescharacteristic
264C22×Dic5C22×D311yescharacteristic
265C22×Dic5C22×D311yescharacteristic
266C22×Dic5C22×D311yescharacteristic
267C2×Dic10—41no—
268C2×Dic10—41no—
269C2×Dic10C4×D314yes—
270C5×C4⋊C4—121no—
271C5×C4⋊C4—121no—
272C5×C22⋊C4—121no—
273C5×C22⋊C4—121no—
274C22⋊Dic5—34no—
275C22⋊Dic5—34no—
276C22⋊Dic5—121no—
277C22⋊Dic5—121no—
278C4⋊Dic5—34no—
279#683—34no—
280#683—34no—
281#683—41no—
282#683—121no—
283#683—121no—
284#683—121no—
285C4×Dic5—41no—
286C4×Dic5—121no—
287C4×Dic5—121no—
288C4×Dic5—121no—
289C2×C22⋊Q8—151no—
290#391—51no—
291#391—151no—
292#389—151no—
293#389—151no—
294#388—151no—
295#388—151no—
296#388—151no—
297#388—151no—
298#387—151no—
299#387—151no—
300#387—151no—
301#387—151no—
302#381—151no—
303#380—31no—
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×C5×D3—22no—
312C2×C5×D3—22no—
313C2×C5×D3—22no—
314C2×C5×D3—41no—
315C2×C5×D3—41no—
316C2×C5×D3—41no—
317C2×C5×D3—41no—
318C3×C4×C5—22no—
319C3×C4×C5—41no—
320C3×C4×C5—41no—
321Dic15—22no—
322Dic15—22no—
323Dic15—41no—
324Dic15—41no—
325C3×Dic5—22no—
326C3×Dic5—22no—
327C3×Dic5—41no—
328C3×Dic5—41no—
329C5×Dic3—22no—
330C5×Dic3—41no—
331C5×Dic3—41no—
332C23×D3C22×D511yescharacteristic
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—51no—
340C22×C3×C4C22×D511yescharacteristic
341C22×C3×C4C22×D511yescharacteristic
342C22×C3×C4C22×D511yescharacteristic
343C22×Dic3—51no—
344C22×Dic3—51no—
345C22×Dic3—51no—
346C22×Dic3—51no—
347C22×Dic3C22×D511yescharacteristic
348C22×Dic3C22×D511yescharacteristic
349C22×Dic3C22×D511yescharacteristic
350C2×C4×D3—41no—
351C2×C4×D3—41no—
352C2×C4×D3C4×D514yes—
353C3×C4⋊C4—201no—
354C3×C42—201no—
355(C2×D3)⋊C4—41no—
356(C2×D3)⋊C4—41no—
357(C2×D3)⋊C4—54no—
358(C2×D3)⋊C4—54no—
359(C2×D3)⋊C4—201no—
360(C2×D3)⋊C4—201no—
361C4⋊Dic3—54no—
362C4⋊Dic3—201no—
363Dic3⋊C4—41no—
364Dic3⋊C4—41no—
365Dic3⋊C4—54no—
366Dic3⋊C4—54no—
367Dic3⋊C4—201no—
368Dic3⋊C4—201no—
369C4×Dic3—201no—
370C4×Dic3—201no—
371C4×Dic3—201no—
372C23×C5—32no—
373C23×C5—61no—
374C23×C5—61no—
375C23×C5—61no—
376C23×C5—61no—
377C23×C5—61no—
378C23×C5—61no—
379C23×C5C23×D311yescharacteristic
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—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×Dic5—21no—
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—61no—
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×Dic5C2×C4×D312yes—
422C2×Dic5C2×C4×D312yes—
423Dic10—44no—
424C22×Q8—51no—
425C23×C4—31no—
426C22⋊Q8—158no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
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⋊C4—151no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—151no—
439C2×C22⋊C4—151no—
440C2×C22⋊C4—151no—
441C2×C22⋊C4—151no—
442C2×C42—51no—
443C2×C42—151no—
444C2×C42—151no—
445C2×C42—151no—
446#95—31no—
447#95—51no—
448#95—51no—
449#95—51no—
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#95D3×D511yescharacteristic
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
467C5×D3—42no—
468C23×C3C23×D511yescharacteristic
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3C2×C4×D512yes—
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—21no—
484C2×C3×C4—21no—
485C2×C3×C4—52no—
486C2×C3×C4—52no—
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×C4—101no—
495C2×C3×C4—101no—
496C2×C3×C4—101no—
497C2×C3×C4C2×C4×D512yes—
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—52no—
507C2×Dic3—52no—
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×Dic3C2×C4×D512yes—
519C4×D3—44no—
520C22×C5—62no—
521C22×C5—62no—
522C22×C5—62no—
523C22×C5—121no—
524C22×C5—121no—
525C22×C5—121no—
526C22×C5—121no—
527C22×C5C22×C4×D311yescharacteristic
528C22×C5#100411yescharacteristic
529C22×C5#100411yescharacteristic
530C22×C5#100711yescharacteristic
531C22×C5#100711yescharacteristic
532C22×C5#100911yescharacteristic
533C22×C5#101011yescharacteristic
534C4×C5—22no—
535C4×C5—41no—
536C4×C5—41no—
537C4×C5—62no—
538C4×C5—121no—
539C4×C5—121no—
540Dic5—22no—
541Dic5—22no—
542Dic5—41no—
543Dic5—41no—
544Dic5—62no—
545Dic5—62no—
546Dic5—121no—
547Dic5—121no—
548C24—31no—
549C2×Q8—54no—
550C2×Q8—201no—
551C2×Q8—201no—
552C22×C4—31no—
553C22×C4—34no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—51no—
557C22×C4—51no—
558C22×C4—51no—
559C22×C4—51no—
560C22×C4—121no—
561C22×C4—121no—
562C22×C4—151no—
563C22×C4—151no—
564C22×C4—151no—
565C22×C4—151no—
566C22×C4C2×D3×D511yescharacteristic
567C22×C4C2×D3×D511yescharacteristic
568C22×C4C2×D3×D511yescharacteristic
569C4⋊C4—121no—
570C4⋊C4—121no—
571C4⋊C4—154no—
572C4⋊C4—154no—
573C4⋊C4—154no—
574C4⋊C4—201no—
575C4⋊C4—601no—
576C4⋊C4—601no—
577C4⋊C4—601no—
578C22⋊C4—121no—
579C22⋊C4—121no—
580C22⋊C4—154no—
581C22⋊C4—154no—
582C22⋊C4—601no—
583C22⋊C4—601no—
584C42—201no—
585C42—601no—
586C42—601no—
587C42—601no—
588C3×C5#237811yescharacteristic, complemented, Hall
589C22×C3C22×C4×D511yescharacteristic
590C22×C3#414411yescharacteristic
591C22×C3#414411yescharacteristic
592C22×C3#414411yescharacteristic
593C22×C3#414711yescharacteristic
594C22×C3#415011yescharacteristic
595C22×C3#415011yescharacteristic
596C2×D3—22no—
597C2×D3—22no—
598C2×D3—22no—
599C2×D3—41no—
600C2×D3—41no—
601C2×D3—41no—
602C2×D3—41no—
603C3×C4—22no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—102no—
607C3×C4—102no—
608C3×C4—201no—
609C3×C4—201no—
610Dic3—22no—
611Dic3—41no—
612Dic3—41no—
613Dic3—102no—
614Dic3—102no—
615Dic3—201no—
616Dic3—201no—
617C2×C5—122no—
618C2×C5#548611yescharacteristic
619C2×C5#557211yescharacteristic
620C2×C5#557411yescharacteristic
621C2×C5#564611yescharacteristic
622C2×C5#564711yescharacteristic
623C2×C5#568411yescharacteristic
624C2×C5#573511yescharacteristic
625C23—32no—
626C23—61no—
627C23—61no—
628C23—61no—
629C23—61no—
630C23—61no—
631C23—61no—
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—21no—
641C2×C4—21no—
642C2×C4—32no—
643C2×C4—52no—
644C2×C4—52no—
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—101no—
654C2×C4—101no—
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—124no—
664C2×C4—152no—
665C2×C4—152no—
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×C4—301no—
675C2×C4—301no—
676C2×C4C4×D3×D512yes—
677C2×C3#6582011yescharacteristic
678C2×C3#6583811yescharacteristic
679C2×C3#6585011yescharacteristic
680C2×C3#6595511yescharacteristic
681C2×C3#6595511yescharacteristic
682C2×C3#6598011yescharacteristic
683C2×C3#6598011yescharacteristic
684D3—42no—
685C5#7661711yescharacteristic, complemented, Sylow
686C22—62no—
687C22—62no—
688C22—62no—
689C22—121no—
690C22—121no—
691C22—121no—
692C22—121no—
693C22#9200111yescharacteristic
694C22#9200411yescharacteristic
695C22C2×C4×D3×D511yescharacteristic
696C22#9202511yescharacteristic
697C22#9202511yescharacteristic
698C22#9202711yescharacteristic
699C22#9202911yescharacteristic
700C4—22no—
701C4—41no—
702C4—41no—
703C4—62no—
704C4—102no—
705C4—102no—
706C4—121no—
707C4—121no—
708C4—201no—
709C4—201no—
710C4—302no—
711C4—302no—
712C4—601no—
713C4—601no—
714C3#1060561711yescharacteristic, complemented, Sylow
715C2—122no—
716C2#1175252311yescharacteristic
717C2#1175306511yescharacteristic
718C2#1175317111yescharacteristic
719C2#1175317611yescharacteristic
720C2#1175333711yescharacteristic
721C2#1175336211yescharacteristic
722C2#1175381311yescharacteristic
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#2378
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #11750755C2semidirect
4. C3×#64935C2semidirect
5. #11748818C2semidirect
6. #11748813C2semidirect
12. #11748689C2semidirect
13. #11748672C2semidirect
14. #11748662C2semidirect
15. #11748633C2semidirect
38. #91369C4semidirect
68. #64935D3semidirect
588. C3×C5#2378semidirect
685. C5#76617semidirect
714. C3#10605617semidirect

Maximal subgroups

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

subgroupindex
C2×#913692
#117507552
C5×#46672
C3×#649352
#117488182
#117488132
#117487772
#117487242
#117487212
#117487182
#117487152
#117486892
#117486722
#117486622
#117486332
#106056173
#766175