Finite Group Databasebeta

← #14326495

Subgroups — #14326495

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×C5×#877C211yesmaximal, characteristic
2#11751051C211yesmaximal, characteristic
3C3×#65239C211yesmaximal, characteristic
4#11749487C211yesmaximal, characteristic
5Dic5×#217C211yesmaximal, characteristic
6#11749472C211yesmaximal, characteristic
7C2×#90994C211yesmaximal, characteristic
8Dic3×C4⋊Dic5C211yesmaximal, characteristic, complemented
9#11748684C211yesmaximal, characteristic, complemented
10#11748684C211yesmaximal, characteristic, complemented
11#11748673C211yesmaximal, characteristic, complemented
12#11748673C211yesmaximal, characteristic, complemented
13#11748643C211yesmaximal, characteristic, complemented
14#11748619C211yesmaximal, characteristic, complemented
15#11748618C211yesmaximal, characteristic, complemented
16#10613968—31nomaximal, Hall
17C23×Dic15C2211yescharacteristic
18C23×C5×Dic3C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×#6719C2211yescharacteristic
22C2×C4⋊Dic15C2211yescharacteristic
23C2×C4⋊Dic15C2211yescharacteristic
24C2×C5×#217C2211yescharacteristic
25C2×C5×Dic3⋊C4C2211yescharacteristic
26C2×C5×Dic3⋊C4C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C4×C5×Dic3C2211yescharacteristic
29C5×#877C418yescomplemented
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C2×C3×C4⋊Dic5C2211yescharacteristic
32C2×C3×C4⋊Dic5C2211yescharacteristic
33C2×Dic3×Dic5C2211yescharacteristic
34C2×Dic3×Dic5C2211yescharacteristic
35C2×Dic3×Dic5C2211yescharacteristic
36C2×Dic3×Dic5C2211yescharacteristic
37#91115C2211yescharacteristic
38#91115C2211yescharacteristic
39C3×#3963C2211yescharacteristic
40C3×#3963C2211yescharacteristic
41#90994C2211yescharacteristic
42#90994C2211yescharacteristic
43#90994C2211yescharacteristic
44#90994C2211yescharacteristic
45#90994C2211yescharacteristic
46#90994C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#74392—51nomaximal, Hall
54C2×C5×#117—31no—
55#65500—31no—
56C2×#3963—31no—
57#65270—31no—
58#65270—31no—
59#65270—31no—
60#65270—31no—
61#65239—31no—
62#65239D311yescharacteristic
63C22⋊C4×Dic5—31no—
64C22⋊C4×Dic5—31no—
65#65226—31no—
66#65225—31no—
67C4×C4⋊Dic5—31no—
68#65221—31no—
69C24×C3×C5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×Dic15—22no—
73C22×Dic15—22no—
74C22×Dic15—41no—
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×C5×Dic3—22no—
80C22×C5×Dic3—22no—
81C22×C5×Dic3C2×C414yes—
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C3×Dic5—22no—
87C22×C3×Dic5—22no—
88C22×C3×Dic5—41no—
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C3×C5×C22⋊C4C2×C414yes—
94#6719—22no—
95C4⋊Dic15—22no—
96C4⋊Dic15—41no—
97C5×#217C2×C414yes—
98C5×Dic3⋊C4C2×C414yescomplemented
99C5×Dic3⋊C4C2×C414yescomplemented
100C4×C5×Dic3C2×C414yescomplemented
101C4×C5×Dic3C2×C414yescomplemented
102C3×C22⋊Dic5—22no—
103C3×C4⋊Dic5—22no—
104C3×C4⋊Dic5—41no—
105Dic3×Dic5—22no—
106Dic3×Dic5—22no—
107Dic3×Dic5—41no—
108Dic3×Dic5—41no—
109C2×#877D511yescharacteristic
110C3×#385—51no—
111C4×#217—51no—
112C2×C3⋊#95—51no—
113#4978—51no—
114#4978—51no—
115#4977—51no—
116Dic3×C4⋊C4—51no—
117#4950—51no—
118#4943—51no—
119Dic3×C22⋊C4—51no—
120#4655—51no—
121#4655—51no—
122#4651—51no—
123#4648—51no—
124C23×C4×C5—31no—
125C23×Dic5—31no—
126C23×Dic5C2×D311yescharacteristic
127C5×#117—38no—
128C2×C5×C4⋊C4—31no—
129C2×C5×C4⋊C4—31no—
130C2×C5×C22⋊C4—31no—
131C2×C5×C22⋊C4C2×D311yescharacteristic
132C2×C42×C5—31no—
133C2×C42×C5—31no—
134C2×C22⋊Dic5—31no—
135C2×C22⋊Dic5C2×D311yescharacteristic
136C2×C4⋊Dic5—31no—
137C2×C4⋊Dic5—31no—
138C2×C4⋊Dic5C2×D311yescharacteristic
139C2×C4⋊Dic5C2×D311yescharacteristic
140C2×C4×Dic5—31no—
141C2×C4×Dic5—31no—
142C2×C4×Dic5—31no—
143C2×C4×Dic5—31no—
144#3963—31no—
145#3963—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#3963—31no—
157#3963—31no—
158#3963C2×D311yescharacteristic
159#3963C2×D311yescharacteristic
160#2343—151noSylow
161C23×C3×C5—21no—
162C23×C3×C5—21no—
163C23×C3×C5—21no—
164C23×C3×C5—21no—
165C23×C3×C5C22×C412yes—
166C23×C3×C5#4112yes—
167C23×C3×C5#4112yes—
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—44no—
187C2×Dic15#4112yes—
188C2×C5×Dic3—28no—
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×Dic3C22×C412yes—
198C2×C5×Dic3C22×C412yes—
199C2×C5×Dic3C22×C412yes—
200C2×C5×Dic3C22×C412yes—
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×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—44no—
213C2×C3×Dic5#4112yes—
214C23×C3×C4—51no—
215C23×Dic3—51no—
216C23×Dic3C2×D511yescharacteristic
217C2×C3×C4⋊C4—51no—
218C2×C3×C4⋊C4—51no—
219C2×C3×C22⋊C4—51no—
220C2×C3×C22⋊C4C2×D511yescharacteristic
221C2×#217—51no—
222C2×#217C2×D511yescharacteristic
223C2×C4⋊Dic3—51no—
224C2×C4⋊Dic3—51no—
225C2×Dic3⋊C4C2×D511yescharacteristic
226C2×Dic3⋊C4C2×D511yescharacteristic
227C2×C4×Dic3—51no—
228C2×C4×Dic3—51no—
229C2×C4×Dic3—51no—
230C2×C4×Dic3—51no—
231C2×C4×Dic3C2×D511yescharacteristic
232C2×C4×Dic3C2×D511yescharacteristic
233#877Dic518yescomplemented
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⋊#95—51no—
249C3⋊#95—51no—
250C24×C5C22×D311yescharacteristic
251C22×C4×C5—34no—
252C22×C4×C5—31no—
253C22×C4×C5—31no—
254C22×C4×C5—31no—
255C22×C4×C5—31no—
256C22×C4×C5—62no—
257C22×C4×C5—62no—
258C22×C4×C5C22×D311yescharacteristic
259C22×C4×C5C22×D311yescharacteristic
260C22×Dic5—22no—
261C22×Dic5—22no—
262C22×Dic5—31no—
263C22×Dic5—31no—
264C22×Dic5—31no—
265C22×Dic5—31no—
266C22×Dic5—41no—
267C22×Dic5—62no—
268C22×Dic5—62no—
269C22×Dic5—121no—
270C22×Dic5C22×D311yescharacteristic
271C22×Dic5C22×D311yescharacteristic
272C22×Dic5C22×D311yescharacteristic
273C22×Dic5C22×D311yescharacteristic
274C5×C4⋊C4—34no—
275C5×C4⋊C4—34no—
276C5×C22⋊C4—34no—
277C5×C22⋊C4C4×D314yes—
278C42×C5—34no—
279C42×C5—34no—
280C22⋊Dic5—22no—
281C22⋊Dic5—62no—
282C4⋊Dic5—22no—
283C4⋊Dic5—41no—
284C4⋊Dic5—62no—
285C4⋊Dic5—121no—
286C4×Dic5—62no—
287C4×Dic5—62no—
288C4×Dic5—121no—
289C4×Dic5—121no—
290C2×#117—31no—
291#387—151no—
292#387—151no—
293#387—151no—
294#387—151no—
295#385—51no—
296#385—151no—
297#383—151no—
298#382—151no—
299#381—151no—
300C4×C4⋊C4—151no—
301C4×C22⋊C4—151no—
302C4×C22⋊C4—151no—
303#376—151no—
304C2×#95—151no—
305C22×C3×C5—22no—
306C22×C3×C5—22no—
307C22×C3×C5—22no—
308C22×C3×C5—22no—
309C22×C3×C5—22no—
310C22×C3×C5—22no—
311C22×C3×C5#11714yes—
312C22×C3×C5C23×C411yescharacteristic
313C22×C3×C5C2×#4111yescharacteristic
314C22×C3×C5C2×#4111yescharacteristic
315C22×C3×C5C2×#4111yescharacteristic
316C22×C3×C5C2×#4111yescharacteristic
317C22×C3×C5H(5,𝔽2)11yescharacteristic
318C22×C3×C52−1+411yescharacteristic
319C3×C4×C5—22no—
320C3×C4×C5—22no—
321Dic15—22no—
322Dic15—41no—
323Dic15—41no—
324Dic15—41no—
325C3×Dic5—22no—
326C3×Dic5—41no—
327C3×Dic5—41no—
328C3×Dic5—41no—
329C5×Dic3—22no—
330C5×Dic3—22no—
331C5×Dic3—22no—
332C5×Dic3—22no—
333C24×C3C22×D511yescharacteristic
334C22×C3×C4—51no—
335C22×C3×C4—51no—
336C22×C3×C4—51no—
337C22×C3×C4—51no—
338C22×C3×C4—102no—
339C22×C3×C4—102no—
340C22×C3×C4—201no—
341C22×C3×C4C22×D511yescharacteristic
342C22×C3×C4C22×D511yescharacteristic
343C22×Dic3—22no—
344C22×Dic3—22no—
345C22×Dic3—51no—
346C22×Dic3—51no—
347C22×Dic3—51no—
348C22×Dic3—51no—
349C22×Dic3—102no—
350C22×Dic3—102no—
351C22×Dic3—201no—
352C22×Dic3C2×Dic514yes—
353C22×Dic3C22×D511yescharacteristic
354C22×Dic3C22×D511yescharacteristic
355C22×Dic3C22×D511yescharacteristic
356C22×Dic3C22×D511yescharacteristic
357C3×C4⋊C4—102no—
358C3×C4⋊C4—201no—
359C3×C22⋊C4—102no—
360C3×C22⋊C4C2×Dic514yes—
361#217—102no—
362#217C2×Dic514yes—
363C4⋊Dic3—102no—
364C4⋊Dic3—201no—
365Dic3⋊C4C2×Dic514yescomplemented
366Dic3⋊C4C2×Dic514yescomplemented
367C4×Dic3—102no—
368C4×Dic3—102no—
369C4×Dic3—201no—
370C4×Dic3—201no—
371C4×Dic3C2×Dic514yescomplemented
372C4×Dic3C2×Dic514yescomplemented
373C23×C5—21no—
374C23×C5—21no—
375C23×C5—21no—
376C23×C5—21no—
377C23×C5C2×C4×D312yes—
378C23×C5#23712yes—
379C23×C5#23912yes—
380C23×C5C23×D311yescharacteristic
381C2×C4×C5—21no—
382C2×C4×C5—21no—
383C2×C4×C5—21no—
384C2×C4×C5—21no—
385C2×C4×C5—32no—
386C2×C4×C5—32no—
387C2×C4×C5—32no—
388C2×C4×C5—32no—
389C2×C4×C5—68no—
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×C5C2×C4×D312yes—
399C2×C4×C5C2×C4×D312yes—
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—21no—
410C2×Dic5—21no—
411C2×Dic5—32no—
412C2×Dic5—44no—
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—61no—
423C2×Dic5—61no—
424C2×Dic5—124no—
425C2×Dic5#23712yes—
426C23×C4—31no—
427C23×C4—51no—
428C23×C4—151no—
429#117—38no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—51no—
433C2×C4⋊C4—51no—
434C2×C4⋊C4—151no—
435C2×C4⋊C4—151no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—51no—
438C2×C22⋊C4—151no—
439C2×C22⋊C4D3×D511yescharacteristic
440C2×C42—31no—
441C2×C42—31no—
442C2×C42—151no—
443C2×C42—151no—
444C2×C42—151no—
445C2×C42—151no—
446#95—51no—
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#95—151no—
458#95—151no—
459#95—151no—
460#95—151no—
461#95—151no—
462C2×C3×C5—24no—
463C2×C3×C5C2×#11711yescharacteristic
464C2×C3×C5C4×#4111yescharacteristic
465C2×C3×C5#52011yescharacteristic
466C2×C3×C5#55111yescharacteristic
467C2×C3×C5#55111yescharacteristic
468C2×C3×C5#55211yescharacteristic
469C2×C3×C5#55211yescharacteristic
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3#70912yes—
475C23×C3#70912yes—
476C23×C3C22×Dic512yes—
477C23×C3C23×D511yescharacteristic
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—52no—
483C2×C3×C4—101no—
484C2×C3×C4—101no—
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×C4—101no—
492C2×C3×C4—101no—
493C2×C3×C4—101no—
494C2×C3×C4—204no—
495C2×C3×C4C22×Dic512yes—
496C2×C3×C4C22×Dic512yes—
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—28no—
506C2×Dic3—52no—
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—
517C2×Dic3—101no—
518C2×Dic3—204no—
519C2×Dic3C22×Dic512yes—
520C2×Dic3C22×Dic512yes—
521C2×Dic3C22×Dic512yes—
522C2×Dic3C22×Dic512yes—
523C22×C5—22no—
524C22×C5—22no—
525C22×C5—22no—
526C22×C5—22no—
527C22×C5—22no—
528C22×C5—22no—
529C22×C5#89214yes—
530C22×C5C22×C4×D311yescharacteristic
531C22×C5C2×#23711yescharacteristic
532C22×C5C2×#23711yescharacteristic
533C22×C5#100411yescharacteristic
534C22×C5C2×#23911yescharacteristic
535C22×C5D3×#4111yescharacteristic
536C22×C5#101011yescharacteristic
537C4×C5—22no—
538C4×C5—22no—
539C4×C5—62no—
540C4×C5—62no—
541C4×C5—62no—
542C4×C5—62no—
543Dic5—22no—
544Dic5—41no—
545Dic5—41no—
546Dic5—41no—
547Dic5—62no—
548Dic5—121no—
549Dic5—121no—
550Dic5—121no—
551C24C2×D3×D511yescharacteristic
552C22×C4—34no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—51no—
558C22×C4—51no—
559C22×C4—51no—
560C22×C4—51no—
561C22×C4—62no—
562C22×C4—62no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—151no—
566C22×C4—151no—
567C22×C4—151no—
568C22×C4—151no—
569C22×C4—201no—
570C22×C4—302no—
571C22×C4—302no—
572C22×C4—601no—
573C22×C4C2×D3×D511yescharacteristic
574C22×C4C2×D3×D511yescharacteristic
575C4⋊C4—34no—
576C4⋊C4—34no—
577C4⋊C4—102no—
578C4⋊C4—201no—
579C4⋊C4—302no—
580C4⋊C4—601no—
581C22⋊C4—34no—
582C22⋊C4—102no—
583C22⋊C4—302no—
584C22⋊C4D3×Dic514yes—
585C42—34no—
586C42—34no—
587C42—302no—
588C42—302no—
589C42—601no—
590C42—601no—
591C3×C5#234311yescharacteristic, complemented, Hall
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3#407214yes—
599C22×C3C2×#70911yescharacteristic
600C22×C3C2×#70911yescharacteristic
601C22×C3D5×#4111yescharacteristic
602C22×C3D5×#4111yescharacteristic
603C22×C3#414911yescharacteristic
604C22×C3#415011yescharacteristic
605C22×C3C23×Dic511yescharacteristic
606C3×C4—22no—
607C3×C4—22no—
608C3×C4—102no—
609C3×C4—201no—
610C3×C4—201no—
611C3×C4—201no—
612Dic3—22no—
613Dic3—22no—
614Dic3—22no—
615Dic3—22no—
616Dic3—102no—
617Dic3—201no—
618Dic3—201no—
619Dic3—201no—
620C2×C5—24no—
621C2×C5C2×#89211yescharacteristic
622C2×C5C4×#23711yescharacteristic
623C2×C5#554611yescharacteristic
624C2×C5#558711yescharacteristic
625C2×C5#563711yescharacteristic
626C2×C5#564211yescharacteristic
627C2×C5#565011yescharacteristic
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23#676512yes—
633C23#676912yes—
634C23C2×D3×Dic512yes—
635C23C22×D3×D511yescharacteristic
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—32no—
641C2×C4—32no—
642C2×C4—32no—
643C2×C4—32no—
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—68no—
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—101no—
664C2×C4—101no—
665C2×C4—152no—
666C2×C4—204no—
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×C4—301no—
677C2×C4—301no—
678C2×C4—604no—
679C2×C4C2×D3×Dic512yes—
680C2×C4C2×D3×Dic512yes—
681C2×C3—24no—
682C2×C3#6586111yescharacteristic
683C2×C3#6586111yescharacteristic
684C2×C3#6586511yescharacteristic
685C2×C3#6586511yescharacteristic
686C2×C3C2×#407211yescharacteristic
687C2×C3#41×Dic511yescharacteristic
688C2×C3#6616111yescharacteristic
689C5#7439211yescharacteristic, complemented, Sylow
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22#9133814yes—
697C22C2×#676511yescharacteristic
698C22C2×#676911yescharacteristic
699C22#9202011yescharacteristic
700C22D5×#23711yescharacteristic
701C22#9202411yescharacteristic
702C22#9202611yescharacteristic
703C22C22×D3×Dic511yescharacteristic
704C4—22no—
705C4—22no—
706C4—62no—
707C4—62no—
708C4—62no—
709C4—62no—
710C4—102no—
711C4—201no—
712C4—201no—
713C4—201no—
714C4—302no—
715C4—601no—
716C4—601no—
717C4—601no—
718C3#1061396811yescharacteristic, complemented, Sylow
719C2—24no—
720C2#1175291611yescharacteristic
721C2#1175295011yescharacteristic
722C2#1175302311yescharacteristic
723C2#1175303511yescharacteristic
724C2C2×#9133811yescharacteristic
725C2Dic5×#23711yescharacteristic
726C2#1175492011yescharacteristic
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#2343
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. Dic3×C4⋊Dic5C2semidirect
9. #11748684C2semidirect
10. #11748684C2semidirect
11. #11748673C2semidirect
12. #11748673C2semidirect
13. #11748643C2semidirect
14. #11748619C2semidirect
15. #11748618C2semidirect
29. C5×#877C4semidirect
98. C5×Dic3⋊C4C2×C4semidirect
99. C5×Dic3⋊C4C2×C4semidirect
100. C4×C5×Dic3C2×C4semidirect
101. C4×C5×Dic3C2×C4semidirect
233. #877Dic5semidirect
365. Dic3⋊C4C2×Dic5semidirect
366. Dic3⋊C4C2×Dic5semidirect
371. C4×Dic3C2×Dic5semidirect
372. C4×Dic3C2×Dic5semidirect
591. C3×C5#2343semidirect
689. C5#74392semidirect
718. C3#10613968semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8772
#117510512
C3×#652392
#117494872
Dic5×#2172
#117494722
C2×#909942
Dic3×C4⋊Dic52
#117486842
#117486732
#117486432
#117486192
#117486182
#106139683
#743925