Finite Group Databasebeta

← #14327506

Subgroups — #14327506

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic15C211yesmaximal, characteristic
2C3×C5×#386C211yesmaximal, characteristic
3#11751321C211yesmaximal, characteristic
4C4×#6719C211yesmaximal, characteristic, complemented
5C2×#91115C211yesmaximal, characteristic, complemented
6#11751046C211yesmaximal, characteristic, complemented
7#11751045C211yesmaximal, characteristic, complemented
8#11751044C211yesmaximal, characteristic, complemented
9#11751043C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic15C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic15C211yesmaximal, characteristic, complemented
12#11750755C211yesmaximal, characteristic, complemented
13#11750754C211yesmaximal, characteristic, complemented
14#11750752C211yesmaximal, characteristic, complemented
15#11750749C211yesmaximal, characteristic, complemented
16#10606405—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C23×Dic15C2211yescharacteristic
21C23×Dic15C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×#6719C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6719C2211yescharacteristic
30D4×Dic15C418yescomplemented
31C2×C4⋊Dic15C2211yescharacteristic
32C2×#6712C2211yescharacteristic
33C2×#6712C2211yescharacteristic
34C2×C4×Dic15C2211yescharacteristic
35C2×C4×Dic15C2211yescharacteristic
36C2×C4×Dic15C2211yescharacteristic
37C2×C4×Dic15C2211yescharacteristic
38C2×C4×Dic15C2211yescharacteristic
39C3×C5×#95C2211yescharacteristic
40C3×C5×#95C2211yescharacteristic
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43#91115C2211yescharacteristic
44#91115C2211yescharacteristic
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53#74674—51nomaximal, Hall
54C2×D4×Dic5—31no—
55C5×#386D311yescharacteristic
56#65509—31no—
57C4×C22⋊Dic5—31no—
58C2×#3963—31no—
59#65234—31no—
60#65233—31no—
61#65232—31no—
62#65231—31no—
63C22⋊C4×Dic5—31no—
64C22⋊C4×Dic5—31no—
65#64943—31no—
66#64942—31no—
67#64940—31no—
68#64937—31no—
69C24×C3×C5C2311yescharacteristic
70C24×C3×C5C2311yescharacteristic
71C2×C3×C5×D4—22no—
72C2×C3×C5×D4—22no—
73C2×C3×C5×D4C2×C414yes—
74C22×C3×C4×C5—22no—
75C22×C3×C4×C5—22no—
76C22×C3×C4×C5—41no—
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×Dic15—22no—
83C22×Dic15—22no—
84C22×Dic15—41no—
85C22×Dic15—41no—
86C22×Dic15—41no—
87C22×Dic15—41no—
88C22×Dic15—41no—
89C22×Dic15C2×C414yes—
90C22×Dic15C2×C414yescomplemented
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C3×C5×C22⋊C4—22no—
100C3×C5×C22⋊C4—22no—
101C3×C5×C22⋊C4—41no—
102#6719—22no—
103#6719—22no—
104#6719—41no—
105#6719C2×C414yes—
106#6719C2×C414yescomplemented
107C4⋊Dic15C2×C414yescomplemented
108#6712—41no—
109#6712—41no—
110C4×Dic15—22no—
111C4×Dic15—22no—
112C4×Dic15—41no—
113C4×Dic15—41no—
114C4×Dic15C2×C414yescomplemented
115C2×D4×Dic3—51no—
116C3×#386D511yescharacteristic
117#5220—51no—
118C4×#217—51no—
119C2×C3⋊#95—51no—
120#4945—51no—
121#4944—51no—
122#4943—51no—
123#4942—51no—
124Dic3×C22⋊C4—51no—
125Dic3×C22⋊C4—51no—
126#4654—51no—
127#4653—51no—
128#4651—51no—
129#4648—51no—
130C22×C5×D4C2×D311yescharacteristic
131C23×C4×C5C2×D311yescharacteristic
132C23×Dic5—31no—
133C23×Dic5—31no—
134C23×Dic5—31no—
135C2×C5×C22⋊C4C2×D311yescharacteristic
136C2×C5×C22⋊C4C2×D311yescharacteristic
137C2×C5×C22⋊C4C2×D311yescharacteristic
138C2×C22⋊Dic5—31no—
139C2×C22⋊Dic5—31no—
140C2×C22⋊Dic5—31no—
141C2×C22⋊Dic5—31no—
142C2×C22⋊Dic5—31no—
143D4×Dic5—38no—
144C2×C4⋊Dic5—31no—
145C2×#683—31no—
146C2×#683—31no—
147C2×C4×Dic5—31no—
148C2×C4×Dic5—31no—
149C2×C4×Dic5—31no—
150C2×C4×Dic5—31no—
151C2×C4×Dic5—31no—
152C5×#95C2×D311yescharacteristic
153C5×#95C2×D311yescharacteristic
154#3963—31no—
155#3963—31no—
156#3963—31no—
157#3963—31no—
158#3963—31no—
159#3963—31no—
160#3963—31no—
161#3963—31no—
162#3963—31no—
163#3963—31no—
164#3963—31no—
165#3963—31no—
166#2353—151noSylow
167C23×C3×C5—21no—
168C23×C3×C5—21no—
169C23×C3×C5—21no—
170C23×C3×C5—21no—
171C23×C3×C5—21no—
172C23×C3×C5—21no—
173C23×C3×C5—21no—
174C23×C3×C5—21no—
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5C22×C412yes—
178C23×C3×C5C22×C412yes—
179C23×C3×C5#4112yes—
180C23×C3×C5#4112yes—
181C23×C3×C5C2411yescharacteristic
182C3×C5×D4—28no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—44no—
197C2×C3×C4×C5C22×C412yes—
198C2×C3×C4×C5#4112yes—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—21no—
207C2×Dic15—21no—
208C2×Dic15—21no—
209C2×Dic15—21no—
210C2×Dic15—21no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—21no—
214C2×Dic15—21no—
215C2×Dic15—21no—
216C2×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15—44no—
219C2×Dic15—44no—
220C2×Dic15—44no—
221C2×Dic15C22×C412yes—
222C2×Dic15C22×C412yes—
223C2×Dic15C22×C412yes—
224C2×Dic15C22×C412yes—
225C2×Dic15#4112yes—
226C22×C3×D4C2×D511yescharacteristic
227C23×C3×C4C2×D511yescharacteristic
228C23×Dic3—51no—
229C23×Dic3—51no—
230C23×Dic3—51no—
231C2×C3×C22⋊C4C2×D511yescharacteristic
232C2×C3×C22⋊C4C2×D511yescharacteristic
233C2×C3×C22⋊C4C2×D511yescharacteristic
234C2×#217—51no—
235C2×#217—51no—
236C2×#217—51no—
237C2×#217—51no—
238C2×#217—51no—
239D4×Dic3—58no—
240C2×C4⋊Dic3—51no—
241C2×Dic3⋊C4—51no—
242C2×Dic3⋊C4—51no—
243C2×C4×Dic3—51no—
244C2×C4×Dic3—51no—
245C2×C4×Dic3—51no—
246C2×C4×Dic3—51no—
247C2×C4×Dic3—51no—
248C3×#95C2×D511yescharacteristic
249C3×#95C2×D511yescharacteristic
250C3⋊#95—51no—
251C3⋊#95—51no—
252C3⋊#95—51no—
253C3⋊#95—51no—
254C3⋊#95—51no—
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95—51no—
258C3⋊#95—51no—
259C3⋊#95—51no—
260C3⋊#95—51no—
261C3⋊#95—51no—
262C24×C5C22×D311yescharacteristic
263C24×C5C22×D311yescharacteristic
264C2×C5×D4—22no—
265C2×C5×D4—22no—
266C2×C5×D4C4×D314yes—
267C22×C4×C5—22no—
268C22×C4×C5—22no—
269C22×C4×C5—41no—
270C22×C4×C5C22×D311yescharacteristic
271C22×C4×C5C22×D311yescharacteristic
272C22×C4×C5C22×D311yescharacteristic
273C22×C4×C5C22×D311yescharacteristic
274C22×C4×C5C22×D311yescharacteristic
275C22×Dic5—31no—
276C22×Dic5—31no—
277C22×Dic5—31no—
278C22×Dic5—31no—
279C22×Dic5—31no—
280C22×Dic5—34no—
281C22×Dic5—34no—
282C22×Dic5—31no—
283C22×Dic5—31no—
284C22×Dic5—31no—
285C22×Dic5—62no—
286C22×Dic5—62no—
287C22×Dic5—121no—
288C22×Dic5—121no—
289C22×Dic5—121no—
290C22×Dic5—121no—
291C22×Dic5—121no—
292C5×C22⋊C4—22no—
293C5×C22⋊C4—22no—
294C5×C22⋊C4—41no—
295C22⋊Dic5—34no—
296C22⋊Dic5—34no—
297C22⋊Dic5—62no—
298C22⋊Dic5—62no—
299C22⋊Dic5—121no—
300C4⋊Dic5—34no—
301#683—121no—
302#683—121no—
303C4×Dic5—34no—
304C4×Dic5—62no—
305C4×Dic5—62no—
306C4×Dic5—121no—
307C4×Dic5—121no—
308C2×C4×D4—151no—
309#388—151no—
310#388—151no—
311#387—151no—
312#387—151no—
313#386—151no—
314#386D1511yescharacteristic
315#383—151no—
316#381—151no—
317#380—151no—
318C4×C22⋊C4—151no—
319C4×C22⋊C4—151no—
320C4×C22⋊C4—151no—
321#376—151no—
322C2×#95—151no—
323C22×C3×C5—22no—
324C22×C3×C5—22no—
325C22×C3×C5—22no—
326C22×C3×C5—22no—
327C22×C3×C5—22no—
328C22×C3×C5—22no—
329C22×C3×C5—22no—
330C22×C3×C5—22no—
331C22×C3×C5—22no—
332C22×C3×C5—41no—
333C22×C3×C5—41no—
334C22×C3×C5—41no—
335C22×C3×C5—41no—
336C22×C3×C5#11714yes—
337C22×C3×C5C23×C411yescharacteristic
338C22×C3×C5C2×#4111yescharacteristic
339C22×C3×C5C2×#4111yescharacteristic
340C22×C3×C5C2×#4111yescharacteristic
341C22×C3×C5C2×#4111yescharacteristic
342C22×C3×C5H(5,𝔽2)11yescharacteristic
343C22×C3×C5H(5,𝔽2)11yescharacteristic
344C3×C4×C5—22no—
345C3×C4×C5—22no—
346C3×C4×C5—41no—
347C3×C4×C5—41no—
348C3×C4×C5—41no—
349Dic15—22no—
350Dic15—22no—
351Dic15—22no—
352Dic15—22no—
353Dic15—22no—
354Dic15—41no—
355Dic15—41no—
356Dic15—41no—
357C24×C3C22×D511yescharacteristic
358C24×C3C22×D511yescharacteristic
359C2×C3×D4—22no—
360C2×C3×D4—22no—
361C2×C3×D4C4×D514yes—
362C22×C3×C4—22no—
363C22×C3×C4—22no—
364C22×C3×C4—41no—
365C22×C3×C4C22×D511yescharacteristic
366C22×C3×C4C22×D511yescharacteristic
367C22×C3×C4C22×D511yescharacteristic
368C22×C3×C4C22×D511yescharacteristic
369C22×C3×C4C22×D511yescharacteristic
370C22×Dic3—51no—
371C22×Dic3—51no—
372C22×Dic3—51no—
373C22×Dic3—51no—
374C22×Dic3—51no—
375C22×Dic3—54no—
376C22×Dic3—54no—
377C22×Dic3—51no—
378C22×Dic3—51no—
379C22×Dic3—51no—
380C22×Dic3—102no—
381C22×Dic3—102no—
382C22×Dic3—201no—
383C22×Dic3—201no—
384C22×Dic3—201no—
385C22×Dic3—201no—
386C22×Dic3—201no—
387C3×C22⋊C4—22no—
388C3×C22⋊C4—22no—
389C3×C22⋊C4—41no—
390#217—54no—
391#217—54no—
392#217—102no—
393#217—102no—
394#217—201no—
395C4⋊Dic3—54no—
396Dic3⋊C4—201no—
397Dic3⋊C4—201no—
398C4×Dic3—54no—
399C4×Dic3—102no—
400C4×Dic3—102no—
401C4×Dic3—201no—
402C4×Dic3—201no—
403C23×C5—21no—
404C23×C5—21no—
405C23×C5—21no—
406C23×C5—21no—
407C23×C5—21no—
408C23×C5—21no—
409C23×C5—21no—
410C23×C5—21no—
411C23×C5—21no—
412C23×C5—21no—
413C23×C5C2×C4×D312yes—
414C23×C5C2×C4×D312yes—
415C23×C5#23712yes—
416C23×C5#23712yes—
417C23×C5C23×D311yescharacteristic
418C5×D4—28no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5—21no—
429C2×C4×C5—21no—
430C2×C4×C5—21no—
431C2×C4×C5—21no—
432C2×C4×C5—44no—
433C2×C4×C5C2×C4×D312yes—
434C2×C4×C5#23712yes—
435C2×Dic5—32no—
436C2×Dic5—32no—
437C2×Dic5—32no—
438C2×Dic5—32no—
439C2×Dic5—32no—
440C2×Dic5—61no—
441C2×Dic5—61no—
442C2×Dic5—61no—
443C2×Dic5—61no—
444C2×Dic5—61no—
445C2×Dic5—61no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5—61no—
452C2×Dic5—61no—
453C2×Dic5—61no—
454C2×Dic5—61no—
455C2×Dic5—61no—
456C2×Dic5—61no—
457C2×Dic5—61no—
458C2×Dic5—61no—
459C2×Dic5—124no—
460C2×Dic5—124no—
461C2×Dic5—124no—
462C22×D4C2×D1511yescharacteristic
463C23×C4—151no—
464C23×C4—151no—
465C23×C4—151no—
466C23×C4C2×D1511yescharacteristic
467C4×D4—158no—
468C2×C4⋊C4—151no—
469C2×C4⋊C4—151no—
470C2×C4⋊C4—151no—
471C2×C22⋊C4—151no—
472C2×C22⋊C4—151no—
473C2×C22⋊C4—151no—
474C2×C22⋊C4—151no—
475C2×C22⋊C4—151no—
476C2×C22⋊C4C2×D1511yescharacteristic
477C2×C22⋊C4C2×D1511yescharacteristic
478C2×C22⋊C4C2×D1511yescharacteristic
479C2×C42—151no—
480C2×C42—151no—
481C2×C42—151no—
482C2×C42—151no—
483C2×C42—151no—
484#95—151no—
485#95—151no—
486#95—151no—
487#95—151no—
488#95—151no—
489#95—151no—
490#95—151no—
491#95—151no—
492#95—151no—
493#95—151no—
494#95—151no—
495#95—151no—
496#95C2×D1511yescharacteristic
497#95C2×D1511yescharacteristic
498C2×C3×C5—24no—
499C2×C3×C5—42no—
500C2×C3×C5C2×#11711yescharacteristic
501C2×C3×C5C4×#4111yescharacteristic
502C2×C3×C5#51811yescharacteristic
503C2×C3×C5#55111yescharacteristic
504C2×C3×C5#55111yescharacteristic
505C2×C3×C5#55311yescharacteristic
506C2×C3×C5#55311yescharacteristic
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3C2×C4×D512yes—
518C23×C3C2×C4×D512yes—
519C23×C3#71112yes—
520C23×C3#71112yes—
521C23×C3C23×D511yescharacteristic
522C3×D4—28no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—44no—
537C2×C3×C4C2×C4×D512yes—
538C2×C3×C4#71112yes—
539C2×Dic3—52no—
540C2×Dic3—52no—
541C2×Dic3—52no—
542C2×Dic3—52no—
543C2×Dic3—52no—
544C2×Dic3—101no—
545C2×Dic3—101no—
546C2×Dic3—101no—
547C2×Dic3—101no—
548C2×Dic3—101no—
549C2×Dic3—101no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—101no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—101no—
558C2×Dic3—101no—
559C2×Dic3—101no—
560C2×Dic3—101no—
561C2×Dic3—101no—
562C2×Dic3—101no—
563C2×Dic3—204no—
564C2×Dic3—204no—
565C2×Dic3—204no—
566C22×C5—22no—
567C22×C5—22no—
568C22×C5—22no—
569C22×C5—22no—
570C22×C5—22no—
571C22×C5—22no—
572C22×C5—22no—
573C22×C5—22no—
574C22×C5—22no—
575C22×C5—41no—
576C22×C5—41no—
577C22×C5—41no—
578C22×C5—41no—
579C22×C5#87714yes—
580C22×C5C22×C4×D311yescharacteristic
581C22×C5C2×#23711yescharacteristic
582C22×C5C2×#23711yescharacteristic
583C22×C5C2×#23711yescharacteristic
584C22×C5#100411yescharacteristic
585C22×C5D3×#4111yescharacteristic
586C22×C5#100911yescharacteristic
587C4×C5—22no—
588C4×C5—22no—
589C4×C5—41no—
590C4×C5—41no—
591C4×C5—41no—
592Dic5—62no—
593Dic5—62no—
594Dic5—62no—
595Dic5—62no—
596Dic5—62no—
597Dic5—121no—
598Dic5—121no—
599Dic5—121no—
600C24C22×D1511yescharacteristic
601C24C22×D1511yescharacteristic
602C2×D4—22no—
603C2×D4—22no—
604C2×D4C4×D1514yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—41no—
608C22×C4—151no—
609C22×C4—151no—
610C22×C4—151no—
611C22×C4—151no—
612C22×C4—151no—
613C22×C4—154no—
614C22×C4—154no—
615C22×C4—151no—
616C22×C4—151no—
617C22×C4—151no—
618C22×C4—302no—
619C22×C4—302no—
620C22×C4—601no—
621C22×C4—601no—
622C22×C4—601no—
623C22×C4—601no—
624C22×C4—601no—
625C22×C4C22×D1511yescharacteristic
626C22×C4C22×D1511yescharacteristic
627C22×C4C22×D1511yescharacteristic
628C22×C4C22×D1511yescharacteristic
629C22×C4C22×D1511yescharacteristic
630C4⋊C4—154no—
631C4⋊C4—601no—
632C4⋊C4—601no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—41no—
636C22⋊C4—154no—
637C22⋊C4—154no—
638C22⋊C4—302no—
639C22⋊C4—302no—
640C22⋊C4—601no—
641C42—154no—
642C42—302no—
643C42—302no—
644C42—601no—
645C42—601no—
646C3×C5#235311yescharacteristic, complemented, Hall
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—22no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3#402314yes—
661C22×C3C22×C4×D511yescharacteristic
662C22×C3C2×#71111yescharacteristic
663C22×C3C2×#71111yescharacteristic
664C22×C3C2×#71111yescharacteristic
665C22×C3#414411yescharacteristic
666C22×C3D5×#4111yescharacteristic
667C22×C3#414911yescharacteristic
668C3×C4—22no—
669C3×C4—22no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673Dic3—102no—
674Dic3—102no—
675Dic3—102no—
676Dic3—102no—
677Dic3—102no—
678Dic3—201no—
679Dic3—201no—
680Dic3—201no—
681C2×C5—24no—
682C2×C5—42no—
683C2×C5C2×#87711yescharacteristic
684C2×C5C4×#23711yescharacteristic
685C2×C5#554511yescharacteristic
686C2×C5#558711yescharacteristic
687C2×C5#560111yescharacteristic
688C2×C5#561811yescharacteristic
689C2×C5#565811yescharacteristic
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23C2×C4×D1512yes—
701C23C2×C4×D1512yes—
702C23#681912yes—
703C23#681912yes—
704C23C23×D1511yescharacteristic
705D4—28no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—44no—
720C2×C4—152no—
721C2×C4—152no—
722C2×C4—152no—
723C2×C4—152no—
724C2×C4—152no—
725C2×C4—301no—
726C2×C4—301no—
727C2×C4—301no—
728C2×C4—301no—
729C2×C4—301no—
730C2×C4—301no—
731C2×C4—301no—
732C2×C4—301no—
733C2×C4—301no—
734C2×C4—301no—
735C2×C4—301no—
736C2×C4—301no—
737C2×C4—301no—
738C2×C4—301no—
739C2×C4—301no—
740C2×C4—301no—
741C2×C4—301no—
742C2×C4—301no—
743C2×C4—301no—
744C2×C4—604no—
745C2×C4—604no—
746C2×C4—604no—
747C2×C4C2×C4×D1512yes—
748C2×C4#681912yes—
749C2×C3—24no—
750C2×C3—42no—
751C2×C3C2×#402311yescharacteristic
752C2×C3C4×#71111yescharacteristic
753C2×C3#6587911yescharacteristic
754C2×C3#6592111yescharacteristic
755C2×C3#6593511yescharacteristic
756C2×C3#6595211yescharacteristic
757C2×C3#6599211yescharacteristic
758C5#7467411yescharacteristic, complemented, Sylow
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22#9176614yes—
773C22C22×C4×D1511yescharacteristic
774C22C2×#681911yescharacteristic
775C22C2×#681911yescharacteristic
776C22C2×#681911yescharacteristic
777C22#9209511yescharacteristic
778C22#41×D1511yescharacteristic
779C22#9210011yescharacteristic
780C4—22no—
781C4—22no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—302no—
786C4—302no—
787C4—302no—
788C4—302no—
789C4—302no—
790C4—601no—
791C4—601no—
792C4—601no—
793C3#1060640511yescharacteristic, complemented, Sylow
794C2—24no—
795C2—42no—
796C2C2×#9176611yescharacteristic
797C2C4×#681911yescharacteristic
798C2#1175630411yescharacteristic
799C2#1175634611yescharacteristic
800C2#1175636011yescharacteristic
801C2#1175637711yescharacteristic
802C2#1175641711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#386C2
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
hypercenter#386D15
hypocenterC3×C5#2353
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
4. C4×#6719C2semidirect
5. C2×#91115C2semidirect
6. #11751046C2semidirect
7. #11751045C2semidirect
8. #11751044C2semidirect
9. #11751043C2semidirect
10. C22⋊C4×Dic15C2semidirect
11. C22⋊C4×Dic15C2semidirect
12. #11750755C2semidirect
13. #11750754C2semidirect
14. #11750752C2semidirect
15. #11750749C2semidirect
30. D4×Dic15C4semidirect
90. C22×Dic15C2×C4semidirect
106. #6719C2×C4semidirect
107. C4⋊Dic15C2×C4semidirect
114. C4×Dic15C2×C4semidirect
646. C3×C5#2353semidirect
758. C5#74674semidirect
793. C3#10606405semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic152
C3×C5×#3862
#117513212
C4×#67192
C2×#911152
#117510462
#117510452
#117510442
#117510432
C22⋊C4×Dic152
#117507552
#117507542
#117507522
#117507492
#106064053
#746745