Finite Group Databasebeta

← #14280056

Subgroups — #14280056

Order 1920.

1560 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6714C211yesmaximal, characteristic
2C22×#6714C211yesmaximal, characteristic
3C22×#6714C211yesmaximal, characteristic
4C22×#6712C211yesmaximal, characteristic, complemented
5C2×C3×C5×#95C211yesmaximal, characteristic, complemented
6C2×#91115C211yesmaximal, characteristic, complemented
7C2×#91115C211yesmaximal, characteristic, complemented
8#10600221—31nomaximal, Hall
9C24×D15C2211yescharacteristic
10C23×C3×C4×C5C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C23×Dic15C2211yescharacteristic
15C23×Dic15C2211yescharacteristic
16C2×#6714—22no—
17C2×#6714—22no—
18C2×#6714—22no—
19C2×#6714—22no—
20C2×#6714—22no—
21C2×#6714—22no—
22C2×#6714—22no—
23C2×#6714—22no—
24C2×#6714C414yescomplemented
25C2×#6712—22no—
26C2×#6712—22no—
27C2×#6712—22no—
28C3×C5×#95—22no—
29#91115—22no—
30#91115—22no—
31#69428—51nomaximal, Hall
32C22×#685—31no—
33C22×#685—31no—
34C22×#685—31no—
35C22×#683—31no—
36C2×C5×#95D311yescharacteristic, complemented
37C2×#3963—31no—
38C2×#3963—31no—
39C24×C3×C5C2311yescharacteristic
40C23×D15—21no—
41C23×D15—21no—
42C23×D15—21no—
43C23×D15—21no—
44C23×D15—21no—
45C23×D15—21no—
46C23×D15—21no—
47C23×D15—21no—
48C23×D15—21no—
49C23×D15—21no—
50C23×D15—21no—
51C23×D15—21no—
52C23×D15C2×C412yes—
53C23×D15D412yes—
54C23×D15Q812yes—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5—21no—
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5—21no—
65C22×C3×C4×C5—21no—
66C22×C3×C4×C5—21no—
67C22×C3×C4×C5—21no—
68C22×C3×C4×C5—21no—
69C22×C3×C4×C5—21no—
70C22×C3×C4×C5—21no—
71C22×C3×C4×C5—21no—
72C22×C3×C4×C5—21no—
73C22×C3×C4×C5C2×C412yes—
74C22×C3×C4×C5D412yes—
75C22×C3×C4×C5D412yes—
76C22×Dic15—21no—
77C22×Dic15—21no—
78C22×Dic15—21no—
79C22×Dic15—21no—
80C22×Dic15—21no—
81C22×Dic15—21no—
82C22×Dic15—21no—
83C22×Dic15—21no—
84C22×Dic15—21no—
85C22×Dic15—21no—
86C22×Dic15—21no—
87C22×Dic15—21no—
88C22×Dic15—21no—
89C22×Dic15—21no—
90C22×Dic15—21no—
91C22×Dic15—21no—
92C22×Dic15C2×C412yes—
93C22×Dic15D412yes—
94C22×Dic15D412yes—
95C22×Dic15D412yes—
96C22×Dic15D412yes—
97#6714—28no—
98#6714—28no—
99#6714—28no—
100#6712—28no—
101C22×(C2×D3)⋊C4—51no—
102C22×(C2×D3)⋊C4—51no—
103C22×(C2×D3)⋊C4—51no—
104C22×Dic3⋊C4—51no—
105C2×C3×#95D511yescharacteristic, complemented
106C2×C3⋊#95—51no—
107C2×C3⋊#95—51no—
108C24×D5—31no—
109C23×C4×C5C2×D311yescharacteristic
110C23×C4×C5C2×D311yescharacteristic
111C23×C4×C5C2×D311yescharacteristic
112C23×Dic5—31no—
113C23×Dic5—31no—
114C23×Dic5—31no—
115C2×#685—34no—
116C2×#685—62no—
117C2×#685—62no—
118C2×#685—62no—
119C2×#685—62no—
120C2×#685—62no—
121C2×#685—62no—
122C2×#685—62no—
123C2×#685—62no—
124C2×#683—62no—
125C2×#683—62no—
126C2×#683—62no—
127C5×#95—22no—
128#3963—62no—
129#3963—62no—
130#1439—151noSylow
131C23×C3×C5C22×C411yescharacteristic
132C23×C3×C5C2×D411yescharacteristic
133C23×C3×C5C2×D411yescharacteristic
134C23×C3×C5C2×D411yescharacteristic
135C23×C3×C5C2×D411yescharacteristic
136C23×C3×C5C2×D411yescharacteristic
137C23×C3×C5C2×D411yescharacteristic
138C23×C3×C5C2×D411yescharacteristic
139C23×C3×C5C2×Q811yescharacteristic
140C23×C3×C5#4111yescharacteristic
141C23×C3×C5#4111yescharacteristic
142C23×C3×C5#4111yescharacteristic
143C23×C3×C5#4111yescharacteristic
144C23×C3×C5#4111yescharacteristic
145C23×C3×C5#4111yescharacteristic
146C22×D15—22no—
147C22×D15—22no—
148C22×D15—22no—
149C22×D15—22no—
150C22×D15—22no—
151C22×D15—22no—
152C22×D15—22no—
153C22×D15—22no—
154C22×D15—22no—
155C22×D15—22no—
156C22×D15—22no—
157C22×D15—22no—
158C22×D15—22no—
159C22×D15—22no—
160C22×D15—22no—
161C22×D15—22no—
162C22×D15—22no—
163C22×D15—22no—
164C22×D15—41no—
165C22×D15—41no—
166C22×D15—41no—
167C22×D15—41no—
168C22×D15—41no—
169C22×D15—41no—
170C22×D15—41no—
171C22×D15—41no—
172C22×D15—41no—
173C22×D15—41no—
174C22×D15—41no—
175C22×D15—41no—
176C22×D15—41no—
177C22×D15—41no—
178C22×D15—41no—
179C22×D15—41no—
180C22×D15C4⋊C414yescomplemented
181C2×C3×C4×C5—22no—
182C2×C3×C4×C5—22no—
183C2×C3×C4×C5—22no—
184C2×C3×C4×C5—22no—
185C2×C3×C4×C5—22no—
186C2×C3×C4×C5—22no—
187C2×C3×C4×C5—22no—
188C2×C3×C4×C5—22no—
189C2×C3×C4×C5—22no—
190C2×C3×C4×C5—41no—
191C2×C3×C4×C5—41no—
192C2×C3×C4×C5—41no—
193C2×C3×C4×C5—41no—
194C2×C3×C4×C5—41no—
195C2×C3×C4×C5—41no—
196C2×C3×C4×C5—41no—
197C2×C3×C4×C5—41no—
198C2×C3×C4×C5—41no—
199C2×C3×C4×C5—41no—
200C2×C3×C4×C5—41no—
201C2×C3×C4×C5—41no—
202C2×Dic15—22no—
203C2×Dic15—22no—
204C2×Dic15—22no—
205C2×Dic15—22no—
206C2×Dic15—22no—
207C2×Dic15—22no—
208C2×Dic15—22no—
209C2×Dic15—22no—
210C2×Dic15—22no—
211C2×Dic15—22no—
212C2×Dic15—22no—
213C2×Dic15—22no—
214C2×Dic15—41no—
215C2×Dic15—41no—
216C2×Dic15—41no—
217C2×Dic15—41no—
218C2×Dic15—41no—
219C2×Dic15—41no—
220C2×Dic15—41no—
221C2×Dic15—41no—
222C2×Dic15C22⋊C414yescomplemented
223C24×D3—51no—
224C23×C3×C4C2×D511yescharacteristic
225C23×C3×C4C2×D511yescharacteristic
226C23×C3×C4C2×D511yescharacteristic
227C23×Dic3—51no—
228C23×Dic3—51no—
229C23×Dic3—51no—
230C2×(C2×D3)⋊C4—54no—
231C2×(C2×D3)⋊C4—102no—
232C2×(C2×D3)⋊C4—102no—
233C2×(C2×D3)⋊C4—102no—
234C2×(C2×D3)⋊C4—102no—
235C2×(C2×D3)⋊C4—102no—
236C2×(C2×D3)⋊C4—102no—
237C2×(C2×D3)⋊C4—102no—
238C2×(C2×D3)⋊C4—102no—
239C2×Dic3⋊C4—102no—
240C2×Dic3⋊C4—102no—
241C2×Dic3⋊C4—102no—
242C3×#95—22no—
243C3⋊#95—102no—
244C3⋊#95—102no—
245C24×C5C22×D311yescharacteristic
246C23×D5—32no—
247C23×D5—32no—
248C23×D5—32no—
249C23×D5—61no—
250C23×D5—61no—
251C23×D5—61no—
252C23×D5—61no—
253C23×D5—61no—
254C23×D5—61no—
255C23×D5—61no—
256C23×D5—61no—
257C23×D5—61no—
258C23×D5—61no—
259C23×D5—61no—
260C23×D5—61no—
261C22×C4×C5—21no—
262C22×C4×C5—21no—
263C22×C4×C5—21no—
264C22×C4×C5—21no—
265C22×C4×C5—21no—
266C22×C4×C5—21no—
267C22×C4×C5—21no—
268C22×C4×C5—21no—
269C22×C4×C5—21no—
270C22×C4×C5—21no—
271C22×C4×C5—21no—
272C22×C4×C5—21no—
273C22×C4×C5—21no—
274C22×C4×C5—21no—
275C22×C4×C5—21no—
276C22×C4×C5—21no—
277C22×C4×C5—21no—
278C22×C4×C5—21no—
279C22×C4×C5C4×D312yes—
280C22×C4×C5D1212yes—
281C22×C4×C5#6712yes—
282C22×Dic5—32no—
283C22×Dic5—32no—
284C22×Dic5—32no—
285C22×Dic5—32no—
286C22×Dic5—32no—
287C22×Dic5—61no—
288C22×Dic5—61no—
289C22×Dic5—61no—
290C22×Dic5—61no—
291C22×Dic5—61no—
292C22×Dic5—61no—
293C22×Dic5—61no—
294C22×Dic5—61no—
295C22×Dic5—61no—
296C22×Dic5—61no—
297C22×Dic5—61no—
298C22×Dic5—61no—
299C22×Dic5—61no—
300C22×Dic5—61no—
301C22×Dic5—61no—
302C22×Dic5—61no—
303#685—68no—
304#685—68no—
305#685—68no—
306#683—68no—
307C22×C4⋊C4—151no—
308C22×C22⋊C4—151no—
309C22×C22⋊C4—151no—
310C22×C22⋊C4—151no—
311C2×#95—151no—
312C2×#95—151no—
313C2×#95D1511yescharacteristic, complemented
314C22×C3×C5C2×C22⋊C411yescharacteristic
315C22×C3×C5C2×C4⋊C411yescharacteristic
316C22×C3×C5#11711yescharacteristic
317C22×C3×C5C4×D411yescharacteristic
318C22×C3×C5C4×D411yescharacteristic
319C22×C3×C5C4×D411yescharacteristic
320C22×C3×C5C4×D411yescharacteristic
321C22×C3×C5#12011yescharacteristic
322C22×C3×C5#12011yescharacteristic
323C22×C3×C5#12011yescharacteristic
324C22×C3×C5#12111yescharacteristic
325C22×C3×C5#12111yescharacteristic
326C22×C3×C5#12111yescharacteristic
327C22×C3×C5#12111yescharacteristic
328C22×C3×C5#12111yescharacteristic
329C22×C3×C5#12111yescharacteristic
330C22×C3×C5#12111yescharacteristic
331C22×C3×C5#12111yescharacteristic
332C22×C3×C5C22⋊Q811yescharacteristic
333C22×C3×C5C22⋊Q811yescharacteristic
334C22×C3×C5C22⋊Q811yescharacteristic
335C22×C3×C5C22⋊Q811yescharacteristic
336C22×C3×C5C22⋊Q811yescharacteristic
337C22×C3×C5C22⋊Q811yescharacteristic
338C22×C3×C5#12311yescharacteristic
339C22×C3×C5#12311yescharacteristic
340C22×C3×C5#12311yescharacteristic
341C22×C3×C5#12311yescharacteristic
342C22×C3×C5#12311yescharacteristic
343C22×C3×C5#12411yescharacteristic
344C22×C3×C5#12411yescharacteristic
345C22×C3×C5#12411yescharacteristic
346C22×C3×C5#12611yescharacteristic
347C22×C3×C5#12611yescharacteristic
348C22×C3×C5#12711yescharacteristic
349C2×D15—24no—
350C2×D15—24no—
351C2×D15—24no—
352C2×D15—42no—
353C2×D15—42no—
354C2×D15—42no—
355C2×D15—42no—
356C2×D15—42no—
357C2×D15—42no—
358C2×D15—42no—
359C2×D15—42no—
360C2×D15—42no—
361C2×D15—42no—
362C2×D15—42no—
363C2×D15—42no—
364C3×C4×C5—42no—
365C3×C4×C5—42no—
366C3×C4×C5—42no—
367Dic15—24no—
368Dic15—42no—
369Dic15—42no—
370C24×C3C22×D511yescharacteristic
371C23×D3—52no—
372C23×D3—52no—
373C23×D3—52no—
374C23×D3—101no—
375C23×D3—101no—
376C23×D3—101no—
377C23×D3—101no—
378C23×D3—101no—
379C23×D3—101no—
380C23×D3—101no—
381C23×D3—101no—
382C23×D3—101no—
383C23×D3—101no—
384C23×D3—101no—
385C23×D3—101no—
386C22×C3×C4—21no—
387C22×C3×C4—21no—
388C22×C3×C4—21no—
389C22×C3×C4—21no—
390C22×C3×C4—21no—
391C22×C3×C4—21no—
392C22×C3×C4—21no—
393C22×C3×C4—21no—
394C22×C3×C4—21no—
395C22×C3×C4—21no—
396C22×C3×C4—21no—
397C22×C3×C4—21no—
398C22×C3×C4—21no—
399C22×C3×C4—21no—
400C22×C3×C4—21no—
401C22×C3×C4—21no—
402C22×C3×C4—21no—
403C22×C3×C4—21no—
404C22×C3×C4C4×D512yes—
405C22×C3×C4D2012yes—
406C22×C3×C4C22⋊D512yes—
407C22×Dic3—52no—
408C22×Dic3—52no—
409C22×Dic3—52no—
410C22×Dic3—52no—
411C22×Dic3—52no—
412C22×Dic3—101no—
413C22×Dic3—101no—
414C22×Dic3—101no—
415C22×Dic3—101no—
416C22×Dic3—101no—
417C22×Dic3—101no—
418C22×Dic3—101no—
419C22×Dic3—101no—
420C22×Dic3—101no—
421C22×Dic3—101no—
422C22×Dic3—101no—
423C22×Dic3—101no—
424C22×Dic3—101no—
425C22×Dic3—101no—
426C22×Dic3—101no—
427C22×Dic3—101no—
428(C2×D3)⋊C4—108no—
429(C2×D3)⋊C4—108no—
430(C2×D3)⋊C4—108no—
431Dic3⋊C4—108no—
432C23×C5C2×C4×D311yescharacteristic
433C23×C5C2×D1211yescharacteristic
434C23×C5#23511yescharacteristic
435C23×C5#23511yescharacteristic
436C23×C5#23511yescharacteristic
437C23×C5#23511yescharacteristic
438C23×C5D3×D411yescharacteristic
439C23×C5D3×D411yescharacteristic
440C23×C5D3×D411yescharacteristic
441C23×C5D3×D411yescharacteristic
442C23×C5D3×D411yescharacteristic
443C23×C5#23711yescharacteristic
444C23×C5D3×Q811yescharacteristic
445C23×C5#23911yescharacteristic
446C23×C5C2×#6711yescharacteristic
447C22×D5—34no—
448C22×D5—62no—
449C22×D5—62no—
450C22×D5—62no—
451C22×D5—62no—
452C22×D5—62no—
453C22×D5—62no—
454C22×D5—62no—
455C22×D5—62no—
456C22×D5—62no—
457C22×D5—62no—
458C22×D5—62no—
459C22×D5—62no—
460C22×D5—62no—
461C22×D5—62no—
462C22×D5—62no—
463C22×D5—62no—
464C22×D5—62no—
465C22×D5—62no—
466C22×D5—121no—
467C22×D5—121no—
468C22×D5—121no—
469C22×D5—121no—
470C22×D5—121no—
471C22×D5—121no—
472C22×D5—121no—
473C22×D5—121no—
474C22×D5—121no—
475C22×D5—121no—
476C22×D5—121no—
477C22×D5—121no—
478C22×D5—121no—
479C22×D5—121no—
480C22×D5—121no—
481C22×D5—121no—
482C2×C4×C5—22no—
483C2×C4×C5—22no—
484C2×C4×C5—22no—
485C2×C4×C5—22no—
486C2×C4×C5—22no—
487C2×C4×C5—22no—
488C2×C4×C5—22no—
489C2×C4×C5—22no—
490C2×C4×C5—22no—
491C2×C4×C5—41no—
492C2×C4×C5—41no—
493C2×C4×C5—41no—
494C2×C4×C5—41no—
495C2×C4×C5—41no—
496C2×C4×C5—41no—
497C2×C4×C5—41no—
498C2×C4×C5—41no—
499C2×C4×C5—41no—
500C2×C4×C5—41no—
501C2×C4×C5—41no—
502C2×C4×C5—41no—
503C2×Dic5—34no—
504C2×Dic5—62no—
505C2×Dic5—62no—
506C2×Dic5—62no—
507C2×Dic5—62no—
508C2×Dic5—62no—
509C2×Dic5—62no—
510C2×Dic5—62no—
511C2×Dic5—62no—
512C2×Dic5—62no—
513C2×Dic5—62no—
514C2×Dic5—62no—
515C2×Dic5—62no—
516C2×Dic5—121no—
517C2×Dic5—121no—
518C2×Dic5—121no—
519C2×Dic5—121no—
520C2×Dic5—121no—
521C2×Dic5—121no—
522C2×Dic5—121no—
523C2×Dic5—121no—
524C25—151no—
525C23×C4—151no—
526C23×C4—151no—
527C23×C4—151no—
528C23×C4C2×D1511yescharacteristic
529C23×C4C2×D1511yescharacteristic
530C23×C4C2×D1511yescharacteristic
531C2×C4⋊C4—302no—
532C2×C4⋊C4—302no—
533C2×C4⋊C4—302no—
534C2×C22⋊C4—154no—
535C2×C22⋊C4—302no—
536C2×C22⋊C4—302no—
537C2×C22⋊C4—302no—
538C2×C22⋊C4—302no—
539C2×C22⋊C4—302no—
540C2×C22⋊C4—302no—
541C2×C22⋊C4—302no—
542C2×C22⋊C4—302no—
543#95—22no—
544#95—302no—
545#95—302no—
546C2×C3×C5#38011yescharacteristic
547C2×C3×C5#38511yescharacteristic
548C2×C3×C5#38511yescharacteristic
549C2×C3×C5#38611yescharacteristic
550C2×C3×C5#38811yescharacteristic
551C2×C3×C5#38811yescharacteristic
552C2×C3×C5#39011yescharacteristic
553C2×C3×C5#39211yescharacteristic
554C2×C3×C5#39311yescharacteristic
555C2×C3×C5#39411yescharacteristic
556C2×C3×C5#39411yescharacteristic
557C2×C3×C5#39611yescharacteristic
558C2×C3×C5#39611yescharacteristic
559C2×C3×C5#39711yescharacteristic
560C2×C3×C5#39911yescharacteristic
561D15—44no—
562C23×C3C2×C4×D511yescharacteristic
563C23×C3C2×D2011yescharacteristic
564C23×C3#70911yescharacteristic
565C23×C3#70911yescharacteristic
566C23×C3#70911yescharacteristic
567C23×C3#70911yescharacteristic
568C23×C3D4×D511yescharacteristic
569C23×C3D4×D511yescharacteristic
570C23×C3D4×D511yescharacteristic
571C23×C3D4×D511yescharacteristic
572C23×C3D4×D511yescharacteristic
573C23×C3#71111yescharacteristic
574C23×C3Q8×D511yescharacteristic
575C23×C3#71311yescharacteristic
576C23×C3C2×C22⋊D511yescharacteristic
577C22×D3—54no—
578C22×D3—102no—
579C22×D3—102no—
580C22×D3—102no—
581C22×D3—102no—
582C22×D3—102no—
583C22×D3—102no—
584C22×D3—102no—
585C22×D3—102no—
586C22×D3—102no—
587C22×D3—102no—
588C22×D3—102no—
589C22×D3—102no—
590C22×D3—102no—
591C22×D3—102no—
592C22×D3—102no—
593C22×D3—102no—
594C22×D3—102no—
595C22×D3—102no—
596C22×D3—201no—
597C22×D3—201no—
598C22×D3—201no—
599C22×D3—201no—
600C22×D3—201no—
601C22×D3—201no—
602C22×D3—201no—
603C22×D3—201no—
604C22×D3—201no—
605C22×D3—201no—
606C22×D3—201no—
607C22×D3—201no—
608C22×D3—201no—
609C22×D3—201no—
610C22×D3—201no—
611C22×D3—201no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—22no—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×Dic3—54no—
634C2×Dic3—102no—
635C2×Dic3—102no—
636C2×Dic3—102no—
637C2×Dic3—102no—
638C2×Dic3—102no—
639C2×Dic3—102no—
640C2×Dic3—102no—
641C2×Dic3—102no—
642C2×Dic3—102no—
643C2×Dic3—102no—
644C2×Dic3—102no—
645C2×Dic3—102no—
646C2×Dic3—201no—
647C2×Dic3—201no—
648C2×Dic3—201no—
649C2×Dic3—201no—
650C2×Dic3—201no—
651C2×Dic3—201no—
652C2×Dic3—201no—
653C2×Dic3—201no—
654C22×C5#87211yescharacteristic
655C22×C5C4×D1211yescharacteristic
656C22×C5#87511yescharacteristic
657C22×C5#87611yescharacteristic
658C22×C5D3×C22⋊C411yescharacteristic
659C22×C5#67⋊C411yescharacteristic
660C22×C5#88211yescharacteristic
661C22×C5#88211yescharacteristic
662C22×C5#88311yescharacteristic
663C22×C5#88411yescharacteristic
664C22×C5#88411yescharacteristic
665C22×C5#88411yescharacteristic
666C22×C5#88411yescharacteristic
667C22×C5#88411yescharacteristic
668C22×C5#88511yescharacteristic
669C22×C5#88511yescharacteristic
670C22×C5D3×C4⋊C411yescharacteristic
671C22×C5#89311yescharacteristic
672C22×C5#89411yescharacteristic
673C22×C5#89411yescharacteristic
674C22×C5#89411yescharacteristic
675C22×C5#89511yescharacteristic
676C22×C5#89611yescharacteristic
677C22×C5#89611yescharacteristic
678C22×C5#89611yescharacteristic
679C22×C5#89611yescharacteristic
680C22×C5#89711yescharacteristic
681C22×C5#89811yescharacteristic
682C22×C5C4×#6711yescharacteristic
683C22×C5#92911yescharacteristic
684C22×C5#93011yescharacteristic
685C22×C5#93711yescharacteristic
686C22×C5#93911yescharacteristic
687C22×C5#94011yescharacteristic
688C22×C5#94611yescharacteristic
689C2×D5—64no—
690C2×D5—64no—
691C2×D5—64no—
692C2×D5—122no—
693C2×D5—122no—
694C2×D5—122no—
695C2×D5—122no—
696C2×D5—122no—
697C2×D5—122no—
698C2×D5—122no—
699C2×D5—122no—
700C2×D5—122no—
701C2×D5—122no—
702C2×D5—122no—
703C2×D5—122no—
704C4×C5—42no—
705C4×C5—42no—
706C4×C5—42no—
707Dic5—64no—
708Dic5—122no—
709Dic5—122no—
710C24—152no—
711C24—152no—
712C24—152no—
713C24—301no—
714C24—301no—
715C24—301no—
716C24—301no—
717C24—301no—
718C24—301no—
719C24—301no—
720C24—301no—
721C24—301no—
722C24—301no—
723C24—301no—
724C24—301no—
725C24C22×D1511yescharacteristic
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—152no—
745C22×C4—152no—
746C22×C4—152no—
747C22×C4—152no—
748C22×C4—152no—
749C22×C4—301no—
750C22×C4—301no—
751C22×C4—301no—
752C22×C4—301no—
753C22×C4—301no—
754C22×C4—301no—
755C22×C4—301no—
756C22×C4—301no—
757C22×C4—301no—
758C22×C4—301no—
759C22×C4—301no—
760C22×C4—301no—
761C22×C4—301no—
762C22×C4—301no—
763C22×C4—301no—
764C22×C4—301no—
765C22×C4C4×D1512yes—
766C22×C4D6012yes—
767C22×C4#122012yes—
768C4⋊C4—308no—
769C22⋊C4—308no—
770C22⋊C4—308no—
771C22⋊C4—308no—
772C3×C5#143911yescharacteristic, complemented, Hall
773C22×C3#401811yescharacteristic
774C22×C3C4×D2011yescharacteristic
775C22×C3#402111yescharacteristic
776C22×C3#402211yescharacteristic
777C22×C3D5×C22⋊C411yescharacteristic
778C22×C3#402711yescharacteristic
779C22×C3#402811yescharacteristic
780C22×C3#402811yescharacteristic
781C22×C3#402911yescharacteristic
782C22×C3#403011yescharacteristic
783C22×C3#403011yescharacteristic
784C22×C3#403011yescharacteristic
785C22×C3#403011yescharacteristic
786C22×C3#403011yescharacteristic
787C22×C3#403111yescharacteristic
788C22×C3#403111yescharacteristic
789C22×C3D5×C4⋊C411yescharacteristic
790C22×C3#403911yescharacteristic
791C22×C3#404011yescharacteristic
792C22×C3#404011yescharacteristic
793C22×C3#404011yescharacteristic
794C22×C3#404111yescharacteristic
795C22×C3#404211yescharacteristic
796C22×C3#404211yescharacteristic
797C22×C3#404211yescharacteristic
798C22×C3#404211yescharacteristic
799C22×C3#404311yescharacteristic
800C22×C3#404411yescharacteristic
801C22×C3C4×C22⋊D511yescharacteristic
802C22×C3#407511yescharacteristic
803C22×C3#407611yescharacteristic
804C22×C3#408311yescharacteristic
805C22×C3#408511yescharacteristic
806C22×C3#408611yescharacteristic
807C22×C3#409211yescharacteristic
808C2×D3—104no—
809C2×D3—104no—
810C2×D3—104no—
811C2×D3—202no—
812C2×D3—202no—
813C2×D3—202no—
814C2×D3—202no—
815C2×D3—202no—
816C2×D3—202no—
817C2×D3—202no—
818C2×D3—202no—
819C2×D3—202no—
820C2×D3—202no—
821C2×D3—202no—
822C2×D3—202no—
823C3×C4—42no—
824C3×C4—42no—
825C3×C4—42no—
826Dic3—104no—
827Dic3—202no—
828Dic3—202no—
829C2×C5#466511yescharacteristic
830C2×C5#466711yescharacteristic
831C2×C5#466811yescharacteristic
832C2×C5#466911yescharacteristic
833C2×C5#467211yescharacteristic
834C2×C5#467311yescharacteristic
835C2×C5#467511yescharacteristic
836C2×C5#467611yescharacteristic
837C2×C5#494011yescharacteristic
838C2×C5#495711yescharacteristic
839C2×C5#495911yescharacteristic
840C2×C5#496011yescharacteristic
841C2×C5#498911yescharacteristic
842C2×C5#499311yescharacteristic
843C2×C5#499411yescharacteristic
844D5—124no—
845C23—154no—
846C23—302no—
847C23—302no—
848C23—302no—
849C23—302no—
850C23—302no—
851C23—302no—
852C23—302no—
853C23—302no—
854C23—302no—
855C23—302no—
856C23—302no—
857C23—302no—
858C23—302no—
859C23—302no—
860C23—302no—
861C23—302no—
862C23—302no—
863C23—302no—
864C23—601no—
865C23—601no—
866C23—601no—
867C23—601no—
868C23—601no—
869C23—601no—
870C23—601no—
871C23—601no—
872C23—601no—
873C23—601no—
874C23—601no—
875C23—601no—
876C23—601no—
877C23—601no—
878C23—601no—
879C23—601no—
880C23C2×C4×D1511yescharacteristic
881C23C2×D6011yescharacteristic
882C23#681711yescharacteristic
883C23#681711yescharacteristic
884C23#681711yescharacteristic
885C23#681711yescharacteristic
886C23D4×D1511yescharacteristic
887C23D4×D1511yescharacteristic
888C23D4×D1511yescharacteristic
889C23D4×D1511yescharacteristic
890C23D4×D1511yescharacteristic
891C23#681911yescharacteristic
892C23Q8×D1511yescharacteristic
893C23#682111yescharacteristic
894C23C2×#122011yescharacteristic
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—154no—
917C2×C4—302no—
918C2×C4—302no—
919C2×C4—302no—
920C2×C4—302no—
921C2×C4—302no—
922C2×C4—302no—
923C2×C4—302no—
924C2×C4—302no—
925C2×C4—302no—
926C2×C4—302no—
927C2×C4—302no—
928C2×C4—302no—
929C2×C4—601no—
930C2×C4—601no—
931C2×C4—601no—
932C2×C4—601no—
933C2×C4—601no—
934C2×C4—601no—
935C2×C4—601no—
936C2×C4—601no—
937C2×C3#6495411yescharacteristic
938C2×C3#6495611yescharacteristic
939C2×C3#6495711yescharacteristic
940C2×C3#6495811yescharacteristic
941C2×C3#6496111yescharacteristic
942C2×C3#6496211yescharacteristic
943C2×C3#6496411yescharacteristic
944C2×C3#6496511yescharacteristic
945C2×C3#6522911yescharacteristic
946C2×C3#6524611yescharacteristic
947C2×C3#6524811yescharacteristic
948C2×C3#6524911yescharacteristic
949C2×C3#6527811yescharacteristic
950C2×C3#6528111yescharacteristic
951C2×C3#6528311yescharacteristic
952D3—204no—
953C5#6942811yescharacteristic, complemented, Sylow
954C22—304no—
955C22—304no—
956C22—304no—
957C22—602no—
958C22—602no—
959C22—602no—
960C22—602no—
961C22—602no—
962C22—602no—
963C22—602no—
964C22—602no—
965C22—602no—
966C22—602no—
967C22—602no—
968C22—602no—
969C22#9176111yescharacteristic
970C22C4×D6011yescharacteristic
971C22#9176411yescharacteristic
972C22#9176511yescharacteristic
973C22C22⋊C4×D1511yescharacteristic
974C22#9177011yescharacteristic
975C22#9177111yescharacteristic
976C22#9177111yescharacteristic
977C22#9177211yescharacteristic
978C22#9177311yescharacteristic
979C22#9177311yescharacteristic
980C22#9177311yescharacteristic
981C22#9177311yescharacteristic
982C22#9177311yescharacteristic
983C22#9177411yescharacteristic
984C22#9177411yescharacteristic
985C22C4⋊C4×D1511yescharacteristic
986C22#9178211yescharacteristic
987C22#9178311yescharacteristic
988C22#9178311yescharacteristic
989C22#9178311yescharacteristic
990C22#9178411yescharacteristic
991C22#9178511yescharacteristic
992C22#9178511yescharacteristic
993C22#9178511yescharacteristic
994C22#9178511yescharacteristic
995C22#9178611yescharacteristic
996C22#9178711yescharacteristic
997C22C4×#122011yescharacteristic
998C22#9181811yescharacteristic
999C22#9181911yescharacteristic
1000C22#9182611yescharacteristic
1001C22#9182811yescharacteristic
1002C22#9182911yescharacteristic
1003C22#9183511yescharacteristic
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—304no—
1008C4—602no—
1009C4—602no—
1010C3#1060022111yescharacteristic, complemented, Sylow
1011C2—604no—
1012C2#1175076611yescharacteristic
1013C2#1175076811yescharacteristic
1014C2#1175076911yescharacteristic
1015C2#1175077011yescharacteristic
1016C2#1175077311yescharacteristic
1017C2#1175077411yescharacteristic
1018C2#1175077611yescharacteristic
1019C2#1175077711yescharacteristic
1020C2#1175104111yescharacteristic
1021C2#1175105811yescharacteristic
1022C2#1175106011yescharacteristic
1023C2#1175106111yescharacteristic
1024C2#1175109011yescharacteristic
1025C2#1175109411yescharacteristic
1026C2#1175109511yescharacteristic
subgroupG/H
center, FrattiniC24C22×D15
commutatorC23×C3×C5C22×C4
FittingC2×C3×C5×#95C2
socle, cosocleC24×C3×C5C23
prime radicalC24×D15C22
hypercenterC2×#95D15
hypocenterC3×C5#1439
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
4. C22×#6712C2semidirect
5. C2×C3×C5×#95C2semidirect
6. C2×#91115C2semidirect
7. C2×#91115C2semidirect
24. C2×#6714C4semidirect
36. C2×C5×#95D3semidirect
105. C2×C3×#95D5semidirect
180. C22×D15C4⋊C4semidirect
222. C2×Dic15C22⋊C4semidirect
313. C2×#95D15semidirect
772. C3×C5#1439semidirect
953. C5#69428semidirect
1010. C3#10600221semidirect

Maximal subgroups

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

subgroupindex
C22×#67142
C22×#67122
C2×C3×C5×#952
C2×#911152
#106002213
#694285