Finite Group Databasebeta

← #14280053

Subgroups — #14280053

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×C3×C5×C22⋊C4C211yesmaximal, characteristic
2C22×#6719C211yesmaximal, characteristic
3C22×#6719C211yesmaximal, characteristic
4C22×#6712C211yesmaximal, characteristic, complemented
5C2×#91115C211yesmaximal, characteristic, complemented
6C2×#91115C211yesmaximal, characteristic, complemented
7C2×#91115C211yesmaximal, characteristic, complemented
8#10602340—31nomaximal, Hall
9C25×C3×C5C2211yescharacteristic
10C23×C3×C4×C5C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×Dic15C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C23×Dic15C2211yescharacteristic
15C23×Dic15C2211yescharacteristic
16C2×C3×C5×C22⋊C4—22no—
17C2×C3×C5×C22⋊C4—22no—
18C2×C3×C5×C22⋊C4—22no—
19C2×#6719—22no—
20C2×#6719—22no—
21C2×#6719—22no—
22C2×#6719—22no—
23C2×#6719—22no—
24C2×#6719C414yescomplemented
25C2×#6712—22no—
26C2×#6712—22no—
27C2×#6712—22no—
28#91115—22no—
29#91115—22no—
30#91115—22no—
31#71547—51nomaximal, Hall
32C22×C5×C22⋊C4D311yescharacteristic
33C22×C22⋊Dic5—31no—
34C22×C22⋊Dic5—31no—
35C22×#683—31no—
36C2×#3963—31no—
37C2×#3963—31no—
38C2×#3963—31no—
39C24×C3×C5—21no—
40C24×C3×C5—21no—
41C24×C3×C5—21no—
42C24×C3×C5—21no—
43C24×C3×C5—21no—
44C24×C3×C5—21no—
45C24×C3×C5—21no—
46C24×C3×C5—21no—
47C24×C3×C5—21no—
48C24×C3×C5—21no—
49C24×C3×C5—21no—
50C24×C3×C5—21no—
51C24×C3×C5C2×C412yes—
52C24×C3×C5D412yes—
53C24×C3×C5Q812yes—
54C24×C3×C5C2311yescharacteristic
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×C5D412yes—
68C22×C3×C4×C5D412yes—
69C22×Dic15—21no—
70C22×Dic15—21no—
71C22×Dic15—21no—
72C22×Dic15—21no—
73C22×Dic15—21no—
74C22×Dic15—21no—
75C22×Dic15—21no—
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×Dic15C2×C412yes—
92C22×Dic15C2×C412yes—
93C22×Dic15D412yes—
94C22×Dic15D412yes—
95C22×Dic15D412yes—
96C22×Dic15D412yes—
97C3×C5×C22⋊C4—28no—
98#6719—28no—
99#6719—28no—
100#6712—28no—
101C22×C3×C22⋊C4D511yescharacteristic
102C22×#217—51no—
103C22×#217—51no—
104C22×Dic3⋊C4—51no—
105C2×C3⋊#95—51no—
106C2×C3⋊#95—51no—
107C2×C3⋊#95—51no—
108C25×C5C2×D311yescharacteristic
109C23×C4×C5C2×D311yescharacteristic
110C23×C4×C5C2×D311yescharacteristic
111C23×Dic5—31no—
112C23×Dic5—31no—
113C23×Dic5—31no—
114C23×Dic5—31no—
115C2×C5×C22⋊C4—22no—
116C2×C5×C22⋊C4—22no—
117C2×C5×C22⋊C4—22no—
118C2×C22⋊Dic5—34no—
119C2×C22⋊Dic5—62no—
120C2×C22⋊Dic5—62no—
121C2×C22⋊Dic5—62no—
122C2×C22⋊Dic5—62no—
123C2×C22⋊Dic5—62no—
124C2×#683—62no—
125C2×#683—62no—
126C2×#683—62no—
127#3963—62no—
128#3963—62no—
129#3963—62no—
130#1439—151noSylow
131C23×C3×C5—22no—
132C23×C3×C5—22no—
133C23×C3×C5—22no—
134C23×C3×C5—22no—
135C23×C3×C5—22no—
136C23×C3×C5—22no—
137C23×C3×C5—22no—
138C23×C3×C5—22no—
139C23×C3×C5—22no—
140C23×C3×C5—22no—
141C23×C3×C5—22no—
142C23×C3×C5—22no—
143C23×C3×C5—22no—
144C23×C3×C5—22no—
145C23×C3×C5—22no—
146C23×C3×C5—22no—
147C23×C3×C5—22no—
148C23×C3×C5—22no—
149C23×C3×C5—41no—
150C23×C3×C5—41no—
151C23×C3×C5—41no—
152C23×C3×C5—41no—
153C23×C3×C5—41no—
154C23×C3×C5—41no—
155C23×C3×C5—41no—
156C23×C3×C5—41no—
157C23×C3×C5—41no—
158C23×C3×C5—41no—
159C23×C3×C5—41no—
160C23×C3×C5—41no—
161C23×C3×C5—41no—
162C23×C3×C5—41no—
163C23×C3×C5—41no—
164C23×C3×C5—41no—
165C23×C3×C5C4⋊C414yescomplemented
166C23×C3×C5C22×C411yescharacteristic
167C23×C3×C5C2×D411yescharacteristic
168C23×C3×C5C2×D411yescharacteristic
169C23×C3×C5C2×D411yescharacteristic
170C23×C3×C5C2×D411yescharacteristic
171C23×C3×C5C2×D411yescharacteristic
172C23×C3×C5C2×D411yescharacteristic
173C23×C3×C5C2×D411yescharacteristic
174C23×C3×C5C2×Q811yescharacteristic
175C23×C3×C5#4111yescharacteristic
176C23×C3×C5#4111yescharacteristic
177C23×C3×C5#4111yescharacteristic
178C23×C3×C5#4111yescharacteristic
179C23×C3×C5#4111yescharacteristic
180C23×C3×C5#4111yescharacteristic
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—41no—
188C2×C3×C4×C5—41no—
189C2×C3×C4×C5—41no—
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×Dic15—22no—
196C2×Dic15—22no—
197C2×Dic15—22no—
198C2×Dic15—22no—
199C2×Dic15—22no—
200C2×Dic15—22no—
201C2×Dic15—22no—
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—41no—
211C2×Dic15—41no—
212C2×Dic15—41no—
213C2×Dic15—41no—
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
223C25×C3C2×D511yescharacteristic
224C23×C3×C4C2×D511yescharacteristic
225C23×C3×C4C2×D511yescharacteristic
226C23×Dic3—51no—
227C23×Dic3—51no—
228C23×Dic3—51no—
229C23×Dic3—51no—
230C2×C3×C22⋊C4—22no—
231C2×C3×C22⋊C4—22no—
232C2×C3×C22⋊C4—22no—
233C2×#217—54no—
234C2×#217—102no—
235C2×#217—102no—
236C2×#217—102no—
237C2×#217—102no—
238C2×#217—102no—
239C2×Dic3⋊C4—102no—
240C2×Dic3⋊C4—102no—
241C2×Dic3⋊C4—102no—
242C3⋊#95—102no—
243C3⋊#95—102no—
244C3⋊#95—102no—
245C24×C5—21no—
246C24×C5—21no—
247C24×C5—21no—
248C24×C5—21no—
249C24×C5—21no—
250C24×C5—21no—
251C24×C5—21no—
252C24×C5—21no—
253C24×C5—21no—
254C24×C5—21no—
255C24×C5—21no—
256C24×C5—21no—
257C24×C5Dic612yes—
258C24×C5C4×D312yes—
259C24×C5#6712yes—
260C24×C5C22×D311yescharacteristic
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#6712yes—
274C22×C4×C5#6712yes—
275C22×Dic5—32no—
276C22×Dic5—32no—
277C22×Dic5—32no—
278C22×Dic5—32no—
279C22×Dic5—32no—
280C22×Dic5—32no—
281C22×Dic5—61no—
282C22×Dic5—61no—
283C22×Dic5—61no—
284C22×Dic5—61no—
285C22×Dic5—61no—
286C22×Dic5—61no—
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—
303C5×C22⋊C4—28no—
304C22⋊Dic5—68no—
305C22⋊Dic5—68no—
306#683—68no—
307C22×C4⋊C4—151no—
308C22×C22⋊C4—151no—
309C22×C22⋊C4—151no—
310C22×C22⋊C4D1511yescharacteristic
311C2×#95—151no—
312C2×#95—151no—
313C2×#95—151no—
314C22×C3×C5—24no—
315C22×C3×C5—24no—
316C22×C3×C5—24no—
317C22×C3×C5—42no—
318C22×C3×C5—42no—
319C22×C3×C5—42no—
320C22×C3×C5—42no—
321C22×C3×C5—42no—
322C22×C3×C5—42no—
323C22×C3×C5—42no—
324C22×C3×C5—42no—
325C22×C3×C5—42no—
326C22×C3×C5—42no—
327C22×C3×C5—42no—
328C22×C3×C5—42no—
329C22×C3×C5C2×C22⋊C411yescharacteristic
330C22×C3×C5C2×C4⋊C411yescharacteristic
331C22×C3×C5#11711yescharacteristic
332C22×C3×C5C4×D411yescharacteristic
333C22×C3×C5C4×D411yescharacteristic
334C22×C3×C5C4×D411yescharacteristic
335C22×C3×C5C4×D411yescharacteristic
336C22×C3×C5#12011yescharacteristic
337C22×C3×C5#12011yescharacteristic
338C22×C3×C5#12011yescharacteristic
339C22×C3×C5#12111yescharacteristic
340C22×C3×C5#12111yescharacteristic
341C22×C3×C5#12111yescharacteristic
342C22×C3×C5#12111yescharacteristic
343C22×C3×C5#12111yescharacteristic
344C22×C3×C5#12111yescharacteristic
345C22×C3×C5#12111yescharacteristic
346C22×C3×C5#12111yescharacteristic
347C22×C3×C5C22⋊Q811yescharacteristic
348C22×C3×C5C22⋊Q811yescharacteristic
349C22×C3×C5C22⋊Q811yescharacteristic
350C22×C3×C5C22⋊Q811yescharacteristic
351C22×C3×C5C22⋊Q811yescharacteristic
352C22×C3×C5C22⋊Q811yescharacteristic
353C22×C3×C5#12311yescharacteristic
354C22×C3×C5#12311yescharacteristic
355C22×C3×C5#12311yescharacteristic
356C22×C3×C5#12311yescharacteristic
357C22×C3×C5#12311yescharacteristic
358C22×C3×C5#12411yescharacteristic
359C22×C3×C5#12411yescharacteristic
360C22×C3×C5#12411yescharacteristic
361C22×C3×C5#12611yescharacteristic
362C22×C3×C5#12611yescharacteristic
363C22×C3×C5#12711yescharacteristic
364C3×C4×C5—42no—
365C3×C4×C5—42no—
366Dic15—24no—
367Dic15—42no—
368Dic15—42no—
369Dic15—42no—
370C24×C3—21no—
371C24×C3—21no—
372C24×C3—21no—
373C24×C3—21no—
374C24×C3—21no—
375C24×C3—21no—
376C24×C3—21no—
377C24×C3—21no—
378C24×C3—21no—
379C24×C3—21no—
380C24×C3—21no—
381C24×C3—21no—
382C24×C3Dic1012yes—
383C24×C3C4×D512yes—
384C24×C3C22⋊D512yes—
385C24×C3C22×D511yescharacteristic
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×C4C22⋊D512yes—
399C22×C3×C4C22⋊D512yes—
400C22×Dic3—52no—
401C22×Dic3—52no—
402C22×Dic3—52no—
403C22×Dic3—52no—
404C22×Dic3—52no—
405C22×Dic3—52no—
406C22×Dic3—101no—
407C22×Dic3—101no—
408C22×Dic3—101no—
409C22×Dic3—101no—
410C22×Dic3—101no—
411C22×Dic3—101no—
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—
428C3×C22⋊C4—28no—
429#217—108no—
430#217—108no—
431Dic3⋊C4—108no—
432C23×C5—22no—
433C23×C5—22no—
434C23×C5—22no—
435C23×C5—22no—
436C23×C5—22no—
437C23×C5—22no—
438C23×C5—22no—
439C23×C5—22no—
440C23×C5—22no—
441C23×C5—22no—
442C23×C5—22no—
443C23×C5—22no—
444C23×C5—22no—
445C23×C5—22no—
446C23×C5—22no—
447C23×C5—22no—
448C23×C5—22no—
449C23×C5—22no—
450C23×C5—41no—
451C23×C5—41no—
452C23×C5—41no—
453C23×C5—41no—
454C23×C5—41no—
455C23×C5—41no—
456C23×C5—41no—
457C23×C5—41no—
458C23×C5—41no—
459C23×C5—41no—
460C23×C5—41no—
461C23×C5—41no—
462C23×C5—41no—
463C23×C5—41no—
464C23×C5—41no—
465C23×C5—41no—
466C23×C5Dic3⋊C414yescomplemented
467C23×C5C2×Dic611yescharacteristic
468C23×C5C2×C4×D311yescharacteristic
469C23×C5#23511yescharacteristic
470C23×C5#23511yescharacteristic
471C23×C5D3×D411yescharacteristic
472C23×C5D3×D411yescharacteristic
473C23×C5D3×D411yescharacteristic
474C23×C5D3×D411yescharacteristic
475C23×C5#23711yescharacteristic
476C23×C5#23711yescharacteristic
477C23×C5#23711yescharacteristic
478C23×C5#23711yescharacteristic
479C23×C5C2×#6711yescharacteristic
480C23×C5C2×#6711yescharacteristic
481C23×C5C2×#6711yescharacteristic
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—41no—
489C2×C4×C5—41no—
490C2×C4×C5—41no—
491C2×C4×C5—41no—
492C2×C4×C5—41no—
493C2×C4×C5—41no—
494C2×C4×C5—41no—
495C2×C4×C5—41no—
496C2×Dic5—34no—
497C2×Dic5—62no—
498C2×Dic5—62no—
499C2×Dic5—62no—
500C2×Dic5—62no—
501C2×Dic5—62no—
502C2×Dic5—62no—
503C2×Dic5—62no—
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—121no—
513C2×Dic5—121no—
514C2×Dic5—121no—
515C2×Dic5—121no—
516C2×Dic5—121no—
517C2×Dic5—121no—
518C2×Dic5—121no—
519C2×Dic5—121no—
520C2×Dic5—121no—
521C2×Dic5—121no—
522C2×Dic5—121no—
523C2×Dic5—121no—
524C25C2×D1511yescharacteristic
525C23×C4—151no—
526C23×C4—151no—
527C23×C4—151no—
528C23×C4—151no—
529C23×C4C2×D1511yescharacteristic
530C23×C4C2×D1511yescharacteristic
531C2×C4⋊C4—302no—
532C2×C4⋊C4—302no—
533C2×C4⋊C4—302no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—154no—
538C2×C22⋊C4—302no—
539C2×C22⋊C4—302no—
540C2×C22⋊C4—302no—
541C2×C22⋊C4—302no—
542C2×C22⋊C4—302no—
543#95—302no—
544#95—302no—
545#95—302no—
546C2×C3×C5—44no—
547C2×C3×C5#38011yescharacteristic
548C2×C3×C5#38511yescharacteristic
549C2×C3×C5#38511yescharacteristic
550C2×C3×C5#38611yescharacteristic
551C2×C3×C5#38811yescharacteristic
552C2×C3×C5#38811yescharacteristic
553C2×C3×C5#39011yescharacteristic
554C2×C3×C5#39211yescharacteristic
555C2×C3×C5#39311yescharacteristic
556C2×C3×C5#39411yescharacteristic
557C2×C3×C5#39411yescharacteristic
558C2×C3×C5#39611yescharacteristic
559C2×C3×C5#39611yescharacteristic
560C2×C3×C5#39711yescharacteristic
561C2×C3×C5#39911yescharacteristic
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—22no—
577C23×C3—22no—
578C23×C3—22no—
579C23×C3—22no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3#68314yescomplemented
597C23×C3C2×Dic1011yescharacteristic
598C23×C3C2×C4×D511yescharacteristic
599C23×C3#70911yescharacteristic
600C23×C3#70911yescharacteristic
601C23×C3D4×D511yescharacteristic
602C23×C3D4×D511yescharacteristic
603C23×C3D4×D511yescharacteristic
604C23×C3D4×D511yescharacteristic
605C23×C3#71111yescharacteristic
606C23×C3#71111yescharacteristic
607C23×C3#71111yescharacteristic
608C23×C3#71111yescharacteristic
609C23×C3C2×C22⋊D511yescharacteristic
610C23×C3C2×C22⋊D511yescharacteristic
611C23×C3C2×C22⋊D511yescharacteristic
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—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×Dic3—54no—
627C2×Dic3—102no—
628C2×Dic3—102no—
629C2×Dic3—102no—
630C2×Dic3—102no—
631C2×Dic3—102no—
632C2×Dic3—102no—
633C2×Dic3—102no—
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—201no—
643C2×Dic3—201no—
644C2×Dic3—201no—
645C2×Dic3—201no—
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—24no—
655C22×C5—24no—
656C22×C5—24no—
657C22×C5—42no—
658C22×C5—42no—
659C22×C5—42no—
660C22×C5—42no—
661C22×C5—42no—
662C22×C5—42no—
663C22×C5—42no—
664C22×C5—42no—
665C22×C5—42no—
666C22×C5—42no—
667C22×C5—42no—
668C22×C5—42no—
669C22×C5#87711yescharacteristic
670C22×C5#87811yescharacteristic
671C22×C5#87811yescharacteristic
672C22×C5#87811yescharacteristic
673C22×C5#87811yescharacteristic
674C22×C5#87911yescharacteristic
675C22×C5#87911yescharacteristic
676C22×C5D3×C22⋊C411yescharacteristic
677C22×C5#67⋊C411yescharacteristic
678C22×C5#67⋊C411yescharacteristic
679C22×C5#88311yescharacteristic
680C22×C5#88311yescharacteristic
681C22×C5#88411yescharacteristic
682C22×C5#88411yescharacteristic
683C22×C5#88511yescharacteristic
684C22×C5#88511yescharacteristic
685C22×C5C2×Dic3⋊C411yescharacteristic
686C22×C5#92411yescharacteristic
687C22×C5#92411yescharacteristic
688C22×C5C4×#6711yescharacteristic
689C22×C5C4×#6711yescharacteristic
690C22×C5#92911yescharacteristic
691C22×C5#93511yescharacteristic
692C22×C5#93511yescharacteristic
693C22×C5#93611yescharacteristic
694C22×C5#93711yescharacteristic
695C22×C5#93711yescharacteristic
696C22×C5#93811yescharacteristic
697C22×C5#93811yescharacteristic
698C22×C5#93911yescharacteristic
699C22×C5#93911yescharacteristic
700C22×C5#93911yescharacteristic
701C22×C5#93911yescharacteristic
702C22×C5#94011yescharacteristic
703C22×C5#95311yescharacteristic
704C4×C5—42no—
705C4×C5—42no—
706Dic5—64no—
707Dic5—122no—
708Dic5—122no—
709Dic5—122no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24Dic3012yes—
723C24C4×D1512yes—
724C24#122012yes—
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—152no—
739C22×C4—152no—
740C22×C4—152no—
741C22×C4—152no—
742C22×C4—152no—
743C22×C4—152no—
744C22×C4—301no—
745C22×C4—301no—
746C22×C4—301no—
747C22×C4—301no—
748C22×C4—301no—
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×C4—301no—
766C22×C4#122012yes—
767C22×C4#122012yes—
768C4⋊C4—308no—
769C22⋊C4—28no—
770C22⋊C4—308no—
771C22⋊C4—308no—
772C3×C5#143911yescharacteristic, complemented, Hall
773C22×C3—24no—
774C22×C3—24no—
775C22×C3—24no—
776C22×C3—42no—
777C22×C3—42no—
778C22×C3—42no—
779C22×C3—42no—
780C22×C3—42no—
781C22×C3—42no—
782C22×C3—42no—
783C22×C3—42no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3—42no—
787C22×C3—42no—
788C22×C3#402311yescharacteristic
789C22×C3#402411yescharacteristic
790C22×C3#402411yescharacteristic
791C22×C3#402411yescharacteristic
792C22×C3#402411yescharacteristic
793C22×C3#402511yescharacteristic
794C22×C3#402511yescharacteristic
795C22×C3D5×C22⋊C411yescharacteristic
796C22×C3#402711yescharacteristic
797C22×C3#402711yescharacteristic
798C22×C3#402911yescharacteristic
799C22×C3#402911yescharacteristic
800C22×C3#403011yescharacteristic
801C22×C3#403011yescharacteristic
802C22×C3#403111yescharacteristic
803C22×C3#403111yescharacteristic
804C22×C3C2×#68311yescharacteristic
805C22×C3#407011yescharacteristic
806C22×C3#407011yescharacteristic
807C22×C3C4×C22⋊D511yescharacteristic
808C22×C3C4×C22⋊D511yescharacteristic
809C22×C3#407511yescharacteristic
810C22×C3#408111yescharacteristic
811C22×C3#408111yescharacteristic
812C22×C3#408211yescharacteristic
813C22×C3#408311yescharacteristic
814C22×C3#408311yescharacteristic
815C22×C3#408411yescharacteristic
816C22×C3#408411yescharacteristic
817C22×C3#408511yescharacteristic
818C22×C3#408511yescharacteristic
819C22×C3#408511yescharacteristic
820C22×C3#408511yescharacteristic
821C22×C3#408611yescharacteristic
822C22×C3#409911yescharacteristic
823C3×C4—42no—
824C3×C4—42no—
825Dic3—104no—
826Dic3—202no—
827Dic3—202no—
828Dic3—202no—
829C2×C5—44no—
830C2×C5#494211yescharacteristic
831C2×C5#494411yescharacteristic
832C2×C5#494511yescharacteristic
833C2×C5#494611yescharacteristic
834C2×C5#494711yescharacteristic
835C2×C5#494811yescharacteristic
836C2×C5#494811yescharacteristic
837C2×C5#494911yescharacteristic
838C2×C5#495211yescharacteristic
839C2×C5#495611yescharacteristic
840C2×C5#495711yescharacteristic
841C2×C5#495911yescharacteristic
842C2×C5#521011yescharacteristic
843C2×C5#522211yescharacteristic
844C2×C5#522311yescharacteristic
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23#671214yescomplemented
880C23C2×Dic3011yescharacteristic
881C23C2×C4×D1511yescharacteristic
882C23#681711yescharacteristic
883C23#681711yescharacteristic
884C23D4×D1511yescharacteristic
885C23D4×D1511yescharacteristic
886C23D4×D1511yescharacteristic
887C23D4×D1511yescharacteristic
888C23#681911yescharacteristic
889C23#681911yescharacteristic
890C23#681911yescharacteristic
891C23#681911yescharacteristic
892C23C2×#122011yescharacteristic
893C23C2×#122011yescharacteristic
894C23C2×#122011yescharacteristic
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—154no—
910C2×C4—302no—
911C2×C4—302no—
912C2×C4—302no—
913C2×C4—302no—
914C2×C4—302no—
915C2×C4—302no—
916C2×C4—302no—
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—601no—
926C2×C4—601no—
927C2×C4—601no—
928C2×C4—601no—
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—44no—
938C2×C3#6523111yescharacteristic
939C2×C3#6523311yescharacteristic
940C2×C3#6523411yescharacteristic
941C2×C3#6523511yescharacteristic
942C2×C3#6523611yescharacteristic
943C2×C3#6523711yescharacteristic
944C2×C3#6523711yescharacteristic
945C2×C3#6523811yescharacteristic
946C2×C3#6524111yescharacteristic
947C2×C3#6524511yescharacteristic
948C2×C3#6524611yescharacteristic
949C2×C3#6524811yescharacteristic
950C2×C3#6549911yescharacteristic
951C2×C3#6551111yescharacteristic
952C2×C3#6551211yescharacteristic
953C5#7154711yescharacteristic, complemented, Sylow
954C22—24no—
955C22—24no—
956C22—24no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22#9176611yescharacteristic
970C22#9176711yescharacteristic
971C22#9176711yescharacteristic
972C22#9176711yescharacteristic
973C22#9176711yescharacteristic
974C22#9176811yescharacteristic
975C22#9176811yescharacteristic
976C22C22⋊C4×D1511yescharacteristic
977C22#9177011yescharacteristic
978C22#9177011yescharacteristic
979C22#9177211yescharacteristic
980C22#9177211yescharacteristic
981C22#9177311yescharacteristic
982C22#9177311yescharacteristic
983C22#9177411yescharacteristic
984C22#9177411yescharacteristic
985C22C2×#671211yescharacteristic
986C22#9181311yescharacteristic
987C22#9181311yescharacteristic
988C22C4×#122011yescharacteristic
989C22C4×#122011yescharacteristic
990C22#9181811yescharacteristic
991C22#9182411yescharacteristic
992C22#9182411yescharacteristic
993C22#9182511yescharacteristic
994C22#9182611yescharacteristic
995C22#9182611yescharacteristic
996C22#9182711yescharacteristic
997C22#9182711yescharacteristic
998C22#9182811yescharacteristic
999C22#9182811yescharacteristic
1000C22#9182811yescharacteristic
1001C22#9182811yescharacteristic
1002C22#9182911yescharacteristic
1003C22#9184211yescharacteristic
1004C4—42no—
1005C4—42no—
1006C4—304no—
1007C4—602no—
1008C4—602no—
1009C4—602no—
1010C3#1060234011yescharacteristic, complemented, Sylow
1011C2—44no—
1012C2#1175104311yescharacteristic
1013C2#1175104511yescharacteristic
1014C2#1175104611yescharacteristic
1015C2#1175104711yescharacteristic
1016C2#1175104811yescharacteristic
1017C2#1175104911yescharacteristic
1018C2#1175104911yescharacteristic
1019C2#1175105011yescharacteristic
1020C2#1175105311yescharacteristic
1021C2#1175105711yescharacteristic
1022C2#1175105811yescharacteristic
1023C2#1175106011yescharacteristic
1024C2#1175131111yescharacteristic
1025C2#1175132311yescharacteristic
1026C2#1175132411yescharacteristic
subgroupG/H
center, FrattiniC24C22×D15
commutatorC23×C3×C5C22×C4
FittingC22×C3×C5×C22⋊C4C2
socle, cosocleC24×C3×C5C23
prime radicalC25×C3×C5C22
hypercenterC22×C22⋊C4D15
hypocenterC3×C5#1439
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C22×#6712C2semidirect
5. C2×#91115C2semidirect
6. C2×#91115C2semidirect
7. C2×#91115C2semidirect
24. C2×#6719C4semidirect
165. C23×C3×C5C4⋊C4semidirect
222. C2×Dic15C22⋊C4semidirect
466. C23×C5Dic3⋊C4semidirect
596. C23×C3#683semidirect
772. C3×C5#1439semidirect
879. C23#6712semidirect
953. C5#71547semidirect
1010. C3#10602340semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C5×C22⋊C42
C22×#67192
C22×#67122
C2×#911152
#106023403
#715475