Finite Group Databasebeta

← #14323356

Subgroups — #14323356

Order 1920.

1616 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91826C211yesmaximal, characteristic
2C2×C4×#1220C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D15C211yesmaximal, characteristic, complemented
4C3×C5×#386C211yesmaximal, characteristic, complemented
5#11751322C211yesmaximal, characteristic, complemented
6#11751314C211yesmaximal, characteristic, complemented
7#11751058C211yesmaximal, characteristic, complemented
8#11751057C211yesmaximal, characteristic, complemented
9#11751056C211yesmaximal, characteristic, complemented
10#11751045C211yesmaximal, characteristic, complemented
11#11751045C211yesmaximal, characteristic, complemented
12#11750771C211yesmaximal, characteristic, complemented
13#11750770C211yesmaximal, characteristic, complemented
14#11750769C211yesmaximal, characteristic, complemented
15#11750767C211yesmaximal, characteristic, complemented
16#10606607—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic, complemented
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic
22C22×C4×D15C2211yescharacteristic
23C22×C4×D15C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
27C2×#6719C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6719C2211yescharacteristic
30C2×#6719C2211yescharacteristic, complemented
31C2×#6719C2211yescharacteristic, complemented
32#91826C418yescomplemented
33C4×#1220—24no—
34C2×#6714C2211yescharacteristic
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic
38C2×#6714C2211yescharacteristic
39C2×#6714C2211yescharacteristic
40C2×#6714C2211yescharacteristic
41C2×#6714C2211yescharacteristic
42C2×C4⋊Dic15C2211yescharacteristic, complemented
43C2×#6712C2211yescharacteristic, complemented
44C2×#6712C2211yescharacteristic, complemented
45C2×C4×Dic15C2211yescharacteristic, complemented
46C2×C4×Dic15C2211yescharacteristic, complemented
47C2×C4×Dic15C2211yescharacteristic, complemented
48C22⋊C4×D15—24no—
49C3×C5×#95C2211yescharacteristic, complemented
50C3×C5×#95C2211yescharacteristic, complemented
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53#91115C2211yescharacteristic, complemented
54#91115C2211yescharacteristic, complemented
55#74876—51nomaximal, Hall
56C2×#4083—31no—
57C2×C4×C22⋊D5—31no—
58C2×D5×C22⋊C4—31no—
59C5×#386D311yescharacteristic, complemented
60#65510—31no—
61#65502—31no—
62#65246—31no—
63#65245—31no—
64#65244—31no—
65#65233—31no—
66#65233—31no—
67#64959—31no—
68#64958—31no—
69#64957—31no—
70#64955—31no—
71C24×C3×C5C2311yescharacteristic
72C24×C3×C5C2311yescharacteristic
73C23×D15—22no—
74C23×D15—22no—
75C23×D15—41no—
76C23×D15—41no—
77C23×D15—41no—
78C23×D15—41no—
79C23×D15C2×C414yescomplemented
80C23×D15C2311yescharacteristic
81C23×D15C2311yescharacteristic
82C2×C3×C5×D4—41no—
83C2×C3×C5×D4—41no—
84C2×C3×C5×D4C2×C414yescomplemented
85C22×C3×C4×C5—22no—
86C22×C3×C4×C5—41no—
87C22×C3×C4×C5—41no—
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C2×#1220—22no—
94C2×#1220—22no—
95C2×#1220—41no—
96C2×#1220—41no—
97C2×#1220C2×C414yes—
98C2×#1220C2×C414yescomplemented
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C22×Dic15C2311yescharacteristic
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C2×C4×D15—22no—
106C2×C4×D15—41no—
107C2×C4×D15—41no—
108C2×C4×D15—41no—
109C2×C4×D15—41no—
110C2×C4×D15D414yescomplemented
111C3×C5×C22⋊C4—22no—
112C3×C5×C22⋊C4—41no—
113C3×C5×C22⋊C4—41no—
114#6719—22no—
115#6719—22no—
116#6719—41no—
117#6719—41no—
118#6719C2×C414yescomplemented
119#6714—22no—
120#6714—22no—
121#6714—22no—
122#6714—22no—
123#6714—41no—
124#6714—41no—
125#6714C2×C414yescomplemented
126#6714C2×C414yescomplemented
127C4⋊Dic15—41no—
128#6712—22no—
129#6712—41no—
130C4×Dic15—22no—
131C4×Dic15—41no—
132C4×Dic15—41no—
133C2×#937—51no—
134C2×C4×#67—51no—
135C2×D3×C22⋊C4—51no—
136C3×#386D511yescharacteristic, complemented
137#5221—51no—
138#5213—51no—
139#4957—51no—
140#4956—51no—
141#4955—51no—
142#4944—51no—
143#4944—51no—
144#4670—51no—
145#4669—51no—
146#4668—51no—
147#4666—51no—
148C24×D5—31no—
149C22×C5×D4C2×D311yescharacteristic
150C23×C4×C5C2×D311yescharacteristic, complemented
151C22×C22⋊D5—31no—
152C22×C22⋊D5—31no—
153C22×C4×D5—31no—
154C22×C4×D5—31no—
155C2×C5×C22⋊C4C2×D311yescharacteristic
156C2×C5×C22⋊C4C2×D311yescharacteristic
157C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
158C2×C22⋊Dic5—31no—
159C2×C22⋊Dic5—31no—
160C2×C22⋊Dic5—31no—
161C2×C22⋊Dic5—31no—
162C2×C22⋊Dic5—31no—
163#4083—38no—
164C4×C22⋊D5—64no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685—31no—
171C2×#685—31no—
172C2×#685—31no—
173C2×C4⋊Dic5—31no—
174C2×#683—31no—
175C2×#683—31no—
176C2×C4×Dic5—31no—
177C2×C4×Dic5—31no—
178C2×C4×Dic5—31no—
179D5×C22⋊C4—64no—
180C5×#95C2×D311yescharacteristic, complemented
181C5×#95C2×D311yescharacteristic, complemented
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#2321—151noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5—21no—
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5C22×C412yes—
200C23×C3×C5C22×C412yes—
201C23×C3×C5C2411yescharacteristic
202C22×D15—21no—
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—21no—
207C22×D15—21no—
208C22×D15—21no—
209C22×D15—21no—
210C22×D15—21no—
211C22×D15—21no—
212C22×D15—28no—
213C22×D15—44no—
214C22×D15—44no—
215C22×D15—44no—
216C22×D15—44no—
217C22×D15—44no—
218C22×D15—44no—
219C22×D15C22×C412yes—
220C22×D15C22×C412yes—
221C22×D15C2×D412yes—
222C22×D15#4112yes—
223C3×C5×D4—44no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5—21no—
236C2×C3×C4×C5—21no—
237C2×C3×C4×C5—44no—
238C2×C3×C4×C5C22×C412yes—
239C2×C3×C4×C5C2×D412yes—
240#1220—28no—
241#1220—44no—
242C2×Dic15—21no—
243C2×Dic15—21no—
244C2×Dic15—21no—
245C2×Dic15—21no—
246C2×Dic15—21no—
247C2×Dic15—21no—
248C2×Dic15—21no—
249C2×Dic15—21no—
250C2×Dic15—21no—
251C2×Dic15—21no—
252C2×Dic15—21no—
253C2×Dic15—21no—
254C2×Dic15—21no—
255C2×Dic15—21no—
256C2×Dic15—21no—
257C2×Dic15C22×C412yes—
258C2×Dic15C22×C412yes—
259C2×Dic15C2×D412yes—
260C4×D15—44no—
261C4×D15—44no—
262C24×D3—51no—
263C22×C3×D4C2×D511yescharacteristic
264C23×C3×C4C2×D511yescharacteristic, complemented
265C22×#67—51no—
266C22×#67—51no—
267C22×C4×D3—51no—
268C22×C4×D3—51no—
269C2×C3×C22⋊C4C2×D511yescharacteristic
270C2×C3×C22⋊C4C2×D511yescharacteristic
271C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
272C2×#217—51no—
273C2×#217—51no—
274C2×#217—51no—
275C2×#217—51no—
276C2×#217—51no—
277#937—58no—
278C4×#67—104no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4—51no—
282C2×(C2×D3)⋊C4—51no—
283C2×(C2×D3)⋊C4—51no—
284C2×(C2×D3)⋊C4—51no—
285C2×(C2×D3)⋊C4—51no—
286C2×(C2×D3)⋊C4—51no—
287C2×C4⋊Dic3—51no—
288C2×Dic3⋊C4—51no—
289C2×Dic3⋊C4—51no—
290C2×C4×Dic3—51no—
291C2×C4×Dic3—51no—
292C2×C4×Dic3—51no—
293D3×C22⋊C4—104no—
294C3×#95C2×D511yescharacteristic, complemented
295C3×#95C2×D511yescharacteristic, complemented
296C3⋊#95—51no—
297C3⋊#95—51no—
298C3⋊#95—51no—
299C3⋊#95—51no—
300C24×C5C22×D311yescharacteristic
301C24×C5C22×D311yescharacteristic
302C23×D5—31no—
303C23×D5—31no—
304C23×D5—34no—
305C23×D5—62no—
306C23×D5—62no—
307C23×D5—121no—
308C23×D5—121no—
309C23×D5—121no—
310C23×D5—121no—
311C2×C5×D4—41no—
312C2×C5×D4—41no—
313C2×C5×D4C4×D314yescomplemented
314C22×C4×C5—22no—
315C22×C4×C5—41no—
316C22×C4×C5—41no—
317C22×C4×C5C22×D311yescharacteristic
318C22×C4×C5C22×D311yescharacteristic
319C22×C4×C5C22×D311yescharacteristic
320C22×C4×C5C22×D311yescharacteristic
321C22×C4×C5C22×D311yescharacteristic
322C2×C22⋊D5—34no—
323C2×C22⋊D5—34no—
324C2×C22⋊D5—62no—
325C2×C22⋊D5—62no—
326C2×C22⋊D5—121no—
327C2×C22⋊D5—121no—
328C22×Dic5—31no—
329C22×Dic5—31no—
330C22×Dic5—31no—
331C22×Dic5—31no—
332C22×Dic5—31no—
333C22×Dic5—31no—
334C2×C4×D5—34no—
335C2×C4×D5—62no—
336C2×C4×D5—121no—
337C2×C4×D5—121no—
338C2×C4×D5—121no—
339C2×C4×D5—121no—
340C5×C22⋊C4—22no—
341C5×C22⋊C4—41no—
342C5×C22⋊C4—41no—
343C22⋊Dic5—34no—
344C22⋊Dic5—62no—
345C22⋊Dic5—62no—
346C22⋊Dic5—121no—
347C22⋊Dic5—121no—
348#685—34no—
349#685—34no—
350#685—62no—
351#685—62no—
352#685—62no—
353#685—62no—
354#685—121no—
355#685—121no—
356C4⋊Dic5—121no—
357#683—62no—
358#683—121no—
359C4×Dic5—62no—
360C4×Dic5—121no—
361C4×Dic5—121no—
362C2×#120—151no—
363C2×C4×D4—151no—
364C22×C22⋊C4—151no—
365#390—151no—
366#390—151no—
367#388—151no—
368#388—151no—
369#388—151no—
370#388—151no—
371#386—151no—
372#386—151no—
373#386D1511yescharacteristic, complemented
374#385—151no—
375#379—151no—
376C4×C22⋊C4—151no—
377C22×C3×C5—22no—
378C22×C3×C5—22no—
379C22×C3×C5—22no—
380C22×C3×C5—22no—
381C22×C3×C5—22no—
382C22×C3×C5—22no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5—41no—
389C22×C3×C5—41no—
390C22×C3×C5—41no—
391C22×C3×C5C23×C411yescharacteristic
392C22×C3×C5C22×D411yescharacteristic
393C22×C3×C5C2×#4111yescharacteristic
394C22×C3×C5H(5,𝔽2)11yescharacteristic
395C22×C3×C5H(5,𝔽2)11yescharacteristic
396C22×C3×C5H(5,𝔽2)11yescharacteristic
397C22×C3×C5H(5,𝔽2)11yescharacteristic
398C2×D15—22no—
399C2×D15—22no—
400C2×D15—22no—
401C2×D15—22no—
402C2×D15—22no—
403C2×D15—22no—
404C2×D15—22no—
405C2×D15—22no—
406C2×D15—22no—
407C2×D15—416no—
408C2×D15—41no—
409C2×D15—41no—
410C2×D15—41no—
411C2×D15—41no—
412C2×D15C4×D414yes—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415C3×C4×C5—41no—
416C3×C4×C5—41no—
417C3×C4×C5—41no—
418Dic15—22no—
419Dic15—22no—
420Dic15—22no—
421Dic15—41no—
422Dic15—41no—
423Dic15—41no—
424C24×C3C22×D511yescharacteristic
425C24×C3C22×D511yescharacteristic
426C23×D3—51no—
427C23×D3—51no—
428C23×D3—54no—
429C23×D3—102no—
430C23×D3—102no—
431C23×D3—201no—
432C23×D3—201no—
433C23×D3—201no—
434C23×D3—201no—
435C2×C3×D4—41no—
436C2×C3×D4—41no—
437C2×C3×D4C4×D514yescomplemented
438C22×C3×C4—22no—
439C22×C3×C4—41no—
440C22×C3×C4—41no—
441C22×C3×C4C22×D511yescharacteristic
442C22×C3×C4C22×D511yescharacteristic
443C22×C3×C4C22×D511yescharacteristic
444C22×C3×C4C22×D511yescharacteristic
445C22×C3×C4C22×D511yescharacteristic
446C2×#67—54no—
447C2×#67—54no—
448C2×#67—102no—
449C2×#67—102no—
450C2×#67—201no—
451C2×#67—201no—
452C22×Dic3—51no—
453C22×Dic3—51no—
454C22×Dic3—51no—
455C22×Dic3—51no—
456C22×Dic3—51no—
457C22×Dic3—51no—
458C2×C4×D3—54no—
459C2×C4×D3—102no—
460C2×C4×D3—201no—
461C2×C4×D3—201no—
462C2×C4×D3—201no—
463C2×C4×D3—201no—
464C3×C22⋊C4—22no—
465C3×C22⋊C4—41no—
466C3×C22⋊C4—41no—
467#217—54no—
468#217—102no—
469#217—102no—
470#217—201no—
471#217—201no—
472(C2×D3)⋊C4—54no—
473(C2×D3)⋊C4—54no—
474(C2×D3)⋊C4—102no—
475(C2×D3)⋊C4—102no—
476(C2×D3)⋊C4—102no—
477(C2×D3)⋊C4—102no—
478(C2×D3)⋊C4—201no—
479(C2×D3)⋊C4—201no—
480C4⋊Dic3—201no—
481Dic3⋊C4—102no—
482Dic3⋊C4—201no—
483C4×Dic3—102no—
484C4×Dic3—201no—
485C4×Dic3—201no—
486C23×C5—21no—
487C23×C5—21no—
488C23×C5—21no—
489C23×C5—21no—
490C23×C5—21no—
491C23×C5—21no—
492C23×C5—21no—
493C23×C5—21no—
494C23×C5—21no—
495C23×C5—21no—
496C23×C5—21no—
497C23×C5—21no—
498C23×C5C2×C4×D312yes—
499C23×C5C2×C4×D312yes—
500C23×C5C23×D311yescharacteristic
501C22×D5—32no—
502C22×D5—32no—
503C22×D5—32no—
504C22×D5—32no—
505C22×D5—68no—
506C22×D5—61no—
507C22×D5—61no—
508C22×D5—61no—
509C22×D5—61no—
510C22×D5—61no—
511C22×D5—61no—
512C22×D5—61no—
513C22×D5—61no—
514C22×D5—61no—
515C22×D5—61no—
516C22×D5—124no—
517C22×D5—124no—
518C22×D5—124no—
519C22×D5—124no—
520C22×D5—124no—
521C22×D5—124no—
522C5×D4—44no—
523C2×C4×C5—21no—
524C2×C4×C5—21no—
525C2×C4×C5—21no—
526C2×C4×C5—21no—
527C2×C4×C5—21no—
528C2×C4×C5—21no—
529C2×C4×C5—21no—
530C2×C4×C5—21no—
531C2×C4×C5—21no—
532C2×C4×C5—21no—
533C2×C4×C5—21no—
534C2×C4×C5—21no—
535C2×C4×C5—21no—
536C2×C4×C5—44no—
537C2×C4×C5C2×C4×D312yes—
538C2×C4×C5D3×D412yes—
539C22⋊D5—68no—
540C22⋊D5—124no—
541C2×Dic5—32no—
542C2×Dic5—32no—
543C2×Dic5—32no—
544C2×Dic5—61no—
545C2×Dic5—61no—
546C2×Dic5—61no—
547C2×Dic5—61no—
548C2×Dic5—61no—
549C2×Dic5—61no—
550C2×Dic5—61no—
551C2×Dic5—61no—
552C2×Dic5—61no—
553C2×Dic5—61no—
554C2×Dic5—61no—
555C2×Dic5—61no—
556C2×Dic5—61no—
557C2×Dic5—61no—
558C2×Dic5—61no—
559C4×D5—124no—
560C4×D5—124no—
561C25—151no—
562C22×D4—151no—
563C22×D4—151no—
564C22×D4C2×D1511yescharacteristic
565C23×C4—151no—
566C23×C4—151no—
567C23×C4C2×D1511yescharacteristic, complemented
568#120—158no—
569C4×D4—304no—
570C2×C4⋊C4—151no—
571C2×C4⋊C4—151no—
572C2×C4⋊C4—151no—
573C2×C22⋊C4—151no—
574C2×C22⋊C4—151no—
575C2×C22⋊C4—151no—
576C2×C22⋊C4—151no—
577C2×C22⋊C4—151no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C22⋊C4—151no—
585C2×C22⋊C4—151no—
586C2×C22⋊C4—304no—
587C2×C22⋊C4C2×D1511yescharacteristic
588C2×C22⋊C4C2×D1511yescharacteristic
589C2×C22⋊C4C2×D1511yescharacteristic, complemented
590C2×C42—151no—
591C2×C42—151no—
592C2×C42—151no—
593#95—151no—
594#95—151no—
595#95—151no—
596#95—151no—
597#95C2×D1511yescharacteristic, complemented
598#95C2×D1511yescharacteristic, complemented
599C2×C3×C5—42no—
600C2×C3×C5—42no—
601C2×C3×C5C2×C4×D411yescharacteristic
602C2×C3×C5#51811yescharacteristic
603C2×C3×C5#51811yescharacteristic
604C2×C3×C5#53411yescharacteristic
605C2×C3×C5#53511yescharacteristic
606C2×C3×C5#53811yescharacteristic
607C2×C3×C5#53811yescharacteristic
608D15—24no—
609D15—42no—
610C23×C3—21no—
611C23×C3—21no—
612C23×C3—21no—
613C23×C3—21no—
614C23×C3—21no—
615C23×C3—21no—
616C23×C3—21no—
617C23×C3—21no—
618C23×C3—21no—
619C23×C3—21no—
620C23×C3—21no—
621C23×C3—21no—
622C23×C3C2×C4×D512yes—
623C23×C3C2×C4×D512yes—
624C23×C3C23×D511yescharacteristic
625C22×D3—52no—
626C22×D3—52no—
627C22×D3—52no—
628C22×D3—52no—
629C22×D3—108no—
630C22×D3—101no—
631C22×D3—101no—
632C22×D3—101no—
633C22×D3—101no—
634C22×D3—101no—
635C22×D3—101no—
636C22×D3—101no—
637C22×D3—101no—
638C22×D3—101no—
639C22×D3—101no—
640C22×D3—204no—
641C22×D3—204no—
642C22×D3—204no—
643C22×D3—204no—
644C22×D3—204no—
645C22×D3—204no—
646C3×D4—44no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—44no—
661C2×C3×C4C2×C4×D512yes—
662C2×C3×C4D4×D512yes—
663#67—108no—
664#67—204no—
665C2×Dic3—52no—
666C2×Dic3—52no—
667C2×Dic3—52no—
668C2×Dic3—101no—
669C2×Dic3—101no—
670C2×Dic3—101no—
671C2×Dic3—101no—
672C2×Dic3—101no—
673C2×Dic3—101no—
674C2×Dic3—101no—
675C2×Dic3—101no—
676C2×Dic3—101no—
677C2×Dic3—101no—
678C2×Dic3—101no—
679C2×Dic3—101no—
680C2×Dic3—101no—
681C2×Dic3—101no—
682C2×Dic3—101no—
683C4×D3—204no—
684C4×D3—204no—
685C22×C5—22no—
686C22×C5—22no—
687C22×C5—22no—
688C22×C5—22no—
689C22×C5—22no—
690C22×C5—22no—
691C22×C5—41no—
692C22×C5—41no—
693C22×C5—41no—
694C22×C5—41no—
695C22×C5—41no—
696C22×C5—41no—
697C22×C5—41no—
698C22×C5—41no—
699C22×C5C22×C4×D311yescharacteristic
700C22×C5C2×D3×D411yescharacteristic
701C22×C5#100411yescharacteristic
702C22×C5#100411yescharacteristic
703C22×C5#100411yescharacteristic
704C22×C5D3×#4111yescharacteristic
705C22×C5#100911yescharacteristic
706C2×D5—34no—
707C2×D5—62no—
708C2×D5—62no—
709C2×D5—62no—
710C2×D5—62no—
711C2×D5—62no—
712C2×D5—62no—
713C2×D5—62no—
714C2×D5—62no—
715C2×D5—62no—
716C2×D5—1216no—
717C2×D5—121no—
718C2×D5—121no—
719C2×D5—121no—
720C2×D5—121no—
721C4×C5—22no—
722C4×C5—22no—
723C4×C5—41no—
724C4×C5—41no—
725C4×C5—41no—
726Dic5—62no—
727Dic5—62no—
728Dic5—62no—
729Dic5—121no—
730Dic5—121no—
731Dic5—121no—
732C24—151no—
733C24—151no—
734C24—154no—
735C24—302no—
736C24—302no—
737C24—601no—
738C24—601no—
739C24—601no—
740C24—601no—
741C24C22×D1511yescharacteristic
742C24C22×D1511yescharacteristic
743C2×D4—41no—
744C2×D4—41no—
745C2×D4—154no—
746C2×D4—154no—
747C2×D4—302no—
748C2×D4—302no—
749C2×D4—601no—
750C2×D4—601no—
751C2×D4C4×D1514yescomplemented
752C22×C4—22no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—151no—
756C22×C4—151no—
757C22×C4—151no—
758C22×C4—154no—
759C22×C4—151no—
760C22×C4—151no—
761C22×C4—151no—
762C22×C4—302no—
763C22×C4—601no—
764C22×C4—601no—
765C22×C4—601no—
766C22×C4—601no—
767C22×C4C22×D1511yescharacteristic
768C22×C4C22×D1511yescharacteristic
769C22×C4C22×D1511yescharacteristic
770C22×C4C22×D1511yescharacteristic
771C22×C4C22×D1511yescharacteristic
772C4⋊C4—302no—
773C4⋊C4—601no—
774C4⋊C4—601no—
775C22⋊C4—22no—
776C22⋊C4—41no—
777C22⋊C4—41no—
778C22⋊C4—154no—
779C22⋊C4—154no—
780C22⋊C4—154no—
781C22⋊C4—302no—
782C22⋊C4—302no—
783C22⋊C4—302no—
784C22⋊C4—302no—
785C22⋊C4—302no—
786C22⋊C4—302no—
787C22⋊C4—601no—
788C22⋊C4—601no—
789C22⋊C4—601no—
790C22⋊C4—601no—
791C42—302no—
792C42—601no—
793C42—601no—
794C3×C5#232111yescharacteristic, complemented, Hall
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—41no—
802C22×C3—41no—
803C22×C3—41no—
804C22×C3—41no—
805C22×C3—41no—
806C22×C3—41no—
807C22×C3—41no—
808C22×C3—41no—
809C22×C3C22×C4×D511yescharacteristic
810C22×C3C2×D4×D511yescharacteristic
811C22×C3#414411yescharacteristic
812C22×C3#414411yescharacteristic
813C22×C3#414411yescharacteristic
814C22×C3D5×#4111yescharacteristic
815C22×C3#414911yescharacteristic
816C2×D3—54no—
817C2×D3—102no—
818C2×D3—102no—
819C2×D3—102no—
820C2×D3—102no—
821C2×D3—102no—
822C2×D3—102no—
823C2×D3—102no—
824C2×D3—102no—
825C2×D3—102no—
826C2×D3—2016no—
827C2×D3—201no—
828C2×D3—201no—
829C2×D3—201no—
830C2×D3—201no—
831C3×C4—22no—
832C3×C4—22no—
833C3×C4—41no—
834C3×C4—41no—
835C3×C4—41no—
836Dic3—102no—
837Dic3—102no—
838Dic3—102no—
839Dic3—201no—
840Dic3—201no—
841Dic3—201no—
842C2×C5—42no—
843C2×C5—42no—
844C2×C5#548611yescharacteristic
845C2×C5C4×D3×D411yescharacteristic
846C2×C5#554511yescharacteristic
847C2×C5#558911yescharacteristic
848C2×C5#560711yescharacteristic
849C2×C5#561311yescharacteristic
850C2×C5#565711yescharacteristic
851D5—64no—
852D5—122no—
853C23—21no—
854C23—21no—
855C23—21no—
856C23—21no—
857C23—21no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—21no—
865C23—152no—
866C23—152no—
867C23—152no—
868C23—152no—
869C23—308no—
870C23—301no—
871C23—301no—
872C23—301no—
873C23—301no—
874C23—301no—
875C23—301no—
876C23—301no—
877C23—301no—
878C23—301no—
879C23—301no—
880C23—604no—
881C23—604no—
882C23—604no—
883C23—604no—
884C23—604no—
885C23—604no—
886C23C2×C4×D1512yes—
887C23C2×C4×D1512yes—
888C23C23×D1511yescharacteristic
889D4—44no—
890D4—308no—
891D4—604no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—44no—
906C2×C4—152no—
907C2×C4—152no—
908C2×C4—152no—
909C2×C4—301no—
910C2×C4—301no—
911C2×C4—301no—
912C2×C4—301no—
913C2×C4—301no—
914C2×C4—301no—
915C2×C4—301no—
916C2×C4—301no—
917C2×C4—301no—
918C2×C4—301no—
919C2×C4—301no—
920C2×C4—301no—
921C2×C4—301no—
922C2×C4—301no—
923C2×C4—301no—
924C2×C4—604no—
925C2×C4—604no—
926C2×C4C2×C4×D1512yes—
927C2×C4D4×D1512yes—
928C2×C3—42no—
929C2×C3—42no—
930C2×C3#6582011yescharacteristic
931C2×C3C4×D4×D511yescharacteristic
932C2×C3#6587911yescharacteristic
933C2×C3#6592311yescharacteristic
934C2×C3#6594111yescharacteristic
935C2×C3#6594711yescharacteristic
936C2×C3#6599111yescharacteristic
937D3—104no—
938D3—202no—
939C5#7487611yescharacteristic, complemented, Sylow
940C22—22no—
941C22—22no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—22no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—154no—
955C22—302no—
956C22—302no—
957C22—302no—
958C22—302no—
959C22—302no—
960C22—302no—
961C22—302no—
962C22—302no—
963C22—302no—
964C22—6016no—
965C22—601no—
966C22—601no—
967C22—601no—
968C22—601no—
969C22C22×C4×D1511yescharacteristic
970C22C2×D4×D1511yescharacteristic
971C22#9209511yescharacteristic
972C22#9209511yescharacteristic
973C22#9209511yescharacteristic
974C22#41×D1511yescharacteristic
975C22#9210011yescharacteristic
976C4—22no—
977C4—22no—
978C4—41no—
979C4—41no—
980C4—41no—
981C4—302no—
982C4—302no—
983C4—302no—
984C4—601no—
985C4—601no—
986C4—601no—
987C3#1060660711yescharacteristic, complemented, Sylow
988C2—42no—
989C2—42no—
990C2—304no—
991C2—602no—
992C2#1175624511yescharacteristic
993C2C4×D4×D1511yescharacteristic
994C2#1175630411yescharacteristic
995C2#1175634811yescharacteristic
996C2#1175636611yescharacteristic
997C2#1175637211yescharacteristic
998C2#1175641611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#386C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91826C2
hypercenter#386D15
hypocenterC3×C5#2321
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×#1220C2semidirect
3. C2×C22⋊C4×D15C2semidirect
4. C3×C5×#386C2semidirect
5. #11751322C2semidirect
6. #11751314C2semidirect
7. #11751058C2semidirect
8. #11751057C2semidirect
9. #11751056C2semidirect
10. #11751045C2semidirect
11. #11751045C2semidirect
12. #11750771C2semidirect
13. #11750770C2semidirect
14. #11750769C2semidirect
15. #11750767C2semidirect
19. C23×C3×C4×C5C22semidirect
26. C2×C3×C5×C22⋊C4C22semidirect
30. C2×#6719C22semidirect
31. C2×#6719C22semidirect
32. #91826C4semidirect
42. C2×C4⋊Dic15C22semidirect
43. C2×#6712C22semidirect
44. C2×#6712C22semidirect
45. C2×C4×Dic15C22semidirect
46. C2×C4×Dic15C22semidirect
47. C2×C4×Dic15C22semidirect
49. C3×C5×#95C22semidirect
50. C3×C5×#95C22semidirect
51. #91115C22semidirect
52. #91115C22semidirect
53. #91115C22semidirect
54. #91115C22semidirect
59. C5×#386D3semidirect
79. C23×D15C2×C4semidirect
84. C2×C3×C5×D4C2×C4semidirect
98. C2×#1220C2×C4semidirect
110. C2×C4×D15D4semidirect
118. #6719C2×C4semidirect
125. #6714C2×C4semidirect
126. #6714C2×C4semidirect
136. C3×#386D5semidirect
150. C23×C4×C5C2×D3semidirect
157. C2×C5×C22⋊C4C2×D3semidirect
180. C5×#95C2×D3semidirect
181. C5×#95C2×D3semidirect
264. C23×C3×C4C2×D5semidirect
271. C2×C3×C22⋊C4C2×D5semidirect
294. C3×#95C2×D5semidirect
295. C3×#95C2×D5semidirect
313. C2×C5×D4C4×D3semidirect
373. #386D15semidirect
437. C2×C3×D4C4×D5semidirect
567. C23×C4C2×D15semidirect
589. C2×C22⋊C4C2×D15semidirect
597. #95C2×D15semidirect
598. #95C2×D15semidirect
751. C2×D4C4×D15semidirect
794. C3×C5#2321semidirect
939. C5#74876semidirect
987. C3#10606607semidirect

Maximal subgroups

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

subgroupindex
C2×#918262
C2×C4×#12202
C2×C22⋊C4×D152
C3×C5×#3862
#117513222
#117513142
#117510582
#117510572
#117510562
#117510452
#117507712
#117507702
#117507692
#117507672
#106066073
#748765