Finite Group Databasebeta

← #14323365

Subgroups — #14323365

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×#91770C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D15C211yesmaximal, characteristic, complemented
4C3×C5×#390C211yesmaximal, characteristic, complemented
5#11751321C211yesmaximal, characteristic, complemented
6#11751091C211yesmaximal, characteristic, complemented
7#11751090C211yesmaximal, characteristic, complemented
8#11751059C211yesmaximal, characteristic, complemented
9#11751058C211yesmaximal, characteristic, complemented
10#11751057C211yesmaximal, characteristic, complemented
11#11751056C211yesmaximal, characteristic, complemented
12#11751046C211yesmaximal, characteristic, complemented
13#11751046C211yesmaximal, characteristic, complemented
14#11751041C211yesmaximal, characteristic, complemented
15C4×#6714C211yesmaximal, characteristic, complemented
16#10608160—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C23×Dic15C2211yescharacteristic, complemented
22C22×C4×D15C2211yescharacteristic
23C22×C4×D15C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
28C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
29C2×C3×C42×C5C2211yescharacteristic, complemented
30C2×#6719C2211yescharacteristic
31C2×#6719C2211yescharacteristic
32C2×#6719C2211yescharacteristic
33C2×#6719C2211yescharacteristic, complemented
34#91826C418yescomplemented
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic
38C2×#6714C2211yescharacteristic
39C2×#6714C2211yescharacteristic
40C2×#6714C2211yescharacteristic
41C2×#6714C2211yescharacteristic
42C2×#6714C2211yescharacteristic
43C2×#6712C2211yescharacteristic, complemented
44C2×#6712C2211yescharacteristic, complemented
45C2×C4×Dic15C2211yescharacteristic, complemented
46C2×C4×Dic15C2211yescharacteristic, complemented
47#91770—24no—
48C22⋊C4×D15—24no—
49#91115C2211yescharacteristic, complemented
50#91115C2211yescharacteristic, complemented
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53#91115C2211yescharacteristic, complemented
54#91115C2211yescharacteristic, complemented
55#76429—51nomaximal, Hall
56C2×#4083—31no—
57C2×#4027—31no—
58C2×D5×C22⋊C4—31no—
59C5×#390D311yescharacteristic, complemented
60#65509—31no—
61#65279—31no—
62#65278—31no—
63#65247—31no—
64#65246—31no—
65#65245—31no—
66#65244—31no—
67#65234—31no—
68#65234—31no—
69#65229—31no—
70C4×#685—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×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C2×#1220—22no—
91C2×#1220—22no—
92C2×#1220—41no—
93C2×#1220—41no—
94C2×#1220C2×C414yes—
95C2×#1220C2×C414yescomplemented
96C22×Dic15—22no—
97C22×Dic15—41no—
98C22×Dic15—41no—
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×C4⋊C4—41no—
112C3×C5×C22⋊C4—22no—
113C3×C5×C22⋊C4—22no—
114C3×C5×C22⋊C4—41no—
115C3×C5×C22⋊C4—41no—
116C3×C42×C5—41no—
117#6719—22no—
118#6719—41no—
119#6719—41no—
120#6719C2×C414yescomplemented
121#6714—22no—
122#6714—22no—
123#6714—22no—
124#6714—22no—
125#6714—41no—
126#6714—41no—
127#6714C2×C414yescomplemented
128#6714C2×C414yescomplemented
129#6712—22no—
130#6712—41no—
131C4×Dic15—22no—
132C4×Dic15—41no—
133C2×#937—51no—
134C2×#67⋊C4—51no—
135C2×D3×C22⋊C4—51no—
136C3×#390D511yescharacteristic, complemented
137#5220—51no—
138#4990—51no—
139#4989—51no—
140#4958—51no—
141#4957—51no—
142#4956—51no—
143#4955—51no—
144#4945—51no—
145#4945—51no—
146#4940—51no—
147C4×(C2×D3)⋊C4—51no—
148C24×D5—31no—
149C22×C5×D4C2×D311yescharacteristic
150C22×C22⋊D5—31no—
151C22×C22⋊D5—31no—
152C23×Dic5—31no—
153C22×C4×D5—31no—
154C22×C4×D5—31no—
155C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
156C2×C5×C22⋊C4C2×D311yescharacteristic
157C2×C5×C22⋊C4C2×D311yescharacteristic
158C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
159C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
160C2×C42×C5C2×D311yescharacteristic, complemented
161C2×C22⋊Dic5—31no—
162C2×C22⋊Dic5—31no—
163C2×C22⋊Dic5—31no—
164C2×C22⋊Dic5—31no—
165#4083—38no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685—31no—
171C2×#685—31no—
172C2×#685—31no—
173C2×#685—31no—
174C2×#683—31no—
175C2×#683—31no—
176C2×C4×Dic5—31no—
177C2×C4×Dic5—31no—
178#4027—64no—
179D5×C22⋊C4—64no—
180#3963—31no—
181#3963—31no—
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×C5C22×C412yes—
238C2×C3×C4×C5C2×D412yes—
239#1220—28no—
240#1220—44no—
241C2×Dic15—21no—
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—44no—
257C2×Dic15C22×C412yes—
258C2×Dic15C22×C412yes—
259C2×Dic15C2×D412yes—
260C4×D15—44no—
261C4×D15—44no—
262C24×D3—51no—
263C22×C3×D4C2×D511yescharacteristic
264C22×#67—51no—
265C22×#67—51no—
266C23×Dic3—51no—
267C22×C4×D3—51no—
268C22×C4×D3—51no—
269C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
270C2×C3×C22⋊C4C2×D511yescharacteristic
271C2×C3×C22⋊C4C2×D511yescharacteristic
272C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
273C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
274C2×C3×C42C2×D511yescharacteristic, complemented
275C2×#217—51no—
276C2×#217—51no—
277C2×#217—51no—
278C2×#217—51no—
279#937—58no—
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×(C2×D3)⋊C4—51no—
288C2×Dic3⋊C4—51no—
289C2×Dic3⋊C4—51no—
290C2×C4×Dic3—51no—
291C2×C4×Dic3—51no—
292#67⋊C4—104no—
293D3×C22⋊C4—104no—
294C3⋊#95—51no—
295C3⋊#95—51no—
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×C5C22×D311yescharacteristic
315C22×C4×C5C22×D311yescharacteristic
316C22×C4×C5C22×D311yescharacteristic
317C22×C4×C5C22×D311yescharacteristic
318C22×C4×C5C22×D311yescharacteristic
319C2×C22⋊D5—34no—
320C2×C22⋊D5—34no—
321C2×C22⋊D5—62no—
322C2×C22⋊D5—62no—
323C2×C22⋊D5—121no—
324C2×C22⋊D5—121no—
325C22×Dic5—31no—
326C22×Dic5—31no—
327C22×Dic5—31no—
328C22×Dic5—31no—
329C22×Dic5—31no—
330C22×Dic5—31no—
331C22×Dic5—62no—
332C22×Dic5—121no—
333C22×Dic5—121no—
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×C4⋊C4—41no—
341C5×C22⋊C4—22no—
342C5×C22⋊C4—22no—
343C5×C22⋊C4—41no—
344C5×C22⋊C4—41no—
345C42×C5—41no—
346C22⋊Dic5—34no—
347C22⋊Dic5—62no—
348C22⋊Dic5—121no—
349C22⋊Dic5—121no—
350#685—34no—
351#685—34no—
352#685—62no—
353#685—62no—
354#685—62no—
355#685—62no—
356#685—121no—
357#685—121no—
358#683—62no—
359#683—121no—
360C4×Dic5—62no—
361C4×Dic5—121no—
362C2×#120—151no—
363C2×C4×D4—151no—
364C22×C22⋊C4—151no—
365#390—151no—
366#390D1511yescharacteristic, complemented
367#388—151no—
368#388—151no—
369#388—151no—
370#388—151no—
371#386—151no—
372#386—151no—
373#386—151no—
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×C4C22×D511yescharacteristic
439C22×C3×C4C22×D511yescharacteristic
440C22×C3×C4C22×D511yescharacteristic
441C22×C3×C4C22×D511yescharacteristic
442C22×C3×C4C22×D511yescharacteristic
443C2×#67—54no—
444C2×#67—54no—
445C2×#67—102no—
446C2×#67—102no—
447C2×#67—201no—
448C2×#67—201no—
449C22×Dic3—51no—
450C22×Dic3—51no—
451C22×Dic3—51no—
452C22×Dic3—51no—
453C22×Dic3—51no—
454C22×Dic3—51no—
455C22×Dic3—102no—
456C22×Dic3—201no—
457C22×Dic3—201no—
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×C4⋊C4—41no—
465C3×C22⋊C4—22no—
466C3×C22⋊C4—22no—
467C3×C22⋊C4—41no—
468C3×C22⋊C4—41no—
469C3×C42—41no—
470#217—54no—
471#217—102no—
472#217—201no—
473#217—201no—
474(C2×D3)⋊C4—54no—
475(C2×D3)⋊C4—54no—
476(C2×D3)⋊C4—102no—
477(C2×D3)⋊C4—102no—
478(C2×D3)⋊C4—102no—
479(C2×D3)⋊C4—102no—
480(C2×D3)⋊C4—201no—
481(C2×D3)⋊C4—201no—
482Dic3⋊C4—102no—
483Dic3⋊C4—201no—
484C4×Dic3—102no—
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×C5C2×C4×D312yes—
537C2×C4×C5D3×D412yes—
538C22⋊D5—68no—
539C22⋊D5—124no—
540C2×Dic5—32no—
541C2×Dic5—32no—
542C2×Dic5—32no—
543C2×Dic5—61no—
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—124no—
559C4×D5—124no—
560C4×D5—124no—
561C25—151no—
562C22×D4—151no—
563C22×D4—151no—
564C22×D4C2×D1511yescharacteristic
565C23×C4—151no—
566C23×C4—151no—
567C23×C4—151no—
568#120—158no—
569C4×D4—304no—
570C2×C4⋊C4—151no—
571C2×C4⋊C4—151no—
572C2×C4⋊C4C2×D1511yescharacteristic, complemented
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—304no—
586C2×C22⋊C4C2×D1511yescharacteristic
587C2×C22⋊C4C2×D1511yescharacteristic
588C2×C22⋊C4C2×D1511yescharacteristic, complemented
589C2×C22⋊C4C2×D1511yescharacteristic, complemented
590C2×C42—151no—
591C2×C42—151no—
592C2×C42C2×D1511yescharacteristic, complemented
593#95—151no—
594#95—151no—
595#95—151no—
596#95—151no—
597#95—151no—
598#95—151no—
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×C4C2×C4×D512yes—
661C2×C3×C4D4×D512yes—
662#67—108no—
663#67—204no—
664C2×Dic3—52no—
665C2×Dic3—52no—
666C2×Dic3—52no—
667C2×Dic3—101no—
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—204no—
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—151no—
753C22×C4—151no—
754C22×C4—151no—
755C22×C4—154no—
756C22×C4—151no—
757C22×C4—151no—
758C22×C4—151no—
759C22×C4—302no—
760C22×C4—302no—
761C22×C4—601no—
762C22×C4—601no—
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—41no—
773C4⋊C4—302no—
774C4⋊C4—601no—
775C22⋊C4—22no—
776C22⋊C4—22no—
777C22⋊C4—41no—
778C22⋊C4—41no—
779C22⋊C4—154no—
780C22⋊C4—154no—
781C22⋊C4—154no—
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—41no—
792C42—302no—
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#560511yescharacteristic
848C2×C5#561311yescharacteristic
849C2×C5#567811yescharacteristic
850C2×C5#571511yescharacteristic
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—152no—
906C2×C4—152no—
907C2×C4—152no—
908C2×C4—301no—
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—604no—
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#6593911yescharacteristic
934C2×C3#6594711yescharacteristic
935C2×C3#6601211yescharacteristic
936C2×C3#6604911yescharacteristic
937D3—104no—
938D3—202no—
939C5#7642911yescharacteristic, 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#1060816011yescharacteristic, complemented, Sylow
988C2—42no—
989C2—42no—
990C2—304no—
991C2—602no—
992C2#1175624511yescharacteristic
993C2C4×D4×D1511yescharacteristic
994C2#1175630411yescharacteristic
995C2#1175636411yescharacteristic
996C2#1175637211yescharacteristic
997C2#1175643711yescharacteristic
998C2#1175647411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#390C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91826C2
hypercenter#390D15
hypocenterC3×C5#2321
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#91770C2semidirect
3. C2×C22⋊C4×D15C2semidirect
4. C3×C5×#390C2semidirect
5. #11751321C2semidirect
6. #11751091C2semidirect
7. #11751090C2semidirect
8. #11751059C2semidirect
9. #11751058C2semidirect
10. #11751057C2semidirect
11. #11751056C2semidirect
12. #11751046C2semidirect
13. #11751046C2semidirect
14. #11751041C2semidirect
15. C4×#6714C2semidirect
21. C23×Dic15C22semidirect
24. C2×C3×C5×C4⋊C4C22semidirect
27. C2×C3×C5×C22⋊C4C22semidirect
28. C2×C3×C5×C22⋊C4C22semidirect
29. C2×C3×C42×C5C22semidirect
33. C2×#6719C22semidirect
34. #91826C4semidirect
43. C2×#6712C22semidirect
44. C2×#6712C22semidirect
45. C2×C4×Dic15C22semidirect
46. C2×C4×Dic15C22semidirect
49. #91115C22semidirect
50. #91115C22semidirect
51. #91115C22semidirect
52. #91115C22semidirect
53. #91115C22semidirect
54. #91115C22semidirect
59. C5×#390D3semidirect
79. C23×D15C2×C4semidirect
84. C2×C3×C5×D4C2×C4semidirect
95. C2×#1220C2×C4semidirect
110. C2×C4×D15D4semidirect
120. #6719C2×C4semidirect
127. #6714C2×C4semidirect
128. #6714C2×C4semidirect
136. C3×#390D5semidirect
155. C2×C5×C4⋊C4C2×D3semidirect
158. C2×C5×C22⋊C4C2×D3semidirect
159. C2×C5×C22⋊C4C2×D3semidirect
160. C2×C42×C5C2×D3semidirect
269. C2×C3×C4⋊C4C2×D5semidirect
272. C2×C3×C22⋊C4C2×D5semidirect
273. C2×C3×C22⋊C4C2×D5semidirect
274. C2×C3×C42C2×D5semidirect
313. C2×C5×D4C4×D3semidirect
366. #390D15semidirect
437. C2×C3×D4C4×D5semidirect
572. C2×C4⋊C4C2×D15semidirect
588. C2×C22⋊C4C2×D15semidirect
589. C2×C22⋊C4C2×D15semidirect
592. C2×C42C2×D15semidirect
751. C2×D4C4×D15semidirect
794. C3×C5#2321semidirect
939. C5#76429semidirect
987. C3#10608160semidirect

Maximal subgroups

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

subgroupindex
C2×#918262
C2×#917702
C2×C22⋊C4×D152
C3×C5×#3902
#117513212
#117510912
#117510902
#117510592
#117510582
#117510572
#117510562
#117510462
#117510412
C4×#67142
#106081603
#764295