Finite Group Databasebeta

← C2×C5×#4959 #14331522

Subgroups — C2×C5×#4959 #14331522

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×#67C211yesmaximal, characteristic
2C22×C3×C5×C22⋊C4C211yesmaximal, characteristic, complemented
3C22×C5×#217C211yesmaximal, characteristic, complemented
4C22×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C22×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C22×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
7C2×C5×C3⋊#95C211yesmaximal, characteristic, complemented
8C5×#4959C218yesmaximal, direct product factor
9C2×C5×#394—31nomaximal, Hall
10C25×C3×C5C2211yescharacteristic
11C24×C5×D3C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×C3×C4×C5C2211yescharacteristic
14C22×C5×#67—24no—
15C22×C5×#67—24no—
16C22×C5×#67—24no—
17C22×C5×#67C2214yes—
18C23×C5×Dic3C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic
20C23×C5×Dic3C2211yescharacteristic
21C2×C3×C5×C22⋊C4—24no—
22C2×C3×C5×C22⋊C4C2214yescomplemented
23C2×C5×#217—24no—
24C2×C5×#217C2214yescomplemented
25C2×C5×(C2×D3)⋊C4—24no—
26C2×C5×(C2×D3)⋊C4—24no—
27C2×C5×(C2×D3)⋊C4C2214yescomplemented
28C2×C5×(C2×D3)⋊C4C2214yescomplemented
29C2×C5×Dic3⋊C4—24no—
30C2×C5×Dic3⋊C4C2214yescomplemented
31C5×C3⋊#95C2214yescomplemented
32C2×#4959C511yesmaximal, characteristic, direct product factor, Hall
33C23×C5×D4—31no—
34C22×C5×C4⋊C4—31no—
35C22×C5×C22⋊C4—31no—
36C22×C5×C22⋊C4—31no—
37C22×C5×C22⋊C4—31no—
38C22×C5×C22⋊C4D311yescharacteristic, complemented
39C5×#394—38no—
40C2×C5×#95—31no—
41C24×C3×C5—22no—
42C24×C3×C5—22no—
43C24×C3×C5—22no—
44C24×C3×C5—22no—
45C24×C3×C5—22no—
46C24×C3×C5—22no—
47C24×C3×C5D414yes—
48C24×C3×C5C2312yes—
49C24×C3×C5C2311yescharacteristic
50C23×C5×D3—22no—
51C23×C5×D3—22no—
52C23×C5×D3—22no—
53C23×C5×D3—22no—
54C23×C5×D3—22no—
55C23×C5×D3—22no—
56C23×C5×D3D414yes—
57C23×C5×D3C2312yes—
58C22×C3×C4×C5—22no—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5—22no—
62C22×C3×C4×C5—22no—
63C22×C3×C4×C5—22no—
64C22×C3×C4×C5C2312yes—
65C22×C3×C4×C5C2312yes—
66C2×C5×#67—232no—
67C2×C5×#67—28no—
68C2×C5×#67—28no—
69C2×C5×#67—28no—
70C22×C5×Dic3—22no—
71C22×C5×Dic3—22no—
72C22×C5×Dic3—22no—
73C22×C5×Dic3—22no—
74C22×C5×Dic3—22no—
75C22×C5×Dic3—22no—
76C22×C5×Dic3—22no—
77C22×C5×Dic3D414yes—
78C22×C5×Dic3D414yescomplemented
79C22×C5×Dic3C2312yes—
80C22×C5×Dic3C2312yes—
81C22×C5×Dic3C2312yes—
82C3×C5×C22⋊C4—28no—
83C5×#217—28no—
84C5×(C2×D3)⋊C4—28no—
85C5×(C2×D3)⋊C4—28no—
86C5×Dic3⋊C4—28no—
87C23×#67C2×C511yescharacteristic
88C22×C3×C22⋊C4C2×C511yescharacteristic, complemented
89C22×#217C2×C511yescharacteristic, complemented
90C22×(C2×D3)⋊C4C2×C511yescharacteristic, complemented
91C22×(C2×D3)⋊C4C2×C511yescharacteristic, complemented
92C22×Dic3⋊C4C2×C511yescharacteristic, complemented
93C2×C3⋊#95C2×C511yescharacteristic, complemented
94#4959C2×C518yesdirect product factor
95C25×C5—31no—
96C25×C5C2×D311yescharacteristic
97C22×C5×D4—34no—
98C22×C5×D4—64no—
99C22×C5×D4—64no—
100C22×C5×D4—64no—
101C23×C4×C5—31no—
102C23×C4×C5—31no—
103C23×C4×C5—31no—
104C23×C4×C5C2×D311yescharacteristic
105C23×C4×C5C2×D311yescharacteristic
106C2×C5×C4⋊C4—34no—
107C2×C5×C4⋊C4—64no—
108C2×C5×C22⋊C4—24no—
109C2×C5×C22⋊C4—34no—
110C2×C5×C22⋊C4—34no—
111C2×C5×C22⋊C4—34no—
112C2×C5×C22⋊C4—64no—
113C2×C5×C22⋊C4—64no—
114C2×C5×C22⋊C4—64no—
115C2×C5×C22⋊C4C2×D314yescomplemented
116C5×#95—34no—
117C2×#394—31noSylow
118C23×C3×C5—28no—
119C23×C3×C5—28no—
120C23×C3×C5—28no—
121C23×C3×C5—22no—
122C23×C3×C5—22no—
123C23×C3×C5—22no—
124C23×C3×C5—22no—
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5—44no—
128C23×C3×C5—44no—
129C23×C3×C5—44no—
130C23×C3×C5—44no—
131C23×C3×C5C2×D414yes—
132C23×C3×C5C2×D412yes—
133C23×C3×C5C2×D412yes—
134C23×C3×C5C2×D412yes—
135C23×C3×C5C2×D412yes—
136C23×C3×C5#4112yes—
137C23×C3×C5#4112yes—
138C23×C3×C5#4112yes—
139C23×C3×C5C2411yescharacteristic
140C22×C5×D3—28no—
141C22×C5×D3—28no—
142C22×C5×D3—28no—
143C22×C5×D3—22no—
144C22×C5×D3—22no—
145C22×C5×D3—22no—
146C22×C5×D3—22no—
147C22×C5×D3—22no—
148C22×C5×D3—22no—
149C22×C5×D3—44no—
150C22×C5×D3—44no—
151C22×C5×D3—44no—
152C22×C5×D3—44no—
153C22×C5×D3C2×D414yes—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—44no—
161C2×C3×C4×C5—44no—
162C5×#67—232no—
163C2×C5×Dic3—28no—
164C2×C5×Dic3—28no—
165C2×C5×Dic3—22no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3—22no—
171C2×C5×Dic3—22no—
172C2×C5×Dic3—44no—
173C2×C5×Dic3C2×D414yes—
174C2×C5×Dic3C2×D414yescomplemented
175C25×C3C22×C511yescharacteristic
176C24×D3C22×C511yescharacteristic
177C23×C3×C4C22×C511yescharacteristic
178C23×C3×C4C22×C511yescharacteristic
179C22×#67—24no—
180C22×#67—24no—
181C22×#67—24no—
182C22×#67C22×C514yes—
183C23×Dic3C22×C511yescharacteristic
184C23×Dic3C22×C511yescharacteristic
185C23×Dic3C22×C511yescharacteristic
186C2×C3×C22⋊C4—24no—
187C2×C3×C22⋊C4C22×C514yescomplemented
188C2×#217—24no—
189C2×#217C22×C514yescomplemented
190C2×(C2×D3)⋊C4—24no—
191C2×(C2×D3)⋊C4—24no—
192C2×(C2×D3)⋊C4C22×C514yescomplemented
193C2×(C2×D3)⋊C4C22×C514yescomplemented
194C2×Dic3⋊C4—24no—
195C2×Dic3⋊C4C22×C514yescomplemented
196C3⋊#95C22×C514yescomplemented
197C24×C5—22no—
198C24×C5—22no—
199C24×C5—22no—
200C24×C5—22no—
201C24×C5—22no—
202C24×C5—22no—
203C24×C5—34no—
204C24×C5—32no—
205C24×C5—62no—
206C24×C5—62no—
207C24×C5—62no—
208C24×C5—62no—
209C24×C5—62no—
210C24×C5—62no—
211C24×C5#6714yes—
212C24×C5C22×D312yes—
213C24×C5C22×D311yescharacteristic
214C2×C5×D4—68no—
215C2×C5×D4—68no—
216C2×C5×D4—632no—
217C2×C5×D4—68no—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—34no—
225C22×C4×C5—34no—
226C22×C4×C5—32no—
227C22×C4×C5—32no—
228C22×C4×C5—32no—
229C22×C4×C5—62no—
230C22×C4×C5—62no—
231C22×C4×C5—62no—
232C22×C4×C5—62no—
233C22×C4×C5—62no—
234C22×C4×C5—62no—
235C22×C4×C5—62no—
236C22×C4×C5C22×D312yes—
237C22×C4×C5C22×D312yes—
238C5×C4⋊C4—68no—
239C5×C22⋊C4—28no—
240C5×C22⋊C4—68no—
241C5×C22⋊C4—68no—
242C5×C22⋊C4—68no—
243C23×D4—31no—
244C22×C4⋊C4—31no—
245C22×C22⋊C4—31no—
246C22×C22⋊C4—31no—
247C22×C22⋊C4—31no—
248C22×C22⋊C4C5×D311yescharacteristic, complemented
249#394—38no—
250C2×#95—31no—
251C22×C3×C5—24no—
252C22×C3×C5—24no—
253C22×C3×C5—24no—
254C22×C3×C5—42no—
255C22×C3×C5—42no—
256C22×C3×C5—42no—
257C22×C3×C5—42no—
258C22×C3×C5—416no—
259C22×C3×C5#12014yes—
260C22×C3×C5#12114yes—
261C22×C3×C5#12114yes—
262C22×C3×C5#12114yes—
263C22×C3×C5#12314yes—
264C22×C3×C5#12314yes—
265C22×C3×C5#12414yes—
266C22×C3×C5C22×D411yescharacteristic
267C22×C3×C5C22×D411yescharacteristic
268C22×C3×C5C22×D411yescharacteristic
269C22×C3×C5C22×D411yescharacteristic
270C22×C3×C5C2×#4111yescharacteristic
271C22×C3×C5C2×#4111yescharacteristic
272C22×C3×C5C2×#4111yescharacteristic
273C2×C5×D3—24no—
274C2×C5×D3—24no—
275C2×C5×D3—24no—
276C2×C5×D3—42no—
277C2×C5×D3—42no—
278C2×C5×D3—42no—
279C2×C5×D3—42no—
280C2×C5×D3—416no—
281C3×C4×C5—42no—
282C3×C4×C5—42no—
283C5×Dic3—24no—
284C5×Dic3—24no—
285C5×Dic3—42no—
286C24×C3—22no—
287C24×C3—22no—
288C24×C3—22no—
289C24×C3—22no—
290C24×C3—22no—
291C24×C3—22no—
292C24×C3C5×D414yes—
293C24×C3C23×C512yes—
294C24×C3C23×C511yescharacteristic
295C23×D3—22no—
296C23×D3—22no—
297C23×D3—22no—
298C23×D3—22no—
299C23×D3—22no—
300C23×D3—22no—
301C23×D3C5×D414yes—
302C23×D3C23×C512yes—
303C22×C3×C4—22no—
304C22×C3×C4—22no—
305C22×C3×C4—22no—
306C22×C3×C4—22no—
307C22×C3×C4—22no—
308C22×C3×C4—22no—
309C22×C3×C4C23×C512yes—
310C22×C3×C4C23×C512yes—
311C2×#67—232no—
312C2×#67—28no—
313C2×#67—28no—
314C2×#67—28no—
315C22×Dic3—22no—
316C22×Dic3—22no—
317C22×Dic3—22no—
318C22×Dic3—22no—
319C22×Dic3—22no—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3C5×D414yes—
323C22×Dic3C5×D414yescomplemented
324C22×Dic3C23×C512yes—
325C22×Dic3C23×C512yes—
326C22×Dic3C23×C512yes—
327C3×C22⋊C4—28no—
328#217—28no—
329(C2×D3)⋊C4—28no—
330(C2×D3)⋊C4—28no—
331Dic3⋊C4—28no—
332C23×C5—28no—
333C23×C5—28no—
334C23×C5—28no—
335C23×C5—22no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—22no—
340C23×C5—22no—
341C23×C5—34no—
342C23×C5—44no—
343C23×C5—44no—
344C23×C5—44no—
345C23×C5—44no—
346C23×C5—68no—
347C23×C5—68no—
348C23×C5—68no—
349C23×C5—62no—
350C23×C5—62no—
351C23×C5—62no—
352C23×C5—62no—
353C23×C5—62no—
354C23×C5—62no—
355C23×C5—124no—
356C23×C5—124no—
357C23×C5—124no—
358C23×C5—124no—
359C23×C5#23512yes—
360C23×C5#23512yes—
361C23×C5D3×D412yes—
362C23×C5D3×D412yes—
363C23×C5D3×D412yes—
364C23×C5#23712yes—
365C23×C5C2×#6714yes—
366C23×C5C2×#6712yes—
367C23×C5C23×D311yescharacteristic
368C5×D4—632no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—34no—
376C2×C4×C5—34no—
377C2×C4×C5—44no—
378C2×C4×C5—44no—
379C2×C4×C5—68no—
380C2×C4×C5—68no—
381C2×C4×C5—62no—
382C2×C4×C5—62no—
383C2×C4×C5—62no—
384C2×C4×C5—62no—
385C2×C4×C5—62no—
386C2×C4×C5—62no—
387C2×C4×C5—62no—
388C2×C4×C5—124no—
389C25—31no—
390C25C2×C5×D311yescharacteristic
391C22×D4—34no—
392C22×D4—64no—
393C22×D4—64no—
394C22×D4—64no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—31no—
398C23×C4C2×C5×D311yescharacteristic
399C23×C4C2×C5×D311yescharacteristic
400C2×C4⋊C4—34no—
401C2×C4⋊C4—64no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—64no—
407C2×C22⋊C4—64no—
408C2×C22⋊C4—64no—
409C2×C22⋊C4C2×C5×D314yescomplemented
410#95—34no—
411C2×C3×C5—44no—
412C2×C3×C5#39418yescomplemented
413C2×C3×C5C2×#12011yescharacteristic
414C2×C3×C5C2×#12111yescharacteristic
415C2×C3×C5C2×#12111yescharacteristic
416C2×C3×C5C2×#12111yescharacteristic
417C2×C3×C5C2×#12311yescharacteristic
418C2×C3×C5C2×#12311yescharacteristic
419C2×C3×C5C2×#12411yescharacteristic
420C5×D3—44no—
421C23×C3—28no—
422C23×C3—28no—
423C23×C3—28no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—44no—
431C23×C3—44no—
432C23×C3—44no—
433C23×C3—44no—
434C23×C3C2×C5×D412yes—
435C23×C3C2×C5×D412yes—
436C23×C3C2×C5×D412yes—
437C23×C3C2×C5×D414yes—
438C23×C3C2×C5×D412yes—
439C23×C3C5×#4112yes—
440C23×C3C5×#4112yes—
441C23×C3C5×#4112yes—
442C23×C3C24×C511yescharacteristic
443C22×D3—28no—
444C22×D3—28no—
445C22×D3—28no—
446C22×D3—22no—
447C22×D3—22no—
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—44no—
453C22×D3—44no—
454C22×D3—44no—
455C22×D3—44no—
456C22×D3C2×C5×D414yes—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—44no—
464C2×C3×C4—44no—
465#67—232no—
466C2×Dic3—28no—
467C2×Dic3—28no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—44no—
476C2×Dic3C2×C5×D414yes—
477C2×Dic3C2×C5×D414yescomplemented
478C22×C5—24no—
479C22×C5—24no—
480C22×C5—24no—
481C22×C5—416no—
482C22×C5—42no—
483C22×C5—42no—
484C22×C5—42no—
485C22×C5—42no—
486C22×C5—64no—
487C22×C5—64no—
488C22×C5—64no—
489C22×C5—1216no—
490C22×C5—122no—
491C22×C5—122no—
492C22×C5—122no—
493C22×C5—122no—
494C22×C5#88314yes—
495C22×C5#88414yes—
496C22×C5#88414yes—
497C22×C5#88514yes—
498C22×C5#92914yes—
499C22×C5#93714yes—
500C22×C5#93914yes—
501C22×C5C2×#23511yescharacteristic
502C22×C5C2×#23511yescharacteristic
503C22×C5C2×D3×D411yescharacteristic
504C22×C5C2×D3×D411yescharacteristic
505C22×C5C2×D3×D411yescharacteristic
506C22×C5C2×#23711yescharacteristic
507C22×C5C22×#6711yescharacteristic
508C4×C5—42no—
509C4×C5—42no—
510C4×C5—64no—
511C4×C5—64no—
512C4×C5—122no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—34no—
520C24—32no—
521C24—62no—
522C24—62no—
523C24—62no—
524C24—62no—
525C24—62no—
526C24—62no—
527C24C5×#6714yes—
528C24C22×C5×D312yes—
529C24C22×C5×D311yescharacteristic
530C2×D4—68no—
531C2×D4—68no—
532C2×D4—632no—
533C2×D4—68no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—34no—
541C22×C4—34no—
542C22×C4—32no—
543C22×C4—32no—
544C22×C4—32no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4C22×C5×D312yes—
553C22×C4C22×C5×D312yes—
554C4⋊C4—68no—
555C22⋊C4—28no—
556C22⋊C4—68no—
557C22⋊C4—68no—
558C22⋊C4—68no—
559C3×C5C2×#39411yescharacteristic, complemented, Hall
560C22×C3—24no—
561C22×C3—24no—
562C22×C3—24no—
563C22×C3—416no—
564C22×C3—42no—
565C22×C3—42no—
566C22×C3—42no—
567C22×C3—42no—
568C22×C3C5×#12014yes—
569C22×C3C5×#12114yes—
570C22×C3C5×#12114yes—
571C22×C3C5×#12114yes—
572C22×C3C5×#12314yes—
573C22×C3C5×#12314yes—
574C22×C3C5×#12414yes—
575C22×C3C22×C5×D411yescharacteristic
576C22×C3C22×C5×D411yescharacteristic
577C22×C3C22×C5×D411yescharacteristic
578C22×C3C22×C5×D411yescharacteristic
579C22×C3C2×C5×#4111yescharacteristic
580C22×C3C2×C5×#4111yescharacteristic
581C22×C3C2×C5×#4111yescharacteristic
582C2×D3—24no—
583C2×D3—24no—
584C2×D3—24no—
585C2×D3—416no—
586C2×D3—42no—
587C2×D3—42no—
588C2×D3—42no—
589C2×D3—42no—
590C3×C4—42no—
591C3×C4—42no—
592Dic3—24no—
593Dic3—24no—
594Dic3—42no—
595C2×C5—44no—
596C2×C5—124no—
597C2×C5#495918yesdirect product factor
598C2×C5C2×#88311yescharacteristic
599C2×C5C2×#88411yescharacteristic
600C2×C5C2×#88411yescharacteristic
601C2×C5C2×#88511yescharacteristic
602C2×C5C2×#92911yescharacteristic
603C2×C5C2×#93711yescharacteristic
604C2×C5C2×#93911yescharacteristic
605C23—28no—
606C23—28no—
607C23—28no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—34no—
615C23—44no—
616C23—44no—
617C23—44no—
618C23—44no—
619C23—68no—
620C23—68no—
621C23—68no—
622C23—62no—
623C23—62no—
624C23—62no—
625C23—62no—
626C23—62no—
627C23—62no—
628C23—124no—
629C23—124no—
630C23—124no—
631C23—124no—
632C23C5×#23512yes—
633C23C5×#23512yes—
634C23C5×D3×D412yes—
635C23C5×D3×D412yes—
636C23C5×D3×D412yes—
637C23C5×#23712yes—
638C23C2×C5×#6714yes—
639C23C2×C5×#6712yes—
640C23C23×C5×D311yescharacteristic
641D4—632no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—34no—
649C2×C4—34no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—68no—
653C2×C4—68no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—62no—
661C2×C4—124no—
662C2×C3—44no—
663C2×C3C5×#39418yescomplemented
664C2×C3C2×C5×#12011yescharacteristic
665C2×C3C2×C5×#12111yescharacteristic
666C2×C3C2×C5×#12111yescharacteristic
667C2×C3C2×C5×#12111yescharacteristic
668C2×C3C2×C5×#12311yescharacteristic
669C2×C3C2×C5×#12311yescharacteristic
670C2×C3C2×C5×#12411yescharacteristic
671D3—44no—
672C5C2×#495911yescharacteristic, direct product factor, Sylow
673C22—24no—
674C22—24no—
675C22—24no—
676C22—416no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—64no—
682C22—64no—
683C22—64no—
684C22—1216no—
685C22—122no—
686C22—122no—
687C22—122no—
688C22—122no—
689C22C5×#88314yes—
690C22C5×#88414yes—
691C22C5×#88414yes—
692C22C5×#88514yes—
693C22C5×#92914yes—
694C22C5×#93714yes—
695C22C5×#93914yes—
696C22C2×C5×#23511yescharacteristic
697C22C2×C5×#23511yescharacteristic
698C22C2×C5×D3×D411yescharacteristic
699C22C2×C5×D3×D411yescharacteristic
700C22C2×C5×D3×D411yescharacteristic
701C22C2×C5×#23711yescharacteristic
702C22C22×C5×#6711yescharacteristic
703C4—42no—
704C4—42no—
705C4—64no—
706C4—64no—
707C4—122no—
708C3C2×C5×#39411yescharacteristic, complemented, Sylow
709C2—44no—
710C2—124no—
711C2C5×#495918yesdirect product factor
712C2C2×C5×#88311yescharacteristic
713C2C2×C5×#88411yescharacteristic
714C2C2×C5×#88411yescharacteristic
715C2C2×C5×#88511yescharacteristic
716C2C2×C5×#92911yescharacteristic
717C2C2×C5×#93711yescharacteristic
718C2C2×C5×#93911yescharacteristic
subgroupG/H
centerC24×C5C22×D3
commutator, cosocleC23×C3C24×C5
FrattiniC23C23×C5×D3
FittingC22×C3×C5×C22⋊C4C2
socleC24×C3×C5C23
prime radicalC23×C5×#67C2
hypercenterC22×C5×C22⋊C4D3
hypocenterC3C2×C5×#394
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C5 ◁ C22×C5×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C5×C22⋊C4C2semidirect
3. C22×C5×#217C2semidirect
4. C22×C5×(C2×D3)⋊C4C2semidirect
5. C22×C5×(C2×D3)⋊C4C2semidirect
6. C22×C5×Dic3⋊C4C2semidirect
7. C2×C5×C3⋊#95C2semidirect
8. C5×#4959C2direct (N × H)
22. C2×C3×C5×C22⋊C4C22semidirect
24. C2×C5×#217C22semidirect
27. C2×C5×(C2×D3)⋊C4C22semidirect
28. C2×C5×(C2×D3)⋊C4C22semidirect
30. C2×C5×Dic3⋊C4C22semidirect
31. C5×C3⋊#95C22semidirect
32. C2×#4959C5direct (N × H)
38. C22×C5×C22⋊C4D3semidirect
78. C22×C5×Dic3D4semidirect
88. C22×C3×C22⋊C4C2×C5semidirect
89. C22×#217C2×C5semidirect
90. C22×(C2×D3)⋊C4C2×C5semidirect
91. C22×(C2×D3)⋊C4C2×C5semidirect
92. C22×Dic3⋊C4C2×C5semidirect
93. C2×C3⋊#95C2×C5semidirect
94. #4959C2×C5direct (N × H)
115. C2×C5×C22⋊C4C2×D3semidirect
174. C2×C5×Dic3C2×D4semidirect
187. C2×C3×C22⋊C4C22×C5semidirect
189. C2×#217C22×C5semidirect
192. C2×(C2×D3)⋊C4C22×C5semidirect
193. C2×(C2×D3)⋊C4C22×C5semidirect
195. C2×Dic3⋊C4C22×C5semidirect
196. C3⋊#95C22×C5semidirect
248. C22×C22⋊C4C5×D3semidirect
323. C22×Dic3C5×D4semidirect
409. C2×C22⋊C4C2×C5×D3semidirect
412. C2×C3×C5#394semidirect
477. C2×Dic3C2×C5×D4semidirect
559. C3×C5C2×#394semidirect
597. C2×C5#4959direct (N × H)
663. C2×C3C5×#394semidirect
672. C5C2×#4959direct (N × H)
708. C3C2×C5×#394semidirect
711. C2C5×#4959direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×#672
C22×C3×C5×C22⋊C42
C22×C5×#2172
C22×C5×(C2×D3)⋊C42
C22×C5×Dic3⋊C42
C2×C5×C3⋊#952
C5×#49592
C2×C5×#3943
C2×#49595