Finite Group Databasebeta

← C2×#11756380 #14495280

Subgroups — C2×#11756380 #14495280

Order 1920.

2304 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#121C211yesmaximal, characteristic, complemented
2C2×#91828C211yesmaximal, characteristic, complemented
3C2×#91828C211yesmaximal, characteristic, complemented
4C2×#91827C211yesmaximal, characteristic, complemented
5C2×#91825C211yesmaximal, characteristic, complemented
6C2×#91824C211yesmaximal, characteristic, complemented
7C2×#91824C211yesmaximal, characteristic, complemented
8C2×#91818C211yesmaximal, characteristic, complemented
9C2×#91813C211yesmaximal, characteristic, complemented
10#11756380C2116yesmaximal, direct product factor
11C2×#91785C211yesmaximal, characteristic, complemented
12C2×#91778C211yesmaximal, characteristic, complemented
13C2×#91774C211yesmaximal, characteristic, complemented
14C2×#91772C211yesmaximal, characteristic, complemented
15C2×#91767C211yesmaximal, characteristic, complemented
16C2×#91767C211yesmaximal, characteristic, complemented
17C2×#65955—31nomaximal, Hall
18C22×C3×C5×D4C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C22×C3×C5×D4C2211yescharacteristic
21C23×C3×C4×C5C2211yescharacteristic
22C22×#1220C2211yescharacteristic
23C22×#1220C2211yescharacteristic
24C22×#1220C2211yescharacteristic
25C23×Dic15C2211yescharacteristic
26C23×Dic15C2211yescharacteristic
27C22×C4×D15C2211yescharacteristic
28C22×Dic30C2211yescharacteristic
29C22×Dic30C2211yescharacteristic
30C3×C5×#121C2218yescomplemented
31C2×C3×C5×C4⋊C4C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×C3×C5×C22⋊C4C2211yescharacteristic
34C2×#6719C2211yescharacteristic
35C2×#6719C2211yescharacteristic
36C2×#6719C2211yescharacteristic
37C2×#6719C2211yescharacteristic
38C2×#6719C2211yescharacteristic
39C2×#6719C2211yescharacteristic
40C2×#6719C2211yescharacteristic
41#91828C2218yescomplemented
42#91828C2218yescomplemented
43#91827C2218yescomplemented
44#91825C2218yescomplemented
45#91824C2218yescomplemented
46#91824C2218yescomplemented
47#91818C2218yescomplemented
48C2×#6714C2211yescharacteristic
49C2×#6714C2211yescharacteristic
50C2×#6714C2211yescharacteristic
51C2×C4⋊Dic15C2211yescharacteristic
52C2×C4⋊Dic15C2211yescharacteristic
53#91813C2218yescomplemented
54C2×#6712C2211yescharacteristic
55C2×#6712C2211yescharacteristic
56C2×#6712C2211yescharacteristic
57C2×#6712C2211yescharacteristic
58C2×#6712C2211yescharacteristic
59C2×#6712C2211yescharacteristic
60C2×#6712C2211yescharacteristic
61C2×C4×Dic15C2211yescharacteristic
62#91785C2218yescomplemented
63#91778C2218yescomplemented
64#91774C2218yescomplemented
65#91772C2218yescomplemented
66#91767C2218yescomplemented
67#91767C2218yescomplemented
68C2×#5621—51nomaximal, Hall
69C2×C5×#121D311yescharacteristic, complemented
70C2×#4085—31no—
71C2×#4085—31no—
72C2×#4084—31no—
73C2×#4082—31no—
74C2×#4081—31no—
75C2×#4081—31no—
76C2×#4075—31no—
77C2×#4070—31no—
78#65955—316no—
79C2×#4042—31no—
80C2×#4035—31no—
81C2×#4031—31no—
82C2×#4029—31no—
83C2×#4024—31no—
84C2×#4024—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C2×C3×C5×D4—42no—
90C2×C3×C5×D4—42no—
91C2×C3×C5×D4—42no—
92C2×C3×C5×D4C2314yes—
93C2×C3×C5×D4C2314yes—
94C2×C3×C5×D4C2314yes—
95C22×C3×C4×C5—42no—
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2311yescharacteristic
99C22×C3×C4×C5C2311yescharacteristic
100C22×C3×C4×C5C2314yes—
101C2×#1220—42no—
102C2×#1220—42no—
103C2×#1220—42no—
104C2×#1220C2314yes—
105C2×#1220C2314yes—
106C2×#1220C2314yes—
107C22×Dic15—42no—
108C22×Dic15—42no—
109C22×Dic15C2311yescharacteristic
110C22×Dic15C2311yescharacteristic
111C22×Dic15C2311yescharacteristic
112C22×Dic15C2311yescharacteristic
113C22×Dic15C2311yescharacteristic
114C22×Dic15C2311yescharacteristic
115C22×Dic15C2311yescharacteristic
116C22×Dic15C2314yes—
117C22×Dic15C2314yes—
118C2×C4×D15—42no—
119C2×C4×D15C2314yes—
120C2×Dic30—42no—
121C2×Dic30—42no—
122C2×Dic30C2314yes—
123C2×Dic30C2314yes—
124C3×C5×C4⋊C4C2314yes—
125C3×C5×C22⋊C4C2314yes—
126C3×C5×C22⋊C4C2314yes—
127#6719C2314yes—
128#6719C2314yes—
129#6719C2314yes—
130#6719C2314yes—
131#6719C2314yes—
132#6719C2314yes—
133#6719C2314yes—
134#6714C2314yes—
135#6714C2314yes—
136#6714C2314yes—
137C4⋊Dic15C2314yes—
138C4⋊Dic15C2314yes—
139#6712C2314yes—
140#6712C2314yes—
141#6712C2314yes—
142#6712C2314yes—
143#6712C2314yes—
144#6712C2314yes—
145#6712C2314yes—
146C4×Dic15C2314yes—
147C2×C3×#121D511yescharacteristic, complemented
148C2×#939—51no—
149C2×#939—51no—
150C2×#938—51no—
151C2×#936—51no—
152C2×#935—51no—
153C2×#935—51no—
154C2×#929—51no—
155C2×#924—51no—
156#5621—516no—
157C2×#896—51no—
158C2×#889—51no—
159C2×#885—51no—
160C2×#883—51no—
161C2×#878—51no—
162C2×#878—51no—
163C22×C5×D4C2×D311yescharacteristic
164C22×C5×D4C2×D311yescharacteristic
165C22×C5×D4C2×D311yescharacteristic
166C23×C4×C5C2×D311yescharacteristic
167C22×C22⋊D5—31no—
168C22×C22⋊D5—31no—
169C22×C22⋊D5—31no—
170C23×Dic5—31no—
171C23×Dic5—31no—
172C22×C4×D5—31no—
173C22×Dic10—31no—
174C22×Dic10—31no—
175C5×#121C2×D318yescomplemented
176C2×C5×C4⋊C4C2×D311yescharacteristic
177C2×C5×C22⋊C4C2×D311yescharacteristic
178C2×C5×C22⋊C4C2×D311yescharacteristic
179C2×C22⋊Dic5—31no—
180C2×C22⋊Dic5—31no—
181C2×C22⋊Dic5—31no—
182C2×C22⋊Dic5—31no—
183C2×C22⋊Dic5—31no—
184C2×C22⋊Dic5—31no—
185C2×C22⋊Dic5—31no—
186#4085—38no—
187#4085—38no—
188#4084—38no—
189#4082—38no—
190#4081—38no—
191#4081—38no—
192#4075—38no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×C4⋊Dic5—31no—
197C2×C4⋊Dic5—31no—
198#4070—38no—
199C2×#683—31no—
200C2×#683—31no—
201C2×#683—31no—
202C2×#683—31no—
203C2×#683—31no—
204C2×#683—31no—
205C2×#683—31no—
206C2×C4×Dic5—31no—
207#4042—38no—
208#4035—38no—
209#4031—38no—
210#4029—38no—
211#4024—38no—
212#4024—38no—
213C2×#562—151noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5—22no—
220C23×C3×C5—22no—
221C23×C3×C5—22no—
222C23×C3×C5—22no—
223C23×C3×C5C2412yes—
224C23×C3×C5C2412yes—
225C23×C3×C5C2412yes—
226C23×C3×C5C2411yescharacteristic
227C22×D15—22no—
228C22×D15—22no—
229C22×D15—22no—
230C22×D15C2412yes—
231C3×C5×D4—44no—
232C3×C5×D4—44no—
233C3×C5×D4—44no—
234C2×C3×C4×C5—22no—
235C2×C3×C4×C5—22no—
236C2×C3×C4×C5—22no—
237C2×C3×C4×C5—22no—
238C2×C3×C4×C5—44no—
239C2×C3×C4×C5C2412yes—
240C2×C3×C4×C5C2412yes—
241C2×C3×C4×C5C2412yes—
242C2×C3×C4×C5C2412yes—
243#1220—44no—
244#1220—44no—
245#1220—44no—
246C2×Dic15—22no—
247C2×Dic15—22no—
248C2×Dic15—22no—
249C2×Dic15—22no—
250C2×Dic15—22no—
251C2×Dic15—22no—
252C2×Dic15—22no—
253C2×Dic15—44no—
254C2×Dic15—44no—
255C2×Dic15C2412yes—
256C2×Dic15C2412yes—
257C2×Dic15C2412yes—
258C2×Dic15C2412yes—
259C2×Dic15C2412yes—
260C2×Dic15C2412yes—
261C2×Dic15C2412yes—
262C4×D15—44no—
263Dic30—44no—
264Dic30—44no—
265C22×C3×D4C2×D511yescharacteristic
266C22×C3×D4C2×D511yescharacteristic
267C22×C3×D4C2×D511yescharacteristic
268C23×C3×C4C2×D511yescharacteristic
269C22×#67—51no—
270C22×#67—51no—
271C22×#67—51no—
272C23×Dic3—51no—
273C23×Dic3—51no—
274C22×C4×D3—51no—
275C22×Dic6—51no—
276C22×Dic6—51no—
277C3×#121C2×D518yescomplemented
278C2×C3×C4⋊C4C2×D511yescharacteristic
279C2×C3×C22⋊C4C2×D511yescharacteristic
280C2×C3×C22⋊C4C2×D511yescharacteristic
281C2×#217—51no—
282C2×#217—51no—
283C2×#217—51no—
284C2×#217—51no—
285C2×#217—51no—
286C2×#217—51no—
287C2×#217—51no—
288#939—58no—
289#939—58no—
290#938—58no—
291#936—58no—
292#935—58no—
293#935—58no—
294#929—58no—
295C2×(C2×D3)⋊C4—51no—
296C2×(C2×D3)⋊C4—51no—
297C2×(C2×D3)⋊C4—51no—
298C2×C4⋊Dic3—51no—
299C2×C4⋊Dic3—51no—
300#924—58no—
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4—51no—
304C2×Dic3⋊C4—51no—
305C2×Dic3⋊C4—51no—
306C2×Dic3⋊C4—51no—
307C2×Dic3⋊C4—51no—
308C2×C4×Dic3—51no—
309#896—58no—
310#889—58no—
311#885—58no—
312#883—58no—
313#878—58no—
314#878—58no—
315C24×C5C22×D311yescharacteristic
316C24×C5C22×D311yescharacteristic
317C24×C5C22×D311yescharacteristic
318C23×D5—31no—
319C2×C5×D4—42no—
320C2×C5×D4—42no—
321C2×C5×D4—42no—
322C2×C5×D4C22×D314yes—
323C2×C5×D4C22×D314yes—
324C2×C5×D4C22×D314yes—
325C22×C4×C5—42no—
326C22×C4×C5C22×D311yescharacteristic
327C22×C4×C5C22×D311yescharacteristic
328C22×C4×C5C22×D311yescharacteristic
329C22×C4×C5C22×D311yescharacteristic
330C22×C4×C5C22×D314yes—
331C2×C22⋊D5—34no—
332C2×C22⋊D5—34no—
333C2×C22⋊D5—34no—
334C2×C22⋊D5—122no—
335C2×C22⋊D5—122no—
336C2×C22⋊D5—122no—
337C22×Dic5—31no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—31no—
341C22×Dic5—31no—
342C22×Dic5—31no—
343C22×Dic5—31no—
344C22×Dic5—34no—
345C22×Dic5—34no—
346C22×Dic5—122no—
347C22×Dic5—122no—
348C2×C4×D5—34no—
349C2×C4×D5—122no—
350C2×Dic10—34no—
351C2×Dic10—34no—
352C2×Dic10—122no—
353C2×Dic10—122no—
354C5×C4⋊C4C22×D314yes—
355C5×C22⋊C4C22×D314yes—
356C5×C22⋊C4C22×D314yes—
357C22⋊Dic5—34no—
358C22⋊Dic5—34no—
359C22⋊Dic5—34no—
360C22⋊Dic5—34no—
361C22⋊Dic5—34no—
362C22⋊Dic5—34no—
363C22⋊Dic5—34no—
364#685—34no—
365#685—34no—
366#685—34no—
367C4⋊Dic5—34no—
368C4⋊Dic5—34no—
369#683—34no—
370#683—34no—
371#683—34no—
372#683—34no—
373#683—34no—
374#683—34no—
375#683—34no—
376C4×Dic5—34no—
377#562—1516no—
378C2×#125—151no—
379C2×#124—151no—
380C2×#124—151no—
381C2×#123—151no—
382C2×#123—151no—
383C2×#123—151no—
384C2×#123—151no—
385C2×C22⋊Q8—151no—
386C2×C22⋊Q8—151no—
387C2×C22⋊Q8—151no—
388C2×C22⋊Q8—151no—
389C2×#121—151no—
390C2×#121—151no—
391C2×#121—151no—
392C2×#121D1511yescharacteristic, complemented
393C22×C3×C5—22no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—22no—
398C22×C3×C5—22no—
399C22×C3×C5—22no—
400C22×C3×C5—22no—
401C22×C3×C5—22no—
402C22×C3×C5—44no—
403C22×C3×C5—44no—
404C22×C3×C5—44no—
405C22×C3×C5H(5,𝔽2)12yes—
406C22×C3×C5H(5,𝔽2)12yes—
407C22×C3×C52−1+412yes—
408C22×C3×C5C2511yescharacteristic
409C2×D15—22no—
410C2×D15—22no—
411C2×D15—22no—
412C2×D15—44no—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415C3×C4×C5—22no—
416C3×C4×C5—22no—
417Dic15—22no—
418Dic15—22no—
419Dic15—22no—
420Dic15—22no—
421Dic15—22no—
422Dic15—22no—
423Dic15—22no—
424C24×C3C22×D511yescharacteristic
425C24×C3C22×D511yescharacteristic
426C24×C3C22×D511yescharacteristic
427C23×D3—51no—
428C2×C3×D4—42no—
429C2×C3×D4—42no—
430C2×C3×D4—42no—
431C2×C3×D4C22×D514yes—
432C2×C3×D4C22×D514yes—
433C2×C3×D4C22×D514yes—
434C22×C3×C4—42no—
435C22×C3×C4C22×D511yescharacteristic
436C22×C3×C4C22×D511yescharacteristic
437C22×C3×C4C22×D511yescharacteristic
438C22×C3×C4C22×D511yescharacteristic
439C22×C3×C4C22×D514yes—
440C2×#67—54no—
441C2×#67—54no—
442C2×#67—54no—
443C2×#67—202no—
444C2×#67—202no—
445C2×#67—202no—
446C22×Dic3—51no—
447C22×Dic3—51no—
448C22×Dic3—51no—
449C22×Dic3—51no—
450C22×Dic3—51no—
451C22×Dic3—51no—
452C22×Dic3—51no—
453C22×Dic3—54no—
454C22×Dic3—54no—
455C22×Dic3—202no—
456C22×Dic3—202no—
457C2×C4×D3—54no—
458C2×C4×D3—202no—
459C2×Dic6—54no—
460C2×Dic6—54no—
461C2×Dic6—202no—
462C2×Dic6—202no—
463C3×C4⋊C4C22×D514yes—
464C3×C22⋊C4C22×D514yes—
465C3×C22⋊C4C22×D514yes—
466#217—54no—
467#217—54no—
468#217—54no—
469#217—54no—
470#217—54no—
471#217—54no—
472#217—54no—
473(C2×D3)⋊C4—54no—
474(C2×D3)⋊C4—54no—
475(C2×D3)⋊C4—54no—
476C4⋊Dic3—54no—
477C4⋊Dic3—54no—
478Dic3⋊C4—54no—
479Dic3⋊C4—54no—
480Dic3⋊C4—54no—
481Dic3⋊C4—54no—
482Dic3⋊C4—54no—
483Dic3⋊C4—54no—
484Dic3⋊C4—54no—
485C4×Dic3—54no—
486C23×C5—22no—
487C23×C5—22no—
488C23×C5—22no—
489C23×C5—22no—
490C23×C5—22no—
491C23×C5—22no—
492C23×C5—22no—
493C23×C5—22no—
494C23×C5—22no—
495C23×C5C23×D312yes—
496C23×C5C23×D312yes—
497C23×C5C23×D312yes—
498C23×C5C23×D311yescharacteristic
499C22×D5—32no—
500C22×D5—62no—
501C22×D5—62no—
502C22×D5—62no—
503C5×D4—44no—
504C5×D4—44no—
505C5×D4—44no—
506C2×C4×C5—22no—
507C2×C4×C5—22no—
508C2×C4×C5—22no—
509C2×C4×C5—22no—
510C2×C4×C5—44no—
511C2×C4×C5C23×D312yes—
512C2×C4×C5C23×D312yes—
513C2×C4×C5C23×D312yes—
514C2×C4×C5C23×D312yes—
515C22⋊D5—124no—
516C22⋊D5—124no—
517C22⋊D5—124no—
518C2×Dic5—32no—
519C2×Dic5—32no—
520C2×Dic5—32no—
521C2×Dic5—32no—
522C2×Dic5—32no—
523C2×Dic5—32no—
524C2×Dic5—32no—
525C2×Dic5—62no—
526C2×Dic5—62no—
527C2×Dic5—62no—
528C2×Dic5—62no—
529C2×Dic5—62no—
530C2×Dic5—62no—
531C2×Dic5—62no—
532C2×Dic5—124no—
533C2×Dic5—124no—
534C4×D5—124no—
535Dic10—124no—
536Dic10—124no—
537C22×Q8—151no—
538C22×Q8—151no—
539C22×D4—151no—
540C22×D4—151no—
541C22×D4—151no—
542C22×D4C2×D1511yescharacteristic
543C22×D4C2×D1511yescharacteristic
544C22×D4C2×D1511yescharacteristic
545C23×C4—151no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4C2×D1511yescharacteristic
549#125—158no—
550#124—158no—
551#124—158no—
552#123—158no—
553#123—158no—
554#123—158no—
555#123—158no—
556C22⋊Q8—158no—
557C22⋊Q8—158no—
558C22⋊Q8—158no—
559C22⋊Q8—158no—
560#121—158no—
561#121—158no—
562#121—158no—
563#121C2×D1518yescomplemented
564C2×C4⋊C4—151no—
565C2×C4⋊C4—151no—
566C2×C4⋊C4—151no—
567C2×C4⋊C4—151no—
568C2×C4⋊C4—151no—
569C2×C4⋊C4—151no—
570C2×C4⋊C4—151no—
571C2×C4⋊C4—151no—
572C2×C4⋊C4—151no—
573C2×C4⋊C4C2×D1511yescharacteristic
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⋊C4C2×D1511yescharacteristic
585C2×C22⋊C4C2×D1511yescharacteristic
586C2×C42—151no—
587C2×C3×C5—42no—
588C2×C3×C5—42no—
589C2×C3×C5—42no—
590C2×C3×C5#56214yescomplemented
591C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
592C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
593C2×C3×C5C2×2−1+411yescharacteristic
594D15—42no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—22no—
604C23×C3C23×D512yes—
605C23×C3C23×D512yes—
606C23×C3C23×D512yes—
607C23×C3C23×D511yescharacteristic
608C22×D3—52no—
609C22×D3—102no—
610C22×D3—102no—
611C22×D3—102no—
612C3×D4—44no—
613C3×D4—44no—
614C3×D4—44no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—22no—
619C2×C3×C4—44no—
620C2×C3×C4C23×D512yes—
621C2×C3×C4C23×D512yes—
622C2×C3×C4C23×D512yes—
623C2×C3×C4C23×D512yes—
624#67—204no—
625#67—204no—
626#67—204no—
627C2×Dic3—52no—
628C2×Dic3—52no—
629C2×Dic3—52no—
630C2×Dic3—52no—
631C2×Dic3—52no—
632C2×Dic3—52no—
633C2×Dic3—52no—
634C2×Dic3—102no—
635C2×Dic3—102no—
636C2×Dic3—102no—
637C2×Dic3—102no—
638C2×Dic3—102no—
639C2×Dic3—102no—
640C2×Dic3—102no—
641C2×Dic3—204no—
642C2×Dic3—204no—
643C4×D3—204no—
644Dic6—204no—
645Dic6—204no—
646C22×C5—22no—
647C22×C5—22no—
648C22×C5—22no—
649C22×C5—22no—
650C22×C5—22no—
651C22×C5—22no—
652C22×C5—22no—
653C22×C5—22no—
654C22×C5—22no—
655C22×C5—44no—
656C22×C5—44no—
657C22×C5—44no—
658C22×C5#100412yes—
659C22×C5#100412yes—
660C22×C5#101012yes—
661C22×C5C24×D311yescharacteristic
662C2×D5—62no—
663C2×D5—62no—
664C2×D5—62no—
665C2×D5—124no—
666C4×C5—22no—
667C4×C5—22no—
668C4×C5—22no—
669C4×C5—22no—
670Dic5—62no—
671Dic5—62no—
672Dic5—62no—
673Dic5—62no—
674Dic5—62no—
675Dic5—62no—
676Dic5—62no—
677C24—151no—
678C24C22×D1511yescharacteristic
679C24C22×D1511yescharacteristic
680C24C22×D1511yescharacteristic
681C2×Q8—154no—
682C2×Q8—154no—
683C2×Q8—602no—
684C2×Q8—602no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—154no—
689C2×D4—154no—
690C2×D4—154no—
691C2×D4—602no—
692C2×D4—602no—
693C2×D4—602no—
694C2×D4C22×D1514yes—
695C2×D4C22×D1514yes—
696C2×D4C22×D1514yes—
697C22×C4—42no—
698C22×C4—151no—
699C22×C4—151no—
700C22×C4—151no—
701C22×C4—151no—
702C22×C4—151no—
703C22×C4—151no—
704C22×C4—151no—
705C22×C4—154no—
706C22×C4—154no—
707C22×C4—154no—
708C22×C4—602no—
709C22×C4—602no—
710C22×C4—602no—
711C22×C4C22×D1511yescharacteristic
712C22×C4C22×D1511yescharacteristic
713C22×C4C22×D1511yescharacteristic
714C22×C4C22×D1511yescharacteristic
715C22×C4C22×D1514yes—
716C4⋊C4—154no—
717C4⋊C4—154no—
718C4⋊C4—154no—
719C4⋊C4—154no—
720C4⋊C4—154no—
721C4⋊C4—154no—
722C4⋊C4—154no—
723C4⋊C4—154no—
724C4⋊C4—154no—
725C4⋊C4C22×D1514yes—
726C22⋊C4—154no—
727C22⋊C4—154no—
728C22⋊C4—154no—
729C22⋊C4—154no—
730C22⋊C4—154no—
731C22⋊C4—154no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C22⋊C4—154no—
736C22⋊C4C22×D1514yes—
737C22⋊C4C22×D1514yes—
738C42—154no—
739C3×C5C2×#56211yescharacteristic, complemented, Hall
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—44no—
750C22×C3—44no—
751C22×C3—44no—
752C22×C3#414412yes—
753C22×C3#414412yes—
754C22×C3#415012yes—
755C22×C3C24×D511yescharacteristic
756C2×D3—102no—
757C2×D3—102no—
758C2×D3—102no—
759C2×D3—204no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—22no—
764Dic3—102no—
765Dic3—102no—
766Dic3—102no—
767Dic3—102no—
768Dic3—102no—
769Dic3—102no—
770Dic3—102no—
771C2×C5—42no—
772C2×C5—42no—
773C2×C5—42no—
774C2×C5#562114yescomplemented
775C2×C5C2×#100411yescharacteristic
776C2×C5C2×#100411yescharacteristic
777C2×C5C2×#101011yescharacteristic
778D5—122no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—152no—
789C23—302no—
790C23—302no—
791C23—302no—
792C23C23×D1512yes—
793C23C23×D1512yes—
794C23C23×D1512yes—
795C23C23×D1511yescharacteristic
796Q8—604no—
797Q8—604no—
798D4—44no—
799D4—44no—
800D4—44no—
801D4—604no—
802D4—604no—
803D4—604no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—44no—
809C2×C4—152no—
810C2×C4—152no—
811C2×C4—152no—
812C2×C4—152no—
813C2×C4—152no—
814C2×C4—152no—
815C2×C4—152no—
816C2×C4—302no—
817C2×C4—302no—
818C2×C4—302no—
819C2×C4—302no—
820C2×C4—302no—
821C2×C4—302no—
822C2×C4—302no—
823C2×C4—604no—
824C2×C4—604no—
825C2×C4—604no—
826C2×C4C23×D1512yes—
827C2×C4C23×D1512yes—
828C2×C4C23×D1512yes—
829C2×C4C23×D1512yes—
830C2×C3—42no—
831C2×C3—42no—
832C2×C3—42no—
833C2×C3#6595514yescomplemented
834C2×C3C2×#414411yescharacteristic
835C2×C3C2×#414411yescharacteristic
836C2×C3C2×#415011yescharacteristic
837D3—202no—
838C5C2×#562111yescharacteristic, complemented, Sylow
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—302no—
852C22—302no—
853C22—302no—
854C22—604no—
855C22#9209512yes—
856C22#9209512yes—
857C22#9210112yes—
858C22C24×D1511yescharacteristic
859C4—22no—
860C4—22no—
861C4—22no—
862C4—22no—
863C4—302no—
864C4—302no—
865C4—302no—
866C4—302no—
867C4—302no—
868C4—302no—
869C4—302no—
870C3C2×#6595511yescharacteristic, complemented, Sylow
871C2—42no—
872C2—42no—
873C2—42no—
874C2—602no—
875C2#1175638014yesdirect product factor
876C2C2×#9209511yescharacteristic
877C2C2×#9209511yescharacteristic
878C2C2×#9210111yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#121C2
socleC23×C3×C5C24
hypercenterC2×#121D15
hypocenterC3×C5C2×#562
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#121C2semidirect
2. C2×#91828C2semidirect
3. C2×#91828C2semidirect
4. C2×#91827C2semidirect
5. C2×#91825C2semidirect
6. C2×#91824C2semidirect
7. C2×#91824C2semidirect
8. C2×#91818C2semidirect
9. C2×#91813C2semidirect
10. #11756380C2direct (N × H)
11. C2×#91785C2semidirect
12. C2×#91778C2semidirect
13. C2×#91774C2semidirect
14. C2×#91772C2semidirect
15. C2×#91767C2semidirect
16. C2×#91767C2semidirect
30. C3×C5×#121C22semidirect
41. #91828C22semidirect
42. #91828C22semidirect
43. #91827C22semidirect
44. #91825C22semidirect
45. #91824C22semidirect
46. #91824C22semidirect
47. #91818C22semidirect
53. #91813C22semidirect
62. #91785C22semidirect
63. #91778C22semidirect
64. #91774C22semidirect
65. #91772C22semidirect
66. #91767C22semidirect
67. #91767C22semidirect
69. C2×C5×#121D3semidirect
147. C2×C3×#121D5semidirect
175. C5×#121C2×D3semidirect
277. C3×#121C2×D5semidirect
392. C2×#121D15semidirect
563. #121C2×D15semidirect
590. C2×C3×C5#562semidirect
739. C3×C5C2×#562semidirect
774. C2×C5#5621semidirect
833. C2×C3#65955semidirect
838. C5C2×#5621semidirect
870. C3C2×#65955semidirect
875. C2#11756380direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1212
C2×#918282
C2×#918272
C2×#918252
C2×#918242
C2×#918182
C2×#918132
#117563802
C2×#917852
C2×#917782
C2×#917742
C2×#917722
C2×#917672
C2×#659553
C2×#56215