Finite Group Databasebeta

← C2×#11756352 #14480760

Subgroups — C2×#11756352 #14480760

Order 1920.

2672 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#120C211yesmaximal, characteristic, complemented
2C2×#91842C211yesmaximal, characteristic, complemented
3C22×#6719C211yesmaximal, characteristic, complemented
4C2×#91828C211yesmaximal, characteristic, complemented
5C2×#91828C211yesmaximal, characteristic, complemented
6C2×#91827C211yesmaximal, characteristic, complemented
7C2×#91825C211yesmaximal, characteristic, complemented
8C2×#91824C211yesmaximal, characteristic, complemented
9C2×D4×Dic15C211yesmaximal, characteristic, complemented
10#11756352C2116yesmaximal, direct product factor
11C2×#91774C211yesmaximal, characteristic, complemented
12C2×#91772C211yesmaximal, characteristic, complemented
13C2×#91770C211yesmaximal, characteristic, complemented
14C2×#91768C211yesmaximal, characteristic, complemented
15C2×#91768C211yesmaximal, characteristic, complemented
16C2×#91767C211yesmaximal, characteristic, complemented
17C2×#65927—31nomaximal, Hall
18C25×C3×C5C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C22×C3×C5×D4C2211yescharacteristic
21C22×C3×C5×D4C2211yescharacteristic
22C22×#1220C2211yescharacteristic
23C22×#1220C2211yescharacteristic
24C22×#1220C2211yescharacteristic
25C22×#1220C2211yescharacteristic, complemented
26C23×Dic15C2211yescharacteristic
27C23×Dic15C2211yescharacteristic
28C23×Dic15C2211yescharacteristic, complemented
29C22×C4×D15C2211yescharacteristic, complemented
30C22×Dic30C2211yescharacteristic, complemented
31C3×C5×#120C2218yescomplemented
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×C3×C5×C22⋊C4C2211yescharacteristic
34C2×C3×C5×C22⋊C4C2211yescharacteristic
35#91842C2218yescomplemented
36C2×#6719C2211yescharacteristic
37C2×#6719C2211yescharacteristic
38C2×#6719C2211yescharacteristic
39C2×#6719C2211yescharacteristic
40C2×#6719C2211yescharacteristic
41C2×#6719C2211yescharacteristic
42C2×#6719C2211yescharacteristic
43C2×#6719C2218yescomplemented
44C2×#6719C2211yescharacteristic, complemented
45C2×#6719C2211yescharacteristic, complemented
46#91828C2218yescomplemented
47#91828C2218yescomplemented
48#91827C2218yescomplemented
49#91825C2218yescomplemented
50#91824C2218yescomplemented
51D4×Dic15C2218yescomplemented
52C2×#6714C2211yescharacteristic, complemented
53C2×#6714C2211yescharacteristic, complemented
54C2×C4⋊Dic15C2211yescharacteristic, complemented
55C2×C4⋊Dic15C2211yescharacteristic, complemented
56C2×#6712C2211yescharacteristic, complemented
57C2×#6712C2211yescharacteristic, complemented
58C2×#6712C2211yescharacteristic, complemented
59C2×#6712C2211yescharacteristic, complemented
60C2×C4×Dic15C2211yescharacteristic, complemented
61C2×C4×Dic15C2211yescharacteristic, complemented
62#91774C2218yescomplemented
63#91772C2218yescomplemented
64#91770C2218yescomplemented
65#91768C2218yescomplemented
66#91768C2218yescomplemented
67#91767C2218yescomplemented
68C2×#5593—51nomaximal, Hall
69C2×C5×#120D311yescharacteristic, complemented
70C2×#4099—31no—
71C22×C22⋊Dic5—31no—
72C2×#4085—31no—
73C2×#4085—31no—
74C2×#4084—31no—
75C2×#4082—31no—
76C2×#4081—31no—
77C2×D4×Dic5—31no—
78#65927—316no—
79C2×#4031—31no—
80C2×#4029—31no—
81C2×#4027—31no—
82C2×#4025—31no—
83C2×#4025—31no—
84C2×#4024—31no—
85C24×C3×C5—24no—
86C24×C3×C5—42no—
87C24×C3×C5—42no—
88C24×C3×C5C2311yescharacteristic
89C24×C3×C5C2311yescharacteristic
90C24×C3×C5C2311yescharacteristic
91C24×C3×C5C2311yescharacteristic
92C24×C3×C5C2314yes—
93C23×D15C2311yescharacteristic
94C2×C3×C5×D4—24no—
95C2×C3×C5×D4—42no—
96C2×C3×C5×D4—42no—
97C2×C3×C5×D4C2314yes—
98C2×C3×C5×D4C2314yes—
99C2×C3×C5×D4C2314yes—
100C22×C3×C4×C5C2311yescharacteristic
101C22×C3×C4×C5C2311yescharacteristic
102C22×C3×C4×C5C2311yescharacteristic
103C2×#1220—24no—
104C2×#1220—42no—
105C2×#1220—42no—
106C2×#1220—42no—
107C2×#1220C2314yes—
108C2×#1220C2314yes—
109C2×#1220C2314yes—
110C2×#1220C2314yescomplemented
111C22×Dic15—42no—
112C22×Dic15—42no—
113C22×Dic15—42no—
114C22×Dic15C2311yescharacteristic
115C22×Dic15C2311yescharacteristic
116C22×Dic15C2311yescharacteristic
117C22×Dic15C2311yescharacteristic
118C22×Dic15C2311yescharacteristic
119C22×Dic15C2311yescharacteristic
120C22×Dic15C2311yescharacteristic
121C22×Dic15C2314yes—
122C22×Dic15C2314yes—
123C22×Dic15C2314yescomplemented
124C2×C4×D15—42no—
125C2×C4×D15C2314yescomplemented
126C2×Dic30—42no—
127C2×Dic30C2314yescomplemented
128C3×C5×C22⋊C4C2314yes—
129C3×C5×C22⋊C4C2314yes—
130C3×C5×C22⋊C4C2314yes—
131#6719C2314yes—
132#6719C2314yes—
133#6719C2314yes—
134#6719C2314yes—
135#6719C2314yes—
136#6719C2314yes—
137#6719C2314yes—
138#6719C2314yescomplemented
139#6719C2314yescomplemented
140#6714C2314yescomplemented
141#6714C2314yescomplemented
142C4⋊Dic15C2314yescomplemented
143C4⋊Dic15C2314yescomplemented
144#6712C2314yescomplemented
145#6712C2314yescomplemented
146#6712C2314yescomplemented
147#6712C2314yescomplemented
148C4×Dic15C2314yescomplemented
149C4×Dic15C2314yescomplemented
150C2×C3×#120D511yescharacteristic, complemented
151C2×#953—51no—
152C22×#217—51no—
153C2×#939—51no—
154C2×#939—51no—
155C2×#938—51no—
156C2×#936—51no—
157C2×#935—51no—
158C2×D4×Dic3—51no—
159#5593—516no—
160C2×#885—51no—
161C2×#883—51no—
162C2×#67⋊C4—51no—
163C2×#879—51no—
164C2×#879—51no—
165C2×#878—51no—
166C25×C5C2×D311yescharacteristic
167C22×C5×D4C2×D311yescharacteristic
168C22×C5×D4C2×D311yescharacteristic
169C22×C5×D4C2×D311yescharacteristic
170C22×C22⋊D5—31no—
171C22×C22⋊D5—31no—
172C22×C22⋊D5—31no—
173C22×C22⋊D5—31no—
174C23×Dic5—31no—
175C23×Dic5—31no—
176C23×Dic5—31no—
177C22×C4×D5—31no—
178C22×Dic10—31no—
179C5×#120C2×D318yescomplemented
180C2×C5×C22⋊C4C2×D311yescharacteristic
181C2×C5×C22⋊C4C2×D311yescharacteristic
182C2×C5×C22⋊C4C2×D311yescharacteristic
183#4099—38no—
184C2×C22⋊Dic5—31no—
185C2×C22⋊Dic5—31no—
186C2×C22⋊Dic5—31no—
187C2×C22⋊Dic5—31no—
188C2×C22⋊Dic5—31no—
189C2×C22⋊Dic5—31no—
190C2×C22⋊Dic5—31no—
191C2×C22⋊Dic5—31no—
192C2×C22⋊Dic5—31no—
193C2×C22⋊Dic5—38no—
194#4085—38no—
195#4085—38no—
196#4084—38no—
197#4082—38no—
198#4081—38no—
199D4×Dic5—38no—
200C2×#685—31no—
201C2×#685—31no—
202C2×C4⋊Dic5—31no—
203C2×C4⋊Dic5—31no—
204C2×#683—31no—
205C2×#683—31no—
206C2×#683—31no—
207C2×#683—31no—
208C2×C4×Dic5—31no—
209C2×C4×Dic5—31no—
210#4031—38no—
211#4029—38no—
212#4027—38no—
213#4025—38no—
214#4025—38no—
215#4024—38no—
216C2×#538—151noSylow
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5—22no—
220C23×C3×C5—28no—
221C23×C3×C5—22no—
222C23×C3×C5—22no—
223C23×C3×C5—22no—
224C23×C3×C5—22no—
225C23×C3×C5—22no—
226C23×C3×C5—22no—
227C23×C3×C5—22no—
228C23×C3×C5—22no—
229C23×C3×C5—44no—
230C23×C3×C5—44no—
231C23×C3×C5—416no—
232C23×C3×C5#4114yes—
233C23×C3×C5C2412yes—
234C23×C3×C5C2412yes—
235C23×C3×C5C2412yes—
236C23×C3×C5C2412yes—
237C23×C3×C5C2411yescharacteristic
238C22×D15—22no—
239C22×D15—22no—
240C22×D15—22no—
241C22×D15C2412yes—
242C3×C5×D4—28no—
243C3×C5×D4—44no—
244C3×C5×D4—44no—
245C2×C3×C4×C5—22no—
246C2×C3×C4×C5—22no—
247C2×C3×C4×C5—22no—
248C2×C3×C4×C5C2412yes—
249C2×C3×C4×C5C2412yes—
250C2×C3×C4×C5C2412yes—
251#1220—28no—
252#1220—44no—
253#1220—44no—
254#1220—44no—
255C2×Dic15—22no—
256C2×Dic15—22no—
257C2×Dic15—22no—
258C2×Dic15—22no—
259C2×Dic15—22no—
260C2×Dic15—22no—
261C2×Dic15—22no—
262C2×Dic15—44no—
263C2×Dic15—44no—
264C2×Dic15—44no—
265C2×Dic15C2412yes—
266C2×Dic15C2412yes—
267C2×Dic15C2412yes—
268C2×Dic15C2412yes—
269C2×Dic15C2412yes—
270C2×Dic15C2412yes—
271C2×Dic15C2412yes—
272C4×D15—44no—
273Dic30—44no—
274C25×C3C2×D511yescharacteristic
275C22×C3×D4C2×D511yescharacteristic
276C22×C3×D4C2×D511yescharacteristic
277C22×C3×D4C2×D511yescharacteristic
278C22×#67—51no—
279C22×#67—51no—
280C22×#67—51no—
281C22×#67—51no—
282C23×Dic3—51no—
283C23×Dic3—51no—
284C23×Dic3—51no—
285C22×C4×D3—51no—
286C22×Dic6—51no—
287C3×#120C2×D518yescomplemented
288C2×C3×C22⋊C4C2×D511yescharacteristic
289C2×C3×C22⋊C4C2×D511yescharacteristic
290C2×C3×C22⋊C4C2×D511yescharacteristic
291#953—58no—
292C2×#217—51no—
293C2×#217—51no—
294C2×#217—51no—
295C2×#217—51no—
296C2×#217—51no—
297C2×#217—51no—
298C2×#217—51no—
299C2×#217—51no—
300C2×#217—51no—
301C2×#217—58no—
302#939—58no—
303#939—58no—
304#938—58no—
305#936—58no—
306#935—58no—
307D4×Dic3—58no—
308C2×(C2×D3)⋊C4—51no—
309C2×(C2×D3)⋊C4—51no—
310C2×C4⋊Dic3—51no—
311C2×C4⋊Dic3—51no—
312C2×Dic3⋊C4—51no—
313C2×Dic3⋊C4—51no—
314C2×Dic3⋊C4—51no—
315C2×Dic3⋊C4—51no—
316C2×C4×Dic3—51no—
317C2×C4×Dic3—51no—
318#885—58no—
319#883—58no—
320#67⋊C4—58no—
321#879—58no—
322#879—58no—
323#878—58no—
324C24×C5—24no—
325C24×C5—42no—
326C24×C5—42no—
327C24×C5C22×D311yescharacteristic
328C24×C5C22×D311yescharacteristic
329C24×C5C22×D311yescharacteristic
330C24×C5C22×D311yescharacteristic
331C24×C5C22×D314yes—
332C23×D5—31no—
333C2×C5×D4—24no—
334C2×C5×D4—42no—
335C2×C5×D4—42no—
336C2×C5×D4C22×D314yes—
337C2×C5×D4C22×D314yes—
338C2×C5×D4C22×D314yes—
339C22×C4×C5C22×D311yescharacteristic
340C22×C4×C5C22×D311yescharacteristic
341C22×C4×C5C22×D311yescharacteristic
342C2×C22⋊D5—34no—
343C2×C22⋊D5—34no—
344C2×C22⋊D5—34no—
345C2×C22⋊D5—34no—
346C2×C22⋊D5—64no—
347C2×C22⋊D5—122no—
348C2×C22⋊D5—122no—
349C2×C22⋊D5—122no—
350C22×Dic5—31no—
351C22×Dic5—31no—
352C22×Dic5—31no—
353C22×Dic5—31no—
354C22×Dic5—31no—
355C22×Dic5—31no—
356C22×Dic5—31no—
357C22×Dic5—34no—
358C22×Dic5—34no—
359C22×Dic5—34no—
360C22×Dic5—122no—
361C22×Dic5—122no—
362C22×Dic5—122no—
363C2×C4×D5—34no—
364C2×C4×D5—122no—
365C2×Dic10—34no—
366C2×Dic10—122no—
367C5×C22⋊C4C22×D314yes—
368C5×C22⋊C4C22×D314yes—
369C5×C22⋊C4C22×D314yes—
370C22⋊Dic5—34no—
371C22⋊Dic5—34no—
372C22⋊Dic5—34no—
373C22⋊Dic5—34no—
374C22⋊Dic5—34no—
375C22⋊Dic5—34no—
376C22⋊Dic5—34no—
377C22⋊Dic5—34no—
378C22⋊Dic5—34no—
379#685—34no—
380#685—34no—
381C4⋊Dic5—34no—
382C4⋊Dic5—34no—
383#683—34no—
384#683—34no—
385#683—34no—
386#683—34no—
387C4×Dic5—34no—
388C4×Dic5—34no—
389#538—1516no—
390C2×#126—151no—
391C2×#126—151no—
392C2×#124—151no—
393C2×#124—151no—
394C2×#123—151no—
395C2×#123—151no—
396C2×C22⋊Q8—151no—
397C2×#121—151no—
398C2×#121—151no—
399C2×#121—151no—
400C2×#120—151no—
401C2×#120D1511yescharacteristic, complemented
402C2×C4×D4—151no—
403C2×C4×D4—151no—
404C22×C22⋊C4—151no—
405C22×C3×C5—28no—
406C22×C3×C5—22no—
407C22×C3×C5—22no—
408C22×C3×C5—22no—
409C22×C3×C5—22no—
410C22×C3×C5—22no—
411C22×C3×C5—22no—
412C22×C3×C5—22no—
413C22×C3×C5—22no—
414C22×C3×C5—22no—
415C22×C3×C5—22no—
416C22×C3×C5—22no—
417C22×C3×C5—416no—
418C22×C3×C5—44no—
419C22×C3×C5—44no—
420C22×C3×C5—44no—
421C22×C3×C5C2×#4114yes—
422C22×C3×C5C2×#4112yes—
423C22×C3×C5H(5,𝔽2)12yes—
424C22×C3×C5H(5,𝔽2)12yes—
425C22×C3×C5C2511yescharacteristic
426C2×D15—22no—
427C2×D15—22no—
428C2×D15—22no—
429C2×D15—44no—
430C3×C4×C5—22no—
431C3×C4×C5—22no—
432C3×C4×C5—22no—
433Dic15—22no—
434Dic15—22no—
435Dic15—22no—
436Dic15—22no—
437Dic15—22no—
438Dic15—22no—
439Dic15—22no—
440C24×C3—24no—
441C24×C3—42no—
442C24×C3—42no—
443C24×C3C22×D511yescharacteristic
444C24×C3C22×D511yescharacteristic
445C24×C3C22×D511yescharacteristic
446C24×C3C22×D511yescharacteristic
447C24×C3C22×D514yes—
448C23×D3—51no—
449C2×C3×D4—24no—
450C2×C3×D4—42no—
451C2×C3×D4—42no—
452C2×C3×D4C22×D514yes—
453C2×C3×D4C22×D514yes—
454C2×C3×D4C22×D514yes—
455C22×C3×C4C22×D511yescharacteristic
456C22×C3×C4C22×D511yescharacteristic
457C22×C3×C4C22×D511yescharacteristic
458C2×#67—54no—
459C2×#67—54no—
460C2×#67—54no—
461C2×#67—54no—
462C2×#67—104no—
463C2×#67—202no—
464C2×#67—202no—
465C2×#67—202no—
466C22×Dic3—51no—
467C22×Dic3—51no—
468C22×Dic3—51no—
469C22×Dic3—51no—
470C22×Dic3—51no—
471C22×Dic3—51no—
472C22×Dic3—51no—
473C22×Dic3—54no—
474C22×Dic3—54no—
475C22×Dic3—54no—
476C22×Dic3—202no—
477C22×Dic3—202no—
478C22×Dic3—202no—
479C2×C4×D3—54no—
480C2×C4×D3—202no—
481C2×Dic6—54no—
482C2×Dic6—202no—
483C3×C22⋊C4C22×D514yes—
484C3×C22⋊C4C22×D514yes—
485C3×C22⋊C4C22×D514yes—
486#217—54no—
487#217—54no—
488#217—54no—
489#217—54no—
490#217—54no—
491#217—54no—
492#217—54no—
493#217—54no—
494#217—54no—
495(C2×D3)⋊C4—54no—
496(C2×D3)⋊C4—54no—
497C4⋊Dic3—54no—
498C4⋊Dic3—54no—
499Dic3⋊C4—54no—
500Dic3⋊C4—54no—
501Dic3⋊C4—54no—
502Dic3⋊C4—54no—
503C4×Dic3—54no—
504C4×Dic3—54no—
505C23×C5—22no—
506C23×C5—22no—
507C23×C5—22no—
508C23×C5—28no—
509C23×C5—22no—
510C23×C5—22no—
511C23×C5—22no—
512C23×C5—22no—
513C23×C5—22no—
514C23×C5—22no—
515C23×C5—22no—
516C23×C5—22no—
517C23×C5—44no—
518C23×C5—44no—
519C23×C5—416no—
520C23×C5#23714yes—
521C23×C5C23×D312yes—
522C23×C5C23×D312yes—
523C23×C5C23×D312yes—
524C23×C5C23×D312yes—
525C23×C5C23×D311yescharacteristic
526C22×D5—32no—
527C22×D5—62no—
528C22×D5—62no—
529C22×D5—62no—
530C5×D4—28no—
531C5×D4—44no—
532C5×D4—44no—
533C2×C4×C5—22no—
534C2×C4×C5—22no—
535C2×C4×C5—22no—
536C2×C4×C5C23×D312yes—
537C2×C4×C5C23×D312yes—
538C2×C4×C5C23×D312yes—
539C22⋊D5—68no—
540C22⋊D5—124no—
541C22⋊D5—124no—
542C22⋊D5—124no—
543C2×Dic5—32no—
544C2×Dic5—32no—
545C2×Dic5—32no—
546C2×Dic5—32no—
547C2×Dic5—32no—
548C2×Dic5—32no—
549C2×Dic5—32no—
550C2×Dic5—62no—
551C2×Dic5—62no—
552C2×Dic5—62no—
553C2×Dic5—62no—
554C2×Dic5—62no—
555C2×Dic5—62no—
556C2×Dic5—62no—
557C2×Dic5—124no—
558C2×Dic5—124no—
559C2×Dic5—124no—
560C4×D5—124no—
561Dic10—124no—
562C25C2×D1511yescharacteristic
563C22×Q8—151no—
564C22×D4—151no—
565C22×D4—151no—
566C22×D4—151no—
567C22×D4—151no—
568C22×D4C2×D1511yescharacteristic
569C22×D4C2×D1511yescharacteristic
570C22×D4C2×D1511yescharacteristic
571C23×C4—151no—
572C23×C4—151no—
573C23×C4—151no—
574C23×C4—151no—
575#126—158no—
576#126—158no—
577#124—158no—
578#124—158no—
579#123—158no—
580#123—158no—
581C22⋊Q8—158no—
582#121—158no—
583#121—158no—
584#121—158no—
585#120—158no—
586#120C2×D1518yescomplemented
587C4×D4—158no—
588C4×D4—158no—
589C2×C4⋊C4—151no—
590C2×C4⋊C4—151no—
591C2×C4⋊C4—151no—
592C2×C4⋊C4—151no—
593C2×C4⋊C4—151no—
594C2×C4⋊C4—151no—
595C2×C22⋊C4—151no—
596C2×C22⋊C4—151no—
597C2×C22⋊C4—151no—
598C2×C22⋊C4—151no—
599C2×C22⋊C4—158no—
600C2×C22⋊C4—151no—
601C2×C22⋊C4—151no—
602C2×C22⋊C4—151no—
603C2×C22⋊C4—151no—
604C2×C22⋊C4—151no—
605C2×C22⋊C4—151no—
606C2×C22⋊C4—151no—
607C2×C22⋊C4C2×D1511yescharacteristic
608C2×C22⋊C4C2×D1511yescharacteristic
609C2×C22⋊C4C2×D1511yescharacteristic
610C2×C42—151no—
611C2×C42—151no—
612C2×C3×C5—24no—
613C2×C3×C5—42no—
614C2×C3×C5—42no—
615C2×C3×C5—42no—
616C2×C3×C5#53814yescomplemented
617C2×C3×C5C22×#4111yescharacteristic
618C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
619C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
620D15—42no—
621C23×C3—22no—
622C23×C3—22no—
623C23×C3—22no—
624C23×C3—28no—
625C23×C3—22no—
626C23×C3—22no—
627C23×C3—22no—
628C23×C3—22no—
629C23×C3—22no—
630C23×C3—22no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—44no—
634C23×C3—44no—
635C23×C3—416no—
636C23×C3#71114yes—
637C23×C3C23×D512yes—
638C23×C3C23×D512yes—
639C23×C3C23×D512yes—
640C23×C3C23×D512yes—
641C23×C3C23×D511yescharacteristic
642C22×D3—52no—
643C22×D3—102no—
644C22×D3—102no—
645C22×D3—102no—
646C3×D4—28no—
647C3×D4—44no—
648C3×D4—44no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4C23×D512yes—
653C2×C3×C4C23×D512yes—
654C2×C3×C4C23×D512yes—
655#67—108no—
656#67—204no—
657#67—204no—
658#67—204no—
659C2×Dic3—52no—
660C2×Dic3—52no—
661C2×Dic3—52no—
662C2×Dic3—52no—
663C2×Dic3—52no—
664C2×Dic3—52no—
665C2×Dic3—52no—
666C2×Dic3—102no—
667C2×Dic3—102no—
668C2×Dic3—102no—
669C2×Dic3—102no—
670C2×Dic3—102no—
671C2×Dic3—102no—
672C2×Dic3—102no—
673C2×Dic3—204no—
674C2×Dic3—204no—
675C2×Dic3—204no—
676C4×D3—204no—
677Dic6—204no—
678C22×C5—22no—
679C22×C5—22no—
680C22×C5—28no—
681C22×C5—22no—
682C22×C5—22no—
683C22×C5—22no—
684C22×C5—22no—
685C22×C5—22no—
686C22×C5—22no—
687C22×C5—22no—
688C22×C5—22no—
689C22×C5—22no—
690C22×C5—416no—
691C22×C5—44no—
692C22×C5—44no—
693C22×C5—44no—
694C22×C5C2×#23714yes—
695C22×C5C2×#23712yes—
696C22×C5#100412yes—
697C22×C5#100412yes—
698C22×C5C24×D311yescharacteristic
699C2×D5—62no—
700C2×D5—62no—
701C2×D5—62no—
702C2×D5—124no—
703C4×C5—22no—
704C4×C5—22no—
705C4×C5—22no—
706Dic5—62no—
707Dic5—62no—
708Dic5—62no—
709Dic5—62no—
710Dic5—62no—
711Dic5—62no—
712Dic5—62no—
713C24—24no—
714C24—42no—
715C24—42no—
716C24—151no—
717C24C22×D1511yescharacteristic
718C24C22×D1511yescharacteristic
719C24C22×D1511yescharacteristic
720C24C22×D1511yescharacteristic
721C24C22×D1514yes—
722C2×Q8—154no—
723C2×Q8—602no—
724C2×D4—24no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—154no—
728C2×D4—154no—
729C2×D4—154no—
730C2×D4—154no—
731C2×D4—304no—
732C2×D4—602no—
733C2×D4—602no—
734C2×D4—602no—
735C2×D4C22×D1514yes—
736C2×D4C22×D1514yes—
737C2×D4C22×D1514yes—
738C22×C4—151no—
739C22×C4—151no—
740C22×C4—151no—
741C22×C4—151no—
742C22×C4—151no—
743C22×C4—151no—
744C22×C4—151no—
745C22×C4—154no—
746C22×C4—154no—
747C22×C4—154no—
748C22×C4—154no—
749C22×C4—602no—
750C22×C4—602no—
751C22×C4—602no—
752C22×C4—602no—
753C22×C4C22×D1511yescharacteristic
754C22×C4C22×D1511yescharacteristic
755C22×C4C22×D1511yescharacteristic
756C4⋊C4—154no—
757C4⋊C4—154no—
758C4⋊C4—154no—
759C4⋊C4—154no—
760C4⋊C4—154no—
761C4⋊C4—154no—
762C22⋊C4—154no—
763C22⋊C4—154no—
764C22⋊C4—154no—
765C22⋊C4—154no—
766C22⋊C4—154no—
767C22⋊C4—154no—
768C22⋊C4—154no—
769C22⋊C4—154no—
770C22⋊C4—154no—
771C22⋊C4—154no—
772C22⋊C4—154no—
773C22⋊C4C22×D1514yes—
774C22⋊C4C22×D1514yes—
775C22⋊C4C22×D1514yes—
776C42—154no—
777C42—154no—
778C3×C5C2×#53811yescharacteristic, complemented, Hall
779C22×C3—28no—
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—22no—
791C22×C3—416no—
792C22×C3—44no—
793C22×C3—44no—
794C22×C3—44no—
795C22×C3C2×#71114yes—
796C22×C3C2×#71112yes—
797C22×C3#414412yes—
798C22×C3#414412yes—
799C22×C3C24×D511yescharacteristic
800C2×D3—102no—
801C2×D3—102no—
802C2×D3—102no—
803C2×D3—204no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—22no—
807Dic3—102no—
808Dic3—102no—
809Dic3—102no—
810Dic3—102no—
811Dic3—102no—
812Dic3—102no—
813Dic3—102no—
814C2×C5—24no—
815C2×C5—42no—
816C2×C5—42no—
817C2×C5—42no—
818C2×C5#559314yescomplemented
819C2×C5C22×#23711yescharacteristic
820C2×C5C2×#100411yescharacteristic
821C2×C5C2×#100411yescharacteristic
822D5—122no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—28no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—44no—
836C23—44no—
837C23—416no—
838C23—152no—
839C23—302no—
840C23—302no—
841C23—302no—
842C23#681914yes—
843C23C23×D1512yes—
844C23C23×D1512yes—
845C23C23×D1512yes—
846C23C23×D1512yes—
847C23C23×D1511yescharacteristic
848Q8—604no—
849D4—28no—
850D4—44no—
851D4—44no—
852D4—308no—
853D4—604no—
854D4—604no—
855D4—604no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—152no—
860C2×C4—152no—
861C2×C4—152no—
862C2×C4—152no—
863C2×C4—152no—
864C2×C4—152no—
865C2×C4—152no—
866C2×C4—302no—
867C2×C4—302no—
868C2×C4—302no—
869C2×C4—302no—
870C2×C4—302no—
871C2×C4—302no—
872C2×C4—302no—
873C2×C4—604no—
874C2×C4—604no—
875C2×C4—604no—
876C2×C4—604no—
877C2×C4C23×D1512yes—
878C2×C4C23×D1512yes—
879C2×C4C23×D1512yes—
880C2×C3—24no—
881C2×C3—42no—
882C2×C3—42no—
883C2×C3—42no—
884C2×C3#6592714yescomplemented
885C2×C3C22×#71111yescharacteristic
886C2×C3C2×#414411yescharacteristic
887C2×C3C2×#414411yescharacteristic
888D3—202no—
889C5C2×#559311yescharacteristic, complemented, Sylow
890C22—28no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—416no—
903C22—44no—
904C22—44no—
905C22—44no—
906C22—302no—
907C22—302no—
908C22—302no—
909C22—604no—
910C22C2×#681914yes—
911C22C2×#681912yes—
912C22#9209512yes—
913C22#9209512yes—
914C22C24×D1511yescharacteristic
915C4—22no—
916C4—22no—
917C4—22no—
918C4—302no—
919C4—302no—
920C4—302no—
921C4—302no—
922C4—302no—
923C4—302no—
924C4—302no—
925C3C2×#6592711yescharacteristic, complemented, Sylow
926C2—24no—
927C2—42no—
928C2—42no—
929C2—42no—
930C2—602no—
931C2#1175635214yesdirect product factor
932C2C22×#681911yescharacteristic
933C2C2×#9209511yescharacteristic
934C2C2×#9209511yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#120C2
socleC23×C3×C5C24
hypercenterC2×#120D15
hypocenterC3×C5C2×#538
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#120C2semidirect
2. C2×#91842C2semidirect
3. C22×#6719C2semidirect
4. C2×#91828C2semidirect
5. C2×#91828C2semidirect
6. C2×#91827C2semidirect
7. C2×#91825C2semidirect
8. C2×#91824C2semidirect
9. C2×D4×Dic15C2semidirect
10. #11756352C2direct (N × H)
11. C2×#91774C2semidirect
12. C2×#91772C2semidirect
13. C2×#91770C2semidirect
14. C2×#91768C2semidirect
15. C2×#91768C2semidirect
16. C2×#91767C2semidirect
25. C22×#1220C22semidirect
28. C23×Dic15C22semidirect
29. C22×C4×D15C22semidirect
30. C22×Dic30C22semidirect
31. C3×C5×#120C22semidirect
35. #91842C22semidirect
43. C2×#6719C22semidirect
44. C2×#6719C22semidirect
45. C2×#6719C22semidirect
46. #91828C22semidirect
47. #91828C22semidirect
48. #91827C22semidirect
49. #91825C22semidirect
50. #91824C22semidirect
51. D4×Dic15C22semidirect
52. C2×#6714C22semidirect
53. C2×#6714C22semidirect
54. C2×C4⋊Dic15C22semidirect
55. C2×C4⋊Dic15C22semidirect
56. C2×#6712C22semidirect
57. C2×#6712C22semidirect
58. C2×#6712C22semidirect
59. C2×#6712C22semidirect
60. C2×C4×Dic15C22semidirect
61. C2×C4×Dic15C22semidirect
62. #91774C22semidirect
63. #91772C22semidirect
64. #91770C22semidirect
65. #91768C22semidirect
66. #91768C22semidirect
67. #91767C22semidirect
69. C2×C5×#120D3semidirect
110. C2×#1220C23semidirect
123. C22×Dic15C23semidirect
125. C2×C4×D15C23semidirect
127. C2×Dic30C23semidirect
138. #6719C23semidirect
139. #6719C23semidirect
140. #6714C23semidirect
141. #6714C23semidirect
142. C4⋊Dic15C23semidirect
143. C4⋊Dic15C23semidirect
144. #6712C23semidirect
145. #6712C23semidirect
146. #6712C23semidirect
147. #6712C23semidirect
148. C4×Dic15C23semidirect
149. C4×Dic15C23semidirect
150. C2×C3×#120D5semidirect
179. C5×#120C2×D3semidirect
287. C3×#120C2×D5semidirect
401. C2×#120D15semidirect
586. #120C2×D15semidirect
616. C2×C3×C5#538semidirect
778. C3×C5C2×#538semidirect
818. C2×C5#5593semidirect
884. C2×C3#65927semidirect
889. C5C2×#5593semidirect
925. C3C2×#65927semidirect
931. C2#11756352direct (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×#1202
C2×#918422
C22×#67192
C2×#918282
C2×#918272
C2×#918252
C2×#918242
C2×D4×Dic152
#117563522
C2×#917742
C2×#917722
C2×#917702
C2×#917682
C2×#917672
C2×#659273
C2×#55935