Finite Group Databasebeta

← C2×#11756416 #14480763

Subgroups — C2×#11756416 #14480763

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×#123C211yesmaximal, characteristic, complemented
2C2×#91827C211yesmaximal, characteristic, complemented
3C2×#91826C211yesmaximal, characteristic, complemented
4C2×#91819C211yesmaximal, characteristic, complemented
5C2×C4×#1220C211yesmaximal, characteristic, complemented
6#11756416C2116yesmaximal, direct product factor
7C2×#91787C211yesmaximal, characteristic, complemented
8C2×#91786C211yesmaximal, characteristic, complemented
9C2×#91783C211yesmaximal, characteristic, complemented
10C2×#91782C211yesmaximal, characteristic, complemented
11C2×#91774C211yesmaximal, characteristic, complemented
12C2×#91774C211yesmaximal, characteristic, complemented
13C2×#91773C211yesmaximal, characteristic, complemented
14C2×#91771C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×D15C211yesmaximal, characteristic, complemented
16C2×#91768C211yesmaximal, characteristic, complemented
17C2×#65991—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C23×C3×C4×C5C2211yescharacteristic, complemented
21C22×#1220C2211yescharacteristic
22C22×#1220C2211yescharacteristic
23C22×#1220C2211yescharacteristic
24C22×#1220C2211yescharacteristic, complemented
25C22×D60C2211yescharacteristic
26C22×D60C2211yescharacteristic
27C22×C4×D15C2211yescharacteristic
28C22×C4×D15C2211yescharacteristic
29C22×C4×D15C2211yescharacteristic, complemented
30C22×Dic30C2211yescharacteristic, complemented
31C3×C5×#123C2218yescomplemented
32C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
33C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
34C2×C3×C5×C22⋊C4C2211yescharacteristic
35C2×C3×C5×C22⋊C4C2211yescharacteristic
36C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
37C2×#6719C2211yescharacteristic
38C2×#6719C2211yescharacteristic
39C2×#6719C2211yescharacteristic, complemented
40#91827C2218yescomplemented
41#91826C2218yescomplemented
42#91819C2218yescomplemented
43C4×#1220C2218yescomplemented
44C2×#6714C2211yescharacteristic
45C2×#6714C2211yescharacteristic
46C2×#6714C2211yescharacteristic
47C2×#6714C2211yescharacteristic
48C2×#6714C2211yescharacteristic
49C2×#6714C2211yescharacteristic
50C2×#6714C2211yescharacteristic, complemented
51C2×#6714C2211yescharacteristic, complemented
52C2×C4⋊Dic15C2211yescharacteristic, complemented
53C2×C4⋊Dic15C2211yescharacteristic, complemented
54C2×#6712C2211yescharacteristic, complemented
55C2×#6712C2211yescharacteristic, complemented
56C2×C4×Dic15C2211yescharacteristic, complemented
57C2×C4×Dic15C2211yescharacteristic, complemented
58#91787C2218yescomplemented
59#91786C2218yescomplemented
60#91783C2218yescomplemented
61#91782C2218yescomplemented
62#91774C2218yescomplemented
63#91774C2218yescomplemented
64#91773C2218yescomplemented
65#91771C2218yescomplemented
66C22⋊C4×D15C2218yescomplemented
67#91768C2218yescomplemented
68C2×#5657—51nomaximal, Hall
69C2×C5×#123D311yescharacteristic, complemented
70C2×#4084—31no—
71C2×#4083—31no—
72C2×#4076—31no—
73C2×C4×C22⋊D5—31no—
74#65991—316no—
75C2×#4044—31no—
76C2×#4043—31no—
77C2×#4040—31no—
78C2×#4039—31no—
79C2×#4031—31no—
80C2×#4031—31no—
81C2×#4030—31no—
82C2×#4028—31no—
83C2×D5×C22⋊C4—31no—
84C2×#4025—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×D15—24no—
88C23×D15—42no—
89C23×D15—42no—
90C23×D15C2311yescharacteristic
91C23×D15C2311yescharacteristic
92C23×D15C2311yescharacteristic
93C23×D15C2314yes—
94C2×C3×C5×D4—42no—
95C2×C3×C5×D4C2314yes—
96C22×C3×C4×C5—42no—
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2311yescharacteristic
99C22×C3×C4×C5C2311yescharacteristic
100C22×C3×C4×C5C2311yescharacteristic
101C22×C3×C4×C5C2311yescharacteristic
102C22×C3×C4×C5C2314yescomplemented
103C2×#1220—24no—
104C2×#1220—42no—
105C2×#1220—42no—
106C2×#1220—42no—
107C2×#1220C2314yes—
108C2×#1220C2314yes—
109C2×#1220C2314yes—
110C2×#1220C2314yescomplemented
111C22×Dic15C2311yescharacteristic
112C22×Dic15C2311yescharacteristic
113C22×Dic15C2311yescharacteristic
114C22×Dic15C2311yescharacteristic
115C22×Dic15C2311yescharacteristic
116C2×D60—24no—
117C2×D60—42no—
118C2×D60C2314yes—
119C2×D60C2314yes—
120C2×C4×D15—42no—
121C2×C4×D15—42no—
122C2×C4×D15—42no—
123C2×C4×D15C2314yes—
124C2×C4×D15C2314yes—
125C2×C4×D15C2314yescomplemented
126C2×Dic30—42no—
127C2×Dic30C2314yescomplemented
128C3×C5×C4⋊C4C2314yescomplemented
129C3×C5×C4⋊C4C2314yescomplemented
130C3×C5×C22⋊C4C2314yes—
131C3×C5×C22⋊C4C2314yes—
132C3×C5×C22⋊C4C2314yescomplemented
133#6719C2314yes—
134#6719C2314yes—
135#6719C2314yescomplemented
136#6714C2314yes—
137#6714C2314yes—
138#6714C2314yes—
139#6714C2314yes—
140#6714C2314yes—
141#6714C2314yes—
142#6714C2314yescomplemented
143#6714C2314yescomplemented
144C4⋊Dic15C2314yescomplemented
145C4⋊Dic15C2314yescomplemented
146#6712C2314yescomplemented
147#6712C2314yescomplemented
148C4×Dic15C2314yescomplemented
149C4×Dic15C2314yescomplemented
150C2×C3×#123D511yescharacteristic, complemented
151C2×#938—51no—
152C2×#937—51no—
153C2×#930—51no—
154C2×C4×#67—51no—
155#5657—516no—
156C2×#898—51no—
157C2×#897—51no—
158C2×#894—51no—
159C2×#893—51no—
160C2×#885—51no—
161C2×#885—51no—
162C2×#884—51no—
163C2×#882—51no—
164C2×D3×C22⋊C4—51no—
165C2×#879—51no—
166C24×D5—31no—
167C22×C5×D4C2×D311yescharacteristic
168C23×C4×C5C2×D311yescharacteristic, complemented
169C22×C22⋊D5—31no—
170C22×C22⋊D5—31no—
171C22×C22⋊D5—31no—
172C22×C22⋊D5—31no—
173C22×D20—31no—
174C22×D20—31no—
175C22×C4×D5—31no—
176C22×C4×D5—31no—
177C22×C4×D5—31no—
178C22×Dic10—31no—
179C5×#123C2×D318yescomplemented
180C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
181C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
182C2×C5×C22⋊C4C2×D311yescharacteristic
183C2×C5×C22⋊C4C2×D311yescharacteristic
184C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
185C2×C22⋊Dic5—31no—
186C2×C22⋊Dic5—31no—
187C2×C22⋊Dic5—31no—
188#4084—38no—
189#4083—38no—
190#4076—38no—
191C4×C22⋊D5—38no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685—31no—
199C2×#685—31no—
200C2×C4⋊Dic5—31no—
201C2×C4⋊Dic5—31no—
202C2×#683—31no—
203C2×#683—31no—
204C2×C4×Dic5—31no—
205C2×C4×Dic5—31no—
206#4044—38no—
207#4043—38no—
208#4040—38no—
209#4039—38no—
210#4031—38no—
211#4031—38no—
212#4030—38no—
213#4028—38no—
214D5×C22⋊C4—38no—
215#4025—38no—
216C2×#538—151noSylow
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×C5C2411yescharacteristic
226C22×D15—22no—
227C22×D15—22no—
228C22×D15—22no—
229C22×D15—22no—
230C22×D15—22no—
231C22×D15—22no—
232C22×D15—22no—
233C22×D15—22no—
234C22×D15—28no—
235C22×D15—44no—
236C22×D15—44no—
237C22×D15—416no—
238C22×D15#4114yes—
239C22×D15C2412yes—
240C22×D15C2412yes—
241C22×D15C2412yes—
242C3×C5×D4—44no—
243C2×C3×C4×C5—22no—
244C2×C3×C4×C5—22no—
245C2×C3×C4×C5—22no—
246C2×C3×C4×C5—22no—
247C2×C3×C4×C5—22no—
248C2×C3×C4×C5—44no—
249C2×C3×C4×C5C2412yes—
250C2×C3×C4×C5C2412yes—
251C2×C3×C4×C5C2412yes—
252C2×C3×C4×C5C2412yes—
253C2×C3×C4×C5C2412yes—
254#1220—28no—
255#1220—44no—
256#1220—44no—
257#1220—44no—
258C2×Dic15—22no—
259C2×Dic15—22no—
260C2×Dic15—22no—
261C2×Dic15—22no—
262C2×Dic15—22no—
263C2×Dic15C2412yes—
264C2×Dic15C2412yes—
265C2×Dic15C2412yes—
266C2×Dic15C2412yes—
267C2×Dic15C2412yes—
268D60—28no—
269D60—44no—
270C4×D15—44no—
271C4×D15—44no—
272C4×D15—44no—
273Dic30—44no—
274C24×D3—51no—
275C22×C3×D4C2×D511yescharacteristic
276C23×C3×C4C2×D511yescharacteristic, complemented
277C22×#67—51no—
278C22×#67—51no—
279C22×#67—51no—
280C22×#67—51no—
281C22×D12—51no—
282C22×D12—51no—
283C22×C4×D3—51no—
284C22×C4×D3—51no—
285C22×C4×D3—51no—
286C22×Dic6—51no—
287C3×#123C2×D518yescomplemented
288C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
289C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
290C2×C3×C22⋊C4C2×D511yescharacteristic
291C2×C3×C22⋊C4C2×D511yescharacteristic
292C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
293C2×#217—51no—
294C2×#217—51no—
295C2×#217—51no—
296#938—58no—
297#937—58no—
298#930—58no—
299C4×#67—58no—
300C2×(C2×D3)⋊C4—51no—
301C2×(C2×D3)⋊C4—51no—
302C2×(C2×D3)⋊C4—51no—
303C2×(C2×D3)⋊C4—51no—
304C2×(C2×D3)⋊C4—51no—
305C2×(C2×D3)⋊C4—51no—
306C2×(C2×D3)⋊C4—51no—
307C2×(C2×D3)⋊C4—51no—
308C2×C4⋊Dic3—51no—
309C2×C4⋊Dic3—51no—
310C2×Dic3⋊C4—51no—
311C2×Dic3⋊C4—51no—
312C2×C4×Dic3—51no—
313C2×C4×Dic3—51no—
314#898—58no—
315#897—58no—
316#894—58no—
317#893—58no—
318#885—58no—
319#885—58no—
320#884—58no—
321#882—58no—
322D3×C22⋊C4—58no—
323#879—58no—
324C24×C5C22×D311yescharacteristic
325C24×C5C22×D311yescharacteristic
326C23×D5—31no—
327C23×D5—31no—
328C23×D5—31no—
329C23×D5—34no—
330C23×D5—64no—
331C23×D5—122no—
332C23×D5—122no—
333C2×C5×D4—42no—
334C2×C5×D4C22×D314yes—
335C22×C4×C5—42no—
336C22×C4×C5C22×D311yescharacteristic
337C22×C4×C5C22×D311yescharacteristic
338C22×C4×C5C22×D311yescharacteristic
339C22×C4×C5C22×D311yescharacteristic
340C22×C4×C5C22×D311yescharacteristic
341C22×C4×C5C22×D314yescomplemented
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—
355C2×D20—34no—
356C2×D20—34no—
357C2×D20—64no—
358C2×D20—122no—
359C2×C4×D5—34no—
360C2×C4×D5—34no—
361C2×C4×D5—34no—
362C2×C4×D5—122no—
363C2×C4×D5—122no—
364C2×C4×D5—122no—
365C2×Dic10—34no—
366C2×Dic10—122no—
367C5×C4⋊C4C22×D314yescomplemented
368C5×C4⋊C4C22×D314yescomplemented
369C5×C22⋊C4C22×D314yes—
370C5×C22⋊C4C22×D314yes—
371C5×C22⋊C4C22×D314yescomplemented
372C22⋊Dic5—34no—
373C22⋊Dic5—34no—
374C22⋊Dic5—34no—
375#685—34no—
376#685—34no—
377#685—34no—
378#685—34no—
379#685—34no—
380#685—34no—
381#685—34no—
382#685—34no—
383C4⋊Dic5—34no—
384C4⋊Dic5—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×#123D1511yescharacteristic, complemented
396C2×C22⋊Q8—151no—
397C2×#121—151no—
398C2×#121—151no—
399C2×#121—151no—
400C2×#120—151no—
401C2×#120—151no—
402C2×C4×D4—151no—
403C2×C4×D4—151no—
404C22×C22⋊C4—151no—
405C22×C3×C5—22no—
406C22×C3×C5—22no—
407C22×C3×C5—22no—
408C22×C3×C5—22no—
409C22×C3×C5—22no—
410C22×C3×C5—22no—
411C22×C3×C5—44no—
412C22×C3×C5—44no—
413C22×C3×C5C2×#4112yes—
414C22×C3×C5H(5,𝔽2)12yes—
415C22×C3×C5H(5,𝔽2)12yes—
416C22×C3×C5C2511yescharacteristic
417C2×D15—28no—
418C2×D15—22no—
419C2×D15—22no—
420C2×D15—22no—
421C2×D15—22no—
422C2×D15—22no—
423C2×D15—22no—
424C2×D15—22no—
425C2×D15—22no—
426C2×D15—416no—
427C2×D15—44no—
428C2×D15—44no—
429C2×D15C2×#4114yes—
430C3×C4×C5—22no—
431C3×C4×C5—22no—
432C3×C4×C5—22no—
433C3×C4×C5—22no—
434C3×C4×C5—22no—
435Dic15—22no—
436Dic15—22no—
437Dic15—22no—
438Dic15—22no—
439Dic15—22no—
440C24×C3C22×D511yescharacteristic
441C24×C3C22×D511yescharacteristic
442C23×D3—51no—
443C23×D3—51no—
444C23×D3—51no—
445C23×D3—54no—
446C23×D3—104no—
447C23×D3—202no—
448C23×D3—202no—
449C2×C3×D4—42no—
450C2×C3×D4C22×D514yes—
451C22×C3×C4—42no—
452C22×C3×C4C22×D511yescharacteristic
453C22×C3×C4C22×D511yescharacteristic
454C22×C3×C4C22×D511yescharacteristic
455C22×C3×C4C22×D511yescharacteristic
456C22×C3×C4C22×D511yescharacteristic
457C22×C3×C4C22×D514yescomplemented
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—
471C2×D12—54no—
472C2×D12—54no—
473C2×D12—104no—
474C2×D12—202no—
475C2×C4×D3—54no—
476C2×C4×D3—54no—
477C2×C4×D3—54no—
478C2×C4×D3—202no—
479C2×C4×D3—202no—
480C2×C4×D3—202no—
481C2×Dic6—54no—
482C2×Dic6—202no—
483C3×C4⋊C4C22×D514yescomplemented
484C3×C4⋊C4C22×D514yescomplemented
485C3×C22⋊C4C22×D514yes—
486C3×C22⋊C4C22×D514yes—
487C3×C22⋊C4C22×D514yescomplemented
488#217—54no—
489#217—54no—
490#217—54no—
491(C2×D3)⋊C4—54no—
492(C2×D3)⋊C4—54no—
493(C2×D3)⋊C4—54no—
494(C2×D3)⋊C4—54no—
495(C2×D3)⋊C4—54no—
496(C2×D3)⋊C4—54no—
497(C2×D3)⋊C4—54no—
498(C2×D3)⋊C4—54no—
499C4⋊Dic3—54no—
500C4⋊Dic3—54no—
501Dic3⋊C4—54no—
502Dic3⋊C4—54no—
503C4×Dic3—54no—
504C4×Dic3—54no—
505C23×C5—22no—
506C23×C5—22no—
507C23×C5—22no—
508C23×C5—22no—
509C23×C5—22no—
510C23×C5—22no—
511C23×C5C23×D312yes—
512C23×C5C23×D312yes—
513C23×C5C23×D311yescharacteristic
514C22×D5—34no—
515C22×D5—32no—
516C22×D5—32no—
517C22×D5—32no—
518C22×D5—68no—
519C22×D5—62no—
520C22×D5—62no—
521C22×D5—62no—
522C22×D5—62no—
523C22×D5—62no—
524C22×D5—62no—
525C22×D5—62no—
526C22×D5—62no—
527C22×D5—124no—
528C22×D5—124no—
529C22×D5—1216no—
530C5×D4—44no—
531C2×C4×C5—22no—
532C2×C4×C5—22no—
533C2×C4×C5—22no—
534C2×C4×C5—22no—
535C2×C4×C5—22no—
536C2×C4×C5—44no—
537C2×C4×C5C23×D312yes—
538C2×C4×C5C23×D312yes—
539C2×C4×C5C23×D312yes—
540C2×C4×C5C23×D312yes—
541C2×C4×C5C23×D312yes—
542C22⋊D5—68no—
543C22⋊D5—124no—
544C22⋊D5—124no—
545C22⋊D5—124no—
546C2×Dic5—32no—
547C2×Dic5—32no—
548C2×Dic5—32no—
549C2×Dic5—32no—
550C2×Dic5—32no—
551C2×Dic5—62no—
552C2×Dic5—62no—
553C2×Dic5—62no—
554C2×Dic5—62no—
555C2×Dic5—62no—
556D20—68no—
557D20—124no—
558C4×D5—124no—
559C4×D5—124no—
560C4×D5—124no—
561Dic10—124no—
562C25—151no—
563C22×Q8—151no—
564C22×D4—151no—
565C22×D4—151no—
566C22×D4—151no—
567C22×D4—151no—
568C22×D4—151no—
569C22×D4—151no—
570C22×D4C2×D1511yescharacteristic
571C23×C4—151no—
572C23×C4—151no—
573C23×C4—151no—
574C23×C4C2×D1511yescharacteristic, complemented
575#126—158no—
576#126—158no—
577#124—158no—
578#124—158no—
579#123—158no—
580#123C2×D1518yescomplemented
581C22⋊Q8—158no—
582#121—158no—
583#121—158no—
584#121—158no—
585#120—158no—
586#120—158no—
587C4×D4—158no—
588C4×D4—158no—
589C2×C4⋊C4—151no—
590C2×C4⋊C4—151no—
591C2×C4⋊C4—151no—
592C2×C4⋊C4—151no—
593C2×C4⋊C4C2×D1511yescharacteristic, complemented
594C2×C4⋊C4C2×D1511yescharacteristic, complemented
595C2×C22⋊C4—151no—
596C2×C22⋊C4—151no—
597C2×C22⋊C4—151no—
598C2×C22⋊C4—151no—
599C2×C22⋊C4—151no—
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—158no—
607C2×C22⋊C4C2×D1511yescharacteristic
608C2×C22⋊C4C2×D1511yescharacteristic
609C2×C22⋊C4C2×D1511yescharacteristic, complemented
610C2×C42—151no—
611C2×C42—151no—
612C2×C3×C5—42no—
613C2×C3×C5—42no—
614C2×C3×C5#53814yescomplemented
615C2×C3×C5C22×#4111yescharacteristic
616C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
617C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
618D15—24no—
619D15—42no—
620D15—42no—
621C23×C3—22no—
622C23×C3—22no—
623C23×C3—22no—
624C23×C3—22no—
625C23×C3—22no—
626C23×C3—22no—
627C23×C3C23×D512yes—
628C23×C3C23×D512yes—
629C23×C3C23×D511yescharacteristic
630C22×D3—54no—
631C22×D3—52no—
632C22×D3—52no—
633C22×D3—52no—
634C22×D3—108no—
635C22×D3—102no—
636C22×D3—102no—
637C22×D3—102no—
638C22×D3—102no—
639C22×D3—102no—
640C22×D3—102no—
641C22×D3—102no—
642C22×D3—102no—
643C22×D3—204no—
644C22×D3—204no—
645C22×D3—2016no—
646C3×D4—44no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—44no—
653C2×C3×C4C23×D512yes—
654C2×C3×C4C23×D512yes—
655C2×C3×C4C23×D512yes—
656C2×C3×C4C23×D512yes—
657C2×C3×C4C23×D512yes—
658#67—108no—
659#67—204no—
660#67—204no—
661#67—204no—
662C2×Dic3—52no—
663C2×Dic3—52no—
664C2×Dic3—52no—
665C2×Dic3—52no—
666C2×Dic3—52no—
667C2×Dic3—102no—
668C2×Dic3—102no—
669C2×Dic3—102no—
670C2×Dic3—102no—
671C2×Dic3—102no—
672D12—108no—
673D12—204no—
674C4×D3—204no—
675C4×D3—204no—
676C4×D3—204no—
677Dic6—204no—
678C22×C5—22no—
679C22×C5—22no—
680C22×C5—22no—
681C22×C5—22no—
682C22×C5—22no—
683C22×C5—22no—
684C22×C5—44no—
685C22×C5—44no—
686C22×C5#100412yes—
687C22×C5D3×#4112yes—
688C22×C5#100912yes—
689C22×C5C24×D311yescharacteristic
690C2×D5—34no—
691C2×D5—68no—
692C2×D5—62no—
693C2×D5—62no—
694C2×D5—62no—
695C2×D5—62no—
696C2×D5—62no—
697C2×D5—62no—
698C2×D5—62no—
699C2×D5—62no—
700C2×D5—1216no—
701C2×D5—124no—
702C2×D5—124no—
703C4×C5—22no—
704C4×C5—22no—
705C4×C5—22no—
706C4×C5—22no—
707C4×C5—22no—
708Dic5—62no—
709Dic5—62no—
710Dic5—62no—
711Dic5—62no—
712Dic5—62no—
713C24—151no—
714C24—151no—
715C24—151no—
716C24—154no—
717C24—304no—
718C24—602no—
719C24—602no—
720C24C22×D1511yescharacteristic
721C24C22×D1511yescharacteristic
722C2×Q8—154no—
723C2×Q8—602no—
724C2×D4—42no—
725C2×D4—154no—
726C2×D4—154no—
727C2×D4—154no—
728C2×D4—154no—
729C2×D4—154no—
730C2×D4—154no—
731C2×D4—304no—
732C2×D4—304no—
733C2×D4—602no—
734C2×D4—602no—
735C2×D4—602no—
736C2×D4—602no—
737C2×D4C22×D1514yes—
738C22×C4—42no—
739C22×C4—151no—
740C22×C4—151no—
741C22×C4—151no—
742C22×C4—151no—
743C22×C4—151no—
744C22×C4—154no—
745C22×C4—154no—
746C22×C4—154no—
747C22×C4—602no—
748C22×C4—602no—
749C22×C4—602no—
750C22×C4C22×D1511yescharacteristic
751C22×C4C22×D1511yescharacteristic
752C22×C4C22×D1511yescharacteristic
753C22×C4C22×D1511yescharacteristic
754C22×C4C22×D1511yescharacteristic
755C22×C4C22×D1514yescomplemented
756C4⋊C4—154no—
757C4⋊C4—154no—
758C4⋊C4—154no—
759C4⋊C4—154no—
760C4⋊C4C22×D1514yescomplemented
761C4⋊C4C22×D1514yescomplemented
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×D1514yescomplemented
776C42—154no—
777C42—154no—
778C3×C5C2×#53811yescharacteristic, complemented, Hall
779C22×C3—22no—
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—44no—
786C22×C3—44no—
787C22×C3#414412yes—
788C22×C3D5×#4112yes—
789C22×C3#414912yes—
790C22×C3C24×D511yescharacteristic
791C2×D3—54no—
792C2×D3—108no—
793C2×D3—102no—
794C2×D3—102no—
795C2×D3—102no—
796C2×D3—102no—
797C2×D3—102no—
798C2×D3—102no—
799C2×D3—102no—
800C2×D3—102no—
801C2×D3—2016no—
802C2×D3—204no—
803C2×D3—204no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—22no—
809Dic3—102no—
810Dic3—102no—
811Dic3—102no—
812Dic3—102no—
813Dic3—102no—
814C2×C5—42no—
815C2×C5—42no—
816C2×C5#565714yescomplemented
817C2×C5C2×#100411yescharacteristic
818C2×C5C2×D3×#4111yescharacteristic
819C2×C5C2×#100911yescharacteristic
820D5—64no—
821D5—122no—
822D5—122no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—154no—
830C23—152no—
831C23—152no—
832C23—152no—
833C23—308no—
834C23—302no—
835C23—302no—
836C23—302no—
837C23—302no—
838C23—302no—
839C23—302no—
840C23—302no—
841C23—302no—
842C23—604no—
843C23—604no—
844C23—6016no—
845C23C23×D1512yes—
846C23C23×D1512yes—
847C23C23×D1511yescharacteristic
848Q8—604no—
849D4—44no—
850D4—308no—
851D4—308no—
852D4—604no—
853D4—604no—
854D4—604no—
855D4—604no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—44no—
862C2×C4—152no—
863C2×C4—152no—
864C2×C4—152no—
865C2×C4—152no—
866C2×C4—152no—
867C2×C4—302no—
868C2×C4—302no—
869C2×C4—302no—
870C2×C4—302no—
871C2×C4—302no—
872C2×C4—604no—
873C2×C4—604no—
874C2×C4—604no—
875C2×C4C23×D1512yes—
876C2×C4C23×D1512yes—
877C2×C4C23×D1512yes—
878C2×C4C23×D1512yes—
879C2×C4C23×D1512yes—
880C2×C3—42no—
881C2×C3—42no—
882C2×C3#6599114yescomplemented
883C2×C3C2×#414411yescharacteristic
884C2×C3C2×D5×#4111yescharacteristic
885C2×C3C2×#414911yescharacteristic
886D3—104no—
887D3—202no—
888D3—202no—
889C5C2×#565711yescharacteristic, complemented, Sylow
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—44no—
897C22—44no—
898C22—154no—
899C22—302no—
900C22—302no—
901C22—308no—
902C22—302no—
903C22—302no—
904C22—302no—
905C22—302no—
906C22—302no—
907C22—302no—
908C22—6016no—
909C22—604no—
910C22—604no—
911C22#9209512yes—
912C22#41×D1512yes—
913C22#9210012yes—
914C22C24×D1511yescharacteristic
915C4—22no—
916C4—22no—
917C4—22no—
918C4—22no—
919C4—22no—
920C4—302no—
921C4—302no—
922C4—302no—
923C4—302no—
924C4—302no—
925C3C2×#6599111yescharacteristic, complemented, Sylow
926C2—42no—
927C2—42no—
928C2—304no—
929C2—602no—
930C2—602no—
931C2#1175641614yesdirect product factor
932C2C2×#9209511yescharacteristic
933C2C2×#41×D1511yescharacteristic
934C2C2×#9210011yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#123C2
socleC23×C3×C5C24
hypercenterC2×#123D15
hypocenterC3×C5C2×#538
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#123C2semidirect
2. C2×#91827C2semidirect
3. C2×#91826C2semidirect
4. C2×#91819C2semidirect
5. C2×C4×#1220C2semidirect
6. #11756416C2direct (N × H)
7. C2×#91787C2semidirect
8. C2×#91786C2semidirect
9. C2×#91783C2semidirect
10. C2×#91782C2semidirect
11. C2×#91774C2semidirect
12. C2×#91774C2semidirect
13. C2×#91773C2semidirect
14. C2×#91771C2semidirect
15. C2×C22⋊C4×D15C2semidirect
16. C2×#91768C2semidirect
20. C23×C3×C4×C5C22semidirect
24. C22×#1220C22semidirect
29. C22×C4×D15C22semidirect
30. C22×Dic30C22semidirect
31. C3×C5×#123C22semidirect
32. C2×C3×C5×C4⋊C4C22semidirect
33. C2×C3×C5×C4⋊C4C22semidirect
36. C2×C3×C5×C22⋊C4C22semidirect
39. C2×#6719C22semidirect
40. #91827C22semidirect
41. #91826C22semidirect
42. #91819C22semidirect
43. C4×#1220C22semidirect
50. C2×#6714C22semidirect
51. C2×#6714C22semidirect
52. C2×C4⋊Dic15C22semidirect
53. C2×C4⋊Dic15C22semidirect
54. C2×#6712C22semidirect
55. C2×#6712C22semidirect
56. C2×C4×Dic15C22semidirect
57. C2×C4×Dic15C22semidirect
58. #91787C22semidirect
59. #91786C22semidirect
60. #91783C22semidirect
61. #91782C22semidirect
62. #91774C22semidirect
63. #91774C22semidirect
64. #91773C22semidirect
65. #91771C22semidirect
66. C22⋊C4×D15C22semidirect
67. #91768C22semidirect
69. C2×C5×#123D3semidirect
102. C22×C3×C4×C5C23semidirect
110. C2×#1220C23semidirect
125. C2×C4×D15C23semidirect
127. C2×Dic30C23semidirect
128. C3×C5×C4⋊C4C23semidirect
129. C3×C5×C4⋊C4C23semidirect
132. C3×C5×C22⋊C4C23semidirect
135. #6719C23semidirect
142. #6714C23semidirect
143. #6714C23semidirect
144. C4⋊Dic15C23semidirect
145. C4⋊Dic15C23semidirect
146. #6712C23semidirect
147. #6712C23semidirect
148. C4×Dic15C23semidirect
149. C4×Dic15C23semidirect
150. C2×C3×#123D5semidirect
168. C23×C4×C5C2×D3semidirect
179. C5×#123C2×D3semidirect
180. C2×C5×C4⋊C4C2×D3semidirect
181. C2×C5×C4⋊C4C2×D3semidirect
184. C2×C5×C22⋊C4C2×D3semidirect
276. C23×C3×C4C2×D5semidirect
287. C3×#123C2×D5semidirect
288. C2×C3×C4⋊C4C2×D5semidirect
289. C2×C3×C4⋊C4C2×D5semidirect
292. C2×C3×C22⋊C4C2×D5semidirect
341. C22×C4×C5C22×D3semidirect
367. C5×C4⋊C4C22×D3semidirect
368. C5×C4⋊C4C22×D3semidirect
371. C5×C22⋊C4C22×D3semidirect
395. C2×#123D15semidirect
457. C22×C3×C4C22×D5semidirect
483. C3×C4⋊C4C22×D5semidirect
484. C3×C4⋊C4C22×D5semidirect
487. C3×C22⋊C4C22×D5semidirect
574. C23×C4C2×D15semidirect
580. #123C2×D15semidirect
593. C2×C4⋊C4C2×D15semidirect
594. C2×C4⋊C4C2×D15semidirect
609. C2×C22⋊C4C2×D15semidirect
614. C2×C3×C5#538semidirect
755. C22×C4C22×D15semidirect
760. C4⋊C4C22×D15semidirect
761. C4⋊C4C22×D15semidirect
775. C22⋊C4C22×D15semidirect
778. C3×C5C2×#538semidirect
816. C2×C5#5657semidirect
882. C2×C3#65991semidirect
889. C5C2×#5657semidirect
925. C3C2×#65991semidirect
931. C2#11756416direct (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×#1232
C2×#918272
C2×#918262
C2×#918192
C2×C4×#12202
#117564162
C2×#917872
C2×#917862
C2×#917832
C2×#917822
C2×#917742
C2×#917732
C2×#917712
C2×C22⋊C4×D152
C2×#917682
C2×#659913
C2×#56575