Finite Group Databasebeta

← C2×#11754593 #14480869

Subgroups — C2×#11754593 #14480869

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×C4×#1220C211yesmaximal, characteristic, complemented
2C2×C4×C5×#67C211yesmaximal, characteristic, complemented
3C22×C3×#685C211yesmaximal, characteristic, complemented
4C2×#91574C211yesmaximal, characteristic, complemented
5C2×#91566C211yesmaximal, characteristic, complemented
6C2×#91564C211yesmaximal, characteristic, complemented
7C2×#91563C211yesmaximal, characteristic, complemented
8#11754593C2116yesmaximal, direct product factor
9C2×#91464C211yesmaximal, characteristic, complemented
10C2×#91461C211yesmaximal, characteristic, complemented
11C2×#91454C211yesmaximal, characteristic, complemented
12C2×#91452C211yesmaximal, characteristic, complemented
13C2×#91366C211yesmaximal, characteristic, complemented
14C2×#91363C211yesmaximal, characteristic, complemented
15C2×#91354C211yesmaximal, characteristic, complemented
16C2×#91353C211yesmaximal, characteristic, complemented
17C2×#65894—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic, complemented
22C22×C5×#67C2211yescharacteristic
23C22×C4×C5×D3C2211yescharacteristic, complemented
24C23×C3×Dic5C2211yescharacteristic
25C22×#1204C2211yescharacteristic, complemented
26C22×#1203C2211yescharacteristic, complemented
27C22×#1202C2211yescharacteristic
28C22×#1202C2211yescharacteristic
29C22×#1201C2211yescharacteristic
30C22×#1201C2211yescharacteristic
31C2×#6719C2211yescharacteristic
32C4×#1220C2218yescomplemented
33C2×#6714C2211yescharacteristic, complemented
34C2×#6712C2211yescharacteristic, complemented
35C2×C4×Dic15C2211yescharacteristic, complemented
36C2×C5×#217C2211yescharacteristic
37C4×C5×#67C2218yescomplemented
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
40C2×C4×C5×Dic3C2211yescharacteristic, complemented
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic
43C2×C3×#685C2211yescharacteristic
44C2×C3×#685C2211yescharacteristic
45C2×C3×#685C2218yescomplemented
46#91574C2218yescomplemented
47#91566C2218yescomplemented
48#91564C2218yescomplemented
49#91563C2218yescomplemented
50C2×Dic3⋊Dic5C2211yescharacteristic, complemented
51C2×#6669C2211yescharacteristic, complemented
52C2×#6668C2211yescharacteristic, complemented
53C2×#6668C2211yescharacteristic, complemented
54C2×#6667C2211yescharacteristic, complemented
55C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
56C2×#6665C2211yescharacteristic
57C2×#6665C2211yescharacteristic
58C2×#6665C2211yescharacteristic
59C2×#6665C2211yescharacteristic
60#91464C2218yescomplemented
61#91461C2218yescomplemented
62#91454C2218yescomplemented
63#91452C2218yescomplemented
64#91366C2218yescomplemented
65#91363C2218yescomplemented
66#91354C2218yescomplemented
67#91353C2218yescomplemented
68C2×#5494—51nomaximal, Hall
69C2×C4×C5×D4—31no—
70C2×#4085—31no—
71C2×#4083—31no—
72C2×#4076—31no—
73C2×#4075—31no—
74C2×C4×C22⋊D5—31no—
75C22×#685D311yescharacteristic, complemented
76#65894—316no—
77C2×#4044—31no—
78C2×#4040—31no—
79C2×#4031—31no—
80C2×#4030—31no—
81C2×#4028—31no—
82C2×#4024—31no—
83C2×#4022—31no—
84C2×#4021—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C23×C3×D5—24no—
89C23×C3×D5—42no—
90C23×C3×D5—42no—
91C23×C3×D5C2311yescharacteristic
92C23×C3×D5C2311yescharacteristic
93C23×C3×D5C2314yes—
94C22×C3×C4×C5—42no—
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2314yes—
98C2×#1220—24no—
99C2×#1220C2314yes—
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C22×Dic15C2311yescharacteristic
103C2×C4×D15—42no—
104C2×C4×D15C2314yescomplemented
105C2×C5×#67—24no—
106C2×C5×#67C2314yes—
107C22×C5×Dic3C2311yescharacteristic
108C22×C5×Dic3C2311yescharacteristic
109C22×C5×Dic3C2311yescharacteristic
110C2×C4×C5×D3—42no—
111C2×C4×C5×D3C2314yescomplemented
112C22×C3×Dic5—42no—
113C22×C3×Dic5C2311yescharacteristic
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2314yes—
116C2×#1204—42no—
117C2×#1204C2314yescomplemented
118C2×#1203—42no—
119C2×#1203C2314yescomplemented
120C2×#1202—42no—
121C2×#1202—42no—
122C2×#1202C2314yes—
123C2×#1202C2314yes—
124C2×#1201—42no—
125C2×#1201—42no—
126C2×#1201C2314yes—
127C2×#1201C2314yes—
128#6719C2314yes—
129#6714C2314yescomplemented
130#6712C2314yescomplemented
131C4×Dic15C2314yescomplemented
132C5×#217C2314yes—
133C5×(C2×D3)⋊C4C2314yescomplemented
134C5×Dic3⋊C4C2314yescomplemented
135C4×C5×Dic3C2314yescomplemented
136C3×#685C2314yes—
137C3×#685C2314yes—
138C3×#685C2314yes—
139C3×#685C2314yes—
140Dic3⋊Dic5C2314yescomplemented
141#6669C2314yescomplemented
142#6668C2314yescomplemented
143#6668C2314yescomplemented
144#6667C2314yescomplemented
145(C2×D3)⋊Dic5C2314yescomplemented
146#6665C2314yes—
147#6665C2314yes—
148#6665C2314yes—
149#6665C2314yes—
150C22×C3×C22⋊C4—51no—
151C2×#953—51no—
152C2×#953—51no—
153C2×#930—51no—
154C2×C4×#67—51no—
155C2×C4×#67D511yescharacteristic, complemented
156C2×#924—51no—
157#5494—516no—
158C2×#885—51no—
159C2×#885—51no—
160C2×#884—51no—
161C2×#884—51no—
162C2×#883—51no—
163C2×#883—51no—
164C2×#879—51no—
165C2×#879—51no—
166C24×D5C2×D311yescharacteristic
167C22×C5×D4—31no—
168C23×C4×C5—31no—
169C23×C4×C5C2×D311yescharacteristic
170C22×C22⋊D5—31no—
171C22×C22⋊D5—31no—
172C22×C22⋊D5—31no—
173C22×C22⋊D5—31no—
174C23×Dic5C2×D311yescharacteristic
175C22×D20—31no—
176C22×D20—31no—
177C22×C4×D5—31no—
178C22×Dic10—31no—
179C4×C5×D4—38no—
180C2×C5×C4⋊C4—31no—
181C2×C5×C22⋊C4—31no—
182C2×C5×C22⋊C4—31no—
183C2×C42×C5—31no—
184C2×C22⋊Dic5—31no—
185C2×C22⋊Dic5—31no—
186#4085—38no—
187#4083—38no—
188#4076—38no—
189#4075—38no—
190C4×C22⋊D5—38no—
191C2×#685—31no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685C2×D311yescharacteristic
198C2×#685C2×D311yescharacteristic
199C2×#685C2×D311yescharacteristic
200C2×#685C2×D311yescharacteristic
201C2×#685C2×D318yescomplemented
202C2×C4⋊Dic5—31no—
203C2×#683—31no—
204C2×#683—31no—
205C2×#683—31no—
206C2×#683—31no—
207C2×C4×Dic5—31no—
208#4044—38no—
209#4040—38no—
210#4031—38no—
211#4030—38no—
212#4028—38no—
213#4024—38no—
214#4022—38no—
215#4021—38no—
216C2×#538—151noSylow
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5#4114yes—
220C23×C3×C5C2412yes—
221C23×C3×C5C2411yescharacteristic
222C22×D15—22no—
223C22×D15—22no—
224C22×D15—22no—
225C22×D15C2412yes—
226C22×C5×D3—22no—
227C22×C5×D3—22no—
228C22×C5×D3—22no—
229C22×C5×D3C2412yes—
230C22×C3×D5—28no—
231C22×C3×D5—22no—
232C22×C3×D5—22no—
233C22×C3×D5—22no—
234C22×C3×D5—22no—
235C22×C3×D5—22no—
236C22×C3×D5—22no—
237C22×C3×D5—44no—
238C22×C3×D5—44no—
239C22×C3×D5—416no—
240C22×C3×D5C2412yes—
241C22×C3×D5C2412yes—
242C2×C3×C4×C5—22no—
243C2×C3×C4×C5—22no—
244C2×C3×C4×C5—44no—
245C2×C3×C4×C5C2412yes—
246C2×C3×C4×C5C2412yes—
247#1220—28no—
248C2×Dic15—22no—
249C2×Dic15—22no—
250C2×Dic15—22no—
251C2×Dic15C2412yes—
252C2×Dic15C2412yes—
253C2×Dic15C2412yes—
254C4×D15—44no—
255C5×#67—28no—
256C2×C5×Dic3—22no—
257C2×C5×Dic3—22no—
258C2×C5×Dic3—22no—
259C2×C5×Dic3C2412yes—
260C2×C5×Dic3C2412yes—
261C2×C5×Dic3C2412yes—
262C4×C5×D3—44no—
263C2×C3×Dic5—22no—
264C2×C3×Dic5—22no—
265C2×C3×Dic5—44no—
266C2×C3×Dic5C2412yes—
267C2×C3×Dic5C2412yes—
268#1204—44no—
269#1203—44no—
270#1202—44no—
271#1202—44no—
272#1201—44no—
273#1201—44no—
274C25×C3—51no—
275C23×C3×C4—51no—
276C23×C3×C4C2×D511yescharacteristic
277C22×#67—51no—
278C22×#67—51no—
279C22×#67—51no—
280C22×#67—51no—
281C22×#67—51no—
282C22×#67C2×D511yescharacteristic
283C22×D12—51no—
284C22×C4×D3—51no—
285C22×C4×D3C2×D511yescharacteristic, complemented
286C22×Dic6—51no—
287C2×C3×C22⋊C4—51no—
288C2×C3×C22⋊C4—51no—
289C2×C3×C22⋊C4—51no—
290C2×C3×C22⋊C4—51no—
291C2×C3×C22⋊C4—58no—
292#953—58no—
293#953—58no—
294C2×#217—51no—
295C2×#217—51no—
296C2×#217—51no—
297C2×#217—51no—
298C2×#217—51no—
299C2×#217C2×D511yescharacteristic
300#930—58no—
301C4×#67—58no—
302C4×#67C2×D518yescomplemented
303C2×(C2×D3)⋊C4—51no—
304C2×(C2×D3)⋊C4—51no—
305C2×(C2×D3)⋊C4—51no—
306C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
307C2×C4⋊Dic3—51no—
308C2×C4⋊Dic3—51no—
309#924—58no—
310C2×Dic3⋊C4—51no—
311C2×Dic3⋊C4—51no—
312C2×Dic3⋊C4—51no—
313C2×Dic3⋊C4C2×D511yescharacteristic, complemented
314C2×C4×Dic3—51no—
315C2×C4×Dic3C2×D511yescharacteristic, complemented
316#885—58no—
317#885—58no—
318#884—58no—
319#884—58no—
320#883—58no—
321#883—58no—
322#879—58no—
323#879—58no—
324C24×C5—31no—
325C24×C5C22×D311yescharacteristic
326C23×D5—24no—
327C23×D5—31no—
328C23×D5—42no—
329C23×D5—42no—
330C23×D5C22×D311yescharacteristic
331C23×D5C22×D311yescharacteristic
332C23×D5C22×D314yes—
333C2×C5×D4—34no—
334C2×C5×D4—64no—
335C22×C4×C5—31no—
336C22×C4×C5—31no—
337C22×C4×C5—31no—
338C22×C4×C5—34no—
339C22×C4×C5—42no—
340C22×C4×C5—122no—
341C22×C4×C5C22×D311yescharacteristic
342C22×C4×C5C22×D311yescharacteristic
343C22×C4×C5C22×D314yes—
344C2×C22⋊D5—34no—
345C2×C22⋊D5—34no—
346C2×C22⋊D5—34no—
347C2×C22⋊D5—34no—
348C2×C22⋊D5—64no—
349C2×C22⋊D5—122no—
350C2×C22⋊D5—122no—
351C2×C22⋊D5—122no—
352C22×Dic5—31no—
353C22×Dic5—31no—
354C22×Dic5—31no—
355C22×Dic5—42no—
356C22×Dic5C22×D311yescharacteristic
357C22×Dic5C22×D311yescharacteristic
358C22×Dic5C22×D314yes—
359C2×D20—34no—
360C2×D20—34no—
361C2×D20—122no—
362C2×D20—122no—
363C2×C4×D5—34no—
364C2×C4×D5—122no—
365C2×Dic10—34no—
366C2×Dic10—122no—
367C5×C4⋊C4—34no—
368C5×C22⋊C4—34no—
369C5×C22⋊C4—34no—
370C42×C5—34no—
371C22⋊Dic5—34no—
372C22⋊Dic5—34no—
373#685—34no—
374#685—34no—
375#685—34no—
376#685—34no—
377#685—34no—
378#685—34no—
379#685C22×D314yes—
380#685C22×D314yes—
381#685C22×D314yes—
382#685C22×D314yes—
383C4⋊Dic5—34no—
384#683—34no—
385#683—34no—
386#683—34no—
387#683—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×#120—151no—
402C2×C4×D4—31no—
403C2×C4×D4—151no—
404C22×C22⋊C4—51no—
405C22×C3×C5—28no—
406C22×C3×C5—22no—
407C22×C3×C5—22no—
408C22×C3×C5C2×#4114yes—
409C22×C3×C5C2×#4112yes—
410C22×C3×C5H(5,𝔽2)12yes—
411C22×C3×C5H(5,𝔽2)12yes—
412C22×C3×C5C2511yescharacteristic
413C2×D15—22no—
414C2×D15—22no—
415C2×D15—22no—
416C2×D15—44no—
417C2×C5×D3—22no—
418C2×C5×D3—22no—
419C2×C5×D3—22no—
420C2×C5×D3—44no—
421C2×C3×D5—22no—
422C2×C3×D5—22no—
423C2×C3×D5—22no—
424C2×C3×D5—22no—
425C2×C3×D5—22no—
426C2×C3×D5—22no—
427C2×C3×D5—416no—
428C2×C3×D5—44no—
429C2×C3×D5—44no—
430C3×C4×C5—22no—
431C3×C4×C5—22no—
432Dic15—22no—
433Dic15—22no—
434Dic15—22no—
435C3×Dic5—22no—
436C3×Dic5—22no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—22no—
440C24×C3—51no—
441C24×C3—51no—
442C24×C3—54no—
443C24×C3—104no—
444C24×C3—202no—
445C24×C3—202no—
446C24×C3C22×D511yescharacteristic
447C23×D3—51no—
448C23×D3C22×D511yescharacteristic
449C22×C3×C4—42no—
450C22×C3×C4—51no—
451C22×C3×C4—51no—
452C22×C3×C4—54no—
453C22×C3×C4—202no—
454C22×C3×C4C22×D511yescharacteristic
455C22×C3×C4C22×D511yescharacteristic
456C22×C3×C4C22×D514yes—
457C2×#67—24no—
458C2×#67—54no—
459C2×#67—54no—
460C2×#67—54no—
461C2×#67—54no—
462C2×#67—54no—
463C2×#67—104no—
464C2×#67—202no—
465C2×#67—202no—
466C2×#67—202no—
467C2×#67—202no—
468C2×#67C22×D514yes—
469C22×Dic3—51no—
470C22×Dic3—51no—
471C22×Dic3—51no—
472C22×Dic3C22×D511yescharacteristic
473C22×Dic3C22×D511yescharacteristic
474C22×Dic3C22×D511yescharacteristic
475C2×D12—54no—
476C2×D12—202no—
477C2×C4×D3—42no—
478C2×C4×D3—54no—
479C2×C4×D3—202no—
480C2×C4×D3C22×D514yescomplemented
481C2×Dic6—54no—
482C2×Dic6—202no—
483C3×C22⋊C4—54no—
484C3×C22⋊C4—54no—
485C3×C22⋊C4—54no—
486C3×C22⋊C4—54no—
487#217—54no—
488#217—54no—
489#217—54no—
490#217—54no—
491#217—54no—
492#217C22×D514yes—
493(C2×D3)⋊C4—54no—
494(C2×D3)⋊C4—54no—
495(C2×D3)⋊C4—54no—
496(C2×D3)⋊C4C22×D514yescomplemented
497C4⋊Dic3—54no—
498C4⋊Dic3—54no—
499Dic3⋊C4—54no—
500Dic3⋊C4—54no—
501Dic3⋊C4—54no—
502Dic3⋊C4C22×D514yescomplemented
503C4×Dic3—54no—
504C4×Dic3C22×D514yescomplemented
505C23×C5—22no—
506C23×C5—22no—
507C23×C5—32no—
508C23×C5—62no—
509C23×C5—62no—
510C23×C5—62no—
511C23×C5#23514yes—
512C23×C5C23×D312yes—
513C23×C5C23×D311yescharacteristic
514C22×D5—28no—
515C22×D5—22no—
516C22×D5—22no—
517C22×D5—22no—
518C22×D5—22no—
519C22×D5—22no—
520C22×D5—22no—
521C22×D5—32no—
522C22×D5—44no—
523C22×D5—44no—
524C22×D5—416no—
525C22×D5—62no—
526C22×D5—62no—
527C22×D5—62no—
528C22×D5C23×D312yes—
529C22×D5C23×D312yes—
530C5×D4—68no—
531C2×C4×C5—22no—
532C2×C4×C5—22no—
533C2×C4×C5—32no—
534C2×C4×C5—32no—
535C2×C4×C5—32no—
536C2×C4×C5—44no—
537C2×C4×C5—62no—
538C2×C4×C5—62no—
539C2×C4×C5—62no—
540C2×C4×C5—124no—
541C2×C4×C5C23×D312yes—
542C2×C4×C5C23×D312yes—
543C22⋊D5—68no—
544C22⋊D5—124no—
545C22⋊D5—124no—
546C22⋊D5—124no—
547C2×Dic5—22no—
548C2×Dic5—22no—
549C2×Dic5—32no—
550C2×Dic5—32no—
551C2×Dic5—32no—
552C2×Dic5—44no—
553C2×Dic5—62no—
554C2×Dic5—62no—
555C2×Dic5—62no—
556C2×Dic5C23×D312yes—
557C2×Dic5C23×D312yes—
558D20—124no—
559D20—124no—
560C4×D5—124no—
561Dic10—124no—
562C25—51no—
563C22×Q8—151no—
564C22×D4—31no—
565C22×D4—151no—
566C22×D4—151no—
567C22×D4—151no—
568C22×D4—151no—
569C22×D4—151no—
570C22×D4—151no—
571C23×C4—31no—
572C23×C4—51no—
573C23×C4—151no—
574C23×C4D3×D511yescharacteristic
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#120—158no—
587C4×D4—38no—
588C4×D4—158no—
589C2×C4⋊C4—31no—
590C2×C4⋊C4—151no—
591C2×C4⋊C4—151no—
592C2×C4⋊C4—151no—
593C2×C4⋊C4—151no—
594C2×C4⋊C4—151no—
595C2×C22⋊C4—31no—
596C2×C22⋊C4—31no—
597C2×C22⋊C4—51no—
598C2×C22⋊C4—51no—
599C2×C22⋊C4—51no—
600C2×C22⋊C4—51no—
601C2×C22⋊C4—58no—
602C2×C22⋊C4—151no—
603C2×C22⋊C4—151no—
604C2×C22⋊C4—151no—
605C2×C22⋊C4—151no—
606C2×C22⋊C4—151no—
607C2×C22⋊C4—151no—
608C2×C22⋊C4—151no—
609C2×C22⋊C4—151no—
610C2×C42—31no—
611C2×C42—151no—
612C2×C3×C5—24no—
613C2×C3×C5#53814yescomplemented
614C2×C3×C5C22×#4111yescharacteristic
615C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
616C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
617D15—42no—
618C3×D5—42no—
619C3×D5—42no—
620C5×D3—42no—
621C23×C3—22no—
622C23×C3—22no—
623C23×C3—52no—
624C23×C3—52no—
625C23×C3—108no—
626C23×C3—102no—
627C23×C3—102no—
628C23×C3—102no—
629C23×C3—102no—
630C23×C3—102no—
631C23×C3—102no—
632C23×C3—204no—
633C23×C3—204no—
634C23×C3—2016no—
635C23×C3#70914yes—
636C23×C3C23×D512yes—
637C23×C3C23×D511yescharacteristic
638C22×D3—22no—
639C22×D3—22no—
640C22×D3—22no—
641C22×D3—52no—
642C22×D3—102no—
643C22×D3—102no—
644C22×D3—102no—
645C22×D3C23×D512yes—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—44no—
649C2×C3×C4—52no—
650C2×C3×C4—52no—
651C2×C3×C4—102no—
652C2×C3×C4—102no—
653C2×C3×C4—204no—
654C2×C3×C4C23×D512yes—
655C2×C3×C4C23×D512yes—
656#67—28no—
657#67—108no—
658#67—204no—
659#67—204no—
660#67—204no—
661#67—204no—
662C2×Dic3—22no—
663C2×Dic3—22no—
664C2×Dic3—22no—
665C2×Dic3—52no—
666C2×Dic3—52no—
667C2×Dic3—52no—
668C2×Dic3—102no—
669C2×Dic3—102no—
670C2×Dic3—102no—
671C2×Dic3C23×D512yes—
672C2×Dic3C23×D512yes—
673C2×Dic3C23×D512yes—
674D12—204no—
675C4×D3—44no—
676C4×D3—204no—
677Dic6—204no—
678C22×C5—22no—
679C22×C5—22no—
680C22×C5—28no—
681C22×C5—62no—
682C22×C5—62no—
683C22×C5—62no—
684C22×C5—124no—
685C22×C5C2×#23514yes—
686C22×C5C2×#23512yes—
687C22×C5#100412yes—
688C22×C5#100412yes—
689C22×C5C24×D311yescharacteristic
690C2×D5—22no—
691C2×D5—22no—
692C2×D5—22no—
693C2×D5—22no—
694C2×D5—22no—
695C2×D5—22no—
696C2×D5—416no—
697C2×D5—44no—
698C2×D5—44no—
699C2×D5—62no—
700C2×D5—62no—
701C2×D5—62no—
702C2×D5—124no—
703C4×C5—22no—
704C4×C5—22no—
705C4×C5—62no—
706C4×C5—62no—
707C4×C5—62no—
708Dic5—22no—
709Dic5—22no—
710Dic5—62no—
711Dic5—62no—
712Dic5—62no—
713C24—31no—
714C24—51no—
715C24—51no—
716C24—54no—
717C24—104no—
718C24—151no—
719C24—202no—
720C24—202no—
721C24C2×D3×D511yescharacteristic
722C2×Q8—154no—
723C2×Q8—602no—
724C2×D4—34no—
725C2×D4—64no—
726C2×D4—154no—
727C2×D4—154no—
728C2×D4—154no—
729C2×D4—154no—
730C2×D4—154no—
731C2×D4—154no—
732C2×D4—304no—
733C2×D4—602no—
734C2×D4—602no—
735C2×D4—602no—
736C2×D4—602no—
737C2×D4—602no—
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—31no—
741C22×C4—34no—
742C22×C4—42no—
743C22×C4—51no—
744C22×C4—51no—
745C22×C4—54no—
746C22×C4—122no—
747C22×C4—151no—
748C22×C4—151no—
749C22×C4—151no—
750C22×C4—154no—
751C22×C4—202no—
752C22×C4—602no—
753C22×C4C2×D3×D511yescharacteristic
754C22×C4C2×D3×D511yescharacteristic
755C22×C4C2×D3×D514yes—
756C4⋊C4—34no—
757C4⋊C4—154no—
758C4⋊C4—154no—
759C4⋊C4—154no—
760C4⋊C4—154no—
761C4⋊C4—154no—
762C22⋊C4—34no—
763C22⋊C4—34no—
764C22⋊C4—54no—
765C22⋊C4—54no—
766C22⋊C4—54no—
767C22⋊C4—54no—
768C22⋊C4—154no—
769C22⋊C4—154no—
770C22⋊C4—154no—
771C22⋊C4—154no—
772C22⋊C4—154no—
773C22⋊C4—154no—
774C22⋊C4—154no—
775C22⋊C4—154no—
776C42—34no—
777C42—154no—
778C3×C5C2×#53811yescharacteristic, complemented, Hall
779C22×C3—28no—
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—102no—
783C22×C3—102no—
784C22×C3—102no—
785C22×C3—102no—
786C22×C3—102no—
787C22×C3—102no—
788C22×C3—2016no—
789C22×C3—204no—
790C22×C3—204no—
791C22×C3C2×#70914yes—
792C22×C3C2×#70912yes—
793C22×C3#414412yes—
794C22×C3#414912yes—
795C22×C3C24×D511yescharacteristic
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—22no—
799C2×D3—44no—
800C2×D3—102no—
801C2×D3—102no—
802C2×D3—102no—
803C2×D3—204no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—102no—
807C3×C4—102no—
808Dic3—22no—
809Dic3—22no—
810Dic3—22no—
811Dic3—102no—
812Dic3—102no—
813Dic3—102no—
814C2×C5—24no—
815C2×C5—122no—
816C2×C5#549414yescomplemented
817C2×C5C22×#23511yescharacteristic
818C2×C5C2×#100411yescharacteristic
819C2×C5C2×#100411yescharacteristic
820D5—42no—
821D5—42no—
822D5—122no—
823C23—22no—
824C23—22no—
825C23—32no—
826C23—52no—
827C23—52no—
828C23—62no—
829C23—62no—
830C23—62no—
831C23—108no—
832C23—102no—
833C23—102no—
834C23—102no—
835C23—102no—
836C23—102no—
837C23—102no—
838C23—152no—
839C23—204no—
840C23—204no—
841C23—2016no—
842C23—302no—
843C23—302no—
844C23—302no—
845C23#677114yes—
846C23C22×D3×D512yes—
847C23C22×D3×D511yescharacteristic
848Q8—604no—
849D4—68no—
850D4—308no—
851D4—604no—
852D4—604no—
853D4—604no—
854D4—604no—
855D4—604no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—32no—
861C2×C4—44no—
862C2×C4—52no—
863C2×C4—52no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—62no—
867C2×C4—102no—
868C2×C4—102no—
869C2×C4—124no—
870C2×C4—152no—
871C2×C4—152no—
872C2×C4—152no—
873C2×C4—204no—
874C2×C4—302no—
875C2×C4—302no—
876C2×C4—302no—
877C2×C4—604no—
878C2×C4C22×D3×D512yes—
879C2×C4C22×D3×D512yes—
880C2×C3—24no—
881C2×C3—202no—
882C2×C3—202no—
883C2×C3#6589414yescomplemented
884C2×C3C22×#70911yescharacteristic
885C2×C3C2×#414411yescharacteristic
886C2×C3C2×#414911yescharacteristic
887D3—42no—
888D3—202no—
889C5C2×#549411yescharacteristic, complemented, Sylow
890C22—22no—
891C22—28no—
892C22—22no—
893C22—62no—
894C22—62no—
895C22—62no—
896C22—102no—
897C22—102no—
898C22—102no—
899C22—102no—
900C22—102no—
901C22—102no—
902C22—124no—
903C22—2016no—
904C22—204no—
905C22—204no—
906C22—302no—
907C22—302no—
908C22—302no—
909C22—604no—
910C22C2×#677114yes—
911C22C2×#677112yes—
912C22#9201712yes—
913C22#9204912yes—
914C22C23×D3×D511yescharacteristic
915C4—22no—
916C4—22no—
917C4—62no—
918C4—62no—
919C4—62no—
920C4—102no—
921C4—102no—
922C4—302no—
923C4—302no—
924C4—302no—
925C3C2×#6589411yescharacteristic, complemented, Sylow
926C2—24no—
927C2—122no—
928C2—202no—
929C2—202no—
930C2—602no—
931C2#1175459314yesdirect product factor
932C2C22×#677111yescharacteristic
933C2C2×#9201711yescharacteristic
934C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#538
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#1220C2semidirect
2. C2×C4×C5×#67C2semidirect
3. C22×C3×#685C2semidirect
4. C2×#91574C2semidirect
5. C2×#91566C2semidirect
6. C2×#91564C2semidirect
7. C2×#91563C2semidirect
8. #11754593C2direct (N × H)
9. C2×#91464C2semidirect
10. C2×#91461C2semidirect
11. C2×#91454C2semidirect
12. C2×#91452C2semidirect
13. C2×#91366C2semidirect
14. C2×#91363C2semidirect
15. C2×#91354C2semidirect
16. C2×#91353C2semidirect
21. C22×C4×D15C22semidirect
23. C22×C4×C5×D3C22semidirect
25. C22×#1204C22semidirect
26. C22×#1203C22semidirect
32. C4×#1220C22semidirect
33. C2×#6714C22semidirect
34. C2×#6712C22semidirect
35. C2×C4×Dic15C22semidirect
37. C4×C5×#67C22semidirect
38. C2×C5×(C2×D3)⋊C4C22semidirect
39. C2×C5×Dic3⋊C4C22semidirect
40. C2×C4×C5×Dic3C22semidirect
45. C2×C3×#685C22semidirect
46. #91574C22semidirect
47. #91566C22semidirect
48. #91564C22semidirect
49. #91563C22semidirect
50. C2×Dic3⋊Dic5C22semidirect
51. C2×#6669C22semidirect
52. C2×#6668C22semidirect
53. C2×#6668C22semidirect
54. C2×#6667C22semidirect
55. C2×(C2×D3)⋊Dic5C22semidirect
60. #91464C22semidirect
61. #91461C22semidirect
62. #91454C22semidirect
63. #91452C22semidirect
64. #91366C22semidirect
65. #91363C22semidirect
66. #91354C22semidirect
67. #91353C22semidirect
75. C22×#685D3semidirect
104. C2×C4×D15C23semidirect
111. C2×C4×C5×D3C23semidirect
117. C2×#1204C23semidirect
119. C2×#1203C23semidirect
129. #6714C23semidirect
130. #6712C23semidirect
131. C4×Dic15C23semidirect
133. C5×(C2×D3)⋊C4C23semidirect
134. C5×Dic3⋊C4C23semidirect
135. C4×C5×Dic3C23semidirect
140. Dic3⋊Dic5C23semidirect
141. #6669C23semidirect
142. #6668C23semidirect
143. #6668C23semidirect
144. #6667C23semidirect
145. (C2×D3)⋊Dic5C23semidirect
155. C2×C4×#67D5semidirect
201. C2×#685C2×D3semidirect
285. C22×C4×D3C2×D5semidirect
302. C4×#67C2×D5semidirect
306. C2×(C2×D3)⋊C4C2×D5semidirect
313. C2×Dic3⋊C4C2×D5semidirect
315. C2×C4×Dic3C2×D5semidirect
480. C2×C4×D3C22×D5semidirect
496. (C2×D3)⋊C4C22×D5semidirect
502. Dic3⋊C4C22×D5semidirect
504. C4×Dic3C22×D5semidirect
613. C2×C3×C5#538semidirect
778. C3×C5C2×#538semidirect
816. C2×C5#5494semidirect
883. C2×C3#65894semidirect
889. C5C2×#5494semidirect
925. C3C2×#65894semidirect
931. C2#11754593direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C2×C4×C5×#672
C22×C3×#6852
C2×#915742
C2×#915662
C2×#915642
C2×#915632
#117545932
C2×#914642
C2×#914612
C2×#914542
C2×#914522
C2×#913662
C2×#913632
C2×#913542
C2×#913532
C2×#658943
C2×#54945