Finite Group Databasebeta

← C2×#11748909 #14320792

Subgroups — C2×#11748909 #14320792

Order 1920.

2720 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#1203C211yesmaximal, characteristic
2C22×#6714C211yesmaximal, characteristic, complemented
3C22×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C22×C3×#683C211yesmaximal, characteristic, complemented
5C22×#6667C211yesmaximal, characteristic, complemented
6C22×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
7C22×Dic3×Dic5C211yesmaximal, characteristic, complemented
8#11748909C218yesmaximal, direct product factor
9C2×#65246—31nomaximal, Hall
10C24×D15C2211yescharacteristic
11C24×C5×D3C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C22×#1203—24no—
18C22×#1203—24no—
19C22×#1203C418yescomplemented
20C22×#1203C2214yes—
21C2×#6714—24no—
22C2×#6714C2214yescomplemented
23C2×C5×(C2×D3)⋊C4—24no—
24C2×C5×(C2×D3)⋊C4C2214yescomplemented
25C2×C3×#683—24no—
26C2×C3×#683C2214yescomplemented
27C2×#6667—24no—
28C2×#6667C2214yescomplemented
29C2×(C2×D3)⋊Dic5—24no—
30C2×(C2×D3)⋊Dic5C2214yescomplemented
31C2×Dic3×Dic5—24no—
32C2×Dic3×Dic5C2214yescomplemented
33C2×#4988—51nomaximal, Hall
34C23×C22⋊D5—31no—
35C22×C5×C22⋊C4—31no—
36C22×C22⋊Dic5—31no—
37C22×#685—31no—
38C22×#685—31no—
39C22×#683D311yescharacteristic, complemented
40C22×C4×Dic5—31no—
41#65246—38no—
42C24×C3×C5C2311yescharacteristic
43C23×D15—22no—
44C23×D15—22no—
45C23×D15—22no—
46C23×D15—22no—
47C23×D15—22no—
48C23×D15—22no—
49C23×D15C2×C414yes—
50C23×D15C2312yes—
51C23×C5×D3—22no—
52C23×C5×D3—22no—
53C23×C5×D3—22no—
54C23×C5×D3—22no—
55C23×C5×D3—22no—
56C23×C5×D3—22no—
57C23×C5×D3C2×C414yes—
58C23×C5×D3C2312yes—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5—22no—
62C22×C3×C4×C5C2312yes—
63C22×Dic15—22no—
64C22×Dic15—22no—
65C22×Dic15D414yescomplemented
66C22×Dic15C2312yes—
67C22×C5×Dic3—22no—
68C22×C5×Dic3—22no—
69C22×C5×Dic3D414yescomplemented
70C22×C5×Dic3C2312yes—
71C22×C3×Dic5—22no—
72C22×C3×Dic5—22no—
73C22×C3×Dic5—22no—
74C22×C3×Dic5C2×C414yes—
75C22×C3×Dic5D414yes—
76C22×C3×Dic5D414yes—
77C22×C3×Dic5C2312yes—
78C22×C3×Dic5C2312yes—
79C2×#1203—232no—
80C2×#1203—28no—
81C2×#1203—28no—
82C2×#1203C2×C4116yescomplemented
83#6714—28no—
84C5×(C2×D3)⋊C4—28no—
85C3×#683—28no—
86#6667—28no—
87(C2×D3)⋊Dic5—28no—
88Dic3×Dic5—28no—
89C23×D12—51no—
90C22×C3×C4⋊C4—51no—
91C22×(C2×D3)⋊C4—51no—
92C22×(C2×D3)⋊C4—51no—
93C22×(C2×D3)⋊C4—51no—
94C22×(C2×D3)⋊C4D511yescharacteristic, complemented
95C22×C4×Dic3—51no—
96#4988—58no—
97C25×C5—31no—
98C24×D5—31no—
99C23×C4×C5—31no—
100C23×C4×C5C2×D311yescharacteristic
101C22×C22⋊D5—38no—
102C22×C22⋊D5—34no—
103C22×C22⋊D5—64no—
104C22×C22⋊D5—64no—
105C23×Dic5—31no—
106C23×Dic5C2×D311yescharacteristic
107C23×Dic5C2×D311yescharacteristic
108C2×C5×C22⋊C4—34no—
109C2×C5×C22⋊C4—64no—
110C2×C22⋊Dic5—34no—
111C2×C22⋊Dic5—64no—
112C2×#685—34no—
113C2×#685—34no—
114C2×#685—64no—
115C2×#685—64no—
116C2×#683—24no—
117C2×#683C2×D314yescomplemented
118C2×C4×Dic5—34no—
119C2×C4×Dic5—64no—
120C2×#390—151noSylow
121C23×C3×C5C22×C412yes—
122C23×C3×C5C2×D412yes—
123C23×C3×C5C2×D412yes—
124C23×C3×C5C2×D412yes—
125C23×C3×C5C2×D412yes—
126C23×C3×C5#4112yes—
127C23×C3×C5#4112yes—
128C23×C3×C5C2411yescharacteristic
129C22×D15—28no—
130C22×D15—28no—
131C22×D15—28no—
132C22×D15—22no—
133C22×D15—22no—
134C22×D15—22no—
135C22×D15—22no—
136C22×D15—22no—
137C22×D15—22no—
138C22×D15—44no—
139C22×D15—44no—
140C22×D15—44no—
141C22×D15—44no—
142C22×D15C22×C414yes—
143C22×C5×D3—28no—
144C22×C5×D3—28no—
145C22×C5×D3—28no—
146C22×C5×D3—22no—
147C22×C5×D3—22no—
148C22×C5×D3—22no—
149C22×C5×D3—22no—
150C22×C5×D3—22no—
151C22×C5×D3—22no—
152C22×C5×D3—44no—
153C22×C5×D3—44no—
154C22×C5×D3—44no—
155C22×C5×D3—44no—
156C22×C5×D3C22×C414yes—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—44no—
161C2×Dic15—28no—
162C2×Dic15—22no—
163C2×Dic15—22no—
164C2×Dic15C2×D414yescomplemented
165C2×C5×Dic3—28no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3C2×D414yescomplemented
169C2×C3×Dic5—22no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—44no—
173C2×C3×Dic5C22⋊C4116yescomplemented
174C2×C3×Dic5C22×C414yes—
175C2×C3×Dic5C2×D414yes—
176C2×C3×Dic5C2×D414yes—
177#1203—232no—
178C24×D3—51no—
179C24×D3C2×D511yescharacteristic
180C23×C3×C4—51no—
181C23×C3×C4—51no—
182C23×C3×C4C2×D511yescharacteristic
183C23×Dic3—51no—
184C23×Dic3C2×D511yescharacteristic
185C22×D12—58no—
186C22×D12—54no—
187C22×D12—104no—
188C22×D12—104no—
189C2×C3×C4⋊C4—54no—
190C2×C3×C4⋊C4—104no—
191C2×(C2×D3)⋊C4—24no—
192C2×(C2×D3)⋊C4—54no—
193C2×(C2×D3)⋊C4—54no—
194C2×(C2×D3)⋊C4—54no—
195C2×(C2×D3)⋊C4—104no—
196C2×(C2×D3)⋊C4—104no—
197C2×(C2×D3)⋊C4—104no—
198C2×(C2×D3)⋊C4C2×D514yescomplemented
199C2×C4×Dic3—54no—
200C2×C4×Dic3—104no—
201C24×C5—34no—
202C24×C5—32no—
203C24×C5—62no—
204C24×C5—62no—
205C24×C5—62no—
206C24×C5—62no—
207C24×C5—62no—
208C24×C5—62no—
209C24×C5C22×D311yescharacteristic
210C23×D5—34no—
211C23×D5—32no—
212C23×D5—62no—
213C23×D5—62no—
214C23×D5—62no—
215C23×D5—62no—
216C23×D5—62no—
217C23×D5—62no—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—34no—
222C22×C4×C5—32no—
223C22×C4×C5—62no—
224C22×C4×C5—62no—
225C22×C4×C5C22×D312yes—
226C2×C22⋊D5—316no—
227C2×C22⋊D5—632no—
228C2×C22⋊D5—68no—
229C2×C22⋊D5—68no—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—34no—
234C22×Dic5—32no—
235C22×Dic5—62no—
236C22×Dic5—62no—
237C22×Dic5C4×D314yes—
238C22×Dic5D1214yes—
239C22×Dic5#6714yes—
240C22×Dic5C22×D312yes—
241C22×Dic5C22×D312yes—
242C5×C22⋊C4—68no—
243C22⋊Dic5—68no—
244#685—68no—
245#685—68no—
246#683—28no—
247C4×Dic5—68no—
248C23×D4—151no—
249C22×C4⋊C4—51no—
250C22×C22⋊C4—31no—
251C22×C22⋊C4—151no—
252C22×C22⋊C4—151no—
253C22×C22⋊C4—151no—
254C22×C42—151no—
255#390—158no—
256C22×C3×C5C2×C22⋊C414yes—
257C22×C3×C5C4×D414yes—
258C22×C3×C5C4×D414yes—
259C22×C3×C5#12114yes—
260C22×C3×C5#12114yes—
261C22×C3×C5#12414yes—
262C22×C3×C5#12714yes—
263C22×C3×C5C23×C411yescharacteristic
264C22×C3×C5C22×D411yescharacteristic
265C22×C3×C5C22×D411yescharacteristic
266C22×C3×C5C22×D411yescharacteristic
267C22×C3×C5C22×D411yescharacteristic
268C22×C3×C5C2×#4111yescharacteristic
269C22×C3×C5C2×#4111yescharacteristic
270C2×D15—24no—
271C2×D15—24no—
272C2×D15—24no—
273C2×D15—42no—
274C2×D15—42no—
275C2×D15—42no—
276C2×D15—42no—
277C2×D15—416no—
278C2×C5×D3—24no—
279C2×C5×D3—24no—
280C2×C5×D3—24no—
281C2×C5×D3—42no—
282C2×C5×D3—42no—
283C2×C5×D3—42no—
284C2×C5×D3—42no—
285C2×C5×D3—416no—
286C3×C4×C5—42no—
287Dic15—24no—
288C3×Dic5—42no—
289C3×Dic5C2×C22⋊C418yescomplemented
290C5×Dic3—24no—
291C24×C3C22×D511yescharacteristic
292C23×D3—22no—
293C23×D3—22no—
294C23×D3—22no—
295C23×D3—22no—
296C23×D3—22no—
297C23×D3—22no—
298C23×D3—54no—
299C23×D3—52no—
300C23×D3—102no—
301C23×D3—102no—
302C23×D3—102no—
303C23×D3—102no—
304C23×D3—102no—
305C23×D3—102no—
306C23×D3C4×D514yes—
307C23×D3C22×D512yes—
308C22×C3×C4—22no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—54no—
312C22×C3×C4—54no—
313C22×C3×C4—54no—
314C22×C3×C4—52no—
315C22×C3×C4—52no—
316C22×C3×C4—102no—
317C22×C3×C4—102no—
318C22×C3×C4—102no—
319C22×C3×C4C22×D512yes—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—54no—
323C22×Dic3—52no—
324C22×Dic3—102no—
325C22×Dic3—102no—
326C22×Dic3C22⋊D514yescomplemented
327C22×Dic3C22×D512yes—
328C2×D12—516no—
329C2×D12—108no—
330C2×D12—108no—
331C2×D12—1032no—
332C3×C4⋊C4—108no—
333(C2×D3)⋊C4—28no—
334(C2×D3)⋊C4—108no—
335(C2×D3)⋊C4—108no—
336(C2×D3)⋊C4—108no—
337C4×Dic3—108no—
338C23×C5—34no—
339C23×C5—68no—
340C23×C5—68no—
341C23×C5—68no—
342C23×C5—62no—
343C23×C5—62no—
344C23×C5—62no—
345C23×C5—62no—
346C23×C5—62no—
347C23×C5—62no—
348C23×C5—124no—
349C23×C5—124no—
350C23×C5—124no—
351C23×C5—124no—
352C23×C5C2×C4×D312yes—
353C23×C5C2×D1212yes—
354C23×C5D3×D412yes—
355C23×C5D3×D412yes—
356C23×C5#23912yes—
357C23×C5#23912yes—
358C23×C5C2×#6712yes—
359C23×C5C23×D311yescharacteristic
360C22×D5—34no—
361C22×D5—68no—
362C22×D5—68no—
363C22×D5—68no—
364C22×D5—62no—
365C22×D5—62no—
366C22×D5—62no—
367C22×D5—62no—
368C22×D5—62no—
369C22×D5—62no—
370C22×D5—124no—
371C22×D5—124no—
372C22×D5—124no—
373C22×D5—124no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—34no—
378C2×C4×C5—44no—
379C2×C4×C5—68no—
380C2×C4×C5—62no—
381C2×C4×C5—62no—
382C22⋊D5—632no—
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—34no—
387C2×Dic5—44no—
388C2×Dic5—68no—
389C2×Dic5—62no—
390C2×Dic5—62no—
391C2×Dic5(C2×D3)⋊C4116yescomplemented
392C2×Dic5C2×C4×D314yes—
393C2×Dic5C2×D1214yes—
394C2×Dic5C2×#6714yes—
395C25—31no—
396C25—151no—
397C22×D4—154no—
398C22×D4—158no—
399C22×D4—304no—
400C22×D4—304no—
401C23×C4—31no—
402C23×C4—51no—
403C23×C4—51no—
404C23×C4—151no—
405C23×C4D3×D511yescharacteristic
406C2×C4⋊C4—54no—
407C2×C4⋊C4—104no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—64no—
410C2×C22⋊C4—154no—
411C2×C22⋊C4—154no—
412C2×C22⋊C4—154no—
413C2×C22⋊C4—304no—
414C2×C22⋊C4—304no—
415C2×C22⋊C4—304no—
416C2×C42—154no—
417C2×C42—304no—
418C2×C3×C5#39018yescomplemented
419C2×C3×C5C22×C22⋊C411yescharacteristic
420C2×C3×C5C2×C4×D411yescharacteristic
421C2×C3×C5C2×C4×D411yescharacteristic
422C2×C3×C5C2×#12111yescharacteristic
423C2×C3×C5C2×#12111yescharacteristic
424C2×C3×C5C2×#12411yescharacteristic
425C2×C3×C5C2×#12711yescharacteristic
426D15—44no—
427C5×D3—44no—
428C23×C3C2×C4×D512yes—
429C23×C3#70912yes—
430C23×C3D4×D512yes—
431C23×C3D4×D512yes—
432C23×C3D4×D512yes—
433C23×C3#71112yes—
434C23×C3C2×C22⋊D512yes—
435C23×C3C23×D511yescharacteristic
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—22no—
441C22×D3—22no—
442C22×D3—28no—
443C22×D3—28no—
444C22×D3—28no—
445C22×D3—44no—
446C22×D3—44no—
447C22×D3—44no—
448C22×D3—44no—
449C22×D3—54no—
450C22×D3—102no—
451C22×D3—102no—
452C22×D3—102no—
453C22×D3—102no—
454C22×D3—102no—
455C22×D3—102no—
456C22×D3—108no—
457C22×D3—108no—
458C22×D3—108no—
459C22×D3—204no—
460C22×D3—204no—
461C22×D3—204no—
462C22×D3—204no—
463C22×D3C2×C4×D514yes—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—44no—
468C2×C3×C4—54no—
469C2×C3×C4—54no—
470C2×C3×C4—54no—
471C2×C3×C4—516no—
472C2×C3×C4—102no—
473C2×C3×C4—102no—
474C2×C3×C4—102no—
475C2×C3×C4—204no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—28no—
479C2×Dic3—54no—
480C2×Dic3—102no—
481C2×Dic3—102no—
482C2×Dic3—108no—
483C2×Dic3C2×C22⋊D514yescomplemented
484D12—1032no—
485C22×C5—64no—
486C22×C5—64no—
487C22×C5—64no—
488C22×C5—1216no—
489C22×C5—122no—
490C22×C5—122no—
491C22×C5—122no—
492C22×C5—122no—
493C22×C5#89314yes—
494C22×C5#89314yes—
495C22×C5#89514yes—
496C22×C5#89514yes—
497C22×C5C2×(C2×D3)⋊C414yes—
498C22×C5#94014yes—
499C22×C5#94714yes—
500C22×C5C22×C4×D311yescharacteristic
501C22×C5C22×D1211yescharacteristic
502C22×C5C2×D3×D411yescharacteristic
503C22×C5C2×D3×D411yescharacteristic
504C22×C5C2×#23911yescharacteristic
505C22×C5C2×#23911yescharacteristic
506C22×C5C22×#6711yescharacteristic
507C2×D5—64no—
508C2×D5—64no—
509C2×D5—64no—
510C2×D5—1216no—
511C2×D5—122no—
512C2×D5—122no—
513C2×D5—122no—
514C2×D5—122no—
515C4×C5—42no—
516C4×C5—64no—
517Dic5—42no—
518Dic5—64no—
519Dic5C2×(C2×D3)⋊C418yescomplemented
520C24—34no—
521C24—32no—
522C24—62no—
523C24—62no—
524C24—62no—
525C24—62no—
526C24—62no—
527C24—62no—
528C24—154no—
529C24—152no—
530C24—302no—
531C24—302no—
532C24—302no—
533C24—302no—
534C24—302no—
535C24—302no—
536C24C2×D3×D511yescharacteristic
537C2×D4—1516no—
538C2×D4—3032no—
539C2×D4—308no—
540C2×D4—308no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—34no—
545C22×C4—32no—
546C22×C4—54no—
547C22×C4—54no—
548C22×C4—54no—
549C22×C4—52no—
550C22×C4—52no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—102no—
554C22×C4—102no—
555C22×C4—102no—
556C22×C4—154no—
557C22×C4—152no—
558C22×C4—302no—
559C22×C4—302no—
560C22×C4C2×D3×D512yes—
561C4⋊C4—108no—
562C22⋊C4—68no—
563C22⋊C4—308no—
564C22⋊C4—308no—
565C22⋊C4—308no—
566C42—308no—
567C3×C5C2×#39011yescharacteristic, complemented, Hall
568C22×C3D5×C22⋊C414yes—
569C22×C3#402714yes—
570C22×C3#403014yes—
571C22×C3#403114yes—
572C22×C3C4×C22⋊D514yes—
573C22×C3#408514yes—
574C22×C3#408614yes—
575C22×C3C22×C4×D511yescharacteristic
576C22×C3C2×#70911yescharacteristic
577C22×C3C2×D4×D511yescharacteristic
578C22×C3C2×D4×D511yescharacteristic
579C22×C3C2×D4×D511yescharacteristic
580C22×C3C2×#71111yescharacteristic
581C22×C3C22×C22⋊D511yescharacteristic
582C2×D3—24no—
583C2×D3—24no—
584C2×D3—24no—
585C2×D3—42no—
586C2×D3—42no—
587C2×D3—42no—
588C2×D3—42no—
589C2×D3—416no—
590C2×D3—104no—
591C2×D3—104no—
592C2×D3—104no—
593C2×D3—202no—
594C2×D3—202no—
595C2×D3—202no—
596C2×D3—202no—
597C2×D3—2016no—
598C3×C4—42no—
599C3×C4—58no—
600C3×C4—202no—
601Dic3—24no—
602Dic3—104no—
603C2×C5—124no—
604C2×C5#498818yescomplemented
605C2×C5C2×#89311yescharacteristic
606C2×C5C2×#89311yescharacteristic
607C2×C5C2×#89511yescharacteristic
608C2×C5C2×#89511yescharacteristic
609C2×C5C22×(C2×D3)⋊C411yescharacteristic
610C2×C5C2×#94011yescharacteristic
611C2×C5C2×#94711yescharacteristic
612D5—124no—
613C23—34no—
614C23—68no—
615C23—68no—
616C23—68no—
617C23—62no—
618C23—62no—
619C23—62no—
620C23—62no—
621C23—62no—
622C23—62no—
623C23—124no—
624C23—124no—
625C23—124no—
626C23—124no—
627C23—154no—
628C23—308no—
629C23—308no—
630C23—308no—
631C23—302no—
632C23—302no—
633C23—302no—
634C23—302no—
635C23—302no—
636C23—302no—
637C23—604no—
638C23—604no—
639C23—604no—
640C23—604no—
641C23#676812yes—
642C23#676912yes—
643C23C4×D3×D512yes—
644C23D5×D1212yes—
645C23D5×#6712yes—
646C23D3×C22⋊D512yes—
647C23#679012yes—
648C23C22×D3×D511yescharacteristic
649D4—3032no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—34no—
654C2×C4—44no—
655C2×C4—516no—
656C2×C4—54no—
657C2×C4—54no—
658C2×C4—54no—
659C2×C4—68no—
660C2×C4—62no—
661C2×C4—62no—
662C2×C4—102no—
663C2×C4—102no—
664C2×C4—102no—
665C2×C4—154no—
666C2×C4—204no—
667C2×C4—308no—
668C2×C4—302no—
669C2×C4—302no—
670C2×C3#6524618yescomplemented
671C2×C3C2×D5×C22⋊C411yescharacteristic
672C2×C3C2×#402711yescharacteristic
673C2×C3C2×#403011yescharacteristic
674C2×C3C2×#403111yescharacteristic
675C2×C3C2×C4×C22⋊D511yescharacteristic
676C2×C3C2×#408511yescharacteristic
677C2×C3C2×#408611yescharacteristic
678D3—44no—
679D3—204no—
680C5C2×#498811yescharacteristic, complemented, Sylow
681C22—64no—
682C22—64no—
683C22—64no—
684C22—1216no—
685C22—122no—
686C22—122no—
687C22—122no—
688C22—122no—
689C22—304no—
690C22—304no—
691C22—304no—
692C22—6016no—
693C22—602no—
694C22—602no—
695C22—602no—
696C22—602no—
697C22#9132614yes—
698C22#9140614yes—
699C22#9141614yes—
700C22#9142014yes—
701C22#9144614yes—
702C22D5×(C2×D3)⋊C414yes—
703C22#9156714yes—
704C22C2×#676811yescharacteristic
705C22C2×#676911yescharacteristic
706C22C2×C4×D3×D511yescharacteristic
707C22C2×D5×D1211yescharacteristic
708C22C2×D5×#6711yescharacteristic
709C22C2×D3×C22⋊D511yescharacteristic
710C22C2×#679011yescharacteristic
711C4—42no—
712C4—58no—
713C4—64no—
714C4—202no—
715C4—304no—
716C3C2×#6524611yescharacteristic, complemented, Sylow
717C2—124no—
718C2—604no—
719C2#1174890918yesdirect product factor
720C2C2×#9132611yescharacteristic
721C2C2×#9140611yescharacteristic
722C2C2×#9141611yescharacteristic
723C2C2×#9142011yescharacteristic
724C2C2×#9144611yescharacteristic
725C2C2×D5×(C2×D3)⋊C411yescharacteristic
726C2C2×#9156711yescharacteristic
subgroupG/H
centerC24C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socleC24×C3×C5C23
prime radicalC23×#1203C2
cosocleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#390
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×#6714C2semidirect
3. C22×C5×(C2×D3)⋊C4C2semidirect
4. C22×C3×#683C2semidirect
5. C22×#6667C2semidirect
6. C22×(C2×D3)⋊Dic5C2semidirect
7. C22×Dic3×Dic5C2semidirect
8. #11748909C2direct (N × H)
19. C22×#1203C4semidirect
22. C2×#6714C22semidirect
24. C2×C5×(C2×D3)⋊C4C22semidirect
26. C2×C3×#683C22semidirect
28. C2×#6667C22semidirect
30. C2×(C2×D3)⋊Dic5C22semidirect
32. C2×Dic3×Dic5C22semidirect
39. C22×#683D3semidirect
65. C22×Dic15D4semidirect
69. C22×C5×Dic3D4semidirect
82. C2×#1203C2×C4semidirect
94. C22×(C2×D3)⋊C4D5semidirect
117. C2×#683C2×D3semidirect
164. C2×Dic15C2×D4semidirect
168. C2×C5×Dic3C2×D4semidirect
173. C2×C3×Dic5C22⋊C4semidirect
198. C2×(C2×D3)⋊C4C2×D5semidirect
289. C3×Dic5C2×C22⋊C4semidirect
326. C22×Dic3C22⋊D5semidirect
391. C2×Dic5(C2×D3)⋊C4semidirect
418. C2×C3×C5#390semidirect
483. C2×Dic3C2×C22⋊D5semidirect
519. Dic5C2×(C2×D3)⋊C4semidirect
567. C3×C5C2×#390semidirect
604. C2×C5#4988semidirect
670. C2×C3#65246semidirect
680. C5C2×#4988semidirect
716. C3C2×#65246semidirect
719. C2#11748909direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#12032
C22×#67142
C22×C5×(C2×D3)⋊C42
C22×C3×#6832
C22×#66672
C22×(C2×D3)⋊Dic52
C22×Dic3×Dic52
#117489092
C2×#652463
C2×#49885