Finite Group Databasebeta

← C2×#11749489 #14320804

Subgroups — C2×#11749489 #14320804

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×C3×C22⋊D5C211yesmaximal, characteristic
2C22×#6719C211yesmaximal, characteristic, complemented
3C22×C5×#217C211yesmaximal, characteristic, complemented
4C22×#6668C211yesmaximal, characteristic, complemented
5C22×#6665C211yesmaximal, characteristic, complemented
6C22×#6665C211yesmaximal, characteristic, complemented
7C22×Dic3×Dic5C211yesmaximal, characteristic, complemented
8#11749489C218yesmaximal, direct product factor
9C2×#65246—31nomaximal, Hall
10C25×C3×C5C2211yescharacteristic
11C24×C3×D5C2211yescharacteristic
12C23×Dic15C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C22×C3×C22⋊D5—24no—
17C22×C3×C22⋊D5—24no—
18C22×C3×C22⋊D5C418yescomplemented
19C22×C3×C22⋊D5C2214yes—
20C23×C3×Dic5C2211yescharacteristic
21C2×#6719—24no—
22C2×#6719C2214yescomplemented
23C2×C5×#217—24no—
24C2×C5×#217C2214yescomplemented
25C2×#6668—24no—
26C2×#6668C2214yescomplemented
27C2×#6665—24no—
28C2×#6665—24no—
29C2×#6665C2214yescomplemented
30C2×#6665C2214yescomplemented
31C2×Dic3×Dic5—24no—
32C2×Dic3×Dic5C2214yescomplemented
33C2×#5221—51nomaximal, Hall
34C23×C22⋊D5D311yescharacteristic
35C22×C5×C22⋊C4—31no—
36C22×C22⋊Dic5—31no—
37C22×#685—31no—
38C22×#685—31no—
39C22×#683—31no—
40C22×C4×Dic5—31no—
41#65246—38no—
42C24×C3×C5—22no—
43C24×C3×C5—22no—
44C24×C3×C5—22no—
45C24×C3×C5—22no—
46C24×C3×C5—22no—
47C24×C3×C5—22no—
48C24×C3×C5C2×C414yes—
49C24×C3×C5C2312yes—
50C24×C3×C5C2311yescharacteristic
51C23×C3×D5—22no—
52C23×C3×D5—22no—
53C23×C3×D5—22no—
54C23×C3×D5—22no—
55C23×C3×D5—22no—
56C23×C3×D5—22no—
57C23×C3×D5C2×C414yes—
58C23×C3×D5C2312yes—
59C22×Dic15—22no—
60C22×Dic15—22no—
61C22×Dic15—22no—
62C22×Dic15—22no—
63C22×Dic15—22no—
64C22×Dic15D414yescomplemented
65C22×Dic15C2312yes—
66C22×Dic15C2312yes—
67C22×C5×Dic3—22no—
68C22×C5×Dic3—22no—
69C22×C5×Dic3—22no—
70C22×C5×Dic3—22no—
71C22×C5×Dic3—22no—
72C22×C5×Dic3D414yescomplemented
73C22×C5×Dic3C2312yes—
74C22×C5×Dic3C2312yes—
75C2×C3×C22⋊D5—232no—
76C2×C3×C22⋊D5—28no—
77C2×C3×C22⋊D5—28no—
78C2×C3×C22⋊D5C2×C4116yescomplemented
79C22×C3×Dic5C2×C414yes—
80C22×C3×Dic5D414yes—
81C22×C3×Dic5D414yes—
82C22×C3×Dic5C2312yes—
83#6719—28no—
84C5×#217—28no—
85#6668—28no—
86#6665—28no—
87#6665—28no—
88Dic3×Dic5—28no—
89C23×C3×D4—51no—
90C22×#217—51no—
91C22×#217—51no—
92C22×#217—51no—
93C22×#217D511yescharacteristic, complemented
94C22×C4⋊Dic3—51no—
95C22×C4×Dic3—51no—
96#5221—58no—
97C25×C5C2×D311yescharacteristic
98C24×D5C2×D311yescharacteristic
99C23×C4×C5—31no—
100C23×C4×C5—31no—
101C22×C22⋊D5—24no—
102C22×C22⋊D5—24no—
103C22×C22⋊D5Dic318yescomplemented
104C22×C22⋊D5C2×D314yes—
105C23×Dic5—31no—
106C23×Dic5—31no—
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—34no—
117C2×#683—64no—
118C2×C4×Dic5—34no—
119C2×C4×Dic5—64no—
120C2×#390—151noSylow
121C23×C3×C5—28no—
122C23×C3×C5—28no—
123C23×C3×C5—28no—
124C23×C3×C5—22no—
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5—22no—
128C23×C3×C5—22no—
129C23×C3×C5—22no—
130C23×C3×C5—44no—
131C23×C3×C5—44no—
132C23×C3×C5—44no—
133C23×C3×C5—44no—
134C23×C3×C5C22×C414yes—
135C23×C3×C5C22×C412yes—
136C23×C3×C5C2×D412yes—
137C23×C3×C5C2×D412yes—
138C23×C3×C5C2×D412yes—
139C23×C3×C5C2×D412yes—
140C23×C3×C5#4112yes—
141C23×C3×C5#4112yes—
142C23×C3×C5C2411yescharacteristic
143C22×C3×D5—28no—
144C22×C3×D5—28no—
145C22×C3×D5—28no—
146C22×C3×D5—22no—
147C22×C3×D5—22no—
148C22×C3×D5—22no—
149C22×C3×D5—22no—
150C22×C3×D5—22no—
151C22×C3×D5—22no—
152C22×C3×D5—44no—
153C22×C3×D5—44no—
154C22×C3×D5—44no—
155C22×C3×D5—44no—
156C22×C3×D5C22×C414yes—
157C2×Dic15—28no—
158C2×Dic15—22no—
159C2×Dic15—22no—
160C2×Dic15—22no—
161C2×Dic15—22no—
162C2×Dic15—22no—
163C2×Dic15—44no—
164C2×Dic15C2×D414yescomplemented
165C2×C5×Dic3—28no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3—22no—
171C2×C5×Dic3—44no—
172C2×C5×Dic3C2×D414yescomplemented
173C3×C22⋊D5—232no—
174C2×C3×Dic5C22⋊C4116yescomplemented
175C2×C3×Dic5C22×C414yes—
176C2×C3×Dic5C2×D414yes—
177C2×C3×Dic5C2×D414yes—
178C25×C3—51no—
179C25×C3C2×D511yescharacteristic
180C22×C3×D4—58no—
181C22×C3×D4—54no—
182C22×C3×D4—104no—
183C22×C3×D4—104no—
184C23×C3×C4—51no—
185C23×Dic3—51no—
186C23×Dic3—51no—
187C23×Dic3C2×D511yescharacteristic
188C23×Dic3C2×D511yescharacteristic
189C2×#217—24no—
190C2×#217—54no—
191C2×#217—54no—
192C2×#217—54no—
193C2×#217—104no—
194C2×#217—104no—
195C2×#217—104no—
196C2×#217C2×D514yescomplemented
197C2×C4⋊Dic3—54no—
198C2×C4⋊Dic3—104no—
199C2×C4×Dic3—54no—
200C2×C4×Dic3—104no—
201C24×C5—22no—
202C24×C5—22no—
203C24×C5—22no—
204C24×C5—22no—
205C24×C5—22no—
206C24×C5—22no—
207C24×C5C2×Dic314yes—
208C24×C5C22×D312yes—
209C24×C5C22×D311yescharacteristic
210C23×D5—22no—
211C23×D5—22no—
212C23×D5—22no—
213C23×D5—22no—
214C23×D5—22no—
215C23×D5—22no—
216C23×D5C2×Dic314yes—
217C23×D5C22×D312yes—
218C22×C4×C5—34no—
219C22×C4×C5—32no—
220C22×C4×C5—32no—
221C22×C4×C5—62no—
222C22×C4×C5—62no—
223C22×C4×C5—62no—
224C22×C4×C5—62no—
225C22×C4×C5—62no—
226C2×C22⋊D5—232no—
227C2×C22⋊D5—28no—
228C2×C22⋊D5—28no—
229C2×C22⋊D5C2×Dic3116yescomplemented
230C22×Dic5—34no—
231C22×Dic5—32no—
232C22×Dic5—32no—
233C22×Dic5—62no—
234C22×Dic5—62no—
235C22×Dic5—62no—
236C22×Dic5—62no—
237C22×Dic5—62no—
238C22×Dic5C2×Dic314yes—
239C22×Dic5#6714yes—
240C22×Dic5#6714yes—
241C22×Dic5C22×D312yes—
242C5×C22⋊C4—68no—
243C22⋊Dic5—68no—
244#685—68no—
245#685—68no—
246#683—68no—
247C4×Dic5—68no—
248C23×D4—51no—
249C22×C4⋊C4—151no—
250C22×C22⋊C4—31no—
251C22×C22⋊C4—151no—
252C22×C22⋊C4—151no—
253C22×C22⋊C4—151no—
254C22×C42—151no—
255#390—158no—
256C22×C3×C5—24no—
257C22×C3×C5—24no—
258C22×C3×C5—24no—
259C22×C3×C5—42no—
260C22×C3×C5—42no—
261C22×C3×C5—42no—
262C22×C3×C5—42no—
263C22×C3×C5—416no—
264C22×C3×C5C2×C22⋊C414yes—
265C22×C3×C5C4×D414yes—
266C22×C3×C5C4×D414yes—
267C22×C3×C5#12114yes—
268C22×C3×C5#12114yes—
269C22×C3×C5#12414yes—
270C22×C3×C5#12714yes—
271C22×C3×C5C23×C411yescharacteristic
272C22×C3×C5C22×D411yescharacteristic
273C22×C3×C5C22×D411yescharacteristic
274C22×C3×C5C22×D411yescharacteristic
275C22×C3×C5C22×D411yescharacteristic
276C22×C3×C5C2×#4111yescharacteristic
277C22×C3×C5C2×#4111yescharacteristic
278C2×C3×D5—24no—
279C2×C3×D5—24no—
280C2×C3×D5—24no—
281C2×C3×D5—42no—
282C2×C3×D5—42no—
283C2×C3×D5—42no—
284C2×C3×D5—42no—
285C2×C3×D5—416no—
286Dic15—24no—
287Dic15—42no—
288C3×Dic5C2×C22⋊C418yescomplemented
289C5×Dic3—24no—
290C5×Dic3—42no—
291C24×C3—22no—
292C24×C3—22no—
293C24×C3—22no—
294C24×C3—22no—
295C24×C3—22no—
296C24×C3—22no—
297C24×C3—54no—
298C24×C3—52no—
299C24×C3—102no—
300C24×C3—102no—
301C24×C3—102no—
302C24×C3—102no—
303C24×C3—102no—
304C24×C3—102no—
305C24×C3C4×D514yes—
306C24×C3C22×D512yes—
307C24×C3C22×D511yescharacteristic
308C2×C3×D4—516no—
309C2×C3×D4—108no—
310C2×C3×D4—108no—
311C2×C3×D4—1032no—
312C22×C3×C4—54no—
313C22×C3×C4—54no—
314C22×C3×C4—54no—
315C22×C3×C4—52no—
316C22×Dic3—22no—
317C22×Dic3—22no—
318C22×Dic3—22no—
319C22×Dic3—22no—
320C22×Dic3—22no—
321C22×Dic3—54no—
322C22×Dic3—52no—
323C22×Dic3—52no—
324C22×Dic3—102no—
325C22×Dic3—102no—
326C22×Dic3—102no—
327C22×Dic3—102no—
328C22×Dic3—102no—
329C22×Dic3C22⋊D514yescomplemented
330C22×Dic3C22×D512yes—
331C22×Dic3C22×D512yes—
332#217—28no—
333#217—108no—
334#217—108no—
335#217—108no—
336C4⋊Dic3—108no—
337C4×Dic3—108no—
338C23×C5—28no—
339C23×C5—28no—
340C23×C5—28no—
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—44no—
348C23×C5—44no—
349C23×C5—44no—
350C23×C5—44no—
351C23×C5D3×D412yes—
352C23×C5D3×D412yes—
353C23×C5#23712yes—
354C23×C5#23712yes—
355C23×C5C22×Dic314yes—
356C23×C5C22×Dic312yes—
357C23×C5C2×#6712yes—
358C23×C5C2×#6712yes—
359C23×C5C23×D311yescharacteristic
360C22×D5—28no—
361C22×D5—28no—
362C22×D5—28no—
363C22×D5—22no—
364C22×D5—22no—
365C22×D5—22no—
366C22×D5—22no—
367C22×D5—22no—
368C22×D5—22no—
369C22×D5—44no—
370C22×D5—44no—
371C22×D5—44no—
372C22×D5—44no—
373C22×D5C22×Dic314yes—
374C2×C4×C5—34no—
375C2×C4×C5—68no—
376C2×C4×C5—62no—
377C2×C4×C5—62no—
378C2×C4×C5—62no—
379C2×C4×C5—62no—
380C2×C4×C5—62no—
381C2×C4×C5—124no—
382C22⋊D5—232no—
383C2×Dic5—34no—
384C2×Dic5—68no—
385C2×Dic5—62no—
386C2×Dic5—62no—
387C2×Dic5—62no—
388C2×Dic5—62no—
389C2×Dic5—62no—
390C2×Dic5—124no—
391C2×Dic5#217116yescomplemented
392C2×Dic5C22×Dic314yes—
393C2×Dic5C2×#6714yes—
394C2×Dic5C2×#6714yes—
395C25—51no—
396C25D3×D511yescharacteristic
397C22×D4—58no—
398C22×D4—54no—
399C22×D4—104no—
400C22×D4—104no—
401C23×C4—31no—
402C23×C4—31no—
403C23×C4—51no—
404C23×C4—151no—
405C23×C4—151no—
406C2×C4⋊C4—154no—
407C2×C4⋊C4—304no—
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—44no—
419C2×C3×C5#39018yescomplemented
420C2×C3×C5C22×C22⋊C411yescharacteristic
421C2×C3×C5C2×C4×D411yescharacteristic
422C2×C3×C5C2×C4×D411yescharacteristic
423C2×C3×C5C2×#12111yescharacteristic
424C2×C3×C5C2×#12111yescharacteristic
425C2×C3×C5C2×#12411yescharacteristic
426C2×C3×C5C2×#12711yescharacteristic
427C3×D5—44no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—28no—
435C23×C3—28no—
436C23×C3—28no—
437C23×C3—44no—
438C23×C3—44no—
439C23×C3—44no—
440C23×C3—44no—
441C23×C3—54no—
442C23×C3—102no—
443C23×C3—102no—
444C23×C3—102no—
445C23×C3—102no—
446C23×C3—102no—
447C23×C3—102no—
448C23×C3—108no—
449C23×C3—108no—
450C23×C3—108no—
451C23×C3—204no—
452C23×C3—204no—
453C23×C3—204no—
454C23×C3—204no—
455C23×C3C2×C4×D514yes—
456C23×C3C2×C4×D512yes—
457C23×C3#70912yes—
458C23×C3D4×D512yes—
459C23×C3D4×D512yes—
460C23×C3D4×D512yes—
461C23×C3#71112yes—
462C23×C3C2×C22⋊D512yes—
463C23×C3C23×D511yescharacteristic
464C3×D4—1032no—
465C2×C3×C4—54no—
466C2×C3×C4—54no—
467C2×C3×C4—54no—
468C2×C3×C4—516no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—28no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—44no—
476C2×Dic3—54no—
477C2×Dic3—102no—
478C2×Dic3—102no—
479C2×Dic3—108no—
480C2×Dic3—102no—
481C2×Dic3—102no—
482C2×Dic3—102no—
483C2×Dic3—204no—
484C2×Dic3C2×C22⋊D514yescomplemented
485C22×C5—24no—
486C22×C5—24no—
487C22×C5—24no—
488C22×C5—416no—
489C22×C5—42no—
490C22×C5—42no—
491C22×C5—42no—
492C22×C5—42no—
493C22×C5D4×Dic314yes—
494C22×C5D4×Dic314yes—
495C22×C5#93614yes—
496C22×C5#93814yes—
497C22×C5#93814yes—
498C22×C5#94014yes—
499C22×C5C2×#21714yes—
500C22×C5C2×D3×D411yescharacteristic
501C22×C5C2×D3×D411yescharacteristic
502C22×C5C2×#23711yescharacteristic
503C22×C5C2×#23711yescharacteristic
504C22×C5C23×Dic311yescharacteristic
505C22×C5C22×#6711yescharacteristic
506C22×C5C22×#6711yescharacteristic
507C2×D5—24no—
508C2×D5—24no—
509C2×D5—24no—
510C2×D5—416no—
511C2×D5—42no—
512C2×D5—42no—
513C2×D5—42no—
514C2×D5—42no—
515C4×C5—64no—
516C4×C5—122no—
517Dic5—64no—
518Dic5—122no—
519Dic5C2×#21718yescomplemented
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—54no—
527C24—52no—
528C24—102no—
529C24—102no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24—102no—
534C24D5×Dic314yes—
535C24C2×D3×D512yes—
536C24C2×D3×D511yescharacteristic
537C2×D4—516no—
538C2×D4—108no—
539C2×D4—108no—
540C2×D4—1032no—
541C22×C4—34no—
542C22×C4—32no—
543C22×C4—32no—
544C22×C4—54no—
545C22×C4—54no—
546C22×C4—54no—
547C22×C4—52no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—154no—
554C22×C4—152no—
555C22×C4—152no—
556C22×C4—302no—
557C22×C4—302no—
558C22×C4—302no—
559C22×C4—302no—
560C22×C4—302no—
561C4⋊C4—308no—
562C22⋊C4—68no—
563C22⋊C4—308no—
564C22⋊C4—308no—
565C22⋊C4—308no—
566C42—308no—
567C3×C5C2×#39011yescharacteristic, complemented, Hall
568C22×C3—24no—
569C22×C3—24no—
570C22×C3—24no—
571C22×C3—42no—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—416no—
576C22×C3—104no—
577C22×C3—104no—
578C22×C3—104no—
579C22×C3—202no—
580C22×C3—202no—
581C22×C3—202no—
582C22×C3—202no—
583C22×C3—2016no—
584C22×C3D5×C22⋊C414yes—
585C22×C3#402714yes—
586C22×C3#403014yes—
587C22×C3#403114yes—
588C22×C3C4×C22⋊D514yes—
589C22×C3#408514yes—
590C22×C3#408614yes—
591C22×C3C22×C4×D511yescharacteristic
592C22×C3C2×#70911yescharacteristic
593C22×C3C2×D4×D511yescharacteristic
594C22×C3C2×D4×D511yescharacteristic
595C22×C3C2×D4×D511yescharacteristic
596C22×C3C2×#71111yescharacteristic
597C22×C3C22×C22⋊D511yescharacteristic
598C3×C4—58no—
599Dic3—24no—
600Dic3—42no—
601Dic3—104no—
602Dic3—202no—
603C2×C5—44no—
604C2×C5#522118yescomplemented
605C2×C5C2×D4×Dic311yescharacteristic
606C2×C5C2×D4×Dic311yescharacteristic
607C2×C5C2×#93611yescharacteristic
608C2×C5C2×#93811yescharacteristic
609C2×C5C2×#93811yescharacteristic
610C2×C5C2×#94011yescharacteristic
611C2×C5C22×#21711yescharacteristic
612D5—44no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—28no—
620C23—28no—
621C23—28no—
622C23—44no—
623C23—44no—
624C23—44no—
625C23—44no—
626C23—54no—
627C23—102no—
628C23—102no—
629C23—102no—
630C23—102no—
631C23—102no—
632C23—102no—
633C23—108no—
634C23—108no—
635C23—108no—
636C23—204no—
637C23—204no—
638C23—204no—
639C23—204no—
640C23C2×D5×Dic314yes—
641C23C2×D5×Dic312yes—
642C23#677912yes—
643C23#678012yes—
644C23D5×#6712yes—
645C23D5×#6712yes—
646C23D3×C22⋊D512yes—
647C23#679012yes—
648C23C22×D3×D511yescharacteristic
649D4—1032no—
650C2×C4—34no—
651C2×C4—54no—
652C2×C4—54no—
653C2×C4—54no—
654C2×C4—516no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—68no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—62no—
661C2×C4—124no—
662C2×C4—154no—
663C2×C4—302no—
664C2×C4—308no—
665C2×C4—302no—
666C2×C4—302no—
667C2×C4—302no—
668C2×C4—302no—
669C2×C4—604no—
670C2×C3—44no—
671C2×C3—204no—
672C2×C3#6524618yescomplemented
673C2×C3C2×D5×C22⋊C411yescharacteristic
674C2×C3C2×#402711yescharacteristic
675C2×C3C2×#403011yescharacteristic
676C2×C3C2×#403111yescharacteristic
677C2×C3C2×C4×C22⋊D511yescharacteristic
678C2×C3C2×#408511yescharacteristic
679C2×C3C2×#408611yescharacteristic
680C5C2×#522111yescharacteristic, complemented, Sylow
681C22—24no—
682C22—24no—
683C22—24no—
684C22—42no—
685C22—42no—
686C22—416no—
687C22—42no—
688C22—42no—
689C22—104no—
690C22—104no—
691C22—104no—
692C22—202no—
693C22—202no—
694C22—2016no—
695C22—202no—
696C22—202no—
697C22#9153314yes—
698C22#9153414yes—
699C22D5×#21714yes—
700C22Dic3×C22⋊D514yes—
701C22#9155914yes—
702C22#9156514yes—
703C22#9156714yes—
704C22C22×D5×Dic311yescharacteristic
705C22C2×#677911yescharacteristic
706C22C2×#678011yescharacteristic
707C22C2×D5×#6711yescharacteristic
708C22C2×D5×#6711yescharacteristic
709C22C2×D3×C22⋊D511yescharacteristic
710C22C2×#679011yescharacteristic
711C4—58no—
712C4—64no—
713C4—122no—
714C4—304no—
715C4—602no—
716C3C2×#6524611yescharacteristic, complemented, Sylow
717C2—44no—
718C2—204no—
719C2#1174948918yesdirect product factor
720C2C2×#9153311yescharacteristic
721C2C2×#9153411yescharacteristic
722C2C2×D5×#21711yescharacteristic
723C2C2×Dic3×C22⋊D511yescharacteristic
724C2C2×#9155911yescharacteristic
725C2C2×#9156511yescharacteristic
726C2C2×#9156711yescharacteristic
subgroupG/H
centerC24C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC25×C3×C5C22
socleC24×C3×C5C23
prime radicalC23×C3×C22⋊D5C2
cosocleC23×C3×C5C24
hypercenterC25D3×D5
hypocenterC3×C5C2×#390
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
2. C22×#6719C2semidirect
3. C22×C5×#217C2semidirect
4. C22×#6668C2semidirect
5. C22×#6665C2semidirect
6. C22×#6665C2semidirect
7. C22×Dic3×Dic5C2semidirect
8. #11749489C2direct (N × H)
18. C22×C3×C22⋊D5C4semidirect
22. C2×#6719C22semidirect
24. C2×C5×#217C22semidirect
26. C2×#6668C22semidirect
29. C2×#6665C22semidirect
30. C2×#6665C22semidirect
32. C2×Dic3×Dic5C22semidirect
64. C22×Dic15D4semidirect
72. C22×C5×Dic3D4semidirect
78. C2×C3×C22⋊D5C2×C4semidirect
93. C22×#217D5semidirect
103. C22×C22⋊D5Dic3semidirect
164. C2×Dic15C2×D4semidirect
172. C2×C5×Dic3C2×D4semidirect
174. C2×C3×Dic5C22⋊C4semidirect
196. C2×#217C2×D5semidirect
229. C2×C22⋊D5C2×Dic3semidirect
288. C3×Dic5C2×C22⋊C4semidirect
329. C22×Dic3C22⋊D5semidirect
391. C2×Dic5#217semidirect
419. C2×C3×C5#390semidirect
484. C2×Dic3C2×C22⋊D5semidirect
519. Dic5C2×#217semidirect
567. C3×C5C2×#390semidirect
604. C2×C5#5221semidirect
672. C2×C3#65246semidirect
680. C5C2×#5221semidirect
716. C3C2×#65246semidirect
719. C2#11749489direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C22⋊D52
C22×#67192
C22×C5×#2172
C22×#66682
C22×#66652
C22×Dic3×Dic52
#117494892
C2×#652463
C2×#52215