Finite Group Databasebeta

← C2×#11752008 #14412149

Subgroups — C2×#11752008 #14412149

Order 1920.

1512 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6782C211yesmaximal, characteristic
2C22×#6762C211yesmaximal, characteristic, complemented
3C22×C3×#704C211yesmaximal, characteristic, complemented
4C2×#91175C212yesmaximal, complemented
5#11752008C218yesmaximal, direct product factor
6C2×#91174C212yesmaximal, complemented
7C2×#65777—31nomaximal, Hall
8C22×#1220C411yescharacteristic
9C22×C5×#67C411yescharacteristic
10C23×C3×Dic5C2211yescharacteristic
11C22×#1204C2211yescharacteristic
12C22×#1203C2211yescharacteristic
13C22×#1200C411yescharacteristic
14C2×#6782—21no—
15C2×#6782—22no—
16C2×#6782—21no—
17C2×#6782—21no—
18C2×#6782—22no—
19C2×#6782—21no—
20C2×#6782C414yes—
21C2×#6782C2214yes—
22C22×D3×Dic5C411yescharacteristic
23C2×#6762—21no—
24C2×#6762—22no—
25C2×#6762C2212yes—
26C2×#6762C2214yescomplemented
27C22×C3⋊#170—21no—
28C2×C3×#704—21no—
29C2×C3×#704—22no—
30C2×C3×#704C2212yes—
31C2×C3×#704C2214yescomplemented
32C22×C3×#170—21no—
33#91175C2218yescomplemented
34#91174C2218yescomplemented
35C2×#5132—51nomaximal, Hall
36C22×#711—31no—
37C22×#704—31no—
38C22×#704D311yescharacteristic, complemented
39C2×#4013—32no—
40#65777—38no—
41C2×#4005—32no—
42C24×C3×C5C2×C411yescharacteristic
43C23×D15C2×C411yescharacteristic
44C23×C5×D3C2×C411yescharacteristic
45C2×#1220—21no—
46C2×#1220—21no—
47C2×#1220—22no—
48C2×#1220C2×C414yes—
49C22×Dic15C2×C411yescharacteristic
50C2×C5×#67—21no—
51C2×C5×#67—21no—
52C2×C5×#67—22no—
53C2×C5×#67C2×C414yes—
54C22×C5×Dic3C2×C411yescharacteristic
55C22×C3×Dic5C2×C411yescharacteristic
56C22×C3×Dic5C2×C412yes—
57C22×C3×Dic5D411yescharacteristic
58C22×C3×Dic5D412yes—
59C22×C3×Dic5D411yescharacteristic
60C22×C3×Dic5D411yescharacteristic
61C22×C3×Dic5D412yes—
62C22×C3×Dic5D411yescharacteristic
63C22×C3×Dic5C2311yescharacteristic
64C22×C3×Dic5C2312yes—
65C2×#1204—21no—
66C2×#1204—21no—
67C2×#1204—21no—
68C2×#1204—21no—
69C2×#1204C2×C412yes—
70C2×#1204C2312yes—
71C2×#1203—21no—
72C2×#1203—21no—
73C2×#1203—21no—
74C2×#1203—21no—
75C2×#1203C2×C412yes—
76C2×#1203C2312yes—
77C2×#1200—22no—
78C2×#1200—21no—
79C2×#1200—21no—
80C2×#1200C2×C414yes—
81#6782—24no—
82#6782—24no—
83#6782—24no—
84#6782—24no—
85#6782—24no—
86#6782—24no—
87#6782—24no—
88#6782—24no—
89C2×D3×Dic5—22no—
90C2×D3×Dic5—21no—
91C2×D3×Dic5—21no—
92C2×D3×Dic5C2×C414yes—
93#6762—22no—
94#6762—24no—
95#6762C2314yes—
96C2×C3⋊#170—22no—
97C2×C3⋊#170—24no—
98C3×#704—22no—
99C3×#704—24no—
100C3×#704C2314yes—
101C2×C3×#170—22no—
102C2×C3×#170—24no—
103C22×#235—51no—
104C22×C3×M16—51no—
105C22×#208—51no—
106C2×#824—52no—
107#5132—58no—
108C2×#823—52no—
109C22×C5×D4—31no—
110C22×C22⋊D5—31no—
111C22×C22⋊D5—31no—
112C23×Dic5—31no—
113C23×Dic5C2×D311yescharacteristic
114C2×#711—34no—
115C2×#711—34no—
116C2×#711—61no—
117C2×#711—61no—
118C2×#711—62no—
119C2×#711—61no—
120C2×#711—61no—
121C2×#711—62no—
122C22×C4×D5—31no—
123C22×Dic10—31no—
124C2×#704—21no—
125C2×#704—22no—
126C2×#704—32no—
127C2×#704—34no—
128C2×#704—61no—
129C2×#704—62no—
130C2×#704C2×D312yes—
131C2×#704C2×D314yescomplemented
132C22×#170—21no—
133C22×#170—61no—
134#4013—38no—
135#4005—38no—
136C2×#413—151noSylow
137C23×C3×C5—42no—
138C23×C3×C5C22⋊C411yescharacteristic
139C23×C3×C5C22⋊C411yescharacteristic
140C23×C3×C5C22⋊C412yes—
141C23×C3×C5C22×C411yescharacteristic
142C23×C3×C5C22×C412yes—
143C22×D15—21no—
144C22×D15—21no—
145C22×D15—42no—
146C22×D15C22×C412yes—
147C22×C5×D3—21no—
148C22×C5×D3—21no—
149C22×C5×D3—42no—
150C22×C5×D3C22×C412yes—
151#1220—24no—
152#1220—24no—
153C2×Dic15—21no—
154C2×Dic15—21no—
155C2×Dic15C22×C412yes—
156C5×#67—24no—
157C5×#67—24no—
158C2×C5×Dic3—21no—
159C2×C5×Dic3—21no—
160C2×C5×Dic3C22×C412yes—
161C2×C3×Dic5C22⋊C412yes—
162C2×C3×Dic5C22⋊C411yescharacteristic
163C2×C3×Dic5C22⋊C411yescharacteristic
164C2×C3×Dic5C22⋊C412yes—
165C2×C3×Dic5C22⋊C412yes—
166C2×C3×Dic5C22⋊C412yes—
167C2×C3×Dic5C22⋊C412yes—
168C2×C3×Dic5C22×C412yes—
169C2×C3×Dic5C22×C411yescharacteristic
170C2×C3×Dic5C2×D412yes—
171C2×C3×Dic5C2×D411yescharacteristic
172C2×C3×Dic5C2×D412yes—
173C2×C3×Dic5C2×D411yescharacteristic
174C2×C3×Dic5C2×D412yes—
175C2×C3×Dic5C2×D411yescharacteristic
176C2×C3×Dic5C2×D412yes—
177C2×C3×Dic5C2×D411yescharacteristic
178C2×C3×Dic5C2411yescharacteristic
179#1204—22no—
180#1204—22no—
181#1204—22no—
182#1204—22no—
183#1203—22no—
184#1203—22no—
185#1203—22no—
186#1203—22no—
187#1200—24no—
188#1200—24no—
189D3×Dic5—24no—
190D3×Dic5—24no—
191C3⋊#170—24no—
192C3×#170—24no—
193C23×C3×C4—51no—
194C22×#67—51no—
195C22×#67AGL(1,𝔽5)11yescharacteristic
196C2×#235—54no—
197C2×#235—54no—
198C2×#235—101no—
199C2×#235—101no—
200C2×#235—102no—
201C2×#235—101no—
202C2×#235—101no—
203C2×#235—102no—
204C22×D12—51no—
205C22×C4×D3—51no—
206C22×C4×D3—51no—
207C22×Dic6—51no—
208C2×C3×M16—52no—
209C2×C3×M16—54no—
210C2×C3×M16—101no—
211C2×C3×M16—102no—
212C22×C3×C8—101no—
213C2×#208—52no—
214C2×#208—54no—
215C2×#208—101no—
216C2×#208—102no—
217C22×C3⋊C8—101no—
218#824—58no—
219#823—58no—
220C24×C5—31no—
221C24×C5C4×D311yescharacteristic
222C23×D5—31no—
223C2×C5×D4—34no—
224C2×C5×D4—61no—
225C2×C5×D4—61no—
226C2×C5×D4—62no—
227C22×C4×C5—31no—
228C2×C22⋊D5—34no—
229C2×C22⋊D5—32no—
230C2×C22⋊D5—32no—
231C2×C22⋊D5—61no—
232C2×C22⋊D5—61no—
233C2×C22⋊D5—62no—
234C2×C22⋊D5—61no—
235C2×C22⋊D5—61no—
236C2×C22⋊D5—61no—
237C2×C22⋊D5—61no—
238C22×Dic5—31no—
239C22×Dic5—34no—
240C22×Dic5—62no—
241C22×Dic5—61no—
242C22×Dic5—61no—
243C22×Dic5C4×D311yescharacteristic
244C22×Dic5C4×D312yes—
245C22×Dic5D1211yescharacteristic
246C22×Dic5D1211yescharacteristic
247C22×Dic5D1212yes—
248C22×Dic5#6711yescharacteristic
249C22×Dic5#6711yescharacteristic
250C22×Dic5#6712yes—
251C22×Dic5C22×D311yescharacteristic
252C22×Dic5C22×D312yes—
253#711—64no—
254#711—64no—
255#711—64no—
256#711—64no—
257#711—64no—
258#711—64no—
259#711—64no—
260#711—64no—
261C2×C4×D5—34no—
262C2×C4×D5—62no—
263C2×C4×D5—61no—
264C2×C4×D5—61no—
265C2×Dic10—32no—
266C2×Dic10—32no—
267C2×Dic10—61no—
268C2×Dic10—61no—
269C2×Dic10—61no—
270C2×Dic10—61no—
271#704—22no—
272#704—24no—
273#704—34no—
274#704—62no—
275#704—64no—
276#704C22×D314yes—
277C2×#170—22no—
278C2×#170—24no—
279C2×#170—62no—
280C2×#170—64no—
281C22×#41—151no—
282C22×M16—51no—
283C22×M16—151no—
284#413—158no—
285C2×#101—152no—
286C2×#100—152no—
287C22×C3×C5—22no—
288C22×C3×C5—22no—
289C22×C3×C5—22no—
290C22×C3×C5—42no—
291C22×C3×C5—42no—
292C22×C3×C5C2×C22⋊C411yescharacteristic
293C22×C3×C5C2×C22⋊C412yes—
294C22×C3×C5C2×C22⋊C412yes—
295C22×C3×C5C2×C22⋊C411yescharacteristic
296C22×C3×C5C23×C411yescharacteristic
297C2×D15—22no—
298C2×D15—42no—
299C2×D15—42no—
300C2×D15—42no—
301C2×C5×D3—22no—
302C2×C5×D3—42no—
303C2×C5×D3—42no—
304C2×C5×D3—42no—
305Dic15—22no—
306C3×Dic5C2×C22⋊C412yes—
307C3×Dic5C2×C22⋊C412yes—
308C3×Dic5C2×C22⋊C411yescharacteristic
309C3×Dic5C2×C22⋊C411yescharacteristic
310C3×Dic5C22×D411yescharacteristic
311C3×Dic5C22×D411yescharacteristic
312C5×Dic3—22no—
313C24×C3C2×AGL(1,𝔽5)11yescharacteristic
314C23×D3—51no—
315C23×D3C2×AGL(1,𝔽5)11yescharacteristic
316C22×C3×C4—51no—
317C22×C3×C4—51no—
318C22×C3×C4—52no—
319C22×C3×C4—51no—
320C22×C3×C4—51no—
321C22×C3×C4—52no—
322C22×C3×C4—51no—
323C22×C3×C4—52no—
324C22×C3×C4—51no—
325C22×C3×C4—52no—
326C2×#67—21no—
327C2×#67—21no—
328C2×#67—22no—
329C2×#67—54no—
330C2×#67—101no—
331C2×#67—101no—
332C2×#67—102no—
333C2×#67C2×AGL(1,𝔽5)14yes—
334C22×Dic3—51no—
335C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
336#235—104no—
337#235—104no—
338#235—104no—
339#235—104no—
340#235—104no—
341#235—104no—
342#235—104no—
343#235—104no—
344C2×D12—52no—
345C2×D12—52no—
346C2×D12—101no—
347C2×D12—101no—
348C2×D12—101no—
349C2×D12—101no—
350C2×C4×D3—54no—
351C2×C4×D3—54no—
352C2×C4×D3—102no—
353C2×C4×D3—101no—
354C2×C4×D3—101no—
355C2×C4×D3—102no—
356C2×C4×D3—101no—
357C2×C4×D3—101no—
358C2×Dic6—52no—
359C2×Dic6—52no—
360C2×Dic6—101no—
361C2×Dic6—101no—
362C2×Dic6—101no—
363C2×Dic6—101no—
364C3×M16—54no—
365C3×M16—102no—
366C3×M16—104no—
367C2×C3×C8—102no—
368C2×C3×C8—104no—
369#208—54no—
370#208—102no—
371#208—104no—
372C2×C3⋊C8—102no—
373C2×C3⋊C8—104no—
374C23×C5—32no—
375C23×C5—42no—
376C23×C5—61no—
377C23×C5—61no—
378C23×C5—122no—
379C23×C5(C2×D3)⋊C411yescharacteristic
380C23×C5(C2×D3)⋊C411yescharacteristic
381C23×C5(C2×D3)⋊C412yes—
382C23×C5C2×C4×D311yescharacteristic
383C23×C5C2×C4×D312yes—
384C22×D5—32no—
385C22×D5—61no—
386C22×D5—61no—
387C22×D5—122no—
388C5×D4—64no—
389C5×D4—64no—
390C2×C4×C5—32no—
391C2×C4×C5—61no—
392C2×C4×C5—61no—
393C22⋊D5—64no—
394C22⋊D5—64no—
395C22⋊D5—62no—
396C22⋊D5—62no—
397C22⋊D5—62no—
398C22⋊D5—62no—
399C2×Dic5—32no—
400C2×Dic5—61no—
401C2×Dic5—61no—
402C2×Dic5—64no—
403C2×Dic5—64no—
404C2×Dic5(C2×D3)⋊C412yes—
405C2×Dic5(C2×D3)⋊C411yescharacteristic
406C2×Dic5(C2×D3)⋊C411yescharacteristic
407C2×Dic5(C2×D3)⋊C412yes—
408C2×Dic5(C2×D3)⋊C412yes—
409C2×Dic5(C2×D3)⋊C412yes—
410C2×Dic5(C2×D3)⋊C412yes—
411C2×Dic5C2×C4×D311yescharacteristic
412C2×Dic5C2×C4×D312yes—
413C2×Dic5C2×D1211yescharacteristic
414C2×Dic5C2×D1212yes—
415C2×Dic5C2×D1211yescharacteristic
416C2×Dic5C2×D1212yes—
417C2×Dic5C2×#6711yescharacteristic
418C2×Dic5C2×#6712yes—
419C2×Dic5C2×#6711yescharacteristic
420C2×Dic5C2×#6712yes—
421C2×Dic5C23×D311yescharacteristic
422C4×D5—64no—
423C4×D5—64no—
424Dic10—62no—
425Dic10—62no—
426Dic10—62no—
427Dic10—62no—
428#170—24no—
429#170—64no—
430C2×#41—154no—
431C2×#41—154no—
432C2×#41—301no—
433C2×#41—301no—
434C2×#41—302no—
435C2×#41—301no—
436C2×#41—302no—
437C2×#41—301no—
438C22×Q8—151no—
439C22×D4—31no—
440C22×D4—151no—
441C22×D4—151no—
442C23×C4—51no—
443C23×C4—151no—
444C23×C4—151no—
445C2×M16—52no—
446C2×M16—54no—
447C2×M16—102no—
448C2×M16—101no—
449C2×M16—152no—
450C2×M16—154no—
451C2×M16—302no—
452C2×M16—301no—
453C22×C8—101no—
454C22×C8—301no—
455#101—158no—
456#100—158no—
457C2×C3×C5—21no—
458C2×C3×C5—21no—
459C2×C3×C5—22no—
460C2×C3×C5—22no—
461C2×C3×C5#41312yescomplemented
462C2×C3×C5C22×C22⋊C411yescharacteristic
463D15—42no—
464C5×D3—42no—
465C23×C3—42no—
466C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
467C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
468C23×C3C22⋊AGL(1,𝔽5)12yes—
469C23×C3C22×AGL(1,𝔽5)11yescharacteristic
470C23×C3C22×AGL(1,𝔽5)12yes—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—42no—
474C22×D3—52no—
475C22×D3—101no—
476C22×D3—101no—
477C22×D3—202no—
478C22×D3C22×AGL(1,𝔽5)12yes—
479C2×C3×C4—52no—
480C2×C3×C4—51no—
481C2×C3×C4—51no—
482C2×C3×C4—52no—
483C2×C3×C4—52no—
484C2×C3×C4—52no—
485C2×C3×C4—52no—
486C2×C3×C4—51no—
487C2×C3×C4—52no—
488C2×C3×C4—51no—
489C2×C3×C4—52no—
490C2×C3×C4—51no—
491C2×C3×C4—52no—
492C2×C3×C4—51no—
493C2×C3×C4—52no—
494C2×C3×C4—51no—
495C2×C3×C4—52no—
496C2×C3×C4—51no—
497#67—24no—
498#67—24no—
499#67—104no—
500#67—104no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—52no—
504C2×Dic3—101no—
505C2×Dic3—101no—
506C2×Dic3C22×AGL(1,𝔽5)12yes—
507D12—102no—
508D12—102no—
509D12—102no—
510D12—102no—
511C4×D3—104no—
512C4×D3—104no—
513C4×D3—104no—
514C4×D3—104no—
515Dic6—102no—
516Dic6—102no—
517Dic6—102no—
518Dic6—102no—
519C3×C8—104no—
520C3⋊C8—104no—
521C22×C5—22no—
522C22×C5—22no—
523C22×C5—22no—
524C22×C5—42no—
525C22×C5—42no—
526C22×C5—62no—
527C22×C5—122no—
528C22×C5—122no—
529C22×C5—122no—
530C22×C5C2×(C2×D3)⋊C411yescharacteristic
531C22×C5C2×(C2×D3)⋊C412yes—
532C22×C5C2×(C2×D3)⋊C412yes—
533C22×C5C2×(C2×D3)⋊C411yescharacteristic
534C22×C5C22×C4×D311yescharacteristic
535C2×D5—62no—
536C2×D5—122no—
537C2×D5—122no—
538C2×D5—122no—
539C4×C5—62no—
540Dic5—62no—
541Dic5C2×(C2×D3)⋊C411yescharacteristic
542Dic5C2×(C2×D3)⋊C411yescharacteristic
543Dic5C2×(C2×D3)⋊C412yes—
544Dic5C2×(C2×D3)⋊C412yes—
545Dic5C22×D1211yescharacteristic
546Dic5C22×#6711yescharacteristic
547C24—31no—
548C24—151no—
549C24D3×AGL(1,𝔽5)11yescharacteristic
550#41—304no—
551#41—304no—
552#41—304no—
553#41—304no—
554#41—304no—
555#41—304no—
556#41—304no—
557#41—304no—
558C2×Q8—152no—
559C2×Q8—152no—
560C2×Q8—301no—
561C2×Q8—301no—
562C2×Q8—301no—
563C2×Q8—301no—
564C2×D4—34no—
565C2×D4—62no—
566C2×D4—61no—
567C2×D4—61no—
568C2×D4—152no—
569C2×D4—152no—
570C2×D4—154no—
571C2×D4—301no—
572C2×D4—301no—
573C2×D4—301no—
574C2×D4—301no—
575C2×D4—302no—
576C2×D4—301no—
577C2×D4—301no—
578C22×C4—31no—
579C22×C4—51no—
580C22×C4—51no—
581C22×C4—52no—
582C22×C4—51no—
583C22×C4—52no—
584C22×C4—51no—
585C22×C4—51no—
586C22×C4—52no—
587C22×C4—51no—
588C22×C4—52no—
589C22×C4—154no—
590C22×C4—154no—
591C22×C4—151no—
592C22×C4—302no—
593C22×C4—301no—
594C22×C4—301no—
595C22×C4—302no—
596C22×C4—301no—
597C22×C4—301no—
598M16—54no—
599M16—102no—
600M16—104no—
601M16—154no—
602M16—302no—
603M16—304no—
604C2×C8—104no—
605C2×C8—102no—
606C2×C8—304no—
607C2×C8—302no—
608C3×C5C2×#41311yescharacteristic, complemented, Hall
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
615C22×C3C2×C22⋊AGL(1,𝔽5)12yes—
616C22×C3C2×C22⋊AGL(1,𝔽5)12yes—
617C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
618C22×C3C23×AGL(1,𝔽5)11yescharacteristic
619C2×D3—22no—
620C2×D3—42no—
621C2×D3—42no—
622C2×D3—42no—
623C2×D3—102no—
624C2×D3—202no—
625C2×D3—202no—
626C2×D3—202no—
627C3×C4—51no—
628C3×C4—51no—
629C3×C4—52no—
630C3×C4—52no—
631C3×C4—51no—
632C3×C4—51no—
633Dic3—22no—
634Dic3—102no—
635C2×C5—21no—
636C2×C5—21no—
637C2×C5—22no—
638C2×C5—22no—
639C2×C5—122no—
640C2×C5#513212yescomplemented
641C2×C5C22×(C2×D3)⋊C411yescharacteristic
642D5—122no—
643C23—32no—
644C23—42no—
645C23—61no—
646C23—61no—
647C23—122no—
648C23—152no—
649C23—301no—
650C23—301no—
651C23—602no—
652C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
653C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
654C23(C2×D3)⋊AGL(1,𝔽5)12yes—
655C23C2×D3×AGL(1,𝔽5)11yescharacteristic
656C23C2×D3×AGL(1,𝔽5)12yes—
657Q8—302no—
658Q8—302no—
659Q8—302no—
660Q8—302no—
661D4—64no—
662D4—64no—
663D4—302no—
664D4—302no—
665D4—302no—
666D4—302no—
667D4—304no—
668D4—304no—
669C2×C4—32no—
670C2×C4—52no—
671C2×C4—52no—
672C2×C4—51no—
673C2×C4—52no—
674C2×C4—51no—
675C2×C4—52no—
676C2×C4—52no—
677C2×C4—52no—
678C2×C4—52no—
679C2×C4—52no—
680C2×C4—52no—
681C2×C4—51no—
682C2×C4—51no—
683C2×C4—51no—
684C2×C4—51no—
685C2×C4—51no—
686C2×C4—52no—
687C2×C4—51no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—152no—
691C2×C4—304no—
692C2×C4—304no—
693C2×C4—304no—
694C2×C4—304no—
695C2×C4—301no—
696C2×C4—301no—
697C8—104no—
698C8—304no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—22no—
702C2×C3—22no—
703C2×C3#6577712yescomplemented
704C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
705D3—42no—
706D3—202no—
707C5C2×#513211yescharacteristic, complemented, Sylow
708C22—22no—
709C22—22no—
710C22—22no—
711C22—42no—
712C22—42no—
713C22—62no—
714C22—122no—
715C22—122no—
716C22—122no—
717C22—302no—
718C22—602no—
719C22—602no—
720C22—602no—
721C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
722C22C2×(C2×D3)⋊AGL(1,𝔽5)12yes—
723C22C2×(C2×D3)⋊AGL(1,𝔽5)12yes—
724C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
725C22C22×D3×AGL(1,𝔽5)11yescharacteristic
726C4—51no—
727C4—51no—
728C4—52no—
729C4—52no—
730C4—51no—
731C4—51no—
732C4—62no—
733C4—302no—
734C3C2×#6577711yescharacteristic, complemented, Sylow
735C2—21no—
736C2—21no—
737C2—22no—
738C2—22no—
739C2—122no—
740C2—602no—
741C2#1175200812yesdirect product factor
742C2C22×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC22×C3×C5C23×C4
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC24×C3×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#6782C2
cosocleC2×C3×Dic5C24
hypercenterC24D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#413
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C22×#6762C2semidirect
3. C22×C3×#704C2semidirect
4. C2×#91175C2semidirect
5. #11752008C2direct (N × H)
6. C2×#91174C2semidirect
26. C2×#6762C22semidirect
31. C2×C3×#704C22semidirect
33. #91175C22semidirect
34. #91174C22semidirect
38. C22×#704D3semidirect
131. C2×#704C2×D3semidirect
461. C2×C3×C5#413semidirect
608. C3×C5C2×#413semidirect
640. C2×C5#5132semidirect
703. C2×C3#65777semidirect
707. C5C2×#5132semidirect
734. C3C2×#65777semidirect
741. C2#11752008direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67822
C22×#67622
C22×C3×#7042
C2×#911752
#117520082
C2×#911742
C2×#657773
C2×#51325