Finite Group Databasebeta

← C5×#11013 #11933733

Subgroups — C5×#11013 #11933733

Order 1280.

1262 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#137C211yesmaximal, characteristic
2C2×C5×#421C211yesmaximal, characteristic
3C2×C5×#419C211yesmaximal, characteristic, complemented
4C2×C5×#410C211yesmaximal, characteristic
5C5×#2310C211yesmaximal, characteristic, complemented
6C2×C5×#344C211yesmaximal, characteristic, complemented
7C2×C5×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×C5×#41C2211yescharacteristic
9C23×C5×Q8C2211yescharacteristic
10C2×C5×#137—22no—
11C2×C5×#137—22no—
12C2×C5×#137—22no—
13C2×C5×#137—22no—
14C2×C5×#137—22no—
15C2×C5×#137—22no—
16C22×C5×Q16C412yescomplemented
17C22×C5×SD16C412yescomplemented
18C22×C5×M16C2211yescharacteristic
19C22×C5×M16C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C2×C5×#117C2211yescharacteristic
22C2×C5×#117C2211yescharacteristic
23C5×#421—22no—
24C5×#421—22no—
25C2×C5×#104—22no—
26C5×#419—22no—
27C5×#419—22no—
28C2×C5×#103—22no—
29C5×#410—22no—
30C5×#410—22no—
31C2×C5×#99—22no—
32C5×#391—22no—
33C5×#391—22no—
34C5×#381—22no—
35C5×#344—22no—
36C5×H(3,ℤ/4)—22no—
37#11013C511yesmaximal, characteristic, direct product factor, Sylow
38C2×C5×#41—21no—
39C2×C5×#41—21no—
40C2×C5×#41—21no—
41C2×C5×#41—21no—
42C2×C5×#41—21no—
43C2×C5×#41—21no—
44C2×C5×#41—21no—
45C2×C5×#41—21no—
46C2×C5×#41—21no—
47C2×C5×#41—21no—
48C2×C5×#41D412yes—
49C2×C5×#41D412yes—
50C22×C5×Q8—21no—
51C22×C5×Q8—21no—
52C22×C5×Q8—21no—
53C22×C5×Q8—21no—
54C22×C5×Q8—21no—
55C22×C5×Q8—21no—
56C22×C5×Q8—21no—
57C22×C5×Q8—21no—
58C22×C5×Q8—21no—
59C22×C5×Q8—21no—
60C22×C5×Q8—21no—
61C22×C5×Q8C2×C412yes—
62C22×C5×Q8C2×C411yescharacteristic
63C22×C5×Q8D412yes—
64C22×C5×Q8D412yes—
65C22×C5×D4—21no—
66C22×C5×D4C2×C411yescharacteristic
67C23×C4×C5—21no—
68C23×C4×C5—21no—
69C23×C4×C5C2311yescharacteristic
70C5×#137—28no—
71C5×#137—28no—
72C5×#137—28no—
73C5×#137—28no—
74C2×C5×Q16—24no—
75C2×C5×Q16—24no—
76C2×C5×Q16—24no—
77C2×C5×SD16—24no—
78C2×C5×SD16—24no—
79C2×C5×SD16—24no—
80C2×C5×M16—21no—
81C2×C5×M16—21no—
82C2×C5×M16—21no—
83C2×C5×M16—21no—
84C2×C5×M16—21no—
85C2×C5×M16—21no—
86C2×C5×M16—21no—
87C2×C5×M16—21no—
88C2×C5×M16—21no—
89C2×C5×M16D412yes—
90C2×C5×M16D412yes—
91C2×C5×M16D412yes—
92C22×C5×C8—21no—
93C22×C5×C8C2×C412yes—
94C5×#117—21no—
95C5×#117—21no—
96C5×#117—21no—
97C5×#117—21no—
98C5×#117—21no—
99C5×#117—21no—
100C5×#117—21no—
101C5×#117—21no—
102C5×#117—21no—
103C5×#117—21no—
104C5×#117—21no—
105C5×#117D412yes—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C22⋊C4—21no—
110C2×C5×C22⋊C4—21no—
111C2×C5×C22⋊C4D412yes—
112C2×C42×C5—21no—
113C2×C42×C5—21no—
114C2×C42×C5D412yes—
115C5×#104—28no—
116C5×#103—28no—
117C5×#99—28no—
118C5×#95—28no—
119C22×#137C2×C511yescharacteristic
120C2×#421C2×C511yescharacteristic
121C2×#419C2×C511yescharacteristic, complemented
122C2×#410C2×C511yescharacteristic
123#2310C2×C511yescharacteristic, complemented
124C2×#344C2×C511yescharacteristic, complemented
125C2×H(3,ℤ/4)C2×C511yescharacteristic, complemented
126C24×C5—21no—
127C24×C5C2×D411yescharacteristic
128C5×#41—22no—
129C5×#41—22no—
130C5×#41—22no—
131C5×#41—22no—
132C5×#41—22no—
133C5×#41—22no—
134C5×#41—22no—
135C5×#41—22no—
136C5×#41—41no—
137C5×#41—41no—
138C5×#41—41no—
139C5×#41—41no—
140C5×#41—41no—
141C5×#41—41no—
142C5×#41—41no—
143C5×#41—41no—
144C2×C5×Q8—22no—
145C2×C5×Q8—21no—
146C2×C5×Q8—22no—
147C2×C5×Q8—22no—
148C2×C5×Q8—22no—
149C2×C5×Q8—22no—
150C2×C5×Q8—21no—
151C2×C5×Q8—21no—
152C2×C5×Q8—22no—
153C2×C5×Q8—22no—
154C2×C5×Q8—21no—
155C2×C5×Q8—21no—
156C2×C5×Q8—22no—
157C2×C5×Q8—22no—
158C2×C5×Q8—22no—
159C2×C5×Q8—22no—
160C2×C5×Q8—22no—
161C2×C5×Q8—22no—
162C2×C5×Q8—22no—
163C2×C5×Q8—22no—
164C2×C5×Q8—41no—
165C2×C5×Q8—41no—
166C2×C5×Q8—41no—
167C2×C5×Q8—41no—
168C2×C5×Q8—41no—
169C2×C5×Q8—41no—
170C2×C5×Q8—41no—
171C2×C5×Q8—41no—
172C2×C5×Q8—41no—
173C2×C5×Q8—41no—
174C2×C5×Q8—41no—
175C2×C5×Q8—41no—
176C2×C5×Q8C22⋊C414yes—
177C2×C5×Q8C22⋊C412yes—
178C2×C5×D4—22no—
179C2×C5×D4—22no—
180C2×C5×D4—21no—
181C2×C5×D4—21no—
182C2×C5×D4—21no—
183C2×C5×D4—21no—
184C2×C5×D4—21no—
185C2×C5×D4—41no—
186C2×C5×D4—41no—
187C2×C5×D4—41no—
188C2×C5×D4—41no—
189C2×C5×D4C22⋊C412yes—
190C22×C4×C5—21no—
191C22×C4×C5—22no—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5—22no—
198C22×C4×C5—41no—
199C22×C4×C5—41no—
200C22×C4×C5—41no—
201C22×C4×C5—41no—
202C22×C4×C5—41no—
203C22×C4×C5—41no—
204C22×C4×C5—41no—
205C22×C4×C5—41no—
206C22×C4×C5—41no—
207C22×C4×C5C22×C411yescharacteristic
208C22×C4×C5C2×D411yescharacteristic
209C22×C4×C5C2×D411yescharacteristic
210C22×C4×C5C2×D411yescharacteristic
211C22×C4×C5C2×D411yescharacteristic
212C22×C4×C5C2×D411yescharacteristic
213C22×C4×C5C2×D411yescharacteristic
214C22×C4×C5C2×D411yescharacteristic
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5#4111yescharacteristic
218C22×C4×C5#4111yescharacteristic
219C22×C4×C5#4111yescharacteristic
220C22×C4×C5#4111yescharacteristic
221C5×Q16—216no—
222C5×SD16—216no—
223C5×M16—22no—
224C5×M16—22no—
225C5×M16—22no—
226C5×M16—22no—
227C5×M16—22no—
228C5×M16—22no—
229C5×M16—41no—
230C5×M16—41no—
231C2×C5×C8—22no—
232C2×C5×C8—22no—
233C2×C5×C8—22no—
234C2×C5×C8—41no—
235C2×C5×C8—41no—
236C2×C5×C8C22⋊C414yes—
237C5×C4⋊C4—22no—
238C5×C4⋊C4—41no—
239C5×C4⋊C4—41no—
240C5×C4⋊C4—41no—
241C5×C4⋊C4—41no—
242C5×C4⋊C4—41no—
243C5×C22⋊C4—22no—
244C5×C22⋊C4—22no—
245C5×C22⋊C4—22no—
246C5×C22⋊C4—41no—
247C5×C22⋊C4—41no—
248C5×C22⋊C4—41no—
249C42×C5—22no—
250C42×C5—22no—
251C42×C5—22no—
252C42×C5—41no—
253C42×C5—41no—
254C42×C5—41no—
255C22×#41C22×C511yescharacteristic
256C23×Q8C22×C511yescharacteristic
257C2×#137—22no—
258C2×#137—22no—
259C2×#137—22no—
260C2×#137—22no—
261C2×#137—22no—
262C2×#137—22no—
263C22×Q16C4×C512yescomplemented
264C22×SD16C4×C512yescomplemented
265C22×M16C22×C511yescharacteristic
266C22×M16C22×C511yescharacteristic
267C2×#117C22×C511yescharacteristic
268C2×#117C22×C511yescharacteristic
269C2×#117C22×C511yescharacteristic
270#421—22no—
271#421—22no—
272C2×#104—22no—
273#419—22no—
274#419—22no—
275C2×#103—22no—
276#410—22no—
277#410—22no—
278C2×#99—22no—
279#391—22no—
280#391—22no—
281#381—22no—
282#344—22no—
283H(3,ℤ/4)—22no—
284C23×C5—22no—
285C23×C5—42no—
286C23×C5—41no—
287C23×C5—41no—
288C23×C5—82no—
289C23×C5C4×D411yescharacteristic
290C23×C5#12011yescharacteristic
291C23×C5#12011yescharacteristic
292C23×C5#12111yescharacteristic
293C23×C5#12111yescharacteristic
294C23×C5#12111yescharacteristic
295C23×C5#12711yescharacteristic
296C5×Q8—24no—
297C5×Q8—22no—
298C5×Q8—24no—
299C5×Q8—22no—
300C5×Q8—42no—
301C5×Q8—41no—
302C5×Q8—42no—
303C5×Q8—41no—
304C5×Q8—42no—
305C5×Q8—42no—
306C5×Q8—42no—
307C5×Q8—42no—
308C5×D4—22no—
309C5×D4—22no—
310C5×D4—42no—
311C5×D4—42no—
312C5×D4—42no—
313C5×D4—42no—
314C5×D4—41no—
315C5×D4—41no—
316C2×C4×C5—22no—
317C2×C4×C5—24no—
318C2×C4×C5—42no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—42no—
322C2×C4×C5—42no—
323C2×C4×C5—42no—
324C2×C4×C5—42no—
325C2×C4×C5—42no—
326C2×C4×C5—42no—
327C2×C4×C5—42no—
328C2×C4×C5—42no—
329C2×C4×C5—42no—
330C2×C4×C5—44no—
331C2×C4×C5—44no—
332C2×C4×C5—42no—
333C2×C4×C5—42no—
334C2×C4×C5—42no—
335C2×C4×C5—82no—
336C2×C4×C5C2×C22⋊C411yescharacteristic
337C2×C4×C5C2×C22⋊C411yescharacteristic
338C2×C4×C5C2×C22⋊C411yescharacteristic
339C2×C4×C5C4×D411yescharacteristic
340C2×C4×C5C4×D411yescharacteristic
341C2×C4×C5C4×D411yescharacteristic
342C2×C4×C5#12011yescharacteristic
343C2×C4×C5#12011yescharacteristic
344C2×C4×C5#12011yescharacteristic
345C2×C4×C5#12011yescharacteristic
346C2×C4×C5#12011yescharacteristic
347C2×C4×C5#12011yescharacteristic
348C2×C4×C5#12111yescharacteristic
349C2×C4×C5#12111yescharacteristic
350C2×C4×C5#12111yescharacteristic
351C2×C4×C5#12111yescharacteristic
352C2×C4×C5#12111yescharacteristic
353C2×C4×C5#12111yescharacteristic
354C2×C4×C5#12111yescharacteristic
355C2×C4×C5#12111yescharacteristic
356C2×C4×C5#12111yescharacteristic
357C2×C4×C5#12311yescharacteristic
358C2×C4×C5#12311yescharacteristic
359C2×C4×C5#12311yescharacteristic
360C2×C4×C5#12311yescharacteristic
361C2×C4×C5#12411yescharacteristic
362C2×C4×C5#12411yescharacteristic
363C2×C4×C5#12711yescharacteristic
364C5×C8—24no—
365C5×C8—42no—
366C2×#41—21no—
367C2×#41—21no—
368C2×#41—21no—
369C2×#41—21no—
370C2×#41—21no—
371C2×#41—21no—
372C2×#41—21no—
373C2×#41—21no—
374C2×#41—21no—
375C2×#41—21no—
376C2×#41C5×D412yes—
377C2×#41C5×D412yes—
378C22×Q8—21no—
379C22×Q8—21no—
380C22×Q8—21no—
381C22×Q8—21no—
382C22×Q8—21no—
383C22×Q8—21no—
384C22×Q8—21no—
385C22×Q8—21no—
386C22×Q8—21no—
387C22×Q8—21no—
388C22×Q8—21no—
389C22×Q8C2×C4×C512yes—
390C22×Q8C2×C4×C511yescharacteristic
391C22×Q8C5×D412yes—
392C22×Q8C5×D412yes—
393C22×D4—21no—
394C22×D4C2×C4×C511yescharacteristic
395C23×C4—21no—
396C23×C4—21no—
397C23×C4C23×C511yescharacteristic
398#137—28no—
399#137—28no—
400#137—28no—
401#137—28no—
402C2×Q16—24no—
403C2×Q16—24no—
404C2×Q16—24no—
405C2×SD16—24no—
406C2×SD16—24no—
407C2×SD16—24no—
408C2×M16—21no—
409C2×M16—21no—
410C2×M16—21no—
411C2×M16—21no—
412C2×M16—21no—
413C2×M16—21no—
414C2×M16—21no—
415C2×M16—21no—
416C2×M16—21no—
417C2×M16C5×D412yes—
418C2×M16C5×D412yes—
419C2×M16C5×D412yes—
420C22×C8—21no—
421C22×C8C2×C4×C512yes—
422#117—21no—
423#117—21no—
424#117—21no—
425#117—21no—
426#117—21no—
427#117—21no—
428#117—21no—
429#117—21no—
430#117—21no—
431#117—21no—
432#117—21no—
433#117C5×D412yes—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4C5×D412yes—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42C5×D412yes—
443#104—28no—
444#103—28no—
445#99—28no—
446#95—28no—
447C22×C5—22no—
448C22×C5—22no—
449C22×C5—22no—
450C22×C5—41no—
451C22×C5—41no—
452C22×C5—41no—
453C22×C5—41no—
454C22×C5—42no—
455C22×C5—82no—
456C22×C5—82no—
457C22×C5—82no—
458C22×C5#38611yescharacteristic
459C22×C5#38611yescharacteristic
460C22×C5#39011yescharacteristic
461C22×C5#39211yescharacteristic
462C22×C5#39211yescharacteristic
463C22×C5#39211yescharacteristic
464C22×C5#39411yescharacteristic
465C4×C5—42no—
466C4×C5—44no—
467C4×C5—82no—
468C4×C5—82no—
469C4×C5—82no—
470C4×C5#37911yescharacteristic
471C4×C5#38611yescharacteristic
472C4×C5#38611yescharacteristic
473C4×C5#39011yescharacteristic
474C4×C5#39211yescharacteristic
475C4×C5#39411yescharacteristic
476C4×C5#39411yescharacteristic
477C4×C5#39411yescharacteristic
478C24—21no—
479C24C2×C5×D411yescharacteristic
480#41—22no—
481#41—22no—
482#41—22no—
483#41—22no—
484#41—22no—
485#41—22no—
486#41—22no—
487#41—22no—
488#41—41no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493#41—41no—
494#41—41no—
495#41—41no—
496C2×Q8—22no—
497C2×Q8—21no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—41no—
517C2×Q8—41no—
518C2×Q8—41no—
519C2×Q8—41no—
520C2×Q8—41no—
521C2×Q8—41no—
522C2×Q8—41no—
523C2×Q8—41no—
524C2×Q8—41no—
525C2×Q8—41no—
526C2×Q8—41no—
527C2×Q8—41no—
528C2×Q8C5×C22⋊C414yes—
529C2×Q8C5×C22⋊C412yes—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—41no—
538C2×D4—41no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4C5×C22⋊C412yes—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4C22×C4×C511yescharacteristic
560C22×C4C2×C5×D411yescharacteristic
561C22×C4C2×C5×D411yescharacteristic
562C22×C4C2×C5×D411yescharacteristic
563C22×C4C2×C5×D411yescharacteristic
564C22×C4C2×C5×D411yescharacteristic
565C22×C4C2×C5×D411yescharacteristic
566C22×C4C2×C5×D411yescharacteristic
567C22×C4C2×C5×D411yescharacteristic
568C22×C4C2×C5×D411yescharacteristic
569C22×C4C5×#4111yescharacteristic
570C22×C4C5×#4111yescharacteristic
571C22×C4C5×#4111yescharacteristic
572C22×C4C5×#4111yescharacteristic
573Q16—216no—
574SD16—216no—
575M16—22no—
576M16—22no—
577M16—22no—
578M16—22no—
579M16—22no—
580M16—22no—
581M16—41no—
582M16—41no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8C5×C22⋊C414yes—
589C4⋊C4—22no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—41no—
599C22⋊C4—41no—
600C22⋊C4—41no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—41no—
605C42—41no—
606C42—41no—
607C2×C5—21no—
608C2×C5—21no—
609C2×C5—21no—
610C2×C5—21no—
611C2×C5—21no—
612C2×C5—21no—
613C2×C5—82no—
614C2×C5#143811yescharacteristic
615C2×C5#190512yes—
616C23—22no—
617C23—42no—
618C23—41no—
619C23—41no—
620C23—82no—
621C23C4×C5×D411yescharacteristic
622C23C5×#12011yescharacteristic
623C23C5×#12011yescharacteristic
624C23C5×#12111yescharacteristic
625C23C5×#12111yescharacteristic
626C23C5×#12111yescharacteristic
627C23C5×#12711yescharacteristic
628Q8—24no—
629Q8—22no—
630Q8—24no—
631Q8—22no—
632Q8—42no—
633Q8—41no—
634Q8—42no—
635Q8—41no—
636Q8—42no—
637Q8—42no—
638Q8—42no—
639Q8—42no—
640D4—22no—
641D4—22no—
642D4—42no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—41no—
647D4—41no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—82no—
668C2×C4C2×C5×C22⋊C411yescharacteristic
669C2×C4C2×C5×C22⋊C411yescharacteristic
670C2×C4C2×C5×C22⋊C411yescharacteristic
671C2×C4C4×C5×D411yescharacteristic
672C2×C4C4×C5×D411yescharacteristic
673C2×C4C4×C5×D411yescharacteristic
674C2×C4C5×#12011yescharacteristic
675C2×C4C5×#12011yescharacteristic
676C2×C4C5×#12011yescharacteristic
677C2×C4C5×#12011yescharacteristic
678C2×C4C5×#12011yescharacteristic
679C2×C4C5×#12011yescharacteristic
680C2×C4C5×#12111yescharacteristic
681C2×C4C5×#12111yescharacteristic
682C2×C4C5×#12111yescharacteristic
683C2×C4C5×#12111yescharacteristic
684C2×C4C5×#12111yescharacteristic
685C2×C4C5×#12111yescharacteristic
686C2×C4C5×#12111yescharacteristic
687C2×C4C5×#12111yescharacteristic
688C2×C4C5×#12111yescharacteristic
689C2×C4C5×#12311yescharacteristic
690C2×C4C5×#12311yescharacteristic
691C2×C4C5×#12311yescharacteristic
692C2×C4C5×#12311yescharacteristic
693C2×C4C5×#12411yescharacteristic
694C2×C4C5×#12411yescharacteristic
695C2×C4C5×#12711yescharacteristic
696C8—24no—
697C8—42no—
698C5#1101311yescharacteristic, direct product factor, Sylow
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—42no—
707C22—82no—
708C22—82no—
709C22—82no—
710C22C5×#38611yescharacteristic
711C22C5×#38611yescharacteristic
712C22C5×#39011yescharacteristic
713C22C5×#39211yescharacteristic
714C22C5×#39211yescharacteristic
715C22C5×#39211yescharacteristic
716C22C5×#39411yescharacteristic
717C4—42no—
718C4—44no—
719C4—82no—
720C4—82no—
721C4—82no—
722C4C5×#37911yescharacteristic
723C4C5×#38611yescharacteristic
724C4C5×#38611yescharacteristic
725C4C5×#39011yescharacteristic
726C4C5×#39211yescharacteristic
727C4C5×#39411yescharacteristic
728C4C5×#39411yescharacteristic
729C4C5×#39411yescharacteristic
730C2—21no—
731C2—21no—
732C2—21no—
733C2—21no—
734C2—21no—
735C2—21no—
736C2—82no—
737C2C5×#143811yescharacteristic
738C2C5×#190512yes—
subgroupG/H
center, socleC22×C5#386
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC22×C5×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C5×#419C2semidirect
5. C5×#2310C2semidirect
6. C2×C5×#344C2semidirect
7. C2×C5×H(3,ℤ/4)C2semidirect
16. C22×C5×Q16C4semidirect
17. C22×C5×SD16C4semidirect
37. #11013C5direct (N × H)
121. C2×#419C2×C5semidirect
123. #2310C2×C5semidirect
124. C2×#344C2×C5semidirect
125. C2×H(3,ℤ/4)C2×C5semidirect
263. C22×Q16C4×C5semidirect
264. C22×SD16C4×C5semidirect
698. C5#11013direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1372
C2×C5×#4212
C2×C5×#4192
C2×C5×#4102
C5×#23102
C2×C5×#3442
C2×C5×H(3,ℤ/4)2
#110135