Finite Group Databasebeta

← C5×#11005 #11933725

Subgroups — C5×#11005 #11933725

Order 1280.

1270 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
1C2×C5×#536C211yesmaximal, characteristic
2C2×C5×#421C211yesmaximal, characteristic
3C5×#2896C211yesmaximal, characteristic
4C2×C5×#419C211yesmaximal, characteristic, complemented
5C2×C5×#419C211yesmaximal, characteristic, complemented
6C2×C5×#344C211yesmaximal, characteristic, complemented
7C5×#1740C211yesmaximal, characteristic, complemented
8C22×C5×#41C2211yescharacteristic
9C23×C5×Q8C2211yescharacteristic
10C22×C5×M16C2211yescharacteristic
11C22×C5×M16C2211yescharacteristic
12C5×#536—22no—
13C5×#536—22no—
14C5×#536—22no—
15C5×#536C414yescomplemented
16C2×C5×C4⋊Q8—21no—
17C2×C5×#124—21no—
18C2×C5×#123—22no—
19C2×C5×C22⋊Q8—22no—
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—
28C5×#419—21no—
29C5×#419—22no—
30C5×#419—22no—
31C5×#418—21no—
32C5×#417—22no—
33C5×#416—22no—
34C2×C5×#103—22no—
35C2×C5×#103—22no—
36C5×#344—22no—
37C5×#342—22no—
38#11005C511yesmaximal, characteristic, direct product factor, Sylow
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×#41—21no—
49C2×C5×#41C2×C412yes—
50C2×C5×#41D412yes—
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×Q8—21no—
62C22×C5×Q8C2×C412yes—
63C22×C5×Q8D412yes—
64C22×C5×Q8D411yescharacteristic
65C22×C5×Q8D412yes—
66C22×C5×D4—21no—
67C22×C5×D4D411yescharacteristic
68C23×C4×C5—21no—
69C23×C4×C5—21no—
70C23×C4×C5C2311yescharacteristic
71C2×C5×M16—21no—
72C2×C5×M16—21no—
73C2×C5×M16—21no—
74C2×C5×M16—21no—
75C2×C5×M16—21no—
76C2×C5×M16—21no—
77C2×C5×M16—21no—
78C2×C5×M16—21no—
79C2×C5×M16—21no—
80C2×C5×M16—21no—
81C2×C5×M16—21no—
82C2×C5×M16D412yes—
83C22×C5×C8—21no—
84C22×C5×C8D412yes—
85C5×C4⋊Q8—24no—
86C5×C4⋊Q8—24no—
87C5×#124—24no—
88C5×#124—24no—
89C5×#123—28no—
90C5×#123—28no—
91C5×C22⋊Q8—28no—
92C5×C22⋊Q8—28no—
93C5×#117—21no—
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×#117C2×C412yes—
103C5×#117D412yes—
104C5×#117D412yes—
105C2×C5×C4⋊C4—24no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4D412yes—
109C2×C5×C22⋊C4—24no—
110C2×C5×C22⋊C4—21no—
111C2×C5×C22⋊C4—21no—
112C2×C5×C22⋊C4D412yes—
113C2×C42×C5—21no—
114C2×C42×C5—21no—
115C2×C42×C5—21no—
116C5×#104—28no—
117C5×#103—28no—
118C5×#103—28no—
119C5×#103—24no—
120C5×#102—24no—
121C2×#536C2×C511yescharacteristic
122C2×#421C2×C511yescharacteristic
123#2896C2×C511yescharacteristic
124C2×#419C2×C511yescharacteristic, complemented
125C2×#419C2×C511yescharacteristic, complemented
126C2×#344C2×C511yescharacteristic, complemented
127#1740C2×C511yescharacteristic, complemented
128C24×C5—21no—
129C24×C5C2×D411yescharacteristic
130C5×#41—22no—
131C5×#41—22no—
132C5×#41—22no—
133C5×#41—22no—
134C5×#41—22no—
135C5×#41—22no—
136C5×#41—22no—
137C5×#41—22no—
138C5×#41—41no—
139C5×#41—41no—
140C5×#41—41no—
141C5×#41—41no—
142C5×#41—41no—
143C5×#41—41no—
144C5×#41—41no—
145C5×#41—41no—
146C2×C5×Q8—22no—
147C2×C5×Q8—22no—
148C2×C5×Q8—22no—
149C2×C5×Q8—21no—
150C2×C5×Q8—22no—
151C2×C5×Q8—22no—
152C2×C5×Q8—22no—
153C2×C5×Q8—22no—
154C2×C5×Q8—22no—
155C2×C5×Q8—22no—
156C2×C5×Q8—21no—
157C2×C5×Q8—22no—
158C2×C5×Q8—22no—
159C2×C5×Q8—22no—
160C2×C5×Q8—22no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—22no—
164C2×C5×Q8—22no—
165C2×C5×Q8—21no—
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×Q8—41no—
177C2×C5×Q8—41no—
178C2×C5×Q8C22⋊C414yes—
179C2×C5×Q8C22⋊C412yes—
180C2×C5×D4—22no—
181C2×C5×D4—22no—
182C2×C5×D4—21no—
183C2×C5×D4—21no—
184C2×C5×D4—21no—
185C2×C5×D4—21no—
186C2×C5×D4—21no—
187C2×C5×D4—41no—
188C2×C5×D4—41no—
189C2×C5×D4—41no—
190C2×C5×D4—41no—
191C2×C5×D4C22⋊C412yes—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5—21no—
196C22×C4×C5—22no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
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×C5—41no—
208C22×C4×C5—41no—
209C22×C4×C5C22×C411yescharacteristic
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×C5C2×D411yescharacteristic
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5#4111yescharacteristic
220C22×C4×C5#4111yescharacteristic
221C22×C4×C5#4111yescharacteristic
222C22×C4×C5#4111yescharacteristic
223C5×M16—22no—
224C5×M16—22no—
225C5×M16—41no—
226C5×M16—41no—
227C5×M16—41no—
228C5×M16—41no—
229C5×M16—41no—
230C5×M16—41no—
231C2×C5×C8—22no—
232C2×C5×C8—22no—
233C2×C5×C8—22no—
234C2×C5×C8—22no—
235C2×C5×C8—41no—
236C2×C5×C8—41no—
237C5×C4⋊C4—216no—
238C5×C4⋊C4—22no—
239C5×C4⋊C4—22no—
240C5×C4⋊C4—22no—
241C5×C4⋊C4—22no—
242C5×C4⋊C4—22no—
243C5×C4⋊C4—41no—
244C5×C22⋊C4—216no—
245C5×C22⋊C4—22no—
246C5×C22⋊C4—22no—
247C5×C22⋊C4—41no—
248C5×C22⋊C4—41no—
249C5×C22⋊C4—41no—
250C5×C22⋊C4C22⋊C414yes—
251C42×C5—22no—
252C42×C5—22no—
253C42×C5—22no—
254C42×C5—41no—
255C42×C5—41no—
256C42×C5—41no—
257C22×#41C22×C511yescharacteristic
258C23×Q8C22×C511yescharacteristic
259C22×M16C22×C511yescharacteristic
260C22×M16C22×C511yescharacteristic
261#536—22no—
262#536—22no—
263#536—22no—
264#536C4×C514yescomplemented
265C2×C4⋊Q8—21no—
266C2×#124—21no—
267C2×#123—22no—
268C2×C22⋊Q8—22no—
269C2×#117C22×C511yescharacteristic
270C2×#117C22×C511yescharacteristic
271C2×#117C22×C511yescharacteristic
272#421—22no—
273#421—22no—
274C2×#104—22no—
275#419—22no—
276#419—22no—
277#419—21no—
278#419—22no—
279#419—22no—
280#418—21no—
281#417—22no—
282#416—22no—
283C2×#103—22no—
284C2×#103—22no—
285#344—22no—
286#342—22no—
287C23×C5—22no—
288C23×C5—42no—
289C23×C5—44no—
290C23×C5—41no—
291C23×C5—41no—
292C23×C5C2×C22⋊C411yescharacteristic
293C23×C5#12011yescharacteristic
294C23×C5#12011yescharacteristic
295C23×C5#12111yescharacteristic
296C23×C5#12111yescharacteristic
297C23×C5#12411yescharacteristic
298C23×C5#12711yescharacteristic
299C5×Q8—24no—
300C5×Q8—24no—
301C5×Q8—22no—
302C5×Q8—22no—
303C5×Q8—42no—
304C5×Q8—42no—
305C5×Q8—42no—
306C5×Q8—42no—
307C5×Q8—41no—
308C5×Q8—42no—
309C5×Q8—42no—
310C5×Q8—41no—
311C5×D4—22no—
312C5×D4—22no—
313C5×D4—42no—
314C5×D4—42no—
315C5×D4—42no—
316C5×D4—42no—
317C5×D4—41no—
318C5×D4—41no—
319C2×C4×C5—24no—
320C2×C4×C5—24no—
321C2×C4×C5—22no—
322C2×C4×C5—44no—
323C2×C4×C5—42no—
324C2×C4×C5—42no—
325C2×C4×C5—42no—
326C2×C4×C5—41no—
327C2×C4×C5—42no—
328C2×C4×C5—41no—
329C2×C4×C5—42no—
330C2×C4×C5—42no—
331C2×C4×C5—42no—
332C2×C4×C5—42no—
333C2×C4×C5—42no—
334C2×C4×C5—42no—
335C2×C4×C5—42no—
336C2×C4×C5—42no—
337C2×C4×C5—82no—
338C2×C4×C5—82no—
339C2×C4×C5C2×C22⋊C411yescharacteristic
340C2×C4×C5C2×C22⋊C411yescharacteristic
341C2×C4×C5C4×D411yescharacteristic
342C2×C4×C5C4×D411yescharacteristic
343C2×C4×C5C4×D411yescharacteristic
344C2×C4×C5C4×D411yescharacteristic
345C2×C4×C5#12011yescharacteristic
346C2×C4×C5#12011yescharacteristic
347C2×C4×C5#12011yescharacteristic
348C2×C4×C5#12011yescharacteristic
349C2×C4×C5#12011yescharacteristic
350C2×C4×C5#12011yescharacteristic
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#12111yescharacteristic
358C2×C4×C5#12111yescharacteristic
359C2×C4×C5#12111yescharacteristic
360C2×C4×C5#12111yescharacteristic
361C2×C4×C5#12311yescharacteristic
362C2×C4×C5#12311yescharacteristic
363C2×C4×C5#12311yescharacteristic
364C2×C4×C5#12311yescharacteristic
365C2×C4×C5#12411yescharacteristic
366C2×C4×C5#12711yescharacteristic
367C5×C8—42no—
368C5×C8—42no—
369C2×#41—21no—
370C2×#41—21no—
371C2×#41—21no—
372C2×#41—21no—
373C2×#41—21no—
374C2×#41—21no—
375C2×#41—21no—
376C2×#41—21no—
377C2×#41—21no—
378C2×#41—21no—
379C2×#41C2×C4×C512yes—
380C2×#41C5×D412yes—
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×Q8—21no—
390C22×Q8—21no—
391C22×Q8—21no—
392C22×Q8C2×C4×C512yes—
393C22×Q8C5×D412yes—
394C22×Q8C5×D411yescharacteristic
395C22×Q8C5×D412yes—
396C22×D4—21no—
397C22×D4C5×D411yescharacteristic
398C23×C4—21no—
399C23×C4—21no—
400C23×C4C23×C511yescharacteristic
401C2×M16—21no—
402C2×M16—21no—
403C2×M16—21no—
404C2×M16—21no—
405C2×M16—21no—
406C2×M16—21no—
407C2×M16—21no—
408C2×M16—21no—
409C2×M16—21no—
410C2×M16—21no—
411C2×M16—21no—
412C2×M16C5×D412yes—
413C22×C8—21no—
414C22×C8C5×D412yes—
415C4⋊Q8—24no—
416C4⋊Q8—24no—
417#124—24no—
418#124—24no—
419#123—28no—
420#123—28no—
421C22⋊Q8—28no—
422C22⋊Q8—28no—
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#117C2×C4×C512yes—
433#117C5×D412yes—
434#117C5×D412yes—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4C5×D412yes—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4C5×D412yes—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—21no—
446#104—28no—
447#103—28no—
448#103—28no—
449#103—24no—
450#102—24no—
451C22×C5—22no—
452C22×C5—22no—
453C22×C5—22no—
454C22×C5—41no—
455C22×C5—41no—
456C22×C5—41no—
457C22×C5—41no—
458C22×C5—44no—
459C22×C5—42no—
460C22×C5—82no—
461C22×C5—82no—
462C22×C5#37911yescharacteristic
463C22×C5#39011yescharacteristic
464C22×C5#39011yescharacteristic
465C22×C5#39211yescharacteristic
466C22×C5#39211yescharacteristic
467C22×C5#39411yescharacteristic
468C22×C5#39411yescharacteristic
469C4×C5—44no—
470C4×C5—42no—
471C4×C5—44no—
472C4×C5—82no—
473C4×C5—82no—
474C4×C5#38611yescharacteristic
475C4×C5#38611yescharacteristic
476C4×C5#38611yescharacteristic
477C4×C5#38611yescharacteristic
478C4×C5#39211yescharacteristic
479C4×C5#39211yescharacteristic
480C4×C5#39411yescharacteristic
481C4×C5#39411yescharacteristic
482C24—21no—
483C24C2×C5×D411yescharacteristic
484#41—22no—
485#41—22no—
486#41—22no—
487#41—22no—
488#41—22no—
489#41—22no—
490#41—22no—
491#41—22no—
492#41—41no—
493#41—41no—
494#41—41no—
495#41—41no—
496#41—41no—
497#41—41no—
498#41—41no—
499#41—41no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—21no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—21no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8—22no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—21no—
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×Q8—41no—
529C2×Q8—41no—
530C2×Q8—41no—
531C2×Q8—41no—
532C2×Q8C5×C22⋊C414yes—
533C2×Q8C5×C22⋊C412yes—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—41no—
542C2×D4—41no—
543C2×D4—41no—
544C2×D4—41no—
545C2×D4C5×C22⋊C412yes—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4C22×C4×C511yescharacteristic
564C22×C4C2×C5×D411yescharacteristic
565C22×C4C2×C5×D411yescharacteristic
566C22×C4C2×C5×D411yescharacteristic
567C22×C4C2×C5×D411yescharacteristic
568C22×C4C2×C5×D411yescharacteristic
569C22×C4C2×C5×D411yescharacteristic
570C22×C4C2×C5×D411yescharacteristic
571C22×C4C2×C5×D411yescharacteristic
572C22×C4C2×C5×D411yescharacteristic
573C22×C4C5×#4111yescharacteristic
574C22×C4C5×#4111yescharacteristic
575C22×C4C5×#4111yescharacteristic
576C22×C4C5×#4111yescharacteristic
577M16—22no—
578M16—22no—
579M16—41no—
580M16—41no—
581M16—41no—
582M16—41no—
583M16—41no—
584M16—41no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—41no—
590C2×C8—41no—
591C4⋊C4—216no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—41no—
598C22⋊C4—216no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—41no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4C5×C22⋊C414yes—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—41no—
609C42—41no—
610C42—41no—
611C2×C5—21no—
612C2×C5—21no—
613C2×C5—21no—
614C2×C5—21no—
615C2×C5—21no—
616C2×C5—21no—
617C2×C5—82no—
618C2×C5#143811yescharacteristic
619C2×C5#200912yes—
620C23—22no—
621C23—42no—
622C23—44no—
623C23—41no—
624C23—41no—
625C23C2×C5×C22⋊C411yescharacteristic
626C23C5×#12011yescharacteristic
627C23C5×#12011yescharacteristic
628C23C5×#12111yescharacteristic
629C23C5×#12111yescharacteristic
630C23C5×#12411yescharacteristic
631C23C5×#12711yescharacteristic
632Q8—24no—
633Q8—24no—
634Q8—22no—
635Q8—22no—
636Q8—42no—
637Q8—42no—
638Q8—42no—
639Q8—42no—
640Q8—41no—
641Q8—42no—
642Q8—42no—
643Q8—41no—
644D4—22no—
645D4—22no—
646D4—42no—
647D4—42no—
648D4—42no—
649D4—42no—
650D4—41no—
651D4—41no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—44no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—82no—
671C2×C4—82no—
672C2×C4C2×C5×C22⋊C411yescharacteristic
673C2×C4C2×C5×C22⋊C411yescharacteristic
674C2×C4C4×C5×D411yescharacteristic
675C2×C4C4×C5×D411yescharacteristic
676C2×C4C4×C5×D411yescharacteristic
677C2×C4C4×C5×D411yescharacteristic
678C2×C4C5×#12011yescharacteristic
679C2×C4C5×#12011yescharacteristic
680C2×C4C5×#12011yescharacteristic
681C2×C4C5×#12011yescharacteristic
682C2×C4C5×#12011yescharacteristic
683C2×C4C5×#12011yescharacteristic
684C2×C4C5×#12111yescharacteristic
685C2×C4C5×#12111yescharacteristic
686C2×C4C5×#12111yescharacteristic
687C2×C4C5×#12111yescharacteristic
688C2×C4C5×#12111yescharacteristic
689C2×C4C5×#12111yescharacteristic
690C2×C4C5×#12111yescharacteristic
691C2×C4C5×#12111yescharacteristic
692C2×C4C5×#12111yescharacteristic
693C2×C4C5×#12111yescharacteristic
694C2×C4C5×#12311yescharacteristic
695C2×C4C5×#12311yescharacteristic
696C2×C4C5×#12311yescharacteristic
697C2×C4C5×#12311yescharacteristic
698C2×C4C5×#12411yescharacteristic
699C2×C4C5×#12711yescharacteristic
700C8—42no—
701C8—42no—
702C5#1100511yescharacteristic, direct product factor, Sylow
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—44no—
711C22—42no—
712C22—82no—
713C22—82no—
714C22C5×#37911yescharacteristic
715C22C5×#39011yescharacteristic
716C22C5×#39011yescharacteristic
717C22C5×#39211yescharacteristic
718C22C5×#39211yescharacteristic
719C22C5×#39411yescharacteristic
720C22C5×#39411yescharacteristic
721C4—44no—
722C4—42no—
723C4—44no—
724C4—82no—
725C4—82no—
726C4C5×#38611yescharacteristic
727C4C5×#38611yescharacteristic
728C4C5×#38611yescharacteristic
729C4C5×#38611yescharacteristic
730C4C5×#39211yescharacteristic
731C4C5×#39211yescharacteristic
732C4C5×#39411yescharacteristic
733C4C5×#39411yescharacteristic
734C2—21no—
735C2—21no—
736C2—21no—
737C2—21no—
738C2—21no—
739C2—21no—
740C2—82no—
741C2C5×#143811yescharacteristic
742C2C5×#200912yes—
subgroupG/H
center, socleC22×C5#392
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
4. C2×C5×#419C2semidirect
5. C2×C5×#419C2semidirect
6. C2×C5×#344C2semidirect
7. C5×#1740C2semidirect
15. C5×#536C4semidirect
38. #11005C5direct (N × H)
124. C2×#419C2×C5semidirect
125. C2×#419C2×C5semidirect
126. C2×#344C2×C5semidirect
127. #1740C2×C5semidirect
264. #536C4×C5semidirect
702. C5#11005direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5362
C2×C5×#4212
C5×#28962
C2×C5×#4192
C2×C5×#3442
C5×#17402
#110055