Finite Group Databasebeta

← C2×C5×#3013 #11983085

Subgroups — C2×C5×#3013 #11983085

Order 1280.

4782 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×2−1+4C211yesmaximal, characteristic, complemented
2C22×C5×#137C211yesmaximal, characteristic, complemented
3C22×C5×#135C211yesmaximal, characteristic, complemented
4C2×C5×#537C211yesmaximal, characteristic, complemented
5C5×#3013C2116yesmaximal, direct product factor
6C2×C5×#452C212yesmaximal, complemented
7C2×C5×#449C212yesmaximal, complemented
8C2×C5×#451C212yesmaximal, complemented
9C2×C5×#448C212yesmaximal, complemented
10C2×C5×#417C211yesmaximal, characteristic, complemented
11C22×C5×#103C211yesmaximal, characteristic, complemented
12C2×C5×#408C211yesmaximal, characteristic, complemented
13C2×C5×2−1+4—24no—
14C2×C5×2−1+4—28no—
15C2×C5×2−1+4—28no—
16C2×C5×2−1+4C2218yescomplemented
17C22×C5×#41—21no—
18C22×C5×#41—22no—
19C22×C5×#41C2212yes—
20C22×C5×#41C2211yescharacteristic
21C22×C5×#41C2211yescharacteristic
22C22×C5×#41C2211yescharacteristic
23C23×C5×Q8—21no—
24C23×C5×Q8C2212yes—
25C23×C5×Q8C2211yescharacteristic
26C2×C5×#137—28no—
27C2×C5×#137C2218yescomplemented
28C2×C5×#135—28no—
29C2×C5×#135C2218yescomplemented
30C22×C5×Q16C2211yescharacteristic
31C22×C5×Q16C2212yes—
32C22×C5×SD16C2211yescharacteristic
33C22×C5×SD16C2212yes—
34C22×C5×SD16C2211yescharacteristic
35C22×C5×D8C2211yescharacteristic
36C22×C5×M16C2211yescharacteristic
37C23×C5×C8C2211yescharacteristic
38C5×#537—24no—
39C5×#537C2218yescomplemented
40C2×C5×C22⋊Q8—21no—
41C2×C5×C22⋊Q8C2212yes—
42C2×C5×#121—21no—
43C2×C5×#121—22no—
44C2×C5×#121C2212yes—
45C22×C5×C4⋊C4C2211yescharacteristic
46C5×#452C22116yescomplemented
47C5×#451C22116yescomplemented
48C5×#449C22116yescomplemented
49C5×#448C22116yescomplemented
50C5×#417C2218yescomplemented
51C2×C5×#103C2212yes—
52C2×C5×#103C2212yes—
53C2×C5×#103C2212yes—
54C2×C5×#103C2218yescomplemented
55C2×C5×#102C2212yes—
56C5×#408C2218yescomplemented
57C2×C5×C22⋊C8C2212yes—
58C2×C5×C22⋊C8C2212yes—
59C2×#3013C511yesmaximal, characteristic, direct product factor, Sylow
60C5×2−1+4—264no—
61C5×2−1+4—232no—
62C5×2−1+4—232no—
63C2×C5×#41—232no—
64C2×C5×#41—216no—
65C2×C5×#41—28no—
66C2×C5×#41—28no—
67C2×C5×#41—216no—
68C2×C5×#41—28no—
69C2×C5×#41—24no—
70C2×C5×#41—24no—
71C2×C5×#41—22no—
72C2×C5×#41—24no—
73C2×C5×#41—24no—
74C2×C5×#41—22no—
75C2×C5×#41—24no—
76C2×C5×#41—24no—
77C2×C5×#41D414yes—
78C2×C5×#41D418yescomplemented
79C2×C5×#41C2318yes—
80C2×C5×#41C2314yes—
81C2×C5×#41C2314yes—
82C2×C5×#41C2314yes—
83C22×C5×Q8—216no—
84C22×C5×Q8—28no—
85C22×C5×Q8—28no—
86C22×C5×Q8—28no—
87C22×C5×Q8—22no—
88C22×C5×Q8—21no—
89C22×C5×Q8—24no—
90C22×C5×Q8—24no—
91C22×C5×Q8—22no—
92C22×C5×Q8D411yescharacteristic
93C22×C5×Q8D418yescomplemented
94C22×C5×Q8C2318yes—
95C22×C5×Q8C2311yescharacteristic
96C22×C5×Q8C2311yescharacteristic
97C22×C5×Q8C2312yes—
98C22×C5×Q8C2314yes—
99C22×C5×D4—22no—
100C22×C5×D4—21no—
101C22×C5×D4—21no—
102C22×C5×D4—22no—
103C22×C5×D4D412yes—
104C22×C5×D4D411yescharacteristic
105C22×C5×D4C2311yescharacteristic
106C22×C5×D4C2311yescharacteristic
107C23×C4×C5—22no—
108C23×C4×C5—21no—
109C23×C4×C5—22no—
110C23×C4×C5—21no—
111C23×C4×C5—21no—
112C23×C4×C5—21no—
113C23×C4×C5C2312yes—
114C23×C4×C5C2311yescharacteristic
115C5×#137—232no—
116C5×#135—232no—
117C2×C5×Q16—24no—
118C2×C5×Q16—28no—
119C2×C5×Q16C2314yes—
120C2×C5×Q16C2318yes—
121C2×C5×SD16—24no—
122C2×C5×SD16—28no—
123C2×C5×SD16—24no—
124C2×C5×SD16C2314yes—
125C2×C5×SD16C2318yes—
126C2×C5×SD16C2314yes—
127C2×C5×D8—24no—
128C2×C5×D8C2314yes—
129C2×C5×M16—24no—
130C2×C5×M16C2314yes—
131C22×C5×C8—24no—
132C22×C5×C8C2312yes—
133C22×C5×C8C2311yescharacteristic
134C22×C5×C8C2311yescharacteristic
135C22×C5×C8C2314yes—
136C5×C22⋊Q8—28no—
137C5×C22⋊Q8—24no—
138C5×C22⋊Q8C2318yes—
139C5×#121—28no—
140C5×#121—216no—
141C5×#121—24no—
142C5×#121C2318yes—
143C2×C5×C4⋊C4—21no—
144C2×C5×C4⋊C4—22no—
145C2×C5×C4⋊C4—22no—
146C2×C5×C4⋊C4C2312yes—
147C2×C5×C4⋊C4C2314yes—
148C2×C5×C22⋊C4—22no—
149C2×C5×C22⋊C4—22no—
150C5×#103C2318yes—
151C5×#103C2318yes—
152C5×#103C2318yes—
153C5×#102C2318yes—
154C5×C22⋊C8C2318yes—
155C5×C22⋊C8C2318yes—
156C22×2−1+4C2×C511yescharacteristic, complemented
157C22×#137C2×C511yescharacteristic, complemented
158C22×#135C2×C511yescharacteristic, complemented
159C2×#537C2×C511yescharacteristic, complemented
160#3013C2×C5116yesdirect product factor
161C2×#452C2×C512yescomplemented
162C2×#449C2×C512yescomplemented
163C2×#451C2×C512yescomplemented
164C2×#448C2×C512yescomplemented
165C2×#417C2×C511yescharacteristic, complemented
166C22×#103C2×C511yescharacteristic, complemented
167C2×#408C2×C511yescharacteristic, complemented
168C24×C5—21no—
169C24×C5—21no—
170C24×C5C2×D412yes—
171C24×C5C2×D411yescharacteristic
172C5×#41—2128no—
173C5×#41—264no—
174C5×#41—232no—
175C5×#41—216no—
176C5×#41—216no—
177C5×#41—216no—
178C5×#41—216no—
179C5×#41—28no—
180C5×#41—28no—
181C5×#41—28no—
182C5×#41—28no—
183C5×#41—28no—
184C5×#41—48no—
185C5×#41C2×D4116yescomplemented
186C2×C5×Q8—216no—
187C2×C5×Q8—264no—
188C2×C5×Q8—232no—
189C2×C5×Q8—216no—
190C2×C5×Q8—216no—
191C2×C5×Q8—24no—
192C2×C5×Q8—28no—
193C2×C5×Q8—216no—
194C2×C5×Q8—22no—
195C2×C5×Q8—24no—
196C2×C5×Q8—28no—
197C2×C5×Q8—24no—
198C2×C5×Q8—21no—
199C2×C5×Q8—22no—
200C2×C5×Q8—28no—
201C2×C5×Q8—21no—
202C2×C5×Q8—22no—
203C2×C5×Q8—22no—
204C2×C5×Q8C2×D414yes—
205C2×C5×Q8C2×D418yes—
206C2×C5×Q8C2×D414yes—
207C2×C5×Q8C2×D4116yescomplemented
208C2×C5×Q8C2412yes—
209C2×C5×Q8C2412yes—
210C2×C5×Q8C2414yes—
211C2×C5×D4—216no—
212C2×C5×D4—28no—
213C2×C5×D4—28no—
214C2×C5×D4—28no—
215C2×C5×D4—24no—
216C2×C5×D4—24no—
217C2×C5×D4—28no—
218C2×C5×D4—24no—
219C2×C5×D4—21no—
220C2×C5×D4—22no—
221C2×C5×D4—22no—
222C2×C5×D4—22no—
223C2×C5×D4—21no—
224C2×C5×D4—44no—
225C2×C5×D4—84no—
226C2×C5×D4C2×D418yes—
227C2×C5×D4C2×D414yes—
228C2×C5×D4C2×D414yes—
229C2×C5×D4C2412yes—
230C2×C5×D4C2412yes—
231C22×C4×C5—216no—
232C22×C4×C5—216no—
233C22×C4×C5—28no—
234C22×C4×C5—28no—
235C22×C4×C5—24no—
236C22×C4×C5—22no—
237C22×C4×C5—21no—
238C22×C4×C5—28no—
239C22×C4×C5—28no—
240C22×C4×C5—24no—
241C22×C4×C5—24no—
242C22×C4×C5—24no—
243C22×C4×C5—22no—
244C22×C4×C5—21no—
245C22×C4×C5—24no—
246C22×C4×C5—24no—
247C22×C4×C5—44no—
248C22×C4×C5—82no—
249C22×C4×C5C2×D414yes—
250C22×C4×C5C2×D412yes—
251C22×C4×C5C2×D412yes—
252C22×C4×C5C2×D411yescharacteristic
253C22×C4×C5C2×D414yes—
254C22×C4×C5C2×D414yes—
255C22×C4×C5C2414yes—
256C22×C4×C5C2412yes—
257C22×C4×C5C2411yescharacteristic
258C5×Q16—28no—
259C5×Q16—216no—
260C5×SD16—28no—
261C5×SD16—216no—
262C5×SD16—28no—
263C5×D8—28no—
264C5×M16—28no—
265C2×C5×C8—22no—
266C2×C5×C8—22no—
267C2×C5×C8—28no—
268C2×C5×C8—24no—
269C2×C5×C8C2412yes—
270C2×C5×C8C2412yes—
271C2×C5×C8C2414yes—
272C5×C4⋊C4—24no—
273C5×C4⋊C4—22no—
274C5×C4⋊C4—28no—
275C5×C4⋊C4C2414yes—
276C5×C22⋊C4—28no—
277C5×C22⋊C4—28no—
278C2×2−1+4—24no—
279C2×2−1+4—28no—
280C2×2−1+4—28no—
281C2×2−1+4C22×C518yescomplemented
282C22×#41—21no—
283C22×#41—22no—
284C22×#41C22×C512yes—
285C22×#41C22×C511yescharacteristic
286C22×#41C22×C511yescharacteristic
287C22×#41C22×C511yescharacteristic
288C23×Q8—21no—
289C23×Q8C22×C512yes—
290C23×Q8C22×C511yescharacteristic
291C2×#137—28no—
292C2×#137C22×C518yescomplemented
293C2×#135—28no—
294C2×#135C22×C518yescomplemented
295C22×Q16C22×C511yescharacteristic
296C22×Q16C22×C512yes—
297C22×SD16C22×C511yescharacteristic
298C22×SD16C22×C512yes—
299C22×SD16C22×C511yescharacteristic
300C22×D8C22×C511yescharacteristic
301C22×M16C22×C511yescharacteristic
302C23×C8C22×C511yescharacteristic
303#537—24no—
304#537C22×C518yescomplemented
305C2×C22⋊Q8—21no—
306C2×C22⋊Q8C22×C512yes—
307C2×#121—21no—
308C2×#121—22no—
309C2×#121C22×C512yes—
310C22×C4⋊C4C22×C511yescharacteristic
311#452C22×C5116yescomplemented
312#451C22×C5116yescomplemented
313#449C22×C5116yescomplemented
314#448C22×C5116yescomplemented
315#417C22×C518yescomplemented
316C2×#103C22×C512yes—
317C2×#103C22×C512yes—
318C2×#103C22×C512yes—
319C2×#103C22×C518yescomplemented
320C2×#102C22×C512yes—
321#408C22×C518yescomplemented
322C2×C22⋊C8C22×C512yes—
323C2×C22⋊C8C22×C512yes—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—24no—
327C23×C5—24no—
328C23×C5—24no—
329C23×C5—24no—
330C23×C5—22no—
331C23×C5—22no—
332C23×C5—42no—
333C23×C5—42no—
334C23×C5—42no—
335C23×C5—42no—
336C23×C5—42no—
337C23×C5#12014yes—
338C23×C5C22×D414yes—
339C23×C5C22×D412yes—
340C23×C5C22×D411yescharacteristic
341C5×Q8—232no—
342C5×Q8—24no—
343C5×Q8—28no—
344C5×Q8—28no—
345C5×Q8—216no—
346C5×Q8—22no—
347C5×Q8—24no—
348C5×Q8—22no—
349C5×Q8—22no—
350C5×Q8—42no—
351C5×Q8C22×D414yes—
352C5×Q8C22×D418yes—
353C5×D4—232no—
354C5×D4—216no—
355C5×D4—216no—
356C5×D4—28no—
357C5×D4—24no—
358C5×D4—22no—
359C5×D4—22no—
360C5×D4—22no—
361C5×D4—48no—
362C5×D4—42no—
363C5×D4—88no—
364C5×D4C22×D414yes—
365C2×C4×C5—232no—
366C2×C4×C5—232no—
367C2×C4×C5—28no—
368C2×C4×C5—24no—
369C2×C4×C5—24no—
370C2×C4×C5—216no—
371C2×C4×C5—24no—
372C2×C4×C5—22no—
373C2×C4×C5—216no—
374C2×C4×C5—28no—
375C2×C4×C5—24no—
376C2×C4×C5—24no—
377C2×C4×C5—24no—
378C2×C4×C5—22no—
379C2×C4×C5—42no—
380C2×C4×C5—44no—
381C2×C4×C5—48no—
382C2×C4×C5—84no—
383C2×C4×C5#12014yes—
384C2×C4×C5#12018yes—
385C2×C4×C5C22×D414yes—
386C2×C4×C5C22×D412yes—
387C2×C4×C5C22×D411yescharacteristic
388C2×C4×C5C22×D412yes—
389C2×C4×C5C22×D412yes—
390C2×C4×C5C22×D414yes—
391C2×C4×C5C22×D414yes—
392C2×C4×C5C2511yescharacteristic
393C5×C8—22no—
394C5×C8—22no—
395C5×C8—24no—
3962−1+4—264no—
3972−1+4—232no—
3982−1+4—232no—
399C2×#41—232no—
400C2×#41—216no—
401C2×#41—28no—
402C2×#41—28no—
403C2×#41—216no—
404C2×#41—28no—
405C2×#41—24no—
406C2×#41—24no—
407C2×#41—22no—
408C2×#41—24no—
409C2×#41—24no—
410C2×#41—22no—
411C2×#41—24no—
412C2×#41—24no—
413C2×#41C5×D414yes—
414C2×#41C5×D418yescomplemented
415C2×#41C23×C514yes—
416C2×#41C23×C518yes—
417C2×#41C23×C514yes—
418C2×#41C23×C514yes—
419C22×Q8—216no—
420C22×Q8—28no—
421C22×Q8—28no—
422C22×Q8—28no—
423C22×Q8—22no—
424C22×Q8—21no—
425C22×Q8—24no—
426C22×Q8—24no—
427C22×Q8—22no—
428C22×Q8C5×D411yescharacteristic
429C22×Q8C5×D418yescomplemented
430C22×Q8C23×C511yescharacteristic
431C22×Q8C23×C518yes—
432C22×Q8C23×C511yescharacteristic
433C22×Q8C23×C512yes—
434C22×Q8C23×C514yes—
435C22×D4—22no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4—22no—
439C22×D4C5×D412yes—
440C22×D4C5×D411yescharacteristic
441C22×D4C23×C511yescharacteristic
442C22×D4C23×C511yescharacteristic
443C23×C4—22no—
444C23×C4—21no—
445C23×C4—22no—
446C23×C4—21no—
447C23×C4—21no—
448C23×C4—21no—
449C23×C4C23×C512yes—
450C23×C4C23×C511yescharacteristic
451#137—232no—
452#135—232no—
453C2×Q16—24no—
454C2×Q16—28no—
455C2×Q16C23×C514yes—
456C2×Q16C23×C518yes—
457C2×SD16—24no—
458C2×SD16—28no—
459C2×SD16—24no—
460C2×SD16C23×C514yes—
461C2×SD16C23×C514yes—
462C2×SD16C23×C518yes—
463C2×D8—24no—
464C2×D8C23×C514yes—
465C2×M16—24no—
466C2×M16C23×C514yes—
467C22×C8—24no—
468C22×C8C23×C511yescharacteristic
469C22×C8C23×C511yescharacteristic
470C22×C8C23×C514yes—
471C22×C8C23×C512yes—
472C22⋊Q8—28no—
473C22⋊Q8—24no—
474C22⋊Q8C23×C518yes—
475#121—28no—
476#121—216no—
477#121—24no—
478#121C23×C518yes—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4C23×C512yes—
483C2×C4⋊C4C23×C514yes—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486#103C23×C518yes—
487#103C23×C518yes—
488#103C23×C518yes—
489#102C23×C518yes—
490C22⋊C8C23×C518yes—
491C22⋊C8C23×C518yes—
492C22×C5—28no—
493C22×C5—22no—
494C22×C5—22no—
495C22×C5—24no—
496C22×C5—24no—
497C22×C5—24no—
498C22×C5—24no—
499C22×C5—48no—
500C22×C5—48no—
501C22×C5—42no—
502C22×C5—42no—
503C22×C5—42no—
504C22×C5—42no—
505C22×C5—42no—
506C22×C5—84no—
507C22×C5C2×#12014yes—
508C22×C5C2×#12012yes—
509C22×C5#57712yes—
510C22×C5#57812yes—
511C22×C5C23×D411yescharacteristic
512C4×C5—28no—
513C4×C5—24no—
514C4×C5—24no—
515C4×C5—42no—
516C4×C5—44no—
517C4×C5C2×#12014yes—
518C4×C5C2×#12012yes—
519C4×C5C23×D411yescharacteristic
520C4×C5C23×D411yescharacteristic
521C24—21no—
522C24—21no—
523C24C2×C5×D412yes—
524C24C2×C5×D411yescharacteristic
525#41—2128no—
526#41—264no—
527#41—232no—
528#41—216no—
529#41—216no—
530#41—216no—
531#41—216no—
532#41—28no—
533#41—28no—
534#41—28no—
535#41—28no—
536#41—28no—
537#41—48no—
538#41C2×C5×D4116yescomplemented
539C2×Q8—216no—
540C2×Q8—264no—
541C2×Q8—232no—
542C2×Q8—216no—
543C2×Q8—216no—
544C2×Q8—24no—
545C2×Q8—28no—
546C2×Q8—216no—
547C2×Q8—22no—
548C2×Q8—24no—
549C2×Q8—28no—
550C2×Q8—24no—
551C2×Q8—21no—
552C2×Q8—22no—
553C2×Q8—28no—
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8C2×C5×D414yes—
558C2×Q8C2×C5×D418yes—
559C2×Q8C2×C5×D414yes—
560C2×Q8C2×C5×D4116yescomplemented
561C2×Q8C24×C512yes—
562C2×Q8C24×C512yes—
563C2×Q8C24×C514yes—
564C2×D4—216no—
565C2×D4—28no—
566C2×D4—28no—
567C2×D4—28no—
568C2×D4—24no—
569C2×D4—24no—
570C2×D4—28no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—21no—
577C2×D4—44no—
578C2×D4—84no—
579C2×D4C2×C5×D418yes—
580C2×D4C2×C5×D414yes—
581C2×D4C2×C5×D414yes—
582C2×D4C24×C512yes—
583C2×D4C24×C512yes—
584C22×C4—216no—
585C22×C4—216no—
586C22×C4—28no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—28no—
590C22×C4—24no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—44no—
601C22×C4—82no—
602C22×C4C2×C5×D412yes—
603C22×C4C2×C5×D414yes—
604C22×C4C2×C5×D411yescharacteristic
605C22×C4C2×C5×D412yes—
606C22×C4C2×C5×D414yes—
607C22×C4C2×C5×D414yes—
608C22×C4C24×C514yes—
609C22×C4C24×C511yescharacteristic
610C22×C4C24×C512yes—
611Q16—28no—
612Q16—216no—
613SD16—28no—
614SD16—216no—
615SD16—28no—
616D8—28no—
617M16—28no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—28no—
621C2×C8—24no—
622C2×C8C24×C514yes—
623C2×C8C24×C512yes—
624C2×C8C24×C512yes—
625C4⋊C4—24no—
626C4⋊C4—22no—
627C4⋊C4—28no—
628C4⋊C4C24×C514yes—
629C22⋊C4—28no—
630C22⋊C4—28no—
631C2×C5—24no—
632C2×C5—44no—
633C2×C5—44no—
634C2×C5—82no—
635C2×C5#301314yesdirect product factor
636C2×C5C22×#12011yescharacteristic
637C2×C5C2×#57711yescharacteristic
638C2×C5C2×#57811yescharacteristic
639C23—22no—
640C23—22no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23C5×#12014yes—
653C23C22×C5×D414yes—
654C23C22×C5×D412yes—
655C23C22×C5×D411yescharacteristic
656Q8—232no—
657Q8—24no—
658Q8—28no—
659Q8—28no—
660Q8—216no—
661Q8—22no—
662Q8—24no—
663Q8—22no—
664Q8—22no—
665Q8—42no—
666Q8C22×C5×D414yes—
667Q8C22×C5×D418yes—
668D4—232no—
669D4—216no—
670D4—216no—
671D4—28no—
672D4—24no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—48no—
677D4—42no—
678D4—88no—
679D4C22×C5×D414yes—
680C2×C4—232no—
681C2×C4—232no—
682C2×C4—28no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—216no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—216no—
689C2×C4—28no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—48no—
697C2×C4—84no—
698C2×C4C5×#12014yes—
699C2×C4C5×#12018yes—
700C2×C4C22×C5×D414yes—
701C2×C4C22×C5×D412yes—
702C2×C4C22×C5×D411yescharacteristic
703C2×C4C22×C5×D412yes—
704C2×C4C22×C5×D412yes—
705C2×C4C22×C5×D414yes—
706C2×C4C22×C5×D414yes—
707C2×C4C25×C511yescharacteristic
708C8—22no—
709C8—22no—
710C8—24no—
711C5C2×#301311yescharacteristic, direct product factor, Sylow
712C22—28no—
713C22—22no—
714C22—22no—
715C22—24no—
716C22—24no—
717C22—24no—
718C22—24no—
719C22—48no—
720C22—48no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—84no—
727C22C2×C5×#12014yes—
728C22C2×C5×#12012yes—
729C22C5×#57712yes—
730C22C5×#57812yes—
731C22C23×C5×D411yescharacteristic
732C4—28no—
733C4—24no—
734C4—24no—
735C4—42no—
736C4—44no—
737C4C2×C5×#12014yes—
738C4C2×C5×#12012yes—
739C4C23×C5×D411yescharacteristic
740C4C23×C5×D411yescharacteristic
741C2—24no—
742C2—44no—
743C2—44no—
744C2—82no—
745C2C5×#301314yesdirect product factor
746C2C22×C5×#12011yescharacteristic
747C2C2×C5×#57711yescharacteristic
748C2C2×C5×#57811yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC2×C4C25×C5
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C5×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C5×2−1+4C2semidirect
2. C22×C5×#137C2semidirect
3. C22×C5×#135C2semidirect
4. C2×C5×#537C2semidirect
5. C5×#3013C2direct (N × H)
6. C2×C5×#452C2semidirect
7. C2×C5×#449C2semidirect
8. C2×C5×#451C2semidirect
9. C2×C5×#448C2semidirect
10. C2×C5×#417C2semidirect
11. C22×C5×#103C2semidirect
12. C2×C5×#408C2semidirect
16. C2×C5×2−1+4C22semidirect
27. C2×C5×#137C22semidirect
29. C2×C5×#135C22semidirect
39. C5×#537C22semidirect
46. C5×#452C22semidirect
47. C5×#451C22semidirect
48. C5×#449C22semidirect
49. C5×#448C22semidirect
50. C5×#417C22semidirect
54. C2×C5×#103C22semidirect
56. C5×#408C22semidirect
59. C2×#3013C5direct (N × H)
78. C2×C5×#41D4semidirect
93. C22×C5×Q8D4semidirect
156. C22×2−1+4C2×C5semidirect
157. C22×#137C2×C5semidirect
158. C22×#135C2×C5semidirect
159. C2×#537C2×C5semidirect
160. #3013C2×C5direct (N × H)
161. C2×#452C2×C5semidirect
162. C2×#449C2×C5semidirect
163. C2×#451C2×C5semidirect
164. C2×#448C2×C5semidirect
165. C2×#417C2×C5semidirect
166. C22×#103C2×C5semidirect
167. C2×#408C2×C5semidirect
185. C5×#41C2×D4semidirect
207. C2×C5×Q8C2×D4semidirect
281. C2×2−1+4C22×C5semidirect
292. C2×#137C22×C5semidirect
294. C2×#135C22×C5semidirect
304. #537C22×C5semidirect
311. #452C22×C5semidirect
312. #451C22×C5semidirect
313. #449C22×C5semidirect
314. #448C22×C5semidirect
315. #417C22×C5semidirect
319. C2×#103C22×C5semidirect
321. #408C22×C5semidirect
414. C2×#41C5×D4semidirect
429. C22×Q8C5×D4semidirect
538. #41C2×C5×D4semidirect
560. C2×Q8C2×C5×D4semidirect
635. C2×C5#3013direct (N × H)
711. C5C2×#3013direct (N × H)
745. C2C5×#3013direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×2−1+42
C22×C5×#1372
C22×C5×#1352
C2×C5×#5372
C5×#30132
C2×C5×#4522
C2×C5×#4492
C2×C5×#4512
C2×C5×#4482
C2×C5×#4172
C22×C5×#1032
C2×C5×#4082
C2×#30135