Finite Group Databasebeta

← C5×#25938 #11948658

Subgroups — C5×#25938 #11948658

Order 1280.

1104 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#554C211yesmaximal, characteristic, complemented
2C2×C5×#488C211yesmaximal, characteristic, complemented
3C2×C5×#463C211yesmaximal, characteristic
4C5×#2592C211yesmaximal, characteristic, complemented
5C5×#2026C211yesmaximal, characteristic, complemented
6C5×#2025C211yesmaximal, characteristic, complemented
7C5×#2024C211yesmaximal, characteristic, complemented
8C5×#2023C211yesmaximal, characteristic, complemented
9C5×#1989C211yesmaximal, characteristic, complemented
10C5×#1984C211yesmaximal, characteristic, complemented
11C5×#1879C211yesmaximal, characteristic
12C5×#1879C211yesmaximal, characteristic
13C5×#1877C211yesmaximal, characteristic, complemented
14C5×#1877C211yesmaximal, characteristic, complemented
15C4×C5×#102C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C22×C5×D8C2211yescharacteristic
18C5×#554—24no—
19C5×#554—24no—
20C2×C5×C4⋊Q8C2211yescharacteristic
21C2×C5×#125C2211yescharacteristic
22C2×C5×#125C2211yescharacteristic
23C2×C5×#124C2211yescharacteristic
24C2×C5×C22⋊Q8—21no—
25C2×C5×C22⋊Q8—21no—
26C2×C5×C22⋊Q8—21no—
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×D4C2211yescharacteristic
29C2×C4×C5×D4C2211yescharacteristic
30C2×C4×C5×D4C2211yescharacteristic
31C22×C5×C4⋊C4—21no—
32C5×#488—24no—
33C5×#463—24no—
34C2×C5×C4⋊C8C2211yescharacteristic
35C2×C5×#103C2211yescharacteristic
36C2×C5×#103C2211yescharacteristic
37C2×C5×#103C2211yescharacteristic
38C2×C5×#102C2211yescharacteristic
39C2×C5×#102C2211yescharacteristic
40C2×C5×#102C2211yescharacteristic
41C2×C5×#102C2211yescharacteristic
42C2×C5×#102C2211yescharacteristic
43C2×C4×C5×C8C2211yescharacteristic
44C5×#397—21no—
45C5×#393—21no—
46C5×#391C2211yescharacteristic
47C5×#391C2211yescharacteristic
48C5×#390C2211yescharacteristic
49C5×#390C2211yescharacteristic
50C5×#388—21no—
51C5×#388—21no—
52C4×C5×C4⋊C4C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61C5×#336C2211yescharacteristic
62C5×#336C2211yescharacteristic
63#25938C511yesmaximal, characteristic, direct product factor, Sylow
64C22×C5×Q8—21no—
65C22×C5×Q8D411yescharacteristic
66C22×C5×Q8C2311yescharacteristic
67C22×C5×D4C2311yescharacteristic
68C22×C5×D4C2311yescharacteristic
69C23×C4×C5—21no—
70C23×C4×C5—21no—
71C23×C4×C5—21no—
72C2×C5×SD16—22no—
73C2×C5×SD16—22no—
74C2×C5×SD16—22no—
75C2×C5×D8—22no—
76C2×C5×D8—22no—
77C2×C5×D8—22no—
78C22×C5×C8C2311yescharacteristic
79C22×C5×C8C2311yescharacteristic
80C22×C5×C8C2311yescharacteristic
81C22×C5×C8C2311yescharacteristic
82C5×C4⋊Q8—22no—
83C5×C4⋊Q8—22no—
84C5×#125—22no—
85C5×#125—22no—
86C5×#125—22no—
87C5×#125D414yes—
88C5×#124—22no—
89C5×#124—22no—
90C5×C22⋊Q8—28no—
91C5×C22⋊Q8—28no—
92C5×C22⋊Q8—28no—
93C4×C5×Q8—22no—
94C4×C5×Q8—22no—
95C4×C5×D4—22no—
96C4×C5×D4—22no—
97C4×C5×D4—22no—
98C4×C5×D4—22no—
99C4×C5×D4—22no—
100C4×C5×D4D414yes—
101C2×C5×C4⋊C4—28no—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4D411yescharacteristic
108C2×C5×C4⋊C4D411yescharacteristic
109C2×C5×C4⋊C4D411yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4—21no—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4—21no—
123C2×C5×C22⋊C4—21no—
124C2×C42×C5—21no—
125C2×C42×C5C2311yescharacteristic
126C2×C42×C5C2311yescharacteristic
127C2×C42×C5C2311yescharacteristic
128C5×C4⋊C8—22no—
129C5×#103—22no—
130C5×#103—22no—
131C5×#103—22no—
132C5×#102—22no—
133C5×#102—22no—
134C5×#102—22no—
135C5×#102—22no—
136C5×#102—22no—
137C4×C5×C8—22no—
138C5×#95—21no—
139C5×#95—21no—
140C5×#95—21no—
141C5×#95—21no—
142C5×#95—21no—
143C2×#554C2×C511yescharacteristic, complemented
144C2×#488C2×C511yescharacteristic, complemented
145C2×#463C2×C511yescharacteristic
146#2592C2×C511yescharacteristic, complemented
147#2026C2×C511yescharacteristic, complemented
148#2025C2×C511yescharacteristic, complemented
149#2024C2×C511yescharacteristic, complemented
150#2023C2×C511yescharacteristic, complemented
151#1989C2×C511yescharacteristic, complemented
152#1984C2×C511yescharacteristic, complemented
153#1879C2×C511yescharacteristic
154#1879C2×C511yescharacteristic
155#1877C2×C511yescharacteristic, complemented
156#1877C2×C511yescharacteristic, complemented
157C4×#102C2×C511yescharacteristic, complemented
158C24×C5—21no—
159C24×C5—21no—
160C2×C5×Q8—24no—
161C2×C5×Q8—22no—
162C2×C5×Q8—22no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8—21no—
166C2×C5×Q8—21no—
167C2×C5×Q8—21no—
168C2×C5×Q8—21no—
169C2×C5×Q8—41no—
170C2×C5×Q8—81no—
171C2×C5×Q8—81no—
172C2×C5×D4—21no—
173C2×C5×D4—21no—
174C2×C5×D4—21no—
175C2×C5×D4—21no—
176C2×C5×D4—21no—
177C2×C5×D4—21no—
178C2×C5×D4—21no—
179C2×C5×D4—21no—
180C2×C5×D4—21no—
181C2×C5×D4C2×D412yes—
182C2×C5×D4#4112yes—
183C2×C5×D4#4112yes—
184C22×C4×C5—24no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—24no—
189C22×C4×C5—24no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—42no—
194C22×C4×C5—42no—
195C22×C4×C5—81no—
196C22×C4×C5—81no—
197C22×C4×C5—81no—
198C22×C4×C5—81no—
199C22×C4×C5C2×D411yescharacteristic
200C22×C4×C5C2×D411yescharacteristic
201C22×C4×C5C2×D411yescharacteristic
202C22×C4×C5C2×D411yescharacteristic
203C22×C4×C5C2×D411yescharacteristic
204C22×C4×C5C2×D411yescharacteristic
205C22×C4×C5C2411yescharacteristic
206C5×SD16—44no—
207C5×D8—44no—
208C2×C5×C8—21no—
209C2×C5×C8—21no—
210C2×C5×C8—21no—
211C2×C5×C8—21no—
212C2×C5×C8—21no—
213C2×C5×C8—21no—
214C2×C5×C8—21no—
215C2×C5×C8—21no—
216C2×C5×C8—21no—
217C2×C5×C8—21no—
218C2×C5×C8—21no—
219C2×C5×C8—21no—
220C5×C4⋊C4—24no—
221C5×C4⋊C4—24no—
222C5×C4⋊C4—24no—
223C5×C4⋊C4—22no—
224C5×C4⋊C4—24no—
225C5×C4⋊C4—24no—
226C5×C4⋊C4—22no—
227C5×C4⋊C4—22no—
228C5×C4⋊C4—21no—
229C5×C4⋊C4—21no—
230C5×C4⋊C4—21no—
231C5×C4⋊C4—21no—
232C5×C4⋊C4—21no—
233C5×C4⋊C4—21no—
234C5×C4⋊C4—21no—
235C5×C4⋊C4C2×D412yes—
236C5×C4⋊C4C2×D412yes—
237C5×C4⋊C4C2×D412yes—
238C5×C22⋊C4—24no—
239C5×C22⋊C4—24no—
240C5×C22⋊C4—24no—
241C5×C22⋊C4—42no—
242C5×C22⋊C4—42no—
243C5×C22⋊C4—42no—
244C5×C22⋊C4—42no—
245C5×C22⋊C4—81no—
246C5×C22⋊C4—81no—
247C42×C5—21no—
248C42×C5—21no—
249C42×C5—21no—
250C42×C5—21no—
251C42×C5—81no—
252C42×C5C2×D412yes—
253C42×C5C2×D412yes—
254C22×SD16C22×C511yescharacteristic
255C22×D8C22×C511yescharacteristic
256#554—24no—
257#554—24no—
258C2×C4⋊Q8C22×C511yescharacteristic
259C2×#125C22×C511yescharacteristic
260C2×#125C22×C511yescharacteristic
261C2×#124C22×C511yescharacteristic
262C2×C22⋊Q8—21no—
263C2×C22⋊Q8—21no—
264C2×C22⋊Q8—21no—
265C2×C4×Q8C22×C511yescharacteristic
266C2×C4×D4C22×C511yescharacteristic
267C2×C4×D4C22×C511yescharacteristic
268C2×C4×D4C22×C511yescharacteristic
269C22×C4⋊C4—21no—
270#488—24no—
271#463—24no—
272C2×C4⋊C8C22×C511yescharacteristic
273C2×#103C22×C511yescharacteristic
274C2×#103C22×C511yescharacteristic
275C2×#103C22×C511yescharacteristic
276C2×#102C22×C511yescharacteristic
277C2×#102C22×C511yescharacteristic
278C2×#102C22×C511yescharacteristic
279C2×#102C22×C511yescharacteristic
280C2×#102C22×C511yescharacteristic
281C2×C4×C8C22×C511yescharacteristic
282#397—21no—
283#393—21no—
284#391C22×C511yescharacteristic
285#391C22×C511yescharacteristic
286#390C22×C511yescharacteristic
287#390C22×C511yescharacteristic
288#388—21no—
289#388—21no—
290C4×C4⋊C4C22×C511yescharacteristic
291#340C22×C511yescharacteristic
292#340C22×C511yescharacteristic
293#340C22×C511yescharacteristic
294#340C22×C511yescharacteristic
295#340C22×C511yescharacteristic
296#340C22×C511yescharacteristic
297#336C22×C511yescharacteristic
298#336C22×C511yescharacteristic
299#336C22×C511yescharacteristic
300#336C22×C511yescharacteristic
301C23×C5—22no—
302C23×C5—22no—
303C23×C5—22no—
304C23×C5—41no—
305C23×C5—41no—
306C23×C5—41no—
307C23×C5—41no—
308C23×C5—41no—
309C23×C5—41no—
310C23×C5—41no—
311C23×C5—41no—
312C23×C5—41no—
313C23×C5—41no—
314C23×C5—41no—
315C23×C5C22×D411yescharacteristic
316C5×Q8—44no—
317C5×Q8—41no—
318C5×Q8—41no—
319C5×Q8—41no—
320C5×Q8—41no—
321C5×Q8—84no—
322C5×D4—22no—
323C5×D4—22no—
324C5×D4—22no—
325C5×D4—41no—
326C5×D4—41no—
327C5×D4—41no—
328C5×D4—41no—
329C5×D4#12414yes—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—22no—
340C2×C4×C5—22no—
341C2×C4×C5—22no—
342C2×C4×C5—21no—
343C2×C4×C5—21no—
344C2×C4×C5—21no—
345C2×C4×C5—21no—
346C2×C4×C5—21no—
347C2×C4×C5—21no—
348C2×C4×C5—48no—
349C2×C4×C5—41no—
350C2×C4×C5—41no—
351C2×C4×C5—41no—
352C2×C4×C5—41no—
353C2×C4×C5—41no—
354C2×C4×C5—41no—
355C2×C4×C5—41no—
356C2×C4×C5—41no—
357C2×C4×C5—41no—
358C2×C4×C5—41no—
359C2×C4×C5—41no—
360C2×C4×C5—41no—
361C2×C4×C5—41no—
362C2×C4×C5—41no—
363C2×C4×C5—41no—
364C2×C4×C5—84no—
365C2×C4×C5—84no—
366C2×C4×C5#12012yes—
367C2×C4×C5#12012yes—
368C2×C4×C5#13512yes—
369C2×C4×C5C22×D411yescharacteristic
370C2×C4×C5C22×D411yescharacteristic
371C2×C4×C5C2×#4111yescharacteristic
372C2×C4×C5C2×#4111yescharacteristic
373C2×C4×C52−1+411yescharacteristic
374C2×C4×C52−1+411yescharacteristic
375C5×C8—41no—
376C5×C8—41no—
377C5×C8—41no—
378C5×C8—41no—
379C22×Q8—21no—
380C22×Q8C5×D411yescharacteristic
381C22×Q8C23×C511yescharacteristic
382C22×D4C23×C511yescharacteristic
383C22×D4C23×C511yescharacteristic
384C23×C4—21no—
385C23×C4—21no—
386C23×C4—21no—
387C2×SD16—22no—
388C2×SD16—22no—
389C2×SD16—22no—
390C2×D8—22no—
391C2×D8—22no—
392C2×D8—22no—
393C22×C8C23×C511yescharacteristic
394C22×C8C23×C511yescharacteristic
395C22×C8C23×C511yescharacteristic
396C22×C8C23×C511yescharacteristic
397C4⋊Q8—22no—
398C4⋊Q8—22no—
399#125—22no—
400#125—22no—
401#125—22no—
402#125C5×D414yes—
403#124—22no—
404#124—22no—
405C22⋊Q8—28no—
406C22⋊Q8—28no—
407C22⋊Q8—28no—
408C4×Q8—22no—
409C4×Q8—22no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4—22no—
413C4×D4—22no—
414C4×D4—22no—
415C4×D4C5×D414yes—
416C2×C4⋊C4—28no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4C5×D411yescharacteristic
423C2×C4⋊C4C5×D411yescharacteristic
424C2×C4⋊C4C5×D411yescharacteristic
425C2×C4⋊C4C23×C511yescharacteristic
426C2×C4⋊C4C23×C511yescharacteristic
427C2×C4⋊C4C23×C511yescharacteristic
428C2×C4⋊C4C23×C511yescharacteristic
429C2×C4⋊C4C23×C511yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C42—21no—
440C2×C42C23×C511yescharacteristic
441C2×C42C23×C511yescharacteristic
442C2×C42C23×C511yescharacteristic
443C4⋊C8—22no—
444#103—22no—
445#103—22no—
446#103—22no—
447#102—22no—
448#102—22no—
449#102—22no—
450#102—22no—
451#102—22no—
452C4×C8—22no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458C22×C5—24no—
459C22×C5—42no—
460C22×C5—42no—
461C22×C5—42no—
462C22×C5—42no—
463C22×C5—42no—
464C22×C5—42no—
465C22×C5—81no—
466C22×C5—81no—
467C22×C5—81no—
468C22×C5—81no—
469C22×C5—81no—
470C22×C5—81no—
471C22×C5—81no—
472C22×C5C2×#12011yescharacteristic
473C22×C5#54811yescharacteristic
474C22×C5#54811yescharacteristic
475C22×C5C2×#13511yescharacteristic
476C22×C5#57511yescharacteristic
477C22×C5#57611yescharacteristic
478C22×C5#57711yescharacteristic
479C4×C5—22no—
480C4×C5—22no—
481C4×C5—22no—
482C4×C5—41no—
483C4×C5—42no—
484C4×C5—41no—
485C4×C5—41no—
486C4×C5—42no—
487C4×C5—42no—
488C4×C5—81no—
489C4×C5—81no—
490C4×C5—81no—
491C4×C5C2×#12411yescharacteristic
492C4×C5#53611yescharacteristic
493C4×C5#54811yescharacteristic
494C4×C5#54811yescharacteristic
495C24—21no—
496C24—21no—
497C2×Q8—24no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—41no—
507C2×Q8—81no—
508C2×Q8—81no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4C2×C5×D412yes—
519C2×D4C5×#4112yes—
520C2×D4C5×#4112yes—
521C22×C4—24no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4C2×C5×D411yescharacteristic
537C22×C4C2×C5×D411yescharacteristic
538C22×C4C2×C5×D411yescharacteristic
539C22×C4C2×C5×D411yescharacteristic
540C22×C4C2×C5×D411yescharacteristic
541C22×C4C2×C5×D411yescharacteristic
542C22×C4C24×C511yescharacteristic
543SD16—44no—
544D8—44no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4C2×C5×D412yes—
573C4⋊C4C2×C5×D412yes—
574C4⋊C4C2×C5×D412yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—81no—
589C42C2×C5×D412yes—
590C42C2×C5×D412yes—
591C2×C5—44no—
592C2×C5—161no—
593C2×C5#243611yescharacteristic
594C2×C5#300211yescharacteristic
595C2×C5#301211yescharacteristic
596C2×C5#336011yescharacteristic
597C2×C5#336111yescharacteristic
598C2×C5#337011yescharacteristic
599C2×C5#337611yescharacteristic
600C23—22no—
601C23—22no—
602C23—22no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23C22×C5×D411yescharacteristic
615Q8—44no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620Q8—84no—
621D4—22no—
622D4—22no—
623D4—22no—
624D4—41no—
625D4—41no—
626D4—41no—
627D4—41no—
628D4C5×#12414yes—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—48no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—84no—
664C2×C4—84no—
665C2×C4C5×#12012yes—
666C2×C4C5×#12012yes—
667C2×C4C5×#13512yes—
668C2×C4C22×C5×D411yescharacteristic
669C2×C4C22×C5×D411yescharacteristic
670C2×C4C2×C5×#4111yescharacteristic
671C2×C4C2×C5×#4111yescharacteristic
672C2×C4C5×2−1+411yescharacteristic
673C2×C4C5×2−1+411yescharacteristic
674C8—41no—
675C8—41no—
676C8—41no—
677C8—41no—
678C5#2593811yescharacteristic, direct product factor, Sylow
679C22—24no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22C2×C5×#12011yescharacteristic
694C22C5×#54811yescharacteristic
695C22C5×#54811yescharacteristic
696C22C2×C5×#13511yescharacteristic
697C22C5×#57511yescharacteristic
698C22C5×#57611yescharacteristic
699C22C5×#57711yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—41no—
704C4—42no—
705C4—41no—
706C4—41no—
707C4—42no—
708C4—42no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4C2×C5×#12411yescharacteristic
713C4C5×#53611yescharacteristic
714C4C5×#54811yescharacteristic
715C4C5×#54811yescharacteristic
716C2—44no—
717C2—161no—
718C2C5×#243611yescharacteristic
719C2C5×#300211yescharacteristic
720C2C5×#301211yescharacteristic
721C2C5×#336011yescharacteristic
722C2C5×#336111yescharacteristic
723C2C5×#337011yescharacteristic
724C2C5×#337611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#554C2semidirect
2. C2×C5×#488C2semidirect
4. C5×#2592C2semidirect
5. C5×#2026C2semidirect
6. C5×#2025C2semidirect
7. C5×#2024C2semidirect
8. C5×#2023C2semidirect
9. C5×#1989C2semidirect
10. C5×#1984C2semidirect
13. C5×#1877C2semidirect
14. C5×#1877C2semidirect
15. C4×C5×#102C2semidirect
63. #25938C5direct (N × H)
143. C2×#554C2×C5semidirect
144. C2×#488C2×C5semidirect
146. #2592C2×C5semidirect
147. #2026C2×C5semidirect
148. #2025C2×C5semidirect
149. #2024C2×C5semidirect
150. #2023C2×C5semidirect
151. #1989C2×C5semidirect
152. #1984C2×C5semidirect
155. #1877C2×C5semidirect
156. #1877C2×C5semidirect
157. C4×#102C2×C5semidirect
678. C5#25938direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5542
C2×C5×#4882
C2×C5×#4632
C5×#25922
C5×#20262
C5×#20252
C5×#20242
C5×#20232
C5×#19892
C5×#19842
C5×#18792
C5×#18772
C4×C5×#1022
#259385