Finite Group Databasebeta

← C5×#23712 #11946432

Subgroups — C5×#23712 #11946432

Order 1280.

932 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#442C211yesmaximal, characteristic, complemented
2C2×C5×#433C211yesmaximal, characteristic, complemented
3C5×#2324C211yesmaximal, characteristic, complemented
4C5×#2324C211yesmaximal, characteristic, complemented
5C5×#2088C211yesmaximal, characteristic, complemented
6C5×#2077C211yesmaximal, characteristic, complemented
7C5×#2067C211yesmaximal, characteristic, complemented
8C5×#2065C211yesmaximal, characteristic, complemented
9C5×#2054C211yesmaximal, characteristic, complemented
10C5×#2034C211yesmaximal, characteristic, complemented
11C5×#2033C211yesmaximal, characteristic, complemented
12C5×#1999C211yesmaximal, characteristic
13C5×#1776C211yesmaximal, characteristic, complemented
14C4×C5×#102C211yesmaximal, characteristic, complemented
15C4×C5×#102C211yesmaximal, characteristic, complemented
16C22×C5×D8C2211yescharacteristic
17C2×C5×#121C2211yescharacteristic
18C2×C5×#121C2211yescharacteristic
19C2×C4×C5×D4C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×C5×#117C2211yescharacteristic
22C5×#442—24no—
23C5×#433—24no—
24C2×C5×#107C2211yescharacteristic
25C2×C5×#106C2211yescharacteristic
26C2×C5×#106C2211yescharacteristic
27C2×C5×C4⋊C8C2211yescharacteristic
28C2×C5×C4⋊C8C2211yescharacteristic
29C2×C5×#102C2211yescharacteristic
30C2×C5×#102C2211yescharacteristic
31C2×C5×#102C2211yescharacteristic
32C2×C5×#102C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×C22⋊C8C2211yescharacteristic
36C2×C5×C22⋊C8C2211yescharacteristic
37C2×C5×#97C2211yescharacteristic
38C2×C4×C5×C8C2211yescharacteristic
39C5×#390—21no—
40C5×#390—21no—
41C5×#390C2211yescharacteristic
42C5×#390C2211yescharacteristic
43C5×#389C2211yescharacteristic
44C5×#389C2211yescharacteristic
45C5×#388—21no—
46C5×#388—21no—
47C5×#386—21no—
48C5×#386—21no—
49C5×#385—21no—
50C5×#385—21no—
51C5×#380C2211yescharacteristic
52C5×#380C2211yescharacteristic
53C4×C5×C4⋊C4C2211yescharacteristic
54C4×C5×C4⋊C4C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61#23712C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×D4—21no—
63C22×C5×D4—21no—
64C22×C5×D4C2311yescharacteristic
65C22×C5×D4C2311yescharacteristic
66C23×C4×C5—21no—
67C23×C4×C5—21no—
68C23×C4×C5C2311yescharacteristic
69C2×C5×D8—22no—
70C2×C5×D8—22no—
71C2×C5×D8—22no—
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C5×#121—22no—
77C5×#121—22no—
78C5×#121—22no—
79C5×#121—22no—
80C4×C5×D4—22no—
81C4×C5×D4—22no—
82C4×C5×D4—22no—
83C4×C5×D4—22no—
84C5×#117—22no—
85C5×#117—22no—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4D411yescharacteristic
89C2×C5×C4⋊C4D411yescharacteristic
90C2×C5×C4⋊C4C2311yescharacteristic
91C2×C5×C4⋊C4C2311yescharacteristic
92C2×C5×C4⋊C4C2311yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C22⋊C4—21no—
97C2×C5×C22⋊C4—21no—
98C2×C5×C22⋊C4—21no—
99C2×C5×C22⋊C4—21no—
100C2×C5×C22⋊C4—21no—
101C2×C5×C22⋊C4—21no—
102C2×C5×C22⋊C4—21no—
103C2×C5×C22⋊C4—21no—
104C2×C5×C22⋊C4—21no—
105C2×C5×C22⋊C4—21no—
106C2×C5×C22⋊C4D411yescharacteristic
107C2×C5×C22⋊C4D411yescharacteristic
108C2×C42×C5—21no—
109C2×C42×C5—21no—
110C2×C42×C5C2311yescharacteristic
111C2×C42×C5C2311yescharacteristic
112C5×#107—22no—
113C5×#106—22no—
114C5×#106—22no—
115C5×C4⋊C8—22no—
116C5×C4⋊C8—22no—
117C5×#102—22no—
118C5×#102—22no—
119C5×#102—22no—
120C5×#102—22no—
121C5×#102—22no—
122C5×#102—22no—
123C5×C22⋊C8—22no—
124C5×C22⋊C8—22no—
125C5×#97D414yescomplemented
126C4×C5×C8—22no—
127C5×#95—21no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133C2×#442C2×C511yescharacteristic, complemented
134C2×#433C2×C511yescharacteristic, complemented
135#2324C2×C511yescharacteristic, complemented
136#2324C2×C511yescharacteristic, complemented
137#2088C2×C511yescharacteristic, complemented
138#2077C2×C511yescharacteristic, complemented
139#2067C2×C511yescharacteristic, complemented
140#2065C2×C511yescharacteristic, complemented
141#2054C2×C511yescharacteristic, complemented
142#2034C2×C511yescharacteristic, complemented
143#2033C2×C511yescharacteristic, complemented
144#1999C2×C511yescharacteristic
145#1776C2×C511yescharacteristic, complemented
146C4×#102C2×C511yescharacteristic, complemented
147C4×#102C2×C511yescharacteristic, complemented
148C24×C5—21no—
149C24×C5—21no—
150C24×C5C2×D411yescharacteristic
151C2×C5×D4—24no—
152C2×C5×D4—24no—
153C2×C5×D4—21no—
154C2×C5×D4—21no—
155C2×C5×D4—21no—
156C2×C5×D4—21no—
157C2×C5×D4—21no—
158C2×C5×D4—21no—
159C2×C5×D4—21no—
160C2×C5×D4—21no—
161C2×C5×D4—21no—
162C2×C5×D4—21no—
163C2×C5×D4—81no—
164C2×C5×D4—81no—
165C2×C5×D4—81no—
166C2×C5×D4—81no—
167C2×C5×D4#4112yes—
168C2×C5×D4#4112yes—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—42no—
182C22×C4×C5—42no—
183C22×C4×C5—81no—
184C22×C4×C5—81no—
185C22×C4×C5—81no—
186C22×C4×C5—81no—
187C22×C4×C5C2×D411yescharacteristic
188C22×C4×C5C2×D411yescharacteristic
189C22×C4×C5C2×D411yescharacteristic
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2411yescharacteristic
193C5×D8—28no—
194C2×C5×C8—21no—
195C2×C5×C8—21no—
196C2×C5×C8—21no—
197C2×C5×C8—21no—
198C2×C5×C8—21no—
199C2×C5×C8—21no—
200C2×C5×C8—21no—
201C2×C5×C8—21no—
202C2×C5×C8—21no—
203C2×C5×C8—21no—
204C2×C5×C8C2×D412yes—
205C2×C5×C8C2×D412yes—
206C5×C4⋊C4—22no—
207C5×C4⋊C4—22no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—21no—
213C5×C4⋊C4—21no—
214C5×C4⋊C4—21no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4—21no—
218C5×C4⋊C4—81no—
219C5×C4⋊C4—81no—
220C5×C4⋊C4#4112yes—
221C5×C4⋊C4#4112yes—
222C5×C22⋊C4—24no—
223C5×C22⋊C4—24no—
224C5×C22⋊C4—22no—
225C5×C22⋊C4—22no—
226C5×C22⋊C4—42no—
227C5×C22⋊C4—42no—
228C5×C22⋊C4—81no—
229C5×C22⋊C4—81no—
230C5×C22⋊C4—81no—
231C5×C22⋊C4—81no—
232C5×C22⋊C4—81no—
233C5×C22⋊C4—81no—
234C42×C5—21no—
235C42×C5—21no—
236C42×C5—81no—
237C42×C5—81no—
238C42×C5C2×D412yes—
239C42×C5#4112yes—
240C22×D8C22×C511yescharacteristic
241C2×#121C22×C511yescharacteristic
242C2×#121C22×C511yescharacteristic
243C2×C4×D4C22×C511yescharacteristic
244C2×C4×D4C22×C511yescharacteristic
245C2×#117C22×C511yescharacteristic
246#442—24no—
247#433—24no—
248C2×#107C22×C511yescharacteristic
249C2×#106C22×C511yescharacteristic
250C2×#106C22×C511yescharacteristic
251C2×C4⋊C8C22×C511yescharacteristic
252C2×C4⋊C8C22×C511yescharacteristic
253C2×#102C22×C511yescharacteristic
254C2×#102C22×C511yescharacteristic
255C2×#102C22×C511yescharacteristic
256C2×#102C22×C511yescharacteristic
257C2×#102C22×C511yescharacteristic
258C2×#102C22×C511yescharacteristic
259C2×C22⋊C8C22×C511yescharacteristic
260C2×C22⋊C8C22×C511yescharacteristic
261C2×#97C22×C511yescharacteristic
262C2×C4×C8C22×C511yescharacteristic
263#390—21no—
264#390—21no—
265#390C22×C511yescharacteristic
266#390C22×C511yescharacteristic
267#389C22×C511yescharacteristic
268#389C22×C511yescharacteristic
269#388—21no—
270#388—21no—
271#386—21no—
272#386—21no—
273#385—21no—
274#385—21no—
275#380C22×C511yescharacteristic
276#380C22×C511yescharacteristic
277C4×C4⋊C4C22×C511yescharacteristic
278C4×C4⋊C4C22×C511yescharacteristic
279#340C22×C511yescharacteristic
280#340C22×C511yescharacteristic
281#340C22×C511yescharacteristic
282#340C22×C511yescharacteristic
283#340C22×C511yescharacteristic
284#340C22×C511yescharacteristic
285C23×C5—21no—
286C23×C5—22no—
287C23×C5—22no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5—21no—
293C23×C5—21no—
294C23×C5—41no—
295C23×C5—41no—
296C23×C5—41no—
297C23×C5—41no—
298C23×C5—41no—
299C23×C5—41no—
300C23×C5—41no—
301C23×C5—41no—
302C23×C5—41no—
303C23×C5—41no—
304C23×C5—41no—
305C23×C5—41no—
306C23×C5C22×D411yescharacteristic
307C5×D4—22no—
308C5×D4—22no—
309C5×D4—22no—
310C5×D4—22no—
311C5×D4—41no—
312C5×D4—41no—
313C5×D4—41no—
314C5×D4—41no—
315C5×D4—84no—
316C5×D4—84no—
317C2×C4×C5—21no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—41no—
333C2×C4×C5—41no—
334C2×C4×C5—41no—
335C2×C4×C5—41no—
336C2×C4×C5—41no—
337C2×C4×C5—41no—
338C2×C4×C5—41no—
339C2×C4×C5—41no—
340C2×C4×C5—41no—
341C2×C4×C5—41no—
342C2×C4×C5—41no—
343C2×C4×C5—41no—
344C2×C4×C5—41no—
345C2×C4×C5—41no—
346C2×C4×C5—41no—
347C2×C4×C5—41no—
348C2×C4×C5—41no—
349C2×C4×C5—41no—
350C2×C4×C5—41no—
351C2×C4×C5—41no—
352C2×C4×C5—84no—
353C2×C4×C5—84no—
354C2×C4×C5#12112yes—
355C2×C4×C5#12112yes—
356C2×C4×C5C22×D411yescharacteristic
357C2×C4×C5C2×#4111yescharacteristic
358C2×C4×C5C2×#4111yescharacteristic
359C2×C4×C5C2×#4111yescharacteristic
360C2×C4×C5C2×#4111yescharacteristic
361C2×C4×C5C2×#4111yescharacteristic
362C5×C8—22no—
363C5×C8—22no—
364C5×C8—41no—
365C5×C8—41no—
366C22×D4—21no—
367C22×D4—21no—
368C22×D4C23×C511yescharacteristic
369C22×D4C23×C511yescharacteristic
370C23×C4—21no—
371C23×C4—21no—
372C23×C4C23×C511yescharacteristic
373C2×D8—22no—
374C2×D8—22no—
375C2×D8—22no—
376C22×C8C23×C511yescharacteristic
377C22×C8C23×C511yescharacteristic
378C22×C8C23×C511yescharacteristic
379C22×C8C23×C511yescharacteristic
380#121—22no—
381#121—22no—
382#121—22no—
383#121—22no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—22no—
388#117—22no—
389#117—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4C5×D411yescharacteristic
393C2×C4⋊C4C5×D411yescharacteristic
394C2×C4⋊C4C23×C511yescharacteristic
395C2×C4⋊C4C23×C511yescharacteristic
396C2×C4⋊C4C23×C511yescharacteristic
397C2×C4⋊C4C23×C511yescharacteristic
398C2×C4⋊C4C23×C511yescharacteristic
399C2×C4⋊C4C23×C511yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4C5×D411yescharacteristic
411C2×C22⋊C4C5×D411yescharacteristic
412C2×C42—21no—
413C2×C42—21no—
414C2×C42C23×C511yescharacteristic
415C2×C42C23×C511yescharacteristic
416#107—22no—
417#106—22no—
418#106—22no—
419C4⋊C8—22no—
420C4⋊C8—22no—
421#102—22no—
422#102—22no—
423#102—22no—
424#102—22no—
425#102—22no—
426#102—22no—
427C22⋊C8—22no—
428C22⋊C8—22no—
429#97C5×D414yescomplemented
430C4×C8—22no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437C22×C5—41no—
438C22×C5—42no—
439C22×C5—41no—
440C22×C5—42no—
441C22×C5—41no—
442C22×C5—42no—
443C22×C5—41no—
444C22×C5—42no—
445C22×C5—41no—
446C22×C5—42no—
447C22×C5—42no—
448C22×C5—41no—
449C22×C5—41no—
450C22×C5—81no—
451C22×C5—81no—
452C22×C5—81no—
453C22×C5—81no—
454C22×C5—81no—
455C22×C5—81no—
456C22×C5—81no—
457C22×C5—81no—
458C22×C5C2×#12111yescharacteristic
459C22×C5#52511yescharacteristic
460C22×C5#52511yescharacteristic
461C22×C5#57611yescharacteristic
462C22×C5#57611yescharacteristic
463C22×C5#57711yescharacteristic
464C22×C5#57711yescharacteristic
465C4×C5—22no—
466C4×C5—22no—
467C4×C5—42no—
468C4×C5—42no—
469C4×C5—41no—
470C4×C5—41no—
471C4×C5—41no—
472C4×C5—81no—
473C4×C5—81no—
474C4×C5—81no—
475C4×C5—81no—
476C4×C5#52511yescharacteristic
477C4×C5#52911yescharacteristic
478C4×C5#52911yescharacteristic
479C4×C5#53211yescharacteristic
480C24—21no—
481C24—21no—
482C24C2×C5×D411yescharacteristic
483C2×D4—24no—
484C2×D4—24no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—81no—
496C2×D4—81no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4C5×#4112yes—
500C2×D4C5×#4112yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—81no—
516C22×C4—81no—
517C22×C4—81no—
518C22×C4—81no—
519C22×C4C2×C5×D411yescharacteristic
520C22×C4C2×C5×D411yescharacteristic
521C22×C4C2×C5×D411yescharacteristic
522C22×C4C2×C5×D411yescharacteristic
523C22×C4C2×C5×D411yescharacteristic
524C22×C4C24×C511yescharacteristic
525D8—28no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8C2×C5×D412yes—
537C2×C8C2×C5×D412yes—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—81no—
551C4⋊C4—81no—
552C4⋊C4C5×#4112yes—
553C4⋊C4C5×#4112yes—
554C22⋊C4—24no—
555C22⋊C4—24no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—81no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C22⋊C4—81no—
565C22⋊C4—81no—
566C42—21no—
567C42—21no—
568C42—81no—
569C42—81no—
570C42C2×C5×D412yes—
571C42C5×#4112yes—
572C2×C5—81no—
573C2×C5—82no—
574C2×C5—82no—
575C2×C5#239211yescharacteristic
576C2×C5#306211yescharacteristic
577C2×C5#306211yescharacteristic
578C2×C5#311811yescharacteristic
579C2×C5#311911yescharacteristic
580C2×C5#312211yescharacteristic
581C2×C5#312511yescharacteristic
582C23—21no—
583C23—22no—
584C23—22no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23C22×C5×D411yescharacteristic
604D4—22no—
605D4—22no—
606D4—22no—
607D4—22no—
608D4—41no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—84no—
613D4—84no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4C5×#12112yes—
652C2×C4C5×#12112yes—
653C2×C4C22×C5×D411yescharacteristic
654C2×C4C2×C5×#4111yescharacteristic
655C2×C4C2×C5×#4111yescharacteristic
656C2×C4C2×C5×#4111yescharacteristic
657C2×C4C2×C5×#4111yescharacteristic
658C2×C4C2×C5×#4111yescharacteristic
659C8—22no—
660C8—22no—
661C8—41no—
662C8—41no—
663C5#2371211yescharacteristic, direct product factor, Sylow
664C22—41no—
665C22—41no—
666C22—41no—
667C22—42no—
668C22—41no—
669C22—42no—
670C22—41no—
671C22—42no—
672C22—41no—
673C22—42no—
674C22—41no—
675C22—42no—
676C22—42no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22C2×C5×#12111yescharacteristic
686C22C5×#52511yescharacteristic
687C22C5×#52511yescharacteristic
688C22C5×#57611yescharacteristic
689C22C5×#57611yescharacteristic
690C22C5×#57711yescharacteristic
691C22C5×#57711yescharacteristic
692C4—22no—
693C4—22no—
694C4—41no—
695C4—41no—
696C4—42no—
697C4—42no—
698C4—41no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4C5×#52511yescharacteristic
704C4C5×#52911yescharacteristic
705C4C5×#52911yescharacteristic
706C4C5×#53211yescharacteristic
707C2—81no—
708C2—82no—
709C2—82no—
710C2C5×#239211yescharacteristic
711C2C5×#306211yescharacteristic
712C2C5×#306211yescharacteristic
713C2C5×#311811yescharacteristic
714C2C5×#311911yescharacteristic
715C2C5×#312211yescharacteristic
716C2C5×#312511yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C5×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#442C2semidirect
2. C2×C5×#433C2semidirect
3. C5×#2324C2semidirect
4. C5×#2324C2semidirect
5. C5×#2088C2semidirect
6. C5×#2077C2semidirect
7. C5×#2067C2semidirect
8. C5×#2065C2semidirect
9. C5×#2054C2semidirect
10. C5×#2034C2semidirect
11. C5×#2033C2semidirect
13. C5×#1776C2semidirect
14. C4×C5×#102C2semidirect
15. C4×C5×#102C2semidirect
61. #23712C5direct (N × H)
125. C5×#97D4semidirect
133. C2×#442C2×C5semidirect
134. C2×#433C2×C5semidirect
135. #2324C2×C5semidirect
136. #2324C2×C5semidirect
137. #2088C2×C5semidirect
138. #2077C2×C5semidirect
139. #2067C2×C5semidirect
140. #2065C2×C5semidirect
141. #2054C2×C5semidirect
142. #2034C2×C5semidirect
143. #2033C2×C5semidirect
145. #1776C2×C5semidirect
146. C4×#102C2×C5semidirect
147. C4×#102C2×C5semidirect
429. #97C5×D4semidirect
663. C5#23712direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4422
C2×C5×#4332
C5×#23242
C5×#20882
C5×#20772
C5×#20672
C5×#20652
C5×#20542
C5×#20342
C5×#20332
C5×#19992
C5×#17762
C4×C5×#1022
#237125