Finite Group Databasebeta

← C5×#14013 #11936733

Subgroups — C5×#14013 #11936733

Order 1280.

1462 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#388C211yesmaximal, characteristic
2C2×C5×#388C211yesmaximal, characteristic
3C2×C5×#383C211yesmaximal, characteristic, complemented
4C5×#1443C211yesmaximal, characteristic, complemented
5C5×#1441C211yesmaximal, characteristic, complemented
6C5×#1440C211yesmaximal, characteristic
7C5×#1439C211yesmaximal, characteristic
8C5×#1437C211yesmaximal, characteristic
9C5×#1437C211yesmaximal, characteristic
10C5×#1437C211yesmaximal, characteristic
11C5×#1436C211yesmaximal, characteristic, complemented
12C5×#1436C211yesmaximal, characteristic, complemented
13C5×C4⋊#95C211yesmaximal, characteristic, complemented
14C4×C5×#95C211yesmaximal, characteristic, complemented
15C4×C5×#95C211yesmaximal, characteristic, complemented
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C22⋊C4C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C42×C5C2211yescharacteristic
27C22×C42×C5C2211yescharacteristic
28C22×C42×C5C2211yescharacteristic
29C22×C42×C5C2211yescharacteristic
30C22×C42×C5C2211yescharacteristic
31C5×#388—24no—
32C5×#388C418yescomplemented
33C5×#383—24no—
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2211yescharacteristic
37C2×C5×#95C2211yescharacteristic
38C2×C5×#95C2211yescharacteristic
39C2×C5×#95C2211yescharacteristic
40C2×C5×#95C2211yescharacteristic
41C2×C5×#95C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2211yescharacteristic
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×C5×#95C2211yescharacteristic
52C2×C5×#95C2211yescharacteristic
53C2×C5×#95C2211yescharacteristic
54#14013C511yesmaximal, characteristic, direct product factor, Sylow
55C25×C5C2311yescharacteristic
56C23×C4×C5C2311yescharacteristic
57C23×C4×C5C2311yescharacteristic
58C23×C4×C5C2311yescharacteristic
59C23×C4×C5C2311yescharacteristic
60C23×C4×C5C2311yescharacteristic
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2311yescharacteristic
70C2×C5×C4⋊C4—22no—
71C2×C5×C4⋊C4—22no—
72C2×C5×C4⋊C4—22no—
73C2×C5×C4⋊C4—22no—
74C2×C5×C4⋊C4—41no—
75C2×C5×C4⋊C4—41no—
76C2×C5×C4⋊C4—41no—
77C2×C5×C4⋊C4—41no—
78C2×C5×C4⋊C4C2×C414yes—
79C2×C5×C22⋊C4—22no—
80C2×C5×C22⋊C4—22no—
81C2×C5×C22⋊C4—22no—
82C2×C5×C22⋊C4—22no—
83C2×C5×C22⋊C4—22no—
84C2×C5×C22⋊C4—22no—
85C2×C5×C22⋊C4—22no—
86C2×C5×C22⋊C4—22no—
87C2×C5×C22⋊C4—22no—
88C2×C5×C22⋊C4—22no—
89C2×C5×C22⋊C4—22no—
90C2×C5×C22⋊C4—22no—
91C2×C5×C22⋊C4—41no—
92C2×C5×C22⋊C4—41no—
93C2×C5×C22⋊C4—41no—
94C2×C5×C22⋊C4—41no—
95C2×C5×C22⋊C4—41no—
96C2×C5×C22⋊C4—41no—
97C2×C5×C22⋊C4C2×C414yes—
98C2×C5×C22⋊C4C2×C414yes—
99C2×C5×C22⋊C4C2×C414yes—
100C2×C42×C5—22no—
101C2×C42×C5—22no—
102C2×C42×C5—22no—
103C2×C42×C5—22no—
104C2×C42×C5—22no—
105C2×C42×C5—22no—
106C2×C42×C5—22no—
107C2×C42×C5—22no—
108C2×C42×C5—22no—
109C2×C42×C5—41no—
110C2×C42×C5—41no—
111C2×C42×C5—41no—
112C2×C42×C5—41no—
113C2×C42×C5—41no—
114C2×C42×C5C2×C414yes—
115C5×#95—22no—
116C5×#95—22no—
117C5×#95—22no—
118C5×#95—22no—
119C5×#95—22no—
120C5×#95—22no—
121C5×#95—22no—
122C5×#95—22no—
123C5×#95—22no—
124C5×#95—22no—
125C5×#95—22no—
126C5×#95—22no—
127C5×#95—22no—
128C5×#95—22no—
129C5×#95—41no—
130C5×#95—41no—
131C5×#95—41no—
132C5×#95C2×C414yes—
133C5×#95C2×C414yes—
134C5×#95D414yes—
135C2×#388C2×C511yescharacteristic
136C2×#388C2×C511yescharacteristic
137C2×#383C2×C511yescharacteristic, complemented
138#1443C2×C511yescharacteristic, complemented
139#1441C2×C511yescharacteristic, complemented
140#1440C2×C511yescharacteristic
141#1439C2×C511yescharacteristic
142#1437C2×C511yescharacteristic
143#1437C2×C511yescharacteristic
144#1437C2×C511yescharacteristic
145#1436C2×C511yescharacteristic, complemented
146#1436C2×C511yescharacteristic, complemented
147C4⋊#95C2×C511yescharacteristic, complemented
148C4×#95C2×C511yescharacteristic, complemented
149C4×#95C2×C511yescharacteristic, complemented
150C24×C5—21no—
151C24×C5—21no—
152C24×C5—21no—
153C24×C5—21no—
154C24×C5—21no—
155C24×C5—21no—
156C24×C5—21no—
157C24×C5—21no—
158C24×C5—21no—
159C24×C5—21no—
160C24×C5—21no—
161C24×C5—21no—
162C24×C5—21no—
163C24×C5—21no—
164C24×C5C22×C412yes—
165C24×C5C2411yescharacteristic
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
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—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5—21no—
228C22×C4×C5—21no—
229C22×C4×C5—21no—
230C22×C4×C5—21no—
231C22×C4×C5—21no—
232C22×C4×C5—21no—
233C22×C4×C5—21no—
234C22×C4×C5—21no—
235C22×C4×C5—21no—
236C22×C4×C5—21no—
237C22×C4×C5—21no—
238C22×C4×C5—21no—
239C22×C4×C5—21no—
240C22×C4×C5—21no—
241C22×C4×C5—21no—
242C22×C4×C5—21no—
243C22×C4×C5—21no—
244C22×C4×C5—21no—
245C22×C4×C5—21no—
246C22×C4×C5C22×C412yes—
247C22×C4×C5C22×C412yes—
248C22×C4×C5C22×C412yes—
249C22×C4×C5C22×C412yes—
250C22×C4×C5C22×C412yes—
251C22×C4×C5C22×C412yes—
252C22×C4×C5C2×D412yes—
253C22×C4×C5C2×D412yes—
254C22×C4×C5C2×D412yes—
255C22×C4×C5#4112yes—
256C22×C4×C5#4112yes—
257C22×C4×C5#4112yes—
258C22×C4×C5#4112yes—
259C22×C4×C5#4112yes—
260C22×C4×C5#4112yes—
261C22×C4×C5#4112yes—
262C22×C4×C5#4112yes—
263C22×C4×C5#4112yes—
264C5×C4⋊C4—44no—
265C5×C4⋊C4—44no—
266C5×C4⋊C4—44no—
267C5×C22⋊C4—28no—
268C5×C22⋊C4—28no—
269C5×C22⋊C4—44no—
270C5×C22⋊C4—44no—
271C5×C22⋊C4—44no—
272C5×C22⋊C4—44no—
273C5×C22⋊C4—44no—
274C42×C5—28no—
275C42×C5—44no—
276C42×C5—44no—
277C42×C5—44no—
278C42×C5—44no—
279C22×C4⋊C4C22×C511yescharacteristic
280C22×C4⋊C4C22×C511yescharacteristic
281C22×C4⋊C4C22×C511yescharacteristic
282C22×C22⋊C4C22×C511yescharacteristic
283C22×C22⋊C4C22×C511yescharacteristic
284C22×C22⋊C4C22×C511yescharacteristic
285C22×C22⋊C4C22×C511yescharacteristic
286C22×C22⋊C4C22×C511yescharacteristic
287C22×C22⋊C4C22×C511yescharacteristic
288C22×C22⋊C4C22×C511yescharacteristic
289C22×C42C22×C511yescharacteristic
290C22×C42C22×C511yescharacteristic
291C22×C42C22×C511yescharacteristic
292C22×C42C22×C511yescharacteristic
293C22×C42C22×C511yescharacteristic
294#388—24no—
295#388C4×C518yescomplemented
296#383—24no—
297C2×#95C22×C511yescharacteristic
298C2×#95C22×C511yescharacteristic
299C2×#95C22×C511yescharacteristic
300C2×#95C22×C511yescharacteristic
301C2×#95C22×C511yescharacteristic
302C2×#95C22×C511yescharacteristic
303C2×#95C22×C511yescharacteristic
304C2×#95C22×C511yescharacteristic
305C2×#95C22×C511yescharacteristic
306C2×#95C22×C511yescharacteristic
307C2×#95C22×C511yescharacteristic
308C2×#95C22×C511yescharacteristic
309C2×#95C22×C511yescharacteristic
310C2×#95C22×C511yescharacteristic
311C2×#95C22×C511yescharacteristic
312C2×#95C22×C511yescharacteristic
313C2×#95C22×C511yescharacteristic
314C2×#95C22×C511yescharacteristic
315C2×#95C22×C511yescharacteristic
316C2×#95C22×C511yescharacteristic
317C23×C5—22no—
318C23×C5—22no—
319C23×C5—22no—
320C23×C5—22no—
321C23×C5—22no—
322C23×C5—22no—
323C23×C5—22no—
324C23×C5—41no—
325C23×C5—41no—
326C23×C5—41no—
327C23×C5—41no—
328C23×C5—41no—
329C23×C5—41no—
330C23×C5—41no—
331C23×C5—41no—
332C23×C5—41no—
333C23×C5—41no—
334C23×C5—41no—
335C23×C5—41no—
336C23×C5—41no—
337C23×C5—41no—
338C23×C5—41no—
339C23×C5—41no—
340C23×C5—41no—
341C23×C5—41no—
342C23×C5—41no—
343C23×C5—41no—
344C23×C5—41no—
345C23×C5—41no—
346C23×C5—41no—
347C23×C5—41no—
348C23×C5—41no—
349C23×C5—41no—
350C23×C5—41no—
351C23×C5—41no—
352C23×C5C23×C411yescharacteristic
353C23×C5C22×D411yescharacteristic
354C23×C5C2×#4111yescharacteristic
355C23×C5C2×#4111yescharacteristic
356C23×C5C2×#4111yescharacteristic
357C23×C5C2×#4111yescharacteristic
358C23×C5C2×#4111yescharacteristic
359C23×C5C2×#4111yescharacteristic
360C23×C5C2×#4111yescharacteristic
361C23×C5C2×#4111yescharacteristic
362C23×C5C2×#4111yescharacteristic
363C23×C5H(5,𝔽2)11yescharacteristic
364C23×C5H(5,𝔽2)11yescharacteristic
365C23×C5H(5,𝔽2)11yescharacteristic
366C23×C52−1+411yescharacteristic
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—41no—
413C2×C4×C5—41no—
414C2×C4×C5—41no—
415C2×C4×C5—41no—
416C2×C4×C5—41no—
417C2×C4×C5—41no—
418C2×C4×C5—41no—
419C2×C4×C5—41no—
420C2×C4×C5—41no—
421C2×C4×C5—41no—
422C2×C4×C5—41no—
423C2×C4×C5—41no—
424C2×C4×C5—41no—
425C2×C4×C5—41no—
426C2×C4×C5—41no—
427C2×C4×C5—41no—
428C2×C4×C5—41no—
429C2×C4×C5—41no—
430C2×C4×C5—41no—
431C2×C4×C5—41no—
432C2×C4×C5—41no—
433C2×C4×C5—41no—
434C2×C4×C5—41no—
435C2×C4×C5—41no—
436C2×C4×C5—41no—
437C2×C4×C5—41no—
438C2×C4×C5—41no—
439C2×C4×C5—41no—
440C2×C4×C5—41no—
441C2×C4×C5—41no—
442C2×C4×C5—41no—
443C2×C4×C5—41no—
444C2×C4×C5—41no—
445C2×C4×C5—41no—
446C2×C4×C5—41no—
447C2×C4×C5—41no—
448C2×C4×C5—41no—
449C2×C4×C5—41no—
450C2×C4×C5—41no—
451C2×C4×C5—41no—
452C2×C4×C5—41no—
453C2×C4×C5—41no—
454C2×C4×C5—41no—
455C2×C4×C5—41no—
456C2×C4×C5—41no—
457C2×C4×C5—41no—
458C2×C4×C5—41no—
459C2×C4×C5—41no—
460C2×C4×C5—41no—
461C2×C4×C5—41no—
462C2×C4×C5#11714yes—
463C2×C4×C5C4×D414yes—
464C2×C4×C5#12614yes—
465C25C23×C511yescharacteristic
466C23×C4C23×C511yescharacteristic
467C23×C4C23×C511yescharacteristic
468C23×C4C23×C511yescharacteristic
469C23×C4C23×C511yescharacteristic
470C23×C4C23×C511yescharacteristic
471C23×C4C23×C511yescharacteristic
472C23×C4C23×C511yescharacteristic
473C23×C4C23×C511yescharacteristic
474C23×C4C23×C511yescharacteristic
475C23×C4C23×C511yescharacteristic
476C23×C4C23×C511yescharacteristic
477C23×C4C23×C511yescharacteristic
478C23×C4C23×C511yescharacteristic
479C23×C4C23×C511yescharacteristic
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—41no—
485C2×C4⋊C4—41no—
486C2×C4⋊C4—41no—
487C2×C4⋊C4—41no—
488C2×C4⋊C4C2×C4×C514yes—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—41no—
502C2×C22⋊C4—41no—
503C2×C22⋊C4—41no—
504C2×C22⋊C4—41no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—41no—
507C2×C22⋊C4C2×C4×C514yes—
508C2×C22⋊C4C2×C4×C514yes—
509C2×C22⋊C4C2×C4×C514yes—
510C2×C42—22no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—22no—
515C2×C42—22no—
516C2×C42—22no—
517C2×C42—22no—
518C2×C42—22no—
519C2×C42—41no—
520C2×C42—41no—
521C2×C42—41no—
522C2×C42—41no—
523C2×C42—41no—
524C2×C42C2×C4×C514yes—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—41no—
540#95—41no—
541#95—41no—
542#95C2×C4×C514yes—
543#95C2×C4×C514yes—
544#95C5×D414yes—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—42no—
551C22×C5—42no—
552C22×C5—81no—
553C22×C5—81no—
554C22×C5—81no—
555C22×C5—81no—
556C22×C5—81no—
557C22×C5—81no—
558C22×C5—81no—
559C22×C5—81no—
560C22×C5C2×#11711yescharacteristic
561C22×C5C2×C4×D411yescharacteristic
562C22×C5C4×#4111yescharacteristic
563C22×C5C4×#4111yescharacteristic
564C22×C5C4×#4111yescharacteristic
565C22×C5#51811yescharacteristic
566C22×C5#52011yescharacteristic
567C22×C5C2×#12611yescharacteristic
568C22×C5#52911yescharacteristic
569C22×C5#52911yescharacteristic
570C22×C5#52911yescharacteristic
571C22×C5#52911yescharacteristic
572C22×C5#52911yescharacteristic
573C22×C5#53211yescharacteristic
574C22×C5#53211yescharacteristic
575C22×C5#53811yescharacteristic
576C22×C5#53811yescharacteristic
577C22×C5#54211yescharacteristic
578C22×C5#54211yescharacteristic
579C22×C5#54611yescharacteristic
580C22×C5#54611yescharacteristic
581C22×C5#54711yescharacteristic
582C22×C5#55011yescharacteristic
583C22×C5#55111yescharacteristic
584C22×C5#55111yescharacteristic
585C22×C5#55111yescharacteristic
586C22×C5#55211yescharacteristic
587C22×C5#55311yescharacteristic
588C22×C5#55311yescharacteristic
589C22×C5#55311yescharacteristic
590C22×C5#55311yescharacteristic
591C22×C5#55311yescharacteristic
592C22×C5#55511yescharacteristic
593C22×C5#55611yescharacteristic
594C22×C5#55611yescharacteristic
595C4×C5—24no—
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—42no—
599C4×C5—42no—
600C4×C5—42no—
601C4×C5—42no—
602C4×C5—42no—
603C4×C5—42no—
604C4×C5—42no—
605C4×C5—42no—
606C4×C5—42no—
607C4×C5—81no—
608C4×C5—81no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24C22×C4×C512yes—
624C24C24×C511yescharacteristic
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4C22×C4×C512yes—
706C22×C4C22×C4×C512yes—
707C22×C4C22×C4×C512yes—
708C22×C4C22×C4×C512yes—
709C22×C4C22×C4×C512yes—
710C22×C4C22×C4×C512yes—
711C22×C4C2×C5×D412yes—
712C22×C4C2×C5×D412yes—
713C22×C4C2×C5×D412yes—
714C22×C4C5×#4112yes—
715C22×C4C5×#4112yes—
716C22×C4C5×#4112yes—
717C22×C4C5×#4112yes—
718C22×C4C5×#4112yes—
719C22×C4C5×#4112yes—
720C22×C4C5×#4112yes—
721C22×C4C5×#4112yes—
722C22×C4C5×#4112yes—
723C4⋊C4—44no—
724C4⋊C4—44no—
725C4⋊C4—44no—
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—44no—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C22⋊C4—44no—
732C22⋊C4—44no—
733C42—28no—
734C42—44no—
735C42—44no—
736C42—44no—
737C42—44no—
738C2×C5—82no—
739C2×C5#229311yescharacteristic
740C2×C5C4×#12611yescharacteristic
741C2×C5#233711yescharacteristic
742C2×C5#234711yescharacteristic
743C2×C5#235311yescharacteristic
744C2×C5#235911yescharacteristic
745C2×C5#236311yescharacteristic
746C2×C5#251011yescharacteristic
747C2×C5#251211yescharacteristic
748C2×C5#251811yescharacteristic
749C2×C5#252111yescharacteristic
750C2×C5#252511yescharacteristic
751C2×C5#253211yescharacteristic
752C2×C5#255411yescharacteristic
753C2×C5#255911yescharacteristic
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23C23×C4×C511yescharacteristic
790C23C22×C5×D411yescharacteristic
791C23C2×C5×#4111yescharacteristic
792C23C2×C5×#4111yescharacteristic
793C23C2×C5×#4111yescharacteristic
794C23C2×C5×#4111yescharacteristic
795C23C2×C5×#4111yescharacteristic
796C23C2×C5×#4111yescharacteristic
797C23C2×C5×#4111yescharacteristic
798C23C2×C5×#4111yescharacteristic
799C23C2×C5×#4111yescharacteristic
800C23C5×H(5,𝔽2)11yescharacteristic
801C23C5×H(5,𝔽2)11yescharacteristic
802C23C5×H(5,𝔽2)11yescharacteristic
803C23C5×2−1+411yescharacteristic
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4C5×#11714yes—
900C2×C4C4×C5×D414yes—
901C2×C4C5×#12614yes—
902C5#1401311yescharacteristic, direct product factor, Sylow
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22C2×C5×#11711yescharacteristic
919C22C2×C4×C5×D411yescharacteristic
920C22C4×C5×#4111yescharacteristic
921C22C4×C5×#4111yescharacteristic
922C22C4×C5×#4111yescharacteristic
923C22C5×#51811yescharacteristic
924C22C5×#52011yescharacteristic
925C22C2×C5×#12611yescharacteristic
926C22C5×#52911yescharacteristic
927C22C5×#52911yescharacteristic
928C22C5×#52911yescharacteristic
929C22C5×#52911yescharacteristic
930C22C5×#52911yescharacteristic
931C22C5×#53211yescharacteristic
932C22C5×#53211yescharacteristic
933C22C5×#53811yescharacteristic
934C22C5×#53811yescharacteristic
935C22C5×#54211yescharacteristic
936C22C5×#54211yescharacteristic
937C22C5×#54611yescharacteristic
938C22C5×#54611yescharacteristic
939C22C5×#54711yescharacteristic
940C22C5×#55011yescharacteristic
941C22C5×#55111yescharacteristic
942C22C5×#55111yescharacteristic
943C22C5×#55111yescharacteristic
944C22C5×#55211yescharacteristic
945C22C5×#55311yescharacteristic
946C22C5×#55311yescharacteristic
947C22C5×#55311yescharacteristic
948C22C5×#55311yescharacteristic
949C22C5×#55311yescharacteristic
950C22C5×#55511yescharacteristic
951C22C5×#55611yescharacteristic
952C22C5×#55611yescharacteristic
953C4—24no—
954C4—24no—
955C4—24no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—81no—
966C4—81no—
967C2—82no—
968C2C5×#229311yescharacteristic
969C2C4×C5×#12611yescharacteristic
970C2C5×#233711yescharacteristic
971C2C5×#234711yescharacteristic
972C2C5×#235311yescharacteristic
973C2C5×#235911yescharacteristic
974C2C5×#236311yescharacteristic
975C2C5×#251011yescharacteristic
976C2C5×#251211yescharacteristic
977C2C5×#251811yescharacteristic
978C2C5×#252111yescharacteristic
979C2C5×#252511yescharacteristic
980C2C5×#253211yescharacteristic
981C2C5×#255411yescharacteristic
982C2C5×#255911yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C5×#383C2semidirect
4. C5×#1443C2semidirect
5. C5×#1441C2semidirect
11. C5×#1436C2semidirect
12. C5×#1436C2semidirect
13. C5×C4⋊#95C2semidirect
14. C4×C5×#95C2semidirect
15. C4×C5×#95C2semidirect
32. C5×#388C4semidirect
54. #14013C5direct (N × H)
137. C2×#383C2×C5semidirect
138. #1443C2×C5semidirect
139. #1441C2×C5semidirect
145. #1436C2×C5semidirect
146. #1436C2×C5semidirect
147. C4⋊#95C2×C5semidirect
148. C4×#95C2×C5semidirect
149. C4×#95C2×C5semidirect
295. #388C4×C5semidirect
902. C5#14013direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3882
C2×C5×#3832
C5×#14432
C5×#14412
C5×#14402
C5×#14392
C5×#14372
C5×#14362
C5×C4⋊#952
C4×C5×#952
#140135