Finite Group Databasebeta

← C5×#14754 #11937474

Subgroups — C5×#14754 #11937474

Order 1280.

2302 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#396C211yesmaximal, characteristic, complemented
2C2×C5×#394C211yesmaximal, characteristic, complemented
3C2×C5×#392C211yesmaximal, characteristic
4C2×C5×#390C211yesmaximal, characteristic, complemented
5C2×C5×#388C211yesmaximal, characteristic, complemented
6C2×C5×#386C211yesmaximal, characteristic, complemented
7C2×C5×#386C211yesmaximal, characteristic, complemented
8C2×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
9C5×#1442C211yesmaximal, characteristic, complemented
10C5×#1440C211yesmaximal, characteristic, complemented
11C5×#1439C211yesmaximal, characteristic, complemented
12C5×#1438C211yesmaximal, characteristic, complemented
13C5×#1438C211yesmaximal, characteristic, complemented
14C5×#1437C211yesmaximal, characteristic, complemented
15C5×#1436C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C23×C5×D4C2211yescharacteristic
18C23×C5×D4C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C5×C22⋊C4C2211yescharacteristic
31C22×C5×C22⋊C4C2211yescharacteristic
32C22×C5×C22⋊C4C2211yescharacteristic
33C22×C5×C22⋊C4C2211yescharacteristic
34C22×C5×C22⋊C4C2211yescharacteristic
35C22×C5×C22⋊C4C2211yescharacteristic
36C22×C5×C22⋊C4C2211yescharacteristic
37C22×C42×C5C2211yescharacteristic
38C22×C42×C5C2211yescharacteristic
39C5×#396—24no—
40C5×#394—24no—
41C5×#392—24no—
42C5×#390—24no—
43C5×#388—24no—
44C5×#386—24no—
45C5×#386—24no—
46C4×C5×C22⋊C4—24no—
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×C5×#95C2211yescharacteristic
52C2×C5×#95C2211yescharacteristic
53C2×C5×#95C2211yescharacteristic
54C2×C5×#95C2211yescharacteristic
55C2×C5×#95C2211yescharacteristic
56C2×C5×#95C2211yescharacteristic
57C2×C5×#95C2211yescharacteristic
58C2×C5×#95C2211yescharacteristic
59#14754C511yesmaximal, characteristic, direct product factor, Sylow
60C25×C5C2311yescharacteristic
61C25×C5C2311yescharacteristic
62C25×C5C2311yescharacteristic
63C22×C5×D4—22no—
64C22×C5×D4—22no—
65C22×C5×D4—22no—
66C22×C5×D4—22no—
67C22×C5×D4—22no—
68C22×C5×D4—22no—
69C22×C5×D4—22no—
70C22×C5×D4—22no—
71C22×C5×D4—22no—
72C22×C5×D4—22no—
73C22×C5×D4—22no—
74C22×C5×D4—22no—
75C22×C5×D4—22no—
76C22×C5×D4—22no—
77C22×C5×D4—22no—
78C22×C5×D4—41no—
79C22×C5×D4—41no—
80C22×C5×D4—41no—
81C22×C5×D4—41no—
82C22×C5×D4—41no—
83C22×C5×D4—41no—
84C23×C4×C5—22no—
85C23×C4×C5—22no—
86C23×C4×C5—22no—
87C23×C4×C5—22no—
88C23×C4×C5—22no—
89C23×C4×C5—41no—
90C23×C4×C5—41no—
91C23×C4×C5C2311yescharacteristic
92C23×C4×C5C2311yescharacteristic
93C23×C4×C5C2311yescharacteristic
94C23×C4×C5C2311yescharacteristic
95C23×C4×C5C2311yescharacteristic
96C23×C4×C5C2311yescharacteristic
97C23×C4×C5C2311yescharacteristic
98C23×C4×C5C2311yescharacteristic
99C23×C4×C5C2311yescharacteristic
100C23×C4×C5C2311yescharacteristic
101C23×C4×C5C2311yescharacteristic
102C23×C4×C5C2311yescharacteristic
103C2×C5×C4⋊C4—22no—
104C2×C5×C4⋊C4—22no—
105C2×C5×C4⋊C4—22no—
106C2×C5×C4⋊C4—22no—
107C2×C5×C4⋊C4—22no—
108C2×C5×C4⋊C4—22no—
109C2×C5×C4⋊C4—22no—
110C2×C5×C4⋊C4—41no—
111C2×C5×C4⋊C4—41no—
112C2×C5×C22⋊C4—22no—
113C2×C5×C22⋊C4—22no—
114C2×C5×C22⋊C4—22no—
115C2×C5×C22⋊C4—22no—
116C2×C5×C22⋊C4—22no—
117C2×C5×C22⋊C4—22no—
118C2×C5×C22⋊C4—22no—
119C2×C5×C22⋊C4—22no—
120C2×C5×C22⋊C4—22no—
121C2×C5×C22⋊C4—22no—
122C2×C5×C22⋊C4—22no—
123C2×C5×C22⋊C4—22no—
124C2×C5×C22⋊C4—22no—
125C2×C5×C22⋊C4—22no—
126C2×C5×C22⋊C4—22no—
127C2×C5×C22⋊C4—22no—
128C2×C5×C22⋊C4—22no—
129C2×C5×C22⋊C4—22no—
130C2×C5×C22⋊C4—22no—
131C2×C5×C22⋊C4—22no—
132C2×C5×C22⋊C4—22no—
133C2×C5×C22⋊C4—22no—
134C2×C5×C22⋊C4—22no—
135C2×C5×C22⋊C4—22no—
136C2×C5×C22⋊C4—22no—
137C2×C5×C22⋊C4—22no—
138C2×C5×C22⋊C4—22no—
139C2×C5×C22⋊C4—22no—
140C2×C5×C22⋊C4—22no—
141C2×C5×C22⋊C4—22no—
142C2×C5×C22⋊C4—41no—
143C2×C5×C22⋊C4—41no—
144C2×C5×C22⋊C4—41no—
145C2×C5×C22⋊C4—41no—
146C2×C5×C22⋊C4—41no—
147C2×C5×C22⋊C4—41no—
148C2×C5×C22⋊C4—41no—
149C2×C5×C22⋊C4—41no—
150C2×C5×C22⋊C4—41no—
151C2×C5×C22⋊C4—41no—
152C2×C5×C22⋊C4D414yes—
153C2×C5×C22⋊C4D414yescomplemented
154C2×C42×C5—22no—
155C2×C42×C5—22no—
156C2×C42×C5—22no—
157C2×C42×C5—22no—
158C2×C42×C5—41no—
159C2×C42×C5—41no—
160C5×#95—22no—
161C5×#95—22no—
162C5×#95—22no—
163C5×#95—22no—
164C5×#95—22no—
165C5×#95—22no—
166C5×#95—22no—
167C5×#95—22no—
168C5×#95—41no—
169C5×#95—41no—
170C5×#95D414yescomplemented
171C5×#95D414yescomplemented
172C2×#396C2×C511yescharacteristic, complemented
173C2×#394C2×C511yescharacteristic, complemented
174C2×#392C2×C511yescharacteristic
175C2×#390C2×C511yescharacteristic, complemented
176C2×#388C2×C511yescharacteristic, complemented
177C2×#386C2×C511yescharacteristic, complemented
178C2×#386C2×C511yescharacteristic, complemented
179C2×C4×C22⋊C4C2×C511yescharacteristic, complemented
180#1442C2×C511yescharacteristic, complemented
181#1440C2×C511yescharacteristic, complemented
182#1439C2×C511yescharacteristic, complemented
183#1438C2×C511yescharacteristic, complemented
184#1438C2×C511yescharacteristic, complemented
185#1437C2×C511yescharacteristic, complemented
186#1436C2×C511yescharacteristic, complemented
187C24×C5—21no—
188C24×C5—21no—
189C24×C5—21no—
190C24×C5—21no—
191C24×C5—21no—
192C24×C5—21no—
193C24×C5—21no—
194C24×C5—21no—
195C24×C5—21no—
196C24×C5—21no—
197C24×C5—21no—
198C24×C5—21no—
199C24×C5—21no—
200C24×C5—21no—
201C24×C5—21no—
202C24×C5—21no—
203C24×C5—21no—
204C24×C5—21no—
205C24×C5—21no—
206C24×C5—21no—
207C24×C5—21no—
208C24×C5—21no—
209C24×C5—21no—
210C24×C5—21no—
211C24×C5—21no—
212C24×C5—21no—
213C24×C5—21no—
214C24×C5—21no—
215C24×C5—21no—
216C24×C5—21no—
217C24×C5—21no—
218C24×C5—21no—
219C24×C5—21no—
220C24×C5—21no—
221C24×C5—21no—
222C24×C5—21no—
223C24×C5—21no—
224C24×C5—21no—
225C24×C5—21no—
226C24×C5—21no—
227C24×C5C2×D412yes—
228C24×C5C2×D412yes—
229C24×C5#4112yes—
230C24×C5#4112yes—
231C24×C5#4112yes—
232C24×C5C2411yescharacteristic
233C2×C5×D4—28no—
234C2×C5×D4—28no—
235C2×C5×D4—28no—
236C2×C5×D4—44no—
237C2×C5×D4—44no—
238C2×C5×D4—44no—
239C2×C5×D4—44no—
240C2×C5×D4—44no—
241C2×C5×D4—44no—
242C2×C5×D4—44no—
243C2×C5×D4—44no—
244C2×C5×D4—44no—
245C2×C5×D4—44no—
246C2×C5×D4—44no—
247C2×C5×D4—44no—
248C2×C5×D4—44no—
249C2×C5×D4—44no—
250C2×C5×D4—44no—
251C2×C5×D4—44no—
252C2×C5×D4—44no—
253C2×C5×D4—44no—
254C22×C4×C5—21no—
255C22×C4×C5—21no—
256C22×C4×C5—21no—
257C22×C4×C5—21no—
258C22×C4×C5—21no—
259C22×C4×C5—21no—
260C22×C4×C5—21no—
261C22×C4×C5—21no—
262C22×C4×C5—28no—
263C22×C4×C5—21no—
264C22×C4×C5—21no—
265C22×C4×C5—21no—
266C22×C4×C5—21no—
267C22×C4×C5—21no—
268C22×C4×C5—21no—
269C22×C4×C5—21no—
270C22×C4×C5—21no—
271C22×C4×C5—21no—
272C22×C4×C5—21no—
273C22×C4×C5—21no—
274C22×C4×C5—21no—
275C22×C4×C5—21no—
276C22×C4×C5—21no—
277C22×C4×C5—21no—
278C22×C4×C5—21no—
279C22×C4×C5—21no—
280C22×C4×C5—21no—
281C22×C4×C5—21no—
282C22×C4×C5—21no—
283C22×C4×C5—21no—
284C22×C4×C5—21no—
285C22×C4×C5—21no—
286C22×C4×C5—21no—
287C22×C4×C5—21no—
288C22×C4×C5—21no—
289C22×C4×C5—21no—
290C22×C4×C5—21no—
291C22×C4×C5—21no—
292C22×C4×C5—21no—
293C22×C4×C5—21no—
294C22×C4×C5—21no—
295C22×C4×C5—21no—
296C22×C4×C5—21no—
297C22×C4×C5—21no—
298C22×C4×C5—21no—
299C22×C4×C5—21no—
300C22×C4×C5—21no—
301C22×C4×C5—21no—
302C22×C4×C5—21no—
303C22×C4×C5—21no—
304C22×C4×C5—21no—
305C22×C4×C5—21no—
306C22×C4×C5—21no—
307C22×C4×C5—21no—
308C22×C4×C5—21no—
309C22×C4×C5—21no—
310C22×C4×C5—21no—
311C22×C4×C5—21no—
312C22×C4×C5—21no—
313C22×C4×C5—21no—
314C22×C4×C5—21no—
315C22×C4×C5—21no—
316C22×C4×C5—21no—
317C22×C4×C5—21no—
318C22×C4×C5—21no—
319C22×C4×C5—21no—
320C22×C4×C5—21no—
321C22×C4×C5—21no—
322C22×C4×C5—21no—
323C22×C4×C5—21no—
324C22×C4×C5—21no—
325C22×C4×C5—44no—
326C22×C4×C5—44no—
327C22×C4×C5—44no—
328C22×C4×C5—44no—
329C22×C4×C5—44no—
330C22×C4×C5—44no—
331C22×C4×C5C2×D412yes—
332C22×C4×C5C2×D412yes—
333C22×C4×C5C2×D412yes—
334C22×C4×C5C2×D412yes—
335C22×C4×C5C2×D412yes—
336C22×C4×C5C2×D412yes—
337C22×C4×C5C2×D412yes—
338C22×C4×C5C2×D412yes—
339C22×C4×C5C2×D412yes—
340C22×C4×C5C2×D412yes—
341C22×C4×C5#4112yes—
342C22×C4×C5#4112yes—
343C22×C4×C5#4112yes—
344C22×C4×C5#4112yes—
345C5×C4⋊C4—44no—
346C5×C4⋊C4—44no—
347C5×C4⋊C4—44no—
348C5×C22⋊C4—28no—
349C5×C22⋊C4—28no—
350C5×C22⋊C4—28no—
351C5×C22⋊C4—44no—
352C5×C22⋊C4—44no—
353C5×C22⋊C4—44no—
354C5×C22⋊C4—44no—
355C5×C22⋊C4—44no—
356C5×C22⋊C4—44no—
357C5×C22⋊C4—44no—
358C5×C22⋊C4—44no—
359C5×C22⋊C4—44no—
360C5×C22⋊C4—44no—
361C5×C22⋊C4—44no—
362C42×C5—44no—
363C42×C5—44no—
364C23×D4C22×C511yescharacteristic
365C23×D4C22×C511yescharacteristic
366C23×D4C22×C511yescharacteristic
367C24×C4C22×C511yescharacteristic
368C22×C4⋊C4C22×C511yescharacteristic
369C22×C4⋊C4C22×C511yescharacteristic
370C22×C4⋊C4C22×C511yescharacteristic
371C22×C22⋊C4C22×C511yescharacteristic
372C22×C22⋊C4C22×C511yescharacteristic
373C22×C22⋊C4C22×C511yescharacteristic
374C22×C22⋊C4C22×C511yescharacteristic
375C22×C22⋊C4C22×C511yescharacteristic
376C22×C22⋊C4C22×C511yescharacteristic
377C22×C22⋊C4C22×C511yescharacteristic
378C22×C22⋊C4C22×C511yescharacteristic
379C22×C22⋊C4C22×C511yescharacteristic
380C22×C22⋊C4C22×C511yescharacteristic
381C22×C22⋊C4C22×C511yescharacteristic
382C22×C22⋊C4C22×C511yescharacteristic
383C22×C22⋊C4C22×C511yescharacteristic
384C22×C22⋊C4C22×C511yescharacteristic
385C22×C42C22×C511yescharacteristic
386C22×C42C22×C511yescharacteristic
387#396—24no—
388#394—24no—
389#392—24no—
390#390—24no—
391#388—24no—
392#386—24no—
393#386—24no—
394C4×C22⋊C4—24no—
395C2×#95C22×C511yescharacteristic
396C2×#95C22×C511yescharacteristic
397C2×#95C22×C511yescharacteristic
398C2×#95C22×C511yescharacteristic
399C2×#95C22×C511yescharacteristic
400C2×#95C22×C511yescharacteristic
401C2×#95C22×C511yescharacteristic
402C2×#95C22×C511yescharacteristic
403C2×#95C22×C511yescharacteristic
404C2×#95C22×C511yescharacteristic
405C2×#95C22×C511yescharacteristic
406C2×#95C22×C511yescharacteristic
407C23×C5—22no—
408C23×C5—22no—
409C23×C5—22no—
410C23×C5—22no—
411C23×C5—22no—
412C23×C5—22no—
413C23×C5—22no—
414C23×C5—22no—
415C23×C5—22no—
416C23×C5—22no—
417C23×C5—22no—
418C23×C5—22no—
419C23×C5—22no—
420C23×C5—22no—
421C23×C5—22no—
422C23×C5—22no—
423C23×C5—22no—
424C23×C5—22no—
425C23×C5—22no—
426C23×C5—22no—
427C23×C5—22no—
428C23×C5—22no—
429C23×C5—22no—
430C23×C5—22no—
431C23×C5—22no—
432C23×C5—22no—
433C23×C5—22no—
434C23×C5—22no—
435C23×C5—22no—
436C23×C5—22no—
437C23×C5—22no—
438C23×C5—22no—
439C23×C5—41no—
440C23×C5—41no—
441C23×C5—41no—
442C23×C5—41no—
443C23×C5—41no—
444C23×C5—41no—
445C23×C5—41no—
446C23×C5—41no—
447C23×C5—41no—
448C23×C5—41no—
449C23×C5—41no—
450C23×C5—41no—
451C23×C5—41no—
452C23×C5—41no—
453C23×C5—41no—
454C23×C5—41no—
455C23×C5—41no—
456C23×C5—41no—
457C23×C5—41no—
458C23×C5—41no—
459C23×C5—41no—
460C23×C5—41no—
461C23×C5—41no—
462C23×C5—41no—
463C23×C5—41no—
464C23×C5—41no—
465C23×C5—41no—
466C23×C5—41no—
467C23×C5—41no—
468C23×C5—41no—
469C23×C5—41no—
470C23×C5—41no—
471C23×C5—41no—
472C23×C5—41no—
473C23×C5—41no—
474C23×C5—41no—
475C23×C5—41no—
476C23×C5—41no—
477C23×C5—41no—
478C23×C5—41no—
479C23×C5—41no—
480C23×C5—41no—
481C23×C5—41no—
482C23×C5—41no—
483C23×C5—41no—
484C23×C5—41no—
485C23×C5—41no—
486C23×C5—41no—
487C23×C5—41no—
488C23×C5—41no—
489C23×C5—41no—
490C23×C5—41no—
491C23×C5—41no—
492C23×C5—41no—
493C23×C5—41no—
494C23×C5—41no—
495C23×C5—41no—
496C23×C5—41no—
497C23×C5—41no—
498C23×C5—41no—
499C23×C5—41no—
500C23×C5—41no—
501C23×C5—41no—
502C23×C5—41no—
503C23×C5—41no—
504C23×C5—41no—
505C23×C5—41no—
506C23×C5—41no—
507C23×C5—41no—
508C23×C5—41no—
509C23×C5—41no—
510C23×C5—41no—
511C23×C5#12414yes—
512C23×C5C22×D411yescharacteristic
513C23×C5C22×D411yescharacteristic
514C23×C5C22×D411yescharacteristic
515C23×C5C22×D411yescharacteristic
516C23×C5C2×#4111yescharacteristic
517C23×C5C2×#4111yescharacteristic
518C23×C5C2×#4111yescharacteristic
519C23×C5C2×#4111yescharacteristic
520C23×C5C2×#4111yescharacteristic
521C23×C5C2×#4111yescharacteristic
522C23×C5C2×#4111yescharacteristic
523C23×C5H(5,𝔽2)11yescharacteristic
524C23×C5H(5,𝔽2)11yescharacteristic
525C23×C5H(5,𝔽2)11yescharacteristic
526C23×C5H(5,𝔽2)11yescharacteristic
527C5×D4—416no—
528C5×D4—416no—
529C5×D4—416no—
530C2×C4×C5—22no—
531C2×C4×C5—22no—
532C2×C4×C5—22no—
533C2×C4×C5—22no—
534C2×C4×C5—22no—
535C2×C4×C5—22no—
536C2×C4×C5—22no—
537C2×C4×C5—22no—
538C2×C4×C5—22no—
539C2×C4×C5—22no—
540C2×C4×C5—22no—
541C2×C4×C5—22no—
542C2×C4×C5—22no—
543C2×C4×C5—22no—
544C2×C4×C5—22no—
545C2×C4×C5—22no—
546C2×C4×C5—22no—
547C2×C4×C5—22no—
548C2×C4×C5—22no—
549C2×C4×C5—22no—
550C2×C4×C5—22no—
551C2×C4×C5—22no—
552C2×C4×C5—22no—
553C2×C4×C5—22no—
554C2×C4×C5—22no—
555C2×C4×C5—22no—
556C2×C4×C5—22no—
557C2×C4×C5—22no—
558C2×C4×C5—22no—
559C2×C4×C5—22no—
560C2×C4×C5—22no—
561C2×C4×C5—22no—
562C2×C4×C5—22no—
563C2×C4×C5—22no—
564C2×C4×C5—22no—
565C2×C4×C5—22no—
566C2×C4×C5—416no—
567C2×C4×C5—41no—
568C2×C4×C5—41no—
569C2×C4×C5—41no—
570C2×C4×C5—41no—
571C2×C4×C5—41no—
572C2×C4×C5—41no—
573C2×C4×C5—41no—
574C2×C4×C5—41no—
575C2×C4×C5—41no—
576C2×C4×C5—41no—
577C2×C4×C5—41no—
578C2×C4×C5—41no—
579C2×C4×C5—41no—
580C2×C4×C5—41no—
581C2×C4×C5—41no—
582C2×C4×C5—41no—
583C2×C4×C5—41no—
584C2×C4×C5—41no—
585C2×C4×C5—41no—
586C2×C4×C5—41no—
587C2×C4×C5—41no—
588C2×C4×C5—41no—
589C2×C4×C5—41no—
590C2×C4×C5—41no—
591C2×C4×C5—41no—
592C2×C4×C5—41no—
593C2×C4×C5—41no—
594C2×C4×C5—41no—
595C2×C4×C5—41no—
596C2×C4×C5—41no—
597C2×C4×C5—41no—
598C2×C4×C5—41no—
599C2×C4×C5—41no—
600C2×C4×C5—41no—
601C2×C4×C5—41no—
602C2×C4×C5—41no—
603C2×C4×C5—41no—
604C2×C4×C5—41no—
605C2×C4×C5—41no—
606C2×C4×C5—41no—
607C2×C4×C5—41no—
608C2×C4×C5—41no—
609C2×C4×C5—41no—
610C2×C4×C5—41no—
611C2×C4×C5—41no—
612C2×C4×C5—41no—
613C2×C4×C5#12114yes—
614C2×C4×C5#12114yes—
615C25C23×C511yescharacteristic
616C25C23×C511yescharacteristic
617C25C23×C511yescharacteristic
618C22×D4—22no—
619C22×D4—22no—
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—22no—
623C22×D4—22no—
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—22no—
630C22×D4—22no—
631C22×D4—22no—
632C22×D4—22no—
633C22×D4—41no—
634C22×D4—41no—
635C22×D4—41no—
636C22×D4—41no—
637C22×D4—41no—
638C22×D4—41no—
639C23×C4—22no—
640C23×C4—22no—
641C23×C4—22no—
642C23×C4—22no—
643C23×C4—22no—
644C23×C4—41no—
645C23×C4—41no—
646C23×C4C23×C511yescharacteristic
647C23×C4C23×C511yescharacteristic
648C23×C4C23×C511yescharacteristic
649C23×C4C23×C511yescharacteristic
650C23×C4C23×C511yescharacteristic
651C23×C4C23×C511yescharacteristic
652C23×C4C23×C511yescharacteristic
653C23×C4C23×C511yescharacteristic
654C23×C4C23×C511yescharacteristic
655C23×C4C23×C511yescharacteristic
656C23×C4C23×C511yescharacteristic
657C23×C4C23×C511yescharacteristic
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—41no—
666C2×C4⋊C4—41no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4C5×D414yes—
708C2×C22⋊C4C5×D414yescomplemented
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—22no—
712C2×C42—22no—
713C2×C42—41no—
714C2×C42—41no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—41no—
724#95—41no—
725#95C5×D414yescomplemented
726#95C5×D414yescomplemented
727C22×C5—24no—
728C22×C5—24no—
729C22×C5—24no—
730C22×C5—42no—
731C22×C5—42no—
732C22×C5—42no—
733C22×C5—42no—
734C22×C5—42no—
735C22×C5—42no—
736C22×C5—42no—
737C22×C5—42no—
738C22×C5—42no—
739C22×C5—42no—
740C22×C5—42no—
741C22×C5—42no—
742C22×C5—42no—
743C22×C5—42no—
744C22×C5—42no—
745C22×C5—42no—
746C22×C5—42no—
747C22×C5—42no—
748C22×C5—42no—
749C22×C5—42no—
750C22×C5—42no—
751C22×C5—42no—
752C22×C5—42no—
753C22×C5—42no—
754C22×C5—42no—
755C22×C5—42no—
756C22×C5—81no—
757C22×C5—81no—
758C22×C5—81no—
759C22×C5—81no—
760C22×C5—81no—
761C22×C5—81no—
762C22×C5—81no—
763C22×C5—81no—
764C22×C5—81no—
765C22×C5—81no—
766C22×C5—81no—
767C22×C5—81no—
768C22×C5—81no—
769C22×C5—81no—
770C22×C5—81no—
771C22×C5—81no—
772C22×C5C2×#12111yescharacteristic
773C22×C5C2×#12111yescharacteristic
774C22×C5#52511yescharacteristic
775C22×C5#52511yescharacteristic
776C22×C5#52511yescharacteristic
777C22×C5#52511yescharacteristic
778C22×C5#52511yescharacteristic
779C22×C5C2×#12411yescharacteristic
780C22×C5#52911yescharacteristic
781C22×C5#52911yescharacteristic
782C22×C5#52911yescharacteristic
783C22×C5#53211yescharacteristic
784C22×C5#53211yescharacteristic
785C22×C5#53811yescharacteristic
786C22×C5#53811yescharacteristic
787C22×C5#53811yescharacteristic
788C22×C5#53811yescharacteristic
789C22×C5#54011yescharacteristic
790C22×C5#54011yescharacteristic
791C22×C5D4211yescharacteristic
792C22×C5D4211yescharacteristic
793C22×C5D4211yescharacteristic
794C22×C5D4211yescharacteristic
795C22×C5#54611yescharacteristic
796C22×C5#54611yescharacteristic
797C22×C5#54611yescharacteristic
798C22×C5#54611yescharacteristic
799C22×C5#54611yescharacteristic
800C22×C5#54611yescharacteristic
801C22×C5#55011yescharacteristic
802C22×C5#55011yescharacteristic
803C22×C5#55111yescharacteristic
804C22×C5#55111yescharacteristic
805C22×C5#55311yescharacteristic
806C22×C5#55311yescharacteristic
807C4×C5—24no—
808C4×C5—24no—
809C4×C5—42no—
810C4×C5—42no—
811C4×C5—42no—
812C4×C5—42no—
813C4×C5—42no—
814C4×C5—42no—
815C4×C5—42no—
816C4×C5—42no—
817C4×C5—81no—
818C4×C5—81no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24C2×C5×D412yes—
860C24C2×C5×D412yes—
861C24C5×#4112yes—
862C24C5×#4112yes—
863C24C5×#4112yes—
864C24C24×C511yescharacteristic
865C2×D4—28no—
866C2×D4—28no—
867C2×D4—28no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—28no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4C2×C5×D412yes—
964C22×C4C2×C5×D412yes—
965C22×C4C2×C5×D412yes—
966C22×C4C2×C5×D412yes—
967C22×C4C2×C5×D412yes—
968C22×C4C2×C5×D412yes—
969C22×C4C2×C5×D412yes—
970C22×C4C2×C5×D412yes—
971C22×C4C2×C5×D412yes—
972C22×C4C2×C5×D412yes—
973C22×C4C5×#4112yes—
974C22×C4C5×#4112yes—
975C22×C4C5×#4112yes—
976C22×C4C5×#4112yes—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C22⋊C4—28no—
981C22⋊C4—28no—
982C22⋊C4—28no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C42—44no—
995C42—44no—
996C2×C5—44no—
997C2×C5—82no—
998C2×C5—82no—
999C2×C5#239211yescharacteristic
1000C2×C5#242411yescharacteristic
1001C2×C5#242411yescharacteristic
1002C2×C5#242811yescharacteristic
1003C2×C5#242811yescharacteristic
1004C2×C5#245611yescharacteristic
1005C2×C5#245611yescharacteristic
1006C2×C5#245711yescharacteristic
1007C2×C5#247111yescharacteristic
1008C2×C5#247211yescharacteristic
1009C2×C5#247211yescharacteristic
1010C2×C5#255411yescharacteristic
1011C2×C5#255911yescharacteristic
1012C2×C5#264811yescharacteristic
1013C2×C5#285011yescharacteristic
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23C5×#12414yes—
1119C23C22×C5×D411yescharacteristic
1120C23C22×C5×D411yescharacteristic
1121C23C22×C5×D411yescharacteristic
1122C23C22×C5×D411yescharacteristic
1123C23C2×C5×#4111yescharacteristic
1124C23C2×C5×#4111yescharacteristic
1125C23C2×C5×#4111yescharacteristic
1126C23C2×C5×#4111yescharacteristic
1127C23C2×C5×#4111yescharacteristic
1128C23C2×C5×#4111yescharacteristic
1129C23C2×C5×#4111yescharacteristic
1130C23C5×H(5,𝔽2)11yescharacteristic
1131C23C5×H(5,𝔽2)11yescharacteristic
1132C23C5×H(5,𝔽2)11yescharacteristic
1133C23C5×H(5,𝔽2)11yescharacteristic
1134D4—416no—
1135D4—416no—
1136D4—416no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—416no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4C5×#12114yes—
1221C2×C4C5×#12114yes—
1222C5#1475411yescharacteristic, direct product factor, Sylow
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22C2×C5×#12111yescharacteristic
1269C22C2×C5×#12111yescharacteristic
1270C22C5×#52511yescharacteristic
1271C22C5×#52511yescharacteristic
1272C22C5×#52511yescharacteristic
1273C22C5×#52511yescharacteristic
1274C22C5×#52511yescharacteristic
1275C22C2×C5×#12411yescharacteristic
1276C22C5×#52911yescharacteristic
1277C22C5×#52911yescharacteristic
1278C22C5×#52911yescharacteristic
1279C22C5×#53211yescharacteristic
1280C22C5×#53211yescharacteristic
1281C22C5×#53811yescharacteristic
1282C22C5×#53811yescharacteristic
1283C22C5×#53811yescharacteristic
1284C22C5×#53811yescharacteristic
1285C22C5×#54011yescharacteristic
1286C22C5×#54011yescharacteristic
1287C22C5×D4211yescharacteristic
1288C22C5×D4211yescharacteristic
1289C22C5×D4211yescharacteristic
1290C22C5×D4211yescharacteristic
1291C22C5×#54611yescharacteristic
1292C22C5×#54611yescharacteristic
1293C22C5×#54611yescharacteristic
1294C22C5×#54611yescharacteristic
1295C22C5×#54611yescharacteristic
1296C22C5×#54611yescharacteristic
1297C22C5×#55011yescharacteristic
1298C22C5×#55011yescharacteristic
1299C22C5×#55111yescharacteristic
1300C22C5×#55111yescharacteristic
1301C22C5×#55311yescharacteristic
1302C22C5×#55311yescharacteristic
1303C4—24no—
1304C4—24no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—81no—
1314C4—81no—
1315C2—44no—
1316C2—82no—
1317C2—82no—
1318C2C5×#239211yescharacteristic
1319C2C5×#242411yescharacteristic
1320C2C5×#242411yescharacteristic
1321C2C5×#242811yescharacteristic
1322C2C5×#242811yescharacteristic
1323C2C5×#245611yescharacteristic
1324C2C5×#245611yescharacteristic
1325C2C5×#245711yescharacteristic
1326C2C5×#247111yescharacteristic
1327C2C5×#247211yescharacteristic
1328C2C5×#247211yescharacteristic
1329C2C5×#255411yescharacteristic
1330C2C5×#255911yescharacteristic
1331C2C5×#264811yescharacteristic
1332C2C5×#285011yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutator, Frattini, cosocleC24C24×C5
prime radicalC2×C5×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#396C2semidirect
2. C2×C5×#394C2semidirect
4. C2×C5×#390C2semidirect
5. C2×C5×#388C2semidirect
6. C2×C5×#386C2semidirect
7. C2×C5×#386C2semidirect
8. C2×C4×C5×C22⋊C4C2semidirect
9. C5×#1442C2semidirect
10. C5×#1440C2semidirect
11. C5×#1439C2semidirect
12. C5×#1438C2semidirect
13. C5×#1438C2semidirect
14. C5×#1437C2semidirect
15. C5×#1436C2semidirect
59. #14754C5direct (N × H)
153. C2×C5×C22⋊C4D4semidirect
170. C5×#95D4semidirect
171. C5×#95D4semidirect
172. C2×#396C2×C5semidirect
173. C2×#394C2×C5semidirect
175. C2×#390C2×C5semidirect
176. C2×#388C2×C5semidirect
177. C2×#386C2×C5semidirect
178. C2×#386C2×C5semidirect
179. C2×C4×C22⋊C4C2×C5semidirect
180. #1442C2×C5semidirect
181. #1440C2×C5semidirect
182. #1439C2×C5semidirect
183. #1438C2×C5semidirect
184. #1438C2×C5semidirect
185. #1437C2×C5semidirect
186. #1436C2×C5semidirect
708. C2×C22⋊C4C5×D4semidirect
725. #95C5×D4semidirect
726. #95C5×D4semidirect
1222. C5#14754direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3962
C2×C5×#3942
C2×C5×#3922
C2×C5×#3902
C2×C5×#3882
C2×C5×#3862
C2×C4×C5×C22⋊C42
C5×#14422
C5×#14402
C5×#14392
C5×#14382
C5×#14372
C5×#14362
#147545