Finite Group Databasebeta

← C5×#14553 #11937273

Subgroups — C5×#14553 #11937273

Order 1280.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#393C211yesmaximal, characteristic
2C2×C5×#391C211yesmaximal, characteristic, complemented
3C2×C5×#385C211yesmaximal, characteristic
4C5×#1446C211yesmaximal, characteristic, complemented
5C5×#1443C211yesmaximal, characteristic, complemented
6C5×#1442C211yesmaximal, characteristic, complemented
7C5×#1442C211yesmaximal, characteristic, complemented
8C5×#1439C211yesmaximal, characteristic
9C5×#1437C211yesmaximal, characteristic
10C5×#1437C211yesmaximal, characteristic
11C5×#1436C211yesmaximal, characteristic, complemented
12C5×#1436C211yesmaximal, characteristic, complemented
13C5×#1436C211yesmaximal, characteristic, complemented
14C5×C22⋊#95C211yesmaximal, characteristic
15C5×C22⋊#95C211yesmaximal, characteristic
16C23×C5×Q8C2211yescharacteristic
17C24×C4×C5C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C42×C5C2211yescharacteristic
28C22×C42×C5C2211yescharacteristic
29C5×#393C418yescomplemented
30C5×#391—24no—
31C5×#385—24no—
32C2×C5×#95C2211yescharacteristic
33C2×C5×#95C2211yescharacteristic
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#14553C511yesmaximal, characteristic, direct product factor, Sylow
55C25×C5C2311yescharacteristic
56C22×C5×Q8—22no—
57C22×C5×Q8—22no—
58C22×C5×Q8—41no—
59C22×C5×Q8—41no—
60C22×C5×Q8—41no—
61C22×C5×Q8—41no—
62C22×C5×Q8C2×C414yescomplemented
63C23×C4×C5—22no—
64C23×C4×C5—22no—
65C23×C4×C5—22no—
66C23×C4×C5—41no—
67C23×C4×C5—41no—
68C23×C4×C5—41no—
69C23×C4×C5—41no—
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—22no—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4—41no—
88C2×C5×C4⋊C4—41no—
89C2×C5×C4⋊C4—41no—
90C2×C5×C4⋊C4—41no—
91C2×C5×C4⋊C4—41no—
92C2×C5×C4⋊C4D414yes—
93C2×C5×C22⋊C4—22no—
94C2×C5×C22⋊C4—22no—
95C2×C5×C22⋊C4—22no—
96C2×C5×C22⋊C4—22no—
97C2×C5×C22⋊C4—22no—
98C2×C5×C22⋊C4—22no—
99C2×C5×C22⋊C4—41no—
100C2×C5×C22⋊C4—41no—
101C2×C5×C22⋊C4—41no—
102C2×C5×C22⋊C4—41no—
103C2×C5×C22⋊C4—41no—
104C2×C5×C22⋊C4—41no—
105C2×C5×C22⋊C4—41no—
106C2×C5×C22⋊C4—41no—
107C2×C5×C22⋊C4C2×C414yes—
108C2×C5×C22⋊C4C2×C414yes—
109C2×C5×C22⋊C4C2×C414yes—
110C2×C5×C22⋊C4Q814yescomplemented
111C2×C42×C5—22no—
112C2×C42×C5—41no—
113C2×C42×C5—41no—
114C2×C42×C5—41no—
115C2×C42×C5—41no—
116C2×C42×C5—41no—
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—41no—
127C5×#95—41no—
128C5×#95—41no—
129C5×#95—41no—
130C5×#95—41no—
131C5×#95—41no—
132C5×#95—41no—
133C5×#95—41no—
134C5×#95—41no—
135C5×#95—41no—
136C5×#95C2×C414yescomplemented
137C5×#95C2×C414yescomplemented
138C5×#95C2×C414yescomplemented
139C2×#393C2×C511yescharacteristic
140C2×#391C2×C511yescharacteristic, complemented
141C2×#385C2×C511yescharacteristic
142#1446C2×C511yescharacteristic, complemented
143#1443C2×C511yescharacteristic, complemented
144#1442C2×C511yescharacteristic, complemented
145#1442C2×C511yescharacteristic, complemented
146#1439C2×C511yescharacteristic
147#1437C2×C511yescharacteristic
148#1437C2×C511yescharacteristic
149#1436C2×C511yescharacteristic, complemented
150#1436C2×C511yescharacteristic, complemented
151#1436C2×C511yescharacteristic, complemented
152C22⋊#95C2×C511yescharacteristic
153C22⋊#95C2×C511yescharacteristic
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×C5—21no—
165C24×C5—21no—
166C24×C5C22×C412yes—
167C24×C5C2×Q812yes—
168C24×C5#4112yes—
169C24×C5C2411yescharacteristic
170C2×C5×Q8—28no—
171C2×C5×Q8—44no—
172C2×C5×Q8—44no—
173C2×C5×Q8—44no—
174C2×C5×Q8—44no—
175C2×C5×Q8—44no—
176C2×C5×Q8—44no—
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×C5—21no—
247C22×C4×C5—21no—
248C22×C4×C5—21no—
249C22×C4×C5—21no—
250C22×C4×C5—21no—
251C22×C4×C5—21no—
252C22×C4×C5—21no—
253C22×C4×C5—21no—
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—44no—
262C22×C4×C5—44no—
263C22×C4×C5—44no—
264C22×C4×C5—44no—
265C22×C4×C5—44no—
266C22×C4×C5—44no—
267C22×C4×C5—44no—
268C22×C4×C5C22×C412yes—
269C22×C4×C5C22×C412yes—
270C22×C4×C5C22×C412yes—
271C22×C4×C5C22×C412yes—
272C22×C4×C5C22×C412yes—
273C22×C4×C5C22×C412yes—
274C22×C4×C5C2×D412yes—
275C22×C4×C5C2×D412yes—
276C22×C4×C5C2×D412yes—
277C22×C4×C5C2×Q812yes—
278C22×C4×C5C2×Q812yes—
279C22×C4×C5#4112yes—
280C22×C4×C5#4112yes—
281C22×C4×C5#4112yes—
282C5×C4⋊C4—44no—
283C5×C4⋊C4—44no—
284C5×C4⋊C4—44no—
285C5×C22⋊C4—28no—
286C5×C22⋊C4—44no—
287C5×C22⋊C4—44no—
288C5×C22⋊C4—44no—
289C5×C22⋊C4—44no—
290C5×C22⋊C4—44no—
291C42×C5—44no—
292C42×C5—44no—
293C23×Q8C22×C511yescharacteristic
294C24×C4C22×C511yescharacteristic
295C22×C4⋊C4C22×C511yescharacteristic
296C22×C4⋊C4C22×C511yescharacteristic
297C22×C4⋊C4C22×C511yescharacteristic
298C22×C22⋊C4C22×C511yescharacteristic
299C22×C22⋊C4C22×C511yescharacteristic
300C22×C22⋊C4C22×C511yescharacteristic
301C22×C22⋊C4C22×C511yescharacteristic
302C22×C22⋊C4C22×C511yescharacteristic
303C22×C22⋊C4C22×C511yescharacteristic
304C22×C42C22×C511yescharacteristic
305C22×C42C22×C511yescharacteristic
306#393C4×C518yescomplemented
307#391—24no—
308#385—24no—
309C2×#95C22×C511yescharacteristic
310C2×#95C22×C511yescharacteristic
311C2×#95C22×C511yescharacteristic
312C2×#95C22×C511yescharacteristic
313C2×#95C22×C511yescharacteristic
314C2×#95C22×C511yescharacteristic
315C2×#95C22×C511yescharacteristic
316C2×#95C22×C511yescharacteristic
317C2×#95C22×C511yescharacteristic
318C2×#95C22×C511yescharacteristic
319C2×#95C22×C511yescharacteristic
320C2×#95C22×C511yescharacteristic
321C2×#95C22×C511yescharacteristic
322C2×#95C22×C511yescharacteristic
323C2×#95C22×C511yescharacteristic
324C2×#95C22×C511yescharacteristic
325C2×#95C22×C511yescharacteristic
326C2×#95C22×C511yescharacteristic
327C2×#95C22×C511yescharacteristic
328C2×#95C22×C511yescharacteristic
329C2×#95C22×C511yescharacteristic
330C2×#95C22×C511yescharacteristic
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—22no—
334C23×C5—22no—
335C23×C5—22no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—22no—
340C23×C5—22no—
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—41no—
350C23×C5—41no—
351C23×C5—41no—
352C23×C5—41no—
353C23×C5—41no—
354C23×C5—41no—
355C23×C5—41no—
356C23×C5—41no—
357C23×C5—41no—
358C23×C5—41no—
359C23×C5—41no—
360C23×C5—41no—
361C23×C5—41no—
362C23×C5—41no—
363C23×C5—41no—
364C23×C5—41no—
365C23×C5C4×Q814yes—
366C23×C5C23×C411yescharacteristic
367C23×C5C22×D411yescharacteristic
368C23×C5C22×Q811yescharacteristic
369C23×C5C2×#4111yescharacteristic
370C23×C5C2×#4111yescharacteristic
371C23×C5C2×#4111yescharacteristic
372C23×C5C2×#4111yescharacteristic
373C23×C5H(5,𝔽2)11yescharacteristic
374C23×C5H(5,𝔽2)11yescharacteristic
375C23×C5H(5,𝔽2)11yescharacteristic
376C23×C5H(5,𝔽2)11yescharacteristic
377C23×C5H(5,𝔽2)11yescharacteristic
378C23×C5H(5,𝔽2)11yescharacteristic
379C23×C52−1+411yescharacteristic
380C23×C52−1+411yescharacteristic
381C5×Q8—416no—
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—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—416no—
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—41no—
463C2×C4×C5—41no—
464C2×C4×C5—41no—
465C2×C4×C5—41no—
466C2×C4×C5—41no—
467C2×C4×C5—41no—
468C2×C4×C5—41no—
469C2×C4×C5—41no—
470C2×C4×C5—41no—
471C2×C4×C5—41no—
472C2×C4×C5—41no—
473C2×C4×C5—41no—
474C2×C4×C5—41no—
475C2×C4×C5—41no—
476C2×C4×C5—41no—
477C2×C4×C5—41no—
478C2×C4×C5—41no—
479C2×C4×C5—41no—
480C2×C4×C5C4×D414yes—
481C25C23×C511yescharacteristic
482C22×Q8—22no—
483C22×Q8—22no—
484C22×Q8—41no—
485C22×Q8—41no—
486C22×Q8—41no—
487C22×Q8—41no—
488C22×Q8C2×C4×C514yescomplemented
489C23×C4—22no—
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—41no—
493C23×C4—41no—
494C23×C4—41no—
495C23×C4—41no—
496C23×C4C23×C511yescharacteristic
497C23×C4C23×C511yescharacteristic
498C23×C4C23×C511yescharacteristic
499C23×C4C23×C511yescharacteristic
500C23×C4C23×C511yescharacteristic
501C23×C4C23×C511yescharacteristic
502C23×C4C23×C511yescharacteristic
503C23×C4C23×C511yescharacteristic
504C23×C4C23×C511yescharacteristic
505C23×C4C23×C511yescharacteristic
506C23×C4C23×C511yescharacteristic
507C23×C4C23×C511yescharacteristic
508C23×C4C23×C511yescharacteristic
509C23×C4C23×C511yescharacteristic
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—41no—
514C2×C4⋊C4—41no—
515C2×C4⋊C4—41no—
516C2×C4⋊C4—41no—
517C2×C4⋊C4—41no—
518C2×C4⋊C4C5×D414yes—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—41no—
526C2×C22⋊C4—41no—
527C2×C22⋊C4—41no—
528C2×C22⋊C4—41no—
529C2×C22⋊C4—41no—
530C2×C22⋊C4—41no—
531C2×C22⋊C4—41no—
532C2×C22⋊C4—41no—
533C2×C22⋊C4C2×C4×C514yes—
534C2×C22⋊C4C2×C4×C514yes—
535C2×C22⋊C4C2×C4×C514yes—
536C2×C22⋊C4C5×Q814yescomplemented
537C2×C42—22no—
538C2×C42—41no—
539C2×C42—41no—
540C2×C42—41no—
541C2×C42—41no—
542C2×C42—41no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—41no—
553#95—41no—
554#95—41no—
555#95—41no—
556#95—41no—
557#95—41no—
558#95—41no—
559#95—41no—
560#95—41no—
561#95—41no—
562#95C2×C4×C514yescomplemented
563#95C2×C4×C514yescomplemented
564#95C2×C4×C514yescomplemented
565C22×C5—24no—
566C22×C5—24no—
567C22×C5—24no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—42no—
572C22×C5—42no—
573C22×C5—42no—
574C22×C5—42no—
575C22×C5—42no—
576C22×C5—42no—
577C22×C5—42no—
578C22×C5—42no—
579C22×C5—42no—
580C22×C5C2×C4×D411yescharacteristic
581C22×C5C2×C4×Q811yescharacteristic
582C22×C5C4×#4111yescharacteristic
583C22×C5#51811yescharacteristic
584C22×C5#51811yescharacteristic
585C22×C5#52011yescharacteristic
586C22×C5#52011yescharacteristic
587C22×C5#53411yescharacteristic
588C22×C5#53511yescharacteristic
589C22×C5#53811yescharacteristic
590C22×C5#53811yescharacteristic
591C22×C5#53811yescharacteristic
592C22×C5#53811yescharacteristic
593C22×C5#53811yescharacteristic
594C22×C5#53911yescharacteristic
595C22×C5#54211yescharacteristic
596C22×C5#54211yescharacteristic
597C22×C5#54311yescharacteristic
598C22×C5#54411yescharacteristic
599C22×C5#54611yescharacteristic
600C22×C5#54611yescharacteristic
601C22×C5#54811yescharacteristic
602C22×C5D4×Q811yescharacteristic
603C22×C5#55111yescharacteristic
604C22×C5#55111yescharacteristic
605C22×C5#55211yescharacteristic
606C22×C5#55411yescharacteristic
607C22×C5#55411yescharacteristic
608C22×C5#55411yescharacteristic
609C22×C5#55611yescharacteristic
610C22×C5#55911yescharacteristic
611C22×C5H(3,𝔽4)11yescharacteristic
612C22×C5#56211yescharacteristic
613C22×C5#56211yescharacteristic
614C22×C5#56311yescharacteristic
615C4×C5—24no—
616C4×C5—42no—
617C4×C5—42no—
618C4×C5—42no—
619C4×C5—42no—
620C4×C5—42no—
621C4×C5—42no—
622C4×C5—42no—
623C4×C5—42no—
624C4×C5—42no—
625C4×C5—42no—
626C4×C5—42no—
627C4×C5—81no—
628C4×C5—81no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24C22×C4×C512yes—
642C24C2×C5×Q812yes—
643C24C5×#4112yes—
644C24C24×C511yescharacteristic
645C2×Q8—28no—
646C2×Q8—44no—
647C2×Q8—44no—
648C2×Q8—44no—
649C2×Q8—44no—
650C2×Q8—44no—
651C2×Q8—44no—
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×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4C22×C4×C512yes—
744C22×C4C22×C4×C512yes—
745C22×C4C22×C4×C512yes—
746C22×C4C22×C4×C512yes—
747C22×C4C22×C4×C512yes—
748C22×C4C22×C4×C512yes—
749C22×C4C2×C5×D412yes—
750C22×C4C2×C5×D412yes—
751C22×C4C2×C5×D412yes—
752C22×C4C2×C5×Q812yes—
753C22×C4C2×C5×Q812yes—
754C22×C4C5×#4112yes—
755C22×C4C5×#4112yes—
756C22×C4C5×#4112yes—
757C4⋊C4—44no—
758C4⋊C4—44no—
759C4⋊C4—44no—
760C22⋊C4—28no—
761C22⋊C4—44no—
762C22⋊C4—44no—
763C22⋊C4—44no—
764C22⋊C4—44no—
765C22⋊C4—44no—
766C42—44no—
767C42—44no—
768C2×C5—44no—
769C2×C5#232111yescharacteristic
770C2×C5#232911yescharacteristic
771C2×C5#233711yescharacteristic
772C2×C5#236011yescharacteristic
773C2×C5#236711yescharacteristic
774C2×C5#236811yescharacteristic
775C2×C5#237911yescharacteristic
776C2×C5#268411yescharacteristic
777C2×C5#269211yescharacteristic
778C2×C5#269611yescharacteristic
779C2×C5#272911yescharacteristic
780C2×C5#274511yescharacteristic
781C2×C5#275111yescharacteristic
782C2×C5#278811yescharacteristic
783C2×C5#280411yescharacteristic
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23C4×C5×Q814yes—
819C23C23×C4×C511yescharacteristic
820C23C22×C5×D411yescharacteristic
821C23C22×C5×Q811yescharacteristic
822C23C2×C5×#4111yescharacteristic
823C23C2×C5×#4111yescharacteristic
824C23C2×C5×#4111yescharacteristic
825C23C2×C5×#4111yescharacteristic
826C23C5×H(5,𝔽2)11yescharacteristic
827C23C5×H(5,𝔽2)11yescharacteristic
828C23C5×H(5,𝔽2)11yescharacteristic
829C23C5×H(5,𝔽2)11yescharacteristic
830C23C5×H(5,𝔽2)11yescharacteristic
831C23C5×H(5,𝔽2)11yescharacteristic
832C23C5×2−1+411yescharacteristic
833C23C5×2−1+411yescharacteristic
834Q8—416no—
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—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—416no—
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×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4C4×C5×D414yes—
934C5#1455311yescharacteristic, direct product factor, Sylow
935C22—24no—
936C22—24no—
937C22—24no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22C2×C4×C5×D411yescharacteristic
951C22C2×C4×C5×Q811yescharacteristic
952C22C4×C5×#4111yescharacteristic
953C22C5×#51811yescharacteristic
954C22C5×#51811yescharacteristic
955C22C5×#52011yescharacteristic
956C22C5×#52011yescharacteristic
957C22C5×#53411yescharacteristic
958C22C5×#53511yescharacteristic
959C22C5×#53811yescharacteristic
960C22C5×#53811yescharacteristic
961C22C5×#53811yescharacteristic
962C22C5×#53811yescharacteristic
963C22C5×#53811yescharacteristic
964C22C5×#53911yescharacteristic
965C22C5×#54211yescharacteristic
966C22C5×#54211yescharacteristic
967C22C5×#54311yescharacteristic
968C22C5×#54411yescharacteristic
969C22C5×#54611yescharacteristic
970C22C5×#54611yescharacteristic
971C22C5×#54811yescharacteristic
972C22C5×D4×Q811yescharacteristic
973C22C5×#55111yescharacteristic
974C22C5×#55111yescharacteristic
975C22C5×#55211yescharacteristic
976C22C5×#55411yescharacteristic
977C22C5×#55411yescharacteristic
978C22C5×#55411yescharacteristic
979C22C5×#55611yescharacteristic
980C22C5×#55911yescharacteristic
981C22C5×H(3,𝔽4)11yescharacteristic
982C22C5×#56211yescharacteristic
983C22C5×#56211yescharacteristic
984C22C5×#56311yescharacteristic
985C4—24no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—42no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—81no—
998C4—81no—
999C2—44no—
1000C2C5×#232111yescharacteristic
1001C2C5×#232911yescharacteristic
1002C2C5×#233711yescharacteristic
1003C2C5×#236011yescharacteristic
1004C2C5×#236711yescharacteristic
1005C2C5×#236811yescharacteristic
1006C2C5×#237911yescharacteristic
1007C2C5×#268411yescharacteristic
1008C2C5×#269211yescharacteristic
1009C2C5×#269611yescharacteristic
1010C2C5×#272911yescharacteristic
1011C2C5×#274511yescharacteristic
1012C2C5×#275111yescharacteristic
1013C2C5×#278811yescharacteristic
1014C2C5×#280411yescharacteristic
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
2. C2×C5×#391C2semidirect
4. C5×#1446C2semidirect
5. C5×#1443C2semidirect
6. C5×#1442C2semidirect
7. C5×#1442C2semidirect
11. C5×#1436C2semidirect
12. C5×#1436C2semidirect
13. C5×#1436C2semidirect
29. C5×#393C4semidirect
54. #14553C5direct (N × H)
62. C22×C5×Q8C2×C4semidirect
110. C2×C5×C22⋊C4Q8semidirect
136. C5×#95C2×C4semidirect
137. C5×#95C2×C4semidirect
138. C5×#95C2×C4semidirect
140. C2×#391C2×C5semidirect
142. #1446C2×C5semidirect
143. #1443C2×C5semidirect
144. #1442C2×C5semidirect
145. #1442C2×C5semidirect
149. #1436C2×C5semidirect
150. #1436C2×C5semidirect
151. #1436C2×C5semidirect
306. #393C4×C5semidirect
488. C22×Q8C2×C4×C5semidirect
536. C2×C22⋊C4C5×Q8semidirect
562. #95C2×C4×C5semidirect
563. #95C2×C4×C5semidirect
564. #95C2×C4×C5semidirect
934. C5#14553direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3932
C2×C5×#3912
C2×C5×#3852
C5×#14462
C5×#14432
C5×#14422
C5×#14392
C5×#14372
C5×#14362
C5×C22⋊#952
#145535