Finite Group Databasebeta

← C5×#14393 #11937113

Subgroups — C5×#14393 #11937113

Order 1280.

1506 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#388C211yesmaximal, characteristic
2C2×C5×#385C211yesmaximal, characteristic
3C2×C5×#382C211yesmaximal, characteristic, complemented
4C5×#1445C211yesmaximal, characteristic, complemented
5C5×#1443C211yesmaximal, characteristic, complemented
6C5×#1442C211yesmaximal, characteristic, complemented
7C5×#1441C211yesmaximal, characteristic, complemented
8C5×#1440C211yesmaximal, characteristic
9C5×#1439C211yesmaximal, characteristic
10C5×#1437C211yesmaximal, characteristic
11C5×#1436C211yesmaximal, characteristic, complemented
12C5×#1436C211yesmaximal, characteristic, complemented
13C5×#1434C211yesmaximal, characteristic, complemented
14C5×C22⋊#95C211yesmaximal, characteristic
15C5×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C5C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
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×#388C418yescomplemented
30C5×#385—24no—
31C5×#382—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#14393C511yesmaximal, characteristic, direct product factor, Sylow
55C25×C5C2311yescharacteristic
56C23×C4×C5—22no—
57C23×C4×C5—22no—
58C23×C4×C5—22no—
59C23×C4×C5—41no—
60C23×C4×C5—41no—
61C23×C4×C5—41no—
62C23×C4×C5—41no—
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C2×C5×C4⋊C4—22no—
78C2×C5×C4⋊C4—22no—
79C2×C5×C4⋊C4—22no—
80C2×C5×C4⋊C4—41no—
81C2×C5×C4⋊C4—41no—
82C2×C5×C4⋊C4—41no—
83C2×C5×C4⋊C4—41no—
84C2×C5×C4⋊C4—41no—
85C2×C5×C4⋊C4—41no—
86C2×C5×C4⋊C4—41no—
87C2×C5×C4⋊C4C2×C414yescomplemented
88C2×C5×C4⋊C4D414yes—
89C2×C5×C22⋊C4—22no—
90C2×C5×C22⋊C4—22no—
91C2×C5×C22⋊C4—22no—
92C2×C5×C22⋊C4—22no—
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—41no—
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⋊C4C2×C414yes—
105C2×C5×C22⋊C4C2×C414yes—
106C2×C5×C22⋊C4C2×C414yes—
107C2×C42×C5—22no—
108C2×C42×C5—22no—
109C2×C42×C5—41no—
110C2×C42×C5—41no—
111C2×C42×C5—41no—
112C2×C42×C5C2×C414yescomplemented
113C5×#95—22no—
114C5×#95—22no—
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—41no—
124C5×#95—41no—
125C5×#95—41no—
126C5×#95—41no—
127C5×#95—41no—
128C5×#95—41no—
129C5×#95—41no—
130C5×#95—41no—
131C5×#95—41no—
132C5×#95—41no—
133C5×#95C2×C414yescomplemented
134C5×#95C2×C414yescomplemented
135C2×#388C2×C511yescharacteristic
136C2×#385C2×C511yescharacteristic
137C2×#382C2×C511yescharacteristic, complemented
138#1445C2×C511yescharacteristic, complemented
139#1443C2×C511yescharacteristic, complemented
140#1442C2×C511yescharacteristic, complemented
141#1441C2×C511yescharacteristic, complemented
142#1440C2×C511yescharacteristic
143#1439C2×C511yescharacteristic
144#1437C2×C511yescharacteristic
145#1436C2×C511yescharacteristic, complemented
146#1436C2×C511yescharacteristic, complemented
147#1434C2×C511yescharacteristic, complemented
148C22⋊#95C2×C511yescharacteristic
149C22⋊#95C2×C511yescharacteristic
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×C5C22×C412yes—
163C24×C5#4112yes—
164C24×C5#4112yes—
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×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—44no—
253C22×C4×C5—44no—
254C22×C4×C5—44no—
255C22×C4×C5—44no—
256C22×C4×C5—44no—
257C22×C4×C5—44no—
258C22×C4×C5—44no—
259C22×C4×C5C22×C412yes—
260C22×C4×C5C22×C412yes—
261C22×C4×C5C22×C412yes—
262C22×C4×C5C22×C412yes—
263C22×C4×C5C22×C412yes—
264C22×C4×C5C22×C412yes—
265C22×C4×C5C2×D412yes—
266C22×C4×C5C2×D412yes—
267C22×C4×C5C2×D412yes—
268C22×C4×C5#4112yes—
269C22×C4×C5#4112yes—
270C22×C4×C5#4112yes—
271C5×C4⋊C4—44no—
272C5×C4⋊C4—44no—
273C5×C4⋊C4—44no—
274C5×C4⋊C4—44no—
275C5×C22⋊C4—28no—
276C5×C22⋊C4—28no—
277C5×C22⋊C4—44no—
278C5×C22⋊C4—44no—
279C5×C22⋊C4—44no—
280C5×C22⋊C4—44no—
281C42×C5—28no—
282C42×C5—44no—
283C24×C4C22×C511yescharacteristic
284C22×C4⋊C4C22×C511yescharacteristic
285C22×C4⋊C4C22×C511yescharacteristic
286C22×C4⋊C4C22×C511yescharacteristic
287C22×C4⋊C4C22×C511yescharacteristic
288C22×C22⋊C4C22×C511yescharacteristic
289C22×C22⋊C4C22×C511yescharacteristic
290C22×C22⋊C4C22×C511yescharacteristic
291C22×C22⋊C4C22×C511yescharacteristic
292C22×C22⋊C4C22×C511yescharacteristic
293C22×C22⋊C4C22×C511yescharacteristic
294C22×C42C22×C511yescharacteristic
295C22×C42C22×C511yescharacteristic
296#388C4×C518yescomplemented
297#385—24no—
298#382—24no—
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
317C2×#95C22×C511yescharacteristic
318C2×#95C22×C511yescharacteristic
319C2×#95C22×C511yescharacteristic
320C2×#95C22×C511yescharacteristic
321C23×C5—22no—
322C23×C5—22no—
323C23×C5—22no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
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—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×C5—41no—
353C23×C5—41no—
354C23×C5—41no—
355C23×C5#11714yes—
356C23×C5C23×C411yescharacteristic
357C23×C5C22×D411yescharacteristic
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×C5H(5,𝔽2)11yescharacteristic
367C23×C5H(5,𝔽2)11yescharacteristic
368C23×C52−1+411yescharacteristic
369C23×C52−1+411yescharacteristic
370C23×C52−1+411yescharacteristic
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—416no—
405C2×C4×C5—41no—
406C2×C4×C5—41no—
407C2×C4×C5—41no—
408C2×C4×C5—41no—
409C2×C4×C5—41no—
410C2×C4×C5—41no—
411C2×C4×C5—41no—
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—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×C5C4×D414yes—
470C25C23×C511yescharacteristic
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—41no—
475C23×C4—41no—
476C23×C4—41no—
477C23×C4—41no—
478C23×C4C23×C511yescharacteristic
479C23×C4C23×C511yescharacteristic
480C23×C4C23×C511yescharacteristic
481C23×C4C23×C511yescharacteristic
482C23×C4C23×C511yescharacteristic
483C23×C4C23×C511yescharacteristic
484C23×C4C23×C511yescharacteristic
485C23×C4C23×C511yescharacteristic
486C23×C4C23×C511yescharacteristic
487C23×C4C23×C511yescharacteristic
488C23×C4C23×C511yescharacteristic
489C23×C4C23×C511yescharacteristic
490C23×C4C23×C511yescharacteristic
491C23×C4C23×C511yescharacteristic
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—41no—
496C2×C4⋊C4—41no—
497C2×C4⋊C4—41no—
498C2×C4⋊C4—41no—
499C2×C4⋊C4—41no—
500C2×C4⋊C4—41no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4C2×C4×C514yescomplemented
503C2×C4⋊C4C5×D414yes—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—41no—
514C2×C22⋊C4—41no—
515C2×C22⋊C4—41no—
516C2×C22⋊C4—41no—
517C2×C22⋊C4—41no—
518C2×C22⋊C4—41no—
519C2×C22⋊C4C2×C4×C514yes—
520C2×C22⋊C4C2×C4×C514yes—
521C2×C22⋊C4C2×C4×C514yes—
522C2×C42—22no—
523C2×C42—22no—
524C2×C42—41no—
525C2×C42—41no—
526C2×C42—41no—
527C2×C42C2×C4×C514yescomplemented
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—41no—
539#95—41no—
540#95—41no—
541#95—41no—
542#95—41no—
543#95—41no—
544#95—41no—
545#95—41no—
546#95—41no—
547#95—41no—
548#95C2×C4×C514yescomplemented
549#95C2×C4×C514yescomplemented
550C22×C5—24no—
551C22×C5—24no—
552C22×C5—24no—
553C22×C5—42no—
554C22×C5—42no—
555C22×C5—42no—
556C22×C5—42no—
557C22×C5—42no—
558C22×C5—42no—
559C22×C5—42no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—42no—
564C22×C5—42no—
565C22×C5C2×#11711yescharacteristic
566C22×C5C2×C4×D411yescharacteristic
567C22×C5C4×#4111yescharacteristic
568C22×C5#51811yescharacteristic
569C22×C5#52011yescharacteristic
570C22×C5#52011yescharacteristic
571C22×C5#52011yescharacteristic
572C22×C5#53411yescharacteristic
573C22×C5#53611yescharacteristic
574C22×C5#53811yescharacteristic
575C22×C5#53811yescharacteristic
576C22×C5#53811yescharacteristic
577C22×C5#53911yescharacteristic
578C22×C5#53911yescharacteristic
579C22×C5#53911yescharacteristic
580C22×C5#53911yescharacteristic
581C22×C5#53911yescharacteristic
582C22×C5#54111yescharacteristic
583C22×C5#54211yescharacteristic
584C22×C5#54611yescharacteristic
585C22×C5#54611yescharacteristic
586C22×C5#54811yescharacteristic
587C22×C5#55011yescharacteristic
588C22×C5#55111yescharacteristic
589C22×C5#55111yescharacteristic
590C22×C5#55211yescharacteristic
591C22×C5#55211yescharacteristic
592C22×C5#55211yescharacteristic
593C22×C5#55311yescharacteristic
594C22×C5#55311yescharacteristic
595C22×C5#55511yescharacteristic
596C22×C5H(3,𝔽4)11yescharacteristic
597C22×C5#56211yescharacteristic
598C22×C5#56211yescharacteristic
599C22×C5#56311yescharacteristic
600C4×C5—24no—
601C4×C5—42no—
602C4×C5—42no—
603C4×C5—42no—
604C4×C5—42no—
605C4×C5—42no—
606C4×C5—42no—
607C4×C5—42no—
608C4×C5—42no—
609C4×C5—42no—
610C4×C5—81no—
611C4×C5—81no—
612C4×C5—81no—
613C4×C5—81no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24C22×C4×C512yes—
627C24C5×#4112yes—
628C24C5×#4112yes—
629C24C24×C511yescharacteristic
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×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—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4C22×C4×C512yes—
724C22×C4C22×C4×C512yes—
725C22×C4C22×C4×C512yes—
726C22×C4C22×C4×C512yes—
727C22×C4C22×C4×C512yes—
728C22×C4C22×C4×C512yes—
729C22×C4C2×C5×D412yes—
730C22×C4C2×C5×D412yes—
731C22×C4C2×C5×D412yes—
732C22×C4C5×#4112yes—
733C22×C4C5×#4112yes—
734C22×C4C5×#4112yes—
735C4⋊C4—44no—
736C4⋊C4—44no—
737C4⋊C4—44no—
738C4⋊C4—44no—
739C22⋊C4—28no—
740C22⋊C4—28no—
741C22⋊C4—44no—
742C22⋊C4—44no—
743C22⋊C4—44no—
744C22⋊C4—44no—
745C42—28no—
746C42—44no—
747C2×C5—44no—
748C2×C5#231811yescharacteristic
749C2×C5#232211yescharacteristic
750C2×C5#233411yescharacteristic
751C2×C5#234311yescharacteristic
752C2×C5#235211yescharacteristic
753C2×C5#236311yescharacteristic
754C2×C5#237911yescharacteristic
755C2×C5#268411yescharacteristic
756C2×C5#269011yescharacteristic
757C2×C5#269411yescharacteristic
758C2×C5#273011yescharacteristic
759C2×C5#274411yescharacteristic
760C2×C5#276511yescharacteristic
761C2×C5#278111yescharacteristic
762C2×C5#278211yescharacteristic
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23C5×#11714yes—
798C23C23×C4×C511yescharacteristic
799C23C22×C5×D411yescharacteristic
800C23C2×C5×#4111yescharacteristic
801C23C2×C5×#4111yescharacteristic
802C23C2×C5×#4111yescharacteristic
803C23C2×C5×#4111yescharacteristic
804C23C2×C5×#4111yescharacteristic
805C23C5×H(5,𝔽2)11yescharacteristic
806C23C5×H(5,𝔽2)11yescharacteristic
807C23C5×H(5,𝔽2)11yescharacteristic
808C23C5×H(5,𝔽2)11yescharacteristic
809C23C5×H(5,𝔽2)11yescharacteristic
810C23C5×2−1+411yescharacteristic
811C23C5×2−1+411yescharacteristic
812C23C5×2−1+411yescharacteristic
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—416no—
847C2×C4—41no—
848C2×C4—41no—
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×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×C4C4×C5×D414yes—
912C5#1439311yescharacteristic, direct product factor, Sylow
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22C2×C5×#11711yescharacteristic
929C22C2×C4×C5×D411yescharacteristic
930C22C4×C5×#4111yescharacteristic
931C22C5×#51811yescharacteristic
932C22C5×#52011yescharacteristic
933C22C5×#52011yescharacteristic
934C22C5×#52011yescharacteristic
935C22C5×#53411yescharacteristic
936C22C5×#53611yescharacteristic
937C22C5×#53811yescharacteristic
938C22C5×#53811yescharacteristic
939C22C5×#53811yescharacteristic
940C22C5×#53911yescharacteristic
941C22C5×#53911yescharacteristic
942C22C5×#53911yescharacteristic
943C22C5×#53911yescharacteristic
944C22C5×#53911yescharacteristic
945C22C5×#54111yescharacteristic
946C22C5×#54211yescharacteristic
947C22C5×#54611yescharacteristic
948C22C5×#54611yescharacteristic
949C22C5×#54811yescharacteristic
950C22C5×#55011yescharacteristic
951C22C5×#55111yescharacteristic
952C22C5×#55111yescharacteristic
953C22C5×#55211yescharacteristic
954C22C5×#55211yescharacteristic
955C22C5×#55211yescharacteristic
956C22C5×#55311yescharacteristic
957C22C5×#55311yescharacteristic
958C22C5×#55511yescharacteristic
959C22C5×H(3,𝔽4)11yescharacteristic
960C22C5×#56211yescharacteristic
961C22C5×#56211yescharacteristic
962C22C5×#56311yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—81no—
974C4—81no—
975C4—81no—
976C4—81no—
977C2—44no—
978C2C5×#231811yescharacteristic
979C2C5×#232211yescharacteristic
980C2C5×#233411yescharacteristic
981C2C5×#234311yescharacteristic
982C2C5×#235211yescharacteristic
983C2C5×#236311yescharacteristic
984C2C5×#237911yescharacteristic
985C2C5×#268411yescharacteristic
986C2C5×#269011yescharacteristic
987C2C5×#269411yescharacteristic
988C2C5×#273011yescharacteristic
989C2C5×#274411yescharacteristic
990C2C5×#276511yescharacteristic
991C2C5×#278111yescharacteristic
992C2C5×#278211yescharacteristic
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×#382C2semidirect
4. C5×#1445C2semidirect
5. C5×#1443C2semidirect
6. C5×#1442C2semidirect
7. C5×#1441C2semidirect
11. C5×#1436C2semidirect
12. C5×#1436C2semidirect
13. C5×#1434C2semidirect
29. C5×#388C4semidirect
54. #14393C5direct (N × H)
87. C2×C5×C4⋊C4C2×C4semidirect
112. C2×C42×C5C2×C4semidirect
133. C5×#95C2×C4semidirect
134. C5×#95C2×C4semidirect
137. C2×#382C2×C5semidirect
138. #1445C2×C5semidirect
139. #1443C2×C5semidirect
140. #1442C2×C5semidirect
141. #1441C2×C5semidirect
145. #1436C2×C5semidirect
146. #1436C2×C5semidirect
147. #1434C2×C5semidirect
296. #388C4×C5semidirect
502. C2×C4⋊C4C2×C4×C5semidirect
527. C2×C42C2×C4×C5semidirect
548. #95C2×C4×C5semidirect
549. #95C2×C4×C5semidirect
912. C5#14393direct (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×#3852
C2×C5×#3822
C5×#14452
C5×#14432
C5×#14422
C5×#14412
C5×#14402
C5×#14392
C5×#14372
C5×#14362
C5×#14342
C5×C22⋊#952
#143935