Finite Group Databasebeta

← C5×#14633 #11937353

Subgroups — C5×#14633 #11937353

Order 1280.

1326 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×#396C211yesmaximal, characteristic
2C2×C5×#388C211yesmaximal, characteristic
3C2×C5×#387C211yesmaximal, characteristic, complemented
4C5×#1445C211yesmaximal, characteristic, complemented
5C5×#1444C211yesmaximal, characteristic, complemented
6C5×#1443C211yesmaximal, characteristic, complemented
7C5×#1441C211yesmaximal, characteristic, complemented
8C5×#1441C211yesmaximal, characteristic, complemented
9C5×#1441C211yesmaximal, characteristic, complemented
10C5×#1440C211yesmaximal, characteristic
11C5×#1440C211yesmaximal, characteristic
12C5×#1439C211yesmaximal, characteristic
13C5×#1439C211yesmaximal, characteristic
14C5×#1439C211yesmaximal, characteristic
15C5×C4⋊#95C211yesmaximal, characteristic, complemented
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
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×C42×C5C2211yescharacteristic
31C5×#396C418yescomplemented
32C5×#388—24no—
33C5×#387—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#14633C511yesmaximal, 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—22no—
75C2×C5×C4⋊C4—41no—
76C2×C5×C4⋊C4—41no—
77C2×C5×C4⋊C4—41no—
78C2×C5×C4⋊C4—41no—
79C2×C5×C4⋊C4—41no—
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⋊C4—41no—
88C2×C5×C4⋊C4C2×C414yes—
89C2×C5×C4⋊C4C2×C414yes—
90C2×C5×C4⋊C4C2×C414yes—
91C2×C5×C22⋊C4—22no—
92C2×C5×C22⋊C4—22no—
93C2×C5×C22⋊C4—22no—
94C2×C5×C22⋊C4—22no—
95C2×C5×C22⋊C4—41no—
96C2×C5×C22⋊C4—41no—
97C2×C5×C22⋊C4—41no—
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⋊C4—41no—
105C2×C5×C22⋊C4—41no—
106C2×C5×C22⋊C4—41no—
107C2×C5×C22⋊C4—41no—
108C2×C5×C22⋊C4—41no—
109C2×C5×C22⋊C4C2×C414yes—
110C2×C5×C22⋊C4C2×C414yes—
111C2×C5×C22⋊C4C2×C414yes—
112C2×C42×C5—41no—
113C2×C42×C5—41no—
114C2×C42×C5D414yes—
115C5×#95—22no—
116C5×#95—22no—
117C5×#95—22no—
118C5×#95—22no—
119C5×#95—22no—
120C5×#95—22no—
121C5×#95—41no—
122C5×#95—41no—
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×#95—41no—
134C5×#95C2×C414yes—
135C2×#396C2×C511yescharacteristic
136C2×#388C2×C511yescharacteristic
137C2×#387C2×C511yescharacteristic, complemented
138#1445C2×C511yescharacteristic, complemented
139#1444C2×C511yescharacteristic, complemented
140#1443C2×C511yescharacteristic, complemented
141#1441C2×C511yescharacteristic, complemented
142#1441C2×C511yescharacteristic, complemented
143#1441C2×C511yescharacteristic, complemented
144#1440C2×C511yescharacteristic
145#1440C2×C511yescharacteristic
146#1439C2×C511yescharacteristic
147#1439C2×C511yescharacteristic
148#1439C2×C511yescharacteristic
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×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×C5C22×C412yes—
255C22×C4×C5C22×C412yes—
256C22×C4×C5C22×C412yes—
257C22×C4×C5C22×C412yes—
258C22×C4×C5C22×C412yes—
259C22×C4×C5C22×C412yes—
260C22×C4×C5C2×D412yes—
261C22×C4×C5C2×D412yes—
262C22×C4×C5C2×D412yes—
263C22×C4×C5#4112yes—
264C5×C4⋊C4—28no—
265C5×C4⋊C4—44no—
266C5×C4⋊C4—44no—
267C5×C4⋊C4—44no—
268C5×C4⋊C4—44no—
269C5×C4⋊C4—44no—
270C5×C4⋊C4—44no—
271C5×C22⋊C4—28no—
272C5×C22⋊C4—44no—
273C5×C22⋊C4—44no—
274C5×C22⋊C4—44no—
275C5×C22⋊C4—44no—
276C5×C22⋊C4—44no—
277C5×C22⋊C4—44no—
278C42×C5—44no—
279C22×C4⋊C4C22×C511yescharacteristic
280C22×C4⋊C4C22×C511yescharacteristic
281C22×C4⋊C4C22×C511yescharacteristic
282C22×C4⋊C4C22×C511yescharacteristic
283C22×C4⋊C4C22×C511yescharacteristic
284C22×C4⋊C4C22×C511yescharacteristic
285C22×C4⋊C4C22×C511yescharacteristic
286C22×C22⋊C4C22×C511yescharacteristic
287C22×C22⋊C4C22×C511yescharacteristic
288C22×C22⋊C4C22×C511yescharacteristic
289C22×C22⋊C4C22×C511yescharacteristic
290C22×C22⋊C4C22×C511yescharacteristic
291C22×C22⋊C4C22×C511yescharacteristic
292C22×C22⋊C4C22×C511yescharacteristic
293C22×C42C22×C511yescharacteristic
294#396C4×C518yescomplemented
295#388—24no—
296#387—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×C5H(5,𝔽2)11yescharacteristic
356C23×C5H(5,𝔽2)11yescharacteristic
357C23×C5H(5,𝔽2)11yescharacteristic
358C23×C5H(5,𝔽2)11yescharacteristic
359C23×C5H(5,𝔽2)11yescharacteristic
360C23×C5H(5,𝔽2)11yescharacteristic
361C23×C5H(5,𝔽2)11yescharacteristic
362C23×C52−1+411yescharacteristic
363C23×C52−1+411yescharacteristic
364C23×C52−1+411yescharacteristic
365C23×C52−1+411yescharacteristic
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—41no—
395C2×C4×C5—41no—
396C2×C4×C5—41no—
397C2×C4×C5—41no—
398C2×C4×C5—41no—
399C2×C4×C5—41no—
400C2×C4×C5—41no—
401C2×C4×C5—41no—
402C2×C4×C5—41no—
403C2×C4×C5—41no—
404C2×C4×C5—41no—
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×C5C4×D414yes—
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—22no—
485C2×C4⋊C4—41no—
486C2×C4⋊C4—41no—
487C2×C4⋊C4—41no—
488C2×C4⋊C4—41no—
489C2×C4⋊C4—41no—
490C2×C4⋊C4—41no—
491C2×C4⋊C4—41no—
492C2×C4⋊C4—41no—
493C2×C4⋊C4—41no—
494C2×C4⋊C4—41no—
495C2×C4⋊C4—41no—
496C2×C4⋊C4—41no—
497C2×C4⋊C4—41no—
498C2×C4⋊C4C2×C4×C514yes—
499C2×C4⋊C4C2×C4×C514yes—
500C2×C4⋊C4C2×C4×C514yes—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—41no—
507C2×C22⋊C4—41no—
508C2×C22⋊C4—41no—
509C2×C22⋊C4—41no—
510C2×C22⋊C4—41no—
511C2×C22⋊C4—41no—
512C2×C22⋊C4—41no—
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—41no—
523C2×C42—41no—
524C2×C42C5×D414yes—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—41no—
532#95—41no—
533#95—41no—
534#95—41no—
535#95—41no—
536#95—41no—
537#95—41no—
538#95—41no—
539#95—41no—
540#95—41no—
541#95—41no—
542#95—41no—
543#95—41no—
544#95C2×C4×C514yes—
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×C4×D411yescharacteristic
561C22×C5#51811yescharacteristic
562C22×C5#51811yescharacteristic
563C22×C5#51911yescharacteristic
564C22×C5#52011yescharacteristic
565C22×C5#52011yescharacteristic
566C22×C5#52011yescharacteristic
567C22×C5#53411yescharacteristic
568C22×C5#53511yescharacteristic
569C22×C5#53611yescharacteristic
570C22×C5#53711yescharacteristic
571C22×C5#53711yescharacteristic
572C22×C5#53711yescharacteristic
573C22×C5#53811yescharacteristic
574C22×C5#53911yescharacteristic
575C22×C5#54011yescharacteristic
576C22×C5#54111yescharacteristic
577C22×C5#54211yescharacteristic
578C22×C5#54211yescharacteristic
579C22×C5#56011yescharacteristic
580C22×C5#56011yescharacteristic
581C22×C5#56011yescharacteristic
582C22×C5#56211yescharacteristic
583C22×C5#56211yescharacteristic
584C22×C5#56211yescharacteristic
585C22×C5#56211yescharacteristic
586C22×C5#56211yescharacteristic
587C22×C5#56211yescharacteristic
588C22×C5#56311yescharacteristic
589C22×C5#56311yescharacteristic
590C22×C5#56311yescharacteristic
591C22×C5#56311yescharacteristic
592C22×C5#56311yescharacteristic
593C22×C5#56311yescharacteristic
594C22×C5#56311yescharacteristic
595C4×C5—24no—
596C4×C5—42no—
597C4×C5—42no—
598C4×C5—42no—
599C4×C5—42no—
600C4×C5—42no—
601C4×C5—42no—
602C4×C5—42no—
603C4×C5—81no—
604C4×C5—81no—
605C4×C5—81no—
606C4×C5—81no—
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×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4C22×C4×C512yes—
714C22×C4C22×C4×C512yes—
715C22×C4C22×C4×C512yes—
716C22×C4C22×C4×C512yes—
717C22×C4C22×C4×C512yes—
718C22×C4C22×C4×C512yes—
719C22×C4C2×C5×D412yes—
720C22×C4C2×C5×D412yes—
721C22×C4C2×C5×D412yes—
722C22×C4C5×#4112yes—
723C4⋊C4—28no—
724C4⋊C4—44no—
725C4⋊C4—44no—
726C4⋊C4—44no—
727C4⋊C4—44no—
728C4⋊C4—44no—
729C4⋊C4—44no—
730C22⋊C4—28no—
731C22⋊C4—44no—
732C22⋊C4—44no—
733C22⋊C4—44no—
734C22⋊C4—44no—
735C22⋊C4—44no—
736C22⋊C4—44no—
737C42—44no—
738C2×C5—82no—
739C2×C5#232311yescharacteristic
740C2×C5#232411yescharacteristic
741C2×C5#232511yescharacteristic
742C2×C5#237711yescharacteristic
743C2×C5#237811yescharacteristic
744C2×C5#237811yescharacteristic
745C2×C5#238311yescharacteristic
746C2×C5#281311yescharacteristic
747C2×C5#281411yescharacteristic
748C2×C5#282011yescharacteristic
749C2×C5#282311yescharacteristic
750C2×C5#282911yescharacteristic
751C2×C5#283111yescharacteristic
752C2×C5#283611yescharacteristic
753C2×C5#283811yescharacteristic
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
792C23C5×H(5,𝔽2)11yescharacteristic
793C23C5×H(5,𝔽2)11yescharacteristic
794C23C5×H(5,𝔽2)11yescharacteristic
795C23C5×H(5,𝔽2)11yescharacteristic
796C23C5×H(5,𝔽2)11yescharacteristic
797C23C5×H(5,𝔽2)11yescharacteristic
798C23C5×H(5,𝔽2)11yescharacteristic
799C23C5×2−1+411yescharacteristic
800C23C5×2−1+411yescharacteristic
801C23C5×2−1+411yescharacteristic
802C23C5×2−1+411yescharacteristic
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—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
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×C4C4×C5×D414yes—
902C5#1463311yescharacteristic, 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×C4×C5×D411yescharacteristic
919C22C5×#51811yescharacteristic
920C22C5×#51811yescharacteristic
921C22C5×#51911yescharacteristic
922C22C5×#52011yescharacteristic
923C22C5×#52011yescharacteristic
924C22C5×#52011yescharacteristic
925C22C5×#53411yescharacteristic
926C22C5×#53511yescharacteristic
927C22C5×#53611yescharacteristic
928C22C5×#53711yescharacteristic
929C22C5×#53711yescharacteristic
930C22C5×#53711yescharacteristic
931C22C5×#53811yescharacteristic
932C22C5×#53911yescharacteristic
933C22C5×#54011yescharacteristic
934C22C5×#54111yescharacteristic
935C22C5×#54211yescharacteristic
936C22C5×#54211yescharacteristic
937C22C5×#56011yescharacteristic
938C22C5×#56011yescharacteristic
939C22C5×#56011yescharacteristic
940C22C5×#56211yescharacteristic
941C22C5×#56211yescharacteristic
942C22C5×#56211yescharacteristic
943C22C5×#56211yescharacteristic
944C22C5×#56211yescharacteristic
945C22C5×#56211yescharacteristic
946C22C5×#56311yescharacteristic
947C22C5×#56311yescharacteristic
948C22C5×#56311yescharacteristic
949C22C5×#56311yescharacteristic
950C22C5×#56311yescharacteristic
951C22C5×#56311yescharacteristic
952C22C5×#56311yescharacteristic
953C4—24no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—42no—
961C4—81no—
962C4—81no—
963C4—81no—
964C4—81no—
965C4—81no—
966C4—81no—
967C2—82no—
968C2C5×#232311yescharacteristic
969C2C5×#232411yescharacteristic
970C2C5×#232511yescharacteristic
971C2C5×#237711yescharacteristic
972C2C5×#237811yescharacteristic
973C2C5×#237811yescharacteristic
974C2C5×#238311yescharacteristic
975C2C5×#281311yescharacteristic
976C2C5×#281411yescharacteristic
977C2C5×#282011yescharacteristic
978C2C5×#282311yescharacteristic
979C2C5×#282911yescharacteristic
980C2C5×#283111yescharacteristic
981C2C5×#283611yescharacteristic
982C2C5×#283811yescharacteristic
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×#387C2semidirect
4. C5×#1445C2semidirect
5. C5×#1444C2semidirect
6. C5×#1443C2semidirect
7. C5×#1441C2semidirect
8. C5×#1441C2semidirect
9. C5×#1441C2semidirect
15. C5×C4⋊#95C2semidirect
31. C5×#396C4semidirect
54. #14633C5direct (N × H)
137. C2×#387C2×C5semidirect
138. #1445C2×C5semidirect
139. #1444C2×C5semidirect
140. #1443C2×C5semidirect
141. #1441C2×C5semidirect
142. #1441C2×C5semidirect
143. #1441C2×C5semidirect
149. C4⋊#95C2×C5semidirect
294. #396C4×C5semidirect
902. C5#14633direct (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×#3882
C2×C5×#3872
C5×#14452
C5×#14442
C5×#14432
C5×#14412
C5×#14402
C5×#14392
C5×C4⋊#952
#146335