Finite Group Databasebeta

← C5×#14591 #11937311

Subgroups — C5×#14591 #11937311

Order 1280.

1442 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#396C211yesmaximal, characteristic
2C5×#1445C211yesmaximal, characteristic, complemented
3C5×#1445C211yesmaximal, characteristic, complemented
4C5×#1445C211yesmaximal, characteristic, complemented
5C5×#1441C211yesmaximal, characteristic, complemented
6C5×#1439C211yesmaximal, characteristic
7C5×#1437C211yesmaximal, characteristic
8C5×#1437C211yesmaximal, characteristic
9C5×#1436C211yesmaximal, characteristic, complemented
10C5×#1436C211yesmaximal, characteristic, complemented
11C5×#1436C211yesmaximal, characteristic, complemented
12C5×#1434C211yesmaximal, characteristic, complemented
13C5×C22⋊#95C211yesmaximal, characteristic
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×#396C418yescomplemented
30C2×C5×#95C2211yescharacteristic
31C2×C5×#95C2211yescharacteristic
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
52#14591C511yesmaximal, characteristic, direct product factor, Sylow
53C25×C5C2311yescharacteristic
54C23×C4×C5—22no—
55C23×C4×C5—22no—
56C23×C4×C5—22no—
57C23×C4×C5—41no—
58C23×C4×C5—41no—
59C23×C4×C5—41no—
60C23×C4×C5—41no—
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
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C2×C5×C4⋊C4—22no—
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⋊C4C2×C414yescomplemented
85C2×C5×C4⋊C4C2×C414yescomplemented
86C2×C5×C4⋊C4C2×C414yescomplemented
87C2×C5×C22⋊C4—22no—
88C2×C5×C22⋊C4—22no—
89C2×C5×C22⋊C4—22no—
90C2×C5×C22⋊C4—22no—
91C2×C5×C22⋊C4—41no—
92C2×C5×C22⋊C4—41no—
93C2×C5×C22⋊C4—41no—
94C2×C5×C22⋊C4—41no—
95C2×C5×C22⋊C4—41no—
96C2×C5×C22⋊C4—41no—
97C2×C5×C22⋊C4—41no—
98C2×C5×C22⋊C4—41no—
99C2×C5×C22⋊C4—41no—
100C2×C5×C22⋊C4—41no—
101C2×C5×C22⋊C4C2×C414yes—
102C2×C5×C22⋊C4C2×C414yes—
103C2×C5×C22⋊C4C2×C414yes—
104C2×C5×C22⋊C4Q814yes—
105C2×C42×C5—22no—
106C2×C42×C5—41no—
107C2×C42×C5—41no—
108C2×C42×C5—41no—
109C2×C42×C5—41no—
110C2×C42×C5—41no—
111C5×#95—22no—
112C5×#95—22no—
113C5×#95—22no—
114C5×#95—22no—
115C5×#95—22no—
116C5×#95—22no—
117C5×#95—41no—
118C5×#95—41no—
119C5×#95—41no—
120C5×#95—41no—
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×#95C2×C414yescomplemented
133C2×#396C2×C511yescharacteristic
134#1445C2×C511yescharacteristic, complemented
135#1445C2×C511yescharacteristic, complemented
136#1445C2×C511yescharacteristic, complemented
137#1441C2×C511yescharacteristic, complemented
138#1439C2×C511yescharacteristic
139#1437C2×C511yescharacteristic
140#1437C2×C511yescharacteristic
141#1436C2×C511yescharacteristic, complemented
142#1436C2×C511yescharacteristic, complemented
143#1436C2×C511yescharacteristic, complemented
144#1434C2×C511yescharacteristic, complemented
145C22⋊#95C2×C511yescharacteristic
146C22⋊#95C2×C511yescharacteristic
147C22⋊#95C2×C511yescharacteristic
148C24×C5—21no—
149C24×C5—21no—
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×C5C22×C412yes—
161C24×C5C2×Q812yes—
162C24×C5#4112yes—
163C24×C5C2411yescharacteristic
164C22×C4×C5—21no—
165C22×C4×C5—21no—
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—44no—
251C22×C4×C5—44no—
252C22×C4×C5—44no—
253C22×C4×C5—44no—
254C22×C4×C5—44no—
255C22×C4×C5—44no—
256C22×C4×C5—44no—
257C22×C4×C5C22×C412yes—
258C22×C4×C5C22×C412yes—
259C22×C4×C5C22×C412yes—
260C22×C4×C5C22×C412yes—
261C22×C4×C5C22×C412yes—
262C22×C4×C5C22×C412yes—
263C22×C4×C5C2×Q812yes—
264C22×C4×C5C2×Q812yes—
265C22×C4×C5#4112yes—
266C22×C4×C5#4112yes—
267C22×C4×C5#4112yes—
268C22×C4×C5#4112yes—
269C5×C4⋊C4—44no—
270C5×C4⋊C4—44no—
271C5×C4⋊C4—44no—
272C5×C4⋊C4—44no—
273C5×C22⋊C4—44no—
274C5×C22⋊C4—44no—
275C5×C22⋊C4—44no—
276C5×C22⋊C4—44no—
277C5×C22⋊C4—44no—
278C5×C22⋊C4—44no—
279C42×C5—44no—
280C42×C5—44no—
281C24×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×C42C22×C511yescharacteristic
293C22×C42C22×C511yescharacteristic
294#396C4×C518yescomplemented
295C2×#95C22×C511yescharacteristic
296C2×#95C22×C511yescharacteristic
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—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—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×C5C4×Q814yes—
352C23×C5C23×C411yescharacteristic
353C23×C5C22×Q811yescharacteristic
354C23×C5C2×#4111yescharacteristic
355C23×C5C2×#4111yescharacteristic
356C23×C5C2×#4111yescharacteristic
357C23×C5C2×#4111yescharacteristic
358C23×C5C2×#4111yescharacteristic
359C23×C5H(5,𝔽2)11yescharacteristic
360C23×C5H(5,𝔽2)11yescharacteristic
361C23×C5H(5,𝔽2)11yescharacteristic
362C23×C5H(5,𝔽2)11yescharacteristic
363C23×C5H(5,𝔽2)11yescharacteristic
364C23×C5H(5,𝔽2)11yescharacteristic
365C23×C5H(5,𝔽2)11yescharacteristic
366C23×C52−1+411yescharacteristic
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—416no—
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×C5—41no—
465C2×C4×C5—41no—
466C25C23×C511yescharacteristic
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—41no—
471C23×C4—41no—
472C23×C4—41no—
473C23×C4—41no—
474C23×C4C23×C511yescharacteristic
475C23×C4C23×C511yescharacteristic
476C23×C4C23×C511yescharacteristic
477C23×C4C23×C511yescharacteristic
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
488C2×C4⋊C4—22no—
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⋊C4C2×C4×C514yescomplemented
498C2×C4⋊C4C2×C4×C514yescomplemented
499C2×C4⋊C4C2×C4×C514yescomplemented
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—41no—
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⋊C4C2×C4×C514yes—
515C2×C22⋊C4C2×C4×C514yes—
516C2×C22⋊C4C2×C4×C514yes—
517C2×C22⋊C4C5×Q814yes—
518C2×C42—22no—
519C2×C42—41no—
520C2×C42—41no—
521C2×C42—41no—
522C2×C42—41no—
523C2×C42—41no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—41no—
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#95—41no—
545#95C2×C4×C514yescomplemented
546C22×C5—24no—
547C22×C5—24no—
548C22×C5—24no—
549C22×C5—42no—
550C22×C5—42no—
551C22×C5—42no—
552C22×C5—42no—
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×C5C2×C4×Q811yescharacteristic
562C22×C5C4×#4111yescharacteristic
563C22×C5C4×#4111yescharacteristic
564C22×C5#51811yescharacteristic
565C22×C5#51811yescharacteristic
566C22×C5#51811yescharacteristic
567C22×C5#52011yescharacteristic
568C22×C5#53811yescharacteristic
569C22×C5#53811yescharacteristic
570C22×C5#53811yescharacteristic
571C22×C5#53811yescharacteristic
572C22×C5#53811yescharacteristic
573C22×C5#53911yescharacteristic
574C22×C5#54011yescharacteristic
575C22×C5#54011yescharacteristic
576C22×C5#54011yescharacteristic
577C22×C5#54011yescharacteristic
578C22×C5#54311yescharacteristic
579C22×C5#54411yescharacteristic
580C22×C5#55111yescharacteristic
581C22×C5#55111yescharacteristic
582C22×C5#55111yescharacteristic
583C22×C5#55111yescharacteristic
584C22×C5#55111yescharacteristic
585C22×C5#55211yescharacteristic
586C22×C5#55311yescharacteristic
587C22×C5#55411yescharacteristic
588C22×C5#55411yescharacteristic
589C22×C5#55411yescharacteristic
590C22×C5#55411yescharacteristic
591C22×C5#55611yescharacteristic
592C22×C5#56011yescharacteristic
593C22×C5#56011yescharacteristic
594C22×C5#56211yescharacteristic
595C22×C5#56211yescharacteristic
596C4×C5—42no—
597C4×C5—42no—
598C4×C5—42no—
599C4×C5—42no—
600C4×C5—42no—
601C4×C5—42no—
602C4×C5—42no—
603C4×C5—42no—
604C4×C5—42no—
605C4×C5—42no—
606C4×C5—42no—
607C4×C5—42no—
608C4×C5—81no—
609C4×C5—81no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24C22×C4×C512yes—
623C24C2×C5×Q812yes—
624C24C5×#4112yes—
625C24C24×C511yescharacteristic
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—44no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4C22×C4×C512yes—
720C22×C4C22×C4×C512yes—
721C22×C4C22×C4×C512yes—
722C22×C4C22×C4×C512yes—
723C22×C4C22×C4×C512yes—
724C22×C4C22×C4×C512yes—
725C22×C4C2×C5×Q812yes—
726C22×C4C2×C5×Q812yes—
727C22×C4C5×#4112yes—
728C22×C4C5×#4112yes—
729C22×C4C5×#4112yes—
730C22×C4C5×#4112yes—
731C4⋊C4—44no—
732C4⋊C4—44no—
733C4⋊C4—44no—
734C4⋊C4—44no—
735C22⋊C4—44no—
736C22⋊C4—44no—
737C22⋊C4—44no—
738C22⋊C4—44no—
739C22⋊C4—44no—
740C22⋊C4—44no—
741C42—44no—
742C42—44no—
743C2×C5—44no—
744C2×C5#232911yescharacteristic
745C2×C5#233311yescharacteristic
746C2×C5#233311yescharacteristic
747C2×C5#236811yescharacteristic
748C2×C5#236811yescharacteristic
749C2×C5#237311yescharacteristic
750C2×C5#237711yescharacteristic
751C2×C5#273511yescharacteristic
752C2×C5#274011yescharacteristic
753C2×C5#274311yescharacteristic
754C2×C5#274811yescharacteristic
755C2×C5#274911yescharacteristic
756C2×C5#276811yescharacteristic
757C2×C5#278011yescharacteristic
758C2×C5#278811yescharacteristic
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
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—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23C4×C5×Q814yes—
794C23C23×C4×C511yescharacteristic
795C23C22×C5×Q811yescharacteristic
796C23C2×C5×#4111yescharacteristic
797C23C2×C5×#4111yescharacteristic
798C23C2×C5×#4111yescharacteristic
799C23C2×C5×#4111yescharacteristic
800C23C2×C5×#4111yescharacteristic
801C23C5×H(5,𝔽2)11yescharacteristic
802C23C5×H(5,𝔽2)11yescharacteristic
803C23C5×H(5,𝔽2)11yescharacteristic
804C23C5×H(5,𝔽2)11yescharacteristic
805C23C5×H(5,𝔽2)11yescharacteristic
806C23C5×H(5,𝔽2)11yescharacteristic
807C23C5×H(5,𝔽2)11yescharacteristic
808C23C5×2−1+411yescharacteristic
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—416no—
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×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C5#1459111yescharacteristic, direct product factor, Sylow
909C22—24no—
910C22—24no—
911C22—24no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22C2×C4×C5×Q811yescharacteristic
925C22C4×C5×#4111yescharacteristic
926C22C4×C5×#4111yescharacteristic
927C22C5×#51811yescharacteristic
928C22C5×#51811yescharacteristic
929C22C5×#51811yescharacteristic
930C22C5×#52011yescharacteristic
931C22C5×#53811yescharacteristic
932C22C5×#53811yescharacteristic
933C22C5×#53811yescharacteristic
934C22C5×#53811yescharacteristic
935C22C5×#53811yescharacteristic
936C22C5×#53911yescharacteristic
937C22C5×#54011yescharacteristic
938C22C5×#54011yescharacteristic
939C22C5×#54011yescharacteristic
940C22C5×#54011yescharacteristic
941C22C5×#54311yescharacteristic
942C22C5×#54411yescharacteristic
943C22C5×#55111yescharacteristic
944C22C5×#55111yescharacteristic
945C22C5×#55111yescharacteristic
946C22C5×#55111yescharacteristic
947C22C5×#55111yescharacteristic
948C22C5×#55211yescharacteristic
949C22C5×#55311yescharacteristic
950C22C5×#55411yescharacteristic
951C22C5×#55411yescharacteristic
952C22C5×#55411yescharacteristic
953C22C5×#55411yescharacteristic
954C22C5×#55611yescharacteristic
955C22C5×#56011yescharacteristic
956C22C5×#56011yescharacteristic
957C22C5×#56211yescharacteristic
958C22C5×#56211yescharacteristic
959C4—42no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—81no—
972C4—81no—
973C2—44no—
974C2C5×#232911yescharacteristic
975C2C5×#233311yescharacteristic
976C2C5×#233311yescharacteristic
977C2C5×#236811yescharacteristic
978C2C5×#236811yescharacteristic
979C2C5×#237311yescharacteristic
980C2C5×#237711yescharacteristic
981C2C5×#273511yescharacteristic
982C2C5×#274011yescharacteristic
983C2C5×#274311yescharacteristic
984C2C5×#274811yescharacteristic
985C2C5×#274911yescharacteristic
986C2C5×#276811yescharacteristic
987C2C5×#278011yescharacteristic
988C2C5×#278811yescharacteristic
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. C5×#1445C2semidirect
3. C5×#1445C2semidirect
4. C5×#1445C2semidirect
5. C5×#1441C2semidirect
9. C5×#1436C2semidirect
10. C5×#1436C2semidirect
11. C5×#1436C2semidirect
12. C5×#1434C2semidirect
29. C5×#396C4semidirect
52. #14591C5direct (N × H)
84. C2×C5×C4⋊C4C2×C4semidirect
85. C2×C5×C4⋊C4C2×C4semidirect
86. C2×C5×C4⋊C4C2×C4semidirect
132. C5×#95C2×C4semidirect
134. #1445C2×C5semidirect
135. #1445C2×C5semidirect
136. #1445C2×C5semidirect
137. #1441C2×C5semidirect
141. #1436C2×C5semidirect
142. #1436C2×C5semidirect
143. #1436C2×C5semidirect
144. #1434C2×C5semidirect
294. #396C4×C5semidirect
497. C2×C4⋊C4C2×C4×C5semidirect
498. C2×C4⋊C4C2×C4×C5semidirect
499. C2×C4⋊C4C2×C4×C5semidirect
545. #95C2×C4×C5semidirect
908. C5#14591direct (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
C5×#14452
C5×#14412
C5×#14392
C5×#14372
C5×#14362
C5×#14342
C5×C22⋊#952
#145915