Finite Group Databasebeta

← C5×#14060 #11936780

Subgroups — C5×#14060 #11936780

Order 1280.

1426 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#389C211yesmaximal, characteristic
2C2×C5×#389C211yesmaximal, characteristic
3C2×C5×#387C211yesmaximal, characteristic
4C2×C5×#387C211yesmaximal, characteristic
5C2×C4×C5×C4⋊C4C211yesmaximal, characteristic
6C5×#1445C211yesmaximal, characteristic
7C5×#1441C211yesmaximal, characteristic
8C5×#1441C211yesmaximal, characteristic
9C5×#1441C211yesmaximal, characteristic
10C5×#1436C211yesmaximal, characteristic
11C5×#1436C211yesmaximal, characteristic
12C5×#1436C211yesmaximal, characteristic
13C5×#1434C211yesmaximal, characteristic
14C5×#1434C211yesmaximal, characteristic
15C4×C5×#95C211yesmaximal, characteristic
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×C4⋊C4C2211yescharacteristic
24C22×C42×C5C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic
26C22×C42×C5C2211yescharacteristic
27C22×C42×C5C2211yescharacteristic
28C22×C42×C5C2211yescharacteristic
29C5×#389—24no—
30C5×#389C418yescomplemented
31C5×#387—24no—
32C5×#387—24no—
33C4×C5×C4⋊C4—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
54C2×C5×#95C2211yescharacteristic
55C2×C5×#95C2211yescharacteristic
56#14060C511yesmaximal, characteristic, direct product factor, Sylow
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
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C2×C5×C4⋊C4—22no—
73C2×C5×C4⋊C4—22no—
74C2×C5×C4⋊C4—22no—
75C2×C5×C4⋊C4—22no—
76C2×C5×C4⋊C4—22no—
77C2×C5×C4⋊C4—22no—
78C2×C5×C4⋊C4—22no—
79C2×C5×C4⋊C4—22no—
80C2×C5×C4⋊C4—22no—
81C2×C5×C4⋊C4—22no—
82C2×C5×C4⋊C4—22no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—22no—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4—22no—
88C2×C5×C4⋊C4—22no—
89C2×C5×C4⋊C4—22no—
90C2×C5×C4⋊C4—41no—
91C2×C5×C4⋊C4C2×C414yes—
92C2×C5×C4⋊C4C2×C414yes—
93C2×C5×C4⋊C4C2×C414yes—
94C2×C5×C4⋊C4C2×C414yes—
95C2×C5×C4⋊C4D414yes—
96C2×C42×C5—22no—
97C2×C42×C5—22no—
98C2×C42×C5—22no—
99C2×C42×C5—22no—
100C2×C42×C5—22no—
101C2×C42×C5—22no—
102C2×C42×C5—22no—
103C2×C42×C5—22no—
104C2×C42×C5—22no—
105C2×C42×C5—22no—
106C2×C42×C5—22no—
107C2×C42×C5—41no—
108C2×C42×C5—41no—
109C2×C42×C5—41no—
110C2×C42×C5C2×C414yes—
111C5×#95—22no—
112C5×#95—22no—
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—22no—
124C5×#95—22no—
125C5×#95—22no—
126C5×#95—22no—
127C5×#95—41no—
128C5×#95—41no—
129C5×#95C2×C414yes—
130C5×#95C2×C414yes—
131C5×#95D414yes—
132C5×#95Q814yes—
133C2×#389C2×C511yescharacteristic
134C2×#389C2×C511yescharacteristic
135C2×#387C2×C511yescharacteristic
136C2×#387C2×C511yescharacteristic
137C2×C4×C4⋊C4C2×C511yescharacteristic
138#1445C2×C511yescharacteristic
139#1441C2×C511yescharacteristic
140#1441C2×C511yescharacteristic
141#1441C2×C511yescharacteristic
142#1436C2×C511yescharacteristic
143#1436C2×C511yescharacteristic
144#1436C2×C511yescharacteristic
145#1434C2×C511yescharacteristic
146#1434C2×C511yescharacteristic
147C4×#95C2×C511yescharacteristic
148C24×C5C2411yescharacteristic
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
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×C5C22×C412yes—
232C22×C4×C5C22×C412yes—
233C22×C4×C5C22×C412yes—
234C22×C4×C5C22×C412yes—
235C22×C4×C5C22×C412yes—
236C22×C4×C5C22×C412yes—
237C22×C4×C5C22×C412yes—
238C22×C4×C5C2×D412yes—
239C22×C4×C5C2×D412yes—
240C22×C4×C5C2×D412yes—
241C22×C4×C5C2×D412yes—
242C22×C4×C5C2×D412yes—
243C22×C4×C5C2×D412yes—
244C22×C4×C5C2×Q812yes—
245C22×C4×C5C2×Q812yes—
246C22×C4×C5C2×Q812yes—
247C22×C4×C5#4112yes—
248C22×C4×C5#4112yes—
249C22×C4×C5#4112yes—
250C22×C4×C5#4112yes—
251C22×C4×C5#4112yes—
252C22×C4×C5#4112yes—
253C22×C4×C5#4112yes—
254C5×C4⋊C4—28no—
255C5×C4⋊C4—28no—
256C5×C4⋊C4—28no—
257C5×C4⋊C4—28no—
258C5×C4⋊C4—28no—
259C5×C4⋊C4—28no—
260C5×C4⋊C4—44no—
261C5×C4⋊C4—44no—
262C42×C5—28no—
263C42×C5—44no—
264C42×C5—44no—
265C42×C5—44no—
266C42×C5—44no—
267C22×C4⋊C4C22×C511yescharacteristic
268C22×C4⋊C4C22×C511yescharacteristic
269C22×C4⋊C4C22×C511yescharacteristic
270C22×C4⋊C4C22×C511yescharacteristic
271C22×C4⋊C4C22×C511yescharacteristic
272C22×C4⋊C4C22×C511yescharacteristic
273C22×C4⋊C4C22×C511yescharacteristic
274C22×C4⋊C4C22×C511yescharacteristic
275C22×C42C22×C511yescharacteristic
276C22×C42C22×C511yescharacteristic
277C22×C42C22×C511yescharacteristic
278C22×C42C22×C511yescharacteristic
279C22×C42C22×C511yescharacteristic
280#389—24no—
281#389C4×C518yescomplemented
282#387—24no—
283#387—24no—
284C4×C4⋊C4—24no—
285C2×#95C22×C511yescharacteristic
286C2×#95C22×C511yescharacteristic
287C2×#95C22×C511yescharacteristic
288C2×#95C22×C511yescharacteristic
289C2×#95C22×C511yescharacteristic
290C2×#95C22×C511yescharacteristic
291C2×#95C22×C511yescharacteristic
292C2×#95C22×C511yescharacteristic
293C2×#95C22×C511yescharacteristic
294C2×#95C22×C511yescharacteristic
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
307C23×C5C23×C411yescharacteristic
308C23×C5C22×D411yescharacteristic
309C23×C5C22×D411yescharacteristic
310C23×C5C22×Q811yescharacteristic
311C23×C5C2×#4111yescharacteristic
312C23×C5C2×#4111yescharacteristic
313C23×C5C2×#4111yescharacteristic
314C23×C5C2×#4111yescharacteristic
315C23×C5C2×#4111yescharacteristic
316C23×C5C2×#4111yescharacteristic
317C23×C5C2×#4111yescharacteristic
318C23×C5H(5,𝔽2)11yescharacteristic
319C23×C52−1+411yescharacteristic
320C23×C52−1+411yescharacteristic
321C23×C52−1+411yescharacteristic
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—22no—
338C2×C4×C5—22no—
339C2×C4×C5—22no—
340C2×C4×C5—22no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
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—41no—
377C2×C4×C5—41no—
378C2×C4×C5—41no—
379C2×C4×C5—41no—
380C2×C4×C5—41no—
381C2×C4×C5—41no—
382C2×C4×C5—41no—
383C2×C4×C5—41no—
384C2×C4×C5—41no—
385C2×C4×C5—41no—
386C2×C4×C5—41no—
387C2×C4×C5—41no—
388C2×C4×C5—41no—
389C2×C4×C5—41no—
390C2×C4×C5—41no—
391C2×C4×C5—41no—
392C2×C4×C5—41no—
393C2×C4×C5—41no—
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#11714yes—
423C2×C4×C5C4×D414yes—
424C2×C4×C5C4×D414yes—
425C2×C4×C5C4×Q814yes—
426C2×C4×C5#12114yes—
427C23×C4C23×C511yescharacteristic
428C23×C4C23×C511yescharacteristic
429C23×C4C23×C511yescharacteristic
430C23×C4C23×C511yescharacteristic
431C23×C4C23×C511yescharacteristic
432C23×C4C23×C511yescharacteristic
433C23×C4C23×C511yescharacteristic
434C23×C4C23×C511yescharacteristic
435C23×C4C23×C511yescharacteristic
436C23×C4C23×C511yescharacteristic
437C23×C4C23×C511yescharacteristic
438C23×C4C23×C511yescharacteristic
439C23×C4C23×C511yescharacteristic
440C23×C4C23×C511yescharacteristic
441C23×C4C23×C511yescharacteristic
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—41no—
461C2×C4⋊C4C2×C4×C514yes—
462C2×C4⋊C4C2×C4×C514yes—
463C2×C4⋊C4C2×C4×C514yes—
464C2×C4⋊C4C2×C4×C514yes—
465C2×C4⋊C4C5×D414yes—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—41no—
478C2×C42—41no—
479C2×C42—41no—
480C2×C42C2×C4×C514yes—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95—22no—
495#95—22no—
496#95—22no—
497#95—41no—
498#95—41no—
499#95C2×C4×C514yes—
500#95C2×C4×C514yes—
501#95C5×D414yes—
502#95C5×Q814yes—
503C22×C5C2×#11711yescharacteristic
504C22×C5C2×C4×D411yescharacteristic
505C22×C5C2×C4×D411yescharacteristic
506C22×C5C2×C4×Q811yescharacteristic
507C22×C5C4×#4111yescharacteristic
508C22×C5#51911yescharacteristic
509C22×C5#52011yescharacteristic
510C22×C5C2×#12111yescharacteristic
511C22×C5#52511yescharacteristic
512C22×C5#52911yescharacteristic
513C22×C5#52911yescharacteristic
514C22×C5#52911yescharacteristic
515C22×C5#53211yescharacteristic
516C22×C5#53311yescharacteristic
517C22×C5#53311yescharacteristic
518C22×C5#53911yescharacteristic
519C22×C5#53911yescharacteristic
520C22×C5#54111yescharacteristic
521C22×C5#54111yescharacteristic
522C22×C5#54611yescharacteristic
523C22×C5#54611yescharacteristic
524C22×C5#54711yescharacteristic
525C22×C5#54711yescharacteristic
526C22×C5#54711yescharacteristic
527C22×C5#54811yescharacteristic
528C22×C5D4×Q811yescharacteristic
529C22×C5D4×Q811yescharacteristic
530C22×C5#55211yescharacteristic
531C22×C5#55211yescharacteristic
532C22×C5#55211yescharacteristic
533C22×C5#55211yescharacteristic
534C22×C5#55311yescharacteristic
535C22×C5#55411yescharacteristic
536C22×C5#55611yescharacteristic
537C22×C5#55711yescharacteristic
538C4×C5—24no—
539C4×C5—24no—
540C4×C5—24no—
541C4×C5—24no—
542C4×C5—24no—
543C4×C5—42no—
544C4×C5—42no—
545C4×C5—42no—
546C4×C5—42no—
547C4×C5—42no—
548C4×C5—42no—
549C4×C5—42no—
550C4×C5—42no—
551C4×C5—81no—
552C4×C5—81no—
553C24C24×C511yescharacteristic
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
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×C4C22×C4×C512yes—
637C22×C4C22×C4×C512yes—
638C22×C4C22×C4×C512yes—
639C22×C4C22×C4×C512yes—
640C22×C4C22×C4×C512yes—
641C22×C4C22×C4×C512yes—
642C22×C4C22×C4×C512yes—
643C22×C4C2×C5×D412yes—
644C22×C4C2×C5×D412yes—
645C22×C4C2×C5×D412yes—
646C22×C4C2×C5×D412yes—
647C22×C4C2×C5×D412yes—
648C22×C4C2×C5×D412yes—
649C22×C4C2×C5×Q812yes—
650C22×C4C2×C5×Q812yes—
651C22×C4C2×C5×Q812yes—
652C22×C4C5×#4112yes—
653C22×C4C5×#4112yes—
654C22×C4C5×#4112yes—
655C22×C4C5×#4112yes—
656C22×C4C5×#4112yes—
657C22×C4C5×#4112yes—
658C22×C4C5×#4112yes—
659C4⋊C4—28no—
660C4⋊C4—28no—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—28no—
664C4⋊C4—28no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C42—28no—
668C42—44no—
669C42—44no—
670C42—44no—
671C42—44no—
672C2×C5#229511yescharacteristic
673C2×C5C4×#12111yescharacteristic
674C2×C5#233611yescharacteristic
675C2×C5#234411yescharacteristic
676C2×C5#235211yescharacteristic
677C2×C5#236011yescharacteristic
678C2×C5#236511yescharacteristic
679C2×C5#242511yescharacteristic
680C2×C5#242911yescharacteristic
681C2×C5#246211yescharacteristic
682C2×C5#246611yescharacteristic
683C2×C5#251911yescharacteristic
684C2×C5#253311yescharacteristic
685C2×C5#255611yescharacteristic
686C2×C5#259011yescharacteristic
687C23C23×C4×C511yescharacteristic
688C23C22×C5×D411yescharacteristic
689C23C22×C5×D411yescharacteristic
690C23C22×C5×Q811yescharacteristic
691C23C2×C5×#4111yescharacteristic
692C23C2×C5×#4111yescharacteristic
693C23C2×C5×#4111yescharacteristic
694C23C2×C5×#4111yescharacteristic
695C23C2×C5×#4111yescharacteristic
696C23C2×C5×#4111yescharacteristic
697C23C2×C5×#4111yescharacteristic
698C23C5×H(5,𝔽2)11yescharacteristic
699C23C5×2−1+411yescharacteristic
700C23C5×2−1+411yescharacteristic
701C23C5×2−1+411yescharacteristic
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4C5×#11714yes—
803C2×C4C4×C5×D414yes—
804C2×C4C4×C5×D414yes—
805C2×C4C4×C5×Q814yes—
806C2×C4C5×#12114yes—
807C5#1406011yescharacteristic, direct product factor, Sylow
808C22C2×C5×#11711yescharacteristic
809C22C2×C4×C5×D411yescharacteristic
810C22C2×C4×C5×D411yescharacteristic
811C22C2×C4×C5×Q811yescharacteristic
812C22C4×C5×#4111yescharacteristic
813C22C5×#51911yescharacteristic
814C22C5×#52011yescharacteristic
815C22C2×C5×#12111yescharacteristic
816C22C5×#52511yescharacteristic
817C22C5×#52911yescharacteristic
818C22C5×#52911yescharacteristic
819C22C5×#52911yescharacteristic
820C22C5×#53211yescharacteristic
821C22C5×#53311yescharacteristic
822C22C5×#53311yescharacteristic
823C22C5×#53911yescharacteristic
824C22C5×#53911yescharacteristic
825C22C5×#54111yescharacteristic
826C22C5×#54111yescharacteristic
827C22C5×#54611yescharacteristic
828C22C5×#54611yescharacteristic
829C22C5×#54711yescharacteristic
830C22C5×#54711yescharacteristic
831C22C5×#54711yescharacteristic
832C22C5×#54811yescharacteristic
833C22C5×D4×Q811yescharacteristic
834C22C5×D4×Q811yescharacteristic
835C22C5×#55211yescharacteristic
836C22C5×#55211yescharacteristic
837C22C5×#55211yescharacteristic
838C22C5×#55211yescharacteristic
839C22C5×#55311yescharacteristic
840C22C5×#55411yescharacteristic
841C22C5×#55611yescharacteristic
842C22C5×#55711yescharacteristic
843C4—24no—
844C4—24no—
845C4—24no—
846C4—24no—
847C4—24no—
848C4—42no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—81no—
857C4—81no—
858C2C5×#229511yescharacteristic
859C2C4×C5×#12111yescharacteristic
860C2C5×#233611yescharacteristic
861C2C5×#234411yescharacteristic
862C2C5×#235211yescharacteristic
863C2C5×#236011yescharacteristic
864C2C5×#236511yescharacteristic
865C2C5×#242511yescharacteristic
866C2C5×#242911yescharacteristic
867C2C5×#246211yescharacteristic
868C2C5×#246611yescharacteristic
869C2C5×#251911yescharacteristic
870C2C5×#253311yescharacteristic
871C2C5×#255611yescharacteristic
872C2C5×#259011yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
30. C5×#389C4semidirect
56. #14060C5direct (N × H)
281. #389C4×C5semidirect
807. C5#14060direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3892
C2×C5×#3872
C2×C4×C5×C4⋊C42
C5×#14452
C5×#14412
C5×#14362
C5×#14342
C4×C5×#952
#140605