Finite Group Databasebeta

← C5×#14518 #11937238

Subgroups — C5×#14518 #11937238

Order 1280.

1958 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#394C211yesmaximal, characteristic
2C2×C5×#390C211yesmaximal, characteristic
3C2×C5×#389C211yesmaximal, characteristic, complemented
4C2×C5×#388C211yesmaximal, characteristic, complemented
5C2×C5×#386C211yesmaximal, characteristic
6C2×C5×#385C211yesmaximal, characteristic, complemented
7C2×C5×#385C211yesmaximal, characteristic, complemented
8C5×#1444C211yesmaximal, characteristic, complemented
9C5×#1440C211yesmaximal, characteristic, complemented
10C5×#1439C211yesmaximal, characteristic, complemented
11C5×#1439C211yesmaximal, characteristic, complemented
12C5×#1439C211yesmaximal, characteristic, complemented
13C5×#1437C211yesmaximal, characteristic, complemented
14C5×#1436C211yesmaximal, characteristic, complemented
15C5×#1434C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C24×C4×C5C2211yescharacteristic
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×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C5×C22⋊C4C2211yescharacteristic
31C22×C5×C22⋊C4C2211yescharacteristic
32C22×C5×C22⋊C4C2211yescharacteristic
33C22×C5×C22⋊C4C2211yescharacteristic
34C22×C5×C22⋊C4C2211yescharacteristic
35C22×C42×C5C2211yescharacteristic
36C22×C42×C5C2211yescharacteristic
37C5×#394C418yescomplemented
38C5×#390—24no—
39C5×#389—24no—
40C5×#388—24no—
41C5×#386—24no—
42C5×#385—24no—
43C5×#385—24no—
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
56C2×C5×#95C2211yescharacteristic
57C2×C5×#95C2211yescharacteristic
58#14518C511yesmaximal, characteristic, direct product factor, Sylow
59C25×C5C2311yescharacteristic
60C25×C5C2311yescharacteristic
61C22×C5×D4—22no—
62C22×C5×D4—22no—
63C22×C5×D4—22no—
64C22×C5×D4—22no—
65C22×C5×D4—41no—
66C22×C5×D4—41no—
67C22×C5×D4C2×C414yes—
68C23×C4×C5—22no—
69C23×C4×C5—22no—
70C23×C4×C5—22no—
71C23×C4×C5—41no—
72C23×C4×C5—41no—
73C23×C4×C5—41no—
74C23×C4×C5—41no—
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
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C2×C5×C4⋊C4—22no—
89C2×C5×C4⋊C4—22no—
90C2×C5×C4⋊C4—22no—
91C2×C5×C4⋊C4—22no—
92C2×C5×C4⋊C4—22no—
93C2×C5×C4⋊C4—22no—
94C2×C5×C4⋊C4—22no—
95C2×C5×C4⋊C4—22no—
96C2×C5×C4⋊C4—22no—
97C2×C5×C4⋊C4—22no—
98C2×C5×C4⋊C4—22no—
99C2×C5×C4⋊C4—41no—
100C2×C5×C4⋊C4—41no—
101C2×C5×C4⋊C4—41no—
102C2×C5×C4⋊C4—41no—
103C2×C5×C4⋊C4—41no—
104C2×C5×C4⋊C4—41no—
105C2×C5×C4⋊C4C2×C414yescomplemented
106C2×C5×C22⋊C4—22no—
107C2×C5×C22⋊C4—22no—
108C2×C5×C22⋊C4—22no—
109C2×C5×C22⋊C4—22no—
110C2×C5×C22⋊C4—22no—
111C2×C5×C22⋊C4—22no—
112C2×C5×C22⋊C4—22no—
113C2×C5×C22⋊C4—22no—
114C2×C5×C22⋊C4—22no—
115C2×C5×C22⋊C4—22no—
116C2×C5×C22⋊C4—22no—
117C2×C5×C22⋊C4—22no—
118C2×C5×C22⋊C4—22no—
119C2×C5×C22⋊C4—22no—
120C2×C5×C22⋊C4—22no—
121C2×C5×C22⋊C4—22no—
122C2×C5×C22⋊C4—41no—
123C2×C5×C22⋊C4—41no—
124C2×C5×C22⋊C4—41no—
125C2×C5×C22⋊C4—41no—
126C2×C5×C22⋊C4—41no—
127C2×C5×C22⋊C4—41no—
128C2×C5×C22⋊C4—41no—
129C2×C5×C22⋊C4—41no—
130C2×C5×C22⋊C4—41no—
131C2×C5×C22⋊C4—41no—
132C2×C5×C22⋊C4—41no—
133C2×C5×C22⋊C4—41no—
134C2×C5×C22⋊C4C2×C414yes—
135C2×C5×C22⋊C4C2×C414yes—
136C2×C5×C22⋊C4C2×C414yescomplemented
137C2×C5×C22⋊C4C2×C414yescomplemented
138C2×C5×C22⋊C4D414yes—
139C2×C42×C5—22no—
140C2×C42×C5—22no—
141C2×C42×C5—22no—
142C2×C42×C5—22no—
143C2×C42×C5—41no—
144C2×C42×C5—41no—
145C5×#95—22no—
146C5×#95—22no—
147C5×#95—22no—
148C5×#95—22no—
149C5×#95—22no—
150C5×#95—22no—
151C5×#95—22no—
152C5×#95—41no—
153C5×#95—41no—
154C5×#95—41no—
155C5×#95—41no—
156C5×#95C2×C414yescomplemented
157C5×#95D414yes—
158C5×#95D414yescomplemented
159C2×#394C2×C511yescharacteristic
160C2×#390C2×C511yescharacteristic
161C2×#389C2×C511yescharacteristic, complemented
162C2×#388C2×C511yescharacteristic, complemented
163C2×#386C2×C511yescharacteristic
164C2×#385C2×C511yescharacteristic, complemented
165C2×#385C2×C511yescharacteristic, complemented
166#1444C2×C511yescharacteristic, complemented
167#1440C2×C511yescharacteristic, complemented
168#1439C2×C511yescharacteristic, complemented
169#1439C2×C511yescharacteristic, complemented
170#1439C2×C511yescharacteristic, complemented
171#1437C2×C511yescharacteristic, complemented
172#1436C2×C511yescharacteristic, complemented
173#1434C2×C511yescharacteristic, complemented
174C24×C5—21no—
175C24×C5—21no—
176C24×C5—21no—
177C24×C5—21no—
178C24×C5—21no—
179C24×C5—21no—
180C24×C5—21no—
181C24×C5—21no—
182C24×C5—21no—
183C24×C5—21no—
184C24×C5—21no—
185C24×C5—21no—
186C24×C5—21no—
187C24×C5—21no—
188C24×C5—21no—
189C24×C5—21no—
190C24×C5—21no—
191C24×C5—21no—
192C24×C5—21no—
193C24×C5—21no—
194C24×C5—21no—
195C24×C5—21no—
196C24×C5—21no—
197C24×C5—21no—
198C24×C5—21no—
199C24×C5—21no—
200C24×C5C22×C412yes—
201C24×C5C22×C412yes—
202C24×C5C2×D412yes—
203C24×C5#4112yes—
204C24×C5C2411yescharacteristic
205C2×C5×D4—28no—
206C2×C5×D4—28no—
207C2×C5×D4—44no—
208C2×C5×D4—44no—
209C2×C5×D4—44no—
210C2×C5×D4—44no—
211C2×C5×D4—44no—
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—21no—
262C22×C4×C5—21no—
263C22×C4×C5—21no—
264C22×C4×C5—21no—
265C22×C4×C5—21no—
266C22×C4×C5—21no—
267C22×C4×C5—21no—
268C22×C4×C5—21no—
269C22×C4×C5—21no—
270C22×C4×C5—21no—
271C22×C4×C5—21no—
272C22×C4×C5—21no—
273C22×C4×C5—21no—
274C22×C4×C5—21no—
275C22×C4×C5—21no—
276C22×C4×C5—21no—
277C22×C4×C5—21no—
278C22×C4×C5—21no—
279C22×C4×C5—21no—
280C22×C4×C5—21no—
281C22×C4×C5—21no—
282C22×C4×C5—21no—
283C22×C4×C5—21no—
284C22×C4×C5—21no—
285C22×C4×C5—21no—
286C22×C4×C5—21no—
287C22×C4×C5—21no—
288C22×C4×C5—44no—
289C22×C4×C5—44no—
290C22×C4×C5—44no—
291C22×C4×C5—44no—
292C22×C4×C5—44no—
293C22×C4×C5—44no—
294C22×C4×C5—44no—
295C22×C4×C5C22×C412yes—
296C22×C4×C5C22×C412yes—
297C22×C4×C5C22×C412yes—
298C22×C4×C5C22×C412yes—
299C22×C4×C5C22×C412yes—
300C22×C4×C5C2×D412yes—
301C22×C4×C5C2×D412yes—
302C22×C4×C5C2×D412yes—
303C22×C4×C5C2×D412yes—
304C22×C4×C5C2×D412yes—
305C22×C4×C5C2×D412yes—
306C22×C4×C5C2×D412yes—
307C22×C4×C5C2×D412yes—
308C22×C4×C5#4112yes—
309C22×C4×C5#4112yes—
310C5×C4⋊C4—28no—
311C5×C4⋊C4—44no—
312C5×C4⋊C4—44no—
313C5×C4⋊C4—44no—
314C5×C4⋊C4—44no—
315C5×C4⋊C4—44no—
316C5×C22⋊C4—28no—
317C5×C22⋊C4—28no—
318C5×C22⋊C4—28no—
319C5×C22⋊C4—44no—
320C5×C22⋊C4—44no—
321C5×C22⋊C4—44no—
322C5×C22⋊C4—44no—
323C5×C22⋊C4—44no—
324C5×C22⋊C4—44no—
325C5×C22⋊C4—44no—
326C5×C22⋊C4—44no—
327C42×C5—44no—
328C42×C5—44no—
329C23×D4C22×C511yescharacteristic
330C24×C4C22×C511yescharacteristic
331C22×C4⋊C4C22×C511yescharacteristic
332C22×C4⋊C4C22×C511yescharacteristic
333C22×C4⋊C4C22×C511yescharacteristic
334C22×C4⋊C4C22×C511yescharacteristic
335C22×C4⋊C4C22×C511yescharacteristic
336C22×C4⋊C4C22×C511yescharacteristic
337C22×C22⋊C4C22×C511yescharacteristic
338C22×C22⋊C4C22×C511yescharacteristic
339C22×C22⋊C4C22×C511yescharacteristic
340C22×C22⋊C4C22×C511yescharacteristic
341C22×C22⋊C4C22×C511yescharacteristic
342C22×C22⋊C4C22×C511yescharacteristic
343C22×C22⋊C4C22×C511yescharacteristic
344C22×C22⋊C4C22×C511yescharacteristic
345C22×C22⋊C4C22×C511yescharacteristic
346C22×C22⋊C4C22×C511yescharacteristic
347C22×C22⋊C4C22×C511yescharacteristic
348C22×C42C22×C511yescharacteristic
349C22×C42C22×C511yescharacteristic
350#394C4×C518yescomplemented
351#390—24no—
352#389—24no—
353#388—24no—
354#386—24no—
355#385—24no—
356#385—24no—
357C2×#95C22×C511yescharacteristic
358C2×#95C22×C511yescharacteristic
359C2×#95C22×C511yescharacteristic
360C2×#95C22×C511yescharacteristic
361C2×#95C22×C511yescharacteristic
362C2×#95C22×C511yescharacteristic
363C2×#95C22×C511yescharacteristic
364C2×#95C22×C511yescharacteristic
365C2×#95C22×C511yescharacteristic
366C2×#95C22×C511yescharacteristic
367C2×#95C22×C511yescharacteristic
368C2×#95C22×C511yescharacteristic
369C2×#95C22×C511yescharacteristic
370C2×#95C22×C511yescharacteristic
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—22no—
376C23×C5—22no—
377C23×C5—22no—
378C23×C5—22no—
379C23×C5—22no—
380C23×C5—22no—
381C23×C5—22no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—22no—
385C23×C5—22no—
386C23×C5—22no—
387C23×C5—22no—
388C23×C5—22no—
389C23×C5—22no—
390C23×C5—22no—
391C23×C5—22no—
392C23×C5—22no—
393C23×C5—22no—
394C23×C5—22no—
395C23×C5—22no—
396C23×C5—41no—
397C23×C5—41no—
398C23×C5—41no—
399C23×C5—41no—
400C23×C5—41no—
401C23×C5—41no—
402C23×C5—41no—
403C23×C5—41no—
404C23×C5—41no—
405C23×C5—41no—
406C23×C5—41no—
407C23×C5—41no—
408C23×C5—41no—
409C23×C5—41no—
410C23×C5—41no—
411C23×C5—41no—
412C23×C5—41no—
413C23×C5—41no—
414C23×C5—41no—
415C23×C5—41no—
416C23×C5—41no—
417C23×C5—41no—
418C23×C5—41no—
419C23×C5—41no—
420C23×C5—41no—
421C23×C5—41no—
422C23×C5—41no—
423C23×C5—41no—
424C23×C5—41no—
425C23×C5—41no—
426C23×C5—41no—
427C23×C5—41no—
428C23×C5—41no—
429C23×C5—41no—
430C23×C5—41no—
431C23×C5—41no—
432C23×C5—41no—
433C23×C5—41no—
434C23×C5—41no—
435C23×C5—41no—
436C23×C5—41no—
437C23×C5—41no—
438C23×C5—41no—
439C23×C5—41no—
440C23×C5C4×D414yes—
441C23×C5C23×C411yescharacteristic
442C23×C5C22×D411yescharacteristic
443C23×C5C22×D411yescharacteristic
444C23×C5C22×D411yescharacteristic
445C23×C5C2×#4111yescharacteristic
446C23×C5C2×#4111yescharacteristic
447C23×C5C2×#4111yescharacteristic
448C23×C5H(5,𝔽2)11yescharacteristic
449C23×C5H(5,𝔽2)11yescharacteristic
450C23×C5H(5,𝔽2)11yescharacteristic
451C23×C5H(5,𝔽2)11yescharacteristic
452C23×C5H(5,𝔽2)11yescharacteristic
453C23×C52−1+411yescharacteristic
454C23×C52−1+411yescharacteristic
455C23×C52−1+411yescharacteristic
456C5×D4—416no—
457C2×C4×C5—22no—
458C2×C4×C5—22no—
459C2×C4×C5—22no—
460C2×C4×C5—22no—
461C2×C4×C5—22no—
462C2×C4×C5—22no—
463C2×C4×C5—22no—
464C2×C4×C5—22no—
465C2×C4×C5—22no—
466C2×C4×C5—22no—
467C2×C4×C5—22no—
468C2×C4×C5—22no—
469C2×C4×C5—22no—
470C2×C4×C5—22no—
471C2×C4×C5—22no—
472C2×C4×C5—22no—
473C2×C4×C5—22no—
474C2×C4×C5—22no—
475C2×C4×C5—22no—
476C2×C4×C5—22no—
477C2×C4×C5—22no—
478C2×C4×C5—22no—
479C2×C4×C5—22no—
480C2×C4×C5—22no—
481C2×C4×C5—22no—
482C2×C4×C5—22no—
483C2×C4×C5—22no—
484C2×C4×C5—22no—
485C2×C4×C5—22no—
486C2×C4×C5—22no—
487C2×C4×C5—22no—
488C2×C4×C5—22no—
489C2×C4×C5—22no—
490C2×C4×C5—22no—
491C2×C4×C5—22no—
492C2×C4×C5—22no—
493C2×C4×C5—22no—
494C2×C4×C5—22no—
495C2×C4×C5—22no—
496C2×C4×C5—416no—
497C2×C4×C5—41no—
498C2×C4×C5—41no—
499C2×C4×C5—41no—
500C2×C4×C5—41no—
501C2×C4×C5—41no—
502C2×C4×C5—41no—
503C2×C4×C5—41no—
504C2×C4×C5—41no—
505C2×C4×C5—41no—
506C2×C4×C5—41no—
507C2×C4×C5—41no—
508C2×C4×C5—41no—
509C2×C4×C5—41no—
510C2×C4×C5—41no—
511C2×C4×C5—41no—
512C2×C4×C5—41no—
513C2×C4×C5—41no—
514C2×C4×C5—41no—
515C2×C4×C5—41no—
516C2×C4×C5—41no—
517C2×C4×C5—41no—
518C2×C4×C5—41no—
519C2×C4×C5—41no—
520C2×C4×C5—41no—
521C2×C4×C5—41no—
522C2×C4×C5—41no—
523C2×C4×C5—41no—
524C2×C4×C5—41no—
525C2×C4×C5—41no—
526C2×C4×C5—41no—
527C2×C4×C5—41no—
528C2×C4×C5—41no—
529C2×C4×C5—41no—
530C2×C4×C5—41no—
531C2×C4×C5—41no—
532C2×C4×C5—41no—
533C2×C4×C5—41no—
534C2×C4×C5—41no—
535C2×C4×C5—41no—
536C2×C4×C5—41no—
537C2×C4×C5—41no—
538C2×C4×C5—41no—
539C2×C4×C5—41no—
540C2×C4×C5—41no—
541C2×C4×C5—41no—
542C2×C4×C5—41no—
543C2×C4×C5—41no—
544C2×C4×C5—41no—
545C2×C4×C5—41no—
546C2×C4×C5—41no—
547C2×C4×C5C4×D414yes—
548C2×C4×C5C4×D414yes—
549C25C23×C511yescharacteristic
550C25C23×C511yescharacteristic
551C22×D4—22no—
552C22×D4—22no—
553C22×D4—22no—
554C22×D4—22no—
555C22×D4—41no—
556C22×D4—41no—
557C22×D4C2×C4×C514yes—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—41no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4—41no—
565C23×C4C23×C511yescharacteristic
566C23×C4C23×C511yescharacteristic
567C23×C4C23×C511yescharacteristic
568C23×C4C23×C511yescharacteristic
569C23×C4C23×C511yescharacteristic
570C23×C4C23×C511yescharacteristic
571C23×C4C23×C511yescharacteristic
572C23×C4C23×C511yescharacteristic
573C23×C4C23×C511yescharacteristic
574C23×C4C23×C511yescharacteristic
575C23×C4C23×C511yescharacteristic
576C23×C4C23×C511yescharacteristic
577C23×C4C23×C511yescharacteristic
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4C2×C4×C514yescomplemented
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—41no—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—41no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4—41no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4C2×C4×C514yes—
625C2×C22⋊C4C2×C4×C514yes—
626C2×C22⋊C4C2×C4×C514yescomplemented
627C2×C22⋊C4C2×C4×C514yescomplemented
628C2×C22⋊C4C5×D414yes—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—41no—
634C2×C42—41no—
635#95—22no—
636#95—22no—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—41no—
643#95—41no—
644#95—41no—
645#95—41no—
646#95C2×C4×C514yescomplemented
647#95C5×D414yes—
648#95C5×D414yescomplemented
649C22×C5—24no—
650C22×C5—24no—
651C22×C5—24no—
652C22×C5—42no—
653C22×C5—42no—
654C22×C5—42no—
655C22×C5—42no—
656C22×C5—42no—
657C22×C5—42no—
658C22×C5—42no—
659C22×C5—42no—
660C22×C5—42no—
661C22×C5—42no—
662C22×C5—42no—
663C22×C5—42no—
664C22×C5—42no—
665C22×C5—42no—
666C22×C5—42no—
667C22×C5—42no—
668C22×C5—42no—
669C22×C5—42no—
670C22×C5—42no—
671C22×C5—81no—
672C22×C5—81no—
673C22×C5—81no—
674C22×C5—81no—
675C22×C5—81no—
676C22×C5—81no—
677C22×C5—81no—
678C22×C5—81no—
679C22×C5C2×C4×D411yescharacteristic
680C22×C5C2×C4×D411yescharacteristic
681C22×C5C2×C4×D411yescharacteristic
682C22×C5#51811yescharacteristic
683C22×C5#52011yescharacteristic
684C22×C5#52011yescharacteristic
685C22×C5#52011yescharacteristic
686C22×C5#53411yescharacteristic
687C22×C5#53511yescharacteristic
688C22×C5#53511yescharacteristic
689C22×C5#53611yescharacteristic
690C22×C5#53611yescharacteristic
691C22×C5#53711yescharacteristic
692C22×C5#53911yescharacteristic
693C22×C5#53911yescharacteristic
694C22×C5#54011yescharacteristic
695C22×C5#54211yescharacteristic
696C22×C5#54211yescharacteristic
697C22×C5#54211yescharacteristic
698C22×C5D4211yescharacteristic
699C22×C5D4211yescharacteristic
700C22×C5D4211yescharacteristic
701C22×C5#54611yescharacteristic
702C22×C5#54611yescharacteristic
703C22×C5#54711yescharacteristic
704C22×C5#54711yescharacteristic
705C22×C5#54811yescharacteristic
706C22×C5#54811yescharacteristic
707C22×C5#55111yescharacteristic
708C22×C5#55311yescharacteristic
709C22×C5#55311yescharacteristic
710C22×C5#56011yescharacteristic
711C22×C5#56211yescharacteristic
712C22×C5#56211yescharacteristic
713C22×C5#56311yescharacteristic
714C4×C5—24no—
715C4×C5—24no—
716C4×C5—42no—
717C4×C5—42no—
718C4×C5—42no—
719C4×C5—42no—
720C4×C5—42no—
721C4×C5—42no—
722C4×C5—42no—
723C4×C5—42no—
724C4×C5—42no—
725C4×C5—81no—
726C4×C5—81no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24C22×C4×C512yes—
754C24C22×C4×C512yes—
755C24C2×C5×D412yes—
756C24C5×#4112yes—
757C24C24×C511yescharacteristic
758C2×D4—28no—
759C2×D4—28no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4C22×C4×C512yes—
849C22×C4C22×C4×C512yes—
850C22×C4C22×C4×C512yes—
851C22×C4C22×C4×C512yes—
852C22×C4C22×C4×C512yes—
853C22×C4C2×C5×D412yes—
854C22×C4C2×C5×D412yes—
855C22×C4C2×C5×D412yes—
856C22×C4C2×C5×D412yes—
857C22×C4C2×C5×D412yes—
858C22×C4C2×C5×D412yes—
859C22×C4C2×C5×D412yes—
860C22×C4C2×C5×D412yes—
861C22×C4C5×#4112yes—
862C22×C4C5×#4112yes—
863C4⋊C4—28no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—28no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C42—44no—
881C42—44no—
882C2×C5—44no—
883C2×C5—82no—
884C2×C5#232211yescharacteristic
885C2×C5#232411yescharacteristic
886C2×C5#232611yescharacteristic
887C2×C5#235811yescharacteristic
888C2×C5#236111yescharacteristic
889C2×C5#236111yescharacteristic
890C2×C5#237611yescharacteristic
891C2×C5#266911yescharacteristic
892C2×C5#267211yescharacteristic
893C2×C5#267411yescharacteristic
894C2×C5#268111yescharacteristic
895C2×C5#270111yescharacteristic
896C2×C5#271111yescharacteristic
897C2×C5#272311yescharacteristic
898C2×C5#275711yescharacteristic
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23C4×C5×D414yes—
969C23C23×C4×C511yescharacteristic
970C23C22×C5×D411yescharacteristic
971C23C22×C5×D411yescharacteristic
972C23C22×C5×D411yescharacteristic
973C23C2×C5×#4111yescharacteristic
974C23C2×C5×#4111yescharacteristic
975C23C2×C5×#4111yescharacteristic
976C23C5×H(5,𝔽2)11yescharacteristic
977C23C5×H(5,𝔽2)11yescharacteristic
978C23C5×H(5,𝔽2)11yescharacteristic
979C23C5×H(5,𝔽2)11yescharacteristic
980C23C5×H(5,𝔽2)11yescharacteristic
981C23C5×2−1+411yescharacteristic
982C23C5×2−1+411yescharacteristic
983C23C5×2−1+411yescharacteristic
984D4—416no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—416no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4C4×C5×D414yes—
1076C2×C4C4×C5×D414yes—
1077C5#1451811yescharacteristic, direct product factor, Sylow
1078C22—24no—
1079C22—24no—
1080C22—24no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22C2×C4×C5×D411yescharacteristic
1109C22C2×C4×C5×D411yescharacteristic
1110C22C2×C4×C5×D411yescharacteristic
1111C22C5×#51811yescharacteristic
1112C22C5×#52011yescharacteristic
1113C22C5×#52011yescharacteristic
1114C22C5×#52011yescharacteristic
1115C22C5×#53411yescharacteristic
1116C22C5×#53511yescharacteristic
1117C22C5×#53511yescharacteristic
1118C22C5×#53611yescharacteristic
1119C22C5×#53611yescharacteristic
1120C22C5×#53711yescharacteristic
1121C22C5×#53911yescharacteristic
1122C22C5×#53911yescharacteristic
1123C22C5×#54011yescharacteristic
1124C22C5×#54211yescharacteristic
1125C22C5×#54211yescharacteristic
1126C22C5×#54211yescharacteristic
1127C22C5×D4211yescharacteristic
1128C22C5×D4211yescharacteristic
1129C22C5×D4211yescharacteristic
1130C22C5×#54611yescharacteristic
1131C22C5×#54611yescharacteristic
1132C22C5×#54711yescharacteristic
1133C22C5×#54711yescharacteristic
1134C22C5×#54811yescharacteristic
1135C22C5×#54811yescharacteristic
1136C22C5×#55111yescharacteristic
1137C22C5×#55311yescharacteristic
1138C22C5×#55311yescharacteristic
1139C22C5×#56011yescharacteristic
1140C22C5×#56211yescharacteristic
1141C22C5×#56211yescharacteristic
1142C22C5×#56311yescharacteristic
1143C4—24no—
1144C4—24no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—81no—
1155C4—81no—
1156C2—44no—
1157C2—82no—
1158C2C5×#232211yescharacteristic
1159C2C5×#232411yescharacteristic
1160C2C5×#232611yescharacteristic
1161C2C5×#235811yescharacteristic
1162C2C5×#236111yescharacteristic
1163C2C5×#236111yescharacteristic
1164C2C5×#237611yescharacteristic
1165C2C5×#266911yescharacteristic
1166C2C5×#267211yescharacteristic
1167C2C5×#267411yescharacteristic
1168C2C5×#268111yescharacteristic
1169C2C5×#270111yescharacteristic
1170C2C5×#271111yescharacteristic
1171C2C5×#272311yescharacteristic
1172C2C5×#275711yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC23×C5×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C5×#389C2semidirect
4. C2×C5×#388C2semidirect
6. C2×C5×#385C2semidirect
7. C2×C5×#385C2semidirect
8. C5×#1444C2semidirect
9. C5×#1440C2semidirect
10. C5×#1439C2semidirect
11. C5×#1439C2semidirect
12. C5×#1439C2semidirect
13. C5×#1437C2semidirect
14. C5×#1436C2semidirect
15. C5×#1434C2semidirect
37. C5×#394C4semidirect
58. #14518C5direct (N × H)
105. C2×C5×C4⋊C4C2×C4semidirect
136. C2×C5×C22⋊C4C2×C4semidirect
137. C2×C5×C22⋊C4C2×C4semidirect
156. C5×#95C2×C4semidirect
158. C5×#95D4semidirect
161. C2×#389C2×C5semidirect
162. C2×#388C2×C5semidirect
164. C2×#385C2×C5semidirect
165. C2×#385C2×C5semidirect
166. #1444C2×C5semidirect
167. #1440C2×C5semidirect
168. #1439C2×C5semidirect
169. #1439C2×C5semidirect
170. #1439C2×C5semidirect
171. #1437C2×C5semidirect
172. #1436C2×C5semidirect
173. #1434C2×C5semidirect
350. #394C4×C5semidirect
595. C2×C4⋊C4C2×C4×C5semidirect
626. C2×C22⋊C4C2×C4×C5semidirect
627. C2×C22⋊C4C2×C4×C5semidirect
646. #95C2×C4×C5semidirect
648. #95C5×D4semidirect
1077. C5#14518direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3942
C2×C5×#3902
C2×C5×#3892
C2×C5×#3882
C2×C5×#3862
C2×C5×#3852
C5×#14442
C5×#14402
C5×#14392
C5×#14372
C5×#14362
C5×#14342
#145185