Finite Group Databasebeta

← C5×#16432 #11939152

Subgroups — C5×#16432 #11939152

Order 1280.

1614 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#394C211yesmaximal, characteristic
2C2×C5×#386C211yesmaximal, characteristic
3C5×#1443C211yesmaximal, characteristic, complemented
4C5×#1442C211yesmaximal, characteristic, complemented
5C5×#1442C211yesmaximal, characteristic, complemented
6C5×#1442C211yesmaximal, characteristic, complemented
7C5×#1440C211yesmaximal, characteristic, complemented
8C5×#1440C211yesmaximal, characteristic, complemented
9C5×#1440C211yesmaximal, characteristic, complemented
10C5×#1440C211yesmaximal, characteristic, complemented
11C5×#1439C211yesmaximal, characteristic, complemented
12C5×#1439C211yesmaximal, characteristic, complemented
13C5×#1438C211yesmaximal, characteristic
14C5×C22⋊#95C211yesmaximal, characteristic, complemented
15C5×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C24×C4×C5C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C22⋊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×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C5×C22⋊C4C2211yescharacteristic
31C5×#394—24no—
32C5×#386—24no—
33C2×C5×#95C2211yescharacteristic
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2211yescharacteristic
37C2×C5×#95C2211yescharacteristic
38C2×C5×#95C2211yescharacteristic
39C2×C5×#95C2211yescharacteristic
40C2×C5×#95C2211yescharacteristic
41C2×C5×#95C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2211yescharacteristic
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×C5×#95C2211yescharacteristic
52C2×C5×#95C2211yescharacteristic
53#16432C511yesmaximal, characteristic, direct product factor, Sylow
54C25×C5C2311yescharacteristic
55C25×C5C2311yescharacteristic
56C22×C5×D4—22no—
57C22×C5×D4—22no—
58C22×C5×D4—41no—
59C22×C5×D4—41no—
60C22×C5×D4—41no—
61C22×C5×D4—41no—
62C22×C5×D4D414yes—
63C23×C4×C5—22no—
64C23×C4×C5—22no—
65C23×C4×C5—22no—
66C23×C4×C5—41no—
67C23×C4×C5—41no—
68C23×C4×C5—41no—
69C23×C4×C5—41no—
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4—41no—
85C2×C5×C4⋊C4—41no—
86C2×C5×C4⋊C4—41no—
87C2×C5×C4⋊C4—41no—
88C2×C5×C4⋊C4—41no—
89C2×C5×C22⋊C4—22no—
90C2×C5×C22⋊C4—22no—
91C2×C5×C22⋊C4—22no—
92C2×C5×C22⋊C4—22no—
93C2×C5×C22⋊C4—22no—
94C2×C5×C22⋊C4—22no—
95C2×C5×C22⋊C4—22no—
96C2×C5×C22⋊C4—22no—
97C2×C5×C22⋊C4—22no—
98C2×C5×C22⋊C4—22no—
99C2×C5×C22⋊C4—22no—
100C2×C5×C22⋊C4—22no—
101C2×C5×C22⋊C4—22no—
102C2×C5×C22⋊C4—22no—
103C2×C5×C22⋊C4—22no—
104C2×C5×C22⋊C4—22no—
105C2×C5×C22⋊C4—22no—
106C2×C5×C22⋊C4—41no—
107C2×C5×C22⋊C4—41no—
108C2×C5×C22⋊C4—41no—
109C2×C5×C22⋊C4—41no—
110C2×C5×C22⋊C4—41no—
111C2×C5×C22⋊C4—41no—
112C2×C5×C22⋊C4—41no—
113C2×C5×C22⋊C4—41no—
114C2×C5×C22⋊C4—41no—
115C2×C5×C22⋊C4—41no—
116C2×C5×C22⋊C4—41no—
117C2×C5×C22⋊C4—41no—
118C2×C5×C22⋊C4—41no—
119C2×C5×C22⋊C4—41no—
120C2×C5×C22⋊C4—41no—
121C2×C5×C22⋊C4—41no—
122C5×#95—22no—
123C5×#95—22no—
124C5×#95—22no—
125C5×#95—22no—
126C5×#95—22no—
127C5×#95—22no—
128C5×#95—22no—
129C5×#95—41no—
130C5×#95—41no—
131C5×#95—41no—
132C5×#95—41no—
133C5×#95—41no—
134C5×#95—41no—
135C5×#95—41no—
136C5×#95—41no—
137C5×#95—41no—
138C5×#95—41no—
139C5×#95—41no—
140C5×#95—41no—
141C5×#95—41no—
142C2×#394C2×C511yescharacteristic
143C2×#386C2×C511yescharacteristic
144#1443C2×C511yescharacteristic, complemented
145#1442C2×C511yescharacteristic, complemented
146#1442C2×C511yescharacteristic, complemented
147#1442C2×C511yescharacteristic, complemented
148#1440C2×C511yescharacteristic, complemented
149#1440C2×C511yescharacteristic, complemented
150#1440C2×C511yescharacteristic, complemented
151#1440C2×C511yescharacteristic, complemented
152#1439C2×C511yescharacteristic, complemented
153#1439C2×C511yescharacteristic, complemented
154#1438C2×C511yescharacteristic
155C22⋊#95C2×C511yescharacteristic, complemented
156C22⋊#95C2×C511yescharacteristic, complemented
157C24×C5—21no—
158C24×C5—21no—
159C24×C5—21no—
160C24×C5—21no—
161C24×C5—21no—
162C24×C5—21no—
163C24×C5—21no—
164C24×C5—21no—
165C24×C5—21no—
166C24×C5—21no—
167C24×C5—21no—
168C24×C5—21no—
169C24×C5—21no—
170C24×C5—21no—
171C24×C5—21no—
172C24×C5—21no—
173C24×C5—21no—
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×C5C2×D412yes—
184C24×C5C2×D412yes—
185C24×C5#4112yes—
186C24×C5#4112yes—
187C24×C5C2411yescharacteristic
188C2×C5×D4—28no—
189C2×C5×D4—44no—
190C2×C5×D4—44no—
191C2×C5×D4—44no—
192C2×C5×D4—44no—
193C2×C5×D4—44no—
194C2×C5×D4—44no—
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×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—44no—
282C22×C4×C5—44no—
283C22×C4×C5—44no—
284C22×C4×C5—44no—
285C22×C4×C5—44no—
286C22×C4×C5—44no—
287C22×C4×C5—44no—
288C22×C4×C5C2×D412yes—
289C22×C4×C5#4112yes—
290C22×C4×C5#4112yes—
291C22×C4×C5#4112yes—
292C22×C4×C5#4112yes—
293C5×C4⋊C4—44no—
294C5×C4⋊C4—44no—
295C5×C22⋊C4—44no—
296C5×C22⋊C4—44no—
297C5×C22⋊C4—44no—
298C5×C22⋊C4—44no—
299C5×C22⋊C4—44no—
300C5×C22⋊C4—44no—
301C5×C22⋊C4—44no—
302C5×C22⋊C4—44no—
303C5×C22⋊C4—44no—
304C5×C22⋊C4—44no—
305C5×C22⋊C4—44no—
306C23×D4C22×C511yescharacteristic
307C24×C4C22×C511yescharacteristic
308C22×C4⋊C4C22×C511yescharacteristic
309C22×C4⋊C4C22×C511yescharacteristic
310C22×C22⋊C4C22×C511yescharacteristic
311C22×C22⋊C4C22×C511yescharacteristic
312C22×C22⋊C4C22×C511yescharacteristic
313C22×C22⋊C4C22×C511yescharacteristic
314C22×C22⋊C4C22×C511yescharacteristic
315C22×C22⋊C4C22×C511yescharacteristic
316C22×C22⋊C4C22×C511yescharacteristic
317C22×C22⋊C4C22×C511yescharacteristic
318C22×C22⋊C4C22×C511yescharacteristic
319C22×C22⋊C4C22×C511yescharacteristic
320C22×C22⋊C4C22×C511yescharacteristic
321#394—24no—
322#386—24no—
323C2×#95C22×C511yescharacteristic
324C2×#95C22×C511yescharacteristic
325C2×#95C22×C511yescharacteristic
326C2×#95C22×C511yescharacteristic
327C2×#95C22×C511yescharacteristic
328C2×#95C22×C511yescharacteristic
329C2×#95C22×C511yescharacteristic
330C2×#95C22×C511yescharacteristic
331C2×#95C22×C511yescharacteristic
332C2×#95C22×C511yescharacteristic
333C2×#95C22×C511yescharacteristic
334C2×#95C22×C511yescharacteristic
335C2×#95C22×C511yescharacteristic
336C2×#95C22×C511yescharacteristic
337C2×#95C22×C511yescharacteristic
338C2×#95C22×C511yescharacteristic
339C2×#95C22×C511yescharacteristic
340C2×#95C22×C511yescharacteristic
341C2×#95C22×C511yescharacteristic
342C2×#95C22×C511yescharacteristic
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—41no—
369C23×C5—41no—
370C23×C5—41no—
371C23×C5—41no—
372C23×C5—41no—
373C23×C5—41no—
374C23×C5—41no—
375C23×C5—41no—
376C23×C5—41no—
377C23×C5—41no—
378C23×C5—41no—
379C23×C5—41no—
380C23×C5—41no—
381C23×C5—41no—
382C23×C5—41no—
383C23×C5—41no—
384C23×C5—41no—
385C23×C5—41no—
386C23×C5—41no—
387C23×C5—41no—
388C23×C5—41no—
389C23×C5—41no—
390C23×C5—41no—
391C23×C5—41no—
392C23×C5—41no—
393C23×C5—41no—
394C23×C5—41no—
395C23×C5—41no—
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#12314yes—
413C23×C5C22×D411yescharacteristic
414C23×C5C2×#4111yescharacteristic
415C23×C5C2×#4111yescharacteristic
416C23×C5C2×#4111yescharacteristic
417C23×C5C2×#4111yescharacteristic
418C23×C5C2×#4111yescharacteristic
419C23×C5C2×#4111yescharacteristic
420C23×C5H(5,𝔽2)11yescharacteristic
421C23×C5H(5,𝔽2)11yescharacteristic
422C23×C5H(5,𝔽2)11yescharacteristic
423C23×C5H(5,𝔽2)11yescharacteristic
424C23×C5H(5,𝔽2)11yescharacteristic
425C23×C5H(5,𝔽2)11yescharacteristic
426C23×C5H(5,𝔽2)11yescharacteristic
427C23×C52−1+411yescharacteristic
428C5×D4—416no—
429C2×C4×C5—22no—
430C2×C4×C5—22no—
431C2×C4×C5—22no—
432C2×C4×C5—22no—
433C2×C4×C5—22no—
434C2×C4×C5—22no—
435C2×C4×C5—22no—
436C2×C4×C5—22no—
437C2×C4×C5—22no—
438C2×C4×C5—22no—
439C2×C4×C5—22no—
440C2×C4×C5—22no—
441C2×C4×C5—22no—
442C2×C4×C5—22no—
443C2×C4×C5—22no—
444C2×C4×C5—416no—
445C2×C4×C5—41no—
446C2×C4×C5—41no—
447C2×C4×C5—41no—
448C2×C4×C5—41no—
449C2×C4×C5—41no—
450C2×C4×C5—41no—
451C2×C4×C5—41no—
452C2×C4×C5—41no—
453C2×C4×C5—41no—
454C2×C4×C5—41no—
455C2×C4×C5—41no—
456C2×C4×C5—41no—
457C2×C4×C5—41no—
458C2×C4×C5—41no—
459C2×C4×C5—41no—
460C2×C4×C5—41no—
461C2×C4×C5—41no—
462C2×C4×C5—41no—
463C2×C4×C5—41no—
464C2×C4×C5—41no—
465C2×C4×C5—41no—
466C2×C4×C5—41no—
467C2×C4×C5—41no—
468C2×C4×C5—41no—
469C2×C4×C5—41no—
470C2×C4×C5—41no—
471C2×C4×C5—41no—
472C2×C4×C5—41no—
473C2×C4×C5—41no—
474C2×C4×C5—41no—
475C2×C4×C5—41no—
476C2×C4×C5—41no—
477C2×C4×C5—41no—
478C2×C4×C5—41no—
479C2×C4×C5—41no—
480C2×C4×C5—41no—
481C2×C4×C5—41no—
482C2×C4×C5—41no—
483C2×C4×C5—41no—
484C2×C4×C5—41no—
485C2×C4×C5—41no—
486C2×C4×C5—41no—
487C2×C4×C5—41no—
488C2×C4×C5—41no—
489C2×C4×C5—41no—
490C2×C4×C5—41no—
491C2×C4×C5—41no—
492C2×C4×C5—41no—
493C2×C4×C5—41no—
494C2×C4×C5—41no—
495C2×C4×C5—41no—
496C2×C4×C5—41no—
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—
521C25C23×C511yescharacteristic
522C25C23×C511yescharacteristic
523C22×D4—22no—
524C22×D4—22no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4C5×D414yes—
530C23×C4—22no—
531C23×C4—22no—
532C23×C4—22no—
533C23×C4—41no—
534C23×C4—41no—
535C23×C4—41no—
536C23×C4—41no—
537C23×C4C23×C511yescharacteristic
538C23×C4C23×C511yescharacteristic
539C23×C4C23×C511yescharacteristic
540C23×C4C23×C511yescharacteristic
541C23×C4C23×C511yescharacteristic
542C23×C4C23×C511yescharacteristic
543C23×C4C23×C511yescharacteristic
544C23×C4C23×C511yescharacteristic
545C23×C4C23×C511yescharacteristic
546C23×C4C23×C511yescharacteristic
547C23×C4C23×C511yescharacteristic
548C23×C4C23×C511yescharacteristic
549C23×C4C23×C511yescharacteristic
550C2×C4⋊C4—22no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4—41no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—41no—
575C2×C22⋊C4—41no—
576C2×C22⋊C4—41no—
577C2×C22⋊C4—41no—
578C2×C22⋊C4—41no—
579C2×C22⋊C4—41no—
580C2×C22⋊C4—41no—
581C2×C22⋊C4—41no—
582C2×C22⋊C4—41no—
583C2×C22⋊C4—41no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—41no—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—41no—
597#95—41no—
598#95—41no—
599#95—41no—
600#95—41no—
601#95—41no—
602#95—41no—
603#95—41no—
604#95—41no—
605#95—41no—
606#95—41no—
607#95—41no—
608#95—41no—
609C22×C5—24no—
610C22×C5—24no—
611C22×C5—24no—
612C22×C5—42no—
613C22×C5—42no—
614C22×C5—42no—
615C22×C5—42no—
616C22×C5—42no—
617C22×C5—42no—
618C22×C5—42no—
619C22×C5—42no—
620C22×C5—42no—
621C22×C5—42no—
622C22×C5—42no—
623C22×C5—42no—
624C22×C5—42no—
625C22×C5—42no—
626C22×C5—42no—
627C22×C5—42no—
628C22×C5—42no—
629C22×C5—42no—
630C22×C5—42no—
631C22×C5—81no—
632C22×C5—81no—
633C22×C5—81no—
634C22×C5—81no—
635C22×C5—81no—
636C22×C5—81no—
637C22×C5—81no—
638C22×C5—81no—
639C22×C5C2×#12311yescharacteristic
640C22×C5#52911yescharacteristic
641C22×C5#52911yescharacteristic
642C22×C5#53411yescharacteristic
643C22×C5#53411yescharacteristic
644C22×C5#53811yescharacteristic
645C22×C5#53811yescharacteristic
646C22×C5#53811yescharacteristic
647C22×C5#53811yescharacteristic
648C22×C5#53811yescharacteristic
649C22×C5#53811yescharacteristic
650C22×C5#53811yescharacteristic
651C22×C5#53811yescharacteristic
652C22×C5#53911yescharacteristic
653C22×C5#53911yescharacteristic
654C22×C5#54011yescharacteristic
655C22×C5#54011yescharacteristic
656C22×C5#54011yescharacteristic
657C22×C5#54211yescharacteristic
658C22×C5#54611yescharacteristic
659C22×C5#54611yescharacteristic
660C22×C5#54611yescharacteristic
661C22×C5#54711yescharacteristic
662C22×C5#55111yescharacteristic
663C22×C5#55111yescharacteristic
664C22×C5#55211yescharacteristic
665C22×C5#55311yescharacteristic
666C22×C5#55311yescharacteristic
667C22×C5#55311yescharacteristic
668C22×C5#55311yescharacteristic
669C22×C5#55511yescharacteristic
670C22×C5#56011yescharacteristic
671C22×C5H(3,𝔽4)11yescharacteristic
672C22×C5#56211yescharacteristic
673C22×C5#56211yescharacteristic
674C4×C5—42no—
675C4×C5—42no—
676C4×C5—42no—
677C4×C5—42no—
678C4×C5—42no—
679C4×C5—81no—
680C4×C5—81no—
681C4×C5—81no—
682C4×C5—81no—
683C4×C5—81no—
684C4×C5—81no—
685C4×C5—81no—
686C4×C5—81no—
687C24—21no—
688C24—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24C2×C5×D412yes—
714C24C2×C5×D412yes—
715C24C5×#4112yes—
716C24C5×#4112yes—
717C24C24×C511yescharacteristic
718C2×D4—28no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
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—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4C2×C5×D412yes—
819C22×C4C5×#4112yes—
820C22×C4C5×#4112yes—
821C22×C4C5×#4112yes—
822C22×C4C5×#4112yes—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C22⋊C4—44no—
826C22⋊C4—44no—
827C22⋊C4—44no—
828C22⋊C4—44no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—44no—
832C22⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C2×C5—44no—
837C2×C5—82no—
838C2×C5#241911yescharacteristic
839C2×C5#244411yescharacteristic
840C2×C5#251811yescharacteristic
841C2×C5#262211yescharacteristic
842C2×C5#264811yescharacteristic
843C2×C5#264911yescharacteristic
844C2×C5#268411yescharacteristic
845C2×C5#269911yescharacteristic
846C2×C5#270111yescharacteristic
847C2×C5#270811yescharacteristic
848C2×C5#274111yescharacteristic
849C2×C5#275311yescharacteristic
850C2×C5#277811yescharacteristic
851C2×C5#278111yescharacteristic
852C2×C5#282411yescharacteristic
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23C5×#12314yes—
923C23C22×C5×D411yescharacteristic
924C23C2×C5×#4111yescharacteristic
925C23C2×C5×#4111yescharacteristic
926C23C2×C5×#4111yescharacteristic
927C23C2×C5×#4111yescharacteristic
928C23C2×C5×#4111yescharacteristic
929C23C2×C5×#4111yescharacteristic
930C23C5×H(5,𝔽2)11yescharacteristic
931C23C5×H(5,𝔽2)11yescharacteristic
932C23C5×H(5,𝔽2)11yescharacteristic
933C23C5×H(5,𝔽2)11yescharacteristic
934C23C5×H(5,𝔽2)11yescharacteristic
935C23C5×H(5,𝔽2)11yescharacteristic
936C23C5×H(5,𝔽2)11yescharacteristic
937C23C5×2−1+411yescharacteristic
938D4—416no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—416no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C5#1643211yescharacteristic, direct product factor, Sylow
1032C22—24no—
1033C22—24no—
1034C22—24no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22C2×C5×#12311yescharacteristic
1063C22C5×#52911yescharacteristic
1064C22C5×#52911yescharacteristic
1065C22C5×#53411yescharacteristic
1066C22C5×#53411yescharacteristic
1067C22C5×#53811yescharacteristic
1068C22C5×#53811yescharacteristic
1069C22C5×#53811yescharacteristic
1070C22C5×#53811yescharacteristic
1071C22C5×#53811yescharacteristic
1072C22C5×#53811yescharacteristic
1073C22C5×#53811yescharacteristic
1074C22C5×#53811yescharacteristic
1075C22C5×#53911yescharacteristic
1076C22C5×#53911yescharacteristic
1077C22C5×#54011yescharacteristic
1078C22C5×#54011yescharacteristic
1079C22C5×#54011yescharacteristic
1080C22C5×#54211yescharacteristic
1081C22C5×#54611yescharacteristic
1082C22C5×#54611yescharacteristic
1083C22C5×#54611yescharacteristic
1084C22C5×#54711yescharacteristic
1085C22C5×#55111yescharacteristic
1086C22C5×#55111yescharacteristic
1087C22C5×#55211yescharacteristic
1088C22C5×#55311yescharacteristic
1089C22C5×#55311yescharacteristic
1090C22C5×#55311yescharacteristic
1091C22C5×#55311yescharacteristic
1092C22C5×#55511yescharacteristic
1093C22C5×#56011yescharacteristic
1094C22C5×H(3,𝔽4)11yescharacteristic
1095C22C5×#56211yescharacteristic
1096C22C5×#56211yescharacteristic
1097C4—42no—
1098C4—42no—
1099C4—42no—
1100C4—42no—
1101C4—42no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C2—44no—
1111C2—82no—
1112C2C5×#241911yescharacteristic
1113C2C5×#244411yescharacteristic
1114C2C5×#251811yescharacteristic
1115C2C5×#262211yescharacteristic
1116C2C5×#264811yescharacteristic
1117C2C5×#264911yescharacteristic
1118C2C5×#268411yescharacteristic
1119C2C5×#269911yescharacteristic
1120C2C5×#270111yescharacteristic
1121C2C5×#270811yescharacteristic
1122C2C5×#274111yescharacteristic
1123C2C5×#275311yescharacteristic
1124C2C5×#277811yescharacteristic
1125C2C5×#278111yescharacteristic
1126C2C5×#282411yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutator, Frattini, cosocleC24C24×C5
prime radicalC23×C5×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1443C2semidirect
4. C5×#1442C2semidirect
5. C5×#1442C2semidirect
6. C5×#1442C2semidirect
7. C5×#1440C2semidirect
8. C5×#1440C2semidirect
9. C5×#1440C2semidirect
10. C5×#1440C2semidirect
11. C5×#1439C2semidirect
12. C5×#1439C2semidirect
14. C5×C22⋊#95C2semidirect
15. C5×C22⋊#95C2semidirect
53. #16432C5direct (N × H)
144. #1443C2×C5semidirect
145. #1442C2×C5semidirect
146. #1442C2×C5semidirect
147. #1442C2×C5semidirect
148. #1440C2×C5semidirect
149. #1440C2×C5semidirect
150. #1440C2×C5semidirect
151. #1440C2×C5semidirect
152. #1439C2×C5semidirect
153. #1439C2×C5semidirect
155. C22⋊#95C2×C5semidirect
156. C22⋊#95C2×C5semidirect
1031. C5#16432direct (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×#3862
C5×#14432
C5×#14422
C5×#14402
C5×#14392
C5×#14382
C5×C22⋊#952
#164325