Finite Group Databasebeta

← C5×#16532 #11939252

Subgroups — C5×#16532 #11939252

Order 1280.

1330 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#400C211yesmaximal, characteristic, complemented
2C2×C5×#399C211yesmaximal, characteristic
3C2×C5×#397C211yesmaximal, characteristic
4C2×C5×#389C211yesmaximal, characteristic, complemented
5C5×#1445C211yesmaximal, characteristic, complemented
6C5×#1442C211yesmaximal, characteristic, complemented
7C5×#1442C211yesmaximal, characteristic, complemented
8C5×#1441C211yesmaximal, characteristic, complemented
9C5×#1441C211yesmaximal, characteristic, complemented
10C5×#1440C211yesmaximal, characteristic
11C5×#1439C211yesmaximal, characteristic
12C5×#1439C211yesmaximal, characteristic
13C5×#1439C211yesmaximal, characteristic
14C5×#1437C211yesmaximal, characteristic
15C5×#1436C211yesmaximal, characteristic, complemented
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C42×C5C2211yescharacteristic
31C5×#400—24no—
32C5×#399—24no—
33C5×#397—24no—
34C5×#389—24no—
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
55#16532C511yesmaximal, characteristic, direct product factor, Sylow
56C25×C5C2311yescharacteristic
57C23×C4×C5C2311yescharacteristic
58C23×C4×C5C2311yescharacteristic
59C23×C4×C5C2311yescharacteristic
60C23×C4×C5C2311yescharacteristic
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C2×C5×C4⋊C4—22no—
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—41no—
85C2×C5×C4⋊C4—41no—
86C2×C5×C4⋊C4—41no—
87C2×C5×C4⋊C4—41no—
88C2×C5×C4⋊C4—41no—
89C2×C5×C4⋊C4—41no—
90C2×C5×C4⋊C4—41no—
91C2×C5×C4⋊C4D414yes—
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—41no—
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×C42×C5—22no—
114C2×C42×C5—41no—
115C2×C42×C5—41no—
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—22no—
128C5×#95—41no—
129C5×#95—41no—
130C5×#95—41no—
131C5×#95—41no—
132C5×#95—41no—
133C5×#95—41no—
134C5×#95—41no—
135C5×#95D414yes—
136C2×#400C2×C511yescharacteristic, complemented
137C2×#399C2×C511yescharacteristic
138C2×#397C2×C511yescharacteristic
139C2×#389C2×C511yescharacteristic, complemented
140#1445C2×C511yescharacteristic, complemented
141#1442C2×C511yescharacteristic, complemented
142#1442C2×C511yescharacteristic, complemented
143#1441C2×C511yescharacteristic, complemented
144#1441C2×C511yescharacteristic, complemented
145#1440C2×C511yescharacteristic
146#1439C2×C511yescharacteristic
147#1439C2×C511yescharacteristic
148#1439C2×C511yescharacteristic
149#1437C2×C511yescharacteristic
150#1436C2×C511yescharacteristic, complemented
151C24×C5—21no—
152C24×C5—21no—
153C24×C5—21no—
154C24×C5—21no—
155C24×C5—21no—
156C24×C5—21no—
157C24×C5—21no—
158C24×C5—21no—
159C24×C5—21no—
160C24×C5—21no—
161C24×C5—21no—
162C24×C5—21no—
163C24×C5—21no—
164C24×C5—21no—
165C24×C5#4112yes—
166C24×C5C2411yescharacteristic
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5—21no—
228C22×C4×C5—21no—
229C22×C4×C5—21no—
230C22×C4×C5—21no—
231C22×C4×C5—21no—
232C22×C4×C5—21no—
233C22×C4×C5—21no—
234C22×C4×C5—21no—
235C22×C4×C5—21no—
236C22×C4×C5—21no—
237C22×C4×C5—21no—
238C22×C4×C5—21no—
239C22×C4×C5—21no—
240C22×C4×C5—21no—
241C22×C4×C5—21no—
242C22×C4×C5—21no—
243C22×C4×C5—21no—
244C22×C4×C5—21no—
245C22×C4×C5—21no—
246C22×C4×C5—21no—
247C22×C4×C5—21no—
248C22×C4×C5—21no—
249C22×C4×C5—21no—
250C22×C4×C5—21no—
251C22×C4×C5—21no—
252C22×C4×C5—21no—
253C22×C4×C5—21no—
254C22×C4×C5—21no—
255C22×C4×C5C2×D412yes—
256C22×C4×C5C2×D412yes—
257C22×C4×C5C2×D412yes—
258C22×C4×C5C2×D412yes—
259C22×C4×C5C2×D412yes—
260C22×C4×C5C2×D412yes—
261C22×C4×C5#4112yes—
262C22×C4×C5#4112yes—
263C22×C4×C5#4112yes—
264C22×C4×C5#4112yes—
265C5×C4⋊C4—28no—
266C5×C4⋊C4—44no—
267C5×C4⋊C4—44no—
268C5×C4⋊C4—44no—
269C5×C4⋊C4—44no—
270C5×C4⋊C4—44no—
271C5×C4⋊C4—44no—
272C5×C22⋊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—
280C22×C4⋊C4C22×C511yescharacteristic
281C22×C4⋊C4C22×C511yescharacteristic
282C22×C4⋊C4C22×C511yescharacteristic
283C22×C4⋊C4C22×C511yescharacteristic
284C22×C4⋊C4C22×C511yescharacteristic
285C22×C4⋊C4C22×C511yescharacteristic
286C22×C4⋊C4C22×C511yescharacteristic
287C22×C22⋊C4C22×C511yescharacteristic
288C22×C22⋊C4C22×C511yescharacteristic
289C22×C22⋊C4C22×C511yescharacteristic
290C22×C22⋊C4C22×C511yescharacteristic
291C22×C22⋊C4C22×C511yescharacteristic
292C22×C22⋊C4C22×C511yescharacteristic
293C22×C22⋊C4C22×C511yescharacteristic
294C22×C42C22×C511yescharacteristic
295#400—24no—
296#399—24no—
297#397—24no—
298#389—24no—
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
317C2×#95C22×C511yescharacteristic
318C2×#95C22×C511yescharacteristic
319C23×C5—22no—
320C23×C5—22no—
321C23×C5—22no—
322C23×C5—22no—
323C23×C5—22no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—41no—
327C23×C5—41no—
328C23×C5—41no—
329C23×C5—41no—
330C23×C5—41no—
331C23×C5—41no—
332C23×C5—41no—
333C23×C5—41no—
334C23×C5—41no—
335C23×C5—41no—
336C23×C5—41no—
337C23×C5—41no—
338C23×C5—41no—
339C23×C5—41no—
340C23×C5—41no—
341C23×C5—41no—
342C23×C5—41no—
343C23×C5—41no—
344C23×C5—41no—
345C23×C5—41no—
346C23×C5—41no—
347C23×C5—41no—
348C23×C5—41no—
349C23×C5—41no—
350C23×C5—41no—
351C23×C5—41no—
352C23×C5—41no—
353C23×C5—41no—
354C23×C5C22×D411yescharacteristic
355C23×C5C22×D411yescharacteristic
356C23×C5C2×#4111yescharacteristic
357C23×C5C2×#4111yescharacteristic
358C23×C5C2×#4111yescharacteristic
359C23×C5C2×#4111yescharacteristic
360C23×C5C2×#4111yescharacteristic
361C23×C5H(5,𝔽2)11yescharacteristic
362C23×C5H(5,𝔽2)11yescharacteristic
363C23×C5H(5,𝔽2)11yescharacteristic
364C23×C5H(5,𝔽2)11yescharacteristic
365C23×C52−1+411yescharacteristic
366C23×C52−1+411yescharacteristic
367C23×C52−1+411yescharacteristic
368C23×C52−1+411yescharacteristic
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—41no—
397C2×C4×C5—41no—
398C2×C4×C5—41no—
399C2×C4×C5—41no—
400C2×C4×C5—41no—
401C2×C4×C5—41no—
402C2×C4×C5—41no—
403C2×C4×C5—41no—
404C2×C4×C5—41no—
405C2×C4×C5—41no—
406C2×C4×C5—41no—
407C2×C4×C5—41no—
408C2×C4×C5—41no—
409C2×C4×C5—41no—
410C2×C4×C5—41no—
411C2×C4×C5—41no—
412C2×C4×C5—41no—
413C2×C4×C5—41no—
414C2×C4×C5—41no—
415C2×C4×C5—41no—
416C2×C4×C5—41no—
417C2×C4×C5—41no—
418C2×C4×C5—41no—
419C2×C4×C5—41no—
420C2×C4×C5—41no—
421C2×C4×C5—41no—
422C2×C4×C5—41no—
423C2×C4×C5—41no—
424C2×C4×C5—41no—
425C2×C4×C5—41no—
426C2×C4×C5—41no—
427C2×C4×C5—41no—
428C2×C4×C5—41no—
429C2×C4×C5—41no—
430C2×C4×C5—41no—
431C2×C4×C5—41no—
432C2×C4×C5—41no—
433C2×C4×C5—41no—
434C2×C4×C5—41no—
435C2×C4×C5—41no—
436C2×C4×C5—41no—
437C2×C4×C5—41no—
438C2×C4×C5—41no—
439C2×C4×C5—41no—
440C2×C4×C5—41no—
441C2×C4×C5—41no—
442C2×C4×C5—41no—
443C2×C4×C5—41no—
444C2×C4×C5—41no—
445C2×C4×C5—41no—
446C2×C4×C5—41no—
447C2×C4×C5—41no—
448C2×C4×C5—41no—
449C2×C4×C5—41no—
450C2×C4×C5—41no—
451C2×C4×C5—41no—
452C2×C4×C5—41no—
453C2×C4×C5—41no—
454C2×C4×C5—41no—
455C2×C4×C5—41no—
456C2×C4×C5—41no—
457C2×C4×C5—41no—
458C2×C4×C5—41no—
459C2×C4×C5—41no—
460C2×C4×C5—41no—
461C2×C4×C5—41no—
462C2×C4×C5—41no—
463C2×C4×C5—41no—
464C2×C4×C5—41no—
465C2×C4×C5—41no—
466C2×C4×C5#12314yes—
467C25C23×C511yescharacteristic
468C23×C4C23×C511yescharacteristic
469C23×C4C23×C511yescharacteristic
470C23×C4C23×C511yescharacteristic
471C23×C4C23×C511yescharacteristic
472C23×C4C23×C511yescharacteristic
473C23×C4C23×C511yescharacteristic
474C23×C4C23×C511yescharacteristic
475C23×C4C23×C511yescharacteristic
476C23×C4C23×C511yescharacteristic
477C23×C4C23×C511yescharacteristic
478C23×C4C23×C511yescharacteristic
479C23×C4C23×C511yescharacteristic
480C23×C4C23×C511yescharacteristic
481C23×C4C23×C511yescharacteristic
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—41no—
496C2×C4⋊C4—41no—
497C2×C4⋊C4—41no—
498C2×C4⋊C4—41no—
499C2×C4⋊C4—41no—
500C2×C4⋊C4—41no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4C5×D414yes—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—41no—
517C2×C22⋊C4—41no—
518C2×C22⋊C4—41no—
519C2×C22⋊C4—41no—
520C2×C22⋊C4—41no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—41no—
523C2×C22⋊C4—41no—
524C2×C42—22no—
525C2×C42—41no—
526C2×C42—41no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—41no—
540#95—41no—
541#95—41no—
542#95—41no—
543#95—41no—
544#95—41no—
545#95—41no—
546#95C5×D414yes—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—42no—
551C22×C5—42no—
552C22×C5—42no—
553C22×C5—42no—
554C22×C5—81no—
555C22×C5—81no—
556C22×C5—81no—
557C22×C5—81no—
558C22×C5—81no—
559C22×C5—81no—
560C22×C5—81no—
561C22×C5—81no—
562C22×C5C2×#12311yescharacteristic
563C22×C5#52911yescharacteristic
564C22×C5#53211yescharacteristic
565C22×C5#53511yescharacteristic
566C22×C5#53611yescharacteristic
567C22×C5#53611yescharacteristic
568C22×C5#53711yescharacteristic
569C22×C5#53811yescharacteristic
570C22×C5#53811yescharacteristic
571C22×C5#53911yescharacteristic
572C22×C5#53911yescharacteristic
573C22×C5#53911yescharacteristic
574C22×C5#53911yescharacteristic
575C22×C5#53911yescharacteristic
576C22×C5#53911yescharacteristic
577C22×C5#54011yescharacteristic
578C22×C5#54111yescharacteristic
579C22×C5#54111yescharacteristic
580C22×C5#54211yescharacteristic
581C22×C5D4211yescharacteristic
582C22×C5#54611yescharacteristic
583C22×C5#54611yescharacteristic
584C22×C5#54711yescharacteristic
585C22×C5#54811yescharacteristic
586C22×C5#54811yescharacteristic
587C22×C5#55011yescharacteristic
588C22×C5#55111yescharacteristic
589C22×C5#55211yescharacteristic
590C22×C5#55211yescharacteristic
591C22×C5#55611yescharacteristic
592C22×C5#55911yescharacteristic
593C22×C5#56211yescharacteristic
594C22×C5#56211yescharacteristic
595C22×C5#56311yescharacteristic
596C22×C5#56311yescharacteristic
597C4×C5—24no—
598C4×C5—42no—
599C4×C5—42no—
600C4×C5—42no—
601C4×C5—42no—
602C4×C5—42no—
603C4×C5—42no—
604C4×C5—42no—
605C4×C5—81no—
606C4×C5—81no—
607C4×C5—81no—
608C4×C5—81no—
609C4×C5—81no—
610C4×C5—81no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24C5×#4112yes—
626C24C24×C511yescharacteristic
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4C2×C5×D412yes—
716C22×C4C2×C5×D412yes—
717C22×C4C2×C5×D412yes—
718C22×C4C2×C5×D412yes—
719C22×C4C2×C5×D412yes—
720C22×C4C2×C5×D412yes—
721C22×C4C5×#4112yes—
722C22×C4C5×#4112yes—
723C22×C4C5×#4112yes—
724C22×C4C5×#4112yes—
725C4⋊C4—28no—
726C4⋊C4—44no—
727C4⋊C4—44no—
728C4⋊C4—44no—
729C4⋊C4—44no—
730C4⋊C4—44no—
731C4⋊C4—44no—
732C22⋊C4—44no—
733C22⋊C4—44no—
734C22⋊C4—44no—
735C22⋊C4—44no—
736C22⋊C4—44no—
737C22⋊C4—44no—
738C22⋊C4—44no—
739C42—44no—
740C2×C5—82no—
741C2×C5#242111yescharacteristic
742C2×C5#244511yescharacteristic
743C2×C5#255311yescharacteristic
744C2×C5#262311yescharacteristic
745C2×C5#264911yescharacteristic
746C2×C5#266411yescharacteristic
747C2×C5#267411yescharacteristic
748C2×C5#267611yescharacteristic
749C2×C5#269011yescharacteristic
750C2×C5#269411yescharacteristic
751C2×C5#269611yescharacteristic
752C2×C5#272711yescharacteristic
753C2×C5#277111yescharacteristic
754C2×C5#279811yescharacteristic
755C2×C5#283611yescharacteristic
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23C22×C5×D411yescharacteristic
792C23C22×C5×D411yescharacteristic
793C23C2×C5×#4111yescharacteristic
794C23C2×C5×#4111yescharacteristic
795C23C2×C5×#4111yescharacteristic
796C23C2×C5×#4111yescharacteristic
797C23C2×C5×#4111yescharacteristic
798C23C5×H(5,𝔽2)11yescharacteristic
799C23C5×H(5,𝔽2)11yescharacteristic
800C23C5×H(5,𝔽2)11yescharacteristic
801C23C5×H(5,𝔽2)11yescharacteristic
802C23C5×2−1+411yescharacteristic
803C23C5×2−1+411yescharacteristic
804C23C5×2−1+411yescharacteristic
805C23C5×2−1+411yescharacteristic
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4C5×#12314yes—
904C5#1653211yescharacteristic, direct product factor, Sylow
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22C2×C5×#12311yescharacteristic
921C22C5×#52911yescharacteristic
922C22C5×#53211yescharacteristic
923C22C5×#53511yescharacteristic
924C22C5×#53611yescharacteristic
925C22C5×#53611yescharacteristic
926C22C5×#53711yescharacteristic
927C22C5×#53811yescharacteristic
928C22C5×#53811yescharacteristic
929C22C5×#53911yescharacteristic
930C22C5×#53911yescharacteristic
931C22C5×#53911yescharacteristic
932C22C5×#53911yescharacteristic
933C22C5×#53911yescharacteristic
934C22C5×#53911yescharacteristic
935C22C5×#54011yescharacteristic
936C22C5×#54111yescharacteristic
937C22C5×#54111yescharacteristic
938C22C5×#54211yescharacteristic
939C22C5×D4211yescharacteristic
940C22C5×#54611yescharacteristic
941C22C5×#54611yescharacteristic
942C22C5×#54711yescharacteristic
943C22C5×#54811yescharacteristic
944C22C5×#54811yescharacteristic
945C22C5×#55011yescharacteristic
946C22C5×#55111yescharacteristic
947C22C5×#55211yescharacteristic
948C22C5×#55211yescharacteristic
949C22C5×#55611yescharacteristic
950C22C5×#55911yescharacteristic
951C22C5×#56211yescharacteristic
952C22C5×#56211yescharacteristic
953C22C5×#56311yescharacteristic
954C22C5×#56311yescharacteristic
955C4—24no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—81no—
964C4—81no—
965C4—81no—
966C4—81no—
967C4—81no—
968C4—81no—
969C2—82no—
970C2C5×#242111yescharacteristic
971C2C5×#244511yescharacteristic
972C2C5×#255311yescharacteristic
973C2C5×#262311yescharacteristic
974C2C5×#264911yescharacteristic
975C2C5×#266411yescharacteristic
976C2C5×#267411yescharacteristic
977C2C5×#267611yescharacteristic
978C2C5×#269011yescharacteristic
979C2C5×#269411yescharacteristic
980C2C5×#269611yescharacteristic
981C2C5×#272711yescharacteristic
982C2C5×#277111yescharacteristic
983C2C5×#279811yescharacteristic
984C2C5×#283611yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutator, Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#400C2semidirect
4. C2×C5×#389C2semidirect
5. C5×#1445C2semidirect
6. C5×#1442C2semidirect
7. C5×#1442C2semidirect
8. C5×#1441C2semidirect
9. C5×#1441C2semidirect
15. C5×#1436C2semidirect
55. #16532C5direct (N × H)
136. C2×#400C2×C5semidirect
139. C2×#389C2×C5semidirect
140. #1445C2×C5semidirect
141. #1442C2×C5semidirect
142. #1442C2×C5semidirect
143. #1441C2×C5semidirect
144. #1441C2×C5semidirect
150. #1436C2×C5semidirect
904. C5#16532direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4002
C2×C5×#3992
C2×C5×#3972
C2×C5×#3892
C5×#14452
C5×#14422
C5×#14412
C5×#14402
C5×#14392
C5×#14372
C5×#14362
#165325