Finite Group Databasebeta

← C2×C5×#3524 #11985512

Subgroups — C2×C5×#3524 #11985512

Order 1280.

7226 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3524C2132yesmaximal, direct product factor
2C2×C5×#559C213yesmaximal, complemented
3C2×C5×#557C211yesmaximal, characteristic, complemented
4C2×C5×#555C213yesmaximal, complemented
5C2×C5×#553C213yesmaximal, complemented
6C2×C5×#552C213yesmaximal, complemented
7C2×C5×#550C211yesmaximal, characteristic, complemented
8C2×C5×#548C211yesmaximal, characteristic, complemented
9C2×C5×#548C211yesmaximal, characteristic, complemented
10C2×C5×#542C213yesmaximal, complemented
11C2×C5×#540C213yesmaximal, complemented
12C2×C5×#529C213yesmaximal, complemented
13C2×C5×#529C213yesmaximal, complemented
14C2×C5×#520C211yesmaximal, characteristic, complemented
15C2×C5×#519C211yesmaximal, characteristic, complemented
16C2×C4×C5×#41C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C22×C5×#41C2211yescharacteristic
19C23×C5×Q8C2211yescharacteristic
20C5×#559C22148yescomplemented
21C5×#557C22116yescomplemented
22C5×#555C22148yescomplemented
23C5×#553C22148yescomplemented
24C5×#552C22148yescomplemented
25C5×#550C22116yescomplemented
26C5×#548C22116yescomplemented
27C5×#548C22116yescomplemented
28C5×#542C22148yescomplemented
29C5×#540C22148yescomplemented
30C2×C5×C4⋊Q8C2213yes—
31C2×C5×#127C2213yes—
32C5×#529C22148yescomplemented
33C5×#529C22148yescomplemented
34C2×C5×#126C2211yescharacteristic
35C2×C5×#126C2213yes—
36C2×C5×#126C2216yes—
37C2×C5×#125C2213yes—
38C2×C5×#125C2213yes—
39C2×C5×#125C2213yes—
40C2×C5×#124C2213yes—
41C2×C5×#124C2213yes—
42C2×C5×#124C2213yes—
43C2×C5×#124C2216yes—
44C2×C5×#123C2216yes—
45C2×C5×#123C2213yes—
46C2×C5×#123C2213yes—
47C2×C5×#123C2216yes—
48C2×C5×C22⋊Q8C2213yes—
49C2×C5×C22⋊Q8C2213yes—
50C2×C5×C22⋊Q8C2213yes—
51C2×C5×#121C2213yes—
52C2×C5×#121C2213yes—
53C2×C5×#121C2213yes—
54C2×C5×#121C2213yes—
55C2×C5×#121C2216yes—
56C2×C5×#121C2213yes—
57C5×#520C22116yescomplemented
58C5×#519C22116yescomplemented
59C4×C5×#41C22116yescomplemented
60C2×C4×C5×Q8C2211yescharacteristic
61C2×C4×C5×Q8C2211yescharacteristic
62C2×C4×C5×Q8C2213yes—
63C2×C4×C5×Q8C2211yescharacteristic
64C2×C4×C5×Q8C2213yes—
65C2×C4×C5×Q8C2211yescharacteristic
66C2×C4×C5×Q8C2213yes—
67C2×C4×C5×D4C2213yes—
68C2×C4×C5×D4C2213yes—
69C2×C4×C5×D4C2213yes—
70C2×C4×C5×D4C2213yes—
71C2×C4×C5×D4C2213yes—
72C2×C4×C5×D4C2213yes—
73C2×C4×C5×D4C2213yes—
74C2×C4×C5×D4C2216yes—
75C2×C5×#117C2213yes—
76C2×C5×#117C2213yes—
77C2×C5×#117C2213yes—
78C2×C5×#117C2213yes—
79C2×C5×#117C2216yes—
80C22×C5×C4⋊C4C2213yes—
81C22×C42×C5C2213yes—
82C2×#3524C511yesmaximal, characteristic, direct product factor, Sylow
83C2×C5×#41—28no—
84C2×C5×#41—28no—
85C2×C5×#41C2318yes—
86C2×C5×#41C2318yes—
87C22×C5×Q8—28no—
88C22×C5×Q8C2313yes—
89C22×C5×Q8C2318yes—
90C22×C5×Q8C2313yes—
91C22×C5×Q8C2311yescharacteristic
92C22×C5×D4C2313yes—
93C22×C5×D4C2313yes—
94C22×C5×D4C2313yes—
95C22×C5×D4C2313yes—
96C22×C5×D4C2316yes—
97C22×C5×D4C2313yes—
98C23×C4×C5C2313yes—
99C23×C4×C5C2313yes—
100C23×C4×C5C2313yes—
101C23×C4×C5C2313yes—
102C23×C4×C5C2313yes—
103C23×C4×C5C2316yes—
104C5×C4⋊Q8C23124yes—
105C5×#127C23124yes—
106C5×#126C2318yes—
107C5×#126C23124yes—
108C5×#126C23148yes—
109C5×#125C23124yes—
110C5×#125C23124yes—
111C5×#125C23124yes—
112C5×#124C23124yes—
113C5×#124C23124yes—
114C5×#124C23124yes—
115C5×#124C23148yes—
116C5×#123C23148yes—
117C5×#123C23124yes—
118C5×#123C23124yes—
119C5×#123C23148yes—
120C5×C22⋊Q8C23124yes—
121C5×C22⋊Q8C23124yes—
122C5×C22⋊Q8C23124yes—
123C5×#121C23124yes—
124C5×#121C23124yes—
125C5×#121C23124yes—
126C5×#121C23124yes—
127C5×#121C23148yes—
128C5×#121C23124yes—
129C4×C5×Q8C2318yes—
130C4×C5×Q8C2318yes—
131C4×C5×Q8C23124yes—
132C4×C5×Q8C2318yes—
133C4×C5×Q8C23124yes—
134C4×C5×Q8C2318yes—
135C4×C5×Q8C23124yes—
136C4×C5×D4C23124yes—
137C4×C5×D4C23124yes—
138C4×C5×D4C23124yes—
139C4×C5×D4C23124yes—
140C4×C5×D4C23124yes—
141C4×C5×D4C23124yes—
142C4×C5×D4C23124yes—
143C4×C5×D4C23148yes—
144C5×#117C23124yes—
145C5×#117C23124yes—
146C5×#117C23124yes—
147C5×#117C23124yes—
148C5×#117C23148yes—
149C2×C5×C4⋊C4C2313yes—
150C2×C5×C4⋊C4C2313yes—
151C2×C5×C4⋊C4C2313yes—
152C2×C5×C4⋊C4C23124yes—
153C2×C5×C4⋊C4C2311yescharacteristic
154C2×C5×C4⋊C4C2313yes—
155C2×C5×C4⋊C4C2313yes—
156C2×C5×C4⋊C4C2313yes—
157C2×C5×C4⋊C4C2313yes—
158C2×C5×C4⋊C4C2313yes—
159C2×C5×C4⋊C4C2316yes—
160C2×C5×C4⋊C4C2311yescharacteristic
161C2×C5×C4⋊C4C2313yes—
162C2×C5×C4⋊C4C2313yes—
163C2×C5×C4⋊C4C2311yescharacteristic
164C2×C5×C4⋊C4C2313yes—
165C2×C5×C22⋊C4C2311yescharacteristic
166C2×C5×C22⋊C4C2313yes—
167C2×C5×C22⋊C4C2313yes—
168C2×C5×C22⋊C4C2313yes—
169C2×C5×C22⋊C4C2316yes—
170C2×C5×C22⋊C4C2313yes—
171C2×C5×C22⋊C4C2316yes—
172C2×C5×C22⋊C4C2311yescharacteristic
173C2×C5×C22⋊C4C2313yes—
174C2×C5×C22⋊C4C2311yescharacteristic
175C2×C5×C22⋊C4C2313yes—
176C2×C5×C22⋊C4C2316yes—
177C2×C5×C22⋊C4C2313yes—
178C2×C42×C5C2311yescharacteristic
179C2×C42×C5C2313yes—
180C2×C42×C5C2313yes—
181C2×C42×C5C2313yes—
182C2×C42×C5C23124yes—
183C2×C42×C5C2316yes—
184C2×C42×C5C2313yes—
185C2×C42×C5C2313yes—
186#3524C2×C5132yesdirect product factor
187C2×#559C2×C513yescomplemented
188C2×#557C2×C511yescharacteristic, complemented
189C2×#555C2×C513yescomplemented
190C2×#553C2×C513yescomplemented
191C2×#552C2×C513yescomplemented
192C2×#550C2×C511yescharacteristic, complemented
193C2×#548C2×C511yescharacteristic, complemented
194C2×#548C2×C511yescharacteristic, complemented
195C2×#542C2×C513yescomplemented
196C2×#540C2×C513yescomplemented
197C2×#529C2×C513yescomplemented
198C2×#529C2×C513yescomplemented
199C2×#520C2×C511yescharacteristic, complemented
200C2×#519C2×C511yescharacteristic, complemented
201C2×C4×#41C2×C511yescharacteristic, complemented
202C24×C5C2411yescharacteristic
203C24×C5C2413yes—
204C24×C5C2413yes—
205C5×#41—232no—
206C5×#41—232no—
207C2×C5×Q8—232no—
208C2×C5×Q8—212no—
209C2×C5×Q8—46no—
210C2×C5×Q8#4118yes—
211C2×C5×Q8C24112yes—
212C2×C5×Q8C24112yes—
213C2×C5×Q8C2414yes—
214C2×C5×D4—212no—
215C2×C5×D4—212no—
216C2×C5×D4—46no—
217C2×C5×D4—46no—
218C2×C5×D4—46no—
219C2×C5×D4—412no—
220C2×C5×D4C24112yes—
221C2×C5×D4C24112yes—
222C2×C5×D4C24112yes—
223C2×C5×D4C24112yes—
224C2×C5×D4C24124yes—
225C2×C5×D4C24112yes—
226C22×C4×C5—212no—
227C22×C4×C5—212no—
228C22×C4×C5—212no—
229C22×C4×C5—46no—
230C22×C4×C5—412no—
231C22×C4×C5—46no—
232C22×C4×C5C24112yes—
233C22×C4×C5C24112yes—
234C22×C4×C5C24112yes—
235C22×C4×C5C2411yescharacteristic
236C22×C4×C5C2411yescharacteristic
237C22×C4×C5C2411yescharacteristic
238C22×C4×C5C2413yes—
239C22×C4×C5C2411yescharacteristic
240C22×C4×C5C2413yes—
241C22×C4×C5C2411yescharacteristic
242C22×C4×C5C2413yes—
243C22×C4×C5C2413yes—
244C22×C4×C5C2413yes—
245C22×C4×C5C2411yescharacteristic
246C22×C4×C5C24112yes—
247C22×C4×C5C24112yes—
248C22×C4×C5C24124yes—
249C22×C4×C5C2413yes—
250C5×C4⋊C4C24112yes—
251C5×C4⋊C4C24112yes—
252C5×C4⋊C4C24112yes—
253C5×C4⋊C4C2414yes—
254C5×C4⋊C4C24112yes—
255C5×C4⋊C4C24112yes—
256C5×C4⋊C4C24112yes—
257C5×C4⋊C4C24112yes—
258C5×C4⋊C4C24112yes—
259C5×C4⋊C4C24124yes—
260C5×C4⋊C4C2414yes—
261C5×C4⋊C4C24112yes—
262C5×C4⋊C4C24112yes—
263C5×C4⋊C4C2414yes—
264C5×C4⋊C4C24112yes—
265C5×C22⋊C4C2414yes—
266C5×C22⋊C4C24112yes—
267C5×C22⋊C4C24112yes—
268C5×C22⋊C4C24112yes—
269C5×C22⋊C4C24124yes—
270C5×C22⋊C4C24112yes—
271C5×C22⋊C4C24124yes—
272C5×C22⋊C4C2414yes—
273C5×C22⋊C4C24112yes—
274C5×C22⋊C4C2414yes—
275C5×C22⋊C4C24112yes—
276C5×C22⋊C4C24124yes—
277C5×C22⋊C4C24112yes—
278C42×C5C2414yes—
279C42×C5C24112yes—
280C42×C5C24112yes—
281C42×C5C24112yes—
282C42×C5C24124yes—
283C42×C5C24112yes—
284C42×C5C24112yes—
285C22×#41C22×C511yescharacteristic
286C22×#41C22×C511yescharacteristic
287C23×Q8C22×C511yescharacteristic
288#559C22×C5148yescomplemented
289#557C22×C5116yescomplemented
290#555C22×C5148yescomplemented
291#553C22×C5148yescomplemented
292#552C22×C5148yescomplemented
293#550C22×C5116yescomplemented
294#548C22×C5116yescomplemented
295#548C22×C5116yescomplemented
296#542C22×C5148yescomplemented
297#540C22×C5148yescomplemented
298C2×C4⋊Q8C22×C513yes—
299C2×#127C22×C513yes—
300#529C22×C5148yescomplemented
301#529C22×C5148yescomplemented
302C2×#126C22×C511yescharacteristic
303C2×#126C22×C513yes—
304C2×#126C22×C516yes—
305C2×#125C22×C513yes—
306C2×#125C22×C513yes—
307C2×#125C22×C513yes—
308C2×#124C22×C513yes—
309C2×#124C22×C513yes—
310C2×#124C22×C513yes—
311C2×#124C22×C516yes—
312C2×#123C22×C516yes—
313C2×#123C22×C513yes—
314C2×#123C22×C513yes—
315C2×#123C22×C516yes—
316C2×C22⋊Q8C22×C513yes—
317C2×C22⋊Q8C22×C513yes—
318C2×C22⋊Q8C22×C513yes—
319C2×#121C22×C513yes—
320C2×#121C22×C513yes—
321C2×#121C22×C513yes—
322C2×#121C22×C513yes—
323C2×#121C22×C516yes—
324C2×#121C22×C513yes—
325#520C22×C5116yescomplemented
326#519C22×C5116yescomplemented
327C4×#41C22×C5116yescomplemented
328C2×C4×Q8C22×C511yescharacteristic
329C2×C4×Q8C22×C511yescharacteristic
330C2×C4×Q8C22×C513yes—
331C2×C4×Q8C22×C511yescharacteristic
332C2×C4×Q8C22×C513yes—
333C2×C4×Q8C22×C511yescharacteristic
334C2×C4×Q8C22×C513yes—
335C2×C4×D4C22×C513yes—
336C2×C4×D4C22×C513yes—
337C2×C4×D4C22×C513yes—
338C2×C4×D4C22×C513yes—
339C2×C4×D4C22×C513yes—
340C2×C4×D4C22×C513yes—
341C2×C4×D4C22×C513yes—
342C2×C4×D4C22×C516yes—
343C2×#117C22×C513yes—
344C2×#117C22×C513yes—
345C2×#117C22×C513yes—
346C2×#117C22×C513yes—
347C2×#117C22×C516yes—
348C22×C4⋊C4C22×C513yes—
349C22×C42C22×C513yes—
350C23×C5—22no—
351C23×C5—26no—
352C23×C5—26no—
353C23×C5—26no—
354C23×C5—26no—
355C23×C5—26no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—26no—
359C23×C5C2512yes—
360C23×C5C2516yes—
361C23×C5C2516yes—
362C23×C5C2511yescharacteristic
363C5×Q8—224no—
364C5×Q8—412no—
365C5×Q8C2×#41116yes—
366C5×D4—224no—
367C5×D4—224no—
368C5×D4—412no—
369C5×D4—412no—
370C5×D4—412no—
371C5×D4—424no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—26no—
375C2×C4×C5—22no—
376C2×C4×C5—26no—
377C2×C4×C5—22no—
378C2×C4×C5—26no—
379C2×C4×C5—26no—
380C2×C4×C5—22no—
381C2×C4×C5—26no—
382C2×C4×C5—22no—
383C2×C4×C5—224no—
384C2×C4×C5—224no—
385C2×C4×C5—224no—
386C2×C4×C5—412no—
387C2×C4×C5—424no—
388C2×C4×C5—412no—
389C2×C4×C5C2×#41112yes—
390C2×C4×C5C2512yes—
391C2×C4×C5C2512yes—
392C2×C4×C5C2512yes—
393C2×C4×C5C2516yes—
394C2×C4×C5C2512yes—
395C2×C4×C5C2516yes—
396C2×C4×C5C2512yes—
397C2×C4×C5C2516yes—
398C2×C4×C5C2516yes—
399C2×C4×C5C2516yes—
400C2×C4×C5C2512yes—
401C2×C4×C5C2516yes—
402C2×#41—28no—
403C2×#41—28no—
404C2×#41C23×C518yes—
405C2×#41C23×C518yes—
406C22×Q8—28no—
407C22×Q8C23×C513yes—
408C22×Q8C23×C518yes—
409C22×Q8C23×C513yes—
410C22×Q8C23×C511yescharacteristic
411C22×D4C23×C513yes—
412C22×D4C23×C513yes—
413C22×D4C23×C513yes—
414C22×D4C23×C513yes—
415C22×D4C23×C516yes—
416C22×D4C23×C513yes—
417C23×C4C23×C513yes—
418C23×C4C23×C513yes—
419C23×C4C23×C513yes—
420C23×C4C23×C516yes—
421C23×C4C23×C513yes—
422C23×C4C23×C513yes—
423C4⋊Q8C23×C5124yes—
424#127C23×C5124yes—
425#126C23×C518yes—
426#126C23×C5124yes—
427#126C23×C5148yes—
428#125C23×C5124yes—
429#125C23×C5124yes—
430#125C23×C5124yes—
431#124C23×C5124yes—
432#124C23×C5124yes—
433#124C23×C5124yes—
434#124C23×C5148yes—
435#123C23×C5148yes—
436#123C23×C5124yes—
437#123C23×C5124yes—
438#123C23×C5148yes—
439C22⋊Q8C23×C5124yes—
440C22⋊Q8C23×C5124yes—
441C22⋊Q8C23×C5124yes—
442#121C23×C5124yes—
443#121C23×C5124yes—
444#121C23×C5124yes—
445#121C23×C5124yes—
446#121C23×C5148yes—
447#121C23×C5124yes—
448C4×Q8C23×C518yes—
449C4×Q8C23×C518yes—
450C4×Q8C23×C5124yes—
451C4×Q8C23×C518yes—
452C4×Q8C23×C5124yes—
453C4×Q8C23×C518yes—
454C4×Q8C23×C5124yes—
455C4×D4C23×C5124yes—
456C4×D4C23×C5124yes—
457C4×D4C23×C5124yes—
458C4×D4C23×C5124yes—
459C4×D4C23×C5124yes—
460C4×D4C23×C5124yes—
461C4×D4C23×C5124yes—
462C4×D4C23×C5148yes—
463#117C23×C5124yes—
464#117C23×C5124yes—
465#117C23×C5124yes—
466#117C23×C5124yes—
467#117C23×C5148yes—
468C2×C4⋊C4C23×C513yes—
469C2×C4⋊C4C23×C513yes—
470C2×C4⋊C4C23×C513yes—
471C2×C4⋊C4C23×C5124yes—
472C2×C4⋊C4C23×C511yescharacteristic
473C2×C4⋊C4C23×C513yes—
474C2×C4⋊C4C23×C513yes—
475C2×C4⋊C4C23×C513yes—
476C2×C4⋊C4C23×C513yes—
477C2×C4⋊C4C23×C513yes—
478C2×C4⋊C4C23×C516yes—
479C2×C4⋊C4C23×C511yescharacteristic
480C2×C4⋊C4C23×C513yes—
481C2×C4⋊C4C23×C513yes—
482C2×C4⋊C4C23×C511yescharacteristic
483C2×C4⋊C4C23×C513yes—
484C2×C22⋊C4C23×C511yescharacteristic
485C2×C22⋊C4C23×C513yes—
486C2×C22⋊C4C23×C513yes—
487C2×C22⋊C4C23×C513yes—
488C2×C22⋊C4C23×C516yes—
489C2×C22⋊C4C23×C513yes—
490C2×C22⋊C4C23×C516yes—
491C2×C22⋊C4C23×C511yescharacteristic
492C2×C22⋊C4C23×C513yes—
493C2×C22⋊C4C23×C511yescharacteristic
494C2×C22⋊C4C23×C513yes—
495C2×C22⋊C4C23×C516yes—
496C2×C22⋊C4C23×C513yes—
497C2×C42C23×C513yes—
498C2×C42C23×C513yes—
499C2×C42C23×C516yes—
500C2×C42C23×C513yes—
501C2×C42C23×C513yes—
502C2×C42C23×C513yes—
503C2×C42C23×C5124yes—
504C2×C42C23×C511yescharacteristic
505C22×C5—22no—
506C22×C5—26no—
507C22×C5—26no—
508C22×C5—26no—
509C22×C5—26no—
510C22×C5—26no—
511C22×C5—22no—
512C22×C5—22no—
513C22×C5—26no—
514C22×C5—44no—
515C22×C5—412no—
516C22×C5—412no—
517C22×C5C22×#4112yes—
518C22×C5#58512yes—
519C22×C5#58512yes—
520C22×C5C2611yescharacteristic
521C4×C5—22no—
522C4×C5—22no—
523C4×C5—26no—
524C4×C5—22no—
525C4×C5—26no—
526C4×C5—22no—
527C4×C5—26no—
528C4×C5—26no—
529C4×C5—22no—
530C4×C5—26no—
531C4×C5—22no—
532C4×C5C22×#41112yes—
533C24C24×C511yescharacteristic
534C24C24×C513yes—
535C24C24×C513yes—
536#41—232no—
537#41—232no—
538C2×Q8—232no—
539C2×Q8—212no—
540C2×Q8—46no—
541C2×Q8C5×#4118yes—
542C2×Q8C24×C5112yes—
543C2×Q8C24×C5112yes—
544C2×Q8C24×C514yes—
545C2×D4—212no—
546C2×D4—212no—
547C2×D4—46no—
548C2×D4—46no—
549C2×D4—46no—
550C2×D4—412no—
551C2×D4C24×C5112yes—
552C2×D4C24×C5112yes—
553C2×D4C24×C5112yes—
554C2×D4C24×C5112yes—
555C2×D4C24×C5124yes—
556C2×D4C24×C5112yes—
557C22×C4—212no—
558C22×C4—212no—
559C22×C4—212no—
560C22×C4—46no—
561C22×C4—412no—
562C22×C4—46no—
563C22×C4C24×C511yescharacteristic
564C22×C4C24×C513yes—
565C22×C4C24×C511yescharacteristic
566C22×C4C24×C511yescharacteristic
567C22×C4C24×C511yescharacteristic
568C22×C4C24×C513yes—
569C22×C4C24×C511yescharacteristic
570C22×C4C24×C513yes—
571C22×C4C24×C513yes—
572C22×C4C24×C5112yes—
573C22×C4C24×C513yes—
574C22×C4C24×C511yescharacteristic
575C22×C4C24×C5112yes—
576C22×C4C24×C5112yes—
577C22×C4C24×C5112yes—
578C22×C4C24×C5112yes—
579C22×C4C24×C5124yes—
580C22×C4C24×C513yes—
581C4⋊C4C24×C5112yes—
582C4⋊C4C24×C5112yes—
583C4⋊C4C24×C5112yes—
584C4⋊C4C24×C514yes—
585C4⋊C4C24×C5112yes—
586C4⋊C4C24×C5112yes—
587C4⋊C4C24×C5112yes—
588C4⋊C4C24×C5112yes—
589C4⋊C4C24×C5112yes—
590C4⋊C4C24×C5124yes—
591C4⋊C4C24×C514yes—
592C4⋊C4C24×C5112yes—
593C4⋊C4C24×C5112yes—
594C4⋊C4C24×C514yes—
595C4⋊C4C24×C5112yes—
596C22⋊C4C24×C514yes—
597C22⋊C4C24×C5112yes—
598C22⋊C4C24×C5112yes—
599C22⋊C4C24×C5112yes—
600C22⋊C4C24×C5124yes—
601C22⋊C4C24×C5112yes—
602C22⋊C4C24×C5124yes—
603C22⋊C4C24×C514yes—
604C22⋊C4C24×C5112yes—
605C22⋊C4C24×C514yes—
606C22⋊C4C24×C5112yes—
607C22⋊C4C24×C5124yes—
608C22⋊C4C24×C5112yes—
609C42C24×C514yes—
610C42C24×C5112yes—
611C42C24×C5112yes—
612C42C24×C5112yes—
613C42C24×C5124yes—
614C42C24×C5112yes—
615C42C24×C5112yes—
616C2×C5—42no—
617C2×C5—46no—
618C2×C5—46no—
619C2×C5#352414yesdirect product factor
620C2×C5C23×#4111yescharacteristic
621C2×C5C2×#58511yescharacteristic
622C2×C5C2×#58511yescharacteristic
623C23—22no—
624C23—26no—
625C23—26no—
626C23—26no—
627C23—26no—
628C23—26no—
629C23—22no—
630C23—22no—
631C23—26no—
632C23C25×C512yes—
633C23C25×C516yes—
634C23C25×C516yes—
635C23C25×C511yescharacteristic
636Q8—224no—
637Q8—412no—
638Q8C2×C5×#41116yes—
639D4—224no—
640D4—224no—
641D4—412no—
642D4—412no—
643D4—412no—
644D4—424no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—26no—
648C2×C4—22no—
649C2×C4—26no—
650C2×C4—22no—
651C2×C4—26no—
652C2×C4—26no—
653C2×C4—22no—
654C2×C4—26no—
655C2×C4—22no—
656C2×C4—224no—
657C2×C4—224no—
658C2×C4—224no—
659C2×C4—412no—
660C2×C4—424no—
661C2×C4—412no—
662C2×C4C2×C5×#41112yes—
663C2×C4C25×C512yes—
664C2×C4C25×C512yes—
665C2×C4C25×C512yes—
666C2×C4C25×C516yes—
667C2×C4C25×C512yes—
668C2×C4C25×C516yes—
669C2×C4C25×C512yes—
670C2×C4C25×C516yes—
671C2×C4C25×C516yes—
672C2×C4C25×C516yes—
673C2×C4C25×C512yes—
674C2×C4C25×C516yes—
675C5C2×#352411yescharacteristic, direct product factor, Sylow
676C22—22no—
677C22—26no—
678C22—26no—
679C22—26no—
680C22—26no—
681C22—26no—
682C22—22no—
683C22—22no—
684C22—26no—
685C22—44no—
686C22—412no—
687C22—412no—
688C22C22×C5×#4112yes—
689C22C5×#58512yes—
690C22C5×#58512yes—
691C22C26×C511yescharacteristic
692C4—22no—
693C4—22no—
694C4—26no—
695C4—22no—
696C4—26no—
697C4—22no—
698C4—26no—
699C4—26no—
700C4—22no—
701C4—26no—
702C4—22no—
703C4C22×C5×#41112yes—
704C2—42no—
705C2—46no—
706C2—46no—
707C2C5×#352414yesdirect product factor
708C2C23×C5×#4111yescharacteristic
709C2C2×C5×#58511yescharacteristic
710C2C2×C5×#58511yescharacteristic
subgroupG/H
center, socleC23×C5C25
commutator, Frattini, cosocleC22C26×C5
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3524C2direct (N × H)
2. C2×C5×#559C2semidirect
3. C2×C5×#557C2semidirect
4. C2×C5×#555C2semidirect
5. C2×C5×#553C2semidirect
6. C2×C5×#552C2semidirect
7. C2×C5×#550C2semidirect
8. C2×C5×#548C2semidirect
9. C2×C5×#548C2semidirect
10. C2×C5×#542C2semidirect
11. C2×C5×#540C2semidirect
12. C2×C5×#529C2semidirect
13. C2×C5×#529C2semidirect
14. C2×C5×#520C2semidirect
15. C2×C5×#519C2semidirect
16. C2×C4×C5×#41C2semidirect
20. C5×#559C22semidirect
21. C5×#557C22semidirect
22. C5×#555C22semidirect
23. C5×#553C22semidirect
24. C5×#552C22semidirect
25. C5×#550C22semidirect
26. C5×#548C22semidirect
27. C5×#548C22semidirect
28. C5×#542C22semidirect
29. C5×#540C22semidirect
32. C5×#529C22semidirect
33. C5×#529C22semidirect
57. C5×#520C22semidirect
58. C5×#519C22semidirect
59. C4×C5×#41C22semidirect
82. C2×#3524C5direct (N × H)
186. #3524C2×C5direct (N × H)
187. C2×#559C2×C5semidirect
188. C2×#557C2×C5semidirect
189. C2×#555C2×C5semidirect
190. C2×#553C2×C5semidirect
191. C2×#552C2×C5semidirect
192. C2×#550C2×C5semidirect
193. C2×#548C2×C5semidirect
194. C2×#548C2×C5semidirect
195. C2×#542C2×C5semidirect
196. C2×#540C2×C5semidirect
197. C2×#529C2×C5semidirect
198. C2×#529C2×C5semidirect
199. C2×#520C2×C5semidirect
200. C2×#519C2×C5semidirect
201. C2×C4×#41C2×C5semidirect
288. #559C22×C5semidirect
289. #557C22×C5semidirect
290. #555C22×C5semidirect
291. #553C22×C5semidirect
292. #552C22×C5semidirect
293. #550C22×C5semidirect
294. #548C22×C5semidirect
295. #548C22×C5semidirect
296. #542C22×C5semidirect
297. #540C22×C5semidirect
300. #529C22×C5semidirect
301. #529C22×C5semidirect
325. #520C22×C5semidirect
326. #519C22×C5semidirect
327. C4×#41C22×C5semidirect
619. C2×C5#3524direct (N × H)
675. C5C2×#3524direct (N × H)
707. C2C5×#3524direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35242
C2×C5×#5592
C2×C5×#5572
C2×C5×#5552
C2×C5×#5532
C2×C5×#5522
C2×C5×#5502
C2×C5×#5482
C2×C5×#5422
C2×C5×#5402
C2×C5×#5292
C2×C5×#5202
C2×C5×#5192
C2×C4×C5×#412
C2×#35245