Finite Group Databasebeta

← C2×C5×#3516 #11985505

Subgroups — C2×C5×#3516 #11985505

Order 1280.

7130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3516C2132yesmaximal, direct product factor
2C2×C5×#557C211yesmaximal, characteristic, complemented
3C2×C5×#556C213yesmaximal, complemented
4C2×C5×#554C213yesmaximal, complemented
5C2×C5×#553C213yesmaximal, complemented
6C2×C5×#552C213yesmaximal, complemented
7C2×C5×D4×Q8C211yesmaximal, characteristic, complemented
8C2×C5×#548C211yesmaximal, characteristic, complemented
9C2×C5×#548C211yesmaximal, characteristic, complemented
10C2×C5×#542C213yesmaximal, complemented
11C2×C5×#541C213yesmaximal, complemented
12C2×C5×#529C213yesmaximal, complemented
13C2×C5×#529C213yesmaximal, complemented
14C2×C5×#520C211yesmaximal, characteristic, complemented
15C2×C5×#519C211yesmaximal, characteristic, complemented
16C22×C4×C5×Q8C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C23×C5×Q8C2211yescharacteristic
19C23×C5×Q8C2211yescharacteristic
20C5×#557C22116yescomplemented
21C5×#556C22148yescomplemented
22C5×#554C22148yescomplemented
23C5×#553C22148yescomplemented
24C5×#552C22148yescomplemented
25C5×D4×Q8C22116yescomplemented
26C5×#548C22116yescomplemented
27C5×#548C22116yescomplemented
28C5×#542C22148yescomplemented
29C5×#541C22148yescomplemented
30C2×C5×C4⋊Q8C2213yes—
31C2×C5×C4⋊Q8C2213yes—
32C5×#529C22148yescomplemented
33C5×#529C22148yescomplemented
34C2×C5×#126C2216yes—
35C2×C5×#126C2213yes—
36C2×C5×#126C2213yes—
37C2×C5×#126C2216yes—
38C2×C5×#125C2213yes—
39C2×C5×#125C2213yes—
40C2×C5×#125C2216yes—
41C2×C5×#125C2213yes—
42C2×C5×#124C2213yes—
43C2×C5×#124C2213yes—
44C2×C5×#124C2213yes—
45C2×C5×#123C2211yescharacteristic
46C2×C5×#123C2213yes—
47C2×C5×#123C2216yes—
48C2×C5×C22⋊Q8C2213yes—
49C2×C5×C22⋊Q8C2213yes—
50C2×C5×C22⋊Q8C2213yes—
51C2×C5×C22⋊Q8C2213yes—
52C2×C5×C22⋊Q8C2213yes—
53C2×C5×C22⋊Q8C2216yes—
54C2×C5×#121C2213yes—
55C2×C5×#121C2213yes—
56C2×C5×#121C2213yes—
57C5×#520C22116yescomplemented
58C5×#519C22116yescomplemented
59C2×C4×C5×Q8C2211yescharacteristic
60C2×C4×C5×Q8C2213yes—
61C2×C4×C5×Q8C2211yescharacteristic
62C2×C4×C5×Q8C2213yes—
63C2×C4×C5×Q8C2213yes—
64C2×C4×C5×Q8C2211yescharacteristic
65C2×C4×C5×Q8C2213yes—
66C2×C4×C5×Q8C2211yescharacteristic
67C2×C4×C5×Q8C2213yes—
68C2×C4×C5×Q8C22116yescomplemented
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×#117C2216yes—
79C22×C5×C4⋊C4C2213yes—
80C22×C5×C4⋊C4C2213yes—
81C22×C42×C5C2213yes—
82C2×#3516C511yesmaximal, characteristic, direct product factor, Sylow
83C2×C5×#41—28no—
84C2×C5×#41C2318yes—
85C22×C5×Q8—28no—
86C22×C5×Q8—28no—
87C22×C5×Q8C2313yes—
88C22×C5×Q8C2313yes—
89C22×C5×Q8C2318yes—
90C22×C5×Q8C2318yes—
91C22×C5×Q8C2313yes—
92C22×C5×Q8C2311yescharacteristic
93C22×C5×D4C2313yes—
94C22×C5×D4C2311yescharacteristic
95C22×C5×D4C2313yes—
96C22×C5×D4C2313yes—
97C23×C4×C5C2311yescharacteristic
98C23×C4×C5C2313yes—
99C23×C4×C5C2313yes—
100C23×C4×C5C2313yes—
101C23×C4×C5C2313yes—
102C23×C4×C5C2316yes—
103C5×C4⋊Q8C23124yes—
104C5×C4⋊Q8C23124yes—
105C5×#126C23148yes—
106C5×#126C23124yes—
107C5×#126C23124yes—
108C5×#126C23148yes—
109C5×#125C23124yes—
110C5×#125C23124yes—
111C5×#125C23148yes—
112C5×#125C23124yes—
113C5×#124C23124yes—
114C5×#124C23124yes—
115C5×#124C23124yes—
116C5×#123C2318yes—
117C5×#123C23124yes—
118C5×#123C23148yes—
119C5×C22⋊Q8C23124yes—
120C5×C22⋊Q8C23124yes—
121C5×C22⋊Q8C23124yes—
122C5×C22⋊Q8C23124yes—
123C5×C22⋊Q8C23124yes—
124C5×C22⋊Q8C23148yes—
125C5×#121C23124yes—
126C5×#121C23124yes—
127C5×#121C23124yes—
128C4×C5×Q8C2318yes—
129C4×C5×Q8C23124yes—
130C4×C5×Q8C2318yes—
131C4×C5×Q8C23124yes—
132C4×C5×Q8C23124yes—
133C4×C5×Q8C2318yes—
134C4×C5×Q8C23124yes—
135C4×C5×Q8C2318yes—
136C4×C5×Q8C23124yes—
137C4×C5×D4C23124yes—
138C4×C5×D4C23124yes—
139C4×C5×D4C23124yes—
140C4×C5×D4C23124yes—
141C4×C5×D4C23124yes—
142C4×C5×D4C23148yes—
143C5×#117C23124yes—
144C5×#117C23124yes—
145C5×#117C23124yes—
146C5×#117C23148yes—
147C2×C5×C4⋊C4C2313yes—
148C2×C5×C4⋊C4C2313yes—
149C2×C5×C4⋊C4C2313yes—
150C2×C5×C4⋊C4C2313yes—
151C2×C5×C4⋊C4C2316yes—
152C2×C5×C4⋊C4C23124yes—
153C2×C5×C4⋊C4C23124yes—
154C2×C5×C4⋊C4C2311yescharacteristic
155C2×C5×C4⋊C4C2313yes—
156C2×C5×C4⋊C4C2313yes—
157C2×C5×C4⋊C4C2313yes—
158C2×C5×C4⋊C4C2313yes—
159C2×C5×C4⋊C4C2316yes—
160C2×C5×C4⋊C4C2313yes—
161C2×C5×C4⋊C4C2313yes—
162C2×C5×C4⋊C4C2316yes—
163C2×C5×C4⋊C4C2313yes—
164C2×C5×C4⋊C4C2311yescharacteristic
165C2×C5×C4⋊C4C2313yes—
166C2×C5×C22⋊C4C2313yes—
167C2×C5×C22⋊C4C2311yescharacteristic
168C2×C5×C22⋊C4C2313yes—
169C2×C5×C22⋊C4C2313yes—
170C2×C5×C22⋊C4C2313yes—
171C2×C5×C22⋊C4C2316yes—
172C2×C5×C22⋊C4C2311yescharacteristic
173C2×C5×C22⋊C4C2313yes—
174C2×C5×C22⋊C4C2311yescharacteristic
175C2×C5×C22⋊C4C2316yes—
176C2×C5×C22⋊C4C2313yes—
177C2×C5×C22⋊C4C2313yes—
178C2×C42×C5C2313yes—
179C2×C42×C5C2313yes—
180C2×C42×C5C2313yes—
181C2×C42×C5C2313yes—
182C2×C42×C5C23124yes—
183C2×C42×C5C2316yes—
184C2×C42×C5C2313yes—
185C2×C42×C5C2313yes—
186#3516C2×C5132yesdirect product factor
187C2×#557C2×C511yescharacteristic, complemented
188C2×#556C2×C513yescomplemented
189C2×#554C2×C513yescomplemented
190C2×#553C2×C513yescomplemented
191C2×#552C2×C513yescomplemented
192C2×D4×Q8C2×C511yescharacteristic, complemented
193C2×#548C2×C511yescharacteristic, complemented
194C2×#548C2×C511yescharacteristic, complemented
195C2×#542C2×C513yescomplemented
196C2×#541C2×C513yescomplemented
197C2×#529C2×C513yescomplemented
198C2×#529C2×C513yescomplemented
199C2×#520C2×C511yescharacteristic, complemented
200C2×#519C2×C511yescharacteristic, complemented
201C22×C4×Q8C2×C511yescharacteristic, complemented
202C24×C5C2411yescharacteristic
203C24×C5C2413yes—
204C24×C5C2411yescharacteristic
205C5×#41—232no—
206C2×C5×Q8—232no—
207C2×C5×Q8—232no—
208C2×C5×Q8—212no—
209C2×C5×Q8—212no—
210C2×C5×Q8—46no—
211C2×C5×Q8#4118yes—
212C2×C5×Q8C24112yes—
213C2×C5×Q8C24112yes—
214C2×C5×Q8C24112yes—
215C2×C5×Q8C2414yes—
216C2×C5×D4—212no—
217C2×C5×D4—24no—
218C2×C5×D4—212no—
219C2×C5×D4—46no—
220C2×C5×D4C24112yes—
221C2×C5×D4C2414yes—
222C2×C5×D4C24112yes—
223C2×C5×D4C24112yes—
224C22×C4×C5—24no—
225C22×C4×C5—212no—
226C22×C4×C5—212no—
227C22×C4×C5—212no—
228C22×C4×C5—412no—
229C22×C4×C5—46no—
230C22×C4×C5C2414yes—
231C22×C4×C5C24112yes—
232C22×C4×C5C24112yes—
233C22×C4×C5C24112yes—
234C22×C4×C5C2411yescharacteristic
235C22×C4×C5C2411yescharacteristic
236C22×C4×C5C2413yes—
237C22×C4×C5C2411yescharacteristic
238C22×C4×C5C2413yes—
239C22×C4×C5C2411yescharacteristic
240C22×C4×C5C2413yes—
241C22×C4×C5C2413yes—
242C22×C4×C5C2413yes—
243C22×C4×C5C2413yes—
244C22×C4×C5C2411yescharacteristic
245C22×C4×C5C24112yes—
246C22×C4×C5C24124yes—
247C22×C4×C5C2413yes—
248C5×C4⋊C4C24112yes—
249C5×C4⋊C4C24112yes—
250C5×C4⋊C4C24112yes—
251C5×C4⋊C4C24112yes—
252C5×C4⋊C4C24124yes—
253C5×C4⋊C4C2414yes—
254C5×C4⋊C4C24112yes—
255C5×C4⋊C4C24112yes—
256C5×C4⋊C4C24112yes—
257C5×C4⋊C4C24112yes—
258C5×C4⋊C4C24124yes—
259C5×C4⋊C4C24112yes—
260C5×C4⋊C4C24112yes—
261C5×C4⋊C4C24124yes—
262C5×C4⋊C4C24112yes—
263C5×C4⋊C4C2414yes—
264C5×C4⋊C4C24112yes—
265C5×C22⋊C4C24112yes—
266C5×C22⋊C4C2414yes—
267C5×C22⋊C4C24112yes—
268C5×C22⋊C4C24112yes—
269C5×C22⋊C4C24112yes—
270C5×C22⋊C4C24124yes—
271C5×C22⋊C4C2414yes—
272C5×C22⋊C4C24112yes—
273C5×C22⋊C4C2414yes—
274C5×C22⋊C4C24124yes—
275C5×C22⋊C4C24112yes—
276C5×C22⋊C4C24112yes—
277C42×C5C24112yes—
278C42×C5C24112yes—
279C42×C5C24112yes—
280C42×C5C24112yes—
281C42×C5C24124yes—
282C42×C5C24112yes—
283C42×C5C24112yes—
284C22×#41C22×C511yescharacteristic
285C23×Q8C22×C511yescharacteristic
286C23×Q8C22×C511yescharacteristic
287#557C22×C5116yescomplemented
288#556C22×C5148yescomplemented
289#554C22×C5148yescomplemented
290#553C22×C5148yescomplemented
291#552C22×C5148yescomplemented
292D4×Q8C22×C5116yescomplemented
293#548C22×C5116yescomplemented
294#548C22×C5116yescomplemented
295#542C22×C5148yescomplemented
296#541C22×C5148yescomplemented
297C2×C4⋊Q8C22×C513yes—
298C2×C4⋊Q8C22×C513yes—
299#529C22×C5148yescomplemented
300#529C22×C5148yescomplemented
301C2×#126C22×C516yes—
302C2×#126C22×C513yes—
303C2×#126C22×C513yes—
304C2×#126C22×C516yes—
305C2×#125C22×C513yes—
306C2×#125C22×C513yes—
307C2×#125C22×C516yes—
308C2×#125C22×C513yes—
309C2×#124C22×C513yes—
310C2×#124C22×C513yes—
311C2×#124C22×C513yes—
312C2×#123C22×C511yescharacteristic
313C2×#123C22×C513yes—
314C2×#123C22×C516yes—
315C2×C22⋊Q8C22×C513yes—
316C2×C22⋊Q8C22×C513yes—
317C2×C22⋊Q8C22×C513yes—
318C2×C22⋊Q8C22×C513yes—
319C2×C22⋊Q8C22×C513yes—
320C2×C22⋊Q8C22×C516yes—
321C2×#121C22×C513yes—
322C2×#121C22×C513yes—
323C2×#121C22×C513yes—
324#520C22×C5116yescomplemented
325#519C22×C5116yescomplemented
326C2×C4×Q8C22×C511yescharacteristic
327C2×C4×Q8C22×C513yes—
328C2×C4×Q8C22×C511yescharacteristic
329C2×C4×Q8C22×C513yes—
330C2×C4×Q8C22×C513yes—
331C2×C4×Q8C22×C511yescharacteristic
332C2×C4×Q8C22×C513yes—
333C2×C4×Q8C22×C511yescharacteristic
334C2×C4×Q8C22×C513yes—
335C2×C4×Q8C22×C5116yescomplemented
336C2×C4×D4C22×C513yes—
337C2×C4×D4C22×C513yes—
338C2×C4×D4C22×C513yes—
339C2×C4×D4C22×C513yes—
340C2×C4×D4C22×C513yes—
341C2×C4×D4C22×C516yes—
342C2×#117C22×C513yes—
343C2×#117C22×C513yes—
344C2×#117C22×C513yes—
345C2×#117C22×C516yes—
346C22×C4⋊C4C22×C513yes—
347C22×C4⋊C4C22×C513yes—
348C22×C42C22×C513yes—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—26no—
353C23×C5—22no—
354C23×C5—26no—
355C23×C5—26no—
356C23×C5—22no—
357C23×C52−1+414yes—
358C23×C5C2512yes—
359C23×C5C2516yes—
360C23×C5C2512yes—
361C23×C5C2511yescharacteristic
362C5×Q8—224no—
363C5×Q8—224no—
364C5×Q8—412no—
365C5×Q8C2×#41116yes—
366C5×D4—224no—
367C5×D4—28no—
368C5×D4—224no—
369C5×D4—412no—
370C2×C4×C5—22no—
371C2×C4×C5—26no—
372C2×C4×C5—26no—
373C2×C4×C5—28no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—26no—
377C2×C4×C5—22no—
378C2×C4×C5—26no—
379C2×C4×C5—26no—
380C2×C4×C5—26no—
381C2×C4×C5—22no—
382C2×C4×C5—224no—
383C2×C4×C5—224no—
384C2×C4×C5—224no—
385C2×C4×C5—424no—
386C2×C4×C5—412no—
387C2×C4×C5C2×#41112yes—
388C2×C4×C5C2512yes—
389C2×C4×C5C2512yes—
390C2×C4×C5C2516yes—
391C2×C4×C5C2512yes—
392C2×C4×C5C2516yes—
393C2×C4×C5C2512yes—
394C2×C4×C5C2516yes—
395C2×C4×C5C2516yes—
396C2×C4×C5C2516yes—
397C2×C4×C5C2516yes—
398C2×C4×C5C2512yes—
399C2×C4×C5C2516yes—
400C2×#41—28no—
401C2×#41C23×C518yes—
402C22×Q8—28no—
403C22×Q8—28no—
404C22×Q8C23×C513yes—
405C22×Q8C23×C513yes—
406C22×Q8C23×C518yes—
407C22×Q8C23×C518yes—
408C22×Q8C23×C513yes—
409C22×Q8C23×C511yescharacteristic
410C22×D4C23×C513yes—
411C22×D4C23×C511yescharacteristic
412C22×D4C23×C513yes—
413C22×D4C23×C513yes—
414C23×C4C23×C513yes—
415C23×C4C23×C513yes—
416C23×C4C23×C513yes—
417C23×C4C23×C511yescharacteristic
418C23×C4C23×C513yes—
419C23×C4C23×C516yes—
420C4⋊Q8C23×C5124yes—
421C4⋊Q8C23×C5124yes—
422#126C23×C5148yes—
423#126C23×C5124yes—
424#126C23×C5124yes—
425#126C23×C5148yes—
426#125C23×C5124yes—
427#125C23×C5124yes—
428#125C23×C5148yes—
429#125C23×C5124yes—
430#124C23×C5124yes—
431#124C23×C5124yes—
432#124C23×C5124yes—
433#123C23×C518yes—
434#123C23×C5124yes—
435#123C23×C5148yes—
436C22⋊Q8C23×C5124yes—
437C22⋊Q8C23×C5124yes—
438C22⋊Q8C23×C5124yes—
439C22⋊Q8C23×C5124yes—
440C22⋊Q8C23×C5124yes—
441C22⋊Q8C23×C5148yes—
442#121C23×C5124yes—
443#121C23×C5124yes—
444#121C23×C5124yes—
445C4×Q8C23×C518yes—
446C4×Q8C23×C5124yes—
447C4×Q8C23×C518yes—
448C4×Q8C23×C5124yes—
449C4×Q8C23×C5124yes—
450C4×Q8C23×C518yes—
451C4×Q8C23×C5124yes—
452C4×Q8C23×C518yes—
453C4×Q8C23×C5124yes—
454C4×D4C23×C5124yes—
455C4×D4C23×C5124yes—
456C4×D4C23×C5124yes—
457C4×D4C23×C5124yes—
458C4×D4C23×C5124yes—
459C4×D4C23×C5148yes—
460#117C23×C5124yes—
461#117C23×C5124yes—
462#117C23×C5124yes—
463#117C23×C5148yes—
464C2×C4⋊C4C23×C513yes—
465C2×C4⋊C4C23×C513yes—
466C2×C4⋊C4C23×C513yes—
467C2×C4⋊C4C23×C513yes—
468C2×C4⋊C4C23×C516yes—
469C2×C4⋊C4C23×C5124yes—
470C2×C4⋊C4C23×C5124yes—
471C2×C4⋊C4C23×C511yescharacteristic
472C2×C4⋊C4C23×C513yes—
473C2×C4⋊C4C23×C513yes—
474C2×C4⋊C4C23×C513yes—
475C2×C4⋊C4C23×C513yes—
476C2×C4⋊C4C23×C516yes—
477C2×C4⋊C4C23×C513yes—
478C2×C4⋊C4C23×C513yes—
479C2×C4⋊C4C23×C516yes—
480C2×C4⋊C4C23×C513yes—
481C2×C4⋊C4C23×C511yescharacteristic
482C2×C4⋊C4C23×C513yes—
483C2×C22⋊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×C511yescharacteristic
490C2×C22⋊C4C23×C513yes—
491C2×C22⋊C4C23×C511yescharacteristic
492C2×C22⋊C4C23×C516yes—
493C2×C22⋊C4C23×C513yes—
494C2×C22⋊C4C23×C513yes—
495C2×C42C23×C513yes—
496C2×C42C23×C516yes—
497C2×C42C23×C513yes—
498C2×C42C23×C513yes—
499C2×C42C23×C513yes—
500C2×C42C23×C513yes—
501C2×C42C23×C513yes—
502C2×C42C23×C5124yes—
503C22×C5—22no—
504C22×C5—22no—
505C22×C5—28no—
506C22×C5—22no—
507C22×C5—26no—
508C22×C5—22no—
509C22×C5—26no—
510C22×C5—26no—
511C22×C5—22no—
512C22×C5—44no—
513C22×C5—412no—
514C22×C5C22×#4112yes—
515C22×C5C2×2−1+414yes—
516C22×C5C2×2−1+412yes—
517C22×C5#58512yes—
518C22×C5C2611yescharacteristic
519C4×C5—22no—
520C4×C5—26no—
521C4×C5—26no—
522C4×C5—22no—
523C4×C5—22no—
524C4×C5—26no—
525C4×C5—22no—
526C4×C5—26no—
527C4×C5—26no—
528C4×C5—26no—
529C4×C5—22no—
530C4×C5C22×#41112yes—
531C24C24×C511yescharacteristic
532C24C24×C513yes—
533C24C24×C511yescharacteristic
534#41—232no—
535C2×Q8—232no—
536C2×Q8—232no—
537C2×Q8—212no—
538C2×Q8—212no—
539C2×Q8—46no—
540C2×Q8C5×#4118yes—
541C2×Q8C24×C5112yes—
542C2×Q8C24×C5112yes—
543C2×Q8C24×C5112yes—
544C2×Q8C24×C514yes—
545C2×D4—212no—
546C2×D4—24no—
547C2×D4—212no—
548C2×D4—46no—
549C2×D4C24×C5112yes—
550C2×D4C24×C514yes—
551C2×D4C24×C5112yes—
552C2×D4C24×C5112yes—
553C22×C4—24no—
554C22×C4—212no—
555C22×C4—212no—
556C22×C4—212no—
557C22×C4—412no—
558C22×C4—46no—
559C22×C4C24×C511yescharacteristic
560C22×C4C24×C511yescharacteristic
561C22×C4C24×C514yes—
562C22×C4C24×C513yes—
563C22×C4C24×C511yescharacteristic
564C22×C4C24×C513yes—
565C22×C4C24×C511yescharacteristic
566C22×C4C24×C513yes—
567C22×C4C24×C513yes—
568C22×C4C24×C513yes—
569C22×C4C24×C5112yes—
570C22×C4C24×C513yes—
571C22×C4C24×C511yescharacteristic
572C22×C4C24×C5112yes—
573C22×C4C24×C5112yes—
574C22×C4C24×C5112yes—
575C22×C4C24×C5124yes—
576C22×C4C24×C513yes—
577C4⋊C4C24×C5112yes—
578C4⋊C4C24×C5112yes—
579C4⋊C4C24×C5112yes—
580C4⋊C4C24×C5112yes—
581C4⋊C4C24×C5124yes—
582C4⋊C4C24×C514yes—
583C4⋊C4C24×C5112yes—
584C4⋊C4C24×C5112yes—
585C4⋊C4C24×C5112yes—
586C4⋊C4C24×C5112yes—
587C4⋊C4C24×C5124yes—
588C4⋊C4C24×C5112yes—
589C4⋊C4C24×C5112yes—
590C4⋊C4C24×C5124yes—
591C4⋊C4C24×C5112yes—
592C4⋊C4C24×C514yes—
593C4⋊C4C24×C5112yes—
594C22⋊C4C24×C5112yes—
595C22⋊C4C24×C514yes—
596C22⋊C4C24×C5112yes—
597C22⋊C4C24×C5112yes—
598C22⋊C4C24×C5112yes—
599C22⋊C4C24×C5124yes—
600C22⋊C4C24×C514yes—
601C22⋊C4C24×C5112yes—
602C22⋊C4C24×C514yes—
603C22⋊C4C24×C5124yes—
604C22⋊C4C24×C5112yes—
605C22⋊C4C24×C5112yes—
606C42C24×C5112yes—
607C42C24×C5112yes—
608C42C24×C5112yes—
609C42C24×C5112yes—
610C42C24×C5124yes—
611C42C24×C5112yes—
612C42C24×C5112yes—
613C2×C5—24no—
614C2×C5—42no—
615C2×C5—46no—
616C2×C5#351614yesdirect product factor
617C2×C5C23×#4111yescharacteristic
618C2×C5C22×2−1+411yescharacteristic
619C2×C5C2×#58511yescharacteristic
620C23—22no—
621C23—22no—
622C23—22no—
623C23—26no—
624C23—22no—
625C23—26no—
626C23—26no—
627C23—22no—
628C23C5×2−1+414yes—
629C23C25×C512yes—
630C23C25×C516yes—
631C23C25×C512yes—
632C23C25×C511yescharacteristic
633Q8—224no—
634Q8—224no—
635Q8—412no—
636Q8C2×C5×#41116yes—
637D4—224no—
638D4—28no—
639D4—224no—
640D4—412no—
641C2×C4—22no—
642C2×C4—26no—
643C2×C4—26no—
644C2×C4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—26no—
648C2×C4—22no—
649C2×C4—26no—
650C2×C4—26no—
651C2×C4—26no—
652C2×C4—22no—
653C2×C4—224no—
654C2×C4—224no—
655C2×C4—224no—
656C2×C4—424no—
657C2×C4—412no—
658C2×C4C2×C5×#41112yes—
659C2×C4C25×C512yes—
660C2×C4C25×C512yes—
661C2×C4C25×C516yes—
662C2×C4C25×C512yes—
663C2×C4C25×C516yes—
664C2×C4C25×C512yes—
665C2×C4C25×C516yes—
666C2×C4C25×C516yes—
667C2×C4C25×C516yes—
668C2×C4C25×C516yes—
669C2×C4C25×C512yes—
670C2×C4C25×C516yes—
671C5C2×#351611yescharacteristic, direct product factor, Sylow
672C22—22no—
673C22—22no—
674C22—28no—
675C22—22no—
676C22—26no—
677C22—22no—
678C22—26no—
679C22—26no—
680C22—22no—
681C22—44no—
682C22—412no—
683C22C22×C5×#4112yes—
684C22C2×C5×2−1+414yes—
685C22C2×C5×2−1+412yes—
686C22C5×#58512yes—
687C22C26×C511yescharacteristic
688C4—22no—
689C4—26no—
690C4—26no—
691C4—22no—
692C4—22no—
693C4—26no—
694C4—22no—
695C4—26no—
696C4—26no—
697C4—26no—
698C4—22no—
699C4C22×C5×#41112yes—
700C2—24no—
701C2—42no—
702C2—46no—
703C2C5×#351614yesdirect product factor
704C2C23×C5×#4111yescharacteristic
705C2C22×C5×2−1+411yescharacteristic
706C2C2×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×#3516C2direct (N × H)
2. C2×C5×#557C2semidirect
3. C2×C5×#556C2semidirect
4. C2×C5×#554C2semidirect
5. C2×C5×#553C2semidirect
6. C2×C5×#552C2semidirect
7. C2×C5×D4×Q8C2semidirect
8. C2×C5×#548C2semidirect
9. C2×C5×#548C2semidirect
10. C2×C5×#542C2semidirect
11. C2×C5×#541C2semidirect
12. C2×C5×#529C2semidirect
13. C2×C5×#529C2semidirect
14. C2×C5×#520C2semidirect
15. C2×C5×#519C2semidirect
16. C22×C4×C5×Q8C2semidirect
20. C5×#557C22semidirect
21. C5×#556C22semidirect
22. C5×#554C22semidirect
23. C5×#553C22semidirect
24. C5×#552C22semidirect
25. C5×D4×Q8C22semidirect
26. C5×#548C22semidirect
27. C5×#548C22semidirect
28. C5×#542C22semidirect
29. C5×#541C22semidirect
32. C5×#529C22semidirect
33. C5×#529C22semidirect
57. C5×#520C22semidirect
58. C5×#519C22semidirect
68. C2×C4×C5×Q8C22semidirect
82. C2×#3516C5direct (N × H)
186. #3516C2×C5direct (N × H)
187. C2×#557C2×C5semidirect
188. C2×#556C2×C5semidirect
189. C2×#554C2×C5semidirect
190. C2×#553C2×C5semidirect
191. C2×#552C2×C5semidirect
192. C2×D4×Q8C2×C5semidirect
193. C2×#548C2×C5semidirect
194. C2×#548C2×C5semidirect
195. C2×#542C2×C5semidirect
196. C2×#541C2×C5semidirect
197. C2×#529C2×C5semidirect
198. C2×#529C2×C5semidirect
199. C2×#520C2×C5semidirect
200. C2×#519C2×C5semidirect
201. C22×C4×Q8C2×C5semidirect
287. #557C22×C5semidirect
288. #556C22×C5semidirect
289. #554C22×C5semidirect
290. #553C22×C5semidirect
291. #552C22×C5semidirect
292. D4×Q8C22×C5semidirect
293. #548C22×C5semidirect
294. #548C22×C5semidirect
295. #542C22×C5semidirect
296. #541C22×C5semidirect
299. #529C22×C5semidirect
300. #529C22×C5semidirect
324. #520C22×C5semidirect
325. #519C22×C5semidirect
335. C2×C4×Q8C22×C5semidirect
616. C2×C5#3516direct (N × H)
671. C5C2×#3516direct (N × H)
703. C2C5×#3516direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35162
C2×C5×#5572
C2×C5×#5562
C2×C5×#5542
C2×C5×#5532
C2×C5×#5522
C2×C5×D4×Q82
C2×C5×#5482
C2×C5×#5422
C2×C5×#5412
C2×C5×#5292
C2×C5×#5202
C2×C5×#5192
C22×C4×C5×Q82
C2×#35165