Finite Group Databasebeta

← C5×#74947 #14323705

Subgroups — C5×#74947 #14323705

Order 1920.

1112 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#896C211yesmaximal, characteristic
2C2×C5×#892C211yesmaximal, characteristic
3C2×C4×C5×Dic6C211yesmaximal, characteristic, complemented
4C3×C5×#387C211yesmaximal, characteristic, complemented
5C5×#4984C211yesmaximal, characteristic, complemented
6C5×#4978C211yesmaximal, characteristic, complemented
7C5×#4940C211yesmaximal, characteristic
8C5×#4670C211yesmaximal, characteristic
9C5×#4670C211yesmaximal, characteristic
10C5×#4669C211yesmaximal, characteristic
11C5×#4667C211yesmaximal, characteristic
12C5×#4649C211yesmaximal, characteristic, complemented
13C5×#4647C211yesmaximal, characteristic, complemented
14C5×#4647C211yesmaximal, characteristic, complemented
15C5×#4646C211yesmaximal, characteristic, complemented
16C5×#2323—31nomaximal, Hall
17C22×C4×C5×D3C2211yescharacteristic
18C22×C5×Dic6C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C42×C5C2211yescharacteristic
22C2×C5×(C2×D3)⋊C4C2211yescharacteristic
23C2×C5×(C2×D3)⋊C4C2211yescharacteristic
24C2×C5×(C2×D3)⋊C4C2211yescharacteristic
25C2×C5×(C2×D3)⋊C4C2211yescharacteristic
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×C4⋊Dic3C2211yescharacteristic
29C2×C5×C4⋊Dic3C2211yescharacteristic
30C2×C5×C4⋊Dic3C2211yescharacteristic
31C2×C5×Dic3⋊C4C2211yescharacteristic
32C2×C5×Dic3⋊C4C2211yescharacteristic
33C2×C5×Dic3⋊C4C2211yescharacteristic
34C2×C5×Dic3⋊C4C2211yescharacteristic
35C2×C5×Dic3⋊C4C2211yescharacteristic
36C2×C5×Dic3⋊C4C2211yescharacteristic
37C2×C4×C5×Dic3C2211yescharacteristic
38C2×C4×C5×Dic3C2211yescharacteristic
39C2×C4×C5×Dic3C2211yescharacteristic
40C2×C4×C5×Dic3C2211yescharacteristic
41C2×C4×C5×Dic3C2211yescharacteristic
42C5×#896C418yescomplemented
43C5×#892—24no—
44C4×C5×Dic6—24no—
45C3×C5×#95C2211yescharacteristic
46C3×C5×#95C2211yescharacteristic
47C3×C5×#95C2211yescharacteristic
48C3×C5×#95C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C5×C3⋊#95C2211yescharacteristic
51C5×C3⋊#95C2211yescharacteristic
52C5×C3⋊#95C2211yescharacteristic
53C5×C3⋊#95C2211yescharacteristic
54C5×C3⋊#95C2211yescharacteristic
55#74947C511yesmaximal, characteristic, direct product factor, Hall
56C2×C5×C22⋊Q8—31no—
57C2×C4×C5×Q8—31no—
58C2×C5×#117—31no—
59C5×#391—31no—
60C5×#389—31no—
61C5×#389—31no—
62C5×#389—31no—
63C5×#388—31no—
64C5×#388—31no—
65C5×#388—31no—
66C5×#388—31no—
67C5×#387—31no—
68C5×#387D311yescharacteristic, complemented
69C5×#380—31no—
70C4×C5×C4⋊C4—31no—
71C23×C5×D3C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C2×C4×C5×D3—22no—
87C2×C4×C5×D3—22no—
88C2×C4×C5×D3C2×C414yes—
89C2×C5×Dic6—22no—
90C2×C5×Dic6—22no—
91C2×C5×Dic6C2×C414yes—
92C3×C5×C4⋊C4—22no—
93C3×C5×C4⋊C4C2×C414yes—
94C3×C42×C5—22no—
95C5×(C2×D3)⋊C4—22no—
96C5×(C2×D3)⋊C4—22no—
97C5×(C2×D3)⋊C4—41no—
98C5×(C2×D3)⋊C4—41no—
99C5×(C2×D3)⋊C4C2×C414yes—
100C5×(C2×D3)⋊C4C2×C414yes—
101C5×C4⋊Dic3—22no—
102C5×C4⋊Dic3—22no—
103C5×C4⋊Dic3—41no—
104C5×Dic3⋊C4—22no—
105C5×Dic3⋊C4—22no—
106C5×Dic3⋊C4—22no—
107C5×Dic3⋊C4—41no—
108C5×Dic3⋊C4C2×C414yes—
109C5×Dic3⋊C4C2×C414yes—
110C4×C5×Dic3—22no—
111C4×C5×Dic3—22no—
112C4×C5×Dic3—41no—
113C4×C5×Dic3—41no—
114C4×C5×Dic3D414yes—
115C2×#896C2×C511yescharacteristic
116C2×#892C2×C511yescharacteristic
117C2×C4×Dic6C2×C511yescharacteristic, complemented
118C3×#387C2×C511yescharacteristic, complemented
119#4984C2×C511yescharacteristic, complemented
120#4978C2×C511yescharacteristic, complemented
121#4940C2×C511yescharacteristic
122#4670C2×C511yescharacteristic
123#4670C2×C511yescharacteristic
124#4669C2×C511yescharacteristic
125#4667C2×C511yescharacteristic
126#4649C2×C511yescharacteristic, complemented
127#4647C2×C511yescharacteristic, complemented
128#4647C2×C511yescharacteristic, complemented
129#4646C2×C511yescharacteristic, complemented
130C22×C5×Q8—31no—
131C23×C4×C5—31no—
132C5×C22⋊Q8—38no—
133C4×C5×Q8—64no—
134C5×#117—64no—
135C2×C5×C4⋊C4—31no—
136C2×C5×C4⋊C4—31no—
137C2×C5×C4⋊C4—31no—
138C2×C5×C4⋊C4—31no—
139C2×C5×C4⋊C4—31no—
140C2×C5×C4⋊C4—31no—
141C2×C5×C4⋊C4—31no—
142C2×C5×C4⋊C4—31no—
143C2×C5×C4⋊C4—31no—
144C2×C5×C4⋊C4C2×D311yescharacteristic
145C2×C5×C4⋊C4C2×D311yescharacteristic
146C2×C5×C22⋊C4—31no—
147C2×C5×C22⋊C4—31no—
148C2×C5×C22⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4—31no—
151C2×C5×C22⋊C4—31no—
152C2×C42×C5—31no—
153C2×C42×C5—31no—
154C2×C42×C5—31no—
155C2×C42×C5—31no—
156C2×C42×C5—31no—
157C2×C42×C5C2×D311yescharacteristic
158C5×#95—31no—
159C5×#95—31no—
160C5×#95—31no—
161C5×#95—31no—
162C5×#95—31no—
163C5×#95—31no—
164C5×#95C2×D311yescharacteristic
165C5×#95C2×D311yescharacteristic
166C5×#95C2×D311yescharacteristic
167C5×#95C2×D311yescharacteristic
168#2323—31noSylow
169C23×C3×C5C2411yescharacteristic
170C22×C5×D3—21no—
171C22×C5×D3—21no—
172C22×C5×D3—21no—
173C22×C5×D3—21no—
174C22×C5×D3—21no—
175C22×C5×D3—21no—
176C22×C5×D3C22×C412yes—
177C2×C3×C4×C5—21no—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—21no—
180C2×C3×C4×C5—21no—
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5—21no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5C22×C412yes—
195C2×C3×C4×C5C22×C412yes—
196C2×C3×C4×C5C22×C412yes—
197C2×C3×C4×C5C2×D412yes—
198C2×C5×Dic3—21no—
199C2×C5×Dic3—21no—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3C22×C412yes—
214C2×C5×Dic3C22×C412yes—
215C2×C5×Dic3C22×C412yes—
216C2×C5×Dic3C2×D412yes—
217C2×C5×Dic3C2×D412yes—
218C2×C5×Dic3#4112yes—
219C4×C5×D3—28no—
220C5×Dic6—28no—
221C22×C4×D3C22×C511yescharacteristic
222C22×Dic6C22×C511yescharacteristic
223C2×C3×C4⋊C4C22×C511yescharacteristic
224C2×C3×C4⋊C4C22×C511yescharacteristic
225C2×C3×C42C22×C511yescharacteristic
226C2×(C2×D3)⋊C4C22×C511yescharacteristic
227C2×(C2×D3)⋊C4C22×C511yescharacteristic
228C2×(C2×D3)⋊C4C22×C511yescharacteristic
229C2×(C2×D3)⋊C4C22×C511yescharacteristic
230C2×(C2×D3)⋊C4C22×C511yescharacteristic
231C2×(C2×D3)⋊C4C22×C511yescharacteristic
232C2×C4⋊Dic3C22×C511yescharacteristic
233C2×C4⋊Dic3C22×C511yescharacteristic
234C2×C4⋊Dic3C22×C511yescharacteristic
235C2×Dic3⋊C4C22×C511yescharacteristic
236C2×Dic3⋊C4C22×C511yescharacteristic
237C2×Dic3⋊C4C22×C511yescharacteristic
238C2×Dic3⋊C4C22×C511yescharacteristic
239C2×Dic3⋊C4C22×C511yescharacteristic
240C2×Dic3⋊C4C22×C511yescharacteristic
241C2×C4×Dic3C22×C511yescharacteristic
242C2×C4×Dic3C22×C511yescharacteristic
243C2×C4×Dic3C22×C511yescharacteristic
244C2×C4×Dic3C22×C511yescharacteristic
245C2×C4×Dic3C22×C511yescharacteristic
246#896C4×C518yescomplemented
247#892—24no—
248C4×Dic6—24no—
249C3×#95C22×C511yescharacteristic
250C3×#95C22×C511yescharacteristic
251C3×#95C22×C511yescharacteristic
252C3×#95C22×C511yescharacteristic
253C3⋊#95C22×C511yescharacteristic
254C3⋊#95C22×C511yescharacteristic
255C3⋊#95C22×C511yescharacteristic
256C3⋊#95C22×C511yescharacteristic
257C3⋊#95C22×C511yescharacteristic
258C3⋊#95C22×C511yescharacteristic
259C24×C5—31no—
260C2×C5×Q8—34no—
261C2×C5×Q8—62no—
262C2×C5×Q8—62no—
263C22×C4×C5—31no—
264C22×C4×C5—31no—
265C22×C4×C5—31no—
266C22×C4×C5—31no—
267C22×C4×C5—34no—
268C22×C4×C5—31no—
269C22×C4×C5—31no—
270C22×C4×C5—31no—
271C22×C4×C5—62no—
272C22×C4×C5—62no—
273C22×C4×C5C22×D311yescharacteristic
274C22×C4×C5C22×D311yescharacteristic
275C22×C4×C5C22×D311yescharacteristic
276C22×C4×C5C22×D311yescharacteristic
277C22×C4×C5C22×D311yescharacteristic
278C22×C4×C5C22×D311yescharacteristic
279C22×C4×C5C22×D311yescharacteristic
280C5×C4⋊C4—22no—
281C5×C4⋊C4—34no—
282C5×C4⋊C4—34no—
283C5×C4⋊C4—62no—
284C5×C4⋊C4—62no—
285C5×C4⋊C4—62no—
286C5×C4⋊C4—62no—
287C5×C4⋊C4—62no—
288C5×C4⋊C4—121no—
289C5×C4⋊C4—121no—
290C5×C4⋊C4C4×D314yes—
291C5×C22⋊C4—34no—
292C5×C22⋊C4—34no—
293C5×C22⋊C4—62no—
294C5×C22⋊C4—62no—
295C5×C22⋊C4—121no—
296C5×C22⋊C4—121no—
297C42×C5—22no—
298C42×C5—34no—
299C42×C5—62no—
300C42×C5—62no—
301C42×C5—121no—
302C42×C5—121no—
303C2×C22⋊Q8—31no—
304C2×C4×Q8—31no—
305C2×#117—31no—
306#391—31no—
307#389—31no—
308#389—31no—
309#389—31no—
310#388—31no—
311#388—31no—
312#388—31no—
313#388—31no—
314#387—31no—
315#387C5×D311yescharacteristic, complemented
316#380—31no—
317C4×C4⋊C4—31no—
318C22×C3×C5C23×C411yescharacteristic
319C22×C3×C5C22×D411yescharacteristic
320C22×C3×C5C2×#4111yescharacteristic
321C22×C3×C5H(5,𝔽2)11yescharacteristic
322C22×C3×C52−1+411yescharacteristic
323C22×C3×C52−1+411yescharacteristic
324C22×C3×C52−1+411yescharacteristic
325C2×C5×D3—22no—
326C2×C5×D3—22no—
327C2×C5×D3—22no—
328C2×C5×D3—41no—
329C2×C5×D3—41no—
330C2×C5×D3—41no—
331C2×C5×D3—41no—
332C3×C4×C5—22no—
333C3×C4×C5—22no—
334C3×C4×C5—22no—
335C3×C4×C5—22no—
336C3×C4×C5—41no—
337C3×C4×C5—41no—
338C3×C4×C5—41no—
339C5×Dic3—22no—
340C5×Dic3—22no—
341C5×Dic3—22no—
342C5×Dic3—41no—
343C5×Dic3—41no—
344C5×Dic3—41no—
345C5×Dic3C4×D414yes—
346C23×D3C23×C511yescharacteristic
347C22×C3×C4C23×C511yescharacteristic
348C22×C3×C4C23×C511yescharacteristic
349C22×C3×C4C23×C511yescharacteristic
350C22×C3×C4C23×C511yescharacteristic
351C22×C3×C4C23×C511yescharacteristic
352C22×C3×C4C23×C511yescharacteristic
353C22×C3×C4C23×C511yescharacteristic
354C22×Dic3C23×C511yescharacteristic
355C22×Dic3C23×C511yescharacteristic
356C22×Dic3C23×C511yescharacteristic
357C22×Dic3C23×C511yescharacteristic
358C22×Dic3C23×C511yescharacteristic
359C22×Dic3C23×C511yescharacteristic
360C22×Dic3C23×C511yescharacteristic
361C2×C4×D3—22no—
362C2×C4×D3—22no—
363C2×C4×D3C2×C4×C514yes—
364C2×Dic6—22no—
365C2×Dic6—22no—
366C2×Dic6C2×C4×C514yes—
367C3×C4⋊C4—22no—
368C3×C4⋊C4C2×C4×C514yes—
369C3×C42—22no—
370(C2×D3)⋊C4—22no—
371(C2×D3)⋊C4—22no—
372(C2×D3)⋊C4—41no—
373(C2×D3)⋊C4—41no—
374(C2×D3)⋊C4C2×C4×C514yes—
375(C2×D3)⋊C4C2×C4×C514yes—
376C4⋊Dic3—22no—
377C4⋊Dic3—22no—
378C4⋊Dic3—41no—
379Dic3⋊C4—22no—
380Dic3⋊C4—22no—
381Dic3⋊C4—22no—
382Dic3⋊C4—41no—
383Dic3⋊C4C2×C4×C514yes—
384Dic3⋊C4C2×C4×C514yes—
385C4×Dic3—22no—
386C4×Dic3—22no—
387C4×Dic3—41no—
388C4×Dic3—41no—
389C4×Dic3C5×D414yes—
390C23×C5—32no—
391C23×C5—61no—
392C23×C5—61no—
393C23×C5—61no—
394C23×C5—61no—
395C23×C5—61no—
396C23×C5—61no—
397C23×C5C23×D311yescharacteristic
398C5×Q8—68no—
399C2×C4×C5—21no—
400C2×C4×C5—21no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—21no—
407C2×C4×C5—21no—
408C2×C4×C5—21no—
409C2×C4×C5—21no—
410C2×C4×C5—21no—
411C2×C4×C5—21no—
412C2×C4×C5—21no—
413C2×C4×C5—21no—
414C2×C4×C5—21no—
415C2×C4×C5—21no—
416C2×C4×C5—32no—
417C2×C4×C5—32no—
418C2×C4×C5—32no—
419C2×C4×C5—32no—
420C2×C4×C5—32no—
421C2×C4×C5—32no—
422C2×C4×C5—68no—
423C2×C4×C5—61no—
424C2×C4×C5—61no—
425C2×C4×C5—61no—
426C2×C4×C5—61no—
427C2×C4×C5—61no—
428C2×C4×C5—61no—
429C2×C4×C5—61no—
430C2×C4×C5—61no—
431C2×C4×C5—61no—
432C2×C4×C5—61no—
433C2×C4×C5—61no—
434C2×C4×C5—61no—
435C2×C4×C5—61no—
436C2×C4×C5—61no—
437C2×C4×C5—61no—
438C2×C4×C5C2×C4×D312yes—
439C2×C4×C5C2×C4×D312yes—
440C2×C4×C5C2×C4×D312yes—
441C2×C4×C5D3×D412yes—
442C22×Q8—31no—
443C23×C4—31no—
444C22⋊Q8—38no—
445C4×Q8—64no—
446#117—64no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—31no—
451C2×C4⋊C4—31no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—31no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—31no—
456C2×C4⋊C4C2×C5×D311yescharacteristic
457C2×C4⋊C4C2×C5×D311yescharacteristic
458C2×C22⋊C4—31no—
459C2×C22⋊C4—31no—
460C2×C22⋊C4—31no—
461C2×C22⋊C4—31no—
462C2×C22⋊C4—31no—
463C2×C22⋊C4—31no—
464C2×C42—31no—
465C2×C42—31no—
466C2×C42—31no—
467C2×C42—31no—
468C2×C42—31no—
469C2×C42C2×C5×D311yescharacteristic
470#95—31no—
471#95—31no—
472#95—31no—
473#95—31no—
474#95—31no—
475#95—31no—
476#95C2×C5×D311yescharacteristic
477#95C2×C5×D311yescharacteristic
478#95C2×C5×D311yescharacteristic
479#95C2×C5×D311yescharacteristic
480C2×C3×C5C2×C4×D411yescharacteristic
481C2×C3×C5#51911yescharacteristic
482C2×C3×C5#52011yescharacteristic
483C2×C3×C5#53611yescharacteristic
484C2×C3×C5#53711yescharacteristic
485C2×C3×C5#54111yescharacteristic
486C2×C3×C5#54211yescharacteristic
487C5×D3—42no—
488C23×C3C24×C511yescharacteristic
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3C22×C4×C512yes—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4C22×C4×C512yes—
514C2×C3×C4C22×C4×C512yes—
515C2×C3×C4C22×C4×C512yes—
516C2×C3×C4C2×C5×D412yes—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3C22×C4×C512yes—
533C2×Dic3C22×C4×C512yes—
534C2×Dic3C22×C4×C512yes—
535C2×Dic3C2×C5×D412yes—
536C2×Dic3C2×C5×D412yes—
537C2×Dic3C5×#4112yes—
538C4×D3—28no—
539Dic6—28no—
540C22×C5—62no—
541C22×C5—62no—
542C22×C5—62no—
543C22×C5—121no—
544C22×C5—121no—
545C22×C5—121no—
546C22×C5—121no—
547C22×C5C22×C4×D311yescharacteristic
548C22×C5C2×D3×D411yescharacteristic
549C22×C5#100711yescharacteristic
550C22×C5D3×#4111yescharacteristic
551C22×C5#100911yescharacteristic
552C22×C5#101011yescharacteristic
553C22×C5#101011yescharacteristic
554C4×C5—22no—
555C4×C5—22no—
556C4×C5—22no—
557C4×C5—22no—
558C4×C5—34no—
559C4×C5—41no—
560C4×C5—41no—
561C4×C5—41no—
562C4×C5—62no—
563C4×C5—62no—
564C4×C5—62no—
565C4×C5—121no—
566C4×C5—121no—
567C4×C5—121no—
568C24—31no—
569C2×Q8—34no—
570C2×Q8—62no—
571C2×Q8—62no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—34no—
577C22×C4—31no—
578C22×C4—31no—
579C22×C4—31no—
580C22×C4—62no—
581C22×C4—62no—
582C22×C4C22×C5×D311yescharacteristic
583C22×C4C22×C5×D311yescharacteristic
584C22×C4C22×C5×D311yescharacteristic
585C22×C4C22×C5×D311yescharacteristic
586C22×C4C22×C5×D311yescharacteristic
587C22×C4C22×C5×D311yescharacteristic
588C22×C4C22×C5×D311yescharacteristic
589C4⋊C4—22no—
590C4⋊C4—34no—
591C4⋊C4—34no—
592C4⋊C4—62no—
593C4⋊C4—62no—
594C4⋊C4—62no—
595C4⋊C4—62no—
596C4⋊C4—62no—
597C4⋊C4—121no—
598C4⋊C4—121no—
599C4⋊C4C4×C5×D314yes—
600C22⋊C4—34no—
601C22⋊C4—34no—
602C22⋊C4—62no—
603C22⋊C4—62no—
604C22⋊C4—121no—
605C22⋊C4—121no—
606C42—22no—
607C42—34no—
608C42—62no—
609C42—62no—
610C42—121no—
611C42—121no—
612C3×C5#232311yescharacteristic, complemented, Hall
613C22×C3C23×C4×C511yescharacteristic
614C22×C3C22×C5×D411yescharacteristic
615C22×C3C2×C5×#4111yescharacteristic
616C22×C3C5×H(5,𝔽2)11yescharacteristic
617C22×C3C5×2−1+411yescharacteristic
618C22×C3C5×2−1+411yescharacteristic
619C22×C3C5×2−1+411yescharacteristic
620C2×D3—22no—
621C2×D3—22no—
622C2×D3—22no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—41no—
626C2×D3—41no—
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—22no—
630C3×C4—22no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—41no—
634Dic3—22no—
635Dic3—22no—
636Dic3—22no—
637Dic3—41no—
638Dic3—41no—
639Dic3—41no—
640Dic3C4×C5×D414yes—
641C2×C5—122no—
642C2×C5#552311yescharacteristic
643C2×C5C4×D3×D411yescharacteristic
644C2×C5#557211yescharacteristic
645C2×C5#562911yescharacteristic
646C2×C5#564811yescharacteristic
647C2×C5#569611yescharacteristic
648C2×C5#571011yescharacteristic
649C23—32no—
650C23—61no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23—61no—
655C23—61no—
656C23C23×C5×D311yescharacteristic
657Q8—68no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—32no—
676C2×C4—32no—
677C2×C4—32no—
678C2×C4—32no—
679C2×C4—32no—
680C2×C4—32no—
681C2×C4—68no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4C2×C4×C5×D312yes—
698C2×C4C2×C4×C5×D312yes—
699C2×C4C2×C4×C5×D312yes—
700C2×C4C5×D3×D412yes—
701C2×C3C2×C4×C5×D411yescharacteristic
702C2×C3C5×#51911yescharacteristic
703C2×C3C5×#52011yescharacteristic
704C2×C3C5×#53611yescharacteristic
705C2×C3C5×#53711yescharacteristic
706C2×C3C5×#54111yescharacteristic
707C2×C3C5×#54211yescharacteristic
708D3—42no—
709C5#7494711yescharacteristic, direct product factor, Sylow
710C22—62no—
711C22—62no—
712C22—62no—
713C22—121no—
714C22—121no—
715C22—121no—
716C22—121no—
717C22C22×C4×C5×D311yescharacteristic
718C22C2×C5×D3×D411yescharacteristic
719C22C5×#100711yescharacteristic
720C22C5×D3×#4111yescharacteristic
721C22C5×#100911yescharacteristic
722C22C5×#101011yescharacteristic
723C22C5×#101011yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—34no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—62no—
733C4—62no—
734C4—62no—
735C4—121no—
736C4—121no—
737C4—121no—
738C3C5×#232311yescharacteristic, complemented, Sylow
739C2—122no—
740C2C5×#552311yescharacteristic
741C2C4×C5×D3×D411yescharacteristic
742C2C5×#557211yescharacteristic
743C2C5×#562911yescharacteristic
744C2C5×#564811yescharacteristic
745C2C5×#569611yescharacteristic
746C2C5×#571011yescharacteristic
subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#387C2
socleC23×C3×C5C24
prime radicalC23×C5×D3C23
cosocleC23×C3C24×C5
hypercenterC5×#387D3
hypocenterC3C5×#2323
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C5×#387

Complements

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

NH ≅ G/Ntype
3. C2×C4×C5×Dic6C2semidirect
4. C3×C5×#387C2semidirect
5. C5×#4984C2semidirect
6. C5×#4978C2semidirect
12. C5×#4649C2semidirect
13. C5×#4647C2semidirect
14. C5×#4647C2semidirect
15. C5×#4646C2semidirect
42. C5×#896C4semidirect
55. #74947C5direct (N × H)
68. C5×#387D3semidirect
117. C2×C4×Dic6C2×C5semidirect
118. C3×#387C2×C5semidirect
119. #4984C2×C5semidirect
120. #4978C2×C5semidirect
126. #4649C2×C5semidirect
127. #4647C2×C5semidirect
128. #4647C2×C5semidirect
129. #4646C2×C5semidirect
246. #896C4×C5semidirect
315. #387C5×D3semidirect
612. C3×C5#2323semidirect
709. C5#74947direct (N × H)
738. C3C5×#2323semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8962
C2×C5×#8922
C2×C4×C5×Dic62
C3×C5×#3872
C5×#49842
C5×#49782
C5×#49402
C5×#46702
C5×#46692
C5×#46672
C5×#46492
C5×#46472
C5×#46462
C5×#23233
#749475