Finite Group Databasebeta

← C5×#69429 #14280096

Subgroups — C5×#69429 #14280096

Order 1920.

1472 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×(C2×D3)⋊C4C211yesmaximal, characteristic
2C22×C5×(C2×D3)⋊C4C211yesmaximal, characteristic
3C22×C5×(C2×D3)⋊C4C211yesmaximal, characteristic
4C2×C3×C5×#95C211yesmaximal, characteristic, complemented
5C2×C5×C3⋊#95C211yesmaximal, characteristic, complemented
6C2×C5×C3⋊#95C211yesmaximal, characteristic, complemented
7C2×C5×C3⋊#95C211yesmaximal, characteristic, complemented
8C5×#1440—31nomaximal, Hall
9C24×C5×D3C2211yescharacteristic
10C23×C3×C4×C5C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×C5×Dic3C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C2×C5×(C2×D3)⋊C4—22no—
17C2×C5×(C2×D3)⋊C4—22no—
18C2×C5×(C2×D3)⋊C4—22no—
19C2×C5×(C2×D3)⋊C4—22no—
20C2×C5×(C2×D3)⋊C4—22no—
21C2×C5×(C2×D3)⋊C4—22no—
22C2×C5×(C2×D3)⋊C4—22no—
23C2×C5×(C2×D3)⋊C4—22no—
24C2×C5×(C2×D3)⋊C4C414yescomplemented
25C3×C5×#95—22no—
26C5×C3⋊#95—22no—
27C5×C3⋊#95—22no—
28C5×C3⋊#95—22no—
29#69429C511yesmaximal, characteristic, direct product factor, Hall
30C22×C5×C22⋊C4—31no—
31C22×C5×C22⋊C4—31no—
32C22×C5×C22⋊C4—31no—
33C2×C5×#95—31no—
34C2×C5×#95—31no—
35C2×C5×#95—31no—
36C2×C5×#95D311yescharacteristic, complemented
37C24×C3×C5C2311yescharacteristic
38C23×C5×D3—21no—
39C23×C5×D3—21no—
40C23×C5×D3—21no—
41C23×C5×D3—21no—
42C23×C5×D3—21no—
43C23×C5×D3—21no—
44C23×C5×D3—21no—
45C23×C5×D3—21no—
46C23×C5×D3—21no—
47C23×C5×D3—21no—
48C23×C5×D3—21no—
49C23×C5×D3—21no—
50C23×C5×D3C2×C412yes—
51C23×C5×D3D412yes—
52C23×C5×D3D412yes—
53C22×C3×C4×C5—21no—
54C22×C3×C4×C5—21no—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5—21no—
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5—21no—
65C22×C3×C4×C5—21no—
66C22×C3×C4×C5—21no—
67C22×C3×C4×C5—21no—
68C22×C3×C4×C5—21no—
69C22×C3×C4×C5—21no—
70C22×C3×C4×C5—21no—
71C22×C3×C4×C5C2×C412yes—
72C22×C3×C4×C5D412yes—
73C22×C3×C4×C5D412yes—
74C22×C5×Dic3—21no—
75C22×C5×Dic3—21no—
76C22×C5×Dic3—21no—
77C22×C5×Dic3—21no—
78C22×C5×Dic3—21no—
79C22×C5×Dic3—21no—
80C22×C5×Dic3—21no—
81C22×C5×Dic3—21no—
82C22×C5×Dic3—21no—
83C22×C5×Dic3—21no—
84C22×C5×Dic3—21no—
85C22×C5×Dic3—21no—
86C22×C5×Dic3—21no—
87C22×C5×Dic3—21no—
88C22×C5×Dic3—21no—
89C22×C5×Dic3—21no—
90C22×C5×Dic3—21no—
91C22×C5×Dic3—21no—
92C22×C5×Dic3C2×C412yes—
93C22×C5×Dic3D412yes—
94C22×C5×Dic3D412yes—
95C5×(C2×D3)⋊C4—28no—
96C5×(C2×D3)⋊C4—28no—
97C5×(C2×D3)⋊C4—28no—
98C22×(C2×D3)⋊C4C2×C511yescharacteristic
99C22×(C2×D3)⋊C4C2×C511yescharacteristic
100C22×(C2×D3)⋊C4C2×C511yescharacteristic
101C2×C3×#95C2×C511yescharacteristic, complemented
102C2×C3⋊#95C2×C511yescharacteristic, complemented
103C2×C3⋊#95C2×C511yescharacteristic, complemented
104C2×C3⋊#95C2×C511yescharacteristic, complemented
105C25×C5—31no—
106C23×C4×C5—31no—
107C23×C4×C5—31no—
108C23×C4×C5—31no—
109C23×C4×C5C2×D311yescharacteristic
110C23×C4×C5C2×D311yescharacteristic
111C23×C4×C5C2×D311yescharacteristic
112C2×C5×C22⋊C4—34no—
113C2×C5×C22⋊C4—62no—
114C2×C5×C22⋊C4—62no—
115C2×C5×C22⋊C4—62no—
116C2×C5×C22⋊C4—62no—
117C2×C5×C22⋊C4—62no—
118C2×C5×C22⋊C4—62no—
119C2×C5×C22⋊C4—62no—
120C2×C5×C22⋊C4—62no—
121C5×#95—22no—
122C5×#95—62no—
123C5×#95—62no—
124C5×#95—62no—
125#1440—31noSylow
126C23×C3×C5C22×C411yescharacteristic
127C23×C3×C5C2×D411yescharacteristic
128C23×C3×C5C2×D411yescharacteristic
129C23×C3×C5C2×D411yescharacteristic
130C23×C3×C5C2×D411yescharacteristic
131C23×C3×C5C2×D411yescharacteristic
132C23×C3×C5C2×D411yescharacteristic
133C23×C3×C5#4111yescharacteristic
134C23×C3×C5#4111yescharacteristic
135C23×C3×C5#4111yescharacteristic
136C23×C3×C5#4111yescharacteristic
137C23×C3×C5#4111yescharacteristic
138C23×C3×C5#4111yescharacteristic
139C23×C3×C5#4111yescharacteristic
140C23×C3×C5#4111yescharacteristic
141C22×C5×D3—22no—
142C22×C5×D3—22no—
143C22×C5×D3—22no—
144C22×C5×D3—22no—
145C22×C5×D3—22no—
146C22×C5×D3—22no—
147C22×C5×D3—22no—
148C22×C5×D3—22no—
149C22×C5×D3—22no—
150C22×C5×D3—22no—
151C22×C5×D3—22no—
152C22×C5×D3—22no—
153C22×C5×D3—22no—
154C22×C5×D3—22no—
155C22×C5×D3—22no—
156C22×C5×D3—22no—
157C22×C5×D3—22no—
158C22×C5×D3—22no—
159C22×C5×D3—41no—
160C22×C5×D3—41no—
161C22×C5×D3—41no—
162C22×C5×D3—41no—
163C22×C5×D3—41no—
164C22×C5×D3—41no—
165C22×C5×D3—41no—
166C22×C5×D3—41no—
167C22×C5×D3—41no—
168C22×C5×D3—41no—
169C22×C5×D3—41no—
170C22×C5×D3—41no—
171C22×C5×D3—41no—
172C22×C5×D3—41no—
173C22×C5×D3—41no—
174C22×C5×D3—41no—
175C22×C5×D3C22⋊C414yes—
176C2×C3×C4×C5—22no—
177C2×C3×C4×C5—22no—
178C2×C3×C4×C5—22no—
179C2×C3×C4×C5—22no—
180C2×C3×C4×C5—22no—
181C2×C3×C4×C5—22no—
182C2×C3×C4×C5—22no—
183C2×C3×C4×C5—22no—
184C2×C3×C4×C5—22no—
185C2×C3×C4×C5—41no—
186C2×C3×C4×C5—41no—
187C2×C3×C4×C5—41no—
188C2×C3×C4×C5—41no—
189C2×C3×C4×C5—41no—
190C2×C3×C4×C5—41no—
191C2×C3×C4×C5—41no—
192C2×C3×C4×C5—41no—
193C2×C3×C4×C5—41no—
194C2×C3×C4×C5—41no—
195C2×C3×C4×C5—41no—
196C2×C3×C4×C5—41no—
197C2×C5×Dic3—22no—
198C2×C5×Dic3—22no—
199C2×C5×Dic3—22no—
200C2×C5×Dic3—22no—
201C2×C5×Dic3—22no—
202C2×C5×Dic3—22no—
203C2×C5×Dic3—22no—
204C2×C5×Dic3—22no—
205C2×C5×Dic3—22no—
206C2×C5×Dic3—41no—
207C2×C5×Dic3—41no—
208C2×C5×Dic3—41no—
209C2×C5×Dic3—41no—
210C2×C5×Dic3—41no—
211C2×C5×Dic3—41no—
212C2×C5×Dic3—41no—
213C2×C5×Dic3—41no—
214C2×C5×Dic3—41no—
215C2×C5×Dic3—41no—
216C2×C5×Dic3—41no—
217C2×C5×Dic3—41no—
218C24×D3C22×C511yescharacteristic
219C23×C3×C4C22×C511yescharacteristic
220C23×C3×C4C22×C511yescharacteristic
221C23×C3×C4C22×C511yescharacteristic
222C23×Dic3C22×C511yescharacteristic
223C23×Dic3C22×C511yescharacteristic
224C23×Dic3C22×C511yescharacteristic
225C2×(C2×D3)⋊C4—22no—
226C2×(C2×D3)⋊C4—22no—
227C2×(C2×D3)⋊C4—22no—
228C2×(C2×D3)⋊C4—22no—
229C2×(C2×D3)⋊C4—22no—
230C2×(C2×D3)⋊C4—22no—
231C2×(C2×D3)⋊C4—22no—
232C2×(C2×D3)⋊C4—22no—
233C2×(C2×D3)⋊C4C4×C514yescomplemented
234C3×#95—22no—
235C3⋊#95—22no—
236C3⋊#95—22no—
237C3⋊#95—22no—
238C24×C5—32no—
239C24×C5—32no—
240C24×C5—32no—
241C24×C5—61no—
242C24×C5—61no—
243C24×C5—61no—
244C24×C5—61no—
245C24×C5—61no—
246C24×C5—61no—
247C24×C5—61no—
248C24×C5—61no—
249C24×C5—61no—
250C24×C5—61no—
251C24×C5—61no—
252C24×C5—61no—
253C24×C5C22×D311yescharacteristic
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—32no—
273C22×C4×C5—32no—
274C22×C4×C5—32no—
275C22×C4×C5—61no—
276C22×C4×C5—61no—
277C22×C4×C5—61no—
278C22×C4×C5—61no—
279C22×C4×C5—61no—
280C22×C4×C5—61no—
281C22×C4×C5—61no—
282C22×C4×C5—61no—
283C22×C4×C5—61no—
284C22×C4×C5—61no—
285C22×C4×C5—61no—
286C22×C4×C5—61no—
287C22×C4×C5—61no—
288C22×C4×C5—61no—
289C22×C4×C5—61no—
290C22×C4×C5—61no—
291C22×C4×C5—61no—
292C22×C4×C5—61no—
293C22×C4×C5C4×D312yes—
294C22×C4×C5D1212yes—
295C22×C4×C5#6712yes—
296C5×C22⋊C4—68no—
297C5×C22⋊C4—68no—
298C5×C22⋊C4—68no—
299C22×C22⋊C4—31no—
300C22×C22⋊C4—31no—
301C22×C22⋊C4—31no—
302C2×#95—31no—
303C2×#95—31no—
304C2×#95—31no—
305C2×#95C5×D311yescharacteristic, complemented
306C22×C3×C5C2×C22⋊C411yescharacteristic
307C22×C3×C5#11711yescharacteristic
308C22×C3×C5#11711yescharacteristic
309C22×C3×C5C4×D411yescharacteristic
310C22×C3×C5C4×D411yescharacteristic
311C22×C3×C5C4×D411yescharacteristic
312C22×C3×C5C4×D411yescharacteristic
313C22×C3×C5#12011yescharacteristic
314C22×C3×C5#12011yescharacteristic
315C22×C3×C5#12111yescharacteristic
316C22×C3×C5#12111yescharacteristic
317C22×C3×C5#12111yescharacteristic
318C22×C3×C5#12111yescharacteristic
319C22×C3×C5#12111yescharacteristic
320C22×C3×C5#12111yescharacteristic
321C22×C3×C5#12111yescharacteristic
322C22×C3×C5#12111yescharacteristic
323C22×C3×C5#12311yescharacteristic
324C22×C3×C5#12311yescharacteristic
325C22×C3×C5#12311yescharacteristic
326C22×C3×C5#12311yescharacteristic
327C22×C3×C5#12311yescharacteristic
328C22×C3×C5#12311yescharacteristic
329C22×C3×C5#12311yescharacteristic
330C22×C3×C5#12311yescharacteristic
331C22×C3×C5#12311yescharacteristic
332C22×C3×C5#12311yescharacteristic
333C22×C3×C5#12411yescharacteristic
334C22×C3×C5#12411yescharacteristic
335C22×C3×C5#12411yescharacteristic
336C22×C3×C5#12411yescharacteristic
337C22×C3×C5#12611yescharacteristic
338C22×C3×C5#12611yescharacteristic
339C22×C3×C5#12611yescharacteristic
340C22×C3×C5#12611yescharacteristic
341C2×C5×D3—24no—
342C2×C5×D3—24no—
343C2×C5×D3—24no—
344C2×C5×D3—42no—
345C2×C5×D3—42no—
346C2×C5×D3—42no—
347C2×C5×D3—42no—
348C2×C5×D3—42no—
349C2×C5×D3—42no—
350C2×C5×D3—42no—
351C2×C5×D3—42no—
352C2×C5×D3—42no—
353C2×C5×D3—42no—
354C2×C5×D3—42no—
355C2×C5×D3—42no—
356C3×C4×C5—42no—
357C3×C4×C5—42no—
358C3×C4×C5—42no—
359C5×Dic3—42no—
360C5×Dic3—42no—
361C5×Dic3—42no—
362C24×C3C23×C511yescharacteristic
363C23×D3—21no—
364C23×D3—21no—
365C23×D3—21no—
366C23×D3—21no—
367C23×D3—21no—
368C23×D3—21no—
369C23×D3—21no—
370C23×D3—21no—
371C23×D3—21no—
372C23×D3—21no—
373C23×D3—21no—
374C23×D3—21no—
375C23×D3C2×C4×C512yes—
376C23×D3C5×D412yes—
377C23×D3C5×D412yes—
378C22×C3×C4—21no—
379C22×C3×C4—21no—
380C22×C3×C4—21no—
381C22×C3×C4—21no—
382C22×C3×C4—21no—
383C22×C3×C4—21no—
384C22×C3×C4—21no—
385C22×C3×C4—21no—
386C22×C3×C4—21no—
387C22×C3×C4—21no—
388C22×C3×C4—21no—
389C22×C3×C4—21no—
390C22×C3×C4—21no—
391C22×C3×C4—21no—
392C22×C3×C4—21no—
393C22×C3×C4—21no—
394C22×C3×C4—21no—
395C22×C3×C4—21no—
396C22×C3×C4C2×C4×C512yes—
397C22×C3×C4C5×D412yes—
398C22×C3×C4C5×D412yes—
399C22×Dic3—21no—
400C22×Dic3—21no—
401C22×Dic3—21no—
402C22×Dic3—21no—
403C22×Dic3—21no—
404C22×Dic3—21no—
405C22×Dic3—21no—
406C22×Dic3—21no—
407C22×Dic3—21no—
408C22×Dic3—21no—
409C22×Dic3—21no—
410C22×Dic3—21no—
411C22×Dic3—21no—
412C22×Dic3—21no—
413C22×Dic3—21no—
414C22×Dic3—21no—
415C22×Dic3—21no—
416C22×Dic3—21no—
417C22×Dic3C2×C4×C512yes—
418C22×Dic3C5×D412yes—
419C22×Dic3C5×D412yes—
420(C2×D3)⋊C4—28no—
421(C2×D3)⋊C4—28no—
422(C2×D3)⋊C4—28no—
423C23×C5—34no—
424C23×C5—62no—
425C23×C5—62no—
426C23×C5—62no—
427C23×C5—62no—
428C23×C5—62no—
429C23×C5—62no—
430C23×C5—62no—
431C23×C5—62no—
432C23×C5—62no—
433C23×C5—62no—
434C23×C5—62no—
435C23×C5—62no—
436C23×C5—62no—
437C23×C5—62no—
438C23×C5—62no—
439C23×C5—62no—
440C23×C5—62no—
441C23×C5—62no—
442C23×C5—121no—
443C23×C5—121no—
444C23×C5—121no—
445C23×C5—121no—
446C23×C5—121no—
447C23×C5—121no—
448C23×C5—121no—
449C23×C5—121no—
450C23×C5—121no—
451C23×C5—121no—
452C23×C5—121no—
453C23×C5—121no—
454C23×C5—121no—
455C23×C5—121no—
456C23×C5—121no—
457C23×C5—121no—
458C23×C5C2×C4×D311yescharacteristic
459C23×C5C2×D1211yescharacteristic
460C23×C5#23511yescharacteristic
461C23×C5#23511yescharacteristic
462C23×C5#23511yescharacteristic
463C23×C5#23511yescharacteristic
464C23×C5D3×D411yescharacteristic
465C23×C5D3×D411yescharacteristic
466C23×C5D3×D411yescharacteristic
467C23×C5D3×D411yescharacteristic
468C23×C5#23711yescharacteristic
469C23×C5#23711yescharacteristic
470C23×C5#23911yescharacteristic
471C23×C5#23911yescharacteristic
472C23×C5C2×#6711yescharacteristic
473C2×C4×C5—22no—
474C2×C4×C5—22no—
475C2×C4×C5—22no—
476C2×C4×C5—22no—
477C2×C4×C5—22no—
478C2×C4×C5—22no—
479C2×C4×C5—22no—
480C2×C4×C5—22no—
481C2×C4×C5—22no—
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—62no—
495C2×C4×C5—62no—
496C2×C4×C5—62no—
497C2×C4×C5—62no—
498C2×C4×C5—62no—
499C2×C4×C5—62no—
500C2×C4×C5—62no—
501C2×C4×C5—62no—
502C2×C4×C5—62no—
503C2×C4×C5—121no—
504C2×C4×C5—121no—
505C2×C4×C5—121no—
506C2×C4×C5—121no—
507C2×C4×C5—121no—
508C2×C4×C5—121no—
509C2×C4×C5—121no—
510C2×C4×C5—121no—
511C2×C4×C5—121no—
512C2×C4×C5—121no—
513C2×C4×C5—121no—
514C2×C4×C5—121no—
515C25—31no—
516C23×C4—31no—
517C23×C4—31no—
518C23×C4—31no—
519C23×C4C2×C5×D311yescharacteristic
520C23×C4C2×C5×D311yescharacteristic
521C23×C4C2×C5×D311yescharacteristic
522C2×C22⋊C4—34no—
523C2×C22⋊C4—62no—
524C2×C22⋊C4—62no—
525C2×C22⋊C4—62no—
526C2×C22⋊C4—62no—
527C2×C22⋊C4—62no—
528C2×C22⋊C4—62no—
529C2×C22⋊C4—62no—
530C2×C22⋊C4—62no—
531#95—22no—
532#95—62no—
533#95—62no—
534#95—62no—
535C2×C3×C5#38111yescharacteristic
536C2×C3×C5#38611yescharacteristic
537C2×C3×C5#38611yescharacteristic
538C2×C3×C5#38811yescharacteristic
539C2×C3×C5#38811yescharacteristic
540C2×C3×C5#38811yescharacteristic
541C2×C3×C5#38811yescharacteristic
542C2×C3×C5#39411yescharacteristic
543C2×C3×C5#39411yescharacteristic
544C2×C3×C5#39411yescharacteristic
545C2×C3×C5#39411yescharacteristic
546C2×C3×C5#39711yescharacteristic
547C2×C3×C5#39711yescharacteristic
548C2×C3×C5#39711yescharacteristic
549C2×C3×C5#39711yescharacteristic
550C5×D3—44no—
551C23×C3C22×C4×C511yescharacteristic
552C23×C3C2×C5×D411yescharacteristic
553C23×C3C2×C5×D411yescharacteristic
554C23×C3C2×C5×D411yescharacteristic
555C23×C3C2×C5×D411yescharacteristic
556C23×C3C2×C5×D411yescharacteristic
557C23×C3C2×C5×D411yescharacteristic
558C23×C3C5×#4111yescharacteristic
559C23×C3C5×#4111yescharacteristic
560C23×C3C5×#4111yescharacteristic
561C23×C3C5×#4111yescharacteristic
562C23×C3C5×#4111yescharacteristic
563C23×C3C5×#4111yescharacteristic
564C23×C3C5×#4111yescharacteristic
565C23×C3C5×#4111yescharacteristic
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—22no—
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3—41no—
585C22×D3—41no—
586C22×D3—41no—
587C22×D3—41no—
588C22×D3—41no—
589C22×D3—41no—
590C22×D3—41no—
591C22×D3—41no—
592C22×D3—41no—
593C22×D3—41no—
594C22×D3—41no—
595C22×D3—41no—
596C22×D3—41no—
597C22×D3—41no—
598C22×D3—41no—
599C22×D3—41no—
600C22×D3C5×C22⋊C414yes—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C2×Dic3—41no—
641C2×Dic3—41no—
642C2×Dic3—41no—
643C22×C5—64no—
644C22×C5—64no—
645C22×C5—64no—
646C22×C5—122no—
647C22×C5—122no—
648C22×C5—122no—
649C22×C5—122no—
650C22×C5—122no—
651C22×C5—122no—
652C22×C5—122no—
653C22×C5—122no—
654C22×C5—122no—
655C22×C5—122no—
656C22×C5—122no—
657C22×C5—122no—
658C22×C5#87211yescharacteristic
659C22×C5C4×D1211yescharacteristic
660C22×C5#87511yescharacteristic
661C22×C5#87611yescharacteristic
662C22×C5D3×C22⋊C411yescharacteristic
663C22×C5#67⋊C411yescharacteristic
664C22×C5#88211yescharacteristic
665C22×C5#88311yescharacteristic
666C22×C5#88311yescharacteristic
667C22×C5#88311yescharacteristic
668C22×C5#88411yescharacteristic
669C22×C5#88411yescharacteristic
670C22×C5#88411yescharacteristic
671C22×C5#88511yescharacteristic
672C22×C5#88511yescharacteristic
673C22×C5#88611yescharacteristic
674C22×C5#89211yescharacteristic
675C22×C5#89311yescharacteristic
676C22×C5#89411yescharacteristic
677C22×C5#89411yescharacteristic
678C22×C5#89411yescharacteristic
679C22×C5#89411yescharacteristic
680C22×C5#89411yescharacteristic
681C22×C5#89511yescharacteristic
682C22×C5#89511yescharacteristic
683C22×C5#89811yescharacteristic
684C22×C5#89811yescharacteristic
685C22×C5#89811yescharacteristic
686C22×C5C4×#6711yescharacteristic
687C22×C5#92911yescharacteristic
688C22×C5#93011yescharacteristic
689C22×C5#93711yescharacteristic
690C22×C5#93811yescharacteristic
691C22×C5#93911yescharacteristic
692C22×C5#94711yescharacteristic
693C4×C5—42no—
694C4×C5—42no—
695C4×C5—42no—
696C4×C5—122no—
697C4×C5—122no—
698C4×C5—122no—
699C24—32no—
700C24—32no—
701C24—32no—
702C24—61no—
703C24—61no—
704C24—61no—
705C24—61no—
706C24—61no—
707C24—61no—
708C24—61no—
709C24—61no—
710C24—61no—
711C24—61no—
712C24—61no—
713C24—61no—
714C24C22×C5×D311yescharacteristic
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
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—32no—
734C22×C4—32no—
735C22×C4—32no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4C4×C5×D312yes—
755C22×C4C5×D1212yes—
756C22×C4C5×#6712yes—
757C22⋊C4—68no—
758C22⋊C4—68no—
759C22⋊C4—68no—
760C3×C5#144011yescharacteristic, complemented, Hall
761C22×C3C2×C5×C22⋊C411yescharacteristic
762C22×C3C5×#11711yescharacteristic
763C22×C3C5×#11711yescharacteristic
764C22×C3C4×C5×D411yescharacteristic
765C22×C3C4×C5×D411yescharacteristic
766C22×C3C4×C5×D411yescharacteristic
767C22×C3C4×C5×D411yescharacteristic
768C22×C3C5×#12011yescharacteristic
769C22×C3C5×#12011yescharacteristic
770C22×C3C5×#12111yescharacteristic
771C22×C3C5×#12111yescharacteristic
772C22×C3C5×#12111yescharacteristic
773C22×C3C5×#12111yescharacteristic
774C22×C3C5×#12111yescharacteristic
775C22×C3C5×#12111yescharacteristic
776C22×C3C5×#12111yescharacteristic
777C22×C3C5×#12111yescharacteristic
778C22×C3C5×#12311yescharacteristic
779C22×C3C5×#12311yescharacteristic
780C22×C3C5×#12311yescharacteristic
781C22×C3C5×#12311yescharacteristic
782C22×C3C5×#12311yescharacteristic
783C22×C3C5×#12311yescharacteristic
784C22×C3C5×#12311yescharacteristic
785C22×C3C5×#12311yescharacteristic
786C22×C3C5×#12311yescharacteristic
787C22×C3C5×#12311yescharacteristic
788C22×C3C5×#12411yescharacteristic
789C22×C3C5×#12411yescharacteristic
790C22×C3C5×#12411yescharacteristic
791C22×C3C5×#12411yescharacteristic
792C22×C3C5×#12611yescharacteristic
793C22×C3C5×#12611yescharacteristic
794C22×C3C5×#12611yescharacteristic
795C22×C3C5×#12611yescharacteristic
796C2×D3—24no—
797C2×D3—24no—
798C2×D3—24no—
799C2×D3—42no—
800C2×D3—42no—
801C2×D3—42no—
802C2×D3—42no—
803C2×D3—42no—
804C2×D3—42no—
805C2×D3—42no—
806C2×D3—42no—
807C2×D3—42no—
808C2×D3—42no—
809C2×D3—42no—
810C2×D3—42no—
811C3×C4—42no—
812C3×C4—42no—
813C3×C4—42no—
814Dic3—42no—
815Dic3—42no—
816Dic3—42no—
817C2×C5—124no—
818C2×C5#466411yescharacteristic
819C2×C5#466511yescharacteristic
820C2×C5#466911yescharacteristic
821C2×C5#467011yescharacteristic
822C2×C5#467211yescharacteristic
823C2×C5#467411yescharacteristic
824C2×C5#467511yescharacteristic
825C2×C5#467511yescharacteristic
826C2×C5#494011yescharacteristic
827C2×C5#495611yescharacteristic
828C2×C5#495911yescharacteristic
829C2×C5#496111yescharacteristic
830C2×C5#499011yescharacteristic
831C2×C5#499111yescharacteristic
832C2×C5#499211yescharacteristic
833C23—34no—
834C23—62no—
835C23—62no—
836C23—62no—
837C23—62no—
838C23—62no—
839C23—62no—
840C23—62no—
841C23—62no—
842C23—62no—
843C23—62no—
844C23—62no—
845C23—62no—
846C23—62no—
847C23—62no—
848C23—62no—
849C23—62no—
850C23—62no—
851C23—62no—
852C23—121no—
853C23—121no—
854C23—121no—
855C23—121no—
856C23—121no—
857C23—121no—
858C23—121no—
859C23—121no—
860C23—121no—
861C23—121no—
862C23—121no—
863C23—121no—
864C23—121no—
865C23—121no—
866C23—121no—
867C23—121no—
868C23C2×C4×C5×D311yescharacteristic
869C23C2×C5×D1211yescharacteristic
870C23C5×#23511yescharacteristic
871C23C5×#23511yescharacteristic
872C23C5×#23511yescharacteristic
873C23C5×#23511yescharacteristic
874C23C5×D3×D411yescharacteristic
875C23C5×D3×D411yescharacteristic
876C23C5×D3×D411yescharacteristic
877C23C5×D3×D411yescharacteristic
878C23C5×#23711yescharacteristic
879C23C5×#23711yescharacteristic
880C23C5×#23911yescharacteristic
881C23C5×#23911yescharacteristic
882C23C2×C5×#6711yescharacteristic
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
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×C4—41no—
904C2×C4—62no—
905C2×C4—62no—
906C2×C4—62no—
907C2×C4—62no—
908C2×C4—62no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—121no—
914C2×C4—121no—
915C2×C4—121no—
916C2×C4—121no—
917C2×C4—121no—
918C2×C4—121no—
919C2×C4—121no—
920C2×C4—121no—
921C2×C4—121no—
922C2×C4—121no—
923C2×C4—121no—
924C2×C4—121no—
925C2×C3C5×#38111yescharacteristic
926C2×C3C5×#38611yescharacteristic
927C2×C3C5×#38611yescharacteristic
928C2×C3C5×#38811yescharacteristic
929C2×C3C5×#38811yescharacteristic
930C2×C3C5×#38811yescharacteristic
931C2×C3C5×#38811yescharacteristic
932C2×C3C5×#39411yescharacteristic
933C2×C3C5×#39411yescharacteristic
934C2×C3C5×#39411yescharacteristic
935C2×C3C5×#39411yescharacteristic
936C2×C3C5×#39711yescharacteristic
937C2×C3C5×#39711yescharacteristic
938C2×C3C5×#39711yescharacteristic
939C2×C3C5×#39711yescharacteristic
940D3—44no—
941C5#6942911yescharacteristic, direct product factor, Sylow
942C22—64no—
943C22—64no—
944C22—64no—
945C22—122no—
946C22—122no—
947C22—122no—
948C22—122no—
949C22—122no—
950C22—122no—
951C22—122no—
952C22—122no—
953C22—122no—
954C22—122no—
955C22—122no—
956C22—122no—
957C22C5×#87211yescharacteristic
958C22C4×C5×D1211yescharacteristic
959C22C5×#87511yescharacteristic
960C22C5×#87611yescharacteristic
961C22C5×D3×C22⋊C411yescharacteristic
962C22C5×#67⋊C411yescharacteristic
963C22C5×#88211yescharacteristic
964C22C5×#88311yescharacteristic
965C22C5×#88311yescharacteristic
966C22C5×#88311yescharacteristic
967C22C5×#88411yescharacteristic
968C22C5×#88411yescharacteristic
969C22C5×#88411yescharacteristic
970C22C5×#88511yescharacteristic
971C22C5×#88511yescharacteristic
972C22C5×#88611yescharacteristic
973C22C5×#89211yescharacteristic
974C22C5×#89311yescharacteristic
975C22C5×#89411yescharacteristic
976C22C5×#89411yescharacteristic
977C22C5×#89411yescharacteristic
978C22C5×#89411yescharacteristic
979C22C5×#89411yescharacteristic
980C22C5×#89511yescharacteristic
981C22C5×#89511yescharacteristic
982C22C5×#89811yescharacteristic
983C22C5×#89811yescharacteristic
984C22C5×#89811yescharacteristic
985C22C4×C5×#6711yescharacteristic
986C22C5×#92911yescharacteristic
987C22C5×#93011yescharacteristic
988C22C5×#93711yescharacteristic
989C22C5×#93811yescharacteristic
990C22C5×#93911yescharacteristic
991C22C5×#94711yescharacteristic
992C4—42no—
993C4—42no—
994C4—42no—
995C4—122no—
996C4—122no—
997C4—122no—
998C3C5×#144011yescharacteristic, complemented, Sylow
999C2—124no—
1000C2C5×#466411yescharacteristic
1001C2C5×#466511yescharacteristic
1002C2C5×#466911yescharacteristic
1003C2C5×#467011yescharacteristic
1004C2C5×#467211yescharacteristic
1005C2C5×#467411yescharacteristic
1006C2C5×#467511yescharacteristic
1007C2C5×#467511yescharacteristic
1008C2C5×#494011yescharacteristic
1009C2C5×#495611yescharacteristic
1010C2C5×#495911yescharacteristic
1011C2C5×#496111yescharacteristic
1012C2C5×#499011yescharacteristic
1013C2C5×#499111yescharacteristic
1014C2C5×#499211yescharacteristic
subgroupG/H
centerC24×C5C22×D3
commutatorC23×C3C22×C4×C5
FrattiniC24C22×C5×D3
FittingC2×C3×C5×#95C2
socleC24×C3×C5C23
prime radicalC24×C5×D3C22
cosocleC24×C3C23×C5
hypercenterC2×C5×#95D3
hypocenterC3C5×#1440
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C5 ◁ C2×C5×#95

Complements

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

NH ≅ G/Ntype
4. C2×C3×C5×#95C2semidirect
5. C2×C5×C3⋊#95C2semidirect
6. C2×C5×C3⋊#95C2semidirect
7. C2×C5×C3⋊#95C2semidirect
24. C2×C5×(C2×D3)⋊C4C4semidirect
29. #69429C5direct (N × H)
36. C2×C5×#95D3semidirect
101. C2×C3×#95C2×C5semidirect
102. C2×C3⋊#95C2×C5semidirect
103. C2×C3⋊#95C2×C5semidirect
104. C2×C3⋊#95C2×C5semidirect
233. C2×(C2×D3)⋊C4C4×C5semidirect
305. C2×#95C5×D3semidirect
760. C3×C5#1440semidirect
941. C5#69429direct (N × H)
998. C3C5×#1440semidirect

Maximal subgroups

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

subgroupindex
C22×C5×(C2×D3)⋊C42
C2×C3×C5×#952
C2×C5×C3⋊#952
C5×#14403
#694295