Finite Group Databasebeta

← C5×#69421 #14280258

Subgroups — C5×#69421 #14280258

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×Dic3⋊C4C211yesmaximal, characteristic
2C2×C3×C5×#95C211yesmaximal, characteristic
3C2×C5×C3⋊#95C211yesmaximal, characteristic
4C2×C5×C3⋊#95C211yesmaximal, characteristic
5C2×C5×C3⋊#95C211yesmaximal, characteristic
6C2×C5×C3⋊#95C211yesmaximal, characteristic
7C2×C5×C3⋊#95C211yesmaximal, characteristic
8C5×#1445—31nomaximal, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C23×C3×C4×C5C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×C5×Dic3C2211yescharacteristic
13C23×C5×Dic3C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C2×C5×Dic3⋊C4—22no—
17C2×C5×Dic3⋊C4—22no—
18C2×C5×Dic3⋊C4C414yescomplemented
19C3×C5×#95—22no—
20C5×C3⋊#95—22no—
21C5×C3⋊#95—22no—
22C5×C3⋊#95—22no—
23C5×C3⋊#95—22no—
24C5×C3⋊#95—22no—
25#69421C511yesmaximal, characteristic, direct product factor, Hall
26C22×C5×C4⋊C4—31no—
27C2×C5×#95—31no—
28C2×C5×#95—31no—
29C2×C5×#95—31no—
30C2×C5×#95—31no—
31C2×C5×#95—31no—
32C2×C5×#95D311yescharacteristic
33C24×C3×C5C2311yescharacteristic
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5—21no—
46C22×C3×C4×C5—21no—
47C22×C3×C4×C5—21no—
48C22×C3×C4×C5—21no—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5—21no—
52C22×C3×C4×C5C2×C412yes—
53C22×C3×C4×C5D412yes—
54C22×C3×C4×C5Q812yes—
55C22×C5×Dic3—21no—
56C22×C5×Dic3—21no—
57C22×C5×Dic3—21no—
58C22×C5×Dic3—21no—
59C22×C5×Dic3—21no—
60C22×C5×Dic3—21no—
61C22×C5×Dic3—21no—
62C22×C5×Dic3—21no—
63C22×C5×Dic3—21no—
64C22×C5×Dic3—21no—
65C22×C5×Dic3—21no—
66C22×C5×Dic3—21no—
67C22×C5×Dic3—21no—
68C22×C5×Dic3—21no—
69C22×C5×Dic3—21no—
70C22×C5×Dic3—21no—
71C22×C5×Dic3—21no—
72C22×C5×Dic3—21no—
73C22×C5×Dic3—21no—
74C22×C5×Dic3—21no—
75C22×C5×Dic3—21no—
76C22×C5×Dic3—21no—
77C22×C5×Dic3C2×C412yes—
78C22×C5×Dic3C2×C412yes—
79C22×C5×Dic3D412yes—
80C22×C5×Dic3D412yes—
81C22×C5×Dic3D412yes—
82C22×C5×Dic3Q812yes—
83C5×Dic3⋊C4—28no—
84C22×Dic3⋊C4C2×C511yescharacteristic
85C2×C3×#95C2×C511yescharacteristic
86C2×C3⋊#95C2×C511yescharacteristic
87C2×C3⋊#95C2×C511yescharacteristic
88C2×C3⋊#95C2×C511yescharacteristic
89C2×C3⋊#95C2×C511yescharacteristic
90C2×C3⋊#95C2×C511yescharacteristic
91C23×C4×C5—31no—
92C23×C4×C5—31no—
93C23×C4×C5—31no—
94C23×C4×C5—31no—
95C23×C4×C5C2×D311yescharacteristic
96C23×C4×C5C2×D311yescharacteristic
97C23×C4×C5C2×D311yescharacteristic
98C2×C5×C4⋊C4—34no—
99C2×C5×C4⋊C4—62no—
100C2×C5×C4⋊C4—62no—
101C5×#95—22no—
102C5×#95—62no—
103C5×#95—62no—
104C5×#95—62no—
105C5×#95—62no—
106C5×#95—62no—
107#1445—31noSylow
108C23×C3×C5C22×C411yescharacteristic
109C23×C3×C5C2×D411yescharacteristic
110C23×C3×C5C2×D411yescharacteristic
111C23×C3×C5C2×D411yescharacteristic
112C23×C3×C5C2×D411yescharacteristic
113C23×C3×C5C2×Q811yescharacteristic
114C23×C3×C5C2×Q811yescharacteristic
115C23×C3×C5#4111yescharacteristic
116C23×C3×C5#4111yescharacteristic
117C23×C3×C5#4111yescharacteristic
118C23×C3×C5#4111yescharacteristic
119C23×C3×C5#4111yescharacteristic
120C23×C3×C5#4111yescharacteristic
121C23×C3×C5#4111yescharacteristic
122C23×C3×C5#4111yescharacteristic
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—41no—
133C2×C3×C4×C5—41no—
134C2×C3×C4×C5—41no—
135C2×C3×C4×C5—41no—
136C2×C3×C4×C5—41no—
137C2×C3×C4×C5—41no—
138C2×C3×C4×C5—41no—
139C2×C3×C4×C5—41no—
140C2×C3×C4×C5—41no—
141C2×C3×C4×C5—41no—
142C2×C3×C4×C5—41no—
143C2×C3×C4×C5—41no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—22no—
153C2×C5×Dic3—22no—
154C2×C5×Dic3—22no—
155C2×C5×Dic3—22no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3—22no—
158C2×C5×Dic3—22no—
159C2×C5×Dic3—41no—
160C2×C5×Dic3—41no—
161C2×C5×Dic3—41no—
162C2×C5×Dic3—41no—
163C2×C5×Dic3—41no—
164C2×C5×Dic3—41no—
165C2×C5×Dic3—41no—
166C2×C5×Dic3—41no—
167C2×C5×Dic3—41no—
168C2×C5×Dic3—41no—
169C2×C5×Dic3—41no—
170C2×C5×Dic3—41no—
171C2×C5×Dic3C22⋊C414yes—
172C23×C3×C4C22×C511yescharacteristic
173C23×C3×C4C22×C511yescharacteristic
174C23×C3×C4C22×C511yescharacteristic
175C23×Dic3C22×C511yescharacteristic
176C23×Dic3C22×C511yescharacteristic
177C23×Dic3C22×C511yescharacteristic
178C23×Dic3C22×C511yescharacteristic
179C2×Dic3⋊C4—22no—
180C2×Dic3⋊C4—22no—
181C2×Dic3⋊C4C4×C514yescomplemented
182C3×#95—22no—
183C3⋊#95—22no—
184C3⋊#95—22no—
185C3⋊#95—22no—
186C3⋊#95—22no—
187C3⋊#95—22no—
188C24×C5C22×D311yescharacteristic
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—32no—
208C22×C4×C5—32no—
209C22×C4×C5—32no—
210C22×C4×C5—32no—
211C22×C4×C5—32no—
212C22×C4×C5—32no—
213C22×C4×C5—61no—
214C22×C4×C5—61no—
215C22×C4×C5—61no—
216C22×C4×C5—61no—
217C22×C4×C5—61no—
218C22×C4×C5—61no—
219C22×C4×C5—61no—
220C22×C4×C5—61no—
221C22×C4×C5—61no—
222C22×C4×C5—61no—
223C22×C4×C5—61no—
224C22×C4×C5—61no—
225C22×C4×C5—61no—
226C22×C4×C5—61no—
227C22×C4×C5—61no—
228C22×C4×C5—61no—
229C22×C4×C5—61no—
230C22×C4×C5—61no—
231C22×C4×C5—61no—
232C22×C4×C5—61no—
233C22×C4×C5—61no—
234C22×C4×C5—61no—
235C22×C4×C5Dic612yes—
236C22×C4×C5C4×D312yes—
237C22×C4×C5#6712yes—
238C5×C4⋊C4—68no—
239C22×C4⋊C4—31no—
240C2×#95—31no—
241C2×#95—31no—
242C2×#95—31no—
243C2×#95—31no—
244C2×#95—31no—
245C2×#95C5×D311yescharacteristic
246C22×C3×C5C2×C22⋊C411yescharacteristic
247C22×C3×C5#11711yescharacteristic
248C22×C3×C5#11711yescharacteristic
249C22×C3×C5C4×D411yescharacteristic
250C22×C3×C5C4×D411yescharacteristic
251C22×C3×C5C4×Q811yescharacteristic
252C22×C3×C5C4×Q811yescharacteristic
253C22×C3×C5#12111yescharacteristic
254C22×C3×C5#12111yescharacteristic
255C22×C3×C5C22⋊Q811yescharacteristic
256C22×C3×C5C22⋊Q811yescharacteristic
257C22×C3×C5C22⋊Q811yescharacteristic
258C22×C3×C5C22⋊Q811yescharacteristic
259C22×C3×C5C22⋊Q811yescharacteristic
260C22×C3×C5C22⋊Q811yescharacteristic
261C22×C3×C5#12311yescharacteristic
262C22×C3×C5#12311yescharacteristic
263C22×C3×C5#12311yescharacteristic
264C22×C3×C5#12311yescharacteristic
265C22×C3×C5#12311yescharacteristic
266C22×C3×C5#12311yescharacteristic
267C22×C3×C5#12311yescharacteristic
268C22×C3×C5#12311yescharacteristic
269C22×C3×C5#12411yescharacteristic
270C22×C3×C5#12411yescharacteristic
271C22×C3×C5#12511yescharacteristic
272C22×C3×C5#12511yescharacteristic
273C22×C3×C5#12511yescharacteristic
274C22×C3×C5#12511yescharacteristic
275C22×C3×C5#12611yescharacteristic
276C22×C3×C5#12611yescharacteristic
277C22×C3×C5#12611yescharacteristic
278C22×C3×C5#12611yescharacteristic
279C22×C3×C5#12711yescharacteristic
280C22×C3×C5C4⋊Q811yescharacteristic
281C3×C4×C5—42no—
282C3×C4×C5—42no—
283C3×C4×C5—42no—
284C5×Dic3—24no—
285C5×Dic3—42no—
286C5×Dic3—42no—
287C5×Dic3—42no—
288C24×C3C23×C511yescharacteristic
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4C2×C4×C512yes—
308C22×C3×C4C5×D412yes—
309C22×C3×C4C5×Q812yes—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3C2×C4×C512yes—
333C22×Dic3C2×C4×C512yes—
334C22×Dic3C5×D412yes—
335C22×Dic3C5×D412yes—
336C22×Dic3C5×D412yes—
337C22×Dic3C5×Q812yes—
338Dic3⋊C4—28no—
339C23×C5C2×Dic611yescharacteristic
340C23×C5C2×C4×D311yescharacteristic
341C23×C5#23511yescharacteristic
342C23×C5#23511yescharacteristic
343C23×C5#23511yescharacteristic
344C23×C5#23511yescharacteristic
345C23×C5D3×D411yescharacteristic
346C23×C5D3×D411yescharacteristic
347C23×C5D3×D411yescharacteristic
348C23×C5#23711yescharacteristic
349C23×C5#23711yescharacteristic
350C23×C5#23711yescharacteristic
351C23×C5D3×Q811yescharacteristic
352C23×C5#23911yescharacteristic
353C23×C5C2×#6711yescharacteristic
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—34no—
364C2×C4×C5—41no—
365C2×C4×C5—41no—
366C2×C4×C5—41no—
367C2×C4×C5—41no—
368C2×C4×C5—41no—
369C2×C4×C5—41no—
370C2×C4×C5—41no—
371C2×C4×C5—41no—
372C2×C4×C5—41no—
373C2×C4×C5—41no—
374C2×C4×C5—41no—
375C2×C4×C5—41no—
376C2×C4×C5—62no—
377C2×C4×C5—62no—
378C2×C4×C5—62no—
379C2×C4×C5—62no—
380C2×C4×C5—62no—
381C2×C4×C5—62no—
382C2×C4×C5—62no—
383C2×C4×C5—62no—
384C2×C4×C5—62no—
385C2×C4×C5—62no—
386C2×C4×C5—62no—
387C2×C4×C5—62no—
388C2×C4×C5—62no—
389C2×C4×C5—62no—
390C2×C4×C5—62no—
391C2×C4×C5—121no—
392C2×C4×C5—121no—
393C2×C4×C5—121no—
394C2×C4×C5—121no—
395C2×C4×C5—121no—
396C2×C4×C5—121no—
397C2×C4×C5—121no—
398C2×C4×C5—121no—
399C2×C4×C5—121no—
400C2×C4×C5—121no—
401C2×C4×C5—121no—
402C2×C4×C5—121no—
403C23×C4—31no—
404C23×C4—31no—
405C23×C4—31no—
406C23×C4—31no—
407C23×C4C2×C5×D311yescharacteristic
408C23×C4C2×C5×D311yescharacteristic
409C23×C4C2×C5×D311yescharacteristic
410C2×C4⋊C4—34no—
411C2×C4⋊C4—62no—
412C2×C4⋊C4—62no—
413#95—22no—
414#95—62no—
415#95—62no—
416#95—62no—
417#95—62no—
418#95—62no—
419C2×C3×C5#38111yescharacteristic
420C2×C3×C5#38711yescharacteristic
421C2×C3×C5#38711yescharacteristic
422C2×C3×C5#38711yescharacteristic
423C2×C3×C5#38711yescharacteristic
424C2×C3×C5#39011yescharacteristic
425C2×C3×C5#39111yescharacteristic
426C2×C3×C5#39711yescharacteristic
427C2×C3×C5#39711yescharacteristic
428C2×C3×C5#39811yescharacteristic
429C2×C3×C5#39811yescharacteristic
430C2×C3×C5#39911yescharacteristic
431C2×C3×C5#39911yescharacteristic
432C2×C3×C5#40011yescharacteristic
433C2×C3×C5#40011yescharacteristic
434C23×C3C22×C4×C511yescharacteristic
435C23×C3C2×C5×D411yescharacteristic
436C23×C3C2×C5×D411yescharacteristic
437C23×C3C2×C5×D411yescharacteristic
438C23×C3C2×C5×D411yescharacteristic
439C23×C3C2×C5×Q811yescharacteristic
440C23×C3C2×C5×Q811yescharacteristic
441C23×C3C5×#4111yescharacteristic
442C23×C3C5×#4111yescharacteristic
443C23×C3C5×#4111yescharacteristic
444C23×C3C5×#4111yescharacteristic
445C23×C3C5×#4111yescharacteristic
446C23×C3C5×#4111yescharacteristic
447C23×C3C5×#4111yescharacteristic
448C23×C3C5×#4111yescharacteristic
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3C5×C22⋊C414yes—
498C22×C5C4×Dic611yescharacteristic
499C22×C5#87011yescharacteristic
500C22×C5#87211yescharacteristic
501C22×C5#87611yescharacteristic
502C22×C5#87811yescharacteristic
503C22×C5#87811yescharacteristic
504C22×C5#87911yescharacteristic
505C22×C5#87911yescharacteristic
506C22×C5D3×C22⋊C411yescharacteristic
507C22×C5#67⋊C411yescharacteristic
508C22×C5#88311yescharacteristic
509C22×C5#88311yescharacteristic
510C22×C5#88311yescharacteristic
511C22×C5#88411yescharacteristic
512C22×C5#88511yescharacteristic
513C22×C5#88511yescharacteristic
514C22×C5#88711yescharacteristic
515C22×C5#88811yescharacteristic
516C22×C5#88911yescharacteristic
517C22×C5#88911yescharacteristic
518C22×C5#89011yescharacteristic
519C22×C5#89211yescharacteristic
520C22×C5#89411yescharacteristic
521C22×C5#89411yescharacteristic
522C22×C5#89411yescharacteristic
523C22×C5#89611yescharacteristic
524C22×C5#89611yescharacteristic
525C22×C5#89811yescharacteristic
526C22×C5#92411yescharacteristic
527C22×C5C4×#6711yescharacteristic
528C22×C5#92911yescharacteristic
529C22×C5#93511yescharacteristic
530C22×C5#93911yescharacteristic
531C22×C5#94011yescharacteristic
532C22×C5#94611yescharacteristic
533C4×C5—42no—
534C4×C5—42no—
535C4×C5—42no—
536C4×C5—64no—
537C4×C5—122no—
538C4×C5—122no—
539C4×C5—122no—
540C24C22×C5×D311yescharacteristic
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—32no—
560C22×C4—32no—
561C22×C4—32no—
562C22×C4—32no—
563C22×C4—32no—
564C22×C4—32no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4C5×Dic612yes—
588C22×C4C4×C5×D312yes—
589C22×C4C5×#6712yes—
590C4⋊C4—68no—
591C3×C5#144511yescharacteristic, complemented, Hall
592C22×C3C2×C5×C22⋊C411yescharacteristic
593C22×C3C5×#11711yescharacteristic
594C22×C3C5×#11711yescharacteristic
595C22×C3C4×C5×D411yescharacteristic
596C22×C3C4×C5×D411yescharacteristic
597C22×C3C4×C5×Q811yescharacteristic
598C22×C3C4×C5×Q811yescharacteristic
599C22×C3C5×#12111yescharacteristic
600C22×C3C5×#12111yescharacteristic
601C22×C3C5×C22⋊Q811yescharacteristic
602C22×C3C5×C22⋊Q811yescharacteristic
603C22×C3C5×C22⋊Q811yescharacteristic
604C22×C3C5×C22⋊Q811yescharacteristic
605C22×C3C5×C22⋊Q811yescharacteristic
606C22×C3C5×C22⋊Q811yescharacteristic
607C22×C3C5×#12311yescharacteristic
608C22×C3C5×#12311yescharacteristic
609C22×C3C5×#12311yescharacteristic
610C22×C3C5×#12311yescharacteristic
611C22×C3C5×#12311yescharacteristic
612C22×C3C5×#12311yescharacteristic
613C22×C3C5×#12311yescharacteristic
614C22×C3C5×#12311yescharacteristic
615C22×C3C5×#12411yescharacteristic
616C22×C3C5×#12411yescharacteristic
617C22×C3C5×#12511yescharacteristic
618C22×C3C5×#12511yescharacteristic
619C22×C3C5×#12511yescharacteristic
620C22×C3C5×#12511yescharacteristic
621C22×C3C5×#12611yescharacteristic
622C22×C3C5×#12611yescharacteristic
623C22×C3C5×#12611yescharacteristic
624C22×C3C5×#12611yescharacteristic
625C22×C3C5×#12711yescharacteristic
626C22×C3C5×C4⋊Q811yescharacteristic
627C3×C4—42no—
628C3×C4—42no—
629C3×C4—42no—
630Dic3—24no—
631Dic3—42no—
632Dic3—42no—
633Dic3—42no—
634C2×C5#464611yescharacteristic
635C2×C5#465211yescharacteristic
636C2×C5#465511yescharacteristic
637C2×C5#465711yescharacteristic
638C2×C5#465811yescharacteristic
639C2×C5#466011yescharacteristic
640C2×C5#466411yescharacteristic
641C2×C5#467511yescharacteristic
642C2×C5#493311yescharacteristic
643C2×C5#494911yescharacteristic
644C2×C5#495211yescharacteristic
645C2×C5#495711yescharacteristic
646C2×C5#497811yescharacteristic
647C2×C5#498211yescharacteristic
648C2×C5#499311yescharacteristic
649C23C2×C5×Dic611yescharacteristic
650C23C2×C4×C5×D311yescharacteristic
651C23C5×#23511yescharacteristic
652C23C5×#23511yescharacteristic
653C23C5×#23511yescharacteristic
654C23C5×#23511yescharacteristic
655C23C5×D3×D411yescharacteristic
656C23C5×D3×D411yescharacteristic
657C23C5×D3×D411yescharacteristic
658C23C5×#23711yescharacteristic
659C23C5×#23711yescharacteristic
660C23C5×#23711yescharacteristic
661C23C5×D3×Q811yescharacteristic
662C23C5×#23911yescharacteristic
663C23C2×C5×#6711yescharacteristic
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—34no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C3C5×#38111yescharacteristic
714C2×C3C5×#38711yescharacteristic
715C2×C3C5×#38711yescharacteristic
716C2×C3C5×#38711yescharacteristic
717C2×C3C5×#38711yescharacteristic
718C2×C3C5×#39011yescharacteristic
719C2×C3C5×#39111yescharacteristic
720C2×C3C5×#39711yescharacteristic
721C2×C3C5×#39711yescharacteristic
722C2×C3C5×#39811yescharacteristic
723C2×C3C5×#39811yescharacteristic
724C2×C3C5×#39911yescharacteristic
725C2×C3C5×#39911yescharacteristic
726C2×C3C5×#40011yescharacteristic
727C2×C3C5×#40011yescharacteristic
728C5#6942111yescharacteristic, direct product factor, Sylow
729C22C4×C5×Dic611yescharacteristic
730C22C5×#87011yescharacteristic
731C22C5×#87211yescharacteristic
732C22C5×#87611yescharacteristic
733C22C5×#87811yescharacteristic
734C22C5×#87811yescharacteristic
735C22C5×#87911yescharacteristic
736C22C5×#87911yescharacteristic
737C22C5×D3×C22⋊C411yescharacteristic
738C22C5×#67⋊C411yescharacteristic
739C22C5×#88311yescharacteristic
740C22C5×#88311yescharacteristic
741C22C5×#88311yescharacteristic
742C22C5×#88411yescharacteristic
743C22C5×#88511yescharacteristic
744C22C5×#88511yescharacteristic
745C22C5×#88711yescharacteristic
746C22C5×#88811yescharacteristic
747C22C5×#88911yescharacteristic
748C22C5×#88911yescharacteristic
749C22C5×#89011yescharacteristic
750C22C5×#89211yescharacteristic
751C22C5×#89411yescharacteristic
752C22C5×#89411yescharacteristic
753C22C5×#89411yescharacteristic
754C22C5×#89611yescharacteristic
755C22C5×#89611yescharacteristic
756C22C5×#89811yescharacteristic
757C22C5×#92411yescharacteristic
758C22C4×C5×#6711yescharacteristic
759C22C5×#92911yescharacteristic
760C22C5×#93511yescharacteristic
761C22C5×#93911yescharacteristic
762C22C5×#94011yescharacteristic
763C22C5×#94611yescharacteristic
764C4—42no—
765C4—42no—
766C4—42no—
767C4—64no—
768C4—122no—
769C4—122no—
770C4—122no—
771C3C5×#144511yescharacteristic, complemented, Sylow
772C2C5×#464611yescharacteristic
773C2C5×#465211yescharacteristic
774C2C5×#465511yescharacteristic
775C2C5×#465711yescharacteristic
776C2C5×#465811yescharacteristic
777C2C5×#466011yescharacteristic
778C2C5×#466411yescharacteristic
779C2C5×#467511yescharacteristic
780C2C5×#493311yescharacteristic
781C2C5×#494911yescharacteristic
782C2C5×#495211yescharacteristic
783C2C5×#495711yescharacteristic
784C2C5×#497811yescharacteristic
785C2C5×#498211yescharacteristic
786C2C5×#499311yescharacteristic
subgroupG/H
centerC24×C5C22×D3
commutatorC23×C3C22×C4×C5
FrattiniC24C22×C5×D3
FittingC2×C3×C5×#95C2
socle, prime radicalC24×C3×C5C23
cosocleC24×C3C23×C5
hypercenterC2×C5×#95D3
hypocenterC3C5×#1445
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C5 ◁ C2×C5×#95

Complements

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

NH ≅ G/Ntype
18. C2×C5×Dic3⋊C4C4semidirect
25. #69421C5direct (N × H)
181. C2×Dic3⋊C4C4×C5semidirect
591. C3×C5#1445semidirect
728. C5#69421direct (N × H)
771. C3C5×#1445semidirect

Maximal subgroups

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

subgroupindex
C22×C5×Dic3⋊C42
C2×C3×C5×#952
C2×C5×C3⋊#952
C5×#14453
#694215