Finite Group Databasebeta

← C3×#10602340 #14280052

Subgroups — C3×#10602340 #14280052

Order 1920.

1560 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×C22⋊C4C211yesmaximal, characteristic
2C22×C3×C22⋊Dic5C211yesmaximal, characteristic
3C22×C3×C22⋊Dic5C211yesmaximal, characteristic
4C22×C3×#683C211yesmaximal, characteristic, complemented
5C2×C3×#3963C211yesmaximal, characteristic, complemented
6C2×C3×#3963C211yesmaximal, characteristic, complemented
7C2×C3×#3963C211yesmaximal, characteristic, complemented
8#10602340C311yesmaximal, characteristic, direct product factor, Hall
9C25×C3×C5C2211yescharacteristic
10C23×C3×C4×C5C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×C3×Dic5C2211yescharacteristic
13C23×C3×Dic5C2211yescharacteristic
14C23×C3×Dic5C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C2×C3×C5×C22⋊C4—22no—
17C2×C3×C5×C22⋊C4—22no—
18C2×C3×C5×C22⋊C4—22no—
19C2×C3×C22⋊Dic5—22no—
20C2×C3×C22⋊Dic5—22no—
21C2×C3×C22⋊Dic5—22no—
22C2×C3×C22⋊Dic5—22no—
23C2×C3×C22⋊Dic5—22no—
24C2×C3×C22⋊Dic5C414yescomplemented
25C2×C3×#683—22no—
26C2×C3×#683—22no—
27C2×C3×#683—22no—
28C3×#3963—22no—
29C3×#3963—22no—
30C3×#3963—22no—
31C3×#1439—51nomaximal, Hall
32C22×C5×C22⋊C4C2×C311yescharacteristic
33C22×C22⋊Dic5C2×C311yescharacteristic
34C22×C22⋊Dic5C2×C311yescharacteristic
35C22×#683C2×C311yescharacteristic, complemented
36C2×#3963C2×C311yescharacteristic, complemented
37C2×#3963C2×C311yescharacteristic, complemented
38C2×#3963C2×C311yescharacteristic, complemented
39C24×C3×C5—21no—
40C24×C3×C5—21no—
41C24×C3×C5—21no—
42C24×C3×C5—21no—
43C24×C3×C5—21no—
44C24×C3×C5—21no—
45C24×C3×C5—21no—
46C24×C3×C5—21no—
47C24×C3×C5—21no—
48C24×C3×C5—21no—
49C24×C3×C5—21no—
50C24×C3×C5—21no—
51C24×C3×C5C2×C412yes—
52C24×C3×C5D412yes—
53C24×C3×C5Q812yes—
54C24×C3×C5C2311yescharacteristic
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×C5D412yes—
68C22×C3×C4×C5D412yes—
69C22×C3×Dic5—21no—
70C22×C3×Dic5—21no—
71C22×C3×Dic5—21no—
72C22×C3×Dic5—21no—
73C22×C3×Dic5—21no—
74C22×C3×Dic5—21no—
75C22×C3×Dic5—21no—
76C22×C3×Dic5—21no—
77C22×C3×Dic5—21no—
78C22×C3×Dic5—21no—
79C22×C3×Dic5—21no—
80C22×C3×Dic5—21no—
81C22×C3×Dic5—21no—
82C22×C3×Dic5—21no—
83C22×C3×Dic5—21no—
84C22×C3×Dic5—21no—
85C22×C3×Dic5—21no—
86C22×C3×Dic5—21no—
87C22×C3×Dic5—21no—
88C22×C3×Dic5—21no—
89C22×C3×Dic5—21no—
90C22×C3×Dic5—21no—
91C22×C3×Dic5C2×C412yes—
92C22×C3×Dic5C2×C412yes—
93C22×C3×Dic5D412yes—
94C22×C3×Dic5D412yes—
95C22×C3×Dic5D412yes—
96C22×C3×Dic5D412yes—
97C3×C5×C22⋊C4—28no—
98C3×C22⋊Dic5—28no—
99C3×C22⋊Dic5—28no—
100C3×#683—28no—
101C22×C3×C4⋊C4—51no—
102C22×C3×C22⋊C4—51no—
103C22×C3×C22⋊C4—51no—
104C22×C3×C22⋊C4D511yescharacteristic
105C2×C3×#95—51no—
106C2×C3×#95—51no—
107C2×C3×#95—51no—
108C25×C5C22×C311yescharacteristic
109C23×C4×C5C22×C311yescharacteristic
110C23×C4×C5C22×C311yescharacteristic
111C23×Dic5C22×C311yescharacteristic
112C23×Dic5C22×C311yescharacteristic
113C23×Dic5C22×C311yescharacteristic
114C23×Dic5C22×C311yescharacteristic
115C2×C5×C22⋊C4—22no—
116C2×C5×C22⋊C4—22no—
117C2×C5×C22⋊C4—22no—
118C2×C22⋊Dic5—22no—
119C2×C22⋊Dic5—22no—
120C2×C22⋊Dic5—22no—
121C2×C22⋊Dic5—22no—
122C2×C22⋊Dic5—22no—
123C2×C22⋊Dic5C3×C414yescomplemented
124C2×#683—22no—
125C2×#683—22no—
126C2×#683—22no—
127#3963—22no—
128#3963—22no—
129#3963—22no—
130#1439—51noSylow
131C23×C3×C5—22no—
132C23×C3×C5—22no—
133C23×C3×C5—22no—
134C23×C3×C5—22no—
135C23×C3×C5—22no—
136C23×C3×C5—22no—
137C23×C3×C5—22no—
138C23×C3×C5—22no—
139C23×C3×C5—22no—
140C23×C3×C5—22no—
141C23×C3×C5—22no—
142C23×C3×C5—22no—
143C23×C3×C5—22no—
144C23×C3×C5—22no—
145C23×C3×C5—22no—
146C23×C3×C5—22no—
147C23×C3×C5—22no—
148C23×C3×C5—22no—
149C23×C3×C5—41no—
150C23×C3×C5—41no—
151C23×C3×C5—41no—
152C23×C3×C5—41no—
153C23×C3×C5—41no—
154C23×C3×C5—41no—
155C23×C3×C5—41no—
156C23×C3×C5—41no—
157C23×C3×C5—41no—
158C23×C3×C5—41no—
159C23×C3×C5—41no—
160C23×C3×C5—41no—
161C23×C3×C5—41no—
162C23×C3×C5—41no—
163C23×C3×C5—41no—
164C23×C3×C5—41no—
165C23×C3×C5C4⋊C414yescomplemented
166C23×C3×C5C22×C411yescharacteristic
167C23×C3×C5C2×D411yescharacteristic
168C23×C3×C5C2×D411yescharacteristic
169C23×C3×C5C2×D411yescharacteristic
170C23×C3×C5C2×D411yescharacteristic
171C23×C3×C5C2×D411yescharacteristic
172C23×C3×C5C2×D411yescharacteristic
173C23×C3×C5C2×D411yescharacteristic
174C23×C3×C5C2×Q811yescharacteristic
175C23×C3×C5#4111yescharacteristic
176C23×C3×C5#4111yescharacteristic
177C23×C3×C5#4111yescharacteristic
178C23×C3×C5#4111yescharacteristic
179C23×C3×C5#4111yescharacteristic
180C23×C3×C5#4111yescharacteristic
181C2×C3×C4×C5—22no—
182C2×C3×C4×C5—22no—
183C2×C3×C4×C5—22no—
184C2×C3×C4×C5—22no—
185C2×C3×C4×C5—22no—
186C2×C3×C4×C5—22no—
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×Dic5—22no—
196C2×C3×Dic5—22no—
197C2×C3×Dic5—22no—
198C2×C3×Dic5—22no—
199C2×C3×Dic5—22no—
200C2×C3×Dic5—22no—
201C2×C3×Dic5—22no—
202C2×C3×Dic5—22no—
203C2×C3×Dic5—22no—
204C2×C3×Dic5—22no—
205C2×C3×Dic5—22no—
206C2×C3×Dic5—22no—
207C2×C3×Dic5—22no—
208C2×C3×Dic5—22no—
209C2×C3×Dic5—22no—
210C2×C3×Dic5—41no—
211C2×C3×Dic5—41no—
212C2×C3×Dic5—41no—
213C2×C3×Dic5—41no—
214C2×C3×Dic5—41no—
215C2×C3×Dic5—41no—
216C2×C3×Dic5—41no—
217C2×C3×Dic5—41no—
218C2×C3×Dic5—41no—
219C2×C3×Dic5—41no—
220C2×C3×Dic5—41no—
221C2×C3×Dic5—41no—
222C2×C3×Dic5C22⋊C414yescomplemented
223C25×C3C2×D511yescharacteristic
224C23×C3×C4—51no—
225C23×C3×C4—51no—
226C23×C3×C4—51no—
227C23×C3×C4—51no—
228C23×C3×C4C2×D511yescharacteristic
229C23×C3×C4C2×D511yescharacteristic
230C2×C3×C4⋊C4—102no—
231C2×C3×C4⋊C4—102no—
232C2×C3×C4⋊C4—102no—
233C2×C3×C22⋊C4—22no—
234C2×C3×C22⋊C4—22no—
235C2×C3×C22⋊C4—22no—
236C2×C3×C22⋊C4—54no—
237C2×C3×C22⋊C4—102no—
238C2×C3×C22⋊C4—102no—
239C2×C3×C22⋊C4—102no—
240C2×C3×C22⋊C4—102no—
241C2×C3×C22⋊C4—102no—
242C3×#95—102no—
243C3×#95—102no—
244C3×#95—102no—
245C24×C5—21no—
246C24×C5—21no—
247C24×C5—21no—
248C24×C5—21no—
249C24×C5—21no—
250C24×C5—21no—
251C24×C5—21no—
252C24×C5—21no—
253C24×C5—21no—
254C24×C5—21no—
255C24×C5—21no—
256C24×C5—21no—
257C24×C5C2×C3×C412yes—
258C24×C5C3×D412yes—
259C24×C5C3×Q812yes—
260C24×C5C23×C311yescharacteristic
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—21no—
273C22×C4×C5C3×D412yes—
274C22×C4×C5C3×D412yes—
275C22×Dic5—21no—
276C22×Dic5—21no—
277C22×Dic5—21no—
278C22×Dic5—21no—
279C22×Dic5—21no—
280C22×Dic5—21no—
281C22×Dic5—21no—
282C22×Dic5—21no—
283C22×Dic5—21no—
284C22×Dic5—21no—
285C22×Dic5—21no—
286C22×Dic5—21no—
287C22×Dic5—21no—
288C22×Dic5—21no—
289C22×Dic5—21no—
290C22×Dic5—21no—
291C22×Dic5—21no—
292C22×Dic5—21no—
293C22×Dic5—21no—
294C22×Dic5—21no—
295C22×Dic5—21no—
296C22×Dic5—21no—
297C22×Dic5C2×C3×C412yes—
298C22×Dic5C2×C3×C412yes—
299C22×Dic5C3×D412yes—
300C22×Dic5C3×D412yes—
301C22×Dic5C3×D412yes—
302C22×Dic5C3×D412yes—
303C5×C22⋊C4—28no—
304C22⋊Dic5—28no—
305C22⋊Dic5—28no—
306#683—28no—
307C22×C4⋊C4—51no—
308C22×C22⋊C4—51no—
309C22×C22⋊C4—51no—
310C22×C22⋊C4C3×D511yescharacteristic
311C2×#95—51no—
312C2×#95—51no—
313C2×#95—51no—
314C22×C3×C5—24no—
315C22×C3×C5—24no—
316C22×C3×C5—24no—
317C22×C3×C5—42no—
318C22×C3×C5—42no—
319C22×C3×C5—42no—
320C22×C3×C5—42no—
321C22×C3×C5—42no—
322C22×C3×C5—42no—
323C22×C3×C5—42no—
324C22×C3×C5—42no—
325C22×C3×C5—42no—
326C22×C3×C5—42no—
327C22×C3×C5—42no—
328C22×C3×C5—42no—
329C22×C3×C5C2×C22⋊C411yescharacteristic
330C22×C3×C5C2×C4⋊C411yescharacteristic
331C22×C3×C5#11711yescharacteristic
332C22×C3×C5C4×D411yescharacteristic
333C22×C3×C5C4×D411yescharacteristic
334C22×C3×C5C4×D411yescharacteristic
335C22×C3×C5C4×D411yescharacteristic
336C22×C3×C5#12011yescharacteristic
337C22×C3×C5#12011yescharacteristic
338C22×C3×C5#12011yescharacteristic
339C22×C3×C5#12111yescharacteristic
340C22×C3×C5#12111yescharacteristic
341C22×C3×C5#12111yescharacteristic
342C22×C3×C5#12111yescharacteristic
343C22×C3×C5#12111yescharacteristic
344C22×C3×C5#12111yescharacteristic
345C22×C3×C5#12111yescharacteristic
346C22×C3×C5#12111yescharacteristic
347C22×C3×C5C22⋊Q811yescharacteristic
348C22×C3×C5C22⋊Q811yescharacteristic
349C22×C3×C5C22⋊Q811yescharacteristic
350C22×C3×C5C22⋊Q811yescharacteristic
351C22×C3×C5C22⋊Q811yescharacteristic
352C22×C3×C5C22⋊Q811yescharacteristic
353C22×C3×C5#12311yescharacteristic
354C22×C3×C5#12311yescharacteristic
355C22×C3×C5#12311yescharacteristic
356C22×C3×C5#12311yescharacteristic
357C22×C3×C5#12311yescharacteristic
358C22×C3×C5#12411yescharacteristic
359C22×C3×C5#12411yescharacteristic
360C22×C3×C5#12411yescharacteristic
361C22×C3×C5#12611yescharacteristic
362C22×C3×C5#12611yescharacteristic
363C22×C3×C5#12711yescharacteristic
364C3×C4×C5—42no—
365C3×C4×C5—42no—
366C3×Dic5—24no—
367C3×Dic5—42no—
368C3×Dic5—42no—
369C3×Dic5—42no—
370C24×C3—21no—
371C24×C3—21no—
372C24×C3—21no—
373C24×C3—21no—
374C24×C3—21no—
375C24×C3—21no—
376C24×C3—21no—
377C24×C3—21no—
378C24×C3—21no—
379C24×C3—21no—
380C24×C3—21no—
381C24×C3—21no—
382C24×C3Dic1012yes—
383C24×C3C4×D512yes—
384C24×C3C22⋊D512yes—
385C24×C3C22×D511yescharacteristic
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×C4—21no—
397C22×C3×C4—21no—
398C22×C3×C4—52no—
399C22×C3×C4—52no—
400C22×C3×C4—52no—
401C22×C3×C4—52no—
402C22×C3×C4—52no—
403C22×C3×C4—52no—
404C22×C3×C4—101no—
405C22×C3×C4—101no—
406C22×C3×C4—101no—
407C22×C3×C4—101no—
408C22×C3×C4—101no—
409C22×C3×C4—101no—
410C22×C3×C4—101no—
411C22×C3×C4—101no—
412C22×C3×C4—101no—
413C22×C3×C4—101no—
414C22×C3×C4—101no—
415C22×C3×C4—101no—
416C22×C3×C4—101no—
417C22×C3×C4—101no—
418C22×C3×C4—101no—
419C22×C3×C4—101no—
420C22×C3×C4—101no—
421C22×C3×C4—101no—
422C22×C3×C4—101no—
423C22×C3×C4—101no—
424C22×C3×C4—101no—
425C22×C3×C4—101no—
426C22×C3×C4C22⋊D512yes—
427C22×C3×C4C22⋊D512yes—
428C3×C4⋊C4—108no—
429C3×C22⋊C4—28no—
430C3×C22⋊C4—108no—
431C3×C22⋊C4—108no—
432C23×C5—22no—
433C23×C5—22no—
434C23×C5—22no—
435C23×C5—22no—
436C23×C5—22no—
437C23×C5—22no—
438C23×C5—22no—
439C23×C5—22no—
440C23×C5—22no—
441C23×C5—22no—
442C23×C5—22no—
443C23×C5—22no—
444C23×C5—22no—
445C23×C5—22no—
446C23×C5—22no—
447C23×C5—22no—
448C23×C5—22no—
449C23×C5—22no—
450C23×C5—41no—
451C23×C5—41no—
452C23×C5—41no—
453C23×C5—41no—
454C23×C5—41no—
455C23×C5—41no—
456C23×C5—41no—
457C23×C5—41no—
458C23×C5—41no—
459C23×C5—41no—
460C23×C5—41no—
461C23×C5—41no—
462C23×C5—41no—
463C23×C5—41no—
464C23×C5—41no—
465C23×C5—41no—
466C23×C5C3×C4⋊C414yescomplemented
467C23×C5C22×C3×C411yescharacteristic
468C23×C5C2×C3×D411yescharacteristic
469C23×C5C2×C3×D411yescharacteristic
470C23×C5C2×C3×D411yescharacteristic
471C23×C5C2×C3×D411yescharacteristic
472C23×C5C2×C3×D411yescharacteristic
473C23×C5C2×C3×D411yescharacteristic
474C23×C5C2×C3×D411yescharacteristic
475C23×C5C2×C3×Q811yescharacteristic
476C23×C5C3×#4111yescharacteristic
477C23×C5C3×#4111yescharacteristic
478C23×C5C3×#4111yescharacteristic
479C23×C5C3×#4111yescharacteristic
480C23×C5C3×#4111yescharacteristic
481C23×C5C3×#4111yescharacteristic
482C2×C4×C5—22no—
483C2×C4×C5—22no—
484C2×C4×C5—22no—
485C2×C4×C5—22no—
486C2×C4×C5—22no—
487C2×C4×C5—22no—
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—41no—
495C2×C4×C5—41no—
496C2×Dic5—22no—
497C2×Dic5—22no—
498C2×Dic5—22no—
499C2×Dic5—22no—
500C2×Dic5—22no—
501C2×Dic5—22no—
502C2×Dic5—22no—
503C2×Dic5—22no—
504C2×Dic5—22no—
505C2×Dic5—22no—
506C2×Dic5—22no—
507C2×Dic5—22no—
508C2×Dic5—22no—
509C2×Dic5—22no—
510C2×Dic5—22no—
511C2×Dic5—41no—
512C2×Dic5—41no—
513C2×Dic5—41no—
514C2×Dic5—41no—
515C2×Dic5—41no—
516C2×Dic5—41no—
517C2×Dic5—41no—
518C2×Dic5—41no—
519C2×Dic5—41no—
520C2×Dic5—41no—
521C2×Dic5—41no—
522C2×Dic5—41no—
523C2×Dic5C3×C22⋊C414yescomplemented
524C25C2×C3×D511yescharacteristic
525C23×C4—51no—
526C23×C4—51no—
527C23×C4—51no—
528C23×C4—51no—
529C23×C4C2×C3×D511yescharacteristic
530C23×C4C2×C3×D511yescharacteristic
531C2×C4⋊C4—102no—
532C2×C4⋊C4—102no—
533C2×C4⋊C4—102no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—54no—
538C2×C22⋊C4—102no—
539C2×C22⋊C4—102no—
540C2×C22⋊C4—102no—
541C2×C22⋊C4—102no—
542C2×C22⋊C4—102no—
543#95—102no—
544#95—102no—
545#95—102no—
546C2×C3×C5—44no—
547C2×C3×C5#38011yescharacteristic
548C2×C3×C5#38511yescharacteristic
549C2×C3×C5#38511yescharacteristic
550C2×C3×C5#38611yescharacteristic
551C2×C3×C5#38811yescharacteristic
552C2×C3×C5#38811yescharacteristic
553C2×C3×C5#39011yescharacteristic
554C2×C3×C5#39211yescharacteristic
555C2×C3×C5#39311yescharacteristic
556C2×C3×C5#39411yescharacteristic
557C2×C3×C5#39411yescharacteristic
558C2×C3×C5#39611yescharacteristic
559C2×C3×C5#39611yescharacteristic
560C2×C3×C5#39711yescharacteristic
561C2×C3×C5#39911yescharacteristic
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—22no—
577C23×C3—22no—
578C23×C3—22no—
579C23×C3—22no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3#68314yescomplemented
597C23×C3C2×Dic1011yescharacteristic
598C23×C3C2×C4×D511yescharacteristic
599C23×C3#70911yescharacteristic
600C23×C3#70911yescharacteristic
601C23×C3D4×D511yescharacteristic
602C23×C3D4×D511yescharacteristic
603C23×C3D4×D511yescharacteristic
604C23×C3D4×D511yescharacteristic
605C23×C3#71111yescharacteristic
606C23×C3#71111yescharacteristic
607C23×C3#71111yescharacteristic
608C23×C3#71111yescharacteristic
609C23×C3C2×C22⋊D511yescharacteristic
610C23×C3C2×C22⋊D511yescharacteristic
611C23×C3C2×C22⋊D511yescharacteristic
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—54no—
627C2×C3×C4—102no—
628C2×C3×C4—102no—
629C2×C3×C4—102no—
630C2×C3×C4—102no—
631C2×C3×C4—102no—
632C2×C3×C4—102no—
633C2×C3×C4—102no—
634C2×C3×C4—102no—
635C2×C3×C4—102no—
636C2×C3×C4—102no—
637C2×C3×C4—102no—
638C2×C3×C4—102no—
639C2×C3×C4—102no—
640C2×C3×C4—102no—
641C2×C3×C4—102no—
642C2×C3×C4—201no—
643C2×C3×C4—201no—
644C2×C3×C4—201no—
645C2×C3×C4—201no—
646C2×C3×C4—201no—
647C2×C3×C4—201no—
648C2×C3×C4—201no—
649C2×C3×C4—201no—
650C2×C3×C4—201no—
651C2×C3×C4—201no—
652C2×C3×C4—201no—
653C2×C3×C4—201no—
654C22×C5—24no—
655C22×C5—24no—
656C22×C5—24no—
657C22×C5—42no—
658C22×C5—42no—
659C22×C5—42no—
660C22×C5—42no—
661C22×C5—42no—
662C22×C5—42no—
663C22×C5—42no—
664C22×C5—42no—
665C22×C5—42no—
666C22×C5—42no—
667C22×C5—42no—
668C22×C5—42no—
669C22×C5C2×C3×C22⋊C411yescharacteristic
670C22×C5C2×C3×C4⋊C411yescharacteristic
671C22×C5C3×#11711yescharacteristic
672C22×C5C3×C4×D411yescharacteristic
673C22×C5C3×C4×D411yescharacteristic
674C22×C5C3×C4×D411yescharacteristic
675C22×C5C3×C4×D411yescharacteristic
676C22×C5C3×#12011yescharacteristic
677C22×C5C3×#12011yescharacteristic
678C22×C5C3×#12011yescharacteristic
679C22×C5C3×#12111yescharacteristic
680C22×C5C3×#12111yescharacteristic
681C22×C5C3×#12111yescharacteristic
682C22×C5C3×#12111yescharacteristic
683C22×C5C3×#12111yescharacteristic
684C22×C5C3×#12111yescharacteristic
685C22×C5C3×#12111yescharacteristic
686C22×C5C3×#12111yescharacteristic
687C22×C5C3×C22⋊Q811yescharacteristic
688C22×C5C3×C22⋊Q811yescharacteristic
689C22×C5C3×C22⋊Q811yescharacteristic
690C22×C5C3×C22⋊Q811yescharacteristic
691C22×C5C3×C22⋊Q811yescharacteristic
692C22×C5C3×C22⋊Q811yescharacteristic
693C22×C5C3×#12311yescharacteristic
694C22×C5C3×#12311yescharacteristic
695C22×C5C3×#12311yescharacteristic
696C22×C5C3×#12311yescharacteristic
697C22×C5C3×#12311yescharacteristic
698C22×C5C3×#12411yescharacteristic
699C22×C5C3×#12411yescharacteristic
700C22×C5C3×#12411yescharacteristic
701C22×C5C3×#12611yescharacteristic
702C22×C5C3×#12611yescharacteristic
703C22×C5C3×#12711yescharacteristic
704C4×C5—42no—
705C4×C5—42no—
706Dic5—24no—
707Dic5—42no—
708Dic5—42no—
709Dic5—42no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24C3×Dic1012yes—
723C24C3×C4×D512yes—
724C24C3×C22⋊D512yes—
725C24C22×C3×D511yescharacteristic
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—52no—
739C22×C4—52no—
740C22×C4—52no—
741C22×C4—52no—
742C22×C4—52no—
743C22×C4—52no—
744C22×C4—101no—
745C22×C4—101no—
746C22×C4—101no—
747C22×C4—101no—
748C22×C4—101no—
749C22×C4—101no—
750C22×C4—101no—
751C22×C4—101no—
752C22×C4—101no—
753C22×C4—101no—
754C22×C4—101no—
755C22×C4—101no—
756C22×C4—101no—
757C22×C4—101no—
758C22×C4—101no—
759C22×C4—101no—
760C22×C4—101no—
761C22×C4—101no—
762C22×C4—101no—
763C22×C4—101no—
764C22×C4—101no—
765C22×C4—101no—
766C22×C4C3×C22⋊D512yes—
767C22×C4C3×C22⋊D512yes—
768C4⋊C4—108no—
769C22⋊C4—28no—
770C22⋊C4—108no—
771C22⋊C4—108no—
772C3×C5#143911yescharacteristic, complemented, Hall
773C22×C3—24no—
774C22×C3—24no—
775C22×C3—24no—
776C22×C3—42no—
777C22×C3—42no—
778C22×C3—42no—
779C22×C3—42no—
780C22×C3—42no—
781C22×C3—42no—
782C22×C3—42no—
783C22×C3—42no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3—42no—
787C22×C3—42no—
788C22×C3#402311yescharacteristic
789C22×C3#402411yescharacteristic
790C22×C3#402411yescharacteristic
791C22×C3#402411yescharacteristic
792C22×C3#402411yescharacteristic
793C22×C3#402511yescharacteristic
794C22×C3#402511yescharacteristic
795C22×C3D5×C22⋊C411yescharacteristic
796C22×C3#402711yescharacteristic
797C22×C3#402711yescharacteristic
798C22×C3#402911yescharacteristic
799C22×C3#402911yescharacteristic
800C22×C3#403011yescharacteristic
801C22×C3#403011yescharacteristic
802C22×C3#403111yescharacteristic
803C22×C3#403111yescharacteristic
804C22×C3C2×#68311yescharacteristic
805C22×C3#407011yescharacteristic
806C22×C3#407011yescharacteristic
807C22×C3C4×C22⋊D511yescharacteristic
808C22×C3C4×C22⋊D511yescharacteristic
809C22×C3#407511yescharacteristic
810C22×C3#408111yescharacteristic
811C22×C3#408111yescharacteristic
812C22×C3#408211yescharacteristic
813C22×C3#408311yescharacteristic
814C22×C3#408311yescharacteristic
815C22×C3#408411yescharacteristic
816C22×C3#408411yescharacteristic
817C22×C3#408511yescharacteristic
818C22×C3#408511yescharacteristic
819C22×C3#408511yescharacteristic
820C22×C3#408511yescharacteristic
821C22×C3#408611yescharacteristic
822C22×C3#409911yescharacteristic
823C3×C4—42no—
824C3×C4—42no—
825C3×C4—104no—
826C3×C4—202no—
827C3×C4—202no—
828C3×C4—202no—
829C2×C5—44no—
830C2×C5C3×#38011yescharacteristic
831C2×C5C3×#38511yescharacteristic
832C2×C5C3×#38511yescharacteristic
833C2×C5C3×#38611yescharacteristic
834C2×C5C3×#38811yescharacteristic
835C2×C5C3×#38811yescharacteristic
836C2×C5C3×#39011yescharacteristic
837C2×C5C3×#39211yescharacteristic
838C2×C5C3×#39311yescharacteristic
839C2×C5C3×#39411yescharacteristic
840C2×C5C3×#39411yescharacteristic
841C2×C5C3×#39611yescharacteristic
842C2×C5C3×#39611yescharacteristic
843C2×C5C3×#39711yescharacteristic
844C2×C5C3×#39911yescharacteristic
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23C3×#68314yescomplemented
880C23C2×C3×Dic1011yescharacteristic
881C23C2×C3×C4×D511yescharacteristic
882C23C3×#70911yescharacteristic
883C23C3×#70911yescharacteristic
884C23C3×D4×D511yescharacteristic
885C23C3×D4×D511yescharacteristic
886C23C3×D4×D511yescharacteristic
887C23C3×D4×D511yescharacteristic
888C23C3×#71111yescharacteristic
889C23C3×#71111yescharacteristic
890C23C3×#71111yescharacteristic
891C23C3×#71111yescharacteristic
892C23C2×C3×C22⋊D511yescharacteristic
893C23C2×C3×C22⋊D511yescharacteristic
894C23C2×C3×C22⋊D511yescharacteristic
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—54no—
910C2×C4—102no—
911C2×C4—102no—
912C2×C4—102no—
913C2×C4—102no—
914C2×C4—102no—
915C2×C4—102no—
916C2×C4—102no—
917C2×C4—102no—
918C2×C4—102no—
919C2×C4—102no—
920C2×C4—102no—
921C2×C4—102no—
922C2×C4—102no—
923C2×C4—102no—
924C2×C4—102no—
925C2×C4—201no—
926C2×C4—201no—
927C2×C4—201no—
928C2×C4—201no—
929C2×C4—201no—
930C2×C4—201no—
931C2×C4—201no—
932C2×C4—201no—
933C2×C4—201no—
934C2×C4—201no—
935C2×C4—201no—
936C2×C4—201no—
937C2×C3—44no—
938C2×C3#6523111yescharacteristic
939C2×C3#6523311yescharacteristic
940C2×C3#6523411yescharacteristic
941C2×C3#6523511yescharacteristic
942C2×C3#6523611yescharacteristic
943C2×C3#6523711yescharacteristic
944C2×C3#6523711yescharacteristic
945C2×C3#6523811yescharacteristic
946C2×C3#6524111yescharacteristic
947C2×C3#6524511yescharacteristic
948C2×C3#6524611yescharacteristic
949C2×C3#6524811yescharacteristic
950C2×C3#6549911yescharacteristic
951C2×C3#6551111yescharacteristic
952C2×C3#6551211yescharacteristic
953C5C3×#143911yescharacteristic, complemented, Sylow
954C22—24no—
955C22—24no—
956C22—24no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22C3×#402311yescharacteristic
970C22C3×#402411yescharacteristic
971C22C3×#402411yescharacteristic
972C22C3×#402411yescharacteristic
973C22C3×#402411yescharacteristic
974C22C3×#402511yescharacteristic
975C22C3×#402511yescharacteristic
976C22C3×D5×C22⋊C411yescharacteristic
977C22C3×#402711yescharacteristic
978C22C3×#402711yescharacteristic
979C22C3×#402911yescharacteristic
980C22C3×#402911yescharacteristic
981C22C3×#403011yescharacteristic
982C22C3×#403011yescharacteristic
983C22C3×#403111yescharacteristic
984C22C3×#403111yescharacteristic
985C22C2×C3×#68311yescharacteristic
986C22C3×#407011yescharacteristic
987C22C3×#407011yescharacteristic
988C22C3×C4×C22⋊D511yescharacteristic
989C22C3×C4×C22⋊D511yescharacteristic
990C22C3×#407511yescharacteristic
991C22C3×#408111yescharacteristic
992C22C3×#408111yescharacteristic
993C22C3×#408211yescharacteristic
994C22C3×#408311yescharacteristic
995C22C3×#408311yescharacteristic
996C22C3×#408411yescharacteristic
997C22C3×#408411yescharacteristic
998C22C3×#408511yescharacteristic
999C22C3×#408511yescharacteristic
1000C22C3×#408511yescharacteristic
1001C22C3×#408511yescharacteristic
1002C22C3×#408611yescharacteristic
1003C22C3×#409911yescharacteristic
1004C4—42no—
1005C4—42no—
1006C4—104no—
1007C4—202no—
1008C4—202no—
1009C4—202no—
1010C3#1060234011yescharacteristic, direct product factor, Sylow
1011C2—44no—
1012C2C3×#6523111yescharacteristic
1013C2C3×#6523311yescharacteristic
1014C2C3×#6523411yescharacteristic
1015C2C3×#6523511yescharacteristic
1016C2C3×#6523611yescharacteristic
1017C2C3×#6523711yescharacteristic
1018C2C3×#6523711yescharacteristic
1019C2C3×#6523811yescharacteristic
1020C2C3×#6524111yescharacteristic
1021C2C3×#6524511yescharacteristic
1022C2C3×#6524611yescharacteristic
1023C2C3×#6524811yescharacteristic
1024C2C3×#6549911yescharacteristic
1025C2C3×#6551111yescharacteristic
1026C2C3×#6551211yescharacteristic
subgroupG/H
centerC24×C3C22×D5
commutatorC23×C5C22×C3×C4
FrattiniC24C22×C3×D5
FittingC22×C3×C5×C22⋊C4C2
socleC24×C3×C5C23
prime radicalC25×C3×C5C22
cosocleC24×C5C23×C3
hypercenterC22×C3×C22⋊C4D5
hypocenterC5C3×#1439
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C22×C3×#683C2semidirect
5. C2×C3×#3963C2semidirect
6. C2×C3×#3963C2semidirect
7. C2×C3×#3963C2semidirect
8. #10602340C3direct (N × H)
24. C2×C3×C22⋊Dic5C4semidirect
35. C22×#683C2×C3semidirect
36. C2×#3963C2×C3semidirect
37. C2×#3963C2×C3semidirect
38. C2×#3963C2×C3semidirect
123. C2×C22⋊Dic5C3×C4semidirect
165. C23×C3×C5C4⋊C4semidirect
222. C2×C3×Dic5C22⋊C4semidirect
466. C23×C5C3×C4⋊C4semidirect
523. C2×Dic5C3×C22⋊C4semidirect
596. C23×C3#683semidirect
772. C3×C5#1439semidirect
879. C23C3×#683semidirect
953. C5C3×#1439semidirect
1010. C3#10602340direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×C22⋊C42
C22×C3×C22⋊Dic52
C22×C3×#6832
C2×C3×#39632
#106023403
C3×#14395