Finite Group Databasebeta

← C3×#10606389 #14321146

Subgroups — C3×#10606389 #14321146

Order 1920.

1872 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#711C211yesmaximal, characteristic
2C22×C3×C4×Dic5C211yesmaximal, characteristic, complemented
3C2×C3×#4023C211yesmaximal, characteristic, complemented
4C3×C5×#386C211yesmaximal, characteristic, complemented
5C3×#65509C211yesmaximal, characteristic, complemented
6C3×#65502C211yesmaximal, characteristic, complemented
7C3×#65247C211yesmaximal, characteristic, complemented
8C3×#65246C212yesmaximal, complemented
9C3×C22⋊C4×Dic5C212yesmaximal, complemented
10C3×#64955C212yesmaximal, complemented
11C3×#64935C212yesmaximal, complemented
12#10606389C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C22×C3×C22⋊D5C2211yescharacteristic
16C22×C3×C22⋊D5C2211yescharacteristic
17C23×C3×Dic5C2211yescharacteristic
18C23×C3×Dic5C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C2×C3×#711—24no—
21C2×C3×#711—24no—
22C2×C3×#711C418yescomplemented
23C22×C3×C4×D5C2211yescharacteristic
24C22×C3×Dic10C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2212yes—
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊Dic5C2212yes—
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C2×C3×#685C2212yes—
30C2×C3×#685C2212yes—
31C2×C3×#683C2212yes—
32C2×C3×C4×Dic5—24no—
33C2×C3×C4×Dic5C2212yes—
34C2×C3×C4×Dic5C2212yes—
35C2×C3×C4×Dic5C2212yes—
36C3×#4023—24no—
37C3×C5×#95C2212yes—
38C3×#3963C2212yes—
39C3×#3963C2212yes—
40C3×#3963C2212yes—
41C3×#2297—51nomaximal, Hall
42C22×#711C2×C311yescharacteristic
43C22×C4×Dic5C2×C311yescharacteristic, complemented
44C2×#4023C2×C311yescharacteristic, complemented
45C5×#386C2×C311yescharacteristic, complemented
46#65509C2×C311yescharacteristic, complemented
47#65502C2×C311yescharacteristic, complemented
48#65247C2×C311yescharacteristic, complemented
49#65246C2×C312yescomplemented
50C22⋊C4×Dic5C2×C312yescomplemented
51#64955C2×C312yescomplemented
52#64935C2×C312yescomplemented
53C24×C3×C5C2311yescharacteristic
54C24×C3×C5C2311yescharacteristic
55C23×C3×D5C2311yescharacteristic
56C2×C3×C5×D4—22no—
57C2×C3×C5×D4—22no—
58C2×C3×C5×D4C2×C414yes—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—24no—
61C22×C3×C4×C5C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C22×C3×C4×C5C2312yes—
64C2×C3×C22⋊D5—22no—
65C2×C3×C22⋊D5—22no—
66C2×C3×C22⋊D5—22no—
67C2×C3×C22⋊D5—22no—
68C2×C3×C22⋊D5C2×C414yes—
69C2×C3×C22⋊D5C2×C414yescomplemented
70C22×C3×Dic5—22no—
71C22×C3×Dic5—22no—
72C22×C3×Dic5—22no—
73C22×C3×Dic5—24no—
74C22×C3×Dic5C2×C414yes—
75C22×C3×Dic5C2×C414yescomplemented
76C22×C3×Dic5D414yes—
77C22×C3×Dic5D414yes—
78C22×C3×Dic5C2312yes—
79C22×C3×Dic5C2311yescharacteristic
80C22×C3×Dic5C2312yes—
81C22×C3×Dic5C2311yescharacteristic
82C22×C3×Dic5C2311yescharacteristic
83C3×#711—232no—
84C2×C3×C4×D5—22no—
85C2×C3×C4×D5—22no—
86C2×C3×C4×D5C2×C414yescomplemented
87C2×C3×Dic10—22no—
88C2×C3×Dic10—22no—
89C2×C3×Dic10C2×C414yescomplemented
90C3×C5×C22⋊C4—22no—
91C3×C5×C22⋊C4—24no—
92C3×C22⋊Dic5—22no—
93C3×C22⋊Dic5—24no—
94C3×#685—24no—
95C3×#685—24no—
96C3×#683—24no—
97C3×C4×Dic5—24no—
98C3×C4×Dic5—24no—
99C3×C4×Dic5—24no—
100C22×C3×#41—51no—
101C2×C3×#117—51no—
102C22×C3×C42—51no—
103C3×#391—52no—
104C3×#390—52no—
105C3×#386—51no—
106C3×#386—51no—
107C3×#386—51no—
108C3×#386D511yescharacteristic, complemented
109C3×C4×C22⋊C4—52no—
110C3×C4×C22⋊C4—52no—
111C22×C5×D4C22×C311yescharacteristic
112C23×C4×C5C22×C311yescharacteristic
113C22×C22⋊D5C22×C311yescharacteristic
114C22×C22⋊D5C22×C311yescharacteristic
115C23×Dic5C22×C311yescharacteristic
116C23×Dic5C22×C311yescharacteristic
117C23×Dic5C22×C311yescharacteristic
118C2×#711—24no—
119C2×#711—24no—
120C2×#711C3×C418yescomplemented
121C22×C4×D5C22×C311yescharacteristic
122C22×Dic10C22×C311yescharacteristic
123C2×C5×C22⋊C4C22×C311yescharacteristic
124C2×C5×C22⋊C4C22×C312yes—
125C2×C22⋊Dic5C22×C311yescharacteristic
126C2×C22⋊Dic5C22×C312yes—
127C2×#685C22×C312yes—
128C2×#685C22×C312yes—
129C2×#683C22×C312yes—
130C2×C4×Dic5—24no—
131C2×C4×Dic5C22×C312yes—
132C2×C4×Dic5C22×C312yes—
133C2×C4×Dic5C22×C312yes—
134#4023—24no—
135C5×#95C22×C312yes—
136#3963C22×C312yes—
137#3963C22×C312yes—
138#3963C22×C312yes—
139#2297—51noSylow
140C23×C3×C5—22no—
141C23×C3×C5—22no—
142C23×C3×C5—21no—
143C23×C3×C5—21no—
144C23×C3×C5—22no—
145C23×C3×C5—22no—
146C23×C3×C5C22×C412yes—
147C23×C3×C5C22×C412yes—
148C23×C3×C5C2×D412yes—
149C23×C3×C5C2×D412yes—
150C23×C3×C5C2411yescharacteristic
151C22×C3×D5—21no—
152C22×C3×D5—21no—
153C22×C3×D5—22no—
154C22×C3×D5—22no—
155C22×C3×D5C22×C412yes—
156C3×C5×D4—28no—
157C2×C3×C4×C5—28no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—21no—
160C2×C3×C4×C5—21no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—22no—
164C2×C3×C4×C5—22no—
165C2×C3×C4×C5C22×C412yes—
166C2×C3×C4×C5#4114yescomplemented
167C3×C22⋊D5—28no—
168C3×C22⋊D5—28no—
169C2×C3×Dic5—28no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—21no—
172C2×C3×Dic5—21no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—28no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—22no—
177C2×C3×Dic5—22no—
178C2×C3×Dic5C22⋊C4116yescomplemented
179C2×C3×Dic5C22×C412yes—
180C2×C3×Dic5C22×C412yes—
181C2×C3×Dic5C22×C412yes—
182C2×C3×Dic5C2×D412yes—
183C2×C3×Dic5C2×D412yes—
184C2×C3×Dic5C2×D412yes—
185C2×C3×Dic5C2×D412yes—
186C2×C3×Dic5#4114yescomplemented
187C3×C4×D5—28no—
188C3×Dic10—28no—
189C2×C3×#41—58no—
190C2×C3×#41—104no—
191C2×C3×#41—104no—
192C22×C3×Q8—51no—
193C22×C3×D4—51no—
194C22×C3×D4—51no—
195C22×C3×D4C2×D511yescharacteristic
196C23×C3×C4—51no—
197C23×C3×C4—51no—
198C23×C3×C4—51no—
199C23×C3×C4—51no—
200C23×C3×C4C2×D511yescharacteristic
201C3×#117—104no—
202C2×C3×C4⋊C4—52no—
203C2×C3×C22⋊C4—52no—
204C2×C3×C22⋊C4—51no—
205C2×C3×C22⋊C4—52no—
206C2×C3×C22⋊C4—52no—
207C2×C3×C22⋊C4C2×D512yes—
208C2×C3×C22⋊C4C2×D511yescharacteristic
209C2×C3×C42—52no—
210C2×C3×C42—52no—
211C2×C3×C42—52no—
212C2×C3×C42—104no—
213C3×#95—52no—
214C3×#95—52no—
215C3×#95—52no—
216C3×#95C2×D512yes—
217C24×C5C23×C311yescharacteristic
218C24×C5C23×C311yescharacteristic
219C23×D5C23×C311yescharacteristic
220C2×C5×D4—22no—
221C2×C5×D4—22no—
222C2×C5×D4C2×C3×C414yes—
223C22×C4×C5—22no—
224C22×C4×C5—24no—
225C22×C4×C5C23×C312yes—
226C22×C4×C5C23×C311yescharacteristic
227C22×C4×C5C23×C312yes—
228C2×C22⋊D5—22no—
229C2×C22⋊D5—22no—
230C2×C22⋊D5—22no—
231C2×C22⋊D5—22no—
232C2×C22⋊D5C2×C3×C414yes—
233C2×C22⋊D5C2×C3×C414yescomplemented
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5—24no—
238C22×Dic5C2×C3×C414yes—
239C22×Dic5C2×C3×C414yescomplemented
240C22×Dic5C3×D414yes—
241C22×Dic5C3×D414yes—
242C22×Dic5C23×C312yes—
243C22×Dic5C23×C311yescharacteristic
244C22×Dic5C23×C312yes—
245C22×Dic5C23×C311yescharacteristic
246C22×Dic5C23×C311yescharacteristic
247#711—232no—
248C2×C4×D5—22no—
249C2×C4×D5—22no—
250C2×C4×D5C2×C3×C414yescomplemented
251C2×Dic10—22no—
252C2×Dic10—22no—
253C2×Dic10C2×C3×C414yescomplemented
254C5×C22⋊C4—22no—
255C5×C22⋊C4—24no—
256C22⋊Dic5—22no—
257C22⋊Dic5—24no—
258#685—24no—
259#685—24no—
260#683—24no—
261C4×Dic5—24no—
262C4×Dic5—24no—
263C4×Dic5—24no—
264C22×#41—51no—
265C2×#117—51no—
266C22×C42—51no—
267#391—52no—
268#390—52no—
269#386—51no—
270#386—51no—
271#386—51no—
272#386C3×D511yescharacteristic, complemented
273C4×C22⋊C4—52no—
274C4×C22⋊C4—52no—
275C22×C3×C5—24no—
276C22×C3×C5—22no—
277C22×C3×C5—22no—
278C22×C3×C5—24no—
279C22×C3×C5—22no—
280C22×C3×C5—24no—
281C22×C3×C5—41no—
282C22×C3×C5—41no—
283C22×C3×C5—42no—
284C22×C3×C5C2×C22⋊C414yes—
285C22×C3×C5C23×C411yescharacteristic
286C22×C3×C5C22×D411yescharacteristic
287C22×C3×C5C22×D411yescharacteristic
288C22×C3×C5C2×#4112yes—
289C22×C3×C5C2×#4112yes—
290C2×C3×D5—22no—
291C2×C3×D5—24no—
292C2×C3×D5—41no—
293C2×C3×D5—41no—
294C2×C3×D5—42no—
295C3×C4×C5—22no—
296C3×C4×C5—24no—
297C3×C4×C5—42no—
298C3×Dic5—22no—
299C3×Dic5—24no—
300C3×Dic5—42no—
301C3×Dic5C2×C22⋊C414yes—
302C3×Dic5C2×C22⋊C414yes—
303C24×C3—51no—
304C24×C3C22×D511yescharacteristic
305C24×C3C22×D511yescharacteristic
306C3×#41—1032no—
307C2×C3×Q8—54no—
308C2×C3×Q8—102no—
309C2×C3×Q8—102no—
310C2×C3×D4—22no—
311C2×C3×D4—22no—
312C2×C3×D4—54no—
313C2×C3×D4—54no—
314C2×C3×D4—102no—
315C2×C3×D4—102no—
316C2×C3×D4—102no—
317C2×C3×D4—102no—
318C2×C3×D4C4×D514yes—
319C22×C3×C4—22no—
320C22×C3×C4—24no—
321C22×C3×C4—54no—
322C22×C3×C4—54no—
323C22×C3×C4—54no—
324C22×C3×C4—51no—
325C22×C3×C4—51no—
326C22×C3×C4—54no—
327C22×C3×C4—51no—
328C22×C3×C4—52no—
329C22×C3×C4—54no—
330C22×C3×C4—52no—
331C22×C3×C4—102no—
332C22×C3×C4—102no—
333C22×C3×C4—104no—
334C22×C3×C4—102no—
335C22×C3×C4—102no—
336C22×C3×C4—102no—
337C22×C3×C4C22×D512yes—
338C22×C3×C4C22×D511yescharacteristic
339C22×C3×C4C22×D512yes—
340C3×C4⋊C4—104no—
341C3×C22⋊C4—22no—
342C3×C22⋊C4—24no—
343C3×C22⋊C4—104no—
344C3×C22⋊C4—104no—
345C3×C22⋊C4—102no—
346C3×C22⋊C4—104no—
347C3×C42—104no—
348C3×C42—104no—
349C3×C42—104no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—21no—
353C23×C5—21no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5C22×C3×C412yes—
357C23×C5C22×C3×C412yes—
358C23×C5C2×C3×D412yes—
359C23×C5C2×C3×D412yes—
360C23×C5C24×C311yescharacteristic
361C22×D5—21no—
362C22×D5—21no—
363C22×D5—22no—
364C22×D5—22no—
365C22×D5C22×C3×C412yes—
366C5×D4—28no—
367C2×C4×C5—28no—
368C2×C4×C5—22no—
369C2×C4×C5—21no—
370C2×C4×C5—21no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5C22×C3×C412yes—
376C2×C4×C5C3×#4114yescomplemented
377C22⋊D5—28no—
378C22⋊D5—28no—
379C2×Dic5—28no—
380C2×Dic5—22no—
381C2×Dic5—21no—
382C2×Dic5—21no—
383C2×Dic5—22no—
384C2×Dic5—28no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5C3×C22⋊C4116yescomplemented
389C2×Dic5C22×C3×C412yes—
390C2×Dic5C22×C3×C412yes—
391C2×Dic5C22×C3×C412yes—
392C2×Dic5C2×C3×D412yes—
393C2×Dic5C2×C3×D412yes—
394C2×Dic5C2×C3×D412yes—
395C2×Dic5C2×C3×D412yes—
396C2×Dic5C3×#4114yescomplemented
397C4×D5—28no—
398Dic10—28no—
399C2×#41—58no—
400C2×#41—104no—
401C2×#41—104no—
402C22×Q8—51no—
403C22×D4—51no—
404C22×D4—51no—
405C22×D4C2×C3×D511yescharacteristic
406C23×C4—51no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4—51no—
410C23×C4C2×C3×D511yescharacteristic
411#117—104no—
412C2×C4⋊C4—52no—
413C2×C22⋊C4—51no—
414C2×C22⋊C4—52no—
415C2×C22⋊C4—52no—
416C2×C22⋊C4—52no—
417C2×C22⋊C4C2×C3×D511yescharacteristic
418C2×C22⋊C4C2×C3×D512yes—
419C2×C42—52no—
420C2×C42—52no—
421C2×C42—52no—
422C2×C42—104no—
423#95—52no—
424#95—52no—
425#95—52no—
426#95C2×C3×D512yes—
427C2×C3×C5—24no—
428C2×C3×C5—42no—
429C2×C3×C5C22×C22⋊C411yescharacteristic
430C2×C3×C5C4×#4112yes—
431C2×C3×C5#52511yescharacteristic
432C2×C3×C5#52511yescharacteristic
433C2×C3×C5#53212yes—
434C3×D5—42no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—52no—
442C23×C3—101no—
443C23×C3—101no—
444C23×C3—102no—
445C23×C3—102no—
446C23×C3C2×C4×D512yes—
447C23×C3C2×C4×D512yes—
448C23×C3D4×D512yes—
449C23×C3D4×D512yes—
450C23×C3C23×D511yescharacteristic
451C3×Q8—108no—
452C3×D4—28no—
453C3×D4—108no—
454C3×D4—108no—
455C2×C3×C4—28no—
456C2×C3×C4—22no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—52no—
464C2×C3×C4—52no—
465C2×C3×C4—52no—
466C2×C3×C4—52no—
467C2×C3×C4—52no—
468C2×C3×C4—52no—
469C2×C3×C4—516no—
470C2×C3×C4—52no—
471C2×C3×C4—54no—
472C2×C3×C4—108no—
473C2×C3×C4—108no—
474C2×C3×C4—108no—
475C2×C3×C4—102no—
476C2×C3×C4—101no—
477C2×C3×C4—101no—
478C2×C3×C4—102no—
479C2×C3×C4—102no—
480C2×C3×C4—102no—
481C2×C3×C4—102no—
482C2×C3×C4C2×C4×D512yes—
483C2×C3×C4#71114yescomplemented
484C22×C5—24no—
485C22×C5—22no—
486C22×C5—22no—
487C22×C5—24no—
488C22×C5—22no—
489C22×C5—24no—
490C22×C5—41no—
491C22×C5—41no—
492C22×C5—42no—
493C22×C5C2×C3×C22⋊C414yes—
494C22×C5C23×C3×C411yescharacteristic
495C22×C5C22×C3×D411yescharacteristic
496C22×C5C22×C3×D411yescharacteristic
497C22×C5C2×C3×#4112yes—
498C22×C5C2×C3×#4112yes—
499C2×D5—22no—
500C2×D5—24no—
501C2×D5—41no—
502C2×D5—41no—
503C2×D5—42no—
504C4×C5—22no—
505C4×C5—24no—
506C4×C5—42no—
507Dic5—22no—
508Dic5—24no—
509Dic5—42no—
510Dic5C2×C3×C22⋊C414yes—
511Dic5C2×C3×C22⋊C414yes—
512C24—51no—
513C24C22×C3×D511yescharacteristic
514C24C22×C3×D511yescharacteristic
515#41—1032no—
516C2×Q8—54no—
517C2×Q8—102no—
518C2×Q8—102no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—54no—
522C2×D4—54no—
523C2×D4—102no—
524C2×D4—102no—
525C2×D4—102no—
526C2×D4—102no—
527C2×D4C3×C4×D514yes—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—54no—
531C22×C4—54no—
532C22×C4—54no—
533C22×C4—51no—
534C22×C4—51no—
535C22×C4—54no—
536C22×C4—51no—
537C22×C4—52no—
538C22×C4—54no—
539C22×C4—52no—
540C22×C4—102no—
541C22×C4—102no—
542C22×C4—102no—
543C22×C4—102no—
544C22×C4—104no—
545C22×C4—102no—
546C22×C4C22×C3×D512yes—
547C22×C4C22×C3×D511yescharacteristic
548C22×C4C22×C3×D512yes—
549C4⋊C4—104no—
550C22⋊C4—22no—
551C22⋊C4—24no—
552C22⋊C4—104no—
553C22⋊C4—104no—
554C22⋊C4—102no—
555C22⋊C4—104no—
556C42—104no—
557C42—104no—
558C42—104no—
559C3×C5#229711yescharacteristic, complemented, Hall
560C22×C3—24no—
561C22×C3—22no—
562C22×C3—24no—
563C22×C3—22no—
564C22×C3—22no—
565C22×C3—24no—
566C22×C3—41no—
567C22×C3—42no—
568C22×C3—41no—
569C22×C3—102no—
570C22×C3—104no—
571C22×C3—201no—
572C22×C3—202no—
573C22×C3—201no—
574C22×C3D5×C22⋊C414yes—
575C22×C3C22×C4×D511yescharacteristic
576C22×C3C2×D4×D511yescharacteristic
577C22×C3C2×D4×D511yescharacteristic
578C22×C3C2×#71112yes—
579C22×C3D5×#4112yes—
580C3×C4—22no—
581C3×C4—24no—
582C3×C4—42no—
583C3×C4—54no—
584C3×C4—54no—
585C3×C4—102no—
586C3×C4—104no—
587C3×C4—202no—
588C2×C5—24no—
589C2×C5—42no—
590C2×C5C22×C3×C22⋊C411yescharacteristic
591C2×C5C3×C4×#4112yes—
592C2×C5C3×#52511yescharacteristic
593C2×C5C3×#52511yescharacteristic
594C2×C5C3×#53212yes—
595D5—42no—
596C23—22no—
597C23—22no—
598C23—21no—
599C23—21no—
600C23—22no—
601C23—22no—
602C23—52no—
603C23—101no—
604C23—101no—
605C23—102no—
606C23—102no—
607C23C2×C3×C4×D512yes—
608C23C2×C3×C4×D512yes—
609C23C3×D4×D512yes—
610C23C3×D4×D512yes—
611C23C23×C3×D511yescharacteristic
612Q8—108no—
613D4—28no—
614D4—108no—
615D4—108no—
616C2×C4—28no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—52no—
625C2×C4—52no—
626C2×C4—52no—
627C2×C4—52no—
628C2×C4—52no—
629C2×C4—52no—
630C2×C4—516no—
631C2×C4—52no—
632C2×C4—54no—
633C2×C4—108no—
634C2×C4—108no—
635C2×C4—108no—
636C2×C4—102no—
637C2×C4—101no—
638C2×C4—101no—
639C2×C4—102no—
640C2×C4—102no—
641C2×C4—102no—
642C2×C4—102no—
643C2×C4C2×C3×C4×D512yes—
644C2×C4C3×#71114yescomplemented
645C2×C3—24no—
646C2×C3—42no—
647C2×C3—202no—
648C2×C3C2×D5×C22⋊C411yescharacteristic
649C2×C3C4×#71112yes—
650C2×C3#6592011yescharacteristic
651C2×C3#6593012yes—
652C2×C3#6599011yescharacteristic
653C5C3×#229711yescharacteristic, complemented, Sylow
654C22—24no—
655C22—22no—
656C22—24no—
657C22—22no—
658C22—24no—
659C22—22no—
660C22—41no—
661C22—42no—
662C22—41no—
663C22—104no—
664C22—102no—
665C22—201no—
666C22—202no—
667C22—201no—
668C22C3×D5×C22⋊C414yes—
669C22C22×C3×C4×D511yescharacteristic
670C22C2×C3×D4×D511yescharacteristic
671C22C2×C3×D4×D511yescharacteristic
672C22C2×C3×#71112yes—
673C22C3×D5×#4112yes—
674C4—24no—
675C4—22no—
676C4—42no—
677C4—54no—
678C4—54no—
679C4—104no—
680C4—102no—
681C4—202no—
682C3#1060638911yescharacteristic, direct product factor, Sylow
683C2—24no—
684C2—42no—
685C2—202no—
686C2C2×C3×D5×C22⋊C411yescharacteristic
687C2C3×C4×#71112yes—
688C2C3×#6592011yescharacteristic
689C2C3×#6593012yes—
690C2C3×#6599011yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#386C2
socleC23×C3×C5C24
prime radicalC22×C3×#711C2
cosocleC23×C5C24×C3
hypercenterC3×#386D5
hypocenterC5C3×#2297
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4×Dic5C2semidirect
3. C2×C3×#4023C2semidirect
4. C3×C5×#386C2semidirect
5. C3×#65509C2semidirect
6. C3×#65502C2semidirect
7. C3×#65247C2semidirect
8. C3×#65246C2semidirect
9. C3×C22⋊C4×Dic5C2semidirect
10. C3×#64955C2semidirect
11. C3×#64935C2semidirect
12. #10606389C3direct (N × H)
22. C2×C3×#711C4semidirect
43. C22×C4×Dic5C2×C3semidirect
44. C2×#4023C2×C3semidirect
45. C5×#386C2×C3semidirect
46. #65509C2×C3semidirect
47. #65502C2×C3semidirect
48. #65247C2×C3semidirect
49. #65246C2×C3semidirect
50. C22⋊C4×Dic5C2×C3semidirect
51. #64955C2×C3semidirect
52. #64935C2×C3semidirect
69. C2×C3×C22⋊D5C2×C4semidirect
75. C22×C3×Dic5C2×C4semidirect
86. C2×C3×C4×D5C2×C4semidirect
89. C2×C3×Dic10C2×C4semidirect
108. C3×#386D5semidirect
120. C2×#711C3×C4semidirect
166. C2×C3×C4×C5#41semidirect
178. C2×C3×Dic5C22⋊C4semidirect
186. C2×C3×Dic5#41semidirect
233. C2×C22⋊D5C2×C3×C4semidirect
239. C22×Dic5C2×C3×C4semidirect
250. C2×C4×D5C2×C3×C4semidirect
253. C2×Dic10C2×C3×C4semidirect
272. #386C3×D5semidirect
376. C2×C4×C5C3×#41semidirect
388. C2×Dic5C3×C22⋊C4semidirect
396. C2×Dic5C3×#41semidirect
483. C2×C3×C4#711semidirect
559. C3×C5#2297semidirect
644. C2×C4C3×#711semidirect
653. C5C3×#2297semidirect
682. C3#10606389direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7112
C22×C3×C4×Dic52
C2×C3×#40232
C3×C5×#3862
C3×#655092
C3×#655022
C3×#652472
C3×#652462
C3×C22⋊C4×Dic52
C3×#649552
C3×#649352
#106063893
C3×#22975