Finite Group Databasebeta

← C3×#10605200 #14329031

Subgroups — C3×#10605200 #14329031

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4076C211yesmaximal, characteristic
2C2×C3×#4072C211yesmaximal, characteristic, complemented
3C2×C3×C4×D20C211yesmaximal, characteristic, complemented
4C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#65246C212yesmaximal, complemented
6C3×#65245C212yesmaximal, complemented
7C3×#65228C211yesmaximal, characteristic, complemented
8C3×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
9C3×#65217C211yesmaximal, characteristic, complemented
10C3×#64958C212yesmaximal, complemented
11C3×#64955C212yesmaximal, complemented
12#10605200C311yesmaximal, characteristic, direct product factor, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5C2212yes—
15C22×C3×D20C2211yescharacteristic
16C22×C3×C4×D5C2212yes—
17C2×C3×C5×C22⋊C4C2211yescharacteristic
18C2×C3×C5×C22⋊C4C2211yescharacteristic
19C2×C3×C42×C5C2211yescharacteristic
20C2×C3×C42×C5C2211yescharacteristic
21C2×C3×C22⋊Dic5C2212yes—
22C3×#4076C418yescomplemented
23C2×C3×#685C2212yes—
24C2×C3×#685C2212yes—
25C2×C3×#685C2212yes—
26C2×C3×#685C2212yes—
27C3×#4072—24no—
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×C4⋊Dic5C2211yescharacteristic
31C2×C3×#683C2212yes—
32C2×C3×C4×Dic5C2212yes—
33C2×C3×C4×Dic5C2212yes—
34C3×C4×D20—24no—
35C3×C5×#95C2211yescharacteristic
36C3×C5×#95C2211yescharacteristic
37C3×#3963C2212yes—
38C3×#3963C2212yes—
39C3×#2363—51nomaximal, Hall
40C2×#4076C2×C311yescharacteristic
41C2×#4072C2×C311yescharacteristic, complemented
42C2×C4×D20C2×C311yescharacteristic, complemented
43C4×C5×C22⋊C4C2×C311yescharacteristic, complemented
44#65246C2×C312yescomplemented
45#65245C2×C312yescomplemented
46#65228C2×C311yescharacteristic, complemented
47C4×C4⋊Dic5C2×C311yescharacteristic, complemented
48#65217C2×C311yescharacteristic, complemented
49#64958C2×C312yescomplemented
50#64955C2×C312yescomplemented
51C24×C3×C5C2311yescharacteristic
52C23×C3×D5C2312yes—
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5C2×C414yescomplemented
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×C3×C4×C5C2311yescharacteristic
60C22×C3×C4×C5C2311yescharacteristic
61C22×C3×C4×C5C2311yescharacteristic
62C2×C3×C22⋊D5—42no—
63C2×C3×C22⋊D5—42no—
64C2×C3×C22⋊D5C2×C418yescomplemented
65C22×C3×Dic5C2312yes—
66C22×C3×Dic5C2312yes—
67C22×C3×Dic5C2312yes—
68C2×C3×D20—22no—
69C2×C3×D20—22no—
70C2×C3×D20C2×C414yes—
71C2×C3×C4×D5—24no—
72C2×C3×C4×D5—24no—
73C2×C3×C4×D5—42no—
74C3×C5×C22⋊C4—22no—
75C3×C5×C22⋊C4—22no—
76C3×C42×C5—22no—
77C3×C42×C5—22no—
78C3×C22⋊Dic5—24no—
79C3×#685—24no—
80C3×#685—24no—
81C3×#685—42no—
82C3×#685C2×C418yescomplemented
83C3×C4⋊Dic5—22no—
84C3×C4⋊Dic5C2×C414yescomplemented
85C3×C4⋊Dic5D414yescomplemented
86C3×#683—42no—
87C3×C4×Dic5—24no—
88C3×C4×Dic5—42no—
89C2×C3×#121—51no—
90C2×C3×C4×D4—51no—
91C2×C3×#117—51no—
92C3×#390—52no—
93C3×#390—51no—
94C3×#389—51no—
95C3×#388—52no—
96C3×#386—52no—
97C3×C4×C4⋊C4—51no—
98C3×C4×C22⋊C4—52no—
99C3×C4×C22⋊C4D511yescharacteristic, complemented
100C23×C4×C5C22×C311yescharacteristic
101C22×C22⋊D5C22×C312yes—
102C22×D20C22×C311yescharacteristic
103C22×C4×D5C22×C312yes—
104C2×C5×C22⋊C4C22×C311yescharacteristic
105C2×C5×C22⋊C4C22×C311yescharacteristic
106C2×C42×C5C22×C311yescharacteristic
107C2×C42×C5C22×C311yescharacteristic
108C2×C22⋊Dic5C22×C312yes—
109#4076C3×C418yescomplemented
110C2×#685C22×C312yes—
111C2×#685C22×C312yes—
112C2×#685C22×C312yes—
113C2×#685C22×C312yes—
114#4072—24no—
115C2×C4⋊Dic5C22×C311yescharacteristic
116C2×C4⋊Dic5C22×C311yescharacteristic
117C2×C4⋊Dic5C22×C311yescharacteristic
118C2×#683C22×C312yes—
119C2×C4×Dic5C22×C312yes—
120C2×C4×Dic5C22×C312yes—
121C4×D20—24no—
122C5×#95C22×C311yescharacteristic
123C5×#95C22×C311yescharacteristic
124#3963C22×C312yes—
125#3963C22×C312yes—
126#2363—51noSylow
127C23×C3×C5—21no—
128C23×C3×C5—21no—
129C23×C3×C5—21no—
130C23×C3×C5—21no—
131C23×C3×C5—21no—
132C23×C3×C5—21no—
133C23×C3×C5C22×C412yes—
134C23×C3×C5C2411yescharacteristic
135C22×C3×D5—22no—
136C22×C3×D5—22no—
137C22×C3×D5—22no—
138C22×C3×D5—22no—
139C22×C3×D5—22no—
140C22×C3×D5—22no—
141C22×C3×D5C22×C414yes—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5—28no—
149C2×C3×C4×C5—21no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—21no—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5C22×C412yes—
156C2×C3×C4×C5C22×C412yes—
157C2×C3×C4×C5C2×D412yes—
158C2×C3×C4×C5#4112yes—
159C2×C3×C4×C5#4112yes—
160C2×C3×C4×C5#4112yes—
161C3×C22⋊D5—48no—
162C2×C3×Dic5—22no—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5—22no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5C22×C414yes—
170C2×C3×Dic5C2×D414yes—
171C3×D20—28no—
172C3×C4×D5—48no—
173C22×C3×D4—52no—
174C22×C3×D4—51no—
175C23×C3×C4—52no—
176C23×C3×C4C2×D511yescharacteristic
177C3×#121—58no—
178C3×C4×D4—104no—
179C3×#117—104no—
180C2×C3×C4⋊C4—51no—
181C2×C3×C4⋊C4—51no—
182C2×C3×C4⋊C4—51no—
183C2×C3×C4⋊C4—52no—
184C2×C3×C22⋊C4—52no—
185C2×C3×C22⋊C4—52no—
186C2×C3×C22⋊C4—52no—
187C2×C3×C22⋊C4—52no—
188C2×C3×C22⋊C4—52no—
189C2×C3×C22⋊C4C2×D511yescharacteristic
190C2×C3×C22⋊C4C2×D511yescharacteristic
191C2×C3×C42—52no—
192C2×C3×C42—52no—
193C2×C3×C42C2×D511yescharacteristic
194C2×C3×C42C2×D511yescharacteristic
195C3×#95—52no—
196C3×#95—52no—
197C3×#95C2×D511yescharacteristic
198C3×#95C2×D511yescharacteristic
199C24×C5C23×C311yescharacteristic
200C23×D5C23×C312yes—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5C2×C3×C414yescomplemented
204C22×C4×C5C23×C311yescharacteristic
205C22×C4×C5C23×C311yescharacteristic
206C22×C4×C5C23×C311yescharacteristic
207C22×C4×C5C23×C311yescharacteristic
208C22×C4×C5C23×C311yescharacteristic
209C22×C4×C5C23×C311yescharacteristic
210C2×C22⋊D5—42no—
211C2×C22⋊D5—42no—
212C2×C22⋊D5C2×C3×C418yescomplemented
213C22×Dic5C23×C312yes—
214C22×Dic5C23×C312yes—
215C22×Dic5C23×C312yes—
216C2×D20—22no—
217C2×D20—22no—
218C2×D20C2×C3×C414yes—
219C2×C4×D5—24no—
220C2×C4×D5—24no—
221C2×C4×D5—42no—
222C5×C22⋊C4—22no—
223C5×C22⋊C4—22no—
224C42×C5—22no—
225C42×C5—22no—
226C22⋊Dic5—24no—
227#685—24no—
228#685—24no—
229#685—42no—
230#685C2×C3×C418yescomplemented
231C4⋊Dic5—22no—
232C4⋊Dic5C2×C3×C414yescomplemented
233C4⋊Dic5C3×D414yescomplemented
234#683—42no—
235C4×Dic5—24no—
236C4×Dic5—42no—
237C2×#121—51no—
238C2×C4×D4—51no—
239C2×#117—51no—
240#390—52no—
241#390—51no—
242#389—51no—
243#388—52no—
244#386—52no—
245C4×C4⋊C4—51no—
246C4×C22⋊C4—52no—
247C4×C22⋊C4C3×D511yescharacteristic, complemented
248C22×C3×C5—22no—
249C22×C3×C5—22no—
250C22×C3×C5—22no—
251C22×C3×C5—41no—
252C22×C3×C5—41no—
253C22×C3×C5—41no—
254C22×C3×C5—41no—
255C22×C3×C5C23×C411yescharacteristic
256C22×C3×C5C22×D411yescharacteristic
257C22×C3×C5C2×#4111yescharacteristic
258C22×C3×C5C2×#4111yescharacteristic
259C22×C3×C5C2×#4111yescharacteristic
260C22×C3×C5H(5,𝔽2)11yescharacteristic
261C22×C3×C5H(5,𝔽2)11yescharacteristic
262C2×C3×D5—24no—
263C2×C3×D5—24no—
264C2×C3×D5—24no—
265C2×C3×D5—42no—
266C2×C3×D5—42no—
267C2×C3×D5—42no—
268C2×C3×D5—42no—
269C3×C4×C5—22no—
270C3×C4×C5—22no—
271C3×C4×C5—22no—
272C3×C4×C5—41no—
273C3×C4×C5—41no—
274C3×C4×C5C4×D414yes—
275C3×Dic5—24no—
276C3×Dic5—24no—
277C3×Dic5—42no—
278C24×C3—52no—
279C24×C3C22×D511yescharacteristic
280C2×C3×D4—58no—
281C2×C3×D4—54no—
282C2×C3×D4—102no—
283C2×C3×D4—102no—
284C2×C3×D4—202no—
285C2×C3×D4—202no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—52no—
289C22×C3×C4—52no—
290C22×C3×C4—52no—
291C22×C3×C4—104no—
292C22×C3×C4—104no—
293C22×C3×C4—202no—
294C22×C3×C4C4×D514yescomplemented
295C22×C3×C4C22×D511yescharacteristic
296C22×C3×C4C22×D511yescharacteristic
297C22×C3×C4C22×D511yescharacteristic
298C22×C3×C4C22×D511yescharacteristic
299C22×C3×C4C22×D511yescharacteristic
300C22×C3×C4C22×D511yescharacteristic
301C3×C4⋊C4—54no—
302C3×C4⋊C4—54no—
303C3×C4⋊C4—102no—
304C3×C4⋊C4—202no—
305C3×C22⋊C4—22no—
306C3×C22⋊C4—22no—
307C3×C22⋊C4—58no—
308C3×C22⋊C4—104no—
309C3×C22⋊C4—104no—
310C3×C22⋊C4—104no—
311C3×C22⋊C4—202no—
312C3×C42—22no—
313C3×C42—22no—
314C3×C42—104no—
315C3×C42—202no—
316C23×C5—21no—
317C23×C5—21no—
318C23×C5—21no—
319C23×C5—21no—
320C23×C5—21no—
321C23×C5—21no—
322C23×C5C22×C3×C412yes—
323C23×C5C24×C311yescharacteristic
324C22×D5—22no—
325C22×D5—22no—
326C22×D5—22no—
327C22×D5—22no—
328C22×D5—22no—
329C22×D5—22no—
330C22×D5C22×C3×C414yes—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—28no—
338C2×C4×C5—21no—
339C2×C4×C5—21no—
340C2×C4×C5—21no—
341C2×C4×C5—21no—
342C2×C4×C5—21no—
343C2×C4×C5—21no—
344C2×C4×C5C22×C3×C412yes—
345C2×C4×C5C22×C3×C412yes—
346C2×C4×C5C2×C3×D412yes—
347C2×C4×C5C3×#4112yes—
348C2×C4×C5C3×#4112yes—
349C2×C4×C5C3×#4112yes—
350C22⋊D5—48no—
351C2×Dic5—22no—
352C2×Dic5—22no—
353C2×Dic5—22no—
354C2×Dic5—22no—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5C22×C3×C414yes—
359C2×Dic5C2×C3×D414yes—
360D20—28no—
361C4×D5—48no—
362C22×D4—52no—
363C22×D4—51no—
364C23×C4—52no—
365C23×C4C2×C3×D511yescharacteristic
366#121—58no—
367C4×D4—104no—
368#117—104no—
369C2×C4⋊C4—51no—
370C2×C4⋊C4—51no—
371C2×C4⋊C4—51no—
372C2×C4⋊C4—52no—
373C2×C22⋊C4—52no—
374C2×C22⋊C4—52no—
375C2×C22⋊C4—52no—
376C2×C22⋊C4—52no—
377C2×C22⋊C4—52no—
378C2×C22⋊C4C2×C3×D511yescharacteristic
379C2×C22⋊C4C2×C3×D511yescharacteristic
380C2×C42—52no—
381C2×C42—52no—
382C2×C42C2×C3×D511yescharacteristic
383C2×C42C2×C3×D511yescharacteristic
384#95—52no—
385#95—52no—
386#95C2×C3×D511yescharacteristic
387#95C2×C3×D511yescharacteristic
388C2×C3×C5—42no—
389C2×C3×C5C2×C4×D411yescharacteristic
390C2×C3×C5C4×#4111yescharacteristic
391C2×C3×C5#51811yescharacteristic
392C2×C3×C5#54611yescharacteristic
393C2×C3×C5#55011yescharacteristic
394C2×C3×C5#55311yescharacteristic
395C2×C3×C5#55511yescharacteristic
396C3×D5—44no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—54no—
404C23×C3—102no—
405C23×C3—102no—
406C23×C3—102no—
407C23×C3—102no—
408C23×C3—102no—
409C23×C3—102no—
410C23×C3C2×C4×D512yes—
411C23×C3C23×D511yescharacteristic
412C3×D4—108no—
413C3×D4—208no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—28no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—54no—
428C2×C3×C4—54no—
429C2×C3×C4—102no—
430C2×C3×C4—102no—
431C2×C3×C4—102no—
432C2×C3×C4—102no—
433C2×C3×C4—102no—
434C2×C3×C4—102no—
435C2×C3×C4—102no—
436C2×C3×C4—208no—
437C2×C3×C4C2×C4×D512yes—
438C2×C3×C4C2×C4×D512yes—
439C2×C3×C4#70912yes—
440C2×C3×C4#70912yes—
441C2×C3×C4D4×D512yes—
442C2×C3×C4#71112yes—
443C22×C5—22no—
444C22×C5—22no—
445C22×C5—22no—
446C22×C5—41no—
447C22×C5—41no—
448C22×C5—41no—
449C22×C5—41no—
450C22×C5C23×C3×C411yescharacteristic
451C22×C5C22×C3×D411yescharacteristic
452C22×C5C2×C3×#4111yescharacteristic
453C22×C5C2×C3×#4111yescharacteristic
454C22×C5C2×C3×#4111yescharacteristic
455C22×C5C3×H(5,𝔽2)11yescharacteristic
456C22×C5C3×H(5,𝔽2)11yescharacteristic
457C2×D5—24no—
458C2×D5—24no—
459C2×D5—24no—
460C2×D5—42no—
461C2×D5—42no—
462C2×D5—42no—
463C2×D5—42no—
464C4×C5—22no—
465C4×C5—22no—
466C4×C5—22no—
467C4×C5—41no—
468C4×C5—41no—
469C4×C5C3×C4×D414yes—
470Dic5—24no—
471Dic5—24no—
472Dic5—42no—
473C24—52no—
474C24C22×C3×D511yescharacteristic
475C2×D4—58no—
476C2×D4—54no—
477C2×D4—102no—
478C2×D4—102no—
479C2×D4—202no—
480C2×D4—202no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—52no—
484C22×C4—52no—
485C22×C4—52no—
486C22×C4—104no—
487C22×C4—104no—
488C22×C4—202no—
489C22×C4C3×C4×D514yescomplemented
490C22×C4C22×C3×D511yescharacteristic
491C22×C4C22×C3×D511yescharacteristic
492C22×C4C22×C3×D511yescharacteristic
493C22×C4C22×C3×D511yescharacteristic
494C22×C4C22×C3×D511yescharacteristic
495C22×C4C22×C3×D511yescharacteristic
496C4⋊C4—54no—
497C4⋊C4—54no—
498C4⋊C4—102no—
499C4⋊C4—202no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—58no—
503C22⋊C4—104no—
504C22⋊C4—104no—
505C22⋊C4—104no—
506C22⋊C4—202no—
507C42—22no—
508C42—22no—
509C42—104no—
510C42—202no—
511C3×C5#236311yescharacteristic, complemented, Hall
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—41no—
516C22×C3—41no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—104no—
520C22×C3—104no—
521C22×C3—104no—
522C22×C3—202no—
523C22×C3—202no—
524C22×C3—202no—
525C22×C3—202no—
526C22×C3C22×C4×D511yescharacteristic
527C22×C3C2×#70911yescharacteristic
528C22×C3C2×#70911yescharacteristic
529C22×C3C2×D4×D511yescharacteristic
530C22×C3C2×#71111yescharacteristic
531C22×C3#414911yescharacteristic
532C22×C3#414911yescharacteristic
533C3×C4—22no—
534C3×C4—22no—
535C3×C4—22no—
536C3×C4—41no—
537C3×C4—41no—
538C3×C4—104no—
539C3×C4—104no—
540C3×C4—202no—
541C3×C4#402714yes—
542C2×C5—42no—
543C2×C5C2×C3×C4×D411yescharacteristic
544C2×C5C3×C4×#4111yescharacteristic
545C2×C5C3×#51811yescharacteristic
546C2×C5C3×#54611yescharacteristic
547C2×C5C3×#55011yescharacteristic
548C2×C5C3×#55311yescharacteristic
549C2×C5C3×#55511yescharacteristic
550D5—44no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—54no—
558C23—102no—
559C23—102no—
560C23—102no—
561C23—102no—
562C23—102no—
563C23—102no—
564C23C2×C3×C4×D512yes—
565C23C23×C3×D511yescharacteristic
566D4—108no—
567D4—208no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—28no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—54no—
582C2×C4—54no—
583C2×C4—102no—
584C2×C4—102no—
585C2×C4—102no—
586C2×C4—102no—
587C2×C4—102no—
588C2×C4—102no—
589C2×C4—102no—
590C2×C4—208no—
591C2×C4C2×C3×C4×D512yes—
592C2×C4C2×C3×C4×D512yes—
593C2×C4C3×#70912yes—
594C2×C4C3×#70912yes—
595C2×C4C3×D4×D512yes—
596C2×C4C3×#71112yes—
597C2×C3—42no—
598C2×C3—204no—
599C2×C3C4×#70911yescharacteristic
600C2×C3C2×#402711yescharacteristic
601C2×C3#6585511yescharacteristic
602C2×C3#6588411yescharacteristic
603C2×C3#6588711yescharacteristic
604C2×C3#6589711yescharacteristic
605C2×C3#6589911yescharacteristic
606C5C3×#236311yescharacteristic, complemented, Sylow
607C22—22no—
608C22—22no—
609C22—22no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—104no—
615C22—104no—
616C22—104no—
617C22—202no—
618C22—202no—
619C22—202no—
620C22—202no—
621C22C22×C3×C4×D511yescharacteristic
622C22C2×C3×#70911yescharacteristic
623C22C2×C3×#70911yescharacteristic
624C22C2×C3×D4×D511yescharacteristic
625C22C2×C3×#71111yescharacteristic
626C22C3×#414911yescharacteristic
627C22C3×#414911yescharacteristic
628C4—22no—
629C4—22no—
630C4—22no—
631C4—41no—
632C4—41no—
633C4—104no—
634C4—104no—
635C4—202no—
636C4C3×#402714yes—
637C3#1060520011yescharacteristic, direct product factor, Sylow
638C2—42no—
639C2—204no—
640C2C3×C4×#70911yescharacteristic
641C2C2×C3×#402711yescharacteristic
642C2C3×#6585511yescharacteristic
643C2C3×#6588411yescharacteristic
644C2C3×#6588711yescharacteristic
645C2C3×#6589711yescharacteristic
646C2C3×#6589911yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC2×C3×#4076C2
cosocleC23×C5C24×C3
hypercenterC3×C4×C22⋊C4D5
hypocenterC5C3×#2363
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4072C2semidirect
3. C2×C3×C4×D20C2semidirect
4. C3×C4×C5×C22⋊C4C2semidirect
5. C3×#65246C2semidirect
6. C3×#65245C2semidirect
7. C3×#65228C2semidirect
8. C3×C4×C4⋊Dic5C2semidirect
9. C3×#65217C2semidirect
10. C3×#64958C2semidirect
11. C3×#64955C2semidirect
12. #10605200C3direct (N × H)
22. C3×#4076C4semidirect
41. C2×#4072C2×C3semidirect
42. C2×C4×D20C2×C3semidirect
43. C4×C5×C22⋊C4C2×C3semidirect
44. #65246C2×C3semidirect
45. #65245C2×C3semidirect
46. #65228C2×C3semidirect
47. C4×C4⋊Dic5C2×C3semidirect
48. #65217C2×C3semidirect
49. #64958C2×C3semidirect
50. #64955C2×C3semidirect
55. C22×C3×C4×C5C2×C4semidirect
64. C2×C3×C22⋊D5C2×C4semidirect
82. C3×#685C2×C4semidirect
84. C3×C4⋊Dic5C2×C4semidirect
85. C3×C4⋊Dic5D4semidirect
99. C3×C4×C22⋊C4D5semidirect
109. #4076C3×C4semidirect
203. C22×C4×C5C2×C3×C4semidirect
212. C2×C22⋊D5C2×C3×C4semidirect
230. #685C2×C3×C4semidirect
232. C4⋊Dic5C2×C3×C4semidirect
233. C4⋊Dic5C3×D4semidirect
247. C4×C22⋊C4C3×D5semidirect
294. C22×C3×C4C4×D5semidirect
489. C22×C4C3×C4×D5semidirect
511. C3×C5#2363semidirect
606. C5C3×#2363semidirect
637. C3#10605200direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40762
C2×C3×#40722
C2×C3×C4×D202
C3×C4×C5×C22⋊C42
C3×#652462
C3×#652452
C3×#652282
C3×C4×C4⋊Dic52
C3×#652172
C3×#649582
C3×#649552
#106052003
C3×#23635