Finite Group Databasebeta

← #14327036

Subgroups — #14327036

Order 1920.

1552 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊Dic15C211yesmaximal, characteristic, complemented
2C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
3C2×#91559C212yesmaximal
4C2×D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C5×#5212C211yesmaximal, characteristic, complemented
6#11749515C212yesmaximal, complemented
7#11748900C212yesmaximal, complemented
8#11748834C211yesmaximal, characteristic, complemented
9#11748759C211yesmaximal, characteristic, complemented
10#11748680C212yesmaximal, complemented
11Dic5×C4⋊Dic3C211yesmaximal, characteristic, complemented
12#10605741—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×Dic15C2212yes—
15C22×C3×C22⋊D5C2211yescharacteristic
16C22×C3×C4×D5C2211yescharacteristic
17C22×D5×Dic3C2212yes—
18C2×C4⋊Dic15—24no—
19C2×C4⋊Dic15C2212yes—
20C2×C4⋊Dic15C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C5×#217C2212yes—
23C2×C5×C4⋊Dic3C2211yescharacteristic
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C3×C22⋊Dic5C2211yescharacteristic
26C3×C4×C22⋊D5C418yescomplemented
27C2×C3×#685C2211yescharacteristic
28C2×C3×#683C2211yescharacteristic
29C2×C3×C4×Dic5C2211yescharacteristic
30#91559—28no—
31C2×#6668C2212yes—
32C2×#6668C2212yes—
33C2×#6668C2212yes—
34C2×#6665C2212yes—
35C2×Dic3×Dic5C2212yes—
36D5×C4⋊Dic3—24no—
37C5×C3⋊#95C2212yes—
38#90994C2212yes—
39#90994C2212yes—
40D4×C4⋊Dic3—51nomaximal, Hall
41C2×C4×C22⋊D5D311yescharacteristic
42C22×C4⋊Dic5—31no—
43C2×D5×C4⋊C4—31no—
44C2×#4027—32no—
45C5×#380—31no—
46#65276—31no—
47#65265—31no—
48C4⋊C4×Dic5—31no—
49#65235—32no—
50#64957—32no—
51#64936—32no—
52C24×C3×C5C2311yescharacteristic
53C23×C3×D5C2311yescharacteristic
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5—22no—
56C22×C3×C4×C5C2×C414yescomplemented
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15—24no—
60C22×Dic15—24no—
61C22×Dic15—42no—
62C22×Dic15C2312yes—
63C22×Dic15C2312yes—
64C22×C5×Dic3C2312yes—
65C22×C5×Dic3C2312yes—
66C2×C3×C22⋊D5C2×C414yes—
67C2×C3×C22⋊D5D414yes—
68C2×C3×C22⋊D5Q814yes—
69C22×C3×Dic5C2311yescharacteristic
70C22×C3×Dic5C2311yescharacteristic
71C22×C3×Dic5C2311yescharacteristic
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5C2×C414yescomplemented
75C2×D5×Dic3—24no—
76C2×D5×Dic3—24no—
77C2×D5×Dic3—42no—
78C4⋊Dic15—22no—
79C4⋊Dic15—24no—
80C4⋊Dic15D414yescomplemented
81C5×#217—24no—
82C5×C4⋊Dic3—22no—
83C5×C4⋊Dic3—22no—
84C3×C22⋊Dic5C2×C414yescomplemented
85C3×#685C2×C414yescomplemented
86C3×#683C2×C414yescomplemented
87C3×C4×Dic5C2×C414yescomplemented
88#6668—24no—
89#6668—24no—
90#6668—42no—
91#6665—24no—
92Dic3×Dic5—24no—
93C2×C3×C4×D4—51no—
94C2×D4×Dic3—52no—
95C22×C4⋊Dic3—51no—
96C22×C4⋊Dic3—51no—
97#5212—51no—
98#5212D511yescharacteristic, complemented
99#4984—52no—
100#4950—52no—
101#4950—52no—
102#4935—51no—
103C4×C4⋊Dic3—51no—
104C23×C4×C5C2×D311yescharacteristic
105C22×C22⋊D5C2×D311yescharacteristic
106C23×Dic5—32no—
107C22×C4×D5—32no—
108C22×C4×D5C2×D311yescharacteristic
109C2×C5×C4⋊C4—31no—
110C2×C5×C4⋊C4—31no—
111C2×C5×C22⋊C4—32no—
112C2×C22⋊Dic5C2×D311yescharacteristic
113C4×C22⋊D5Dic318yescomplemented
114C2×#685—32no—
115C2×#685C2×D311yescharacteristic
116C2×C4⋊Dic5—31no—
117C2×C4⋊Dic5—32no—
118C2×C4⋊Dic5—31no—
119C2×C4⋊Dic5—64no—
120C2×#683—32no—
121C2×#683—32no—
122C2×#683—32no—
123C2×#683C2×D311yescharacteristic
124C2×C4×Dic5—32no—
125C2×C4×Dic5C2×D311yescharacteristic
126D5×C4⋊C4—64no—
127#4027—68no—
128C5×#95—32no—
129#3963—32no—
130#3963—32no—
131D4×C4⋊C4—151noSylow
132C23×C3×C5—21no—
133C23×C3×C5—21no—
134C23×C3×C5—21no—
135C23×C3×C5—21no—
136C23×C3×C5C22×C412yes—
137C23×C3×C5C2×D412yes—
138C23×C3×C5C2×Q812yes—
139C23×C3×C5C2411yescharacteristic
140C22×C3×D5—21no—
141C22×C3×D5—21no—
142C22×C3×D5—21no—
143C22×C3×D5—21no—
144C22×C3×D5C22×C412yes—
145C22×C3×D5C2×D412yes—
146C22×C3×D5C2×Q812yes—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—28no—
150C2×C3×C4×C5C22×C412yes—
151C2×C3×C4×C5C22×C412yes—
152C2×C3×C4×C5C2×D412yes—
153C2×C3×C4×C5#4112yes—
154C2×Dic15—22no—
155C2×Dic15—22no—
156C2×Dic15—22no—
157C2×Dic15—22no—
158C2×Dic15—22no—
159C2×Dic15—48no—
160C2×Dic15C2×D414yes—
161C2×C5×Dic3—22no—
162C2×C5×Dic3—22no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—22no—
166C2×C5×Dic3—22no—
167C3×C22⋊D5C4⋊C4116yescomplemented
168C2×C3×Dic5—21no—
169C2×C3×Dic5—21no—
170C2×C3×Dic5—21no—
171C2×C3×Dic5—21no—
172C2×C3×Dic5C22×C412yes—
173C2×C3×Dic5C22×C412yes—
174C2×C3×Dic5C22×C412yes—
175C2×C3×Dic5C2×D412yes—
176C2×C3×Dic5C2×Q812yes—
177C3×C4×D5—28no—
178D5×Dic3—48no—
179C22×C3×D4—51no—
180C23×C3×C4—51no—
181C23×C3×C4C2×D511yescharacteristic
182C23×Dic3—52no—
183C23×Dic3—52no—
184C3×C4×D4—58no—
185C2×C3×C4⋊C4—51no—
186C2×C3×C22⋊C4—51no—
187C2×C3×C22⋊C4—51no—
188C2×C3×C42—51no—
189C2×#217—52no—
190C2×#217C2×D512yes—
191D4×Dic3—108no—
192C2×C4⋊Dic3—51no—
193C2×C4⋊Dic3—51no—
194C2×C4⋊Dic3—52no—
195C2×C4⋊Dic3—52no—
196C2×C4⋊Dic3—52no—
197C2×C4⋊Dic3—52no—
198C2×C4⋊Dic3—104no—
199C2×C4⋊Dic3—104no—
200C2×C4⋊Dic3C2×D511yescharacteristic
201C2×C4⋊Dic3C2×D511yescharacteristic
202C2×C4×Dic3—52no—
203C3⋊#95—52no—
204C3⋊#95—52no—
205C3⋊#95C2×D512yes—
206C24×C5C22×D311yescharacteristic
207C23×D5C22×D311yescharacteristic
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—32no—
211C22×C4×C5—32no—
212C22×C4×C5C2×Dic314yescomplemented
213C22×C4×C5C22×D311yescharacteristic
214C22×C4×C5C22×D311yescharacteristic
215C2×C22⋊D5Dic614yes—
216C2×C22⋊D5D1214yes—
217C2×C22⋊D5C2×Dic314yes—
218C22×Dic5—32no—
219C22×Dic5—32no—
220C22×Dic5—64no—
221C22×Dic5—64no—
222C22×Dic5—122no—
223C22×Dic5C22×D311yescharacteristic
224C22×Dic5C22×D311yescharacteristic
225C22×Dic5C22×D311yescharacteristic
226C2×C4×D5—22no—
227C2×C4×D5—22no—
228C2×C4×D5—64no—
229C2×C4×D5—64no—
230C2×C4×D5—122no—
231C2×C4×D5C2×Dic314yescomplemented
232C5×C4⋊C4—62no—
233C5×C4⋊C4—62no—
234C5×C22⋊C4—64no—
235C22⋊Dic5C2×Dic314yescomplemented
236#685—64no—
237#685C2×Dic314yescomplemented
238C4⋊Dic5—34no—
239C4⋊Dic5—64no—
240C4⋊Dic5—62no—
241#683—64no—
242#683—64no—
243#683—122no—
244#683C2×Dic314yescomplemented
245C4×Dic5—64no—
246C4×Dic5C2×Dic314yescomplemented
247C2×C4×D4—51no—
248C2×C4×D4—152no—
249C22×C4⋊C4—151no—
250C22×C4⋊C4—151no—
251#389—152no—
252#385—152no—
253#385—152no—
254#384—151no—
255#380—31no—
256#380—151no—
257C4×C4⋊C4—151no—
258C22×C3×C5—22no—
259C22×C3×C5—22no—
260C22×C3×C5—22no—
261C22×C3×C5—22no—
262C22×C3×C5—22no—
263C22×C3×C5—22no—
264C22×C3×C5C2×C4⋊C414yescomplemented
265C22×C3×C5C23×C411yescharacteristic
266C22×C3×C5C22×D411yescharacteristic
267C22×C3×C5C22×D411yescharacteristic
268C22×C3×C5C22×Q811yescharacteristic
269C22×C3×C5C2×#4111yescharacteristic
270C22×C3×C5H(5,𝔽2)11yescharacteristic
271C22×C3×C52−1+411yescharacteristic
272C2×C3×D5—22no—
273C2×C3×D5—22no—
274C2×C3×D5—22no—
275C2×C3×D5—22no—
276C2×C3×D5—22no—
277C2×C3×D5—22no—
278C2×C3×D5C2×C4⋊C414yescomplemented
279C3×C4×C5—22no—
280C3×C4×C5C4×D414yescomplemented
281Dic15—24no—
282Dic15—42no—
283C3×Dic5—22no—
284C3×Dic5—22no—
285C3×Dic5C2×C4⋊C414yescomplemented
286C5×Dic3—42no—
287C5×Dic3—42no—
288C24×C3—51no—
289C24×C3C22×D511yescharacteristic
290C2×C3×D4—54no—
291C2×C3×D4—54no—
292C2×C3×D4—54no—
293C22×C3×C4—22no—
294C22×C3×C4—22no—
295C22×C3×C4—51no—
296C22×C3×C4—51no—
297C22×C3×C4—51no—
298C22×C3×C4—54no—
299C22×C3×C4—102no—
300C22×C3×C4—102no—
301C22×C3×C4C4×D514yescomplemented
302C22×C3×C4C22×D511yescharacteristic
303C22×C3×C4C22×D511yescharacteristic
304C22×Dic3—52no—
305C22×Dic3—52no—
306C22×Dic3—104no—
307C22×Dic3—104no—
308C22×Dic3—104no—
309C22×Dic3—104no—
310C22×Dic3—202no—
311C22×Dic3—202no—
312C22×Dic3C22×D512yes—
313C22×Dic3C22×D512yes—
314C3×C4⋊C4—54no—
315C3×C22⋊C4—54no—
316C3×C22⋊C4—54no—
317C3×C42—54no—
318#217—24no—
319#217—104no—
320C4⋊Dic3—22no—
321C4⋊Dic3—22no—
322C4⋊Dic3—54no—
323C4⋊Dic3—104no—
324C4⋊Dic3—104no—
325C4⋊Dic3—104no—
326C4⋊Dic3—102no—
327C4⋊Dic3—202no—
328C4×Dic3—104no—
329C23×C5—21no—
330C23×C5—21no—
331C23×C5—21no—
332C23×C5—21no—
333C23×C5C2×Dic612yes—
334C23×C5C2×D1212yes—
335C23×C5C22×Dic312yes—
336C23×C5C23×D311yescharacteristic
337C22×D5—21no—
338C22×D5—21no—
339C22×D5—21no—
340C22×D5—21no—
341C22×D5C2×Dic612yes—
342C22×D5C2×D1212yes—
343C22×D5C22×Dic312yes—
344C2×C4×C5—21no—
345C2×C4×C5—21no—
346C2×C4×C5—28no—
347C2×C4×C5—62no—
348C2×C4×C5—62no—
349C2×C4×C5—62no—
350C2×C4×C5—62no—
351C2×C4×C5—62no—
352C2×C4×C5—62no—
353C2×C4×C5D3×D412yes—
354C2×C4×C5#23712yes—
355C2×C4×C5C22×Dic312yes—
356C2×C4×C5C22×Dic312yes—
357C22⋊D5C4⋊Dic3116yescomplemented
358C2×Dic5—21no—
359C2×Dic5—21no—
360C2×Dic5—21no—
361C2×Dic5—21no—
362C2×Dic5—34no—
363C2×Dic5—62no—
364C2×Dic5—62no—
365C2×Dic5—62no—
366C2×Dic5—62no—
367C2×Dic5—62no—
368C2×Dic5—128no—
369C2×Dic5C2×Dic612yes—
370C2×Dic5C2×D1212yes—
371C2×Dic5C22×Dic312yes—
372C2×Dic5C22×Dic312yes—
373C2×Dic5C22×Dic312yes—
374C4×D5—28no—
375C4×D5—128no—
376C22×D4—51no—
377C23×C4—51no—
378C23×C4—152no—
379C23×C4—152no—
380C23×C4D3×D511yescharacteristic
381C4×D4—58no—
382C4×D4—308no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—51no—
386C2×C4⋊C4—151no—
387C2×C4⋊C4—152no—
388C2×C4⋊C4—152no—
389C2×C4⋊C4—151no—
390C2×C4⋊C4—152no—
391C2×C4⋊C4—152no—
392C2×C4⋊C4—304no—
393C2×C4⋊C4—304no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—51no—
396C2×C22⋊C4—51no—
397C2×C22⋊C4—152no—
398C2×C42—51no—
399C2×C42—152no—
400#95—32no—
401#95—152no—
402#95—152no—
403C2×C3×C5—24no—
404C2×C3×C5C22×C4⋊C411yescharacteristic
405C2×C3×C5C2×C4×D411yescharacteristic
406C2×C3×C5#52011yescharacteristic
407C2×C3×C5D4211yescharacteristic
408C2×C3×C5#54711yescharacteristic
409C2×C3×C5D4×Q811yescharacteristic
410C2×C3×C5#55411yescharacteristic
411C3×D5—24no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—52no—
417C23×C3—52no—
418C23×C3—52no—
419C23×C3—101no—
420C23×C3—101no—
421C23×C3—101no—
422C23×C3—101no—
423C23×C3C2×C4×D512yes—
424C23×C3D4×D512yes—
425C23×C3Q8×D512yes—
426C23×C3C23×D511yescharacteristic
427C3×D4—516no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—28no—
431C2×C3×C4—52no—
432C2×C3×C4—52no—
433C2×C3×C4—52no—
434C2×C3×C4—52no—
435C2×C3×C4—52no—
436C2×C3×C4—101no—
437C2×C3×C4—101no—
438C2×C3×C4—101no—
439C2×C3×C4—101no—
440C2×C3×C4—108no—
441C2×C3×C4C2×C4×D512yes—
442C2×C3×C4C2×C4×D512yes—
443C2×C3×C4D4×D512yes—
444C2×C3×C4#71112yes—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—54no—
452C2×Dic3—102no—
453C2×Dic3—102no—
454C2×Dic3—102no—
455C2×Dic3—102no—
456C2×Dic3—102no—
457C2×Dic3—208no—
458C2×Dic3—208no—
459C22×C5—22no—
460C22×C5—22no—
461C22×C5—22no—
462C22×C5—22no—
463C22×C5—22no—
464C22×C5—22no—
465C22×C5C2×C4⋊Dic314yescomplemented
466C22×C5C22×Dic611yescharacteristic
467C22×C5C22×D1211yescharacteristic
468C22×C5C2×D3×D411yescharacteristic
469C22×C5C2×#23711yescharacteristic
470C22×C5#100911yescharacteristic
471C22×C5#101011yescharacteristic
472C22×C5C23×Dic311yescharacteristic
473C2×D5—22no—
474C2×D5—22no—
475C2×D5—22no—
476C2×D5—22no—
477C2×D5—22no—
478C2×D5—22no—
479C2×D5C2×C4⋊Dic314yescomplemented
480C4×C5—22no—
481C4×C5—122no—
482C4×C5—122no—
483C4×C5D4×Dic314yescomplemented
484Dic5—22no—
485Dic5—22no—
486Dic5—64no—
487Dic5—122no—
488Dic5C2×C4⋊Dic314yescomplemented
489C24—51no—
490C24C2×D3×D511yescharacteristic
491C2×D4—54no—
492C2×D4—54no—
493C2×D4—54no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—32no—
497C22×C4—32no—
498C22×C4—51no—
499C22×C4—51no—
500C22×C4—51no—
501C22×C4—54no—
502C22×C4—102no—
503C22×C4—102no—
504C22×C4—152no—
505C22×C4—152no—
506C22×C4—304no—
507C22×C4—304no—
508C22×C4—304no—
509C22×C4—304no—
510C22×C4—602no—
511C22×C4—602no—
512C22×C4D5×Dic314yescomplemented
513C22×C4C2×D3×D511yescharacteristic
514C22×C4C2×D3×D511yescharacteristic
515C4⋊C4—54no—
516C4⋊C4—62no—
517C4⋊C4—62no—
518C4⋊C4—154no—
519C4⋊C4—304no—
520C4⋊C4—304no—
521C4⋊C4—304no—
522C4⋊C4—302no—
523C4⋊C4—602no—
524C22⋊C4—54no—
525C22⋊C4—54no—
526C22⋊C4—64no—
527C22⋊C4—304no—
528C42—54no—
529C42—304no—
530C3×C5D4×C4⋊C411yescharacteristic, complemented, Hall
531C22×C3—22no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—22no—
535C22×C3—22no—
536C22×C3—22no—
537C22×C3—54no—
538C22×C3—102no—
539C22×C3—102no—
540C22×C3—102no—
541C22×C3—102no—
542C22×C3—102no—
543C22×C3—102no—
544C22×C3D5×C4⋊C414yescomplemented
545C22×C3C22×C4×D511yescharacteristic
546C22×C3C2×D4×D511yescharacteristic
547C22×C3C2×D4×D511yescharacteristic
548C22×C3C2×#71111yescharacteristic
549C22×C3C2×Q8×D511yescharacteristic
550C22×C3#414911yescharacteristic
551C22×C3#415011yescharacteristic
552C3×C4—22no—
553C3×C4—54no—
554C3×C4—102no—
555C3×C4—102no—
556C3×C4#402714yescomplemented
557Dic3—42no—
558Dic3—42no—
559Dic3—104no—
560Dic3—202no—
561C2×C5—24no—
562C2×C5D4×Dic611yescharacteristic
563C2×C5#554311yescharacteristic
564C2×C5D4×D1211yescharacteristic
565C2×C5#555511yescharacteristic
566C2×C5C22×C4⋊Dic311yescharacteristic
567C2×C5C2×D4×Dic311yescharacteristic
568C2×C5#582711yescharacteristic
569D5—24no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—52no—
575C23—52no—
576C23—52no—
577C23—101no—
578C23—101no—
579C23—101no—
580C23—101no—
581C23D5×Dic612yes—
582C23D5×D1212yes—
583C23C2×D5×Dic312yes—
584C23C22×D3×D511yescharacteristic
585D4—516no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—28no—
589C2×C4—52no—
590C2×C4—52no—
591C2×C4—52no—
592C2×C4—52no—
593C2×C4—52no—
594C2×C4—62no—
595C2×C4—62no—
596C2×C4—62no—
597C2×C4—62no—
598C2×C4—62no—
599C2×C4—62no—
600C2×C4—101no—
601C2×C4—101no—
602C2×C4—101no—
603C2×C4—101no—
604C2×C4—108no—
605C2×C4—154no—
606C2×C4—302no—
607C2×C4—302no—
608C2×C4—302no—
609C2×C4—302no—
610C2×C4—302no—
611C2×C4—608no—
612C2×C4—608no—
613C2×C4C2×D5×Dic312yes—
614C2×C4C2×D5×Dic312yes—
615C2×C4#678012yes—
616C2×C4#679012yes—
617C2×C3—24no—
618C2×C3—104no—
619C2×C3C2×#402711yescharacteristic
620C2×C3C2×D5×C4⋊C411yescharacteristic
621C2×C3#6585711yescharacteristic
622C2×C3#6594311yescharacteristic
623C2×C3#6594511yescharacteristic
624C2×C3#6596611yescharacteristic
625C2×C3#6596911yescharacteristic
626C5D4×C4⋊Dic311yescharacteristic, complemented, Sylow
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—54no—
634C22—102no—
635C22—102no—
636C22—102no—
637C22—102no—
638C22—102no—
639C22—102no—
640C22D5×C4⋊Dic314yescomplemented
641C22C2×D5×Dic611yescharacteristic
642C22#9200111yescharacteristic
643C22C2×D5×D1211yescharacteristic
644C22#9201911yescharacteristic
645C22C22×D5×Dic311yescharacteristic
646C22C2×#678011yescharacteristic
647C22C2×#679011yescharacteristic
648C4—22no—
649C4—54no—
650C4—102no—
651C4—102no—
652C4—122no—
653C4—122no—
654C4—304no—
655C4—602no—
656C4#9155914yescomplemented
657C3#1060574111yescharacteristic, complemented, Sylow
658C2—24no—
659C2—104no—
660C2C2×D5×C4⋊Dic311yescharacteristic
661C2#1175432611yescharacteristic
662C2#1175436611yescharacteristic
663C2#1175450911yescharacteristic
664C2#1175451011yescharacteristic
665C2#1175464711yescharacteristic
666C2C2×#9155911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC23×C4D3×D5
hypocenterC3×C5D4×C4⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊Dic15C2semidirect
4. C2×D5×C4⋊Dic3C2semidirect
5. C5×#5212C2semidirect
6. #11749515C2semidirect
7. #11748900C2semidirect
8. #11748834C2semidirect
9. #11748759C2semidirect
10. #11748680C2semidirect
11. Dic5×C4⋊Dic3C2semidirect
26. C3×C4×C22⋊D5C4semidirect
56. C22×C3×C4×C5C2×C4semidirect
74. C2×C3×C4×D5C2×C4semidirect
80. C4⋊Dic15D4semidirect
84. C3×C22⋊Dic5C2×C4semidirect
85. C3×#685C2×C4semidirect
86. C3×#683C2×C4semidirect
87. C3×C4×Dic5C2×C4semidirect
98. #5212D5semidirect
113. C4×C22⋊D5Dic3semidirect
167. C3×C22⋊D5C4⋊C4semidirect
212. C22×C4×C5C2×Dic3semidirect
231. C2×C4×D5C2×Dic3semidirect
235. C22⋊Dic5C2×Dic3semidirect
237. #685C2×Dic3semidirect
244. #683C2×Dic3semidirect
246. C4×Dic5C2×Dic3semidirect
264. C22×C3×C5C2×C4⋊C4semidirect
278. C2×C3×D5C2×C4⋊C4semidirect
280. C3×C4×C5C4×D4semidirect
285. C3×Dic5C2×C4⋊C4semidirect
301. C22×C3×C4C4×D5semidirect
357. C22⋊D5C4⋊Dic3semidirect
465. C22×C5C2×C4⋊Dic3semidirect
479. C2×D5C2×C4⋊Dic3semidirect
483. C4×C5D4×Dic3semidirect
488. Dic5C2×C4⋊Dic3semidirect
512. C22×C4D5×Dic3semidirect
530. C3×C5D4×C4⋊C4semidirect
544. C22×C3D5×C4⋊C4semidirect
556. C3×C4#4027semidirect
626. C5D4×C4⋊Dic3semidirect
640. C22D5×C4⋊Dic3semidirect
656. C4#91559semidirect
657. C3#10605741semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊Dic152
C2×C3×C4×C22⋊D52
C2×#915592
C2×D5×C4⋊Dic32
C5×#52122
#117495152
#117489002
#117488342
#117487592
#117486802
Dic5×C4⋊Dic32
#106057413
D4×C4⋊Dic35