Finite Group Databasebeta

← D3×C4⋊C4×Dic5 #14319449

Subgroups — D3×C4⋊C4×Dic5 #14319449

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×C4⋊C4C211yesmaximal, characteristic
2C2×D3×C4⋊Dic5C211yesmaximal, characteristic
3C2×C4×D3×Dic5C212yesmaximal
4C2×C4×D3×Dic5C211yesmaximal, characteristic
5C4⋊C4×Dic15C211yesmaximal, characteristic, complemented
6C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
7D3×#3963C212yesmaximal
8#11748699C211yesmaximal, characteristic, complemented
9Dic5×C4⋊Dic3C211yesmaximal, characteristic, complemented
10#11748651C212yesmaximal, complemented
11Dic5×Dic3⋊C4C212yesmaximal, complemented
12C2×C4⋊C4×Dic5—31nomaximal, Hall
13C22×C4×C5×D3C2212yes—
14C22×C4×C5×D3C2211yescharacteristic
15C22×D3×Dic5C2211yescharacteristic
16C22×D3×Dic5C2212yes—
17C22×D3×Dic5C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20C2×C4×Dic15C2212yes—
21C2×C4×Dic15C2211yescharacteristic
22C2×C5×C4⋊Dic3C2211yescharacteristic
23C2×C5×Dic3⋊C4C2212yes—
24C5×D3×C4⋊C4C418yescomplemented
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×C3×C4×Dic5C2212yes—
27C2×C3×C4×Dic5C2211yescharacteristic
28C2×Dic3⋊Dic5C2212yes—
29C2×Dic3×Dic5C2212yes—
30C2×Dic3×Dic5C2212yes—
31C2×Dic3×Dic5C2211yescharacteristic
32C2×Dic3×Dic5C2211yescharacteristic
33D3×C4⋊Dic5C418yescomplemented
34C4×D3×Dic5—28no—
35C4×D3×Dic5C418yescomplemented
36#91115C2212yes—
37C3×#3963C2212yes—
38#90994C2212yes—
39#90994C2212yes—
40C4×D3×C4⋊C4—51nomaximal, Hall
41C22×C5×C4⋊C4—31no—
42C22×C4⋊Dic5—31no—
43C22×C4×Dic5—31no—
44C22×C4×Dic5—32no—
45C2×#3963—32no—
46C4⋊C4×Dic5—31no—
47C4⋊C4×Dic5—32no—
48C4⋊C4×Dic5—31no—
49C4⋊C4×Dic5—32no—
50C4⋊C4×Dic5—31no—
51C4⋊C4×Dic5D311yescharacteristic, direct product factor
52C23×C5×D3C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C22×Dic15C2312yes—
57C22×Dic15C2311yescharacteristic
58C22×C5×Dic3C2312yes—
59C22×C5×Dic3C2311yescharacteristic
60C2×C4×C5×D3—24no—
61C2×C4×C5×D3—24no—
62C2×C4×C5×D3C2×C418yes—
63C2×C4×C5×D3C2×C414yes—
64C2×C4×C5×D3C2×C414yes—
65C2×C4×C5×D3C2×C414yes—
66C22×C3×Dic5C2311yescharacteristic
67C22×C3×Dic5C2312yes—
68C22×C3×Dic5C2311yescharacteristic
69C2×D3×Dic5—24no—
70C2×D3×Dic5—22no—
71C2×D3×Dic5—22no—
72C2×D3×Dic5—24no—
73C2×D3×Dic5C2×C414yes—
74C2×D3×Dic5C2×C418yes—
75C2×D3×Dic5C2×C414yes—
76C2×D3×Dic5D414yes—
77C2×D3×Dic5Q814yes—
78C3×C5×C4⋊C4C2×C414yescomplemented
79C4⋊Dic15C2×C414yescomplemented
80C4×Dic15—24no—
81C4×Dic15C2×C414yescomplemented
82C5×C4⋊Dic3C2×C414yescomplemented
83C5×Dic3⋊C4C2×C418yescomplemented
84C3×C4⋊Dic5C2×C414yescomplemented
85C3×C4×Dic5—24no—
86C3×C4×Dic5C2×C414yescomplemented
87Dic3⋊Dic5C2×C418yescomplemented
88Dic3×Dic5—24no—
89Dic3×Dic5—24no—
90Dic3×Dic5C2×C414yescomplemented
91Dic3×Dic5C2×C414yescomplemented
92C2×D3×C4⋊C4—51no—
93C2×D3×C4⋊C4D511yescharacteristic
94C2×C42×D3—51no—
95C2×C42×D3—52no—
96C3×C4×C4⋊C4—51no—
97Dic3×C4⋊C4—51no—
98Dic3×C4⋊C4—51no—
99C4×C4⋊Dic3—51no—
100C4×Dic3⋊C4—52no—
101D3×#95—52no—
102#4649—52no—
103C23×C4×C5—31no—
104C23×C4×C5—32no—
105C23×Dic5—31no—
106C23×Dic5—32no—
107C23×Dic5—31no—
108C2×C5×C4⋊C4—32no—
109C2×C5×C4⋊C4—31no—
110C2×C5×C4⋊C4—38no—
111C2×C5×C4⋊C4C2×D311yescharacteristic
112C2×C4⋊Dic5—31no—
113C2×C4⋊Dic5—32no—
114C2×C4⋊Dic5—38no—
115C2×C4⋊Dic5C2×D311yescharacteristic
116C2×C4×Dic5—31no—
117C2×C4×Dic5—31no—
118C2×C4×Dic5—31no—
119C2×C4×Dic5—38no—
120C2×C4×Dic5—32no—
121C2×C4×Dic5—32no—
122C2×C4×Dic5—32no—
123C2×C4×Dic5—68no—
124C2×C4×Dic5C2×D312yes—
125C2×C4×Dic5C2×D311yescharacteristic
126#3963—32no—
127#3963—32no—
128#3963—32no—
129#3963C2×D312yes—
130C2×C4×C4⋊C4—151noSylow
131C23×C3×C5C2411yescharacteristic
132C22×C5×D3C22×C412yes—
133C22×C5×D3C22×C412yes—
134C22×C5×D3C22×C412yes—
135C22×C5×D3C2×D412yes—
136C22×C5×D3C2×Q812yes—
137C22×C5×D3#4112yes—
138C22×C5×D3#4112yes—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5C22×C414yes—
142C2×C3×C4×C5C22×C412yes—
143C2×C3×C4×C5C22×C412yes—
144C2×C3×C4×C5C22×C412yes—
145C2×Dic15—22no—
146C2×Dic15—21no—
147C2×Dic15—21no—
148C2×Dic15—22no—
149C2×Dic15C22×C412yes—
150C2×Dic15C22×C414yes—
151C2×Dic15C22×C412yes—
152C2×Dic15C2×D412yes—
153C2×Dic15C2×Q812yes—
154C2×C5×Dic3—22no—
155C2×C5×Dic3—22no—
156C2×C5×Dic3C22×C414yes—
157C2×C5×Dic3C22×C412yes—
158C2×C5×Dic3C22×C412yes—
159C2×C5×Dic3C22×C412yes—
160C4×C5×D3—216no—
161C4×C5×D3C42116yescomplemented
162C2×C3×Dic5—22no—
163C2×C3×Dic5—21no—
164C2×C3×Dic5—21no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5C22×C412yes—
167C2×C3×Dic5C22×C414yes—
168C2×C3×Dic5C22×C412yes—
169C2×C3×Dic5C2×D412yes—
170C2×C3×Dic5C2×Q812yes—
171D3×Dic5—28no—
172D3×Dic5—216no—
173D3×Dic5C4⋊C4116yesdirect product factor
174C22×C4×D3—51no—
175C22×C4×D3—51no—
176C22×C4×D3—52no—
177C22×C4×D3C2×D512yes—
178C22×C4×D3C2×D511yescharacteristic
179C2×C3×C4⋊C4—51no—
180C2×C3×C4⋊C4C2×D511yescharacteristic
181C2×C3×C42—51no—
182C2×C3×C42—52no—
183C2×C4⋊Dic3—51no—
184C2×C4⋊Dic3C2×D511yescharacteristic
185C2×Dic3⋊C4—52no—
186C2×Dic3⋊C4C2×D512yes—
187C2×C4×Dic3—51no—
188C2×C4×Dic3—51no—
189C2×C4×Dic3—51no—
190C2×C4×Dic3—52no—
191C2×C4×Dic3—52no—
192C2×C4×Dic3—52no—
193D3×C4⋊C4—58no—
194D3×C4⋊C4Dic518yesdirect product factor
195C42×D3—58no—
196C42×D3—108no—
197C3×#95—52no—
198C3⋊#95—52no—
199C3⋊#95—52no—
200C3⋊#95—52no—
201C24×C5—31no—
202C22×C4×C5—31no—
203C22×C4×C5—34no—
204C22×C4×C5—34no—
205C22×C4×C5—34no—
206C22×C4×C5—32no—
207C22×C4×C5—38no—
208C22×C4×C5—64no—
209C22×C4×C5—64no—
210C22×C4×C5C22×D312yes—
211C22×C4×C5C22×D311yescharacteristic
212C22×Dic5—31no—
213C22×Dic5—34no—
214C22×Dic5—34no—
215C22×Dic5—34no—
216C22×Dic5—31no—
217C22×Dic5—32no—
218C22×Dic5—34no—
219C22×Dic5—38no—
220C22×Dic5—64no—
221C22×Dic5—62no—
222C22×Dic5—62no—
223C22×Dic5—64no—
224C22×Dic5C22×D311yescharacteristic
225C22×Dic5C22×D312yes—
226C22×Dic5C22×D311yescharacteristic
227C5×C4⋊C4—38no—
228C5×C4⋊C4—34no—
229C5×C4⋊C4C4×D314yescomplemented
230C4⋊Dic5—34no—
231C4⋊Dic5—38no—
232C4⋊Dic5C4×D314yescomplemented
233C4×Dic5—24no—
234C4×Dic5—34no—
235C4×Dic5—34no—
236C4×Dic5—34no—
237C4×Dic5—64no—
238C4×Dic5—64no—
239C4×Dic5—64no—
240C4×Dic5C4×D314yescomplemented
241C22×C4⋊C4—31no—
242C22×C4⋊C4—151no—
243C22×C42—151no—
244C22×C42—152no—
245C4×C4⋊C4—51no—
246C4×C4⋊C4—152no—
247C4×C4⋊C4—152no—
248C4×C4⋊C4—151no—
249C4×C4⋊C4—151no—
250C4×C4⋊C4—151no—
251C2×#95—152no—
252C22×C3×C5C23×C411yescharacteristic
253C22×C3×C5C23×C411yescharacteristic
254C22×C3×C5C23×C411yescharacteristic
255C22×C3×C5C22×D411yescharacteristic
256C22×C3×C5C22×Q811yescharacteristic
257C22×C3×C5C2×#4111yescharacteristic
258C22×C3×C5C2×#4111yescharacteristic
259C2×C5×D3C2×C4214yes—
260C2×C5×D3C2×C4⋊C414yes—
261C2×C5×D3#11714yes—
262C2×C5×D3C4×D414yes—
263C2×C5×D3C4×D414yes—
264C2×C5×D3C4×Q814yes—
265C2×C5×D3C4×Q814yes—
266C3×C4×C5—24no—
267C3×C4×C5C2×C4214yescomplemented
268Dic15—22no—
269Dic15—24no—
270Dic15C2×C4⋊C414yescomplemented
271C3×Dic5—22no—
272C3×Dic5—24no—
273C3×Dic5C2×C4⋊C414yescomplemented
274C5×Dic3—24no—
275C5×Dic3C2×C4214yescomplemented
276C23×D3C22×D511yescharacteristic
277C22×C3×C4—51no—
278C22×C3×C4—51no—
279C22×C3×C4—52no—
280C22×C3×C4C22×D512yes—
281C22×C3×C4C22×D511yescharacteristic
282C22×Dic3—51no—
283C22×Dic3—51no—
284C22×Dic3—52no—
285C22×Dic3C22×D512yes—
286C22×Dic3C22×D511yescharacteristic
287C2×C4×D3—24no—
288C2×C4×D3—24no—
289C2×C4×D3—54no—
290C2×C4×D3—54no—
291C2×C4×D3—54no—
292C2×C4×D3—54no—
293C2×C4×D3—58no—
294C2×C4×D3—104no—
295C2×C4×D3—102no—
296C2×C4×D3—102no—
297C2×C4×D3—104no—
298C2×C4×D3C4×D514yes—
299C2×C4×D3C4×D514yes—
300C2×C4×D3C2×Dic518yes—
301C2×C4×D3C2×Dic514yes—
302C3×C4⋊C4—54no—
303C3×C4⋊C4C2×Dic514yescomplemented
304C3×C42—54no—
305C3×C42—104no—
306C4⋊Dic3—54no—
307C4⋊Dic3C2×Dic514yescomplemented
308Dic3⋊C4—58no—
309Dic3⋊C4C2×Dic518yescomplemented
310C4×Dic3—54no—
311C4×Dic3—54no—
312C4×Dic3—54no—
313C4×Dic3—104no—
314C4×Dic3—104no—
315C4×Dic3—104no—
316C23×C5—32no—
317C23×C5—32no—
318C23×C5—32no—
319C23×C5—32no—
320C23×C5—32no—
321C23×C5—32no—
322C23×C5—32no—
323C23×C5C23×D311yescharacteristic
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—32no—
327C2×C4×C5—32no—
328C2×C4×C5—32no—
329C2×C4×C5—316no—
330C2×C4×C5—34no—
331C2×C4×C5—616no—
332C2×C4×C5—62no—
333C2×C4×C5—62no—
334C2×C4×C5C2×C4×D312yes—
335C2×C4×C5C2×C4×D312yes—
336C2×C4×C5C2×C4×D314yes—
337C2×C4×C5C2×C4×D312yes—
338C2×Dic5—22no—
339C2×Dic5—21no—
340C2×Dic5—21no—
341C2×Dic5—22no—
342C2×Dic5—32no—
343C2×Dic5—32no—
344C2×Dic5—32no—
345C2×Dic5—316no—
346C2×Dic5—32no—
347C2×Dic5—34no—
348C2×Dic5—68no—
349C2×Dic5—616no—
350C2×Dic5—62no—
351C2×Dic5—61no—
352C2×Dic5—61no—
353C2×Dic5—62no—
354C2×Dic5C2×C4×D312yes—
355C2×Dic5C2×C4×D314yes—
356C2×Dic5C2×C4×D312yes—
357C2×Dic5D3×D412yes—
358C2×Dic5D3×Q812yes—
359C23×C4—31no—
360C23×C4—32no—
361C23×C4—151no—
362C23×C4—152no—
363C23×C4—151no—
364C2×C4⋊C4—32no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—38no—
367C2×C4⋊C4—51no—
368C2×C4⋊C4—158no—
369C2×C4⋊C4—152no—
370C2×C4⋊C4—151no—
371C2×C4⋊C4D3×D511yescharacteristic
372C2×C42—51no—
373C2×C42—52no—
374C2×C42—158no—
375C2×C42—151no—
376C2×C42—151no—
377C2×C42—151no—
378C2×C42—152no—
379C2×C42—152no—
380C2×C42—152no—
381C2×C42—308no—
382#95—52no—
383#95—152no—
384#95—152no—
385#95—152no—
386C2×C3×C5C22×C4211yescharacteristic
387C2×C3×C5C22×C4⋊C411yescharacteristic
388C2×C3×C5C2×#11711yescharacteristic
389C2×C3×C5C2×C4×D411yescharacteristic
390C2×C3×C5C2×C4×D411yescharacteristic
391C2×C3×C5C2×C4×Q811yescharacteristic
392C2×C3×C5C2×C4×Q811yescharacteristic
393C5×D3C4×C4⋊C418yescomplemented
394C23×C3C23×D511yescharacteristic
395C22×D3C2×C4×D512yes—
396C22×D3C2×C4×D512yes—
397C22×D3D4×D512yes—
398C22×D3#71112yes—
399C22×D3Q8×D512yes—
400C22×D3#71312yes—
401C22×D3C22×Dic512yes—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—52no—
405C2×C3×C4—52no—
406C2×C3×C4—52no—
407C2×C3×C4—52no—
408C2×C3×C4—54no—
409C2×C3×C4—102no—
410C2×C3×C4—101no—
411C2×C3×C4—101no—
412C2×C3×C4—102no—
413C2×C3×C4C2×C4×D512yes—
414C2×C3×C4C2×C4×D512yes—
415C2×C3×C4C22×Dic514yes—
416C2×C3×C4C22×Dic512yes—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—52no—
420C2×Dic3—52no—
421C2×Dic3—52no—
422C2×Dic3—52no—
423C2×Dic3—54no—
424C2×Dic3—102no—
425C2×Dic3—101no—
426C2×Dic3—101no—
427C2×Dic3—102no—
428C2×Dic3C2×C4×D512yes—
429C2×Dic3C2×C4×D512yes—
430C2×Dic3C22×Dic514yes—
431C2×Dic3C22×Dic512yes—
432C4×D3—216no—
433C4×D3—516no—
434C4×D3—108no—
435C4×D3—1016no—
436C4×D3C4×Dic5116yescomplemented
437C22×C5—34no—
438C22×C5—34no—
439C22×C5—34no—
440C22×C5—34no—
441C22×C5—34no—
442C22×C5—34no—
443C22×C5—34no—
444C22×C5C22×C4×D311yescharacteristic
445C22×C5C22×C4×D311yescharacteristic
446C22×C5C22×C4×D311yescharacteristic
447C22×C5C2×D3×D411yescharacteristic
448C22×C5C2×D3×Q811yescharacteristic
449C22×C5D3×#4111yescharacteristic
450C22×C5D3×#4111yescharacteristic
451C4×C5—24no—
452C4×C5—34no—
453C4×C5—64no—
454C4×C5C42×D314yescomplemented
455Dic5—22no—
456Dic5—24no—
457Dic5—34no—
458Dic5—62no—
459Dic5—64no—
460Dic5D3×C4⋊C414yesdirect product factor
461C24—31no—
462C22×C4—31no—
463C22×C4—34no—
464C22×C4—34no—
465C22×C4—34no—
466C22×C4—32no—
467C22×C4—38no—
468C22×C4—51no—
469C22×C4—51no—
470C22×C4—52no—
471C22×C4—64no—
472C22×C4—64no—
473C22×C4—154no—
474C22×C4—154no—
475C22×C4—154no—
476C22×C4—154no—
477C22×C4—158no—
478C22×C4—151no—
479C22×C4—151no—
480C22×C4—152no—
481C22×C4—304no—
482C22×C4—302no—
483C22×C4—304no—
484C22×C4—302no—
485C22×C4C2×D3×D512yes—
486C22×C4C2×D3×D511yescharacteristic
487C4⋊C4—38no—
488C4⋊C4—34no—
489C4⋊C4—54no—
490C4⋊C4—158no—
491C4⋊C4—154no—
492C4⋊C4D3×Dic514yesdirect product factor
493C42—54no—
494C42—104no—
495C42—154no—
496C42—154no—
497C42—154no—
498C42—304no—
499C42—304no—
500C42—304no—
501C3×C5C2×C4×C4⋊C411yescharacteristic, complemented, Hall
502C22×C3C22×C4×D511yescharacteristic
503C22×C3C22×C4×D511yescharacteristic
504C22×C3C2×D4×D511yescharacteristic
505C22×C3C2×#71111yescharacteristic
506C22×C3C2×Q8×D511yescharacteristic
507C22×C3C2×#71311yescharacteristic
508C22×C3C23×Dic511yescharacteristic
509C2×D3#403314yes—
510C2×D3D5×C4⋊C414yes—
511C2×D3#403814yes—
512C2×D3#403914yes—
513C2×D3C2×C4×Dic514yes—
514C2×D3D4×Dic514yes—
515C2×D3Q8×Dic514yes—
516C3×C4—24no—
517C3×C4—54no—
518C3×C4—102no—
519C3×C4—104no—
520C3×C4C2×C4×Dic514yescomplemented
521Dic3—24no—
522Dic3—54no—
523Dic3—102no—
524Dic3—104no—
525Dic3C2×C4×Dic514yescomplemented
526C2×C5—38no—
527C2×C5C2×C42×D311yescharacteristic
528C2×C5C2×D3×C4⋊C411yescharacteristic
529C2×C5D3×#11711yescharacteristic
530C2×C5C4×D3×D411yescharacteristic
531C2×C5C4×D3×D411yescharacteristic
532C2×C5C4×D3×Q811yescharacteristic
533C2×C5C4×D3×Q811yescharacteristic
534C23—32no—
535C23—32no—
536C23—32no—
537C23—32no—
538C23—32no—
539C23—32no—
540C23—32no—
541C23C22×D3×D511yescharacteristic
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—32no—
545C2×C4—32no—
546C2×C4—32no—
547C2×C4—316no—
548C2×C4—34no—
549C2×C4—52no—
550C2×C4—52no—
551C2×C4—52no—
552C2×C4—52no—
553C2×C4—54no—
554C2×C4—616no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—102no—
558C2×C4—101no—
559C2×C4—101no—
560C2×C4—102no—
561C2×C4—1516no—
562C2×C4—152no—
563C2×C4—152no—
564C2×C4—152no—
565C2×C4—152no—
566C2×C4—154no—
567C2×C4—308no—
568C2×C4—3016no—
569C2×C4—302no—
570C2×C4—301no—
571C2×C4—301no—
572C2×C4—302no—
573C2×C4C4×D3×D512yes—
574C2×C4C4×D3×D512yes—
575C2×C4C2×D3×Dic514yes—
576C2×C4C2×D3×Dic512yes—
577C2×C3C2×#403311yescharacteristic
578C2×C3C2×D5×C4⋊C411yescharacteristic
579C2×C3C2×#403811yescharacteristic
580C2×C3C2×#403911yescharacteristic
581C2×C3C22×C4×Dic511yescharacteristic
582C2×C3C2×D4×Dic511yescharacteristic
583C2×C3C2×Q8×Dic511yescharacteristic
584D3C4⋊C4×Dic518yesdirect product factor
585C5C4×D3×C4⋊C411yescharacteristic, complemented, Sylow
586C22—34no—
587C22—34no—
588C22—34no—
589C22—34no—
590C22—34no—
591C22—34no—
592C22—34no—
593C22C2×C4×D3×D511yescharacteristic
594C22C2×C4×D3×D511yescharacteristic
595C22D3×D4×D511yescharacteristic
596C22D3×#71111yescharacteristic
597C22D3×Q8×D511yescharacteristic
598C22D3×#71311yescharacteristic
599C22C22×D3×Dic511yescharacteristic
600C4—24no—
601C4—34no—
602C4—54no—
603C4—64no—
604C4—102no—
605C4—104no—
606C4—154no—
607C4—302no—
608C4—304no—
609C4C4×D3×Dic514yescomplemented
610C3C2×C4⋊C4×Dic511yescharacteristic, complemented, Sylow
611C2—38no—
612C2D3×#403311yescharacteristic
613C2D3×D5×C4⋊C411yescharacteristic
614C2D3×#403811yescharacteristic
615C2D3×#403911yescharacteristic
616C2C2×C4×D3×Dic511yescharacteristic
617C2D3×D4×Dic511yescharacteristic
618C2D3×Q8×Dic511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC2×C3×C5C22×C42
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×C4×C4⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. C4⋊C4×Dic15C2semidirect
6. C3×C4⋊C4×Dic5C2semidirect
8. #11748699C2semidirect
9. Dic5×C4⋊Dic3C2semidirect
10. #11748651C2semidirect
11. Dic5×Dic3⋊C4C2semidirect
24. C5×D3×C4⋊C4C4semidirect
33. D3×C4⋊Dic5C4semidirect
35. C4×D3×Dic5C4semidirect
51. C4⋊C4×Dic5D3direct (N × H)
78. C3×C5×C4⋊C4C2×C4semidirect
79. C4⋊Dic15C2×C4semidirect
81. C4×Dic15C2×C4semidirect
82. C5×C4⋊Dic3C2×C4semidirect
83. C5×Dic3⋊C4C2×C4semidirect
84. C3×C4⋊Dic5C2×C4semidirect
86. C3×C4×Dic5C2×C4semidirect
87. Dic3⋊Dic5C2×C4semidirect
90. Dic3×Dic5C2×C4semidirect
91. Dic3×Dic5C2×C4semidirect
161. C4×C5×D3C42semidirect
173. D3×Dic5C4⋊C4direct (N × H)
194. D3×C4⋊C4Dic5direct (N × H)
229. C5×C4⋊C4C4×D3semidirect
232. C4⋊Dic5C4×D3semidirect
240. C4×Dic5C4×D3semidirect
267. C3×C4×C5C2×C42semidirect
270. Dic15C2×C4⋊C4semidirect
273. C3×Dic5C2×C4⋊C4semidirect
275. C5×Dic3C2×C42semidirect
303. C3×C4⋊C4C2×Dic5semidirect
307. C4⋊Dic3C2×Dic5semidirect
309. Dic3⋊C4C2×Dic5semidirect
393. C5×D3C4×C4⋊C4semidirect
436. C4×D3C4×Dic5semidirect
454. C4×C5C42×D3semidirect
460. Dic5D3×C4⋊C4direct (N × H)
492. C4⋊C4D3×Dic5direct (N × H)
501. C3×C5C2×C4×C4⋊C4semidirect
520. C3×C4C2×C4×Dic5semidirect
525. Dic3C2×C4×Dic5semidirect
584. D3C4⋊C4×Dic5direct (N × H)
585. C5C4×D3×C4⋊C4semidirect
609. C4C4×D3×Dic5semidirect
610. C3C2×C4⋊C4×Dic5semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×C4⋊C42
C2×D3×C4⋊Dic52
C2×C4×D3×Dic52
C4⋊C4×Dic152
C3×C4⋊C4×Dic52
D3×#39632
#117486992
Dic5×C4⋊Dic32
#117486512
Dic5×Dic3⋊C42
C2×C4⋊C4×Dic53
C4×D3×C4⋊C45