Finite Group Databasebeta

← C2×D3×D5×C4⋊C4 #14478711

Subgroups — C2×D3×D5×C4⋊C4 #14478711

Order 1920.

4976 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D3×D5C212yesmaximal
2C22×C4×D3×D5C211yesmaximal, characteristic
3C2×C4⋊C4×D15C211yesmaximal, characteristic, complemented
4C2×C5×D3×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
6C2×#91437C211yesmaximal, characteristic, complemented
7C2×D3×C4⋊Dic5C211yesmaximal, characteristic, complemented
8C2×D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
9C2×#91404C212yesmaximal, complemented
10C2×D3×#683C212yesmaximal, complemented
11C2×D5×Dic3⋊C4C212yesmaximal, complemented
12D3×D5×C4⋊C4C2116yesmaximal, direct product factor
13C22×D5×C4⋊C4—31nomaximal, Hall
14C23×D3×D5C2211yescharacteristic
15C22×C4×D15C2212yes—
16C22×C4×D15C2211yescharacteristic
17C22×C4×C5×D3C2212yes—
18C22×C4×C5×D3C2211yescharacteristic
19C22×C3×C4×D5C2212yes—
20C22×C3×C4×D5C2211yescharacteristic
21C22×#1200C2212yes—
22C22×#1200C2211yescharacteristic
23C22×D3×Dic5C2212yes—
24C22×D3×Dic5C2211yescharacteristic
25C22×D5×Dic3C2212yes—
26C22×D5×Dic3C2211yescharacteristic
27C2×C4×D3×D5—216no—
28C2×C4×D3×D5C4116yescomplemented
29C2×C4×D3×D5C22116yes—
30C2×C4×D3×D5C2218yes—
31C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
32C2×C4⋊Dic15C2211yescharacteristic, complemented
33C2×#6712C2212yescomplemented
34C4⋊C4×D15C2218yescomplemented
35C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
36C2×C5×Dic3⋊C4C2212yescomplemented
37C5×D3×C4⋊C4C2218yescomplemented
38C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
39C2×C3×#683C2212yescomplemented
40C3×D5×C4⋊C4C2218yescomplemented
41C2×Dic3⋊Dic5C2212yescomplemented
42C2×#6669C2212yescomplemented
43C2×#6668C2212yescomplemented
44#91437C2218yescomplemented
45D3×C4⋊Dic5C2218yescomplemented
46D5×C4⋊Dic3C2218yescomplemented
47#91404C22116yescomplemented
48D3×#683C22116yescomplemented
49D5×Dic3⋊C4C22116yescomplemented
50C22×D3×C4⋊C4—51nomaximal, Hall
51C23×C4×D5—31no—
52C23×C4×D5—32no—
53C22×C5×C4⋊C4—31no—
54C22×C4⋊Dic5—31no—
55C22×#683—32no—
56C2×D5×C4⋊C4—31no—
57C2×D5×C4⋊C4—32no—
58C2×D5×C4⋊C4—316no—
59C2×D5×C4⋊C4—32no—
60C2×D5×C4⋊C4—31no—
61C2×D5×C4⋊C4—31no—
62C2×D5×C4⋊C4D311yescharacteristic, direct product factor
63C23×D15C2311yescharacteristic
64C23×C5×D3C2311yescharacteristic
65C23×C3×D5C2311yescharacteristic
66C22×D3×D5C2×C418yes—
67C22×D3×D5D418yes—
68C22×D3×D5Q818yes—
69C22×D3×D5C2314yes—
70C22×C3×C4×C5C2312yes—
71C22×C3×C4×C5C2311yescharacteristic
72C22×Dic15C2312yes—
73C22×Dic15C2311yescharacteristic
74C2×C4×D15—28no—
75C2×C4×D15C2×C418yescomplemented
76C2×C4×D15C2318yes—
77C2×C4×D15C2314yes—
78C22×C5×Dic3C2312yes—
79C22×C5×Dic3C2311yescharacteristic
80C2×C4×C5×D3—28no—
81C2×C4×C5×D3C2×C418yescomplemented
82C2×C4×C5×D3C2318yes—
83C2×C4×C5×D3C2314yes—
84C22×C3×Dic5C2312yes—
85C22×C3×Dic5C2311yescharacteristic
86C2×C3×C4×D5—28no—
87C2×C3×C4×D5C2×C418yescomplemented
88C2×C3×C4×D5C2318yes—
89C2×C3×C4×D5C2314yes—
90C2×#1200—28no—
91C2×#1200C2×C418yescomplemented
92C2×#1200C2318yes—
93C2×#1200C2314yes—
94C2×D3×Dic5—28no—
95C2×D3×Dic5C2×C418yescomplemented
96C2×D3×Dic5C2318yes—
97C2×D3×Dic5C2314yes—
98C2×D5×Dic3—28no—
99C2×D5×Dic3C2×C418yescomplemented
100C2×D5×Dic3C2318yes—
101C2×D5×Dic3C2314yes—
102C4×D3×D5—264no—
103C4×D3×D5C2×C4164yescomplemented
104C3×C5×C4⋊C4C2314yescomplemented
105C4⋊Dic15C2314yescomplemented
106#6712C2318yescomplemented
107C5×C4⋊Dic3C2314yescomplemented
108C5×Dic3⋊C4C2318yescomplemented
109C3×C4⋊Dic5C2314yescomplemented
110C3×#683C2318yescomplemented
111Dic3⋊Dic5C2318yescomplemented
112#6669C2318yescomplemented
113#6668C2318yescomplemented
114C23×C4×D3—51no—
115C23×C4×D3—52no—
116C22×C3×C4⋊C4—51no—
117C22×C4⋊Dic3—51no—
118C22×Dic3⋊C4—52no—
119C2×D3×C4⋊C4—52no—
120C2×D3×C4⋊C4—51no—
121C2×D3×C4⋊C4—51no—
122C2×D3×C4⋊C4—51no—
123C2×D3×C4⋊C4—52no—
124C2×D3×C4⋊C4—516no—
125C2×D3×C4⋊C4D511yescharacteristic, direct product factor
126C24×D5—31no—
127C23×C4×C5—31no—
128C23×C4×C5—32no—
129C23×Dic5—31no—
130C23×Dic5—32no—
131C22×C4×D5—31no—
132C22×C4×D5—31no—
133C22×C4×D5—31no—
134C22×C4×D5—316no—
135C22×C4×D5—38no—
136C22×C4×D5—32no—
137C22×C4×D5—32no—
138C22×C4×D5—32no—
139C22×C4×D5—316no—
140C22×C4×D5—616no—
141C22×C4×D5C2×D312yes—
142C22×C4×D5C2×D311yescharacteristic
143C2×C5×C4⋊C4—32no—
144C2×C5×C4⋊C4—31no—
145C2×C5×C4⋊C4—38no—
146C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
147C2×C4⋊Dic5—31no—
148C2×C4⋊Dic5—32no—
149C2×C4⋊Dic5—38no—
150C2×C4⋊Dic5C2×D311yescharacteristic, complemented
151C2×#683—32no—
152C2×#683—32no—
153C2×#683—32no—
154C2×#683—316no—
155C2×#683C2×D312yescomplemented
156D5×C4⋊C4—316no—
157D5×C4⋊C4—38no—
158D5×C4⋊C4—38no—
159D5×C4⋊C4—38no—
160D5×C4⋊C4—316no—
161D5×C4⋊C4C2×D318yesdirect product factor
162C23×C4⋊C4—151noSylow
163C23×C3×C5C2411yescharacteristic
164C22×D15C22×C414yes—
165C22×D15C2×D414yes—
166C22×D15C2×Q814yes—
167C22×D15C2412yes—
168C22×C5×D3C22×C414yes—
169C22×C5×D3C2×D414yes—
170C22×C5×D3C2×Q814yes—
171C22×C5×D3C2412yes—
172C22×C3×D5C22×C414yes—
173C22×C3×D5C2×D414yes—
174C22×C3×D5C2×Q814yes—
175C22×C3×D5C2412yes—
176C2×D3×D5C4⋊C4164yesdirect product factor
177C2×D3×D5C22×C4116yes—
178C2×D3×D5C2×D4116yes—
179C2×D3×D5C2×Q8116yes—
180C2×C3×C4×C5—24no—
181C2×C3×C4×C5C22×C414yescomplemented
182C2×C3×C4×C5C2414yes—
183C2×C3×C4×C5C2412yes—
184C2×Dic15—24no—
185C2×Dic15C22×C414yescomplemented
186C2×Dic15C2414yes—
187C2×Dic15C2412yes—
188C4×D15—216no—
189C4×D15C22×C4116yescomplemented
190C2×C5×Dic3—24no—
191C2×C5×Dic3C22×C414yescomplemented
192C2×C5×Dic3C2414yes—
193C2×C5×Dic3C2412yes—
194C4×C5×D3—216no—
195C4×C5×D3C22×C4116yescomplemented
196C2×C3×Dic5—24no—
197C2×C3×Dic5C22×C414yescomplemented
198C2×C3×Dic5C2414yes—
199C2×C3×Dic5C2412yes—
200C3×C4×D5—216no—
201C3×C4×D5C22×C4116yescomplemented
202#1200—216no—
203#1200C22×C4116yescomplemented
204D3×Dic5—216no—
205D3×Dic5C22×C4116yescomplemented
206D5×Dic3—216no—
207D5×Dic3C22×C4116yescomplemented
208C24×D3—51no—
209C23×C3×C4—51no—
210C23×C3×C4—52no—
211C23×Dic3—51no—
212C23×Dic3—52no—
213C22×C4×D3—51no—
214C22×C4×D3—51no—
215C22×C4×D3—51no—
216C22×C4×D3—516no—
217C22×C4×D3—58no—
218C22×C4×D3—52no—
219C22×C4×D3—52no—
220C22×C4×D3—52no—
221C22×C4×D3—516no—
222C22×C4×D3—1016no—
223C22×C4×D3C2×D512yes—
224C22×C4×D3C2×D511yescharacteristic
225C2×C3×C4⋊C4—52no—
226C2×C3×C4⋊C4—51no—
227C2×C3×C4⋊C4—58no—
228C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
229C2×C4⋊Dic3—51no—
230C2×C4⋊Dic3—52no—
231C2×C4⋊Dic3—58no—
232C2×C4⋊Dic3C2×D511yescharacteristic, complemented
233C2×Dic3⋊C4—52no—
234C2×Dic3⋊C4—52no—
235C2×Dic3⋊C4—52no—
236C2×Dic3⋊C4—516no—
237C2×Dic3⋊C4C2×D512yescomplemented
238D3×C4⋊C4—516no—
239D3×C4⋊C4—58no—
240D3×C4⋊C4—58no—
241D3×C4⋊C4—58no—
242D3×C4⋊C4—516no—
243D3×C4⋊C4C2×D518yesdirect product factor
244C24×C5—31no—
245C23×D5—31no—
246C23×D5—38no—
247C23×D5—38no—
248C23×D5—38no—
249C23×D5—34no—
250C23×D5C22×D311yescharacteristic
251C22×C4×C5—31no—
252C22×C4×C5—38no—
253C22×C4×C5—34no—
254C22×C4×C5—32no—
255C22×C4×C5—38no—
256C22×C4×C5—68no—
257C22×C4×C5C22×D312yes—
258C22×C4×C5C22×D311yescharacteristic
259C22×Dic5—31no—
260C22×Dic5—38no—
261C22×Dic5—34no—
262C22×Dic5—32no—
263C22×Dic5—38no—
264C22×Dic5—68no—
265C22×Dic5C22×D312yes—
266C22×Dic5C22×D311yescharacteristic
267C2×C4×D5—28no—
268C2×C4×D5—38no—
269C2×C4×D5—34no—
270C2×C4×D5—38no—
271C2×C4×D5—34no—
272C2×C4×D5—38no—
273C2×C4×D5—34no—
274C2×C4×D5—364no—
275C2×C4×D5—38no—
276C2×C4×D5—38no—
277C2×C4×D5—38no—
278C2×C4×D5—664no—
279C2×C4×D5—68no—
280C2×C4×D5—68no—
281C2×C4×D5—68no—
282C2×C4×D5C4×D318yescomplemented
283C2×C4×D5C22×D318yes—
284C2×C4×D5C22×D314yes—
285C5×C4⋊C4—38no—
286C5×C4⋊C4—34no—
287C5×C4⋊C4C22×D314yescomplemented
288C4⋊Dic5—34no—
289C4⋊Dic5—38no—
290C4⋊Dic5C22×D314yescomplemented
291#683—38no—
292#683—38no—
293#683—38no—
294#683C22×D318yescomplemented
295C24×C4—151no—
296C24×C4—152no—
297C22×C4⋊C4—31no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4—152no—
300C22×C4⋊C4—151no—
301C22×C4⋊C4—1516no—
302C22×C4⋊C4—152no—
303C22×C4⋊C4—151no—
304C22×C4⋊C4—152no—
305C22×C4⋊C4—151no—
306C22×C4⋊C4—151no—
307C22×C3×C5C23×C412yes—
308C22×C3×C5C22×D412yes—
309C22×C3×C5C22×Q812yes—
310C22×C3×C5C2511yescharacteristic
311C2×D15C2×C4⋊C4116yescomplemented
312C2×D15C23×C414yes—
313C2×D15C22×D414yes—
314C2×D15C22×Q814yes—
315C2×C5×D3C2×C4⋊C4116yescomplemented
316C2×C5×D3C23×C414yes—
317C2×C5×D3C22×D414yes—
318C2×C5×D3C22×Q814yes—
319C2×C3×D5C2×C4⋊C4116yescomplemented
320C2×C3×D5C23×C414yes—
321C2×C3×D5C22×D414yes—
322C2×C3×D5C22×Q814yes—
323D3×D5C2×C4⋊C4164yesdirect product factor
324C3×C4×C5—24no—
325C3×C4×C5C23×C414yescomplemented
326Dic15—24no—
327Dic15C23×C414yescomplemented
328C3×Dic5—24no—
329C3×Dic5C23×C414yescomplemented
330C5×Dic3—24no—
331C5×Dic3C23×C414yescomplemented
332C24×C3—51no—
333C23×D3—51no—
334C23×D3—58no—
335C23×D3—58no—
336C23×D3—58no—
337C23×D3—54no—
338C23×D3C22×D511yescharacteristic
339C22×C3×C4—51no—
340C22×C3×C4—58no—
341C22×C3×C4—54no—
342C22×C3×C4—52no—
343C22×C3×C4—58no—
344C22×C3×C4—108no—
345C22×C3×C4C22×D512yes—
346C22×C3×C4C22×D511yescharacteristic
347C22×Dic3—51no—
348C22×Dic3—58no—
349C22×Dic3—54no—
350C22×Dic3—52no—
351C22×Dic3—58no—
352C22×Dic3—108no—
353C22×Dic3C22×D512yes—
354C22×Dic3C22×D511yescharacteristic
355C2×C4×D3—28no—
356C2×C4×D3—58no—
357C2×C4×D3—54no—
358C2×C4×D3—58no—
359C2×C4×D3—54no—
360C2×C4×D3—58no—
361C2×C4×D3—54no—
362C2×C4×D3—564no—
363C2×C4×D3—58no—
364C2×C4×D3—58no—
365C2×C4×D3—58no—
366C2×C4×D3—1064no—
367C2×C4×D3—108no—
368C2×C4×D3—108no—
369C2×C4×D3—108no—
370C2×C4×D3C4×D518yescomplemented
371C2×C4×D3C22×D518yes—
372C2×C4×D3C22×D514yes—
373C3×C4⋊C4—58no—
374C3×C4⋊C4—54no—
375C3×C4⋊C4C22×D514yescomplemented
376C4⋊Dic3—54no—
377C4⋊Dic3—58no—
378C4⋊Dic3C22×D514yescomplemented
379Dic3⋊C4—58no—
380Dic3⋊C4—58no—
381Dic3⋊C4—58no—
382Dic3⋊C4C22×D518yescomplemented
383C23×C5—34no—
384C23×C5—34no—
385C23×C5—34no—
386C23×C5—32no—
387C23×C5C23×D311yescharacteristic
388C22×D5—34no—
389C22×D5—34no—
390C22×D5—34no—
391C22×D5—32no—
392C22×D5—364no—
393C22×D5—316no—
394C22×D5—316no—
395C22×D5—316no—
396C22×D5C2×C4×D314yes—
397C22×D5D3×D414yes—
398C22×D5D3×Q814yes—
399C22×D5C23×D312yes—
400C2×C4×C5—24no—
401C2×C4×C5—34no—
402C2×C4×C5—32no—
403C2×C4×C5—316no—
404C2×C4×C5—34no—
405C2×C4×C5—616no—
406C2×C4×C5—64no—
407C2×C4×C5C2×C4×D314yescomplemented
408C2×C4×C5C23×D314yes—
409C2×C4×C5C23×D312yes—
410C2×Dic5—24no—
411C2×Dic5—34no—
412C2×Dic5—32no—
413C2×Dic5—316no—
414C2×Dic5—34no—
415C2×Dic5—616no—
416C2×Dic5—64no—
417C2×Dic5C2×C4×D314yescomplemented
418C2×Dic5C23×D314yes—
419C2×Dic5C23×D312yes—
420C4×D5—216no—
421C4×D5—316no—
422C4×D5—316no—
423C4×D5—316no—
424C4×D5—616no—
425C4×D5—616no—
426C4×D5—616no—
427C4×D5C2×C4×D3116yescomplemented
428C25—151no—
429C23×C4—31no—
430C23×C4—32no—
431C23×C4—51no—
432C23×C4—52no—
433C23×C4—151no—
434C23×C4—158no—
435C23×C4—1516no—
436C23×C4—152no—
437C23×C4—1516no—
438C23×C4—151no—
439C23×C4—152no—
440C23×C4—151no—
441C23×C4—152no—
442C23×C4—151no—
443C23×C4—152no—
444C23×C4—3016no—
445C2×C4⋊C4—32no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—38no—
448C2×C4⋊C4—52no—
449C2×C4⋊C4—51no—
450C2×C4⋊C4—58no—
451C2×C4⋊C4—1516no—
452C2×C4⋊C4—158no—
453C2×C4⋊C4—1516no—
454C2×C4⋊C4—158no—
455C2×C4⋊C4—1516no—
456C2×C4⋊C4—158no—
457C2×C4⋊C4—152no—
458C2×C4⋊C4—152no—
459C2×C4⋊C4—152no—
460C2×C4⋊C4—152no—
461C2×C4⋊C4—151no—
462C2×C4⋊C4—158no—
463C2×C4⋊C4D3×D511yescharacteristic, direct product factor
464C2×C3×C5C22×C4⋊C414yescomplemented
465C2×C3×C5C24×C411yescharacteristic
466C2×C3×C5C23×D411yescharacteristic
467C2×C3×C5C23×Q811yescharacteristic
468D15C22×C4⋊C418yescomplemented
469C3×D5C22×C4⋊C418yescomplemented
470C5×D3C22×C4⋊C418yescomplemented
471C23×C3—54no—
472C23×C3—54no—
473C23×C3—54no—
474C23×C3—52no—
475C23×C3C23×D511yescharacteristic
476C22×D3—54no—
477C22×D3—54no—
478C22×D3—54no—
479C22×D3—52no—
480C22×D3—516no—
481C22×D3—516no—
482C22×D3—516no—
483C22×D3—564no—
484C22×D3C2×C4×D514yes—
485C22×D3D4×D514yes—
486C22×D3Q8×D514yes—
487C22×D3C23×D512yes—
488C2×C3×C4—24no—
489C2×C3×C4—54no—
490C2×C3×C4—52no—
491C2×C3×C4—516no—
492C2×C3×C4—54no—
493C2×C3×C4—1016no—
494C2×C3×C4—104no—
495C2×C3×C4C2×C4×D514yescomplemented
496C2×C3×C4C23×D514yes—
497C2×C3×C4C23×D512yes—
498C2×Dic3—24no—
499C2×Dic3—54no—
500C2×Dic3—52no—
501C2×Dic3—516no—
502C2×Dic3—54no—
503C2×Dic3—1016no—
504C2×Dic3—104no—
505C2×Dic3C2×C4×D514yescomplemented
506C2×Dic3C23×D514yes—
507C2×Dic3C23×D512yes—
508C4×D3—216no—
509C4×D3—516no—
510C4×D3—516no—
511C4×D3—516no—
512C4×D3—1016no—
513C4×D3—1016no—
514C4×D3—1016no—
515C4×D3C2×C4×D5116yescomplemented
516C22×C5—34no—
517C22×C5—34no—
518C22×C5—34no—
519C22×C5—316no—
520C22×C5C22×C4×D312yes—
521C22×C5C2×D3×D412yes—
522C22×C5C2×D3×Q812yes—
523C22×C5C24×D311yescharacteristic
524C2×D5—34no—
525C2×D5—34no—
526C2×D5—34no—
527C2×D5—316no—
528C2×D5—364no—
529C2×D5D3×C4⋊C4116yesdirect product factor
530C2×D5C22×C4×D314yes—
531C2×D5C2×D3×D414yes—
532C2×D5C2×D3×Q814yes—
533C4×C5—24no—
534C4×C5—34no—
535C4×C5—64no—
536C4×C5C22×C4×D314yescomplemented
537Dic5—24no—
538Dic5—34no—
539Dic5—64no—
540Dic5C22×C4×D314yescomplemented
541C24—31no—
542C24—51no—
543C24—154no—
544C24—158no—
545C24—158no—
546C24—158no—
547C24—151no—
548C22×C4—31no—
549C22×C4—38no—
550C22×C4—34no—
551C22×C4—32no—
552C22×C4—38no—
553C22×C4—51no—
554C22×C4—58no—
555C22×C4—54no—
556C22×C4—52no—
557C22×C4—58no—
558C22×C4—68no—
559C22×C4—108no—
560C22×C4—154no—
561C22×C4—158no—
562C22×C4—1564no—
563C22×C4—158no—
564C22×C4—154no—
565C22×C4—158no—
566C22×C4—158no—
567C22×C4—154no—
568C22×C4—158no—
569C22×C4—158no—
570C22×C4—151no—
571C22×C4—158no—
572C22×C4—154no—
573C22×C4—152no—
574C22×C4—158no—
575C22×C4—308no—
576C22×C4—3064no—
577C22×C4—308no—
578C22×C4—308no—
579C22×C4—308no—
580C22×C4C2×D3×D512yes—
581C22×C4C2×D3×D511yescharacteristic
582C4⋊C4—38no—
583C4⋊C4—34no—
584C4⋊C4—58no—
585C4⋊C4—54no—
586C4⋊C4—158no—
587C4⋊C4—158no—
588C4⋊C4—158no—
589C4⋊C4—158no—
590C4⋊C4—154no—
591C4⋊C4C2×D3×D514yesdirect product factor
592C3×C5C23×C4⋊C411yescharacteristic, complemented, Hall
593C22×C3—516no—
594C22×C3—54no—
595C22×C3—54no—
596C22×C3—54no—
597C22×C3C22×C4×D512yes—
598C22×C3C2×D4×D512yes—
599C22×C3C2×Q8×D512yes—
600C22×C3C24×D511yescharacteristic
601C2×D3—516no—
602C2×D3—54no—
603C2×D3—54no—
604C2×D3—54no—
605C2×D3—564no—
606C2×D3D5×C4⋊C4116yesdirect product factor
607C2×D3C22×C4×D514yes—
608C2×D3C2×D4×D514yes—
609C2×D3C2×Q8×D514yes—
610C3×C4—24no—
611C3×C4—54no—
612C3×C4—104no—
613C3×C4C22×C4×D514yescomplemented
614Dic3—24no—
615Dic3—54no—
616Dic3—104no—
617Dic3C22×C4×D514yescomplemented
618C2×C5—38no—
619C2×C5C2×D3×C4⋊C414yescomplemented
620C2×C5C23×C4×D311yescharacteristic
621C2×C5C22×D3×D411yescharacteristic
622C2×C5C22×D3×Q811yescharacteristic
623D5—38no—
624D5C2×D3×C4⋊C418yesdirect product factor
625C23—34no—
626C23—34no—
627C23—34no—
628C23—32no—
629C23—54no—
630C23—54no—
631C23—54no—
632C23—52no—
633C23—1516no—
634C23—1516no—
635C23—1564no—
636C23—1516no—
637C23—154no—
638C23—154no—
639C23—154no—
640C23—152no—
641C23C22×D3×D511yescharacteristic
642C2×C4—24no—
643C2×C4—34no—
644C2×C4—32no—
645C2×C4—316no—
646C2×C4—34no—
647C2×C4—54no—
648C2×C4—52no—
649C2×C4—516no—
650C2×C4—54no—
651C2×C4—616no—
652C2×C4—64no—
653C2×C4—1016no—
654C2×C4—104no—
655C2×C4—1516no—
656C2×C4—1516no—
657C2×C4—1516no—
658C2×C4—154no—
659C2×C4—152no—
660C2×C4—1516no—
661C2×C4—154no—
662C2×C4—3016no—
663C2×C4—3016no—
664C2×C4—3016no—
665C2×C4—3016no—
666C2×C4—304no—
667C2×C4C4×D3×D514yescomplemented
668C2×C4C22×D3×D514yes—
669C2×C4C22×D3×D512yes—
670C2×C3—58no—
671C2×C3C2×D5×C4⋊C414yescomplemented
672C2×C3C23×C4×D511yescharacteristic
673C2×C3C22×D4×D511yescharacteristic
674C2×C3C22×Q8×D511yescharacteristic
675D3—58no—
676D3C2×D5×C4⋊C418yesdirect product factor
677C5C22×D3×C4⋊C411yescharacteristic, complemented, Sylow
678C22—316no—
679C22—34no—
680C22—34no—
681C22—34no—
682C22—516no—
683C22—54no—
684C22—54no—
685C22—54no—
686C22—1564no—
687C22—1516no—
688C22—154no—
689C22—154no—
690C22—154no—
691C22C2×C4×D3×D512yes—
692C22D3×D4×D512yes—
693C22D3×Q8×D512yes—
694C22C23×D3×D511yescharacteristic
695C4—24no—
696C4—34no—
697C4—54no—
698C4—64no—
699C4—104no—
700C4—154no—
701C4—304no—
702C4C2×C4×D3×D514yescomplemented
703C3C22×D5×C4⋊C411yescharacteristic, complemented, Sylow
704C2—38no—
705C2—58no—
706C2—158no—
707C2D3×D5×C4⋊C414yesdirect product factor
708C2C22×C4×D3×D511yescharacteristic
709C2C2×D3×D4×D511yescharacteristic
710C2C2×D3×Q8×D511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC23×D3×D5C22
cosocleC22×C3×C5C25
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C23×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
3. C2×C4⋊C4×D15C2semidirect
4. C2×C5×D3×C4⋊C4C2semidirect
5. C2×C3×D5×C4⋊C4C2semidirect
6. C2×#91437C2semidirect
7. C2×D3×C4⋊Dic5C2semidirect
8. C2×D5×C4⋊Dic3C2semidirect
9. C2×#91404C2semidirect
10. C2×D3×#683C2semidirect
11. C2×D5×Dic3⋊C4C2semidirect
12. D3×D5×C4⋊C4C2direct (N × H)
28. C2×C4×D3×D5C4semidirect
31. C2×C3×C5×C4⋊C4C22semidirect
32. C2×C4⋊Dic15C22semidirect
33. C2×#6712C22semidirect
34. C4⋊C4×D15C22semidirect
35. C2×C5×C4⋊Dic3C22semidirect
36. C2×C5×Dic3⋊C4C22semidirect
37. C5×D3×C4⋊C4C22semidirect
38. C2×C3×C4⋊Dic5C22semidirect
39. C2×C3×#683C22semidirect
40. C3×D5×C4⋊C4C22semidirect
41. C2×Dic3⋊Dic5C22semidirect
42. C2×#6669C22semidirect
43. C2×#6668C22semidirect
44. #91437C22semidirect
45. D3×C4⋊Dic5C22semidirect
46. D5×C4⋊Dic3C22semidirect
47. #91404C22semidirect
48. D3×#683C22semidirect
49. D5×Dic3⋊C4C22semidirect
62. C2×D5×C4⋊C4D3direct (N × H)
75. C2×C4×D15C2×C4semidirect
81. C2×C4×C5×D3C2×C4semidirect
87. C2×C3×C4×D5C2×C4semidirect
91. C2×#1200C2×C4semidirect
95. C2×D3×Dic5C2×C4semidirect
99. C2×D5×Dic3C2×C4semidirect
103. C4×D3×D5C2×C4semidirect
104. C3×C5×C4⋊C4C23semidirect
105. C4⋊Dic15C23semidirect
106. #6712C23semidirect
107. C5×C4⋊Dic3C23semidirect
108. C5×Dic3⋊C4C23semidirect
109. C3×C4⋊Dic5C23semidirect
110. C3×#683C23semidirect
111. Dic3⋊Dic5C23semidirect
112. #6669C23semidirect
113. #6668C23semidirect
125. C2×D3×C4⋊C4D5direct (N × H)
146. C2×C5×C4⋊C4C2×D3semidirect
150. C2×C4⋊Dic5C2×D3semidirect
155. C2×#683C2×D3semidirect
161. D5×C4⋊C4C2×D3direct (N × H)
176. C2×D3×D5C4⋊C4direct (N × H)
181. C2×C3×C4×C5C22×C4semidirect
185. C2×Dic15C22×C4semidirect
189. C4×D15C22×C4semidirect
191. C2×C5×Dic3C22×C4semidirect
195. C4×C5×D3C22×C4semidirect
197. C2×C3×Dic5C22×C4semidirect
201. C3×C4×D5C22×C4semidirect
203. #1200C22×C4semidirect
205. D3×Dic5C22×C4semidirect
207. D5×Dic3C22×C4semidirect
228. C2×C3×C4⋊C4C2×D5semidirect
232. C2×C4⋊Dic3C2×D5semidirect
237. C2×Dic3⋊C4C2×D5semidirect
243. D3×C4⋊C4C2×D5direct (N × H)
282. C2×C4×D5C4×D3semidirect
287. C5×C4⋊C4C22×D3semidirect
290. C4⋊Dic5C22×D3semidirect
294. #683C22×D3semidirect
311. C2×D15C2×C4⋊C4semidirect
315. C2×C5×D3C2×C4⋊C4semidirect
319. C2×C3×D5C2×C4⋊C4semidirect
323. D3×D5C2×C4⋊C4direct (N × H)
325. C3×C4×C5C23×C4semidirect
327. Dic15C23×C4semidirect
329. C3×Dic5C23×C4semidirect
331. C5×Dic3C23×C4semidirect
370. C2×C4×D3C4×D5semidirect
375. C3×C4⋊C4C22×D5semidirect
378. C4⋊Dic3C22×D5semidirect
382. Dic3⋊C4C22×D5semidirect
407. C2×C4×C5C2×C4×D3semidirect
417. C2×Dic5C2×C4×D3semidirect
427. C4×D5C2×C4×D3semidirect
463. C2×C4⋊C4D3×D5direct (N × H)
464. C2×C3×C5C22×C4⋊C4semidirect
468. D15C22×C4⋊C4semidirect
469. C3×D5C22×C4⋊C4semidirect
470. C5×D3C22×C4⋊C4semidirect
495. C2×C3×C4C2×C4×D5semidirect
505. C2×Dic3C2×C4×D5semidirect
515. C4×D3C2×C4×D5semidirect
529. C2×D5D3×C4⋊C4direct (N × H)
536. C4×C5C22×C4×D3semidirect
540. Dic5C22×C4×D3semidirect
591. C4⋊C4C2×D3×D5direct (N × H)
592. C3×C5C23×C4⋊C4semidirect
606. C2×D3D5×C4⋊C4direct (N × H)
613. C3×C4C22×C4×D5semidirect
617. Dic3C22×C4×D5semidirect
619. C2×C5C2×D3×C4⋊C4semidirect
624. D5C2×D3×C4⋊C4direct (N × H)
667. C2×C4C4×D3×D5semidirect
671. C2×C3C2×D5×C4⋊C4semidirect
676. D3C2×D5×C4⋊C4direct (N × H)
677. C5C22×D3×C4⋊C4semidirect
702. C4C2×C4×D3×D5semidirect
703. C3C22×D5×C4⋊C4semidirect
707. C2D3×D5×C4⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D3×D52
C2×C4⋊C4×D152
C2×C5×D3×C4⋊C42
C2×C3×D5×C4⋊C42
C2×#914372
C2×D3×C4⋊Dic52
C2×D5×C4⋊Dic32
C2×#914042
C2×D3×#6832
C2×D5×Dic3⋊C42
D3×D5×C4⋊C42
C22×D5×C4⋊C43
C22×D3×C4⋊C45