Finite Group Databasebeta

← C4×#91473 #14319399

Subgroups — C4×#91473 #14319399

Order 1920.

2720 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D3×D5C211yesmaximal, characteristic
2C2×C42×D15C211yesmaximal, characteristic, complemented
3C2×#91473C212yesmaximal
4C2×C4×#1200C211yesmaximal, characteristic, complemented
5C4×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C3×C4×#685C211yesmaximal, characteristic, complemented
7#11748888C212yesmaximal, complemented
8#11748886C212yesmaximal, complemented
9#11748884C212yesmaximal, complemented
10C4×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
11C4×#6665C211yesmaximal, characteristic, complemented
12C4×D5×C22⋊C4—31nomaximal, Hall
13C23×D3×D5C2211yescharacteristic
14C22×C4×D15C2212yes—
15C22×C4×D15C2211yescharacteristic
16C22×C4×C5×D3C2211yescharacteristic
17C22×C3×C4×D5C2211yescharacteristic
18C22×#1200C2211yescharacteristic
19C22×#1200C2212yes—
20C22×D3×Dic5C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C2×C4×D3×D5—24no—
23C2×C4×D3×D5—24no—
24C2×C4×D3×D5C418yescomplemented
25C2×C3×C42×C5C2211yescharacteristic, complemented
26C2×C4×Dic15C2212yescomplemented
27C2×C4×Dic15C2211yescharacteristic, complemented
28C42×D15—24no—
29C2×C5×(C2×D3)⋊C4C2212yes—
30C2×C4×C5×Dic3C2211yescharacteristic, complemented
31C2×C3×#685C2212yes—
32C2×C3×C4×Dic5C2211yescharacteristic, complemented
33C2×(C2×D3)⋊Dic5C2212yes—
34C2×#6665C2212yes—
35C2×Dic3×Dic5C2212yescomplemented
36#91473C4116yesdirect product factor
37C4×#1200—24no—
38C5×C3⋊#95C2212yescomplemented
39C3×#3963C2212yescomplemented
40#90994C2212yescomplemented
41#90994C2212yescomplemented
42C4×D3×C22⋊C4—51nomaximal, Hall
43C23×C4×D5—31no—
44C2×D5×C22⋊C4—32no—
45C2×C42×D5—31no—
46C2×C42×D5—31no—
47C4×C5×C22⋊C4—31no—
48C4×C22⋊Dic5—31no—
49C22⋊C4×Dic5—32no—
50C4×#685—31no—
51C4×#685D311yescharacteristic, complemented
52#64955—32no—
53D5×#95—32no—
54C23×D15C2311yescharacteristic
55C23×C5×D3C2311yescharacteristic
56C23×C3×D5C2311yescharacteristic
57C22×D3×D5—22no—
58C22×D3×D5—22no—
59C22×D3×D5—24no—
60C22×D3×D5C2×C418yes—
61C22×D3×D5C2×C414yes—
62C22×C3×C4×C5C2312yes—
63C22×C3×C4×C5C2311yescharacteristic
64C22×Dic15C2312yes—
65C22×Dic15C2311yescharacteristic
66C2×C4×D15—24no—
67C2×C4×D15—24no—
68C2×C4×D15C2×C414yes—
69C2×C4×D15C2×C418yescomplemented
70C2×C4×D15D414yes—
71C2×C4×D15D414yes—
72C22×C5×Dic3C2311yescharacteristic
73C22×C5×Dic3C2312yes—
74C2×C4×C5×D3—22no—
75C2×C4×C5×D3—22no—
76C2×C4×C5×D3C2×C414yescomplemented
77C22×C3×Dic5C2311yescharacteristic
78C22×C3×Dic5C2312yes—
79C2×C3×C4×D5—22no—
80C2×C3×C4×D5—22no—
81C2×C3×C4×D5C2×C414yescomplemented
82C2×#1200—24no—
83C2×#1200—22no—
84C2×#1200—22no—
85C2×#1200—24no—
86C2×#1200C2×C414yes—
87C2×#1200C2×C418yescomplemented
88C2×D3×Dic5—22no—
89C2×D3×Dic5—22no—
90C2×D3×Dic5C2×C414yescomplemented
91C2×D5×Dic3—22no—
92C2×D5×Dic3—22no—
93C2×D5×Dic3C2×C414yescomplemented
94C4×D3×D5—232no—
95C3×C42×C5—22no—
96C4×Dic15—22no—
97C4×Dic15—24no—
98C5×(C2×D3)⋊C4C2×C418yescomplemented
99C4×C5×Dic3—22no—
100C3×#685C2×C418yescomplemented
101C3×C4×Dic5—22no—
102(C2×D3)⋊Dic5C2×C418yescomplemented
103#6665C2×C418yescomplemented
104Dic3×Dic5—24no—
105C23×C4×D3—51no—
106C2×D3×C22⋊C4—52no—
107C2×C42×D3—51no—
108C2×C42×D3—51no—
109C3×C4×C22⋊C4—51no—
110C4×#217—51no—
111Dic3×C22⋊C4—52no—
112C4×(C2×D3)⋊C4—51no—
113C4×(C2×D3)⋊C4D511yescharacteristic, complemented
114#4666—52no—
115D3×#95—52no—
116C24×D5—31no—
117C23×C4×C5—31no—
118C23×Dic5—31no—
119C22×C4×D5—31no—
120C22×C4×D5—31no—
121C22×C4×D5—32no—
122C22×C4×D5—32no—
123C22×C4×D5—31no—
124C22×C4×D5—38no—
125C22×C4×D5—64no—
126C22×C4×D5—64no—
127C22×C4×D5C2×D311yescharacteristic
128C2×C5×C22⋊C4—32no—
129C2×C42×C5—31no—
130C2×C42×C5C2×D311yescharacteristic, complemented
131C2×C22⋊Dic5—32no—
132C2×#685—32no—
133C2×#685C2×D312yes—
134C2×C4×Dic5—32no—
135C2×C4×Dic5—31no—
136C2×C4×Dic5—32no—
137C2×C4×Dic5C2×D311yescharacteristic, complemented
138D5×C22⋊C4—316no—
139C42×D5—64no—
140C42×D5—64no—
141C5×#95—32no—
142#3963—32no—
143#3963—32no—
144#3963C2×D312yescomplemented
145C2×C4×C22⋊C4—151noSylow
146C23×C3×C5C2411yescharacteristic
147C22×D15C22×C412yes—
148C22×D15C22×C414yes—
149C22×D15C2×D412yes—
150C22×D15C2×D412yes—
151C22×D15#4114yes—
152C22×C5×D3—21no—
153C22×C5×D3—21no—
154C22×C5×D3—22no—
155C22×C5×D3C22×C414yes—
156C22×C5×D3C22×C412yes—
157C22×C3×D5—21no—
158C22×C3×D5—21no—
159C22×C3×D5—22no—
160C22×C3×D5C22×C414yes—
161C22×C3×D5C22×C412yes—
162C2×D3×D5—28no—
163C2×D3×D5—28no—
164C2×D3×D5—216no—
165C2×D3×D5—216no—
166C2×D3×D5C42116yescomplemented
167C2×C3×C4×C5—22no—
168C2×C3×C4×C5—22no—
169C2×C3×C4×C5C22×C412yes—
170C2×C3×C4×C5C22×C414yescomplemented
171C2×C3×C4×C5C2×D412yes—
172C2×C3×C4×C5C2×D412yes—
173C2×Dic15—22no—
174C2×Dic15—22no—
175C2×Dic15C22×C412yes—
176C2×Dic15C22×C414yescomplemented
177C2×Dic15C2×D412yes—
178C2×Dic15C2×D412yes—
179C4×D15—216no—
180C4×D15C22⋊C4116yescomplemented
181C2×C5×Dic3—22no—
182C2×C5×Dic3—21no—
183C2×C5×Dic3—21no—
184C2×C5×Dic3—22no—
185C2×C5×Dic3C22×C412yes—
186C2×C5×Dic3C22×C414yescomplemented
187C4×C5×D3—28no—
188C2×C3×Dic5—22no—
189C2×C3×Dic5—21no—
190C2×C3×Dic5—21no—
191C2×C3×Dic5—22no—
192C2×C3×Dic5C22×C412yes—
193C2×C3×Dic5C22×C414yescomplemented
194C3×C4×D5—28no—
195#1200—28no—
196#1200—216no—
197D3×Dic5—28no—
198D5×Dic3—28no—
199C24×D3—51no—
200C23×C3×C4—51no—
201C23×Dic3—51no—
202C22×C4×D3—51no—
203C22×C4×D3—51no—
204C22×C4×D3—52no—
205C22×C4×D3—51no—
206C22×C4×D3—52no—
207C22×C4×D3—58no—
208C22×C4×D3—104no—
209C22×C4×D3—104no—
210C22×C4×D3C2×D511yescharacteristic
211C2×C3×C22⋊C4—52no—
212C2×C3×C42—51no—
213C2×C3×C42C2×D511yescharacteristic, complemented
214C2×#217—52no—
215C2×(C2×D3)⋊C4—52no—
216C2×(C2×D3)⋊C4C2×D512yes—
217C2×C4×Dic3—52no—
218C2×C4×Dic3—51no—
219C2×C4×Dic3—52no—
220C2×C4×Dic3C2×D511yescharacteristic, complemented
221D3×C22⋊C4—516no—
222C42×D3—104no—
223C42×D3—104no—
224C3×#95—52no—
225C3⋊#95—52no—
226C3⋊#95—52no—
227C3⋊#95C2×D512yescomplemented
228C24×C5—31no—
229C23×D5—31no—
230C23×D5—34no—
231C23×D5—38no—
232C23×D5—62no—
233C23×D5—62no—
234C23×D5—64no—
235C23×D5C22×D311yescharacteristic
236C22×C4×C5—32no—
237C22×C4×C5—31no—
238C22×C4×C5—34no—
239C22×C4×C5—62no—
240C22×C4×C5—62no—
241C22×C4×C5C22×D312yes—
242C22×C4×C5C22×D311yescharacteristic
243C22×Dic5—31no—
244C22×Dic5—32no—
245C22×Dic5—34no—
246C22×Dic5—62no—
247C22×Dic5—62no—
248C22×Dic5C22×D311yescharacteristic
249C22×Dic5C22×D312yes—
250C2×C4×D5—22no—
251C2×C4×D5—22no—
252C2×C4×D5—34no—
253C2×C4×D5—34no—
254C2×C4×D5—34no—
255C2×C4×D5—34no—
256C2×C4×D5—38no—
257C2×C4×D5—34no—
258C2×C4×D5—38no—
259C2×C4×D5—632no—
260C2×C4×D5—62no—
261C2×C4×D5—62no—
262C2×C4×D5—64no—
263C2×C4×D5—64no—
264C2×C4×D5—62no—
265C2×C4×D5—62no—
266C2×C4×D5—64no—
267C2×C4×D5—64no—
268C2×C4×D5C4×D314yescomplemented
269C5×C22⋊C4—38no—
270C42×C5—22no—
271C42×C5—62no—
272C22⋊Dic5—38no—
273#685—38no—
274#685C4×D318yescomplemented
275C4×Dic5—22no—
276C4×Dic5—64no—
277C4×Dic5—64no—
278C4×Dic5—62no—
279C24×C4—151no—
280C22×C22⋊C4—152no—
281C22×C42—151no—
282C22×C42—151no—
283C4×C22⋊C4—31no—
284C4×C22⋊C4—51no—
285C4×C22⋊C4—152no—
286C4×C22⋊C4—152no—
287C4×C22⋊C4—151no—
288C4×C22⋊C4—151no—
289C2×#95—152no—
290C22×C3×C5C23×C411yescharacteristic
291C22×C3×C5C23×C412yes—
292C22×C3×C5C22×D411yescharacteristic
293C22×C3×C5C22×D411yescharacteristic
294C22×C3×C5C2×#4112yes—
295C2×D15C2×C4214yes—
296C2×D15C2×C22⋊C414yes—
297C2×D15#11714yes—
298C2×D15C4×D418yes—
299C2×D15C4×D418yes—
300C2×C5×D3—22no—
301C2×C5×D3—22no—
302C2×C5×D3—24no—
303C2×C5×D3—24no—
304C2×C5×D3C2×C4214yescomplemented
305C2×C3×D5—22no—
306C2×C3×D5—22no—
307C2×C3×D5—24no—
308C2×C3×D5—24no—
309C2×C3×D5C2×C4214yescomplemented
310D3×D5—232no—
311C3×C4×C5—24no—
312C3×C4×C5C2×C22⋊C414yescomplemented
313Dic15—24no—
314Dic15C2×C22⋊C414yescomplemented
315C3×Dic5—22no—
316C3×Dic5—24no—
317C5×Dic3—22no—
318C5×Dic3—24no—
319C24×C3—51no—
320C23×D3—51no—
321C23×D3—58no—
322C23×D3—54no—
323C23×D3—102no—
324C23×D3—102no—
325C23×D3—104no—
326C23×D3C22×D511yescharacteristic
327C22×C3×C4—51no—
328C22×C3×C4—52no—
329C22×C3×C4—54no—
330C22×C3×C4—102no—
331C22×C3×C4—102no—
332C22×C3×C4C22×D512yes—
333C22×C3×C4C22×D511yescharacteristic
334C22×Dic3—51no—
335C22×Dic3—52no—
336C22×Dic3—54no—
337C22×Dic3—102no—
338C22×Dic3—102no—
339C22×Dic3C22×D511yescharacteristic
340C22×Dic3C22×D512yes—
341C2×C4×D3—22no—
342C2×C4×D3—22no—
343C2×C4×D3—54no—
344C2×C4×D3—54no—
345C2×C4×D3—54no—
346C2×C4×D3—54no—
347C2×C4×D3—58no—
348C2×C4×D3—54no—
349C2×C4×D3—58no—
350C2×C4×D3—1032no—
351C2×C4×D3—104no—
352C2×C4×D3—104no—
353C2×C4×D3—102no—
354C2×C4×D3—102no—
355C2×C4×D3—102no—
356C2×C4×D3—102no—
357C2×C4×D3—104no—
358C2×C4×D3—104no—
359C2×C4×D3C4×D514yescomplemented
360C3×C22⋊C4—58no—
361C3×C42—22no—
362C3×C42—102no—
363#217—58no—
364(C2×D3)⋊C4—58no—
365(C2×D3)⋊C4C4×D518yescomplemented
366C4×Dic3—22no—
367C4×Dic3—104no—
368C4×Dic3—104no—
369C4×Dic3—102no—
370C23×C5—34no—
371C23×C5—32no—
372C23×C5—61no—
373C23×C5—61no—
374C23×C5—62no—
375C23×C5C23×D311yescharacteristic
376C22×D5—21no—
377C22×D5—21no—
378C22×D5—22no—
379C22×D5—32no—
380C22×D5—34no—
381C22×D5—32no—
382C22×D5—32no—
383C22×D5—34no—
384C22×D5—316no—
385C22×D5—68no—
386C22×D5—68no—
387C22×D5—616no—
388C22×D5—616no—
389C22×D5C2×C4×D314yes—
390C22×D5C2×C4×D312yes—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—34no—
394C2×C4×C5—32no—
395C2×C4×C5—62no—
396C2×C4×C5—61no—
397C2×C4×C5—61no—
398C2×C4×C5—62no—
399C2×C4×C5—68no—
400C2×C4×C5C2×C4×D312yes—
401C2×C4×C5C2×C4×D314yescomplemented
402C2×C4×C5D3×D412yes—
403C2×C4×C5D3×D412yes—
404C2×Dic5—22no—
405C2×Dic5—21no—
406C2×Dic5—21no—
407C2×Dic5—22no—
408C2×Dic5—32no—
409C2×Dic5—32no—
410C2×Dic5—32no—
411C2×Dic5—34no—
412C2×Dic5—68no—
413C2×Dic5—62no—
414C2×Dic5—62no—
415C2×Dic5C2×C4×D312yes—
416C2×Dic5C2×C4×D314yescomplemented
417C4×D5—28no—
418C4×D5—316no—
419C4×D5—616no—
420C4×D5—68no—
421C4×D5—68no—
422C4×D5—616no—
423C25—151no—
424C23×C4—31no—
425C23×C4—51no—
426C23×C4—152no—
427C23×C4—151no—
428C23×C4—158no—
429C23×C4—151no—
430C23×C4—151no—
431C23×C4—151no—
432C23×C4—152no—
433C23×C4—304no—
434C23×C4—304no—
435C2×C22⋊C4—32no—
436C2×C22⋊C4—52no—
437C2×C22⋊C4—1516no—
438C2×C22⋊C4—152no—
439C2×C22⋊C4—152no—
440C2×C42—31no—
441C2×C42—51no—
442C2×C42—152no—
443C2×C42—152no—
444C2×C42—151no—
445C2×C42—304no—
446C2×C42—304no—
447C2×C42D3×D511yescharacteristic, complemented
448#95—32no—
449#95—52no—
450#95—152no—
451#95—152no—
452C2×C3×C5C22×C4211yescharacteristic
453C2×C3×C5C22×C22⋊C411yescharacteristic
454C2×C3×C5C2×#11711yescharacteristic
455C2×C3×C5C2×C4×D412yes—
456C2×C3×C5C2×C4×D412yes—
457D15C4×C22⋊C418yescomplemented
458C3×D5—24no—
459C5×D3—24no—
460C23×C3—54no—
461C23×C3—52no—
462C23×C3—101no—
463C23×C3—101no—
464C23×C3—102no—
465C23×C3C23×D511yescharacteristic
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—22no—
469C22×D3—52no—
470C22×D3—54no—
471C22×D3—52no—
472C22×D3—52no—
473C22×D3—54no—
474C22×D3—516no—
475C22×D3—108no—
476C22×D3—108no—
477C22×D3—1016no—
478C22×D3—1016no—
479C22×D3C2×C4×D514yes—
480C22×D3C2×C4×D512yes—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—52no—
484C2×C3×C4—54no—
485C2×C3×C4—102no—
486C2×C3×C4—101no—
487C2×C3×C4—101no—
488C2×C3×C4—102no—
489C2×C3×C4—108no—
490C2×C3×C4C2×C4×D512yes—
491C2×C3×C4C2×C4×D514yescomplemented
492C2×C3×C4D4×D512yes—
493C2×C3×C4D4×D512yes—
494C2×Dic3—22no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—22no—
498C2×Dic3—52no—
499C2×Dic3—52no—
500C2×Dic3—52no—
501C2×Dic3—54no—
502C2×Dic3—108no—
503C2×Dic3—102no—
504C2×Dic3—102no—
505C2×Dic3C2×C4×D512yes—
506C2×Dic3C2×C4×D514yescomplemented
507C4×D3—28no—
508C4×D3—516no—
509C4×D3—1016no—
510C4×D3—108no—
511C4×D3—108no—
512C4×D3—1016no—
513C22×C5—34no—
514C22×C5—62no—
515C22×C5—62no—
516C22×C5—64no—
517C22×C5—64no—
518C22×C5C22×C4×D311yescharacteristic
519C22×C5C22×C4×D312yes—
520C22×C5C2×D3×D411yescharacteristic
521C22×C5C2×D3×D411yescharacteristic
522C22×C5D3×#4112yes—
523C2×D5—22no—
524C2×D5—22no—
525C2×D5—24no—
526C2×D5—24no—
527C2×D5—34no—
528C2×D5—34no—
529C2×D5—34no—
530C2×D5—38no—
531C2×D5—38no—
532C2×D5—632no—
533C2×D5C42×D314yescomplemented
534C4×C5—24no—
535C4×C5—62no—
536C4×C5—64no—
537C4×C5D3×C22⋊C414yescomplemented
538Dic5—22no—
539Dic5—24no—
540Dic5—34no—
541Dic5—64no—
542C24—31no—
543C24—51no—
544C24—158no—
545C24—154no—
546C24—151no—
547C24—302no—
548C24—302no—
549C24—304no—
550C22×C4—31no—
551C22×C4—32no—
552C22×C4—34no—
553C22×C4—51no—
554C22×C4—52no—
555C22×C4—54no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—102no—
559C22×C4—102no—
560C22×C4—158no—
561C22×C4—154no—
562C22×C4—154no—
563C22×C4—154no—
564C22×C4—151no—
565C22×C4—154no—
566C22×C4—154no—
567C22×C4—154no—
568C22×C4—152no—
569C22×C4—158no—
570C22×C4—304no—
571C22×C4—304no—
572C22×C4—3032no—
573C22×C4—304no—
574C22×C4—302no—
575C22×C4—302no—
576C22×C4—304no—
577C22×C4—302no—
578C22×C4—302no—
579C22×C4—302no—
580C22×C4—302no—
581C22×C4C2×D3×D512yes—
582C22×C4C2×D3×D511yescharacteristic
583C22⋊C4—38no—
584C22⋊C4—58no—
585C22⋊C4—158no—
586C22⋊C4—158no—
587C42—22no—
588C42—62no—
589C42—102no—
590C42—304no—
591C42—304no—
592C42—302no—
593C3×C5C2×C4×C22⋊C411yescharacteristic, complemented, Hall
594C22×C3—54no—
595C22×C3—102no—
596C22×C3—102no—
597C22×C3—104no—
598C22×C3—104no—
599C22×C3C22×C4×D511yescharacteristic
600C22×C3C22×C4×D512yes—
601C22×C3C2×D4×D511yescharacteristic
602C22×C3C2×D4×D511yescharacteristic
603C22×C3D5×#4112yes—
604C2×D3—22no—
605C2×D3—22no—
606C2×D3—24no—
607C2×D3—24no—
608C2×D3—54no—
609C2×D3—54no—
610C2×D3—54no—
611C2×D3—58no—
612C2×D3—58no—
613C2×D3—1032no—
614C2×D3C42×D514yescomplemented
615C3×C4—24no—
616C3×C4—102no—
617C3×C4—104no—
618C3×C4D5×C22⋊C414yescomplemented
619Dic3—22no—
620Dic3—24no—
621Dic3—54no—
622Dic3—104no—
623C2×C5—64no—
624C2×C5C2×C42×D311yescharacteristic
625C2×C5C2×D3×C22⋊C411yescharacteristic
626C2×C5D3×#11711yescharacteristic
627C2×C5C4×D3×D412yes—
628C2×C5C4×D3×D412yes—
629D5—24no—
630D5—38no—
631C23—34no—
632C23—32no—
633C23—54no—
634C23—52no—
635C23—61no—
636C23—62no—
637C23—61no—
638C23—101no—
639C23—102no—
640C23—101no—
641C23—1516no—
642C23—152no—
643C23—154no—
644C23—152no—
645C23—154no—
646C23—152no—
647C23—308no—
648C23—308no—
649C23—3016no—
650C23—3016no—
651C23C22×D3×D511yescharacteristic
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—34no—
655C2×C4—32no—
656C2×C4—54no—
657C2×C4—52no—
658C2×C4—62no—
659C2×C4—61no—
660C2×C4—62no—
661C2×C4—61no—
662C2×C4—68no—
663C2×C4—102no—
664C2×C4—101no—
665C2×C4—102no—
666C2×C4—101no—
667C2×C4—108no—
668C2×C4—152no—
669C2×C4—152no—
670C2×C4—152no—
671C2×C4—1516no—
672C2×C4—154no—
673C2×C4—3016no—
674C2×C4—308no—
675C2×C4—3016no—
676C2×C4—308no—
677C2×C4—308no—
678C2×C4—302no—
679C2×C4—302no—
680C2×C4C4×D3×D512yes—
681C2×C4C4×D3×D514yescomplemented
682C2×C4#677712yes—
683C2×C4#679012yes—
684C2×C3—104no—
685C2×C3C2×C42×D511yescharacteristic
686C2×C3C2×D5×C22⋊C411yescharacteristic
687C2×C3D5×#11711yescharacteristic
688C2×C3C4×D4×D512yes—
689C2×C3C4×D4×D512yes—
690D3—24no—
691D3—58no—
692C5C4×D3×C22⋊C411yescharacteristic, complemented, Sylow
693C22—34no—
694C22—54no—
695C22—62no—
696C22—64no—
697C22—62no—
698C22—64no—
699C22—102no—
700C22—104no—
701C22—102no—
702C22—104no—
703C22—154no—
704C22—154no—
705C22—158no—
706C22—154no—
707C22—158no—
708C22—3032no—
709C22C2×C4×D3×D511yescharacteristic
710C22C2×C4×D3×D512yes—
711C22C2×#677711yescharacteristic
712C22#9201612yes—
713C22C2×#679011yescharacteristic
714C4—24no—
715C4—64no—
716C4—62no—
717C4—104no—
718C4—102no—
719C4—154no—
720C4—304no—
721C4#9147314yesdirect product factor
722C3C4×D5×C22⋊C411yescharacteristic, complemented, Sylow
723C2—64no—
724C2—104no—
725C2—158no—
726C2C42×D3×D511yescharacteristic
727C2#1175272311yescharacteristic
728C2C4×#677712yes—
729C2C2×#9147311yescharacteristic
730C2C4×#679012yes—
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC2×C3×C5C22×C42
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D3×D5C22
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×C4×C22⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C42×D15C2semidirect
4. C2×C4×#1200C2semidirect
5. C4×C5×(C2×D3)⋊C4C2semidirect
6. C3×C4×#685C2semidirect
7. #11748888C2semidirect
8. #11748886C2semidirect
9. #11748884C2semidirect
10. C4×(C2×D3)⋊Dic5C2semidirect
11. C4×#6665C2semidirect
24. C2×C4×D3×D5C4semidirect
25. C2×C3×C42×C5C22semidirect
26. C2×C4×Dic15C22semidirect
27. C2×C4×Dic15C22semidirect
30. C2×C4×C5×Dic3C22semidirect
32. C2×C3×C4×Dic5C22semidirect
35. C2×Dic3×Dic5C22semidirect
36. #91473C4direct (N × H)
38. C5×C3⋊#95C22semidirect
39. C3×#3963C22semidirect
40. #90994C22semidirect
41. #90994C22semidirect
51. C4×#685D3semidirect
69. C2×C4×D15C2×C4semidirect
76. C2×C4×C5×D3C2×C4semidirect
81. C2×C3×C4×D5C2×C4semidirect
87. C2×#1200C2×C4semidirect
90. C2×D3×Dic5C2×C4semidirect
93. C2×D5×Dic3C2×C4semidirect
98. C5×(C2×D3)⋊C4C2×C4semidirect
100. C3×#685C2×C4semidirect
102. (C2×D3)⋊Dic5C2×C4semidirect
103. #6665C2×C4semidirect
113. C4×(C2×D3)⋊C4D5semidirect
130. C2×C42×C5C2×D3semidirect
137. C2×C4×Dic5C2×D3semidirect
144. #3963C2×D3semidirect
166. C2×D3×D5C42semidirect
170. C2×C3×C4×C5C22×C4semidirect
176. C2×Dic15C22×C4semidirect
180. C4×D15C22⋊C4semidirect
186. C2×C5×Dic3C22×C4semidirect
193. C2×C3×Dic5C22×C4semidirect
213. C2×C3×C42C2×D5semidirect
220. C2×C4×Dic3C2×D5semidirect
227. C3⋊#95C2×D5semidirect
268. C2×C4×D5C4×D3semidirect
274. #685C4×D3semidirect
304. C2×C5×D3C2×C42semidirect
309. C2×C3×D5C2×C42semidirect
312. C3×C4×C5C2×C22⋊C4semidirect
314. Dic15C2×C22⋊C4semidirect
359. C2×C4×D3C4×D5semidirect
365. (C2×D3)⋊C4C4×D5semidirect
401. C2×C4×C5C2×C4×D3semidirect
416. C2×Dic5C2×C4×D3semidirect
447. C2×C42D3×D5semidirect
457. D15C4×C22⋊C4semidirect
491. C2×C3×C4C2×C4×D5semidirect
506. C2×Dic3C2×C4×D5semidirect
533. C2×D5C42×D3semidirect
537. C4×C5D3×C22⋊C4semidirect
593. C3×C5C2×C4×C22⋊C4semidirect
614. C2×D3C42×D5semidirect
618. C3×C4D5×C22⋊C4semidirect
681. C2×C4C4×D3×D5semidirect
692. C5C4×D3×C22⋊C4semidirect
721. C4#91473direct (N × H)
722. C3C4×D5×C22⋊C4semidirect

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×C42×D152
C2×#914732
C2×C4×#12002
C4×C5×(C2×D3)⋊C42
C3×C4×#6852
#117488882
#117488862
#117488842
C4×(C2×D3)⋊Dic52
C4×#66652
C4×D5×C22⋊C43
C4×D3×C22⋊C45