Finite Group Databasebeta

← C4×#91327 #14322348

Subgroups — C4×#91327 #14322348

Order 1920.

1176 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
1C2×C3×C4×Dic10C211yesmaximal, characteristic
2C2×C4×#1204C211yesmaximal, characteristic
3C2×#91327C211yesmaximal, characteristic
4C4×#6712C211yesmaximal, characteristic
5C4×C5×Dic3⋊C4C211yesmaximal, characteristic
6C4×Dic3⋊Dic5C211yesmaximal, characteristic
7C4×#6669C211yesmaximal, characteristic
8#11748677C211yesmaximal, characteristic
9#11748676C211yesmaximal, characteristic
10#11748672C211yesmaximal, characteristic
11#11748664C211yesmaximal, characteristic
12#11748658C211yesmaximal, characteristic
13#11748641C211yesmaximal, characteristic
14C4×Dic3×Dic5C211yesmaximal, characteristic
15#11748628C211yesmaximal, characteristic
16C4×#4034—31nomaximal, Hall
17C22×C3×Dic10C2211yescharacteristic
18C22×#1204C2211yescharacteristic
19C2×C3×C42×C5C2211yescharacteristic
20C2×#6712C2211yescharacteristic
21C2×#6712C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C4×Dic15C2211yescharacteristic
24C2×C5×Dic3⋊C4C2211yescharacteristic
25C2×C5×Dic3⋊C4C2211yescharacteristic
26C2×C4×C5×Dic3C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×#683C2211yescharacteristic
30C2×C3×#683C2211yescharacteristic
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×C3×C4×Dic5C2211yescharacteristic
33C3×C4×Dic10—24no—
34C2×Dic3⋊Dic5C2211yescharacteristic
35C2×Dic3⋊Dic5C2211yescharacteristic
36C2×Dic3⋊Dic5C2211yescharacteristic
37C2×#6669C2211yescharacteristic
38C2×#6669C2211yescharacteristic
39C2×#6669C2211yescharacteristic
40C2×#6668C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45C4×#1204—24no—
46#91327C418yesdirect product factor
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C5×C3⋊#95C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55C4×#944—51nomaximal, Hall
56C2×#4034—31no—
57C2×C4×Dic10—31no—
58C2×C4×Dic10D311yescharacteristic
59C4×C5×C4⋊C4—31no—
60#65274—31no—
61#65265—31no—
62#65262—31no—
63C4×C4⋊Dic5—31no—
64C4×#683—31no—
65C4×#683—31no—
66C42×Dic5—31no—
67#64936—31no—
68#64936—31no—
69#64935—31no—
70#64935—31no—
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C22×C3×Dic5C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C2×C3×Dic10—22no—
87C2×C3×Dic10—22no—
88C2×C3×Dic10C2×C414yes—
89C2×#1204—22no—
90C2×#1204—22no—
91C2×#1204C2×C414yes—
92C3×C42×C5—22no—
93#6712—22no—
94#6712C2×C414yes—
95C4×Dic15—22no—
96C4×Dic15Q814yescomplemented
97C5×Dic3⋊C4—22no—
98C5×Dic3⋊C4C2×C414yes—
99C4×C5×Dic3—22no—
100C4×C5×Dic3Q814yescomplemented
101C3×C4⋊Dic5—22no—
102C3×#683—22no—
103C3×#683—22no—
104C3×C4×Dic5—22no—
105C3×C4×Dic5D414yes—
106Dic3⋊Dic5—22no—
107Dic3⋊Dic5—22no—
108Dic3⋊Dic5C2×C414yes—
109#6669—22no—
110#6669—22no—
111#6669C2×C414yes—
112#6668—22no—
113Dic3×Dic5—22no—
114Dic3×Dic5—22no—
115Dic3×Dic5—22no—
116Dic3×Dic5C2×C414yes—
117C2×C3×C4×Q8—51no—
118C2×#944—51no—
119C2×C4×Dic6—51no—
120#5229—51no—
121#4976—51no—
122#4976—51no—
123#4976—51no—
124#4976—51no—
125#4975—51no—
126#4973—51no—
127C4×Dic3⋊C4—51no—
128C4×Dic3⋊C4—51no—
129C4×Dic3⋊C4—51no—
130C4×Dic3⋊C4D511yescharacteristic
131C42×Dic3—51no—
132C22×Dic10—31no—
133C22×Dic10C2×D311yescharacteristic
134C2×C5×C4⋊C4—31no—
135C2×C5×C4⋊C4—31no—
136C2×C42×C5—31no—
137C2×C42×C5—31no—
138C2×C42×C5C2×D311yescharacteristic
139C2×C4⋊Dic5—31no—
140C2×C4⋊Dic5—31no—
141C2×C4⋊Dic5—31no—
142C2×C4⋊Dic5C2×D311yescharacteristic
143C2×#683—31no—
144C2×#683—31no—
145C2×#683—31no—
146C2×#683—31no—
147C2×#683—31no—
148C2×#683—31no—
149C2×#683C2×D311yescharacteristic
150C2×#683C2×D311yescharacteristic
151C2×C4×Dic5—31no—
152C2×C4×Dic5—31no—
153C2×C4×Dic5—31no—
154C2×C4×Dic5—31no—
155C2×C4×Dic5—31no—
156C2×C4×Dic5—31no—
157C2×C4×Dic5C2×D311yescharacteristic
158C2×C4×Dic5C2×D311yescharacteristic
159#4034—38no—
160C4×Dic10—24no—
161C4×Dic10—64no—
162C5×#95—31no—
163C5×#95—31no—
164#3963—31no—
165#3963—31no—
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170C4×C4⋊Q8—151noSylow
171C23×C3×C5C2411yescharacteristic
172C2×C3×C4×C5—21no—
173C2×C3×C4×C5—21no—
174C2×C3×C4×C5—21no—
175C2×C3×C4×C5—21no—
176C2×C3×C4×C5—21no—
177C2×C3×C4×C5C22×C412yes—
178C2×C3×C4×C5C2×D412yes—
179C2×C3×C4×C5C2×Q812yes—
180C2×C3×C4×C5C2×Q812yes—
181C2×Dic15—21no—
182C2×Dic15—21no—
183C2×Dic15—21no—
184C2×Dic15—21no—
185C2×Dic15—21no—
186C2×Dic15—21no—
187C2×Dic15—21no—
188C2×Dic15C22×C412yes—
189C2×Dic15C22×C412yes—
190C2×Dic15C2×Q812yes—
191C2×Dic15C2×Q812yes—
192C2×Dic15#4112yes—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3—21no—
199C2×C5×Dic3—21no—
200C2×C5×Dic3C22×C412yes—
201C2×C5×Dic3C22×C412yes—
202C2×C5×Dic3C2×Q812yes—
203C2×C5×Dic3C2×Q812yes—
204C2×C5×Dic3#4112yes—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5C22×C412yes—
213C2×C3×Dic5C22×C412yes—
214C2×C3×Dic5C2×D412yes—
215C2×C3×Dic5C2×D412yes—
216C2×C3×Dic5#4112yes—
217C3×Dic10—28no—
218#1204—28no—
219C22×C3×Q8—51no—
220C22×Dic6—51no—
221C3×C4×Q8—104no—
222C2×C3×C4⋊C4—51no—
223C2×C3×C4⋊C4—51no—
224C2×C3×C4⋊C4—51no—
225C2×C3×C42—51no—
226C2×C3×C42—51no—
227C2×C3×C42C2×D511yescharacteristic
228#944—58no—
229C2×C4⋊Dic3—51no—
230C2×Dic3⋊C4—51no—
231C2×Dic3⋊C4—51no—
232C2×Dic3⋊C4—51no—
233C2×Dic3⋊C4—51no—
234C2×Dic3⋊C4—51no—
235C2×Dic3⋊C4—51no—
236C2×Dic3⋊C4—51no—
237C2×Dic3⋊C4—51no—
238C2×Dic3⋊C4C2×D511yescharacteristic
239C2×Dic3⋊C4C2×D511yescharacteristic
240C2×C4×Dic3—51no—
241C2×C4×Dic3—51no—
242C2×C4×Dic3—51no—
243C2×C4×Dic3—51no—
244C2×C4×Dic3—51no—
245C2×C4×Dic3—51no—
246C2×C4×Dic3C2×D511yescharacteristic
247C2×C4×Dic3C2×D511yescharacteristic
248C4×Dic6—104no—
249C3⋊#95—51no—
250C3⋊#95—51no—
251C3⋊#95—51no—
252C3⋊#95—51no—
253C3⋊#95—51no—
254C3⋊#95—51no—
255C3⋊#95C2×D511yescharacteristic
256C3⋊#95C2×D511yescharacteristic
257C22×C4×C5—31no—
258C22×C4×C5—31no—
259C22×C4×C5—31no—
260C22×C4×C5—31no—
261C22×C4×C5C22×D311yescharacteristic
262C22×C4×C5C22×D311yescharacteristic
263C22×C4×C5C22×D311yescharacteristic
264C22×Dic5—31no—
265C22×Dic5—31no—
266C22×Dic5—31no—
267C22×Dic5—31no—
268C22×Dic5C22×D311yescharacteristic
269C22×Dic5C22×D311yescharacteristic
270C22×Dic5C22×D311yescharacteristic
271C22×Dic5C22×D311yescharacteristic
272C2×Dic10—22no—
273C2×Dic10—22no—
274C2×Dic10—34no—
275C2×Dic10—62no—
276C2×Dic10—62no—
277C2×Dic10C4×D314yes—
278C5×C4⋊C4—34no—
279C5×C4⋊C4—62no—
280C42×C5—22no—
281C42×C5—34no—
282C42×C5—62no—
283C4⋊Dic5—22no—
284C4⋊Dic5—34no—
285C4⋊Dic5—62no—
286C4⋊Dic5—62no—
287#683—22no—
288#683—22no—
289#683—34no—
290#683—34no—
291#683—62no—
292#683—62no—
293#683—62no—
294#683—62no—
295C4×Dic5—22no—
296C4×Dic5—34no—
297C4×Dic5—34no—
298C4×Dic5—62no—
299C4×Dic5—62no—
300C4×Dic5—62no—
301C4×Dic5—62no—
302C4×Dic5#6714yes—
303C2×C4⋊Q8—151no—
304C2×C4×Q8—51no—
305C2×C4×Q8—151no—
306#391—151no—
307#391—151no—
308#389—151no—
309#389—151no—
310#389—151no—
311#389—151no—
312#384—151no—
313C4×C4⋊C4—31no—
314C4×C4⋊C4—151no—
315C4×C4⋊C4—151no—
316C4×C4⋊C4—151no—
317C43—151no—
318C22×C3×C5C23×C411yescharacteristic
319C22×C3×C5C22×D411yescharacteristic
320C22×C3×C5C22×Q811yescharacteristic
321C22×C3×C5C22×Q811yescharacteristic
322C22×C3×C5C2×#4111yescharacteristic
323C22×C3×C5C2×#4111yescharacteristic
324C22×C3×C5C2×#4111yescharacteristic
325C3×C4×C5—22no—
326C3×C4×C5—41no—
327C3×C4×C5C4⋊Q814yescomplemented
328Dic15—22no—
329Dic15—22no—
330Dic15—41no—
331Dic15C4×Q814yescomplemented
332C3×Dic5—22no—
333C3×Dic5—22no—
334C3×Dic5—41no—
335C3×Dic5C4×D414yes—
336C5×Dic3—22no—
337C5×Dic3—22no—
338C5×Dic3—41no—
339C5×Dic3C4×Q814yescomplemented
340C2×C3×Q8—54no—
341C2×C3×Q8—102no—
342C2×C3×Q8—102no—
343C22×C3×C4—51no—
344C22×C3×C4—51no—
345C22×C3×C4—51no—
346C22×C3×C4—51no—
347C22×C3×C4C22×D511yescharacteristic
348C22×C3×C4C22×D511yescharacteristic
349C22×C3×C4C22×D511yescharacteristic
350C22×Dic3—51no—
351C22×Dic3—51no—
352C22×Dic3—51no—
353C22×Dic3—51no—
354C22×Dic3C22×D511yescharacteristic
355C22×Dic3C22×D511yescharacteristic
356C22×Dic3C22×D511yescharacteristic
357C22×Dic3C22×D511yescharacteristic
358C2×Dic6—54no—
359C2×Dic6—102no—
360C2×Dic6—102no—
361C3×C4⋊C4—102no—
362C3×C4⋊C4—102no—
363C3×C4⋊C4—102no—
364C3×C42—22no—
365C3×C42—54no—
366C3×C42—102no—
367C4⋊Dic3—102no—
368Dic3⋊C4—22no—
369Dic3⋊C4—54no—
370Dic3⋊C4—54no—
371Dic3⋊C4—54no—
372Dic3⋊C4—102no—
373Dic3⋊C4—102no—
374Dic3⋊C4—102no—
375Dic3⋊C4—102no—
376Dic3⋊C4—102no—
377Dic3⋊C4C4×D514yes—
378C4×Dic3—22no—
379C4×Dic3—54no—
380C4×Dic3—54no—
381C4×Dic3—102no—
382C4×Dic3—102no—
383C4×Dic3—102no—
384C4×Dic3—102no—
385C4×Dic3Dic1014yescomplemented
386C23×C5C23×D311yescharacteristic
387C2×C4×C5—21no—
388C2×C4×C5—21no—
389C2×C4×C5—21no—
390C2×C4×C5—21no—
391C2×C4×C5—21no—
392C2×C4×C5—32no—
393C2×C4×C5—32no—
394C2×C4×C5—32no—
395C2×C4×C5—32no—
396C2×C4×C5—32no—
397C2×C4×C5—61no—
398C2×C4×C5—61no—
399C2×C4×C5—61no—
400C2×C4×C5—61no—
401C2×C4×C5—61no—
402C2×C4×C5—61no—
403C2×C4×C5—61no—
404C2×C4×C5C2×C4×D312yes—
405C2×C4×C5D3×Q812yes—
406C2×C4×C5D3×Q812yes—
407C2×C4×C5C2×#6712yes—
408C2×Dic5—21no—
409C2×Dic5—21no—
410C2×Dic5—21no—
411C2×Dic5—21no—
412C2×Dic5—21no—
413C2×Dic5—21no—
414C2×Dic5—21no—
415C2×Dic5—32no—
416C2×Dic5—32no—
417C2×Dic5—32no—
418C2×Dic5—32no—
419C2×Dic5—32no—
420C2×Dic5—61no—
421C2×Dic5—61no—
422C2×Dic5—61no—
423C2×Dic5—61no—
424C2×Dic5—61no—
425C2×Dic5—61no—
426C2×Dic5—61no—
427C2×Dic5C2×C4×D312yes—
428C2×Dic5C2×C4×D312yes—
429C2×Dic5#23512yes—
430C2×Dic5C2×#6712yes—
431C2×Dic5C2×#6712yes—
432Dic10—28no—
433Dic10—68no—
434C22×Q8—51no—
435C22×Q8—151no—
436C4⋊Q8—158no—
437C4×Q8—104no—
438C4×Q8—304no—
439C2×C4⋊C4—31no—
440C2×C4⋊C4—31no—
441C2×C4⋊C4—51no—
442C2×C4⋊C4—51no—
443C2×C4⋊C4—51no—
444C2×C4⋊C4—151no—
445C2×C4⋊C4—151no—
446C2×C4⋊C4—151no—
447C2×C4⋊C4—151no—
448C2×C4⋊C4—151no—
449C2×C4⋊C4—151no—
450C2×C4⋊C4—151no—
451C2×C4⋊C4—151no—
452C2×C4⋊C4—151no—
453C2×C42—31no—
454C2×C42—31no—
455C2×C42—51no—
456C2×C42—51no—
457C2×C42—151no—
458C2×C42—151no—
459C2×C42—151no—
460C2×C42—151no—
461C2×C42—151no—
462C2×C42—151no—
463C2×C42D3×D511yescharacteristic
464#95—31no—
465#95—31no—
466#95—151no—
467#95—151no—
468#95—151no—
469#95—151no—
470#95—151no—
471#95—151no—
472C2×C3×C5C2×C4×D411yescharacteristic
473C2×C3×C5C2×C4×Q811yescharacteristic
474C2×C3×C5C2×C4×Q811yescharacteristic
475C2×C3×C5C2×C4⋊Q811yescharacteristic
476C2×C3×C5#53211yescharacteristic
477C2×C3×C5#53311yescharacteristic
478C2×C3×C5#53311yescharacteristic
479C23×C3C23×D511yescharacteristic
480C3×Q8—108no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—52no—
487C2×C3×C4—52no—
488C2×C3×C4—52no—
489C2×C3×C4—52no—
490C2×C3×C4—52no—
491C2×C3×C4—101no—
492C2×C3×C4—101no—
493C2×C3×C4—101no—
494C2×C3×C4—101no—
495C2×C3×C4—101no—
496C2×C3×C4—101no—
497C2×C3×C4—101no—
498C2×C3×C4C2×Dic1012yes—
499C2×C3×C4C2×C4×D512yes—
500C2×C3×C4D4×D512yes—
501C2×C3×C4Q8×D512yes—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—52no—
510C2×Dic3—52no—
511C2×Dic3—52no—
512C2×Dic3—52no—
513C2×Dic3—52no—
514C2×Dic3—101no—
515C2×Dic3—101no—
516C2×Dic3—101no—
517C2×Dic3—101no—
518C2×Dic3—101no—
519C2×Dic3—101no—
520C2×Dic3—101no—
521C2×Dic3C2×Dic1012yes—
522C2×Dic3C2×Dic1012yes—
523C2×Dic3C2×C4×D512yes—
524C2×Dic3C2×C4×D512yes—
525C2×Dic3#70912yes—
526Dic6—108no—
527C22×C5C22×C4×D311yescharacteristic
528C22×C5C2×#23511yescharacteristic
529C22×C5C2×D3×Q811yescharacteristic
530C22×C5C2×D3×Q811yescharacteristic
531C22×C5D3×#4111yescharacteristic
532C22×C5D3×#4111yescharacteristic
533C22×C5C22×#6711yescharacteristic
534C4×C5—22no—
535C4×C5—34no—
536C4×C5—41no—
537C4×C5—62no—
538C4×C5—62no—
539C4×C5—121no—
540C4×C5#94414yescomplemented
541Dic5—22no—
542Dic5—22no—
543Dic5—34no—
544Dic5—41no—
545Dic5—62no—
546Dic5—62no—
547Dic5—121no—
548Dic5C4×#6714yes—
549C2×Q8—54no—
550C2×Q8—102no—
551C2×Q8—102no—
552C2×Q8—154no—
553C2×Q8—302no—
554C2×Q8—302no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—51no—
560C22×C4—51no—
561C22×C4—51no—
562C22×C4—51no—
563C22×C4—151no—
564C22×C4—151no—
565C22×C4—151no—
566C22×C4—151no—
567C22×C4C2×D3×D511yescharacteristic
568C22×C4C2×D3×D511yescharacteristic
569C22×C4C2×D3×D511yescharacteristic
570C4⋊C4—34no—
571C4⋊C4—62no—
572C4⋊C4—102no—
573C4⋊C4—102no—
574C4⋊C4—102no—
575C4⋊C4—154no—
576C4⋊C4—154no—
577C4⋊C4—154no—
578C4⋊C4—302no—
579C4⋊C4—302no—
580C4⋊C4—302no—
581C4⋊C4—302no—
582C4⋊C4—302no—
583C4⋊C4—302no—
584C42—22no—
585C42—34no—
586C42—54no—
587C42—62no—
588C42—102no—
589C42—154no—
590C42—154no—
591C42—302no—
592C42—302no—
593C42—302no—
594C42—302no—
595C3×C5C4×C4⋊Q811yescharacteristic, complemented, Hall
596C22×C3C22×Dic1011yescharacteristic
597C22×C3C22×C4×D511yescharacteristic
598C22×C3C2×#70911yescharacteristic
599C22×C3C2×D4×D511yescharacteristic
600C22×C3C2×Q8×D511yescharacteristic
601C22×C3D5×#4111yescharacteristic
602C22×C3D5×#4111yescharacteristic
603C3×C4—22no—
604C3×C4—41no—
605C3×C4—54no—
606C3×C4—102no—
607C3×C4—102no—
608C3×C4—201no—
609C3×C4#403414yescomplemented
610Dic3—22no—
611Dic3—22no—
612Dic3—41no—
613Dic3—54no—
614Dic3—102no—
615Dic3—102no—
616Dic3—201no—
617Dic3C4×Dic1014yescomplemented
618C2×C5C4×D3×Q811yescharacteristic
619C2×C5C4×D3×Q811yescharacteristic
620C2×C5#557811yescharacteristic
621C2×C5#557811yescharacteristic
622C2×C5C2×C4×#6711yescharacteristic
623C2×C5C2×#94411yescharacteristic
624C2×C5#583211yescharacteristic
625C23C22×D3×D511yescharacteristic
626Q8—108no—
627Q8—308no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—32no—
634C2×C4—32no—
635C2×C4—32no—
636C2×C4—32no—
637C2×C4—32no—
638C2×C4—52no—
639C2×C4—52no—
640C2×C4—52no—
641C2×C4—52no—
642C2×C4—52no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—101no—
651C2×C4—101no—
652C2×C4—101no—
653C2×C4—101no—
654C2×C4—101no—
655C2×C4—101no—
656C2×C4—101no—
657C2×C4—152no—
658C2×C4—152no—
659C2×C4—152no—
660C2×C4—152no—
661C2×C4—152no—
662C2×C4—301no—
663C2×C4—301no—
664C2×C4—301no—
665C2×C4—301no—
666C2×C4—301no—
667C2×C4—301no—
668C2×C4—301no—
669C2×C4D3×Dic1012yes—
670C2×C4D15⋊Q812yes—
671C2×C4C4×D3×D512yes—
672C2×C4D5×#6712yes—
673C2×C3C2×C4×Dic1011yescharacteristic
674C2×C3C2×#403411yescharacteristic
675C2×C3#6585111yescharacteristic
676C2×C3C4×D4×D511yescharacteristic
677C2×C3#6588211yescharacteristic
678C2×C3C4×Q8×D511yescharacteristic
679C2×C3#6591211yescharacteristic
680C5C4×#94411yescharacteristic, complemented, Sylow
681C22C2×D3×Dic1011yescharacteristic
682C22C2×D15⋊Q811yescharacteristic
683C22C2×C4×D3×D511yescharacteristic
684C22D5×#23511yescharacteristic
685C22D3×#70911yescharacteristic
686C22#9201611yescharacteristic
687C22C2×D5×#6711yescharacteristic
688C4—22no—
689C4—34no—
690C4—41no—
691C4—54no—
692C4—62no—
693C4—62no—
694C4—102no—
695C4—102no—
696C4—121no—
697C4—154no—
698C4—201no—
699C4—302no—
700C4—302no—
701C4—601no—
702C4#9132714yesdirect product factor
703C3C4×#403411yescharacteristic, complemented, Sylow
704C2C4×D3×Dic1011yescharacteristic
705C2C4×D15⋊Q811yescharacteristic
706C2#1175257811yescharacteristic
707C2#1175258811yescharacteristic
708C2C2×#9132711yescharacteristic
709C2#1175431111yescharacteristic
710C2C4×D5×#6711yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
socle, prime radical, cosocleC23×C3×C5C24
hypercenterC2×C42D3×D5
hypocenterC3×C5C4×C4⋊Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
46. #91327C4direct (N × H)
96. C4×Dic15Q8semidirect
100. C4×C5×Dic3Q8semidirect
327. C3×C4×C5C4⋊Q8semidirect
331. Dic15C4×Q8semidirect
339. C5×Dic3C4×Q8semidirect
385. C4×Dic3Dic10semidirect
540. C4×C5#944semidirect
595. C3×C5C4×C4⋊Q8semidirect
609. C3×C4#4034semidirect
617. Dic3C4×Dic10semidirect
680. C5C4×#944semidirect
702. C4#91327direct (N × H)
703. C3C4×#4034semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic102
C2×C4×#12042
C2×#913272
C4×#67122
C4×C5×Dic3⋊C42
C4×Dic3⋊Dic52
C4×#66692
#117486772
#117486762
#117486722
#117486642
#117486582
#117486412
C4×Dic3×Dic52
#117486282
C4×#40343
C4×#9445