Finite Group Databasebeta

← #14326157

Subgroups — #14326157

Order 1920.

1640 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D15⋊Q8C211yesmaximal, characteristic
2C2×C4×#1204C211yesmaximal, characteristic, complemented
3C2×#91325C211yesmaximal, characteristic, complemented
4#11750767C211yesmaximal, characteristic
5C5×#4646C211yesmaximal, characteristic, complemented
6C3×#64935C211yesmaximal, characteristic, complemented
7#11748935C211yesmaximal, characteristic, complemented
8#11748935C211yesmaximal, characteristic, complemented
9#11748882C211yesmaximal, characteristic
10#11748881C211yesmaximal, characteristic
11#11748876C211yesmaximal, characteristic
12#11748875C211yesmaximal, characteristic
13#11748863C211yesmaximal, characteristic
14#11748692C211yesmaximal, characteristic, complemented
15#11748672C211yesmaximal, characteristic, complemented
16#10608345—31nomaximal, Hall
17C22×C4×D15C2211yescharacteristic
18C22×C5×Dic6C2211yescharacteristic
19C22×C3×Dic10C2211yescharacteristic
20C22×#1204C2211yescharacteristic
21C22×#1204C2211yescharacteristic
22C22×#1200C2211yescharacteristic
23C22×#1200C2211yescharacteristic
24C2×D15⋊Q8—24no—
25C2×D15⋊Q8—24no—
26C2×D15⋊Q8C418yescomplemented
27C2×#6714C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×C4×Dic15C2211yescharacteristic
30C2×C4×Dic15C2211yescharacteristic
31C2×C5×Dic3⋊C4C2211yescharacteristic
32C2×C4×C5×Dic3C2211yescharacteristic
33C2×C3×#683C2211yescharacteristic
34C2×C3×C4×Dic5C2211yescharacteristic
35C2×Dic3⋊Dic5C2211yescharacteristic
36C2×#6669C2211yescharacteristic
37C2×#6669C2211yescharacteristic
38C2×#6668C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C4×#1204—24no—
44#91325—24no—
45C3×C5×#95C2211yescharacteristic
46#91115C2211yescharacteristic
47C5×C3⋊#95C2211yescharacteristic
48C5×C3⋊#95C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#76614—51nomaximal, Hall
58C22×Q8×D5—31no—
59C2×#4033—31no—
60C2×C4×Dic10—31no—
61C5×#391—31no—
62#65519—31no—
63#65276—31no—
64C4×#685—31no—
65#64956—31no—
66#64956—31no—
67#64955—31no—
68#64955—31no—
69#64935—31no—
70#64935—31no—
71#64935—31no—
72#64935D311yescharacteristic, complemented
73C23×D15C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C2×C4×D15—22no—
81C2×C4×D15—22no—
82C2×C4×D15C2×C414yes—
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C2×C5×Dic6—22no—
88C2×C5×Dic6—22no—
89C2×C5×Dic6C2×C414yes—
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C2×C3×Dic10—22no—
95C2×C3×Dic10—22no—
96C2×C3×Dic10C2×C414yes—
97C2×#1204—22no—
98C2×#1204—22no—
99C2×#1204C2×C414yes—
100C2×#1204C2×C414yes—
101C2×#1204D414yes—
102C2×#1204D414yes—
103C2×#1200—22no—
104C2×#1200—22no—
105C2×#1200—22no—
106C2×#1200—22no—
107C2×#1200C2×C414yes—
108C2×#1200C2×C414yes—
109D15⋊Q8—232no—
110#6714—22no—
111#6714Q814yescomplemented
112C4×Dic15—22no—
113C4×Dic15—22no—
114C5×Dic3⋊C4—22no—
115C4×C5×Dic3—22no—
116C3×#683—22no—
117C3×C4×Dic5—22no—
118Dic3⋊Dic5—22no—
119#6669—22no—
120#6669—22no—
121#6668—22no—
122#6667—22no—
123#6667—22no—
124Dic3×Dic5—22no—
125Dic3×Dic5—22no—
126C22×D3×Q8—51no—
127C2×#887—51no—
128C2×C4×Dic6—51no—
129C3×#391—51no—
130#5229—51no—
131#4987—51no—
132C4×(C2×D3)⋊C4—51no—
133#4667—51no—
134#4667—51no—
135#4666—51no—
136#4666—51no—
137#4646—51no—
138#4646—51no—
139#4646—51no—
140#4646D511yescharacteristic, complemented
141C22×C5×Q8—31no—
142C2×Q8×D5—38no—
143C2×Q8×D5—64no—
144C2×Q8×D5—64no—
145C22×C4×D5—31no—
146C22×C4×D5—31no—
147C22×C4×D5—31no—
148C22×Dic10—31no—
149C22×Dic10—31no—
150C22×Dic10C2×D311yescharacteristic
151C2×C5×C4⋊C4—31no—
152C2×C42×C5—31no—
153C2×#685—31no—
154C2×#685—31no—
155C2×#685—31no—
156C2×#685—31no—
157C2×C4⋊Dic5—31no—
158C2×#683—31no—
159C2×#683—31no—
160C2×#683—31no—
161C2×#683C2×D311yescharacteristic
162C2×C4×Dic5—31no—
163C2×C4×Dic5—31no—
164C2×C4×Dic5—31no—
165C2×C4×Dic5—31no—
166C2×C4×Dic5C2×D311yescharacteristic
167#4033—64no—
168C4×Dic10—64no—
169C5×#95—31no—
170C5×#95—31no—
171C5×#95—31no—
172C5×#95C2×D311yescharacteristic
173#3963—31no—
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#3963C2×D311yescharacteristic
179#3963C2×D311yescharacteristic
180#3963C2×D311yescharacteristic
181Q8×C22⋊C4—151noSylow
182C23×C3×C5C2411yescharacteristic
183C22×D15—21no—
184C22×D15—21no—
185C22×D15—21no—
186C22×D15—21no—
187C22×D15C22×C412yes—
188C22×D15C2×Q812yes—
189C22×D15#4112yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5C22×C412yes—
198C2×C3×C4×C5C2×Q812yescomplemented
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15C22×C412yes—
205C2×Dic15C2×D412yes—
206C2×Dic15C2×D412yes—
207C2×Dic15C2×Q812yescomplemented
208C4×D15—28no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3—21no—
216C2×C5×Dic3—21no—
217C2×C5×Dic3C22×C412yes—
218C2×C5×Dic3C22×C412yes—
219C2×C5×Dic3C2×D412yes—
220C2×C5×Dic3C2×D412yes—
221C5×Dic6—28no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5C22×C412yes—
231C2×C3×Dic5C22×C412yes—
232C2×C3×Dic5C2×D412yes—
233C2×C3×Dic5C2×D412yes—
234C3×Dic10—28no—
235#1204—28no—
236#1204C22⋊C4116yescomplemented
237#1200—28no—
238#1200—28no—
239C22×C3×Q8—51no—
240C2×D3×Q8—58no—
241C2×D3×Q8—104no—
242C2×D3×Q8—104no—
243C22×C4×D3—51no—
244C22×C4×D3—51no—
245C22×C4×D3—51no—
246C22×Dic6—51no—
247C22×Dic6—51no—
248C22×Dic6C2×D511yescharacteristic
249C2×C3×C4⋊C4—51no—
250C2×C3×C42—51no—
251C2×(C2×D3)⋊C4—51no—
252C2×(C2×D3)⋊C4—51no—
253C2×(C2×D3)⋊C4—51no—
254C2×(C2×D3)⋊C4—51no—
255C2×C4⋊Dic3—51no—
256C2×Dic3⋊C4—51no—
257C2×Dic3⋊C4—51no—
258C2×Dic3⋊C4—51no—
259C2×Dic3⋊C4C2×D511yescharacteristic
260C2×C4×Dic3—51no—
261C2×C4×Dic3—51no—
262C2×C4×Dic3—51no—
263C2×C4×Dic3—51no—
264C2×C4×Dic3C2×D511yescharacteristic
265#887—104no—
266C4×Dic6—104no—
267C3×#95—51no—
268C3×#95—51no—
269C3×#95—51no—
270C3×#95C2×D511yescharacteristic
271C3⋊#95—51no—
272C3⋊#95—51no—
273C3⋊#95—51no—
274C3⋊#95—51no—
275C3⋊#95—51no—
276C3⋊#95C2×D511yescharacteristic
277C3⋊#95C2×D511yescharacteristic
278C3⋊#95C2×D511yescharacteristic
279C23×D5—31no—
280C2×C5×Q8—34no—
281C2×C5×Q8—62no—
282C2×C5×Q8—62no—
283C22×C4×C5—31no—
284C22×C4×C5—31no—
285C22×C4×C5—31no—
286C22×C4×C5—31no—
287C22×C4×C5C22×D311yescharacteristic
288C22×C4×C5C22×D311yescharacteristic
289C22×C4×C5C22×D311yescharacteristic
290C22×Dic5—31no—
291C22×Dic5—31no—
292C22×Dic5—31no—
293C22×Dic5C22×D311yescharacteristic
294C22×Dic5C22×D311yescharacteristic
295C22×Dic5C22×D311yescharacteristic
296C22×Dic5C22×D311yescharacteristic
297Q8×D5—632no—
298C2×C4×D5—34no—
299C2×C4×D5—34no—
300C2×C4×D5—34no—
301C2×C4×D5—62no—
302C2×C4×D5—62no—
303C2×C4×D5—62no—
304C2×C4×D5—62no—
305C2×C4×D5—62no—
306C2×C4×D5—62no—
307C2×Dic10—22no—
308C2×Dic10—22no—
309C2×Dic10—34no—
310C2×Dic10—34no—
311C2×Dic10—34no—
312C2×Dic10—34no—
313C2×Dic10—62no—
314C2×Dic10—62no—
315C2×Dic10C4×D314yes—
316C5×C4⋊C4—62no—
317C42×C5—62no—
318#685—34no—
319#685—62no—
320#685—62no—
321#685—62no—
322C4⋊Dic5—62no—
323#683—22no—
324#683—62no—
325#683—62no—
326#683—62no—
327C4×Dic5—22no—
328C4×Dic5—62no—
329C4×Dic5—62no—
330C4×Dic5—62no—
331C4×Dic5—62no—
332C23×Q8—151no—
333C2×C4×Q8—151no—
334C2×C4×Q8—151no—
335#391—31no—
336#391—51no—
337#391—151no—
338#391—151no—
339#391—151no—
340#391—151no—
341#380—151no—
342#380—151no—
343#380—151no—
344C4×C22⋊C4—151no—
345C4×C22⋊C4—151no—
346C4×C22⋊C4—151no—
347C22×C3×C5C23×C411yescharacteristic
348C22×C3×C5C22×D411yescharacteristic
349C22×C3×C5C22×D411yescharacteristic
350C22×C3×C5C22×Q811yescharacteristic
351C22×C3×C5C2×#4111yescharacteristic
352C22×C3×C52−1+411yescharacteristic
353C22×C3×C52−1+411yescharacteristic
354C2×D15—22no—
355C2×D15—22no—
356C2×D15—22no—
357C2×D15—22no—
358C2×D15—22no—
359C2×D15—22no—
360C2×D15C4×Q814yescomplemented
361C3×C4×C5—22no—
362C3×C4×C5—22no—
363C3×C4×C5—41no—
364Dic15—22no—
365Dic15—41no—
366Dic15C2×C22⋊C414yes—
367C3×Dic5—22no—
368C3×Dic5—41no—
369C3×Dic5—41no—
370C3×Dic5C2×C22⋊C414yes—
371C5×Dic3—22no—
372C5×Dic3—41no—
373C5×Dic3—41no—
374C5×Dic3C2×C22⋊C414yes—
375C23×D3—51no—
376C2×C3×Q8—54no—
377C2×C3×Q8—102no—
378C2×C3×Q8—102no—
379C22×C3×C4—51no—
380C22×C3×C4—51no—
381C22×C3×C4—51no—
382C22×C3×C4—51no—
383C22×C3×C4C22×D511yescharacteristic
384C22×C3×C4C22×D511yescharacteristic
385C22×C3×C4C22×D511yescharacteristic
386C22×Dic3—51no—
387C22×Dic3—51no—
388C22×Dic3—51no—
389C22×Dic3C22×D511yescharacteristic
390C22×Dic3C22×D511yescharacteristic
391C22×Dic3C22×D511yescharacteristic
392C22×Dic3C22×D511yescharacteristic
393D3×Q8—1032no—
394C2×C4×D3—54no—
395C2×C4×D3—54no—
396C2×C4×D3—54no—
397C2×C4×D3—102no—
398C2×C4×D3—102no—
399C2×C4×D3—102no—
400C2×C4×D3—102no—
401C2×C4×D3—102no—
402C2×C4×D3—102no—
403C2×Dic6—22no—
404C2×Dic6—22no—
405C2×Dic6—54no—
406C2×Dic6—54no—
407C2×Dic6—54no—
408C2×Dic6—54no—
409C2×Dic6—102no—
410C2×Dic6—102no—
411C2×Dic6C4×D514yes—
412C3×C4⋊C4—102no—
413C3×C42—102no—
414(C2×D3)⋊C4—54no—
415(C2×D3)⋊C4—102no—
416(C2×D3)⋊C4—102no—
417(C2×D3)⋊C4—102no—
418C4⋊Dic3—102no—
419Dic3⋊C4—22no—
420Dic3⋊C4—102no—
421Dic3⋊C4—102no—
422Dic3⋊C4—102no—
423C4×Dic3—22no—
424C4×Dic3—102no—
425C4×Dic3—102no—
426C4×Dic3—102no—
427C4×Dic3—102no—
428C23×C5C23×D311yescharacteristic
429C22×D5—32no—
430C22×D5—32no—
431C22×D5—32no—
432C22×D5—61no—
433C22×D5—61no—
434C22×D5—61no—
435C22×D5—61no—
436C5×Q8—68no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—21no—
444C2×C4×C5—32no—
445C2×C4×C5—32no—
446C2×C4×C5—32no—
447C2×C4×C5—32no—
448C2×C4×C5—61no—
449C2×C4×C5—61no—
450C2×C4×C5—61no—
451C2×C4×C5—61no—
452C2×C4×C5—61no—
453C2×C4×C5—61no—
454C2×C4×C5—61no—
455C2×C4×C5—61no—
456C2×C4×C5C2×C4×D312yes—
457C2×C4×C5D3×Q812yescomplemented
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—21no—
462C2×Dic5—21no—
463C2×Dic5—21no—
464C2×Dic5—21no—
465C2×Dic5—21no—
466C2×Dic5—32no—
467C2×Dic5—32no—
468C2×Dic5—32no—
469C2×Dic5—32no—
470C2×Dic5—61no—
471C2×Dic5—61no—
472C2×Dic5—61no—
473C2×Dic5—61no—
474C2×Dic5—61no—
475C2×Dic5C2×C4×D312yes—
476C2×Dic5C2×C4×D312yes—
477C2×Dic5D3×D412yes—
478C2×Dic5D3×D412yes—
479C4×D5—68no—
480C4×D5—68no—
481C4×D5—68no—
482Dic10—28no—
483Dic10—316no—
484Dic10—68no—
485C22×Q8—31no—
486C22×Q8—51no—
487C22×Q8—151no—
488C22×Q8—151no—
489C22×Q8—158no—
490C22×Q8—304no—
491C22×Q8—304no—
492C23×C4—151no—
493C23×C4—151no—
494C23×C4—151no—
495C4×Q8—304no—
496C4×Q8—304no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—51no—
499C2×C4⋊C4—151no—
500C2×C4⋊C4—151no—
501C2×C4⋊C4—151no—
502C2×C4⋊C4—151no—
503C2×C22⋊C4—151no—
504C2×C22⋊C4—151no—
505C2×C22⋊C4—151no—
506C2×C22⋊C4—151no—
507C2×C42—31no—
508C2×C42—51no—
509C2×C42—151no—
510C2×C42—151no—
511C2×C42—151no—
512C2×C42—151no—
513#95—31no—
514#95—31no—
515#95—31no—
516#95—51no—
517#95—51no—
518#95—51no—
519#95—151no—
520#95—151no—
521#95—151no—
522#95—151no—
523#95—151no—
524#95D3×D511yescharacteristic
525C2×C3×C5C22×C22⋊C411yescharacteristic
526C2×C3×C5C2×C4×Q811yescharacteristic
527C2×C3×C5#51911yescharacteristic
528C2×C3×C5#54811yescharacteristic
529C2×C3×C5#54811yescharacteristic
530C2×C3×C5D4×Q811yescharacteristic
531C2×C3×C5D4×Q811yescharacteristic
532D15—24no—
533C23×C3C23×D511yescharacteristic
534C22×D3—52no—
535C22×D3—52no—
536C22×D3—52no—
537C22×D3—101no—
538C22×D3—101no—
539C22×D3—101no—
540C22×D3—101no—
541C3×Q8—108no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—52no—
550C2×C3×C4—52no—
551C2×C3×C4—52no—
552C2×C3×C4—52no—
553C2×C3×C4—101no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4—101no—
557C2×C3×C4—101no—
558C2×C3×C4—101no—
559C2×C3×C4—101no—
560C2×C3×C4—101no—
561C2×C3×C4C2×C4×D512yes—
562C2×C3×C4Q8×D512yescomplemented
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—52no—
572C2×Dic3—52no—
573C2×Dic3—52no—
574C2×Dic3—52no—
575C2×Dic3—101no—
576C2×Dic3—101no—
577C2×Dic3—101no—
578C2×Dic3—101no—
579C2×Dic3—101no—
580C2×Dic3C2×C4×D512yes—
581C2×Dic3C2×C4×D512yes—
582C2×Dic3D4×D512yes—
583C2×Dic3D4×D512yes—
584C4×D3—108no—
585C4×D3—108no—
586C4×D3—108no—
587Dic6—28no—
588Dic6—516no—
589Dic6—108no—
590C22×C5C22×C4×D311yescharacteristic
591C22×C5C2×D3×D411yescharacteristic
592C22×C5C2×D3×D411yescharacteristic
593C22×C5C2×D3×Q811yescharacteristic
594C22×C5#100711yescharacteristic
595C22×C5D3×#4111yescharacteristic
596C22×C5#101011yescharacteristic
597C2×D5—34no—
598C2×D5—62no—
599C2×D5—62no—
600C2×D5—62no—
601C2×D5—62no—
602C2×D5—62no—
603C2×D5—62no—
604C4×C5—22no—
605C4×C5—22no—
606C4×C5—34no—
607C4×C5—41no—
608C4×C5—62no—
609C4×C5—121no—
610C4×C5—121no—
611Dic5—22no—
612Dic5—34no—
613Dic5—41no—
614Dic5—41no—
615Dic5—62no—
616Dic5—121no—
617Dic5D3×C22⋊C414yes—
618C24—151no—
619C2×Q8—34no—
620C2×Q8—54no—
621C2×Q8—62no—
622C2×Q8—62no—
623C2×Q8—102no—
624C2×Q8—102no—
625C2×Q8—154no—
626C2×Q8—154no—
627C2×Q8—154no—
628C2×Q8—154no—
629C2×Q8—302no—
630C2×Q8—302no—
631C2×Q8—3032no—
632C22×C4—31no—
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—51no—
637C22×C4—51no—
638C22×C4—51no—
639C22×C4—51no—
640C22×C4—154no—
641C22×C4—154no—
642C22×C4—151no—
643C22×C4—151no—
644C22×C4—154no—
645C22×C4—151no—
646C22×C4—302no—
647C22×C4—302no—
648C22×C4—302no—
649C22×C4—302no—
650C22×C4—302no—
651C22×C4—302no—
652C22×C4C2×D3×D511yescharacteristic
653C22×C4C2×D3×D511yescharacteristic
654C22×C4C2×D3×D511yescharacteristic
655C4⋊C4—62no—
656C4⋊C4—102no—
657C4⋊C4—302no—
658C4⋊C4—302no—
659C4⋊C4—302no—
660C4⋊C4—302no—
661C22⋊C4—154no—
662C22⋊C4—302no—
663C22⋊C4—302no—
664C22⋊C4—302no—
665C42—62no—
666C42—102no—
667C42—302no—
668C42—302no—
669C42—302no—
670C42—302no—
671C3×C5Q8×C22⋊C411yescharacteristic, complemented, Hall
672C22×C3C22×C4×D511yescharacteristic
673C22×C3C2×D4×D511yescharacteristic
674C22×C3C2×D4×D511yescharacteristic
675C22×C3C2×Q8×D511yescharacteristic
676C22×C3#414711yescharacteristic
677C22×C3D5×#4111yescharacteristic
678C22×C3#415011yescharacteristic
679C2×D3—54no—
680C2×D3—102no—
681C2×D3—102no—
682C2×D3—102no—
683C2×D3—102no—
684C2×D3—102no—
685C2×D3—102no—
686C3×C4—22no—
687C3×C4—22no—
688C3×C4—41no—
689C3×C4—54no—
690C3×C4—102no—
691C3×C4—201no—
692C3×C4—201no—
693Dic3—22no—
694Dic3—41no—
695Dic3—41no—
696Dic3—54no—
697Dic3—102no—
698Dic3—201no—
699Dic3D5×C22⋊C414yes—
700C2×C5C2×D3×C22⋊C411yescharacteristic
701C2×C5C4×D3×Q811yescharacteristic
702C2×C5#557211yescharacteristic
703C2×C5#563211yescharacteristic
704C2×C5#563311yescharacteristic
705C2×C5#567711yescharacteristic
706C2×C5#572711yescharacteristic
707D5—64no—
708C23—152no—
709C23—152no—
710C23—152no—
711C23—301no—
712C23—301no—
713C23—301no—
714C23—301no—
715C23C22×D3×D511yescharacteristic
716Q8—68no—
717Q8—108no—
718Q8—1516no—
719Q8—308no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—32no—
728C2×C4—32no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—52no—
732C2×C4—52no—
733C2×C4—52no—
734C2×C4—52no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—101no—
744C2×C4—101no—
745C2×C4—101no—
746C2×C4—101no—
747C2×C4—101no—
748C2×C4—101no—
749C2×C4—101no—
750C2×C4—101no—
751C2×C4—152no—
752C2×C4—152no—
753C2×C4—152no—
754C2×C4—152no—
755C2×C4—308no—
756C2×C4—308no—
757C2×C4—308no—
758C2×C4—301no—
759C2×C4—301no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—301no—
763C2×C4D15⋊Q812yescomplemented
764C2×C4C4×D3×D512yes—
765C2×C3C2×D5×C22⋊C411yescharacteristic
766C2×C3C4×Q8×D511yescharacteristic
767C2×C3#6590611yescharacteristic
768C2×C3#6596611yescharacteristic
769C2×C3#6596711yescharacteristic
770C2×C3#6601111yescharacteristic
771C2×C3#6606111yescharacteristic
772D3—104no—
773C5#7661411yescharacteristic, complemented, Sylow
774C22—154no—
775C22—302no—
776C22—302no—
777C22—302no—
778C22—302no—
779C22—302no—
780C22—302no—
781C22C2×D15⋊Q811yescharacteristic
782C22C2×C4×D3×D511yescharacteristic
783C22#9201611yescharacteristic
784C22#9202011yescharacteristic
785C22D3×D4×D511yescharacteristic
786C22D3×D4×D511yescharacteristic
787C22#9202911yescharacteristic
788C4—22no—
789C4—22no—
790C4—34no—
791C4—41no—
792C4—54no—
793C4—62no—
794C4—102no—
795C4—121no—
796C4—121no—
797C4—154no—
798C4—201no—
799C4—201no—
800C4—302no—
801C4—601no—
802C3#1060834511yescharacteristic, complemented, Sylow
803C2—304no—
804C2C4×D15⋊Q811yescharacteristic
805C2#1175286211yescharacteristic
806C2#1175308211yescharacteristic
807C2D3×D5×C22⋊C411yescharacteristic
808C2#1175338111yescharacteristic
809C2#1175343411yescharacteristic
810C2#1175368911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenter#95D3×D5
hypocenterC3×C5Q8×C22⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×C4×#1204C2semidirect
3. C2×#91325C2semidirect
5. C5×#4646C2semidirect
6. C3×#64935C2semidirect
7. #11748935C2semidirect
8. #11748935C2semidirect
14. #11748692C2semidirect
15. #11748672C2semidirect
26. C2×D15⋊Q8C4semidirect
72. #64935D3semidirect
111. #6714Q8semidirect
140. #4646D5semidirect
198. C2×C3×C4×C5C2×Q8semidirect
207. C2×Dic15C2×Q8semidirect
236. #1204C22⋊C4semidirect
360. C2×D15C4×Q8semidirect
457. C2×C4×C5D3×Q8semidirect
562. C2×C3×C4Q8×D5semidirect
671. C3×C5Q8×C22⋊C4semidirect
763. C2×C4D15⋊Q8semidirect
773. C5#76614semidirect
802. C3#10608345semidirect

Maximal subgroups

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

subgroupindex
C22×D15⋊Q82
C2×C4×#12042
C2×#913252
#117507672
C5×#46462
C3×#649352
#117489352
#117488822
#117488812
#117488762
#117488752
#117488632
#117486922
#117486722
#106083453
#766145