Finite Group Databasebeta

← #14326156

Subgroups — #14326156

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×D5×Dic6C211yesmaximal, characteristic
2C2×C4×#1204C211yesmaximal, characteristic, complemented
3C2×#91323C211yesmaximal, characteristic, complemented
4#11750747C211yesmaximal, characteristic, complemented
5C5×#4646C211yesmaximal, characteristic, complemented
6C3×#64955C211yesmaximal, characteristic
7#11748933C211yesmaximal, characteristic, complemented
8#11748933C211yesmaximal, characteristic, complemented
9#11748885C211yesmaximal, characteristic
10#11748884C211yesmaximal, characteristic
11#11748878C211yesmaximal, characteristic
12Dic3×#685C211yesmaximal, characteristic
13#11748738C211yesmaximal, characteristic
14#11748694C211yesmaximal, characteristic, complemented
15#11748692C211yesmaximal, characteristic, complemented
16#10608345—31nomaximal, Hall
17C22×Dic30C2211yescharacteristic
18C22×C5×Dic6C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×#1204C2211yescharacteristic
21C22×#1204C2211yescharacteristic
22C22×D5×Dic3C2211yescharacteristic
23C22×D5×Dic3C2211yescharacteristic
24C2×D5×Dic6—24no—
25C2×D5×Dic6—24no—
26C2×D5×Dic6C418yescomplemented
27C2×#6712C2211yescharacteristic
28C2×C4×Dic15C2211yescharacteristic
29C2×C5×Dic3⋊C4C2211yescharacteristic
30C2×C4×C5×Dic3C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34C2×C3×C4×Dic5C2211yescharacteristic
35C2×Dic3⋊Dic5C2211yescharacteristic
36C2×#6669C2211yescharacteristic
37C2×#6668C2211yescharacteristic
38C2×#6668C2211yescharacteristic
39C2×#6665C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C4×#1204—24no—
44#91323—24no—
45C3×C5×#95C2211yescharacteristic
46#91115C2211yescharacteristic
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C5×C3⋊#95C2211yescharacteristic
51C5×C3⋊#95C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57C22⋊C4×Dic6—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#64955D311yescharacteristic
69#64935—31no—
70#64935—31no—
71#64935—31no—
72#64935—31no—
73C23×C3×D5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C2×Dic30—22no—
82C2×Dic30—22no—
83C2×Dic30C2×C414yes—
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C2×C5×Dic6—22no—
89C2×C5×Dic6—22no—
90C2×C5×Dic6C2×C414yes—
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C2×C3×C4×D5—22no—
95C2×C3×C4×D5—22no—
96C2×C3×C4×D5C2×C414yes—
97C2×#1204—22no—
98C2×#1204—22no—
99C2×#1204C2×C414yes—
100C2×#1204C2×C414yes—
101C2×#1204D414yes—
102C2×#1204D414yes—
103C2×D5×Dic3—22no—
104C2×D5×Dic3—22no—
105C2×D5×Dic3—22no—
106C2×D5×Dic3—22no—
107C2×D5×Dic3C2×C414yes—
108C2×D5×Dic3C2×C414yes—
109D5×Dic6—232no—
110#6712—22no—
111C4×Dic15—22no—
112C5×Dic3⋊C4—22no—
113C4×C5×Dic3—22no—
114C3×#685—22no—
115C3×#685Q814yescomplemented
116C3×C4×Dic5—22no—
117C3×C4×Dic5—22no—
118Dic3⋊Dic5—22no—
119#6669—22no—
120#6668—22no—
121#6668—22no—
122#6665—22no—
123#6665—22no—
124Dic3×Dic5—22no—
125Dic3×Dic5—22no—
126C23×Dic6—51no—
127C2×C4×Dic6—51no—
128C2×C4×Dic6—51no—
129C3×C4×C22⋊C4—51no—
130#5212—51no—
131#4942—51no—
132#4942—51no—
133Dic3×C22⋊C4—51no—
134Dic3×C22⋊C4—51no—
135#4929—51no—
136#4929—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×D5C2×D311yescharacteristic
148C22×Dic10—31no—
149C22×Dic10—31no—
150C22×Dic10—31no—
151C2×C5×C4⋊C4—31no—
152C2×C42×C5—31no—
153C2×#685—31no—
154C2×#685—31no—
155C2×#685C2×D311yescharacteristic
156C2×#685C2×D311yescharacteristic
157C2×C4⋊Dic5—31no—
158C2×#683—31no—
159C2×#683—31no—
160C2×#683—31no—
161C2×#683—31no—
162C2×C4×Dic5—31no—
163C2×C4×Dic5—31no—
164C2×C4×Dic5—31no—
165C2×C4×Dic5C2×D311yescharacteristic
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#3963—31no—
179#3963—31no—
180#3963C2×D311yescharacteristic
181Q8×C22⋊C4—151noSylow
182C23×C3×C5C2411yescharacteristic
183C22×C3×D5—21no—
184C22×C3×D5—21no—
185C22×C3×D5—21no—
186C22×C3×D5—21no—
187C22×C3×D5C22×C412yes—
188C22×C3×D5C2×Q812yes—
189C22×C3×D5#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×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—21no—
207C2×Dic15C22×C412yes—
208C2×Dic15C22×C412yes—
209C2×Dic15C2×D412yes—
210C2×Dic15C2×D412yes—
211Dic30—28no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3—21no—
216C2×C5×Dic3—21no—
217C2×C5×Dic3—21no—
218C2×C5×Dic3—21no—
219C2×C5×Dic3—21no—
220C2×C5×Dic3C22×C412yes—
221C2×C5×Dic3C22×C412yes—
222C2×C5×Dic3C2×D412yes—
223C2×C5×Dic3C2×D412yes—
224C5×Dic6—28no—
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×Dic5C2×D412yes—
232C2×C3×Dic5C2×D412yes—
233C2×C3×Dic5C2×Q812yescomplemented
234C3×C4×D5—28no—
235#1204—28no—
236#1204C22⋊C4116yescomplemented
237D5×Dic3—28no—
238D5×Dic3—28no—
239C23×C3×C4—51no—
240C23×Dic3—51no—
241C23×Dic3—51no—
242C22×Dic6—51no—
243C22×Dic6—51no—
244C22×Dic6—51no—
245C22×Dic6—58no—
246C22×Dic6—104no—
247C22×Dic6—104no—
248C22×Dic6C2×D511yescharacteristic
249C2×C3×C22⋊C4—51no—
250C2×C3×C22⋊C4—51no—
251C2×C3×C42—51no—
252C2×C3×C42—51no—
253C2×#217—51no—
254C2×#217—51no—
255C2×C4⋊Dic3—51no—
256C2×C4⋊Dic3—51no—
257C2×Dic3⋊C4—51no—
258C2×Dic3⋊C4—51no—
259C2×Dic3⋊C4—51no—
260C2×Dic3⋊C4C2×D511yescharacteristic
261C2×C4×Dic3—51no—
262C2×C4×Dic3—51no—
263C2×C4×Dic3—51no—
264C2×C4×Dic3C2×D511yescharacteristic
265C4×Dic6—104no—
266C4×Dic6—104no—
267C3×#95—51no—
268C3×#95C2×D511yescharacteristic
269C3⋊#95—51no—
270C3⋊#95—51no—
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×D5C22×D311yescharacteristic
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×Dic5—31no—
294C22×Dic5C22×D311yescharacteristic
295C22×Dic5C22×D311yescharacteristic
296C22×Dic5C22×D311yescharacteristic
297Q8×D5—632no—
298C2×C4×D5—22no—
299C2×C4×D5—22no—
300C2×C4×D5—34no—
301C2×C4×D5—34no—
302C2×C4×D5—62no—
303C2×C4×D5—62no—
304C2×C4×D5—62no—
305C2×C4×D5—62no—
306C2×C4×D5C4×D314yes—
307C2×Dic10—34no—
308C2×Dic10—34no—
309C2×Dic10—34no—
310C2×Dic10—34no—
311C2×Dic10—34no—
312C2×Dic10—62no—
313C2×Dic10—62no—
314C2×Dic10—62no—
315C2×Dic10—62no—
316C5×C4⋊C4—62no—
317C42×C5—62no—
318#685—22no—
319#685—62no—
320#685—62no—
321#685Dic614yescomplemented
322C4⋊Dic5—62no—
323#683—62no—
324#683—62no—
325#683—62no—
326#683—62no—
327C4×Dic5—22no—
328C4×Dic5—22no—
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—151no—
337#391—151no—
338#391—151no—
339#391—151no—
340#391—151no—
341#380—151no—
342#380—151no—
343#380—151no—
344C4×C22⋊C4—51no—
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×C3×D5—22no—
355C2×C3×D5—22no—
356C2×C3×D5—22no—
357C2×C3×D5—22no—
358C2×C3×D5—22no—
359C2×C3×D5—22no—
360C2×C3×D5C4×Q814yescomplemented
361C3×C4×C5—22no—
362C3×C4×C5—22no—
363C3×C4×C5—41no—
364Dic15—22no—
365Dic15—41no—
366Dic15—41no—
367Dic15C2×C22⋊C414yes—
368C3×Dic5—22no—
369C3×Dic5—41no—
370C3×Dic5C2×C22⋊C414yes—
371C5×Dic3—22no—
372C5×Dic3—41no—
373C5×Dic3—41no—
374C5×Dic3C2×C22⋊C414yes—
375C24×C3—51no—
376C22×C3×C4—51no—
377C22×C3×C4—51no—
378C22×C3×C4—54no—
379C22×C3×C4—51no—
380C22×C3×C4—102no—
381C22×C3×C4—102no—
382C22×C3×C4C22×D511yescharacteristic
383C22×C3×C4C22×D511yescharacteristic
384C22×C3×C4C22×D511yescharacteristic
385C22×Dic3—51no—
386C22×Dic3—51no—
387C22×Dic3—54no—
388C22×Dic3—54no—
389C22×Dic3—51no—
390C22×Dic3—51no—
391C22×Dic3—102no—
392C22×Dic3—102no—
393C22×Dic3—102no—
394C22×Dic3—102no—
395C22×Dic3C22×D511yescharacteristic
396C22×Dic3C22×D511yescharacteristic
397C22×Dic3C22×D511yescharacteristic
398C22×Dic3C22×D511yescharacteristic
399C2×Dic6—22no—
400C2×Dic6—22no—
401C2×Dic6—54no—
402C2×Dic6—54no—
403C2×Dic6—54no—
404C2×Dic6—54no—
405C2×Dic6—54no—
406C2×Dic6—1032no—
407C2×Dic6—102no—
408C2×Dic6—102no—
409C2×Dic6—102no—
410C2×Dic6—102no—
411C2×Dic6C4×D514yes—
412C3×C22⋊C4—54no—
413C3×C22⋊C4—102no—
414C3×C42—102no—
415C3×C42—102no—
416#217—102no—
417#217—102no—
418C4⋊Dic3—102no—
419C4⋊Dic3—102no—
420Dic3⋊C4—22no—
421Dic3⋊C4—102no—
422Dic3⋊C4—102no—
423Dic3⋊C4—102no—
424C4×Dic3—22no—
425C4×Dic3—102no—
426C4×Dic3—102no—
427C4×Dic3—102no—
428C23×C5C23×D311yescharacteristic
429C22×D5—21no—
430C22×D5—21no—
431C22×D5—21no—
432C22×D5—21no—
433C22×D5C2×Dic612yes—
434C22×D5C2×C4×D312yes—
435C22×D5#23512yes—
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×Dic612yescomplemented
457C2×C4×C5C2×C4×D312yes—
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—21no—
462C2×Dic5—21no—
463C2×Dic5—32no—
464C2×Dic5—32no—
465C2×Dic5—32no—
466C2×Dic5—32no—
467C2×Dic5—61no—
468C2×Dic5—61no—
469C2×Dic5—61no—
470C2×Dic5—61no—
471C2×Dic5—61no—
472C2×Dic5—61no—
473C2×Dic5—61no—
474C2×Dic5—61no—
475C2×Dic5C2×Dic612yescomplemented
476C2×Dic5C2×C4×D312yes—
477C2×Dic5D3×D412yes—
478C2×Dic5D3×D412yes—
479C4×D5—28no—
480C4×D5—68no—
481C4×D5—68no—
482Dic10—316no—
483Dic10—68no—
484Dic10—68no—
485C22×Q8—31no—
486C22×Q8—151no—
487C22×Q8—151no—
488C22×Q8—158no—
489C22×Q8—151no—
490C22×Q8—304no—
491C22×Q8—304no—
492C23×C4—51no—
493C23×C4—151no—
494C23×C4—151no—
495C4×Q8—304no—
496C4×Q8—304no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—151no—
499C2×C4⋊C4—151no—
500C2×C4⋊C4—151no—
501C2×C4⋊C4—151no—
502C2×C4⋊C4—151no—
503C2×C22⋊C4—51no—
504C2×C22⋊C4—51no—
505C2×C22⋊C4—151no—
506C2×C22⋊C4—151no—
507C2×C42—31no—
508C2×C42—51no—
509C2×C42—51no—
510C2×C42—151no—
511C2×C42—151no—
512C2×C42—151no—
513#95—31no—
514#95—31no—
515#95—31no—
516#95—51no—
517#95—151no—
518#95—151no—
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
532C3×D5—24no—
533C23×C3—52no—
534C23×C3—52no—
535C23×C3—52no—
536C23×C3—101no—
537C23×C3—101no—
538C23×C3—101no—
539C23×C3—101no—
540C23×C3C23×D511yescharacteristic
541C2×C3×C4—21no—
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—52no—
549C2×C3×C4—52no—
550C2×C3×C4—52no—
551C2×C3×C4—52no—
552C2×C3×C4—108no—
553C2×C3×C4—101no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4—101no—
557C2×C3×C4—101no—
558C2×C3×C4C2×C4×D512yes—
559C2×C3×C4Q8×D512yescomplemented
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—52no—
569C2×Dic3—52no—
570C2×Dic3—52no—
571C2×Dic3—52no—
572C2×Dic3—108no—
573C2×Dic3—101no—
574C2×Dic3—101no—
575C2×Dic3—108no—
576C2×Dic3—101no—
577C2×Dic3—101no—
578C2×Dic3—101no—
579C2×Dic3—101no—
580C2×Dic3—101no—
581C2×Dic3—101no—
582C2×Dic3C2×C4×D512yes—
583C2×Dic3C2×C4×D512yes—
584C2×Dic3D4×D512yes—
585C2×Dic3D4×D512yes—
586Dic6—28no—
587Dic6—516no—
588Dic6—108no—
589Dic6—108no—
590C22×C5C22×Dic611yescharacteristic
591C22×C5C22×C4×D311yescharacteristic
592C22×C5C2×#23511yescharacteristic
593C22×C5C2×D3×D411yescharacteristic
594C22×C5C2×D3×D411yescharacteristic
595C22×C5#101011yescharacteristic
596C22×C5#101011yescharacteristic
597C2×D5—22no—
598C2×D5—22no—
599C2×D5—22no—
600C2×D5—22no—
601C2×D5—22no—
602C2×D5—22no—
603C2×D5C4×Dic614yescomplemented
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—62no—
615Dic5—121no—
616Dic5—121no—
617Dic5D3×C22⋊C414yes—
618C24—51no—
619C2×Q8—34no—
620C2×Q8—62no—
621C2×Q8—62no—
622C2×Q8—154no—
623C2×Q8—154no—
624C2×Q8—154no—
625C2×Q8—154no—
626C2×Q8—154no—
627C2×Q8—302no—
628C2×Q8—302no—
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—54no—
639C22×C4—51no—
640C22×C4—102no—
641C22×C4—102no—
642C22×C4—154no—
643C22×C4—154no—
644C22×C4—151no—
645C22×C4—151no—
646C22×C4—151no—
647C22×C4—151no—
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—302no—
657C4⋊C4—302no—
658C4⋊C4—302no—
659C4⋊C4—302no—
660C4⋊C4—302no—
661C22⋊C4—54no—
662C22⋊C4—102no—
663C22⋊C4—302no—
664C22⋊C4—302no—
665C42—62no—
666C42—102no—
667C42—102no—
668C42—302no—
669C42—302no—
670C42—302no—
671C3×C5Q8×C22⋊C411yescharacteristic, complemented, Hall
672C22×C3—54no—
673C22×C3—102no—
674C22×C3—102no—
675C22×C3—102no—
676C22×C3—102no—
677C22×C3—102no—
678C22×C3—102no—
679C22×C3C22×C4×D511yescharacteristic
680C22×C3C2×D4×D511yescharacteristic
681C22×C3C2×D4×D511yescharacteristic
682C22×C3C2×Q8×D511yescharacteristic
683C22×C3#414711yescharacteristic
684C22×C3D5×#4111yescharacteristic
685C22×C3#415011yescharacteristic
686C3×C4—22no—
687C3×C4—22no—
688C3×C4—41no—
689C3×C4—54no—
690C3×C4—102no—
691C3×C4—201no—
692Dic3—22no—
693Dic3—41no—
694Dic3—41no—
695Dic3—54no—
696Dic3—102no—
697Dic3—201no—
698Dic3—201no—
699Dic3D5×C22⋊C414yes—
700C2×C5C2×C4×Dic611yescharacteristic
701C2×C5C2×D3×C22⋊C411yescharacteristic
702C2×C5#551611yescharacteristic
703C2×C5D4×Dic611yescharacteristic
704C2×C5D4×Dic611yescharacteristic
705C2×C5#555211yescharacteristic
706C2×C5#555211yescharacteristic
707D5—24no—
708C23—52no—
709C23—52no—
710C23—52no—
711C23—101no—
712C23—101no—
713C23—101no—
714C23—101no—
715C23C22×D3×D511yescharacteristic
716Q8—68no—
717Q8—1516no—
718Q8—308no—
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—108no—
744C2×C4—101no—
745C2×C4—101no—
746C2×C4—101no—
747C2×C4—101no—
748C2×C4—101no—
749C2×C4—152no—
750C2×C4—152no—
751C2×C4—152no—
752C2×C4—152no—
753C2×C4—308no—
754C2×C4—308no—
755C2×C4—301no—
756C2×C4—301no—
757C2×C4—301no—
758C2×C4—301no—
759C2×C4—301no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—301no—
763C2×C4D5×Dic612yescomplemented
764C2×C4C4×D3×D512yes—
765C2×C3—104no—
766C2×C3C2×D5×C22⋊C411yescharacteristic
767C2×C3C4×Q8×D511yescharacteristic
768C2×C3#6590611yescharacteristic
769C2×C3#6596611yescharacteristic
770C2×C3#6596711yescharacteristic
771C2×C3#6601111yescharacteristic
772C2×C3#6606111yescharacteristic
773C5C22⋊C4×Dic611yescharacteristic, complemented, Sylow
774C22—54no—
775C22—102no—
776C22—102no—
777C22—102no—
778C22—102no—
779C22—102no—
780C22—102no—
781C22C2×D5×Dic611yescharacteristic
782C22C2×C4×D3×D511yescharacteristic
783C22D5×#23511yescharacteristic
784C22#9202011yescharacteristic
785C22D3×D4×D511yescharacteristic
786C22D3×D4×D511yescharacteristic
787C22#9202811yescharacteristic
788C4—22no—
789C4—22no—
790C4—34no—
791C4—41no—
792C4—54no—
793C4—62no—
794C4—102no—
795C4—121no—
796C4—121no—
797C4—154no—
798C4—201no—
799C4—302no—
800C4—601no—
801C4—601no—
802C3#1060834511yescharacteristic, complemented, Sylow
803C2—104no—
804C2C4×D5×Dic611yescharacteristic
805C2#1175286011yescharacteristic
806C2#1175286311yescharacteristic
807C2D3×D5×C22⋊C411yescharacteristic
808C2#1175339711yescharacteristic
809C2#1175342811yescharacteristic
810C2#1175342911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
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×#91323C2semidirect
4. #11750747C2semidirect
5. C5×#4646C2semidirect
7. #11748933C2semidirect
8. #11748933C2semidirect
14. #11748694C2semidirect
15. #11748692C2semidirect
26. C2×D5×Dic6C4semidirect
115. C3×#685Q8semidirect
140. #4646D5semidirect
198. C2×C3×C4×C5C2×Q8semidirect
233. C2×C3×Dic5C2×Q8semidirect
236. #1204C22⋊C4semidirect
321. #685Dic6semidirect
360. C2×C3×D5C4×Q8semidirect
456. C2×C4×C5C2×Dic6semidirect
475. C2×Dic5C2×Dic6semidirect
559. C2×C3×C4Q8×D5semidirect
603. C2×D5C4×Dic6semidirect
671. C3×C5Q8×C22⋊C4semidirect
763. C2×C4D5×Dic6semidirect
773. C5C22⋊C4×Dic6semidirect
802. C3#10608345semidirect

Maximal subgroups

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

subgroupindex
C22×D5×Dic62
C2×C4×#12042
C2×#913232
#117507472
C5×#46462
C3×#649552
#117489332
#117488852
#117488842
#117488782
Dic3×#6852
#117487382
#117486942
#117486922
#106083453
C22⋊C4×Dic65