Finite Group Databasebeta

← #14418633

Subgroups — #14418633

Order 1920.

696 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752596C211yesmaximal, characteristic
2#11750929C211yesmaximal, characteristic, complemented
3C5×#4831C211yesmaximal, characteristic, complemented
4C3×#65128C211yesmaximal, characteristic
5#11748051C211yesmaximal, characteristic
6#11747825C211yesmaximal, characteristic, complemented
7#11747647C211yesmaximal, characteristic
8#11747596C211yesmaximal, characteristic
9D5×#815C211yesmaximal, characteristic
10#11747569C211yesmaximal, characteristic, complemented
11#11747567C211yesmaximal, characteristic, complemented
12#11747567C211yesmaximal, characteristic, complemented
13#11746974C211yesmaximal, characteristic
14#11746865C211yesmaximal, characteristic, complemented
15#11746858C211yesmaximal, characteristic, complemented
16#10611690—31nomaximal, Hall
17C4×Dic30C2211yescharacteristic
18C4×C5×Dic6C2211yescharacteristic
19C2×C3×#676C2211yescharacteristic
20C2×C3×C8×D5C2211yescharacteristic
21C3×#4018C2211yescharacteristic
22C4×#1204C2211yescharacteristic
23C4×#1204C2211yescharacteristic
24#91431C411yescharacteristic
25#91430C411yescharacteristic
26#91422C411yescharacteristic
27#91421C411yescharacteristic
28C4×D5×Dic3C2211yescharacteristic
29#91357C2211yescharacteristic
30#91335C411yescharacteristic
31#91334C411yescharacteristic
32#91329C411yescharacteristic
33#91328C411yescharacteristic
34C2×#6649C2211yescharacteristic
35C2×D5×C3⋊C8C2211yescharacteristic
36C3×C5×C4⋊C8C2211yescharacteristic
37#91099C2211yescharacteristic
38#91098C2211yescharacteristic
39#91098C2211yescharacteristic
40C8×Dic15C2211yescharacteristic
41#91087C2211yescharacteristic
42C5×#815C2211yescharacteristic
43C5×#815C2211yescharacteristic
44C5×Dic3⋊C8C2211yescharacteristic
45C5×Dic3⋊C8C2211yescharacteristic
46C4×C5×C3⋊C8C2211yescharacteristic
47C3×#3946C2211yescharacteristic
48C3×#3946C2211yescharacteristic
49C3×C4⋊#168C2211yescharacteristic
50Dic3⋊#168C2211yescharacteristic
51Dic3⋊#168C2211yescharacteristic
52#90983C2211yescharacteristic
53#90983C2211yescharacteristic
54#90954C2211yescharacteristic
55#90954C2211yescharacteristic
56#90953C2211yescharacteristic
57#90952C2211yescharacteristic
58Dic3×#168C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic
60#79077—51nomaximal, Hall
61#65912—31no—
62C5×#446—31no—
63#65313—31no—
64#65128—31no—
65#65128D311yescharacteristic
66#65126—31no—
67#65120—31no—
68#65117—31no—
69#65117—31no—
70#64997—31no—
71D5×#97—31no—
72#64990—31no—
73#64990—31no—
74#64978—31no—
75#64968—31no—
76C2×Dic30C2×C411yescharacteristic
77C2×C5×Dic6C2×C411yescharacteristic
78C2×C3×C4×D5C2311yescharacteristic
79C2×#1204C2×C411yescharacteristic
80C2×#1204C2×C411yescharacteristic
81C2×D5×Dic3C2×C411yescharacteristic
82C2×D5×Dic3C2×C411yescharacteristic
83C2×C3×C5×C8C2311yescharacteristic
84C2×C3×C5×C8C2311yescharacteristic
85C3×C42×C5C2311yescharacteristic
86C4⋊Dic15C2×C411yescharacteristic
87#6712C2×C411yescharacteristic
88#6712C2×C411yescharacteristic
89C4×Dic15C2311yescharacteristic
90C4×Dic15C2311yescharacteristic
91C2×C3⋊#168C2311yescharacteristic
92C2×C3⋊#168C2311yescharacteristic
93C5×C4⋊Dic3C2×C411yescharacteristic
94C5×Dic3⋊C4C2×C411yescharacteristic
95C5×Dic3⋊C4C2×C411yescharacteristic
96C4×C5×Dic3C2311yescharacteristic
97C4×C5×Dic3C2311yescharacteristic
98C2×C5×C3⋊C8C2311yescharacteristic
99C2×C5×C3⋊C8C2311yescharacteristic
100C3×#685C2×C411yescharacteristic
101C3×#685C2×C411yescharacteristic
102C3×#683C2×C411yescharacteristic
103C3×#683C2×C411yescharacteristic
104C3×C4×Dic5C2311yescharacteristic
105C2×C3×#168C2311yescharacteristic
106C2×C3×#168C2311yescharacteristic
107C3×#676—22no—
108C3×C8×D5—22no—
109Dic3⋊Dic5C2×C411yescharacteristic
110Dic3⋊Dic5C2×C411yescharacteristic
111#6669C2×C411yescharacteristic
112#6669C2×C411yescharacteristic
113#6668C2×C411yescharacteristic
114#6668C2×C411yescharacteristic
115#6668C2×C411yescharacteristic
116#6668C2×C411yescharacteristic
117#6665C2×C411yescharacteristic
118#6665C2×C411yescharacteristic
119Dic3×Dic5C2×C411yescharacteristic
120Dic3×Dic5C2×C411yescharacteristic
121#6649—22no—
122D5×C3⋊C8Q814yescomplemented
123#5517—51no—
124C3×#424—51no—
125#5122—51no—
126#5118—51no—
127#5102—51no—
128C2×#815—51no—
129#4997—51no—
130#4831—51no—
131#4831—51no—
132#4831—51no—
133#4831D511yescharacteristic, complemented
134#4828—51no—
135#4828—51no—
136#4828—51no—
137#4828—51no—
138C4×C5×Q8—31no—
139#4092—31no—
140#4090—31no—
141C2×#676—31no—
142C2×#676C2×D311yescharacteristic
143C2×C8×D5—31no—
144C2×C8×D5C2×D311yescharacteristic
145#4043—31no—
146#4042—31no—
147#4042—31no—
148#4035—31no—
149#4035—31no—
150#4034—31no—
151#4018—31no—
152#4018C2×D311yescharacteristic
153C42×D5—31no—
154C4×Dic10—31no—
155C4×Dic10—31no—
156C4×Dic10—31no—
157C5×C4⋊C8—31no—
158C5×C4⋊C8—31no—
159C5×C4⋊C8C2×D311yescharacteristic
160C5×#97—31no—
161C5×#97—31no—
162C4×C5×C8—31no—
163#3947—31no—
164#3947—31no—
165#3947—31no—
166#3947—31no—
167#3946—31no—
168#3946—31no—
169#3946—31no—
170#3946—31no—
171#3946C2×D311yescharacteristic
172#3946C2×D311yescharacteristic
173C8×Dic5—31no—
174C8×Dic5—31no—
175C4⋊#168—31no—
176C4⋊#168—31no—
177C4⋊#168C2×D311yescharacteristic
178#3935—31no—
179#3935—31no—
180C4×#168—31no—
181#2961—151noSylow
182C22×C3×D5C22×C411yescharacteristic
183C2×C3×C4×C5C22×C411yescharacteristic
184C2×C3×C4×C5C22×C411yescharacteristic
185C2×C3×C4×C5C2411yescharacteristic
186C2×Dic15C22×C411yescharacteristic
187C2×Dic15C22×C411yescharacteristic
188C2×Dic15C22×C411yescharacteristic
189C2×Dic15C22×C411yescharacteristic
190Dic30—41no—
191C2×C5×Dic3C22×C411yescharacteristic
192C2×C5×Dic3C22×C411yescharacteristic
193C2×C5×Dic3C22×C411yescharacteristic
194C2×C5×Dic3C22×C411yescharacteristic
195C5×Dic6—41no—
196C2×C3×Dic5C22×C411yescharacteristic
197C2×C3×Dic5C22×C411yescharacteristic
198C2×C3×Dic5C22×C411yescharacteristic
199C3×C4×D5C2×Q812yes—
200C3×C4×D5#4112yes—
201#1204—41no—
202#1204—41no—
203D5×Dic3—41no—
204D5×Dic3—41no—
205C3×C5×C8—21no—
206C3×C5×C8—21no—
207C3⋊#168—21no—
208C3⋊#168C2×Q812yes—
209C3×#168—21no—
210C3×#168—21no—
211C5×C3⋊C8—21no—
212C5×C3⋊C8C2×Q812yes—
213C2×C3×M16—51no—
214C22×C3×C8—51no—
215C3×#117—51no—
216#926—51no—
217C2×C4×Dic3—51no—
218C2×#208—51no—
219C22×C3⋊C8—51no—
220#890—51no—
221#890—51no—
222#888—51no—
223#888—51no—
224#878—51no—
225#878—51no—
226#878—51no—
227#878—51no—
228C4×Dic6—51no—
229C4×Dic6—51no—
230C4×Dic6—51no—
231C4×Dic6C2×D511yescharacteristic
232C3×C4⋊C8—51no—
233C3×C4⋊C8—51no—
234C3×C4⋊C8—51no—
235C3×C4⋊C8C2×D511yescharacteristic
236#815—51no—
237#815—51no—
238#815—51no—
239#815—51no—
240#815C2×D511yescharacteristic
241#815C2×D511yescharacteristic
242Dic3⋊C8—51no—
243Dic3⋊C8—51no—
244Dic3⋊C8—51no—
245Dic3⋊C8—51no—
246Dic3⋊C8—51no—
247Dic3⋊C8—51no—
248Dic3⋊C8C2×D511yescharacteristic
249Dic3⋊C8C2×D511yescharacteristic
250C8×Dic3—51no—
251C8×Dic3—51no—
252#803—51no—
253#803—51no—
254C4×C3⋊C8—51no—
255C4×C3⋊C8C2×D511yescharacteristic
256C2×C5×Q8—31no—
257C2×C4×D5—31no—
258C2×C4×D5—31no—
259C2×C4×D5C22×D311yescharacteristic
260C2×Dic10—31no—
261C2×Dic10—31no—
262C2×Dic10—31no—
263C2×C5×C8—31no—
264C2×C5×C8—31no—
265C2×C5×C8C22×D311yescharacteristic
266C2×C5×C8C22×D311yescharacteristic
267C5×C4⋊C4—31no—
268C5×C4⋊C4—31no—
269C5×C4⋊C4—31no—
270C42×C5—31no—
271C42×C5—31no—
272C42×C5C22×D311yescharacteristic
273#685—31no—
274#685—31no—
275#685C4×D311yescharacteristic
276#685C4×D311yescharacteristic
277C4⋊Dic5—31no—
278C4⋊Dic5—31no—
279C4⋊Dic5—31no—
280#683—31no—
281#683—31no—
282#683—31no—
283#683—31no—
284#683—31no—
285#683—31no—
286#683—31no—
287#683—31no—
288#683C4×D311yescharacteristic
289#683C4×D311yescharacteristic
290C4×Dic5—31no—
291C4×Dic5—31no—
292C4×Dic5—31no—
293C4×Dic5—31no—
294C4×Dic5C22×D311yescharacteristic
295C2×#168—31no—
296C2×#168—31no—
297C2×#168C22×D311yescharacteristic
298C2×#168C22×D311yescharacteristic
299#676—22no—
300#676—62no—
301C8×D5—22no—
302C8×D5—34no—
303#533—151no—
304#446—31no—
305#446—151no—
306#446—151no—
307#446—151no—
308#446—151no—
309#446—151no—
310#446—151no—
311#446—151no—
312#424—51no—
313#424—151no—
314#423—151no—
315#405—151no—
316#405—151no—
317C2×#97—151no—
318C22×C3×C5C23×C411yescharacteristic
319C2×C3×D5—21no—
320C2×C3×D5—21no—
321C2×C3×D5C4×Q812yes—
322C3×C4×C5—21no—
323C3×C4×C5—21no—
324C3×C4×C5C22×Q811yescharacteristic
325C3×C4×C5C2×#4111yescharacteristic
326Dic15—21no—
327Dic15—21no—
328Dic15—21no—
329Dic15—21no—
330C3×Dic5—21no—
331C3×Dic5—21no—
332C3×Dic5C4×Q812yes—
333C5×Dic3—21no—
334C5×Dic3—21no—
335C5×Dic3—21no—
336C5×Dic3—21no—
337C22×C3×C4—51no—
338C22×Dic3—51no—
339C22×Dic3—51no—
340C2×Dic6—51no—
341C2×Dic6—51no—
342C2×Dic6—51no—
343C2×Dic6C4×D511yescharacteristic
344C3×M16—102no—
345C2×C3×C8—51no—
346C2×C3×C8—51no—
347C2×C3×C8—102no—
348C2×C3×C8C22×D511yescharacteristic
349C2×C3×C8C22×D511yescharacteristic
350C3×C4⋊C4—51no—
351C3×C4⋊C4—51no—
352C3×C22⋊C4—51no—
353C3×C22⋊C4—51no—
354C3×C42—51no—
355C3×C42C22×D511yescharacteristic
356#217—51no—
357#217—51no—
358C4⋊Dic3—51no—
359C4⋊Dic3—51no—
360C4⋊Dic3—51no—
361C4⋊Dic3—51no—
362C4⋊Dic3—51no—
363C4⋊Dic3C4×D511yescharacteristic
364Dic3⋊C4—51no—
365Dic3⋊C4—51no—
366Dic3⋊C4—51no—
367Dic3⋊C4—51no—
368Dic3⋊C4—51no—
369Dic3⋊C4—51no—
370Dic3⋊C4C4×D511yescharacteristic
371Dic3⋊C4C4×D511yescharacteristic
372C4×Dic3—51no—
373C4×Dic3—51no—
374C4×Dic3—51no—
375C4×Dic3—51no—
376C4×Dic3C22×D511yescharacteristic
377C4×Dic3C22×D511yescharacteristic
378#208—102no—
379C2×C3⋊C8—51no—
380C2×C3⋊C8—54no—
381C2×C3⋊C8—51no—
382C2×C3⋊C8C22×D511yescharacteristic
383C2×C3⋊C8C22×D511yescharacteristic
384C22×D5C2×C4×D311yescharacteristic
385C5×Q8—121no—
386C2×C4×C5—31no—
387C2×C4×C5—31no—
388C2×C4×C5—31no—
389C2×C4×C5—31no—
390C2×C4×C5C2×C4×D311yescharacteristic
391C2×C4×C5C2×C4×D311yescharacteristic
392C2×C4×C5C23×D311yescharacteristic
393C2×Dic5—31no—
394C2×Dic5—31no—
395C2×Dic5—31no—
396C2×Dic5—31no—
397C2×Dic5C2×C4×D311yescharacteristic
398C2×Dic5C2×C4×D311yescharacteristic
399C2×Dic5C2×C4×D311yescharacteristic
400C4×D5—121no—
401C4×D5—121no—
402C4×D5#23712yes—
403C4×D5D3×Q812yes—
404Dic10—121no—
405Dic10—121no—
406Dic10—121no—
407C5×C8—21no—
408C5×C8—21no—
409C5×C8—32no—
410C5×C8—61no—
411#168—21no—
412#168—21no—
413#168—32no—
414#168—61no—
415C2×M16—51no—
416C2×M16—151no—
417C22×C8—51no—
418C22×C8—151no—
419C4⋊Q8—151no—
420C4⋊Q8—151no—
421#125—151no—
422#125—151no—
423C22⋊Q8—151no—
424C22⋊Q8—151no—
425C22⋊Q8—151no—
426C22⋊Q8—151no—
427C4×Q8—31no—
428C4×Q8—151no—
429C4×Q8—151no—
430C4×Q8—151no—
431#117—51no—
432#117—151no—
433C2×C42—151no—
434C4⋊C8—31no—
435C4⋊C8—31no—
436C4⋊C8—51no—
437C4⋊C8—51no—
438C4⋊C8—51no—
439C4⋊C8—151no—
440C4⋊C8—151no—
441C4⋊C8—151no—
442C4⋊C8—151no—
443C4⋊C8—151no—
444C4⋊C8—151no—
445C4⋊C8D3×D511yescharacteristic
446#97—31no—
447#97—31no—
448#97—151no—
449#97—151no—
450#97—151no—
451#97—151no—
452#97—151no—
453#97—151no—
454C4×C8—31no—
455C4×C8—151no—
456C4×C8—151no—
457C4×C8—151no—
458C2×C3×C5C2×C4×Q811yescharacteristic
459C2×C3×C5#56811yescharacteristic
460C2×C3×C5#56811yescharacteristic
461C3×D5—22no—
462C23×C3—51no—
463C2×C3×C4—51no—
464C2×C3×C4—52no—
465C2×C3×C4—52no—
466C2×C3×C4—51no—
467C2×C3×C4—51no—
468C2×C3×C4C2×C4×D511yescharacteristic
469C2×C3×C4C2×C4×D511yescharacteristic
470C2×C3×C4C23×D511yescharacteristic
471C2×Dic3—51no—
472C2×Dic3—51no—
473C2×Dic3—51no—
474C2×Dic3—51no—
475C2×Dic3—201no—
476C2×Dic3—201no—
477C2×Dic3C2×C4×D511yescharacteristic
478C2×Dic3C2×C4×D511yescharacteristic
479C2×Dic3C2×C4×D511yescharacteristic
480C2×Dic3C2×C4×D511yescharacteristic
481Dic6—41no—
482Dic6—201no—
483Dic6—201no—
484Dic6—201no—
485C3×C8—21no—
486C3×C8—21no—
487C3×C8—101no—
488C3×C8—101no—
489C3⋊C8—21no—
490C3⋊C8—52no—
491C3⋊C8—101no—
492C3⋊C8Q8×D512yes—
493C22×C5C22×C4×D311yescharacteristic
494C2×D5—21no—
495C2×D5—21no—
496C2×D5#88712yes—
497C4×C5—21no—
498C4×C5—21no—
499C4×C5—61no—
500C4×C5—61no—
501C4×C5—61no—
502C4×C5—61no—
503C4×C5C2×#23711yescharacteristic
504C4×C5C2×D3×Q811yescharacteristic
505Dic5—21no—
506Dic5—21no—
507Dic5—61no—
508Dic5—61no—
509Dic5—61no—
510Dic5—61no—
511Dic5#88712yes—
512C2×Q8—31no—
513C2×Q8—151no—
514C2×Q8—151no—
515C2×Q8—151no—
516C22×C4—51no—
517C22×C4—151no—
518C22×C4—151no—
519M16—102no—
520M16—302no—
521C2×C8—31no—
522C2×C8—31no—
523C2×C8—51no—
524C2×C8—51no—
525C2×C8—102no—
526C2×C8—154no—
527C2×C8—151no—
528C2×C8—151no—
529C2×C8C2×D3×D511yescharacteristic
530C2×C8C2×D3×D511yescharacteristic
531C4⋊C4—31no—
532C4⋊C4—31no—
533C4⋊C4—31no—
534C4⋊C4—51no—
535C4⋊C4—51no—
536C4⋊C4—151no—
537C4⋊C4—151no—
538C4⋊C4—151no—
539C4⋊C4—151no—
540C4⋊C4—151no—
541C4⋊C4—151no—
542C4⋊C4—151no—
543C4⋊C4—151no—
544C4⋊C4—151no—
545C4⋊C4—151no—
546C4⋊C4—151no—
547C22⋊C4—51no—
548C22⋊C4—51no—
549C22⋊C4—151no—
550C22⋊C4—151no—
551C42—31no—
552C42—31no—
553C42—51no—
554C42—151no—
555C42—151no—
556C42—151no—
557C42—151no—
558C42C2×D3×D511yescharacteristic
559C3×C5#296111yescharacteristic, complemented, Hall
560C22×C3—52no—
561C22×C3—101no—
562C22×C3—101no—
563C22×C3C22×C4×D511yescharacteristic
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—52no—
567C3×C4—101no—
568C3×C4—101no—
569C3×C4C2×Q8×D511yescharacteristic
570C3×C4D5×#4111yescharacteristic
571Dic3—21no—
572Dic3—21no—
573Dic3—21no—
574Dic3—21no—
575Dic3—101no—
576Dic3—101no—
577Dic3—101no—
578Dic3—101no—
579C2×C5C2×#88711yescharacteristic
580C2×C5#575011yescharacteristic
581C2×C5#575011yescharacteristic
582D5—22no—
583C23—51no—
584Q8—121no—
585Q8—601no—
586Q8—601no—
587Q8—601no—
588C2×C4—31no—
589C2×C4—31no—
590C2×C4—31no—
591C2×C4—31no—
592C2×C4—51no—
593C2×C4—52no—
594C2×C4—52no—
595C2×C4—51no—
596C2×C4—51no—
597C2×C4—151no—
598C2×C4—151no—
599C2×C4—151no—
600C2×C4—151no—
601C2×C4—601no—
602C2×C4—601no—
603C2×C4C4×D3×D511yescharacteristic
604C2×C4C4×D3×D511yescharacteristic
605C2×C4C22×D3×D511yescharacteristic
606C8—21no—
607C8—21no—
608C8—32no—
609C8—61no—
610C8—101no—
611C8—101no—
612C8—152no—
613C8—301no—
614C2×C3—102no—
615C2×C3C4×Q8×D511yescharacteristic
616C2×C3#6607911yescharacteristic
617C2×C3#6608411yescharacteristic
618C5#7907711yescharacteristic, complemented, Sylow
619C22—52no—
620C22—101no—
621C22—101no—
622C22C2×C4×D3×D511yescharacteristic
623C4—21no—
624C4—21no—
625C4—52no—
626C4—61no—
627C4—61no—
628C4—61no—
629C4—61no—
630C4—101no—
631C4—101no—
632C4—301no—
633C4—301no—
634C4—301no—
635C4—301no—
636C4D5×#23711yescharacteristic
637C4D3×Q8×D511yescharacteristic
638C3#1061169011yescharacteristic, complemented, Sylow
639C2—102no—
640C2D5×#88711yescharacteristic
641C2#1175395111yescharacteristic
642C2#1175401811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C8C22
prime radicalC22×C3×D5C22×C4
cosocleC2×C3×C4×C5C24
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#2961
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750929C2semidirect
3. C5×#4831C2semidirect
6. #11747825C2semidirect
10. #11747569C2semidirect
11. #11747567C2semidirect
12. #11747567C2semidirect
14. #11746865C2semidirect
15. #11746858C2semidirect
122. D5×C3⋊C8Q8semidirect
133. #4831D5semidirect
559. C3×C5#2961semidirect
618. C5#79077semidirect
638. C3#10611690semidirect

Maximal subgroups

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

subgroupindex
#117525962
#117509292
C5×#48312
C3×#651282
#117480512
#117478252
#117476472
#117475962
D5×#8152
#117475692
#117475672
#117469742
#117468652
#117468582
#106116903
#790775