Finite Group Databasebeta

← #14329029

Subgroups — #14329029

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91828C211yesmaximal, characteristic
2C2×#91770C211yesmaximal, characteristic, complemented
3C2×#91766C211yesmaximal, characteristic, complemented
4C3×C5×#390C211yesmaximal, characteristic, complemented
5#11751321C211yesmaximal, characteristic, complemented
6#11751091C211yesmaximal, characteristic, complemented
7#11751077C211yesmaximal, characteristic, complemented
8#11751058C211yesmaximal, characteristic, complemented
9#11751058C211yesmaximal, characteristic, complemented
10#11751057C211yesmaximal, characteristic, complemented
11#11751045C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic15C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic15C211yesmaximal, characteristic, complemented
14C4×#6714C211yesmaximal, characteristic, complemented
15C4×#6712C211yesmaximal, characteristic, complemented
16#10608036—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C23×Dic15C2211yescharacteristic
21C23×Dic15C2211yescharacteristic
22C22×C4×D15C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C42×C5C2211yescharacteristic
29C2×#6719C2211yescharacteristic
30C2×#6719C2211yescharacteristic
31C2×#6719C2211yescharacteristic
32C2×#6719C2211yescharacteristic
33#91828C418yescomplemented
34C2×#6714C2211yescharacteristic
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic
38C2×#6712C2211yescharacteristic
39C2×#6712C2211yescharacteristic
40C2×#6712C2211yescharacteristic
41C2×#6712C2211yescharacteristic
42C2×C4×Dic15C2211yescharacteristic
43C2×C4×Dic15C2211yescharacteristic
44C2×C4×Dic15C2211yescharacteristic
45C2×C4×Dic15C2211yescharacteristic
46C2×C4×Dic15C2211yescharacteristic
47#91770—24no—
48#91766—24no—
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53#91115C2211yescharacteristic
54#91115C2211yescharacteristic
55#76305—51nomaximal, Hall
56C2×#4085—31no—
57C2×#4027—31no—
58C2×#4023—31no—
59C5×#390D311yescharacteristic, complemented
60#65509—31no—
61#65279—31no—
62#65261—31no—
63#65246—31no—
64#65246—31no—
65#65245—31no—
66#65233—31no—
67C22⋊C4×Dic5—31no—
68C22⋊C4×Dic5—31no—
69C4×#685—31no—
70C4×#683—31no—
71C24×C3×C5C2311yescharacteristic
72C24×C3×C5C2311yescharacteristic
73C23×D15C2311yescharacteristic
74C2×C3×C5×D4—41no—
75C2×C3×C5×D4—41no—
76C2×C3×C5×D4C2×C414yescomplemented
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×#1220—22no—
83C2×#1220—22no—
84C2×#1220—41no—
85C2×#1220—41no—
86C2×#1220C2×C414yes—
87C2×#1220C2×C414yescomplemented
88C22×Dic15—22no—
89C22×Dic15—22no—
90C22×Dic15—22no—
91C22×Dic15—22no—
92C22×Dic15—41no—
93C22×Dic15C2×C414yescomplemented
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C2×C4×D15—22no—
102C2×C4×D15—22no—
103C2×C4×D15—41no—
104C3×C5×C4⋊C4—41no—
105C3×C5×C22⋊C4—22no—
106C3×C5×C22⋊C4—22no—
107C3×C5×C22⋊C4—22no—
108C3×C5×C22⋊C4—22no—
109C3×C42×C5—41no—
110#6719—22no—
111#6719—22no—
112#6719—41no—
113#6719C2×C414yescomplemented
114#6714—22no—
115#6714—22no—
116#6714—41no—
117#6714C2×C414yescomplemented
118#6712—22no—
119#6712—41no—
120#6712C2×C414yescomplemented
121#6712D414yescomplemented
122C4×Dic15—22no—
123C4×Dic15—22no—
124C4×Dic15—22no—
125C4×Dic15—22no—
126C4×Dic15—41no—
127C2×#939—51no—
128C2×#67⋊C4—51no—
129C2×#877—51no—
130C3×#390D511yescharacteristic, complemented
131#5220—51no—
132#4990—51no—
133#4976—51no—
134#4957—51no—
135#4957—51no—
136#4956—51no—
137#4944—51no—
138Dic3×C22⋊C4—51no—
139Dic3×C22⋊C4—51no—
140C4×(C2×D3)⋊C4—51no—
141C4×Dic3⋊C4—51no—
142C22×C5×D4C2×D311yescharacteristic
143C22×C22⋊D5—31no—
144C22×C22⋊D5—31no—
145C23×Dic5—31no—
146C23×Dic5—31no—
147C22×C4×D5—31no—
148C2×C5×C4⋊C4C2×D311yescharacteristic
149C2×C5×C22⋊C4C2×D311yescharacteristic
150C2×C5×C22⋊C4C2×D311yescharacteristic
151C2×C5×C22⋊C4C2×D311yescharacteristic
152C2×C5×C22⋊C4C2×D311yescharacteristic
153C2×C42×C5C2×D311yescharacteristic
154C2×C22⋊Dic5—31no—
155C2×C22⋊Dic5—31no—
156C2×C22⋊Dic5—31no—
157C2×C22⋊Dic5—31no—
158#4085—38no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—31no—
162C2×#685—31no—
163C2×#683—31no—
164C2×#683—31no—
165C2×#683—31no—
166C2×#683—31no—
167C2×C4×Dic5—31no—
168C2×C4×Dic5—31no—
169C2×C4×Dic5—31no—
170C2×C4×Dic5—31no—
171C2×C4×Dic5—31no—
172#4027—64no—
173#4023—64no—
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#3963—31no—
179#3963—31no—
180#2363—151noSylow
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5C22×C412yes—
194C23×C3×C5C22×C412yes—
195C23×C3×C5C2411yescharacteristic
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15—21no—
201C22×D15—21no—
202C22×D15C22×C412yes—
203C3×C5×D4—44no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5C22×C412yes—
217C2×C3×C4×C5C2×D412yes—
218C2×C3×C4×C5#4112yes—
219#1220—28no—
220#1220—44no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—28no—
230C2×Dic15—21no—
231C2×Dic15—21no—
232C2×Dic15—21no—
233C2×Dic15—21no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—44no—
237C2×Dic15C22×C412yes—
238C2×Dic15C22×C412yes—
239C2×Dic15C22×C412yes—
240C2×Dic15C2×D412yes—
241C2×Dic15C2×D412yes—
242C2×Dic15#4112yes—
243C2×Dic15#4112yes—
244C4×D15—44no—
245C22×C3×D4C2×D511yescharacteristic
246C22×#67—51no—
247C22×#67—51no—
248C23×Dic3—51no—
249C23×Dic3—51no—
250C22×C4×D3—51no—
251C2×C3×C4⋊C4C2×D511yescharacteristic
252C2×C3×C22⋊C4C2×D511yescharacteristic
253C2×C3×C22⋊C4C2×D511yescharacteristic
254C2×C3×C22⋊C4C2×D511yescharacteristic
255C2×C3×C22⋊C4C2×D511yescharacteristic
256C2×C3×C42C2×D511yescharacteristic
257C2×#217—51no—
258C2×#217—51no—
259C2×#217—51no—
260C2×#217—51no—
261#939—58no—
262C2×(C2×D3)⋊C4—51no—
263C2×(C2×D3)⋊C4—51no—
264C2×(C2×D3)⋊C4—51no—
265C2×(C2×D3)⋊C4—51no—
266C2×Dic3⋊C4—51no—
267C2×Dic3⋊C4—51no—
268C2×Dic3⋊C4—51no—
269C2×Dic3⋊C4—51no—
270C2×C4×Dic3—51no—
271C2×C4×Dic3—51no—
272C2×C4×Dic3—51no—
273C2×C4×Dic3—51no—
274C2×C4×Dic3—51no—
275#67⋊C4—104no—
276#877—104no—
277C3⋊#95—51no—
278C3⋊#95—51no—
279C3⋊#95—51no—
280C3⋊#95—51no—
281C3⋊#95—51no—
282C3⋊#95—51no—
283C24×C5C22×D311yescharacteristic
284C24×C5C22×D311yescharacteristic
285C23×D5—31no—
286C2×C5×D4—41no—
287C2×C5×D4—41no—
288C2×C5×D4C4×D314yescomplemented
289C22×C4×C5C22×D311yescharacteristic
290C22×C4×C5C22×D311yescharacteristic
291C22×C4×C5C22×D311yescharacteristic
292C22×C4×C5C22×D311yescharacteristic
293C22×C4×C5C22×D311yescharacteristic
294C2×C22⋊D5—34no—
295C2×C22⋊D5—34no—
296C2×C22⋊D5—62no—
297C2×C22⋊D5—62no—
298C2×C22⋊D5—121no—
299C2×C22⋊D5—121no—
300C22×Dic5—31no—
301C22×Dic5—34no—
302C22×Dic5—31no—
303C22×Dic5—31no—
304C22×Dic5—31no—
305C22×Dic5—31no—
306C22×Dic5—31no—
307C22×Dic5—31no—
308C22×Dic5—62no—
309C22×Dic5—62no—
310C22×Dic5—62no—
311C22×Dic5—62no—
312C22×Dic5—121no—
313C2×C4×D5—62no—
314C2×C4×D5—62no—
315C2×C4×D5—121no—
316C5×C4⋊C4—41no—
317C5×C22⋊C4—22no—
318C5×C22⋊C4—22no—
319C5×C22⋊C4—22no—
320C5×C22⋊C4—22no—
321C42×C5—41no—
322C22⋊Dic5—34no—
323C22⋊Dic5—62no—
324C22⋊Dic5—62no—
325C22⋊Dic5—121no—
326#685—34no—
327#685—62no—
328#685—62no—
329#685—121no—
330#683—34no—
331#683—34no—
332#683—62no—
333#683—121no—
334C4×Dic5—62no—
335C4×Dic5—62no—
336C4×Dic5—62no—
337C4×Dic5—62no—
338C4×Dic5—121no—
339C2×#121—151no—
340C2×C4×D4—151no—
341C2×#117—151no—
342#390—151no—
343#390—151no—
344#390D1511yescharacteristic, complemented
345#389—151no—
346#388—151no—
347#388—151no—
348#386—151no—
349#386—151no—
350C4×C4⋊C4—151no—
351C4×C22⋊C4—151no—
352C4×C22⋊C4—151no—
353C4×C22⋊C4—151no—
354C22×C3×C5—22no—
355C22×C3×C5—22no—
356C22×C3×C5—22no—
357C22×C3×C5—22no—
358C22×C3×C5—22no—
359C22×C3×C5—22no—
360C22×C3×C5—41no—
361C22×C3×C5—41no—
362C22×C3×C5—41no—
363C22×C3×C5—41no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
366C22×C3×C5—41no—
367C22×C3×C5—41no—
368C22×C3×C5C23×C411yescharacteristic
369C22×C3×C5C22×D411yescharacteristic
370C22×C3×C5C2×#4111yescharacteristic
371C22×C3×C5C2×#4111yescharacteristic
372C22×C3×C5C2×#4111yescharacteristic
373C22×C3×C5H(5,𝔽2)11yescharacteristic
374C22×C3×C5H(5,𝔽2)11yescharacteristic
375C2×D15—22no—
376C2×D15—22no—
377C2×D15—22no—
378C2×D15—41no—
379C2×D15—41no—
380C2×D15—41no—
381C2×D15—41no—
382C3×C4×C5—22no—
383C3×C4×C5—22no—
384C3×C4×C5—22no—
385C3×C4×C5—41no—
386C3×C4×C5—41no—
387Dic15—22no—
388Dic15—22no—
389Dic15—22no—
390Dic15—22no—
391Dic15—41no—
392Dic15—41no—
393Dic15C4×D414yes—
394C24×C3C22×D511yescharacteristic
395C24×C3C22×D511yescharacteristic
396C23×D3—51no—
397C2×C3×D4—41no—
398C2×C3×D4—41no—
399C2×C3×D4C4×D514yescomplemented
400C22×C3×C4C22×D511yescharacteristic
401C22×C3×C4C22×D511yescharacteristic
402C22×C3×C4C22×D511yescharacteristic
403C22×C3×C4C22×D511yescharacteristic
404C22×C3×C4C22×D511yescharacteristic
405C2×#67—54no—
406C2×#67—54no—
407C2×#67—102no—
408C2×#67—102no—
409C2×#67—201no—
410C2×#67—201no—
411C22×Dic3—51no—
412C22×Dic3—54no—
413C22×Dic3—51no—
414C22×Dic3—51no—
415C22×Dic3—51no—
416C22×Dic3—51no—
417C22×Dic3—51no—
418C22×Dic3—51no—
419C22×Dic3—102no—
420C22×Dic3—102no—
421C22×Dic3—102no—
422C22×Dic3—102no—
423C22×Dic3—201no—
424C2×C4×D3—102no—
425C2×C4×D3—102no—
426C2×C4×D3—201no—
427C3×C4⋊C4—41no—
428C3×C22⋊C4—22no—
429C3×C22⋊C4—22no—
430C3×C22⋊C4—22no—
431C3×C22⋊C4—22no—
432C3×C42—41no—
433#217—54no—
434#217—102no—
435#217—102no—
436#217—201no—
437(C2×D3)⋊C4—54no—
438(C2×D3)⋊C4—102no—
439(C2×D3)⋊C4—102no—
440(C2×D3)⋊C4—201no—
441Dic3⋊C4—54no—
442Dic3⋊C4—54no—
443Dic3⋊C4—102no—
444Dic3⋊C4—201no—
445C4×Dic3—102no—
446C4×Dic3—102no—
447C4×Dic3—102no—
448C4×Dic3—102no—
449C4×Dic3—201no—
450C23×C5—21no—
451C23×C5—21no—
452C23×C5—21no—
453C23×C5—21no—
454C23×C5—21no—
455C23×C5—21no—
456C23×C5—21no—
457C23×C5—21no—
458C23×C5—21no—
459C23×C5—21no—
460C23×C5—21no—
461C23×C5—21no—
462C23×C5C2×C4×D312yes—
463C23×C5C2×C4×D312yes—
464C23×C5C23×D311yescharacteristic
465C22×D5—32no—
466C22×D5—61no—
467C22×D5—61no—
468C22×D5—61no—
469C22×D5—61no—
470C22×D5—61no—
471C22×D5—61no—
472C5×D4—44no—
473C2×C4×C5—21no—
474C2×C4×C5—21no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—21no—
483C2×C4×C5—21no—
484C2×C4×C5—21no—
485C2×C4×C5C2×C4×D312yes—
486C2×C4×C5D3×D412yes—
487C2×C4×C5#23712yes—
488C22⋊D5—68no—
489C22⋊D5—124no—
490C2×Dic5—32no—
491C2×Dic5—32no—
492C2×Dic5—32no—
493C2×Dic5—32no—
494C2×Dic5—32no—
495C2×Dic5—32no—
496C2×Dic5—32no—
497C2×Dic5—68no—
498C2×Dic5—61no—
499C2×Dic5—61no—
500C2×Dic5—61no—
501C2×Dic5—61no—
502C2×Dic5—61no—
503C2×Dic5—61no—
504C2×Dic5—61no—
505C2×Dic5—61no—
506C2×Dic5—61no—
507C2×Dic5—61no—
508C2×Dic5—61no—
509C2×Dic5—61no—
510C2×Dic5—61no—
511C2×Dic5—61no—
512C2×Dic5—124no—
513C4×D5—124no—
514C22×D4—151no—
515C22×D4—151no—
516C22×D4C2×D1511yescharacteristic
517C23×C4—151no—
518C23×C4—151no—
519C23×C4—151no—
520#121—158no—
521C4×D4—304no—
522#117—304no—
523C2×C4⋊C4—151no—
524C2×C4⋊C4—151no—
525C2×C4⋊C4—151no—
526C2×C4⋊C4—151no—
527C2×C4⋊C4C2×D1511yescharacteristic
528C2×C22⋊C4—151no—
529C2×C22⋊C4—151no—
530C2×C22⋊C4—151no—
531C2×C22⋊C4—151no—
532C2×C22⋊C4—151no—
533C2×C22⋊C4—151no—
534C2×C22⋊C4—151no—
535C2×C22⋊C4—151no—
536C2×C22⋊C4C2×D1511yescharacteristic
537C2×C22⋊C4C2×D1511yescharacteristic
538C2×C22⋊C4C2×D1511yescharacteristic
539C2×C22⋊C4C2×D1511yescharacteristic
540C2×C42—151no—
541C2×C42—151no—
542C2×C42—151no—
543C2×C42—151no—
544C2×C42—151no—
545C2×C42C2×D1511yescharacteristic
546#95—151no—
547#95—151no—
548#95—151no—
549#95—151no—
550#95—151no—
551#95—151no—
552C2×C3×C5—42no—
553C2×C3×C5—42no—
554C2×C3×C5C2×C4×D411yescharacteristic
555C2×C3×C5C4×#4111yescharacteristic
556C2×C3×C5#51811yescharacteristic
557C2×C3×C5#54611yescharacteristic
558C2×C3×C5#55011yescharacteristic
559C2×C3×C5#55311yescharacteristic
560C2×C3×C5#55511yescharacteristic
561D15—42no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3C2×C4×D512yes—
575C23×C3C2×C4×D512yes—
576C23×C3C23×D511yescharacteristic
577C22×D3—52no—
578C22×D3—101no—
579C22×D3—101no—
580C22×D3—101no—
581C22×D3—101no—
582C22×D3—101no—
583C22×D3—101no—
584C3×D4—44no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4C2×C4×D512yes—
598C2×C3×C4D4×D512yes—
599C2×C3×C4#71112yes—
600#67—108no—
601#67—204no—
602C2×Dic3—52no—
603C2×Dic3—52no—
604C2×Dic3—52no—
605C2×Dic3—52no—
606C2×Dic3—52no—
607C2×Dic3—52no—
608C2×Dic3—52no—
609C2×Dic3—108no—
610C2×Dic3—101no—
611C2×Dic3—101no—
612C2×Dic3—101no—
613C2×Dic3—101no—
614C2×Dic3—101no—
615C2×Dic3—101no—
616C2×Dic3—101no—
617C2×Dic3—101no—
618C2×Dic3—101no—
619C2×Dic3—101no—
620C2×Dic3—101no—
621C2×Dic3—101no—
622C2×Dic3—101no—
623C2×Dic3—101no—
624C2×Dic3—204no—
625C4×D3—204no—
626C22×C5—22no—
627C22×C5—22no—
628C22×C5—22no—
629C22×C5—22no—
630C22×C5—22no—
631C22×C5—22no—
632C22×C5—41no—
633C22×C5—41no—
634C22×C5—41no—
635C22×C5—41no—
636C22×C5—41no—
637C22×C5—41no—
638C22×C5—41no—
639C22×C5—41no—
640C22×C5C22×C4×D311yescharacteristic
641C22×C5C2×D3×D411yescharacteristic
642C22×C5C2×#23711yescharacteristic
643C22×C5#100411yescharacteristic
644C22×C5#100411yescharacteristic
645C22×C5D3×#4111yescharacteristic
646C22×C5D3×#4111yescharacteristic
647C2×D5—62no—
648C2×D5—62no—
649C2×D5—62no—
650C2×D5—121no—
651C2×D5—121no—
652C2×D5—121no—
653C2×D5—121no—
654C4×C5—22no—
655C4×C5—22no—
656C4×C5—22no—
657C4×C5—41no—
658C4×C5—41no—
659Dic5—34no—
660Dic5—62no—
661Dic5—62no—
662Dic5—62no—
663Dic5—62no—
664Dic5—121no—
665Dic5—121no—
666C24—151no—
667C24C22×D1511yescharacteristic
668C24C22×D1511yescharacteristic
669C2×D4—41no—
670C2×D4—41no—
671C2×D4—154no—
672C2×D4—154no—
673C2×D4—302no—
674C2×D4—302no—
675C2×D4—601no—
676C2×D4—601no—
677C2×D4C4×D1514yescomplemented
678C22×C4—151no—
679C22×C4—154no—
680C22×C4—151no—
681C22×C4—151no—
682C22×C4—151no—
683C22×C4—151no—
684C22×C4—151no—
685C22×C4—151no—
686C22×C4—302no—
687C22×C4—302no—
688C22×C4—302no—
689C22×C4—302no—
690C22×C4—302no—
691C22×C4—302no—
692C22×C4—601no—
693C22×C4—601no—
694C22×C4C22×D1511yescharacteristic
695C22×C4C22×D1511yescharacteristic
696C22×C4C22×D1511yescharacteristic
697C22×C4C22×D1511yescharacteristic
698C22×C4C22×D1511yescharacteristic
699C4⋊C4—41no—
700C4⋊C4—154no—
701C4⋊C4—154no—
702C4⋊C4—302no—
703C4⋊C4—601no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—154no—
709C22⋊C4—154no—
710C22⋊C4—302no—
711C22⋊C4—302no—
712C22⋊C4—302no—
713C22⋊C4—302no—
714C22⋊C4—601no—
715C22⋊C4—601no—
716C42—41no—
717C42—302no—
718C42—302no—
719C42—302no—
720C42—302no—
721C42—601no—
722C3×C5#236311yescharacteristic, complemented, Hall
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3C22×C4×D511yescharacteristic
738C22×C3C2×D4×D511yescharacteristic
739C22×C3C2×#71111yescharacteristic
740C22×C3#414411yescharacteristic
741C22×C3#414411yescharacteristic
742C22×C3D5×#4111yescharacteristic
743C22×C3D5×#4111yescharacteristic
744C2×D3—102no—
745C2×D3—102no—
746C2×D3—102no—
747C2×D3—201no—
748C2×D3—201no—
749C2×D3—201no—
750C2×D3—201no—
751C3×C4—22no—
752C3×C4—22no—
753C3×C4—22no—
754C3×C4—41no—
755C3×C4—41no—
756Dic3—54no—
757Dic3—102no—
758Dic3—102no—
759Dic3—102no—
760Dic3—102no—
761Dic3—201no—
762Dic3—201no—
763C2×C5—42no—
764C2×C5—42no—
765C2×C5#548611yescharacteristic
766C2×C5C4×#23711yescharacteristic
767C2×C5C4×D3×D411yescharacteristic
768C2×C5#560111yescharacteristic
769C2×C5#561011yescharacteristic
770C2×C5#567011yescharacteristic
771C2×C5#571811yescharacteristic
772D5—122no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—152no—
786C23—301no—
787C23—301no—
788C23—301no—
789C23—301no—
790C23—301no—
791C23—301no—
792C23C2×C4×D1512yes—
793C23C2×C4×D1512yes—
794C23C23×D1511yescharacteristic
795D4—44no—
796D4—308no—
797D4—604no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—152no—
811C2×C4—152no—
812C2×C4—152no—
813C2×C4—152no—
814C2×C4—152no—
815C2×C4—152no—
816C2×C4—152no—
817C2×C4—308no—
818C2×C4—301no—
819C2×C4—301no—
820C2×C4—301no—
821C2×C4—301no—
822C2×C4—301no—
823C2×C4—301no—
824C2×C4—301no—
825C2×C4—301no—
826C2×C4—301no—
827C2×C4—301no—
828C2×C4—301no—
829C2×C4—301no—
830C2×C4—301no—
831C2×C4—301no—
832C2×C4—604no—
833C2×C4—604no—
834C2×C4C2×C4×D1512yes—
835C2×C4D4×D1512yes—
836C2×C4#681912yes—
837C2×C3—42no—
838C2×C3—42no—
839C2×C3#6582011yescharacteristic
840C2×C3C4×#71111yescharacteristic
841C2×C3C4×D4×D511yescharacteristic
842C2×C3#6593511yescharacteristic
843C2×C3#6594411yescharacteristic
844C2×C3#6600411yescharacteristic
845C2×C3#6605211yescharacteristic
846D3—202no—
847C5#7630511yescharacteristic, complemented, Sylow
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—302no—
863C22—302no—
864C22—302no—
865C22—601no—
866C22—601no—
867C22—601no—
868C22—601no—
869C22C22×C4×D1511yescharacteristic
870C22C2×D4×D1511yescharacteristic
871C22C2×#681911yescharacteristic
872C22#9209511yescharacteristic
873C22#9209511yescharacteristic
874C22#41×D1511yescharacteristic
875C22#41×D1511yescharacteristic
876C4—22no—
877C4—22no—
878C4—22no—
879C4—41no—
880C4—41no—
881C4—154no—
882C4—302no—
883C4—302no—
884C4—302no—
885C4—302no—
886C4—601no—
887C4—601no—
888C3#1060803611yescharacteristic, complemented, Sylow
889C2—42no—
890C2—42no—
891C2—602no—
892C2#1175624511yescharacteristic
893C2C4×#681911yescharacteristic
894C2C4×D4×D1511yescharacteristic
895C2#1175636011yescharacteristic
896C2#1175636911yescharacteristic
897C2#1175642911yescharacteristic
898C2#1175647711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#390C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91828C2
hypercenter#390D15
hypocenterC3×C5#2363
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#91770C2semidirect
3. C2×#91766C2semidirect
4. C3×C5×#390C2semidirect
5. #11751321C2semidirect
6. #11751091C2semidirect
7. #11751077C2semidirect
8. #11751058C2semidirect
9. #11751058C2semidirect
10. #11751057C2semidirect
11. #11751045C2semidirect
12. C22⋊C4×Dic15C2semidirect
13. C22⋊C4×Dic15C2semidirect
14. C4×#6714C2semidirect
15. C4×#6712C2semidirect
33. #91828C4semidirect
59. C5×#390D3semidirect
76. C2×C3×C5×D4C2×C4semidirect
87. C2×#1220C2×C4semidirect
93. C22×Dic15C2×C4semidirect
113. #6719C2×C4semidirect
117. #6714C2×C4semidirect
120. #6712C2×C4semidirect
121. #6712D4semidirect
130. C3×#390D5semidirect
288. C2×C5×D4C4×D3semidirect
344. #390D15semidirect
399. C2×C3×D4C4×D5semidirect
677. C2×D4C4×D15semidirect
722. C3×C5#2363semidirect
847. C5#76305semidirect
888. C3#10608036semidirect

Maximal subgroups

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

subgroupindex
C2×#918282
C2×#917702
C2×#917662
C3×C5×#3902
#117513212
#117510912
#117510772
#117510582
#117510572
#117510452
C22⋊C4×Dic152
C4×#67142
C4×#67122
#106080363
#763055