Finite Group Databasebeta

← #14331635

Subgroups — #14331635

Order 1920.

1888 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6780C211yesmaximal, characteristic, complemented
2C2×#91559C211yesmaximal, characteristic, complemented
3C2×#91442C211yesmaximal, characteristic, complemented
4C2×#91434C211yesmaximal, characteristic, complemented
5C22⋊C4×Dic15C211yesmaximal, characteristic, complemented
6C5×#4961C211yesmaximal, characteristic, complemented
7C3×#65249C211yesmaximal, characteristic, complemented
8#11749521C211yesmaximal, characteristic, complemented
9#11749490C211yesmaximal, characteristic, complemented
10#11748937C211yesmaximal, characteristic, complemented
11#11748926C211yesmaximal, characteristic, complemented
12#11748921C211yesmaximal, characteristic, complemented
13#11748886C211yesmaximal, characteristic, complemented
14#11748884C211yesmaximal, characteristic, complemented
15#11748736C211yesmaximal, characteristic, complemented
16#10608620—31nomaximal, Hall
17C23×Dic15C2211yescharacteristic
18C22×C5×#67C2211yescharacteristic
19C22×C3×C22⋊D5C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×D20C2211yescharacteristic
22C22×#1204C2211yescharacteristic
23C22×#1201C2211yescharacteristic
24C22×#1201C2211yescharacteristic
25C22×D3×Dic5C2211yescharacteristic
26C2×#6780—24no—
27C2×#6780—24no—
28C2×#6780—24no—
29C22×D5×Dic3C2211yescharacteristic
30C22×D5×Dic3C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×#6719C2211yescharacteristic
33C2×C4×Dic15C2211yescharacteristic
34C2×C4×Dic15C2211yescharacteristic
35C2×C5×#217C2211yescharacteristic
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic
38C2×C5×C4⋊Dic3C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic
40C2×C3×#685C2211yescharacteristic
41#91559—24no—
42C2×#6669C2211yescharacteristic
43C2×#6668C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47C2×#6665C2211yescharacteristic
48C2×#6665C2211yescharacteristic
49C2×Dic3×Dic5C2211yescharacteristic
50#91442—24no—
51#91434—24no—
52#91115C2211yescharacteristic
53#91115C2211yescharacteristic
54C5×C3⋊#95C2211yescharacteristic
55C3×#3963C2211yescharacteristic
56#90994C2211yescharacteristic
57#90994C2211yescharacteristic
58#76665—51nomaximal, Hall
59C22×#711—31no—
60C2×#4039—31no—
61C2×#4027—31no—
62C2×#4027—31no—
63C5×#394—31no—
64#65512—31no—
65#65268—31no—
66#65249—31no—
67#65249D311yescharacteristic, complemented
68#65248—31no—
69#65248—31no—
70C22⋊C4×Dic5—31no—
71C22⋊C4×Dic5—31no—
72#64962—31no—
73#64955—31no—
74C24×C3×C5C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
76C23×C3×D5C2311yescharacteristic
77C23×C3×D5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×Dic15—22no—
81C22×Dic15—22no—
82C22×Dic15D414yescomplemented
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C2×C5×#67—22no—
88C2×C5×#67—22no—
89C2×C5×#67—22no—
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
93C2×C3×C22⋊D5—22no—
94C2×C3×C22⋊D5—22no—
95C2×C3×C22⋊D5—22no—
96C2×C3×C22⋊D5—22no—
97C2×C3×C22⋊D5—22no—
98C2×C3×C22⋊D5—22no—
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C2×C3×D20—22no—
102C2×C3×D20—22no—
103C2×C3×D20—22no—
104C2×#1204—22no—
105C2×#1204—22no—
106C2×#1204—22no—
107C2×#1201—22no—
108C2×#1201—22no—
109C2×#1201—22no—
110C2×#1201—22no—
111C2×#1201—22no—
112C2×#1201—22no—
113C2×D3×Dic5—22no—
114C2×D3×Dic5—22no—
115C2×D3×Dic5D414yescomplemented
116#6780—232no—
117C2×D5×Dic3—22no—
118C2×D5×Dic3—22no—
119C2×D5×Dic3—22no—
120C2×D5×Dic3—22no—
121C2×D5×Dic3—22no—
122C2×D5×Dic3D414yescomplemented
123C3×C5×C22⋊C4—22no—
124#6719—22no—
125C4×Dic15—22no—
126C4×Dic15—22no—
127C5×#217—22no—
128C5×(C2×D3)⋊C4—22no—
129C5×(C2×D3)⋊C4—22no—
130C5×C4⋊Dic3—22no—
131C3×#685—22no—
132C3×#685—22no—
133#6669—22no—
134#6668—22no—
135(C2×D3)⋊Dic5—22no—
136#6665—22no—
137#6665—22no—
138#6665—22no—
139#6665—22no—
140Dic3×Dic5—22no—
141C22×#237—51no—
142C2×D4×Dic3—51no—
143C2×D4×Dic3—51no—
144C2×#67⋊C4—51no—
145C3×#392—51no—
146#5223—51no—
147#5223—51no—
148#5222—51no—
149#4961—51no—
150#4961D511yescharacteristic, complemented
151#4947—51no—
152Dic3×C22⋊C4—51no—
153Dic3×C22⋊C4—51no—
154#4666—51no—
155#4656—51no—
156C22×C5×D4—31no—
157C22×C22⋊D5—31no—
158C22×C22⋊D5—31no—
159C22×C22⋊D5C2×D311yescharacteristic
160C22×C22⋊D5C2×D311yescharacteristic
161C23×Dic5—31no—
162C23×Dic5—31no—
163C2×#711—64no—
164C2×#711—64no—
165C2×#711—64no—
166C22×D20C2×D311yescharacteristic
167C22×C4×D5—31no—
168C22×C4×D5—31no—
169C22×Dic10—31no—
170C2×C5×C4⋊C4—31no—
171C2×C5×C22⋊C4—31no—
172C2×C5×C22⋊C4—31no—
173C2×C5×C22⋊C4—31no—
174C2×C5×C22⋊C4C2×D311yescharacteristic
175C2×C22⋊Dic5—31no—
176C2×C22⋊Dic5—31no—
177C2×#685—31no—
178C2×#685—31no—
179C2×#685—31no—
180C2×#685—31no—
181C2×#685C2×D311yescharacteristic
182C2×#685C2×D311yescharacteristic
183C2×#683—31no—
184C2×#683—31no—
185C2×C4×Dic5—31no—
186C2×C4×Dic5—31no—
187C2×C4×Dic5—31no—
188#4039—64no—
189#4027—64no—
190#4027—64no—
191C5×#95—31no—
192#3963—31no—
193#3963—31no—
194#3963—31no—
195#3963—31no—
196#3963C2×D311yescharacteristic
197#2388—151noSylow
198C23×C3×C5—21no—
199C23×C3×C5—21no—
200C23×C3×C5—21no—
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5C2×D412yes—
205C23×C3×C5C2411yescharacteristic
206C22×C5×D3—21no—
207C22×C5×D3—21no—
208C22×C5×D3—21no—
209C22×C5×D3—21no—
210C22×C5×D3—21no—
211C22×C5×D3—21no—
212C22×C5×D3C2×D412yes—
213C22×C3×D5—21no—
214C22×C3×D5—21no—
215C22×C3×D5—21no—
216C22×C3×D5—21no—
217C22×C3×D5—21no—
218C22×C3×D5—21no—
219C22×C3×D5—21no—
220C22×C3×D5—21no—
221C22×C3×D5—21no—
222C22×C3×D5—21no—
223C22×C3×D5—21no—
224C22×C3×D5—21no—
225C22×C3×D5C2×D412yes—
226C22×C3×D5#4112yescomplemented
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5#4112yescomplemented
233C2×Dic15—21no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237C2×Dic15—28no—
238C2×Dic15—21no—
239C2×Dic15—21no—
240C2×Dic15—21no—
241C2×Dic15C2×D412yes—
242C2×Dic15C2×D412yes—
243C2×Dic15C2×D412yes—
244C2×Dic15C2×D412yes—
245C2×Dic15#4112yescomplemented
246C5×#67—28no—
247C2×C5×Dic3—21no—
248C2×C5×Dic3—21no—
249C2×C5×Dic3—21no—
250C2×C5×Dic3—21no—
251C2×C5×Dic3—21no—
252C2×C5×Dic3—21no—
253C2×C5×Dic3—21no—
254C2×C5×Dic3—21no—
255C2×C5×Dic3C2×D412yes—
256C3×C22⋊D5—28no—
257C3×C22⋊D5—28no—
258C2×C3×Dic5—21no—
259C2×C3×Dic5—21no—
260C2×C3×Dic5—21no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5C2×D412yes—
263C2×C3×Dic5#4112yescomplemented
264C3×D20—28no—
265#1204—28no—
266#1201—28no—
267#1201—28no—
268D3×Dic5—28no—
269D5×Dic3—28no—
270D5×Dic3—44no—
271C22×C3×D4—51no—
272C22×C3×D4—51no—
273C22×C3×D4—51no—
274C22×#67—51no—
275C22×#67—51no—
276C22×#67C2×D511yescharacteristic
277C23×Dic3—51no—
278C23×Dic3—51no—
279C23×Dic3—51no—
280C2×#237—104no—
281C2×#237—104no—
282C2×#237—104no—
283C22×C4×D3—51no—
284C22×Dic6—51no—
285C2×C3×C22⋊C4—51no—
286C2×C3×C22⋊C4—51no—
287C2×C3×C22⋊C4C2×D511yescharacteristic
288C2×#217—51no—
289C2×#217—51no—
290C2×#217—51no—
291C2×#217—51no—
292C2×#217—51no—
293C2×#217C2×D511yescharacteristic
294D4×Dic3—104no—
295D4×Dic3—104no—
296C2×(C2×D3)⋊C4—51no—
297C2×(C2×D3)⋊C4C2×D511yescharacteristic
298C2×(C2×D3)⋊C4C2×D511yescharacteristic
299C2×C4⋊Dic3—51no—
300C2×C4⋊Dic3C2×D511yescharacteristic
301C2×Dic3⋊C4—51no—
302C2×C4×Dic3—51no—
303C2×C4×Dic3—51no—
304C2×C4×Dic3—51no—
305#67⋊C4—104no—
306C3×#95—51no—
307C3⋊#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
311C3⋊#95C2×D511yescharacteristic
312C24×C5—31no—
313C24×C5C22×D311yescharacteristic
314C23×D5C22×D311yescharacteristic
315C23×D5C22×D311yescharacteristic
316C2×C5×D4—62no—
317C2×C5×D4—62no—
318C2×C5×D4—62no—
319C22×C4×C5—31no—
320C22×C4×C5—31no—
321C22×C4×C5—31no—
322C22×C4×C5C22×D311yescharacteristic
323C22×C4×C5C22×D311yescharacteristic
324C2×C22⋊D5—22no—
325C2×C22⋊D5—22no—
326C2×C22⋊D5—22no—
327C2×C22⋊D5—22no—
328C2×C22⋊D5—22no—
329C2×C22⋊D5—22no—
330C2×C22⋊D5—62no—
331C2×C22⋊D5—62no—
332C2×C22⋊D5—62no—
333C2×C22⋊D5—62no—
334C2×C22⋊D5—62no—
335C2×C22⋊D5—62no—
336C22×Dic5—31no—
337C22×Dic5—34no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—34no—
341C22×Dic5—31no—
342C22×Dic5—62no—
343C22×Dic5—62no—
344C22×Dic5—62no—
345C22×Dic5—62no—
346C22×Dic5C22×D311yescharacteristic
347C22×Dic5C22×D311yescharacteristic
348#711—632no—
349C2×D20—22no—
350C2×D20—22no—
351C2×D20—22no—
352C2×C4×D5—34no—
353C2×C4×D5—62no—
354C2×C4×D5—62no—
355C2×C4×D5—62no—
356C2×C4×D5—62no—
357C2×C4×D5—62no—
358C2×Dic10—62no—
359C2×Dic10—62no—
360C2×Dic10—62no—
361C5×C4⋊C4—62no—
362C5×C22⋊C4—22no—
363C5×C22⋊C4—62no—
364C5×C22⋊C4—62no—
365C5×C22⋊C4—62no—
366C22⋊Dic5—62no—
367C22⋊Dic5—62no—
368#685—22no—
369#685—22no—
370#685—62no—
371#685—62no—
372#685—62no—
373#685—62no—
374#683—62no—
375#683—62no—
376C4×Dic5—62no—
377C4×Dic5—62no—
378C4×Dic5—62no—
379C22×#41—151no—
380C2×C4×D4—151no—
381C2×C4×D4—151no—
382C2×C4×D4—151no—
383#395—151no—
384#394—31no—
385#394—151no—
386#394—151no—
387#393—151no—
388#392—51no—
389#392—151no—
390#392—151no—
391C4×C22⋊C4—151no—
392C4×C22⋊C4—151no—
393C4×C22⋊C4—151no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—41no—
398C22×C3×C5—41no—
399C22×C3×C5—41no—
400C22×C3×C5—41no—
401C22×C3×C5C22×D411yescharacteristic
402C22×C3×C5C22×D411yescharacteristic
403C22×C3×C5C22×D411yescharacteristic
404C22×C3×C5C2×#4111yescharacteristic
405C22×C3×C5C2×#4111yescharacteristic
406C22×C3×C5C2×#4111yescharacteristic
407C22×C3×C5C2×#4111yescharacteristic
408C2×C5×D3—22no—
409C2×C5×D3—22no—
410C2×C5×D3—22no—
411C2×C5×D3—41no—
412C2×C5×D3—41no—
413C2×C5×D3—41no—
414C2×C5×D3—41no—
415C2×C3×D5—22no—
416C2×C3×D5—22no—
417C2×C3×D5—22no—
418C2×C3×D5—22no—
419C2×C3×D5—22no—
420C2×C3×D5—22no—
421C2×C3×D5—41no—
422C2×C3×D5—41no—
423C2×C3×D5—41no—
424C2×C3×D5—41no—
425C2×C3×D5—41no—
426C2×C3×D5—41no—
427C2×C3×D5—41no—
428C2×C3×D5—41no—
429C3×C4×C5—22no—
430C3×C4×C5—41no—
431Dic15—22no—
432Dic15—22no—
433Dic15—41no—
434Dic15#12014yes—
435C3×Dic5—22no—
436C3×Dic5—22no—
437C5×Dic3—22no—
438C5×Dic3—41no—
439C5×Dic3—41no—
440C24×C3—51no—
441C24×C3—51no—
442C24×C3C22×D511yescharacteristic
443C23×D3C22×D511yescharacteristic
444C2×C3×D4—102no—
445C2×C3×D4—102no—
446C2×C3×D4—102no—
447C2×C3×D4—102no—
448C2×C3×D4—102no—
449C2×C3×D4—102no—
450C2×C3×D4—102no—
451C2×C3×D4—102no—
452C2×C3×D4—102no—
453C22×C3×C4—51no—
454C22×C3×C4—51no—
455C22×C3×C4C22×D511yescharacteristic
456C22×C3×C4C22×D511yescharacteristic
457C2×#67—22no—
458C2×#67—22no—
459C2×#67—22no—
460C2×#67—102no—
461C2×#67—102no—
462C2×#67—102no—
463C2×#67—102no—
464C2×#67—102no—
465C2×#67—102no—
466C22×Dic3—51no—
467C22×Dic3—54no—
468C22×Dic3—51no—
469C22×Dic3—51no—
470C22×Dic3—54no—
471C22×Dic3—51no—
472C22×Dic3—102no—
473C22×Dic3—102no—
474C22×Dic3—102no—
475C22×Dic3—102no—
476C22×Dic3—102no—
477C22×Dic3—102no—
478C22×Dic3—102no—
479C22×Dic3C22×D511yescharacteristic
480C22×Dic3C22×D511yescharacteristic
481C22×Dic3C22×D511yescharacteristic
482#237—1032no—
483C2×C4×D3—54no—
484C2×C4×D3—102no—
485C2×C4×D3—102no—
486C2×Dic6—102no—
487C2×Dic6—102no—
488C2×Dic6—102no—
489C3×C22⋊C4—22no—
490C3×C22⋊C4—102no—
491C3×C22⋊C4—102no—
492#217—22no—
493#217—102no—
494#217—102no—
495#217—102no—
496#217—102no—
497#217—102no—
498(C2×D3)⋊C4—22no—
499(C2×D3)⋊C4—22no—
500(C2×D3)⋊C4—102no—
501C4⋊Dic3—22no—
502C4⋊Dic3—102no—
503Dic3⋊C4—102no—
504C4×Dic3—102no—
505C4×Dic3—102no—
506C4×Dic3—102no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5—21no—
511C23×C5—21no—
512C23×C5—21no—
513C23×C5—32no—
514C23×C5—61no—
515C23×C5—61no—
516C23×C5—61no—
517C23×C5—61no—
518C23×C5—61no—
519C23×C5—61no—
520C23×C5D3×D412yes—
521C23×C5C23×D311yescharacteristic
522C22×D5—21no—
523C22×D5—21no—
524C22×D5—21no—
525C22×D5—21no—
526C22×D5—21no—
527C22×D5—21no—
528C22×D5—21no—
529C22×D5—21no—
530C22×D5—21no—
531C22×D5—21no—
532C22×D5—21no—
533C22×D5—21no—
534C22×D5D3×D412yes—
535C22×D5#23712yescomplemented
536C5×D4—68no—
537C2×C4×C5—21no—
538C2×C4×C5—21no—
539C2×C4×C5—21no—
540C2×C4×C5—21no—
541C2×C4×C5—21no—
542C2×C4×C5—32no—
543C2×C4×C5—61no—
544C2×C4×C5—61no—
545C2×C4×C5—61no—
546C2×C4×C5—61no—
547C2×C4×C5—61no—
548C2×C4×C5—61no—
549C2×C4×C5—61no—
550C2×C4×C5—61no—
551C2×C4×C5#23712yescomplemented
552C22⋊D5—28no—
553C22⋊D5—28no—
554C22⋊D5—68no—
555C22⋊D5—68no—
556C2×Dic5—21no—
557C2×Dic5—21no—
558C2×Dic5—21no—
559C2×Dic5—21no—
560C2×Dic5—32no—
561C2×Dic5—32no—
562C2×Dic5—32no—
563C2×Dic5—32no—
564C2×Dic5—32no—
565C2×Dic5—68no—
566C2×Dic5—68no—
567C2×Dic5—61no—
568C2×Dic5—61no—
569C2×Dic5—61no—
570C2×Dic5—61no—
571C2×Dic5—61no—
572C2×Dic5—61no—
573C2×Dic5—61no—
574C2×Dic5D3×D412yes—
575C2×Dic5#23712yescomplemented
576D20—28no—
577C4×D5—68no—
578C4×D5—124no—
579Dic10—68no—
580C2×#41—304no—
581C2×#41—304no—
582C2×#41—304no—
583C22×Q8—151no—
584C22×D4—31no—
585C22×D4—51no—
586C22×D4—51no—
587C22×D4—51no—
588C22×D4—151no—
589C22×D4—151no—
590C23×C4—151no—
591C23×C4—151no—
592C23×C4—151no—
593C23×C4—151no—
594C4×D4—304no—
595C4×D4—304no—
596C4×D4—304no—
597C2×C4⋊C4—31no—
598C2×C4⋊C4—151no—
599C2×C4⋊C4—151no—
600C2×C22⋊C4—31no—
601C2×C22⋊C4—31no—
602C2×C22⋊C4—31no—
603C2×C22⋊C4—51no—
604C2×C22⋊C4—51no—
605C2×C22⋊C4—151no—
606C2×C22⋊C4—151no—
607C2×C22⋊C4—151no—
608C2×C22⋊C4—151no—
609C2×C22⋊C4—151no—
610C2×C22⋊C4—151no—
611C2×C22⋊C4D3×D511yescharacteristic
612C2×C42—151no—
613C2×C42—151no—
614C2×C42—151no—
615#95—31no—
616#95—51no—
617#95—151no—
618#95—151no—
619#95—151no—
620#95—151no—
621C2×C3×C5—42no—
622C2×C3×C5C2×#12011yescharacteristic
623C2×C3×C5#52511yescharacteristic
624C2×C3×C5#52511yescharacteristic
625C2×C3×C5#52511yescharacteristic
626C2×C3×C5#53211yescharacteristic
627C2×C3×C5#53211yescharacteristic
628C2×C3×C5#53211yescharacteristic
629C3×D5—42no—
630C3×D5—42no—
631C5×D3—42no—
632C23×C3—21no—
633C23×C3—21no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3—52no—
639C23×C3—52no—
640C23×C3—101no—
641C23×C3—101no—
642C23×C3—101no—
643C23×C3—101no—
644C23×C3—101no—
645C23×C3—101no—
646C23×C3—101no—
647C23×C3—101no—
648C23×C3—101no—
649C23×C3—101no—
650C23×C3—101no—
651C23×C3—101no—
652C23×C3D4×D512yes—
653C23×C3C23×D511yescharacteristic
654C22×D3—21no—
655C22×D3—21no—
656C22×D3—21no—
657C22×D3—21no—
658C22×D3—21no—
659C22×D3—21no—
660C22×D3D4×D512yes—
661C3×D4—108no—
662C3×D4—108no—
663C3×D4—108no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—52no—
670C2×C3×C4—52no—
671C2×C3×C4—101no—
672C2×C3×C4—101no—
673C2×C3×C4—101no—
674C2×C3×C4—101no—
675C2×C3×C4#71112yescomplemented
676#67—28no—
677#67—108no—
678#67—108no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—52no—
688C2×Dic3—52no—
689C2×Dic3—52no—
690C2×Dic3—52no—
691C2×Dic3—52no—
692C2×Dic3—108no—
693C2×Dic3—108no—
694C2×Dic3—101no—
695C2×Dic3—101no—
696C2×Dic3—101no—
697C2×Dic3—101no—
698C2×Dic3—101no—
699C2×Dic3—101no—
700C2×Dic3—101no—
701C2×Dic3—204no—
702C2×Dic3D4×D512yes—
703C4×D3—108no—
704Dic6—108no—
705C22×C5—22no—
706C22×C5—22no—
707C22×C5—22no—
708C22×C5—41no—
709C22×C5—41no—
710C22×C5—41no—
711C22×C5—41no—
712C22×C5—62no—
713C22×C5—62no—
714C22×C5—62no—
715C22×C5—121no—
716C22×C5—121no—
717C22×C5—121no—
718C22×C5—121no—
719C22×C5C2×D3×D411yescharacteristic
720C22×C5C2×D3×D411yescharacteristic
721C22×C5C2×D3×D411yescharacteristic
722C22×C5C2×#23711yescharacteristic
723C22×C5C2×#23711yescharacteristic
724C22×C5C2×#23711yescharacteristic
725C22×C5D3×#4111yescharacteristic
726C2×D5—22no—
727C2×D5—22no—
728C2×D5—22no—
729C2×D5—22no—
730C2×D5—22no—
731C2×D5—22no—
732C2×D5—41no—
733C2×D5—41no—
734C2×D5—41no—
735C2×D5—41no—
736C2×D5—41no—
737C2×D5—41no—
738C2×D5—41no—
739C2×D5—41no—
740C4×C5—22no—
741C4×C5—41no—
742C4×C5—62no—
743C4×C5—121no—
744C4×C5—121no—
745Dic5—22no—
746Dic5—22no—
747Dic5—34no—
748Dic5—62no—
749Dic5—62no—
750Dic5—121no—
751C24—31no—
752C24—51no—
753C24—51no—
754C24C2×D3×D511yescharacteristic
755#41—3032no—
756C2×Q8—302no—
757C2×Q8—302no—
758C2×Q8—302no—
759C2×D4—62no—
760C2×D4—62no—
761C2×D4—62no—
762C2×D4—102no—
763C2×D4—102no—
764C2×D4—102no—
765C2×D4—102no—
766C2×D4—102no—
767C2×D4—102no—
768C2×D4—102no—
769C2×D4—102no—
770C2×D4—102no—
771C2×D4—302no—
772C2×D4—302no—
773C2×D4—302no—
774C2×D4—302no—
775C2×D4—302no—
776C2×D4—302no—
777C22×C4—31no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—51no—
781C22×C4—51no—
782C22×C4—154no—
783C22×C4—154no—
784C22×C4—151no—
785C22×C4—154no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—151no—
789C22×C4—302no—
790C22×C4—302no—
791C22×C4—302no—
792C22×C4—302no—
793C22×C4—302no—
794C22×C4—302no—
795C22×C4—302no—
796C22×C4—302no—
797C22×C4—302no—
798C22×C4C2×D3×D511yescharacteristic
799C22×C4C2×D3×D511yescharacteristic
800C4⋊C4—62no—
801C4⋊C4—302no—
802C4⋊C4—302no—
803C22⋊C4—22no—
804C22⋊C4—62no—
805C22⋊C4—62no—
806C22⋊C4—62no—
807C22⋊C4—102no—
808C22⋊C4—102no—
809C22⋊C4—302no—
810C22⋊C4—302no—
811C22⋊C4—302no—
812C22⋊C4—302no—
813C22⋊C4—302no—
814C22⋊C4—302no—
815C42—302no—
816C42—302no—
817C42—302no—
818C3×C5#238811yescharacteristic, complemented, Hall
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—102no—
827C22×C3—102no—
828C22×C3—102no—
829C22×C3—102no—
830C22×C3—102no—
831C22×C3—102no—
832C22×C3—201no—
833C22×C3—201no—
834C22×C3—201no—
835C22×C3—201no—
836C22×C3—201no—
837C22×C3—201no—
838C22×C3—201no—
839C22×C3—201no—
840C22×C3C2×D4×D511yescharacteristic
841C22×C3C2×D4×D511yescharacteristic
842C22×C3C2×D4×D511yescharacteristic
843C22×C3C2×#71111yescharacteristic
844C22×C3D5×#4111yescharacteristic
845C22×C3D5×#4111yescharacteristic
846C22×C3D5×#4111yescharacteristic
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—41no—
851C2×D3—41no—
852C2×D3—41no—
853C2×D3—41no—
854C3×C4—22no—
855C3×C4—41no—
856C3×C4—102no—
857C3×C4—102no—
858Dic3—22no—
859Dic3—41no—
860Dic3—41no—
861Dic3—54no—
862Dic3—102no—
863Dic3—102no—
864Dic3—201no—
865C2×C5—42no—
866C2×C5—122no—
867C2×C5#558611yescharacteristic
868C2×C5#558611yescharacteristic
869C2×C5D3×#12011yescharacteristic
870C2×C5#559611yescharacteristic
871C2×C5#559611yescharacteristic
872C2×C5#560611yescharacteristic
873C2×C5#571611yescharacteristic
874D5—42no—
875D5—42no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—32no—
883C23—52no—
884C23—52no—
885C23—61no—
886C23—61no—
887C23—61no—
888C23—61no—
889C23—61no—
890C23—61no—
891C23—101no—
892C23—101no—
893C23—101no—
894C23—101no—
895C23—101no—
896C23—101no—
897C23—101no—
898C23—101no—
899C23—101no—
900C23—101no—
901C23—101no—
902C23—101no—
903C23#677712yes—
904C23C22×D3×D511yescharacteristic
905Q8—308no—
906D4—68no—
907D4—108no—
908D4—108no—
909D4—108no—
910D4—308no—
911D4—308no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—32no—
918C2×C4—52no—
919C2×C4—52no—
920C2×C4—61no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—101no—
929C2×C4—101no—
930C2×C4—101no—
931C2×C4—101no—
932C2×C4—152no—
933C2×C4—152no—
934C2×C4—152no—
935C2×C4—152no—
936C2×C4—152no—
937C2×C4—308no—
938C2×C4—308no—
939C2×C4—308no—
940C2×C4—301no—
941C2×C4—301no—
942C2×C4—301no—
943C2×C4—301no—
944C2×C4—301no—
945C2×C4—301no—
946C2×C4—301no—
947C2×C4—604no—
948C2×C4#678012yescomplemented
949C2×C3—42no—
950C2×C3—202no—
951C2×C3—202no—
952C2×C3D5×#12011yescharacteristic
953C2×C3#6593011yescharacteristic
954C2×C3#6593011yescharacteristic
955C2×C3#6594011yescharacteristic
956C2×C3#6599011yescharacteristic
957C2×C3#6599011yescharacteristic
958C2×C3#6600211yescharacteristic
959D3—42no—
960C5#7666511yescharacteristic, complemented, Sylow
961C22—22no—
962C22—22no—
963C22—22no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—62no—
969C22—62no—
970C22—62no—
971C22—102no—
972C22—102no—
973C22—102no—
974C22—102no—
975C22—102no—
976C22—102no—
977C22—121no—
978C22—121no—
979C22—121no—
980C22—121no—
981C22—201no—
982C22—201no—
983C22—201no—
984C22—201no—
985C22—201no—
986C22—201no—
987C22—201no—
988C22—201no—
989C22C2×#677711yescharacteristic
990C22#9201611yescharacteristic
991C22D3×D4×D511yescharacteristic
992C22D3×D4×D511yescharacteristic
993C22D5×#23711yescharacteristic
994C22D5×#23711yescharacteristic
995C22C2×#678011yescharacteristic
996C4—22no—
997C4—41no—
998C4—62no—
999C4—102no—
1000C4—102no—
1001C4—121no—
1002C4—121no—
1003C4—154no—
1004C4—302no—
1005C4—302no—
1006C4—601no—
1007C3#1060862011yescharacteristic, complemented, Sylow
1008C2—42no—
1009C2—122no—
1010C2—202no—
1011C2—202no—
1012C2#1175283411yescharacteristic
1013C2#1175288011yescharacteristic
1014C2#1175320711yescharacteristic
1015C2#1175324511yescharacteristic
1016C2#1175438611yescharacteristic
1017C2#1175475911yescharacteristic
1018C2#1175477111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutator, socle, cosocleC23×C3×C5C24
FittingC2×C3×C5×C22⋊C4C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2388
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6780C2semidirect
2. C2×#91559C2semidirect
3. C2×#91442C2semidirect
4. C2×#91434C2semidirect
5. C22⋊C4×Dic15C2semidirect
6. C5×#4961C2semidirect
7. C3×#65249C2semidirect
8. #11749521C2semidirect
9. #11749490C2semidirect
10. #11748937C2semidirect
11. #11748926C2semidirect
12. #11748921C2semidirect
13. #11748886C2semidirect
14. #11748884C2semidirect
15. #11748736C2semidirect
67. #65249D3semidirect
82. C22×Dic15D4semidirect
115. C2×D3×Dic5D4semidirect
122. C2×D5×Dic3D4semidirect
150. #4961D5semidirect
226. C22×C3×D5#41semidirect
232. C2×C3×C4×C5#41semidirect
245. C2×Dic15#41semidirect
263. C2×C3×Dic5#41semidirect
535. C22×D5#237semidirect
551. C2×C4×C5#237semidirect
575. C2×Dic5#237semidirect
675. C2×C3×C4#711semidirect
818. C3×C5#2388semidirect
948. C2×C4#6780semidirect
960. C5#76665semidirect
1007. C3#10608620semidirect

Maximal subgroups

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

subgroupindex
C22×#67802
C2×#915592
C2×#914422
C2×#914342
C22⋊C4×Dic152
C5×#49612
C3×#652492
#117495212
#117494902
#117489372
#117489262
#117489212
#117488862
#117488842
#117487362
#106086203
#766655