Finite Group Databasebeta

← #14328103

Subgroups — #14328103

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×#91842C211yesmaximal, characteristic
3C22×#6719C211yesmaximal, characteristic, complemented
4C2×C4×#1220C211yesmaximal, characteristic, complemented
5C2×#91770C211yesmaximal, characteristic, complemented
6#11751314C211yesmaximal, characteristic, complemented
7#11751311C211yesmaximal, characteristic, complemented
8C4×#6719C211yesmaximal, characteristic, complemented
9#11751059C211yesmaximal, characteristic, complemented
10#11751058C211yesmaximal, characteristic, complemented
11#11751057C211yesmaximal, characteristic, complemented
12#11751047C211yesmaximal, characteristic, complemented
13#11751046C211yesmaximal, characteristic, complemented
14#11751045C211yesmaximal, characteristic, complemented
15C22⋊C4×Dic15C211yesmaximal, characteristic, complemented
16#10613830—31nomaximal, Hall
17C25×C3×C5C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic
22C22×#1220C2211yescharacteristic
23C23×Dic15C2211yescharacteristic
24C23×Dic15C2211yescharacteristic
25C22×C4×D15C2211yescharacteristic, complemented
26C2×C3×C5×C22⋊C4—24no—
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2211yescharacteristic
30C2×C3×C5×C22⋊C4C2211yescharacteristic
31#91842C418yescomplemented
32C2×#6719—24no—
33C2×#6719C2211yescharacteristic
34C2×#6719C2211yescharacteristic
35C2×#6719C2211yescharacteristic
36C2×#6719C2211yescharacteristic
37C2×#6719C2211yescharacteristic
38C2×#6719C2211yescharacteristic
39C2×#6719C2211yescharacteristic
40C4×#1220—24no—
41C2×#6714C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43C2×#6714C2211yescharacteristic, complemented
44C2×#6712C2211yescharacteristic, complemented
45C2×#6712C2211yescharacteristic, complemented
46C2×#6712C2211yescharacteristic, complemented
47C2×C4×Dic15C2211yescharacteristic, complemented
48C2×C4×Dic15C2211yescharacteristic, complemented
49C2×C4×Dic15C2211yescharacteristic, complemented
50#91770—24no—
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53#91115C2211yescharacteristic, complemented
54#91115C2211yescharacteristic, complemented
55#91115C2211yescharacteristic, complemented
56#91115C2211yescharacteristic, complemented
57#82099—51nomaximal, Hall
58C22×C5×C22⋊C4D311yescharacteristic, complemented
59C2×#4099—31no—
60C22×C22⋊Dic5—31no—
61C2×C4×C22⋊D5—31no—
62C2×#4027—31no—
63#65502—31no—
64#65499—31no—
65C4×C22⋊Dic5—31no—
66#65247—31no—
67#65246—31no—
68#65245—31no—
69#65235—31no—
70#65234—31no—
71#65233—31no—
72C22⋊C4×Dic5—31no—
73C24×C3×C5—22no—
74C24×C3×C5—22no—
75C24×C3×C5—22no—
76C24×C3×C5—22no—
77C24×C3×C5—41no—
78C24×C3×C5—41no—
79C24×C3×C5C2×C414yescomplemented
80C24×C3×C5C2311yescharacteristic
81C24×C3×C5C2311yescharacteristic
82C24×C3×C5C2311yescharacteristic
83C23×D15C2311yescharacteristic
84C22×C3×C4×C5—22no—
85C22×C3×C4×C5—22no—
86C22×C3×C4×C5—22no—
87C22×C3×C4×C5—22no—
88C22×C3×C4×C5—41no—
89C22×C3×C4×C5—41no—
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C2×#1220—22no—
95C2×#1220—22no—
96C2×#1220—22no—
97C2×#1220—22no—
98C2×#1220—41no—
99C2×#1220—41no—
100C2×#1220C2×C414yescomplemented
101C2×#1220C2×C414yescomplemented
102C2×#1220C2×C414yescomplemented
103C22×Dic15—22no—
104C22×Dic15—22no—
105C22×Dic15—22no—
106C22×Dic15—22no—
107C22×Dic15—41no—
108C22×Dic15—41no—
109C22×Dic15C2311yescharacteristic
110C22×Dic15C2311yescharacteristic
111C22×Dic15C2311yescharacteristic
112C22×Dic15C2311yescharacteristic
113C22×Dic15C2311yescharacteristic
114C22×Dic15C2311yescharacteristic
115C22×Dic15C2311yescharacteristic
116C2×C4×D15—22no—
117C2×C4×D15—22no—
118C2×C4×D15—41no—
119C3×C5×C22⋊C4—22no—
120C3×C5×C22⋊C4—22no—
121C3×C5×C22⋊C4—22no—
122C3×C5×C22⋊C4D414yescomplemented
123#6719—22no—
124#6719—22no—
125#6719—22no—
126#6719C2×C414yescomplemented
127#6719C2×C414yescomplemented
128#6719C2×C414yescomplemented
129#6719D414yescomplemented
130#6714—22no—
131#6714—22no—
132#6714—41no—
133#6712—22no—
134#6712—22no—
135#6712—41no—
136C4×Dic15—22no—
137C4×Dic15—22no—
138C4×Dic15—41no—
139C22×C3×C22⋊C4D511yescharacteristic, complemented
140C2×#953—51no—
141C22×#217—51no—
142C2×C4×#67—51no—
143C2×#67⋊C4—51no—
144#5213—51no—
145#5210—51no—
146C4×#217—51no—
147#4958—51no—
148#4957—51no—
149#4956—51no—
150#4946—51no—
151#4945—51no—
152#4944—51no—
153Dic3×C22⋊C4—51no—
154C25×C5C2×D311yescharacteristic
155C23×C4×C5C2×D311yescharacteristic
156C23×C4×C5C2×D311yescharacteristic
157C22×C22⋊D5—31no—
158C22×C22⋊D5—31no—
159C22×C22⋊D5—31no—
160C23×Dic5—31no—
161C23×Dic5—31no—
162C22×C4×D5—31no—
163C2×C5×C22⋊C4—24no—
164C2×C5×C22⋊C4C2×D311yescharacteristic
165C2×C5×C22⋊C4C2×D311yescharacteristic
166C2×C5×C22⋊C4C2×D311yescharacteristic
167C2×C5×C22⋊C4C2×D311yescharacteristic
168#4099—38no—
169C2×C22⋊Dic5—31no—
170C2×C22⋊Dic5—31no—
171C2×C22⋊Dic5—31no—
172C2×C22⋊Dic5—31no—
173C2×C22⋊Dic5—31no—
174C2×C22⋊Dic5—31no—
175C2×C22⋊Dic5—31no—
176C2×C22⋊Dic5—64no—
177C4×C22⋊D5—64no—
178C2×#685—31no—
179C2×#685—31no—
180C2×#685—31no—
181C2×#683—31no—
182C2×#683—31no—
183C2×#683—31no—
184C2×C4×Dic5—31no—
185C2×C4×Dic5—31no—
186C2×C4×Dic5—31no—
187#4027—64no—
188#3963—31no—
189#3963—31no—
190#3963—31no—
191#3963—31no—
192#3963—31no—
193#3963—31no—
194#2358—151noSylow
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5—21no—
200C23×C3×C5—21no—
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5—28no—
204C23×C3×C5—28no—
205C23×C3×C5—21no—
206C23×C3×C5—21no—
207C23×C3×C5—21no—
208C23×C3×C5—21no—
209C23×C3×C5—21no—
210C23×C3×C5—21no—
211C23×C3×C5—44no—
212C23×C3×C5—44no—
213C23×C3×C5—44no—
214C23×C3×C5—44no—
215C23×C3×C5—44no—
216C23×C3×C5C22×C412yes—
217C23×C3×C5C22×C412yes—
218C23×C3×C5C22×C412yes—
219C23×C3×C5C2×D412yes—
220C23×C3×C5C2×D412yes—
221C23×C3×C5#4112yes—
222C23×C3×C5#4112yes—
223C23×C3×C5C2411yescharacteristic
224C22×D15—21no—
225C22×D15—21no—
226C22×D15—21no—
227C22×D15—21no—
228C22×D15—21no—
229C22×D15—21no—
230C22×D15C22×C412yes—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5—21no—
236C2×C3×C4×C5—21no—
237C2×C3×C4×C5—21no—
238C2×C3×C4×C5—21no—
239C2×C3×C4×C5—21no—
240C2×C3×C4×C5—21no—
241C2×C3×C4×C5—44no—
242C2×C3×C4×C5—44no—
243C2×C3×C4×C5C2×D412yes—
244C2×C3×C4×C5C2×D412yes—
245#1220—28no—
246#1220—28no—
247#1220—44no—
248C2×Dic15—21no—
249C2×Dic15—21no—
250C2×Dic15—21no—
251C2×Dic15—21no—
252C2×Dic15—21no—
253C2×Dic15—21no—
254C2×Dic15—21no—
255C2×Dic15—21no—
256C2×Dic15—21no—
257C2×Dic15—21no—
258C2×Dic15—21no—
259C2×Dic15—21no—
260C2×Dic15—21no—
261C2×Dic15—21no—
262C2×Dic15—21no—
263C2×Dic15—21no—
264C2×Dic15—44no—
265C2×Dic15—44no—
266C2×Dic15C22×C412yes—
267C2×Dic15C22×C412yes—
268C2×Dic15C22×C412yes—
269C2×Dic15C2×D412yes—
270C2×Dic15C2×D412yes—
271C4×D15—44no—
272C25×C3C2×D511yescharacteristic
273C23×C3×C4C2×D511yescharacteristic
274C23×C3×C4C2×D511yescharacteristic
275C22×#67—51no—
276C22×#67—51no—
277C22×#67—51no—
278C23×Dic3—51no—
279C23×Dic3—51no—
280C22×C4×D3—51no—
281C2×C3×C22⋊C4—24no—
282C2×C3×C22⋊C4C2×D511yescharacteristic
283C2×C3×C22⋊C4C2×D511yescharacteristic
284C2×C3×C22⋊C4C2×D511yescharacteristic
285C2×C3×C22⋊C4C2×D511yescharacteristic
286#953—58no—
287C2×#217—51no—
288C2×#217—51no—
289C2×#217—51no—
290C2×#217—51no—
291C2×#217—51no—
292C2×#217—51no—
293C2×#217—51no—
294C2×#217—104no—
295C4×#67—104no—
296C2×(C2×D3)⋊C4—51no—
297C2×(C2×D3)⋊C4—51no—
298C2×(C2×D3)⋊C4—51no—
299C2×Dic3⋊C4—51no—
300C2×Dic3⋊C4—51no—
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⋊#95—51no—
312C24×C5—22no—
313C24×C5—22no—
314C24×C5—22no—
315C24×C5—22no—
316C24×C5—41no—
317C24×C5—41no—
318C24×C5C4×D314yescomplemented
319C24×C5C22×D311yescharacteristic
320C24×C5C22×D311yescharacteristic
321C24×C5C22×D311yescharacteristic
322C23×D5—31no—
323C22×C4×C5—22no—
324C22×C4×C5—22no—
325C22×C4×C5—22no—
326C22×C4×C5—22no—
327C22×C4×C5—41no—
328C22×C4×C5—41no—
329C22×C4×C5C22×D311yescharacteristic
330C22×C4×C5C22×D311yescharacteristic
331C22×C4×C5C22×D311yescharacteristic
332C22×C4×C5C22×D311yescharacteristic
333C2×C22⋊D5—34no—
334C2×C22⋊D5—34no—
335C2×C22⋊D5—34no—
336C2×C22⋊D5—62no—
337C2×C22⋊D5—62no—
338C2×C22⋊D5—62no—
339C2×C22⋊D5—62no—
340C2×C22⋊D5—121no—
341C2×C22⋊D5—121no—
342C22×Dic5—31no—
343C22×Dic5—31no—
344C22×Dic5—31no—
345C22×Dic5—31no—
346C22×Dic5—31no—
347C22×Dic5—31no—
348C22×Dic5—31no—
349C22×Dic5—62no—
350C22×Dic5—62no—
351C22×Dic5—62no—
352C22×Dic5—62no—
353C22×Dic5—121no—
354C22×Dic5—121no—
355C2×C4×D5—62no—
356C2×C4×D5—62no—
357C2×C4×D5—121no—
358C5×C22⋊C4—22no—
359C5×C22⋊C4—22no—
360C5×C22⋊C4—22no—
361C5×C22⋊C4#6714yescomplemented
362C22⋊Dic5—34no—
363C22⋊Dic5—34no—
364C22⋊Dic5—34no—
365C22⋊Dic5—34no—
366C22⋊Dic5—62no—
367C22⋊Dic5—62no—
368C22⋊Dic5—62no—
369#685—62no—
370#685—62no—
371#685—121no—
372#683—62no—
373#683—62no—
374#683—121no—
375C4×Dic5—62no—
376C4×Dic5—62no—
377C4×Dic5—121no—
378C2×#120—151no—
379C2×C4×D4—151no—
380C2×C4×D4—151no—
381C22×C22⋊C4—151no—
382C22×C22⋊C4D1511yescharacteristic, complemented
383#390—151no—
384#388—151no—
385#388—151no—
386#386—151no—
387#386—151no—
388#386—151no—
389#385—151no—
390#385—151no—
391C4×C22⋊C4—151no—
392C4×C22⋊C4—151no—
393C22×C3×C5—22no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—22no—
398C22×C3×C5—22no—
399C22×C3×C5—22no—
400C22×C3×C5—22no—
401C22×C3×C5—22no—
402C22×C3×C5—22no—
403C22×C3×C5—22no—
404C22×C3×C5—22no—
405C22×C3×C5—22no—
406C22×C3×C5—22no—
407C22×C3×C5—22no—
408C22×C3×C5—416no—
409C22×C3×C5—41no—
410C22×C3×C5—41no—
411C22×C3×C5—41no—
412C22×C3×C5—41no—
413C22×C3×C5C4×D414yescomplemented
414C22×C3×C5C4×D414yescomplemented
415C22×C3×C5C23×C411yescharacteristic
416C22×C3×C5C22×D411yescharacteristic
417C22×C3×C5C22×D411yescharacteristic
418C22×C3×C5C2×#4111yescharacteristic
419C22×C3×C5C2×#4111yescharacteristic
420C22×C3×C5H(5,𝔽2)11yescharacteristic
421C22×C3×C5H(5,𝔽2)11yescharacteristic
422C2×D15—22no—
423C2×D15—22no—
424C2×D15—22no—
425C2×D15—41no—
426C2×D15—41no—
427C2×D15—41no—
428C2×D15—41no—
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431C3×C4×C5—41no—
432C3×C4×C5—41no—
433Dic15—22no—
434Dic15—22no—
435Dic15—22no—
436Dic15—22no—
437Dic15—22no—
438Dic15—41no—
439Dic15—41no—
440C24×C3—22no—
441C24×C3—22no—
442C24×C3—22no—
443C24×C3—22no—
444C24×C3—41no—
445C24×C3—41no—
446C24×C3C4×D514yescomplemented
447C24×C3C22×D511yescharacteristic
448C24×C3C22×D511yescharacteristic
449C24×C3C22×D511yescharacteristic
450C23×D3—51no—
451C22×C3×C4—22no—
452C22×C3×C4—22no—
453C22×C3×C4—22no—
454C22×C3×C4—22no—
455C22×C3×C4—41no—
456C22×C3×C4—41no—
457C22×C3×C4C22×D511yescharacteristic
458C22×C3×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C22×C3×C4C22×D511yescharacteristic
461C2×#67—54no—
462C2×#67—54no—
463C2×#67—54no—
464C2×#67—102no—
465C2×#67—102no—
466C2×#67—102no—
467C2×#67—102no—
468C2×#67—201no—
469C2×#67—201no—
470C22×Dic3—51no—
471C22×Dic3—51no—
472C22×Dic3—51no—
473C22×Dic3—51no—
474C22×Dic3—51no—
475C22×Dic3—51no—
476C22×Dic3—51no—
477C22×Dic3—102no—
478C22×Dic3—102no—
479C22×Dic3—102no—
480C22×Dic3—102no—
481C22×Dic3—201no—
482C22×Dic3—201no—
483C2×C4×D3—102no—
484C2×C4×D3—102no—
485C2×C4×D3—201no—
486C3×C22⋊C4—22no—
487C3×C22⋊C4—22no—
488C3×C22⋊C4—22no—
489C3×C22⋊C4C22⋊D514yescomplemented
490#217—54no—
491#217—54no—
492#217—54no—
493#217—54no—
494#217—102no—
495#217—102no—
496#217—102no—
497(C2×D3)⋊C4—102no—
498(C2×D3)⋊C4—102no—
499(C2×D3)⋊C4—201no—
500Dic3⋊C4—102no—
501Dic3⋊C4—102no—
502Dic3⋊C4—201no—
503C4×Dic3—102no—
504C4×Dic3—102no—
505C4×Dic3—201no—
506C23×C5—21no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5—21no—
511C23×C5—21no—
512C23×C5—21no—
513C23×C5—21no—
514C23×C5—28no—
515C23×C5—28no—
516C23×C5—21no—
517C23×C5—21no—
518C23×C5—21no—
519C23×C5—21no—
520C23×C5—21no—
521C23×C5—21no—
522C23×C5—44no—
523C23×C5—44no—
524C23×C5—44no—
525C23×C5—44no—
526C23×C5—44no—
527C23×C5C2×C4×D312yes—
528C23×C5C2×C4×D312yes—
529C23×C5C2×C4×D312yes—
530C23×C5#23512yes—
531C23×C5D3×D412yes—
532C23×C5#23712yes—
533C23×C5C2×#6712yes—
534C23×C5C23×D311yescharacteristic
535C22×D5—32no—
536C22×D5—61no—
537C22×D5—61no—
538C22×D5—61no—
539C22×D5—61no—
540C22×D5—61no—
541C22×D5—61no—
542C2×C4×C5—21no—
543C2×C4×C5—21no—
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—21no—
547C2×C4×C5—21no—
548C2×C4×C5—21no—
549C2×C4×C5—21no—
550C2×C4×C5—21no—
551C2×C4×C5—21no—
552C2×C4×C5—44no—
553C2×C4×C5—44no—
554C2×C4×C5C2×#6712yes—
555C2×C4×C5C2×#6712yes—
556C22⋊D5—68no—
557C22⋊D5—68no—
558C22⋊D5—124no—
559C2×Dic5—32no—
560C2×Dic5—32no—
561C2×Dic5—32no—
562C2×Dic5—32no—
563C2×Dic5—32no—
564C2×Dic5—61no—
565C2×Dic5—61no—
566C2×Dic5—61no—
567C2×Dic5—61no—
568C2×Dic5—61no—
569C2×Dic5—61no—
570C2×Dic5—61no—
571C2×Dic5—61no—
572C2×Dic5—61no—
573C2×Dic5—61no—
574C2×Dic5—61no—
575C2×Dic5—61no—
576C2×Dic5—61no—
577C2×Dic5—61no—
578C2×Dic5—61no—
579C2×Dic5—61no—
580C2×Dic5—124no—
581C2×Dic5—124no—
582C4×D5—124no—
583C25C2×D1511yescharacteristic
584C22×D4—151no—
585C22×D4—151no—
586C22×D4—151no—
587C23×C4—151no—
588C23×C4—151no—
589C23×C4—151no—
590C23×C4C2×D1511yescharacteristic
591C23×C4C2×D1511yescharacteristic
592#120—158no—
593C4×D4—304no—
594C4×D4—304no—
595C2×C4⋊C4—151no—
596C2×C4⋊C4—151no—
597C2×C4⋊C4—151no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—151no—
600C2×C22⋊C4—151no—
601C2×C22⋊C4—151no—
602C2×C22⋊C4—151no—
603C2×C22⋊C4—151no—
604C2×C22⋊C4—151no—
605C2×C22⋊C4—151no—
606C2×C22⋊C4—151no—
607C2×C22⋊C4—151no—
608C2×C22⋊C4—151no—
609C2×C22⋊C4—304no—
610C2×C22⋊C4C2×D1511yescharacteristic
611C2×C22⋊C4C2×D1511yescharacteristic
612C2×C22⋊C4C2×D1511yescharacteristic
613C2×C22⋊C4C2×D1511yescharacteristic
614C2×C42—151no—
615C2×C42—151no—
616C2×C42—151no—
617#95—151no—
618#95—151no—
619#95—151no—
620#95—151no—
621#95—151no—
622#95—151no—
623C2×C3×C5—24no—
624C2×C3×C5—24no—
625C2×C3×C5—42no—
626C2×C3×C5C2×C4×D411yescharacteristic
627C2×C3×C5C2×C4×D411yescharacteristic
628C2×C3×C5#51811yescharacteristic
629C2×C3×C5D4211yescharacteristic
630C2×C3×C5#54611yescharacteristic
631C2×C3×C5#54611yescharacteristic
632C2×C3×C5#55111yescharacteristic
633D15—42no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3—21no—
639C23×C3—21no—
640C23×C3—21no—
641C23×C3—21no—
642C23×C3—21no—
643C23×C3—21no—
644C23×C3—21no—
645C23×C3—21no—
646C23×C3—21no—
647C23×C3—21no—
648C23×C3—28no—
649C23×C3—28no—
650C23×C3—44no—
651C23×C3—44no—
652C23×C3—44no—
653C23×C3—44no—
654C23×C3—44no—
655C23×C3C2×C4×D512yes—
656C23×C3C2×C4×D512yes—
657C23×C3C2×C4×D512yes—
658C23×C3#70912yes—
659C23×C3D4×D512yes—
660C23×C3#71112yes—
661C23×C3C2×C22⋊D512yes—
662C23×C3C23×D511yescharacteristic
663C22×D3—52no—
664C22×D3—101no—
665C22×D3—101no—
666C22×D3—101no—
667C22×D3—101no—
668C22×D3—101no—
669C22×D3—101no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—21no—
680C2×C3×C4—44no—
681C2×C3×C4—44no—
682C2×C3×C4C2×C22⋊D512yes—
683C2×C3×C4C2×C22⋊D512yes—
684#67—108no—
685#67—108no—
686#67—204no—
687C2×Dic3—52no—
688C2×Dic3—52no—
689C2×Dic3—52no—
690C2×Dic3—52no—
691C2×Dic3—52no—
692C2×Dic3—101no—
693C2×Dic3—101no—
694C2×Dic3—101no—
695C2×Dic3—101no—
696C2×Dic3—101no—
697C2×Dic3—101no—
698C2×Dic3—101no—
699C2×Dic3—101no—
700C2×Dic3—101no—
701C2×Dic3—101no—
702C2×Dic3—101no—
703C2×Dic3—101no—
704C2×Dic3—101no—
705C2×Dic3—101no—
706C2×Dic3—101no—
707C2×Dic3—101no—
708C2×Dic3—204no—
709C2×Dic3—204no—
710C4×D3—204no—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—22no—
715C22×C5—22no—
716C22×C5—22no—
717C22×C5—22no—
718C22×C5—22no—
719C22×C5—22no—
720C22×C5—22no—
721C22×C5—22no—
722C22×C5—22no—
723C22×C5—22no—
724C22×C5—22no—
725C22×C5—22no—
726C22×C5—416no—
727C22×C5—41no—
728C22×C5—41no—
729C22×C5—41no—
730C22×C5—41no—
731C22×C5#67⋊C414yescomplemented
732C22×C5C4×#6714yescomplemented
733C22×C5C22×C4×D311yescharacteristic
734C22×C5C2×#23511yescharacteristic
735C22×C5C2×D3×D411yescharacteristic
736C22×C5C2×#23711yescharacteristic
737C22×C5#100411yescharacteristic
738C22×C5#100411yescharacteristic
739C22×C5C22×#6711yescharacteristic
740C2×D5—62no—
741C2×D5—62no—
742C2×D5—62no—
743C2×D5—121no—
744C2×D5—121no—
745C2×D5—121no—
746C2×D5—121no—
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—41no—
750C4×C5—41no—
751Dic5—62no—
752Dic5—62no—
753Dic5—62no—
754Dic5—62no—
755Dic5—62no—
756Dic5—121no—
757Dic5—121no—
758C24—22no—
759C24—22no—
760C24—22no—
761C24—22no—
762C24—41no—
763C24—41no—
764C24—151no—
765C24C4×D1514yescomplemented
766C24C22×D1511yescharacteristic
767C24C22×D1511yescharacteristic
768C24C22×D1511yescharacteristic
769C2×D4—154no—
770C2×D4—154no—
771C2×D4—154no—
772C2×D4—302no—
773C2×D4—302no—
774C2×D4—302no—
775C2×D4—302no—
776C2×D4—601no—
777C2×D4—601no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—151no—
785C22×C4—151no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—151no—
789C22×C4—151no—
790C22×C4—151no—
791C22×C4—302no—
792C22×C4—302no—
793C22×C4—302no—
794C22×C4—302no—
795C22×C4—302no—
796C22×C4—302no—
797C22×C4—601no—
798C22×C4—601no—
799C22×C4—601no—
800C22×C4C22×D1511yescharacteristic
801C22×C4C22×D1511yescharacteristic
802C22×C4C22×D1511yescharacteristic
803C22×C4C22×D1511yescharacteristic
804C4⋊C4—302no—
805C4⋊C4—302no—
806C4⋊C4—601no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—154no—
811C22⋊C4—154no—
812C22⋊C4—154no—
813C22⋊C4—154no—
814C22⋊C4—302no—
815C22⋊C4—302no—
816C22⋊C4—302no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—601no—
820C22⋊C4#122014yescomplemented
821C42—302no—
822C42—302no—
823C42—601no—
824C3×C5#235811yescharacteristic, complemented, Hall
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—416no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3#402714yescomplemented
846C22×C3C4×C22⋊D514yescomplemented
847C22×C3C22×C4×D511yescharacteristic
848C22×C3C2×#70911yescharacteristic
849C22×C3C2×D4×D511yescharacteristic
850C22×C3C2×#71111yescharacteristic
851C22×C3#414411yescharacteristic
852C22×C3#414411yescharacteristic
853C22×C3C22×C22⋊D511yescharacteristic
854C2×D3—102no—
855C2×D3—102no—
856C2×D3—102no—
857C2×D3—201no—
858C2×D3—201no—
859C2×D3—201no—
860C2×D3—201no—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—41no—
864C3×C4—41no—
865Dic3—102no—
866Dic3—102no—
867Dic3—102no—
868Dic3—102no—
869Dic3—102no—
870Dic3—201no—
871Dic3—201no—
872C2×C5—24no—
873C2×C5—24no—
874C2×C5—42no—
875C2×C5C2×#67⋊C411yescharacteristic
876C2×C5#548611yescharacteristic
877C2×C5#549011yescharacteristic
878C2×C5#549511yescharacteristic
879C2×C5C2×C4×#6711yescharacteristic
880C2×C5D4×#6711yescharacteristic
881C2×C5#580611yescharacteristic
882D5—122no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—21no—
890C23—21no—
891C23—28no—
892C23—28no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—44no—
900C23—44no—
901C23—44no—
902C23—44no—
903C23—44no—
904C23—152no—
905C23—301no—
906C23—301no—
907C23—301no—
908C23—301no—
909C23—301no—
910C23—301no—
911C23C2×C4×D1512yes—
912C23C2×C4×D1512yes—
913C23C2×C4×D1512yes—
914C23#681712yes—
915C23D4×D1512yes—
916C23#681912yes—
917C23C2×#122012yes—
918C23C23×D1511yescharacteristic
919D4—308no—
920D4—308no—
921D4—604no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—44no—
933C2×C4—44no—
934C2×C4—152no—
935C2×C4—152no—
936C2×C4—152no—
937C2×C4—152no—
938C2×C4—152no—
939C2×C4—301no—
940C2×C4—301no—
941C2×C4—301no—
942C2×C4—301no—
943C2×C4—301no—
944C2×C4—301no—
945C2×C4—301no—
946C2×C4—301no—
947C2×C4—301no—
948C2×C4—301no—
949C2×C4—301no—
950C2×C4—301no—
951C2×C4—301no—
952C2×C4—301no—
953C2×C4—301no—
954C2×C4—301no—
955C2×C4—604no—
956C2×C4—604no—
957C2×C4—604no—
958C2×C4C2×#122012yes—
959C2×C4C2×#122012yes—
960C2×C3—24no—
961C2×C3—24no—
962C2×C3—42no—
963C2×C3C2×#402711yescharacteristic
964C2×C3#6582011yescharacteristic
965C2×C3#6582411yescharacteristic
966C2×C3#6582911yescharacteristic
967C2×C3C2×C4×C22⋊D511yescharacteristic
968C2×C3D4×C22⋊D511yescharacteristic
969C2×C3#6614011yescharacteristic
970D3—202no—
971C5#8209911yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—22no—
981C22—22no—
982C22—22no—
983C22—22no—
984C22—22no—
985C22—22no—
986C22—22no—
987C22—416no—
988C22—41no—
989C22—41no—
990C22—41no—
991C22—41no—
992C22—302no—
993C22—302no—
994C22—302no—
995C22—601no—
996C22—601no—
997C22—601no—
998C22—601no—
999C22#9177014yescomplemented
1000C22C4×#122014yescomplemented
1001C22C22×C4×D1511yescharacteristic
1002C22C2×#681711yescharacteristic
1003C22C2×D4×D1511yescharacteristic
1004C22C2×#681911yescharacteristic
1005C22#9209511yescharacteristic
1006C22#9209511yescharacteristic
1007C22C22×#122011yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—41no—
1011C4—41no—
1012C4—302no—
1013C4—302no—
1014C4—302no—
1015C4—302no—
1016C4—302no—
1017C4—601no—
1018C4—601no—
1019C3#1061383011yescharacteristic, complemented, Sylow
1020C2—24no—
1021C2—24no—
1022C2—42no—
1023C2—602no—
1024C2C2×#9177011yescharacteristic
1025C2#1175624511yescharacteristic
1026C2#1175624911yescharacteristic
1027C2#1175625411yescharacteristic
1028C2C2×C4×#122011yescharacteristic
1029C2D4×#122011yescharacteristic
1030C2#1175656511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×C22⋊C4C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91842C2
hypercenterC22×C22⋊C4D15
hypocenterC3×C5#2358
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×C22⋊C4C2semidirect
3. C22×#6719C2semidirect
4. C2×C4×#1220C2semidirect
5. C2×#91770C2semidirect
6. #11751314C2semidirect
7. #11751311C2semidirect
8. C4×#6719C2semidirect
9. #11751059C2semidirect
10. #11751058C2semidirect
11. #11751057C2semidirect
12. #11751047C2semidirect
13. #11751046C2semidirect
14. #11751045C2semidirect
15. C22⋊C4×Dic15C2semidirect
25. C22×C4×D15C22semidirect
31. #91842C4semidirect
41. C2×#6714C22semidirect
42. C2×#6714C22semidirect
43. C2×#6714C22semidirect
44. C2×#6712C22semidirect
45. C2×#6712C22semidirect
46. C2×#6712C22semidirect
47. C2×C4×Dic15C22semidirect
48. C2×C4×Dic15C22semidirect
49. C2×C4×Dic15C22semidirect
51. #91115C22semidirect
52. #91115C22semidirect
53. #91115C22semidirect
54. #91115C22semidirect
55. #91115C22semidirect
56. #91115C22semidirect
58. C22×C5×C22⋊C4D3semidirect
79. C24×C3×C5C2×C4semidirect
100. C2×#1220C2×C4semidirect
101. C2×#1220C2×C4semidirect
102. C2×#1220C2×C4semidirect
122. C3×C5×C22⋊C4D4semidirect
126. #6719C2×C4semidirect
127. #6719C2×C4semidirect
128. #6719C2×C4semidirect
129. #6719D4semidirect
139. C22×C3×C22⋊C4D5semidirect
318. C24×C5C4×D3semidirect
361. C5×C22⋊C4#67semidirect
382. C22×C22⋊C4D15semidirect
413. C22×C3×C5C4×D4semidirect
414. C22×C3×C5C4×D4semidirect
446. C24×C3C4×D5semidirect
489. C3×C22⋊C4C22⋊D5semidirect
731. C22×C5#67⋊C4semidirect
732. C22×C5C4×#67semidirect
765. C24C4×D15semidirect
820. C22⋊C4#1220semidirect
824. C3×C5#2358semidirect
845. C22×C3#4027semidirect
846. C22×C3C4×C22⋊D5semidirect
971. C5#82099semidirect
999. C22#91770semidirect
1000. C22C4×#1220semidirect
1019. C3#10613830semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C5×C22⋊C42
C2×#918422
C22×#67192
C2×C4×#12202
C2×#917702
#117513142
#117513112
C4×#67192
#117510592
#117510582
#117510572
#117510472
#117510462
#117510452
C22⋊C4×Dic152
#106138303
#820995