Finite Group Databasebeta

← Dic3×#4027 #14319599

Subgroups — Dic3×#4027 #14319599

Order 1920.

1848 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4027C211yesmaximal, characteristic
2C2×#91559C211yesmaximal, characteristic
3C2×Dic3×C22⋊D5C211yesmaximal, characteristic
4C22×Dic3×Dic5C211yesmaximal, characteristic, complemented
5C2×C4×D5×Dic3C211yesmaximal, characteristic, complemented
6C22⋊C4×Dic15C211yesmaximal, characteristic, complemented
7C5×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
8Dic5×#217C211yesmaximal, characteristic, complemented
9#11748884C211yesmaximal, characteristic, complemented
10Dic3×#685C211yesmaximal, characteristic, complemented
11#11748702C211yesmaximal, characteristic, complemented
12#11748638C211yesmaximal, characteristic, complemented
13#11748637C211yesmaximal, characteristic, complemented
14Dic3×#683C211yesmaximal, characteristic, complemented
15C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
16C4×#4027—31nomaximal, Hall
17C23×Dic15C2211yescharacteristic
18C23×C5×Dic3C2211yescharacteristic
19C22×C3×C22⋊D5C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×D5×Dic3C2211yescharacteristic
23C22×D5×Dic3C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×C4×Dic15C2211yescharacteristic
27C2×C4×Dic15C2211yescharacteristic
28C2×C5×#217C2211yescharacteristic
29C2×C4×C5×Dic3C2211yescharacteristic
30C2×C4×C5×Dic3C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#683C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34C3×#4027C418yescomplemented
35#91559C418yescomplemented
36Dic3×C22⋊D5C418yescomplemented
37C2×#6668C2211yescharacteristic
38C2×#6668C2211yescharacteristic
39C2×#6665C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×Dic3×Dic5—24no—
42C2×Dic3×Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic
47C2×Dic3×Dic5C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic
49C2×Dic3×Dic5C2211yescharacteristic
50C4×D5×Dic3—24no—
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53C5×C3⋊#95C2211yescharacteristic
54C5×C3⋊#95C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57C4×D4×Dic3—51nomaximal, Hall
58C2×C4×C22⋊D5—31no—
59C22×C4×Dic5—31no—
60C2×#4027—31no—
61C2×#4027D311yescharacteristic
62C2×C42×D5—31no—
63C4×C5×C22⋊C4—31no—
64C22⋊C4×Dic5—31no—
65C22⋊C4×Dic5—31no—
66C4×#685—31no—
67C4×#683—31no—
68C42×Dic5—31no—
69#64955—31no—
70#64955—31no—
71#64938—31no—
72#64938—31no—
73C24×C3×C5C2311yescharacteristic
74C23×C3×D5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×Dic15—22no—
78C22×Dic15—22no—
79C22×Dic15C2×C414yescomplemented
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×C5×Dic3—22no—
85C22×C5×Dic3—22no—
86C22×C5×Dic3C2×C414yescomplemented
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C2×C3×C22⋊D5C2×C414yes—
92C2×C3×C22⋊D5C2×C414yes—
93C2×C3×C22⋊D5C2×C414yes—
94C22×C3×Dic5—22no—
95C22×C3×Dic5—22no—
96C22×C3×Dic5C2×C414yescomplemented
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C2×C3×C4×D5—22no—
101C2×C3×C4×D5—22no—
102C2×C3×C4×D5C2×C414yescomplemented
103C2×D5×Dic3—22no—
104C2×D5×Dic3—22no—
105C2×D5×Dic3—22no—
106C2×D5×Dic3—22no—
107C2×D5×Dic3C2×C414yescomplemented
108C2×D5×Dic3C2×C414yescomplemented
109C3×C5×C22⋊C4C2×C414yescomplemented
110#6719C2×C414yescomplemented
111C4×Dic15—22no—
112C4×Dic15—22no—
113C5×#217C2×C414yescomplemented
114C4×C5×Dic3—22no—
115C4×C5×Dic3—22no—
116C3×#685C2×C414yescomplemented
117C3×#683C2×C414yescomplemented
118C3×C4×Dic5C2×C414yescomplemented
119#6668C2×C414yescomplemented
120#6668C2×C414yescomplemented
121#6665C2×C414yescomplemented
122#6665C2×C414yescomplemented
123Dic3×Dic5—22no—
124Dic3×Dic5—22no—
125Dic3×Dic5—22no—
126Dic3×Dic5—22no—
127Dic3×Dic5—22no—
128Dic3×Dic5C2×C414yescomplemented
129Dic3×Dic5C2×C414yescomplemented
130Dic3×Dic5D414yescomplemented
131C2×C3×C4×D4—51no—
132C2×D4×Dic3—51no—
133C2×D4×Dic3—51no—
134C22×C4×Dic3—51no—
135C22×C4×Dic3—51no—
136C4×#217—51no—
137C4×#217—51no—
138Dic3×C4⋊C4—51no—
139Dic3×C4⋊C4—51no—
140Dic3×C22⋊C4—51no—
141Dic3×C22⋊C4—51no—
142Dic3×C22⋊C4—51no—
143Dic3×C22⋊C4D511yescharacteristic, complemented
144C4×C4⋊Dic3—51no—
145C42×Dic3—51no—
146C23×C4×C5—31no—
147C22×C22⋊D5C2×D311yescharacteristic
148C23×Dic5—31no—
149C23×Dic5C2×D311yescharacteristic
150C22×C4×D5—31no—
151C22×C4×D5—31no—
152C22×C4×D5C2×D311yescharacteristic
153C2×C5×C22⋊C4—31no—
154C2×C5×C22⋊C4C2×D311yescharacteristic
155C2×C42×C5—31no—
156C2×C42×C5—31no—
157C2×C22⋊Dic5—31no—
158C4×C22⋊D5—38no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685C2×D311yescharacteristic
162C2×#683—31no—
163C2×#683—31no—
164C2×#683C2×D311yescharacteristic
165C2×C4×Dic5—31no—
166C2×C4×Dic5—31no—
167C2×C4×Dic5—31no—
168C2×C4×Dic5—31no—
169C2×C4×Dic5—31no—
170C2×C4×Dic5—31no—
171C2×C4×Dic5—31no—
172C2×C4×Dic5—31no—
173C2×C4×Dic5—31no—
174C2×C4×Dic5—31no—
175C2×C4×Dic5—64no—
176C2×C4×Dic5C2×D311yescharacteristic
177#4027—38no—
178#4027Dic318yesdirect product factor
179C42×D5—64no—
180C5×#95—31no—
181C5×#95—31no—
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186C42×D4—151noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5C22×C412yes—
192C23×C3×C5C22×C412yes—
193C23×C3×C5C22×C412yes—
194C23×C3×C5C2411yescharacteristic
195C22×C3×D5—21no—
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5C22×C412yes—
200C22×C3×D5C22×C412yes—
201C22×C3×D5C22×C412yes—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5C22×C412yes—
207C2×C3×C4×C5C22×C412yes—
208C2×Dic15—21no—
209C2×Dic15—21no—
210C2×Dic15—21no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—21no—
214C2×Dic15—28no—
215C2×Dic15C22×C412yes—
216C2×Dic15C22×C412yes—
217C2×Dic15C22×C412yes—
218C2×Dic15C22×C412yes—
219C2×Dic15C2×D412yes—
220C2×Dic15#4112yes—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—21no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—21no—
226C2×C5×Dic3—21no—
227C2×C5×Dic3—28no—
228C2×C5×Dic3C22×C412yes—
229C2×C5×Dic3C22×C412yes—
230C2×C5×Dic3C22×C412yes—
231C2×C5×Dic3C22×C412yes—
232C2×C5×Dic3C2×D412yes—
233C2×C5×Dic3#4112yes—
234C3×C22⋊D5C42116yescomplemented
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—28no—
238C2×C3×Dic5C22×C412yes—
239C2×C3×Dic5C22×C412yes—
240C2×C3×Dic5C22×C412yes—
241C2×C3×Dic5C22×C412yes—
242C2×C3×Dic5C22×C412yes—
243C2×C3×Dic5C2×D412yes—
244C2×C3×Dic5#4112yes—
245C3×C4×D5—28no—
246D5×Dic3—28no—
247D5×Dic3—28no—
248C22×C3×D4—51no—
249C23×C3×C4—51no—
250C23×C3×C4—51no—
251C23×Dic3—51no—
252C23×Dic3—51no—
253C23×Dic3—51no—
254C23×Dic3C2×D511yescharacteristic
255C3×C4×D4—58no—
256C2×C3×C4⋊C4—51no—
257C2×C3×C22⋊C4—51no—
258C2×C3×C22⋊C4C2×D511yescharacteristic
259C2×C3×C42—51no—
260C2×#217—51no—
261C2×#217—51no—
262C2×#217—51no—
263C2×#217C2×D511yescharacteristic
264D4×Dic3—58no—
265D4×Dic3—58no—
266C2×C4⋊Dic3—51no—
267C2×C4⋊Dic3—51no—
268C2×C4×Dic3—51no—
269C2×C4×Dic3—51no—
270C2×C4×Dic3—51no—
271C2×C4×Dic3—51no—
272C2×C4×Dic3—51no—
273C2×C4×Dic3—51no—
274C2×C4×Dic3—51no—
275C2×C4×Dic3—51no—
276C2×C4×Dic3—51no—
277C2×C4×Dic3—51no—
278C2×C4×Dic3—104no—
279C2×C4×Dic3—104no—
280C2×C4×Dic3C2×D511yescharacteristic
281C2×C4×Dic3C2×D511yescharacteristic
282C3⋊#95—51no—
283C3⋊#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95C2×D511yescharacteristic
287C3⋊#95C2×D511yescharacteristic
288C24×C5C22×D311yescharacteristic
289C23×D5C22×D311yescharacteristic
290C22×C4×C5—31no—
291C22×C4×C5—34no—
292C22×C4×C5—31no—
293C22×C4×C5—31no—
294C22×C4×C5—31no—
295C22×C4×C5—62no—
296C22×C4×C5—62no—
297C22×C4×C5C22×D311yescharacteristic
298C22×C4×C5C22×D311yescharacteristic
299C2×C22⋊D5C4×D314yes—
300C2×C22⋊D5C4×D314yes—
301C2×C22⋊D5C2×Dic314yes—
302C22×Dic5—22no—
303C22×Dic5—22no—
304C22×Dic5—31no—
305C22×Dic5—34no—
306C22×Dic5—31no—
307C22×Dic5—31no—
308C22×Dic5—31no—
309C22×Dic5—62no—
310C22×Dic5—62no—
311C22×Dic5C2×Dic314yescomplemented
312C22×Dic5C22×D311yescharacteristic
313C22×Dic5C22×D311yescharacteristic
314C22×Dic5C22×D311yescharacteristic
315C2×C4×D5—22no—
316C2×C4×D5—22no—
317C2×C4×D5—34no—
318C2×C4×D5—34no—
319C2×C4×D5—62no—
320C2×C4×D5—62no—
321C2×C4×D5—62no—
322C2×C4×D5—62no—
323C2×C4×D5C2×Dic314yescomplemented
324C5×C22⋊C4—34no—
325C5×C22⋊C4C2×Dic314yescomplemented
326C42×C5—62no—
327C42×C5—62no—
328C22⋊Dic5—34no—
329#685—34no—
330#685—34no—
331#685C2×Dic314yescomplemented
332#683—34no—
333#683—34no—
334#683C2×Dic314yescomplemented
335C4×Dic5—34no—
336C4×Dic5—34no—
337C4×Dic5—34no—
338C4×Dic5—62no—
339C4×Dic5—62no—
340C4×Dic5—62no—
341C4×Dic5—62no—
342C4×Dic5—62no—
343C4×Dic5—62no—
344C4×Dic5—62no—
345C4×Dic5C2×Dic314yescomplemented
346C2×C4×D4—51no—
347C2×C4×D4—151no—
348C2×C4×D4—151no—
349C22×C42—151no—
350C22×C42—151no—
351C4×C4⋊C4—151no—
352C4×C4⋊C4—151no—
353C4×C4⋊C4—151no—
354C4×C22⋊C4—31no—
355C4×C22⋊C4—151no—
356C4×C22⋊C4—151no—
357C4×C22⋊C4—151no—
358C4×C22⋊C4—151no—
359C4×C22⋊C4—151no—
360C43—151no—
361C22×C3×C5—22no—
362C22×C3×C5—22no—
363C22×C3×C5—22no—
364C22×C3×C5—22no—
365C22×C3×C5—22no—
366C22×C3×C5—22no—
367C22×C3×C5C2×C4214yescomplemented
368C22×C3×C5C23×C411yescharacteristic
369C22×C3×C5C23×C411yescharacteristic
370C22×C3×C5C23×C411yescharacteristic
371C22×C3×C5C22×D411yescharacteristic
372C22×C3×C5C2×#4111yescharacteristic
373C22×C3×C5C2×#4111yescharacteristic
374C22×C3×C5C2×#4111yescharacteristic
375C2×C3×D5—22no—
376C2×C3×D5—22no—
377C2×C3×D5—22no—
378C2×C3×D5—22no—
379C2×C3×D5—22no—
380C2×C3×D5—22no—
381C2×C3×D5C2×C4214yescomplemented
382C3×C4×C5—22no—
383C3×C4×C5—22no—
384Dic15—22no—
385Dic15—22no—
386Dic15—22no—
387Dic15C4×D414yescomplemented
388C3×Dic5—22no—
389C3×Dic5C2×C4214yescomplemented
390C3×Dic5C4×D414yescomplemented
391C5×Dic3—22no—
392C5×Dic3—22no—
393C5×Dic3—22no—
394C5×Dic3C4×D414yescomplemented
395C24×C3—51no—
396C24×C3C22×D511yescharacteristic
397C2×C3×D4—54no—
398C2×C3×D4—54no—
399C2×C3×D4—54no—
400C22×C3×C4—51no—
401C22×C3×C4—51no—
402C22×C3×C4—54no—
403C22×C3×C4—51no—
404C22×C3×C4—54no—
405C22×C3×C4—102no—
406C22×C3×C4—102no—
407C22×C3×C4—102no—
408C22×C3×C4—102no—
409C22×C3×C4C22×D511yescharacteristic
410C22×C3×C4C22×D511yescharacteristic
411C22×Dic3—22no—
412C22×Dic3—22no—
413C22×Dic3—51no—
414C22×Dic3—54no—
415C22×Dic3—51no—
416C22×Dic3—51no—
417C22×Dic3—51no—
418C22×Dic3—54no—
419C22×Dic3—54no—
420C22×Dic3—102no—
421C22×Dic3—102no—
422C22×Dic3—102no—
423C22×Dic3—102no—
424C22×Dic3—102no—
425C22×Dic3—102no—
426C22×Dic3C4×D514yescomplemented
427C22×Dic3C22×D511yescharacteristic
428C22×Dic3C22×D511yescharacteristic
429C22×Dic3C22×D511yescharacteristic
430C22×Dic3C22×D511yescharacteristic
431C3×C4⋊C4—54no—
432C3×C22⋊C4—54no—
433C3×C22⋊C4C4×D514yescomplemented
434C3×C42—54no—
435#217—54no—
436#217—54no—
437#217—54no—
438#217C4×D514yescomplemented
439C4⋊Dic3—54no—
440C4⋊Dic3—54no—
441C4×Dic3—22no—
442C4×Dic3—22no—
443C4×Dic3—54no—
444C4×Dic3—54no—
445C4×Dic3—54no—
446C4×Dic3—102no—
447C4×Dic3—102no—
448C4×Dic3—102no—
449C4×Dic3—102no—
450C4×Dic3—102no—
451C4×Dic3—102no—
452C4×Dic3—102no—
453C23×C5—21no—
454C23×C5—21no—
455C23×C5—21no—
456C23×C5—21no—
457C23×C5C2×C4×D312yes—
458C23×C5C2×C4×D312yes—
459C23×C5C22×Dic312yes—
460C23×C5C23×D311yescharacteristic
461C22×D5—21no—
462C22×D5—21no—
463C22×D5—21no—
464C22×D5—21no—
465C22×D5C2×C4×D312yes—
466C22×D5C2×C4×D312yes—
467C22×D5C22×Dic312yes—
468C2×C4×C5—21no—
469C2×C4×C5—21no—
470C2×C4×C5—21no—
471C2×C4×C5—21no—
472C2×C4×C5—32no—
473C2×C4×C5—32no—
474C2×C4×C5—32no—
475C2×C4×C5—32no—
476C2×C4×C5—32no—
477C2×C4×C5—32no—
478C2×C4×C5—68no—
479C2×C4×C5—61no—
480C2×C4×C5—61no—
481C2×C4×C5—61no—
482C2×C4×C5—61no—
483C2×C4×C5—61no—
484C2×C4×C5—61no—
485C2×C4×C5C22×Dic312yes—
486C2×C4×C5C22×Dic312yes—
487C22⋊D5C4×Dic3116yescomplemented
488C2×Dic5—21no—
489C2×Dic5—21no—
490C2×Dic5—28no—
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×Dic5C2×C4×D312yes—
505C2×Dic5C2×C4×D312yes—
506C2×Dic5D3×D412yes—
507C2×Dic5#23712yes—
508C2×Dic5C22×Dic312yes—
509C2×Dic5C22×Dic312yes—
510C2×Dic5C22×Dic312yes—
511C4×D5—28no—
512C4×D5—68no—
513C4×D5—68no—
514C22×D4—51no—
515C23×C4—31no—
516C23×C4—51no—
517C23×C4—51no—
518C23×C4—151no—
519C23×C4—151no—
520C23×C4—151no—
521C4×D4—58no—
522C4×D4—158no—
523C4×D4—158no—
524C2×C4⋊C4—51no—
525C2×C4⋊C4—151no—
526C2×C4⋊C4—151no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—51no—
529C2×C22⋊C4—151no—
530C2×C22⋊C4—151no—
531C2×C22⋊C4—151no—
532C2×C22⋊C4D3×D511yescharacteristic
533C2×C42—31no—
534C2×C42—31no—
535C2×C42—51no—
536C2×C42—151no—
537C2×C42—151no—
538C2×C42—151no—
539C2×C42—151no—
540C2×C42—151no—
541C2×C42—151no—
542C2×C42—151no—
543C2×C42—151no—
544C2×C42—151no—
545C2×C42—151no—
546C2×C42—304no—
547C2×C42—304no—
548#95—31no—
549#95—31no—
550#95—151no—
551#95—151no—
552#95—151no—
553#95—151no—
554C2×C3×C5—24no—
555C2×C3×C5C22×C4211yescharacteristic
556C2×C3×C5C2×C4×D411yescharacteristic
557C2×C3×C5C2×C4×D411yescharacteristic
558C2×C3×C5C2×C4×D411yescharacteristic
559C2×C3×C5C4×#4111yescharacteristic
560C2×C3×C5C4×#4111yescharacteristic
561C2×C3×C5C4×#4111yescharacteristic
562C3×D5—24no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—52no—
568C23×C3—52no—
569C23×C3—52no—
570C23×C3—101no—
571C23×C3—101no—
572C23×C3—101no—
573C23×C3—101no—
574C23×C3C2×C4×D512yes—
575C23×C3C2×C4×D512yes—
576C23×C3C2×C4×D512yes—
577C23×C3C23×D511yescharacteristic
578C3×D4—516no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—52no—
584C2×C3×C4—52no—
585C2×C3×C4—52no—
586C2×C3×C4—52no—
587C2×C3×C4—52no—
588C2×C3×C4—52no—
589C2×C3×C4—52no—
590C2×C3×C4—108no—
591C2×C3×C4—108no—
592C2×C3×C4—101no—
593C2×C3×C4—101no—
594C2×C3×C4C2×C4×D512yes—
595C2×C3×C4C2×C4×D512yes—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—28no—
603C2×Dic3—52no—
604C2×Dic3—52no—
605C2×Dic3—52no—
606C2×Dic3—52no—
607C2×Dic3—52no—
608C2×Dic3—52no—
609C2×Dic3—108no—
610C2×Dic3—108no—
611C2×Dic3—101no—
612C2×Dic3—101no—
613C2×Dic3—101no—
614C2×Dic3—101no—
615C2×Dic3—101no—
616C2×Dic3—101no—
617C2×Dic3—108no—
618C2×Dic3C2×C4×D512yes—
619C2×Dic3C2×C4×D512yes—
620C2×Dic3C2×C4×D512yes—
621C2×Dic3C2×C4×D512yes—
622C2×Dic3D4×D512yes—
623C2×Dic3#71112yes—
624C22×C5—22no—
625C22×C5—22no—
626C22×C5—22no—
627C22×C5—22no—
628C22×C5—22no—
629C22×C5—22no—
630C22×C5C2×C4×Dic314yescomplemented
631C22×C5C22×C4×D311yescharacteristic
632C22×C5C22×C4×D311yescharacteristic
633C22×C5C2×D3×D411yescharacteristic
634C22×C5C2×#23711yescharacteristic
635C22×C5D3×#4111yescharacteristic
636C22×C5D3×#4111yescharacteristic
637C22×C5C23×Dic311yescharacteristic
638C2×D5—22no—
639C2×D5—22no—
640C2×D5—22no—
641C2×D5—22no—
642C2×D5—22no—
643C2×D5—22no—
644C2×D5C2×C4×Dic314yescomplemented
645C4×C5—22no—
646C4×C5—22no—
647C4×C5—34no—
648C4×C5—62no—
649C4×C5—62no—
650C4×C5—62no—
651Dic5—22no—
652Dic5—34no—
653Dic5—62no—
654Dic5—62no—
655Dic5—62no—
656Dic5C2×C4×Dic314yescomplemented
657Dic5D4×Dic314yescomplemented
658C24—51no—
659C24C2×D3×D511yescharacteristic
660C2×D4—54no—
661C2×D4—54no—
662C2×D4—54no—
663C22×C4—31no—
664C22×C4—34no—
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—51no—
669C22×C4—51no—
670C22×C4—54no—
671C22×C4—51no—
672C22×C4—54no—
673C22×C4—62no—
674C22×C4—62no—
675C22×C4—102no—
676C22×C4—102no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—154no—
680C22×C4—154no—
681C22×C4—151no—
682C22×C4—154no—
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×C4C2×D3×D511yescharacteristic
693C22×C4C2×D3×D511yescharacteristic
694C4⋊C4—54no—
695C4⋊C4—154no—
696C4⋊C4—154no—
697C22⋊C4—34no—
698C22⋊C4—54no—
699C22⋊C4—154no—
700C22⋊C4—154no—
701C22⋊C4—154no—
702C22⋊C4D5×Dic314yescomplemented
703C42—54no—
704C42—62no—
705C42—62no—
706C42—154no—
707C42—154no—
708C42—154no—
709C42—302no—
710C42—302no—
711C42—302no—
712C42—302no—
713C42—302no—
714C42—302no—
715C42—302no—
716C3×C5C42×D411yescharacteristic, complemented, Hall
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—54no—
724C22×C3—102no—
725C22×C3—102no—
726C22×C3—102no—
727C22×C3—102no—
728C22×C3—102no—
729C22×C3—102no—
730C22×C3C42×D514yescomplemented
731C22×C3C22×C4×D511yescharacteristic
732C22×C3C22×C4×D511yescharacteristic
733C22×C3C22×C4×D511yescharacteristic
734C22×C3C2×D4×D511yescharacteristic
735C22×C3C2×#71111yescharacteristic
736C22×C3D5×#4111yescharacteristic
737C22×C3D5×#4111yescharacteristic
738C3×C4—22no—
739C3×C4—22no—
740C3×C4—54no—
741C3×C4—54no—
742C3×C4—102no—
743Dic3—22no—
744Dic3—22no—
745Dic3—22no—
746Dic3—54no—
747Dic3—102no—
748Dic3—102no—
749Dic3—102no—
750Dic3#402714yesdirect product factor
751C2×C5—24no—
752C2×C5C4×#23711yescharacteristic
753C2×C5C4×#23711yescharacteristic
754C2×C5C4×D3×D411yescharacteristic
755C2×C5C4×D3×D411yescharacteristic
756C2×C5C22×C4×Dic311yescharacteristic
757C2×C5C2×D4×Dic311yescharacteristic
758C2×C5Dic3×#4111yescharacteristic
759D5—24no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—52no—
765C23—52no—
766C23—52no—
767C23—101no—
768C23—101no—
769C23—101no—
770C23—101no—
771C23C4×D3×D512yes—
772C23C4×D3×D512yes—
773C23C2×D5×Dic312yes—
774C23C22×D3×D511yescharacteristic
775D4—516no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—32no—
781C2×C4—32no—
782C2×C4—32no—
783C2×C4—32no—
784C2×C4—32no—
785C2×C4—32no—
786C2×C4—52no—
787C2×C4—52no—
788C2×C4—52no—
789C2×C4—52no—
790C2×C4—52no—
791C2×C4—52no—
792C2×C4—52no—
793C2×C4—68no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—108no—
801C2×C4—108no—
802C2×C4—101no—
803C2×C4—101no—
804C2×C4—152no—
805C2×C4—152no—
806C2×C4—152no—
807C2×C4—152no—
808C2×C4—152no—
809C2×C4—152no—
810C2×C4—308no—
811C2×C4—308no—
812C2×C4—308no—
813C2×C4—301no—
814C2×C4—301no—
815C2×C4—301no—
816C2×C4—301no—
817C2×C4—301no—
818C2×C4—301no—
819C2×C4C2×D5×Dic312yes—
820C2×C4C2×D5×Dic312yes—
821C2×C3—24no—
822C2×C3—104no—
823C2×C3C2×C42×D511yescharacteristic
824C2×C3C2×#402711yescharacteristic
825C2×C3#6585611yescharacteristic
826C2×C3C4×#71111yescharacteristic
827C2×C3C4×#71111yescharacteristic
828C2×C3C4×D4×D511yescharacteristic
829C2×C3C4×D4×D511yescharacteristic
830C5C4×D4×Dic311yescharacteristic, complemented, Sylow
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—54no—
838C22—102no—
839C22—102no—
840C22—102no—
841C22—102no—
842C22—102no—
843C22—102no—
844C22C4×D5×Dic314yescomplemented
845C22C2×C4×D3×D511yescharacteristic
846C22C2×C4×D3×D511yescharacteristic
847C22D3×D4×D511yescharacteristic
848C22D5×#23711yescharacteristic
849C22D3×#71111yescharacteristic
850C22#9202411yescharacteristic
851C22C22×D5×Dic311yescharacteristic
852C4—22no—
853C4—22no—
854C4—34no—
855C4—54no—
856C4—54no—
857C4—62no—
858C4—62no—
859C4—62no—
860C4—102no—
861C4—154no—
862C4—302no—
863C4—302no—
864C4—302no—
865C3C4×#402711yescharacteristic, complemented, Sylow
866C2—24no—
867C2—104no—
868C2#1175281811yescharacteristic
869C2#1175282011yescharacteristic
870C2D3×#402711yescharacteristic
871C2#1175320311yescharacteristic
872C2C2×C4×D5×Dic311yescharacteristic
873C2D4×D5×Dic311yescharacteristic
874C2Dic3×#71111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC2×C3×C5C22×C42
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C42×D4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C22×Dic3×Dic5C2semidirect
5. C2×C4×D5×Dic3C2semidirect
6. C22⋊C4×Dic15C2semidirect
7. C5×Dic3×C22⋊C4C2semidirect
8. Dic5×#217C2semidirect
9. #11748884C2semidirect
10. Dic3×#685C2semidirect
11. #11748702C2semidirect
12. #11748638C2semidirect
13. #11748637C2semidirect
14. Dic3×#683C2semidirect
15. C4×Dic3×Dic5C2semidirect
34. C3×#4027C4semidirect
35. #91559C4semidirect
36. Dic3×C22⋊D5C4semidirect
79. C22×Dic15C2×C4semidirect
86. C22×C5×Dic3C2×C4semidirect
96. C22×C3×Dic5C2×C4semidirect
102. C2×C3×C4×D5C2×C4semidirect
107. C2×D5×Dic3C2×C4semidirect
108. C2×D5×Dic3C2×C4semidirect
109. C3×C5×C22⋊C4C2×C4semidirect
110. #6719C2×C4semidirect
113. C5×#217C2×C4semidirect
116. C3×#685C2×C4semidirect
117. C3×#683C2×C4semidirect
118. C3×C4×Dic5C2×C4semidirect
119. #6668C2×C4semidirect
120. #6668C2×C4semidirect
121. #6665C2×C4semidirect
122. #6665C2×C4semidirect
128. Dic3×Dic5C2×C4semidirect
129. Dic3×Dic5C2×C4semidirect
130. Dic3×Dic5D4semidirect
143. Dic3×C22⋊C4D5semidirect
178. #4027Dic3direct (N × H)
234. C3×C22⋊D5C42semidirect
311. C22×Dic5C2×Dic3semidirect
323. C2×C4×D5C2×Dic3semidirect
325. C5×C22⋊C4C2×Dic3semidirect
331. #685C2×Dic3semidirect
334. #683C2×Dic3semidirect
345. C4×Dic5C2×Dic3semidirect
367. C22×C3×C5C2×C42semidirect
381. C2×C3×D5C2×C42semidirect
387. Dic15C4×D4semidirect
389. C3×Dic5C2×C42semidirect
390. C3×Dic5C4×D4semidirect
394. C5×Dic3C4×D4semidirect
426. C22×Dic3C4×D5semidirect
433. C3×C22⋊C4C4×D5semidirect
438. #217C4×D5semidirect
487. C22⋊D5C4×Dic3semidirect
630. C22×C5C2×C4×Dic3semidirect
644. C2×D5C2×C4×Dic3semidirect
656. Dic5C2×C4×Dic3semidirect
657. Dic5D4×Dic3semidirect
702. C22⋊C4D5×Dic3semidirect
716. C3×C5C42×D4semidirect
730. C22×C3C42×D5semidirect
750. Dic3#4027direct (N × H)
830. C5C4×D4×Dic3semidirect
844. C22C4×D5×Dic3semidirect
865. C3C4×#4027semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40272
C2×#915592
C2×Dic3×C22⋊D52
C22×Dic3×Dic52
C2×C4×D5×Dic32
C22⋊C4×Dic152
C5×Dic3×C22⋊C42
Dic5×#2172
#117488842
Dic3×#6852
#117487022
#117486382
#117486372
Dic3×#6832
C4×Dic3×Dic52
C4×#40273
C4×D4×Dic35