Finite Group Databasebeta

← #14321534

Subgroups — #14321534

Order 1920.

1648 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×D20C211yesmaximal, characteristic, complemented
2C2×#91409C211yesmaximal, characteristic
3C2×#91395C211yesmaximal, characteristic, complemented
4C2×#91395C211yesmaximal, characteristic, complemented
5C2×C4×D5×Dic3C211yesmaximal, characteristic, complemented
6#11750771C211yesmaximal, characteristic, complemented
7C5×#4649C211yesmaximal, characteristic, complemented
8C3×#64954C211yesmaximal, characteristic, complemented
9#11748913C211yesmaximal, characteristic, complemented
10#11748907C211yesmaximal, characteristic, complemented
11#11748881C211yesmaximal, characteristic, complemented
12#11748878C211yesmaximal, characteristic, complemented
13Dic3×#685C211yesmaximal, characteristic, complemented
14#11748710C211yesmaximal, characteristic, complemented
15#11748693C211yesmaximal, characteristic, complemented
16C4×#4041—31nomaximal, Hall
17C22×C3×D20C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×#1202C2211yescharacteristic
20C22×#1202C2211yescharacteristic
21C22×#1200C2211yescharacteristic
22C22×D5×Dic3C2211yescharacteristic
23C22×D5×Dic3C2211yescharacteristic
24C22×D5×Dic3C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×C4⋊Dic15C2211yescharacteristic
29C2×C4×Dic15C2211yescharacteristic
30C2×C5×Dic3⋊C4C2211yescharacteristic
31C2×C5×Dic3⋊C4C2211yescharacteristic
32C2×C4×C5×Dic3C2211yescharacteristic
33C2×C4×C5×Dic3C2211yescharacteristic
34C2×C4×C5×Dic3C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×Dic3⋊Dic5C2211yescharacteristic
39C2×Dic3⋊Dic5C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46Dic3×D20—24no—
47#91409C418yescomplemented
48#91395—24no—
49#91395—24no—
50C4×D5×Dic3—24no—
51C3×C5×#95C2211yescharacteristic
52#91115C2211yescharacteristic
53C5×C3⋊#95C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#74660—51nomaximal, Hall
58C2×#4041—31no—
59C2×C4×D20—31no—
60C2×C4×D20—31no—
61C2×C4×D20—31no—
62C2×C42×D5—31no—
63C4×C5×C4⋊C4—31no—
64#65277—31no—
65#65276—31no—
66#65274—31no—
67C4×#685—31no—
68C4×#685—31no—
69#64959—31no—
70#64959—31no—
71#64954—31no—
72#64954D311yescharacteristic, complemented
73C23×D15C2311yescharacteristic
74C23×C3×D5C2311yescharacteristic
75C23×C3×D5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C2×C3×D20—22no—
89C2×C3×D20—22no—
90C2×C3×D20C2×C414yescomplemented
91C2×C3×C4×D5—22no—
92C2×C3×C4×D5—22no—
93C2×C3×C4×D5—22no—
94C2×#1202—22no—
95C2×#1202—22no—
96C2×#1202—22no—
97C2×#1202—22no—
98C2×#1202C2×C414yescomplemented
99C2×#1202C2×C414yescomplemented
100C2×#1200—22no—
101C2×#1200—22no—
102C2×#1200—22no—
103C2×D5×Dic3—22no—
104C2×D5×Dic3—22no—
105C2×D5×Dic3—22no—
106C2×D5×Dic3—22no—
107C2×D5×Dic3—22no—
108C2×D5×Dic3—22no—
109C2×D5×Dic3—22no—
110C2×D5×Dic3C2×C414yescomplemented
111C2×D5×Dic3D414yescomplemented
112#6714—22no—
113#6714—22no—
114#6714C2×C414yescomplemented
115C4⋊Dic15—22no—
116C4×Dic15—22no—
117C5×Dic3⋊C4—22no—
118C5×Dic3⋊C4C2×C414yescomplemented
119C4×C5×Dic3—22no—
120C4×C5×Dic3—22no—
121C4×C5×Dic3D414yescomplemented
122C3×#685—22no—
123C3×#685—22no—
124C3×#685—22no—
125Dic3⋊Dic5—22no—
126Dic3⋊Dic5—22no—
127#6667—22no—
128#6665—22no—
129#6665—22no—
130#6665C2×C414yescomplemented
131Dic3×Dic5—22no—
132Dic3×Dic5—22no—
133C2×#939—51no—
134C2×D4×Dic3—51no—
135C22×C4×Dic3—51no—
136C2×#67⋊C4—51no—
137C2×#67⋊C4—51no—
138C3×#386—51no—
139#5213—51no—
140#4957—51no—
141#4944—51no—
142#4942—51no—
143Dic3×C22⋊C4—51no—
144#4670—51no—
145#4666—51no—
146#4649D511yescharacteristic, complemented
147#4647—51no—
148C22×D20—31no—
149C22×D20—31no—
150C22×D20C2×D311yescharacteristic
151C22×C4×D5—31no—
152C22×C4×D5—31no—
153C22×C4×D5—31no—
154C22×C4×D5—31no—
155C22×C4×D5C2×D311yescharacteristic
156C2×C5×C4⋊C4—31no—
157C2×C5×C4⋊C4—31no—
158C2×C42×C5—31no—
159C2×C42×C5—31no—
160C2×C42×C5—31no—
161C2×#685—31no—
162C2×#685—31no—
163C2×#685—31no—
164C2×#685—31no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685C2×D311yescharacteristic
169C2×#685C2×D311yescharacteristic
170C2×#685C2×D311yescharacteristic
171C2×C4⋊Dic5—31no—
172C2×C4⋊Dic5—31no—
173C2×C4⋊Dic5—31no—
174C2×C4×Dic5—31no—
175C2×C4×Dic5—31no—
176C2×C4×Dic5—31no—
177#4041—38no—
178C4×D20—64no—
179C4×D20—64no—
180C4×D20—64no—
181C42×D5—64no—
182C5×#95—31no—
183C5×#95C2×D311yescharacteristic
184#3963—31no—
185#3963—31no—
186#3963—31no—
187#3963C2×D311yescharacteristic
188C4×#121—151noSylow
189C23×C3×C5C2411yescharacteristic
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—21no—
194C22×D15—21no—
195C22×D15—21no—
196C22×D15C22×C412yes—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—21no—
201C22×C3×D5—21no—
202C22×C3×D5—21no—
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5C22×C412yes—
208C22×C3×D5C22×C412yes—
209C22×C3×D5C2×D412yes—
210C22×C3×D5#4112yes—
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×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5C22×C412yes—
219C2×C3×C4×C5C2×D412yes—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15C22×C412yes—
228C2×Dic15C2×D412yes—
229C2×C5×Dic3—21no—
230C2×C5×Dic3—21no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3C22×C412yes—
235C2×C5×Dic3C22×C412yes—
236C2×C5×Dic3C2×D412yes—
237C2×C5×Dic3C2×D412yes—
238C2×C5×Dic3C2×D412yes—
239C2×C5×Dic3#4112yes—
240C2×C5×Dic3#4112yes—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5#4112yes—
247C3×D20—28no—
248C3×C4×D5—28no—
249#1202—28no—
250#1202—28no—
251#1200—44no—
252D5×Dic3—28no—
253D5×Dic3—28no—
254D5×Dic3—44no—
255C22×C3×D4—51no—
256C23×C3×C4—51no—
257C22×#67—51no—
258C22×#67—51no—
259C23×Dic3—51no—
260C23×Dic3—51no—
261C23×Dic3—51no—
262C22×C4×D3—51no—
263C2×C3×C22⋊C4—51no—
264C2×C3×C22⋊C4—51no—
265C2×C3×C22⋊C4—51no—
266C2×#217—51no—
267C2×#217—51no—
268C2×#217—51no—
269#939—58no—
270D4×Dic3—104no—
271C2×(C2×D3)⋊C4—51no—
272C2×(C2×D3)⋊C4—51no—
273C2×(C2×D3)⋊C4—51no—
274C2×(C2×D3)⋊C4—51no—
275C2×C4⋊Dic3—51no—
276C2×Dic3⋊C4—51no—
277C2×Dic3⋊C4—51no—
278C2×Dic3⋊C4C2×D511yescharacteristic
279C2×Dic3⋊C4C2×D511yescharacteristic
280C2×C4×Dic3—51no—
281C2×C4×Dic3—51no—
282C2×C4×Dic3—51no—
283C2×C4×Dic3—104no—
284C2×C4×Dic3C2×D511yescharacteristic
285C2×C4×Dic3C2×D511yescharacteristic
286C2×C4×Dic3C2×D511yescharacteristic
287#67⋊C4—104no—
288#67⋊C4—104no—
289C3×#95—51no—
290C3×#95C2×D511yescharacteristic
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95C2×D511yescharacteristic
295C23×D5—31no—
296C23×D5C22×D311yescharacteristic
297C23×D5C22×D311yescharacteristic
298C22×C4×C5—31no—
299C22×C4×C5—31no—
300C22×C4×C5—31no—
301C22×C4×C5—31no—
302C22×C4×C5C22×D311yescharacteristic
303C22×C4×C5C22×D311yescharacteristic
304C22×C4×C5C22×D311yescharacteristic
305C22×Dic5—31no—
306C22×Dic5—31no—
307C22×Dic5—31no—
308C22×Dic5C22×D311yescharacteristic
309C22×Dic5C22×D311yescharacteristic
310C2×D20—22no—
311C2×D20—22no—
312C2×D20—34no—
313C2×D20—34no—
314C2×D20—62no—
315C2×D20—62no—
316C2×D20—62no—
317C2×D20—62no—
318C2×D20C4×D314yescomplemented
319C2×C4×D5—22no—
320C2×C4×D5—22no—
321C2×C4×D5—22no—
322C2×C4×D5—34no—
323C2×C4×D5—34no—
324C2×C4×D5—62no—
325C2×C4×D5—62no—
326C2×C4×D5—62no—
327C2×C4×D5—62no—
328C2×C4×D5—62no—
329C2×C4×D5—62no—
330C2×C4×D5—62no—
331C2×C4×D5—62no—
332C2×C4×D5—62no—
333C2×C4×D5—62no—
334C5×C4⋊C4—34no—
335C5×C4⋊C4—62no—
336C42×C5—34no—
337C42×C5—62no—
338C42×C5—62no—
339#685—22no—
340#685—22no—
341#685—22no—
342#685—34no—
343#685—34no—
344#685—62no—
345#685—62no—
346#685—62no—
347#685—62no—
348#685—62no—
349C4⋊Dic5—62no—
350C4⋊Dic5—62no—
351C4⋊Dic5—62no—
352C4×Dic5—62no—
353C4×Dic5—62no—
354C4×Dic5—62no—
355C2×#121—151no—
356C2×C4×D4—151no—
357C2×C4×D4—151no—
358C2×C4×D4—151no—
359C22×C42—151no—
360#390—151no—
361#389—151no—
362#388—151no—
363#388—151no—
364#386—51no—
365#386—151no—
366#380—151no—
367C4×C4⋊C4—31no—
368C4×C22⋊C4—151no—
369C4×C22⋊C4—151no—
370C22×C3×C5C23×C411yescharacteristic
371C22×C3×C5C22×D411yescharacteristic
372C22×C3×C5C22×D411yescharacteristic
373C22×C3×C5C2×#4111yescharacteristic
374C22×C3×C5C2×#4111yescharacteristic
375C22×C3×C5C2×#4111yescharacteristic
376C22×C3×C5C2×#4111yescharacteristic
377C2×D15—22no—
378C2×D15—22no—
379C2×D15—22no—
380C2×D15—41no—
381C2×D15—41no—
382C2×D15—41no—
383C2×D15—41no—
384C2×C3×D5—22no—
385C2×C3×D5—22no—
386C2×C3×D5—22no—
387C2×C3×D5—22no—
388C2×C3×D5—22no—
389C2×C3×D5—22no—
390C2×C3×D5—22no—
391C2×C3×D5—22no—
392C2×C3×D5—22no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C2×C3×D5C4×D414yescomplemented
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400C3×C4×C5—41no—
401Dic15—22no—
402Dic15—22no—
403Dic15—41no—
404C3×Dic5—22no—
405C3×Dic5—41no—
406C5×Dic3—22no—
407C5×Dic3—41no—
408C5×Dic3C4×D414yescomplemented
409C5×Dic3#12114yescomplemented
410C24×C3—51no—
411C24×C3—51no—
412C23×D3—51no—
413C2×C3×D4—54no—
414C2×C3×D4—102no—
415C2×C3×D4—102no—
416C22×C3×C4—51no—
417C22×C3×C4—51no—
418C22×C3×C4—102no—
419C22×C3×C4—102no—
420C22×C3×C4—102no—
421C22×C3×C4C22×D511yescharacteristic
422C22×C3×C4C22×D511yescharacteristic
423C22×C3×C4C22×D511yescharacteristic
424C2×#67—54no—
425C2×#67—54no—
426C2×#67—102no—
427C2×#67—102no—
428C2×#67—102no—
429C2×#67—102no—
430C22×Dic3—51no—
431C22×Dic3—51no—
432C22×Dic3—54no—
433C22×Dic3—54no—
434C22×Dic3—51no—
435C22×Dic3—102no—
436C22×Dic3—102no—
437C22×Dic3—102no—
438C22×Dic3—102no—
439C22×Dic3—102no—
440C22×Dic3—102no—
441C22×Dic3—102no—
442C22×Dic3C22×D511yescharacteristic
443C22×Dic3C22×D511yescharacteristic
444C22×Dic3C22×D511yescharacteristic
445C22×Dic3C22×D511yescharacteristic
446C2×C4×D3—102no—
447C2×C4×D3—102no—
448C2×C4×D3—102no—
449C3×C22⋊C4—102no—
450C3×C22⋊C4—102no—
451C3×C22⋊C4—102no—
452#217—54no—
453#217—102no—
454#217—102no—
455(C2×D3)⋊C4—54no—
456(C2×D3)⋊C4—102no—
457(C2×D3)⋊C4—102no—
458(C2×D3)⋊C4—102no—
459C4⋊Dic3—102no—
460Dic3⋊C4—22no—
461Dic3⋊C4—102no—
462Dic3⋊C4—102no—
463Dic3⋊C4C4×D514yescomplemented
464C4×Dic3—22no—
465C4×Dic3—22no—
466C4×Dic3—102no—
467C4×Dic3—102no—
468C4×Dic3—102no—
469C4×Dic3D2014yescomplemented
470C23×C5C23×D311yescharacteristic
471C22×D5—21no—
472C22×D5—21no—
473C22×D5—21no—
474C22×D5—21no—
475C22×D5—21no—
476C22×D5—21no—
477C22×D5—21no—
478C22×D5—21no—
479C22×D5—21no—
480C22×D5—21no—
481C22×D5—32no—
482C22×D5—61no—
483C22×D5—61no—
484C22×D5—61no—
485C22×D5—61no—
486C22×D5—61no—
487C22×D5—61no—
488C22×D5C2×C4×D312yes—
489C22×D5C2×C4×D312yes—
490C22×D5D3×D412yes—
491C22×D5#23712yes—
492C2×C4×C5—21no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—21no—
499C2×C4×C5—32no—
500C2×C4×C5—32no—
501C2×C4×C5—32no—
502C2×C4×C5—32no—
503C2×C4×C5—32no—
504C2×C4×C5—32no—
505C2×C4×C5—32no—
506C2×C4×C5—61no—
507C2×C4×C5—61no—
508C2×C4×C5—61no—
509C2×C4×C5—61no—
510C2×C4×C5—61no—
511C2×C4×C5C2×C4×D312yes—
512C2×C4×C5D3×D412yes—
513C2×Dic5—21no—
514C2×Dic5—21no—
515C2×Dic5—21no—
516C2×Dic5—21no—
517C2×Dic5—21no—
518C2×Dic5—32no—
519C2×Dic5—32no—
520C2×Dic5—61no—
521C2×Dic5—61no—
522C2×Dic5—61no—
523C2×Dic5—61no—
524C2×Dic5—61no—
525C2×Dic5—61no—
526C2×Dic5—61no—
527C2×Dic5#23712yes—
528D20—28no—
529D20—68no—
530D20—68no—
531C4×D5—28no—
532C4×D5—68no—
533C4×D5—68no—
534C4×D5—124no—
535C4×D5—124no—
536C22×D4—51no—
537C22×D4—151no—
538C22×D4—151no—
539C23×C4—51no—
540C23×C4—151no—
541C23×C4—151no—
542C23×C4—151no—
543C23×C4—151no—
544#121—158no—
545C4×D4—304no—
546C4×D4—304no—
547C4×D4—304no—
548C2×C4⋊C4—31no—
549C2×C4⋊C4—31no—
550C2×C4⋊C4—151no—
551C2×C4⋊C4—151no—
552C2×C4⋊C4—151no—
553C2×C22⋊C4—51no—
554C2×C22⋊C4—51no—
555C2×C22⋊C4—51no—
556C2×C22⋊C4—151no—
557C2×C22⋊C4—151no—
558C2×C22⋊C4—151no—
559C2×C22⋊C4—151no—
560C2×C22⋊C4—151no—
561C2×C22⋊C4—151no—
562C2×C22⋊C4—151no—
563C2×C42—31no—
564C2×C42—31no—
565C2×C42—31no—
566C2×C42—151no—
567C2×C42—151no—
568C2×C42—151no—
569C2×C42—304no—
570#95—31no—
571#95—51no—
572#95—151no—
573#95—151no—
574#95—151no—
575#95D3×D511yescharacteristic
576C2×C3×C5C2×C4×D411yescharacteristic
577C2×C3×C5C2×C4×D411yescharacteristic
578C2×C3×C5C4×#4111yescharacteristic
579C2×C3×C5C2×#12111yescharacteristic
580C2×C3×C5#52511yescharacteristic
581C2×C3×C5#52911yescharacteristic
582C2×C3×C5#53211yescharacteristic
583D15—42no—
584C3×D5—24no—
585C3×D5—42no—
586C23×C3—52no—
587C23×C3—52no—
588C23×C3—52no—
589C23×C3—52no—
590C23×C3—101no—
591C23×C3—101no—
592C23×C3—101no—
593C23×C3—101no—
594C23×C3—101no—
595C23×C3—101no—
596C23×C3—101no—
597C23×C3—101no—
598C23×C3—101no—
599C23×C3—101no—
600C23×C3C23×D511yescharacteristic
601C22×D3—52no—
602C22×D3—101no—
603C22×D3—101no—
604C22×D3—101no—
605C22×D3—101no—
606C22×D3—101no—
607C22×D3—101no—
608C3×D4—108no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—52no—
617C2×C3×C4—108no—
618C2×C3×C4—101no—
619C2×C3×C4—101no—
620C2×C3×C4—101no—
621C2×C3×C4—101no—
622C2×C3×C4—101no—
623C2×C3×C4C2×C4×D512yes—
624C2×C3×C4C2×D2012yes—
625#67—108no—
626#67—108no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—52no—
633C2×Dic3—52no—
634C2×Dic3—101no—
635C2×Dic3—101no—
636C2×Dic3—101no—
637C2×Dic3—101no—
638C2×Dic3—108no—
639C2×Dic3—108no—
640C2×Dic3—101no—
641C2×Dic3—101no—
642C2×Dic3—101no—
643C2×Dic3—204no—
644C2×Dic3C2×C4×D512yes—
645C2×Dic3C2×C4×D512yes—
646C2×Dic3C2×D2012yes—
647C2×Dic3C2×D2012yes—
648C2×Dic3#70912yes—
649C2×Dic3D4×D512yes—
650C2×Dic3#71312yes—
651C4×D3—204no—
652C22×C5C22×C4×D311yescharacteristic
653C22×C5C2×D3×D411yescharacteristic
654C22×C5C2×D3×D411yescharacteristic
655C22×C5C2×#23711yescharacteristic
656C22×C5C2×#23711yescharacteristic
657C22×C5D3×#4111yescharacteristic
658C22×C5D3×#4111yescharacteristic
659C2×D5—22no—
660C2×D5—22no—
661C2×D5—22no—
662C2×D5—22no—
663C2×D5—22no—
664C2×D5—22no—
665C2×D5—22no—
666C2×D5—22no—
667C2×D5—22no—
668C2×D5—41no—
669C2×D5—41no—
670C2×D5—41no—
671C2×D5—41no—
672C2×D5—62no—
673C2×D5—62no—
674C2×D5—62no—
675C2×D5—121no—
676C2×D5—121no—
677C2×D5—121no—
678C2×D5—121no—
679C2×D5#67⋊C414yescomplemented
680C4×C5—22no—
681C4×C5—22no—
682C4×C5—34no—
683C4×C5—34no—
684C4×C5—41no—
685C4×C5—62no—
686C4×C5—121no—
687Dic5—22no—
688Dic5—41no—
689Dic5—62no—
690Dic5—62no—
691Dic5—121no—
692C24—51no—
693C24—51no—
694C24—151no—
695C2×D4—54no—
696C2×D4—102no—
697C2×D4—102no—
698C2×D4—154no—
699C2×D4—154no—
700C2×D4—302no—
701C2×D4—302no—
702C2×D4—302no—
703C2×D4—302no—
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—51no—
709C22×C4—51no—
710C22×C4—102no—
711C22×C4—102no—
712C22×C4—102no—
713C22×C4—154no—
714C22×C4—154no—
715C22×C4—151no—
716C22×C4—151no—
717C22×C4—151no—
718C22×C4—302no—
719C22×C4—302no—
720C22×C4—302no—
721C22×C4—302no—
722C22×C4—302no—
723C22×C4—302no—
724C22×C4—302no—
725C22×C4—302no—
726C22×C4—302no—
727C22×C4—302no—
728C22×C4C2×D3×D511yescharacteristic
729C22×C4C2×D3×D511yescharacteristic
730C22×C4C2×D3×D511yescharacteristic
731C4⋊C4—34no—
732C4⋊C4—62no—
733C4⋊C4—302no—
734C4⋊C4—302no—
735C4⋊C4—302no—
736C22⋊C4—102no—
737C22⋊C4—102no—
738C22⋊C4—102no—
739C22⋊C4—154no—
740C22⋊C4—154no—
741C22⋊C4—302no—
742C22⋊C4—302no—
743C22⋊C4—302no—
744C22⋊C4—302no—
745C22⋊C4—302no—
746C42—34no—
747C42—62no—
748C42—62no—
749C42—302no—
750C42—302no—
751C42—302no—
752C3×C5C4×#12111yescharacteristic, complemented, Hall
753C22×C3—54no—
754C22×C3—102no—
755C22×C3—102no—
756C22×C3—102no—
757C22×C3—102no—
758C22×C3—102no—
759C22×C3—102no—
760C22×C3—102no—
761C22×C3—102no—
762C22×C3—102no—
763C22×C3—201no—
764C22×C3—201no—
765C22×C3—201no—
766C22×C3—201no—
767C22×C3C22×C4×D511yescharacteristic
768C22×C3C22×D2011yescharacteristic
769C22×C3C2×#70911yescharacteristic
770C22×C3C2×D4×D511yescharacteristic
771C22×C3C2×#71311yescharacteristic
772C22×C3D5×#4111yescharacteristic
773C22×C3D5×#4111yescharacteristic
774C2×D3—102no—
775C2×D3—102no—
776C2×D3—102no—
777C2×D3—201no—
778C2×D3—201no—
779C2×D3—201no—
780C2×D3—201no—
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—41no—
784C3×C4—102no—
785C3×C4—201no—
786Dic3—22no—
787Dic3—41no—
788Dic3—102no—
789Dic3—102no—
790Dic3—201no—
791Dic3C4×D2014yescomplemented
792Dic3#404114yescomplemented
793C2×C5C2×#67⋊C411yescharacteristic
794C2×C5C4×#23711yescharacteristic
795C2×C5C4×D3×D411yescharacteristic
796C2×C5#558611yescharacteristic
797C2×C5#559611yescharacteristic
798C2×C5D3×#12111yescharacteristic
799C2×C5#564911yescharacteristic
800D5—24no—
801D5—42no—
802D5—122no—
803C23—52no—
804C23—52no—
805C23—52no—
806C23—52no—
807C23—101no—
808C23—101no—
809C23—101no—
810C23—101no—
811C23—101no—
812C23—101no—
813C23—101no—
814C23—101no—
815C23—101no—
816C23—101no—
817C23—152no—
818C23—301no—
819C23—301no—
820C23—301no—
821C23—301no—
822C23—301no—
823C23—301no—
824C23C22×D3×D511yescharacteristic
825D4—108no—
826D4—308no—
827D4—308no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—32no—
836C2×C4—32no—
837C2×C4—32no—
838C2×C4—32no—
839C2×C4—32no—
840C2×C4—32no—
841C2×C4—32no—
842C2×C4—52no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—108no—
849C2×C4—101no—
850C2×C4—101no—
851C2×C4—101no—
852C2×C4—101no—
853C2×C4—101no—
854C2×C4—152no—
855C2×C4—152no—
856C2×C4—308no—
857C2×C4—308no—
858C2×C4—301no—
859C2×C4—301no—
860C2×C4—301no—
861C2×C4—301no—
862C2×C4—301no—
863C2×C4—301no—
864C2×C4—301no—
865C2×C4—604no—
866C2×C4—604no—
867C2×C4C4×D3×D512yes—
868C2×C4D3×D2012yes—
869C2×C3—104no—
870C2×C3—202no—
871C2×C3C2×C4×D2011yescharacteristic
872C2×C3C2×#404111yescharacteristic
873C2×C3#6585811yescharacteristic
874C2×C3C4×D4×D511yescharacteristic
875C2×C3#6588211yescharacteristic
876C2×C3C4×#71311yescharacteristic
877C2×C3#6591411yescharacteristic
878D3—202no—
879C5#7466011yescharacteristic, complemented, Sylow
880C22—54no—
881C22—102no—
882C22—102no—
883C22—102no—
884C22—102no—
885C22—102no—
886C22—102no—
887C22—102no—
888C22—102no—
889C22—102no—
890C22—201no—
891C22—201no—
892C22—201no—
893C22—201no—
894C22—302no—
895C22—302no—
896C22—302no—
897C22—601no—
898C22—601no—
899C22—601no—
900C22—601no—
901C22C2×C4×D3×D511yescharacteristic
902C22C2×D3×D2011yescharacteristic
903C22D3×#70911yescharacteristic
904C22D3×D4×D511yescharacteristic
905C22D5×#23711yescharacteristic
906C22D5×#23711yescharacteristic
907C22D3×#71311yescharacteristic
908C4—22no—
909C4—22no—
910C4—34no—
911C4—34no—
912C4—41no—
913C4—62no—
914C4—102no—
915C4—121no—
916C4—201no—
917C4—302no—
918C4—302no—
919C4—601no—
920C3C4×#404111yescharacteristic, complemented, Sylow
921C2—104no—
922C2—202no—
923C2—602no—
924C2C4×D3×D2011yescharacteristic
925C2#1175283111yescharacteristic
926C2#1175287511yescharacteristic
927C2D5×#67⋊C411yescharacteristic
928C2#1175340011yescharacteristic
929C2#1175351311yescharacteristic
930C2D3×#404111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91409C2
hypercenter#95D3×D5
hypocenterC3×C5C4×#121
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×Dic3×D20C2semidirect
3. C2×#91395C2semidirect
4. C2×#91395C2semidirect
5. C2×C4×D5×Dic3C2semidirect
6. #11750771C2semidirect
7. C5×#4649C2semidirect
8. C3×#64954C2semidirect
9. #11748913C2semidirect
10. #11748907C2semidirect
11. #11748881C2semidirect
12. #11748878C2semidirect
13. Dic3×#685C2semidirect
14. #11748710C2semidirect
15. #11748693C2semidirect
47. #91409C4semidirect
72. #64954D3semidirect
90. C2×C3×D20C2×C4semidirect
98. C2×#1202C2×C4semidirect
99. C2×#1202C2×C4semidirect
110. C2×D5×Dic3C2×C4semidirect
111. C2×D5×Dic3D4semidirect
114. #6714C2×C4semidirect
118. C5×Dic3⋊C4C2×C4semidirect
121. C4×C5×Dic3D4semidirect
130. #6665C2×C4semidirect
146. #4649D5semidirect
318. C2×D20C4×D3semidirect
397. C2×C3×D5C4×D4semidirect
408. C5×Dic3C4×D4semidirect
409. C5×Dic3#121semidirect
463. Dic3⋊C4C4×D5semidirect
469. C4×Dic3D20semidirect
679. C2×D5#67⋊C4semidirect
752. C3×C5C4×#121semidirect
791. Dic3C4×D20semidirect
792. Dic3#4041semidirect
879. C5#74660semidirect
920. C3C4×#4041semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×D202
C2×#914092
C2×#913952
C2×C4×D5×Dic32
#117507712
C5×#46492
C3×#649542
#117489132
#117489072
#117488812
#117488782
Dic3×#6852
#117487102
#117486932
C4×#40413
#746605