Finite Group Databasebeta

← #14321473

Subgroups — #14321473

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×#91770C211yesmaximal, characteristic, complemented
2C2×#91566C211yesmaximal, characteristic
3C2×#67⋊Dic5C211yesmaximal, characteristic, complemented
4C22×Dic3×Dic5C211yesmaximal, characteristic, complemented
5C2×#91406C211yesmaximal, characteristic, complemented
6C5×#4958C211yesmaximal, characteristic, complemented
7C3×#65231C211yesmaximal, characteristic, complemented
8#11749498C211yesmaximal, characteristic, complemented
9#11748909C211yesmaximal, characteristic, complemented
10#11748886C211yesmaximal, characteristic, complemented
11#11748720C211yesmaximal, characteristic, complemented
12#11748670C211yesmaximal, characteristic, complemented
13#11748668C211yesmaximal, characteristic, complemented
14#11748637C211yesmaximal, characteristic, complemented
15#11748627C211yesmaximal, characteristic, complemented
16#10606391—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C23×C5×Dic3C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C22×#1203C2211yescharacteristic
24C22×D3×Dic5C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6712C2211yescharacteristic
28C2×C4×Dic15C2211yescharacteristic
29#91770—24no—
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×C3×#683C2211yescharacteristic
34C2×C3×#683C2211yescharacteristic
35#91566C418yescomplemented
36#67⋊Dic5—24no—
37C2×Dic3⋊Dic5C2211yescharacteristic
38C2×#6668C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×Dic3×Dic5—24no—
45C2×Dic3×Dic5C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic
47C2×Dic3×Dic5C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic
49C2×Dic3×Dic5C2211yescharacteristic
50#91406—24no—
51C5×C3⋊#95C2211yescharacteristic
52C5×C3⋊#95C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#73865—51nomaximal, Hall
58C2×#4085—31no—
59C2×D4×Dic5—31no—
60C22×C4×Dic5—31no—
61C2×#4027—31no—
62C2×#4027—31no—
63C5×#386—31no—
64#65502—31no—
65#65246—31no—
66#65233—31no—
67#65231D311yescharacteristic, complemented
68C22⋊C4×Dic5—31no—
69#64959—31no—
70#64955—31no—
71#64938—31no—
72#64936—31no—
73C24×C3×C5C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C2×#1220—22no—
79C2×#1220—22no—
80C2×#1220C2×C414yescomplemented
81C22×Dic15—22no—
82C22×Dic15—22no—
83C22×Dic15D414yescomplemented
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C2×C4×D15—22no—
88C2×C4×D15—22no—
89C2×C4×D15—22no—
90C2×C5×#67—22no—
91C2×C5×#67—22no—
92C2×C5×#67C2×C414yescomplemented
93C22×C5×Dic3—22no—
94C22×C5×Dic3—22no—
95C22×C5×Dic3—22no—
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C22×C5×Dic3C2311yescharacteristic
99C22×C3×Dic5—22no—
100C22×C3×Dic5—22no—
101C22×C3×Dic5C2×C414yescomplemented
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C2×#1203—22no—
107C2×#1203—22no—
108C2×#1203C2×C414yescomplemented
109C2×D3×Dic5—22no—
110C2×D3×Dic5—22no—
111C2×D3×Dic5—22no—
112C3×C5×C22⋊C4—22no—
113#6714—22no—
114#6712—22no—
115C4×Dic15—22no—
116C5×(C2×D3)⋊C4—22no—
117C5×(C2×D3)⋊C4—22no—
118C3×C22⋊Dic5—22no—
119C3×#683—22no—
120C3×#683—22no—
121Dic3⋊Dic5—22no—
122#6668C2×C414yescomplemented
123#6667—22no—
124#6667—22no—
125#6667C2×C414yescomplemented
126(C2×D3)⋊Dic5—22no—
127(C2×D3)⋊Dic5C2×C414yescomplemented
128Dic3×Dic5—22no—
129Dic3×Dic5—22no—
130Dic3×Dic5—22no—
131Dic3×Dic5—22no—
132Dic3×Dic5D414yescomplemented
133C2×#930—51no—
134C22×C4×Dic3—51no—
135C2×#893—51no—
136C2×#67⋊C4—51no—
137C2×#67⋊C4—51no—
138C3×#380—51no—
139#4988—51no—
140Dic3×C4⋊C4—51no—
141#4972—51no—
142#4958—51no—
143#4958D511yescharacteristic, complemented
144#4669—51no—
145#4669—51no—
146#4666—51no—
147#4666—51no—
148C22×C5×D4—31no—
149C23×C4×C5—31no—
150C22×C22⋊D5—31no—
151C22×C22⋊D5—31no—
152C23×Dic5—31no—
153C23×Dic5—31no—
154C23×Dic5C2×D311yescharacteristic
155C22×C4×D5—31no—
156C2×C5×C22⋊C4—31no—
157C2×C5×C22⋊C4—31no—
158C2×C5×C22⋊C4C2×D311yescharacteristic
159C2×C22⋊Dic5—31no—
160C2×C22⋊Dic5—31no—
161C2×C22⋊Dic5C2×D311yescharacteristic
162#4085—38no—
163D4×Dic5—64no—
164C2×#685—31no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×C4⋊Dic5—31no—
169C2×#683—31no—
170C2×#683—31no—
171C2×#683C2×D311yescharacteristic
172C2×#683C2×D311yescharacteristic
173C2×C4×Dic5—31no—
174C2×C4×Dic5—31no—
175C2×C4×Dic5—31no—
176C2×C4×Dic5—31no—
177C2×C4×Dic5—31no—
178C2×C4×Dic5—31no—
179C2×C4×Dic5—64no—
180#4027—64no—
181#4027—64no—
182C5×#95—31no—
183C5×#95—31no—
184#3963—31no—
185#3963—31no—
186#3963C2×D311yescharacteristic
187#3963C2×D311yescharacteristic
188C4×#121—151noSylow
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5C22×C412yes—
194C23×C3×C5C2×D412yes—
195C23×C3×C5#4112yes—
196C23×C3×C5C2411yescharacteristic
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15—21no—
201C22×D15—21no—
202C22×D15—21no—
203C22×D15C22×C412yes—
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—21no—
207C22×C5×D3—21no—
208C22×C5×D3—21no—
209C22×C5×D3—21no—
210C22×C5×D3C22×C412yes—
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—
217#1220—28no—
218C2×Dic15—21no—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—28no—
223C2×Dic15C22×C412yes—
224C2×Dic15C2×D412yes—
225C2×Dic15C2×D412yes—
226C2×Dic15C2×D412yes—
227C2×Dic15#4112yes—
228C4×D15—44no—
229C5×#67—28no—
230C2×C5×Dic3—28no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3C22×C412yes—
238C2×C5×Dic3C2×D412yes—
239C2×C5×Dic3#4112yes—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—28no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5C22×C412yes—
250C2×C3×Dic5C22×C412yes—
251C2×C3×Dic5C2×D412yes—
252C2×C3×Dic5#4112yes—
253#1203—28no—
254D3×Dic5—44no—
255C23×C3×C4—51no—
256C22×#67—51no—
257C22×#67C2×D511yescharacteristic
258C23×Dic3—51no—
259C23×Dic3C2×D511yescharacteristic
260C22×D12—51no—
261C22×C4×D3—51no—
262C22×C4×D3—51no—
263C2×C3×C4⋊C4—51no—
264C2×C3×C4⋊C4—51no—
265C2×C3×C22⋊C4—51no—
266C2×C3×C22⋊C4C2×D511yescharacteristic
267#930—58no—
268C2×(C2×D3)⋊C4—51no—
269C2×(C2×D3)⋊C4—51no—
270C2×(C2×D3)⋊C4—51no—
271C2×(C2×D3)⋊C4—51no—
272C2×(C2×D3)⋊C4—51no—
273C2×(C2×D3)⋊C4—51no—
274C2×(C2×D3)⋊C4C2×D511yescharacteristic
275C2×(C2×D3)⋊C4C2×D511yescharacteristic
276C2×C4⋊Dic3—51no—
277C2×Dic3⋊C4—51no—
278C2×Dic3⋊C4—51no—
279C2×C4×Dic3—51no—
280C2×C4×Dic3—51no—
281C2×C4×Dic3—51no—
282C2×C4×Dic3—51no—
283C2×C4×Dic3—51no—
284C2×C4×Dic3—51no—
285C2×C4×Dic3—104no—
286#893—104no—
287#67⋊C4—104no—
288#67⋊C4—104no—
289C3×#95—51no—
290C3×#95—51no—
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95C2×D511yescharacteristic
294C3⋊#95C2×D511yescharacteristic
295C24×C5—31no—
296C24×C5C22×D311yescharacteristic
297C23×D5—31no—
298C2×C5×D4—34no—
299C2×C5×D4—62no—
300C2×C5×D4—62no—
301C22×C4×C5—31no—
302C22×C4×C5—31no—
303C22×C4×C5—31no—
304C22×C4×C5—62no—
305C22×C4×C5—62no—
306C22×C4×C5—62no—
307C22×C4×C5C22×D311yescharacteristic
308C22×C4×C5C22×D311yescharacteristic
309C2×C22⋊D5—34no—
310C2×C22⋊D5—34no—
311C2×C22⋊D5—62no—
312C2×C22⋊D5—62no—
313C2×C22⋊D5—62no—
314C2×C22⋊D5—62no—
315C22×Dic5—22no—
316C22×Dic5—22no—
317C22×Dic5—31no—
318C22×Dic5—34no—
319C22×Dic5—31no—
320C22×Dic5—31no—
321C22×Dic5—62no—
322C22×Dic5—62no—
323C22×Dic5—62no—
324C22×Dic5—62no—
325C22×Dic5—62no—
326C22×Dic5C4×D314yescomplemented
327C22×Dic5C22×D311yescharacteristic
328C22×Dic5C22×D311yescharacteristic
329C22×Dic5C22×D311yescharacteristic
330C22×Dic5C22×D311yescharacteristic
331C2×C4×D5—62no—
332C2×C4×D5—62no—
333C2×C4×D5—62no—
334C5×C22⋊C4—22no—
335C5×C22⋊C4—62no—
336C5×C22⋊C4—62no—
337C22⋊Dic5—22no—
338C22⋊Dic5—34no—
339C22⋊Dic5—62no—
340#685—34no—
341#685—62no—
342#685—62no—
343#685—62no—
344C4⋊Dic5—62no—
345#683—22no—
346#683—22no—
347#683—34no—
348#683—62no—
349C4×Dic5—34no—
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—31no—
365#386—151no—
366#380—51no—
367C4×C4⋊C4—151no—
368C4×C22⋊C4—151no—
369C4×C22⋊C4—151no—
370C22×C3×C5—22no—
371C22×C3×C5—22no—
372C22×C3×C5—22no—
373C22×C3×C5—22no—
374C22×C3×C5—22no—
375C22×C3×C5—22no—
376C22×C3×C5C4×D414yescomplemented
377C22×C3×C5C23×C411yescharacteristic
378C22×C3×C5C22×D411yescharacteristic
379C22×C3×C5C22×D411yescharacteristic
380C22×C3×C5C2×#4111yescharacteristic
381C22×C3×C5C2×#4111yescharacteristic
382C22×C3×C5C2×#4111yescharacteristic
383C22×C3×C5C2×#4111yescharacteristic
384C2×D15—22no—
385C2×D15—22no—
386C2×D15—22no—
387C2×D15—41no—
388C2×D15—41no—
389C2×D15—41no—
390C2×D15—41no—
391C2×C5×D3—22no—
392C2×C5×D3—22no—
393C2×C5×D3—22no—
394C2×C5×D3—41no—
395C2×C5×D3—41no—
396C2×C5×D3—41no—
397C2×C5×D3—41no—
398C3×C4×C5—41no—
399C3×C4×C5—41no—
400Dic15—22no—
401Dic15—22no—
402Dic15#12114yescomplemented
403C3×Dic5—22no—
404C3×Dic5—41no—
405C3×Dic5—41no—
406C3×Dic5C4×D414yescomplemented
407C5×Dic3—22no—
408C5×Dic3—22no—
409C5×Dic3—22no—
410C24×C3C22×D511yescharacteristic
411C23×D3—51no—
412C23×D3C22×D511yescharacteristic
413C22×C3×C4—51no—
414C22×C3×C4—54no—
415C22×C3×C4—51no—
416C22×C3×C4—51no—
417C22×C3×C4—51no—
418C22×C3×C4—102no—
419C22×C3×C4—102no—
420C22×C3×C4C22×D511yescharacteristic
421C22×C3×C4C22×D511yescharacteristic
422C2×#67—22no—
423C2×#67—22no—
424C2×#67—54no—
425C2×#67—102no—
426C2×#67—102no—
427C2×#67C4×D514yescomplemented
428C22×Dic3—22no—
429C22×Dic3—22no—
430C22×Dic3—22no—
431C22×Dic3—51no—
432C22×Dic3—54no—
433C22×Dic3—51no—
434C22×Dic3—51no—
435C22×Dic3—102no—
436C22×Dic3—102no—
437C22×Dic3C22×D511yescharacteristic
438C22×Dic3C22×D511yescharacteristic
439C22×Dic3C22×D511yescharacteristic
440C2×D12—54no—
441C2×D12—102no—
442C2×D12—102no—
443C2×C4×D3—102no—
444C2×C4×D3—102no—
445C2×C4×D3—102no—
446C2×C4×D3—102no—
447C2×C4×D3—102no—
448C2×C4×D3—102no—
449C3×C4⋊C4—102no—
450C3×C4⋊C4—102no—
451C3×C22⋊C4—22no—
452C3×C22⋊C4—102no—
453(C2×D3)⋊C4—22no—
454(C2×D3)⋊C4—22no—
455(C2×D3)⋊C4—54no—
456(C2×D3)⋊C4—54no—
457(C2×D3)⋊C4—102no—
458(C2×D3)⋊C4—102no—
459(C2×D3)⋊C4—102no—
460(C2×D3)⋊C4—102no—
461C4⋊Dic3—54no—
462Dic3⋊C4—102no—
463Dic3⋊C4—102no—
464C4×Dic3—54no—
465C4×Dic3—102no—
466C4×Dic3—102no—
467C4×Dic3—102no—
468C4×Dic3—102no—
469C4×Dic3—102no—
470C23×C5—21no—
471C23×C5—21no—
472C23×C5—21no—
473C23×C5—21no—
474C23×C5—32no—
475C23×C5—61no—
476C23×C5—61no—
477C23×C5—61no—
478C23×C5—61no—
479C23×C5—61no—
480C23×C5—61no—
481C23×C5C2×C4×D312yes—
482C23×C5D3×D412yes—
483C23×C5#23912yes—
484C23×C5C23×D311yescharacteristic
485C22×D5—32no—
486C22×D5—61no—
487C22×D5—61no—
488C22×D5—61no—
489C22×D5—61no—
490C22×D5—61no—
491C22×D5—61no—
492C5×D4—68no—
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—68no—
503C2×C4×C5—61no—
504C2×C4×C5—61no—
505C2×C4×C5—61no—
506C2×C4×C5—61no—
507C2×C4×C5—61no—
508C2×C4×C5—61no—
509C22⋊D5—68no—
510C22⋊D5—68no—
511C2×Dic5—21no—
512C2×Dic5—21no—
513C2×Dic5—28no—
514C2×Dic5—21no—
515C2×Dic5—21no—
516C2×Dic5—21no—
517C2×Dic5—21no—
518C2×Dic5—21no—
519C2×Dic5—21no—
520C2×Dic5—32no—
521C2×Dic5—32no—
522C2×Dic5—32no—
523C2×Dic5—32no—
524C2×Dic5—32no—
525C2×Dic5—68no—
526C2×Dic5—61no—
527C2×Dic5—61no—
528C2×Dic5—61no—
529C2×Dic5—61no—
530C2×Dic5—124no—
531C2×Dic5C2×C4×D312yes—
532C2×Dic5C2×C4×D312yes—
533C2×Dic5D3×D412yes—
534C2×Dic5#23712yes—
535C4×D5—124no—
536C22×D4—31no—
537C22×D4—151no—
538C22×D4—151no—
539C23×C4—31no—
540C23×C4—51no—
541C23×C4—151no—
542C23×C4—151no—
543C23×C4—151no—
544#121—158no—
545C4×D4—304no—
546C4×D4—304no—
547C4×D4—304no—
548C2×C4⋊C4—51no—
549C2×C4⋊C4—51no—
550C2×C4⋊C4—151no—
551C2×C4⋊C4—151no—
552C2×C4⋊C4—151no—
553C2×C22⋊C4—31no—
554C2×C22⋊C4—31no—
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⋊C4D3×D511yescharacteristic
563C2×C42—151no—
564C2×C42—151no—
565C2×C42—151no—
566C2×C42—151no—
567C2×C42—151no—
568C2×C42—151no—
569C2×C42—304no—
570#95—31no—
571#95—31no—
572#95—51no—
573#95—51no—
574#95—151no—
575#95—151no—
576C2×C3×C5—24no—
577C2×C3×C5C2×C4×D411yescharacteristic
578C2×C3×C5C2×C4×D411yescharacteristic
579C2×C3×C5C4×#4111yescharacteristic
580C2×C3×C5C2×#12111yescharacteristic
581C2×C3×C5#52511yescharacteristic
582C2×C3×C5#52911yescharacteristic
583C2×C3×C5#53211yescharacteristic
584D15—42no—
585C5×D3—42no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3C2×C4×D512yes—
591C23×C3D4×D512yes—
592C23×C3#71112yes—
593C23×C3C23×D511yescharacteristic
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—52no—
601C22×D3—101no—
602C22×D3—101no—
603C22×D3—101no—
604C22×D3—101no—
605C22×D3—101no—
606C22×D3—101no—
607C22×D3C2×C4×D512yes—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—52no—
615C2×C3×C4—52no—
616C2×C3×C4—52no—
617C2×C3×C4—52no—
618C2×C3×C4—108no—
619C2×C3×C4—101no—
620C2×C3×C4—101no—
621C2×C3×C4—101no—
622C2×C3×C4—101no—
623C2×C3×C4—101no—
624C2×C3×C4—101no—
625C2×C3×C4—101no—
626C2×C3×C4—101no—
627#67—28no—
628#67—108no—
629C2×Dic3—28no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—52no—
637C2×Dic3—52no—
638C2×Dic3—52no—
639C2×Dic3—52no—
640C2×Dic3—52no—
641C2×Dic3—108no—
642C2×Dic3—101no—
643C2×Dic3—101no—
644C2×Dic3—101no—
645C2×Dic3—101no—
646C2×Dic3C2×C4×D512yes—
647C2×Dic3D4×D512yes—
648C2×Dic3#71112yes—
649D12—108no—
650C4×D3—204no—
651C4×D3—204no—
652C22×C5—22no—
653C22×C5—22no—
654C22×C5—22no—
655C22×C5—22no—
656C22×C5—22no—
657C22×C5—22no—
658C22×C5—62no—
659C22×C5—62no—
660C22×C5—62no—
661C22×C5—121no—
662C22×C5—121no—
663C22×C5—121no—
664C22×C5—121no—
665C22×C5#89314yescomplemented
666C22×C5C22×C4×D311yescharacteristic
667C22×C5C2×D3×D411yescharacteristic
668C22×C5C2×D3×D411yescharacteristic
669C22×C5C2×#23711yescharacteristic
670C22×C5C2×#23911yescharacteristic
671C22×C5D3×#4111yescharacteristic
672C22×C5D3×#4111yescharacteristic
673C2×D5—62no—
674C2×D5—62no—
675C2×D5—62no—
676C2×D5—121no—
677C2×D5—121no—
678C2×D5—121no—
679C2×D5—121no—
680C4×C5—41no—
681C4×C5—41no—
682C4×C5—62no—
683C4×C5—62no—
684C4×C5—62no—
685Dic5—22no—
686Dic5—34no—
687Dic5—41no—
688Dic5—41no—
689Dic5—62no—
690Dic5—62no—
691Dic5#67⋊C414yescomplemented
692C24—31no—
693C24—151no—
694C24C2×D3×D511yescharacteristic
695C2×D4—34no—
696C2×D4—62no—
697C2×D4—62no—
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—51no—
708C22×C4—54no—
709C22×C4—51no—
710C22×C4—51no—
711C22×C4—51no—
712C22×C4—62no—
713C22×C4—62no—
714C22×C4—62no—
715C22×C4—102no—
716C22×C4—102no—
717C22×C4—151no—
718C22×C4—154no—
719C22×C4—151no—
720C22×C4—151no—
721C22×C4—302no—
722C22×C4—302no—
723C22×C4—302no—
724C22×C4—302no—
725C22×C4—302no—
726C22×C4—302no—
727C22×C4—302no—
728C22×C4—302no—
729C22×C4C2×D3×D511yescharacteristic
730C22×C4C2×D3×D511yescharacteristic
731C4⋊C4—102no—
732C4⋊C4—102no—
733C4⋊C4—154no—
734C4⋊C4—302no—
735C4⋊C4—302no—
736C22⋊C4—22no—
737C22⋊C4—62no—
738C22⋊C4—62no—
739C22⋊C4—102no—
740C22⋊C4—154no—
741C22⋊C4—154no—
742C22⋊C4—302no—
743C22⋊C4—302no—
744C22⋊C4—302no—
745C22⋊C4—302no—
746C42—154no—
747C42—302no—
748C42—302no—
749C42—302no—
750C42—302no—
751C42—302no—
752C3×C5C4×#12111yescharacteristic, complemented, Hall
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3#402714yescomplemented
760C22×C3C22×C4×D511yescharacteristic
761C22×C3C2×D4×D511yescharacteristic
762C22×C3C2×D4×D511yescharacteristic
763C22×C3C2×#71111yescharacteristic
764C22×C3C2×#71111yescharacteristic
765C22×C3D5×#4111yescharacteristic
766C22×C3D5×#4111yescharacteristic
767C2×D3—22no—
768C2×D3—22no—
769C2×D3—22no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—102no—
775C2×D3—102no—
776C2×D3—102no—
777C2×D3—201no—
778C2×D3—201no—
779C2×D3—201no—
780C2×D3—201no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—54no—
784C3×C4—102no—
785C3×C4—201no—
786C3×C4—201no—
787Dic3—22no—
788Dic3—22no—
789Dic3—22no—
790Dic3—54no—
791Dic3—102no—
792Dic3—102no—
793C2×C5—24no—
794C2×C5—122no—
795C2×C5C2×#67⋊C411yescharacteristic
796C2×C5C2×#89311yescharacteristic
797C2×C5#552211yescharacteristic
798C2×C5#559611yescharacteristic
799C2×C5D3×#12111yescharacteristic
800C2×C5#562411yescharacteristic
801C2×C5#562711yescharacteristic
802D5—122no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—32no—
808C23—61no—
809C23—61no—
810C23—61no—
811C23—61no—
812C23—61no—
813C23—61no—
814C23—152no—
815C23—301no—
816C23—301no—
817C23—301no—
818C23—301no—
819C23—301no—
820C23—301no—
821C23#676812yes—
822C23C4×D3×D512yes—
823C23#679012yes—
824C23C22×D3×D511yescharacteristic
825D4—68no—
826D4—308no—
827D4—308no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—32no—
835C2×C4—32no—
836C2×C4—32no—
837C2×C4—52no—
838C2×C4—52no—
839C2×C4—52no—
840C2×C4—52no—
841C2×C4—68no—
842C2×C4—61no—
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—101no—
855C2×C4—101no—
856C2×C4—101no—
857C2×C4—152no—
858C2×C4—152no—
859C2×C4—152no—
860C2×C4—152no—
861C2×C4—152no—
862C2×C4—308no—
863C2×C4—301no—
864C2×C4—301no—
865C2×C4—301no—
866C2×C4—301no—
867C2×C4—604no—
868C2×C4—604no—
869C2×C3—24no—
870C2×C3C2×#402711yescharacteristic
871C2×C3C4×#71111yescharacteristic
872C2×C3C4×D4×D511yescharacteristic
873C2×C3#6592011yescharacteristic
874C2×C3#6593011yescharacteristic
875C2×C3D5×#12111yescharacteristic
876C2×C3#6598311yescharacteristic
877D3—42no—
878D3—202no—
879C5#7386511yescharacteristic, complemented, Sylow
880C22—22no—
881C22—22no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—62no—
887C22—62no—
888C22—62no—
889C22—121no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—302no—
894C22—302no—
895C22—302no—
896C22—601no—
897C22—601no—
898C22—601no—
899C22—601no—
900C22#9140614yescomplemented
901C22C2×#676811yescharacteristic
902C22C2×C4×D3×D511yescharacteristic
903C22D3×D4×D511yescharacteristic
904C22D5×#23711yescharacteristic
905C22D3×#71111yescharacteristic
906C22#9202411yescharacteristic
907C22C2×#679011yescharacteristic
908C4—41no—
909C4—41no—
910C4—54no—
911C4—62no—
912C4—62no—
913C4—62no—
914C4—102no—
915C4—154no—
916C4—201no—
917C4—201no—
918C4—302no—
919C4—302no—
920C3#1060639111yescharacteristic, complemented, Sylow
921C2—24no—
922C2—122no—
923C2—602no—
924C2#1175282311yescharacteristic
925C2#1175284211yescharacteristic
926C2#1175295911yescharacteristic
927C2D5×#67⋊C411yescharacteristic
928C2C2×#9140611yescharacteristic
929C2#1175482011yescharacteristic
930C2#1175504911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91566C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C4×#121
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91770C2semidirect
3. C2×#67⋊Dic5C2semidirect
4. C22×Dic3×Dic5C2semidirect
5. C2×#91406C2semidirect
6. C5×#4958C2semidirect
7. C3×#65231C2semidirect
8. #11749498C2semidirect
9. #11748909C2semidirect
10. #11748886C2semidirect
11. #11748720C2semidirect
12. #11748670C2semidirect
13. #11748668C2semidirect
14. #11748637C2semidirect
15. #11748627C2semidirect
35. #91566C4semidirect
67. #65231D3semidirect
80. C2×#1220C2×C4semidirect
83. C22×Dic15D4semidirect
92. C2×C5×#67C2×C4semidirect
101. C22×C3×Dic5C2×C4semidirect
108. C2×#1203C2×C4semidirect
122. #6668C2×C4semidirect
125. #6667C2×C4semidirect
127. (C2×D3)⋊Dic5C2×C4semidirect
132. Dic3×Dic5D4semidirect
143. #4958D5semidirect
326. C22×Dic5C4×D3semidirect
376. C22×C3×C5C4×D4semidirect
402. Dic15#121semidirect
406. C3×Dic5C4×D4semidirect
427. C2×#67C4×D5semidirect
665. C22×C5#893semidirect
691. Dic5#67⋊C4semidirect
752. C3×C5C4×#121semidirect
759. C22×C3#4027semidirect
879. C5#73865semidirect
900. C22#91406semidirect
920. C3#10606391semidirect

Maximal subgroups

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

subgroupindex
C2×#917702
C2×#915662
C2×#67⋊Dic52
C22×Dic3×Dic52
C2×#914062
C5×#49582
C3×#652312
#117494982
#117489092
#117488862
#117487202
#117486702
#117486682
#117486372
#117486272
#106063913
#738655