Finite Group Databasebeta

← C4×#91448 #14321511

Subgroups — C4×#91448 #14321511

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×C3×C42×D5C211yesmaximal, characteristic, complemented
2C2×#91448C211yesmaximal, characteristic
3C2×C4×#1203C211yesmaximal, characteristic, complemented
4C2×C4×#1202C211yesmaximal, characteristic, complemented
5C2×C4×#1201C211yesmaximal, characteristic, complemented
6C4×#6714C211yesmaximal, characteristic, complemented
7C4×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
8#11748908C211yesmaximal, characteristic, complemented
9#11748907C211yesmaximal, characteristic, complemented
10#11748905C211yesmaximal, characteristic, complemented
11#11748829C211yesmaximal, characteristic, complemented
12C4×#6668C211yesmaximal, characteristic, complemented
13#11748802C211yesmaximal, characteristic, complemented
14#11748747C211yesmaximal, characteristic, complemented
15#11748738C211yesmaximal, characteristic, complemented
16C4×#4030—31nomaximal, Hall
17C22×C4×D15C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×#1203C2211yescharacteristic
23C22×#1202C2211yescharacteristic
24C22×#1201C2211yescharacteristic
25C2×C3×C42×C5C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×C4×Dic15C2211yescharacteristic
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C4×C5×Dic3C2211yescharacteristic
32C2×C3×C4×Dic5C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34C2×C3×C4×Dic5C2211yescharacteristic
35C3×C42×D5—24no—
36C2×Dic3⋊Dic5C2211yescharacteristic
37C2×#6669C2211yescharacteristic
38C2×#6668C2211yescharacteristic
39C2×#6668C2211yescharacteristic
40C2×#6668C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47#91448C418yesdirect product factor
48C4×#1203—24no—
49C4×#1202—24no—
50C4×#1201—24no—
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53C5×C3⋊#95C2211yescharacteristic
54C5×C3⋊#95C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57C4×#930—51nomaximal, Hall
58C2×C4×C22⋊D5—31no—
59C2×C4×C22⋊D5—31no—
60C2×#4030—31no—
61C2×C4×D20—31no—
62C2×C42×D5D311yescharacteristic, complemented
63C4×C5×C22⋊C4—31no—
64#65246—31no—
65#65245—31no—
66#65240—31no—
67C4×#685—31no—
68C4×#683—31no—
69#64958—31no—
70#64956—31no—
71#64954—31no—
72#64936—31no—
73C23×D15C2311yescharacteristic
74C23×C5×D3C2311yescharacteristic
75C23×C3×D5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C2×C4×D15—22no—
83C2×C4×D15—22no—
84C2×C4×D15—22no—
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C2×C4×C5×D3—22no—
89C2×C4×C5×D3—22no—
90C2×C4×C5×D3—22no—
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C2×C3×C4×D5—22no—
95C2×C3×C4×D5—22no—
96C2×C3×C4×D5—22no—
97C2×C3×C4×D5—22no—
98C2×C3×C4×D5—22no—
99C2×C3×C4×D5—22no—
100C2×C3×C4×D5—22no—
101C2×C3×C4×D5C2×C414yescomplemented
102C2×C3×C4×D5D414yescomplemented
103C2×#1203—22no—
104C2×#1203—22no—
105C2×#1203C2×C414yescomplemented
106C2×#1202—22no—
107C2×#1202—22no—
108C2×#1202C2×C414yescomplemented
109C2×#1201—22no—
110C2×#1201—22no—
111C2×#1201C2×C414yescomplemented
112C3×C42×C5—22no—
113#6714—22no—
114#6714C2×C414yescomplemented
115C4×Dic15—22no—
116C5×(C2×D3)⋊C4—22no—
117C5×(C2×D3)⋊C4C2×C414yescomplemented
118C4×C5×Dic3—22no—
119C3×C4×Dic5—22no—
120C3×C4×Dic5—22no—
121C3×C4×Dic5D414yescomplemented
122Dic3⋊Dic5—22no—
123#6669—22no—
124#6668—22no—
125#6668—22no—
126#6668C2×C414yescomplemented
127#6667—22no—
128#6667—22no—
129(C2×D3)⋊Dic5—22no—
130(C2×D3)⋊Dic5—22no—
131#6665—22no—
132#6665—22no—
133C22×C3×C42—51no—
134C2×#930—51no—
135C2×C4×#67—51no—
136C2×C4×#67—51no—
137C2×C4×D12—51no—
138#5213—51no—
139#5213—51no—
140#5212—51no—
141#4940—51no—
142#4940—51no—
143#4939—51no—
144C4×(C2×D3)⋊C4—51no—
145C4×(C2×D3)⋊C4D511yescharacteristic, complemented
146C4×C4⋊Dic3—51no—
147#4928—51no—
148C23×C4×C5—31no—
149C22×C22⋊D5—31no—
150C22×C22⋊D5—31no—
151C22×D20—31no—
152C22×C4×D5—31no—
153C22×C4×D5C2×D311yescharacteristic
154C22×C4×D5C2×D311yescharacteristic
155C22×C4×D5C2×D311yescharacteristic
156C2×C5×C22⋊C4—31no—
157C2×C5×C22⋊C4—31no—
158C2×C42×C5—31no—
159C2×C42×C5C2×D311yescharacteristic
160C2×C22⋊Dic5—31no—
161C2×C22⋊Dic5—31no—
162C4×C22⋊D5—64no—
163C4×C22⋊D5—64no—
164C2×#685—31no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685—31no—
170C2×C4⋊Dic5—31no—
171C2×#683—31no—
172C2×#683—31no—
173C2×#683—31no—
174C2×#683—31no—
175C2×C4×Dic5—31no—
176C2×C4×Dic5C2×D311yescharacteristic
177C2×C4×Dic5C2×D311yescharacteristic
178C2×C4×Dic5C2×D311yescharacteristic
179#4030—38no—
180C4×D20—64no—
181C42×D5—24no—
182C5×#95—31no—
183C5×#95—31no—
184#3963—31no—
185#3963—31no—
186#3963—31no—
187#3963—31no—
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×C5×D3—21no—
198C22×C5×D3—21no—
199C22×C5×D3—21no—
200C22×C5×D3—21no—
201C22×C5×D3—21no—
202C22×C5×D3—21no—
203C22×C5×D3C22×C412yes—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
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×C5C22×C412yes—
216C2×C3×C4×C5C2×D412yes—
217C2×C3×C4×C5C2×D412yes—
218C2×C3×C4×C5#4112yes—
219C2×C3×C4×C5#4112yes—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15C22×C412yes—
229C4×D15—44no—
230C2×C5×Dic3—21no—
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×Dic3—21no—
238C2×C5×Dic3C22×C412yes—
239C4×C5×D3—44no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5C22×C412yes—
245C2×C3×Dic5C2×D412yes—
246C2×C3×Dic5C2×D412yes—
247C2×C3×Dic5C2×D412yes—
248C2×C3×Dic5#4112yes—
249C3×C4×D5—28no—
250C3×C4×D5—28no—
251C3×C4×D5—28no—
252#1203—28no—
253#1202—28no—
254#1201—28no—
255C23×C3×C4—51no—
256C23×C3×C4—51no—
257C23×C3×C4—51no—
258C22×#67—51no—
259C22×#67—51no—
260C22×D12—51no—
261C22×C4×D3—51no—
262C22×C4×D3C2×D511yescharacteristic
263C2×C3×C42—51no—
264C2×C3×C42—51no—
265C2×C3×C42—51no—
266C2×C3×C42—104no—
267C2×C3×C42C2×D511yescharacteristic
268C2×#217—51no—
269C2×#217—51no—
270#930—58no—
271C4×#67—104no—
272C4×#67—104no—
273C2×(C2×D3)⋊C4—51no—
274C2×(C2×D3)⋊C4—51no—
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4C2×D511yescharacteristic
280C2×(C2×D3)⋊C4C2×D511yescharacteristic
281C2×C4⋊Dic3—51no—
282C2×C4⋊Dic3—51no—
283C2×C4⋊Dic3—51no—
284C2×Dic3⋊C4—51no—
285C2×Dic3⋊C4—51no—
286C2×C4×Dic3—51no—
287C2×C4×Dic3C2×D511yescharacteristic
288C4×D12—104no—
289C3⋊#95—51no—
290C3⋊#95—51no—
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95C2×D511yescharacteristic
294C3⋊#95C2×D511yescharacteristic
295C24×C5—31no—
296C23×D5—31no—
297C23×D5C22×D311yescharacteristic
298C22×C4×C5—31no—
299C22×C4×C5—31no—
300C22×C4×C5—31no—
301C22×C4×C5—62no—
302C22×C4×C5—62no—
303C22×C4×C5—62no—
304C22×C4×C5C22×D311yescharacteristic
305C22×C4×C5C22×D311yescharacteristic
306C22×C4×C5C22×D311yescharacteristic
307C2×C22⋊D5—34no—
308C2×C22⋊D5—34no—
309C2×C22⋊D5—62no—
310C2×C22⋊D5—62no—
311C2×C22⋊D5—62no—
312C2×C22⋊D5—62no—
313C22×Dic5—31no—
314C22×Dic5—31no—
315C22×Dic5—31no—
316C22×Dic5C22×D311yescharacteristic
317C22×Dic5C22×D311yescharacteristic
318C22×Dic5C22×D311yescharacteristic
319C2×D20—34no—
320C2×D20—62no—
321C2×D20—62no—
322C2×C4×D5—22no—
323C2×C4×D5—22no—
324C2×C4×D5—22no—
325C2×C4×D5—22no—
326C2×C4×D5—22no—
327C2×C4×D5—22no—
328C2×C4×D5—22no—
329C2×C4×D5—62no—
330C2×C4×D5—62no—
331C2×C4×D5—62no—
332C2×C4×D5C4×D314yescomplemented
333C2×C4×D5D1214yescomplemented
334C5×C22⋊C4—34no—
335C5×C22⋊C4—62no—
336C42×C5—22no—
337C42×C5—62no—
338C22⋊Dic5—62no—
339C22⋊Dic5—62no—
340#685—34no—
341#685—62no—
342#685—62no—
343#685—62no—
344#685—62no—
345#685—62no—
346C4⋊Dic5—62no—
347#683—34no—
348#683—62no—
349#683—62no—
350#683—62no—
351C4×Dic5—22no—
352C4×Dic5—22no—
353C4×Dic5—62no—
354C4×Dic5#6714yescomplemented
355C2×#121—151no—
356C2×C4×D4—151no—
357C2×C4×D4—151no—
358C2×C4×D4—151no—
359C22×C42—51no—
360#390—151no—
361#389—151no—
362#388—151no—
363#388—151no—
364#386—151no—
365#386—151no—
366#380—151no—
367C4×C4⋊C4—151no—
368C4×C22⋊C4—31no—
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×C5×D3—22no—
385C2×C5×D3—22no—
386C2×C5×D3—22no—
387C2×C5×D3—41no—
388C2×C5×D3—41no—
389C2×C5×D3—41no—
390C2×C5×D3—41no—
391C2×C3×D5—22no—
392C2×C3×D5—22no—
393C2×C3×D5—22no—
394C2×C3×D5—22no—
395C2×C3×D5—22no—
396C2×C3×D5—22no—
397C2×C3×D5C4×D414yescomplemented
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400C3×C4×C5#12114yescomplemented
401Dic15—22no—
402Dic15—41no—
403Dic15—41no—
404C3×Dic5—22no—
405C3×Dic5—22no—
406C3×Dic5C4×D414yescomplemented
407C5×Dic3—22no—
408C5×Dic3—41no—
409C5×Dic3—41no—
410C24×C3—51no—
411C23×D3—51no—
412C23×D3C22×D511yescharacteristic
413C22×C3×C4—51no—
414C22×C3×C4—51no—
415C22×C3×C4—51no—
416C22×C3×C4—54no—
417C22×C3×C4—54no—
418C22×C3×C4—102no—
419C22×C3×C4—102no—
420C22×C3×C4—102no—
421C22×C3×C4—102no—
422C22×C3×C4—102no—
423C22×C3×C4—102no—
424C22×C3×C4—102no—
425C22×C3×C4C22×D511yescharacteristic
426C22×C3×C4C22×D511yescharacteristic
427C22×C3×C4C22×D511yescharacteristic
428C2×#67—54no—
429C2×#67—54no—
430C2×#67—102no—
431C2×#67—102no—
432C2×#67—102no—
433C2×#67—102no—
434C22×Dic3—51no—
435C22×Dic3—51no—
436C22×Dic3—51no—
437C22×Dic3C22×D511yescharacteristic
438C22×Dic3C22×D511yescharacteristic
439C22×Dic3C22×D511yescharacteristic
440C2×D12—54no—
441C2×D12—102no—
442C2×D12—102no—
443C2×C4×D3—22no—
444C2×C4×D3—22no—
445C2×C4×D3—22no—
446C2×C4×D3—102no—
447C2×C4×D3—102no—
448C2×C4×D3—102no—
449C3×C42—22no—
450C3×C42—54no—
451C3×C42—102no—
452C3×C42—102no—
453#217—102no—
454#217—102no—
455(C2×D3)⋊C4—22no—
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—
461(C2×D3)⋊C4—102no—
462(C2×D3)⋊C4C4×D514yescomplemented
463C4⋊Dic3—54no—
464C4⋊Dic3—102no—
465C4⋊Dic3—102no—
466Dic3⋊C4—102no—
467Dic3⋊C4—102no—
468C4×Dic3—22no—
469C4×Dic3—102no—
470C23×C5—32no—
471C23×C5—61no—
472C23×C5—61no—
473C23×C5—61no—
474C23×C5—61no—
475C23×C5—61no—
476C23×C5—61no—
477C23×C5C23×D311yescharacteristic
478C22×D5—21no—
479C22×D5—21no—
480C22×D5—21no—
481C22×D5—21no—
482C22×D5—32no—
483C22×D5—61no—
484C22×D5—61no—
485C22×D5—61no—
486C22×D5—61no—
487C22×D5—61no—
488C22×D5—61no—
489C22×D5C2×C4×D312yes—
490C22×D5C2×D1212yes—
491C22×D5#23512yes—
492C2×C4×C5—21no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5—21no—
496C2×C4×C5—32no—
497C2×C4×C5—61no—
498C2×C4×C5—61no—
499C2×C4×C5—61no—
500C2×C4×C5—61no—
501C2×C4×C5—61no—
502C2×C4×C5—61no—
503C2×C4×C5—61no—
504C2×C4×C5—61no—
505C2×C4×C5—124no—
506C2×C4×C5C2×C4×D312yes—
507C2×C4×C5C2×D1212yes—
508C2×C4×C5#23512yes—
509C2×C4×C5#23512yes—
510C2×C4×C5C2×#6712yes—
511C22⋊D5—68no—
512C22⋊D5—68no—
513C2×Dic5—21no—
514C2×Dic5—21no—
515C2×Dic5—21no—
516C2×Dic5—21no—
517C2×Dic5—32no—
518C2×Dic5—61no—
519C2×Dic5—61no—
520C2×Dic5—61no—
521C2×Dic5—61no—
522C2×Dic5—61no—
523C2×Dic5—61no—
524C2×Dic5—61no—
525C2×Dic5—61no—
526C2×Dic5C2×C4×D312yes—
527C2×Dic5C2×D1212yes—
528C2×Dic5#23512yes—
529C2×Dic5C2×#6712yes—
530C2×Dic5C2×#6712yes—
531D20—68no—
532C4×D5—28no—
533C4×D5—28no—
534C4×D5—28no—
535C4×D5—124no—
536C22×D4—151no—
537C22×D4—151no—
538C22×D4—151no—
539C23×C4—31no—
540C23×C4—51no—
541C23×C4—51no—
542C23×C4—51no—
543C23×C4—151no—
544#121—158no—
545C4×D4—304no—
546C4×D4—304no—
547C4×D4—304no—
548C2×C4⋊C4—151no—
549C2×C4⋊C4—151no—
550C2×C4⋊C4—151no—
551C2×C4⋊C4—151no—
552C2×C4⋊C4—151no—
553C2×C22⋊C4—31no—
554C2×C22⋊C4—31no—
555C2×C22⋊C4—151no—
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—51no—
565C2×C42—51no—
566C2×C42—51no—
567C2×C42—104no—
568C2×C42—151no—
569C2×C42D3×D511yescharacteristic
570#95—31no—
571#95—31no—
572#95—151no—
573#95—151no—
574#95—151no—
575#95—151no—
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—
585C5×D3—42no—
586C23×C3—52no—
587C23×C3—52no—
588C23×C3—52no—
589C23×C3—101no—
590C23×C3—101no—
591C23×C3—101no—
592C23×C3—101no—
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—52no—
613C2×C3×C4—52no—
614C2×C3×C4—52no—
615C2×C3×C4—52no—
616C2×C3×C4—52no—
617C2×C3×C4—108no—
618C2×C3×C4—108no—
619C2×C3×C4—101no—
620C2×C3×C4—101no—
621C2×C3×C4—101no—
622C2×C3×C4—101no—
623C2×C3×C4—108no—
624C2×C3×C4C2×C4×D512yes—
625C2×C3×C4#70912yes—
626C2×C3×C4#70912yes—
627C2×C3×C4D4×D512yes—
628C2×C3×C4D4×D512yes—
629#67—108no—
630#67—108no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—52no—
640C2×Dic3—101no—
641C2×Dic3—101no—
642C2×Dic3—101no—
643C2×Dic3—101no—
644C2×Dic3—101no—
645C2×Dic3—101no—
646C2×Dic3—101no—
647C2×Dic3—101no—
648C2×Dic3C2×C4×D512yes—
649D12—108no—
650C4×D3—44no—
651C4×D3—204no—
652C22×C5—62no—
653C22×C5—62no—
654C22×C5—62no—
655C22×C5—121no—
656C22×C5—121no—
657C22×C5—121no—
658C22×C5—121no—
659C22×C5C22×C4×D311yescharacteristic
660C22×C5C22×D1211yescharacteristic
661C22×C5C2×#23511yescharacteristic
662C22×C5C2×#23511yescharacteristic
663C22×C5C2×#23511yescharacteristic
664C22×C5C2×#23511yescharacteristic
665C22×C5C22×#6711yescharacteristic
666C2×D5—22no—
667C2×D5—22no—
668C2×D5—22no—
669C2×D5—22no—
670C2×D5—22no—
671C2×D5—22no—
672C2×D5—62no—
673C2×D5—62no—
674C2×D5—62no—
675C2×D5—121no—
676C2×D5—121no—
677C2×D5—121no—
678C2×D5—121no—
679C2×D5C4×D1214yescomplemented
680C4×C5—22no—
681C4×C5—22no—
682C4×C5—62no—
683C4×C5—121no—
684C4×C5—121no—
685C4×C5#93014yescomplemented
686Dic5—22no—
687Dic5—22no—
688Dic5—62no—
689Dic5—121no—
690Dic5—121no—
691Dic5C4×#6714yescomplemented
692C24—31no—
693C24—51no—
694C24—151no—
695C2×D4—154no—
696C2×D4—154no—
697C2×D4—154no—
698C2×D4—302no—
699C2×D4—302no—
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—51no—
709C22×C4—51no—
710C22×C4—54no—
711C22×C4—54no—
712C22×C4—62no—
713C22×C4—62no—
714C22×C4—62no—
715C22×C4—102no—
716C22×C4—102no—
717C22×C4—102no—
718C22×C4—102no—
719C22×C4—102no—
720C22×C4—102no—
721C22×C4—102no—
722C22×C4—151no—
723C22×C4—151no—
724C22×C4—151no—
725C22×C4—302no—
726C22×C4—302no—
727C22×C4—302no—
728C22×C4C2×D3×D511yescharacteristic
729C22×C4C2×D3×D511yescharacteristic
730C22×C4C2×D3×D511yescharacteristic
731C4⋊C4—154no—
732C4⋊C4—302no—
733C4⋊C4—302no—
734C4⋊C4—302no—
735C4⋊C4—302no—
736C22⋊C4—34no—
737C22⋊C4—62no—
738C22⋊C4—154no—
739C22⋊C4—302no—
740C22⋊C4—302no—
741C22⋊C4—302no—
742C22⋊C4—302no—
743C22⋊C4—302no—
744C22⋊C4—302no—
745C22⋊C4—302no—
746C42—22no—
747C42—54no—
748C42—62no—
749C42—102no—
750C42—102no—
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×C3C22×C4×D511yescharacteristic
761C22×C3C2×#70911yescharacteristic
762C22×C3C2×#70911yescharacteristic
763C22×C3C2×D4×D511yescharacteristic
764C22×C3C2×D4×D511yescharacteristic
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—22no—
782C3×C4—22no—
783C3×C4—54no—
784C3×C4—102no—
785C3×C4—102no—
786C3×C4#403014yescomplemented
787Dic3—22no—
788Dic3—41no—
789Dic3—41no—
790Dic3—102no—
791Dic3—201no—
792Dic3—201no—
793C2×C5—122no—
794C2×C5C2×C4×D1211yescharacteristic
795C2×C5C4×#23511yescharacteristic
796C2×C5#547711yescharacteristic
797C2×C5#547911yescharacteristic
798C2×C5C2×C4×#6711yescharacteristic
799C2×C5C2×#93011yescharacteristic
800C2×C5#579111yescharacteristic
801D5—24no—
802D5—122no—
803C23—32no—
804C23—52no—
805C23—52no—
806C23—52no—
807C23—61no—
808C23—61no—
809C23—61no—
810C23—61no—
811C23—61no—
812C23—61no—
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—308no—
826D4—308no—
827D4—308no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—32no—
833C2×C4—52no—
834C2×C4—52no—
835C2×C4—52no—
836C2×C4—52no—
837C2×C4—52no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—108no—
847C2×C4—108no—
848C2×C4—101no—
849C2×C4—101no—
850C2×C4—101no—
851C2×C4—101no—
852C2×C4—108no—
853C2×C4—124no—
854C2×C4—152no—
855C2×C4—301no—
856C2×C4—301no—
857C2×C4—301no—
858C2×C4—301no—
859C2×C4—301no—
860C2×C4—301no—
861C2×C4—301no—
862C2×C4—301no—
863C2×C4—604no—
864C2×C4#677112yes—
865C2×C4#677112yes—
866C2×C4C4×D3×D512yes—
867C2×C4D5×D1212yes—
868C2×C4D5×#6712yes—
869C2×C3—104no—
870C2×C3C4×#70911yescharacteristic
871C2×C3C2×#403011yescharacteristic
872C2×C3#6586211yescharacteristic
873C2×C3C4×D4×D511yescharacteristic
874C2×C3C4×D4×D511yescharacteristic
875C2×C3#6588111yescharacteristic
876C2×C3#6588211yescharacteristic
877D3—42no—
878D3—202no—
879C5C4×#93011yescharacteristic, complemented, Sylow
880C22—54no—
881C22—62no—
882C22—62no—
883C22—62no—
884C22—102no—
885C22—102no—
886C22—102no—
887C22—102no—
888C22—102no—
889C22—102no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—302no—
895C22—302no—
896C22—302no—
897C22—601no—
898C22—601no—
899C22—601no—
900C22—601no—
901C22C2×#677111yescharacteristic
902C22C2×#677111yescharacteristic
903C22C2×C4×D3×D511yescharacteristic
904C22C2×D5×D1211yescharacteristic
905C22D5×#23511yescharacteristic
906C22D5×#23511yescharacteristic
907C22C2×D5×#6711yescharacteristic
908C4—22no—
909C4—22no—
910C4—54no—
911C4—62no—
912C4—102no—
913C4—102no—
914C4—121no—
915C4—121no—
916C4—302no—
917C4—601no—
918C4—601no—
919C4#9144814yesdirect product factor
920C3C4×#403011yescharacteristic, complemented, Sylow
921C2—104no—
922C2—122no—
923C2—602no—
924C2C4×#677111yescharacteristic
925C2#1175267111yescharacteristic
926C2#1175268111yescharacteristic
927C2C4×D5×D1211yescharacteristic
928C2#1175452511yescharacteristic
929C2C2×#9144811yescharacteristic
930C2C4×D5×#6711yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91448C2
hypercenterC2×C42D3×D5
hypocenterC3×C5C4×#121
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C3×C42×D5C2semidirect
3. C2×C4×#1203C2semidirect
4. C2×C4×#1202C2semidirect
5. C2×C4×#1201C2semidirect
6. C4×#6714C2semidirect
7. C4×C5×(C2×D3)⋊C4C2semidirect
8. #11748908C2semidirect
9. #11748907C2semidirect
10. #11748905C2semidirect
11. #11748829C2semidirect
12. C4×#6668C2semidirect
13. #11748802C2semidirect
14. #11748747C2semidirect
15. #11748738C2semidirect
47. #91448C4direct (N × H)
62. C2×C42×D5D3semidirect
101. C2×C3×C4×D5C2×C4semidirect
102. C2×C3×C4×D5D4semidirect
105. C2×#1203C2×C4semidirect
108. C2×#1202C2×C4semidirect
111. C2×#1201C2×C4semidirect
114. #6714C2×C4semidirect
117. C5×(C2×D3)⋊C4C2×C4semidirect
121. C3×C4×Dic5D4semidirect
126. #6668C2×C4semidirect
145. C4×(C2×D3)⋊C4D5semidirect
332. C2×C4×D5C4×D3semidirect
333. C2×C4×D5D12semidirect
354. C4×Dic5#67semidirect
397. C2×C3×D5C4×D4semidirect
400. C3×C4×C5#121semidirect
406. C3×Dic5C4×D4semidirect
462. (C2×D3)⋊C4C4×D5semidirect
679. C2×D5C4×D12semidirect
685. C4×C5#930semidirect
691. Dic5C4×#67semidirect
752. C3×C5C4×#121semidirect
786. C3×C4#4030semidirect
879. C5C4×#930semidirect
919. C4#91448direct (N × H)
920. C3C4×#4030semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C42×D52
C2×#914482
C2×C4×#12032
C2×C4×#12022
C2×C4×#12012
C4×#67142
C4×C5×(C2×D3)⋊C42
#117489082
#117489072
#117489052
#117488292
C4×#66682
#117488022
#117487472
#117487382
C4×#40303
C4×#9305