Finite Group Databasebeta

← C4×#91566 #14321502

Subgroups — C4×#91566 #14321502

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×C4×#1220C211yesmaximal, characteristic, complemented
2C2×C4×C5×#67C211yesmaximal, characteristic, complemented
3C22×C3×C4×Dic5C211yesmaximal, characteristic, complemented
4C2×#91566C211yesmaximal, characteristic
5C2×C4×#1203C211yesmaximal, characteristic, complemented
6#11749506C211yesmaximal, characteristic, complemented
7#11749494C211yesmaximal, characteristic, complemented
8#11749492C211yesmaximal, characteristic, complemented
9#11748908C211yesmaximal, characteristic, complemented
10C4×#6668C211yesmaximal, characteristic, complemented
11#11748801C211yesmaximal, characteristic, complemented
12#11748727C211yesmaximal, characteristic, complemented
13C4×#6667C211yesmaximal, characteristic, complemented
14#11748715C211yesmaximal, characteristic, complemented
15C4×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
16C4×#4085—31nomaximal, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic
24C22×#1203C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C4×#1220—24no—
27C2×#6714C2211yescharacteristic
28C2×#6712C2211yescharacteristic
29C2×C4×Dic15C2211yescharacteristic
30C2×C5×#217C2211yescharacteristic
31C4×C5×#67—24no—
32C2×C5×(C2×D3)⋊C4C2211yescharacteristic
33C2×C5×Dic3⋊C4C2211yescharacteristic
34C2×C4×C5×Dic3C2211yescharacteristic
35C2×C3×C4×Dic5—24no—
36C2×C3×C4×Dic5C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic
38C2×C3×C4×Dic5C2211yescharacteristic
39C2×C3×C4×Dic5C2211yescharacteristic
40#91566C418yesdirect product factor
41C2×#6668C2211yescharacteristic
42C2×#6668C2211yescharacteristic
43C2×#6668C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×#6667C2211yescharacteristic
46C2×#6667C2211yescharacteristic
47C2×(C2×D3)⋊Dic5C2211yescharacteristic
48C2×(C2×D3)⋊Dic5C2211yescharacteristic
49C2×(C2×D3)⋊Dic5C2211yescharacteristic
50C4×#1203—24no—
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57C4×#930—51nomaximal, Hall
58C2×C4×C5×D4—31no—
59C2×#4085—31no—
60C2×C4×C22⋊D5—31no—
61C2×C4×C22⋊D5—31no—
62C22×C4×Dic5D311yescharacteristic, complemented
63#65509—31no—
64C4×C22⋊Dic5—31no—
65#65279—31no—
66#65261—31no—
67#65247—31no—
68#65246—31no—
69#65234—31no—
70#65231—31no—
71C4×#685—31no—
72C4×#683—31no—
73C24×C3×C5C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
76C22×C3×C4×C5—22no—
77C22×C3×C4×C5—22no—
78C22×C3×C4×C5D414yescomplemented
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C2×#1220—22no—
82C2×#1220—22no—
83C2×#1220C2×C414yescomplemented
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×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C2×C4×C5×D3—22no—
97C2×C4×C5×D3—22no—
98C2×C4×C5×D3—22no—
99C22×C3×Dic5—22no—
100C22×C3×Dic5—22no—
101C22×C3×Dic5—22no—
102C22×C3×Dic5—22no—
103C22×C3×Dic5—22no—
104C22×C3×Dic5C2×C414yescomplemented
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C2×#1203—22no—
110C2×#1203—22no—
111C2×#1203C2×C414yescomplemented
112#6719—22no—
113#6714—22no—
114#6712—22no—
115C4×Dic15—22no—
116C5×#217—22no—
117C5×(C2×D3)⋊C4—22no—
118C5×Dic3⋊C4—22no—
119C4×C5×Dic3—22no—
120C3×C4×Dic5—22no—
121C3×C4×Dic5—22no—
122C3×C4×Dic5—22no—
123C3×C4×Dic5D414yescomplemented
124#6668—22no—
125#6668—22no—
126#6668C2×C414yescomplemented
127#6667—22no—
128#6667—22no—
129#6667C2×C414yescomplemented
130(C2×D3)⋊Dic5—22no—
131(C2×D3)⋊Dic5—22no—
132(C2×D3)⋊Dic5C2×C414yescomplemented
133C22×C3×C42—51no—
134C2×#930—51no—
135C2×C4×#67—51no—
136C2×C4×#67D511yescharacteristic, complemented
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)⋊C4—51no—
146C4×C4⋊Dic3—51no—
147#4928—51no—
148C22×C5×D4—31no—
149C23×C4×C5—31no—
150C23×C4×C5C2×D311yescharacteristic
151C22×C22⋊D5—31no—
152C22×C22⋊D5—31no—
153C23×Dic5C2×D311yescharacteristic
154C23×Dic5C2×D311yescharacteristic
155C22×C4×D5—31no—
156C4×C5×D4—64no—
157C2×C5×C4⋊C4—31no—
158C2×C5×C22⋊C4—31no—
159C2×C5×C22⋊C4—31no—
160C2×C42×C5—31no—
161C2×C22⋊Dic5—31no—
162C2×C22⋊Dic5—31no—
163C2×C22⋊Dic5—31no—
164C2×C22⋊Dic5—31no—
165#4085—38no—
166C4×C22⋊D5—64no—
167C4×C22⋊D5—64no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685—31no—
171C2×#685—31no—
172C2×#683—31no—
173C2×#683—31no—
174C2×#683—31no—
175C2×#683—31no—
176C2×C4×Dic5—24no—
177C2×C4×Dic5—31no—
178C2×C4×Dic5C2×D311yescharacteristic
179C2×C4×Dic5C2×D311yescharacteristic
180C2×C4×Dic5C2×D311yescharacteristic
181C2×C4×Dic5C2×D311yescharacteristic
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#3963—31no—
187#3963—31no—
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—28no—
214C2×C3×C4×C5C2×D412yes—
215C2×C3×C4×C5C2×D412yes—
216C2×C3×C4×C5C2×D412yes—
217C2×C3×C4×C5#4112yes—
218#1220—28no—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15C22×C412yes—
228C4×D15—44no—
229C5×#67—28no—
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—28no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—28no—
248C2×C3×Dic5C22×C412yes—
249C2×C3×Dic5C22×C412yes—
250C2×C3×Dic5C2×D412yes—
251C2×C3×Dic5C2×D412yes—
252C2×C3×Dic5#4112yes—
253C2×C3×Dic5#4112yes—
254#1203—28no—
255C23×C3×C4—51no—
256C23×C3×C4—51no—
257C23×C3×C4C2×D511yescharacteristic
258C22×#67—51no—
259C22×#67C2×D511yescharacteristic
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—51no—
267C2×C3×C42—104no—
268C2×#217—51no—
269C2×#217C2×D511yescharacteristic
270#930—58no—
271C4×#67—24no—
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)⋊C4—51no—
280C2×(C2×D3)⋊C4C2×D511yescharacteristic
281C2×C4⋊Dic3—51no—
282C2×C4⋊Dic3—51no—
283C2×C4⋊Dic3—51no—
284C2×Dic3⋊C4—51no—
285C2×Dic3⋊C4C2×D511yescharacteristic
286C2×C4×Dic3—51no—
287C2×C4×Dic3C2×D511yescharacteristic
288C4×D12—104no—
289C3⋊#95—51no—
290C3⋊#95—51no—
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C24×C5—31no—
296C24×C5C22×D311yescharacteristic
297C23×D5—31no—
298C2×C5×D4—34no—
299C2×C5×D4—62no—
300C2×C5×D4—62no—
301C22×C4×C5—22no—
302C22×C4×C5—22no—
303C22×C4×C5—31no—
304C22×C4×C5—31no—
305C22×C4×C5—31no—
306C22×C4×C5—62no—
307C22×C4×C5—62no—
308C22×C4×C5—62no—
309C22×C4×C5D1214yescomplemented
310C22×C4×C5C22×D311yescharacteristic
311C22×C4×C5C22×D311yescharacteristic
312C2×C22⋊D5—34no—
313C2×C22⋊D5—34no—
314C2×C22⋊D5—62no—
315C2×C22⋊D5—62no—
316C2×C22⋊D5—62no—
317C2×C22⋊D5—62no—
318C22×Dic5—22no—
319C22×Dic5—22no—
320C22×Dic5—22no—
321C22×Dic5—22no—
322C22×Dic5—22no—
323C22×Dic5—31no—
324C22×Dic5—31no—
325C22×Dic5—31no—
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×C4⋊C4—62no—
335C5×C22⋊C4—62no—
336C5×C22⋊C4—62no—
337C42×C5—62no—
338C22⋊Dic5—34no—
339C22⋊Dic5—62no—
340C22⋊Dic5—62no—
341C22⋊Dic5—62no—
342#685—34no—
343#685—62no—
344#685—62no—
345#685—62no—
346#683—34no—
347#683—62no—
348#683—62no—
349#683—62no—
350C4×Dic5—22no—
351C4×Dic5—22no—
352C4×Dic5—22no—
353C4×Dic5—62no—
354C4×Dic5#6714yescomplemented
355C2×#121—151no—
356C2×C4×D4—31no—
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—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—22no—
399C3×C4×C5#12114yescomplemented
400Dic15—22no—
401Dic15—41no—
402Dic15—41no—
403C3×Dic5—22no—
404C3×Dic5—22no—
405C3×Dic5—22no—
406C3×Dic5C4×D414yescomplemented
407C5×Dic3—22no—
408C5×Dic3—41no—
409C5×Dic3—41no—
410C24×C3C22×D511yescharacteristic
411C23×D3—51no—
412C23×D3C22×D511yescharacteristic
413C22×C3×C4—22no—
414C22×C3×C4—22no—
415C22×C3×C4—51no—
416C22×C3×C4—54no—
417C22×C3×C4—51no—
418C22×C3×C4—51no—
419C22×C3×C4—51no—
420C22×C3×C4—102no—
421C22×C3×C4—102no—
422C22×C3×C4—102no—
423C22×C3×C4—102no—
424C22×C3×C4—102no—
425C22×C3×C4C22⋊D514yescomplemented
426C22×C3×C4C22×D511yescharacteristic
427C22×C3×C4C22×D511yescharacteristic
428C2×#67—22no—
429C2×#67—22no—
430C2×#67—54no—
431C2×#67—102no—
432C2×#67—102no—
433C2×#67C4×D514yescomplemented
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—54no—
450C3×C42—102no—
451C3×C42—102no—
452C3×C42—102no—
453#217—22no—
454#217—102no—
455(C2×D3)⋊C4—22no—
456(C2×D3)⋊C4—54no—
457(C2×D3)⋊C4—54no—
458(C2×D3)⋊C4—102no—
459(C2×D3)⋊C4—102no—
460(C2×D3)⋊C4—102no—
461(C2×D3)⋊C4—102no—
462(C2×D3)⋊C4—102no—
463C4⋊Dic3—54no—
464C4⋊Dic3—102no—
465C4⋊Dic3—102no—
466Dic3⋊C4—22no—
467Dic3⋊C4—102no—
468C4×Dic3—22no—
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×C5C2×D1212yes—
483C23×C5#23512yes—
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—28no—
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×D1212yes—
507C2×C4×C5C2×D1212yes—
508C2×C4×C5#23512yes—
509C2×C4×C5C2×#6712yes—
510C22⋊D5—68no—
511C22⋊D5—68no—
512C2×Dic5—28no—
513C2×Dic5—21no—
514C2×Dic5—21no—
515C2×Dic5—21no—
516C2×Dic5—21no—
517C2×Dic5—21no—
518C2×Dic5—21no—
519C2×Dic5—28no—
520C2×Dic5—32no—
521C2×Dic5—61no—
522C2×Dic5—61no—
523C2×Dic5—61no—
524C2×Dic5—61no—
525C2×Dic5—61no—
526C2×Dic5—61no—
527C2×Dic5—61no—
528C2×Dic5—61no—
529C2×Dic5C2×C4×D312yes—
530C2×Dic5C2×C4×D312yes—
531C2×Dic5#23512yes—
532C2×Dic5#23512yes—
533C2×Dic5C2×#6712yes—
534C2×Dic5C2×#6712yes—
535C4×D5—124no—
536C22×D4—31no—
537C22×D4—151no—
538C22×D4—151no—
539C23×C4—31no—
540C23×C4—51no—
541C23×C4—51no—
542C23×C4—151no—
543C23×C4D3×D511yescharacteristic
544#121—158no—
545C4×D4—64no—
546C4×D4—304no—
547C4×D4—304no—
548C2×C4⋊C4—31no—
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—51no—
568C2×C42—104no—
569C2×C42—151no—
570#95—151no—
571#95—151no—
572#95—151no—
573#95—151no—
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×C3#70912yes—
592C23×C3C2×C22⋊D512yes—
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—28no—
611C2×C3×C4—52no—
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—101no—
624C2×C3×C4—101no—
625C2×C3×C4D4×D512yes—
626C2×C3×C4#71112yes—
627C2×C3×C4C2×C22⋊D512yes—
628C2×C3×C4C2×C22⋊D512yes—
629#67—28no—
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—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×C5C4×D1214yescomplemented
666C22×C5C22×C4×D311yescharacteristic
667C22×C5C22×D1211yescharacteristic
668C22×C5C2×#23511yescharacteristic
669C22×C5C2×#23511yescharacteristic
670C22×C5C2×#23511yescharacteristic
671C22×C5C2×#23511yescharacteristic
672C22×C5C22×#6711yescharacteristic
673C2×D5—62no—
674C2×D5—62no—
675C2×D5—62no—
676C2×D5—121no—
677C2×D5—121no—
678C2×D5—121no—
679C2×D5—121no—
680C4×C5—22no—
681C4×C5—62no—
682C4×C5—121no—
683C4×C5—121no—
684C4×C5#93014yescomplemented
685Dic5—22no—
686Dic5—22no—
687Dic5—22no—
688Dic5—62no—
689Dic5—121no—
690Dic5—121no—
691Dic5C4×#6714yescomplemented
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—22no—
705C22×C4—22no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—51no—
710C22×C4—54no—
711C22×C4—51no—
712C22×C4—51no—
713C22×C4—51no—
714C22×C4—62no—
715C22×C4—62no—
716C22×C4—62no—
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×C4#120314yescomplemented
729C22×C4C2×D3×D511yescharacteristic
730C22×C4C2×D3×D511yescharacteristic
731C4⋊C4—62no—
732C4⋊C4—154no—
733C4⋊C4—302no—
734C4⋊C4—302no—
735C4⋊C4—302no—
736C22⋊C4—62no—
737C22⋊C4—62no—
738C22⋊C4—154no—
739C22⋊C4—154no—
740C22⋊C4—302no—
741C22⋊C4—302no—
742C22⋊C4—302no—
743C22⋊C4—302no—
744C22⋊C4—302no—
745C22⋊C4—302no—
746C42—54no—
747C42—62no—
748C42—102no—
749C42—102no—
750C42—102no—
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×C3C4×C22⋊D514yescomplemented
760C22×C3C22×C4×D511yescharacteristic
761C22×C3C2×#70911yescharacteristic
762C22×C3C2×D4×D511yescharacteristic
763C22×C3C2×#71111yescharacteristic
764C22×C3D5×#4111yescharacteristic
765C22×C3D5×#4111yescharacteristic
766C22×C3C22×C22⋊D511yescharacteristic
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—54no—
783C3×C4—102no—
784C3×C4—102no—
785C3×C4—102no—
786C3×C4#408514yescomplemented
787Dic3—22no—
788Dic3—41no—
789Dic3—41no—
790Dic3—102no—
791Dic3—201no—
792Dic3—201no—
793C2×C5—24no—
794C2×C5—122no—
795C2×C5C2×C4×D1211yescharacteristic
796C2×C5C4×#23511yescharacteristic
797C2×C5#547711yescharacteristic
798C2×C5#547911yescharacteristic
799C2×C5C2×C4×#6711yescharacteristic
800C2×C5C2×#93011yescharacteristic
801C2×C5#579111yescharacteristic
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#677112yes—
822C23C4×D3×D512yes—
823C23C2×#120312yes—
824C23C22×D3×D511yescharacteristic
825D4—68no—
826D4—308no—
827D4—308no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—28no—
831C2×C4—32no—
832C2×C4—52no—
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—101no—
853C2×C4—101no—
854C2×C4—124no—
855C2×C4—152no—
856C2×C4—301no—
857C2×C4—301no—
858C2×C4—301no—
859C2×C4—301no—
860C2×C4—301no—
861C2×C4—301no—
862C2×C4—301no—
863C2×C4—301no—
864C2×C4—604no—
865C2×C4#678212yes—
866C2×C4C2×#120312yes—
867C2×C4C2×#120312yes—
868C2×C4D5×#6712yes—
869C2×C3—24no—
870C2×C3C4×#71111yescharacteristic
871C2×C3#6587211yescharacteristic
872C2×C3C4×D4×D511yescharacteristic
873C2×C3#6588111yescharacteristic
874C2×C3C2×C4×C22⋊D511yescharacteristic
875C2×C3C2×#408511yescharacteristic
876C2×C3#6616611yescharacteristic
877D3—42no—
878D3—202no—
879C5C4×#93011yescharacteristic, 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—
900C22C4×#120314yescomplemented
901C22C2×#677111yescharacteristic
902C22C2×C4×D3×D511yescharacteristic
903C22D5×#23511yescharacteristic
904C22D5×#23511yescharacteristic
905C22C2×#678211yescharacteristic
906C22C22×#120311yescharacteristic
907C22C2×D5×#6711yescharacteristic
908C4—22no—
909C4—54no—
910C4—62no—
911C4—102no—
912C4—102no—
913C4—102no—
914C4—121no—
915C4—121no—
916C4—302no—
917C4—601no—
918C4—601no—
919C4#9156614yesdirect product factor
920C3C4×#408511yescharacteristic, complemented, Sylow
921C2—24no—
922C2—122no—
923C2—602no—
924C2#1175422911yescharacteristic
925C2C4×#678211yescharacteristic
926C2C2×C4×#120311yescharacteristic
927C2#1175452511yescharacteristic
928C2#1175457211yescharacteristic
929C2C4×D5×#6711yescharacteristic
930C2C2×#9156611yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91566C2
hypercenterC23×C4D3×D5
hypocenterC3×C5C4×#121
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#1220C2semidirect
2. C2×C4×C5×#67C2semidirect
3. C22×C3×C4×Dic5C2semidirect
5. C2×C4×#1203C2semidirect
6. #11749506C2semidirect
7. #11749494C2semidirect
8. #11749492C2semidirect
9. #11748908C2semidirect
10. C4×#6668C2semidirect
11. #11748801C2semidirect
12. #11748727C2semidirect
13. C4×#6667C2semidirect
14. #11748715C2semidirect
15. C4×(C2×D3)⋊Dic5C2semidirect
40. #91566C4direct (N × H)
62. C22×C4×Dic5D3semidirect
78. C22×C3×C4×C5D4semidirect
83. C2×#1220C2×C4semidirect
92. C2×C5×#67C2×C4semidirect
104. C22×C3×Dic5C2×C4semidirect
111. C2×#1203C2×C4semidirect
123. C3×C4×Dic5D4semidirect
126. #6668C2×C4semidirect
129. #6667C2×C4semidirect
132. (C2×D3)⋊Dic5C2×C4semidirect
136. C2×C4×#67D5semidirect
309. C22×C4×C5D12semidirect
326. C22×Dic5C4×D3semidirect
354. C4×Dic5#67semidirect
376. C22×C3×C5C4×D4semidirect
399. C3×C4×C5#121semidirect
406. C3×Dic5C4×D4semidirect
425. C22×C3×C4C22⋊D5semidirect
433. C2×#67C4×D5semidirect
665. C22×C5C4×D12semidirect
684. C4×C5#930semidirect
691. Dic5C4×#67semidirect
728. C22×C4#1203semidirect
752. C3×C5C4×#121semidirect
759. C22×C3C4×C22⋊D5semidirect
786. C3×C4#4085semidirect
879. C5C4×#930semidirect
900. C22C4×#1203semidirect
919. C4#91566direct (N × H)
920. C3C4×#4085semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C2×C4×C5×#672
C22×C3×C4×Dic52
C2×#915662
C2×C4×#12032
#117495062
#117494942
#117494922
#117489082
C4×#66682
#117488012
#117487272
C4×#66672
#117487152
C4×(C2×D3)⋊Dic52
C4×#40853
C4×#9305