Finite Group Databasebeta

← #14327067

Subgroups — #14327067

Order 1920.

1552 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×C5×D3×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#91446C211yesmaximal, characteristic
3C2×#91446C211yesmaximal, characteristic
4C2×C4×#1203C211yesmaximal, characteristic
5C2×#91404C211yesmaximal, characteristic, complemented
6#11751090C211yesmaximal, characteristic, complemented
7C3×#65261C211yesmaximal, characteristic, complemented
8#11748902C211yesmaximal, characteristic, complemented
9#11748882C211yesmaximal, characteristic, complemented
10#11748782C211yesmaximal, characteristic, complemented
11#11748722C211yesmaximal, characteristic, complemented
12#11748716C211yesmaximal, characteristic, complemented
13#11748681C211yesmaximal, characteristic, complemented
14#11748641C211yesmaximal, characteristic, complemented
15Dic5×Dic3⋊C4C211yesmaximal, characteristic, complemented
16C4⋊C4×C22⋊D5—31nomaximal, Hall
17C22×C4×D15C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic
21C22×#1203C2211yescharacteristic
22C22×#1200C2211yescharacteristic
23C22×#1200C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6712C2211yescharacteristic
28C2×C5×C4⋊Dic3C2211yescharacteristic
29C2×C5×Dic3⋊C4C2211yescharacteristic
30C2×C5×Dic3⋊C4C2211yescharacteristic
31C5×D3×C4⋊C4—24no—
32C2×C3×#683C2211yescharacteristic
33C2×C3×#683C2211yescharacteristic
34C2×C3×#683C2211yescharacteristic
35C2×C3×C4×Dic5C2211yescharacteristic
36C2×Dic3⋊Dic5C2211yescharacteristic
37C2×Dic3⋊Dic5C2211yescharacteristic
38C2×#6669C2211yescharacteristic
39C2×#6668C2211yescharacteristic
40C2×#6668C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic
47#91446—24no—
48#91446C418yescomplemented
49C4×#1203—24no—
50#91404—24no—
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#76202—51nomaximal, Hall
58C22×C5×C4⋊C4—31no—
59C2×C4×C22⋊D5—31no—
60C2×C4×C22⋊D5—31no—
61C2×C4×C22⋊D5—31no—
62C2×D5×C4⋊C4—31no—
63#65501—31no—
64#65499—31no—
65#65499—31no—
66#65278—31no—
67#65278—31no—
68#65276—31no—
69#65265—31no—
70C4⋊C4×Dic5—31no—
71#65261—31no—
72#65261D311yescharacteristic, complemented
73C23×D15C2311yescharacteristic
74C23×C5×D3C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C2×C4×D15—22no—
82C2×C4×D15—22no—
83C2×C4×D15—41no—
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C2×C4×C5×D3—22no—
88C2×C4×C5×D3—22no—
89C2×C4×C5×D3—22no—
90C2×C4×C5×D3—22no—
91C2×C4×C5×D3—22no—
92C2×C4×C5×D3—22no—
93C2×C4×C5×D3—41no—
94C2×C4×C5×D3—41no—
95C2×C4×C5×D3C2×C414yescomplemented
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C2×#1203C2×C414yes—
101C2×#1203D414yes—
102C2×#1203Q814yes—
103C2×#1200—22no—
104C2×#1200—22no—
105C2×#1200—22no—
106C2×#1200—22no—
107C2×#1200—41no—
108C2×#1200C2×C414yescomplemented
109C3×C5×C4⋊C4—22no—
110#6714—22no—
111#6714C2×C414yescomplemented
112#6712—41no—
113C5×C4⋊Dic3—22no—
114C5×Dic3⋊C4—22no—
115C5×Dic3⋊C4D414yescomplemented
116C3×#683—22no—
117C3×#683—22no—
118C3×#683C2×C414yescomplemented
119C3×C4×Dic5—22no—
120Dic3⋊Dic5—22no—
121Dic3⋊Dic5—22no—
122#6669—41no—
123#6668—22no—
124#6668—22no—
125#6667—22no—
126(C2×D3)⋊Dic5—22no—
127(C2×D3)⋊Dic5—22no—
128(C2×D3)⋊Dic5C2×C414yescomplemented
129Dic3×Dic5—22no—
130Dic3×Dic5C2×C414yescomplemented
131C2×#893—51no—
132C2×#893—51no—
133C2×D3×C4⋊C4—51no—
134C2×D3×C4⋊C4D511yescharacteristic, complemented
135C2×C4×D12—51no—
136C3×#389—51no—
137#4989—51no—
138#4989—51no—
139#4984—51no—
140#4975—51no—
141C4×Dic3⋊C4—51no—
142#4668—51no—
143#4668—51no—
144#4667—51no—
145#4667—51no—
146C23×C4×C5—31no—
147C23×C4×C5—31no—
148C23×C4×C5—31no—
149C22×C22⋊D5—31no—
150C22×C4×D5—31no—
151C22×C4×D5—31no—
152C22×C4×D5—31no—
153C2×C5×C4⋊C4—31no—
154C2×C5×C4⋊C4—31no—
155C2×C5×C4⋊C4—31no—
156C2×C5×C4⋊C4—64no—
157C2×C5×C4⋊C4C2×D311yescharacteristic
158C2×C22⋊Dic5—31no—
159C2×C22⋊Dic5—31no—
160C2×C22⋊Dic5—31no—
161C4×C22⋊D5—38no—
162C4×C22⋊D5—64no—
163C4×C22⋊D5—64no—
164C2×#685—31no—
165C2×#685—31no—
166C2×#685—31no—
167C2×C4⋊Dic5—31no—
168C2×C4⋊Dic5—31no—
169C2×#683—31no—
170C2×#683—31no—
171C2×#683—31no—
172C2×#683—31no—
173C2×#683C2×D311yescharacteristic
174C2×#683C2×D311yescharacteristic
175C2×#683C2×D311yescharacteristic
176C2×C4×Dic5—31no—
177C2×C4×Dic5—31no—
178C2×C4×Dic5C2×D311yescharacteristic
179D5×C4⋊C4—64no—
180#3963—31no—
181#3963—31no—
182#3963—31no—
183#3963—31no—
184#3963C2×D311yescharacteristic
185#3963C2×D311yescharacteristic
186D4×C4⋊C4—151noSylow
187C23×C3×C5C2411yescharacteristic
188C22×D15—21no—
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—21no—
192C22×D15C22×C412yes—
193C22×D15C2×D412yes—
194C22×D15C2×Q812yes—
195C22×C5×D3—21no—
196C22×C5×D3—21no—
197C22×C5×D3—21no—
198C22×C5×D3—21no—
199C22×C5×D3C22×C412yes—
200C22×C5×D3C2×D412yes—
201C22×C5×D3C2×Q812yes—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5C22×C412yes—
210C2×C3×C4×C5C2×D412yes—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—21no—
214C2×Dic15—21no—
215C2×Dic15—21no—
216C2×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15C22×C412yes—
220C4×D15—44no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—21no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—21no—
226C2×C5×Dic3C22×C412yes—
227C2×C5×Dic3C2×D412yes—
228C2×C5×Dic3C2×D412yes—
229C2×C5×Dic3#4112yes—
230C4×C5×D3—28no—
231C4×C5×D3—44no—
232C4×C5×D3—44no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5C22×C412yes—
242C2×C3×Dic5C22×C412yes—
243C2×C3×Dic5C2×D412yes—
244C2×C3×Dic5C2×Q812yes—
245#1203C4⋊C4116yescomplemented
246#1200—28no—
247#1200—44no—
248C22×D12—51no—
249C22×C4×D3—51no—
250C22×C4×D3—51no—
251C22×C4×D3—51no—
252C22×C4×D3C2×D511yescharacteristic
253C22×C4×D3C2×D511yescharacteristic
254C22×C4×D3C2×D511yescharacteristic
255C2×C3×C4⋊C4—51no—
256C2×C3×C4⋊C4—51no—
257C2×C3×C4⋊C4—51no—
258C2×C3×C4⋊C4C2×D511yescharacteristic
259C2×C3×C42—51no—
260C2×(C2×D3)⋊C4—51no—
261C2×(C2×D3)⋊C4—51no—
262C2×(C2×D3)⋊C4—51no—
263C2×(C2×D3)⋊C4—51no—
264C2×(C2×D3)⋊C4—51no—
265C2×(C2×D3)⋊C4—51no—
266C2×C4⋊Dic3—51no—
267C2×C4⋊Dic3—51no—
268C2×C4⋊Dic3C2×D511yescharacteristic
269C2×Dic3⋊C4—51no—
270C2×Dic3⋊C4—51no—
271C2×Dic3⋊C4—51no—
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4C2×D511yescharacteristic
274C2×Dic3⋊C4C2×D511yescharacteristic
275C2×C4×Dic3—51no—
276C2×C4×Dic3—51no—
277#893—58no—
278#893—104no—
279D3×C4⋊C4—24no—
280D3×C4⋊C4—104no—
281C4×D12—104no—
282C3×#95—51no—
283C3×#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95—51no—
287C3⋊#95—51no—
288C24×C5—31no—
289C23×D5—31no—
290C22×C4×C5—31no—
291C22×C4×C5—31no—
292C22×C4×C5—34no—
293C22×C4×C5—31no—
294C22×C4×C5—62no—
295C22×C4×C5—62no—
296C22×C4×C5—62no—
297C22×C4×C5—62no—
298C22×C4×C5—62no—
299C22×C4×C5—62no—
300C22×C4×C5—121no—
301C22×C4×C5—121no—
302C22×C4×C5C22×D311yescharacteristic
303C22×C4×C5C22×D311yescharacteristic
304C22×C4×C5C22×D311yescharacteristic
305C2×C22⋊D5—34no—
306C2×C22⋊D5—34no—
307C2×C22⋊D5—34no—
308C22×Dic5—31no—
309C22×Dic5—31no—
310C22×Dic5—31no—
311C22×Dic5C22×D311yescharacteristic
312C22×Dic5C22×D311yescharacteristic
313C22×Dic5C22×D311yescharacteristic
314C22×Dic5C22×D311yescharacteristic
315C2×C4×D5—34no—
316C2×C4×D5—62no—
317C2×C4×D5—62no—
318C2×C4×D5—62no—
319C2×C4×D5—62no—
320C2×C4×D5—62no—
321C2×C4×D5—62no—
322C2×C4×D5—121no—
323C2×C4×D5—121no—
324C5×C4⋊C4—22no—
325C5×C4⋊C4—34no—
326C5×C4⋊C4—62no—
327C5×C4⋊C4—62no—
328C22⋊Dic5—34no—
329C22⋊Dic5—62no—
330C22⋊Dic5—62no—
331#685—34no—
332#685—62no—
333#685—62no—
334C4⋊Dic5—62no—
335C4⋊Dic5—62no—
336#683—22no—
337#683—22no—
338#683—62no—
339#683—62no—
340#683—121no—
341#683—121no—
342#683C4×D314yescomplemented
343C4×Dic5—22no—
344C4×Dic5—34no—
345C4×Dic5—62no—
346C2×C4×D4—151no—
347C2×C4×D4—151no—
348C2×C4×D4—151no—
349C22×C4⋊C4—31no—
350C22×C4⋊C4—151no—
351#389—51no—
352#389—151no—
353#385—151no—
354#385—151no—
355#385—151no—
356#385—151no—
357#384—151no—
358#380—151no—
359#380—151no—
360C4×C4⋊C4—151no—
361C22×C3×C5C23×C411yescharacteristic
362C22×C3×C5C22×D411yescharacteristic
363C22×C3×C5C22×D411yescharacteristic
364C22×C3×C5C22×Q811yescharacteristic
365C22×C3×C5C2×#4111yescharacteristic
366C22×C3×C5H(5,𝔽2)11yescharacteristic
367C22×C3×C52−1+411yescharacteristic
368C2×D15—22no—
369C2×D15—22no—
370C2×D15—22no—
371C2×D15—22no—
372C2×D15—22no—
373C2×D15—22no—
374C2×D15C2×C4⋊C414yescomplemented
375C2×C5×D3—22no—
376C2×C5×D3—22no—
377C2×C5×D3—22no—
378C2×C5×D3—22no—
379C2×C5×D3—22no—
380C2×C5×D3—22no—
381C2×C5×D3C2×C4⋊C414yescomplemented
382C3×C4×C5—22no—
383C3×C4×C5—22no—
384C3×C4×C5—41no—
385Dic15—22no—
386Dic15—41no—
387Dic15—41no—
388C3×Dic5—22no—
389C3×Dic5—41no—
390C3×Dic5—41no—
391C3×Dic5C2×C4⋊C414yescomplemented
392C5×Dic3—22no—
393C5×Dic3—41no—
394C5×Dic3C4×D414yescomplemented
395C23×D3—51no—
396C23×D3C22×D511yescharacteristic
397C22×C3×C4—51no—
398C22×C3×C4—51no—
399C22×C3×C4—51no—
400C22×C3×C4—51no—
401C22×C3×C4C22×D511yescharacteristic
402C22×C3×C4C22×D511yescharacteristic
403C22×C3×C4C22×D511yescharacteristic
404C22×Dic3—51no—
405C22×Dic3—51no—
406C22×Dic3—51no—
407C22×Dic3C22×D511yescharacteristic
408C22×Dic3C22×D511yescharacteristic
409C22×Dic3C22×D511yescharacteristic
410C2×D12—54no—
411C2×D12—54no—
412C2×D12—54no—
413C2×C4×D3—22no—
414C2×C4×D3—22no—
415C2×C4×D3—22no—
416C2×C4×D3—22no—
417C2×C4×D3—22no—
418C2×C4×D3—22no—
419C2×C4×D3—41no—
420C2×C4×D3—41no—
421C2×C4×D3—54no—
422C2×C4×D3—102no—
423C2×C4×D3—102no—
424C2×C4×D3—102no—
425C2×C4×D3—102no—
426C2×C4×D3—102no—
427C2×C4×D3—102no—
428C2×C4×D3—201no—
429C2×C4×D3—201no—
430C2×C4×D3C4×D514yescomplemented
431C3×C4⋊C4—22no—
432C3×C4⋊C4—54no—
433C3×C4⋊C4—102no—
434C3×C4⋊C4—102no—
435C3×C42—102no—
436(C2×D3)⋊C4—54no—
437(C2×D3)⋊C4—54no—
438(C2×D3)⋊C4—102no—
439(C2×D3)⋊C4—102no—
440(C2×D3)⋊C4—102no—
441(C2×D3)⋊C4—102no—
442C4⋊Dic3—22no—
443C4⋊Dic3—102no—
444C4⋊Dic3—102no—
445Dic3⋊C4—22no—
446Dic3⋊C4—102no—
447Dic3⋊C4—102no—
448Dic3⋊C4—201no—
449Dic3⋊C4—201no—
450Dic3⋊C4C22⋊D514yescomplemented
451C4×Dic3—54no—
452C4×Dic3—102no—
453C23×C5—32no—
454C23×C5—32no—
455C23×C5—32no—
456C23×C5—61no—
457C23×C5—61no—
458C23×C5—61no—
459C23×C5—61no—
460C23×C5C23×D311yescharacteristic
461C22×D5—32no—
462C22×D5—32no—
463C22×D5—32no—
464C22×D5—61no—
465C22×D5—61no—
466C22×D5—61no—
467C22×D5—61no—
468C2×C4×C5—21no—
469C2×C4×C5—21no—
470C2×C4×C5—21no—
471C2×C4×C5—21no—
472C2×C4×C5—21no—
473C2×C4×C5—21no—
474C2×C4×C5—21no—
475C2×C4×C5—32no—
476C2×C4×C5—32no—
477C2×C4×C5—32no—
478C2×C4×C5—32no—
479C2×C4×C5—68no—
480C2×C4×C5—61no—
481C2×C4×C5—61no—
482C2×C4×C5—61no—
483C2×C4×C5—61no—
484C2×C4×C5—61no—
485C2×C4×C5—124no—
486C2×C4×C5—124no—
487C2×C4×C5C2×C4×D312yes—
488C2×C4×C5D3×D412yes—
489C22⋊D5—316no—
490C2×Dic5—21no—
491C2×Dic5—21no—
492C2×Dic5—21no—
493C2×Dic5—21no—
494C2×Dic5—21no—
495C2×Dic5—21no—
496C2×Dic5—21no—
497C2×Dic5—21no—
498C2×Dic5—32no—
499C2×Dic5—61no—
500C2×Dic5—61no—
501C2×Dic5—61no—
502C2×Dic5—61no—
503C2×Dic5—61no—
504C2×Dic5—61no—
505C2×Dic5—61no—
506C2×Dic5—61no—
507C2×Dic5C2×C4×D312yes—
508C2×Dic5C2×C4×D312yes—
509C2×Dic5D3×D412yes—
510C2×Dic5D3×Q812yes—
511C4×D5—68no—
512C4×D5—124no—
513C4×D5—124no—
514C22×D4—151no—
515C23×C4—31no—
516C23×C4—31no—
517C23×C4—31no—
518C23×C4—151no—
519C23×C4—151no—
520C23×C4—151no—
521C4×D4—158no—
522C4×D4—304no—
523C4×D4—304no—
524C2×C4⋊C4—31no—
525C2×C4⋊C4—31no—
526C2×C4⋊C4—31no—
527C2×C4⋊C4—51no—
528C2×C4⋊C4—51no—
529C2×C4⋊C4—51no—
530C2×C4⋊C4—64no—
531C2×C4⋊C4—151no—
532C2×C4⋊C4—151no—
533C2×C4⋊C4—151no—
534C2×C4⋊C4—151no—
535C2×C4⋊C4—151no—
536C2×C4⋊C4—151no—
537C2×C4⋊C4—304no—
538C2×C4⋊C4D3×D511yescharacteristic
539C2×C22⋊C4—151no—
540C2×C22⋊C4—151no—
541C2×C22⋊C4—151no—
542C2×C22⋊C4—151no—
543C2×C22⋊C4—151no—
544C2×C22⋊C4—151no—
545C2×C42—51no—
546C2×C42—151no—
547C2×C42—151no—
548#95—51no—
549#95—51no—
550#95—151no—
551#95—151no—
552#95—151no—
553#95—151no—
554C2×C3×C5C22×C4⋊C411yescharacteristic
555C2×C3×C5C2×C4×D411yescharacteristic
556C2×C3×C5#52011yescharacteristic
557C2×C3×C5D4211yescharacteristic
558C2×C3×C5#54711yescharacteristic
559C2×C3×C5D4×Q811yescharacteristic
560C2×C3×C5#55411yescharacteristic
561D15—24no—
562C5×D3—24no—
563C23×C3C23×D511yescharacteristic
564C22×D3—21no—
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—21no—
568C22×D3—52no—
569C22×D3—52no—
570C22×D3—52no—
571C22×D3—101no—
572C22×D3—101no—
573C22×D3—101no—
574C22×D3—101no—
575C22×D3C2×C4×D512yes—
576C22×D3D4×D512yes—
577C22×D3Q8×D512yes—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—52no—
586C2×C3×C4—52no—
587C2×C3×C4—52no—
588C2×C3×C4—52no—
589C2×C3×C4—101no—
590C2×C3×C4—101no—
591C2×C3×C4—101no—
592C2×C3×C4—101no—
593C2×C3×C4—101no—
594C2×C3×C4—101no—
595C2×C3×C4—101no—
596C2×C3×C4—101no—
597C2×C3×C4C2×C4×D512yes—
598C2×C3×C4C2×C22⋊D512yes—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—52no—
605C2×Dic3—101no—
606C2×Dic3—101no—
607C2×Dic3—101no—
608C2×Dic3—101no—
609C2×Dic3—101no—
610C2×Dic3—101no—
611C2×Dic3—101no—
612C2×Dic3—101no—
613C2×Dic3C2×C4×D512yes—
614C2×Dic3#70912yes—
615C2×Dic3C2×C22⋊D512yes—
616C2×Dic3C2×C22⋊D512yes—
617D12—516no—
618C4×D3—28no—
619C4×D3—44no—
620C4×D3—44no—
621C4×D3—108no—
622C4×D3—204no—
623C4×D3—204no—
624C22×C5—34no—
625C22×C5—62no—
626C22×C5—62no—
627C22×C5—62no—
628C22×C5—62no—
629C22×C5—62no—
630C22×C5—62no—
631C22×C5C22×C4×D311yescharacteristic
632C22×C5C2×D3×D411yescharacteristic
633C22×C5C2×D3×D411yescharacteristic
634C22×C5C2×D3×Q811yescharacteristic
635C22×C5#100711yescharacteristic
636C22×C5D3×#4111yescharacteristic
637C22×C5#100911yescharacteristic
638C2×D5—34no—
639C2×D5—62no—
640C2×D5—62no—
641C2×D5—62no—
642C2×D5—62no—
643C2×D5—62no—
644C2×D5—62no—
645C4×C5—22no—
646C4×C5—22no—
647C4×C5—34no—
648C4×C5—41no—
649C4×C5—62no—
650C4×C5—121no—
651Dic5—22no—
652Dic5—41no—
653Dic5—41no—
654Dic5—62no—
655Dic5—121no—
656Dic5—121no—
657Dic5D3×C4⋊C414yescomplemented
658C24—31no—
659C24—151no—
660C2×D4—154no—
661C2×D4—154no—
662C2×D4—154no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—34no—
666C22×C4—31no—
667C22×C4—51no—
668C22×C4—51no—
669C22×C4—51no—
670C22×C4—51no—
671C22×C4—62no—
672C22×C4—62no—
673C22×C4—62no—
674C22×C4—62no—
675C22×C4—62no—
676C22×C4—62no—
677C22×C4—121no—
678C22×C4—121no—
679C22×C4—154no—
680C22×C4—151no—
681C22×C4—151no—
682C22×C4—151no—
683C22×C4—302no—
684C22×C4—302no—
685C22×C4—302no—
686C22×C4—302no—
687C22×C4—302no—
688C22×C4—302no—
689C22×C4—601no—
690C22×C4—601no—
691C22×C4C2×D3×D511yescharacteristic
692C22×C4C2×D3×D511yescharacteristic
693C22×C4C2×D3×D511yescharacteristic
694C4⋊C4—22no—
695C4⋊C4—34no—
696C4⋊C4—54no—
697C4⋊C4—62no—
698C4⋊C4—62no—
699C4⋊C4—102no—
700C4⋊C4—102no—
701C4⋊C4—302no—
702C4⋊C4—302no—
703C4⋊C4—302no—
704C4⋊C4—302no—
705C4⋊C4—601no—
706C4⋊C4—601no—
707C22⋊C4—154no—
708C22⋊C4—154no—
709C22⋊C4—302no—
710C22⋊C4—302no—
711C22⋊C4—302no—
712C22⋊C4—302no—
713C42—102no—
714C42—154no—
715C42—302no—
716C3×C5D4×C4⋊C411yescharacteristic, complemented, Hall
717C22×C3C22×C4×D511yescharacteristic
718C22×C3C2×#70911yescharacteristic
719C22×C3C2×D4×D511yescharacteristic
720C22×C3#414411yescharacteristic
721C22×C3C2×Q8×D511yescharacteristic
722C22×C3#414711yescharacteristic
723C22×C3C22×C22⋊D511yescharacteristic
724C2×D3—22no—
725C2×D3—22no—
726C2×D3—22no—
727C2×D3—22no—
728C2×D3—22no—
729C2×D3—22no—
730C2×D3—54no—
731C2×D3—102no—
732C2×D3—102no—
733C2×D3—102no—
734C2×D3—102no—
735C2×D3—102no—
736C2×D3—102no—
737C2×D3D5×C4⋊C414yescomplemented
738C3×C4—22no—
739C3×C4—22no—
740C3×C4—41no—
741C3×C4—54no—
742C3×C4—102no—
743C3×C4—201no—
744C3×C4—201no—
745Dic3—22no—
746Dic3—41no—
747Dic3—102no—
748Dic3—201no—
749Dic3—201no—
750Dic3C4×C22⋊D514yescomplemented
751C2×C5—64no—
752C2×C5C2×D3×C4⋊C411yescharacteristic
753C2×C5C4×D3×D411yescharacteristic
754C2×C5#557411yescharacteristic
755C2×C5#560911yescharacteristic
756C2×C5#563111yescharacteristic
757C2×C5#569011yescharacteristic
758C2×C5#572711yescharacteristic
759D5—64no—
760C23—32no—
761C23—32no—
762C23—32no—
763C23—61no—
764C23—61no—
765C23—61no—
766C23—61no—
767C23—152no—
768C23—152no—
769C23—152no—
770C23—301no—
771C23—301no—
772C23—301no—
773C23—301no—
774C23C22×D3×D511yescharacteristic
775D4—1516no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—32no—
784C2×C4—32no—
785C2×C4—32no—
786C2×C4—32no—
787C2×C4—52no—
788C2×C4—52no—
789C2×C4—52no—
790C2×C4—52no—
791C2×C4—68no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—101no—
798C2×C4—101no—
799C2×C4—101no—
800C2×C4—101no—
801C2×C4—101no—
802C2×C4—101no—
803C2×C4—101no—
804C2×C4—101no—
805C2×C4—124no—
806C2×C4—124no—
807C2×C4—152no—
808C2×C4—308no—
809C2×C4—301no—
810C2×C4—301no—
811C2×C4—301no—
812C2×C4—301no—
813C2×C4—301no—
814C2×C4—301no—
815C2×C4—301no—
816C2×C4—301no—
817C2×C4—604no—
818C2×C4—604no—
819C2×C4C4×D3×D512yes—
820C2×C4D3×C22⋊D512yes—
821C2×C3C2×D5×C4⋊C411yescharacteristic
822C2×C3#6583811yescharacteristic
823C2×C3#6584111yescharacteristic
824C2×C3#6584511yescharacteristic
825C2×C3C2×C4×C22⋊D511yescharacteristic
826C2×C3D4×C22⋊D511yescharacteristic
827C2×C3Q8×C22⋊D511yescharacteristic
828D3—24no—
829D3—104no—
830C5#7620211yescharacteristic, complemented, Sylow
831C22—34no—
832C22—62no—
833C22—62no—
834C22—62no—
835C22—62no—
836C22—62no—
837C22—62no—
838C22—154no—
839C22—302no—
840C22—302no—
841C22—302no—
842C22—302no—
843C22—302no—
844C22—302no—
845C22C2×C4×D3×D511yescharacteristic
846C22D3×#70911yescharacteristic
847C22D3×D4×D511yescharacteristic
848C22#9202711yescharacteristic
849C22#9202911yescharacteristic
850C22D3×Q8×D511yescharacteristic
851C22C2×D3×C22⋊D511yescharacteristic
852C4—22no—
853C4—22no—
854C4—34no—
855C4—41no—
856C4—54no—
857C4—62no—
858C4—102no—
859C4—121no—
860C4—201no—
861C4—201no—
862C4—302no—
863C4—601no—
864C4—601no—
865C3C4⋊C4×C22⋊D511yescharacteristic, complemented, Sylow
866C2—64no—
867C2—304no—
868C2#1175333711yescharacteristic
869C2#1175368511yescharacteristic
870C2#1175371811yescharacteristic
871C2D3×D5×C4⋊C411yescharacteristic
872C2C4×D3×C22⋊D511yescharacteristic
873C2#1175505311yescharacteristic
874C2#1175523511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1203C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5D4×C4⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C5×D3×C4⋊C4C2semidirect
5. C2×#91404C2semidirect
6. #11751090C2semidirect
7. C3×#65261C2semidirect
8. #11748902C2semidirect
9. #11748882C2semidirect
10. #11748782C2semidirect
11. #11748722C2semidirect
12. #11748716C2semidirect
13. #11748681C2semidirect
14. #11748641C2semidirect
15. Dic5×Dic3⋊C4C2semidirect
48. #91446C4semidirect
72. #65261D3semidirect
95. C2×C4×C5×D3C2×C4semidirect
108. C2×#1200C2×C4semidirect
111. #6714C2×C4semidirect
115. C5×Dic3⋊C4D4semidirect
118. C3×#683C2×C4semidirect
128. (C2×D3)⋊Dic5C2×C4semidirect
130. Dic3×Dic5C2×C4semidirect
134. C2×D3×C4⋊C4D5semidirect
245. #1203C4⋊C4semidirect
342. #683C4×D3semidirect
374. C2×D15C2×C4⋊C4semidirect
381. C2×C5×D3C2×C4⋊C4semidirect
391. C3×Dic5C2×C4⋊C4semidirect
394. C5×Dic3C4×D4semidirect
430. C2×C4×D3C4×D5semidirect
450. Dic3⋊C4C22⋊D5semidirect
657. Dic5D3×C4⋊C4semidirect
716. C3×C5D4×C4⋊C4semidirect
737. C2×D3D5×C4⋊C4semidirect
750. Dic3C4×C22⋊D5semidirect
830. C5#76202semidirect
865. C3C4⋊C4×C22⋊D5semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×C4⋊C42
C2×#914462
C2×C4×#12032
C2×#914042
#117510902
C3×#652612
#117489022
#117488822
#117487822
#117487222
#117487162
#117486812
#117486412
Dic5×Dic3⋊C42
C4⋊C4×C22⋊D53
#762025