Finite Group Databasebeta

← #14327090

Subgroups — #14327090

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×C4×#1202C211yesmaximal, characteristic
2C2×#91404C211yesmaximal, characteristic, complemented
3C2×#91395C211yesmaximal, characteristic
4C2×#91395C211yesmaximal, characteristic
5C2×D5×Dic3⋊C4C211yesmaximal, characteristic, complemented
6#11750769C211yesmaximal, characteristic, complemented
7C5×#4649C211yesmaximal, characteristic, complemented
8C3×#64957C211yesmaximal, characteristic, complemented
9#11748900C211yesmaximal, characteristic, complemented
10#11748898C211yesmaximal, characteristic, complemented
11#11748882C211yesmaximal, characteristic, complemented
12#11748878C211yesmaximal, characteristic, complemented
13#11748861C211yesmaximal, characteristic, complemented
14#11748820C211yesmaximal, characteristic, complemented
15#11748803C211yesmaximal, characteristic, complemented
16C4⋊C4×D20—31nomaximal, Hall
17C22×C4×D15C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×#1202C2211yescharacteristic
20C22×#1200C2211yescharacteristic
21C22×#1200C2211yescharacteristic
22C22×D5×Dic3C2211yescharacteristic
23C22×D5×Dic3C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×C4⋊Dic15C2211yescharacteristic
27C2×#6712C2211yescharacteristic
28C2×C5×Dic3⋊C4C2211yescharacteristic
29C2×C5×Dic3⋊C4C2211yescharacteristic
30C2×C4×C5×Dic3C2211yescharacteristic
31C2×C4×C5×Dic3C2211yescharacteristic
32C2×C4×C5×Dic3C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×C4⋊Dic5C2211yescharacteristic
36C2×C3×#683C2211yescharacteristic
37C2×Dic3⋊Dic5C2211yescharacteristic
38C2×Dic3⋊Dic5C2211yescharacteristic
39C2×Dic3⋊Dic5C2211yescharacteristic
40C2×Dic3⋊Dic5C2211yescharacteristic
41C2×Dic3⋊Dic5C2211yescharacteristic
42C2×#6669C2211yescharacteristic
43C2×#6668C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C4×#1202—24no—
47#91404—24no—
48#91395—24no—
49#91395C418yescomplemented
50D5×Dic3⋊C4—24no—
51C3×C5×#95C2211yescharacteristic
52#91115C2211yescharacteristic
53C5×C3⋊#95C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#74393—51nomaximal, Hall
58C2×D5×C4⋊C4—31no—
59C2×D5×C4⋊C4—31no—
60C2×C4×D20—31no—
61C2×C4×D20—31no—
62C2×C4×D20—31no—
63C4×C5×C4⋊C4—31no—
64#65276—31no—
65#65276—31no—
66#65224—31no—
67#65217—31no—
68#65217—31no—
69#64957—31no—
70#64957—31no—
71#64957—31no—
72#64957D311yescharacteristic, complemented
73C23×D15C2311yescharacteristic
74C23×C3×D5C2311yescharacteristic
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
87C22×C5×Dic3C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C2×C3×C4×D5—22no—
92C2×C3×C4×D5—22no—
93C2×C3×C4×D5—41no—
94C2×#1202C2×C414yes—
95C2×#1202D414yes—
96C2×#1202Q814yes—
97C2×#1200—22no—
98C2×#1200—22no—
99C2×#1200—22no—
100C2×#1200—22no—
101C2×#1200—41no—
102C2×#1200C2×C414yescomplemented
103C2×D5×Dic3—22no—
104C2×D5×Dic3—22no—
105C2×D5×Dic3—22no—
106C2×D5×Dic3—22no—
107C2×D5×Dic3—41no—
108C2×D5×Dic3C2×C414yescomplemented
109#6714—22no—
110#6714C2×C414yescomplemented
111C4⋊Dic15—41no—
112#6712—22no—
113C5×Dic3⋊C4—22no—
114C5×Dic3⋊C4D414yescomplemented
115C4×C5×Dic3—22no—
116C4×C5×Dic3—22no—
117C4×C5×Dic3C2×C414yescomplemented
118C3×#685—22no—
119C3×#685C2×C414yescomplemented
120C3×C4⋊Dic5—41no—
121C3×#683—22no—
122Dic3⋊Dic5—22no—
123Dic3⋊Dic5—22no—
124Dic3⋊Dic5—22no—
125Dic3⋊Dic5—22no—
126Dic3⋊Dic5C2×C414yescomplemented
127#6669—22no—
128#6668—22no—
129#6667—22no—
130#6665—22no—
131C2×C4×#67—51no—
132C22×Dic3⋊C4—51no—
133C2×D3×C4⋊C4—51no—
134C2×#67⋊C4—51no—
135C2×#67⋊C4—51no—
136C3×#385—51no—
137#4989—51no—
138#4976—51no—
139#4975—51no—
140#4950—51no—
141#4942—51no—
142#4668—51no—
143#4667—51no—
144#4649D511yescharacteristic, complemented
145#4647—51no—
146C22×D20—31no—
147C22×C4×D5—31no—
148C22×C4×D5—31no—
149C22×C4×D5—31no—
150C22×C4×D5—31no—
151C22×C4×D5—31no—
152C22×C4×D5C2×D311yescharacteristic
153C2×C5×C4⋊C4—31no—
154C2×C5×C4⋊C4—31no—
155C2×C42×C5—31no—
156C2×C42×C5—31no—
157C2×C42×C5—31no—
158C2×#685—31no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—31no—
162C2×#685C2×D311yescharacteristic
163C2×#685C2×D311yescharacteristic
164C2×C4⋊Dic5—31no—
165C2×C4⋊Dic5—31no—
166C2×C4⋊Dic5—31no—
167C2×C4⋊Dic5—31no—
168C2×C4⋊Dic5—31no—
169C2×C4⋊Dic5—31no—
170C2×C4⋊Dic5C2×D311yescharacteristic
171C2×#683—31no—
172C2×#683—31no—
173C2×#683—31no—
174C2×#683C2×D311yescharacteristic
175D5×C4⋊C4—64no—
176D5×C4⋊C4—64no—
177C4×D20—38no—
178C4×D20—64no—
179C4×D20—64no—
180C5×#95—31no—
181C5×#95C2×D311yescharacteristic
182#3963—31no—
183#3963—31no—
184#3963—31no—
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×C3×D5—21no—
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5C22×C412yes—
200C22×C3×D5C2×D412yes—
201C22×C3×D5C2×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×Dic3C22×C412yes—
228C2×C5×Dic3C2×D412yes—
229C2×C5×Dic3C2×D412yes—
230C2×C5×Dic3C2×D412yes—
231C2×C5×Dic3C2×Q812yes—
232C2×C5×Dic3#4112yes—
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—
242C3×C4×D5—44no—
243#1202C4⋊C4116yescomplemented
244#1200—28no—
245#1200—44no—
246D5×Dic3—28no—
247D5×Dic3—44no—
248C23×C3×C4—51no—
249C22×#67—51no—
250C23×Dic3—51no—
251C23×Dic3—51no—
252C22×C4×D3—51no—
253C22×C4×D3—51no—
254C22×C4×D3—51no—
255C2×C3×C4⋊C4—51no—
256C2×C3×C4⋊C4—51no—
257C2×C3×C22⋊C4—51no—
258C2×C3×C22⋊C4—51no—
259C2×#217—51no—
260C4×#67—104no—
261C2×(C2×D3)⋊C4—51no—
262C2×(C2×D3)⋊C4—51no—
263C2×(C2×D3)⋊C4—51no—
264C2×C4⋊Dic3—51no—
265C2×C4⋊Dic3—51no—
266C2×Dic3⋊C4—51no—
267C2×Dic3⋊C4—51no—
268C2×Dic3⋊C4—51no—
269C2×Dic3⋊C4—51no—
270C2×Dic3⋊C4—51no—
271C2×Dic3⋊C4—51no—
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4—104no—
274C2×Dic3⋊C4C2×D511yescharacteristic
275C2×Dic3⋊C4C2×D511yescharacteristic
276C2×C4×Dic3C2×D511yescharacteristic
277C2×C4×Dic3C2×D511yescharacteristic
278C2×C4×Dic3C2×D511yescharacteristic
279D3×C4⋊C4—104no—
280#67⋊C4—58no—
281#67⋊C4—104no—
282C3×#95—51no—
283C3×#95C2×D511yescharacteristic
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95—51no—
287C3⋊#95C2×D511yescharacteristic
288C23×D5—31no—
289C23×D5C22×D311yescharacteristic
290C22×C4×C5—31no—
291C22×C4×C5—31no—
292C22×C4×C5—31no—
293C22×C4×C5—31no—
294C22×C4×C5C22×D311yescharacteristic
295C22×C4×C5C22×D311yescharacteristic
296C22×C4×C5C22×D311yescharacteristic
297C22×Dic5—31no—
298C22×Dic5—31no—
299C22×Dic5—31no—
300C22×Dic5C22×D311yescharacteristic
301C22×Dic5C22×D311yescharacteristic
302C22×Dic5C22×D311yescharacteristic
303C2×D20—34no—
304C2×D20—34no—
305C2×D20—34no—
306C2×C4×D5—22no—
307C2×C4×D5—22no—
308C2×C4×D5—34no—
309C2×C4×D5—34no—
310C2×C4×D5—41no—
311C2×C4×D5—62no—
312C2×C4×D5—62no—
313C2×C4×D5—62no—
314C2×C4×D5—62no—
315C2×C4×D5—62no—
316C2×C4×D5—62no—
317C2×C4×D5—62no—
318C2×C4×D5—62no—
319C2×C4×D5—62no—
320C2×C4×D5—62no—
321C2×C4×D5—121no—
322C2×C4×D5—121no—
323C2×C4×D5—121no—
324C5×C4⋊C4—34no—
325C5×C4⋊C4—62no—
326C42×C5—34no—
327C42×C5—62no—
328C42×C5—62no—
329#685—22no—
330#685—34no—
331#685—62no—
332#685—62no—
333#685—62no—
334#685C4×D314yescomplemented
335C4⋊Dic5—34no—
336C4⋊Dic5—41no—
337C4⋊Dic5—62no—
338C4⋊Dic5—62no—
339C4⋊Dic5—62no—
340C4⋊Dic5—62no—
341C4⋊Dic5—121no—
342#683—22no—
343#683—62no—
344#683—62no—
345#683—62no—
346C2×C4×D4—151no—
347C2×C4×D4—151no—
348C2×C4×D4—151no—
349C22×C4⋊C4—151no—
350C22×C4⋊C4—151no—
351#389—151no—
352#389—151no—
353#385—51no—
354#385—151no—
355#385—151no—
356#385—151no—
357#384—151no—
358#380—151no—
359#380—151no—
360C4×C4⋊C4—31no—
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×C3×D5—22no—
376C2×C3×D5—22no—
377C2×C3×D5—22no—
378C2×C3×D5—22no—
379C2×C3×D5—22no—
380C2×C3×D5—22no—
381C2×C3×D5C2×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—
391C5×Dic3—22no—
392C5×Dic3—41no—
393C5×Dic3C2×C4⋊C414yescomplemented
394C5×Dic3C4×D414yescomplemented
395C24×C3—51no—
396C23×D3—51no—
397C22×C3×C4—51no—
398C22×C3×C4—51no—
399C22×C3×C4—51no—
400C22×C3×C4—102no—
401C22×C3×C4—102no—
402C22×C3×C4—201no—
403C22×C3×C4C22×D511yescharacteristic
404C22×C3×C4C22×D511yescharacteristic
405C22×C3×C4C22×D511yescharacteristic
406C2×#67—54no—
407C2×#67—54no—
408C2×#67—54no—
409C22×Dic3—51no—
410C22×Dic3—54no—
411C22×Dic3—51no—
412C22×Dic3—51no—
413C22×Dic3—102no—
414C22×Dic3—102no—
415C22×Dic3—102no—
416C22×Dic3—102no—
417C22×Dic3—201no—
418C22×Dic3C22×D511yescharacteristic
419C22×Dic3C22×D511yescharacteristic
420C22×Dic3C22×D511yescharacteristic
421C22×Dic3C22×D511yescharacteristic
422C2×C4×D3—54no—
423C2×C4×D3—102no—
424C2×C4×D3—102no—
425C2×C4×D3—102no—
426C2×C4×D3—102no—
427C2×C4×D3—102no—
428C2×C4×D3—102no—
429C2×C4×D3—201no—
430C2×C4×D3—201no—
431C3×C4⋊C4—102no—
432C3×C4⋊C4—201no—
433C3×C22⋊C4—54no—
434C3×C22⋊C4—102no—
435#217—102no—
436(C2×D3)⋊C4—54no—
437(C2×D3)⋊C4—102no—
438(C2×D3)⋊C4—102no—
439C4⋊Dic3—102no—
440C4⋊Dic3—201no—
441Dic3⋊C4—22no—
442Dic3⋊C4—54no—
443Dic3⋊C4—102no—
444Dic3⋊C4—102no—
445Dic3⋊C4—102no—
446Dic3⋊C4—102no—
447Dic3⋊C4—102no—
448Dic3⋊C4—102no—
449Dic3⋊C4D2014yescomplemented
450C4×Dic3—22no—
451C4×Dic3—22no—
452C4×Dic3C4×D514yescomplemented
453C23×C5C23×D311yescharacteristic
454C22×D5—21no—
455C22×D5—21no—
456C22×D5—21no—
457C22×D5—21no—
458C22×D5—32no—
459C22×D5—32no—
460C22×D5—32no—
461C22×D5—61no—
462C22×D5—61no—
463C22×D5—61no—
464C22×D5—61no—
465C22×D5C2×C4×D312yes—
466C22×D5D3×D412yes—
467C22×D5D3×Q812yes—
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—32no—
480C2×C4×C5—32no—
481C2×C4×C5—32no—
482C2×C4×C5—61no—
483C2×C4×C5—61no—
484C2×C4×C5—61no—
485C2×C4×C5—61no—
486C2×C4×C5—61no—
487C2×C4×C5C2×C4×D312yes—
488C2×C4×C5D3×D412yes—
489C2×Dic5—21no—
490C2×Dic5—21no—
491C2×Dic5—21no—
492C2×Dic5—21no—
493C2×Dic5—21no—
494C2×Dic5—21no—
495C2×Dic5—21no—
496C2×Dic5—21no—
497C2×Dic5—32no—
498C2×Dic5—61no—
499C2×Dic5—61no—
500C2×Dic5—61no—
501C2×Dic5—61no—
502C2×Dic5—61no—
503C2×Dic5—61no—
504C2×Dic5—61no—
505C2×Dic5—61no—
506C2×Dic5C2×C4×D312yes—
507D20—316no—
508C4×D5—44no—
509C4×D5—68no—
510C4×D5—68no—
511C4×D5—124no—
512C4×D5—124no—
513C4×D5—124no—
514C22×D4—151no—
515C23×C4—51no—
516C23×C4—151no—
517C23×C4—151no—
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—51no—
527C2×C4⋊C4—51no—
528C2×C4⋊C4—151no—
529C2×C4⋊C4—151no—
530C2×C4⋊C4—151no—
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⋊C4—304no—
539C2×C22⋊C4—51no—
540C2×C22⋊C4—51no—
541C2×C22⋊C4—151no—
542C2×C22⋊C4—151no—
543C2×C22⋊C4—151no—
544C2×C22⋊C4—151no—
545C2×C42—31no—
546C2×C42—31no—
547C2×C42—31no—
548#95—31no—
549#95—51no—
550#95—151no—
551#95—151no—
552#95—151no—
553#95D3×D511yescharacteristic
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—
562C3×D5—24no—
563C23×C3—52no—
564C23×C3—52no—
565C23×C3—52no—
566C23×C3—101no—
567C23×C3—101no—
568C23×C3—101no—
569C23×C3—101no—
570C23×C3C23×D511yescharacteristic
571C22×D3—52no—
572C22×D3—52no—
573C22×D3—52no—
574C22×D3—101no—
575C22×D3—101no—
576C22×D3—101no—
577C22×D3—101no—
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—101no—
587C2×C3×C4—101no—
588C2×C3×C4—101no—
589C2×C3×C4—101no—
590C2×C3×C4—101no—
591C2×C3×C4—101no—
592C2×C3×C4—101no—
593C2×C3×C4—101no—
594C2×C3×C4—204no—
595C2×C3×C4C2×C4×D512yes—
596C2×C3×C4C2×D2012yes—
597#67—516no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—52no—
604C2×Dic3—101no—
605C2×Dic3—101no—
606C2×Dic3—108no—
607C2×Dic3—101no—
608C2×Dic3—101no—
609C2×Dic3—101no—
610C2×Dic3—101no—
611C2×Dic3—101no—
612C2×Dic3—101no—
613C2×Dic3—204no—
614C2×Dic3C2×C4×D512yes—
615C2×Dic3C2×C4×D512yes—
616C2×Dic3C2×D2012yes—
617C2×Dic3C2×D2012yes—
618C2×Dic3#70912yes—
619C2×Dic3D4×D512yes—
620C2×Dic3Q8×D512yes—
621C4×D3—108no—
622C4×D3—204no—
623C4×D3—204no—
624C22×C5C22×C4×D311yescharacteristic
625C22×C5C2×D3×D411yescharacteristic
626C22×C5C2×D3×D411yescharacteristic
627C22×C5#100411yescharacteristic
628C22×C5C2×D3×Q811yescharacteristic
629C22×C5D3×#4111yescharacteristic
630C22×C5#101011yescharacteristic
631C2×D5—22no—
632C2×D5—22no—
633C2×D5—22no—
634C2×D5—22no—
635C2×D5—22no—
636C2×D5—22no—
637C2×D5—34no—
638C2×D5—62no—
639C2×D5—62no—
640C2×D5—62no—
641C2×D5—62no—
642C2×D5—62no—
643C2×D5—62no—
644C2×D5D3×C4⋊C414yescomplemented
645C4×C5—22no—
646C4×C5—22no—
647C4×C5—34no—
648C4×C5—34no—
649C4×C5—41no—
650C4×C5—62no—
651C4×C5—121no—
652Dic5—22no—
653Dic5—41no—
654Dic5—41no—
655Dic5—62no—
656Dic5—121no—
657Dic5—121no—
658C24—51no—
659C24—151no—
660C2×D4—154no—
661C2×D4—154no—
662C2×D4—154no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—51no—
668C22×C4—51no—
669C22×C4—51no—
670C22×C4—102no—
671C22×C4—102no—
672C22×C4—154no—
673C22×C4—154no—
674C22×C4—151no—
675C22×C4—151no—
676C22×C4—151no—
677C22×C4—201no—
678C22×C4—302no—
679C22×C4—302no—
680C22×C4—302no—
681C22×C4—302no—
682C22×C4—302no—
683C22×C4—302no—
684C22×C4—302no—
685C22×C4—302no—
686C22×C4—302no—
687C22×C4—302no—
688C22×C4—601no—
689C22×C4—601no—
690C22×C4—601no—
691C22×C4C2×D3×D511yescharacteristic
692C22×C4C2×D3×D511yescharacteristic
693C22×C4C2×D3×D511yescharacteristic
694C4⋊C4—34no—
695C4⋊C4—62no—
696C4⋊C4—102no—
697C4⋊C4—154no—
698C4⋊C4—201no—
699C4⋊C4—302no—
700C4⋊C4—302no—
701C4⋊C4—302no—
702C4⋊C4—302no—
703C4⋊C4—302no—
704C4⋊C4—302no—
705C4⋊C4—302no—
706C4⋊C4—601no—
707C22⋊C4—54no—
708C22⋊C4—102no—
709C22⋊C4—154no—
710C22⋊C4—302no—
711C22⋊C4—302no—
712C22⋊C4—302no—
713C42—34no—
714C42—62no—
715C42—62no—
716C3×C5D4×C4⋊C411yescharacteristic, complemented, Hall
717C22×C3—54no—
718C22×C3—102no—
719C22×C3—102no—
720C22×C3—102no—
721C22×C3—102no—
722C22×C3—102no—
723C22×C3—102no—
724C22×C3C22×C4×D511yescharacteristic
725C22×C3C22×D2011yescharacteristic
726C22×C3C2×#70911yescharacteristic
727C22×C3C2×D4×D511yescharacteristic
728C22×C3C2×Q8×D511yescharacteristic
729C22×C3#414911yescharacteristic
730C22×C3#415011yescharacteristic
731C2×D3—54no—
732C2×D3—102no—
733C2×D3—102no—
734C2×D3—102no—
735C2×D3—102no—
736C2×D3—102no—
737C2×D3—102no—
738C3×C4—22no—
739C3×C4—22no—
740C3×C4—41no—
741C3×C4—102no—
742C3×C4—201no—
743C3×C4—201no—
744Dic3—22no—
745Dic3—41no—
746Dic3—102no—
747Dic3—201no—
748Dic3—201no—
749Dic3C4×D2014yescomplemented
750Dic3D5×C4⋊C414yescomplemented
751C2×C5C2×D3×C4⋊C411yescharacteristic
752C2×C5C4×D3×D411yescharacteristic
753C2×C5#554611yescharacteristic
754C2×C5#559011yescharacteristic
755C2×C5#563211yescharacteristic
756C2×C5#563611yescharacteristic
757C2×C5#565511yescharacteristic
758D5—24no—
759D5—64no—
760C23—52no—
761C23—52no—
762C23—52no—
763C23—101no—
764C23—101no—
765C23—101no—
766C23—101no—
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—32no—
788C2×C4—32no—
789C2×C4—32no—
790C2×C4—52no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—101no—
797C2×C4—101no—
798C2×C4—101no—
799C2×C4—101no—
800C2×C4—101no—
801C2×C4—101no—
802C2×C4—101no—
803C2×C4—101no—
804C2×C4—152no—
805C2×C4—204no—
806C2×C4—308no—
807C2×C4—308no—
808C2×C4—301no—
809C2×C4—301no—
810C2×C4—301no—
811C2×C4—301no—
812C2×C4—301no—
813C2×C4—301no—
814C2×C4—301no—
815C2×C4—301no—
816C2×C4—604no—
817C2×C4—604no—
818C2×C4—604no—
819C2×C4C4×D3×D512yes—
820C2×C4D3×D2012yes—
821C2×C3—104no—
822C2×C3C2×C4×D2011yescharacteristic
823C2×C3C2×D5×C4⋊C411yescharacteristic
824C2×C3#6585711yescharacteristic
825C2×C3D4×D2011yescharacteristic
826C2×C3#6588511yescharacteristic
827C2×C3Q8×D2011yescharacteristic
828C2×C3#6591311yescharacteristic
829D3—104no—
830C5#7439311yescharacteristic, complemented, Sylow
831C22—54no—
832C22—102no—
833C22—102no—
834C22—102no—
835C22—102no—
836C22—102no—
837C22—102no—
838C22—154no—
839C22—302no—
840C22—302no—
841C22—302no—
842C22—302no—
843C22—302no—
844C22—302no—
845C22C2×C4×D3×D511yescharacteristic
846C22C2×D3×D2011yescharacteristic
847C22D3×#70911yescharacteristic
848C22#9202011yescharacteristic
849C22D3×D4×D511yescharacteristic
850C22#9202611yescharacteristic
851C22D3×Q8×D511yescharacteristic
852C4—22no—
853C4—22no—
854C4—34no—
855C4—34no—
856C4—41no—
857C4—62no—
858C4—102no—
859C4—121no—
860C4—201no—
861C4—201no—
862C4—302no—
863C4—601no—
864C4—601no—
865C3C4⋊C4×D2011yescharacteristic, complemented, Sylow
866C2—104no—
867C2—304no—
868C2C4×D3×D2011yescharacteristic
869C2#1175281911yescharacteristic
870C2#1175307411yescharacteristic
871C2#1175323511yescharacteristic
872C2#1175344011yescharacteristic
873C2#1175345111yescharacteristic
874C2D3×D5×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1202C22
hypercenter#95D3×D5
hypocenterC3×C5D4×C4⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#91404C2semidirect
5. C2×D5×Dic3⋊C4C2semidirect
6. #11750769C2semidirect
7. C5×#4649C2semidirect
8. C3×#64957C2semidirect
9. #11748900C2semidirect
10. #11748898C2semidirect
11. #11748882C2semidirect
12. #11748878C2semidirect
13. #11748861C2semidirect
14. #11748820C2semidirect
15. #11748803C2semidirect
49. #91395C4semidirect
72. #64957D3semidirect
102. C2×#1200C2×C4semidirect
108. C2×D5×Dic3C2×C4semidirect
110. #6714C2×C4semidirect
114. C5×Dic3⋊C4D4semidirect
117. C4×C5×Dic3C2×C4semidirect
119. C3×#685C2×C4semidirect
126. Dic3⋊Dic5C2×C4semidirect
144. #4649D5semidirect
243. #1202C4⋊C4semidirect
334. #685C4×D3semidirect
374. C2×D15C2×C4⋊C4semidirect
381. C2×C3×D5C2×C4⋊C4semidirect
393. C5×Dic3C2×C4⋊C4semidirect
394. C5×Dic3C4×D4semidirect
449. Dic3⋊C4D20semidirect
452. C4×Dic3C4×D5semidirect
644. C2×D5D3×C4⋊C4semidirect
716. C3×C5D4×C4⋊C4semidirect
749. Dic3C4×D20semidirect
750. Dic3D5×C4⋊C4semidirect
830. C5#74393semidirect
865. C3C4⋊C4×D20semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12022
C2×#914042
C2×#913952
C2×D5×Dic3⋊C42
#117507692
C5×#46492
C3×#649572
#117489002
#117488982
#117488822
#117488782
#117488612
#117488202
#117488032
C4⋊C4×D203
#743935