Finite Group Databasebeta

← #14479179

Subgroups — #14479179

Order 1920.

3080 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92016C211yesmaximal, characteristic
2D15×#117C211yesmaximal, characteristic, complemented
3C5×#5523C211yesmaximal, characteristic, complemented
4C3×#65857C211yesmaximal, characteristic, complemented
5#11754499C211yesmaximal, characteristic, complemented
6#11754492C211yesmaximal, characteristic, complemented
7C2×#91347C211yesmaximal, characteristic, complemented
8D3×#4038C212yesmaximal, complemented
9D5×#892C212yesmaximal, complemented
10#11753669C212yesmaximal, complemented
11#11753668C212yesmaximal, complemented
12#11753204C214yesmaximal, complemented
13#11752820C214yesmaximal, complemented
14#11752729C212yesmaximal, complemented
15C4×#6768C212yesmaximal, complemented
16C4×#6766C212yesmaximal, complemented
17#11752460C212yesmaximal, complemented
18#10617786—31nomaximal, Hall
19C22×C4×D15C2211yescharacteristic
20C2×C5×#235C2211yescharacteristic
21C2×C3×#709C2211yescharacteristic
22C2×#6790C2212yes—
23C2×#6780C2212yes—
24#92016C4116yescomplemented
25C2×#6777C2211yescharacteristic
26C2×C4×D3×D5C2212yes—
27C2×#6771C2212yes—
28C2×D15⋊Q8C2211yescharacteristic
29C2×#6768C2211yescharacteristic
30C2×#6766C2211yescharacteristic
31C3×C5×#117C2211yescharacteristic, complemented
32#91815C2211yescharacteristic, complemented
33#91781C2211yescharacteristic
34#91781C2211yescharacteristic
35C4⋊C4×D15C2211yescharacteristic, complemented
36C4⋊C4×D15C2211yescharacteristic, complemented
37C22⋊C4×D15C2212yes—
38#91766C2212yescomplemented
39#91761C2212yes—
40C42×D15C2212yescomplemented
41C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
42C5×#892C2212yescomplemented
43C5×D3×C4⋊C4C2212yescomplemented
44C5×#67⋊C4C2214yescomplemented
45C4×C5×D12C2212yescomplemented
46C4×C5×Dic6C2212yescomplemented
47C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
48C3×#4038C2212yescomplemented
49C3×D5×C4⋊C4C2212yescomplemented
50C3×#4027C2214yescomplemented
51C3×C4×D20C2212yescomplemented
52C3×C4×Dic10C2212yescomplemented
53Dic3×C22⋊D5C2214yescomplemented
54Dic5×#67C2214yescomplemented
55C2×#6667C2212yes—
56C2×Dic3×Dic5C2212yescomplemented
57D3×#685C2214yes—
58D5×(C2×D3)⋊C4C2214yes—
59C4×#1203C2214yescomplemented
60C4×#1202C2214yescomplemented
61#91441C2214yescomplemented
62#91440C2214yescomplemented
63#91435C2212yescomplemented
64#91434C2212yescomplemented
65D3×C4⋊Dic5C2212yescomplemented
66D5×C4⋊Dic3C2212yescomplemented
67#91406C2214yescomplemented
68#91403C2214yes—
69#91402C2214yes—
70#91400C2214yescomplemented
71C4×D3×Dic5C2214yescomplemented
72#91396C2214yescomplemented
73#91394C2214yescomplemented
74C4×D5×Dic3C2214yescomplemented
75#91358C2212yescomplemented
76#91347C2212yes—
77#91347C2212yes—
78#91347C2212yescomplemented
79#91347C2212yescomplemented
80#91344C2212yescomplemented
81#91338C2212yescomplemented
82#91331C2212yescomplemented
83#91324C2214yescomplemented
84#91323C2214yescomplemented
85#85885—51nomaximal, Hall
86C2×D5×#41—31no—
87C5×#520—31no—
88#66161—31no—
89C4×#713—32no—
90#65906—32no—
91#65879—34no—
92#65879—32no—
93C4×#711—34no—
94C4×#711—32no—
95#65857—32no—
96#65857D311yescharacteristic, complemented
97D5×#117—32no—
98D5×#117—31no—
99#65838—32no—
100#65838—31no—
101C2×#4038—31no—
102C2×#4038—32no—
103C23×D15C2311yescharacteristic
104C22×D3×D5C2312yes—
105C22×C3×C4×C5C2311yescharacteristic
106C22×Dic15C2311yescharacteristic
107C2×C4×D15C2×C418yescomplemented
108C2×C4×D15C2312yes—
109C2×C4×D15C2312yes—
110C2×C4×D15C2311yescharacteristic
111C2×C4×D15C2311yescharacteristic
112C2×C4×D15C2311yescharacteristic
113C2×C4×D15C2311yescharacteristic
114C2×C5×#67C2312yes—
115C22×C5×Dic3C2312yes—
116C5×#235C2×C418yescomplemented
117C2×C5×D12C2311yescharacteristic
118C2×C4×C5×D3C2314yes—
119C2×C4×C5×D3C2312yes—
120C2×C5×Dic6C2311yescharacteristic
121C2×C3×C22⋊D5C2312yes—
122C22×C3×Dic5C2312yes—
123C3×#709C2×C418yescomplemented
124C2×C3×D20C2311yescharacteristic
125C2×C3×C4×D5C2314yes—
126C2×C3×C4×D5C2312yes—
127C2×C3×Dic10C2311yescharacteristic
128#6790C2×C4116yescomplemented
129C2×#1204C2312yes—
130C2×#1203C2312yes—
131C2×#1202C2312yes—
132C2×#1201C2312yes—
133C2×#1200C2312yes—
134C2×D3×Dic5C2314yes—
135C2×D3×Dic5C2312yes—
136#6780C2×C4116yescomplemented
137C2×D5×Dic3C2314yes—
138C2×D5×Dic3C2312yes—
139#6777C2×C418yescomplemented
140C4×D3×D5C2×C4116yescomplemented
141#6771C2×C4116yescomplemented
142D15⋊Q8C2×C418yescomplemented
143#6768C2×C418yescomplemented
144#6766C2×C418yescomplemented
145C3×C5×C4⋊C4C2311yescharacteristic
146C3×C5×C4⋊C4C2311yescharacteristic
147C3×C5×C22⋊C4C2312yes—
148C3×C42×C5C2312yes—
149#6719C2312yes—
150#6714C2312yes—
151#6714C2312yes—
152C4⋊Dic15C2311yescharacteristic
153C4⋊Dic15C2311yescharacteristic
154#6712C2312yes—
155#6712C2312yes—
156C4×Dic15C2312yes—
157C4×Dic15C2312yes—
158C4×Dic15C2312yes—
159C5×(C2×D3)⋊C4C2314yes—
160C5×C4⋊Dic3C2312yes—
161C5×C4⋊Dic3C2312yes—
162C5×Dic3⋊C4C2314yes—
163C4×C5×Dic3C2314yes—
164C3×#685C2314yes—
165C3×C4⋊Dic5C2312yes—
166C3×C4⋊Dic5C2312yes—
167C3×#683C2314yes—
168C3×C4×Dic5C2314yes—
169Dic3⋊Dic5C2314yes—
170#6668C2314yes—
171#6667C2314yes—
172#6667C2314yes—
173(C2×D3)⋊Dic5C2314yes—
174#6665C2314yes—
175Dic3×Dic5C2314yes—
176Dic3×Dic5C2314yes—
177Dic3×Dic5C2314yes—
178Dic3×Dic5C2314yes—
179C2×D3×#41—51no—
180C3×#520—51no—
181#5827—51no—
182C4×#239—52no—
183#5572—52no—
184#5545—54no—
185#5545—52no—
186C4×#237—54no—
187C4×#237—52no—
188#5523—52no—
189#5523D511yescharacteristic, complemented
190D3×#117—51no—
191D3×#117—52no—
192#5504—51no—
193#5504—52no—
194C2×#892—51no—
195C2×#892—52no—
196C2×C5×#41—31no—
197D5×#41—316no—
198C2×#713—31no—
199C2×Q8×D5—31no—
200C2×#711—32no—
201C2×#711—31no—
202C2×D4×D5—32no—
203C2×D4×D5—31no—
204C2×#709—32no—
205C2×#709C2×D311yescharacteristic
206C22×C4×D5—31no—
207C22×C4×D5—32no—
208C4×C5×Q8—32no—
209C4×C5×D4—34no—
210C4×C5×D4—32no—
211C5×#117—32no—
212C5×#117C2×D311yescharacteristic, complemented
213C2×C5×C4⋊C4—31no—
214C2×C5×C4⋊C4—32no—
215Q8×Dic5—32no—
216D4×Dic5—34no—
217D4×Dic5—32no—
218C4×C22⋊D5—34no—
219C4×C22⋊D5—34no—
220C4×C22⋊D5—34no—
221C2×#685—32no—
222C2×#685—34no—
223#4072—31no—
224#4072—32no—
225C2×C4⋊Dic5—32no—
226C2×C4⋊Dic5C2×D311yescharacteristic, complemented
227C2×C4×Dic5—32no—
228C2×C4×Dic5—34no—
229#4039—32no—
230#4039—34no—
231#4038—32no—
232#4038—31no—
233#4038—31no—
234#4038—34no—
235#4038—32no—
236#4038—32no—
237#4038—32no—
238#4038—32no—
239#4038—34no—
240#4038C2×D312yescomplemented
241D5×C4⋊C4—32no—
242D5×C4⋊C4—31no—
243D5×C4⋊C4—31no—
244D5×C4⋊C4C2×D312yescomplemented
245#4033—32no—
246#4033—34no—
247#4027—34no—
248#4027—34no—
249#4027C2×D314yescomplemented
250D5×C22⋊C4—34no—
251D5×C22⋊C4—32no—
252#4023—32no—
253#4023—34no—
254C4×D20—34no—
255C4×D20C2×D312yescomplemented
256#4018—32no—
257#4018—34no—
258C42×D5—34no—
259C42×D5—32no—
260C4×Dic10—34no—
261C4×Dic10C2×D312yescomplemented
262#3428—151noSylow
263C23×C3×C5C2411yescharacteristic
264C22×D15—41no—
265C22×D15—41no—
266C22×D15C22×C414yes—
267C22×D15C2411yescharacteristic
268C22×D15C2411yescharacteristic
269C22×C5×D3C2412yes—
270C22×C3×D5C2412yes—
271C2×D3×D5—42no—
272C2×D3×D5—42no—
273C2×D3×D5C22×C418yes—
274C2×C3×C4×C5C22×C414yes—
275C2×C3×C4×C5C2412yes—
276C2×C3×C4×C5C2412yes—
277C2×C3×C4×C5C2411yescharacteristic
278C2×C3×C4×C5C2411yescharacteristic
279C2×Dic15C22×C414yes—
280C2×Dic15C2412yes—
281C2×Dic15C2412yes—
282C2×Dic15C2411yescharacteristic
283C2×Dic15C2411yescharacteristic
284C4×D15—42no—
285C4×D15—42no—
286C4×D15C22×C414yes—
287C4×D15C22×C414yes—
288C4×D15C22×C414yes—
289C4×D15C22×C414yes—
290C5×#67C22×C418yes—
291C2×C5×Dic3—42no—
292C2×C5×Dic3C2414yes—
293C2×C5×Dic3C2412yes—
294C5×D12C22×C414yes—
295C4×C5×D3—44no—
296C4×C5×D3C22×C418yes—
297C5×Dic6C22×C414yes—
298C3×C22⋊D5C22×C418yes—
299C2×C3×Dic5—42no—
300C2×C3×Dic5C2414yes—
301C2×C3×Dic5C2412yes—
302C3×D20C22×C414yes—
303C3×C4×D5—44no—
304C3×C4×D5C22×C418yes—
305C3×Dic10C22×C414yes—
306#1204C22×C418yes—
307#1203C22×C418yes—
308#1202C22×C418yes—
309#1201C22×C418yes—
310#1200C22×C418yes—
311D3×Dic5—44no—
312D3×Dic5C22×C418yes—
313D5×Dic3—44no—
314D5×Dic3C22×C418yes—
315C2×C3×#41—51no—
316D3×#41—516no—
317C2×#239—51no—
318C2×D3×Q8—51no—
319C2×#237—52no—
320C2×#237—51no—
321C2×D3×D4—52no—
322C2×D3×D4—51no—
323C2×#235—52no—
324C2×#235C2×D511yescharacteristic
325C22×C4×D3—51no—
326C22×C4×D3—52no—
327C3×C4×Q8—52no—
328C3×C4×D4—54no—
329C3×C4×D4—52no—
330C3×#117—52no—
331C3×#117C2×D511yescharacteristic, complemented
332C2×C3×C4⋊C4—51no—
333C2×C3×C4⋊C4—52no—
334Q8×Dic3—52no—
335D4×Dic3—54no—
336D4×Dic3—52no—
337C4×#67—54no—
338C4×#67—54no—
339C4×#67—54no—
340C2×(C2×D3)⋊C4—52no—
341C2×(C2×D3)⋊C4—54no—
342#926—51no—
343#926—52no—
344C2×C4⋊Dic3—52no—
345C2×C4⋊Dic3C2×D511yescharacteristic, complemented
346C2×C4×Dic3—52no—
347C2×C4×Dic3—54no—
348#893—52no—
349#893—54no—
350#892—52no—
351#892—51no—
352#892—51no—
353#892—54no—
354#892—52no—
355#892—52no—
356#892—52no—
357#892—52no—
358#892—54no—
359#892C2×D512yescomplemented
360D3×C4⋊C4—52no—
361D3×C4⋊C4—51no—
362D3×C4⋊C4—51no—
363D3×C4⋊C4C2×D512yescomplemented
364#887—52no—
365#887—54no—
366#67⋊C4—54no—
367#67⋊C4—54no—
368#67⋊C4C2×D514yescomplemented
369D3×C22⋊C4—54no—
370D3×C22⋊C4—52no—
371#877—52no—
372#877—54no—
373C4×D12—54no—
374C4×D12C2×D512yescomplemented
375#872—52no—
376#872—54no—
377C42×D3—54no—
378C42×D3—52no—
379C4×Dic6—54no—
380C4×Dic6C2×D512yescomplemented
381C23×D5—31no—
382C23×D5—32no—
383C5×#41—38no—
384C2×C5×Q8—31no—
385C2×C5×D4—32no—
386C2×C5×D4—31no—
387C22×C4×C5—32no—
388C22×C4×C5—32no—
389C22×C4×C5—34no—
390C22×C4×C5C22×D311yescharacteristic
391C2×C22⋊D5—32no—
392C2×C22⋊D5—32no—
393C2×C22⋊D5C22×D312yes—
394C22×Dic5—31no—
395C22×Dic5—32no—
396C22×Dic5—34no—
397C22×Dic5C22×D312yes—
398#713—38no—
399Q8×D5—38no—
400#711—316no—
401#711—38no—
402D4×D5—316no—
403D4×D5—38no—
404#709—316no—
405#709C4×D318yescomplemented
406C2×D20—32no—
407C2×D20C22×D311yescharacteristic
408C2×C4×D5—32no—
409C2×C4×D5—38no—
410C2×C4×D5—31no—
411C2×C4×D5—31no—
412C2×C4×D5—31no—
413C2×C4×D5—31no—
414C2×C4×D5—32no—
415C2×C4×D5—316no—
416C2×C4×D5—34no—
417C2×C4×D5—32no—
418C2×C4×D5—32no—
419C2×C4×D5C22×D314yes—
420C2×C4×D5C22×D312yes—
421C2×Dic10—32no—
422C2×Dic10C22×D311yescharacteristic
423C5×C4⋊C4—32no—
424C5×C4⋊C4—34no—
425C5×C4⋊C4—32no—
426C5×C4⋊C4C22×D311yescharacteristic
427C5×C4⋊C4C22×D311yescharacteristic
428C5×C22⋊C4—34no—
429C5×C22⋊C4C22×D312yes—
430C42×C5—34no—
431C42×C5C22×D312yes—
432C22⋊Dic5—32no—
433C22⋊Dic5—34no—
434#685—34no—
435#685—32no—
436#685—32no—
437#685—34no—
438#685—34no—
439#685C22×D314yes—
440C4⋊Dic5—31no—
441C4⋊Dic5—31no—
442C4⋊Dic5—34no—
443C4⋊Dic5C22×D312yes—
444C4⋊Dic5C22×D312yes—
445#683—32no—
446#683—32no—
447#683—34no—
448#683C22×D314yes—
449C4×Dic5—32no—
450C4×Dic5—32no—
451C4×Dic5—32no—
452C4×Dic5—34no—
453C4×Dic5—34no—
454C4×Dic5—34no—
455C4×Dic5—34no—
456C4×Dic5C22×D314yes—
457C22×#41—151no—
458#520—31no—
459#520—51no—
460#520—152no—
461#520—151no—
462#520—152no—
463#520—151no—
464#519—152no—
465#518—152no—
466#518—154no—
467C4×#41—154no—
468C4×#41—152no—
469C4×#41—152no—
470C2×#117—151no—
471C2×#117—152no—
472C2×#117—152no—
473C2×#117—151no—
474C22×C3×C5—21no—
475C22×C3×C5—21no—
476C22×C3×C5C23×C412yes—
477C22×C3×C5C2511yescharacteristic
478C2×D15—21no—
479C2×D15—21no—
480C2×D15—21no—
481C2×D15—21no—
482C2×D15—44no—
483C2×D15C23×C412yes—
484C2×D15C23×C412yes—
485C2×C5×D3—22no—
486C2×C5×D3—22no—
487C2×C5×D3C23×C414yes—
488C2×C3×D5—22no—
489C2×C3×D5—22no—
490C2×C3×D5C23×C414yes—
491D3×D5—48no—
492C3×C4×C5—22no—
493C3×C4×C5—22no—
494C3×C4×C5C23×C412yes—
495C3×C4×C5C23×C412yes—
496Dic15—22no—
497Dic15—22no—
498Dic15C23×C412yes—
499Dic15C23×C412yes—
500C3×Dic5—24no—
501C3×Dic5C23×C414yes—
502C5×Dic3—24no—
503C5×Dic3C23×C414yes—
504C23×D3—51no—
505C23×D3—52no—
506C3×#41—58no—
507C2×C3×Q8—51no—
508C2×C3×D4—52no—
509C2×C3×D4—51no—
510C22×C3×C4—52no—
511C22×C3×C4—52no—
512C22×C3×C4—54no—
513C22×C3×C4C22×D511yescharacteristic
514C2×#67—52no—
515C2×#67—52no—
516C2×#67C22×D512yes—
517C22×Dic3—51no—
518C22×Dic3—52no—
519C22×Dic3—54no—
520C22×Dic3C22×D512yes—
521#239—58no—
522D3×Q8—58no—
523#237—516no—
524#237—58no—
525D3×D4—516no—
526D3×D4—58no—
527#235—516no—
528#235C4×D518yescomplemented
529C2×D12—52no—
530C2×D12C22×D511yescharacteristic
531C2×C4×D3—52no—
532C2×C4×D3—58no—
533C2×C4×D3—51no—
534C2×C4×D3—51no—
535C2×C4×D3—51no—
536C2×C4×D3—51no—
537C2×C4×D3—52no—
538C2×C4×D3—516no—
539C2×C4×D3—54no—
540C2×C4×D3—52no—
541C2×C4×D3—52no—
542C2×C4×D3C22×D514yes—
543C2×C4×D3C22×D512yes—
544C2×Dic6—52no—
545C2×Dic6C22×D511yescharacteristic
546C3×C4⋊C4—54no—
547C3×C4⋊C4—52no—
548C3×C4⋊C4—52no—
549C3×C4⋊C4C22×D511yescharacteristic
550C3×C4⋊C4C22×D511yescharacteristic
551C3×C22⋊C4—54no—
552C3×C22⋊C4C22×D512yes—
553C3×C42—54no—
554C3×C42C22×D512yes—
555#217—52no—
556#217—54no—
557(C2×D3)⋊C4—54no—
558(C2×D3)⋊C4—52no—
559(C2×D3)⋊C4—52no—
560(C2×D3)⋊C4—54no—
561(C2×D3)⋊C4—54no—
562(C2×D3)⋊C4C22×D514yes—
563C4⋊Dic3—51no—
564C4⋊Dic3—51no—
565C4⋊Dic3—54no—
566C4⋊Dic3C22×D512yes—
567C4⋊Dic3C22×D512yes—
568Dic3⋊C4—52no—
569Dic3⋊C4—52no—
570Dic3⋊C4—54no—
571Dic3⋊C4C22×D514yes—
572C4×Dic3—52no—
573C4×Dic3—52no—
574C4×Dic3—52no—
575C4×Dic3—54no—
576C4×Dic3—54no—
577C4×Dic3—54no—
578C4×Dic3—54no—
579C4×Dic3C22×D514yes—
580C23×C5—32no—
581C23×C5C23×D311yescharacteristic
582C22×D5—31no—
583C22×D5—31no—
584C22×D5—34no—
585C22×D5—38no—
586C22×D5—122no—
587C22×D5—122no—
588C22×D5—121no—
589C22×D5—121no—
590C22×D5C23×D312yes—
591C5×Q8—34no—
592C5×D4—38no—
593C5×D4—34no—
594C2×C4×C5—32no—
595C2×C4×C5—38no—
596C2×C4×C5—34no—
597C2×C4×C5—124no—
598C2×C4×C5—122no—
599C2×C4×C5C2×C4×D314yes—
600C2×C4×C5C23×D312yes—
601C2×C4×C5C23×D312yes—
602C2×C4×C5C23×D311yescharacteristic
603C2×C4×C5C23×D311yescharacteristic
604C22⋊D5—38no—
605C22⋊D5—38no—
606C22⋊D5C2×C4×D318yes—
607C2×Dic5—34no—
608C2×Dic5—31no—
609C2×Dic5—31no—
610C2×Dic5—38no—
611C2×Dic5—32no—
612C2×Dic5—32no—
613C2×Dic5—42no—
614C2×Dic5—124no—
615C2×Dic5C23×D314yes—
616C2×Dic5C23×D312yes—
617D20—38no—
618D20C2×C4×D314yes—
619C4×D5—38no—
620C4×D5—34no—
621C4×D5—34no—
622C4×D5—34no—
623C4×D5—34no—
624C4×D5—38no—
625C4×D5—44no—
626C4×D5—122no—
627C4×D5—122no—
628C4×D5—124no—
629C4×D5C2×C4×D318yes—
630Dic10—38no—
631Dic10C2×C4×D314yes—
632C2×#41—31no—
633C2×#41—51no—
634C2×#41—152no—
635C2×#41—152no—
636C2×#41—151no—
637C2×#41—151no—
638C2×#41—1516no—
639C22×Q8—151no—
640C22×D4—152no—
641C22×D4—151no—
642C23×C4—152no—
643C23×C4—151no—
644C4×Q8—32no—
645C4×Q8—52no—
646C4×Q8—154no—
647C4×Q8—154no—
648C4×Q8—152no—
649C4×Q8—152no—
650C4×D4—34no—
651C4×D4—32no—
652C4×D4—54no—
653C4×D4—52no—
654C4×D4—154no—
655C4×D4—154no—
656C4×D4—154no—
657C4×D4—154no—
658C4×D4—154no—
659C4×D4—154no—
660C4×D4—152no—
661C4×D4—152no—
662C4×D4—154no—
663C4×D4—154no—
664#117—32no—
665#117—52no—
666#117—154no—
667#117—154no—
668#117—154no—
669#117—154no—
670#117—152no—
671#117—152no—
672#117—152no—
673#117—152no—
674#117—152no—
675#117—152no—
676#117—151no—
677#117—151no—
678#117—151no—
679#117—152no—
680#117—152no—
681#117D3×D511yescharacteristic, complemented
682C2×C4⋊C4—31no—
683C2×C4⋊C4—32no—
684C2×C4⋊C4—51no—
685C2×C4⋊C4—52no—
686C2×C4⋊C4—152no—
687C2×C4⋊C4—152no—
688C2×C4⋊C4—151no—
689C2×C4⋊C4—151no—
690C2×C22⋊C4—154no—
691C2×C22⋊C4—154no—
692C2×C22⋊C4—152no—
693C2×C22⋊C4—152no—
694C2×C42—154no—
695C2×C42—154no—
696C2×C42—152no—
697C2×C42—152no—
698C2×C3×C5—22no—
699C2×C3×C5C24×C411yescharacteristic
700C2×C3×C5#58511yescharacteristic
701C2×C3×C5#58511yescharacteristic
702D15—22no—
703D15—22no—
704C3×D5—24no—
705C5×D3—24no—
706C23×C3—52no—
707C23×C3C23×D511yescharacteristic
708C22×D3—51no—
709C22×D3—51no—
710C22×D3—54no—
711C22×D3—58no—
712C22×D3—202no—
713C22×D3—202no—
714C22×D3—201no—
715C22×D3—201no—
716C22×D3C23×D512yes—
717C3×Q8—54no—
718C3×D4—58no—
719C3×D4—54no—
720C2×C3×C4—52no—
721C2×C3×C4—58no—
722C2×C3×C4—54no—
723C2×C3×C4—204no—
724C2×C3×C4—202no—
725C2×C3×C4C2×C4×D514yes—
726C2×C3×C4C23×D512yes—
727C2×C3×C4C23×D512yes—
728C2×C3×C4C23×D511yescharacteristic
729C2×C3×C4C23×D511yescharacteristic
730#67—58no—
731#67—58no—
732#67C2×C4×D518yes—
733C2×Dic3—42no—
734C2×Dic3—54no—
735C2×Dic3—51no—
736C2×Dic3—51no—
737C2×Dic3—58no—
738C2×Dic3—52no—
739C2×Dic3—52no—
740C2×Dic3—204no—
741C2×Dic3C23×D514yes—
742C2×Dic3C23×D512yes—
743D12—58no—
744D12C2×C4×D514yes—
745C4×D3—44no—
746C4×D3—58no—
747C4×D3—54no—
748C4×D3—54no—
749C4×D3—54no—
750C4×D3—54no—
751C4×D3—58no—
752C4×D3—202no—
753C4×D3—202no—
754C4×D3—204no—
755C4×D3C2×C4×D518yes—
756Dic6—58no—
757Dic6C2×C4×D514yes—
758C22×C5—21no—
759C22×C5—21no—
760C22×C5—34no—
761C22×C5—62no—
762C22×C5—62no—
763C22×C5C22×C4×D312yes—
764C22×C5C24×D311yescharacteristic
765C2×D5—22no—
766C2×D5—22no—
767C2×D5—32no—
768C2×D5—32no—
769C2×D5—61no—
770C2×D5—61no—
771C2×D5—61no—
772C2×D5—61no—
773C2×D5—128no—
774C2×D5—124no—
775C2×D5C22×C4×D314yes—
776C4×C5—22no—
777C4×C5—22no—
778C4×C5—34no—
779C4×C5—64no—
780C4×C5C22×C4×D312yes—
781C4×C5C22×C4×D312yes—
782Dic5—24no—
783Dic5—32no—
784Dic5—32no—
785Dic5—62no—
786Dic5—62no—
787Dic5C22×C4×D314yes—
788C24—152no—
789C24—151no—
790#41—38no—
791#41—58no—
792#41—1516no—
793#41—1516no—
794#41—158no—
795#41—158no—
796C2×Q8—31no—
797C2×Q8—51no—
798C2×Q8—152no—
799C2×Q8—158no—
800C2×D4—32no—
801C2×D4—31no—
802C2×D4—52no—
803C2×D4—51no—
804C2×D4—152no—
805C2×D4—152no—
806C2×D4—1516no—
807C2×D4—158no—
808C2×D4—152no—
809C22×C4—32no—
810C22×C4—32no—
811C22×C4—34no—
812C22×C4—52no—
813C22×C4—52no—
814C22×C4—54no—
815C22×C4—152no—
816C22×C4—1516no—
817C22×C4—152no—
818C22×C4—154no—
819C22×C4—152no—
820C22×C4—154no—
821C22×C4—151no—
822C22×C4—158no—
823C22×C4—151no—
824C22×C4—151no—
825C22×C4—151no—
826C22×C4—151no—
827C22×C4—152no—
828C22×C4—152no—
829C22×C4C2×D3×D511yescharacteristic
830C4⋊C4—32no—
831C4⋊C4—34no—
832C4⋊C4—32no—
833C4⋊C4—52no—
834C4⋊C4—54no—
835C4⋊C4—52no—
836C4⋊C4—154no—
837C4⋊C4—154no—
838C4⋊C4—151no—
839C4⋊C4—151no—
840C4⋊C4—152no—
841C4⋊C4—152no—
842C4⋊C4C2×D3×D511yescharacteristic
843C4⋊C4C2×D3×D511yescharacteristic
844C22⋊C4—34no—
845C22⋊C4—54no—
846C22⋊C4—154no—
847C22⋊C4—154no—
848C22⋊C4—154no—
849C22⋊C4—154no—
850C22⋊C4—152no—
851C22⋊C4—152no—
852C22⋊C4—152no—
853C22⋊C4C2×D3×D512yes—
854C42—34no—
855C42—54no—
856C42—154no—
857C42—154no—
858C42—154no—
859C42—154no—
860C42—152no—
861C42—152no—
862C42—152no—
863C42C2×D3×D512yes—
864C3×C5#342811yescharacteristic, complemented, Hall
865C22×C3—21no—
866C22×C3—21no—
867C22×C3—54no—
868C22×C3—102no—
869C22×C3—102no—
870C22×C3C22×C4×D512yes—
871C22×C3C24×D511yescharacteristic
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—52no—
875C2×D3—52no—
876C2×D3—101no—
877C2×D3—101no—
878C2×D3—101no—
879C2×D3—101no—
880C2×D3—208no—
881C2×D3—204no—
882C2×D3C22×C4×D514yes—
883C3×C4—22no—
884C3×C4—22no—
885C3×C4—54no—
886C3×C4—104no—
887C3×C4C22×C4×D512yes—
888C3×C4C22×C4×D512yes—
889Dic3—24no—
890Dic3—52no—
891Dic3—52no—
892Dic3—102no—
893Dic3—102no—
894Dic3C22×C4×D514yes—
895C2×C5—22no—
896C2×C5—64no—
897C2×C5C23×C4×D311yescharacteristic
898C2×C5#596611yescharacteristic
899C2×C5#596811yescharacteristic
900D5—24no—
901D5—62no—
902D5—62no—
903C23—32no—
904C23—52no—
905C23—158no—
906C23—151no—
907C23—151no—
908C23—154no—
909C23—601no—
910C23—601no—
911C23—602no—
912C23—602no—
913C23C22×D3×D511yescharacteristic
914Q8—34no—
915Q8—54no—
916Q8—158no—
917D4—38no—
918D4—34no—
919D4—58no—
920D4—54no—
921D4—158no—
922D4—158no—
923D4—158no—
924C2×C4—32no—
925C2×C4—38no—
926C2×C4—34no—
927C2×C4—52no—
928C2×C4—58no—
929C2×C4—54no—
930C2×C4—124no—
931C2×C4—122no—
932C2×C4—158no—
933C2×C4—158no—
934C2×C4—158no—
935C2×C4—154no—
936C2×C4—151no—
937C2×C4—151no—
938C2×C4—154no—
939C2×C4—154no—
940C2×C4—154no—
941C2×C4—154no—
942C2×C4—152no—
943C2×C4—152no—
944C2×C4—204no—
945C2×C4—202no—
946C2×C4—602no—
947C2×C4—602no—
948C2×C4—604no—
949C2×C4—604no—
950C2×C4C4×D3×D514yes—
951C2×C4C22×D3×D512yes—
952C2×C4C22×D3×D512yes—
953C2×C4C22×D3×D511yescharacteristic
954C2×C4C22×D3×D511yescharacteristic
955C2×C3—22no—
956C2×C3—104no—
957C2×C3C23×C4×D511yescharacteristic
958C2×C3#6628511yescharacteristic
959C2×C3#6628711yescharacteristic
960D3—24no—
961D3—102no—
962D3—102no—
963C5#8588511yescharacteristic, complemented, Sylow
964C22—21no—
965C22—21no—
966C22—34no—
967C22—54no—
968C22—62no—
969C22—62no—
970C22—102no—
971C22—102no—
972C22—152no—
973C22—152no—
974C22—301no—
975C22—301no—
976C22—301no—
977C22—301no—
978C22—604no—
979C22—608no—
980C22C2×C4×D3×D512yes—
981C22C23×D3×D511yescharacteristic
982C4—22no—
983C4—22no—
984C4—34no—
985C4—54no—
986C4—64no—
987C4—104no—
988C4—152no—
989C4—152no—
990C4—302no—
991C4—302no—
992C4C2×C4×D3×D512yes—
993C4C2×C4×D3×D512yes—
994C3#1061778611yescharacteristic, complemented, Sylow
995C2—22no—
996C2—64no—
997C2—104no—
998C2—302no—
999C2—302no—
1000C2C22×C4×D3×D511yescharacteristic
1001C2#1175706211yescharacteristic
1002C2#1175706411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC3×C5×#117C22
socle, cosocleC22×C3×C5C25
prime radicalC2×#92016C2
hypercenter#117D3×D5
hypocenterC3×C5#3428
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
2. D15×#117C2semidirect
3. C5×#5523C2semidirect
4. C3×#65857C2semidirect
5. #11754499C2semidirect
6. #11754492C2semidirect
7. C2×#91347C2semidirect
8. D3×#4038C2semidirect
9. D5×#892C2semidirect
10. #11753669C2semidirect
11. #11753668C2semidirect
12. #11753204C2semidirect
13. #11752820C2semidirect
14. #11752729C2semidirect
15. C4×#6768C2semidirect
16. C4×#6766C2semidirect
17. #11752460C2semidirect
24. #92016C4semidirect
31. C3×C5×#117C22semidirect
32. #91815C22semidirect
35. C4⋊C4×D15C22semidirect
36. C4⋊C4×D15C22semidirect
38. #91766C22semidirect
40. C42×D15C22semidirect
41. C2×C5×C4⋊Dic3C22semidirect
42. C5×#892C22semidirect
43. C5×D3×C4⋊C4C22semidirect
44. C5×#67⋊C4C22semidirect
45. C4×C5×D12C22semidirect
46. C4×C5×Dic6C22semidirect
47. C2×C3×C4⋊Dic5C22semidirect
48. C3×#4038C22semidirect
49. C3×D5×C4⋊C4C22semidirect
50. C3×#4027C22semidirect
51. C3×C4×D20C22semidirect
52. C3×C4×Dic10C22semidirect
53. Dic3×C22⋊D5C22semidirect
54. Dic5×#67C22semidirect
56. C2×Dic3×Dic5C22semidirect
59. C4×#1203C22semidirect
60. C4×#1202C22semidirect
61. #91441C22semidirect
62. #91440C22semidirect
63. #91435C22semidirect
64. #91434C22semidirect
65. D3×C4⋊Dic5C22semidirect
66. D5×C4⋊Dic3C22semidirect
67. #91406C22semidirect
70. #91400C22semidirect
71. C4×D3×Dic5C22semidirect
72. #91396C22semidirect
73. #91394C22semidirect
74. C4×D5×Dic3C22semidirect
75. #91358C22semidirect
78. #91347C22semidirect
79. #91347C22semidirect
80. #91344C22semidirect
81. #91338C22semidirect
82. #91331C22semidirect
83. #91324C22semidirect
84. #91323C22semidirect
96. #65857D3semidirect
107. C2×C4×D15C2×C4semidirect
116. C5×#235C2×C4semidirect
123. C3×#709C2×C4semidirect
128. #6790C2×C4semidirect
136. #6780C2×C4semidirect
139. #6777C2×C4semidirect
140. C4×D3×D5C2×C4semidirect
141. #6771C2×C4semidirect
142. D15⋊Q8C2×C4semidirect
143. #6768C2×C4semidirect
144. #6766C2×C4semidirect
189. #5523D5semidirect
212. C5×#117C2×D3semidirect
226. C2×C4⋊Dic5C2×D3semidirect
240. #4038C2×D3semidirect
244. D5×C4⋊C4C2×D3semidirect
249. #4027C2×D3semidirect
255. C4×D20C2×D3semidirect
261. C4×Dic10C2×D3semidirect
331. C3×#117C2×D5semidirect
345. C2×C4⋊Dic3C2×D5semidirect
359. #892C2×D5semidirect
363. D3×C4⋊C4C2×D5semidirect
368. #67⋊C4C2×D5semidirect
374. C4×D12C2×D5semidirect
380. C4×Dic6C2×D5semidirect
405. #709C4×D3semidirect
528. #235C4×D5semidirect
681. #117D3×D5semidirect
864. C3×C5#3428semidirect
963. C5#85885semidirect
994. C3#10617786semidirect

Maximal subgroups

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

subgroupindex
C2×#920162
D15×#1172
C5×#55232
C3×#658572
#117544992
#117544922
C2×#913472
D3×#40382
D5×#8922
#117536692
#117536682
#117532042
#117528202
#117527292
C4×#67682
C4×#67662
#117524602
#106177863
#858855