Finite Group Databasebeta

← #14321535

Subgroups — #14321535

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×#91459C211yesmaximal, characteristic
2C2×#91428C211yesmaximal, characteristic, complemented
3C2×C4×#1200C211yesmaximal, characteristic, complemented
4C2×#91395C211yesmaximal, characteristic, complemented
5C2×#91395C211yesmaximal, characteristic, complemented
6#11750766C211yesmaximal, characteristic, complemented
7C5×#4649C211yesmaximal, characteristic, complemented
8C3×#64959C211yesmaximal, characteristic, complemented
9#11748917C211yesmaximal, characteristic, complemented
10#11748913C211yesmaximal, characteristic, complemented
11#11748882C211yesmaximal, characteristic, complemented
12#11748881C211yesmaximal, characteristic, complemented
13Dic3×#685C211yesmaximal, characteristic, complemented
14#11748726C211yesmaximal, characteristic, complemented
15#11748677C211yesmaximal, characteristic, complemented
16C4×#4041—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×#1202C2211yescharacteristic
20C22×#1202C2211yescharacteristic
21C22×#1200C2211yescharacteristic
22C22×#1200C2211yescharacteristic
23C22×#1200C2211yescharacteristic
24C22×D5×Dic3C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6714C2211yescharacteristic
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×#685C2211yescharacteristic
36C2×C3×C4⋊Dic5C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic
38C2×Dic3⋊Dic5C2211yescharacteristic
39C2×Dic3⋊Dic5C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46#91459C418yescomplemented
47#91428—24no—
48C4×#1200—24no—
49#91395—24no—
50#91395—24no—
51C3×C5×#95C2211yescharacteristic
52#91115C2211yescharacteristic
53C5×C3⋊#95C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#75452—51nomaximal, Hall
58C2×#4041—31no—
59C2×C4×D20—31no—
60C2×C4×D20—31no—
61C2×C4×D20—31no—
62C2×C42×D5—31no—
63C4×C5×C4⋊C4—31no—
64#65277—31no—
65#65276—31no—
66#65274—31no—
67C4×#685—31no—
68C4×#685—31no—
69#64959—31no—
70#64959D311yescharacteristic, complemented
71#64954—31no—
72#64954—31no—
73C23×D15C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C23×C3×D5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C2×D60—22no—
82C2×D60—22no—
83C2×D60C2×C414yescomplemented
84C2×C4×D15—22no—
85C2×C4×D15—22no—
86C2×C4×D15—22no—
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C2×#1202—22no—
95C2×#1202—22no—
96C2×#1202—22no—
97C2×#1202—22no—
98C2×#1202C2×C414yescomplemented
99C2×#1202C2×C414yescomplemented
100C2×#1200—22no—
101C2×#1200—22no—
102C2×#1200—22no—
103C2×#1200—22no—
104C2×#1200—22no—
105C2×#1200—22no—
106C2×#1200—22no—
107C2×#1200C2×C414yescomplemented
108C2×#1200D414yescomplemented
109C2×D5×Dic3—22no—
110C2×D5×Dic3—22no—
111C2×D5×Dic3—22no—
112#6714—22no—
113#6714—22no—
114#6714—22no—
115C5×Dic3⋊C4—22no—
116C5×Dic3⋊C4C2×C414yescomplemented
117C4×C5×Dic3—22no—
118C4×C5×Dic3—22no—
119C4×C5×Dic3D414yescomplemented
120C3×#685—22no—
121C3×#685—22no—
122C3×#685C2×C414yescomplemented
123C3×C4⋊Dic5—22no—
124C3×C4×Dic5—22no—
125Dic3⋊Dic5—22no—
126Dic3⋊Dic5—22no—
127#6667—22no—
128#6667—22no—
129#6667C2×C414yescomplemented
130#6665—22no—
131Dic3×Dic5—22no—
132Dic3×Dic5—22no—
133C2×#893—51no—
134C2×#884—51no—
135C2×#67⋊C4—51no—
136C2×#67⋊C4—51no—
137C2×C42×D3—51no—
138C3×#388—51no—
139#4976—51no—
140#4957—51no—
141#4956—51no—
142Dic3×C22⋊C4—51no—
143#4940—51no—
144#4667—51no—
145#4666—51no—
146#4665—51no—
147#4649D511yescharacteristic, complemented
148C22×D20—31no—
149C22×D20—31no—
150C22×D20—31no—
151C22×C4×D5—31no—
152C22×C4×D5—31no—
153C22×C4×D5—31no—
154C22×C4×D5—31no—
155C22×C4×D5—31no—
156C2×C5×C4⋊C4—31no—
157C2×C5×C4⋊C4—31no—
158C2×C42×C5—31no—
159C2×C42×C5—31no—
160C2×C42×C5—31no—
161C2×#685—31no—
162C2×#685—31no—
163C2×#685—31no—
164C2×#685—31no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685C2×D311yescharacteristic
169C2×#685C2×D311yescharacteristic
170C2×#685C2×D311yescharacteristic
171C2×C4⋊Dic5—31no—
172C2×C4⋊Dic5—31no—
173C2×C4⋊Dic5C2×D311yescharacteristic
174C2×C4×Dic5—31no—
175C2×C4×Dic5—31no—
176C2×C4×Dic5C2×D311yescharacteristic
177#4041—38no—
178C4×D20—64no—
179C4×D20—64no—
180C4×D20—64no—
181C42×D5—64no—
182C5×#95—31no—
183C5×#95C2×D311yescharacteristic
184#3963—31no—
185#3963—31no—
186#3963—31no—
187#3963C2×D311yescharacteristic
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×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15C22×C412yes—
201C22×D15C22×C412yes—
202C22×D15C2×D412yes—
203C22×D15#4112yes—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—21no—
209C22×C3×D5—21no—
210C22×C3×D5C22×C412yes—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5C22×C412yes—
219C2×C3×C4×C5C2×D412yes—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15#4112yes—
226D60—28no—
227C4×D15—28no—
228C2×C5×Dic3—21no—
229C2×C5×Dic3—21no—
230C2×C5×Dic3—21no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3C22×C412yes—
234C2×C5×Dic3C22×C412yes—
235C2×C5×Dic3C2×D412yes—
236C2×C5×Dic3C2×D412yes—
237C2×C5×Dic3C2×D412yes—
238C2×C5×Dic3#4112yes—
239C2×C5×Dic3#4112yes—
240C2×C3×Dic5—21no—
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×Dic5C22×C412yes—
248C2×C3×Dic5C2×D412yes—
249#1202—28no—
250#1202—28no—
251#1200—28no—
252#1200—28no—
253#1200—44no—
254D5×Dic3—44no—
255C22×#67—51no—
256C22×#67—51no—
257C23×Dic3—51no—
258C22×D12—51no—
259C22×C4×D3—51no—
260C22×C4×D3—51no—
261C22×C4×D3—51no—
262C22×C4×D3—51no—
263C2×C3×C4⋊C4—51no—
264C2×C3×C22⋊C4—51no—
265C2×C3×C22⋊C4—51no—
266C2×C3×C22⋊C4—51no—
267C2×C3×C42—51no—
268C2×#217—51no—
269C2×(C2×D3)⋊C4—51no—
270C2×(C2×D3)⋊C4—51no—
271C2×(C2×D3)⋊C4—51no—
272C2×(C2×D3)⋊C4—51no—
273C2×(C2×D3)⋊C4—51no—
274C2×(C2×D3)⋊C4—51no—
275C2×Dic3⋊C4—51no—
276C2×Dic3⋊C4—51no—
277C2×Dic3⋊C4C2×D511yescharacteristic
278C2×Dic3⋊C4C2×D511yescharacteristic
279C2×C4×Dic3—51no—
280C2×C4×Dic3—51no—
281C2×C4×Dic3C2×D511yescharacteristic
282C2×C4×Dic3C2×D511yescharacteristic
283C2×C4×Dic3C2×D511yescharacteristic
284#893—104no—
285#884—58no—
286#67⋊C4—104no—
287#67⋊C4—104no—
288C42×D3—104no—
289C3×#95—51no—
290C3×#95C2×D511yescharacteristic
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95C2×D511yescharacteristic
295C23×D5—31no—
296C23×D5—31no—
297C23×D5C22×D311yescharacteristic
298C22×C4×C5—31no—
299C22×C4×C5—31no—
300C22×C4×C5—31no—
301C22×C4×C5—31no—
302C22×C4×C5C22×D311yescharacteristic
303C22×C4×C5C22×D311yescharacteristic
304C22×C4×C5C22×D311yescharacteristic
305C22×Dic5—31no—
306C22×Dic5—31no—
307C22×Dic5C22×D311yescharacteristic
308C22×Dic5C22×D311yescharacteristic
309C22×Dic5C22×D311yescharacteristic
310C2×D20—34no—
311C2×D20—34no—
312C2×D20—34no—
313C2×D20—62no—
314C2×D20—62no—
315C2×D20—62no—
316C2×D20—62no—
317C2×D20—62no—
318C2×D20—62no—
319C2×C4×D5—34no—
320C2×C4×D5—34no—
321C2×C4×D5—62no—
322C2×C4×D5—62no—
323C2×C4×D5—62no—
324C2×C4×D5—62no—
325C2×C4×D5—62no—
326C2×C4×D5—62no—
327C2×C4×D5—62no—
328C2×C4×D5—62no—
329C2×C4×D5—62no—
330C2×C4×D5—62no—
331C2×C4×D5—62no—
332C2×C4×D5—62no—
333C2×C4×D5—62no—
334C5×C4⋊C4—34no—
335C5×C4⋊C4—62no—
336C42×C5—34no—
337C42×C5—62no—
338C42×C5—62no—
339#685—22no—
340#685—22no—
341#685—34no—
342#685—62no—
343#685—62no—
344#685—62no—
345#685—62no—
346#685—62no—
347#685—62no—
348#685C4×D314yescomplemented
349C4⋊Dic5—22no—
350C4⋊Dic5—62no—
351C4⋊Dic5—62no—
352C4×Dic5—22no—
353C4×Dic5—62no—
354C4×Dic5—62no—
355C2×#121—151no—
356C2×C4×D4—151no—
357C2×C4×D4—151no—
358C2×C4×D4—151no—
359C22×C42—151no—
360#390—151no—
361#389—151no—
362#388—51no—
363#388—151no—
364#386—151no—
365#386—151no—
366#380—151no—
367C4×C4⋊C4—31no—
368C4×C22⋊C4—151no—
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—22no—
381C2×D15—22no—
382C2×D15—22no—
383C2×D15—22no—
384C2×D15—22no—
385C2×D15—22no—
386C2×D15—41no—
387C2×D15—41no—
388C2×D15—41no—
389C2×D15—41no—
390C2×D15C4×D414yescomplemented
391C2×C3×D5—22no—
392C2×C3×D5—22no—
393C2×C3×D5—22no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C2×C3×D5—41no—
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400C3×C4×C5—41no—
401Dic15—22no—
402Dic15—41no—
403C3×Dic5—22no—
404C3×Dic5—22no—
405C3×Dic5—41no—
406C5×Dic3—22no—
407C5×Dic3—41no—
408C5×Dic3C4×D414yescomplemented
409C5×Dic3#12114yescomplemented
410C24×C3—51no—
411C23×D3—51no—
412C23×D3—51no—
413C22×C3×C4—51no—
414C22×C3×C4—51no—
415C22×C3×C4—51no—
416C22×C3×C4C22×D511yescharacteristic
417C22×C3×C4C22×D511yescharacteristic
418C22×C3×C4C22×D511yescharacteristic
419C2×#67—54no—
420C2×#67—54no—
421C2×#67—102no—
422C2×#67—102no—
423C2×#67—102no—
424C2×#67—102no—
425C22×Dic3—51no—
426C22×Dic3—51no—
427C22×Dic3—102no—
428C22×Dic3—102no—
429C22×Dic3—102no—
430C22×Dic3C22×D511yescharacteristic
431C22×Dic3C22×D511yescharacteristic
432C22×Dic3C22×D511yescharacteristic
433C22×Dic3C22×D511yescharacteristic
434C2×D12—54no—
435C2×D12—102no—
436C2×D12—102no—
437C2×C4×D3—54no—
438C2×C4×D3—54no—
439C2×C4×D3—102no—
440C2×C4×D3—102no—
441C2×C4×D3—102no—
442C2×C4×D3—102no—
443C2×C4×D3—102no—
444C2×C4×D3—102no—
445C2×C4×D3—102no—
446C2×C4×D3—102no—
447C2×C4×D3—102no—
448C2×C4×D3—102no—
449C3×C4⋊C4—102no—
450C3×C22⋊C4—54no—
451C3×C22⋊C4—102no—
452C3×C22⋊C4—102no—
453C3×C42—102no—
454#217—102no—
455(C2×D3)⋊C4—54no—
456(C2×D3)⋊C4—102no—
457(C2×D3)⋊C4—102no—
458(C2×D3)⋊C4—102no—
459(C2×D3)⋊C4—102no—
460(C2×D3)⋊C4—102no—
461Dic3⋊C4—22no—
462Dic3⋊C4—102no—
463Dic3⋊C4—102no—
464Dic3⋊C4C4×D514yescomplemented
465C4×Dic3—22no—
466C4×Dic3—22no—
467C4×Dic3—102no—
468C4×Dic3—102no—
469C4×Dic3D2014yescomplemented
470C23×C5C23×D311yescharacteristic
471C22×D5—21no—
472C22×D5—21no—
473C22×D5—21no—
474C22×D5—21no—
475C22×D5—21no—
476C22×D5—21no—
477C22×D5—32no—
478C22×D5—32no—
479C22×D5—32no—
480C22×D5—32no—
481C22×D5—61no—
482C22×D5—61no—
483C22×D5—61no—
484C22×D5—61no—
485C22×D5—61no—
486C22×D5—61no—
487C22×D5—61no—
488C22×D5—61no—
489C22×D5—61no—
490C22×D5—61no—
491C22×D5C2×C4×D312yes—
492C2×C4×C5—21no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—21no—
499C2×C4×C5—32no—
500C2×C4×C5—32no—
501C2×C4×C5—32no—
502C2×C4×C5—32no—
503C2×C4×C5—32no—
504C2×C4×C5—32no—
505C2×C4×C5—32no—
506C2×C4×C5—61no—
507C2×C4×C5—61no—
508C2×C4×C5—61no—
509C2×C4×C5—61no—
510C2×C4×C5—61no—
511C2×C4×C5C2×C4×D312yes—
512C2×C4×C5D3×D412yes—
513C2×Dic5—21no—
514C2×Dic5—21no—
515C2×Dic5—21no—
516C2×Dic5—21no—
517C2×Dic5—21no—
518C2×Dic5—21no—
519C2×Dic5—21no—
520C2×Dic5—32no—
521C2×Dic5—61no—
522C2×Dic5—61no—
523C2×Dic5—61no—
524C2×Dic5—61no—
525C2×Dic5—61no—
526C2×Dic5C2×C4×D312yes—
527C2×Dic5D3×D412yes—
528D20—68no—
529D20—68no—
530D20—68no—
531C4×D5—68no—
532C4×D5—68no—
533C4×D5—68no—
534C4×D5—124no—
535C4×D5—124no—
536C22×D4—151no—
537C22×D4—151no—
538C22×D4—151no—
539C23×C4—151no—
540C23×C4—151no—
541C23×C4—151no—
542C23×C4—151no—
543C23×C4—151no—
544#121—158no—
545C4×D4—304no—
546C4×D4—304no—
547C4×D4—304no—
548C2×C4⋊C4—31no—
549C2×C4⋊C4—31no—
550C2×C4⋊C4—51no—
551C2×C4⋊C4—151no—
552C2×C4⋊C4—151no—
553C2×C22⋊C4—51no—
554C2×C22⋊C4—51no—
555C2×C22⋊C4—51no—
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—31no—
565C2×C42—31no—
566C2×C42—51no—
567C2×C42—151no—
568C2×C42—151no—
569C2×C42—304no—
570#95—31no—
571#95—51no—
572#95—151no—
573#95—151no—
574#95—151no—
575#95D3×D511yescharacteristic
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—24no—
584D15—42no—
585C3×D5—42no—
586C23×C3—52no—
587C23×C3—101no—
588C23×C3—101no—
589C23×C3—101no—
590C23×C3—101no—
591C23×C3—101no—
592C23×C3—101no—
593C23×C3C23×D511yescharacteristic
594C22×D3—52no—
595C22×D3—52no—
596C22×D3—52no—
597C22×D3—52no—
598C22×D3—101no—
599C22×D3—101no—
600C22×D3—101no—
601C22×D3—101no—
602C22×D3—101no—
603C22×D3—101no—
604C22×D3—101no—
605C22×D3—101no—
606C22×D3—101no—
607C22×D3—101no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—52no—
616C2×C3×C4—52no—
617C2×C3×C4—101no—
618C2×C3×C4—101no—
619C2×C3×C4—101no—
620C2×C3×C4—101no—
621C2×C3×C4—101no—
622C2×C3×C4—101no—
623C2×C3×C4—101no—
624C2×C3×C4C2×C4×D512yes—
625C2×C3×C4C2×D2012yes—
626#67—108no—
627#67—108no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—52no—
634C2×Dic3—101no—
635C2×Dic3—101no—
636C2×Dic3—101no—
637C2×Dic3—101no—
638C2×Dic3—101no—
639C2×Dic3—204no—
640C2×Dic3C2×C4×D512yes—
641C2×Dic3C2×C4×D512yes—
642C2×Dic3C2×D2012yes—
643C2×Dic3C2×D2012yes—
644C2×Dic3#70912yes—
645C2×Dic3D4×D512yes—
646C2×Dic3#71312yes—
647D12—108no—
648C4×D3—108no—
649C4×D3—108no—
650C4×D3—108no—
651C4×D3—204no—
652C22×C5C22×C4×D311yescharacteristic
653C22×C5C2×D3×D411yescharacteristic
654C22×C5C2×D3×D411yescharacteristic
655C22×C5D3×#4111yescharacteristic
656C22×C5D3×#4111yescharacteristic
657C22×C5D3×#4111yescharacteristic
658C22×C5D3×#4111yescharacteristic
659C2×D5—22no—
660C2×D5—22no—
661C2×D5—22no—
662C2×D5—34no—
663C2×D5—41no—
664C2×D5—41no—
665C2×D5—41no—
666C2×D5—41no—
667C2×D5—62no—
668C2×D5—62no—
669C2×D5—62no—
670C2×D5—62no—
671C2×D5—62no—
672C2×D5—62no—
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—22no—
682C4×C5—34no—
683C4×C5—34no—
684C4×C5—41no—
685C4×C5—62no—
686C4×C5—121no—
687Dic5—22no—
688Dic5—22no—
689Dic5—41no—
690Dic5—62no—
691Dic5—121no—
692C24—51no—
693C24—151no—
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—31no—
708C22×C4—51no—
709C22×C4—51no—
710C22×C4—51no—
711C22×C4—154no—
712C22×C4—154no—
713C22×C4—151no—
714C22×C4—151no—
715C22×C4—302no—
716C22×C4—302no—
717C22×C4—302no—
718C22×C4—302no—
719C22×C4—302no—
720C22×C4—302no—
721C22×C4—302no—
722C22×C4—302no—
723C22×C4—302no—
724C22×C4—302no—
725C22×C4—302no—
726C22×C4—302no—
727C22×C4—302no—
728C22×C4C2×D3×D511yescharacteristic
729C22×C4C2×D3×D511yescharacteristic
730C22×C4C2×D3×D511yescharacteristic
731C4⋊C4—34no—
732C4⋊C4—62no—
733C4⋊C4—102no—
734C4⋊C4—302no—
735C4⋊C4—302no—
736C22⋊C4—54no—
737C22⋊C4—102no—
738C22⋊C4—102no—
739C22⋊C4—154no—
740C22⋊C4—302no—
741C22⋊C4—302no—
742C22⋊C4—302no—
743C22⋊C4—302no—
744C22⋊C4—302no—
745C22⋊C4—302no—
746C42—34no—
747C42—62no—
748C42—62no—
749C42—102no—
750C42—302no—
751C42—302no—
752C3×C5C4×#12111yescharacteristic, complemented, Hall
753C22×C3—102no—
754C22×C3—102no—
755C22×C3—102no—
756C22×C3—201no—
757C22×C3—201no—
758C22×C3—201no—
759C22×C3—201no—
760C22×C3C22×C4×D511yescharacteristic
761C22×C3C22×D2011yescharacteristic
762C22×C3C2×#70911yescharacteristic
763C22×C3C2×D4×D511yescharacteristic
764C22×C3C2×#71311yescharacteristic
765C22×C3D5×#4111yescharacteristic
766C22×C3D5×#4111yescharacteristic
767C2×D3—54no—
768C2×D3—102no—
769C2×D3—102no—
770C2×D3—102no—
771C2×D3—102no—
772C2×D3—102no—
773C2×D3—102no—
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—41no—
784C3×C4—102no—
785C3×C4—102no—
786C3×C4—201no—
787Dic3—22no—
788Dic3—41no—
789Dic3—102no—
790Dic3—201no—
791Dic3C4×D2014yescomplemented
792Dic3#404114yescomplemented
793C2×C5#552211yescharacteristic
794C2×C5C4×D3×D411yescharacteristic
795C2×C5C4×D3×D411yescharacteristic
796C2×C5D3×#12111yescharacteristic
797C2×C5#565611yescharacteristic
798C2×C5#566811yescharacteristic
799C2×C5#570611yescharacteristic
800D5—42no—
801D5—64no—
802D5—122no—
803C23—52no—
804C23—101no—
805C23—101no—
806C23—101no—
807C23—101no—
808C23—101no—
809C23—101no—
810C23—152no—
811C23—152no—
812C23—152no—
813C23—152no—
814C23—301no—
815C23—301no—
816C23—301no—
817C23—301no—
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—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—32no—
836C2×C4—32no—
837C2×C4—32no—
838C2×C4—32no—
839C2×C4—32no—
840C2×C4—32no—
841C2×C4—32no—
842C2×C4—52no—
843C2×C4—52no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—101no—
850C2×C4—101no—
851C2×C4—101no—
852C2×C4—101no—
853C2×C4—101no—
854C2×C4—101no—
855C2×C4—101no—
856C2×C4—152no—
857C2×C4—308no—
858C2×C4—308no—
859C2×C4—308no—
860C2×C4—301no—
861C2×C4—301no—
862C2×C4—301no—
863C2×C4—301no—
864C2×C4—301no—
865C2×C4—604no—
866C2×C4—604no—
867C2×C4C4×D3×D512yes—
868C2×C4D3×D2012yes—
869C2×C3—202no—
870C2×C3C2×C4×D2011yescharacteristic
871C2×C3C2×#404111yescharacteristic
872C2×C3#6585811yescharacteristic
873C2×C3C4×D4×D511yescharacteristic
874C2×C3#6588211yescharacteristic
875C2×C3C4×#71311yescharacteristic
876C2×C3#6591411yescharacteristic
877D3—104no—
878D3—202no—
879C5#7545211yescharacteristic, complemented, Sylow
880C22—102no—
881C22—102no—
882C22—102no—
883C22—154no—
884C22—201no—
885C22—201no—
886C22—201no—
887C22—201no—
888C22—302no—
889C22—302no—
890C22—302no—
891C22—302no—
892C22—302no—
893C22—302no—
894C22—302no—
895C22—302no—
896C22—302no—
897C22—601no—
898C22—601no—
899C22—601no—
900C22—601no—
901C22C2×C4×D3×D511yescharacteristic
902C22C2×D3×D2011yescharacteristic
903C22D3×#70911yescharacteristic
904C22D3×D4×D511yescharacteristic
905C22#9202411yescharacteristic
906C22#9202411yescharacteristic
907C22D3×#71311yescharacteristic
908C4—22no—
909C4—22no—
910C4—34no—
911C4—34no—
912C4—41no—
913C4—62no—
914C4—102no—
915C4—102no—
916C4—121no—
917C4—201no—
918C4—302no—
919C4—601no—
920C3C4×#404111yescharacteristic, complemented, Sylow
921C2—202no—
922C2—304no—
923C2—602no—
924C2C4×D3×D2011yescharacteristic
925C2#1175285511yescharacteristic
926C2#1175287611yescharacteristic
927C2#1175320311yescharacteristic
928C2#1175340311yescharacteristic
929C2#1175356311yescharacteristic
930C2D3×#404111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91459C2
hypercenter#95D3×D5
hypocenterC3×C5C4×#121
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×#91428C2semidirect
3. C2×C4×#1200C2semidirect
4. C2×#91395C2semidirect
5. C2×#91395C2semidirect
6. #11750766C2semidirect
7. C5×#4649C2semidirect
8. C3×#64959C2semidirect
9. #11748917C2semidirect
10. #11748913C2semidirect
11. #11748882C2semidirect
12. #11748881C2semidirect
13. Dic3×#685C2semidirect
14. #11748726C2semidirect
15. #11748677C2semidirect
46. #91459C4semidirect
70. #64959D3semidirect
83. C2×D60C2×C4semidirect
98. C2×#1202C2×C4semidirect
99. C2×#1202C2×C4semidirect
107. C2×#1200C2×C4semidirect
108. C2×#1200D4semidirect
116. C5×Dic3⋊C4C2×C4semidirect
119. C4×C5×Dic3D4semidirect
122. C3×#685C2×C4semidirect
129. #6667C2×C4semidirect
147. #4649D5semidirect
348. #685C4×D3semidirect
390. C2×D15C4×D4semidirect
408. C5×Dic3C4×D4semidirect
409. C5×Dic3#121semidirect
464. Dic3⋊C4C4×D5semidirect
469. C4×Dic3D20semidirect
752. C3×C5C4×#121semidirect
791. Dic3C4×D20semidirect
792. Dic3#4041semidirect
879. C5#75452semidirect
920. C3C4×#4041semidirect

Maximal subgroups

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

subgroupindex
C2×#914592
C2×#914282
C2×C4×#12002
C2×#913952
#117507662
C5×#46492
C3×#649592
#117489172
#117489132
#117488822
#117488812
Dic3×#6852
#117487262
#117486772
C4×#40413
#754525