Finite Group Databasebeta

← #14321174

Subgroups — #14321174

Order 1920.

1872 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6772C211yesmaximal, characteristic
2C2×#91398C211yesmaximal, characteristic, complemented
3C2×C4×D3×Dic5C211yesmaximal, characteristic, complemented
4#11750747C211yesmaximal, characteristic, complemented
5C5×#4665C211yesmaximal, characteristic, complemented
6C3×#64955C211yesmaximal, characteristic, complemented
7#11748916C211yesmaximal, characteristic, complemented
8#11748915C211yesmaximal, characteristic, complemented
9#11748911C211yesmaximal, characteristic, complemented
10#11748910C211yesmaximal, characteristic, complemented
11#11748901C211yesmaximal, characteristic, complemented
12Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
13Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
14#11748702C211yesmaximal, characteristic, complemented
15#11748694C211yesmaximal, characteristic, complemented
16#10606389—31nomaximal, Hall
17C22×Dic30C2211yescharacteristic
18C22×C5×D12C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×#1201C2211yescharacteristic
22C22×#1201C2211yescharacteristic
23C22×D3×Dic5C2211yescharacteristic
24C22×D3×Dic5C2211yescharacteristic
25C22×D3×Dic5C2211yescharacteristic
26C2×#6772—24no—
27C2×#6772—24no—
28C2×#6772C418yescomplemented
29C2×#6712C2211yescharacteristic
30C2×C4×Dic15C2211yescharacteristic
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C5×(C2×D3)⋊C4C2211yescharacteristic
33C2×C5×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×C4×Dic5C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic
38C2×#6669C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic
47#91398—24no—
48C4×D3×Dic5—24no—
49C3×C5×#95C2211yescharacteristic
50#91115C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53C5×C3⋊#95C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#73563—51nomaximal, Hall
58C22×#711—31no—
59C22×C4×Dic5—31no—
60C2×#4023—31no—
61C5×#386—31no—
62#65509—31no—
63#65502—31no—
64#65247—31no—
65#65246—31no—
66#65246—31no—
67C22⋊C4×Dic5—31no—
68C22⋊C4×Dic5—31no—
69#64955—31no—
70#64955D311yescharacteristic, complemented
71#64935—31no—
72#64935—31no—
73C23×C5×D3C2311yescharacteristic
74C23×C5×D3C2311yescharacteristic
75C23×C3×D5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C2×Dic30—22no—
84C2×Dic30—22no—
85C2×Dic30C2×C414yescomplemented
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C2×C5×D12—22no—
89C2×C5×D12—22no—
90C2×C5×D12C2×C414yes—
91C2×C4×C5×D3—22no—
92C2×C4×C5×D3—22no—
93C2×C4×C5×D3—22no—
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C2×C3×C4×D5—22no—
98C2×C3×C4×D5—22no—
99C2×C3×C4×D5C2×C414yescomplemented
100C2×#1201—22no—
101C2×#1201—22no—
102C2×#1201—22no—
103C2×#1201—22no—
104C2×#1201C2×C414yes—
105C2×#1201C2×C414yescomplemented
106C2×D3×Dic5—22no—
107C2×D3×Dic5—22no—
108C2×D3×Dic5—22no—
109C2×D3×Dic5—22no—
110C2×D3×Dic5—22no—
111C2×D3×Dic5C2×C414yes—
112C2×D3×Dic5C2×C414yescomplemented
113C2×D3×Dic5D414yes—
114C2×D3×Dic5D414yes—
115#6772—232no—
116#6712—22no—
117C4×Dic15—22no—
118C5×(C2×D3)⋊C4—22no—
119C5×(C2×D3)⋊C4—22no—
120C5×(C2×D3)⋊C4—22no—
121C3×#685—22no—
122C3×#685—22no—
123C3×C4×Dic5—22no—
124C3×C4×Dic5—22no—
125#6669—22no—
126(C2×D3)⋊Dic5—22no—
127(C2×D3)⋊Dic5—22no—
128(C2×D3)⋊Dic5—22no—
129#6665—22no—
130#6665—22no—
131Dic3×Dic5—22no—
132Dic3×Dic5—22no—
133Dic3×Dic5—22no—
134C22×#235—51no—
135C2×#872—51no—
136C2×C42×D3—51no—
137C3×C4×C22⋊C4—51no—
138C4×#217—51no—
139#4957—51no—
140#4957—51no—
141#4956—51no—
142#4956—51no—
143C4×(C2×D3)⋊C4—51no—
144C4×(C2×D3)⋊C4—51no—
145#4665—51no—
146#4665D511yescharacteristic, complemented
147#4646—51no—
148#4646—51no—
149C22×C5×D4—31no—
150C23×C4×C5—31no—
151C22×C22⋊D5—31no—
152C22×C22⋊D5—31no—
153C23×Dic5—31no—
154C23×Dic5—31no—
155C23×Dic5—31no—
156C2×#711—38no—
157C2×#711—64no—
158C2×#711—64no—
159C22×C4×D5C2×D311yescharacteristic
160C22×Dic10—31no—
161C2×C5×C22⋊C4—31no—
162C2×C5×C22⋊C4—31no—
163C2×C5×C22⋊C4—31no—
164C2×C22⋊Dic5—31no—
165C2×C22⋊Dic5—31no—
166C2×C22⋊Dic5—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685C2×D311yescharacteristic
170C2×#685C2×D311yescharacteristic
171C2×#683—31no—
172C2×#683—31no—
173C2×C4×Dic5—31no—
174C2×C4×Dic5—31no—
175C2×C4×Dic5—31no—
176C2×C4×Dic5—31no—
177C2×C4×Dic5—64no—
178C2×C4×Dic5C2×D311yescharacteristic
179C2×C4×Dic5C2×D311yescharacteristic
180#4023—64no—
181C5×#95—31no—
182C5×#95C2×D311yescharacteristic
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#3963—31no—
187#3963—31no—
188#3963C2×D311yescharacteristic
189#2297—151noSylow
190C23×C3×C5C2411yescharacteristic
191C22×C5×D3—21no—
192C22×C5×D3—21no—
193C22×C5×D3—21no—
194C22×C5×D3—21no—
195C22×C5×D3—21no—
196C22×C5×D3—21no—
197C22×C5×D3—21no—
198C22×C5×D3—21no—
199C22×C5×D3—21no—
200C22×C5×D3—21no—
201C22×C5×D3C22×C412yes—
202C22×C5×D3C22×C412yes—
203C22×C5×D3C2×D412yes—
204C22×C5×D3C2×D412yes—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—21no—
209C22×C3×D5—21no—
210C22×C3×D5—21no—
211C22×C3×D5C22×C412yes—
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×C5—21no—
219C2×C3×C4×C5C22×C412yes—
220C2×C3×C4×C5#4112yescomplemented
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15C22×C412yes—
229C2×Dic15C22×C412yes—
230C2×Dic15C2×D412yes—
231C2×Dic15C2×D412yes—
232C2×Dic15#4112yescomplemented
233Dic30—28no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3#4112yescomplemented
240C5×D12—28no—
241C4×C5×D3—28no—
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—
249C2×C3×Dic5C2×D412yes—
250C2×C3×Dic5#4112yescomplemented
251C3×C4×D5—28no—
252#1201—28no—
253#1201—28no—
254D3×Dic5—28no—
255D3×Dic5—28no—
256D3×Dic5C22⋊C4116yescomplemented
257C23×C3×C4—51no—
258C22×#67—51no—
259C22×#67—51no—
260C2×#235—58no—
261C2×#235—104no—
262C2×#235—104no—
263C22×D12C2×D511yescharacteristic
264C22×C4×D3—51no—
265C22×C4×D3—51no—
266C22×C4×D3—51no—
267C22×C4×D3C2×D511yescharacteristic
268C22×Dic6—51no—
269C2×C3×C22⋊C4—51no—
270C2×C3×C22⋊C4—51no—
271C2×C3×C42—51no—
272C2×C3×C42—51no—
273C2×#217—51no—
274C2×#217—51no—
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4C2×D511yescharacteristic
279C2×(C2×D3)⋊C4C2×D511yescharacteristic
280C2×(C2×D3)⋊C4C2×D511yescharacteristic
281C2×Dic3⋊C4—51no—
282C2×Dic3⋊C4—51no—
283C2×C4×Dic3—51no—
284C2×C4×Dic3—51no—
285C2×C4×Dic3—51no—
286C2×C4×Dic3—51no—
287#872—104no—
288C42×D3—104no—
289C3×#95—51no—
290C3×#95C2×D511yescharacteristic
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95C2×D511yescharacteristic
297C24×C5—31no—
298C24×C5—31no—
299C23×D5C22×D311yescharacteristic
300C2×C5×D4—34no—
301C2×C5×D4—62no—
302C2×C5×D4—62no—
303C22×C4×C5—31no—
304C22×C4×C5—31no—
305C22×C4×C5—62no—
306C22×C4×C5—62no—
307C22×C4×C5—62no—
308C22×C4×C5C22×D311yescharacteristic
309C22×C4×C5C22×D311yescharacteristic
310C22×C4×C5C22×D311yescharacteristic
311C2×C22⋊D5—34no—
312C2×C22⋊D5—34no—
313C2×C22⋊D5—62no—
314C2×C22⋊D5—62no—
315C2×C22⋊D5—62no—
316C2×C22⋊D5—62no—
317C22×Dic5—31no—
318C22×Dic5—34no—
319C22×Dic5—34no—
320C22×Dic5—34no—
321C22×Dic5—31no—
322C22×Dic5—31no—
323C22×Dic5—34no—
324C22×Dic5—31no—
325C22×Dic5—62no—
326C22×Dic5—62no—
327C22×Dic5—62no—
328C22×Dic5—62no—
329C22×Dic5—62no—
330C22×Dic5C22×D311yescharacteristic
331C22×Dic5C22×D311yescharacteristic
332C22×Dic5C22×D311yescharacteristic
333#711—632no—
334C2×C4×D5—22no—
335C2×C4×D5—22no—
336C2×C4×D5C4×D314yescomplemented
337C2×Dic10—34no—
338C2×Dic10—62no—
339C2×Dic10—62no—
340C5×C22⋊C4—62no—
341C5×C22⋊C4—62no—
342C5×C22⋊C4—62no—
343C22⋊Dic5—62no—
344C22⋊Dic5—62no—
345C22⋊Dic5—62no—
346#685—22no—
347#685—22no—
348#685—62no—
349#685—62no—
350#683—62no—
351#683—62no—
352C4×Dic5—22no—
353C4×Dic5—22no—
354C4×Dic5—62no—
355C4×Dic5—62no—
356C4×Dic5—62no—
357C4×Dic5—62no—
358C22×#41—151no—
359C2×#117—151no—
360C22×C42—151no—
361#391—151no—
362#391—151no—
363#390—151no—
364#390—151no—
365#386—31no—
366#386—151no—
367#386—151no—
368#386—151no—
369C4×C22⋊C4—51no—
370C4×C22⋊C4—151no—
371C4×C22⋊C4—151no—
372C4×C22⋊C4—151no—
373C22×C3×C5C23×C411yescharacteristic
374C22×C3×C5C22×D411yescharacteristic
375C22×C3×C5C22×D411yescharacteristic
376C22×C3×C5C2×#4111yescharacteristic
377C22×C3×C5C2×#4111yescharacteristic
378C22×C3×C5C2×#4111yescharacteristic
379C22×C3×C5C2×#4111yescharacteristic
380C2×C5×D3—22no—
381C2×C5×D3—22no—
382C2×C5×D3—22no—
383C2×C5×D3—22no—
384C2×C5×D3—22no—
385C2×C5×D3—22no—
386C2×C5×D3—22no—
387C2×C5×D3—22no—
388C2×C5×D3—22no—
389C2×C5×D3—41no—
390C2×C5×D3—41no—
391C2×C5×D3—41no—
392C2×C5×D3—41no—
393C2×C5×D3C2×C22⋊C414yes—
394C2×C3×D5—22no—
395C2×C3×D5—22no—
396C2×C3×D5—22no—
397C2×C3×D5—41no—
398C2×C3×D5—41no—
399C2×C3×D5—41no—
400C2×C3×D5—41no—
401C3×C4×C5—22no—
402C3×C4×C5—22no—
403C3×C4×C5—41no—
404Dic15—22no—
405Dic15—22no—
406Dic15—41no—
407Dic15C2×C22⋊C414yes—
408C3×Dic5—22no—
409C3×Dic5—41no—
410C3×Dic5C2×C22⋊C414yes—
411C5×Dic3—22no—
412C5×Dic3—41no—
413C24×C3—51no—
414C23×D3C22×D511yescharacteristic
415C23×D3C22×D511yescharacteristic
416C22×C3×C4—51no—
417C22×C3×C4—51no—
418C22×C3×C4—54no—
419C22×C3×C4—51no—
420C22×C3×C4—102no—
421C22×C3×C4—102no—
422C22×C3×C4C22×D511yescharacteristic
423C22×C3×C4C22×D511yescharacteristic
424C22×C3×C4C22×D511yescharacteristic
425C2×#67—54no—
426C2×#67—54no—
427C2×#67—102no—
428C2×#67—102no—
429C2×#67—102no—
430C2×#67—102no—
431C22×Dic3—51no—
432C22×Dic3—51no—
433C22×Dic3—51no—
434C22×Dic3—51no—
435C22×Dic3C22×D511yescharacteristic
436C22×Dic3C22×D511yescharacteristic
437#235—1032no—
438C2×D12—22no—
439C2×D12—22no—
440C2×D12C4×D514yes—
441C2×C4×D3—22no—
442C2×C4×D3—22no—
443C2×C4×D3—22no—
444C2×C4×D3—54no—
445C2×C4×D3—54no—
446C2×C4×D3—54no—
447C2×C4×D3—54no—
448C2×C4×D3—102no—
449C2×C4×D3—102no—
450C2×C4×D3—102no—
451C2×C4×D3—102no—
452C2×C4×D3—102no—
453C2×Dic6—54no—
454C2×Dic6—102no—
455C2×Dic6—102no—
456C3×C22⋊C4—102no—
457C3×C22⋊C4—102no—
458C3×C42—102no—
459C3×C42—102no—
460#217—102no—
461#217—102no—
462(C2×D3)⋊C4—22no—
463(C2×D3)⋊C4—22no—
464(C2×D3)⋊C4—22no—
465(C2×D3)⋊C4—102no—
466(C2×D3)⋊C4—102no—
467(C2×D3)⋊C4—102no—
468Dic3⋊C4—102no—
469Dic3⋊C4—102no—
470C4×Dic3—102no—
471C4×Dic3—102no—
472C4×Dic3—102no—
473C4×Dic3—102no—
474C23×C5—32no—
475C23×C5—32no—
476C23×C5—32no—
477C23×C5—32no—
478C23×C5—61no—
479C23×C5—61no—
480C23×C5—61no—
481C23×C5—61no—
482C23×C5—61no—
483C23×C5—61no—
484C23×C5—61no—
485C23×C5—61no—
486C23×C5—61no—
487C23×C5—61no—
488C23×C5C23×D311yescharacteristic
489C22×D5—21no—
490C22×D5—21no—
491C22×D5—21no—
492C22×D5—21no—
493C22×D5—21no—
494C22×D5—21no—
495C22×D5C2×C4×D312yes—
496C5×D4—68no—
497C2×C4×C5—21no—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—21no—
503C2×C4×C5—21no—
504C2×C4×C5—32no—
505C2×C4×C5—68no—
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×C5#23512yescomplemented
513C22⋊D5—68no—
514C22⋊D5—68no—
515C2×Dic5—21no—
516C2×Dic5—21no—
517C2×Dic5—21no—
518C2×Dic5—21no—
519C2×Dic5—21no—
520C2×Dic5—32no—
521C2×Dic5—32no—
522C2×Dic5—32no—
523C2×Dic5—316no—
524C2×Dic5—32no—
525C2×Dic5—32no—
526C2×Dic5—68no—
527C2×Dic5—61no—
528C2×Dic5—61no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5—68no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5C2×C4×D312yes—
536C2×Dic5#23512yescomplemented
537C2×Dic5D3×D412yes—
538C2×Dic5D3×D412yes—
539C4×D5—28no—
540Dic10—68no—
541C2×#41—158no—
542C2×#41—304no—
543C2×#41—304no—
544C22×Q8—151no—
545C22×D4—31no—
546C22×D4—151no—
547C22×D4—151no—
548C23×C4—31no—
549C23×C4—51no—
550C23×C4—151no—
551C23×C4—151no—
552C23×C4—151no—
553#117—304no—
554C2×C4⋊C4—151no—
555C2×C4⋊C4—151no—
556C2×C22⋊C4—31no—
557C2×C22⋊C4—31no—
558C2×C22⋊C4—31no—
559C2×C22⋊C4—51no—
560C2×C22⋊C4—51no—
561C2×C22⋊C4—151no—
562C2×C22⋊C4—151no—
563C2×C22⋊C4—151no—
564C2×C22⋊C4—151no—
565C2×C22⋊C4—151no—
566C2×C42—51no—
567C2×C42—51no—
568C2×C42—151no—
569C2×C42—151no—
570C2×C42—151no—
571C2×C42—151no—
572C2×C42—304no—
573#95—31no—
574#95—51no—
575#95—151no—
576#95—151no—
577#95—151no—
578#95—151no—
579#95—151no—
580#95D3×D511yescharacteristic
581C2×C3×C5C22×C22⋊C411yescharacteristic
582C2×C3×C5C4×#4111yescharacteristic
583C2×C3×C5C4×#4111yescharacteristic
584C2×C3×C5#52511yescharacteristic
585C2×C3×C5#52511yescharacteristic
586C2×C3×C5#53211yescharacteristic
587C2×C3×C5#53211yescharacteristic
588C3×D5—42no—
589C5×D3—24no—
590C5×D3—42no—
591C23×C3—52no—
592C23×C3—101no—
593C23×C3—101no—
594C23×C3—101no—
595C23×C3—101no—
596C23×C3—101no—
597C23×C3—101no—
598C23×C3C23×D511yescharacteristic
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3C2×C4×D512yes—
610C22×D3C2×C4×D512yes—
611C22×D3D4×D512yes—
612C22×D3D4×D512yes—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—52no—
621C2×C3×C4—52no—
622C2×C3×C4—52no—
623C2×C3×C4—52no—
624C2×C3×C4—108no—
625C2×C3×C4—101no—
626C2×C3×C4—101no—
627C2×C3×C4—101no—
628C2×C3×C4—101no—
629C2×C3×C4—101no—
630C2×C3×C4C2×C4×D512yes—
631C2×C3×C4#71112yescomplemented
632#67—108no—
633#67—108no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—52no—
640C2×Dic3—52no—
641C2×Dic3—52no—
642C2×Dic3—52no—
643C2×Dic3—52no—
644C2×Dic3—101no—
645C2×Dic3—101no—
646C2×Dic3—101no—
647C2×Dic3—101no—
648C2×Dic3—101no—
649C2×Dic3—101no—
650C2×Dic3—101no—
651C2×Dic3#71112yescomplemented
652D12—28no—
653C4×D3—28no—
654C4×D3—516no—
655C4×D3—108no—
656C4×D3—108no—
657Dic6—108no—
658C22×C5—34no—
659C22×C5—62no—
660C22×C5—62no—
661C22×C5—62no—
662C22×C5—62no—
663C22×C5—62no—
664C22×C5—62no—
665C22×C5—62no—
666C22×C5—62no—
667C22×C5—62no—
668C22×C5—121no—
669C22×C5—121no—
670C22×C5—121no—
671C22×C5—121no—
672C22×C5C22×C4×D311yescharacteristic
673C22×C5C2×#23511yescharacteristic
674C22×C5C2×#23511yescharacteristic
675C22×C5C2×D3×D411yescharacteristic
676C22×C5C2×D3×D411yescharacteristic
677C22×C5D3×#4111yescharacteristic
678C22×C5D3×#4111yescharacteristic
679C2×D5—22no—
680C2×D5—22no—
681C2×D5—22no—
682C2×D5—41no—
683C2×D5—41no—
684C2×D5—41no—
685C2×D5—41no—
686C4×C5—22no—
687C4×C5—22no—
688C4×C5—41no—
689C4×C5—62no—
690C4×C5—121no—
691Dic5—22no—
692Dic5—34no—
693Dic5—41no—
694Dic5—62no—
695Dic5—62no—
696Dic5—121no—
697Dic5D3×C22⋊C414yes—
698C24—31no—
699C24—31no—
700C24—51no—
701#41—3032no—
702C2×Q8—154no—
703C2×Q8—302no—
704C2×Q8—302no—
705C2×D4—34no—
706C2×D4—62no—
707C2×D4—62no—
708C2×D4—154no—
709C2×D4—154no—
710C2×D4—302no—
711C2×D4—302no—
712C2×D4—302no—
713C2×D4—302no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—51no—
717C22×C4—51no—
718C22×C4—54no—
719C22×C4—51no—
720C22×C4—62no—
721C22×C4—62no—
722C22×C4—62no—
723C22×C4—102no—
724C22×C4—102no—
725C22×C4—154no—
726C22×C4—154no—
727C22×C4—154no—
728C22×C4—154no—
729C22×C4—151no—
730C22×C4—151no—
731C22×C4—151no—
732C22×C4—151no—
733C22×C4—302no—
734C22×C4—302no—
735C22×C4—302no—
736C22×C4—302no—
737C22×C4—302no—
738C22×C4C2×D3×D511yescharacteristic
739C22×C4C2×D3×D511yescharacteristic
740C22×C4C2×D3×D511yescharacteristic
741C4⋊C4—302no—
742C4⋊C4—302no—
743C22⋊C4—62no—
744C22⋊C4—62no—
745C22⋊C4—62no—
746C22⋊C4—102no—
747C22⋊C4—102no—
748C22⋊C4—302no—
749C22⋊C4—302no—
750C22⋊C4—302no—
751C22⋊C4—302no—
752C22⋊C4—302no—
753C42—102no—
754C42—102no—
755C42—302no—
756C42—302no—
757C42—302no—
758C42—302no—
759C3×C5#229711yescharacteristic, complemented, Hall
760C22×C3—102no—
761C22×C3—102no—
762C22×C3—102no—
763C22×C3—201no—
764C22×C3—201no—
765C22×C3—201no—
766C22×C3—201no—
767C22×C3C22×C4×D511yescharacteristic
768C22×C3C2×D4×D511yescharacteristic
769C22×C3C2×D4×D511yescharacteristic
770C22×C3C2×#71111yescharacteristic
771C22×C3C2×#71111yescharacteristic
772C22×C3D5×#4111yescharacteristic
773C22×C3D5×#4111yescharacteristic
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—22no—
779C2×D3—22no—
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3D5×C22⋊C414yes—
788C3×C4—22no—
789C3×C4—22no—
790C3×C4—41no—
791C3×C4—54no—
792C3×C4—102no—
793C3×C4—201no—
794Dic3—22no—
795Dic3—41no—
796Dic3—54no—
797Dic3—102no—
798Dic3—102no—
799Dic3—201no—
800C2×C5—64no—
801C2×C5—122no—
802C2×C5C4×#23511yescharacteristic
803C2×C5C2×D3×C22⋊C411yescharacteristic
804C2×C5#552211yescharacteristic
805C2×C5#554711yescharacteristic
806C2×C5#554711yescharacteristic
807C2×C5#554811yescharacteristic
808C2×C5#554811yescharacteristic
809D5—42no—
810C23—32no—
811C23—32no—
812C23—32no—
813C23—32no—
814C23—52no—
815C23—61no—
816C23—61no—
817C23—61no—
818C23—61no—
819C23—61no—
820C23—61no—
821C23—61no—
822C23—61no—
823C23—61no—
824C23—61no—
825C23—101no—
826C23—101no—
827C23—101no—
828C23—101no—
829C23—101no—
830C23—101no—
831C23C22×D3×D511yescharacteristic
832Q8—308no—
833D4—68no—
834D4—308no—
835D4—308no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—32no—
844C2×C4—52no—
845C2×C4—52no—
846C2×C4—52no—
847C2×C4—52no—
848C2×C4—68no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—108no—
855C2×C4—101no—
856C2×C4—101no—
857C2×C4—101no—
858C2×C4—101no—
859C2×C4—101no—
860C2×C4—1516no—
861C2×C4—152no—
862C2×C4—152no—
863C2×C4—152no—
864C2×C4—152no—
865C2×C4—152no—
866C2×C4—308no—
867C2×C4—308no—
868C2×C4—301no—
869C2×C4—301no—
870C2×C4—301no—
871C2×C4—301no—
872C2×C4—301no—
873C2×C4—301no—
874C2×C4—301no—
875C2×C4#677212yescomplemented
876C2×C4C4×D3×D512yes—
877C2×C3—202no—
878C2×C3C2×D5×C22⋊C411yescharacteristic
879C2×C3C4×#71111yescharacteristic
880C2×C3C4×#71111yescharacteristic
881C2×C3#6592011yescharacteristic
882C2×C3#6593011yescharacteristic
883C2×C3#6593011yescharacteristic
884C2×C3#6599011yescharacteristic
885D3—24no—
886D3—42no—
887C5#7356311yescharacteristic, complemented, Sylow
888C22—34no—
889C22—62no—
890C22—62no—
891C22—62no—
892C22—62no—
893C22—62no—
894C22—62no—
895C22—62no—
896C22—62no—
897C22—62no—
898C22—102no—
899C22—102no—
900C22—102no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—201no—
906C22—201no—
907C22—201no—
908C22—201no—
909C22C2×#677211yescharacteristic
910C22C2×C4×D3×D511yescharacteristic
911C22D5×#23511yescharacteristic
912C22D3×D4×D511yescharacteristic
913C22D3×D4×D511yescharacteristic
914C22D3×#71111yescharacteristic
915C22#9203411yescharacteristic
916C4—22no—
917C4—22no—
918C4—41no—
919C4—54no—
920C4—62no—
921C4—102no—
922C4—121no—
923C4—154no—
924C4—201no—
925C4—302no—
926C4—302no—
927C4—601no—
928C3#1060638911yescharacteristic, complemented, Sylow
929C2—64no—
930C2—122no—
931C2—202no—
932C2C4×#677211yescharacteristic
933C2#1175284011yescharacteristic
934C2#1175284311yescharacteristic
935C2D3×D5×C22⋊C411yescharacteristic
936C2#1175340211yescharacteristic
937C2#1175368011yescharacteristic
938C2#1175386211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#6772C2
hypercenter#95D3×D5
hypocenterC3×C5#2297
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×#91398C2semidirect
3. C2×C4×D3×Dic5C2semidirect
4. #11750747C2semidirect
5. C5×#4665C2semidirect
6. C3×#64955C2semidirect
7. #11748916C2semidirect
8. #11748915C2semidirect
9. #11748911C2semidirect
10. #11748910C2semidirect
11. #11748901C2semidirect
12. Dic5×(C2×D3)⋊C4C2semidirect
13. Dic5×(C2×D3)⋊C4C2semidirect
14. #11748702C2semidirect
15. #11748694C2semidirect
28. C2×#6772C4semidirect
70. #64955D3semidirect
85. C2×Dic30C2×C4semidirect
99. C2×C3×C4×D5C2×C4semidirect
105. C2×#1201C2×C4semidirect
112. C2×D3×Dic5C2×C4semidirect
146. #4665D5semidirect
220. C2×C3×C4×C5#41semidirect
232. C2×Dic15#41semidirect
239. C2×C5×Dic3#41semidirect
250. C2×C3×Dic5#41semidirect
256. D3×Dic5C22⋊C4semidirect
336. C2×C4×D5C4×D3semidirect
512. C2×C4×C5#235semidirect
536. C2×Dic5#235semidirect
631. C2×C3×C4#711semidirect
651. C2×Dic3#711semidirect
759. C3×C5#2297semidirect
875. C2×C4#6772semidirect
887. C5#73563semidirect
928. C3#10606389semidirect

Maximal subgroups

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

subgroupindex
C22×#67722
C2×#913982
C2×C4×D3×Dic52
#117507472
C5×#46652
C3×#649552
#117489162
#117489152
#117489112
#117489102
#117489012
Dic5×(C2×D3)⋊C42
#117487022
#117486942
#106063893
#735635