Finite Group Databasebeta

← #14324394

Subgroups — #14324394

Order 1920.

1480 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91451C211yesmaximal, characteristic
2C2×C4×#1203C211yesmaximal, characteristic, complemented
3C2×#91405C211yesmaximal, characteristic, complemented
4#11750766C211yesmaximal, characteristic, complemented
5C5×#4665C211yesmaximal, characteristic, complemented
6C3×#64937C211yesmaximal, characteristic, complemented
7#11748919C211yesmaximal, characteristic, complemented
8#11748918C211yesmaximal, characteristic, complemented
9#11748914C211yesmaximal, characteristic, complemented
10#11748908C211yesmaximal, characteristic, complemented
11#11748908C211yesmaximal, characteristic, complemented
12#11748904C211yesmaximal, characteristic, complemented
13#11748901C211yesmaximal, characteristic, complemented
14#11748883C211yesmaximal, characteristic, complemented
15#11748580C211yesmaximal, characteristic, complemented
16#10606398—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C5×D12C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic
21C22×#1203C2211yescharacteristic
22C22×#1203C2211yescharacteristic
23C22×#1203C2211yescharacteristic
24C22×#1203C2211yescharacteristic
25C22×#1200C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C5×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34C2×C3×C4×Dic5C2211yescharacteristic
35C2×C3×C4×Dic5C2211yescharacteristic
36C2×#6668C2211yescharacteristic
37C2×#6668C2211yescharacteristic
38C2×#6667C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44#91451C418yescomplemented
45C4×#1203—24no—
46#91405—24no—
47C3×C5×#95C2211yescharacteristic
48#91115C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#73389—51nomaximal, Hall
56C2×#4086—31no—
57C2×C4×C22⋊D5—31no—
58C2×#4027—31no—
59C5×#386—31no—
60#65509—31no—
61#65502—31no—
62#65247—31no—
63#65246—31no—
64#65246—31no—
65#65245—31no—
66#65245—31no—
67#64954—31no—
68#64954—31no—
69#64939—31no—
70#64937D311yescharacteristic, complemented
71C23×D15C2311yescharacteristic
72C23×D15C2311yescharacteristic
73C23×C5×D3C2311yescharacteristic
74C23×C5×D3C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C2×D60—41no—
81C2×D60—41no—
82C2×D60C2×C414yescomplemented
83C2×C4×D15—22no—
84C2×C4×D15—41no—
85C2×C4×D15—41no—
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C2×C5×D12—41no—
89C2×C5×D12—41no—
90C2×C5×D12C2×C414yescomplemented
91C2×C4×C5×D3—22no—
92C2×C4×C5×D3—41no—
93C2×C4×C5×D3—41no—
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C2×#1203—22no—
99C2×#1203—22no—
100C2×#1203—22no—
101C2×#1203—22no—
102C2×#1203—41no—
103C2×#1203—41no—
104C2×#1203—41no—
105C2×#1203—41no—
106C2×#1203C2×C414yescomplemented
107C2×#1203C2×C414yescomplemented
108C2×#1203C2×C414yescomplemented
109C2×#1203C2×C414yescomplemented
110C2×#1200—22no—
111C2×#1200—41no—
112C2×#1200—41no—
113C2×D3×Dic5—22no—
114C2×D3×Dic5—41no—
115C2×D3×Dic5—41no—
116#6714—22no—
117#6714—41no—
118#6714—41no—
119C5×(C2×D3)⋊C4—22no—
120C5×(C2×D3)⋊C4—41no—
121C5×(C2×D3)⋊C4—41no—
122C3×C4×Dic5—22no—
123C3×C4×Dic5C2×C414yescomplemented
124C3×C4×Dic5D414yescomplemented
125#6668—22no—
126#6668—22no—
127#6667—22no—
128#6667—41no—
129#6667—41no—
130(C2×D3)⋊Dic5—22no—
131(C2×D3)⋊Dic5—41no—
132(C2×D3)⋊Dic5—41no—
133C2×#874—51no—
134C2×C4×D12—51no—
135C2×C4×D12—51no—
136C3×#376—51no—
137#4939—51no—
138#4939—51no—
139#4936—51no—
140#4665—51no—
141#4665—51no—
142#4665—51no—
143#4665—51no—
144#4665—51no—
145#4665—51no—
146#4665—51no—
147#4665D511yescharacteristic, complemented
148C22×C5×D4—31no—
149C23×C4×C5—31no—
150C22×C22⋊D5—31no—
151C22×C22⋊D5—31no—
152C22×C22⋊D5—31no—
153C22×C22⋊D5—31no—
154C23×Dic5—31no—
155C22×D20—31no—
156C22×C4×D5—31no—
157C22×C4×D5—31no—
158C2×C5×C22⋊C4—31no—
159C2×C5×C22⋊C4—31no—
160C2×C5×C22⋊C4—31no—
161C2×C22⋊Dic5—31no—
162C2×C22⋊Dic5—31no—
163C2×C22⋊Dic5—31no—
164#4086—38no—
165C4×C22⋊D5—64no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685—31no—
171C2×#685—31no—
172C2×#683—31no—
173C2×#683—31no—
174C2×C4×Dic5C2×D311yescharacteristic
175C2×C4×Dic5C2×D311yescharacteristic
176C2×C4×Dic5C2×D311yescharacteristic
177#4027—64no—
178C5×#95—31no—
179C5×#95C2×D311yescharacteristic
180#3963—31no—
181#3963—31no—
182#3963—31no—
183#3963C2×D311yescharacteristic
184#3963C2×D311yescharacteristic
185#3963C2×D311yescharacteristic
186#2328—151noSylow
187C23×C3×C5C2411yescharacteristic
188C22×D15—21no—
189C22×D15—21no—
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×C5×D3—21no—
203C22×C5×D3—21no—
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—21no—
207C22×C5×D3—21no—
208C22×C5×D3—21no—
209C22×C5×D3—21no—
210C22×C5×D3—21no—
211C22×C5×D3—21no—
212C22×C5×D3—21no—
213C22×C5×D3—21no—
214C22×C5×D3C22×C412yes—
215C22×C5×D3C22×C412yes—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5C22×C412yes—
224C2×C3×C4×C5C2×D412yes—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231D60—44no—
232C4×D15—44no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C5×D12—44no—
240C4×C5×D3—44no—
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×Dic5—21no—
248C2×C3×Dic5C22×C412yes—
249C2×C3×Dic5C22×C412yes—
250C2×C3×Dic5C2×D412yes—
251C2×C3×Dic5C2×D412yes—
252C2×C3×Dic5#4112yes—
253#1203—28no—
254#1203—28no—
255#1203—44no—
256#1203—44no—
257#1200—44no—
258D3×Dic5—44no—
259C22×D12—51no—
260C22×D12—51no—
261C22×D12—51no—
262C22×D12—51no—
263C22×D12—51no—
264C22×D12C2×D511yescharacteristic
265C22×C4×D3—51no—
266C22×C4×D3—51no—
267C22×C4×D3—51no—
268C22×C4×D3C2×D511yescharacteristic
269C2×C3×C42—51no—
270C2×C3×C42—51no—
271C2×C3×C42—51no—
272C2×(C2×D3)⋊C4—51no—
273C2×(C2×D3)⋊C4—51no—
274C2×(C2×D3)⋊C4—51no—
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4C2×D511yescharacteristic
282C2×(C2×D3)⋊C4C2×D511yescharacteristic
283C2×(C2×D3)⋊C4C2×D511yescharacteristic
284C2×C4⋊Dic3—51no—
285C2×C4⋊Dic3—51no—
286#874—58no—
287C4×D12—104no—
288C4×D12—104no—
289C3×#95—51no—
290C3×#95—51no—
291C3×#95—51no—
292C3×#95C2×D511yescharacteristic
293C3⋊#95—51no—
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95C2×D511yescharacteristic
297C24×C5—31no—
298C24×C5—31no—
299C23×D5—31no—
300C23×D5—31no—
301C2×C5×D4—34no—
302C2×C5×D4—121no—
303C2×C5×D4—121no—
304C22×C4×C5—31no—
305C22×C4×C5—31no—
306C22×C4×C5—62no—
307C22×C4×C5—121no—
308C22×C4×C5—121no—
309C22×C4×C5C22×D311yescharacteristic
310C22×C4×C5C22×D311yescharacteristic
311C22×C4×C5C22×D311yescharacteristic
312C2×C22⋊D5—34no—
313C2×C22⋊D5—34no—
314C2×C22⋊D5—34no—
315C2×C22⋊D5—34no—
316C2×C22⋊D5—62no—
317C2×C22⋊D5—62no—
318C2×C22⋊D5—62no—
319C2×C22⋊D5—62no—
320C2×C22⋊D5—121no—
321C2×C22⋊D5—121no—
322C2×C22⋊D5—121no—
323C2×C22⋊D5—121no—
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—62no—
327C22×Dic5—121no—
328C22×Dic5—121no—
329C22×Dic5C22×D311yescharacteristic
330C22×Dic5C22×D311yescharacteristic
331C22×Dic5C22×D311yescharacteristic
332C22×Dic5C22×D311yescharacteristic
333C2×D20—34no—
334C2×D20—121no—
335C2×D20—121no—
336C2×C4×D5—62no—
337C2×C4×D5—62no—
338C2×C4×D5—121no—
339C2×C4×D5—121no—
340C2×C4×D5—121no—
341C2×C4×D5—121no—
342C5×C22⋊C4—62no—
343C5×C22⋊C4—121no—
344C5×C22⋊C4—121no—
345C22⋊Dic5—62no—
346C22⋊Dic5—121no—
347C22⋊Dic5—121no—
348#685—62no—
349#685—62no—
350#685—121no—
351#685—121no—
352#685—121no—
353#685—121no—
354#683—62no—
355#683—62no—
356C4×Dic5—22no—
357C4×Dic5C4×D314yescomplemented
358C4×Dic5D1214yescomplemented
359C2×#127—151no—
360C2×C4×D4—151no—
361C2×C4×D4—151no—
362#390—151no—
363#390—151no—
364#386—31no—
365#386—151no—
366#386—151no—
367#386—151no—
368#386—151no—
369#386—151no—
370#386—151no—
371#386—151no—
372#382—151no—
373#376—51no—
374C22×C3×C5C23×C411yescharacteristic
375C22×C3×C5C22×D411yescharacteristic
376C22×C3×C5C2×#4111yescharacteristic
377C22×C3×C5H(5,𝔽2)11yescharacteristic
378C22×C3×C5H(5,𝔽2)11yescharacteristic
379C22×C3×C5H(5,𝔽2)11yescharacteristic
380C22×C3×C5H(5,𝔽2)11yescharacteristic
381C2×D15—22no—
382C2×D15—22no—
383C2×D15—22no—
384C2×D15—22no—
385C2×D15—22no—
386C2×D15—22no—
387C2×D15—41no—
388C2×D15—41no—
389C2×D15—41no—
390C2×D15—41no—
391C2×D15—41no—
392C2×D15—41no—
393C2×D15—41no—
394C2×D15—41no—
395C2×C5×D3—22no—
396C2×C5×D3—22no—
397C2×C5×D3—22no—
398C2×C5×D3—22no—
399C2×C5×D3—22no—
400C2×C5×D3—22no—
401C2×C5×D3—41no—
402C2×C5×D3—41no—
403C2×C5×D3—41no—
404C2×C5×D3—41no—
405C2×C5×D3—41no—
406C2×C5×D3—41no—
407C2×C5×D3—41no—
408C2×C5×D3—41no—
409C3×C4×C5—22no—
410C3×C4×C5—22no—
411C3×C4×C5—41no—
412Dic15—41no—
413Dic15—41no—
414C3×Dic5—22no—
415C3×Dic5—22no—
416C3×Dic5—41no—
417C3×Dic5C4×D414yes—
418C5×Dic3—41no—
419C5×Dic3—41no—
420C23×D3—51no—
421C23×D3—51no—
422C23×D3C22×D511yescharacteristic
423C23×D3C22×D511yescharacteristic
424C22×C3×C4—51no—
425C22×C3×C4—51no—
426C22×C3×C4—51no—
427C22×C3×C4—51no—
428C22×C3×C4C22×D511yescharacteristic
429C22×C3×C4C22×D511yescharacteristic
430C22×C3×C4C22×D511yescharacteristic
431C22×Dic3—51no—
432C22×Dic3—51no—
433C22×Dic3C22×D511yescharacteristic
434C22×Dic3C22×D511yescharacteristic
435C2×D12—41no—
436C2×D12—41no—
437C2×D12—54no—
438C2×D12—54no—
439C2×D12—54no—
440C2×D12—54no—
441C2×D12—54no—
442C2×D12—102no—
443C2×D12—102no—
444C2×D12—102no—
445C2×D12—102no—
446C2×D12—201no—
447C2×D12—201no—
448C2×D12—201no—
449C2×D12—201no—
450C2×D12—201no—
451C2×D12—201no—
452C2×D12C4×D514yescomplemented
453C2×C4×D3—22no—
454C2×C4×D3—41no—
455C2×C4×D3—41no—
456C2×C4×D3—102no—
457C2×C4×D3—102no—
458C2×C4×D3—102no—
459C2×C4×D3—201no—
460C2×C4×D3—201no—
461C2×C4×D3—201no—
462C2×C4×D3—201no—
463C2×C4×D3—201no—
464C2×C4×D3—201no—
465C3×C42—54no—
466C3×C42—54no—
467C3×C42—102no—
468(C2×D3)⋊C4—22no—
469(C2×D3)⋊C4—41no—
470(C2×D3)⋊C4—41no—
471(C2×D3)⋊C4—102no—
472(C2×D3)⋊C4—102no—
473(C2×D3)⋊C4—102no—
474(C2×D3)⋊C4—201no—
475(C2×D3)⋊C4—201no—
476(C2×D3)⋊C4—201no—
477(C2×D3)⋊C4—201no—
478(C2×D3)⋊C4—201no—
479(C2×D3)⋊C4—201no—
480C4⋊Dic3—102no—
481C4⋊Dic3—102no—
482C23×C5—32no—
483C23×C5—32no—
484C23×C5—61no—
485C23×C5—61no—
486C23×C5—61no—
487C23×C5—61no—
488C23×C5—61no—
489C23×C5—61no—
490C23×C5—61no—
491C23×C5—61no—
492C23×C5—61no—
493C23×C5—61no—
494C23×C5—61no—
495C23×C5—61no—
496C23×C5C23×D311yescharacteristic
497C22×D5—32no—
498C22×D5—32no—
499C22×D5—61no—
500C22×D5—61no—
501C22×D5—61no—
502C22×D5—61no—
503C22×D5—61no—
504C22×D5—61no—
505C22×D5—61no—
506C22×D5—61no—
507C22×D5—61no—
508C22×D5—61no—
509C22×D5—61no—
510C22×D5—61no—
511C5×D4—124no—
512C2×C4×C5—21no—
513C2×C4×C5—21no—
514C2×C4×C5—21no—
515C2×C4×C5—21no—
516C2×C4×C5—21no—
517C2×C4×C5—21no—
518C2×C4×C5—21no—
519C2×C4×C5—61no—
520C2×C4×C5—61no—
521C2×C4×C5—61no—
522C2×C4×C5—61no—
523C2×C4×C5—61no—
524C2×C4×C5—61no—
525C2×C4×C5—124no—
526C2×C4×C5C2×C4×D312yes—
527C2×C4×C5C2×D1212yes—
528C22⋊D5—68no—
529C22⋊D5—68no—
530C22⋊D5—124no—
531C22⋊D5—124no—
532C2×Dic5—21no—
533C2×Dic5—21no—
534C2×Dic5—21no—
535C2×Dic5—21no—
536C2×Dic5—21no—
537C2×Dic5—21no—
538C2×Dic5—21no—
539C2×Dic5—61no—
540C2×Dic5—61no—
541C2×Dic5—61no—
542C2×Dic5—61no—
543C2×Dic5—61no—
544C2×Dic5—61no—
545C2×Dic5—124no—
546C2×Dic5C2×C4×D312yes—
547C2×Dic5C2×C4×D312yes—
548C2×Dic5C2×D1212yes—
549C2×Dic5C2×D1212yes—
550C2×Dic5#23512yes—
551D20—124no—
552C4×D5—124no—
553C4×D5—124no—
554C22×D4—31no—
555C22×D4—151no—
556C22×D4—151no—
557C22×D4—151no—
558C22×D4—151no—
559C22×D4—151no—
560C23×C4—31no—
561C23×C4—151no—
562C23×C4—151no—
563C23×C4—151no—
564#127—158no—
565C4×D4—304no—
566C4×D4—304no—
567C2×C4⋊C4—151no—
568C2×C4⋊C4—151no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—31no—
572C2×C22⋊C4—151no—
573C2×C22⋊C4—151no—
574C2×C22⋊C4—151no—
575C2×C22⋊C4—151no—
576C2×C22⋊C4—151no—
577C2×C22⋊C4—151no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C42—51no—
582C2×C42—51no—
583C2×C42—51no—
584#95—31no—
585#95—51no—
586#95—51no—
587#95—51no—
588#95—151no—
589#95—151no—
590#95—151no—
591#95D3×D511yescharacteristic
592C2×C3×C5C2×C4×D411yescharacteristic
593C2×C3×C5#51811yescharacteristic
594C2×C3×C5#51811yescharacteristic
595C2×C3×C5#53511yescharacteristic
596C2×C3×C5#53511yescharacteristic
597C2×C3×C5#54011yescharacteristic
598C2×C3×C5#54011yescharacteristic
599D15—42no—
600D15—42no—
601C5×D3—42no—
602C5×D3—42no—
603C23×C3C23×D511yescharacteristic
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—21no—
615C22×D3—21no—
616C22×D3—52no—
617C22×D3—52no—
618C22×D3—101no—
619C22×D3—101no—
620C22×D3—101no—
621C22×D3—101no—
622C22×D3—101no—
623C22×D3—101no—
624C22×D3—101no—
625C22×D3—101no—
626C22×D3—101no—
627C22×D3—101no—
628C22×D3—101no—
629C22×D3—101no—
630C22×D3C2×C4×D512yes—
631C22×D3C2×C4×D512yes—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—52no—
640C2×C3×C4—52no—
641C2×C3×C4—52no—
642C2×C3×C4—52no—
643C2×C3×C4—52no—
644C2×C3×C4—101no—
645C2×C3×C4—101no—
646C2×C3×C4—101no—
647C2×C3×C4—101no—
648C2×C3×C4—101no—
649C2×C3×C4—101no—
650C2×C3×C4—101no—
651C2×C3×C4C2×C4×D512yes—
652C2×C3×C4D4×D512yes—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—101no—
660C2×Dic3—101no—
661C2×Dic3—101no—
662C2×Dic3—101no—
663C2×Dic3—101no—
664C2×Dic3—101no—
665D12—44no—
666D12—108no—
667D12—108no—
668D12—204no—
669D12—204no—
670D12—204no—
671C4×D3—44no—
672C4×D3—204no—
673C4×D3—204no—
674C4×D3—204no—
675C22×C5—62no—
676C22×C5—62no—
677C22×C5—62no—
678C22×C5—62no—
679C22×C5—62no—
680C22×C5—62no—
681C22×C5—121no—
682C22×C5—121no—
683C22×C5—121no—
684C22×C5—121no—
685C22×C5—121no—
686C22×C5—121no—
687C22×C5—121no—
688C22×C5—121no—
689C22×C5C22×C4×D311yescharacteristic
690C22×C5C22×D1211yescharacteristic
691C22×C5C2×#23511yescharacteristic
692C22×C5#100911yescharacteristic
693C22×C5#100911yescharacteristic
694C22×C5#100911yescharacteristic
695C22×C5#100911yescharacteristic
696C2×D5—62no—
697C2×D5—62no—
698C2×D5—62no—
699C2×D5—62no—
700C2×D5—62no—
701C2×D5—62no—
702C2×D5—121no—
703C2×D5—121no—
704C2×D5—121no—
705C2×D5—121no—
706C2×D5—121no—
707C2×D5—121no—
708C2×D5—121no—
709C2×D5—121no—
710C4×C5—22no—
711C4×C5—22no—
712C4×C5—41no—
713C4×C5—121no—
714C4×C5—121no—
715Dic5—22no—
716Dic5—22no—
717Dic5—41no—
718Dic5—121no—
719Dic5—121no—
720Dic5C4×D1214yes—
721C24—31no—
722C24—31no—
723C24—151no—
724C24—151no—
725C2×D4—34no—
726C2×D4—121no—
727C2×D4—121no—
728C2×D4—154no—
729C2×D4—154no—
730C2×D4—154no—
731C2×D4—154no—
732C2×D4—154no—
733C2×D4—302no—
734C2×D4—302no—
735C2×D4—302no—
736C2×D4—302no—
737C2×D4—601no—
738C2×D4—601no—
739C2×D4—601no—
740C2×D4—601no—
741C2×D4—601no—
742C2×D4—601no—
743C22×C4—31no—
744C22×C4—31no—
745C22×C4—51no—
746C22×C4—51no—
747C22×C4—51no—
748C22×C4—51no—
749C22×C4—62no—
750C22×C4—121no—
751C22×C4—121no—
752C22×C4—151no—
753C22×C4—151no—
754C22×C4—302no—
755C22×C4—302no—
756C22×C4—302no—
757C22×C4—601no—
758C22×C4—601no—
759C22×C4—601no—
760C22×C4—601no—
761C22×C4—601no—
762C22×C4—601no—
763C22×C4C2×D3×D511yescharacteristic
764C22×C4C2×D3×D511yescharacteristic
765C22×C4C2×D3×D511yescharacteristic
766C4⋊C4—302no—
767C4⋊C4—302no—
768C22⋊C4—62no—
769C22⋊C4—121no—
770C22⋊C4—121no—
771C22⋊C4—302no—
772C22⋊C4—302no—
773C22⋊C4—302no—
774C22⋊C4—601no—
775C22⋊C4—601no—
776C22⋊C4—601no—
777C22⋊C4—601no—
778C22⋊C4—601no—
779C22⋊C4—601no—
780C42—54no—
781C42—54no—
782C42—102no—
783C3×C5#232811yescharacteristic, complemented, Hall
784C22×C3C22×C4×D511yescharacteristic
785C22×C3C2×D4×D511yescharacteristic
786C22×C3#414411yescharacteristic
787C22×C3#414411yescharacteristic
788C22×C3#414411yescharacteristic
789C22×C3D5×#4111yescharacteristic
790C22×C3#414911yescharacteristic
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—22no—
796C2×D3—22no—
797C2×D3—41no—
798C2×D3—41no—
799C2×D3—41no—
800C2×D3—41no—
801C2×D3—41no—
802C2×D3—41no—
803C2×D3—41no—
804C2×D3—41no—
805C2×D3—102no—
806C2×D3—102no—
807C2×D3—102no—
808C2×D3—102no—
809C2×D3—102no—
810C2×D3—102no—
811C2×D3—201no—
812C2×D3—201no—
813C2×D3—201no—
814C2×D3—201no—
815C2×D3—201no—
816C2×D3—201no—
817C2×D3—201no—
818C2×D3—201no—
819C3×C4—22no—
820C3×C4—22no—
821C3×C4—41no—
822C3×C4—54no—
823C3×C4—102no—
824C3×C4—102no—
825C3×C4—201no—
826Dic3—41no—
827Dic3—41no—
828Dic3—201no—
829Dic3—201no—
830C2×C5—122no—
831C2×C5—122no—
832C2×C5C2×C4×D1211yescharacteristic
833C2×C5#552111yescharacteristic
834C2×C5#552111yescharacteristic
835C2×C5#552511yescharacteristic
836C2×C5#552511yescharacteristic
837C2×C5#553511yescharacteristic
838C2×C5#553511yescharacteristic
839D5—122no—
840D5—122no—
841C23—32no—
842C23—32no—
843C23—61no—
844C23—61no—
845C23—61no—
846C23—61no—
847C23—61no—
848C23—61no—
849C23—61no—
850C23—61no—
851C23—61no—
852C23—61no—
853C23—61no—
854C23—61no—
855C23—152no—
856C23—152no—
857C23—301no—
858C23—301no—
859C23—301no—
860C23—301no—
861C23—301no—
862C23—301no—
863C23—301no—
864C23—301no—
865C23—301no—
866C23—301no—
867C23—301no—
868C23—301no—
869C23C22×D3×D511yescharacteristic
870D4—124no—
871D4—308no—
872D4—308no—
873D4—604no—
874D4—604no—
875D4—604no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—52no—
884C2×C4—52no—
885C2×C4—52no—
886C2×C4—52no—
887C2×C4—52no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—101no—
895C2×C4—101no—
896C2×C4—101no—
897C2×C4—101no—
898C2×C4—101no—
899C2×C4—101no—
900C2×C4—101no—
901C2×C4—124no—
902C2×C4—301no—
903C2×C4—301no—
904C2×C4—301no—
905C2×C4—301no—
906C2×C4—301no—
907C2×C4—301no—
908C2×C4—604no—
909C2×C4—604no—
910C2×C4—604no—
911C2×C4C4×D3×D512yes—
912C2×C4D5×D1212yes—
913C2×C3#6582011yescharacteristic
914C2×C3C4×D4×D511yescharacteristic
915C2×C3#6587911yescharacteristic
916C2×C3#6592611yescharacteristic
917C2×C3#6594111yescharacteristic
918C2×C3#6594911yescharacteristic
919C2×C3#6599711yescharacteristic
920D3—42no—
921D3—42no—
922D3—202no—
923D3—202no—
924C5#7338911yescharacteristic, complemented, Sylow
925C22—62no—
926C22—62no—
927C22—62no—
928C22—62no—
929C22—62no—
930C22—62no—
931C22—121no—
932C22—121no—
933C22—121no—
934C22—121no—
935C22—121no—
936C22—121no—
937C22—121no—
938C22—121no—
939C22—302no—
940C22—302no—
941C22—302no—
942C22—302no—
943C22—302no—
944C22—302no—
945C22—601no—
946C22—601no—
947C22—601no—
948C22—601no—
949C22—601no—
950C22—601no—
951C22—601no—
952C22—601no—
953C22C2×C4×D3×D511yescharacteristic
954C22C2×D5×D1211yescharacteristic
955C22D5×#23511yescharacteristic
956C22#9202711yescharacteristic
957C22#9202711yescharacteristic
958C22#9202711yescharacteristic
959C22#9203511yescharacteristic
960C4—22no—
961C4—22no—
962C4—41no—
963C4—54no—
964C4—102no—
965C4—102no—
966C4—121no—
967C4—121no—
968C4—201no—
969C4—601no—
970C4—601no—
971C3#1060639811yescharacteristic, complemented, Sylow
972C2—122no—
973C2—122no—
974C2—602no—
975C2—602no—
976C2C4×D5×D1211yescharacteristic
977C2#1175287311yescharacteristic
978C2#1175306711yescharacteristic
979C2#1175309711yescharacteristic
980C2#1175372711yescharacteristic
981C2#1175383711yescharacteristic
982C2#1175387511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91451C2
hypercenter#95D3×D5
hypocenterC3×C5#2328
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×C4×#1203C2semidirect
3. C2×#91405C2semidirect
4. #11750766C2semidirect
5. C5×#4665C2semidirect
6. C3×#64937C2semidirect
7. #11748919C2semidirect
8. #11748918C2semidirect
9. #11748914C2semidirect
10. #11748908C2semidirect
11. #11748908C2semidirect
12. #11748904C2semidirect
13. #11748901C2semidirect
14. #11748883C2semidirect
15. #11748580C2semidirect
44. #91451C4semidirect
70. #64937D3semidirect
82. C2×D60C2×C4semidirect
90. C2×C5×D12C2×C4semidirect
106. C2×#1203C2×C4semidirect
107. C2×#1203C2×C4semidirect
108. C2×#1203C2×C4semidirect
109. C2×#1203C2×C4semidirect
123. C3×C4×Dic5C2×C4semidirect
124. C3×C4×Dic5D4semidirect
147. #4665D5semidirect
357. C4×Dic5C4×D3semidirect
358. C4×Dic5D12semidirect
452. C2×D12C4×D5semidirect
783. C3×C5#2328semidirect
924. C5#73389semidirect
971. C3#10606398semidirect

Maximal subgroups

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

subgroupindex
C2×#914512
C2×C4×#12032
C2×#914052
#117507662
C5×#46652
C3×#649372
#117489192
#117489182
#117489142
#117489082
#117489042
#117489012
#117488832
#117485802
#106063983
#733895