Finite Group Databasebeta

← D3×#65697 #14413880

Subgroups — D3×#65697 #14413880

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#4023C211yesmaximal, characteristic
2#11752356C211yesmaximal, characteristic, complemented
3C3×#65697C211yesmaximal, characteristic, complemented
4D3×C22⋊#170C211yesmaximal, characteristic
5D3×C22⋊#170C211yesmaximal, characteristic
6#11751990C211yesmaximal, characteristic, complemented
7#11751989C211yesmaximal, characteristic, complemented
8D3×#4004C211yesmaximal, characteristic, complemented
9D3×#4002C211yesmaximal, characteristic, complemented
10D3×C4⋊#170C211yesmaximal, characteristic, complemented
11C4×D3×#170C211yesmaximal, characteristic, complemented
12#11751809C211yesmaximal, characteristic, complemented
13#11751799C211yesmaximal, characteristic, complemented
14#11751798C211yesmaximal, characteristic, complemented
15#11751772C211yesmaximal, characteristic, complemented
16C2×#65697—31nomaximal, Hall
17C22×D3×Dic5C2211yescharacteristic
18C2×D3×#170C2211yescharacteristic
19C2×D3×#170C2211yescharacteristic
20C2×D3×#170C2211yescharacteristic
21C2×D3×#170C2211yescharacteristic
22#91766C411yescharacteristic
23C5×D3×C22⋊C4C411yescharacteristic
24C3×#4023C2211yescharacteristic
25D3×C22⋊Dic5C411yescharacteristic
26#91532C411yescharacteristic
27#91528C2211yescharacteristic
28#91400C411yescharacteristic
29#91400C411yescharacteristic
30D3×#683C411yescharacteristic
31D3×#683C411yescharacteristic
32#91398C2211yescharacteristic
33#91398C2211yescharacteristic
34C4×D3×Dic5C2211yescharacteristic
35C4×D3×Dic5C2211yescharacteristic
36#91241C2211yescharacteristic
37#91241C2211yescharacteristic
38#91233C2211yescharacteristic, complemented
39#91231C2211yescharacteristic, complemented
40C4⋊(C3⋊#170)C2211yescharacteristic, complemented
41C4×C3⋊#170C2211yescharacteristic, complemented
42C3×C22⋊#170C2211yescharacteristic
43C3×C22⋊#170C2211yescharacteristic
44C3×#4004C2211yescharacteristic, complemented
45C3×#4002C2211yescharacteristic, complemented
46C3×C4⋊#170C2211yescharacteristic, complemented
47C3×C4×#170C2211yescharacteristic, complemented
48#91177C2211yescharacteristic, complemented
49#91177C2211yescharacteristic, complemented
50Dic3⋊#170C2211yescharacteristic, complemented
51Dic3⋊#170C2211yescharacteristic, complemented
52(C2×D3)⋊#170C2211yescharacteristic
53(C2×D3)⋊#170C2211yescharacteristic
54(C2×D3)⋊#170C2211yescharacteristic
55(C2×D3)⋊#170C2211yescharacteristic
56#91169C2211yescharacteristic, complemented
57#91169C2211yescharacteristic, complemented
58Dic3×#170C2211yescharacteristic, complemented
59Dic3×#170C2211yescharacteristic, complemented
60D3×#433—51nomaximal, Hall
61C2×#4023—31no—
62C2×C22⋊#170—31no—
63C2×C22⋊#170—31no—
64C2×#4004—31no—
65C2×#4002—31no—
66C2×C4⋊#170—31no—
67C2×C4×#170—31no—
68#65697—31no—
69#65697—31no—
70#65697—31no—
71#65697—31no—
72#65697—31no—
73#65697—31no—
74#65697—31no—
75#65697D311yescharacteristic, direct product factor
76C23×C5×D3C2×C411yescharacteristic
77C22×Dic15C2×C411yescharacteristic
78C2×C4×C5×D3C2×C411yescharacteristic
79C2×C4×C5×D3C2×C411yescharacteristic
80C22×C3×Dic5C2311yescharacteristic
81C2×D3×Dic5—22no—
82C2×D3×Dic5—22no—
83C2×D3×Dic5C2×C411yescharacteristic
84C2×D3×Dic5C2×C411yescharacteristic
85C2×D3×Dic5C2×C411yescharacteristic
86C2×D3×Dic5C2×C411yescharacteristic
87C2×D3×Dic5C2311yescharacteristic
88C2×D3×Dic5C2311yescharacteristic
89C2×C3⋊#170C2311yescharacteristic
90C2×C3⋊#170C2311yescharacteristic
91C2×C3⋊#170C2311yescharacteristic
92C2×C3⋊#170C2311yescharacteristic
93C2×C3×#170C2311yescharacteristic
94C2×C3×#170C2311yescharacteristic
95C2×C3×#170C2311yescharacteristic
96C2×C3×#170C2311yescharacteristic
97D3×#170—22no—
98D3×#170—22no—
99D3×#170—22no—
100D3×#170—22no—
101C3×C5×C22⋊C4C2×C411yescharacteristic
102#6719C2×C411yescharacteristic
103#6712C2×C411yescharacteristic
104#6712C2×C411yescharacteristic
105C4×Dic15C2×C411yescharacteristic
106C4×Dic15C2×C411yescharacteristic
107C5×#217C2×C411yescharacteristic
108C5×(C2×D3)⋊C4C2×C411yescharacteristic
109C5×(C2×D3)⋊C4C2×C411yescharacteristic
110C3×C22⋊Dic5C2×C411yescharacteristic
111C3×#683C2×C411yescharacteristic
112C3×#683C2×C411yescharacteristic
113C3×C4×Dic5C2311yescharacteristic
114C3×C4×Dic5C2311yescharacteristic
115#6669C2×C411yescharacteristic
116#6669C2×C411yescharacteristic
117#6668C2×C411yescharacteristic
118#6668C2×C411yescharacteristic
119(C2×D3)⋊Dic5C2×C411yescharacteristic
120(C2×D3)⋊Dic5C2×C411yescharacteristic
121Dic3×Dic5C2×C411yescharacteristic
122Dic3×Dic5C2×C411yescharacteristic
123Dic3×Dic5C2311yescharacteristic
124Dic3×Dic5C2311yescharacteristic
125D3×#117—51no—
126C3×#433—51no—
127#5000—51no—
128#4840—51no—
129#4840—51no—
130D3×C4⋊C8—51no—
131D3×C4⋊C8—51no—
132D3×C22⋊C8—51no—
133D3×C22⋊C8—51no—
134#4720—51no—
135#4720—51no—
136#4709—51no—
137D3×#97—51no—
138#4690—51no—
139C4×D3×C8—51no—
140C23×Dic5—31no—
141C22×#170—31no—
142C22×#170—31no—
143C22×#170—31no—
144C22×#170—31no—
145C2×C5×C22⋊C4—31no—
146C2×C22⋊Dic5—31no—
147C2×#683—31no—
148C2×#683—31no—
149C2×C4×Dic5—31no—
150C2×C4×Dic5—31no—
151#4023—31no—
152#4023—31no—
153#4023—31no—
154#4023—31no—
155#4023—31no—
156#4023—31no—
157#4023—31no—
158#4023C2×D311yescharacteristic
159C22⋊#170—31no—
160C22⋊#170—31no—
161C22⋊#170—31no—
162C22⋊#170—31no—
163C22⋊#170—31no—
164C22⋊#170—31no—
165C22⋊#170C2×D311yescharacteristic
166C22⋊#170C2×D311yescharacteristic
167#4004—31no—
168#4004—31no—
169#4004—31no—
170#4004C2×D311yescharacteristic, complemented
171#4002—31no—
172#4002—31no—
173#4002—31no—
174#4002C2×D311yescharacteristic, complemented
175C4⋊#170—31no—
176C4⋊#170—31no—
177C4⋊#170—31no—
178C4⋊#170C2×D311yescharacteristic, complemented
179C4×#170—31no—
180C4×#170—31no—
181C4×#170—31no—
182C4×#170C2×D311yescharacteristic, complemented
183C2×#433—151noSylow
184C23×C3×C5C22×C411yescharacteristic
185C22×C5×D3—22no—
186C22×C5×D3—22no—
187C22×C5×D3—22no—
188C22×C5×D3C22×C411yescharacteristic
189C22×C5×D3C22×C411yescharacteristic
190C2×C3×C4×C5C22×C411yescharacteristic
191C2×C3×C4×C5C22×C411yescharacteristic
192C2×Dic15—22no—
193C2×Dic15C22×C411yescharacteristic
194C2×Dic15C22×C411yescharacteristic
195C2×Dic15C22×C411yescharacteristic
196C2×Dic15C22×C411yescharacteristic
197C2×C5×Dic3C22×C411yescharacteristic
198C2×C5×Dic3C22×C411yescharacteristic
199C4×C5×D3—22no—
200C4×C5×D3—22no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5C22×C411yescharacteristic
204C2×C3×Dic5C22×C411yescharacteristic
205C2×C3×Dic5C22×C411yescharacteristic
206C2×C3×Dic5C2411yescharacteristic
207D3×Dic5—22no—
208D3×Dic5—22no—
209D3×Dic5—22no—
210D3×Dic5—22no—
211D3×Dic5—21no—
212D3×Dic5—21no—
213D3×Dic5#4112yes—
214D3×Dic5#4112yes—
215C3⋊#170—21no—
216C3⋊#170—21no—
217C3⋊#170—21no—
218C3⋊#170—21no—
219C3×#170—21no—
220C3×#170—21no—
221C3×#170—21no—
222C3×#170—21no—
223C22×C4×D3—51no—
224C3×#117—51no—
225#926—51no—
226C2×D3×C8—51no—
227C2×D3×C8—51no—
228C2×D3×C8—51no—
229C2×D3×C8—51no—
230#892—51no—
231#892—51no—
232D3×C4⋊C4—51no—
233D3×C4⋊C4—51no—
234D3×C22⋊C4—51no—
235D3×C22⋊C4AGL(1,𝔽5)11yescharacteristic
236#877—51no—
237#877—51no—
238#872—51no—
239#872—51no—
240C42×D3—51no—
241C42×D3—51no—
242C3×C4⋊C8—51no—
243C3×C4⋊C8—51no—
244C3×C22⋊C8—51no—
245C3×C22⋊C8—51no—
246C3×#97—51no—
247C3×C4×C8—51no—
248#830—51no—
249#830—51no—
250(C2×D3)⋊C8—51no—
251(C2×D3)⋊C8—51no—
252(C2×D3)⋊C8—51no—
253(C2×D3)⋊C8—51no—
254#815—51no—
255#815—51no—
256Dic3⋊C8—51no—
257Dic3⋊C8—51no—
258Dic3⋊C8—51no—
259Dic3⋊C8—51no—
260C8×Dic3—51no—
261C8×Dic3—51no—
262C4⋊(C3⋊C8)—51no—
263C4⋊(C3⋊C8)—51no—
264#803—51no—
265C4×C3⋊C8—51no—
266C24×C5—31no—
267C22×C4×C5—31no—
268C22×C4×C5—31no—
269C22×Dic5—31no—
270C22×Dic5—31no—
271C22×Dic5—31no—
272C22×Dic5—31no—
273C22×Dic5—31no—
274C22×Dic5—31no—
275C22×Dic5—31no—
276C22×Dic5—62no—
277C22×Dic5—62no—
278C22×Dic5C22×D311yescharacteristic
279C2×#170—31no—
280C2×#170—31no—
281C2×#170—31no—
282C2×#170—31no—
283C2×#170—62no—
284C2×#170—62no—
285C2×#170—62no—
286C2×#170—62no—
287C2×#170C22×D311yescharacteristic
288C2×#170C22×D311yescharacteristic
289C2×#170C22×D311yescharacteristic
290C2×#170C22×D311yescharacteristic
291C5×C22⋊C4—31no—
292C5×C22⋊C4—31no—
293C5×C22⋊C4—31no—
294C5×C22⋊C4C4×D311yescharacteristic
295C22⋊Dic5—31no—
296C22⋊Dic5—31no—
297C22⋊Dic5—31no—
298C22⋊Dic5C4×D311yescharacteristic
299#683—31no—
300#683—31no—
301#683—31no—
302#683—31no—
303#683—31no—
304#683—31no—
305#683C4×D311yescharacteristic
306#683C4×D311yescharacteristic
307C4×Dic5—31no—
308C4×Dic5—31no—
309C4×Dic5—31no—
310C4×Dic5—31no—
311C4×Dic5—31no—
312C4×Dic5—31no—
313C4×Dic5C22×D311yescharacteristic
314C4×Dic5C22×D311yescharacteristic
315C2×#117—151no—
316#433—51no—
317#433—151no—
318#433—151no—
319#433—151no—
320#433—151no—
321#433—151no—
322#433—151no—
323#433—151no—
324C2×C4⋊C8—151no—
325C2×C4⋊C8—151no—
326C2×C22⋊C8—151no—
327C2×C22⋊C8—151no—
328C2×#97—151no—
329C2×C4×C8—151no—
330C22×C3×C5—21no—
331C22×C3×C5—21no—
332C22×C3×C5—21no—
333C22×C3×C5C23×C411yescharacteristic
334C2×C5×D3—21no—
335C2×C5×D3—21no—
336C2×C5×D3—21no—
337C2×C5×D3—44no—
338C2×C5×D3#11712yes—
339C2×C5×D3#13112yes—
340C2×C5×D3#13112yes—
341C3×C4×C5—21no—
342C3×C4×C5—21no—
343Dic15—21no—
344Dic15—21no—
345Dic15—21no—
346Dic15#11712yes—
347C3×Dic5—21no—
348C3×Dic5—21no—
349C3×Dic5—21no—
350C3×Dic5C2×#4111yescharacteristic
351C3×Dic5C2×#4111yescharacteristic
352C5×Dic3—21no—
353C5×Dic3—21no—
354C23×D3C2×AGL(1,𝔽5)11yescharacteristic
355C22×C3×C4—51no—
356C22×Dic3—51no—
357C2×C4×D3—51no—
358C2×C4×D3—51no—
359C2×C4×D3—51no—
360C2×C4×D3—51no—
361C2×C4×D3—51no—
362C2×C4×D3—51no—
363C2×C4×D3—102no—
364C2×C4×D3—102no—
365C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
366C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
367C2×C3×C8—51no—
368C2×C3×C8—51no—
369C2×C3×C8—51no—
370C2×C3×C8—51no—
371C3×C4⋊C4—51no—
372C3×C4⋊C4—51no—
373C3×C22⋊C4—51no—
374C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
375C3×C42—51no—
376C3×C42—51no—
377#217—51no—
378#217C2×AGL(1,𝔽5)11yescharacteristic
379(C2×D3)⋊C4—51no—
380(C2×D3)⋊C4—51no—
381(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
382(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
383C4⋊Dic3—51no—
384C4⋊Dic3—51no—
385Dic3⋊C4—51no—
386Dic3⋊C4—51no—
387Dic3⋊C4—51no—
388Dic3⋊C4—51no—
389C4×Dic3—51no—
390C4×Dic3—51no—
391C4×Dic3—51no—
392C4×Dic3—51no—
393C4×Dic3—51no—
394C4×Dic3—51no—
395C2×C3⋊C8—51no—
396C2×C3⋊C8—51no—
397C2×C3⋊C8—51no—
398C2×C3⋊C8—51no—
399D3×C8—102no—
400D3×C8—102no—
401D3×C8—102no—
402D3×C8—102no—
403C23×C5—31no—
404C23×C5—31no—
405C23×C5—62no—
406C23×C5—62no—
407C23×C5—62no—
408C23×C5C2×C4×D311yescharacteristic
409C2×C4×C5—31no—
410C2×C4×C5—31no—
411C2×C4×C5—62no—
412C2×C4×C5—62no—
413C2×C4×C5C2×C4×D311yescharacteristic
414C2×C4×C5C2×C4×D311yescharacteristic
415C2×Dic5—21no—
416C2×Dic5—21no—
417C2×Dic5—31no—
418C2×Dic5—32no—
419C2×Dic5—32no—
420C2×Dic5—31no—
421C2×Dic5—31no—
422C2×Dic5—31no—
423C2×Dic5—62no—
424C2×Dic5—62no—
425C2×Dic5—62no—
426C2×Dic5—62no—
427C2×Dic5—62no—
428C2×Dic5—61no—
429C2×Dic5—61no—
430C2×Dic5C2×C4×D311yescharacteristic
431C2×Dic5C2×C4×D311yescharacteristic
432C2×Dic5C2×C4×D311yescharacteristic
433C2×Dic5C23×D311yescharacteristic
434#170—21no—
435#170—21no—
436#170—21no—
437#170—21no—
438#170—61no—
439#170—61no—
440#170—61no—
441#170—61no—
442C23×C4—151no—
443C22×C8—151no—
444C22×C8—151no—
445C22×C8—151no—
446C22×C8—151no—
447#117—51no—
448#117—151no—
449#117—151no—
450#117—151no—
451#117—151no—
452#117—151no—
453#117—151no—
454#117—151no—
455C2×C4⋊C4—151no—
456C2×C4⋊C4—151no—
457C2×C22⋊C4—31no—
458C2×C22⋊C4—151no—
459C2×C42—151no—
460C2×C42—151no—
461C4⋊C8—51no—
462C4⋊C8—51no—
463C4⋊C8—151no—
464C4⋊C8—151no—
465C4⋊C8—151no—
466C4⋊C8—151no—
467C4⋊C8—151no—
468C4⋊C8—151no—
469C22⋊C8—51no—
470C22⋊C8—51no—
471C22⋊C8—151no—
472C22⋊C8—151no—
473C22⋊C8—151no—
474C22⋊C8—151no—
475C22⋊C8—151no—
476C22⋊C8—151no—
477#97—51no—
478#97—151no—
479#97—151no—
480#97—151no—
481C4×C8—51no—
482C4×C8—151no—
483C4×C8—151no—
484C4×C8—151no—
485C2×C3×C5—41no—
486C2×C3×C5C2×#11711yescharacteristic
487C2×C3×C5C2×#13111yescharacteristic
488C2×C3×C5C2×#13111yescharacteristic
489C5×D3—41no—
490C5×D3#43314yescomplemented
491C23×C3C22×AGL(1,𝔽5)11yescharacteristic
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3C22×AGL(1,𝔽5)11yescharacteristic
496C22×D3C22×AGL(1,𝔽5)11yescharacteristic
497C2×C3×C4—51no—
498C2×C3×C4—51no—
499C2×C3×C4—51no—
500C2×C3×C4—51no—
501C2×C3×C4—101no—
502C2×C3×C4—101no—
503C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
504C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
505C2×Dic3—51no—
506C2×Dic3—51no—
507C2×Dic3—51no—
508C2×Dic3—51no—
509C2×Dic3—102no—
510C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
511C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
512C4×D3—22no—
513C4×D3—22no—
514C4×D3—52no—
515C4×D3—52no—
516C4×D3—102no—
517C4×D3—101no—
518C4×D3—101no—
519C4×D3—102no—
520C4×D3—102no—
521C4×D3—102no—
522C3×C8—101no—
523C3×C8—101no—
524C3×C8—101no—
525C3×C8—101no—
526C3⋊C8—101no—
527C3⋊C8—101no—
528C3⋊C8—101no—
529C3⋊C8—101no—
530C22×C5—21no—
531C22×C5—21no—
532C22×C5—21no—
533C22×C5—32no—
534C22×C5—32no—
535C22×C5—32no—
536C22×C5—61no—
537C22×C5—61no—
538C22×C5—61no—
539C22×C5—124no—
540C22×C5C22×C4×D311yescharacteristic
541C4×C5—21no—
542C4×C5—21no—
543C4×C5—61no—
544C4×C5—61no—
545Dic5—21no—
546Dic5—21no—
547Dic5—21no—
548Dic5—32no—
549Dic5—61no—
550Dic5—61no—
551Dic5—61no—
552Dic5D3×#4111yescharacteristic
553Dic5D3×#4111yescharacteristic
554C24—31no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—51no—
558C22×C4—151no—
559C22×C4—151no—
560C22×C4—151no—
561C22×C4—151no—
562C22×C4—151no—
563C22×C4—151no—
564C22×C4—151no—
565C22×C4—302no—
566C22×C4—302no—
567C2×C8—51no—
568C2×C8—51no—
569C2×C8—51no—
570C2×C8—51no—
571C2×C8—151no—
572C2×C8—151no—
573C2×C8—151no—
574C2×C8—151no—
575C2×C8—302no—
576C2×C8—302no—
577C2×C8—302no—
578C2×C8—302no—
579C4⋊C4—51no—
580C4⋊C4—51no—
581C4⋊C4—151no—
582C4⋊C4—151no—
583C4⋊C4—151no—
584C4⋊C4—151no—
585C4⋊C4—151no—
586C4⋊C4—151no—
587C22⋊C4—31no—
588C22⋊C4—31no—
589C22⋊C4—31no—
590C22⋊C4—51no—
591C22⋊C4—151no—
592C22⋊C4—151no—
593C22⋊C4—151no—
594C22⋊C4D3×AGL(1,𝔽5)11yescharacteristic
595C42—51no—
596C42—51no—
597C42—151no—
598C42—151no—
599C42—151no—
600C42—151no—
601C42—151no—
602C42—151no—
603C3×C5C2×#43311yescharacteristic, complemented, Hall
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3C23×AGL(1,𝔽5)11yescharacteristic
608C2×D3—21no—
609C2×D3—21no—
610C2×D3—21no—
611C2×D3—44no—
612C2×D3#413012yes—
613C2×D3#413112yes—
614C2×D3#413112yes—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—51no—
618C3×C4—51no—
619C3×C4—101no—
620C3×C4—101no—
621C3×C4—101no—
622Dic3—21no—
623Dic3—21no—
624Dic3—52no—
625Dic3—101no—
626Dic3—101no—
627Dic3—101no—
628C2×C5—34no—
629C2×C5—41no—
630C2×C5—121no—
631C2×C5D3×#11711yescharacteristic
632C2×C5D3×#13111yescharacteristic
633C2×C5D3×#13111yescharacteristic
634C23—31no—
635C23—31no—
636C23—62no—
637C23—62no—
638C23—62no—
639C23C2×D3×AGL(1,𝔽5)11yescharacteristic
640C2×C4—31no—
641C2×C4—31no—
642C2×C4—51no—
643C2×C4—51no—
644C2×C4—51no—
645C2×C4—51no—
646C2×C4—62no—
647C2×C4—62no—
648C2×C4—101no—
649C2×C4—101no—
650C2×C4—152no—
651C2×C4—152no—
652C2×C4—151no—
653C2×C4—151no—
654C2×C4—151no—
655C2×C4—151no—
656C2×C4—301no—
657C2×C4—301no—
658C2×C4—302no—
659C2×C4—302no—
660C2×C4—302no—
661C2×C4—302no—
662C2×C4—302no—
663C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
664C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
665C8—101no—
666C8—101no—
667C8—101no—
668C8—101no—
669C8—301no—
670C8—301no—
671C8—301no—
672C8—301no—
673C2×C3—41no—
674C2×C3C2×#413011yescharacteristic
675C2×C3C2×#413111yescharacteristic
676C2×C3C2×#413111yescharacteristic
677D3—41no—
678D3#6569714yesdirect product factor
679C5D3×#43311yescharacteristic, complemented, Sylow
680C22—21no—
681C22—21no—
682C22—21no—
683C22—32no—
684C22—32no—
685C22—32no—
686C22—61no—
687C22—61no—
688C22—61no—
689C22—124no—
690C22C22×D3×AGL(1,𝔽5)11yescharacteristic
691C4—21no—
692C4—21no—
693C4—51no—
694C4—51no—
695C4—61no—
696C4—61no—
697C4—101no—
698C4—101no—
699C4—101no—
700C4—152no—
701C4—301no—
702C4—301no—
703C4—301no—
704C3C2×#6569711yescharacteristic, complemented, Sylow
705C2—34no—
706C2—41no—
707C2—121no—
708C2D3×#413011yescharacteristic
709C2D3×#413111yescharacteristic
710C2D3×#413111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C22⋊C4C2×C4
prime radicalC23×C5×D3C2×C4
cosocleC2×C3×Dic5C24
hypercenterC22⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#433
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #11752356C2semidirect
3. C3×#65697C2semidirect
6. #11751990C2semidirect
7. #11751989C2semidirect
8. D3×#4004C2semidirect
9. D3×#4002C2semidirect
10. D3×C4⋊#170C2semidirect
11. C4×D3×#170C2semidirect
12. #11751809C2semidirect
13. #11751799C2semidirect
14. #11751798C2semidirect
15. #11751772C2semidirect
38. #91233C22semidirect
39. #91231C22semidirect
40. C4⋊(C3⋊#170)C22semidirect
41. C4×C3⋊#170C22semidirect
44. C3×#4004C22semidirect
45. C3×#4002C22semidirect
46. C3×C4⋊#170C22semidirect
47. C3×C4×#170C22semidirect
48. #91177C22semidirect
49. #91177C22semidirect
50. Dic3⋊#170C22semidirect
51. Dic3⋊#170C22semidirect
56. #91169C22semidirect
57. #91169C22semidirect
58. Dic3×#170C22semidirect
59. Dic3×#170C22semidirect
75. #65697D3direct (N × H)
170. #4004C2×D3semidirect
174. #4002C2×D3semidirect
178. C4⋊#170C2×D3semidirect
182. C4×#170C2×D3semidirect
490. C5×D3#433semidirect
603. C3×C5C2×#433semidirect
678. D3#65697direct (N × H)
679. C5D3×#433semidirect
704. C3C2×#65697semidirect

Maximal subgroups

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

subgroupindex
D3×#40232
#117523562
C3×#656972
D3×C22⋊#1702
#117519902
#117519892
D3×#40042
D3×#40022
D3×C4⋊#1702
C4×D3×#1702
#117518092
#117517992
#117517982
#117517722
C2×#656973
D3×#4335