Finite Group Databasebeta

← D3×#65706 #14413882

Subgroups — D3×#65706 #14413882

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×#4038C211yesmaximal, characteristic
2#11752365C211yesmaximal, characteristic, complemented
3C3×#65706C211yesmaximal, characteristic, complemented
4D3×#4004C211yesmaximal, characteristic, complemented
5D3×#4003C211yesmaximal, characteristic
6D3×#4003C211yesmaximal, characteristic
7D3×#4002C211yesmaximal, characteristic, complemented
8D3×C4⋊#170C211yesmaximal, characteristic, complemented
9C4×D3×#170C211yesmaximal, characteristic, complemented
10#11751810C211yesmaximal, characteristic, complemented
11#11751800C211yesmaximal, characteristic, complemented
12#11751781C211yesmaximal, characteristic, complemented
13#11751770C211yesmaximal, characteristic, complemented
14#11751769C211yesmaximal, characteristic, complemented
15#11751764C211yesmaximal, characteristic, complemented
16C2×#65706—31nomaximal, Hall
17C2×C4×D3×D5C2211yescharacteristic
18C2×D3×#170C2211yescharacteristic
19C2×D3×#170C2211yescharacteristic
20C2×D3×#170C2211yescharacteristic
21C2×D3×#170C2211yescharacteristic
22#91781C411yescharacteristic
23C5×D3×C4⋊C4C411yescharacteristic
24C3×#4038C2211yescharacteristic
25D3×#685C411yescharacteristic
26D3×#685C411yescharacteristic
27D3×C4⋊Dic5C411yescharacteristic
28#91402C2211yescharacteristic
29#91402C2211yescharacteristic
30C4×D3×Dic5C2211yescharacteristic
31C4×D3×Dic5C2211yescharacteristic
32#91394C411yescharacteristic
33#91394C411yescharacteristic
34#91358C2211yescharacteristic
35#91347C411yescharacteristic
36#91233C2211yescharacteristic, complemented
37#91232C2211yescharacteristic
38#91232C2211yescharacteristic
39#91231C2211yescharacteristic, complemented
40C4⋊(C3⋊#170)C2211yescharacteristic, complemented
41C4×C3⋊#170C2211yescharacteristic, complemented
42C3×#4004C2211yescharacteristic, complemented
43C3×#4003C2211yescharacteristic
44C3×#4003C2211yescharacteristic
45C3×#4002C2211yescharacteristic, complemented
46C3×C4⋊#170C2211yescharacteristic, complemented
47C3×C4×#170C2211yescharacteristic, complemented
48#91177C2211yescharacteristic, complemented
49#91177C2211yescharacteristic, complemented
50Dic3⋊#170C2211yescharacteristic, complemented
51Dic3⋊#170C2211yescharacteristic, complemented
52#91171C2211yescharacteristic
53#91171C2211yescharacteristic
54#91171C2211yescharacteristic
55#91171C2211yescharacteristic
56#91169C2211yescharacteristic, complemented
57#91169C2211yescharacteristic, complemented
58Dic3×#170C2211yescharacteristic, complemented
59Dic3×#170C2211yescharacteristic, complemented
60D3×#433—51nomaximal, Hall
61C2×#4038—31no—
62C2×#4004—31no—
63C2×#4003—31no—
64C2×#4003—31no—
65C2×#4002—31no—
66C2×C4⋊#170—31no—
67C2×C4×#170—31no—
68#65706—31no—
69#65706—31no—
70#65706—31no—
71#65706—31no—
72#65706—31no—
73#65706—31no—
74#65706—31no—
75#65706D311yescharacteristic, direct product factor
76C22×D3×D5C2×C411yescharacteristic
77C2×C4×D15C2×C411yescharacteristic
78C2×C4×C5×D3C2×C411yescharacteristic
79C2×C4×C5×D3C2×C411yescharacteristic
80C2×C4×C5×D3C2×C411yescharacteristic
81C2×C3×C4×D5C2311yescharacteristic
82C2×#1200C2311yescharacteristic
83C2×D3×Dic5C2×C411yescharacteristic
84C2×D3×Dic5C2×C411yescharacteristic
85C2×D3×Dic5C2311yescharacteristic
86C2×D5×Dic3C2×C411yescharacteristic
87C4×D3×D5—22no—
88C4×D3×D5—22no—
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×C4⋊C4C2×C411yescharacteristic
102#6714C2×C411yescharacteristic
103#6714C2×C411yescharacteristic
104C4⋊Dic15C2×C411yescharacteristic
105C4×Dic15C2×C411yescharacteristic
106C4×Dic15C2×C411yescharacteristic
107C5×C4⋊Dic3C2×C411yescharacteristic
108C5×Dic3⋊C4C2×C411yescharacteristic
109C5×Dic3⋊C4C2×C411yescharacteristic
110C3×#685C2×C411yescharacteristic
111C3×#685C2×C411yescharacteristic
112C3×C4⋊Dic5C2×C411yescharacteristic
113C3×C4×Dic5C2311yescharacteristic
114C3×C4×Dic5C2311yescharacteristic
115Dic3⋊Dic5C2×C411yescharacteristic
116Dic3⋊Dic5C2×C411yescharacteristic
117#6667C2×C411yescharacteristic
118#6667C2×C411yescharacteristic
119#6665C2×C411yescharacteristic
120#6665C2×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—
140C22×C4×D5—31no—
141C22×#170—31no—
142C22×#170—31no—
143C22×#170—31no—
144C22×#170—31no—
145C2×C5×C4⋊C4—31no—
146C2×#685—31no—
147C2×#685—31no—
148C2×C4⋊Dic5—31no—
149C2×C4×Dic5—31no—
150C2×C4×Dic5—31no—
151#4038—31no—
152#4038—31no—
153#4038—31no—
154#4038—31no—
155#4038—31no—
156#4038—31no—
157#4038—31no—
158#4038C2×D311yescharacteristic
159#4004—31no—
160#4004—31no—
161#4004—31no—
162#4004C2×D311yescharacteristic, complemented
163#4003—31no—
164#4003—31no—
165#4003—31no—
166#4003—31no—
167#4003—31no—
168#4003—31no—
169#4003C2×D311yescharacteristic
170#4003C2×D311yescharacteristic
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
184C22×D15C22×C411yescharacteristic
185C22×C5×D3C22×C411yescharacteristic
186C22×C3×D5C22×C411yescharacteristic
187C2×D3×D5—22no—
188C2×D3×D5—22no—
189C2×D3×D5—22no—
190C2×C3×C4×C5C22×C411yescharacteristic
191C2×C3×C4×C5C22×C411yescharacteristic
192C2×C3×C4×C5C22×C411yescharacteristic
193C2×Dic15C22×C411yescharacteristic
194C2×Dic15C22×C411yescharacteristic
195C2×Dic15C22×C411yescharacteristic
196C4×D15—22no—
197C2×C5×Dic3C22×C411yescharacteristic
198C2×C5×Dic3C22×C411yescharacteristic
199C2×C5×Dic3C22×C411yescharacteristic
200C4×C5×D3—22no—
201C4×C5×D3—22no—
202C4×C5×D3—22no—
203C2×C3×Dic5C22×C411yescharacteristic
204C2×C3×Dic5C22×C411yescharacteristic
205C2×C3×Dic5C2411yescharacteristic
206C3×C4×D5—21no—
207C3×C4×D5—21no—
208#1200—21no—
209#1200—21no—
210D3×Dic5—22no—
211D3×Dic5—22no—
212D3×Dic5#4112yes—
213D3×Dic5#4112yes—
214D5×Dic3—22no—
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⋊C4AGL(1,𝔽5)11yescharacteristic
234D3×C22⋊C4—51no—
235D3×C22⋊C4—51no—
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—
266C23×D5—31no—
267C22×C4×C5—31no—
268C22×C4×C5—31no—
269C22×C4×C5—31no—
270C22×Dic5—31no—
271C22×Dic5—31no—
272C22×Dic5—31no—
273C2×C4×D5—31no—
274C2×C4×D5—31no—
275C2×C4×D5—31no—
276C2×C4×D5—62no—
277C2×C4×D5—62no—
278C2×C4×D5C22×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×C4⋊C4—31no—
292C5×C4⋊C4—31no—
293C5×C4⋊C4—31no—
294C5×C4⋊C4C4×D311yescharacteristic
295#685—31no—
296#685—31no—
297#685—31no—
298#685—31no—
299#685—31no—
300#685—31no—
301#685C4×D311yescharacteristic
302#685C4×D311yescharacteristic
303C4⋊Dic5—31no—
304C4⋊Dic5—31no—
305C4⋊Dic5—31no—
306C4⋊Dic5C4×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×C5C23×C411yescharacteristic
331C2×D15—21no—
332C2×D15—21no—
333C2×D15—21no—
334C2×C5×D3#11712yes—
335C2×C5×D3#13112yes—
336C2×C5×D3#13112yes—
337C2×C3×D5—21no—
338C2×C3×D5—21no—
339C2×C3×D5—21no—
340D3×D5—44no—
341C3×C4×C5—21no—
342C3×C4×C5—21no—
343C3×C4×C5—21no—
344Dic15—21no—
345Dic15—21no—
346Dic15#11712yes—
347C3×Dic5—21no—
348C3×Dic5—21no—
349C3×Dic5C2×#4111yescharacteristic
350C3×Dic5C2×#4111yescharacteristic
351C5×Dic3—21no—
352C5×Dic3—21no—
353C5×Dic3—21no—
354C23×D3—51no—
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—102no—
363C2×C4×D3—102no—
364C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
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⋊C4C2×AGL(1,𝔽5)11yescharacteristic
373C3×C22⋊C4—51no—
374C3×C22⋊C4—51no—
375C3×C42—51no—
376C3×C42—51no—
377#217—51no—
378#217—51no—
379(C2×D3)⋊C4—51no—
380(C2×D3)⋊C4—51no—
381(C2×D3)⋊C4—51no—
382(C2×D3)⋊C4—51no—
383C4⋊Dic3—51no—
384C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
385Dic3⋊C4—51no—
386Dic3⋊C4—51no—
387Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
388Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
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—
404C22×D5—31no—
405C22×D5—62no—
406C22×D5—62no—
407C22×D5—62no—
408C22×D5C2×C4×D311yescharacteristic
409C2×C4×C5—31no—
410C2×C4×C5—31no—
411C2×C4×C5—31no—
412C2×C4×C5—62no—
413C2×C4×C5—62no—
414C2×C4×C5—62no—
415C2×C4×C5C2×C4×D311yescharacteristic
416C2×C4×C5C2×C4×D311yescharacteristic
417C2×C4×C5C2×C4×D311yescharacteristic
418C2×Dic5—31no—
419C2×Dic5—32no—
420C2×Dic5—32no—
421C2×Dic5—31no—
422C2×Dic5—31no—
423C2×Dic5—62no—
424C2×Dic5—62no—
425C2×Dic5C2×C4×D311yescharacteristic
426C2×Dic5C2×C4×D311yescharacteristic
427C2×Dic5C23×D311yescharacteristic
428C4×D5—21no—
429C4×D5—21no—
430C4×D5—62no—
431C4×D5—62no—
432C4×D5—61no—
433C4×D5—61no—
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—31no—
456C2×C4⋊C4—151no—
457C2×C22⋊C4—151no—
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×C5C2×#11711yescharacteristic
486C2×C3×C5C2×#13111yescharacteristic
487C2×C3×C5C2×#13111yescharacteristic
488D15—41no—
489C3×D5—41no—
490C5×D3#43314yescomplemented
491C23×C3—51no—
492C22×D3—51no—
493C22×D3—102no—
494C22×D3—102no—
495C22×D3—102no—
496C22×D3C22×AGL(1,𝔽5)11yescharacteristic
497C2×C3×C4—51no—
498C2×C3×C4—51no—
499C2×C3×C4—51no—
500C2×C3×C4—101no—
501C2×C3×C4—101no—
502C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
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—102no—
509C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
510C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
511C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
512C4×D3—22no—
513C4×D3—22no—
514C4×D3—22no—
515C4×D3—52no—
516C4×D3—52no—
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—32no—
531C22×C5—32no—
532C22×C5—32no—
533C22×C5C22×C4×D311yescharacteristic
534C2×D5—21no—
535C2×D5—21no—
536C2×D5—21no—
537C2×D5—61no—
538C2×D5—61no—
539C2×D5—61no—
540C2×D5—124no—
541C4×C5—21no—
542C4×C5—21no—
543C4×C5—21no—
544C4×C5—61no—
545C4×C5—61no—
546C4×C5—61no—
547Dic5—21no—
548Dic5—21no—
549Dic5—32no—
550Dic5—61no—
551Dic5—61no—
552Dic5D3×#4111yescharacteristic
553Dic5D3×#4111yescharacteristic
554C24—151no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—31no—
558C22×C4—51no—
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—31no—
580C4⋊C4—31no—
581C4⋊C4—31no—
582C4⋊C4—51no—
583C4⋊C4—151no—
584C4⋊C4—151no—
585C4⋊C4—151no—
586C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
587C22⋊C4—51no—
588C22⋊C4—51no—
589C22⋊C4—151no—
590C22⋊C4—151no—
591C22⋊C4—151no—
592C22⋊C4—151no—
593C22⋊C4—151no—
594C22⋊C4—151no—
595C42—51no—
596C42—51no—
597C42—151no—
598C42—151no—
599C42—151no—
600C42—151no—
601C42—151no—
602C42—151no—
603C3×C5C2×#43311yescharacteristic, complemented, Hall
604C22×C3—101no—
605C22×C3—101no—
606C22×C3—101no—
607C22×C3C23×AGL(1,𝔽5)11yescharacteristic
608C2×D3—101no—
609C2×D3—101no—
610C2×D3—101no—
611C2×D3—204no—
612C2×D3#413012yes—
613C2×D3#413112yes—
614C2×D3#413312yes—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—51no—
619C3×C4—51no—
620C3×C4—101no—
621C3×C4—101no—
622Dic3—21no—
623Dic3—21no—
624Dic3—21no—
625Dic3—52no—
626Dic3—101no—
627Dic3—101no—
628C2×C5—34no—
629C2×C5D3×#11711yescharacteristic
630C2×C5D3×#13111yescharacteristic
631C2×C5D3×#13111yescharacteristic
632D5—41no—
633D5—121no—
634C23—31no—
635C23—51no—
636C23—151no—
637C23—302no—
638C23—302no—
639C23—302no—
640C2×C4—31no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—51no—
644C2×C4—51no—
645C2×C4—51no—
646C2×C4—62no—
647C2×C4—62no—
648C2×C4—62no—
649C2×C4—101no—
650C2×C4—101no—
651C2×C4—152no—
652C2×C4—152no—
653C2×C4—151no—
654C2×C4—151no—
655C2×C4—151no—
656C2×C4—302no—
657C2×C4—301no—
658C2×C4—301no—
659C2×C4—302no—
660C2×C4—302no—
661C2×C4—302no—
662C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
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—201no—
674C2×C3C2×#413011yescharacteristic
675C2×C3C2×#413111yescharacteristic
676C2×C3C2×#413311yescharacteristic
677D3—201no—
678D3#6570614yesdirect product factor
679C5D3×#43311yescharacteristic, complemented, Sylow
680C22—32no—
681C22—32no—
682C22—32no—
683C22—101no—
684C22—101no—
685C22—101no—
686C22—301no—
687C22—301no—
688C22—301no—
689C22—604no—
690C22C22×D3×AGL(1,𝔽5)11yescharacteristic
691C4—21no—
692C4—21no—
693C4—21no—
694C4—51no—
695C4—51no—
696C4—61no—
697C4—61no—
698C4—61no—
699C4—101no—
700C4—101no—
701C4—152no—
702C4—301no—
703C4—301no—
704C3C2×#6570611yescharacteristic, complemented, Sylow
705C2—34no—
706C2—201no—
707C2—601no—
708C2D3×#413011yescharacteristic
709C2D3×#413111yescharacteristic
710C2D3×#413311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radicalC22×D3×D5C2×C4
cosocleC2×C3×Dic5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#433
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11752365C2semidirect
3. C3×#65706C2semidirect
4. D3×#4004C2semidirect
7. D3×#4002C2semidirect
8. D3×C4⋊#170C2semidirect
9. C4×D3×#170C2semidirect
10. #11751810C2semidirect
11. #11751800C2semidirect
12. #11751781C2semidirect
13. #11751770C2semidirect
14. #11751769C2semidirect
15. #11751764C2semidirect
36. #91233C22semidirect
39. #91231C22semidirect
40. C4⋊(C3⋊#170)C22semidirect
41. C4×C3⋊#170C22semidirect
42. 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. #65706D3direct (N × H)
162. #4004C2×D3semidirect
174. #4002C2×D3semidirect
178. C4⋊#170C2×D3semidirect
182. C4×#170C2×D3semidirect
490. C5×D3#433semidirect
603. C3×C5C2×#433semidirect
678. D3#65706direct (N × H)
679. C5D3×#433semidirect
704. C3C2×#65706semidirect

Maximal subgroups

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

subgroupindex
D3×#40382
#117523652
C3×#657062
D3×#40042
D3×#40032
D3×#40022
D3×C4⋊#1702
C4×D3×#1702
#117518102
#117518002
#117517812
#117517702
#117517692
#117517642
C2×#657063
D3×#4335