Finite Group Databasebeta

← #14435673

Subgroups — #14435673

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5534C211yesmaximal, characteristic, complemented
2C3×#65855C211yesmaximal, characteristic, complemented
3#11751101C211yesmaximal, characteristic, complemented
4#11748527C211yesmaximal, characteristic, complemented
5#11748510C211yesmaximal, characteristic
6#11748404C211yesmaximal, characteristic, complemented
7#11748383C211yesmaximal, characteristic, complemented
8#11747048C211yesmaximal, characteristic, complemented
9C4×#6655C211yesmaximal, characteristic, complemented
10#11747027C211yesmaximal, characteristic, complemented
11#11747027C211yesmaximal, characteristic, complemented
12#11747021C211yesmaximal, characteristic, complemented
13C4×#6652C211yesmaximal, characteristic, complemented
14#11746886C211yesmaximal, characteristic, complemented
15#11746880C211yesmaximal, characteristic, complemented
16#10615191—31nomaximal, Hall
17C22×C3×D20C2211yescharacteristic
18C3×C5×#117C2211yescharacteristic
19C5×#930C2211yescharacteristic
20C5×#924C2211yescharacteristic
21C5×#898—21no—
22C5×#896—21no—
23C5×#885—21no—
24C5×#883—21no—
25C5×#875C2211yescharacteristic, complemented
26C4×C5×D12C2211yescharacteristic, complemented
27C5×#869C2211yescharacteristic, complemented
28C4×C5×Dic6C2211yescharacteristic, complemented
29C3×#4072C2211yescharacteristic
30C3×#4039—21no—
31C3×#4039—21no—
32C3×D5×C22⋊C4—21no—
33C3×D5×C22⋊C4—21no—
34C3×C4×D20C2211yescharacteristic
35C3×C4×D20C2211yescharacteristic
36C3×C4×D20C2211yescharacteristic
37C3×C4×D20C2211yescharacteristic
38C2×#6655C2211yescharacteristic
39C2×#6655C2211yescharacteristic
40C2×#6652C2211yescharacteristic
41C2×#6652C2211yescharacteristic
42#91114C2211yescharacteristic
43#91114C2211yescharacteristic
44C4⋊(C3⋊#168)C2211yescharacteristic, complemented
45C4⋊(C3⋊#168)C2211yescharacteristic, complemented
46#91087C2211yescharacteristic, complemented
47C4×C3⋊#168C2211yescharacteristic, complemented
48#90989C2211yescharacteristic, complemented
49#90989C2211yescharacteristic, complemented
50#90986C2211yescharacteristic, complemented
51#90986C2211yescharacteristic, complemented
52#90972C2211yescharacteristic, complemented
53#90972C2211yescharacteristic, complemented
54#90966C2211yescharacteristic, complemented
55#90966C2211yescharacteristic, complemented
56#90964C2211yescharacteristic
57#90964C2211yescharacteristic
58#90964C2211yescharacteristic
59#90964C2211yescharacteristic
60#82541—51nomaximal, Hall
61C5×#542—31no—
62#65855D311yescharacteristic, complemented
63#65376—31no—
64#65373—31no—
65#65346—31no—
66#65346—31no—
67#65335—31no—
68#65334—31no—
69#65325—31no—
70#65324—31no—
71#65315—31no—
72C4×#688—31no—
73#65303—31no—
74C4×#686—31no—
75#65289—31no—
76C23×C3×D5—21no—
77C22×C3×C4×C5C2311yescharacteristic
78C2×C5×#67—21no—
79C2×C5×D12C2311yescharacteristic
80C2×C4×C5×D3—21no—
81C2×C5×Dic6—21no—
82C2×C5×Dic6C2311yescharacteristic
83C2×C3×D20—21no—
84C2×C3×D20—22no—
85C2×C3×D20—22no—
86C2×C3×D20C2311yescharacteristic
87C2×C3×D20C2311yescharacteristic
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5—21no—
92C3×C5×C4⋊C4D411yescharacteristic
93C3×C5×C4⋊C4D411yescharacteristic
94C3×C5×C22⋊C4D411yescharacteristic
95C3×C5×C22⋊C4D411yescharacteristic
96C3×C42×C5C2311yescharacteristic
97C3×C42×C5C2311yescharacteristic
98C2×C3⋊#168C2311yescharacteristic
99C2×C3⋊#168C2311yescharacteristic
100C2×C3⋊#168C2311yescharacteristic
101C2×C3⋊#168C2311yescharacteristic
102C5×#217—21no—
103C5×(C2×D3)⋊C4—21no—
104C5×(C2×D3)⋊C4—21no—
105C5×(C2×D3)⋊C4—21no—
106C5×(C2×D3)⋊C4—21no—
107C5×C4⋊Dic3—21no—
108C5×C4⋊Dic3C2311yescharacteristic
109C5×C4⋊Dic3C2311yescharacteristic
110C5×Dic3⋊C4—21no—
111C5×Dic3⋊C4—21no—
112C4×C5×Dic3—21no—
113C3×C22⋊Dic5—21no—
114C3×#685—21no—
115C3×#685—21no—
116C3×#685—21no—
117C3×#685—21no—
118C3×C4⋊Dic5C2311yescharacteristic
119C3×C4⋊Dic5C2311yescharacteristic
120C3×C4×Dic5—21no—
121#6655—22no—
122#6655—22no—
123#6652—22no—
124#6652—22no—
125C3×#518—51no—
126#5534D511yescharacteristic, complemented
127#5218—51no—
128#5217—51no—
129#5018—51no—
130C4×#214—51no—
131#5016—51no—
132#5016—51no—
133#5014—51no—
134C4×#213—51no—
135#5008—51no—
136#5007—51no—
137#5003—51no—
138#5000—51no—
139#4996—51no—
140C22×D20C2×D311yescharacteristic
141C5×C4⋊Q8—31no—
142C5×#126—61no—
143C5×#124—31no—
144C5×#124—61no—
145C5×#123—61no—
146C5×C22⋊Q8—31no—
147C5×C22⋊Q8—61no—
148C5×#121—31no—
149C4×C5×Q8—31no—
150C4×C5×D4—31no—
151C5×#117C2×D311yescharacteristic
152C2×#688—31no—
153C2×#688—31no—
154C2×#686—31no—
155C2×#686—31no—
156#4072C2×D311yescharacteristic
157#4039—21no—
158#4039—21no—
159D5×C22⋊C4—21no—
160D5×C22⋊C4—21no—
161C4×D20C2×D311yescharacteristic
162C4×D20C2×D311yescharacteristic
163C4×D20C2×D311yescharacteristic
164C4×D20C2×D311yescharacteristic
165#3967—31no—
166#3967—31no—
167#3964—31no—
168#3964—31no—
169C22⋊#168—31no—
170C22⋊#168—31no—
171#3941—31no—
172#3941—31no—
173#3941—31no—
174#3941—31no—
175#3940—31no—
176#3940—31no—
177#3939—31no—
178#3939—31no—
179C4⋊#168—31no—
180C4⋊#168—31no—
181#3935—31no—
182C4×#168—31no—
183#3118—151noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×C5×D3—21no—
186C22×C3×D5—21no—
187C22×C3×D5—21no—
188C22×C3×D5—24no—
189C22×C3×D5—81no—
190C22×C3×D5—81no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5C2×D411yescharacteristic
194C2×C3×C4×C5C2×D411yescharacteristic
195C2×C3×C4×C5C2×D411yescharacteristic
196C2×C3×C4×C5C2×D411yescharacteristic
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2411yescharacteristic
199C5×#67—81no—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—21no—
203C5×D12—21no—
204C5×D12—21no—
205C4×C5×D3—81no—
206C5×Dic6—21no—
207C5×Dic6—21no—
208C5×Dic6—81no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C3×D20—24no—
212C3×D20—21no—
213C3×D20—21no—
214C3×D20#4112yes—
215C3×D20#4112yes—
216C3×C4×D5—81no—
217C3×C4×D5—81no—
218C3×C4×D5—81no—
219C3×C4×D5—81no—
220C3⋊#168—21no—
221C3⋊#168—21no—
222C3⋊#168—21no—
223C3⋊#168—21no—
224C22×C3×D4—51no—
225C3×C4×D4—51no—
226C3×C4×D4—51no—
227C3×C4×D4—51no—
228C3×C4×D4—51no—
229C3×C4×D4—101no—
230C3×C4×D4—101no—
231C3×#117—51no—
232C3×#117C2×D511yescharacteristic
233C2×C3×C22⋊C4—101no—
234C2×C3×C22⋊C4—101no—
235C2×#214—51no—
236C2×#214—51no—
237C2×#213—51no—
238C2×#213—51no—
239#930C2×D511yescharacteristic
240#924C2×D511yescharacteristic
241#898—21no—
242#896—21no—
243#885—21no—
244#883—21no—
245#875C2×D511yescharacteristic, complemented
246C4×D12C2×D511yescharacteristic, complemented
247#869C2×D511yescharacteristic, complemented
248C4×Dic6C2×D511yescharacteristic, complemented
249#832—51no—
250#832—51no—
251#832—51no—
252#832—51no—
253#830—51no—
254#830—51no—
255#810—51no—
256#810—51no—
257#809—51no—
258#809—51no—
259#808—51no—
260#808—51no—
261#807—51no—
262#807—51no—
263C4⋊(C3⋊C8)—51no—
264C4⋊(C3⋊C8)—51no—
265#803—51no—
266C4×C3⋊C8—51no—
267C23×D5—21no—
268C2×C5×Q8—31no—
269C2×C5×Q8—61no—
270C2×C5×D4—31no—
271C2×C5×D4—61no—
272C22×C4×C5—61no—
273C22×C4×C5C22×D311yescharacteristic
274C2×D20—21no—
275C2×D20—22no—
276C2×D20—22no—
277C2×D20C22×D311yescharacteristic
278C2×D20C22×D311yescharacteristic
279C2×C4×D5—21no—
280C2×C4×D5—21no—
281C2×C4×D5—21no—
282C2×C4×D5—21no—
283C5×C4⋊C4—31no—
284C5×C4⋊C4—31no—
285C5×C4⋊C4—61no—
286C5×C4⋊C4—61no—
287C5×C4⋊C4—61no—
288C5×C4⋊C4#6711yescharacteristic
289C5×C4⋊C4#6711yescharacteristic
290C5×C22⋊C4—61no—
291C5×C22⋊C4—61no—
292C5×C22⋊C4—61no—
293C5×C22⋊C4—61no—
294C5×C22⋊C4—61no—
295C5×C22⋊C4#6711yescharacteristic
296C5×C22⋊C4#6711yescharacteristic
297C42×C5—61no—
298C42×C5C22×D311yescharacteristic
299C42×C5C22×D311yescharacteristic
300C22⋊Dic5—21no—
301#688—62no—
302#688—62no—
303#686—62no—
304#686—62no—
305#685—21no—
306#685—21no—
307#685—21no—
308#685—21no—
309C4⋊Dic5C22×D311yescharacteristic
310C4⋊Dic5C22×D311yescharacteristic
311C4×Dic5—21no—
312C2×#168—31no—
313C2×#168—31no—
314C2×#168—31no—
315C2×#168—31no—
316#542—31no—
317#518—51no—
318#485—151no—
319#482—151no—
320#476—151no—
321#474—151no—
322#463—151no—
323#463—151no—
324#450—151no—
325#447—151no—
326#442—151no—
327#440—151no—
328C4×SD16—151no—
329C4×D8—151no—
330#433—151no—
331C22×C3×C5—21no—
332C22×C3×C5—21no—
333C22×C3×C5—21no—
334C22×C3×C5C22×D411yescharacteristic
335C2×C5×D3—41no—
336C2×C5×D3—41no—
337C2×C5×D3—41no—
338C2×C3×D5—22no—
339C2×C3×D5—22no—
340C2×C3×D5—41no—
341C2×C3×D5—41no—
342C2×C3×D5—41no—
343C2×C3×D5—41no—
344C2×C3×D5—84no—
345C3×C4×C5—21no—
346C3×C4×C5—21no—
347C3×C4×C5—21no—
348C3×C4×C5—21no—
349C3×C4×C5—21no—
350C3×C4×C5C2×#4111yescharacteristic
351C3×C4×C5C2×#4111yescharacteristic
352C3×Dic5—41no—
353C3×Dic5—41no—
354C5×Dic3—41no—
355C5×Dic3—41no—
356C5×Dic3—41no—
357C24×C3—101no—
358C2×C3×D4—51no—
359C2×C3×D4—51no—
360C2×C3×D4—102no—
361C2×C3×D4—102no—
362C2×C3×D4—101no—
363C22×C3×C4—101no—
364C22×C3×C4—101no—
365C22×C3×C4—101no—
366C22×C3×C4—101no—
367C22×C3×C4C22×D511yescharacteristic
368C2×#67—21no—
369C2×D12C22×D511yescharacteristic
370C2×C4×D3—21no—
371C2×Dic6—21no—
372C2×Dic6C22×D511yescharacteristic
373C3×C4⋊C4—51no—
374C3×C4⋊C4—51no—
375C3×C4⋊C4C22⋊D511yescharacteristic
376C3×C4⋊C4C22⋊D511yescharacteristic
377C3×C22⋊C4—101no—
378C3×C22⋊C4—101no—
379C3×C22⋊C4—101no—
380C3×C22⋊C4—101no—
381C3×C22⋊C4—101no—
382C3×C22⋊C4C22⋊D511yescharacteristic
383C3×C22⋊C4C22⋊D511yescharacteristic
384C3×C42—101no—
385C3×C42C22×D511yescharacteristic
386C3×C42C22×D511yescharacteristic
387#217—21no—
388#214—102no—
389#214—102no—
390#213—102no—
391#213—102no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396C4⋊Dic3—21no—
397C4⋊Dic3C22×D511yescharacteristic
398C4⋊Dic3C22×D511yescharacteristic
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401C4×Dic3—21no—
402C2×C3⋊C8—51no—
403C2×C3⋊C8—51no—
404C2×C3⋊C8—51no—
405C2×C3⋊C8—51no—
406C23×C5—61no—
407C23×C5C2×#6711yescharacteristic
408C22×D5—21no—
409C22×D5—21no—
410C22×D5—24no—
411C22×D5—81no—
412C22×D5—81no—
413C5×Q8—61no—
414C5×Q8—61no—
415C5×Q8—241no—
416C5×D4—61no—
417C5×D4—61no—
418C5×D4—241no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—61no—
422C2×C4×C5—61no—
423C2×C4×C5—61no—
424C2×C4×C5—241no—
425C2×C4×C5C2×#6711yescharacteristic
426C2×C4×C5C2×#6711yescharacteristic
427C2×C4×C5C2×#6711yescharacteristic
428C2×C4×C5C2×#6711yescharacteristic
429C2×C4×C5C2×#6711yescharacteristic
430C2×C4×C5C23×D311yescharacteristic
431C2×Dic5—21no—
432C2×Dic5—21no—
433D20—24no—
434D20—21no—
435D20—21no—
436D20#23512yes—
437D20#23512yes—
438C4×D5—81no—
439C4×D5—81no—
440C4×D5—81no—
441C4×D5—81no—
442#168—61no—
443#168—61no—
444#168—61no—
445#168—61no—
446C22×D4—51no—
447C2×SD16—151no—
448C2×SD16—151no—
449C2×D8—151no—
450C2×D8—151no—
451C4⋊Q8—31no—
452#126—61no—
453#124—31no—
454#124—61no—
455#123—61no—
456C22⋊Q8—31no—
457C22⋊Q8—61no—
458#121—31no—
459C4×Q8—31no—
460C4×D4—31no—
461C4×D4—51no—
462C4×D4—51no—
463C4×D4—51no—
464C4×D4—51no—
465C4×D4—101no—
466C4×D4—101no—
467#117—51no—
468#117D3×D511yescharacteristic
469C2×C22⋊C4—101no—
470C2×C22⋊C4—101no—
471#107—151no—
472#107—151no—
473#106—151no—
474#106—151no—
475C4⋊C8—151no—
476C4⋊C8—151no—
477#103—151no—
478#103—151no—
479#102—151no—
480#102—151no—
481#102—151no—
482#102—151no—
483#102—151no—
484#102—151no—
485C22⋊C8—151no—
486C22⋊C8—151no—
487#97—151no—
488C4×C8—151no—
489C2×C3×C5—41no—
490C2×C3×C5#52511yescharacteristic
491C2×C3×C5#57611yescharacteristic
492C2×C3×C5#57711yescharacteristic
493C3×D5—42no—
494C3×D5—42no—
495C5×D3—81no—
496C23×C3—104no—
497C23×C3—101no—
498C23×C3—101no—
499C23×C3—401no—
500C23×C3—401no—
501C23×C3C2×C22⋊D511yescharacteristic
502C22×D3—21no—
503C3×D4—52no—
504C3×D4—52no—
505C3×D4—104no—
506C3×D4—101no—
507C3×D4—101no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—101no—
511C2×C3×C4—101no—
512C2×C3×C4—401no—
513C2×C3×C4—401no—
514C2×C3×C4—401no—
515C2×C3×C4—401no—
516C2×C3×C4C2×C22⋊D511yescharacteristic
517C2×C3×C4C2×C22⋊D511yescharacteristic
518C2×C3×C4C2×C22⋊D511yescharacteristic
519C2×C3×C4C2×C22⋊D511yescharacteristic
520C2×C3×C4C2×C22⋊D511yescharacteristic
521C2×C3×C4C23×D511yescharacteristic
522#67—81no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526D12—21no—
527D12—21no—
528C4×D3—81no—
529Dic6—21no—
530Dic6—21no—
531Dic6—81no—
532C3⋊C8—101no—
533C3⋊C8—101no—
534C3⋊C8—101no—
535C3⋊C8—101no—
536C22×C5—21no—
537C22×C5—21no—
538C22×C5—21no—
539C22×C5—121no—
540C22×C5—121no—
541C22×C5—121no—
542C22×C5C22×#6711yescharacteristic
543C2×D5—22no—
544C2×D5—22no—
545C2×D5—41no—
546C2×D5—41no—
547C2×D5—41no—
548C2×D5—41no—
549C2×D5—84no—
550C4×C5—21no—
551C4×C5—21no—
552C4×C5—21no—
553C4×C5—21no—
554C4×C5—21no—
555C4×C5—121no—
556C4×C5—121no—
557C4×C5—121no—
558C4×C5C2×#23511yescharacteristic
559C4×C5C2×#23511yescharacteristic
560Dic5—41no—
561Dic5—41no—
562C24—101no—
563C2×Q8—31no—
564C2×Q8—61no—
565C2×D4—31no—
566C2×D4—51no—
567C2×D4—51no—
568C2×D4—61no—
569C2×D4—102no—
570C2×D4—102no—
571C2×D4—101no—
572C22×C4—61no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4C2×D3×D511yescharacteristic
578SD16—302no—
579SD16—302no—
580D8—302no—
581D8—302no—
582C2×C8—151no—
583C2×C8—151no—
584C2×C8—151no—
585C2×C8—151no—
586C4⋊C4—31no—
587C4⋊C4—31no—
588C4⋊C4—51no—
589C4⋊C4—51no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4#120111yescharacteristic
594C4⋊C4#120111yescharacteristic
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—61no—
599C22⋊C4—61no—
600C22⋊C4—101no—
601C22⋊C4—101no—
602C22⋊C4—101no—
603C22⋊C4—101no—
604C22⋊C4—101no—
605C22⋊C4#120111yescharacteristic
606C22⋊C4#120111yescharacteristic
607C42—61no—
608C42—101no—
609C42C2×D3×D511yescharacteristic
610C42C2×D3×D511yescharacteristic
611C3×C5#311811yescharacteristic, complemented, Hall
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—102no—
616C22×C3—102no—
617C22×C3—201no—
618C22×C3—201no—
619C22×C3—201no—
620C22×C3—201no—
621C22×C3—404no—
622C22×C3C22×C22⋊D511yescharacteristic
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—41no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—201no—
632C3×C4—201no—
633C3×C4D5×#4111yescharacteristic
634C3×C4D5×#4111yescharacteristic
635Dic3—41no—
636Dic3—41no—
637Dic3—41no—
638C2×C5—41no—
639C2×C5—241no—
640C2×C5#579111yescharacteristic
641C2×C5#583511yescharacteristic
642C2×C5#583611yescharacteristic
643D5—42no—
644D5—42no—
645C23—61no—
646C23—104no—
647C23—101no—
648C23—101no—
649C23—401no—
650C23—401no—
651C23C2×#120111yescharacteristic
652Q8—61no—
653Q8—61no—
654Q8—241no—
655D4—52no—
656D4—52no—
657D4—61no—
658D4—61no—
659D4—104no—
660D4—101no—
661D4—101no—
662D4—241no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—101no—
669C2×C4—101no—
670C2×C4—241no—
671C2×C4—401no—
672C2×C4—401no—
673C2×C4—401no—
674C2×C4—401no—
675C2×C4C2×#120111yescharacteristic
676C2×C4C2×#120111yescharacteristic
677C2×C4C2×#120111yescharacteristic
678C2×C4C2×#120111yescharacteristic
679C2×C4C2×#120111yescharacteristic
680C2×C4C22×D3×D511yescharacteristic
681C8—301no—
682C8—301no—
683C8—301no—
684C8—301no—
685C2×C3—41no—
686C2×C3—202no—
687C2×C3—202no—
688C2×C3#6616211yescharacteristic
689C2×C3#6616911yescharacteristic
690C2×C3#6617111yescharacteristic
691D3—81no—
692C5#8254111yescharacteristic, complemented, Sylow
693C22—21no—
694C22—21no—
695C22—21no—
696C22—102no—
697C22—102no—
698C22—121no—
699C22—121no—
700C22—121no—
701C22—201no—
702C22—201no—
703C22—201no—
704C22—201no—
705C22—404no—
706C22C22×#120111yescharacteristic
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—121no—
713C4—121no—
714C4—121no—
715C4—201no—
716C4—201no—
717C4D5×#23511yescharacteristic
718C4D5×#23511yescharacteristic
719C3#1061519111yescharacteristic, complemented, Sylow
720C2—41no—
721C2—202no—
722C2—202no—
723C2—241no—
724C2#1175456311yescharacteristic
725C2#1175530111yescharacteristic
726C2#1175530311yescharacteristic
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radical#11748510C2
hypercenter#117D3×D5
hypocenterC3×C5#3118
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C5×#5534C2semidirect
2. C3×#65855C2semidirect
3. #11751101C2semidirect
4. #11748527C2semidirect
6. #11748404C2semidirect
7. #11748383C2semidirect
8. #11747048C2semidirect
9. C4×#6655C2semidirect
10. #11747027C2semidirect
11. #11747027C2semidirect
12. #11747021C2semidirect
13. C4×#6652C2semidirect
14. #11746886C2semidirect
15. #11746880C2semidirect
25. C5×#875C22semidirect
26. C4×C5×D12C22semidirect
27. C5×#869C22semidirect
28. C4×C5×Dic6C22semidirect
44. C4⋊(C3⋊#168)C22semidirect
45. C4⋊(C3⋊#168)C22semidirect
46. #91087C22semidirect
47. C4×C3⋊#168C22semidirect
48. #90989C22semidirect
49. #90989C22semidirect
50. #90986C22semidirect
51. #90986C22semidirect
52. #90972C22semidirect
53. #90972C22semidirect
54. #90966C22semidirect
55. #90966C22semidirect
62. #65855D3semidirect
126. #5534D5semidirect
245. #875C2×D5semidirect
246. C4×D12C2×D5semidirect
247. #869C2×D5semidirect
248. C4×Dic6C2×D5semidirect
611. C3×C5#3118semidirect
692. C5#82541semidirect
719. C3#10615191semidirect

Maximal subgroups

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

subgroupindex
C5×#55342
C3×#658552
#117511012
#117485272
#117485102
#117484042
#117483832
#117470482
C4×#66552
#117470272
#117470212
C4×#66522
#117468862
#117468802
#106151913
#825415