Finite Group Databasebeta

← C3×#11751705 #72230451

Subgroups — C3×#11751705 #72230451

Order 2880.

740 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#235C211yesmaximal, characteristic
2C3×D5⋊#208C211yesmaximal, characteristic, complemented
3C2×C32×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
4C3×#91153C212yesmaximal, complemented
5C3×#91151C212yesmaximal, complemented
6C3×#65793—31nomaximal
7#11751705C311yesmaximal, characteristic, direct product factor
8C22×C32×AGL(1,𝔽5)—21no—
9C3×#6817C411yescharacteristic, complemented
10C3×C5×#235C411yescharacteristic, complemented
11C2×C32×C4×D5C2211yescharacteristic
12C3×D5×#67—21no—
13C3×#6782—21no—
14C3×D5×D12C2211yescharacteristic
15C3×C4×D3×D5—21no—
16C3×#6773C411yescharacteristic, complemented
17C3×#6772C411yescharacteristic, complemented
18C3×#6771—21no—
19C3×D5×Dic6C2211yescharacteristic
20C3×#6762—21no—
21C3×#6758—21no—
22C3×D5⋊(C3⋊C8)C2212yes—
23C32×C4⋊AGL(1,𝔽5)—21no—
24C32×C4⋊AGL(1,𝔽5)C2212yes—
25C3×#4966—51nomaximal, Hall
26C3×D5×#41—31no—
27D5×#235C2×C311yescharacteristic
28D5⋊#208C2×C311yescharacteristic, complemented
29C2×C3×C4⋊AGL(1,𝔽5)—21no—
30C2×C3×C4⋊AGL(1,𝔽5)D311yescharacteristic, complemented
31C2×C3×C4⋊AGL(1,𝔽5)C2×C311yescharacteristic, complemented
32C3×D5⋊M16—31no—
33C3×#4009—32no—
34C3×#4007—32no—
35#91153C2×C312yescomplemented
36#91151C2×C312yescomplemented
37C22×C32×D5D411yescharacteristic
38C2×C3×D3×D5—21no—
39C2×C32×AGL(1,𝔽5)—22no—
40C2×C32×AGL(1,𝔽5)—42no—
41C2×C32×C4×C5C2×C411yescharacteristic
42C3×#1220—21no—
43C3×D60C2×C411yescharacteristic, complemented
44C3×C4×D15—21no—
45C3×Dic30C2×C411yescharacteristic, complemented
46C3×C5×#67—21no—
47C3×C5×D12C2×C411yescharacteristic, complemented
48C3×C4×C5×D3—21no—
49C3×C5×Dic6C2×C411yescharacteristic, complemented
50C2×C32×Dic5D411yescharacteristic
51C32×C4×D5C2×C411yescharacteristic
52C32×C4×D5D411yescharacteristic
53C32×C4×D5D411yescharacteristic
54C32×C4×D5C2311yescharacteristic
55C3×#1204—21no—
56C3×#1203—21no—
57C3×#1202—21no—
58C3×#1201—21no—
59C3×#1200—21no—
60C3×D3×Dic5—21no—
61C3×D5×Dic3—21no—
62C3×C3⋊#170—22no—
63#65793—31noHall
64C2×C3×#235—51no—
65C2×C32×C4⋊C4—51no—
66C2×C3×#208—51no—
67C3×#810—52no—
68C3×#809—52no—
69C22×C3×AGL(1,𝔽5)—21no—
70C22×C3×AGL(1,𝔽5)—21no—
71C22×C3×AGL(1,𝔽5)—21no—
72C22×C3×AGL(1,𝔽5)—21no—
73C3×C5×#41—31no—
74#6817C3×C411yescharacteristic, complemented
75C5×#235C3×C411yescharacteristic, complemented
76C3×#713—31no—
77C3×Q8×D5—31no—
78C3×#711—31no—
79C3×#711—61no—
80C3×D4×D5—31no—
81C3×D4×D5—61no—
82C3×#709—31no—
83C3×#709—61no—
84C2×C3×C4×D5—21no—
85C2×C3×C4×D5—61no—
86C2×C3×C4×D5C2×D311yescharacteristic
87C2×C3×C4×D5C22×C311yescharacteristic
88D5×#67—21no—
89#6782—21no—
90D5×D12C22×C311yescharacteristic
91C4×D3×D5—21no—
92#6773C3×C411yescharacteristic, complemented
93#6772C3×C411yescharacteristic, complemented
94#6771—21no—
95D5×Dic6C22×C311yescharacteristic
96#6762—21no—
97#6758—21no—
98D5⋊(C3⋊C8)C22×C312yes—
99C3×#704—61no—
100C3×C4⋊AGL(1,𝔽5)—21no—
101C3×C4⋊AGL(1,𝔽5)—21no—
102C3×C4⋊AGL(1,𝔽5)—22no—
103C3×C4⋊AGL(1,𝔽5)—21no—
104C3×C4⋊AGL(1,𝔽5)—21no—
105C3×C4⋊AGL(1,𝔽5)C2×D312yes—
106C3×C4⋊AGL(1,𝔽5)C22×C312yes—
107C3×#700—61no—
108C3×D5⋊C8—32no—
109C3×#417—151no—
110#4966—51no—
111C22×C32×C5C22⋊C411yescharacteristic
112C2×C3×D15—21no—
113C2×C3×C5×D3—21no—
114C2×C32×D5—21no—
115C2×C32×D5—21no—
116C2×C32×D5C22⋊C411yescharacteristic
117C2×C32×D5C2×D411yescharacteristic
118C3×D3×D5—41no—
119C3×D3×D5—41no—
120C32×AGL(1,𝔽5)—42no—
121C32×C4×C5C22⋊C411yescharacteristic
122C32×C4×C5C22×C411yescharacteristic
123C3×Dic15—21no—
124C3×C5×Dic3—21no—
125C32×Dic5C22⋊C411yescharacteristic
126C32×Dic5C2×D411yescharacteristic
127D5×#41—31no—
128C2×C4⋊AGL(1,𝔽5)C3×D311yescharacteristic, complemented
129D5⋊M16—31no—
130#4009—32no—
131#4007—32no—
132C22×C32×C4—51no—
133C22×C32×C4—101no—
134C2×C3×#67—101no—
135C3×#235—51no—
136C3×#235—51no—
137C3×#235—51no—
138C3×#235—101no—
139C3×#235—101no—
140C3×#235AGL(1,𝔽5)11yescharacteristic, complemented
141C2×C3×D12—51no—
142C2×C3×C4×D3—101no—
143C2×C3×Dic6—51no—
144C32×C4⋊C4—52no—
145C32×C4⋊C4—101no—
146C3×#208—101no—
147C3×#208—101no—
148C2×C3×C3⋊C8—52no—
149C22×C3×D5—21no—
150C22×C3×D5—61no—
151C22×C3×D5#6711yescharacteristic
152C22×C3×D5C3×D411yescharacteristic
153C2×D3×D5—21no—
154C2×C3×AGL(1,𝔽5)—22no—
155C2×C3×AGL(1,𝔽5)—22no—
156C2×C3×AGL(1,𝔽5)—22no—
157C2×C3×AGL(1,𝔽5)—22no—
158C2×C3×AGL(1,𝔽5)—42no—
159C2×C3×AGL(1,𝔽5)—42no—
160C2×C3×AGL(1,𝔽5)—42no—
161C2×C3×AGL(1,𝔽5)—42no—
162C3×C5×Q8—31no—
163C3×C5×D4—31no—
164C3×C5×D4—61no—
165C2×C3×C4×C5—21no—
166C2×C3×C4×C5—61no—
167C2×C3×C4×C5C4×D311yescharacteristic
168C2×C3×C4×C5C2×C3×C411yescharacteristic
169#1220—21no—
170D60C2×C3×C411yescharacteristic, complemented
171C4×D15—21no—
172Dic30C2×C3×C411yescharacteristic, complemented
173C5×#67—21no—
174C5×D12C2×C3×C411yescharacteristic, complemented
175C4×C5×D3—21no—
176C5×Dic6C2×C3×C411yescharacteristic, complemented
177C3×C22⋊D5—61no—
178C3×C22⋊D5—61no—
179C3×C22⋊D5—61no—
180C2×C3×Dic5—21no—
181C2×C3×Dic5—61no—
182C2×C3×Dic5D1211yescharacteristic
183C2×C3×Dic5C3×D411yescharacteristic
184C3×D20—31no—
185C3×D20—61no—
186C3×C4×D5—21no—
187C3×C4×D5—21no—
188C3×C4×D5—21no—
189C3×C4×D5—21no—
190C3×C4×D5—61no—
191C3×C4×D5—61no—
192C3×C4×D5—61no—
193C3×C4×D5C4×D311yescharacteristic
194C3×C4×D5D1211yescharacteristic
195C3×C4×D5#6711yescharacteristic
196C3×C4×D5C2×C3×C411yescharacteristic
197C3×C4×D5C3×D411yescharacteristic
198C3×C4×D5C3×D411yescharacteristic
199C3×C4×D5C22×D311yescharacteristic
200C3×C4×D5C23×C311yescharacteristic
201C3×Dic10—31no—
202C3×Dic10—61no—
203#1204—21no—
204#1203—21no—
205#1202—21no—
206#1201—21no—
207#1200—21no—
208D3×Dic5—21no—
209D5×Dic3—21no—
210C3⋊#170—22no—
211C3×#170—62no—
212C2×C3×#41—151no—
213C2×#235—51no—
214C2×C3×M16—151no—
215C2×C3×C4⋊C4—51no—
216C2×C3×C4⋊C4—51no—
217C2×C3×C4⋊C4—101no—
218C2×#208—51no—
219C3×#103—152no—
220C3×#102—152no—
221#810—52no—
222#809—52no—
223C2×C32×C5—21no—
224C2×C32×C5C2×C22⋊C411yescharacteristic
225C3×D15—41no—
226C3×C5×D3—41no—
227C32×D5—21no—
228C32×D5AGL(1,ℤ/8)11yescharacteristic
229C32×D5#13711yescharacteristic
230C22×AGL(1,𝔽5)—21no—
231C5×#41—31no—
232#713—31no—
233Q8×D5—31no—
234#711—31no—
235#711—61no—
236D4×D5—31no—
237D4×D5—61no—
238#709—31no—
239#709—61no—
240C2×C4×D5—61no—
241C2×C4×D5C2×C3×D311yescharacteristic
242#704—61no—
243C4⋊AGL(1,𝔽5)—21no—
244C4⋊AGL(1,𝔽5)C2×C3×D312yes—
245#700—61no—
246D5⋊C8—32no—
247C23×C32—51no—
248C22×C3×D3—101no—
249C2×C32×C4—51no—
250C2×C32×C4—51no—
251C2×C32×C4—51no—
252C2×C32×C4—51no—
253C2×C32×C4—51no—
254C2×C32×C4—102no—
255C2×C32×C4—202no—
256C2×C32×C4C2×AGL(1,𝔽5)11yescharacteristic
257C3×#67—21no—
258C3×#67—101no—
259C3×#67—101no—
260C3×#67—101no—
261C2×C3×Dic3—101no—
262C3×D12—51no—
263C3×D12—101no—
264C3×D12C2×AGL(1,𝔽5)11yescharacteristic, complemented
265C3×C4×D3—21no—
266C3×C4×D3—101no—
267C3×C4×D3—101no—
268C3×C4×D3—101no—
269C3×Dic6—51no—
270C3×Dic6—101no—
271C3×Dic6C2×AGL(1,𝔽5)11yescharacteristic, complemented
272C3×C3⋊C8—102no—
273#417—151noSylow
274C22×C3×C5—21no—
275C22×C3×C5—61no—
276C22×C3×C5(C2×D3)⋊C411yescharacteristic
277C22×C3×C5C3×C22⋊C411yescharacteristic
278C2×D15—21no—
279C2×C5×D3—21no—
280C2×C3×D5—21no—
281C2×C3×D5—21no—
282C2×C3×D5—21no—
283C2×C3×D5—21no—
284C2×C3×D5—21no—
285C2×C3×D5—21no—
286C2×C3×D5—21no—
287C2×C3×D5—21no—
288C2×C3×D5—21no—
289C2×C3×D5—21no—
290C2×C3×D5—61no—
291C2×C3×D5—121no—
292C2×C3×D5—121no—
293C2×C3×D5(C2×D3)⋊C411yescharacteristic
294C2×C3×D5C3×C22⋊C411yescharacteristic
295C2×C3×D5C2×#6711yescharacteristic
296C2×C3×D5C2×C3×D411yescharacteristic
297D3×D5—41no—
298D3×D5—41no—
299C3×AGL(1,𝔽5)—42no—
300C3×AGL(1,𝔽5)—42no—
301C3×AGL(1,𝔽5)—42no—
302C3×AGL(1,𝔽5)—42no—
303C3×C4×C5—21no—
304C3×C4×C5—21no—
305C3×C4×C5—61no—
306C3×C4×C5(C2×D3)⋊C411yescharacteristic
307C3×C4×C5C3×C22⋊C411yescharacteristic
308C3×C4×C5C2×C4×D311yescharacteristic
309C3×C4×C5C22×C3×C411yescharacteristic
310Dic15—21no—
311C3×Dic5—21no—
312C3×Dic5—21no—
313C3×Dic5—61no—
314C3×Dic5(C2×D3)⋊C411yescharacteristic
315C3×Dic5C3×C22⋊C411yescharacteristic
316C3×Dic5C2×D1211yescharacteristic
317C3×Dic5C2×C3×D411yescharacteristic
318C5×Dic3—21no—
319C3×#41—31no—
320C3×#41—151no—
321C3×#41—151no—
322C3×#41—151no—
323C3×#41—301no—
324C3×#41—301no—
325C2×C3×Q8—151no—
326C2×C3×D4—151no—
327C2×C3×D4—301no—
328C22×C3×C4—51no—
329C22×C3×C4—51no—
330C22×C3×C4—101no—
331C22×C3×C4—101no—
332C22×C3×C4—101no—
333C22×C3×C4—101no—
334C22×C3×C4—101no—
335C22×C3×C4—301no—
336C2×#67—101no—
337#235—51no—
338#235—51no—
339#235—51no—
340#235—101no—
341#235—101no—
342#235C3×AGL(1,𝔽5)11yescharacteristic, complemented
343C2×D12—51no—
344C2×C4×D3—101no—
345C2×Dic6—51no—
346C3×M16—301no—
347C3×M16—301no—
348C2×C3×C8—152no—
349C3×C4⋊C4—52no—
350C3×C4⋊C4—52no—
351C3×C4⋊C4—102no—
352C3×C4⋊C4—101no—
353C3×C4⋊C4—101no—
354C3×C4⋊C4—101no—
355C3×C4⋊C4—101no—
356#208—101no—
357#208—101no—
358C2×C3⋊C8—52no—
359C32×C5#41711yescharacteristic, complemented, Hall
360C22×D5—61no—
361C22×D5C3×#6711yescharacteristic
362C2×AGL(1,𝔽5)—22no—
363C2×AGL(1,𝔽5)—42no—
364C5×Q8—31no—
365C5×D4—31no—
366C5×D4—61no—
367C2×C4×C5—61no—
368C2×C4×C5C3×C4×D311yescharacteristic
369C22⋊D5—61no—
370C22⋊D5—61no—
371C22⋊D5—61no—
372C2×Dic5—61no—
373C2×Dic5C3×D1211yescharacteristic
374D20—31no—
375D20—61no—
376C4×D5—61no—
377C4×D5—61no—
378C4×D5—61no—
379C4×D5C3×C4×D311yescharacteristic
380C4×D5C3×D1211yescharacteristic
381C4×D5C3×#6711yescharacteristic
382C4×D5C22×C3×D311yescharacteristic
383Dic10—31no—
384Dic10—61no—
385#170—62no—
386C22×C32—51no—
387C22×C32—51no—
388C22×C32—101no—
389C22×C32—101no—
390C22×C32C22⋊AGL(1,𝔽5)11yescharacteristic
391C2×C3×D3—21no—
392C2×C3×D3—101no—
393C2×C3×D3—201no—
394C2×C3×D3—201no—
395C32×C4—51no—
396C32×C4—51no—
397C32×C4—202no—
398C32×C4C22⋊AGL(1,𝔽5)11yescharacteristic
399C32×C4C22×AGL(1,𝔽5)11yescharacteristic
400C3×Dic3—21no—
401C3×Dic3—101no—
402C2×#41—151no—
403C2×M16—151no—
404C2×C4⋊C4—51no—
405#103—152no—
406#102—152no—
407C2×C3×C5—21no—
408C2×C3×C5—21no—
409C2×C3×C5—21no—
410C2×C3×C5—21no—
411C2×C3×C5—21no—
412C2×C3×C5—121no—
413C2×C3×C5C2×(C2×D3)⋊C411yescharacteristic
414C2×C3×C5C2×C3×C22⋊C411yescharacteristic
415D15—41no—
416C3×D5—21no—
417C3×D5—21no—
418C3×D5—21no—
419C3×D5—21no—
420C3×D5—21no—
421C3×D5—21no—
422C3×D5—121no—
423C3×D5#93211yescharacteristic
424C3×D5#94211yescharacteristic
425C3×D5C3×AGL(1,ℤ/8)11yescharacteristic
426C3×D5C3×#13711yescharacteristic
427C5×D3—41no—
428C23×C3—51no—
429C23×C3—51no—
430C23×C3—101no—
431C23×C3—301no—
432C22×D3—101no—
433C3×Q8—31no—
434C3×Q8—151no—
435C3×Q8—301no—
436C3×D4—31no—
437C3×D4—61no—
438C3×D4—151no—
439C3×D4—301no—
440C3×D4—301no—
441C3×D4—301no—
442C3×D4—301no—
443C2×C3×C4—21no—
444C2×C3×C4—51no—
445C2×C3×C4—51no—
446C2×C3×C4—51no—
447C2×C3×C4—51no—
448C2×C3×C4—51no—
449C2×C3×C4—51no—
450C2×C3×C4—51no—
451C2×C3×C4—51no—
452C2×C3×C4—51no—
453C2×C3×C4—51no—
454C2×C3×C4—61no—
455C2×C3×C4—101no—
456C2×C3×C4—101no—
457C2×C3×C4—101no—
458C2×C3×C4—101no—
459C2×C3×C4—101no—
460C2×C3×C4—102no—
461C2×C3×C4—102no—
462C2×C3×C4—102no—
463C2×C3×C4—102no—
464C2×C3×C4—202no—
465C2×C3×C4—202no—
466C2×C3×C4—202no—
467C2×C3×C4—202no—
468C2×C3×C4—301no—
469C2×C3×C4—301no—
470C2×C3×C4—301no—
471C2×C3×C4—301no—
472C2×C3×C4D3×AGL(1,𝔽5)11yescharacteristic
473C2×C3×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
474#67—21no—
475#67—101no—
476#67—101no—
477#67—101no—
478C2×Dic3—101no—
479D12—51no—
480D12—101no—
481D12C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
482C4×D3—21no—
483C4×D3—101no—
484C4×D3—101no—
485C4×D3—101no—
486Dic6—51no—
487Dic6—101no—
488Dic6C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
489C3×C8—302no—
490C3⋊C8—102no—
491C22×C5—61no—
492C22×C5C3×(C2×D3)⋊C411yescharacteristic
493C2×D5—21no—
494C2×D5—21no—
495C2×D5—61no—
496C2×D5—121no—
497C2×D5—121no—
498C2×D5C3×(C2×D3)⋊C411yescharacteristic
499C2×D5C2×C3×#6711yescharacteristic
500AGL(1,𝔽5)—42no—
501C4×C5—61no—
502C4×C5C3×(C2×D3)⋊C411yescharacteristic
503C4×C5C2×C3×C4×D311yescharacteristic
504Dic5—61no—
505Dic5C3×(C2×D3)⋊C411yescharacteristic
506Dic5C2×C3×D1211yescharacteristic
507C2×C32—21no—
508C2×C32—51no—
509C2×C32—51no—
510C2×C32—101no—
511C2×C32C2×C22⋊AGL(1,𝔽5)11yescharacteristic
512C3×D3—41no—
513C3×D3—201no—
514#41—31no—
515#41—151no—
516#41—151no—
517#41—151no—
518#41—301no—
519#41—301no—
520C2×Q8—151no—
521C2×D4—151no—
522C2×D4—301no—
523C22×C4—51no—
524C22×C4—101no—
525C22×C4—301no—
526M16—301no—
527M16—301no—
528C2×C8—152no—
529C4⋊C4—52no—
530C4⋊C4—101no—
531C3×C5—21no—
532C3×C5#496611yescharacteristic, complemented
533C3×C5C3×#41711yescharacteristic, complemented
534C22×C3—21no—
535C22×C3—51no—
536C22×C3—51no—
537C22×C3—51no—
538C22×C3—51no—
539C22×C3—61no—
540C22×C3—101no—
541C22×C3—101no—
542C22×C3—101no—
543C22×C3—101no—
544C22×C3—101no—
545C22×C3—101no—
546C22×C3—101no—
547C22×C3—101no—
548C22×C3—101no—
549C22×C3—101no—
550C22×C3—301no—
551C22×C3—601no—
552C22×C3—601no—
553C22×C3(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
554C22×C3C3×C22⋊AGL(1,𝔽5)11yescharacteristic
555C2×D3—21no—
556C2×D3—101no—
557C2×D3—201no—
558C2×D3—201no—
559C3×C4—21no—
560C3×C4—21no—
561C3×C4—51no—
562C3×C4—51no—
563C3×C4—51no—
564C3×C4—51no—
565C3×C4—61no—
566C3×C4—101no—
567C3×C4—101no—
568C3×C4—202no—
569C3×C4—202no—
570C3×C4—202no—
571C3×C4—202no—
572C3×C4—301no—
573C3×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
574C3×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
575C3×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
576C3×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
577Dic3—21no—
578Dic3—101no—
579C2×C5—21no—
580C2×C5—121no—
581C2×C5C2×C3×(C2×D3)⋊C411yescharacteristic
582D5—21no—
583D5—121no—
584D5C3×#93211yescharacteristic
585D5C3×#94211yescharacteristic
586C32#6579311yescharacteristic, complemented, Sylow
587C23—51no—
588C23—301no—
589Q8—31no—
590Q8—151no—
591Q8—301no—
592D4—31no—
593D4—61no—
594D4—151no—
595D4—301no—
596D4—301no—
597D4—301no—
598D4—301no—
599C2×C4—51no—
600C2×C4—51no—
601C2×C4—51no—
602C2×C4—51no—
603C2×C4—51no—
604C2×C4—61no—
605C2×C4—102no—
606C2×C4—202no—
607C2×C4—301no—
608C2×C4—301no—
609C2×C4—301no—
610C2×C4—301no—
611C2×C4C3×D3×AGL(1,𝔽5)11yescharacteristic
612C8—302no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—51no—
619C2×C3—51no—
620C2×C3—51no—
621C2×C3—51no—
622C2×C3—101no—
623C2×C3—101no—
624C2×C3—101no—
625C2×C3—101no—
626C2×C3—101no—
627C2×C3—101no—
628C2×C3—121no—
629C2×C3—601no—
630C2×C3C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
631C2×C3C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
632D3—41no—
633D3—201no—
634C5C3×#496611yescharacteristic, complemented, Sylow
635C22—51no—
636C22—51no—
637C22—61no—
638C22—101no—
639C22—101no—
640C22—301no—
641C22—601no—
642C22—601no—
643C22C3×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
644C4—51no—
645C4—51no—
646C4—61no—
647C4—202no—
648C4—301no—
649C4C3×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
650C4C2×C3×D3×AGL(1,𝔽5)11yescharacteristic
651C3—21no—
652C3#1175170511yescharacteristic, direct product factor
653C3C3×#6579311yescharacteristic, complemented
654C2—21no—
655C2—51no—
656C2—51no—
657C2—101no—
658C2—121no—
659C2—601no—
660C2C2×C3×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2×C3C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC3×C4×C5C22×C3×C4
FrattiniC4C2×C3×D3×AGL(1,𝔽5)
FittingC2×C32×C4×C5C2×C4
socleC2×C32×C5C2×C22⋊C4
prime radicalC3×D5×#235C2
cosocleC3×C4×D5C23×C3
hypercenterC2×C3×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C3×#417
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
2. C3×D5⋊#208C2semidirect
3. C2×C32×C4⋊AGL(1,𝔽5)C2semidirect
4. C3×#91153C2semidirect
5. C3×#91151C2semidirect
7. #11751705C3direct (N × H)
9. C3×#6817C4semidirect
10. C3×C5×#235C4semidirect
16. C3×#6773C4semidirect
17. C3×#6772C4semidirect
28. D5⋊#208C2×C3semidirect
30. C2×C3×C4⋊AGL(1,𝔽5)D3semidirect
31. C2×C3×C4⋊AGL(1,𝔽5)C2×C3semidirect
35. #91153C2×C3semidirect
36. #91151C2×C3semidirect
43. C3×D60C2×C4semidirect
45. C3×Dic30C2×C4semidirect
47. C3×C5×D12C2×C4semidirect
49. C3×C5×Dic6C2×C4semidirect
74. #6817C3×C4semidirect
75. C5×#235C3×C4semidirect
92. #6773C3×C4semidirect
93. #6772C3×C4semidirect
128. C2×C4⋊AGL(1,𝔽5)C3×D3semidirect
140. C3×#235AGL(1,𝔽5)semidirect
170. D60C2×C3×C4semidirect
172. Dic30C2×C3×C4semidirect
174. C5×D12C2×C3×C4semidirect
176. C5×Dic6C2×C3×C4semidirect
264. C3×D12C2×AGL(1,𝔽5)semidirect
271. C3×Dic6C2×AGL(1,𝔽5)semidirect
342. #235C3×AGL(1,𝔽5)semidirect
359. C32×C5#417semidirect
481. D12C2×C3×AGL(1,𝔽5)semidirect
488. Dic6C2×C3×AGL(1,𝔽5)semidirect
532. C3×C5#4966semidirect
533. C3×C5C3×#417semidirect
586. C32#65793semidirect
634. C5C3×#4966semidirect
652. C3#11751705direct (N × H)
653. C3C3×#65793semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#2352
C3×D5⋊#2082
C2×C32×C4⋊AGL(1,𝔽5)2
C3×#911532
C3×#911512
C3×#657933
#117517053
C3×#49665