Finite Group Databasebeta

← C5×#74962 #14326674

Subgroups — C5×#74962 #14326674

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×C4⋊C4C211yesmaximal, characteristic
2C3×C5×#387C211yesmaximal, characteristic, complemented
3C5×#4987C211yesmaximal, characteristic
4C5×#4980C211yesmaximal, characteristic, complemented
5C5×#4976C211yesmaximal, characteristic, complemented
6C4×C5×(C2×D3)⋊C4C211yesmaximal, characteristic
7C4×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
8C5×#4667C211yesmaximal, characteristic
9C5×#4667C211yesmaximal, characteristic
10C5×#4666C211yesmaximal, characteristic
11C5×#4666C211yesmaximal, characteristic
12C5×#4654C211yesmaximal, characteristic, complemented
13C5×#4653C211yesmaximal, characteristic, complemented
14C5×#4649C211yesmaximal, characteristic, complemented
15C5×#4647C211yesmaximal, characteristic, complemented
16C5×#2345—31nomaximal, Hall
17C22×C4×C5×D3C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C42×C5C2211yescharacteristic
23C2×C5×(C2×D3)⋊C4C2211yescharacteristic
24C2×C5×(C2×D3)⋊C4C2211yescharacteristic
25C2×C5×(C2×D3)⋊C4C2211yescharacteristic
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C2×C5×C4⋊Dic3C2211yescharacteristic
29C2×C5×Dic3⋊C4C2211yescharacteristic
30C2×C5×Dic3⋊C4C2211yescharacteristic
31C2×C5×Dic3⋊C4C2211yescharacteristic
32C2×C5×Dic3⋊C4C2211yescharacteristic
33C2×C5×Dic3⋊C4C2211yescharacteristic
34C2×C5×Dic3⋊C4C2211yescharacteristic
35C2×C4×C5×Dic3C2211yescharacteristic
36C2×C4×C5×Dic3C2211yescharacteristic
37C2×C4×C5×Dic3C2211yescharacteristic
38C2×C4×C5×Dic3C2211yescharacteristic
39C2×C4×C5×Dic3C2211yescharacteristic
40C5×D3×C4⋊C4C418yescomplemented
41C3×C5×#95C2211yescharacteristic
42C3×C5×#95C2211yescharacteristic
43C3×C5×#95C2211yescharacteristic
44C3×C5×#95C2211yescharacteristic
45C5×C3⋊#95C2211yescharacteristic
46C5×C3⋊#95C2211yescharacteristic
47C5×C3⋊#95C2211yescharacteristic
48C5×C3⋊#95C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C5×C3⋊#95C2211yescharacteristic
51C5×C3⋊#95C2211yescharacteristic
52C5×C3⋊#95C2211yescharacteristic
53#74962C511yesmaximal, characteristic, direct product factor, Hall
54C22×C5×C4⋊C4—31no—
55C5×#389—31no—
56C5×#389—31no—
57C5×#387—31no—
58C5×#387—31no—
59C5×#387—31no—
60C5×#387D311yescharacteristic, complemented
61C5×#380—31no—
62C5×#380—31no—
63C5×#380—31no—
64C4×C5×C4⋊C4—31no—
65C4×C5×C4⋊C4—31no—
66C4×C5×C22⋊C4—31no—
67C4×C5×C22⋊C4—31no—
68C4×C5×C22⋊C4—31no—
69C23×C5×D3C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C5×Dic3C2311yescharacteristic
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C2×C4×C5×D3—22no—
85C2×C4×C5×D3—22no—
86C2×C4×C5×D3—41no—
87C2×C4×C5×D3—41no—
88C2×C4×C5×D3—41no—
89C2×C4×C5×D3—41no—
90C2×C4×C5×D3C2×C414yes—
91C2×C4×C5×D3C2×C414yes—
92C2×C4×C5×D3C2×C414yes—
93C3×C5×C4⋊C4—41no—
94C3×C5×C4⋊C4C2×C414yes—
95C3×C42×C5—41no—
96C5×(C2×D3)⋊C4—22no—
97C5×(C2×D3)⋊C4—22no—
98C5×(C2×D3)⋊C4—22no—
99C5×(C2×D3)⋊C4Q814yes—
100C5×C4⋊Dic3—41no—
101C5×C4⋊Dic3C2×C414yes—
102C5×Dic3⋊C4—22no—
103C5×Dic3⋊C4—22no—
104C5×Dic3⋊C4—41no—
105C5×Dic3⋊C4—41no—
106C5×Dic3⋊C4C2×C414yes—
107C5×Dic3⋊C4C2×C414yes—
108C4×C5×Dic3—22no—
109C4×C5×Dic3—22no—
110C4×C5×Dic3—41no—
111C4×C5×Dic3—41no—
112C4×C5×Dic3—41no—
113C2×D3×C4⋊C4C2×C511yescharacteristic
114C3×#387C2×C511yescharacteristic, complemented
115#4987C2×C511yescharacteristic
116#4980C2×C511yescharacteristic, complemented
117#4976C2×C511yescharacteristic, complemented
118C4×(C2×D3)⋊C4C2×C511yescharacteristic
119C4×Dic3⋊C4C2×C511yescharacteristic, complemented
120#4667C2×C511yescharacteristic
121#4667C2×C511yescharacteristic
122#4666C2×C511yescharacteristic
123#4666C2×C511yescharacteristic
124#4654C2×C511yescharacteristic, complemented
125#4653C2×C511yescharacteristic, complemented
126#4649C2×C511yescharacteristic, complemented
127#4647C2×C511yescharacteristic, complemented
128C23×C4×C5—31no—
129C23×C4×C5—31no—
130C23×C4×C5—31no—
131C2×C5×C4⋊C4—31no—
132C2×C5×C4⋊C4—31no—
133C2×C5×C4⋊C4—31no—
134C2×C5×C4⋊C4—38no—
135C2×C5×C4⋊C4—31no—
136C2×C5×C4⋊C4—31no—
137C2×C5×C4⋊C4—31no—
138C2×C5×C4⋊C4—31no—
139C2×C5×C4⋊C4—31no—
140C2×C5×C4⋊C4C2×D311yescharacteristic
141C2×C5×C4⋊C4C2×D311yescharacteristic
142C2×C5×C22⋊C4—31no—
143C2×C5×C22⋊C4—31no—
144C2×C5×C22⋊C4—31no—
145C2×C5×C22⋊C4—31no—
146C2×C42×C5—31no—
147C2×C42×C5—31no—
148C2×C42×C5—31no—
149C2×C42×C5—31no—
150C2×C42×C5—31no—
151C2×C42×C5C2×D311yescharacteristic
152C5×#95—31no—
153C5×#95—31no—
154C5×#95—31no—
155C5×#95—31no—
156C5×#95—31no—
157C5×#95—31no—
158C5×#95—31no—
159C5×#95—31no—
160C5×#95C2×D311yescharacteristic
161C5×#95C2×D311yescharacteristic
162C5×#95C2×D311yescharacteristic
163C5×#95C2×D311yescharacteristic
164#2345—31noSylow
165C23×C3×C5C2411yescharacteristic
166C22×C5×D3—21no—
167C22×C5×D3—21no—
168C22×C5×D3—21no—
169C22×C5×D3—21no—
170C22×C5×D3C22×C412yes—
171C22×C5×D3C2×Q812yes—
172C22×C5×D3#4112yes—
173C2×C3×C4×C5—21no—
174C2×C3×C4×C5—21no—
175C2×C3×C4×C5—21no—
176C2×C3×C4×C5—21no—
177C2×C3×C4×C5—21no—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—21no—
180C2×C3×C4×C5—21no—
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5—21no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5C22×C412yes—
191C2×C3×C4×C5C22×C412yes—
192C2×C3×C4×C5C22×C412yes—
193C2×C3×C4×C5C2×Q812yes—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3—21no—
199C2×C5×Dic3—21no—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3C22×C412yes—
210C2×C5×Dic3C22×C412yes—
211C2×C5×Dic3C22×C412yes—
212C2×C5×Dic3C2×Q812yes—
213C2×C5×Dic3#4112yes—
214C2×C5×Dic3#4112yes—
215C4×C5×D3—28no—
216C4×C5×D3—44no—
217C4×C5×D3—44no—
218C22×C4×D3C22×C511yescharacteristic
219C22×C4×D3C22×C511yescharacteristic
220C22×C4×D3C22×C511yescharacteristic
221C2×C3×C4⋊C4C22×C511yescharacteristic
222C2×C3×C4⋊C4C22×C511yescharacteristic
223C2×C3×C42C22×C511yescharacteristic
224C2×(C2×D3)⋊C4C22×C511yescharacteristic
225C2×(C2×D3)⋊C4C22×C511yescharacteristic
226C2×(C2×D3)⋊C4C22×C511yescharacteristic
227C2×(C2×D3)⋊C4C22×C511yescharacteristic
228C2×C4⋊Dic3C22×C511yescharacteristic
229C2×C4⋊Dic3C22×C511yescharacteristic
230C2×Dic3⋊C4C22×C511yescharacteristic
231C2×Dic3⋊C4C22×C511yescharacteristic
232C2×Dic3⋊C4C22×C511yescharacteristic
233C2×Dic3⋊C4C22×C511yescharacteristic
234C2×Dic3⋊C4C22×C511yescharacteristic
235C2×Dic3⋊C4C22×C511yescharacteristic
236C2×C4×Dic3C22×C511yescharacteristic
237C2×C4×Dic3C22×C511yescharacteristic
238C2×C4×Dic3C22×C511yescharacteristic
239C2×C4×Dic3C22×C511yescharacteristic
240C2×C4×Dic3C22×C511yescharacteristic
241D3×C4⋊C4C4×C518yescomplemented
242C3×#95C22×C511yescharacteristic
243C3×#95C22×C511yescharacteristic
244C3×#95C22×C511yescharacteristic
245C3×#95C22×C511yescharacteristic
246C3⋊#95C22×C511yescharacteristic
247C3⋊#95C22×C511yescharacteristic
248C3⋊#95C22×C511yescharacteristic
249C3⋊#95C22×C511yescharacteristic
250C3⋊#95C22×C511yescharacteristic
251C3⋊#95C22×C511yescharacteristic
252C3⋊#95C22×C511yescharacteristic
253C3⋊#95C22×C511yescharacteristic
254C24×C5—31no—
255C22×C4×C5—31no—
256C22×C4×C5—31no—
257C22×C4×C5—31no—
258C22×C4×C5—31no—
259C22×C4×C5—34no—
260C22×C4×C5—34no—
261C22×C4×C5—34no—
262C22×C4×C5—31no—
263C22×C4×C5—31no—
264C22×C4×C5—31no—
265C22×C4×C5—62no—
266C22×C4×C5—62no—
267C22×C4×C5—121no—
268C22×C4×C5—121no—
269C22×C4×C5—121no—
270C22×C4×C5—121no—
271C22×C4×C5C22×D311yescharacteristic
272C22×C4×C5C22×D311yescharacteristic
273C22×C4×C5C22×D311yescharacteristic
274C22×C4×C5C22×D311yescharacteristic
275C22×C4×C5C22×D311yescharacteristic
276C22×C4×C5C22×D311yescharacteristic
277C22×C4×C5C22×D311yescharacteristic
278C5×C4⋊C4—34no—
279C5×C4⋊C4—34no—
280C5×C4⋊C4—34no—
281C5×C4⋊C4—41no—
282C5×C4⋊C4—62no—
283C5×C4⋊C4—62no—
284C5×C4⋊C4—121no—
285C5×C4⋊C4—121no—
286C5×C4⋊C4—121no—
287C5×C4⋊C4C4×D314yes—
288C5×C22⋊C4—34no—
289C5×C22⋊C4—62no—
290C5×C22⋊C4—62no—
291C5×C22⋊C4—62no—
292C42×C5—41no—
293C42×C5—62no—
294C42×C5—62no—
295C42×C5—121no—
296C42×C5—121no—
297C42×C5—121no—
298C22×C4⋊C4—31no—
299#389—31no—
300#389—31no—
301#387—31no—
302#387—31no—
303#387—31no—
304#387C5×D311yescharacteristic, complemented
305#380—31no—
306#380—31no—
307#380—31no—
308C4×C4⋊C4—31no—
309C4×C4⋊C4—31no—
310C4×C22⋊C4—31no—
311C4×C22⋊C4—31no—
312C4×C22⋊C4—31no—
313C22×C3×C5C23×C411yescharacteristic
314C22×C3×C5C22×Q811yescharacteristic
315C22×C3×C5C2×#4111yescharacteristic
316C22×C3×C5C2×#4111yescharacteristic
317C22×C3×C5C2×#4111yescharacteristic
318C22×C3×C5H(5,𝔽2)11yescharacteristic
319C22×C3×C5H(5,𝔽2)11yescharacteristic
320C2×C5×D3—22no—
321C2×C5×D3—22no—
322C2×C5×D3—22no—
323C2×C5×D3—22no—
324C2×C5×D3—22no—
325C2×C5×D3—22no—
326C2×C5×D3C4×Q814yes—
327C3×C4×C5—22no—
328C3×C4×C5—22no—
329C3×C4×C5—22no—
330C3×C4×C5—22no—
331C3×C4×C5—41no—
332C3×C4×C5—41no—
333C3×C4×C5—41no—
334C5×Dic3—22no—
335C5×Dic3—22no—
336C5×Dic3—22no—
337C5×Dic3—41no—
338C5×Dic3—41no—
339C5×Dic3—41no—
340C5×Dic3#11714yes—
341C23×D3C23×C511yescharacteristic
342C22×C3×C4C23×C511yescharacteristic
343C22×C3×C4C23×C511yescharacteristic
344C22×C3×C4C23×C511yescharacteristic
345C22×C3×C4C23×C511yescharacteristic
346C22×C3×C4C23×C511yescharacteristic
347C22×C3×C4C23×C511yescharacteristic
348C22×C3×C4C23×C511yescharacteristic
349C22×Dic3C23×C511yescharacteristic
350C22×Dic3C23×C511yescharacteristic
351C22×Dic3C23×C511yescharacteristic
352C22×Dic3C23×C511yescharacteristic
353C22×Dic3C23×C511yescharacteristic
354C22×Dic3C23×C511yescharacteristic
355C22×Dic3C23×C511yescharacteristic
356C2×C4×D3—22no—
357C2×C4×D3—22no—
358C2×C4×D3—41no—
359C2×C4×D3—41no—
360C2×C4×D3—41no—
361C2×C4×D3—41no—
362C2×C4×D3C2×C4×C514yes—
363C2×C4×D3C2×C4×C514yes—
364C2×C4×D3C2×C4×C514yes—
365C3×C4⋊C4—41no—
366C3×C4⋊C4C2×C4×C514yes—
367C3×C42—41no—
368(C2×D3)⋊C4—22no—
369(C2×D3)⋊C4—22no—
370(C2×D3)⋊C4—22no—
371(C2×D3)⋊C4C5×Q814yes—
372C4⋊Dic3—41no—
373C4⋊Dic3C2×C4×C514yes—
374Dic3⋊C4—22no—
375Dic3⋊C4—22no—
376Dic3⋊C4—41no—
377Dic3⋊C4—41no—
378Dic3⋊C4C2×C4×C514yes—
379Dic3⋊C4C2×C4×C514yes—
380C4×Dic3—22no—
381C4×Dic3—22no—
382C4×Dic3—41no—
383C4×Dic3—41no—
384C4×Dic3—41no—
385C23×C5—32no—
386C23×C5—32no—
387C23×C5—32no—
388C23×C5—61no—
389C23×C5—61no—
390C23×C5—61no—
391C23×C5—61no—
392C23×C5C23×D311yescharacteristic
393C2×C4×C5—21no—
394C2×C4×C5—21no—
395C2×C4×C5—21no—
396C2×C4×C5—21no—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5—21no—
400C2×C4×C5—21no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—21no—
407C2×C4×C5—21no—
408C2×C4×C5—21no—
409C2×C4×C5—21no—
410C2×C4×C5—32no—
411C2×C4×C5—32no—
412C2×C4×C5—32no—
413C2×C4×C5—32no—
414C2×C4×C5—32no—
415C2×C4×C5—32no—
416C2×C4×C5—68no—
417C2×C4×C5—61no—
418C2×C4×C5—61no—
419C2×C4×C5—61no—
420C2×C4×C5—61no—
421C2×C4×C5—61no—
422C2×C4×C5—61no—
423C2×C4×C5—61no—
424C2×C4×C5—61no—
425C2×C4×C5—61no—
426C2×C4×C5—61no—
427C2×C4×C5—61no—
428C2×C4×C5—61no—
429C2×C4×C5—61no—
430C2×C4×C5—61no—
431C2×C4×C5—61no—
432C2×C4×C5—124no—
433C2×C4×C5—124no—
434C2×C4×C5C2×C4×D312yes—
435C2×C4×C5C2×C4×D312yes—
436C2×C4×C5C2×C4×D312yes—
437C2×C4×C5D3×Q812yes—
438C23×C4—31no—
439C23×C4—31no—
440C23×C4—31no—
441C2×C4⋊C4—31no—
442C2×C4⋊C4—31no—
443C2×C4⋊C4—31no—
444C2×C4⋊C4—38no—
445C2×C4⋊C4—31no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4C2×C5×D311yescharacteristic
451C2×C4⋊C4C2×C5×D311yescharacteristic
452C2×C22⋊C4—31no—
453C2×C22⋊C4—31no—
454C2×C22⋊C4—31no—
455C2×C22⋊C4—31no—
456C2×C42—31no—
457C2×C42—31no—
458C2×C42—31no—
459C2×C42—31no—
460C2×C42—31no—
461C2×C42C2×C5×D311yescharacteristic
462#95—31no—
463#95—31no—
464#95—31no—
465#95—31no—
466#95—31no—
467#95—31no—
468#95—31no—
469#95—31no—
470#95C2×C5×D311yescharacteristic
471#95C2×C5×D311yescharacteristic
472#95C2×C5×D311yescharacteristic
473#95C2×C5×D311yescharacteristic
474C2×C3×C5C2×#11711yescharacteristic
475C2×C3×C5C2×C4×Q811yescharacteristic
476C2×C3×C5#51811yescharacteristic
477C2×C3×C5#55311yescharacteristic
478C2×C3×C5#55311yescharacteristic
479C2×C3×C5#55411yescharacteristic
480C2×C3×C5#55411yescharacteristic
481C5×D3—24no—
482C23×C3C24×C511yescharacteristic
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3C22×C4×C512yes—
488C22×D3C2×C5×Q812yes—
489C22×D3C5×#4112yes—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4C22×C4×C512yes—
508C2×C3×C4C22×C4×C512yes—
509C2×C3×C4C22×C4×C512yes—
510C2×C3×C4C2×C5×Q812yes—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3C22×C4×C512yes—
527C2×Dic3C22×C4×C512yes—
528C2×Dic3C22×C4×C512yes—
529C2×Dic3C2×C5×Q812yes—
530C2×Dic3C5×#4112yes—
531C2×Dic3C5×#4112yes—
532C4×D3—28no—
533C4×D3—44no—
534C4×D3—44no—
535C22×C5—34no—
536C22×C5—62no—
537C22×C5—62no—
538C22×C5—62no—
539C22×C5—62no—
540C22×C5—62no—
541C22×C5—62no—
542C22×C5C22×C4×D311yescharacteristic
543C22×C5#100411yescharacteristic
544C22×C5C2×D3×Q811yescharacteristic
545C22×C5D3×#4111yescharacteristic
546C22×C5D3×#4111yescharacteristic
547C22×C5D3×#4111yescharacteristic
548C22×C5#100911yescharacteristic
549C4×C5—22no—
550C4×C5—22no—
551C4×C5—22no—
552C4×C5—22no—
553C4×C5—34no—
554C4×C5—41no—
555C4×C5—41no—
556C4×C5—41no—
557C4×C5—62no—
558C4×C5—62no—
559C4×C5—62no—
560C4×C5—121no—
561C4×C5—121no—
562C4×C5—121no—
563C24—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—34no—
569C22×C4—34no—
570C22×C4—34no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—121no—
577C22×C4—121no—
578C22×C4—121no—
579C22×C4—121no—
580C22×C4C22×C5×D311yescharacteristic
581C22×C4C22×C5×D311yescharacteristic
582C22×C4C22×C5×D311yescharacteristic
583C22×C4C22×C5×D311yescharacteristic
584C22×C4C22×C5×D311yescharacteristic
585C22×C4C22×C5×D311yescharacteristic
586C22×C4C22×C5×D311yescharacteristic
587C4⋊C4—34no—
588C4⋊C4—34no—
589C4⋊C4—34no—
590C4⋊C4—41no—
591C4⋊C4—62no—
592C4⋊C4—62no—
593C4⋊C4—121no—
594C4⋊C4—121no—
595C4⋊C4—121no—
596C4⋊C4C4×C5×D314yes—
597C22⋊C4—34no—
598C22⋊C4—62no—
599C22⋊C4—62no—
600C22⋊C4—62no—
601C42—41no—
602C42—62no—
603C42—62no—
604C42—121no—
605C42—121no—
606C42—121no—
607C3×C5#234511yescharacteristic, complemented, Hall
608C22×C3C23×C4×C511yescharacteristic
609C22×C3C22×C5×Q811yescharacteristic
610C22×C3C2×C5×#4111yescharacteristic
611C22×C3C2×C5×#4111yescharacteristic
612C22×C3C2×C5×#4111yescharacteristic
613C22×C3C5×H(5,𝔽2)11yescharacteristic
614C22×C3C5×H(5,𝔽2)11yescharacteristic
615C2×D3—22no—
616C2×D3—22no—
617C2×D3—22no—
618C2×D3—22no—
619C2×D3—22no—
620C2×D3—22no—
621C2×D3C4×C5×Q814yes—
622C3×C4—22no—
623C3×C4—22no—
624C3×C4—22no—
625C3×C4—22no—
626C3×C4—41no—
627C3×C4—41no—
628C3×C4—41no—
629Dic3—22no—
630Dic3—22no—
631Dic3—22no—
632Dic3—41no—
633Dic3—41no—
634Dic3—41no—
635Dic3C5×#11714yes—
636C2×C5—64no—
637C2×C5D3×#11711yescharacteristic
638C2×C5#554511yescharacteristic
639C2×C5C4×D3×Q811yescharacteristic
640C2×C5#563611yescharacteristic
641C2×C5#566111yescharacteristic
642C2×C5#569011yescharacteristic
643C2×C5#570911yescharacteristic
644C23—32no—
645C23—32no—
646C23—32no—
647C23—61no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23C23×C5×D311yescharacteristic
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—32no—
670C2×C4—32no—
671C2×C4—32no—
672C2×C4—32no—
673C2×C4—32no—
674C2×C4—32no—
675C2×C4—68no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—124no—
692C2×C4—124no—
693C2×C4C2×C4×C5×D312yes—
694C2×C4C2×C4×C5×D312yes—
695C2×C4C2×C4×C5×D312yes—
696C2×C4C5×D3×Q812yes—
697C2×C3C2×C5×#11711yescharacteristic
698C2×C3C2×C4×C5×Q811yescharacteristic
699C2×C3C5×#51811yescharacteristic
700C2×C3C5×#55311yescharacteristic
701C2×C3C5×#55311yescharacteristic
702C2×C3C5×#55411yescharacteristic
703C2×C3C5×#55411yescharacteristic
704D3—24no—
705C5#7496211yescharacteristic, direct product factor, Sylow
706C22—34no—
707C22—62no—
708C22—62no—
709C22—62no—
710C22—62no—
711C22—62no—
712C22—62no—
713C22C22×C4×C5×D311yescharacteristic
714C22C5×#100411yescharacteristic
715C22C2×C5×D3×Q811yescharacteristic
716C22C5×D3×#4111yescharacteristic
717C22C5×D3×#4111yescharacteristic
718C22C5×D3×#4111yescharacteristic
719C22C5×#100911yescharacteristic
720C4—22no—
721C4—22no—
722C4—22no—
723C4—22no—
724C4—34no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—62no—
729C4—62no—
730C4—62no—
731C4—121no—
732C4—121no—
733C4—121no—
734C3C5×#234511yescharacteristic, complemented, Sylow
735C2—64no—
736C2C5×D3×#11711yescharacteristic
737C2C5×#554511yescharacteristic
738C2C4×C5×D3×Q811yescharacteristic
739C2C5×#563611yescharacteristic
740C2C5×#566111yescharacteristic
741C2C5×#569011yescharacteristic
742C2C5×#570911yescharacteristic
subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#387C2
socleC23×C3×C5C24
prime radicalC23×C5×D3C23
cosocleC23×C3C24×C5
hypercenterC5×#387D3
hypocenterC3C5×#2345
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C5×#387

Complements

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

NH ≅ G/Ntype
2. C3×C5×#387C2semidirect
4. C5×#4980C2semidirect
5. C5×#4976C2semidirect
7. C4×C5×Dic3⋊C4C2semidirect
12. C5×#4654C2semidirect
13. C5×#4653C2semidirect
14. C5×#4649C2semidirect
15. C5×#4647C2semidirect
40. C5×D3×C4⋊C4C4semidirect
53. #74962C5direct (N × H)
60. C5×#387D3semidirect
114. C3×#387C2×C5semidirect
116. #4980C2×C5semidirect
117. #4976C2×C5semidirect
119. C4×Dic3⋊C4C2×C5semidirect
124. #4654C2×C5semidirect
125. #4653C2×C5semidirect
126. #4649C2×C5semidirect
127. #4647C2×C5semidirect
241. D3×C4⋊C4C4×C5semidirect
304. #387C5×D3semidirect
607. C3×C5#2345semidirect
705. C5#74962direct (N × H)
734. C3C5×#2345semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×C4⋊C42
C3×C5×#3872
C5×#49872
C5×#49802
C5×#49762
C4×C5×(C2×D3)⋊C42
C4×C5×Dic3⋊C42
C5×#46672
C5×#46662
C5×#46542
C5×#46532
C5×#46492
C5×#46472
C5×#23453
#749625