Finite Group Databasebeta

← #11752687

Subgroups — #11752687

Order 960.

476 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91765C211yesmaximal, characteristic, complemented
2C4×C5×D12C211yesmaximal, characteristic, complemented
3C3×#4018C211yesmaximal, characteristic, complemented
4#91454C211yesmaximal, characteristic, complemented
5#91453C211yesmaximal, characteristic, complemented
6#91452C211yesmaximal, characteristic, complemented
7#91448C211yesmaximal, characteristic, complemented
8#91446C211yesmaximal, characteristic, complemented
9#91440C211yesmaximal, characteristic, complemented
10#91416C211yesmaximal, characteristic, complemented
11#91405C211yesmaximal, characteristic, complemented
12D3×#683C211yesmaximal, characteristic, complemented
13#91372C211yesmaximal, characteristic, complemented
14#91356C211yesmaximal, characteristic, complemented
15#91335C211yesmaximal, characteristic, complemented
16#65874—31nomaximal, Hall
17C2×C5×D12C2211yescharacteristic
18C2×C4×C5×D3C2211yescharacteristic
19C2×C4×C5×D3C2211yescharacteristic
20C2×C3×C4×D5C2211yescharacteristic
21C2×#1203C2211yescharacteristic
22C2×#1203C2211yescharacteristic
23C2×#1202C2211yescharacteristic
24C2×#1201C2211yescharacteristic
25C2×#1201C2211yescharacteristic
26C2×#1200C2211yescharacteristic
27C2×D3×Dic5C2211yescharacteristic
28C2×D3×Dic5C2211yescharacteristic
29C3×C42×C5C2211yescharacteristic
30#6714C2211yescharacteristic
31#6714C2211yescharacteristic
32#6714C2211yescharacteristic
33#6712C2211yescharacteristic
34#6712C2211yescharacteristic
35#6712C2211yescharacteristic
36C5×(C2×D3)⋊C4C2211yescharacteristic
37C5×(C2×D3)⋊C4C2211yescharacteristic
38C5×C4⋊Dic3C2211yescharacteristic
39C3×#685C2211yescharacteristic
40C3×#685C2211yescharacteristic
41C3×#683C2211yescharacteristic
42C3×#683C2211yescharacteristic
43C3×C4×Dic5C2211yescharacteristic
44Dic3⋊Dic5C2211yescharacteristic
45#6669C2211yescharacteristic
46#6668C2211yescharacteristic
47#6668C2211yescharacteristic
48(C2×D3)⋊Dic5C2211yescharacteristic
49(C2×D3)⋊Dic5C2211yescharacteristic
50#6665C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5530—51nomaximal, Hall
53C4×C5×D4—31no—
54#4085—31no—
55#4085—31no—
56#4076—31no—
57#4075—31no—
58C4×C22⋊D5—31no—
59C2×#683—31no—
60#4040—31no—
61#4035—31no—
62#4030—31no—
63#4027—31no—
64#4027—31no—
65#4025—31no—
66#4022—31no—
67#4018D311yescharacteristic, complemented
68C22×D15C2311yescharacteristic
69C22×C5×D3C2311yescharacteristic
70C22×C5×D3C2311yescharacteristic
71C22×C3×D5C2311yescharacteristic
72C2×C3×C4×C5C2311yescharacteristic
73C2×C3×C4×C5C2311yescharacteristic
74C2×C3×C4×C5C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77C2×Dic15C2311yescharacteristic
78C2×C5×Dic3C2311yescharacteristic
79C2×C5×Dic3C2311yescharacteristic
80C5×D12—22no—
81C4×C5×D3—41no—
82C4×C5×D3—41no—
83C2×C3×Dic5C2311yescharacteristic
84C2×C3×Dic5C2311yescharacteristic
85C2×C3×Dic5C2311yescharacteristic
86C3×C4×D5—22no—
87#1203—22no—
88#1203—22no—
89#1202—41no—
90#1201—22no—
91#1201—41no—
92#1200—41no—
93D3×Dic5—22no—
94D3×Dic5—41no—
95C3×#117—51no—
96#930—51no—
97C4×#67—51no—
98#895—51no—
99#893—51no—
100D3×C4⋊C4—51no—
101#890—51no—
102#884—51no—
103#884—51no—
104#883—51no—
105#883—51no—
106#876—51no—
107#876—51no—
108C4×D12—51no—
109C4×D12D511yescharacteristic, complemented
110C2×C5×D4—31no—
111C22×C4×C5—31no—
112C22×C4×C5—31no—
113C2×C22⋊D5—31no—
114C2×C22⋊D5—31no—
115C2×C22⋊D5—31no—
116C2×C22⋊D5—31no—
117C22×Dic5—31no—
118C22×Dic5—31no—
119C2×D20—31no—
120C2×C4×D5—31no—
121C2×C4×D5C2×D311yescharacteristic
122C5×C4⋊C4—31no—
123C5×C22⋊C4—31no—
124C5×C22⋊C4—31no—
125C42×C5C2×D311yescharacteristic
126C22⋊Dic5—31no—
127C22⋊Dic5—31no—
128#685—31no—
129#685—31no—
130#685—31no—
131#685—31no—
132#685C2×D311yescharacteristic
133#685C2×D311yescharacteristic
134C4⋊Dic5—31no—
135#683—31no—
136#683—31no—
137#683—31no—
138#683—31no—
139#683—31no—
140#683—31no—
141#683C2×D311yescharacteristic
142#683C2×D311yescharacteristic
143C4×Dic5—31no—
144C4×Dic5C2×D311yescharacteristic
145#553—151noSylow
146C22×C3×C5C2411yescharacteristic
147C2×D15—21no—
148C2×D15—21no—
149C2×D15—21no—
150C2×C5×D3—21no—
151C2×C5×D3—21no—
152C2×C5×D3—21no—
153C2×C5×D3—21no—
154C2×C5×D3—21no—
155C2×C5×D3#4112yes—
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162Dic15—21no—
163Dic15—21no—
164Dic15—21no—
165C3×Dic5—21no—
166C3×Dic5—21no—
167C3×Dic5#4112yes—
168C5×Dic3—21no—
169C5×Dic3—21no—
170C22×C3×C4—51no—
171C2×#67—51no—
172C2×#67—51no—
173C2×#67—51no—
174C2×D12—51no—
175C2×D12—51no—
176C2×D12C2×D511yescharacteristic
177C2×C4×D3—51no—
178C2×C4×D3—51no—
179C2×C4×D3—51no—
180C2×C4×D3C2×D511yescharacteristic
181C2×C4×D3C2×D511yescharacteristic
182C3×C4⋊C4—51no—
183C3×C4⋊C4—51no—
184C3×C22⋊C4—51no—
185C3×C22⋊C4—51no—
186C3×C42—51no—
187C3×C42C2×D511yescharacteristic
188#217—51no—
189(C2×D3)⋊C4—51no—
190(C2×D3)⋊C4—51no—
191(C2×D3)⋊C4—51no—
192(C2×D3)⋊C4—51no—
193(C2×D3)⋊C4—51no—
194(C2×D3)⋊C4C2×D511yescharacteristic
195(C2×D3)⋊C4C2×D511yescharacteristic
196C4⋊Dic3—51no—
197C4⋊Dic3—51no—
198C4⋊Dic3C2×D511yescharacteristic
199Dic3⋊C4—51no—
200Dic3⋊C4—51no—
201Dic3⋊C4—51no—
202Dic3⋊C4—51no—
203Dic3⋊C4—51no—
204C4×Dic3—51no—
205C23×C5—31no—
206C23×C5—31no—
207C22×D5—31no—
208C22×D5C22×D311yescharacteristic
209C5×D4—62no—
210C2×C4×C5—31no—
211C2×C4×C5—31no—
212C2×C4×C5—121no—
213C2×C4×C5—121no—
214C2×C4×C5C22×D311yescharacteristic
215C2×C4×C5C22×D311yescharacteristic
216C2×C4×C5C22×D311yescharacteristic
217C22⋊D5—62no—
218C22⋊D5—62no—
219C22⋊D5—62no—
220C22⋊D5—121no—
221C2×Dic5—31no—
222C2×Dic5—31no—
223C2×Dic5—31no—
224C2×Dic5—62no—
225C2×Dic5—121no—
226C2×Dic5C22×D311yescharacteristic
227C2×Dic5C22×D311yescharacteristic
228C2×Dic5C22×D311yescharacteristic
229D20—121no—
230C4×D5—22no—
231C4×D5—121no—
232#126—151no—
233#126—151no—
234#125—151no—
235#123—151no—
236#123—151no—
237#121—151no—
238#121—151no—
239#121—151no—
240#121—151no—
241C4×D4—31no—
242C4×D4—151no—
243C4×D4—151no—
244C4×D4—151no—
245#117—51no—
246C2×C4⋊C4—151no—
247C2×C3×C5C2×#4111yescharacteristic
248C2×C3×C5C2×#4111yescharacteristic
249C2×C3×C5H(5,𝔽2)11yescharacteristic
250D15—41no—
251C3×D5—41no—
252C5×D3—22no—
253C5×D3—41no—
254C23×C3—51no—
255C22×D3—51no—
256C22×D3C22×D511yescharacteristic
257C22×D3C22×D511yescharacteristic
258C2×C3×C4—51no—
259C2×C3×C4—51no—
260C2×C3×C4—51no—
261C2×C3×C4—102no—
262C2×C3×C4C22×D511yescharacteristic
263C2×C3×C4C22×D511yescharacteristic
264C2×C3×C4C22×D511yescharacteristic
265#67—102no—
266#67—201no—
267#67—201no—
268C2×Dic3—51no—
269C2×Dic3—51no—
270C2×Dic3—51no—
271C2×Dic3C22×D511yescharacteristic
272C2×Dic3C22×D511yescharacteristic
273D12—22no—
274D12—102no—
275D12—102no—
276C4×D3—41no—
277C4×D3—41no—
278C4×D3—102no—
279C4×D3—201no—
280C4×D3—201no—
281C22×C5—32no—
282C22×C5—61no—
283C22×C5—61no—
284C22×C5—61no—
285C22×C5—61no—
286C22×C5—61no—
287C22×C5C23×D311yescharacteristic
288C2×D5—21no—
289C2×D5—21no—
290C2×D5—21no—
291C2×D5—61no—
292C2×D5—61no—
293C2×D5—61no—
294C4×C5—21no—
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—61no—
298C4×C5—61no—
299Dic5—21no—
300Dic5—21no—
301Dic5—61no—
302Dic5—61no—
303Dic5—61no—
304Dic5#23512yes—
305C2×D4—31no—
306C2×D4—151no—
307C2×D4—151no—
308C2×D4—151no—
309C2×D4—151no—
310C2×D4—151no—
311C22×C4—31no—
312C22×C4—31no—
313C22×C4—51no—
314C22×C4—151no—
315C22×C4—151no—
316C22×C4—151no—
317C4⋊C4—31no—
318C4⋊C4—51no—
319C4⋊C4—51no—
320C4⋊C4—151no—
321C4⋊C4—151no—
322C4⋊C4—151no—
323C4⋊C4—151no—
324C4⋊C4—151no—
325C4⋊C4—151no—
326C4⋊C4—151no—
327C22⋊C4—31no—
328C22⋊C4—31no—
329C22⋊C4—51no—
330C22⋊C4—51no—
331C22⋊C4—151no—
332C22⋊C4—151no—
333C22⋊C4—151no—
334C22⋊C4—151no—
335C22⋊C4—151no—
336C22⋊C4—151no—
337C42—51no—
338C42—151no—
339C42D3×D511yescharacteristic
340C3×C5#55311yescharacteristic, complemented, Hall
341C22×C3—101no—
342C22×C3—101no—
343C22×C3—101no—
344C22×C3C23×D511yescharacteristic
345C2×D3—21no—
346C2×D3—21no—
347C2×D3—21no—
348C2×D3—21no—
349C2×D3—21no—
350C2×D3—101no—
351C2×D3—101no—
352C2×D3—101no—
353C2×D3#70912yes—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—52no—
358C3×C4—101no—
359C3×C4—101no—
360Dic3—21no—
361Dic3—21no—
362Dic3—101no—
363Dic3—101no—
364Dic3—101no—
365C2×C5—62no—
366C2×C5—121no—
367C2×C5C2×#23511yescharacteristic
368C2×C5D3×#4111yescharacteristic
369C2×C5#100911yescharacteristic
370D5—41no—
371D5—121no—
372C23—31no—
373C23—31no—
374C23—51no—
375C23—151no—
376D4—62no—
377D4—302no—
378D4—302no—
379D4—302no—
380D4—601no—
381D4—601no—
382C2×C4—31no—
383C2×C4—31no—
384C2×C4—51no—
385C2×C4—51no—
386C2×C4—51no—
387C2×C4—102no—
388C2×C4—121no—
389C2×C4—121no—
390C2×C4—151no—
391C2×C4—151no—
392C2×C4—151no—
393C2×C4—302no—
394C2×C4—601no—
395C2×C4—601no—
396C2×C4C2×D3×D511yescharacteristic
397C2×C4C2×D3×D511yescharacteristic
398C2×C4C2×D3×D511yescharacteristic
399C2×C3—201no—
400C2×C3C2×#70911yescharacteristic
401C2×C3#414411yescharacteristic
402C2×C3D5×#4111yescharacteristic
403D3—22no—
404D3—41no—
405D3—201no—
406C5#553011yescharacteristic, complemented, Sylow
407C22—32no—
408C22—61no—
409C22—61no—
410C22—61no—
411C22—61no—
412C22—61no—
413C22—101no—
414C22—101no—
415C22—101no—
416C22—301no—
417C22—301no—
418C22—301no—
419C22C22×D3×D511yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—52no—
424C4—61no—
425C4—61no—
426C4—101no—
427C4—101no—
428C4—301no—
429C4—301no—
430C4—301no—
431C3#6587411yescharacteristic, complemented, Sylow
432C2—62no—
433C2—121no—
434C2—201no—
435C2—601no—
436C2D5×#23511yescharacteristic
437C2D3×#70911yescharacteristic
438C2#9201811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C42×C5C22
hypercenterC42D3×D5
hypocenterC3×C5#553
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #91765C2semidirect
2. C4×C5×D12C2semidirect
3. C3×#4018C2semidirect
4. #91454C2semidirect
5. #91453C2semidirect
6. #91452C2semidirect
7. #91448C2semidirect
8. #91446C2semidirect
9. #91440C2semidirect
10. #91416C2semidirect
11. #91405C2semidirect
12. D3×#683C2semidirect
13. #91372C2semidirect
14. #91356C2semidirect
15. #91335C2semidirect
67. #4018D3semidirect
109. C4×D12D5semidirect
340. C3×C5#553semidirect
406. C5#5530semidirect
431. C3#65874semidirect

Maximal subgroups

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

subgroupindex
#917652
C4×C5×D122
C3×#40182
#914542
#914532
#914522
#914482
#914462
#914402
#914162
#914052
D3×#6832
#913722
#913562
#913352
#658743
#55305