Finite Group Databasebeta

← #11753473

Subgroups — #11753473

Order 960.

456 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊C4×D15C211yesmaximal, characteristic, complemented
2C5×#896C211yesmaximal, characteristic, complemented
3C3×#4035C211yesmaximal, characteristic, complemented
4C4×#1203C211yesmaximal, characteristic
5#91436C211yesmaximal, characteristic, complemented
6#91417C211yesmaximal, characteristic, complemented
7#91406C211yesmaximal, characteristic
8#91406C211yesmaximal, characteristic
9D3×#683C211yesmaximal, characteristic, complemented
10#91383C211yesmaximal, characteristic, complemented
11#91377C211yesmaximal, characteristic, complemented
12#91377C211yesmaximal, characteristic, complemented
13#91334C211yesmaximal, characteristic, complemented
14#91329C211yesmaximal, characteristic, complemented
15#91323C211yesmaximal, characteristic, complemented
16#65970—31nomaximal, Hall
17C2×C4×D15C2211yescharacteristic
18C2×C4×D15C2211yescharacteristic
19C2×C4×D15C2211yescharacteristic
20C2×C4×C5×D3C2211yescharacteristic
21C2×C5×Dic6C2211yescharacteristic
22C2×#1204C2211yescharacteristic
23C2×#1204C2211yescharacteristic
24C2×#1203C2211yescharacteristic
25C2×D3×Dic5C2211yescharacteristic
26C2×D3×Dic5C2211yescharacteristic
27C3×C5×C4⋊C4C2211yescharacteristic
28C4⋊Dic15C2211yescharacteristic
29#6712C2211yescharacteristic
30#6712C2211yescharacteristic
31C5×(C2×D3)⋊C4C2211yescharacteristic
32C5×(C2×D3)⋊C4C2211yescharacteristic
33C5×Dic3⋊C4C2211yescharacteristic
34C5×Dic3⋊C4C2211yescharacteristic
35C3×C4⋊Dic5C2211yescharacteristic
36C3×#683C2211yescharacteristic
37C3×#683C2211yescharacteristic
38C3×#683C2211yescharacteristic
39C3×#683C2211yescharacteristic
40C3×C4×Dic5C2211yescharacteristic
41#6669C2211yescharacteristic
42#6669C2211yescharacteristic
43#6668C2211yescharacteristic
44#6668C2211yescharacteristic
45#6668C2211yescharacteristic
46#6667C2211yescharacteristic
47#6667C2211yescharacteristic
48#6667C2211yescharacteristic
49(C2×D3)⋊Dic5C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5690—51nomaximal, Hall
53C5×C22⋊Q8—31no—
54#4092—31no—
55#4090—31no—
56C4×C22⋊D5—31no—
57C2×#683—31no—
58#4042—31no—
59#4042—31no—
60D5×C4⋊C4—31no—
61#4035—31no—
62#4035D311yescharacteristic, complemented
63#4033—31no—
64#4027—31no—
65#4027—31no—
66#4024—31no—
67#4024—31no—
68C22×D15C2311yescharacteristic
69C22×C5×D3C2311yescharacteristic
70C2×C3×C4×C5C2311yescharacteristic
71C2×C3×C4×C5C2311yescharacteristic
72C2×C3×C4×C5C2311yescharacteristic
73C2×Dic15C2311yescharacteristic
74C2×Dic15C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76C4×D15—22no—
77C4×D15—41no—
78C4×D15—41no—
79C2×C5×Dic3C2311yescharacteristic
80C2×C5×Dic3C2311yescharacteristic
81C2×C5×Dic3C2311yescharacteristic
82C4×C5×D3—41no—
83C5×Dic6—41no—
84C2×C3×Dic5C2311yescharacteristic
85C2×C3×Dic5C2311yescharacteristic
86C2×C3×Dic5C2311yescharacteristic
87C2×C3×Dic5C2311yescharacteristic
88#1204—22no—
89#1204—41no—
90#1203Q814yescomplemented
91D3×Dic5—22no—
92D3×Dic5—41no—
93C3×#125—51no—
94#897—51no—
95#897—51no—
96#896—51no—
97#896—51no—
98#896—51no—
99#896D511yescharacteristic, complemented
100#893—51no—
101#893—51no—
102D3×C4⋊C4—51no—
103D3×C4⋊C4—51no—
104#890—51no—
105#888—51no—
106C4×D12—51no—
107C4×Dic6—51no—
108C2×C5×Q8—31no—
109C22×C4×C5—31no—
110C2×C22⋊D5—31no—
111C22×Dic5—31no—
112C22×Dic5—31no—
113C2×C4×D5—31no—
114C2×C4×D5—31no—
115C2×C4×D5—31no—
116C2×Dic10—31no—
117C2×Dic10—31no—
118C5×C4⋊C4—31no—
119C5×C4⋊C4—31no—
120C5×C4⋊C4C2×D311yescharacteristic
121C5×C22⋊C4—31no—
122C5×C22⋊C4—31no—
123C22⋊Dic5—31no—
124#685—31no—
125#685—31no—
126#685—31no—
127C4⋊Dic5—31no—
128C4⋊Dic5C2×D311yescharacteristic
129#683—31no—
130#683—31no—
131#683—31no—
132#683—31no—
133#683—31no—
134#683—31no—
135#683—31no—
136#683C2×D311yescharacteristic
137#683C2×D311yescharacteristic
138#683C2×D311yescharacteristic
139#683C2×D311yescharacteristic
140C4×Dic5—31no—
141C4×Dic5—31no—
142C4×Dic5C2×D311yescharacteristic
143#554—151noSylow
144C22×C3×C5C2411yescharacteristic
145C2×D15—21no—
146C2×D15—21no—
147C2×D15C2×Q812yes—
148C2×C5×D3—21no—
149C2×C5×D3—21no—
150C2×C5×D3C2×Q812yes—
151C3×C4×C5—21no—
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154Dic15—21no—
155Dic15—21no—
156Dic15#4112yes—
157C3×Dic5—21no—
158C3×Dic5—21no—
159C3×Dic5—21no—
160C3×Dic5C2×Q812yes—
161C5×Dic3—21no—
162C5×Dic3—21no—
163C5×Dic3—21no—
164C2×D12—51no—
165C2×C4×D3—51no—
166C2×C4×D3—51no—
167C2×C4×D3—51no—
168C2×C4×D3—51no—
169C2×C4×D3—51no—
170C2×C4×D3C2×D511yescharacteristic
171C2×Dic6—51no—
172C2×Dic6—51no—
173C2×Dic6C2×D511yescharacteristic
174C3×C4⋊C4—51no—
175C3×C4⋊C4—51no—
176C3×C4⋊C4—51no—
177C3×C4⋊C4—51no—
178C3×C4⋊C4—51no—
179C3×C4⋊C4C2×D511yescharacteristic
180C3×C42—51no—
181(C2×D3)⋊C4—51no—
182(C2×D3)⋊C4—51no—
183(C2×D3)⋊C4—51no—
184(C2×D3)⋊C4—51no—
185(C2×D3)⋊C4C2×D511yescharacteristic
186(C2×D3)⋊C4C2×D511yescharacteristic
187C4⋊Dic3—51no—
188C4⋊Dic3—51no—
189C4⋊Dic3—51no—
190C4⋊Dic3—51no—
191Dic3⋊C4—51no—
192Dic3⋊C4—51no—
193Dic3⋊C4—51no—
194Dic3⋊C4—51no—
195Dic3⋊C4C2×D511yescharacteristic
196Dic3⋊C4C2×D511yescharacteristic
197C4×Dic3—51no—
198C4×Dic3—51no—
199C23×C5—31no—
200C22×D5—31no—
201C5×Q8—121no—
202C2×C4×C5—31no—
203C2×C4×C5—31no—
204C2×C4×C5—31no—
205C2×C4×C5—121no—
206C2×C4×C5C22×D311yescharacteristic
207C2×C4×C5C22×D311yescharacteristic
208C2×C4×C5C22×D311yescharacteristic
209C22⋊D5—34no—
210C2×Dic5—31no—
211C2×Dic5—31no—
212C2×Dic5—31no—
213C2×Dic5—62no—
214C2×Dic5—121no—
215C2×Dic5C22×D311yescharacteristic
216C2×Dic5C22×D311yescharacteristic
217C2×Dic5C22×D311yescharacteristic
218C2×Dic5C22×D311yescharacteristic
219C4×D5—62no—
220C4×D5—121no—
221C4×D5—121no—
222Dic10—62no—
223Dic10—121no—
224C4⋊Q8—151no—
225#125—51no—
226#125—151no—
227C22⋊Q8—31no—
228C22⋊Q8—151no—
229C22⋊Q8—151no—
230C22⋊Q8—151no—
231C22⋊Q8—151no—
232C22⋊Q8—151no—
233C4×Q8—151no—
234C4×D4—151no—
235C4×D4—151no—
236C4×D4—151no—
237C2×C4⋊C4—151no—
238C2×C4⋊C4—151no—
239C2×C3×C5C22×Q811yescharacteristic
240C2×C3×C5C2×#4111yescharacteristic
241C2×C3×C5H(5,𝔽2)11yescharacteristic
242D15—22no—
243C5×D3—22no—
244C22×D3—51no—
245C22×D3C22×D511yescharacteristic
246C2×C3×C4—51no—
247C2×C3×C4—51no—
248C2×C3×C4—51no—
249C2×C3×C4—51no—
250C2×C3×C4C22×D511yescharacteristic
251C2×C3×C4C22×D511yescharacteristic
252C2×C3×C4C22×D511yescharacteristic
253C2×Dic3—51no—
254C2×Dic3—51no—
255C2×Dic3—51no—
256C2×Dic3C22×D511yescharacteristic
257C2×Dic3C22×D511yescharacteristic
258C2×Dic3C22×D511yescharacteristic
259D12—54no—
260C4×D3—41no—
261C4×D3—102no—
262C4×D3—102no—
263C4×D3—201no—
264C4×D3—201no—
265C4×D3—201no—
266Dic6—41no—
267Dic6—102no—
268Dic6—201no—
269C22×C5—32no—
270C22×C5—61no—
271C22×C5—61no—
272C22×C5C23×D311yescharacteristic
273C2×D5—32no—
274C2×D5—61no—
275C2×D5—61no—
276C4×C5—21no—
277C4×C5—21no—
278C4×C5—21no—
279C4×C5—61no—
280C4×C5—61no—
281C4×C5—61no—
282Dic5—21no—
283Dic5—21no—
284Dic5—21no—
285Dic5—32no—
286Dic5—61no—
287Dic5—61no—
288Dic5D3×Q812yes—
289C2×Q8—31no—
290C2×Q8—151no—
291C2×Q8—151no—
292C2×D4—151no—
293C22×C4—31no—
294C22×C4—151no—
295C22×C4—151no—
296C22×C4—151no—
297C22×C4—151no—
298C22×C4—151no—
299C4⋊C4—31no—
300C4⋊C4—31no—
301C4⋊C4—51no—
302C4⋊C4—51no—
303C4⋊C4—51no—
304C4⋊C4—51no—
305C4⋊C4—51no—
306C4⋊C4—151no—
307C4⋊C4—151no—
308C4⋊C4—151no—
309C4⋊C4—151no—
310C4⋊C4—151no—
311C4⋊C4—151no—
312C4⋊C4—151no—
313C4⋊C4—151no—
314C4⋊C4D3×D511yescharacteristic
315C22⋊C4—31no—
316C22⋊C4—31no—
317C22⋊C4—151no—
318C22⋊C4—151no—
319C22⋊C4—151no—
320C22⋊C4—151no—
321C42—51no—
322C42—151no—
323C42—151no—
324C3×C5#55411yescharacteristic, complemented, Hall
325C22×C3C23×D511yescharacteristic
326C2×D3—21no—
327C2×D3—21no—
328C2×D3—52no—
329C2×D3—101no—
330C2×D3—101no—
331C2×D3Q8×D512yes—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—52no—
336C3×C4—101no—
337C3×C4—101no—
338C3×C4—101no—
339Dic3—21no—
340Dic3—21no—
341Dic3—21no—
342Dic3—52no—
343Dic3—101no—
344Dic3—101no—
345C2×C5—62no—
346C2×C5C2×D3×Q811yescharacteristic
347C2×C5D3×#4111yescharacteristic
348C2×C5#100911yescharacteristic
349D5—62no—
350C23—31no—
351C23—151no—
352Q8—121no—
353Q8—302no—
354Q8—601no—
355D4—154no—
356C2×C4—31no—
357C2×C4—31no—
358C2×C4—31no—
359C2×C4—51no—
360C2×C4—51no—
361C2×C4—51no—
362C2×C4—51no—
363C2×C4—121no—
364C2×C4—151no—
365C2×C4—151no—
366C2×C4—151no—
367C2×C4—302no—
368C2×C4—302no—
369C2×C4—601no—
370C2×C4—601no—
371C2×C4—601no—
372C2×C4C2×D3×D511yescharacteristic
373C2×C4C2×D3×D511yescharacteristic
374C2×C4C2×D3×D511yescharacteristic
375C2×C3#414411yescharacteristic
376C2×C3C2×Q8×D511yescharacteristic
377C2×C3D5×#4111yescharacteristic
378D3—22no—
379D3—102no—
380C5#569011yescharacteristic, complemented, Sylow
381C22—32no—
382C22—61no—
383C22—61no—
384C22—152no—
385C22—301no—
386C22—301no—
387C22C22×D3×D511yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—52no—
392C4—61no—
393C4—61no—
394C4—61no—
395C4—101no—
396C4—101no—
397C4—101no—
398C4—152no—
399C4—301no—
400C4—301no—
401C3#6597011yescharacteristic, complemented, Sylow
402C2—62no—
403C2—302no—
404C2#9201611yescharacteristic
405C2#9202711yescharacteristic
406C2D3×Q8×D511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radicalC2×#1203C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#554
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C4⋊C4×D15C2semidirect
2. C5×#896C2semidirect
3. C3×#4035C2semidirect
5. #91436C2semidirect
6. #91417C2semidirect
9. D3×#683C2semidirect
10. #91383C2semidirect
11. #91377C2semidirect
12. #91377C2semidirect
13. #91334C2semidirect
14. #91329C2semidirect
15. #91323C2semidirect
62. #4035D3semidirect
90. #1203Q8semidirect
99. #896D5semidirect
324. C3×C5#554semidirect
380. C5#5690semidirect
401. C3#65970semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×D152
C5×#8962
C3×#40352
C4×#12032
#914362
#914172
#914062
D3×#6832
#913832
#913772
#913342
#913292
#913232
#659703
#56905