Finite Group Databasebeta

← #11754417

Subgroups — #11754417

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×#1220C211yesmaximal, characteristic
2C5×#924C211yesmaximal, characteristic, complemented
3C2×C3×#683C211yesmaximal, characteristic, complemented
4#91574C211yesmaximal, characteristic, complemented
5#91574C211yesmaximal, characteristic, complemented
6#91552C211yesmaximal, characteristic
7#91552C211yesmaximal, characteristic
8#91424C211yesmaximal, characteristic, complemented
9#91419C211yesmaximal, characteristic, complemented
10#91404C211yesmaximal, characteristic, complemented
11#91382C211yesmaximal, characteristic, complemented
12#91377C211yesmaximal, characteristic, complemented
13#91336C211yesmaximal, characteristic, complemented
14#91329C211yesmaximal, characteristic, complemented
15#91325C211yesmaximal, characteristic, complemented
16#65970—31nomaximal, Hall
17C22×C3×C4×C5C2211yescharacteristic
18C2×#1220C2211yescharacteristic
19C2×C4×D15C2211yescharacteristic
20C2×C5×Dic6C2211yescharacteristic
21C22×C3×Dic5C2211yescharacteristic
22C22×C3×Dic5C2211yescharacteristic
23C2×#1204C2211yescharacteristic
24C2×#1204C2211yescharacteristic
25C2×#1200C2211yescharacteristic
26C2×#1200C2211yescharacteristic
27#6719C2211yescharacteristic
28#6714C2211yescharacteristic
29#6712C2211yescharacteristic
30C4×Dic15C2211yescharacteristic
31C5×#217C2211yescharacteristic
32C5×#217C2211yescharacteristic
33C5×C4⋊Dic3C2211yescharacteristic
34C5×Dic3⋊C4C2211yescharacteristic
35C5×Dic3⋊C4C2211yescharacteristic
36C3×#683C2211yescharacteristic
37C3×#683C2211yescharacteristic
38C3×#683C2211yescharacteristic
39C3×#683C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic
41Dic3⋊Dic5C2211yescharacteristic
42#6669C2211yescharacteristic
43#6669C2211yescharacteristic
44#6669C2211yescharacteristic
45#6669C2211yescharacteristic
46#6668C2211yescharacteristic
47#6668C2211yescharacteristic
48#6667C2211yescharacteristic
49#6667C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5511—51nomaximal, Hall
53C5×C22⋊Q8—31no—
54#4092—31no—
55#4090—31no—
56C4×C22⋊D5—31no—
57C2×#683D311yescharacteristic, complemented
58#4042—31no—
59#4042—31no—
60D5×C4⋊C4—31no—
61#4035—31no—
62#4035—31no—
63#4033—31no—
64#4027—31no—
65#4027—31no—
66#4024—31no—
67#4024—31no—
68C23×C3×C5C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C2×C3×C4×C5—41no—
71C2×C3×C4×C5C2311yescharacteristic
72C2×C3×C4×C5C2311yescharacteristic
73#1220Q814yescomplemented
74C2×Dic15C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77C4×D15—41no—
78C2×C5×Dic3C2311yescharacteristic
79C2×C5×Dic3C2311yescharacteristic
80C2×C5×Dic3C2311yescharacteristic
81C2×C5×Dic3C2311yescharacteristic
82C5×Dic6—41no—
83C2×C3×Dic5—22no—
84C2×C3×Dic5—41no—
85C2×C3×Dic5C2311yescharacteristic
86C2×C3×Dic5C2311yescharacteristic
87C2×C3×Dic5C2311yescharacteristic
88C2×C3×Dic5C2311yescharacteristic
89#1204—22no—
90#1204—41no—
91#1200—22no—
92#1200—41no—
93C2×C3×C4⋊C4—51no—
94C4×#67—51no—
95C4×#67—51no—
96C4×#67—51no—
97#924—51no—
98#924—51no—
99#924D511yescharacteristic, complemented
100#897—51no—
101#896—51no—
102#896—51no—
103D3×C4⋊C4—51no—
104#889—51no—
105#889—51no—
106#888—51no—
107#887—51no—
108C2×C5×Q8—31no—
109C22×C4×C5C2×D311yescharacteristic
110C2×C22⋊D5—31no—
111C22×Dic5C2×D311yescharacteristic
112C22×Dic5C2×D311yescharacteristic
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⋊C4—31no—
121C5×C22⋊C4—31no—
122C5×C22⋊C4—31no—
123C22⋊Dic5—31no—
124#685—31no—
125#685—31no—
126#685—31no—
127C4⋊Dic5—31no—
128C4⋊Dic5—31no—
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×Dic5—31no—
143#554—151noSylow
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5C2×Q812yes—
147C22×C3×C5C2411yescharacteristic
148C2×D15—21no—
149C2×D15—21no—
150C2×D15C2×Q812yes—
151C3×C4×C5—21no—
152C3×C4×C5—21no—
153Dic15—21no—
154Dic15—21no—
155Dic15C2×Q812yes—
156C3×Dic5—21no—
157C3×Dic5—21no—
158C3×Dic5—21no—
159C3×Dic5#4112yes—
160C5×Dic3—21no—
161C5×Dic3—21no—
162C5×Dic3—21no—
163C5×Dic3—21no—
164C22×C3×C4—51no—
165C22×C3×C4—51no—
166C22×C3×C4C2×D511yescharacteristic
167C2×#67—51no—
168C2×C4×D3—51no—
169C2×C4×D3—51no—
170C2×C4×D3—51no—
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—
178#217—51no—
179#217C2×D511yescharacteristic
180#217C2×D511yescharacteristic
181(C2×D3)⋊C4—51no—
182(C2×D3)⋊C4—51no—
183(C2×D3)⋊C4—51no—
184C4⋊Dic3—51no—
185C4⋊Dic3—51no—
186C4⋊Dic3C2×D511yescharacteristic
187Dic3⋊C4—51no—
188Dic3⋊C4—51no—
189Dic3⋊C4—51no—
190Dic3⋊C4—51no—
191Dic3⋊C4—51no—
192Dic3⋊C4—51no—
193Dic3⋊C4—51no—
194Dic3⋊C4C2×D511yescharacteristic
195Dic3⋊C4C2×D511yescharacteristic
196C4×Dic3—51no—
197C4×Dic3—51no—
198C4×Dic3—51no—
199C23×C5C22×D311yescharacteristic
200C22×D5—31no—
201C5×Q8—121no—
202C2×C4×C5—31no—
203C2×C4×C5—31no—
204C2×C4×C5—31no—
205C2×C4×C5—31no—
206C2×C4×C5—41no—
207C2×C4×C5C22×D311yescharacteristic
208C2×C4×C5C22×D311yescharacteristic
209C22⋊D5—34no—
210C2×Dic5—22no—
211C2×Dic5—31no—
212C2×Dic5—31no—
213C2×Dic5—31no—
214C2×Dic5—41no—
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—151no—
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—51no—
238C2×C4⋊C4—151no—
239C2×C3×C5—22no—
240C2×C3×C5C22×Q811yescharacteristic
241C2×C3×C5C2×#4111yescharacteristic
242C2×C3×C5H(5,𝔽2)11yescharacteristic
243D15—22no—
244C23×C3C22×D511yescharacteristic
245C22×D3—51no—
246C2×C3×C4—41no—
247C2×C3×C4—51no—
248C2×C3×C4—51no—
249C2×C3×C4—51no—
250C2×C3×C4—51no—
251C2×C3×C4—102no—
252C2×C3×C4—201no—
253C2×C3×C4C22×D511yescharacteristic
254C2×C3×C4C22×D511yescharacteristic
255#67—54no—
256C2×Dic3—51no—
257C2×Dic3—51no—
258C2×Dic3—51no—
259C2×Dic3C22×D511yescharacteristic
260C2×Dic3C22×D511yescharacteristic
261C2×Dic3C22×D511yescharacteristic
262C2×Dic3C22×D511yescharacteristic
263C4×D3—102no—
264C4×D3—201no—
265C4×D3—201no—
266Dic6—41no—
267Dic6—102no—
268Dic6—201no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5D3×Q812yes—
272C22×C5C23×D311yescharacteristic
273C2×D5—32no—
274C2×D5—61no—
275C2×D5—61no—
276C4×C5—21no—
277C4×C5—21no—
278C4×C5—61no—
279C4×C5—61no—
280C4×C5—61no—
281C4×C5—61no—
282Dic5—21no—
283Dic5—21no—
284Dic5—21no—
285Dic5—32no—
286Dic5—61no—
287Dic5—61no—
288Dic5#23512yes—
289C2×Q8—31no—
290C2×Q8—151no—
291C2×Q8—151no—
292C2×D4—151no—
293C22×C4—51no—
294C22×C4—51no—
295C22×C4—151no—
296C22×C4—151no—
297C22×C4—151no—
298C22×C4D3×D511yescharacteristic
299C4⋊C4—31no—
300C4⋊C4—31no—
301C4⋊C4—31no—
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⋊C4—151no—
315C22⋊C4—31no—
316C22⋊C4—31no—
317C22⋊C4—151no—
318C22⋊C4—151no—
319C22⋊C4—151no—
320C22⋊C4—151no—
321C42—151no—
322C42—151no—
323C42—151no—
324C3×C5#55411yescharacteristic, complemented, Hall
325C22×C3—21no—
326C22×C3—21no—
327C22×C3Q8×D512yes—
328C22×C3C23×D511yescharacteristic
329C2×D3—52no—
330C2×D3—101no—
331C2×D3—101no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—52no—
335C3×C4—101no—
336C3×C4—101no—
337C3×C4—101no—
338Dic3—21no—
339Dic3—21no—
340Dic3—21no—
341Dic3—21no—
342Dic3—52no—
343Dic3—101no—
344Dic3—101no—
345C2×C5—22no—
346C2×C5C2×#23511yescharacteristic
347C2×C5#100411yescharacteristic
348C2×C5C2×D3×Q811yescharacteristic
349D5—62no—
350C23—151no—
351C23C2×D3×D511yescharacteristic
352Q8—121no—
353Q8—302no—
354Q8—601no—
355D4—154no—
356C2×C4—31no—
357C2×C4—31no—
358C2×C4—31no—
359C2×C4—31no—
360C2×C4—41no—
361C2×C4—51no—
362C2×C4—51no—
363C2×C4—51no—
364C2×C4—51no—
365C2×C4—102no—
366C2×C4—151no—
367C2×C4—151no—
368C2×C4—151no—
369C2×C4—201no—
370C2×C4—302no—
371C2×C4—601no—
372C2×C4—601no—
373C2×C4C2×D3×D511yescharacteristic
374C2×C4C2×D3×D511yescharacteristic
375C2×C3—22no—
376C2×C3#414411yescharacteristic
377C2×C3C2×Q8×D511yescharacteristic
378C2×C3D5×#4111yescharacteristic
379D3—102no—
380C5#551111yescharacteristic, complemented, Sylow
381C22—21no—
382C22—21no—
383C22—152no—
384C22—301no—
385C22—301no—
386C22D15⋊Q812yes—
387C22C22×D3×D511yescharacteristic
388C4—21no—
389C4—21no—
390C4—52no—
391C4—61no—
392C4—61no—
393C4—61no—
394C4—61no—
395C4—101no—
396C4—101no—
397C4—101no—
398C4—152no—
399C4—301no—
400C4—301no—
401C3#6597011yescharacteristic, complemented, Sylow
402C2—22no—
403C2—302no—
404C2C2×D15⋊Q811yescharacteristic
405C2D5×#23511yescharacteristic
406C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC22×C3×C4×C5C22
prime radicalC2×#1220C22
hypercenterC22×C4D3×D5
hypocenterC3×C5#554
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C5×#924C2semidirect
3. C2×C3×#683C2semidirect
4. #91574C2semidirect
5. #91574C2semidirect
8. #91424C2semidirect
9. #91419C2semidirect
10. #91404C2semidirect
11. #91382C2semidirect
12. #91377C2semidirect
13. #91336C2semidirect
14. #91329C2semidirect
15. #91325C2semidirect
57. C2×#683D3semidirect
73. #1220Q8semidirect
99. #924D5semidirect
324. C3×C5#554semidirect
380. C5#5511semidirect
401. C3#65970semidirect

Maximal subgroups

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

subgroupindex
C4×#12202
C5×#9242
C2×C3×#6832
#915742
#915522
#914242
#914192
#914042
#913822
#913772
#913362
#913292
#913252
#659703
#55115