Finite Group Databasebeta

← C2×#11751570 #14512982

Subgroups — C2×#11751570 #14512982

Order 1920.

670 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5⋊S4C211yesmaximal, characteristic
2C2×A4×#168C211yesmaximal, characteristic, complemented
3C2×C5×A4⋊C8C211yesmaximal, characteristic, complemented
4#11751570C214yesmaximal, direct product factor
5C2×#65014—31nomaximal, Hall
6C22×C5⋊S4C411yescharacteristic
7C2×C4×C5×A4C2211yescharacteristic
8C2×A4⋊Dic5C411yescharacteristic
9C4×C5⋊S4C412yes—
10C4×C5⋊S4C2212yes—
11C2×#6648—41nomaximal
12A4×#168C2212yescomplemented
13C5×A4⋊C8C2212yescomplemented
14C2×C8×S4—51nomaximal, Hall
15C2×C4×C22⋊D5—31no—
16C23×#168D311yescharacteristic, complemented
17C22×C8×D5—31no—
18C2×C5×C22⋊C8—31no—
19C2×#3952—31no—
20C2×#3946—31no—
21C2×C8×Dic5—31no—
22#65014—34no—
23#65014—34no—
24C22×C5×A4C2×C411yescharacteristic
25C2×C5⋊S4C814yescomplemented
26C2×C5⋊S4C2×C412yes—
27C2×C4×D15—41no—
28C4×C5×A4C2×C411yescharacteristic
29C4×C5×A4C2311yescharacteristic
30A4⋊Dic5C2×C412yes—
31C2×C5×C3⋊C8—41no—
32C2×C3×#168—41no—
33#6648—44no—
34C2×C4×S4—51no—
35C2×C8×A4—51no—
36C2×A4⋊C8D511yescharacteristic, complemented
37C8×S4—54no—
38C23×C4×C5C2×D311yescharacteristic
39C22×C22⋊D5—31no—
40C22×C4×D5—31no—
41C22×C5×C8—31no—
42C22×C5×C8—31no—
43C2×C22⋊Dic5—31no—
44C4×C22⋊D5—32no—
45C4×C22⋊D5—32no—
46C4×C22⋊D5—32no—
47C4×C22⋊D5—32no—
48C2×#685—31no—
49C2×#683—31no—
50C2×C4×Dic5—31no—
51C22×#168—31no—
52C22×#168—31no—
53C22×#168—32no—
54C22×#168C2×D312yescomplemented
55C2×C8×D5—34no—
56C2×C8×D5—61no—
57C2×C8×D5—62no—
58C2×C8×D5—61no—
59C5×C22⋊C8—32no—
60C5×C22⋊C8—32no—
61#3952—34no—
62#3946—34no—
63C8×Dic5—34no—
64C2×C8×D4—151noSylow
65C22×D15—41no—
66C2×C5×A4C2×C812yescomplemented
67C2×C5×A4C22×C411yescharacteristic
68C5⋊S4C2×C814yescomplemented
69C2×C3×C4×C5—41no—
70C2×Dic15—41no—
71C4×D15—42no—
72C4×D15—42no—
73C3×#168—42no—
74C5×C3⋊C8—42no—
75C22×S4—51no—
76C2×C4×A4C2×D511yescharacteristic
77C2×SL(2,ℤ/4)—51no—
78C4×S4—52no—
79C4×S4—52no—
80C2×D3×C8—201no—
81C8×A4—52no—
82A4⋊C8C2×D512yescomplemented
83C24×C5C4×D311yescharacteristic
84C23×D5—31no—
85C22×C4×C5—31no—
86C22×C4×C5—31no—
87C22×C4×C5—31no—
88C22×C4×C5—31no—
89C22×C4×C5C4×D311yescharacteristic
90C22×C4×C5C22×D311yescharacteristic
91C2×C22⋊D5—34no—
92C2×C22⋊D5—32no—
93C2×C22⋊D5—34no—
94C2×C22⋊D5—32no—
95C22×Dic5—31no—
96C22×Dic5—31no—
97C22×Dic5—31no—
98C2×C4×D5—32no—
99C2×C4×D5—32no—
100C2×C4×D5—61no—
101C2×C4×D5—61no—
102C2×C4×D5—61no—
103C2×C4×D5—61no—
104C2×C5×C8—32no—
105C2×C5×C8—32no—
106C2×C5×C8—61no—
107C2×C5×C8—61no—
108C2×C5×C8—61no—
109C2×C5×C8—61no—
110C22⋊Dic5—32no—
111C22⋊Dic5—32no—
112#685—32no—
113#685—32no—
114#683—32no—
115#683—32no—
116C4×Dic5—32no—
117C4×Dic5—32no—
118C2×#168—31no—
119C2×#168—32no—
120C2×#168—32no—
121C2×#168—32no—
122C2×#168—61no—
123C2×#168S411yescharacteristic, complemented
124C8×D5—64no—
125C8×D5—64no—
126C23×C8—51no—
127C23×C8—151no—
128C2×C4×D4—151no—
129C8×D4—154no—
130C8×D4—154no—
131C2×C4⋊C8—151no—
132C2×C22⋊C8—31no—
133C2×C22⋊C8—151no—
134C2×C4×C8—151no—
135C22×C3×C5—41no—
136C2×D15—44no—
137C2×D15—42no—
138C5×A4C22×C811yescharacteristic, complemented
139C3×C4×C5—41no—
140C3×C4×C5—41no—
141Dic15—42no—
142C22×A4C4×D511yescharacteristic
143C2×S4—54no—
144C2×S4—52no—
145C2×C4×D3—201no—
146C4×A4C4×D511yescharacteristic
147C4×A4C22×D511yescharacteristic
148SL(2,ℤ/4)—52no—
149C2×C3×C8—201no—
150C2×C3⋊C8—41no—
151D3×C8—204no—
152C23×C5—31no—
153C23×C5—31no—
154C23×C5—32no—
155C23×C5D3×C812yescomplemented
156C23×C5C2×C4×D311yescharacteristic
157C22×D5—32no—
158C22×D5—34no—
159C22×D5—61no—
160C22×D5—62no—
161C22×D5—61no—
162C2×C4×C5—31no—
163C2×C4×C5—31no—
164C2×C4×C5—31no—
165C2×C4×C5—31no—
166C2×C4×C5—31no—
167C2×C4×C5—31no—
168C2×C4×C5—31no—
169C2×C4×C5—61no—
170C2×C4×C5C2×S411yescharacteristic
171C22⋊D5—38no—
172C22⋊D5—34no—
173C22⋊D5—34no—
174C2×Dic5—32no—
175C2×Dic5—34no—
176C2×Dic5—32no—
177C2×Dic5—32no—
178C2×Dic5—61no—
179C2×Dic5—62no—
180C2×Dic5—61no—
181C4×D5—62no—
182C4×D5—62no—
183C4×D5—62no—
184C4×D5—62no—
185C5×C8—62no—
186C5×C8—62no—
187#168—32no—
188#168C2×S412yescomplemented
189C22×D4—151no—
190C23×C4—151no—
191C23×C4D3×D511yescharacteristic
192C22×C8—31no—
193C22×C8—31no—
194C22×C8—52no—
195C22×C8—154no—
196C22×C8—151no—
197C22×C8—151no—
198C22×C8—152no—
199C22×C8—301no—
200C22×C8—302no—
201C22×C8—301no—
202C4×D4—152no—
203C4×D4—152no—
204C4×D4—152no—
205C4×D4—152no—
206C2×C4⋊C4—151no—
207C2×C22⋊C4—151no—
208C2×C22⋊C4—151no—
209C2×C42—151no—
210C4⋊C8—154no—
211C22⋊C8—32no—
212C22⋊C8—32no—
213C22⋊C8—154no—
214C4×C8—154no—
215C2×C3×C5—41no—
216C2×C3×C5—42no—
217D15—44no—
218C22×D3—201no—
219C2×A4C8×D512yescomplemented
220C2×A4C2×C4×D511yescharacteristic
221S4—54no—
222C2×C3×C4—41no—
223C2×Dic3—201no—
224C4×D3—202no—
225C4×D3—202no—
226C3×C8—202no—
227C3⋊C8—42no—
228C22×C5—32no—
229C22×C5—31no—
230C22×C5—31no—
231C22×C5—31no—
232C22×C5—32no—
233C22×C5—32no—
234C22×C5—61no—
235C22×C5C2×D3×C811yescharacteristic, complemented
236C22×C5C4×S411yescharacteristic
237C2×D5—34no—
238C2×D5—62no—
239C2×D5—64no—
240C2×D5—62no—
241C2×D5—64no—
242C4×C5—31no—
243C4×C5—31no—
244C4×C5C4×S411yescharacteristic
245C4×C5C22×S411yescharacteristic
246Dic5—34no—
247Dic5—62no—
248Dic5—62no—
249C24—151no—
250C24#120011yescharacteristic
251C2×D4—152no—
252C2×D4—154no—
253C2×D4—152no—
254C2×D4—154no—
255C22×C4—31no—
256C22×C4—31no—
257C22×C4—31no—
258C22×C4—31no—
259C22×C4—152no—
260C22×C4—152no—
261C22×C4—151no—
262C22×C4—151no—
263C22×C4—151no—
264C22×C4—301no—
265C22×C4—301no—
266C22×C4—301no—
267C22×C4—301no—
268C22×C4#120011yescharacteristic
269C22×C4C2×D3×D511yescharacteristic
270C2×C8—32no—
271C2×C8—32no—
272C2×C8—51no—
273C2×C8—61no—
274C2×C8—61no—
275C2×C8—61no—
276C2×C8—61no—
277C2×C8—152no—
278C2×C8—152no—
279C2×C8—151no—
280C2×C8—152no—
281C2×C8—304no—
282C2×C8—304no—
283C2×C8—301no—
284C4⋊C4—152no—
285C4⋊C4—152no—
286C22⋊C4—152no—
287C22⋊C4—152no—
288C22⋊C4—152no—
289C22⋊C4—152no—
290C42—152no—
291C42—152no—
292C3×C5—41noHall
293C22×C3—41no—
294C2×D3—202no—
295C2×D3—204no—
296A4C2×C8×D511yescharacteristic, complemented
297C3×C4—41no—
298C3×C4—41no—
299Dic3—202no—
300C2×C5—31no—
301C2×C5—31no—
302C2×C5—32no—
303C2×C5C8×S412yescomplemented
304C2×C5C2×C4×S411yescharacteristic
305D5—64no—
306C23—31no—
307C23—31no—
308C23—32no—
309C23—152no—
310C23—154no—
311C23—301no—
312C23—302no—
313C23—301no—
314C23#664812yescomplemented
315C23C2×#120011yescharacteristic
316D4—154no—
317D4—158no—
318D4—154no—
319C2×C4—31no—
320C2×C4—31no—
321C2×C4—31no—
322C2×C4—31no—
323C2×C4—31no—
324C2×C4—31no—
325C2×C4—31no—
326C2×C4—61no—
327C2×C4—152no—
328C2×C4—154no—
329C2×C4—152no—
330C2×C4—152no—
331C2×C4—302no—
332C2×C4—302no—
333C2×C4—301no—
334C2×C4—302no—
335C2×C4—301no—
336C2×C4—302no—
337C2×C4—302no—
338C2×C4D5×S411yescharacteristic
339C8—52no—
340C8—62no—
341C8—62no—
342C8—152no—
343C2×C3—42no—
344C2×C3—41no—
345D3—204no—
346C5C2×C8×S411yescharacteristic, complemented, Sylow
347C22—31no—
348C22—32no—
349C22—32no—
350C22—32no—
351C22—31no—
352C22—31no—
353C22—61no—
354C22—154no—
355C22—302no—
356C22—304no—
357C22—304no—
358C22—302no—
359C22C2×#664811yescharacteristic, complemented
360C22#9190111yescharacteristic
361C4—31no—
362C4—31no—
363C4—154no—
364C4—302no—
365C4—302no—
366C4#9190111yescharacteristic
367C4C2×D5×S411yescharacteristic
368C3—41noSylow
369C2—31no—
370C2—31no—
371C2—32no—
372C2—304no—
373C2#1175157012yesdirect product factor
374C2C2×#9190111yescharacteristic
subgroupG/H
center, hypercenterC2×C4D5×S4
commutator, hypocenterC5×A4C22×C8
FrattiniC4C2×D5×S4
FittingC23×C4×C5C2×D3
socleC24×C5C4×D3
prime radicalC22×C5⋊S4C4
cosocleC4×C5×A4C23
LCSG ▷ C5×A4
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×A4×#168C2semidirect
3. C2×C5×A4⋊C8C2semidirect
4. #11751570C2direct (N × H)
12. A4×#168C22semidirect
13. C5×A4⋊C8C22semidirect
16. C23×#168D3semidirect
25. C2×C5⋊S4C8semidirect
36. C2×A4⋊C8D5semidirect
54. C22×#168C2×D3semidirect
66. C2×C5×A4C2×C8semidirect
68. C5⋊S4C2×C8semidirect
82. A4⋊C8C2×D5semidirect
123. C2×#168S4semidirect
138. C5×A4C22×C8semidirect
155. C23×C5D3×C8semidirect
188. #168C2×S4semidirect
219. C2×A4C8×D5semidirect
235. C22×C5C2×D3×C8semidirect
296. A4C2×C8×D5semidirect
303. C2×C5C8×S4semidirect
314. C23#6648semidirect
346. C5C2×C8×S4semidirect
359. C22C2×#6648semidirect
373. C2#11751570direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C5⋊S42
C2×A4×#1682
C2×C5×A4⋊C82
#117515702
C2×#650143
C2×#66484
C2×C8×S45