Finite Group Databasebeta

← #14289779

Subgroups — #14289779

Order 1920.

456 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 98 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
1Q8×D60C211yesmaximal, characteristic
2C5×#5021C211yesmaximal, characteristic, complemented
3#11746929C211yesmaximal, characteristic, complemented
4#11746885C211yesmaximal, characteristic
5C3×Q8⋊#168C211yesmaximal, characteristic, complemented
6#11745859C211yesmaximal, characteristic, complemented
7#11745839C211yesmaximal, characteristic
8#10601956—31nomaximal, Hall
9C2×Q8×D15—21no—
10C3×C4×C5×Q8C2211yescharacteristic
11#91786—21no—
12#91786—22no—
13C4×D60—21no—
14C4×D60C2211yescharacteristic
15#91758—21no—
16#91758C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C5×#835—21no—
19C5×#807—21no—
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22C3×C4×#168C2211yescharacteristic
23#90985—21no—
24#90973—22no—
25#90969—21no—
26#68269—51nomaximal, Hall
27Q8×D20—31no—
28C5×#477—31no—
29#65373—31no—
30#65370—31no—
31Q8⋊#168D311yescharacteristic, complemented
32#64703—31no—
33#64702—31no—
34C2×C3×C5×Q8D411yescharacteristic
35Q8×D15—42no—
36Q8×D15—42no—
37C2×D60D411yescharacteristic
38C2×C4×D15—22no—
39C2×C4×D15—21no—
40C2×Dic30—22no—
41C2×Dic30—21no—
42C2×C5×Dic6—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C42×C5—21no—
46C3×C42×C5C2311yescharacteristic
47#6714—22no—
48#6714—21no—
49C4⋊Dic15—22no—
50C4⋊Dic15—21no—
51C4⋊Dic15D412yes—
52C4⋊Dic15D411yescharacteristic
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3—21no—
55C2×C5×C3⋊C8—21no—
56C2×C3×#168—21no—
57C2×C3×#168—21no—
58Q8×D12—51no—
59#5021D511yescharacteristic, complemented
60#4842—51no—
61#4681—51no—
62C3×Q8⋊C8—51no—
63#4486—51no—
64#4459—51no—
65C2×Q8×D5—61no—
66C5×C4⋊Q8—31no—
67C4×C5×Q8C2×D311yescharacteristic
68#4043—62no—
69#4043—61no—
70C4×D20—31no—
71C4×D20—61no—
72#4015—31no—
73#4015—61no—
74C5×#107—61no—
75C5×C4⋊C8—31no—
76C5×#103—61no—
77#3967—62no—
78#3941—61no—
79#3940—61no—
80C4⋊#168C2×D311yescharacteristic
81C4×#168C2×D311yescharacteristic
82#1637—151noSylow
83C22×D15—21no—
84C3×C5×Q8—21no—
85C3×C5×Q8SD1612yes—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—21no—
92C2×Dic15—22no—
93D60—21no—
94D60Q1612yes—
95C4×D15—44no—
96C4×D15—41no—
97C4×D15—41no—
98Dic30—44no—
99Dic30—41no—
100Dic30—41no—
101C2×C5×Dic3—41no—
102C5×Dic6—42no—
103C3×#168—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C2×D3×Q8—101no—
107C3×C4×Q8C2×D511yescharacteristic
108#897—102no—
109#897—101no—
110C4×D12—51no—
111C4×D12—101no—
112#869—51no—
113#869—101no—
114#869C2×D511yescharacteristic
115C3×C4⋊C8—51no—
116C3×C4×C8—51no—
117#835—21no—
118#821—101no—
119#817—101no—
120#816—102no—
121#807—21no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C2×C5×Q8—61no—
124C2×C5×Q8D1211yescharacteristic
125Q8×D5—122no—
126Q8×D5—122no—
127C2×D20—31no—
128C2×C4×D5—62no—
129C2×C4×D5—61no—
130C2×Dic10—62no—
131C2×Dic10—61no—
132C2×C5×C8—61no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—61no—
135C5×C4⋊C4—61no—
136C5×C4⋊C4D1211yescharacteristic
137C42×C5—21no—
138C42×C5C22×D311yescharacteristic
139#685—62no—
140#685—61no—
141C4⋊Dic5—31no—
142C4⋊Dic5—32no—
143C4⋊Dic5—62no—
144C4⋊Dic5—61no—
145C2×#168—21no—
146C2×#168—21no—
147D4×Q8—151no—
148#487—151no—
149#477—31no—
150#476—151no—
151#332—151no—
152Q8⋊C8—51no—
153D4⋊C8—151no—
154C22×C3×C5#12011yescharacteristic
155C2×D15—22no—
156C2×D15—41no—
157C2×D15—41no—
158C3×C4×C5—22no—
159C3×C4×C5—21no—
160C3×C4×C5—41no—
161C3×C4×C5C2×SD1611yescharacteristic
162C3×C4×C5C2×Q1611yescharacteristic
163C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C3×C4×C5#13711yescharacteristic
165Dic15—41no—
166Dic15—42no—
167C5×Dic3—81no—
168C2×C3×Q8C22⋊D511yescharacteristic
169D3×Q8—202no—
170D3×Q8—202no—
171C2×D12—51no—
172C2×C4×D3—102no—
173C2×C4×D3—101no—
174C2×Dic6—21no—
175C2×Dic6—102no—
176C2×Dic6—101no—
177C2×C3×C8—101no—
178C2×C3×C8—101no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4C22⋊D511yescharacteristic
181C3×C42—21no—
182C3×C42C22×D511yescharacteristic
183(C2×D3)⋊C4—102no—
184(C2×D3)⋊C4—101no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3—52no—
188C4⋊Dic3—51no—
189C4⋊Dic3—102no—
190C4⋊Dic3—101no—
191C2×C3⋊C8—21no—
192C22×D5—61no—
193C5×Q8—21no—
194C5×Q8—122no—
195C5×Q8#20412yes—
196C2×C4×C5—21no—
197C2×C4×C5—21no—
198C2×C4×C5—121no—
199C2×C4×C5C2×D1211yescharacteristic
200C2×C4×C5D3×D411yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C2×Dic5—61no—
203C2×Dic5—62no—
204D20—32no—
205D20—61no—
206C4×D5—124no—
207C4×D5—121no—
208C4×D5—121no—
209Dic10—124no—
210Dic10—121no—
211Dic10—121no—
212C5×C8—121no—
213#168—41no—
214#168—41no—
215C22×Q8—301no—
216C4⋊Q8—31no—
217C4⋊Q8—151no—
218C4⋊Q8—301no—
219C22⋊Q8—302no—
220C22⋊Q8—301no—
221C4×Q8D3×D511yescharacteristic
222C4×D4—151no—
223C4×D4—301no—
224#107—61no—
225#106—301no—
226C4⋊C8—31no—
227C4⋊C8—51no—
228#103—61no—
229#103—302no—
230#102—301no—
231C4×C8—51no—
232C2×C3×C5#45011yescharacteristic
233C2×C3×C5#45111yescharacteristic
234C2×C3×C5#45411yescharacteristic
235D15—42no—
236C22×D3—101no—
237C3×Q8—21no—
238C3×Q8#68812yes—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4D4×D511yescharacteristic
242C2×C3×C4D4×D511yescharacteristic
243C2×C3×C4C2×C22⋊D511yescharacteristic
244C2×Dic3—41no—
245C2×Dic3—102no—
246C2×Dic3—101no—
247D12—52no—
248D12—101no—
249C4×D3—204no—
250C4×D3—201no—
251C4×D3—201no—
252Dic6—42no—
253Dic6—204no—
254Dic6—201no—
255Dic6—201no—
256C3×C8—201no—
257C3×C8—201no—
258C3⋊C8—41no—
259C22×C5#88211yescharacteristic
260C2×D5—62no—
261C2×D5—121no—
262C2×D5—121no—
263C4×C5—22no—
264C4×C5—21no—
265C4×C5—41no—
266C4×C5—241no—
267C4×C5C2×#20411yescharacteristic
268C4×C5#90811yescharacteristic
269C4×C5#91511yescharacteristic
270C4×C5D3×Q1611yescharacteristic
271Dic5—121no—
272Dic5—122no—
273C2×Q8—61no—
274C2×Q8—302no—
275C2×Q8—301no—
276C2×Q8—602no—
277C2×Q8—602no—
278C2×Q8#120311yescharacteristic
279C2×D4—151no—
280C22×C4—302no—
281C22×C4—301no—
282C2×C8—61no—
283C2×C8—101no—
284C2×C8—101no—
285C4⋊C4—21no—
286C4⋊C4—61no—
287C4⋊C4—61no—
288C4⋊C4—152no—
289C4⋊C4—151no—
290C4⋊C4—302no—
291C4⋊C4—301no—
292C4⋊C4#120311yescharacteristic
293C22⋊C4—302no—
294C22⋊C4—301no—
295C42—21no—
296C42C2×D3×D511yescharacteristic
297C3×C5#163711yescharacteristic, complemented, Hall
298C22×C3#408311yescharacteristic
299C2×D3—102no—
300C2×D3—201no—
301C2×D3—201no—
302C3×C4—22no—
303C3×C4—21no—
304C3×C4—41no—
305C3×C4D5×Q1611yescharacteristic
306C3×C4#406411yescharacteristic
307C3×C4C2×#68811yescharacteristic
308C3×C4#409511yescharacteristic
309Dic3—81no—
310Dic3—201no—
311Dic3—202no—
312C2×C5#473111yescharacteristic
313C2×C5#480911yescharacteristic
314C2×C5#482711yescharacteristic
315D5—122no—
316C23—301no—
317Q8—21no—
318Q8—122no—
319Q8—604no—
320Q8—601no—
321Q8—601no—
322Q8#666012yes—
323D4—152no—
324D4—301no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—121no—
328C2×C4—302no—
329C2×C4—301no—
330C2×C4—604no—
331C2×C4—601no—
332C2×C4—601no—
333C2×C4C2×#120311yescharacteristic
334C2×C4#679011yescharacteristic
335C2×C4#679011yescharacteristic
336C8—121no—
337C8—201no—
338C8—201no—
339C2×C3#6533511yescharacteristic
340C2×C3#6547511yescharacteristic
341C2×C3#6549011yescharacteristic
342D3—202no—
343C5#6826911yescharacteristic, complemented, Sylow
344C22—302no—
345C22—601no—
346C22—601no—
347C22#9157311yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—241no—
352C4—602no—
353C4—601no—
354C4#9130511yescharacteristic
355C4C2×#666011yescharacteristic
356C4#9151111yescharacteristic
357C4#9152211yescharacteristic
358C3#1060195611yescharacteristic, complemented, Sylow
359C2—602no—
360C2#1174855411yescharacteristic
361C2#1174930811yescharacteristic
362C2#1174946111yescharacteristic
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1637
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C5×#5021C2semidirect
3. #11746929C2semidirect
5. C3×Q8⋊#168C2semidirect
6. #11745859C2semidirect
31. Q8⋊#168D3semidirect
59. #5021D5semidirect
297. C3×C5#1637semidirect
343. C5#68269semidirect
358. C3#10601956semidirect

Maximal subgroups

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

subgroupindex
Q8×D602
C5×#50212
#117469292
#117468852
C3×Q8⋊#1682
#117458592
#117458392
#106019563
#682695