Subgroups — #14438927

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91271	C₂	1	4	yes	maximal, complemented
2	#11752674	C₂	1	2	yes	maximal, complemented
3	#11750796	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4699	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	#11747965	C₂	1	4	yes	maximal, complemented
7	#11747067	C₂	1	2	yes	maximal, complemented
8	#10613530	—	3	1	no	maximal, Hall
9	C₂×#6773	C₂²	1	4	yes	—
10	C₂×D₁₂₀	C₂²	1	4	yes	—
11	#91763	C₂²	1	2	yes	—
12	C₂×C₅×Dic₁₂	C₂²	1	4	yes	—
13	C₅×#869	C₂²	1	2	yes	—
14	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
15	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
16	#91450	—	2	4	no	—
17	#91418	—	2	4	no	—
18	#91375	C₂²	1	4	yes	—
19	C₂×#6660	C₂²	1	8	yes	—
20	#91271	—	2	16	no	—
21	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₃×C₈×Dic₅	C₂²	1	2	yes	—
23	C₃×C₄×#168	C₂²	1	1	yes	characteristic
24	#78467	—	5	1	no	maximal, Hall
25	C₂×#4065	—	3	4	no	—
26	#66059	—	3	2	no	—
27	C₅×#494	—	3	1	no	—
28	#65480	—	3	4	no	—
29	#65374	—	3	2	no	—
30	#64984	—	3	1	no	—
31	C₄×C₈×D₅	D₃	1	1	yes	characteristic, complemented
32	C₂×D₆₀	—	2	4	no	—
33	C₂×D₆₀	C₂³	1	4	yes	—
34	C₂×C₅×Dic₆	C₂³	1	4	yes	—
35	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
36	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
37	C₂×#1202	—	2	4	no	—
38	C₂×#1200	—	2	4	no	—
39	#6773	—	2	16	no	—
40	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
41	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
42	D₁₂₀	—	2	8	no	—
43	C₅×C₄⋊Dic₃	—	2	4	no	—
44	C₅×Dic₁₂	—	2	8	no	—
45	C₃×C₄×Dic₅	D₄	1	2	yes	—
46	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
47	C₂×C₃×#168	C₂³	1	2	yes	—
48	C₃×C₈×D₅	D₄	1	8	yes	complemented
49	#6667	—	2	8	no	—
50	#6660	—	2	16	no	—
51	C₂×#904	—	5	4	no	—
52	#5477	—	5	2	no	—
53	C₂×C₃×C₄×C₈	—	5	1	no	—
54	#4699	D₅	1	1	yes	characteristic, complemented
55	#4696	—	5	4	no	—
56	#4695	—	5	1	no	—
57	#4693	—	5	2	no	—
58	C₂×#713	—	3	4	no	—
59	C₂×C₅×Q₁₆	—	3	4	no	—
60	C₅×C₄⋊Q₈	—	3	2	no	—
61	#4093	—	3	4	no	—
62	C₂×#688	—	3	8	no	—
63	#4065	—	6	16	no	—
64	C₂×D₄₀	—	3	4	no	—
65	C₂×C₈×D₅	C₂×D₃	1	2	yes	—
66	#4041	—	6	4	no	—
67	#4039	—	6	4	no	—
68	#4020	—	3	2	no	—
69	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
70	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
71	C₈×Dic₅	C₂×D₃	1	2	yes	—
72	C₄×#168	C₂×D₃	1	1	yes	characteristic
73	#3147	—	15	1	no	Sylow
74	C₂²×D₁₅	—	2	4	no	—
75	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
76	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
77	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
78	D₆₀	—	2	8	no	—
79	D₆₀	—	4	8	no	—
80	C₂×C₅×Dic₃	—	2	4	no	—
81	C₅×Dic₆	—	2	8	no	—
82	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
83	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
84	C₃×C₄×D₅	—	2	4	no	—
85	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
86	#1202	—	4	8	no	—
87	#1200	—	4	8	no	—
88	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
89	C₃×#168	C₂×D₄	1	4	yes	—
90	C₂×#235	—	5	4	no	—
91	C₂²×C₃×C₈	—	5	2	no	—
92	C₂×C₃×C₄²	—	5	1	no	—
93	#930	—	10	4	no	—
94	C₂×Dic₁₂	C₂×D₅	1	4	yes	—
95	#904	—	10	16	no	—
96	C₂×D₂₄	—	5	4	no	—
97	C₂×#204	—	5	8	no	—
98	#875	—	5	4	no	—
99	#874	—	5	2	no	—
100	C₄×D₁₂	—	10	4	no	—
101	#869	C₂×D₅	1	2	yes	—
102	C₃×C₄×C₈	—	5	2	no	—
103	C₃×C₄×C₈	—	5	1	no	—
104	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
105	C₂×C₅×Q₈	—	3	4	no	—
106	#713	—	6	16	no	—
107	C₂×D₂₀	—	3	4	no	—
108	C₂×D₂₀	—	6	4	no	—
109	C₂×D₂₀	—	6	4	no	—
110	C₂×C₄×D₅	—	6	4	no	—
111	C₂×C₄×D₅	D₁₂	1	2	yes	—
112	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
113	C₅×Q₁₆	—	6	8	no	—
114	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
115	C₅×C₄⋊C₄	—	6	4	no	—
116	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
117	#688	—	6	16	no	—
118	#685	—	6	8	no	—
119	C₄×Dic₅	D₁₂	1	2	yes	—
120	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
121	C₂×#168	C₂²×D₃	1	2	yes	—
122	D₄₀	—	6	8	no	—
123	C₈×D₅	D₁₂	1	8	yes	complemented
124	C₂×#135	—	15	4	no	—
125	#532	—	15	2	no	—
126	#495	—	15	4	no	—
127	#494	—	3	1	no	—
128	#493	—	15	1	no	—
129	#492	—	15	2	no	—
130	C₂×C₄×C₈	—	5	1	no	—
131	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
132	C₂×D₁₅	—	4	4	no	—
133	C₂×D₁₅	—	4	8	no	—
134	C₂×C₃×D₅	—	2	2	no	—
135	C₂×C₃×D₅	#127	1	2	yes	—
136	C₃×C₄×C₅	#135	1	4	yes	complemented
137	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
138	C₃×Dic₅	—	2	2	no	—
139	C₃×Dic₅	#127	1	2	yes	—
140	C₅×Dic₃	—	4	4	no	—
141	C₂²×C₃×C₄	—	5	1	no	—
142	C₂²×C₃×C₄	—	5	2	no	—
143	C₂×#67	—	10	4	no	—
144	#235	—	10	16	no	—
145	C₂×D₁₂	—	5	4	no	—
146	C₂×D₁₂	—	10	4	no	—
147	C₂×C₄×D₃	—	10	4	no	—
148	C₂×Dic₆	C₂²×D₅	1	4	yes	—
149	C₂×C₃×C₈	—	5	2	no	—
150	C₂×C₃×C₈	—	5	8	no	—
151	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
152	C₃×C₄²	—	5	2	no	—
153	C₃×C₄²	—	5	1	no	—
154	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
155	(C₂×D₃)⋊C₄	—	10	8	no	—
156	C₄⋊Dic₃	—	2	4	no	—
157	Dic₁₂	—	2	8	no	—
158	D₂₄	—	10	8	no	—
159	#204	—	10	16	no	—
160	C₂²×D₅	—	6	4	no	—
161	C₂²×D₅	C₂×D₁₂	1	1	yes	characteristic
162	C₅×Q₈	—	6	8	no	—
163	C₂×C₄×C₅	—	6	4	no	—
164	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
165	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
166	C₂×Dic₅	C₂×D₁₂	1	2	yes	—
167	C₂×Dic₅	C₂×D₁₂	1	1	yes	characteristic
168	D₂₀	—	6	8	no	—
169	D₂₀	—	12	8	no	—
170	D₂₀	—	12	8	no	—
171	C₄×D₅	—	2	4	no	—
172	C₄×D₅	—	12	8	no	—
173	C₄×D₅	C₂×D₁₂	1	4	yes	—
174	C₅×C₈	C₂×D₁₂	1	4	yes	—
175	#168	C₂×D₁₂	1	4	yes	—
176	C₂×#41	—	15	4	no	—
177	#135	—	30	16	no	—
178	C₂×Q₁₆	—	3	4	no	—
179	C₂×SD₁₆	—	15	8	no	—
180	C₂×D₈	—	15	4	no	—
181	C₂²×C₈	—	5	2	no	—
182	C₄⋊Q₈	—	3	2	no	—
183	#127	—	15	2	no	—
184	#124	—	15	4	no	—
185	#121	—	30	4	no	—
186	C₄×D₄	—	30	4	no	—
187	C₂×C₄²	—	5	1	no	—
188	C₄×C₈	—	5	2	no	—
189	C₄×C₈	—	5	1	no	—
190	C₄×C₈	D₃×D₅	1	1	yes	characteristic
191	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
192	C₂×C₃×C₅	C₂×#135	1	2	yes	—
193	D₁₅	—	8	4	no	—
194	C₃×D₅	—	2	2	no	—
195	C₂³×C₃	—	5	1	no	—
196	C₂²×D₃	—	10	4	no	—
197	C₂×C₃×C₄	—	5	1	no	—
198	C₂×C₃×C₄	—	5	4	no	—
199	C₂×C₃×C₄	—	5	2	no	—
200	C₂×C₃×C₄	—	10	4	no	—
201	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
202	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
203	#67	—	20	8	no	—
204	C₂×Dic₃	—	2	4	no	—
205	D₁₂	—	10	8	no	—
206	D₁₂	—	20	8	no	—
207	C₄×D₃	—	20	8	no	—
208	Dic₆	—	2	8	no	—
209	C₃×C₈	—	5	4	no	—
210	C₃×C₈	D₄×D₅	1	4	yes	—
211	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
212	C₂×D₅	—	2	2	no	—
213	C₂×D₅	—	12	4	no	—
214	C₂×D₅	—	12	8	no	—
215	C₂×D₅	#874	1	2	yes	—
216	C₄×C₅	—	12	4	no	—
217	C₄×C₅	#904	1	4	yes	complemented
218	C₄×C₅	C₂²×D₁₂	1	2	yes	—
219	Dic₅	—	2	2	no	—
220	Dic₅	#874	1	2	yes	—
221	#41	—	30	16	no	—
222	C₂×Q₈	—	3	4	no	—
223	C₂×D₄	—	15	4	no	—
224	C₂×D₄	—	30	4	no	—
225	C₂×D₄	—	30	4	no	—
226	C₂²×C₄	—	5	1	no	—
227	C₂²×C₄	—	5	2	no	—
228	C₂²×C₄	—	30	4	no	—
229	Q₁₆	—	6	8	no	—
230	SD₁₆	—	30	16	no	—
231	D₈	—	30	8	no	—
232	C₂×C₈	—	5	2	no	—
233	C₂×C₈	—	5	8	no	—
234	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
235	C₄⋊C₄	—	6	4	no	—
236	C₂²⋊C₄	—	30	8	no	—
237	C₄²	—	5	2	no	—
238	C₄²	—	5	1	no	—
239	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
240	C₃×C₅	#3147	1	1	yes	characteristic, complemented, Hall
241	C₂²×C₃	—	5	2	no	—
242	C₂²×C₃	—	10	2	no	—
243	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
244	C₂×D₃	—	20	4	no	—
245	C₂×D₃	—	20	8	no	—
246	C₃×C₄	—	5	2	no	—
247	C₃×C₄	—	10	2	no	—
248	C₃×C₄	#4065	1	4	yes	complemented
249	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
250	Dic₃	—	4	4	no	—
251	C₂×C₅	C₂×#874	1	1	yes	characteristic
252	C₂×C₅	C₂×#904	1	2	yes	—
253	D₅	—	2	2	no	—
254	D₅	—	24	4	no	—
255	C₂³	—	5	1	no	—
256	C₂³	—	30	4	no	—
257	Q₈	—	6	8	no	—
258	D₄	—	30	8	no	—
259	D₄	—	60	8	no	—
260	D₄	—	60	8	no	—
261	C₂×C₄	—	5	1	no	—
262	C₂×C₄	—	5	4	no	—
263	C₂×C₄	—	5	2	no	—
264	C₂×C₄	—	6	4	no	—
265	C₂×C₄	—	10	4	no	—
266	C₂×C₄	—	60	8	no	—
267	C₂×C₄	D₅×D₁₂	1	2	yes	—
268	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
269	C₈	—	5	4	no	—
270	C₈	D₅×D₁₂	1	4	yes	—
271	C₂×C₃	—	10	2	no	—
272	C₂×C₃	D₅×#127	1	1	yes	characteristic
273	C₂×C₃	C₂×#4065	1	2	yes	—
274	D₃	—	40	4	no	—
275	C₅	#78467	1	1	yes	characteristic, complemented, Sylow
276	C₂²	—	5	2	no	—
277	C₂²	—	10	2	no	—
278	C₂²	—	60	8	no	—
279	C₂²	—	60	4	no	—
280	C₂²	C₂×D₅×D₁₂	1	1	yes	characteristic
281	C₄	—	5	2	no	—
282	C₄	—	10	2	no	—
283	C₄	—	12	4	no	—
284	C₄	#91271	1	4	yes	complemented
285	C₄	C₂×D₅×D₁₂	1	2	yes	—
286	C₃	#10613530	1	1	yes	characteristic, complemented, Sylow
287	C₂	—	10	2	no	—
288	C₂	—	120	4	no	—
289	C₂	D₅×#874	1	1	yes	characteristic
290	C₂	C₂×#91271	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₅×D₁₂
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	#3147
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#91271	C₂	semidirect
2. #11752674	C₂	semidirect
3. #11750796	C₂	semidirect
4. C₅×#4699	C₂	semidirect
5. C₃×C₄×C₈×D₅	C₂	semidirect
6. #11747965	C₂	semidirect
7. #11747067	C₂	semidirect
31. C₄×C₈×D₅	D₃	semidirect
48. C₃×C₈×D₅	D₄	semidirect
54. #4699	D₅	semidirect
123. C₈×D₅	D₁₂	semidirect
136. C₃×C₄×C₅	#135	semidirect
217. C₄×C₅	#904	semidirect
240. C₃×C₅	#3147	semidirect
248. C₃×C₄	#4065	semidirect
275. C₅	#78467	semidirect
284. C₄	#91271	semidirect
286. C₃	#10613530	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91271	2
#11752674	2
#11750796	2
C₅×#4699	2
C₃×C₄×C₈×D₅	2
#11747965	2
#11747067	2
#10613530	3
#78467	5