Subgroups — C₄×#11926298 #18087685

Order 4864.

1318 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄²×Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926298	C₂	1	4	yes	maximal
4	C₂²×C₄×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₁₉⋊C₈	C₂²	1	2	yes	—
6	C₂²×C₄×Dic₁₉	C₄	1	4	yes	—
7	C₂²×C₄×Dic₁₉	C₂²	1	2	yes	—
8	C₂×C₄×C₁₉⋊C₈	—	2	2	no	—
9	C₂×C₄×C₁₉⋊C₈	—	2	2	no	—
10	C₂×C₄×C₁₉⋊C₈	C₄	1	4	yes	complemented
11	C₄²×Dic₁₉	—	2	2	no	—
12	C₄²×Dic₁₉	—	2	2	no	—
13	#11926298	C₄	1	16	yes	direct product factor
14	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₉	—	2	2	no	—
17	C₂×C₄×C₈×C₁₉	—	2	2	no	—
18	C₂×C₄×C₈×C₁₉	C₄	1	4	yes	complemented
19	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
20	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂³×Dic₁₉	C₂×C₄	1	4	yes	—
22	C₂²×C₈×C₁₉	—	2	2	no	—
23	C₂²×C₈×C₁₉	—	2	2	no	—
24	C₂²×C₈×C₁₉	—	2	4	no	—
25	C₂²×C₈×C₁₉	C₂×C₄	1	8	yes	—
26	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
27	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₉	D₄	1	2	yes	—
30	C₂×C₄²×C₁₉	D₄	1	2	yes	—
31	C₂×C₄²×C₁₉	D₄	1	2	yes	—
32	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
33	C₂×C₄×Dic₁₉	—	2	8	no	—
34	C₂×C₄×Dic₁₉	—	2	8	no	—
35	C₂×C₄×Dic₁₉	—	2	2	no	—
36	C₂×C₄×Dic₁₉	—	2	2	no	—
37	C₂×C₄×Dic₁₉	—	2	4	no	—
38	C₂×C₄×Dic₁₉	C₈	1	16	yes	complemented
39	C₂×C₄×Dic₁₉	C₂×C₄	1	8	yes	—
40	C₂²×C₁₉⋊C₈	—	2	2	no	—
41	C₂²×C₁₉⋊C₈	—	2	2	no	—
42	C₂²×C₁₉⋊C₈	—	2	4	no	—
43	C₂²×C₁₉⋊C₈	C₂×C₄	1	8	yes	—
44	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
45	C₄×C₈×C₁₉	—	2	8	no	—
46	C₄×C₁₉⋊C₈	—	2	8	no	—
47	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₄²	1	4	yes	—
49	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
50	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
51	C₂²×C₄×C₁₉	C₂×C₈	1	8	yes	—
52	C₂²×C₄×C₁₉	M₁₆	1	8	yes	—
53	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
55	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	#41	1	4	yes	—
61	C₂²×Dic₁₉	—	2	4	no	—
62	C₂²×Dic₁₉	—	2	4	no	—
63	C₂²×Dic₁₉	—	2	8	no	—
64	C₂²×Dic₁₉	C₄²	1	8	yes	—
65	C₂²×Dic₁₉	C₂×C₈	1	16	yes	—
66	C₂×C₈×C₁₉	—	2	4	no	—
67	C₂×C₈×C₁₉	—	2	4	no	—
68	C₂×C₈×C₁₉	—	2	8	no	—
69	C₂×C₈×C₁₉	—	2	8	no	—
70	C₂×C₈×C₁₉	C₄²	1	8	yes	complemented
71	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
72	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
73	C₄²×C₁₉	C₄⋊C₄	1	4	yes	—
74	C₄²×C₁₉	C₄⋊C₄	1	4	yes	—
75	C₄×Dic₁₉	—	2	32	no	—
76	C₄×Dic₁₉	—	2	8	no	—
77	C₄×Dic₁₉	—	2	8	no	—
78	C₂×C₁₉⋊C₈	—	2	4	no	—
79	C₂×C₁₉⋊C₈	—	2	4	no	—
80	C₂×C₁₉⋊C₈	—	2	8	no	—
81	C₂×C₁₉⋊C₈	—	2	8	no	—
82	C₂×C₁₉⋊C₈	C₄²	1	8	yes	complemented
83	C₄×#336	—	19	1	no	maximal, Sylow
84	C₂³×C₁₉	C₂×C₄²	1	2	yes	—
85	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
86	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
88	C₂³×C₁₉	#117	1	2	yes	—
89	C₂³×C₁₉	C₂²×C₈	1	4	yes	—
90	C₂³×C₁₉	C₂×M₁₆	1	4	yes	—
91	C₂×C₄×C₁₉	#95	1	8	yes	—
92	C₂×C₄×C₁₉	C₄×C₈	1	8	yes	—
93	C₂×C₄×C₁₉	#97	1	8	yes	—
94	C₂×C₄×C₁₉	C₂²⋊C₈	1	16	yes	—
95	C₂×C₄×C₁₉	C₄⋊C₈	1	16	yes	—
96	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
97	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
98	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#117	1	2	yes	—
103	C₂×C₄×C₁₉	#117	1	2	yes	—
104	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
105	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
106	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
107	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
108	C₂×Dic₁₉	—	2	8	no	—
109	C₂×Dic₁₉	—	2	8	no	—
110	C₂×Dic₁₉	—	2	16	no	—
111	C₂×Dic₁₉	—	2	16	no	—
112	C₂×Dic₁₉	C₄×C₈	1	16	yes	complemented
113	C₈×C₁₉	—	2	8	no	—
114	C₁₉⋊C₈	—	2	8	no	—
115	C₂²×C₄×C₈	—	19	1	no	—
116	C₂²×C₄×C₈	D₁₉	1	1	yes	characteristic
117	C₂×C₄³	—	19	1	no	—
118	C₂×#336	—	19	4	no	—
119	C₂²×C₁₉	C₄³	1	1	yes	characteristic
120	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
121	C₂²×C₁₉	#376	1	1	yes	characteristic
122	C₂²×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
123	C₂²×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
124	C₂²×C₁₉	C₂×C₄×C₈	1	4	yes	—
125	C₂²×C₁₉	C₂×C₄×C₈	1	2	yes	—
126	C₂²×C₁₉	C₂×#97	1	2	yes	—
127	C₂²×C₁₉	C₄×M₁₆	1	4	yes	—
128	C₂²×C₁₉	C₂×C₂²⋊C₈	1	4	yes	—
129	C₂²×C₁₉	C₂×C₄⋊C₈	1	4	yes	—
130	C₂²×C₁₉	#431	1	8	yes	—
131	C₄×C₁₉	#336	1	16	yes	complemented
132	C₄×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
133	C₄×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
134	C₄×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
135	C₄×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
136	Dic₁₉	—	2	16	no	—
137	C₂³×C₈	—	19	2	no	—
138	C₂³×C₈	C₂×D₁₉	1	2	yes	—
139	C₂²×C₄²	—	19	4	no	—
140	C₂²×C₄²	—	19	2	no	—
141	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
142	C₂×C₄×C₈	—	2	2	no	—
143	C₂×C₄×C₈	—	2	2	no	—
144	C₂×C₄×C₈	—	19	4	no	—
145	C₂×C₄×C₈	—	38	2	no	—
146	C₂×C₄×C₈	—	38	2	no	—
147	C₂×C₄×C₈	Dic₁₉	1	4	yes	complemented
148	C₄³	—	38	2	no	—
149	C₄³	—	38	2	no	—
150	#336	—	19	16	no	—
151	C₂×C₁₉	C₄×#95	1	1	yes	characteristic
152	C₂×C₁₉	C₄²×C₈	1	1	yes	characteristic
153	C₂×C₁₉	C₄×#97	1	1	yes	characteristic
154	C₂×C₁₉	C₂×#336	1	2	yes	—
155	C₂×C₁₉	#1744	1	2	yes	—
156	C₂×C₁₉	C₄×C₂²⋊C₈	1	4	yes	—
157	C₂×C₁₉	C₄×C₄⋊C₈	1	4	yes	—
158	C₂³×C₄	—	19	4	no	—
159	C₂³×C₄	C₄×D₁₉	1	2	yes	—
160	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
161	C₂²×C₈	—	2	4	no	—
162	C₂²×C₈	—	2	2	no	—
163	C₂²×C₈	—	2	2	no	—
164	C₂²×C₈	—	19	8	no	—
165	C₂²×C₈	—	19	4	no	—
166	C₂²×C₈	—	38	2	no	—
167	C₂²×C₈	—	38	4	no	—
168	C₂²×C₈	—	38	2	no	—
169	C₂²×C₈	C₄×D₁₉	1	8	yes	—
170	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
171	C₂×C₄²	—	19	16	no	—
172	C₂×C₄²	—	19	8	no	—
173	C₂×C₄²	—	38	8	no	—
174	C₂×C₄²	—	38	8	no	—
175	C₂×C₄²	—	38	2	no	—
176	C₂×C₄²	—	38	4	no	—
177	C₂×C₄²	—	38	2	no	—
178	C₂×C₄²	Dic₃₈	1	2	yes	—
179	C₂×C₄²	C₄×D₁₉	1	2	yes	—
180	C₂×C₄²	D₇₆	1	2	yes	—
181	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
182	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
183	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
184	C₄×C₈	—	2	8	no	—
185	C₄×C₈	—	38	8	no	—
186	C₁₉	C₄×#336	1	1	yes	characteristic, complemented, Sylow
187	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
188	C₂²×C₄	—	19	8	no	—
189	C₂²×C₄	—	19	16	no	—
190	C₂²×C₄	—	38	4	no	—
191	C₂²×C₄	—	38	8	no	—
192	C₂²×C₄	—	38	4	no	—
193	C₂²×C₄	C₈×D₁₉	1	8	yes	—
194	C₂²×C₄	#64515	1	8	yes	—
195	C₂²×C₄	C₄×Dic₁₉	1	4	yes	—
196	C₂²×C₄	Dic₁₉⋊C₄	1	4	yes	—
197	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
198	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
199	C₂²×C₄	C₂×C₄×D₁₉	1	4	yes	—
200	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
201	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
202	C₂²×C₄	#64541	1	4	yes	—
203	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
204	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
205	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
206	C₂×C₈	—	2	4	no	—
207	C₂×C₈	—	2	4	no	—
208	C₂×C₈	—	2	8	no	—
209	C₂×C₈	—	2	8	no	—
210	C₂×C₈	—	19	8	no	—
211	C₂×C₈	—	38	4	no	—
212	C₂×C₈	—	38	8	no	—
213	C₂×C₈	—	38	4	no	—
214	C₂×C₈	—	38	8	no	—
215	C₂×C₈	C₄×Dic₁₉	1	8	yes	complemented
216	C₄²	—	38	32	no	—
217	C₄²	—	38	8	no	—
218	C₄²	—	38	8	no	—
219	C₄²	Dic₁₉⋊C₄	1	4	yes	—
220	C₄²	C₄⋊Dic₁₉	1	4	yes	—
221	C₄²	(C₂×D₁₉)⋊C₄	1	4	yes	—
222	C₄²	C₂²⋊Dic₁₉	1	4	yes	—
223	C₂³	C₄²×D₁₉	1	2	yes	—
224	C₂³	#10597318	1	2	yes	—
225	C₂³	C₂×C₈×D₁₉	1	4	yes	—
226	C₂³	C₂×#64515	1	4	yes	—
227	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
228	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
229	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
230	C₂×C₄	—	19	16	no	—
231	C₂×C₄	—	38	16	no	—
232	C₂×C₄	—	38	8	no	—
233	C₂×C₄	—	38	8	no	—
234	C₂×C₄	—	38	16	no	—
235	C₂×C₄	C₈×Dic₁₉	1	8	yes	—
236	C₂×C₄	Dic₁₉⋊C₈	1	16	yes	—
237	C₂×C₄	#10597272	1	8	yes	—
238	C₂×C₄	(C₂×D₁₉)⋊C₈	1	16	yes	—
239	C₂×C₄	C₁₉⋊#95	1	8	yes	—
240	C₂×C₄	C₄×Dic₃₈	1	4	yes	—
241	C₂×C₄	C₄²×D₁₉	1	2	yes	—
242	C₂×C₄	#10597318	1	2	yes	—
243	C₂×C₄	C₄×D₇₆	1	4	yes	—
244	C₂×C₄	C₂×C₄×Dic₁₉	1	2	yes	—
245	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
246	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
247	C₂×C₄	#10597372	1	2	yes	—
248	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
249	C₂×C₄	C₄×C₂²⋊D₁₉	1	4	yes	—
250	C₂×C₄	C₄×C₂²⋊D₁₉	1	4	yes	—
251	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
252	C₈	—	2	8	no	—
253	C₈	—	38	8	no	—
254	C₂²	C₄²×Dic₁₉	1	1	yes	characteristic
255	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
256	C₂²	#11926390	1	1	yes	characteristic
257	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	2	yes	—
258	C₂²	C₄×Dic₁₉⋊C₄	1	2	yes	—
259	C₂²	C₄×C₈×D₁₉	1	4	yes	—
260	C₂²	C₂×C₈×Dic₁₉	1	2	yes	—
261	C₂²	C₂×#10597272	1	2	yes	—
262	C₂²	C₄×#64515	1	4	yes	—
263	C₂²	C₂×(C₂×D₁₉)⋊C₈	1	4	yes	—
264	C₂²	C₂×Dic₁₉⋊C₈	1	4	yes	—
265	C₂²	#11926595	1	8	yes	—
266	C₄	—	38	16	no	—
267	C₄	#11926298	1	16	yes	direct product factor
268	C₄	C₄×C₂²⋊Dic₁₉	1	2	yes	—
269	C₄	C₄×(C₂×D₁₉)⋊C₄	1	2	yes	—
270	C₄	C₄×C₄⋊Dic₁₉	1	2	yes	—
271	C₄	C₄×Dic₁₉⋊C₄	1	2	yes	—
272	C₂	C₄×C₁₉⋊#95	1	1	yes	characteristic
273	C₂	C₄×C₈×Dic₁₉	1	1	yes	characteristic
274	C₂	C₄×#10597272	1	1	yes	characteristic
275	C₂	C₂×#11926298	1	2	yes	—
276	C₂	#14563380	1	2	yes	—
277	C₂	C₄×(C₂×D₁₉)⋊C₈	1	4	yes	—
278	C₂	C₄×Dic₁₉⋊C₈	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄²	C₂×D₁₉
commutator	C₂×C₁₉	C₄²×C₈
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₄×C₈×C₁₉	C₂
socle, prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×C₄×C₈	D₁₉
hypocenter	C₁₉	C₄×#336
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
10. C₂×C₄×C₁₉⋊C₈	C₄	semidirect
13. #11926298	C₄	direct (N × H)
18. C₂×C₄×C₈×C₁₉	C₄	semidirect
38. C₂×C₄×Dic₁₉	C₈	semidirect
70. C₂×C₈×C₁₉	C₄²	semidirect
82. C₂×C₁₉⋊C₈	C₄²	semidirect
112. C₂×Dic₁₉	C₄×C₈	semidirect
131. C₄×C₁₉	#336	semidirect
147. C₂×C₄×C₈	Dic₁₉	semidirect
186. C₁₉	C₄×#336	semidirect
215. C₂×C₈	C₄×Dic₁₉	semidirect
267. C₄	#11926298	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₁₉⋊C₈	2
C₂×C₄²×Dic₁₉	2
C₂×#11926298	2
C₂²×C₄×C₈×C₁₉	2
C₄×#336	19

Subgroups — C4×#11926298 #18087685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11926298 #18087685