Subgroups — #18088325

Order 4864.

1174 conjugacy classes of subgroups.

The subgroup lattice has 356 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×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₁₉⋊C₈	C₂²	1	2	yes	—
6	C₂²×C₄×Dic₁₉	C₄	1	2	yes	—
7	C₂²×C₄×Dic₁₉	C₄	1	2	yes	—
8	C₂²×C₄×Dic₁₉	C₂²	1	2	yes	—
9	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
10	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
11	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	4	yes	complemented
12	C₄²×Dic₁₉	—	2	2	no	—
13	C₄²×Dic₁₉	—	2	2	no	—
14	#11926298	—	2	8	no	—
15	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
18	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
19	C₂×C₁₉×C₄⋊C₈	C₄	1	4	yes	complemented
20	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₂³×Dic₁₉	C₂×C₄	1	4	yes	—
24	C₂²×C₈×C₁₉	—	2	4	no	—
25	C₂²×C₈×C₁₉	—	2	2	no	—
26	C₂²×C₈×C₁₉	—	2	2	no	—
27	C₂²×C₈×C₁₉	—	2	4	no	—
28	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
29	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₁₉	D₄	1	2	yes	—
32	C₂×C₄²×C₁₉	D₄	1	2	yes	—
33	C₂×C₄²×C₁₉	D₄	1	2	yes	—
34	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
35	C₂×C₄×Dic₁₉	—	2	4	no	—
36	C₂×C₄×Dic₁₉	—	2	4	no	—
37	C₂×C₄×Dic₁₉	—	2	4	no	—
38	C₂×C₄×Dic₁₉	—	2	2	no	—
39	C₂×C₄×Dic₁₉	—	2	2	no	—
40	C₂×C₄×Dic₁₉	—	2	2	no	—
41	C₂×C₄×Dic₁₉	—	2	2	no	—
42	C₂×C₄×Dic₁₉	—	2	8	no	—
43	C₂×C₄×Dic₁₉	C₈	1	8	yes	complemented
44	C₂×C₄×Dic₁₉	D₄	1	4	yes	—
45	C₂×C₄×Dic₁₉	Q₈	1	4	yes	—
46	C₂²×C₁₉⋊C₈	—	2	4	no	—
47	C₂²×C₁₉⋊C₈	—	2	2	no	—
48	C₂²×C₁₉⋊C₈	—	2	2	no	—
49	C₂²×C₁₉⋊C₈	—	2	4	no	—
50	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
51	C₁₉×C₄⋊C₈	—	2	8	no	—
52	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
53	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	—	2	4	no	—
55	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
56	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
59	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
60	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
61	C₂²×C₄×C₁₉	C₂×C₈	1	4	yes	—
62	C₂²×C₄×C₁₉	M₁₆	1	4	yes	—
63	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
67	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
71	C₂²×C₄×C₁₉	#41	1	2	yes	—
72	C₂²×C₄×C₁₉	#41	1	2	yes	—
73	C₂²×Dic₁₉	—	2	4	no	—
74	C₂²×Dic₁₉	—	2	4	no	—
75	C₂²×Dic₁₉	—	2	4	no	—
76	C₂²×Dic₁₉	—	2	4	no	—
77	C₂²×Dic₁₉	C₄⋊C₄	1	8	yes	—
78	C₂²×Dic₁₉	C₂×C₈	1	8	yes	—
79	C₂²×Dic₁₉	M₁₆	1	8	yes	—
80	C₂×C₈×C₁₉	—	2	4	no	—
81	C₂×C₈×C₁₉	—	2	8	no	—
82	C₂×C₈×C₁₉	—	4	4	no	—
83	C₂×C₈×C₁₉	—	4	2	no	—
84	C₂×C₈×C₁₉	—	4	2	no	—
85	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
86	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
87	C₄²×C₁₉	C₄⋊C₄	1	4	yes	—
88	C₄²×C₁₉	C₄⋊C₄	1	4	yes	—
89	C₄×Dic₁₉	—	2	16	no	—
90	C₄×Dic₁₉	—	2	16	no	—
91	C₄×Dic₁₉	—	2	4	no	—
92	C₄×Dic₁₉	—	2	4	no	—
93	C₄×Dic₁₉	—	2	4	no	—
94	C₄×Dic₁₉	—	2	4	no	—
95	C₂×C₁₉⋊C₈	—	2	4	no	—
96	C₂×C₁₉⋊C₈	—	2	8	no	—
97	C₂×C₁₉⋊C₈	—	4	4	no	—
98	C₂×C₁₉⋊C₈	—	4	2	no	—
99	C₂×C₁₉⋊C₈	—	4	2	no	—
100	#10832	—	19	1	no	maximal, Sylow
101	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
102	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
104	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
105	C₂³×C₁₉	#117	1	2	yes	—
106	C₂³×C₁₉	C₂²×C₈	1	2	yes	—
107	C₂³×C₁₉	C₂×M₁₆	1	2	yes	—
108	C₂³×C₁₉	C₂×M₁₆	1	4	yes	—
109	C₂×C₄×C₁₉	—	2	4	no	—
110	C₂×C₄×C₁₉	—	2	4	no	—
111	C₂×C₄×C₁₉	—	2	4	no	—
112	C₂×C₄×C₁₉	#95	1	4	yes	—
113	C₂×C₄×C₁₉	#95	1	4	yes	—
114	C₂×C₄×C₁₉	C₄×C₈	1	4	yes	—
115	C₂×C₄×C₁₉	#97	1	4	yes	—
116	C₂×C₄×C₁₉	C₂²⋊C₈	1	8	yes	—
117	C₂×C₄×C₁₉	C₄⋊C₈	1	8	yes	—
118	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
123	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
124	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
125	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
126	C₂×C₄×C₁₉	#121	1	2	yes	—
127	C₂×C₄×C₁₉	#121	1	2	yes	—
128	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
129	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
130	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
131	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
132	C₂×C₄×C₁₉	#125	1	2	yes	—
133	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
134	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
135	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
136	C₂×Dic₁₉	—	2	8	no	—
137	C₂×Dic₁₉	—	2	8	no	—
138	C₂×Dic₁₉	—	2	8	no	—
139	C₂×Dic₁₉	—	2	8	no	—
140	C₂×Dic₁₉	—	2	8	no	—
141	C₂×Dic₁₉	—	2	8	no	—
142	C₂×Dic₁₉	C₄⋊C₈	1	16	yes	complemented
143	C₈×C₁₉	—	4	4	no	—
144	C₁₉⋊C₈	—	4	4	no	—
145	C₂²×C₄⋊C₈	—	19	1	no	—
146	C₂²×C₄⋊C₈	D₁₉	1	1	yes	characteristic
147	C₂×C₄³	—	19	1	no	—
148	C₂×#336	—	19	4	no	—
149	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
150	C₂²×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
151	C₂²×C₁₉	#380	1	2	yes	—
152	C₂²×C₁₉	#382	1	1	yes	characteristic
153	C₂²×C₁₉	#384	1	1	yes	characteristic
154	C₂²×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
155	C₂²×C₁₉	C₂×#97	1	1	yes	characteristic
156	C₂²×C₁₉	C₄×M₁₆	1	2	yes	—
157	C₂²×C₁₉	C₂×C₂²⋊C₈	1	2	yes	—
158	C₂²×C₁₉	#407	1	2	yes	—
159	C₂²×C₁₉	C₂×C₄⋊C₈	1	4	yes	—
160	C₂²×C₁₉	C₂×C₄⋊C₈	1	2	yes	—
161	C₂²×C₁₉	#423	1	4	yes	—
162	C₂²×C₁₉	#423	1	2	yes	—
163	C₂²×C₁₉	#431	1	4	yes	—
164	C₂²×C₁₉	#432	1	4	yes	—
165	C₄×C₁₉	—	2	4	no	—
166	C₄×C₁₉	#336	1	8	yes	complemented
167	C₄×C₁₉	#389	1	2	yes	—
168	C₄×C₁₉	#389	1	2	yes	—
169	C₄×C₁₉	#390	1	1	yes	characteristic
170	C₄×C₁₉	#390	1	1	yes	characteristic
171	C₄×C₁₉	#391	1	1	yes	characteristic
172	C₄×C₁₉	#391	1	1	yes	characteristic
173	Dic₁₉	—	2	16	no	—
174	C₂³×C₈	—	19	2	no	—
175	C₂³×C₈	C₂×D₁₉	1	2	yes	—
176	C₂²×C₄²	—	19	2	no	—
177	C₂²×C₄²	—	19	2	no	—
178	C₂²×C₄²	—	19	2	no	—
179	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
180	C₂×C₄⋊C₈	—	2	2	no	—
181	C₂×C₄⋊C₈	—	2	2	no	—
182	C₂×C₄⋊C₈	—	19	4	no	—
183	C₂×C₄⋊C₈	—	38	2	no	—
184	C₂×C₄⋊C₈	—	38	2	no	—
185	C₂×C₄⋊C₈	Dic₁₉	1	4	yes	complemented
186	C₄³	—	38	2	no	—
187	C₄³	—	38	2	no	—
188	#336	—	38	8	no	—
189	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
190	C₂×C₁₉	C₂×#336	1	1	yes	characteristic
191	C₂×C₁₉	#1728	1	1	yes	characteristic
192	C₂×C₁₉	C₄×C₄⋊C₈	1	2	yes	—
193	C₂×C₁₉	#1767	1	2	yes	—
194	C₂×C₁₉	#1797	1	4	yes	—
195	C₂×C₁₉	#1831	1	2	yes	—
196	C₂×C₁₉	#1842	1	2	yes	—
197	C₂³×C₄	—	19	4	no	—
198	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
199	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
200	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
201	C₂²×C₈	—	2	4	no	—
202	C₂²×C₈	—	2	4	no	—
203	C₂²×C₈	—	2	2	no	—
204	C₂²×C₈	—	2	2	no	—
205	C₂²×C₈	—	19	4	no	—
206	C₂²×C₈	—	38	2	no	—
207	C₂²×C₈	—	38	4	no	—
208	C₂²×C₈	—	38	4	no	—
209	C₂²×C₈	—	38	2	no	—
210	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
211	C₂×C₄²	—	19	8	no	—
212	C₂×C₄²	—	19	4	no	—
213	C₂×C₄²	—	19	4	no	—
214	C₂×C₄²	—	38	8	no	—
215	C₂×C₄²	—	38	4	no	—
216	C₂×C₄²	—	38	4	no	—
217	C₂×C₄²	—	38	4	no	—
218	C₂×C₄²	—	38	2	no	—
219	C₂×C₄²	—	38	2	no	—
220	C₂×C₄²	—	38	2	no	—
221	C₂×C₄²	—	38	2	no	—
222	C₂×C₄²	Dic₃₈	1	2	yes	—
223	C₂×C₄²	C₄×D₁₉	1	2	yes	—
224	C₂×C₄²	D₇₆	1	2	yes	—
225	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
226	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
227	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
228	C₄⋊C₈	—	2	8	no	—
229	C₄⋊C₈	—	38	8	no	—
230	C₁₉	#10832	1	1	yes	characteristic, complemented, Sylow
231	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	—	19	8	no	—
234	C₂²×C₄	—	19	8	no	—
235	C₂²×C₄	—	19	8	no	—
236	C₂²×C₄	—	38	4	no	—
237	C₂²×C₄	—	38	4	no	—
238	C₂²×C₄	—	38	4	no	—
239	C₂²×C₄	—	38	4	no	—
240	C₂²×C₄	C₈×D₁₉	1	4	yes	—
241	C₂²×C₄	#64515	1	4	yes	—
242	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
243	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
244	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
245	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
246	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
247	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
248	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
249	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
250	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
251	C₂²×C₄	D₄×D₁₉	1	2	yes	—
252	C₂²×C₄	#64543	1	2	yes	—
253	C₂²×C₄	Q₈×D₁₉	1	2	yes	—
254	C₂²×C₄	#64545	1	2	yes	—
255	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
256	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
257	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
258	C₂×C₈	—	2	8	no	—
259	C₂×C₈	—	2	4	no	—
260	C₂×C₈	—	4	2	no	—
261	C₂×C₈	—	4	4	no	—
262	C₂×C₈	—	4	2	no	—
263	C₂×C₈	—	38	8	no	—
264	C₂×C₈	—	38	4	no	—
265	C₂×C₈	—	76	2	no	—
266	C₂×C₈	—	76	2	no	—
267	C₂×C₈	—	76	4	no	—
268	C₄²	—	38	16	no	—
269	C₄²	—	38	4	no	—
270	C₄²	—	38	4	no	—
271	C₄²	—	38	16	no	—
272	C₄²	—	38	4	no	—
273	C₄²	—	38	4	no	—
274	C₄²	Dic₁₉⋊C₄	1	4	yes	—
275	C₄²	C₄⋊Dic₁₉	1	4	yes	—
276	C₄²	(C₂×D₁₉)⋊C₄	1	4	yes	—
277	C₄²	C₂²⋊Dic₁₉	1	4	yes	—
278	C₂³	C₄⋊C₄×D₁₉	1	2	yes	—
279	C₂³	#10597338	1	2	yes	—
280	C₂³	C₂×C₈×D₁₉	1	2	yes	—
281	C₂³	C₂×#64515	1	2	yes	—
282	C₂³	M₁₆×D₁₉	1	4	yes	—
283	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
284	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
285	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	19	16	no	—
290	C₂×C₄	—	38	8	no	—
291	C₂×C₄	—	38	8	no	—
292	C₂×C₄	—	38	8	no	—
293	C₂×C₄	—	38	8	no	—
294	C₂×C₄	—	38	8	no	—
295	C₂×C₄	—	38	8	no	—
296	C₂×C₄	C₈×Dic₁₉	1	4	yes	—
297	C₂×C₄	Dic₁₉⋊C₈	1	8	yes	—
298	C₂×C₄	#10597272	1	4	yes	—
299	C₂×C₄	(C₂×D₁₉)⋊C₈	1	8	yes	—
300	C₂×C₄	C₁₉⋊#95	1	4	yes	—
301	C₂×C₄	C₁₉⋊#95	1	4	yes	—
302	C₂×C₄	#10597333	1	2	yes	—
303	C₂×C₄	#10597334	1	2	yes	—
304	C₂×C₄	#10597336	1	2	yes	—
305	C₂×C₄	#10597339	1	2	yes	—
306	C₂×C₄	#10597341	1	2	yes	—
307	C₂×C₄	#10597343	1	2	yes	—
308	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
309	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
310	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
311	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
312	C₂×C₄	#10597382	1	1	yes	characteristic
313	C₂×C₄	#10597384	1	2	yes	—
314	C₂×C₄	#10597386	1	1	yes	characteristic
315	C₂×C₄	#10597390	1	1	yes	characteristic
316	C₂×C₄	Q₈×Dic₁₉	1	2	yes	—
317	C₂×C₄	#10597392	1	2	yes	—
318	C₂×C₄	#10597393	1	1	yes	characteristic
319	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
320	C₈	—	4	4	no	—
321	C₈	—	76	4	no	—
322	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
323	C₂²	C₄⋊C₄×Dic₁₉	1	2	yes	—
324	C₂²	#11926401	1	2	yes	—
325	C₂²	#11926409	1	1	yes	characteristic
326	C₂²	#11926413	1	1	yes	characteristic
327	C₂²	C₂×C₈×Dic₁₉	1	1	yes	characteristic
328	C₂²	C₂×#10597272	1	1	yes	characteristic
329	C₂²	M₁₆×Dic₁₉	1	2	yes	—
330	C₂²	C₂×(C₂×D₁₉)⋊C₈	1	2	yes	—
331	C₂²	#11926507	1	2	yes	—
332	C₂²	C₄⋊C₈×D₁₉	1	4	yes	—
333	C₂²	C₂×Dic₁₉⋊C₈	1	2	yes	—
334	C₂²	#11926566	1	4	yes	—
335	C₂²	#11926567	1	2	yes	—
336	C₂²	#11926596	1	4	yes	—
337	C₂²	#11926600	1	4	yes	—
338	C₄	—	2	4	no	—
339	C₄	—	38	16	no	—
340	C₄	#11926298	1	8	yes	complemented
341	C₄	#11926440	1	2	yes	—
342	C₄	#11926443	1	2	yes	—
343	C₄	#11926445	1	1	yes	characteristic
344	C₄	#11926447	1	1	yes	characteristic
345	C₄	#11926449	1	1	yes	characteristic
346	C₄	#11926451	1	1	yes	characteristic
347	C₂	#14561864	1	1	yes	characteristic
348	C₂	C₂×#11926298	1	1	yes	characteristic
349	C₂	#14563328	1	1	yes	characteristic
350	C₂	C₄⋊C₈×Dic₁₉	1	2	yes	—
351	C₂	#14563490	1	2	yes	—
352	C₂	#14563612	1	4	yes	—
353	C₂	#14563751	1	2	yes	—
354	C₂	#14563786	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₁₉
commutator	C₂²×C₁₉	C₂×C₄×C₈
Fitting	C₂²×C₁₉×C₄⋊C₈	C₂
socle, prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×C₄⋊C₈	D₁₉
hypocenter	C₁₉	#10832
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
11. C₂×C₄⋊(C₁₉⋊C₈)	C₄	semidirect
19. C₂×C₁₉×C₄⋊C₈	C₄	semidirect
43. C₂×C₄×Dic₁₉	C₈	semidirect
142. C₂×Dic₁₉	C₄⋊C₈	semidirect
166. C₄×C₁₉	#336	semidirect
185. C₂×C₄⋊C₈	Dic₁₉	semidirect
230. C₁₉	#10832	semidirect
340. C₄	#11926298	semidirect

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×C₁₉×C₄⋊C₈	2
#10832	19