Subgroups — C₂²×C₁₉×#464 #18066367

Order 4864.

2918 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×#124	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#464	C₂	1	24	yes	maximal, direct product factor
6	C₂²×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×Q₁₆×C₁₉	—	2	8	no	—
13	C₂²×Q₁₆×C₁₉	C₂²	1	12	yes	complemented
14	C₂²×SD₁₆×C₁₉	—	2	8	no	—
15	C₂²×SD₁₆×C₁₉	C₂²	1	12	yes	—
16	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#124	—	2	6	no	—
19	C₂×C₁₉×#124	C₂²	1	12	yes	—
20	C₂×C₄×Q₈×C₁₉	—	2	6	no	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	12	yes	complemented
22	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
25	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
26	C₂²×C₄²×C₁₉	—	2	1	no	—
27	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#464	C₂²	1	64	yes	direct product factor
29	C₂×C₁₉×C₄⋊C₈	C₂²	1	12	yes	complemented
30	C₂×C₁₉×#103	C₂²	1	12	yes	complemented
31	C₂×C₁₉×#102	C₂²	1	12	yes	—
32	C₂⁵×C₁₉	—	2	1	no	—
33	C₂²×Q₈×C₁₉	—	2	3	no	—
34	C₂²×Q₈×C₁₉	—	2	3	no	—
35	C₂²×Q₈×C₁₉	—	2	4	no	—
36	C₂²×Q₈×C₁₉	—	2	4	no	—
37	C₂²×Q₈×C₁₉	—	2	4	no	—
38	C₂²×Q₈×C₁₉	D₄	1	8	yes	—
39	C₂²×Q₈×C₁₉	C₂³	1	6	yes	—
40	C₂²×Q₈×C₁₉	C₂³	1	6	yes	—
41	C₂²×D₄×C₁₉	—	2	4	no	—
42	C₂²×D₄×C₁₉	—	2	3	no	—
43	C₂²×D₄×C₁₉	—	2	4	no	—
44	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	—	2	1	no	—
48	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂×Q₁₆×C₁₉	—	2	48	no	—
52	C₂×Q₁₆×C₁₉	C₂³	1	16	yes	complemented
53	C₂×SD₁₆×C₁₉	—	2	48	no	—
54	C₂×SD₁₆×C₁₉	C₂³	1	16	yes	—
55	C₂²×C₈×C₁₉	—	2	4	no	—
56	C₂²×C₈×C₁₉	—	2	4	no	—
57	C₂²×C₈×C₁₉	C₂³	1	6	yes	—
58	C₂²×C₈×C₁₉	C₂³	1	6	yes	—
59	C₁₉×#124	—	2	24	no	—
60	C₁₉×#124	C₂³	1	16	yes	—
61	C₄×Q₈×C₁₉	—	2	24	no	—
62	C₄×Q₈×C₁₉	C₂³	1	16	yes	complemented
63	C₂×C₄⋊C₄×C₁₉	—	2	12	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	12	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	12	no	—
68	C₂×C₄²×C₁₉	—	2	12	no	—
69	C₂×C₄²×C₁₉	D₄	1	6	yes	—
70	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
71	C₁₉×C₄⋊C₈	C₂³	1	16	yes	complemented
72	C₁₉×#103	C₂³	1	16	yes	complemented
73	C₁₉×#102	C₂³	1	16	yes	—
74	C₂⁴×C₁₉	—	2	6	no	—
75	C₂⁴×C₁₉	—	4	4	no	—
76	C₂⁴×C₁₉	—	4	4	no	—
77	C₂⁴×C₁₉	—	4	4	no	—
78	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂×Q₈×C₁₉	—	2	24	no	—
80	C₂×Q₈×C₁₉	—	2	6	no	—
81	C₂×Q₈×C₁₉	—	2	6	no	—
82	C₂×Q₈×C₁₉	—	2	12	no	—
83	C₂×Q₈×C₁₉	—	2	12	no	—
84	C₂×Q₈×C₁₉	—	2	12	no	—
85	C₂×Q₈×C₁₉	—	4	12	no	—
86	C₂×Q₈×C₁₉	C₂×D₄	1	24	yes	—
87	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
88	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
89	C₂×D₄×C₁₉	—	2	12	no	—
90	C₂×D₄×C₁₉	—	2	6	no	—
91	C₂×D₄×C₁₉	—	2	12	no	—
92	C₂×D₄×C₁₉	—	4	12	no	—
93	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
94	C₂²×C₄×C₁₉	—	2	8	no	—
95	C₂²×C₄×C₁₉	—	2	4	no	—
96	C₂²×C₄×C₁₉	—	2	4	no	—
97	C₂²×C₄×C₁₉	—	2	6	no	—
98	C₂²×C₄×C₁₉	—	2	6	no	—
99	C₂²×C₄×C₁₉	—	2	6	no	—
100	C₂²×C₄×C₁₉	—	4	4	no	—
101	C₂²×C₄×C₁₉	—	4	4	no	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₁₉	#41	1	4	yes	—
107	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
108	Q₁₆×C₁₉	—	2	32	no	—
109	SD₁₆×C₁₉	—	2	32	no	—
110	C₂×C₈×C₁₉	—	2	12	no	—
111	C₂×C₈×C₁₉	—	2	12	no	—
112	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
113	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
114	C₄⋊C₄×C₁₉	—	2	16	no	—
115	C₄⋊C₄×C₁₉	—	2	6	no	—
116	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
117	C₂²⋊C₄×C₁₉	—	2	16	no	—
118	C₂²⋊C₄×C₁₉	—	2	16	no	—
119	C₄²×C₁₉	—	2	16	no	—
120	C₄²×C₁₉	C₂×D₄	1	12	yes	—
121	C₄²×C₁₉	C₂⁴	1	4	yes	—
122	C₂²×#464	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂³×C₁₉	—	2	4	no	—
124	C₂³×C₁₉	—	4	12	no	—
125	C₂³×C₁₉	—	4	12	no	—
126	C₂³×C₁₉	—	4	12	no	—
127	C₂³×C₁₉	—	8	16	no	—
128	C₂³×C₁₉	#121	1	4	yes	—
129	C₂³×C₁₉	#135	1	4	yes	—
130	C₂³×C₁₉	#137	1	4	yes	—
131	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
132	Q₈×C₁₉	—	2	24	no	—
133	Q₈×C₁₉	—	2	4	no	—
134	Q₈×C₁₉	—	2	4	no	—
135	Q₈×C₁₉	—	2	4	no	—
136	Q₈×C₁₉	—	4	12	no	—
137	Q₈×C₁₉	C₂²×D₄	1	8	yes	—
138	D₄×C₁₉	—	2	4	no	—
139	D₄×C₁₉	—	2	4	no	—
140	D₄×C₁₉	—	4	12	no	—
141	C₂×C₄×C₁₉	—	2	24	no	—
142	C₂×C₄×C₁₉	—	2	12	no	—
143	C₂×C₄×C₁₉	—	2	12	no	—
144	C₂×C₄×C₁₉	—	2	4	no	—
145	C₂×C₄×C₁₉	—	2	4	no	—
146	C₂×C₄×C₁₉	—	2	4	no	—
147	C₂×C₄×C₁₉	—	4	12	no	—
148	C₂×C₄×C₁₉	—	4	12	no	—
149	C₂×C₄×C₁₉	#121	1	12	yes	—
150	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
151	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
152	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
153	C₂×C₄×C₁₉	C₂²×D₄	1	6	yes	—
154	C₂×C₄×C₁₉	C₂×#41	1	6	yes	—
155	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
156	C₈×C₁₉	—	2	4	no	—
157	C₈×C₁₉	—	2	4	no	—
158	C₂³×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
159	C₂³×SD₁₆	C₂×C₁₉	1	1	yes	characteristic
160	C₂²×#124	C₂×C₁₉	1	1	yes	characteristic
161	C₂²×C₄×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
162	C₂×#464	C₂×C₁₉	1	24	yes	direct product factor
163	C₂²×C₄⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
164	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
165	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic
166	C₂²×C₁₉	—	4	4	no	—
167	C₂²×C₁₉	—	4	4	no	—
168	C₂²×C₁₉	—	4	4	no	—
169	C₂²×C₁₉	—	8	24	no	—
170	C₂²×C₁₉	#464	1	16	yes	direct product factor
171	C₂²×C₁₉	C₂×#121	1	6	yes	—
172	C₂²×C₁₉	C₂×#135	1	6	yes	—
173	C₂²×C₁₉	C₂×#137	1	6	yes	—
174	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
175	C₄×C₁₉	—	2	8	no	—
176	C₄×C₁₉	—	2	4	no	—
177	C₄×C₁₉	—	2	4	no	—
178	C₄×C₁₉	—	4	4	no	—
179	C₄×C₁₉	—	4	4	no	—
180	C₄×C₁₉	C₂×#121	1	6	yes	—
181	C₄×C₁₉	C₂³×D₄	1	1	yes	characteristic
182	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
183	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
184	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
185	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
186	C₂²×Q₁₆	—	2	8	no	—
187	C₂²×Q₁₆	C₂²×C₁₉	1	12	yes	complemented
188	C₂²×SD₁₆	—	2	8	no	—
189	C₂²×SD₁₆	C₂²×C₁₉	1	12	yes	—
190	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
191	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
192	C₂×#124	—	2	6	no	—
193	C₂×#124	C₂²×C₁₉	1	12	yes	—
194	C₂×C₄×Q₈	—	2	6	no	—
195	C₂×C₄×Q₈	C₂²×C₁₉	1	12	yes	complemented
196	C₂²×C₄⋊C₄	—	2	1	no	—
197	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
198	C₂²×C₂²⋊C₄	—	2	1	no	—
199	C₂²×C₂²⋊C₄	—	2	1	no	—
200	C₂²×C₄²	—	2	1	no	—
201	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
202	#464	C₂²×C₁₉	1	64	yes	direct product factor
203	C₂×C₄⋊C₈	C₂²×C₁₉	1	12	yes	complemented
204	C₂×#103	C₂²×C₁₉	1	12	yes	complemented
205	C₂×#102	C₂²×C₁₉	1	12	yes	—
206	C₂×C₁₉	—	8	4	no	—
207	C₂×C₁₉	C₂×#464	1	12	yes	direct product factor
208	C₂×C₁₉	C₂²×#121	1	1	yes	characteristic
209	C₂×C₁₉	C₂²×#135	1	1	yes	characteristic
210	C₂×C₁₉	C₂²×#137	1	1	yes	characteristic
211	C₂⁵	—	2	1	no	—
212	C₂²×Q₈	—	2	3	no	—
213	C₂²×Q₈	—	2	3	no	—
214	C₂²×Q₈	—	2	4	no	—
215	C₂²×Q₈	—	2	4	no	—
216	C₂²×Q₈	—	2	4	no	—
217	C₂²×Q₈	D₄×C₁₉	1	8	yes	—
218	C₂²×Q₈	C₂³×C₁₉	1	6	yes	—
219	C₂²×Q₈	C₂³×C₁₉	1	6	yes	—
220	C₂²×D₄	—	2	4	no	—
221	C₂²×D₄	—	2	3	no	—
222	C₂²×D₄	—	2	4	no	—
223	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
224	C₂³×C₄	—	2	1	no	—
225	C₂³×C₄	—	2	1	no	—
226	C₂³×C₄	—	2	1	no	—
227	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
228	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
230	C₂×Q₁₆	—	2	48	no	—
231	C₂×Q₁₆	C₂³×C₁₉	1	16	yes	complemented
232	C₂×SD₁₆	—	2	48	no	—
233	C₂×SD₁₆	C₂³×C₁₉	1	16	yes	—
234	C₂²×C₈	—	2	4	no	—
235	C₂²×C₈	—	2	4	no	—
236	C₂²×C₈	C₂³×C₁₉	1	6	yes	—
237	C₂²×C₈	C₂³×C₁₉	1	6	yes	—
238	#124	—	2	24	no	—
239	#124	C₂³×C₁₉	1	16	yes	—
240	C₄×Q₈	—	2	24	no	—
241	C₄×Q₈	C₂³×C₁₉	1	16	yes	complemented
242	C₂×C₄⋊C₄	—	2	12	no	—
243	C₂×C₄⋊C₄	—	2	3	no	—
244	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
245	C₂×C₂²⋊C₄	—	2	12	no	—
246	C₂×C₂²⋊C₄	—	2	12	no	—
247	C₂×C₄²	—	2	12	no	—
248	C₂×C₄²	D₄×C₁₉	1	6	yes	—
249	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
250	C₄⋊C₈	C₂³×C₁₉	1	16	yes	complemented
251	#103	C₂³×C₁₉	1	16	yes	complemented
252	#102	C₂³×C₁₉	1	16	yes	—
253	C₁₉	C₂²×#464	1	1	yes	characteristic, direct product factor, Sylow
254	C₂⁴	—	2	6	no	—
255	C₂⁴	—	4	4	no	—
256	C₂⁴	—	4	4	no	—
257	C₂⁴	—	4	4	no	—
258	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
259	C₂×Q₈	—	2	24	no	—
260	C₂×Q₈	—	2	6	no	—
261	C₂×Q₈	—	2	6	no	—
262	C₂×Q₈	—	2	12	no	—
263	C₂×Q₈	—	2	12	no	—
264	C₂×Q₈	—	2	12	no	—
265	C₂×Q₈	—	4	12	no	—
266	C₂×Q₈	C₂×D₄×C₁₉	1	24	yes	—
267	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
268	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
269	C₂×D₄	—	2	12	no	—
270	C₂×D₄	—	2	6	no	—
271	C₂×D₄	—	2	12	no	—
272	C₂×D₄	—	4	12	no	—
273	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
274	C₂²×C₄	—	2	8	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	6	no	—
278	C₂²×C₄	—	2	6	no	—
279	C₂²×C₄	—	2	6	no	—
280	C₂²×C₄	—	4	4	no	—
281	C₂²×C₄	—	4	4	no	—
282	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
283	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
284	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
285	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
286	C₂²×C₄	#41×C₁₉	1	4	yes	—
287	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
288	Q₁₆	—	2	32	no	—
289	SD₁₆	—	2	32	no	—
290	C₂×C₈	—	2	12	no	—
291	C₂×C₈	—	2	12	no	—
292	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
293	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
294	C₄⋊C₄	—	2	16	no	—
295	C₄⋊C₄	—	2	6	no	—
296	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
297	C₂²⋊C₄	—	2	16	no	—
298	C₂²⋊C₄	—	2	16	no	—
299	C₄²	—	2	16	no	—
300	C₄²	C₂×D₄×C₁₉	1	12	yes	—
301	C₄²	C₂⁴×C₁₉	1	4	yes	—
302	C₂³	—	2	4	no	—
303	C₂³	—	4	12	no	—
304	C₂³	—	4	12	no	—
305	C₂³	—	4	12	no	—
306	C₂³	—	8	16	no	—
307	C₂³	C₁₉×#121	1	4	yes	—
308	C₂³	C₁₉×#135	1	4	yes	—
309	C₂³	C₁₉×#137	1	4	yes	—
310	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
311	Q₈	—	2	24	no	—
312	Q₈	—	2	4	no	—
313	Q₈	—	2	4	no	—
314	Q₈	—	2	4	no	—
315	Q₈	—	4	12	no	—
316	Q₈	C₂²×D₄×C₁₉	1	8	yes	—
317	D₄	—	2	4	no	—
318	D₄	—	2	4	no	—
319	D₄	—	4	12	no	—
320	C₂×C₄	—	2	24	no	—
321	C₂×C₄	—	2	12	no	—
322	C₂×C₄	—	2	12	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	4	12	no	—
327	C₂×C₄	—	4	12	no	—
328	C₂×C₄	C₁₉×#121	1	12	yes	—
329	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
330	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
331	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
332	C₂×C₄	C₂²×D₄×C₁₉	1	6	yes	—
333	C₂×C₄	C₂×#41×C₁₉	1	6	yes	—
334	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
335	C₈	—	2	4	no	—
336	C₈	—	2	4	no	—
337	C₂²	—	4	4	no	—
338	C₂²	—	4	4	no	—
339	C₂²	—	4	4	no	—
340	C₂²	—	8	24	no	—
341	C₂²	C₁₉×#464	1	16	yes	direct product factor
342	C₂²	C₂×C₁₉×#121	1	6	yes	—
343	C₂²	C₂×C₁₉×#135	1	6	yes	—
344	C₂²	C₂×C₁₉×#137	1	6	yes	—
345	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
346	C₄	—	2	8	no	—
347	C₄	—	2	4	no	—
348	C₄	—	2	4	no	—
349	C₄	—	4	4	no	—
350	C₄	—	4	4	no	—
351	C₄	C₂×C₁₉×#121	1	6	yes	—
352	C₄	C₂³×D₄×C₁₉	1	1	yes	characteristic
353	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
354	C₂	—	8	4	no	—
355	C₂	C₂×C₁₉×#464	1	12	yes	direct product factor
356	C₂	C₂²×C₁₉×#121	1	1	yes	characteristic
357	C₂	C₂²×C₁₉×#135	1	1	yes	characteristic
358	C₂	C₂²×C₁₉×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₁₆×C₁₉	C₂	semidirect
4. C₂²×C₄×Q₈×C₁₉	C₂	semidirect
5. C₂×C₁₉×#464	C₂	direct (N × H)
6. C₂²×C₁₉×C₄⋊C₈	C₂	semidirect
7. C₂²×C₁₉×#103	C₂	semidirect
13. C₂²×Q₁₆×C₁₉	C₂²	semidirect
21. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
28. C₁₉×#464	C₂²	direct (N × H)
29. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
30. C₂×C₁₉×#103	C₂²	semidirect
52. C₂×Q₁₆×C₁₉	C₂³	semidirect
62. C₄×Q₈×C₁₉	C₂³	semidirect
71. C₁₉×C₄⋊C₈	C₂³	semidirect
72. C₁₉×#103	C₂³	semidirect
122. C₂²×#464	C₁₉	direct (N × H)
158. C₂³×Q₁₆	C₂×C₁₉	semidirect
161. C₂²×C₄×Q₈	C₂×C₁₉	semidirect
162. C₂×#464	C₂×C₁₉	direct (N × H)
163. C₂²×C₄⋊C₈	C₂×C₁₉	semidirect
164. C₂²×#103	C₂×C₁₉	semidirect
170. C₂²×C₁₉	#464	direct (N × H)
187. C₂²×Q₁₆	C₂²×C₁₉	semidirect
195. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
202. #464	C₂²×C₁₉	direct (N × H)
203. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
204. C₂×#103	C₂²×C₁₉	semidirect
207. C₂×C₁₉	C₂×#464	direct (N × H)
231. C₂×Q₁₆	C₂³×C₁₉	semidirect
241. C₄×Q₈	C₂³×C₁₉	semidirect
250. C₄⋊C₈	C₂³×C₁₉	semidirect
251. #103	C₂³×C₁₉	semidirect
253. C₁₉	C₂²×#464	direct (N × H)
341. C₂²	C₁₉×#464	direct (N × H)
355. C₂	C₂×C₁₉×#464	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Q₁₆×C₁₉	2
C₂³×SD₁₆×C₁₉	2
C₂²×C₁₉×#124	2
C₂²×C₄×Q₈×C₁₉	2
C₂×C₁₉×#464	2
C₂²×C₁₉×C₄⋊C₈	2
C₂²×C₁₉×#103	2
C₂²×C₁₉×#102	2
C₂²×#464	19

Subgroups — C22×C19×#464 #18066367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₉×#464 #18066367