Subgroups — C₂×C₁₉×#1763 #18026369

Order 4864.

1686 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#103	C₂	1	2	yes	maximal
3	C₂²×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1763	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#340	C₂	1	2	yes	maximal
7	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
9	C₂×C₄×Q₈×C₁₉	—	2	4	no	—
10	C₂×C₄×Q₈×C₁₉	—	2	2	no	—
11	C₂×C₄×Q₈×C₁₉	C₄	1	8	yes	complemented
12	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
13	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₉	—	2	1	no	—
17	C₂²×C₄²×C₁₉	—	2	1	no	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#103	C₄	1	16	yes	complemented
20	C₂×C₁₉×#103	C₂²	1	8	yes	—
21	C₂×C₁₉×#97	—	2	4	no	—
22	C₂×C₁₉×#97	C₂²	1	4	yes	—
23	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
25	C₂×C₁₉×#95	—	2	1	no	—
26	C₁₉×#340	C₂²	1	8	yes	—
27	C₂²×Q₈×C₁₉	—	2	2	no	—
28	C₂²×Q₈×C₁₉	—	2	1	no	—
29	C₂²×Q₈×C₁₉	—	2	4	no	—
30	C₂²×Q₈×C₁₉	C₂×C₄	1	8	yes	—
31	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
32	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₉	—	2	1	no	—
34	C₂³×C₄×C₁₉	—	2	2	no	—
35	C₂³×C₄×C₁₉	—	2	1	no	—
36	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₁₉	—	2	4	no	—
40	C₂²×C₈×C₁₉	—	2	4	no	—
41	C₂²×C₈×C₁₉	C₂×C₄	1	8	yes	—
42	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
43	C₄×Q₈×C₁₉	—	2	16	no	—
44	C₄×Q₈×C₁₉	—	2	8	no	—
45	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	complemented
46	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
53	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
56	C₂×C₄²×C₁₉	—	2	8	no	—
57	C₂×C₄²×C₁₉	—	2	4	no	—
58	C₂×C₄²×C₁₉	—	2	4	no	—
59	C₂×C₄²×C₁₉	—	4	4	no	—
60	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₁₉	D₄	1	2	yes	—
62	C₂×C₄²×C₁₉	D₄	1	4	yes	—
63	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
64	C₁₉×#103	C₂×C₄	1	32	yes	complemented
65	C₁₉×#97	—	2	8	no	—
66	C₁₉×#95	—	2	4	no	—
67	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂×Q₈×C₁₉	—	2	4	no	—
69	C₂×Q₈×C₁₉	—	2	8	no	—
70	C₂×Q₈×C₁₉	—	2	8	no	—
71	C₂×Q₈×C₁₉	—	2	16	no	—
72	C₂×Q₈×C₁₉	—	2	2	no	—
73	C₂×Q₈×C₁₉	—	2	4	no	—
74	C₂×Q₈×C₁₉	C₄²	1	16	yes	complemented
75	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
76	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
77	C₂²×C₄×C₁₉	—	2	4	no	—
78	C₂²×C₄×C₁₉	—	2	8	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	4	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	4	no	—
84	C₂²×C₄×C₁₉	—	2	8	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	4	no	—
87	C₂²×C₄×C₁₉	—	4	4	no	—
88	C₂²×C₄×C₁₉	—	4	2	no	—
89	C₂²×C₄×C₁₉	—	4	2	no	—
90	C₂²×C₄×C₁₉	—	4	4	no	—
91	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
92	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
93	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₉	#41	1	4	yes	—
100	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
101	C₂×C₈×C₁₉	—	2	16	no	—
102	C₂×C₈×C₁₉	—	2	4	no	—
103	C₂×C₈×C₁₉	—	2	4	no	—
104	C₂×C₈×C₁₉	C₂²×C₄	1	8	yes	—
105	C₄⋊C₄×C₁₉	—	2	16	no	—
106	C₄⋊C₄×C₁₉	—	2	4	no	—
107	C₄⋊C₄×C₁₉	—	2	8	no	—
108	C₄⋊C₄×C₁₉	—	2	2	no	—
109	C₄⋊C₄×C₁₉	—	2	4	no	—
110	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
111	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
112	C₄²×C₁₉	—	2	16	no	—
113	C₄²×C₁₉	—	4	8	no	—
114	C₄²×C₁₉	C₂²⋊C₄	1	8	yes	—
115	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
116	C₄²×C₁₉	C₂×D₄	1	4	yes	—
117	C₂×#1763	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
119	C₂³×C₁₉	C₄×D₄	1	4	yes	—
120	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
121	C₂³×C₁₉	#137	1	2	yes	—
122	C₂³×C₁₉	#137	1	4	yes	—
123	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
124	Q₈×C₁₉	—	2	4	no	—
125	Q₈×C₁₉	—	2	8	no	—
126	Q₈×C₁₉	—	2	16	no	—
127	Q₈×C₁₉	C₂×C₄²	1	8	yes	complemented
128	C₂×C₄×C₁₉	—	2	4	no	—
129	C₂×C₄×C₁₉	—	2	8	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	4	no	—
132	C₂×C₄×C₁₉	—	2	2	no	—
133	C₂×C₄×C₁₉	—	2	16	no	—
134	C₂×C₄×C₁₉	—	2	8	no	—
135	C₂×C₄×C₁₉	—	2	8	no	—
136	C₂×C₄×C₁₉	—	2	4	no	—
137	C₂×C₄×C₁₉	—	2	8	no	—
138	C₂×C₄×C₁₉	—	4	4	no	—
139	C₂×C₄×C₁₉	—	4	2	no	—
140	C₂×C₄×C₁₉	—	4	2	no	—
141	C₂×C₄×C₁₉	—	4	4	no	—
142	C₂×C₄×C₁₉	—	4	8	no	—
143	C₂×C₄×C₁₉	—	4	16	no	—
144	C₂×C₄×C₁₉	C₂×C₄²	1	4	yes	—
145	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
146	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
147	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
148	C₂×C₄×C₁₉	#117	1	4	yes	—
149	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
150	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
151	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
153	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
155	C₈×C₁₉	—	2	8	no	—
156	C₂²×C₄×Q₈	C₂×C₁₉	1	1	yes	characteristic
157	C₂²×#103	C₂×C₁₉	1	2	yes	—
158	C₂²×#97	C₂×C₁₉	1	1	yes	characteristic
159	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
160	#1763	C₂×C₁₉	1	8	yes	direct product factor
161	C₂×#340	C₂×C₁₉	1	2	yes	—
162	C₂²×C₁₉	C₄×C₂²⋊C₄	1	4	yes	—
163	C₂²×C₁₉	#417	1	4	yes	—
164	C₂²×C₁₉	#419	1	4	yes	—
165	C₂²×C₁₉	#440	1	8	yes	—
166	C₂²×C₁₉	#441	1	8	yes	—
167	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
169	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂²×C₁₉	C₂×#137	1	2	yes	—
171	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
172	C₄×C₁₉	—	2	4	no	—
173	C₄×C₁₉	—	2	4	no	—
174	C₄×C₁₉	—	2	8	no	—
175	C₄×C₁₉	—	4	4	no	—
176	C₄×C₁₉	—	4	8	no	—
177	C₄×C₁₉	C₄×C₂²⋊C₄	1	4	yes	—
178	C₄×C₁₉	C₂²×C₄²	1	1	yes	characteristic
179	C₄×C₁₉	C₂×#117	1	1	yes	characteristic
180	C₄×C₁₉	C₂×C₄×D₄	1	2	yes	—
181	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
182	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
183	C₂×C₄×Q₈	—	2	4	no	—
184	C₂×C₄×Q₈	—	2	2	no	—
185	C₂×C₄×Q₈	C₄×C₁₉	1	8	yes	complemented
186	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
187	C₂²×C₄⋊C₄	—	2	1	no	—
188	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
189	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
190	C₂²×C₄²	—	2	1	no	—
191	C₂²×C₄²	—	2	1	no	—
192	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
193	C₂×#103	C₄×C₁₉	1	16	yes	complemented
194	C₂×#103	C₂²×C₁₉	1	8	yes	—
195	C₂×#97	—	2	4	no	—
196	C₂×#97	C₂²×C₁₉	1	4	yes	—
197	C₄×C₄⋊C₄	—	2	2	no	—
198	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
199	C₂×#95	—	2	1	no	—
200	#340	C₂²×C₁₉	1	8	yes	—
201	C₂×C₁₉	#1763	1	8	yes	direct product factor
202	C₂×C₁₉	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₁₉	C₂×#419	1	1	yes	characteristic
204	C₂×C₁₉	C₂×#417	1	1	yes	characteristic
205	C₂×C₁₉	C₂×#440	1	2	yes	—
206	C₂×C₁₉	C₂×#441	1	2	yes	—
207	C₂²×Q₈	—	2	2	no	—
208	C₂²×Q₈	—	2	1	no	—
209	C₂²×Q₈	—	2	4	no	—
210	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
211	C₂²×Q₈	C₂×C₄×C₁₉	1	8	yes	—
212	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
213	C₂³×C₄	—	2	1	no	—
214	C₂³×C₄	—	2	1	no	—
215	C₂³×C₄	—	2	2	no	—
216	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
217	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
218	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
219	C₂²×C₈	—	2	4	no	—
220	C₂²×C₈	—	2	4	no	—
221	C₂²×C₈	C₂×C₄×C₁₉	1	8	yes	—
222	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
223	C₄×Q₈	—	2	16	no	—
224	C₄×Q₈	—	2	8	no	—
225	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	complemented
226	C₂×C₄⋊C₄	—	2	8	no	—
227	C₂×C₄⋊C₄	—	2	4	no	—
228	C₂×C₄⋊C₄	—	2	1	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	4	no	—
232	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
233	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
234	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
235	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
236	C₂×C₄²	—	2	8	no	—
237	C₂×C₄²	—	2	4	no	—
238	C₂×C₄²	—	2	4	no	—
239	C₂×C₄²	—	4	4	no	—
240	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
241	C₂×C₄²	D₄×C₁₉	1	2	yes	—
242	C₂×C₄²	D₄×C₁₉	1	4	yes	—
243	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
244	#103	C₂×C₄×C₁₉	1	32	yes	complemented
245	#97	—	2	8	no	—
246	#95	—	2	4	no	—
247	C₁₉	C₂×#1763	1	1	yes	characteristic, direct product factor, Sylow
248	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
249	C₂×Q₈	—	2	4	no	—
250	C₂×Q₈	—	2	8	no	—
251	C₂×Q₈	—	2	16	no	—
252	C₂×Q₈	—	2	8	no	—
253	C₂×Q₈	—	2	2	no	—
254	C₂×Q₈	—	2	4	no	—
255	C₂×Q₈	C₄²×C₁₉	1	16	yes	complemented
256	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
257	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	8	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	8	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	4	4	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	—	4	4	no	—
272	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
273	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
274	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
275	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
276	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
277	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
278	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
279	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
280	C₂²×C₄	#41×C₁₉	1	4	yes	—
281	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
282	C₂×C₈	—	2	16	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	C₂²×C₄×C₁₉	1	8	yes	—
286	C₄⋊C₄	—	2	16	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	8	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
292	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
293	C₄²	—	2	16	no	—
294	C₄²	—	4	8	no	—
295	C₄²	C₂²⋊C₄×C₁₉	1	8	yes	—
296	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
297	C₄²	C₂×D₄×C₁₉	1	4	yes	—
298	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
299	C₂³	C₄×D₄×C₁₉	1	4	yes	—
300	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
301	C₂³	C₁₉×#137	1	2	yes	—
302	C₂³	C₁₉×#137	1	4	yes	—
303	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
304	Q₈	—	2	16	no	—
305	Q₈	—	2	4	no	—
306	Q₈	—	2	8	no	—
307	Q₈	C₂×C₄²×C₁₉	1	8	yes	complemented
308	C₂×C₄	—	2	16	no	—
309	C₂×C₄	—	2	8	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	4	8	no	—
319	C₂×C₄	—	4	16	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	C₂×C₄²×C₁₉	1	4	yes	—
325	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
328	C₂×C₄	C₁₉×#117	1	4	yes	—
329	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
330	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
331	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
332	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
333	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
334	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
335	C₈	—	2	8	no	—
336	C₂²	C₄×C₂²⋊C₄×C₁₉	1	4	yes	—
337	C₂²	C₁₉×#417	1	4	yes	—
338	C₂²	C₁₉×#419	1	4	yes	—
339	C₂²	C₁₉×#440	1	8	yes	—
340	C₂²	C₁₉×#441	1	8	yes	—
341	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
342	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
343	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
344	C₂²	C₂×C₁₉×#137	1	2	yes	—
345	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
346	C₄	—	2	8	no	—
347	C₄	—	2	4	no	—
348	C₄	—	2	4	no	—
349	C₄	—	4	8	no	—
350	C₄	—	4	4	no	—
351	C₄	C₄×C₂²⋊C₄×C₁₉	1	4	yes	—
352	C₄	C₂²×C₄²×C₁₉	1	1	yes	characteristic
353	C₄	C₂×C₁₉×#117	1	1	yes	characteristic
354	C₄	C₂×C₄×D₄×C₁₉	1	2	yes	—
355	C₂	C₁₉×#1763	1	8	yes	direct product factor
356	C₂	C₂×C₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
357	C₂	C₂×C₁₉×#419	1	1	yes	characteristic
358	C₂	C₂×C₁₉×#417	1	1	yes	characteristic
359	C₂	C₂×C₁₉×#440	1	2	yes	—
360	C₂	C₂×C₁₉×#441	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂×D₄
commutator	C₄	C₂²×C₄²×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ 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
5. C₁₉×#1763	C₂	direct (N × H)
11. C₂×C₄×Q₈×C₁₉	C₄	semidirect
19. C₂×C₁₉×#103	C₄	semidirect
45. C₄×Q₈×C₁₉	C₂×C₄	semidirect
64. C₁₉×#103	C₂×C₄	semidirect
74. C₂×Q₈×C₁₉	C₄²	semidirect
117. C₂×#1763	C₁₉	direct (N × H)
127. Q₈×C₁₉	C₂×C₄²	semidirect
160. #1763	C₂×C₁₉	direct (N × H)
185. C₂×C₄×Q₈	C₄×C₁₉	semidirect
193. C₂×#103	C₄×C₁₉	semidirect
201. C₂×C₁₉	#1763	direct (N × H)
225. C₄×Q₈	C₂×C₄×C₁₉	semidirect
244. #103	C₂×C₄×C₁₉	semidirect
247. C₁₉	C₂×#1763	direct (N × H)
255. C₂×Q₈	C₄²×C₁₉	semidirect
307. Q₈	C₂×C₄²×C₁₉	semidirect
355. C₂	C₁₉×#1763	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×Q₈×C₁₉	2
C₂²×C₁₉×#103	2
C₂²×C₁₉×#97	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₁₉×#1763	2
C₂×C₁₉×#340	2
C₂×#1763	19

Subgroups — C2×C19×#1763 #18026369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1763 #18026369