Subgroups — C₁₉×#14159 #18020118

Order 4864.

2166 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×#95	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1446	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1445	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1436	C₂	1	4	yes	maximal, complemented
7	C₁₉×C₂²⋊#95	C₂	1	4	yes	maximal
8	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
10	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₂²⋊Q₈	—	2	4	no	—
12	C₂×C₁₉×C₂²⋊Q₈	—	2	4	no	—
13	C₂×C₁₉×C₂²⋊Q₈	C₄	1	8	yes	complemented
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
19	C₄×C₂²⋊C₄×C₁₉	—	2	4	no	—
20	C₂×C₁₉×#95	—	2	4	no	—
21	C₂×C₁₉×#95	C₂²	1	8	yes	—
22	C₂×C₁₉×#95	C₂²	1	2	yes	—
23	C₂×C₁₉×#95	C₂²	1	2	yes	—
24	C₂×C₁₉×#95	C₂²	1	2	yes	—
25	C₂×C₁₉×#95	C₂²	1	8	yes	—
26	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
27	C₂²×Q₈×C₁₉	—	2	2	no	—
28	C₂²×Q₈×C₁₉	—	2	2	no	—
29	C₂²×Q₈×C₁₉	—	4	4	no	—
30	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	complemented
31	C₂³×C₄×C₁₉	—	2	4	no	—
32	C₂³×C₄×C₁₉	—	2	8	no	—
33	C₂³×C₄×C₁₉	—	2	8	no	—
34	C₂³×C₄×C₁₉	—	4	4	no	—
35	C₂³×C₄×C₁₉	—	4	4	no	—
36	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₁₉	D₄	1	4	yes	—
38	C₂³×C₄×C₁₉	D₄	1	4	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₁₉×C₂²⋊Q₈	—	2	32	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
51	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
52	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
57	C₂×C₂²⋊C₄×C₁₉	Q₈	1	8	yes	complemented
58	C₂×C₄²×C₁₉	—	2	4	no	—
59	C₂×C₄²×C₁₉	—	4	4	no	—
60	C₁₉×#95	—	2	4	no	—
61	C₁₉×#95	—	2	4	no	—
62	C₁₉×#95	—	2	4	no	—
63	C₁₉×#95	—	2	16	no	—
64	C₁₉×#95	—	4	8	no	—
65	C₂⁴×C₁₉	—	2	4	no	—
66	C₂⁴×C₁₉	—	2	4	no	—
67	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
68	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
69	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
70	C₂⁴×C₁₉	C₂×Q₈	1	4	yes	—
71	C₂⁴×C₁₉	#41	1	4	yes	—
72	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
73	C₂×Q₈×C₁₉	—	2	8	no	—
74	C₂×Q₈×C₁₉	—	4	8	no	—
75	C₂×Q₈×C₁₉	—	4	8	no	—
76	C₂×Q₈×C₁₉	—	4	8	no	—
77	C₂²×C₄×C₁₉	—	2	4	no	—
78	C₂²×C₄×C₁₉	—	2	4	no	—
79	C₂²×C₄×C₁₉	—	2	16	no	—
80	C₂²×C₄×C₁₉	—	2	4	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	2	4	no	—
87	C₂²×C₄×C₁₉	—	2	4	no	—
88	C₂²×C₄×C₁₉	—	2	8	no	—
89	C₂²×C₄×C₁₉	—	2	8	no	—
90	C₂²×C₄×C₁₉	—	2	8	no	—
91	C₂²×C₄×C₁₉	—	2	8	no	—
92	C₂²×C₄×C₁₉	—	2	8	no	—
93	C₂²×C₄×C₁₉	—	2	8	no	—
94	C₂²×C₄×C₁₉	—	4	8	no	—
95	C₂²×C₄×C₁₉	—	4	8	no	—
96	C₂²×C₄×C₁₉	—	4	8	no	—
97	C₂²×C₄×C₁₉	—	4	32	no	—
98	C₂²×C₄×C₁₉	—	4	8	no	—
99	C₂²×C₄×C₁₉	—	4	8	no	—
100	C₂²×C₄×C₁₉	C₂²⋊C₄	1	16	yes	—
101	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂×Q₈	1	8	yes	—
110	C₂²×C₄×C₁₉	#41	1	8	yes	—
111	C₄⋊C₄×C₁₉	—	2	8	no	—
112	C₄⋊C₄×C₁₉	—	2	16	no	—
113	C₂²⋊C₄×C₁₉	—	2	16	no	—
114	C₂²⋊C₄×C₁₉	—	2	16	no	—
115	C₄²×C₁₉	—	4	8	no	—
116	#14159	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₁₉	—	2	4	no	—
118	C₂³×C₁₉	—	2	4	no	—
119	C₂³×C₁₉	—	2	4	no	—
120	C₂³×C₁₉	—	2	4	no	—
121	C₂³×C₁₉	—	2	4	no	—
122	C₂³×C₁₉	—	2	4	no	—
123	C₂³×C₁₉	—	2	16	no	—
124	C₂³×C₁₉	—	2	16	no	—
125	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
126	C₂³×C₁₉	C₄×Q₈	1	8	yes	—
127	C₂³×C₁₉	C₂²⋊Q₈	1	8	yes	—
128	C₂³×C₁₉	#124	1	4	yes	—
129	C₂³×C₁₉	C₄⋊Q₈	1	4	yes	—
130	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
131	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
132	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
133	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
134	C₂³×C₁₉	C₂×#41	1	2	yes	—
135	C₂³×C₁₉	C₂×#41	1	4	yes	—
136	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
137	Q₈×C₁₉	—	4	16	no	—
138	C₂×C₄×C₁₉	—	2	4	no	—
139	C₂×C₄×C₁₉	—	2	4	no	—
140	C₂×C₄×C₁₉	—	2	4	no	—
141	C₂×C₄×C₁₉	—	2	4	no	—
142	C₂×C₄×C₁₉	—	2	4	no	—
143	C₂×C₄×C₁₉	—	2	4	no	—
144	C₂×C₄×C₁₉	—	2	4	no	—
145	C₂×C₄×C₁₉	—	2	4	no	—
146	C₂×C₄×C₁₉	—	2	8	no	—
147	C₂×C₄×C₁₉	—	2	8	no	—
148	C₂×C₄×C₁₉	—	2	8	no	—
149	C₂×C₄×C₁₉	—	2	8	no	—
150	C₂×C₄×C₁₉	—	2	16	no	—
151	C₂×C₄×C₁₉	—	2	16	no	—
152	C₂×C₄×C₁₉	—	4	16	no	—
153	C₂×C₄×C₁₉	—	4	32	no	—
154	C₂×C₄×C₁₉	—	4	4	no	—
155	C₂×C₄×C₁₉	—	4	4	no	—
156	C₂×C₄×C₁₉	—	4	4	no	—
157	C₂×C₄×C₁₉	—	4	4	no	—
158	C₂×C₄×C₁₉	—	4	4	no	—
159	C₂×C₄×C₁₉	—	4	4	no	—
160	C₂×C₄×C₁₉	—	4	4	no	—
161	C₂×C₄×C₁₉	—	4	4	no	—
162	C₂×C₄×C₁₉	—	4	8	no	—
163	C₂×C₄×C₁₉	—	4	8	no	—
164	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
165	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
166	C₂²×C₂²⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
167	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
168	C₂²×#95	C₂×C₁₉	1	1	yes	characteristic
169	#1446	C₂×C₁₉	1	2	yes	complemented
170	#1445	C₂×C₁₉	1	2	yes	complemented
171	#1436	C₂×C₁₉	1	4	yes	complemented
172	C₂²⋊#95	C₂×C₁₉	1	4	yes	—
173	C₂²×C₁₉	—	2	8	no	—
174	C₂²×C₁₉	—	2	4	no	—
175	C₂²×C₁₉	—	2	16	no	—
176	C₂²×C₁₉	—	2	8	no	—
177	C₂²×C₁₉	—	2	16	no	—
178	C₂²×C₁₉	—	2	4	no	—
179	C₂²×C₁₉	#391	1	8	yes	—
180	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₁₉	C₂×C₄×Q₈	1	2	yes	—
182	C₂²×C₁₉	C₄×#41	1	2	yes	—
183	C₂²×C₁₉	#518	1	2	yes	—
184	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
185	C₂²×C₁₉	#525	1	2	yes	—
186	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
187	C₂²×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
188	C₂²×C₁₉	#532	1	2	yes	—
189	C₂²×C₁₉	#534	1	2	yes	—
190	C₂²×C₁₉	#534	1	2	yes	—
191	C₂²×C₁₉	#551	1	8	yes	—
192	C₂²×C₁₉	#554	1	8	yes	—
193	C₄×C₁₉	—	2	4	no	—
194	C₄×C₁₉	—	2	4	no	—
195	C₄×C₁₉	—	4	8	no	—
196	C₄×C₁₉	—	4	4	no	—
197	C₄×C₁₉	—	4	8	no	—
198	C₄×C₁₉	—	4	4	no	—
199	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
200	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
201	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
202	C₂×C₂²⋊Q₈	—	2	4	no	—
203	C₂×C₂²⋊Q₈	—	2	4	no	—
204	C₂×C₂²⋊Q₈	C₄×C₁₉	1	8	yes	complemented
205	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
206	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
207	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
208	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
209	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
210	C₄×C₂²⋊C₄	—	2	4	no	—
211	C₂×#95	—	2	4	no	—
212	C₂×#95	C₂²×C₁₉	1	8	yes	—
213	C₂×#95	C₂²×C₁₉	1	2	yes	—
214	C₂×#95	C₂²×C₁₉	1	2	yes	—
215	C₂×#95	C₂²×C₁₉	1	2	yes	—
216	C₂×#95	C₂²×C₁₉	1	8	yes	—
217	C₂×C₁₉	—	2	8	no	—
218	C₂×C₁₉	C₂×#391	1	1	yes	characteristic
219	C₂×C₁₉	#2297	1	1	yes	characteristic
220	C₂×C₁₉	#2308	1	1	yes	characteristic
221	C₂×C₁₉	#2368	1	4	yes	—
222	C₂×C₁₉	#2561	1	2	yes	—
223	C₂×C₁₉	#2564	1	4	yes	—
224	C₂×C₁₉	#2583	1	2	yes	—
225	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
226	C₂²×Q₈	—	2	2	no	—
227	C₂²×Q₈	—	2	2	no	—
228	C₂²×Q₈	—	4	4	no	—
229	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
230	C₂³×C₄	—	2	4	no	—
231	C₂³×C₄	—	2	8	no	—
232	C₂³×C₄	—	2	8	no	—
233	C₂³×C₄	—	4	4	no	—
234	C₂³×C₄	—	4	4	no	—
235	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
236	C₂³×C₄	D₄×C₁₉	1	4	yes	—
237	C₂³×C₄	D₄×C₁₉	1	4	yes	—
238	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
239	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
240	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
241	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
242	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
243	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
244	C₂²⋊Q₈	—	2	32	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	4	no	—
249	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
250	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
251	C₂×C₂²⋊C₄	—	2	4	no	—
252	C₂×C₂²⋊C₄	—	2	4	no	—
253	C₂×C₂²⋊C₄	—	2	4	no	—
254	C₂×C₂²⋊C₄	—	2	4	no	—
255	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
256	C₂×C₂²⋊C₄	Q₈×C₁₉	1	8	yes	complemented
257	C₂×C₄²	—	2	4	no	—
258	C₂×C₄²	—	4	4	no	—
259	#95	—	2	4	no	—
260	#95	—	2	4	no	—
261	#95	—	2	4	no	—
262	#95	—	2	16	no	—
263	#95	—	4	8	no	—
264	C₁₉	#14159	1	1	yes	characteristic, direct product factor, Sylow
265	C₂⁴	—	2	4	no	—
266	C₂⁴	—	2	4	no	—
267	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
268	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
269	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
270	C₂⁴	C₂×Q₈×C₁₉	1	4	yes	—
271	C₂⁴	#41×C₁₉	1	4	yes	—
272	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
273	C₂×Q₈	—	2	8	no	—
274	C₂×Q₈	—	4	8	no	—
275	C₂×Q₈	—	4	8	no	—
276	C₂×Q₈	—	4	8	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	16	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	8	no	—
287	C₂²×C₄	—	2	8	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	8	no	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	8	no	—
294	C₂²×C₄	—	4	8	no	—
295	C₂²×C₄	—	4	8	no	—
296	C₂²×C₄	—	4	8	no	—
297	C₂²×C₄	—	4	32	no	—
298	C₂²×C₄	—	4	8	no	—
299	C₂²×C₄	—	4	8	no	—
300	C₂²×C₄	C₂²⋊C₄×C₁₉	1	16	yes	—
301	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
302	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
303	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
304	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
309	C₂²×C₄	C₂×Q₈×C₁₉	1	8	yes	—
310	C₂²×C₄	#41×C₁₉	1	8	yes	—
311	C₄⋊C₄	—	2	8	no	—
312	C₄⋊C₄	—	2	16	no	—
313	C₂²⋊C₄	—	2	16	no	—
314	C₂²⋊C₄	—	2	16	no	—
315	C₄²	—	4	8	no	—
316	C₂³	—	2	4	no	—
317	C₂³	—	2	4	no	—
318	C₂³	—	2	4	no	—
319	C₂³	—	2	4	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	2	16	no	—
323	C₂³	—	2	16	no	—
324	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
325	C₂³	C₄×Q₈×C₁₉	1	8	yes	—
326	C₂³	C₁₉×C₂²⋊Q₈	1	8	yes	—
327	C₂³	C₁₉×#124	1	4	yes	—
328	C₂³	C₁₉×C₄⋊Q₈	1	4	yes	—
329	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
330	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
331	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
332	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
333	C₂³	C₂×#41×C₁₉	1	2	yes	—
334	C₂³	C₂×#41×C₁₉	1	4	yes	—
335	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
336	Q₈	—	4	16	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	16	no	—
350	C₂×C₄	—	2	16	no	—
351	C₂×C₄	—	4	16	no	—
352	C₂×C₄	—	4	32	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	8	no	—
362	C₂×C₄	—	4	8	no	—
363	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
364	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	8	no	—
367	C₂²	—	2	4	no	—
368	C₂²	—	2	16	no	—
369	C₂²	—	2	8	no	—
370	C₂²	—	2	16	no	—
371	C₂²	C₁₉×#391	1	8	yes	—
372	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
373	C₂²	C₂×C₄×Q₈×C₁₉	1	2	yes	—
374	C₂²	C₄×#41×C₁₉	1	2	yes	—
375	C₂²	C₁₉×#518	1	2	yes	—
376	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
377	C₂²	C₁₉×#525	1	2	yes	—
378	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
379	C₂²	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
380	C₂²	C₁₉×#532	1	2	yes	—
381	C₂²	C₁₉×#534	1	2	yes	—
382	C₂²	C₁₉×#534	1	2	yes	—
383	C₂²	C₁₉×#551	1	8	yes	—
384	C₂²	C₁₉×#554	1	8	yes	—
385	C₄	—	2	4	no	—
386	C₄	—	2	4	no	—
387	C₄	—	4	4	no	—
388	C₄	—	4	8	no	—
389	C₄	—	4	4	no	—
390	C₄	—	4	8	no	—
391	C₂	—	2	8	no	—
392	C₂	C₂×C₁₉×#391	1	1	yes	characteristic
393	C₂	C₁₉×#2297	1	1	yes	characteristic
394	C₂	C₁₉×#2308	1	1	yes	characteristic
395	C₂	C₁₉×#2368	1	4	yes	—
396	C₂	C₁₉×#2561	1	2	yes	—
397	C₂	C₁₉×#2564	1	4	yes	—
398	C₂	C₁₉×#2583	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1446	C₂	semidirect
5. C₁₉×#1445	C₂	semidirect
6. C₁₉×#1436	C₂	semidirect
13. C₂×C₁₉×C₂²⋊Q₈	C₄	semidirect
30. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
50. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
51. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
57. C₂×C₂²⋊C₄×C₁₉	Q₈	semidirect
116. #14159	C₁₉	direct (N × H)
169. #1446	C₂×C₁₉	semidirect
170. #1445	C₂×C₁₉	semidirect
171. #1436	C₂×C₁₉	semidirect
204. C₂×C₂²⋊Q₈	C₄×C₁₉	semidirect
229. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
249. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
250. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
256. C₂×C₂²⋊C₄	Q₈×C₁₉	semidirect
264. C₁₉	#14159	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×C₁₉×C₂²⋊Q₈	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₂²×C₁₉×#95	2
C₁₉×#1446	2
C₁₉×#1445	2
C₁₉×#1436	2
C₁₉×C₂²⋊#95	2
#14159	19

Subgroups — C19×#14159 #18020118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14159 #18020118