Subgroups — C₁₉×#8383 #18014342

Order 4864.

1450 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1545	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1486	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1460	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₄×C₁₉	—	2	1	no	—
7	C₂³×D₄×C₁₉	C₄	1	2	yes	—
8	D₄²×C₁₉	—	2	4	no	—
9	D₄²×C₁₉	—	2	4	no	—
10	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#121	—	2	1	no	—
12	C₂×C₁₉×#121	C₄	1	2	yes	—
13	C₂×C₁₉×#120	—	2	2	no	—
14	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#431	C₂²	1	2	yes	complemented
17	C₁₉×#423	C₂²	1	2	yes	complemented
18	C₂×C₁₉×#100	—	2	1	no	—
19	C₁₉×#343	—	2	1	no	—
20	C₁₉×#331	—	2	4	no	—
21	C₁₉×D₄⋊C₈	—	2	4	no	—
22	C₁₉×#323	—	2	2	no	—
23	C₂⁵×C₁₉	—	2	2	no	—
24	C₂²×D₄×C₁₉	—	2	8	no	—
25	C₂²×D₄×C₁₉	—	2	2	no	—
26	C₂²×D₄×C₁₉	—	2	4	no	—
27	C₂²×D₄×C₁₉	—	2	4	no	—
28	C₂²×D₄×C₁₉	—	2	2	no	—
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	—	4	4	no	—
32	C₂²×D₄×C₁₉	—	4	8	no	—
33	C₂²×D₄×C₁₉	—	4	2	no	—
34	C₂²×D₄×C₁₉	—	4	2	no	—
35	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
37	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	—	2	1	no	—
39	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
40	C₂×M₁₆×C₁₉	—	2	2	no	—
41	C₁₉×#127	—	2	2	no	—
42	C₁₉×#127	D₄	1	4	yes	—
43	C₁₉×#121	—	2	8	no	—
44	C₁₉×#121	—	2	4	no	—
45	C₁₉×#121	—	2	4	no	—
46	C₁₉×#120	—	2	16	no	—
47	C₄×D₄×C₁₉	—	2	2	no	—
48	C₄×D₄×C₁₉	—	2	2	no	—
49	C₄×D₄×C₁₉	—	2	2	no	—
50	C₄×D₄×C₁₉	D₄	1	4	yes	—
51	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
53	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
56	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
57	C₁₉×C₄⋊C₈	—	2	2	no	—
58	C₁₉×C₄⋊C₈	—	2	2	no	—
59	C₁₉×C₄⋊C₈	—	2	2	no	—
60	C₁₉×#100	—	4	2	no	—
61	C₁₉×C₂²⋊C₈	—	2	2	no	—
62	C₄×C₈×C₁₉	—	2	2	no	—
63	C₂⁴×C₁₉	—	2	1	no	—
64	C₂⁴×C₁₉	—	2	8	no	—
65	C₂⁴×C₁₉	—	2	2	no	—
66	C₂⁴×C₁₉	—	4	8	no	—
67	C₂⁴×C₁₉	—	4	4	no	—
68	C₂⁴×C₁₉	—	4	4	no	—
69	C₂⁴×C₁₉	—	8	4	no	—
70	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
71	C₂×D₄×C₁₉	—	2	4	no	—
72	C₂×D₄×C₁₉	—	2	8	no	—
73	C₂×D₄×C₁₉	—	2	8	no	—
74	C₂×D₄×C₁₉	—	2	1	no	—
75	C₂×D₄×C₁₉	—	2	2	no	—
76	C₂×D₄×C₁₉	—	2	2	no	—
77	C₂×D₄×C₁₉	—	2	4	no	—
78	C₂×D₄×C₁₉	—	2	4	no	—
79	C₂×D₄×C₁₉	—	2	2	no	—
80	C₂×D₄×C₁₉	—	4	4	no	—
81	C₂×D₄×C₁₉	—	4	16	no	—
82	C₂×D₄×C₁₉	—	4	8	no	—
83	C₂×D₄×C₁₉	—	4	16	no	—
84	C₂×D₄×C₁₉	—	4	16	no	—
85	C₂×D₄×C₁₉	—	4	4	no	—
86	C₂×D₄×C₁₉	—	4	8	no	—
87	C₂×D₄×C₁₉	—	4	4	no	—
88	C₂×D₄×C₁₉	—	4	8	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂×D₄×C₁₉	—	4	2	no	—
92	C₂×D₄×C₁₉	—	8	2	no	—
93	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
94	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
95	C₂×D₄×C₁₉	D₈	1	2	yes	—
96	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	4	4	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	4	2	no	—
105	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	M₁₆×C₁₉	—	4	2	no	—
110	M₁₆×C₁₉	—	4	2	no	—
111	C₂×C₈×C₁₉	—	4	2	no	—
112	C₂×C₈×C₁₉	—	4	2	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
116	C₂²⋊C₄×C₁₉	—	2	8	no	—
117	C₂²⋊C₄×C₁₉	—	2	4	no	—
118	C₂²⋊C₄×C₁₉	—	2	4	no	—
119	C₄²×C₁₉	C₂×D₄	1	2	yes	—
120	C₄²×C₁₉	C₂×D₄	1	2	yes	—
121	#8383	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂³×C₁₉	—	2	4	no	—
123	C₂³×C₁₉	—	2	2	no	—
124	C₂³×C₁₉	—	2	2	no	—
125	C₂³×C₁₉	—	2	2	no	—
126	C₂³×C₁₉	—	2	4	no	—
127	C₂³×C₁₉	—	4	2	no	—
128	C₂³×C₁₉	—	4	2	no	—
129	C₂³×C₁₉	—	4	2	no	—
130	C₂³×C₁₉	—	4	4	no	—
131	C₂³×C₁₉	—	4	16	no	—
132	C₂³×C₁₉	—	4	16	no	—
133	C₂³×C₁₉	—	4	4	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	—	4	1	no	—
136	C₂³×C₁₉	—	4	2	no	—
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	—	8	8	no	—
139	C₂³×C₁₉	—	8	16	no	—
140	C₂³×C₁₉	—	8	16	no	—
141	C₂³×C₁₉	#102	1	4	yes	—
142	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	D₄×C₁₉	—	2	4	no	—
144	D₄×C₁₉	—	2	2	no	—
145	D₄×C₁₉	—	2	4	no	—
146	D₄×C₁₉	—	2	4	no	—
147	D₄×C₁₉	—	4	4	no	—
148	D₄×C₁₉	—	4	16	no	—
149	D₄×C₁₉	—	4	16	no	—
150	D₄×C₁₉	—	4	4	no	—
151	D₄×C₁₉	—	4	4	no	—
152	D₄×C₁₉	—	4	4	no	—
153	D₄×C₁₉	—	8	4	no	—
154	D₄×C₁₉	#100	1	4	yes	complemented
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	4	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	4	no	—
163	C₂×C₄×C₁₉	—	4	4	no	—
164	C₂×C₄×C₁₉	—	4	4	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#120	1	2	yes	—
169	C₂×C₄×C₁₉	#120	1	2	yes	—
170	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
172	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
173	C₈×C₁₉	—	8	2	no	—
174	C₈×C₁₉	—	8	2	no	—
175	C₂×D₄²	C₂×C₁₉	1	1	yes	characteristic
176	#1800	C₂×C₁₉	1	1	yes	characteristic, complemented
177	#1545	C₂×C₁₉	1	2	yes	complemented
178	#1486	C₂×C₁₉	1	2	yes	complemented
179	#1460	C₂×C₁₉	1	1	yes	characteristic, complemented
180	C₂²×C₁₉	—	2	1	no	—
181	C₂²×C₁₉	—	2	1	no	—
182	C₂²×C₁₉	—	2	4	no	—
183	C₂²×C₁₉	—	2	4	no	—
184	C₂²×C₁₉	—	4	4	no	—
185	C₂²×C₁₉	—	4	4	no	—
186	C₂²×C₁₉	—	4	4	no	—
187	C₂²×C₁₉	—	4	4	no	—
188	C₂²×C₁₉	—	4	2	no	—
189	C₂²×C₁₉	—	4	2	no	—
190	C₂²×C₁₉	—	4	2	no	—
191	C₂²×C₁₉	—	4	2	no	—
192	C₂²×C₁₉	—	4	4	no	—
193	C₂²×C₁₉	—	4	4	no	—
194	C₂²×C₁₉	—	4	4	no	—
195	C₂²×C₁₉	—	8	4	no	—
196	C₂²×C₁₉	—	8	4	no	—
197	C₂²×C₁₉	—	8	32	no	—
198	C₂²×C₁₉	#379	1	1	yes	characteristic
199	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
200	C₂²×C₁₉	#418	1	1	yes	characteristic
201	C₄×C₁₉	—	2	2	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	4	2	no	—
204	C₄×C₁₉	—	4	2	no	—
205	C₄×C₁₉	C₂×#100	1	2	yes	—
206	C₄×C₁₉	#447	1	2	yes	—
207	C₄×C₁₉	#450	1	2	yes	—
208	C₂³×D₄	—	2	1	no	—
209	C₂³×D₄	C₄×C₁₉	1	2	yes	—
210	D₄²	—	2	4	no	—
211	D₄²	—	2	4	no	—
212	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
213	C₂×#121	—	2	1	no	—
214	C₂×#121	C₄×C₁₉	1	2	yes	—
215	C₂×#120	—	2	2	no	—
216	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
218	#431	C₂²×C₁₉	1	2	yes	complemented
219	#423	C₂²×C₁₉	1	2	yes	complemented
220	C₂×#100	—	2	1	no	—
221	#343	—	2	1	no	—
222	#331	—	2	4	no	—
223	D₄⋊C₈	—	2	4	no	—
224	#323	—	2	2	no	—
225	C₂×C₁₉	—	2	1	no	—
226	C₂×C₁₉	—	2	1	no	—
227	C₂×C₁₉	—	4	4	no	—
228	C₂×C₁₉	—	4	4	no	—
229	C₂×C₁₉	—	8	4	no	—
230	C₂×C₁₉	#1783	1	1	yes	characteristic
231	C₂×C₁₉	#1786	1	1	yes	characteristic
232	C₂×C₁₉	#1795	1	1	yes	characteristic
233	C₂⁵	—	2	2	no	—
234	C₂²×D₄	—	2	8	no	—
235	C₂²×D₄	—	2	2	no	—
236	C₂²×D₄	—	2	4	no	—
237	C₂²×D₄	—	2	4	no	—
238	C₂²×D₄	—	2	2	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	4	4	no	—
242	C₂²×D₄	—	4	8	no	—
243	C₂²×D₄	—	4	2	no	—
244	C₂²×D₄	—	4	2	no	—
245	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
246	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
247	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
248	C₂³×C₄	—	2	1	no	—
249	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
250	C₂×M₁₆	—	2	2	no	—
251	#127	—	2	2	no	—
252	#127	D₄×C₁₉	1	4	yes	—
253	#121	—	2	8	no	—
254	#121	—	2	4	no	—
255	#121	—	2	4	no	—
256	#120	—	2	16	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	D₄×C₁₉	1	4	yes	—
261	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
262	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
266	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	2	2	no	—
270	#100	—	4	2	no	—
271	C₂²⋊C₈	—	2	2	no	—
272	C₄×C₈	—	2	2	no	—
273	C₁₉	#8383	1	1	yes	characteristic, direct product factor, Sylow
274	C₂⁴	—	2	1	no	—
275	C₂⁴	—	2	8	no	—
276	C₂⁴	—	2	2	no	—
277	C₂⁴	—	4	8	no	—
278	C₂⁴	—	4	4	no	—
279	C₂⁴	—	4	4	no	—
280	C₂⁴	—	8	4	no	—
281	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	8	no	—
284	C₂×D₄	—	2	8	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	4	4	no	—
292	C₂×D₄	—	4	16	no	—
293	C₂×D₄	—	4	8	no	—
294	C₂×D₄	—	4	16	no	—
295	C₂×D₄	—	4	16	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	—	4	8	no	—
298	C₂×D₄	—	4	4	no	—
299	C₂×D₄	—	4	8	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	8	2	no	—
304	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
305	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
306	C₂×D₄	D₈×C₁₉	1	2	yes	—
307	C₂×D₄	SD₁₆×C₁₉	1	2	yes	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	4	4	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
317	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
320	M₁₆	—	4	2	no	—
321	M₁₆	—	4	2	no	—
322	C₂×C₈	—	4	2	no	—
323	C₂×C₈	—	4	2	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
327	C₂²⋊C₄	—	2	8	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₄²	C₂×D₄×C₁₉	1	2	yes	—
331	C₄²	C₂×D₄×C₁₉	1	2	yes	—
332	C₂³	—	2	4	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	16	no	—
342	C₂³	—	4	16	no	—
343	C₂³	—	4	4	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	8	no	—
349	C₂³	—	8	16	no	—
350	C₂³	—	8	16	no	—
351	C₂³	C₁₉×#102	1	4	yes	—
352	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
353	D₄	—	2	4	no	—
354	D₄	—	2	2	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	4	no	—
357	D₄	—	4	4	no	—
358	D₄	—	4	16	no	—
359	D₄	—	4	16	no	—
360	D₄	—	4	4	no	—
361	D₄	—	4	4	no	—
362	D₄	—	4	4	no	—
363	D₄	—	8	4	no	—
364	D₄	C₁₉×#100	1	4	yes	complemented
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
377	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
378	C₂×C₄	C₁₉×#120	1	2	yes	—
379	C₂×C₄	C₁₉×#120	1	2	yes	—
380	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
381	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
382	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
383	C₈	—	8	2	no	—
384	C₈	—	8	2	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	4	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	8	4	no	—
401	C₂²	—	8	4	no	—
402	C₂²	—	8	32	no	—
403	C₂²	C₁₉×#379	1	1	yes	characteristic
404	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
405	C₂²	C₁₉×#418	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	2	no	—
410	C₄	C₂×C₁₉×#100	1	2	yes	—
411	C₄	C₁₉×#447	1	2	yes	—
412	C₄	C₁₉×#450	1	2	yes	—
413	C₂	—	2	1	no	—
414	C₂	—	2	1	no	—
415	C₂	—	4	4	no	—
416	C₂	—	4	4	no	—
417	C₂	—	8	4	no	—
418	C₂	C₁₉×#1783	1	1	yes	characteristic
419	C₂	C₁₉×#1786	1	1	yes	characteristic
420	C₂	C₁₉×#1795	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂×D₄²×C₁₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1800	C₂	semidirect
3. C₁₉×#1545	C₂	semidirect
4. C₁₉×#1486	C₂	semidirect
5. C₁₉×#1460	C₂	semidirect
16. C₁₉×#431	C₂²	semidirect
17. C₁₉×#423	C₂²	semidirect
121. #8383	C₁₉	direct (N × H)
154. D₄×C₁₉	#100	semidirect
176. #1800	C₂×C₁₉	semidirect
177. #1545	C₂×C₁₉	semidirect
178. #1486	C₂×C₁₉	semidirect
179. #1460	C₂×C₁₉	semidirect
218. #431	C₂²×C₁₉	semidirect
219. #423	C₂²×C₁₉	semidirect
273. C₁₉	#8383	direct (N × H)
364. D₄	C₁₉×#100	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₁₉	2
C₁₉×#1800	2
C₁₉×#1545	2
C₁₉×#1486	2
C₁₉×#1460	2
#8383	19

Subgroups — C19×#8383 #18014342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8383 #18014342