Subgroups — C₁₉×#8373 #18014332

Order 4864.

814 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#553	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1528	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1490	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1466	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#553	—	2	4	no	—
7	C₁₉×#553	—	2	4	no	—
8	C₂×C₁₉×#126	—	2	1	no	—
9	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#123	—	2	1	no	—
11	C₂×C₁₉×#121	—	2	1	no	—
12	C₂×C₁₉×#121	C₄	1	1	yes	characteristic
13	C₂×C₁₉×#121	C₄	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₉	—	2	1	no	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
19	C₁₉×#432	C₂²	1	2	yes	—
20	C₂×C₁₉×#100	—	2	1	no	—
21	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
22	C₁₉×#343	—	2	1	no	—
23	C₁₉×#330	—	2	4	no	—
24	C₁₉×D₄⋊C₈	—	2	4	no	—
25	C₁₉×#323	—	2	1	no	—
26	C₁₉×#323	—	2	1	no	—
27	C₂²×D₄×C₁₉	—	2	1	no	—
28	C₂²×D₄×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	—	2	1	no	—
32	C₂³×C₄×C₁₉	—	2	1	no	—
33	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×M₁₆×C₁₉	—	2	2	no	—
36	C₁₉×#126	—	2	8	no	—
37	C₁₉×#125	—	2	2	no	—
38	C₁₉×#125	D₄	1	4	yes	—
39	C₁₉×#123	—	2	8	no	—
40	C₁₉×#121	—	2	8	no	—
41	C₁₉×#121	—	2	2	no	—
42	C₁₉×#121	—	2	2	no	—
43	C₁₉×#121	—	2	2	no	—
44	C₁₉×#121	—	2	2	no	—
45	C₄×D₄×C₁₉	—	2	8	no	—
46	C₄×D₄×C₁₉	—	2	2	no	—
47	C₄×D₄×C₁₉	—	2	2	no	—
48	C₄×D₄×C₁₉	—	2	2	no	—
49	C₄×D₄×C₁₉	D₄	1	4	yes	—
50	C₁₉×#117	—	2	2	no	—
51	C₁₉×#117	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×C₄⋊C₈	—	2	2	no	—
70	C₁₉×#100	—	2	4	no	—
71	C₁₉×C₂²⋊C₈	—	2	2	no	—
72	C₁₉×#97	—	2	2	no	—
73	C₁₉×#97	—	2	2	no	—
74	C₄×C₈×C₁₉	—	2	2	no	—
75	C₂⁴×C₁₉	—	2	1	no	—
76	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂×D₄×C₁₉	—	2	4	no	—
79	C₂×D₄×C₁₉	—	2	2	no	—
80	C₂×D₄×C₁₉	—	2	4	no	—
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	2	2	no	—
83	C₂×D₄×C₁₉	—	4	2	no	—
84	C₂×D₄×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	4	2	no	—
86	C₂×D₄×C₁₉	—	4	2	no	—
87	C₂×D₄×C₁₉	—	8	2	no	—
88	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	4	no	—
98	C₂²×C₄×C₁₉	—	4	2	no	—
99	C₂²×C₄×C₁₉	—	4	2	no	—
100	C₂²×C₄×C₁₉	—	8	2	no	—
101	C₂²×C₄×C₁₉	—	8	2	no	—
102	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	M₁₆×C₁₉	—	2	4	no	—
108	M₁₆×C₁₉	—	4	2	no	—
109	C₂×C₈×C₁₉	—	4	2	no	—
110	C₂×C₈×C₁₉	—	4	2	no	—
111	C₄⋊C₄×C₁₉	—	2	4	no	—
112	C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	2	4	no	—
116	C₄⋊C₄×C₁₉	—	2	4	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
119	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
120	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
121	C₂²⋊C₄×C₁₉	—	2	4	no	—
122	C₂²⋊C₄×C₁₉	—	2	4	no	—
123	C₂²⋊C₄×C₁₉	—	2	4	no	—
124	C₂²⋊C₄×C₁₉	—	2	4	no	—
125	C₂²⋊C₄×C₁₉	—	2	2	no	—
126	C₂²⋊C₄×C₁₉	—	2	2	no	—
127	C₄²×C₁₉	—	2	4	no	—
128	C₄²×C₁₉	C₂×D₄	1	2	yes	—
129	C₄²×C₁₉	C₂×D₄	1	2	yes	—
130	#8373	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂³×C₁₉	—	2	1	no	—
132	C₂³×C₁₉	—	2	1	no	—
133	C₂³×C₁₉	—	2	1	no	—
134	C₂³×C₁₉	—	2	2	no	—
135	C₂³×C₁₉	—	2	1	no	—
136	C₂³×C₁₉	—	2	1	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	—	4	1	no	—
142	C₂³×C₁₉	—	4	1	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	#104	1	2	yes	—
146	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	D₄×C₁₉	—	2	4	no	—
148	D₄×C₁₉	—	4	4	no	—
149	D₄×C₁₉	—	4	2	no	—
150	D₄×C₁₉	—	4	8	no	—
151	D₄×C₁₉	—	8	4	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	8	4	no	—
172	C₂×C₄×C₁₉	—	8	4	no	—
173	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#120	1	2	yes	—
176	C₂×C₄×C₁₉	#120	1	2	yes	—
177	C₈×C₁₉	—	4	4	no	—
178	C₈×C₁₉	—	8	2	no	—
179	C₂×#553	C₂×C₁₉	1	1	yes	characteristic
180	C₄×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
181	#1528	C₂×C₁₉	1	2	yes	complemented
182	#1490	C₂×C₁₉	1	2	yes	complemented
183	#1466	C₂×C₁₉	1	1	yes	characteristic, complemented
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	2	2	no	—
187	C₂²×C₁₉	—	4	2	no	—
188	C₂²×C₁₉	—	4	2	no	—
189	C₂²×C₁₉	—	4	1	no	—
190	C₂²×C₁₉	—	4	1	no	—
191	C₂²×C₁₉	—	4	2	no	—
192	C₂²×C₁₉	—	4	1	no	—
193	C₂²×C₁₉	—	4	1	no	—
194	C₂²×C₁₉	—	4	2	no	—
195	C₂²×C₁₉	—	4	1	no	—
196	C₂²×C₁₉	—	4	2	no	—
197	C₂²×C₁₉	—	8	1	no	—
198	C₂²×C₁₉	—	8	1	no	—
199	C₂²×C₁₉	—	8	2	no	—
200	C₂²×C₁₉	—	8	2	no	—
201	C₂²×C₁₉	#379	1	1	yes	characteristic
202	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
203	C₂²×C₁₉	#421	1	1	yes	characteristic
204	C₄×C₁₉	—	2	2	no	—
205	C₄×C₁₉	—	2	1	no	—
206	C₄×C₁₉	—	2	2	no	—
207	C₄×C₁₉	—	4	2	no	—
208	C₄×C₁₉	—	4	2	no	—
209	C₄×C₁₉	—	4	1	no	—
210	C₄×C₁₉	—	4	1	no	—
211	C₄×C₁₉	—	4	2	no	—
212	C₄×C₁₉	#413	1	2	yes	—
213	#553	—	2	4	no	—
214	#553	—	2	4	no	—
215	C₂×#126	—	2	1	no	—
216	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×#123	—	2	1	no	—
218	C₂×#121	—	2	1	no	—
219	C₂×#121	C₄×C₁₉	1	1	yes	characteristic
220	C₂×#121	C₄×C₁₉	1	1	yes	characteristic
221	C₂×C₄×D₄	—	2	1	no	—
222	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
223	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×#117	C₄×C₁₉	1	1	yes	characteristic
225	C₂²×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic
226	#432	C₂²×C₁₉	1	2	yes	—
227	C₂×#100	—	2	1	no	—
228	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
229	#343	—	2	1	no	—
230	#330	—	2	4	no	—
231	D₄⋊C₈	—	2	4	no	—
232	#323	—	2	1	no	—
233	#323	—	2	1	no	—
234	C₂×C₁₉	—	2	1	no	—
235	C₂×C₁₉	—	2	1	no	—
236	C₂×C₁₉	—	4	2	no	—
237	C₂×C₁₉	—	8	1	no	—
238	C₂×C₁₉	—	8	2	no	—
239	C₂×C₁₉	#1785	1	1	yes	characteristic
240	C₂×C₁₉	#1789	1	1	yes	characteristic
241	C₂×C₁₉	#1795	1	1	yes	characteristic
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
245	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
246	C₂³×C₄	—	2	1	no	—
247	C₂³×C₄	—	2	1	no	—
248	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
249	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
250	C₂×M₁₆	—	2	2	no	—
251	#126	—	2	8	no	—
252	#125	—	2	2	no	—
253	#125	D₄×C₁₉	1	4	yes	—
254	#123	—	2	8	no	—
255	#121	—	2	8	no	—
256	#121	—	2	2	no	—
257	#121	—	2	2	no	—
258	#121	—	2	2	no	—
259	#121	—	2	2	no	—
260	C₄×D₄	—	2	8	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	—	2	2	no	—
263	C₄×D₄	—	2	2	no	—
264	C₄×D₄	D₄×C₁₉	1	4	yes	—
265	#117	—	2	2	no	—
266	#117	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
275	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
284	C₄⋊C₈	—	2	2	no	—
285	#100	—	2	4	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	#97	—	2	2	no	—
288	#97	—	2	2	no	—
289	C₄×C₈	—	2	2	no	—
290	C₁₉	#8373	1	1	yes	characteristic, direct product factor, Sylow
291	C₂⁴	—	2	1	no	—
292	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
293	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	8	2	no	—
304	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	—	8	2	no	—
317	C₂²×C₄	—	8	2	no	—
318	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
323	M₁₆	—	2	4	no	—
324	M₁₆	—	4	2	no	—
325	C₂×C₈	—	4	2	no	—
326	C₂×C₈	—	4	2	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
335	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
336	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	2	2	no	—
343	C₄²	—	2	4	no	—
344	C₄²	C₂×D₄×C₁₉	1	2	yes	—
345	C₄²	C₂×D₄×C₁₉	1	2	yes	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	4	1	no	—
353	C₂³	—	4	1	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	1	no	—
360	C₂³	C₁₉×#104	1	2	yes	—
361	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
362	D₄	—	2	4	no	—
363	D₄	—	4	4	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	8	no	—
366	D₄	—	8	4	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	8	4	no	—
387	C₂×C₄	—	8	4	no	—
388	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
389	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
390	C₂×C₄	C₁₉×#120	1	2	yes	—
391	C₂×C₄	C₁₉×#120	1	2	yes	—
392	C₈	—	4	4	no	—
393	C₈	—	8	2	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	C₁₉×#379	1	1	yes	characteristic
412	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
413	C₂²	C₁₉×#421	1	1	yes	characteristic
414	C₄	—	2	1	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	C₁₉×#413	1	2	yes	—
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	—	4	2	no	—
426	C₂	—	8	2	no	—
427	C₂	—	8	1	no	—
428	C₂	C₁₉×#1785	1	1	yes	characteristic
429	C₂	C₁₉×#1789	1	1	yes	characteristic
430	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×C₁₉×#553	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. C₄×C₁₉×#100	C₂	semidirect
3. C₁₉×#1528	C₂	semidirect
4. C₁₉×#1490	C₂	semidirect
5. C₁₉×#1466	C₂	semidirect
130. #8373	C₁₉	direct (N × H)
180. C₄×#100	C₂×C₁₉	semidirect
181. #1528	C₂×C₁₉	semidirect
182. #1490	C₂×C₁₉	semidirect
183. #1466	C₂×C₁₉	semidirect
290. C₁₉	#8373	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#553	2
C₄×C₁₉×#100	2
C₁₉×#1528	2
C₁₉×#1490	2
C₁₉×#1466	2
#8373	19

Subgroups — C19×#8373 #18014332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8373 #18014332