Subgroups — C₁₉×#12794 #18018753

Order 4864.

540 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×#123	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#352	C₂	1	2	yes	maximal
3	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1799	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1390	C₂	1	2	yes	maximal
6	C₂×C₁₉×#123	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₄²×C₁₉	C₄	1	1	yes	characteristic, complemented
9	C₁₉×#423	—	2	1	no	—
10	C₂×C₁₉×#100	C₂²	1	2	yes	—
11	C₂×C₁₉×#99	C₂²	1	2	yes	—
12	C₁₉×#388	—	2	1	no	—
13	C₁₉×#387	—	2	1	no	—
14	C₁₉×#386	C₂²	1	1	yes	characteristic
15	C₁₉×#385	C₄	1	1	yes	characteristic, complemented
16	C₁₉×#381	C₄	1	1	yes	characteristic, complemented
17	C₁₉×#380	—	2	1	no	—
18	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
19	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
20	C₄×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
21	C₁₉×#352	—	2	4	no	—
22	C₁₉×#343	—	2	1	no	—
23	C₁₉×#342	—	2	1	no	—
24	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂×M₁₆×C₁₉	—	2	2	no	—
30	C₁₉×#123	—	2	1	no	—
31	C₁₉×#123	—	2	1	no	—
32	C₁₉×#123	D₄	1	2	yes	—
33	C₁₉×#123	Q₈	1	2	yes	—
34	C₄×D₄×C₁₉	—	4	1	no	—
35	C₄×D₄×C₁₉	—	4	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
39	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	—	4	1	no	—
51	C₂×C₄²×C₁₉	—	4	1	no	—
52	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
53	C₁₉×C₄⋊C₈	—	4	1	no	—
54	C₁₉×C₄⋊C₈	—	4	1	no	—
55	C₁₉×#100	—	2	2	no	—
56	C₁₉×#100	—	2	2	no	—
57	C₁₉×#99	—	2	2	no	—
58	C₁₉×#99	—	2	2	no	—
59	C₁₉×#95	—	2	1	no	—
60	C₁₉×#95	—	2	1	no	—
61	C₁₉×#95	—	2	1	no	—
62	C₁₉×#95	—	2	1	no	—
63	C₁₉×#95	—	2	1	no	—
64	C₁₉×#95	—	4	1	no	—
65	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
66	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂×D₄×C₁₉	—	4	1	no	—
68	C₂×D₄×C₁₉	—	4	1	no	—
69	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂×D₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
71	C₂×D₄×C₁₉	#41	1	1	yes	characteristic
72	C₂×D₄×C₁₉	#41	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	4	2	no	—
83	C₂²×C₄×C₁₉	—	4	2	no	—
84	C₂²×C₄×C₁₉	—	4	2	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	—	4	2	no	—
89	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	complemented
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	M₁₆×C₁₉	—	4	2	no	—
96	M₁₆×C₁₉	—	4	2	no	—
97	C₂×C₈×C₁₉	—	4	2	no	—
98	C₄⋊C₄×C₁₉	—	2	2	no	—
99	C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₄⋊C₄×C₁₉	—	4	2	no	—
102	C₄⋊C₄×C₁₉	—	8	2	no	—
103	C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂²⋊C₄×C₁₉	—	2	2	no	—
105	C₂²⋊C₄×C₁₉	—	2	2	no	—
106	C₂²⋊C₄×C₁₉	—	4	1	no	—
107	C₂²⋊C₄×C₁₉	—	4	1	no	—
108	C₂²⋊C₄×C₁₉	—	4	2	no	—
109	C₂²⋊C₄×C₁₉	—	4	1	no	—
110	C₂²⋊C₄×C₁₉	—	4	2	no	—
111	C₂²⋊C₄×C₁₉	—	4	2	no	—
112	C₂²⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	complemented
113	C₄²×C₁₉	—	2	1	no	—
114	C₄²×C₁₉	—	2	1	no	—
115	C₄²×C₁₉	—	4	2	no	—
116	C₄²×C₁₉	—	4	2	no	—
117	C₄²×C₁₉	—	4	1	no	—
118	C₄²×C₁₉	—	4	1	no	—
119	#12794	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₁₉	—	2	1	no	—
121	C₂³×C₁₉	—	2	1	no	—
122	C₂³×C₁₉	—	2	1	no	—
123	C₂³×C₁₉	—	2	1	no	—
124	C₂³×C₁₉	—	4	1	no	—
125	C₂³×C₁₉	—	4	1	no	—
126	C₂³×C₁₉	—	4	1	no	—
127	C₂³×C₁₉	—	4	1	no	—
128	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂³×C₁₉	#117	1	1	yes	characteristic
131	C₂³×C₁₉	#121	1	1	yes	characteristic
132	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
133	D₄×C₁₉	—	4	1	no	—
134	D₄×C₁₉	—	4	1	no	—
135	D₄×C₁₉	—	4	1	no	—
136	D₄×C₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	8	1	no	—
166	C₂×C₄×C₁₉	—	8	2	no	—
167	C₂×C₄×C₁₉	—	8	2	no	—
168	C₂×C₄×C₁₉	—	8	2	no	—
169	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
173	C₈×C₁₉	—	8	2	no	—
174	C₄×#123	C₂×C₁₉	1	1	yes	characteristic
175	C₂×#352	C₂×C₁₉	1	2	yes	—
176	#1800	C₂×C₁₉	1	1	yes	characteristic
177	#1799	C₂×C₁₉	1	1	yes	characteristic
178	#1390	C₂×C₁₉	1	2	yes	—
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	2	1	no	—
181	C₂²×C₁₉	—	2	1	no	—
182	C₂²×C₁₉	—	2	1	no	—
183	C₂²×C₁₉	—	2	1	no	—
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	4	1	no	—
186	C₂²×C₁₉	—	4	1	no	—
187	C₂²×C₁₉	—	4	1	no	—
188	C₂²×C₁₉	—	4	1	no	—
189	C₂²×C₁₉	—	4	2	no	—
190	C₂²×C₁₉	—	4	1	no	—
191	C₂²×C₁₉	—	4	1	no	—
192	C₂²×C₁₉	—	4	1	no	—
193	C₂²×C₁₉	—	4	1	no	—
194	C₂²×C₁₉	—	8	1	no	—
195	C₂²×C₁₉	#380	1	1	yes	characteristic
196	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
197	C₂²×C₁₉	#410	1	1	yes	characteristic
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	2	1	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	4	2	no	—
202	C₄×C₁₉	—	4	2	no	—
203	C₄×C₁₉	—	4	1	no	—
204	C₄×C₁₉	—	4	1	no	—
205	C₄×C₁₉	—	4	1	no	—
206	C₄×C₁₉	—	4	2	no	—
207	C₄×C₁₉	—	8	1	no	—
208	C₄×C₁₉	—	16	2	no	—
209	C₄×C₁₉	#352	1	2	yes	complemented
210	C₂×#123	C₂²×C₁₉	1	1	yes	characteristic
211	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
212	C₂²×C₄²	C₄×C₁₉	1	1	yes	characteristic, complemented
213	#423	—	2	1	no	—
214	C₂×#100	C₂²×C₁₉	1	2	yes	—
215	C₂×#99	C₂²×C₁₉	1	2	yes	—
216	#388	—	2	1	no	—
217	#387	—	2	1	no	—
218	#386	C₂²×C₁₉	1	1	yes	characteristic
219	#385	C₄×C₁₉	1	1	yes	characteristic, complemented
220	#381	C₄×C₁₉	1	1	yes	characteristic, complemented
221	#380	—	2	1	no	—
222	C₄×C₄⋊C₄	—	2	1	no	—
223	C₄×C₂²⋊C₄	—	2	1	no	—
224	C₄×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
225	#352	—	2	4	no	—
226	#343	—	2	1	no	—
227	#342	—	2	1	no	—
228	C₂×C₁₉	—	2	1	no	—
229	C₂×C₁₉	—	2	1	no	—
230	C₂×C₁₉	—	4	1	no	—
231	C₂×C₁₉	—	4	1	no	—
232	C₂×C₁₉	—	4	1	no	—
233	C₂×C₁₉	—	4	1	no	—
234	C₂×C₁₉	#1799	1	1	yes	characteristic
235	C₂×C₁₉	C₂×#352	1	1	yes	characteristic
236	C₂×C₁₉	#2120	1	1	yes	characteristic
237	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
238	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
239	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
240	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
241	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
242	C₂×M₁₆	—	2	2	no	—
243	#123	—	2	1	no	—
244	#123	—	2	1	no	—
245	#123	D₄×C₁₉	1	2	yes	—
246	#123	Q₈×C₁₉	1	2	yes	—
247	C₄×D₄	—	4	1	no	—
248	C₄×D₄	—	4	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	4	1	no	—
252	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
260	C₂×C₄²	—	2	1	no	—
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	—	2	1	no	—
263	C₂×C₄²	—	4	1	no	—
264	C₂×C₄²	—	4	1	no	—
265	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
266	C₄⋊C₈	—	4	1	no	—
267	C₄⋊C₈	—	4	1	no	—
268	#100	—	2	2	no	—
269	#100	—	2	2	no	—
270	#99	—	2	2	no	—
271	#99	—	2	2	no	—
272	#95	—	2	1	no	—
273	#95	—	2	1	no	—
274	#95	—	2	1	no	—
275	#95	—	2	1	no	—
276	#95	—	2	1	no	—
277	#95	—	4	1	no	—
278	C₁₉	#12794	1	1	yes	characteristic, direct product factor, Sylow
279	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
280	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
281	C₂×D₄	—	4	1	no	—
282	C₂×D₄	—	4	1	no	—
283	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
284	C₂×D₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
285	C₂×D₄	#41×C₁₉	1	1	yes	characteristic
286	C₂×D₄	#41×C₁₉	1	1	yes	characteristic
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
304	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
305	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
306	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₄⋊C₄×C₁₉	1	2	yes	complemented
308	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
309	M₁₆	—	4	2	no	—
310	M₁₆	—	4	2	no	—
311	C₂×C₈	—	4	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	8	2	no	—
317	C₂²⋊C₄	—	2	1	no	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	4	1	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	C₄⋊C₄×C₁₉	1	2	yes	complemented
327	C₄²	—	2	1	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	4	2	no	—
330	C₄²	—	4	2	no	—
331	C₄²	—	4	1	no	—
332	C₄²	—	4	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	4	1	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	4	1	no	—
341	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
342	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
343	C₂³	C₁₉×#117	1	1	yes	characteristic
344	C₂³	C₁₉×#121	1	1	yes	characteristic
345	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
346	D₄	—	4	1	no	—
347	D₄	—	4	1	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	8	1	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	—	8	2	no	—
381	C₂×C₄	—	8	2	no	—
382	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
383	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
384	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
385	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
386	C₈	—	8	2	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	C₁₉×#380	1	1	yes	characteristic
404	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
405	C₂²	C₁₉×#410	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	8	1	no	—
416	C₄	—	16	2	no	—
417	C₄	C₁₉×#352	1	2	yes	complemented
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	4	1	no	—
421	C₂	—	4	1	no	—
422	C₂	—	4	1	no	—
423	C₂	—	4	1	no	—
424	C₂	C₁₉×#1799	1	1	yes	characteristic
425	C₂	C₂×C₁₉×#352	1	1	yes	characteristic
426	C₂	C₁₉×#2120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#99
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×D₄	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂³
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₂²×C₄²×C₁₉	C₄	semidirect
15. C₁₉×#385	C₄	semidirect
16. C₁₉×#381	C₄	semidirect
20. C₄×C₂²⋊C₄×C₁₉	C₄	semidirect
93. C₂²×C₄×C₁₉	C₄⋊C₄	semidirect
112. C₂²⋊C₄×C₁₉	C₄⋊C₄	semidirect
119. #12794	C₁₉	direct (N × H)
209. C₄×C₁₉	#352	semidirect
212. C₂²×C₄²	C₄×C₁₉	semidirect
219. #385	C₄×C₁₉	semidirect
220. #381	C₄×C₁₉	semidirect
224. C₄×C₂²⋊C₄	C₄×C₁₉	semidirect
278. C₁₉	#12794	direct (N × H)
307. C₂²×C₄	C₄⋊C₄×C₁₉	semidirect
326. C₂²⋊C₄	C₄⋊C₄×C₁₉	semidirect
417. C₄	C₁₉×#352	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₉×#123	2
C₂×C₁₉×#352	2
C₁₉×#1800	2
C₁₉×#1799	2
C₁₉×#1390	2
#12794	19

Subgroups — C19×#12794 #18018753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12794 #18018753