Subgroups — C₁₉×#32780 #18038739

Order 4864.

652 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2628	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2621	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2097	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2085	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2043	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2036	C₂	1	2	yes	maximal
7	C₁₉×#2035	C₂	1	2	yes	maximal
8	C₁₉×#2024	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1818	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#107	C₂²	1	2	yes	—
15	C₂×C₁₉×#106	C₂²	1	2	yes	—
16	C₂×C₁₉×#103	C₂²	1	2	yes	—
17	C₂×C₁₉×#103	C₂²	1	2	yes	—
18	C₂×C₁₉×#103	C₂²	1	2	yes	—
19	C₂×C₁₉×#103	C₂²	1	2	yes	—
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₁₉×#400	—	2	1	no	—
23	C₁₉×#399	—	2	1	no	—
24	C₁₉×#398	—	2	1	no	—
25	C₁₉×#398	—	2	1	no	—
26	C₁₉×#397	—	2	1	no	—
27	C₁₉×#397	—	2	1	no	—
28	C₁₉×#395	—	2	1	no	—
29	C₁₉×#393	—	2	1	no	—
30	C₁₉×#391	C₂²	1	2	yes	—
31	C₁₉×#389	C₂²	1	2	yes	—
32	C₁₉×#382	C₂²	1	1	yes	characteristic
33	C₁₉×#382	C₂²	1	1	yes	characteristic
34	C₁₉×#380	C₂²	1	2	yes	—
35	C₁₉×#340	C₂²	1	2	yes	—
36	C₁₉×#340	C₂²	1	2	yes	—
37	C₁₉×#336	C₂²	1	2	yes	—
38	C₁₉×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₁₉	—	2	1	no	—
40	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
44	C₁₉×C₄⋊Q₈	—	4	1	no	—
45	C₁₉×C₄⋊Q₈	—	4	1	no	—
46	C₁₉×C₄⋊Q₈	—	4	1	no	—
47	C₁₉×C₄⋊Q₈	—	4	1	no	—
48	C₁₉×C₂²⋊Q₈	—	4	2	no	—
49	C₁₉×C₂²⋊Q₈	—	4	2	no	—
50	C₁₉×#117	—	4	1	no	—
51	C₁₉×#117	—	4	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
68	C₁₉×#107	—	4	2	no	—
69	C₁₉×#106	—	4	2	no	—
70	C₁₉×#103	—	4	2	no	—
71	C₁₉×#103	—	4	2	no	—
72	C₁₉×#103	—	4	2	no	—
73	C₁₉×#103	—	4	2	no	—
74	C₁₉×C₂²⋊C₈	—	4	1	no	—
75	C₁₉×C₂²⋊C₈	—	4	1	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₁₉×#95	—	2	1	no	—
78	C₁₉×#95	—	2	1	no	—
79	C₁₉×#95	—	2	1	no	—
80	C₁₉×#95	—	2	1	no	—
81	C₁₉×#95	—	2	2	no	—
82	C₁₉×#95	—	2	2	no	—
83	C₁₉×#95	—	2	2	no	—
84	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	—	2	2	no	—
87	C₂×Q₈×C₁₉	—	2	2	no	—
88	C₂×Q₈×C₁₉	—	2	2	no	—
89	C₂×Q₈×C₁₉	—	2	2	no	—
90	C₂×Q₈×C₁₉	—	2	2	no	—
91	C₂×Q₈×C₁₉	—	4	2	no	—
92	C₂×Q₈×C₁₉	—	8	2	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	4	1	no	—
120	C₄⋊C₄×C₁₉	—	4	1	no	—
121	C₄⋊C₄×C₁₉	—	4	4	no	—
122	C₄⋊C₄×C₁₉	—	4	2	no	—
123	C₄⋊C₄×C₁₉	—	4	2	no	—
124	C₄⋊C₄×C₁₉	—	4	2	no	—
125	C₄⋊C₄×C₁₉	—	8	2	no	—
126	C₂²⋊C₄×C₁₉	—	4	1	no	—
127	C₂²⋊C₄×C₁₉	—	4	1	no	—
128	C₂²⋊C₄×C₁₉	—	4	4	no	—
129	C₂²⋊C₄×C₁₉	—	8	2	no	—
130	C₄²×C₁₉	—	2	1	no	—
131	C₄²×C₁₉	—	2	1	no	—
132	C₄²×C₁₉	—	2	1	no	—
133	C₄²×C₁₉	—	2	1	no	—
134	#32780	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₁₉	—	2	1	no	—
136	C₂³×C₁₉	—	2	1	no	—
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	—	2	2	no	—
139	C₂³×C₁₉	—	2	2	no	—
140	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₁₉	—	4	2	no	—
142	Q₈×C₁₉	—	4	2	no	—
143	Q₈×C₁₉	—	4	2	no	—
144	Q₈×C₁₉	—	4	2	no	—
145	Q₈×C₁₉	—	8	4	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	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	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
174	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
175	C₈×C₁₉	—	4	2	no	—
176	C₈×C₁₉	—	4	2	no	—
177	#2628	C₂×C₁₉	1	1	yes	characteristic
178	#2621	C₂×C₁₉	1	1	yes	characteristic
179	#2097	C₂×C₁₉	1	2	yes	complemented
180	#2085	C₂×C₁₉	1	2	yes	complemented
181	#2043	C₂×C₁₉	1	2	yes	complemented
182	#2036	C₂×C₁₉	1	2	yes	—
183	#2035	C₂×C₁₉	1	2	yes	—
184	#2024	C₂×C₁₉	1	2	yes	complemented
185	#1818	C₂×C₁₉	1	1	yes	characteristic
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	2	no	—
191	C₂²×C₁₉	#534	1	1	yes	characteristic
192	C₂²×C₁₉	#535	1	1	yes	characteristic
193	C₂²×C₁₉	#536	1	1	yes	characteristic
194	C₂²×C₁₉	#577	1	2	yes	—
195	C₂²×C₁₉	#578	1	2	yes	—
196	C₄×C₁₉	—	4	1	no	—
197	C₄×C₁₉	—	4	1	no	—
198	C₄×C₁₉	—	4	1	no	—
199	C₄×C₁₉	—	4	1	no	—
200	C₄×C₁₉	—	4	1	no	—
201	C₄×C₁₉	—	8	2	no	—
202	C₄×C₁₉	—	8	2	no	—
203	C₄×C₁₉	—	8	2	no	—
204	C₄×C₁₉	—	8	2	no	—
205	C₄×C₁₉	#562	1	2	yes	—
206	C₄×C₁₉	#562	1	2	yes	—
207	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
208	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
209	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
210	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
211	C₂×#107	C₂²×C₁₉	1	2	yes	—
212	C₂×#106	C₂²×C₁₉	1	2	yes	—
213	C₂×#103	C₂²×C₁₉	1	2	yes	—
214	C₂×#103	C₂²×C₁₉	1	2	yes	—
215	C₂×#103	C₂²×C₁₉	1	2	yes	—
216	C₂×#103	C₂²×C₁₉	1	2	yes	—
217	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
218	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
219	#400	—	2	1	no	—
220	#399	—	2	1	no	—
221	#398	—	2	1	no	—
222	#398	—	2	1	no	—
223	#397	—	2	1	no	—
224	#397	—	2	1	no	—
225	#395	—	2	1	no	—
226	#393	—	2	1	no	—
227	#391	C₂²×C₁₉	1	2	yes	—
228	#389	C₂²×C₁₉	1	2	yes	—
229	#382	C₂²×C₁₉	1	1	yes	characteristic
230	#382	C₂²×C₁₉	1	1	yes	characteristic
231	#380	C₂²×C₁₉	1	2	yes	—
232	#340	C₂²×C₁₉	1	2	yes	—
233	#340	C₂²×C₁₉	1	2	yes	—
234	#336	C₂²×C₁₉	1	2	yes	—
235	#336	C₂²×C₁₉	1	2	yes	—
236	C₂×C₁₉	—	8	1	no	—
237	C₂×C₁₉	#2816	1	1	yes	characteristic
238	C₂×C₁₉	#3200	1	1	yes	characteristic
239	C₂×C₁₉	#3202	1	1	yes	characteristic
240	C₂×C₁₉	#3225	1	2	yes	—
241	C₂×C₁₉	#3242	1	2	yes	—
242	C₂²×Q₈	—	2	1	no	—
243	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
244	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
246	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
247	C₄⋊Q₈	—	4	1	no	—
248	C₄⋊Q₈	—	4	1	no	—
249	C₄⋊Q₈	—	4	1	no	—
250	C₄⋊Q₈	—	4	1	no	—
251	C₂²⋊Q₈	—	4	2	no	—
252	C₂²⋊Q₈	—	4	2	no	—
253	#117	—	4	1	no	—
254	#117	—	4	1	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
271	#107	—	4	2	no	—
272	#106	—	4	2	no	—
273	#103	—	4	2	no	—
274	#103	—	4	2	no	—
275	#103	—	4	2	no	—
276	#103	—	4	2	no	—
277	C₂²⋊C₈	—	4	1	no	—
278	C₂²⋊C₈	—	4	1	no	—
279	#95	—	2	2	no	—
280	#95	—	2	1	no	—
281	#95	—	2	1	no	—
282	#95	—	2	1	no	—
283	#95	—	2	1	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	—	2	2	no	—
287	C₁₉	#32780	1	1	yes	characteristic, direct product factor, Sylow
288	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	4	2	no	—
296	C₂×Q₈	—	8	2	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
310	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	4	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	4	2	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	8	2	no	—
330	C₂²⋊C₄	—	4	1	no	—
331	C₂²⋊C₄	—	4	1	no	—
332	C₂²⋊C₄	—	4	4	no	—
333	C₂²⋊C₄	—	8	2	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
344	Q₈	—	4	2	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	4	2	no	—
347	Q₈	—	4	2	no	—
348	Q₈	—	8	4	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
375	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
376	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
377	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
378	C₈	—	4	2	no	—
379	C₈	—	4	2	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	1	no	—
385	C₂²	C₁₉×#534	1	1	yes	characteristic
386	C₂²	C₁₉×#535	1	1	yes	characteristic
387	C₂²	C₁₉×#536	1	1	yes	characteristic
388	C₂²	C₁₉×#577	1	2	yes	—
389	C₂²	C₁₉×#578	1	2	yes	—
390	C₄	—	4	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	8	2	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	2	no	—
399	C₄	C₁₉×#562	1	2	yes	—
400	C₄	C₁₉×#562	1	2	yes	—
401	C₂	—	8	1	no	—
402	C₂	C₁₉×#2816	1	1	yes	characteristic
403	C₂	C₁₉×#3200	1	1	yes	characteristic
404	C₂	C₁₉×#3202	1	1	yes	characteristic
405	C₂	C₁₉×#3225	1	2	yes	—
406	C₂	C₁₉×#3242	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#2097	C₂	semidirect
4. C₁₉×#2085	C₂	semidirect
5. C₁₉×#2043	C₂	semidirect
8. C₁₉×#2024	C₂	semidirect
134. #32780	C₁₉	direct (N × H)
179. #2097	C₂×C₁₉	semidirect
180. #2085	C₂×C₁₉	semidirect
181. #2043	C₂×C₁₉	semidirect
184. #2024	C₂×C₁₉	semidirect
287. C₁₉	#32780	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2628	2
C₁₉×#2621	2
C₁₉×#2097	2
C₁₉×#2085	2
C₁₉×#2043	2
C₁₉×#2036	2
C₁₉×#2035	2
C₁₉×#2024	2
C₁₉×#1818	2
#32780	19

Subgroups — C19×#32780 #18038739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32780 #18038739