Subgroups — C₁₉×#22539 #18028498

Order 4864.

1066 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#559	C₂	1	1	yes	maximal, characteristic
2	Q₈×M₁₆×C₁₉	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1967	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1965	C₂	1	2	yes	maximal
5	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1800	C₂	1	2	yes	maximal, complemented
7	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₁₉×#100	C₂	1	2	yes	maximal, complemented
9	C₁₉×#559	—	2	2	no	—
10	C₁₉×#559	—	2	4	no	—
11	C₁₉×#559	—	2	2	no	—
12	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#124	C₄	1	2	yes	—
14	C₂×C₁₉×#124	C₂²	1	2	yes	—
15	C₂×C₁₉×#123	C₄	1	4	yes	—
16	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	—
19	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
20	C₁₉×#446	—	2	4	no	—
21	C₁₉×#446	—	2	2	no	—
22	C₈×Q₈×C₁₉	—	2	2	no	—
23	C₁₉×#423	C₂²	1	2	yes	—
24	C₁₉×#423	C₂²	1	4	yes	—
25	C₂×C₁₉×#101	C₂²	1	2	yes	—
26	C₂×C₁₉×#101	C₂²	1	2	yes	—
27	C₂×C₁₉×#100	C₂²	1	4	yes	—
28	C₂×C₁₉×#100	C₂²	1	4	yes	—
29	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
30	C₄×M₁₆×C₁₉	C₂²	1	4	yes	—
31	C₁₉×#343	C₂²	1	1	yes	characteristic
32	C₁₉×#343	C₂²	1	2	yes	—
33	C₁₉×#343	C₂²	1	1	yes	characteristic
34	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
37	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
40	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
41	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
42	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
43	C₁₉×#127	—	2	2	no	—
44	C₁₉×#127	—	2	2	no	—
45	C₁₉×#124	—	2	4	no	—
46	C₁₉×#124	—	2	4	no	—
47	C₁₉×#124	—	2	4	no	—
48	C₁₉×#124	—	2	4	no	—
49	C₁₉×#123	—	2	8	no	—
50	C₁₉×#123	—	2	8	no	—
51	C₄×Q₈×C₁₉	—	2	2	no	—
52	C₄×Q₈×C₁₉	—	2	2	no	—
53	C₄×Q₈×C₁₉	D₄	1	2	yes	—
54	C₄×Q₈×C₁₉	D₄	1	4	yes	—
55	C₄×Q₈×C₁₉	D₄	1	2	yes	—
56	C₄×D₄×C₁₉	—	2	4	no	—
57	C₄×D₄×C₁₉	—	2	2	no	—
58	C₄×D₄×C₁₉	—	2	2	no	—
59	C₄×D₄×C₁₉	—	2	4	no	—
60	C₄×D₄×C₁₉	—	2	4	no	—
61	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
66	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
67	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
68	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
71	C₁₉×C₄⋊C₈	—	2	4	no	—
72	C₁₉×C₄⋊C₈	—	2	2	no	—
73	C₁₉×C₄⋊C₈	—	2	4	no	—
74	C₁₉×C₄⋊C₈	—	2	2	no	—
75	C₁₉×#101	—	2	4	no	—
76	C₁₉×#101	—	4	2	no	—
77	C₁₉×#100	—	2	8	no	—
78	C₁₉×#100	—	4	4	no	—
79	C₁₉×#97	—	2	4	no	—
80	C₁₉×#97	—	2	2	no	—
81	C₄×C₈×C₁₉	—	2	4	no	—
82	C₄×C₈×C₁₉	—	2	2	no	—
83	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
84	C₂×Q₈×C₁₉	—	2	2	no	—
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	2	1	no	—
88	C₂×Q₈×C₁₉	—	4	2	no	—
89	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
90	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
91	C₂×D₄×C₁₉	—	2	2	no	—
92	C₂×D₄×C₁₉	—	2	2	no	—
93	C₂×D₄×C₁₉	—	2	4	no	—
94	C₂×D₄×C₁₉	—	2	4	no	—
95	C₂×D₄×C₁₉	—	2	4	no	—
96	C₂×D₄×C₁₉	—	2	2	no	—
97	C₂×D₄×C₁₉	—	2	2	no	—
98	C₂×D₄×C₁₉	—	4	4	no	—
99	C₂×D₄×C₁₉	—	8	2	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	2	4	no	—
102	C₂²×C₄×C₁₉	—	8	4	no	—
103	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
110	M₁₆×C₁₉	—	2	2	no	—
111	M₁₆×C₁₉	—	2	4	no	—
112	M₁₆×C₁₉	—	2	2	no	—
113	M₁₆×C₁₉	—	2	2	no	—
114	M₁₆×C₁₉	—	2	4	no	—
115	M₁₆×C₁₉	#41	1	4	yes	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	2	4	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	2	4	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
122	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
123	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
124	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
125	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
126	C₂²⋊C₄×C₁₉	—	2	4	no	—
127	C₂²⋊C₄×C₁₉	—	2	4	no	—
128	C₂²⋊C₄×C₁₉	—	2	8	no	—
129	C₂²⋊C₄×C₁₉	—	2	8	no	—
130	C₄²×C₁₉	—	2	2	no	—
131	C₄²×C₁₉	—	2	2	no	—
132	C₄²×C₁₉	C₂×D₄	1	4	yes	—
133	C₄²×C₁₉	C₂×D₄	1	4	yes	—
134	C₄²×C₁₉	C₂×D₄	1	2	yes	—
135	C₄²×C₁₉	C₂×D₄	1	2	yes	—
136	#22539	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₁₉	—	2	4	no	—
138	C₂³×C₁₉	—	2	4	no	—
139	C₂³×C₁₉	—	2	4	no	—
140	C₂³×C₁₉	—	4	4	no	—
141	C₂³×C₁₉	—	4	4	no	—
142	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
143	Q₈×C₁₉	—	2	4	no	—
144	Q₈×C₁₉	—	4	2	no	—
145	Q₈×C₁₉	—	4	2	no	—
146	Q₈×C₁₉	—	4	2	no	—
147	D₄×C₁₉	—	4	4	no	—
148	D₄×C₁₉	—	4	4	no	—
149	D₄×C₁₉	—	4	4	no	—
150	D₄×C₁₉	—	4	4	no	—
151	D₄×C₁₉	—	8	4	no	—
152	C₂×C₄×C₁₉	—	2	2	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	1	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	8	4	no	—
162	C₂×C₄×C₁₉	—	8	4	no	—
163	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
165	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
171	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
173	C₈×C₁₉	—	2	4	no	—
174	C₈×C₁₉	—	4	4	no	—
175	C₈×C₁₉	—	4	2	no	—
176	C₂×#559	C₂×C₁₉	1	1	yes	characteristic
177	Q₈×M₁₆	C₂×C₁₉	1	2	yes	complemented
178	#1967	C₂×C₁₉	1	4	yes	complemented
179	#1965	C₂×C₁₉	1	2	yes	—
180	#1801	C₂×C₁₉	1	1	yes	characteristic, complemented
181	#1800	C₂×C₁₉	1	2	yes	complemented
182	C₄×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
183	C₄×#100	C₂×C₁₉	1	2	yes	complemented
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	4	4	no	—
187	C₂²×C₁₉	—	4	4	no	—
188	C₂²×C₁₉	—	4	4	no	—
189	C₂²×C₁₉	—	8	4	no	—
190	C₂²×C₁₉	—	8	4	no	—
191	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
193	C₂²×C₁₉	#520	1	1	yes	characteristic
194	C₄×C₁₉	—	2	1	no	—
195	C₄×C₁₉	—	2	4	no	—
196	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	2	2	no	—
198	C₄×C₁₉	—	2	2	no	—
199	C₄×C₁₉	—	4	2	no	—
200	C₄×C₁₉	—	4	2	no	—
201	C₄×C₁₉	#413	1	2	yes	—
202	C₄×C₁₉	#548	1	2	yes	—
203	C₄×C₁₉	#550	1	2	yes	—
204	#559	—	2	2	no	—
205	#559	—	2	4	no	—
206	#559	—	2	2	no	—
207	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
208	C₂×#124	C₄×C₁₉	1	2	yes	—
209	C₂×#124	C₂²×C₁₉	1	2	yes	—
210	C₂×#123	C₄×C₁₉	1	4	yes	—
211	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
212	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
213	C₂×C₄×D₄	C₄×C₁₉	1	2	yes	—
214	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
215	#446	—	2	4	no	—
216	#446	—	2	2	no	—
217	C₈×Q₈	—	2	2	no	—
218	#423	C₂²×C₁₉	1	4	yes	—
219	#423	C₂²×C₁₉	1	2	yes	—
220	C₂×#101	C₂²×C₁₉	1	2	yes	—
221	C₂×#101	C₂²×C₁₉	1	2	yes	—
222	C₂×#100	C₂²×C₁₉	1	4	yes	—
223	C₂×#100	C₂²×C₁₉	1	4	yes	—
224	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
225	C₄×M₁₆	C₂²×C₁₉	1	4	yes	—
226	#343	C₂²×C₁₉	1	1	yes	characteristic
227	#343	C₂²×C₁₉	1	2	yes	—
228	#343	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×C₁₉	—	2	1	no	—
230	C₂×C₁₉	—	2	1	no	—
231	C₂×C₁₉	—	8	4	no	—
232	C₂×C₁₉	#2341	1	1	yes	characteristic
233	C₂×C₁₉	C₂×#413	1	1	yes	characteristic
234	C₂×C₁₉	#2888	1	1	yes	characteristic
235	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
236	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
237	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
238	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
239	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
240	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
241	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
242	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
243	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
244	#127	—	2	2	no	—
245	#127	—	2	2	no	—
246	#124	—	2	4	no	—
247	#124	—	2	4	no	—
248	#124	—	2	4	no	—
249	#124	—	2	4	no	—
250	#123	—	2	8	no	—
251	#123	—	2	8	no	—
252	C₄×Q₈	—	2	2	no	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	D₄×C₁₉	1	2	yes	—
255	C₄×Q₈	D₄×C₁₉	1	4	yes	—
256	C₄×Q₈	D₄×C₁₉	1	2	yes	—
257	C₄×D₄	—	2	4	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	2	4	no	—
261	C₄×D₄	—	2	4	no	—
262	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
263	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
267	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
268	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
269	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
270	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
271	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
272	C₄⋊C₈	—	2	4	no	—
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	—	2	4	no	—
275	C₄⋊C₈	—	2	2	no	—
276	#101	—	2	4	no	—
277	#101	—	4	2	no	—
278	#100	—	2	8	no	—
279	#100	—	4	4	no	—
280	#97	—	2	4	no	—
281	#97	—	2	2	no	—
282	C₄×C₈	—	2	4	no	—
283	C₄×C₈	—	2	2	no	—
284	C₁₉	#22539	1	1	yes	characteristic, direct product factor, Sylow
285	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
292	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	4	4	no	—
301	C₂×D₄	—	8	2	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	8	4	no	—
305	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
308	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
309	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
310	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
311	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
312	M₁₆	—	2	2	no	—
313	M₁₆	—	2	4	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	2	4	no	—
317	M₁₆	#41×C₁₉	1	4	yes	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	2	2	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
324	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
325	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
326	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
327	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	2	8	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	C₂×D₄×C₁₉	1	4	yes	—
335	C₄²	C₂×D₄×C₁₉	1	2	yes	—
336	C₄²	C₂×D₄×C₁₉	1	4	yes	—
337	C₄²	C₂×D₄×C₁₉	1	2	yes	—
338	C₂³	—	2	4	no	—
339	C₂³	—	2	4	no	—
340	C₂³	—	2	4	no	—
341	C₂³	—	4	4	no	—
342	C₂³	—	4	4	no	—
343	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
344	Q₈	—	2	4	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	4	2	no	—
347	Q₈	—	4	2	no	—
348	D₄	—	4	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	4	4	no	—
352	D₄	—	8	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	8	4	no	—
363	C₂×C₄	—	8	4	no	—
364	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
365	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
366	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
367	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
368	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
371	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
372	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
373	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
374	C₈	—	2	4	no	—
375	C₈	—	4	4	no	—
376	C₈	—	4	2	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	4	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	8	4	no	—
383	C₂²	—	8	4	no	—
384	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
385	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
386	C₂²	C₁₉×#520	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	4	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	2	no	—
394	C₄	C₁₉×#413	1	2	yes	—
395	C₄	C₁₉×#548	1	2	yes	—
396	C₄	C₁₉×#550	1	2	yes	—
397	C₂	—	2	1	no	—
398	C₂	—	2	1	no	—
399	C₂	—	8	4	no	—
400	C₂	C₁₉×#2341	1	1	yes	characteristic
401	C₂	C₂×C₁₉×#413	1	1	yes	characteristic
402	C₂	C₁₉×#2888	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#127	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×M₁₆×C₁₉	C₂	semidirect
3. C₁₉×#1967	C₂	semidirect
5. C₁₉×#1801	C₂	semidirect
6. C₁₉×#1800	C₂	semidirect
7. C₄×C₁₉×#101	C₂	semidirect
8. C₄×C₁₉×#100	C₂	semidirect
136. #22539	C₁₉	direct (N × H)
177. Q₈×M₁₆	C₂×C₁₉	semidirect
178. #1967	C₂×C₁₉	semidirect
180. #1801	C₂×C₁₉	semidirect
181. #1800	C₂×C₁₉	semidirect
182. C₄×#101	C₂×C₁₉	semidirect
183. C₄×#100	C₂×C₁₉	semidirect
284. C₁₉	#22539	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×#559	2
Q₈×M₁₆×C₁₉	2
C₁₉×#1967	2
C₁₉×#1965	2
C₁₉×#1801	2
C₁₉×#1800	2
C₄×C₁₉×#101	2
C₄×C₁₉×#100	2
#22539	19

Subgroups — C19×#22539 #18028498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22539 #18028498