Subgroups — C₁₉×#32770 #18038729

Order 4864.

888 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2856	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2093	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2083	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2041	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2033	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2023	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1817	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
12	C₂×C₁₉×#121	—	2	1	no	—
13	C₂×C₁₉×#121	—	2	1	no	—
14	C₂×C₁₉×#121	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#107	C₂²	1	4	yes	—
17	C₂×C₁₉×#102	C₂²	1	4	yes	—
18	C₂×C₁₉×#102	C₂²	1	4	yes	—
19	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₁₉×#391	—	2	1	no	—
21	C₁₉×#390	—	2	1	no	—
22	C₁₉×#390	—	2	1	no	—
23	C₁₉×#390	C₂²	1	2	yes	—
24	C₁₉×#389	—	2	1	no	—
25	C₁₉×#389	C₂²	1	2	yes	—
26	C₁₉×#384	C₂²	1	1	yes	characteristic
27	C₁₉×#384	C₂²	1	1	yes	characteristic
28	C₁₉×#380	—	2	1	no	—
29	C₁₉×#380	C₂²	1	2	yes	—
30	C₁₉×#340	C₂²	1	4	yes	—
31	C₁₉×#336	C₂²	1	2	yes	—
32	C₁₉×#336	C₂²	1	2	yes	—
33	C₂²×Q₈×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	2	no	—
35	C₂²×D₄×C₁₉	—	2	1	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
42	C₁₉×C₄⋊Q₈	—	4	2	no	—
43	C₁₉×#127	—	4	2	no	—
44	C₁₉×C₂²⋊Q₈	—	4	4	no	—
45	C₁₉×#121	—	4	4	no	—
46	C₁₉×#121	—	4	4	no	—
47	C₁₉×#121	—	4	4	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄²×C₁₉	—	4	2	no	—
62	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
66	C₁₉×#107	—	4	4	no	—
67	C₁₉×#102	—	4	4	no	—
68	C₁₉×#102	—	4	4	no	—
69	C₁₉×C₂²⋊C₈	—	4	2	no	—
70	C₁₉×#95	—	2	2	no	—
71	C₁₉×#95	—	2	2	no	—
72	C₂⁴×C₁₉	—	2	2	no	—
73	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂×Q₈×C₁₉	—	4	2	no	—
75	C₂×Q₈×C₁₉	—	4	2	no	—
76	C₂×Q₈×C₁₉	—	4	2	no	—
77	C₂×D₄×C₁₉	—	2	4	no	—
78	C₂×D₄×C₁₉	—	2	4	no	—
79	C₂×D₄×C₁₉	—	2	4	no	—
80	C₂×D₄×C₁₉	—	4	2	no	—
81	C₂×D₄×C₁₉	—	4	2	no	—
82	C₂×D₄×C₁₉	—	4	2	no	—
83	C₂×D₄×C₁₉	—	4	2	no	—
84	C₂×D₄×C₁₉	—	4	4	no	—
85	C₂×D₄×C₁₉	—	4	4	no	—
86	C₂×D₄×C₁₉	—	4	4	no	—
87	C₂×D₄×C₁₉	—	4	2	no	—
88	C₂×D₄×C₁₉	—	4	2	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	D₈	1	4	yes	—
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	4	no	—
108	C₂×C₈×C₁₉	—	2	4	no	—
109	C₂×C₈×C₁₉	—	2	4	no	—
110	C₄⋊C₄×C₁₉	—	2	4	no	—
111	C₄⋊C₄×C₁₉	—	2	4	no	—
112	C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	4	2	no	—
115	C₄⋊C₄×C₁₉	—	4	2	no	—
116	C₄⋊C₄×C₁₉	—	4	2	no	—
117	C₄⋊C₄×C₁₉	—	4	2	no	—
118	C₄⋊C₄×C₁₉	—	4	4	no	—
119	C₄⋊C₄×C₁₉	—	4	2	no	—
120	C₂²⋊C₄×C₁₉	—	4	4	no	—
121	C₂²⋊C₄×C₁₉	—	4	4	no	—
122	C₂²⋊C₄×C₁₉	—	4	4	no	—
123	C₂²⋊C₄×C₁₉	—	4	4	no	—
124	C₄²×C₁₉	—	2	2	no	—
125	C₄²×C₁₉	—	2	2	no	—
126	C₄²×C₁₉	—	4	1	no	—
127	C₄²×C₁₉	—	4	1	no	—
128	#32770	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₁₉	—	2	1	no	—
130	C₂³×C₁₉	—	2	1	no	—
131	C₂³×C₁₉	—	2	1	no	—
132	C₂³×C₁₉	—	2	1	no	—
133	C₂³×C₁₉	—	2	1	no	—
134	C₂³×C₁₉	—	2	1	no	—
135	C₂³×C₁₉	—	4	2	no	—
136	C₂³×C₁₉	—	4	2	no	—
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	—	4	2	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	C₂×D₈	1	2	yes	—
143	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₁₉	—	8	4	no	—
145	D₄×C₁₉	—	4	8	no	—
146	D₄×C₁₉	—	8	4	no	—
147	D₄×C₁₉	—	8	4	no	—
148	D₄×C₁₉	—	8	8	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	1	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	4	4	no	—
161	C₂×C₄×C₁₉	—	4	4	no	—
162	C₂×C₄×C₁₉	—	4	4	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	—	4	2	no	—
172	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
173	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
174	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
175	C₂×C₄×C₁₉	#137	1	2	yes	—
176	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
177	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
178	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
179	C₈×C₁₉	—	4	4	no	—
180	#2857	C₂×C₁₉	1	1	yes	characteristic, complemented
181	#2856	C₂×C₁₉	1	1	yes	characteristic
182	#2093	C₂×C₁₉	1	2	yes	complemented
183	#2083	C₂×C₁₉	1	2	yes	complemented
184	#2041	C₂×C₁₉	1	2	yes	complemented
185	#2033	C₂×C₁₉	1	4	yes	complemented
186	#2023	C₂×C₁₉	1	2	yes	complemented
187	#1817	C₂×C₁₉	1	1	yes	characteristic, complemented
188	C₂²×C₁₉	—	2	2	no	—
189	C₂²×C₁₉	—	2	2	no	—
190	C₂²×C₁₉	—	2	2	no	—
191	C₂²×C₁₉	—	4	1	no	—
192	C₂²×C₁₉	—	4	1	no	—
193	C₂²×C₁₉	—	4	1	no	—
194	C₂²×C₁₉	—	4	1	no	—
195	C₂²×C₁₉	—	8	2	no	—
196	C₂²×C₁₉	—	8	2	no	—
197	C₂²×C₁₉	—	8	2	no	—
198	C₂²×C₁₉	—	8	2	no	—
199	C₂²×C₁₉	—	8	2	no	—
200	C₂²×C₁₉	—	8	2	no	—
201	C₂²×C₁₉	—	8	2	no	—
202	C₂²×C₁₉	#534	1	1	yes	characteristic
203	C₂²×C₁₉	#535	1	1	yes	characteristic
204	C₂²×C₁₉	#536	1	1	yes	characteristic
205	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
206	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
207	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
208	C₂²×C₁₉	#575	1	1	yes	characteristic
209	C₄×C₁₉	—	2	2	no	—
210	C₄×C₁₉	—	2	2	no	—
211	C₄×C₁₉	—	2	2	no	—
212	C₄×C₁₉	—	2	2	no	—
213	C₄×C₁₉	—	4	1	no	—
214	C₄×C₁₉	—	8	2	no	—
215	C₄×C₁₉	—	8	2	no	—
216	C₄×C₁₉	—	8	2	no	—
217	C₄×C₁₉	#562	1	4	yes	—
218	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
219	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
220	C₂×C₂²⋊Q₈	—	2	1	no	—
221	C₂×#121	—	2	1	no	—
222	C₂×#121	—	2	1	no	—
223	C₂×#121	C₂²×C₁₉	1	2	yes	—
224	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
225	C₂×#107	C₂²×C₁₉	1	4	yes	—
226	C₂×#102	C₂²×C₁₉	1	4	yes	—
227	C₂×#102	C₂²×C₁₉	1	4	yes	—
228	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
229	#391	—	2	1	no	—
230	#390	—	2	1	no	—
231	#390	—	2	1	no	—
232	#390	C₂²×C₁₉	1	2	yes	—
233	#389	—	2	1	no	—
234	#389	C₂²×C₁₉	1	2	yes	—
235	#384	C₂²×C₁₉	1	1	yes	characteristic
236	#384	C₂²×C₁₉	1	1	yes	characteristic
237	#380	—	2	1	no	—
238	#380	C₂²×C₁₉	1	2	yes	—
239	#340	C₂²×C₁₉	1	4	yes	—
240	#336	C₂²×C₁₉	1	2	yes	—
241	#336	C₂²×C₁₉	1	2	yes	—
242	C₂×C₁₉	—	4	2	no	—
243	C₂×C₁₉	—	16	2	no	—
244	C₂×C₁₉	#2816	1	1	yes	characteristic
245	C₂×C₁₉	#3186	1	1	yes	characteristic
246	C₂×C₁₉	#3193	1	1	yes	characteristic
247	C₂×C₁₉	#3205	1	1	yes	characteristic
248	C₂×C₁₉	#3216	1	1	yes	characteristic
249	C₂×C₁₉	#3226	1	1	yes	characteristic
250	C₂×C₁₉	#3235	1	1	yes	characteristic
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×D₄	—	2	2	no	—
253	C₂²×D₄	—	2	1	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
256	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
257	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
260	C₄⋊Q₈	—	4	2	no	—
261	#127	—	4	2	no	—
262	C₂²⋊Q₈	—	4	4	no	—
263	#121	—	4	4	no	—
264	#121	—	4	4	no	—
265	#121	—	4	4	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₄²	—	4	2	no	—
280	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
281	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
284	#107	—	4	4	no	—
285	#102	—	4	4	no	—
286	#102	—	4	4	no	—
287	C₂²⋊C₈	—	4	2	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	C₁₉	#32770	1	1	yes	characteristic, direct product factor, Sylow
291	C₂⁴	—	2	2	no	—
292	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	4	2	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂×D₄	—	4	4	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	D₈×C₁₉	1	4	yes	—
320	C₂²×C₄	C₂×D₄×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	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
325	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
326	C₂×C₈	—	2	4	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	2	4	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₂²⋊C₄	—	4	4	no	—
340	C₂²⋊C₄	—	4	4	no	—
341	C₂²⋊C₄	—	4	4	no	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	4	1	no	—
346	C₄²	—	4	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	C₂×D₈×C₁₉	1	2	yes	—
361	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
362	Q₈	—	8	4	no	—
363	D₄	—	4	8	no	—
364	D₄	—	8	4	no	—
365	D₄	—	8	4	no	—
366	D₄	—	8	8	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
391	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
392	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
393	C₂×C₄	C₁₉×#137	1	2	yes	—
394	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
395	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
396	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
397	C₈	—	4	4	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	2	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	C₁₉×#534	1	1	yes	characteristic
413	C₂²	C₁₉×#535	1	1	yes	characteristic
414	C₂²	C₁₉×#536	1	1	yes	characteristic
415	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
416	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
417	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
418	C₂²	C₁₉×#575	1	1	yes	characteristic
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	4	1	no	—
424	C₄	—	8	2	no	—
425	C₄	—	8	2	no	—
426	C₄	—	8	2	no	—
427	C₄	C₁₉×#562	1	4	yes	—
428	C₂	—	4	2	no	—
429	C₂	—	16	2	no	—
430	C₂	C₁₉×#2816	1	1	yes	characteristic
431	C₂	C₁₉×#3186	1	1	yes	characteristic
432	C₂	C₁₉×#3193	1	1	yes	characteristic
433	C₂	C₁₉×#3205	1	1	yes	characteristic
434	C₂	C₁₉×#3216	1	1	yes	characteristic
435	C₂	C₁₉×#3226	1	1	yes	characteristic
436	C₂	C₁₉×#3235	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2856	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2857	C₂	semidirect
3. C₁₉×#2093	C₂	semidirect
4. C₁₉×#2083	C₂	semidirect
5. C₁₉×#2041	C₂	semidirect
6. C₁₉×#2033	C₂	semidirect
7. C₁₉×#2023	C₂	semidirect
8. C₁₉×#1817	C₂	semidirect
128. #32770	C₁₉	direct (N × H)
180. #2857	C₂×C₁₉	semidirect
182. #2093	C₂×C₁₉	semidirect
183. #2083	C₂×C₁₉	semidirect
184. #2041	C₂×C₁₉	semidirect
185. #2033	C₂×C₁₉	semidirect
186. #2023	C₂×C₁₉	semidirect
187. #1817	C₂×C₁₉	semidirect
290. C₁₉	#32770	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×#2857	2
C₁₉×#2856	2
C₁₉×#2093	2
C₁₉×#2083	2
C₁₉×#2041	2
C₁₉×#2033	2
C₁₉×#2023	2
C₁₉×#1817	2
#32770	19

Subgroups — C19×#32770 #18038729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32770 #18038729