Subgroups — C₁₉×#8428 #18014387

Order 4864.

1020 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3496	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1804	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1540	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1517	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1517	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1480	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×H(5,𝔽₂)	—	2	1	no	—
9	C₁₉×#547	—	2	1	no	—
10	C₁₉×#547	C₄	1	2	yes	complemented
11	C₁₉×#546	—	2	2	no	—
12	C₁₉×#546	—	2	2	no	—
13	D₄²×C₁₉	—	2	1	no	—
14	D₄²×C₁₉	C₄	1	2	yes	complemented
15	C₁₉×#537	—	2	1	no	—
16	C₁₉×#534	—	2	2	no	—
17	C₁₉×#532	C₂²	1	1	yes	characteristic
18	C₁₉×#532	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#121	—	2	2	no	—
20	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#431	C₂²	1	1	yes	characteristic, complemented
22	C₁₉×#431	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₉×#102	—	2	1	no	—
25	C₁₉×#382	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#340	—	2	1	no	—
27	C₁₉×#332	—	2	1	no	—
28	C₁₉×#331	—	2	1	no	—
29	C₁₉×#327	—	2	2	no	—
30	C₁₉×#327	—	2	2	no	—
31	C₁₉×D₄⋊C₈	—	2	2	no	—
32	C₁₉×D₄⋊C₈	—	2	2	no	—
33	C₁₉×H(5,𝔽₂)	—	4	2	no	—
34	C₁₉×H(5,𝔽₂)	—	4	2	no	—
35	C₁₉×H(5,𝔽₂)	—	4	2	no	—
36	C₁₉×H(5,𝔽₂)	—	4	2	no	—
37	C₂×#41×C₁₉	—	2	2	no	—
38	C₂×#41×C₁₉	—	2	2	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	—	2	1	no	—
41	C₂²×D₄×C₁₉	—	2	4	no	—
42	C₂²×D₄×C₁₉	—	2	2	no	—
43	C₂²×D₄×C₁₉	—	2	2	no	—
44	C₂²×D₄×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂²×C₈×C₁₉	—	2	1	no	—
48	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
49	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
50	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
51	C₁₉×#127	D₄	1	1	yes	characteristic
52	C₁₉×#124	—	2	1	no	—
53	C₁₉×#124	—	2	1	no	—
54	C₁₉×#123	—	2	4	no	—
55	C₁₉×#123	—	2	4	no	—
56	C₁₉×C₂²⋊Q₈	—	2	2	no	—
57	C₁₉×C₂²⋊Q₈	—	2	2	no	—
58	C₁₉×#121	—	2	4	no	—
59	C₁₉×#121	—	2	4	no	—
60	C₁₉×#121	—	2	2	no	—
61	C₁₉×#121	—	2	2	no	—
62	C₁₉×#121	—	2	1	no	—
63	C₁₉×#121	—	2	1	no	—
64	C₁₉×#121	—	2	2	no	—
65	C₁₉×#121	—	2	2	no	—
66	C₁₉×#121	D₄	1	2	yes	—
67	C₁₉×#121	D₄	1	2	yes	—
68	C₁₉×#120	—	2	4	no	—
69	C₁₉×#120	—	2	4	no	—
70	C₄×D₄×C₁₉	—	2	1	no	—
71	C₄×D₄×C₁₉	—	2	1	no	—
72	C₄×D₄×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	—	2	1	no	—
74	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
75	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
76	C₄×D₄×C₁₉	D₄	1	2	yes	—
77	C₄×D₄×C₁₉	D₄	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
84	C₁₉×C₄⋊C₈	—	2	1	no	—
85	C₁₉×C₄⋊C₈	—	2	1	no	—
86	C₁₉×C₄⋊C₈	—	2	1	no	—
87	C₁₉×C₄⋊C₈	—	2	1	no	—
88	C₁₉×#102	—	4	2	no	—
89	C₁₉×C₂²⋊C₈	—	2	1	no	—
90	C₁₉×C₂²⋊C₈	—	2	1	no	—
91	C₄×C₈×C₁₉	—	2	1	no	—
92	C₄×C₈×C₁₉	—	2	1	no	—
93	C₁₉×#95	—	2	1	no	—
94	C₁₉×#95	—	2	1	no	—
95	C₂⁴×C₁₉	—	2	1	no	—
96	C₂⁴×C₁₉	—	2	4	no	—
97	#41×C₁₉	—	4	4	no	—
98	#41×C₁₉	—	4	4	no	—
99	#41×C₁₉	—	4	4	no	—
100	#41×C₁₉	—	4	4	no	—
101	#41×C₁₉	—	4	1	no	—
102	#41×C₁₉	—	4	1	no	—
103	#41×C₁₉	—	4	1	no	—
104	#41×C₁₉	—	4	1	no	—
105	#41×C₁₉	—	4	1	no	—
106	#41×C₁₉	—	4	1	no	—
107	#41×C₁₉	—	4	1	no	—
108	#41×C₁₉	—	4	1	no	—
109	C₂×Q₈×C₁₉	—	2	1	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	—	2	4	no	—
112	C₂×D₄×C₁₉	—	2	4	no	—
113	C₂×D₄×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	4	no	—
116	C₂×D₄×C₁₉	—	2	1	no	—
117	C₂×D₄×C₁₉	—	2	1	no	—
118	C₂×D₄×C₁₉	—	2	1	no	—
119	C₂×D₄×C₁₉	—	2	1	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	4	4	no	—
124	C₂×D₄×C₁₉	—	4	4	no	—
125	C₂×D₄×C₁₉	—	4	4	no	—
126	C₂×D₄×C₁₉	—	4	8	no	—
127	C₂×D₄×C₁₉	—	4	8	no	—
128	C₂×D₄×C₁₉	—	4	4	no	—
129	C₂×D₄×C₁₉	—	8	4	no	—
130	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
131	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
132	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
133	C₂×D₄×C₁₉	D₈	1	2	yes	—
134	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
135	C₂²×C₄×C₁₉	—	2	4	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	4	1	no	—
142	C₂²×C₄×C₁₉	—	8	2	no	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₉	—	4	1	no	—
147	C₂×C₈×C₁₉	—	4	1	no	—
148	C₂×C₈×C₁₉	—	4	1	no	—
149	C₂×C₈×C₁₉	—	4	1	no	—
150	C₂×C₈×C₁₉	—	4	1	no	—
151	C₄⋊C₄×C₁₉	—	2	4	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	4	1	no	—
156	C₄⋊C₄×C₁₉	—	4	1	no	—
157	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
158	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
159	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
160	C₂²⋊C₄×C₁₉	—	2	4	no	—
161	C₂²⋊C₄×C₁₉	—	2	4	no	—
162	C₂²⋊C₄×C₁₉	—	2	2	no	—
163	C₂²⋊C₄×C₁₉	—	2	2	no	—
164	C₂²⋊C₄×C₁₉	—	2	2	no	—
165	C₂²⋊C₄×C₁₉	—	2	2	no	—
166	C₂²⋊C₄×C₁₉	—	2	2	no	—
167	C₂²⋊C₄×C₁₉	—	2	2	no	—
168	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
172	#8428	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	—	2	2	no	—
176	C₂³×C₁₉	—	2	2	no	—
177	C₂³×C₁₉	—	2	2	no	—
178	C₂³×C₁₉	—	4	8	no	—
179	C₂³×C₁₉	—	8	1	no	—
180	C₂³×C₁₉	—	8	1	no	—
181	C₂³×C₁₉	—	8	4	no	—
182	C₂³×C₁₉	—	8	4	no	—
183	C₂³×C₁₉	#120	1	1	yes	characteristic
184	Q₈×C₁₉	—	4	1	no	—
185	Q₈×C₁₉	—	4	1	no	—
186	Q₈×C₁₉	—	4	1	no	—
187	Q₈×C₁₉	—	4	1	no	—
188	D₄×C₁₉	—	2	2	no	—
189	D₄×C₁₉	—	2	2	no	—
190	D₄×C₁₉	—	2	2	no	—
191	D₄×C₁₉	—	4	2	no	—
192	D₄×C₁₉	—	4	2	no	—
193	D₄×C₁₉	—	4	2	no	—
194	D₄×C₁₉	—	4	8	no	—
195	D₄×C₁₉	—	4	8	no	—
196	D₄×C₁₉	—	4	2	no	—
197	D₄×C₁₉	—	4	2	no	—
198	D₄×C₁₉	—	4	2	no	—
199	D₄×C₁₉	—	4	2	no	—
200	D₄×C₁₉	—	4	1	no	—
201	D₄×C₁₉	—	4	1	no	—
202	D₄×C₁₉	—	4	1	no	—
203	D₄×C₁₉	—	4	1	no	—
204	D₄×C₁₉	—	8	1	no	—
205	D₄×C₁₉	—	8	4	no	—
206	D₄×C₁₉	#102	1	4	yes	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	4	no	—
213	C₂×C₄×C₁₉	—	4	8	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	8	2	no	—
219	C₂×C₄×C₁₉	—	8	1	no	—
220	C₂×C₄×C₁₉	—	8	1	no	—
221	C₂×C₄×C₁₉	—	8	1	no	—
222	C₂×C₄×C₁₉	—	8	1	no	—
223	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
228	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
231	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
232	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₈×C₁₉	—	8	1	no	—
234	C₈×C₁₉	—	8	1	no	—
235	C₈×C₁₉	—	8	1	no	—
236	#3496	C₂×C₁₉	1	1	yes	characteristic
237	#1804	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#1540	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#1517	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#1517	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#1480	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#1478	C₂×C₁₉	1	1	yes	characteristic, complemented
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	2	1	no	—
245	C₂²×C₁₉	—	2	4	no	—
246	C₂²×C₁₉	—	4	2	no	—
247	C₂²×C₁₉	—	4	2	no	—
248	C₂²×C₁₉	—	4	2	no	—
249	C₂²×C₁₉	—	4	2	no	—
250	C₂²×C₁₉	—	4	2	no	—
251	C₂²×C₁₉	—	4	2	no	—
252	C₂²×C₁₉	—	4	2	no	—
253	C₂²×C₁₉	—	4	2	no	—
254	C₂²×C₁₉	—	8	2	no	—
255	C₂²×C₁₉	—	8	2	no	—
256	C₂²×C₁₉	—	16	8	no	—
257	C₂²×C₁₉	#379	1	1	yes	characteristic
258	C₂²×C₁₉	#447	1	1	yes	characteristic
259	C₂²×C₁₉	#450	1	1	yes	characteristic
260	C₄×C₁₉	—	2	1	no	—
261	C₄×C₁₉	—	2	1	no	—
262	C₄×C₁₉	—	2	1	no	—
263	C₄×C₁₉	—	2	1	no	—
264	C₄×C₁₉	—	4	2	no	—
265	C₄×C₁₉	—	4	2	no	—
266	C₄×C₁₉	—	4	2	no	—
267	C₄×C₁₉	—	16	1	no	—
268	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
269	C₄×C₁₉	#418	1	1	yes	characteristic
270	C₄×C₁₉	#447	1	1	yes	characteristic
271	C₄×C₁₉	#450	1	1	yes	characteristic
272	C₂×H(5,𝔽₂)	—	2	1	no	—
273	#547	—	2	1	no	—
274	#547	C₄×C₁₉	1	2	yes	complemented
275	#546	—	2	2	no	—
276	#546	—	2	2	no	—
277	D₄²	—	2	1	no	—
278	D₄²	C₄×C₁₉	1	2	yes	complemented
279	#537	—	2	1	no	—
280	#534	—	2	2	no	—
281	#532	C₂²×C₁₉	1	1	yes	characteristic
282	#532	C₂²×C₁₉	1	1	yes	characteristic
283	C₂×#121	—	2	2	no	—
284	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
285	#431	C₂²×C₁₉	1	1	yes	characteristic, complemented
286	#431	C₂²×C₁₉	1	1	yes	characteristic, complemented
287	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
288	C₂×#102	—	2	1	no	—
289	#382	C₂²×C₁₉	1	1	yes	characteristic, complemented
290	#340	—	2	1	no	—
291	#332	—	2	1	no	—
292	#331	—	2	1	no	—
293	#327	—	2	2	no	—
294	#327	—	2	2	no	—
295	D₄⋊C₈	—	2	2	no	—
296	D₄⋊C₈	—	2	2	no	—
297	C₂×C₁₉	—	2	1	no	—
298	C₂×C₁₉	—	2	1	no	—
299	C₂×C₁₉	—	4	4	no	—
300	C₂×C₁₉	—	8	2	no	—
301	C₂×C₁₉	—	8	2	no	—
302	C₂×C₁₉	#1786	1	1	yes	characteristic
303	C₂×C₁₉	#1794	1	1	yes	characteristic
304	C₂×C₁₉	#1795	1	1	yes	characteristic
305	H(5,𝔽₂)	—	4	2	no	—
306	H(5,𝔽₂)	—	4	2	no	—
307	H(5,𝔽₂)	—	4	2	no	—
308	H(5,𝔽₂)	—	4	2	no	—
309	C₂×#41	—	2	2	no	—
310	C₂×#41	—	2	2	no	—
311	C₂×#41	—	2	1	no	—
312	C₂×#41	—	2	1	no	—
313	C₂²×D₄	—	2	4	no	—
314	C₂²×D₄	—	2	2	no	—
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	—	2	2	no	—
317	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
318	C₂³×C₄	—	2	1	no	—
319	C₂²×C₈	—	2	1	no	—
320	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
321	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
322	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
323	#127	D₄×C₁₉	1	1	yes	characteristic
324	#124	—	2	1	no	—
325	#124	—	2	1	no	—
326	#123	—	2	4	no	—
327	#123	—	2	4	no	—
328	C₂²⋊Q₈	—	2	2	no	—
329	C₂²⋊Q₈	—	2	2	no	—
330	#121	—	2	4	no	—
331	#121	—	2	4	no	—
332	#121	—	2	2	no	—
333	#121	—	2	2	no	—
334	#121	—	2	1	no	—
335	#121	—	2	1	no	—
336	#121	—	2	2	no	—
337	#121	—	2	2	no	—
338	#121	D₄×C₁₉	1	2	yes	—
339	#121	D₄×C₁₉	1	2	yes	—
340	#120	—	2	4	no	—
341	#120	—	2	4	no	—
342	C₄×D₄	—	2	1	no	—
343	C₄×D₄	—	2	1	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
347	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
348	C₄×D₄	D₄×C₁₉	1	2	yes	—
349	C₄×D₄	D₄×C₁₉	1	2	yes	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
353	C₂×C₂²⋊C₄	—	2	4	no	—
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
356	C₄⋊C₈	—	2	1	no	—
357	C₄⋊C₈	—	2	1	no	—
358	C₄⋊C₈	—	2	1	no	—
359	C₄⋊C₈	—	2	1	no	—
360	#102	—	4	2	no	—
361	C₂²⋊C₈	—	2	1	no	—
362	C₂²⋊C₈	—	2	1	no	—
363	C₄×C₈	—	2	1	no	—
364	C₄×C₈	—	2	1	no	—
365	#95	—	2	1	no	—
366	#95	—	2	1	no	—
367	C₁₉	#8428	1	1	yes	characteristic, direct product factor, Sylow
368	C₂⁴	—	2	1	no	—
369	C₂⁴	—	2	4	no	—
370	#41	—	4	4	no	—
371	#41	—	4	4	no	—
372	#41	—	4	4	no	—
373	#41	—	4	4	no	—
374	#41	—	4	1	no	—
375	#41	—	4	1	no	—
376	#41	—	4	1	no	—
377	#41	—	4	1	no	—
378	#41	—	4	1	no	—
379	#41	—	4	1	no	—
380	#41	—	4	1	no	—
381	#41	—	4	1	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	4	4	no	—
397	C₂×D₄	—	4	4	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	—	4	8	no	—
400	C₂×D₄	—	4	8	no	—
401	C₂×D₄	—	4	4	no	—
402	C₂×D₄	—	8	4	no	—
403	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
404	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
405	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
406	C₂×D₄	D₈×C₁₉	1	2	yes	—
407	C₂×D₄	SD₁₆×C₁₉	1	2	yes	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	4	1	no	—
415	C₂²×C₄	—	8	2	no	—
416	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
419	C₂×C₈	—	4	1	no	—
420	C₂×C₈	—	4	1	no	—
421	C₂×C₈	—	4	1	no	—
422	C₂×C₈	—	4	1	no	—
423	C₂×C₈	—	4	1	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	4	1	no	—
429	C₄⋊C₄	—	4	1	no	—
430	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
431	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
432	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
442	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
445	C₂³	—	2	2	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	4	8	no	—
451	C₂³	—	8	1	no	—
452	C₂³	—	8	1	no	—
453	C₂³	—	8	4	no	—
454	C₂³	—	8	4	no	—
455	C₂³	C₁₉×#120	1	1	yes	characteristic
456	Q₈	—	4	1	no	—
457	Q₈	—	4	1	no	—
458	Q₈	—	4	1	no	—
459	Q₈	—	4	1	no	—
460	D₄	—	2	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	2	no	—
463	D₄	—	4	2	no	—
464	D₄	—	4	2	no	—
465	D₄	—	4	2	no	—
466	D₄	—	4	8	no	—
467	D₄	—	4	8	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	1	no	—
475	D₄	—	4	1	no	—
476	D₄	—	8	1	no	—
477	D₄	—	8	4	no	—
478	D₄	C₁₉×#102	1	4	yes	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	8	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	8	2	no	—
491	C₂×C₄	—	8	1	no	—
492	C₂×C₄	—	8	1	no	—
493	C₂×C₄	—	8	1	no	—
494	C₂×C₄	—	8	1	no	—
495	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
496	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
497	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
498	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
499	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
500	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
501	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
502	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
503	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
504	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
505	C₈	—	8	1	no	—
506	C₈	—	8	1	no	—
507	C₈	—	8	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	8	2	no	—
520	C₂²	—	8	2	no	—
521	C₂²	—	16	8	no	—
522	C₂²	C₁₉×#379	1	1	yes	characteristic
523	C₂²	C₁₉×#447	1	1	yes	characteristic
524	C₂²	C₁₉×#450	1	1	yes	characteristic
525	C₄	—	2	1	no	—
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	2	1	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	2	no	—
531	C₄	—	4	2	no	—
532	C₄	—	16	1	no	—
533	C₄	C₂×C₁₉×#102	1	1	yes	characteristic
534	C₄	C₁₉×#418	1	1	yes	characteristic
535	C₄	C₁₉×#447	1	1	yes	characteristic
536	C₄	C₁₉×#450	1	1	yes	characteristic
537	C₂	—	2	1	no	—
538	C₂	—	2	1	no	—
539	C₂	—	4	4	no	—
540	C₂	—	8	2	no	—
541	C₂	—	8	2	no	—
542	C₂	C₁₉×#1786	1	1	yes	characteristic
543	C₂	C₁₉×#1794	1	1	yes	characteristic
544	C₂	C₁₉×#1795	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3496	C₂
LCS	G ▷ C₄² ▷ 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. C₁₉×#1804	C₂	semidirect
3. C₁₉×#1540	C₂	semidirect
4. C₁₉×#1517	C₂	semidirect
5. C₁₉×#1517	C₂	semidirect
6. C₁₉×#1480	C₂	semidirect
7. C₁₉×#1478	C₂	semidirect
10. C₁₉×#547	C₄	semidirect
14. D₄²×C₁₉	C₄	semidirect
21. C₁₉×#431	C₂²	semidirect
22. C₁₉×#431	C₂²	semidirect
23. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
25. C₁₉×#382	C₂²	semidirect
172. #8428	C₁₉	direct (N × H)
237. #1804	C₂×C₁₉	semidirect
238. #1540	C₂×C₁₉	semidirect
239. #1517	C₂×C₁₉	semidirect
240. #1517	C₂×C₁₉	semidirect
241. #1480	C₂×C₁₉	semidirect
242. #1478	C₂×C₁₉	semidirect
274. #547	C₄×C₁₉	semidirect
278. D₄²	C₄×C₁₉	semidirect
285. #431	C₂²×C₁₉	semidirect
286. #431	C₂²×C₁₉	semidirect
287. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
289. #382	C₂²×C₁₉	semidirect
367. C₁₉	#8428	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×#3496	2
C₁₉×#1804	2
C₁₉×#1540	2
C₁₉×#1517	2
C₁₉×#1480	2
C₁₉×#1478	2
#8428	19

Subgroups — C19×#8428 #18014387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8428 #18014387