Subgroups — C₁₉×#32871 #18038830

Order 4864.

492 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2103	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2103	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2098	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2082	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2081	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2070	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2069	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2049	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2048	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#2046	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2046	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2019	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1903	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1902	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1858	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#568	C₂²	1	1	yes	characteristic
20	C₁₉×#430	C₂²	1	1	yes	characteristic
21	C₁₉×#430	C₂²	1	1	yes	characteristic
22	C₁₉×#430	C₂²	1	1	yes	characteristic
23	C₁₉×#430	C₂²	1	1	yes	characteristic
24	C₁₉×#430	C₂²	1	1	yes	characteristic
25	C₁₉×#424	C₂²	1	1	yes	characteristic
26	C₁₉×#424	C₂²	1	1	yes	characteristic
27	C₁₉×#421	C₂²	1	1	yes	characteristic
28	C₁₉×#421	C₂²	1	1	yes	characteristic
29	C₁₉×#419	C₂²	1	1	yes	characteristic
30	C₁₉×#419	C₂²	1	1	yes	characteristic
31	C₁₉×#418	C₂²	1	1	yes	characteristic
32	C₁₉×#418	C₂²	1	1	yes	characteristic
33	C₁₉×#413	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
40	C₁₉×#408	C₂²	1	1	yes	characteristic
41	C₁₉×#344	C₂²	1	1	yes	characteristic
42	C₁₉×#344	C₂²	1	1	yes	characteristic
43	C₁₉×#344	C₂²	1	1	yes	characteristic
44	C₁₉×#344	C₂²	1	1	yes	characteristic
45	C₁₉×#341	C₂²	1	1	yes	characteristic
46	C₁₉×#341	C₂²	1	1	yes	characteristic
47	C₁₉×#341	C₂²	1	1	yes	characteristic
48	C₁₉×#338	C₂²	1	1	yes	characteristic
49	C₁₉×#338	C₂²	1	1	yes	characteristic
50	C₁₉×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
51	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₁₉×#137	—	4	1	no	—
55	C₁₉×#137	—	4	1	no	—
56	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
57	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
58	C₂×Q₁₆×C₁₉	—	2	1	no	—
59	C₂×SD₁₆×C₁₉	—	2	1	no	—
60	C₂×SD₁₆×C₁₉	—	2	1	no	—
61	C₂×SD₁₆×C₁₉	—	4	1	no	—
62	C₂×SD₁₆×C₁₉	—	4	1	no	—
63	C₂×SD₁₆×C₁₉	—	4	1	no	—
64	C₂×D₈×C₁₉	—	2	1	no	—
65	C₁₉×#131	—	4	1	no	—
66	C₁₉×#131	—	4	1	no	—
67	C₂×M₁₆×C₁₉	—	4	1	no	—
68	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
78	C₁₉×#117	C₂³	1	1	yes	characteristic
79	C₁₉×#117	C₂³	1	1	yes	characteristic
80	C₁₉×#108	—	4	1	no	—
81	C₁₉×#108	—	4	1	no	—
82	C₁₉×#108	—	4	1	no	—
83	C₁₉×#108	—	4	1	no	—
84	C₁₉×#108	—	4	1	no	—
85	C₁₉×C₄⋊C₈	—	4	1	no	—
86	C₁₉×C₄⋊C₈	—	4	1	no	—
87	C₁₉×#104	—	4	1	no	—
88	C₁₉×#104	—	4	1	no	—
89	C₁₉×#103	—	4	1	no	—
90	C₁₉×#103	—	4	1	no	—
91	C₁₉×#102	—	4	1	no	—
92	C₁₉×#102	—	4	1	no	—
93	C₁₉×#101	—	2	1	no	—
94	C₁₉×#101	—	4	1	no	—
95	C₁₉×#101	—	4	1	no	—
96	C₁₉×#101	—	4	1	no	—
97	C₁₉×#100	—	2	1	no	—
98	C₁₉×#100	—	4	1	no	—
99	C₁₉×#100	—	4	1	no	—
100	C₁₉×#100	—	4	1	no	—
101	C₁₉×C₂²⋊C₈	—	4	1	no	—
102	C₂⁴×C₁₉	—	2	1	no	—
103	#41×C₁₉	—	2	1	no	—
104	#41×C₁₉	—	2	1	no	—
105	#41×C₁₉	—	2	1	no	—
106	#41×C₁₉	—	2	1	no	—
107	C₂×Q₈×C₁₉	—	2	1	no	—
108	C₂×Q₈×C₁₉	—	2	1	no	—
109	C₂×Q₈×C₁₉	—	2	1	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	#41	1	1	yes	characteristic
114	C₂×D₄×C₁₉	—	2	1	no	—
115	C₂×D₄×C₁₉	—	2	1	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	#41	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
125	Q₁₆×C₁₉	—	4	2	no	—
126	SD₁₆×C₁₉	—	4	2	no	—
127	SD₁₆×C₁₉	—	4	2	no	—
128	SD₁₆×C₁₉	—	4	4	no	—
129	D₈×C₁₉	—	4	2	no	—
130	M₁₆×C₁₉	—	2	1	no	—
131	M₁₆×C₁₉	—	2	1	no	—
132	M₁₆×C₁₉	—	2	1	no	—
133	M₁₆×C₁₉	—	2	1	no	—
134	M₁₆×C₁₉	—	2	1	no	—
135	M₁₆×C₁₉	—	2	1	no	—
136	M₁₆×C₁₉	—	2	1	no	—
137	M₁₆×C₁₉	—	2	1	no	—
138	M₁₆×C₁₉	—	2	1	no	—
139	M₁₆×C₁₉	—	2	1	no	—
140	M₁₆×C₁₉	—	2	1	no	—
141	M₁₆×C₁₉	—	2	1	no	—
142	M₁₆×C₁₉	—	2	1	no	—
143	M₁₆×C₁₉	—	2	1	no	—
144	M₁₆×C₁₉	—	2	1	no	—
145	M₁₆×C₁₉	—	2	1	no	—
146	M₁₆×C₁₉	—	2	1	no	—
147	M₁₆×C₁₉	—	2	1	no	—
148	M₁₆×C₁₉	—	4	2	no	—
149	C₂×C₈×C₁₉	—	2	1	no	—
150	C₂×C₈×C₁₉	—	2	1	no	—
151	C₂×C₈×C₁₉	—	2	1	no	—
152	C₂×C₈×C₁₉	—	2	1	no	—
153	C₂×C₈×C₁₉	—	2	1	no	—
154	C₂×C₈×C₁₉	—	2	1	no	—
155	C₂×C₈×C₁₉	—	2	1	no	—
156	C₂×C₈×C₁₉	—	2	1	no	—
157	C₂×C₈×C₁₉	—	2	1	no	—
158	C₂×C₈×C₁₉	—	2	1	no	—
159	C₂×C₈×C₁₉	—	2	1	no	—
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₂×C₈×C₁₉	—	4	2	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₂²⋊C₄×C₁₉	—	2	1	no	—
165	C₂²⋊C₄×C₁₉	—	2	1	no	—
166	C₄²×C₁₉	—	2	1	no	—
167	C₄²×C₁₉	—	2	1	no	—
168	#32871	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂³×C₁₉	—	2	1	no	—
170	C₂³×C₁₉	—	4	1	no	—
171	C₂³×C₁₉	—	4	1	no	—
172	C₂³×C₁₉	—	4	1	no	—
173	C₂³×C₁₉	—	16	1	no	—
174	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
175	Q₈×C₁₉	—	2	1	no	—
176	Q₈×C₁₉	—	2	1	no	—
177	Q₈×C₁₉	—	4	1	no	—
178	Q₈×C₁₉	—	4	1	no	—
179	Q₈×C₁₉	—	4	1	no	—
180	Q₈×C₁₉	—	4	1	no	—
181	D₄×C₁₉	—	2	1	no	—
182	D₄×C₁₉	—	2	1	no	—
183	D₄×C₁₉	—	4	1	no	—
184	D₄×C₁₉	—	4	1	no	—
185	D₄×C₁₉	—	4	1	no	—
186	D₄×C₁₉	—	4	1	no	—
187	D₄×C₁₉	—	4	1	no	—
188	D₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
203	C₈×C₁₉	—	4	1	no	—
204	C₈×C₁₉	—	4	1	no	—
205	C₈×C₁₉	—	4	1	no	—
206	C₈×C₁₉	—	4	1	no	—
207	C₈×C₁₉	—	4	1	no	—
208	C₈×C₁₉	—	4	1	no	—
209	C₈×C₁₉	—	4	1	no	—
210	C₈×C₁₉	—	4	1	no	—
211	C₈×C₁₉	—	4	1	no	—
212	C₈×C₁₉	—	4	1	no	—
213	#2103	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#2103	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#2098	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#2082	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#2081	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#2070	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#2069	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#2049	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#2048	C₂×C₁₉	1	1	yes	characteristic
222	#2046	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#2046	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#2019	C₂×C₁₉	1	1	yes	characteristic
225	#1903	C₂×C₁₉	1	1	yes	characteristic
226	#1902	C₂×C₁₉	1	1	yes	characteristic, complemented
227	#1858	C₂×C₁₉	1	1	yes	characteristic, complemented
228	C₂²×C₁₉	—	4	1	no	—
229	C₂²×C₁₉	—	4	1	no	—
230	C₂²×C₁₉	—	8	1	no	—
231	C₂²×C₁₉	—	8	1	no	—
232	C₂²×C₁₉	—	16	1	no	—
233	C₂²×C₁₉	—	16	1	no	—
234	C₂²×C₁₉	—	16	1	no	—
235	C₂²×C₁₉	#539	1	1	yes	characteristic
236	C₂²×C₁₉	#562	1	1	yes	characteristic
237	C₂²×C₁₉	#562	1	1	yes	characteristic
238	C₄×C₁₉	—	4	1	no	—
239	C₄×C₁₉	—	8	1	no	—
240	C₄×C₁₉	—	8	1	no	—
241	C₄×C₁₉	—	8	1	no	—
242	C₄×C₁₉	#538	1	1	yes	characteristic
243	C₄×C₁₉	#538	1	1	yes	characteristic
244	C₄×C₁₉	#560	1	1	yes	characteristic
245	C₄×C₁₉	#560	1	1	yes	characteristic
246	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
248	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
249	#568	C₂²×C₁₉	1	1	yes	characteristic
250	#430	C₂²×C₁₉	1	1	yes	characteristic
251	#430	C₂²×C₁₉	1	1	yes	characteristic
252	#430	C₂²×C₁₉	1	1	yes	characteristic
253	#430	C₂²×C₁₉	1	1	yes	characteristic
254	#430	C₂²×C₁₉	1	1	yes	characteristic
255	#424	C₂²×C₁₉	1	1	yes	characteristic
256	#424	C₂²×C₁₉	1	1	yes	characteristic
257	#421	C₂²×C₁₉	1	1	yes	characteristic
258	#421	C₂²×C₁₉	1	1	yes	characteristic
259	#419	C₂²×C₁₉	1	1	yes	characteristic
260	#419	C₂²×C₁₉	1	1	yes	characteristic
261	#418	C₂²×C₁₉	1	1	yes	characteristic
262	#418	C₂²×C₁₉	1	1	yes	characteristic
263	#413	C₂²×C₁₉	1	1	yes	characteristic
264	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
265	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
267	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
268	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
269	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
270	#408	C₂²×C₁₉	1	1	yes	characteristic
271	#344	C₂²×C₁₉	1	1	yes	characteristic
272	#344	C₂²×C₁₉	1	1	yes	characteristic
273	#344	C₂²×C₁₉	1	1	yes	characteristic
274	#344	C₂²×C₁₉	1	1	yes	characteristic
275	#341	C₂²×C₁₉	1	1	yes	characteristic
276	#341	C₂²×C₁₉	1	1	yes	characteristic
277	#341	C₂²×C₁₉	1	1	yes	characteristic
278	#338	C₂²×C₁₉	1	1	yes	characteristic
279	#338	C₂²×C₁₉	1	1	yes	characteristic
280	H(3,ℤ/4)	C₂²×C₁₉	1	1	yes	characteristic
281	C₂×C₁₉	—	2	1	no	—
282	C₂×C₁₉	—	2	1	no	—
283	C₂×C₁₉	—	2	1	no	—
284	C₂×C₁₉	—	8	1	no	—
285	C₂×C₁₉	—	16	1	no	—
286	C₂×C₁₉	#2826	1	1	yes	characteristic
287	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
288	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
289	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
290	#137	—	4	1	no	—
291	#137	—	4	1	no	—
292	AGL(1,ℤ/8)	—	4	1	no	—
293	AGL(1,ℤ/8)	—	4	1	no	—
294	C₂×Q₁₆	—	2	1	no	—
295	C₂×SD₁₆	—	2	1	no	—
296	C₂×SD₁₆	—	2	1	no	—
297	C₂×SD₁₆	—	4	1	no	—
298	C₂×SD₁₆	—	4	1	no	—
299	C₂×SD₁₆	—	4	1	no	—
300	C₂×D₈	—	2	1	no	—
301	#131	—	4	1	no	—
302	#131	—	4	1	no	—
303	C₂×M₁₆	—	4	1	no	—
304	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
305	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
306	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
307	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
308	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
309	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
310	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
311	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
312	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
314	#117	C₂³×C₁₉	1	1	yes	characteristic
315	#117	C₂³×C₁₉	1	1	yes	characteristic
316	#108	—	4	1	no	—
317	#108	—	4	1	no	—
318	#108	—	4	1	no	—
319	#108	—	4	1	no	—
320	#108	—	4	1	no	—
321	C₄⋊C₈	—	4	1	no	—
322	C₄⋊C₈	—	4	1	no	—
323	#104	—	4	1	no	—
324	#104	—	4	1	no	—
325	#103	—	4	1	no	—
326	#103	—	4	1	no	—
327	#102	—	4	1	no	—
328	#102	—	4	1	no	—
329	#101	—	2	1	no	—
330	#101	—	4	1	no	—
331	#101	—	4	1	no	—
332	#101	—	4	1	no	—
333	#100	—	2	1	no	—
334	#100	—	4	1	no	—
335	#100	—	4	1	no	—
336	#100	—	4	1	no	—
337	C₂²⋊C₈	—	4	1	no	—
338	C₁₉	#32871	1	1	yes	characteristic, direct product factor, Sylow
339	C₂⁴	—	2	1	no	—
340	#41	—	2	1	no	—
341	#41	—	2	1	no	—
342	#41	—	2	1	no	—
343	#41	—	2	1	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	#41×C₁₉	1	1	yes	characteristic
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	#41×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
362	Q₁₆	—	4	2	no	—
363	SD₁₆	—	4	2	no	—
364	SD₁₆	—	4	2	no	—
365	SD₁₆	—	4	4	no	—
366	D₈	—	4	2	no	—
367	M₁₆	—	2	1	no	—
368	M₁₆	—	2	1	no	—
369	M₁₆	—	2	1	no	—
370	M₁₆	—	2	1	no	—
371	M₁₆	—	2	1	no	—
372	M₁₆	—	2	1	no	—
373	M₁₆	—	2	1	no	—
374	M₁₆	—	2	1	no	—
375	M₁₆	—	2	1	no	—
376	M₁₆	—	2	1	no	—
377	M₁₆	—	2	1	no	—
378	M₁₆	—	2	1	no	—
379	M₁₆	—	2	1	no	—
380	M₁₆	—	2	1	no	—
381	M₁₆	—	2	1	no	—
382	M₁₆	—	2	1	no	—
383	M₁₆	—	2	1	no	—
384	M₁₆	—	2	1	no	—
385	M₁₆	—	4	2	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	4	2	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	2	1	no	—
402	C₂²⋊C₄	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	16	1	no	—
410	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
411	Q₈	—	2	1	no	—
412	Q₈	—	2	1	no	—
413	Q₈	—	4	1	no	—
414	Q₈	—	4	1	no	—
415	Q₈	—	4	1	no	—
416	Q₈	—	4	1	no	—
417	D₄	—	2	1	no	—
418	D₄	—	2	1	no	—
419	D₄	—	4	1	no	—
420	D₄	—	4	1	no	—
421	D₄	—	4	1	no	—
422	D₄	—	4	1	no	—
423	D₄	—	4	1	no	—
424	D₄	—	4	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
434	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
435	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
436	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
437	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
439	C₈	—	4	1	no	—
440	C₈	—	4	1	no	—
441	C₈	—	4	1	no	—
442	C₈	—	4	1	no	—
443	C₈	—	4	1	no	—
444	C₈	—	4	1	no	—
445	C₈	—	4	1	no	—
446	C₈	—	4	1	no	—
447	C₈	—	4	1	no	—
448	C₈	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	—	16	1	no	—
454	C₂²	—	16	1	no	—
455	C₂²	—	16	1	no	—
456	C₂²	C₁₉×#539	1	1	yes	characteristic
457	C₂²	C₁₉×#562	1	1	yes	characteristic
458	C₂²	C₁₉×#562	1	1	yes	characteristic
459	C₄	—	4	1	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	1	no	—
462	C₄	—	8	1	no	—
463	C₄	C₁₉×#538	1	1	yes	characteristic
464	C₄	C₁₉×#538	1	1	yes	characteristic
465	C₄	C₁₉×#560	1	1	yes	characteristic
466	C₄	C₁₉×#560	1	1	yes	characteristic
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	—	2	1	no	—
470	C₂	—	8	1	no	—
471	C₂	—	16	1	no	—
472	C₂	C₁₉×#2826	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#2826
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2103	C₂	semidirect
2. C₁₉×#2103	C₂	semidirect
3. C₁₉×#2098	C₂	semidirect
4. C₁₉×#2082	C₂	semidirect
5. C₁₉×#2081	C₂	semidirect
6. C₁₉×#2070	C₂	semidirect
7. C₁₉×#2069	C₂	semidirect
8. C₁₉×#2049	C₂	semidirect
10. C₁₉×#2046	C₂	semidirect
11. C₁₉×#2046	C₂	semidirect
14. C₁₉×#1902	C₂	semidirect
15. C₁₉×#1858	C₂	semidirect
168. #32871	C₁₉	direct (N × H)
213. #2103	C₂×C₁₉	semidirect
214. #2103	C₂×C₁₉	semidirect
215. #2098	C₂×C₁₉	semidirect
216. #2082	C₂×C₁₉	semidirect
217. #2081	C₂×C₁₉	semidirect
218. #2070	C₂×C₁₉	semidirect
219. #2069	C₂×C₁₉	semidirect
220. #2049	C₂×C₁₉	semidirect
222. #2046	C₂×C₁₉	semidirect
223. #2046	C₂×C₁₉	semidirect
226. #1902	C₂×C₁₉	semidirect
227. #1858	C₂×C₁₉	semidirect
338. C₁₉	#32871	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×#2103	2
C₁₉×#2098	2
C₁₉×#2082	2
C₁₉×#2081	2
C₁₉×#2070	2
C₁₉×#2069	2
C₁₉×#2049	2
C₁₉×#2048	2
C₁₉×#2046	2
C₁₉×#2019	2
C₁₉×#1903	2
C₁₉×#1902	2
C₁₉×#1858	2
#32871	19

Subgroups — C19×#32871 #18038830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32871 #18038830