Subgroups — C₁₉×#33864 #18039823

Order 4864.

580 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3339	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3280	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2242	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2236	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2234	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2228	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2217	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2215	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2210	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2186	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2184	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₉×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2138	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×#357	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#553	—	2	1	no	—
19	C₁₉×#546	—	2	1	no	—
20	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₉×D₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×D₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#499	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#495	C₂²	1	1	yes	characteristic
27	C₁₉×#482	—	2	1	no	—
28	C₁₉×#481	—	2	1	no	—
29	C₁₉×#478	—	2	1	no	—
30	C₁₉×#467	C₂²	1	1	yes	characteristic
31	C₁₉×#466	C₂²	1	1	yes	characteristic
32	C₁₉×#466	C₂²	1	1	yes	characteristic
33	C₁₉×#466	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#463	—	2	1	no	—
35	C₁₉×#450	—	2	1	no	—
36	C₁₉×#449	—	2	1	no	—
37	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
38	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
39	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
40	C₁₉×#427	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
42	C₁₉×#367	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#366	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#366	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×#358	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#358	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#358	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#357	C₂²	1	1	yes	characteristic
50	C₁₉×#357	C₂²	1	1	yes	characteristic
51	C₁₉×#357	C₂²	1	1	yes	characteristic
52	C₁₉×#357	C₂²	1	1	yes	characteristic
53	C₁₉×#357	C₂²	1	1	yes	characteristic
54	C₁₉×#357	C₂²	1	1	yes	characteristic
55	C₁₉×#357	C₂²	1	1	yes	characteristic, complemented
56	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
57	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
59	C₂×#41×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₁₉×#135	—	2	2	no	—
62	C₁₉×#135	—	4	1	no	—
63	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×SD₁₆×C₁₉	—	2	1	no	—
65	C₂×SD₁₆×C₁₉	—	2	1	no	—
66	C₂×D₈×C₁₉	—	2	2	no	—
67	C₂×D₈×C₁₉	—	2	1	no	—
68	C₂×D₈×C₁₉	—	4	1	no	—
69	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×#126	—	4	1	no	—
75	C₁₉×#125	—	2	1	no	—
76	C₁₉×#124	—	2	1	no	—
77	C₁₉×#123	—	4	1	no	—
78	C₁₉×#123	—	4	1	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×#121	—	2	1	no	—
81	C₁₉×#121	—	2	1	no	—
82	C₁₉×#121	—	2	1	no	—
83	C₁₉×#121	—	4	1	no	—
84	C₁₉×#121	—	4	1	no	—
85	C₁₉×#120	—	4	1	no	—
86	C₄×D₄×C₁₉	—	2	1	no	—
87	C₄×D₄×C₁₉	—	2	1	no	—
88	C₄×D₄×C₁₉	—	4	1	no	—
89	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
90	C₁₉×#117	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
93	C₁₉×SD₃₂	—	4	1	no	—
94	C₁₉×D₁₆	—	2	2	no	—
95	C₁₉×D₁₆	—	4	1	no	—
96	C₂×C₁₆×C₁₉	—	4	1	no	—
97	C₂×C₁₆×C₁₉	—	4	1	no	—
98	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×#107	—	2	1	no	—
103	C₁₉×#107	C₂³	1	1	yes	characteristic
104	C₁₉×#107	C₂³	1	1	yes	characteristic
105	C₁₉×#107	C₂³	1	1	yes	characteristic
106	C₁₉×#107	C₂³	1	1	yes	characteristic
107	C₁₉×#106	—	2	1	no	—
108	C₁₉×#106	—	2	1	no	—
109	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
110	C₁₉×#103	—	2	1	no	—
111	C₁₉×#102	—	2	1	no	—
112	C₁₉×#102	—	2	1	no	—
113	C₁₉×#102	—	2	1	no	—
114	C₁₉×#102	—	2	1	no	—
115	C₁₉×#102	—	2	1	no	—
116	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
117	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
118	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
119	C₂⁴×C₁₉	—	4	1	no	—
120	#41×C₁₉	—	4	2	no	—
121	#41×C₁₉	—	8	1	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	—	2	1	no	—
126	C₂×D₄×C₁₉	—	4	2	no	—
127	C₂×D₄×C₁₉	—	4	1	no	—
128	C₂×D₄×C₁₉	—	4	1	no	—
129	C₂×D₄×C₁₉	—	4	1	no	—
130	C₂×D₄×C₁₉	—	4	1	no	—
131	C₂×D₄×C₁₉	—	4	1	no	—
132	C₂×D₄×C₁₉	—	8	1	no	—
133	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	—	4	1	no	—
135	C₂²×C₄×C₁₉	—	4	1	no	—
136	C₂²×C₄×C₁₉	—	4	1	no	—
137	C₂²×C₄×C₁₉	—	4	1	no	—
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	Q₁₆×C₁₉	—	2	1	no	—
141	Q₁₆×C₁₉	—	2	1	no	—
142	SD₁₆×C₁₉	—	4	2	no	—
143	SD₁₆×C₁₉	—	8	1	no	—
144	D₈×C₁₉	—	2	1	no	—
145	D₈×C₁₉	—	2	1	no	—
146	D₈×C₁₉	—	2	1	no	—
147	D₈×C₁₉	—	2	1	no	—
148	D₈×C₁₉	—	2	1	no	—
149	D₈×C₁₉	—	4	2	no	—
150	D₈×C₁₉	#41	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	4	1	no	—
164	C₄⋊C₄×C₁₉	—	4	1	no	—
165	C₄⋊C₄×C₁₉	—	4	1	no	—
166	C₄⋊C₄×C₁₉	—	4	1	no	—
167	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
168	C₂²⋊C₄×C₁₉	—	4	1	no	—
169	C₂²⋊C₄×C₁₉	—	4	1	no	—
170	C₂²⋊C₄×C₁₉	—	4	1	no	—
171	C₂²⋊C₄×C₁₉	—	4	1	no	—
172	C₂²⋊C₄×C₁₉	—	4	1	no	—
173	C₂²⋊C₄×C₁₉	—	4	1	no	—
174	C₂²⋊C₄×C₁₉	—	4	1	no	—
175	C₂²⋊C₄×C₁₉	—	4	1	no	—
176	C₂²⋊C₄×C₁₉	—	4	1	no	—
177	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
178	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
179	C₄²×C₁₉	—	4	1	no	—
180	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₁₆×C₁₉	—	2	1	no	—
182	C₁₆×C₁₉	—	2	1	no	—
183	C₁₆×C₁₉	—	2	1	no	—
184	C₁₆×C₁₉	—	2	1	no	—
185	#33864	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂³×C₁₉	—	4	1	no	—
187	C₂³×C₁₉	—	4	1	no	—
188	C₂³×C₁₉	—	4	1	no	—
189	C₂³×C₁₉	—	8	2	no	—
190	C₂³×C₁₉	—	8	2	no	—
191	C₂³×C₁₉	—	16	1	no	—
192	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
193	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
194	Q₈×C₁₉	—	4	1	no	—
195	Q₈×C₁₉	—	4	1	no	—
196	D₄×C₁₉	—	2	2	no	—
197	D₄×C₁₉	—	2	2	no	—
198	D₄×C₁₉	—	4	1	no	—
199	D₄×C₁₉	—	4	1	no	—
200	D₄×C₁₉	—	4	1	no	—
201	D₄×C₁₉	—	4	1	no	—
202	D₄×C₁₉	—	4	1	no	—
203	D₄×C₁₉	—	8	2	no	—
204	D₄×C₁₉	—	8	2	no	—
205	D₄×C₁₉	—	8	2	no	—
206	D₄×C₁₉	—	16	1	no	—
207	D₄×C₁₉	—	16	1	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	8	2	no	—
218	C₂×C₄×C₁₉	—	16	1	no	—
219	C₂×C₄×C₁₉	—	16	1	no	—
220	C₂×C₄×C₁₉	—	16	1	no	—
221	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
223	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
226	C₈×C₁₉	—	2	1	no	—
227	C₈×C₁₉	—	2	1	no	—
228	C₈×C₁₉	—	2	1	no	—
229	C₈×C₁₉	C₂×#41	1	1	yes	characteristic
230	C₈×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
231	#3339	C₂×C₁₉	1	1	yes	characteristic, complemented
232	#3280	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#2242	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#2236	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#2234	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#2228	C₂×C₁₉	1	1	yes	characteristic, complemented
237	#2217	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#2215	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#2210	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#2186	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#2184	C₂×C₁₉	1	1	yes	characteristic, complemented
242	C₄×D₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
243	D₄×C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
244	#2138	C₂×C₁₉	1	1	yes	characteristic, complemented
245	C₂×#357	C₂×C₁₉	1	1	yes	characteristic, complemented
246	C₂²×C₁₉	—	2	1	no	—
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	2	1	no	—
249	C₂²×C₁₉	—	2	1	no	—
250	C₂²×C₁₉	—	2	1	no	—
251	C₂²×C₁₉	—	4	2	no	—
252	C₂²×C₁₉	—	8	1	no	—
253	C₂²×C₁₉	—	8	1	no	—
254	C₂²×C₁₉	—	8	1	no	—
255	C₂²×C₁₉	—	8	1	no	—
256	C₂²×C₁₉	—	8	1	no	—
257	C₂²×C₁₉	—	8	1	no	—
258	C₂²×C₁₉	—	8	1	no	—
259	C₂²×C₁₉	—	8	1	no	—
260	C₂²×C₁₉	—	16	4	no	—
261	C₂²×C₁₉	#508	1	2	yes	—
262	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
263	C₄×C₁₉	—	2	1	no	—
264	C₄×C₁₉	—	2	1	no	—
265	C₄×C₁₉	—	2	1	no	—
266	C₄×C₁₉	—	2	1	no	—
267	C₄×C₁₉	—	8	1	no	—
268	C₄×C₁₉	—	8	1	no	—
269	C₄×C₁₉	—	8	1	no	—
270	C₄×C₁₉	—	8	1	no	—
271	C₄×C₁₉	—	8	1	no	—
272	C₄×C₁₉	#546	1	1	yes	characteristic
273	C₄×C₁₉	#577	1	1	yes	characteristic
274	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
275	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
276	#553	—	2	1	no	—
277	#546	—	2	1	no	—
278	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic, complemented
279	C₂×D₁₆	C₂²×C₁₉	1	1	yes	characteristic
280	C₂×D₁₆	C₂²×C₁₉	1	1	yes	characteristic
281	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
282	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
283	#499	C₂²×C₁₉	1	1	yes	characteristic, complemented
284	#495	C₂²×C₁₉	1	1	yes	characteristic
285	#482	—	2	1	no	—
286	#481	—	2	1	no	—
287	#478	—	2	1	no	—
288	#467	C₂²×C₁₉	1	1	yes	characteristic
289	#466	C₂²×C₁₉	1	1	yes	characteristic
290	#466	C₂²×C₁₉	1	1	yes	characteristic
291	#466	C₂²×C₁₉	1	1	yes	characteristic, complemented
292	#463	—	2	1	no	—
293	#450	—	2	1	no	—
294	#449	—	2	1	no	—
295	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
296	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
297	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
298	#427	C₂²×C₁₉	1	1	yes	characteristic, complemented
299	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
300	#367	C₂²×C₁₉	1	1	yes	characteristic, complemented
301	#366	C₂²×C₁₉	1	1	yes	characteristic, complemented
302	#366	C₂²×C₁₉	1	1	yes	characteristic, complemented
303	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
304	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
305	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
306	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
307	#357	C₂²×C₁₉	1	1	yes	characteristic
308	#357	C₂²×C₁₉	1	1	yes	characteristic
309	#357	C₂²×C₁₉	1	1	yes	characteristic
310	#357	C₂²×C₁₉	1	1	yes	characteristic
311	#357	C₂²×C₁₉	1	1	yes	characteristic
312	#357	C₂²×C₁₉	1	1	yes	characteristic
313	#357	C₂²×C₁₉	1	1	yes	characteristic, complemented
314	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
315	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
316	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
317	C₂×C₁₉	—	2	2	no	—
318	C₂×C₁₉	—	4	1	no	—
319	C₂×C₁₉	—	8	2	no	—
320	C₂×C₁₉	—	16	1	no	—
321	C₂×C₁₉	—	16	1	no	—
322	C₂×C₁₉	#3294	1	1	yes	characteristic
323	C₂×C₁₉	C₂×#508	1	1	yes	characteristic
324	C₂×C₁₉	#3415	1	1	yes	characteristic
325	C₂×#41	—	2	1	no	—
326	C₂²×D₄	—	2	1	no	—
327	#135	—	2	2	no	—
328	#135	—	4	1	no	—
329	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
330	C₂×SD₁₆	—	2	1	no	—
331	C₂×SD₁₆	—	2	1	no	—
332	C₂×D₈	—	2	2	no	—
333	C₂×D₈	—	2	1	no	—
334	C₂×D₈	—	4	1	no	—
335	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
336	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
337	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
340	#126	—	4	1	no	—
341	#125	—	2	1	no	—
342	#124	—	2	1	no	—
343	#123	—	4	1	no	—
344	#123	—	4	1	no	—
345	C₂²⋊Q₈	—	2	1	no	—
346	#121	—	2	1	no	—
347	#121	—	2	1	no	—
348	#121	—	2	1	no	—
349	#121	—	4	1	no	—
350	#121	—	4	1	no	—
351	#120	—	4	1	no	—
352	C₄×D₄	—	2	1	no	—
353	C₄×D₄	—	2	1	no	—
354	C₄×D₄	—	4	1	no	—
355	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
356	#117	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	4	1	no	—
359	SD₃₂	—	4	1	no	—
360	D₁₆	—	2	2	no	—
361	D₁₆	—	4	1	no	—
362	C₂×C₁₆	—	4	1	no	—
363	C₂×C₁₆	—	4	1	no	—
364	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
365	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
366	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
367	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
368	#107	—	2	1	no	—
369	#107	C₂³×C₁₉	1	1	yes	characteristic
370	#107	C₂³×C₁₉	1	1	yes	characteristic
371	#107	C₂³×C₁₉	1	1	yes	characteristic
372	#107	C₂³×C₁₉	1	1	yes	characteristic
373	#106	—	2	1	no	—
374	#106	—	2	1	no	—
375	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
376	#103	—	2	1	no	—
377	#102	—	2	1	no	—
378	#102	—	2	1	no	—
379	#102	—	2	1	no	—
380	#102	—	2	1	no	—
381	#102	—	2	1	no	—
382	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
383	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
384	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
385	C₁₉	#33864	1	1	yes	characteristic, direct product factor, Sylow
386	C₂⁴	—	4	1	no	—
387	#41	—	4	2	no	—
388	#41	—	8	1	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	4	2	no	—
394	C₂×D₄	—	4	1	no	—
395	C₂×D₄	—	4	1	no	—
396	C₂×D₄	—	4	1	no	—
397	C₂×D₄	—	4	1	no	—
398	C₂×D₄	—	4	1	no	—
399	C₂×D₄	—	8	1	no	—
400	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
401	C₂²×C₄	—	4	1	no	—
402	C₂²×C₄	—	4	1	no	—
403	C₂²×C₄	—	4	1	no	—
404	C₂²×C₄	—	4	1	no	—
405	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
407	Q₁₆	—	2	1	no	—
408	Q₁₆	—	2	1	no	—
409	SD₁₆	—	4	2	no	—
410	SD₁₆	—	8	1	no	—
411	D₈	—	2	1	no	—
412	D₈	—	2	1	no	—
413	D₈	—	2	1	no	—
414	D₈	—	2	1	no	—
415	D₈	—	2	1	no	—
416	D₈	—	4	2	no	—
417	D₈	#41×C₁₉	1	2	yes	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
424	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
425	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	4	1	no	—
431	C₄⋊C₄	—	4	1	no	—
432	C₄⋊C₄	—	4	1	no	—
433	C₄⋊C₄	—	4	1	no	—
434	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
435	C₂²⋊C₄	—	4	1	no	—
436	C₂²⋊C₄	—	4	1	no	—
437	C₂²⋊C₄	—	4	1	no	—
438	C₂²⋊C₄	—	4	1	no	—
439	C₂²⋊C₄	—	4	1	no	—
440	C₂²⋊C₄	—	4	1	no	—
441	C₂²⋊C₄	—	4	1	no	—
442	C₂²⋊C₄	—	4	1	no	—
443	C₂²⋊C₄	—	4	1	no	—
444	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
445	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
446	C₄²	—	4	1	no	—
447	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₁₆	—	2	1	no	—
449	C₁₆	—	2	1	no	—
450	C₁₆	—	2	1	no	—
451	C₁₆	—	2	1	no	—
452	C₂³	—	4	1	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	1	no	—
455	C₂³	—	8	2	no	—
456	C₂³	—	8	2	no	—
457	C₂³	—	16	1	no	—
458	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
459	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
460	Q₈	—	4	1	no	—
461	Q₈	—	4	1	no	—
462	D₄	—	2	2	no	—
463	D₄	—	2	2	no	—
464	D₄	—	4	1	no	—
465	D₄	—	4	1	no	—
466	D₄	—	4	1	no	—
467	D₄	—	4	1	no	—
468	D₄	—	4	1	no	—
469	D₄	—	8	2	no	—
470	D₄	—	8	2	no	—
471	D₄	—	8	2	no	—
472	D₄	—	16	1	no	—
473	D₄	—	16	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	8	2	no	—
484	C₂×C₄	—	16	1	no	—
485	C₂×C₄	—	16	1	no	—
486	C₂×C₄	—	16	1	no	—
487	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
488	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
489	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
490	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
492	C₈	—	2	1	no	—
493	C₈	—	2	1	no	—
494	C₈	—	2	1	no	—
495	C₈	C₂×#41×C₁₉	1	1	yes	characteristic
496	C₈	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	8	1	no	—
504	C₂²	—	8	1	no	—
505	C₂²	—	8	1	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	8	1	no	—
508	C₂²	—	8	1	no	—
509	C₂²	—	8	1	no	—
510	C₂²	—	8	1	no	—
511	C₂²	—	16	4	no	—
512	C₂²	C₁₉×#508	1	2	yes	—
513	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	2	1	no	—
518	C₄	—	8	1	no	—
519	C₄	—	8	1	no	—
520	C₄	—	8	1	no	—
521	C₄	—	8	1	no	—
522	C₄	—	8	1	no	—
523	C₄	C₁₉×#546	1	1	yes	characteristic
524	C₄	C₁₉×#577	1	1	yes	characteristic
525	C₂	—	2	2	no	—
526	C₂	—	4	1	no	—
527	C₂	—	8	2	no	—
528	C₂	—	16	1	no	—
529	C₂	—	16	1	no	—
530	C₂	C₁₉×#3294	1	1	yes	characteristic
531	C₂	C₂×C₁₉×#508	1	1	yes	characteristic
532	C₂	C₁₉×#3415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×D₄×C₁₉ ◁ C₈×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3339	C₂	semidirect
2. C₁₉×#3280	C₂	semidirect
3. C₁₉×#2242	C₂	semidirect
4. C₁₉×#2236	C₂	semidirect
5. C₁₉×#2234	C₂	semidirect
6. C₁₉×#2228	C₂	semidirect
7. C₁₉×#2217	C₂	semidirect
8. C₁₉×#2215	C₂	semidirect
9. C₁₉×#2210	C₂	semidirect
10. C₁₉×#2186	C₂	semidirect
11. C₁₉×#2184	C₂	semidirect
12. C₄×C₁₉×D₁₆	C₂	semidirect
13. D₄×C₁₆×C₁₉	C₂	semidirect
14. C₁₉×#2138	C₂	semidirect
15. C₂×C₁₉×#357	C₂	semidirect
20. C₂×C₁₉×SD₃₂	C₂²	semidirect
24. C₂²×C₁₆×C₁₉	C₂²	semidirect
25. C₁₉×#499	C₂²	semidirect
33. C₁₉×#466	C₂²	semidirect
38. C₄×D₈×C₁₉	C₂²	semidirect
40. C₁₉×#427	C₂²	semidirect
42. C₁₉×#367	C₂²	semidirect
43. C₁₉×#366	C₂²	semidirect
44. C₁₉×#366	C₂²	semidirect
45. C₁₉×C₄⋊C₁₆	C₂²	semidirect
46. C₁₉×#358	C₂²	semidirect
47. C₁₉×#358	C₂²	semidirect
48. C₁₉×#358	C₂²	semidirect
55. C₁₉×#357	C₂²	semidirect
57. C₁₉×C₂²⋊C₁₆	C₂²	semidirect
58. C₄×C₁₆×C₁₉	C₂²	semidirect
185. #33864	C₁₉	direct (N × H)
231. #3339	C₂×C₁₉	semidirect
232. #3280	C₂×C₁₉	semidirect
233. #2242	C₂×C₁₉	semidirect
234. #2236	C₂×C₁₉	semidirect
235. #2234	C₂×C₁₉	semidirect
236. #2228	C₂×C₁₉	semidirect
237. #2217	C₂×C₁₉	semidirect
238. #2215	C₂×C₁₉	semidirect
239. #2210	C₂×C₁₉	semidirect
240. #2186	C₂×C₁₉	semidirect
241. #2184	C₂×C₁₉	semidirect
242. C₄×D₁₆	C₂×C₁₉	semidirect
243. D₄×C₁₆	C₂×C₁₉	semidirect
244. #2138	C₂×C₁₉	semidirect
245. C₂×#357	C₂×C₁₉	semidirect
278. C₂×SD₃₂	C₂²×C₁₉	semidirect
282. C₂²×C₁₆	C₂²×C₁₉	semidirect
283. #499	C₂²×C₁₉	semidirect
291. #466	C₂²×C₁₉	semidirect
296. C₄×D₈	C₂²×C₁₉	semidirect
298. #427	C₂²×C₁₉	semidirect
300. #367	C₂²×C₁₉	semidirect
301. #366	C₂²×C₁₉	semidirect
302. #366	C₂²×C₁₉	semidirect
303. C₄⋊C₁₆	C₂²×C₁₉	semidirect
304. #358	C₂²×C₁₉	semidirect
305. #358	C₂²×C₁₉	semidirect
306. #358	C₂²×C₁₉	semidirect
313. #357	C₂²×C₁₉	semidirect
315. C₂²⋊C₁₆	C₂²×C₁₉	semidirect
316. C₄×C₁₆	C₂²×C₁₉	semidirect
385. C₁₉	#33864	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×#3339	2
C₁₉×#3280	2
C₁₉×#2242	2
C₁₉×#2236	2
C₁₉×#2234	2
C₁₉×#2228	2
C₁₉×#2217	2
C₁₉×#2215	2
C₁₉×#2210	2
C₁₉×#2186	2
C₁₉×#2184	2
C₄×C₁₉×D₁₆	2
D₄×C₁₆×C₁₉	2
C₁₉×#2138	2
C₂×C₁₉×#357	2
#33864	19

Subgroups — C19×#33864 #18039823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33864 #18039823