Subgroups — C₁₉×#33863 #18039822

Order 4864.

568 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3336	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3280	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2242	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2235	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×#2216	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2211	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2189	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2187	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₉×SD₃₂	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×#552	—	2	1	no	—
19	C₁₉×#546	—	2	1	no	—
20	C₂×C₁₉×Q₃₂	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×SD₃₂	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×#485	—	2	1	no	—
28	C₁₉×#483	—	2	1	no	—
29	C₁₉×#479	—	2	1	no	—
30	C₁₉×#467	C₂²	1	1	yes	characteristic
31	C₁₉×#467	C₂²	1	1	yes	characteristic
32	C₁₉×#467	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#466	C₂²	1	1	yes	characteristic
34	C₁₉×#463	—	2	1	no	—
35	C₁₉×#450	—	2	1	no	—
36	C₁₉×#449	—	2	1	no	—
37	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
38	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
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×#367	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×#358	C₂²	1	1	yes	characteristic, complemented
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
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×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×SD₁₆×C₁₉	—	2	1	no	—
66	C₂×SD₁₆×C₁₉	—	2	1	no	—
67	C₂×D₈×C₁₉	—	2	2	no	—
68	C₂×D₈×C₁₉	—	2	1	no	—
69	C₂×D₈×C₁₉	—	4	1	no	—
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×#125	—	4	1	no	—
77	C₁₉×#124	—	2	1	no	—
78	C₁₉×#123	—	4	1	no	—
79	C₁₉×#123	—	4	1	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×C₂²⋊Q₈	—	2	1	no	—
82	C₁₉×C₂²⋊Q₈	—	2	1	no	—
83	C₁₉×#121	—	2	1	no	—
84	C₁₉×#121	—	4	1	no	—
85	C₁₉×#120	—	4	1	no	—
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₄×D₄×C₁₉	—	2	1	no	—
88	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
89	C₁₉×#117	—	2	1	no	—
90	C₁₉×#117	—	4	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
93	C₁₉×Q₃₂	—	4	1	no	—
94	C₁₉×SD₃₂	—	2	2	no	—
95	C₁₉×SD₃₂	—	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×#103	—	2	1	no	—
112	C₁₉×#103	—	2	1	no	—
113	C₁₉×#103	—	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×Q₈×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	—	8	1	no	—
131	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	—	4	1	no	—
133	C₂²×C₄×C₁₉	—	4	1	no	—
134	C₂²×C₄×C₁₉	—	4	1	no	—
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	Q₁₆×C₁₉	—	2	1	no	—
138	Q₁₆×C₁₉	—	2	1	no	—
139	Q₁₆×C₁₉	—	2	1	no	—
140	Q₁₆×C₁₉	—	2	1	no	—
141	SD₁₆×C₁₉	—	4	2	no	—
142	SD₁₆×C₁₉	—	8	1	no	—
143	D₈×C₁₉	—	2	1	no	—
144	D₈×C₁₉	—	2	1	no	—
145	D₈×C₁₉	—	2	1	no	—
146	D₈×C₁₉	—	4	2	no	—
147	D₈×C₁₉	#41	1	2	yes	—
148	C₂×C₈×C₁₉	—	2	1	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	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	4	1	no	—
161	C₄⋊C₄×C₁₉	—	4	1	no	—
162	C₄⋊C₄×C₁₉	—	4	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	D₈	1	1	yes	characteristic
177	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
178	C₄²×C₁₉	—	4	1	no	—
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	#33863	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	—	8	2	no	—
189	C₂³×C₁₉	—	8	2	no	—
190	C₂³×C₁₉	—	16	1	no	—
191	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
192	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
193	Q₈×C₁₉	—	4	1	no	—
194	Q₈×C₁₉	—	4	1	no	—
195	Q₈×C₁₉	—	4	1	no	—
196	Q₈×C₁₉	—	4	1	no	—
197	D₄×C₁₉	—	2	2	no	—
198	D₄×C₁₉	—	2	2	no	—
199	D₄×C₁₉	—	4	1	no	—
200	D₄×C₁₉	—	4	1	no	—
201	D₄×C₁₉	—	4	1	no	—
202	D₄×C₁₉	—	8	2	no	—
203	D₄×C₁₉	—	8	2	no	—
204	D₄×C₁₉	—	16	1	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	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	—	8	2	no	—
216	C₂×C₄×C₁₉	—	8	2	no	—
217	C₂×C₄×C₁₉	—	16	1	no	—
218	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
223	C₈×C₁₉	—	2	1	no	—
224	C₈×C₁₉	—	2	1	no	—
225	C₈×C₁₉	—	2	1	no	—
226	C₈×C₁₉	C₂×#41	1	1	yes	characteristic
227	C₈×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
228	#3336	C₂×C₁₉	1	1	yes	characteristic, complemented
229	#3280	C₂×C₁₉	1	1	yes	characteristic
230	#2242	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#2235	C₂×C₁₉	1	1	yes	characteristic, complemented
232	#2234	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#2228	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#2217	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#2216	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#2211	C₂×C₁₉	1	1	yes	characteristic, complemented
237	#2189	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#2187	C₂×C₁₉	1	1	yes	characteristic, complemented
239	C₄×SD₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
240	D₄×C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#2138	C₂×C₁₉	1	1	yes	characteristic, complemented
242	C₂×#357	C₂×C₁₉	1	1	yes	characteristic, complemented
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	2	1	no	—
245	C₂²×C₁₉	—	2	1	no	—
246	C₂²×C₁₉	—	2	1	no	—
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	4	2	no	—
249	C₂²×C₁₉	—	8	1	no	—
250	C₂²×C₁₉	—	8	1	no	—
251	C₂²×C₁₉	—	8	1	no	—
252	C₂²×C₁₉	—	8	1	no	—
253	C₂²×C₁₉	—	8	1	no	—
254	C₂²×C₁₉	—	16	4	no	—
255	C₂²×C₁₉	#508	1	2	yes	—
256	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
257	C₄×C₁₉	—	2	1	no	—
258	C₄×C₁₉	—	2	1	no	—
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	2	1	no	—
261	C₄×C₁₉	—	8	1	no	—
262	C₄×C₁₉	—	8	1	no	—
263	C₄×C₁₉	—	8	1	no	—
264	C₄×C₁₉	—	8	1	no	—
265	C₄×C₁₉	—	8	1	no	—
266	C₄×C₁₉	—	8	1	no	—
267	C₄×C₁₉	#546	1	1	yes	characteristic
268	C₄×C₁₉	#577	1	1	yes	characteristic
269	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
270	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
271	#552	—	2	1	no	—
272	#546	—	2	1	no	—
273	C₂×Q₃₂	C₂²×C₁₉	1	1	yes	characteristic, complemented
274	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
275	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
276	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
277	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
278	#499	C₂²×C₁₉	1	1	yes	characteristic, complemented
279	#495	C₂²×C₁₉	1	1	yes	characteristic
280	#485	—	2	1	no	—
281	#483	—	2	1	no	—
282	#479	—	2	1	no	—
283	#467	C₂²×C₁₉	1	1	yes	characteristic
284	#467	C₂²×C₁₉	1	1	yes	characteristic
285	#467	C₂²×C₁₉	1	1	yes	characteristic, complemented
286	#466	C₂²×C₁₉	1	1	yes	characteristic
287	#463	—	2	1	no	—
288	#450	—	2	1	no	—
289	#449	—	2	1	no	—
290	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
291	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
292	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
293	#427	C₂²×C₁₉	1	1	yes	characteristic, complemented
294	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
295	#367	C₂²×C₁₉	1	1	yes	characteristic, complemented
296	#367	C₂²×C₁₉	1	1	yes	characteristic, complemented
297	#366	C₂²×C₁₉	1	1	yes	characteristic, complemented
298	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
299	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
300	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
301	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
302	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
303	#357	C₂²×C₁₉	1	1	yes	characteristic
304	#357	C₂²×C₁₉	1	1	yes	characteristic
305	#357	C₂²×C₁₉	1	1	yes	characteristic
306	#357	C₂²×C₁₉	1	1	yes	characteristic
307	#357	C₂²×C₁₉	1	1	yes	characteristic
308	#357	C₂²×C₁₉	1	1	yes	characteristic
309	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
310	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
311	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
312	C₂×C₁₉	—	2	2	no	—
313	C₂×C₁₉	—	4	1	no	—
314	C₂×C₁₉	—	8	2	no	—
315	C₂×C₁₉	—	16	1	no	—
316	C₂×C₁₉	#3294	1	1	yes	characteristic
317	C₂×C₁₉	C₂×#508	1	1	yes	characteristic
318	C₂×C₁₉	#3416	1	1	yes	characteristic
319	C₂×#41	—	2	1	no	—
320	C₂²×D₄	—	2	1	no	—
321	#135	—	2	2	no	—
322	#135	—	4	1	no	—
323	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
324	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
325	C₂×SD₁₆	—	2	1	no	—
326	C₂×SD₁₆	—	2	1	no	—
327	C₂×D₈	—	2	2	no	—
328	C₂×D₈	—	2	1	no	—
329	C₂×D₈	—	4	1	no	—
330	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
331	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
333	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
334	#126	—	4	1	no	—
335	#125	—	2	1	no	—
336	#125	—	4	1	no	—
337	#124	—	2	1	no	—
338	#123	—	4	1	no	—
339	#123	—	4	1	no	—
340	C₂²⋊Q₈	—	2	1	no	—
341	C₂²⋊Q₈	—	2	1	no	—
342	C₂²⋊Q₈	—	2	1	no	—
343	#121	—	2	1	no	—
344	#121	—	4	1	no	—
345	#120	—	4	1	no	—
346	C₄×Q₈	—	2	1	no	—
347	C₄×D₄	—	2	1	no	—
348	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
349	#117	—	2	1	no	—
350	#117	—	4	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	4	1	no	—
353	Q₃₂	—	4	1	no	—
354	SD₃₂	—	2	2	no	—
355	SD₃₂	—	4	1	no	—
356	C₂×C₁₆	—	4	1	no	—
357	C₂×C₁₆	—	4	1	no	—
358	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
359	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
360	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
361	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
362	#107	—	2	1	no	—
363	#107	C₂³×C₁₉	1	1	yes	characteristic
364	#107	C₂³×C₁₉	1	1	yes	characteristic
365	#107	C₂³×C₁₉	1	1	yes	characteristic
366	#107	C₂³×C₁₉	1	1	yes	characteristic
367	#106	—	2	1	no	—
368	#106	—	2	1	no	—
369	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
370	#103	—	2	1	no	—
371	#103	—	2	1	no	—
372	#103	—	2	1	no	—
373	#103	—	2	1	no	—
374	#102	—	2	1	no	—
375	#102	—	2	1	no	—
376	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
377	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
378	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
379	C₁₉	#33863	1	1	yes	characteristic, direct product factor, Sylow
380	C₂⁴	—	4	1	no	—
381	#41	—	4	2	no	—
382	#41	—	8	1	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	4	2	no	—
388	C₂×D₄	—	4	1	no	—
389	C₂×D₄	—	4	1	no	—
390	C₂×D₄	—	4	1	no	—
391	C₂×D₄	—	8	1	no	—
392	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	4	1	no	—
395	C₂²×C₄	—	4	1	no	—
396	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
398	Q₁₆	—	2	1	no	—
399	Q₁₆	—	2	1	no	—
400	Q₁₆	—	2	1	no	—
401	Q₁₆	—	2	1	no	—
402	SD₁₆	—	4	2	no	—
403	SD₁₆	—	8	1	no	—
404	D₈	—	2	1	no	—
405	D₈	—	2	1	no	—
406	D₈	—	2	1	no	—
407	D₈	—	4	2	no	—
408	D₈	#41×C₁₉	1	2	yes	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
415	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
416	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	4	1	no	—
422	C₄⋊C₄	—	4	1	no	—
423	C₄⋊C₄	—	4	1	no	—
424	C₄⋊C₄	—	4	1	no	—
425	C₄⋊C₄	—	4	1	no	—
426	C₄⋊C₄	—	4	1	no	—
427	C₄⋊C₄	—	4	1	no	—
428	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
429	C₂²⋊C₄	—	4	1	no	—
430	C₂²⋊C₄	—	4	1	no	—
431	C₂²⋊C₄	—	4	1	no	—
432	C₂²⋊C₄	—	4	1	no	—
433	C₂²⋊C₄	—	4	1	no	—
434	C₂²⋊C₄	—	4	1	no	—
435	C₂²⋊C₄	—	4	1	no	—
436	C₂²⋊C₄	—	4	1	no	—
437	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
438	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
439	C₄²	—	4	1	no	—
440	C₄²	—	4	1	no	—
441	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₁₆	—	2	1	no	—
443	C₁₆	—	2	1	no	—
444	C₁₆	—	2	1	no	—
445	C₁₆	—	2	1	no	—
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	8	2	no	—
449	C₂³	—	8	2	no	—
450	C₂³	—	16	1	no	—
451	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
452	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
453	Q₈	—	4	1	no	—
454	Q₈	—	4	1	no	—
455	Q₈	—	4	1	no	—
456	Q₈	—	4	1	no	—
457	D₄	—	2	2	no	—
458	D₄	—	2	2	no	—
459	D₄	—	4	1	no	—
460	D₄	—	4	1	no	—
461	D₄	—	4	1	no	—
462	D₄	—	8	2	no	—
463	D₄	—	8	2	no	—
464	D₄	—	16	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	8	2	no	—
476	C₂×C₄	—	8	2	no	—
477	C₂×C₄	—	16	1	no	—
478	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
479	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
480	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
481	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
483	C₈	—	2	1	no	—
484	C₈	—	2	1	no	—
485	C₈	—	2	1	no	—
486	C₈	C₂×#41×C₁₉	1	1	yes	characteristic
487	C₈	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	8	1	no	—
495	C₂²	—	8	1	no	—
496	C₂²	—	8	1	no	—
497	C₂²	—	8	1	no	—
498	C₂²	—	8	1	no	—
499	C₂²	—	16	4	no	—
500	C₂²	C₁₉×#508	1	2	yes	—
501	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	8	1	no	—
507	C₄	—	8	1	no	—
508	C₄	—	8	1	no	—
509	C₄	—	8	1	no	—
510	C₄	—	8	1	no	—
511	C₄	—	8	1	no	—
512	C₄	C₁₉×#546	1	1	yes	characteristic
513	C₄	C₁₉×#577	1	1	yes	characteristic
514	C₂	—	2	2	no	—
515	C₂	—	4	1	no	—
516	C₂	—	8	2	no	—
517	C₂	—	16	1	no	—
518	C₂	C₁₉×#3294	1	1	yes	characteristic
519	C₂	C₂×C₁₉×#508	1	1	yes	characteristic
520	C₂	C₁₉×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	C₁₉×#3280	C₂
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×#3336	C₂	semidirect
3. C₁₉×#2242	C₂	semidirect
4. C₁₉×#2235	C₂	semidirect
5. C₁₉×#2234	C₂	semidirect
6. C₁₉×#2228	C₂	semidirect
7. C₁₉×#2217	C₂	semidirect
8. C₁₉×#2216	C₂	semidirect
9. C₁₉×#2211	C₂	semidirect
10. C₁₉×#2189	C₂	semidirect
11. C₁₉×#2187	C₂	semidirect
12. C₄×C₁₉×SD₃₂	C₂	semidirect
13. D₄×C₁₆×C₁₉	C₂	semidirect
14. C₁₉×#2138	C₂	semidirect
15. C₂×C₁₉×#357	C₂	semidirect
20. C₂×C₁₉×Q₃₂	C₂²	semidirect
24. C₂²×C₁₆×C₁₉	C₂²	semidirect
25. C₁₉×#499	C₂²	semidirect
32. C₁₉×#467	C₂²	semidirect
37. C₄×Q₁₆×C₁₉	C₂²	semidirect
40. C₁₉×#427	C₂²	semidirect
42. C₁₉×#367	C₂²	semidirect
43. C₁₉×#367	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
49. C₁₉×#358	C₂²	semidirect
57. C₁₉×C₂²⋊C₁₆	C₂²	semidirect
58. C₄×C₁₆×C₁₉	C₂²	semidirect
185. #33863	C₁₉	direct (N × H)
228. #3336	C₂×C₁₉	semidirect
230. #2242	C₂×C₁₉	semidirect
231. #2235	C₂×C₁₉	semidirect
232. #2234	C₂×C₁₉	semidirect
233. #2228	C₂×C₁₉	semidirect
234. #2217	C₂×C₁₉	semidirect
235. #2216	C₂×C₁₉	semidirect
236. #2211	C₂×C₁₉	semidirect
237. #2189	C₂×C₁₉	semidirect
238. #2187	C₂×C₁₉	semidirect
239. C₄×SD₃₂	C₂×C₁₉	semidirect
240. D₄×C₁₆	C₂×C₁₉	semidirect
241. #2138	C₂×C₁₉	semidirect
242. C₂×#357	C₂×C₁₉	semidirect
273. C₂×Q₃₂	C₂²×C₁₉	semidirect
277. C₂²×C₁₆	C₂²×C₁₉	semidirect
278. #499	C₂²×C₁₉	semidirect
285. #467	C₂²×C₁₉	semidirect
290. C₄×Q₁₆	C₂²×C₁₉	semidirect
293. #427	C₂²×C₁₉	semidirect
295. #367	C₂²×C₁₉	semidirect
296. #367	C₂²×C₁₉	semidirect
297. #366	C₂²×C₁₉	semidirect
298. C₄⋊C₁₆	C₂²×C₁₉	semidirect
299. #358	C₂²×C₁₉	semidirect
300. #358	C₂²×C₁₉	semidirect
301. #358	C₂²×C₁₉	semidirect
302. #358	C₂²×C₁₉	semidirect
310. C₂²⋊C₁₆	C₂²×C₁₉	semidirect
311. C₄×C₁₆	C₂²×C₁₉	semidirect
379. C₁₉	#33863	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×#3336	2
C₁₉×#3280	2
C₁₉×#2242	2
C₁₉×#2235	2
C₁₉×#2234	2
C₁₉×#2228	2
C₁₉×#2217	2
C₁₉×#2216	2
C₁₉×#2211	2
C₁₉×#2189	2
C₁₉×#2187	2
C₄×C₁₉×SD₃₂	2
D₄×C₁₆×C₁₉	2
C₁₉×#2138	2
C₂×C₁₉×#357	2
#33863	19

Subgroups — C19×#33863 #18039822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33863 #18039822