Subgroups — C₁₉×#33877 #18039836

Order 4864.

610 conjugacy classes of subgroups.

The subgroup lattice has 542 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	D₄×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2244	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2234	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2232	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2228	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2220	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2217	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2207	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2187	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2187	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2175	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2140	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×#357	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#552	—	2	1	no	—
19	D₄²×C₁₉	—	2	1	no	—
20	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#499	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#493	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, complemented
31	C₁₉×#467	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#466	C₂²	1	1	yes	characteristic
33	C₁₉×#466	C₂²	1	1	yes	characteristic
34	C₁₉×#459	—	2	1	no	—
35	C₁₉×#447	—	2	1	no	—
36	C₁₉×#447	—	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, complemented
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×#357	C₂²	1	1	yes	characteristic
48	C₁₉×#357	C₂²	1	1	yes	characteristic
49	C₁₉×#357	C₂²	1	1	yes	characteristic
50	C₁₉×#357	C₂²	1	1	yes	characteristic, complemented
51	C₁₉×#357	C₂²	1	1	yes	characteristic, complemented
52	C₁₉×#357	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#357	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#357	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×#357	C₂²	1	1	yes	characteristic, complemented
56	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#346	C₂²	1	1	yes	characteristic, complemented
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	—	4	1	no	—
62	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×D₈×C₁₉	—	2	2	no	—
64	C₂×D₈×C₁₉	—	2	2	no	—
65	C₂×D₈×C₁₉	—	2	1	no	—
66	C₂×D₈×C₁₉	—	2	1	no	—
67	C₂×D₈×C₁₉	—	2	1	no	—
68	C₂×D₈×C₁₉	—	4	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	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×#127	—	2	1	no	—
76	C₁₉×#126	—	4	1	no	—
77	C₁₉×#125	—	2	1	no	—
78	C₁₉×#125	—	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×#121	—	2	1	no	—
83	C₁₉×#121	—	2	1	no	—
84	C₁₉×#121	—	4	1	no	—
85	C₁₉×#120	—	4	1	no	—
86	C₁₉×#120	—	4	1	no	—
87	C₄×Q₈×C₁₉	—	2	1	no	—
88	C₄×D₄×C₁₉	—	2	1	no	—
89	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
90	C₁₉×#117	—	2	1	no	—
91	C₁₉×#117	—	4	1	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₁₉×SD₃₂	—	2	2	no	—
94	C₁₉×SD₃₂	—	4	1	no	—
95	C₁₉×SD₃₂	—	4	1	no	—
96	C₁₉×M₃₂	—	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×#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	C₂⁴×C₁₉	—	4	1	no	—
121	C₂×Q₈×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	—	4	2	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	—	4	1	no	—
133	C₂×D₄×C₁₉	—	8	1	no	—
134	C₂×D₄×C₁₉	—	8	1	no	—
135	C₂×D₄×C₁₉	—	8	4	no	—
136	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	—	4	1	no	—
138	C₂²×C₄×C₁₉	—	4	1	no	—
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	Q₁₆×C₁₉	—	2	1	no	—
142	Q₁₆×C₁₉	—	2	1	no	—
143	D₈×C₁₉	—	2	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	—	4	2	no	—
149	D₈×C₁₉	—	4	2	no	—
150	D₈×C₁₉	—	8	1	no	—
151	D₈×C₁₉	#41	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
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	—	2	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	—	4	1	no	—
168	C₄⋊C₄×C₁₉	—	4	1	no	—
169	C₄⋊C₄×C₁₉	—	4	1	no	—
170	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
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	—	4	1	no	—
181	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₁₆×C₁₉	—	2	1	no	—
183	C₁₆×C₁₉	—	2	1	no	—
184	C₁₆×C₁₉	—	2	1	no	—
185	C₁₆×C₁₉	—	2	1	no	—
186	#33877	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂³×C₁₉	—	4	1	no	—
188	C₂³×C₁₉	—	4	1	no	—
189	C₂³×C₁₉	—	4	1	no	—
190	C₂³×C₁₉	—	8	2	no	—
191	C₂³×C₁₉	—	8	2	no	—
192	C₂³×C₁₉	—	8	2	no	—
193	C₂³×C₁₉	—	8	2	no	—
194	C₂³×C₁₉	—	16	1	no	—
195	C₂³×C₁₉	—	16	1	no	—
196	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
197	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
198	Q₈×C₁₉	—	4	1	no	—
199	Q₈×C₁₉	—	4	1	no	—
200	D₄×C₁₉	—	2	2	no	—
201	D₄×C₁₉	—	2	2	no	—
202	D₄×C₁₉	—	4	1	no	—
203	D₄×C₁₉	—	4	1	no	—
204	D₄×C₁₉	—	4	1	no	—
205	D₄×C₁₉	—	4	1	no	—
206	D₄×C₁₉	—	4	1	no	—
207	D₄×C₁₉	—	8	2	no	—
208	D₄×C₁₉	—	8	2	no	—
209	D₄×C₁₉	—	8	2	no	—
210	D₄×C₁₉	—	8	2	no	—
211	D₄×C₁₉	—	8	2	no	—
212	D₄×C₁₉	—	16	1	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	8	2	no	—
223	C₂×C₄×C₁₉	—	8	2	no	—
224	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
229	C₈×C₁₉	—	2	1	no	—
230	C₈×C₁₉	—	2	1	no	—
231	C₈×C₁₉	—	2	1	no	—
232	C₈×C₁₉	C₂×#41	1	1	yes	characteristic
233	C₈×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
234	#3336	C₂×C₁₉	1	1	yes	characteristic, complemented
235	D₄×D₈	C₂×C₁₉	1	1	yes	characteristic
236	#2244	C₂×C₁₉	1	1	yes	characteristic, complemented
237	#2234	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#2232	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#2228	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#2220	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#2217	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#2207	C₂×C₁₉	1	1	yes	characteristic, complemented
243	#2187	C₂×C₁₉	1	1	yes	characteristic, complemented
244	#2187	C₂×C₁₉	1	1	yes	characteristic, complemented
245	#2175	C₂×C₁₉	1	1	yes	characteristic, complemented
246	#2168	C₂×C₁₉	1	1	yes	characteristic, complemented
247	#2140	C₂×C₁₉	1	1	yes	characteristic, complemented
248	C₂×#357	C₂×C₁₉	1	1	yes	characteristic, complemented
249	C₂²×C₁₉	—	2	1	no	—
250	C₂²×C₁₉	—	2	1	no	—
251	C₂²×C₁₉	—	2	1	no	—
252	C₂²×C₁₉	—	2	1	no	—
253	C₂²×C₁₉	—	2	1	no	—
254	C₂²×C₁₉	—	4	2	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	—	8	1	no	—
261	C₂²×C₁₉	—	8	1	no	—
262	C₂²×C₁₉	—	8	1	no	—
263	C₂²×C₁₉	—	16	4	no	—
264	C₂²×C₁₉	—	16	4	no	—
265	C₂²×C₁₉	#509	1	2	yes	—
266	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
267	C₄×C₁₉	—	2	1	no	—
268	C₄×C₁₉	—	2	1	no	—
269	C₄×C₁₉	—	2	1	no	—
270	C₄×C₁₉	—	2	1	no	—
271	C₄×C₁₉	—	8	1	no	—
272	C₄×C₁₉	—	8	1	no	—
273	C₄×C₁₉	—	8	1	no	—
274	C₄×C₁₉	—	8	1	no	—
275	C₄×C₁₉	—	8	1	no	—
276	C₄×C₁₉	#546	1	1	yes	characteristic
277	C₄×C₁₉	#577	1	1	yes	characteristic
278	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
279	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
280	#552	—	2	1	no	—
281	D₄²	—	2	1	no	—
282	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
283	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic, complemented
284	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic, complemented
285	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic, complemented
286	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
287	#499	C₂²×C₁₉	1	1	yes	characteristic, complemented
288	#493	C₂²×C₁₉	1	1	yes	characteristic
289	#485	—	2	1	no	—
290	#483	—	2	1	no	—
291	#479	—	2	1	no	—
292	#467	C₂²×C₁₉	1	1	yes	characteristic, complemented
293	#467	C₂²×C₁₉	1	1	yes	characteristic, complemented
294	#466	C₂²×C₁₉	1	1	yes	characteristic
295	#466	C₂²×C₁₉	1	1	yes	characteristic
296	#459	—	2	1	no	—
297	#447	—	2	1	no	—
298	#447	—	2	1	no	—
299	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
300	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
301	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
302	#427	C₂²×C₁₉	1	1	yes	characteristic, complemented
303	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
304	#367	C₂²×C₁₉	1	1	yes	characteristic, complemented
305	#366	C₂²×C₁₉	1	1	yes	characteristic, complemented
306	#366	C₂²×C₁₉	1	1	yes	characteristic, complemented
307	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
308	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
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, complemented
313	#357	C₂²×C₁₉	1	1	yes	characteristic, complemented
314	#357	C₂²×C₁₉	1	1	yes	characteristic, complemented
315	#357	C₂²×C₁₉	1	1	yes	characteristic, complemented
316	#357	C₂²×C₁₉	1	1	yes	characteristic, complemented
317	#357	C₂²×C₁₉	1	1	yes	characteristic, complemented
318	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
319	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
320	#346	C₂²×C₁₉	1	1	yes	characteristic, complemented
321	C₂×C₁₉	—	2	2	no	—
322	C₂×C₁₉	—	4	1	no	—
323	C₂×C₁₉	—	8	2	no	—
324	C₂×C₁₉	—	16	1	no	—
325	C₂×C₁₉	—	16	1	no	—
326	C₂×C₁₉	#3294	1	1	yes	characteristic
327	C₂×C₁₉	C₂×#509	1	1	yes	characteristic
328	C₂×C₁₉	#3416	1	1	yes	characteristic
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	—	4	1	no	—
332	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
333	C₂×D₈	—	2	2	no	—
334	C₂×D₈	—	2	2	no	—
335	C₂×D₈	—	2	1	no	—
336	C₂×D₈	—	2	1	no	—
337	C₂×D₈	—	2	1	no	—
338	C₂×D₈	—	4	1	no	—
339	C₂×D₈	—	4	1	no	—
340	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
341	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
342	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
343	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
345	#127	—	2	1	no	—
346	#126	—	4	1	no	—
347	#125	—	2	1	no	—
348	#125	—	4	1	no	—
349	#123	—	4	1	no	—
350	C₂²⋊Q₈	—	2	1	no	—
351	C₂²⋊Q₈	—	2	1	no	—
352	#121	—	2	1	no	—
353	#121	—	2	1	no	—
354	#121	—	4	1	no	—
355	#120	—	4	1	no	—
356	#120	—	4	1	no	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
360	#117	—	2	1	no	—
361	#117	—	4	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	SD₃₂	—	2	2	no	—
364	SD₃₂	—	4	1	no	—
365	SD₃₂	—	4	1	no	—
366	M₃₂	—	4	1	no	—
367	C₂×C₁₆	—	4	1	no	—
368	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
369	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
370	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
371	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
372	#107	—	2	1	no	—
373	#107	C₂³×C₁₉	1	1	yes	characteristic
374	#107	C₂³×C₁₉	1	1	yes	characteristic
375	#107	C₂³×C₁₉	1	1	yes	characteristic
376	#107	C₂³×C₁₉	1	1	yes	characteristic
377	#106	—	2	1	no	—
378	#106	—	2	1	no	—
379	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
380	#103	—	2	1	no	—
381	#103	—	2	1	no	—
382	#103	—	2	1	no	—
383	#102	—	2	1	no	—
384	#102	—	2	1	no	—
385	#102	—	2	1	no	—
386	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
387	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
388	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
389	C₁₉	#33877	1	1	yes	characteristic, direct product factor, Sylow
390	C₂⁴	—	4	1	no	—
391	C₂⁴	—	4	1	no	—
392	C₂×Q₈	—	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	2	no	—
397	C₂×D₄	—	4	2	no	—
398	C₂×D₄	—	4	1	no	—
399	C₂×D₄	—	4	1	no	—
400	C₂×D₄	—	4	1	no	—
401	C₂×D₄	—	4	1	no	—
402	C₂×D₄	—	4	1	no	—
403	C₂×D₄	—	4	1	no	—
404	C₂×D₄	—	8	1	no	—
405	C₂×D₄	—	8	1	no	—
406	C₂×D₄	—	8	4	no	—
407	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
408	C₂²×C₄	—	4	1	no	—
409	C₂²×C₄	—	4	1	no	—
410	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
412	Q₁₆	—	2	1	no	—
413	Q₁₆	—	2	1	no	—
414	D₈	—	2	1	no	—
415	D₈	—	2	1	no	—
416	D₈	—	2	1	no	—
417	D₈	—	2	1	no	—
418	D₈	—	2	1	no	—
419	D₈	—	4	2	no	—
420	D₈	—	4	2	no	—
421	D₈	—	8	1	no	—
422	D₈	#41×C₁₉	1	2	yes	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
429	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	4	1	no	—
436	C₄⋊C₄	—	4	1	no	—
437	C₄⋊C₄	—	4	1	no	—
438	C₄⋊C₄	—	4	1	no	—
439	C₄⋊C₄	—	4	1	no	—
440	C₄⋊C₄	—	4	1	no	—
441	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
442	C₂²⋊C₄	—	4	1	no	—
443	C₂²⋊C₄	—	4	1	no	—
444	C₂²⋊C₄	—	4	1	no	—
445	C₂²⋊C₄	—	4	1	no	—
446	C₂²⋊C₄	—	4	1	no	—
447	C₂²⋊C₄	—	4	1	no	—
448	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
449	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
450	C₄²	—	4	1	no	—
451	C₄²	—	4	1	no	—
452	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
453	C₁₆	—	2	1	no	—
454	C₁₆	—	2	1	no	—
455	C₁₆	—	2	1	no	—
456	C₁₆	—	2	1	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	4	1	no	—
460	C₂³	—	8	2	no	—
461	C₂³	—	8	2	no	—
462	C₂³	—	8	2	no	—
463	C₂³	—	8	2	no	—
464	C₂³	—	16	1	no	—
465	C₂³	—	16	1	no	—
466	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
467	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
468	Q₈	—	4	1	no	—
469	Q₈	—	4	1	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	2	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	1	no	—
475	D₄	—	4	1	no	—
476	D₄	—	4	1	no	—
477	D₄	—	8	2	no	—
478	D₄	—	8	2	no	—
479	D₄	—	8	2	no	—
480	D₄	—	8	2	no	—
481	D₄	—	8	2	no	—
482	D₄	—	16	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	8	2	no	—
493	C₂×C₄	—	8	2	no	—
494	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
495	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
496	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
497	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
499	C₈	—	2	1	no	—
500	C₈	—	2	1	no	—
501	C₈	—	2	1	no	—
502	C₈	C₂×#41×C₁₉	1	1	yes	characteristic
503	C₈	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	8	1	no	—
511	C₂²	—	8	1	no	—
512	C₂²	—	8	1	no	—
513	C₂²	—	8	1	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	1	no	—
516	C₂²	—	8	1	no	—
517	C₂²	—	8	1	no	—
518	C₂²	—	16	4	no	—
519	C₂²	—	16	4	no	—
520	C₂²	C₁₉×#509	1	2	yes	—
521	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	2	1	no	—
526	C₄	—	8	1	no	—
527	C₄	—	8	1	no	—
528	C₄	—	8	1	no	—
529	C₄	—	8	1	no	—
530	C₄	—	8	1	no	—
531	C₄	C₁₉×#546	1	1	yes	characteristic
532	C₄	C₁₉×#577	1	1	yes	characteristic
533	C₂	—	2	2	no	—
534	C₂	—	4	1	no	—
535	C₂	—	8	2	no	—
536	C₂	—	16	1	no	—
537	C₂	—	16	1	no	—
538	C₂	C₁₉×#3294	1	1	yes	characteristic
539	C₂	C₂×C₁₉×#509	1	1	yes	characteristic
540	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	D₄×D₈×C₁₉	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×#2244	C₂	semidirect
4. C₁₉×#2234	C₂	semidirect
5. C₁₉×#2232	C₂	semidirect
6. C₁₉×#2228	C₂	semidirect
7. C₁₉×#2220	C₂	semidirect
8. C₁₉×#2217	C₂	semidirect
9. C₁₉×#2207	C₂	semidirect
10. C₁₉×#2187	C₂	semidirect
11. C₁₉×#2187	C₂	semidirect
12. C₁₉×#2175	C₂	semidirect
13. C₁₉×#2168	C₂	semidirect
14. C₁₉×#2140	C₂	semidirect
15. C₂×C₁₉×#357	C₂	semidirect
21. C₂×C₁₉×SD₃₂	C₂²	semidirect
22. C₂×C₁₉×SD₃₂	C₂²	semidirect
23. C₂×C₁₉×M₃₂	C₂²	semidirect
24. C₂²×C₁₆×C₁₉	C₂²	semidirect
25. C₁₉×#499	C₂²	semidirect
30. C₁₉×#467	C₂²	semidirect
31. C₁₉×#467	C₂²	semidirect
37. C₄×Q₁₆×C₁₉	C₂²	semidirect
40. C₁₉×#427	C₂²	semidirect
41. C₂×C₁₉×#107	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
50. C₁₉×#357	C₂²	semidirect
51. C₁₉×#357	C₂²	semidirect
52. C₁₉×#357	C₂²	semidirect
53. C₁₉×#357	C₂²	semidirect
54. C₁₉×#357	C₂²	semidirect
55. C₁₉×#357	C₂²	semidirect
56. C₁₉×C₂²⋊C₁₆	C₂²	semidirect
57. C₁₉×C₂²⋊C₁₆	C₂²	semidirect
58. C₁₉×#346	C₂²	semidirect
186. #33877	C₁₉	direct (N × H)
234. #3336	C₂×C₁₉	semidirect
236. #2244	C₂×C₁₉	semidirect
237. #2234	C₂×C₁₉	semidirect
238. #2232	C₂×C₁₉	semidirect
239. #2228	C₂×C₁₉	semidirect
240. #2220	C₂×C₁₉	semidirect
241. #2217	C₂×C₁₉	semidirect
242. #2207	C₂×C₁₉	semidirect
243. #2187	C₂×C₁₉	semidirect
244. #2187	C₂×C₁₉	semidirect
245. #2175	C₂×C₁₉	semidirect
246. #2168	C₂×C₁₉	semidirect
247. #2140	C₂×C₁₉	semidirect
248. C₂×#357	C₂×C₁₉	semidirect
283. C₂×SD₃₂	C₂²×C₁₉	semidirect
284. C₂×SD₃₂	C₂²×C₁₉	semidirect
285. C₂×M₃₂	C₂²×C₁₉	semidirect
286. C₂²×C₁₆	C₂²×C₁₉	semidirect
287. #499	C₂²×C₁₉	semidirect
292. #467	C₂²×C₁₉	semidirect
293. #467	C₂²×C₁₉	semidirect
299. C₄×Q₁₆	C₂²×C₁₉	semidirect
302. #427	C₂²×C₁₉	semidirect
303. C₂×#107	C₂²×C₁₉	semidirect
304. #367	C₂²×C₁₉	semidirect
305. #366	C₂²×C₁₉	semidirect
306. #366	C₂²×C₁₉	semidirect
307. C₄⋊C₁₆	C₂²×C₁₉	semidirect
308. #358	C₂²×C₁₉	semidirect
312. #357	C₂²×C₁₉	semidirect
313. #357	C₂²×C₁₉	semidirect
314. #357	C₂²×C₁₉	semidirect
315. #357	C₂²×C₁₉	semidirect
316. #357	C₂²×C₁₉	semidirect
317. #357	C₂²×C₁₉	semidirect
318. C₂²⋊C₁₆	C₂²×C₁₉	semidirect
319. C₂²⋊C₁₆	C₂²×C₁₉	semidirect
320. #346	C₂²×C₁₉	semidirect
389. C₁₉	#33877	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
D₄×D₈×C₁₉	2
C₁₉×#2244	2
C₁₉×#2234	2
C₁₉×#2232	2
C₁₉×#2228	2
C₁₉×#2220	2
C₁₉×#2217	2
C₁₉×#2207	2
C₁₉×#2187	2
C₁₉×#2175	2
C₁₉×#2168	2
C₁₉×#2140	2
C₂×C₁₉×#357	2
#33877	19

Subgroups — C19×#33877 #18039836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33877 #18039836