Subgroups — C₁₉×#33873 #18039832

Order 4864.

602 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3334	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3280	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2243	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2235	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2233	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2226	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2218	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2217	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	C₁₉×#2177	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2139	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×#547	—	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	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#495	C₂²	1	1	yes	characteristic
27	C₁₉×#480	—	2	1	no	—
28	C₁₉×#480	—	2	1	no	—
29	C₁₉×#474	—	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	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×#367	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#367	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#367	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	C₁₉×#346	C₂²	1	1	yes	characteristic, complemented
59	C₂×#41×C₁₉	—	2	1	no	—
60	C₂×#41×C₁₉	—	4	1	no	—
61	C₂²×D₄×C₁₉	—	2	1	no	—
62	C₁₉×#135	—	2	2	no	—
63	C₁₉×#135	—	4	1	no	—
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	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×C₄⋊Q₈	—	2	1	no	—
76	C₁₉×#124	—	2	1	no	—
77	C₁₉×#123	—	4	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	—	4	1	no	—
82	C₁₉×#121	—	2	1	no	—
83	C₁₉×#121	—	2	1	no	—
84	C₁₉×#121	—	2	1	no	—
85	C₁₉×#121	—	4	1	no	—
86	C₁₉×#120	—	4	1	no	—
87	C₄×D₄×C₁₉	—	2	1	no	—
88	C₄×D₄×C₁₉	—	2	1	no	—
89	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	—	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	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	—	2	1	no	—
104	C₁₉×#107	—	2	1	no	—
105	C₁₉×#107	C₂³	1	1	yes	characteristic
106	C₁₉×#107	C₂³	1	1	yes	characteristic
107	C₁₉×#107	C₂³	1	1	yes	characteristic
108	C₁₉×#107	C₂³	1	1	yes	characteristic
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	#41×C₁₉	—	8	4	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	—	4	1	no	—
125	C₂×D₄×C₁₉	—	2	1	no	—
126	C₂×D₄×C₁₉	—	2	1	no	—
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	4	2	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	—	4	1	no	—
134	C₂×D₄×C₁₉	—	8	1	no	—
135	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	—	4	1	no	—
137	C₂²×C₄×C₁₉	—	4	1	no	—
138	C₂²×C₄×C₁₉	—	4	1	no	—
139	C₂²×C₄×C₁₉	—	4	1	no	—
140	C₂²×C₄×C₁₉	—	4	1	no	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	Q₁₆×C₁₉	—	2	1	no	—
144	Q₁₆×C₁₉	—	2	1	no	—
145	SD₁₆×C₁₉	—	4	2	no	—
146	SD₁₆×C₁₉	—	8	1	no	—
147	D₈×C₁₉	—	2	1	no	—
148	D₈×C₁₉	—	2	1	no	—
149	D₈×C₁₉	—	2	1	no	—
150	D₈×C₁₉	—	2	1	no	—
151	D₈×C₁₉	—	2	1	no	—
152	D₈×C₁₉	—	4	2	no	—
153	D₈×C₁₉	#41	1	2	yes	complemented
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	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	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	—	4	1	no	—
178	C₂²⋊C₄×C₁₉	—	4	1	no	—
179	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
180	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
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	#33873	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	—	16	1	no	—
193	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
194	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
195	Q₈×C₁₉	—	4	1	no	—
196	Q₈×C₁₉	—	4	1	no	—
197	Q₈×C₁₉	—	8	2	no	—
198	D₄×C₁₉	—	2	2	no	—
199	D₄×C₁₉	—	2	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	—	4	1	no	—
205	D₄×C₁₉	—	8	2	no	—
206	D₄×C₁₉	—	8	2	no	—
207	D₄×C₁₉	—	8	2	no	—
208	D₄×C₁₉	—	8	2	no	—
209	D₄×C₁₉	—	16	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	8	2	no	—
220	C₂×C₄×C₁₉	—	8	2	no	—
221	C₂×C₄×C₁₉	—	8	2	no	—
222	C₂×C₄×C₁₉	—	8	2	no	—
223	C₂×C₄×C₁₉	—	16	1	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	#3334	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#3280	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#2243	C₂×C₁₉	1	1	yes	characteristic, complemented
237	#2235	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#2233	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#2226	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#2218	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#2217	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#2210	C₂×C₁₉	1	1	yes	characteristic, complemented
243	#2186	C₂×C₁₉	1	1	yes	characteristic, complemented
244	#2184	C₂×C₁₉	1	1	yes	characteristic, complemented
245	#2177	C₂×C₁₉	1	1	yes	characteristic, complemented
246	#2168	C₂×C₁₉	1	1	yes	characteristic, complemented
247	#2139	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	#509	1	2	yes	—
265	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
266	C₄×C₁₉	—	2	1	no	—
267	C₄×C₁₉	—	2	1	no	—
268	C₄×C₁₉	—	2	1	no	—
269	C₄×C₁₉	—	2	1	no	—
270	C₄×C₁₉	—	8	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	#546	1	1	yes	characteristic
276	C₄×C₁₉	#577	1	1	yes	characteristic
277	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
278	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
279	#547	—	2	1	no	—
280	#546	—	2	1	no	—
281	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic, complemented
282	C₂×D₁₆	C₂²×C₁₉	1	1	yes	characteristic
283	C₂×D₁₆	C₂²×C₁₉	1	1	yes	characteristic
284	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic, complemented
285	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
286	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
287	#495	C₂²×C₁₉	1	1	yes	characteristic
288	#480	—	2	1	no	—
289	#480	—	2	1	no	—
290	#474	—	2	1	no	—
291	#467	C₂²×C₁₉	1	1	yes	characteristic
292	#466	C₂²×C₁₉	1	1	yes	characteristic
293	#466	C₂²×C₁₉	1	1	yes	characteristic
294	#466	C₂²×C₁₉	1	1	yes	characteristic, complemented
295	#463	—	2	1	no	—
296	#450	—	2	1	no	—
297	#449	—	2	1	no	—
298	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
299	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
300	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
301	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
303	#367	C₂²×C₁₉	1	1	yes	characteristic, complemented
304	#367	C₂²×C₁₉	1	1	yes	characteristic, complemented
305	#367	C₂²×C₁₉	1	1	yes	characteristic, complemented
306	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
307	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
308	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
309	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
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
314	#357	C₂²×C₁₉	1	1	yes	characteristic
315	#357	C₂²×C₁₉	1	1	yes	characteristic
316	#357	C₂²×C₁₉	1	1	yes	characteristic, complemented
317	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
318	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
319	#346	C₂²×C₁₉	1	1	yes	characteristic, complemented
320	C₂×C₁₉	—	2	2	no	—
321	C₂×C₁₉	—	4	1	no	—
322	C₂×C₁₉	—	8	2	no	—
323	C₂×C₁₉	—	16	1	no	—
324	C₂×C₁₉	—	16	1	no	—
325	C₂×C₁₉	#3294	1	1	yes	characteristic
326	C₂×C₁₉	C₂×#509	1	1	yes	characteristic
327	C₂×C₁₉	#3416	1	1	yes	characteristic
328	C₂×#41	—	2	1	no	—
329	C₂×#41	—	4	1	no	—
330	C₂²×D₄	—	2	1	no	—
331	#135	—	2	2	no	—
332	#135	—	4	1	no	—
333	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
334	C₂×SD₁₆	—	2	1	no	—
335	C₂×SD₁₆	—	2	1	no	—
336	C₂×D₈	—	2	2	no	—
337	C₂×D₈	—	2	1	no	—
338	C₂×D₈	—	4	1	no	—
339	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
340	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
341	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
342	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
343	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
344	C₄⋊Q₈	—	2	1	no	—
345	#124	—	2	1	no	—
346	#123	—	4	1	no	—
347	#123	—	4	1	no	—
348	#123	—	4	1	no	—
349	C₂²⋊Q₈	—	2	1	no	—
350	C₂²⋊Q₈	—	4	1	no	—
351	#121	—	2	1	no	—
352	#121	—	2	1	no	—
353	#121	—	2	1	no	—
354	#121	—	4	1	no	—
355	#120	—	4	1	no	—
356	C₄×D₄	—	2	1	no	—
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	4	1	no	—
362	SD₃₂	—	4	1	no	—
363	D₁₆	—	2	2	no	—
364	D₁₆	—	4	1	no	—
365	M₃₂	—	4	1	no	—
366	C₂×C₁₆	—	4	1	no	—
367	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
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	#107	—	2	1	no	—
372	#107	—	2	1	no	—
373	#107	—	2	1	no	—
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	#107	C₂³×C₁₉	1	1	yes	characteristic
378	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
379	#103	—	2	1	no	—
380	#102	—	2	1	no	—
381	#102	—	2	1	no	—
382	#102	—	2	1	no	—
383	#102	—	2	1	no	—
384	#102	—	2	1	no	—
385	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
386	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
387	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
388	C₁₉	#33873	1	1	yes	characteristic, direct product factor, Sylow
389	C₂⁴	—	4	1	no	—
390	#41	—	4	2	no	—
391	#41	—	8	1	no	—
392	#41	—	8	4	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	4	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	4	2	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	D₈×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	—	4	1	no	—
407	C₂²×C₄	—	4	1	no	—
408	C₂²×C₄	—	4	1	no	—
409	C₂²×C₄	—	4	1	no	—
410	C₂²×C₄	—	4	1	no	—
411	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
413	Q₁₆	—	2	1	no	—
414	Q₁₆	—	2	1	no	—
415	SD₁₆	—	4	2	no	—
416	SD₁₆	—	8	1	no	—
417	D₈	—	2	1	no	—
418	D₈	—	2	1	no	—
419	D₈	—	2	1	no	—
420	D₈	—	2	1	no	—
421	D₈	—	2	1	no	—
422	D₈	—	4	2	no	—
423	D₈	#41×C₁₉	1	2	yes	complemented
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
429	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
431	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	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	D₈×C₁₉	1	1	yes	characteristic
441	C₂²⋊C₄	—	4	1	no	—
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	—	4	1	no	—
449	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
450	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
451	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
452	C₁₆	—	2	1	no	—
453	C₁₆	—	2	1	no	—
454	C₁₆	—	2	1	no	—
455	C₁₆	—	2	1	no	—
456	C₂³	—	4	1	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	8	2	no	—
460	C₂³	—	8	2	no	—
461	C₂³	—	16	1	no	—
462	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
463	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
464	Q₈	—	4	1	no	—
465	Q₈	—	4	1	no	—
466	Q₈	—	8	2	no	—
467	D₄	—	2	2	no	—
468	D₄	—	2	2	no	—
469	D₄	—	4	1	no	—
470	D₄	—	4	1	no	—
471	D₄	—	4	1	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	1	no	—
474	D₄	—	8	2	no	—
475	D₄	—	8	2	no	—
476	D₄	—	8	2	no	—
477	D₄	—	8	2	no	—
478	D₄	—	16	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	8	2	no	—
489	C₂×C₄	—	8	2	no	—
490	C₂×C₄	—	8	2	no	—
491	C₂×C₄	—	8	2	no	—
492	C₂×C₄	—	16	1	no	—
493	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
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	C₂²×D₄×C₁₉	1	1	yes	characteristic
498	C₈	—	2	1	no	—
499	C₈	—	2	1	no	—
500	C₈	—	2	1	no	—
501	C₈	C₂×#41×C₁₉	1	1	yes	characteristic
502	C₈	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	8	1	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	—	16	4	no	—
518	C₂²	C₁₉×#509	1	2	yes	—
519	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	8	1	no	—
525	C₄	—	8	1	no	—
526	C₄	—	8	1	no	—
527	C₄	—	8	1	no	—
528	C₄	—	8	1	no	—
529	C₄	C₁₉×#546	1	1	yes	characteristic
530	C₄	C₁₉×#577	1	1	yes	characteristic
531	C₂	—	2	2	no	—
532	C₂	—	4	1	no	—
533	C₂	—	8	2	no	—
534	C₂	—	16	1	no	—
535	C₂	—	16	1	no	—
536	C₂	C₁₉×#3294	1	1	yes	characteristic
537	C₂	C₂×C₁₉×#509	1	1	yes	characteristic
538	C₂	C₁₉×#3416	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×#3334	C₂	semidirect
2. C₁₉×#3280	C₂	semidirect
3. C₁₉×#2243	C₂	semidirect
4. C₁₉×#2235	C₂	semidirect
5. C₁₉×#2233	C₂	semidirect
6. C₁₉×#2226	C₂	semidirect
7. C₁₉×#2218	C₂	semidirect
8. C₁₉×#2217	C₂	semidirect
9. C₁₉×#2210	C₂	semidirect
10. C₁₉×#2186	C₂	semidirect
11. C₁₉×#2184	C₂	semidirect
12. C₁₉×#2177	C₂	semidirect
13. C₁₉×#2168	C₂	semidirect
14. C₁₉×#2139	C₂	semidirect
15. C₂×C₁₉×#357	C₂	semidirect
20. C₂×C₁₉×SD₃₂	C₂²	semidirect
23. C₂×C₁₉×M₃₂	C₂²	semidirect
25. C₁₉×#500	C₂²	semidirect
33. C₁₉×#466	C₂²	semidirect
38. C₄×D₈×C₁₉	C₂²	semidirect
41. C₂×C₁₉×#107	C₂²	semidirect
42. C₁₉×#367	C₂²	semidirect
43. C₁₉×#367	C₂²	semidirect
44. C₁₉×#367	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. C₁₉×#346	C₂²	semidirect
153. D₈×C₁₉	#41	semidirect
186. #33873	C₁₉	direct (N × H)
234. #3334	C₂×C₁₉	semidirect
235. #3280	C₂×C₁₉	semidirect
236. #2243	C₂×C₁₉	semidirect
237. #2235	C₂×C₁₉	semidirect
238. #2233	C₂×C₁₉	semidirect
239. #2226	C₂×C₁₉	semidirect
240. #2218	C₂×C₁₉	semidirect
241. #2217	C₂×C₁₉	semidirect
242. #2210	C₂×C₁₉	semidirect
243. #2186	C₂×C₁₉	semidirect
244. #2184	C₂×C₁₉	semidirect
245. #2177	C₂×C₁₉	semidirect
246. #2168	C₂×C₁₉	semidirect
247. #2139	C₂×C₁₉	semidirect
248. C₂×#357	C₂×C₁₉	semidirect
281. C₂×SD₃₂	C₂²×C₁₉	semidirect
284. C₂×M₃₂	C₂²×C₁₉	semidirect
286. #500	C₂²×C₁₉	semidirect
294. #466	C₂²×C₁₉	semidirect
299. C₄×D₈	C₂²×C₁₉	semidirect
302. C₂×#107	C₂²×C₁₉	semidirect
303. #367	C₂²×C₁₉	semidirect
304. #367	C₂²×C₁₉	semidirect
305. #367	C₂²×C₁₉	semidirect
306. C₄⋊C₁₆	C₂²×C₁₉	semidirect
307. #358	C₂²×C₁₉	semidirect
308. #358	C₂²×C₁₉	semidirect
309. #358	C₂²×C₁₉	semidirect
316. #357	C₂²×C₁₉	semidirect
318. C₂²⋊C₁₆	C₂²×C₁₉	semidirect
319. #346	C₂²×C₁₉	semidirect
388. C₁₉	#33873	direct (N × H)
423. D₈	#41×C₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3334	2
C₁₉×#3280	2
C₁₉×#2243	2
C₁₉×#2235	2
C₁₉×#2233	2
C₁₉×#2226	2
C₁₉×#2218	2
C₁₉×#2217	2
C₁₉×#2210	2
C₁₉×#2186	2
C₁₉×#2184	2
C₁₉×#2177	2
C₁₉×#2168	2
C₁₉×#2139	2
C₂×C₁₉×#357	2
#33873	19

Subgroups — C19×#33873 #18039832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33873 #18039832