Subgroups — C₁₉×#33823 #18039782

Order 4864.

500 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3176	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3175	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2229	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2228	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2226	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2224	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2220	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2218	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2217	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2215	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2210	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2210	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2207	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2206	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#2151	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#542	—	2	1	no	—
17	C₁₉×#540	—	2	1	no	—
18	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×D₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×D₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
23	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#500	C₂²	1	1	yes	characteristic
25	C₁₉×#499	C₂²	1	1	yes	characteristic
26	C₁₉×#495	C₂²	1	1	yes	characteristic
27	C₁₉×#493	C₂²	1	1	yes	characteristic
28	C₁₉×#490	—	2	1	no	—
29	C₁₉×#489	—	2	1	no	—
30	C₁₉×#469	—	2	1	no	—
31	C₁₉×#468	—	2	1	no	—
32	C₁₉×#467	C₂²	1	1	yes	characteristic
33	C₁₉×#466	C₂²	1	1	yes	characteristic
34	C₁₉×#466	C₂²	1	1	yes	characteristic
35	C₁₉×#466	C₂²	1	1	yes	characteristic
36	C₁₉×#442	—	2	1	no	—
37	C₁₉×#440	—	2	1	no	—
38	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
39	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
40	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
41	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
42	C₁₉×#405	C₂²	1	1	yes	characteristic
43	C₁₉×#367	C₂²	1	1	yes	characteristic
44	C₁₉×#367	C₂²	1	1	yes	characteristic
45	C₁₉×#366	C₂²	1	1	yes	characteristic
46	C₁₉×#366	C₂²	1	1	yes	characteristic
47	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
48	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
49	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
50	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
51	C₁₉×#358	C₂²	1	1	yes	characteristic
52	C₁₉×#358	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×#357	C₂²	1	1	yes	characteristic
57	C₁₉×#357	C₂²	1	1	yes	characteristic
58	C₁₉×#357	C₂²	1	1	yes	characteristic
59	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×SD₁₆×C₁₉	—	2	1	no	—
61	C₂×D₈×C₁₉	—	2	1	no	—
62	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
66	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×#127	—	2	1	no	—
69	C₁₉×#126	—	4	1	no	—
70	C₁₉×#125	—	2	1	no	—
71	C₁₉×#124	—	2	1	no	—
72	C₁₉×#124	—	4	1	no	—
73	C₁₉×#123	—	4	1	no	—
74	C₁₉×#123	—	4	1	no	—
75	C₁₉×#123	—	4	1	no	—
76	C₁₉×C₂²⋊Q₈	—	2	1	no	—
77	C₁₉×C₂²⋊Q₈	—	4	1	no	—
78	C₁₉×#121	—	2	1	no	—
79	C₁₉×#121	—	2	1	no	—
80	C₁₉×#121	—	2	1	no	—
81	C₁₉×#121	—	4	1	no	—
82	C₁₉×#121	—	4	1	no	—
83	C₄×Q₈×C₁₉	—	2	1	no	—
84	C₄×D₄×C₁₉	—	2	1	no	—
85	C₄×D₄×C₁₉	—	2	1	no	—
86	C₄×D₄×C₁₉	—	2	1	no	—
87	C₁₉×#117	D₄	1	1	yes	characteristic
88	C₁₉×SD₃₂	—	4	1	no	—
89	C₁₉×SD₃₂	—	4	1	no	—
90	C₁₉×D₁₆	—	4	1	no	—
91	C₁₉×D₁₆	—	4	1	no	—
92	C₁₉×M₃₂	—	4	1	no	—
93	C₂×C₁₆×C₁₉	—	4	1	no	—
94	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
98	C₁₉×#107	—	2	1	no	—
99	C₁₉×#107	C₂³	1	1	yes	characteristic
100	C₁₉×#107	C₂³	1	1	yes	characteristic
101	C₁₉×#107	C₂³	1	1	yes	characteristic
102	C₁₉×#107	C₂³	1	1	yes	characteristic
103	C₁₉×#106	—	2	1	no	—
104	C₁₉×#103	—	2	1	no	—
105	C₁₉×#103	—	2	1	no	—
106	C₁₉×#102	—	2	1	no	—
107	C₁₉×#102	—	2	1	no	—
108	C₁₉×#102	—	2	1	no	—
109	C₁₉×#102	—	2	1	no	—
110	C₁₉×#102	—	2	1	no	—
111	C₁₉×#102	—	2	1	no	—
112	C₁₉×#97	D₄	1	1	yes	characteristic
113	C₁₉×#97	D₄	1	1	yes	characteristic
114	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
115	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	4	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	—	4	1	no	—
122	C₂×D₄×C₁₉	—	4	1	no	—
123	C₂×D₄×C₁₉	—	4	1	no	—
124	C₂×D₄×C₁₉	—	4	1	no	—
125	C₂×D₄×C₁₉	—	4	1	no	—
126	C₂²×C₄×C₁₉	—	4	1	no	—
127	C₂²×C₄×C₁₉	—	4	1	no	—
128	C₂²×C₄×C₁₉	—	4	1	no	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
130	Q₁₆×C₁₉	—	2	1	no	—
131	Q₁₆×C₁₉	—	2	1	no	—
132	SD₁₆×C₁₉	—	4	2	no	—
133	D₈×C₁₉	—	2	1	no	—
134	D₈×C₁₉	—	2	1	no	—
135	D₈×C₁₉	—	2	1	no	—
136	D₈×C₁₉	—	2	1	no	—
137	D₈×C₁₉	—	2	1	no	—
138	D₈×C₁₉	—	2	1	no	—
139	D₈×C₁₉	—	4	2	no	—
140	M₁₆×C₁₉	—	4	1	no	—
141	C₂×C₈×C₁₉	—	2	1	no	—
142	C₂×C₈×C₁₉	—	2	1	no	—
143	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	4	1	no	—
152	C₄⋊C₄×C₁₉	—	4	1	no	—
153	C₄⋊C₄×C₁₉	—	4	1	no	—
154	C₄⋊C₄×C₁₉	—	4	1	no	—
155	C₄⋊C₄×C₁₉	—	4	1	no	—
156	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
157	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
158	C₂²⋊C₄×C₁₉	—	4	1	no	—
159	C₂²⋊C₄×C₁₉	—	4	1	no	—
160	C₂²⋊C₄×C₁₉	—	4	1	no	—
161	C₂²⋊C₄×C₁₉	—	4	1	no	—
162	C₂²⋊C₄×C₁₉	—	4	1	no	—
163	C₂²⋊C₄×C₁₉	—	4	1	no	—
164	C₂²⋊C₄×C₁₉	—	4	1	no	—
165	C₂²⋊C₄×C₁₉	—	4	1	no	—
166	C₂²⋊C₄×C₁₉	—	4	1	no	—
167	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
168	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
169	C₄²×C₁₉	—	4	1	no	—
170	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₁₆×C₁₉	—	2	1	no	—
173	C₁₆×C₁₉	—	2	1	no	—
174	C₁₆×C₁₉	—	2	1	no	—
175	C₁₆×C₁₉	—	2	1	no	—
176	#33823	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂³×C₁₉	—	4	1	no	—
178	C₂³×C₁₉	—	4	1	no	—
179	C₂³×C₁₉	—	4	1	no	—
180	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
181	Q₈×C₁₉	—	4	1	no	—
182	Q₈×C₁₉	—	4	1	no	—
183	Q₈×C₁₉	—	16	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	D₄×C₁₉	—	4	1	no	—
190	D₄×C₁₉	—	16	1	no	—
191	D₄×C₁₉	—	16	1	no	—
192	D₄×C₁₉	—	16	1	no	—
193	D₄×C₁₉	—	16	1	no	—
194	D₄×C₁₉	—	16	1	no	—
195	C₂×C₄×C₁₉	—	2	1	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	16	1	no	—
203	C₂×C₄×C₁₉	—	16	1	no	—
204	C₂×C₄×C₁₉	—	16	1	no	—
205	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
208	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
211	C₈×C₁₉	—	2	1	no	—
212	C₈×C₁₉	—	2	1	no	—
213	C₈×C₁₉	—	2	1	no	—
214	C₈×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
215	C₈×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
216	#3176	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#3175	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#2229	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#2228	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#2226	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#2224	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#2220	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#2218	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#2217	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#2215	C₂×C₁₉	1	1	yes	characteristic, complemented
226	#2210	C₂×C₁₉	1	1	yes	characteristic, complemented
227	#2210	C₂×C₁₉	1	1	yes	characteristic, complemented
228	#2207	C₂×C₁₉	1	1	yes	characteristic, complemented
229	#2206	C₂×C₁₉	1	1	yes	characteristic, complemented
230	#2151	C₂×C₁₉	1	1	yes	characteristic, complemented
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	2	1	no	—
233	C₂²×C₁₉	—	2	1	no	—
234	C₂²×C₁₉	—	8	1	no	—
235	C₂²×C₁₉	—	8	1	no	—
236	C₂²×C₁₉	—	8	1	no	—
237	C₂²×C₁₉	—	8	1	no	—
238	C₂²×C₁₉	—	8	1	no	—
239	C₂²×C₁₉	—	8	1	no	—
240	C₂²×C₁₉	—	8	1	no	—
241	C₂²×C₁₉	—	8	1	no	—
242	C₂²×C₁₉	—	8	1	no	—
243	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
244	C₄×C₁₉	—	2	1	no	—
245	C₄×C₁₉	—	2	1	no	—
246	C₄×C₁₉	—	2	1	no	—
247	C₄×C₁₉	—	2	1	no	—
248	C₄×C₁₉	—	2	1	no	—
249	C₄×C₁₉	—	8	1	no	—
250	C₄×C₁₉	—	8	1	no	—
251	C₄×C₁₉	—	8	1	no	—
252	C₄×C₁₉	—	8	1	no	—
253	C₄×C₁₉	—	8	1	no	—
254	C₄×C₁₉	#537	1	1	yes	characteristic
255	C₄×C₁₉	#575	1	1	yes	characteristic
256	#542	—	2	1	no	—
257	#540	—	2	1	no	—
258	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
259	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
260	C₂×D₁₆	C₂²×C₁₉	1	1	yes	characteristic
261	C₂×D₁₆	C₂²×C₁₉	1	1	yes	characteristic
262	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
263	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
264	#500	C₂²×C₁₉	1	1	yes	characteristic
265	#499	C₂²×C₁₉	1	1	yes	characteristic
266	#495	C₂²×C₁₉	1	1	yes	characteristic
267	#493	C₂²×C₁₉	1	1	yes	characteristic
268	#490	—	2	1	no	—
269	#489	—	2	1	no	—
270	#469	—	2	1	no	—
271	#468	—	2	1	no	—
272	#467	C₂²×C₁₉	1	1	yes	characteristic
273	#466	C₂²×C₁₉	1	1	yes	characteristic
274	#466	C₂²×C₁₉	1	1	yes	characteristic
275	#466	C₂²×C₁₉	1	1	yes	characteristic
276	#442	—	2	1	no	—
277	#440	—	2	1	no	—
278	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
279	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
280	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
281	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
282	#405	C₂²×C₁₉	1	1	yes	characteristic
283	#367	C₂²×C₁₉	1	1	yes	characteristic
284	#367	C₂²×C₁₉	1	1	yes	characteristic
285	#366	C₂²×C₁₉	1	1	yes	characteristic
286	#366	C₂²×C₁₉	1	1	yes	characteristic
287	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
288	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
289	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
290	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
291	#358	C₂²×C₁₉	1	1	yes	characteristic
292	#358	C₂²×C₁₉	1	1	yes	characteristic
293	#357	C₂²×C₁₉	1	1	yes	characteristic
294	#357	C₂²×C₁₉	1	1	yes	characteristic
295	#357	C₂²×C₁₉	1	1	yes	characteristic
296	#357	C₂²×C₁₉	1	1	yes	characteristic
297	#357	C₂²×C₁₉	1	1	yes	characteristic
298	#357	C₂²×C₁₉	1	1	yes	characteristic
299	C₂×C₁₉	—	4	1	no	—
300	C₂×C₁₉	—	16	1	no	—
301	C₂×C₁₉	—	16	1	no	—
302	C₂×C₁₉	—	16	1	no	—
303	C₂×C₁₉	#3245	1	1	yes	characteristic
304	C₂×C₁₉	#3415	1	1	yes	characteristic
305	C₂×C₁₉	#3416	1	1	yes	characteristic
306	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
307	C₂×SD₁₆	—	2	1	no	—
308	C₂×D₈	—	2	1	no	—
309	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
310	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
311	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
312	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
314	C₄⋊Q₈	—	2	1	no	—
315	#127	—	2	1	no	—
316	#126	—	4	1	no	—
317	#125	—	2	1	no	—
318	#124	—	2	1	no	—
319	#124	—	4	1	no	—
320	#123	—	4	1	no	—
321	#123	—	4	1	no	—
322	#123	—	4	1	no	—
323	C₂²⋊Q₈	—	2	1	no	—
324	C₂²⋊Q₈	—	4	1	no	—
325	#121	—	2	1	no	—
326	#121	—	2	1	no	—
327	#121	—	2	1	no	—
328	#121	—	4	1	no	—
329	#121	—	4	1	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×D₄	—	2	1	no	—
332	C₄×D₄	—	2	1	no	—
333	C₄×D₄	—	2	1	no	—
334	#117	D₄×C₁₉	1	1	yes	characteristic
335	SD₃₂	—	4	1	no	—
336	SD₃₂	—	4	1	no	—
337	D₁₆	—	4	1	no	—
338	D₁₆	—	4	1	no	—
339	M₃₂	—	4	1	no	—
340	C₂×C₁₆	—	4	1	no	—
341	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
342	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
343	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
344	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
345	#107	—	2	1	no	—
346	#107	C₂³×C₁₉	1	1	yes	characteristic
347	#107	C₂³×C₁₉	1	1	yes	characteristic
348	#107	C₂³×C₁₉	1	1	yes	characteristic
349	#107	C₂³×C₁₉	1	1	yes	characteristic
350	#106	—	2	1	no	—
351	#103	—	2	1	no	—
352	#103	—	2	1	no	—
353	#102	—	2	1	no	—
354	#102	—	2	1	no	—
355	#102	—	2	1	no	—
356	#102	—	2	1	no	—
357	#102	—	2	1	no	—
358	#102	—	2	1	no	—
359	#97	D₄×C₁₉	1	1	yes	characteristic
360	#97	D₄×C₁₉	1	1	yes	characteristic
361	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
362	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
363	C₁₉	#33823	1	1	yes	characteristic, direct product factor, Sylow
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	4	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	4	1	no	—
370	C₂×D₄	—	4	1	no	—
371	C₂×D₄	—	4	1	no	—
372	C₂×D₄	—	4	1	no	—
373	C₂×D₄	—	4	1	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	—	4	1	no	—
376	C₂²×C₄	—	4	1	no	—
377	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
378	Q₁₆	—	2	1	no	—
379	Q₁₆	—	2	1	no	—
380	SD₁₆	—	4	2	no	—
381	D₈	—	2	1	no	—
382	D₈	—	2	1	no	—
383	D₈	—	2	1	no	—
384	D₈	—	2	1	no	—
385	D₈	—	2	1	no	—
386	D₈	—	2	1	no	—
387	D₈	—	4	2	no	—
388	M₁₆	—	4	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
392	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
393	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
394	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	4	1	no	—
400	C₄⋊C₄	—	4	1	no	—
401	C₄⋊C₄	—	4	1	no	—
402	C₄⋊C₄	—	4	1	no	—
403	C₄⋊C₄	—	4	1	no	—
404	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
405	C₄⋊C₄	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	—	4	1	no	—
412	C₂²⋊C₄	—	4	1	no	—
413	C₂²⋊C₄	—	4	1	no	—
414	C₂²⋊C₄	—	4	1	no	—
415	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
416	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
417	C₄²	—	4	1	no	—
418	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
419	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
420	C₁₆	—	2	1	no	—
421	C₁₆	—	2	1	no	—
422	C₁₆	—	2	1	no	—
423	C₁₆	—	2	1	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	1	no	—
427	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
428	Q₈	—	4	1	no	—
429	Q₈	—	4	1	no	—
430	Q₈	—	16	1	no	—
431	D₄	—	4	1	no	—
432	D₄	—	4	1	no	—
433	D₄	—	4	1	no	—
434	D₄	—	4	1	no	—
435	D₄	—	4	1	no	—
436	D₄	—	4	1	no	—
437	D₄	—	16	1	no	—
438	D₄	—	16	1	no	—
439	D₄	—	16	1	no	—
440	D₄	—	16	1	no	—
441	D₄	—	16	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	16	1	no	—
450	C₂×C₄	—	16	1	no	—
451	C₂×C₄	—	16	1	no	—
452	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
453	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
454	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
455	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
456	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
458	C₈	—	2	1	no	—
459	C₈	—	2	1	no	—
460	C₈	—	2	1	no	—
461	C₈	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
462	C₈	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	8	1	no	—
467	C₂²	—	8	1	no	—
468	C₂²	—	8	1	no	—
469	C₂²	—	8	1	no	—
470	C₂²	—	8	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	1	no	—
475	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	8	1	no	—
482	C₄	—	8	1	no	—
483	C₄	—	8	1	no	—
484	C₄	—	8	1	no	—
485	C₄	—	8	1	no	—
486	C₄	C₁₉×#537	1	1	yes	characteristic
487	C₄	C₁₉×#575	1	1	yes	characteristic
488	C₂	—	4	1	no	—
489	C₂	—	16	1	no	—
490	C₂	—	16	1	no	—
491	C₂	—	16	1	no	—
492	C₂	C₁₉×#3245	1	1	yes	characteristic
493	C₂	C₁₉×#3415	1	1	yes	characteristic
494	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 ◁ C₁₉×#117 ◁ C₁₉×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3176	C₂	semidirect
2. C₁₉×#3175	C₂	semidirect
3. C₁₉×#2229	C₂	semidirect
4. C₁₉×#2228	C₂	semidirect
5. C₁₉×#2226	C₂	semidirect
6. C₁₉×#2224	C₂	semidirect
7. C₁₉×#2220	C₂	semidirect
8. C₁₉×#2218	C₂	semidirect
9. C₁₉×#2217	C₂	semidirect
10. C₁₉×#2215	C₂	semidirect
11. C₁₉×#2210	C₂	semidirect
12. C₁₉×#2210	C₂	semidirect
13. C₁₉×#2207	C₂	semidirect
14. C₁₉×#2206	C₂	semidirect
15. C₁₉×#2151	C₂	semidirect
176. #33823	C₁₉	direct (N × H)
216. #3176	C₂×C₁₉	semidirect
217. #3175	C₂×C₁₉	semidirect
218. #2229	C₂×C₁₉	semidirect
219. #2228	C₂×C₁₉	semidirect
220. #2226	C₂×C₁₉	semidirect
221. #2224	C₂×C₁₉	semidirect
222. #2220	C₂×C₁₉	semidirect
223. #2218	C₂×C₁₉	semidirect
224. #2217	C₂×C₁₉	semidirect
225. #2215	C₂×C₁₉	semidirect
226. #2210	C₂×C₁₉	semidirect
227. #2210	C₂×C₁₉	semidirect
228. #2207	C₂×C₁₉	semidirect
229. #2206	C₂×C₁₉	semidirect
230. #2151	C₂×C₁₉	semidirect
363. C₁₉	#33823	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×#3176	2
C₁₉×#3175	2
C₁₉×#2229	2
C₁₉×#2228	2
C₁₉×#2226	2
C₁₉×#2224	2
C₁₉×#2220	2
C₁₉×#2218	2
C₁₉×#2217	2
C₁₉×#2215	2
C₁₉×#2210	2
C₁₉×#2207	2
C₁₉×#2206	2
C₁₉×#2151	2
#33823	19

Subgroups — C19×#33823 #18039782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33823 #18039782