Subgroups — C₁₉×#62331 #18068290

Order 4864.

1876 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3548	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3335	C₂	1	4	yes	maximal, complemented
3	C₁₉×#3332	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3331	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3284	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3255	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3253	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3204	C₂	1	4	yes	maximal, complemented
9	C₁₉×#3167	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3060	C₂	1	4	yes	maximal, complemented
11	C₁₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#135	C₂²	1	4	yes	—
13	C₂×C₁₉×#131	C₂²	1	2	yes	—
14	C₁₉×#562	—	2	4	no	—
15	C₁₉×#554	—	2	2	no	—
16	C₁₉×#554	C₂²	1	4	yes	—
17	C₁₉×#550	—	2	2	no	—
18	C₁₉×#550	C₂²	1	4	yes	—
19	C₁₉×#547	C₂²	1	4	yes	—
20	C₁₉×#547	C₂²	1	4	yes	—
21	C₁₉×#540	—	2	4	no	—
22	C₁₉×#537	—	2	4	no	—
23	C₁₉×#537	C₂²	1	8	yes	—
24	C₁₉×#533	C₂²	1	2	yes	—
25	C₁₉×#532	C₂²	1	2	yes	—
26	C₁₉×#532	C₂²	1	1	yes	characteristic
27	C₁₉×#498	C₂²	1	2	yes	—
28	C₁₉×#492	C₂²	1	2	yes	—
29	C₁₉×#487	C₂²	1	2	yes	—
30	C₁₉×#486	C₂²	1	2	yes	—
31	C₁₉×#483	C₂²	1	8	yes	—
32	C₁₉×#481	C₂²	1	8	yes	—
33	C₁₉×#476	C₂²	1	4	yes	—
34	C₁₉×#475	C₂²	1	4	yes	—
35	C₁₉×#470	C₂²	1	4	yes	—
36	C₁₉×#470	C₂²	1	4	yes	—
37	C₁₉×#469	C₂²	1	4	yes	—
38	C₁₉×#469	C₂²	1	4	yes	—
39	C₁₉×#465	C₂²	1	4	yes	—
40	C₁₉×#465	C₂²	1	4	yes	—
41	C₁₉×#465	C₂²	1	8	yes	—
42	C₁₉×#462	C₂²	1	4	yes	—
43	C₁₉×#459	C₂²	1	4	yes	—
44	C₁₉×#452	C₂²	1	8	yes	—
45	C₁₉×#449	C₂²	1	8	yes	—
46	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	—
47	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	—
48	C₁₉×#436	C₂²	1	4	yes	—
49	C₈×D₄×C₁₉	C₂²	1	4	yes	—
50	C₂×C₁₉×#106	C₂²	1	4	yes	—
51	C₁₉×#423	C₂²	1	1	yes	characteristic
52	C₁₉×#417	C₂²	1	8	yes	—
53	C₁₉×#408	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
55	C₂×#41×C₁₉	—	2	4	no	—
56	C₂×#41×C₁₉	—	2	2	no	—
57	C₂×#41×C₁₉	C₂³	1	8	yes	—
58	C₂×#41×C₁₉	C₂³	1	2	yes	—
59	C₁₉×#135	—	4	8	no	—
60	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
61	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
62	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
63	C₂×D₈×C₁₉	C₂³	1	4	yes	—
64	C₁₉×#131	—	4	4	no	—
65	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
66	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
67	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
71	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
72	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
73	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
74	C₁₉×#127	—	2	4	no	—
75	C₁₉×#127	D₄	1	1	yes	characteristic
76	C₁₉×#127	C₂³	1	2	yes	—
77	C₁₉×#125	—	2	4	no	—
78	C₁₉×#125	—	2	2	no	—
79	C₁₉×#124	—	2	2	no	—
80	C₁₉×#124	D₄	1	2	yes	—
81	C₁₉×#123	—	2	8	no	—
82	C₁₉×#123	—	2	8	no	—
83	C₁₉×C₂²⋊Q₈	—	2	8	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	2	4	no	—
86	C₁₉×C₂²⋊Q₈	—	2	8	no	—
87	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
88	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
89	C₁₉×#121	—	2	8	no	—
90	C₁₉×#121	—	2	8	no	—
91	C₁₉×#121	—	2	4	no	—
92	C₁₉×#121	—	2	8	no	—
93	C₁₉×#121	—	2	2	no	—
94	C₁₉×#121	—	2	8	no	—
95	C₁₉×#121	D₄	1	4	yes	—
96	C₁₉×#121	C₂³	1	8	yes	—
97	C₁₉×#121	C₂³	1	4	yes	—
98	C₄×Q₈×C₁₉	—	2	2	no	—
99	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
100	C₄×D₄×C₁₉	—	2	4	no	—
101	C₄×D₄×C₁₉	—	2	4	no	—
102	C₄×D₄×C₁₉	—	2	2	no	—
103	C₄×D₄×C₁₉	C₂³	1	4	yes	—
104	C₄×D₄×C₁₉	C₂³	1	4	yes	—
105	C₁₉×#117	—	2	2	no	—
106	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
107	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
108	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
109	C₁₉×#106	C₂³	1	4	yes	—
110	C₁₉×#106	C₂³	1	4	yes	—
111	C₁₉×#106	C₂³	1	4	yes	—
112	C₁₉×#106	C₂³	1	4	yes	—
113	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
114	C₁₉×#103	C₂³	1	4	yes	—
115	C₁₉×#103	C₂³	1	8	yes	—
116	C₁₉×#103	C₂³	1	4	yes	—
117	C₁₉×#102	C₂³	1	4	yes	—
118	C₁₉×#102	C₂³	1	8	yes	—
119	C₁₉×#102	C₂³	1	4	yes	—
120	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
121	C₄×C₈×C₁₉	C₂³	1	2	yes	—
122	C₄×C₈×C₁₉	C₂³	1	2	yes	—
123	#41×C₁₉	—	4	2	no	—
124	#41×C₁₉	—	4	2	no	—
125	#41×C₁₉	—	4	8	no	—
126	#41×C₁₉	—	4	8	no	—
127	#41×C₁₉	—	8	4	no	—
128	#41×C₁₉	—	8	8	no	—
129	C₂×Q₈×C₁₉	—	2	2	no	—
130	C₂×Q₈×C₁₉	—	2	2	no	—
131	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
132	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
133	C₂×D₄×C₁₉	—	2	4	no	—
134	C₂×D₄×C₁₉	—	2	8	no	—
135	C₂×D₄×C₁₉	—	2	8	no	—
136	C₂×D₄×C₁₉	—	2	2	no	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
139	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
140	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
141	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₁₉	—	2	8	no	—
143	C₂²×C₄×C₁₉	—	2	4	no	—
144	C₂²×C₄×C₁₉	—	2	8	no	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
148	Q₁₆×C₁₉	—	4	4	no	—
149	SD₁₆×C₁₉	—	2	8	no	—
150	SD₁₆×C₁₉	—	4	4	no	—
151	D₈×C₁₉	—	4	4	no	—
152	M₁₆×C₁₉	—	4	4	no	—
153	M₁₆×C₁₉	—	4	2	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₂×C₈×C₁₉	—	2	8	no	—
156	C₂×C₈×C₁₉	—	4	1	no	—
157	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
158	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
159	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
160	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	8	no	—
163	C₄⋊C₄×C₁₉	—	2	8	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	4	no	—
168	C₄⋊C₄×C₁₉	—	2	4	no	—
169	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
170	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
171	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
172	C₂²⋊C₄×C₁₉	—	2	4	no	—
173	C₂²⋊C₄×C₁₉	—	2	8	no	—
174	C₂²⋊C₄×C₁₉	—	2	8	no	—
175	C₂²⋊C₄×C₁₉	—	2	4	no	—
176	C₂²⋊C₄×C₁₉	—	2	4	no	—
177	C₂²⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
178	C₄²×C₁₉	—	2	4	no	—
179	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₉	C₂⁴	1	2	yes	—
182	#62331	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂³×C₁₉	—	2	4	no	—
184	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
185	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
186	Q₈×C₁₉	—	2	4	no	—
187	Q₈×C₁₉	—	2	4	no	—
188	Q₈×C₁₉	—	4	2	no	—
189	Q₈×C₁₉	—	4	4	no	—
190	Q₈×C₁₉	—	8	2	no	—
191	D₄×C₁₉	—	2	8	no	—
192	D₄×C₁₉	—	2	4	no	—
193	D₄×C₁₉	—	2	4	no	—
194	D₄×C₁₉	—	4	4	no	—
195	D₄×C₁₉	—	4	2	no	—
196	D₄×C₁₉	—	4	4	no	—
197	D₄×C₁₉	—	8	2	no	—
198	D₄×C₁₉	—	8	8	no	—
199	D₄×C₁₉	—	8	4	no	—
200	D₄×C₁₉	—	8	8	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	4	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	2	4	no	—
207	C₂×C₄×C₁₉	—	2	4	no	—
208	C₂×C₄×C₁₉	—	2	4	no	—
209	C₂×C₄×C₁₉	—	4	8	no	—
210	C₂×C₄×C₁₉	—	8	8	no	—
211	C₂×C₄×C₁₉	—	8	8	no	—
212	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
215	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
217	C₈×C₁₉	—	2	1	no	—
218	C₈×C₁₉	—	2	4	no	—
219	C₈×C₁₉	—	2	2	no	—
220	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
221	#3548	C₂×C₁₉	1	2	yes	complemented
222	#3335	C₂×C₁₉	1	4	yes	complemented
223	#3332	C₂×C₁₉	1	4	yes	complemented
224	#3331	C₂×C₁₉	1	4	yes	complemented
225	#3284	C₂×C₁₉	1	4	yes	complemented
226	#3255	C₂×C₁₉	1	1	yes	characteristic, complemented
227	#3253	C₂×C₁₉	1	1	yes	characteristic, complemented
228	#3204	C₂×C₁₉	1	4	yes	complemented
229	#3167	C₂×C₁₉	1	2	yes	complemented
230	#3060	C₂×C₁₉	1	4	yes	complemented
231	#2931	C₂×C₁₉	1	1	yes	characteristic, complemented
232	C₂²×C₁₉	—	2	1	no	—
233	C₂²×C₁₉	—	2	4	no	—
234	C₂²×C₁₉	—	2	2	no	—
235	C₂²×C₁₉	—	2	8	no	—
236	C₂²×C₁₉	—	4	4	no	—
237	C₂²×C₁₉	—	4	4	no	—
238	C₂²×C₁₉	—	4	4	no	—
239	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
240	C₄×C₁₉	—	2	4	no	—
241	C₄×C₁₉	—	2	1	no	—
242	C₄×C₁₉	—	2	2	no	—
243	C₄×C₁₉	—	4	4	no	—
244	C₄×C₁₉	—	4	4	no	—
245	C₄×C₁₉	—	4	4	no	—
246	C₄×C₁₉	#577	1	4	yes	—
247	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
248	C₄×C₁₉	#585	1	1	yes	characteristic
249	C₂×#135	C₂²×C₁₉	1	4	yes	—
250	C₂×#131	C₂²×C₁₉	1	2	yes	—
251	#562	—	2	4	no	—
252	#554	—	2	2	no	—
253	#554	C₂²×C₁₉	1	4	yes	—
254	#550	—	2	2	no	—
255	#550	C₂²×C₁₉	1	4	yes	—
256	#547	C₂²×C₁₉	1	4	yes	—
257	#547	C₂²×C₁₉	1	4	yes	—
258	#540	—	2	4	no	—
259	#537	—	2	4	no	—
260	#537	C₂²×C₁₉	1	8	yes	—
261	#533	C₂²×C₁₉	1	2	yes	—
262	#532	C₂²×C₁₉	1	2	yes	—
263	#532	C₂²×C₁₉	1	1	yes	characteristic
264	#498	C₂²×C₁₉	1	2	yes	—
265	#492	C₂²×C₁₉	1	2	yes	—
266	#487	C₂²×C₁₉	1	2	yes	—
267	#486	C₂²×C₁₉	1	2	yes	—
268	#483	C₂²×C₁₉	1	8	yes	—
269	#481	C₂²×C₁₉	1	8	yes	—
270	#476	C₂²×C₁₉	1	4	yes	—
271	#475	C₂²×C₁₉	1	4	yes	—
272	#470	C₂²×C₁₉	1	4	yes	—
273	#470	C₂²×C₁₉	1	4	yes	—
274	#469	C₂²×C₁₉	1	4	yes	—
275	#469	C₂²×C₁₉	1	4	yes	—
276	#465	C₂²×C₁₉	1	8	yes	—
277	#465	C₂²×C₁₉	1	4	yes	—
278	#465	C₂²×C₁₉	1	4	yes	—
279	#462	C₂²×C₁₉	1	4	yes	—
280	#459	C₂²×C₁₉	1	4	yes	—
281	#452	C₂²×C₁₉	1	8	yes	—
282	#449	C₂²×C₁₉	1	8	yes	—
283	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	—
284	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	—
285	#436	C₂²×C₁₉	1	4	yes	—
286	C₈×D₄	C₂²×C₁₉	1	4	yes	—
287	C₂×#106	C₂²×C₁₉	1	4	yes	—
288	#423	C₂²×C₁₉	1	1	yes	characteristic
289	#417	C₂²×C₁₉	1	8	yes	—
290	#408	C₂²×C₁₉	1	2	yes	—
291	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
292	C₂×C₁₉	—	4	1	no	—
293	C₂×C₁₉	—	4	4	no	—
294	C₂×C₁₉	—	8	4	no	—
295	C₂×C₁₉	#3496	1	1	yes	characteristic
296	C₂×C₁₉	C₂×#577	1	2	yes	—
297	C₂×#41	—	2	4	no	—
298	C₂×#41	—	2	2	no	—
299	C₂×#41	C₂³×C₁₉	1	8	yes	—
300	C₂×#41	C₂³×C₁₉	1	2	yes	—
301	#135	—	4	8	no	—
302	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
303	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
304	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
305	C₂×D₈	C₂³×C₁₉	1	4	yes	—
306	#131	—	4	4	no	—
307	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
308	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
309	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
311	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
312	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
313	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
314	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
315	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
316	#127	—	2	4	no	—
317	#127	D₄×C₁₉	1	1	yes	characteristic
318	#127	C₂³×C₁₉	1	2	yes	—
319	#125	—	2	4	no	—
320	#125	—	2	2	no	—
321	#124	—	2	2	no	—
322	#124	D₄×C₁₉	1	2	yes	—
323	#123	—	2	8	no	—
324	#123	—	2	8	no	—
325	C₂²⋊Q₈	—	2	8	no	—
326	C₂²⋊Q₈	—	2	2	no	—
327	C₂²⋊Q₈	—	2	4	no	—
328	C₂²⋊Q₈	—	2	8	no	—
329	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
330	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
331	#121	—	2	8	no	—
332	#121	—	2	8	no	—
333	#121	—	2	4	no	—
334	#121	—	2	8	no	—
335	#121	—	2	2	no	—
336	#121	—	2	8	no	—
337	#121	D₄×C₁₉	1	4	yes	—
338	#121	C₂³×C₁₉	1	4	yes	—
339	#121	C₂³×C₁₉	1	8	yes	—
340	C₄×Q₈	—	2	2	no	—
341	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
342	C₄×D₄	—	2	4	no	—
343	C₄×D₄	—	2	4	no	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	C₂³×C₁₉	1	4	yes	—
346	C₄×D₄	C₂³×C₁₉	1	4	yes	—
347	#117	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	4	no	—
349	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
350	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
351	#106	C₂³×C₁₉	1	4	yes	—
352	#106	C₂³×C₁₉	1	4	yes	—
353	#106	C₂³×C₁₉	1	4	yes	—
354	#106	C₂³×C₁₉	1	4	yes	—
355	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
356	#103	C₂³×C₁₉	1	4	yes	—
357	#103	C₂³×C₁₉	1	8	yes	—
358	#103	C₂³×C₁₉	1	4	yes	—
359	#102	C₂³×C₁₉	1	4	yes	—
360	#102	C₂³×C₁₉	1	8	yes	—
361	#102	C₂³×C₁₉	1	4	yes	—
362	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
363	C₄×C₈	C₂³×C₁₉	1	2	yes	—
364	C₄×C₈	C₂³×C₁₉	1	2	yes	—
365	C₁₉	#62331	1	1	yes	characteristic, direct product factor, Sylow
366	#41	—	4	2	no	—
367	#41	—	4	2	no	—
368	#41	—	4	8	no	—
369	#41	—	4	8	no	—
370	#41	—	8	4	no	—
371	#41	—	8	8	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
375	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	8	no	—
378	C₂×D₄	—	2	8	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
382	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
383	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
384	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
385	C₂²×C₄	—	2	8	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	8	no	—
388	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
389	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
390	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
391	Q₁₆	—	4	4	no	—
392	SD₁₆	—	2	8	no	—
393	SD₁₆	—	4	4	no	—
394	D₈	—	4	4	no	—
395	M₁₆	—	4	4	no	—
396	M₁₆	—	4	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	8	no	—
399	C₂×C₈	—	4	1	no	—
400	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
401	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
402	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
403	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	8	no	—
406	C₄⋊C₄	—	2	8	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
413	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
414	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	8	no	—
417	C₂²⋊C₄	—	2	8	no	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
421	C₄²	—	2	4	no	—
422	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
424	C₄²	C₂⁴×C₁₉	1	2	yes	—
425	C₂³	—	2	4	no	—
426	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
427	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
428	Q₈	—	2	4	no	—
429	Q₈	—	2	4	no	—
430	Q₈	—	4	2	no	—
431	Q₈	—	4	4	no	—
432	Q₈	—	8	2	no	—
433	D₄	—	2	8	no	—
434	D₄	—	2	4	no	—
435	D₄	—	2	4	no	—
436	D₄	—	4	4	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	4	no	—
439	D₄	—	8	2	no	—
440	D₄	—	8	8	no	—
441	D₄	—	8	4	no	—
442	D₄	—	8	8	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	4	8	no	—
452	C₂×C₄	—	8	8	no	—
453	C₂×C₄	—	8	8	no	—
454	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
456	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
457	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
458	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
459	C₈	—	2	1	no	—
460	C₈	—	2	4	no	—
461	C₈	—	2	2	no	—
462	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	8	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	4	4	no	—
470	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
471	C₄	—	2	4	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	2	no	—
474	C₄	—	4	4	no	—
475	C₄	—	4	4	no	—
476	C₄	—	4	4	no	—
477	C₄	C₁₉×#577	1	4	yes	—
478	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
479	C₄	C₁₉×#585	1	1	yes	characteristic
480	C₂	—	4	1	no	—
481	C₂	—	4	4	no	—
482	C₂	—	8	4	no	—
483	C₂	C₁₉×#3496	1	1	yes	characteristic
484	C₂	C₂×C₁₉×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3548	C₂	semidirect
2. C₁₉×#3335	C₂	semidirect
3. C₁₉×#3332	C₂	semidirect
4. C₁₉×#3331	C₂	semidirect
5. C₁₉×#3284	C₂	semidirect
6. C₁₉×#3255	C₂	semidirect
7. C₁₉×#3253	C₂	semidirect
8. C₁₉×#3204	C₂	semidirect
9. C₁₉×#3167	C₂	semidirect
10. C₁₉×#3060	C₂	semidirect
11. C₁₉×#2931	C₂	semidirect
182. #62331	C₁₉	direct (N × H)
221. #3548	C₂×C₁₉	semidirect
222. #3335	C₂×C₁₉	semidirect
223. #3332	C₂×C₁₉	semidirect
224. #3331	C₂×C₁₉	semidirect
225. #3284	C₂×C₁₉	semidirect
226. #3255	C₂×C₁₉	semidirect
227. #3253	C₂×C₁₉	semidirect
228. #3204	C₂×C₁₉	semidirect
229. #3167	C₂×C₁₉	semidirect
230. #3060	C₂×C₁₉	semidirect
231. #2931	C₂×C₁₉	semidirect
365. C₁₉	#62331	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×#3548	2
C₁₉×#3335	2
C₁₉×#3332	2
C₁₉×#3331	2
C₁₉×#3284	2
C₁₉×#3255	2
C₁₉×#3253	2
C₁₉×#3204	2
C₁₉×#3167	2
C₁₉×#3060	2
C₁₉×#2931	2
#62331	19

Subgroups — C19×#62331 #18068290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62331 #18068290