Subgroups — C₁₉×#23601 #18029560

Order 4864.

994 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#108	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2911	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2896	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#416	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#413	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2064	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2063	C₂	1	4	yes	maximal, complemented
9	C₁₉×#1742	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#108	—	2	4	no	—
18	C₂×C₁₉×#108	C₂²	1	4	yes	—
19	C₁₉×#428	—	2	2	no	—
20	C₁₉×#428	C₂²	1	4	yes	—
21	C₁₉×#427	—	2	2	no	—
22	C₁₉×#424	—	2	2	no	—
23	C₁₉×#424	C₂²	1	4	yes	—
24	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
25	C₁₉×#419	C₂²	1	2	yes	—
26	C₁₉×#418	C₂²	1	2	yes	—
27	C₁₉×#417	—	2	2	no	—
28	C₁₉×#416	—	2	2	no	—
29	C₁₉×#416	—	2	2	no	—
30	C₁₉×#416	—	2	2	no	—
31	C₂×C₁₉×#103	C₂²	1	2	yes	—
32	C₂×C₁₉×#102	C₂²	1	2	yes	—
33	C₁₉×#413	—	2	4	no	—
34	C₂×C₁₉×#101	C₂²	1	2	yes	—
35	C₂×C₁₉×#100	C₂²	1	2	yes	—
36	C₁₉×#343	C₂²	1	4	yes	—
37	C₂×#41×C₁₉	—	2	2	no	—
38	C₂×#41×C₁₉	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	—	2	1	no	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	—	2	2	no	—
43	C₂×#41×C₁₉	—	2	2	no	—
44	C₂×#41×C₁₉	Q₈	1	4	yes	—
45	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	—	2	1	no	—
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂×M₁₆×C₁₉	—	2	2	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	—	2	1	no	—
54	C₂×M₁₆×C₁₉	—	2	2	no	—
55	C₂×M₁₆×C₁₉	—	2	2	no	—
56	C₂×M₁₆×C₁₉	—	2	2	no	—
57	C₂×M₁₆×C₁₉	—	2	2	no	—
58	C₂×M₁₆×C₁₉	D₄	1	4	yes	—
59	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
60	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
61	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₉	—	2	1	no	—
63	C₂²×C₈×C₁₉	—	2	2	no	—
64	C₂²×C₈×C₁₉	—	2	2	no	—
65	C₂²×C₈×C₁₉	—	2	1	no	—
66	C₂²×C₈×C₁₉	—	2	1	no	—
67	C₂²×C₈×C₁₉	D₄	1	2	yes	—
68	C₂²×C₈×C₁₉	D₄	1	2	yes	—
69	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
70	C₁₉×#117	—	2	1	no	—
71	C₁₉×#117	—	2	1	no	—
72	C₁₉×#117	—	2	1	no	—
73	C₁₉×#117	—	2	1	no	—
74	C₁₉×#117	—	2	1	no	—
75	C₁₉×#117	—	2	1	no	—
76	C₁₉×#117	D₄	1	2	yes	—
77	C₁₉×#117	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄²×C₁₉	—	2	1	no	—
83	C₂×C₄²×C₁₉	—	2	1	no	—
84	C₁₉×#108	—	2	8	no	—
85	C₁₉×#107	—	2	4	no	—
86	C₁₉×#106	—	2	4	no	—
87	C₁₉×C₄⋊C₈	—	2	8	no	—
88	C₁₉×#103	—	2	4	no	—
89	C₁₉×#103	—	2	4	no	—
90	C₁₉×#102	—	2	4	no	—
91	C₁₉×#102	—	2	4	no	—
92	C₁₉×#101	—	2	4	no	—
93	C₁₉×#100	—	2	4	no	—
94	C₂⁴×C₁₉	—	2	1	no	—
95	C₂⁴×C₁₉	#41	1	1	yes	characteristic
96	#41×C₁₉	—	2	4	no	—
97	#41×C₁₉	—	2	4	no	—
98	#41×C₁₉	—	2	4	no	—
99	#41×C₁₉	—	2	4	no	—
100	#41×C₁₉	—	4	2	no	—
101	#41×C₁₉	—	4	2	no	—
102	#41×C₁₉	—	4	2	no	—
103	#41×C₁₉	—	4	2	no	—
104	C₂×Q₈×C₁₉	—	2	1	no	—
105	C₂×Q₈×C₁₉	—	2	1	no	—
106	C₂×Q₈×C₁₉	—	2	1	no	—
107	C₂×Q₈×C₁₉	—	2	1	no	—
108	C₂×Q₈×C₁₉	—	2	1	no	—
109	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
110	C₂×D₄×C₁₉	—	2	4	no	—
111	C₂×D₄×C₁₉	—	2	1	no	—
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	—	2	1	no	—
115	C₂×D₄×C₁₉	—	2	1	no	—
116	C₂×D₄×C₁₉	—	4	1	no	—
117	C₂×D₄×C₁₉	—	4	1	no	—
118	C₂×D₄×C₁₉	—	4	2	no	—
119	C₂×D₄×C₁₉	C₂×Q₈	1	2	yes	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	4	1	no	—
125	C₂²×C₄×C₁₉	—	4	1	no	—
126	C₂²×C₄×C₁₉	—	4	2	no	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
133	C₂²×C₄×C₁₉	#41	1	2	yes	—
134	C₂²×C₄×C₁₉	#41	1	2	yes	—
135	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
137	M₁₆×C₁₉	—	2	4	no	—
138	M₁₆×C₁₉	—	2	2	no	—
139	M₁₆×C₁₉	—	2	2	no	—
140	M₁₆×C₁₉	—	2	2	no	—
141	M₁₆×C₁₉	—	2	2	no	—
142	M₁₆×C₁₉	—	2	2	no	—
143	M₁₆×C₁₉	—	4	2	no	—
144	M₁₆×C₁₉	—	4	2	no	—
145	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
146	C₂×C₈×C₁₉	—	2	4	no	—
147	C₂×C₈×C₁₉	—	2	4	no	—
148	C₂×C₈×C₁₉	—	2	4	no	—
149	C₂×C₈×C₁₉	—	2	2	no	—
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₂×C₈×C₁₉	—	2	2	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₂×C₈×C₁₉	—	4	2	no	—
155	C₂×C₈×C₁₉	—	4	2	no	—
156	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
161	C₂²⋊C₄×C₁₉	—	2	2	no	—
162	C₂²⋊C₄×C₁₉	—	2	2	no	—
163	C₂²⋊C₄×C₁₉	—	4	1	no	—
164	C₂²⋊C₄×C₁₉	—	4	1	no	—
165	C₄²×C₁₉	—	2	2	no	—
166	C₄²×C₁₉	—	2	2	no	—
167	C₄²×C₁₉	—	4	1	no	—
168	C₄²×C₁₉	—	4	1	no	—
169	#23601	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	—	4	2	no	—
172	C₂³×C₁₉	—	4	1	no	—
173	C₂³×C₁₉	—	4	1	no	—
174	C₂³×C₁₉	—	8	2	no	—
175	C₂³×C₁₉	#121	1	1	yes	characteristic
176	C₂³×C₁₉	#121	1	1	yes	characteristic
177	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
178	C₂³×C₁₉	#126	1	2	yes	—
179	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
180	Q₈×C₁₉	—	2	2	no	—
181	Q₈×C₁₉	—	2	2	no	—
182	Q₈×C₁₉	—	4	1	no	—
183	Q₈×C₁₉	—	4	1	no	—
184	D₄×C₁₉	—	2	2	no	—
185	D₄×C₁₉	—	2	2	no	—
186	D₄×C₁₉	—	4	4	no	—
187	D₄×C₁₉	—	4	4	no	—
188	D₄×C₁₉	—	4	1	no	—
189	D₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	4	4	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	4	no	—
196	C₂×C₄×C₁₉	—	4	4	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	8	2	no	—
199	C₂×C₄×C₁₉	#121	1	2	yes	—
200	C₂×C₄×C₁₉	#121	1	2	yes	—
201	C₂×C₄×C₁₉	#121	1	2	yes	—
202	C₂×C₄×C₁₉	#121	1	2	yes	—
203	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
206	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
207	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
208	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
209	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
210	C₂×C₄×C₁₉	#126	1	2	yes	—
211	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
217	C₈×C₁₉	—	2	4	no	—
218	C₈×C₁₉	—	2	4	no	—
219	C₈×C₁₉	—	4	2	no	—
220	C₈×C₁₉	—	4	2	no	—
221	C₂²×#108	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#2911	C₂×C₁₉	1	1	yes	characteristic, complemented
223	C₂×#424	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#2896	C₂×C₁₉	1	1	yes	characteristic
225	C₂×#416	C₂×C₁₉	1	1	yes	characteristic
226	C₂×#413	C₂×C₁₉	1	1	yes	characteristic
227	#2064	C₂×C₁₉	1	4	yes	complemented
228	#2063	C₂×C₁₉	1	4	yes	complemented
229	#1742	C₂×C₁₉	1	1	yes	characteristic, complemented
230	C₂²×C₁₉	—	2	2	no	—
231	C₂²×C₁₉	—	2	2	no	—
232	C₂²×C₁₉	—	2	2	no	—
233	C₂²×C₁₉	—	4	2	no	—
234	C₂²×C₁₉	—	4	2	no	—
235	C₂²×C₁₉	—	4	2	no	—
236	C₂²×C₁₉	—	8	2	no	—
237	C₂²×C₁₉	—	8	2	no	—
238	C₂²×C₁₉	—	8	2	no	—
239	C₂²×C₁₉	#396	1	2	yes	—
240	C₂²×C₁₉	#396	1	2	yes	—
241	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
242	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
243	C₂²×C₁₉	C₂×#126	1	1	yes	characteristic
244	C₄×C₁₉	—	4	2	no	—
245	C₄×C₁₉	—	4	4	no	—
246	C₄×C₁₉	—	8	2	no	—
247	C₄×C₁₉	#396	1	2	yes	—
248	C₄×C₁₉	#396	1	2	yes	—
249	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
250	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
251	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
252	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
253	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
254	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
255	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
256	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
257	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
258	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
259	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
260	C₂×#108	—	2	4	no	—
261	C₂×#108	C₂²×C₁₉	1	4	yes	—
262	#428	—	2	2	no	—
263	#428	C₂²×C₁₉	1	4	yes	—
264	#427	—	2	2	no	—
265	#424	—	2	2	no	—
266	#424	C₂²×C₁₉	1	4	yes	—
267	C₂×C₄⋊C₈	—	2	2	no	—
268	#419	C₂²×C₁₉	1	2	yes	—
269	#418	C₂²×C₁₉	1	2	yes	—
270	#417	—	2	2	no	—
271	#416	—	2	2	no	—
272	#416	—	2	2	no	—
273	#416	—	2	2	no	—
274	C₂×#103	C₂²×C₁₉	1	2	yes	—
275	C₂×#102	C₂²×C₁₉	1	2	yes	—
276	#413	—	2	4	no	—
277	C₂×#101	C₂²×C₁₉	1	2	yes	—
278	C₂×#100	C₂²×C₁₉	1	2	yes	—
279	#343	C₂²×C₁₉	1	4	yes	—
280	C₂×C₁₉	—	2	1	no	—
281	C₂×C₁₉	—	2	1	no	—
282	C₂×C₁₉	—	2	2	no	—
283	C₂×C₁₉	—	2	2	no	—
284	C₂×C₁₉	—	8	2	no	—
285	C₂×C₁₉	C₂×#396	1	1	yes	characteristic
286	C₂×C₁₉	#3067	1	2	yes	—
287	C₂×#41	—	2	2	no	—
288	C₂×#41	—	2	1	no	—
289	C₂×#41	—	2	1	no	—
290	C₂×#41	—	2	1	no	—
291	C₂×#41	—	2	1	no	—
292	C₂×#41	—	2	2	no	—
293	C₂×#41	—	2	2	no	—
294	C₂×#41	Q₈×C₁₉	1	4	yes	—
295	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
296	C₂²×D₄	—	2	1	no	—
297	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
298	C₂³×C₄	—	2	1	no	—
299	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
300	C₂×M₁₆	—	2	1	no	—
301	C₂×M₁₆	—	2	2	no	—
302	C₂×M₁₆	—	2	1	no	—
303	C₂×M₁₆	—	2	1	no	—
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	—	2	2	no	—
307	C₂×M₁₆	—	2	2	no	—
308	C₂×M₁₆	D₄×C₁₉	1	4	yes	—
309	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
310	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
311	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	—	2	1	no	—
314	C₂²×C₈	—	2	2	no	—
315	C₂²×C₈	—	2	1	no	—
316	C₂²×C₈	—	2	1	no	—
317	C₂²×C₈	D₄×C₁₉	1	2	yes	—
318	C₂²×C₈	D₄×C₁₉	1	2	yes	—
319	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
320	#117	—	2	1	no	—
321	#117	—	2	1	no	—
322	#117	—	2	1	no	—
323	#117	—	2	1	no	—
324	#117	—	2	1	no	—
325	#117	—	2	1	no	—
326	#117	D₄×C₁₉	1	2	yes	—
327	#117	C₂³×C₁₉	1	2	yes	—
328	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	1	no	—
334	#108	—	2	8	no	—
335	#107	—	2	4	no	—
336	#106	—	2	4	no	—
337	C₄⋊C₈	—	2	8	no	—
338	#103	—	2	4	no	—
339	#103	—	2	4	no	—
340	#102	—	2	4	no	—
341	#102	—	2	4	no	—
342	#101	—	2	4	no	—
343	#100	—	2	4	no	—
344	C₁₉	#23601	1	1	yes	characteristic, direct product factor, Sylow
345	C₂⁴	—	2	1	no	—
346	C₂⁴	#41×C₁₉	1	1	yes	characteristic
347	#41	—	2	4	no	—
348	#41	—	2	4	no	—
349	#41	—	2	4	no	—
350	#41	—	2	4	no	—
351	#41	—	4	2	no	—
352	#41	—	4	2	no	—
353	#41	—	4	2	no	—
354	#41	—	4	2	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	4	1	no	—
368	C₂×D₄	—	4	1	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	C₂×Q₈×C₁₉	1	2	yes	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	4	1	no	—
376	C₂²×C₄	—	4	1	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
379	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
383	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
384	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
385	C₂²×C₄	#41×C₁₉	1	2	yes	—
386	C₂²×C₄	#41×C₁₉	1	2	yes	—
387	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
388	M₁₆	—	2	4	no	—
389	M₁₆	—	2	2	no	—
390	M₁₆	—	2	2	no	—
391	M₁₆	—	2	2	no	—
392	M₁₆	—	2	2	no	—
393	M₁₆	—	2	2	no	—
394	M₁₆	—	4	2	no	—
395	M₁₆	—	4	2	no	—
396	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
397	C₂×C₈	—	2	4	no	—
398	C₂×C₈	—	2	4	no	—
399	C₂×C₈	—	2	4	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	4	2	no	—
406	C₂×C₈	—	4	2	no	—
407	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	4	1	no	—
415	C₂²⋊C₄	—	4	1	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	4	1	no	—
419	C₄²	—	4	1	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	8	2	no	—
425	C₂³	C₁₉×#121	1	1	yes	characteristic
426	C₂³	C₁₉×#121	1	1	yes	characteristic
427	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
428	C₂³	C₁₉×#126	1	2	yes	—
429	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
430	Q₈	—	2	2	no	—
431	Q₈	—	2	2	no	—
432	Q₈	—	4	1	no	—
433	Q₈	—	4	1	no	—
434	D₄	—	2	2	no	—
435	D₄	—	2	2	no	—
436	D₄	—	4	4	no	—
437	D₄	—	4	4	no	—
438	D₄	—	4	1	no	—
439	D₄	—	4	1	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	8	2	no	—
449	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
450	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
451	C₂×C₄	C₁₉×#121	1	2	yes	—
452	C₂×C₄	C₁₉×#121	1	2	yes	—
453	C₂×C₄	C₁₉×#121	1	2	yes	—
454	C₂×C₄	C₁₉×#121	1	2	yes	—
455	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
456	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
457	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
458	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
459	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
460	C₂×C₄	C₁₉×#126	1	2	yes	—
461	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
464	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
465	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
466	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
467	C₈	—	2	4	no	—
468	C₈	—	2	4	no	—
469	C₈	—	4	2	no	—
470	C₈	—	4	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	—	8	2	no	—
480	C₂²	C₁₉×#396	1	2	yes	—
481	C₂²	C₁₉×#396	1	2	yes	—
482	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
483	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
484	C₂²	C₂×C₁₉×#126	1	1	yes	characteristic
485	C₄	—	4	4	no	—
486	C₄	—	4	2	no	—
487	C₄	—	8	2	no	—
488	C₄	C₁₉×#396	1	2	yes	—
489	C₄	C₁₉×#396	1	2	yes	—
490	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
491	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
492	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
493	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
494	C₂	—	2	1	no	—
495	C₂	—	2	1	no	—
496	C₂	—	2	2	no	—
497	C₂	—	2	2	no	—
498	C₂	—	8	2	no	—
499	C₂	C₂×C₁₉×#396	1	1	yes	characteristic
500	C₂	C₁₉×#3067	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×#121
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×#108	C₂	semidirect
2. C₁₉×#2911	C₂	semidirect
3. C₂×C₁₉×#424	C₂	semidirect
7. C₁₉×#2064	C₂	semidirect
8. C₁₉×#2063	C₂	semidirect
9. C₁₉×#1742	C₂	semidirect
169. #23601	C₁₉	direct (N × H)
221. C₂²×#108	C₂×C₁₉	semidirect
222. #2911	C₂×C₁₉	semidirect
223. C₂×#424	C₂×C₁₉	semidirect
227. #2064	C₂×C₁₉	semidirect
228. #2063	C₂×C₁₉	semidirect
229. #1742	C₂×C₁₉	semidirect
344. C₁₉	#23601	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#108	2
C₁₉×#2911	2
C₂×C₁₉×#424	2
C₁₉×#2896	2
C₂×C₁₉×#416	2
C₂×C₁₉×#413	2
C₁₉×#2064	2
C₁₉×#2063	2
C₁₉×#1742	2
#23601	19

Subgroups — C19×#23601 #18029560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23601 #18029560