Subgroups — C₁₉×#18998 #18024957

Order 4864.

926 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#562	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3236	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3215	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3140	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1662	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1661	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1533	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1528	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1527	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#562	—	2	2	no	—
11	C₁₉×#562	—	2	2	no	—
12	C₁₉×#562	—	2	2	no	—
13	C₁₉×#562	C₂²	1	4	yes	—
14	C₁₉×#533	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#123	—	2	1	no	—
19	C₂×C₁₉×#123	—	2	1	no	—
20	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
21	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
22	C₂×C₁₉×#121	—	2	1	no	—
23	C₂×C₁₉×#121	—	2	1	no	—
24	C₁₉×#501	C₂²	1	2	yes	complemented
25	C₁₉×#497	C₂²	1	2	yes	complemented
26	C₁₉×#491	C₂²	1	2	yes	complemented
27	C₁₉×#489	C₂²	1	2	yes	complemented
28	C₁₉×#489	C₂²	1	2	yes	complemented
29	C₁₉×#489	C₂²	1	2	yes	complemented
30	C₁₉×#488	—	2	2	no	—
31	C₁₉×#484	—	2	1	no	—
32	C₁₉×#483	—	2	1	no	—
33	C₁₉×#479	—	2	2	no	—
34	C₁₉×#464	—	2	2	no	—
35	C₁₉×#451	—	2	1	no	—
36	C₁₉×#450	—	2	1	no	—
37	C₁₉×#432	C₂²	1	1	yes	characteristic
38	C₁₉×#432	C₂²	1	1	yes	characteristic
39	C₁₉×#419	—	2	1	no	—
40	C₁₉×#418	—	2	1	no	—
41	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
42	C₁₉×#330	C₂²	1	4	yes	complemented
43	C₁₉×#329	C₂²	1	4	yes	complemented
44	C₁₉×#329	C₂²	1	4	yes	complemented
45	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	—	2	1	no	—
53	C₂×Q₁₆×C₁₉	—	2	2	no	—
54	C₂×SD₁₆×C₁₉	—	2	2	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
57	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
58	C₁₉×#125	—	2	1	no	—
59	C₁₉×#125	—	2	1	no	—
60	C₁₉×#125	—	2	1	no	—
61	C₁₉×#125	D₄	1	2	yes	—
62	C₁₉×#125	C₂³	1	2	yes	—
63	C₁₉×#124	—	2	1	no	—
64	C₁₉×#124	—	2	1	no	—
65	C₁₉×#124	—	2	1	no	—
66	C₁₉×#124	—	2	1	no	—
67	C₁₉×#124	D₄	1	2	yes	—
68	C₁₉×#124	D₄	1	2	yes	—
69	C₁₉×#124	C₂³	1	2	yes	—
70	C₁₉×#124	C₂³	1	2	yes	—
71	C₁₉×#123	—	2	4	no	—
72	C₁₉×#123	—	2	4	no	—
73	C₁₉×#123	—	2	4	no	—
74	C₁₉×#123	—	2	4	no	—
75	C₁₉×C₂²⋊Q₈	—	2	4	no	—
76	C₁₉×C₂²⋊Q₈	—	2	4	no	—
77	C₁₉×C₂²⋊Q₈	—	2	4	no	—
78	C₁₉×C₂²⋊Q₈	—	2	4	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×#121	—	2	4	no	—
82	C₁₉×#121	—	2	4	no	—
83	C₁₉×#121	—	2	4	no	—
84	C₁₉×#121	—	2	4	no	—
85	C₄×Q₈×C₁₉	—	2	1	no	—
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₁₉×#117	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×#107	—	2	2	no	—
102	C₁₉×#106	—	2	2	no	—
103	C₁₉×C₄⋊C₈	—	2	1	no	—
104	C₁₉×C₄⋊C₈	—	2	1	no	—
105	C₁₉×#103	—	2	2	no	—
106	C₁₉×#103	—	2	2	no	—
107	C₁₉×#103	—	2	2	no	—
108	C₁₉×#103	—	2	2	no	—
109	C₁₉×#103	—	2	2	no	—
110	C₁₉×#102	—	2	2	no	—
111	C₁₉×#102	—	2	2	no	—
112	C₁₉×#102	—	2	2	no	—
113	C₁₉×C₂²⋊C₈	—	2	1	no	—
114	C₁₉×C₂²⋊C₈	—	2	1	no	—
115	C₁₉×#97	C₂³	1	2	yes	—
116	C₁₉×#97	C₂³	1	2	yes	—
117	C₁₉×#97	C₂³	1	2	yes	—
118	C₄×C₈×C₁₉	—	2	1	no	—
119	C₂⁴×C₁₉	—	2	1	no	—
120	C₂⁴×C₁₉	—	2	1	no	—
121	C₂×Q₈×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	4	2	no	—
126	C₂×Q₈×C₁₉	—	8	1	no	—
127	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
128	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
129	C₂×D₄×C₁₉	—	2	4	no	—
130	C₂×D₄×C₁₉	—	2	4	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	2	1	no	—
133	C₂×D₄×C₁₉	—	4	2	no	—
134	C₂×D₄×C₁₉	—	8	1	no	—
135	C₂×D₄×C₁₉	—	8	2	no	—
136	C₂×D₄×C₁₉	—	8	2	no	—
137	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	4	no	—
144	C₂²×C₄×C₁₉	—	2	4	no	—
145	C₂²×C₄×C₁₉	—	8	2	no	—
146	C₂²×C₄×C₁₉	—	8	2	no	—
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	Q₁₆×C₁₉	—	8	2	no	—
151	SD₁₆×C₁₉	—	8	2	no	—
152	M₁₆×C₁₉	—	4	2	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₂×C₈×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	4	no	—
157	C₄⋊C₄×C₁₉	—	2	4	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	4	1	no	—
169	C₄⋊C₄×C₁₉	—	4	1	no	—
170	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
171	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
172	C₂²⋊C₄×C₁₉	—	2	4	no	—
173	C₂²⋊C₄×C₁₉	—	2	4	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂²⋊C₄×C₁₉	—	2	2	no	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₂²⋊C₄×C₁₉	—	2	2	no	—
181	C₂²⋊C₄×C₁₉	—	2	2	no	—
182	C₂²⋊C₄×C₁₉	—	4	1	no	—
183	C₄²×C₁₉	—	4	1	no	—
184	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
188	#18998	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂³×C₁₉	—	2	2	no	—
190	C₂³×C₁₉	—	2	2	no	—
191	C₂³×C₁₉	—	4	2	no	—
192	C₂³×C₁₉	—	4	2	no	—
193	C₂³×C₁₉	—	4	2	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	—	4	2	no	—
196	C₂³×C₁₉	—	4	2	no	—
197	C₂³×C₁₉	#120	1	1	yes	characteristic
198	Q₈×C₁₉	—	4	2	no	—
199	Q₈×C₁₉	—	4	2	no	—
200	Q₈×C₁₉	—	4	2	no	—
201	Q₈×C₁₉	—	4	2	no	—
202	Q₈×C₁₉	—	8	1	no	—
203	Q₈×C₁₉	—	8	1	no	—
204	D₄×C₁₉	—	4	2	no	—
205	D₄×C₁₉	—	4	2	no	—
206	D₄×C₁₉	—	8	1	no	—
207	D₄×C₁₉	—	8	1	no	—
208	D₄×C₁₉	—	8	4	no	—
209	D₄×C₁₉	—	8	4	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	8	4	no	—
224	C₂×C₄×C₁₉	—	8	4	no	—
225	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
226	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
231	C₈×C₁₉	—	4	2	no	—
232	C₈×C₁₉	—	4	2	no	—
233	C₈×C₁₉	—	4	2	no	—
234	C₂×#562	C₂×C₁₉	1	1	yes	characteristic
235	#3236	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#3215	C₂×C₁₉	1	1	yes	characteristic, complemented
237	#3140	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#1662	C₂×C₁₉	1	4	yes	complemented
239	#1661	C₂×C₁₉	1	4	yes	complemented
240	#1533	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#1528	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#1527	C₂×C₁₉	1	1	yes	characteristic, complemented
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	2	1	no	—
245	C₂²×C₁₉	—	4	2	no	—
246	C₂²×C₁₉	—	4	2	no	—
247	C₂²×C₁₉	—	4	2	no	—
248	C₂²×C₁₉	—	4	2	no	—
249	C₂²×C₁₉	—	4	2	no	—
250	C₂²×C₁₉	—	4	2	no	—
251	C₂²×C₁₉	—	8	4	no	—
252	C₂²×C₁₉	—	8	4	no	—
253	C₂²×C₁₉	#455	1	2	yes	—
254	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
255	C₄×C₁₉	—	2	1	no	—
256	C₄×C₁₉	—	2	1	no	—
257	C₄×C₁₉	—	2	1	no	—
258	C₄×C₁₉	—	2	1	no	—
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	2	1	no	—
261	C₄×C₁₉	—	4	2	no	—
262	C₄×C₁₉	—	4	2	no	—
263	C₄×C₁₉	—	4	2	no	—
264	C₄×C₁₉	—	4	2	no	—
265	C₄×C₁₉	—	8	1	no	—
266	C₄×C₁₉	—	8	1	no	—
267	#562	—	2	2	no	—
268	#562	—	2	2	no	—
269	#562	—	2	2	no	—
270	#562	C₂²×C₁₉	1	4	yes	—
271	#533	C₂²×C₁₉	1	1	yes	characteristic
272	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
273	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
274	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
275	C₂×#123	—	2	1	no	—
276	C₂×#123	—	2	1	no	—
277	C₂×C₂²⋊Q₈	—	2	1	no	—
278	C₂×C₂²⋊Q₈	—	2	1	no	—
279	C₂×#121	—	2	1	no	—
280	C₂×#121	—	2	1	no	—
281	#501	C₂²×C₁₉	1	2	yes	complemented
282	#497	C₂²×C₁₉	1	2	yes	complemented
283	#491	C₂²×C₁₉	1	2	yes	complemented
284	#489	C₂²×C₁₉	1	2	yes	complemented
285	#489	C₂²×C₁₉	1	2	yes	complemented
286	#489	C₂²×C₁₉	1	2	yes	complemented
287	#488	—	2	2	no	—
288	#484	—	2	1	no	—
289	#483	—	2	1	no	—
290	#479	—	2	2	no	—
291	#464	—	2	2	no	—
292	#451	—	2	1	no	—
293	#450	—	2	1	no	—
294	#432	C₂²×C₁₉	1	1	yes	characteristic
295	#432	C₂²×C₁₉	1	1	yes	characteristic
296	#419	—	2	1	no	—
297	#418	—	2	1	no	—
298	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
299	#330	C₂²×C₁₉	1	4	yes	complemented
300	#329	C₂²×C₁₉	1	4	yes	complemented
301	#329	C₂²×C₁₉	1	4	yes	complemented
302	C₂×C₁₉	—	2	2	no	—
303	C₂×C₁₉	—	8	2	no	—
304	C₂×C₁₉	—	8	2	no	—
305	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
306	C₂×C₁₉	#3019	1	1	yes	characteristic
307	C₂×C₁₉	#3020	1	1	yes	characteristic
308	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
309	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
310	C₂²×D₄	—	2	1	no	—
311	C₂²×D₄	—	2	1	no	—
312	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
313	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	—	2	1	no	—
316	C₂×Q₁₆	—	2	2	no	—
317	C₂×SD₁₆	—	2	2	no	—
318	C₂×M₁₆	—	2	1	no	—
319	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
320	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
321	#125	—	2	1	no	—
322	#125	—	2	1	no	—
323	#125	—	2	1	no	—
324	#125	D₄×C₁₉	1	2	yes	—
325	#125	C₂³×C₁₉	1	2	yes	—
326	#124	—	2	1	no	—
327	#124	—	2	1	no	—
328	#124	—	2	1	no	—
329	#124	—	2	1	no	—
330	#124	D₄×C₁₉	1	2	yes	—
331	#124	D₄×C₁₉	1	2	yes	—
332	#124	C₂³×C₁₉	1	2	yes	—
333	#124	C₂³×C₁₉	1	2	yes	—
334	#123	—	2	4	no	—
335	#123	—	2	4	no	—
336	#123	—	2	4	no	—
337	#123	—	2	4	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	—	2	4	no	—
340	C₂²⋊Q₈	—	2	4	no	—
341	C₂²⋊Q₈	—	2	4	no	—
342	C₂²⋊Q₈	—	2	1	no	—
343	C₂²⋊Q₈	—	2	1	no	—
344	#121	—	2	4	no	—
345	#121	—	2	4	no	—
346	#121	—	2	4	no	—
347	#121	—	2	4	no	—
348	C₄×Q₈	—	2	1	no	—
349	C₄×Q₈	—	2	1	no	—
350	#117	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
356	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
364	#107	—	2	2	no	—
365	#106	—	2	2	no	—
366	C₄⋊C₈	—	2	1	no	—
367	C₄⋊C₈	—	2	1	no	—
368	#103	—	2	2	no	—
369	#103	—	2	2	no	—
370	#103	—	2	2	no	—
371	#103	—	2	2	no	—
372	#103	—	2	2	no	—
373	#102	—	2	2	no	—
374	#102	—	2	2	no	—
375	#102	—	2	2	no	—
376	C₂²⋊C₈	—	2	1	no	—
377	C₂²⋊C₈	—	2	1	no	—
378	#97	C₂³×C₁₉	1	2	yes	—
379	#97	C₂³×C₁₉	1	2	yes	—
380	#97	C₂³×C₁₉	1	2	yes	—
381	C₄×C₈	—	2	1	no	—
382	C₁₉	#18998	1	1	yes	characteristic, direct product factor, Sylow
383	C₂⁴	—	2	1	no	—
384	C₂⁴	—	2	1	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	4	2	no	—
390	C₂×Q₈	—	8	1	no	—
391	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
392	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	4	2	no	—
398	C₂×D₄	—	8	1	no	—
399	C₂×D₄	—	8	2	no	—
400	C₂×D₄	—	8	2	no	—
401	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
402	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	8	2	no	—
410	C₂²×C₄	—	8	2	no	—
411	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
414	Q₁₆	—	8	2	no	—
415	SD₁₆	—	8	2	no	—
416	M₁₆	—	4	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	4	1	no	—
433	C₄⋊C₄	—	4	1	no	—
434	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
435	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₂²⋊C₄	—	2	4	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	4	1	no	—
447	C₄²	—	4	1	no	—
448	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	C₁₉×#120	1	1	yes	characteristic
461	Q₈	—	4	2	no	—
462	Q₈	—	4	2	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	8	1	no	—
466	Q₈	—	8	1	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	8	1	no	—
470	D₄	—	8	1	no	—
471	D₄	—	8	4	no	—
472	D₄	—	8	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	8	4	no	—
487	C₂×C₄	—	8	4	no	—
488	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
489	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
490	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
494	C₈	—	4	2	no	—
495	C₈	—	4	2	no	—
496	C₈	—	4	2	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	8	4	no	—
506	C₂²	—	8	4	no	—
507	C₂²	C₁₉×#455	1	2	yes	—
508	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
509	C₄	—	2	1	no	—
510	C₄	—	2	1	no	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	8	1	no	—
520	C₄	—	8	1	no	—
521	C₂	—	2	2	no	—
522	C₂	—	8	2	no	—
523	C₂	—	8	2	no	—
524	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
525	C₂	C₁₉×#3019	1	1	yes	characteristic
526	C₂	C₁₉×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#562	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3236	C₂	semidirect
3. C₁₉×#3215	C₂	semidirect
4. C₁₉×#3140	C₂	semidirect
5. C₁₉×#1662	C₂	semidirect
6. C₁₉×#1661	C₂	semidirect
7. C₁₉×#1533	C₂	semidirect
8. C₁₉×#1528	C₂	semidirect
9. C₁₉×#1527	C₂	semidirect
24. C₁₉×#501	C₂²	semidirect
25. C₁₉×#497	C₂²	semidirect
26. C₁₉×#491	C₂²	semidirect
27. C₁₉×#489	C₂²	semidirect
28. C₁₉×#489	C₂²	semidirect
29. C₁₉×#489	C₂²	semidirect
42. C₁₉×#330	C₂²	semidirect
43. C₁₉×#329	C₂²	semidirect
44. C₁₉×#329	C₂²	semidirect
188. #18998	C₁₉	direct (N × H)
235. #3236	C₂×C₁₉	semidirect
236. #3215	C₂×C₁₉	semidirect
237. #3140	C₂×C₁₉	semidirect
238. #1662	C₂×C₁₉	semidirect
239. #1661	C₂×C₁₉	semidirect
240. #1533	C₂×C₁₉	semidirect
241. #1528	C₂×C₁₉	semidirect
242. #1527	C₂×C₁₉	semidirect
281. #501	C₂²×C₁₉	semidirect
282. #497	C₂²×C₁₉	semidirect
283. #491	C₂²×C₁₉	semidirect
284. #489	C₂²×C₁₉	semidirect
285. #489	C₂²×C₁₉	semidirect
286. #489	C₂²×C₁₉	semidirect
299. #330	C₂²×C₁₉	semidirect
300. #329	C₂²×C₁₉	semidirect
301. #329	C₂²×C₁₉	semidirect
382. C₁₉	#18998	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#562	2
C₁₉×#3236	2
C₁₉×#3215	2
C₁₉×#3140	2
C₁₉×#1662	2
C₁₉×#1661	2
C₁₉×#1533	2
C₁₉×#1528	2
C₁₉×#1527	2
#18998	19

Subgroups — C19×#18998 #18024957

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18998 #18024957