Subgroups — C₁₉×#23589 #18029548

Order 4864.

1138 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3460	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×#137	C₂	1	2	yes	maximal, complemented
3	C₄×C₁₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2061	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2040	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2037	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2028	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2007	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2004	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₉×#104	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#137	C₂²	1	2	yes	—
13	C₁₉×#544	C₂²	1	1	yes	characteristic
14	C₁₉×#542	—	2	2	no	—
15	C₁₉×#540	—	2	2	no	—
16	C₁₉×#538	—	2	2	no	—
17	C₁₉×#537	C₂²	1	1	yes	characteristic
18	C₁₉×#535	C₂²	1	2	yes	—
19	C₁₉×#532	—	2	2	no	—
20	C₁₉×#529	—	2	2	no	—
21	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
22	C₁₉×#525	—	2	2	no	—
23	C₄×#41×C₁₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#441	—	2	2	no	—
27	C₁₉×#440	—	2	2	no	—
28	C₄×Q₁₆×C₁₉	—	2	2	no	—
29	C₄×SD₁₆×C₁₉	—	2	2	no	—
30	C₁₉×#428	C₂²	1	2	yes	—
31	C₂×C₁₉×#104	C₂²	1	2	yes	—
32	C₂×C₁₉×#104	C₂²	1	2	yes	—
33	C₁₉×#419	C₂²	1	2	yes	—
34	C₁₉×#417	C₂²	1	2	yes	—
35	C₂×C₁₉×#100	C₂²	1	2	yes	—
36	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
37	C₁₉×#391	C₂²	1	1	yes	characteristic
38	C₁₉×#390	C₂²	1	1	yes	characteristic
39	C₁₉×#388	—	2	2	no	—
40	C₁₉×#382	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
42	C₄³×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#343	C₂²	1	1	yes	characteristic
44	C₁₉×#343	C₂²	1	1	yes	characteristic
45	C₁₉×#339	C₂²	1	2	yes	—
46	C₁₉×#339	C₂²	1	2	yes	—
47	C₂×#41×C₁₉	—	2	2	no	—
48	C₂×#41×C₁₉	C₂³	1	2	yes	—
49	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	D₄	1	2	yes	—
52	C₁₉×#137	—	2	4	no	—
53	C₁₉×#137	—	2	4	no	—
54	C₂×Q₁₆×C₁₉	—	2	2	no	—
55	C₂×SD₁₆×C₁₉	—	2	2	no	—
56	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
57	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
58	C₁₉×C₄⋊Q₈	—	2	2	no	—
59	C₁₉×#127	—	2	2	no	—
60	C₁₉×#126	—	2	4	no	—
61	C₁₉×#125	—	2	2	no	—
62	C₁₉×#124	—	2	4	no	—
63	C₁₉×#124	—	2	2	no	—
64	C₁₉×#124	—	2	2	no	—
65	C₁₉×#124	—	2	2	no	—
66	C₁₉×#123	—	2	4	no	—
67	C₁₉×#123	—	2	4	no	—
68	C₁₉×C₂²⋊Q₈	—	2	2	no	—
69	C₁₉×C₂²⋊Q₈	—	2	2	no	—
70	C₁₉×C₂²⋊Q₈	—	2	2	no	—
71	C₁₉×#121	—	2	2	no	—
72	C₁₉×#121	—	2	4	no	—
73	C₁₉×#121	—	2	2	no	—
74	C₁₉×#121	—	2	2	no	—
75	C₁₉×#121	—	2	2	no	—
76	C₁₉×#121	—	2	2	no	—
77	C₁₉×#120	—	2	4	no	—
78	C₄×Q₈×C₁₉	—	2	2	no	—
79	C₄×Q₈×C₁₉	—	2	2	no	—
80	C₄×Q₈×C₁₉	D₄	1	2	yes	—
81	C₄×Q₈×C₁₉	D₄	1	2	yes	—
82	C₄×D₄×C₁₉	—	2	4	no	—
83	C₄×D₄×C₁₉	—	2	2	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₄×D₄×C₁₉	—	2	2	no	—
86	C₄×D₄×C₁₉	—	2	2	no	—
87	C₄×D₄×C₁₉	D₄	1	2	yes	—
88	C₄×D₄×C₁₉	D₄	1	2	yes	—
89	C₁₉×#117	—	2	2	no	—
90	C₁₉×#117	—	2	2	no	—
91	C₁₉×#117	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
98	C₂×C₄²×C₁₉	—	2	2	no	—
99	C₂×C₄²×C₁₉	—	2	1	no	—
100	C₂×C₄²×C₁₉	—	2	1	no	—
101	C₂×C₄²×C₁₉	—	2	1	no	—
102	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
105	C₁₉×#107	—	2	2	no	—
106	C₁₉×#106	—	2	2	no	—
107	C₁₉×#104	—	2	4	no	—
108	C₁₉×#104	—	2	4	no	—
109	C₁₉×#103	—	2	2	no	—
110	C₁₉×#103	—	2	2	no	—
111	C₁₉×#103	—	2	2	no	—
112	C₁₉×#102	—	2	2	no	—
113	C₁₉×#100	—	2	4	no	—
114	C₁₉×#97	—	2	2	no	—
115	C₄×C₈×C₁₉	—	2	2	no	—
116	C₁₉×#95	—	2	2	no	—
117	C₁₉×#95	—	2	2	no	—
118	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
119	#41×C₁₉	—	2	2	no	—
120	#41×C₁₉	—	2	2	no	—
121	#41×C₁₉	—	2	2	no	—
122	#41×C₁₉	—	2	2	no	—
123	#41×C₁₉	—	8	4	no	—
124	C₂×Q₈×C₁₉	—	2	2	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	2	no	—
127	C₂×Q₈×C₁₉	—	2	2	no	—
128	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
129	C₂×Q₈×C₁₉	#41	1	2	yes	complemented
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	2	4	no	—
132	C₂×D₄×C₁₉	—	2	4	no	—
133	C₂×D₄×C₁₉	—	2	2	no	—
134	C₂×D₄×C₁₉	—	2	2	no	—
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	2	no	—
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	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	4	4	no	—
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
153	Q₁₆×C₁₉	—	2	8	no	—
154	SD₁₆×C₁₉	—	2	8	no	—
155	M₁₆×C₁₉	—	2	2	no	—
156	M₁₆×C₁₉	—	2	2	no	—
157	M₁₆×C₁₉	—	2	2	no	—
158	M₁₆×C₁₉	#41	1	4	yes	complemented
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	4	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	2	no	—
168	C₄⋊C₄×C₁₉	—	4	2	no	—
169	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
170	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
171	C₂²⋊C₄×C₁₉	—	2	8	no	—
172	C₂²⋊C₄×C₁₉	—	2	4	no	—
173	C₂²⋊C₄×C₁₉	—	2	4	no	—
174	C₂²⋊C₄×C₁₉	—	2	4	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	4	no	—
177	C₂²⋊C₄×C₁₉	—	2	2	no	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	4	4	no	—
180	C₄²×C₁₉	—	2	2	no	—
181	C₄²×C₁₉	—	2	2	no	—
182	C₄²×C₁₉	—	2	2	no	—
183	C₄²×C₁₉	—	2	1	no	—
184	C₄²×C₁₉	—	2	2	no	—
185	C₄²×C₁₉	—	4	2	no	—
186	C₄²×C₁₉	—	4	2	no	—
187	C₄²×C₁₉	—	4	1	no	—
188	C₄²×C₁₉	—	4	1	no	—
189	C₄²×C₁₉	C₂×D₄	1	2	yes	—
190	C₄²×C₁₉	C₂×D₄	1	2	yes	—
191	C₄²×C₁₉	#41	1	2	yes	complemented
192	#23589	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂³×C₁₉	—	2	2	no	—
194	C₂³×C₁₉	—	2	2	no	—
195	C₂³×C₁₉	—	2	2	no	—
196	C₂³×C₁₉	—	2	2	no	—
197	C₂³×C₁₉	—	4	2	no	—
198	C₂³×C₁₉	—	4	2	no	—
199	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₁₉	—	2	4	no	—
201	Q₈×C₁₉	—	2	2	no	—
202	Q₈×C₁₉	—	2	2	no	—
203	Q₈×C₁₉	—	4	2	no	—
204	Q₈×C₁₉	—	8	2	no	—
205	D₄×C₁₉	—	2	2	no	—
206	D₄×C₁₉	—	2	2	no	—
207	D₄×C₁₉	—	4	2	no	—
208	D₄×C₁₉	—	4	2	no	—
209	D₄×C₁₉	—	4	2	no	—
210	D₄×C₁₉	—	4	2	no	—
211	D₄×C₁₉	—	8	4	no	—
212	D₄×C₁₉	—	8	2	no	—
213	D₄×C₁₉	—	8	4	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	4	no	—
232	C₂×C₄×C₁₉	—	4	4	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	8	2	no	—
237	C₂×C₄×C₁₉	—	8	2	no	—
238	C₂×C₄×C₁₉	#120	1	2	yes	—
239	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
242	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
244	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
245	C₈×C₁₉	—	2	4	no	—
246	C₈×C₁₉	—	4	2	no	—
247	#3460	C₂×C₁₉	1	1	yes	characteristic
248	C₄×#137	C₂×C₁₉	1	2	yes	complemented
249	C₄×#124	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#2061	C₂×C₁₉	1	1	yes	characteristic, complemented
251	#2040	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#2037	C₂×C₁₉	1	2	yes	complemented
253	#2028	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#2007	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#2004	C₂×C₁₉	1	2	yes	complemented
256	C₄×#104	C₂×C₁₉	1	2	yes	complemented
257	C₄×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	—	2	1	no	—
260	C₂²×C₁₉	—	4	4	no	—
261	C₂²×C₁₉	—	4	2	no	—
262	C₂²×C₁₉	—	4	2	no	—
263	C₂²×C₁₉	—	4	2	no	—
264	C₂²×C₁₉	—	4	2	no	—
265	C₂²×C₁₉	—	4	2	no	—
266	C₂²×C₁₉	—	4	2	no	—
267	C₂²×C₁₉	—	8	2	no	—
268	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
269	C₂²×C₁₉	#525	1	1	yes	characteristic
270	C₂²×C₁₉	#532	1	1	yes	characteristic
271	C₄×C₁₉	—	2	1	no	—
272	C₄×C₁₉	—	2	2	no	—
273	C₄×C₁₉	—	4	2	no	—
274	C₄×C₁₉	—	4	2	no	—
275	C₄×C₁₉	—	4	2	no	—
276	C₄×C₁₉	—	4	2	no	—
277	C₄×C₁₉	—	4	2	no	—
278	C₄×C₁₉	—	4	2	no	—
279	C₄×C₁₉	—	4	2	no	—
280	C₄×C₁₉	—	8	1	no	—
281	C₄×C₁₉	#455	1	2	yes	—
282	C₄×C₁₉	#525	1	2	yes	—
283	C₄×C₁₉	#532	1	2	yes	—
284	C₂×#137	C₂²×C₁₉	1	2	yes	—
285	#544	C₂²×C₁₉	1	1	yes	characteristic
286	#542	—	2	2	no	—
287	#540	—	2	2	no	—
288	#538	—	2	2	no	—
289	#537	C₂²×C₁₉	1	1	yes	characteristic
290	#535	C₂²×C₁₉	1	2	yes	—
291	#532	—	2	2	no	—
292	#529	—	2	2	no	—
293	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
294	#525	—	2	2	no	—
295	C₄×#41	C₂²×C₁₉	1	2	yes	—
296	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
297	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
298	#441	—	2	2	no	—
299	#440	—	2	2	no	—
300	C₄×Q₁₆	—	2	2	no	—
301	C₄×SD₁₆	—	2	2	no	—
302	#428	C₂²×C₁₉	1	2	yes	—
303	C₂×#104	C₂²×C₁₉	1	2	yes	—
304	C₂×#104	C₂²×C₁₉	1	2	yes	—
305	#419	C₂²×C₁₉	1	2	yes	—
306	#417	C₂²×C₁₉	1	2	yes	—
307	C₂×#100	C₂²×C₁₉	1	2	yes	—
308	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
309	#391	C₂²×C₁₉	1	1	yes	characteristic
310	#390	C₂²×C₁₉	1	1	yes	characteristic
311	#388	—	2	2	no	—
312	#382	C₂²×C₁₉	1	1	yes	characteristic
313	C₄×C₂²⋊C₄	—	2	2	no	—
314	C₄³	C₂²×C₁₉	1	1	yes	characteristic
315	#343	C₂²×C₁₉	1	1	yes	characteristic
316	#343	C₂²×C₁₉	1	1	yes	characteristic
317	#339	C₂²×C₁₉	1	2	yes	—
318	#339	C₂²×C₁₉	1	2	yes	—
319	C₂×C₁₉	—	2	1	no	—
320	C₂×C₁₉	—	2	1	no	—
321	C₂×C₁₉	—	8	2	no	—
322	C₂×C₁₉	—	8	2	no	—
323	C₂×C₁₉	#2388	1	1	yes	characteristic
324	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
325	C₂×C₁₉	#3018	1	1	yes	characteristic
326	C₂×#41	—	2	2	no	—
327	C₂×#41	C₂³×C₁₉	1	2	yes	—
328	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
329	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
330	C₂³×C₄	D₄×C₁₉	1	2	yes	—
331	#137	—	2	4	no	—
332	#137	—	2	4	no	—
333	C₂×Q₁₆	—	2	2	no	—
334	C₂×SD₁₆	—	2	2	no	—
335	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
336	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
337	C₄⋊Q₈	—	2	2	no	—
338	#127	—	2	2	no	—
339	#126	—	2	4	no	—
340	#125	—	2	2	no	—
341	#124	—	2	4	no	—
342	#124	—	2	2	no	—
343	#124	—	2	2	no	—
344	#124	—	2	2	no	—
345	#123	—	2	4	no	—
346	#123	—	2	4	no	—
347	C₂²⋊Q₈	—	2	2	no	—
348	C₂²⋊Q₈	—	2	2	no	—
349	C₂²⋊Q₈	—	2	2	no	—
350	#121	—	2	2	no	—
351	#121	—	2	4	no	—
352	#121	—	2	2	no	—
353	#121	—	2	2	no	—
354	#121	—	2	2	no	—
355	#121	—	2	2	no	—
356	#120	—	2	4	no	—
357	C₄×Q₈	—	2	2	no	—
358	C₄×Q₈	—	2	2	no	—
359	C₄×Q₈	D₄×C₁₉	1	2	yes	—
360	C₄×Q₈	D₄×C₁₉	1	2	yes	—
361	C₄×D₄	—	2	4	no	—
362	C₄×D₄	—	2	2	no	—
363	C₄×D₄	—	2	2	no	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	D₄×C₁₉	1	2	yes	—
367	C₄×D₄	D₄×C₁₉	1	2	yes	—
368	#117	—	2	2	no	—
369	#117	—	2	2	no	—
370	#117	C₂³×C₁₉	1	2	yes	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
377	C₂×C₄²	—	2	2	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	—	2	1	no	—
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
384	#107	—	2	2	no	—
385	#106	—	2	2	no	—
386	#104	—	2	4	no	—
387	#104	—	2	4	no	—
388	#103	—	2	2	no	—
389	#103	—	2	2	no	—
390	#103	—	2	2	no	—
391	#102	—	2	2	no	—
392	#100	—	2	4	no	—
393	#97	—	2	2	no	—
394	C₄×C₈	—	2	2	no	—
395	#95	—	2	2	no	—
396	#95	—	2	2	no	—
397	C₁₉	#23589	1	1	yes	characteristic, direct product factor, Sylow
398	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
399	#41	—	2	2	no	—
400	#41	—	2	2	no	—
401	#41	—	2	2	no	—
402	#41	—	2	2	no	—
403	#41	—	8	4	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
409	C₂×Q₈	#41×C₁₉	1	2	yes	complemented
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	4	no	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	4	4	no	—
429	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
431	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
432	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
433	Q₁₆	—	2	8	no	—
434	SD₁₆	—	2	8	no	—
435	M₁₆	—	2	2	no	—
436	M₁₆	—	2	2	no	—
437	M₁₆	—	2	2	no	—
438	M₁₆	#41×C₁₉	1	4	yes	complemented
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	4	2	no	—
449	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
450	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
451	C₂²⋊C₄	—	2	8	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	4	4	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	2	2	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	2	no	—
465	C₄²	—	4	2	no	—
466	C₄²	—	4	2	no	—
467	C₄²	—	4	1	no	—
468	C₄²	—	4	1	no	—
469	C₄²	C₂×D₄×C₁₉	1	2	yes	—
470	C₄²	C₂×D₄×C₁₉	1	2	yes	—
471	C₄²	#41×C₁₉	1	2	yes	complemented
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	2	no	—
478	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
479	Q₈	—	2	4	no	—
480	Q₈	—	2	2	no	—
481	Q₈	—	2	2	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	8	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	2	no	—
486	D₄	—	4	2	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	8	2	no	—
491	D₄	—	8	4	no	—
492	D₄	—	8	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	4	no	—
509	C₂×C₄	—	4	4	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	8	2	no	—
516	C₂×C₄	—	8	2	no	—
517	C₂×C₄	C₁₉×#120	1	2	yes	—
518	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
519	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
521	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
522	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
523	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
524	C₈	—	2	4	no	—
525	C₈	—	4	2	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	4	4	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	8	2	no	—
536	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
537	C₂²	C₁₉×#525	1	1	yes	characteristic
538	C₂²	C₁₉×#532	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	2	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	2	no	—
548	C₄	—	8	1	no	—
549	C₄	C₁₉×#455	1	2	yes	—
550	C₄	C₁₉×#525	1	2	yes	—
551	C₄	C₁₉×#532	1	2	yes	—
552	C₂	—	2	1	no	—
553	C₂	—	2	1	no	—
554	C₂	—	8	2	no	—
555	C₂	—	8	2	no	—
556	C₂	C₁₉×#2388	1	1	yes	characteristic
557	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
558	C₂	C₁₉×#3018	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×#120
prime radical	C₁₉×#3460	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₉×#137	C₂	semidirect
3. C₄×C₁₉×#124	C₂	semidirect
4. C₁₉×#2061	C₂	semidirect
5. C₁₉×#2040	C₂	semidirect
6. C₁₉×#2037	C₂	semidirect
7. C₁₉×#2028	C₂	semidirect
8. C₁₉×#2007	C₂	semidirect
9. C₁₉×#2004	C₂	semidirect
10. C₄×C₁₉×#104	C₂	semidirect
11. C₄×C₁₉×#100	C₂	semidirect
129. C₂×Q₈×C₁₉	#41	semidirect
158. M₁₆×C₁₉	#41	semidirect
191. C₄²×C₁₉	#41	semidirect
192. #23589	C₁₉	direct (N × H)
248. C₄×#137	C₂×C₁₉	semidirect
249. C₄×#124	C₂×C₁₉	semidirect
250. #2061	C₂×C₁₉	semidirect
251. #2040	C₂×C₁₉	semidirect
252. #2037	C₂×C₁₉	semidirect
253. #2028	C₂×C₁₉	semidirect
254. #2007	C₂×C₁₉	semidirect
255. #2004	C₂×C₁₉	semidirect
256. C₄×#104	C₂×C₁₉	semidirect
257. C₄×#100	C₂×C₁₉	semidirect
397. C₁₉	#23589	direct (N × H)
409. C₂×Q₈	#41×C₁₉	semidirect
438. M₁₆	#41×C₁₉	semidirect
471. C₄²	#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×#3460	2
C₄×C₁₉×#137	2
C₄×C₁₉×#124	2
C₁₉×#2061	2
C₁₉×#2040	2
C₁₉×#2037	2
C₁₉×#2028	2
C₁₉×#2007	2
C₁₉×#2004	2
C₄×C₁₉×#104	2
C₄×C₁₉×#100	2
#23589	19

Subgroups — C19×#23589 #18029548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23589 #18029548