Subgroups — C₁₉×#19028 #18024987

Order 4864.

888 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3217	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3138	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#490	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1658	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1657	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1531	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1528	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1524	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#564	C₂²	1	2	yes	complemented
11	C₁₉×#563	C₂²	1	2	yes	complemented
12	C₁₉×#557	—	2	1	no	—
13	C₁₉×#554	—	2	1	no	—
14	C₁₉×#552	—	2	1	no	—
15	C₁₉×#552	—	2	2	no	—
16	C₁₉×#552	—	2	1	no	—
17	C₁₉×#544	—	2	1	no	—
18	C₁₉×#544	—	2	1	no	—
19	C₁₉×#541	—	2	1	no	—
20	C₁₉×#541	—	2	2	no	—
21	C₁₉×#539	—	2	1	no	—
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
24	C₁₉×#529	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
26	C₁₉×#496	C₂²	1	2	yes	—
27	C₁₉×#490	—	2	2	no	—
28	C₁₉×#490	C₂²	1	4	yes	—
29	C₁₉×#490	C₂²	1	4	yes	—
30	C₁₉×#490	C₂²	1	2	yes	—
31	C₁₉×#486	—	2	1	no	—
32	C₁₉×#486	—	2	1	no	—
33	C₁₉×#460	—	2	1	no	—
34	C₁₉×#459	—	2	1	no	—
35	C₁₉×#450	—	2	1	no	—
36	C₁₉×#447	—	2	1	no	—
37	C₁₉×#432	C₂²	1	1	yes	characteristic
38	C₁₉×#418	—	2	2	no	—
39	C₂×C₁₉×#102	—	2	1	no	—
40	C₂×C₁₉×#102	—	2	1	no	—
41	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
43	C₁₉×#330	C₂²	1	4	yes	complemented
44	C₁₉×#330	C₂²	1	4	yes	complemented
45	C₁₉×#330	C₂²	1	2	yes	complemented
46	C₁₉×#329	C₂²	1	2	yes	complemented
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂×SD₁₆×C₁₉	—	2	2	no	—
51	C₂×D₈×C₁₉	—	2	2	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂²×C₈×C₁₉	—	2	1	no	—
54	C₁₉×C₄⋊Q₈	—	2	2	no	—
55	C₁₉×C₄⋊Q₈	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	2	no	—
57	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
58	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
59	C₁₉×#127	—	2	1	no	—
60	C₁₉×#127	—	2	1	no	—
61	C₁₉×#127	—	2	1	no	—
62	C₁₉×#127	C₂³	1	2	yes	—
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#126	—	2	2	no	—
65	C₁₉×#126	—	2	2	no	—
66	C₁₉×#126	—	2	2	no	—
67	C₁₉×#126	—	2	1	no	—
68	C₁₉×#125	—	2	2	no	—
69	C₁₉×#125	—	2	2	no	—
70	C₁₉×#125	—	2	1	no	—
71	C₁₉×#125	—	2	2	no	—
72	C₁₉×#125	—	2	2	no	—
73	C₁₉×#125	—	2	2	no	—
74	C₁₉×#125	—	2	2	no	—
75	C₁₉×#125	—	2	2	no	—
76	C₁₉×#125	—	2	2	no	—
77	C₁₉×#125	—	2	1	no	—
78	C₁₉×#125	—	2	1	no	—
79	C₁₉×#125	D₄	1	2	yes	—
80	C₁₉×#125	C₂³	1	2	yes	—
81	C₁₉×#125	C₂³	1	1	yes	characteristic
82	C₁₉×#125	C₂³	1	2	yes	—
83	C₁₉×#124	C₂³	1	1	yes	characteristic
84	C₁₉×#123	—	2	2	no	—
85	C₁₉×#123	—	2	2	no	—
86	C₁₉×#123	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	—	2	1	no	—
93	C₁₉×C₂²⋊Q₈	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
96	C₁₉×#121	D₄	1	1	yes	characteristic
97	C₄×Q₈×C₁₉	—	2	1	no	—
98	C₄×Q₈×C₁₉	—	2	2	no	—
99	C₄×Q₈×C₁₉	—	2	1	no	—
100	C₄×Q₈×C₁₉	—	2	1	no	—
101	C₄×Q₈×C₁₉	—	2	1	no	—
102	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
103	C₄×D₄×C₁₉	—	2	2	no	—
104	C₄×D₄×C₁₉	—	2	1	no	—
105	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
106	C₁₉×#117	—	2	2	no	—
107	C₁₉×#117	—	2	1	no	—
108	C₁₉×#117	—	2	2	no	—
109	C₁₉×#117	—	2	1	no	—
110	C₁₉×#117	D₄	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊C₈	—	2	1	no	—
118	C₁₉×#102	—	2	4	no	—
119	C₁₉×#102	—	2	4	no	—
120	C₁₉×#102	—	2	4	no	—
121	C₁₉×#102	—	2	4	no	—
122	C₁₉×#102	—	2	2	no	—
123	C₁₉×#102	—	2	2	no	—
124	C₁₉×C₂²⋊C₈	—	2	1	no	—
125	C₁₉×#97	—	2	1	no	—
126	C₁₉×#97	C₂³	1	2	yes	—
127	C₁₉×#97	C₂³	1	2	yes	—
128	C₁₉×#97	C₂³	1	2	yes	—
129	C₄×C₈×C₁₉	—	2	1	no	—
130	C₂⁴×C₁₉	—	4	1	no	—
131	C₂×Q₈×C₁₉	—	2	2	no	—
132	C₂×Q₈×C₁₉	—	2	1	no	—
133	C₂×Q₈×C₁₉	—	2	1	no	—
134	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	—	2	2	no	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	—	2	2	no	—
139	C₂×D₄×C₁₉	—	4	4	no	—
140	C₂×D₄×C₁₉	—	4	4	no	—
141	C₂×D₄×C₁₉	—	4	1	no	—
142	C₂×D₄×C₁₉	—	4	1	no	—
143	C₂×D₄×C₁₉	—	4	1	no	—
144	C₂×D₄×C₁₉	—	8	2	no	—
145	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	SD₁₆×C₁₉	—	8	2	no	—
154	D₈×C₁₉	—	8	2	no	—
155	M₁₆×C₁₉	—	4	2	no	—
156	C₂×C₈×C₁₉	—	2	2	no	—
157	C₂×C₈×C₁₉	—	2	2	no	—
158	C₂×C₈×C₁₉	—	2	2	no	—
159	C₂×C₈×C₁₉	—	4	2	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
183	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
184	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
185	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
186	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂²⋊C₄×C₁₉	—	2	2	no	—
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	2	2	no	—
191	C₂²⋊C₄×C₁₉	—	2	1	no	—
192	C₂²⋊C₄×C₁₉	—	2	2	no	—
193	C₂²⋊C₄×C₁₉	—	2	1	no	—
194	C₂²⋊C₄×C₁₉	—	2	1	no	—
195	C₂²⋊C₄×C₁₉	—	2	1	no	—
196	C₂²⋊C₄×C₁₉	—	2	1	no	—
197	C₄²×C₁₉	—	2	2	no	—
198	C₄²×C₁₉	—	2	2	no	—
199	C₄²×C₁₉	—	2	2	no	—
200	C₄²×C₁₉	—	2	2	no	—
201	C₄²×C₁₉	—	2	1	no	—
202	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
206	#19028	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₁₉	—	2	1	no	—
208	C₂³×C₁₉	—	4	2	no	—
209	C₂³×C₁₉	—	8	2	no	—
210	C₂³×C₁₉	—	8	2	no	—
211	C₂³×C₁₉	—	8	2	no	—
212	C₂³×C₁₉	#120	1	1	yes	characteristic
213	Q₈×C₁₉	—	4	1	no	—
214	Q₈×C₁₉	—	4	2	no	—
215	Q₈×C₁₉	—	8	1	no	—
216	Q₈×C₁₉	—	8	2	no	—
217	D₄×C₁₉	—	4	1	no	—
218	D₄×C₁₉	—	4	2	no	—
219	D₄×C₁₉	—	4	2	no	—
220	D₄×C₁₉	—	4	4	no	—
221	D₄×C₁₉	—	4	4	no	—
222	D₄×C₁₉	—	4	2	no	—
223	D₄×C₁₉	—	8	2	no	—
224	D₄×C₁₉	—	8	2	no	—
225	D₄×C₁₉	—	8	2	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	2	2	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	8	1	no	—
239	C₂×C₄×C₁₉	—	8	2	no	—
240	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
246	C₈×C₁₉	—	4	2	no	—
247	C₈×C₁₉	—	4	2	no	—
248	C₈×C₁₉	—	4	2	no	—
249	#3563	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#3217	C₂×C₁₉	1	1	yes	characteristic
251	#3138	C₂×C₁₉	1	1	yes	characteristic, complemented
252	C₂×#490	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#1658	C₂×C₁₉	1	4	yes	complemented
254	#1657	C₂×C₁₉	1	4	yes	complemented
255	#1531	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1528	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1524	C₂×C₁₉	1	1	yes	characteristic, complemented
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	—	2	1	no	—
260	C₂²×C₁₉	—	4	1	no	—
261	C₂²×C₁₉	—	4	1	no	—
262	C₂²×C₁₉	—	4	1	no	—
263	C₂²×C₁₉	—	8	2	no	—
264	C₂²×C₁₉	—	8	2	no	—
265	C₂²×C₁₉	—	8	2	no	—
266	C₂²×C₁₉	—	16	4	no	—
267	C₂²×C₁₉	#454	1	2	yes	—
268	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
269	C₄×C₁₉	—	2	1	no	—
270	C₄×C₁₉	—	2	1	no	—
271	C₄×C₁₉	—	2	1	no	—
272	C₄×C₁₉	—	2	1	no	—
273	C₄×C₁₉	—	2	1	no	—
274	C₄×C₁₉	—	4	2	no	—
275	C₄×C₁₉	—	4	1	no	—
276	C₄×C₁₉	—	4	1	no	—
277	C₄×C₁₉	—	4	2	no	—
278	C₄×C₁₉	—	4	2	no	—
279	C₄×C₁₉	—	4	2	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	#454	1	2	yes	—
282	#564	C₂²×C₁₉	1	2	yes	complemented
283	#563	C₂²×C₁₉	1	2	yes	complemented
284	#557	—	2	1	no	—
285	#554	—	2	1	no	—
286	#552	—	2	1	no	—
287	#552	—	2	2	no	—
288	#552	—	2	1	no	—
289	#544	—	2	1	no	—
290	#544	—	2	1	no	—
291	#541	—	2	1	no	—
292	#541	—	2	2	no	—
293	#539	—	2	1	no	—
294	#533	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
296	#529	C₂²×C₁₉	1	1	yes	characteristic
297	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
298	#496	C₂²×C₁₉	1	2	yes	—
299	#490	—	2	2	no	—
300	#490	C₂²×C₁₉	1	4	yes	—
301	#490	C₂²×C₁₉	1	4	yes	—
302	#490	C₂²×C₁₉	1	2	yes	—
303	#486	—	2	1	no	—
304	#486	—	2	1	no	—
305	#460	—	2	1	no	—
306	#459	—	2	1	no	—
307	#450	—	2	1	no	—
308	#447	—	2	1	no	—
309	#432	C₂²×C₁₉	1	1	yes	characteristic
310	#418	—	2	2	no	—
311	C₂×#102	—	2	1	no	—
312	C₂×#102	—	2	1	no	—
313	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
314	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
315	#330	C₂²×C₁₉	1	4	yes	complemented
316	#330	C₂²×C₁₉	1	4	yes	complemented
317	#330	C₂²×C₁₉	1	2	yes	complemented
318	#329	C₂²×C₁₉	1	2	yes	complemented
319	C₂×C₁₉	—	2	2	no	—
320	C₂×C₁₉	—	8	1	no	—
321	C₂×C₁₉	—	16	2	no	—
322	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
323	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
324	C₂×C₁₉	#3021	1	1	yes	characteristic
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	—	2	1	no	—
328	C₂×SD₁₆	—	2	2	no	—
329	C₂×D₈	—	2	2	no	—
330	C₂×M₁₆	—	2	1	no	—
331	C₂²×C₈	—	2	1	no	—
332	C₄⋊Q₈	—	2	2	no	—
333	C₄⋊Q₈	—	2	1	no	—
334	C₄⋊Q₈	—	2	2	no	—
335	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
336	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
337	#127	—	2	1	no	—
338	#127	—	2	1	no	—
339	#127	—	2	1	no	—
340	#127	C₂³×C₁₉	1	2	yes	—
341	#126	—	2	2	no	—
342	#126	—	2	2	no	—
343	#126	—	2	2	no	—
344	#126	—	2	2	no	—
345	#126	—	2	1	no	—
346	#125	—	2	2	no	—
347	#125	—	2	2	no	—
348	#125	—	2	1	no	—
349	#125	—	2	2	no	—
350	#125	—	2	2	no	—
351	#125	—	2	2	no	—
352	#125	—	2	2	no	—
353	#125	—	2	2	no	—
354	#125	—	2	2	no	—
355	#125	—	2	1	no	—
356	#125	—	2	1	no	—
357	#125	D₄×C₁₉	1	2	yes	—
358	#125	C₂³×C₁₉	1	2	yes	—
359	#125	C₂³×C₁₉	1	1	yes	characteristic
360	#125	C₂³×C₁₉	1	2	yes	—
361	#124	C₂³×C₁₉	1	1	yes	characteristic
362	#123	—	2	2	no	—
363	#123	—	2	2	no	—
364	#123	—	2	1	no	—
365	C₂²⋊Q₈	—	2	2	no	—
366	C₂²⋊Q₈	—	2	1	no	—
367	C₂²⋊Q₈	—	2	1	no	—
368	C₂²⋊Q₈	—	2	2	no	—
369	C₂²⋊Q₈	—	2	1	no	—
370	C₂²⋊Q₈	—	2	1	no	—
371	C₂²⋊Q₈	—	2	2	no	—
372	C₂²⋊Q₈	—	2	2	no	—
373	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
374	#121	D₄×C₁₉	1	1	yes	characteristic
375	C₄×Q₈	—	2	1	no	—
376	C₄×Q₈	—	2	2	no	—
377	C₄×Q₈	—	2	1	no	—
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
381	C₄×D₄	—	2	2	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
384	#117	—	2	2	no	—
385	#117	—	2	1	no	—
386	#117	—	2	2	no	—
387	#117	—	2	1	no	—
388	#117	D₄×C₁₉	1	2	yes	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
393	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
395	C₄⋊C₈	—	2	1	no	—
396	#102	—	2	4	no	—
397	#102	—	2	4	no	—
398	#102	—	2	4	no	—
399	#102	—	2	4	no	—
400	#102	—	2	2	no	—
401	#102	—	2	2	no	—
402	C₂²⋊C₈	—	2	1	no	—
403	#97	—	2	1	no	—
404	#97	C₂³×C₁₉	1	2	yes	—
405	#97	C₂³×C₁₉	1	2	yes	—
406	#97	C₂³×C₁₉	1	2	yes	—
407	C₄×C₈	—	2	1	no	—
408	C₁₉	#19028	1	1	yes	characteristic, direct product factor, Sylow
409	C₂⁴	—	4	1	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	—	4	4	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂×D₄	—	4	1	no	—
422	C₂×D₄	—	4	1	no	—
423	C₂×D₄	—	8	2	no	—
424	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
432	SD₁₆	—	8	2	no	—
433	D₈	—	8	2	no	—
434	M₁₆	—	4	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	4	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
462	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
463	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
464	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
465	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₄²	—	2	2	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	1	no	—
481	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
485	C₂³	—	2	1	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	8	2	no	—
488	C₂³	—	8	2	no	—
489	C₂³	—	8	2	no	—
490	C₂³	C₁₉×#120	1	1	yes	characteristic
491	Q₈	—	4	1	no	—
492	Q₈	—	4	2	no	—
493	Q₈	—	8	1	no	—
494	Q₈	—	8	2	no	—
495	D₄	—	4	1	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	4	no	—
499	D₄	—	4	4	no	—
500	D₄	—	4	2	no	—
501	D₄	—	8	2	no	—
502	D₄	—	8	2	no	—
503	D₄	—	8	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	8	1	no	—
517	C₂×C₄	—	8	2	no	—
518	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
519	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
520	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
524	C₈	—	4	2	no	—
525	C₈	—	4	2	no	—
526	C₈	—	4	2	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	4	1	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	8	2	no	—
533	C₂²	—	8	2	no	—
534	C₂²	—	8	2	no	—
535	C₂²	—	16	4	no	—
536	C₂²	C₁₉×#454	1	2	yes	—
537	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	2	no	—
549	C₄	—	4	1	no	—
550	C₄	C₁₉×#454	1	2	yes	—
551	C₂	—	2	2	no	—
552	C₂	—	8	1	no	—
553	C₂	—	16	2	no	—
554	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
555	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
556	C₂	C₁₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3217	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
1. C₁₉×#3563	C₂	semidirect
3. C₁₉×#3138	C₂	semidirect
4. C₂×C₁₉×#490	C₂	semidirect
5. C₁₉×#1658	C₂	semidirect
6. C₁₉×#1657	C₂	semidirect
7. C₁₉×#1531	C₂	semidirect
8. C₁₉×#1528	C₂	semidirect
9. C₁₉×#1524	C₂	semidirect
10. C₁₉×#564	C₂²	semidirect
11. C₁₉×#563	C₂²	semidirect
43. C₁₉×#330	C₂²	semidirect
44. C₁₉×#330	C₂²	semidirect
45. C₁₉×#330	C₂²	semidirect
46. C₁₉×#329	C₂²	semidirect
206. #19028	C₁₉	direct (N × H)
249. #3563	C₂×C₁₉	semidirect
251. #3138	C₂×C₁₉	semidirect
252. C₂×#490	C₂×C₁₉	semidirect
253. #1658	C₂×C₁₉	semidirect
254. #1657	C₂×C₁₉	semidirect
255. #1531	C₂×C₁₉	semidirect
256. #1528	C₂×C₁₉	semidirect
257. #1524	C₂×C₁₉	semidirect
282. #564	C₂²×C₁₉	semidirect
283. #563	C₂²×C₁₉	semidirect
315. #330	C₂²×C₁₉	semidirect
316. #330	C₂²×C₁₉	semidirect
317. #330	C₂²×C₁₉	semidirect
318. #329	C₂²×C₁₉	semidirect
408. C₁₉	#19028	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×#3563	2
C₁₉×#3217	2
C₁₉×#3138	2
C₂×C₁₉×#490	2
C₁₉×#1658	2
C₁₉×#1657	2
C₁₉×#1531	2
C₁₉×#1528	2
C₁₉×#1524	2
#19028	19

Subgroups — C19×#19028 #18024987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19028 #18024987