Subgroups — C₁₉×#18254 #18024213

Order 4864.

1508 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3003	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#447	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2433	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1600	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1595	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1507	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1501	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1471	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
11	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
12	C₂²×D₈×C₁₉	—	2	1	no	—
13	C₁₉×#560	—	2	2	no	—
14	C₁₉×#553	—	2	1	no	—
15	C₁₉×#553	—	2	1	no	—
16	D₄²×C₁₉	—	2	2	no	—
17	D₄²×C₁₉	—	2	1	no	—
18	D₄²×C₁₉	—	2	1	no	—
19	C₁₉×#540	—	2	1	no	—
20	C₁₉×#538	—	2	1	no	—
21	C₁₉×#538	C₂²	1	2	yes	complemented
22	C₁₉×#535	—	2	1	no	—
23	C₁₉×#534	—	2	1	no	—
24	C₁₉×#534	C₂²	1	2	yes	complemented
25	C₂×C₁₉×#127	—	2	1	no	—
26	C₁₉×#525	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#120	—	2	2	no	—
30	C₁₉×#450	—	2	1	no	—
31	C₁₉×#450	C₂²	1	2	yes	complemented
32	C₁₉×#447	—	2	2	no	—
33	C₁₉×#447	—	2	1	no	—
34	C₁₉×#447	C₂²	1	4	yes	complemented
35	C₁₉×#447	C₂²	1	2	yes	complemented
36	C₁₉×#418	—	2	1	no	—
37	C₂×C₁₉×#102	—	2	1	no	—
38	C₁₉×#407	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#392	C₂²	1	4	yes	complemented
41	C₁₉×#390	—	2	1	no	—
42	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#328	C₂²	1	2	yes	complemented
44	C₁₉×#327	C₂²	1	2	yes	complemented
45	C₁₉×#327	C₂²	1	4	yes	complemented
46	C₁₉×#323	C₂²	1	4	yes	complemented
47	C₂⁵×C₁₉	—	2	1	no	—
48	C₂×#41×C₁₉	D₄	1	1	yes	characteristic, complemented
49	C₂²×D₄×C₁₉	—	2	2	no	—
50	C₂²×D₄×C₁₉	—	2	1	no	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂²×D₄×C₁₉	—	2	2	no	—
53	C₂²×D₄×C₁₉	—	2	4	no	—
54	C₂²×D₄×C₁₉	—	2	1	no	—
55	C₂²×D₄×C₁₉	—	2	1	no	—
56	C₂²×D₄×C₁₉	—	2	1	no	—
57	C₂²×D₄×C₁₉	—	2	1	no	—
58	C₂²×D₄×C₁₉	—	2	1	no	—
59	C₂²×D₄×C₁₉	—	4	4	no	—
60	C₂²×D₄×C₁₉	D₄	1	2	yes	—
61	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic, complemented
63	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
66	C₂×SD₁₆×C₁₉	—	2	2	no	—
67	C₂×D₈×C₁₉	—	2	4	no	—
68	C₂×D₈×C₁₉	—	2	2	no	—
69	C₂×D₈×C₁₉	—	4	4	no	—
70	C₂×M₁₆×C₁₉	—	2	1	no	—
71	C₂²×C₈×C₁₉	—	2	1	no	—
72	C₁₉×#127	—	2	2	no	—
73	C₁₉×#127	—	2	1	no	—
74	C₁₉×#127	—	4	4	no	—
75	C₁₉×#126	—	2	2	no	—
76	C₁₉×#126	—	2	2	no	—
77	C₁₉×#125	—	2	1	no	—
78	C₁₉×#124	—	2	2	no	—
79	C₁₉×#123	—	2	2	no	—
80	C₁₉×#123	—	2	1	no	—
81	C₁₉×#123	—	2	2	no	—
82	C₁₉×#123	—	2	2	no	—
83	C₁₉×#123	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
85	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₉×#121	—	2	2	no	—
87	C₁₉×#121	—	2	1	no	—
88	C₁₉×#121	—	2	1	no	—
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#121	—	2	2	no	—
91	C₁₉×#121	—	2	2	no	—
92	C₁₉×#121	—	2	2	no	—
93	C₁₉×#121	—	2	1	no	—
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#121	—	2	1	no	—
98	C₁₉×#121	—	2	1	no	—
99	C₁₉×#121	—	2	2	no	—
100	C₁₉×#121	D₄	1	2	yes	complemented
101	C₁₉×#121	D₄	1	1	yes	characteristic, complemented
102	C₁₉×#121	C₂³	1	2	yes	—
103	C₁₉×#121	C₂³	1	1	yes	characteristic
104	C₁₉×#120	—	2	2	no	—
105	C₁₉×#120	—	2	2	no	—
106	C₁₉×#120	—	2	2	no	—
107	C₁₉×#120	—	2	1	no	—
108	C₁₉×#120	—	2	2	no	—
109	C₁₉×#120	—	2	2	no	—
110	C₁₉×#120	—	2	2	no	—
111	C₁₉×#120	—	4	8	no	—
112	C₄×D₄×C₁₉	—	2	2	no	—
113	C₄×D₄×C₁₉	—	2	1	no	—
114	C₄×D₄×C₁₉	—	2	1	no	—
115	C₄×D₄×C₁₉	—	2	1	no	—
116	C₄×D₄×C₁₉	—	2	1	no	—
117	C₄×D₄×C₁₉	—	2	2	no	—
118	C₁₉×#117	—	2	1	no	—
119	C₁₉×#117	D₄	1	1	yes	characteristic, complemented
120	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic, complemented
122	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
125	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
126	C₂×C₄²×C₁₉	—	2	1	no	—
127	C₁₉×#102	—	2	4	no	—
128	C₁₉×#102	—	2	2	no	—
129	C₁₉×#102	—	2	2	no	—
130	C₁₉×C₂²⋊C₈	—	2	1	no	—
131	C₁₉×C₂²⋊C₈	—	2	1	no	—
132	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
133	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
134	C₁₉×#95	C₂³	1	2	yes	—
135	C₂⁴×C₁₉	—	2	2	no	—
136	C₂⁴×C₁₉	—	2	2	no	—
137	C₂⁴×C₁₉	—	2	1	no	—
138	C₂⁴×C₁₉	—	4	4	no	—
139	C₂⁴×C₁₉	—	4	4	no	—
140	C₂⁴×C₁₉	—	4	1	no	—
141	C₂⁴×C₁₉	—	4	1	no	—
142	C₂⁴×C₁₉	—	8	2	no	—
143	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
145	#41×C₁₉	—	4	2	no	—
146	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂×D₄×C₁₉	—	2	4	no	—
148	C₂×D₄×C₁₉	—	2	4	no	—
149	C₂×D₄×C₁₉	—	2	4	no	—
150	C₂×D₄×C₁₉	—	2	2	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	2	no	—
154	C₂×D₄×C₁₉	—	2	2	no	—
155	C₂×D₄×C₁₉	—	2	2	no	—
156	C₂×D₄×C₁₉	—	2	2	no	—
157	C₂×D₄×C₁₉	—	2	2	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	2	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	2	1	no	—
165	C₂×D₄×C₁₉	—	2	2	no	—
166	C₂×D₄×C₁₉	—	2	2	no	—
167	C₂×D₄×C₁₉	—	4	2	no	—
168	C₂×D₄×C₁₉	—	4	2	no	—
169	C₂×D₄×C₁₉	—	4	2	no	—
170	C₂×D₄×C₁₉	—	4	2	no	—
171	C₂×D₄×C₁₉	—	4	2	no	—
172	C₂×D₄×C₁₉	—	4	8	no	—
173	C₂×D₄×C₁₉	—	4	4	no	—
174	C₂×D₄×C₁₉	—	4	4	no	—
175	C₂×D₄×C₁₉	—	4	4	no	—
176	C₂×D₄×C₁₉	—	4	4	no	—
177	C₂×D₄×C₁₉	—	4	8	no	—
178	C₂×D₄×C₁₉	—	4	1	no	—
179	C₂×D₄×C₁₉	—	4	1	no	—
180	C₂×D₄×C₁₉	—	8	2	no	—
181	C₂×D₄×C₁₉	—	8	4	no	—
182	C₂×D₄×C₁₉	—	8	2	no	—
183	C₂×D₄×C₁₉	—	8	4	no	—
184	C₂×D₄×C₁₉	—	8	4	no	—
185	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₁₉	—	2	2	no	—
188	C₂²×C₄×C₁₉	—	2	2	no	—
189	C₂²×C₄×C₁₉	—	2	2	no	—
190	C₂²×C₄×C₁₉	—	2	1	no	—
191	C₂²×C₄×C₁₉	—	2	1	no	—
192	C₂²×C₄×C₁₉	—	4	2	no	—
193	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
200	SD₁₆×C₁₉	—	4	4	no	—
201	D₈×C₁₉	—	4	8	no	—
202	D₈×C₁₉	—	4	4	no	—
203	M₁₆×C₁₉	—	4	2	no	—
204	C₂×C₈×C₁₉	—	2	2	no	—
205	C₂×C₈×C₁₉	—	2	2	no	—
206	C₂×C₈×C₁₉	—	4	2	no	—
207	C₄⋊C₄×C₁₉	—	2	2	no	—
208	C₄⋊C₄×C₁₉	—	2	2	no	—
209	C₄⋊C₄×C₁₉	—	2	1	no	—
210	C₄⋊C₄×C₁₉	—	2	1	no	—
211	C₄⋊C₄×C₁₉	—	2	1	no	—
212	C₄⋊C₄×C₁₉	—	2	1	no	—
213	C₄⋊C₄×C₁₉	—	2	1	no	—
214	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
215	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₂²⋊C₄×C₁₉	—	2	4	no	—
218	C₂²⋊C₄×C₁₉	—	2	2	no	—
219	C₂²⋊C₄×C₁₉	—	2	2	no	—
220	C₂²⋊C₄×C₁₉	—	2	2	no	—
221	C₂²⋊C₄×C₁₉	—	2	2	no	—
222	C₂²⋊C₄×C₁₉	—	2	2	no	—
223	C₂²⋊C₄×C₁₉	—	2	1	no	—
224	C₂²⋊C₄×C₁₉	—	2	1	no	—
225	C₂²⋊C₄×C₁₉	—	2	1	no	—
226	C₂²⋊C₄×C₁₉	—	2	2	no	—
227	C₂²⋊C₄×C₁₉	—	2	1	no	—
228	C₂²⋊C₄×C₁₉	—	2	2	no	—
229	C₂²⋊C₄×C₁₉	—	2	2	no	—
230	C₂²⋊C₄×C₁₉	—	2	2	no	—
231	C₂²⋊C₄×C₁₉	—	2	1	no	—
232	C₂²⋊C₄×C₁₉	—	4	8	no	—
233	C₄²×C₁₉	—	2	2	no	—
234	C₄²×C₁₉	—	2	1	no	—
235	C₄²×C₁₉	—	4	2	no	—
236	#18254	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂³×C₁₉	—	2	2	no	—
238	C₂³×C₁₉	—	2	2	no	—
239	C₂³×C₁₉	—	2	4	no	—
240	C₂³×C₁₉	—	2	2	no	—
241	C₂³×C₁₉	—	2	2	no	—
242	C₂³×C₁₉	—	2	1	no	—
243	C₂³×C₁₉	—	2	4	no	—
244	C₂³×C₁₉	—	4	1	no	—
245	C₂³×C₁₉	—	4	4	no	—
246	C₂³×C₁₉	—	4	4	no	—
247	C₂³×C₁₉	—	4	4	no	—
248	C₂³×C₁₉	—	4	2	no	—
249	C₂³×C₁₉	—	4	2	no	—
250	C₂³×C₁₉	—	4	2	no	—
251	C₂³×C₁₉	—	4	2	no	—
252	C₂³×C₁₉	—	4	4	no	—
253	C₂³×C₁₉	—	4	2	no	—
254	C₂³×C₁₉	—	8	1	no	—
255	C₂³×C₁₉	—	8	1	no	—
256	C₂³×C₁₉	—	8	2	no	—
257	C₂³×C₁₉	—	8	2	no	—
258	C₂³×C₁₉	—	8	2	no	—
259	C₂³×C₁₉	—	8	2	no	—
260	C₂³×C₁₉	—	8	2	no	—
261	C₂³×C₁₉	—	8	2	no	—
262	C₂³×C₁₉	—	8	16	no	—
263	C₂³×C₁₉	—	8	2	no	—
264	C₂³×C₁₉	#120	1	1	yes	characteristic
265	C₂³×C₁₉	#120	1	1	yes	characteristic
266	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
267	Q₈×C₁₉	—	4	1	no	—
268	D₄×C₁₉	—	2	4	no	—
269	D₄×C₁₉	—	2	4	no	—
270	D₄×C₁₉	—	4	2	no	—
271	D₄×C₁₉	—	4	1	no	—
272	D₄×C₁₉	—	4	2	no	—
273	D₄×C₁₉	—	4	2	no	—
274	D₄×C₁₉	—	4	4	no	—
275	D₄×C₁₉	—	4	4	no	—
276	D₄×C₁₉	—	4	2	no	—
277	D₄×C₁₉	—	4	4	no	—
278	D₄×C₁₉	—	4	2	no	—
279	D₄×C₁₉	—	4	4	no	—
280	D₄×C₁₉	—	4	2	no	—
281	D₄×C₁₉	—	4	2	no	—
282	D₄×C₁₉	—	8	1	no	—
283	D₄×C₁₉	—	8	2	no	—
284	D₄×C₁₉	—	8	2	no	—
285	D₄×C₁₉	—	8	1	no	—
286	D₄×C₁₉	—	8	2	no	—
287	D₄×C₁₉	—	8	2	no	—
288	D₄×C₁₉	—	8	2	no	—
289	D₄×C₁₉	—	8	2	no	—
290	D₄×C₁₉	—	8	2	no	—
291	D₄×C₁₉	—	8	16	no	—
292	C₂×C₄×C₁₉	—	2	2	no	—
293	C₂×C₄×C₁₉	—	2	2	no	—
294	C₂×C₄×C₁₉	—	2	2	no	—
295	C₂×C₄×C₁₉	—	2	4	no	—
296	C₂×C₄×C₁₉	—	2	1	no	—
297	C₂×C₄×C₁₉	—	2	2	no	—
298	C₂×C₄×C₁₉	—	2	2	no	—
299	C₂×C₄×C₁₉	—	2	1	no	—
300	C₂×C₄×C₁₉	—	2	1	no	—
301	C₂×C₄×C₁₉	—	4	1	no	—
302	C₂×C₄×C₁₉	—	4	1	no	—
303	C₂×C₄×C₁₉	—	4	1	no	—
304	C₂×C₄×C₁₉	—	4	2	no	—
305	C₂×C₄×C₁₉	—	4	2	no	—
306	C₂×C₄×C₁₉	—	4	2	no	—
307	C₂×C₄×C₁₉	—	4	2	no	—
308	C₂×C₄×C₁₉	—	8	1	no	—
309	C₂×C₄×C₁₉	—	8	2	no	—
310	C₂×C₄×C₁₉	—	8	2	no	—
311	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
312	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
313	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
315	C₈×C₁₉	—	4	2	no	—
316	C₈×C₁₉	—	4	2	no	—
317	#3537	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#3003	C₂×C₁₉	1	1	yes	characteristic, complemented
319	C₂×#447	C₂×C₁₉	1	1	yes	characteristic, complemented
320	#2433	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#1600	C₂×C₁₉	1	4	yes	complemented
322	#1595	C₂×C₁₉	1	4	yes	complemented
323	#1507	C₂×C₁₉	1	1	yes	characteristic, complemented
324	#1501	C₂×C₁₉	1	1	yes	characteristic, complemented
325	#1471	C₂×C₁₉	1	1	yes	characteristic, complemented
326	C₂²×C₁₉	—	2	1	no	—
327	C₂²×C₁₉	—	2	1	no	—
328	C₂²×C₁₉	—	2	1	no	—
329	C₂²×C₁₉	—	2	1	no	—
330	C₂²×C₁₉	—	2	1	no	—
331	C₂²×C₁₉	—	2	1	no	—
332	C₂²×C₁₉	—	2	1	no	—
333	C₂²×C₁₉	—	4	4	no	—
334	C₂²×C₁₉	—	4	8	no	—
335	C₂²×C₁₉	—	4	2	no	—
336	C₂²×C₁₉	—	4	2	no	—
337	C₂²×C₁₉	—	4	1	no	—
338	C₂²×C₁₉	—	4	2	no	—
339	C₂²×C₁₉	—	4	2	no	—
340	C₂²×C₁₉	—	4	1	no	—
341	C₂²×C₁₉	—	4	1	no	—
342	C₂²×C₁₉	—	4	4	no	—
343	C₂²×C₁₉	—	4	2	no	—
344	C₂²×C₁₉	—	4	2	no	—
345	C₂²×C₁₉	—	8	4	no	—
346	C₂²×C₁₉	—	8	4	no	—
347	C₂²×C₁₉	—	8	8	no	—
348	C₂²×C₁₉	—	8	8	no	—
349	C₂²×C₁₉	—	8	2	no	—
350	C₂²×C₁₉	—	8	2	no	—
351	C₂²×C₁₉	—	16	2	no	—
352	C₂²×C₁₉	—	16	4	no	—
353	C₂²×C₁₉	#453	1	2	yes	—
354	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
355	C₂²×C₁₉	#576	1	2	yes	—
356	C₄×C₁₉	—	2	1	no	—
357	C₄×C₁₉	—	2	1	no	—
358	C₄×C₁₉	—	2	1	no	—
359	C₄×C₁₉	—	4	4	no	—
360	C₄×C₁₉	—	4	2	no	—
361	C₄×C₁₉	—	4	1	no	—
362	C₄×C₁₉	—	4	2	no	—
363	C₄×C₁₉	—	4	1	no	—
364	C₄×C₁₉	—	4	1	no	—
365	C₄×C₁₉	B(4,𝔽₂)	1	2	yes	—
366	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
367	C₂×AGL(1,ℤ/8)	—	2	1	no	—
368	C₂²×D₈	—	2	1	no	—
369	#560	—	2	2	no	—
370	#553	—	2	1	no	—
371	#553	—	2	1	no	—
372	D₄²	—	2	2	no	—
373	D₄²	—	2	1	no	—
374	D₄²	—	2	1	no	—
375	#540	—	2	1	no	—
376	#538	—	2	1	no	—
377	#538	C₂²×C₁₉	1	2	yes	complemented
378	#535	—	2	1	no	—
379	#534	—	2	1	no	—
380	#534	C₂²×C₁₉	1	2	yes	complemented
381	C₂×#127	—	2	1	no	—
382	#525	C₂²×C₁₉	1	1	yes	characteristic
383	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
384	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
385	C₂×#120	—	2	2	no	—
386	#450	—	2	1	no	—
387	#450	C₂²×C₁₉	1	2	yes	complemented
388	#447	—	2	2	no	—
389	#447	—	2	1	no	—
390	#447	C₂²×C₁₉	1	2	yes	complemented
391	#447	C₂²×C₁₉	1	4	yes	complemented
392	#418	—	2	1	no	—
393	C₂×#102	—	2	1	no	—
394	#407	C₂²×C₁₉	1	1	yes	characteristic, complemented
395	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
396	#392	C₂²×C₁₉	1	4	yes	complemented
397	#390	—	2	1	no	—
398	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
399	#328	C₂²×C₁₉	1	2	yes	complemented
400	#327	C₂²×C₁₉	1	2	yes	complemented
401	#327	C₂²×C₁₉	1	4	yes	complemented
402	#323	C₂²×C₁₉	1	4	yes	complemented
403	C₂×C₁₉	—	2	2	no	—
404	C₂×C₁₉	—	2	2	no	—
405	C₂×C₁₉	—	4	1	no	—
406	C₂×C₁₉	—	8	4	no	—
407	C₂×C₁₉	—	8	2	no	—
408	C₂×C₁₉	—	8	2	no	—
409	C₂×C₁₉	—	8	1	no	—
410	C₂×C₁₉	#3008	1	1	yes	characteristic
411	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
412	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
413	C₂⁵	—	2	1	no	—
414	C₂×#41	D₄×C₁₉	1	1	yes	characteristic, complemented
415	C₂²×D₄	—	2	2	no	—
416	C₂²×D₄	—	2	1	no	—
417	C₂²×D₄	—	2	1	no	—
418	C₂²×D₄	—	2	2	no	—
419	C₂²×D₄	—	2	4	no	—
420	C₂²×D₄	—	2	1	no	—
421	C₂²×D₄	—	2	1	no	—
422	C₂²×D₄	—	2	1	no	—
423	C₂²×D₄	—	2	1	no	—
424	C₂²×D₄	—	2	1	no	—
425	C₂²×D₄	—	4	4	no	—
426	C₂²×D₄	D₄×C₁₉	1	2	yes	—
427	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
428	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic, complemented
429	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
430	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
431	AGL(1,ℤ/8)	—	4	4	no	—
432	C₂×SD₁₆	—	2	2	no	—
433	C₂×D₈	—	2	4	no	—
434	C₂×D₈	—	2	2	no	—
435	C₂×D₈	—	4	4	no	—
436	C₂×M₁₆	—	2	1	no	—
437	C₂²×C₈	—	2	1	no	—
438	#127	—	2	2	no	—
439	#127	—	2	1	no	—
440	#127	—	4	4	no	—
441	#126	—	2	2	no	—
442	#126	—	2	2	no	—
443	#125	—	2	1	no	—
444	#124	—	2	2	no	—
445	#123	—	2	2	no	—
446	#123	—	2	1	no	—
447	#123	—	2	2	no	—
448	#123	—	2	2	no	—
449	#123	—	2	2	no	—
450	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
451	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
452	#121	—	2	2	no	—
453	#121	—	2	1	no	—
454	#121	—	2	1	no	—
455	#121	—	2	2	no	—
456	#121	—	2	2	no	—
457	#121	—	2	2	no	—
458	#121	—	2	2	no	—
459	#121	—	2	1	no	—
460	#121	—	2	1	no	—
461	#121	—	2	1	no	—
462	#121	—	2	1	no	—
463	#121	—	2	1	no	—
464	#121	—	2	1	no	—
465	#121	—	2	2	no	—
466	#121	D₄×C₁₉	1	2	yes	complemented
467	#121	D₄×C₁₉	1	1	yes	characteristic, complemented
468	#121	C₂³×C₁₉	1	2	yes	—
469	#121	C₂³×C₁₉	1	1	yes	characteristic
470	#120	—	2	2	no	—
471	#120	—	2	2	no	—
472	#120	—	2	2	no	—
473	#120	—	2	1	no	—
474	#120	—	2	2	no	—
475	#120	—	2	2	no	—
476	#120	—	2	2	no	—
477	#120	—	4	8	no	—
478	C₄×D₄	—	2	2	no	—
479	C₄×D₄	—	2	1	no	—
480	C₄×D₄	—	2	1	no	—
481	C₄×D₄	—	2	1	no	—
482	C₄×D₄	—	2	1	no	—
483	C₄×D₄	—	2	2	no	—
484	#117	—	2	1	no	—
485	#117	D₄×C₁₉	1	1	yes	characteristic, complemented
486	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
487	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic, complemented
488	C₂×C₂²⋊C₄	—	2	1	no	—
489	C₂×C₂²⋊C₄	—	2	1	no	—
490	C₂×C₂²⋊C₄	—	2	4	no	—
491	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
492	C₂×C₄²	—	2	1	no	—
493	#102	—	2	4	no	—
494	#102	—	2	2	no	—
495	#102	—	2	2	no	—
496	C₂²⋊C₈	—	2	1	no	—
497	C₂²⋊C₈	—	2	1	no	—
498	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
499	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
500	#95	C₂³×C₁₉	1	2	yes	—
501	C₁₉	#18254	1	1	yes	characteristic, direct product factor, Sylow
502	C₂⁴	—	2	2	no	—
503	C₂⁴	—	2	2	no	—
504	C₂⁴	—	2	1	no	—
505	C₂⁴	—	4	4	no	—
506	C₂⁴	—	4	4	no	—
507	C₂⁴	—	4	1	no	—
508	C₂⁴	—	4	1	no	—
509	C₂⁴	—	8	2	no	—
510	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
511	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
512	#41	—	4	2	no	—
513	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
514	C₂×D₄	—	2	4	no	—
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	2	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	2	no	—
521	C₂×D₄	—	2	2	no	—
522	C₂×D₄	—	2	2	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	2	2	no	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	4	2	no	—
535	C₂×D₄	—	4	2	no	—
536	C₂×D₄	—	4	2	no	—
537	C₂×D₄	—	4	2	no	—
538	C₂×D₄	—	4	2	no	—
539	C₂×D₄	—	4	8	no	—
540	C₂×D₄	—	4	4	no	—
541	C₂×D₄	—	4	4	no	—
542	C₂×D₄	—	4	4	no	—
543	C₂×D₄	—	4	4	no	—
544	C₂×D₄	—	4	8	no	—
545	C₂×D₄	—	4	1	no	—
546	C₂×D₄	—	4	1	no	—
547	C₂×D₄	—	8	2	no	—
548	C₂×D₄	—	8	4	no	—
549	C₂×D₄	—	8	2	no	—
550	C₂×D₄	—	8	4	no	—
551	C₂×D₄	—	8	4	no	—
552	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
553	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	4	2	no	—
560	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
561	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
564	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
565	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
566	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
567	SD₁₆	—	4	4	no	—
568	D₈	—	4	8	no	—
569	D₈	—	4	4	no	—
570	M₁₆	—	4	2	no	—
571	C₂×C₈	—	2	2	no	—
572	C₂×C₈	—	2	2	no	—
573	C₂×C₈	—	4	2	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
582	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
583	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	1	no	—
591	C₂²⋊C₄	—	2	1	no	—
592	C₂²⋊C₄	—	2	1	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	1	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	1	no	—
599	C₂²⋊C₄	—	4	8	no	—
600	C₄²	—	2	2	no	—
601	C₄²	—	2	1	no	—
602	C₄²	—	4	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	4	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	4	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	4	no	—
612	C₂³	—	4	4	no	—
613	C₂³	—	4	4	no	—
614	C₂³	—	4	2	no	—
615	C₂³	—	4	2	no	—
616	C₂³	—	4	2	no	—
617	C₂³	—	4	2	no	—
618	C₂³	—	4	4	no	—
619	C₂³	—	4	2	no	—
620	C₂³	—	8	1	no	—
621	C₂³	—	8	1	no	—
622	C₂³	—	8	2	no	—
623	C₂³	—	8	2	no	—
624	C₂³	—	8	2	no	—
625	C₂³	—	8	2	no	—
626	C₂³	—	8	2	no	—
627	C₂³	—	8	2	no	—
628	C₂³	—	8	16	no	—
629	C₂³	—	8	2	no	—
630	C₂³	C₁₉×#120	1	1	yes	characteristic
631	C₂³	C₁₉×#120	1	1	yes	characteristic
632	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
633	Q₈	—	4	1	no	—
634	D₄	—	2	4	no	—
635	D₄	—	2	4	no	—
636	D₄	—	4	2	no	—
637	D₄	—	4	1	no	—
638	D₄	—	4	2	no	—
639	D₄	—	4	2	no	—
640	D₄	—	4	4	no	—
641	D₄	—	4	4	no	—
642	D₄	—	4	2	no	—
643	D₄	—	4	4	no	—
644	D₄	—	4	2	no	—
645	D₄	—	4	4	no	—
646	D₄	—	4	2	no	—
647	D₄	—	4	2	no	—
648	D₄	—	8	1	no	—
649	D₄	—	8	2	no	—
650	D₄	—	8	2	no	—
651	D₄	—	8	1	no	—
652	D₄	—	8	2	no	—
653	D₄	—	8	2	no	—
654	D₄	—	8	2	no	—
655	D₄	—	8	2	no	—
656	D₄	—	8	2	no	—
657	D₄	—	8	16	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	2	no	—
671	C₂×C₄	—	4	2	no	—
672	C₂×C₄	—	4	2	no	—
673	C₂×C₄	—	4	2	no	—
674	C₂×C₄	—	8	1	no	—
675	C₂×C₄	—	8	2	no	—
676	C₂×C₄	—	8	2	no	—
677	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
678	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
679	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
680	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
681	C₈	—	4	2	no	—
682	C₈	—	4	2	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	1	no	—
687	C₂²	—	2	1	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	2	1	no	—
690	C₂²	—	4	4	no	—
691	C₂²	—	4	8	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	8	4	no	—
703	C₂²	—	8	4	no	—
704	C₂²	—	8	8	no	—
705	C₂²	—	8	8	no	—
706	C₂²	—	8	2	no	—
707	C₂²	—	8	2	no	—
708	C₂²	—	16	2	no	—
709	C₂²	—	16	4	no	—
710	C₂²	C₁₉×#453	1	2	yes	—
711	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
712	C₂²	C₁₉×#576	1	2	yes	—
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	4	4	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	1	no	—
722	C₄	C₁₉×B(4,𝔽₂)	1	2	yes	—
723	C₂	—	2	2	no	—
724	C₂	—	2	2	no	—
725	C₂	—	4	1	no	—
726	C₂	—	8	4	no	—
727	C₂	—	8	2	no	—
728	C₂	—	8	2	no	—
729	C₂	—	8	1	no	—
730	C₂	C₁₉×#3008	1	1	yes	characteristic
731	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
732	C₂	C₂×C₁₉×B(4,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3537	C₂	semidirect
2. C₁₉×#3003	C₂	semidirect
3. C₂×C₁₉×#447	C₂	semidirect
4. C₁₉×#2433	C₂	semidirect
5. C₁₉×#1600	C₂	semidirect
6. C₁₉×#1595	C₂	semidirect
7. C₁₉×#1507	C₂	semidirect
8. C₁₉×#1501	C₂	semidirect
9. C₁₉×#1471	C₂	semidirect
10. C₂³×D₄×C₁₉	C₂²	semidirect
21. C₁₉×#538	C₂²	semidirect
24. C₁₉×#534	C₂²	semidirect
31. C₁₉×#450	C₂²	semidirect
34. C₁₉×#447	C₂²	semidirect
35. C₁₉×#447	C₂²	semidirect
38. C₁₉×#407	C₂²	semidirect
39. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
40. C₁₉×#392	C₂²	semidirect
42. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
43. C₁₉×#328	C₂²	semidirect
44. C₁₉×#327	C₂²	semidirect
45. C₁₉×#327	C₂²	semidirect
46. C₁₉×#323	C₂²	semidirect
48. C₂×#41×C₁₉	D₄	semidirect
62. C₂²×D₄×C₁₉	D₄	semidirect
84. C₁₉×C₂²⋊Q₈	D₄	semidirect
100. C₁₉×#121	D₄	semidirect
101. C₁₉×#121	D₄	semidirect
119. C₁₉×#117	D₄	semidirect
121. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
236. #18254	C₁₉	direct (N × H)
317. #3537	C₂×C₁₉	semidirect
318. #3003	C₂×C₁₉	semidirect
319. C₂×#447	C₂×C₁₉	semidirect
320. #2433	C₂×C₁₉	semidirect
321. #1600	C₂×C₁₉	semidirect
322. #1595	C₂×C₁₉	semidirect
323. #1507	C₂×C₁₉	semidirect
324. #1501	C₂×C₁₉	semidirect
325. #1471	C₂×C₁₉	semidirect
366. C₂³×D₄	C₂²×C₁₉	semidirect
377. #538	C₂²×C₁₉	semidirect
380. #534	C₂²×C₁₉	semidirect
387. #450	C₂²×C₁₉	semidirect
390. #447	C₂²×C₁₉	semidirect
391. #447	C₂²×C₁₉	semidirect
394. #407	C₂²×C₁₉	semidirect
395. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
396. #392	C₂²×C₁₉	semidirect
398. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
399. #328	C₂²×C₁₉	semidirect
400. #327	C₂²×C₁₉	semidirect
401. #327	C₂²×C₁₉	semidirect
402. #323	C₂²×C₁₉	semidirect
414. C₂×#41	D₄×C₁₉	semidirect
428. C₂²×D₄	D₄×C₁₉	semidirect
450. C₂²⋊Q₈	D₄×C₁₉	semidirect
466. #121	D₄×C₁₉	semidirect
467. #121	D₄×C₁₉	semidirect
485. #117	D₄×C₁₉	semidirect
487. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
501. C₁₉	#18254	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×#3537	2
C₁₉×#3003	2
C₂×C₁₉×#447	2
C₁₉×#2433	2
C₁₉×#1600	2
C₁₉×#1595	2
C₁₉×#1507	2
C₁₉×#1501	2
C₁₉×#1471	2
#18254	19

Subgroups — C19×#18254 #18024213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18254 #18024213