Subgroups — C₁₉×#19016 #18024975

Order 4864.

1008 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3217	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3151	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#490	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1657	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1656	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1530	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	C₂×C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
11	C₁₉×#563	C₂²	1	2	yes	complemented
12	C₁₉×#562	C₂²	1	2	yes	complemented
13	C₁₉×#554	—	2	1	no	—
14	C₁₉×#553	—	2	1	no	—
15	C₁₉×#553	—	2	1	no	—
16	C₁₉×#547	—	2	2	no	—
17	C₁₉×#547	—	2	1	no	—
18	C₁₉×#544	—	2	1	no	—
19	C₁₉×#540	—	2	1	no	—
20	C₁₉×#539	—	2	2	no	—
21	C₁₉×#539	—	2	1	no	—
22	C₁₉×#537	—	2	1	no	—
23	C₁₉×#532	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
25	C₁₉×#529	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
27	C₁₉×#496	C₂²	1	2	yes	—
28	C₁₉×#496	C₂²	1	4	yes	—
29	C₁₉×#493	—	2	1	no	—
30	C₁₉×#492	—	2	1	no	—
31	C₁₉×#490	—	2	2	no	—
32	C₁₉×#490	C₂²	1	4	yes	—
33	C₁₉×#490	C₂²	1	2	yes	—
34	C₁₉×#460	—	2	1	no	—
35	C₁₉×#459	—	2	1	no	—
36	C₁₉×#450	—	2	1	no	—
37	C₁₉×#447	—	2	1	no	—
38	C₁₉×#432	C₂²	1	1	yes	characteristic
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	2	yes	complemented
45	C₁₉×#329	C₂²	1	2	yes	complemented
46	C₁₉×#329	C₂²	1	4	yes	complemented
47	C₂×#41×C₁₉	—	2	2	no	—
48	C₂×#41×C₁₉	D₄	1	2	yes	—
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	—	2	1	no	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₁₉×AGL(1,ℤ/8)	—	4	8	no	—
53	C₂×SD₁₆×C₁₉	—	2	4	no	—
54	C₂×SD₁₆×C₁₉	—	2	2	no	—
55	C₂×D₈×C₁₉	—	2	4	no	—
56	C₂×D₈×C₁₉	—	2	2	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂²×C₈×C₁₉	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	—	2	2	no	—
61	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
62	C₁₉×#127	—	2	1	no	—
63	C₁₉×#127	—	2	1	no	—
64	C₁₉×#127	—	2	1	no	—
65	C₁₉×#127	D₄	1	1	yes	characteristic
66	C₁₉×#127	C₂³	1	2	yes	—
67	C₁₉×#126	—	2	2	no	—
68	C₁₉×#126	—	2	2	no	—
69	C₁₉×#126	—	2	1	no	—
70	C₁₉×#125	—	2	2	no	—
71	C₁₉×#125	—	2	1	no	—
72	C₁₉×#125	—	2	1	no	—
73	C₁₉×#125	—	2	1	no	—
74	C₁₉×#125	D₄	1	2	yes	—
75	C₁₉×#125	C₂³	1	2	yes	—
76	C₁₉×#125	C₂³	1	1	yes	characteristic
77	C₁₉×#124	C₂³	1	1	yes	characteristic
78	C₁₉×#124	C₂³	1	2	yes	—
79	C₁₉×#123	—	2	2	no	—
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×#123	—	2	2	no	—
82	C₁₉×#123	—	2	2	no	—
83	C₁₉×#123	—	2	1	no	—
84	C₁₉×#123	—	2	2	no	—
85	C₁₉×#123	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	2	no	—
87	C₁₉×C₂²⋊Q₈	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	2	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
93	C₁₉×#121	—	2	2	no	—
94	C₁₉×#121	—	2	2	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#121	—	2	2	no	—
98	C₁₉×#121	—	2	2	no	—
99	C₁₉×#121	—	2	1	no	—
100	C₁₉×#121	—	2	1	no	—
101	C₁₉×#121	D₄	1	1	yes	characteristic
102	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
103	C₄×D₄×C₁₉	—	2	2	no	—
104	C₄×D₄×C₁₉	—	2	2	no	—
105	C₄×D₄×C₁₉	—	2	1	no	—
106	C₄×D₄×C₁₉	—	2	1	no	—
107	C₄×D₄×C₁₉	—	2	1	no	—
108	C₄×D₄×C₁₉	—	2	1	no	—
109	C₄×D₄×C₁₉	—	2	1	no	—
110	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
111	C₁₉×#117	—	2	1	no	—
112	C₁₉×#117	—	2	1	no	—
113	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
120	C₁₉×C₄⋊C₈	—	2	1	no	—
121	C₁₉×#102	—	2	4	no	—
122	C₁₉×#102	—	2	4	no	—
123	C₁₉×#102	—	2	2	no	—
124	C₁₉×#102	—	2	2	no	—
125	C₁₉×C₂²⋊C₈	—	2	1	no	—
126	C₁₉×#97	—	2	1	no	—
127	C₁₉×#97	C₂³	1	2	yes	—
128	C₁₉×#97	C₂³	1	2	yes	—
129	C₁₉×#97	C₂³	1	2	yes	—
130	C₄×C₈×C₁₉	—	2	1	no	—
131	C₂⁴×C₁₉	—	4	1	no	—
132	#41×C₁₉	—	4	4	no	—
133	#41×C₁₉	—	8	4	no	—
134	C₂×Q₈×C₁₉	—	2	2	no	—
135	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	—	2	1	no	—
139	C₂×D₄×C₁₉	—	2	2	no	—
140	C₂×D₄×C₁₉	—	2	2	no	—
141	C₂×D₄×C₁₉	—	2	1	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	4	4	no	—
147	C₂×D₄×C₁₉	—	4	4	no	—
148	C₂×D₄×C₁₉	—	4	1	no	—
149	C₂×D₄×C₁₉	—	4	1	no	—
150	C₂×D₄×C₁₉	—	4	1	no	—
151	C₂×D₄×C₁₉	—	8	2	no	—
152	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	2	no	—
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	SD₁₆×C₁₉	—	4	8	no	—
165	SD₁₆×C₁₉	—	8	2	no	—
166	D₈×C₁₉	—	4	8	no	—
167	D₈×C₁₉	—	8	2	no	—
168	M₁₆×C₁₉	—	2	4	no	—
169	C₂×C₈×C₁₉	—	2	2	no	—
170	C₂×C₈×C₁₉	—	2	2	no	—
171	C₂×C₈×C₁₉	—	2	2	no	—
172	C₂×C₈×C₁₉	—	4	2	no	—
173	C₄⋊C₄×C₁₉	—	2	2	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
190	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
191	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	2	2	no	—
195	C₂²⋊C₄×C₁₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₉	—	2	2	no	—
197	C₂²⋊C₄×C₁₉	—	2	2	no	—
198	C₂²⋊C₄×C₁₉	—	2	1	no	—
199	C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂²⋊C₄×C₁₉	—	2	1	no	—
201	C₂²⋊C₄×C₁₉	—	2	1	no	—
202	C₂²⋊C₄×C₁₉	—	2	2	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	1	no	—
205	C₄²×C₁₉	—	2	2	no	—
206	C₄²×C₁₉	—	2	1	no	—
207	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
211	#19016	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂³×C₁₉	—	2	2	no	—
213	C₂³×C₁₉	—	2	1	no	—
214	C₂³×C₁₉	—	4	2	no	—
215	C₂³×C₁₉	—	8	2	no	—
216	C₂³×C₁₉	—	8	2	no	—
217	C₂³×C₁₉	—	8	2	no	—
218	C₂³×C₁₉	#120	1	1	yes	characteristic
219	Q₈×C₁₉	—	4	2	no	—
220	Q₈×C₁₉	—	4	1	no	—
221	Q₈×C₁₉	—	8	2	no	—
222	D₄×C₁₉	—	4	2	no	—
223	D₄×C₁₉	—	4	1	no	—
224	D₄×C₁₉	—	4	4	no	—
225	D₄×C₁₉	—	4	2	no	—
226	D₄×C₁₉	—	4	2	no	—
227	D₄×C₁₉	—	4	4	no	—
228	D₄×C₁₉	—	4	4	no	—
229	D₄×C₁₉	—	4	2	no	—
230	D₄×C₁₉	—	4	2	no	—
231	D₄×C₁₉	—	8	1	no	—
232	D₄×C₁₉	—	8	2	no	—
233	D₄×C₁₉	—	8	2	no	—
234	D₄×C₁₉	—	8	2	no	—
235	D₄×C₁₉	—	8	2	no	—
236	D₄×C₁₉	—	8	2	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	8	2	no	—
249	C₂×C₄×C₁₉	—	8	1	no	—
250	C₂×C₄×C₁₉	—	8	2	no	—
251	C₂×C₄×C₁₉	—	8	2	no	—
252	C₂×C₄×C₁₉	—	8	2	no	—
253	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
254	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
255	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
259	C₈×C₁₉	—	2	4	no	—
260	C₈×C₁₉	—	4	2	no	—
261	C₈×C₁₉	—	4	2	no	—
262	#3559	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#3217	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#3151	C₂×C₁₉	1	1	yes	characteristic, complemented
265	C₂×#490	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1657	C₂×C₁₉	1	4	yes	complemented
267	#1656	C₂×C₁₉	1	4	yes	complemented
268	#1530	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1528	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#1524	C₂×C₁₉	1	1	yes	characteristic, complemented
271	C₂²×C₁₉	—	2	1	no	—
272	C₂²×C₁₉	—	2	1	no	—
273	C₂²×C₁₉	—	4	2	no	—
274	C₂²×C₁₉	—	4	1	no	—
275	C₂²×C₁₉	—	4	1	no	—
276	C₂²×C₁₉	—	4	2	no	—
277	C₂²×C₁₉	—	4	2	no	—
278	C₂²×C₁₉	—	4	1	no	—
279	C₂²×C₁₉	—	8	2	no	—
280	C₂²×C₁₉	—	8	2	no	—
281	C₂²×C₁₉	—	8	2	no	—
282	C₂²×C₁₉	—	16	4	no	—
283	C₂²×C₁₉	#453	1	2	yes	—
284	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
285	C₄×C₁₉	—	2	1	no	—
286	C₄×C₁₉	—	2	1	no	—
287	C₄×C₁₉	—	2	1	no	—
288	C₄×C₁₉	—	2	1	no	—
289	C₄×C₁₉	—	2	1	no	—
290	C₄×C₁₉	—	4	2	no	—
291	C₄×C₁₉	—	4	2	no	—
292	C₄×C₁₉	—	4	1	no	—
293	C₄×C₁₉	—	4	1	no	—
294	C₄×C₁₉	—	4	2	no	—
295	C₄×C₁₉	—	4	1	no	—
296	C₄×C₁₉	#454	1	2	yes	—
297	C₂×AGL(1,ℤ/8)	—	2	2	no	—
298	#563	C₂²×C₁₉	1	2	yes	complemented
299	#562	C₂²×C₁₉	1	2	yes	complemented
300	#554	—	2	1	no	—
301	#553	—	2	1	no	—
302	#553	—	2	1	no	—
303	#547	—	2	2	no	—
304	#547	—	2	1	no	—
305	#544	—	2	1	no	—
306	#540	—	2	1	no	—
307	#539	—	2	2	no	—
308	#539	—	2	1	no	—
309	#537	—	2	1	no	—
310	#532	C₂²×C₁₉	1	1	yes	characteristic
311	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
312	#529	C₂²×C₁₉	1	1	yes	characteristic
313	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
314	#496	C₂²×C₁₉	1	4	yes	—
315	#496	C₂²×C₁₉	1	2	yes	—
316	#493	—	2	1	no	—
317	#492	—	2	1	no	—
318	#490	—	2	2	no	—
319	#490	C₂²×C₁₉	1	4	yes	—
320	#490	C₂²×C₁₉	1	2	yes	—
321	#460	—	2	1	no	—
322	#459	—	2	1	no	—
323	#450	—	2	1	no	—
324	#447	—	2	1	no	—
325	#432	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×#102	—	2	1	no	—
327	C₂×#102	—	2	1	no	—
328	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
329	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
330	#330	C₂²×C₁₉	1	4	yes	complemented
331	#330	C₂²×C₁₉	1	2	yes	complemented
332	#329	C₂²×C₁₉	1	2	yes	complemented
333	#329	C₂²×C₁₉	1	4	yes	complemented
334	C₂×C₁₉	—	2	2	no	—
335	C₂×C₁₉	—	8	2	no	—
336	C₂×C₁₉	—	8	1	no	—
337	C₂×C₁₉	—	16	2	no	—
338	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
339	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
340	C₂×C₁₉	#3021	1	1	yes	characteristic
341	C₂×#41	—	2	2	no	—
342	C₂×#41	D₄×C₁₉	1	2	yes	—
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	—	2	1	no	—
345	C₂²×D₄	—	2	1	no	—
346	AGL(1,ℤ/8)	—	4	8	no	—
347	C₂×SD₁₆	—	2	4	no	—
348	C₂×SD₁₆	—	2	2	no	—
349	C₂×D₈	—	2	4	no	—
350	C₂×D₈	—	2	2	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂²×C₈	—	2	1	no	—
353	C₄⋊Q₈	—	2	1	no	—
354	C₄⋊Q₈	—	2	2	no	—
355	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
356	#127	—	2	1	no	—
357	#127	—	2	1	no	—
358	#127	—	2	1	no	—
359	#127	D₄×C₁₉	1	1	yes	characteristic
360	#127	C₂³×C₁₉	1	2	yes	—
361	#126	—	2	2	no	—
362	#126	—	2	2	no	—
363	#126	—	2	1	no	—
364	#125	—	2	2	no	—
365	#125	—	2	1	no	—
366	#125	—	2	1	no	—
367	#125	—	2	1	no	—
368	#125	D₄×C₁₉	1	2	yes	—
369	#125	C₂³×C₁₉	1	2	yes	—
370	#125	C₂³×C₁₉	1	1	yes	characteristic
371	#124	C₂³×C₁₉	1	1	yes	characteristic
372	#124	C₂³×C₁₉	1	2	yes	—
373	#123	—	2	2	no	—
374	#123	—	2	2	no	—
375	#123	—	2	2	no	—
376	#123	—	2	2	no	—
377	#123	—	2	1	no	—
378	#123	—	2	2	no	—
379	#123	—	2	2	no	—
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	—	2	2	no	—
382	C₂²⋊Q₈	—	2	2	no	—
383	C₂²⋊Q₈	—	2	2	no	—
384	C₂²⋊Q₈	—	2	2	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
387	#121	—	2	2	no	—
388	#121	—	2	2	no	—
389	#121	—	2	1	no	—
390	#121	—	2	1	no	—
391	#121	—	2	2	no	—
392	#121	—	2	2	no	—
393	#121	—	2	1	no	—
394	#121	—	2	1	no	—
395	#121	D₄×C₁₉	1	1	yes	characteristic
396	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
405	#117	—	2	1	no	—
406	#117	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	2	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
412	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
414	C₄⋊C₈	—	2	1	no	—
415	#102	—	2	4	no	—
416	#102	—	2	4	no	—
417	#102	—	2	2	no	—
418	#102	—	2	2	no	—
419	C₂²⋊C₈	—	2	1	no	—
420	#97	—	2	1	no	—
421	#97	C₂³×C₁₉	1	2	yes	—
422	#97	C₂³×C₁₉	1	2	yes	—
423	#97	C₂³×C₁₉	1	2	yes	—
424	C₄×C₈	—	2	1	no	—
425	C₁₉	#19016	1	1	yes	characteristic, direct product factor, Sylow
426	C₂⁴	—	4	1	no	—
427	#41	—	4	4	no	—
428	#41	—	8	4	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
431	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	4	4	no	—
442	C₂×D₄	—	4	4	no	—
443	C₂×D₄	—	4	1	no	—
444	C₂×D₄	—	4	1	no	—
445	C₂×D₄	—	4	1	no	—
446	C₂×D₄	—	8	2	no	—
447	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
459	SD₁₆	—	4	8	no	—
460	SD₁₆	—	8	2	no	—
461	D₈	—	4	8	no	—
462	D₈	—	8	2	no	—
463	M₁₆	—	2	4	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	4	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
485	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
486	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	2	1	no	—
502	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
503	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
505	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
506	C₂³	—	2	2	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	4	2	no	—
509	C₂³	—	8	2	no	—
510	C₂³	—	8	2	no	—
511	C₂³	—	8	2	no	—
512	C₂³	C₁₉×#120	1	1	yes	characteristic
513	Q₈	—	4	2	no	—
514	Q₈	—	4	1	no	—
515	Q₈	—	8	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	4	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	4	no	—
522	D₄	—	4	4	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	8	1	no	—
526	D₄	—	8	2	no	—
527	D₄	—	8	2	no	—
528	D₄	—	8	2	no	—
529	D₄	—	8	2	no	—
530	D₄	—	8	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	8	2	no	—
543	C₂×C₄	—	8	1	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	—	8	2	no	—
546	C₂×C₄	—	8	2	no	—
547	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
548	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
549	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
553	C₈	—	2	4	no	—
554	C₈	—	4	2	no	—
555	C₈	—	4	2	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	8	2	no	—
565	C₂²	—	8	2	no	—
566	C₂²	—	8	2	no	—
567	C₂²	—	16	4	no	—
568	C₂²	C₁₉×#453	1	2	yes	—
569	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	2	no	—
580	C₄	—	4	1	no	—
581	C₄	C₁₉×#454	1	2	yes	—
582	C₂	—	2	2	no	—
583	C₂	—	8	2	no	—
584	C₂	—	8	1	no	—
585	C₂	—	16	2	no	—
586	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
587	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
588	C₂	C₁₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
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×#3559	C₂	semidirect
2. C₁₉×#3217	C₂	semidirect
3. C₁₉×#3151	C₂	semidirect
4. C₂×C₁₉×#490	C₂	semidirect
5. C₁₉×#1657	C₂	semidirect
6. C₁₉×#1656	C₂	semidirect
7. C₁₉×#1530	C₂	semidirect
8. C₁₉×#1528	C₂	semidirect
9. C₁₉×#1524	C₂	semidirect
11. C₁₉×#563	C₂²	semidirect
12. C₁₉×#562	C₂²	semidirect
43. C₁₉×#330	C₂²	semidirect
44. C₁₉×#330	C₂²	semidirect
45. C₁₉×#329	C₂²	semidirect
46. C₁₉×#329	C₂²	semidirect
211. #19016	C₁₉	direct (N × H)
262. #3559	C₂×C₁₉	semidirect
263. #3217	C₂×C₁₉	semidirect
264. #3151	C₂×C₁₉	semidirect
265. C₂×#490	C₂×C₁₉	semidirect
266. #1657	C₂×C₁₉	semidirect
267. #1656	C₂×C₁₉	semidirect
268. #1530	C₂×C₁₉	semidirect
269. #1528	C₂×C₁₉	semidirect
270. #1524	C₂×C₁₉	semidirect
298. #563	C₂²×C₁₉	semidirect
299. #562	C₂²×C₁₉	semidirect
330. #330	C₂²×C₁₉	semidirect
331. #330	C₂²×C₁₉	semidirect
332. #329	C₂²×C₁₉	semidirect
333. #329	C₂²×C₁₉	semidirect
425. C₁₉	#19016	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×#3559	2
C₁₉×#3217	2
C₁₉×#3151	2
C₂×C₁₉×#490	2
C₁₉×#1657	2
C₁₉×#1656	2
C₁₉×#1530	2
C₁₉×#1528	2
C₁₉×#1524	2
#19016	19

Subgroups — C19×#19016 #18024975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19016 #18024975