Subgroups — C₁₉×#62397 #18068356

Order 4864.

1970 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3399	C₂	1	3	yes	maximal, complemented
4	C₁₉×#3391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3384	C₂	1	3	yes	maximal, complemented
6	Q₈×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3373	C₂	1	3	yes	maximal, complemented
8	C₁₉×#3366	C₂	1	3	yes	maximal, complemented
9	C₁₉×#3362	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#3358	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3253	C₂	1	3	yes	maximal, complemented
12	C₁₉×#3251	C₂	1	3	yes	maximal, complemented
13	C₁₉×#3184	C₂	1	3	yes	maximal, complemented
14	C₁₉×#3171	C₂	1	3	yes	maximal, complemented
15	Q₈×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×2₋¹⁺⁴	—	2	1	no	—
17	C₁₉×#559	C₂²	1	3	yes	—
18	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#554	C₂²	1	3	yes	—
20	C₁₉×#550	C₂²	1	1	yes	characteristic
21	C₁₉×#550	C₂²	1	3	yes	—
22	C₁₉×#550	C₂²	1	1	yes	characteristic
23	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	D₄×Q₈×C₁₉	C₂²	1	3	yes	—
25	C₁₉×#548	—	2	1	no	—
26	C₁₉×#548	—	2	1	no	—
27	C₁₉×#548	—	2	3	no	—
28	C₁₉×#547	—	2	3	no	—
29	C₁₉×#542	—	2	3	no	—
30	C₁₉×#537	—	2	3	no	—
31	C₁₉×#532	C₂²	1	3	yes	—
32	C₁₉×#532	C₂²	1	3	yes	—
33	C₁₉×#532	C₂²	1	3	yes	—
34	C₁₉×#529	C₂²	1	3	yes	—
35	C₁₉×#520	—	2	1	no	—
36	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×#501	C₂²	1	3	yes	—
38	C₁₉×#498	C₂²	1	3	yes	—
39	C₁₉×#496	C₂²	1	3	yes	—
40	C₁₉×#493	C₂²	1	3	yes	—
41	C₁₉×#490	C₂²	1	3	yes	—
42	C₁₉×#489	C₂²	1	3	yes	—
43	C₁₉×#486	C₂²	1	3	yes	—
44	C₁₉×#486	C₂²	1	3	yes	—
45	C₁₉×#478	C₂²	1	6	yes	—
46	C₁₉×#476	C₂²	1	3	yes	—
47	C₁₉×#476	C₂²	1	3	yes	—
48	C₁₉×#476	C₂²	1	6	yes	—
49	C₁₉×#475	C₂²	1	3	yes	—
50	C₁₉×#474	C₂²	1	3	yes	—
51	C₁₉×#469	C₂²	1	3	yes	—
52	C₁₉×#469	C₂²	1	3	yes	—
53	C₁₉×#469	C₂²	1	6	yes	—
54	C₁₉×#468	C₂²	1	1	yes	characteristic
55	C₁₉×#468	C₂²	1	3	yes	—
56	C₁₉×#463	C₂²	1	6	yes	—
57	C₁₉×#460	C₂²	1	3	yes	—
58	C₁₉×#459	C₂²	1	3	yes	—
59	C₁₉×#459	C₂²	1	3	yes	—
60	C₁₉×#459	C₂²	1	6	yes	—
61	C₁₉×#459	C₂²	1	3	yes	—
62	C₁₉×#446	C₂²	1	3	yes	—
63	C₁₉×#446	C₂²	1	3	yes	—
64	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
65	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
66	C₁₉×#442	C₂²	1	6	yes	—
67	C₁₉×#442	C₂²	1	6	yes	—
68	C₄×SD₁₆×C₁₉	C₂²	1	3	yes	—
69	C₄×SD₁₆×C₁₉	C₂²	1	3	yes	—
70	C₄×D₈×C₁₉	C₂²	1	3	yes	—
71	C₄×D₈×C₁₉	C₂²	1	3	yes	—
72	C₁₉×#423	C₂²	1	3	yes	—
73	C₄×M₁₆×C₁₉	C₂²	1	3	yes	—
74	C₁₉×2₋¹⁺⁴	—	4	8	no	—
75	C₂×#41×C₁₉	—	2	1	no	—
76	C₂×#41×C₁₉	—	2	3	no	—
77	C₂×#41×C₁₉	—	2	1	no	—
78	C₂×#41×C₁₉	—	2	3	no	—
79	C₂×#41×C₁₉	—	2	3	no	—
80	C₂×#41×C₁₉	—	2	3	no	—
81	C₂²×Q₈×C₁₉	—	2	3	no	—
82	C₂²×Q₈×C₁₉	—	2	1	no	—
83	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
84	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×SD₁₆×C₁₉	C₂³	1	3	yes	—
86	C₂×D₈×C₁₉	C₂³	1	3	yes	—
87	C₂×D₈×C₁₉	C₂³	1	3	yes	—
88	C₂×D₈×C₁₉	C₂³	1	6	yes	—
89	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×M₁₆×C₁₉	C₂³	1	3	yes	—
91	C₁₉×C₄⋊Q₈	—	2	3	no	—
92	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
93	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
94	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
95	C₁₉×#127	C₂³	1	3	yes	—
96	C₁₉×#127	C₂³	1	3	yes	—
97	C₁₉×#127	C₂³	1	3	yes	—
98	C₁₉×#126	—	2	3	no	—
99	C₁₉×#125	C₂³	1	3	yes	—
100	C₁₉×#124	—	2	3	no	—
101	C₁₉×#124	—	2	3	no	—
102	C₁₉×#124	—	2	3	no	—
103	C₁₉×#124	—	2	3	no	—
104	C₁₉×#124	C₂³	1	3	yes	—
105	C₁₉×#123	—	2	3	no	—
106	C₁₉×#123	—	2	6	no	—
107	C₁₉×C₂²⋊Q₈	—	2	3	no	—
108	C₁₉×C₂²⋊Q₈	—	2	3	no	—
109	C₁₉×C₂²⋊Q₈	—	2	3	no	—
110	C₁₉×C₂²⋊Q₈	—	2	6	no	—
111	C₁₉×C₂²⋊Q₈	—	2	6	no	—
112	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₉×#121	—	2	3	no	—
114	C₁₉×#121	—	2	3	no	—
115	C₁₉×#121	—	2	3	no	—
116	C₁₉×#121	—	2	3	no	—
117	C₁₉×#121	—	2	3	no	—
118	C₁₉×#121	—	2	6	no	—
119	C₁₉×#121	—	2	3	no	—
120	C₁₉×#121	C₂³	1	1	yes	characteristic
121	C₁₉×#121	C₂³	1	3	yes	—
122	C₁₉×#121	C₂³	1	3	yes	—
123	C₄×Q₈×C₁₉	—	2	1	no	—
124	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
125	C₄×Q₈×C₁₉	D₄	1	3	yes	—
126	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
127	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
128	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
129	C₄×D₄×C₁₉	—	2	3	no	—
130	C₄×D₄×C₁₉	—	2	3	no	—
131	C₄×D₄×C₁₉	—	2	3	no	—
132	C₄×D₄×C₁₉	—	2	3	no	—
133	C₄×D₄×C₁₉	—	2	3	no	—
134	C₄×D₄×C₁₉	C₂³	1	3	yes	—
135	C₄×D₄×C₁₉	C₂³	1	3	yes	—
136	C₄×D₄×C₁₉	C₂³	1	3	yes	—
137	C₄×D₄×C₁₉	C₂³	1	6	yes	—
138	C₄×D₄×C₁₉	C₂³	1	6	yes	—
139	C₁₉×#117	—	2	3	no	—
140	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
141	C₂×C₄⋊C₄×C₁₉	D₄	1	3	yes	—
142	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
143	C₁₉×#107	C₂³	1	1	yes	characteristic
144	C₁₉×#107	C₂³	1	3	yes	—
145	C₁₉×#106	C₂³	1	3	yes	—
146	C₁₉×#106	C₂³	1	3	yes	—
147	C₁₉×#106	C₂³	1	6	yes	—
148	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
149	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
150	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
151	C₁₉×#103	C₂³	1	1	yes	characteristic
152	C₁₉×#103	C₂³	1	3	yes	—
153	C₁₉×#102	C₂³	1	1	yes	characteristic
154	C₁₉×#102	C₂³	1	3	yes	—
155	C₁₉×#102	C₂³	1	3	yes	—
156	C₁₉×#102	C₂³	1	3	yes	—
157	C₁₉×#102	C₂³	1	3	yes	—
158	C₁₉×#102	C₂³	1	3	yes	—
159	C₁₉×#102	C₂³	1	6	yes	—
160	C₁₉×#102	C₂³	1	6	yes	—
161	C₁₉×#97	C₂³	1	3	yes	—
162	C₁₉×#97	C₂³	1	3	yes	—
163	C₄×C₈×C₁₉	C₂³	1	3	yes	—
164	C₄×C₈×C₁₉	C₂³	1	3	yes	—
165	#41×C₁₉	—	4	12	no	—
166	#41×C₁₉	—	4	12	no	—
167	#41×C₁₉	—	4	12	no	—
168	#41×C₁₉	—	4	4	no	—
169	#41×C₁₉	—	4	4	no	—
170	#41×C₁₉	—	8	6	no	—
171	C₂×Q₈×C₁₉	—	2	4	no	—
172	C₂×Q₈×C₁₉	—	2	3	no	—
173	C₂×Q₈×C₁₉	—	2	3	no	—
174	C₂×Q₈×C₁₉	—	2	3	no	—
175	C₂×Q₈×C₁₉	—	4	12	no	—
176	C₂×Q₈×C₁₉	—	4	4	no	—
177	C₂×Q₈×C₁₉	C₂×D₄	1	3	yes	—
178	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
180	C₂×D₄×C₁₉	—	2	3	no	—
181	C₂×D₄×C₁₉	—	2	1	no	—
182	C₂×D₄×C₁₉	—	2	3	no	—
183	C₂×D₄×C₁₉	—	2	3	no	—
184	C₂×D₄×C₁₉	—	2	3	no	—
185	C₂×D₄×C₁₉	—	2	3	no	—
186	C₂×D₄×C₁₉	—	2	3	no	—
187	C₂×D₄×C₁₉	—	2	3	no	—
188	C₂×D₄×C₁₉	—	2	3	no	—
189	C₂×D₄×C₁₉	C₂⁴	1	3	yes	—
190	C₂×D₄×C₁₉	C₂⁴	1	3	yes	—
191	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₉	—	2	3	no	—
193	C₂²×C₄×C₁₉	—	2	6	no	—
194	C₂²×C₄×C₁₉	—	2	3	no	—
195	C₂²×C₄×C₁₉	—	2	3	no	—
196	C₂²×C₄×C₁₉	—	2	6	no	—
197	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
198	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
199	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
200	SD₁₆×C₁₉	—	2	2	no	—
201	SD₁₆×C₁₉	—	4	3	no	—
202	D₈×C₁₉	—	2	6	no	—
203	D₈×C₁₉	—	4	6	no	—
204	D₈×C₁₉	—	4	3	no	—
205	M₁₆×C₁₉	—	2	2	no	—
206	M₁₆×C₁₉	—	4	3	no	—
207	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
208	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
209	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
210	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
211	C₄⋊C₄×C₁₉	—	2	3	no	—
212	C₄⋊C₄×C₁₉	—	2	3	no	—
213	C₄⋊C₄×C₁₉	—	2	1	no	—
214	C₄⋊C₄×C₁₉	—	2	3	no	—
215	C₄⋊C₄×C₁₉	—	2	3	no	—
216	C₄⋊C₄×C₁₉	—	2	3	no	—
217	C₄⋊C₄×C₁₉	—	2	3	no	—
218	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
219	C₄⋊C₄×C₁₉	C₂×D₄	1	3	yes	—
220	C₄⋊C₄×C₁₉	C₂×D₄	1	6	yes	—
221	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
222	C₄⋊C₄×C₁₉	C₂⁴	1	3	yes	—
223	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
224	C₄⋊C₄×C₁₉	C₂⁴	1	3	yes	—
225	C₂²⋊C₄×C₁₉	—	2	1	no	—
226	C₂²⋊C₄×C₁₉	—	2	3	no	—
227	C₂²⋊C₄×C₁₉	—	2	3	no	—
228	C₂²⋊C₄×C₁₉	—	2	1	no	—
229	C₂²⋊C₄×C₁₉	—	2	3	no	—
230	C₂²⋊C₄×C₁₉	—	2	3	no	—
231	C₂²⋊C₄×C₁₉	—	2	6	no	—
232	C₂²⋊C₄×C₁₉	—	2	3	no	—
233	C₂²⋊C₄×C₁₉	—	2	3	no	—
234	C₂²⋊C₄×C₁₉	—	2	3	no	—
235	C₂²⋊C₄×C₁₉	—	2	6	no	—
236	C₄²×C₁₉	—	2	3	no	—
237	C₄²×C₁₉	C₂×D₄	1	3	yes	—
238	C₄²×C₁₉	C₂×D₄	1	3	yes	—
239	C₄²×C₁₉	C₂⁴	1	3	yes	—
240	C₄²×C₁₉	C₂⁴	1	3	yes	—
241	#62397	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂³×C₁₉	—	2	3	no	—
243	C₂³×C₁₉	—	2	3	no	—
244	C₂³×C₁₉	—	2	1	no	—
245	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
246	Q₈×C₁₉	—	2	6	no	—
247	Q₈×C₁₉	—	2	1	no	—
248	Q₈×C₁₉	—	2	1	no	—
249	Q₈×C₁₉	—	4	6	no	—
250	Q₈×C₁₉	—	4	6	no	—
251	Q₈×C₁₉	—	8	3	no	—
252	Q₈×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
253	D₄×C₁₉	—	2	3	no	—
254	D₄×C₁₉	—	2	3	no	—
255	D₄×C₁₉	—	2	1	no	—
256	D₄×C₁₉	—	2	3	no	—
257	D₄×C₁₉	—	2	1	no	—
258	D₄×C₁₉	—	2	3	no	—
259	D₄×C₁₉	—	4	6	no	—
260	D₄×C₁₉	—	4	6	no	—
261	D₄×C₁₉	—	4	2	no	—
262	D₄×C₁₉	—	4	6	no	—
263	D₄×C₁₉	—	4	6	no	—
264	D₄×C₁₉	—	4	6	no	—
265	D₄×C₁₉	—	8	3	no	—
266	D₄×C₁₉	—	8	3	no	—
267	D₄×C₁₉	—	8	3	no	—
268	C₂×C₄×C₁₉	—	2	6	no	—
269	C₂×C₄×C₁₉	—	2	1	no	—
270	C₂×C₄×C₁₉	—	2	1	no	—
271	C₂×C₄×C₁₉	—	2	1	no	—
272	C₂×C₄×C₁₉	—	2	3	no	—
273	C₂×C₄×C₁₉	—	2	1	no	—
274	C₂×C₄×C₁₉	—	2	3	no	—
275	C₂×C₄×C₁₉	—	2	1	no	—
276	C₂×C₄×C₁₉	—	4	3	no	—
277	C₂×C₄×C₁₉	—	4	12	no	—
278	C₂×C₄×C₁₉	—	4	6	no	—
279	C₂×C₄×C₁₉	—	4	6	no	—
280	C₂×C₄×C₁₉	—	4	6	no	—
281	C₂×C₄×C₁₉	—	8	6	no	—
282	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
284	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
285	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
286	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
287	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
288	C₈×C₁₉	—	2	1	no	—
289	C₈×C₁₉	—	2	3	no	—
290	C₈×C₁₉	—	2	3	no	—
291	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	complemented
292	#3522	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#3497	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#3399	C₂×C₁₉	1	3	yes	complemented
295	#3391	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#3384	C₂×C₁₉	1	3	yes	complemented
297	Q₈×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#3373	C₂×C₁₉	1	3	yes	complemented
299	#3366	C₂×C₁₉	1	3	yes	complemented
300	#3362	C₂×C₁₉	1	1	yes	characteristic, complemented
301	#3358	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#3253	C₂×C₁₉	1	3	yes	complemented
303	#3251	C₂×C₁₉	1	3	yes	complemented
304	#3184	C₂×C₁₉	1	3	yes	complemented
305	#3171	C₂×C₁₉	1	3	yes	complemented
306	Q₈×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
307	C₂²×C₁₉	—	2	1	no	—
308	C₂²×C₁₉	—	2	1	no	—
309	C₂²×C₁₉	—	2	1	no	—
310	C₂²×C₁₉	—	4	3	no	—
311	C₂²×C₁₉	—	4	1	no	—
312	C₂²×C₁₉	—	4	3	no	—
313	C₂²×C₁₉	—	4	3	no	—
314	C₂²×C₁₉	—	4	3	no	—
315	C₂²×C₁₉	—	4	1	no	—
316	C₂²×C₁₉	—	4	3	no	—
317	C₂²×C₁₉	—	4	1	no	—
318	C₂²×C₁₉	—	4	3	no	—
319	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
320	C₄×C₁₉	—	2	3	no	—
321	C₄×C₁₉	—	2	3	no	—
322	C₄×C₁₉	—	2	1	no	—
323	C₄×C₁₉	—	2	3	no	—
324	C₄×C₁₉	—	4	3	no	—
325	C₄×C₁₉	—	4	1	no	—
326	C₄×C₁₉	—	4	1	no	—
327	C₄×C₁₉	—	4	3	no	—
328	C₄×C₁₉	—	4	1	no	—
329	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	6	yes	—
330	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
331	C₄×C₁₉	#585	1	1	yes	characteristic
332	C₂×2₋¹⁺⁴	—	2	1	no	—
333	#559	C₂²×C₁₉	1	3	yes	—
334	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
335	#554	C₂²×C₁₉	1	3	yes	—
336	#550	C₂²×C₁₉	1	1	yes	characteristic
337	#550	C₂²×C₁₉	1	1	yes	characteristic
338	#550	C₂²×C₁₉	1	3	yes	—
339	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
340	D₄×Q₈	C₂²×C₁₉	1	3	yes	—
341	#548	—	2	1	no	—
342	#548	—	2	1	no	—
343	#548	—	2	3	no	—
344	#547	—	2	3	no	—
345	#542	—	2	3	no	—
346	#537	—	2	3	no	—
347	#532	C₂²×C₁₉	1	3	yes	—
348	#532	C₂²×C₁₉	1	3	yes	—
349	#532	C₂²×C₁₉	1	3	yes	—
350	#529	C₂²×C₁₉	1	3	yes	—
351	#520	—	2	1	no	—
352	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
353	#501	C₂²×C₁₉	1	3	yes	—
354	#498	C₂²×C₁₉	1	3	yes	—
355	#496	C₂²×C₁₉	1	3	yes	—
356	#493	C₂²×C₁₉	1	3	yes	—
357	#490	C₂²×C₁₉	1	3	yes	—
358	#489	C₂²×C₁₉	1	3	yes	—
359	#486	C₂²×C₁₉	1	3	yes	—
360	#486	C₂²×C₁₉	1	3	yes	—
361	#478	C₂²×C₁₉	1	6	yes	—
362	#476	C₂²×C₁₉	1	3	yes	—
363	#476	C₂²×C₁₉	1	3	yes	—
364	#476	C₂²×C₁₉	1	6	yes	—
365	#475	C₂²×C₁₉	1	3	yes	—
366	#474	C₂²×C₁₉	1	3	yes	—
367	#469	C₂²×C₁₉	1	3	yes	—
368	#469	C₂²×C₁₉	1	3	yes	—
369	#469	C₂²×C₁₉	1	6	yes	—
370	#468	C₂²×C₁₉	1	1	yes	characteristic
371	#468	C₂²×C₁₉	1	3	yes	—
372	#463	C₂²×C₁₉	1	6	yes	—
373	#460	C₂²×C₁₉	1	3	yes	—
374	#459	C₂²×C₁₉	1	3	yes	—
375	#459	C₂²×C₁₉	1	3	yes	—
376	#459	C₂²×C₁₉	1	6	yes	—
377	#459	C₂²×C₁₉	1	3	yes	—
378	#446	C₂²×C₁₉	1	3	yes	—
379	#446	C₂²×C₁₉	1	3	yes	—
380	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
381	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
382	#442	C₂²×C₁₉	1	6	yes	—
383	#442	C₂²×C₁₉	1	6	yes	—
384	C₄×SD₁₆	C₂²×C₁₉	1	3	yes	—
385	C₄×SD₁₆	C₂²×C₁₉	1	3	yes	—
386	C₄×D₈	C₂²×C₁₉	1	3	yes	—
387	C₄×D₈	C₂²×C₁₉	1	3	yes	—
388	#423	C₂²×C₁₉	1	3	yes	—
389	C₄×M₁₆	C₂²×C₁₉	1	3	yes	—
390	C₂×C₁₉	—	4	1	no	—
391	C₂×C₁₉	—	8	3	no	—
392	C₂×C₁₉	—	8	3	no	—
393	C₂×C₁₉	—	8	1	no	—
394	C₂×C₁₉	#3497	1	1	yes	characteristic
395	C₂×C₁₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
396	C₂×C₁₉	#3585	1	1	yes	characteristic
397	2₋¹⁺⁴	—	4	8	no	—
398	C₂×#41	—	2	1	no	—
399	C₂×#41	—	2	3	no	—
400	C₂×#41	—	2	1	no	—
401	C₂×#41	—	2	3	no	—
402	C₂×#41	—	2	3	no	—
403	C₂×#41	—	2	3	no	—
404	C₂²×Q₈	—	2	3	no	—
405	C₂²×Q₈	—	2	1	no	—
406	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
407	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
408	C₂×SD₁₆	C₂³×C₁₉	1	3	yes	—
409	C₂×D₈	C₂³×C₁₉	1	3	yes	—
410	C₂×D₈	C₂³×C₁₉	1	3	yes	—
411	C₂×D₈	C₂³×C₁₉	1	6	yes	—
412	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
413	C₂×M₁₆	C₂³×C₁₉	1	3	yes	—
414	C₄⋊Q₈	—	2	3	no	—
415	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
416	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
417	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
418	#127	C₂³×C₁₉	1	3	yes	—
419	#127	C₂³×C₁₉	1	3	yes	—
420	#127	C₂³×C₁₉	1	3	yes	—
421	#126	—	2	3	no	—
422	#125	C₂³×C₁₉	1	3	yes	—
423	#124	—	2	3	no	—
424	#124	—	2	3	no	—
425	#124	—	2	3	no	—
426	#124	—	2	3	no	—
427	#124	C₂³×C₁₉	1	3	yes	—
428	#123	—	2	3	no	—
429	#123	—	2	6	no	—
430	C₂²⋊Q₈	—	2	3	no	—
431	C₂²⋊Q₈	—	2	3	no	—
432	C₂²⋊Q₈	—	2	3	no	—
433	C₂²⋊Q₈	—	2	6	no	—
434	C₂²⋊Q₈	—	2	6	no	—
435	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
436	#121	—	2	3	no	—
437	#121	—	2	3	no	—
438	#121	—	2	3	no	—
439	#121	—	2	3	no	—
440	#121	—	2	3	no	—
441	#121	—	2	6	no	—
442	#121	—	2	3	no	—
443	#121	C₂³×C₁₉	1	3	yes	—
444	#121	C₂³×C₁₉	1	1	yes	characteristic
445	#121	C₂³×C₁₉	1	3	yes	—
446	C₄×Q₈	—	2	1	no	—
447	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
448	C₄×Q₈	D₄×C₁₉	1	3	yes	—
449	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
450	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
451	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
452	C₄×D₄	—	2	3	no	—
453	C₄×D₄	—	2	3	no	—
454	C₄×D₄	—	2	3	no	—
455	C₄×D₄	—	2	3	no	—
456	C₄×D₄	—	2	3	no	—
457	C₄×D₄	C₂³×C₁₉	1	3	yes	—
458	C₄×D₄	C₂³×C₁₉	1	3	yes	—
459	C₄×D₄	C₂³×C₁₉	1	3	yes	—
460	C₄×D₄	C₂³×C₁₉	1	6	yes	—
461	C₄×D₄	C₂³×C₁₉	1	6	yes	—
462	#117	—	2	3	no	—
463	C₂×C₄⋊C₄	—	2	3	no	—
464	C₂×C₄⋊C₄	D₄×C₁₉	1	3	yes	—
465	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
466	#107	C₂³×C₁₉	1	1	yes	characteristic
467	#107	C₂³×C₁₉	1	3	yes	—
468	#106	C₂³×C₁₉	1	3	yes	—
469	#106	C₂³×C₁₉	1	3	yes	—
470	#106	C₂³×C₁₉	1	6	yes	—
471	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
472	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
473	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
474	#103	C₂³×C₁₉	1	1	yes	characteristic
475	#103	C₂³×C₁₉	1	3	yes	—
476	#102	C₂³×C₁₉	1	1	yes	characteristic
477	#102	C₂³×C₁₉	1	3	yes	—
478	#102	C₂³×C₁₉	1	3	yes	—
479	#102	C₂³×C₁₉	1	3	yes	—
480	#102	C₂³×C₁₉	1	3	yes	—
481	#102	C₂³×C₁₉	1	3	yes	—
482	#102	C₂³×C₁₉	1	6	yes	—
483	#102	C₂³×C₁₉	1	6	yes	—
484	#97	C₂³×C₁₉	1	3	yes	—
485	#97	C₂³×C₁₉	1	3	yes	—
486	C₄×C₈	C₂³×C₁₉	1	3	yes	—
487	C₄×C₈	C₂³×C₁₉	1	3	yes	—
488	C₁₉	#62397	1	1	yes	characteristic, direct product factor, Sylow
489	#41	—	4	12	no	—
490	#41	—	4	12	no	—
491	#41	—	4	12	no	—
492	#41	—	4	4	no	—
493	#41	—	4	4	no	—
494	#41	—	8	6	no	—
495	C₂×Q₈	—	2	4	no	—
496	C₂×Q₈	—	2	3	no	—
497	C₂×Q₈	—	2	3	no	—
498	C₂×Q₈	—	2	3	no	—
499	C₂×Q₈	—	4	12	no	—
500	C₂×Q₈	—	4	4	no	—
501	C₂×Q₈	C₂×D₄×C₁₉	1	3	yes	—
502	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
503	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
504	C₂×D₄	—	2	3	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	3	no	—
507	C₂×D₄	—	2	3	no	—
508	C₂×D₄	—	2	3	no	—
509	C₂×D₄	—	2	3	no	—
510	C₂×D₄	—	2	3	no	—
511	C₂×D₄	—	2	3	no	—
512	C₂×D₄	—	2	3	no	—
513	C₂×D₄	C₂⁴×C₁₉	1	3	yes	—
514	C₂×D₄	C₂⁴×C₁₉	1	3	yes	—
515	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
516	C₂²×C₄	—	2	3	no	—
517	C₂²×C₄	—	2	6	no	—
518	C₂²×C₄	—	2	3	no	—
519	C₂²×C₄	—	2	3	no	—
520	C₂²×C₄	—	2	6	no	—
521	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
522	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
523	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
524	SD₁₆	—	2	2	no	—
525	SD₁₆	—	4	3	no	—
526	D₈	—	2	6	no	—
527	D₈	—	4	6	no	—
528	D₈	—	4	3	no	—
529	M₁₆	—	2	2	no	—
530	M₁₆	—	4	3	no	—
531	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
532	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
533	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
534	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
535	C₄⋊C₄	—	2	3	no	—
536	C₄⋊C₄	—	2	3	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	3	no	—
539	C₄⋊C₄	—	2	3	no	—
540	C₄⋊C₄	—	2	3	no	—
541	C₄⋊C₄	—	2	3	no	—
542	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
543	C₄⋊C₄	C₂×D₄×C₁₉	1	3	yes	—
544	C₄⋊C₄	C₂×D₄×C₁₉	1	6	yes	—
545	C₄⋊C₄	C₂⁴×C₁₉	1	3	yes	—
546	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
547	C₄⋊C₄	C₂⁴×C₁₉	1	3	yes	—
548	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
549	C₂²⋊C₄	—	2	1	no	—
550	C₂²⋊C₄	—	2	3	no	—
551	C₂²⋊C₄	—	2	3	no	—
552	C₂²⋊C₄	—	2	1	no	—
553	C₂²⋊C₄	—	2	3	no	—
554	C₂²⋊C₄	—	2	3	no	—
555	C₂²⋊C₄	—	2	6	no	—
556	C₂²⋊C₄	—	2	3	no	—
557	C₂²⋊C₄	—	2	3	no	—
558	C₂²⋊C₄	—	2	3	no	—
559	C₂²⋊C₄	—	2	6	no	—
560	C₄²	—	2	3	no	—
561	C₄²	C₂×D₄×C₁₉	1	3	yes	—
562	C₄²	C₂×D₄×C₁₉	1	3	yes	—
563	C₄²	C₂⁴×C₁₉	1	3	yes	—
564	C₄²	C₂⁴×C₁₉	1	3	yes	—
565	C₂³	—	2	3	no	—
566	C₂³	—	2	3	no	—
567	C₂³	—	2	1	no	—
568	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
569	Q₈	—	2	6	no	—
570	Q₈	—	2	1	no	—
571	Q₈	—	2	1	no	—
572	Q₈	—	4	6	no	—
573	Q₈	—	4	6	no	—
574	Q₈	—	8	3	no	—
575	Q₈	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
576	D₄	—	2	3	no	—
577	D₄	—	2	3	no	—
578	D₄	—	2	1	no	—
579	D₄	—	2	3	no	—
580	D₄	—	2	1	no	—
581	D₄	—	2	3	no	—
582	D₄	—	4	6	no	—
583	D₄	—	4	6	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	6	no	—
586	D₄	—	4	6	no	—
587	D₄	—	4	6	no	—
588	D₄	—	8	3	no	—
589	D₄	—	8	3	no	—
590	D₄	—	8	3	no	—
591	C₂×C₄	—	2	6	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	3	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	3	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	4	3	no	—
600	C₂×C₄	—	4	12	no	—
601	C₂×C₄	—	4	6	no	—
602	C₂×C₄	—	4	6	no	—
603	C₂×C₄	—	4	6	no	—
604	C₂×C₄	—	8	6	no	—
605	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
606	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
607	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
608	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
609	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
610	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
611	C₈	—	2	1	no	—
612	C₈	—	2	3	no	—
613	C₈	—	2	3	no	—
614	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	complemented
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	4	3	no	—
619	C₂²	—	4	3	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	3	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	3	no	—
624	C₂²	—	4	3	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	3	no	—
627	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
628	C₄	—	2	1	no	—
629	C₄	—	2	3	no	—
630	C₄	—	2	3	no	—
631	C₄	—	2	3	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	3	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	1	no	—
636	C₄	—	4	3	no	—
637	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	6	yes	—
638	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
639	C₄	C₁₉×#585	1	1	yes	characteristic
640	C₂	—	4	1	no	—
641	C₂	—	8	3	no	—
642	C₂	—	8	1	no	—
643	C₂	—	8	3	no	—
644	C₂	C₁₉×#3497	1	1	yes	characteristic
645	C₂	C₂²×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
646	C₂	C₁₉×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3522	C₂	semidirect
2. C₁₉×#3497	C₂	semidirect
3. C₁₉×#3399	C₂	semidirect
4. C₁₉×#3391	C₂	semidirect
5. C₁₉×#3384	C₂	semidirect
6. Q₈×SD₁₆×C₁₉	C₂	semidirect
7. C₁₉×#3373	C₂	semidirect
8. C₁₉×#3366	C₂	semidirect
9. C₁₉×#3362	C₂	semidirect
10. C₁₉×#3358	C₂	semidirect
11. C₁₉×#3253	C₂	semidirect
12. C₁₉×#3251	C₂	semidirect
13. C₁₉×#3184	C₂	semidirect
14. C₁₉×#3171	C₂	semidirect
15. Q₈×M₁₆×C₁₉	C₂	semidirect
241. #62397	C₁₉	direct (N × H)
291. C₈×C₁₉	2₋¹⁺⁴	semidirect
292. #3522	C₂×C₁₉	semidirect
293. #3497	C₂×C₁₉	semidirect
294. #3399	C₂×C₁₉	semidirect
295. #3391	C₂×C₁₉	semidirect
296. #3384	C₂×C₁₉	semidirect
297. Q₈×SD₁₆	C₂×C₁₉	semidirect
298. #3373	C₂×C₁₉	semidirect
299. #3366	C₂×C₁₉	semidirect
300. #3362	C₂×C₁₉	semidirect
301. #3358	C₂×C₁₉	semidirect
302. #3253	C₂×C₁₉	semidirect
303. #3251	C₂×C₁₉	semidirect
304. #3184	C₂×C₁₉	semidirect
305. #3171	C₂×C₁₉	semidirect
306. Q₈×M₁₆	C₂×C₁₉	semidirect
488. C₁₉	#62397	direct (N × H)
614. C₈	C₁₉×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3522	2
C₁₉×#3497	2
C₁₉×#3399	2
C₁₉×#3391	2
C₁₉×#3384	2
Q₈×SD₁₆×C₁₉	2
C₁₉×#3373	2
C₁₉×#3366	2
C₁₉×#3362	2
C₁₉×#3358	2
C₁₉×#3253	2
C₁₉×#3251	2
C₁₉×#3184	2
C₁₉×#3171	2
Q₈×M₁₆×C₁₉	2
#62397	19

Subgroups — C19×#62397 #18068356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62397 #18068356