Subgroups — C₁₉×#18694 #18024653

Order 4864.

942 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3217	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3217	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1628	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1627	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1626	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1625	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1494	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#563	—	2	2	no	—
13	C₁₉×#557	C₂²	1	1	yes	characteristic, complemented
14	C₁₉×#556	C₂²	1	1	yes	characteristic, complemented
15	C₁₉×#554	—	2	1	no	—
16	C₁₉×#553	—	2	1	no	—
17	D₄×Q₈×C₁₉	—	2	1	no	—
18	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
19	C₁₉×#548	—	2	1	no	—
20	C₁₉×#547	C₂²	1	1	yes	characteristic, complemented
21	C₁₉×#544	—	2	1	no	—
22	C₁₉×#542	—	2	1	no	—
23	C₁₉×#541	—	2	1	no	—
24	C₁₉×#539	—	2	2	no	—
25	C₁₉×#536	—	2	1	no	—
26	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
28	C₁₉×#529	C₂²	1	1	yes	characteristic
29	C₁₉×#529	C₂²	1	1	yes	characteristic
30	C₁₉×#496	—	2	1	no	—
31	C₁₉×#496	—	2	1	no	—
32	C₁₉×#490	—	2	1	no	—
33	C₁₉×#490	—	2	1	no	—
34	C₁₉×#486	—	2	2	no	—
35	C₁₉×#486	C₂²	1	2	yes	—
36	C₁₉×#486	C₂²	1	2	yes	—
37	C₁₉×#460	C₂²	1	2	yes	—
38	C₁₉×#460	C₂²	1	2	yes	—
39	C₁₉×#459	C₂²	1	2	yes	—
40	C₁₉×#459	C₂²	1	2	yes	—
41	C₁₉×#450	—	2	1	no	—
42	C₁₉×#450	—	2	1	no	—
43	C₁₉×#447	—	2	1	no	—
44	C₁₉×#447	—	2	1	no	—
45	C₁₉×#432	C₂²	1	1	yes	characteristic
46	C₁₉×#432	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#102	—	2	2	no	—
48	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#332	C₂²	1	2	yes	complemented
50	C₁₉×#332	C₂²	1	2	yes	complemented
51	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	complemented
52	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	complemented
53	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
54	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂²×Q₈×C₁₉	—	2	1	no	—
57	C₂²×Q₈×C₁₉	—	2	1	no	—
58	C₂²×D₄×C₁₉	—	2	1	no	—
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂×SD₁₆×C₁₉	—	2	2	no	—
62	C₂×SD₁₆×C₁₉	—	2	2	no	—
63	C₂×D₈×C₁₉	—	2	2	no	—
64	C₂×D₈×C₁₉	—	2	2	no	—
65	C₂²×C₈×C₁₉	—	2	1	no	—
66	C₁₉×C₄⋊Q₈	—	2	2	no	—
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	—	2	1	no	—
69	C₁₉×C₄⋊Q₈	—	2	1	no	—
70	C₁₉×C₄⋊Q₈	—	2	1	no	—
71	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
72	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
73	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
74	C₁₉×#127	—	2	1	no	—
75	C₁₉×#127	—	2	1	no	—
76	C₁₉×#127	—	2	1	no	—
77	C₁₉×#127	C₂³	1	2	yes	—
78	C₁₉×#126	—	2	2	no	—
79	C₁₉×#126	—	2	2	no	—
80	C₁₉×#126	—	2	2	no	—
81	C₁₉×#126	—	2	1	no	—
82	C₁₉×#126	—	2	1	no	—
83	C₁₉×#125	—	2	2	no	—
84	C₁₉×#125	—	2	2	no	—
85	C₁₉×#125	—	2	2	no	—
86	C₁₉×#125	—	2	1	no	—
87	C₁₉×#125	D₄	1	1	yes	characteristic
88	C₁₉×#125	D₄	1	1	yes	characteristic
89	C₁₉×#124	—	2	2	no	—
90	C₁₉×#124	—	2	1	no	—
91	C₁₉×#124	D₄	1	1	yes	characteristic
92	C₁₉×#124	D₄	1	1	yes	characteristic
93	C₁₉×#123	—	2	2	no	—
94	C₁₉×#123	—	2	2	no	—
95	C₁₉×#123	—	2	1	no	—
96	C₁₉×#123	—	2	1	no	—
97	C₁₉×#123	—	2	2	no	—
98	C₁₉×C₂²⋊Q₈	—	2	2	no	—
99	C₁₉×C₂²⋊Q₈	—	2	2	no	—
100	C₁₉×C₂²⋊Q₈	—	2	2	no	—
101	C₁₉×C₂²⋊Q₈	—	2	2	no	—
102	C₁₉×C₂²⋊Q₈	—	2	2	no	—
103	C₁₉×C₂²⋊Q₈	—	2	1	no	—
104	C₁₉×C₂²⋊Q₈	—	2	2	no	—
105	C₁₉×C₂²⋊Q₈	—	2	1	no	—
106	C₁₉×C₂²⋊Q₈	—	2	1	no	—
107	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
108	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
109	C₁₉×#121	—	2	2	no	—
110	C₁₉×#121	—	2	1	no	—
111	C₁₉×#121	D₄	1	1	yes	characteristic
112	C₁₉×#121	D₄	1	1	yes	characteristic
113	C₄×Q₈×C₁₉	—	2	1	no	—
114	C₄×Q₈×C₁₉	—	2	1	no	—
115	C₄×Q₈×C₁₉	—	2	1	no	—
116	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
117	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
118	C₄×D₄×C₁₉	—	2	2	no	—
119	C₄×D₄×C₁₉	—	2	2	no	—
120	C₄×D₄×C₁₉	—	2	1	no	—
121	C₄×D₄×C₁₉	—	2	1	no	—
122	C₄×D₄×C₁₉	—	2	1	no	—
123	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
124	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
125	C₁₉×#117	—	2	1	no	—
126	C₁₉×#117	—	2	1	no	—
127	C₁₉×#117	—	2	1	no	—
128	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
131	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
132	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
133	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
134	C₁₉×#102	—	2	4	no	—
135	C₁₉×#102	—	2	4	no	—
136	C₁₉×#102	—	2	2	no	—
137	C₁₉×#102	—	2	2	no	—
138	C₁₉×#102	—	2	2	no	—
139	C₁₉×#102	—	2	2	no	—
140	C₁₉×C₂²⋊C₈	—	2	1	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₁₉×#97	—	2	1	no	—
143	C₁₉×#97	—	2	1	no	—
144	C₄×C₈×C₁₉	—	2	1	no	—
145	C₄×C₈×C₁₉	C₂³	1	2	yes	—
146	C₂⁴×C₁₉	—	4	1	no	—
147	#41×C₁₉	—	8	2	no	—
148	C₂×Q₈×C₁₉	—	2	2	no	—
149	C₂×Q₈×C₁₉	—	2	2	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	—	8	2	no	—
153	C₂×Q₈×C₁₉	—	8	2	no	—
154	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	2	2	no	—
160	C₂×D₄×C₁₉	—	2	2	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	4	4	no	—
163	C₂×D₄×C₁₉	—	4	1	no	—
164	C₂×D₄×C₁₉	—	4	1	no	—
165	C₂×D₄×C₁₉	—	4	1	no	—
166	C₂×D₄×C₁₉	—	8	2	no	—
167	C₂×D₄×C₁₉	—	8	2	no	—
168	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	—	2	2	no	—
171	C₂²×C₄×C₁₉	—	2	2	no	—
172	C₂²×C₄×C₁₉	—	2	2	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	SD₁₆×C₁₉	—	8	2	no	—
179	SD₁₆×C₁₉	—	8	2	no	—
180	D₈×C₁₉	—	8	2	no	—
181	D₈×C₁₉	—	8	2	no	—
182	C₂×C₈×C₁₉	—	2	2	no	—
183	C₂×C₈×C₁₉	—	2	2	no	—
184	C₂×C₈×C₁₉	—	2	2	no	—
185	C₂×C₈×C₁₉	—	4	2	no	—
186	C₄⋊C₄×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
206	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
207	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₂²⋊C₄×C₁₉	—	2	2	no	—
211	C₂²⋊C₄×C₁₉	—	2	2	no	—
212	C₂²⋊C₄×C₁₉	—	2	2	no	—
213	C₂²⋊C₄×C₁₉	—	2	2	no	—
214	C₂²⋊C₄×C₁₉	—	2	1	no	—
215	C₂²⋊C₄×C₁₉	—	2	1	no	—
216	C₂²⋊C₄×C₁₉	—	2	1	no	—
217	C₂²⋊C₄×C₁₉	—	2	1	no	—
218	C₂²⋊C₄×C₁₉	—	2	1	no	—
219	C₂²⋊C₄×C₁₉	—	2	1	no	—
220	C₂²⋊C₄×C₁₉	—	2	1	no	—
221	C₂²⋊C₄×C₁₉	—	2	1	no	—
222	C₂²⋊C₄×C₁₉	—	2	1	no	—
223	C₂²⋊C₄×C₁₉	—	2	1	no	—
224	C₄²×C₁₉	—	2	2	no	—
225	C₄²×C₁₉	—	2	2	no	—
226	C₄²×C₁₉	—	2	1	no	—
227	C₄²×C₁₉	—	2	1	no	—
228	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
229	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
231	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
232	#18694	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂³×C₁₉	—	2	1	no	—
234	C₂³×C₁₉	—	2	1	no	—
235	C₂³×C₁₉	—	4	2	no	—
236	C₂³×C₁₉	—	8	2	no	—
237	C₂³×C₁₉	—	8	2	no	—
238	C₂³×C₁₉	—	8	2	no	—
239	C₂³×C₁₉	#120	1	1	yes	characteristic
240	Q₈×C₁₉	—	2	2	no	—
241	Q₈×C₁₉	—	2	2	no	—
242	Q₈×C₁₉	—	4	2	no	—
243	Q₈×C₁₉	—	4	2	no	—
244	Q₈×C₁₉	—	8	2	no	—
245	Q₈×C₁₉	—	8	2	no	—
246	D₄×C₁₉	—	2	2	no	—
247	D₄×C₁₉	—	2	2	no	—
248	D₄×C₁₉	—	4	4	no	—
249	D₄×C₁₉	—	4	2	no	—
250	D₄×C₁₉	—	4	2	no	—
251	D₄×C₁₉	—	4	2	no	—
252	D₄×C₁₉	—	4	2	no	—
253	D₄×C₁₉	—	4	2	no	—
254	D₄×C₁₉	—	4	2	no	—
255	D₄×C₁₉	—	8	2	no	—
256	D₄×C₁₉	—	8	2	no	—
257	D₄×C₁₉	—	8	2	no	—
258	D₄×C₁₉	—	8	2	no	—
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	2	2	no	—
268	C₂×C₄×C₁₉	—	2	2	no	—
269	C₂×C₄×C₁₉	—	2	1	no	—
270	C₂×C₄×C₁₉	—	4	2	no	—
271	C₂×C₄×C₁₉	—	4	2	no	—
272	C₂×C₄×C₁₉	—	8	2	no	—
273	C₂×C₄×C₁₉	—	8	2	no	—
274	C₂×C₄×C₁₉	—	8	2	no	—
275	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
276	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
277	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
278	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
281	C₈×C₁₉	—	4	2	no	—
282	C₈×C₁₉	—	4	2	no	—
283	C₈×C₁₉	—	4	2	no	—
284	#3552	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#3217	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#3217	C₂×C₁₉	1	1	yes	characteristic, complemented
287	C₂×#486	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1628	C₂×C₁₉	1	2	yes	complemented
289	#1627	C₂×C₁₉	1	2	yes	complemented
290	#1626	C₂×C₁₉	1	2	yes	complemented
291	#1625	C₂×C₁₉	1	2	yes	complemented
292	#1556	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#1494	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1494	C₂×C₁₉	1	1	yes	characteristic, complemented
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	—	2	1	no	—
297	C₂²×C₁₉	—	4	1	no	—
298	C₂²×C₁₉	—	4	1	no	—
299	C₂²×C₁₉	—	4	1	no	—
300	C₂²×C₁₉	—	4	1	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	—	4	1	no	—
303	C₂²×C₁₉	—	8	2	no	—
304	C₂²×C₁₉	—	8	2	no	—
305	C₂²×C₁₉	—	8	2	no	—
306	C₂²×C₁₉	—	16	4	no	—
307	C₂²×C₁₉	#454	1	2	yes	—
308	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
309	C₄×C₁₉	—	2	1	no	—
310	C₄×C₁₉	—	2	1	no	—
311	C₄×C₁₉	—	2	1	no	—
312	C₄×C₁₉	—	2	1	no	—
313	C₄×C₁₉	—	4	1	no	—
314	C₄×C₁₉	—	4	2	no	—
315	C₄×C₁₉	—	4	1	no	—
316	C₄×C₁₉	—	4	2	no	—
317	C₄×C₁₉	—	4	1	no	—
318	C₄×C₁₉	—	4	1	no	—
319	C₄×C₁₉	—	4	1	no	—
320	C₄×C₁₉	—	4	1	no	—
321	C₄×C₁₉	#576	1	2	yes	—
322	C₄×C₁₉	#577	1	2	yes	—
323	#563	—	2	2	no	—
324	#557	C₂²×C₁₉	1	1	yes	characteristic, complemented
325	#556	C₂²×C₁₉	1	1	yes	characteristic, complemented
326	#554	—	2	1	no	—
327	#553	—	2	1	no	—
328	D₄×Q₈	—	2	1	no	—
329	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
330	#548	—	2	1	no	—
331	#547	C₂²×C₁₉	1	1	yes	characteristic, complemented
332	#544	—	2	1	no	—
333	#542	—	2	1	no	—
334	#541	—	2	1	no	—
335	#539	—	2	2	no	—
336	#536	—	2	1	no	—
337	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
339	#529	C₂²×C₁₉	1	1	yes	characteristic
340	#529	C₂²×C₁₉	1	1	yes	characteristic
341	#496	—	2	1	no	—
342	#496	—	2	1	no	—
343	#490	—	2	1	no	—
344	#490	—	2	1	no	—
345	#486	—	2	2	no	—
346	#486	C₂²×C₁₉	1	2	yes	—
347	#486	C₂²×C₁₉	1	2	yes	—
348	#460	C₂²×C₁₉	1	2	yes	—
349	#460	C₂²×C₁₉	1	2	yes	—
350	#459	C₂²×C₁₉	1	2	yes	—
351	#459	C₂²×C₁₉	1	2	yes	—
352	#450	—	2	1	no	—
353	#450	—	2	1	no	—
354	#447	—	2	1	no	—
355	#447	—	2	1	no	—
356	#432	C₂²×C₁₉	1	1	yes	characteristic
357	#432	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×#102	—	2	2	no	—
359	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
360	#332	C₂²×C₁₉	1	2	yes	complemented
361	#332	C₂²×C₁₉	1	2	yes	complemented
362	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	complemented
363	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	complemented
364	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
365	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
366	C₂×C₁₉	—	2	2	no	—
367	C₂×C₁₉	—	8	1	no	—
368	C₂×C₁₉	—	8	1	no	—
369	C₂×C₁₉	—	16	2	no	—
370	C₂×C₁₉	#3008	1	1	yes	characteristic
371	C₂×C₁₉	#3010	1	1	yes	characteristic
372	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
373	C₂×#41	—	2	1	no	—
374	C₂²×Q₈	—	2	1	no	—
375	C₂²×Q₈	—	2	1	no	—
376	C₂²×D₄	—	2	1	no	—
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	—	2	1	no	—
379	C₂×SD₁₆	—	2	2	no	—
380	C₂×SD₁₆	—	2	2	no	—
381	C₂×D₈	—	2	2	no	—
382	C₂×D₈	—	2	2	no	—
383	C₂²×C₈	—	2	1	no	—
384	C₄⋊Q₈	—	2	2	no	—
385	C₄⋊Q₈	—	2	1	no	—
386	C₄⋊Q₈	—	2	1	no	—
387	C₄⋊Q₈	—	2	1	no	—
388	C₄⋊Q₈	—	2	1	no	—
389	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
390	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
391	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
392	#127	—	2	1	no	—
393	#127	—	2	1	no	—
394	#127	—	2	1	no	—
395	#127	C₂³×C₁₉	1	2	yes	—
396	#126	—	2	2	no	—
397	#126	—	2	2	no	—
398	#126	—	2	2	no	—
399	#126	—	2	1	no	—
400	#126	—	2	1	no	—
401	#125	—	2	2	no	—
402	#125	—	2	2	no	—
403	#125	—	2	2	no	—
404	#125	—	2	1	no	—
405	#125	D₄×C₁₉	1	1	yes	characteristic
406	#125	D₄×C₁₉	1	1	yes	characteristic
407	#124	—	2	2	no	—
408	#124	—	2	1	no	—
409	#124	D₄×C₁₉	1	1	yes	characteristic
410	#124	D₄×C₁₉	1	1	yes	characteristic
411	#123	—	2	2	no	—
412	#123	—	2	2	no	—
413	#123	—	2	1	no	—
414	#123	—	2	1	no	—
415	#123	—	2	2	no	—
416	C₂²⋊Q₈	—	2	2	no	—
417	C₂²⋊Q₈	—	2	2	no	—
418	C₂²⋊Q₈	—	2	2	no	—
419	C₂²⋊Q₈	—	2	2	no	—
420	C₂²⋊Q₈	—	2	2	no	—
421	C₂²⋊Q₈	—	2	1	no	—
422	C₂²⋊Q₈	—	2	2	no	—
423	C₂²⋊Q₈	—	2	1	no	—
424	C₂²⋊Q₈	—	2	1	no	—
425	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
426	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
427	#121	—	2	2	no	—
428	#121	—	2	1	no	—
429	#121	D₄×C₁₉	1	1	yes	characteristic
430	#121	D₄×C₁₉	1	1	yes	characteristic
431	C₄×Q₈	—	2	1	no	—
432	C₄×Q₈	—	2	1	no	—
433	C₄×Q₈	—	2	1	no	—
434	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
435	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
436	C₄×D₄	—	2	2	no	—
437	C₄×D₄	—	2	2	no	—
438	C₄×D₄	—	2	1	no	—
439	C₄×D₄	—	2	1	no	—
440	C₄×D₄	—	2	1	no	—
441	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
442	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
443	#117	—	2	1	no	—
444	#117	—	2	1	no	—
445	#117	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
449	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
450	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
451	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
452	#102	—	2	4	no	—
453	#102	—	2	4	no	—
454	#102	—	2	2	no	—
455	#102	—	2	2	no	—
456	#102	—	2	2	no	—
457	#102	—	2	2	no	—
458	C₂²⋊C₈	—	2	1	no	—
459	C₂²⋊C₈	—	2	1	no	—
460	#97	—	2	1	no	—
461	#97	—	2	1	no	—
462	C₄×C₈	—	2	1	no	—
463	C₄×C₈	C₂³×C₁₉	1	2	yes	—
464	C₁₉	#18694	1	1	yes	characteristic, direct product factor, Sylow
465	C₂⁴	—	4	1	no	—
466	#41	—	8	2	no	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	—	2	2	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	8	2	no	—
472	C₂×Q₈	—	8	2	no	—
473	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	4	4	no	—
482	C₂×D₄	—	4	1	no	—
483	C₂×D₄	—	4	1	no	—
484	C₂×D₄	—	4	1	no	—
485	C₂×D₄	—	8	2	no	—
486	C₂×D₄	—	8	2	no	—
487	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
497	SD₁₆	—	8	2	no	—
498	SD₁₆	—	8	2	no	—
499	D₈	—	8	2	no	—
500	D₈	—	8	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	4	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
524	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
525	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
526	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
527	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	1	no	—
534	C₂²⋊C₄	—	2	1	no	—
535	C₂²⋊C₄	—	2	1	no	—
536	C₂²⋊C₄	—	2	1	no	—
537	C₂²⋊C₄	—	2	1	no	—
538	C₂²⋊C₄	—	2	1	no	—
539	C₂²⋊C₄	—	2	1	no	—
540	C₂²⋊C₄	—	2	1	no	—
541	C₂²⋊C₄	—	2	1	no	—
542	C₂²⋊C₄	—	2	1	no	—
543	C₄²	—	2	2	no	—
544	C₄²	—	2	2	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
548	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
549	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
550	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	8	2	no	—
555	C₂³	—	8	2	no	—
556	C₂³	—	8	2	no	—
557	C₂³	C₁₉×#120	1	1	yes	characteristic
558	Q₈	—	2	2	no	—
559	Q₈	—	2	2	no	—
560	Q₈	—	4	2	no	—
561	Q₈	—	4	2	no	—
562	Q₈	—	8	2	no	—
563	Q₈	—	8	2	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	—	4	4	no	—
567	D₄	—	4	2	no	—
568	D₄	—	4	2	no	—
569	D₄	—	4	2	no	—
570	D₄	—	4	2	no	—
571	D₄	—	4	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	8	2	no	—
574	D₄	—	8	2	no	—
575	D₄	—	8	2	no	—
576	D₄	—	8	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	8	2	no	—
591	C₂×C₄	—	8	2	no	—
592	C₂×C₄	—	8	2	no	—
593	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
594	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
595	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
596	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
597	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
598	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
599	C₈	—	4	2	no	—
600	C₈	—	4	2	no	—
601	C₈	—	4	2	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	8	2	no	—
611	C₂²	—	8	2	no	—
612	C₂²	—	8	2	no	—
613	C₂²	—	16	4	no	—
614	C₂²	C₁₉×#454	1	2	yes	—
615	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	2	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	1	no	—
628	C₄	C₁₉×#576	1	2	yes	—
629	C₄	C₁₉×#577	1	2	yes	—
630	C₂	—	2	2	no	—
631	C₂	—	8	1	no	—
632	C₂	—	8	1	no	—
633	C₂	—	16	2	no	—
634	C₂	C₁₉×#3008	1	1	yes	characteristic
635	C₂	C₁₉×#3010	1	1	yes	characteristic
636	C₂	C₂×C₁₉×#454	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×#3552	C₂	semidirect
2. C₁₉×#3217	C₂	semidirect
3. C₁₉×#3217	C₂	semidirect
4. C₂×C₁₉×#486	C₂	semidirect
5. C₁₉×#1628	C₂	semidirect
6. C₁₉×#1627	C₂	semidirect
7. C₁₉×#1626	C₂	semidirect
8. C₁₉×#1625	C₂	semidirect
9. C₁₉×#1556	C₂	semidirect
10. C₁₉×#1494	C₂	semidirect
11. C₁₉×#1494	C₂	semidirect
13. C₁₉×#557	C₂²	semidirect
14. C₁₉×#556	C₂²	semidirect
18. D₄×Q₈×C₁₉	C₂²	semidirect
20. C₁₉×#547	C₂²	semidirect
49. C₁₉×#332	C₂²	semidirect
50. C₁₉×#332	C₂²	semidirect
51. C₁₉×Q₈⋊C₈	C₂²	semidirect
52. C₁₉×Q₈⋊C₈	C₂²	semidirect
53. C₁₉×D₄⋊C₈	C₂²	semidirect
54. C₁₉×D₄⋊C₈	C₂²	semidirect
232. #18694	C₁₉	direct (N × H)
284. #3552	C₂×C₁₉	semidirect
285. #3217	C₂×C₁₉	semidirect
286. #3217	C₂×C₁₉	semidirect
287. C₂×#486	C₂×C₁₉	semidirect
288. #1628	C₂×C₁₉	semidirect
289. #1627	C₂×C₁₉	semidirect
290. #1626	C₂×C₁₉	semidirect
291. #1625	C₂×C₁₉	semidirect
292. #1556	C₂×C₁₉	semidirect
293. #1494	C₂×C₁₉	semidirect
294. #1494	C₂×C₁₉	semidirect
324. #557	C₂²×C₁₉	semidirect
325. #556	C₂²×C₁₉	semidirect
329. D₄×Q₈	C₂²×C₁₉	semidirect
331. #547	C₂²×C₁₉	semidirect
360. #332	C₂²×C₁₉	semidirect
361. #332	C₂²×C₁₉	semidirect
362. Q₈⋊C₈	C₂²×C₁₉	semidirect
363. Q₈⋊C₈	C₂²×C₁₉	semidirect
364. D₄⋊C₈	C₂²×C₁₉	semidirect
365. D₄⋊C₈	C₂²×C₁₉	semidirect
464. C₁₉	#18694	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×#3552	2
C₁₉×#3217	2
C₂×C₁₉×#486	2
C₁₉×#1628	2
C₁₉×#1627	2
C₁₉×#1626	2
C₁₉×#1625	2
C₁₉×#1556	2
C₁₉×#1494	2
#18694	19

Subgroups — C19×#18694 #18024653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18694 #18024653