Subgroups — C₁₉×#61705 #18067664

Order 4864.

1742 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3501	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#552	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3344	C₂	1	8	yes	maximal, complemented
4	C₁₉×#3312	C₂	1	8	yes	maximal, complemented
5	C₁₉×#3236	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3195	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3189	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3113	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3095	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₉×#483	C₂	1	2	yes	maximal, complemented
11	C₁₉×#2973	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#554	—	2	4	no	—
13	C₁₉×#554	C₂²	1	4	yes	—
14	C₁₉×#552	—	2	4	no	—
15	C₁₉×#552	C₂²	1	8	yes	—
16	D₄×Q₈×C₁₉	C₂²	1	4	yes	—
17	C₁₉×#544	—	2	1	no	—
18	C₁₉×#543	—	2	1	no	—
19	C₁₉×#543	—	2	1	no	—
20	C₁₉×#533	C₂²	1	2	yes	—
21	C₂×C₁₉×#126	—	2	1	no	—
22	C₂×C₁₉×#125	—	2	1	no	—
23	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#123	—	2	1	no	—
25	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₁₉×#518	—	2	1	no	—
30	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#117	—	2	1	no	—
33	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₁₉×#501	C₂²	1	4	yes	complemented
36	C₁₉×#491	C₂²	1	4	yes	complemented
37	C₁₉×#485	C₂²	1	8	yes	complemented
38	C₁₉×#484	C₂²	1	4	yes	—
39	C₁₉×#484	C₂²	1	4	yes	complemented
40	C₁₉×#483	C₂²	1	4	yes	—
41	C₁₉×#483	C₂²	1	4	yes	—
42	C₁₉×#483	C₂²	1	4	yes	complemented
43	C₁₉×#483	C₂²	1	8	yes	complemented
44	C₁₉×#479	C₂²	1	8	yes	complemented
45	C₁₉×#475	C₂²	1	4	yes	complemented
46	C₁₉×#470	C₂²	1	8	yes	complemented
47	C₁₉×#467	C₂²	1	8	yes	complemented
48	C₁₉×#462	C₂²	1	4	yes	complemented
49	C₁₉×#451	C₂²	1	4	yes	—
50	C₁₉×#451	C₂²	1	4	yes	complemented
51	C₁₉×#451	C₂²	1	4	yes	complemented
52	C₁₉×#441	C₂²	1	8	yes	complemented
53	C₁₉×#435	C₂²	1	8	yes	—
54	C₁₉×#432	C₂²	1	2	yes	—
55	C₁₉×#428	C₂²	1	4	yes	complemented
56	C₂×C₁₉×#106	C₂²	1	4	yes	complemented
57	C₁₉×#419	C₂²	1	4	yes	complemented
58	C₂×C₁₉×#103	C₂²	1	4	yes	complemented
59	C₁₉×#407	C₂²	1	2	yes	—
60	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
61	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
62	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
63	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₁₉	—	2	1	no	—
66	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×Q₁₆×C₁₉	C₂³	1	8	yes	—
69	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
70	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
71	C₁₉×C₄⋊Q₈	—	2	4	no	—
72	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
73	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
74	C₁₉×#126	—	2	8	no	—
75	C₁₉×#125	—	2	8	no	—
76	C₁₉×#125	—	2	4	no	—
77	C₁₉×#125	—	2	2	no	—
78	C₁₉×#125	—	2	2	no	—
79	C₁₉×#125	C₂³	1	4	yes	—
80	C₁₉×#123	—	2	8	no	—
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	2	no	—
87	C₁₉×C₂²⋊Q₈	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	—	2	4	no	—
89	C₁₉×C₂²⋊Q₈	—	2	4	no	—
90	C₁₉×C₂²⋊Q₈	—	2	4	no	—
91	C₁₉×C₂²⋊Q₈	—	2	4	no	—
92	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
93	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
94	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
95	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
96	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
97	C₄×Q₈×C₁₉	—	2	2	no	—
98	C₄×Q₈×C₁₉	—	2	2	no	—
99	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
100	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
101	C₄×D₄×C₁₉	—	2	4	no	—
102	C₄×D₄×C₁₉	—	2	4	no	—
103	C₄×D₄×C₁₉	D₄	1	4	yes	—
104	C₄×D₄×C₁₉	C₂³	1	4	yes	—
105	C₁₉×#117	—	2	2	no	—
106	C₁₉×#117	—	2	2	no	—
107	C₁₉×#117	—	2	8	no	—
108	C₁₉×#117	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
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	—	2	1	no	—
115	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
128	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
129	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
132	C₂×C₄²×C₁₉	—	2	1	no	—
133	C₂×C₄²×C₁₉	—	2	1	no	—
134	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
135	C₁₉×#107	C₂³	1	8	yes	—
136	C₁₉×#106	C₂³	1	8	yes	—
137	C₁₉×#106	C₂³	1	8	yes	—
138	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
139	C₁₉×#103	C₂³	1	8	yes	—
140	C₁₉×#103	C₂³	1	8	yes	—
141	C₁₉×#103	C₂³	1	8	yes	—
142	C₁₉×#103	C₂³	1	8	yes	—
143	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
144	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
145	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
146	C₁₉×#97	C₂³	1	4	yes	—
147	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	2	no	—
151	C₂×Q₈×C₁₉	—	2	2	no	—
152	C₂×Q₈×C₁₉	—	2	2	no	—
153	C₂×Q₈×C₁₉	—	4	2	no	—
154	C₂×Q₈×C₁₉	—	4	4	no	—
155	C₂×Q₈×C₁₉	—	4	4	no	—
156	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
157	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
158	C₂×D₄×C₁₉	—	2	4	no	—
159	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	4	no	—
165	C₂²×C₄×C₁₉	—	2	2	no	—
166	C₂²×C₄×C₁₉	—	2	2	no	—
167	C₂²×C₄×C₁₉	—	2	2	no	—
168	C₂²×C₄×C₁₉	—	2	2	no	—
169	C₂²×C₄×C₁₉	—	4	2	no	—
170	C₂²×C₄×C₁₉	—	4	2	no	—
171	C₂²×C₄×C₁₉	—	4	4	no	—
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
181	Q₁₆×C₁₉	—	4	8	no	—
182	M₁₆×C₁₉	—	4	4	no	—
183	C₂×C₈×C₁₉	—	4	4	no	—
184	C₂×C₈×C₁₉	C₂⁴	1	8	yes	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	4	no	—
188	C₄⋊C₄×C₁₉	—	2	4	no	—
189	C₄⋊C₄×C₁₉	—	2	4	no	—
190	C₄⋊C₄×C₁₉	—	2	4	no	—
191	C₄⋊C₄×C₁₉	—	2	4	no	—
192	C₄⋊C₄×C₁₉	—	2	4	no	—
193	C₄⋊C₄×C₁₉	—	2	4	no	—
194	C₄⋊C₄×C₁₉	—	2	4	no	—
195	C₄⋊C₄×C₁₉	—	2	4	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	2	no	—
198	C₄⋊C₄×C₁₉	—	2	2	no	—
199	C₄⋊C₄×C₁₉	—	2	2	no	—
200	C₄⋊C₄×C₁₉	—	2	2	no	—
201	C₄⋊C₄×C₁₉	—	2	2	no	—
202	C₄⋊C₄×C₁₉	—	2	4	no	—
203	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
204	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
205	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
206	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
207	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
208	C₂²⋊C₄×C₁₉	—	2	4	no	—
209	C₂²⋊C₄×C₁₉	—	2	4	no	—
210	C₂²⋊C₄×C₁₉	—	2	4	no	—
211	C₂²⋊C₄×C₁₉	—	2	4	no	—
212	C₂²⋊C₄×C₁₉	—	2	4	no	—
213	C₂²⋊C₄×C₁₉	—	2	4	no	—
214	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
215	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
216	C₄²×C₁₉	—	2	4	no	—
217	C₄²×C₁₉	—	2	4	no	—
218	C₄²×C₁₉	—	2	4	no	—
219	C₄²×C₁₉	C₂×D₄	1	2	yes	—
220	C₄²×C₁₉	C₂⁴	1	2	yes	—
221	#61705	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂³×C₁₉	—	2	2	no	—
223	C₂³×C₁₉	—	4	1	no	—
224	C₂³×C₁₉	—	4	1	no	—
225	C₂³×C₁₉	—	4	1	no	—
226	C₂³×C₁₉	—	4	1	no	—
227	C₂³×C₁₉	#137	1	4	yes	—
228	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
229	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
230	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
231	Q₈×C₁₉	—	2	4	no	—
232	Q₈×C₁₉	—	2	8	no	—
233	Q₈×C₁₉	—	4	2	no	—
234	Q₈×C₁₉	—	8	2	no	—
235	Q₈×C₁₉	—	8	2	no	—
236	Q₈×C₁₉	—	8	2	no	—
237	D₄×C₁₉	—	2	8	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	4	no	—
240	C₂×C₄×C₁₉	—	2	4	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	2	4	no	—
246	C₂×C₄×C₁₉	—	2	4	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	—	4	2	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	2	no	—
254	C₂×C₄×C₁₉	—	4	2	no	—
255	C₂×C₄×C₁₉	—	4	2	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	4	8	no	—
258	C₂×C₄×C₁₉	—	8	2	no	—
259	C₂×C₄×C₁₉	—	8	2	no	—
260	C₂×C₄×C₁₉	—	8	2	no	—
261	C₂×C₄×C₁₉	—	8	2	no	—
262	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
265	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
268	C₈×C₁₉	—	2	8	no	—
269	#3501	C₂×C₁₉	1	1	yes	characteristic
270	C₂×#552	C₂×C₁₉	1	1	yes	characteristic
271	#3344	C₂×C₁₉	1	8	yes	complemented
272	#3312	C₂×C₁₉	1	8	yes	complemented
273	#3236	C₂×C₁₉	1	2	yes	complemented
274	#3195	C₂×C₁₉	1	2	yes	complemented
275	#3189	C₂×C₁₉	1	2	yes	complemented
276	#3113	C₂×C₁₉	1	2	yes	complemented
277	#3095	C₂×C₁₉	1	2	yes	complemented
278	C₂×#483	C₂×C₁₉	1	2	yes	complemented
279	#2973	C₂×C₁₉	1	1	yes	characteristic
280	C₂²×C₁₉	—	2	1	no	—
281	C₂²×C₁₉	—	2	2	no	—
282	C₂²×C₁₉	—	2	1	no	—
283	C₂²×C₁₉	—	2	2	no	—
284	C₂²×C₁₉	—	2	2	no	—
285	C₂²×C₁₉	—	2	2	no	—
286	C₂²×C₁₉	—	2	2	no	—
287	C₂²×C₁₉	—	4	4	no	—
288	C₂²×C₁₉	—	8	2	no	—
289	C₂²×C₁₉	C₂×#137	1	2	yes	—
290	C₂²×C₁₉	C₂×#137	1	4	yes	—
291	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
292	C₄×C₁₉	—	2	2	no	—
293	C₄×C₁₉	—	2	1	no	—
294	C₄×C₁₉	—	2	2	no	—
295	C₄×C₁₉	—	2	2	no	—
296	C₄×C₁₉	—	2	2	no	—
297	C₄×C₁₉	—	4	2	no	—
298	C₄×C₁₉	—	4	4	no	—
299	C₄×C₁₉	—	4	2	no	—
300	C₄×C₁₉	—	4	4	no	—
301	C₄×C₁₉	—	4	2	no	—
302	C₄×C₁₉	—	4	2	no	—
303	C₄×C₁₉	#585	1	2	yes	—
304	#554	—	2	4	no	—
305	#554	C₂²×C₁₉	1	4	yes	—
306	#552	—	2	4	no	—
307	#552	C₂²×C₁₉	1	8	yes	—
308	D₄×Q₈	C₂²×C₁₉	1	4	yes	—
309	#544	—	2	1	no	—
310	#543	—	2	1	no	—
311	#543	—	2	1	no	—
312	#533	C₂²×C₁₉	1	2	yes	—
313	C₂×#126	—	2	1	no	—
314	C₂×#125	—	2	1	no	—
315	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
316	C₂×#123	—	2	1	no	—
317	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
318	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
319	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
320	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
321	#518	—	2	1	no	—
322	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
324	C₂×#117	—	2	1	no	—
325	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
326	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
327	#501	C₂²×C₁₉	1	4	yes	complemented
328	#491	C₂²×C₁₉	1	4	yes	complemented
329	#485	C₂²×C₁₉	1	8	yes	complemented
330	#484	C₂²×C₁₉	1	4	yes	—
331	#484	C₂²×C₁₉	1	4	yes	complemented
332	#483	C₂²×C₁₉	1	4	yes	—
333	#483	C₂²×C₁₉	1	4	yes	—
334	#483	C₂²×C₁₉	1	8	yes	complemented
335	#483	C₂²×C₁₉	1	4	yes	complemented
336	#479	C₂²×C₁₉	1	8	yes	complemented
337	#475	C₂²×C₁₉	1	4	yes	complemented
338	#470	C₂²×C₁₉	1	8	yes	complemented
339	#467	C₂²×C₁₉	1	8	yes	complemented
340	#462	C₂²×C₁₉	1	4	yes	complemented
341	#451	C₂²×C₁₉	1	4	yes	—
342	#451	C₂²×C₁₉	1	4	yes	complemented
343	#451	C₂²×C₁₉	1	4	yes	complemented
344	#441	C₂²×C₁₉	1	8	yes	complemented
345	#435	C₂²×C₁₉	1	8	yes	—
346	#432	C₂²×C₁₉	1	2	yes	—
347	#428	C₂²×C₁₉	1	4	yes	complemented
348	C₂×#106	C₂²×C₁₉	1	4	yes	complemented
349	#419	C₂²×C₁₉	1	4	yes	complemented
350	C₂×#103	C₂²×C₁₉	1	4	yes	complemented
351	#407	C₂²×C₁₉	1	2	yes	—
352	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
353	C₂×C₁₉	—	2	2	no	—
354	C₂×C₁₉	—	2	4	no	—
355	C₂×C₁₉	—	4	2	no	—
356	C₂×C₁₉	#3485	1	1	yes	characteristic
357	C₂×C₁₉	C₂²×#137	1	1	yes	characteristic
358	C₂×C₁₉	#3586	1	1	yes	characteristic
359	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
360	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
361	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
362	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
363	C₂³×C₄	—	2	1	no	—
364	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
365	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
366	C₂×Q₁₆	C₂³×C₁₉	1	8	yes	—
367	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
368	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
369	C₄⋊Q₈	—	2	4	no	—
370	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
371	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
372	#126	—	2	8	no	—
373	#125	—	2	8	no	—
374	#125	—	2	4	no	—
375	#125	—	2	2	no	—
376	#125	—	2	2	no	—
377	#125	C₂³×C₁₉	1	4	yes	—
378	#123	—	2	8	no	—
379	C₂²⋊Q₈	—	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	—	2	4	no	—
387	C₂²⋊Q₈	—	2	4	no	—
388	C₂²⋊Q₈	—	2	4	no	—
389	C₂²⋊Q₈	—	2	4	no	—
390	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
391	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
392	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
393	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
394	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
395	C₄×Q₈	—	2	2	no	—
396	C₄×Q₈	—	2	2	no	—
397	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
398	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
399	C₄×D₄	—	2	4	no	—
400	C₄×D₄	—	2	4	no	—
401	C₄×D₄	D₄×C₁₉	1	4	yes	—
402	C₄×D₄	C₂³×C₁₉	1	4	yes	—
403	#117	—	2	2	no	—
404	#117	—	2	2	no	—
405	#117	—	2	8	no	—
406	#117	C₂³×C₁₉	1	4	yes	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	2	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	2	no	—
414	C₂×C₄⋊C₄	—	2	2	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
420	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	2	no	—
426	C₂×C₂²⋊C₄	—	2	2	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
430	C₂×C₄²	—	2	1	no	—
431	C₂×C₄²	—	2	1	no	—
432	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
433	#107	C₂³×C₁₉	1	8	yes	—
434	#106	C₂³×C₁₉	1	8	yes	—
435	#106	C₂³×C₁₉	1	8	yes	—
436	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
437	#103	C₂³×C₁₉	1	8	yes	—
438	#103	C₂³×C₁₉	1	8	yes	—
439	#103	C₂³×C₁₉	1	8	yes	—
440	#103	C₂³×C₁₉	1	8	yes	—
441	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
442	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
443	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
444	#97	C₂³×C₁₉	1	4	yes	—
445	C₁₉	#61705	1	1	yes	characteristic, direct product factor, Sylow
446	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	—	2	2	no	—
451	C₂×Q₈	—	2	2	no	—
452	C₂×Q₈	—	4	2	no	—
453	C₂×Q₈	—	4	4	no	—
454	C₂×Q₈	—	4	4	no	—
455	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
456	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	4	2	no	—
469	C₂²×C₄	—	4	2	no	—
470	C₂²×C₄	—	4	4	no	—
471	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
476	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
477	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
478	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
479	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
480	Q₁₆	—	4	8	no	—
481	M₁₆	—	4	4	no	—
482	C₂×C₈	—	4	4	no	—
483	C₂×C₈	C₂⁴×C₁₉	1	8	yes	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	4	no	—
491	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
503	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
504	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
505	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
506	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
507	C₂²⋊C₄	—	2	4	no	—
508	C₂²⋊C₄	—	2	4	no	—
509	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	2	4	no	—
511	C₂²⋊C₄	—	2	4	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
514	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
515	C₄²	—	2	4	no	—
516	C₄²	—	2	4	no	—
517	C₄²	—	2	4	no	—
518	C₄²	C₂×D₄×C₁₉	1	2	yes	—
519	C₄²	C₂⁴×C₁₉	1	2	yes	—
520	C₂³	—	2	2	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	4	1	no	—
524	C₂³	—	4	1	no	—
525	C₂³	C₁₉×#137	1	4	yes	—
526	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
527	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
528	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
529	Q₈	—	2	4	no	—
530	Q₈	—	2	8	no	—
531	Q₈	—	4	2	no	—
532	Q₈	—	8	2	no	—
533	Q₈	—	8	2	no	—
534	Q₈	—	8	2	no	—
535	D₄	—	2	8	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	8	no	—
556	C₂×C₄	—	8	2	no	—
557	C₂×C₄	—	8	2	no	—
558	C₂×C₄	—	8	2	no	—
559	C₂×C₄	—	8	2	no	—
560	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
561	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
562	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
563	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
564	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
565	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
566	C₈	—	2	8	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	4	4	no	—
575	C₂²	—	8	2	no	—
576	C₂²	C₂×C₁₉×#137	1	2	yes	—
577	C₂²	C₂×C₁₉×#137	1	4	yes	—
578	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
579	C₄	—	2	1	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	2	no	—
584	C₄	—	4	2	no	—
585	C₄	—	4	4	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	2	no	—
589	C₄	—	4	4	no	—
590	C₄	C₁₉×#585	1	2	yes	—
591	C₂	—	2	2	no	—
592	C₂	—	2	4	no	—
593	C₂	—	4	2	no	—
594	C₂	C₁₉×#3485	1	1	yes	characteristic
595	C₂	C₂²×C₁₉×#137	1	1	yes	characteristic
596	C₂	C₁₉×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₁₉×#3344	C₂	semidirect
4. C₁₉×#3312	C₂	semidirect
5. C₁₉×#3236	C₂	semidirect
6. C₁₉×#3195	C₂	semidirect
7. C₁₉×#3189	C₂	semidirect
8. C₁₉×#3113	C₂	semidirect
9. C₁₉×#3095	C₂	semidirect
10. C₂×C₁₉×#483	C₂	semidirect
35. C₁₉×#501	C₂²	semidirect
36. C₁₉×#491	C₂²	semidirect
37. C₁₉×#485	C₂²	semidirect
39. C₁₉×#484	C₂²	semidirect
42. C₁₉×#483	C₂²	semidirect
43. C₁₉×#483	C₂²	semidirect
44. C₁₉×#479	C₂²	semidirect
45. C₁₉×#475	C₂²	semidirect
46. C₁₉×#470	C₂²	semidirect
47. C₁₉×#467	C₂²	semidirect
48. C₁₉×#462	C₂²	semidirect
50. C₁₉×#451	C₂²	semidirect
51. C₁₉×#451	C₂²	semidirect
52. C₁₉×#441	C₂²	semidirect
55. C₁₉×#428	C₂²	semidirect
56. C₂×C₁₉×#106	C₂²	semidirect
57. C₁₉×#419	C₂²	semidirect
58. C₂×C₁₉×#103	C₂²	semidirect
221. #61705	C₁₉	direct (N × H)
271. #3344	C₂×C₁₉	semidirect
272. #3312	C₂×C₁₉	semidirect
273. #3236	C₂×C₁₉	semidirect
274. #3195	C₂×C₁₉	semidirect
275. #3189	C₂×C₁₉	semidirect
276. #3113	C₂×C₁₉	semidirect
277. #3095	C₂×C₁₉	semidirect
278. C₂×#483	C₂×C₁₉	semidirect
327. #501	C₂²×C₁₉	semidirect
328. #491	C₂²×C₁₉	semidirect
329. #485	C₂²×C₁₉	semidirect
331. #484	C₂²×C₁₉	semidirect
334. #483	C₂²×C₁₉	semidirect
335. #483	C₂²×C₁₉	semidirect
336. #479	C₂²×C₁₉	semidirect
337. #475	C₂²×C₁₉	semidirect
338. #470	C₂²×C₁₉	semidirect
339. #467	C₂²×C₁₉	semidirect
340. #462	C₂²×C₁₉	semidirect
342. #451	C₂²×C₁₉	semidirect
343. #451	C₂²×C₁₉	semidirect
344. #441	C₂²×C₁₉	semidirect
347. #428	C₂²×C₁₉	semidirect
348. C₂×#106	C₂²×C₁₉	semidirect
349. #419	C₂²×C₁₉	semidirect
350. C₂×#103	C₂²×C₁₉	semidirect
445. C₁₉	#61705	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×#3501	2
C₂×C₁₉×#552	2
C₁₉×#3344	2
C₁₉×#3312	2
C₁₉×#3236	2
C₁₉×#3195	2
C₁₉×#3189	2
C₁₉×#3113	2
C₁₉×#3095	2
C₂×C₁₉×#483	2
C₁₉×#2973	2
#61705	19

Subgroups — C19×#61705 #18067664

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61705 #18067664