Subgroups — C₁₉×#17748 #18023707

Order 4864.

952 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2920	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#432	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1558	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1556	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1554	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1550	C₂	1	4	yes	maximal, complemented
8	C₁₉×#533	—	2	1	no	—
9	C₁₉×#533	—	2	1	no	—
10	C₁₉×#533	—	2	1	no	—
11	C₁₉×#533	—	2	1	no	—
12	C₁₉×#533	C₄	1	2	yes	—
13	C₁₉×#533	C₄	1	2	yes	—
14	C₁₉×#533	C₂²	1	2	yes	—
15	C₁₉×#533	C₂²	1	2	yes	—
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#125	—	2	1	no	—
19	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₁₉×C₂²⋊Q₈	C₄	1	2	yes	—
21	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
22	C₂×C₄×Q₈×C₁₉	C₄	1	2	yes	—
23	C₂×C₁₉×#117	—	2	1	no	—
24	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#432	—	2	1	no	—
26	C₁₉×#432	—	2	1	no	—
27	C₁₉×#432	—	2	1	no	—
28	C₁₉×#432	C₂²	1	2	yes	—
29	C₁₉×#432	C₂²	1	2	yes	—
30	C₁₉×#432	C₂²	1	2	yes	—
31	C₁₉×#431	—	2	1	no	—
32	C₁₉×#431	C₂²	1	2	yes	—
33	C₁₉×#423	C₂²	1	2	yes	—
34	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
35	C₁₉×#407	—	2	1	no	—
36	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
37	C₄×M₁₆×C₁₉	—	2	1	no	—
38	C₂×C₁₉×#97	—	2	1	no	—
39	C₁₉×#333	C₂²	1	8	yes	complemented
40	C₁₉×#332	C₂²	1	8	yes	complemented
41	C₂²×Q₈×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂²×C₈×C₁₉	—	2	2	no	—
48	C₁₉×C₄⋊Q₈	—	2	1	no	—
49	C₁₉×C₄⋊Q₈	—	2	1	no	—
50	C₁₉×C₄⋊Q₈	—	2	1	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
53	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
54	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
55	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₁₉×#125	—	2	2	no	—
57	C₁₉×#125	—	2	2	no	—
58	C₁₉×#125	—	2	2	no	—
59	C₁₉×#125	—	2	2	no	—
60	C₁₉×C₂²⋊Q₈	—	2	2	no	—
61	C₁₉×C₂²⋊Q₈	—	2	2	no	—
62	C₁₉×C₂²⋊Q₈	—	2	2	no	—
63	C₁₉×C₂²⋊Q₈	—	2	2	no	—
64	C₁₉×C₂²⋊Q₈	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
67	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
68	C₄×Q₈×C₁₉	—	2	2	no	—
69	C₄×Q₈×C₁₉	—	2	2	no	—
70	C₄×Q₈×C₁₉	—	2	2	no	—
71	C₄×Q₈×C₁₉	—	2	2	no	—
72	C₄×Q₈×C₁₉	—	2	2	no	—
73	C₄×Q₈×C₁₉	—	2	2	no	—
74	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
75	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
76	C₁₉×#117	—	2	2	no	—
77	C₁₉×#117	—	2	2	no	—
78	C₁₉×#117	—	2	2	no	—
79	C₁₉×#117	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
87	C₂×C₄²×C₁₉	—	2	2	no	—
88	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
100	C₁₉×C₄⋊C₈	—	2	2	no	—
101	C₁₉×C₄⋊C₈	—	2	2	no	—
102	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
103	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
104	C₁₉×C₂²⋊C₈	—	2	2	no	—
105	C₁₉×C₂²⋊C₈	—	2	2	no	—
106	C₁₉×C₂²⋊C₈	—	2	2	no	—
107	C₁₉×C₂²⋊C₈	—	2	2	no	—
108	C₁₉×#97	—	2	2	no	—
109	C₁₉×#97	—	2	2	no	—
110	C₁₉×#97	—	2	2	no	—
111	C₄×C₈×C₁₉	—	2	2	no	—
112	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	—	2	2	no	—
116	C₂×Q₈×C₁₉	—	4	4	no	—
117	C₂×Q₈×C₁₉	—	4	4	no	—
118	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₁₉	—	2	4	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	4	2	no	—
123	C₂²×C₄×C₁₉	—	4	2	no	—
124	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	M₁₆×C₁₉	—	4	4	no	—
143	C₂×C₈×C₁₉	—	2	4	no	—
144	C₂×C₈×C₁₉	—	2	4	no	—
145	C₂×C₈×C₁₉	—	4	4	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	4	no	—
150	C₄⋊C₄×C₁₉	—	2	4	no	—
151	C₄⋊C₄×C₁₉	—	2	4	no	—
152	C₄⋊C₄×C₁₉	—	2	4	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
158	C₂²⋊C₄×C₁₉	—	2	4	no	—
159	C₂²⋊C₄×C₁₉	—	2	4	no	—
160	C₄²×C₁₉	—	2	4	no	—
161	C₄²×C₁₉	—	2	4	no	—
162	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
163	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
164	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
165	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
166	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
167	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
178	#17748	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂³×C₁₉	—	2	2	no	—
180	C₂³×C₁₉	—	2	2	no	—
181	C₂³×C₁₉	—	4	1	no	—
182	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	Q₈×C₁₉	—	4	4	no	—
186	Q₈×C₁₉	—	4	4	no	—
187	Q₈×C₁₉	—	4	4	no	—
188	Q₈×C₁₉	—	4	4	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	4	no	—
209	C₂×C₄×C₁₉	—	4	4	no	—
210	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#137	1	4	yes	—
220	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
223	C₈×C₁₉	—	4	4	no	—
224	C₈×C₁₉	—	4	4	no	—
225	C₂×#533	C₂×C₁₉	1	1	yes	characteristic
226	#2920	C₂×C₁₉	1	1	yes	characteristic
227	C₂×#432	C₂×C₁₉	1	1	yes	characteristic
228	#1558	C₂×C₁₉	1	2	yes	complemented
229	#1556	C₂×C₁₉	1	2	yes	complemented
230	#1554	C₂×C₁₉	1	4	yes	complemented
231	#1550	C₂×C₁₉	1	4	yes	complemented
232	C₂²×C₁₉	—	2	1	no	—
233	C₂²×C₁₉	—	2	1	no	—
234	C₂²×C₁₉	—	2	1	no	—
235	C₂²×C₁₉	—	2	1	no	—
236	C₂²×C₁₉	—	2	1	no	—
237	C₂²×C₁₉	—	2	1	no	—
238	C₂²×C₁₉	—	2	1	no	—
239	C₂²×C₁₉	—	4	4	no	—
240	C₂²×C₁₉	#413	1	2	yes	—
241	C₂²×C₁₉	#419	1	2	yes	—
242	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
243	C₄×C₁₉	—	2	1	no	—
244	C₄×C₁₉	—	2	1	no	—
245	C₄×C₁₉	—	2	1	no	—
246	C₄×C₁₉	—	2	1	no	—
247	C₄×C₁₉	—	2	1	no	—
248	C₄×C₁₉	—	2	1	no	—
249	C₄×C₁₉	—	2	1	no	—
250	C₄×C₁₉	—	2	1	no	—
251	C₄×C₁₉	—	2	1	no	—
252	C₄×C₁₉	—	4	4	no	—
253	C₄×C₁₉	—	4	4	no	—
254	C₄×C₁₉	#419	1	2	yes	—
255	C₄×C₁₉	C₂×#137	1	2	yes	—
256	C₄×C₁₉	#575	1	2	yes	—
257	#533	—	2	1	no	—
258	#533	—	2	1	no	—
259	#533	—	2	1	no	—
260	#533	—	2	1	no	—
261	#533	C₄×C₁₉	1	2	yes	—
262	#533	C₄×C₁₉	1	2	yes	—
263	#533	C₂²×C₁₉	1	2	yes	—
264	#533	C₂²×C₁₉	1	2	yes	—
265	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
267	C₂×#125	—	2	1	no	—
268	C₂×C₂²⋊Q₈	—	2	1	no	—
269	C₂×C₂²⋊Q₈	C₄×C₁₉	1	2	yes	—
270	C₂×C₄×Q₈	—	2	1	no	—
271	C₂×C₄×Q₈	C₄×C₁₉	1	2	yes	—
272	C₂×#117	—	2	1	no	—
273	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
274	#432	—	2	1	no	—
275	#432	—	2	1	no	—
276	#432	—	2	1	no	—
277	#432	C₂²×C₁₉	1	2	yes	—
278	#432	C₂²×C₁₉	1	2	yes	—
279	#432	C₂²×C₁₉	1	2	yes	—
280	#431	—	2	1	no	—
281	#431	C₂²×C₁₉	1	2	yes	—
282	#423	C₂²×C₁₉	1	2	yes	—
283	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
284	#407	—	2	1	no	—
285	C₂×C₂²⋊C₈	—	2	1	no	—
286	C₄×M₁₆	—	2	1	no	—
287	C₂×#97	—	2	1	no	—
288	#333	C₂²×C₁₉	1	8	yes	complemented
289	#332	C₂²×C₁₉	1	8	yes	complemented
290	C₂×C₁₉	—	2	2	no	—
291	C₂×C₁₉	—	2	2	no	—
292	C₂×C₁₉	—	4	1	no	—
293	C₂×C₁₉	C₂×#413	1	1	yes	characteristic
294	C₂×C₁₉	C₂×#419	1	1	yes	characteristic
295	C₂×C₁₉	#2896	1	1	yes	characteristic
296	C₂²×Q₈	—	2	1	no	—
297	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
298	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
299	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
300	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
301	C₂×M₁₆	—	2	2	no	—
302	C₂²×C₈	—	2	2	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	—	2	1	no	—
306	C₄⋊Q₈	—	2	1	no	—
307	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
308	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
309	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
310	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
311	#125	—	2	2	no	—
312	#125	—	2	2	no	—
313	#125	—	2	2	no	—
314	#125	—	2	2	no	—
315	C₂²⋊Q₈	—	2	2	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	C₂²⋊Q₈	—	2	2	no	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
322	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
330	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
331	#117	—	2	2	no	—
332	#117	—	2	2	no	—
333	#117	—	2	2	no	—
334	#117	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
344	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
345	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
346	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
347	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
348	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
349	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
350	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
351	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
355	C₄⋊C₈	—	2	2	no	—
356	C₄⋊C₈	—	2	2	no	—
357	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
358	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
359	C₂²⋊C₈	—	2	2	no	—
360	C₂²⋊C₈	—	2	2	no	—
361	C₂²⋊C₈	—	2	2	no	—
362	C₂²⋊C₈	—	2	2	no	—
363	#97	—	2	2	no	—
364	#97	—	2	2	no	—
365	#97	—	2	2	no	—
366	C₄×C₈	—	2	2	no	—
367	C₁₉	#17748	1	1	yes	characteristic, direct product factor, Sylow
368	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	4	4	no	—
373	C₂×Q₈	—	4	4	no	—
374	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
381	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
382	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
383	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
384	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
385	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
386	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
387	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
388	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
389	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
390	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
391	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
398	M₁₆	—	4	4	no	—
399	C₂×C₈	—	2	4	no	—
400	C₂×C₈	—	2	4	no	—
401	C₂×C₈	—	4	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₄²	—	2	4	no	—
417	C₄²	—	2	4	no	—
418	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
419	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
420	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
421	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
422	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
423	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
424	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
425	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
426	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
427	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
429	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
431	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
432	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
433	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	4	1	no	—
437	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
438	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
439	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
440	Q₈	—	4	4	no	—
441	Q₈	—	4	4	no	—
442	Q₈	—	4	4	no	—
443	Q₈	—	4	4	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
466	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
467	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
468	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
469	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
470	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
471	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
472	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
473	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
474	C₂×C₄	C₁₉×#137	1	4	yes	—
475	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
476	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
477	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
478	C₈	—	4	4	no	—
479	C₈	—	4	4	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	4	4	no	—
488	C₂²	C₁₉×#413	1	2	yes	—
489	C₂²	C₁₉×#419	1	2	yes	—
490	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	4	4	no	—
501	C₄	—	4	4	no	—
502	C₄	C₁₉×#419	1	2	yes	—
503	C₄	C₂×C₁₉×#137	1	2	yes	—
504	C₄	C₁₉×#575	1	2	yes	—
505	C₂	—	2	2	no	—
506	C₂	—	2	2	no	—
507	C₂	—	4	1	no	—
508	C₂	C₂×C₁₉×#413	1	1	yes	characteristic
509	C₂	C₂×C₁₉×#419	1	1	yes	characteristic
510	C₂	C₁₉×#2896	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1558	C₂	semidirect
5. C₁₉×#1556	C₂	semidirect
6. C₁₉×#1554	C₂	semidirect
7. C₁₉×#1550	C₂	semidirect
39. C₁₉×#333	C₂²	semidirect
40. C₁₉×#332	C₂²	semidirect
178. #17748	C₁₉	direct (N × H)
228. #1558	C₂×C₁₉	semidirect
229. #1556	C₂×C₁₉	semidirect
230. #1554	C₂×C₁₉	semidirect
231. #1550	C₂×C₁₉	semidirect
288. #333	C₂²×C₁₉	semidirect
289. #332	C₂²×C₁₉	semidirect
367. C₁₉	#17748	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#533	2
C₁₉×#2920	2
C₂×C₁₉×#432	2
C₁₉×#1558	2
C₁₉×#1556	2
C₁₉×#1554	2
C₁₉×#1550	2
#17748	19

Subgroups — C19×#17748 #18023707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17748 #18023707