Subgroups — C₁₉×#14241 #18020200

Order 4864.

1470 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#395	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#391	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1446	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1444	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1441	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1436	C₂	1	2	yes	maximal
8	C₁₉×#1436	C₂	1	2	yes	maximal
9	C₁₉×#1436	C₂	1	2	yes	maximal
10	C₁₉×C₄⋊#95	C₂	1	2	yes	maximal
11	C₄×C₁₉×#95	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#395	C₄	1	8	yes	complemented
23	C₁₉×#391	—	2	4	no	—
24	C₄×C₄⋊C₄×C₁₉	—	2	4	no	—
25	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#95	C₂²	1	2	yes	—
28	C₂×C₁₉×#95	C₂²	1	2	yes	—
29	C₂×C₁₉×#95	C₂²	1	2	yes	—
30	C₂×C₁₉×#95	C₂²	1	2	yes	—
31	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#95	C₂²	1	2	yes	—
33	C₂×C₁₉×#95	C₂²	1	2	yes	—
34	C₂×C₁₉×#95	C₂²	1	2	yes	—
35	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#95	C₂²	1	2	yes	—
37	C₂×C₁₉×#95	C₂²	1	2	yes	—
38	C₂²×Q₈×C₁₉	—	2	2	no	—
39	C₂²×Q₈×C₁₉	—	2	2	no	—
40	C₂²×Q₈×C₁₉	—	4	2	no	—
41	C₂²×Q₈×C₁₉	—	4	2	no	—
42	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
61	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
62	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
63	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
65	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
67	C₂×C₄⋊C₄×C₁₉	Q₈	1	4	yes	complemented
68	C₂×C₄²×C₁₉	—	2	2	no	—
69	C₂×C₄²×C₁₉	—	2	2	no	—
70	C₂×C₄²×C₁₉	—	2	2	no	—
71	C₂×C₄²×C₁₉	—	2	2	no	—
72	C₂×C₄²×C₁₉	—	2	4	no	—
73	C₂×C₄²×C₁₉	—	2	4	no	—
74	C₂×C₄²×C₁₉	—	4	2	no	—
75	C₂×C₄²×C₁₉	—	4	2	no	—
76	C₂×C₄²×C₁₉	—	4	2	no	—
77	C₂×C₄²×C₁₉	D₄	1	4	yes	—
78	C₁₉×#95	—	2	2	no	—
79	C₁₉×#95	—	2	2	no	—
80	C₁₉×#95	—	2	4	no	—
81	C₁₉×#95	—	2	4	no	—
82	C₁₉×#95	—	2	2	no	—
83	C₁₉×#95	—	2	4	no	—
84	C₁₉×#95	—	2	4	no	—
85	C₁₉×#95	—	4	2	no	—
86	C₁₉×#95	—	4	2	no	—
87	C₁₉×#95	—	4	2	no	—
88	C₁₉×#95	C₂×C₄	1	8	yes	—
89	C₁₉×#95	C₂×C₄	1	4	yes	—
90	C₁₉×#95	Q₈	1	8	yes	complemented
91	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
92	C₂×Q₈×C₁₉	—	2	8	no	—
93	C₂×Q₈×C₁₉	—	4	8	no	—
94	C₂×Q₈×C₁₉	—	4	4	no	—
95	C₂×Q₈×C₁₉	—	4	4	no	—
96	C₂×Q₈×C₁₉	—	4	8	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	1	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	1	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
145	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
146	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
147	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
148	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
152	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
153	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
154	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
155	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
156	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
157	C₂²×C₄×C₁₉	#41	1	2	yes	—
158	C₂²×C₄×C₁₉	#41	1	2	yes	—
159	C₂²×C₄×C₁₉	#41	1	4	yes	—
160	C₂²×C₄×C₁₉	#41	1	2	yes	—
161	C₂²×C₄×C₁₉	#41	1	2	yes	—
162	C₄⋊C₄×C₁₉	—	2	8	no	—
163	C₄⋊C₄×C₁₉	—	2	8	no	—
164	C₄⋊C₄×C₁₉	—	4	8	no	—
165	C₄⋊C₄×C₁₉	—	4	8	no	—
166	C₄⋊C₄×C₁₉	—	4	4	no	—
167	C₄²×C₁₉	—	2	8	no	—
168	C₄²×C₁₉	—	4	4	no	—
169	C₄²×C₁₉	—	4	8	no	—
170	C₄²×C₁₉	—	4	4	no	—
171	#14241	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
173	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
174	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
175	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
176	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
177	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
178	C₂³×C₁₉	C₂×#41	1	2	yes	—
179	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
180	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
181	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
182	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
183	Q₈×C₁₉	—	4	16	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	2	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	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	4	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	2	4	no	—
207	C₂×C₄×C₁₉	—	2	4	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	4	no	—
210	C₂×C₄×C₁₉	—	2	4	no	—
211	C₂×C₄×C₁₉	—	2	4	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	2	4	no	—
217	C₂×C₄×C₁₉	—	2	4	no	—
218	C₂×C₄×C₁₉	—	2	4	no	—
219	C₂×C₄×C₁₉	—	2	4	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
245	C₂×C₄×C₁₉	C₄×Q₈	1	8	yes	—
246	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
247	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
248	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
249	C₂×#395	C₂×C₁₉	1	1	yes	characteristic
250	C₂×#391	C₂×C₁₉	1	1	yes	characteristic
251	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
252	#1446	C₂×C₁₉	1	1	yes	characteristic
253	#1444	C₂×C₁₉	1	1	yes	characteristic
254	#1441	C₂×C₁₉	1	1	yes	characteristic
255	#1436	C₂×C₁₉	1	2	yes	—
256	#1436	C₂×C₁₉	1	2	yes	—
257	#1436	C₂×C₁₉	1	2	yes	—
258	C₄⋊#95	C₂×C₁₉	1	2	yes	—
259	C₄×#95	C₂×C₁₉	1	1	yes	characteristic
260	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
261	C₂²×C₁₉	C₂×C₄×Q₈	1	2	yes	—
262	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
263	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
264	C₂²×C₁₉	#518	1	2	yes	—
265	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
266	C₂²×C₁₉	#525	1	1	yes	characteristic
267	C₂²×C₁₉	#529	1	1	yes	characteristic
268	C₂²×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
269	C₂²×C₁₉	#532	1	1	yes	characteristic
270	C₂²×C₁₉	#533	1	2	yes	—
271	C₂²×C₁₉	#533	1	1	yes	characteristic
272	C₂²×C₁₉	#534	1	1	yes	characteristic
273	C₂²×C₁₉	#535	1	1	yes	characteristic
274	C₂²×C₁₉	#538	1	2	yes	—
275	C₂²×C₁₉	#551	1	2	yes	—
276	C₂²×C₁₉	#551	1	2	yes	—
277	C₂²×C₁₉	#554	1	2	yes	—
278	C₂²×C₁₉	#554	1	2	yes	—
279	C₂²×C₁₉	#554	1	2	yes	—
280	C₂²×C₁₉	#554	1	2	yes	—
281	C₂²×C₁₉	#555	1	2	yes	—
282	C₂²×C₁₉	Q₈²	1	2	yes	—
283	C₄×C₁₉	—	2	4	no	—
284	C₄×C₁₉	—	2	4	no	—
285	C₄×C₁₉	—	2	4	no	—
286	C₄×C₁₉	—	2	8	no	—
287	C₄×C₁₉	—	2	4	no	—
288	C₄×C₁₉	—	4	2	no	—
289	C₄×C₁₉	—	4	4	no	—
290	C₄×C₁₉	—	4	2	no	—
291	C₄×C₁₉	—	4	4	no	—
292	C₄×C₁₉	—	4	2	no	—
293	C₄×C₁₉	—	8	2	no	—
294	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
295	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
296	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
297	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
298	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
299	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
300	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
301	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
302	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
303	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
304	#395	C₄×C₁₉	1	8	yes	complemented
305	#391	—	2	4	no	—
306	C₄×C₄⋊C₄	—	2	4	no	—
307	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
308	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
309	C₂×#95	C₂²×C₁₉	1	2	yes	—
310	C₂×#95	C₂²×C₁₉	1	2	yes	—
311	C₂×#95	C₂²×C₁₉	1	2	yes	—
312	C₂×#95	C₂²×C₁₉	1	2	yes	—
313	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
314	C₂×#95	C₂²×C₁₉	1	2	yes	—
315	C₂×#95	C₂²×C₁₉	1	2	yes	—
316	C₂×#95	C₂²×C₁₉	1	2	yes	—
317	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×#95	C₂²×C₁₉	1	2	yes	—
319	C₂×#95	C₂²×C₁₉	1	2	yes	—
320	C₂×C₁₉	C₄×C₂²⋊Q₈	1	1	yes	characteristic
321	C₂×C₁₉	C₄×C₄⋊Q₈	1	1	yes	characteristic
322	C₂×C₁₉	#2321	1	1	yes	characteristic
323	C₂×C₁₉	#2368	1	2	yes	—
324	C₂×C₁₉	#2369	1	2	yes	—
325	C₂×C₁₉	#2564	1	1	yes	characteristic
326	C₂×C₁₉	#2567	1	1	yes	characteristic
327	C₂×C₁₉	#2574	1	2	yes	—
328	C₂×C₁₉	#2583	1	1	yes	characteristic
329	C₂×C₁₉	#2586	1	2	yes	—
330	C₂×C₁₉	#2610	1	1	yes	characteristic
331	C₂²×Q₈	—	2	2	no	—
332	C₂²×Q₈	—	2	2	no	—
333	C₂²×Q₈	—	4	2	no	—
334	C₂²×Q₈	—	4	2	no	—
335	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
336	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
337	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
338	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
339	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
340	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
341	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
342	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
343	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
344	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
345	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	4	no	—
353	C₂×C₄⋊C₄	—	2	4	no	—
354	C₂×C₄⋊C₄	—	4	2	no	—
355	C₂×C₄⋊C₄	—	4	2	no	—
356	C₂×C₄⋊C₄	—	4	2	no	—
357	C₂×C₄⋊C₄	—	4	2	no	—
358	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
359	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
360	C₂×C₄⋊C₄	Q₈×C₁₉	1	4	yes	complemented
361	C₂×C₄²	—	2	2	no	—
362	C₂×C₄²	—	2	2	no	—
363	C₂×C₄²	—	2	2	no	—
364	C₂×C₄²	—	2	2	no	—
365	C₂×C₄²	—	2	4	no	—
366	C₂×C₄²	—	2	4	no	—
367	C₂×C₄²	—	4	2	no	—
368	C₂×C₄²	—	4	2	no	—
369	C₂×C₄²	—	4	2	no	—
370	C₂×C₄²	D₄×C₁₉	1	4	yes	—
371	#95	—	2	2	no	—
372	#95	—	2	2	no	—
373	#95	—	2	4	no	—
374	#95	—	2	4	no	—
375	#95	—	2	2	no	—
376	#95	—	2	4	no	—
377	#95	—	2	4	no	—
378	#95	—	4	2	no	—
379	#95	—	4	2	no	—
380	#95	—	4	2	no	—
381	#95	C₂×C₄×C₁₉	1	8	yes	—
382	#95	C₂×C₄×C₁₉	1	4	yes	—
383	#95	Q₈×C₁₉	1	8	yes	complemented
384	C₁₉	#14241	1	1	yes	characteristic, direct product factor, Sylow
385	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
386	C₂×Q₈	—	2	8	no	—
387	C₂×Q₈	—	4	8	no	—
388	C₂×Q₈	—	4	4	no	—
389	C₂×Q₈	—	4	4	no	—
390	C₂×Q₈	—	4	8	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
438	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
439	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
440	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
441	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
442	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
444	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
445	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
446	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
447	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
448	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
449	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
450	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
451	C₂²×C₄	#41×C₁₉	1	2	yes	—
452	C₂²×C₄	#41×C₁₉	1	2	yes	—
453	C₂²×C₄	#41×C₁₉	1	2	yes	—
454	C₂²×C₄	#41×C₁₉	1	4	yes	—
455	C₂²×C₄	#41×C₁₉	1	2	yes	—
456	C₄⋊C₄	—	2	8	no	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	4	8	no	—
459	C₄⋊C₄	—	4	8	no	—
460	C₄⋊C₄	—	4	4	no	—
461	C₄²	—	2	8	no	—
462	C₄²	—	4	4	no	—
463	C₄²	—	4	8	no	—
464	C₄²	—	4	4	no	—
465	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
466	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
467	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
468	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
469	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
470	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
471	C₂³	C₂×#41×C₁₉	1	2	yes	—
472	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
473	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
474	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
475	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
476	Q₈	—	4	16	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
538	C₂×C₄	C₄×Q₈×C₁₉	1	4	yes	—
539	C₂×C₄	C₄×Q₈×C₁₉	1	8	yes	—
540	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
541	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
542	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
543	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
544	C₂²	C₂×C₄×Q₈×C₁₉	1	2	yes	—
545	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
546	C₂²	C₁₉×#518	1	2	yes	—
547	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
548	C₂²	C₁₉×#525	1	1	yes	characteristic
549	C₂²	C₁₉×#529	1	1	yes	characteristic
550	C₂²	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
551	C₂²	C₁₉×#532	1	1	yes	characteristic
552	C₂²	C₁₉×#533	1	1	yes	characteristic
553	C₂²	C₁₉×#533	1	2	yes	—
554	C₂²	C₁₉×#534	1	1	yes	characteristic
555	C₂²	C₁₉×#535	1	1	yes	characteristic
556	C₂²	C₁₉×#538	1	2	yes	—
557	C₂²	C₁₉×#551	1	2	yes	—
558	C₂²	C₁₉×#551	1	2	yes	—
559	C₂²	C₁₉×#554	1	2	yes	—
560	C₂²	C₁₉×#554	1	2	yes	—
561	C₂²	C₁₉×#554	1	2	yes	—
562	C₂²	C₁₉×#554	1	2	yes	—
563	C₂²	C₁₉×#555	1	2	yes	—
564	C₂²	Q₈²×C₁₉	1	2	yes	—
565	C₄	—	2	4	no	—
566	C₄	—	2	4	no	—
567	C₄	—	2	4	no	—
568	C₄	—	2	4	no	—
569	C₄	—	2	8	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	4	no	—
572	C₄	—	4	4	no	—
573	C₄	—	4	2	no	—
574	C₄	—	4	2	no	—
575	C₄	—	8	2	no	—
576	C₂	C₄×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
577	C₂	C₄×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
578	C₂	C₁₉×#2321	1	1	yes	characteristic
579	C₂	C₁₉×#2368	1	2	yes	—
580	C₂	C₁₉×#2369	1	2	yes	—
581	C₂	C₁₉×#2564	1	1	yes	characteristic
582	C₂	C₁₉×#2567	1	1	yes	characteristic
583	C₂	C₁₉×#2574	1	2	yes	—
584	C₂	C₁₉×#2583	1	1	yes	characteristic
585	C₂	C₁₉×#2586	1	2	yes	—
586	C₂	C₁₉×#2610	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
22. C₁₉×#395	C₄	semidirect
67. C₂×C₄⋊C₄×C₁₉	Q₈	semidirect
90. C₁₉×#95	Q₈	semidirect
171. #14241	C₁₉	direct (N × H)
304. #395	C₄×C₁₉	semidirect
360. C₂×C₄⋊C₄	Q₈×C₁₉	semidirect
383. #95	Q₈×C₁₉	semidirect
384. C₁₉	#14241	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×#395	2
C₂×C₁₉×#391	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₁₉×#1446	2
C₁₉×#1444	2
C₁₉×#1441	2
C₁₉×#1436	2
C₁₉×C₄⋊#95	2
C₄×C₁₉×#95	2
#14241	19

Subgroups — C19×#14241 #18020200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14241 #18020200