Subgroups — C₁₉×#14138 #18020097

Order 4864.

2222 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#391	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1440	C₂	1	4	yes	maximal
6	C₁₉×#1436	C₂	1	4	yes	maximal, complemented
7	C₁₉×C₄⋊#95	C₂	1	2	yes	maximal, complemented
8	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₂²⋊Q₈	—	2	4	no	—
11	C₂×C₁₉×C₂²⋊Q₈	—	2	4	no	—
12	C₂×C₁₉×C₂²⋊Q₈	C₄	1	8	yes	complemented
13	C₂×C₁₉×#117	—	2	4	no	—
14	C₂×C₁₉×#117	—	2	8	no	—
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
22	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
23	C₁₉×#391	—	2	8	no	—
24	C₄×C₂²⋊C₄×C₁₉	—	2	4	no	—
25	C₂×C₁₉×#95	C₂²	1	8	yes	—
26	C₂×C₁₉×#95	C₂²	1	2	yes	—
27	C₂×C₁₉×#95	C₂²	1	8	yes	—
28	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×Q₈×C₁₉	—	2	4	no	—
30	C₂²×Q₈×C₁₉	—	2	2	no	—
31	C₂²×Q₈×C₁₉	—	2	2	no	—
32	C₂²×Q₈×C₁₉	—	2	4	no	—
33	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
34	C₂³×C₄×C₁₉	—	2	4	no	—
35	C₂³×C₄×C₁₉	—	2	4	no	—
36	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₁₉	D₄	1	4	yes	—
38	C₂³×C₄×C₁₉	D₄	1	4	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₁₉×C₂²⋊Q₈	—	2	32	no	—
46	C₁₉×#117	—	2	32	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
55	C₂×C₄⋊C₄×C₁₉	D₄	1	8	yes	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
62	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
63	C₂×C₄²×C₁₉	—	2	8	no	—
64	C₂×C₄²×C₁₉	—	2	4	no	—
65	C₂×C₄²×C₁₉	—	2	4	no	—
66	C₂×C₄²×C₁₉	—	2	4	no	—
67	C₂×C₄²×C₁₉	—	2	4	no	—
68	C₁₉×#95	—	2	4	no	—
69	C₁₉×#95	—	2	16	no	—
70	C₁₉×#95	—	2	16	no	—
71	C₂⁴×C₁₉	—	2	2	no	—
72	C₂⁴×C₁₉	—	2	4	no	—
73	C₂⁴×C₁₉	—	2	2	no	—
74	C₂⁴×C₁₉	—	2	4	no	—
75	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
76	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
77	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
78	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
79	C₂×Q₈×C₁₉	—	2	8	no	—
80	C₂×Q₈×C₁₉	—	2	16	no	—
81	C₂×Q₈×C₁₉	—	4	4	no	—
82	C₂×Q₈×C₁₉	—	4	8	no	—
83	C₂×Q₈×C₁₉	—	4	4	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	16	no	—
87	C₂²×C₄×C₁₉	—	2	8	no	—
88	C₂²×C₄×C₁₉	—	2	16	no	—
89	C₂²×C₄×C₁₉	—	2	8	no	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	4	no	—
99	C₂²×C₄×C₁₉	—	2	4	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	2	4	no	—
102	C₂²×C₄×C₁₉	—	2	8	no	—
103	C₂²×C₄×C₁₉	—	2	8	no	—
104	C₂²×C₄×C₁₉	—	2	8	no	—
105	C₂²×C₄×C₁₉	—	2	4	no	—
106	C₂²×C₄×C₁₉	—	2	4	no	—
107	C₂²×C₄×C₁₉	C₂²⋊C₄	1	16	yes	—
108	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
110	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₁₉	#41	1	8	yes	—
119	C₂²×C₄×C₁₉	#41	1	4	yes	—
120	C₄⋊C₄×C₁₉	—	2	8	no	—
121	C₄⋊C₄×C₁₉	—	2	16	no	—
122	C₄⋊C₄×C₁₉	—	2	16	no	—
123	C₂²⋊C₄×C₁₉	—	2	16	no	—
124	C₂²⋊C₄×C₁₉	—	2	16	no	—
125	C₂²⋊C₄×C₁₉	—	2	16	no	—
126	C₄²×C₁₉	—	2	16	no	—
127	C₄²×C₁₉	—	4	8	no	—
128	#14138	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₁₉	—	2	4	no	—
130	C₂³×C₁₉	—	2	4	no	—
131	C₂³×C₁₉	—	2	4	no	—
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	2	4	no	—
134	C₂³×C₁₉	—	2	2	no	—
135	C₂³×C₁₉	—	2	4	no	—
136	C₂³×C₁₉	—	2	4	no	—
137	C₂³×C₁₉	—	2	4	no	—
138	C₂³×C₁₉	—	2	4	no	—
139	C₂³×C₁₉	—	4	4	no	—
140	C₂³×C₁₉	—	4	4	no	—
141	C₂³×C₁₉	—	4	4	no	—
142	C₂³×C₁₉	—	4	4	no	—
143	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
144	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
145	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
146	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
147	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
148	C₂³×C₁₉	C₂×#41	1	2	yes	—
149	C₂³×C₁₉	C₂×#41	1	4	yes	—
150	C₂³×C₁₉	2₋¹⁺⁴	1	4	yes	—
151	Q₈×C₁₉	—	4	16	no	—
152	C₂×C₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	32	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	8	no	—
160	C₂×C₄×C₁₉	—	2	8	no	—
161	C₂×C₄×C₁₉	—	2	8	no	—
162	C₂×C₄×C₁₉	—	2	8	no	—
163	C₂×C₄×C₁₉	—	2	16	no	—
164	C₂×C₄×C₁₉	—	2	8	no	—
165	C₂×C₄×C₁₉	—	2	8	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	4	no	—
171	C₂×C₄×C₁₉	—	4	4	no	—
172	C₂×C₄×C₁₉	—	4	4	no	—
173	C₂×C₄×C₁₉	—	4	4	no	—
174	C₂×C₄×C₁₉	—	4	4	no	—
175	C₂×C₄×C₁₉	—	4	4	no	—
176	C₂×C₄×C₁₉	—	4	8	no	—
177	C₂×C₄×C₁₉	—	4	4	no	—
178	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
179	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
180	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
181	C₂×C₄×C₁₉	#120	1	4	yes	—
182	C₂×C₄×C₁₉	#121	1	8	yes	—
183	C₂×C₄×C₁₉	#123	1	4	yes	—
184	C₂²×C₂²⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
185	C₂²×#117	C₂×C₁₉	1	1	yes	characteristic
186	C₂×#391	C₂×C₁₉	1	2	yes	complemented
187	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
188	#1440	C₂×C₁₉	1	4	yes	—
189	#1436	C₂×C₁₉	1	4	yes	complemented
190	C₄⋊#95	C₂×C₁₉	1	2	yes	complemented
191	C₂²×C₁₉	—	2	4	no	—
192	C₂²×C₁₉	—	2	4	no	—
193	C₂²×C₁₉	—	2	4	no	—
194	C₂²×C₁₉	—	4	8	no	—
195	C₂²×C₁₉	—	4	8	no	—
196	C₂²×C₁₉	—	4	4	no	—
197	C₂²×C₁₉	—	4	4	no	—
198	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
200	C₂²×C₁₉	C₄×#41	1	2	yes	—
201	C₂²×C₁₉	#519	1	2	yes	—
202	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
203	C₂²×C₁₉	C₂×#121	1	2	yes	—
204	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
205	C₂²×C₁₉	#525	1	2	yes	—
206	C₂²×C₁₉	#532	1	2	yes	—
207	C₂²×C₁₉	#536	1	2	yes	—
208	C₂²×C₁₉	#536	1	2	yes	—
209	C₂²×C₁₉	#547	1	4	yes	—
210	C₂²×C₁₉	#548	1	4	yes	—
211	C₂²×C₁₉	#552	1	4	yes	—
212	C₂²×C₁₉	#556	1	4	yes	—
213	C₄×C₁₉	—	2	4	no	—
214	C₄×C₁₉	—	4	8	no	—
215	C₄×C₁₉	—	4	8	no	—
216	C₄×C₁₉	—	4	4	no	—
217	C₄×C₁₉	—	4	4	no	—
218	C₄×C₁₉	#386	1	8	yes	—
219	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
220	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×C₂²⋊Q₈	—	2	4	no	—
222	C₂×C₂²⋊Q₈	—	2	4	no	—
223	C₂×C₂²⋊Q₈	C₄×C₁₉	1	8	yes	complemented
224	C₂×#117	—	2	4	no	—
225	C₂×#117	—	2	8	no	—
226	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
227	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
228	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
229	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
230	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
231	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
232	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
233	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
234	#391	—	2	8	no	—
235	C₄×C₂²⋊C₄	—	2	4	no	—
236	C₂×#95	C₂²×C₁₉	1	8	yes	—
237	C₂×#95	C₂²×C₁₉	1	2	yes	—
238	C₂×#95	C₂²×C₁₉	1	8	yes	—
239	C₂×C₁₉	—	4	4	no	—
240	C₂×C₁₉	C₂×#386	1	1	yes	characteristic
241	C₂×C₁₉	#2297	1	1	yes	characteristic
242	C₂×C₁₉	#2310	1	1	yes	characteristic
243	C₂×C₁₉	#2362	1	4	yes	—
244	C₂×C₁₉	#2415	1	4	yes	—
245	C₂×C₁₉	#2432	1	2	yes	—
246	C₂×C₁₉	#2499	1	2	yes	—
247	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
248	C₂²×Q₈	—	2	2	no	—
249	C₂²×Q₈	—	2	2	no	—
250	C₂²×Q₈	—	2	4	no	—
251	C₂²×Q₈	—	2	4	no	—
252	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
253	C₂³×C₄	—	2	4	no	—
254	C₂³×C₄	—	2	4	no	—
255	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
256	C₂³×C₄	D₄×C₁₉	1	4	yes	—
257	C₂³×C₄	D₄×C₁₉	1	4	yes	—
258	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
259	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
260	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
261	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
262	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
263	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
264	C₂²⋊Q₈	—	2	32	no	—
265	#117	—	2	32	no	—
266	C₂×C₄⋊C₄	—	2	4	no	—
267	C₂×C₄⋊C₄	—	2	4	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	—	2	4	no	—
272	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
273	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
274	C₂×C₄⋊C₄	D₄×C₁₉	1	8	yes	—
275	C₂×C₂²⋊C₄	—	2	4	no	—
276	C₂×C₂²⋊C₄	—	2	4	no	—
277	C₂×C₂²⋊C₄	—	2	4	no	—
278	C₂×C₂²⋊C₄	—	2	4	no	—
279	C₂×C₂²⋊C₄	—	2	8	no	—
280	C₂×C₂²⋊C₄	—	2	8	no	—
281	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
282	C₂×C₄²	—	2	8	no	—
283	C₂×C₄²	—	2	4	no	—
284	C₂×C₄²	—	2	4	no	—
285	C₂×C₄²	—	2	4	no	—
286	C₂×C₄²	—	2	4	no	—
287	#95	—	2	4	no	—
288	#95	—	2	16	no	—
289	#95	—	2	16	no	—
290	C₁₉	#14138	1	1	yes	characteristic, direct product factor, Sylow
291	C₂⁴	—	2	2	no	—
292	C₂⁴	—	2	4	no	—
293	C₂⁴	—	2	2	no	—
294	C₂⁴	—	2	4	no	—
295	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
296	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
297	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
298	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
299	C₂×Q₈	—	2	8	no	—
300	C₂×Q₈	—	2	16	no	—
301	C₂×Q₈	—	4	4	no	—
302	C₂×Q₈	—	4	8	no	—
303	C₂×Q₈	—	4	4	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	16	no	—
307	C₂²×C₄	—	2	8	no	—
308	C₂²×C₄	—	2	16	no	—
309	C₂²×C₄	—	2	8	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	8	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	C₂²⋊C₄×C₁₉	1	16	yes	—
328	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
329	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
330	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
331	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
333	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
338	C₂²×C₄	#41×C₁₉	1	8	yes	—
339	C₂²×C₄	#41×C₁₉	1	4	yes	—
340	C₄⋊C₄	—	2	8	no	—
341	C₄⋊C₄	—	2	16	no	—
342	C₄⋊C₄	—	2	16	no	—
343	C₂²⋊C₄	—	2	16	no	—
344	C₂²⋊C₄	—	2	16	no	—
345	C₂²⋊C₄	—	2	16	no	—
346	C₄²	—	2	16	no	—
347	C₄²	—	4	8	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	4	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	4	no	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	4	4	no	—
359	C₂³	—	4	4	no	—
360	C₂³	—	4	4	no	—
361	C₂³	—	4	4	no	—
362	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
363	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
364	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
365	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
366	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
367	C₂³	C₂×#41×C₁₉	1	2	yes	—
368	C₂³	C₂×#41×C₁₉	1	4	yes	—
369	C₂³	C₁₉×2₋¹⁺⁴	1	4	yes	—
370	Q₈	—	4	16	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	32	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	8	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	8	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	16	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
398	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
399	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
400	C₂×C₄	C₁₉×#120	1	4	yes	—
401	C₂×C₄	C₁₉×#121	1	8	yes	—
402	C₂×C₄	C₁₉×#123	1	4	yes	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	4	8	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	8	no	—
410	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
411	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
412	C₂²	C₄×#41×C₁₉	1	2	yes	—
413	C₂²	C₁₉×#519	1	2	yes	—
414	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
415	C₂²	C₂×C₁₉×#121	1	2	yes	—
416	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
417	C₂²	C₁₉×#525	1	2	yes	—
418	C₂²	C₁₉×#532	1	2	yes	—
419	C₂²	C₁₉×#536	1	2	yes	—
420	C₂²	C₁₉×#536	1	2	yes	—
421	C₂²	C₁₉×#547	1	4	yes	—
422	C₂²	C₁₉×#548	1	4	yes	—
423	C₂²	C₁₉×#552	1	4	yes	—
424	C₂²	C₁₉×#556	1	4	yes	—
425	C₄	—	2	4	no	—
426	C₄	—	4	8	no	—
427	C₄	—	4	8	no	—
428	C₄	—	4	4	no	—
429	C₄	—	4	4	no	—
430	C₄	C₁₉×#386	1	8	yes	—
431	C₂	—	4	4	no	—
432	C₂	C₂×C₁₉×#386	1	1	yes	characteristic
433	C₂	C₁₉×#2297	1	1	yes	characteristic
434	C₂	C₁₉×#2310	1	1	yes	characteristic
435	C₂	C₁₉×#2362	1	4	yes	—
436	C₂	C₁₉×#2415	1	4	yes	—
437	C₂	C₁₉×#2432	1	2	yes	—
438	C₂	C₁₉×#2499	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
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
3. C₂×C₁₉×#391	C₂	semidirect
6. C₁₉×#1436	C₂	semidirect
7. C₁₉×C₄⋊#95	C₂	semidirect
12. C₂×C₁₉×C₂²⋊Q₈	C₄	semidirect
128. #14138	C₁₉	direct (N × H)
186. C₂×#391	C₂×C₁₉	semidirect
189. #1436	C₂×C₁₉	semidirect
190. C₄⋊#95	C₂×C₁₉	semidirect
223. C₂×C₂²⋊Q₈	C₄×C₁₉	semidirect
290. C₁₉	#14138	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×C₂²⋊Q₈	2
C₂²×C₁₉×#117	2
C₂×C₁₉×#391	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₁₉×#1440	2
C₁₉×#1436	2
C₁₉×C₄⋊#95	2
#14138	19

Subgroups — C19×#14138 #18020097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14138 #18020097