Subgroups — C₁₉×#23456 #18029415

Order 4864.

1362 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#418	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2309	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2025	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2023	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1735	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#544	—	2	4	no	—
14	C₁₉×#544	—	2	4	no	—
15	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
17	C₂×C₁₉×#125	—	2	1	no	—
18	C₂×C₁₉×#125	C₂²	1	2	yes	complemented
19	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#418	—	2	4	no	—
25	C₂×C₁₉×#102	—	2	4	no	—
26	C₂×C₁₉×#102	C₂²	1	2	yes	—
27	C₂×C₁₉×#102	C₂²	1	4	yes	—
28	C₂×C₁₉×#102	C₂²	1	2	yes	—
29	C₁₉×#390	—	2	1	no	—
30	C₁₉×#390	—	2	1	no	—
31	C₁₉×#390	C₂²	1	4	yes	—
32	C₁₉×#379	—	2	2	no	—
33	C₁₉×#340	C₂²	1	2	yes	complemented
34	C₁₉×#340	C₂²	1	2	yes	complemented
35	C₁₉×#340	C₂²	1	4	yes	complemented
36	C₁₉×#336	C₂²	1	4	yes	complemented
37	C₂⁵×C₁₉	—	2	1	no	—
38	C₂²×Q₈×C₁₉	—	2	2	no	—
39	C₂²×D₄×C₁₉	—	2	2	no	—
40	C₂²×D₄×C₁₉	—	2	2	no	—
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	—	2	2	no	—
43	C₂²×D₄×C₁₉	—	2	2	no	—
44	C₂²×D₄×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	Q₈	1	4	yes	complemented
46	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₉	—	2	1	no	—
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₁₉	—	2	2	no	—
50	C₂×M₁₆×C₁₉	—	2	2	no	—
51	C₂×M₁₆×C₁₉	—	2	2	no	—
52	C₂²×C₈×C₁₉	—	2	2	no	—
53	C₂²×C₈×C₁₉	—	2	2	no	—
54	C₂²×C₈×C₁₉	—	2	2	no	—
55	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
57	C₁₉×C₄⋊Q₈	—	2	8	no	—
58	C₁₉×C₄⋊Q₈	—	2	4	no	—
59	C₁₉×C₄⋊Q₈	—	2	4	no	—
60	C₁₉×#125	—	2	8	no	—
61	C₁₉×#125	—	2	4	no	—
62	C₁₉×#125	—	2	4	no	—
63	C₁₉×C₂²⋊Q₈	—	2	16	no	—
64	C₁₉×#117	—	2	2	no	—
65	C₁₉×#117	—	2	2	no	—
66	C₁₉×#117	—	2	2	no	—
67	C₁₉×#117	—	2	2	no	—
68	C₁₉×#117	—	2	2	no	—
69	C₁₉×#117	D₄	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
86	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
87	C₂×C₄²×C₁₉	—	2	1	no	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
90	C₁₉×#102	—	2	8	no	—
91	C₁₉×#102	—	2	4	no	—
92	C₁₉×#102	—	2	4	no	—
93	C₂⁴×C₁₉	—	2	2	no	—
94	C₂⁴×C₁₉	—	2	4	no	—
95	C₂⁴×C₁₉	—	4	2	no	—
96	C₂⁴×C₁₉	—	4	2	no	—
97	C₂⁴×C₁₉	—	8	2	no	—
98	C₂⁴×C₁₉	—	8	2	no	—
99	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₁₉	—	2	8	no	—
101	C₂×Q₈×C₁₉	—	8	4	no	—
102	C₂×D₄×C₁₉	—	2	8	no	—
103	C₂×D₄×C₁₉	—	2	8	no	—
104	C₂×D₄×C₁₉	—	2	4	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	2	no	—
110	C₂×D₄×C₁₉	—	4	2	no	—
111	C₂×D₄×C₁₉	—	4	4	no	—
112	C₂×D₄×C₁₉	—	4	4	no	—
113	C₂×D₄×C₁₉	—	4	2	no	—
114	C₂×D₄×C₁₉	C₂×Q₈	1	4	yes	—
115	C₂²×C₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	2	1	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	4	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	8	2	no	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
127	C₂²×C₄×C₁₉	#41	1	2	yes	—
128	C₂²×C₄×C₁₉	#41	1	2	yes	—
129	C₂²×C₄×C₁₉	#41	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
131	M₁₆×C₁₉	—	4	4	no	—
132	C₂×C₈×C₁₉	—	2	2	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₂×C₈×C₁₉	—	4	4	no	—
139	C₄⋊C₄×C₁₉	—	2	8	no	—
140	C₄⋊C₄×C₁₉	—	2	8	no	—
141	C₄⋊C₄×C₁₉	—	2	8	no	—
142	C₄⋊C₄×C₁₉	—	2	4	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
151	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
152	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
153	C₂²⋊C₄×C₁₉	—	2	4	no	—
154	C₂²⋊C₄×C₁₉	—	2	4	no	—
155	C₂²⋊C₄×C₁₉	—	4	2	no	—
156	C₂²⋊C₄×C₁₉	—	8	4	no	—
157	C₂²⋊C₄×C₁₉	—	8	4	no	—
158	C₄²×C₁₉	—	2	4	no	—
159	C₄²×C₁₉	—	2	2	no	—
160	C₄²×C₁₉	—	2	2	no	—
161	C₄²×C₁₉	—	4	2	no	—
162	#23456	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂³×C₁₉	—	2	2	no	—
164	C₂³×C₁₉	—	2	2	no	—
165	C₂³×C₁₉	—	2	4	no	—
166	C₂³×C₁₉	—	4	2	no	—
167	C₂³×C₁₉	—	4	2	no	—
168	C₂³×C₁₉	—	4	4	no	—
169	C₂³×C₁₉	—	4	4	no	—
170	C₂³×C₁₉	—	4	8	no	—
171	C₂³×C₁₉	—	8	8	no	—
172	C₂³×C₁₉	—	8	8	no	—
173	C₂³×C₁₉	—	8	4	no	—
174	C₂³×C₁₉	—	8	4	no	—
175	C₂³×C₁₉	#120	1	2	yes	—
176	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
177	C₂³×C₁₉	#124	1	2	yes	—
178	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₁₉	—	8	8	no	—
180	D₄×C₁₉	—	2	4	no	—
181	D₄×C₁₉	—	2	4	no	—
182	D₄×C₁₉	—	4	2	no	—
183	D₄×C₁₉	—	4	2	no	—
184	D₄×C₁₉	—	4	8	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	4	4	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	8	4	no	—
199	C₂×C₄×C₁₉	#120	1	2	yes	—
200	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
201	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
202	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
203	C₂×C₄×C₁₉	#124	1	4	yes	—
204	C₂×C₄×C₁₉	#124	1	4	yes	—
205	C₂×C₄×C₁₉	#124	1	2	yes	—
206	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
212	C₈×C₁₉	—	4	2	no	—
213	C₈×C₁₉	—	4	2	no	—
214	C₂×#544	C₂×C₁₉	1	1	yes	characteristic, complemented
215	C₂×#418	C₂×C₁₉	1	1	yes	characteristic
216	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic
217	#2309	C₂×C₁₉	1	1	yes	characteristic
218	#2025	C₂×C₁₉	1	4	yes	complemented
219	#2023	C₂×C₁₉	1	4	yes	complemented
220	#1736	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#1735	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#1729	C₂×C₁₉	1	1	yes	characteristic, complemented
223	C₂²×C₁₉	—	2	4	no	—
224	C₂²×C₁₉	—	2	4	no	—
225	C₂²×C₁₉	—	2	2	no	—
226	C₂²×C₁₉	—	2	2	no	—
227	C₂²×C₁₉	—	4	8	no	—
228	C₂²×C₁₉	—	4	4	no	—
229	C₂²×C₁₉	—	8	16	no	—
230	C₂²×C₁₉	—	8	4	no	—
231	C₂²×C₁₉	—	8	2	no	—
232	C₂²×C₁₉	—	8	2	no	—
233	C₂²×C₁₉	#393	1	4	yes	—
234	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
235	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
236	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
237	C₂²×C₁₉	#576	1	2	yes	—
238	C₂²×C₁₉	#577	1	2	yes	—
239	C₄×C₁₉	—	4	2	no	—
240	C₄×C₁₉	—	4	4	no	—
241	C₄×C₁₉	—	4	2	no	—
242	C₄×C₁₉	—	4	2	no	—
243	C₄×C₁₉	—	4	2	no	—
244	C₄×C₁₉	—	8	2	no	—
245	C₄×C₁₉	#393	1	4	yes	—
246	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
247	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
248	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
249	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
250	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
251	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
252	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
253	#544	—	2	4	no	—
254	#544	—	2	4	no	—
255	C₂×C₄⋊Q₈	—	2	1	no	—
256	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	complemented
257	C₂×#125	—	2	1	no	—
258	C₂×#125	C₂²×C₁₉	1	2	yes	complemented
259	C₂×C₂²⋊Q₈	—	2	2	no	—
260	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
261	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
262	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
263	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
264	#418	—	2	4	no	—
265	C₂×#102	—	2	4	no	—
266	C₂×#102	C₂²×C₁₉	1	4	yes	—
267	C₂×#102	C₂²×C₁₉	1	2	yes	—
268	C₂×#102	C₂²×C₁₉	1	2	yes	—
269	#390	—	2	1	no	—
270	#390	—	2	1	no	—
271	#390	C₂²×C₁₉	1	4	yes	—
272	#379	—	2	2	no	—
273	#340	C₂²×C₁₉	1	2	yes	complemented
274	#340	C₂²×C₁₉	1	2	yes	complemented
275	#340	C₂²×C₁₉	1	4	yes	complemented
276	#336	C₂²×C₁₉	1	4	yes	complemented
277	C₂×C₁₉	—	2	4	no	—
278	C₂×C₁₉	—	8	4	no	—
279	C₂×C₁₉	C₂×#393	1	1	yes	characteristic
280	C₂×C₁₉	#3008	1	1	yes	characteristic
281	C₂×C₁₉	#3010	1	1	yes	characteristic
282	C₂×C₁₉	#3081	1	2	yes	—
283	C₂×C₁₉	#3136	1	2	yes	—
284	C₂⁵	—	2	1	no	—
285	C₂²×Q₈	—	2	2	no	—
286	C₂²×D₄	—	2	2	no	—
287	C₂²×D₄	—	2	2	no	—
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	—	2	2	no	—
290	C₂²×D₄	—	2	2	no	—
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	Q₈×C₁₉	1	4	yes	complemented
293	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
294	C₂³×C₄	—	2	1	no	—
295	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂²×C₈	—	2	2	no	—
300	C₂²×C₈	—	2	2	no	—
301	C₂²×C₈	—	2	2	no	—
302	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
303	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
304	C₄⋊Q₈	—	2	8	no	—
305	C₄⋊Q₈	—	2	4	no	—
306	C₄⋊Q₈	—	2	4	no	—
307	#125	—	2	8	no	—
308	#125	—	2	4	no	—
309	#125	—	2	4	no	—
310	C₂²⋊Q₈	—	2	16	no	—
311	#117	—	2	2	no	—
312	#117	—	2	2	no	—
313	#117	—	2	2	no	—
314	#117	—	2	2	no	—
315	#117	—	2	2	no	—
316	#117	D₄×C₁₉	1	4	yes	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
323	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
324	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	4	no	—
332	C₂×C₂²⋊C₄	—	2	4	no	—
333	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
337	#102	—	2	8	no	—
338	#102	—	2	4	no	—
339	#102	—	2	4	no	—
340	C₁₉	#23456	1	1	yes	characteristic, direct product factor, Sylow
341	C₂⁴	—	2	2	no	—
342	C₂⁴	—	2	4	no	—
343	C₂⁴	—	4	2	no	—
344	C₂⁴	—	4	2	no	—
345	C₂⁴	—	8	2	no	—
346	C₂⁴	—	8	2	no	—
347	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
348	C₂×Q₈	—	2	8	no	—
349	C₂×Q₈	—	8	4	no	—
350	C₂×D₄	—	2	8	no	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	4	no	—
361	C₂×D₄	—	4	4	no	—
362	C₂×D₄	C₂×Q₈×C₁₉	1	4	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	8	2	no	—
369	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
374	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
375	C₂²×C₄	#41×C₁₉	1	2	yes	—
376	C₂²×C₄	#41×C₁₉	1	2	yes	—
377	C₂²×C₄	#41×C₁₉	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
379	M₁₆	—	4	4	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	4	4	no	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	2	8	no	—
389	C₄⋊C₄	—	2	8	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
399	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
400	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	4	2	no	—
404	C₂²⋊C₄	—	8	4	no	—
405	C₂²⋊C₄	—	8	4	no	—
406	C₄²	—	2	4	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	4	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	4	8	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	4	no	—
417	C₂³	—	4	4	no	—
418	C₂³	—	8	8	no	—
419	C₂³	—	8	4	no	—
420	C₂³	—	8	4	no	—
421	C₂³	—	8	8	no	—
422	C₂³	C₁₉×#120	1	2	yes	—
423	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
424	C₂³	C₁₉×#124	1	2	yes	—
425	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
426	Q₈	—	8	8	no	—
427	D₄	—	2	4	no	—
428	D₄	—	2	4	no	—
429	D₄	—	4	8	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	8	4	no	—
446	C₂×C₄	C₁₉×#120	1	2	yes	—
447	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
448	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
449	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
450	C₂×C₄	C₁₉×#124	1	2	yes	—
451	C₂×C₄	C₁₉×#124	1	4	yes	—
452	C₂×C₄	C₁₉×#124	1	4	yes	—
453	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
454	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
455	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
456	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
457	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
458	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
459	C₈	—	4	2	no	—
460	C₈	—	4	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	4	8	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	8	16	no	—
468	C₂²	—	8	2	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	8	4	no	—
471	C₂²	C₁₉×#393	1	4	yes	—
472	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
473	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
474	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
475	C₂²	C₁₉×#576	1	2	yes	—
476	C₂²	C₁₉×#577	1	2	yes	—
477	C₄	—	4	2	no	—
478	C₄	—	4	4	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	8	2	no	—
483	C₄	C₁₉×#393	1	4	yes	—
484	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
485	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
486	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
487	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
488	C₂	—	2	4	no	—
489	C₂	—	8	4	no	—
490	C₂	C₂×C₁₉×#393	1	1	yes	characteristic
491	C₂	C₁₉×#3008	1	1	yes	characteristic
492	C₂	C₁₉×#3010	1	1	yes	characteristic
493	C₂	C₁₉×#3081	1	2	yes	—
494	C₂	C₁₉×#3136	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#544	C₂	semidirect
5. C₁₉×#2025	C₂	semidirect
6. C₁₉×#2023	C₂	semidirect
7. C₁₉×#1736	C₂	semidirect
8. C₁₉×#1735	C₂	semidirect
9. C₁₉×#1729	C₂	semidirect
16. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
18. C₂×C₁₉×#125	C₂²	semidirect
33. C₁₉×#340	C₂²	semidirect
34. C₁₉×#340	C₂²	semidirect
35. C₁₉×#340	C₂²	semidirect
36. C₁₉×#336	C₂²	semidirect
45. C₂²×D₄×C₁₉	Q₈	semidirect
162. #23456	C₁₉	direct (N × H)
214. C₂×#544	C₂×C₁₉	semidirect
218. #2025	C₂×C₁₉	semidirect
219. #2023	C₂×C₁₉	semidirect
220. #1736	C₂×C₁₉	semidirect
221. #1735	C₂×C₁₉	semidirect
222. #1729	C₂×C₁₉	semidirect
256. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
258. C₂×#125	C₂²×C₁₉	semidirect
273. #340	C₂²×C₁₉	semidirect
274. #340	C₂²×C₁₉	semidirect
275. #340	C₂²×C₁₉	semidirect
276. #336	C₂²×C₁₉	semidirect
292. C₂²×D₄	Q₈×C₁₉	semidirect
340. C₁₉	#23456	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×#544	2
C₂×C₁₉×#418	2
C₂²×C₁₉×#102	2
C₁₉×#2309	2
C₁₉×#2025	2
C₁₉×#2023	2
C₁₉×#1736	2
C₁₉×#1735	2
C₁₉×#1729	2
#23456	19

Subgroups — C19×#23456 #18029415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23456 #18029415