Subgroups — C₁₉×#23486 #18029445

Order 4864.

1610 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#535	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#427	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#418	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#408	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2034	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2033	C₂	1	4	yes	maximal, complemented
9	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#535	—	2	4	no	—
15	C₁₉×#535	—	2	4	no	—
16	C₂×C₁₉×#127	—	2	1	no	—
17	C₂×C₁₉×#124	—	2	1	no	—
18	C₂×C₁₉×#121	C₂²	1	4	yes	—
19	C₂×C₁₉×#120	—	2	2	no	—
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#427	—	2	4	no	—
24	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
25	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
26	C₁₉×#418	—	2	4	no	—
27	C₂×C₁₉×#102	—	2	4	no	—
28	C₂×C₁₉×#102	C₂²	1	2	yes	—
29	C₂×C₁₉×#102	C₂²	1	4	yes	—
30	C₂×C₁₉×#102	C₂²	1	2	yes	—
31	C₁₉×#408	—	2	4	no	—
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
34	C₁₉×#391	—	2	1	no	—
35	C₁₉×#390	—	2	1	no	—
36	C₁₉×#386	—	2	2	no	—
37	C₁₉×#380	C₂²	1	4	yes	complemented
38	C₁₉×#340	C₂²	1	4	yes	complemented
39	C₂⁵×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	—	2	2	no	—
41	C₂×#41×C₁₉	—	2	2	no	—
42	C₂×#41×C₁₉	—	2	2	no	—
43	C₂×#41×C₁₉	—	2	2	no	—
44	C₂×#41×C₁₉	—	2	2	no	—
45	C₂×#41×C₁₉	—	2	2	no	—
46	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₉	—	2	4	no	—
48	C₂²×D₄×C₁₉	—	2	2	no	—
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	—	2	2	no	—
51	C₂²×D₄×C₁₉	—	2	2	no	—
52	C₂²×D₄×C₁₉	—	2	2	no	—
53	C₂²×D₄×C₁₉	—	2	2	no	—
54	C₂²×D₄×C₁₉	D₄	1	2	yes	—
55	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
56	C₂²×D₄×C₁₉	D₄	1	4	yes	—
57	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₉	—	2	1	no	—
59	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×M₁₆×C₁₉	—	2	2	no	—
62	C₂×M₁₆×C₁₉	—	2	2	no	—
63	C₂×M₁₆×C₁₉	—	2	2	no	—
64	C₂²×C₈×C₁₉	—	2	2	no	—
65	C₂²×C₈×C₁₉	—	2	2	no	—
66	C₂²×C₈×C₁₉	D₄	1	4	yes	complemented
67	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×#127	—	2	8	no	—
71	C₁₉×#124	—	2	8	no	—
72	C₁₉×#121	—	2	8	no	—
73	C₁₉×#121	—	2	8	no	—
74	C₁₉×#120	—	2	16	no	—
75	C₁₉×#117	—	2	2	no	—
76	C₁₉×#117	—	2	2	no	—
77	C₁₉×#117	—	2	2	no	—
78	C₁₉×#117	D₄	1	4	yes	—
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
89	C₂×C₄²×C₁₉	—	2	1	no	—
90	C₂×C₄²×C₁₉	—	2	1	no	—
91	C₁₉×#107	—	2	4	no	—
92	C₁₉×#106	—	2	4	no	—
93	C₁₉×#102	—	2	8	no	—
94	C₁₉×#102	—	2	4	no	—
95	C₁₉×#102	—	2	4	no	—
96	C₁₉×C₂²⋊C₈	—	2	4	no	—
97	C₁₉×C₂²⋊C₈	—	2	4	no	—
98	C₁₉×#95	—	2	4	no	—
99	C₂⁴×C₁₉	—	2	2	no	—
100	C₂⁴×C₁₉	—	2	4	no	—
101	C₂⁴×C₁₉	—	4	2	no	—
102	C₂⁴×C₁₉	—	4	2	no	—
103	C₂⁴×C₁₉	—	8	2	no	—
104	C₂⁴×C₁₉	—	8	2	no	—
105	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
106	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
107	#41×C₁₉	—	4	4	no	—
108	#41×C₁₉	—	4	4	no	—
109	#41×C₁₉	—	4	4	no	—
110	#41×C₁₉	—	4	4	no	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	2	4	no	—
115	C₂×D₄×C₁₉	—	2	4	no	—
116	C₂×D₄×C₁₉	—	2	4	no	—
117	C₂×D₄×C₁₉	—	2	16	no	—
118	C₂×D₄×C₁₉	—	2	4	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	8	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	8	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	4	4	no	—
130	C₂×D₄×C₁₉	—	4	2	no	—
131	C₂×D₄×C₁₉	—	4	2	no	—
132	C₂×D₄×C₁₉	—	4	4	no	—
133	C₂×D₄×C₁₉	—	8	4	no	—
134	C₂×D₄×C₁₉	—	8	4	no	—
135	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
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	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	4	2	no	—
146	C₂²×C₄×C₁₉	—	8	2	no	—
147	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₉	#41	1	2	yes	—
153	C₂²×C₄×C₁₉	#41	1	2	yes	—
154	C₂²×C₄×C₁₉	#41	1	2	yes	—
155	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
156	M₁₆×C₁₉	—	4	4	no	—
157	C₂×C₈×C₁₉	—	2	8	no	—
158	C₂×C₈×C₁₉	—	2	1	no	—
159	C₂×C₈×C₁₉	—	2	1	no	—
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₂×C₈×C₁₉	—	2	1	no	—
162	C₂×C₈×C₁₉	—	2	2	no	—
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
166	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	4	2	no	—
173	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
174	C₂²⋊C₄×C₁₉	—	2	16	no	—
175	C₂²⋊C₄×C₁₉	—	2	4	no	—
176	C₂²⋊C₄×C₁₉	—	4	2	no	—
177	C₂²⋊C₄×C₁₉	—	8	4	no	—
178	C₄²×C₁₉	—	2	4	no	—
179	C₄²×C₁₉	—	4	2	no	—
180	#23486	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂³×C₁₉	—	2	2	no	—
182	C₂³×C₁₉	—	2	2	no	—
183	C₂³×C₁₉	—	2	4	no	—
184	C₂³×C₁₉	—	2	2	no	—
185	C₂³×C₁₉	—	2	2	no	—
186	C₂³×C₁₉	—	2	2	no	—
187	C₂³×C₁₉	—	2	4	no	—
188	C₂³×C₁₉	—	2	4	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	—	4	2	no	—
191	C₂³×C₁₉	—	4	4	no	—
192	C₂³×C₁₉	—	4	4	no	—
193	C₂³×C₁₉	—	4	8	no	—
194	C₂³×C₁₉	—	8	8	no	—
195	C₂³×C₁₉	—	8	8	no	—
196	C₂³×C₁₉	—	8	4	no	—
197	C₂³×C₁₉	—	8	4	no	—
198	C₂³×C₁₉	#120	1	2	yes	—
199	C₂³×C₁₉	#121	1	2	yes	—
200	C₂³×C₁₉	#123	1	2	yes	—
201	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
202	Q₈×C₁₉	—	4	4	no	—
203	D₄×C₁₉	—	2	4	no	—
204	D₄×C₁₉	—	2	4	no	—
205	D₄×C₁₉	—	4	8	no	—
206	D₄×C₁₉	—	4	2	no	—
207	D₄×C₁₉	—	4	2	no	—
208	D₄×C₁₉	—	4	8	no	—
209	D₄×C₁₉	—	4	4	no	—
210	D₄×C₁₉	—	8	16	no	—
211	C₂×C₄×C₁₉	—	2	4	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	4	2	no	—
224	C₂×C₄×C₁₉	—	4	4	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	8	4	no	—
227	C₂×C₄×C₁₉	#120	1	2	yes	—
228	C₂×C₄×C₁₉	#121	1	4	yes	—
229	C₂×C₄×C₁₉	#121	1	4	yes	—
230	C₂×C₄×C₁₉	#121	1	2	yes	—
231	C₂×C₄×C₁₉	#123	1	4	yes	—
232	C₂×C₄×C₁₉	#123	1	2	yes	—
233	C₂×C₄×C₁₉	#124	1	4	yes	—
234	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
240	C₈×C₁₉	—	2	2	no	—
241	C₈×C₁₉	—	2	2	no	—
242	C₈×C₁₉	—	4	2	no	—
243	C₂×#535	C₂×C₁₉	1	1	yes	characteristic
244	C₂×#427	C₂×C₁₉	1	1	yes	characteristic, complemented
245	C₂×#418	C₂×C₁₉	1	1	yes	characteristic, complemented
246	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
247	C₂×#408	C₂×C₁₉	1	1	yes	characteristic, complemented
248	#2311	C₂×C₁₉	1	1	yes	characteristic, complemented
249	#2034	C₂×C₁₉	1	4	yes	complemented
250	#2033	C₂×C₁₉	1	4	yes	complemented
251	#1736	C₂×C₁₉	1	1	yes	characteristic, complemented
252	C₂²×C₁₉	—	2	4	no	—
253	C₂²×C₁₉	—	2	4	no	—
254	C₂²×C₁₉	—	2	2	no	—
255	C₂²×C₁₉	—	2	2	no	—
256	C₂²×C₁₉	—	4	4	no	—
257	C₂²×C₁₉	—	4	2	no	—
258	C₂²×C₁₉	—	4	4	no	—
259	C₂²×C₁₉	—	4	4	no	—
260	C₂²×C₁₉	—	4	8	no	—
261	C₂²×C₁₉	—	4	2	no	—
262	C₂²×C₁₉	—	4	2	no	—
263	C₂²×C₁₉	—	8	16	no	—
264	C₂²×C₁₉	—	8	4	no	—
265	C₂²×C₁₉	—	8	2	no	—
266	C₂²×C₁₉	—	8	2	no	—
267	C₂²×C₁₉	#394	1	4	yes	—
268	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
269	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
270	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
271	C₂²×C₁₉	#576	1	2	yes	—
272	C₂²×C₁₉	#577	1	2	yes	—
273	C₄×C₁₉	—	4	2	no	—
274	C₄×C₁₉	—	4	4	no	—
275	C₄×C₁₉	—	8	2	no	—
276	C₄×C₁₉	—	8	2	no	—
277	C₄×C₁₉	#394	1	4	yes	—
278	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
279	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
280	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
281	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
282	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
283	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
284	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
285	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
286	#535	—	2	4	no	—
287	#535	—	2	4	no	—
288	C₂×#127	—	2	1	no	—
289	C₂×#124	—	2	1	no	—
290	C₂×#121	C₂²×C₁₉	1	4	yes	—
291	C₂×#120	—	2	2	no	—
292	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
294	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
295	#427	—	2	4	no	—
296	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
297	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
298	#418	—	2	4	no	—
299	C₂×#102	—	2	4	no	—
300	C₂×#102	C₂²×C₁₉	1	2	yes	—
301	C₂×#102	C₂²×C₁₉	1	2	yes	—
302	C₂×#102	C₂²×C₁₉	1	4	yes	—
303	#408	—	2	4	no	—
304	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	complemented
305	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	complemented
306	#391	—	2	1	no	—
307	#390	—	2	1	no	—
308	#386	—	2	2	no	—
309	#380	C₂²×C₁₉	1	4	yes	complemented
310	#340	C₂²×C₁₉	1	4	yes	complemented
311	C₂×C₁₉	—	2	4	no	—
312	C₂×C₁₉	—	8	2	no	—
313	C₂×C₁₉	—	8	4	no	—
314	C₂×C₁₉	C₂×#394	1	1	yes	characteristic
315	C₂×C₁₉	#3012	1	2	yes	—
316	C₂×C₁₉	#3057	1	1	yes	characteristic
317	C₂×C₁₉	#3058	1	1	yes	characteristic
318	C₂×C₁₉	#3096	1	2	yes	—
319	C₂⁵	—	2	1	no	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	—	2	2	no	—
324	C₂×#41	—	2	2	no	—
325	C₂×#41	—	2	2	no	—
326	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
327	C₂²×D₄	—	2	4	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	—	2	2	no	—
331	C₂²×D₄	—	2	2	no	—
332	C₂²×D₄	—	2	2	no	—
333	C₂²×D₄	—	2	2	no	—
334	C₂²×D₄	D₄×C₁₉	1	2	yes	—
335	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
336	C₂²×D₄	D₄×C₁₉	1	4	yes	—
337	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
338	C₂³×C₄	—	2	1	no	—
339	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
340	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
341	C₂×M₁₆	—	2	2	no	—
342	C₂×M₁₆	—	2	2	no	—
343	C₂×M₁₆	—	2	2	no	—
344	C₂²×C₈	—	2	2	no	—
345	C₂²×C₈	—	2	2	no	—
346	C₂²×C₈	D₄×C₁₉	1	4	yes	complemented
347	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
348	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
350	#127	—	2	8	no	—
351	#124	—	2	8	no	—
352	#121	—	2	8	no	—
353	#121	—	2	8	no	—
354	#120	—	2	16	no	—
355	#117	—	2	2	no	—
356	#117	—	2	2	no	—
357	#117	—	2	2	no	—
358	#117	D₄×C₁₉	1	4	yes	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	4	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	4	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	—	2	1	no	—
371	#107	—	2	4	no	—
372	#106	—	2	4	no	—
373	#102	—	2	8	no	—
374	#102	—	2	4	no	—
375	#102	—	2	4	no	—
376	C₂²⋊C₈	—	2	4	no	—
377	C₂²⋊C₈	—	2	4	no	—
378	#95	—	2	4	no	—
379	C₁₉	#23486	1	1	yes	characteristic, direct product factor, Sylow
380	C₂⁴	—	2	2	no	—
381	C₂⁴	—	2	4	no	—
382	C₂⁴	—	4	2	no	—
383	C₂⁴	—	4	2	no	—
384	C₂⁴	—	8	2	no	—
385	C₂⁴	—	8	2	no	—
386	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
387	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
388	#41	—	4	4	no	—
389	#41	—	4	4	no	—
390	#41	—	4	4	no	—
391	#41	—	4	4	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	2	16	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	8	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	8	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	4	2	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂×D₄	—	4	2	no	—
413	C₂×D₄	—	4	4	no	—
414	C₂×D₄	—	8	4	no	—
415	C₂×D₄	—	8	4	no	—
416	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
417	C₂²×C₄	—	2	2	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	—	4	2	no	—
427	C₂²×C₄	—	8	2	no	—
428	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
431	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
432	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
433	C₂²×C₄	#41×C₁₉	1	2	yes	—
434	C₂²×C₄	#41×C₁₉	1	2	yes	—
435	C₂²×C₄	#41×C₁₉	1	2	yes	—
436	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
437	M₁₆	—	4	4	no	—
438	C₂×C₈	—	2	8	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
447	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	4	2	no	—
454	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
455	C₂²⋊C₄	—	2	16	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	4	2	no	—
458	C₂²⋊C₄	—	8	4	no	—
459	C₄²	—	2	4	no	—
460	C₄²	—	4	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	4	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	4	no	—
469	C₂³	—	4	8	no	—
470	C₂³	—	4	2	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	4	no	—
473	C₂³	—	4	4	no	—
474	C₂³	—	8	8	no	—
475	C₂³	—	8	4	no	—
476	C₂³	—	8	4	no	—
477	C₂³	—	8	8	no	—
478	C₂³	C₁₉×#120	1	2	yes	—
479	C₂³	C₁₉×#121	1	2	yes	—
480	C₂³	C₁₉×#123	1	2	yes	—
481	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
482	Q₈	—	4	4	no	—
483	D₄	—	2	4	no	—
484	D₄	—	2	4	no	—
485	D₄	—	4	8	no	—
486	D₄	—	4	8	no	—
487	D₄	—	4	4	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	8	16	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	4	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	8	4	no	—
507	C₂×C₄	C₁₉×#120	1	2	yes	—
508	C₂×C₄	C₁₉×#121	1	2	yes	—
509	C₂×C₄	C₁₉×#121	1	4	yes	—
510	C₂×C₄	C₁₉×#121	1	4	yes	—
511	C₂×C₄	C₁₉×#123	1	2	yes	—
512	C₂×C₄	C₁₉×#123	1	4	yes	—
513	C₂×C₄	C₁₉×#124	1	4	yes	—
514	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
517	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
518	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
519	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
520	C₈	—	2	2	no	—
521	C₈	—	2	2	no	—
522	C₈	—	4	2	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	4	4	no	—
528	C₂²	—	4	8	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	4	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	4	no	—
534	C₂²	—	8	16	no	—
535	C₂²	—	8	2	no	—
536	C₂²	—	8	2	no	—
537	C₂²	—	8	4	no	—
538	C₂²	C₁₉×#394	1	4	yes	—
539	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
540	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
541	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
542	C₂²	C₁₉×#576	1	2	yes	—
543	C₂²	C₁₉×#577	1	2	yes	—
544	C₄	—	4	4	no	—
545	C₄	—	4	2	no	—
546	C₄	—	8	2	no	—
547	C₄	—	8	2	no	—
548	C₄	C₁₉×#394	1	4	yes	—
549	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
550	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
551	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
552	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
553	C₂	—	2	4	no	—
554	C₂	—	8	2	no	—
555	C₂	—	8	4	no	—
556	C₂	C₂×C₁₉×#394	1	1	yes	characteristic
557	C₂	C₁₉×#3012	1	2	yes	—
558	C₂	C₁₉×#3057	1	1	yes	characteristic
559	C₂	C₁₉×#3058	1	1	yes	characteristic
560	C₂	C₁₉×#3096	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#535	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#427	C₂	semidirect
3. C₂×C₁₉×#418	C₂	semidirect
4. C₂²×C₁₉×#102	C₂	semidirect
5. C₂×C₁₉×#408	C₂	semidirect
6. C₁₉×#2311	C₂	semidirect
7. C₁₉×#2034	C₂	semidirect
8. C₁₉×#2033	C₂	semidirect
9. C₁₉×#1736	C₂	semidirect
24. C₂×C₁₉×#107	C₂²	semidirect
25. C₂×C₁₉×#106	C₂²	semidirect
32. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
33. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
37. C₁₉×#380	C₂²	semidirect
38. C₁₉×#340	C₂²	semidirect
66. C₂²×C₈×C₁₉	D₄	semidirect
180. #23486	C₁₉	direct (N × H)
244. C₂×#427	C₂×C₁₉	semidirect
245. C₂×#418	C₂×C₁₉	semidirect
246. C₂²×#102	C₂×C₁₉	semidirect
247. C₂×#408	C₂×C₁₉	semidirect
248. #2311	C₂×C₁₉	semidirect
249. #2034	C₂×C₁₉	semidirect
250. #2033	C₂×C₁₉	semidirect
251. #1736	C₂×C₁₉	semidirect
296. C₂×#107	C₂²×C₁₉	semidirect
297. C₂×#106	C₂²×C₁₉	semidirect
304. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
305. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
309. #380	C₂²×C₁₉	semidirect
310. #340	C₂²×C₁₉	semidirect
346. C₂²×C₈	D₄×C₁₉	semidirect
379. C₁₉	#23486	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×#535	2
C₂×C₁₉×#427	2
C₂×C₁₉×#418	2
C₂²×C₁₉×#102	2
C₂×C₁₉×#408	2
C₁₉×#2311	2
C₁₉×#2034	2
C₁₉×#2033	2
C₁₉×#1736	2
#23486	19

Subgroups — C19×#23486 #18029445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23486 #18029445