Subgroups — C₁₉×#10975 #18016934

Order 4864.

2054 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#418	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2309	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#339	C₂	1	2	yes	maximal, complemented
6	C₂³×D₄×C₁₉	—	2	2	no	—
7	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
10	C₂×C₁₉×#127	—	2	2	no	—
11	C₂×C₁₉×#127	—	2	4	no	—
12	C₂×C₁₉×#127	—	2	4	no	—
13	C₂×C₁₉×#127	C₄	1	4	yes	complemented
14	C₂×C₁₉×#117	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#418	—	2	4	no	—
17	C₁₉×#418	—	2	4	no	—
18	C₂×C₁₉×#102	—	2	4	no	—
19	C₂×C₁₉×#100	—	2	2	no	—
20	C₂×C₁₉×#100	—	2	4	no	—
21	C₁₉×#390	—	2	4	no	—
22	C₁₉×#379	—	2	2	no	—
23	C₁₉×#339	—	2	4	no	—
24	C₂⁵×C₁₉	—	2	1	no	—
25	C₂⁵×C₁₉	D₄	1	2	yes	—
26	C₂²×D₄×C₁₉	—	2	16	no	—
27	C₂²×D₄×C₁₉	—	2	8	no	—
28	C₂²×D₄×C₁₉	—	2	2	no	—
29	C₂²×D₄×C₁₉	—	2	2	no	—
30	C₂²×D₄×C₁₉	—	2	2	no	—
31	C₂²×D₄×C₁₉	—	2	2	no	—
32	C₂²×D₄×C₁₉	—	2	2	no	—
33	C₂²×D₄×C₁₉	—	2	2	no	—
34	C₂²×D₄×C₁₉	—	2	2	no	—
35	C₂²×D₄×C₁₉	—	2	1	no	—
36	C₂²×D₄×C₁₉	—	2	2	no	—
37	C₂²×D₄×C₁₉	—	2	2	no	—
38	C₂²×D₄×C₁₉	—	2	2	no	—
39	C₂²×D₄×C₁₉	—	2	2	no	—
40	C₂²×D₄×C₁₉	—	4	16	no	—
41	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
42	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₁₉	D₄	1	2	yes	—
44	C₂²×D₄×C₁₉	D₄	1	4	yes	—
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂×M₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	—	2	2	no	—
49	C₂×M₁₆×C₁₉	—	2	2	no	—
50	C₂×M₁₆×C₁₉	—	2	2	no	—
51	C₂×M₁₆×C₁₉	—	2	2	no	—
52	C₂×M₁₆×C₁₉	D₄	1	4	yes	complemented
53	C₂²×C₈×C₁₉	—	2	2	no	—
54	C₁₉×#127	—	2	16	no	—
55	C₁₉×#127	—	2	8	no	—
56	C₁₉×#127	—	2	8	no	—
57	C₁₉×#117	—	2	2	no	—
58	C₁₉×#117	—	2	2	no	—
59	C₁₉×#117	—	2	2	no	—
60	C₁₉×#117	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	complemented
62	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
64	C₂×C₄²×C₁₉	—	2	2	no	—
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	2	no	—
67	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₁₉	D₄	1	4	yes	—
69	C₁₉×#102	—	2	16	no	—
70	C₁₉×#100	—	2	8	no	—
71	C₂⁴×C₁₉	—	2	2	no	—
72	C₂⁴×C₁₉	—	2	4	no	—
73	C₂⁴×C₁₉	—	2	4	no	—
74	C₂⁴×C₁₉	—	2	2	no	—
75	C₂⁴×C₁₉	—	2	4	no	—
76	C₂⁴×C₁₉	—	2	2	no	—
77	C₂⁴×C₁₉	—	4	8	no	—
78	C₂⁴×C₁₉	—	4	8	no	—
79	C₂⁴×C₁₉	—	4	1	no	—
80	C₂⁴×C₁₉	—	4	2	no	—
81	C₂⁴×C₁₉	—	4	1	no	—
82	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	—
83	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂×D₄×C₁₉	—	2	32	no	—
85	C₂×D₄×C₁₉	—	2	2	no	—
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	—	2	2	no	—
88	C₂×D₄×C₁₉	—	2	4	no	—
89	C₂×D₄×C₁₉	—	2	4	no	—
90	C₂×D₄×C₁₉	—	2	4	no	—
91	C₂×D₄×C₁₉	—	2	4	no	—
92	C₂×D₄×C₁₉	—	2	4	no	—
93	C₂×D₄×C₁₉	—	2	4	no	—
94	C₂×D₄×C₁₉	—	2	4	no	—
95	C₂×D₄×C₁₉	—	2	2	no	—
96	C₂×D₄×C₁₉	—	2	4	no	—
97	C₂×D₄×C₁₉	—	2	4	no	—
98	C₂×D₄×C₁₉	—	2	4	no	—
99	C₂×D₄×C₁₉	—	2	4	no	—
100	C₂×D₄×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	4	32	no	—
102	C₂×D₄×C₁₉	—	4	64	no	—
103	C₂×D₄×C₁₉	—	4	2	no	—
104	C₂×D₄×C₁₉	—	4	1	no	—
105	C₂×D₄×C₁₉	—	4	2	no	—
106	C₂×D₄×C₁₉	—	4	2	no	—
107	C₂×D₄×C₁₉	—	4	2	no	—
108	C₂×D₄×C₁₉	—	4	2	no	—
109	C₂×D₄×C₁₉	—	4	2	no	—
110	C₂×D₄×C₁₉	—	4	2	no	—
111	C₂×D₄×C₁₉	—	4	2	no	—
112	C₂×D₄×C₁₉	—	4	2	no	—
113	C₂×D₄×C₁₉	—	4	1	no	—
114	C₂×D₄×C₁₉	—	4	2	no	—
115	C₂×D₄×C₁₉	—	4	2	no	—
116	C₂×D₄×C₁₉	—	4	2	no	—
117	C₂×D₄×C₁₉	—	4	2	no	—
118	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	complemented
119	C₂²×C₄×C₁₉	—	2	8	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
123	C₂²×C₄×C₁₉	C₂²×C₄	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×D₄	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	#41	1	2	yes	—
130	C₂²×C₄×C₁₉	#41	1	2	yes	—
131	M₁₆×C₁₉	—	2	4	no	—
132	M₁₆×C₁₉	—	2	4	no	—
133	M₁₆×C₁₉	—	4	2	no	—
134	M₁₆×C₁₉	—	4	2	no	—
135	C₂×C₈×C₁₉	—	2	4	no	—
136	C₂×C₈×C₁₉	—	4	2	no	—
137	C₂×C₈×C₁₉	—	4	2	no	—
138	C₄⋊C₄×C₁₉	—	2	4	no	—
139	C₄⋊C₄×C₁₉	—	2	4	no	—
140	C₂²⋊C₄×C₁₉	—	4	2	no	—
141	C₂²⋊C₄×C₁₉	—	4	2	no	—
142	C₂²⋊C₄×C₁₉	—	8	8	no	—
143	C₄²×C₁₉	—	2	2	no	—
144	C₄²×C₁₉	—	2	4	no	—
145	C₄²×C₁₉	—	4	2	no	—
146	C₄²×C₁₉	—	4	2	no	—
147	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	complemented
148	#10975	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂³×C₁₉	—	2	4	no	—
150	C₂³×C₁₉	—	2	4	no	—
151	C₂³×C₁₉	—	2	4	no	—
152	C₂³×C₁₉	—	2	4	no	—
153	C₂³×C₁₉	—	2	4	no	—
154	C₂³×C₁₉	—	4	8	no	—
155	C₂³×C₁₉	—	4	8	no	—
156	C₂³×C₁₉	—	4	16	no	—
157	C₂³×C₁₉	—	4	16	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	4	4	no	—
161	C₂³×C₁₉	—	4	4	no	—
162	C₂³×C₁₉	—	4	4	no	—
163	C₂³×C₁₉	—	4	4	no	—
164	C₂³×C₁₉	—	4	8	no	—
165	C₂³×C₁₉	—	8	4	no	—
166	C₂³×C₁₉	—	8	8	no	—
167	C₂³×C₁₉	—	8	4	no	—
168	C₂³×C₁₉	—	8	8	no	—
169	C₂³×C₁₉	—	8	4	no	—
170	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂³×C₁₉	#120	1	2	yes	—
172	C₂³×C₁₉	#120	1	1	yes	characteristic
173	C₂³×C₁₉	#121	1	2	yes	—
174	C₂³×C₁₉	#123	1	1	yes	characteristic
175	D₄×C₁₉	—	2	8	no	—
176	D₄×C₁₉	—	4	64	no	—
177	D₄×C₁₉	—	4	4	no	—
178	D₄×C₁₉	—	4	4	no	—
179	D₄×C₁₉	—	4	4	no	—
180	D₄×C₁₉	—	4	4	no	—
181	D₄×C₁₉	—	4	4	no	—
182	D₄×C₁₉	—	4	4	no	—
183	D₄×C₁₉	—	4	4	no	—
184	C₂×C₄×C₁₉	—	2	8	no	—
185	C₂×C₄×C₁₉	—	2	16	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	—	4	8	no	—
189	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
193	C₂×C₄×C₁₉	#120	1	2	yes	—
194	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#120	1	2	yes	—
196	C₂×C₄×C₁₉	#121	1	2	yes	—
197	C₂×C₄×C₁₉	#121	1	2	yes	—
198	C₂×C₄×C₁₉	#121	1	2	yes	—
199	C₂×C₄×C₁₉	#121	1	2	yes	—
200	C₂×C₄×C₁₉	#121	1	2	yes	—
201	C₂×C₄×C₁₉	#123	1	2	yes	—
202	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#124	1	2	yes	—
204	C₂×C₄×C₁₉	#127	1	2	yes	—
205	C₈×C₁₉	—	4	4	no	—
206	C₂²×#127	C₂×C₁₉	1	1	yes	characteristic
207	C₂×#418	C₂×C₁₉	1	2	yes	complemented
208	C₂²×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#2309	C₂×C₁₉	1	1	yes	characteristic, complemented
210	C₂×#339	C₂×C₁₉	1	2	yes	complemented
211	C₂²×C₁₉	—	2	2	no	—
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	2	4	no	—
214	C₂²×C₁₉	—	2	4	no	—
215	C₂²×C₁₉	—	4	8	no	—
216	C₂²×C₁₉	—	4	8	no	—
217	C₂²×C₁₉	—	4	8	no	—
218	C₂²×C₁₉	—	4	4	no	—
219	C₂²×C₁₉	—	4	4	no	—
220	C₂²×C₁₉	—	8	4	no	—
221	C₂²×C₁₉	—	8	4	no	—
222	C₂²×C₁₉	—	8	8	no	—
223	C₂²×C₁₉	—	8	8	no	—
224	C₂²×C₁₉	—	8	4	no	—
225	C₂²×C₁₉	—	8	8	no	—
226	C₂²×C₁₉	—	8	8	no	—
227	C₂²×C₁₉	#379	1	1	yes	characteristic
228	C₂²×C₁₉	#386	1	1	yes	characteristic
229	C₂²×C₁₉	#386	1	1	yes	characteristic
230	C₂²×C₁₉	#392	1	2	yes	—
231	C₂²×C₁₉	#394	1	2	yes	—
232	C₂²×C₁₉	#453	1	4	yes	—
233	C₄×C₁₉	—	2	8	no	—
234	C₄×C₁₉	—	8	4	no	—
235	C₄×C₁₉	#386	1	2	yes	—
236	C₄×C₁₉	#390	1	2	yes	—
237	C₄×C₁₉	#392	1	2	yes	—
238	C₄×C₁₉	#394	1	2	yes	—
239	C₂³×D₄	—	2	2	no	—
240	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
241	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
242	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
243	C₂×#127	—	2	2	no	—
244	C₂×#127	—	2	4	no	—
245	C₂×#127	—	2	4	no	—
246	C₂×#127	C₄×C₁₉	1	4	yes	complemented
247	C₂×#117	C₂²×C₁₉	1	2	yes	—
248	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
249	#418	—	2	4	no	—
250	#418	—	2	4	no	—
251	C₂×#102	—	2	4	no	—
252	C₂×#100	—	2	2	no	—
253	C₂×#100	—	2	4	no	—
254	#390	—	2	4	no	—
255	#379	—	2	2	no	—
256	#339	—	2	4	no	—
257	C₂×C₁₉	—	2	1	no	—
258	C₂×C₁₉	—	2	1	no	—
259	C₂×C₁₉	—	2	2	no	—
260	C₂×C₁₉	—	8	4	no	—
261	C₂×C₁₉	—	8	4	no	—
262	C₂×C₁₉	#1438	1	1	yes	characteristic
263	C₂×C₁₉	#1887	1	2	yes	—
264	C₂×C₁₉	#2002	1	4	yes	—
265	C₂⁵	—	2	1	no	—
266	C₂⁵	D₄×C₁₉	1	2	yes	—
267	C₂²×D₄	—	2	16	no	—
268	C₂²×D₄	—	2	8	no	—
269	C₂²×D₄	—	2	2	no	—
270	C₂²×D₄	—	2	2	no	—
271	C₂²×D₄	—	2	2	no	—
272	C₂²×D₄	—	2	2	no	—
273	C₂²×D₄	—	2	2	no	—
274	C₂²×D₄	—	2	1	no	—
275	C₂²×D₄	—	2	2	no	—
276	C₂²×D₄	—	2	2	no	—
277	C₂²×D₄	—	2	2	no	—
278	C₂²×D₄	—	2	2	no	—
279	C₂²×D₄	—	2	2	no	—
280	C₂²×D₄	—	2	2	no	—
281	C₂²×D₄	—	4	16	no	—
282	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
283	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
284	C₂²×D₄	D₄×C₁₉	1	2	yes	—
285	C₂²×D₄	D₄×C₁₉	1	4	yes	—
286	C₂³×C₄	—	2	1	no	—
287	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	—	2	2	no	—
292	C₂×M₁₆	—	2	2	no	—
293	C₂×M₁₆	D₄×C₁₉	1	4	yes	complemented
294	C₂²×C₈	—	2	2	no	—
295	#127	—	2	16	no	—
296	#127	—	2	8	no	—
297	#127	—	2	8	no	—
298	#117	—	2	2	no	—
299	#117	—	2	2	no	—
300	#117	—	2	2	no	—
301	#117	—	2	2	no	—
302	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	complemented
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	2	8	no	—
305	C₂×C₄²	—	2	2	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
309	C₂×C₄²	D₄×C₁₉	1	4	yes	—
310	#102	—	2	16	no	—
311	#100	—	2	8	no	—
312	C₁₉	#10975	1	1	yes	characteristic, direct product factor, Sylow
313	C₂⁴	—	2	2	no	—
314	C₂⁴	—	2	2	no	—
315	C₂⁴	—	2	4	no	—
316	C₂⁴	—	2	4	no	—
317	C₂⁴	—	2	4	no	—
318	C₂⁴	—	2	2	no	—
319	C₂⁴	—	4	8	no	—
320	C₂⁴	—	4	8	no	—
321	C₂⁴	—	4	1	no	—
322	C₂⁴	—	4	2	no	—
323	C₂⁴	—	4	1	no	—
324	C₂⁴	C₂²⋊C₄×C₁₉	1	4	yes	—
325	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
326	C₂×D₄	—	2	32	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	4	32	no	—
344	C₂×D₄	—	4	64	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	4	2	no	—
355	C₂×D₄	—	4	1	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	complemented
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
371	C₂²×C₄	#41×C₁₉	1	2	yes	—
372	C₂²×C₄	#41×C₁₉	1	2	yes	—
373	M₁₆	—	2	4	no	—
374	M₁₆	—	2	4	no	—
375	M₁₆	—	4	2	no	—
376	M₁₆	—	4	2	no	—
377	C₂×C₈	—	2	4	no	—
378	C₂×C₈	—	4	2	no	—
379	C₂×C₈	—	4	2	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₂²⋊C₄	—	8	8	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	4	no	—
387	C₄²	—	4	2	no	—
388	C₄²	—	4	2	no	—
389	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	complemented
390	C₂³	—	2	4	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	2	4	no	—
395	C₂³	—	4	8	no	—
396	C₂³	—	4	8	no	—
397	C₂³	—	4	16	no	—
398	C₂³	—	4	16	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	4	no	—
402	C₂³	—	4	4	no	—
403	C₂³	—	4	4	no	—
404	C₂³	—	4	4	no	—
405	C₂³	—	4	8	no	—
406	C₂³	—	8	4	no	—
407	C₂³	—	8	8	no	—
408	C₂³	—	8	4	no	—
409	C₂³	—	8	8	no	—
410	C₂³	—	8	4	no	—
411	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
412	C₂³	C₁₉×#120	1	2	yes	—
413	C₂³	C₁₉×#120	1	1	yes	characteristic
414	C₂³	C₁₉×#121	1	2	yes	—
415	C₂³	C₁₉×#123	1	1	yes	characteristic
416	D₄	—	2	8	no	—
417	D₄	—	4	64	no	—
418	D₄	—	4	4	no	—
419	D₄	—	4	4	no	—
420	D₄	—	4	4	no	—
421	D₄	—	4	4	no	—
422	D₄	—	4	4	no	—
423	D₄	—	4	4	no	—
424	D₄	—	4	4	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	16	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	8	no	—
430	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
431	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
432	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
433	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
434	C₂×C₄	C₁₉×#120	1	2	yes	—
435	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
436	C₂×C₄	C₁₉×#120	1	2	yes	—
437	C₂×C₄	C₁₉×#121	1	2	yes	—
438	C₂×C₄	C₁₉×#121	1	2	yes	—
439	C₂×C₄	C₁₉×#121	1	2	yes	—
440	C₂×C₄	C₁₉×#121	1	2	yes	—
441	C₂×C₄	C₁₉×#121	1	2	yes	—
442	C₂×C₄	C₁₉×#123	1	2	yes	—
443	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
444	C₂×C₄	C₁₉×#124	1	2	yes	—
445	C₂×C₄	C₁₉×#127	1	2	yes	—
446	C₈	—	4	4	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	4	8	no	—
452	C₂²	—	4	8	no	—
453	C₂²	—	4	8	no	—
454	C₂²	—	4	4	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	8	4	no	—
457	C₂²	—	8	4	no	—
458	C₂²	—	8	8	no	—
459	C₂²	—	8	8	no	—
460	C₂²	—	8	4	no	—
461	C₂²	—	8	8	no	—
462	C₂²	—	8	8	no	—
463	C₂²	C₁₉×#379	1	1	yes	characteristic
464	C₂²	C₁₉×#386	1	1	yes	characteristic
465	C₂²	C₁₉×#386	1	1	yes	characteristic
466	C₂²	C₁₉×#392	1	2	yes	—
467	C₂²	C₁₉×#394	1	2	yes	—
468	C₂²	C₁₉×#453	1	4	yes	—
469	C₄	—	2	8	no	—
470	C₄	—	8	4	no	—
471	C₄	C₁₉×#386	1	2	yes	—
472	C₄	C₁₉×#390	1	2	yes	—
473	C₄	C₁₉×#392	1	2	yes	—
474	C₄	C₁₉×#394	1	2	yes	—
475	C₂	—	2	1	no	—
476	C₂	—	2	1	no	—
477	C₂	—	2	2	no	—
478	C₂	—	8	4	no	—
479	C₂	—	8	4	no	—
480	C₂	C₁₉×#1438	1	1	yes	characteristic
481	C₂	C₁₉×#1887	1	2	yes	—
482	C₂	C₁₉×#2002	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂²×C₁₉×#127	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#418	C₂	semidirect
3. C₂²×C₁₉×#100	C₂	semidirect
4. C₁₉×#2309	C₂	semidirect
5. C₂×C₁₉×#339	C₂	semidirect
13. C₂×C₁₉×#127	C₄	semidirect
52. C₂×M₁₆×C₁₉	D₄	semidirect
61. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
118. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
147. C₄²×C₁₉	C₂²⋊C₄	semidirect
148. #10975	C₁₉	direct (N × H)
207. C₂×#418	C₂×C₁₉	semidirect
208. C₂²×#100	C₂×C₁₉	semidirect
209. #2309	C₂×C₁₉	semidirect
210. C₂×#339	C₂×C₁₉	semidirect
246. C₂×#127	C₄×C₁₉	semidirect
293. C₂×M₁₆	D₄×C₁₉	semidirect
302. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
312. C₁₉	#10975	direct (N × H)
360. C₂×D₄	C₂²⋊C₄×C₁₉	semidirect
389. C₄²	C₂²⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#127	2
C₂×C₁₉×#418	2
C₂²×C₁₉×#100	2
C₁₉×#2309	2
C₂×C₁₉×#339	2
#10975	19

Subgroups — C19×#10975 #18016934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10975 #18016934