Subgroups — C₁₉×#18527 #18024486

Order 4864.

1176 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3481	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3151	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3038	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1622	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1620	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1619	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1560	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1489	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
10	C₂×C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
11	C₁₉×#559	C₂²	1	1	yes	characteristic, complemented
12	C₁₉×#554	C₂²	1	2	yes	complemented
13	C₁₉×#553	—	2	2	no	—
14	C₁₉×#551	—	2	2	no	—
15	C₁₉×#546	—	2	2	no	—
16	D₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
17	C₁₉×#532	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic, complemented
19	C₁₉×#529	—	2	2	no	—
20	C₁₉×#525	—	2	2	no	—
21	C₄×#41×C₁₉	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₉	—	2	2	no	—
23	C₁₉×#496	—	2	2	no	—
24	C₁₉×#493	C₂²	1	2	yes	—
25	C₁₉×#492	C₂²	1	2	yes	complemented
26	C₁₉×#460	—	2	2	no	—
27	C₁₉×#460	C₂²	1	4	yes	complemented
28	C₁₉×#459	—	2	2	no	—
29	C₁₉×#459	C₂²	1	4	yes	—
30	C₁₉×#423	C₂²	1	2	yes	complemented
31	C₁₉×#418	—	2	2	no	—
32	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#333	C₂²	1	2	yes	complemented
34	C₁₉×#331	C₂²	1	2	yes	complemented
35	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	complemented
36	C₁₉×D₄⋊C₈	C₂²	1	4	yes	complemented
37	C₂×#41×C₁₉	D₄	1	2	yes	—
38	C₂×#41×C₁₉	D₄	1	2	yes	—
39	C₂²×D₄×C₁₉	—	2	2	no	—
40	C₂²×D₄×C₁₉	—	2	2	no	—
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂³×C₄×C₁₉	—	2	2	no	—
43	C₁₉×AGL(1,ℤ/8)	—	4	8	no	—
44	C₁₉×AGL(1,ℤ/8)	—	4	8	no	—
45	C₂×SD₁₆×C₁₉	—	2	4	no	—
46	C₂×SD₁₆×C₁₉	—	2	4	no	—
47	C₂×D₈×C₁₉	—	2	4	no	—
48	C₂×D₈×C₁₉	—	2	4	no	—
49	C₂×M₁₆×C₁₉	—	2	1	no	—
50	C₂×M₁₆×C₁₉	—	2	2	no	—
51	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
52	C₁₉×#127	—	2	2	no	—
53	C₁₉×#127	—	2	1	no	—
54	C₁₉×#127	C₂³	1	2	yes	—
55	C₁₉×#127	C₂³	1	1	yes	characteristic
56	C₁₉×#126	—	2	4	no	—
57	C₁₉×#125	—	2	2	no	—
58	C₁₉×#124	—	2	2	no	—
59	C₁₉×#124	D₄	1	2	yes	—
60	C₁₉×#123	—	2	2	no	—
61	C₁₉×#123	—	2	4	no	—
62	C₁₉×#123	—	2	2	no	—
63	C₁₉×C₂²⋊Q₈	—	2	4	no	—
64	C₁₉×C₂²⋊Q₈	—	2	2	no	—
65	C₁₉×#121	—	2	4	no	—
66	C₁₉×#121	—	2	2	no	—
67	C₁₉×#121	—	2	2	no	—
68	C₁₉×#120	—	2	2	no	—
69	C₁₉×#120	—	2	2	no	—
70	C₄×Q₈×C₁₉	D₄	1	2	yes	—
71	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
72	C₄×D₄×C₁₉	—	2	4	no	—
73	C₄×D₄×C₁₉	—	2	4	no	—
74	C₄×D₄×C₁₉	—	2	2	no	—
75	C₄×D₄×C₁₉	—	2	2	no	—
76	C₄×D₄×C₁₉	—	2	2	no	—
77	C₄×D₄×C₁₉	—	2	2	no	—
78	C₄×D₄×C₁₉	—	2	2	no	—
79	C₄×D₄×C₁₉	D₄	1	2	yes	—
80	C₄×D₄×C₁₉	C₂³	1	2	yes	—
81	C₁₉×#117	—	2	2	no	—
82	C₁₉×#117	—	2	2	no	—
83	C₁₉×#117	D₄	1	2	yes	—
84	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
86	C₂×C₄²×C₁₉	—	2	2	no	—
87	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
88	C₁₉×C₄⋊C₈	—	2	2	no	—
89	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
90	C₁₉×#102	—	2	4	no	—
91	C₁₉×#102	—	2	4	no	—
92	C₁₉×#97	—	2	1	no	—
93	C₄×C₈×C₁₉	C₂³	1	2	yes	—
94	C₂⁴×C₁₉	—	2	2	no	—
95	C₂⁴×C₁₉	—	4	1	no	—
96	#41×C₁₉	—	2	4	no	—
97	#41×C₁₉	—	4	2	no	—
98	#41×C₁₉	—	4	4	no	—
99	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
100	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
101	C₂×D₄×C₁₉	—	2	4	no	—
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	4	no	—
107	C₂×D₄×C₁₉	—	4	4	no	—
108	C₂×D₄×C₁₉	—	4	4	no	—
109	C₂×D₄×C₁₉	—	4	4	no	—
110	C₂×D₄×C₁₉	—	4	4	no	—
111	C₂×D₄×C₁₉	—	4	4	no	—
112	C₂×D₄×C₁₉	—	4	2	no	—
113	C₂×D₄×C₁₉	—	4	1	no	—
114	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
115	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	8	4	no	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	SD₁₆×C₁₉	—	4	8	no	—
126	SD₁₆×C₁₉	—	4	8	no	—
127	D₈×C₁₉	—	4	8	no	—
128	D₈×C₁₉	—	4	8	no	—
129	M₁₆×C₁₉	—	2	4	no	—
130	M₁₆×C₁₉	—	4	4	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	2	4	no	—
133	C₄⋊C₄×C₁₉	—	2	4	no	—
134	C₄⋊C₄×C₁₉	—	2	4	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
140	C₂²⋊C₄×C₁₉	—	2	4	no	—
141	C₂²⋊C₄×C₁₉	—	2	4	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	—	2	2	no	—
146	C₂²⋊C₄×C₁₉	—	2	4	no	—
147	C₂²⋊C₄×C₁₉	—	2	2	no	—
148	C₄²×C₁₉	—	2	2	no	—
149	C₄²×C₁₉	—	2	2	no	—
150	C₄²×C₁₉	—	2	2	no	—
151	C₄²×C₁₉	C₂×D₄	1	2	yes	—
152	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
154	#18527	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	4	8	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	8	4	no	—
160	C₂³×C₁₉	—	8	2	no	—
161	C₂³×C₁₉	—	8	2	no	—
162	C₂³×C₁₉	#120	1	1	yes	characteristic
163	Q₈×C₁₉	—	2	2	no	—
164	Q₈×C₁₉	—	2	2	no	—
165	Q₈×C₁₉	—	4	2	no	—
166	D₄×C₁₉	—	2	2	no	—
167	D₄×C₁₉	—	4	2	no	—
168	D₄×C₁₉	—	4	4	no	—
169	D₄×C₁₉	—	4	4	no	—
170	D₄×C₁₉	—	4	8	no	—
171	D₄×C₁₉	—	4	2	no	—
172	D₄×C₁₉	—	4	4	no	—
173	D₄×C₁₉	—	4	2	no	—
174	D₄×C₁₉	—	4	4	no	—
175	D₄×C₁₉	—	8	4	no	—
176	D₄×C₁₉	—	8	2	no	—
177	D₄×C₁₉	—	8	2	no	—
178	D₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	complemented
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	4	no	—
190	C₂×C₄×C₁₉	—	4	4	no	—
191	C₂×C₄×C₁₉	—	8	2	no	—
192	C₂×C₄×C₁₉	—	8	4	no	—
193	C₂×C₄×C₁₉	#120	1	2	yes	—
194	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
197	C₈×C₁₉	—	2	4	no	—
198	C₈×C₁₉	—	4	4	no	—
199	#3481	C₂×C₁₉	1	1	yes	characteristic, complemented
200	#3151	C₂×C₁₉	1	1	yes	characteristic, complemented
201	#3038	C₂×C₁₉	1	2	yes	complemented
202	#1622	C₂×C₁₉	1	4	yes	complemented
203	#1620	C₂×C₁₉	1	2	yes	complemented
204	#1619	C₂×C₁₉	1	2	yes	complemented
205	#1560	C₂×C₁₉	1	1	yes	characteristic, complemented
206	#1489	C₂×C₁₉	1	2	yes	complemented
207	C₂²×C₁₉	—	2	2	no	—
208	C₂²×C₁₉	—	2	4	no	—
209	C₂²×C₁₉	—	2	1	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	—	4	2	no	—
212	C₂²×C₁₉	—	4	4	no	—
213	C₂²×C₁₉	—	4	2	no	—
214	C₂²×C₁₉	—	8	8	no	—
215	C₂²×C₁₉	—	8	4	no	—
216	C₂²×C₁₉	—	8	2	no	—
217	C₂²×C₁₉	—	16	4	no	—
218	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
219	C₄×C₁₉	—	2	2	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	4	2	no	—
222	C₄×C₁₉	—	4	2	no	—
223	C₄×C₁₉	—	4	2	no	—
224	C₄×C₁₉	—	4	2	no	—
225	C₄×C₁₉	#453	1	2	yes	—
226	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
227	C₄×C₁₉	#575	1	2	yes	—
228	C₂×AGL(1,ℤ/8)	—	2	2	no	—
229	C₂×AGL(1,ℤ/8)	—	2	2	no	—
230	#559	C₂²×C₁₉	1	1	yes	characteristic, complemented
231	#554	C₂²×C₁₉	1	2	yes	complemented
232	#553	—	2	2	no	—
233	#551	—	2	2	no	—
234	#546	—	2	2	no	—
235	D₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
236	#532	C₂²×C₁₉	1	1	yes	characteristic
237	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic, complemented
238	#529	—	2	2	no	—
239	#525	—	2	2	no	—
240	C₄×#41	C₂²×C₁₉	1	2	yes	—
241	C₂×C₄×D₄	—	2	2	no	—
242	#496	—	2	2	no	—
243	#493	C₂²×C₁₉	1	2	yes	—
244	#492	C₂²×C₁₉	1	2	yes	complemented
245	#460	—	2	2	no	—
246	#460	C₂²×C₁₉	1	4	yes	complemented
247	#459	—	2	2	no	—
248	#459	C₂²×C₁₉	1	4	yes	—
249	#423	C₂²×C₁₉	1	2	yes	complemented
250	#418	—	2	2	no	—
251	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
252	#333	C₂²×C₁₉	1	2	yes	complemented
253	#331	C₂²×C₁₉	1	2	yes	complemented
254	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	complemented
255	D₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
256	C₂×C₁₉	—	4	1	no	—
257	C₂×C₁₉	—	4	4	no	—
258	C₂×C₁₉	—	8	2	no	—
259	C₂×C₁₉	—	16	2	no	—
260	C₂×C₁₉	#3006	1	2	yes	—
261	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
262	C₂×#41	D₄×C₁₉	1	2	yes	—
263	C₂×#41	D₄×C₁₉	1	2	yes	—
264	C₂²×D₄	—	2	2	no	—
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	—	2	2	no	—
267	C₂³×C₄	—	2	2	no	—
268	AGL(1,ℤ/8)	—	4	8	no	—
269	AGL(1,ℤ/8)	—	4	8	no	—
270	C₂×SD₁₆	—	2	4	no	—
271	C₂×SD₁₆	—	2	4	no	—
272	C₂×D₈	—	2	4	no	—
273	C₂×D₈	—	2	4	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	2	2	no	—
276	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
277	#127	—	2	2	no	—
278	#127	—	2	1	no	—
279	#127	C₂³×C₁₉	1	2	yes	—
280	#127	C₂³×C₁₉	1	1	yes	characteristic
281	#126	—	2	4	no	—
282	#125	—	2	2	no	—
283	#124	—	2	2	no	—
284	#124	D₄×C₁₉	1	2	yes	—
285	#123	—	2	2	no	—
286	#123	—	2	4	no	—
287	#123	—	2	2	no	—
288	C₂²⋊Q₈	—	2	4	no	—
289	C₂²⋊Q₈	—	2	2	no	—
290	#121	—	2	4	no	—
291	#121	—	2	2	no	—
292	#121	—	2	2	no	—
293	#120	—	2	2	no	—
294	#120	—	2	2	no	—
295	C₄×Q₈	D₄×C₁₉	1	2	yes	—
296	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
297	C₄×D₄	—	2	4	no	—
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	D₄×C₁₉	1	2	yes	—
305	C₄×D₄	C₂³×C₁₉	1	2	yes	—
306	#117	—	2	2	no	—
307	#117	—	2	2	no	—
308	#117	D₄×C₁₉	1	2	yes	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	4	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
315	#102	—	2	4	no	—
316	#102	—	2	4	no	—
317	#97	—	2	1	no	—
318	C₄×C₈	C₂³×C₁₉	1	2	yes	—
319	C₁₉	#18527	1	1	yes	characteristic, direct product factor, Sylow
320	C₂⁴	—	2	2	no	—
321	C₂⁴	—	4	1	no	—
322	#41	—	2	4	no	—
323	#41	—	4	2	no	—
324	#41	—	4	4	no	—
325	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
326	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	—	4	4	no	—
335	C₂×D₄	—	4	4	no	—
336	C₂×D₄	—	4	4	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
341	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	8	4	no	—
349	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
351	SD₁₆	—	4	8	no	—
352	SD₁₆	—	4	8	no	—
353	D₈	—	4	8	no	—
354	D₈	—	4	8	no	—
355	M₁₆	—	2	4	no	—
356	M₁₆	—	4	4	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	4	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
365	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
378	C₄²	C₂×D₄×C₁₉	1	2	yes	—
379	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	4	8	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	8	4	no	—
385	C₂³	—	8	2	no	—
386	C₂³	—	8	2	no	—
387	C₂³	C₁₉×#120	1	1	yes	characteristic
388	Q₈	—	2	2	no	—
389	Q₈	—	2	2	no	—
390	Q₈	—	4	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	4	no	—
395	D₄	—	4	8	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	4	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	4	no	—
400	D₄	—	8	4	no	—
401	D₄	—	8	2	no	—
402	D₄	—	8	2	no	—
403	D₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	complemented
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	8	2	no	—
417	C₂×C₄	—	8	4	no	—
418	C₂×C₄	C₁₉×#120	1	2	yes	—
419	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
420	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
421	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
422	C₈	—	2	4	no	—
423	C₈	—	4	4	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	8	8	no	—
432	C₂²	—	8	4	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	16	4	no	—
435	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	C₁₉×#453	1	2	yes	—
443	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
444	C₄	C₁₉×#575	1	2	yes	—
445	C₂	—	4	1	no	—
446	C₂	—	4	4	no	—
447	C₂	—	8	2	no	—
448	C₂	—	16	2	no	—
449	C₂	C₁₉×#3006	1	2	yes	—
450	C₂	C₂×C₁₉×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3481	C₂	semidirect
2. C₁₉×#3151	C₂	semidirect
3. C₁₉×#3038	C₂	semidirect
4. C₁₉×#1622	C₂	semidirect
5. C₁₉×#1620	C₂	semidirect
6. C₁₉×#1619	C₂	semidirect
7. C₁₉×#1560	C₂	semidirect
8. C₁₉×#1489	C₂	semidirect
11. C₁₉×#559	C₂²	semidirect
12. C₁₉×#554	C₂²	semidirect
16. D₄²×C₁₉	C₂²	semidirect
18. C₂×C₁₉×#127	C₂²	semidirect
25. C₁₉×#492	C₂²	semidirect
27. C₁₉×#460	C₂²	semidirect
30. C₁₉×#423	C₂²	semidirect
32. C₄×M₁₆×C₁₉	C₂²	semidirect
33. C₁₉×#333	C₂²	semidirect
34. C₁₉×#331	C₂²	semidirect
35. C₁₉×Q₈⋊C₈	C₂²	semidirect
36. C₁₉×D₄⋊C₈	C₂²	semidirect
154. #18527	C₁₉	direct (N × H)
178. D₄×C₁₉	AGL(1,ℤ/8)	semidirect
199. #3481	C₂×C₁₉	semidirect
200. #3151	C₂×C₁₉	semidirect
201. #3038	C₂×C₁₉	semidirect
202. #1622	C₂×C₁₉	semidirect
203. #1620	C₂×C₁₉	semidirect
204. #1619	C₂×C₁₉	semidirect
205. #1560	C₂×C₁₉	semidirect
206. #1489	C₂×C₁₉	semidirect
230. #559	C₂²×C₁₉	semidirect
231. #554	C₂²×C₁₉	semidirect
235. D₄²	C₂²×C₁₉	semidirect
237. C₂×#127	C₂²×C₁₉	semidirect
244. #492	C₂²×C₁₉	semidirect
246. #460	C₂²×C₁₉	semidirect
249. #423	C₂²×C₁₉	semidirect
251. C₄×M₁₆	C₂²×C₁₉	semidirect
252. #333	C₂²×C₁₉	semidirect
253. #331	C₂²×C₁₉	semidirect
254. Q₈⋊C₈	C₂²×C₁₉	semidirect
255. D₄⋊C₈	C₂²×C₁₉	semidirect
319. C₁₉	#18527	direct (N × H)
403. D₄	C₁₉×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3481	2
C₁₉×#3151	2
C₁₉×#3038	2
C₁₉×#1622	2
C₁₉×#1620	2
C₁₉×#1619	2
C₁₉×#1560	2
C₁₉×#1489	2
#18527	19

Subgroups — C19×#18527 #18024486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18527 #18024486