Subgroups — C₁₉×#18480 #18024439

Order 4864.

1082 conjugacy classes of subgroups.

The subgroup lattice has 498 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×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3106	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1632	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1630	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1629	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1622	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1620	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1619	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1543	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1476	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₉×#135	—	2	2	no	—
13	C₁₉×#559	C₂²	1	1	yes	characteristic
14	C₁₉×#554	C₂²	1	2	yes	—
15	C₁₉×#553	—	2	2	no	—
16	C₁₉×#551	—	2	2	no	—
17	C₁₉×#546	—	2	2	no	—
18	D₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#532	C₂²	1	1	yes	characteristic
20	C₁₉×#532	C₂²	1	1	yes	characteristic, complemented
21	C₁₉×#529	—	2	2	no	—
22	C₁₉×#525	—	2	2	no	—
23	C₄×#41×C₁₉	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₁₉	—	2	2	no	—
25	C₁₉×#495	—	2	2	no	—
26	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
27	C₁₉×#493	C₂²	1	1	yes	characteristic
28	C₁₉×#492	C₂²	1	1	yes	characteristic
29	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#482	—	2	2	no	—
31	C₁₉×#477	C₂²	1	2	yes	complemented
32	C₁₉×#476	C₂²	1	2	yes	—
33	C₁₉×#460	C₂²	1	2	yes	complemented
34	C₁₉×#459	C₂²	1	2	yes	—
35	C₁₉×#449	—	2	2	no	—
36	C₄×SD₁₆×C₁₉	—	2	2	no	—
37	C₄×D₈×C₁₉	—	2	2	no	—
38	C₁₉×#431	C₂²	1	2	yes	complemented
39	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#333	C₂²	1	2	yes	complemented
41	C₁₉×#331	C₂²	1	1	yes	characteristic
42	C₁₉×#331	C₂²	1	1	yes	characteristic
43	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	complemented
44	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	complemented
45	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
46	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂×#41×C₁₉	D₄	1	2	yes	—
49	C₂×#41×C₁₉	D₄	1	2	yes	—
50	C₂²×D₄×C₁₉	—	2	2	no	—
51	C₂³×C₄×C₁₉	—	2	2	no	—
52	C₁₉×#135	—	4	8	no	—
53	C₂×Q₁₆×C₁₉	—	2	2	no	—
54	C₂×SD₁₆×C₁₉	—	2	2	no	—
55	C₂×SD₁₆×C₁₉	—	2	2	no	—
56	C₂×SD₁₆×C₁₉	—	2	2	no	—
57	C₂×D₈×C₁₉	—	2	2	no	—
58	C₂×D₈×C₁₉	—	2	2	no	—
59	C₂²×C₈×C₁₉	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₉×#127	C₂³	1	1	yes	characteristic
63	C₁₉×#127	C₂³	1	1	yes	characteristic
64	C₁₉×#126	—	2	4	no	—
65	C₁₉×#125	—	2	2	no	—
66	C₁₉×#124	—	2	2	no	—
67	C₁₉×#124	—	2	1	no	—
68	C₁₉×#124	D₄	1	2	yes	—
69	C₁₉×#123	—	2	2	no	—
70	C₁₉×#123	—	2	4	no	—
71	C₁₉×#123	—	2	2	no	—
72	C₁₉×C₂²⋊Q₈	—	2	4	no	—
73	C₁₉×C₂²⋊Q₈	—	2	2	no	—
74	C₁₉×#121	—	2	4	no	—
75	C₁₉×#121	—	2	2	no	—
76	C₁₉×#121	—	2	2	no	—
77	C₁₉×#121	—	2	2	no	—
78	C₁₉×#120	—	2	2	no	—
79	C₁₉×#120	—	2	2	no	—
80	C₄×Q₈×C₁₉	D₄	1	2	yes	—
81	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
82	C₄×D₄×C₁₉	—	2	4	no	—
83	C₄×D₄×C₁₉	—	2	4	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₄×D₄×C₁₉	—	2	2	no	—
86	C₄×D₄×C₁₉	—	2	2	no	—
87	C₄×D₄×C₁₉	—	2	2	no	—
88	C₄×D₄×C₁₉	—	2	2	no	—
89	C₄×D₄×C₁₉	—	2	2	no	—
90	C₄×D₄×C₁₉	D₄	1	2	yes	—
91	C₄×D₄×C₁₉	C₂³	1	2	yes	—
92	C₁₉×#117	—	2	2	no	—
93	C₁₉×#117	—	2	2	no	—
94	C₁₉×#117	D₄	1	2	yes	—
95	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
97	C₂×C₄²×C₁₉	—	2	2	no	—
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₁₉×#107	—	2	2	no	—
100	C₁₉×#106	—	2	2	no	—
101	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
102	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
103	C₁₉×#103	—	2	2	no	—
104	C₁₉×#102	—	2	2	no	—
105	C₁₉×#102	—	2	2	no	—
106	C₁₉×#102	—	2	2	no	—
107	C₁₉×C₂²⋊C₈	—	2	2	no	—
108	C₄×C₈×C₁₉	—	2	1	no	—
109	C₄×C₈×C₁₉	—	2	2	no	—
110	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
112	C₂⁴×C₁₉	—	2	2	no	—
113	#41×C₁₉	—	2	4	no	—
114	#41×C₁₉	—	4	2	no	—
115	#41×C₁₉	—	4	4	no	—
116	#41×C₁₉	—	4	4	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
119	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
120	C₂×D₄×C₁₉	—	2	4	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	1	no	—
126	C₂×D₄×C₁₉	—	4	4	no	—
127	C₂×D₄×C₁₉	—	4	4	no	—
128	C₂×D₄×C₁₉	—	4	1	no	—
129	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
130	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₉	—	2	4	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	4	1	no	—
138	C₂²×C₄×C₁₉	—	8	4	no	—
139	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	Q₁₆×C₁₉	—	4	4	no	—
142	SD₁₆×C₁₉	—	4	4	no	—
143	SD₁₆×C₁₉	—	4	4	no	—
144	SD₁₆×C₁₉	—	4	4	no	—
145	D₈×C₁₉	—	4	4	no	—
146	D₈×C₁₉	—	4	4	no	—
147	C₂×C₈×C₁₉	—	2	4	no	—
148	C₂×C₈×C₁₉	—	2	1	no	—
149	C₂×C₈×C₁₉	—	2	1	no	—
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	4	no	—
153	C₄⋊C₄×C₁₉	—	2	4	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
160	C₂²⋊C₄×C₁₉	—	2	4	no	—
161	C₂²⋊C₄×C₁₉	—	2	4	no	—
162	C₂²⋊C₄×C₁₉	—	2	2	no	—
163	C₂²⋊C₄×C₁₉	—	2	2	no	—
164	C₂²⋊C₄×C₁₉	—	2	2	no	—
165	C₂²⋊C₄×C₁₉	—	2	2	no	—
166	C₂²⋊C₄×C₁₉	—	2	4	no	—
167	C₂²⋊C₄×C₁₉	—	2	2	no	—
168	C₂²⋊C₄×C₁₉	—	4	2	no	—
169	C₄²×C₁₉	—	2	2	no	—
170	C₄²×C₁₉	—	2	2	no	—
171	C₄²×C₁₉	—	2	2	no	—
172	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₉	C₂×D₄	1	2	yes	—
174	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
175	#18480	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂³×C₁₉	—	2	2	no	—
177	C₂³×C₁₉	—	2	2	no	—
178	C₂³×C₁₉	—	4	8	no	—
179	C₂³×C₁₉	—	4	1	no	—
180	C₂³×C₁₉	—	8	2	no	—
181	C₂³×C₁₉	#120	1	1	yes	characteristic
182	Q₈×C₁₉	—	2	2	no	—
183	Q₈×C₁₉	—	2	2	no	—
184	Q₈×C₁₉	—	4	2	no	—
185	Q₈×C₁₉	—	4	2	no	—
186	D₄×C₁₉	—	2	2	no	—
187	D₄×C₁₉	—	4	2	no	—
188	D₄×C₁₉	—	4	2	no	—
189	D₄×C₁₉	—	4	4	no	—
190	D₄×C₁₉	—	4	8	no	—
191	D₄×C₁₉	—	4	2	no	—
192	D₄×C₁₉	—	4	2	no	—
193	D₄×C₁₉	—	4	2	no	—
194	D₄×C₁₉	—	4	2	no	—
195	D₄×C₁₉	—	8	2	no	—
196	D₄×C₁₉	—	8	2	no	—
197	D₄×C₁₉	#135	1	4	yes	complemented
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	4	4	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	4	no	—
209	C₂×C₄×C₁₉	—	4	4	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	8	2	no	—
212	C₂×C₄×C₁₉	—	8	4	no	—
213	C₂×C₄×C₁₉	—	8	2	no	—
214	C₂×C₄×C₁₉	#120	1	2	yes	—
215	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
218	C₈×C₁₉	—	2	2	no	—
219	C₈×C₁₉	—	2	2	no	—
220	C₈×C₁₉	—	4	2	no	—
221	C₈×C₁₉	—	4	2	no	—
222	#3481	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#3147	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#3106	C₂×C₁₉	1	2	yes	complemented
225	#1632	C₂×C₁₉	1	2	yes	complemented
226	#1630	C₂×C₁₉	1	1	yes	characteristic, complemented
227	#1629	C₂×C₁₉	1	1	yes	characteristic, complemented
228	#1622	C₂×C₁₉	1	2	yes	complemented
229	#1620	C₂×C₁₉	1	1	yes	characteristic, complemented
230	#1619	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#1543	C₂×C₁₉	1	1	yes	characteristic, complemented
232	#1476	C₂×C₁₉	1	2	yes	complemented
233	C₂²×C₁₉	—	2	2	no	—
234	C₂²×C₁₉	—	2	4	no	—
235	C₂²×C₁₉	—	2	1	no	—
236	C₂²×C₁₉	—	4	2	no	—
237	C₂²×C₁₉	—	4	2	no	—
238	C₂²×C₁₉	—	4	4	no	—
239	C₂²×C₁₉	—	4	2	no	—
240	C₂²×C₁₉	—	8	8	no	—
241	C₂²×C₁₉	—	8	2	no	—
242	C₂²×C₁₉	—	8	1	no	—
243	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
244	C₄×C₁₉	—	2	2	no	—
245	C₄×C₁₉	—	2	1	no	—
246	C₄×C₁₉	—	4	2	no	—
247	C₄×C₁₉	—	4	2	no	—
248	C₄×C₁₉	—	4	2	no	—
249	C₄×C₁₉	—	4	2	no	—
250	C₄×C₁₉	—	8	1	no	—
251	C₄×C₁₉	#453	1	2	yes	—
252	C₄×C₁₉	C₂×#135	1	2	yes	—
253	C₄×C₁₉	#575	1	2	yes	—
254	C₂×#135	—	2	2	no	—
255	#559	C₂²×C₁₉	1	1	yes	characteristic
256	#554	C₂²×C₁₉	1	2	yes	—
257	#553	—	2	2	no	—
258	#551	—	2	2	no	—
259	#546	—	2	2	no	—
260	D₄²	C₂²×C₁₉	1	1	yes	characteristic
261	#532	C₂²×C₁₉	1	1	yes	characteristic
262	#532	C₂²×C₁₉	1	1	yes	characteristic, complemented
263	#529	—	2	2	no	—
264	#525	—	2	2	no	—
265	C₄×#41	C₂²×C₁₉	1	2	yes	—
266	C₂×C₄×D₄	—	2	2	no	—
267	#495	—	2	2	no	—
268	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
269	#493	C₂²×C₁₉	1	1	yes	characteristic
270	#492	C₂²×C₁₉	1	1	yes	characteristic
271	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
272	#482	—	2	2	no	—
273	#477	C₂²×C₁₉	1	2	yes	complemented
274	#476	C₂²×C₁₉	1	2	yes	—
275	#460	C₂²×C₁₉	1	2	yes	complemented
276	#459	C₂²×C₁₉	1	2	yes	—
277	#449	—	2	2	no	—
278	C₄×SD₁₆	—	2	2	no	—
279	C₄×D₈	—	2	2	no	—
280	#431	C₂²×C₁₉	1	2	yes	complemented
281	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
282	#333	C₂²×C₁₉	1	2	yes	complemented
283	#331	C₂²×C₁₉	1	1	yes	characteristic
284	#331	C₂²×C₁₉	1	1	yes	characteristic
285	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	complemented
286	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	complemented
287	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
288	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
289	C₂×C₁₉	—	4	1	no	—
290	C₂×C₁₉	—	4	4	no	—
291	C₂×C₁₉	—	8	2	no	—
292	C₂×C₁₉	—	16	1	no	—
293	C₂×C₁₉	#3002	1	2	yes	—
294	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
295	C₂×#41	—	2	1	no	—
296	C₂×#41	D₄×C₁₉	1	2	yes	—
297	C₂×#41	D₄×C₁₉	1	2	yes	—
298	C₂²×D₄	—	2	2	no	—
299	C₂³×C₄	—	2	2	no	—
300	#135	—	4	8	no	—
301	C₂×Q₁₆	—	2	2	no	—
302	C₂×SD₁₆	—	2	2	no	—
303	C₂×SD₁₆	—	2	2	no	—
304	C₂×SD₁₆	—	2	2	no	—
305	C₂×D₈	—	2	2	no	—
306	C₂×D₈	—	2	2	no	—
307	C₂²×C₈	—	2	1	no	—
308	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
309	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
310	#127	C₂³×C₁₉	1	1	yes	characteristic
311	#127	C₂³×C₁₉	1	1	yes	characteristic
312	#126	—	2	4	no	—
313	#125	—	2	2	no	—
314	#124	—	2	2	no	—
315	#124	—	2	1	no	—
316	#124	D₄×C₁₉	1	2	yes	—
317	#123	—	2	2	no	—
318	#123	—	2	4	no	—
319	#123	—	2	2	no	—
320	C₂²⋊Q₈	—	2	4	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	#121	—	2	4	no	—
323	#121	—	2	2	no	—
324	#121	—	2	2	no	—
325	#121	—	2	2	no	—
326	#120	—	2	2	no	—
327	#120	—	2	2	no	—
328	C₄×Q₈	D₄×C₁₉	1	2	yes	—
329	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
330	C₄×D₄	—	2	4	no	—
331	C₄×D₄	—	2	4	no	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	—	2	2	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	D₄×C₁₉	1	2	yes	—
339	C₄×D₄	C₂³×C₁₉	1	2	yes	—
340	#117	—	2	2	no	—
341	#117	—	2	2	no	—
342	#117	D₄×C₁₉	1	2	yes	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	4	no	—
345	C₂×C₄²	—	2	2	no	—
346	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
347	#107	—	2	2	no	—
348	#106	—	2	2	no	—
349	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
350	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
351	#103	—	2	2	no	—
352	#102	—	2	2	no	—
353	#102	—	2	2	no	—
354	#102	—	2	2	no	—
355	C₂²⋊C₈	—	2	2	no	—
356	C₄×C₈	—	2	1	no	—
357	C₄×C₈	—	2	2	no	—
358	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
359	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
360	C₁₉	#18480	1	1	yes	characteristic, direct product factor, Sylow
361	C₂⁴	—	2	2	no	—
362	#41	—	2	4	no	—
363	#41	—	4	2	no	—
364	#41	—	4	4	no	—
365	#41	—	4	4	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
368	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	—	4	4	no	—
377	C₂×D₄	—	4	1	no	—
378	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
379	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	—	8	4	no	—
388	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
390	Q₁₆	—	4	4	no	—
391	SD₁₆	—	4	4	no	—
392	SD₁₆	—	4	4	no	—
393	SD₁₆	—	4	4	no	—
394	D₈	—	4	4	no	—
395	D₈	—	4	4	no	—
396	C₂×C₈	—	2	4	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
408	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	C₂×D₄×C₁₉	1	2	yes	—
422	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	4	8	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	8	2	no	—
429	C₂³	C₁₉×#120	1	1	yes	characteristic
430	Q₈	—	2	2	no	—
431	Q₈	—	2	2	no	—
432	Q₈	—	4	2	no	—
433	Q₈	—	4	2	no	—
434	D₄	—	2	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	2	no	—
437	D₄	—	4	4	no	—
438	D₄	—	4	8	no	—
439	D₄	—	4	2	no	—
440	D₄	—	4	2	no	—
441	D₄	—	4	2	no	—
442	D₄	—	4	2	no	—
443	D₄	—	8	2	no	—
444	D₄	—	8	2	no	—
445	D₄	C₁₉×#135	1	4	yes	complemented
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	8	2	no	—
460	C₂×C₄	—	8	4	no	—
461	C₂×C₄	—	8	2	no	—
462	C₂×C₄	C₁₉×#120	1	2	yes	—
463	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
466	C₈	—	2	2	no	—
467	C₈	—	2	2	no	—
468	C₈	—	4	2	no	—
469	C₈	—	4	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	8	8	no	—
478	C₂²	—	8	2	no	—
479	C₂²	—	8	1	no	—
480	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
481	C₄	—	2	2	no	—
482	C₄	—	2	1	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	8	1	no	—
488	C₄	C₁₉×#453	1	2	yes	—
489	C₄	C₂×C₁₉×#135	1	2	yes	—
490	C₄	C₁₉×#575	1	2	yes	—
491	C₂	—	4	1	no	—
492	C₂	—	4	4	no	—
493	C₂	—	8	2	no	—
494	C₂	—	16	1	no	—
495	C₂	C₁₉×#3002	1	2	yes	—
496	C₂	C₂×C₁₉×#453	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×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×#3147	C₂	semidirect
3. C₁₉×#3106	C₂	semidirect
4. C₁₉×#1632	C₂	semidirect
5. C₁₉×#1630	C₂	semidirect
6. C₁₉×#1629	C₂	semidirect
7. C₁₉×#1622	C₂	semidirect
8. C₁₉×#1620	C₂	semidirect
9. C₁₉×#1619	C₂	semidirect
10. C₁₉×#1543	C₂	semidirect
11. C₁₉×#1476	C₂	semidirect
20. C₁₉×#532	C₂²	semidirect
26. C₁₉×#494	C₂²	semidirect
29. C₁₉×#492	C₂²	semidirect
31. C₁₉×#477	C₂²	semidirect
33. C₁₉×#460	C₂²	semidirect
38. C₁₉×#431	C₂²	semidirect
39. C₂×C₄×C₈×C₁₉	C₂²	semidirect
40. C₁₉×#333	C₂²	semidirect
43. C₁₉×Q₈⋊C₈	C₂²	semidirect
44. C₁₉×Q₈⋊C₈	C₂²	semidirect
175. #18480	C₁₉	direct (N × H)
197. D₄×C₁₉	#135	semidirect
222. #3481	C₂×C₁₉	semidirect
223. #3147	C₂×C₁₉	semidirect
224. #3106	C₂×C₁₉	semidirect
225. #1632	C₂×C₁₉	semidirect
226. #1630	C₂×C₁₉	semidirect
227. #1629	C₂×C₁₉	semidirect
228. #1622	C₂×C₁₉	semidirect
229. #1620	C₂×C₁₉	semidirect
230. #1619	C₂×C₁₉	semidirect
231. #1543	C₂×C₁₉	semidirect
232. #1476	C₂×C₁₉	semidirect
262. #532	C₂²×C₁₉	semidirect
268. #494	C₂²×C₁₉	semidirect
271. #492	C₂²×C₁₉	semidirect
273. #477	C₂²×C₁₉	semidirect
275. #460	C₂²×C₁₉	semidirect
280. #431	C₂²×C₁₉	semidirect
281. C₂×C₄×C₈	C₂²×C₁₉	semidirect
282. #333	C₂²×C₁₉	semidirect
285. Q₈⋊C₈	C₂²×C₁₉	semidirect
286. Q₈⋊C₈	C₂²×C₁₉	semidirect
360. C₁₉	#18480	direct (N × H)
445. D₄	C₁₉×#135	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×#3147	2
C₁₉×#3106	2
C₁₉×#1632	2
C₁₉×#1630	2
C₁₉×#1629	2
C₁₉×#1622	2
C₁₉×#1620	2
C₁₉×#1619	2
C₁₉×#1543	2
C₁₉×#1476	2
#18480	19

Subgroups — C19×#18480 #18024439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18480 #18024439