Subgroups — C₁₉×#12781 #18018740

Order 4864.

758 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	C₁₉×#3545	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2133	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#355	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1912	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1888	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#563	C₄	1	1	yes	characteristic, complemented
7	C₁₉×#562	—	2	1	no	—
8	C₁₉×H(3,𝔽₄)	C₄	1	1	yes	characteristic, complemented
9	C₁₉×#555	C₄	1	2	yes	complemented
10	C₁₉×#551	—	2	1	no	—
11	C₁₉×#551	—	2	2	no	—
12	C₁₉×#546	—	2	2	no	—
13	C₁₉×#542	—	2	2	no	—
14	C₁₉×#538	—	2	2	no	—
15	C₁₉×#536	C₂²	1	2	yes	—
16	C₁₉×#534	—	2	1	no	—
17	C₁₉×#529	—	2	1	no	—
18	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
19	C₁₉×#519	C₂²	1	1	yes	characteristic, complemented
20	C₁₉×#421	—	2	2	no	—
21	C₁₉×#418	—	2	1	no	—
22	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₉×#101	C₂²	1	2	yes	complemented
24	C₁₉×#356	—	2	2	no	—
25	C₁₉×#355	—	2	1	no	—
26	C₁₉×#355	—	2	1	no	—
27	C₁₉×#355	—	2	2	no	—
28	C₁₉×#339	—	2	1	no	—
29	C₁₉×H(3,ℤ/4)	—	2	2	no	—
30	C₂×#41×C₁₉	D₄	1	2	yes	—
31	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	2	no	—
36	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
37	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
38	C₁₉×#126	—	2	2	no	—
39	C₁₉×#126	—	2	2	no	—
40	C₁₉×#126	—	2	2	no	—
41	C₁₉×#125	—	2	1	no	—
42	C₁₉×#124	—	2	2	no	—
43	C₁₉×#124	—	2	2	no	—
44	C₁₉×#124	—	2	1	no	—
45	C₁₉×#124	—	2	2	no	—
46	C₁₉×#124	C₂×C₄	1	1	yes	characteristic
47	C₁₉×#124	C₂×C₄	1	1	yes	characteristic
48	C₁₉×#124	C₂×C₄	1	2	yes	—
49	C₁₉×#124	D₄	1	1	yes	characteristic
50	C₁₉×#124	D₄	1	1	yes	characteristic
51	C₁₉×#124	D₄	1	2	yes	—
52	C₁₉×#123	—	2	1	no	—
53	C₁₉×#123	—	2	2	no	—
54	C₁₉×#123	—	2	2	no	—
55	C₁₉×#123	—	2	2	no	—
56	C₁₉×#123	—	2	1	no	—
57	C₁₉×#123	—	2	2	no	—
58	C₁₉×#123	—	2	2	no	—
59	C₁₉×C₂²⋊Q₈	—	2	1	no	—
60	C₁₉×C₂²⋊Q₈	—	2	2	no	—
61	C₁₉×C₂²⋊Q₈	—	2	2	no	—
62	C₁₉×C₂²⋊Q₈	—	2	2	no	—
63	C₁₉×C₂²⋊Q₈	—	2	2	no	—
64	C₁₉×#121	—	2	1	no	—
65	C₁₉×#121	—	2	2	no	—
66	C₁₉×#121	—	2	2	no	—
67	C₁₉×#121	—	2	2	no	—
68	C₁₉×#121	—	2	2	no	—
69	C₁₉×#120	—	2	1	no	—
70	C₁₉×#120	—	2	2	no	—
71	C₁₉×#120	—	2	1	no	—
72	C₁₉×#120	—	2	2	no	—
73	C₄×Q₈×C₁₉	—	2	1	no	—
74	C₄×Q₈×C₁₉	—	4	2	no	—
75	C₄×D₄×C₁₉	—	2	1	no	—
76	C₄×D₄×C₁₉	—	2	2	no	—
77	C₄×D₄×C₁₉	—	2	2	no	—
78	C₄×D₄×C₁₉	—	2	2	no	—
79	C₁₉×#117	—	2	2	no	—
80	C₁₉×#117	—	2	2	no	—
81	C₁₉×#117	—	2	2	no	—
82	C₁₉×#117	—	2	1	no	—
83	C₁₉×#117	D₄	1	2	yes	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
87	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
88	C₁₉×#104	—	4	4	no	—
89	C₁₉×#102	—	4	2	no	—
90	C₁₉×#101	—	2	2	no	—
91	C₁₉×#101	—	2	2	no	—
92	C₁₉×#101	—	2	2	no	—
93	C₂⁴×C₁₉	—	2	1	no	—
94	C₂⁴×C₁₉	—	2	1	no	—
95	#41×C₁₉	—	4	2	no	—
96	#41×C₁₉	—	4	2	no	—
97	C₂×Q₈×C₁₉	—	2	1	no	—
98	C₂×Q₈×C₁₉	—	4	1	no	—
99	C₂×Q₈×C₁₉	—	4	1	no	—
100	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
101	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
102	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	—	4	1	no	—
111	C₂×D₄×C₁₉	—	4	1	no	—
112	C₂×D₄×C₁₉	—	8	1	no	—
113	C₂×D₄×C₁₉	—	8	1	no	—
114	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
115	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	M₁₆×C₁₉	—	4	1	no	—
125	M₁₆×C₁₉	—	4	2	no	—
126	M₁₆×C₁₉	—	4	1	no	—
127	M₁₆×C₁₉	—	4	2	no	—
128	C₂×C₈×C₁₉	—	4	2	no	—
129	C₂×C₈×C₁₉	—	4	1	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	2	1	no	—
134	C₄⋊C₄×C₁₉	—	2	2	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	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	4	2	no	—
141	C₂²⋊C₄×C₁₉	—	2	2	no	—
142	C₂²⋊C₄×C₁₉	—	2	2	no	—
143	C₂²⋊C₄×C₁₉	—	2	1	no	—
144	C₂²⋊C₄×C₁₉	—	2	1	no	—
145	C₂²⋊C₄×C₁₉	—	2	2	no	—
146	C₂²⋊C₄×C₁₉	—	2	2	no	—
147	C₂²⋊C₄×C₁₉	—	2	2	no	—
148	C₂²⋊C₄×C₁₉	—	2	2	no	—
149	C₂²⋊C₄×C₁₉	—	2	2	no	—
150	C₂²⋊C₄×C₁₉	—	2	2	no	—
151	C₂²⋊C₄×C₁₉	—	2	2	no	—
152	C₂²⋊C₄×C₁₉	—	2	2	no	—
153	C₂²⋊C₄×C₁₉	—	2	2	no	—
154	C₂²⋊C₄×C₁₉	—	2	2	no	—
155	C₂²⋊C₄×C₁₉	—	2	2	no	—
156	C₂²⋊C₄×C₁₉	—	4	1	no	—
157	C₄²×C₁₉	—	2	2	no	—
158	C₄²×C₁₉	—	2	1	no	—
159	C₄²×C₁₉	—	2	4	no	—
160	C₄²×C₁₉	—	4	1	no	—
161	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
162	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
163	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
164	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
165	#12781	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₁₉	—	2	1	no	—
167	C₂³×C₁₉	—	2	1	no	—
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	4	1	no	—
170	C₂³×C₁₉	—	4	1	no	—
171	C₂³×C₁₉	—	8	1	no	—
172	C₂³×C₁₉	—	8	2	no	—
173	C₂³×C₁₉	—	8	2	no	—
174	C₂³×C₁₉	#120	1	1	yes	characteristic
175	Q₈×C₁₉	—	4	1	no	—
176	Q₈×C₁₉	—	4	1	no	—
177	Q₈×C₁₉	—	4	2	no	—
178	Q₈×C₁₉	—	4	2	no	—
179	Q₈×C₁₉	—	8	1	no	—
180	D₄×C₁₉	—	4	1	no	—
181	D₄×C₁₉	—	4	1	no	—
182	D₄×C₁₉	—	4	2	no	—
183	D₄×C₁₉	—	4	2	no	—
184	D₄×C₁₉	—	4	2	no	—
185	D₄×C₁₉	—	8	1	no	—
186	D₄×C₁₉	—	8	2	no	—
187	D₄×C₁₉	—	8	2	no	—
188	D₄×C₁₉	—	8	1	no	—
189	D₄×C₁₉	—	8	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	—	2	1	no	—
194	C₂×C₄×C₁₉	—	2	1	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	8	2	no	—
201	C₂×C₄×C₁₉	—	8	2	no	—
202	C₂×C₄×C₁₉	—	8	1	no	—
203	C₂×C₄×C₁₉	—	8	2	no	—
204	C₂×C₄×C₁₉	—	8	1	no	—
205	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
206	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
208	C₂×C₄×C₁₉	#120	1	2	yes	—
209	C₈×C₁₉	—	8	2	no	—
210	C₈×C₁₉	—	8	1	no	—
211	#3545	C₂×C₁₉	1	1	yes	characteristic
212	#2133	C₂×C₁₉	1	2	yes	complemented
213	C₂×#355	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#1912	C₂×C₁₉	1	2	yes	complemented
215	#1888	C₂×C₁₉	1	1	yes	characteristic, complemented
216	C₂²×C₁₉	—	4	1	no	—
217	C₂²×C₁₉	—	4	2	no	—
218	C₂²×C₁₉	—	4	2	no	—
219	C₂²×C₁₉	—	4	2	no	—
220	C₂²×C₁₉	—	4	2	no	—
221	C₂²×C₁₉	—	4	2	no	—
222	C₂²×C₁₉	—	4	1	no	—
223	C₂²×C₁₉	—	4	1	no	—
224	C₂²×C₁₉	—	16	1	no	—
225	C₂²×C₁₉	—	16	1	no	—
226	C₂²×C₁₉	—	16	2	no	—
227	C₂²×C₁₉	#379	1	1	yes	characteristic
228	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
229	C₂²×C₁₉	#458	1	1	yes	characteristic
230	C₄×C₁₉	—	2	2	no	—
231	C₄×C₁₉	—	2	1	no	—
232	C₄×C₁₉	—	2	1	no	—
233	C₄×C₁₉	—	2	2	no	—
234	C₄×C₁₉	—	4	1	no	—
235	C₄×C₁₉	—	4	2	no	—
236	C₄×C₁₉	—	4	2	no	—
237	C₄×C₁₉	—	4	1	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	8	2	no	—
240	#563	C₄×C₁₉	1	1	yes	characteristic, complemented
241	#562	—	2	1	no	—
242	H(3,𝔽₄)	C₄×C₁₉	1	1	yes	characteristic, complemented
243	#555	C₄×C₁₉	1	2	yes	complemented
244	#551	—	2	1	no	—
245	#551	—	2	2	no	—
246	#546	—	2	2	no	—
247	#542	—	2	2	no	—
248	#538	—	2	2	no	—
249	#536	C₂²×C₁₉	1	2	yes	—
250	#534	—	2	1	no	—
251	#529	—	2	1	no	—
252	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
253	#519	C₂²×C₁₉	1	1	yes	characteristic, complemented
254	#421	—	2	2	no	—
255	#418	—	2	1	no	—
256	C₂×#101	C₂²×C₁₉	1	2	yes	complemented
257	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic, complemented
258	#356	—	2	2	no	—
259	#355	—	2	1	no	—
260	#355	—	2	1	no	—
261	#355	—	2	2	no	—
262	#339	—	2	1	no	—
263	H(3,ℤ/4)	—	2	2	no	—
264	C₂×C₁₉	—	2	1	no	—
265	C₂×C₁₉	—	2	1	no	—
266	C₂×C₁₉	—	2	1	no	—
267	C₂×C₁₉	—	8	1	no	—
268	C₂×C₁₉	—	8	2	no	—
269	C₂×C₁₉	—	8	1	no	—
270	C₂×C₁₉	#1790	1	1	yes	characteristic
271	C₂×#41	D₄×C₁₉	1	2	yes	—
272	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
273	C₂²×D₄	—	2	1	no	—
274	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
275	C₂×M₁₆	—	2	2	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
278	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
279	#126	—	2	2	no	—
280	#126	—	2	2	no	—
281	#126	—	2	2	no	—
282	#125	—	2	1	no	—
283	#124	—	2	2	no	—
284	#124	—	2	2	no	—
285	#124	—	2	1	no	—
286	#124	—	2	2	no	—
287	#124	C₂×C₄×C₁₉	1	1	yes	characteristic
288	#124	C₂×C₄×C₁₉	1	1	yes	characteristic
289	#124	C₂×C₄×C₁₉	1	2	yes	—
290	#124	D₄×C₁₉	1	1	yes	characteristic
291	#124	D₄×C₁₉	1	1	yes	characteristic
292	#124	D₄×C₁₉	1	2	yes	—
293	#123	—	2	1	no	—
294	#123	—	2	2	no	—
295	#123	—	2	2	no	—
296	#123	—	2	2	no	—
297	#123	—	2	1	no	—
298	#123	—	2	2	no	—
299	#123	—	2	2	no	—
300	C₂²⋊Q₈	—	2	1	no	—
301	C₂²⋊Q₈	—	2	2	no	—
302	C₂²⋊Q₈	—	2	2	no	—
303	C₂²⋊Q₈	—	2	2	no	—
304	C₂²⋊Q₈	—	2	2	no	—
305	#121	—	2	1	no	—
306	#121	—	2	2	no	—
307	#121	—	2	2	no	—
308	#121	—	2	2	no	—
309	#121	—	2	2	no	—
310	#120	—	2	1	no	—
311	#120	—	2	2	no	—
312	#120	—	2	1	no	—
313	#120	—	2	2	no	—
314	C₄×Q₈	—	2	1	no	—
315	C₄×Q₈	—	4	2	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	2	no	—
318	C₄×D₄	—	2	2	no	—
319	C₄×D₄	—	2	2	no	—
320	#117	—	2	2	no	—
321	#117	—	2	2	no	—
322	#117	—	2	2	no	—
323	#117	—	2	1	no	—
324	#117	D₄×C₁₉	1	2	yes	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
329	#104	—	4	4	no	—
330	#102	—	4	2	no	—
331	#101	—	2	2	no	—
332	#101	—	2	2	no	—
333	#101	—	2	2	no	—
334	C₁₉	#12781	1	1	yes	characteristic, direct product factor, Sylow
335	C₂⁴	—	2	1	no	—
336	C₂⁴	—	2	1	no	—
337	#41	—	4	2	no	—
338	#41	—	4	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	4	1	no	—
341	C₂×Q₈	—	4	1	no	—
342	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
343	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
344	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
345	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	4	1	no	—
353	C₂×D₄	—	4	1	no	—
354	C₂×D₄	—	8	1	no	—
355	C₂×D₄	—	8	1	no	—
356	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
357	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
358	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
366	M₁₆	—	4	2	no	—
367	M₁₆	—	4	1	no	—
368	M₁₆	—	4	1	no	—
369	M₁₆	—	4	2	no	—
370	C₂×C₈	—	4	1	no	—
371	C₂×C₈	—	4	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	4	1	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	2	4	no	—
402	C₄²	—	4	1	no	—
403	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
404	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
405	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
406	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	4	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	8	1	no	—
413	C₂³	—	8	2	no	—
414	C₂³	—	8	2	no	—
415	C₂³	C₁₉×#120	1	1	yes	characteristic
416	Q₈	—	4	1	no	—
417	Q₈	—	4	1	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	8	1	no	—
421	D₄	—	4	1	no	—
422	D₄	—	4	1	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	2	no	—
426	D₄	—	8	1	no	—
427	D₄	—	8	2	no	—
428	D₄	—	8	2	no	—
429	D₄	—	8	2	no	—
430	D₄	—	8	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	8	2	no	—
442	C₂×C₄	—	8	1	no	—
443	C₂×C₄	—	8	2	no	—
444	C₂×C₄	—	8	1	no	—
445	C₂×C₄	—	8	2	no	—
446	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
447	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
448	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
449	C₂×C₄	C₁₉×#120	1	2	yes	—
450	C₈	—	8	2	no	—
451	C₈	—	8	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	4	1	no	—
460	C₂²	—	16	1	no	—
461	C₂²	—	16	1	no	—
462	C₂²	—	16	2	no	—
463	C₂²	C₁₉×#379	1	1	yes	characteristic
464	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
465	C₂²	C₁₉×#458	1	1	yes	characteristic
466	C₄	—	2	2	no	—
467	C₄	—	2	1	no	—
468	C₄	—	2	1	no	—
469	C₄	—	2	2	no	—
470	C₄	—	4	1	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	2	no	—
475	C₄	—	8	2	no	—
476	C₂	—	2	1	no	—
477	C₂	—	2	1	no	—
478	C₂	—	2	1	no	—
479	C₂	—	8	1	no	—
480	C₂	—	8	1	no	—
481	C₂	—	8	2	no	—
482	C₂	C₁₉×#1790	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#1790
commutator	C₂×Q₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×Q₈	C₂³×C₁₉
prime radical	C₁₉×#3545	C₂
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2133	C₂	semidirect
3. C₂×C₁₉×#355	C₂	semidirect
4. C₁₉×#1912	C₂	semidirect
5. C₁₉×#1888	C₂	semidirect
6. C₁₉×#563	C₄	semidirect
8. C₁₉×H(3,𝔽₄)	C₄	semidirect
9. C₁₉×#555	C₄	semidirect
19. C₁₉×#519	C₂²	semidirect
22. C₂×C₁₉×#101	C₂²	semidirect
23. C₂×C₁₉×#101	C₂²	semidirect
165. #12781	C₁₉	direct (N × H)
212. #2133	C₂×C₁₉	semidirect
213. C₂×#355	C₂×C₁₉	semidirect
214. #1912	C₂×C₁₉	semidirect
215. #1888	C₂×C₁₉	semidirect
240. #563	C₄×C₁₉	semidirect
242. H(3,𝔽₄)	C₄×C₁₉	semidirect
243. #555	C₄×C₁₉	semidirect
253. #519	C₂²×C₁₉	semidirect
256. C₂×#101	C₂²×C₁₉	semidirect
257. C₂×#101	C₂²×C₁₉	semidirect
334. C₁₉	#12781	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3545	2
C₁₉×#2133	2
C₂×C₁₉×#355	2
C₁₉×#1912	2
C₁₉×#1888	2
#12781	19

Subgroups — C19×#12781 #18018740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12781 #18018740