Subgroups — C₁₉×#62326 #18068285

Order 4864.

1892 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3549	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3340	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3329	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3324	C₂	1	4	yes	maximal, complemented
6	D₄×SD₁₆×C₁₉	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3254	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3200	C₂	1	4	yes	maximal, complemented
9	C₁₉×#3167	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3057	C₂	1	4	yes	maximal, complemented
11	C₁₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₉	C₂²	1	4	yes	complemented
13	C₂×C₁₉×#131	C₂²	1	2	yes	complemented
14	C₁₉×#563	—	2	2	no	—
15	C₁₉×H(3,𝔽₄)	—	2	2	no	—
16	C₁₉×#559	—	2	1	no	—
17	Q₈²×C₁₉	—	2	1	no	—
18	C₁₉×#556	C₂²	1	4	yes	complemented
19	C₁₉×#555	—	2	1	no	—
20	C₁₉×#555	C₂²	1	4	yes	—
21	D₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
22	D₄²×C₁₉	—	2	1	no	—
23	D₄²×C₁₉	C₂²	1	4	yes	—
24	C₁₉×#542	—	2	4	no	—
25	C₁₉×#536	C₂²	1	4	yes	complemented
26	C₁₉×#535	—	2	4	no	—
27	C₁₉×#535	C₂²	1	4	yes	—
28	C₁₉×#533	C₂²	1	2	yes	complemented
29	C₁₉×#532	C₂²	1	2	yes	—
30	C₁₉×#532	C₂²	1	1	yes	characteristic
31	C₁₉×#498	C₂²	1	2	yes	complemented
32	C₁₉×#492	C₂²	1	2	yes	—
33	C₁₉×#487	C₂²	1	2	yes	complemented
34	C₁₉×#486	C₂²	1	2	yes	—
35	C₁₉×#485	C₂²	1	8	yes	complemented
36	C₁₉×#482	C₂²	1	8	yes	complemented
37	C₁₉×#477	C₂²	1	4	yes	complemented
38	C₁₉×#474	C₂²	1	4	yes	complemented
39	C₁₉×#468	C₂²	1	8	yes	complemented
40	C₁₉×#468	C₂²	1	8	yes	complemented
41	C₁₉×#465	C₂²	1	4	yes	complemented
42	C₁₉×#465	C₂²	1	4	yes	complemented
43	C₁₉×#465	C₂²	1	8	yes	complemented
44	C₁₉×#461	C₂²	1	4	yes	complemented
45	C₁₉×#460	C₂²	1	4	yes	—
46	C₁₉×#450	C₂²	1	8	yes	complemented
47	C₁₉×#448	C₂²	1	8	yes	complemented
48	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	complemented
49	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	complemented
50	C₁₉×#436	C₂²	1	4	yes	complemented
51	C₈×D₄×C₁₉	C₂²	1	4	yes	complemented
52	C₁₉×#427	C₂²	1	4	yes	complemented
53	C₁₉×#423	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#419	C₂²	1	4	yes	complemented
55	C₁₉×#418	C₂²	1	4	yes	complemented
56	C₁₉×#408	C₂²	1	2	yes	complemented
57	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
58	C₂×#41×C₁₉	—	2	2	no	—
59	C₂×#41×C₁₉	C₂³	1	2	yes	—
60	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
61	C₂²×D₄×C₁₉	—	2	4	no	—
62	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
63	C₂×SD₁₆×C₁₉	—	4	8	no	—
64	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
65	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
66	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	—
67	C₁₉×#131	—	4	4	no	—
68	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
69	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
70	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×C₄⋊Q₈	—	2	4	no	—
74	C₁₉×C₄⋊Q₈	—	2	4	no	—
75	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
76	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
77	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
78	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
79	C₁₉×#127	—	2	4	no	—
80	C₁₉×#127	D₄	1	1	yes	characteristic
81	C₁₉×#127	C₂³	1	2	yes	—
82	C₁₉×#126	—	2	8	no	—
83	C₁₉×#125	—	2	2	no	—
84	C₁₉×#124	—	2	4	no	—
85	C₁₉×#124	—	2	4	no	—
86	C₁₉×#124	—	2	4	no	—
87	C₁₉×#124	—	2	8	no	—
88	C₁₉×#124	—	2	2	no	—
89	C₁₉×#124	D₄	1	2	yes	—
90	C₁₉×#123	—	2	4	no	—
91	C₁₉×#123	—	2	4	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	no	—
93	C₁₉×C₂²⋊Q₈	—	2	8	no	—
94	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
95	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
96	C₁₉×#121	—	2	4	no	—
97	C₁₉×#121	—	2	2	no	—
98	C₁₉×#121	—	2	4	no	—
99	C₁₉×#121	D₄	1	4	yes	—
100	C₁₉×#121	C₂³	1	8	yes	—
101	C₁₉×#121	C₂³	1	4	yes	—
102	C₁₉×#120	—	2	4	no	—
103	C₁₉×#120	—	2	4	no	—
104	C₁₉×#120	—	2	8	no	—
105	C₄×Q₈×C₁₉	—	2	4	no	—
106	C₄×Q₈×C₁₉	—	2	2	no	—
107	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
108	C₄×D₄×C₁₉	—	2	4	no	—
109	C₄×D₄×C₁₉	—	2	2	no	—
110	C₄×D₄×C₁₉	C₂³	1	4	yes	—
111	C₄×D₄×C₁₉	C₂³	1	4	yes	—
112	C₁₉×#117	—	2	2	no	—
113	C₁₉×#117	—	2	4	no	—
114	C₁₉×#117	C₂³	1	4	yes	—
115	C₁₉×#117	C₂³	1	4	yes	—
116	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
117	C₁₉×#107	C₂³	1	8	yes	—
118	C₁₉×#106	C₂³	1	4	yes	—
119	C₁₉×#106	C₂³	1	4	yes	—
120	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
121	C₁₉×#103	C₂³	1	4	yes	—
122	C₁₉×#103	C₂³	1	8	yes	—
123	C₁₉×#103	C₂³	1	4	yes	—
124	C₁₉×#102	C₂³	1	4	yes	—
125	C₁₉×#102	C₂³	1	8	yes	—
126	C₁₉×#102	C₂³	1	4	yes	—
127	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
128	C₄×C₈×C₁₉	C₂³	1	2	yes	—
129	C₄×C₈×C₁₉	C₂³	1	2	yes	—
130	C₂⁴×C₁₉	—	2	4	no	—
131	#41×C₁₉	—	4	2	no	—
132	#41×C₁₉	—	4	2	no	—
133	#41×C₁₉	—	8	4	no	—
134	C₂×Q₈×C₁₉	—	2	2	no	—
135	C₂×Q₈×C₁₉	—	2	4	no	—
136	C₂×Q₈×C₁₉	—	2	2	no	—
137	C₂×Q₈×C₁₉	—	4	4	no	—
138	C₂×Q₈×C₁₉	—	4	4	no	—
139	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
140	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
141	C₂×D₄×C₁₉	—	2	8	no	—
142	C₂×D₄×C₁₉	—	2	4	no	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	2	4	no	—
146	C₂×D₄×C₁₉	—	4	4	no	—
147	C₂×D₄×C₁₉	—	4	4	no	—
148	C₂×D₄×C₁₉	—	8	8	no	—
149	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
150	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
151	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
152	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₉	—	2	4	no	—
154	C₂²×C₄×C₁₉	—	2	4	no	—
155	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
158	SD₁₆×C₁₉	—	2	8	no	—
159	SD₁₆×C₁₉	—	4	8	no	—
160	SD₁₆×C₁₉	—	4	4	no	—
161	M₁₆×C₁₉	—	4	4	no	—
162	M₁₆×C₁₉	—	4	2	no	—
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	8	no	—
165	C₂×C₈×C₁₉	—	4	1	no	—
166	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
167	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
168	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
169	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	2	2	no	—
174	C₄⋊C₄×C₁₉	—	2	8	no	—
175	C₄⋊C₄×C₁₉	—	2	4	no	—
176	C₄⋊C₄×C₁₉	—	2	4	no	—
177	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
178	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
179	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
180	C₂²⋊C₄×C₁₉	—	2	4	no	—
181	C₂²⋊C₄×C₁₉	—	2	4	no	—
182	C₂²⋊C₄×C₁₉	—	2	4	no	—
183	C₂²⋊C₄×C₁₉	—	2	8	no	—
184	C₂²⋊C₄×C₁₉	—	2	8	no	—
185	C₂²⋊C₄×C₁₉	—	2	4	no	—
186	C₂²⋊C₄×C₁₉	—	2	4	no	—
187	C₂²⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
188	C₄²×C₁₉	—	2	4	no	—
189	C₄²×C₁₉	—	2	4	no	—
190	C₄²×C₁₉	—	2	4	no	—
191	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₁₉	C₂⁴	1	2	yes	—
194	#62326	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂³×C₁₉	—	2	4	no	—
196	C₂³×C₁₉	—	8	4	no	—
197	C₂³×C₁₉	—	8	8	no	—
198	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
199	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₁₉	—	2	4	no	—
201	Q₈×C₁₉	—	2	4	no	—
202	Q₈×C₁₉	—	4	2	no	—
203	Q₈×C₁₉	—	4	4	no	—
204	Q₈×C₁₉	—	8	4	no	—
205	Q₈×C₁₉	—	8	2	no	—
206	D₄×C₁₉	—	2	8	no	—
207	D₄×C₁₉	—	2	4	no	—
208	D₄×C₁₉	—	2	4	no	—
209	D₄×C₁₉	—	4	2	no	—
210	D₄×C₁₉	—	4	4	no	—
211	D₄×C₁₉	—	4	4	no	—
212	D₄×C₁₉	—	8	4	no	—
213	D₄×C₁₉	—	8	2	no	—
214	D₄×C₁₉	—	8	8	no	—
215	D₄×C₁₉	—	8	4	no	—
216	C₂×C₄×C₁₉	—	2	4	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	4	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	4	no	—
221	C₂×C₄×C₁₉	—	2	4	no	—
222	C₂×C₄×C₁₉	—	2	4	no	—
223	C₂×C₄×C₁₉	—	2	4	no	—
224	C₂×C₄×C₁₉	—	4	8	no	—
225	C₂×C₄×C₁₉	—	8	4	no	—
226	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
227	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
231	C₈×C₁₉	—	2	1	no	—
232	C₈×C₁₉	—	2	4	no	—
233	C₈×C₁₉	—	2	2	no	—
234	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
235	#3550	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#3549	C₂×C₁₉	1	1	yes	characteristic
237	#3340	C₂×C₁₉	1	4	yes	complemented
238	#3329	C₂×C₁₉	1	4	yes	complemented
239	#3324	C₂×C₁₉	1	4	yes	complemented
240	D₄×SD₁₆	C₂×C₁₉	1	4	yes	complemented
241	#3254	C₂×C₁₉	1	2	yes	complemented
242	#3200	C₂×C₁₉	1	4	yes	complemented
243	#3167	C₂×C₁₉	1	2	yes	complemented
244	#3057	C₂×C₁₉	1	4	yes	complemented
245	#2931	C₂×C₁₉	1	1	yes	characteristic, complemented
246	C₂²×C₁₉	—	2	4	no	—
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	2	2	no	—
249	C₂²×C₁₉	—	2	8	no	—
250	C₂²×C₁₉	—	4	4	no	—
251	C₂²×C₁₉	—	4	4	no	—
252	C₂²×C₁₉	—	4	4	no	—
253	C₂²×C₁₉	—	16	8	no	—
254	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
255	C₄×C₁₉	—	2	1	no	—
256	C₄×C₁₉	—	2	4	no	—
257	C₄×C₁₉	—	2	2	no	—
258	C₄×C₁₉	—	4	4	no	—
259	C₄×C₁₉	—	4	4	no	—
260	C₄×C₁₉	—	4	4	no	—
261	C₄×C₁₉	#577	1	4	yes	—
262	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
263	C₄×C₁₉	#585	1	1	yes	characteristic
264	C₂²×SD₁₆	C₂²×C₁₉	1	4	yes	complemented
265	C₂×#131	C₂²×C₁₉	1	2	yes	complemented
266	#563	—	2	2	no	—
267	H(3,𝔽₄)	—	2	2	no	—
268	#559	—	2	1	no	—
269	Q₈²	—	2	1	no	—
270	#556	C₂²×C₁₉	1	4	yes	complemented
271	#555	—	2	1	no	—
272	#555	C₂²×C₁₉	1	4	yes	—
273	D₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
274	D₄²	—	2	1	no	—
275	D₄²	C₂²×C₁₉	1	4	yes	—
276	#542	—	2	4	no	—
277	#536	C₂²×C₁₉	1	4	yes	complemented
278	#535	—	2	4	no	—
279	#535	C₂²×C₁₉	1	4	yes	—
280	#533	C₂²×C₁₉	1	2	yes	complemented
281	#532	C₂²×C₁₉	1	2	yes	—
282	#532	C₂²×C₁₉	1	1	yes	characteristic
283	#498	C₂²×C₁₉	1	2	yes	complemented
284	#492	C₂²×C₁₉	1	2	yes	—
285	#487	C₂²×C₁₉	1	2	yes	complemented
286	#486	C₂²×C₁₉	1	2	yes	—
287	#485	C₂²×C₁₉	1	8	yes	complemented
288	#482	C₂²×C₁₉	1	8	yes	complemented
289	#477	C₂²×C₁₉	1	4	yes	complemented
290	#474	C₂²×C₁₉	1	4	yes	complemented
291	#468	C₂²×C₁₉	1	8	yes	complemented
292	#468	C₂²×C₁₉	1	8	yes	complemented
293	#465	C₂²×C₁₉	1	8	yes	complemented
294	#465	C₂²×C₁₉	1	4	yes	complemented
295	#465	C₂²×C₁₉	1	4	yes	complemented
296	#461	C₂²×C₁₉	1	4	yes	complemented
297	#460	C₂²×C₁₉	1	4	yes	—
298	#450	C₂²×C₁₉	1	8	yes	complemented
299	#448	C₂²×C₁₉	1	8	yes	complemented
300	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	complemented
301	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	complemented
302	#436	C₂²×C₁₉	1	4	yes	complemented
303	C₈×D₄	C₂²×C₁₉	1	4	yes	complemented
304	#427	C₂²×C₁₉	1	4	yes	complemented
305	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
306	#419	C₂²×C₁₉	1	4	yes	complemented
307	#418	C₂²×C₁₉	1	4	yes	complemented
308	#408	C₂²×C₁₉	1	2	yes	complemented
309	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
310	C₂×C₁₉	—	4	1	no	—
311	C₂×C₁₉	—	4	4	no	—
312	C₂×C₁₉	—	8	4	no	—
313	C₂×C₁₉	#3496	1	1	yes	characteristic
314	C₂×C₁₉	C₂×#577	1	2	yes	—
315	C₂×#41	—	2	2	no	—
316	C₂×#41	C₂³×C₁₉	1	2	yes	—
317	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
318	C₂²×D₄	—	2	4	no	—
319	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
320	C₂×SD₁₆	—	4	8	no	—
321	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
322	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	—
323	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
324	#131	—	4	4	no	—
325	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
326	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
327	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
329	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
330	C₄⋊Q₈	—	2	4	no	—
331	C₄⋊Q₈	—	2	4	no	—
332	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
333	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
334	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
335	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
336	#127	—	2	4	no	—
337	#127	D₄×C₁₉	1	1	yes	characteristic
338	#127	C₂³×C₁₉	1	2	yes	—
339	#126	—	2	8	no	—
340	#125	—	2	2	no	—
341	#124	—	2	4	no	—
342	#124	—	2	4	no	—
343	#124	—	2	4	no	—
344	#124	—	2	8	no	—
345	#124	—	2	2	no	—
346	#124	D₄×C₁₉	1	2	yes	—
347	#123	—	2	4	no	—
348	#123	—	2	4	no	—
349	C₂²⋊Q₈	—	2	2	no	—
350	C₂²⋊Q₈	—	2	8	no	—
351	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
352	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
353	#121	—	2	4	no	—
354	#121	—	2	2	no	—
355	#121	—	2	4	no	—
356	#121	D₄×C₁₉	1	4	yes	—
357	#121	C₂³×C₁₉	1	4	yes	—
358	#121	C₂³×C₁₉	1	8	yes	—
359	#120	—	2	4	no	—
360	#120	—	2	4	no	—
361	#120	—	2	8	no	—
362	C₄×Q₈	—	2	4	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
365	C₄×D₄	—	2	4	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	C₂³×C₁₉	1	4	yes	—
368	C₄×D₄	C₂³×C₁₉	1	4	yes	—
369	#117	—	2	2	no	—
370	#117	—	2	4	no	—
371	#117	C₂³×C₁₉	1	4	yes	—
372	#117	C₂³×C₁₉	1	4	yes	—
373	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
374	#107	C₂³×C₁₉	1	8	yes	—
375	#106	C₂³×C₁₉	1	4	yes	—
376	#106	C₂³×C₁₉	1	4	yes	—
377	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
378	#103	C₂³×C₁₉	1	4	yes	—
379	#103	C₂³×C₁₉	1	8	yes	—
380	#103	C₂³×C₁₉	1	4	yes	—
381	#102	C₂³×C₁₉	1	4	yes	—
382	#102	C₂³×C₁₉	1	8	yes	—
383	#102	C₂³×C₁₉	1	4	yes	—
384	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
385	C₄×C₈	C₂³×C₁₉	1	2	yes	—
386	C₄×C₈	C₂³×C₁₉	1	2	yes	—
387	C₁₉	#62326	1	1	yes	characteristic, direct product factor, Sylow
388	C₂⁴	—	2	4	no	—
389	#41	—	4	2	no	—
390	#41	—	4	2	no	—
391	#41	—	8	4	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	4	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	4	4	no	—
396	C₂×Q₈	—	4	4	no	—
397	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
398	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
399	C₂×D₄	—	2	8	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	4	4	no	—
405	C₂×D₄	—	4	4	no	—
406	C₂×D₄	—	8	8	no	—
407	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
408	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
409	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
410	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
414	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
415	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
416	SD₁₆	—	2	8	no	—
417	SD₁₆	—	4	8	no	—
418	SD₁₆	—	4	4	no	—
419	M₁₆	—	4	4	no	—
420	M₁₆	—	4	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	8	no	—
423	C₂×C₈	—	4	1	no	—
424	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
425	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
426	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
427	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	8	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
436	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
437	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
438	C₂²⋊C₄	—	2	4	no	—
439	C₂²⋊C₄	—	2	4	no	—
440	C₂²⋊C₄	—	2	4	no	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₂²⋊C₄	—	2	8	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
446	C₄²	—	2	4	no	—
447	C₄²	—	2	4	no	—
448	C₄²	—	2	4	no	—
449	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₄²	C₂⁴×C₁₉	1	2	yes	—
452	C₂³	—	2	4	no	—
453	C₂³	—	8	4	no	—
454	C₂³	—	8	8	no	—
455	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
456	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
457	Q₈	—	2	4	no	—
458	Q₈	—	2	4	no	—
459	Q₈	—	4	2	no	—
460	Q₈	—	4	4	no	—
461	Q₈	—	8	4	no	—
462	Q₈	—	8	2	no	—
463	D₄	—	2	8	no	—
464	D₄	—	2	4	no	—
465	D₄	—	2	4	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	4	no	—
468	D₄	—	4	4	no	—
469	D₄	—	8	4	no	—
470	D₄	—	8	2	no	—
471	D₄	—	8	8	no	—
472	D₄	—	8	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	4	8	no	—
482	C₂×C₄	—	8	4	no	—
483	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
484	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
486	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
487	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
488	C₈	—	2	1	no	—
489	C₈	—	2	4	no	—
490	C₈	—	2	2	no	—
491	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
492	C₂²	—	2	4	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	8	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	4	4	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	16	8	no	—
500	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
501	C₄	—	2	1	no	—
502	C₄	—	2	4	no	—
503	C₄	—	2	2	no	—
504	C₄	—	4	4	no	—
505	C₄	—	4	4	no	—
506	C₄	—	4	4	no	—
507	C₄	C₁₉×#577	1	4	yes	—
508	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
509	C₄	C₁₉×#585	1	1	yes	characteristic
510	C₂	—	4	4	no	—
511	C₂	—	4	1	no	—
512	C₂	—	8	4	no	—
513	C₂	C₁₉×#3496	1	1	yes	characteristic
514	C₂	C₂×C₁₉×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3549	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3550	C₂	semidirect
3. C₁₉×#3340	C₂	semidirect
4. C₁₉×#3329	C₂	semidirect
5. C₁₉×#3324	C₂	semidirect
6. D₄×SD₁₆×C₁₉	C₂	semidirect
7. C₁₉×#3254	C₂	semidirect
8. C₁₉×#3200	C₂	semidirect
9. C₁₉×#3167	C₂	semidirect
10. C₁₉×#3057	C₂	semidirect
11. C₁₉×#2931	C₂	semidirect
12. C₂²×SD₁₆×C₁₉	C₂²	semidirect
13. C₂×C₁₉×#131	C₂²	semidirect
18. C₁₉×#556	C₂²	semidirect
21. D₄×Q₈×C₁₉	C₂²	semidirect
25. C₁₉×#536	C₂²	semidirect
28. C₁₉×#533	C₂²	semidirect
31. C₁₉×#498	C₂²	semidirect
33. C₁₉×#487	C₂²	semidirect
35. C₁₉×#485	C₂²	semidirect
36. C₁₉×#482	C₂²	semidirect
37. C₁₉×#477	C₂²	semidirect
38. C₁₉×#474	C₂²	semidirect
39. C₁₉×#468	C₂²	semidirect
40. C₁₉×#468	C₂²	semidirect
41. C₁₉×#465	C₂²	semidirect
42. C₁₉×#465	C₂²	semidirect
43. C₁₉×#465	C₂²	semidirect
44. C₁₉×#461	C₂²	semidirect
46. C₁₉×#450	C₂²	semidirect
47. C₁₉×#448	C₂²	semidirect
48. C₄×SD₁₆×C₁₉	C₂²	semidirect
49. C₄×SD₁₆×C₁₉	C₂²	semidirect
50. C₁₉×#436	C₂²	semidirect
51. C₈×D₄×C₁₉	C₂²	semidirect
52. C₁₉×#427	C₂²	semidirect
53. C₁₉×#423	C₂²	semidirect
54. C₁₉×#419	C₂²	semidirect
55. C₁₉×#418	C₂²	semidirect
56. C₁₉×#408	C₂²	semidirect
57. C₂×C₄×C₈×C₁₉	C₂²	semidirect
194. #62326	C₁₉	direct (N × H)
235. #3550	C₂×C₁₉	semidirect
237. #3340	C₂×C₁₉	semidirect
238. #3329	C₂×C₁₉	semidirect
239. #3324	C₂×C₁₉	semidirect
240. D₄×SD₁₆	C₂×C₁₉	semidirect
241. #3254	C₂×C₁₉	semidirect
242. #3200	C₂×C₁₉	semidirect
243. #3167	C₂×C₁₉	semidirect
244. #3057	C₂×C₁₉	semidirect
245. #2931	C₂×C₁₉	semidirect
264. C₂²×SD₁₆	C₂²×C₁₉	semidirect
265. C₂×#131	C₂²×C₁₉	semidirect
270. #556	C₂²×C₁₉	semidirect
273. D₄×Q₈	C₂²×C₁₉	semidirect
277. #536	C₂²×C₁₉	semidirect
280. #533	C₂²×C₁₉	semidirect
283. #498	C₂²×C₁₉	semidirect
285. #487	C₂²×C₁₉	semidirect
287. #485	C₂²×C₁₉	semidirect
288. #482	C₂²×C₁₉	semidirect
289. #477	C₂²×C₁₉	semidirect
290. #474	C₂²×C₁₉	semidirect
291. #468	C₂²×C₁₉	semidirect
292. #468	C₂²×C₁₉	semidirect
293. #465	C₂²×C₁₉	semidirect
294. #465	C₂²×C₁₉	semidirect
295. #465	C₂²×C₁₉	semidirect
296. #461	C₂²×C₁₉	semidirect
298. #450	C₂²×C₁₉	semidirect
299. #448	C₂²×C₁₉	semidirect
300. C₄×SD₁₆	C₂²×C₁₉	semidirect
301. C₄×SD₁₆	C₂²×C₁₉	semidirect
302. #436	C₂²×C₁₉	semidirect
303. C₈×D₄	C₂²×C₁₉	semidirect
304. #427	C₂²×C₁₉	semidirect
305. #423	C₂²×C₁₉	semidirect
306. #419	C₂²×C₁₉	semidirect
307. #418	C₂²×C₁₉	semidirect
308. #408	C₂²×C₁₉	semidirect
309. C₂×C₄×C₈	C₂²×C₁₉	semidirect
387. C₁₉	#62326	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×#3550	2
C₁₉×#3549	2
C₁₉×#3340	2
C₁₉×#3329	2
C₁₉×#3324	2
D₄×SD₁₆×C₁₉	2
C₁₉×#3254	2
C₁₉×#3200	2
C₁₉×#3167	2
C₁₉×#3057	2
C₁₉×#2931	2
#62326	19

Subgroups — C19×#62326 #18068285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62326 #18068285