Subgroups — C₁₉×#62332 #18068291

Order 4864.

1876 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3548	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3338	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3334	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3333	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3330	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3287	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3283	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3254	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3203	C₂	1	4	yes	maximal, complemented
10	C₁₉×#3170	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3061	C₂	1	4	yes	maximal, complemented
13	C₁₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₉×#135	C₂²	1	4	yes	—
15	C₂×C₁₉×#131	C₂²	1	2	yes	—
16	C₁₉×#562	—	2	4	no	—
17	C₁₉×#554	—	2	2	no	—
18	C₁₉×#554	C₂²	1	4	yes	—
19	C₁₉×#550	—	2	2	no	—
20	C₁₉×#550	C₂²	1	4	yes	—
21	C₁₉×#547	C₂²	1	4	yes	—
22	C₁₉×#547	C₂²	1	4	yes	—
23	C₁₉×#540	—	2	4	no	—
24	C₁₉×#537	—	2	4	no	—
25	C₁₉×#537	C₂²	1	8	yes	—
26	C₁₉×#533	C₂²	1	2	yes	—
27	C₁₉×#532	C₂²	1	2	yes	—
28	C₁₉×#532	C₂²	1	1	yes	characteristic
29	C₁₉×#500	C₂²	1	1	yes	characteristic
30	C₁₉×#500	C₂²	1	1	yes	characteristic
31	C₁₉×#494	C₂²	1	1	yes	characteristic
32	C₁₉×#493	C₂²	1	1	yes	characteristic
33	C₁₉×#487	C₂²	1	2	yes	—
34	C₁₉×#486	C₂²	1	2	yes	—
35	C₁₉×#484	C₂²	1	8	yes	—
36	C₁₉×#480	C₂²	1	8	yes	—
37	C₁₉×#477	C₂²	1	4	yes	—
38	C₁₉×#474	C₂²	1	4	yes	—
39	C₁₉×#468	C₂²	1	8	yes	—
40	C₁₉×#468	C₂²	1	8	yes	—
41	C₁₉×#467	C₂²	1	2	yes	—
42	C₁₉×#467	C₂²	1	2	yes	—
43	C₁₉×#467	C₂²	1	4	yes	—
44	C₁₉×#466	C₂²	1	2	yes	—
45	C₁₉×#466	C₂²	1	2	yes	—
46	C₁₉×#466	C₂²	1	4	yes	—
47	C₁₉×#461	C₂²	1	4	yes	—
48	C₁₉×#460	C₂²	1	4	yes	—
49	C₁₉×#452	C₂²	1	8	yes	—
50	C₁₉×#449	C₂²	1	8	yes	—
51	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
52	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
53	C₄×D₈×C₁₉	C₂²	1	2	yes	—
54	C₄×D₈×C₁₉	C₂²	1	2	yes	—
55	C₁₉×#436	C₂²	1	2	yes	—
56	C₁₉×#436	C₂²	1	2	yes	—
57	C₈×D₄×C₁₉	C₂²	1	2	yes	—
58	C₈×D₄×C₁₉	C₂²	1	2	yes	—
59	C₂×C₁₉×#107	C₂²	1	4	yes	—
60	C₁₉×#423	C₂²	1	1	yes	characteristic
61	C₁₉×#417	C₂²	1	8	yes	—
62	C₁₉×#408	C₂²	1	2	yes	—
63	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
64	C₂×#41×C₁₉	—	2	4	no	—
65	C₂×#41×C₁₉	—	2	2	no	—
66	C₂×#41×C₁₉	C₂³	1	8	yes	—
67	C₂×#41×C₁₉	C₂³	1	2	yes	—
68	C₁₉×#135	—	4	8	no	—
69	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
70	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
71	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	—
72	C₂×D₈×C₁₉	C₂³	1	2	yes	—
73	C₂×D₈×C₁₉	C₂³	1	2	yes	—
74	C₁₉×#131	—	4	4	no	—
75	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
76	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
77	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
79	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
81	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
82	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
83	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
84	C₁₉×#127	—	2	4	no	—
85	C₁₉×#127	D₄	1	1	yes	characteristic
86	C₁₉×#127	C₂³	1	2	yes	—
87	C₁₉×#125	—	2	4	no	—
88	C₁₉×#125	—	2	2	no	—
89	C₁₉×#124	—	2	2	no	—
90	C₁₉×#124	D₄	1	2	yes	—
91	C₁₉×#123	—	2	8	no	—
92	C₁₉×#123	—	2	8	no	—
93	C₁₉×C₂²⋊Q₈	—	2	8	no	—
94	C₁₉×C₂²⋊Q₈	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	—	2	4	no	—
96	C₁₉×C₂²⋊Q₈	—	2	8	no	—
97	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
98	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
99	C₁₉×#121	—	2	8	no	—
100	C₁₉×#121	—	2	8	no	—
101	C₁₉×#121	—	2	4	no	—
102	C₁₉×#121	—	2	8	no	—
103	C₁₉×#121	—	2	2	no	—
104	C₁₉×#121	—	2	8	no	—
105	C₁₉×#121	D₄	1	2	yes	—
106	C₁₉×#121	D₄	1	2	yes	—
107	C₁₉×#121	C₂³	1	8	yes	—
108	C₁₉×#121	C₂³	1	4	yes	—
109	C₄×Q₈×C₁₉	—	2	2	no	—
110	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
111	C₄×D₄×C₁₉	—	2	4	no	—
112	C₄×D₄×C₁₉	—	2	4	no	—
113	C₄×D₄×C₁₉	—	2	2	no	—
114	C₄×D₄×C₁₉	C₂³	1	4	yes	—
115	C₄×D₄×C₁₉	C₂³	1	2	yes	—
116	C₄×D₄×C₁₉	C₂³	1	2	yes	—
117	C₁₉×#117	—	2	2	no	—
118	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
119	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
120	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
121	C₁₉×#107	C₂³	1	2	yes	—
122	C₁₉×#107	C₂³	1	2	yes	—
123	C₁₉×#107	C₂³	1	8	yes	—
124	C₁₉×#107	C₂³	1	2	yes	—
125	C₁₉×#107	C₂³	1	2	yes	—
126	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
127	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
128	C₁₉×#103	C₂³	1	4	yes	—
129	C₁₉×#103	C₂³	1	8	yes	—
130	C₁₉×#103	C₂³	1	4	yes	—
131	C₁₉×#102	C₂³	1	4	yes	—
132	C₁₉×#102	C₂³	1	8	yes	—
133	C₁₉×#102	C₂³	1	4	yes	—
134	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
135	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
136	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
140	#41×C₁₉	—	4	2	no	—
141	#41×C₁₉	—	4	2	no	—
142	#41×C₁₉	—	4	8	no	—
143	#41×C₁₉	—	4	8	no	—
144	#41×C₁₉	—	8	4	no	—
145	#41×C₁₉	—	8	8	no	—
146	C₂×Q₈×C₁₉	—	2	2	no	—
147	C₂×Q₈×C₁₉	—	2	2	no	—
148	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
149	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
150	C₂×D₄×C₁₉	—	2	4	no	—
151	C₂×D₄×C₁₉	—	2	8	no	—
152	C₂×D₄×C₁₉	—	2	8	no	—
153	C₂×D₄×C₁₉	—	2	2	no	—
154	C₂×D₄×C₁₉	—	2	2	no	—
155	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
157	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
158	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
159	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₉	—	2	8	no	—
161	C₂²×C₄×C₁₉	—	2	4	no	—
162	C₂²×C₄×C₁₉	—	2	8	no	—
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
167	Q₁₆×C₁₉	—	2	4	no	—
168	Q₁₆×C₁₉	—	4	2	no	—
169	SD₁₆×C₁₉	—	4	8	no	—
170	D₈×C₁₉	—	2	4	no	—
171	D₈×C₁₉	—	4	2	no	—
172	M₁₆×C₁₉	—	4	4	no	—
173	M₁₆×C₁₉	—	4	2	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₂×C₈×C₁₉	—	2	8	no	—
176	C₂×C₈×C₁₉	—	4	1	no	—
177	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
178	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
179	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
180	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
181	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	8	no	—
184	C₄⋊C₄×C₁₉	—	2	8	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	4	no	—
189	C₄⋊C₄×C₁₉	—	2	4	no	—
190	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
191	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
192	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
193	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
194	C₂²⋊C₄×C₁₉	—	2	4	no	—
195	C₂²⋊C₄×C₁₉	—	2	8	no	—
196	C₂²⋊C₄×C₁₉	—	2	8	no	—
197	C₂²⋊C₄×C₁₉	—	2	4	no	—
198	C₂²⋊C₄×C₁₉	—	2	4	no	—
199	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
200	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
201	C₄²×C₁₉	—	2	4	no	—
202	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
205	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
206	#62332	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₁₉	—	2	4	no	—
208	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
209	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
210	Q₈×C₁₉	—	2	4	no	—
211	Q₈×C₁₉	—	2	4	no	—
212	Q₈×C₁₉	—	4	2	no	—
213	Q₈×C₁₉	—	4	4	no	—
214	Q₈×C₁₉	—	8	2	no	—
215	D₄×C₁₉	—	2	4	no	—
216	D₄×C₁₉	—	2	4	no	—
217	D₄×C₁₉	—	2	4	no	—
218	D₄×C₁₉	—	2	4	no	—
219	D₄×C₁₉	—	4	4	no	—
220	D₄×C₁₉	—	4	2	no	—
221	D₄×C₁₉	—	4	4	no	—
222	D₄×C₁₉	—	8	2	no	—
223	D₄×C₁₉	—	8	8	no	—
224	D₄×C₁₉	—	8	4	no	—
225	D₄×C₁₉	—	8	8	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	4	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	4	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	4	no	—
235	C₂×C₄×C₁₉	—	4	8	no	—
236	C₂×C₄×C₁₉	—	8	8	no	—
237	C₂×C₄×C₁₉	—	8	8	no	—
238	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
242	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
245	C₈×C₁₉	—	2	1	no	—
246	C₈×C₁₉	—	2	4	no	—
247	C₈×C₁₉	—	2	1	no	—
248	C₈×C₁₉	—	2	1	no	—
249	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
250	#3548	C₂×C₁₉	1	2	yes	complemented
251	#3338	C₂×C₁₉	1	2	yes	complemented
252	#3334	C₂×C₁₉	1	2	yes	complemented
253	#3333	C₂×C₁₉	1	4	yes	complemented
254	#3330	C₂×C₁₉	1	4	yes	complemented
255	#3287	C₂×C₁₉	1	2	yes	complemented
256	#3283	C₂×C₁₉	1	2	yes	complemented
257	#3254	C₂×C₁₉	1	2	yes	complemented
258	#3203	C₂×C₁₉	1	4	yes	complemented
259	#3170	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#3169	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#3061	C₂×C₁₉	1	4	yes	complemented
262	#2931	C₂×C₁₉	1	1	yes	characteristic, complemented
263	C₂²×C₁₉	—	2	1	no	—
264	C₂²×C₁₉	—	2	4	no	—
265	C₂²×C₁₉	—	2	1	no	—
266	C₂²×C₁₉	—	2	4	no	—
267	C₂²×C₁₉	—	2	1	no	—
268	C₂²×C₁₉	—	2	4	no	—
269	C₂²×C₁₉	—	4	4	no	—
270	C₂²×C₁₉	—	4	4	no	—
271	C₂²×C₁₉	—	4	4	no	—
272	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
273	C₄×C₁₉	—	2	4	no	—
274	C₄×C₁₉	—	2	1	no	—
275	C₄×C₁₉	—	2	1	no	—
276	C₄×C₁₉	—	2	1	no	—
277	C₄×C₁₉	—	4	4	no	—
278	C₄×C₁₉	—	4	4	no	—
279	C₄×C₁₉	—	4	4	no	—
280	C₄×C₁₉	#576	1	2	yes	—
281	C₄×C₁₉	#578	1	2	yes	—
282	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
283	C₄×C₁₉	#585	1	1	yes	characteristic
284	C₂×#135	C₂²×C₁₉	1	4	yes	—
285	C₂×#131	C₂²×C₁₉	1	2	yes	—
286	#562	—	2	4	no	—
287	#554	—	2	2	no	—
288	#554	C₂²×C₁₉	1	4	yes	—
289	#550	—	2	2	no	—
290	#550	C₂²×C₁₉	1	4	yes	—
291	#547	C₂²×C₁₉	1	4	yes	—
292	#547	C₂²×C₁₉	1	4	yes	—
293	#540	—	2	4	no	—
294	#537	—	2	4	no	—
295	#537	C₂²×C₁₉	1	8	yes	—
296	#533	C₂²×C₁₉	1	2	yes	—
297	#532	C₂²×C₁₉	1	2	yes	—
298	#532	C₂²×C₁₉	1	1	yes	characteristic
299	#500	C₂²×C₁₉	1	1	yes	characteristic
300	#500	C₂²×C₁₉	1	1	yes	characteristic
301	#494	C₂²×C₁₉	1	1	yes	characteristic
302	#493	C₂²×C₁₉	1	1	yes	characteristic
303	#487	C₂²×C₁₉	1	2	yes	—
304	#486	C₂²×C₁₉	1	2	yes	—
305	#484	C₂²×C₁₉	1	8	yes	—
306	#480	C₂²×C₁₉	1	8	yes	—
307	#477	C₂²×C₁₉	1	4	yes	—
308	#474	C₂²×C₁₉	1	4	yes	—
309	#468	C₂²×C₁₉	1	8	yes	—
310	#468	C₂²×C₁₉	1	8	yes	—
311	#467	C₂²×C₁₉	1	4	yes	—
312	#467	C₂²×C₁₉	1	2	yes	—
313	#467	C₂²×C₁₉	1	2	yes	—
314	#466	C₂²×C₁₉	1	4	yes	—
315	#466	C₂²×C₁₉	1	2	yes	—
316	#466	C₂²×C₁₉	1	2	yes	—
317	#461	C₂²×C₁₉	1	4	yes	—
318	#460	C₂²×C₁₉	1	4	yes	—
319	#452	C₂²×C₁₉	1	8	yes	—
320	#449	C₂²×C₁₉	1	8	yes	—
321	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
322	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
323	C₄×D₈	C₂²×C₁₉	1	2	yes	—
324	C₄×D₈	C₂²×C₁₉	1	2	yes	—
325	#436	C₂²×C₁₉	1	2	yes	—
326	#436	C₂²×C₁₉	1	2	yes	—
327	C₈×D₄	C₂²×C₁₉	1	2	yes	—
328	C₈×D₄	C₂²×C₁₉	1	2	yes	—
329	C₂×#107	C₂²×C₁₉	1	4	yes	—
330	#423	C₂²×C₁₉	1	1	yes	characteristic
331	#417	C₂²×C₁₉	1	8	yes	—
332	#408	C₂²×C₁₉	1	2	yes	—
333	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
334	C₂×C₁₉	—	4	1	no	—
335	C₂×C₁₉	—	4	4	no	—
336	C₂×C₁₉	—	8	4	no	—
337	C₂×C₁₉	#3496	1	1	yes	characteristic
338	C₂×C₁₉	C₂×#576	1	1	yes	characteristic
339	C₂×C₁₉	C₂×#578	1	1	yes	characteristic
340	C₂×#41	—	2	4	no	—
341	C₂×#41	—	2	2	no	—
342	C₂×#41	C₂³×C₁₉	1	8	yes	—
343	C₂×#41	C₂³×C₁₉	1	2	yes	—
344	#135	—	4	8	no	—
345	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
346	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
347	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	—
348	C₂×D₈	C₂³×C₁₉	1	2	yes	—
349	C₂×D₈	C₂³×C₁₉	1	2	yes	—
350	#131	—	4	4	no	—
351	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
352	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
353	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
355	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
356	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
357	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
358	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
359	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
360	#127	—	2	4	no	—
361	#127	D₄×C₁₉	1	1	yes	characteristic
362	#127	C₂³×C₁₉	1	2	yes	—
363	#125	—	2	4	no	—
364	#125	—	2	2	no	—
365	#124	—	2	2	no	—
366	#124	D₄×C₁₉	1	2	yes	—
367	#123	—	2	8	no	—
368	#123	—	2	8	no	—
369	C₂²⋊Q₈	—	2	8	no	—
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	—	2	4	no	—
372	C₂²⋊Q₈	—	2	8	no	—
373	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
374	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
375	#121	—	2	8	no	—
376	#121	—	2	8	no	—
377	#121	—	2	4	no	—
378	#121	—	2	8	no	—
379	#121	—	2	2	no	—
380	#121	—	2	8	no	—
381	#121	D₄×C₁₉	1	2	yes	—
382	#121	D₄×C₁₉	1	2	yes	—
383	#121	C₂³×C₁₉	1	4	yes	—
384	#121	C₂³×C₁₉	1	8	yes	—
385	C₄×Q₈	—	2	2	no	—
386	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
387	C₄×D₄	—	2	4	no	—
388	C₄×D₄	—	2	4	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	C₂³×C₁₉	1	4	yes	—
391	C₄×D₄	C₂³×C₁₉	1	2	yes	—
392	C₄×D₄	C₂³×C₁₉	1	2	yes	—
393	#117	—	2	2	no	—
394	C₂×C₄⋊C₄	—	2	4	no	—
395	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
396	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
397	#107	C₂³×C₁₉	1	2	yes	—
398	#107	C₂³×C₁₉	1	2	yes	—
399	#107	C₂³×C₁₉	1	8	yes	—
400	#107	C₂³×C₁₉	1	2	yes	—
401	#107	C₂³×C₁₉	1	2	yes	—
402	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
403	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
404	#103	C₂³×C₁₉	1	4	yes	—
405	#103	C₂³×C₁₉	1	8	yes	—
406	#103	C₂³×C₁₉	1	4	yes	—
407	#102	C₂³×C₁₉	1	4	yes	—
408	#102	C₂³×C₁₉	1	8	yes	—
409	#102	C₂³×C₁₉	1	4	yes	—
410	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
411	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
412	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
413	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
414	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
415	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
416	C₁₉	#62332	1	1	yes	characteristic, direct product factor, Sylow
417	#41	—	4	2	no	—
418	#41	—	4	2	no	—
419	#41	—	4	8	no	—
420	#41	—	4	8	no	—
421	#41	—	8	4	no	—
422	#41	—	8	8	no	—
423	C₂×Q₈	—	2	2	no	—
424	C₂×Q₈	—	2	2	no	—
425	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
426	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	2	8	no	—
429	C₂×D₄	—	2	8	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
433	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
434	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
435	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
436	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
437	C₂²×C₄	—	2	8	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	8	no	—
440	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
443	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
444	Q₁₆	—	2	4	no	—
445	Q₁₆	—	4	2	no	—
446	SD₁₆	—	4	8	no	—
447	D₈	—	2	4	no	—
448	D₈	—	4	2	no	—
449	M₁₆	—	4	4	no	—
450	M₁₆	—	4	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	2	8	no	—
453	C₂×C₈	—	4	1	no	—
454	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
455	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
456	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
457	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
458	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	8	no	—
461	C₄⋊C₄	—	2	8	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
468	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
469	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
470	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	8	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
477	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
478	C₄²	—	2	4	no	—
479	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
481	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
482	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
483	C₂³	—	2	4	no	—
484	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
485	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
486	Q₈	—	2	4	no	—
487	Q₈	—	2	4	no	—
488	Q₈	—	4	2	no	—
489	Q₈	—	4	4	no	—
490	Q₈	—	8	2	no	—
491	D₄	—	2	4	no	—
492	D₄	—	2	4	no	—
493	D₄	—	2	4	no	—
494	D₄	—	2	4	no	—
495	D₄	—	4	4	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	4	no	—
498	D₄	—	8	2	no	—
499	D₄	—	8	8	no	—
500	D₄	—	8	4	no	—
501	D₄	—	8	8	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	4	8	no	—
512	C₂×C₄	—	8	8	no	—
513	C₂×C₄	—	8	8	no	—
514	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
518	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
520	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
521	C₈	—	2	1	no	—
522	C₈	—	2	4	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	4	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	4	4	no	—
533	C₂²	—	4	4	no	—
534	C₂²	—	4	4	no	—
535	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
536	C₄	—	2	4	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	4	4	no	—
541	C₄	—	4	4	no	—
542	C₄	—	4	4	no	—
543	C₄	C₁₉×#576	1	2	yes	—
544	C₄	C₁₉×#578	1	2	yes	—
545	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
546	C₄	C₁₉×#585	1	1	yes	characteristic
547	C₂	—	4	1	no	—
548	C₂	—	4	4	no	—
549	C₂	—	8	4	no	—
550	C₂	C₁₉×#3496	1	1	yes	characteristic
551	C₂	C₂×C₁₉×#576	1	1	yes	characteristic
552	C₂	C₂×C₁₉×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
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×#3548	C₂	semidirect
2. C₁₉×#3338	C₂	semidirect
3. C₁₉×#3334	C₂	semidirect
4. C₁₉×#3333	C₂	semidirect
5. C₁₉×#3330	C₂	semidirect
6. C₁₉×#3287	C₂	semidirect
7. C₁₉×#3283	C₂	semidirect
8. C₁₉×#3254	C₂	semidirect
9. C₁₉×#3203	C₂	semidirect
10. C₁₉×#3170	C₂	semidirect
11. C₁₉×#3169	C₂	semidirect
12. C₁₉×#3061	C₂	semidirect
13. C₁₉×#2931	C₂	semidirect
206. #62332	C₁₉	direct (N × H)
250. #3548	C₂×C₁₉	semidirect
251. #3338	C₂×C₁₉	semidirect
252. #3334	C₂×C₁₉	semidirect
253. #3333	C₂×C₁₉	semidirect
254. #3330	C₂×C₁₉	semidirect
255. #3287	C₂×C₁₉	semidirect
256. #3283	C₂×C₁₉	semidirect
257. #3254	C₂×C₁₉	semidirect
258. #3203	C₂×C₁₉	semidirect
259. #3170	C₂×C₁₉	semidirect
260. #3169	C₂×C₁₉	semidirect
261. #3061	C₂×C₁₉	semidirect
262. #2931	C₂×C₁₉	semidirect
416. C₁₉	#62332	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×#3548	2
C₁₉×#3338	2
C₁₉×#3334	2
C₁₉×#3333	2
C₁₉×#3330	2
C₁₉×#3287	2
C₁₉×#3283	2
C₁₉×#3254	2
C₁₉×#3203	2
C₁₉×#3170	2
C₁₉×#3169	2
C₁₉×#3061	2
C₁₉×#2931	2
#62332	19

Subgroups — C19×#62332 #18068291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62332 #18068291