Subgroups — C₁₉×#23885 #18029844

Order 4864.

1662 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3586	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3025	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3022	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3004	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2010	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2009	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1909	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1905	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1891	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1796	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#585	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
15	C₁₉×#578	—	2	4	no	—
16	C₁₉×#577	—	2	4	no	—
17	C₁₉×#575	—	2	2	no	—
18	C₁₉×#575	C₂²	1	2	yes	—
19	C₂×C₁₉×#137	—	2	2	no	—
20	C₂×C₁₉×#137	C₂²	1	2	yes	—
21	C₂×C₁₉×#137	C₂²	1	2	yes	—
22	C₁₉×#568	C₂²	1	1	yes	characteristic
23	D₄×Q₈×C₁₉	—	2	2	no	—
24	D₄×Q₈×C₁₉	—	2	2	no	—
25	C₁₉×#548	—	2	2	no	—
26	C₁₉×#548	—	2	2	no	—
27	C₁₉×#536	—	2	2	no	—
28	C₁₉×#536	C₂²	1	1	yes	characteristic
29	C₁₉×#536	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#525	—	2	2	no	—
31	C₁₉×#525	C₂²	1	1	yes	characteristic
32	C₁₉×#525	C₂²	1	2	yes	—
33	C₁₉×#525	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#519	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#458	—	2	2	no	—
36	C₁₉×B(4,𝔽₂)	—	2	2	no	—
37	C₁₉×#456	—	2	2	no	—
38	C₁₉×#455	—	2	2	no	—
39	C₁₉×#451	—	2	4	no	—
40	C₁₉×#448	—	2	4	no	—
41	C₁₉×#421	C₂²	1	2	yes	—
42	C₁₉×#421	C₂²	1	2	yes	complemented
43	C₁₉×#419	C₂²	1	2	yes	complemented
44	C₁₉×#419	C₂²	1	2	yes	complemented
45	C₁₉×#413	C₂²	1	1	yes	characteristic
46	C₁₉×#410	C₂²	1	2	yes	—
47	C₁₉×#410	C₂²	1	1	yes	characteristic
48	C₁₉×#407	C₂²	1	2	yes	complemented
49	C₁₉×#344	C₂²	1	2	yes	complemented
50	C₁₉×H(3,ℤ/4)	C₂²	1	2	yes	complemented
51	C₁₉×2₋¹⁺⁴	—	2	4	no	—
52	C₁₉×2₋¹⁺⁴	—	2	2	no	—
53	C₁₉×2₋¹⁺⁴	—	2	1	no	—
54	C₁₉×2₋¹⁺⁴	—	4	2	no	—
55	C₁₉×H(5,𝔽₂)	—	2	2	no	—
56	C₁₉×H(5,𝔽₂)	—	2	2	no	—
57	C₁₉×H(5,𝔽₂)	—	2	1	no	—
58	C₂×#41×C₁₉	—	2	2	no	—
59	C₂×#41×C₁₉	—	2	1	no	—
60	C₂×#41×C₁₉	—	2	2	no	—
61	C₂×#41×C₁₉	—	4	2	no	—
62	C₂×#41×C₁₉	D₄	1	2	yes	complemented
63	C₂×#41×C₁₉	C₂³	1	2	yes	—
64	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×Q₈×C₁₉	—	2	2	no	—
67	C₂²×Q₈×C₁₉	—	2	2	no	—
68	C₂²×Q₈×C₁₉	—	2	1	no	—
69	C₂²×Q₈×C₁₉	—	2	1	no	—
70	C₂²×Q₈×C₁₉	—	2	4	no	—
71	C₂²×Q₈×C₁₉	—	4	2	no	—
72	C₂²×Q₈×C₁₉	D₄	1	2	yes	complemented
73	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₉	—	2	1	no	—
76	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₁₉×#137	—	2	8	no	—
78	C₁₉×#137	—	2	4	no	—
79	C₁₉×#137	—	2	2	no	—
80	C₁₉×#137	—	2	4	no	—
81	C₁₉×#137	—	2	4	no	—
82	C₁₉×#137	—	2	2	no	—
83	C₁₉×#137	—	2	4	no	—
84	C₁₉×#137	—	4	2	no	—
85	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
86	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
87	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
88	C₁₉×#135	—	2	8	no	—
89	C₁₉×#135	—	2	4	no	—
90	C₂×Q₁₆×C₁₉	—	2	4	no	—
91	C₂×Q₁₆×C₁₉	—	2	2	no	—
92	C₂×Q₁₆×C₁₉	D₄	1	4	yes	complemented
93	C₂×SD₁₆×C₁₉	—	2	4	no	—
94	C₂×SD₁₆×C₁₉	—	2	2	no	—
95	C₂×SD₁₆×C₁₉	D₄	1	4	yes	complemented
96	C₁₉×#131	—	2	4	no	—
97	C₂×M₁₆×C₁₉	—	2	2	no	—
98	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
99	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
100	C₁₉×C₄⋊Q₈	—	2	4	no	—
101	C₁₉×C₄⋊Q₈	—	2	1	no	—
102	C₁₉×C₄⋊Q₈	D₄	1	2	yes	complemented
103	C₁₉×#124	—	2	4	no	—
104	C₁₉×#124	—	2	1	no	—
105	C₁₉×#124	D₄	1	2	yes	complemented
106	C₁₉×#123	—	2	2	no	—
107	C₁₉×#123	—	2	1	no	—
108	C₁₉×#123	—	2	2	no	—
109	C₁₉×#123	—	2	2	no	—
110	C₁₉×#123	D₄	1	2	yes	—
111	C₁₉×C₂²⋊Q₈	—	2	4	no	—
112	C₁₉×C₂²⋊Q₈	—	2	4	no	—
113	C₁₉×C₂²⋊Q₈	—	2	4	no	—
114	C₁₉×C₂²⋊Q₈	—	2	1	no	—
115	C₁₉×C₂²⋊Q₈	—	2	1	no	—
116	C₁₉×C₂²⋊Q₈	—	2	2	no	—
117	C₁₉×C₂²⋊Q₈	—	2	2	no	—
118	C₁₉×C₂²⋊Q₈	—	2	2	no	—
119	C₁₉×#121	—	2	4	no	—
120	C₁₉×#121	—	2	1	no	—
121	C₁₉×#121	—	2	1	no	—
122	C₁₉×#121	—	2	2	no	—
123	C₁₉×#120	—	2	1	no	—
124	C₁₉×#120	—	2	2	no	—
125	C₁₉×#120	D₄	1	2	yes	—
126	C₄×Q₈×C₁₉	—	2	2	no	—
127	C₄×Q₈×C₁₉	—	2	2	no	—
128	C₄×D₄×C₁₉	—	2	4	no	—
129	C₄×D₄×C₁₉	—	2	4	no	—
130	C₄×D₄×C₁₉	—	2	2	no	—
131	C₄×D₄×C₁₉	—	2	2	no	—
132	C₄×D₄×C₁₉	—	4	2	no	—
133	C₁₉×#117	—	2	2	no	—
134	C₁₉×#117	C₂³	1	2	yes	—
135	C₁₉×#117	C₂³	1	1	yes	characteristic
136	C₁₉×#117	C₂³	1	1	yes	characteristic
137	C₁₉×#104	—	2	4	no	—
138	C₁₉×#104	—	4	2	no	—
139	C₁₉×#103	—	2	4	no	—
140	C₁₉×#103	—	2	4	no	—
141	C₁₉×#101	—	2	1	no	—
142	C₁₉×#100	—	2	1	no	—
143	C₁₉×#99	—	2	2	no	—
144	C₁₉×#99	—	2	4	no	—
145	C₁₉×C₂²⋊C₈	—	2	4	no	—
146	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
147	#41×C₁₉	—	2	2	no	—
148	#41×C₁₉	—	2	2	no	—
149	#41×C₁₉	—	2	4	no	—
150	#41×C₁₉	—	2	4	no	—
151	#41×C₁₉	—	2	2	no	—
152	#41×C₁₉	—	2	2	no	—
153	#41×C₁₉	—	2	2	no	—
154	#41×C₁₉	—	2	2	no	—
155	#41×C₁₉	—	2	2	no	—
156	#41×C₁₉	—	2	2	no	—
157	#41×C₁₉	—	4	2	no	—
158	#41×C₁₉	—	4	8	no	—
159	#41×C₁₉	—	4	4	no	—
160	#41×C₁₉	—	4	2	no	—
161	#41×C₁₉	—	4	4	no	—
162	#41×C₁₉	—	4	2	no	—
163	#41×C₁₉	—	4	2	no	—
164	#41×C₁₉	—	4	2	no	—
165	C₂×Q₈×C₁₉	—	2	4	no	—
166	C₂×Q₈×C₁₉	—	2	2	no	—
167	C₂×Q₈×C₁₉	—	2	1	no	—
168	C₂×Q₈×C₁₉	—	2	1	no	—
169	C₂×Q₈×C₁₉	—	2	2	no	—
170	C₂×Q₈×C₁₉	—	2	2	no	—
171	C₂×Q₈×C₁₉	—	2	4	no	—
172	C₂×Q₈×C₁₉	—	2	2	no	—
173	C₂×Q₈×C₁₉	—	2	2	no	—
174	C₂×Q₈×C₁₉	—	4	4	no	—
175	C₂×Q₈×C₁₉	—	4	2	no	—
176	C₂×Q₈×C₁₉	—	4	8	no	—
177	C₂×Q₈×C₁₉	—	4	4	no	—
178	C₂×Q₈×C₁₉	—	4	2	no	—
179	C₂×Q₈×C₁₉	—	4	4	no	—
180	C₂×Q₈×C₁₉	—	4	4	no	—
181	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
182	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
184	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
185	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
186	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂×D₄×C₁₉	—	2	2	no	—
188	C₂×D₄×C₁₉	—	2	2	no	—
189	C₂×D₄×C₁₉	—	2	2	no	—
190	C₂×D₄×C₁₉	—	2	2	no	—
191	C₂×D₄×C₁₉	—	2	1	no	—
192	C₂×D₄×C₁₉	—	2	2	no	—
193	C₂×D₄×C₁₉	—	4	2	no	—
194	C₂×D₄×C₁₉	—	4	4	no	—
195	C₂×D₄×C₁₉	—	4	2	no	—
196	C₂×D₄×C₁₉	—	4	2	no	—
197	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
198	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
200	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₉	—	2	1	no	—
202	C₂²×C₄×C₁₉	—	2	4	no	—
203	C₂²×C₄×C₁₉	—	2	2	no	—
204	C₂²×C₄×C₁₉	—	2	1	no	—
205	C₂²×C₄×C₁₉	—	2	2	no	—
206	C₂²×C₄×C₁₉	—	2	1	no	—
207	C₂²×C₄×C₁₉	—	2	1	no	—
208	C₂²×C₄×C₁₉	—	2	1	no	—
209	C₂²×C₄×C₁₉	—	2	2	no	—
210	C₂²×C₄×C₁₉	—	2	2	no	—
211	C₂²×C₄×C₁₉	—	2	2	no	—
212	C₂²×C₄×C₁₉	—	4	4	no	—
213	C₂²×C₄×C₁₉	—	4	2	no	—
214	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
216	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
217	Q₁₆×C₁₉	—	2	4	no	—
218	Q₁₆×C₁₉	—	2	8	no	—
219	Q₁₆×C₁₉	—	4	4	no	—
220	SD₁₆×C₁₉	—	2	4	no	—
221	SD₁₆×C₁₉	—	2	4	no	—
222	SD₁₆×C₁₉	—	2	8	no	—
223	SD₁₆×C₁₉	—	4	4	no	—
224	D₈×C₁₉	—	2	4	no	—
225	M₁₆×C₁₉	—	2	4	no	—
226	M₁₆×C₁₉	—	2	2	no	—
227	M₁₆×C₁₉	—	2	2	no	—
228	M₁₆×C₁₉	—	2	2	no	—
229	M₁₆×C₁₉	—	2	2	no	—
230	C₂×C₈×C₁₉	—	2	4	no	—
231	C₂×C₈×C₁₉	—	2	2	no	—
232	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
233	C₄⋊C₄×C₁₉	—	2	4	no	—
234	C₄⋊C₄×C₁₉	—	2	4	no	—
235	C₄⋊C₄×C₁₉	—	2	2	no	—
236	C₄⋊C₄×C₁₉	—	2	4	no	—
237	C₄⋊C₄×C₁₉	—	2	2	no	—
238	C₄⋊C₄×C₁₉	—	2	1	no	—
239	C₄⋊C₄×C₁₉	—	2	1	no	—
240	C₄⋊C₄×C₁₉	—	2	2	no	—
241	C₄⋊C₄×C₁₉	—	4	2	no	—
242	C₂²⋊C₄×C₁₉	—	2	2	no	—
243	C₂²⋊C₄×C₁₉	—	2	4	no	—
244	C₂²⋊C₄×C₁₉	—	2	2	no	—
245	C₂²⋊C₄×C₁₉	—	2	4	no	—
246	C₂²⋊C₄×C₁₉	—	2	2	no	—
247	C₂²⋊C₄×C₁₉	—	2	1	no	—
248	C₂²⋊C₄×C₁₉	—	2	2	no	—
249	C₂²⋊C₄×C₁₉	—	2	2	no	—
250	C₂²⋊C₄×C₁₉	—	4	2	no	—
251	C₂²⋊C₄×C₁₉	—	4	2	no	—
252	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
253	C₄²×C₁₉	—	2	4	no	—
254	C₄²×C₁₉	—	2	1	no	—
255	C₄²×C₁₉	—	2	2	no	—
256	C₄²×C₁₉	C₂×D₄	1	2	yes	—
257	#23885	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
258	C₂³×C₁₉	—	2	1	no	—
259	C₂³×C₁₉	—	2	2	no	—
260	C₂³×C₁₉	—	2	1	no	—
261	C₂³×C₁₉	—	2	2	no	—
262	C₂³×C₁₉	—	4	2	no	—
263	C₂³×C₁₉	—	4	2	no	—
264	C₂³×C₁₉	#120	1	2	yes	—
265	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
266	Q₈×C₁₉	—	2	2	no	—
267	Q₈×C₁₉	—	2	4	no	—
268	Q₈×C₁₉	—	2	2	no	—
269	Q₈×C₁₉	—	2	1	no	—
270	Q₈×C₁₉	—	2	2	no	—
271	Q₈×C₁₉	—	2	1	no	—
272	Q₈×C₁₉	—	2	4	no	—
273	Q₈×C₁₉	—	2	2	no	—
274	Q₈×C₁₉	—	4	4	no	—
275	Q₈×C₁₉	—	4	8	no	—
276	Q₈×C₁₉	—	4	2	no	—
277	Q₈×C₁₉	—	4	1	no	—
278	Q₈×C₁₉	—	4	1	no	—
279	Q₈×C₁₉	#120	1	4	yes	—
280	D₄×C₁₉	—	2	4	no	—
281	D₄×C₁₉	—	2	1	no	—
282	D₄×C₁₉	—	2	2	no	—
283	D₄×C₁₉	—	2	1	no	—
284	D₄×C₁₉	—	2	2	no	—
285	D₄×C₁₉	—	2	2	no	—
286	D₄×C₁₉	—	4	4	no	—
287	D₄×C₁₉	—	4	2	no	—
288	D₄×C₁₉	—	4	4	no	—
289	D₄×C₁₉	—	4	4	no	—
290	D₄×C₁₉	—	4	4	no	—
291	D₄×C₁₉	—	4	2	no	—
292	D₄×C₁₉	—	4	2	no	—
293	D₄×C₁₉	—	4	2	no	—
294	D₄×C₁₉	—	8	4	no	—
295	C₂×C₄×C₁₉	—	2	2	no	—
296	C₂×C₄×C₁₉	—	2	4	no	—
297	C₂×C₄×C₁₉	—	2	2	no	—
298	C₂×C₄×C₁₉	—	2	2	no	—
299	C₂×C₄×C₁₉	—	2	2	no	—
300	C₂×C₄×C₁₉	—	2	2	no	—
301	C₂×C₄×C₁₉	—	2	2	no	—
302	C₂×C₄×C₁₉	—	2	1	no	—
303	C₂×C₄×C₁₉	—	2	1	no	—
304	C₂×C₄×C₁₉	—	2	2	no	—
305	C₂×C₄×C₁₉	—	2	2	no	—
306	C₂×C₄×C₁₉	—	4	4	no	—
307	C₂×C₄×C₁₉	—	4	4	no	—
308	C₂×C₄×C₁₉	—	4	8	no	—
309	C₂×C₄×C₁₉	—	4	4	no	—
310	C₂×C₄×C₁₉	—	4	2	no	—
311	C₂×C₄×C₁₉	—	4	2	no	—
312	C₂×C₄×C₁₉	—	4	1	no	—
313	C₂×C₄×C₁₉	—	4	1	no	—
314	C₂×C₄×C₁₉	—	4	2	no	—
315	C₂×C₄×C₁₉	—	4	2	no	—
316	C₂×C₄×C₁₉	—	4	2	no	—
317	C₂×C₄×C₁₉	—	4	2	no	—
318	C₂×C₄×C₁₉	—	4	2	no	—
319	C₂×C₄×C₁₉	#120	1	2	yes	—
320	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
324	C₈×C₁₉	—	2	4	no	—
325	C₈×C₁₉	—	4	2	no	—
326	#3586	C₂×C₁₉	1	1	yes	characteristic, complemented
327	#3486	C₂×C₁₉	1	1	yes	characteristic, complemented
328	#3025	C₂×C₁₉	1	1	yes	characteristic, complemented
329	#3022	C₂×C₁₉	1	1	yes	characteristic, complemented
330	#3004	C₂×C₁₉	1	2	yes	complemented
331	#2010	C₂×C₁₉	1	2	yes	complemented
332	#2009	C₂×C₁₉	1	2	yes	complemented
333	#1909	C₂×C₁₉	1	1	yes	characteristic, complemented
334	#1905	C₂×C₁₉	1	2	yes	complemented
335	#1891	C₂×C₁₉	1	1	yes	characteristic, complemented
336	#1796	C₂×C₁₉	1	1	yes	characteristic, complemented
337	C₂²×C₁₉	—	2	2	no	—
338	C₂²×C₁₉	—	2	4	no	—
339	C₂²×C₁₉	—	2	2	no	—
340	C₂²×C₁₉	—	4	1	no	—
341	C₂²×C₁₉	—	4	2	no	—
342	C₂²×C₁₉	—	4	1	no	—
343	C₂²×C₁₉	—	4	2	no	—
344	C₂²×C₁₉	—	4	2	no	—
345	C₂²×C₁₉	—	4	1	no	—
346	C₂²×C₁₉	—	4	1	no	—
347	C₂²×C₁₉	—	4	2	no	—
348	C₂²×C₁₉	—	8	2	no	—
349	C₂²×C₁₉	—	16	2	no	—
350	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
351	C₂²×C₁₉	D₄²	1	2	yes	—
352	C₄×C₁₉	—	2	4	no	—
353	C₄×C₁₉	—	2	2	no	—
354	C₄×C₁₉	—	4	2	no	—
355	C₄×C₁₉	—	4	2	no	—
356	C₄×C₁₉	—	4	1	no	—
357	C₄×C₁₉	—	4	2	no	—
358	C₄×C₁₉	—	4	1	no	—
359	C₄×C₁₉	—	4	2	no	—
360	C₄×C₁₉	—	8	2	no	—
361	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
362	C₄×C₁₉	#534	1	1	yes	characteristic
363	C₄×C₁₉	D₄²	1	2	yes	—
364	#585	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic
366	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
367	#578	—	2	4	no	—
368	#577	—	2	4	no	—
369	#575	—	2	2	no	—
370	#575	C₂²×C₁₉	1	2	yes	—
371	C₂×#137	—	2	2	no	—
372	C₂×#137	C₂²×C₁₉	1	2	yes	—
373	C₂×#137	C₂²×C₁₉	1	2	yes	—
374	#568	C₂²×C₁₉	1	1	yes	characteristic
375	D₄×Q₈	—	2	2	no	—
376	D₄×Q₈	—	2	2	no	—
377	#548	—	2	2	no	—
378	#548	—	2	2	no	—
379	#536	—	2	2	no	—
380	#536	C₂²×C₁₉	1	1	yes	characteristic
381	#536	C₂²×C₁₉	1	1	yes	characteristic, complemented
382	#525	—	2	2	no	—
383	#525	C₂²×C₁₉	1	1	yes	characteristic
384	#525	C₂²×C₁₉	1	2	yes	—
385	#525	C₂²×C₁₉	1	1	yes	characteristic, complemented
386	#519	C₂²×C₁₉	1	1	yes	characteristic, complemented
387	#458	—	2	2	no	—
388	B(4,𝔽₂)	—	2	2	no	—
389	#456	—	2	2	no	—
390	#455	—	2	2	no	—
391	#451	—	2	4	no	—
392	#448	—	2	4	no	—
393	#421	C₂²×C₁₉	1	2	yes	—
394	#421	C₂²×C₁₉	1	2	yes	complemented
395	#419	C₂²×C₁₉	1	2	yes	complemented
396	#419	C₂²×C₁₉	1	2	yes	complemented
397	#413	C₂²×C₁₉	1	1	yes	characteristic
398	#410	C₂²×C₁₉	1	1	yes	characteristic
399	#410	C₂²×C₁₉	1	2	yes	—
400	#407	C₂²×C₁₉	1	2	yes	complemented
401	#344	C₂²×C₁₉	1	2	yes	complemented
402	H(3,ℤ/4)	C₂²×C₁₉	1	2	yes	complemented
403	C₂×C₁₉	—	2	1	no	—
404	C₂×C₁₉	—	2	2	no	—
405	C₂×C₁₉	—	4	2	no	—
406	C₂×C₁₉	—	4	2	no	—
407	C₂×C₁₉	—	8	1	no	—
408	C₂×C₁₉	—	8	2	no	—
409	C₂×C₁₉	#2403	1	1	yes	characteristic
410	2₋¹⁺⁴	—	2	4	no	—
411	2₋¹⁺⁴	—	2	2	no	—
412	2₋¹⁺⁴	—	2	1	no	—
413	2₋¹⁺⁴	—	4	2	no	—
414	H(5,𝔽₂)	—	2	2	no	—
415	H(5,𝔽₂)	—	2	2	no	—
416	H(5,𝔽₂)	—	2	1	no	—
417	C₂×#41	—	2	2	no	—
418	C₂×#41	—	2	1	no	—
419	C₂×#41	—	2	2	no	—
420	C₂×#41	—	4	2	no	—
421	C₂×#41	D₄×C₁₉	1	2	yes	complemented
422	C₂×#41	C₂³×C₁₉	1	2	yes	—
423	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
424	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
425	C₂²×Q₈	—	2	2	no	—
426	C₂²×Q₈	—	2	2	no	—
427	C₂²×Q₈	—	2	1	no	—
428	C₂²×Q₈	—	2	1	no	—
429	C₂²×Q₈	—	2	4	no	—
430	C₂²×Q₈	—	4	2	no	—
431	C₂²×Q₈	D₄×C₁₉	1	2	yes	complemented
432	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
433	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
434	C₂³×C₄	—	2	1	no	—
435	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
436	#137	—	2	8	no	—
437	#137	—	2	4	no	—
438	#137	—	2	2	no	—
439	#137	—	2	4	no	—
440	#137	—	2	4	no	—
441	#137	—	2	2	no	—
442	#137	—	2	4	no	—
443	#137	—	4	2	no	—
444	AGL(1,ℤ/8)	—	2	4	no	—
445	AGL(1,ℤ/8)	—	2	2	no	—
446	AGL(1,ℤ/8)	—	2	2	no	—
447	#135	—	2	8	no	—
448	#135	—	2	4	no	—
449	C₂×Q₁₆	—	2	4	no	—
450	C₂×Q₁₆	—	2	2	no	—
451	C₂×Q₁₆	D₄×C₁₉	1	4	yes	complemented
452	C₂×SD₁₆	—	2	4	no	—
453	C₂×SD₁₆	—	2	2	no	—
454	C₂×SD₁₆	D₄×C₁₉	1	4	yes	complemented
455	#131	—	2	4	no	—
456	C₂×M₁₆	—	2	2	no	—
457	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
458	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
459	C₄⋊Q₈	—	2	4	no	—
460	C₄⋊Q₈	—	2	1	no	—
461	C₄⋊Q₈	D₄×C₁₉	1	2	yes	complemented
462	#124	—	2	4	no	—
463	#124	—	2	1	no	—
464	#124	D₄×C₁₉	1	2	yes	complemented
465	#123	—	2	2	no	—
466	#123	—	2	1	no	—
467	#123	—	2	2	no	—
468	#123	—	2	2	no	—
469	#123	D₄×C₁₉	1	2	yes	—
470	C₂²⋊Q₈	—	2	4	no	—
471	C₂²⋊Q₈	—	2	4	no	—
472	C₂²⋊Q₈	—	2	4	no	—
473	C₂²⋊Q₈	—	2	1	no	—
474	C₂²⋊Q₈	—	2	1	no	—
475	C₂²⋊Q₈	—	2	2	no	—
476	C₂²⋊Q₈	—	2	2	no	—
477	C₂²⋊Q₈	—	2	2	no	—
478	#121	—	2	4	no	—
479	#121	—	2	1	no	—
480	#121	—	2	1	no	—
481	#121	—	2	2	no	—
482	#120	—	2	1	no	—
483	#120	—	2	2	no	—
484	#120	D₄×C₁₉	1	2	yes	—
485	C₄×Q₈	—	2	2	no	—
486	C₄×Q₈	—	2	2	no	—
487	C₄×D₄	—	2	4	no	—
488	C₄×D₄	—	2	4	no	—
489	C₄×D₄	—	2	2	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	—	4	2	no	—
492	#117	—	2	2	no	—
493	#117	C₂³×C₁₉	1	2	yes	—
494	#117	C₂³×C₁₉	1	1	yes	characteristic
495	#117	C₂³×C₁₉	1	1	yes	characteristic
496	#104	—	2	4	no	—
497	#104	—	4	2	no	—
498	#103	—	2	4	no	—
499	#103	—	2	4	no	—
500	#101	—	2	1	no	—
501	#100	—	2	1	no	—
502	#99	—	2	2	no	—
503	#99	—	2	4	no	—
504	C₂²⋊C₈	—	2	4	no	—
505	C₁₉	#23885	1	1	yes	characteristic, direct product factor, Sylow
506	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
507	#41	—	2	2	no	—
508	#41	—	2	2	no	—
509	#41	—	2	4	no	—
510	#41	—	2	4	no	—
511	#41	—	2	2	no	—
512	#41	—	2	2	no	—
513	#41	—	2	2	no	—
514	#41	—	2	2	no	—
515	#41	—	2	2	no	—
516	#41	—	2	2	no	—
517	#41	—	4	2	no	—
518	#41	—	4	8	no	—
519	#41	—	4	4	no	—
520	#41	—	4	2	no	—
521	#41	—	4	4	no	—
522	#41	—	4	2	no	—
523	#41	—	4	2	no	—
524	#41	—	4	2	no	—
525	C₂×Q₈	—	2	4	no	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	2	no	—
530	C₂×Q₈	—	2	2	no	—
531	C₂×Q₈	—	2	4	no	—
532	C₂×Q₈	—	2	2	no	—
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	—	4	4	no	—
535	C₂×Q₈	—	4	2	no	—
536	C₂×Q₈	—	4	8	no	—
537	C₂×Q₈	—	4	4	no	—
538	C₂×Q₈	—	4	2	no	—
539	C₂×Q₈	—	4	4	no	—
540	C₂×Q₈	—	4	4	no	—
541	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
542	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
543	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
544	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
545	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
546	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	4	2	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	—	4	2	no	—
556	C₂×D₄	—	4	2	no	—
557	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
558	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
559	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
560	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	4	4	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
575	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
577	Q₁₆	—	2	4	no	—
578	Q₁₆	—	2	8	no	—
579	Q₁₆	—	4	4	no	—
580	SD₁₆	—	2	4	no	—
581	SD₁₆	—	2	4	no	—
582	SD₁₆	—	2	8	no	—
583	SD₁₆	—	4	4	no	—
584	D₈	—	2	4	no	—
585	M₁₆	—	2	4	no	—
586	M₁₆	—	2	2	no	—
587	M₁₆	—	2	2	no	—
588	M₁₆	—	2	2	no	—
589	M₁₆	—	2	2	no	—
590	C₂×C₈	—	2	4	no	—
591	C₂×C₈	—	2	2	no	—
592	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	4	2	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	1	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	4	2	no	—
611	C₂²⋊C₄	—	4	2	no	—
612	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
613	C₄²	—	2	4	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	2	no	—
616	C₄²	C₂×D₄×C₁₉	1	2	yes	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	4	2	no	—
622	C₂³	—	4	2	no	—
623	C₂³	C₁₉×#120	1	2	yes	—
624	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
625	Q₈	—	2	2	no	—
626	Q₈	—	2	4	no	—
627	Q₈	—	2	2	no	—
628	Q₈	—	2	1	no	—
629	Q₈	—	2	2	no	—
630	Q₈	—	2	1	no	—
631	Q₈	—	2	4	no	—
632	Q₈	—	2	2	no	—
633	Q₈	—	4	4	no	—
634	Q₈	—	4	8	no	—
635	Q₈	—	4	2	no	—
636	Q₈	—	4	1	no	—
637	Q₈	—	4	1	no	—
638	Q₈	C₁₉×#120	1	4	yes	—
639	D₄	—	2	4	no	—
640	D₄	—	2	1	no	—
641	D₄	—	2	2	no	—
642	D₄	—	2	1	no	—
643	D₄	—	2	2	no	—
644	D₄	—	2	2	no	—
645	D₄	—	4	4	no	—
646	D₄	—	4	2	no	—
647	D₄	—	4	4	no	—
648	D₄	—	4	4	no	—
649	D₄	—	4	4	no	—
650	D₄	—	4	2	no	—
651	D₄	—	4	2	no	—
652	D₄	—	4	2	no	—
653	D₄	—	8	4	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	8	no	—
668	C₂×C₄	—	4	4	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	2	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	2	no	—
674	C₂×C₄	—	4	2	no	—
675	C₂×C₄	—	4	2	no	—
676	C₂×C₄	—	4	2	no	—
677	C₂×C₄	—	4	2	no	—
678	C₂×C₄	C₁₉×#120	1	2	yes	—
679	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
680	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
681	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
682	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
683	C₈	—	2	4	no	—
684	C₈	—	4	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	4	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	8	2	no	—
697	C₂²	—	16	2	no	—
698	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
699	C₂²	D₄²×C₁₉	1	2	yes	—
700	C₄	—	2	4	no	—
701	C₄	—	2	2	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	1	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	1	no	—
707	C₄	—	4	2	no	—
708	C₄	—	8	2	no	—
709	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
710	C₄	C₁₉×#534	1	1	yes	characteristic
711	C₄	D₄²×C₁₉	1	2	yes	—
712	C₂	—	2	1	no	—
713	C₂	—	2	2	no	—
714	C₂	—	4	2	no	—
715	C₂	—	4	2	no	—
716	C₂	—	8	1	no	—
717	C₂	—	8	2	no	—
718	C₂	C₁₉×#2403	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#2403
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3586	C₂	semidirect
2. C₁₉×#3486	C₂	semidirect
3. C₁₉×#3025	C₂	semidirect
4. C₁₉×#3022	C₂	semidirect
5. C₁₉×#3004	C₂	semidirect
6. C₁₉×#2010	C₂	semidirect
7. C₁₉×#2009	C₂	semidirect
8. C₁₉×#1909	C₂	semidirect
9. C₁₉×#1905	C₂	semidirect
10. C₁₉×#1891	C₂	semidirect
11. C₁₉×#1796	C₂	semidirect
14. C₂³×Q₈×C₁₉	C₂²	semidirect
29. C₁₉×#536	C₂²	semidirect
33. C₁₉×#525	C₂²	semidirect
34. C₁₉×#519	C₂²	semidirect
42. C₁₉×#421	C₂²	semidirect
43. C₁₉×#419	C₂²	semidirect
44. C₁₉×#419	C₂²	semidirect
48. C₁₉×#407	C₂²	semidirect
49. C₁₉×#344	C₂²	semidirect
50. C₁₉×H(3,ℤ/4)	C₂²	semidirect
62. C₂×#41×C₁₉	D₄	semidirect
72. C₂²×Q₈×C₁₉	D₄	semidirect
92. C₂×Q₁₆×C₁₉	D₄	semidirect
95. C₂×SD₁₆×C₁₉	D₄	semidirect
102. C₁₉×C₄⋊Q₈	D₄	semidirect
105. C₁₉×#124	D₄	semidirect
257. #23885	C₁₉	direct (N × H)
326. #3586	C₂×C₁₉	semidirect
327. #3486	C₂×C₁₉	semidirect
328. #3025	C₂×C₁₉	semidirect
329. #3022	C₂×C₁₉	semidirect
330. #3004	C₂×C₁₉	semidirect
331. #2010	C₂×C₁₉	semidirect
332. #2009	C₂×C₁₉	semidirect
333. #1909	C₂×C₁₉	semidirect
334. #1905	C₂×C₁₉	semidirect
335. #1891	C₂×C₁₉	semidirect
336. #1796	C₂×C₁₉	semidirect
366. C₂³×Q₈	C₂²×C₁₉	semidirect
381. #536	C₂²×C₁₉	semidirect
385. #525	C₂²×C₁₉	semidirect
386. #519	C₂²×C₁₉	semidirect
394. #421	C₂²×C₁₉	semidirect
395. #419	C₂²×C₁₉	semidirect
396. #419	C₂²×C₁₉	semidirect
400. #407	C₂²×C₁₉	semidirect
401. #344	C₂²×C₁₉	semidirect
402. H(3,ℤ/4)	C₂²×C₁₉	semidirect
421. C₂×#41	D₄×C₁₉	semidirect
431. C₂²×Q₈	D₄×C₁₉	semidirect
451. C₂×Q₁₆	D₄×C₁₉	semidirect
454. C₂×SD₁₆	D₄×C₁₉	semidirect
461. C₄⋊Q₈	D₄×C₁₉	semidirect
464. #124	D₄×C₁₉	semidirect
505. C₁₉	#23885	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×#3586	2
C₁₉×#3486	2
C₁₉×#3025	2
C₁₉×#3022	2
C₁₉×#3004	2
C₁₉×#2010	2
C₁₉×#2009	2
C₁₉×#1909	2
C₁₉×#1905	2
C₁₉×#1891	2
C₁₉×#1796	2
#23885	19

Subgroups — C19×#23885 #18029844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23885 #18029844