Subgroups — C₁₉×#33560 #18039519

Order 4864.

1132 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3551	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3028	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3027	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3018	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2200	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2197	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2126	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2123	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2122	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#585	C₂²	1	1	yes	characteristic
11	C₁₉×#575	—	2	1	no	—
12	C₁₉×#563	—	2	1	no	—
13	C₁₉×#560	C₂²	1	2	yes	complemented
14	C₁₉×#555	—	2	1	no	—
15	C₁₉×#553	—	2	1	no	—
16	C₁₉×#552	—	2	1	no	—
17	C₁₉×#551	C₂²	1	2	yes	complemented
18	C₁₉×#548	—	2	1	no	—
19	C₁₉×#546	—	2	1	no	—
20	C₁₉×#540	—	2	2	no	—
21	C₁₉×#538	—	2	2	no	—
22	C₁₉×#537	—	2	1	no	—
23	C₁₉×#536	—	2	1	no	—
24	C₁₉×#536	C₂²	1	1	yes	characteristic
25	C₁₉×#535	—	2	1	no	—
26	C₁₉×#535	C₂²	1	1	yes	characteristic
27	C₁₉×#532	C₂²	1	1	yes	characteristic
28	C₁₉×#529	—	2	1	no	—
29	C₁₉×#458	—	2	2	no	—
30	C₁₉×#458	C₂²	1	4	yes	—
31	C₁₉×B(4,𝔽₂)	—	2	2	no	—
32	C₁₉×B(4,𝔽₂)	C₂²	1	4	yes	—
33	C₁₉×#456	—	2	1	no	—
34	C₁₉×#455	C₂²	1	2	yes	—
35	C₁₉×#454	—	2	1	no	—
36	C₁₉×#453	C₂²	1	2	yes	—
37	C₂×C₁₉×#104	—	2	1	no	—
38	C₁₉×#413	C₂²	1	1	yes	characteristic
39	C₁₉×#410	—	2	1	no	—
40	C₁₉×#410	—	2	1	no	—
41	C₁₉×#410	C₂²	1	1	yes	characteristic
42	C₁₉×#410	C₂²	1	1	yes	characteristic
43	C₁₉×#354	C₂²	1	2	yes	complemented
44	C₁₉×#353	C₂²	1	2	yes	complemented
45	C₁₉×#352	C₂²	1	4	yes	complemented
46	C₁₉×AΣL(1,𝔽₁₆)	C₂²	1	4	yes	complemented
47	C₁₉×2₋¹⁺⁴	—	2	1	no	—
48	C₁₉×2₋¹⁺⁴	—	4	1	no	—
49	C₁₉×H(5,𝔽₂)	—	2	1	no	—
50	C₁₉×H(5,𝔽₂)	—	2	1	no	—
51	C₁₉×H(5,𝔽₂)	—	4	1	no	—
52	C₁₉×H(5,𝔽₂)	C₂³	1	2	yes	—
53	C₂×#41×C₁₉	—	2	1	no	—
54	C₂×#41×C₁₉	—	2	1	no	—
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂×#41×C₁₉	—	4	2	no	—
58	C₂×#41×C₁₉	D₄	1	1	yes	characteristic, complemented
59	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic, complemented
61	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
62	C₁₉×#137	—	2	2	no	—
63	C₁₉×#137	—	4	1	no	—
64	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
65	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
66	C₁₉×#135	—	4	2	no	—
67	C₂×M₁₆×C₁₉	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	—	2	1	no	—
69	C₁₉×C₄⋊Q₈	—	4	1	no	—
70	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
71	C₁₉×#127	—	2	1	no	—
72	C₁₉×#127	—	4	1	no	—
73	C₁₉×#127	C₂³	1	1	yes	characteristic
74	C₁₉×#126	—	2	2	no	—
75	C₁₉×#126	—	2	2	no	—
76	C₁₉×#126	—	2	2	no	—
77	C₁₉×#125	—	2	1	no	—
78	C₁₉×#125	—	2	2	no	—
79	C₁₉×#124	—	2	1	no	—
80	C₁₉×#124	—	2	2	no	—
81	C₁₉×#124	—	2	1	no	—
82	C₁₉×#124	—	2	1	no	—
83	C₁₉×#124	—	4	1	no	—
84	C₁₉×#124	—	4	1	no	—
85	C₁₉×#124	D₄	1	1	yes	characteristic, complemented
86	C₁₉×#124	C₂³	1	1	yes	characteristic
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×#123	—	2	2	no	—
89	C₁₉×#123	—	2	2	no	—
90	C₁₉×#123	—	2	2	no	—
91	C₁₉×#123	—	2	4	no	—
92	C₁₉×#123	D₄	1	2	yes	complemented
93	C₁₉×#123	C₂³	1	2	yes	—
94	C₁₉×C₂²⋊Q₈	—	2	1	no	—
95	C₁₉×C₂²⋊Q₈	—	2	2	no	—
96	C₁₉×C₂²⋊Q₈	—	2	2	no	—
97	C₁₉×C₂²⋊Q₈	—	2	1	no	—
98	C₁₉×C₂²⋊Q₈	—	2	1	no	—
99	C₁₉×C₂²⋊Q₈	—	4	2	no	—
100	C₁₉×#121	—	2	2	no	—
101	C₁₉×#121	—	2	2	no	—
102	C₁₉×#121	—	2	1	no	—
103	C₁₉×#121	—	2	2	no	—
104	C₁₉×#121	—	2	1	no	—
105	C₁₉×#121	—	2	1	no	—
106	C₁₉×#121	—	2	2	no	—
107	C₁₉×#121	—	2	1	no	—
108	C₁₉×#121	—	2	1	no	—
109	C₁₉×#121	—	2	2	no	—
110	C₁₉×#121	—	2	2	no	—
111	C₁₉×#121	—	4	2	no	—
112	C₁₉×#120	—	2	2	no	—
113	C₁₉×#120	—	2	4	no	—
114	C₁₉×#120	D₄	1	2	yes	—
115	C₁₉×#120	C₂³	1	2	yes	—
116	C₄×Q₈×C₁₉	—	2	1	no	—
117	C₄×D₄×C₁₉	—	2	2	no	—
118	C₄×D₄×C₁₉	—	2	1	no	—
119	C₄×D₄×C₁₉	—	2	2	no	—
120	C₄×D₄×C₁₉	—	2	1	no	—
121	C₄×D₄×C₁₉	—	2	1	no	—
122	C₄×D₄×C₁₉	—	2	2	no	—
123	C₁₉×#117	—	2	2	no	—
124	C₁₉×#117	—	2	2	no	—
125	C₁₉×#117	—	2	1	no	—
126	C₁₉×#117	—	2	1	no	—
127	C₁₉×#117	D₄	1	1	yes	characteristic
128	C₁₉×#117	D₄	1	1	yes	characteristic, complemented
129	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
131	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic, complemented
132	C₁₉×#104	—	2	2	no	—
133	C₁₉×#104	—	2	2	no	—
134	C₁₉×#101	—	2	1	no	—
135	C₁₉×#100	C₂³	1	2	yes	—
136	C₁₉×#99	—	2	1	no	—
137	C₁₉×#99	—	2	1	no	—
138	C₁₉×#99	—	2	4	no	—
139	C₁₉×#99	—	2	4	no	—
140	C₁₉×#99	C₂³	1	2	yes	—
141	C₁₉×#99	C₂³	1	2	yes	—
142	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
143	#41×C₁₉	—	2	2	no	—
144	#41×C₁₉	—	2	2	no	—
145	#41×C₁₉	—	4	1	no	—
146	#41×C₁₉	—	4	1	no	—
147	#41×C₁₉	—	4	2	no	—
148	#41×C₁₉	—	4	1	no	—
149	#41×C₁₉	—	4	1	no	—
150	#41×C₁₉	—	4	1	no	—
151	#41×C₁₉	—	4	1	no	—
152	#41×C₁₉	—	4	1	no	—
153	#41×C₁₉	—	4	2	no	—
154	#41×C₁₉	—	4	2	no	—
155	#41×C₁₉	—	4	1	no	—
156	#41×C₁₉	—	4	1	no	—
157	#41×C₁₉	—	4	2	no	—
158	#41×C₁₉	—	4	1	no	—
159	#41×C₁₉	—	4	1	no	—
160	#41×C₁₉	—	4	1	no	—
161	#41×C₁₉	—	8	1	no	—
162	#41×C₁₉	—	8	1	no	—
163	C₂×Q₈×C₁₉	—	2	1	no	—
164	C₂×Q₈×C₁₉	—	2	1	no	—
165	C₂×Q₈×C₁₉	—	2	1	no	—
166	C₂×Q₈×C₁₉	—	2	1	no	—
167	C₂×Q₈×C₁₉	—	2	1	no	—
168	C₂×Q₈×C₁₉	—	4	1	no	—
169	C₂×Q₈×C₁₉	—	4	1	no	—
170	C₂×Q₈×C₁₉	—	4	2	no	—
171	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂×D₄×C₁₉	—	2	1	no	—
174	C₂×D₄×C₁₉	—	2	1	no	—
175	C₂×D₄×C₁₉	—	2	1	no	—
176	C₂×D₄×C₁₉	—	2	2	no	—
177	C₂×D₄×C₁₉	—	2	2	no	—
178	C₂×D₄×C₁₉	—	2	2	no	—
179	C₂×D₄×C₁₉	—	2	2	no	—
180	C₂×D₄×C₁₉	—	2	2	no	—
181	C₂×D₄×C₁₉	—	2	1	no	—
182	C₂×D₄×C₁₉	—	2	1	no	—
183	C₂×D₄×C₁₉	—	2	2	no	—
184	C₂×D₄×C₁₉	—	2	1	no	—
185	C₂×D₄×C₁₉	—	2	1	no	—
186	C₂×D₄×C₁₉	—	2	1	no	—
187	C₂×D₄×C₁₉	—	4	1	no	—
188	C₂×D₄×C₁₉	—	4	1	no	—
189	C₂×D₄×C₁₉	—	4	2	no	—
190	C₂×D₄×C₁₉	—	4	2	no	—
191	C₂×D₄×C₁₉	—	4	2	no	—
192	C₂×D₄×C₁₉	—	4	1	no	—
193	C₂×D₄×C₁₉	—	4	4	no	—
194	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₁₉	—	2	2	no	—
199	C₂²×C₄×C₁₉	—	2	2	no	—
200	C₂²×C₄×C₁₉	—	2	2	no	—
201	C₂²×C₄×C₁₉	—	2	2	no	—
202	C₂²×C₄×C₁₉	—	2	2	no	—
203	C₂²×C₄×C₁₉	—	2	1	no	—
204	C₂²×C₄×C₁₉	—	2	1	no	—
205	C₂²×C₄×C₁₉	—	4	1	no	—
206	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
210	Q₁₆×C₁₉	—	4	2	no	—
211	SD₁₆×C₁₉	—	4	2	no	—
212	SD₁₆×C₁₉	—	4	2	no	—
213	D₈×C₁₉	—	4	2	no	—
214	M₁₆×C₁₉	—	2	2	no	—
215	M₁₆×C₁₉	—	4	1	no	—
216	C₂×C₈×C₁₉	—	4	1	no	—
217	C₄⋊C₄×C₁₉	—	2	2	no	—
218	C₄⋊C₄×C₁₉	—	2	2	no	—
219	C₄⋊C₄×C₁₉	—	2	2	no	—
220	C₄⋊C₄×C₁₉	—	2	2	no	—
221	C₄⋊C₄×C₁₉	—	2	2	no	—
222	C₄⋊C₄×C₁₉	—	2	2	no	—
223	C₄⋊C₄×C₁₉	—	2	1	no	—
224	C₄⋊C₄×C₁₉	—	2	1	no	—
225	C₄⋊C₄×C₁₉	—	2	1	no	—
226	C₄⋊C₄×C₁₉	—	2	1	no	—
227	C₄⋊C₄×C₁₉	—	2	2	no	—
228	C₄⋊C₄×C₁₉	—	4	1	no	—
229	C₄⋊C₄×C₁₉	—	4	1	no	—
230	C₄⋊C₄×C₁₉	—	4	4	no	—
231	C₂²⋊C₄×C₁₉	—	2	2	no	—
232	C₂²⋊C₄×C₁₉	—	2	2	no	—
233	C₂²⋊C₄×C₁₉	—	2	2	no	—
234	C₂²⋊C₄×C₁₉	—	2	2	no	—
235	C₂²⋊C₄×C₁₉	—	2	2	no	—
236	C₂²⋊C₄×C₁₉	—	2	2	no	—
237	C₂²⋊C₄×C₁₉	—	2	1	no	—
238	C₂²⋊C₄×C₁₉	—	2	2	no	—
239	C₂²⋊C₄×C₁₉	—	2	1	no	—
240	C₂²⋊C₄×C₁₉	—	2	1	no	—
241	C₂²⋊C₄×C₁₉	—	2	1	no	—
242	C₂²⋊C₄×C₁₉	—	2	2	no	—
243	C₂²⋊C₄×C₁₉	—	2	2	no	—
244	C₂²⋊C₄×C₁₉	—	2	2	no	—
245	C₂²⋊C₄×C₁₉	—	2	2	no	—
246	C₂²⋊C₄×C₁₉	—	4	4	no	—
247	C₂²⋊C₄×C₁₉	—	4	4	no	—
248	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
249	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
250	C₄²×C₁₉	—	2	2	no	—
251	C₄²×C₁₉	—	2	1	no	—
252	C₄²×C₁₉	—	2	1	no	—
253	C₄²×C₁₉	—	2	1	no	—
254	C₄²×C₁₉	—	4	1	no	—
255	C₄²×C₁₉	—	4	1	no	—
256	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
257	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
258	#33560	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂³×C₁₉	—	2	2	no	—
260	C₂³×C₁₉	—	2	2	no	—
261	C₂³×C₁₉	—	2	2	no	—
262	C₂³×C₁₉	—	2	1	no	—
263	C₂³×C₁₉	—	4	1	no	—
264	C₂³×C₁₉	—	4	2	no	—
265	C₂³×C₁₉	—	8	2	no	—
266	C₂³×C₁₉	#120	1	1	yes	characteristic
267	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
268	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
269	Q₈×C₁₉	—	2	2	no	—
270	Q₈×C₁₉	—	4	1	no	—
271	Q₈×C₁₉	—	4	1	no	—
272	Q₈×C₁₉	—	4	1	no	—
273	Q₈×C₁₉	—	4	1	no	—
274	Q₈×C₁₉	—	4	1	no	—
275	Q₈×C₁₉	—	4	1	no	—
276	Q₈×C₁₉	—	4	1	no	—
277	Q₈×C₁₉	—	8	1	no	—
278	D₄×C₁₉	—	2	2	no	—
279	D₄×C₁₉	—	4	1	no	—
280	D₄×C₁₉	—	4	1	no	—
281	D₄×C₁₉	—	4	1	no	—
282	D₄×C₁₉	—	4	1	no	—
283	D₄×C₁₉	—	4	1	no	—
284	D₄×C₁₉	—	4	1	no	—
285	D₄×C₁₉	—	4	2	no	—
286	D₄×C₁₉	—	4	2	no	—
287	D₄×C₁₉	—	4	2	no	—
288	D₄×C₁₉	—	4	2	no	—
289	D₄×C₁₉	—	4	1	no	—
290	D₄×C₁₉	—	4	1	no	—
291	D₄×C₁₉	—	4	1	no	—
292	D₄×C₁₉	—	8	1	no	—
293	D₄×C₁₉	—	8	1	no	—
294	D₄×C₁₉	—	8	2	no	—
295	D₄×C₁₉	—	8	2	no	—
296	D₄×C₁₉	—	8	2	no	—
297	D₄×C₁₉	—	8	1	no	—
298	D₄×C₁₉	—	8	1	no	—
299	D₄×C₁₉	—	8	2	no	—
300	D₄×C₁₉	—	16	4	no	—
301	C₂×C₄×C₁₉	—	2	1	no	—
302	C₂×C₄×C₁₉	—	2	1	no	—
303	C₂×C₄×C₁₉	—	2	1	no	—
304	C₂×C₄×C₁₉	—	2	1	no	—
305	C₂×C₄×C₁₉	—	2	1	no	—
306	C₂×C₄×C₁₉	—	2	1	no	—
307	C₂×C₄×C₁₉	—	2	2	no	—
308	C₂×C₄×C₁₉	—	2	2	no	—
309	C₂×C₄×C₁₉	—	2	1	no	—
310	C₂×C₄×C₁₉	—	2	2	no	—
311	C₂×C₄×C₁₉	—	2	1	no	—
312	C₂×C₄×C₁₉	—	2	2	no	—
313	C₂×C₄×C₁₉	—	2	2	no	—
314	C₂×C₄×C₁₉	—	2	1	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	1	no	—
319	C₂×C₄×C₁₉	—	4	2	no	—
320	C₂×C₄×C₁₉	—	4	1	no	—
321	C₂×C₄×C₁₉	—	4	1	no	—
322	C₂×C₄×C₁₉	—	4	2	no	—
323	C₂×C₄×C₁₉	—	4	2	no	—
324	C₂×C₄×C₁₉	—	4	2	no	—
325	C₂×C₄×C₁₉	—	8	2	no	—
326	C₂×C₄×C₁₉	—	8	1	no	—
327	C₂×C₄×C₁₉	—	8	2	no	—
328	C₂×C₄×C₁₉	—	8	2	no	—
329	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
330	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
331	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
332	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
333	C₈×C₁₉	—	4	2	no	—
334	#3551	C₂×C₁₉	1	1	yes	characteristic, complemented
335	#3028	C₂×C₁₉	1	1	yes	characteristic, complemented
336	#3027	C₂×C₁₉	1	1	yes	characteristic, complemented
337	#3018	C₂×C₁₉	1	1	yes	characteristic, complemented
338	#2200	C₂×C₁₉	1	4	yes	complemented
339	#2197	C₂×C₁₉	1	4	yes	complemented
340	#2126	C₂×C₁₉	1	1	yes	characteristic, complemented
341	#2123	C₂×C₁₉	1	1	yes	characteristic, complemented
342	#2122	C₂×C₁₉	1	1	yes	characteristic, complemented
343	C₂²×C₁₉	—	2	1	no	—
344	C₂²×C₁₉	—	2	1	no	—
345	C₂²×C₁₉	—	2	1	no	—
346	C₂²×C₁₉	—	4	1	no	—
347	C₂²×C₁₉	—	4	1	no	—
348	C₂²×C₁₉	—	4	1	no	—
349	C₂²×C₁₉	—	4	1	no	—
350	C₂²×C₁₉	—	4	2	no	—
351	C₂²×C₁₉	—	4	1	no	—
352	C₂²×C₁₉	—	4	2	no	—
353	C₂²×C₁₉	—	4	2	no	—
354	C₂²×C₁₉	—	4	1	no	—
355	C₂²×C₁₉	—	4	2	no	—
356	C₂²×C₁₉	—	8	2	no	—
357	C₂²×C₁₉	—	8	4	no	—
358	C₂²×C₁₉	—	8	2	no	—
359	C₂²×C₁₉	—	16	1	no	—
360	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
361	C₄×C₁₉	—	2	1	no	—
362	C₄×C₁₉	—	2	1	no	—
363	C₄×C₁₉	—	2	1	no	—
364	C₄×C₁₉	—	4	1	no	—
365	C₄×C₁₉	—	4	2	no	—
366	C₄×C₁₉	—	4	2	no	—
367	C₄×C₁₉	—	4	1	no	—
368	C₄×C₁₉	—	4	2	no	—
369	C₄×C₁₉	—	4	1	no	—
370	C₄×C₁₉	—	4	2	no	—
371	C₄×C₁₉	—	8	2	no	—
372	C₄×C₁₉	—	8	2	no	—
373	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
374	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
375	#585	C₂²×C₁₉	1	1	yes	characteristic
376	#575	—	2	1	no	—
377	#563	—	2	1	no	—
378	#560	C₂²×C₁₉	1	2	yes	complemented
379	#555	—	2	1	no	—
380	#553	—	2	1	no	—
381	#552	—	2	1	no	—
382	#551	C₂²×C₁₉	1	2	yes	complemented
383	#548	—	2	1	no	—
384	#546	—	2	1	no	—
385	#540	—	2	2	no	—
386	#538	—	2	2	no	—
387	#537	—	2	1	no	—
388	#536	—	2	1	no	—
389	#536	C₂²×C₁₉	1	1	yes	characteristic
390	#535	—	2	1	no	—
391	#535	C₂²×C₁₉	1	1	yes	characteristic
392	#532	C₂²×C₁₉	1	1	yes	characteristic
393	#529	—	2	1	no	—
394	#458	—	2	2	no	—
395	#458	C₂²×C₁₉	1	4	yes	—
396	B(4,𝔽₂)	—	2	2	no	—
397	B(4,𝔽₂)	C₂²×C₁₉	1	4	yes	—
398	#456	—	2	1	no	—
399	#455	C₂²×C₁₉	1	2	yes	—
400	#454	—	2	1	no	—
401	#453	C₂²×C₁₉	1	2	yes	—
402	C₂×#104	—	2	1	no	—
403	#413	C₂²×C₁₉	1	1	yes	characteristic
404	#410	—	2	1	no	—
405	#410	—	2	1	no	—
406	#410	C₂²×C₁₉	1	1	yes	characteristic
407	#410	C₂²×C₁₉	1	1	yes	characteristic
408	#354	C₂²×C₁₉	1	2	yes	complemented
409	#353	C₂²×C₁₉	1	2	yes	complemented
410	#352	C₂²×C₁₉	1	4	yes	complemented
411	AΣL(1,𝔽₁₆)	C₂²×C₁₉	1	4	yes	complemented
412	C₂×C₁₉	—	2	1	no	—
413	C₂×C₁₉	—	4	1	no	—
414	C₂×C₁₉	—	4	1	no	—
415	C₂×C₁₉	—	4	1	no	—
416	C₂×C₁₉	—	8	1	no	—
417	C₂×C₁₉	—	8	2	no	—
418	C₂×C₁₉	—	8	2	no	—
419	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
420	2₋¹⁺⁴	—	2	1	no	—
421	2₋¹⁺⁴	—	4	1	no	—
422	H(5,𝔽₂)	—	2	1	no	—
423	H(5,𝔽₂)	—	2	1	no	—
424	H(5,𝔽₂)	—	4	1	no	—
425	H(5,𝔽₂)	C₂³×C₁₉	1	2	yes	—
426	C₂×#41	—	2	1	no	—
427	C₂×#41	—	2	1	no	—
428	C₂×#41	—	2	1	no	—
429	C₂×#41	—	2	1	no	—
430	C₂×#41	—	4	2	no	—
431	C₂×#41	D₄×C₁₉	1	1	yes	characteristic, complemented
432	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
433	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
434	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
435	#137	—	2	2	no	—
436	#137	—	4	1	no	—
437	AGL(1,ℤ/8)	—	2	2	no	—
438	AGL(1,ℤ/8)	—	4	1	no	—
439	#135	—	4	2	no	—
440	C₂×M₁₆	—	2	1	no	—
441	C₄⋊Q₈	—	2	1	no	—
442	C₄⋊Q₈	—	4	1	no	—
443	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
444	#127	—	2	1	no	—
445	#127	—	4	1	no	—
446	#127	C₂³×C₁₉	1	1	yes	characteristic
447	#126	—	2	2	no	—
448	#126	—	2	2	no	—
449	#126	—	2	2	no	—
450	#125	—	2	1	no	—
451	#125	—	2	2	no	—
452	#124	—	2	1	no	—
453	#124	—	2	2	no	—
454	#124	—	2	1	no	—
455	#124	—	2	1	no	—
456	#124	—	4	1	no	—
457	#124	—	4	1	no	—
458	#124	D₄×C₁₉	1	1	yes	characteristic, complemented
459	#124	C₂³×C₁₉	1	1	yes	characteristic
460	#123	—	2	2	no	—
461	#123	—	2	2	no	—
462	#123	—	2	2	no	—
463	#123	—	2	2	no	—
464	#123	—	2	4	no	—
465	#123	D₄×C₁₉	1	2	yes	complemented
466	#123	C₂³×C₁₉	1	2	yes	—
467	C₂²⋊Q₈	—	2	1	no	—
468	C₂²⋊Q₈	—	2	2	no	—
469	C₂²⋊Q₈	—	2	2	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	—	2	1	no	—
472	C₂²⋊Q₈	—	4	2	no	—
473	#121	—	2	2	no	—
474	#121	—	2	2	no	—
475	#121	—	2	1	no	—
476	#121	—	2	2	no	—
477	#121	—	2	1	no	—
478	#121	—	2	1	no	—
479	#121	—	2	2	no	—
480	#121	—	2	1	no	—
481	#121	—	2	1	no	—
482	#121	—	2	2	no	—
483	#121	—	2	2	no	—
484	#121	—	4	2	no	—
485	#120	—	2	2	no	—
486	#120	—	2	4	no	—
487	#120	D₄×C₁₉	1	2	yes	—
488	#120	C₂³×C₁₉	1	2	yes	—
489	C₄×Q₈	—	2	1	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	—	2	1	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	1	no	—
494	C₄×D₄	—	2	1	no	—
495	C₄×D₄	—	2	2	no	—
496	#117	—	2	2	no	—
497	#117	—	2	2	no	—
498	#117	—	2	1	no	—
499	#117	—	2	1	no	—
500	#117	D₄×C₁₉	1	1	yes	characteristic
501	#117	D₄×C₁₉	1	1	yes	characteristic, complemented
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	2	no	—
504	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic, complemented
505	#104	—	2	2	no	—
506	#104	—	2	2	no	—
507	#101	—	2	1	no	—
508	#100	C₂³×C₁₉	1	2	yes	—
509	#99	—	2	1	no	—
510	#99	—	2	1	no	—
511	#99	—	2	4	no	—
512	#99	—	2	4	no	—
513	#99	C₂³×C₁₉	1	2	yes	—
514	#99	C₂³×C₁₉	1	2	yes	—
515	C₁₉	#33560	1	1	yes	characteristic, direct product factor, Sylow
516	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
517	#41	—	2	2	no	—
518	#41	—	2	2	no	—
519	#41	—	4	1	no	—
520	#41	—	4	1	no	—
521	#41	—	4	2	no	—
522	#41	—	4	1	no	—
523	#41	—	4	1	no	—
524	#41	—	4	1	no	—
525	#41	—	4	1	no	—
526	#41	—	4	1	no	—
527	#41	—	4	2	no	—
528	#41	—	4	2	no	—
529	#41	—	4	1	no	—
530	#41	—	4	1	no	—
531	#41	—	4	2	no	—
532	#41	—	4	1	no	—
533	#41	—	4	1	no	—
534	#41	—	4	1	no	—
535	#41	—	8	1	no	—
536	#41	—	8	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	4	1	no	—
543	C₂×Q₈	—	4	1	no	—
544	C₂×Q₈	—	4	2	no	—
545	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
546	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	4	1	no	—
562	C₂×D₄	—	4	1	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	2	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	1	no	—
567	C₂×D₄	—	4	4	no	—
568	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
569	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
570	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
571	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	4	1	no	—
580	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
584	Q₁₆	—	4	2	no	—
585	SD₁₆	—	4	2	no	—
586	SD₁₆	—	4	2	no	—
587	D₈	—	4	2	no	—
588	M₁₆	—	2	2	no	—
589	M₁₆	—	4	1	no	—
590	C₂×C₈	—	4	1	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	4	1	no	—
603	C₄⋊C₄	—	4	1	no	—
604	C₄⋊C₄	—	4	4	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	1	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	1	no	—
614	C₂²⋊C₄	—	2	1	no	—
615	C₂²⋊C₄	—	2	1	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	—	4	4	no	—
621	C₂²⋊C₄	—	4	4	no	—
622	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
623	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
624	C₄²	—	2	2	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	2	1	no	—
628	C₄²	—	4	1	no	—
629	C₄²	—	4	1	no	—
630	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
631	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	—	4	2	no	—
638	C₂³	—	8	2	no	—
639	C₂³	C₁₉×#120	1	1	yes	characteristic
640	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
641	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
642	Q₈	—	2	2	no	—
643	Q₈	—	4	1	no	—
644	Q₈	—	4	1	no	—
645	Q₈	—	4	1	no	—
646	Q₈	—	4	1	no	—
647	Q₈	—	4	1	no	—
648	Q₈	—	4	1	no	—
649	Q₈	—	4	1	no	—
650	Q₈	—	8	1	no	—
651	D₄	—	2	2	no	—
652	D₄	—	4	1	no	—
653	D₄	—	4	1	no	—
654	D₄	—	4	1	no	—
655	D₄	—	4	1	no	—
656	D₄	—	4	1	no	—
657	D₄	—	4	1	no	—
658	D₄	—	4	2	no	—
659	D₄	—	4	2	no	—
660	D₄	—	4	2	no	—
661	D₄	—	4	2	no	—
662	D₄	—	4	1	no	—
663	D₄	—	4	1	no	—
664	D₄	—	4	1	no	—
665	D₄	—	8	1	no	—
666	D₄	—	8	1	no	—
667	D₄	—	8	2	no	—
668	D₄	—	8	2	no	—
669	D₄	—	8	2	no	—
670	D₄	—	8	2	no	—
671	D₄	—	8	1	no	—
672	D₄	—	8	1	no	—
673	D₄	—	16	4	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	2	no	—
696	C₂×C₄	—	4	2	no	—
697	C₂×C₄	—	4	2	no	—
698	C₂×C₄	—	8	2	no	—
699	C₂×C₄	—	8	2	no	—
700	C₂×C₄	—	8	1	no	—
701	C₂×C₄	—	8	2	no	—
702	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
703	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
704	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
706	C₈	—	4	2	no	—
707	C₂²	—	2	1	no	—
708	C₂²	—	2	1	no	—
709	C₂²	—	2	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	1	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	8	2	no	—
721	C₂²	—	8	4	no	—
722	C₂²	—	8	2	no	—
723	C₂²	—	16	1	no	—
724	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
725	C₄	—	2	1	no	—
726	C₄	—	2	1	no	—
727	C₄	—	2	1	no	—
728	C₄	—	4	1	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	1	no	—
734	C₄	—	4	2	no	—
735	C₄	—	8	2	no	—
736	C₄	—	8	2	no	—
737	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
738	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
739	C₂	—	2	1	no	—
740	C₂	—	4	1	no	—
741	C₂	—	4	1	no	—
742	C₂	—	4	1	no	—
743	C₂	—	8	2	no	—
744	C₂	—	8	1	no	—
745	C₂	—	8	2	no	—
746	C₂	C₂×C₁₉×B(4,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×D₄	C₂⁴×C₁₉
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3551	C₂	semidirect
2. C₁₉×#3028	C₂	semidirect
3. C₁₉×#3027	C₂	semidirect
4. C₁₉×#3018	C₂	semidirect
5. C₁₉×#2200	C₂	semidirect
6. C₁₉×#2197	C₂	semidirect
7. C₁₉×#2126	C₂	semidirect
8. C₁₉×#2123	C₂	semidirect
9. C₁₉×#2122	C₂	semidirect
13. C₁₉×#560	C₂²	semidirect
17. C₁₉×#551	C₂²	semidirect
43. C₁₉×#354	C₂²	semidirect
44. C₁₉×#353	C₂²	semidirect
45. C₁₉×#352	C₂²	semidirect
46. C₁₉×AΣL(1,𝔽₁₆)	C₂²	semidirect
58. C₂×#41×C₁₉	D₄	semidirect
60. C₂²×Q₈×C₁₉	D₄	semidirect
70. C₁₉×C₄⋊Q₈	D₄	semidirect
85. C₁₉×#124	D₄	semidirect
92. C₁₉×#123	D₄	semidirect
128. C₁₉×#117	D₄	semidirect
131. C₂×C₄²×C₁₉	D₄	semidirect
258. #33560	C₁₉	direct (N × H)
334. #3551	C₂×C₁₉	semidirect
335. #3028	C₂×C₁₉	semidirect
336. #3027	C₂×C₁₉	semidirect
337. #3018	C₂×C₁₉	semidirect
338. #2200	C₂×C₁₉	semidirect
339. #2197	C₂×C₁₉	semidirect
340. #2126	C₂×C₁₉	semidirect
341. #2123	C₂×C₁₉	semidirect
342. #2122	C₂×C₁₉	semidirect
378. #560	C₂²×C₁₉	semidirect
382. #551	C₂²×C₁₉	semidirect
408. #354	C₂²×C₁₉	semidirect
409. #353	C₂²×C₁₉	semidirect
410. #352	C₂²×C₁₉	semidirect
411. AΣL(1,𝔽₁₆)	C₂²×C₁₉	semidirect
431. C₂×#41	D₄×C₁₉	semidirect
433. C₂²×Q₈	D₄×C₁₉	semidirect
443. C₄⋊Q₈	D₄×C₁₉	semidirect
458. #124	D₄×C₁₉	semidirect
465. #123	D₄×C₁₉	semidirect
501. #117	D₄×C₁₉	semidirect
504. C₂×C₄²	D₄×C₁₉	semidirect
515. C₁₉	#33560	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×#3551	2
C₁₉×#3028	2
C₁₉×#3027	2
C₁₉×#3018	2
C₁₉×#2200	2
C₁₉×#2197	2
C₁₉×#2126	2
C₁₉×#2123	2
C₁₉×#2122	2
#33560	19

Subgroups — C19×#33560 #18039519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33560 #18039519