Subgroups — C₁₉×#33546 #18039505

Order 4864.

1236 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3481	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3025	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3018	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2198	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2197	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2196	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2126	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2120	C₂	1	2	yes	maximal, complemented
9	C₁₉×#585	C₂²	1	1	yes	characteristic, complemented
10	C₁₉×#575	—	2	1	no	—
11	C₁₉×#559	C₂²	1	1	yes	characteristic, complemented
12	C₁₉×#554	—	2	1	no	—
13	C₁₉×#553	—	2	2	no	—
14	C₁₉×#551	—	2	1	no	—
15	C₁₉×#551	C₂²	1	2	yes	complemented
16	C₁₉×#546	—	2	2	no	—
17	D₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#532	C₂²	1	1	yes	characteristic
19	C₁₉×#529	—	2	2	no	—
20	C₁₉×#525	—	2	1	no	—
21	C₁₉×#525	—	2	2	no	—
22	C₁₉×#525	C₂²	1	2	yes	—
23	C₄×#41×C₁₉	—	2	1	no	—
24	C₂×C₄×D₄×C₁₉	—	2	2	no	—
25	C₁₉×#458	—	2	2	no	—
26	C₁₉×#458	C₂²	1	4	yes	complemented
27	C₁₉×B(4,𝔽₂)	—	2	2	no	—
28	C₁₉×B(4,𝔽₂)	C₂²	1	4	yes	—
29	C₁₉×#456	—	2	1	no	—
30	C₁₉×#455	C₂²	1	2	yes	complemented
31	C₁₉×#454	—	2	1	no	—
32	C₁₉×#453	C₂²	1	2	yes	—
33	C₂×C₁₉×#104	—	2	1	no	—
34	C₁₉×#413	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#410	—	2	2	no	—
36	C₁₉×#410	C₂²	1	2	yes	complemented
37	C₁₉×#354	C₂²	1	2	yes	complemented
38	C₁₉×#353	C₂²	1	2	yes	complemented
39	C₁₉×#352	C₂²	1	4	yes	complemented
40	C₁₉×AΣL(1,𝔽₁₆)	C₂²	1	4	yes	complemented
41	C₁₉×2₋¹⁺⁴	—	2	1	no	—
42	C₁₉×2₋¹⁺⁴	—	4	1	no	—
43	C₁₉×H(5,𝔽₂)	—	2	2	no	—
44	C₁₉×H(5,𝔽₂)	—	4	1	no	—
45	C₁₉×H(5,𝔽₂)	C₂³	1	2	yes	—
46	C₂×#41×C₁₉	—	2	1	no	—
47	C₂×#41×C₁₉	—	2	2	no	—
48	C₂×#41×C₁₉	—	2	1	no	—
49	C₂×#41×C₁₉	—	4	2	no	—
50	C₂×#41×C₁₉	D₄	1	1	yes	characteristic, complemented
51	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₉	—	2	2	no	—
53	C₂³×C₄×C₁₉	—	2	1	no	—
54	C₂³×C₄×C₁₉	D₄	1	2	yes	complemented
55	C₁₉×#137	—	2	2	no	—
56	C₁₉×#137	—	4	1	no	—
57	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
58	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
59	C₁₉×#135	—	4	2	no	—
60	C₂×M₁₆×C₁₉	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
62	C₁₉×#127	C₂³	1	1	yes	characteristic
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#126	—	2	2	no	—
65	C₁₉×#125	—	2	2	no	—
66	C₁₉×#124	—	2	2	no	—
67	C₁₉×#124	D₄	1	1	yes	characteristic, complemented
68	C₁₉×#124	C₂³	1	1	yes	characteristic
69	C₁₉×#123	—	2	1	no	—
70	C₁₉×#123	—	2	2	no	—
71	C₁₉×#123	—	2	1	no	—
72	C₁₉×#123	—	2	2	no	—
73	C₁₉×#123	—	2	4	no	—
74	C₁₉×#123	D₄	1	2	yes	complemented
75	C₁₉×#123	C₂³	1	2	yes	—
76	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	—	2	2	no	—
78	C₁₉×C₂²⋊Q₈	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	—	4	2	no	—
80	C₁₉×#121	—	2	2	no	—
81	C₁₉×#121	—	2	2	no	—
82	C₁₉×#121	—	2	2	no	—
83	C₁₉×#121	—	2	2	no	—
84	C₁₉×#121	—	4	2	no	—
85	C₁₉×#120	—	2	1	no	—
86	C₁₉×#120	—	2	1	no	—
87	C₁₉×#120	—	2	4	no	—
88	C₁₉×#120	D₄	1	2	yes	complemented
89	C₁₉×#120	C₂³	1	2	yes	—
90	C₄×Q₈×C₁₉	—	2	1	no	—
91	C₄×Q₈×C₁₉	—	2	1	no	—
92	C₄×D₄×C₁₉	—	2	1	no	—
93	C₄×D₄×C₁₉	—	2	2	no	—
94	C₄×D₄×C₁₉	—	2	2	no	—
95	C₄×D₄×C₁₉	—	2	2	no	—
96	C₄×D₄×C₁₉	—	2	2	no	—
97	C₄×D₄×C₁₉	—	2	2	no	—
98	C₄×D₄×C₁₉	—	2	2	no	—
99	C₄×D₄×C₁₉	—	2	2	no	—
100	C₄×D₄×C₁₉	—	2	2	no	—
101	C₄×D₄×C₁₉	—	2	2	no	—
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	—	4	4	no	—
104	C₁₉×#117	—	2	1	no	—
105	C₁₉×#117	—	2	1	no	—
106	C₁₉×#117	—	2	2	no	—
107	C₁₉×#117	—	2	2	no	—
108	C₁₉×#117	D₄	1	2	yes	complemented
109	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
110	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
111	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
112	C₂×C₄²×C₁₉	—	2	2	no	—
113	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic, complemented
114	C₁₉×#104	—	2	2	no	—
115	C₁₉×#104	—	2	2	no	—
116	C₁₉×#101	—	2	1	no	—
117	C₁₉×#100	C₂³	1	2	yes	—
118	C₁₉×#99	—	2	2	no	—
119	C₁₉×#99	—	2	4	no	—
120	C₁₉×#99	—	2	4	no	—
121	C₁₉×#99	C₂³	1	4	yes	—
122	C₂⁴×C₁₉	—	2	1	no	—
123	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
124	#41×C₁₉	—	2	2	no	—
125	#41×C₁₉	—	2	2	no	—
126	#41×C₁₉	—	4	1	no	—
127	#41×C₁₉	—	4	1	no	—
128	#41×C₁₉	—	4	2	no	—
129	#41×C₁₉	—	4	2	no	—
130	#41×C₁₉	—	4	2	no	—
131	#41×C₁₉	—	4	1	no	—
132	#41×C₁₉	—	4	4	no	—
133	#41×C₁₉	—	4	1	no	—
134	#41×C₁₉	—	4	1	no	—
135	#41×C₁₉	—	4	4	no	—
136	#41×C₁₉	—	4	2	no	—
137	#41×C₁₉	—	4	2	no	—
138	#41×C₁₉	—	4	1	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	2	2	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	—	4	2	no	—
143	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂×D₄×C₁₉	—	2	1	no	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	2	2	no	—
150	C₂×D₄×C₁₉	—	2	2	no	—
151	C₂×D₄×C₁₉	—	2	2	no	—
152	C₂×D₄×C₁₉	—	2	4	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	4	2	no	—
155	C₂×D₄×C₁₉	—	4	8	no	—
156	C₂×D₄×C₁₉	—	4	4	no	—
157	C₂×D₄×C₁₉	—	4	1	no	—
158	C₂×D₄×C₁₉	—	4	4	no	—
159	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	—	2	2	no	—
163	C₂²×C₄×C₁₉	—	2	2	no	—
164	C₂²×C₄×C₁₉	—	2	4	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	2	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	2	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	2	no	—
171	C₂²×C₄×C₁₉	—	4	1	no	—
172	C₂²×C₄×C₁₉	—	4	2	no	—
173	C₂²×C₄×C₁₉	—	4	2	no	—
174	C₂²×C₄×C₁₉	—	8	1	no	—
175	C₂²×C₄×C₁₉	—	8	1	no	—
176	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
179	Q₁₆×C₁₉	—	4	2	no	—
180	SD₁₆×C₁₉	—	4	2	no	—
181	SD₁₆×C₁₉	—	4	2	no	—
182	D₈×C₁₉	—	4	2	no	—
183	M₁₆×C₁₉	—	2	2	no	—
184	M₁₆×C₁₉	—	4	1	no	—
185	C₂×C₈×C₁₉	—	4	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	4	2	no	—
196	C₄⋊C₄×C₁₉	—	4	4	no	—
197	C₂²⋊C₄×C₁₉	—	2	2	no	—
198	C₂²⋊C₄×C₁₉	—	2	2	no	—
199	C₂²⋊C₄×C₁₉	—	2	2	no	—
200	C₂²⋊C₄×C₁₉	—	2	1	no	—
201	C₂²⋊C₄×C₁₉	—	2	1	no	—
202	C₂²⋊C₄×C₁₉	—	2	2	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂²⋊C₄×C₁₉	—	2	2	no	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	2	4	no	—
209	C₂²⋊C₄×C₁₉	—	4	4	no	—
210	C₂²⋊C₄×C₁₉	—	4	4	no	—
211	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
212	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
213	C₄²×C₁₉	—	2	2	no	—
214	C₄²×C₁₉	—	2	2	no	—
215	C₄²×C₁₉	—	2	1	no	—
216	C₄²×C₁₉	—	2	2	no	—
217	C₄²×C₁₉	—	4	2	no	—
218	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
220	#33546	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂³×C₁₉	—	2	2	no	—
222	C₂³×C₁₉	—	2	4	no	—
223	C₂³×C₁₉	—	2	1	no	—
224	C₂³×C₁₉	—	4	2	no	—
225	C₂³×C₁₉	—	4	4	no	—
226	C₂³×C₁₉	—	4	4	no	—
227	C₂³×C₁₉	—	4	1	no	—
228	C₂³×C₁₉	—	8	1	no	—
229	C₂³×C₁₉	#120	1	1	yes	characteristic
230	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
231	Q₈×C₁₉	—	2	2	no	—
232	Q₈×C₁₉	—	4	1	no	—
233	Q₈×C₁₉	—	4	1	no	—
234	Q₈×C₁₉	—	4	2	no	—
235	Q₈×C₁₉	—	4	2	no	—
236	Q₈×C₁₉	—	4	1	no	—
237	D₄×C₁₉	—	2	4	no	—
238	D₄×C₁₉	—	2	2	no	—
239	D₄×C₁₉	—	4	2	no	—
240	D₄×C₁₉	—	4	1	no	—
241	D₄×C₁₉	—	4	1	no	—
242	D₄×C₁₉	—	4	4	no	—
243	D₄×C₁₉	—	4	2	no	—
244	D₄×C₁₉	—	4	4	no	—
245	D₄×C₁₉	—	4	4	no	—
246	D₄×C₁₉	—	4	4	no	—
247	D₄×C₁₉	—	4	4	no	—
248	D₄×C₁₉	—	4	2	no	—
249	D₄×C₁₉	—	4	2	no	—
250	D₄×C₁₉	—	4	1	no	—
251	D₄×C₁₉	—	8	1	no	—
252	D₄×C₁₉	—	8	8	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	2	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	2	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	4	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	2	2	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	4	4	no	—
265	C₂×C₄×C₁₉	—	4	4	no	—
266	C₂×C₄×C₁₉	—	4	2	no	—
267	C₂×C₄×C₁₉	—	4	2	no	—
268	C₂×C₄×C₁₉	—	4	4	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	2	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	2	no	—
273	C₂×C₄×C₁₉	—	4	2	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	2	no	—
276	C₂×C₄×C₁₉	—	4	4	no	—
277	C₂×C₄×C₁₉	—	8	2	no	—
278	C₂×C₄×C₁₉	—	8	1	no	—
279	C₂×C₄×C₁₉	—	8	2	no	—
280	C₂×C₄×C₁₉	#120	1	2	yes	—
281	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
282	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
283	C₈×C₁₉	—	4	2	no	—
284	#3481	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#3025	C₂×C₁₉	1	2	yes	complemented
286	#3018	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#2198	C₂×C₁₉	1	2	yes	complemented
288	#2197	C₂×C₁₉	1	4	yes	complemented
289	#2196	C₂×C₁₉	1	2	yes	complemented
290	#2126	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#2120	C₂×C₁₉	1	2	yes	complemented
292	C₂²×C₁₉	—	2	4	no	—
293	C₂²×C₁₉	—	2	2	no	—
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	—	4	2	no	—
297	C₂²×C₁₉	—	4	2	no	—
298	C₂²×C₁₉	—	4	2	no	—
299	C₂²×C₁₉	—	4	4	no	—
300	C₂²×C₁₉	—	4	2	no	—
301	C₂²×C₁₉	—	4	2	no	—
302	C₂²×C₁₉	—	4	1	no	—
303	C₂²×C₁₉	—	8	2	no	—
304	C₂²×C₁₉	—	8	4	no	—
305	C₂²×C₁₉	—	8	4	no	—
306	C₂²×C₁₉	—	16	1	no	—
307	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
308	C₄×C₁₉	—	2	2	no	—
309	C₄×C₁₉	—	2	1	no	—
310	C₄×C₁₉	—	2	2	no	—
311	C₄×C₁₉	—	4	1	no	—
312	C₄×C₁₉	—	4	2	no	—
313	C₄×C₁₉	—	4	2	no	—
314	C₄×C₁₉	—	4	2	no	—
315	C₄×C₁₉	—	4	2	no	—
316	C₄×C₁₉	—	4	1	no	—
317	C₄×C₁₉	—	8	4	no	—
318	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
319	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
320	#585	C₂²×C₁₉	1	1	yes	characteristic, complemented
321	#575	—	2	1	no	—
322	#559	C₂²×C₁₉	1	1	yes	characteristic, complemented
323	#554	—	2	1	no	—
324	#553	—	2	2	no	—
325	#551	—	2	1	no	—
326	#551	C₂²×C₁₉	1	2	yes	complemented
327	#546	—	2	2	no	—
328	D₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
329	#532	C₂²×C₁₉	1	1	yes	characteristic
330	#529	—	2	2	no	—
331	#525	—	2	1	no	—
332	#525	—	2	2	no	—
333	#525	C₂²×C₁₉	1	2	yes	—
334	C₄×#41	—	2	1	no	—
335	C₂×C₄×D₄	—	2	2	no	—
336	#458	—	2	2	no	—
337	#458	C₂²×C₁₉	1	4	yes	complemented
338	B(4,𝔽₂)	—	2	2	no	—
339	B(4,𝔽₂)	C₂²×C₁₉	1	4	yes	—
340	#456	—	2	1	no	—
341	#455	C₂²×C₁₉	1	2	yes	complemented
342	#454	—	2	1	no	—
343	#453	C₂²×C₁₉	1	2	yes	—
344	C₂×#104	—	2	1	no	—
345	#413	C₂²×C₁₉	1	1	yes	characteristic, complemented
346	#410	—	2	2	no	—
347	#410	C₂²×C₁₉	1	2	yes	complemented
348	#354	C₂²×C₁₉	1	2	yes	complemented
349	#353	C₂²×C₁₉	1	2	yes	complemented
350	#352	C₂²×C₁₉	1	4	yes	complemented
351	AΣL(1,𝔽₁₆)	C₂²×C₁₉	1	4	yes	complemented
352	C₂×C₁₉	—	2	1	no	—
353	C₂×C₁₉	—	4	2	no	—
354	C₂×C₁₉	—	4	4	no	—
355	C₂×C₁₉	—	4	1	no	—
356	C₂×C₁₉	—	8	1	no	—
357	C₂×C₁₉	—	8	2	no	—
358	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
359	2₋¹⁺⁴	—	2	1	no	—
360	2₋¹⁺⁴	—	4	1	no	—
361	H(5,𝔽₂)	—	2	2	no	—
362	H(5,𝔽₂)	—	4	1	no	—
363	H(5,𝔽₂)	C₂³×C₁₉	1	2	yes	—
364	C₂×#41	—	2	1	no	—
365	C₂×#41	—	2	2	no	—
366	C₂×#41	—	2	1	no	—
367	C₂×#41	—	4	2	no	—
368	C₂×#41	D₄×C₁₉	1	1	yes	characteristic, complemented
369	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
370	C₂²×D₄	—	2	2	no	—
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	D₄×C₁₉	1	2	yes	complemented
373	#137	—	2	2	no	—
374	#137	—	4	1	no	—
375	AGL(1,ℤ/8)	—	2	2	no	—
376	AGL(1,ℤ/8)	—	4	1	no	—
377	#135	—	4	2	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
380	#127	C₂³×C₁₉	1	1	yes	characteristic
381	#126	—	2	2	no	—
382	#126	—	2	2	no	—
383	#125	—	2	2	no	—
384	#124	—	2	2	no	—
385	#124	D₄×C₁₉	1	1	yes	characteristic, complemented
386	#124	C₂³×C₁₉	1	1	yes	characteristic
387	#123	—	2	1	no	—
388	#123	—	2	2	no	—
389	#123	—	2	1	no	—
390	#123	—	2	2	no	—
391	#123	—	2	4	no	—
392	#123	D₄×C₁₉	1	2	yes	complemented
393	#123	C₂³×C₁₉	1	2	yes	—
394	C₂²⋊Q₈	—	2	2	no	—
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	4	2	no	—
398	#121	—	2	2	no	—
399	#121	—	2	2	no	—
400	#121	—	2	2	no	—
401	#121	—	2	2	no	—
402	#121	—	4	2	no	—
403	#120	—	2	1	no	—
404	#120	—	2	1	no	—
405	#120	—	2	4	no	—
406	#120	D₄×C₁₉	1	2	yes	complemented
407	#120	C₂³×C₁₉	1	2	yes	—
408	C₄×Q₈	—	2	1	no	—
409	C₄×Q₈	—	2	1	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	—	2	2	no	—
412	C₄×D₄	—	2	2	no	—
413	C₄×D₄	—	2	2	no	—
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	2	2	no	—
420	C₄×D₄	—	2	1	no	—
421	C₄×D₄	—	4	4	no	—
422	#117	—	2	1	no	—
423	#117	—	2	1	no	—
424	#117	—	2	2	no	—
425	#117	—	2	2	no	—
426	#117	D₄×C₁₉	1	2	yes	complemented
427	C₂×C₄⋊C₄	—	2	2	no	—
428	C₂×C₂²⋊C₄	—	2	2	no	—
429	C₂×C₂²⋊C₄	—	2	2	no	—
430	C₂×C₄²	—	2	2	no	—
431	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic, complemented
432	#104	—	2	2	no	—
433	#104	—	2	2	no	—
434	#101	—	2	1	no	—
435	#100	C₂³×C₁₉	1	2	yes	—
436	#99	—	2	2	no	—
437	#99	—	2	4	no	—
438	#99	—	2	4	no	—
439	#99	C₂³×C₁₉	1	4	yes	—
440	C₁₉	#33546	1	1	yes	characteristic, direct product factor, Sylow
441	C₂⁴	—	2	1	no	—
442	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
443	#41	—	2	2	no	—
444	#41	—	2	2	no	—
445	#41	—	4	1	no	—
446	#41	—	4	1	no	—
447	#41	—	4	2	no	—
448	#41	—	4	2	no	—
449	#41	—	4	2	no	—
450	#41	—	4	1	no	—
451	#41	—	4	4	no	—
452	#41	—	4	1	no	—
453	#41	—	4	1	no	—
454	#41	—	4	4	no	—
455	#41	—	4	2	no	—
456	#41	—	4	1	no	—
457	#41	—	4	2	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	2	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	4	2	no	—
462	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
463	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	4	2	no	—
474	C₂×D₄	—	4	8	no	—
475	C₂×D₄	—	4	4	no	—
476	C₂×D₄	—	4	1	no	—
477	C₂×D₄	—	4	4	no	—
478	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
479	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	4	1	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	8	1	no	—
494	C₂²×C₄	—	8	1	no	—
495	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
496	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
498	Q₁₆	—	4	2	no	—
499	SD₁₆	—	4	2	no	—
500	SD₁₆	—	4	2	no	—
501	D₈	—	4	2	no	—
502	M₁₆	—	2	2	no	—
503	M₁₆	—	4	1	no	—
504	C₂×C₈	—	4	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	4	2	no	—
515	C₄⋊C₄	—	4	4	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	1	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	4	no	—
528	C₂²⋊C₄	—	4	4	no	—
529	C₂²⋊C₄	—	4	4	no	—
530	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
531	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
532	C₄²	—	2	2	no	—
533	C₄²	—	2	2	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	4	2	no	—
537	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
538	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
539	C₂³	—	2	2	no	—
540	C₂³	—	2	4	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	4	2	no	—
543	C₂³	—	4	4	no	—
544	C₂³	—	4	4	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	8	1	no	—
547	C₂³	C₁₉×#120	1	1	yes	characteristic
548	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
549	Q₈	—	2	2	no	—
550	Q₈	—	4	1	no	—
551	Q₈	—	4	1	no	—
552	Q₈	—	4	2	no	—
553	Q₈	—	4	2	no	—
554	Q₈	—	4	1	no	—
555	D₄	—	2	4	no	—
556	D₄	—	2	2	no	—
557	D₄	—	4	2	no	—
558	D₄	—	4	1	no	—
559	D₄	—	4	1	no	—
560	D₄	—	4	2	no	—
561	D₄	—	4	4	no	—
562	D₄	—	4	4	no	—
563	D₄	—	4	4	no	—
564	D₄	—	4	4	no	—
565	D₄	—	4	4	no	—
566	D₄	—	4	2	no	—
567	D₄	—	4	2	no	—
568	D₄	—	4	1	no	—
569	D₄	—	8	1	no	—
570	D₄	—	8	8	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	4	4	no	—
583	C₂×C₄	—	4	4	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	4	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	4	no	—
595	C₂×C₄	—	8	2	no	—
596	C₂×C₄	—	8	1	no	—
597	C₂×C₄	—	8	2	no	—
598	C₂×C₄	C₁₉×#120	1	2	yes	—
599	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
600	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
601	C₈	—	4	2	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	1	no	—
613	C₂²	—	8	2	no	—
614	C₂²	—	8	4	no	—
615	C₂²	—	8	4	no	—
616	C₂²	—	16	1	no	—
617	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
618	C₄	—	2	2	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	2	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	2	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	1	no	—
627	C₄	—	8	4	no	—
628	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
629	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
630	C₂	—	2	1	no	—
631	C₂	—	4	2	no	—
632	C₂	—	4	4	no	—
633	C₂	—	4	1	no	—
634	C₂	—	8	1	no	—
635	C₂	—	8	2	no	—
636	C₂	C₂×C₁₉×B(4,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₉	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×D₄	C₂⁴×C₁₉
socle	C₂×C₁₉	C₂×B(4,𝔽₂)
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×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×#3481	C₂	semidirect
2. C₁₉×#3025	C₂	semidirect
3. C₁₉×#3018	C₂	semidirect
4. C₁₉×#2198	C₂	semidirect
5. C₁₉×#2197	C₂	semidirect
6. C₁₉×#2196	C₂	semidirect
7. C₁₉×#2126	C₂	semidirect
8. C₁₉×#2120	C₂	semidirect
9. C₁₉×#585	C₂²	semidirect
11. C₁₉×#559	C₂²	semidirect
15. C₁₉×#551	C₂²	semidirect
17. D₄²×C₁₉	C₂²	semidirect
26. C₁₉×#458	C₂²	semidirect
30. C₁₉×#455	C₂²	semidirect
34. C₁₉×#413	C₂²	semidirect
36. C₁₉×#410	C₂²	semidirect
37. C₁₉×#354	C₂²	semidirect
38. C₁₉×#353	C₂²	semidirect
39. C₁₉×#352	C₂²	semidirect
40. C₁₉×AΣL(1,𝔽₁₆)	C₂²	semidirect
50. C₂×#41×C₁₉	D₄	semidirect
54. C₂³×C₄×C₁₉	D₄	semidirect
61. C₁₉×C₄⋊Q₈	D₄	semidirect
67. C₁₉×#124	D₄	semidirect
74. C₁₉×#123	D₄	semidirect
88. C₁₉×#120	D₄	semidirect
108. C₁₉×#117	D₄	semidirect
113. C₂×C₄²×C₁₉	D₄	semidirect
220. #33546	C₁₉	direct (N × H)
284. #3481	C₂×C₁₉	semidirect
285. #3025	C₂×C₁₉	semidirect
286. #3018	C₂×C₁₉	semidirect
287. #2198	C₂×C₁₉	semidirect
288. #2197	C₂×C₁₉	semidirect
289. #2196	C₂×C₁₉	semidirect
290. #2126	C₂×C₁₉	semidirect
291. #2120	C₂×C₁₉	semidirect
320. #585	C₂²×C₁₉	semidirect
322. #559	C₂²×C₁₉	semidirect
326. #551	C₂²×C₁₉	semidirect
328. D₄²	C₂²×C₁₉	semidirect
337. #458	C₂²×C₁₉	semidirect
341. #455	C₂²×C₁₉	semidirect
345. #413	C₂²×C₁₉	semidirect
347. #410	C₂²×C₁₉	semidirect
348. #354	C₂²×C₁₉	semidirect
349. #353	C₂²×C₁₉	semidirect
350. #352	C₂²×C₁₉	semidirect
351. AΣL(1,𝔽₁₆)	C₂²×C₁₉	semidirect
368. C₂×#41	D₄×C₁₉	semidirect
372. C₂³×C₄	D₄×C₁₉	semidirect
379. C₄⋊Q₈	D₄×C₁₉	semidirect
385. #124	D₄×C₁₉	semidirect
392. #123	D₄×C₁₉	semidirect
406. #120	D₄×C₁₉	semidirect
426. #117	D₄×C₁₉	semidirect
431. C₂×C₄²	D₄×C₁₉	semidirect
440. C₁₉	#33546	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×#3481	2
C₁₉×#3025	2
C₁₉×#3018	2
C₁₉×#2198	2
C₁₉×#2197	2
C₁₉×#2196	2
C₁₉×#2126	2
C₁₉×#2120	2
#33546	19

Subgroups — C19×#33546 #18039505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33546 #18039505