Subgroups — C₁₉×#33550 #18039509

Order 4864.

1144 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3529	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×#2201	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2200	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2199	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
10	C₁₉×#575	—	2	1	no	—
11	C₁₉×#563	—	2	1	no	—
12	C₁₉×#563	C₂²	1	1	yes	characteristic, complemented
13	C₁₉×#562	—	2	1	no	—
14	C₁₉×#562	—	2	2	no	—
15	C₁₉×H(3,𝔽₄)	C₂²	1	1	yes	characteristic, complemented
16	C₁₉×#560	—	2	2	no	—
17	C₁₉×#560	C₂²	1	2	yes	complemented
18	C₁₉×#532	—	2	1	no	—
19	C₁₉×#532	C₂²	1	1	yes	characteristic
20	C₁₉×#529	—	2	2	no	—
21	C₁₉×#529	—	2	1	no	—
22	C₁₉×#525	—	2	2	no	—
23	C₁₉×#525	—	2	2	no	—
24	C₁₉×#525	C₂²	1	2	yes	—
25	C₁₉×#458	—	2	2	no	—
26	C₁₉×#458	C₂²	1	4	yes	—
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	—
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
35	C₁₉×#410	—	2	2	no	—
36	C₁₉×#410	C₂²	1	2	yes	—
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	C₂³×C₄×C₁₉	D₄	1	2	yes	complemented
53	C₁₉×#137	—	2	2	no	—
54	C₁₉×#137	—	4	1	no	—
55	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
56	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
57	C₁₉×#135	—	4	2	no	—
58	C₂×M₁₆×C₁₉	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
61	C₁₉×#127	—	2	1	no	—
62	C₁₉×#127	C₂³	1	1	yes	characteristic
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#126	—	2	2	no	—
65	C₁₉×#126	—	2	2	no	—
66	C₁₉×#125	—	2	2	no	—
67	C₁₉×#125	—	2	1	no	—
68	C₁₉×#124	—	2	1	no	—
69	C₁₉×#124	—	2	1	no	—
70	C₁₉×#124	—	2	2	no	—
71	C₁₉×#124	—	2	1	no	—
72	C₁₉×#124	D₄	1	1	yes	characteristic, complemented
73	C₁₉×#124	C₂³	1	1	yes	characteristic
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×#123	—	2	2	no	—
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×#123	—	2	2	no	—
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×#123	—	2	4	no	—
80	C₁₉×#123	D₄	1	2	yes	complemented
81	C₁₉×#123	C₂³	1	2	yes	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	2	no	—
87	C₁₉×C₂²⋊Q₈	—	4	2	no	—
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	—	2	1	no	—
90	C₁₉×#121	—	2	2	no	—
91	C₁₉×#121	—	2	2	no	—
92	C₁₉×#121	—	2	2	no	—
93	C₁₉×#121	—	2	2	no	—
94	C₁₉×#121	—	2	2	no	—
95	C₁₉×#121	—	2	2	no	—
96	C₁₉×#121	—	4	2	no	—
97	C₁₉×#120	—	2	2	no	—
98	C₁₉×#120	—	2	2	no	—
99	C₁₉×#120	—	2	4	no	—
100	C₁₉×#120	D₄	1	2	yes	complemented
101	C₁₉×#120	C₂³	1	2	yes	—
102	C₄×Q₈×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	—	2	1	no	—
104	C₄×D₄×C₁₉	—	2	2	no	—
105	C₄×D₄×C₁₉	—	2	2	no	—
106	C₄×D₄×C₁₉	—	2	2	no	—
107	C₄×D₄×C₁₉	—	2	2	no	—
108	C₄×D₄×C₁₉	—	4	4	no	—
109	C₁₉×#117	—	2	2	no	—
110	C₁₉×#117	—	2	2	no	—
111	C₁₉×#117	D₄	1	2	yes	complemented
112	C₂×C₄²×C₁₉	—	2	1	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	C₂×D₄	1	2	yes	—
123	#41×C₁₉	—	2	2	no	—
124	#41×C₁₉	—	2	2	no	—
125	#41×C₁₉	—	4	1	no	—
126	#41×C₁₉	—	4	1	no	—
127	#41×C₁₉	—	4	2	no	—
128	#41×C₁₉	—	4	2	no	—
129	#41×C₁₉	—	4	2	no	—
130	#41×C₁₉	—	4	1	no	—
131	#41×C₁₉	—	4	4	no	—
132	#41×C₁₉	—	4	1	no	—
133	#41×C₁₉	—	4	1	no	—
134	#41×C₁₉	—	4	2	no	—
135	#41×C₁₉	—	4	2	no	—
136	#41×C₁₉	—	4	1	no	—
137	#41×C₁₉	—	8	1	no	—
138	#41×C₁₉	—	8	1	no	—
139	C₂×Q₈×C₁₉	—	2	2	no	—
140	C₂×Q₈×C₁₉	—	2	1	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	—	2	1	no	—
143	C₂×Q₈×C₁₉	—	4	2	no	—
144	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	2	4	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	—	2	2	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	2	no	—
153	C₂×D₄×C₁₉	—	2	2	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	2	no	—
156	C₂×D₄×C₁₉	—	2	2	no	—
157	C₂×D₄×C₁₉	—	4	2	no	—
158	C₂×D₄×C₁₉	—	4	4	no	—
159	C₂×D₄×C₁₉	—	4	1	no	—
160	C₂×D₄×C₁₉	—	4	4	no	—
161	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
162	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	—	2	4	no	—
165	C₂²×C₄×C₁₉	—	2	2	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	2	no	—
169	C₂²×C₄×C₁₉	—	2	2	no	—
170	C₂²×C₄×C₁₉	—	4	1	no	—
171	C₂²×C₄×C₁₉	—	4	2	no	—
172	C₂²×C₄×C₁₉	—	4	2	no	—
173	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
176	Q₁₆×C₁₉	—	4	2	no	—
177	SD₁₆×C₁₉	—	4	2	no	—
178	SD₁₆×C₁₉	—	4	2	no	—
179	D₈×C₁₉	—	4	2	no	—
180	M₁₆×C₁₉	—	2	2	no	—
181	M₁₆×C₁₉	—	4	1	no	—
182	C₂×C₈×C₁₉	—	4	1	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	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	—	4	2	no	—
194	C₄⋊C₄×C₁₉	—	4	4	no	—
195	C₂²⋊C₄×C₁₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₉	—	2	2	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	2	no	—
201	C₂²⋊C₄×C₁₉	—	2	2	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	4	no	—
207	C₂²⋊C₄×C₁₉	—	4	4	no	—
208	C₂²⋊C₄×C₁₉	—	4	4	no	—
209	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
210	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
211	C₄²×C₁₉	—	2	1	no	—
212	C₄²×C₁₉	—	2	1	no	—
213	C₄²×C₁₉	—	2	2	no	—
214	C₄²×C₁₉	—	2	1	no	—
215	C₄²×C₁₉	—	4	2	no	—
216	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
218	#33550	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂³×C₁₉	—	2	4	no	—
220	C₂³×C₁₉	—	2	2	no	—
221	C₂³×C₁₉	—	2	1	no	—
222	C₂³×C₁₉	—	4	2	no	—
223	C₂³×C₁₉	—	4	1	no	—
224	C₂³×C₁₉	—	8	2	no	—
225	C₂³×C₁₉	#120	1	1	yes	characteristic
226	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
227	Q₈×C₁₉	—	2	2	no	—
228	Q₈×C₁₉	—	4	1	no	—
229	Q₈×C₁₉	—	4	1	no	—
230	Q₈×C₁₉	—	4	2	no	—
231	Q₈×C₁₉	—	4	1	no	—
232	Q₈×C₁₉	—	8	1	no	—
233	Q₈×C₁₉	—	8	1	no	—
234	D₄×C₁₉	—	2	2	no	—
235	D₄×C₁₉	—	4	2	no	—
236	D₄×C₁₉	—	4	1	no	—
237	D₄×C₁₉	—	4	1	no	—
238	D₄×C₁₉	—	4	2	no	—
239	D₄×C₁₉	—	4	4	no	—
240	D₄×C₁₉	—	4	2	no	—
241	D₄×C₁₉	—	4	2	no	—
242	D₄×C₁₉	—	4	1	no	—
243	D₄×C₁₉	—	8	1	no	—
244	D₄×C₁₉	—	8	2	no	—
245	D₄×C₁₉	—	8	2	no	—
246	D₄×C₁₉	—	8	2	no	—
247	D₄×C₁₉	—	8	2	no	—
248	D₄×C₁₉	—	8	1	no	—
249	D₄×C₁₉	—	8	2	no	—
250	D₄×C₁₉	—	8	1	no	—
251	D₄×C₁₉	—	8	8	no	—
252	C₂×C₄×C₁₉	—	2	2	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	4	no	—
257	C₂×C₄×C₁₉	—	2	2	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	2	no	—
263	C₂×C₄×C₁₉	—	4	4	no	—
264	C₂×C₄×C₁₉	—	4	2	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	2	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	2	no	—
269	C₂×C₄×C₁₉	—	4	2	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	4	2	no	—
272	C₂×C₄×C₁₉	—	4	4	no	—
273	C₂×C₄×C₁₉	—	8	2	no	—
274	C₂×C₄×C₁₉	—	8	1	no	—
275	C₂×C₄×C₁₉	—	8	2	no	—
276	C₂×C₄×C₁₉	#120	1	2	yes	—
277	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
278	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
279	C₈×C₁₉	—	4	2	no	—
280	#3529	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#3025	C₂×C₁₉	1	2	yes	complemented
282	#3018	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#2201	C₂×C₁₉	1	2	yes	complemented
284	#2200	C₂×C₁₉	1	4	yes	complemented
285	#2199	C₂×C₁₉	1	2	yes	complemented
286	#2126	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#2120	C₂×C₁₉	1	2	yes	complemented
288	C₂²×C₁₉	—	2	2	no	—
289	C₂²×C₁₉	—	2	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	2	no	—
292	C₂²×C₁₉	—	4	2	no	—
293	C₂²×C₁₉	—	4	2	no	—
294	C₂²×C₁₉	—	4	2	no	—
295	C₂²×C₁₉	—	4	4	no	—
296	C₂²×C₁₉	—	4	2	no	—
297	C₂²×C₁₉	—	4	2	no	—
298	C₂²×C₁₉	—	4	1	no	—
299	C₂²×C₁₉	—	8	4	no	—
300	C₂²×C₁₉	—	8	2	no	—
301	C₂²×C₁₉	—	16	1	no	—
302	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
303	C₄×C₁₉	—	2	1	no	—
304	C₄×C₁₉	—	2	2	no	—
305	C₄×C₁₉	—	4	2	no	—
306	C₄×C₁₉	—	4	1	no	—
307	C₄×C₁₉	—	4	2	no	—
308	C₄×C₁₉	—	4	1	no	—
309	C₄×C₁₉	—	4	2	no	—
310	C₄×C₁₉	—	4	2	no	—
311	C₄×C₁₉	—	4	1	no	—
312	C₄×C₁₉	—	8	4	no	—
313	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
314	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
315	#585	C₂²×C₁₉	1	1	yes	characteristic
316	#575	—	2	1	no	—
317	#563	—	2	1	no	—
318	#563	C₂²×C₁₉	1	1	yes	characteristic, complemented
319	#562	—	2	1	no	—
320	#562	—	2	2	no	—
321	H(3,𝔽₄)	C₂²×C₁₉	1	1	yes	characteristic, complemented
322	#560	—	2	2	no	—
323	#560	C₂²×C₁₉	1	2	yes	complemented
324	#532	—	2	1	no	—
325	#532	C₂²×C₁₉	1	1	yes	characteristic
326	#529	—	2	2	no	—
327	#529	—	2	1	no	—
328	#525	—	2	2	no	—
329	#525	—	2	2	no	—
330	#525	C₂²×C₁₉	1	2	yes	—
331	#458	—	2	2	no	—
332	#458	C₂²×C₁₉	1	4	yes	—
333	B(4,𝔽₂)	—	2	2	no	—
334	B(4,𝔽₂)	C₂²×C₁₉	1	4	yes	—
335	#456	—	2	1	no	—
336	#455	C₂²×C₁₉	1	2	yes	—
337	#454	—	2	1	no	—
338	#453	C₂²×C₁₉	1	2	yes	—
339	C₂×#104	—	2	1	no	—
340	#413	C₂²×C₁₉	1	1	yes	characteristic
341	#410	—	2	2	no	—
342	#410	C₂²×C₁₉	1	2	yes	—
343	#354	C₂²×C₁₉	1	2	yes	complemented
344	#353	C₂²×C₁₉	1	2	yes	complemented
345	#352	C₂²×C₁₉	1	4	yes	complemented
346	AΣL(1,𝔽₁₆)	C₂²×C₁₉	1	4	yes	complemented
347	C₂×C₁₉	—	2	1	no	—
348	C₂×C₁₉	—	4	2	no	—
349	C₂×C₁₉	—	4	1	no	—
350	C₂×C₁₉	—	8	1	no	—
351	C₂×C₁₉	—	8	2	no	—
352	C₂×C₁₉	—	8	2	no	—
353	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
354	2₋¹⁺⁴	—	2	1	no	—
355	2₋¹⁺⁴	—	4	1	no	—
356	H(5,𝔽₂)	—	2	2	no	—
357	H(5,𝔽₂)	—	4	1	no	—
358	H(5,𝔽₂)	C₂³×C₁₉	1	2	yes	—
359	C₂×#41	—	2	1	no	—
360	C₂×#41	—	2	2	no	—
361	C₂×#41	—	2	1	no	—
362	C₂×#41	—	4	2	no	—
363	C₂×#41	D₄×C₁₉	1	1	yes	characteristic, complemented
364	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
365	C₂³×C₄	D₄×C₁₉	1	2	yes	complemented
366	#137	—	2	2	no	—
367	#137	—	4	1	no	—
368	AGL(1,ℤ/8)	—	2	2	no	—
369	AGL(1,ℤ/8)	—	4	1	no	—
370	#135	—	4	2	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₄⋊Q₈	—	2	1	no	—
373	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
374	#127	—	2	1	no	—
375	#127	C₂³×C₁₉	1	1	yes	characteristic
376	#126	—	2	2	no	—
377	#126	—	2	2	no	—
378	#126	—	2	2	no	—
379	#125	—	2	2	no	—
380	#125	—	2	1	no	—
381	#124	—	2	1	no	—
382	#124	—	2	1	no	—
383	#124	—	2	2	no	—
384	#124	—	2	1	no	—
385	#124	D₄×C₁₉	1	1	yes	characteristic, complemented
386	#124	C₂³×C₁₉	1	1	yes	characteristic
387	#123	—	2	2	no	—
388	#123	—	2	2	no	—
389	#123	—	2	2	no	—
390	#123	—	2	2	no	—
391	#123	—	2	2	no	—
392	#123	—	2	4	no	—
393	#123	D₄×C₁₉	1	2	yes	complemented
394	#123	C₂³×C₁₉	1	2	yes	—
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	2	1	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	C₂²⋊Q₈	—	4	2	no	—
401	#121	—	2	2	no	—
402	#121	—	2	1	no	—
403	#121	—	2	2	no	—
404	#121	—	2	2	no	—
405	#121	—	2	2	no	—
406	#121	—	2	2	no	—
407	#121	—	2	2	no	—
408	#121	—	2	2	no	—
409	#121	—	4	2	no	—
410	#120	—	2	2	no	—
411	#120	—	2	2	no	—
412	#120	—	2	4	no	—
413	#120	D₄×C₁₉	1	2	yes	complemented
414	#120	C₂³×C₁₉	1	2	yes	—
415	C₄×Q₈	—	2	1	no	—
416	C₄×D₄	—	2	1	no	—
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	2	2	no	—
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	—	4	4	no	—
422	#117	—	2	2	no	—
423	#117	—	2	2	no	—
424	#117	D₄×C₁₉	1	2	yes	complemented
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic, complemented
427	#104	—	2	2	no	—
428	#104	—	2	2	no	—
429	#101	—	2	1	no	—
430	#100	C₂³×C₁₉	1	2	yes	—
431	#99	—	2	2	no	—
432	#99	—	2	4	no	—
433	#99	—	2	4	no	—
434	#99	C₂³×C₁₉	1	4	yes	—
435	C₁₉	#33550	1	1	yes	characteristic, direct product factor, Sylow
436	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
437	#41	—	2	2	no	—
438	#41	—	2	2	no	—
439	#41	—	4	1	no	—
440	#41	—	4	1	no	—
441	#41	—	4	2	no	—
442	#41	—	4	2	no	—
443	#41	—	4	2	no	—
444	#41	—	4	1	no	—
445	#41	—	4	4	no	—
446	#41	—	4	1	no	—
447	#41	—	4	1	no	—
448	#41	—	4	2	no	—
449	#41	—	4	1	no	—
450	#41	—	4	2	no	—
451	#41	—	8	1	no	—
452	#41	—	8	1	no	—
453	C₂×Q₈	—	2	2	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	4	2	no	—
458	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	4	2	no	—
472	C₂×D₄	—	4	4	no	—
473	C₂×D₄	—	4	1	no	—
474	C₂×D₄	—	4	4	no	—
475	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
476	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	4	1	no	—
485	C₂²×C₄	—	4	2	no	—
486	C₂²×C₄	—	4	2	no	—
487	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
488	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
490	Q₁₆	—	4	2	no	—
491	SD₁₆	—	4	2	no	—
492	SD₁₆	—	4	2	no	—
493	D₈	—	4	2	no	—
494	M₁₆	—	2	2	no	—
495	M₁₆	—	4	1	no	—
496	C₂×C₈	—	4	1	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	4	2	no	—
508	C₄⋊C₄	—	4	4	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	4	4	no	—
522	C₂²⋊C₄	—	4	4	no	—
523	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
524	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	2	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	4	2	no	—
530	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
532	C₂³	—	2	4	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	4	2	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	8	2	no	—
538	C₂³	C₁₉×#120	1	1	yes	characteristic
539	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
540	Q₈	—	2	2	no	—
541	Q₈	—	4	1	no	—
542	Q₈	—	4	1	no	—
543	Q₈	—	4	2	no	—
544	Q₈	—	4	1	no	—
545	Q₈	—	8	1	no	—
546	Q₈	—	8	1	no	—
547	D₄	—	2	2	no	—
548	D₄	—	4	2	no	—
549	D₄	—	4	1	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	4	no	—
553	D₄	—	4	2	no	—
554	D₄	—	4	2	no	—
555	D₄	—	4	1	no	—
556	D₄	—	8	1	no	—
557	D₄	—	8	2	no	—
558	D₄	—	8	1	no	—
559	D₄	—	8	2	no	—
560	D₄	—	8	2	no	—
561	D₄	—	8	2	no	—
562	D₄	—	8	2	no	—
563	D₄	—	8	1	no	—
564	D₄	—	8	8	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	4	4	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	4	no	—
586	C₂×C₄	—	8	2	no	—
587	C₂×C₄	—	8	1	no	—
588	C₂×C₄	—	8	2	no	—
589	C₂×C₄	C₁₉×#120	1	2	yes	—
590	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
591	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
592	C₈	—	4	2	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	4	4	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	8	4	no	—
605	C₂²	—	8	2	no	—
606	C₂²	—	16	1	no	—
607	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
608	C₄	—	2	1	no	—
609	C₄	—	2	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	2	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	2	no	—
615	C₄	—	4	2	no	—
616	C₄	—	4	1	no	—
617	C₄	—	8	4	no	—
618	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
619	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
620	C₂	—	2	1	no	—
621	C₂	—	4	2	no	—
622	C₂	—	4	1	no	—
623	C₂	—	8	2	no	—
624	C₂	—	8	1	no	—
625	C₂	—	8	2	no	—
626	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×#3529	C₂	semidirect
2. C₁₉×#3025	C₂	semidirect
3. C₁₉×#3018	C₂	semidirect
4. C₁₉×#2201	C₂	semidirect
5. C₁₉×#2200	C₂	semidirect
6. C₁₉×#2199	C₂	semidirect
7. C₁₉×#2126	C₂	semidirect
8. C₁₉×#2120	C₂	semidirect
12. C₁₉×#563	C₂²	semidirect
15. C₁₉×H(3,𝔽₄)	C₂²	semidirect
17. C₁₉×#560	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
52. C₂³×C₄×C₁₉	D₄	semidirect
60. C₁₉×C₄⋊Q₈	D₄	semidirect
72. C₁₉×#124	D₄	semidirect
80. C₁₉×#123	D₄	semidirect
100. C₁₉×#120	D₄	semidirect
111. C₁₉×#117	D₄	semidirect
113. C₂×C₄²×C₁₉	D₄	semidirect
218. #33550	C₁₉	direct (N × H)
280. #3529	C₂×C₁₉	semidirect
281. #3025	C₂×C₁₉	semidirect
282. #3018	C₂×C₁₉	semidirect
283. #2201	C₂×C₁₉	semidirect
284. #2200	C₂×C₁₉	semidirect
285. #2199	C₂×C₁₉	semidirect
286. #2126	C₂×C₁₉	semidirect
287. #2120	C₂×C₁₉	semidirect
318. #563	C₂²×C₁₉	semidirect
321. H(3,𝔽₄)	C₂²×C₁₉	semidirect
323. #560	C₂²×C₁₉	semidirect
343. #354	C₂²×C₁₉	semidirect
344. #353	C₂²×C₁₉	semidirect
345. #352	C₂²×C₁₉	semidirect
346. AΣL(1,𝔽₁₆)	C₂²×C₁₉	semidirect
363. C₂×#41	D₄×C₁₉	semidirect
365. C₂³×C₄	D₄×C₁₉	semidirect
373. C₄⋊Q₈	D₄×C₁₉	semidirect
385. #124	D₄×C₁₉	semidirect
393. #123	D₄×C₁₉	semidirect
413. #120	D₄×C₁₉	semidirect
424. #117	D₄×C₁₉	semidirect
426. C₂×C₄²	D₄×C₁₉	semidirect
435. C₁₉	#33550	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×#3529	2
C₁₉×#3025	2
C₁₉×#3018	2
C₁₉×#2201	2
C₁₉×#2200	2
C₁₉×#2199	2
C₁₉×#2126	2
C₁₉×#2120	2
#33550	19

Subgroups — C19×#33550 #18039509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33550 #18039509