Subgroups — C₁₉×#33561 #18039520

Order 4864.

1096 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3028	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3018	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2201	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2198	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2126	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2123	C₂	1	2	yes	maximal, complemented
8	C₁₉×#585	C₂²	1	1	yes	characteristic
9	C₁₉×#575	—	2	1	no	—
10	C₁₉×#563	—	2	1	no	—
11	C₁₉×#563	C₂²	1	2	yes	complemented
12	C₁₉×#559	C₂²	1	2	yes	complemented
13	Q₈²×C₁₉	—	2	1	no	—
14	C₁₉×#556	—	2	2	no	—
15	D₄×Q₈×C₁₉	—	2	2	no	—
16	C₁₉×#542	—	2	4	no	—
17	C₁₉×#536	—	2	1	no	—
18	C₁₉×#536	—	2	2	no	—
19	C₁₉×#536	C₂²	1	2	yes	—
20	C₁₉×#533	—	2	1	no	—
21	C₁₉×#532	C₂²	1	1	yes	characteristic
22	C₁₉×#458	—	2	4	no	—
23	C₁₉×#458	C₂²	1	8	yes	—
24	C₁₉×#456	—	2	1	no	—
25	C₁₉×#455	C₂²	1	2	yes	—
26	C₁₉×#454	—	2	1	no	—
27	C₁₉×#453	C₂²	1	2	yes	—
28	C₂×C₁₉×#104	—	2	1	no	—
29	C₁₉×#413	C₂²	1	1	yes	characteristic
30	C₁₉×#410	—	2	2	no	—
31	C₁₉×#410	C₂²	1	2	yes	—
32	C₁₉×#354	C₂²	1	2	yes	complemented
33	C₁₉×#353	C₂²	1	2	yes	complemented
34	C₁₉×#352	C₂²	1	8	yes	complemented
35	C₁₉×2₋¹⁺⁴	—	2	1	no	—
36	C₁₉×2₋¹⁺⁴	—	4	1	no	—
37	C₁₉×H(5,𝔽₂)	—	2	2	no	—
38	C₁₉×H(5,𝔽₂)	—	4	1	no	—
39	C₁₉×H(5,𝔽₂)	C₂³	1	2	yes	—
40	C₂×#41×C₁₉	—	2	2	no	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	—	4	2	no	—
43	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
44	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₁₉	—	2	1	no	—
46	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
47	C₁₉×#137	—	2	2	no	—
48	C₁₉×#137	—	4	1	no	—
49	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
50	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
51	C₁₉×#135	—	4	2	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	—	2	1	no	—
54	C₁₉×C₄⋊Q₈	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	—	2	4	no	—
56	C₁₉×C₄⋊Q₈	—	2	2	no	—
57	C₁₉×C₄⋊Q₈	—	2	2	no	—
58	C₁₉×C₄⋊Q₈	—	4	2	no	—
59	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₁₉×#127	C₂³	1	1	yes	characteristic
61	C₁₉×#126	—	2	4	no	—
62	C₁₉×#126	—	2	4	no	—
63	C₁₉×#125	—	2	2	no	—
64	C₁₉×#124	—	2	2	no	—
65	C₁₉×#124	—	2	2	no	—
66	C₁₉×#124	—	2	4	no	—
67	C₁₉×#124	—	4	2	no	—
68	C₁₉×#124	D₄	1	1	yes	characteristic
69	C₁₉×#124	C₂³	1	1	yes	characteristic
70	C₁₉×#123	—	2	2	no	—
71	C₁₉×#123	—	2	2	no	—
72	C₁₉×#123	—	2	8	no	—
73	C₁₉×#123	D₄	1	4	yes	—
74	C₁₉×#123	C₂³	1	4	yes	—
75	C₁₉×C₂²⋊Q₈	—	2	2	no	—
76	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	—	2	4	no	—
78	C₁₉×C₂²⋊Q₈	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	—	2	2	no	—
80	C₁₉×C₂²⋊Q₈	—	2	4	no	—
81	C₁₉×C₂²⋊Q₈	—	4	4	no	—
82	C₁₉×#121	—	2	2	no	—
83	C₄×Q₈×C₁₉	—	2	2	no	—
84	C₄×Q₈×C₁₉	—	2	4	no	—
85	C₄×Q₈×C₁₉	—	2	2	no	—
86	C₄×D₄×C₁₉	—	2	2	no	—
87	C₄×D₄×C₁₉	—	2	4	no	—
88	C₁₉×#117	—	2	2	no	—
89	C₁₉×#117	—	2	1	no	—
90	C₁₉×#117	—	2	2	no	—
91	C₁₉×#117	D₄	1	2	yes	—
92	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
93	C₁₉×#104	—	2	2	no	—
94	C₁₉×#104	—	2	2	no	—
95	C₁₉×#101	—	2	1	no	—
96	C₁₉×#100	C₂³	1	2	yes	—
97	C₁₉×#99	—	2	2	no	—
98	C₁₉×#99	—	2	8	no	—
99	C₁₉×#99	C₂³	1	4	yes	—
100	#41×C₁₉	—	2	2	no	—
101	#41×C₁₉	—	2	2	no	—
102	#41×C₁₉	—	4	1	no	—
103	#41×C₁₉	—	4	1	no	—
104	#41×C₁₉	—	4	2	no	—
105	#41×C₁₉	—	4	2	no	—
106	#41×C₁₉	—	4	2	no	—
107	#41×C₁₉	—	4	1	no	—
108	#41×C₁₉	—	4	4	no	—
109	#41×C₁₉	—	4	1	no	—
110	#41×C₁₉	—	4	1	no	—
111	#41×C₁₉	—	4	2	no	—
112	#41×C₁₉	—	4	2	no	—
113	#41×C₁₉	—	4	1	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	—	2	2	no	—
116	C₂×Q₈×C₁₉	—	2	2	no	—
117	C₂×Q₈×C₁₉	—	2	2	no	—
118	C₂×Q₈×C₁₉	—	2	2	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	4	2	no	—
121	C₂×Q₈×C₁₉	—	4	2	no	—
122	C₂×Q₈×C₁₉	—	4	2	no	—
123	C₂×Q₈×C₁₉	—	8	1	no	—
124	C₂×Q₈×C₁₉	—	8	1	no	—
125	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	4	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	4	2	no	—
133	C₂×D₄×C₁₉	—	4	4	no	—
134	C₂×D₄×C₁₉	—	4	1	no	—
135	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
136	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	—	2	4	no	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	4	1	no	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
146	Q₁₆×C₁₉	—	4	2	no	—
147	SD₁₆×C₁₉	—	4	2	no	—
148	SD₁₆×C₁₉	—	4	2	no	—
149	D₈×C₁₉	—	4	2	no	—
150	M₁₆×C₁₉	—	2	2	no	—
151	M₁₆×C₁₉	—	4	1	no	—
152	C₂×C₈×C₁₉	—	4	1	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	4	no	—
157	C₄⋊C₄×C₁₉	—	2	4	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	4	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	4	no	—
162	C₄⋊C₄×C₁₉	—	4	2	no	—
163	C₄⋊C₄×C₁₉	—	4	8	no	—
164	C₂²⋊C₄×C₁₉	—	2	2	no	—
165	C₂²⋊C₄×C₁₉	—	2	4	no	—
166	C₂²⋊C₄×C₁₉	—	2	4	no	—
167	C₂²⋊C₄×C₁₉	—	2	2	no	—
168	C₂²⋊C₄×C₁₉	—	2	4	no	—
169	C₂²⋊C₄×C₁₉	—	2	2	no	—
170	C₂²⋊C₄×C₁₉	—	2	4	no	—
171	C₂²⋊C₄×C₁₉	—	4	8	no	—
172	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
173	C₄²×C₁₉	—	2	4	no	—
174	C₄²×C₁₉	—	2	2	no	—
175	C₄²×C₁₉	—	2	2	no	—
176	C₄²×C₁₉	—	2	1	no	—
177	C₄²×C₁₉	—	4	2	no	—
178	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
180	#33561	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂³×C₁₉	—	2	4	no	—
182	C₂³×C₁₉	—	2	1	no	—
183	C₂³×C₁₉	—	4	1	no	—
184	C₂³×C₁₉	#120	1	1	yes	characteristic
185	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
186	Q₈×C₁₉	—	2	2	no	—
187	Q₈×C₁₉	—	4	1	no	—
188	Q₈×C₁₉	—	4	1	no	—
189	Q₈×C₁₉	—	4	4	no	—
190	Q₈×C₁₉	—	4	2	no	—
191	Q₈×C₁₉	—	4	1	no	—
192	Q₈×C₁₉	—	4	2	no	—
193	Q₈×C₁₉	—	4	2	no	—
194	Q₈×C₁₉	—	8	2	no	—
195	Q₈×C₁₉	—	8	2	no	—
196	D₄×C₁₉	—	2	2	no	—
197	D₄×C₁₉	—	4	2	no	—
198	D₄×C₁₉	—	4	1	no	—
199	D₄×C₁₉	—	4	1	no	—
200	D₄×C₁₉	—	4	4	no	—
201	D₄×C₁₉	—	4	2	no	—
202	D₄×C₁₉	—	4	4	no	—
203	D₄×C₁₉	—	4	2	no	—
204	D₄×C₁₉	—	4	2	no	—
205	D₄×C₁₉	—	4	1	no	—
206	D₄×C₁₉	—	8	1	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	2	4	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	4	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	4	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	4	no	—
225	C₂×C₄×C₁₉	—	4	4	no	—
226	C₂×C₄×C₁₉	—	8	2	no	—
227	C₂×C₄×C₁₉	#120	1	2	yes	—
228	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
230	C₈×C₁₉	—	4	2	no	—
231	#3550	C₂×C₁₉	1	1	yes	characteristic, complemented
232	#3028	C₂×C₁₉	1	2	yes	complemented
233	#3018	C₂×C₁₉	1	1	yes	characteristic
234	#2201	C₂×C₁₉	1	4	yes	complemented
235	#2198	C₂×C₁₉	1	4	yes	complemented
236	#2126	C₂×C₁₉	1	1	yes	characteristic, complemented
237	#2123	C₂×C₁₉	1	2	yes	complemented
238	C₂²×C₁₉	—	2	2	no	—
239	C₂²×C₁₉	—	2	1	no	—
240	C₂²×C₁₉	—	4	1	no	—
241	C₂²×C₁₉	—	4	2	no	—
242	C₂²×C₁₉	—	4	2	no	—
243	C₂²×C₁₉	—	4	2	no	—
244	C₂²×C₁₉	—	4	1	no	—
245	C₂²×C₁₉	—	8	4	no	—
246	C₂²×C₁₉	—	16	1	no	—
247	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
248	C₄×C₁₉	—	2	2	no	—
249	C₄×C₁₉	—	2	1	no	—
250	C₄×C₁₉	—	2	2	no	—
251	C₄×C₁₉	—	4	1	no	—
252	C₄×C₁₉	—	4	4	no	—
253	C₄×C₁₉	—	4	2	no	—
254	C₄×C₁₉	—	4	1	no	—
255	C₄×C₁₉	—	4	4	no	—
256	C₄×C₁₉	—	8	4	no	—
257	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
258	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
259	#585	C₂²×C₁₉	1	1	yes	characteristic
260	#575	—	2	1	no	—
261	#563	—	2	1	no	—
262	#563	C₂²×C₁₉	1	2	yes	complemented
263	#559	C₂²×C₁₉	1	2	yes	complemented
264	Q₈²	—	2	1	no	—
265	#556	—	2	2	no	—
266	D₄×Q₈	—	2	2	no	—
267	#542	—	2	4	no	—
268	#536	—	2	1	no	—
269	#536	—	2	2	no	—
270	#536	C₂²×C₁₉	1	2	yes	—
271	#533	—	2	1	no	—
272	#532	C₂²×C₁₉	1	1	yes	characteristic
273	#458	—	2	4	no	—
274	#458	C₂²×C₁₉	1	8	yes	—
275	#456	—	2	1	no	—
276	#455	C₂²×C₁₉	1	2	yes	—
277	#454	—	2	1	no	—
278	#453	C₂²×C₁₉	1	2	yes	—
279	C₂×#104	—	2	1	no	—
280	#413	C₂²×C₁₉	1	1	yes	characteristic
281	#410	—	2	2	no	—
282	#410	C₂²×C₁₉	1	2	yes	—
283	#354	C₂²×C₁₉	1	2	yes	complemented
284	#353	C₂²×C₁₉	1	2	yes	complemented
285	#352	C₂²×C₁₉	1	8	yes	complemented
286	C₂×C₁₉	—	2	1	no	—
287	C₂×C₁₉	—	4	2	no	—
288	C₂×C₁₉	—	4	1	no	—
289	C₂×C₁₉	—	8	1	no	—
290	C₂×C₁₉	—	8	2	no	—
291	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
292	2₋¹⁺⁴	—	2	1	no	—
293	2₋¹⁺⁴	—	4	1	no	—
294	H(5,𝔽₂)	—	2	2	no	—
295	H(5,𝔽₂)	—	4	1	no	—
296	H(5,𝔽₂)	C₂³×C₁₉	1	2	yes	—
297	C₂×#41	—	2	2	no	—
298	C₂×#41	—	2	1	no	—
299	C₂×#41	—	4	2	no	—
300	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
301	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
302	C₂²×Q₈	—	2	1	no	—
303	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
304	#137	—	2	2	no	—
305	#137	—	4	1	no	—
306	AGL(1,ℤ/8)	—	2	2	no	—
307	AGL(1,ℤ/8)	—	4	1	no	—
308	#135	—	4	2	no	—
309	C₂×M₁₆	—	2	1	no	—
310	C₄⋊Q₈	—	2	1	no	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	4	no	—
313	C₄⋊Q₈	—	2	2	no	—
314	C₄⋊Q₈	—	2	2	no	—
315	C₄⋊Q₈	—	4	2	no	—
316	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
317	#127	C₂³×C₁₉	1	1	yes	characteristic
318	#126	—	2	4	no	—
319	#126	—	2	4	no	—
320	#125	—	2	2	no	—
321	#124	—	2	2	no	—
322	#124	—	2	2	no	—
323	#124	—	2	4	no	—
324	#124	—	4	2	no	—
325	#124	D₄×C₁₉	1	1	yes	characteristic
326	#124	C₂³×C₁₉	1	1	yes	characteristic
327	#123	—	2	2	no	—
328	#123	—	2	2	no	—
329	#123	—	2	8	no	—
330	#123	D₄×C₁₉	1	4	yes	—
331	#123	C₂³×C₁₉	1	4	yes	—
332	C₂²⋊Q₈	—	2	2	no	—
333	C₂²⋊Q₈	—	2	2	no	—
334	C₂²⋊Q₈	—	2	4	no	—
335	C₂²⋊Q₈	—	2	2	no	—
336	C₂²⋊Q₈	—	2	2	no	—
337	C₂²⋊Q₈	—	2	4	no	—
338	C₂²⋊Q₈	—	4	4	no	—
339	#121	—	2	2	no	—
340	C₄×Q₈	—	2	2	no	—
341	C₄×Q₈	—	2	4	no	—
342	C₄×Q₈	—	2	2	no	—
343	C₄×D₄	—	2	2	no	—
344	C₄×D₄	—	2	4	no	—
345	#117	—	2	2	no	—
346	#117	—	2	1	no	—
347	#117	—	2	2	no	—
348	#117	D₄×C₁₉	1	2	yes	—
349	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
350	#104	—	2	2	no	—
351	#104	—	2	2	no	—
352	#101	—	2	1	no	—
353	#100	C₂³×C₁₉	1	2	yes	—
354	#99	—	2	2	no	—
355	#99	—	2	8	no	—
356	#99	C₂³×C₁₉	1	4	yes	—
357	C₁₉	#33561	1	1	yes	characteristic, direct product factor, Sylow
358	#41	—	2	2	no	—
359	#41	—	2	2	no	—
360	#41	—	4	1	no	—
361	#41	—	4	1	no	—
362	#41	—	4	2	no	—
363	#41	—	4	2	no	—
364	#41	—	4	2	no	—
365	#41	—	4	1	no	—
366	#41	—	4	4	no	—
367	#41	—	4	1	no	—
368	#41	—	4	1	no	—
369	#41	—	4	2	no	—
370	#41	—	4	1	no	—
371	#41	—	4	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	4	2	no	—
379	C₂×Q₈	—	4	2	no	—
380	C₂×Q₈	—	4	2	no	—
381	C₂×Q₈	—	8	1	no	—
382	C₂×Q₈	—	8	1	no	—
383	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	4	2	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂×D₄	—	4	1	no	—
393	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
394	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
395	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
402	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
404	Q₁₆	—	4	2	no	—
405	SD₁₆	—	4	2	no	—
406	SD₁₆	—	4	2	no	—
407	D₈	—	4	2	no	—
408	M₁₆	—	2	2	no	—
409	M₁₆	—	4	1	no	—
410	C₂×C₈	—	4	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	4	2	no	—
421	C₄⋊C₄	—	4	8	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	4	no	—
424	C₂²⋊C₄	—	2	4	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	4	no	—
429	C₂²⋊C₄	—	4	8	no	—
430	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
431	C₄²	—	2	4	no	—
432	C₄²	—	2	2	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	4	2	no	—
436	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂³	—	2	4	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	4	1	no	—
441	C₂³	C₁₉×#120	1	1	yes	characteristic
442	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
443	Q₈	—	2	2	no	—
444	Q₈	—	4	1	no	—
445	Q₈	—	4	1	no	—
446	Q₈	—	4	2	no	—
447	Q₈	—	4	4	no	—
448	Q₈	—	4	1	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	4	2	no	—
451	Q₈	—	8	2	no	—
452	Q₈	—	8	2	no	—
453	D₄	—	2	2	no	—
454	D₄	—	4	2	no	—
455	D₄	—	4	1	no	—
456	D₄	—	4	1	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	4	no	—
459	D₄	—	4	4	no	—
460	D₄	—	4	2	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	1	no	—
463	D₄	—	8	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	8	2	no	—
484	C₂×C₄	C₁₉×#120	1	2	yes	—
485	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
487	C₈	—	4	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	8	4	no	—
496	C₂²	—	16	1	no	—
497	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
498	C₄	—	2	2	no	—
499	C₄	—	2	1	no	—
500	C₄	—	2	2	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	4	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	1	no	—
505	C₄	—	4	4	no	—
506	C₄	—	8	4	no	—
507	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
508	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
509	C₂	—	2	1	no	—
510	C₂	—	4	2	no	—
511	C₂	—	4	1	no	—
512	C₂	—	8	1	no	—
513	C₂	—	8	2	no	—
514	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
prime radical	C₁₉×#3018	C₂
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×#3550	C₂	semidirect
2. C₁₉×#3028	C₂	semidirect
4. C₁₉×#2201	C₂	semidirect
5. C₁₉×#2198	C₂	semidirect
6. C₁₉×#2126	C₂	semidirect
7. C₁₉×#2123	C₂	semidirect
11. C₁₉×#563	C₂²	semidirect
12. C₁₉×#559	C₂²	semidirect
32. C₁₉×#354	C₂²	semidirect
33. C₁₉×#353	C₂²	semidirect
34. C₁₉×#352	C₂²	semidirect
180. #33561	C₁₉	direct (N × H)
231. #3550	C₂×C₁₉	semidirect
232. #3028	C₂×C₁₉	semidirect
234. #2201	C₂×C₁₉	semidirect
235. #2198	C₂×C₁₉	semidirect
236. #2126	C₂×C₁₉	semidirect
237. #2123	C₂×C₁₉	semidirect
262. #563	C₂²×C₁₉	semidirect
263. #559	C₂²×C₁₉	semidirect
283. #354	C₂²×C₁₉	semidirect
284. #353	C₂²×C₁₉	semidirect
285. #352	C₂²×C₁₉	semidirect
357. C₁₉	#33561	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×#3550	2
C₁₉×#3028	2
C₁₉×#3018	2
C₁₉×#2201	2
C₁₉×#2198	2
C₁₉×#2126	2
C₁₉×#2123	2
#33561	19

Subgroups — C19×#33561 #18039520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33561 #18039520