Subgroups — C₄×C₁₉×#456 #18027431

Order 4864.

1358 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#456	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉×#137	C₂	1	2	yes	maximal, complemented
4	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1886	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1882	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1859	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1857	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1793	C₂	1	1	yes	maximal, characteristic
10	C₄×C₁₉×#104	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#137	C₂²	1	2	yes	—
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₁₉×#520	—	2	2	no	—
16	C₁₉×#520	—	2	2	no	—
17	C₁₉×#520	C₂²	1	2	yes	—
18	C₁₉×#519	—	2	2	no	—
19	C₁₉×#519	C₂²	1	1	yes	characteristic
20	C₄×#41×C₁₉	—	2	2	no	—
21	C₄×#41×C₁₉	—	2	2	no	—
22	C₄×#41×C₁₉	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₉	—	2	2	no	—
24	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#456	C₄	1	8	yes	direct product factor
27	C₁₉×#441	—	2	2	no	—
28	C₁₉×#440	—	2	2	no	—
29	C₄×Q₁₆×C₁₉	—	2	2	no	—
30	C₄×SD₁₆×C₁₉	—	2	2	no	—
31	C₁₉×#428	C₂²	1	2	yes	—
32	C₂×C₁₉×#104	C₂²	1	2	yes	—
33	C₂×C₁₉×#104	C₂²	1	2	yes	—
34	C₁₉×#419	C₂²	1	2	yes	—
35	C₁₉×#417	C₂²	1	2	yes	—
36	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
39	C₁₉×#391	C₂²	1	1	yes	characteristic
40	C₁₉×#391	C₂²	1	1	yes	characteristic
41	C₁₉×#389	—	2	2	no	—
42	C₁₉×#384	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
44	C₄³×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#343	C₂²	1	2	yes	—
46	C₁₉×#339	C₂²	1	2	yes	—
47	C₁₉×#339	C₂²	1	2	yes	—
48	C₁₉×2₋¹⁺⁴	—	2	4	no	—
49	C₁₉×2₋¹⁺⁴	—	2	2	no	—
50	C₁₉×2₋¹⁺⁴	C₂×C₄	1	4	yes	—
51	C₂×#41×C₁₉	—	2	2	no	—
52	C₂×#41×C₁₉	—	2	2	no	—
53	C₂×#41×C₁₉	C₂³	1	2	yes	—
54	C₂²×Q₈×C₁₉	—	2	2	no	—
55	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₁₉×#137	—	2	4	no	—
58	C₁₉×#137	C₂×C₄	1	8	yes	complemented
59	C₂×Q₁₆×C₁₉	—	2	2	no	—
60	C₂×SD₁₆×C₁₉	—	2	2	no	—
61	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
62	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
63	C₁₉×C₄⋊Q₈	—	2	2	no	—
64	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
65	C₄×Q₈×C₁₉	—	2	2	no	—
66	C₄×Q₈×C₁₉	—	2	4	no	—
67	C₄×Q₈×C₁₉	—	2	2	no	—
68	C₄×Q₈×C₁₉	—	2	2	no	—
69	C₄×Q₈×C₁₉	—	2	2	no	—
70	C₄×Q₈×C₁₉	—	2	2	no	—
71	C₄×Q₈×C₁₉	—	2	2	no	—
72	C₄×Q₈×C₁₉	—	2	2	no	—
73	C₄×Q₈×C₁₉	—	2	2	no	—
74	C₄×Q₈×C₁₉	—	2	2	no	—
75	C₄×Q₈×C₁₉	D₄	1	2	yes	—
76	C₄×Q₈×C₁₉	D₄	1	2	yes	—
77	C₄×D₄×C₁₉	—	2	2	no	—
78	C₄×D₄×C₁₉	—	2	4	no	—
79	C₄×D₄×C₁₉	—	2	2	no	—
80	C₄×D₄×C₁₉	—	2	2	no	—
81	C₄×D₄×C₁₉	—	2	2	no	—
82	C₄×D₄×C₁₉	—	2	4	no	—
83	C₄×D₄×C₁₉	—	2	2	no	—
84	C₄×D₄×C₁₉	D₄	1	2	yes	—
85	C₄×D₄×C₁₉	D₄	1	2	yes	—
86	C₁₉×#117	—	2	4	no	—
87	C₁₉×#117	—	2	4	no	—
88	C₁₉×#117	—	2	2	no	—
89	C₁₉×#117	—	2	2	no	—
90	C₁₉×#117	—	2	2	no	—
91	C₁₉×#117	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₉	—	2	4	no	—
101	C₂×C₄²×C₁₉	—	2	1	no	—
102	C₂×C₄²×C₁₉	—	2	2	no	—
103	C₂×C₄²×C₁₉	—	2	1	no	—
104	C₂×C₄²×C₁₉	—	2	1	no	—
105	C₂×C₄²×C₁₉	D₄	1	2	yes	—
106	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
109	C₁₉×#107	—	2	2	no	—
110	C₁₉×#106	—	2	2	no	—
111	C₁₉×#104	—	2	4	no	—
112	C₁₉×#104	C₂×C₄	1	8	yes	complemented
113	C₁₉×#103	—	2	2	no	—
114	C₁₉×#103	—	2	2	no	—
115	C₁₉×#103	—	2	2	no	—
116	C₁₉×#102	—	2	2	no	—
117	C₁₉×#101	—	2	2	no	—
118	C₁₉×#101	C₂×C₄	1	4	yes	complemented
119	C₁₉×#97	—	2	2	no	—
120	C₄×C₈×C₁₉	—	2	2	no	—
121	C₁₉×#95	—	2	2	no	—
122	C₁₉×#95	—	2	2	no	—
123	#41×C₁₉	—	2	8	no	—
124	#41×C₁₉	—	2	8	no	—
125	#41×C₁₉	—	2	8	no	—
126	#41×C₁₉	—	2	8	no	—
127	#41×C₁₉	—	2	2	no	—
128	#41×C₁₉	—	2	2	no	—
129	#41×C₁₉	C₂²×C₄	1	4	yes	—
130	#41×C₁₉	#41	1	4	yes	—
131	C₂×Q₈×C₁₉	—	2	2	no	—
132	C₂×Q₈×C₁₉	—	2	8	no	—
133	C₂×Q₈×C₁₉	—	2	8	no	—
134	C₂×Q₈×C₁₉	—	2	2	no	—
135	C₂×Q₈×C₁₉	—	2	2	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	—	2	2	no	—
138	C₂×Q₈×C₁₉	—	2	2	no	—
139	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
140	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
141	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
142	C₂×Q₈×C₁₉	#41	1	2	yes	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₉	—	2	4	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	4	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	2	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
160	Q₁₆×C₁₉	—	2	8	no	—
161	SD₁₆×C₁₉	—	2	8	no	—
162	M₁₆×C₁₉	—	2	2	no	—
163	M₁₆×C₁₉	—	2	2	no	—
164	M₁₆×C₁₉	—	2	2	no	—
165	M₁₆×C₁₉	C₂²×C₄	1	4	yes	—
166	C₂×C₈×C₁₉	—	2	2	no	—
167	C₂×C₈×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	4	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	8	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	2	4	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	4	4	no	—
178	C₄⋊C₄×C₁₉	—	4	2	no	—
179	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
180	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
181	C₂²⋊C₄×C₁₉	—	2	4	no	—
182	C₂²⋊C₄×C₁₉	—	2	2	no	—
183	C₂²⋊C₄×C₁₉	—	2	2	no	—
184	C₂²⋊C₄×C₁₉	—	2	2	no	—
185	C₄²×C₁₉	—	2	4	no	—
186	C₄²×C₁₉	—	2	4	no	—
187	C₄²×C₁₉	—	2	4	no	—
188	C₄²×C₁₉	—	2	2	no	—
189	C₄²×C₁₉	—	2	2	no	—
190	C₄²×C₁₉	—	2	2	no	—
191	C₄²×C₁₉	—	2	2	no	—
192	C₄²×C₁₉	—	2	2	no	—
193	C₄²×C₁₉	—	2	1	no	—
194	C₄²×C₁₉	—	2	2	no	—
195	C₄²×C₁₉	—	4	2	no	—
196	C₄²×C₁₉	—	4	1	no	—
197	C₄²×C₁₉	—	4	1	no	—
198	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
199	C₄²×C₁₉	C₂×D₄	1	2	yes	—
200	C₄²×C₁₉	C₂×D₄	1	2	yes	—
201	C₄×#456	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂³×C₁₉	—	2	2	no	—
203	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₁₉	—	2	8	no	—
205	Q₈×C₁₉	—	2	4	no	—
206	Q₈×C₁₉	—	2	2	no	—
207	Q₈×C₁₉	—	2	4	no	—
208	Q₈×C₁₉	—	2	4	no	—
209	Q₈×C₁₉	—	4	2	no	—
210	Q₈×C₁₉	C₄×D₄	1	4	yes	—
211	D₄×C₁₉	—	2	8	no	—
212	D₄×C₁₉	—	2	4	no	—
213	D₄×C₁₉	—	2	4	no	—
214	D₄×C₁₉	—	2	2	no	—
215	D₄×C₁₉	C₄×D₄	1	4	yes	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	16	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	4	no	—
224	C₂×C₄×C₁₉	—	2	4	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	4	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	8	2	no	—
241	C₂×C₄×C₁₉	—	8	4	no	—
242	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
243	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#120	1	2	yes	—
245	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
249	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
250	C₈×C₁₉	—	2	4	no	—
251	C₈×C₁₉	—	4	2	no	—
252	C₄×2₋¹⁺⁴	C₂×C₁₉	1	1	yes	characteristic
253	C₂×#456	C₂×C₁₉	1	1	yes	characteristic
254	C₄×#137	C₂×C₁₉	1	2	yes	complemented
255	C₄×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1886	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1882	C₂×C₁₉	1	2	yes	complemented
258	#1859	C₂×C₁₉	1	2	yes	complemented
259	#1857	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1793	C₂×C₁₉	1	1	yes	characteristic
261	C₄×#104	C₂×C₁₉	1	2	yes	complemented
262	C₄×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
263	C₂²×C₁₉	—	2	1	no	—
264	C₂²×C₁₉	—	2	1	no	—
265	C₂²×C₁₉	—	2	4	no	—
266	C₂²×C₁₉	—	4	2	no	—
267	C₂²×C₁₉	—	4	2	no	—
268	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
269	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
270	C₂²×C₁₉	#525	1	1	yes	characteristic
271	C₄×C₁₉	—	2	4	no	—
272	C₄×C₁₉	—	2	1	no	—
273	C₄×C₁₉	—	2	2	no	—
274	C₄×C₁₉	—	2	4	no	—
275	C₄×C₁₉	—	2	4	no	—
276	C₄×C₁₉	—	4	2	no	—
277	C₄×C₁₉	—	4	2	no	—
278	C₄×C₁₉	—	4	2	no	—
279	C₄×C₁₉	—	4	2	no	—
280	C₄×C₁₉	—	4	2	no	—
281	C₄×C₁₉	—	8	1	no	—
282	C₄×C₁₉	#456	1	2	yes	direct product factor
283	C₄×C₁₉	C₂×C₄×D₄	1	2	yes	—
284	C₄×C₁₉	#525	1	2	yes	—
285	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic
286	C₂×#137	C₂²×C₁₉	1	2	yes	—
287	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
288	#520	—	2	2	no	—
289	#520	—	2	2	no	—
290	#520	C₂²×C₁₉	1	2	yes	—
291	#519	—	2	2	no	—
292	#519	C₂²×C₁₉	1	1	yes	characteristic
293	C₄×#41	—	2	2	no	—
294	C₄×#41	—	2	2	no	—
295	C₄×#41	C₂²×C₁₉	1	2	yes	—
296	C₂×C₄×Q₈	—	2	2	no	—
297	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
298	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
299	#456	C₄×C₁₉	1	8	yes	direct product factor
300	#441	—	2	2	no	—
301	#440	—	2	2	no	—
302	C₄×Q₁₆	—	2	2	no	—
303	C₄×SD₁₆	—	2	2	no	—
304	#428	C₂²×C₁₉	1	2	yes	—
305	C₂×#104	C₂²×C₁₉	1	2	yes	—
306	C₂×#104	C₂²×C₁₉	1	2	yes	—
307	#419	C₂²×C₁₉	1	2	yes	—
308	#417	C₂²×C₁₉	1	2	yes	—
309	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
310	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
311	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
312	#391	C₂²×C₁₉	1	1	yes	characteristic
313	#391	C₂²×C₁₉	1	1	yes	characteristic
314	#389	—	2	2	no	—
315	#384	C₂²×C₁₉	1	1	yes	characteristic
316	C₄×C₄⋊C₄	—	2	2	no	—
317	C₄³	C₂²×C₁₉	1	1	yes	characteristic
318	#343	C₂²×C₁₉	1	2	yes	—
319	#339	C₂²×C₁₉	1	2	yes	—
320	#339	C₂²×C₁₉	1	2	yes	—
321	C₂×C₁₉	—	2	1	no	—
322	C₂×C₁₉	—	2	1	no	—
323	C₂×C₁₉	—	4	4	no	—
324	C₂×C₁₉	C₄×#120	1	1	yes	characteristic
325	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
326	C₂×C₁₉	#3018	1	1	yes	characteristic
327	2₋¹⁺⁴	—	2	4	no	—
328	2₋¹⁺⁴	—	2	2	no	—
329	2₋¹⁺⁴	C₂×C₄×C₁₉	1	4	yes	—
330	C₂×#41	—	2	2	no	—
331	C₂×#41	—	2	2	no	—
332	C₂×#41	C₂³×C₁₉	1	2	yes	—
333	C₂²×Q₈	—	2	2	no	—
334	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
335	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
336	#137	—	2	4	no	—
337	#137	C₂×C₄×C₁₉	1	8	yes	complemented
338	C₂×Q₁₆	—	2	2	no	—
339	C₂×SD₁₆	—	2	2	no	—
340	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
341	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
342	C₄⋊Q₈	—	2	2	no	—
343	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
344	C₄×Q₈	—	2	2	no	—
345	C₄×Q₈	—	2	4	no	—
346	C₄×Q₈	—	2	2	no	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	—	2	2	no	—
349	C₄×Q₈	—	2	2	no	—
350	C₄×Q₈	—	2	2	no	—
351	C₄×Q₈	—	2	2	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	—	2	2	no	—
354	C₄×Q₈	D₄×C₁₉	1	2	yes	—
355	C₄×Q₈	D₄×C₁₉	1	2	yes	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	4	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	—	2	4	no	—
362	C₄×D₄	—	2	2	no	—
363	C₄×D₄	D₄×C₁₉	1	2	yes	—
364	C₄×D₄	D₄×C₁₉	1	2	yes	—
365	#117	—	2	4	no	—
366	#117	—	2	4	no	—
367	#117	—	2	2	no	—
368	#117	—	2	2	no	—
369	#117	—	2	2	no	—
370	#117	C₂³×C₁₉	1	2	yes	—
371	C₂×C₄⋊C₄	—	2	4	no	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	2	no	—
376	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
379	C₂×C₄²	—	2	4	no	—
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	—	2	2	no	—
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	D₄×C₁₉	1	2	yes	—
385	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
388	#107	—	2	2	no	—
389	#106	—	2	2	no	—
390	#104	—	2	4	no	—
391	#104	C₂×C₄×C₁₉	1	8	yes	complemented
392	#103	—	2	2	no	—
393	#103	—	2	2	no	—
394	#103	—	2	2	no	—
395	#102	—	2	2	no	—
396	#101	—	2	2	no	—
397	#101	C₂×C₄×C₁₉	1	4	yes	complemented
398	#97	—	2	2	no	—
399	C₄×C₈	—	2	2	no	—
400	#95	—	2	2	no	—
401	#95	—	2	2	no	—
402	C₁₉	C₄×#456	1	1	yes	characteristic, direct product factor, Sylow
403	#41	—	2	8	no	—
404	#41	—	2	8	no	—
405	#41	—	2	8	no	—
406	#41	—	2	8	no	—
407	#41	—	2	2	no	—
408	#41	—	2	2	no	—
409	#41	C₂²×C₄×C₁₉	1	4	yes	—
410	#41	#41×C₁₉	1	4	yes	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	8	no	—
413	C₂×Q₈	—	2	8	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
420	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
421	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
422	C₂×Q₈	#41×C₁₉	1	2	yes	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
436	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
438	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
440	Q₁₆	—	2	8	no	—
441	SD₁₆	—	2	8	no	—
442	M₁₆	—	2	2	no	—
443	M₁₆	—	2	2	no	—
444	M₁₆	—	2	2	no	—
445	M₁₆	C₂²×C₄×C₁₉	1	4	yes	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	8	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	4	4	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
460	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
461	C₂²⋊C₄	—	2	4	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₄²	—	2	4	no	—
466	C₄²	—	2	4	no	—
467	C₄²	—	2	4	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	2	2	no	—
472	C₄²	—	2	2	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	2	no	—
475	C₄²	—	4	2	no	—
476	C₄²	—	4	1	no	—
477	C₄²	—	4	1	no	—
478	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
479	C₄²	C₂×D₄×C₁₉	1	2	yes	—
480	C₄²	C₂×D₄×C₁₉	1	2	yes	—
481	C₂³	—	2	2	no	—
482	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
483	Q₈	—	2	8	no	—
484	Q₈	—	2	4	no	—
485	Q₈	—	2	2	no	—
486	Q₈	—	2	4	no	—
487	Q₈	—	2	4	no	—
488	Q₈	—	4	2	no	—
489	Q₈	C₄×D₄×C₁₉	1	4	yes	—
490	D₄	—	2	8	no	—
491	D₄	—	2	4	no	—
492	D₄	—	2	4	no	—
493	D₄	—	2	2	no	—
494	D₄	C₄×D₄×C₁₉	1	4	yes	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	16	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	8	2	no	—
520	C₂×C₄	—	8	4	no	—
521	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
522	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
523	C₂×C₄	C₁₉×#120	1	2	yes	—
524	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
525	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
527	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
528	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
529	C₈	—	2	4	no	—
530	C₈	—	4	2	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
537	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
538	C₂²	C₁₉×#525	1	1	yes	characteristic
539	C₄	—	2	4	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	4	no	—
543	C₄	—	2	4	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	2	no	—
549	C₄	—	8	1	no	—
550	C₄	C₁₉×#456	1	2	yes	direct product factor
551	C₄	C₂×C₄×D₄×C₁₉	1	2	yes	—
552	C₄	C₁₉×#525	1	2	yes	—
553	C₂	—	2	1	no	—
554	C₂	—	2	1	no	—
555	C₂	—	4	4	no	—
556	C₂	C₄×C₁₉×#120	1	1	yes	characteristic
557	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
558	C₂	C₁₉×#3018	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×#120
prime radical	C₂×C₁₉×2₋¹⁺⁴	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×C₁₉×#137	C₂	semidirect
4. C₄×C₁₉×C₄⋊Q₈	C₂	semidirect
5. C₁₉×#1886	C₂	semidirect
6. C₁₉×#1882	C₂	semidirect
7. C₁₉×#1859	C₂	semidirect
8. C₁₉×#1857	C₂	semidirect
10. C₄×C₁₉×#104	C₂	semidirect
11. C₄×C₁₉×#101	C₂	semidirect
26. C₁₉×#456	C₄	direct (N × H)
58. C₁₉×#137	C₂×C₄	semidirect
64. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
112. C₁₉×#104	C₂×C₄	semidirect
118. C₁₉×#101	C₂×C₄	semidirect
201. C₄×#456	C₁₉	direct (N × H)
254. C₄×#137	C₂×C₁₉	semidirect
255. C₄×C₄⋊Q₈	C₂×C₁₉	semidirect
256. #1886	C₂×C₁₉	semidirect
257. #1882	C₂×C₁₉	semidirect
258. #1859	C₂×C₁₉	semidirect
259. #1857	C₂×C₁₉	semidirect
261. C₄×#104	C₂×C₁₉	semidirect
262. C₄×#101	C₂×C₁₉	semidirect
282. C₄×C₁₉	#456	direct (N × H)
299. #456	C₄×C₁₉	direct (N × H)
337. #137	C₂×C₄×C₁₉	semidirect
343. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
391. #104	C₂×C₄×C₁₉	semidirect
397. #101	C₂×C₄×C₁₉	semidirect
402. C₁₉	C₄×#456	direct (N × H)
550. C₄	C₁₉×#456	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₁₉×2₋¹⁺⁴	2
C₂×C₁₉×#456	2
C₄×C₁₉×#137	2
C₄×C₁₉×C₄⋊Q₈	2
C₁₉×#1886	2
C₁₉×#1882	2
C₁₉×#1859	2
C₁₉×#1857	2
C₁₉×#1793	2
C₄×C₁₉×#104	2
C₄×C₁₉×#101	2
C₄×#456	19

Subgroups — C4×C19×#456 #18027431

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉×#456 #18027431