Subgroups — C₁₉×#24830 #18030789

Order 4864.

900 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#474	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#442	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2563	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2349	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2085	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2067	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1940	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1879	C₂	1	2	yes	maximal
10	C₁₉×#1804	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1804	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#474	—	2	4	no	—
18	C₁₉×#442	—	2	4	no	—
19	C₂×C₁₉×#107	C₂²	1	2	yes	—
20	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#102	C₂²	1	2	yes	—
26	C₂×C₁₉×#102	C₂²	1	2	yes	—
27	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
28	C₁₉×#393	—	2	1	no	—
29	C₁₉×#393	—	2	1	no	—
30	C₁₉×#390	C₂²	1	2	yes	—
31	C₁₉×#389	C₂²	1	2	yes	—
32	C₁₉×#385	—	2	2	no	—
33	C₁₉×#382	C₂²	1	1	yes	characteristic
34	C₁₉×#382	C₂²	1	2	yes	—
35	C₁₉×#380	—	2	1	no	—
36	C₁₉×#380	—	2	2	no	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#95	—	2	1	no	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	—	2	1	no	—
48	C₂³×C₄×C₁₉	—	2	2	no	—
49	C₂×D₈×C₁₉	—	2	2	no	—
50	C₂×D₈×C₁₉	—	2	2	no	—
51	C₂×D₈×C₁₉	Q₈	1	4	yes	complemented
52	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
55	C₁₉×C₄⋊Q₈	—	2	2	no	—
56	C₁₉×C₄⋊Q₈	—	2	2	no	—
57	C₄×D₄×C₁₉	—	2	4	no	—
58	C₄×D₄×C₁₉	—	2	2	no	—
59	C₄×D₄×C₁₉	—	2	2	no	—
60	C₄×D₄×C₁₉	—	2	2	no	—
61	C₄×D₄×C₁₉	—	4	2	no	—
62	C₄×D₄×C₁₉	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
76	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
77	C₁₉×#107	—	2	4	no	—
78	C₁₉×#106	—	2	2	no	—
79	C₁₉×C₄⋊C₈	—	2	2	no	—
80	C₁₉×C₄⋊C₈	—	4	2	no	—
81	C₁₉×#102	—	2	2	no	—
82	C₁₉×#102	—	2	4	no	—
83	C₁₉×#102	—	2	2	no	—
84	C₁₉×#102	—	4	2	no	—
85	C₁₉×#97	—	2	2	no	—
86	C₁₉×#95	—	2	1	no	—
87	C₁₉×#95	—	2	2	no	—
88	C₁₉×#95	—	2	2	no	—
89	C₁₉×#95	—	2	2	no	—
90	C₁₉×#95	—	2	1	no	—
91	C₁₉×#95	D₄	1	1	yes	characteristic
92	C₁₉×#95	D₄	1	1	yes	characteristic
93	C₂⁴×C₁₉	—	2	1	no	—
94	C₂⁴×C₁₉	—	2	1	no	—
95	C₂×Q₈×C₁₉	—	4	2	no	—
96	C₂×Q₈×C₁₉	—	8	2	no	—
97	C₂×D₄×C₁₉	—	2	1	no	—
98	C₂×D₄×C₁₉	—	2	1	no	—
99	C₂×D₄×C₁₉	—	2	1	no	—
100	C₂×D₄×C₁₉	—	2	1	no	—
101	C₂×D₄×C₁₉	—	2	1	no	—
102	C₂×D₄×C₁₉	—	2	1	no	—
103	C₂×D₄×C₁₉	—	2	1	no	—
104	C₂×D₄×C₁₉	—	2	1	no	—
105	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₁₉	C₂×Q₈	1	2	yes	—
107	C₂×D₄×C₁₉	C₂×Q₈	1	2	yes	—
108	C₂×D₄×C₁₉	#41	1	2	yes	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	4	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	4	4	no	—
115	C₂²×C₄×C₁₉	—	4	4	no	—
116	C₂²×C₄×C₁₉	—	4	4	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	—	8	2	no	—
119	C₂²×C₄×C₁₉	—	8	2	no	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
125	D₈×C₁₉	—	2	8	no	—
126	C₂×C₈×C₁₉	—	2	1	no	—
127	C₂×C₈×C₁₉	—	2	1	no	—
128	C₂×C₈×C₁₉	—	2	1	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	2	1	no	—
132	C₂×C₈×C₁₉	—	2	1	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	4	2	no	—
143	C₄⋊C₄×C₁₉	—	4	2	no	—
144	C₄⋊C₄×C₁₉	—	8	2	no	—
145	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²⋊C₄×C₁₉	—	2	4	no	—
147	C₂²⋊C₄×C₁₉	—	4	4	no	—
148	C₂²⋊C₄×C₁₉	—	4	2	no	—
149	C₂²⋊C₄×C₁₉	—	8	2	no	—
150	C₂²⋊C₄×C₁₉	—	8	2	no	—
151	C₄²×C₁₉	—	2	2	no	—
152	C₄²×C₁₉	—	2	2	no	—
153	C₄²×C₁₉	C₂×D₄	1	2	yes	—
154	C₄²×C₁₉	#41	1	2	yes	—
155	#24830	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	2	2	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	—	4	2	no	—
162	C₂³×C₁₉	—	4	1	no	—
163	C₂³×C₁₉	—	4	1	no	—
164	C₂³×C₁₉	—	4	2	no	—
165	C₂³×C₁₉	—	4	2	no	—
166	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₉	—	8	4	no	—
168	D₄×C₁₉	—	2	2	no	—
169	D₄×C₁₉	—	2	2	no	—
170	D₄×C₁₉	—	2	2	no	—
171	D₄×C₁₉	—	2	2	no	—
172	D₄×C₁₉	—	2	2	no	—
173	D₄×C₁₉	—	4	1	no	—
174	D₄×C₁₉	—	4	1	no	—
175	D₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	8	4	no	—
195	C₂×C₄×C₁₉	—	8	4	no	—
196	C₂×C₄×C₁₉	—	8	8	no	—
197	C₂×C₄×C₁₉	#121	1	2	yes	—
198	C₂×C₄×C₁₉	#121	1	2	yes	—
199	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
205	C₈×C₁₉	—	2	2	no	—
206	C₈×C₁₉	—	4	1	no	—
207	C₈×C₁₉	—	4	2	no	—
208	C₂×#474	C₂×C₁₉	1	1	yes	characteristic, complemented
209	C₂×#442	C₂×C₁₉	1	1	yes	characteristic
210	#2563	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#2349	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#2085	C₂×C₁₉	1	2	yes	complemented
213	#2067	C₂×C₁₉	1	2	yes	complemented
214	#1993	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#1940	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#1879	C₂×C₁₉	1	2	yes	—
217	#1804	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#1804	C₂×C₁₉	1	2	yes	complemented
219	C₂²×C₁₉	—	2	4	no	—
220	C₂²×C₁₉	—	4	4	no	—
221	C₂²×C₁₉	—	4	2	no	—
222	C₂²×C₁₉	—	4	2	no	—
223	C₂²×C₁₉	—	4	4	no	—
224	C₂²×C₁₉	—	4	4	no	—
225	C₂²×C₁₉	—	4	2	no	—
226	C₂²×C₁₉	—	8	1	no	—
227	C₂²×C₁₉	—	8	1	no	—
228	C₂²×C₁₉	—	8	2	no	—
229	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
230	C₂²×C₁₉	#546	1	1	yes	characteristic
231	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
232	C₂²×C₁₉	#575	1	2	yes	—
233	C₂²×C₁₉	#576	1	2	yes	—
234	C₄×C₁₉	—	2	2	no	—
235	C₄×C₁₉	—	2	2	no	—
236	C₄×C₁₉	—	4	2	no	—
237	C₄×C₁₉	—	4	2	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	8	1	no	—
240	C₄×C₁₉	—	8	2	no	—
241	C₄×C₁₉	—	8	2	no	—
242	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
243	C₄×C₁₉	#537	1	1	yes	characteristic
244	C₄×C₁₉	#552	1	1	yes	characteristic
245	C₄×C₁₉	#554	1	1	yes	characteristic
246	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
250	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
251	#474	—	2	4	no	—
252	#442	—	2	4	no	—
253	C₂×#107	C₂²×C₁₉	1	2	yes	—
254	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
257	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
258	C₂×#102	C₂²×C₁₉	1	2	yes	—
259	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
260	C₂×#102	C₂²×C₁₉	1	2	yes	—
261	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
262	#393	—	2	1	no	—
263	#393	—	2	1	no	—
264	#390	C₂²×C₁₉	1	2	yes	—
265	#389	C₂²×C₁₉	1	2	yes	—
266	#385	—	2	2	no	—
267	#382	C₂²×C₁₉	1	2	yes	—
268	#382	C₂²×C₁₉	1	1	yes	characteristic
269	#380	—	2	2	no	—
270	#380	—	2	1	no	—
271	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
272	C₂×#95	—	2	1	no	—
273	#340	C₂²×C₁₉	1	2	yes	—
274	#340	C₂²×C₁₉	1	2	yes	—
275	#340	C₂²×C₁₉	1	2	yes	—
276	#336	C₂²×C₁₉	1	2	yes	—
277	C₂×C₁₉	—	4	4	no	—
278	C₂×C₁₉	—	8	2	no	—
279	C₂×C₁₉	#2417	1	1	yes	characteristic
280	C₂×C₁₉	#3040	1	1	yes	characteristic
281	C₂×C₁₉	#3041	1	1	yes	characteristic
282	C₂×C₁₉	#3319	1	2	yes	—
283	C₂×C₁₉	#3389	1	2	yes	—
284	C₂²×Q₈	—	2	1	no	—
285	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
286	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
287	C₂³×C₄	—	2	1	no	—
288	C₂³×C₄	—	2	1	no	—
289	C₂³×C₄	—	2	2	no	—
290	C₂×D₈	—	2	2	no	—
291	C₂×D₈	—	2	2	no	—
292	C₂×D₈	Q₈×C₁₉	1	4	yes	complemented
293	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
294	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
296	C₄⋊Q₈	—	2	2	no	—
297	C₄⋊Q₈	—	2	2	no	—
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	—	4	2	no	—
303	C₄×D₄	D₄×C₁₉	1	4	yes	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
317	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
318	#107	—	2	4	no	—
319	#106	—	2	2	no	—
320	C₄⋊C₈	—	2	2	no	—
321	C₄⋊C₈	—	4	2	no	—
322	#102	—	2	2	no	—
323	#102	—	2	4	no	—
324	#102	—	2	2	no	—
325	#102	—	4	2	no	—
326	#97	—	2	2	no	—
327	#95	—	2	1	no	—
328	#95	—	2	2	no	—
329	#95	—	2	2	no	—
330	#95	—	2	2	no	—
331	#95	—	2	1	no	—
332	#95	D₄×C₁₉	1	1	yes	characteristic
333	#95	D₄×C₁₉	1	1	yes	characteristic
334	C₁₉	#24830	1	1	yes	characteristic, direct product factor, Sylow
335	C₂⁴	—	2	1	no	—
336	C₂⁴	—	2	1	no	—
337	C₂×Q₈	—	4	2	no	—
338	C₂×Q₈	—	8	2	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
348	C₂×D₄	C₂×Q₈×C₁₉	1	2	yes	—
349	C₂×D₄	C₂×Q₈×C₁₉	1	2	yes	—
350	C₂×D₄	#41×C₁₉	1	2	yes	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	4	4	no	—
357	C₂²×C₄	—	4	4	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	8	2	no	—
361	C₂²×C₄	—	8	2	no	—
362	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
367	D₈	—	2	8	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	8	2	no	—
387	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	4	4	no	—
390	C₂²⋊C₄	—	4	2	no	—
391	C₂²⋊C₄	—	8	2	no	—
392	C₂²⋊C₄	—	8	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	C₂×D₄×C₁₉	1	2	yes	—
396	C₄²	#41×C₁₉	1	2	yes	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
408	Q₈	—	8	4	no	—
409	D₄	—	2	2	no	—
410	D₄	—	2	2	no	—
411	D₄	—	2	2	no	—
412	D₄	—	2	2	no	—
413	D₄	—	2	2	no	—
414	D₄	—	4	1	no	—
415	D₄	—	4	1	no	—
416	D₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	8	4	no	—
436	C₂×C₄	—	8	4	no	—
437	C₂×C₄	—	8	8	no	—
438	C₂×C₄	C₁₉×#121	1	2	yes	—
439	C₂×C₄	C₁₉×#121	1	2	yes	—
440	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
441	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
442	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
443	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
444	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
445	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
446	C₈	—	2	2	no	—
447	C₈	—	4	1	no	—
448	C₈	—	4	2	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	4	4	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	2	no	—
459	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
460	C₂²	C₁₉×#546	1	1	yes	characteristic
461	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
462	C₂²	C₁₉×#575	1	2	yes	—
463	C₂²	C₁₉×#576	1	2	yes	—
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	8	1	no	—
470	C₄	—	8	2	no	—
471	C₄	—	8	2	no	—
472	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
473	C₄	C₁₉×#537	1	1	yes	characteristic
474	C₄	C₁₉×#552	1	1	yes	characteristic
475	C₄	C₁₉×#554	1	1	yes	characteristic
476	C₂	—	4	4	no	—
477	C₂	—	8	2	no	—
478	C₂	C₁₉×#2417	1	1	yes	characteristic
479	C₂	C₁₉×#3040	1	1	yes	characteristic
480	C₂	C₁₉×#3041	1	1	yes	characteristic
481	C₂	C₁₉×#3319	1	2	yes	—
482	C₂	C₁₉×#3389	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₈×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₄⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#474	C₂	semidirect
3. C₁₉×#2563	C₂	semidirect
4. C₁₉×#2349	C₂	semidirect
5. C₁₉×#2085	C₂	semidirect
6. C₁₉×#2067	C₂	semidirect
7. C₁₉×#1993	C₂	semidirect
8. C₁₉×#1940	C₂	semidirect
10. C₁₉×#1804	C₂	semidirect
11. C₁₉×#1804	C₂	semidirect
51. C₂×D₈×C₁₉	Q₈	semidirect
155. #24830	C₁₉	direct (N × H)
208. C₂×#474	C₂×C₁₉	semidirect
210. #2563	C₂×C₁₉	semidirect
211. #2349	C₂×C₁₉	semidirect
212. #2085	C₂×C₁₉	semidirect
213. #2067	C₂×C₁₉	semidirect
214. #1993	C₂×C₁₉	semidirect
215. #1940	C₂×C₁₉	semidirect
217. #1804	C₂×C₁₉	semidirect
218. #1804	C₂×C₁₉	semidirect
292. C₂×D₈	Q₈×C₁₉	semidirect
334. C₁₉	#24830	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#474	2
C₂×C₁₉×#442	2
C₁₉×#2563	2
C₁₉×#2349	2
C₁₉×#2085	2
C₁₉×#2067	2
C₁₉×#1993	2
C₁₉×#1940	2
C₁₉×#1879	2
C₁₉×#1804	2
#24830	19

Subgroups — C19×#24830 #18030789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24830 #18030789