Subgroups — C₁₉×#32953 #18038912

Order 4864.

1764 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#474	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1862	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1852	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1802	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1786	C₂	1	2	yes	maximal
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₉	—	2	1	no	—
11	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
13	C₂×C₄×D₄×C₁₉	—	2	8	no	—
14	C₂×C₄×D₄×C₁₉	—	2	1	no	—
15	C₂×C₄×D₄×C₁₉	—	2	1	no	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
20	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#474	—	2	8	no	—
22	C₂×C₁₉×#107	C₂²	1	4	yes	complemented
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
24	C₂×C₁₉×#102	C₂²	1	4	yes	—
25	C₂×C₁₉×#102	C₂²	1	4	yes	—
26	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₁₉×#391	—	2	1	no	—
28	C₁₉×#389	—	2	1	no	—
29	C₁₉×#389	C₂²	1	2	yes	complemented
30	C₁₉×#384	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#380	—	2	1	no	—
32	C₁₉×#380	C₂²	1	2	yes	—
33	C₁₉×#340	C₂²	1	4	yes	complemented
34	C₁₉×#336	C₂²	1	2	yes	complemented
35	C₂⁵×C₁₉	—	2	1	no	—
36	C₂²×Q₈×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	4	no	—
38	C₂²×D₄×C₁₉	—	2	4	no	—
39	C₂²×D₄×C₁₉	—	2	1	no	—
40	C₂²×D₄×C₁₉	—	2	2	no	—
41	C₂²×D₄×C₁₉	Q₈	1	4	yes	complemented
42	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₉	—	2	8	no	—
44	C₂³×C₄×C₁₉	—	2	1	no	—
45	C₂³×C₄×C₁₉	—	2	2	no	—
46	C₂³×C₄×C₁₉	—	2	2	no	—
47	C₂³×C₄×C₁₉	—	4	4	no	—
48	C₂³×C₄×C₁₉	—	4	4	no	—
49	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
53	C₁₉×C₄⋊Q₈	—	2	4	no	—
54	C₁₉×C₂²⋊Q₈	—	4	4	no	—
55	C₄×D₄×C₁₉	—	2	8	no	—
56	C₄×D₄×C₁₉	—	2	8	no	—
57	C₄×D₄×C₁₉	—	2	4	no	—
58	C₄×D₄×C₁₉	—	2	4	no	—
59	C₄×D₄×C₁₉	—	2	4	no	—
60	C₄×D₄×C₁₉	D₄	1	8	yes	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄²×C₁₉	—	2	4	no	—
75	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
79	C₁₉×#107	—	2	8	no	—
80	C₁₉×C₄⋊C₈	—	2	4	no	—
81	C₁₉×#102	—	2	8	no	—
82	C₁₉×#102	—	2	8	no	—
83	C₁₉×C₂²⋊C₈	—	2	4	no	—
84	C₁₉×#95	—	2	2	no	—
85	C₁₉×#95	—	2	2	no	—
86	C₂⁴×C₁₉	—	2	4	no	—
87	C₂⁴×C₁₉	—	2	4	no	—
88	C₂⁴×C₁₉	—	2	4	no	—
89	C₂⁴×C₁₉	—	2	2	no	—
90	C₂⁴×C₁₉	—	4	2	no	—
91	C₂⁴×C₁₉	—	4	2	no	—
92	C₂⁴×C₁₉	—	4	2	no	—
93	C₂⁴×C₁₉	—	4	2	no	—
94	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₁₉	—	4	2	no	—
96	C₂×Q₈×C₁₉	—	4	2	no	—
97	C₂×Q₈×C₁₉	—	4	2	no	—
98	C₂×D₄×C₁₉	—	2	4	no	—
99	C₂×D₄×C₁₉	—	2	4	no	—
100	C₂×D₄×C₁₉	—	2	16	no	—
101	C₂×D₄×C₁₉	—	2	16	no	—
102	C₂×D₄×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
107	C₂×D₄×C₁₉	C₂×Q₈	1	4	yes	—
108	C₂×D₄×C₁₉	#41	1	4	yes	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	4	no	—
114	C₂²×C₄×C₁₉	—	2	8	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	8	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	4	1	no	—
122	C₂²×C₄×C₁₉	—	4	4	no	—
123	C₂²×C₄×C₁₉	—	4	32	no	—
124	C₂²×C₄×C₁₉	—	4	2	no	—
125	C₂²×C₄×C₁₉	—	4	2	no	—
126	C₂²×C₄×C₁₉	—	4	4	no	—
127	C₂²×C₄×C₁₉	—	4	4	no	—
128	C₂²×C₄×C₁₉	—	4	4	no	—
129	C₂²×C₄×C₁₉	D₈	1	4	yes	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
136	C₂²×C₄×C₁₉	#41	1	2	yes	—
137	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
138	C₂×C₈×C₁₉	—	2	4	no	—
139	C₂×C₈×C₁₉	—	2	4	no	—
140	C₂×C₈×C₁₉	—	2	4	no	—
141	C₄⋊C₄×C₁₉	—	2	4	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	4	no	—
144	C₄⋊C₄×C₁₉	—	2	4	no	—
145	C₄⋊C₄×C₁₉	—	4	2	no	—
146	C₄⋊C₄×C₁₉	—	4	2	no	—
147	C₄⋊C₄×C₁₉	—	4	2	no	—
148	C₄⋊C₄×C₁₉	—	4	4	no	—
149	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
150	C₂²⋊C₄×C₁₉	—	2	8	no	—
151	C₂²⋊C₄×C₁₉	—	2	8	no	—
152	C₂²⋊C₄×C₁₉	—	4	4	no	—
153	C₄²×C₁₉	—	2	2	no	—
154	C₄²×C₁₉	—	2	2	no	—
155	C₄²×C₁₉	—	2	2	no	—
156	C₄²×C₁₉	C₂×D₄	1	4	yes	—
157	#32953	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂³×C₁₉	—	2	1	no	—
159	C₂³×C₁₉	—	2	1	no	—
160	C₂³×C₁₉	—	2	1	no	—
161	C₂³×C₁₉	—	2	1	no	—
162	C₂³×C₁₉	—	2	16	no	—
163	C₂³×C₁₉	—	2	4	no	—
164	C₂³×C₁₉	—	2	4	no	—
165	C₂³×C₁₉	—	2	4	no	—
166	C₂³×C₁₉	—	4	8	no	—
167	C₂³×C₁₉	—	4	8	no	—
168	C₂³×C₁₉	—	4	8	no	—
169	C₂³×C₁₉	—	4	8	no	—
170	C₂³×C₁₉	—	4	8	no	—
171	C₂³×C₁₉	—	4	2	no	—
172	C₂³×C₁₉	—	4	2	no	—
173	C₂³×C₁₉	—	4	2	no	—
174	C₂³×C₁₉	—	4	2	no	—
175	C₂³×C₁₉	—	4	8	no	—
176	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
177	C₂³×C₁₉	C₂×D₈	1	2	yes	—
178	C₂³×C₁₉	#137	1	2	yes	—
179	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₁₉	—	8	4	no	—
181	D₄×C₁₉	—	2	16	no	—
182	D₄×C₁₉	—	2	4	no	—
183	D₄×C₁₉	—	2	4	no	—
184	D₄×C₁₉	—	2	4	no	—
185	D₄×C₁₉	C₂²⋊Q₈	1	8	yes	complemented
186	C₂×C₄×C₁₉	—	2	1	no	—
187	C₂×C₄×C₁₉	—	2	1	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	2	4	no	—
194	C₂×C₄×C₁₉	—	2	8	no	—
195	C₂×C₄×C₁₉	—	2	1	no	—
196	C₂×C₄×C₁₉	—	2	4	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	4	4	no	—
200	C₂×C₄×C₁₉	—	4	16	no	—
201	C₂×C₄×C₁₉	—	4	8	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	16	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	#120	1	2	yes	—
212	C₂×C₄×C₁₉	#120	1	2	yes	—
213	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
214	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
215	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
216	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
217	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
220	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
221	C₈×C₁₉	—	4	4	no	—
222	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic
223	C₂×#474	C₂×C₁₉	1	2	yes	complemented
224	#2857	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#1862	C₂×C₁₉	1	4	yes	complemented
226	#1852	C₂×C₁₉	1	2	yes	complemented
227	#1802	C₂×C₁₉	1	2	yes	complemented
228	#1797	C₂×C₁₉	1	1	yes	characteristic, complemented
229	#1786	C₂×C₁₉	1	2	yes	—
230	C₂²×C₁₉	—	2	2	no	—
231	C₂²×C₁₉	—	2	2	no	—
232	C₂²×C₁₉	—	2	2	no	—
233	C₂²×C₁₉	—	2	2	no	—
234	C₂²×C₁₉	—	2	2	no	—
235	C₂²×C₁₉	—	2	2	no	—
236	C₂²×C₁₉	—	2	8	no	—
237	C₂²×C₁₉	—	4	32	no	—
238	C₂²×C₁₉	—	4	4	no	—
239	C₂²×C₁₉	—	4	4	no	—
240	C₂²×C₁₉	—	4	4	no	—
241	C₂²×C₁₉	—	4	4	no	—
242	C₂²×C₁₉	—	4	4	no	—
243	C₂²×C₁₉	—	4	4	no	—
244	C₂²×C₁₉	#474	1	4	yes	complemented
245	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
246	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
247	C₂²×C₁₉	#525	1	1	yes	characteristic
248	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
249	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
250	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
251	C₂²×C₁₉	#575	1	1	yes	characteristic
252	C₄×C₁₉	—	2	2	no	—
253	C₄×C₁₉	—	2	2	no	—
254	C₄×C₁₉	—	2	2	no	—
255	C₄×C₁₉	—	4	4	no	—
256	C₄×C₁₉	—	4	1	no	—
257	C₄×C₁₉	—	8	2	no	—
258	C₄×C₁₉	—	8	2	no	—
259	C₄×C₁₉	#447	1	4	yes	—
260	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
261	C₄×C₁₉	#525	1	2	yes	—
262	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
263	C₂⁴×C₄	—	2	1	no	—
264	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
265	C₂×C₂²⋊Q₈	—	2	1	no	—
266	C₂×C₄×D₄	—	2	8	no	—
267	C₂×C₄×D₄	—	2	1	no	—
268	C₂×C₄×D₄	—	2	1	no	—
269	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
270	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
271	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
272	C₂²×C₂²⋊C₄	—	2	1	no	—
273	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
274	#474	—	2	8	no	—
275	C₂×#107	C₂²×C₁₉	1	4	yes	complemented
276	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
277	C₂×#102	C₂²×C₁₉	1	4	yes	—
278	C₂×#102	C₂²×C₁₉	1	4	yes	—
279	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
280	#391	—	2	1	no	—
281	#389	—	2	1	no	—
282	#389	C₂²×C₁₉	1	2	yes	complemented
283	#384	C₂²×C₁₉	1	1	yes	characteristic, complemented
284	#380	—	2	1	no	—
285	#380	C₂²×C₁₉	1	2	yes	—
286	#340	C₂²×C₁₉	1	4	yes	complemented
287	#336	C₂²×C₁₉	1	2	yes	complemented
288	C₂×C₁₉	—	2	4	no	—
289	C₂×C₁₉	—	4	8	no	—
290	C₂×C₁₉	#2848	1	1	yes	characteristic
291	C₂×C₁₉	C₂×#447	1	1	yes	characteristic
292	C₂×C₁₉	#3007	1	1	yes	characteristic
293	C₂×C₁₉	C₂×#474	1	1	yes	characteristic
294	C₂×C₁₉	#3077	1	1	yes	characteristic
295	C₂×C₁₉	#3100	1	1	yes	characteristic
296	C₂×C₁₉	#3110	1	1	yes	characteristic
297	C₂⁵	—	2	1	no	—
298	C₂²×Q₈	—	2	1	no	—
299	C₂²×D₄	—	2	4	no	—
300	C₂²×D₄	—	2	4	no	—
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	—	2	2	no	—
303	C₂²×D₄	Q₈×C₁₉	1	4	yes	complemented
304	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
305	C₂³×C₄	—	2	8	no	—
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	—	2	2	no	—
308	C₂³×C₄	—	2	2	no	—
309	C₂³×C₄	—	4	4	no	—
310	C₂³×C₄	—	4	4	no	—
311	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
312	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
313	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
314	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
315	C₄⋊Q₈	—	2	4	no	—
316	C₂²⋊Q₈	—	4	4	no	—
317	C₄×D₄	—	2	8	no	—
318	C₄×D₄	—	2	8	no	—
319	C₄×D₄	—	2	4	no	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	—	2	4	no	—
322	C₄×D₄	D₄×C₁₉	1	8	yes	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	4	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
331	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
332	C₂×C₂²⋊C₄	—	2	8	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₄²	—	2	4	no	—
337	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
338	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
341	#107	—	2	8	no	—
342	C₄⋊C₈	—	2	4	no	—
343	#102	—	2	8	no	—
344	#102	—	2	8	no	—
345	C₂²⋊C₈	—	2	4	no	—
346	#95	—	2	2	no	—
347	#95	—	2	2	no	—
348	C₁₉	#32953	1	1	yes	characteristic, direct product factor, Sylow
349	C₂⁴	—	2	4	no	—
350	C₂⁴	—	2	4	no	—
351	C₂⁴	—	2	4	no	—
352	C₂⁴	—	2	2	no	—
353	C₂⁴	—	4	2	no	—
354	C₂⁴	—	4	2	no	—
355	C₂⁴	—	4	2	no	—
356	C₂⁴	—	4	2	no	—
357	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
358	C₂×Q₈	—	4	2	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×Q₈	—	4	2	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	16	no	—
364	C₂×D₄	—	2	16	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
370	C₂×D₄	C₂×Q₈×C₁₉	1	4	yes	—
371	C₂×D₄	#41×C₁₉	1	4	yes	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	8	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	—	4	4	no	—
386	C₂²×C₄	—	4	32	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	4	no	—
390	C₂²×C₄	—	4	4	no	—
391	C₂²×C₄	—	4	4	no	—
392	C₂²×C₄	D₈×C₁₉	1	4	yes	—
393	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
398	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
399	C₂²×C₄	#41×C₁₉	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
401	C₂×C₈	—	2	4	no	—
402	C₂×C₈	—	2	4	no	—
403	C₂×C₈	—	2	4	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	4	4	no	—
412	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
413	C₂²⋊C₄	—	2	8	no	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	—	4	4	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	C₂×D₄×C₁₉	1	4	yes	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	16	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	4	8	no	—
429	C₂³	—	4	8	no	—
430	C₂³	—	4	8	no	—
431	C₂³	—	4	8	no	—
432	C₂³	—	4	8	no	—
433	C₂³	—	4	8	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
439	C₂³	C₂×D₈×C₁₉	1	2	yes	—
440	C₂³	C₁₉×#137	1	2	yes	—
441	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
442	Q₈	—	8	4	no	—
443	D₄	—	2	16	no	—
444	D₄	—	2	4	no	—
445	D₄	—	2	4	no	—
446	D₄	—	2	4	no	—
447	D₄	C₁₉×C₂²⋊Q₈	1	8	yes	complemented
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	16	no	—
463	C₂×C₄	—	4	8	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	16	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	C₁₉×#120	1	2	yes	—
474	C₂×C₄	C₁₉×#120	1	2	yes	—
475	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
476	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
477	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
478	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
479	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
480	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
481	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
482	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
483	C₈	—	4	4	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	8	no	—
491	C₂²	—	4	32	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	4	4	no	—
498	C₂²	C₁₉×#474	1	4	yes	complemented
499	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
500	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
501	C₂²	C₁₉×#525	1	1	yes	characteristic
502	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
503	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
504	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
505	C₂²	C₁₉×#575	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	1	no	—
511	C₄	—	8	2	no	—
512	C₄	—	8	2	no	—
513	C₄	C₁₉×#447	1	4	yes	—
514	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
515	C₄	C₁₉×#525	1	2	yes	—
516	C₂	—	2	4	no	—
517	C₂	—	4	8	no	—
518	C₂	C₁₉×#2848	1	1	yes	characteristic
519	C₂	C₂×C₁₉×#447	1	1	yes	characteristic
520	C₂	C₁₉×#3007	1	1	yes	characteristic
521	C₂	C₂×C₁₉×#474	1	1	yes	characteristic
522	C₂	C₁₉×#3077	1	1	yes	characteristic
523	C₂	C₁₉×#3100	1	1	yes	characteristic
524	C₂	C₁₉×#3110	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#474	C₂	semidirect
3. C₁₉×#2857	C₂	semidirect
4. C₁₉×#1862	C₂	semidirect
5. C₁₉×#1852	C₂	semidirect
6. C₁₉×#1802	C₂	semidirect
7. C₁₉×#1797	C₂	semidirect
11. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₁₉×#107	C₂²	semidirect
23. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
29. C₁₉×#389	C₂²	semidirect
30. C₁₉×#384	C₂²	semidirect
33. C₁₉×#340	C₂²	semidirect
34. C₁₉×#336	C₂²	semidirect
41. C₂²×D₄×C₁₉	Q₈	semidirect
157. #32953	C₁₉	direct (N × H)
185. D₄×C₁₉	C₂²⋊Q₈	semidirect
223. C₂×#474	C₂×C₁₉	semidirect
224. #2857	C₂×C₁₉	semidirect
225. #1862	C₂×C₁₉	semidirect
226. #1852	C₂×C₁₉	semidirect
227. #1802	C₂×C₁₉	semidirect
228. #1797	C₂×C₁₉	semidirect
244. C₂²×C₁₉	#474	semidirect
264. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
275. C₂×#107	C₂²×C₁₉	semidirect
276. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
282. #389	C₂²×C₁₉	semidirect
283. #384	C₂²×C₁₉	semidirect
286. #340	C₂²×C₁₉	semidirect
287. #336	C₂²×C₁₉	semidirect
303. C₂²×D₄	Q₈×C₁₉	semidirect
348. C₁₉	#32953	direct (N × H)
447. D₄	C₁₉×C₂²⋊Q₈	semidirect
498. C₂²	C₁₉×#474	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₁₉	2
C₂×C₁₉×#474	2
C₁₉×#2857	2
C₁₉×#1862	2
C₁₉×#1852	2
C₁₉×#1802	2
C₁₉×#1797	2
C₁₉×#1786	2
#32953	19

Subgroups — C19×#32953 #18038912

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32953 #18038912