Subgroups — C₁₉×#32987 #18038946

Order 4864.

1358 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#482	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2615	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1875	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1874	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1854	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1853	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1825	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1823	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1780	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#121	C₂²	1	2	yes	—
15	C₁₉×#520	—	2	4	no	—
16	C₁₉×#520	—	2	4	no	—
17	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
18	C₂×C₄×D₄×C₁₉	—	2	2	no	—
19	C₂×C₄×D₄×C₁₉	—	2	1	no	—
20	C₂×C₁₉×#117	C₂²	1	2	yes	—
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#482	—	2	4	no	—
25	C₁₉×#481	—	2	4	no	—
26	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#106	C₂²	1	2	yes	—
29	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#102	C₂²	1	2	yes	—
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₁₉×#393	—	2	1	no	—
37	C₁₉×#392	—	2	1	no	—
38	C₁₉×#392	—	2	2	no	—
39	C₁₉×#380	C₂²	1	1	yes	characteristic
40	C₁₉×#380	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#340	C₂²	1	2	yes	—
43	C₁₉×#340	C₂²	1	2	yes	—
44	C₁₉×#340	C₂²	1	2	yes	—
45	C₂×#41×C₁₉	—	2	2	no	—
46	C₂×#41×C₁₉	—	2	2	no	—
47	C₂×#41×C₁₉	—	2	4	no	—
48	C₂×#41×C₁₉	—	2	4	no	—
49	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₉	—	2	1	no	—
51	C₂²×D₄×C₁₉	—	2	2	no	—
52	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
53	C₂²×D₄×C₁₉	D₄	1	2	yes	—
54	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	—	2	2	no	—
56	C₂³×C₄×C₁₉	—	2	1	no	—
57	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₁₉×#121	—	2	2	no	—
63	C₁₉×#121	—	2	2	no	—
64	C₁₉×#121	—	2	4	no	—
65	C₁₉×#121	—	2	4	no	—
66	C₄×Q₈×C₁₉	—	2	8	no	—
67	C₄×D₄×C₁₉	—	2	16	no	—
68	C₄×D₄×C₁₉	—	2	8	no	—
69	C₁₉×#117	—	2	2	no	—
70	C₁₉×#117	—	2	4	no	—
71	C₁₉×#117	—	2	4	no	—
72	C₁₉×#117	D₄	1	4	yes	complemented
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
78	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	complemented
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
90	C₂×C₄²×C₁₉	—	2	2	no	—
91	C₂×C₄²×C₁₉	—	2	1	no	—
92	C₁₉×#107	—	2	2	no	—
93	C₁₉×#106	—	2	4	no	—
94	C₁₉×#106	—	2	2	no	—
95	C₁₉×#102	—	2	4	no	—
96	C₁₉×#102	—	2	2	no	—
97	C₁₉×#102	—	2	2	no	—
98	C₁₉×C₂²⋊C₈	—	2	2	no	—
99	C₁₉×C₂²⋊C₈	—	2	2	no	—
100	C₁₉×C₂²⋊C₈	—	2	4	no	—
101	C₁₉×C₂²⋊C₈	—	2	4	no	—
102	C₁₉×#95	—	2	1	no	—
103	C₁₉×#95	—	2	2	no	—
104	C₂⁴×C₁₉	—	2	1	no	—
105	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
107	#41×C₁₉	—	2	8	no	—
108	#41×C₁₉	—	2	8	no	—
109	#41×C₁₉	—	2	16	no	—
110	C₂×Q₈×C₁₉	—	2	2	no	—
111	C₂×Q₈×C₁₉	—	2	4	no	—
112	C₂×D₄×C₁₉	—	2	4	no	—
113	C₂×D₄×C₁₉	—	2	4	no	—
114	C₂×D₄×C₁₉	—	2	4	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	4	no	—
117	C₂×D₄×C₁₉	—	2	1	no	—
118	C₂×D₄×C₁₉	—	2	1	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	2	no	—
121	C₂×D₄×C₁₉	—	4	2	no	—
122	C₂×D₄×C₁₉	—	4	4	no	—
123	C₂×D₄×C₁₉	—	8	2	no	—
124	C₂×D₄×C₁₉	—	8	2	no	—
125	C₂×D₄×C₁₉	—	8	2	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	8	no	—
136	C₂²×C₄×C₁₉	—	2	4	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	8	1	no	—
140	C₂²×C₄×C₁₉	—	8	2	no	—
141	C₂²×C₄×C₁₉	—	8	1	no	—
142	C₂²×C₄×C₁₉	—	8	2	no	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₉	#41	1	4	yes	—
148	C₂²×C₄×C₁₉	#41	1	4	yes	—
149	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	2	1	no	—
152	C₂×C₈×C₁₉	—	2	1	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₂×C₈×C₁₉	—	2	2	no	—
156	C₂×C₈×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	8	no	—
158	C₄⋊C₄×C₁₉	—	2	4	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
167	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
168	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
169	C₂²⋊C₄×C₁₉	—	2	8	no	—
170	C₂²⋊C₄×C₁₉	—	2	4	no	—
171	C₂²⋊C₄×C₁₉	—	4	2	no	—
172	C₂²⋊C₄×C₁₉	—	4	4	no	—
173	C₂²⋊C₄×C₁₉	—	8	1	no	—
174	C₂²⋊C₄×C₁₉	—	8	2	no	—
175	C₄²×C₁₉	—	2	8	no	—
176	C₄²×C₁₉	—	2	4	no	—
177	#32987	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂³×C₁₉	—	2	2	no	—
179	C₂³×C₁₉	—	2	2	no	—
180	C₂³×C₁₉	—	2	2	no	—
181	C₂³×C₁₉	—	2	1	no	—
182	C₂³×C₁₉	—	2	2	no	—
183	C₂³×C₁₉	—	2	2	no	—
184	C₂³×C₁₉	—	2	2	no	—
185	C₂³×C₁₉	—	2	1	no	—
186	C₂³×C₁₉	—	2	2	no	—
187	C₂³×C₁₉	—	2	2	no	—
188	C₂³×C₁₉	—	4	1	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	—	4	1	no	—
191	C₂³×C₁₉	—	4	2	no	—
192	C₂³×C₁₉	—	4	1	no	—
193	C₂³×C₁₉	#120	1	2	yes	—
194	C₂³×C₁₉	#123	1	4	yes	—
195	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₁₉	—	2	8	no	—
197	D₄×C₁₉	—	2	8	no	—
198	D₄×C₁₉	—	2	16	no	—
199	D₄×C₁₉	—	4	2	no	—
200	D₄×C₁₉	—	4	1	no	—
201	D₄×C₁₉	—	4	1	no	—
202	D₄×C₁₉	—	8	8	no	—
203	D₄×C₁₉	—	8	4	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	4	no	—
210	C₂×C₄×C₁₉	—	2	4	no	—
211	C₂×C₄×C₁₉	—	2	4	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	2	4	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	2	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	8	4	no	—
228	C₂×C₄×C₁₉	—	8	8	no	—
229	C₂×C₄×C₁₉	#120	1	2	yes	—
230	C₂×C₄×C₁₉	#123	1	4	yes	—
231	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
234	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
235	C₈×C₁₉	—	4	2	no	—
236	C₈×C₁₉	—	4	1	no	—
237	C₈×C₁₉	—	4	1	no	—
238	C₂×#520	C₂×C₁₉	1	1	yes	characteristic, complemented
239	C₂×#481	C₂×C₁₉	1	1	yes	characteristic, complemented
240	C₂×#482	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#2615	C₂×C₁₉	1	1	yes	characteristic
242	#1875	C₂×C₁₉	1	2	yes	complemented
243	#1874	C₂×C₁₉	1	2	yes	complemented
244	#1854	C₂×C₁₉	1	2	yes	complemented
245	#1853	C₂×C₁₉	1	2	yes	complemented
246	#1825	C₂×C₁₉	1	1	yes	characteristic, complemented
247	#1823	C₂×C₁₉	1	1	yes	characteristic, complemented
248	#1780	C₂×C₁₉	1	1	yes	characteristic, complemented
249	C₂²×C₁₉	—	2	4	no	—
250	C₂²×C₁₉	—	2	4	no	—
251	C₂²×C₁₉	—	2	2	no	—
252	C₂²×C₁₉	—	2	4	no	—
253	C₂²×C₁₉	—	2	2	no	—
254	C₂²×C₁₉	—	2	2	no	—
255	C₂²×C₁₉	—	4	2	no	—
256	C₂²×C₁₉	—	4	2	no	—
257	C₂²×C₁₉	—	4	2	no	—
258	C₂²×C₁₉	—	4	2	no	—
259	C₂²×C₁₉	—	4	2	no	—
260	C₂²×C₁₉	—	4	2	no	—
261	C₂²×C₁₉	—	8	2	no	—
262	C₂²×C₁₉	—	8	2	no	—
263	C₂²×C₁₉	—	8	1	no	—
264	C₂²×C₁₉	—	8	1	no	—
265	C₂²×C₁₉	—	8	1	no	—
266	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
267	C₂²×C₁₉	C₂×#123	1	2	yes	—
268	C₂²×C₁₉	#576	1	1	yes	characteristic
269	C₂²×C₁₉	#577	1	2	yes	—
270	C₂²×C₁₉	#577	1	1	yes	characteristic
271	C₄×C₁₉	—	2	2	no	—
272	C₄×C₁₉	—	2	4	no	—
273	C₄×C₁₉	—	4	2	no	—
274	C₄×C₁₉	—	4	4	no	—
275	C₄×C₁₉	—	4	2	no	—
276	C₄×C₁₉	—	8	2	no	—
277	C₄×C₁₉	—	8	1	no	—
278	C₄×C₁₉	#525	1	1	yes	characteristic
279	C₄×C₁₉	#525	1	2	yes	—
280	C₄×C₁₉	#525	1	1	yes	characteristic
281	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
282	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
283	C₂×#121	C₂²×C₁₉	1	2	yes	—
284	#520	—	2	4	no	—
285	#520	—	2	4	no	—
286	C₂×C₄×Q₈	—	2	1	no	—
287	C₂×C₄×D₄	—	2	2	no	—
288	C₂×C₄×D₄	—	2	1	no	—
289	C₂×#117	C₂²×C₁₉	1	2	yes	—
290	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
291	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
292	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
293	#482	—	2	4	no	—
294	#481	—	2	4	no	—
295	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
296	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
297	C₂×#106	C₂²×C₁₉	1	2	yes	—
298	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
299	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
300	C₂×#102	C₂²×C₁₉	1	2	yes	—
301	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
303	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
304	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
305	#393	—	2	1	no	—
306	#392	—	2	1	no	—
307	#392	—	2	2	no	—
308	#380	C₂²×C₁₉	1	1	yes	characteristic
309	#380	C₂²×C₁₉	1	2	yes	—
310	#340	C₂²×C₁₉	1	2	yes	—
311	#340	C₂²×C₁₉	1	2	yes	—
312	#340	C₂²×C₁₉	1	2	yes	—
313	#340	C₂²×C₁₉	1	2	yes	—
314	C₂×C₁₉	—	4	4	no	—
315	C₂×C₁₉	—	4	2	no	—
316	C₂×C₁₉	—	16	1	no	—
317	C₂×C₁₉	#2849	1	1	yes	characteristic
318	C₂×C₁₉	#3010	1	1	yes	characteristic
319	C₂×C₁₉	#3012	1	1	yes	characteristic
320	C₂×C₁₉	#3096	1	2	yes	—
321	C₂×C₁₉	#3099	1	2	yes	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	—	2	2	no	—
324	C₂×#41	—	2	4	no	—
325	C₂×#41	—	2	4	no	—
326	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
330	C₂²×D₄	D₄×C₁₉	1	2	yes	—
331	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
332	C₂³×C₄	—	2	2	no	—
333	C₂³×C₄	—	2	1	no	—
334	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
336	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
338	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
339	#121	—	2	2	no	—
340	#121	—	2	2	no	—
341	#121	—	2	4	no	—
342	#121	—	2	4	no	—
343	C₄×Q₈	—	2	8	no	—
344	C₄×D₄	—	2	16	no	—
345	C₄×D₄	—	2	8	no	—
346	#117	—	2	2	no	—
347	#117	—	2	4	no	—
348	#117	—	2	4	no	—
349	#117	D₄×C₁₉	1	4	yes	complemented
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	4	no	—
354	C₂×C₄⋊C₄	—	2	4	no	—
355	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	complemented
356	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₄²	—	2	2	no	—
368	C₂×C₄²	—	2	1	no	—
369	#107	—	2	2	no	—
370	#106	—	2	4	no	—
371	#106	—	2	2	no	—
372	#102	—	2	4	no	—
373	#102	—	2	2	no	—
374	#102	—	2	2	no	—
375	C₂²⋊C₈	—	2	2	no	—
376	C₂²⋊C₈	—	2	2	no	—
377	C₂²⋊C₈	—	2	4	no	—
378	C₂²⋊C₈	—	2	4	no	—
379	#95	—	2	1	no	—
380	#95	—	2	2	no	—
381	C₁₉	#32987	1	1	yes	characteristic, direct product factor, Sylow
382	C₂⁴	—	2	1	no	—
383	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
385	#41	—	2	8	no	—
386	#41	—	2	8	no	—
387	#41	—	2	16	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	—	2	4	no	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	4	2	no	—
400	C₂×D₄	—	4	4	no	—
401	C₂×D₄	—	8	2	no	—
402	C₂×D₄	—	8	2	no	—
403	C₂×D₄	—	8	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	8	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	8	1	no	—
418	C₂²×C₄	—	8	2	no	—
419	C₂²×C₄	—	8	1	no	—
420	C₂²×C₄	—	8	2	no	—
421	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
423	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
424	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
425	C₂²×C₄	#41×C₁₉	1	4	yes	—
426	C₂²×C₄	#41×C₁₉	1	4	yes	—
427	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
445	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
446	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
447	C₂²⋊C₄	—	2	8	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	4	2	no	—
450	C₂²⋊C₄	—	4	4	no	—
451	C₂²⋊C₄	—	8	1	no	—
452	C₂²⋊C₄	—	8	2	no	—
453	C₄²	—	2	8	no	—
454	C₄²	—	2	4	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	1	no	—
470	C₂³	C₁₉×#120	1	2	yes	—
471	C₂³	C₁₉×#123	1	4	yes	—
472	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
473	Q₈	—	2	8	no	—
474	D₄	—	2	8	no	—
475	D₄	—	2	16	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	1	no	—
478	D₄	—	4	1	no	—
479	D₄	—	8	4	no	—
480	D₄	—	8	8	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	8	4	no	—
505	C₂×C₄	—	8	8	no	—
506	C₂×C₄	C₁₉×#120	1	2	yes	—
507	C₂×C₄	C₁₉×#123	1	4	yes	—
508	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
509	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
510	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
511	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
512	C₈	—	4	2	no	—
513	C₈	—	4	1	no	—
514	C₈	—	4	1	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	8	1	no	—
528	C₂²	—	8	1	no	—
529	C₂²	—	8	2	no	—
530	C₂²	—	8	2	no	—
531	C₂²	—	8	1	no	—
532	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
533	C₂²	C₂×C₁₉×#123	1	2	yes	—
534	C₂²	C₁₉×#576	1	1	yes	characteristic
535	C₂²	C₁₉×#577	1	2	yes	—
536	C₂²	C₁₉×#577	1	1	yes	characteristic
537	C₄	—	2	2	no	—
538	C₄	—	2	4	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	4	no	—
541	C₄	—	4	2	no	—
542	C₄	—	8	1	no	—
543	C₄	—	8	2	no	—
544	C₄	C₁₉×#525	1	1	yes	characteristic
545	C₄	C₁₉×#525	1	2	yes	—
546	C₄	C₁₉×#525	1	1	yes	characteristic
547	C₂	—	4	2	no	—
548	C₂	—	4	4	no	—
549	C₂	—	16	1	no	—
550	C₂	C₁₉×#2849	1	1	yes	characteristic
551	C₂	C₁₉×#3010	1	1	yes	characteristic
552	C₂	C₁₉×#3012	1	1	yes	characteristic
553	C₂	C₁₉×#3096	1	2	yes	—
554	C₂	C₁₉×#3099	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2615	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#520	C₂	semidirect
2. C₂×C₁₉×#481	C₂	semidirect
3. C₂×C₁₉×#482	C₂	semidirect
5. C₁₉×#1875	C₂	semidirect
6. C₁₉×#1874	C₂	semidirect
7. C₁₉×#1854	C₂	semidirect
8. C₁₉×#1853	C₂	semidirect
9. C₁₉×#1825	C₂	semidirect
10. C₁₉×#1823	C₂	semidirect
11. C₁₉×#1780	C₂	semidirect
72. C₁₉×#117	D₄	semidirect
78. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
177. #32987	C₁₉	direct (N × H)
238. C₂×#520	C₂×C₁₉	semidirect
239. C₂×#481	C₂×C₁₉	semidirect
240. C₂×#482	C₂×C₁₉	semidirect
242. #1875	C₂×C₁₉	semidirect
243. #1874	C₂×C₁₉	semidirect
244. #1854	C₂×C₁₉	semidirect
245. #1853	C₂×C₁₉	semidirect
246. #1825	C₂×C₁₉	semidirect
247. #1823	C₂×C₁₉	semidirect
248. #1780	C₂×C₁₉	semidirect
349. #117	D₄×C₁₉	semidirect
355. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
381. C₁₉	#32987	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×#520	2
C₂×C₁₉×#481	2
C₂×C₁₉×#482	2
C₁₉×#2615	2
C₁₉×#1875	2
C₁₉×#1874	2
C₁₉×#1854	2
C₁₉×#1853	2
C₁₉×#1825	2
C₁₉×#1823	2
C₁₉×#1780	2
#32987	19

Subgroups — C19×#32987 #18038946

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32987 #18038946