Subgroups — C₁₉×#12574 #18018533

Order 4864.

994 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#100	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#99	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2308	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1390	C₂	1	4	yes	maximal, complemented
5	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
6	C₂²×M₁₆×C₁₉	—	2	1	no	—
7	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
8	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
9	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
10	C₂×C₁₉×#100	—	2	2	no	—
11	C₂×C₁₉×#100	—	2	1	no	—
12	C₂×C₁₉×#100	C₄	1	4	yes	complemented
13	C₂×C₁₉×#100	C₂²	1	2	yes	—
14	C₂×C₁₉×#99	—	2	2	no	—
15	C₂×C₁₉×#99	—	2	1	no	—
16	C₂×C₁₉×#99	C₄	1	4	yes	complemented
17	C₂×C₁₉×#99	C₂²	1	2	yes	—
18	C₁₉×#386	—	2	1	no	—
19	C₁₉×#386	—	2	1	no	—
20	C₁₉×#386	C₄	1	2	yes	complemented
21	C₁₉×#386	C₂²	1	2	yes	—
22	C₁₉×#381	—	2	1	no	—
23	C₁₉×#379	—	2	1	no	—
24	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×D₄×C₁₉	—	4	1	no	—
27	C₂²×D₄×C₁₉	—	4	1	no	—
28	C₂²×D₄×C₁₉	—	4	2	no	—
29	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
31	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₉	D₄	1	2	yes	—
34	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₉	Q₈	1	2	yes	—
36	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	—	2	1	no	—
38	C₂³×C₄×C₁₉	—	4	1	no	—
39	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	complemented
40	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂×M₁₆×C₁₉	—	2	4	no	—
42	C₂×M₁₆×C₁₉	—	2	2	no	—
43	C₂×M₁₆×C₁₉	—	4	2	no	—
44	C₂×M₁₆×C₁₉	—	4	1	no	—
45	C₂²×C₈×C₁₉	—	4	1	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
58	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	complemented
59	C₁₉×#100	—	2	4	no	—
60	C₁₉×#100	—	2	2	no	—
61	C₁₉×#100	C₂×C₄	1	4	yes	complemented
62	C₁₉×#99	—	2	4	no	—
63	C₁₉×#99	—	2	2	no	—
64	C₁₉×#99	C₂×C₄	1	4	yes	complemented
65	C₁₉×#95	—	2	2	no	—
66	C₁₉×#95	—	2	2	no	—
67	C₂⁴×C₁₉	—	2	1	no	—
68	C₂⁴×C₁₉	—	2	2	no	—
69	C₂⁴×C₁₉	—	2	1	no	—
70	C₂⁴×C₁₉	—	2	1	no	—
71	C₂⁴×C₁₉	—	2	2	no	—
72	C₂⁴×C₁₉	—	2	1	no	—
73	C₂⁴×C₁₉	—	8	2	no	—
74	C₂⁴×C₁₉	—	8	2	no	—
75	C₂⁴×C₁₉	C₄²	1	2	yes	—
76	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
79	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
81	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
82	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
83	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂×D₄×C₁₉	—	4	2	no	—
85	C₂×D₄×C₁₉	—	4	2	no	—
86	C₂×D₄×C₁₉	—	4	2	no	—
87	C₂×D₄×C₁₉	—	4	2	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	4	2	no	—
91	C₂×D₄×C₁₉	—	4	2	no	—
92	C₂×D₄×C₁₉	—	4	1	no	—
93	C₂×D₄×C₁₉	—	4	1	no	—
94	C₂×D₄×C₁₉	—	4	1	no	—
95	C₂×D₄×C₁₉	—	4	1	no	—
96	C₂×D₄×C₁₉	—	4	2	no	—
97	C₂×D₄×C₁₉	—	4	2	no	—
98	C₂×D₄×C₁₉	—	4	1	no	—
99	C₂×D₄×C₁₉	—	4	1	no	—
100	C₂×D₄×C₁₉	C₄²	1	2	yes	—
101	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
102	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
103	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
104	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
105	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
106	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
107	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
108	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂×D₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	—	2	1	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	1	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	4	4	no	—
116	C₂²×C₄×C₁₉	—	4	2	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	—	4	2	no	—
119	C₂²×C₄×C₁₉	—	8	2	no	—
120	C₂²×C₄×C₁₉	—	8	2	no	—
121	C₂²×C₄×C₁₉	—	8	4	no	—
122	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	M₁₆×C₁₉	—	2	4	no	—
127	M₁₆×C₁₉	—	4	4	no	—
128	M₁₆×C₁₉	—	4	2	no	—
129	C₂×C₈×C₁₉	—	4	4	no	—
130	C₂×C₈×C₁₉	—	4	2	no	—
131	C₂²⋊C₄×C₁₉	—	2	4	no	—
132	C₂²⋊C₄×C₁₉	—	4	4	no	—
133	C₂²⋊C₄×C₁₉	—	4	2	no	—
134	C₂²⋊C₄×C₁₉	—	4	2	no	—
135	C₂²⋊C₄×C₁₉	—	4	2	no	—
136	C₂²⋊C₄×C₁₉	—	4	1	no	—
137	C₂²⋊C₄×C₁₉	—	4	1	no	—
138	C₂²⋊C₄×C₁₉	—	4	2	no	—
139	C₂²⋊C₄×C₁₉	—	8	2	no	—
140	C₂²⋊C₄×C₁₉	—	8	2	no	—
141	#12574	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	2	2	no	—
144	C₂³×C₁₉	—	2	1	no	—
145	C₂³×C₁₉	—	2	1	no	—
146	C₂³×C₁₉	—	2	1	no	—
147	C₂³×C₁₉	—	2	1	no	—
148	C₂³×C₁₉	—	2	1	no	—
149	C₂³×C₁₉	—	2	1	no	—
150	C₂³×C₁₉	—	2	2	no	—
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	—	2	2	no	—
153	C₂³×C₁₉	—	2	2	no	—
154	C₂³×C₁₉	—	2	2	no	—
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	2	1	no	—
157	C₂³×C₁₉	—	2	1	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	—	4	4	no	—
162	C₂³×C₁₉	—	4	2	no	—
163	C₂³×C₁₉	—	4	2	no	—
164	C₂³×C₁₉	—	8	2	no	—
165	C₂³×C₁₉	—	8	2	no	—
166	C₂³×C₁₉	—	8	2	no	—
167	C₂³×C₁₉	—	8	2	no	—
168	C₂³×C₁₉	—	8	2	no	—
169	C₂³×C₁₉	—	8	2	no	—
170	C₂³×C₁₉	—	8	2	no	—
171	C₂³×C₁₉	—	8	4	no	—
172	C₂³×C₁₉	—	8	4	no	—
173	C₂³×C₁₉	#95	1	2	yes	—
174	C₂³×C₁₉	#95	1	2	yes	—
175	C₂³×C₁₉	#95	1	2	yes	—
176	C₂³×C₁₉	#99	1	1	yes	characteristic
177	C₂³×C₁₉	#99	1	1	yes	characteristic
178	C₂³×C₁₉	#99	1	2	yes	—
179	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
180	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
184	D₄×C₁₉	—	4	2	no	—
185	D₄×C₁₉	—	4	2	no	—
186	D₄×C₁₉	—	4	2	no	—
187	D₄×C₁₉	—	4	2	no	—
188	D₄×C₁₉	—	4	2	no	—
189	D₄×C₁₉	—	4	2	no	—
190	D₄×C₁₉	—	4	1	no	—
191	D₄×C₁₉	—	4	1	no	—
192	D₄×C₁₉	—	4	1	no	—
193	D₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	4	4	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	2	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	—	8	4	no	—
210	C₂×C₄×C₁₉	—	8	8	no	—
211	C₂×C₄×C₁₉	—	8	4	no	—
212	C₂×C₄×C₁₉	—	8	4	no	—
213	C₂×C₄×C₁₉	#95	1	2	yes	—
214	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
216	C₈×C₁₉	—	4	4	no	—
217	C₂²×#100	C₂×C₁₉	1	1	yes	characteristic
218	C₂²×#99	C₂×C₁₉	1	1	yes	characteristic
219	#2308	C₂×C₁₉	1	1	yes	characteristic
220	#1390	C₂×C₁₉	1	4	yes	complemented
221	C₂²×C₁₉	—	2	2	no	—
222	C₂²×C₁₉	—	2	2	no	—
223	C₂²×C₁₉	—	2	2	no	—
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	2	2	no	—
226	C₂²×C₁₉	—	2	2	no	—
227	C₂²×C₁₉	—	2	1	no	—
228	C₂²×C₁₉	—	2	1	no	—
229	C₂²×C₁₉	—	2	1	no	—
230	C₂²×C₁₉	—	4	2	no	—
231	C₂²×C₁₉	—	4	2	no	—
232	C₂²×C₁₉	—	4	2	no	—
233	C₂²×C₁₉	—	4	2	no	—
234	C₂²×C₁₉	—	4	1	no	—
235	C₂²×C₁₉	—	4	1	no	—
236	C₂²×C₁₉	—	4	1	no	—
237	C₂²×C₁₉	—	4	1	no	—
238	C₂²×C₁₉	—	4	2	no	—
239	C₂²×C₁₉	—	4	4	no	—
240	C₂²×C₁₉	—	4	2	no	—
241	C₂²×C₁₉	—	4	4	no	—
242	C₂²×C₁₉	—	4	2	no	—
243	C₂²×C₁₉	—	4	2	no	—
244	C₂²×C₁₉	—	4	2	no	—
245	C₂²×C₁₉	—	4	2	no	—
246	C₂²×C₁₉	—	8	1	no	—
247	C₂²×C₁₉	—	8	1	no	—
248	C₂²×C₁₉	—	8	2	no	—
249	C₂²×C₁₉	—	8	2	no	—
250	C₂²×C₁₉	—	8	2	no	—
251	C₂²×C₁₉	—	8	2	no	—
252	C₂²×C₁₉	—	8	2	no	—
253	C₂²×C₁₉	—	8	2	no	—
254	C₂²×C₁₉	#342	1	2	yes	—
255	C₂²×C₁₉	#342	1	2	yes	—
256	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
257	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
258	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	2	2	no	—
261	C₄×C₁₉	—	2	1	no	—
262	C₄×C₁₉	—	8	2	no	—
263	C₄×C₁₉	—	8	4	no	—
264	C₄×C₁₉	—	8	2	no	—
265	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
266	C₂²×M₁₆	—	2	1	no	—
267	C₂²×C₂²⋊C₄	—	2	1	no	—
268	C₂²×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
269	C₂²×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
270	C₂×#100	—	2	1	no	—
271	C₂×#100	—	2	2	no	—
272	C₂×#100	C₄×C₁₉	1	4	yes	complemented
273	C₂×#100	C₂²×C₁₉	1	2	yes	—
274	C₂×#99	—	2	1	no	—
275	C₂×#99	—	2	2	no	—
276	C₂×#99	C₄×C₁₉	1	4	yes	complemented
277	C₂×#99	C₂²×C₁₉	1	2	yes	—
278	#386	—	2	1	no	—
279	#386	—	2	1	no	—
280	#386	C₄×C₁₉	1	2	yes	complemented
281	#386	C₂²×C₁₉	1	2	yes	—
282	#381	—	2	1	no	—
283	#379	—	2	1	no	—
284	C₂×C₁₉	—	2	1	no	—
285	C₂×C₁₉	—	2	1	no	—
286	C₂×C₁₉	—	2	2	no	—
287	C₂×C₁₉	—	2	2	no	—
288	C₂×C₁₉	—	4	1	no	—
289	C₂×C₁₉	—	4	2	no	—
290	C₂×C₁₉	—	4	1	no	—
291	C₂×C₁₉	—	4	2	no	—
292	C₂×C₁₉	—	4	1	no	—
293	C₂×C₁₉	—	4	1	no	—
294	C₂×C₁₉	C₂×#342	1	1	yes	characteristic
295	C₂×C₁₉	#2121	1	2	yes	—
296	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
297	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
298	C₂²×D₄	—	4	1	no	—
299	C₂²×D₄	—	4	1	no	—
300	C₂²×D₄	—	4	2	no	—
301	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
302	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
303	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
304	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
305	C₂²×D₄	D₄×C₁₉	1	2	yes	—
306	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
307	C₂²×D₄	Q₈×C₁₉	1	2	yes	—
308	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
309	C₂³×C₄	—	2	1	no	—
310	C₂³×C₄	—	4	1	no	—
311	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	complemented
312	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
313	C₂×M₁₆	—	2	4	no	—
314	C₂×M₁₆	—	2	2	no	—
315	C₂×M₁₆	—	4	2	no	—
316	C₂×M₁₆	—	4	1	no	—
317	C₂²×C₈	—	4	1	no	—
318	C₂×C₂²⋊C₄	—	2	4	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	4	1	no	—
326	C₂×C₂²⋊C₄	—	4	2	no	—
327	C₂×C₂²⋊C₄	—	4	1	no	—
328	C₂×C₂²⋊C₄	—	4	1	no	—
329	C₂×C₂²⋊C₄	—	4	2	no	—
330	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	complemented
331	#100	—	2	4	no	—
332	#100	—	2	2	no	—
333	#100	C₂×C₄×C₁₉	1	4	yes	complemented
334	#99	—	2	4	no	—
335	#99	—	2	2	no	—
336	#99	C₂×C₄×C₁₉	1	4	yes	complemented
337	#95	—	2	2	no	—
338	#95	—	2	2	no	—
339	C₁₉	#12574	1	1	yes	characteristic, direct product factor, Sylow
340	C₂⁴	—	2	1	no	—
341	C₂⁴	—	2	1	no	—
342	C₂⁴	—	2	1	no	—
343	C₂⁴	—	2	2	no	—
344	C₂⁴	—	2	2	no	—
345	C₂⁴	—	2	1	no	—
346	C₂⁴	—	8	2	no	—
347	C₂⁴	—	8	2	no	—
348	C₂⁴	C₄²×C₁₉	1	2	yes	—
349	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
350	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
351	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
352	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
353	C₂⁴	C₄⋊C₄×C₁₉	1	2	yes	—
354	C₂⁴	C₄⋊C₄×C₁₉	1	2	yes	—
355	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
356	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	4	1	no	—
362	C₂×D₄	—	4	1	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	—	4	2	no	—
365	C₂×D₄	—	4	1	no	—
366	C₂×D₄	—	4	1	no	—
367	C₂×D₄	—	4	1	no	—
368	C₂×D₄	—	4	1	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	—	4	1	no	—
372	C₂×D₄	—	4	1	no	—
373	C₂×D₄	C₄²×C₁₉	1	2	yes	—
374	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
375	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
376	C₂×D₄	C₄⋊C₄×C₁₉	1	2	yes	—
377	C₂×D₄	C₄⋊C₄×C₁₉	1	2	yes	—
378	C₂×D₄	C₄⋊C₄×C₁₉	1	2	yes	—
379	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
380	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
381	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
382	C₂×D₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	4	4	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	8	2	no	—
393	C₂²×C₄	—	8	2	no	—
394	C₂²×C₄	—	8	4	no	—
395	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
396	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
397	C₂²×C₄	C₄⋊C₄×C₁₉	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
399	M₁₆	—	2	4	no	—
400	M₁₆	—	4	4	no	—
401	M₁₆	—	4	2	no	—
402	C₂×C₈	—	4	4	no	—
403	C₂×C₈	—	4	2	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	4	4	no	—
406	C₂²⋊C₄	—	4	2	no	—
407	C₂²⋊C₄	—	4	2	no	—
408	C₂²⋊C₄	—	4	1	no	—
409	C₂²⋊C₄	—	4	1	no	—
410	C₂²⋊C₄	—	4	2	no	—
411	C₂²⋊C₄	—	4	2	no	—
412	C₂²⋊C₄	—	8	2	no	—
413	C₂²⋊C₄	—	8	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	4	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	8	2	no	—
437	C₂³	—	8	2	no	—
438	C₂³	—	8	2	no	—
439	C₂³	—	8	2	no	—
440	C₂³	—	8	2	no	—
441	C₂³	—	8	2	no	—
442	C₂³	—	8	2	no	—
443	C₂³	—	8	4	no	—
444	C₂³	—	8	4	no	—
445	C₂³	C₁₉×#95	1	2	yes	—
446	C₂³	C₁₉×#95	1	2	yes	—
447	C₂³	C₁₉×#95	1	2	yes	—
448	C₂³	C₁₉×#99	1	1	yes	characteristic
449	C₂³	C₁₉×#99	1	1	yes	characteristic
450	C₂³	C₁₉×#99	1	2	yes	—
451	C₂³	C₂×C₄²×C₁₉	1	1	yes	characteristic
452	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
453	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
454	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
455	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
456	D₄	—	4	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	1	no	—
463	D₄	—	4	1	no	—
464	D₄	—	4	1	no	—
465	D₄	—	4	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	8	4	no	—
482	C₂×C₄	—	8	8	no	—
483	C₂×C₄	—	8	4	no	—
484	C₂×C₄	—	8	4	no	—
485	C₂×C₄	C₁₉×#95	1	2	yes	—
486	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
487	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
488	C₈	—	4	4	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	1	no	—
516	C₂²	—	8	2	no	—
517	C₂²	—	8	2	no	—
518	C₂²	—	8	2	no	—
519	C₂²	—	8	2	no	—
520	C₂²	—	8	2	no	—
521	C₂²	—	8	2	no	—
522	C₂²	C₁₉×#342	1	2	yes	—
523	C₂²	C₁₉×#342	1	2	yes	—
524	C₂²	C₂×C₁₉×#95	1	1	yes	characteristic
525	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
526	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
527	C₄	—	2	1	no	—
528	C₄	—	2	1	no	—
529	C₄	—	2	2	no	—
530	C₄	—	8	2	no	—
531	C₄	—	8	4	no	—
532	C₄	—	8	2	no	—
533	C₂	—	2	1	no	—
534	C₂	—	2	1	no	—
535	C₂	—	2	2	no	—
536	C₂	—	2	2	no	—
537	C₂	—	4	1	no	—
538	C₂	—	4	1	no	—
539	C₂	—	4	2	no	—
540	C₂	—	4	1	no	—
541	C₂	—	4	1	no	—
542	C₂	—	4	2	no	—
543	C₂	C₂×C₁₉×#342	1	1	yes	characteristic
544	C₂	C₁₉×#2121	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#99
commutator	C₂³	C₂×C₄²×C₁₉
Frattini, cosocle	C₂²×D₄	C₂³×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁴×C₁₉ ◁ C₂³×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1390	C₂	semidirect
8. C₂²×C₂²⋊C₄×C₁₉	C₄	semidirect
9. C₂²×C₂²⋊C₄×C₁₉	C₄	semidirect
12. C₂×C₁₉×#100	C₄	semidirect
16. C₂×C₁₉×#99	C₄	semidirect
20. C₁₉×#386	C₄	semidirect
39. C₂³×C₄×C₁₉	C₂×C₄	semidirect
58. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
61. C₁₉×#100	C₂×C₄	semidirect
64. C₁₉×#99	C₂×C₄	semidirect
141. #12574	C₁₉	direct (N × H)
220. #1390	C₂×C₁₉	semidirect
268. C₂²×C₂²⋊C₄	C₄×C₁₉	semidirect
269. C₂²×C₂²⋊C₄	C₄×C₁₉	semidirect
272. C₂×#100	C₄×C₁₉	semidirect
276. C₂×#99	C₄×C₁₉	semidirect
280. #386	C₄×C₁₉	semidirect
311. C₂³×C₄	C₂×C₄×C₁₉	semidirect
330. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
333. #100	C₂×C₄×C₁₉	semidirect
336. #99	C₂×C₄×C₁₉	semidirect
339. C₁₉	#12574	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#100	2
C₂²×C₁₉×#99	2
C₁₉×#2308	2
C₁₉×#1390	2
#12574	19

Subgroups — C19×#12574 #18018533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12574 #18018533