Subgroups — C₁₉×#20708 #18026667

Order 4864.

1260 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3428	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#413	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#410	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1827	C₂	1	8	yes	maximal, complemented
5	C₁₉×#1733	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×H(3,ℤ/4)	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
9	C₁₉×#520	—	2	2	no	—
10	C₁₉×#520	—	2	2	no	—
11	C₁₉×#519	—	2	1	no	—
12	C₁₉×#518	—	2	1	no	—
13	C₁₉×#518	—	2	2	no	—
14	C₄×#41×C₁₉	C₄	1	4	yes	complemented
15	C₄×#41×C₁₉	C₂²	1	4	yes	—
16	C₂×C₁₉×#117	C₄	1	4	yes	complemented
17	C₂×C₁₉×#117	C₂²	1	2	yes	—
18	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₁₉×#413	—	2	2	no	—
21	C₁₉×#413	C₂²	1	4	yes	—
22	C₂×C₁₉×#101	—	2	1	no	—
23	C₂×C₁₉×#100	—	2	1	no	—
24	C₁₉×#410	—	2	2	no	—
25	C₁₉×#410	C₂²	1	4	yes	—
26	C₂×C₁₉×#99	—	2	2	no	—
27	C₁₉×#339	C₂²	1	8	yes	complemented
28	C₁₉×H(3,ℤ/4)	C₂²	1	8	yes	complemented
29	C₂×#41×C₁₉	—	2	2	no	—
30	C₂×#41×C₁₉	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	2	no	—
32	C₂×#41×C₁₉	—	2	2	no	—
33	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
34	C₂×#41×C₁₉	D₄	1	2	yes	—
35	C₂×#41×C₁₉	D₄	1	2	yes	—
36	C₂×#41×C₁₉	C₂³	1	2	yes	—
37	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
38	C₂²×D₄×C₁₉	D₄	1	2	yes	—
39	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂×M₁₆×C₁₉	—	2	2	no	—
43	C₂×M₁₆×C₁₉	—	2	2	no	—
44	C₂×M₁₆×C₁₉	—	2	2	no	—
45	C₂×M₁₆×C₁₉	—	2	2	no	—
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
48	C₂²×C₈×C₁₉	—	2	2	no	—
49	C₄×Q₈×C₁₉	—	2	4	no	—
50	C₄×Q₈×C₁₉	—	2	4	no	—
51	C₄×D₄×C₁₉	—	2	4	no	—
52	C₄×D₄×C₁₉	—	2	8	no	—
53	C₄×D₄×C₁₉	—	2	8	no	—
54	C₄×D₄×C₁₉	—	2	4	no	—
55	C₁₉×#117	—	2	4	no	—
56	C₁₉×#117	—	2	4	no	—
57	C₁₉×#117	—	2	1	no	—
58	C₁₉×#117	—	2	1	no	—
59	C₁₉×#117	—	2	1	no	—
60	C₁₉×#117	—	2	1	no	—
61	C₁₉×#117	—	2	2	no	—
62	C₁₉×#117	—	2	2	no	—
63	C₁₉×#117	—	2	2	no	—
64	C₁₉×#117	C₂×C₄	1	2	yes	—
65	C₁₉×#117	C₂×C₄	1	2	yes	—
66	C₁₉×#117	C₂×C₄	1	2	yes	—
67	C₁₉×#117	C₂×C₄	1	8	yes	complemented
68	C₁₉×#117	C₂³	1	4	yes	—
69	C₁₉×#117	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄²×C₁₉	—	2	2	no	—
79	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
80	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	complemented
81	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
82	C₁₉×#101	—	2	4	no	—
83	C₁₉×#100	—	2	4	no	—
84	C₁₉×#99	—	2	8	no	—
85	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
86	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
87	#41×C₁₉	—	2	4	no	—
88	#41×C₁₉	—	2	4	no	—
89	#41×C₁₉	—	2	4	no	—
90	#41×C₁₉	—	2	4	no	—
91	#41×C₁₉	—	2	4	no	—
92	#41×C₁₉	—	2	4	no	—
93	#41×C₁₉	—	2	4	no	—
94	#41×C₁₉	—	2	4	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
98	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
99	C₂×D₄×C₁₉	—	2	4	no	—
100	C₂×D₄×C₁₉	—	2	4	no	—
101	C₂×D₄×C₁₉	—	2	2	no	—
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
104	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
105	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
106	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
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	8	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
116	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
117	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	#41	1	2	yes	—
124	C₂²×C₄×C₁₉	#41	1	2	yes	—
125	C₂²×C₄×C₁₉	#41	1	2	yes	—
126	C₂²×C₄×C₁₉	#41	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
128	M₁₆×C₁₉	—	2	4	no	—
129	M₁₆×C₁₉	—	2	4	no	—
130	M₁₆×C₁₉	—	4	2	no	—
131	M₁₆×C₁₉	—	4	2	no	—
132	C₂×C₈×C₁₉	—	2	4	no	—
133	C₂×C₈×C₁₉	—	4	2	no	—
134	C₂×C₈×C₁₉	—	4	2	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	8	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	4	no	—
141	C₄⋊C₄×C₁₉	—	4	2	no	—
142	C₂²⋊C₄×C₁₉	—	2	2	no	—
143	C₂²⋊C₄×C₁₉	—	2	2	no	—
144	C₂²⋊C₄×C₁₉	—	2	2	no	—
145	C₂²⋊C₄×C₁₉	—	2	8	no	—
146	C₂²⋊C₄×C₁₉	—	2	2	no	—
147	C₂²⋊C₄×C₁₉	—	2	4	no	—
148	C₂²⋊C₄×C₁₉	—	4	2	no	—
149	C₄²×C₁₉	—	2	2	no	—
150	C₄²×C₁₉	—	2	8	no	—
151	C₄²×C₁₉	—	2	2	no	—
152	C₄²×C₁₉	—	2	4	no	—
153	C₄²×C₁₉	—	4	2	no	—
154	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
155	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
156	#20708	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	8	1	no	—
160	C₂³×C₁₉	—	8	2	no	—
161	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
162	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂³×C₁₉	#123	1	2	yes	—
165	C₂³×C₁₉	#123	1	2	yes	—
166	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₉	—	2	4	no	—
168	Q₈×C₁₉	—	2	4	no	—
169	D₄×C₁₉	—	2	8	no	—
170	D₄×C₁₉	—	2	8	no	—
171	D₄×C₁₉	—	2	4	no	—
172	D₄×C₁₉	—	2	4	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	2	4	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	2	4	no	—
181	C₂×C₄×C₁₉	—	4	4	no	—
182	C₂×C₄×C₁₉	—	8	2	no	—
183	C₂×C₄×C₁₉	—	8	2	no	—
184	C₂×C₄×C₁₉	—	8	8	no	—
185	C₂×C₄×C₁₉	—	8	4	no	—
186	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
187	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#117	1	2	yes	—
192	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#117	1	2	yes	—
195	C₂×C₄×C₁₉	#123	1	2	yes	—
196	C₂×C₄×C₁₉	#123	1	2	yes	—
197	C₂×C₄×C₁₉	#123	1	2	yes	—
198	C₂×C₄×C₁₉	#123	1	2	yes	—
199	C₂×C₄×C₁₉	#123	1	2	yes	—
200	C₂×C₄×C₁₉	#123	1	2	yes	—
201	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
204	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
205	C₈×C₁₉	—	4	4	no	—
206	#3428	C₂×C₁₉	1	1	yes	characteristic
207	C₂×#413	C₂×C₁₉	1	1	yes	characteristic
208	C₂×#410	C₂×C₁₉	1	1	yes	characteristic
209	#1827	C₂×C₁₉	1	8	yes	complemented
210	#1733	C₂×C₁₉	1	2	yes	complemented
211	C₂×H(3,ℤ/4)	C₂×C₁₉	1	2	yes	complemented
212	C₂²×C₁₉	—	2	4	no	—
213	C₂²×C₁₉	—	4	1	no	—
214	C₂²×C₁₉	—	4	2	no	—
215	C₂²×C₁₉	—	4	1	no	—
216	C₂²×C₁₉	—	4	1	no	—
217	C₂²×C₁₉	—	4	2	no	—
218	C₂²×C₁₉	—	4	4	no	—
219	C₂²×C₁₉	—	8	2	no	—
220	C₂²×C₁₉	—	8	2	no	—
221	C₂²×C₁₉	#381	1	1	yes	characteristic
222	C₂²×C₁₉	#381	1	1	yes	characteristic
223	C₂²×C₁₉	#381	1	2	yes	—
224	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
225	C₂²×C₁₉	C₂×#123	1	2	yes	—
226	C₄×C₁₉	—	2	4	no	—
227	C₄×C₁₉	—	4	4	no	—
228	C₄×C₁₉	—	4	4	no	—
229	C₄×C₁₉	—	8	4	no	—
230	C₄×C₁₉	#381	1	1	yes	characteristic
231	C₄×C₁₉	#381	1	1	yes	characteristic
232	C₄×C₁₉	#381	1	2	yes	—
233	C₄×C₁₉	C₂×#117	1	1	yes	characteristic
234	C₄×C₁₉	C₂×#117	1	1	yes	characteristic
235	C₄×C₁₉	C₂×#123	1	2	yes	—
236	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
237	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
238	#520	—	2	2	no	—
239	#520	—	2	2	no	—
240	#519	—	2	1	no	—
241	#518	—	2	1	no	—
242	#518	—	2	2	no	—
243	C₄×#41	C₄×C₁₉	1	4	yes	complemented
244	C₄×#41	C₂²×C₁₉	1	4	yes	—
245	C₂×#117	C₄×C₁₉	1	4	yes	complemented
246	C₂×#117	C₂²×C₁₉	1	2	yes	—
247	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
249	#413	—	2	2	no	—
250	#413	C₂²×C₁₉	1	4	yes	—
251	C₂×#101	—	2	1	no	—
252	C₂×#100	—	2	1	no	—
253	#410	—	2	2	no	—
254	#410	C₂²×C₁₉	1	4	yes	—
255	C₂×#99	—	2	2	no	—
256	#339	C₂²×C₁₉	1	8	yes	complemented
257	H(3,ℤ/4)	C₂²×C₁₉	1	8	yes	complemented
258	C₂×C₁₉	—	2	1	no	—
259	C₂×C₁₉	—	2	2	no	—
260	C₂×C₁₉	—	2	1	no	—
261	C₂×C₁₉	—	2	1	no	—
262	C₂×C₁₉	—	2	2	no	—
263	C₂×C₁₉	—	4	4	no	—
264	C₂×C₁₉	C₂×#381	1	1	yes	characteristic
265	C₂×#41	—	2	2	no	—
266	C₂×#41	—	2	2	no	—
267	C₂×#41	—	2	2	no	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
270	C₂×#41	D₄×C₁₉	1	2	yes	—
271	C₂×#41	D₄×C₁₉	1	2	yes	—
272	C₂×#41	C₂³×C₁₉	1	2	yes	—
273	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
274	C₂²×D₄	D₄×C₁₉	1	2	yes	—
275	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
276	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
277	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
284	C₂²×C₈	—	2	2	no	—
285	C₄×Q₈	—	2	4	no	—
286	C₄×Q₈	—	2	4	no	—
287	C₄×D₄	—	2	4	no	—
288	C₄×D₄	—	2	8	no	—
289	C₄×D₄	—	2	8	no	—
290	C₄×D₄	—	2	4	no	—
291	#117	—	2	4	no	—
292	#117	—	2	4	no	—
293	#117	—	2	1	no	—
294	#117	—	2	1	no	—
295	#117	—	2	1	no	—
296	#117	—	2	1	no	—
297	#117	—	2	2	no	—
298	#117	—	2	2	no	—
299	#117	—	2	2	no	—
300	#117	C₂×C₄×C₁₉	1	2	yes	—
301	#117	C₂×C₄×C₁₉	1	2	yes	—
302	#117	C₂×C₄×C₁₉	1	2	yes	—
303	#117	C₂×C₄×C₁₉	1	8	yes	complemented
304	#117	C₂³×C₁₉	1	4	yes	—
305	#117	C₂³×C₁₉	1	2	yes	—
306	C₂×C₄⋊C₄	—	2	4	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	4	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₄²	—	2	2	no	—
315	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
316	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	complemented
317	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
318	#101	—	2	4	no	—
319	#100	—	2	4	no	—
320	#99	—	2	8	no	—
321	C₁₉	#20708	1	1	yes	characteristic, direct product factor, Sylow
322	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
323	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
324	#41	—	2	4	no	—
325	#41	—	2	4	no	—
326	#41	—	2	4	no	—
327	#41	—	2	4	no	—
328	#41	—	2	4	no	—
329	#41	—	2	4	no	—
330	#41	—	2	4	no	—
331	#41	—	2	4	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
335	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
341	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
342	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
343	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	8	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
353	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
354	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
355	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
356	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
360	C₂²×C₄	#41×C₁₉	1	2	yes	—
361	C₂²×C₄	#41×C₁₉	1	2	yes	—
362	C₂²×C₄	#41×C₁₉	1	2	yes	—
363	C₂²×C₄	#41×C₁₉	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
365	M₁₆	—	2	4	no	—
366	M₁₆	—	2	4	no	—
367	M₁₆	—	4	2	no	—
368	M₁₆	—	4	2	no	—
369	C₂×C₈	—	2	4	no	—
370	C₂×C₈	—	4	2	no	—
371	C₂×C₈	—	4	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	—	4	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	8	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	4	no	—
390	C₄²	—	4	2	no	—
391	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
392	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	8	1	no	—
396	C₂³	—	8	2	no	—
397	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
398	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
399	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
400	C₂³	C₁₉×#123	1	2	yes	—
401	C₂³	C₁₉×#123	1	2	yes	—
402	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
403	Q₈	—	2	4	no	—
404	Q₈	—	2	4	no	—
405	D₄	—	2	8	no	—
406	D₄	—	2	8	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	—	8	2	no	—
420	C₂×C₄	—	8	8	no	—
421	C₂×C₄	—	8	4	no	—
422	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
423	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
424	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
425	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
426	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
427	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
428	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
429	C₂×C₄	C₁₉×#117	1	2	yes	—
430	C₂×C₄	C₁₉×#117	1	2	yes	—
431	C₂×C₄	C₁₉×#123	1	2	yes	—
432	C₂×C₄	C₁₉×#123	1	2	yes	—
433	C₂×C₄	C₁₉×#123	1	2	yes	—
434	C₂×C₄	C₁₉×#123	1	2	yes	—
435	C₂×C₄	C₁₉×#123	1	2	yes	—
436	C₂×C₄	C₁₉×#123	1	2	yes	—
437	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
438	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
439	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
440	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
441	C₈	—	4	4	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	8	2	no	—
451	C₂²	C₁₉×#381	1	1	yes	characteristic
452	C₂²	C₁₉×#381	1	1	yes	characteristic
453	C₂²	C₁₉×#381	1	2	yes	—
454	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
455	C₂²	C₂×C₁₉×#123	1	2	yes	—
456	C₄	—	2	4	no	—
457	C₄	—	4	4	no	—
458	C₄	—	4	4	no	—
459	C₄	—	8	4	no	—
460	C₄	C₁₉×#381	1	1	yes	characteristic
461	C₄	C₁₉×#381	1	1	yes	characteristic
462	C₄	C₁₉×#381	1	2	yes	—
463	C₄	C₂×C₁₉×#117	1	1	yes	characteristic
464	C₄	C₂×C₁₉×#117	1	1	yes	characteristic
465	C₄	C₂×C₁₉×#123	1	2	yes	—
466	C₂	—	2	1	no	—
467	C₂	—	2	2	no	—
468	C₂	—	2	1	no	—
469	C₂	—	2	1	no	—
470	C₂	—	2	2	no	—
471	C₂	—	4	4	no	—
472	C₂	C₂×C₁₉×#381	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₉	C₂×#117
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂×C₁₉	C₂×#381
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1827	C₂	semidirect
5. C₁₉×#1733	C₂	semidirect
6. C₂×C₁₉×H(3,ℤ/4)	C₂	semidirect
14. C₄×#41×C₁₉	C₄	semidirect
16. C₂×C₁₉×#117	C₄	semidirect
27. C₁₉×#339	C₂²	semidirect
28. C₁₉×H(3,ℤ/4)	C₂²	semidirect
67. C₁₉×#117	C₂×C₄	semidirect
80. C₂×C₄²×C₁₉	C₂×C₄	semidirect
156. #20708	C₁₉	direct (N × H)
209. #1827	C₂×C₁₉	semidirect
210. #1733	C₂×C₁₉	semidirect
211. C₂×H(3,ℤ/4)	C₂×C₁₉	semidirect
243. C₄×#41	C₄×C₁₉	semidirect
245. C₂×#117	C₄×C₁₉	semidirect
256. #339	C₂²×C₁₉	semidirect
257. H(3,ℤ/4)	C₂²×C₁₉	semidirect
303. #117	C₂×C₄×C₁₉	semidirect
316. C₂×C₄²	C₂×C₄×C₁₉	semidirect
321. C₁₉	#20708	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3428	2
C₂×C₁₉×#413	2
C₂×C₁₉×#410	2
C₁₉×#1827	2
C₁₉×#1733	2
C₂×C₁₉×H(3,ℤ/4)	2
#20708	19

Subgroups — C19×#20708 #18026667

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20708 #18026667