Subgroups — C₁₉×#20679 #18026638

Order 4864.

1330 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	C₂×C₁₉×#568	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#430	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2896	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#417	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1816	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1815	C₂	1	4	yes	maximal, complemented
8	C₁₉×#1742	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#568	—	2	4	no	—
12	C₁₉×#568	C₄	1	8	yes	complemented
13	C₂×C₁₉×#131	—	2	2	no	—
14	C₂×C₁₉×#131	C₂²	1	4	yes	—
15	C₂²×M₁₆×C₁₉	—	2	2	no	—
16	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#430	—	2	4	no	—
23	C₂×C₁₉×#108	C₂²	1	4	yes	complemented
24	C₁₉×#428	—	2	2	no	—
25	C₁₉×#428	—	2	2	no	—
26	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
27	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
28	C₁₉×#419	—	2	1	no	—
29	C₁₉×#418	—	2	1	no	—
30	C₁₉×#417	—	2	2	no	—
31	C₁₉×#417	C₂²	1	2	yes	—
32	C₁₉×#417	C₂²	1	4	yes	—
33	C₁₉×#417	C₂²	1	2	yes	—
34	C₁₉×#416	—	2	2	no	—
35	C₂×C₁₉×#103	—	2	1	no	—
36	C₂×C₁₉×#102	—	2	1	no	—
37	C₁₉×#343	C₂²	1	4	yes	complemented
38	C₁₉×#343	C₂²	1	2	yes	complemented
39	C₁₉×#343	C₂²	1	2	yes	complemented
40	C₂×#41×C₁₉	—	2	1	no	—
41	C₂×#41×C₁₉	—	2	2	no	—
42	C₂×#41×C₁₉	—	2	1	no	—
43	C₂×#41×C₁₉	—	2	2	no	—
44	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
45	C₂×#41×C₁₉	D₄	1	2	yes	—
46	C₂×#41×C₁₉	Q₈	1	4	yes	—
47	C₂×#41×C₁₉	C₂³	1	2	yes	—
48	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	—	2	1	no	—
53	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₁₉×#131	—	2	16	no	—
55	C₁₉×#131	—	2	8	no	—
56	C₁₉×#131	C₂×C₄	1	16	yes	complemented
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	—	2	2	no	—
59	C₂×M₁₆×C₁₉	—	2	16	no	—
60	C₂×M₁₆×C₁₉	—	2	1	no	—
61	C₂×M₁₆×C₁₉	—	2	1	no	—
62	C₂×M₁₆×C₁₉	—	2	4	no	—
63	C₂×M₁₆×C₁₉	—	2	2	no	—
64	C₂×M₁₆×C₁₉	—	2	2	no	—
65	C₂×M₁₆×C₁₉	—	2	2	no	—
66	C₂×M₁₆×C₁₉	—	2	2	no	—
67	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
68	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
69	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
70	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
71	C₂×M₁₆×C₁₉	D₄	1	4	yes	—
72	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
73	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
74	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
75	C₂²×C₈×C₁₉	—	2	1	no	—
76	C₂²×C₈×C₁₉	—	2	4	no	—
77	C₂²×C₈×C₁₉	—	2	1	no	—
78	C₂²×C₈×C₁₉	—	2	1	no	—
79	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
80	C₁₉×#117	—	2	1	no	—
81	C₁₉×#117	—	2	1	no	—
82	C₁₉×#117	—	2	1	no	—
83	C₁₉×#117	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄²×C₁₉	—	2	1	no	—
94	C₁₉×#108	—	2	8	no	—
95	C₁₉×#107	—	2	4	no	—
96	C₁₉×#106	—	2	4	no	—
97	C₁₉×#103	—	2	4	no	—
98	C₁₉×#103	—	2	2	no	—
99	C₁₉×#103	—	2	2	no	—
100	C₁₉×#102	—	2	4	no	—
101	C₁₉×#102	—	2	2	no	—
102	C₁₉×#102	—	2	2	no	—
103	C₂⁴×C₁₉	—	2	1	no	—
104	C₂⁴×C₁₉	#41	1	1	yes	characteristic
105	#41×C₁₉	—	2	4	no	—
106	#41×C₁₉	—	2	4	no	—
107	#41×C₁₉	—	2	4	no	—
108	#41×C₁₉	—	2	4	no	—
109	#41×C₁₉	—	2	4	no	—
110	#41×C₁₉	—	2	2	no	—
111	#41×C₁₉	—	2	2	no	—
112	#41×C₁₉	C₄⋊C₄	1	8	yes	—
113	#41×C₁₉	C₂²×C₄	1	4	yes	—
114	#41×C₁₉	C₂×Q₈	1	4	yes	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	—	2	2	no	—
117	C₂×Q₈×C₁₉	C₄⋊C₄	1	4	yes	—
118	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₁₉	—	2	4	no	—
120	C₂×D₄×C₁₉	—	2	2	no	—
121	C₂×D₄×C₁₉	—	2	4	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
126	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	4	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	4	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	4	1	no	—
136	C₂²×C₄×C₁₉	—	4	1	no	—
137	C₂²×C₄×C₁₉	—	8	2	no	—
138	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
145	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	#41	1	2	yes	—
147	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
148	M₁₆×C₁₉	—	2	4	no	—
149	M₁₆×C₁₉	—	2	2	no	—
150	M₁₆×C₁₉	—	2	16	no	—
151	M₁₆×C₁₉	—	2	2	no	—
152	M₁₆×C₁₉	—	2	2	no	—
153	M₁₆×C₁₉	—	2	2	no	—
154	M₁₆×C₁₉	—	2	2	no	—
155	M₁₆×C₁₉	—	4	2	no	—
156	M₁₆×C₁₉	—	4	2	no	—
157	M₁₆×C₁₉	C₂²⋊C₄	1	8	yes	—
158	M₁₆×C₁₉	C₂²⋊C₄	1	8	yes	—
159	M₁₆×C₁₉	C₂²×C₄	1	4	yes	—
160	C₂×C₈×C₁₉	—	2	4	no	—
161	C₂×C₈×C₁₉	—	2	2	no	—
162	C₂×C₈×C₁₉	—	2	16	no	—
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	4	2	no	—
166	C₂×C₈×C₁₉	—	4	2	no	—
167	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
168	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
169	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	4	1	no	—
177	C₄⋊C₄×C₁₉	—	4	1	no	—
178	C₂²⋊C₄×C₁₉	—	4	1	no	—
179	C₂²⋊C₄×C₁₉	—	4	1	no	—
180	C₄²×C₁₉	—	4	1	no	—
181	C₄²×C₁₉	—	4	1	no	—
182	#20679	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂³×C₁₉	—	2	2	no	—
184	C₂³×C₁₉	—	2	4	no	—
185	C₂³×C₁₉	—	4	1	no	—
186	C₂³×C₁₉	—	4	1	no	—
187	C₂³×C₁₉	—	8	1	no	—
188	C₂³×C₁₉	—	8	1	no	—
189	C₂³×C₁₉	#117	1	2	yes	—
190	C₂³×C₁₉	#121	1	1	yes	characteristic
191	C₂³×C₁₉	#121	1	1	yes	characteristic
192	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
193	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
194	Q₈×C₁₉	—	2	2	no	—
195	Q₈×C₁₉	—	2	4	no	—
196	Q₈×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
197	D₄×C₁₉	—	2	4	no	—
198	D₄×C₁₉	—	2	4	no	—
199	D₄×C₁₉	—	2	8	no	—
200	D₄×C₁₉	—	2	2	no	—
201	D₄×C₁₉	—	2	4	no	—
202	D₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	2	4	no	—
207	C₂×C₄×C₁₉	—	2	8	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	8	2	no	—
212	C₂×C₄×C₁₉	—	8	2	no	—
213	C₂×C₄×C₁₉	—	8	1	no	—
214	C₂×C₄×C₁₉	—	8	1	no	—
215	C₂×C₄×C₁₉	—	8	2	no	—
216	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
218	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
219	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
220	C₂×C₄×C₁₉	#117	1	2	yes	—
221	C₂×C₄×C₁₉	#121	1	2	yes	—
222	C₂×C₄×C₁₉	#121	1	2	yes	—
223	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
224	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
226	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
227	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
228	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
234	C₈×C₁₉	—	2	4	no	—
235	C₈×C₁₉	—	4	2	no	—
236	C₈×C₁₉	—	4	2	no	—
237	C₈×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
238	C₂×#568	C₂×C₁₉	1	1	yes	characteristic
239	C₂×#430	C₂×C₁₉	1	1	yes	characteristic, complemented
240	C₂×#428	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#2896	C₂×C₁₉	1	1	yes	characteristic
242	C₂×#417	C₂×C₁₉	1	1	yes	characteristic
243	#1816	C₂×C₁₉	1	4	yes	complemented
244	#1815	C₂×C₁₉	1	4	yes	complemented
245	#1742	C₂×C₁₉	1	1	yes	characteristic, complemented
246	C₂×#343	C₂×C₁₉	1	1	yes	characteristic, complemented
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	2	1	no	—
249	C₂²×C₁₉	—	2	1	no	—
250	C₂²×C₁₉	—	2	1	no	—
251	C₂²×C₁₉	—	2	1	no	—
252	C₂²×C₁₉	—	2	1	no	—
253	C₂²×C₁₉	—	2	4	no	—
254	C₂²×C₁₉	—	4	2	no	—
255	C₂²×C₁₉	—	4	2	no	—
256	C₂²×C₁₉	—	4	2	no	—
257	C₂²×C₁₉	—	4	2	no	—
258	C₂²×C₁₉	—	8	4	no	—
259	C₂²×C₁₉	#380	1	2	yes	—
260	C₂²×C₁₉	#380	1	2	yes	—
261	C₂²×C₁₉	C₂×#117	1	1	yes	characteristic
262	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
263	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
264	C₄×C₁₉	—	2	4	no	—
265	C₄×C₁₉	—	8	1	no	—
266	C₄×C₁₉	—	8	2	no	—
267	C₄×C₁₉	—	8	1	no	—
268	C₄×C₁₉	#380	1	2	yes	—
269	C₄×C₁₉	#380	1	2	yes	—
270	C₄×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
271	C₄×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
272	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
273	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
274	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
275	#568	—	2	4	no	—
276	#568	C₄×C₁₉	1	8	yes	complemented
277	C₂×#131	—	2	2	no	—
278	C₂×#131	C₂²×C₁₉	1	4	yes	—
279	C₂²×M₁₆	—	2	2	no	—
280	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
281	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
282	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
283	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
284	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
285	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
286	#430	—	2	4	no	—
287	C₂×#108	C₂²×C₁₉	1	4	yes	complemented
288	#428	—	2	2	no	—
289	#428	—	2	2	no	—
290	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
291	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
292	#419	—	2	1	no	—
293	#418	—	2	1	no	—
294	#417	—	2	2	no	—
295	#417	C₂²×C₁₉	1	2	yes	—
296	#417	C₂²×C₁₉	1	4	yes	—
297	#417	C₂²×C₁₉	1	2	yes	—
298	#416	—	2	2	no	—
299	C₂×#103	—	2	1	no	—
300	C₂×#102	—	2	1	no	—
301	#343	C₂²×C₁₉	1	2	yes	complemented
302	#343	C₂²×C₁₉	1	4	yes	complemented
303	#343	C₂²×C₁₉	1	2	yes	complemented
304	C₂×C₁₉	—	2	2	no	—
305	C₂×C₁₉	—	2	1	no	—
306	C₂×C₁₉	—	2	1	no	—
307	C₂×C₁₉	—	2	2	no	—
308	C₂×C₁₉	—	4	4	no	—
309	C₂×C₁₉	C₂×#380	1	1	yes	characteristic
310	C₂×C₁₉	#3068	1	1	yes	characteristic
311	C₂×C₁₉	#3069	1	1	yes	characteristic
312	C₂×#41	—	2	1	no	—
313	C₂×#41	—	2	2	no	—
314	C₂×#41	—	2	1	no	—
315	C₂×#41	—	2	2	no	—
316	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
317	C₂×#41	D₄×C₁₉	1	2	yes	—
318	C₂×#41	Q₈×C₁₉	1	4	yes	—
319	C₂×#41	C₂³×C₁₉	1	2	yes	—
320	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
321	C₂²×D₄	—	2	1	no	—
322	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
323	C₂³×C₄	—	2	1	no	—
324	C₂³×C₄	—	2	1	no	—
325	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
326	#131	—	2	16	no	—
327	#131	—	2	8	no	—
328	#131	C₂×C₄×C₁₉	1	16	yes	complemented
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	2	2	no	—
331	C₂×M₁₆	—	2	16	no	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	2	4	no	—
335	C₂×M₁₆	—	2	2	no	—
336	C₂×M₁₆	—	2	2	no	—
337	C₂×M₁₆	—	2	2	no	—
338	C₂×M₁₆	—	2	2	no	—
339	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	—
340	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	—
341	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
342	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
343	C₂×M₁₆	D₄×C₁₉	1	4	yes	—
344	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
345	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
346	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
347	C₂²×C₈	—	2	1	no	—
348	C₂²×C₈	—	2	4	no	—
349	C₂²×C₈	—	2	1	no	—
350	C₂²×C₈	—	2	1	no	—
351	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
352	#117	—	2	1	no	—
353	#117	—	2	1	no	—
354	#117	—	2	1	no	—
355	#117	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₄²	—	2	1	no	—
366	#108	—	2	8	no	—
367	#107	—	2	4	no	—
368	#106	—	2	4	no	—
369	#103	—	2	4	no	—
370	#103	—	2	2	no	—
371	#103	—	2	2	no	—
372	#102	—	2	4	no	—
373	#102	—	2	2	no	—
374	#102	—	2	2	no	—
375	C₁₉	#20679	1	1	yes	characteristic, direct product factor, Sylow
376	C₂⁴	—	2	1	no	—
377	C₂⁴	#41×C₁₉	1	1	yes	characteristic
378	#41	—	2	4	no	—
379	#41	—	2	4	no	—
380	#41	—	2	4	no	—
381	#41	—	2	4	no	—
382	#41	—	2	4	no	—
383	#41	—	2	2	no	—
384	#41	—	2	2	no	—
385	#41	C₄⋊C₄×C₁₉	1	8	yes	—
386	#41	C₂²×C₄×C₁₉	1	4	yes	—
387	#41	C₂×Q₈×C₁₉	1	4	yes	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	C₄⋊C₄×C₁₉	1	4	yes	—
391	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	C₄⋊C₄×C₁₉	1	4	yes	—
399	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	4	1	no	—
409	C₂²×C₄	—	4	1	no	—
410	C₂²×C₄	—	8	2	no	—
411	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
412	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
413	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
417	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
418	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
419	C₂²×C₄	#41×C₁₉	1	2	yes	—
420	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
421	M₁₆	—	2	4	no	—
422	M₁₆	—	2	2	no	—
423	M₁₆	—	2	16	no	—
424	M₁₆	—	2	2	no	—
425	M₁₆	—	2	2	no	—
426	M₁₆	—	2	2	no	—
427	M₁₆	—	2	2	no	—
428	M₁₆	—	4	2	no	—
429	M₁₆	—	4	2	no	—
430	M₁₆	C₂²⋊C₄×C₁₉	1	8	yes	—
431	M₁₆	C₂²⋊C₄×C₁₉	1	8	yes	—
432	M₁₆	C₂²×C₄×C₁₉	1	4	yes	—
433	C₂×C₈	—	2	4	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	16	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	4	2	no	—
439	C₂×C₈	—	4	2	no	—
440	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
441	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
442	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	4	1	no	—
450	C₄⋊C₄	—	4	1	no	—
451	C₂²⋊C₄	—	4	1	no	—
452	C₂²⋊C₄	—	4	1	no	—
453	C₄²	—	4	1	no	—
454	C₄²	—	4	1	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	8	1	no	—
460	C₂³	—	8	1	no	—
461	C₂³	C₁₉×#117	1	2	yes	—
462	C₂³	C₁₉×#121	1	1	yes	characteristic
463	C₂³	C₁₉×#121	1	1	yes	characteristic
464	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
465	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
466	Q₈	—	2	4	no	—
467	Q₈	—	2	2	no	—
468	Q₈	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
469	D₄	—	2	8	no	—
470	D₄	—	2	4	no	—
471	D₄	—	2	4	no	—
472	D₄	—	2	4	no	—
473	D₄	—	2	2	no	—
474	D₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	8	2	no	—
484	C₂×C₄	—	8	2	no	—
485	C₂×C₄	—	8	2	no	—
486	C₂×C₄	—	8	1	no	—
487	C₂×C₄	—	8	1	no	—
488	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
489	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
490	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
491	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
492	C₂×C₄	C₁₉×#117	1	2	yes	—
493	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
494	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
495	C₂×C₄	C₁₉×#121	1	2	yes	—
496	C₂×C₄	C₁₉×#121	1	2	yes	—
497	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
498	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
499	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
500	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
502	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
504	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
505	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
506	C₈	—	2	4	no	—
507	C₈	—	4	2	no	—
508	C₈	—	4	2	no	—
509	C₈	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	8	4	no	—
522	C₂²	C₁₉×#380	1	2	yes	—
523	C₂²	C₁₉×#380	1	2	yes	—
524	C₂²	C₂×C₁₉×#117	1	1	yes	characteristic
525	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
526	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
527	C₄	—	2	4	no	—
528	C₄	—	8	2	no	—
529	C₄	—	8	1	no	—
530	C₄	—	8	1	no	—
531	C₄	C₁₉×#380	1	2	yes	—
532	C₄	C₁₉×#380	1	2	yes	—
533	C₄	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
534	C₄	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
535	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
536	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
537	C₂	—	2	2	no	—
538	C₂	—	2	2	no	—
539	C₂	—	2	1	no	—
540	C₂	—	2	1	no	—
541	C₂	—	4	4	no	—
542	C₂	C₂×C₁₉×#380	1	1	yes	characteristic
543	C₂	C₁₉×#3068	1	1	yes	characteristic
544	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#430	C₂	semidirect
3. C₂×C₁₉×#428	C₂	semidirect
6. C₁₉×#1816	C₂	semidirect
7. C₁₉×#1815	C₂	semidirect
8. C₁₉×#1742	C₂	semidirect
9. C₂×C₁₉×#343	C₂	semidirect
12. C₁₉×#568	C₄	semidirect
23. C₂×C₁₉×#108	C₂²	semidirect
26. C₂×C₁₉×#107	C₂²	semidirect
27. C₂×C₁₉×#106	C₂²	semidirect
37. C₁₉×#343	C₂²	semidirect
38. C₁₉×#343	C₂²	semidirect
39. C₁₉×#343	C₂²	semidirect
56. C₁₉×#131	C₂×C₄	semidirect
182. #20679	C₁₉	direct (N × H)
239. C₂×#430	C₂×C₁₉	semidirect
240. C₂×#428	C₂×C₁₉	semidirect
243. #1816	C₂×C₁₉	semidirect
244. #1815	C₂×C₁₉	semidirect
245. #1742	C₂×C₁₉	semidirect
246. C₂×#343	C₂×C₁₉	semidirect
276. #568	C₄×C₁₉	semidirect
287. C₂×#108	C₂²×C₁₉	semidirect
290. C₂×#107	C₂²×C₁₉	semidirect
291. C₂×#106	C₂²×C₁₉	semidirect
301. #343	C₂²×C₁₉	semidirect
302. #343	C₂²×C₁₉	semidirect
303. #343	C₂²×C₁₉	semidirect
328. #131	C₂×C₄×C₁₉	semidirect
375. C₁₉	#20679	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×#568	2
C₂×C₁₉×#430	2
C₂×C₁₉×#428	2
C₁₉×#2896	2
C₂×C₁₉×#417	2
C₁₉×#1816	2
C₁₉×#1815	2
C₁₉×#1742	2
C₂×C₁₉×#343	2
#20679	19

Subgroups — C19×#20679 #18026638

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20679 #18026638