Subgroups — C₂×C₁₉×#1815 #18026635

Order 4864.

1374 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#131	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#108	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#417	C₂	1	2	yes	maximal
5	C₁₉×#1815	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#343	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₁₉×#131	—	2	4	no	—
9	C₂×C₁₉×#131	—	2	2	no	—
10	C₂×C₁₉×#131	C₄	1	8	yes	complemented
11	C₂×C₁₉×#131	C₂²	1	4	yes	—
12	C₂²×M₁₆×C₁₉	—	2	1	no	—
13	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₉	—	2	1	no	—
16	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂×C₁₉×#108	—	2	4	no	—
19	C₂×C₁₉×#108	C₂²	1	4	yes	complemented
20	C₂×C₁₉×#106	—	2	1	no	—
21	C₂×C₁₉×#106	—	2	1	no	—
22	C₂×C₁₉×#106	—	2	2	no	—
23	C₂×C₁₉×#106	C₂²	1	4	yes	complemented
24	C₁₉×#417	—	2	4	no	—
25	C₁₉×#417	C₂²	1	8	yes	—
26	C₂×C₁₉×#103	—	2	2	no	—
27	C₂×C₁₉×#102	—	2	2	no	—
28	C₁₉×#343	C₂²	1	8	yes	complemented
29	C₂×#41×C₁₉	—	2	2	no	—
30	C₂×#41×C₁₉	—	2	1	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂×#41×C₁₉	—	2	2	no	—
33	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
34	C₂×#41×C₁₉	D₄	1	2	yes	—
35	C₂×#41×C₁₉	Q₈	1	4	yes	—
36	C₂×#41×C₁₉	C₂³	1	2	yes	—
37	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
38	C₂²×D₄×C₁₉	—	2	1	no	—
39	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	—	2	1	no	—
41	C₂³×C₄×C₁₉	—	2	2	no	—
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₁₉×#131	—	2	16	no	—
44	C₁₉×#131	—	2	8	no	—
45	C₁₉×#131	C₂×C₄	1	16	yes	complemented
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	—	2	1	no	—
48	C₂×M₁₆×C₁₉	—	2	2	no	—
49	C₂×M₁₆×C₁₉	—	2	8	no	—
50	C₂×M₁₆×C₁₉	—	2	4	no	—
51	C₂×M₁₆×C₁₉	—	2	4	no	—
52	C₂×M₁₆×C₁₉	—	2	4	no	—
53	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
54	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
55	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₉	—	2	1	no	—
57	C₂²×C₈×C₁₉	—	2	8	no	—
58	C₂²×C₈×C₁₉	—	2	4	no	—
59	C₂²×C₈×C₁₉	—	2	2	no	—
60	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
61	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	D₄	1	2	yes	—
64	C₂²×C₈×C₁₉	D₄	1	4	yes	—
65	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
72	C₁₉×#108	—	2	8	no	—
73	C₁₉×#106	—	2	4	no	—
74	C₁₉×#106	—	2	4	no	—
75	C₁₉×#103	—	2	8	no	—
76	C₁₉×#102	—	2	8	no	—
77	C₂⁴×C₁₉	—	2	1	no	—
78	C₂⁴×C₁₉	#41	1	1	yes	characteristic
79	#41×C₁₉	—	2	4	no	—
80	#41×C₁₉	—	2	4	no	—
81	#41×C₁₉	—	2	4	no	—
82	#41×C₁₉	—	2	4	no	—
83	#41×C₁₉	—	2	4	no	—
84	#41×C₁₉	—	2	2	no	—
85	#41×C₁₉	—	2	2	no	—
86	#41×C₁₉	C₄⋊C₄	1	8	yes	—
87	#41×C₁₉	C₂²×C₄	1	4	yes	—
88	#41×C₁₉	C₂×Q₈	1	4	yes	—
89	C₂×Q₈×C₁₉	—	2	1	no	—
90	C₂×Q₈×C₁₉	—	2	2	no	—
91	C₂×Q₈×C₁₉	C₄⋊C₄	1	4	yes	—
92	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
93	C₂×D₄×C₁₉	—	2	4	no	—
94	C₂×D₄×C₁₉	—	2	2	no	—
95	C₂×D₄×C₁₉	—	2	4	no	—
96	C₂×D₄×C₁₉	—	2	2	no	—
97	C₂×D₄×C₁₉	—	2	2	no	—
98	C₂×D₄×C₁₉	—	2	1	no	—
99	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
100	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	4	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	4	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	4	no	—
107	C₂²×C₄×C₁₉	—	4	2	no	—
108	C₂²×C₄×C₁₉	—	4	2	no	—
109	C₂²×C₄×C₁₉	—	8	4	no	—
110	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
117	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	#41	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
120	M₁₆×C₁₉	—	2	4	no	—
121	M₁₆×C₁₉	—	2	2	no	—
122	M₁₆×C₁₉	—	2	16	no	—
123	M₁₆×C₁₉	—	2	4	no	—
124	M₁₆×C₁₉	—	2	4	no	—
125	M₁₆×C₁₉	—	4	4	no	—
126	M₁₆×C₁₉	C₂²×C₄	1	4	yes	—
127	C₂×C₈×C₁₉	—	2	4	no	—
128	C₂×C₈×C₁₉	—	2	2	no	—
129	C₂×C₈×C₁₉	—	2	16	no	—
130	C₂×C₈×C₁₉	—	2	4	no	—
131	C₂×C₈×C₁₉	—	4	4	no	—
132	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
133	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
134	C₂×C₈×C₁₉	C₂²⋊C₄	1	8	yes	—
135	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
136	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
139	C₄⋊C₄×C₁₉	—	2	4	no	—
140	C₄⋊C₄×C₁₉	—	2	4	no	—
141	C₄⋊C₄×C₁₉	—	4	2	no	—
142	C₄⋊C₄×C₁₉	—	4	2	no	—
143	C₂×#1815	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
144	C₂³×C₁₉	—	2	4	no	—
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	—	2	4	no	—
147	C₂³×C₁₉	—	4	4	no	—
148	C₂³×C₁₉	#117	1	2	yes	—
149	C₂³×C₁₉	#121	1	1	yes	characteristic
150	C₂³×C₁₉	#121	1	1	yes	characteristic
151	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
152	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
153	Q₈×C₁₉	—	2	2	no	—
154	Q₈×C₁₉	—	2	4	no	—
155	Q₈×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
156	D₄×C₁₉	—	2	4	no	—
157	D₄×C₁₉	—	2	4	no	—
158	D₄×C₁₉	—	2	8	no	—
159	D₄×C₁₉	—	2	2	no	—
160	D₄×C₁₉	—	2	4	no	—
161	D₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	8	no	—
167	C₂×C₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	8	4	no	—
169	C₂×C₄×C₁₉	—	8	4	no	—
170	C₂×C₄×C₁₉	—	8	4	no	—
171	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
175	C₂×C₄×C₁₉	#117	1	2	yes	—
176	C₂×C₄×C₁₉	#121	1	2	yes	—
177	C₂×C₄×C₁₉	#121	1	2	yes	—
178	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
181	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
182	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
183	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
189	C₈×C₁₉	—	2	4	no	—
190	C₈×C₁₉	—	4	4	no	—
191	C₈×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
192	C₈×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
193	C₂²×#131	C₂×C₁₉	1	1	yes	characteristic
194	C₂²×#108	C₂×C₁₉	1	1	yes	characteristic, complemented
195	C₂²×#106	C₂×C₁₉	1	1	yes	characteristic, complemented
196	C₂×#417	C₂×C₁₉	1	2	yes	—
197	#1815	C₂×C₁₉	1	8	yes	direct product factor
198	C₂×#343	C₂×C₁₉	1	2	yes	complemented
199	C₂²×C₁₉	—	2	4	no	—
200	C₂²×C₁₉	—	2	4	no	—
201	C₂²×C₁₉	—	2	2	no	—
202	C₂²×C₁₉	—	2	2	no	—
203	C₂²×C₁₉	—	2	4	no	—
204	C₂²×C₁₉	—	4	8	no	—
205	C₂²×C₁₉	—	4	4	no	—
206	C₂²×C₁₉	#380	1	2	yes	—
207	C₂²×C₁₉	#380	1	2	yes	—
208	C₂²×C₁₉	#471	1	4	yes	—
209	C₂²×C₁₉	C₂×#117	1	1	yes	characteristic
210	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
211	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
212	C₄×C₁₉	—	2	4	no	—
213	C₄×C₁₉	—	8	4	no	—
214	C₄×C₁₉	#380	1	2	yes	—
215	C₄×C₁₉	#380	1	2	yes	—
216	C₄×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
217	C₄×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
218	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
219	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
220	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×#131	—	2	4	no	—
222	C₂×#131	—	2	2	no	—
223	C₂×#131	C₄×C₁₉	1	8	yes	complemented
224	C₂×#131	C₂²×C₁₉	1	4	yes	—
225	C₂²×M₁₆	—	2	1	no	—
226	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
227	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
228	C₂³×C₈	—	2	1	no	—
229	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
230	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
231	C₂×#108	—	2	4	no	—
232	C₂×#108	C₂²×C₁₉	1	4	yes	complemented
233	C₂×#106	—	2	1	no	—
234	C₂×#106	—	2	1	no	—
235	C₂×#106	—	2	2	no	—
236	C₂×#106	C₂²×C₁₉	1	4	yes	complemented
237	#417	—	2	4	no	—
238	#417	C₂²×C₁₉	1	8	yes	—
239	C₂×#103	—	2	2	no	—
240	C₂×#102	—	2	2	no	—
241	#343	C₂²×C₁₉	1	8	yes	complemented
242	C₂×C₁₉	—	2	1	no	—
243	C₂×C₁₉	—	2	1	no	—
244	C₂×C₁₉	—	2	2	no	—
245	C₂×C₁₉	—	4	4	no	—
246	C₂×C₁₉	#1815	1	4	yes	direct product factor
247	C₂×C₁₉	C₂×#380	1	1	yes	characteristic
248	C₂×C₁₉	C₂×#471	1	2	yes	—
249	C₂×#41	—	2	2	no	—
250	C₂×#41	—	2	1	no	—
251	C₂×#41	—	2	1	no	—
252	C₂×#41	—	2	2	no	—
253	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
254	C₂×#41	D₄×C₁₉	1	2	yes	—
255	C₂×#41	Q₈×C₁₉	1	4	yes	—
256	C₂×#41	C₂³×C₁₉	1	2	yes	—
257	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
260	C₂³×C₄	—	2	1	no	—
261	C₂³×C₄	—	2	2	no	—
262	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
263	#131	—	2	16	no	—
264	#131	—	2	8	no	—
265	#131	C₂×C₄×C₁₉	1	16	yes	complemented
266	C₂×M₁₆	—	2	2	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	8	no	—
270	C₂×M₁₆	—	2	4	no	—
271	C₂×M₁₆	—	2	4	no	—
272	C₂×M₁₆	—	2	4	no	—
273	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	—
274	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
275	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	2	8	no	—
278	C₂²×C₈	—	2	4	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	C₂×C₄×C₁₉	1	4	yes	—
281	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
282	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
283	C₂²×C₈	D₄×C₁₉	1	2	yes	—
284	C₂²×C₈	D₄×C₁₉	1	4	yes	—
285	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
292	#108	—	2	8	no	—
293	#106	—	2	4	no	—
294	#106	—	2	4	no	—
295	#103	—	2	8	no	—
296	#102	—	2	8	no	—
297	C₁₉	C₂×#1815	1	1	yes	characteristic, direct product factor, Sylow
298	C₂⁴	—	2	1	no	—
299	C₂⁴	#41×C₁₉	1	1	yes	characteristic
300	#41	—	2	4	no	—
301	#41	—	2	4	no	—
302	#41	—	2	4	no	—
303	#41	—	2	4	no	—
304	#41	—	2	4	no	—
305	#41	—	2	2	no	—
306	#41	—	2	2	no	—
307	#41	C₄⋊C₄×C₁₉	1	8	yes	—
308	#41	C₂²×C₄×C₁₉	1	4	yes	—
309	#41	C₂×Q₈×C₁₉	1	4	yes	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	C₄⋊C₄×C₁₉	1	4	yes	—
313	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	C₄⋊C₄×C₁₉	1	4	yes	—
321	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	8	4	no	—
331	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
338	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
339	C₂²×C₄	#41×C₁₉	1	2	yes	—
340	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
341	M₁₆	—	2	4	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	2	16	no	—
344	M₁₆	—	2	4	no	—
345	M₁₆	—	2	4	no	—
346	M₁₆	—	4	4	no	—
347	M₁₆	C₂²×C₄×C₁₉	1	4	yes	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	16	no	—
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	4	4	no	—
353	C₂×C₈	C₂²⋊C₄×C₁₉	1	4	yes	—
354	C₂×C₈	C₂²⋊C₄×C₁₉	1	4	yes	—
355	C₂×C₈	C₂²⋊C₄×C₁₉	1	8	yes	—
356	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
357	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
358	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
359	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	4	4	no	—
368	C₂³	C₁₉×#117	1	2	yes	—
369	C₂³	C₁₉×#121	1	1	yes	characteristic
370	C₂³	C₁₉×#121	1	1	yes	characteristic
371	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
372	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
373	Q₈	—	2	4	no	—
374	Q₈	—	2	2	no	—
375	Q₈	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
376	D₄	—	2	8	no	—
377	D₄	—	2	4	no	—
378	D₄	—	2	4	no	—
379	D₄	—	2	4	no	—
380	D₄	—	2	2	no	—
381	D₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	8	4	no	—
389	C₂×C₄	—	8	4	no	—
390	C₂×C₄	—	8	4	no	—
391	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
392	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
393	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
394	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
395	C₂×C₄	C₁₉×#117	1	2	yes	—
396	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
397	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
398	C₂×C₄	C₁₉×#121	1	2	yes	—
399	C₂×C₄	C₁₉×#121	1	2	yes	—
400	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
401	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
402	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
403	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
404	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
405	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
407	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
408	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
409	C₈	—	2	4	no	—
410	C₈	—	4	4	no	—
411	C₈	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
412	C₈	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	4	8	no	—
420	C₂²	C₁₉×#380	1	2	yes	—
421	C₂²	C₁₉×#380	1	2	yes	—
422	C₂²	C₁₉×#471	1	4	yes	—
423	C₂²	C₂×C₁₉×#117	1	1	yes	characteristic
424	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
425	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
426	C₄	—	2	4	no	—
427	C₄	—	8	4	no	—
428	C₄	C₁₉×#380	1	2	yes	—
429	C₄	C₁₉×#380	1	2	yes	—
430	C₄	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
431	C₄	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
432	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
433	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
434	C₂	—	2	2	no	—
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	4	4	no	—
438	C₂	C₁₉×#1815	1	4	yes	direct product factor
439	C₂	C₂×C₁₉×#380	1	1	yes	characteristic
440	C₂	C₂×C₁₉×#471	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	#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 ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#108	C₂	semidirect
3. C₂²×C₁₉×#106	C₂	semidirect
5. C₁₉×#1815	C₂	direct (N × H)
6. C₂×C₁₉×#343	C₂	semidirect
10. C₂×C₁₉×#131	C₄	semidirect
19. C₂×C₁₉×#108	C₂²	semidirect
23. C₂×C₁₉×#106	C₂²	semidirect
28. C₁₉×#343	C₂²	semidirect
45. C₁₉×#131	C₂×C₄	semidirect
143. C₂×#1815	C₁₉	direct (N × H)
194. C₂²×#108	C₂×C₁₉	semidirect
195. C₂²×#106	C₂×C₁₉	semidirect
197. #1815	C₂×C₁₉	direct (N × H)
198. C₂×#343	C₂×C₁₉	semidirect
223. C₂×#131	C₄×C₁₉	semidirect
232. C₂×#108	C₂²×C₁₉	semidirect
236. C₂×#106	C₂²×C₁₉	semidirect
241. #343	C₂²×C₁₉	semidirect
246. C₂×C₁₉	#1815	direct (N × H)
265. #131	C₂×C₄×C₁₉	semidirect
297. C₁₉	C₂×#1815	direct (N × H)
438. C₂	C₁₉×#1815	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×#131	2
C₂²×C₁₉×#108	2
C₂²×C₁₉×#106	2
C₂×C₁₉×#417	2
C₁₉×#1815	2
C₂×C₁₉×#343	2
C₂×#1815	19

Subgroups — C2×C19×#1815 #18026635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1815 #18026635