Subgroups — C₂×C₁₉×#1912 #18026970

Order 4864.

1694 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#536	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#421	C₂	1	2	yes	maximal
4	C₂²×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1912	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×H(3,ℤ/4)	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
8	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
10	C₁₉×#536	—	2	2	no	—
11	C₁₉×#536	—	2	2	no	—
12	C₁₉×#536	C₄	1	4	yes	complemented
13	C₁₉×#536	C₂²	1	4	yes	—
14	C₂×C₁₉×C₄⋊Q₈	C₄	1	2	yes	complemented
15	C₂×C₁₉×#124	C₄	1	2	yes	complemented
16	C₂×C₁₉×#123	—	2	2	no	—
17	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
18	C₁₉×#519	—	2	2	no	—
19	C₁₉×#519	—	2	4	no	—
20	C₁₉×#519	C₂²	1	4	yes	complemented
21	C₂×C₄×Q₈×C₁₉	—	2	4	no	—
22	C₂×C₁₉×#117	—	2	2	no	—
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#117	C₂²	1	2	yes	—
25	C₁₉×#421	—	2	4	no	—
26	C₁₉×#421	C₂²	1	8	yes	—
27	C₂×C₁₉×#104	—	2	4	no	—
28	C₂×C₁₉×#101	—	2	2	no	—
29	C₂×C₁₉×#101	—	2	2	no	—
30	C₂×C₁₉×#101	C₂²	1	4	yes	complemented
31	C₁₉×H(3,ℤ/4)	C₂²	1	8	yes	complemented
32	C₂×#41×C₁₉	—	2	1	no	—
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂×#41×C₁₉	—	2	2	no	—
35	C₂×#41×C₁₉	—	2	2	no	—
36	C₂×#41×C₁₉	—	2	2	no	—
37	C₂×#41×C₁₉	—	2	2	no	—
38	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
39	C₂×#41×C₁₉	C₂³	1	2	yes	—
40	C₂²×Q₈×C₁₉	—	2	2	no	—
41	C₂²×Q₈×C₁₉	—	2	2	no	—
42	C₂²×Q₈×C₁₉	—	2	2	no	—
43	C₂²×Q₈×C₁₉	—	2	2	no	—
44	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
46	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
47	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
48	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
49	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
50	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₉	—	2	1	no	—
54	C₂³×C₄×C₁₉	D₄	1	2	yes	—
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₁₉	—	2	2	no	—
57	C₂×M₁₆×C₁₉	—	2	2	no	—
58	C₂×M₁₆×C₁₉	—	2	2	no	—
59	C₂×M₁₆×C₁₉	—	2	2	no	—
60	C₂×M₁₆×C₁₉	—	2	2	no	—
61	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
62	C₂²×C₈×C₁₉	—	2	2	no	—
63	C₁₉×C₄⋊Q₈	—	2	4	no	—
64	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
65	C₁₉×#124	—	2	4	no	—
66	C₁₉×#124	C₂×C₄	1	8	yes	complemented
67	C₁₉×#123	—	2	8	no	—
68	C₁₉×#123	—	2	8	no	—
69	C₁₉×C₂²⋊Q₈	—	2	8	no	—
70	C₁₉×C₂²⋊Q₈	—	2	8	no	—
71	C₄×Q₈×C₁₉	—	2	16	no	—
72	C₄×Q₈×C₁₉	—	2	16	no	—
73	C₁₉×#117	—	2	8	no	—
74	C₁₉×#117	—	2	8	no	—
75	C₁₉×#117	—	2	2	no	—
76	C₁₉×#117	—	2	2	no	—
77	C₁₉×#117	—	2	1	no	—
78	C₁₉×#117	—	2	1	no	—
79	C₁₉×#117	C₂×C₄	1	2	yes	—
80	C₁₉×#117	D₄	1	4	yes	—
81	C₁₉×#117	C₂³	1	2	yes	—
82	C₁₉×#117	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₄⋊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	4	no	—
90	C₂×C₄²×C₁₉	—	2	4	no	—
91	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
92	C₂×C₄²×C₁₉	D₄	1	4	yes	—
93	C₁₉×#104	—	2	16	no	—
94	C₁₉×#101	—	2	8	no	—
95	C₂⁴×C₁₉	—	2	1	no	—
96	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
97	#41×C₁₉	—	2	4	no	—
98	#41×C₁₉	—	2	4	no	—
99	#41×C₁₉	—	2	4	no	—
100	#41×C₁₉	—	2	4	no	—
101	#41×C₁₉	—	4	2	no	—
102	#41×C₁₉	—	4	2	no	—
103	#41×C₁₉	—	4	2	no	—
104	#41×C₁₉	—	4	2	no	—
105	C₂×Q₈×C₁₉	—	2	1	no	—
106	C₂×Q₈×C₁₉	—	2	4	no	—
107	C₂×Q₈×C₁₉	—	2	4	no	—
108	C₂×Q₈×C₁₉	—	2	4	no	—
109	C₂×Q₈×C₁₉	—	2	4	no	—
110	C₂×Q₈×C₁₉	—	2	4	no	—
111	C₂×Q₈×C₁₉	—	2	4	no	—
112	C₂×Q₈×C₁₉	—	2	4	no	—
113	C₂×Q₈×C₁₉	—	2	4	no	—
114	C₂×Q₈×C₁₉	—	2	4	no	—
115	C₂×Q₈×C₁₉	—	2	4	no	—
116	C₂×Q₈×C₁₉	—	2	4	no	—
117	C₂×Q₈×C₁₉	—	2	4	no	—
118	C₂×Q₈×C₁₉	—	2	2	no	—
119	C₂×Q₈×C₁₉	—	2	2	no	—
120	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
121	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
122	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
123	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
124	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	4	1	no	—
131	C₂×D₄×C₁₉	—	4	1	no	—
132	C₂×D₄×C₁₉	—	4	1	no	—
133	C₂×D₄×C₁₉	—	4	1	no	—
134	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	4	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	4	2	no	—
145	C₂²×C₄×C₁₉	—	4	2	no	—
146	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
147	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
148	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₁₉	#41	1	2	yes	—
157	C₂²×C₄×C₁₉	#41	1	2	yes	—
158	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
159	M₁₆×C₁₉	—	2	4	no	—
160	M₁₆×C₁₉	—	2	4	no	—
161	M₁₆×C₁₉	—	4	2	no	—
162	M₁₆×C₁₉	—	4	2	no	—
163	C₂×C₈×C₁₉	—	2	4	no	—
164	C₂×C₈×C₁₉	—	4	2	no	—
165	C₂×C₈×C₁₉	—	4	2	no	—
166	C₄⋊C₄×C₁₉	—	2	16	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	16	no	—
169	C₄⋊C₄×C₁₉	—	2	4	no	—
170	C₄⋊C₄×C₁₉	—	2	4	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	4	no	—
174	C₂²⋊C₄×C₁₉	—	2	4	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	16	no	—
177	C₄²×C₁₉	—	2	16	no	—
178	C₄²×C₁₉	—	2	2	no	—
179	C₄²×C₁₉	—	2	4	no	—
180	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
181	C₄²×C₁₉	C₂×D₄	1	8	yes	—
182	C₂×#1912	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂³×C₁₉	—	2	2	no	—
184	C₂³×C₁₉	—	4	2	no	—
185	C₂³×C₁₉	—	4	4	no	—
186	C₂³×C₁₉	—	4	1	no	—
187	C₂³×C₁₉	—	4	1	no	—
188	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂³×C₁₉	#120	1	1	yes	characteristic
191	C₂³×C₁₉	#120	1	1	yes	characteristic
192	C₂³×C₁₉	#123	1	1	yes	characteristic
193	C₂³×C₁₉	#123	1	1	yes	characteristic
194	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₁₉	—	2	8	no	—
196	Q₈×C₁₉	—	2	8	no	—
197	Q₈×C₁₉	—	2	8	no	—
198	Q₈×C₁₉	—	2	8	no	—
199	Q₈×C₁₉	—	2	4	no	—
200	Q₈×C₁₉	—	4	2	no	—
201	D₄×C₁₉	—	2	4	no	—
202	D₄×C₁₉	—	4	2	no	—
203	D₄×C₁₉	—	4	2	no	—
204	D₄×C₁₉	—	4	2	no	—
205	D₄×C₁₉	—	4	2	no	—
206	D₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	2	4	no	—
208	C₂×C₄×C₁₉	—	2	4	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	8	no	—
216	C₂×C₄×C₁₉	—	4	8	no	—
217	C₂×C₄×C₁₉	—	4	4	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	4	no	—
221	C₂×C₄×C₁₉	—	4	4	no	—
222	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
223	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
226	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
229	C₂×C₄×C₁₉	#120	1	2	yes	—
230	C₂×C₄×C₁₉	#121	1	2	yes	—
231	C₂×C₄×C₁₉	#121	1	2	yes	—
232	C₂×C₄×C₁₉	#121	1	2	yes	—
233	C₂×C₄×C₁₉	#121	1	2	yes	—
234	C₂×C₄×C₁₉	#123	1	2	yes	—
235	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
237	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
239	C₈×C₁₉	—	4	4	no	—
240	C₂×#536	C₂×C₁₉	1	1	yes	characteristic
241	C₂×#519	C₂×C₁₉	1	1	yes	characteristic, complemented
242	C₂×#421	C₂×C₁₉	1	2	yes	—
243	C₂²×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
244	#1912	C₂×C₁₉	1	8	yes	direct product factor
245	C₂×H(3,ℤ/4)	C₂×C₁₉	1	2	yes	complemented
246	C₂²×C₁₉	—	2	2	no	—
247	C₂²×C₁₉	—	2	2	no	—
248	C₂²×C₁₉	—	2	2	no	—
249	C₂²×C₁₉	—	4	1	no	—
250	C₂²×C₁₉	—	4	1	no	—
251	C₂²×C₁₉	—	4	1	no	—
252	C₂²×C₁₉	—	4	1	no	—
253	C₂²×C₁₉	—	4	4	no	—
254	C₂²×C₁₉	—	4	2	no	—
255	C₂²×C₁₉	—	8	2	no	—
256	C₂²×C₁₉	—	8	2	no	—
257	C₂²×C₁₉	#386	1	1	yes	characteristic
258	C₂²×C₁₉	#386	1	1	yes	characteristic
259	C₂²×C₁₉	#386	1	1	yes	characteristic
260	C₂²×C₁₉	#386	1	1	yes	characteristic
261	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
262	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
263	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
264	C₄×C₁₉	—	2	8	no	—
265	C₄×C₁₉	—	4	8	no	—
266	C₄×C₁₉	—	4	4	no	—
267	C₄×C₁₉	—	4	2	no	—
268	C₄×C₁₉	#386	1	2	yes	—
269	C₄×C₁₉	#386	1	2	yes	—
270	C₄×C₁₉	C₂×C₄×D₄	1	2	yes	—
271	C₄×C₁₉	C₂×#121	1	2	yes	—
272	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
273	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
274	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
275	#536	—	2	2	no	—
276	#536	—	2	2	no	—
277	#536	C₄×C₁₉	1	4	yes	complemented
278	#536	C₂²×C₁₉	1	4	yes	—
279	C₂×C₄⋊Q₈	C₄×C₁₉	1	2	yes	complemented
280	C₂×#124	C₄×C₁₉	1	2	yes	complemented
281	C₂×#123	—	2	2	no	—
282	C₂×C₂²⋊Q₈	—	2	2	no	—
283	#519	—	2	2	no	—
284	#519	—	2	4	no	—
285	#519	C₂²×C₁₉	1	4	yes	complemented
286	C₂×C₄×Q₈	—	2	4	no	—
287	C₂×#117	—	2	2	no	—
288	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×#117	C₂²×C₁₉	1	2	yes	—
290	#421	—	2	4	no	—
291	#421	C₂²×C₁₉	1	8	yes	—
292	C₂×#104	—	2	4	no	—
293	C₂×#101	—	2	2	no	—
294	C₂×#101	—	2	2	no	—
295	C₂×#101	C₂²×C₁₉	1	4	yes	complemented
296	H(3,ℤ/4)	C₂²×C₁₉	1	8	yes	complemented
297	C₂×C₁₉	—	2	1	no	—
298	C₂×C₁₉	—	2	1	no	—
299	C₂×C₁₉	—	2	1	no	—
300	C₂×C₁₉	—	2	1	no	—
301	C₂×C₁₉	—	2	1	no	—
302	C₂×C₁₉	—	2	1	no	—
303	C₂×C₁₉	—	8	2	no	—
304	C₂×C₁₉	#1912	1	2	yes	direct product factor
305	C₂×C₁₉	C₂×#386	1	1	yes	characteristic
306	C₂×#41	—	2	1	no	—
307	C₂×#41	—	2	1	no	—
308	C₂×#41	—	2	2	no	—
309	C₂×#41	—	2	2	no	—
310	C₂×#41	—	2	2	no	—
311	C₂×#41	—	2	2	no	—
312	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
313	C₂×#41	C₂³×C₁₉	1	2	yes	—
314	C₂²×Q₈	—	2	2	no	—
315	C₂²×Q₈	—	2	2	no	—
316	C₂²×Q₈	—	2	2	no	—
317	C₂²×Q₈	—	2	2	no	—
318	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
319	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
320	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
321	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
322	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
323	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
324	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
327	C₂³×C₄	—	2	1	no	—
328	C₂³×C₄	D₄×C₁₉	1	2	yes	—
329	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
330	C₂×M₁₆	—	2	2	no	—
331	C₂×M₁₆	—	2	2	no	—
332	C₂×M₁₆	—	2	2	no	—
333	C₂×M₁₆	—	2	2	no	—
334	C₂×M₁₆	—	2	2	no	—
335	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
336	C₂²×C₈	—	2	2	no	—
337	C₄⋊Q₈	—	2	4	no	—
338	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
339	#124	—	2	4	no	—
340	#124	C₂×C₄×C₁₉	1	8	yes	complemented
341	#123	—	2	8	no	—
342	#123	—	2	8	no	—
343	C₂²⋊Q₈	—	2	8	no	—
344	C₂²⋊Q₈	—	2	8	no	—
345	C₄×Q₈	—	2	16	no	—
346	C₄×Q₈	—	2	16	no	—
347	#117	—	2	8	no	—
348	#117	—	2	8	no	—
349	#117	—	2	2	no	—
350	#117	—	2	2	no	—
351	#117	—	2	1	no	—
352	#117	—	2	1	no	—
353	#117	C₂×C₄×C₁₉	1	2	yes	—
354	#117	D₄×C₁₉	1	4	yes	—
355	#117	C₂³×C₁₉	1	2	yes	—
356	#117	C₂³×C₁₉	1	4	yes	—
357	C₂×C₄⋊C₄	—	2	4	no	—
358	C₂×C₄⋊C₄	—	2	4	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	4	no	—
364	C₂×C₄²	—	2	4	no	—
365	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
366	C₂×C₄²	D₄×C₁₉	1	4	yes	—
367	#104	—	2	16	no	—
368	#101	—	2	8	no	—
369	C₁₉	C₂×#1912	1	1	yes	characteristic, direct product factor, Sylow
370	C₂⁴	—	2	1	no	—
371	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
372	#41	—	2	4	no	—
373	#41	—	2	4	no	—
374	#41	—	2	4	no	—
375	#41	—	2	4	no	—
376	#41	—	4	2	no	—
377	#41	—	4	2	no	—
378	#41	—	4	2	no	—
379	#41	—	4	2	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	4	no	—
382	C₂×Q₈	—	2	4	no	—
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	2	4	no	—
385	C₂×Q₈	—	2	4	no	—
386	C₂×Q₈	—	2	4	no	—
387	C₂×Q₈	—	2	4	no	—
388	C₂×Q₈	—	2	4	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	2	4	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
396	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
397	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
398	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
399	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	4	1	no	—
406	C₂×D₄	—	4	1	no	—
407	C₂×D₄	—	4	1	no	—
408	C₂×D₄	—	4	1	no	—
409	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	4	2	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
422	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
423	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
424	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
426	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
430	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
431	C₂²×C₄	#41×C₁₉	1	2	yes	—
432	C₂²×C₄	#41×C₁₉	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
434	M₁₆	—	2	4	no	—
435	M₁₆	—	2	4	no	—
436	M₁₆	—	4	2	no	—
437	M₁₆	—	4	2	no	—
438	C₂×C₈	—	2	4	no	—
439	C₂×C₈	—	4	2	no	—
440	C₂×C₈	—	4	2	no	—
441	C₄⋊C₄	—	2	16	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	16	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	16	no	—
452	C₄²	—	2	16	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	2	4	no	—
455	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
456	C₄²	C₂×D₄×C₁₉	1	8	yes	—
457	C₂³	—	2	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	4	no	—
460	C₂³	—	4	1	no	—
461	C₂³	—	4	1	no	—
462	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
463	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
464	C₂³	C₁₉×#120	1	1	yes	characteristic
465	C₂³	C₁₉×#120	1	1	yes	characteristic
466	C₂³	C₁₉×#123	1	1	yes	characteristic
467	C₂³	C₁₉×#123	1	1	yes	characteristic
468	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
469	Q₈	—	2	8	no	—
470	Q₈	—	2	8	no	—
471	Q₈	—	2	8	no	—
472	Q₈	—	2	8	no	—
473	Q₈	—	2	4	no	—
474	Q₈	—	4	2	no	—
475	D₄	—	2	4	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	2	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	8	no	—
490	C₂×C₄	—	4	8	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
497	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
498	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
499	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
500	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
501	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
502	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
503	C₂×C₄	C₁₉×#120	1	2	yes	—
504	C₂×C₄	C₁₉×#121	1	2	yes	—
505	C₂×C₄	C₁₉×#121	1	2	yes	—
506	C₂×C₄	C₁₉×#121	1	2	yes	—
507	C₂×C₄	C₁₉×#121	1	2	yes	—
508	C₂×C₄	C₁₉×#123	1	2	yes	—
509	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
511	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
512	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
513	C₈	—	4	4	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	1	no	—
519	C₂²	—	4	1	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	2	no	—
525	C₂²	C₁₉×#386	1	1	yes	characteristic
526	C₂²	C₁₉×#386	1	1	yes	characteristic
527	C₂²	C₁₉×#386	1	1	yes	characteristic
528	C₂²	C₁₉×#386	1	1	yes	characteristic
529	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
530	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
531	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
532	C₄	—	2	8	no	—
533	C₄	—	4	8	no	—
534	C₄	—	4	4	no	—
535	C₄	—	4	2	no	—
536	C₄	C₁₉×#386	1	2	yes	—
537	C₄	C₁₉×#386	1	2	yes	—
538	C₄	C₂×C₄×D₄×C₁₉	1	2	yes	—
539	C₄	C₂×C₁₉×#121	1	2	yes	—
540	C₂	—	2	1	no	—
541	C₂	—	2	1	no	—
542	C₂	—	2	1	no	—
543	C₂	—	2	1	no	—
544	C₂	—	2	1	no	—
545	C₂	—	2	1	no	—
546	C₂	—	8	2	no	—
547	C₂	C₁₉×#1912	1	2	yes	direct product factor
548	C₂	C₂×C₁₉×#386	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
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×#519	C₂	semidirect
4. C₂²×C₁₉×#101	C₂	semidirect
5. C₁₉×#1912	C₂	direct (N × H)
6. C₂×C₁₉×H(3,ℤ/4)	C₂	semidirect
12. C₁₉×#536	C₄	semidirect
14. C₂×C₁₉×C₄⋊Q₈	C₄	semidirect
15. C₂×C₁₉×#124	C₄	semidirect
20. C₁₉×#519	C₂²	semidirect
30. C₂×C₁₉×#101	C₂²	semidirect
31. C₁₉×H(3,ℤ/4)	C₂²	semidirect
64. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
66. C₁₉×#124	C₂×C₄	semidirect
182. C₂×#1912	C₁₉	direct (N × H)
241. C₂×#519	C₂×C₁₉	semidirect
243. C₂²×#101	C₂×C₁₉	semidirect
244. #1912	C₂×C₁₉	direct (N × H)
245. C₂×H(3,ℤ/4)	C₂×C₁₉	semidirect
277. #536	C₄×C₁₉	semidirect
279. C₂×C₄⋊Q₈	C₄×C₁₉	semidirect
280. C₂×#124	C₄×C₁₉	semidirect
285. #519	C₂²×C₁₉	semidirect
295. C₂×#101	C₂²×C₁₉	semidirect
296. H(3,ℤ/4)	C₂²×C₁₉	semidirect
304. C₂×C₁₉	#1912	direct (N × H)
338. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
340. #124	C₂×C₄×C₁₉	semidirect
369. C₁₉	C₂×#1912	direct (N × H)
547. C₂	C₁₉×#1912	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×#536	2
C₂×C₁₉×#519	2
C₂×C₁₉×#421	2
C₂²×C₁₉×#101	2
C₁₉×#1912	2
C₂×C₁₉×H(3,ℤ/4)	2
C₂×#1912	19

Subgroups — C2×C19×#1912 #18026970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1912 #18026970