Subgroups — C₁₉×#20723 #18026682

Order 4864.

1378 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2283	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1820	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1799	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1782	C₂	1	2	yes	maximal
6	C₄×C₁₉×#99	C₂	1	4	yes	maximal, complemented
7	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
8	C₄×#41×C₁₉	—	2	2	no	—
9	C₄×#41×C₁₉	—	2	2	no	—
10	C₄×#41×C₁₉	—	2	2	no	—
11	C₄×#41×C₁₉	—	2	2	no	—
12	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
13	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
14	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic, complemented
15	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic, complemented
16	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
18	C₂×C₁₉×#117	C₄	1	2	yes	complemented
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₁₉	C₄	1	2	yes	complemented
21	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#99	C₂²	1	8	yes	—
23	C₁₉×#383	—	2	2	no	—
24	C₁₉×#382	—	2	2	no	—
25	C₁₉×#381	C₂²	1	4	yes	—
26	C₁₉×#380	C₂²	1	4	yes	—
27	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
29	C₁₉×#376	—	2	2	no	—
30	C₁₉×#342	C₂²	1	8	yes	—
31	C₂×#41×C₁₉	—	2	8	no	—
32	C₂×#41×C₁₉	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	2	no	—
34	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
39	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₄×Q₈×C₁₉	—	2	2	no	—
44	C₄×Q₈×C₁₉	—	2	2	no	—
45	C₄×Q₈×C₁₉	—	2	2	no	—
46	C₄×Q₈×C₁₉	—	2	2	no	—
47	C₄×D₄×C₁₉	—	2	4	no	—
48	C₄×D₄×C₁₉	—	2	4	no	—
49	C₄×D₄×C₁₉	—	2	4	no	—
50	C₄×D₄×C₁₉	—	2	4	no	—
51	C₄×D₄×C₁₉	—	2	2	no	—
52	C₄×D₄×C₁₉	—	2	2	no	—
53	C₄×D₄×C₁₉	—	2	2	no	—
54	C₄×D₄×C₁₉	—	2	2	no	—
55	C₁₉×#117	—	2	2	no	—
56	C₁₉×#117	—	2	2	no	—
57	C₁₉×#117	—	2	4	no	—
58	C₁₉×#117	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
60	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
67	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₉	—	2	2	no	—
69	C₂×C₄²×C₁₉	—	2	2	no	—
70	C₂×C₄²×C₁₉	—	2	2	no	—
71	C₂×C₄²×C₁₉	—	2	2	no	—
72	C₂×C₄²×C₁₉	—	2	4	no	—
73	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
76	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₁₉	D₄	1	2	yes	—
81	C₂×C₄²×C₁₉	D₄	1	2	yes	—
82	C₂×C₄²×C₁₉	D₄	1	2	yes	—
83	C₂×C₄²×C₁₉	D₄	1	2	yes	—
84	C₁₉×#99	—	2	16	no	—
85	C₁₉×#95	—	2	4	no	—
86	C₁₉×#95	—	2	4	no	—
87	C₁₉×#95	—	2	4	no	—
88	C₁₉×#95	—	2	4	no	—
89	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
90	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
91	#41×C₁₉	—	2	16	no	—
92	#41×C₁₉	—	2	16	no	—
93	C₂×Q₈×C₁₉	—	2	2	no	—
94	C₂×Q₈×C₁₉	—	2	4	no	—
95	C₂×D₄×C₁₉	—	2	4	no	—
96	C₂×D₄×C₁₉	—	2	4	no	—
97	C₂×D₄×C₁₉	—	2	4	no	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	#41	1	8	yes	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	2	4	no	—
102	C₂²×C₄×C₁₉	—	2	2	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	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	8	no	—
110	C₂²×C₄×C₁₉	—	4	2	no	—
111	C₂²×C₄×C₁₉	—	4	2	no	—
112	C₂²×C₄×C₁₉	—	4	4	no	—
113	C₂²×C₄×C₁₉	—	4	4	no	—
114	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₁₉	—	2	4	no	—
130	C₄⋊C₄×C₁₉	—	2	4	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	4	8	no	—
134	C₂²⋊C₄×C₁₉	—	2	4	no	—
135	C₂²⋊C₄×C₁₉	—	2	4	no	—
136	C₂²⋊C₄×C₁₉	—	2	4	no	—
137	C₂²⋊C₄×C₁₉	—	2	16	no	—
138	C₄²×C₁₉	—	2	2	no	—
139	C₄²×C₁₉	—	2	2	no	—
140	C₄²×C₁₉	—	2	2	no	—
141	C₄²×C₁₉	—	2	2	no	—
142	C₄²×C₁₉	—	2	2	no	—
143	C₄²×C₁₉	—	2	2	no	—
144	C₄²×C₁₉	—	4	8	no	—
145	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
146	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
147	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
148	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
149	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
150	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
151	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
152	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
153	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
154	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
155	#20723	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	—	4	1	no	—
159	C₂³×C₁₉	—	4	1	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	—	4	2	no	—
162	C₂³×C₁₉	#117	1	4	yes	—
163	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
164	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
165	C₂³×C₁₉	C₂×#41	1	4	yes	—
166	Q₈×C₁₉	—	2	8	no	—
167	D₄×C₁₉	—	2	8	no	—
168	D₄×C₁₉	—	2	16	no	—
169	C₂×C₄×C₁₉	—	2	8	no	—
170	C₂×C₄×C₁₉	—	2	8	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	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	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	—	4	4	no	—
189	C₂×C₄×C₁₉	—	4	4	no	—
190	C₂×C₄×C₁₉	—	4	4	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	8	no	—
194	C₂×C₄×C₁₉	—	4	8	no	—
195	C₂×C₄×C₁₉	—	4	8	no	—
196	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
201	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
202	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
203	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₉	#117	1	4	yes	—
206	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic
207	#2283	C₂×C₁₉	1	2	yes	complemented
208	#1820	C₂×C₁₉	1	2	yes	complemented
209	#1799	C₂×C₁₉	1	4	yes	complemented
210	#1782	C₂×C₁₉	1	2	yes	—
211	C₄×#99	C₂×C₁₉	1	4	yes	complemented
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	4	no	—
217	C₂²×C₁₉	—	4	4	no	—
218	C₂²×C₁₉	—	4	4	no	—
219	C₂²×C₁₉	—	4	4	no	—
220	C₂²×C₁₉	—	4	2	no	—
221	C₂²×C₁₉	—	4	2	no	—
222	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
223	C₂²×C₁₉	C₂×#117	1	2	yes	—
224	C₂²×C₁₉	#525	1	4	yes	—
225	C₄×C₁₉	—	2	1	no	—
226	C₄×C₁₉	—	2	1	no	—
227	C₄×C₁₉	—	2	2	no	—
228	C₄×C₁₉	—	2	2	no	—
229	C₄×C₁₉	—	2	1	no	—
230	C₄×C₁₉	—	2	1	no	—
231	C₄×C₁₉	—	2	2	no	—
232	C₄×C₁₉	—	2	4	no	—
233	C₄×C₁₉	—	4	2	no	—
234	C₄×C₁₉	—	4	2	no	—
235	C₄×C₁₉	—	8	8	no	—
236	C₄×C₁₉	#410	1	2	yes	—
237	C₄×C₁₉	#410	1	2	yes	—
238	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
239	C₄×#41	—	2	2	no	—
240	C₄×#41	—	2	2	no	—
241	C₄×#41	—	2	2	no	—
242	C₄×#41	—	2	2	no	—
243	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
244	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
245	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic, complemented
246	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic, complemented
247	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
248	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
249	C₂×#117	C₄×C₁₉	1	2	yes	complemented
250	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
251	C₂²×C₄²	C₄×C₁₉	1	2	yes	complemented
252	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
253	C₂×#99	C₂²×C₁₉	1	8	yes	—
254	#383	—	2	2	no	—
255	#382	—	2	2	no	—
256	#381	C₂²×C₁₉	1	4	yes	—
257	#380	C₂²×C₁₉	1	4	yes	—
258	C₄×C₄⋊C₄	—	2	2	no	—
259	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
260	#376	—	2	2	no	—
261	#342	C₂²×C₁₉	1	8	yes	—
262	C₂×C₁₉	—	2	4	no	—
263	C₂×C₁₉	—	2	2	no	—
264	C₂×C₁₉	—	4	4	no	—
265	C₂×C₁₉	#2280	1	1	yes	characteristic
266	C₂×C₁₉	C₂×#410	1	1	yes	characteristic
267	C₂×C₁₉	C₂×#410	1	1	yes	characteristic
268	C₂×#41	—	2	8	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
272	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
273	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
274	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
275	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
276	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
277	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
279	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
280	C₄×Q₈	—	2	2	no	—
281	C₄×Q₈	—	2	2	no	—
282	C₄×Q₈	—	2	2	no	—
283	C₄×Q₈	—	2	2	no	—
284	C₄×D₄	—	2	4	no	—
285	C₄×D₄	—	2	4	no	—
286	C₄×D₄	—	2	4	no	—
287	C₄×D₄	—	2	4	no	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	2	2	no	—
291	C₄×D₄	—	2	2	no	—
292	#117	—	2	2	no	—
293	#117	—	2	2	no	—
294	#117	—	2	4	no	—
295	#117	—	2	4	no	—
296	C₂×C₄⋊C₄	—	2	4	no	—
297	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
298	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
299	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
302	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
305	C₂×C₄²	—	2	2	no	—
306	C₂×C₄²	—	2	2	no	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	—	2	2	no	—
309	C₂×C₄²	—	2	4	no	—
310	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
311	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
312	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
313	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
314	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
315	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
316	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
317	C₂×C₄²	D₄×C₁₉	1	2	yes	—
318	C₂×C₄²	D₄×C₁₉	1	2	yes	—
319	C₂×C₄²	D₄×C₁₉	1	2	yes	—
320	C₂×C₄²	D₄×C₁₉	1	2	yes	—
321	#99	—	2	16	no	—
322	#95	—	2	4	no	—
323	#95	—	2	4	no	—
324	#95	—	2	4	no	—
325	#95	—	2	4	no	—
326	C₁₉	#20723	1	1	yes	characteristic, direct product factor, Sylow
327	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
328	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
329	#41	—	2	16	no	—
330	#41	—	2	16	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	4	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	#41×C₁₉	1	8	yes	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	8	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	4	no	—
351	C₂²×C₄	—	4	4	no	—
352	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
353	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
356	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
357	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
358	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
359	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
360	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	4	8	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	16	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	4	8	no	—
383	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
384	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
385	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
386	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
387	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
388	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
389	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
390	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
391	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
392	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	C₁₉×#117	1	4	yes	—
400	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
401	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
402	C₂³	C₂×#41×C₁₉	1	4	yes	—
403	Q₈	—	2	8	no	—
404	D₄	—	2	8	no	—
405	D₄	—	2	16	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	2	8	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	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	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	8	no	—
431	C₂×C₄	—	4	8	no	—
432	C₂×C₄	—	4	8	no	—
433	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
434	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
435	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
436	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
437	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
438	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
439	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
440	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
441	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
442	C₂×C₄	C₁₉×#117	1	4	yes	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
454	C₂²	C₂×C₁₉×#117	1	2	yes	—
455	C₂²	C₁₉×#525	1	4	yes	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	4	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	8	8	no	—
467	C₄	C₁₉×#410	1	2	yes	—
468	C₄	C₁₉×#410	1	2	yes	—
469	C₂	—	2	4	no	—
470	C₂	—	2	2	no	—
471	C₂	—	4	4	no	—
472	C₂	C₁₉×#2280	1	1	yes	characteristic
473	C₂	C₂×C₁₉×#410	1	1	yes	characteristic
474	C₂	C₂×C₁₉×#410	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2283	C₂	semidirect
3. C₁₉×#1820	C₂	semidirect
4. C₁₉×#1799	C₂	semidirect
6. C₄×C₁₉×#99	C₂	semidirect
12. C₂×C₄×Q₈×C₁₉	C₄	semidirect
13. C₂×C₄×Q₈×C₁₉	C₄	semidirect
14. C₂×C₄×D₄×C₁₉	C₄	semidirect
15. C₂×C₄×D₄×C₁₉	C₄	semidirect
18. C₂×C₁₉×#117	C₄	semidirect
20. C₂²×C₄²×C₁₉	C₄	semidirect
155. #20723	C₁₉	direct (N × H)
207. #2283	C₂×C₁₉	semidirect
208. #1820	C₂×C₁₉	semidirect
209. #1799	C₂×C₁₉	semidirect
211. C₄×#99	C₂×C₁₉	semidirect
243. C₂×C₄×Q₈	C₄×C₁₉	semidirect
244. C₂×C₄×Q₈	C₄×C₁₉	semidirect
245. C₂×C₄×D₄	C₄×C₁₉	semidirect
246. C₂×C₄×D₄	C₄×C₁₉	semidirect
249. C₂×#117	C₄×C₁₉	semidirect
251. C₂²×C₄²	C₄×C₁₉	semidirect
326. C₁₉	#20723	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×C₄×#41×C₁₉	2
C₁₉×#2283	2
C₁₉×#1820	2
C₁₉×#1799	2
C₁₉×#1782	2
C₄×C₁₉×#99	2
#20723	19

Subgroups — C19×#20723 #18026682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20723 #18026682