Subgroups — C₁₉×#32988 #18038947

Order 4864.

1300 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#520	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#483	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2616	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1873	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1872	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1854	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1853	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1825	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1824	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1780	C₂	1	1	yes	maximal, characteristic
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₁₉×#520	—	2	4	no	—
16	C₁₉×#520	—	2	4	no	—
17	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
18	C₂×C₄×D₄×C₁₉	—	2	2	no	—
19	C₂×C₄×D₄×C₁₉	—	2	1	no	—
20	C₂×C₁₉×#117	C₂²	1	2	yes	—
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#485	—	2	4	no	—
25	C₁₉×#483	—	2	4	no	—
26	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#106	C₂²	1	2	yes	—
28	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#103	C₂²	1	2	yes	—
30	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₁₉×#395	—	2	1	no	—
37	C₁₉×#394	—	2	2	no	—
38	C₁₉×#394	—	2	1	no	—
39	C₁₉×#380	C₂²	1	1	yes	characteristic
40	C₁₉×#380	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#340	C₂²	1	2	yes	—
43	C₁₉×#340	C₂²	1	2	yes	—
44	C₁₉×#340	C₂²	1	2	yes	—
45	C₂×#41×C₁₉	—	2	2	no	—
46	C₂×#41×C₁₉	—	2	2	no	—
47	C₂×#41×C₁₉	—	2	4	no	—
48	C₂×#41×C₁₉	—	2	4	no	—
49	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
50	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂²×D₄×C₁₉	D₄	1	2	yes	—
53	C₂³×C₄×C₁₉	—	2	2	no	—
54	C₂³×C₄×C₁₉	—	2	1	no	—
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₁₉×C₂²⋊Q₈	—	2	2	no	—
61	C₁₉×C₂²⋊Q₈	—	2	2	no	—
62	C₁₉×C₂²⋊Q₈	—	2	4	no	—
63	C₁₉×C₂²⋊Q₈	—	2	4	no	—
64	C₄×Q₈×C₁₉	—	2	8	no	—
65	C₄×D₄×C₁₉	—	2	16	no	—
66	C₄×D₄×C₁₉	—	2	8	no	—
67	C₁₉×#117	—	2	2	no	—
68	C₁₉×#117	—	2	4	no	—
69	C₁₉×#117	—	2	4	no	—
70	C₁₉×#117	D₄	1	4	yes	—
71	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₂²⋊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	2	no	—
90	C₂×C₄²×C₁₉	—	2	2	no	—
91	C₂×C₄²×C₁₉	—	2	1	no	—
92	C₁₉×#107	—	2	2	no	—
93	C₁₉×#106	—	2	4	no	—
94	C₁₉×#106	—	2	2	no	—
95	C₁₉×#103	—	2	4	no	—
96	C₁₉×#103	—	2	2	no	—
97	C₁₉×#103	—	2	2	no	—
98	C₁₉×C₂²⋊C₈	—	2	2	no	—
99	C₁₉×C₂²⋊C₈	—	2	2	no	—
100	C₁₉×C₂²⋊C₈	—	2	4	no	—
101	C₁₉×C₂²⋊C₈	—	2	4	no	—
102	C₁₉×#95	—	2	1	no	—
103	C₁₉×#95	—	2	2	no	—
104	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
106	#41×C₁₉	—	2	8	no	—
107	#41×C₁₉	—	2	8	no	—
108	#41×C₁₉	—	2	16	no	—
109	C₂×Q₈×C₁₉	—	2	2	no	—
110	C₂×Q₈×C₁₉	—	2	4	no	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	4	no	—
116	C₂×D₄×C₁₉	—	2	4	no	—
117	C₂×D₄×C₁₉	—	2	4	no	—
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	2	4	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	8	no	—
130	C₂²×C₄×C₁₉	—	2	4	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	8	2	no	—
135	C₂²×C₄×C₁₉	—	8	2	no	—
136	C₂²×C₄×C₁₉	—	8	2	no	—
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₉	#41	1	4	yes	—
142	C₂²×C₄×C₁₉	#41	1	4	yes	—
143	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
144	C₂×C₈×C₁₉	—	2	2	no	—
145	C₂×C₈×C₁₉	—	2	1	no	—
146	C₂×C₈×C₁₉	—	2	1	no	—
147	C₂×C₈×C₁₉	—	2	2	no	—
148	C₂×C₈×C₁₉	—	2	2	no	—
149	C₂×C₈×C₁₉	—	2	2	no	—
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	8	no	—
152	C₄⋊C₄×C₁₉	—	2	4	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	4	2	no	—
161	C₄⋊C₄×C₁₉	—	4	4	no	—
162	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
164	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
165	C₂²⋊C₄×C₁₉	—	2	8	no	—
166	C₂²⋊C₄×C₁₉	—	2	4	no	—
167	C₂²⋊C₄×C₁₉	—	4	2	no	—
168	C₂²⋊C₄×C₁₉	—	4	4	no	—
169	C₂²⋊C₄×C₁₉	—	8	1	no	—
170	C₂²⋊C₄×C₁₉	—	8	2	no	—
171	C₄²×C₁₉	—	2	8	no	—
172	C₄²×C₁₉	—	2	4	no	—
173	#32988	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	—	2	2	no	—
176	C₂³×C₁₉	—	2	2	no	—
177	C₂³×C₁₉	—	2	2	no	—
178	C₂³×C₁₉	—	2	1	no	—
179	C₂³×C₁₉	—	2	2	no	—
180	C₂³×C₁₉	—	2	2	no	—
181	C₂³×C₁₉	—	2	2	no	—
182	C₂³×C₁₉	—	2	2	no	—
183	C₂³×C₁₉	—	2	1	no	—
184	C₂³×C₁₉	#120	1	2	yes	—
185	C₂³×C₁₉	#123	1	4	yes	—
186	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
187	Q₈×C₁₉	—	2	8	no	—
188	Q₈×C₁₉	—	4	2	no	—
189	Q₈×C₁₉	—	4	1	no	—
190	Q₈×C₁₉	—	4	1	no	—
191	D₄×C₁₉	—	2	8	no	—
192	D₄×C₁₉	—	2	16	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	4	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	8	4	no	—
220	C₂×C₄×C₁₉	—	8	8	no	—
221	C₂×C₄×C₁₉	#120	1	2	yes	—
222	C₂×C₄×C₁₉	#123	1	4	yes	—
223	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
226	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
227	C₈×C₁₉	—	4	2	no	—
228	C₈×C₁₉	—	4	1	no	—
229	C₈×C₁₉	—	4	1	no	—
230	C₂×#520	C₂×C₁₉	1	1	yes	characteristic
231	C₂×#485	C₂×C₁₉	1	1	yes	characteristic, complemented
232	C₂×#483	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#2616	C₂×C₁₉	1	1	yes	characteristic
234	#1873	C₂×C₁₉	1	2	yes	complemented
235	#1872	C₂×C₁₉	1	2	yes	complemented
236	#1854	C₂×C₁₉	1	2	yes	complemented
237	#1853	C₂×C₁₉	1	2	yes	complemented
238	#1825	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#1824	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#1780	C₂×C₁₉	1	1	yes	characteristic
241	C₂²×C₁₉	—	2	4	no	—
242	C₂²×C₁₉	—	2	4	no	—
243	C₂²×C₁₉	—	2	2	no	—
244	C₂²×C₁₉	—	2	4	no	—
245	C₂²×C₁₉	—	2	2	no	—
246	C₂²×C₁₉	—	2	2	no	—
247	C₂²×C₁₉	—	4	2	no	—
248	C₂²×C₁₉	—	4	2	no	—
249	C₂²×C₁₉	—	4	2	no	—
250	C₂²×C₁₉	—	4	2	no	—
251	C₂²×C₁₉	—	4	2	no	—
252	C₂²×C₁₉	—	4	2	no	—
253	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
254	C₂²×C₁₉	C₂×#123	1	2	yes	—
255	C₂²×C₁₉	#577	1	2	yes	—
256	C₂²×C₁₉	#577	1	1	yes	characteristic
257	C₂²×C₁₉	#578	1	1	yes	characteristic
258	C₄×C₁₉	—	2	2	no	—
259	C₄×C₁₉	—	2	4	no	—
260	C₄×C₁₉	—	4	4	no	—
261	C₄×C₁₉	—	4	2	no	—
262	C₄×C₁₉	—	4	2	no	—
263	C₄×C₁₉	—	8	2	no	—
264	C₄×C₁₉	—	8	1	no	—
265	C₄×C₁₉	—	8	1	no	—
266	C₄×C₁₉	#525	1	1	yes	characteristic
267	C₄×C₁₉	#525	1	2	yes	—
268	C₄×C₁₉	#525	1	1	yes	characteristic
269	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
270	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
271	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
272	#520	—	2	4	no	—
273	#520	—	2	4	no	—
274	C₂×C₄×Q₈	—	2	1	no	—
275	C₂×C₄×D₄	—	2	2	no	—
276	C₂×C₄×D₄	—	2	1	no	—
277	C₂×#117	C₂²×C₁₉	1	2	yes	—
278	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
280	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
281	#485	—	2	4	no	—
282	#483	—	2	4	no	—
283	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
284	C₂×#106	C₂²×C₁₉	1	2	yes	—
285	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
286	C₂×#103	C₂²×C₁₉	1	2	yes	—
287	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
290	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
291	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
292	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
293	#395	—	2	1	no	—
294	#394	—	2	1	no	—
295	#394	—	2	2	no	—
296	#380	C₂²×C₁₉	1	1	yes	characteristic
297	#380	C₂²×C₁₉	1	2	yes	—
298	#340	C₂²×C₁₉	1	2	yes	—
299	#340	C₂²×C₁₉	1	2	yes	—
300	#340	C₂²×C₁₉	1	2	yes	—
301	#340	C₂²×C₁₉	1	2	yes	—
302	C₂×C₁₉	—	4	4	no	—
303	C₂×C₁₉	—	4	2	no	—
304	C₂×C₁₉	#2849	1	1	yes	characteristic
305	C₂×C₁₉	#3009	1	1	yes	characteristic
306	C₂×C₁₉	#3013	1	1	yes	characteristic
307	C₂×C₁₉	#3097	1	2	yes	—
308	C₂×C₁₉	#3099	1	2	yes	—
309	C₂×#41	—	2	2	no	—
310	C₂×#41	—	2	2	no	—
311	C₂×#41	—	2	4	no	—
312	C₂×#41	—	2	4	no	—
313	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
314	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
315	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
316	C₂²×D₄	D₄×C₁₉	1	2	yes	—
317	C₂³×C₄	—	2	2	no	—
318	C₂³×C₄	—	2	1	no	—
319	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
321	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
322	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
323	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
324	C₂²⋊Q₈	—	2	2	no	—
325	C₂²⋊Q₈	—	2	2	no	—
326	C₂²⋊Q₈	—	2	4	no	—
327	C₂²⋊Q₈	—	2	4	no	—
328	C₄×Q₈	—	2	8	no	—
329	C₄×D₄	—	2	16	no	—
330	C₄×D₄	—	2	8	no	—
331	#117	—	2	2	no	—
332	#117	—	2	4	no	—
333	#117	—	2	4	no	—
334	#117	D₄×C₁₉	1	4	yes	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	4	no	—
339	C₂×C₄⋊C₄	—	2	4	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
343	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
344	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₂²⋊C₄	—	2	1	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₄²	—	2	2	no	—
355	C₂×C₄²	—	2	1	no	—
356	#107	—	2	2	no	—
357	#106	—	2	4	no	—
358	#106	—	2	2	no	—
359	#103	—	2	4	no	—
360	#103	—	2	2	no	—
361	#103	—	2	2	no	—
362	C₂²⋊C₈	—	2	2	no	—
363	C₂²⋊C₈	—	2	2	no	—
364	C₂²⋊C₈	—	2	4	no	—
365	C₂²⋊C₈	—	2	4	no	—
366	#95	—	2	1	no	—
367	#95	—	2	2	no	—
368	C₁₉	#32988	1	1	yes	characteristic, direct product factor, Sylow
369	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
370	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
371	#41	—	2	8	no	—
372	#41	—	2	8	no	—
373	#41	—	2	16	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	8	2	no	—
400	C₂²×C₄	—	8	2	no	—
401	C₂²×C₄	—	8	2	no	—
402	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
404	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
405	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
406	C₂²×C₄	#41×C₁₉	1	4	yes	—
407	C₂²×C₄	#41×C₁₉	1	4	yes	—
408	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₄⋊C₄	—	4	4	no	—
427	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
428	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
429	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
430	C₂²⋊C₄	—	2	8	no	—
431	C₂²⋊C₄	—	2	4	no	—
432	C₂²⋊C₄	—	4	2	no	—
433	C₂²⋊C₄	—	4	4	no	—
434	C₂²⋊C₄	—	8	2	no	—
435	C₂²⋊C₄	—	8	1	no	—
436	C₄²	—	2	8	no	—
437	C₄²	—	2	4	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	2	no	—
448	C₂³	C₁₉×#120	1	2	yes	—
449	C₂³	C₁₉×#123	1	4	yes	—
450	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
451	Q₈	—	2	8	no	—
452	Q₈	—	4	2	no	—
453	Q₈	—	4	1	no	—
454	Q₈	—	4	1	no	—
455	D₄	—	2	8	no	—
456	D₄	—	2	16	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	8	4	no	—
484	C₂×C₄	—	8	8	no	—
485	C₂×C₄	C₁₉×#120	1	2	yes	—
486	C₂×C₄	C₁₉×#123	1	4	yes	—
487	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
489	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
490	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
491	C₈	—	4	2	no	—
492	C₈	—	4	1	no	—
493	C₈	—	4	1	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	4	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	4	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
507	C₂²	C₂×C₁₉×#123	1	2	yes	—
508	C₂²	C₁₉×#577	1	2	yes	—
509	C₂²	C₁₉×#577	1	1	yes	characteristic
510	C₂²	C₁₉×#578	1	1	yes	characteristic
511	C₄	—	2	2	no	—
512	C₄	—	2	4	no	—
513	C₄	—	4	4	no	—
514	C₄	—	4	2	no	—
515	C₄	—	4	2	no	—
516	C₄	—	8	1	no	—
517	C₄	—	8	2	no	—
518	C₄	—	8	1	no	—
519	C₄	C₁₉×#525	1	1	yes	characteristic
520	C₄	C₁₉×#525	1	2	yes	—
521	C₄	C₁₉×#525	1	1	yes	characteristic
522	C₂	—	4	2	no	—
523	C₂	—	4	4	no	—
524	C₂	C₁₉×#2849	1	1	yes	characteristic
525	C₂	C₁₉×#3009	1	1	yes	characteristic
526	C₂	C₁₉×#3013	1	1	yes	characteristic
527	C₂	C₁₉×#3097	1	2	yes	—
528	C₂	C₁₉×#3099	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#485	C₂	semidirect
3. C₂×C₁₉×#483	C₂	semidirect
5. C₁₉×#1873	C₂	semidirect
6. C₁₉×#1872	C₂	semidirect
7. C₁₉×#1854	C₂	semidirect
8. C₁₉×#1853	C₂	semidirect
9. C₁₉×#1825	C₂	semidirect
10. C₁₉×#1824	C₂	semidirect
173. #32988	C₁₉	direct (N × H)
231. C₂×#485	C₂×C₁₉	semidirect
232. C₂×#483	C₂×C₁₉	semidirect
234. #1873	C₂×C₁₉	semidirect
235. #1872	C₂×C₁₉	semidirect
236. #1854	C₂×C₁₉	semidirect
237. #1853	C₂×C₁₉	semidirect
238. #1825	C₂×C₁₉	semidirect
239. #1824	C₂×C₁₉	semidirect
368. C₁₉	#32988	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×#520	2
C₂×C₁₉×#485	2
C₂×C₁₉×#483	2
C₁₉×#2616	2
C₁₉×#1873	2
C₁₉×#1872	2
C₁₉×#1854	2
C₁₉×#1853	2
C₁₉×#1825	2
C₁₉×#1824	2
C₁₉×#1780	2
#32988	19

Subgroups — C19×#32988 #18038947

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32988 #18038947