Subgroups — C₁₉×#23488 #18029447

Order 4864.

1482 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#537	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#417	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#416	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#408	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2036	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2033	C₂	1	4	yes	maximal, complemented
9	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#537	—	2	4	no	—
15	C₁₉×#537	—	2	4	no	—
16	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₉×#121	—	2	1	no	—
19	C₂×C₁₉×#121	—	2	2	no	—
20	C₂×C₁₉×#121	C₂²	1	2	yes	—
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#107	—	2	4	no	—
25	C₂×C₁₉×#107	C₂²	1	4	yes	—
26	C₁₉×#417	—	2	4	no	—
27	C₁₉×#416	—	2	4	no	—
28	C₂×C₁₉×#103	C₂²	1	2	yes	—
29	C₂×C₁₉×#103	C₂²	1	2	yes	—
30	C₂×C₁₉×#102	C₂²	1	2	yes	—
31	C₂×C₁₉×#102	C₂²	1	2	yes	—
32	C₁₉×#408	—	2	4	no	—
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
34	C₁₉×#391	—	2	1	no	—
35	C₁₉×#390	—	2	1	no	—
36	C₁₉×#386	—	2	2	no	—
37	C₁₉×#380	C₂²	1	4	yes	—
38	C₁₉×#340	C₂²	1	4	yes	—
39	C₂×#41×C₁₉	—	2	2	no	—
40	C₂×#41×C₁₉	—	2	2	no	—
41	C₂×#41×C₁₉	—	2	2	no	—
42	C₂×#41×C₁₉	—	2	2	no	—
43	C₂×#41×C₁₉	—	2	2	no	—
44	C₂×#41×C₁₉	—	2	2	no	—
45	C₂×#41×C₁₉	—	2	2	no	—
46	C₂×#41×C₁₉	—	2	2	no	—
47	C₂×#41×C₁₉	—	2	2	no	—
48	C₂×#41×C₁₉	—	2	2	no	—
49	C₂×#41×C₁₉	—	2	2	no	—
50	C₂×#41×C₁₉	D₄	1	4	yes	—
51	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
52	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₉	—	2	1	no	—
54	C₂²×D₄×C₁₉	—	2	2	no	—
55	C₂²×D₄×C₁₉	D₄	1	2	yes	—
56	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₉	—	2	1	no	—
59	C₂³×C₄×C₁₉	—	2	1	no	—
60	C₂³×C₄×C₁₉	—	2	1	no	—
61	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×M₁₆×C₁₉	—	2	2	no	—
64	C₂×M₁₆×C₁₉	—	2	2	no	—
65	C₂×M₁₆×C₁₉	—	2	2	no	—
66	C₂²×C₈×C₁₉	—	2	2	no	—
67	C₂²×C₈×C₁₉	—	2	2	no	—
68	C₂²×C₈×C₁₉	D₄	1	4	yes	complemented
69	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
70	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
71	C₁₉×C₂²⋊Q₈	—	2	8	no	—
72	C₁₉×C₂²⋊Q₈	—	2	4	no	—
73	C₁₉×C₂²⋊Q₈	—	2	4	no	—
74	C₁₉×#121	—	2	16	no	—
75	C₁₉×#121	—	2	8	no	—
76	C₁₉×#121	—	2	4	no	—
77	C₁₉×#121	—	2	4	no	—
78	C₁₉×#117	—	2	2	no	—
79	C₁₉×#117	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
94	C₂×C₄²×C₁₉	—	2	1	no	—
95	C₁₉×#107	—	2	8	no	—
96	C₁₉×#103	—	2	4	no	—
97	C₁₉×#103	—	2	4	no	—
98	C₁₉×#102	—	2	4	no	—
99	C₁₉×#102	—	2	4	no	—
100	C₁₉×C₂²⋊C₈	—	2	8	no	—
101	C₁₉×#95	—	2	4	no	—
102	C₂⁴×C₁₉	—	2	1	no	—
103	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
104	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
105	#41×C₁₉	—	2	8	no	—
106	#41×C₁₉	—	2	8	no	—
107	#41×C₁₉	—	4	4	no	—
108	#41×C₁₉	—	4	4	no	—
109	#41×C₁₉	—	4	4	no	—
110	#41×C₁₉	—	4	4	no	—
111	#41×C₁₉	—	4	4	no	—
112	#41×C₁₉	—	4	4	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	—	2	2	no	—
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	2	1	no	—
121	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
122	C₂×D₄×C₁₉	—	2	4	no	—
123	C₂×D₄×C₁₉	—	2	4	no	—
124	C₂×D₄×C₁₉	—	2	4	no	—
125	C₂×D₄×C₁₉	—	2	4	no	—
126	C₂×D₄×C₁₉	—	2	8	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	1	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	2	1	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	4	2	no	—
136	C₂×D₄×C₁₉	—	4	2	no	—
137	C₂×D₄×C₁₉	—	8	4	no	—
138	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
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	4	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	4	2	no	—
152	C₂²×C₄×C₁₉	—	4	2	no	—
153	C₂²×C₄×C₁₉	—	4	2	no	—
154	C₂²×C₄×C₁₉	—	8	2	no	—
155	C₂²×C₄×C₁₉	—	8	2	no	—
156	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₉	#41	1	2	yes	—
162	C₂²×C₄×C₁₉	#41	1	2	yes	—
163	C₂²×C₄×C₁₉	#41	1	2	yes	—
164	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
165	M₁₆×C₁₉	—	4	4	no	—
166	C₂×C₈×C₁₉	—	2	8	no	—
167	C₂×C₈×C₁₉	—	2	2	no	—
168	C₂×C₈×C₁₉	—	2	2	no	—
169	C₂×C₈×C₁₉	—	2	2	no	—
170	C₂×C₈×C₁₉	—	2	2	no	—
171	C₂×C₈×C₁₉	—	2	2	no	—
172	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
173	C₄⋊C₄×C₁₉	—	2	8	no	—
174	C₄⋊C₄×C₁₉	—	2	4	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	4	2	no	—
181	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
182	C₂²⋊C₄×C₁₉	—	2	8	no	—
183	C₂²⋊C₄×C₁₉	—	2	8	no	—
184	C₂²⋊C₄×C₁₉	—	4	2	no	—
185	C₂²⋊C₄×C₁₉	—	8	4	no	—
186	C₄²×C₁₉	—	4	2	no	—
187	#23488	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂³×C₁₉	—	2	2	no	—
189	C₂³×C₁₉	—	2	2	no	—
190	C₂³×C₁₉	—	2	2	no	—
191	C₂³×C₁₉	—	2	2	no	—
192	C₂³×C₁₉	—	2	2	no	—
193	C₂³×C₁₉	—	2	2	no	—
194	C₂³×C₁₉	—	2	4	no	—
195	C₂³×C₁₉	—	2	4	no	—
196	C₂³×C₁₉	—	4	1	no	—
197	C₂³×C₁₉	—	4	1	no	—
198	C₂³×C₁₉	—	4	2	no	—
199	C₂³×C₁₉	—	4	2	no	—
200	C₂³×C₁₉	#120	1	2	yes	—
201	C₂³×C₁₉	#121	1	2	yes	—
202	C₂³×C₁₉	#123	1	2	yes	—
203	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₁₉	—	2	2	no	—
205	Q₈×C₁₉	—	2	2	no	—
206	Q₈×C₁₉	—	4	1	no	—
207	Q₈×C₁₉	—	4	1	no	—
208	Q₈×C₁₉	—	4	4	no	—
209	D₄×C₁₉	—	2	2	no	—
210	D₄×C₁₉	—	2	2	no	—
211	D₄×C₁₉	—	4	8	no	—
212	D₄×C₁₉	—	4	8	no	—
213	D₄×C₁₉	—	4	1	no	—
214	D₄×C₁₉	—	4	1	no	—
215	D₄×C₁₉	—	4	4	no	—
216	D₄×C₁₉	—	8	8	no	—
217	C₂×C₄×C₁₉	—	2	4	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	4	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	4	8	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	4	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	8	4	no	—
236	C₂×C₄×C₁₉	—	8	4	no	—
237	C₂×C₄×C₁₉	#120	1	2	yes	—
238	C₂×C₄×C₁₉	#121	1	4	yes	—
239	C₂×C₄×C₁₉	#121	1	4	yes	—
240	C₂×C₄×C₁₉	#121	1	2	yes	—
241	C₂×C₄×C₁₉	#123	1	4	yes	—
242	C₂×C₄×C₁₉	#123	1	2	yes	—
243	C₂×C₄×C₁₉	#124	1	4	yes	—
244	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
250	C₈×C₁₉	—	2	4	no	—
251	C₈×C₁₉	—	4	2	no	—
252	C₂×#537	C₂×C₁₉	1	1	yes	characteristic
253	C₂²×#107	C₂×C₁₉	1	1	yes	characteristic, complemented
254	C₂×#417	C₂×C₁₉	1	1	yes	characteristic, complemented
255	C₂×#416	C₂×C₁₉	1	1	yes	characteristic, complemented
256	C₂×#408	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#2311	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#2036	C₂×C₁₉	1	4	yes	complemented
259	#2033	C₂×C₁₉	1	4	yes	complemented
260	#1736	C₂×C₁₉	1	1	yes	characteristic, complemented
261	C₂²×C₁₉	—	2	4	no	—
262	C₂²×C₁₉	—	2	2	no	—
263	C₂²×C₁₉	—	2	2	no	—
264	C₂²×C₁₉	—	2	4	no	—
265	C₂²×C₁₉	—	4	4	no	—
266	C₂²×C₁₉	—	4	2	no	—
267	C₂²×C₁₉	—	4	2	no	—
268	C₂²×C₁₉	—	4	2	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	—	4	2	no	—
271	C₂²×C₁₉	—	4	2	no	—
272	C₂²×C₁₉	—	4	4	no	—
273	C₂²×C₁₉	—	8	2	no	—
274	C₂²×C₁₉	—	8	2	no	—
275	C₂²×C₁₉	#394	1	4	yes	—
276	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
277	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
278	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
279	C₂²×C₁₉	#576	1	2	yes	—
280	C₂²×C₁₉	#578	1	2	yes	—
281	C₄×C₁₉	—	4	2	no	—
282	C₄×C₁₉	—	4	2	no	—
283	C₄×C₁₉	—	4	4	no	—
284	C₄×C₁₉	—	8	2	no	—
285	C₄×C₁₉	—	8	2	no	—
286	C₄×C₁₉	#394	1	4	yes	—
287	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
288	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
289	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
290	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
291	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
292	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
293	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
294	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
295	#537	—	2	4	no	—
296	#537	—	2	4	no	—
297	C₂×C₂²⋊Q₈	—	2	1	no	—
298	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
299	C₂×#121	—	2	1	no	—
300	C₂×#121	—	2	2	no	—
301	C₂×#121	C₂²×C₁₉	1	2	yes	—
302	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
303	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
304	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
305	C₂×#107	—	2	4	no	—
306	C₂×#107	C₂²×C₁₉	1	4	yes	—
307	#417	—	2	4	no	—
308	#416	—	2	4	no	—
309	C₂×#103	C₂²×C₁₉	1	2	yes	—
310	C₂×#103	C₂²×C₁₉	1	2	yes	—
311	C₂×#102	C₂²×C₁₉	1	2	yes	—
312	C₂×#102	C₂²×C₁₉	1	2	yes	—
313	#408	—	2	4	no	—
314	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
315	#391	—	2	1	no	—
316	#390	—	2	1	no	—
317	#386	—	2	2	no	—
318	#380	C₂²×C₁₉	1	4	yes	—
319	#340	C₂²×C₁₉	1	4	yes	—
320	C₂×C₁₉	—	2	4	no	—
321	C₂×C₁₉	—	8	2	no	—
322	C₂×C₁₉	—	8	2	no	—
323	C₂×C₁₉	C₂×#394	1	1	yes	characteristic
324	C₂×C₁₉	#3008	1	1	yes	characteristic
325	C₂×C₁₉	#3011	1	1	yes	characteristic
326	C₂×C₁₉	#3061	1	2	yes	—
327	C₂×C₁₉	#3098	1	2	yes	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	2	2	no	—
330	C₂×#41	—	2	2	no	—
331	C₂×#41	—	2	2	no	—
332	C₂×#41	—	2	2	no	—
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	2	2	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	—	2	2	no	—
337	C₂×#41	—	2	2	no	—
338	C₂×#41	—	2	2	no	—
339	C₂×#41	D₄×C₁₉	1	4	yes	—
340	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
341	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	—	2	2	no	—
344	C₂²×D₄	D₄×C₁₉	1	2	yes	—
345	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
346	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
347	C₂³×C₄	—	2	1	no	—
348	C₂³×C₄	—	2	1	no	—
349	C₂³×C₄	—	2	1	no	—
350	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
351	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
352	C₂×M₁₆	—	2	2	no	—
353	C₂×M₁₆	—	2	2	no	—
354	C₂×M₁₆	—	2	2	no	—
355	C₂²×C₈	—	2	2	no	—
356	C₂²×C₈	—	2	2	no	—
357	C₂²×C₈	D₄×C₁₉	1	4	yes	complemented
358	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
359	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
360	C₂²⋊Q₈	—	2	8	no	—
361	C₂²⋊Q₈	—	2	4	no	—
362	C₂²⋊Q₈	—	2	4	no	—
363	#121	—	2	16	no	—
364	#121	—	2	8	no	—
365	#121	—	2	4	no	—
366	#121	—	2	4	no	—
367	#117	—	2	2	no	—
368	#117	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	—	2	2	no	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	4	no	—
383	C₂×C₄²	—	2	1	no	—
384	#107	—	2	8	no	—
385	#103	—	2	4	no	—
386	#103	—	2	4	no	—
387	#102	—	2	4	no	—
388	#102	—	2	4	no	—
389	C₂²⋊C₈	—	2	8	no	—
390	#95	—	2	4	no	—
391	C₁₉	#23488	1	1	yes	characteristic, direct product factor, Sylow
392	C₂⁴	—	2	1	no	—
393	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
394	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
395	#41	—	2	8	no	—
396	#41	—	2	8	no	—
397	#41	—	4	4	no	—
398	#41	—	4	4	no	—
399	#41	—	4	4	no	—
400	#41	—	4	4	no	—
401	#41	—	4	4	no	—
402	#41	—	4	4	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	4	2	no	—
426	C₂×D₄	—	4	2	no	—
427	C₂×D₄	—	8	4	no	—
428	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	2	no	—
444	C₂²×C₄	—	8	2	no	—
445	C₂²×C₄	—	8	2	no	—
446	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
447	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
449	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
450	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
451	C₂²×C₄	#41×C₁₉	1	2	yes	—
452	C₂²×C₄	#41×C₁₉	1	2	yes	—
453	C₂²×C₄	#41×C₁₉	1	2	yes	—
454	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
455	M₁₆	—	4	4	no	—
456	C₂×C₈	—	2	8	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
463	C₄⋊C₄	—	2	8	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	4	2	no	—
471	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
472	C₂²⋊C₄	—	2	8	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	4	2	no	—
475	C₂²⋊C₄	—	8	4	no	—
476	C₄²	—	4	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	C₁₉×#120	1	2	yes	—
490	C₂³	C₁₉×#121	1	2	yes	—
491	C₂³	C₁₉×#123	1	2	yes	—
492	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
493	Q₈	—	2	2	no	—
494	Q₈	—	2	2	no	—
495	Q₈	—	4	4	no	—
496	Q₈	—	4	1	no	—
497	Q₈	—	4	1	no	—
498	D₄	—	2	2	no	—
499	D₄	—	2	2	no	—
500	D₄	—	4	8	no	—
501	D₄	—	4	8	no	—
502	D₄	—	4	4	no	—
503	D₄	—	4	1	no	—
504	D₄	—	4	1	no	—
505	D₄	—	8	8	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	4	no	—
514	C₂×C₄	—	4	8	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	8	4	no	—
525	C₂×C₄	—	8	4	no	—
526	C₂×C₄	C₁₉×#120	1	2	yes	—
527	C₂×C₄	C₁₉×#121	1	2	yes	—
528	C₂×C₄	C₁₉×#121	1	4	yes	—
529	C₂×C₄	C₁₉×#121	1	4	yes	—
530	C₂×C₄	C₁₉×#123	1	2	yes	—
531	C₂×C₄	C₁₉×#123	1	4	yes	—
532	C₂×C₄	C₁₉×#124	1	4	yes	—
533	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
536	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
537	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
538	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
539	C₈	—	2	4	no	—
540	C₈	—	4	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	4	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	8	2	no	—
554	C₂²	—	8	2	no	—
555	C₂²	C₁₉×#394	1	4	yes	—
556	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
557	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
558	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
559	C₂²	C₁₉×#576	1	2	yes	—
560	C₂²	C₁₉×#578	1	2	yes	—
561	C₄	—	4	4	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	2	no	—
564	C₄	—	8	2	no	—
565	C₄	—	8	2	no	—
566	C₄	C₁₉×#394	1	4	yes	—
567	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
568	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
569	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
570	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
571	C₂	—	2	4	no	—
572	C₂	—	8	2	no	—
573	C₂	—	8	2	no	—
574	C₂	C₂×C₁₉×#394	1	1	yes	characteristic
575	C₂	C₁₉×#3008	1	1	yes	characteristic
576	C₂	C₁₉×#3011	1	1	yes	characteristic
577	C₂	C₁₉×#3061	1	2	yes	—
578	C₂	C₁₉×#3098	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#537	C₂
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. C₂²×C₁₉×#107	C₂	semidirect
3. C₂×C₁₉×#417	C₂	semidirect
4. C₂×C₁₉×#416	C₂	semidirect
5. C₂×C₁₉×#408	C₂	semidirect
6. C₁₉×#2311	C₂	semidirect
7. C₁₉×#2036	C₂	semidirect
8. C₁₉×#2033	C₂	semidirect
9. C₁₉×#1736	C₂	semidirect
68. C₂²×C₈×C₁₉	D₄	semidirect
187. #23488	C₁₉	direct (N × H)
253. C₂²×#107	C₂×C₁₉	semidirect
254. C₂×#417	C₂×C₁₉	semidirect
255. C₂×#416	C₂×C₁₉	semidirect
256. C₂×#408	C₂×C₁₉	semidirect
257. #2311	C₂×C₁₉	semidirect
258. #2036	C₂×C₁₉	semidirect
259. #2033	C₂×C₁₉	semidirect
260. #1736	C₂×C₁₉	semidirect
357. C₂²×C₈	D₄×C₁₉	semidirect
391. C₁₉	#23488	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×#537	2
C₂²×C₁₉×#107	2
C₂×C₁₉×#417	2
C₂×C₁₉×#416	2
C₂×C₁₉×#408	2
C₁₉×#2311	2
C₁₉×#2036	2
C₁₉×#2033	2
C₁₉×#1736	2
#23488	19

Subgroups — C19×#23488 #18029447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23488 #18029447