Subgroups — D₄×C₁₉×#103 #18028374

Order 4864.

1530 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×#103	C₂	1	2	yes	maximal, complemented
4	D₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1981	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1956	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1892	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1872	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1787	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₉	C₂²	1	2	yes	—
13	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
14	D₄×Q₈×C₁₉	—	2	4	no	—
15	D₄×Q₈×C₁₉	C₄	1	8	yes	complemented
16	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
19	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	—	2	1	no	—
22	C₂×C₄×D₄×C₁₉	—	2	1	no	—
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
25	C₈×D₄×C₁₉	—	2	4	no	—
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	—	2	8	no	—
28	C₂×C₁₉×#103	C₂²	1	2	yes	—
29	C₂×C₁₉×#103	C₂²	1	2	yes	—
30	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#103	C₂²	1	2	yes	—
32	C₂×C₁₉×#103	C₂²	1	2	yes	—
33	C₂×C₁₉×#103	C₂²	1	2	yes	—
34	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×#389	—	2	1	no	—
38	C₁₉×#385	—	2	2	no	—
39	C₁₉×#384	C₂²	1	1	yes	characteristic
40	C₁₉×#380	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
42	C₁₉×#340	C₂²	1	1	yes	characteristic
43	C₁₉×#340	C₂²	1	2	yes	—
44	C₁₉×#340	C₂²	1	1	yes	characteristic
45	C₂²×Q₈×C₁₉	—	2	2	no	—
46	C₂²×Q₈×C₁₉	—	2	4	no	—
47	C₂²×Q₈×C₁₉	—	2	4	no	—
48	C₂²×Q₈×C₁₉	—	2	4	no	—
49	C₂²×Q₈×C₁₉	—	4	2	no	—
50	C₂²×Q₈×C₁₉	—	4	2	no	—
51	C₂²×Q₈×C₁₉	C₂×C₄	1	8	yes	complemented
52	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
53	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	—	2	2	no	—
56	C₂³×C₄×C₁₉	—	2	2	no	—
57	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₉	—	2	4	no	—
59	C₂²×C₈×C₁₉	—	2	4	no	—
60	C₂²×C₈×C₁₉	—	4	2	no	—
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₁₉×C₄⋊Q₈	—	2	8	no	—
65	C₁₉×C₄⋊Q₈	—	2	2	no	—
66	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
67	C₁₉×C₂²⋊Q₈	—	2	4	no	—
68	C₁₉×C₂²⋊Q₈	—	2	16	no	—
69	C₁₉×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
70	C₄×Q₈×C₁₉	—	2	2	no	—
71	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	complemented
72	C₄×D₄×C₁₉	—	2	8	no	—
73	C₄×D₄×C₁₉	—	4	4	no	—
74	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
75	C₄×D₄×C₁₉	D₄	1	4	yes	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
85	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
93	C₂×C₄²×C₁₉	—	2	1	no	—
94	C₂×C₄²×C₁₉	—	2	1	no	—
95	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
96	C₁₉×C₄⋊C₈	—	2	2	no	—
97	C₁₉×#103	—	2	4	no	—
98	C₁₉×#103	—	2	2	no	—
99	C₁₉×#103	—	2	4	no	—
100	C₁₉×#103	—	2	4	no	—
101	C₁₉×#103	—	4	2	no	—
102	C₁₉×#103	—	4	2	no	—
103	C₁₉×#103	D₄	1	4	yes	direct product factor
104	C₁₉×C₂²⋊C₈	—	2	4	no	—
105	C₄×C₈×C₁₉	—	2	2	no	—
106	C₁₉×#95	—	2	1	no	—
107	C₁₉×#95	—	2	2	no	—
108	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₁₉	—	2	8	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	16	no	—
115	C₂×Q₈×C₁₉	—	2	2	no	—
116	C₂×Q₈×C₁₉	—	2	2	no	—
117	C₂×Q₈×C₁₉	—	2	2	no	—
118	C₂×Q₈×C₁₉	—	2	2	no	—
119	C₂×Q₈×C₁₉	—	4	4	no	—
120	C₂×Q₈×C₁₉	—	4	4	no	—
121	C₂×Q₈×C₁₉	—	4	8	no	—
122	C₂×Q₈×C₁₉	—	4	8	no	—
123	C₂×Q₈×C₁₉	—	4	8	no	—
124	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
125	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
126	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
127	C₂×Q₈×C₁₉	#41	1	2	yes	—
128	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
129	C₂×D₄×C₁₉	SD₁₆	1	4	yes	—
130	C₂×D₄×C₁₉	Q₁₆	1	4	yes	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	8	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	4	4	no	—
143	C₂²×C₄×C₁₉	—	4	4	no	—
144	C₂²×C₄×C₁₉	—	4	4	no	—
145	C₂²×C₄×C₁₉	—	4	4	no	—
146	C₂²×C₄×C₁₉	—	8	2	no	—
147	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
153	C₂×C₈×C₁₉	—	2	1	no	—
154	C₂×C₈×C₁₉	—	2	1	no	—
155	C₂×C₈×C₁₉	—	2	2	no	—
156	C₂×C₈×C₁₉	—	2	2	no	—
157	C₂×C₈×C₁₉	—	2	1	no	—
158	C₂×C₈×C₁₉	—	2	1	no	—
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₂×C₈×C₁₉	—	4	8	no	—
162	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₁₉	—	2	4	no	—
164	C₄⋊C₄×C₁₉	—	2	4	no	—
165	C₄⋊C₄×C₁₉	—	2	4	no	—
166	C₄⋊C₄×C₁₉	—	2	8	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	4	4	no	—
174	C₄⋊C₄×C₁₉	—	4	2	no	—
175	C₄⋊C₄×C₁₉	—	8	1	no	—
176	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
177	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
178	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
179	C₂²⋊C₄×C₁₉	—	2	8	no	—
180	C₂²⋊C₄×C₁₉	—	4	4	no	—
181	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
182	C₄²×C₁₉	—	2	4	no	—
183	C₄²×C₁₉	—	4	2	no	—
184	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
185	C₄²×C₁₉	C₂×D₄	1	2	yes	—
186	D₄×#103	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂³×C₁₉	—	2	2	no	—
188	C₂³×C₁₉	—	2	2	no	—
189	C₂³×C₁₉	—	2	2	no	—
190	C₂³×C₁₉	—	2	2	no	—
191	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
192	C₂³×C₁₉	C₂×SD₁₆	1	4	yes	—
193	C₂³×C₁₉	C₂×Q₁₆	1	4	yes	—
194	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₁₉	—	2	2	no	—
196	Q₈×C₁₉	—	2	2	no	—
197	Q₈×C₁₉	—	2	2	no	—
198	Q₈×C₁₉	—	2	4	no	—
199	Q₈×C₁₉	—	2	4	no	—
200	Q₈×C₁₉	—	4	16	no	—
201	Q₈×C₁₉	—	4	2	no	—
202	Q₈×C₁₉	—	4	2	no	—
203	Q₈×C₁₉	C₄×D₄	1	4	yes	complemented
204	D₄×C₁₉	#103	1	16	yes	direct product factor
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	2	4	no	—
214	C₂×C₄×C₁₉	—	2	4	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	4	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	4	16	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	8	8	no	—
233	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
234	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
235	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
236	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
237	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
238	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
242	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
243	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
244	C₈×C₁₉	—	2	2	no	—
245	C₈×C₁₉	—	4	2	no	—
246	C₈×C₁₉	—	4	1	no	—
247	C₂×D₄×Q₈	C₂×C₁₉	1	1	yes	characteristic
248	C₂×C₈×D₄	C₂×C₁₉	1	1	yes	characteristic
249	C₂²×#103	C₂×C₁₉	1	2	yes	complemented
250	D₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
251	#1981	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#1956	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#1892	C₂×C₁₉	1	2	yes	complemented
254	#1872	C₂×C₁₉	1	2	yes	complemented
255	#1803	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1787	C₂×C₁₉	1	2	yes	complemented
257	C₄×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
258	C₂²×C₁₉	—	2	4	no	—
259	C₂²×C₁₉	—	2	4	no	—
260	C₂²×C₁₉	—	2	4	no	—
261	C₂²×C₁₉	—	2	4	no	—
262	C₂²×C₁₉	—	2	4	no	—
263	C₂²×C₁₉	—	2	4	no	—
264	C₂²×C₁₉	C₂×#103	1	8	yes	complemented
265	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
266	C₂²×C₁₉	D₄²	1	1	yes	characteristic
267	C₂²×C₁₉	#546	1	1	yes	characteristic
268	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
269	C₂²×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
270	C₂²×C₁₉	#577	1	1	yes	characteristic
271	C₂²×C₁₉	#578	1	1	yes	characteristic
272	C₄×C₁₉	—	2	4	no	—
273	C₄×C₁₉	—	2	4	no	—
274	C₄×C₁₉	—	2	2	no	—
275	C₄×C₁₉	—	4	4	no	—
276	C₄×C₁₉	—	4	2	no	—
277	C₄×C₁₉	—	4	2	no	—
278	C₄×C₁₉	—	8	2	no	—
279	C₄×C₁₉	—	8	1	no	—
280	C₄×C₁₉	C₂×#103	1	4	yes	complemented
281	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
282	C₄×C₁₉	#518	1	1	yes	characteristic
283	C₄×C₁₉	D₄²	1	1	yes	characteristic
284	C₄×C₁₉	#546	1	1	yes	characteristic
285	C₂³×Q₈	C₂²×C₁₉	1	2	yes	—
286	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
287	D₄×Q₈	—	2	4	no	—
288	D₄×Q₈	C₄×C₁₉	1	8	yes	complemented
289	C₂×C₄⋊Q₈	—	2	1	no	—
290	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
291	C₂×C₂²⋊Q₈	—	2	2	no	—
292	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
293	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×C₄×D₄	—	2	1	no	—
295	C₂×C₄×D₄	—	2	1	no	—
296	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
297	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
298	C₈×D₄	—	2	4	no	—
299	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
300	C₂×#103	—	2	8	no	—
301	C₂×#103	C₂²×C₁₉	1	2	yes	—
302	C₂×#103	C₂²×C₁₉	1	2	yes	—
303	C₂×#103	C₂²×C₁₉	1	2	yes	—
304	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
305	C₂×#103	C₂²×C₁₉	1	2	yes	—
306	C₂×#103	C₂²×C₁₉	1	2	yes	—
307	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
308	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
309	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
310	#389	—	2	1	no	—
311	#385	—	2	2	no	—
312	#384	C₂²×C₁₉	1	1	yes	characteristic
313	#380	C₂²×C₁₉	1	2	yes	—
314	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
315	#340	C₂²×C₁₉	1	2	yes	—
316	#340	C₂²×C₁₉	1	1	yes	characteristic
317	#340	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×C₁₉	—	2	8	no	—
319	C₂×C₁₉	D₄×C₂²⋊C₄	1	1	yes	characteristic
320	C₂×C₁₉	C₂²×#103	1	1	yes	characteristic
321	C₂×C₁₉	#2898	1	1	yes	characteristic
322	C₂×C₁₉	D₄×SD₁₆	1	1	yes	characteristic
323	C₂×C₁₉	D₄×Q₁₆	1	1	yes	characteristic
324	C₂×C₁₉	#3298	1	1	yes	characteristic
325	C₂×C₁₉	#3299	1	1	yes	characteristic
326	C₂²×Q₈	—	2	2	no	—
327	C₂²×Q₈	—	2	4	no	—
328	C₂²×Q₈	—	2	4	no	—
329	C₂²×Q₈	—	2	4	no	—
330	C₂²×Q₈	—	4	2	no	—
331	C₂²×Q₈	—	4	2	no	—
332	C₂²×Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
333	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
334	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
335	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
336	C₂³×C₄	—	2	2	no	—
337	C₂³×C₄	—	2	2	no	—
338	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
339	C₂²×C₈	—	2	4	no	—
340	C₂²×C₈	—	2	4	no	—
341	C₂²×C₈	—	4	2	no	—
342	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
343	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
345	C₄⋊Q₈	—	2	8	no	—
346	C₄⋊Q₈	—	2	2	no	—
347	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
348	C₂²⋊Q₈	—	2	4	no	—
349	C₂²⋊Q₈	—	2	16	no	—
350	C₂²⋊Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
351	C₄×Q₈	—	2	2	no	—
352	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
353	C₄×D₄	—	2	8	no	—
354	C₄×D₄	—	4	4	no	—
355	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
356	C₄×D₄	D₄×C₁₉	1	4	yes	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	—	2	4	no	—
362	C₂×C₄⋊C₄	—	2	2	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	4	2	no	—
366	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	—	2	2	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
377	C₄⋊C₈	—	2	2	no	—
378	#103	—	2	4	no	—
379	#103	—	2	2	no	—
380	#103	—	2	4	no	—
381	#103	—	2	4	no	—
382	#103	—	4	2	no	—
383	#103	—	4	2	no	—
384	#103	D₄×C₁₉	1	4	yes	direct product factor
385	C₂²⋊C₈	—	2	4	no	—
386	C₄×C₈	—	2	2	no	—
387	#95	—	2	1	no	—
388	#95	—	2	2	no	—
389	C₁₉	D₄×#103	1	1	yes	characteristic, direct product factor, Sylow
390	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
391	C₂×Q₈	—	2	8	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	2	16	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	4	4	no	—
402	C₂×Q₈	—	4	4	no	—
403	C₂×Q₈	—	4	8	no	—
404	C₂×Q₈	—	4	8	no	—
405	C₂×Q₈	—	4	8	no	—
406	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
407	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
408	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
409	C₂×Q₈	#41×C₁₉	1	2	yes	—
410	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
411	C₂×D₄	SD₁₆×C₁₉	1	4	yes	—
412	C₂×D₄	Q₁₆×C₁₉	1	4	yes	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	8	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	4	4	no	—
425	C₂²×C₄	—	4	4	no	—
426	C₂²×C₄	—	4	4	no	—
427	C₂²×C₄	—	4	4	no	—
428	C₂²×C₄	—	8	2	no	—
429	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
430	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
432	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
433	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
434	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	4	8	no	—
444	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	8	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	4	4	no	—
456	C₄⋊C₄	—	4	2	no	—
457	C₄⋊C₄	—	8	1	no	—
458	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
459	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
460	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	4	4	no	—
463	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
464	C₄²	—	2	4	no	—
465	C₄²	—	4	2	no	—
466	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
467	C₄²	C₂×D₄×C₁₉	1	2	yes	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	2	no	—
472	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
473	C₂³	C₂×SD₁₆×C₁₉	1	4	yes	—
474	C₂³	C₂×Q₁₆×C₁₉	1	4	yes	—
475	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
476	Q₈	—	2	2	no	—
477	Q₈	—	2	2	no	—
478	Q₈	—	2	2	no	—
479	Q₈	—	2	4	no	—
480	Q₈	—	2	4	no	—
481	Q₈	—	4	16	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	4	2	no	—
484	Q₈	C₄×D₄×C₁₉	1	4	yes	complemented
485	D₄	C₁₉×#103	1	16	yes	direct product factor
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	4	16	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	8	8	no	—
514	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
515	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
516	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
517	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
518	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
519	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
522	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
523	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
525	C₈	—	2	2	no	—
526	C₈	—	4	2	no	—
527	C₈	—	4	1	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	2	4	no	—
530	C₂²	—	2	4	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	2	4	no	—
534	C₂²	C₂×C₁₉×#103	1	8	yes	complemented
535	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
536	C₂²	D₄²×C₁₉	1	1	yes	characteristic
537	C₂²	C₁₉×#546	1	1	yes	characteristic
538	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
539	C₂²	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
540	C₂²	C₁₉×#577	1	1	yes	characteristic
541	C₂²	C₁₉×#578	1	1	yes	characteristic
542	C₄	—	2	4	no	—
543	C₄	—	2	4	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	4	no	—
547	C₄	—	4	2	no	—
548	C₄	—	8	2	no	—
549	C₄	—	8	1	no	—
550	C₄	C₂×C₁₉×#103	1	4	yes	complemented
551	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
552	C₄	C₁₉×#518	1	1	yes	characteristic
553	C₄	D₄²×C₁₉	1	1	yes	characteristic
554	C₄	C₁₉×#546	1	1	yes	characteristic
555	C₂	—	2	8	no	—
556	C₂	D₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
557	C₂	C₂²×C₁₉×#103	1	1	yes	characteristic
558	C₂	C₁₉×#2898	1	1	yes	characteristic
559	C₂	D₄×SD₁₆×C₁₉	1	1	yes	characteristic
560	C₂	D₄×Q₁₆×C₁₉	1	1	yes	characteristic
561	C₂	C₁₉×#3298	1	1	yes	characteristic
562	C₂	C₁₉×#3299	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂²×C₁₉×#103	C₂	semidirect
5. C₁₉×#1981	C₂	semidirect
6. C₁₉×#1956	C₂	semidirect
7. C₁₉×#1892	C₂	semidirect
8. C₁₉×#1872	C₂	semidirect
9. C₁₉×#1803	C₂	semidirect
10. C₁₉×#1787	C₂	semidirect
11. C₄×C₁₉×#103	C₂	semidirect
15. D₄×Q₈×C₁₉	C₄	semidirect
51. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
66. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
69. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
71. C₄×Q₈×C₁₉	C₂×C₄	semidirect
103. C₁₉×#103	D₄	direct (N × H)
186. D₄×#103	C₁₉	direct (N × H)
203. Q₈×C₁₉	C₄×D₄	semidirect
204. D₄×C₁₉	#103	direct (N × H)
249. C₂²×#103	C₂×C₁₉	semidirect
251. #1981	C₂×C₁₉	semidirect
252. #1956	C₂×C₁₉	semidirect
253. #1892	C₂×C₁₉	semidirect
254. #1872	C₂×C₁₉	semidirect
255. #1803	C₂×C₁₉	semidirect
256. #1787	C₂×C₁₉	semidirect
257. C₄×#103	C₂×C₁₉	semidirect
264. C₂²×C₁₉	C₂×#103	semidirect
280. C₄×C₁₉	C₂×#103	semidirect
288. D₄×Q₈	C₄×C₁₉	semidirect
332. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
347. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
350. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
352. C₄×Q₈	C₂×C₄×C₁₉	semidirect
384. #103	D₄×C₁₉	direct (N × H)
389. C₁₉	D₄×#103	direct (N × H)
484. Q₈	C₄×D₄×C₁₉	semidirect
485. D₄	C₁₉×#103	direct (N × H)
534. C₂²	C₂×C₁₉×#103	semidirect
550. C₄	C₂×C₁₉×#103	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₄×Q₈×C₁₉	2
C₂×C₈×D₄×C₁₉	2
C₂²×C₁₉×#103	2
D₄×C₄⋊C₄×C₁₉	2
C₁₉×#1981	2
C₁₉×#1956	2
C₁₉×#1892	2
C₁₉×#1872	2
C₁₉×#1803	2
C₁₉×#1787	2
C₄×C₁₉×#103	2
D₄×#103	19

Subgroups — D4×C19×#103 #18028374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₁₉×#103 #18028374