Subgroups — C₂×C₁₉×#1793 #18026573

Order 4864.

3682 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#104	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#417	C₂	1	2	yes	maximal, complemented
4	C₂²×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1793	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₁₉×2₋¹⁺⁴	—	2	8	no	—
8	C₂×C₁₉×2₋¹⁺⁴	—	2	4	no	—
9	C₂×C₁₉×2₋¹⁺⁴	—	2	4	no	—
10	C₂×C₁₉×2₋¹⁺⁴	—	2	2	no	—
11	C₂×C₁₉×2₋¹⁺⁴	C₄	1	8	yes	complemented
12	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	4	yes	—
13	C₂²×#41×C₁₉	—	2	2	no	—
14	C₂²×#41×C₁₉	—	2	2	no	—
15	C₂²×#41×C₁₉	C₂²	1	2	yes	—
16	C₂³×Q₈×C₁₉	—	2	2	no	—
17	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#104	—	2	8	no	—
22	C₂×C₁₉×#104	C₂²	1	8	yes	complemented
23	C₁₉×#417	—	2	4	no	—
24	C₁₉×#417	C₂²	1	8	yes	complemented
25	C₂×C₁₉×#103	—	2	2	no	—
26	C₂×C₁₉×#102	—	2	2	no	—
27	C₂×C₁₉×#101	—	2	4	no	—
28	C₂×C₁₉×#101	C₂²	1	4	yes	complemented
29	C₁₉×#391	—	2	2	no	—
30	C₁₉×#391	C₂²	1	4	yes	complemented
31	C₂×C₁₉×#95	—	2	2	no	—
32	C₁₉×2₋¹⁺⁴	—	2	32	no	—
33	C₁₉×2₋¹⁺⁴	—	2	16	no	—
34	C₁₉×2₋¹⁺⁴	—	2	32	no	—
35	C₁₉×2₋¹⁺⁴	—	2	16	no	—
36	C₁₉×2₋¹⁺⁴	—	2	16	no	—
37	C₁₉×2₋¹⁺⁴	—	2	8	no	—
38	C₁₉×2₋¹⁺⁴	C₂×C₄	1	16	yes	complemented
39	C₂×#41×C₁₉	—	2	8	no	—
40	C₂×#41×C₁₉	—	2	16	no	—
41	C₂×#41×C₁₉	—	2	8	no	—
42	C₂×#41×C₁₉	—	2	16	no	—
43	C₂×#41×C₁₉	—	2	16	no	—
44	C₂×#41×C₁₉	—	2	8	no	—
45	C₂×#41×C₁₉	—	2	16	no	—
46	C₂×#41×C₁₉	—	2	8	no	—
47	C₂×#41×C₁₉	—	2	4	no	—
48	C₂×#41×C₁₉	—	2	2	no	—
49	C₂×#41×C₁₉	—	2	4	no	—
50	C₂×#41×C₁₉	—	2	2	no	—
51	C₂×#41×C₁₉	C₂×C₄	1	8	yes	—
52	C₂×#41×C₁₉	D₄	1	8	yes	—
53	C₂×#41×C₁₉	D₄	1	4	yes	—
54	C₂×#41×C₁₉	C₂³	1	4	yes	—
55	C₂²×Q₈×C₁₉	—	2	2	no	—
56	C₂²×Q₈×C₁₉	—	2	8	no	—
57	C₂²×Q₈×C₁₉	—	2	16	no	—
58	C₂²×Q₈×C₁₉	—	2	16	no	—
59	C₂²×Q₈×C₁₉	—	2	8	no	—
60	C₂²×Q₈×C₁₉	—	2	2	no	—
61	C₂²×Q₈×C₁₉	—	2	4	no	—
62	C₂²×Q₈×C₁₉	—	2	2	no	—
63	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
64	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
65	C₂²×Q₈×C₁₉	D₄	1	4	yes	—
66	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
67	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₉	—	2	2	no	—
69	C₂²×D₄×C₁₉	—	2	2	no	—
70	C₂²×D₄×C₁₉	D₄	1	2	yes	—
71	C₂³×C₄×C₁₉	—	2	4	no	—
72	C₂³×C₄×C₁₉	—	2	2	no	—
73	C₂³×C₄×C₁₉	—	2	1	no	—
74	C₂³×C₄×C₁₉	—	2	1	no	—
75	C₂³×C₄×C₁₉	D₄	1	2	yes	—
76	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×M₁₆×C₁₉	—	2	2	no	—
78	C₂×M₁₆×C₁₉	—	2	4	no	—
79	C₂×M₁₆×C₁₉	—	2	4	no	—
80	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
81	C₂²×C₈×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	1	no	—
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₉	—	2	4	no	—
87	C₂×C₄²×C₁₉	—	2	1	no	—
88	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
89	C₁₉×#104	—	2	16	no	—
90	C₁₉×#103	—	2	8	no	—
91	C₁₉×#102	—	2	8	no	—
92	C₁₉×#101	—	2	8	no	—
93	C₁₉×#95	—	2	8	no	—
94	C₂⁴×C₁₉	—	2	2	no	—
95	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
96	#41×C₁₉	—	2	32	no	—
97	#41×C₁₉	—	2	64	no	—
98	#41×C₁₉	—	2	32	no	—
99	#41×C₁₉	—	2	64	no	—
100	#41×C₁₉	—	2	32	no	—
101	#41×C₁₉	—	2	32	no	—
102	#41×C₁₉	—	2	8	no	—
103	#41×C₁₉	—	2	8	no	—
104	#41×C₁₉	—	2	8	no	—
105	#41×C₁₉	—	2	8	no	—
106	#41×C₁₉	—	2	8	no	—
107	#41×C₁₉	—	2	4	no	—
108	#41×C₁₉	—	2	4	no	—
109	#41×C₁₉	C₂²⋊C₄	1	16	yes	—
110	#41×C₁₉	C₂²×C₄	1	8	yes	—
111	#41×C₁₉	C₂×D₄	1	8	yes	—
112	C₂×Q₈×C₁₉	—	2	8	no	—
113	C₂×Q₈×C₁₉	—	2	16	no	—
114	C₂×Q₈×C₁₉	—	2	32	no	—
115	C₂×Q₈×C₁₉	—	2	64	no	—
116	C₂×Q₈×C₁₉	—	2	32	no	—
117	C₂×Q₈×C₁₉	—	2	8	no	—
118	C₂×Q₈×C₁₉	—	2	8	no	—
119	C₂×Q₈×C₁₉	—	2	2	no	—
120	C₂×Q₈×C₁₉	—	2	4	no	—
121	C₂×Q₈×C₁₉	—	2	4	no	—
122	C₂×Q₈×C₁₉	—	2	8	no	—
123	C₂×Q₈×C₁₉	—	2	4	no	—
124	C₂×Q₈×C₁₉	—	2	8	no	—
125	C₂×Q₈×C₁₉	—	2	4	no	—
126	C₂×Q₈×C₁₉	—	2	4	no	—
127	C₂×Q₈×C₁₉	C₂²⋊C₄	1	8	yes	—
128	C₂×Q₈×C₁₉	C₂²⋊C₄	1	8	yes	—
129	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
130	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
131	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
132	C₂×D₄×C₁₉	—	2	8	no	—
133	C₂×D₄×C₁₉	—	2	16	no	—
134	C₂×D₄×C₁₉	—	2	8	no	—
135	C₂×D₄×C₁₉	—	2	4	no	—
136	C₂×D₄×C₁₉	—	2	8	no	—
137	C₂×D₄×C₁₉	—	2	4	no	—
138	C₂×D₄×C₁₉	—	2	4	no	—
139	C₂×D₄×C₁₉	—	2	2	no	—
140	C₂×D₄×C₁₉	C₂²⋊C₄	1	8	yes	—
141	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₁₉	—	2	16	no	—
143	C₂²×C₄×C₁₉	—	2	32	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	4	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	8	no	—
149	C₂²×C₄×C₁₉	—	2	4	no	—
150	C₂²×C₄×C₁₉	—	2	8	no	—
151	C₂²×C₄×C₁₉	—	2	4	no	—
152	C₂²×C₄×C₁₉	—	2	4	no	—
153	C₂²×C₄×C₁₉	—	2	2	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	4	2	no	—
156	C₂²×C₄×C₁₉	—	4	2	no	—
157	C₂²×C₄×C₁₉	—	4	4	no	—
158	C₂²×C₄×C₁₉	—	4	1	no	—
159	C₂²×C₄×C₁₉	—	4	1	no	—
160	C₂²×C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
161	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
162	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
165	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
169	M₁₆×C₁₉	—	2	4	no	—
170	M₁₆×C₁₉	—	2	4	no	—
171	M₁₆×C₁₉	—	4	4	no	—
172	C₂×C₈×C₁₉	—	2	4	no	—
173	C₂×C₈×C₁₉	—	4	4	no	—
174	C₄⋊C₄×C₁₉	—	2	4	no	—
175	C₄⋊C₄×C₁₉	—	4	2	no	—
176	C₄²×C₁₉	—	2	4	no	—
177	C₄²×C₁₉	—	4	2	no	—
178	C₂×#1793	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂³×C₁₉	—	2	2	no	—
180	C₂³×C₁₉	—	2	2	no	—
181	C₂³×C₁₉	—	2	4	no	—
182	C₂³×C₁₉	—	2	8	no	—
183	C₂³×C₁₉	—	4	4	no	—
184	C₂³×C₁₉	—	4	4	no	—
185	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂³×C₁₉	#120	1	2	yes	—
187	C₂³×C₁₉	#120	1	1	yes	characteristic
188	C₂³×C₁₉	#120	1	1	yes	characteristic
189	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₁₉	—	2	32	no	—
191	Q₈×C₁₉	—	2	8	no	—
192	Q₈×C₁₉	—	2	4	no	—
193	Q₈×C₁₉	—	2	8	no	—
194	Q₈×C₁₉	—	2	8	no	—
195	Q₈×C₁₉	—	2	16	no	—
196	Q₈×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
197	D₄×C₁₉	—	2	32	no	—
198	D₄×C₁₉	—	2	8	no	—
199	D₄×C₁₉	—	2	8	no	—
200	D₄×C₁₉	—	2	16	no	—
201	D₄×C₁₉	—	2	4	no	—
202	D₄×C₁₉	—	2	8	no	—
203	D₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
204	C₂×C₄×C₁₉	—	2	64	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	2	4	no	—
207	C₂×C₄×C₁₉	—	2	4	no	—
208	C₂×C₄×C₁₉	—	2	8	no	—
209	C₂×C₄×C₁₉	—	2	8	no	—
210	C₂×C₄×C₁₉	—	2	8	no	—
211	C₂×C₄×C₁₉	—	2	8	no	—
212	C₂×C₄×C₁₉	—	2	8	no	—
213	C₂×C₄×C₁₉	—	2	16	no	—
214	C₂×C₄×C₁₉	—	2	4	no	—
215	C₂×C₄×C₁₉	—	4	8	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	4	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	8	2	no	—
221	C₂×C₄×C₁₉	—	8	2	no	—
222	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
223	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
224	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
225	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
226	C₂×C₄×C₁₉	#120	1	4	yes	—
227	C₂×C₄×C₁₉	#120	1	4	yes	—
228	C₂×C₄×C₁₉	#120	1	2	yes	—
229	C₂×C₄×C₁₉	#120	1	2	yes	—
230	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
234	C₈×C₁₉	—	4	4	no	—
235	C₂²×2₋¹⁺⁴	C₂×C₁₉	1	1	yes	characteristic
236	C₂²×#104	C₂×C₁₉	1	2	yes	complemented
237	C₂×#417	C₂×C₁₉	1	2	yes	complemented
238	C₂²×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
239	C₂×#391	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#1793	C₂×C₁₉	1	8	yes	direct product factor
241	C₂²×C₁₉	—	2	4	no	—
242	C₂²×C₁₉	—	2	4	no	—
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	2	1	no	—
245	C₂²×C₁₉	—	2	1	no	—
246	C₂²×C₁₉	—	2	1	no	—
247	C₂²×C₁₉	—	2	8	no	—
248	C₂²×C₁₉	—	4	16	no	—
249	C₂²×C₁₉	—	4	4	no	—
250	C₂²×C₁₉	—	4	4	no	—
251	C₂²×C₁₉	#379	1	2	yes	—
252	C₂²×C₁₉	#379	1	2	yes	—
253	C₂²×C₁₉	#454	1	2	yes	—
254	C₂²×C₁₉	#456	1	2	yes	—
255	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
257	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
258	C₄×C₁₉	—	2	8	no	—
259	C₄×C₁₉	—	2	8	no	—
260	C₄×C₁₉	—	4	4	no	—
261	C₄×C₁₉	—	8	2	no	—
262	C₄×C₁₉	#379	1	4	yes	—
263	C₄×C₁₉	C₂²×C₂²⋊C₄	1	2	yes	—
264	C₄×C₁₉	C₂×#120	1	2	yes	—
265	C₂×2₋¹⁺⁴	—	2	8	no	—
266	C₂×2₋¹⁺⁴	—	2	4	no	—
267	C₂×2₋¹⁺⁴	—	2	4	no	—
268	C₂×2₋¹⁺⁴	—	2	2	no	—
269	C₂×2₋¹⁺⁴	C₄×C₁₉	1	8	yes	complemented
270	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	4	yes	—
271	C₂²×#41	—	2	2	no	—
272	C₂²×#41	—	2	2	no	—
273	C₂²×#41	C₂²×C₁₉	1	2	yes	—
274	C₂³×Q₈	—	2	2	no	—
275	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
276	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
277	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
278	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
279	C₂×#104	—	2	8	no	—
280	C₂×#104	C₂²×C₁₉	1	8	yes	complemented
281	#417	—	2	4	no	—
282	#417	C₂²×C₁₉	1	8	yes	complemented
283	C₂×#103	—	2	2	no	—
284	C₂×#102	—	2	2	no	—
285	C₂×#101	—	2	4	no	—
286	C₂×#101	C₂²×C₁₉	1	4	yes	complemented
287	#391	—	2	2	no	—
288	#391	C₂²×C₁₉	1	4	yes	complemented
289	C₂×#95	—	2	2	no	—
290	C₂×C₁₉	—	2	1	no	—
291	C₂×C₁₉	—	2	1	no	—
292	C₂×C₁₉	—	2	2	no	—
293	C₂×C₁₉	—	4	8	no	—
294	C₂×C₁₉	#1793	1	4	yes	direct product factor
295	C₂×C₁₉	C₂×#379	1	1	yes	characteristic
296	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
297	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
298	2₋¹⁺⁴	—	2	16	no	—
299	2₋¹⁺⁴	—	2	32	no	—
300	2₋¹⁺⁴	—	2	32	no	—
301	2₋¹⁺⁴	—	2	16	no	—
302	2₋¹⁺⁴	—	2	16	no	—
303	2₋¹⁺⁴	—	2	8	no	—
304	2₋¹⁺⁴	C₂×C₄×C₁₉	1	16	yes	complemented
305	C₂×#41	—	2	16	no	—
306	C₂×#41	—	2	8	no	—
307	C₂×#41	—	2	16	no	—
308	C₂×#41	—	2	8	no	—
309	C₂×#41	—	2	16	no	—
310	C₂×#41	—	2	8	no	—
311	C₂×#41	—	2	16	no	—
312	C₂×#41	—	2	8	no	—
313	C₂×#41	—	2	4	no	—
314	C₂×#41	—	2	2	no	—
315	C₂×#41	—	2	4	no	—
316	C₂×#41	—	2	2	no	—
317	C₂×#41	C₂×C₄×C₁₉	1	8	yes	—
318	C₂×#41	D₄×C₁₉	1	8	yes	—
319	C₂×#41	D₄×C₁₉	1	4	yes	—
320	C₂×#41	C₂³×C₁₉	1	4	yes	—
321	C₂²×Q₈	—	2	2	no	—
322	C₂²×Q₈	—	2	16	no	—
323	C₂²×Q₈	—	2	8	no	—
324	C₂²×Q₈	—	2	16	no	—
325	C₂²×Q₈	—	2	8	no	—
326	C₂²×Q₈	—	2	2	no	—
327	C₂²×Q₈	—	2	4	no	—
328	C₂²×Q₈	—	2	2	no	—
329	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
330	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
331	C₂²×Q₈	D₄×C₁₉	1	4	yes	—
332	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
333	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
334	C₂²×D₄	—	2	2	no	—
335	C₂²×D₄	—	2	2	no	—
336	C₂²×D₄	D₄×C₁₉	1	2	yes	—
337	C₂³×C₄	—	2	4	no	—
338	C₂³×C₄	—	2	2	no	—
339	C₂³×C₄	—	2	1	no	—
340	C₂³×C₄	—	2	1	no	—
341	C₂³×C₄	D₄×C₁₉	1	2	yes	—
342	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
343	C₂×M₁₆	—	2	2	no	—
344	C₂×M₁₆	—	2	4	no	—
345	C₂×M₁₆	—	2	4	no	—
346	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
347	C₂²×C₈	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
352	C₂×C₄²	—	2	4	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
355	#104	—	2	16	no	—
356	#103	—	2	8	no	—
357	#102	—	2	8	no	—
358	#101	—	2	8	no	—
359	#95	—	2	8	no	—
360	C₁₉	C₂×#1793	1	1	yes	characteristic, direct product factor, Sylow
361	C₂⁴	—	2	2	no	—
362	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
363	#41	—	2	64	no	—
364	#41	—	2	32	no	—
365	#41	—	2	64	no	—
366	#41	—	2	32	no	—
367	#41	—	2	32	no	—
368	#41	—	2	32	no	—
369	#41	—	2	8	no	—
370	#41	—	2	8	no	—
371	#41	—	2	8	no	—
372	#41	—	2	8	no	—
373	#41	—	2	8	no	—
374	#41	—	2	4	no	—
375	#41	—	2	4	no	—
376	#41	C₂²⋊C₄×C₁₉	1	16	yes	—
377	#41	C₂²×C₄×C₁₉	1	8	yes	—
378	#41	C₂×D₄×C₁₉	1	8	yes	—
379	C₂×Q₈	—	2	16	no	—
380	C₂×Q₈	—	2	8	no	—
381	C₂×Q₈	—	2	64	no	—
382	C₂×Q₈	—	2	32	no	—
383	C₂×Q₈	—	2	32	no	—
384	C₂×Q₈	—	2	8	no	—
385	C₂×Q₈	—	2	8	no	—
386	C₂×Q₈	—	2	4	no	—
387	C₂×Q₈	—	2	8	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	8	no	—
391	C₂×Q₈	—	2	4	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	4	no	—
394	C₂×Q₈	C₂²⋊C₄×C₁₉	1	8	yes	—
395	C₂×Q₈	C₂²⋊C₄×C₁₉	1	8	yes	—
396	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
397	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
398	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
399	C₂×D₄	—	2	16	no	—
400	C₂×D₄	—	2	8	no	—
401	C₂×D₄	—	2	8	no	—
402	C₂×D₄	—	2	8	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	—
408	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
409	C₂²×C₄	—	2	32	no	—
410	C₂²×C₄	—	2	16	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	2	8	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	4	4	no	—
425	C₂²×C₄	—	4	1	no	—
426	C₂²×C₄	—	4	1	no	—
427	C₂²×C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
428	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
430	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
432	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
433	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
434	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
436	M₁₆	—	2	4	no	—
437	M₁₆	—	2	4	no	—
438	M₁₆	—	4	4	no	—
439	C₂×C₈	—	2	4	no	—
440	C₂×C₈	—	4	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	4	2	no	—
443	C₄²	—	2	4	no	—
444	C₄²	—	4	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	8	no	—
448	C₂³	—	2	4	no	—
449	C₂³	—	4	4	no	—
450	C₂³	—	4	4	no	—
451	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
452	C₂³	C₁₉×#120	1	1	yes	characteristic
453	C₂³	C₁₉×#120	1	2	yes	—
454	C₂³	C₁₉×#120	1	1	yes	characteristic
455	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
456	Q₈	—	2	32	no	—
457	Q₈	—	2	8	no	—
458	Q₈	—	2	16	no	—
459	Q₈	—	2	8	no	—
460	Q₈	—	2	4	no	—
461	Q₈	—	2	8	no	—
462	Q₈	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
463	D₄	—	2	32	no	—
464	D₄	—	2	16	no	—
465	D₄	—	2	8	no	—
466	D₄	—	2	8	no	—
467	D₄	—	2	8	no	—
468	D₄	—	2	4	no	—
469	D₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
470	C₂×C₄	—	2	64	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	2	8	no	—
473	C₂×C₄	—	2	8	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	16	no	—
478	C₂×C₄	—	2	8	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	8	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	8	2	no	—
487	C₂×C₄	—	8	2	no	—
488	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
489	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
490	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
491	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
492	C₂×C₄	C₁₉×#120	1	2	yes	—
493	C₂×C₄	C₁₉×#120	1	2	yes	—
494	C₂×C₄	C₁₉×#120	1	4	yes	—
495	C₂×C₄	C₁₉×#120	1	4	yes	—
496	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
498	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
499	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
500	C₈	—	4	4	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	4	no	—
507	C₂²	—	2	8	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	4	16	no	—
511	C₂²	C₁₉×#379	1	2	yes	—
512	C₂²	C₁₉×#379	1	2	yes	—
513	C₂²	C₁₉×#454	1	2	yes	—
514	C₂²	C₁₉×#456	1	2	yes	—
515	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
516	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
517	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
518	C₄	—	2	8	no	—
519	C₄	—	2	8	no	—
520	C₄	—	4	4	no	—
521	C₄	—	8	2	no	—
522	C₄	C₁₉×#379	1	4	yes	—
523	C₄	C₂²×C₂²⋊C₄×C₁₉	1	2	yes	—
524	C₄	C₂×C₁₉×#120	1	2	yes	—
525	C₂	—	2	1	no	—
526	C₂	—	2	2	no	—
527	C₂	—	2	1	no	—
528	C₂	—	4	8	no	—
529	C₂	C₁₉×#1793	1	4	yes	direct product factor
530	C₂	C₂×C₁₉×#379	1	1	yes	characteristic
531	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
532	C₂	C₂×C₁₉×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×2₋¹⁺⁴	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#104	C₂	semidirect
3. C₂×C₁₉×#417	C₂	semidirect
4. C₂²×C₁₉×#101	C₂	semidirect
5. C₂×C₁₉×#391	C₂	semidirect
6. C₁₉×#1793	C₂	direct (N × H)
11. C₂×C₁₉×2₋¹⁺⁴	C₄	semidirect
22. C₂×C₁₉×#104	C₂²	semidirect
24. C₁₉×#417	C₂²	semidirect
28. C₂×C₁₉×#101	C₂²	semidirect
30. C₁₉×#391	C₂²	semidirect
38. C₁₉×2₋¹⁺⁴	C₂×C₄	semidirect
178. C₂×#1793	C₁₉	direct (N × H)
236. C₂²×#104	C₂×C₁₉	semidirect
237. C₂×#417	C₂×C₁₉	semidirect
238. C₂²×#101	C₂×C₁₉	semidirect
239. C₂×#391	C₂×C₁₉	semidirect
240. #1793	C₂×C₁₉	direct (N × H)
269. C₂×2₋¹⁺⁴	C₄×C₁₉	semidirect
280. C₂×#104	C₂²×C₁₉	semidirect
282. #417	C₂²×C₁₉	semidirect
286. C₂×#101	C₂²×C₁₉	semidirect
288. #391	C₂²×C₁₉	semidirect
294. C₂×C₁₉	#1793	direct (N × H)
304. 2₋¹⁺⁴	C₂×C₄×C₁₉	semidirect
360. C₁₉	C₂×#1793	direct (N × H)
529. C₂	C₁₉×#1793	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×2₋¹⁺⁴	2
C₂²×C₁₉×#104	2
C₂×C₁₉×#417	2
C₂²×C₁₉×#101	2
C₂×C₁₉×#391	2
C₁₉×#1793	2
C₂×#1793	19

Subgroups — C2×C19×#1793 #18026573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1793 #18026573