Subgroups — C₁₉×#20617 #18026576

Order 4864.

3610 conjugacy classes of subgroups.

The subgroup lattice has 506 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	C₂×C₁₉×#421	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2896	C₂	1	2	yes	maximal, complemented
4	C₂²×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2310	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1793	C₂	1	8	yes	maximal, complemented
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	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₁₉×#421	—	2	8	no	—
22	C₂×C₁₉×#104	C₂²	1	8	yes	complemented
23	C₁₉×#419	—	2	2	no	—
24	C₁₉×#418	—	2	2	no	—
25	C₁₉×#417	C₂²	1	8	yes	complemented
26	C₁₉×#416	—	2	4	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	C₁₉×#381	—	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	—
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	2	no	—
62	C₂²×Q₈×C₁₉	—	2	4	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	D₄	1	2	yes	—
74	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×M₁₆×C₁₉	—	2	2	no	—
76	C₂×M₁₆×C₁₉	—	2	4	no	—
77	C₂×M₁₆×C₁₉	—	2	4	no	—
78	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
79	C₂²×C₈×C₁₉	—	2	2	no	—
80	C₁₉×#117	—	2	4	no	—
81	C₁₉×#117	—	2	2	no	—
82	C₁₉×#117	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	1	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	2	no	—
146	C₂²×C₄×C₁₉	—	2	4	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	2	no	—
153	C₂²×C₄×C₁₉	—	2	2	no	—
154	C₂²×C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
155	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₁₉	C₂×D₄	1	4	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	4	yes	—
161	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
163	M₁₆×C₁₉	—	2	4	no	—
164	M₁₆×C₁₉	—	2	4	no	—
165	M₁₆×C₁₉	—	4	4	no	—
166	C₂×C₈×C₁₉	—	2	4	no	—
167	C₂×C₈×C₁₉	—	4	4	no	—
168	C₄⋊C₄×C₁₉	—	2	4	no	—
169	C₄⋊C₄×C₁₉	—	4	2	no	—
170	C₂²⋊C₄×C₁₉	—	4	2	no	—
171	C₂²⋊C₄×C₁₉	—	4	1	no	—
172	C₂²⋊C₄×C₁₉	—	4	1	no	—
173	C₄²×C₁₉	—	2	4	no	—
174	C₄²×C₁₉	—	4	2	no	—
175	#20617	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂³×C₁₉	—	2	4	no	—
177	C₂³×C₁₉	—	2	8	no	—
178	C₂³×C₁₉	—	4	2	no	—
179	C₂³×C₁₉	—	4	8	no	—
180	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂³×C₁₉	#120	1	1	yes	characteristic
182	C₂³×C₁₉	#120	1	1	yes	characteristic
183	C₂³×C₁₉	#120	1	2	yes	—
184	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
185	Q₈×C₁₉	—	2	32	no	—
186	Q₈×C₁₉	—	2	8	no	—
187	Q₈×C₁₉	—	2	4	no	—
188	Q₈×C₁₉	—	2	8	no	—
189	Q₈×C₁₉	—	2	8	no	—
190	Q₈×C₁₉	—	2	16	no	—
191	Q₈×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
192	D₄×C₁₉	—	2	32	no	—
193	D₄×C₁₉	—	2	8	no	—
194	D₄×C₁₉	—	2	8	no	—
195	D₄×C₁₉	—	2	16	no	—
196	D₄×C₁₉	—	2	4	no	—
197	D₄×C₁₉	—	2	8	no	—
198	D₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
199	C₂×C₄×C₁₉	—	2	64	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	8	no	—
204	C₂×C₄×C₁₉	—	2	8	no	—
205	C₂×C₄×C₁₉	—	2	8	no	—
206	C₂×C₄×C₁₉	—	2	8	no	—
207	C₂×C₄×C₁₉	—	2	8	no	—
208	C₂×C₄×C₁₉	—	2	16	no	—
209	C₂×C₄×C₁₉	—	4	4	no	—
210	C₂×C₄×C₁₉	—	4	4	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
214	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
215	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
216	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂×C₄×C₁₉	#120	1	4	yes	—
218	C₂×C₄×C₁₉	#120	1	4	yes	—
219	C₂×C₄×C₁₉	#120	1	2	yes	—
220	C₂×C₄×C₁₉	#120	1	2	yes	—
221	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
223	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
225	C₈×C₁₉	—	4	4	no	—
226	C₂²×2₋¹⁺⁴	C₂×C₁₉	1	1	yes	characteristic
227	C₂×#421	C₂×C₁₉	1	2	yes	complemented
228	#2896	C₂×C₁₉	1	2	yes	complemented
229	C₂²×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
230	#2310	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#1793	C₂×C₁₉	1	8	yes	complemented
232	C₂²×C₁₉	—	2	2	no	—
233	C₂²×C₁₉	—	2	2	no	—
234	C₂²×C₁₉	—	2	2	no	—
235	C₂²×C₁₉	—	2	8	no	—
236	C₂²×C₁₉	—	4	2	no	—
237	C₂²×C₁₉	—	4	2	no	—
238	C₂²×C₁₉	—	4	16	no	—
239	C₂²×C₁₉	—	4	8	no	—
240	C₂²×C₁₉	#379	1	2	yes	—
241	C₂²×C₁₉	#379	1	2	yes	—
242	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
243	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
244	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
245	C₄×C₁₉	—	2	8	no	—
246	C₄×C₁₉	—	2	8	no	—
247	C₄×C₁₉	—	8	2	no	—
248	C₄×C₁₉	—	8	2	no	—
249	C₄×C₁₉	#379	1	4	yes	—
250	C₄×C₁₉	C₂²×C₂²⋊C₄	1	2	yes	—
251	C₄×C₁₉	C₂×#120	1	2	yes	—
252	C₂×2₋¹⁺⁴	—	2	8	no	—
253	C₂×2₋¹⁺⁴	—	2	4	no	—
254	C₂×2₋¹⁺⁴	—	2	4	no	—
255	C₂×2₋¹⁺⁴	—	2	2	no	—
256	C₂×2₋¹⁺⁴	C₄×C₁₉	1	8	yes	complemented
257	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	4	yes	—
258	C₂²×#41	—	2	2	no	—
259	C₂²×#41	—	2	2	no	—
260	C₂²×#41	C₂²×C₁₉	1	2	yes	—
261	C₂³×Q₈	—	2	2	no	—
262	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
263	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
264	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
265	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
266	#421	—	2	8	no	—
267	C₂×#104	C₂²×C₁₉	1	8	yes	complemented
268	#419	—	2	2	no	—
269	#418	—	2	2	no	—
270	#417	C₂²×C₁₉	1	8	yes	complemented
271	#416	—	2	4	no	—
272	C₂×#101	—	2	4	no	—
273	C₂×#101	C₂²×C₁₉	1	4	yes	complemented
274	#391	—	2	2	no	—
275	#391	C₂²×C₁₉	1	4	yes	complemented
276	#381	—	2	2	no	—
277	C₂×C₁₉	—	2	1	no	—
278	C₂×C₁₉	—	2	2	no	—
279	C₂×C₁₉	—	2	1	no	—
280	C₂×C₁₉	—	2	2	no	—
281	C₂×C₁₉	—	4	8	no	—
282	C₂×C₁₉	C₂×#379	1	1	yes	characteristic
283	C₂×C₁₉	#3020	1	2	yes	—
284	2₋¹⁺⁴	—	2	16	no	—
285	2₋¹⁺⁴	—	2	32	no	—
286	2₋¹⁺⁴	—	2	32	no	—
287	2₋¹⁺⁴	—	2	16	no	—
288	2₋¹⁺⁴	—	2	16	no	—
289	2₋¹⁺⁴	—	2	8	no	—
290	2₋¹⁺⁴	C₂×C₄×C₁₉	1	16	yes	—
291	C₂×#41	—	2	16	no	—
292	C₂×#41	—	2	8	no	—
293	C₂×#41	—	2	16	no	—
294	C₂×#41	—	2	8	no	—
295	C₂×#41	—	2	16	no	—
296	C₂×#41	—	2	8	no	—
297	C₂×#41	—	2	16	no	—
298	C₂×#41	—	2	8	no	—
299	C₂×#41	—	2	4	no	—
300	C₂×#41	—	2	2	no	—
301	C₂×#41	—	2	4	no	—
302	C₂×#41	—	2	2	no	—
303	C₂×#41	C₂×C₄×C₁₉	1	8	yes	—
304	C₂×#41	D₄×C₁₉	1	8	yes	—
305	C₂×#41	D₄×C₁₉	1	4	yes	—
306	C₂×#41	C₂³×C₁₉	1	4	yes	—
307	C₂²×Q₈	—	2	2	no	—
308	C₂²×Q₈	—	2	16	no	—
309	C₂²×Q₈	—	2	8	no	—
310	C₂²×Q₈	—	2	16	no	—
311	C₂²×Q₈	—	2	8	no	—
312	C₂²×Q₈	—	2	2	no	—
313	C₂²×Q₈	—	2	2	no	—
314	C₂²×Q₈	—	2	4	no	—
315	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
316	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
317	C₂²×Q₈	D₄×C₁₉	1	4	yes	—
318	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
319	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	D₄×C₁₉	1	2	yes	—
323	C₂³×C₄	—	2	4	no	—
324	C₂³×C₄	—	2	2	no	—
325	C₂³×C₄	D₄×C₁₉	1	2	yes	—
326	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
327	C₂×M₁₆	—	2	2	no	—
328	C₂×M₁₆	—	2	4	no	—
329	C₂×M₁₆	—	2	4	no	—
330	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
331	C₂²×C₈	—	2	2	no	—
332	#117	—	2	4	no	—
333	#117	—	2	2	no	—
334	#117	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₄²	—	2	1	no	—
340	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
341	#104	—	2	16	no	—
342	#103	—	2	8	no	—
343	#102	—	2	8	no	—
344	#101	—	2	8	no	—
345	#95	—	2	8	no	—
346	C₁₉	#20617	1	1	yes	characteristic, direct product factor, Sylow
347	C₂⁴	—	2	2	no	—
348	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
349	#41	—	2	64	no	—
350	#41	—	2	32	no	—
351	#41	—	2	64	no	—
352	#41	—	2	32	no	—
353	#41	—	2	32	no	—
354	#41	—	2	32	no	—
355	#41	—	2	8	no	—
356	#41	—	2	8	no	—
357	#41	—	2	8	no	—
358	#41	—	2	8	no	—
359	#41	—	2	8	no	—
360	#41	—	2	4	no	—
361	#41	—	2	4	no	—
362	#41	C₂²⋊C₄×C₁₉	1	16	yes	—
363	#41	C₂²×C₄×C₁₉	1	8	yes	—
364	#41	C₂×D₄×C₁₉	1	8	yes	—
365	C₂×Q₈	—	2	16	no	—
366	C₂×Q₈	—	2	8	no	—
367	C₂×Q₈	—	2	64	no	—
368	C₂×Q₈	—	2	32	no	—
369	C₂×Q₈	—	2	32	no	—
370	C₂×Q₈	—	2	8	no	—
371	C₂×Q₈	—	2	8	no	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	—	2	8	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	8	no	—
377	C₂×Q₈	—	2	4	no	—
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	—	2	4	no	—
380	C₂×Q₈	C₂²⋊C₄×C₁₉	1	8	yes	—
381	C₂×Q₈	C₂²⋊C₄×C₁₉	1	8	yes	—
382	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
383	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
384	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
385	C₂×D₄	—	2	16	no	—
386	C₂×D₄	—	2	8	no	—
387	C₂×D₄	—	2	8	no	—
388	C₂×D₄	—	2	8	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	—
394	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
395	C₂²×C₄	—	2	32	no	—
396	C₂²×C₄	—	2	16	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	8	no	—
402	C₂²×C₄	—	2	8	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
408	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
409	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
410	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
412	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
413	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
414	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
416	M₁₆	—	2	4	no	—
417	M₁₆	—	2	4	no	—
418	M₁₆	—	4	4	no	—
419	C₂×C₈	—	2	4	no	—
420	C₂×C₈	—	4	4	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	4	2	no	—
423	C₂²⋊C₄	—	4	2	no	—
424	C₂²⋊C₄	—	4	1	no	—
425	C₂²⋊C₄	—	4	1	no	—
426	C₄²	—	2	4	no	—
427	C₄²	—	4	2	no	—
428	C₂³	—	2	8	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	8	no	—
432	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
433	C₂³	C₁₉×#120	1	1	yes	characteristic
434	C₂³	C₁₉×#120	1	1	yes	characteristic
435	C₂³	C₁₉×#120	1	2	yes	—
436	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
437	Q₈	—	2	32	no	—
438	Q₈	—	2	8	no	—
439	Q₈	—	2	16	no	—
440	Q₈	—	2	8	no	—
441	Q₈	—	2	4	no	—
442	Q₈	—	2	8	no	—
443	Q₈	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
444	D₄	—	2	32	no	—
445	D₄	—	2	16	no	—
446	D₄	—	2	8	no	—
447	D₄	—	2	8	no	—
448	D₄	—	2	8	no	—
449	D₄	—	2	4	no	—
450	D₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
451	C₂×C₄	—	2	64	no	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	2	8	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	16	no	—
459	C₂×C₄	—	2	8	no	—
460	C₂×C₄	—	2	8	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
466	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
467	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
468	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
469	C₂×C₄	C₁₉×#120	1	2	yes	—
470	C₂×C₄	C₁₉×#120	1	2	yes	—
471	C₂×C₄	C₁₉×#120	1	4	yes	—
472	C₂×C₄	C₁₉×#120	1	4	yes	—
473	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
474	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
475	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
476	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
477	C₈	—	4	4	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	8	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	16	no	—
485	C₂²	—	4	8	no	—
486	C₂²	C₁₉×#379	1	2	yes	—
487	C₂²	C₁₉×#379	1	2	yes	—
488	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
489	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
490	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
491	C₄	—	2	8	no	—
492	C₄	—	2	8	no	—
493	C₄	—	8	2	no	—
494	C₄	—	8	2	no	—
495	C₄	C₁₉×#379	1	4	yes	—
496	C₄	C₂²×C₂²⋊C₄×C₁₉	1	2	yes	—
497	C₄	C₂×C₁₉×#120	1	2	yes	—
498	C₂	—	2	1	no	—
499	C₂	—	2	2	no	—
500	C₂	—	2	2	no	—
501	C₂	—	2	1	no	—
502	C₂	—	4	8	no	—
503	C₂	C₂×C₁₉×#379	1	1	yes	characteristic
504	C₂	C₁₉×#3020	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#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 ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#421	C₂	semidirect
3. C₁₉×#2896	C₂	semidirect
4. C₂²×C₁₉×#101	C₂	semidirect
5. C₁₉×#2310	C₂	semidirect
6. C₁₉×#1793	C₂	semidirect
11. C₂×C₁₉×2₋¹⁺⁴	C₄	semidirect
22. C₂×C₁₉×#104	C₂²	semidirect
25. C₁₉×#417	C₂²	semidirect
28. C₂×C₁₉×#101	C₂²	semidirect
30. C₁₉×#391	C₂²	semidirect
175. #20617	C₁₉	direct (N × H)
227. C₂×#421	C₂×C₁₉	semidirect
228. #2896	C₂×C₁₉	semidirect
229. C₂²×#101	C₂×C₁₉	semidirect
230. #2310	C₂×C₁₉	semidirect
231. #1793	C₂×C₁₉	semidirect
256. C₂×2₋¹⁺⁴	C₄×C₁₉	semidirect
267. C₂×#104	C₂²×C₁₉	semidirect
270. #417	C₂²×C₁₉	semidirect
273. C₂×#101	C₂²×C₁₉	semidirect
275. #391	C₂²×C₁₉	semidirect
346. C₁₉	#20617	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
C₂×C₁₉×#421	2
C₁₉×#2896	2
C₂²×C₁₉×#101	2
C₁₉×#2310	2
C₁₉×#1793	2
#20617	19

Subgroups — C19×#20617 #18026576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20617 #18026576