Subgroups — C₁₉×#32889 #18038848

Order 4864.

3606 conjugacy classes of subgroups.

The subgroup lattice has 484 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, complemented
2	C₂×C₁₉×#454	C₂	1	4	yes	maximal, complemented
3	C₁₉×#3006	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2436	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1793	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1789	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1784	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×2₋¹⁺⁴	—	2	16	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	C₂²	1	4	yes	—
12	C₂²×#41×C₁₉	—	2	2	no	—
13	C₂²×#41×C₁₉	—	2	2	no	—
14	C₂²×#41×C₁₉	C₂²	1	2	yes	—
15	C₂³×Q₈×C₁₉	—	2	2	no	—
16	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
18	C₂×C₁₉×#124	C₂²	1	2	yes	complemented
19	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
20	C₁₉×#454	—	2	16	no	—
21	C₁₉×#449	—	2	4	no	—
22	C₁₉×#448	—	2	2	no	—
23	C₁₉×#447	—	2	2	no	—
24	C₂×C₁₉×#104	C₂²	1	8	yes	complemented
25	C₁₉×#417	C₂²	1	4	yes	complemented
26	C₂×C₁₉×#101	C₂²	1	4	yes	complemented
27	C₁₉×#407	C₂²	1	2	yes	—
28	C₁₉×#393	—	2	2	no	—
29	C₁₉×#391	C₂²	1	2	yes	complemented
30	C₁₉×#386	—	2	2	no	—
31	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×2₋¹⁺⁴	—	2	32	no	—
33	C₁₉×2₋¹⁺⁴	—	2	32	no	—
34	C₁₉×2₋¹⁺⁴	—	2	32	no	—
35	C₁₉×2₋¹⁺⁴	—	2	16	no	—
36	C₁₉×2₋¹⁺⁴	—	2	8	no	—
37	C₁₉×2₋¹⁺⁴	D₄	1	16	yes	complemented
38	C₂×#41×C₁₉	—	2	32	no	—
39	C₂×#41×C₁₉	—	2	8	no	—
40	C₂×#41×C₁₉	—	2	8	no	—
41	C₂×#41×C₁₉	—	2	32	no	—
42	C₂×#41×C₁₉	—	2	16	no	—
43	C₂×#41×C₁₉	—	2	8	no	—
44	C₂×#41×C₁₉	—	2	8	no	—
45	C₂×#41×C₁₉	—	2	2	no	—
46	C₂×#41×C₁₉	—	2	2	no	—
47	C₂×#41×C₁₉	D₄	1	4	yes	—
48	C₂×#41×C₁₉	C₂³	1	4	yes	—
49	C₂²×Q₈×C₁₉	—	2	2	no	—
50	C₂²×Q₈×C₁₉	—	2	32	no	—
51	C₂²×Q₈×C₁₉	—	2	8	no	—
52	C₂²×Q₈×C₁₉	—	2	8	no	—
53	C₂²×Q₈×C₁₉	—	2	8	no	—
54	C₂²×Q₈×C₁₉	—	2	2	no	—
55	C₂²×Q₈×C₁₉	—	2	2	no	—
56	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
57	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
58	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₉	—	2	2	no	—
60	C₂²×D₄×C₁₉	—	2	2	no	—
61	C₂²×D₄×C₁₉	—	2	1	no	—
62	C₂²×D₄×C₁₉	D₄	1	2	yes	—
63	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	—	2	4	no	—
65	C₂³×C₄×C₁₉	—	2	2	no	—
66	C₂³×C₄×C₁₉	D₄	1	2	yes	—
67	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₁₉×AGL(1,ℤ/8)	—	2	16	no	—
69	C₂×SD₁₆×C₁₉	—	2	4	no	—
70	C₂×D₈×C₁₉	—	2	4	no	—
71	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
72	C₁₉×#124	—	2	8	no	—
73	C₁₉×#121	—	2	2	no	—
74	C₁₉×#121	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
80	C₁₉×#104	—	2	16	no	—
81	C₁₉×#103	—	2	4	no	—
82	C₁₉×#102	—	2	4	no	—
83	C₁₉×#101	—	2	8	no	—
84	C₁₉×C₂²⋊C₈	—	2	2	no	—
85	C₁₉×C₂²⋊C₈	—	2	2	no	—
86	C₁₉×#95	—	2	1	no	—
87	C₁₉×#95	—	2	4	no	—
88	C₂⁴×C₁₉	—	2	2	no	—
89	C₂⁴×C₁₉	—	2	1	no	—
90	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
91	#41×C₁₉	—	2	64	no	—
92	#41×C₁₉	—	2	64	no	—
93	#41×C₁₉	—	2	32	no	—
94	#41×C₁₉	—	2	16	no	—
95	#41×C₁₉	—	2	32	no	—
96	#41×C₁₉	—	2	16	no	—
97	#41×C₁₉	—	2	8	no	—
98	#41×C₁₉	—	2	32	no	—
99	#41×C₁₉	—	2	8	no	—
100	#41×C₁₉	—	2	32	no	—
101	#41×C₁₉	—	2	8	no	—
102	#41×C₁₉	C₂×D₄	1	16	yes	—
103	C₂×Q₈×C₁₉	—	2	16	no	—
104	C₂×Q₈×C₁₉	—	2	16	no	—
105	C₂×Q₈×C₁₉	—	2	8	no	—
106	C₂×Q₈×C₁₉	—	2	64	no	—
107	C₂×Q₈×C₁₉	—	2	32	no	—
108	C₂×Q₈×C₁₉	—	2	16	no	—
109	C₂×Q₈×C₁₉	—	2	8	no	—
110	C₂×Q₈×C₁₉	—	2	32	no	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	4	no	—
113	C₂×Q₈×C₁₉	—	2	8	no	—
114	C₂×Q₈×C₁₉	—	2	4	no	—
115	C₂×Q₈×C₁₉	—	2	4	no	—
116	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
117	C₂×Q₈×C₁₉	C₂×D₄	1	8	yes	—
118	C₂×D₄×C₁₉	—	2	16	no	—
119	C₂×D₄×C₁₉	—	2	16	no	—
120	C₂×D₄×C₁₉	—	2	8	no	—
121	C₂×D₄×C₁₉	—	2	4	no	—
122	C₂×D₄×C₁₉	—	2	4	no	—
123	C₂×D₄×C₁₉	—	2	8	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	4	no	—
127	C₂×D₄×C₁₉	—	4	4	no	—
128	C₂×D₄×C₁₉	—	4	1	no	—
129	C₂×D₄×C₁₉	—	4	1	no	—
130	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₉	—	2	32	no	—
132	C₂²×C₄×C₁₉	—	2	16	no	—
133	C₂²×C₄×C₁₉	—	2	16	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	4	no	—
138	C₂²×C₄×C₁₉	—	2	8	no	—
139	C₂²×C₄×C₁₉	—	2	4	no	—
140	C₂²×C₄×C₁₉	—	2	4	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
148	SD₁₆×C₁₉	—	4	8	no	—
149	D₈×C₁₉	—	4	8	no	—
150	M₁₆×C₁₉	—	2	8	no	—
151	C₂×C₈×C₁₉	—	2	4	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₂²⋊C₄×C₁₉	—	4	2	no	—
154	C₂²⋊C₄×C₁₉	—	4	2	no	—
155	C₂²⋊C₄×C₁₉	—	4	8	no	—
156	C₄²×C₁₉	—	2	4	no	—
157	#32889	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂³×C₁₉	—	2	8	no	—
159	C₂³×C₁₉	—	2	2	no	—
160	C₂³×C₁₉	—	2	4	no	—
161	C₂³×C₁₉	—	2	2	no	—
162	C₂³×C₁₉	—	4	1	no	—
163	C₂³×C₁₉	—	4	4	no	—
164	C₂³×C₁₉	—	4	2	no	—
165	C₂³×C₁₉	—	4	2	no	—
166	C₂³×C₁₉	—	4	4	no	—
167	C₂³×C₁₉	—	4	2	no	—
168	C₂³×C₁₉	—	4	1	no	—
169	C₂³×C₁₉	#120	1	1	yes	characteristic
170	C₂³×C₁₉	#120	1	1	yes	characteristic
171	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₁₉	—	2	32	no	—
173	Q₈×C₁₉	—	2	8	no	—
174	Q₈×C₁₉	—	2	16	no	—
175	Q₈×C₁₉	—	2	4	no	—
176	Q₈×C₁₉	—	2	16	no	—
177	Q₈×C₁₉	#120	1	8	yes	—
178	D₄×C₁₉	—	2	16	no	—
179	D₄×C₁₉	—	2	32	no	—
180	D₄×C₁₉	—	2	8	no	—
181	D₄×C₁₉	—	2	16	no	—
182	D₄×C₁₉	—	2	4	no	—
183	D₄×C₁₉	—	4	4	no	—
184	D₄×C₁₉	—	8	2	no	—
185	D₄×C₁₉	—	8	2	no	—
186	D₄×C₁₉	#120	1	8	yes	—
187	C₂×C₄×C₁₉	—	2	8	no	—
188	C₂×C₄×C₁₉	—	2	8	no	—
189	C₂×C₄×C₁₉	—	2	64	no	—
190	C₂×C₄×C₁₉	—	2	16	no	—
191	C₂×C₄×C₁₉	—	2	8	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	4	no	—
195	C₂×C₄×C₁₉	—	2	4	no	—
196	C₂×C₄×C₁₉	—	2	4	no	—
197	C₂×C₄×C₁₉	—	2	16	no	—
198	C₂×C₄×C₁₉	—	2	4	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	#120	1	8	yes	—
205	C₂×C₄×C₁₉	#120	1	2	yes	—
206	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
207	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
208	C₈×C₁₉	—	4	4	no	—
209	C₂²×2₋¹⁺⁴	C₂×C₁₉	1	1	yes	characteristic, complemented
210	C₂×#454	C₂×C₁₉	1	4	yes	complemented
211	#3006	C₂×C₁₉	1	2	yes	complemented
212	#2436	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#1793	C₂×C₁₉	1	4	yes	complemented
214	#1789	C₂×C₁₉	1	2	yes	complemented
215	#1784	C₂×C₁₉	1	1	yes	characteristic, complemented
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	2	1	no	—
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	2	1	no	—
221	C₂²×C₁₉	—	2	8	no	—
222	C₂²×C₁₉	—	2	1	no	—
223	C₂²×C₁₉	—	2	1	no	—
224	C₂²×C₁₉	—	4	4	no	—
225	C₂²×C₁₉	—	4	16	no	—
226	C₂²×C₁₉	—	4	4	no	—
227	C₂²×C₁₉	—	4	4	no	—
228	C₂²×C₁₉	—	8	4	no	—
229	C₂²×C₁₉	—	8	1	no	—
230	C₂²×C₁₉	—	8	1	no	—
231	C₂²×C₁₉	—	8	1	no	—
232	C₂²×C₁₉	#454	1	2	yes	complemented
233	C₂²×C₁₉	C₂×#120	1	2	yes	—
234	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
235	C₄×C₁₉	—	2	8	no	—
236	C₄×C₁₉	—	2	8	no	—
237	C₄×C₁₉	—	2	2	no	—
238	C₄×C₁₉	—	8	2	no	—
239	C₄×C₁₉	—	8	1	no	—
240	C₄×C₁₉	C₂×#120	1	4	yes	—
241	C₂×2₋¹⁺⁴	—	2	16	no	—
242	C₂×2₋¹⁺⁴	—	2	4	no	—
243	C₂×2₋¹⁺⁴	—	2	2	no	—
244	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	4	yes	—
245	C₂²×#41	—	2	2	no	—
246	C₂²×#41	—	2	2	no	—
247	C₂²×#41	C₂²×C₁₉	1	2	yes	—
248	C₂³×Q₈	—	2	2	no	—
249	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	4	yes	complemented
251	C₂×#124	C₂²×C₁₉	1	2	yes	complemented
252	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
253	#454	—	2	16	no	—
254	#449	—	2	4	no	—
255	#448	—	2	2	no	—
256	#447	—	2	2	no	—
257	C₂×#104	C₂²×C₁₉	1	8	yes	complemented
258	#417	C₂²×C₁₉	1	4	yes	complemented
259	C₂×#101	C₂²×C₁₉	1	4	yes	complemented
260	#407	C₂²×C₁₉	1	2	yes	—
261	#393	—	2	2	no	—
262	#391	C₂²×C₁₉	1	2	yes	complemented
263	#386	—	2	2	no	—
264	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
265	C₂×C₁₉	—	2	2	no	—
266	C₂×C₁₉	—	2	2	no	—
267	C₂×C₁₉	—	4	1	no	—
268	C₂×C₁₉	—	4	8	no	—
269	C₂×C₁₉	—	16	1	no	—
270	C₂×C₁₉	#2846	1	1	yes	characteristic
271	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
272	C₂×C₁₉	#3020	1	1	yes	characteristic
273	2₋¹⁺⁴	—	2	32	no	—
274	2₋¹⁺⁴	—	2	32	no	—
275	2₋¹⁺⁴	—	2	32	no	—
276	2₋¹⁺⁴	—	2	16	no	—
277	2₋¹⁺⁴	—	2	8	no	—
278	2₋¹⁺⁴	D₄×C₁₉	1	16	yes	complemented
279	C₂×#41	—	2	32	no	—
280	C₂×#41	—	2	8	no	—
281	C₂×#41	—	2	8	no	—
282	C₂×#41	—	2	32	no	—
283	C₂×#41	—	2	16	no	—
284	C₂×#41	—	2	8	no	—
285	C₂×#41	—	2	8	no	—
286	C₂×#41	—	2	2	no	—
287	C₂×#41	—	2	2	no	—
288	C₂×#41	D₄×C₁₉	1	4	yes	—
289	C₂×#41	C₂³×C₁₉	1	4	yes	—
290	C₂²×Q₈	—	2	2	no	—
291	C₂²×Q₈	—	2	32	no	—
292	C₂²×Q₈	—	2	8	no	—
293	C₂²×Q₈	—	2	8	no	—
294	C₂²×Q₈	—	2	8	no	—
295	C₂²×Q₈	—	2	2	no	—
296	C₂²×Q₈	—	2	2	no	—
297	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
298	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
299	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
300	C₂²×D₄	—	2	2	no	—
301	C₂²×D₄	—	2	2	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	D₄×C₁₉	1	2	yes	—
304	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
305	C₂³×C₄	—	2	4	no	—
306	C₂³×C₄	—	2	2	no	—
307	C₂³×C₄	D₄×C₁₉	1	2	yes	—
308	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
309	AGL(1,ℤ/8)	—	2	16	no	—
310	C₂×SD₁₆	—	2	4	no	—
311	C₂×D₈	—	2	4	no	—
312	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
313	#124	—	2	8	no	—
314	#121	—	2	2	no	—
315	#121	—	2	2	no	—
316	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	4	no	—
320	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
321	#104	—	2	16	no	—
322	#103	—	2	4	no	—
323	#102	—	2	4	no	—
324	#101	—	2	8	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	#95	—	2	1	no	—
328	#95	—	2	4	no	—
329	C₁₉	#32889	1	1	yes	characteristic, direct product factor, Sylow
330	C₂⁴	—	2	2	no	—
331	C₂⁴	—	2	1	no	—
332	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
333	#41	—	2	64	no	—
334	#41	—	2	64	no	—
335	#41	—	2	32	no	—
336	#41	—	2	16	no	—
337	#41	—	2	32	no	—
338	#41	—	2	16	no	—
339	#41	—	2	8	no	—
340	#41	—	2	32	no	—
341	#41	—	2	8	no	—
342	#41	—	2	32	no	—
343	#41	—	2	8	no	—
344	#41	C₂×D₄×C₁₉	1	16	yes	—
345	C₂×Q₈	—	2	16	no	—
346	C₂×Q₈	—	2	16	no	—
347	C₂×Q₈	—	2	8	no	—
348	C₂×Q₈	—	2	64	no	—
349	C₂×Q₈	—	2	32	no	—
350	C₂×Q₈	—	2	16	no	—
351	C₂×Q₈	—	2	8	no	—
352	C₂×Q₈	—	2	32	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	4	no	—
355	C₂×Q₈	—	2	8	no	—
356	C₂×Q₈	—	2	4	no	—
357	C₂×Q₈	—	2	4	no	—
358	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
359	C₂×Q₈	C₂×D₄×C₁₉	1	8	yes	—
360	C₂×D₄	—	2	16	no	—
361	C₂×D₄	—	2	16	no	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	4	4	no	—
370	C₂×D₄	—	4	1	no	—
371	C₂×D₄	—	4	1	no	—
372	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
373	C₂²×C₄	—	2	32	no	—
374	C₂²×C₄	—	2	16	no	—
375	C₂²×C₄	—	2	16	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	8	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
386	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
389	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
390	SD₁₆	—	4	8	no	—
391	D₈	—	4	8	no	—
392	M₁₆	—	2	8	no	—
393	C₂×C₈	—	2	4	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	—	4	8	no	—
398	C₄²	—	2	4	no	—
399	C₂³	—	2	8	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	4	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	4	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	1	no	—
410	C₂³	C₁₉×#120	1	1	yes	characteristic
411	C₂³	C₁₉×#120	1	1	yes	characteristic
412	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
413	Q₈	—	2	32	no	—
414	Q₈	—	2	8	no	—
415	Q₈	—	2	16	no	—
416	Q₈	—	2	4	no	—
417	Q₈	—	2	16	no	—
418	Q₈	C₁₉×#120	1	8	yes	—
419	D₄	—	2	16	no	—
420	D₄	—	2	32	no	—
421	D₄	—	2	8	no	—
422	D₄	—	2	16	no	—
423	D₄	—	2	4	no	—
424	D₄	—	4	4	no	—
425	D₄	—	8	2	no	—
426	D₄	—	8	2	no	—
427	D₄	C₁₉×#120	1	8	yes	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	64	no	—
431	C₂×C₄	—	2	16	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	16	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	C₁₉×#120	1	2	yes	—
446	C₂×C₄	C₁₉×#120	1	8	yes	—
447	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
448	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
449	C₈	—	4	4	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	8	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	16	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	8	4	no	—
463	C₂²	—	8	1	no	—
464	C₂²	—	8	1	no	—
465	C₂²	—	8	1	no	—
466	C₂²	C₁₉×#454	1	2	yes	complemented
467	C₂²	C₂×C₁₉×#120	1	2	yes	—
468	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
469	C₄	—	2	8	no	—
470	C₄	—	2	8	no	—
471	C₄	—	2	2	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	1	no	—
474	C₄	C₂×C₁₉×#120	1	4	yes	—
475	C₂	—	2	2	no	—
476	C₂	—	2	2	no	—
477	C₂	—	4	1	no	—
478	C₂	—	4	8	no	—
479	C₂	—	16	1	no	—
480	C₂	C₁₉×#2846	1	1	yes	characteristic
481	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
482	C₂	C₁₉×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×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
1. C₂²×C₁₉×2₋¹⁺⁴	C₂	semidirect
2. C₂×C₁₉×#454	C₂	semidirect
3. C₁₉×#3006	C₂	semidirect
4. C₁₉×#2436	C₂	semidirect
5. C₁₉×#1793	C₂	semidirect
6. C₁₉×#1789	C₂	semidirect
7. C₁₉×#1784	C₂	semidirect
17. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
18. C₂×C₁₉×#124	C₂²	semidirect
24. C₂×C₁₉×#104	C₂²	semidirect
25. C₁₉×#417	C₂²	semidirect
26. C₂×C₁₉×#101	C₂²	semidirect
29. C₁₉×#391	C₂²	semidirect
37. C₁₉×2₋¹⁺⁴	D₄	semidirect
157. #32889	C₁₉	direct (N × H)
209. C₂²×2₋¹⁺⁴	C₂×C₁₉	semidirect
210. C₂×#454	C₂×C₁₉	semidirect
211. #3006	C₂×C₁₉	semidirect
212. #2436	C₂×C₁₉	semidirect
213. #1793	C₂×C₁₉	semidirect
214. #1789	C₂×C₁₉	semidirect
215. #1784	C₂×C₁₉	semidirect
232. C₂²×C₁₉	#454	semidirect
250. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
251. C₂×#124	C₂²×C₁₉	semidirect
257. C₂×#104	C₂²×C₁₉	semidirect
258. #417	C₂²×C₁₉	semidirect
259. C₂×#101	C₂²×C₁₉	semidirect
262. #391	C₂²×C₁₉	semidirect
278. 2₋¹⁺⁴	D₄×C₁₉	semidirect
329. C₁₉	#32889	direct (N × H)
466. C₂²	C₁₉×#454	semidirect

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×#454	2
C₁₉×#3006	2
C₁₉×#2436	2
C₁₉×#1793	2
C₁₉×#1789	2
C₁₉×#1784	2
#32889	19

Subgroups — C19×#32889 #18038848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32889 #18038848