Subgroups — C₁₉×#32921 #18038880

Order 4864.

1402 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3038	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#454	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2548	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1888	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1883	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1806	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	—
11	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#124	C₂²	1	2	yes	—
13	C₁₉×#520	—	2	2	no	—
14	C₁₉×#520	—	2	2	no	—
15	C₁₉×#520	C₂²	1	2	yes	—
16	C₁₉×#519	—	2	2	no	—
17	C₁₉×#519	C₂²	1	1	yes	characteristic
18	C₄×#41×C₁₉	—	2	2	no	—
19	C₄×#41×C₁₉	—	2	2	no	—
20	C₄×#41×C₁₉	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₉	—	2	2	no	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#460	—	2	2	no	—
24	C₁₉×#460	—	2	2	no	—
25	C₁₉×#459	—	2	2	no	—
26	C₁₉×#459	—	2	2	no	—
27	C₁₉×#454	—	2	8	no	—
28	C₁₉×#423	C₂²	1	2	yes	—
29	C₂×C₁₉×#104	C₂²	1	4	yes	—
30	C₁₉×#418	C₂²	1	4	yes	—
31	C₂×C₁₉×#101	C₂²	1	2	yes	—
32	C₁₉×#394	—	2	2	no	—
33	C₁₉×#390	—	2	2	no	—
34	C₁₉×#390	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#343	C₂²	1	2	yes	—
37	C₁₉×#339	C₂²	1	4	yes	—
38	C₁₉×2₋¹⁺⁴	—	2	4	no	—
39	C₁₉×2₋¹⁺⁴	—	2	2	no	—
40	C₁₉×2₋¹⁺⁴	D₄	1	4	yes	complemented
41	C₂×#41×C₁₉	—	2	2	no	—
42	C₂×#41×C₁₉	—	2	2	no	—
43	C₂×#41×C₁₉	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₉	—	2	2	no	—
45	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
49	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
50	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
51	C₂×SD₁₆×C₁₉	—	2	4	no	—
52	C₂×D₈×C₁₉	—	2	4	no	—
53	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
54	C₁₉×#127	—	2	2	no	—
55	C₁₉×#127	—	2	2	no	—
56	C₁₉×#124	—	2	4	no	—
57	C₁₉×#124	—	2	4	no	—
58	C₄×Q₈×C₁₉	—	2	2	no	—
59	C₄×Q₈×C₁₉	—	2	4	no	—
60	C₄×Q₈×C₁₉	—	2	2	no	—
61	C₄×Q₈×C₁₉	—	2	2	no	—
62	C₄×Q₈×C₁₉	—	2	2	no	—
63	C₄×Q₈×C₁₉	—	2	2	no	—
64	C₄×Q₈×C₁₉	—	2	2	no	—
65	C₄×Q₈×C₁₉	—	2	2	no	—
66	C₄×Q₈×C₁₉	D₄	1	2	yes	—
67	C₄×Q₈×C₁₉	D₄	1	2	yes	—
68	C₄×D₄×C₁₉	—	2	2	no	—
69	C₄×D₄×C₁₉	—	2	4	no	—
70	C₄×D₄×C₁₉	—	2	2	no	—
71	C₄×D₄×C₁₉	—	2	2	no	—
72	C₄×D₄×C₁₉	—	2	2	no	—
73	C₄×D₄×C₁₉	—	2	4	no	—
74	C₄×D₄×C₁₉	—	2	2	no	—
75	C₄×D₄×C₁₉	D₄	1	2	yes	—
76	C₄×D₄×C₁₉	D₄	1	2	yes	—
77	C₁₉×#117	—	2	4	no	—
78	C₁₉×#117	—	2	4	no	—
79	C₁₉×#117	—	2	2	no	—
80	C₁₉×#117	—	2	2	no	—
81	C₁₉×#117	—	2	2	no	—
82	C₁₉×#117	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
90	C₂×C₄²×C₁₉	—	2	4	no	—
91	C₂×C₄²×C₁₉	—	2	2	no	—
92	C₂×C₄²×C₁₉	D₄	1	2	yes	—
93	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
94	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
95	C₁₉×C₄⋊C₈	—	2	2	no	—
96	C₁₉×C₄⋊C₈	—	2	2	no	—
97	C₁₉×#104	—	2	8	no	—
98	C₁₉×#102	—	2	4	no	—
99	C₁₉×#102	—	2	4	no	—
100	C₁₉×#101	—	2	4	no	—
101	C₁₉×#95	—	2	1	no	—
102	C₂⁴×C₁₉	—	2	2	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	2	no	—
108	#41×C₁₉	—	2	2	no	—
109	#41×C₁₉	C₂×D₄	1	4	yes	—
110	#41×C₁₉	#41	1	4	yes	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	8	no	—
113	C₂×Q₈×C₁₉	—	2	8	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	—	2	2	no	—
116	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
117	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
118	C₂×Q₈×C₁₉	#41	1	2	yes	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	2	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	4	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	4	no	—
125	C₂×D₄×C₁₉	—	4	4	no	—
126	C₂×D₄×C₁₉	—	4	1	no	—
127	C₂×D₄×C₁₉	—	4	2	no	—
128	C₂×D₄×C₁₉	—	4	1	no	—
129	C₂×D₄×C₁₉	—	8	2	no	—
130	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₉	—	2	4	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	4	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	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
142	SD₁₆×C₁₉	—	4	8	no	—
143	D₈×C₁₉	—	4	8	no	—
144	M₁₆×C₁₉	—	2	4	no	—
145	M₁₆×C₁₉	—	2	4	no	—
146	C₂×C₈×C₁₉	—	2	4	no	—
147	C₄⋊C₄×C₁₉	—	2	4	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	4	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	4	2	no	—
155	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
156	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
157	C₂²⋊C₄×C₁₉	—	2	4	no	—
158	C₂²⋊C₄×C₁₉	—	2	2	no	—
159	C₂²⋊C₄×C₁₉	—	2	2	no	—
160	C₂²⋊C₄×C₁₉	—	2	2	no	—
161	C₂²⋊C₄×C₁₉	—	4	8	no	—
162	C₂²⋊C₄×C₁₉	—	8	4	no	—
163	C₄²×C₁₉	—	2	4	no	—
164	C₄²×C₁₉	—	2	4	no	—
165	C₄²×C₁₉	—	2	2	no	—
166	C₄²×C₁₉	—	2	2	no	—
167	C₄²×C₁₉	—	2	2	no	—
168	C₄²×C₁₉	—	2	2	no	—
169	C₄²×C₁₉	—	2	2	no	—
170	C₄²×C₁₉	—	2	2	no	—
171	C₄²×C₁₉	—	2	2	no	—
172	C₄²×C₁₉	C₂×D₄	1	2	yes	—
173	C₄²×C₁₉	C₂×D₄	1	2	yes	—
174	#32921	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂³×C₁₉	—	2	2	no	—
176	C₂³×C₁₉	—	4	4	no	—
177	C₂³×C₁₉	—	4	4	no	—
178	C₂³×C₁₉	—	4	2	no	—
179	C₂³×C₁₉	—	4	2	no	—
180	C₂³×C₁₉	—	4	2	no	—
181	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₁₉	—	2	8	no	—
183	Q₈×C₁₉	—	2	4	no	—
184	Q₈×C₁₉	—	2	2	no	—
185	Q₈×C₁₉	—	2	4	no	—
186	Q₈×C₁₉	#121	1	4	yes	—
187	D₄×C₁₉	—	2	8	no	—
188	D₄×C₁₉	—	2	4	no	—
189	D₄×C₁₉	—	2	4	no	—
190	D₄×C₁₉	—	2	2	no	—
191	D₄×C₁₉	—	4	4	no	—
192	D₄×C₁₉	—	4	4	no	—
193	D₄×C₁₉	—	8	2	no	—
194	D₄×C₁₉	—	8	4	no	—
195	D₄×C₁₉	—	8	2	no	—
196	D₄×C₁₉	#121	1	4	yes	—
197	C₂×C₄×C₁₉	—	2	16	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	4	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	8	2	no	—
214	C₂×C₄×C₁₉	—	8	4	no	—
215	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
216	C₂×C₄×C₁₉	#120	1	2	yes	—
217	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
218	C₂×C₄×C₁₉	#121	1	4	yes	—
219	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
222	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
223	C₈×C₁₉	—	4	4	no	—
224	C₄×2₋¹⁺⁴	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#3038	C₂×C₁₉	1	2	yes	complemented
226	C₂×#454	C₂×C₁₉	1	2	yes	complemented
227	#2548	C₂×C₁₉	1	1	yes	characteristic, complemented
228	#1888	C₂×C₁₉	1	2	yes	complemented
229	#1883	C₂×C₁₉	1	4	yes	complemented
230	#1806	C₂×C₁₉	1	2	yes	complemented
231	#1801	C₂×C₁₉	1	1	yes	characteristic, complemented
232	C₂²×C₁₉	—	2	1	no	—
233	C₂²×C₁₉	—	2	1	no	—
234	C₂²×C₁₉	—	2	4	no	—
235	C₂²×C₁₉	—	4	2	no	—
236	C₂²×C₁₉	—	4	2	no	—
237	C₂²×C₁₉	—	8	4	no	—
238	C₂²×C₁₉	—	8	4	no	—
239	C₂²×C₁₉	—	8	2	no	—
240	C₂²×C₁₉	—	8	2	no	—
241	C₂²×C₁₉	—	8	2	no	—
242	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
243	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
244	C₂²×C₁₉	#525	1	1	yes	characteristic
245	C₄×C₁₉	—	2	4	no	—
246	C₄×C₁₉	—	2	4	no	—
247	C₄×C₁₉	—	2	1	no	—
248	C₄×C₁₉	—	2	2	no	—
249	C₄×C₁₉	—	4	2	no	—
250	C₄×C₁₉	—	4	2	no	—
251	C₄×C₁₉	—	4	2	no	—
252	C₄×C₁₉	—	8	2	no	—
253	C₄×C₁₉	#454	1	2	yes	complemented
254	C₄×C₁₉	C₂×#121	1	2	yes	—
255	C₄×C₁₉	#525	1	2	yes	—
256	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic
257	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	4	yes	—
258	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
259	C₂×#124	C₂²×C₁₉	1	2	yes	—
260	#520	—	2	2	no	—
261	#520	—	2	2	no	—
262	#520	C₂²×C₁₉	1	2	yes	—
263	#519	—	2	2	no	—
264	#519	C₂²×C₁₉	1	1	yes	characteristic
265	C₄×#41	—	2	2	no	—
266	C₄×#41	—	2	2	no	—
267	C₄×#41	C₂²×C₁₉	1	2	yes	—
268	C₂×C₄×Q₈	—	2	2	no	—
269	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
270	#460	—	2	2	no	—
271	#460	—	2	2	no	—
272	#459	—	2	2	no	—
273	#459	—	2	2	no	—
274	#454	—	2	8	no	—
275	#423	C₂²×C₁₉	1	2	yes	—
276	C₂×#104	C₂²×C₁₉	1	4	yes	—
277	#418	C₂²×C₁₉	1	4	yes	—
278	C₂×#101	C₂²×C₁₉	1	2	yes	—
279	#394	—	2	2	no	—
280	#390	—	2	2	no	—
281	#390	C₂²×C₁₉	1	2	yes	—
282	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
283	#343	C₂²×C₁₉	1	2	yes	—
284	#339	C₂²×C₁₉	1	4	yes	—
285	C₂×C₁₉	—	2	1	no	—
286	C₂×C₁₉	—	2	1	no	—
287	C₂×C₁₉	—	4	4	no	—
288	C₂×C₁₉	—	16	2	no	—
289	C₂×C₁₉	#2847	1	1	yes	characteristic
290	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
291	C₂×C₁₉	#3021	1	1	yes	characteristic
292	2₋¹⁺⁴	—	2	4	no	—
293	2₋¹⁺⁴	—	2	2	no	—
294	2₋¹⁺⁴	D₄×C₁₉	1	4	yes	complemented
295	C₂×#41	—	2	2	no	—
296	C₂×#41	—	2	2	no	—
297	C₂×#41	C₂³×C₁₉	1	2	yes	—
298	C₂²×Q₈	—	2	2	no	—
299	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
300	C₂²×D₄	—	2	1	no	—
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
303	AGL(1,ℤ/8)	—	2	8	no	—
304	AGL(1,ℤ/8)	—	2	8	no	—
305	C₂×SD₁₆	—	2	4	no	—
306	C₂×D₈	—	2	4	no	—
307	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
308	#127	—	2	2	no	—
309	#127	—	2	2	no	—
310	#124	—	2	4	no	—
311	#124	—	2	4	no	—
312	C₄×Q₈	—	2	2	no	—
313	C₄×Q₈	—	2	4	no	—
314	C₄×Q₈	—	2	2	no	—
315	C₄×Q₈	—	2	2	no	—
316	C₄×Q₈	—	2	2	no	—
317	C₄×Q₈	—	2	2	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	D₄×C₁₉	1	2	yes	—
321	C₄×Q₈	D₄×C₁₉	1	2	yes	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	4	no	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	—	2	2	no	—
326	C₄×D₄	—	2	2	no	—
327	C₄×D₄	—	2	4	no	—
328	C₄×D₄	—	2	2	no	—
329	C₄×D₄	D₄×C₁₉	1	2	yes	—
330	C₄×D₄	D₄×C₁₉	1	2	yes	—
331	#117	—	2	4	no	—
332	#117	—	2	4	no	—
333	#117	—	2	2	no	—
334	#117	—	2	2	no	—
335	#117	—	2	2	no	—
336	#117	C₂³×C₁₉	1	2	yes	—
337	C₂×C₄⋊C₄	—	2	4	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	4	no	—
343	C₂×C₂²⋊C₄	—	2	4	no	—
344	C₂×C₄²	—	2	4	no	—
345	C₂×C₄²	—	2	2	no	—
346	C₂×C₄²	D₄×C₁₉	1	2	yes	—
347	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
348	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
349	C₄⋊C₈	—	2	2	no	—
350	C₄⋊C₈	—	2	2	no	—
351	#104	—	2	8	no	—
352	#102	—	2	4	no	—
353	#102	—	2	4	no	—
354	#101	—	2	4	no	—
355	#95	—	2	1	no	—
356	C₁₉	#32921	1	1	yes	characteristic, direct product factor, Sylow
357	C₂⁴	—	2	2	no	—
358	#41	—	2	8	no	—
359	#41	—	2	8	no	—
360	#41	—	2	8	no	—
361	#41	—	2	8	no	—
362	#41	—	2	2	no	—
363	#41	—	2	2	no	—
364	#41	C₂×D₄×C₁₉	1	4	yes	—
365	#41	#41×C₁₉	1	4	yes	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	8	no	—
368	C₂×Q₈	—	2	8	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
372	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
373	C₂×Q₈	#41×C₁₉	1	2	yes	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	4	4	no	—
381	C₂×D₄	—	4	1	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	1	no	—
384	C₂×D₄	—	8	2	no	—
385	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
394	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
395	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
397	SD₁₆	—	4	8	no	—
398	D₈	—	4	8	no	—
399	M₁₆	—	2	4	no	—
400	M₁₆	—	2	4	no	—
401	C₂×C₈	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
411	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	4	8	no	—
417	C₂²⋊C₄	—	8	4	no	—
418	C₄²	—	2	4	no	—
419	C₄²	—	2	4	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	C₂×D₄×C₁₉	1	2	yes	—
428	C₄²	C₂×D₄×C₁₉	1	2	yes	—
429	C₂³	—	2	2	no	—
430	C₂³	—	4	4	no	—
431	C₂³	—	4	4	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
436	Q₈	—	2	8	no	—
437	Q₈	—	2	4	no	—
438	Q₈	—	2	2	no	—
439	Q₈	—	2	4	no	—
440	Q₈	C₁₉×#121	1	4	yes	—
441	D₄	—	2	8	no	—
442	D₄	—	2	4	no	—
443	D₄	—	2	4	no	—
444	D₄	—	2	2	no	—
445	D₄	—	4	4	no	—
446	D₄	—	4	4	no	—
447	D₄	—	8	2	no	—
448	D₄	—	8	4	no	—
449	D₄	—	8	2	no	—
450	D₄	C₁₉×#121	1	4	yes	—
451	C₂×C₄	—	2	16	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	8	2	no	—
468	C₂×C₄	—	8	4	no	—
469	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
470	C₂×C₄	C₁₉×#120	1	2	yes	—
471	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
472	C₂×C₄	C₁₉×#121	1	4	yes	—
473	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
474	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
475	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
476	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
477	C₈	—	4	4	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	8	4	no	—
484	C₂²	—	8	4	no	—
485	C₂²	—	8	2	no	—
486	C₂²	—	8	2	no	—
487	C₂²	—	8	2	no	—
488	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
489	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
490	C₂²	C₁₉×#525	1	1	yes	characteristic
491	C₄	—	2	1	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	4	no	—
494	C₄	—	2	4	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	8	2	no	—
499	C₄	C₁₉×#454	1	2	yes	complemented
500	C₄	C₂×C₁₉×#121	1	2	yes	—
501	C₄	C₁₉×#525	1	2	yes	—
502	C₂	—	2	1	no	—
503	C₂	—	2	1	no	—
504	C₂	—	4	4	no	—
505	C₂	—	16	2	no	—
506	C₂	C₁₉×#2847	1	1	yes	characteristic
507	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
508	C₂	C₁₉×#3021	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 ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×C₁₉×2₋¹⁺⁴	C₂	semidirect
2. C₁₉×#3038	C₂	semidirect
3. C₂×C₁₉×#454	C₂	semidirect
4. C₁₉×#2548	C₂	semidirect
5. C₁₉×#1888	C₂	semidirect
6. C₁₉×#1883	C₂	semidirect
7. C₁₉×#1806	C₂	semidirect
8. C₁₉×#1801	C₂	semidirect
40. C₁₉×2₋¹⁺⁴	D₄	semidirect
174. #32921	C₁₉	direct (N × H)
224. C₄×2₋¹⁺⁴	C₂×C₁₉	semidirect
225. #3038	C₂×C₁₉	semidirect
226. C₂×#454	C₂×C₁₉	semidirect
227. #2548	C₂×C₁₉	semidirect
228. #1888	C₂×C₁₉	semidirect
229. #1883	C₂×C₁₉	semidirect
230. #1806	C₂×C₁₉	semidirect
231. #1801	C₂×C₁₉	semidirect
253. C₄×C₁₉	#454	semidirect
294. 2₋¹⁺⁴	D₄×C₁₉	semidirect
356. C₁₉	#32921	direct (N × H)
499. C₄	C₁₉×#454	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₉×2₋¹⁺⁴	2
C₁₉×#3038	2
C₂×C₁₉×#454	2
C₁₉×#2548	2
C₁₉×#1888	2
C₁₉×#1883	2
C₁₉×#1806	2
C₁₉×#1801	2
#32921	19

Subgroups — C19×#32921 #18038880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32921 #18038880