Subgroups — C₁₉×#19026 #18024985

Order 4864.

1012 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3217	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3138	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1657	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1656	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1531	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1527	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1524	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₁₉	—	2	1	no	—
11	C₂²×D₈×C₁₉	—	2	1	no	—
12	C₁₉×#563	C₂²	1	2	yes	complemented
13	C₁₉×#562	C₂²	1	2	yes	complemented
14	C₁₉×#556	—	2	1	no	—
15	C₁₉×#551	—	2	2	no	—
16	D₄×Q₈×C₁₉	—	2	1	no	—
17	C₁₉×#548	—	2	1	no	—
18	C₁₉×#546	—	2	1	no	—
19	C₁₉×#543	—	2	1	no	—
20	C₁₉×#542	—	2	1	no	—
21	C₁₉×#542	—	2	2	no	—
22	C₁₉×#538	—	2	1	no	—
23	C₁₉×#536	—	2	1	no	—
24	C₁₉×#533	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
26	C₁₉×#529	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
28	C₁₉×#496	—	2	2	no	—
29	C₁₉×#496	C₂²	1	4	yes	—
30	C₁₉×#496	C₂²	1	2	yes	complemented
31	C₁₉×#490	C₂²	1	4	yes	complemented
32	C₁₉×#490	C₂²	1	2	yes	complemented
33	C₁₉×#486	—	2	1	no	—
34	C₁₉×#486	—	2	1	no	—
35	C₁₉×#460	—	2	1	no	—
36	C₁₉×#459	—	2	1	no	—
37	C₁₉×#450	—	2	1	no	—
38	C₁₉×#447	—	2	1	no	—
39	C₁₉×#432	C₂²	1	1	yes	characteristic
40	C₁₉×#418	—	2	2	no	—
41	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
43	C₁₉×#330	C₂²	1	4	yes	complemented
44	C₁₉×#330	C₂²	1	2	yes	complemented
45	C₁₉×#329	C₂²	1	2	yes	complemented
46	C₁₉×#329	C₂²	1	4	yes	complemented
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂²×Q₈×C₁₉	—	2	1	no	—
49	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₉	—	2	1	no	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
54	C₂×SD₁₆×C₁₉	—	2	4	no	—
55	C₂×SD₁₆×C₁₉	—	2	2	no	—
56	C₂×SD₁₆×C₁₉	—	4	4	no	—
57	C₂×D₈×C₁₉	—	2	4	no	—
58	C₂×D₈×C₁₉	—	2	2	no	—
59	C₂×D₈×C₁₉	—	4	4	no	—
60	C₂×M₁₆×C₁₉	—	2	1	no	—
61	C₂²×C₈×C₁₉	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	—	2	2	no	—
64	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₁₉×#127	—	2	1	no	—
67	C₁₉×#127	—	2	1	no	—
68	C₁₉×#127	—	2	1	no	—
69	C₁₉×#127	C₂³	1	2	yes	—
70	C₁₉×#126	—	2	2	no	—
71	C₁₉×#126	—	2	2	no	—
72	C₁₉×#126	—	2	2	no	—
73	C₁₉×#126	—	2	1	no	—
74	C₁₉×#125	C₂³	1	1	yes	characteristic
75	C₁₉×#125	C₂³	1	2	yes	—
76	C₁₉×#124	—	2	1	no	—
77	C₁₉×#124	—	2	2	no	—
78	C₁₉×#124	—	2	2	no	—
79	C₁₉×#124	—	2	1	no	—
80	C₁₉×#124	—	2	1	no	—
81	C₁₉×#124	D₄	1	2	yes	—
82	C₁₉×#124	C₂³	1	2	yes	—
83	C₁₉×#124	C₂³	1	1	yes	characteristic
84	C₁₉×#123	—	2	2	no	—
85	C₁₉×#123	—	2	2	no	—
86	C₁₉×#123	—	2	1	no	—
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×#123	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	2	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	no	—
93	C₁₉×C₂²⋊Q₈	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	—	2	1	no	—
96	C₁₉×C₂²⋊Q₈	—	2	1	no	—
97	C₁₉×C₂²⋊Q₈	—	2	2	no	—
98	C₁₉×C₂²⋊Q₈	—	2	2	no	—
99	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
100	C₁₉×#121	—	2	1	no	—
101	C₁₉×#121	—	2	2	no	—
102	C₁₉×#121	—	2	2	no	—
103	C₁₉×#121	D₄	1	1	yes	characteristic
104	C₁₉×#120	—	2	2	no	—
105	C₄×Q₈×C₁₉	—	2	1	no	—
106	C₄×Q₈×C₁₉	—	2	1	no	—
107	C₄×Q₈×C₁₉	—	2	1	no	—
108	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
109	C₄×D₄×C₁₉	—	2	2	no	—
110	C₄×D₄×C₁₉	—	2	1	no	—
111	C₄×D₄×C₁₉	—	2	2	no	—
112	C₄×D₄×C₁₉	—	2	1	no	—
113	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
114	C₁₉×#117	—	2	2	no	—
115	C₁₉×#117	—	2	1	no	—
116	C₁₉×#117	D₄	1	2	yes	—
117	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
118	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
120	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	—	2	1	no	—
122	C₁₉×#102	—	2	4	no	—
123	C₁₉×#102	—	2	4	no	—
124	C₁₉×#102	—	2	2	no	—
125	C₁₉×#102	—	2	2	no	—
126	C₁₉×C₂²⋊C₈	—	2	1	no	—
127	C₁₉×#97	—	2	1	no	—
128	C₁₉×#97	C₂³	1	2	yes	—
129	C₁₉×#97	C₂³	1	2	yes	—
130	C₁₉×#97	C₂³	1	2	yes	—
131	C₄×C₈×C₁₉	—	2	1	no	—
132	C₂⁴×C₁₉	—	2	1	no	—
133	C₂⁴×C₁₉	—	4	1	no	—
134	#41×C₁₉	—	8	2	no	—
135	C₂×Q₈×C₁₉	—	2	2	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	—	4	2	no	—
140	C₂×Q₈×C₁₉	—	8	2	no	—
141	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	2	2	no	—
150	C₂×D₄×C₁₉	—	4	2	no	—
151	C₂×D₄×C₁₉	—	4	2	no	—
152	C₂×D₄×C₁₉	—	4	2	no	—
153	C₂×D₄×C₁₉	—	4	4	no	—
154	C₂×D₄×C₁₉	—	4	1	no	—
155	C₂×D₄×C₁₉	—	4	1	no	—
156	C₂×D₄×C₁₉	—	4	1	no	—
157	C₂×D₄×C₁₉	—	8	2	no	—
158	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₉	—	2	2	no	—
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	2	2	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	SD₁₆×C₁₉	—	4	8	no	—
169	SD₁₆×C₁₉	—	8	2	no	—
170	D₈×C₁₉	—	4	8	no	—
171	D₈×C₁₉	—	8	2	no	—
172	M₁₆×C₁₉	—	4	2	no	—
173	C₂×C₈×C₁₉	—	2	4	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₂×C₈×C₁₉	—	2	2	no	—
176	C₂×C₈×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
190	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
191	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	2	2	no	—
195	C₂²⋊C₄×C₁₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₉	—	2	2	no	—
197	C₂²⋊C₄×C₁₉	—	2	2	no	—
198	C₂²⋊C₄×C₁₉	—	2	1	no	—
199	C₂²⋊C₄×C₁₉	—	2	2	no	—
200	C₂²⋊C₄×C₁₉	—	2	2	no	—
201	C₂²⋊C₄×C₁₉	—	2	2	no	—
202	C₂²⋊C₄×C₁₉	—	2	1	no	—
203	C₂²⋊C₄×C₁₉	—	2	1	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂²⋊C₄×C₁₉	—	2	2	no	—
206	C₂²⋊C₄×C₁₉	—	2	1	no	—
207	C₂²⋊C₄×C₁₉	—	2	1	no	—
208	C₄²×C₁₉	—	2	2	no	—
209	C₄²×C₁₉	—	2	2	no	—
210	C₄²×C₁₉	—	2	1	no	—
211	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
215	#19026	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂³×C₁₉	—	2	2	no	—
217	C₂³×C₁₉	—	2	1	no	—
218	C₂³×C₁₉	—	4	2	no	—
219	C₂³×C₁₉	—	4	2	no	—
220	C₂³×C₁₉	—	8	1	no	—
221	C₂³×C₁₉	—	8	1	no	—
222	C₂³×C₁₉	—	8	2	no	—
223	C₂³×C₁₉	—	8	2	no	—
224	C₂³×C₁₉	—	8	2	no	—
225	C₂³×C₁₉	#120	1	1	yes	characteristic
226	Q₈×C₁₉	—	4	2	no	—
227	Q₈×C₁₉	—	4	1	no	—
228	Q₈×C₁₉	—	4	2	no	—
229	Q₈×C₁₉	—	4	2	no	—
230	Q₈×C₁₉	—	8	1	no	—
231	Q₈×C₁₉	—	8	2	no	—
232	D₄×C₁₉	—	4	2	no	—
233	D₄×C₁₉	—	4	1	no	—
234	D₄×C₁₉	—	4	2	no	—
235	D₄×C₁₉	—	4	2	no	—
236	D₄×C₁₉	—	4	2	no	—
237	D₄×C₁₉	—	4	2	no	—
238	D₄×C₁₉	—	4	4	no	—
239	D₄×C₁₉	—	4	2	no	—
240	D₄×C₁₉	—	4	2	no	—
241	D₄×C₁₉	—	8	2	no	—
242	D₄×C₁₉	—	8	2	no	—
243	D₄×C₁₉	—	8	2	no	—
244	D₄×C₁₉	—	8	2	no	—
245	D₄×C₁₉	—	8	2	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	2	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	2	no	—
256	C₂×C₄×C₁₉	—	8	1	no	—
257	C₂×C₄×C₁₉	—	8	2	no	—
258	C₂×C₄×C₁₉	—	8	2	no	—
259	C₂×C₄×C₁₉	—	8	2	no	—
260	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
261	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
263	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
266	C₈×C₁₉	—	2	4	no	—
267	C₈×C₁₉	—	4	2	no	—
268	C₈×C₁₉	—	4	2	no	—
269	#3561	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#3217	C₂×C₁₉	1	1	yes	characteristic, complemented
271	C₂×#496	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#3138	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1657	C₂×C₁₉	1	4	yes	complemented
274	#1656	C₂×C₁₉	1	4	yes	complemented
275	#1531	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1527	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1524	C₂×C₁₉	1	1	yes	characteristic, complemented
278	C₂²×C₁₉	—	2	1	no	—
279	C₂²×C₁₉	—	2	1	no	—
280	C₂²×C₁₉	—	4	1	no	—
281	C₂²×C₁₉	—	4	2	no	—
282	C₂²×C₁₉	—	4	1	no	—
283	C₂²×C₁₉	—	4	2	no	—
284	C₂²×C₁₉	—	4	2	no	—
285	C₂²×C₁₉	—	4	1	no	—
286	C₂²×C₁₉	—	8	2	no	—
287	C₂²×C₁₉	—	8	2	no	—
288	C₂²×C₁₉	—	8	2	no	—
289	C₂²×C₁₉	—	16	2	no	—
290	C₂²×C₁₉	—	16	4	no	—
291	C₂²×C₁₉	#454	1	2	yes	—
292	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
293	C₄×C₁₉	—	2	1	no	—
294	C₄×C₁₉	—	2	1	no	—
295	C₄×C₁₉	—	2	1	no	—
296	C₄×C₁₉	—	2	1	no	—
297	C₄×C₁₉	—	2	1	no	—
298	C₄×C₁₉	—	4	1	no	—
299	C₄×C₁₉	—	4	2	no	—
300	C₄×C₁₉	—	4	2	no	—
301	C₄×C₁₉	—	4	1	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	4	2	no	—
304	C₄×C₁₉	#453	1	2	yes	—
305	C₂²×SD₁₆	—	2	1	no	—
306	C₂²×D₈	—	2	1	no	—
307	#563	C₂²×C₁₉	1	2	yes	complemented
308	#562	C₂²×C₁₉	1	2	yes	complemented
309	#556	—	2	1	no	—
310	#551	—	2	2	no	—
311	D₄×Q₈	—	2	1	no	—
312	#548	—	2	1	no	—
313	#546	—	2	1	no	—
314	#543	—	2	1	no	—
315	#542	—	2	1	no	—
316	#542	—	2	2	no	—
317	#538	—	2	1	no	—
318	#536	—	2	1	no	—
319	#533	C₂²×C₁₉	1	1	yes	characteristic
320	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
321	#529	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
323	#496	—	2	2	no	—
324	#496	C₂²×C₁₉	1	4	yes	—
325	#496	C₂²×C₁₉	1	2	yes	complemented
326	#490	C₂²×C₁₉	1	4	yes	complemented
327	#490	C₂²×C₁₉	1	2	yes	complemented
328	#486	—	2	1	no	—
329	#486	—	2	1	no	—
330	#460	—	2	1	no	—
331	#459	—	2	1	no	—
332	#450	—	2	1	no	—
333	#447	—	2	1	no	—
334	#432	C₂²×C₁₉	1	1	yes	characteristic
335	#418	—	2	2	no	—
336	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
338	#330	C₂²×C₁₉	1	4	yes	complemented
339	#330	C₂²×C₁₉	1	2	yes	complemented
340	#329	C₂²×C₁₉	1	2	yes	complemented
341	#329	C₂²×C₁₉	1	4	yes	complemented
342	C₂×C₁₉	—	2	2	no	—
343	C₂×C₁₉	—	8	1	no	—
344	C₂×C₁₉	—	8	2	no	—
345	C₂×C₁₉	—	16	2	no	—
346	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
347	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
348	C₂×C₁₉	#3021	1	1	yes	characteristic
349	C₂×#41	—	2	1	no	—
350	C₂²×Q₈	—	2	1	no	—
351	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
352	C₂²×D₄	—	2	1	no	—
353	C₂²×D₄	—	2	1	no	—
354	C₂²×D₄	—	2	1	no	—
355	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
356	C₂×SD₁₆	—	2	4	no	—
357	C₂×SD₁₆	—	2	2	no	—
358	C₂×SD₁₆	—	4	4	no	—
359	C₂×D₈	—	2	4	no	—
360	C₂×D₈	—	2	2	no	—
361	C₂×D₈	—	4	4	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂²×C₈	—	2	1	no	—
364	C₄⋊Q₈	—	2	1	no	—
365	C₄⋊Q₈	—	2	2	no	—
366	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
367	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
368	#127	—	2	1	no	—
369	#127	—	2	1	no	—
370	#127	—	2	1	no	—
371	#127	C₂³×C₁₉	1	2	yes	—
372	#126	—	2	2	no	—
373	#126	—	2	2	no	—
374	#126	—	2	2	no	—
375	#126	—	2	1	no	—
376	#125	C₂³×C₁₉	1	1	yes	characteristic
377	#125	C₂³×C₁₉	1	2	yes	—
378	#124	—	2	1	no	—
379	#124	—	2	2	no	—
380	#124	—	2	2	no	—
381	#124	—	2	1	no	—
382	#124	—	2	1	no	—
383	#124	D₄×C₁₉	1	2	yes	—
384	#124	C₂³×C₁₉	1	2	yes	—
385	#124	C₂³×C₁₉	1	1	yes	characteristic
386	#123	—	2	2	no	—
387	#123	—	2	2	no	—
388	#123	—	2	1	no	—
389	#123	—	2	2	no	—
390	#123	—	2	2	no	—
391	C₂²⋊Q₈	—	2	2	no	—
392	C₂²⋊Q₈	—	2	2	no	—
393	C₂²⋊Q₈	—	2	1	no	—
394	C₂²⋊Q₈	—	2	2	no	—
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	2	1	no	—
398	C₂²⋊Q₈	—	2	1	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	C₂²⋊Q₈	—	2	2	no	—
401	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
402	#121	—	2	1	no	—
403	#121	—	2	2	no	—
404	#121	—	2	2	no	—
405	#121	D₄×C₁₉	1	1	yes	characteristic
406	#120	—	2	2	no	—
407	C₄×Q₈	—	2	1	no	—
408	C₄×Q₈	—	2	1	no	—
409	C₄×Q₈	—	2	1	no	—
410	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
411	C₄×D₄	—	2	2	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	2	no	—
414	C₄×D₄	—	2	1	no	—
415	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
416	#117	—	2	2	no	—
417	#117	—	2	1	no	—
418	#117	D₄×C₁₉	1	2	yes	—
419	C₂×C₂²⋊C₄	—	2	2	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
423	C₄⋊C₈	—	2	1	no	—
424	#102	—	2	4	no	—
425	#102	—	2	4	no	—
426	#102	—	2	2	no	—
427	#102	—	2	2	no	—
428	C₂²⋊C₈	—	2	1	no	—
429	#97	—	2	1	no	—
430	#97	C₂³×C₁₉	1	2	yes	—
431	#97	C₂³×C₁₉	1	2	yes	—
432	#97	C₂³×C₁₉	1	2	yes	—
433	C₄×C₈	—	2	1	no	—
434	C₁₉	#19026	1	1	yes	characteristic, direct product factor, Sylow
435	C₂⁴	—	2	1	no	—
436	C₂⁴	—	4	1	no	—
437	#41	—	8	2	no	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	4	2	no	—
443	C₂×Q₈	—	8	2	no	—
444	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
445	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	—	4	2	no	—
455	C₂×D₄	—	4	2	no	—
456	C₂×D₄	—	4	4	no	—
457	C₂×D₄	—	4	1	no	—
458	C₂×D₄	—	4	1	no	—
459	C₂×D₄	—	4	1	no	—
460	C₂×D₄	—	8	2	no	—
461	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
471	SD₁₆	—	4	8	no	—
472	SD₁₆	—	8	2	no	—
473	D₈	—	4	8	no	—
474	D₈	—	8	2	no	—
475	M₁₆	—	4	2	no	—
476	C₂×C₈	—	2	4	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
493	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
494	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	2	1	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	2	2	no	—
513	C₄²	—	2	1	no	—
514	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
515	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
516	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
518	C₂³	—	2	2	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	4	2	no	—
521	C₂³	—	4	2	no	—
522	C₂³	—	8	1	no	—
523	C₂³	—	8	1	no	—
524	C₂³	—	8	2	no	—
525	C₂³	—	8	2	no	—
526	C₂³	—	8	2	no	—
527	C₂³	C₁₉×#120	1	1	yes	characteristic
528	Q₈	—	4	2	no	—
529	Q₈	—	4	1	no	—
530	Q₈	—	4	2	no	—
531	Q₈	—	4	2	no	—
532	Q₈	—	8	1	no	—
533	Q₈	—	8	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	1	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	2	no	—
540	D₄	—	4	4	no	—
541	D₄	—	4	2	no	—
542	D₄	—	4	2	no	—
543	D₄	—	8	2	no	—
544	D₄	—	8	2	no	—
545	D₄	—	8	2	no	—
546	D₄	—	8	2	no	—
547	D₄	—	8	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	8	1	no	—
559	C₂×C₄	—	8	2	no	—
560	C₂×C₄	—	8	2	no	—
561	C₂×C₄	—	8	2	no	—
562	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
563	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
564	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
565	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
566	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
568	C₈	—	2	4	no	—
569	C₈	—	4	2	no	—
570	C₈	—	4	2	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	8	2	no	—
580	C₂²	—	8	2	no	—
581	C₂²	—	8	2	no	—
582	C₂²	—	16	2	no	—
583	C₂²	—	16	4	no	—
584	C₂²	C₁₉×#454	1	2	yes	—
585	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	2	no	—
597	C₄	C₁₉×#453	1	2	yes	—
598	C₂	—	2	2	no	—
599	C₂	—	8	2	no	—
600	C₂	—	8	1	no	—
601	C₂	—	16	2	no	—
602	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
603	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
604	C₂	C₁₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ 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. C₁₉×#3561	C₂	semidirect
2. C₁₉×#3217	C₂	semidirect
3. C₂×C₁₉×#496	C₂	semidirect
4. C₁₉×#3138	C₂	semidirect
5. C₁₉×#1657	C₂	semidirect
6. C₁₉×#1656	C₂	semidirect
7. C₁₉×#1531	C₂	semidirect
8. C₁₉×#1527	C₂	semidirect
9. C₁₉×#1524	C₂	semidirect
12. C₁₉×#563	C₂²	semidirect
13. C₁₉×#562	C₂²	semidirect
30. C₁₉×#496	C₂²	semidirect
31. C₁₉×#490	C₂²	semidirect
32. C₁₉×#490	C₂²	semidirect
43. C₁₉×#330	C₂²	semidirect
44. C₁₉×#330	C₂²	semidirect
45. C₁₉×#329	C₂²	semidirect
46. C₁₉×#329	C₂²	semidirect
215. #19026	C₁₉	direct (N × H)
269. #3561	C₂×C₁₉	semidirect
270. #3217	C₂×C₁₉	semidirect
271. C₂×#496	C₂×C₁₉	semidirect
272. #3138	C₂×C₁₉	semidirect
273. #1657	C₂×C₁₉	semidirect
274. #1656	C₂×C₁₉	semidirect
275. #1531	C₂×C₁₉	semidirect
276. #1527	C₂×C₁₉	semidirect
277. #1524	C₂×C₁₉	semidirect
307. #563	C₂²×C₁₉	semidirect
308. #562	C₂²×C₁₉	semidirect
325. #496	C₂²×C₁₉	semidirect
326. #490	C₂²×C₁₉	semidirect
327. #490	C₂²×C₁₉	semidirect
338. #330	C₂²×C₁₉	semidirect
339. #330	C₂²×C₁₉	semidirect
340. #329	C₂²×C₁₉	semidirect
341. #329	C₂²×C₁₉	semidirect
434. C₁₉	#19026	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3561	2
C₁₉×#3217	2
C₂×C₁₉×#496	2
C₁₉×#3138	2
C₁₉×#1657	2
C₁₉×#1656	2
C₁₉×#1531	2
C₁₉×#1527	2
C₁₉×#1524	2
#19026	19

Subgroups — C19×#19026 #18024985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19026 #18024985