Subgroups — C₁₉×#23602 #18029561

Order 4864.

1098 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#430	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2911	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2905	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#418	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#418	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₉×#100	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2063	C₂	1	8	yes	maximal, complemented
8	C₁₉×#1742	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₁₉×#430	—	2	4	no	—
17	C₂×C₁₉×#108	C₂²	1	4	yes	complemented
18	C₁₉×#428	—	2	2	no	—
19	C₁₉×#428	C₂²	1	4	yes	complemented
20	C₁₉×#427	—	2	2	no	—
21	C₁₉×#424	—	2	2	no	—
22	C₁₉×#424	C₂²	1	4	yes	complemented
23	C₁₉×#423	—	2	2	no	—
24	C₁₉×#418	—	2	2	no	—
25	C₁₉×#418	—	2	2	no	—
26	C₁₉×#418	—	2	2	no	—
27	C₁₉×#418	C₂²	1	4	yes	—
28	C₂×C₁₉×#102	—	2	2	no	—
29	C₂×C₁₉×#102	C₂²	1	4	yes	—
30	C₂×C₁₉×#100	—	2	4	no	—
31	C₂×C₁₉×#100	C₂²	1	4	yes	—
32	C₁₉×#343	C₂²	1	4	yes	complemented
33	C₂⁵×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	—	2	1	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	—	2	2	no	—
39	C₂²×D₄×C₁₉	—	2	2	no	—
40	C₂²×D₄×C₁₉	—	2	2	no	—
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	Q₈	1	4	yes	—
43	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₁₉	—	2	1	no	—
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	—	2	2	no	—
49	C₂×M₁₆×C₁₉	—	2	1	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂×M₁₆×C₁₉	—	2	2	no	—
52	C₂×M₁₆×C₁₉	—	2	2	no	—
53	C₂×M₁₆×C₁₉	—	2	2	no	—
54	C₂×M₁₆×C₁₉	—	2	2	no	—
55	C₂×M₁₆×C₁₉	D₄	1	4	yes	—
56	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
57	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
58	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
59	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
60	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₉	—	2	1	no	—
62	C₂²×C₈×C₁₉	—	2	1	no	—
63	C₂²×C₈×C₁₉	—	2	1	no	—
64	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
65	C₁₉×#117	—	2	1	no	—
66	C₁₉×#117	—	2	1	no	—
67	C₁₉×#117	—	2	1	no	—
68	C₁₉×#117	—	2	1	no	—
69	C₁₉×#117	—	2	1	no	—
70	C₁₉×#117	—	2	1	no	—
71	C₁₉×#117	D₄	1	2	yes	—
72	C₁₉×#117	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄²×C₁₉	—	2	1	no	—
78	C₂×C₄²×C₁₉	—	2	1	no	—
79	C₁₉×#108	—	2	8	no	—
80	C₁₉×#107	—	2	4	no	—
81	C₁₉×#106	—	2	4	no	—
82	C₁₉×C₄⋊C₈	—	2	8	no	—
83	C₁₉×#102	—	2	8	no	—
84	C₁₉×#102	—	2	8	no	—
85	C₁₉×#100	—	2	8	no	—
86	C₂⁴×C₁₉	—	2	4	no	—
87	C₂⁴×C₁₉	—	2	2	no	—
88	C₂⁴×C₁₉	—	4	1	no	—
89	C₂⁴×C₁₉	—	4	1	no	—
90	C₂⁴×C₁₉	—	4	2	no	—
91	C₂⁴×C₁₉	—	8	4	no	—
92	C₂⁴×C₁₉	#41	1	1	yes	characteristic
93	C₂×D₄×C₁₉	—	2	4	no	—
94	C₂×D₄×C₁₉	—	2	4	no	—
95	C₂×D₄×C₁₉	—	2	4	no	—
96	C₂×D₄×C₁₉	—	2	4	no	—
97	C₂×D₄×C₁₉	—	2	4	no	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	—	2	2	no	—
100	C₂×D₄×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	2	2	no	—
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂×D₄×C₁₉	—	4	2	no	—
104	C₂×D₄×C₁₉	—	4	2	no	—
105	C₂×D₄×C₁₉	—	4	2	no	—
106	C₂×D₄×C₁₉	—	4	2	no	—
107	C₂×D₄×C₁₉	—	4	1	no	—
108	C₂×D₄×C₁₉	—	4	1	no	—
109	C₂×D₄×C₁₉	—	4	2	no	—
110	C₂×D₄×C₁₉	C₂×Q₈	1	4	yes	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
119	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	#41	1	2	yes	—
121	C₂²×C₄×C₁₉	#41	1	2	yes	—
122	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
123	M₁₆×C₁₉	—	2	4	no	—
124	M₁₆×C₁₉	—	2	4	no	—
125	M₁₆×C₁₉	—	2	4	no	—
126	M₁₆×C₁₉	—	2	2	no	—
127	M₁₆×C₁₉	—	2	2	no	—
128	M₁₆×C₁₉	—	2	2	no	—
129	M₁₆×C₁₉	—	2	2	no	—
130	M₁₆×C₁₉	—	2	2	no	—
131	M₁₆×C₁₉	—	4	2	no	—
132	M₁₆×C₁₉	—	4	2	no	—
133	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
134	C₂×C₈×C₁₉	—	2	4	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₂×C₈×C₁₉	—	2	2	no	—
139	C₂×C₈×C₁₉	—	2	2	no	—
140	C₂×C₈×C₁₉	—	4	2	no	—
141	C₂×C₈×C₁₉	—	4	2	no	—
142	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
147	C₂²⋊C₄×C₁₉	—	2	2	no	—
148	C₂²⋊C₄×C₁₉	—	2	2	no	—
149	C₂²⋊C₄×C₁₉	—	4	1	no	—
150	C₂²⋊C₄×C₁₉	—	4	1	no	—
151	C₄²×C₁₉	—	2	2	no	—
152	C₄²×C₁₉	—	2	2	no	—
153	C₄²×C₁₉	—	4	1	no	—
154	C₄²×C₁₉	—	4	1	no	—
155	#23602	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂³×C₁₉	—	2	4	no	—
157	C₂³×C₁₉	—	4	2	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	4	4	no	—
161	C₂³×C₁₉	—	4	4	no	—
162	C₂³×C₁₉	—	8	4	no	—
163	C₂³×C₁₉	—	8	4	no	—
164	C₂³×C₁₉	—	8	4	no	—
165	C₂³×C₁₉	—	8	8	no	—
166	C₂³×C₁₉	—	8	8	no	—
167	C₂³×C₁₉	#121	1	1	yes	characteristic
168	C₂³×C₁₉	#121	1	1	yes	characteristic
169	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
170	C₂³×C₁₉	#126	1	2	yes	—
171	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
172	D₄×C₁₉	—	2	4	no	—
173	D₄×C₁₉	—	2	4	no	—
174	D₄×C₁₉	—	4	2	no	—
175	D₄×C₁₉	—	4	2	no	—
176	D₄×C₁₉	—	4	4	no	—
177	D₄×C₁₉	—	4	4	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	8	2	no	—
181	C₂×C₄×C₁₉	—	8	2	no	—
182	C₂×C₄×C₁₉	#121	1	2	yes	—
183	C₂×C₄×C₁₉	#121	1	2	yes	—
184	C₂×C₄×C₁₉	#121	1	2	yes	—
185	C₂×C₄×C₁₉	#121	1	2	yes	—
186	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
189	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
190	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
191	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
192	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
193	C₂×C₄×C₁₉	#126	1	2	yes	—
194	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
200	C₈×C₁₉	—	2	4	no	—
201	C₈×C₁₉	—	2	4	no	—
202	C₈×C₁₉	—	4	2	no	—
203	C₈×C₁₉	—	4	2	no	—
204	C₂×#430	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#2911	C₂×C₁₉	1	1	yes	characteristic, complemented
206	#2905	C₂×C₁₉	1	1	yes	characteristic, complemented
207	C₂×#418	C₂×C₁₉	1	1	yes	characteristic
208	C₂×#418	C₂×C₁₉	1	1	yes	characteristic
209	C₂²×#100	C₂×C₁₉	1	1	yes	characteristic
210	#2063	C₂×C₁₉	1	8	yes	complemented
211	#1742	C₂×C₁₉	1	1	yes	characteristic, complemented
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	2	2	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	—	4	2	no	—
217	C₂²×C₁₉	—	4	4	no	—
218	C₂²×C₁₉	—	8	4	no	—
219	C₂²×C₁₉	—	8	8	no	—
220	C₂²×C₁₉	—	8	4	no	—
221	C₂²×C₁₉	—	8	8	no	—
222	C₂²×C₁₉	—	8	4	no	—
223	C₂²×C₁₉	#396	1	2	yes	—
224	C₂²×C₁₉	#396	1	2	yes	—
225	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
226	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
227	C₂²×C₁₉	C₂×#126	1	1	yes	characteristic
228	C₄×C₁₉	—	4	4	no	—
229	C₄×C₁₉	—	8	2	no	—
230	C₄×C₁₉	#396	1	2	yes	—
231	C₄×C₁₉	#396	1	2	yes	—
232	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
233	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
234	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
235	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
236	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
237	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
238	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
239	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
240	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
241	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
242	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
243	#430	—	2	4	no	—
244	C₂×#108	C₂²×C₁₉	1	4	yes	complemented
245	#428	—	2	2	no	—
246	#428	C₂²×C₁₉	1	4	yes	complemented
247	#427	—	2	2	no	—
248	#424	—	2	2	no	—
249	#424	C₂²×C₁₉	1	4	yes	complemented
250	#423	—	2	2	no	—
251	#418	—	2	2	no	—
252	#418	—	2	2	no	—
253	#418	—	2	2	no	—
254	#418	C₂²×C₁₉	1	4	yes	—
255	C₂×#102	—	2	2	no	—
256	C₂×#102	C₂²×C₁₉	1	4	yes	—
257	C₂×#100	—	2	4	no	—
258	C₂×#100	C₂²×C₁₉	1	4	yes	—
259	#343	C₂²×C₁₉	1	4	yes	complemented
260	C₂×C₁₉	—	2	1	no	—
261	C₂×C₁₉	—	2	1	no	—
262	C₂×C₁₉	—	2	2	no	—
263	C₂×C₁₉	—	2	2	no	—
264	C₂×C₁₉	—	8	4	no	—
265	C₂×C₁₉	C₂×#396	1	1	yes	characteristic
266	C₂×C₁₉	#3068	1	2	yes	—
267	C₂⁵	—	2	1	no	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂²×D₄	—	2	2	no	—
273	C₂²×D₄	—	2	2	no	—
274	C₂²×D₄	—	2	2	no	—
275	C₂²×D₄	—	2	1	no	—
276	C₂²×D₄	Q₈×C₁₉	1	4	yes	—
277	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
278	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	2	1	no	—
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	—	2	2	no	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	D₄×C₁₉	1	4	yes	—
290	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
291	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
292	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
293	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
294	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
295	C₂²×C₈	—	2	1	no	—
296	C₂²×C₈	—	2	1	no	—
297	C₂²×C₈	—	2	1	no	—
298	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
299	#117	—	2	1	no	—
300	#117	—	2	1	no	—
301	#117	—	2	1	no	—
302	#117	—	2	1	no	—
303	#117	—	2	1	no	—
304	#117	—	2	1	no	—
305	#117	D₄×C₁₉	1	2	yes	—
306	#117	C₂³×C₁₉	1	2	yes	—
307	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	#108	—	2	8	no	—
314	#107	—	2	4	no	—
315	#106	—	2	4	no	—
316	C₄⋊C₈	—	2	8	no	—
317	#102	—	2	8	no	—
318	#102	—	2	8	no	—
319	#100	—	2	8	no	—
320	C₁₉	#23602	1	1	yes	characteristic, direct product factor, Sylow
321	C₂⁴	—	2	4	no	—
322	C₂⁴	—	2	2	no	—
323	C₂⁴	—	4	1	no	—
324	C₂⁴	—	4	1	no	—
325	C₂⁴	—	4	2	no	—
326	C₂⁴	—	8	4	no	—
327	C₂⁴	#41×C₁₉	1	1	yes	characteristic
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	C₂×Q₈×C₁₉	1	4	yes	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
353	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
354	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
355	C₂²×C₄	#41×C₁₉	1	2	yes	—
356	C₂²×C₄	#41×C₁₉	1	2	yes	—
357	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
358	M₁₆	—	2	4	no	—
359	M₁₆	—	2	4	no	—
360	M₁₆	—	2	4	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	2	2	no	—
365	M₁₆	—	2	2	no	—
366	M₁₆	—	4	2	no	—
367	M₁₆	—	4	2	no	—
368	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
369	C₂×C₈	—	2	4	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	4	2	no	—
376	C₂×C₈	—	4	2	no	—
377	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	4	1	no	—
389	C₄²	—	4	1	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	4	no	—
393	C₂³	—	4	4	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	8	4	no	—
397	C₂³	—	8	4	no	—
398	C₂³	—	8	4	no	—
399	C₂³	—	8	8	no	—
400	C₂³	—	8	8	no	—
401	C₂³	C₁₉×#121	1	1	yes	characteristic
402	C₂³	C₁₉×#121	1	1	yes	characteristic
403	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
404	C₂³	C₁₉×#126	1	2	yes	—
405	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	4	4	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	—	8	2	no	—
416	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
417	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
418	C₂×C₄	C₁₉×#121	1	2	yes	—
419	C₂×C₄	C₁₉×#121	1	2	yes	—
420	C₂×C₄	C₁₉×#121	1	2	yes	—
421	C₂×C₄	C₁₉×#121	1	2	yes	—
422	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
423	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
424	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
425	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
426	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
427	C₂×C₄	C₁₉×#126	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
430	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
431	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
432	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
434	C₈	—	2	4	no	—
435	C₈	—	2	4	no	—
436	C₈	—	4	2	no	—
437	C₈	—	4	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	8	4	no	—
445	C₂²	—	8	8	no	—
446	C₂²	—	8	4	no	—
447	C₂²	—	8	8	no	—
448	C₂²	—	8	4	no	—
449	C₂²	C₁₉×#396	1	2	yes	—
450	C₂²	C₁₉×#396	1	2	yes	—
451	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
452	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
453	C₂²	C₂×C₁₉×#126	1	1	yes	characteristic
454	C₄	—	4	4	no	—
455	C₄	—	8	2	no	—
456	C₄	C₁₉×#396	1	2	yes	—
457	C₄	C₁₉×#396	1	2	yes	—
458	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
459	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
460	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
461	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
462	C₂	—	2	2	no	—
463	C₂	—	2	2	no	—
464	C₂	—	2	1	no	—
465	C₂	—	2	1	no	—
466	C₂	—	8	4	no	—
467	C₂	C₂×C₁₉×#396	1	1	yes	characteristic
468	C₂	C₁₉×#3068	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
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. C₂×C₁₉×#430	C₂	semidirect
2. C₁₉×#2911	C₂	semidirect
3. C₁₉×#2905	C₂	semidirect
7. C₁₉×#2063	C₂	semidirect
8. C₁₉×#1742	C₂	semidirect
17. C₂×C₁₉×#108	C₂²	semidirect
19. C₁₉×#428	C₂²	semidirect
22. C₁₉×#424	C₂²	semidirect
32. C₁₉×#343	C₂²	semidirect
155. #23602	C₁₉	direct (N × H)
204. C₂×#430	C₂×C₁₉	semidirect
205. #2911	C₂×C₁₉	semidirect
206. #2905	C₂×C₁₉	semidirect
210. #2063	C₂×C₁₉	semidirect
211. #1742	C₂×C₁₉	semidirect
244. C₂×#108	C₂²×C₁₉	semidirect
246. #428	C₂²×C₁₉	semidirect
249. #424	C₂²×C₁₉	semidirect
259. #343	C₂²×C₁₉	semidirect
320. C₁₉	#23602	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#430	2
C₁₉×#2911	2
C₁₉×#2905	2
C₂×C₁₉×#418	2
C₂²×C₁₉×#100	2
C₁₉×#2063	2
C₁₉×#1742	2
#23602	19

Subgroups — C19×#23602 #18029561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23602 #18029561