Subgroups — C₂×C₁₉×#1604 #18024068

Order 4864.

1480 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#537	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#448	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#395	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1604	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₉×#327	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#324	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#41×C₁₉	—	2	1	no	—
8	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×SD₁₆×C₁₉	—	2	2	no	—
10	C₁₉×#537	—	2	4	no	—
11	C₁₉×#537	—	2	2	no	—
12	C₁₉×#537	C₂²	1	4	yes	—
13	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
14	C₂×C₁₉×#121	—	2	2	no	—
15	C₂×C₁₉×#121	—	2	1	no	—
16	C₂×C₁₉×#121	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#448	—	2	4	no	—
20	C₁₉×#448	C₂²	1	8	yes	complemented
21	C₂×C₁₉×#103	—	2	2	no	—
22	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₁₉×#395	—	2	2	no	—
24	C₁₉×#395	C₂²	1	4	yes	complemented
25	C₂×C₁₉×#95	—	2	1	no	—
26	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
27	C₁₉×#327	C₂²	1	8	yes	complemented
28	C₁₉×#324	C₂²	1	4	yes	complemented
29	C₂×#41×C₁₉	—	2	4	no	—
30	C₂×#41×C₁₉	—	2	4	no	—
31	C₂×#41×C₁₉	—	4	4	no	—
32	C₂×#41×C₁₉	—	4	4	no	—
33	C₂²×Q₈×C₁₉	—	2	1	no	—
34	C₂²×Q₈×C₁₉	—	2	1	no	—
35	C₂²×Q₈×C₁₉	—	2	2	no	—
36	C₂²×Q₈×C₁₉	—	2	2	no	—
37	C₂²×Q₈×C₁₉	—	4	4	no	—
38	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
39	C₂²×D₄×C₁₉	—	2	1	no	—
40	C₂²×D₄×C₁₉	—	2	2	no	—
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	D₄	1	2	yes	—
43	C₂³×C₄×C₁₉	—	2	2	no	—
44	C₂³×C₄×C₁₉	—	2	1	no	—
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×SD₁₆×C₁₉	—	2	8	no	—
50	C₂×SD₁₆×C₁₉	—	4	8	no	—
51	C₂²×C₈×C₁₉	—	2	2	no	—
52	C₁₉×C₂²⋊Q₈	—	2	8	no	—
53	C₁₉×C₂²⋊Q₈	—	2	8	no	—
54	C₁₉×#121	—	2	4	no	—
55	C₁₉×#121	—	2	8	no	—
56	C₁₉×#121	—	2	8	no	—
57	C₁₉×#121	—	2	4	no	—
58	C₁₉×#121	—	2	2	no	—
59	C₁₉×#121	—	2	2	no	—
60	C₁₉×#121	D₄	1	4	yes	—
61	C₁₉×#121	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
66	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
67	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
72	C₁₉×#103	—	2	8	no	—
73	C₁₉×C₂²⋊C₈	—	2	2	no	—
74	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
75	C₁₉×#95	—	2	4	no	—
76	C₁₉×#95	—	2	1	no	—
77	C₁₉×#95	C₂³	1	2	yes	—
78	C₂⁴×C₁₉	—	2	2	no	—
79	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
80	#41×C₁₉	—	4	8	no	—
81	#41×C₁₉	—	4	16	no	—
82	#41×C₁₉	—	4	8	no	—
83	C₂×Q₈×C₁₉	—	2	4	no	—
84	C₂×Q₈×C₁₉	—	2	8	no	—
85	C₂×Q₈×C₁₉	—	2	4	no	—
86	C₂×Q₈×C₁₉	—	4	4	no	—
87	C₂×Q₈×C₁₉	—	4	4	no	—
88	C₂×Q₈×C₁₉	—	4	4	no	—
89	C₂×Q₈×C₁₉	—	4	4	no	—
90	C₂×Q₈×C₁₉	—	4	8	no	—
91	C₂×Q₈×C₁₉	—	4	2	no	—
92	C₂×D₄×C₁₉	—	2	4	no	—
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	2	no	—
97	C₂×D₄×C₁₉	—	4	4	no	—
98	C₂×D₄×C₁₉	—	4	4	no	—
99	C₂×D₄×C₁₉	—	4	4	no	—
100	C₂×D₄×C₁₉	—	4	4	no	—
101	C₂×D₄×C₁₉	—	8	2	no	—
102	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	4	no	—
107	C₂²×C₄×C₁₉	—	2	8	no	—
108	C₂²×C₄×C₁₉	—	2	4	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	—	4	8	no	—
116	C₂²×C₄×C₁₉	—	4	2	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	—	4	1	no	—
119	C₂²×C₄×C₁₉	—	4	1	no	—
120	C₂²×C₄×C₁₉	—	4	2	no	—
121	C₂²×C₄×C₁₉	—	4	2	no	—
122	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	complemented
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
129	SD₁₆×C₁₉	—	4	16	no	—
130	C₂×C₈×C₁₉	—	2	4	no	—
131	C₂×C₈×C₁₉	—	4	4	no	—
132	C₄⋊C₄×C₁₉	—	2	4	no	—
133	C₄⋊C₄×C₁₉	—	2	4	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	2	4	no	—
136	C₄⋊C₄×C₁₉	—	4	8	no	—
137	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
138	C₂²⋊C₄×C₁₉	—	2	8	no	—
139	C₂²⋊C₄×C₁₉	—	2	4	no	—
140	C₂²⋊C₄×C₁₉	—	2	4	no	—
141	C₂×#1604	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	2	2	no	—
144	C₂³×C₁₉	—	2	4	no	—
145	C₂³×C₁₉	—	4	4	no	—
146	C₂³×C₁₉	—	4	4	no	—
147	C₂³×C₁₉	—	4	4	no	—
148	C₂³×C₁₉	#120	1	1	yes	characteristic
149	C₂³×C₁₉	#120	1	1	yes	characteristic
150	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
151	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
152	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₁₉	—	2	8	no	—
154	Q₈×C₁₉	—	4	4	no	—
155	Q₈×C₁₉	—	4	8	no	—
156	Q₈×C₁₉	—	4	8	no	—
157	D₄×C₁₉	—	4	4	no	—
158	D₄×C₁₉	—	4	8	no	—
159	D₄×C₁₉	—	4	4	no	—
160	D₄×C₁₉	—	4	4	no	—
161	D₄×C₁₉	—	4	8	no	—
162	D₄×C₁₉	—	8	2	no	—
163	D₄×C₁₉	—	8	4	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	4	no	—
169	C₂×C₄×C₁₉	—	2	4	no	—
170	C₂×C₄×C₁₉	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	4	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	16	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	8	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	4	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	4	no	—
184	C₂×C₄×C₁₉	—	4	4	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	8	1	no	—
188	C₂×C₄×C₁₉	#120	1	2	yes	—
189	C₂×C₄×C₁₉	C₂×SD₁₆	1	4	yes	complemented
190	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
191	C₈×C₁₉	—	4	4	no	—
192	C₂×#537	C₂×C₁₉	1	1	yes	characteristic
193	C₂×#448	C₂×C₁₉	1	2	yes	complemented
194	C₂×#395	C₂×C₁₉	1	1	yes	characteristic, complemented
195	#1604	C₂×C₁₉	1	8	yes	direct product factor
196	C₂×#327	C₂×C₁₉	1	2	yes	complemented
197	C₂×#324	C₂×C₁₉	1	1	yes	characteristic, complemented
198	C₂²×C₁₉	—	2	4	no	—
199	C₂²×C₁₉	—	2	4	no	—
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	2	1	no	—
203	C₂²×C₁₉	—	2	1	no	—
204	C₂²×C₁₉	—	4	4	no	—
205	C₂²×C₁₉	—	4	4	no	—
206	C₂²×C₁₉	—	4	4	no	—
207	C₂²×C₁₉	—	8	8	no	—
208	C₂²×C₁₉	#450	1	2	yes	—
209	C₂²×C₁₉	#450	1	2	yes	—
210	C₂²×C₁₉	#456	1	2	yes	—
211	C₂²×C₁₉	B(4,𝔽₂)	1	2	yes	—
212	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
213	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
214	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₄×C₁₉	—	2	4	no	—
216	C₄×C₁₉	—	2	2	no	—
217	C₄×C₁₉	—	2	2	no	—
218	C₄×C₁₉	—	4	4	no	—
219	C₄×C₁₉	—	4	4	no	—
220	C₄×C₁₉	—	4	4	no	—
221	C₄×C₁₉	—	4	2	no	—
222	C₂²×#41	—	2	1	no	—
223	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
224	C₂²×SD₁₆	—	2	2	no	—
225	#537	—	2	4	no	—
226	#537	—	2	2	no	—
227	#537	C₂²×C₁₉	1	4	yes	—
228	C₂×C₂²⋊Q₈	—	2	2	no	—
229	C₂×#121	—	2	2	no	—
230	C₂×#121	—	2	1	no	—
231	C₂×#121	C₂²×C₁₉	1	2	yes	—
232	C₂²×C₄⋊C₄	—	2	1	no	—
233	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
234	#448	—	2	4	no	—
235	#448	C₂²×C₁₉	1	8	yes	complemented
236	C₂×#103	—	2	2	no	—
237	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
238	#395	—	2	2	no	—
239	#395	C₂²×C₁₉	1	4	yes	complemented
240	C₂×#95	—	2	1	no	—
241	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
242	#327	C₂²×C₁₉	1	8	yes	complemented
243	#324	C₂²×C₁₉	1	4	yes	complemented
244	C₂×C₁₉	—	2	1	no	—
245	C₂×C₁₉	—	2	1	no	—
246	C₂×C₁₉	—	2	2	no	—
247	C₂×C₁₉	—	8	4	no	—
248	C₂×C₁₉	#1604	1	4	yes	direct product factor
249	C₂×C₁₉	C₂×#450	1	1	yes	characteristic
250	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
251	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
252	C₂×#41	—	2	4	no	—
253	C₂×#41	—	2	4	no	—
254	C₂×#41	—	4	4	no	—
255	C₂×#41	—	4	4	no	—
256	C₂²×Q₈	—	2	1	no	—
257	C₂²×Q₈	—	2	1	no	—
258	C₂²×Q₈	—	2	2	no	—
259	C₂²×Q₈	—	2	2	no	—
260	C₂²×Q₈	—	4	4	no	—
261	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	—	2	2	no	—
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	D₄×C₁₉	1	2	yes	—
266	C₂³×C₄	—	2	2	no	—
267	C₂³×C₄	—	2	1	no	—
268	C₂³×C₄	—	2	1	no	—
269	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
270	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
271	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
272	C₂×SD₁₆	—	2	8	no	—
273	C₂×SD₁₆	—	4	8	no	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²⋊Q₈	—	2	8	no	—
276	C₂²⋊Q₈	—	2	8	no	—
277	#121	—	2	4	no	—
278	#121	—	2	8	no	—
279	#121	—	2	8	no	—
280	#121	—	2	4	no	—
281	#121	—	2	2	no	—
282	#121	—	2	2	no	—
283	#121	D₄×C₁₉	1	4	yes	—
284	#121	C₂³×C₁₉	1	4	yes	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	4	no	—
289	C₂×C₄⋊C₄	—	4	4	no	—
290	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
291	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	#103	—	2	8	no	—
296	C₂²⋊C₈	—	2	2	no	—
297	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
298	#95	—	2	4	no	—
299	#95	—	2	1	no	—
300	#95	C₂³×C₁₉	1	2	yes	—
301	C₁₉	C₂×#1604	1	1	yes	characteristic, direct product factor, Sylow
302	C₂⁴	—	2	2	no	—
303	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
304	#41	—	4	16	no	—
305	#41	—	4	8	no	—
306	#41	—	4	8	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	—	2	8	no	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	4	4	no	—
311	C₂×Q₈	—	4	4	no	—
312	C₂×Q₈	—	4	4	no	—
313	C₂×Q₈	—	4	4	no	—
314	C₂×Q₈	—	4	8	no	—
315	C₂×Q₈	—	4	2	no	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	4	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	4	4	no	—
322	C₂×D₄	—	4	4	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	—	4	4	no	—
325	C₂×D₄	—	8	2	no	—
326	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	8	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	SD₁₆×C₁₉	1	4	yes	complemented
347	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
352	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
353	SD₁₆	—	4	16	no	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	4	4	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	4	8	no	—
361	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	4	4	no	—
369	C₂³	—	4	4	no	—
370	C₂³	—	4	4	no	—
371	C₂³	C₁₉×#120	1	1	yes	characteristic
372	C₂³	C₁₉×#120	1	1	yes	characteristic
373	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
374	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
375	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
376	Q₈	—	2	8	no	—
377	Q₈	—	4	4	no	—
378	Q₈	—	4	8	no	—
379	Q₈	—	4	8	no	—
380	D₄	—	4	4	no	—
381	D₄	—	4	8	no	—
382	D₄	—	4	8	no	—
383	D₄	—	4	4	no	—
384	D₄	—	4	4	no	—
385	D₄	—	8	2	no	—
386	D₄	—	8	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	16	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	8	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	8	1	no	—
411	C₂×C₄	C₁₉×#120	1	2	yes	—
412	C₂×C₄	C₂×SD₁₆×C₁₉	1	4	yes	complemented
413	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
414	C₈	—	4	4	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	8	8	no	—
425	C₂²	C₁₉×#450	1	2	yes	—
426	C₂²	C₁₉×#450	1	2	yes	—
427	C₂²	C₁₉×#456	1	2	yes	—
428	C₂²	C₁₉×B(4,𝔽₂)	1	2	yes	—
429	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
430	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
431	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
432	C₄	—	2	4	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	4	4	no	—
436	C₄	—	4	4	no	—
437	C₄	—	4	4	no	—
438	C₄	—	4	2	no	—
439	C₂	—	2	1	no	—
440	C₂	—	2	2	no	—
441	C₂	—	2	1	no	—
442	C₂	—	8	4	no	—
443	C₂	C₁₉×#1604	1	4	yes	direct product factor
444	C₂	C₂×C₁₉×#450	1	1	yes	characteristic
445	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
446	C₂	C₂×C₁₉×B(4,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#537	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#448	C₂	semidirect
3. C₂×C₁₉×#395	C₂	semidirect
4. C₁₉×#1604	C₂	direct (N × H)
5. C₂×C₁₉×#327	C₂	semidirect
6. C₂×C₁₉×#324	C₂	semidirect
20. C₁₉×#448	C₂²	semidirect
24. C₁₉×#395	C₂²	semidirect
27. C₁₉×#327	C₂²	semidirect
28. C₁₉×#324	C₂²	semidirect
122. C₂²×C₄×C₁₉	SD₁₆	semidirect
141. C₂×#1604	C₁₉	direct (N × H)
189. C₂×C₄×C₁₉	C₂×SD₁₆	semidirect
193. C₂×#448	C₂×C₁₉	semidirect
194. C₂×#395	C₂×C₁₉	semidirect
195. #1604	C₂×C₁₉	direct (N × H)
196. C₂×#327	C₂×C₁₉	semidirect
197. C₂×#324	C₂×C₁₉	semidirect
235. #448	C₂²×C₁₉	semidirect
239. #395	C₂²×C₁₉	semidirect
242. #327	C₂²×C₁₉	semidirect
243. #324	C₂²×C₁₉	semidirect
248. C₂×C₁₉	#1604	direct (N × H)
301. C₁₉	C₂×#1604	direct (N × H)
346. C₂²×C₄	SD₁₆×C₁₉	semidirect
412. C₂×C₄	C₂×SD₁₆×C₁₉	semidirect
443. C₂	C₁₉×#1604	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×#537	2
C₂×C₁₉×#448	2
C₂×C₁₉×#395	2
C₁₉×#1604	2
C₂×C₁₉×#327	2
C₂×C₁₉×#324	2
C₂×#1604	19

Subgroups — C2×C19×#1604 #18024068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1604 #18024068