Subgroups — D₄×C₁₉×#100 #18028366

Order 4864.

1862 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₁₉	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₁₉	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₉×#100	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1965	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1900	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1783	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₉	C₄	1	2	yes	—
10	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
11	C₂²×M₁₆×C₁₉	C₂²	1	4	yes	complemented
12	D₄²×C₁₉	—	2	2	no	—
13	D₄²×C₁₉	—	2	4	no	—
14	D₄²×C₁₉	—	2	2	no	—
15	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#121	C₄	1	2	yes	—
17	C₂×C₁₉×#121	C₂²	1	2	yes	—
18	C₂×C₁₉×#120	C₄	1	4	yes	—
19	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#436	—	2	2	no	—
22	C₁₉×#435	—	2	4	no	—
23	C₈×D₄×C₁₉	—	2	2	no	—
24	C₁₉×#423	C₂²	1	2	yes	complemented
25	C₂×C₁₉×#100	—	2	8	no	—
26	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#100	C₂²	1	2	yes	—
28	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#100	C₂²	1	4	yes	complemented
30	C₂×C₁₉×#100	C₂²	1	4	yes	complemented
31	C₁₉×#407	C₂²	1	4	yes	complemented
32	C₄×M₁₆×C₁₉	C₂²	1	2	yes	complemented
33	C₁₉×#343	C₂²	1	2	yes	complemented
34	C₁₉×#343	C₂²	1	2	yes	complemented
35	C₂⁵×C₁₉	C₂×C₄	1	4	yes	—
36	C₂²×D₄×C₁₉	—	2	4	no	—
37	C₂²×D₄×C₁₉	—	2	2	no	—
38	C₂²×D₄×C₁₉	—	2	2	no	—
39	C₂²×D₄×C₁₉	—	2	4	no	—
40	C₂²×D₄×C₁₉	—	2	4	no	—
41	C₂²×D₄×C₁₉	—	2	4	no	—
42	C₂²×D₄×C₁₉	—	2	4	no	—
43	C₂²×D₄×C₁₉	—	4	4	no	—
44	C₂²×D₄×C₁₉	—	4	8	no	—
45	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
46	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
48	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
49	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
50	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
53	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
54	C₂×M₁₆×C₁₉	—	2	4	no	—
55	C₂×M₁₆×C₁₉	—	2	8	no	—
56	C₂×M₁₆×C₁₉	—	4	4	no	—
57	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
58	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
59	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₉	—	2	4	no	—
61	C₁₉×#127	—	2	2	no	—
62	C₁₉×#127	—	2	2	no	—
63	C₁₉×#121	—	2	4	no	—
64	C₁₉×#121	—	2	4	no	—
65	C₁₉×#121	—	2	4	no	—
66	C₁₉×#121	—	2	4	no	—
67	C₁₉×#120	—	2	8	no	—
68	C₁₉×#120	—	2	8	no	—
69	C₄×D₄×C₁₉	—	2	2	no	—
70	C₄×D₄×C₁₉	—	2	2	no	—
71	C₄×D₄×C₁₉	D₄	1	2	yes	—
72	C₄×D₄×C₁₉	D₄	1	4	yes	—
73	C₄×D₄×C₁₉	D₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
77	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
78	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
79	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×C₄⋊C₈	—	2	2	no	—
81	C₁₉×C₄⋊C₈	—	2	2	no	—
82	C₁₉×#100	—	2	4	no	—
83	C₁₉×#100	—	2	2	no	—
84	C₁₉×#100	—	2	8	no	—
85	C₁₉×#100	—	4	4	no	—
86	C₁₉×#100	D₄	1	4	yes	direct product factor
87	C₁₉×C₂²⋊C₈	—	2	4	no	—
88	C₁₉×C₂²⋊C₈	—	2	4	no	—
89	C₁₉×#97	—	2	2	no	—
90	C₄×C₈×C₁₉	—	2	2	no	—
91	C₂⁴×C₁₉	—	2	4	no	—
92	C₂⁴×C₁₉	—	2	4	no	—
93	C₂⁴×C₁₉	—	2	8	no	—
94	C₂⁴×C₁₉	—	4	4	no	—
95	C₂⁴×C₁₉	—	4	8	no	—
96	C₂⁴×C₁₉	—	8	4	no	—
97	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
98	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
99	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
100	C₂×D₄×C₁₉	—	2	4	no	—
101	C₂×D₄×C₁₉	—	2	4	no	—
102	C₂×D₄×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	2	8	no	—
104	C₂×D₄×C₁₉	—	2	8	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	—	2	4	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	4	no	—
110	C₂×D₄×C₁₉	—	2	2	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	4	no	—
114	C₂×D₄×C₁₉	—	4	8	no	—
115	C₂×D₄×C₁₉	—	4	8	no	—
116	C₂×D₄×C₁₉	—	4	8	no	—
117	C₂×D₄×C₁₉	—	4	8	no	—
118	C₂×D₄×C₁₉	—	4	4	no	—
119	C₂×D₄×C₁₉	—	4	4	no	—
120	C₂×D₄×C₁₉	—	4	16	no	—
121	C₂×D₄×C₁₉	—	4	8	no	—
122	C₂×D₄×C₁₉	—	4	8	no	—
123	C₂×D₄×C₁₉	—	4	8	no	—
124	C₂×D₄×C₁₉	—	8	2	no	—
125	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
126	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
127	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
128	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
129	C₂×D₄×C₁₉	#41	1	2	yes	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	4	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	4	4	no	—
136	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
143	M₁₆×C₁₉	—	2	2	no	—
144	M₁₆×C₁₉	—	2	4	no	—
145	M₁₆×C₁₉	—	2	2	no	—
146	M₁₆×C₁₉	—	2	4	no	—
147	M₁₆×C₁₉	—	2	2	no	—
148	M₁₆×C₁₉	—	4	8	no	—
149	M₁₆×C₁₉	C₂×D₄	1	4	yes	complemented
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	2	4	no	—
152	C₂×C₈×C₁₉	—	2	2	no	—
153	C₂×C₈×C₁₉	—	4	8	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
156	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
157	C₂²⋊C₄×C₁₉	—	2	4	no	—
158	C₂²⋊C₄×C₁₉	—	2	8	no	—
159	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
160	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
161	C₄²×C₁₉	C₂×D₄	1	2	yes	—
162	C₄²×C₁₉	C₂×D₄	1	2	yes	—
163	D₄×#100	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₁₉	—	2	2	no	—
165	C₂³×C₁₉	—	2	2	no	—
166	C₂³×C₁₉	—	2	2	no	—
167	C₂³×C₁₉	—	2	2	no	—
168	C₂³×C₁₉	—	2	4	no	—
169	C₂³×C₁₉	—	2	4	no	—
170	C₂³×C₁₉	—	2	4	no	—
171	C₂³×C₁₉	—	2	4	no	—
172	C₂³×C₁₉	—	4	2	no	—
173	C₂³×C₁₉	—	4	8	no	—
174	C₂³×C₁₉	—	4	8	no	—
175	C₂³×C₁₉	—	4	2	no	—
176	C₂³×C₁₉	—	4	2	no	—
177	C₂³×C₁₉	—	4	8	no	—
178	C₂³×C₁₉	—	4	4	no	—
179	C₂³×C₁₉	—	4	4	no	—
180	C₂³×C₁₉	—	4	8	no	—
181	C₂³×C₁₉	—	8	4	no	—
182	C₂³×C₁₉	—	8	4	no	—
183	C₂³×C₁₉	—	8	16	no	—
184	C₂³×C₁₉	—	8	16	no	—
185	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂³×C₁₉	C₄×D₄	1	4	yes	—
188	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
189	D₄×C₁₉	—	2	4	no	—
190	D₄×C₁₉	—	2	4	no	—
191	D₄×C₁₉	—	2	4	no	—
192	D₄×C₁₉	—	2	2	no	—
193	D₄×C₁₉	—	4	16	no	—
194	D₄×C₁₉	—	4	4	no	—
195	D₄×C₁₉	—	4	8	no	—
196	D₄×C₁₉	—	4	8	no	—
197	D₄×C₁₉	—	4	4	no	—
198	D₄×C₁₉	—	4	4	no	—
199	D₄×C₁₉	—	4	4	no	—
200	D₄×C₁₉	—	8	4	no	—
201	D₄×C₁₉	#100	1	4	yes	direct product factor
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	2	4	no	—
207	C₂×C₄×C₁₉	—	2	4	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	4	no	—
212	C₂×C₄×C₁₉	—	4	4	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
215	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
217	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
222	C₈×C₁₉	—	2	4	no	—
223	C₈×C₁₉	—	4	4	no	—
224	C₈×C₁₉	—	4	2	no	—
225	C₂×D₄²	C₂×C₁₉	1	1	yes	characteristic
226	D₄×M₁₆	C₂×C₁₉	1	2	yes	complemented
227	C₂²×#100	C₂×C₁₉	1	2	yes	complemented
228	#1965	C₂×C₁₉	1	2	yes	complemented
229	#1900	C₂×C₁₉	1	4	yes	complemented
230	#1800	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#1783	C₂×C₁₉	1	2	yes	complemented
232	C₄×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
233	C₂²×C₁₉	—	2	2	no	—
234	C₂²×C₁₉	—	2	1	no	—
235	C₂²×C₁₉	—	2	1	no	—
236	C₂²×C₁₉	—	2	2	no	—
237	C₂²×C₁₉	—	2	2	no	—
238	C₂²×C₁₉	—	2	4	no	—
239	C₂²×C₁₉	—	2	2	no	—
240	C₂²×C₁₉	—	2	2	no	—
241	C₂²×C₁₉	—	4	4	no	—
242	C₂²×C₁₉	—	4	4	no	—
243	C₂²×C₁₉	—	4	4	no	—
244	C₂²×C₁₉	—	4	4	no	—
245	C₂²×C₁₉	—	4	2	no	—
246	C₂²×C₁₉	—	4	2	no	—
247	C₂²×C₁₉	—	4	4	no	—
248	C₂²×C₁₉	—	4	4	no	—
249	C₂²×C₁₉	—	4	4	no	—
250	C₂²×C₁₉	—	8	16	no	—
251	C₂²×C₁₉	—	8	4	no	—
252	C₂²×C₁₉	—	8	4	no	—
253	C₂²×C₁₉	—	8	16	no	—
254	C₂²×C₁₉	C₂×#100	1	4	yes	complemented
255	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
257	C₂²×C₁₉	#518	1	1	yes	characteristic
258	C₄×C₁₉	—	2	4	no	—
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	2	2	no	—
261	C₄×C₁₉	—	4	2	no	—
262	C₄×C₁₉	C₂×#100	1	2	yes	complemented
263	C₄×C₁₉	D₄²	1	2	yes	—
264	C₄×C₁₉	#546	1	2	yes	—
265	C₂³×D₄	C₄×C₁₉	1	2	yes	—
266	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
267	C₂²×M₁₆	C₂²×C₁₉	1	4	yes	complemented
268	D₄²	—	2	2	no	—
269	D₄²	—	2	4	no	—
270	D₄²	—	2	2	no	—
271	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
272	C₂×#121	C₄×C₁₉	1	2	yes	—
273	C₂×#121	C₂²×C₁₉	1	2	yes	—
274	C₂×#120	C₄×C₁₉	1	4	yes	—
275	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
277	#436	—	2	2	no	—
278	#435	—	2	4	no	—
279	C₈×D₄	—	2	2	no	—
280	#423	C₂²×C₁₉	1	2	yes	complemented
281	C₂×#100	—	2	8	no	—
282	C₂×#100	C₂²×C₁₉	1	2	yes	—
283	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
284	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
285	C₂×#100	C₂²×C₁₉	1	4	yes	complemented
286	C₂×#100	C₂²×C₁₉	1	4	yes	complemented
287	#407	C₂²×C₁₉	1	4	yes	complemented
288	C₄×M₁₆	C₂²×C₁₉	1	2	yes	complemented
289	#343	C₂²×C₁₉	1	2	yes	complemented
290	#343	C₂²×C₁₉	1	2	yes	complemented
291	C₂×C₁₉	—	2	1	no	—
292	C₂×C₁₉	—	2	1	no	—
293	C₂×C₁₉	—	2	4	no	—
294	C₂×C₁₉	—	4	2	no	—
295	C₂×C₁₉	—	4	4	no	—
296	C₂×C₁₉	—	8	4	no	—
297	C₂×C₁₉	D₄×C₂²⋊C₄	1	1	yes	characteristic
298	C₂×C₁₉	C₂²×#100	1	1	yes	characteristic
299	C₂×C₁₉	#2888	1	1	yes	characteristic
300	C₂⁵	C₂×C₄×C₁₉	1	4	yes	—
301	C₂²×D₄	—	2	4	no	—
302	C₂²×D₄	—	2	2	no	—
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	—	2	4	no	—
305	C₂²×D₄	—	2	4	no	—
306	C₂²×D₄	—	2	4	no	—
307	C₂²×D₄	—	2	4	no	—
308	C₂²×D₄	—	4	4	no	—
309	C₂²×D₄	—	4	8	no	—
310	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
311	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
312	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
313	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
314	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
315	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
316	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
317	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
318	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
319	C₂×M₁₆	—	2	4	no	—
320	C₂×M₁₆	—	2	8	no	—
321	C₂×M₁₆	—	4	4	no	—
322	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
323	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
324	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
325	C₂²×C₈	—	2	4	no	—
326	#127	—	2	2	no	—
327	#127	—	2	2	no	—
328	#121	—	2	4	no	—
329	#121	—	2	4	no	—
330	#121	—	2	4	no	—
331	#121	—	2	4	no	—
332	#120	—	2	8	no	—
333	#120	—	2	8	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	D₄×C₁₉	1	2	yes	—
337	C₄×D₄	D₄×C₁₉	1	4	yes	—
338	C₄×D₄	D₄×C₁₉	1	2	yes	—
339	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
342	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
343	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
344	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
345	C₄⋊C₈	—	2	2	no	—
346	C₄⋊C₈	—	2	2	no	—
347	#100	—	2	4	no	—
348	#100	—	2	2	no	—
349	#100	—	2	8	no	—
350	#100	—	4	4	no	—
351	#100	D₄×C₁₉	1	4	yes	direct product factor
352	C₂²⋊C₈	—	2	4	no	—
353	C₂²⋊C₈	—	2	4	no	—
354	#97	—	2	2	no	—
355	C₄×C₈	—	2	2	no	—
356	C₁₉	D₄×#100	1	1	yes	characteristic, direct product factor, Sylow
357	C₂⁴	—	2	4	no	—
358	C₂⁴	—	2	4	no	—
359	C₂⁴	—	2	8	no	—
360	C₂⁴	—	4	4	no	—
361	C₂⁴	—	4	8	no	—
362	C₂⁴	—	8	4	no	—
363	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
364	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
365	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	8	no	—
370	C₂×D₄	—	2	8	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	4	no	—
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	8	no	—
381	C₂×D₄	—	4	8	no	—
382	C₂×D₄	—	4	8	no	—
383	C₂×D₄	—	4	8	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂×D₄	—	4	4	no	—
386	C₂×D₄	—	4	16	no	—
387	C₂×D₄	—	4	8	no	—
388	C₂×D₄	—	4	8	no	—
389	C₂×D₄	—	4	8	no	—
390	C₂×D₄	—	8	2	no	—
391	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
392	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
393	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
394	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
395	C₂×D₄	#41×C₁₉	1	2	yes	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	4	4	no	—
402	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
403	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
404	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
405	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
407	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
408	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
409	M₁₆	—	2	2	no	—
410	M₁₆	—	2	4	no	—
411	M₁₆	—	2	2	no	—
412	M₁₆	—	2	2	no	—
413	M₁₆	—	2	4	no	—
414	M₁₆	—	4	8	no	—
415	M₁₆	C₂×D₄×C₁₉	1	4	yes	complemented
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	4	no	—
419	C₂×C₈	—	4	8	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
422	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
423	C₂²⋊C₄	—	2	4	no	—
424	C₂²⋊C₄	—	2	8	no	—
425	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
426	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
427	C₄²	C₂×D₄×C₁₉	1	2	yes	—
428	C₄²	C₂×D₄×C₁₉	1	2	yes	—
429	C₂³	—	2	4	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	4	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	8	no	—
439	C₂³	—	4	8	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	8	no	—
443	C₂³	—	4	4	no	—
444	C₂³	—	4	4	no	—
445	C₂³	—	4	8	no	—
446	C₂³	—	8	4	no	—
447	C₂³	—	8	4	no	—
448	C₂³	—	8	16	no	—
449	C₂³	—	8	16	no	—
450	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
451	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
452	C₂³	C₄×D₄×C₁₉	1	4	yes	—
453	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
454	D₄	—	2	4	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	4	no	—
457	D₄	—	2	4	no	—
458	D₄	—	4	16	no	—
459	D₄	—	4	4	no	—
460	D₄	—	4	8	no	—
461	D₄	—	4	8	no	—
462	D₄	—	4	4	no	—
463	D₄	—	4	4	no	—
464	D₄	—	4	4	no	—
465	D₄	—	8	4	no	—
466	D₄	C₁₉×#100	1	4	yes	direct product factor
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
480	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
481	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
482	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
485	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
486	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
487	C₈	—	2	4	no	—
488	C₈	—	4	4	no	—
489	C₈	—	4	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	8	16	no	—
508	C₂²	—	8	4	no	—
509	C₂²	—	8	4	no	—
510	C₂²	—	8	16	no	—
511	C₂²	C₂×C₁₉×#100	1	4	yes	complemented
512	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
513	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
514	C₂²	C₁₉×#518	1	1	yes	characteristic
515	C₄	—	2	4	no	—
516	C₄	—	2	1	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	2	no	—
519	C₄	C₂×C₁₉×#100	1	2	yes	complemented
520	C₄	D₄²×C₁₉	1	2	yes	—
521	C₄	C₁₉×#546	1	2	yes	—
522	C₂	—	2	1	no	—
523	C₂	—	2	1	no	—
524	C₂	—	2	4	no	—
525	C₂	—	4	2	no	—
526	C₂	—	4	4	no	—
527	C₂	—	8	4	no	—
528	C₂	D₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
529	C₂	C₂²×C₁₉×#100	1	1	yes	characteristic
530	C₂	C₁₉×#2888	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×D₄²×C₁₉	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×M₁₆×C₁₉	C₂	semidirect
3. C₂²×C₁₉×#100	C₂	semidirect
4. C₁₉×#1965	C₂	semidirect
5. C₁₉×#1900	C₂	semidirect
6. C₁₉×#1800	C₂	semidirect
7. C₁₉×#1783	C₂	semidirect
8. C₄×C₁₉×#100	C₂	semidirect
11. C₂²×M₁₆×C₁₉	C₂²	semidirect
24. C₁₉×#423	C₂²	semidirect
29. C₂×C₁₉×#100	C₂²	semidirect
30. C₂×C₁₉×#100	C₂²	semidirect
31. C₁₉×#407	C₂²	semidirect
32. C₄×M₁₆×C₁₉	C₂²	semidirect
33. C₁₉×#343	C₂²	semidirect
34. C₁₉×#343	C₂²	semidirect
86. C₁₉×#100	D₄	direct (N × H)
149. M₁₆×C₁₉	C₂×D₄	semidirect
163. D₄×#100	C₁₉	direct (N × H)
201. D₄×C₁₉	#100	direct (N × H)
226. D₄×M₁₆	C₂×C₁₉	semidirect
227. C₂²×#100	C₂×C₁₉	semidirect
228. #1965	C₂×C₁₉	semidirect
229. #1900	C₂×C₁₉	semidirect
230. #1800	C₂×C₁₉	semidirect
231. #1783	C₂×C₁₉	semidirect
232. C₄×#100	C₂×C₁₉	semidirect
254. C₂²×C₁₉	C₂×#100	semidirect
262. C₄×C₁₉	C₂×#100	semidirect
267. C₂²×M₁₆	C₂²×C₁₉	semidirect
280. #423	C₂²×C₁₉	semidirect
285. C₂×#100	C₂²×C₁₉	semidirect
286. C₂×#100	C₂²×C₁₉	semidirect
287. #407	C₂²×C₁₉	semidirect
288. C₄×M₁₆	C₂²×C₁₉	semidirect
289. #343	C₂²×C₁₉	semidirect
290. #343	C₂²×C₁₉	semidirect
351. #100	D₄×C₁₉	direct (N × H)
356. C₁₉	D₄×#100	direct (N × H)
415. M₁₆	C₂×D₄×C₁₉	semidirect
466. D₄	C₁₉×#100	direct (N × H)
511. C₂²	C₂×C₁₉×#100	semidirect
519. C₄	C₂×C₁₉×#100	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₁₉	2
D₄×M₁₆×C₁₉	2
C₂²×C₁₉×#100	2
C₁₉×#1965	2
C₁₉×#1900	2
C₁₉×#1800	2
C₁₉×#1783	2
C₄×C₁₉×#100	2
D₄×#100	19

Subgroups — D4×C19×#100 #18028366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₁₉×#100 #18028366