Subgroups — C₂×C₁₉×#2329 #18040030

Order 4864.

2982 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2329	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₉×#391	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#389	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#387	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#387	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₉×#385	C₂	1	2	yes	maximal
8	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	2	yes	maximal
10	C₂²×C₁₉×#95	C₂	1	1	yes	maximal, characteristic
11	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₂²⋊Q₈	C₄	1	16	yes	complemented
16	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	8	yes	—
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
26	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
27	C₁₉×#391	C₂²	1	16	yes	complemented
28	C₁₉×#389	C₂²	1	16	yes	complemented
29	C₁₉×#387	C₂²	1	16	yes	complemented
30	C₁₉×#387	C₂²	1	16	yes	complemented
31	C₁₉×#385	C₂²	1	16	yes	—
32	C₁₉×#380	C₂²	1	8	yes	—
33	C₄×C₂²⋊C₄×C₁₉	C₂²	1	16	yes	—
34	C₂×C₁₉×#95	C₂²	1	2	yes	—
35	C₂×C₁₉×#95	C₂²	1	2	yes	—
36	C₂×C₁₉×#95	C₂²	1	8	yes	—
37	C₂×C₁₉×#95	C₂²	1	2	yes	—
38	C₂×C₁₉×#95	C₂²	1	2	yes	—
39	C₂×C₁₉×#95	C₂²	1	2	yes	—
40	C₂×C₁₉×#95	C₂²	1	2	yes	—
41	C₂×C₁₉×#95	C₂²	1	2	yes	—
42	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₁₉	—	4	2	no	—
44	C₂²×Q₈×C₁₉	—	4	2	no	—
45	C₂²×Q₈×C₁₉	C₂×C₄	1	8	yes	complemented
46	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
47	C₂³×C₄×C₁₉	—	2	4	no	—
48	C₂³×C₄×C₁₉	—	4	2	no	—
49	C₂³×C₄×C₁₉	—	4	2	no	—
50	C₂³×C₄×C₁₉	—	4	2	no	—
51	C₂³×C₄×C₁₉	—	4	2	no	—
52	C₂³×C₄×C₁₉	—	4	2	no	—
53	C₂³×C₄×C₁₉	—	4	2	no	—
54	C₂³×C₄×C₁₉	C₂×C₄	1	8	yes	—
55	C₂³×C₄×C₁₉	Q₈	1	8	yes	complemented
56	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
65	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
66	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
67	C₁₉×C₂²⋊Q₈	C₂×C₄	1	64	yes	complemented
68	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
69	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
70	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
71	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
72	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
73	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	16	yes	complemented
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
81	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	16	yes	—
82	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
83	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
84	C₂×C₄²×C₁₉	—	4	4	no	—
85	C₂×C₄²×C₁₉	—	4	4	no	—
86	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
87	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
88	C₁₉×#95	C₂³	1	8	yes	—
89	C₁₉×#95	C₂³	1	8	yes	—
90	C₁₉×#95	C₂³	1	8	yes	—
91	C₁₉×#95	C₂³	1	8	yes	—
92	C₁₉×#95	C₂³	1	8	yes	—
93	C₁₉×#95	C₂³	1	8	yes	—
94	C₁₉×#95	C₂³	1	8	yes	—
95	C₂⁴×C₁₉	—	2	2	no	—
96	C₂⁴×C₁₉	—	2	2	no	—
97	C₂⁴×C₁₉	—	2	2	no	—
98	C₂⁴×C₁₉	—	2	2	no	—
99	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
100	C₂⁴×C₁₉	C₂×Q₈	1	4	yes	—
101	C₂⁴×C₁₉	#41	1	4	yes	—
102	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
103	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
104	C₂×Q₈×C₁₉	—	4	16	no	—
105	C₂×Q₈×C₁₉	—	4	4	no	—
106	C₂×Q₈×C₁₉	—	4	4	no	—
107	C₂×Q₈×C₁₉	C₂²×C₄	1	16	yes	complemented
108	C₂²×C₄×C₁₉	—	2	4	no	—
109	C₂²×C₄×C₁₉	—	2	4	no	—
110	C₂²×C₄×C₁₉	—	2	4	no	—
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	4	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	4	no	—
118	C₂²×C₄×C₁₉	—	2	4	no	—
119	C₂²×C₄×C₁₉	—	2	4	no	—
120	C₂²×C₄×C₁₉	—	2	8	no	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
123	C₂²×C₄×C₁₉	—	2	4	no	—
124	C₂²×C₄×C₁₉	—	2	4	no	—
125	C₂²×C₄×C₁₉	—	2	4	no	—
126	C₂²×C₄×C₁₉	—	2	4	no	—
127	C₂²×C₄×C₁₉	—	2	4	no	—
128	C₂²×C₄×C₁₉	—	4	16	no	—
129	C₂²×C₄×C₁₉	—	4	16	no	—
130	C₂²×C₄×C₁₉	—	4	4	no	—
131	C₂²×C₄×C₁₉	—	4	4	no	—
132	C₂²×C₄×C₁₉	—	4	4	no	—
133	C₂²×C₄×C₁₉	—	4	4	no	—
134	C₂²×C₄×C₁₉	—	4	4	no	—
135	C₂²×C₄×C₁₉	—	4	4	no	—
136	C₂²×C₄×C₁₉	—	4	16	no	—
137	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
138	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
139	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
141	C₂²×C₄×C₁₉	C₂²×C₄	1	16	yes	—
142	C₂²×C₄×C₁₉	C₂×Q₈	1	8	yes	—
143	C₂²×C₄×C₁₉	C₂×Q₈	1	16	yes	complemented
144	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
152	C₄⋊C₄×C₁₉	—	4	8	no	—
153	C₄⋊C₄×C₁₉	—	4	4	no	—
154	C₄⋊C₄×C₁₉	—	4	4	no	—
155	C₄⋊C₄×C₁₉	—	4	8	no	—
156	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	complemented
157	C₄⋊C₄×C₁₉	C₂²×C₄	1	32	yes	complemented
158	C₂²⋊C₄×C₁₉	—	2	16	no	—
159	C₂²⋊C₄×C₁₉	C₂²×C₄	1	32	yes	—
160	C₄²×C₁₉	—	4	8	no	—
161	C₄²×C₁₉	—	4	8	no	—
162	C₂×#2329	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂³×C₁₉	—	2	8	no	—
164	C₂³×C₁₉	—	2	8	no	—
165	C₂³×C₁₉	—	2	8	no	—
166	C₂³×C₁₉	—	2	8	no	—
167	C₂³×C₁₉	—	2	8	no	—
168	C₂³×C₁₉	—	2	8	no	—
169	C₂³×C₁₉	—	2	2	no	—
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	—	2	2	no	—
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	C₄×Q₈	1	16	yes	—
174	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
175	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
176	C₂³×C₁₉	C₂²×Q₈	1	4	yes	—
177	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
178	C₂³×C₁₉	C₂×#41	1	4	yes	—
179	C₂³×C₁₉	C₂×#41	1	2	yes	—
180	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
181	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
182	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
183	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
184	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
185	Q₈×C₁₉	—	4	16	no	—
186	C₂×C₄×C₁₉	—	2	8	no	—
187	C₂×C₄×C₁₉	—	2	8	no	—
188	C₂×C₄×C₁₉	—	2	16	no	—
189	C₂×C₄×C₁₉	—	2	16	no	—
190	C₂×C₄×C₁₉	—	2	16	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	2	4	no	—
194	C₂×C₄×C₁₉	—	2	4	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	4	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	4	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	4	no	—
209	C₂×C₄×C₁₉	—	2	4	no	—
210	C₂×C₄×C₁₉	—	4	16	no	—
211	C₂×C₄×C₁₉	—	4	16	no	—
212	C₂×C₄×C₁₉	—	4	16	no	—
213	C₂×C₄×C₁₉	—	4	8	no	—
214	C₂×C₄×C₁₉	—	4	8	no	—
215	C₂×C₄×C₁₉	—	4	8	no	—
216	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
217	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
218	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
219	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
220	C₂×C₄×C₁₉	C₂²×Q₈	1	8	yes	—
221	C₂²×C₂²⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
222	#2329	C₂×C₁₉	1	16	yes	direct product factor
223	C₂×#391	C₂×C₁₉	1	2	yes	complemented
224	C₂×#389	C₂×C₁₉	1	2	yes	complemented
225	C₂×#387	C₂×C₁₉	1	2	yes	complemented
226	C₂×#387	C₂×C₁₉	1	2	yes	complemented
227	C₂×#385	C₂×C₁₉	1	2	yes	—
228	C₂×#380	C₂×C₁₉	1	1	yes	characteristic
229	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	2	yes	—
230	C₂²×#95	C₂×C₁₉	1	1	yes	characteristic
231	C₂²×C₁₉	—	2	32	no	—
232	C₂²×C₁₉	—	2	4	no	—
233	C₂²×C₁₉	—	2	4	no	—
234	C₂²×C₁₉	—	2	4	no	—
235	C₂²×C₁₉	—	2	4	no	—
236	C₂²×C₁₉	—	2	4	no	—
237	C₂²×C₁₉	—	2	4	no	—
238	C₂²×C₁₉	C₂×C₄×Q₈	1	8	yes	—
239	C₂²×C₁₉	C₂×C₄×Q₈	1	4	yes	—
240	C₂²×C₁₉	#518	1	4	yes	—
241	C₂²×C₁₉	#520	1	4	yes	—
242	C₂²×C₁₉	#538	1	4	yes	—
243	C₂²×C₁₉	#539	1	4	yes	—
244	C₂²×C₁₉	#543	1	4	yes	—
245	C₂²×C₁₉	#544	1	4	yes	—
246	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
247	C₂²×C₁₉	C₂³×Q₈	1	1	yes	characteristic
248	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
249	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
250	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
251	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
252	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
253	C₄×C₁₉	—	2	4	no	—
254	C₄×C₁₉	—	2	4	no	—
255	C₄×C₁₉	—	2	8	no	—
256	C₄×C₁₉	—	2	8	no	—
257	C₄×C₁₉	—	2	8	no	—
258	C₄×C₁₉	—	4	4	no	—
259	C₄×C₁₉	—	4	4	no	—
260	C₄×C₁₉	—	4	4	no	—
261	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
262	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
263	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
264	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
265	C₂×C₂²⋊Q₈	C₄×C₁₉	1	16	yes	complemented
266	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	8	yes	—
267	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
269	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
270	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
271	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
272	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
273	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
274	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
275	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
276	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
277	#391	C₂²×C₁₉	1	16	yes	complemented
278	#389	C₂²×C₁₉	1	16	yes	complemented
279	#387	C₂²×C₁₉	1	16	yes	complemented
280	#387	C₂²×C₁₉	1	16	yes	complemented
281	#385	C₂²×C₁₉	1	16	yes	—
282	#380	C₂²×C₁₉	1	8	yes	—
283	C₄×C₂²⋊C₄	C₂²×C₁₉	1	16	yes	—
284	C₂×#95	C₂²×C₁₉	1	8	yes	—
285	C₂×#95	C₂²×C₁₉	1	2	yes	—
286	C₂×#95	C₂²×C₁₉	1	2	yes	—
287	C₂×#95	C₂²×C₁₉	1	2	yes	—
288	C₂×#95	C₂²×C₁₉	1	2	yes	—
289	C₂×#95	C₂²×C₁₉	1	2	yes	—
290	C₂×#95	C₂²×C₁₉	1	2	yes	—
291	C₂×#95	C₂²×C₁₉	1	2	yes	—
292	C₂×C₁₉	—	2	8	no	—
293	C₂×C₁₉	#2329	1	8	yes	direct product factor
294	C₂×C₁₉	C₂²×C₄×Q₈	1	1	yes	characteristic
295	C₂×C₁₉	C₂×#518	1	1	yes	characteristic
296	C₂×C₁₉	C₂×#520	1	1	yes	characteristic
297	C₂×C₁₉	C₂×#538	1	1	yes	characteristic
298	C₂×C₁₉	C₂×#539	1	1	yes	characteristic
299	C₂×C₁₉	C₂×#543	1	1	yes	characteristic
300	C₂×C₁₉	C₂×#544	1	1	yes	characteristic
301	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
302	C₂²×Q₈	—	4	2	no	—
303	C₂²×Q₈	—	4	2	no	—
304	C₂²×Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
305	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
306	C₂³×C₄	—	2	4	no	—
307	C₂³×C₄	—	4	2	no	—
308	C₂³×C₄	—	4	2	no	—
309	C₂³×C₄	—	4	2	no	—
310	C₂³×C₄	—	4	2	no	—
311	C₂³×C₄	—	4	2	no	—
312	C₂³×C₄	—	4	2	no	—
313	C₂³×C₄	C₂×C₄×C₁₉	1	8	yes	—
314	C₂³×C₄	Q₈×C₁₉	1	8	yes	complemented
315	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
316	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
317	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
318	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
319	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
320	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
323	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
324	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
325	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
326	C₂²⋊Q₈	C₂×C₄×C₁₉	1	64	yes	complemented
327	C₂×C₄⋊C₄	—	4	4	no	—
328	C₂×C₄⋊C₄	—	4	2	no	—
329	C₂×C₄⋊C₄	—	4	2	no	—
330	C₂×C₄⋊C₄	—	4	4	no	—
331	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
332	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	16	yes	complemented
333	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
335	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
336	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
337	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
338	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
339	C₂×C₂²⋊C₄	—	2	8	no	—
340	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	16	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
343	C₂×C₄²	—	4	4	no	—
344	C₂×C₄²	—	4	4	no	—
345	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
346	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
347	#95	C₂³×C₁₉	1	8	yes	—
348	#95	C₂³×C₁₉	1	8	yes	—
349	#95	C₂³×C₁₉	1	8	yes	—
350	#95	C₂³×C₁₉	1	8	yes	—
351	#95	C₂³×C₁₉	1	8	yes	—
352	#95	C₂³×C₁₉	1	8	yes	—
353	#95	C₂³×C₁₉	1	8	yes	—
354	C₁₉	C₂×#2329	1	1	yes	characteristic, direct product factor, Sylow
355	C₂⁴	—	2	2	no	—
356	C₂⁴	—	2	2	no	—
357	C₂⁴	—	2	2	no	—
358	C₂⁴	—	2	2	no	—
359	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
360	C₂⁴	C₂×Q₈×C₁₉	1	4	yes	—
361	C₂⁴	#41×C₁₉	1	4	yes	—
362	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
363	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
364	C₂×Q₈	—	4	16	no	—
365	C₂×Q₈	—	4	4	no	—
366	C₂×Q₈	—	4	4	no	—
367	C₂×Q₈	C₂²×C₄×C₁₉	1	16	yes	complemented
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	8	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	4	16	no	—
389	C₂²×C₄	—	4	16	no	—
390	C₂²×C₄	—	4	4	no	—
391	C₂²×C₄	—	4	4	no	—
392	C₂²×C₄	—	4	4	no	—
393	C₂²×C₄	—	4	4	no	—
394	C₂²×C₄	—	4	4	no	—
395	C₂²×C₄	—	4	4	no	—
396	C₂²×C₄	—	4	16	no	—
397	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
398	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
399	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
400	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
401	C₂²×C₄	C₂²×C₄×C₁₉	1	16	yes	—
402	C₂²×C₄	C₂×Q₈×C₁₉	1	8	yes	—
403	C₂²×C₄	C₂×Q₈×C₁₉	1	16	yes	complemented
404	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
405	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
406	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
407	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
408	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
409	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
410	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
411	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
412	C₄⋊C₄	—	4	8	no	—
413	C₄⋊C₄	—	4	4	no	—
414	C₄⋊C₄	—	4	4	no	—
415	C₄⋊C₄	—	4	8	no	—
416	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	complemented
417	C₄⋊C₄	C₂²×C₄×C₁₉	1	32	yes	complemented
418	C₂²⋊C₄	—	2	16	no	—
419	C₂²⋊C₄	C₂²×C₄×C₁₉	1	32	yes	—
420	C₄²	—	4	8	no	—
421	C₄²	—	4	8	no	—
422	C₂³	—	2	8	no	—
423	C₂³	—	2	8	no	—
424	C₂³	—	2	8	no	—
425	C₂³	—	2	8	no	—
426	C₂³	—	2	8	no	—
427	C₂³	—	2	8	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	C₄×Q₈×C₁₉	1	16	yes	—
433	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
434	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
435	C₂³	C₂²×Q₈×C₁₉	1	4	yes	—
436	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
437	C₂³	C₂×#41×C₁₉	1	4	yes	—
438	C₂³	C₂×#41×C₁₉	1	2	yes	—
439	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
440	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
441	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
442	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
443	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
444	Q₈	—	4	16	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	16	no	—
448	C₂×C₄	—	2	16	no	—
449	C₂×C₄	—	2	16	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	4	16	no	—
470	C₂×C₄	—	4	16	no	—
471	C₂×C₄	—	4	16	no	—
472	C₂×C₄	—	4	8	no	—
473	C₂×C₄	—	4	8	no	—
474	C₂×C₄	—	4	8	no	—
475	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
476	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
477	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
478	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
479	C₂×C₄	C₂²×Q₈×C₁₉	1	8	yes	—
480	C₂²	—	2	4	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	2	4	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	2	32	no	—
487	C₂²	C₂×C₄×Q₈×C₁₉	1	8	yes	—
488	C₂²	C₂×C₄×Q₈×C₁₉	1	4	yes	—
489	C₂²	C₁₉×#518	1	4	yes	—
490	C₂²	C₁₉×#520	1	4	yes	—
491	C₂²	C₁₉×#538	1	4	yes	—
492	C₂²	C₁₉×#539	1	4	yes	—
493	C₂²	C₁₉×#543	1	4	yes	—
494	C₂²	C₁₉×#544	1	4	yes	—
495	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
496	C₂²	C₂³×Q₈×C₁₉	1	1	yes	characteristic
497	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
498	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
499	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
500	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
501	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
502	C₄	—	2	4	no	—
503	C₄	—	2	4	no	—
504	C₄	—	2	8	no	—
505	C₄	—	2	8	no	—
506	C₄	—	2	8	no	—
507	C₄	—	4	4	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	4	no	—
510	C₂	—	2	8	no	—
511	C₂	C₁₉×#2329	1	8	yes	direct product factor
512	C₂	C₂²×C₄×Q₈×C₁₉	1	1	yes	characteristic
513	C₂	C₂×C₁₉×#518	1	1	yes	characteristic
514	C₂	C₂×C₁₉×#520	1	1	yes	characteristic
515	C₂	C₂×C₁₉×#538	1	1	yes	characteristic
516	C₂	C₂×C₁₉×#539	1	1	yes	characteristic
517	C₂	C₂×C₁₉×#543	1	1	yes	characteristic
518	C₂	C₂×C₁₉×#544	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2329	C₂	direct (N × H)
3. C₂×C₁₉×#391	C₂	semidirect
4. C₂×C₁₉×#389	C₂	semidirect
5. C₂×C₁₉×#387	C₂	semidirect
6. C₂×C₁₉×#387	C₂	semidirect
15. C₂×C₁₉×C₂²⋊Q₈	C₄	semidirect
27. C₁₉×#391	C₂²	semidirect
28. C₁₉×#389	C₂²	semidirect
29. C₁₉×#387	C₂²	semidirect
30. C₁₉×#387	C₂²	semidirect
45. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
55. C₂³×C₄×C₁₉	Q₈	semidirect
67. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
72. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
73. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
107. C₂×Q₈×C₁₉	C₂²×C₄	semidirect
143. C₂²×C₄×C₁₉	C₂×Q₈	semidirect
156. C₄⋊C₄×C₁₉	C₂²×C₄	semidirect
157. C₄⋊C₄×C₁₉	C₂²×C₄	semidirect
162. C₂×#2329	C₁₉	direct (N × H)
222. #2329	C₂×C₁₉	direct (N × H)
223. C₂×#391	C₂×C₁₉	semidirect
224. C₂×#389	C₂×C₁₉	semidirect
225. C₂×#387	C₂×C₁₉	semidirect
226. C₂×#387	C₂×C₁₉	semidirect
265. C₂×C₂²⋊Q₈	C₄×C₁₉	semidirect
277. #391	C₂²×C₁₉	semidirect
278. #389	C₂²×C₁₉	semidirect
279. #387	C₂²×C₁₉	semidirect
280. #387	C₂²×C₁₉	semidirect
293. C₂×C₁₉	#2329	direct (N × H)
304. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
314. C₂³×C₄	Q₈×C₁₉	semidirect
326. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
331. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
332. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
354. C₁₉	C₂×#2329	direct (N × H)
367. C₂×Q₈	C₂²×C₄×C₁₉	semidirect
403. C₂²×C₄	C₂×Q₈×C₁₉	semidirect
416. C₄⋊C₄	C₂²×C₄×C₁₉	semidirect
417. C₄⋊C₄	C₂²×C₄×C₁₉	semidirect
511. C₂	C₁₉×#2329	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×C₂²⋊Q₈	2
C₁₉×#2329	2
C₂×C₁₉×#391	2
C₂×C₁₉×#389	2
C₂×C₁₉×#387	2
C₂×C₁₉×#385	2
C₂×C₁₉×#380	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₂²×C₁₉×#95	2
C₂×#2329	19

Subgroups — C2×C19×#2329 #18040030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2329 #18040030