Subgroups — C₁₉×#34216 #18040175

Order 4864.

2422 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2369	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2365	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2345	C₂	1	4	yes	maximal
5	Q₈×C₂²⋊C₄×C₁₉	C₂	1	4	yes	maximal
6	C₁₉×#2331	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2316	C₂	1	2	yes	maximal
8	C₄×C₁₉×C₄⋊Q₈	C₂	1	4	yes	maximal, complemented
9	C₁₉×#2285	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#2274	C₂	1	2	yes	maximal
11	C₄×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₁₉	C₂²	1	2	yes	—
13	C₂×C₁₉×C₄⋊Q₈	C₄	1	16	yes	complemented
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₉	C₂²	1	8	yes	—
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	2	yes	—
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#391	C₂²	1	8	yes	—
26	C₁₉×#391	C₂²	1	16	yes	—
27	C₁₉×#389	C₂²	1	8	yes	—
28	C₁₉×#389	C₂²	1	8	yes	—
29	C₁₉×#389	C₂²	1	8	yes	—
30	C₁₉×#387	C₂²	1	16	yes	—
31	C₁₉×#384	C₂²	1	2	yes	—
32	C₁₉×#382	C₂²	1	2	yes	—
33	C₁₉×#380	C₂²	1	2	yes	—
34	C₁₉×#380	C₂²	1	2	yes	—
35	C₁₉×#380	C₂²	1	8	yes	—
36	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
38	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
39	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
40	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
42	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
43	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
44	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
45	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
46	C₁₉×#376	C₂²	1	2	yes	—
47	C₄³×C₁₉	C₂²	1	2	yes	—
48	C₂²×Q₈×C₁₉	—	4	8	no	—
49	C₂²×Q₈×C₁₉	C₂×C₄	1	16	yes	—
50	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
51	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	C₂×C₄	1	16	yes	—
57	C₁₉×C₄⋊Q₈	C₂×C₄	1	16	yes	—
58	C₁₉×C₄⋊Q₈	C₂×C₄	1	16	yes	—
59	C₁₉×C₄⋊Q₈	C₂×C₄	1	16	yes	—
60	C₄×Q₈×C₁₉	—	4	16	no	—
61	C₁₉×#117	—	2	4	no	—
62	C₁₉×#117	—	2	8	no	—
63	C₁₉×#117	Q₈	1	8	yes	complemented
64	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	16	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	16	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
76	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
78	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
79	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	—
80	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
81	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
82	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
83	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
84	C₂×C₄²×C₁₉	C₂³	1	16	yes	—
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
90	C₁₉×#95	C₂³	1	4	yes	—
91	C₁₉×#95	C₂³	1	4	yes	—
92	C₁₉×#95	C₂³	1	16	yes	—
93	C₁₉×#95	C₂³	1	4	yes	—
94	C₁₉×#95	C₂³	1	4	yes	—
95	C₁₉×#95	C₂³	1	16	yes	—
96	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
97	C₂×Q₈×C₁₉	—	2	16	no	—
98	C₂×Q₈×C₁₉	—	4	8	no	—
99	C₂×Q₈×C₁₉	—	4	32	no	—
100	C₂×Q₈×C₁₉	C₂²×C₄	1	16	yes	—
101	C₂×Q₈×C₁₉	C₂²×C₄	1	16	yes	—
102	C₂²×C₄×C₁₉	—	2	4	no	—
103	C₂²×C₄×C₁₉	—	2	4	no	—
104	C₂²×C₄×C₁₉	—	4	8	no	—
105	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₁₉	C₂²×C₄	1	16	yes	—
108	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
110	C₂²×C₄×C₁₉	#41	1	4	yes	—
111	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
112	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
113	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
114	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
117	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
121	C₄⋊C₄×C₁₉	—	2	4	no	—
122	C₄⋊C₄×C₁₉	—	2	8	no	—
123	C₄⋊C₄×C₁₉	—	2	8	no	—
124	C₄⋊C₄×C₁₉	—	2	8	no	—
125	C₄⋊C₄×C₁₉	—	4	16	no	—
126	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
127	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
128	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
129	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
130	C₄⋊C₄×C₁₉	C₂×Q₈	1	8	yes	complemented
131	C₂²⋊C₄×C₁₉	—	2	4	no	—
132	C₂²⋊C₄×C₁₉	—	2	8	no	—
133	C₂²⋊C₄×C₁₉	C₂×Q₈	1	8	yes	—
134	C₄²×C₁₉	—	2	8	no	—
135	C₄²×C₁₉	—	2	4	no	—
136	C₄²×C₁₉	—	2	8	no	—
137	C₄²×C₁₉	—	2	8	no	—
138	C₄²×C₁₉	—	4	16	no	—
139	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
140	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
141	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
142	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
143	C₄²×C₁₉	C₂×Q₈	1	8	yes	complemented
144	#34216	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	—	2	2	no	—
147	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
148	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
149	C₂³×C₁₉	C₂×#41	1	2	yes	—
150	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
151	Q₈×C₁₉	—	2	32	no	—
152	Q₈×C₁₉	—	4	16	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	16	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	8	no	—
159	C₂×C₄×C₁₉	—	2	8	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	8	no	—
162	C₂×C₄×C₁₉	—	2	4	no	—
163	C₂×C₄×C₁₉	—	2	8	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	2	8	no	—
166	C₂×C₄×C₁₉	—	4	16	no	—
167	C₂×C₄×C₁₉	C₄×Q₈	1	16	yes	complemented
168	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
169	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
170	C₂×C₄×C₁₉	C₂³×C₄	1	16	yes	—
171	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
172	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
173	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
174	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
175	C₂×C₄×C₁₉	C₂²×Q₈	1	8	yes	—
176	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
177	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
178	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
179	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
180	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
181	C₂×C₄×C₁₉	2₋¹⁺⁴	1	4	yes	—
182	C₂²×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
183	#2369	C₂×C₁₉	1	4	yes	complemented
184	#2365	C₂×C₁₉	1	4	yes	complemented
185	#2345	C₂×C₁₉	1	4	yes	—
186	Q₈×C₂²⋊C₄	C₂×C₁₉	1	4	yes	—
187	#2331	C₂×C₁₉	1	4	yes	complemented
188	#2316	C₂×C₁₉	1	2	yes	—
189	C₄×C₄⋊Q₈	C₂×C₁₉	1	4	yes	complemented
190	#2285	C₂×C₁₉	1	1	yes	characteristic
191	#2274	C₂×C₁₉	1	2	yes	—
192	C₄×#117	C₂×C₁₉	1	1	yes	characteristic
193	C₂²×C₁₉	—	2	2	no	—
194	C₂²×C₁₉	—	2	2	no	—
195	C₂²×C₁₉	—	2	4	no	—
196	C₂²×C₁₉	—	2	4	no	—
197	C₂²×C₁₉	C₂×C₄×Q₈	1	4	yes	—
198	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
199	C₂²×C₁₉	C₂³×Q₈	1	1	yes	characteristic
200	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
201	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
202	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	2	16	no	—
205	C₄×C₁₉	—	2	2	no	—
206	C₄×C₁₉	—	2	8	no	—
207	C₄×C₁₉	—	4	4	no	—
208	C₄×C₁₉	—	4	8	no	—
209	C₄×C₁₉	C₂×C₄×Q₈	1	4	yes	—
210	C₄×C₁₉	C₂×C₄×Q₈	1	4	yes	—
211	C₄×C₁₉	#518	1	4	yes	—
212	C₄×C₁₉	#519	1	4	yes	—
213	C₂³×Q₈	C₂²×C₁₉	1	2	yes	—
214	C₂×C₄⋊Q₈	C₄×C₁₉	1	16	yes	complemented
215	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
216	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
217	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
218	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
219	C₂×C₄×Q₈	C₂²×C₁₉	1	8	yes	—
220	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×#117	C₂²×C₁₉	1	2	yes	—
222	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
223	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
224	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
225	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
226	#391	C₂²×C₁₉	1	8	yes	—
227	#391	C₂²×C₁₉	1	16	yes	—
228	#389	C₂²×C₁₉	1	8	yes	—
229	#389	C₂²×C₁₉	1	8	yes	—
230	#389	C₂²×C₁₉	1	8	yes	—
231	#387	C₂²×C₁₉	1	16	yes	—
232	#384	C₂²×C₁₉	1	2	yes	—
233	#382	C₂²×C₁₉	1	2	yes	—
234	#380	C₂²×C₁₉	1	8	yes	—
235	#380	C₂²×C₁₉	1	2	yes	—
236	#380	C₂²×C₁₉	1	2	yes	—
237	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
238	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
239	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
240	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
241	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
242	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
243	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
244	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
245	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
246	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
247	#376	C₂²×C₁₉	1	2	yes	—
248	C₄³	C₂²×C₁₉	1	2	yes	—
249	C₂×C₁₉	—	2	4	no	—
250	C₂×C₁₉	C₂²×C₄×Q₈	1	1	yes	characteristic
251	C₂×C₁₉	C₂×#518	1	1	yes	characteristic
252	C₂×C₁₉	C₂×#519	1	1	yes	characteristic
253	C₂×C₁₉	#3503	1	2	yes	—
254	C₂×C₁₉	#3511	1	2	yes	—
255	C₂²×Q₈	—	4	8	no	—
256	C₂²×Q₈	C₂×C₄×C₁₉	1	16	yes	—
257	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
258	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
259	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
260	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
261	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
262	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
263	C₄⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
264	C₄⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
265	C₄⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
266	C₄⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
267	C₄×Q₈	—	4	16	no	—
268	#117	—	2	4	no	—
269	#117	—	2	8	no	—
270	#117	Q₈×C₁₉	1	8	yes	complemented
271	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	16	yes	—
272	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	16	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
276	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
277	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
279	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
283	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
284	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
286	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	—
287	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
288	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
289	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
290	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
291	C₂×C₄²	C₂³×C₁₉	1	16	yes	—
292	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
293	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
294	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
296	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
297	#95	C₂³×C₁₉	1	4	yes	—
298	#95	C₂³×C₁₉	1	4	yes	—
299	#95	C₂³×C₁₉	1	16	yes	—
300	#95	C₂³×C₁₉	1	4	yes	—
301	#95	C₂³×C₁₉	1	4	yes	—
302	#95	C₂³×C₁₉	1	16	yes	—
303	C₁₉	#34216	1	1	yes	characteristic, direct product factor, Sylow
304	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
305	C₂×Q₈	—	2	16	no	—
306	C₂×Q₈	—	4	8	no	—
307	C₂×Q₈	—	4	32	no	—
308	C₂×Q₈	C₂²×C₄×C₁₉	1	16	yes	—
309	C₂×Q₈	C₂²×C₄×C₁₉	1	16	yes	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	4	8	no	—
313	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
314	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
315	C₂²×C₄	C₂²×C₄×C₁₉	1	16	yes	—
316	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
317	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
318	C₂²×C₄	#41×C₁₉	1	4	yes	—
319	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
320	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
321	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
322	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
323	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
324	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
325	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
326	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
327	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
328	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	4	16	no	—
334	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
335	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
336	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
337	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
338	C₄⋊C₄	C₂×Q₈×C₁₉	1	8	yes	complemented
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₂²⋊C₄	C₂×Q₈×C₁₉	1	8	yes	—
342	C₄²	—	2	8	no	—
343	C₄²	—	2	4	no	—
344	C₄²	—	2	8	no	—
345	C₄²	—	2	8	no	—
346	C₄²	—	4	16	no	—
347	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
348	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
349	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
350	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
351	C₄²	C₂×Q₈×C₁₉	1	8	yes	complemented
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
355	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
356	C₂³	C₂×#41×C₁₉	1	2	yes	—
357	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
358	Q₈	—	2	32	no	—
359	Q₈	—	4	16	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	16	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	4	16	no	—
374	C₂×C₄	C₄×Q₈×C₁₉	1	16	yes	complemented
375	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
376	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
377	C₂×C₄	C₂³×C₄×C₁₉	1	16	yes	—
378	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
379	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
380	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
381	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
382	C₂×C₄	C₂²×Q₈×C₁₉	1	8	yes	—
383	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
384	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
385	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
386	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
387	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
388	C₂×C₄	C₁₉×2₋¹⁺⁴	1	4	yes	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	2	4	no	—
393	C₂²	C₂×C₄×Q₈×C₁₉	1	4	yes	—
394	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
395	C₂²	C₂³×Q₈×C₁₉	1	1	yes	characteristic
396	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
397	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
398	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
399	C₄	—	2	2	no	—
400	C₄	—	2	16	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	8	no	—
403	C₄	—	4	4	no	—
404	C₄	—	4	8	no	—
405	C₄	C₂×C₄×Q₈×C₁₉	1	4	yes	—
406	C₄	C₂×C₄×Q₈×C₁₉	1	4	yes	—
407	C₄	C₁₉×#518	1	4	yes	—
408	C₄	C₁₉×#519	1	4	yes	—
409	C₂	—	2	4	no	—
410	C₂	C₂²×C₄×Q₈×C₁₉	1	1	yes	characteristic
411	C₂	C₂×C₁₉×#518	1	1	yes	characteristic
412	C₂	C₂×C₁₉×#519	1	1	yes	characteristic
413	C₂	C₁₉×#3503	1	2	yes	—
414	C₂	C₁₉×#3511	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2369	C₂	semidirect
3. C₁₉×#2365	C₂	semidirect
6. C₁₉×#2331	C₂	semidirect
8. C₄×C₁₉×C₄⋊Q₈	C₂	semidirect
13. C₂×C₁₉×C₄⋊Q₈	C₄	semidirect
63. C₁₉×#117	Q₈	semidirect
130. C₄⋊C₄×C₁₉	C₂×Q₈	semidirect
143. C₄²×C₁₉	C₂×Q₈	semidirect
144. #34216	C₁₉	direct (N × H)
167. C₂×C₄×C₁₉	C₄×Q₈	semidirect
183. #2369	C₂×C₁₉	semidirect
184. #2365	C₂×C₁₉	semidirect
187. #2331	C₂×C₁₉	semidirect
189. C₄×C₄⋊Q₈	C₂×C₁₉	semidirect
214. C₂×C₄⋊Q₈	C₄×C₁₉	semidirect
270. #117	Q₈×C₁₉	semidirect
303. C₁₉	#34216	direct (N × H)
338. C₄⋊C₄	C₂×Q₈×C₁₉	semidirect
351. C₄²	C₂×Q₈×C₁₉	semidirect
374. C₂×C₄	C₄×Q₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×C₄⋊Q₈	2
C₁₉×#2369	2
C₁₉×#2365	2
C₁₉×#2345	2
Q₈×C₂²⋊C₄×C₁₉	2
C₁₉×#2331	2
C₁₉×#2316	2
C₄×C₁₉×C₄⋊Q₈	2
C₁₉×#2285	2
C₁₉×#2274	2
C₄×C₁₉×#117	2
#34216	19

Subgroups — C19×#34216 #18040175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34216 #18040175