Subgroups — C₁₉×#34175 #18040134

Order 4864.

5502 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#520	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2341	C₂	1	2	yes	maximal, complemented
4	Q₈×C₂²⋊C₄×C₁₉	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2339	C₂	1	6	yes	maximal, complemented
6	D₄×C₂²⋊C₄×C₁₉	C₂	1	6	yes	maximal, complemented
7	C₁₉×#2311	C₂	1	6	yes	maximal, complemented
8	C₁₉×#2280	C₂	1	3	yes	maximal, complemented
9	C₂×C₁₉×#380	C₂	1	3	yes	maximal, complemented
10	C₂²×#41×C₁₉	—	2	16	no	—
11	C₂²×#41×C₁₉	C₄	1	16	yes	complemented
12	C₂²×#41×C₁₉	C₂²	1	3	yes	—
13	C₂²×#41×C₁₉	C₂²	1	3	yes	—
14	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
16	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₉	C₂²	1	3	yes	—
18	C₂⁴×C₄×C₁₉	C₂²	1	3	yes	—
19	C₁₉×#520	—	2	16	no	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
21	C₂×C₄×D₄×C₁₉	C₂²	1	12	yes	complemented
22	C₂×C₁₉×#117	C₂²	1	6	yes	complemented
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	6	yes	complemented
24	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	6	yes	—
25	C₁₉×#391	C₂²	1	12	yes	complemented
26	C₁₉×#390	C₂²	1	12	yes	complemented
27	C₁₉×#386	C₂²	1	24	yes	complemented
28	C₁₉×#381	C₂²	1	6	yes	complemented
29	C₁₉×#380	C₂²	1	3	yes	—
30	C₁₉×#380	C₂²	1	6	yes	—
31	C₁₉×#380	C₂²	1	1	yes	characteristic
32	C₁₉×#380	C₂²	1	6	yes	complemented
33	C₁₉×#380	C₂²	1	6	yes	complemented
34	C₁₉×#380	C₂²	1	6	yes	complemented
35	C₁₉×#379	C₂²	1	6	yes	—
36	C₄×C₂²⋊C₄×C₁₉	C₂²	1	6	yes	—
37	C₄×C₂²⋊C₄×C₁₉	C₂²	1	6	yes	complemented
38	C₂×C₁₉×#95	C₂²	1	6	yes	complemented
39	C₂⁵×C₁₉	C₂³	1	3	yes	—
40	C₂×#41×C₁₉	—	2	128	no	—
41	C₂×#41×C₁₉	—	2	8	no	—
42	C₂×#41×C₁₉	—	2	24	no	—
43	C₂×#41×C₁₉	—	2	24	no	—
44	C₂×#41×C₁₉	C₂×C₄	1	8	yes	—
45	C₂×#41×C₁₉	C₂×C₄	1	8	yes	complemented
46	C₂×#41×C₁₉	C₂×C₄	1	24	yes	complemented
47	C₂×#41×C₁₉	C₂×C₄	1	24	yes	complemented
48	C₂×#41×C₁₉	D₄	1	16	yes	—
49	C₂²×Q₈×C₁₉	—	2	8	no	—
50	C₂²×Q₈×C₁₉	C₂×C₄	1	8	yes	complemented
51	C₂²×Q₈×C₁₉	C₂³	1	3	yes	—
52	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₉	—	2	24	no	—
54	C₂²×D₄×C₁₉	C₂×C₄	1	24	yes	complemented
55	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
56	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
57	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
58	C₂³×C₄×C₁₉	—	2	24	no	—
59	C₂³×C₄×C₁₉	C₂×C₄	1	24	yes	complemented
60	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
61	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
62	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
63	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
65	C₂³×C₄×C₁₉	C₂³	1	12	yes	—
66	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
67	C₄×Q₈×C₁₉	—	2	16	no	—
68	C₄×D₄×C₁₉	—	2	48	no	—
69	C₁₉×#117	—	2	24	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	24	no	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
74	C₂×C₂²⋊C₄×C₁₉	—	4	12	no	—
75	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
76	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
77	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
78	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
79	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
80	C₂×C₄²×C₁₉	C₂³	1	12	yes	—
81	C₁₉×#95	C₂³	1	6	yes	—
82	C₁₉×#95	C₂³	1	12	yes	—
83	C₁₉×#95	C₂³	1	12	yes	—
84	C₁₉×#95	C₂³	1	2	yes	—
85	C₂⁴×C₁₉	—	2	12	no	—
86	C₂⁴×C₁₉	—	2	6	no	—
87	C₂⁴×C₁₉	—	2	6	no	—
88	C₂⁴×C₁₉	—	4	6	no	—
89	C₂⁴×C₁₉	C₂²×C₄	1	12	yes	—
90	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
91	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
92	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
93	#41×C₁₉	—	2	32	no	—
94	#41×C₁₉	—	2	96	no	—
95	#41×C₁₉	—	2	96	no	—
96	#41×C₁₉	C₂²⋊C₄	1	64	yes	complemented
97	C₂×Q₈×C₁₉	—	2	32	no	—
98	C₂×Q₈×C₁₉	—	2	12	no	—
99	C₂×Q₈×C₁₉	C₂²×C₄	1	12	yes	—
100	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
101	C₂×Q₈×C₁₉	C₂×D₄	1	8	yes	—
102	C₂×D₄×C₁₉	—	2	24	no	—
103	C₂×D₄×C₁₉	—	2	96	no	—
104	C₂×D₄×C₁₉	—	2	12	no	—
105	C₂×D₄×C₁₉	C₂²×C₄	1	24	yes	—
106	C₂×D₄×C₁₉	C₂²×C₄	1	12	yes	—
107	C₂×D₄×C₁₉	C₂²×C₄	1	12	yes	—
108	C₂×D₄×C₁₉	C₂×D₄	1	24	yes	—
109	C₂²×C₄×C₁₉	—	2	12	no	—
110	C₂²×C₄×C₁₉	—	2	96	no	—
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	—	2	12	no	—
113	C₂²×C₄×C₁₉	—	2	12	no	—
114	C₂²×C₄×C₁₉	—	2	12	no	—
115	C₂²×C₄×C₁₉	—	2	24	no	—
116	C₂²×C₄×C₁₉	—	4	12	no	—
117	C₂²×C₄×C₁₉	—	4	12	no	—
118	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
120	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
121	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
122	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
123	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	24	yes	—
125	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
127	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
130	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
131	C₄⋊C₄×C₁₉	—	2	12	no	—
132	C₄⋊C₄×C₁₉	—	2	24	no	—
133	C₄⋊C₄×C₁₉	—	2	4	no	—
134	C₂²⋊C₄×C₁₉	—	2	24	no	—
135	C₂²⋊C₄×C₁₉	—	2	12	no	—
136	C₂²⋊C₄×C₁₉	—	2	4	no	—
137	C₂²⋊C₄×C₁₉	—	4	12	no	—
138	C₂²⋊C₄×C₁₉	—	4	12	no	—
139	C₄²×C₁₉	—	2	24	no	—
140	#34175	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₁₉	—	2	2	no	—
142	C₂³×C₁₉	—	2	3	no	—
143	C₂³×C₁₉	—	2	3	no	—
144	C₂³×C₁₉	—	2	6	no	—
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	—	2	24	no	—
147	C₂³×C₁₉	—	2	24	no	—
148	C₂³×C₁₉	—	2	6	no	—
149	C₂³×C₁₉	—	2	3	no	—
150	C₂³×C₁₉	—	2	3	no	—
151	C₂³×C₁₉	—	2	6	no	—
152	C₂³×C₁₉	—	4	12	no	—
153	C₂³×C₁₉	—	4	24	no	—
154	C₂³×C₁₉	—	4	24	no	—
155	C₂³×C₁₉	C₂³×C₄	1	6	yes	—
156	C₂³×C₁₉	C₂³×C₄	1	6	yes	—
157	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
158	C₂³×C₁₉	C₂²×D₄	1	12	yes	—
159	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
160	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
161	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
162	Q₈×C₁₉	—	2	24	no	—
163	Q₈×C₁₉	C₂×C₂²⋊C₄	1	16	yes	complemented
164	D₄×C₁₉	—	2	48	no	—
165	D₄×C₁₉	—	2	24	no	—
166	D₄×C₁₉	C₂×C₂²⋊C₄	1	48	yes	complemented
167	C₂×C₄×C₁₉	—	2	24	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	6	no	—
170	C₂×C₄×C₁₉	—	2	8	no	—
171	C₂×C₄×C₁₉	—	2	24	no	—
172	C₂×C₄×C₁₉	—	2	24	no	—
173	C₂×C₄×C₁₉	—	2	24	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	2	12	no	—
176	C₂×C₄×C₁₉	—	2	12	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	2	12	no	—
180	C₂×C₄×C₁₉	—	8	24	no	—
181	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	48	yes	complemented
182	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
183	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
184	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
185	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
186	C₂×C₄×C₁₉	C₂²×D₄	1	12	yes	—
187	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
188	C₂³×#41	C₂×C₁₉	1	1	yes	characteristic
189	C₂×#520	C₂×C₁₉	1	2	yes	complemented
190	#2341	C₂×C₁₉	1	2	yes	complemented
191	Q₈×C₂²⋊C₄	C₂×C₁₉	1	2	yes	complemented
192	#2339	C₂×C₁₉	1	6	yes	complemented
193	D₄×C₂²⋊C₄	C₂×C₁₉	1	6	yes	complemented
194	#2311	C₂×C₁₉	1	6	yes	complemented
195	#2280	C₂×C₁₉	1	3	yes	complemented
196	C₂×#380	C₂×C₁₉	1	3	yes	complemented
197	C₂²×C₁₉	—	2	2	no	—
198	C₂²×C₁₉	—	2	6	no	—
199	C₂²×C₁₉	—	2	2	no	—
200	C₂²×C₁₉	—	2	6	no	—
201	C₂²×C₁₉	—	2	12	no	—
202	C₂²×C₁₉	—	2	4	no	—
203	C₂²×C₁₉	—	2	4	no	—
204	C₂²×C₁₉	—	2	12	no	—
205	C₂²×C₁₉	—	2	6	no	—
206	C₂²×C₁₉	—	2	6	no	—
207	C₂²×C₁₉	—	2	6	no	—
208	C₂²×C₁₉	—	4	48	no	—
209	C₂²×C₁₉	—	4	6	no	—
210	C₂²×C₁₉	—	4	6	no	—
211	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	12	yes	—
212	C₂²×C₁₉	#520	1	4	yes	complemented
213	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
214	C₂²×C₁₉	C₂³×D₄	1	2	yes	—
215	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
216	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
217	C₂²×C₁₉	#585	1	2	yes	—
218	C₄×C₁₉	—	2	2	no	—
219	C₄×C₁₉	—	2	6	no	—
220	C₄×C₁₉	—	4	12	no	—
221	C₄×C₁₉	—	4	4	no	—
222	C₄×C₁₉	C₂²×C₂²⋊C₄	1	4	yes	—
223	C₄×C₁₉	C₂²×C₂²⋊C₄	1	12	yes	—
224	C₂²×#41	—	2	16	no	—
225	C₂²×#41	C₄×C₁₉	1	16	yes	complemented
226	C₂²×#41	C₂²×C₁₉	1	3	yes	—
227	C₂²×#41	C₂²×C₁₉	1	3	yes	—
228	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
229	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
230	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
231	C₂³×D₄	C₂²×C₁₉	1	3	yes	—
232	C₂⁴×C₄	C₂²×C₁₉	1	3	yes	—
233	#520	—	2	16	no	—
234	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
235	C₂×C₄×D₄	C₂²×C₁₉	1	12	yes	complemented
236	C₂×#117	C₂²×C₁₉	1	6	yes	complemented
237	C₂²×C₄⋊C₄	C₂²×C₁₉	1	6	yes	complemented
238	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	6	yes	—
239	#391	C₂²×C₁₉	1	12	yes	complemented
240	#390	C₂²×C₁₉	1	12	yes	complemented
241	#386	C₂²×C₁₉	1	24	yes	complemented
242	#381	C₂²×C₁₉	1	6	yes	complemented
243	#380	C₂²×C₁₉	1	6	yes	—
244	#380	C₂²×C₁₉	1	3	yes	—
245	#380	C₂²×C₁₉	1	1	yes	characteristic
246	#380	C₂²×C₁₉	1	6	yes	complemented
247	#380	C₂²×C₁₉	1	6	yes	complemented
248	#380	C₂²×C₁₉	1	6	yes	complemented
249	#379	C₂²×C₁₉	1	6	yes	—
250	C₄×C₂²⋊C₄	C₂²×C₁₉	1	6	yes	—
251	C₄×C₂²⋊C₄	C₂²×C₁₉	1	6	yes	complemented
252	C₂×#95	C₂²×C₁₉	1	6	yes	complemented
253	C₂×C₁₉	—	2	4	no	—
254	C₂×C₁₉	—	2	12	no	—
255	C₂×C₁₉	—	4	6	no	—
256	C₂×C₁₉	C₂³×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×C₁₉	C₂×#520	1	1	yes	characteristic
258	C₂×C₁₉	#3428	1	1	yes	characteristic
259	C₂×C₁₉	#3488	1	2	yes	—
260	C₂×C₁₉	#3489	1	2	yes	—
261	C₂⁵	C₂³×C₁₉	1	3	yes	—
262	C₂×#41	—	2	128	no	—
263	C₂×#41	—	2	8	no	—
264	C₂×#41	—	2	24	no	—
265	C₂×#41	—	2	24	no	—
266	C₂×#41	C₂×C₄×C₁₉	1	8	yes	—
267	C₂×#41	C₂×C₄×C₁₉	1	8	yes	complemented
268	C₂×#41	C₂×C₄×C₁₉	1	24	yes	complemented
269	C₂×#41	C₂×C₄×C₁₉	1	24	yes	complemented
270	C₂×#41	D₄×C₁₉	1	16	yes	—
271	C₂²×Q₈	—	2	8	no	—
272	C₂²×Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
273	C₂²×Q₈	C₂³×C₁₉	1	3	yes	—
274	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
275	C₂²×D₄	—	2	24	no	—
276	C₂²×D₄	C₂×C₄×C₁₉	1	24	yes	complemented
277	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
278	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
279	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
280	C₂³×C₄	—	2	24	no	—
281	C₂³×C₄	C₂×C₄×C₁₉	1	24	yes	complemented
282	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
283	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
284	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
285	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
286	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
287	C₂³×C₄	C₂³×C₁₉	1	12	yes	—
288	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
289	C₄×Q₈	—	2	16	no	—
290	C₄×D₄	—	2	48	no	—
291	#117	—	2	24	no	—
292	C₂×C₄⋊C₄	—	2	24	no	—
293	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
296	C₂×C₂²⋊C₄	—	4	12	no	—
297	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
298	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
299	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
300	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
301	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
302	C₂×C₄²	C₂³×C₁₉	1	12	yes	—
303	#95	C₂³×C₁₉	1	6	yes	—
304	#95	C₂³×C₁₉	1	12	yes	—
305	#95	C₂³×C₁₉	1	12	yes	—
306	#95	C₂³×C₁₉	1	2	yes	—
307	C₁₉	#34175	1	1	yes	characteristic, direct product factor, Sylow
308	C₂⁴	—	2	12	no	—
309	C₂⁴	—	2	6	no	—
310	C₂⁴	—	2	6	no	—
311	C₂⁴	—	4	6	no	—
312	C₂⁴	C₂²×C₄×C₁₉	1	12	yes	—
313	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
314	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
315	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
316	#41	—	2	32	no	—
317	#41	—	2	96	no	—
318	#41	—	2	96	no	—
319	#41	C₂²⋊C₄×C₁₉	1	64	yes	complemented
320	C₂×Q₈	—	2	32	no	—
321	C₂×Q₈	—	2	12	no	—
322	C₂×Q₈	C₂²×C₄×C₁₉	1	12	yes	—
323	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
324	C₂×Q₈	C₂×D₄×C₁₉	1	8	yes	—
325	C₂×D₄	—	2	24	no	—
326	C₂×D₄	—	2	96	no	—
327	C₂×D₄	—	2	12	no	—
328	C₂×D₄	C₂²×C₄×C₁₉	1	24	yes	—
329	C₂×D₄	C₂²×C₄×C₁₉	1	12	yes	—
330	C₂×D₄	C₂²×C₄×C₁₉	1	12	yes	—
331	C₂×D₄	C₂×D₄×C₁₉	1	24	yes	—
332	C₂²×C₄	—	2	12	no	—
333	C₂²×C₄	—	2	96	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	12	no	—
336	C₂²×C₄	—	2	12	no	—
337	C₂²×C₄	—	2	12	no	—
338	C₂²×C₄	—	2	24	no	—
339	C₂²×C₄	—	4	12	no	—
340	C₂²×C₄	—	4	12	no	—
341	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
342	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
343	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
344	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
345	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
346	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
347	C₂²×C₄	C₂×D₄×C₁₉	1	24	yes	—
348	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
349	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
350	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
352	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
353	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
354	C₄⋊C₄	—	2	12	no	—
355	C₄⋊C₄	—	2	24	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	—	2	24	no	—
358	C₂²⋊C₄	—	2	12	no	—
359	C₂²⋊C₄	—	2	4	no	—
360	C₂²⋊C₄	—	4	12	no	—
361	C₂²⋊C₄	—	4	12	no	—
362	C₄²	—	2	24	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	2	3	no	—
365	C₂³	—	2	3	no	—
366	C₂³	—	2	6	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	24	no	—
369	C₂³	—	2	24	no	—
370	C₂³	—	2	6	no	—
371	C₂³	—	2	3	no	—
372	C₂³	—	2	3	no	—
373	C₂³	—	2	6	no	—
374	C₂³	—	4	12	no	—
375	C₂³	—	4	24	no	—
376	C₂³	—	4	24	no	—
377	C₂³	C₂³×C₄×C₁₉	1	6	yes	—
378	C₂³	C₂³×C₄×C₁₉	1	6	yes	—
379	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
380	C₂³	C₂²×D₄×C₁₉	1	12	yes	—
381	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
382	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
383	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
384	Q₈	—	2	24	no	—
385	Q₈	C₂×C₂²⋊C₄×C₁₉	1	16	yes	complemented
386	D₄	—	2	48	no	—
387	D₄	—	2	24	no	—
388	D₄	C₂×C₂²⋊C₄×C₁₉	1	48	yes	complemented
389	C₂×C₄	—	2	24	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	6	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	24	no	—
394	C₂×C₄	—	2	24	no	—
395	C₂×C₄	—	2	24	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	12	no	—
398	C₂×C₄	—	2	12	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	12	no	—
402	C₂×C₄	—	8	24	no	—
403	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	48	yes	complemented
404	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
405	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
406	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
407	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
408	C₂×C₄	C₂²×D₄×C₁₉	1	12	yes	—
409	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
410	C₂²	—	2	6	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	6	no	—
413	C₂²	—	2	12	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	12	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	6	no	—
419	C₂²	—	2	6	no	—
420	C₂²	—	2	6	no	—
421	C₂²	—	4	48	no	—
422	C₂²	—	4	6	no	—
423	C₂²	—	4	6	no	—
424	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	12	yes	—
425	C₂²	C₁₉×#520	1	4	yes	complemented
426	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
427	C₂²	C₂³×D₄×C₁₉	1	2	yes	—
428	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
429	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
430	C₂²	C₁₉×#585	1	2	yes	—
431	C₄	—	2	2	no	—
432	C₄	—	2	6	no	—
433	C₄	—	4	12	no	—
434	C₄	—	4	4	no	—
435	C₄	C₂²×C₂²⋊C₄×C₁₉	1	4	yes	—
436	C₄	C₂²×C₂²⋊C₄×C₁₉	1	12	yes	—
437	C₂	—	2	4	no	—
438	C₂	—	2	12	no	—
439	C₂	—	4	6	no	—
440	C₂	C₂³×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
441	C₂	C₂×C₁₉×#520	1	1	yes	characteristic
442	C₂	C₁₉×#3428	1	1	yes	characteristic
443	C₂	C₁₉×#3488	1	2	yes	—
444	C₂	C₁₉×#3489	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂³×#41×C₁₉	C₂
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. C₂×C₁₉×#520	C₂	semidirect
3. C₁₉×#2341	C₂	semidirect
4. Q₈×C₂²⋊C₄×C₁₉	C₂	semidirect
5. C₁₉×#2339	C₂	semidirect
6. D₄×C₂²⋊C₄×C₁₉	C₂	semidirect
7. C₁₉×#2311	C₂	semidirect
8. C₁₉×#2280	C₂	semidirect
9. C₂×C₁₉×#380	C₂	semidirect
11. C₂²×#41×C₁₉	C₄	semidirect
20. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
21. C₂×C₄×D₄×C₁₉	C₂²	semidirect
22. C₂×C₁₉×#117	C₂²	semidirect
23. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
25. C₁₉×#391	C₂²	semidirect
26. C₁₉×#390	C₂²	semidirect
27. C₁₉×#386	C₂²	semidirect
28. C₁₉×#381	C₂²	semidirect
32. C₁₉×#380	C₂²	semidirect
33. C₁₉×#380	C₂²	semidirect
34. C₁₉×#380	C₂²	semidirect
37. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
38. C₂×C₁₉×#95	C₂²	semidirect
45. C₂×#41×C₁₉	C₂×C₄	semidirect
46. C₂×#41×C₁₉	C₂×C₄	semidirect
47. C₂×#41×C₁₉	C₂×C₄	semidirect
50. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
54. C₂²×D₄×C₁₉	C₂×C₄	semidirect
59. C₂³×C₄×C₁₉	C₂×C₄	semidirect
96. #41×C₁₉	C₂²⋊C₄	semidirect
140. #34175	C₁₉	direct (N × H)
163. Q₈×C₁₉	C₂×C₂²⋊C₄	semidirect
166. D₄×C₁₉	C₂×C₂²⋊C₄	semidirect
181. C₂×C₄×C₁₉	C₂×C₂²⋊C₄	semidirect
189. C₂×#520	C₂×C₁₉	semidirect
190. #2341	C₂×C₁₉	semidirect
191. Q₈×C₂²⋊C₄	C₂×C₁₉	semidirect
192. #2339	C₂×C₁₉	semidirect
193. D₄×C₂²⋊C₄	C₂×C₁₉	semidirect
194. #2311	C₂×C₁₉	semidirect
195. #2280	C₂×C₁₉	semidirect
196. C₂×#380	C₂×C₁₉	semidirect
212. C₂²×C₁₉	#520	semidirect
225. C₂²×#41	C₄×C₁₉	semidirect
234. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
235. C₂×C₄×D₄	C₂²×C₁₉	semidirect
236. C₂×#117	C₂²×C₁₉	semidirect
237. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
239. #391	C₂²×C₁₉	semidirect
240. #390	C₂²×C₁₉	semidirect
241. #386	C₂²×C₁₉	semidirect
242. #381	C₂²×C₁₉	semidirect
246. #380	C₂²×C₁₉	semidirect
247. #380	C₂²×C₁₉	semidirect
248. #380	C₂²×C₁₉	semidirect
251. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
252. C₂×#95	C₂²×C₁₉	semidirect
267. C₂×#41	C₂×C₄×C₁₉	semidirect
268. C₂×#41	C₂×C₄×C₁₉	semidirect
269. C₂×#41	C₂×C₄×C₁₉	semidirect
272. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
276. C₂²×D₄	C₂×C₄×C₁₉	semidirect
281. C₂³×C₄	C₂×C₄×C₁₉	semidirect
307. C₁₉	#34175	direct (N × H)
319. #41	C₂²⋊C₄×C₁₉	semidirect
385. Q₈	C₂×C₂²⋊C₄×C₁₉	semidirect
388. D₄	C₂×C₂²⋊C₄×C₁₉	semidirect
403. C₂×C₄	C₂×C₂²⋊C₄×C₁₉	semidirect
425. C₂²	C₁₉×#520	semidirect

Maximal subgroups

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

subgroup	index
C₂³×#41×C₁₉	2
C₂×C₁₉×#520	2
C₁₉×#2341	2
Q₈×C₂²⋊C₄×C₁₉	2
C₁₉×#2339	2
D₄×C₂²⋊C₄×C₁₉	2
C₁₉×#2311	2
C₁₉×#2280	2
C₂×C₁₉×#380	2
#34175	19

Subgroups — C19×#34175 #18040134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34175 #18040134