Subgroups — C₁₉×#35033 #18040992

Order 4864.

1986 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2857	C₂	1	2	yes	maximal, complemented
2	C₁₉×#2851	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2626	C₂	1	4	yes	maximal
4	C₁₉×#2608	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2607	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2441	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2439	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2329	C₂	1	4	yes	maximal, complemented
9	C₁₉×#2280	C₂	1	2	yes	maximal
10	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
11	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
13	C₂×C₁₉×#125	C₂²	1	2	yes	complemented
14	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
15	C₂×C₁₉×#117	C₂²	1	2	yes	—
16	C₂×C₁₉×#117	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#399	C₂²	1	8	yes	—
21	C₁₉×#396	C₂²	1	8	yes	—
22	C₁₉×#396	C₂²	1	8	yes	—
23	C₁₉×#393	C₂²	1	8	yes	—
24	C₁₉×#391	C₂²	1	8	yes	complemented
25	C₁₉×#391	C₂²	1	4	yes	complemented
26	C₁₉×#389	C₂²	1	4	yes	complemented
27	C₁₉×#389	C₂²	1	4	yes	complemented
28	C₁₉×#389	C₂²	1	8	yes	complemented
29	C₁₉×#389	C₂²	1	4	yes	complemented
30	C₁₉×#387	C₂²	1	8	yes	complemented
31	C₁₉×#387	C₂²	1	8	yes	complemented
32	C₁₉×#387	C₂²	1	8	yes	complemented
33	C₁₉×#385	C₂²	1	8	yes	—
34	C₁₉×#384	C₂²	1	2	yes	complemented
35	C₁₉×#382	C₂²	1	2	yes	complemented
36	C₁₉×#381	C₂²	1	4	yes	—
37	C₁₉×#380	C₂²	1	4	yes	—
38	C₁₉×#380	C₂²	1	4	yes	—
39	C₁₉×#380	C₂²	1	4	yes	—
40	C₁₉×#379	C₂²	1	4	yes	—
41	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
42	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
43	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
44	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
45	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
46	C₂×C₁₉×#95	C₂²	1	2	yes	—
47	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
49	C₂³×C₄×C₁₉	—	4	2	no	—
50	C₂³×C₄×C₁₉	—	4	2	no	—
51	C₂³×C₄×C₁₉	Q₈	1	8	yes	complemented
52	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
58	C₁₉×C₄⋊Q₈	—	4	4	no	—
59	C₁₉×#125	—	4	4	no	—
60	C₁₉×C₂²⋊Q₈	—	2	16	no	—
61	C₁₉×#117	—	4	4	no	—
62	C₁₉×#117	—	4	4	no	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
72	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
73	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
74	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
75	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
76	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
77	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
78	C₂×C₄²×C₁₉	—	4	2	no	—
79	C₂×C₄²×C₁₉	—	4	2	no	—
80	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
81	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
82	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
83	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
84	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
87	C₁₉×#95	C₂³	1	4	yes	—
88	C₁₉×#95	C₂³	1	4	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	C₂⁴×C₁₉	—	2	4	no	—
95	C₂⁴×C₁₉	—	4	1	no	—
96	C₂⁴×C₁₉	—	4	1	no	—
97	C₂⁴×C₁₉	—	4	2	no	—
98	C₂⁴×C₁₉	C₂×Q₈	1	4	yes	—
99	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
100	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
101	C₂×Q₈×C₁₉	—	2	8	no	—
102	C₂×Q₈×C₁₉	—	4	4	no	—
103	C₂×Q₈×C₁₉	—	4	4	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	4	no	—
107	C₂²×C₄×C₁₉	—	2	4	no	—
108	C₂²×C₄×C₁₉	—	2	4	no	—
109	C₂²×C₄×C₁₉	—	4	16	no	—
110	C₂²×C₄×C₁₉	—	4	2	no	—
111	C₂²×C₄×C₁₉	—	4	2	no	—
112	C₂²×C₄×C₁₉	—	4	1	no	—
113	C₂²×C₄×C₁₉	—	4	1	no	—
114	C₂²×C₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	—	4	2	no	—
116	C₂²×C₄×C₁₉	—	4	2	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	C₂×Q₈	1	8	yes	—
119	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
120	C₂²×C₄×C₁₉	C₂×Q₈	1	8	yes	—
121	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
122	C₂²×C₄×C₁₉	#41	1	8	yes	—
123	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
125	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
126	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
131	C₄⋊C₄×C₁₉	—	2	8	no	—
132	C₄⋊C₄×C₁₉	—	2	16	no	—
133	C₄⋊C₄×C₁₉	—	2	8	no	—
134	C₄⋊C₄×C₁₉	—	2	8	no	—
135	C₄⋊C₄×C₁₉	—	4	4	no	—
136	C₄⋊C₄×C₁₉	—	4	8	no	—
137	C₄⋊C₄×C₁₉	—	4	8	no	—
138	C₄⋊C₄×C₁₉	—	4	4	no	—
139	C₂²⋊C₄×C₁₉	—	2	16	no	—
140	C₂²⋊C₄×C₁₉	—	2	8	no	—
141	C₂²⋊C₄×C₁₉	—	2	8	no	—
142	C₂²⋊C₄×C₁₉	—	4	8	no	—
143	C₂²⋊C₄×C₁₉	—	4	4	no	—
144	C₂²⋊C₄×C₁₉	—	4	4	no	—
145	C₄²×C₁₉	—	2	4	no	—
146	C₄²×C₁₉	—	2	4	no	—
147	C₄²×C₁₉	—	4	1	no	—
148	C₄²×C₁₉	—	4	1	no	—
149	C₄²×C₁₉	—	4	2	no	—
150	C₄²×C₁₉	—	4	4	no	—
151	C₄²×C₁₉	—	4	4	no	—
152	#35033	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂³×C₁₉	—	2	1	no	—
154	C₂³×C₁₉	—	2	1	no	—
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	2	8	no	—
157	C₂³×C₁₉	—	2	4	no	—
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	2	2	no	—
160	C₂³×C₁₉	—	2	4	no	—
161	C₂³×C₁₉	—	4	4	no	—
162	C₂³×C₁₉	—	4	4	no	—
163	C₂³×C₁₉	—	4	8	no	—
164	C₂³×C₁₉	—	4	8	no	—
165	C₂³×C₁₉	C₂²×Q₈	1	4	yes	—
166	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
167	C₂³×C₁₉	C₂×#41	1	4	yes	—
168	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
169	Q₈×C₁₉	—	8	8	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	8	no	—
179	C₂×C₄×C₁₉	—	2	16	no	—
180	C₂×C₄×C₁₉	—	2	4	no	—
181	C₂×C₄×C₁₉	—	2	8	no	—
182	C₂×C₄×C₁₉	—	2	8	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	8	no	—
185	C₂×C₄×C₁₉	—	2	8	no	—
186	C₂×C₄×C₁₉	—	2	8	no	—
187	C₂×C₄×C₁₉	—	2	8	no	—
188	C₂×C₄×C₁₉	—	2	4	no	—
189	C₂×C₄×C₁₉	—	4	4	no	—
190	C₂×C₄×C₁₉	—	4	8	no	—
191	C₂×C₄×C₁₉	—	4	8	no	—
192	C₂×C₄×C₁₉	—	4	8	no	—
193	C₂×C₄×C₁₉	C₂²×Q₈	1	4	yes	—
194	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
195	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
196	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
197	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
198	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
199	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
200	#2857	C₂×C₁₉	1	2	yes	complemented
201	#2851	C₂×C₁₉	1	2	yes	complemented
202	#2626	C₂×C₁₉	1	4	yes	—
203	#2608	C₂×C₁₉	1	4	yes	complemented
204	#2607	C₂×C₁₉	1	4	yes	complemented
205	#2441	C₂×C₁₉	1	4	yes	complemented
206	#2439	C₂×C₁₉	1	4	yes	complemented
207	#2329	C₂×C₁₉	1	4	yes	complemented
208	#2280	C₂×C₁₉	1	2	yes	—
209	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	2	2	no	—
212	C₂²×C₁₉	—	2	4	no	—
213	C₂²×C₁₉	—	2	4	no	—
214	C₂²×C₁₉	—	2	4	no	—
215	C₂²×C₁₉	—	2	4	no	—
216	C₂²×C₁₉	—	2	4	no	—
217	C₂²×C₁₉	—	4	16	no	—
218	C₂²×C₁₉	—	4	4	no	—
219	C₂²×C₁₉	—	4	4	no	—
220	C₂²×C₁₉	#533	1	4	yes	—
221	C₂²×C₁₉	C₂³×Q₈	1	1	yes	characteristic
222	C₂²×C₁₉	C₂²×#41	1	2	yes	—
223	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
224	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
225	C₂²×C₁₉	#585	1	2	yes	—
226	C₄×C₁₉	—	2	2	no	—
227	C₄×C₁₉	—	2	4	no	—
228	C₄×C₁₉	—	2	4	no	—
229	C₄×C₁₉	—	2	4	no	—
230	C₄×C₁₉	—	4	8	no	—
231	C₄×C₁₉	—	4	8	no	—
232	C₄×C₁₉	—	4	4	no	—
233	C₄×C₁₉	#543	1	4	yes	—
234	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
235	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	complemented
236	C₂×#125	C₂²×C₁₉	1	2	yes	complemented
237	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
238	C₂×#117	C₂²×C₁₉	1	2	yes	—
239	C₂×#117	C₂²×C₁₉	1	2	yes	—
240	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
241	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
242	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
243	#399	C₂²×C₁₉	1	8	yes	—
244	#396	C₂²×C₁₉	1	8	yes	—
245	#396	C₂²×C₁₉	1	8	yes	—
246	#393	C₂²×C₁₉	1	8	yes	—
247	#391	C₂²×C₁₉	1	8	yes	complemented
248	#391	C₂²×C₁₉	1	4	yes	complemented
249	#389	C₂²×C₁₉	1	8	yes	complemented
250	#389	C₂²×C₁₉	1	4	yes	complemented
251	#389	C₂²×C₁₉	1	4	yes	complemented
252	#389	C₂²×C₁₉	1	4	yes	complemented
253	#387	C₂²×C₁₉	1	8	yes	complemented
254	#387	C₂²×C₁₉	1	8	yes	complemented
255	#387	C₂²×C₁₉	1	8	yes	complemented
256	#385	C₂²×C₁₉	1	8	yes	—
257	#384	C₂²×C₁₉	1	2	yes	complemented
258	#382	C₂²×C₁₉	1	2	yes	complemented
259	#381	C₂²×C₁₉	1	4	yes	—
260	#380	C₂²×C₁₉	1	4	yes	—
261	#380	C₂²×C₁₉	1	4	yes	—
262	#380	C₂²×C₁₉	1	4	yes	—
263	#379	C₂²×C₁₉	1	4	yes	—
264	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
265	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
266	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
267	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
268	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
269	C₂×#95	C₂²×C₁₉	1	2	yes	—
270	C₂×C₁₉	—	2	4	no	—
271	C₂×C₁₉	—	4	4	no	—
272	C₂×C₁₉	C₂×#533	1	1	yes	characteristic
273	C₂×C₁₉	C₂×#543	1	1	yes	characteristic
274	C₂×C₁₉	#3458	1	1	yes	characteristic
275	C₂×C₁₉	#3505	1	2	yes	—
276	C₂×C₁₉	#3506	1	2	yes	—
277	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
278	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
279	C₂³×C₄	—	4	2	no	—
280	C₂³×C₄	—	4	2	no	—
281	C₂³×C₄	Q₈×C₁₉	1	8	yes	complemented
282	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
283	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
285	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
287	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
288	C₄⋊Q₈	—	4	4	no	—
289	#125	—	4	4	no	—
290	C₂²⋊Q₈	—	2	16	no	—
291	#117	—	4	4	no	—
292	#117	—	4	4	no	—
293	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
296	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
298	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
301	C₂×C₂²⋊C₄	—	2	8	no	—
302	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
306	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
307	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
308	C₂×C₄²	—	4	2	no	—
309	C₂×C₄²	—	4	2	no	—
310	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
311	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
312	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
313	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
314	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
315	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
317	#95	C₂³×C₁₉	1	4	yes	—
318	#95	C₂³×C₁₉	1	4	yes	—
319	#95	C₂³×C₁₉	1	8	yes	—
320	#95	C₂³×C₁₉	1	8	yes	—
321	#95	C₂³×C₁₉	1	8	yes	—
322	#95	C₂³×C₁₉	1	8	yes	—
323	#95	C₂³×C₁₉	1	8	yes	—
324	C₁₉	#35033	1	1	yes	characteristic, direct product factor, Sylow
325	C₂⁴	—	2	4	no	—
326	C₂⁴	—	4	1	no	—
327	C₂⁴	—	4	1	no	—
328	C₂⁴	—	4	2	no	—
329	C₂⁴	C₂×Q₈×C₁₉	1	4	yes	—
330	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
331	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
332	C₂×Q₈	—	2	8	no	—
333	C₂×Q₈	—	4	4	no	—
334	C₂×Q₈	—	4	4	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	4	16	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	C₂×Q₈×C₁₉	1	8	yes	—
350	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
351	C₂²×C₄	C₂×Q₈×C₁₉	1	8	yes	—
352	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
353	C₂²×C₄	#41×C₁₉	1	8	yes	—
354	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
355	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
356	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
357	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
361	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	16	no	—
364	C₄⋊C₄	—	2	8	no	—
365	C₄⋊C₄	—	2	8	no	—
366	C₄⋊C₄	—	4	4	no	—
367	C₄⋊C₄	—	4	8	no	—
368	C₄⋊C₄	—	4	8	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₂²⋊C₄	—	2	16	no	—
371	C₂²⋊C₄	—	2	8	no	—
372	C₂²⋊C₄	—	2	8	no	—
373	C₂²⋊C₄	—	4	8	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₄²	—	2	4	no	—
377	C₄²	—	2	4	no	—
378	C₄²	—	4	1	no	—
379	C₄²	—	4	1	no	—
380	C₄²	—	4	2	no	—
381	C₄²	—	4	4	no	—
382	C₄²	—	4	4	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	8	no	—
387	C₂³	—	2	4	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	4	4	no	—
392	C₂³	—	4	4	no	—
393	C₂³	—	4	8	no	—
394	C₂³	—	4	8	no	—
395	C₂³	C₂²×Q₈×C₁₉	1	4	yes	—
396	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
397	C₂³	C₂×#41×C₁₉	1	4	yes	—
398	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
399	Q₈	—	8	8	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	8	no	—
409	C₂×C₄	—	2	16	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	8	no	—
421	C₂×C₄	—	4	8	no	—
422	C₂×C₄	—	4	8	no	—
423	C₂×C₄	C₂²×Q₈×C₁₉	1	4	yes	—
424	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
425	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
426	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
427	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
428	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
429	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	4	16	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	4	no	—
440	C₂²	C₁₉×#533	1	4	yes	—
441	C₂²	C₂³×Q₈×C₁₉	1	1	yes	characteristic
442	C₂²	C₂²×#41×C₁₉	1	2	yes	—
443	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
444	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
445	C₂²	C₁₉×#585	1	2	yes	—
446	C₄	—	2	2	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	4	no	—
449	C₄	—	2	4	no	—
450	C₄	—	4	8	no	—
451	C₄	—	4	4	no	—
452	C₄	—	4	8	no	—
453	C₄	C₁₉×#543	1	4	yes	—
454	C₂	—	2	4	no	—
455	C₂	—	4	4	no	—
456	C₂	C₂×C₁₉×#533	1	1	yes	characteristic
457	C₂	C₂×C₁₉×#543	1	1	yes	characteristic
458	C₂	C₁₉×#3458	1	1	yes	characteristic
459	C₂	C₁₉×#3505	1	2	yes	—
460	C₂	C₁₉×#3506	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2857	C₂	semidirect
2. C₁₉×#2851	C₂	semidirect
4. C₁₉×#2608	C₂	semidirect
5. C₁₉×#2607	C₂	semidirect
6. C₁₉×#2441	C₂	semidirect
7. C₁₉×#2439	C₂	semidirect
8. C₁₉×#2329	C₂	semidirect
12. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
13. C₂×C₁₉×#125	C₂²	semidirect
24. C₁₉×#391	C₂²	semidirect
25. C₁₉×#391	C₂²	semidirect
26. C₁₉×#389	C₂²	semidirect
27. C₁₉×#389	C₂²	semidirect
28. C₁₉×#389	C₂²	semidirect
29. C₁₉×#389	C₂²	semidirect
30. C₁₉×#387	C₂²	semidirect
31. C₁₉×#387	C₂²	semidirect
32. C₁₉×#387	C₂²	semidirect
34. C₁₉×#384	C₂²	semidirect
35. C₁₉×#382	C₂²	semidirect
51. C₂³×C₄×C₁₉	Q₈	semidirect
152. #35033	C₁₉	direct (N × H)
200. #2857	C₂×C₁₉	semidirect
201. #2851	C₂×C₁₉	semidirect
203. #2608	C₂×C₁₉	semidirect
204. #2607	C₂×C₁₉	semidirect
205. #2441	C₂×C₁₉	semidirect
206. #2439	C₂×C₁₉	semidirect
207. #2329	C₂×C₁₉	semidirect
235. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
236. C₂×#125	C₂²×C₁₉	semidirect
247. #391	C₂²×C₁₉	semidirect
248. #391	C₂²×C₁₉	semidirect
249. #389	C₂²×C₁₉	semidirect
250. #389	C₂²×C₁₉	semidirect
251. #389	C₂²×C₁₉	semidirect
252. #389	C₂²×C₁₉	semidirect
253. #387	C₂²×C₁₉	semidirect
254. #387	C₂²×C₁₉	semidirect
255. #387	C₂²×C₁₉	semidirect
257. #384	C₂²×C₁₉	semidirect
258. #382	C₂²×C₁₉	semidirect
281. C₂³×C₄	Q₈×C₁₉	semidirect
324. C₁₉	#35033	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2857	2
C₁₉×#2851	2
C₁₉×#2626	2
C₁₉×#2608	2
C₁₉×#2607	2
C₁₉×#2441	2
C₁₉×#2439	2
C₁₉×#2329	2
C₁₉×#2280	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
#35033	19

Subgroups — C19×#35033 #18040992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#35033 #18040992