Subgroups — C₁₉×#23543 #18029502

Order 4864.

1458 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#417	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2311	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2056	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2055	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2054	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₉	C₂²	1	2	yes	—
10	C₂×C₁₉×#135	—	2	8	no	—
11	C₂×C₁₉×#135	—	2	4	no	—
12	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₁₉×#424	—	2	4	no	—
20	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
22	C₁₉×#417	—	2	8	no	—
23	C₂×C₁₉×#103	C₂²	1	4	yes	—
24	C₂×C₁₉×#102	C₂²	1	4	yes	—
25	C₁₉×#391	C₂²	1	4	yes	—
26	C₁₉×#390	C₂²	1	4	yes	—
27	C₁₉×#386	—	2	4	no	—
28	C₁₉×#380	—	2	2	no	—
29	C₁₉×#380	—	2	2	no	—
30	C₁₉×#340	C₂²	1	2	yes	—
31	C₁₉×#340	C₂²	1	2	yes	—
32	C₂×#41×C₁₉	—	2	4	no	—
33	C₂×#41×C₁₉	—	2	4	no	—
34	C₂×#41×C₁₉	—	2	4	no	—
35	C₂×#41×C₁₉	—	2	4	no	—
36	C₂×#41×C₁₉	—	2	4	no	—
37	C₂×#41×C₁₉	D₄	1	8	yes	—
38	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
39	C₂²×D₄×C₁₉	—	2	2	no	—
40	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₉	—	2	2	no	—
42	C₂³×C₄×C₁₉	—	2	2	no	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₁₉×#135	—	2	32	no	—
45	C₂×Q₁₆×C₁₉	—	2	4	no	—
46	C₂×Q₁₆×C₁₉	—	2	2	no	—
47	C₂×SD₁₆×C₁₉	—	2	4	no	—
48	C₂×SD₁₆×C₁₉	—	2	4	no	—
49	C₂×SD₁₆×C₁₉	—	2	4	no	—
50	C₂×D₈×C₁₉	—	2	4	no	—
51	C₂×D₈×C₁₉	—	2	2	no	—
52	C₂×M₁₆×C₁₉	—	2	4	no	—
53	C₂×M₁₆×C₁₉	—	2	2	no	—
54	C₂²×C₈×C₁₉	—	2	4	no	—
55	C₂²×C₈×C₁₉	D₄	1	4	yes	—
56	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
59	C₁₉×#117	—	2	2	no	—
60	C₁₉×#117	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
70	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
71	C₁₉×C₄⋊C₈	—	2	4	no	—
72	C₁₉×C₄⋊C₈	—	2	4	no	—
73	C₁₉×#103	—	2	8	no	—
74	C₁₉×#102	—	2	8	no	—
75	C₁₉×#95	—	2	4	no	—
76	C₁₉×#95	—	2	4	no	—
77	C₂⁴×C₁₉	—	2	2	no	—
78	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
79	#41×C₁₉	—	2	16	no	—
80	#41×C₁₉	—	2	16	no	—
81	#41×C₁₉	—	4	8	no	—
82	#41×C₁₉	—	4	8	no	—
83	C₂×Q₈×C₁₉	—	2	2	no	—
84	C₂×Q₈×C₁₉	—	2	2	no	—
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	—	2	2	no	—
87	C₂×Q₈×C₁₉	—	2	2	no	—
88	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
89	C₂×D₄×C₁₉	—	2	8	no	—
90	C₂×D₄×C₁₉	—	2	2	no	—
91	C₂×D₄×C₁₉	—	2	2	no	—
92	C₂×D₄×C₁₉	—	2	2	no	—
93	C₂×D₄×C₁₉	—	2	2	no	—
94	C₂×D₄×C₁₉	—	2	2	no	—
95	C₂×D₄×C₁₉	—	4	4	no	—
96	C₂×D₄×C₁₉	—	4	4	no	—
97	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	8	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	4	4	no	—
102	C₂²×C₄×C₁₉	—	4	4	no	—
103	C₂²×C₄×C₁₉	—	4	4	no	—
104	C₂²×C₄×C₁₉	—	8	2	no	—
105	C₂²×C₄×C₁₉	—	8	2	no	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	#41	1	2	yes	—
112	C₂²×C₄×C₁₉	#41	1	4	yes	—
113	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
114	Q₁₆×C₁₉	—	2	8	no	—
115	SD₁₆×C₁₉	—	2	16	no	—
116	D₈×C₁₉	—	2	8	no	—
117	M₁₆×C₁₉	—	4	4	no	—
118	C₂×C₈×C₁₉	—	2	8	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	2	4	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	4	no	—
128	C₄⋊C₄×C₁₉	—	2	4	no	—
129	C₄⋊C₄×C₁₉	—	4	4	no	—
130	C₂²⋊C₄×C₁₉	—	2	4	no	—
131	C₂²⋊C₄×C₁₉	—	8	4	no	—
132	C₂²⋊C₄×C₁₉	—	8	4	no	—
133	C₄²×C₁₉	—	2	2	no	—
134	C₄²×C₁₉	—	2	2	no	—
135	#23543	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂³×C₁₉	—	2	1	no	—
137	C₂³×C₁₉	—	2	2	no	—
138	C₂³×C₁₉	—	2	1	no	—
139	C₂³×C₁₉	—	2	4	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	—	4	2	no	—
143	C₂³×C₁₉	—	4	2	no	—
144	C₂³×C₁₉	—	4	2	no	—
145	C₂³×C₁₉	—	4	2	no	—
146	C₂³×C₁₉	#121	1	2	yes	—
147	C₂³×C₁₉	#121	1	4	yes	—
148	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₁₉	—	2	4	no	—
150	Q₈×C₁₉	—	2	4	no	—
151	Q₈×C₁₉	—	4	2	no	—
152	Q₈×C₁₉	—	4	2	no	—
153	D₄×C₁₉	—	2	4	no	—
154	D₄×C₁₉	—	2	4	no	—
155	D₄×C₁₉	—	4	16	no	—
156	D₄×C₁₉	—	4	2	no	—
157	D₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	4	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	16	no	—
167	C₂×C₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	—	4	4	no	—
170	C₂×C₄×C₁₉	—	8	8	no	—
171	C₂×C₄×C₁₉	#120	1	4	yes	—
172	C₂×C₄×C₁₉	#121	1	2	yes	—
173	C₂×C₄×C₁₉	#121	1	4	yes	—
174	C₂×C₄×C₁₉	#123	1	8	yes	—
175	C₂×C₄×C₁₉	#124	1	4	yes	—
176	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
177	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
180	C₈×C₁₉	—	2	2	no	—
181	C₈×C₁₉	—	2	2	no	—
182	C₈×C₁₉	—	4	2	no	—
183	C₂²×#135	C₂×C₁₉	1	1	yes	characteristic
184	C₂×#424	C₂×C₁₉	1	1	yes	characteristic, complemented
185	C₂×#417	C₂×C₁₉	1	2	yes	complemented
186	#2311	C₂×C₁₉	1	2	yes	complemented
187	#2056	C₂×C₁₉	1	2	yes	complemented
188	#2055	C₂×C₁₉	1	4	yes	complemented
189	#2054	C₂×C₁₉	1	2	yes	complemented
190	C₂×#340	C₂×C₁₉	1	1	yes	characteristic, complemented
191	C₂²×C₁₉	—	2	4	no	—
192	C₂²×C₁₉	—	2	4	no	—
193	C₂²×C₁₉	—	2	2	no	—
194	C₂²×C₁₉	—	2	2	no	—
195	C₂²×C₁₉	—	4	4	no	—
196	C₂²×C₁₉	—	4	4	no	—
197	C₂²×C₁₉	—	4	4	no	—
198	C₂²×C₁₉	—	8	2	no	—
199	C₂²×C₁₉	—	8	2	no	—
200	C₂²×C₁₉	—	8	2	no	—
201	C₂²×C₁₉	—	8	2	no	—
202	C₂²×C₁₉	#394	1	4	yes	—
203	C₂²×C₁₉	C₂×#121	1	2	yes	—
204	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
205	C₂²×C₁₉	#576	1	1	yes	characteristic
206	C₂²×C₁₉	#577	1	2	yes	—
207	C₂²×C₁₉	#578	1	1	yes	characteristic
208	C₄×C₁₉	—	4	4	no	—
209	C₄×C₁₉	—	4	2	no	—
210	C₄×C₁₉	—	4	2	no	—
211	C₄×C₁₉	—	8	4	no	—
212	C₄×C₁₉	#394	1	4	yes	—
213	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
214	C₄×C₁₉	C₂×#123	1	2	yes	—
215	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
216	C₂²×#41	C₂²×C₁₉	1	2	yes	—
217	C₂×#135	—	2	8	no	—
218	C₂×#135	—	2	4	no	—
219	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
220	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
221	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
222	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
223	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
225	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
226	#424	—	2	4	no	—
227	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
228	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
229	#417	—	2	8	no	—
230	C₂×#103	C₂²×C₁₉	1	4	yes	—
231	C₂×#102	C₂²×C₁₉	1	4	yes	—
232	#391	C₂²×C₁₉	1	4	yes	—
233	#390	C₂²×C₁₉	1	4	yes	—
234	#386	—	2	4	no	—
235	#380	—	2	2	no	—
236	#380	—	2	2	no	—
237	#340	C₂²×C₁₉	1	2	yes	—
238	#340	C₂²×C₁₉	1	2	yes	—
239	C₂×C₁₉	—	2	4	no	—
240	C₂×C₁₉	—	8	4	no	—
241	C₂×C₁₉	C₂×#394	1	1	yes	characteristic
242	C₂×C₁₉	#3045	1	2	yes	—
243	C₂×C₁₉	#3046	1	2	yes	—
244	C₂×C₁₉	#3060	1	1	yes	characteristic
245	C₂×C₁₉	#3061	1	1	yes	characteristic
246	C₂×#41	—	2	4	no	—
247	C₂×#41	—	2	4	no	—
248	C₂×#41	—	2	4	no	—
249	C₂×#41	—	2	4	no	—
250	C₂×#41	—	2	4	no	—
251	C₂×#41	D₄×C₁₉	1	8	yes	—
252	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
253	C₂²×D₄	—	2	2	no	—
254	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
255	C₂³×C₄	—	2	2	no	—
256	C₂³×C₄	—	2	2	no	—
257	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
258	#135	—	2	32	no	—
259	C₂×Q₁₆	—	2	4	no	—
260	C₂×Q₁₆	—	2	2	no	—
261	C₂×SD₁₆	—	2	4	no	—
262	C₂×SD₁₆	—	2	4	no	—
263	C₂×SD₁₆	—	2	4	no	—
264	C₂×D₈	—	2	4	no	—
265	C₂×D₈	—	2	2	no	—
266	C₂×M₁₆	—	2	4	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂²×C₈	—	2	4	no	—
269	C₂²×C₈	D₄×C₁₉	1	4	yes	—
270	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
271	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
273	#117	—	2	2	no	—
274	#117	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	4	no	—
276	C₂×C₄⋊C₄	—	2	4	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
279	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
281	C₂×C₂²⋊C₄	—	2	4	no	—
282	C₂×C₂²⋊C₄	—	2	4	no	—
283	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
284	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
285	C₄⋊C₈	—	2	4	no	—
286	C₄⋊C₈	—	2	4	no	—
287	#103	—	2	8	no	—
288	#102	—	2	8	no	—
289	#95	—	2	4	no	—
290	#95	—	2	4	no	—
291	C₁₉	#23543	1	1	yes	characteristic, direct product factor, Sylow
292	C₂⁴	—	2	2	no	—
293	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
294	#41	—	2	16	no	—
295	#41	—	2	16	no	—
296	#41	—	4	8	no	—
297	#41	—	4	8	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
304	C₂×D₄	—	2	8	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	4	4	no	—
311	C₂×D₄	—	4	4	no	—
312	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	8	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	4	4	no	—
317	C₂²×C₄	—	4	4	no	—
318	C₂²×C₄	—	4	4	no	—
319	C₂²×C₄	—	8	2	no	—
320	C₂²×C₄	—	8	2	no	—
321	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
323	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
324	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
326	C₂²×C₄	#41×C₁₉	1	2	yes	—
327	C₂²×C₄	#41×C₁₉	1	4	yes	—
328	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
329	Q₁₆	—	2	8	no	—
330	SD₁₆	—	2	16	no	—
331	D₈	—	2	8	no	—
332	M₁₆	—	4	4	no	—
333	C₂×C₈	—	2	8	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
339	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₂²⋊C₄	—	2	4	no	—
346	C₂²⋊C₄	—	8	4	no	—
347	C₂²⋊C₄	—	8	4	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	2	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	4	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	C₁₉×#121	1	2	yes	—
361	C₂³	C₁₉×#121	1	4	yes	—
362	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
363	Q₈	—	2	4	no	—
364	Q₈	—	2	4	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	4	2	no	—
367	D₄	—	2	4	no	—
368	D₄	—	2	4	no	—
369	D₄	—	4	16	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	16	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	8	8	no	—
385	C₂×C₄	C₁₉×#120	1	4	yes	—
386	C₂×C₄	C₁₉×#121	1	2	yes	—
387	C₂×C₄	C₁₉×#121	1	4	yes	—
388	C₂×C₄	C₁₉×#123	1	8	yes	—
389	C₂×C₄	C₁₉×#124	1	4	yes	—
390	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
391	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
392	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
393	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
394	C₈	—	2	2	no	—
395	C₈	—	2	2	no	—
396	C₈	—	4	2	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	C₁₉×#394	1	4	yes	—
409	C₂²	C₂×C₁₉×#121	1	2	yes	—
410	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
411	C₂²	C₁₉×#576	1	1	yes	characteristic
412	C₂²	C₁₉×#577	1	2	yes	—
413	C₂²	C₁₉×#578	1	1	yes	characteristic
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	4	no	—
417	C₄	—	8	4	no	—
418	C₄	C₁₉×#394	1	4	yes	—
419	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
420	C₄	C₂×C₁₉×#123	1	2	yes	—
421	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
422	C₂	—	2	4	no	—
423	C₂	—	8	4	no	—
424	C₂	C₂×C₁₉×#394	1	1	yes	characteristic
425	C₂	C₁₉×#3045	1	2	yes	—
426	C₂	C₁₉×#3046	1	2	yes	—
427	C₂	C₁₉×#3060	1	1	yes	characteristic
428	C₂	C₁₉×#3061	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×#135	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#424	C₂	semidirect
3. C₂×C₁₉×#417	C₂	semidirect
4. C₁₉×#2311	C₂	semidirect
5. C₁₉×#2056	C₂	semidirect
6. C₁₉×#2055	C₂	semidirect
7. C₁₉×#2054	C₂	semidirect
8. C₂×C₁₉×#340	C₂	semidirect
135. #23543	C₁₉	direct (N × H)
184. C₂×#424	C₂×C₁₉	semidirect
185. C₂×#417	C₂×C₁₉	semidirect
186. #2311	C₂×C₁₉	semidirect
187. #2056	C₂×C₁₉	semidirect
188. #2055	C₂×C₁₉	semidirect
189. #2054	C₂×C₁₉	semidirect
190. C₂×#340	C₂×C₁₉	semidirect
291. C₁₉	#23543	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×#135	2
C₂×C₁₉×#424	2
C₂×C₁₉×#417	2
C₁₉×#2311	2
C₁₉×#2056	2
C₁₉×#2055	2
C₁₉×#2054	2
C₂×C₁₉×#340	2
#23543	19

Subgroups — C19×#23543 #18029502

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23543 #18029502