Subgroups — C₁₉×#13317 #18019276

Order 4864.

552 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3054	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#470	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#360	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2141	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#349	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1386	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
9	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#525	—	2	1	no	—
12	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
13	C₁₉×#510	—	2	2	no	—
14	C₁₉×#510	—	2	2	no	—
15	C₂×C₁₉×Q₃₂	—	2	1	no	—
16	C₂×C₁₉×SD₃₂	—	2	1	no	—
17	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
19	C₁₉×#470	—	2	2	no	—
20	C₁₉×#470	—	2	1	no	—
21	C₁₉×#470	—	2	2	no	—
22	C₁₉×#469	—	2	1	no	—
23	C₁₉×#468	—	2	2	no	—
24	C₁₉×#427	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
26	C₁₉×#416	—	2	1	no	—
27	C₂×C₁₉×#103	—	2	1	no	—
28	C₁₉×#360	—	2	2	no	—
29	C₁₉×#358	—	2	2	no	—
30	C₁₉×#349	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂²×Q₈×C₁₉	—	2	1	no	—
33	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
34	C₁₉×#135	—	2	1	no	—
35	C₁₉×#135	—	2	1	no	—
36	C₁₉×#135	—	2	1	no	—
37	C₁₉×#135	—	2	1	no	—
38	C₂×Q₁₆×C₁₉	—	2	1	no	—
39	C₂×Q₁₆×C₁₉	—	2	1	no	—
40	C₂×Q₁₆×C₁₉	—	2	1	no	—
41	C₂×Q₁₆×C₁₉	—	2	1	no	—
42	C₂×Q₁₆×C₁₉	—	2	1	no	—
43	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
44	C₂×Q₁₆×C₁₉	D₄	1	2	yes	complemented
45	C₂×SD₁₆×C₁₉	—	2	1	no	—
46	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
47	C₂×M₁₆×C₁₉	—	2	1	no	—
48	C₂×M₁₆×C₁₉	—	2	1	no	—
49	C₂×M₁₆×C₁₉	—	2	1	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
55	C₁₉×#123	—	4	1	no	—
56	C₁₉×C₂²⋊Q₈	—	2	2	no	—
57	C₁₉×C₂²⋊Q₈	—	2	4	no	—
58	C₁₉×C₂²⋊Q₈	—	4	2	no	—
59	C₁₉×#121	—	2	2	no	—
60	C₁₉×#120	—	4	1	no	—
61	C₄×D₄×C₁₉	—	4	2	no	—
62	C₁₉×#117	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
66	C₁₉×Q₃₂	—	2	4	no	—
67	C₁₉×SD₃₂	—	2	4	no	—
68	C₁₉×M₃₂	—	2	1	no	—
69	C₁₉×M₃₂	—	2	1	no	—
70	C₁₉×M₃₂	—	2	1	no	—
71	C₁₉×M₃₂	D₄	1	2	yes	complemented
72	C₂×C₁₆×C₁₉	—	2	1	no	—
73	C₂×C₁₆×C₁₉	—	2	1	no	—
74	C₁₉×#107	D₄	1	2	yes	—
75	C₁₉×#106	—	2	1	no	—
76	C₁₉×#106	—	2	1	no	—
77	C₁₉×#106	D₄	1	2	yes	complemented
78	C₁₉×#103	—	2	4	no	—
79	C₁₉×#103	—	2	2	no	—
80	C₁₉×#102	—	2	2	no	—
81	C₂⁴×C₁₉	D₈	1	1	yes	characteristic
82	#41×C₁₉	—	4	1	no	—
83	#41×C₁₉	—	4	1	no	—
84	#41×C₁₉	—	4	1	no	—
85	#41×C₁₉	—	4	1	no	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	2	2	no	—
88	C₂×Q₈×C₁₉	—	4	1	no	—
89	C₂×Q₈×C₁₉	—	4	1	no	—
90	C₂×Q₈×C₁₉	—	4	1	no	—
91	C₂×Q₈×C₁₉	—	4	1	no	—
92	C₂×Q₈×C₁₉	—	4	1	no	—
93	C₂×D₄×C₁₉	—	2	1	no	—
94	C₂×D₄×C₁₉	—	4	2	no	—
95	C₂×D₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	Q₁₆×C₁₉	—	2	2	no	—
108	Q₁₆×C₁₉	—	2	1	no	—
109	Q₁₆×C₁₉	—	2	2	no	—
110	Q₁₆×C₁₉	—	2	1	no	—
111	Q₁₆×C₁₉	—	4	1	no	—
112	Q₁₆×C₁₉	—	4	1	no	—
113	SD₁₆×C₁₉	—	4	1	no	—
114	SD₁₆×C₁₉	—	4	1	no	—
115	D₈×C₁₉	—	2	1	no	—
116	D₈×C₁₉	—	2	1	no	—
117	M₁₆×C₁₉	—	4	1	no	—
118	M₁₆×C₁₉	—	4	1	no	—
119	M₁₆×C₁₉	—	4	1	no	—
120	M₁₆×C₁₉	—	4	1	no	—
121	C₂×C₈×C₁₉	—	2	1	no	—
122	C₂×C₈×C₁₉	—	2	1	no	—
123	C₂×C₈×C₁₉	—	2	1	no	—
124	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	4	4	no	—
133	C₄⋊C₄×C₁₉	—	4	2	no	—
134	C₄⋊C₄×C₁₉	—	4	1	no	—
135	C₂²⋊C₄×C₁₉	—	4	2	no	—
136	C₂²⋊C₄×C₁₉	—	4	4	no	—
137	C₂²⋊C₄×C₁₉	—	4	2	no	—
138	C₂²⋊C₄×C₁₉	—	4	1	no	—
139	C₄²×C₁₉	—	4	1	no	—
140	C₁₆×C₁₉	—	2	2	no	—
141	C₁₆×C₁₉	—	4	1	no	—
142	#13317	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂³×C₁₉	—	2	1	no	—
144	C₂³×C₁₉	—	2	1	no	—
145	C₂³×C₁₉	—	2	1	no	—
146	C₂³×C₁₉	—	4	2	no	—
147	C₂³×C₁₉	—	4	1	no	—
148	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
149	Q₈×C₁₉	—	4	1	no	—
150	Q₈×C₁₉	—	4	2	no	—
151	Q₈×C₁₉	—	4	2	no	—
152	Q₈×C₁₉	—	4	1	no	—
153	Q₈×C₁₉	—	8	1	no	—
154	Q₈×C₁₉	—	8	1	no	—
155	D₄×C₁₉	—	4	1	no	—
156	D₄×C₁₉	—	4	1	no	—
157	D₄×C₁₉	—	8	4	no	—
158	D₄×C₁₉	—	8	1	no	—
159	D₄×C₁₉	—	8	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	8	2	no	—
172	C₂×C₄×C₁₉	—	8	1	no	—
173	C₂×C₄×C₁₉	—	8	1	no	—
174	C₂×C₄×C₁₉	—	8	1	no	—
175	C₂×C₄×C₁₉	—	8	1	no	—
176	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
180	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₈×C₁₉	—	4	1	no	—
183	C₈×C₁₉	#120	1	1	yes	characteristic
184	C₈×C₁₉	#121	1	1	yes	characteristic
185	C₈×C₁₉	#121	1	1	yes	characteristic
186	C₈×C₁₉	#127	1	1	yes	characteristic
187	C₂×#510	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#3054	C₂×C₁₉	1	1	yes	characteristic
189	C₂×#470	C₂×C₁₉	1	1	yes	characteristic, complemented
190	C₂×#360	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#2141	C₂×C₁₉	1	1	yes	characteristic, complemented
192	C₂×#349	C₂×C₁₉	1	1	yes	characteristic, complemented
193	#1386	C₂×C₁₉	1	1	yes	characteristic, complemented
194	C₂²×C₁₉	—	2	2	no	—
195	C₂²×C₁₉	—	4	2	no	—
196	C₂²×C₁₉	—	4	2	no	—
197	C₂²×C₁₉	—	4	1	no	—
198	C₂²×C₁₉	—	8	1	no	—
199	C₂²×C₁₉	—	8	2	no	—
200	C₂²×C₁₉	—	8	1	no	—
201	C₂²×C₁₉	#447	1	1	yes	characteristic
202	C₂²×C₁₉	#447	1	1	yes	characteristic
203	C₂²×C₁₉	#466	1	1	yes	characteristic
204	C₄×C₁₉	—	4	1	no	—
205	C₄×C₁₉	—	8	2	no	—
206	C₄×C₁₉	—	8	2	no	—
207	C₄×C₁₉	—	8	1	no	—
208	C₄×C₁₉	—	8	2	no	—
209	C₄×C₁₉	#392	1	1	yes	characteristic
210	C₄×C₁₉	#449	1	1	yes	characteristic
211	C₄×C₁₉	#449	1	1	yes	characteristic
212	C₄×C₁₉	#469	1	1	yes	characteristic
213	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
214	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
215	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
216	#525	—	2	1	no	—
217	C₂×C₂²⋊Q₈	—	2	1	no	—
218	#510	—	2	2	no	—
219	#510	—	2	2	no	—
220	C₂×Q₃₂	—	2	1	no	—
221	C₂×SD₃₂	—	2	1	no	—
222	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
223	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
224	#470	—	2	1	no	—
225	#470	—	2	2	no	—
226	#470	—	2	2	no	—
227	#469	—	2	1	no	—
228	#468	—	2	2	no	—
229	#427	C₂²×C₁₉	1	1	yes	characteristic
230	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
231	#416	—	2	1	no	—
232	C₂×#103	—	2	1	no	—
233	#360	—	2	2	no	—
234	#358	—	2	2	no	—
235	#349	—	2	2	no	—
236	C₂×C₁₉	—	2	1	no	—
237	C₂×C₁₉	—	2	1	no	—
238	C₂×C₁₉	—	8	1	no	—
239	C₂×C₁₉	—	16	1	no	—
240	C₂×C₁₉	#1999	1	1	yes	characteristic
241	C₂×C₁₉	#2191	1	2	yes	—
242	C₂×#41	—	2	1	no	—
243	C₂²×Q₈	—	2	1	no	—
244	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
245	#135	—	2	1	no	—
246	#135	—	2	1	no	—
247	#135	—	2	1	no	—
248	#135	—	2	1	no	—
249	C₂×Q₁₆	—	2	1	no	—
250	C₂×Q₁₆	—	2	1	no	—
251	C₂×Q₁₆	—	2	1	no	—
252	C₂×Q₁₆	—	2	1	no	—
253	C₂×Q₁₆	—	2	1	no	—
254	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
255	C₂×Q₁₆	D₄×C₁₉	1	2	yes	complemented
256	C₂×SD₁₆	—	2	1	no	—
257	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂×M₁₆	—	2	1	no	—
263	C₂×M₁₆	—	2	1	no	—
264	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
266	#123	—	4	1	no	—
267	C₂²⋊Q₈	—	2	4	no	—
268	C₂²⋊Q₈	—	2	2	no	—
269	C₂²⋊Q₈	—	4	2	no	—
270	#121	—	2	2	no	—
271	#120	—	4	1	no	—
272	C₄×D₄	—	4	2	no	—
273	#117	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	4	1	no	—
276	C₂×C₂²⋊C₄	—	4	1	no	—
277	Q₃₂	—	2	4	no	—
278	SD₃₂	—	2	4	no	—
279	M₃₂	—	2	1	no	—
280	M₃₂	—	2	1	no	—
281	M₃₂	—	2	1	no	—
282	M₃₂	D₄×C₁₉	1	2	yes	complemented
283	C₂×C₁₆	—	2	1	no	—
284	C₂×C₁₆	—	2	1	no	—
285	#107	D₄×C₁₉	1	2	yes	—
286	#106	—	2	1	no	—
287	#106	—	2	1	no	—
288	#106	D₄×C₁₉	1	2	yes	complemented
289	#103	—	2	4	no	—
290	#103	—	2	2	no	—
291	#102	—	2	2	no	—
292	C₁₉	#13317	1	1	yes	characteristic, direct product factor, Sylow
293	C₂⁴	D₈×C₁₉	1	1	yes	characteristic
294	#41	—	4	1	no	—
295	#41	—	4	1	no	—
296	#41	—	4	1	no	—
297	#41	—	4	1	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	4	1	no	—
301	C₂×Q₈	—	4	1	no	—
302	C₂×Q₈	—	4	1	no	—
303	C₂×Q₈	—	4	1	no	—
304	C₂×Q₈	—	4	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
319	Q₁₆	—	2	2	no	—
320	Q₁₆	—	2	1	no	—
321	Q₁₆	—	2	2	no	—
322	Q₁₆	—	2	1	no	—
323	Q₁₆	—	4	1	no	—
324	Q₁₆	—	4	1	no	—
325	SD₁₆	—	4	1	no	—
326	SD₁₆	—	4	1	no	—
327	D₈	—	2	1	no	—
328	D₈	—	2	1	no	—
329	M₁₆	—	4	1	no	—
330	M₁₆	—	4	1	no	—
331	M₁₆	—	4	1	no	—
332	M₁₆	—	4	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
337	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
338	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
339	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
340	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
341	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	4	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₄²	—	4	1	no	—
352	C₁₆	—	2	2	no	—
353	C₁₆	—	4	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	1	no	—
359	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
360	Q₈	—	4	1	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	4	1	no	—
364	Q₈	—	8	1	no	—
365	Q₈	—	8	1	no	—
366	D₄	—	4	1	no	—
367	D₄	—	4	1	no	—
368	D₄	—	8	4	no	—
369	D₄	—	8	1	no	—
370	D₄	—	8	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	—	8	1	no	—
384	C₂×C₄	—	8	1	no	—
385	C₂×C₄	—	8	1	no	—
386	C₂×C₄	—	8	1	no	—
387	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
388	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
389	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
390	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
391	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
392	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
393	C₈	—	4	1	no	—
394	C₈	C₁₉×#120	1	1	yes	characteristic
395	C₈	C₁₉×#121	1	1	yes	characteristic
396	C₈	C₁₉×#121	1	1	yes	characteristic
397	C₈	C₁₉×#127	1	1	yes	characteristic
398	C₂²	—	2	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	1	no	—
405	C₂²	C₁₉×#447	1	1	yes	characteristic
406	C₂²	C₁₉×#447	1	1	yes	characteristic
407	C₂²	C₁₉×#466	1	1	yes	characteristic
408	C₄	—	4	1	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	2	no	—
413	C₄	C₁₉×#392	1	1	yes	characteristic
414	C₄	C₁₉×#449	1	1	yes	characteristic
415	C₄	C₁₉×#449	1	1	yes	characteristic
416	C₄	C₁₉×#469	1	1	yes	characteristic
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	8	1	no	—
420	C₂	—	16	1	no	—
421	C₂	C₁₉×#1999	1	1	yes	characteristic
422	C₂	C₁₉×#2191	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₁₉×#3054	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×M₁₆×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#510	C₂	semidirect
3. C₂×C₁₉×#470	C₂	semidirect
4. C₂×C₁₉×#360	C₂	semidirect
5. C₁₉×#2141	C₂	semidirect
6. C₂×C₁₉×#349	C₂	semidirect
7. C₁₉×#1386	C₂	semidirect
44. C₂×Q₁₆×C₁₉	D₄	semidirect
71. C₁₉×M₃₂	D₄	semidirect
77. C₁₉×#106	D₄	semidirect
142. #13317	C₁₉	direct (N × H)
187. C₂×#510	C₂×C₁₉	semidirect
189. C₂×#470	C₂×C₁₉	semidirect
190. C₂×#360	C₂×C₁₉	semidirect
191. #2141	C₂×C₁₉	semidirect
192. C₂×#349	C₂×C₁₉	semidirect
193. #1386	C₂×C₁₉	semidirect
255. C₂×Q₁₆	D₄×C₁₉	semidirect
282. M₃₂	D₄×C₁₉	semidirect
288. #106	D₄×C₁₉	semidirect
292. C₁₉	#13317	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#510	2
C₁₉×#3054	2
C₂×C₁₉×#470	2
C₂×C₁₉×#360	2
C₁₉×#2141	2
C₂×C₁₉×#349	2
C₁₉×#1386	2
#13317	19

Subgroups — C19×#13317 #18019276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13317 #18019276