Subgroups — C₁₉×#13318 #18019277

Order 4864.

532 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3414	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3067	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3060	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#360	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2143	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2117	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1383	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#575	—	2	1	no	—
9	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
12	C₁₉×#537	—	2	1	no	—
13	C₁₉×#510	—	2	1	no	—
14	C₁₉×#510	—	2	1	no	—
15	C₁₉×#509	—	2	1	no	—
16	C₁₉×#509	—	2	1	no	—
17	C₁₉×#508	—	2	2	no	—
18	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
20	C₁₉×#473	—	2	1	no	—
21	C₁₉×#472	—	2	1	no	—
22	C₁₉×#471	—	2	2	no	—
23	C₁₉×#470	—	2	1	no	—
24	C₁₉×#469	—	2	1	no	—
25	C₁₉×#465	—	2	2	no	—
26	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
28	C₁₉×#417	—	2	1	no	—
29	C₁₉×#413	—	2	1	no	—
30	C₁₉×#360	—	2	2	no	—
31	C₁₉×#359	—	2	2	no	—
32	C₁₉×#350	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂×#41×C₁₉	—	2	1	no	—
35	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
36	C₁₉×#137	—	2	2	no	—
37	C₁₉×#137	—	4	1	no	—
38	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
39	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
40	C₁₉×#135	—	2	1	no	—
41	C₁₉×#135	—	2	1	no	—
42	C₁₉×#135	—	2	1	no	—
43	C₁₉×#135	—	2	1	no	—
44	C₁₉×#135	—	2	1	no	—
45	C₁₉×#135	—	2	1	no	—
46	C₁₉×#135	—	2	1	no	—
47	C₁₉×#135	—	2	1	no	—
48	C₁₉×#135	—	4	2	no	—
49	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
50	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic, complemented
51	C₂×SD₁₆×C₁₉	—	2	1	no	—
52	C₂×SD₁₆×C₁₉	—	2	1	no	—
53	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
54	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic, complemented
55	C₁₉×#131	—	2	1	no	—
56	C₁₉×#131	—	2	1	no	—
57	C₁₉×#131	—	2	1	no	—
58	C₁₉×#131	—	2	1	no	—
59	C₂×M₁₆×C₁₉	—	2	1	no	—
60	C₂×M₁₆×C₁₉	—	2	1	no	—
61	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	—	2	1	no	—
63	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₁₉×C₂²⋊Q₈	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	—	4	1	no	—
66	C₁₉×#121	—	2	2	no	—
67	C₁₉×#121	—	4	2	no	—
68	C₁₉×#121	—	4	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₁₉×Q₃₂	—	2	2	no	—
71	C₁₉×SD₃₂	—	2	2	no	—
72	C₁₉×SD₃₂	—	2	2	no	—
73	C₁₉×D₁₆	—	2	2	no	—
74	C₁₉×M₃₂	—	2	1	no	—
75	C₁₉×M₃₂	—	2	1	no	—
76	C₁₉×M₃₂	—	2	1	no	—
77	C₁₉×M₃₂	—	2	1	no	—
78	C₂×C₁₆×C₁₉	—	2	1	no	—
79	C₂×C₁₆×C₁₉	D₄	1	2	yes	complemented
80	C₁₉×#108	—	2	1	no	—
81	C₁₉×#108	D₄	1	2	yes	complemented
82	C₁₉×#106	—	2	1	no	—
83	C₁₉×#106	D₄	1	2	yes	—
84	C₁₉×#103	—	2	2	no	—
85	C₁₉×#102	—	2	2	no	—
86	C₁₉×#101	—	2	2	no	—
87	C₁₉×#100	—	2	2	no	—
88	#41×C₁₉	—	2	1	no	—
89	#41×C₁₉	—	2	1	no	—
90	#41×C₁₉	—	2	1	no	—
91	#41×C₁₉	—	2	1	no	—
92	#41×C₁₉	—	4	1	no	—
93	#41×C₁₉	—	4	1	no	—
94	#41×C₁₉	—	4	1	no	—
95	#41×C₁₉	—	4	1	no	—
96	#41×C₁₉	—	4	1	no	—
97	#41×C₁₉	—	4	1	no	—
98	#41×C₁₉	—	4	1	no	—
99	#41×C₁₉	—	4	1	no	—
100	C₂×Q₈×C₁₉	—	2	1	no	—
101	C₂×Q₈×C₁₉	—	2	1	no	—
102	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
103	C₂×D₄×C₁₉	—	2	1	no	—
104	C₂×D₄×C₁₉	—	2	1	no	—
105	C₂×D₄×C₁₉	—	2	1	no	—
106	C₂×D₄×C₁₉	—	4	1	no	—
107	C₂×D₄×C₁₉	—	4	1	no	—
108	C₂×D₄×C₁₉	—	4	2	no	—
109	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	—	2	1	no	—
111	C₂²×C₄×C₁₉	—	4	1	no	—
112	C₂²×C₄×C₁₉	—	4	1	no	—
113	C₂²×C₄×C₁₉	—	4	1	no	—
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	Q₁₆×C₁₉	—	2	1	no	—
116	Q₁₆×C₁₉	—	2	1	no	—
117	Q₁₆×C₁₉	—	2	1	no	—
118	Q₁₆×C₁₉	—	2	1	no	—
119	Q₁₆×C₁₉	—	4	2	no	—
120	SD₁₆×C₁₉	—	4	2	no	—
121	SD₁₆×C₁₉	—	4	2	no	—
122	SD₁₆×C₁₉	—	4	1	no	—
123	SD₁₆×C₁₉	—	4	1	no	—
124	SD₁₆×C₁₉	—	4	1	no	—
125	SD₁₆×C₁₉	—	4	1	no	—
126	D₈×C₁₉	—	2	1	no	—
127	D₈×C₁₉	—	2	1	no	—
128	D₈×C₁₉	—	2	1	no	—
129	D₈×C₁₉	—	2	1	no	—
130	D₈×C₁₉	—	4	2	no	—
131	M₁₆×C₁₉	—	2	2	no	—
132	M₁₆×C₁₉	—	2	1	no	—
133	M₁₆×C₁₉	—	2	1	no	—
134	M₁₆×C₁₉	—	4	1	no	—
135	M₁₆×C₁₉	—	4	1	no	—
136	M₁₆×C₁₉	—	4	1	no	—
137	C₂×C₈×C₁₉	—	2	1	no	—
138	C₂×C₈×C₁₉	—	4	1	no	—
139	C₂×C₈×C₁₉	—	4	1	no	—
140	C₂×C₈×C₁₉	—	4	1	no	—
141	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	4	2	no	—
149	C₄⋊C₄×C₁₉	—	4	1	no	—
150	C₂²⋊C₄×C₁₉	—	4	2	no	—
151	C₂²⋊C₄×C₁₉	—	4	2	no	—
152	C₁₆×C₁₉	—	2	2	no	—
153	C₁₆×C₁₉	—	4	1	no	—
154	#13318	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂³×C₁₉	—	2	1	no	—
156	C₂³×C₁₉	—	4	1	no	—
157	C₂³×C₁₉	—	4	1	no	—
158	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
159	Q₈×C₁₉	—	2	1	no	—
160	Q₈×C₁₉	—	2	1	no	—
161	Q₈×C₁₉	—	4	1	no	—
162	Q₈×C₁₉	—	4	1	no	—
163	Q₈×C₁₉	—	4	1	no	—
164	Q₈×C₁₉	—	4	1	no	—
165	D₄×C₁₉	—	2	1	no	—
166	D₄×C₁₉	—	2	1	no	—
167	D₄×C₁₉	—	4	1	no	—
168	D₄×C₁₉	—	4	1	no	—
169	D₄×C₁₉	—	4	1	no	—
170	D₄×C₁₉	—	4	1	no	—
171	D₄×C₁₉	—	4	1	no	—
172	D₄×C₁₉	—	4	1	no	—
173	D₄×C₁₉	—	8	1	no	—
174	D₄×C₁₉	—	8	1	no	—
175	D₄×C₁₉	—	8	1	no	—
176	D₄×C₁₉	—	8	1	no	—
177	D₄×C₁₉	—	16	2	no	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	8	1	no	—
185	C₂×C₄×C₁₉	—	8	1	no	—
186	C₂×C₄×C₁₉	—	8	1	no	—
187	C₂×C₄×C₁₉	—	8	1	no	—
188	C₂×C₄×C₁₉	—	16	1	no	—
189	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
194	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₈×C₁₉	—	4	1	no	—
196	C₈×C₁₉	—	4	2	no	—
197	C₈×C₁₉	#120	1	1	yes	characteristic
198	C₈×C₁₉	#121	1	1	yes	characteristic
199	C₈×C₁₉	#121	1	1	yes	characteristic
200	C₈×C₁₉	#127	1	1	yes	characteristic
201	#3414	C₂×C₁₉	1	1	yes	characteristic, complemented
202	#3067	C₂×C₁₉	1	1	yes	characteristic, complemented
203	#3060	C₂×C₁₉	1	1	yes	characteristic, complemented
204	C₂×#360	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#2143	C₂×C₁₉	1	1	yes	characteristic, complemented
206	#2117	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#1383	C₂×C₁₉	1	1	yes	characteristic, complemented
208	C₂²×C₁₉	—	4	1	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	—	4	1	no	—
211	C₂²×C₁₉	—	8	1	no	—
212	C₂²×C₁₉	—	8	1	no	—
213	C₂²×C₁₉	—	8	1	no	—
214	C₂²×C₁₉	—	8	1	no	—
215	C₂²×C₁₉	—	16	1	no	—
216	C₂²×C₁₉	#447	1	1	yes	characteristic
217	C₂²×C₁₉	#449	1	1	yes	characteristic
218	C₂²×C₁₉	#469	1	1	yes	characteristic
219	C₄×C₁₉	—	4	1	no	—
220	C₄×C₁₉	—	8	2	no	—
221	C₄×C₁₉	—	8	1	no	—
222	C₄×C₁₉	—	8	1	no	—
223	C₄×C₁₉	#392	1	1	yes	characteristic
224	C₄×C₁₉	#447	1	1	yes	characteristic
225	C₄×C₁₉	#449	1	1	yes	characteristic
226	C₄×C₁₉	#466	1	1	yes	characteristic
227	#575	—	2	1	no	—
228	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
230	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
231	#537	—	2	1	no	—
232	#510	—	2	1	no	—
233	#510	—	2	1	no	—
234	#509	—	2	1	no	—
235	#509	—	2	1	no	—
236	#508	—	2	2	no	—
237	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
239	#473	—	2	1	no	—
240	#472	—	2	1	no	—
241	#471	—	2	2	no	—
242	#470	—	2	1	no	—
243	#469	—	2	1	no	—
244	#465	—	2	2	no	—
245	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
246	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
247	#417	—	2	1	no	—
248	#413	—	2	1	no	—
249	#360	—	2	2	no	—
250	#359	—	2	2	no	—
251	#350	—	2	2	no	—
252	C₂×C₁₉	—	2	1	no	—
253	C₂×C₁₉	—	2	1	no	—
254	C₂×C₁₉	—	2	1	no	—
255	C₂×C₁₉	—	8	1	no	—
256	C₂×C₁₉	—	16	1	no	—
257	C₂×C₁₉	—	16	1	no	—
258	C₂×C₁₉	#1999	1	1	yes	characteristic
259	C₂×#41	—	2	1	no	—
260	C₂×#41	—	2	1	no	—
261	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
262	#137	—	2	2	no	—
263	#137	—	4	1	no	—
264	AGL(1,ℤ/8)	—	2	2	no	—
265	AGL(1,ℤ/8)	—	4	1	no	—
266	#135	—	2	1	no	—
267	#135	—	2	1	no	—
268	#135	—	2	1	no	—
269	#135	—	2	1	no	—
270	#135	—	2	1	no	—
271	#135	—	2	1	no	—
272	#135	—	2	1	no	—
273	#135	—	2	1	no	—
274	#135	—	4	2	no	—
275	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
276	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic, complemented
277	C₂×SD₁₆	—	2	1	no	—
278	C₂×SD₁₆	—	2	1	no	—
279	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
280	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic, complemented
281	#131	—	2	1	no	—
282	#131	—	2	1	no	—
283	#131	—	2	1	no	—
284	#131	—	2	1	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₂×M₁₆	—	2	1	no	—
287	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
288	C₂²×C₈	—	2	1	no	—
289	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
290	C₂²⋊Q₈	—	2	2	no	—
291	C₂²⋊Q₈	—	4	1	no	—
292	#121	—	2	2	no	—
293	#121	—	4	2	no	—
294	#121	—	4	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	Q₃₂	—	2	2	no	—
297	SD₃₂	—	2	2	no	—
298	SD₃₂	—	2	2	no	—
299	D₁₆	—	2	2	no	—
300	M₃₂	—	2	1	no	—
301	M₃₂	—	2	1	no	—
302	M₃₂	—	2	1	no	—
303	M₃₂	—	2	1	no	—
304	C₂×C₁₆	—	2	1	no	—
305	C₂×C₁₆	D₄×C₁₉	1	2	yes	complemented
306	#108	—	2	1	no	—
307	#108	D₄×C₁₉	1	2	yes	complemented
308	#106	—	2	1	no	—
309	#106	D₄×C₁₉	1	2	yes	—
310	#103	—	2	2	no	—
311	#102	—	2	2	no	—
312	#101	—	2	2	no	—
313	#100	—	2	2	no	—
314	C₁₉	#13318	1	1	yes	characteristic, direct product factor, Sylow
315	#41	—	2	1	no	—
316	#41	—	2	1	no	—
317	#41	—	2	1	no	—
318	#41	—	2	1	no	—
319	#41	—	4	1	no	—
320	#41	—	4	1	no	—
321	#41	—	4	1	no	—
322	#41	—	4	1	no	—
323	#41	—	4	1	no	—
324	#41	—	4	1	no	—
325	#41	—	4	1	no	—
326	#41	—	4	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	D₈×C₁₉	1	1	yes	characteristic
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	1	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
342	Q₁₆	—	2	1	no	—
343	Q₁₆	—	2	1	no	—
344	Q₁₆	—	2	1	no	—
345	Q₁₆	—	2	1	no	—
346	Q₁₆	—	4	2	no	—
347	SD₁₆	—	4	2	no	—
348	SD₁₆	—	4	2	no	—
349	SD₁₆	—	4	1	no	—
350	SD₁₆	—	4	1	no	—
351	SD₁₆	—	4	1	no	—
352	SD₁₆	—	4	1	no	—
353	D₈	—	2	1	no	—
354	D₈	—	2	1	no	—
355	D₈	—	2	1	no	—
356	D₈	—	2	1	no	—
357	D₈	—	4	2	no	—
358	M₁₆	—	2	1	no	—
359	M₁₆	—	2	2	no	—
360	M₁₆	—	2	1	no	—
361	M₁₆	—	4	1	no	—
362	M₁₆	—	4	1	no	—
363	M₁₆	—	4	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	4	1	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
369	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
370	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
371	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
372	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
373	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	—	4	2	no	—
378	C₂²⋊C₄	—	4	2	no	—
379	C₁₆	—	2	2	no	—
380	C₁₆	—	4	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	1	no	—
384	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
385	Q₈	—	2	1	no	—
386	Q₈	—	2	1	no	—
387	Q₈	—	4	1	no	—
388	Q₈	—	4	1	no	—
389	Q₈	—	4	1	no	—
390	Q₈	—	4	1	no	—
391	D₄	—	2	1	no	—
392	D₄	—	2	1	no	—
393	D₄	—	4	1	no	—
394	D₄	—	4	1	no	—
395	D₄	—	4	1	no	—
396	D₄	—	4	1	no	—
397	D₄	—	4	1	no	—
398	D₄	—	4	1	no	—
399	D₄	—	8	1	no	—
400	D₄	—	8	1	no	—
401	D₄	—	8	1	no	—
402	D₄	—	8	1	no	—
403	D₄	—	16	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	8	1	no	—
411	C₂×C₄	—	8	1	no	—
412	C₂×C₄	—	8	1	no	—
413	C₂×C₄	—	8	1	no	—
414	C₂×C₄	—	16	1	no	—
415	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
416	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
417	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
418	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
419	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
420	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
421	C₈	—	4	1	no	—
422	C₈	—	4	2	no	—
423	C₈	C₁₉×#120	1	1	yes	characteristic
424	C₈	C₁₉×#121	1	1	yes	characteristic
425	C₈	C₁₉×#121	1	1	yes	characteristic
426	C₈	C₁₉×#127	1	1	yes	characteristic
427	C₂²	—	4	1	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	—	8	1	no	—
434	C₂²	—	16	1	no	—
435	C₂²	C₁₉×#447	1	1	yes	characteristic
436	C₂²	C₁₉×#449	1	1	yes	characteristic
437	C₂²	C₁₉×#469	1	1	yes	characteristic
438	C₄	—	4	1	no	—
439	C₄	—	8	2	no	—
440	C₄	—	8	1	no	—
441	C₄	—	8	1	no	—
442	C₄	C₁₉×#392	1	1	yes	characteristic
443	C₄	C₁₉×#447	1	1	yes	characteristic
444	C₄	C₁₉×#449	1	1	yes	characteristic
445	C₄	C₁₉×#466	1	1	yes	characteristic
446	C₂	—	2	1	no	—
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	8	1	no	—
450	C₂	—	16	1	no	—
451	C₂	—	16	1	no	—
452	C₂	C₁₉×#1999	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#1999
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3414	C₂	semidirect
2. C₁₉×#3067	C₂	semidirect
3. C₁₉×#3060	C₂	semidirect
4. C₂×C₁₉×#360	C₂	semidirect
5. C₁₉×#2143	C₂	semidirect
6. C₁₉×#2117	C₂	semidirect
7. C₁₉×#1383	C₂	semidirect
50. C₂×Q₁₆×C₁₉	D₄	semidirect
54. C₂×D₈×C₁₉	D₄	semidirect
79. C₂×C₁₆×C₁₉	D₄	semidirect
81. C₁₉×#108	D₄	semidirect
154. #13318	C₁₉	direct (N × H)
201. #3414	C₂×C₁₉	semidirect
202. #3067	C₂×C₁₉	semidirect
203. #3060	C₂×C₁₉	semidirect
204. C₂×#360	C₂×C₁₉	semidirect
205. #2143	C₂×C₁₉	semidirect
206. #2117	C₂×C₁₉	semidirect
207. #1383	C₂×C₁₉	semidirect
276. C₂×Q₁₆	D₄×C₁₉	semidirect
280. C₂×D₈	D₄×C₁₉	semidirect
305. C₂×C₁₆	D₄×C₁₉	semidirect
307. #108	D₄×C₁₉	semidirect
314. C₁₉	#13318	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×#3414	2
C₁₉×#3067	2
C₁₉×#3060	2
C₂×C₁₉×#360	2
C₁₉×#2143	2
C₁₉×#2117	2
C₁₉×#1383	2
#13318	19

Subgroups — C19×#13318 #18019277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13318 #18019277