Subgroups — C₁₉×#33531 #18039490

Order 4864.

1122 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3584	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#509	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3058	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2190	C₂	1	8	yes	maximal, complemented
5	C₁₉×#2145	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2115	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#585	—	2	1	no	—
8	C₁₉×#578	—	2	2	no	—
9	C₁₉×#577	—	2	4	no	—
10	C₁₉×#576	—	2	2	no	—
11	C₁₉×#575	—	2	1	no	—
12	C₁₉×#575	C₂²	1	4	yes	complemented
13	C₂×C₁₉×#135	—	2	2	no	—
14	C₂×C₁₉×#135	C₂²	1	2	yes	—
15	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
17	C₁₉×#535	—	2	1	no	—
18	C₁₉×#509	—	2	4	no	—
19	C₁₉×#509	C₂²	1	8	yes	complemented
20	C₂×C₁₉×SD₃₂	—	2	2	no	—
21	C₂×C₁₉×D₁₆	—	2	2	no	—
22	C₂×C₁₉×M₃₂	C₂²	1	2	yes	complemented
23	C₁₉×#469	C₂²	1	4	yes	complemented
24	C₁₉×#466	—	2	2	no	—
25	C₁₉×#427	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#418	—	2	1	no	—
27	C₁₉×#360	C₂²	1	8	yes	complemented
28	C₁₉×#349	C₂²	1	4	yes	complemented
29	C₁₉×2₋¹⁺⁴	—	2	4	no	—
30	C₁₉×2₋¹⁺⁴	—	4	1	no	—
31	C₁₉×H(5,𝔽₂)	—	2	4	no	—
32	C₁₉×H(5,𝔽₂)	—	4	2	no	—
33	C₁₉×H(5,𝔽₂)	—	4	1	no	—
34	C₂×#41×C₁₉	—	2	4	no	—
35	C₂×#41×C₁₉	—	2	2	no	—
36	C₂×#41×C₁₉	—	4	4	no	—
37	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
38	C₂²×D₄×C₁₉	—	2	1	no	—
39	C₁₉×#137	—	2	4	no	—
40	C₁₉×#137	—	2	8	no	—
41	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
42	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
43	C₁₉×#135	—	2	4	no	—
44	C₁₉×#135	—	2	4	no	—
45	C₁₉×#135	—	2	2	no	—
46	C₁₉×#135	—	2	4	no	—
47	C₁₉×#135	—	2	2	no	—
48	C₁₉×#135	D₄	1	4	yes	complemented
49	C₁₉×#135	C₂³	1	4	yes	—
50	C₂×Q₁₆×C₁₉	—	2	2	no	—
51	C₂×Q₁₆×C₁₉	D₄	1	2	yes	complemented
52	C₂×SD₁₆×C₁₉	—	2	4	no	—
53	C₂×SD₁₆×C₁₉	—	2	2	no	—
54	C₂×D₈×C₁₉	—	2	2	no	—
55	C₂×D₈×C₁₉	—	2	2	no	—
56	C₂×D₈×C₁₉	—	2	2	no	—
57	C₂×D₈×C₁₉	—	2	1	no	—
58	C₂×D₈×C₁₉	D₄	1	2	yes	complemented
59	C₂×D₈×C₁₉	C₂³	1	2	yes	—
60	C₁₉×#131	—	2	2	no	—
61	C₁₉×#131	—	2	2	no	—
62	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
63	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
64	C₂²×C₈×C₁₉	D₄	1	2	yes	—
65	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₁₉×#127	—	4	1	no	—
67	C₁₉×#124	—	4	1	no	—
68	C₁₉×#121	—	2	4	no	—
69	C₁₉×#120	—	4	2	no	—
70	C₁₉×#117	—	2	1	no	—
71	C₁₉×SD₃₂	—	2	8	no	—
72	C₁₉×D₁₆	—	2	8	no	—
73	C₁₉×M₃₂	—	2	2	no	—
74	C₁₉×M₃₂	C₂³	1	4	yes	—
75	C₂×C₁₆×C₁₉	—	2	2	no	—
76	C₁₉×#107	—	2	1	no	—
77	C₁₉×#106	C₂³	1	2	yes	—
78	C₁₉×#102	—	2	4	no	—
79	C₂⁴×C₁₉	—	4	1	no	—
80	#41×C₁₉	—	2	2	no	—
81	#41×C₁₉	—	2	2	no	—
82	#41×C₁₉	—	2	8	no	—
83	#41×C₁₉	—	2	4	no	—
84	#41×C₁₉	—	2	4	no	—
85	#41×C₁₉	—	4	4	no	—
86	#41×C₁₉	—	4	8	no	—
87	#41×C₁₉	—	4	4	no	—
88	#41×C₁₉	—	4	4	no	—
89	#41×C₁₉	—	4	4	no	—
90	#41×C₁₉	—	4	2	no	—
91	#41×C₁₉	—	4	2	no	—
92	C₂×Q₈×C₁₉	—	2	4	no	—
93	C₂×Q₈×C₁₉	—	2	2	no	—
94	C₂×Q₈×C₁₉	—	4	4	no	—
95	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
96	C₂×D₄×C₁₉	—	2	4	no	—
97	C₂×D₄×C₁₉	—	2	2	no	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	—	4	8	no	—
100	C₂×D₄×C₁₉	—	4	4	no	—
101	C₂×D₄×C₁₉	—	4	4	no	—
102	C₂×D₄×C₁₉	—	4	2	no	—
103	C₂×D₄×C₁₉	—	4	4	no	—
104	C₂×D₄×C₁₉	—	4	2	no	—
105	C₂×D₄×C₁₉	—	4	1	no	—
106	C₂×D₄×C₁₉	—	4	2	no	—
107	C₂×D₄×C₁₉	D₈	1	2	yes	—
108	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	—	4	4	no	—
110	C₂²×C₄×C₁₉	—	4	2	no	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	Q₁₆×C₁₉	—	2	4	no	—
114	Q₁₆×C₁₉	—	2	2	no	—
115	Q₁₆×C₁₉	C₂×D₄	1	4	yes	—
116	SD₁₆×C₁₉	—	2	8	no	—
117	SD₁₆×C₁₉	—	2	4	no	—
118	SD₁₆×C₁₉	—	2	4	no	—
119	D₈×C₁₉	—	2	4	no	—
120	D₈×C₁₉	—	2	2	no	—
121	D₈×C₁₉	—	2	4	no	—
122	D₈×C₁₉	—	4	1	no	—
123	D₈×C₁₉	—	4	1	no	—
124	D₈×C₁₉	C₂×D₄	1	4	yes	—
125	M₁₆×C₁₉	—	2	2	no	—
126	M₁₆×C₁₉	—	2	4	no	—
127	C₂×C₈×C₁₉	—	2	2	no	—
128	C₂×C₈×C₁₉	—	2	2	no	—
129	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₂²⋊C₄×C₁₉	—	4	1	no	—
136	C₂²⋊C₄×C₁₉	—	4	4	no	—
137	C₄²×C₁₉	—	4	1	no	—
138	C₁₆×C₁₉	—	2	4	no	—
139	#33531	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₁₉	—	4	4	no	—
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	—	4	2	no	—
143	C₂³×C₁₉	—	8	2	no	—
144	C₂³×C₁₉	—	16	2	no	—
145	C₂³×C₁₉	C₂×D₈	1	2	yes	—
146	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
147	Q₈×C₁₉	—	2	2	no	—
148	Q₈×C₁₉	—	2	4	no	—
149	Q₈×C₁₉	—	4	4	no	—
150	Q₈×C₁₉	—	4	2	no	—
151	D₄×C₁₉	—	2	4	no	—
152	D₄×C₁₉	—	2	4	no	—
153	D₄×C₁₉	—	2	2	no	—
154	D₄×C₁₉	—	4	4	no	—
155	D₄×C₁₉	—	4	8	no	—
156	D₄×C₁₉	—	4	4	no	—
157	D₄×C₁₉	—	4	4	no	—
158	D₄×C₁₉	—	4	2	no	—
159	D₄×C₁₉	—	4	2	no	—
160	D₄×C₁₉	—	4	2	no	—
161	D₄×C₁₉	—	8	2	no	—
162	D₄×C₁₉	—	16	4	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	4	8	no	—
166	C₂×C₄×C₁₉	—	4	4	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	—	4	4	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	#120	1	2	yes	—
172	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
173	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
175	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
176	C₈×C₁₉	—	2	2	no	—
177	C₈×C₁₉	#120	1	1	yes	characteristic
178	C₈×C₁₉	#120	1	1	yes	characteristic
179	C₈×C₁₉	C₂²×D₄	1	2	yes	—
180	#3584	C₂×C₁₉	1	1	yes	characteristic, complemented
181	C₂×#509	C₂×C₁₉	1	2	yes	complemented
182	#3058	C₂×C₁₉	1	1	yes	characteristic, complemented
183	#2190	C₂×C₁₉	1	8	yes	complemented
184	#2145	C₂×C₁₉	1	2	yes	complemented
185	#2115	C₂×C₁₉	1	1	yes	characteristic, complemented
186	C₂²×C₁₉	—	2	2	no	—
187	C₂²×C₁₉	—	4	1	no	—
188	C₂²×C₁₉	—	4	2	no	—
189	C₂²×C₁₉	—	4	4	no	—
190	C₂²×C₁₉	—	8	4	no	—
191	C₂²×C₁₉	—	8	2	no	—
192	C₂²×C₁₉	—	16	2	no	—
193	C₂²×C₁₉	—	16	4	no	—
194	C₂²×C₁₉	—	16	4	no	—
195	C₂²×C₁₉	#447	1	2	yes	—
196	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
197	C₄×C₁₉	—	2	2	no	—
198	C₄×C₁₉	—	4	4	no	—
199	C₄×C₁₉	—	8	2	no	—
200	C₄×C₁₉	#447	1	2	yes	—
201	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
202	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	#585	—	2	1	no	—
204	#578	—	2	2	no	—
205	#577	—	2	4	no	—
206	#576	—	2	2	no	—
207	#575	—	2	1	no	—
208	#575	C₂²×C₁₉	1	4	yes	complemented
209	C₂×#135	—	2	2	no	—
210	C₂×#135	C₂²×C₁₉	1	2	yes	—
211	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
212	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
213	#535	—	2	1	no	—
214	#509	—	2	4	no	—
215	#509	C₂²×C₁₉	1	8	yes	complemented
216	C₂×SD₃₂	—	2	2	no	—
217	C₂×D₁₆	—	2	2	no	—
218	C₂×M₃₂	C₂²×C₁₉	1	2	yes	complemented
219	#469	C₂²×C₁₉	1	4	yes	complemented
220	#466	—	2	2	no	—
221	#427	C₂²×C₁₉	1	1	yes	characteristic, complemented
222	#418	—	2	1	no	—
223	#360	C₂²×C₁₉	1	8	yes	complemented
224	#349	C₂²×C₁₉	1	4	yes	complemented
225	C₂×C₁₉	—	2	1	no	—
226	C₂×C₁₉	—	2	2	no	—
227	C₂×C₁₉	—	4	2	no	—
228	C₂×C₁₉	—	8	4	no	—
229	C₂×C₁₉	—	16	2	no	—
230	C₂×C₁₉	C₂×#447	1	1	yes	characteristic
231	2₋¹⁺⁴	—	2	4	no	—
232	2₋¹⁺⁴	—	4	1	no	—
233	H(5,𝔽₂)	—	2	4	no	—
234	H(5,𝔽₂)	—	4	2	no	—
235	H(5,𝔽₂)	—	4	1	no	—
236	C₂×#41	—	2	4	no	—
237	C₂×#41	—	2	2	no	—
238	C₂×#41	—	4	4	no	—
239	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
240	C₂²×D₄	—	2	1	no	—
241	#137	—	2	4	no	—
242	#137	—	2	8	no	—
243	AGL(1,ℤ/8)	—	2	4	no	—
244	AGL(1,ℤ/8)	—	2	8	no	—
245	#135	—	2	4	no	—
246	#135	—	2	4	no	—
247	#135	—	2	2	no	—
248	#135	—	2	4	no	—
249	#135	—	2	2	no	—
250	#135	D₄×C₁₉	1	4	yes	complemented
251	#135	C₂³×C₁₉	1	4	yes	—
252	C₂×Q₁₆	—	2	2	no	—
253	C₂×Q₁₆	D₄×C₁₉	1	2	yes	complemented
254	C₂×SD₁₆	—	2	4	no	—
255	C₂×SD₁₆	—	2	2	no	—
256	C₂×D₈	—	2	2	no	—
257	C₂×D₈	—	2	2	no	—
258	C₂×D₈	—	2	2	no	—
259	C₂×D₈	—	2	1	no	—
260	C₂×D₈	D₄×C₁₉	1	2	yes	complemented
261	C₂×D₈	C₂³×C₁₉	1	2	yes	—
262	#131	—	2	2	no	—
263	#131	—	2	2	no	—
264	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
265	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
266	C₂²×C₈	D₄×C₁₉	1	2	yes	—
267	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
268	#127	—	4	1	no	—
269	#124	—	4	1	no	—
270	#121	—	2	4	no	—
271	#120	—	4	2	no	—
272	#117	—	2	1	no	—
273	SD₃₂	—	2	8	no	—
274	D₁₆	—	2	8	no	—
275	M₃₂	—	2	2	no	—
276	M₃₂	C₂³×C₁₉	1	4	yes	—
277	C₂×C₁₆	—	2	2	no	—
278	#107	—	2	1	no	—
279	#106	C₂³×C₁₉	1	2	yes	—
280	#102	—	2	4	no	—
281	C₁₉	#33531	1	1	yes	characteristic, direct product factor, Sylow
282	C₂⁴	—	4	1	no	—
283	#41	—	2	2	no	—
284	#41	—	2	2	no	—
285	#41	—	2	8	no	—
286	#41	—	2	4	no	—
287	#41	—	2	4	no	—
288	#41	—	4	4	no	—
289	#41	—	4	8	no	—
290	#41	—	4	4	no	—
291	#41	—	4	4	no	—
292	#41	—	4	4	no	—
293	#41	—	4	2	no	—
294	#41	—	4	2	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	4	4	no	—
298	C₂×Q₈	D₈×C₁₉	1	1	yes	characteristic
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	4	8	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	4	4	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	D₈×C₁₉	1	2	yes	—
311	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
312	C₂²×C₄	—	4	4	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
316	Q₁₆	—	2	4	no	—
317	Q₁₆	—	2	2	no	—
318	Q₁₆	C₂×D₄×C₁₉	1	4	yes	—
319	SD₁₆	—	2	8	no	—
320	SD₁₆	—	2	4	no	—
321	SD₁₆	—	2	4	no	—
322	D₈	—	2	4	no	—
323	D₈	—	2	2	no	—
324	D₈	—	2	4	no	—
325	D₈	—	4	1	no	—
326	D₈	—	4	1	no	—
327	D₈	C₂×D₄×C₁₉	1	4	yes	—
328	M₁₆	—	2	2	no	—
329	M₁₆	—	2	4	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
333	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
334	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
335	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
336	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
337	C₄⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	4	4	no	—
340	C₄²	—	4	1	no	—
341	C₁₆	—	2	4	no	—
342	C₂³	—	4	4	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	8	2	no	—
346	C₂³	—	16	2	no	—
347	C₂³	C₂×D₈×C₁₉	1	2	yes	—
348	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
349	Q₈	—	2	2	no	—
350	Q₈	—	2	4	no	—
351	Q₈	—	4	4	no	—
352	Q₈	—	4	2	no	—
353	D₄	—	2	4	no	—
354	D₄	—	2	2	no	—
355	D₄	—	2	4	no	—
356	D₄	—	4	4	no	—
357	D₄	—	4	8	no	—
358	D₄	—	4	4	no	—
359	D₄	—	4	4	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	8	2	no	—
364	D₄	—	16	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	8	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	C₁₉×#120	1	2	yes	—
374	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
375	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
376	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
377	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	C₁₉×#120	1	1	yes	characteristic
380	C₈	C₁₉×#120	1	1	yes	characteristic
381	C₈	C₂²×D₄×C₁₉	1	2	yes	—
382	C₂²	—	2	2	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	8	4	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	16	2	no	—
389	C₂²	—	16	4	no	—
390	C₂²	—	16	4	no	—
391	C₂²	C₁₉×#447	1	2	yes	—
392	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	4	4	no	—
395	C₄	—	8	2	no	—
396	C₄	C₁₉×#447	1	2	yes	—
397	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
398	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
399	C₂	—	2	1	no	—
400	C₂	—	2	2	no	—
401	C₂	—	4	2	no	—
402	C₂	—	8	4	no	—
403	C₂	—	16	2	no	—
404	C₂	C₂×C₁₉×#447	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
LCS	G ▷ C₂×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×#3584	C₂	semidirect
2. C₂×C₁₉×#509	C₂	semidirect
3. C₁₉×#3058	C₂	semidirect
4. C₁₉×#2190	C₂	semidirect
5. C₁₉×#2145	C₂	semidirect
6. C₁₉×#2115	C₂	semidirect
12. C₁₉×#575	C₂²	semidirect
15. C₂²×D₈×C₁₉	C₂²	semidirect
19. C₁₉×#509	C₂²	semidirect
22. C₂×C₁₉×M₃₂	C₂²	semidirect
23. C₁₉×#469	C₂²	semidirect
25. C₁₉×#427	C₂²	semidirect
27. C₁₉×#360	C₂²	semidirect
28. C₁₉×#349	C₂²	semidirect
48. C₁₉×#135	D₄	semidirect
51. C₂×Q₁₆×C₁₉	D₄	semidirect
58. C₂×D₈×C₁₉	D₄	semidirect
139. #33531	C₁₉	direct (N × H)
180. #3584	C₂×C₁₉	semidirect
181. C₂×#509	C₂×C₁₉	semidirect
182. #3058	C₂×C₁₉	semidirect
183. #2190	C₂×C₁₉	semidirect
184. #2145	C₂×C₁₉	semidirect
185. #2115	C₂×C₁₉	semidirect
208. #575	C₂²×C₁₉	semidirect
211. C₂²×D₈	C₂²×C₁₉	semidirect
215. #509	C₂²×C₁₉	semidirect
218. C₂×M₃₂	C₂²×C₁₉	semidirect
219. #469	C₂²×C₁₉	semidirect
221. #427	C₂²×C₁₉	semidirect
223. #360	C₂²×C₁₉	semidirect
224. #349	C₂²×C₁₉	semidirect
250. #135	D₄×C₁₉	semidirect
253. C₂×Q₁₆	D₄×C₁₉	semidirect
260. C₂×D₈	D₄×C₁₉	semidirect
281. C₁₉	#33531	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×#3584	2
C₂×C₁₉×#509	2
C₁₉×#3058	2
C₁₉×#2190	2
C₁₉×#2145	2
C₁₉×#2115	2
#33531	19

Subgroups — C19×#33531 #18039490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33531 #18039490