Subgroups — C₁₉×#32884 #18038843

Order 4864.

3994 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#449	C₂	1	3	yes	maximal, complemented
3	C₂×C₁₉×#447	C₂	1	3	yes	maximal, complemented
4	C₁₉×#2615	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1788	C₂	1	3	yes	maximal, complemented
6	C₁₉×#1786	C₂	1	3	yes	maximal, complemented
7	C₁₉×#1780	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×H(5,𝔽₂)	—	2	12	no	—
9	C₂×C₁₉×H(5,𝔽₂)	—	2	12	no	—
10	C₂²×#41×C₁₉	—	2	1	no	—
11	C₂²×#41×C₁₉	C₂²	1	3	yes	—
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₉	—	2	3	no	—
14	C₂³×D₄×C₁₉	C₂²	1	3	yes	—
15	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
16	C₂²×D₈×C₁₉	C₂²	1	3	yes	complemented
17	C₂×C₁₉×#121	C₂²	1	3	yes	complemented
18	C₁₉×#449	—	2	12	no	—
19	C₁₉×#447	—	2	12	no	—
20	C₂×C₁₉×#103	C₂²	1	3	yes	complemented
21	C₂×C₁₉×#102	C₂²	1	6	yes	complemented
22	C₂×C₁₉×#102	C₂²	1	3	yes	complemented
23	C₂×C₁₉×C₂²⋊C₈	C₂²	1	3	yes	complemented
24	C₂×C₁₉×C₂²⋊C₈	C₂²	1	3	yes	complemented
25	C₁₉×#393	—	2	1	no	—
26	C₁₉×#392	—	2	3	no	—
27	C₁₉×#380	C₂²	1	3	yes	complemented
28	C₂⁵×C₁₉	—	2	3	no	—
29	C₁₉×H(5,𝔽₂)	—	2	32	no	—
30	C₁₉×H(5,𝔽₂)	—	2	96	no	—
31	C₂×#41×C₁₉	—	2	24	no	—
32	C₂×#41×C₁₉	—	2	12	no	—
33	C₂×#41×C₁₉	—	2	12	no	—
34	C₂×#41×C₁₉	—	2	6	no	—
35	C₂×#41×C₁₉	—	2	6	no	—
36	C₂×#41×C₁₉	—	2	6	no	—
37	C₂×#41×C₁₉	D₄	1	12	yes	complemented
38	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₉	—	2	48	no	—
41	C₂²×D₄×C₁₉	—	2	24	no	—
42	C₂²×D₄×C₁₉	—	2	3	no	—
43	C₂²×D₄×C₁₉	—	2	12	no	—
44	C₂²×D₄×C₁₉	—	2	12	no	—
45	C₂²×D₄×C₁₉	—	2	3	no	—
46	C₂²×D₄×C₁₉	—	2	3	no	—
47	C₂²×D₄×C₁₉	—	2	6	no	—
48	C₂²×D₄×C₁₉	D₄	1	3	yes	—
49	C₂²×D₄×C₁₉	D₄	1	12	yes	complemented
50	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
52	C₂³×C₄×C₁₉	—	2	3	no	—
53	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
54	C₂×SD₁₆×C₁₉	—	2	6	no	—
55	C₂×D₈×C₁₉	—	2	12	no	—
56	C₂×D₈×C₁₉	—	2	6	no	—
57	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
59	C₁₉×#121	—	2	6	no	—
60	C₁₉×#121	—	2	6	no	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
64	C₁₉×#103	—	2	6	no	—
65	C₁₉×#102	—	2	12	no	—
66	C₁₉×#102	—	2	6	no	—
67	C₁₉×C₂²⋊C₈	—	2	6	no	—
68	C₁₉×C₂²⋊C₈	—	2	6	no	—
69	C₁₉×#95	—	2	3	no	—
70	C₂⁴×C₁₉	—	2	24	no	—
71	C₂⁴×C₁₉	—	2	3	no	—
72	C₂⁴×C₁₉	—	2	12	no	—
73	C₂⁴×C₁₉	—	2	1	no	—
74	C₂⁴×C₁₉	—	8	3	no	—
75	C₂⁴×C₁₉	—	8	6	no	—
76	C₂⁴×C₁₉	—	8	3	no	—
77	C₂⁴×C₁₉	C₂×D₄	1	3	yes	—
78	#41×C₁₉	—	2	64	no	—
79	#41×C₁₉	—	2	48	no	—
80	#41×C₁₉	—	2	8	no	—
81	#41×C₁₉	—	2	24	no	—
82	#41×C₁₉	—	2	24	no	—
83	#41×C₁₉	—	2	24	no	—
84	C₂×Q₈×C₁₉	—	2	6	no	—
85	C₂×Q₈×C₁₉	—	2	3	no	—
86	C₂×Q₈×C₁₉	C₂×D₄	1	6	yes	—
87	C₂×D₄×C₁₉	—	2	24	no	—
88	C₂×D₄×C₁₉	—	2	24	no	—
89	C₂×D₄×C₁₉	—	2	192	no	—
90	C₂×D₄×C₁₉	—	2	24	no	—
91	C₂×D₄×C₁₉	—	2	24	no	—
92	C₂×D₄×C₁₉	—	2	12	no	—
93	C₂×D₄×C₁₉	—	2	12	no	—
94	C₂×D₄×C₁₉	—	2	48	no	—
95	C₂×D₄×C₁₉	—	2	6	no	—
96	C₂×D₄×C₁₉	—	2	12	no	—
97	C₂×D₄×C₁₉	—	2	6	no	—
98	C₂×D₄×C₁₉	—	2	3	no	—
99	C₂×D₄×C₁₉	—	2	3	no	—
100	C₂×D₄×C₁₉	—	2	3	no	—
101	C₂×D₄×C₁₉	—	4	6	no	—
102	C₂×D₄×C₁₉	—	8	6	no	—
103	C₂×D₄×C₁₉	C₂×D₄	1	6	yes	—
104	C₂×D₄×C₁₉	C₂×D₄	1	12	yes	—
105	C₂²×C₄×C₁₉	—	2	24	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	12	no	—
108	C₂²×C₄×C₁₉	—	2	6	no	—
109	C₂²×C₄×C₁₉	—	2	6	no	—
110	C₂²×C₄×C₁₉	—	2	3	no	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
114	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
115	SD₁₆×C₁₉	—	4	4	no	—
116	D₈×C₁₉	—	4	12	no	—
117	C₂×C₈×C₁₉	—	2	6	no	—
118	C₂×C₈×C₁₉	—	2	3	no	—
119	C₂×C₈×C₁₉	—	2	3	no	—
120	C₄⋊C₄×C₁₉	—	2	3	no	—
121	C₄⋊C₄×C₁₉	—	2	3	no	—
122	C₂²⋊C₄×C₁₉	—	4	6	no	—
123	C₂²⋊C₄×C₁₉	—	8	3	no	—
124	#32884	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂³×C₁₉	—	2	48	no	—
126	C₂³×C₁₉	—	2	6	no	—
127	C₂³×C₁₉	—	2	12	no	—
128	C₂³×C₁₉	—	2	6	no	—
129	C₂³×C₁₉	—	2	3	no	—
130	C₂³×C₁₉	—	2	6	no	—
131	C₂³×C₁₉	—	2	3	no	—
132	C₂³×C₁₉	—	4	3	no	—
133	C₂³×C₁₉	—	4	6	no	—
134	C₂³×C₁₉	—	4	3	no	—
135	C₂³×C₁₉	—	4	3	no	—
136	C₂³×C₁₉	—	4	3	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	8	12	no	—
139	C₂³×C₁₉	—	8	12	no	—
140	C₂³×C₁₉	—	8	24	no	—
141	C₂³×C₁₉	—	8	24	no	—
142	C₂³×C₁₉	#120	1	6	yes	—
143	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₁₉	—	2	8	no	—
145	Q₈×C₁₉	—	2	6	no	—
146	Q₈×C₁₉	#120	1	4	yes	—
147	D₄×C₁₉	—	2	48	no	—
148	D₄×C₁₉	—	2	24	no	—
149	D₄×C₁₉	—	2	48	no	—
150	D₄×C₁₉	—	2	6	no	—
151	D₄×C₁₉	—	2	12	no	—
152	D₄×C₁₉	—	4	3	no	—
153	D₄×C₁₉	—	4	1	no	—
154	D₄×C₁₉	—	8	12	no	—
155	D₄×C₁₉	#120	1	12	yes	—
156	C₂×C₄×C₁₉	—	2	48	no	—
157	C₂×C₄×C₁₉	—	2	6	no	—
158	C₂×C₄×C₁₉	—	2	6	no	—
159	C₂×C₄×C₁₉	—	2	6	no	—
160	C₂×C₄×C₁₉	—	2	6	no	—
161	C₂×C₄×C₁₉	—	2	12	no	—
162	C₂×C₄×C₁₉	—	4	3	no	—
163	C₂×C₄×C₁₉	—	4	6	no	—
164	C₂×C₄×C₁₉	#120	1	6	yes	—
165	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
166	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
167	C₈×C₁₉	—	4	3	no	—
168	C₈×C₁₉	—	4	1	no	—
169	C₂²×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic, complemented
170	C₂×#449	C₂×C₁₉	1	3	yes	complemented
171	C₂×#447	C₂×C₁₉	1	3	yes	complemented
172	#2615	C₂×C₁₉	1	1	yes	characteristic, complemented
173	#1788	C₂×C₁₉	1	3	yes	complemented
174	#1786	C₂×C₁₉	1	3	yes	complemented
175	#1780	C₂×C₁₉	1	1	yes	characteristic, complemented
176	C₂²×C₁₉	—	2	6	no	—
177	C₂²×C₁₉	—	2	12	no	—
178	C₂²×C₁₉	—	2	6	no	—
179	C₂²×C₁₉	—	2	6	no	—
180	C₂²×C₁₉	—	4	6	no	—
181	C₂²×C₁₉	—	4	12	no	—
182	C₂²×C₁₉	—	4	6	no	—
183	C₂²×C₁₉	—	4	6	no	—
184	C₂²×C₁₉	—	4	12	no	—
185	C₂²×C₁₉	—	4	6	no	—
186	C₂²×C₁₉	—	8	48	no	—
187	C₂²×C₁₉	—	8	1	no	—
188	C₂²×C₁₉	—	8	3	no	—
189	C₂²×C₁₉	—	8	3	no	—
190	C₂²×C₁₉	C₂×#120	1	3	yes	—
191	C₂²×C₁₉	#576	1	3	yes	—
192	C₂²×C₁₉	#577	1	1	yes	characteristic
193	C₄×C₁₉	—	2	4	no	—
194	C₄×C₁₉	—	2	6	no	—
195	C₄×C₁₉	—	8	3	no	—
196	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
197	C₄×C₁₉	C₂×#120	1	3	yes	—
198	C₂×H(5,𝔽₂)	—	2	12	no	—
199	C₂×H(5,𝔽₂)	—	2	12	no	—
200	C₂²×#41	—	2	1	no	—
201	C₂²×#41	C₂²×C₁₉	1	3	yes	—
202	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
203	C₂³×D₄	—	2	3	no	—
204	C₂³×D₄	C₂²×C₁₉	1	3	yes	—
205	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
206	C₂²×D₈	C₂²×C₁₉	1	3	yes	complemented
207	C₂×#121	C₂²×C₁₉	1	3	yes	complemented
208	#449	—	2	12	no	—
209	#447	—	2	12	no	—
210	C₂×#103	C₂²×C₁₉	1	3	yes	complemented
211	C₂×#102	C₂²×C₁₉	1	6	yes	complemented
212	C₂×#102	C₂²×C₁₉	1	3	yes	complemented
213	C₂×C₂²⋊C₈	C₂²×C₁₉	1	3	yes	complemented
214	C₂×C₂²⋊C₈	C₂²×C₁₉	1	3	yes	complemented
215	#393	—	2	1	no	—
216	#392	—	2	3	no	—
217	#380	C₂²×C₁₉	1	3	yes	complemented
218	C₂×C₁₉	—	4	6	no	—
219	C₂×C₁₉	—	4	12	no	—
220	C₂×C₁₉	—	16	1	no	—
221	C₂×C₁₉	#2846	1	1	yes	characteristic
222	C₂×C₁₉	#3008	1	3	yes	—
223	C₂×C₁₉	#3012	1	3	yes	—
224	C₂⁵	—	2	3	no	—
225	H(5,𝔽₂)	—	2	32	no	—
226	H(5,𝔽₂)	—	2	96	no	—
227	C₂×#41	—	2	24	no	—
228	C₂×#41	—	2	12	no	—
229	C₂×#41	—	2	12	no	—
230	C₂×#41	—	2	6	no	—
231	C₂×#41	—	2	6	no	—
232	C₂×#41	—	2	6	no	—
233	C₂×#41	D₄×C₁₉	1	12	yes	complemented
234	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
235	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
236	C₂²×D₄	—	2	48	no	—
237	C₂²×D₄	—	2	24	no	—
238	C₂²×D₄	—	2	3	no	—
239	C₂²×D₄	—	2	12	no	—
240	C₂²×D₄	—	2	12	no	—
241	C₂²×D₄	—	2	3	no	—
242	C₂²×D₄	—	2	3	no	—
243	C₂²×D₄	—	2	6	no	—
244	C₂²×D₄	D₄×C₁₉	1	3	yes	—
245	C₂²×D₄	D₄×C₁₉	1	12	yes	complemented
246	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
247	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
248	C₂³×C₄	—	2	3	no	—
249	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
250	C₂×SD₁₆	—	2	6	no	—
251	C₂×D₈	—	2	12	no	—
252	C₂×D₈	—	2	6	no	—
253	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
254	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
255	#121	—	2	6	no	—
256	#121	—	2	6	no	—
257	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
258	C₂×C₂²⋊C₄	—	2	3	no	—
259	C₂×C₂²⋊C₄	—	2	3	no	—
260	#103	—	2	6	no	—
261	#102	—	2	12	no	—
262	#102	—	2	6	no	—
263	C₂²⋊C₈	—	2	6	no	—
264	C₂²⋊C₈	—	2	6	no	—
265	#95	—	2	3	no	—
266	C₁₉	#32884	1	1	yes	characteristic, direct product factor, Sylow
267	C₂⁴	—	2	24	no	—
268	C₂⁴	—	2	3	no	—
269	C₂⁴	—	2	12	no	—
270	C₂⁴	—	2	1	no	—
271	C₂⁴	—	8	3	no	—
272	C₂⁴	—	8	6	no	—
273	C₂⁴	—	8	3	no	—
274	C₂⁴	C₂×D₄×C₁₉	1	3	yes	—
275	#41	—	2	64	no	—
276	#41	—	2	48	no	—
277	#41	—	2	8	no	—
278	#41	—	2	24	no	—
279	#41	—	2	24	no	—
280	#41	—	2	24	no	—
281	C₂×Q₈	—	2	6	no	—
282	C₂×Q₈	—	2	3	no	—
283	C₂×Q₈	C₂×D₄×C₁₉	1	6	yes	—
284	C₂×D₄	—	2	24	no	—
285	C₂×D₄	—	2	24	no	—
286	C₂×D₄	—	2	192	no	—
287	C₂×D₄	—	2	24	no	—
288	C₂×D₄	—	2	24	no	—
289	C₂×D₄	—	2	12	no	—
290	C₂×D₄	—	2	12	no	—
291	C₂×D₄	—	2	48	no	—
292	C₂×D₄	—	2	6	no	—
293	C₂×D₄	—	2	12	no	—
294	C₂×D₄	—	2	6	no	—
295	C₂×D₄	—	2	3	no	—
296	C₂×D₄	—	2	3	no	—
297	C₂×D₄	—	2	3	no	—
298	C₂×D₄	—	4	6	no	—
299	C₂×D₄	—	8	6	no	—
300	C₂×D₄	C₂×D₄×C₁₉	1	6	yes	—
301	C₂×D₄	C₂×D₄×C₁₉	1	12	yes	—
302	C₂²×C₄	—	2	24	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	12	no	—
305	C₂²×C₄	—	2	6	no	—
306	C₂²×C₄	—	2	6	no	—
307	C₂²×C₄	—	2	3	no	—
308	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
309	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
310	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
311	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
312	SD₁₆	—	4	4	no	—
313	D₈	—	4	12	no	—
314	C₂×C₈	—	2	6	no	—
315	C₂×C₈	—	2	3	no	—
316	C₂×C₈	—	2	3	no	—
317	C₄⋊C₄	—	2	3	no	—
318	C₄⋊C₄	—	2	3	no	—
319	C₂²⋊C₄	—	4	6	no	—
320	C₂²⋊C₄	—	8	3	no	—
321	C₂³	—	2	48	no	—
322	C₂³	—	2	6	no	—
323	C₂³	—	2	12	no	—
324	C₂³	—	2	6	no	—
325	C₂³	—	2	3	no	—
326	C₂³	—	2	6	no	—
327	C₂³	—	2	3	no	—
328	C₂³	—	4	3	no	—
329	C₂³	—	4	6	no	—
330	C₂³	—	4	3	no	—
331	C₂³	—	4	3	no	—
332	C₂³	—	4	3	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	8	12	no	—
335	C₂³	—	8	12	no	—
336	C₂³	—	8	24	no	—
337	C₂³	—	8	24	no	—
338	C₂³	C₁₉×#120	1	6	yes	—
339	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
340	Q₈	—	2	8	no	—
341	Q₈	—	2	6	no	—
342	Q₈	C₁₉×#120	1	4	yes	—
343	D₄	—	2	48	no	—
344	D₄	—	2	24	no	—
345	D₄	—	2	48	no	—
346	D₄	—	2	6	no	—
347	D₄	—	2	12	no	—
348	D₄	—	4	3	no	—
349	D₄	—	4	1	no	—
350	D₄	—	8	12	no	—
351	D₄	C₁₉×#120	1	12	yes	—
352	C₂×C₄	—	2	48	no	—
353	C₂×C₄	—	2	6	no	—
354	C₂×C₄	—	2	6	no	—
355	C₂×C₄	—	2	6	no	—
356	C₂×C₄	—	2	6	no	—
357	C₂×C₄	—	2	12	no	—
358	C₂×C₄	—	4	3	no	—
359	C₂×C₄	—	4	6	no	—
360	C₂×C₄	C₁₉×#120	1	6	yes	—
361	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
362	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
363	C₈	—	4	3	no	—
364	C₈	—	4	1	no	—
365	C₂²	—	2	6	no	—
366	C₂²	—	2	6	no	—
367	C₂²	—	2	6	no	—
368	C₂²	—	2	12	no	—
369	C₂²	—	4	6	no	—
370	C₂²	—	4	12	no	—
371	C₂²	—	4	6	no	—
372	C₂²	—	4	6	no	—
373	C₂²	—	4	12	no	—
374	C₂²	—	4	6	no	—
375	C₂²	—	8	48	no	—
376	C₂²	—	8	3	no	—
377	C₂²	—	8	3	no	—
378	C₂²	—	8	1	no	—
379	C₂²	C₂×C₁₉×#120	1	3	yes	—
380	C₂²	C₁₉×#576	1	3	yes	—
381	C₂²	C₁₉×#577	1	1	yes	characteristic
382	C₄	—	2	4	no	—
383	C₄	—	2	6	no	—
384	C₄	—	8	3	no	—
385	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
386	C₄	C₂×C₁₉×#120	1	3	yes	—
387	C₂	—	4	6	no	—
388	C₂	—	4	12	no	—
389	C₂	—	16	1	no	—
390	C₂	C₁₉×#2846	1	1	yes	characteristic
391	C₂	C₁₉×#3008	1	3	yes	—
392	C₂	C₁₉×#3012	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×H(5,𝔽₂)	C₂	semidirect
2. C₂×C₁₉×#449	C₂	semidirect
3. C₂×C₁₉×#447	C₂	semidirect
4. C₁₉×#2615	C₂	semidirect
5. C₁₉×#1788	C₂	semidirect
6. C₁₉×#1786	C₂	semidirect
7. C₁₉×#1780	C₂	semidirect
15. C₂²×SD₁₆×C₁₉	C₂²	semidirect
16. C₂²×D₈×C₁₉	C₂²	semidirect
17. C₂×C₁₉×#121	C₂²	semidirect
20. C₂×C₁₉×#103	C₂²	semidirect
21. C₂×C₁₉×#102	C₂²	semidirect
22. C₂×C₁₉×#102	C₂²	semidirect
23. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
24. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
27. C₁₉×#380	C₂²	semidirect
37. C₂×#41×C₁₉	D₄	semidirect
49. C₂²×D₄×C₁₉	D₄	semidirect
124. #32884	C₁₉	direct (N × H)
169. C₂²×H(5,𝔽₂)	C₂×C₁₉	semidirect
170. C₂×#449	C₂×C₁₉	semidirect
171. C₂×#447	C₂×C₁₉	semidirect
172. #2615	C₂×C₁₉	semidirect
173. #1788	C₂×C₁₉	semidirect
174. #1786	C₂×C₁₉	semidirect
175. #1780	C₂×C₁₉	semidirect
205. C₂²×SD₁₆	C₂²×C₁₉	semidirect
206. C₂²×D₈	C₂²×C₁₉	semidirect
207. C₂×#121	C₂²×C₁₉	semidirect
210. C₂×#103	C₂²×C₁₉	semidirect
211. C₂×#102	C₂²×C₁₉	semidirect
212. C₂×#102	C₂²×C₁₉	semidirect
213. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
214. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
217. #380	C₂²×C₁₉	semidirect
233. C₂×#41	D₄×C₁₉	semidirect
245. C₂²×D₄	D₄×C₁₉	semidirect
266. C₁₉	#32884	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×H(5,𝔽₂)	2
C₂×C₁₉×#449	2
C₂×C₁₉×#447	2
C₁₉×#2615	2
C₁₉×#1788	2
C₁₉×#1786	2
C₁₉×#1780	2
#32884	19

Subgroups — C19×#32884 #18038843

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32884 #18038843