Subgroups — C₂²×C₁₉×#448 #18066308

Order 4864.

5326 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×SD₁₆×C₁₉	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₉×#121	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#448	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₁₉×#103	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×Q₈×C₁₉	—	2	16	no	—
8	C₂³×Q₈×C₁₉	—	2	6	no	—
9	C₂³×Q₈×C₁₉	—	2	1	no	—
10	C₂³×Q₈×C₁₉	C₂²	1	2	yes	—
11	C₂³×Q₈×C₁₉	C₂²	1	12	yes	complemented
12	C₂³×D₄×C₁₉	—	2	1	no	—
13	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₉	—	2	1	no	—
15	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×SD₁₆×C₁₉	—	2	16	no	—
17	C₂²×SD₁₆×C₁₉	C₂²	1	24	yes	complemented
18	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
19	C₂×C₁₉×#121	—	2	6	no	—
20	C₂×C₁₉×#121	C₂²	1	12	yes	—
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
23	C₁₉×#448	C₂²	1	64	yes	direct product factor
24	C₂×C₁₉×#103	C₂²	1	24	yes	complemented
25	C₂×C₁₉×C₂²⋊C₈	C₂²	1	12	yes	complemented
26	C₂⁵×C₁₉	—	2	1	no	—
27	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
28	C₂²×Q₈×C₁₉	—	2	96	no	—
29	C₂²×Q₈×C₁₉	—	2	16	no	—
30	C₂²×Q₈×C₁₉	—	2	96	no	—
31	C₂²×Q₈×C₁₉	—	2	8	no	—
32	C₂²×Q₈×C₁₉	—	2	6	no	—
33	C₂²×Q₈×C₁₉	—	2	12	no	—
34	C₂²×Q₈×C₁₉	—	2	24	no	—
35	C₂²×Q₈×C₁₉	D₄	1	16	yes	complemented
36	C₂²×Q₈×C₁₉	C₂³	1	12	yes	—
37	C₂²×Q₈×C₁₉	C₂³	1	16	yes	complemented
38	C₂²×D₄×C₁₉	—	2	12	no	—
39	C₂²×D₄×C₁₉	—	2	8	no	—
40	C₂²×D₄×C₁₉	—	2	3	no	—
41	C₂²×D₄×C₁₉	—	4	8	no	—
42	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
43	C₂³×C₄×C₁₉	—	2	16	no	—
44	C₂³×C₄×C₁₉	—	2	12	no	—
45	C₂³×C₄×C₁₉	—	2	2	no	—
46	C₂³×C₄×C₁₉	—	2	8	no	—
47	C₂³×C₄×C₁₉	—	2	1	no	—
48	C₂³×C₄×C₁₉	D₄	1	6	yes	—
49	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×SD₁₆×C₁₉	—	2	96	no	—
53	C₂×SD₁₆×C₁₉	C₂³	1	32	yes	complemented
54	C₂²×C₈×C₁₉	—	2	8	no	—
55	C₂²×C₈×C₁₉	C₂³	1	12	yes	—
56	C₁₉×#121	—	2	24	no	—
57	C₁₉×#121	C₂³	1	16	yes	—
58	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	12	no	—
61	C₁₉×#103	C₂³	1	32	yes	complemented
62	C₁₉×C₂²⋊C₈	C₂³	1	16	yes	complemented
63	C₂⁴×C₁₉	—	2	4	no	—
64	C₂⁴×C₁₉	—	2	4	no	—
65	C₂⁴×C₁₉	—	2	6	no	—
66	C₂⁴×C₁₉	—	4	4	no	—
67	C₂⁴×C₁₉	—	4	4	no	—
68	C₂⁴×C₁₉	—	4	4	no	—
69	C₂⁴×C₁₉	SD₁₆	1	8	yes	complemented
70	C₂⁴×C₁₉	C₂×D₄	1	6	yes	—
71	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₂×Q₈×C₁₉	—	2	192	no	—
73	C₂×Q₈×C₁₉	—	2	96	no	—
74	C₂×Q₈×C₁₉	—	2	64	no	—
75	C₂×Q₈×C₁₉	—	2	48	no	—
76	C₂×Q₈×C₁₉	—	2	24	no	—
77	C₂×Q₈×C₁₉	—	2	12	no	—
78	C₂×Q₈×C₁₉	—	2	16	no	—
79	C₂×Q₈×C₁₉	C₂×D₄	1	48	yes	complemented
80	C₂×Q₈×C₁₉	C₂⁴	1	8	yes	—
81	C₂×D₄×C₁₉	—	2	16	no	—
82	C₂×D₄×C₁₉	—	2	24	no	—
83	C₂×D₄×C₁₉	—	2	6	no	—
84	C₂×D₄×C₁₉	—	4	48	no	—
85	C₂×D₄×C₁₉	—	4	12	no	—
86	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
87	C₂²×C₄×C₁₉	—	2	96	no	—
88	C₂²×C₄×C₁₉	—	2	16	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	12	no	—
91	C₂²×C₄×C₁₉	—	2	16	no	—
92	C₂²×C₄×C₁₉	—	2	24	no	—
93	C₂²×C₄×C₁₉	—	2	24	no	—
94	C₂²×C₄×C₁₉	—	2	6	no	—
95	C₂²×C₄×C₁₉	—	4	4	no	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
97	C₂²×C₄×C₁₉	C₂×D₄	1	12	yes	—
98	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
100	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
101	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
102	SD₁₆×C₁₉	—	2	64	no	—
103	C₂×C₈×C₁₉	—	2	24	no	—
104	C₂×C₈×C₁₉	C₂⁴	1	8	yes	—
105	C₄⋊C₄×C₁₉	—	2	6	no	—
106	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
107	C₂²⋊C₄×C₁₉	—	2	16	no	—
108	C₂²×#448	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂³×C₁₉	—	2	12	no	—
110	C₂³×C₁₉	—	2	12	no	—
111	C₂³×C₁₉	—	2	32	no	—
112	C₂³×C₁₉	—	2	4	no	—
113	C₂³×C₁₉	—	4	12	no	—
114	C₂³×C₁₉	—	4	12	no	—
115	C₂³×C₁₉	—	4	12	no	—
116	C₂³×C₁₉	—	8	16	no	—
117	C₂³×C₁₉	#120	1	4	yes	—
118	C₂³×C₁₉	C₂×SD₁₆	1	4	yes	—
119	C₂³×C₁₉	C₂×SD₁₆	1	24	yes	complemented
120	C₂³×C₁₉	#137	1	4	yes	—
121	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
122	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
123	Q₈×C₁₉	—	2	64	no	—
124	Q₈×C₁₉	—	2	48	no	—
125	Q₈×C₁₉	—	2	8	no	—
126	Q₈×C₁₉	C₂²×D₄	1	16	yes	complemented
127	D₄×C₁₉	—	2	8	no	—
128	D₄×C₁₉	—	4	32	no	—
129	D₄×C₁₉	—	4	12	no	—
130	C₂×C₄×C₁₉	—	2	64	no	—
131	C₂×C₄×C₁₉	—	2	48	no	—
132	C₂×C₄×C₁₉	—	2	12	no	—
133	C₂×C₄×C₁₉	—	2	8	no	—
134	C₂×C₄×C₁₉	—	2	24	no	—
135	C₂×C₄×C₁₉	—	2	8	no	—
136	C₂×C₄×C₁₉	—	2	4	no	—
137	C₂×C₄×C₁₉	—	4	12	no	—
138	C₂×C₄×C₁₉	#120	1	12	yes	—
139	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
140	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
141	C₂×C₄×C₁₉	C₂²×D₄	1	12	yes	—
142	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
143	C₈×C₁₉	—	2	8	no	—
144	C₂⁴×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
145	C₂³×SD₁₆	C₂×C₁₉	1	2	yes	complemented
146	C₂²×#121	C₂×C₁₉	1	1	yes	characteristic
147	C₂×#448	C₂×C₁₉	1	24	yes	direct product factor
148	C₂²×#103	C₂×C₁₉	1	2	yes	complemented
149	C₂²×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
150	C₂²×C₁₉	—	2	4	no	—
151	C₂²×C₁₉	—	2	48	no	—
152	C₂²×C₁₉	—	2	4	no	—
153	C₂²×C₁₉	—	4	4	no	—
154	C₂²×C₁₉	—	4	4	no	—
155	C₂²×C₁₉	—	4	4	no	—
156	C₂²×C₁₉	—	8	24	no	—
157	C₂²×C₁₉	#448	1	16	yes	direct product factor
158	C₂²×C₁₉	C₂×#120	1	6	yes	—
159	C₂²×C₁₉	C₂²×SD₁₆	1	6	yes	—
160	C₂²×C₁₉	C₂²×SD₁₆	1	8	yes	complemented
161	C₂²×C₁₉	C₂×#137	1	6	yes	—
162	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
163	C₄×C₁₉	—	2	16	no	—
164	C₄×C₁₉	—	2	4	no	—
165	C₄×C₁₉	—	4	4	no	—
166	C₄×C₁₉	C₂×#120	1	6	yes	—
167	C₄×C₁₉	C₂³×D₄	1	2	yes	—
168	C₂³×Q₈	—	2	16	no	—
169	C₂³×Q₈	—	2	1	no	—
170	C₂³×Q₈	—	2	6	no	—
171	C₂³×Q₈	C₂²×C₁₉	1	2	yes	—
172	C₂³×Q₈	C₂²×C₁₉	1	12	yes	complemented
173	C₂³×D₄	—	2	1	no	—
174	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
175	C₂⁴×C₄	—	2	1	no	—
176	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
177	C₂²×SD₁₆	—	2	16	no	—
178	C₂²×SD₁₆	C₂²×C₁₉	1	24	yes	complemented
179	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
180	C₂×#121	—	2	6	no	—
181	C₂×#121	C₂²×C₁₉	1	12	yes	—
182	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
183	C₂²×C₂²⋊C₄	—	2	1	no	—
184	#448	C₂²×C₁₉	1	64	yes	direct product factor
185	C₂×#103	C₂²×C₁₉	1	24	yes	complemented
186	C₂×C₂²⋊C₈	C₂²×C₁₉	1	12	yes	complemented
187	C₂×C₁₉	—	2	8	no	—
188	C₂×C₁₉	—	8	4	no	—
189	C₂×C₁₉	C₂×#448	1	12	yes	direct product factor
190	C₂×C₁₉	C₂²×#120	1	1	yes	characteristic
191	C₂×C₁₉	C₂³×SD₁₆	1	1	yes	characteristic
192	C₂×C₁₉	C₂²×#137	1	1	yes	characteristic
193	C₂⁵	—	2	1	no	—
194	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
195	C₂²×Q₈	—	2	96	no	—
196	C₂²×Q₈	—	2	16	no	—
197	C₂²×Q₈	—	2	96	no	—
198	C₂²×Q₈	—	2	8	no	—
199	C₂²×Q₈	—	2	6	no	—
200	C₂²×Q₈	—	2	12	no	—
201	C₂²×Q₈	—	2	24	no	—
202	C₂²×Q₈	D₄×C₁₉	1	16	yes	complemented
203	C₂²×Q₈	C₂³×C₁₉	1	12	yes	—
204	C₂²×Q₈	C₂³×C₁₉	1	16	yes	complemented
205	C₂²×D₄	—	2	12	no	—
206	C₂²×D₄	—	2	8	no	—
207	C₂²×D₄	—	2	3	no	—
208	C₂²×D₄	—	4	8	no	—
209	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
210	C₂³×C₄	—	2	16	no	—
211	C₂³×C₄	—	2	2	no	—
212	C₂³×C₄	—	2	12	no	—
213	C₂³×C₄	—	2	8	no	—
214	C₂³×C₄	—	2	1	no	—
215	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
216	C₂³×C₄	D₄×C₁₉	1	6	yes	—
217	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
218	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
219	C₂×SD₁₆	—	2	96	no	—
220	C₂×SD₁₆	C₂³×C₁₉	1	32	yes	complemented
221	C₂²×C₈	—	2	8	no	—
222	C₂²×C₈	C₂³×C₁₉	1	12	yes	—
223	#121	—	2	24	no	—
224	#121	C₂³×C₁₉	1	16	yes	—
225	C₂×C₄⋊C₄	—	2	3	no	—
226	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
227	C₂×C₂²⋊C₄	—	2	12	no	—
228	#103	C₂³×C₁₉	1	32	yes	complemented
229	C₂²⋊C₈	C₂³×C₁₉	1	16	yes	complemented
230	C₁₉	C₂²×#448	1	1	yes	characteristic, direct product factor, Sylow
231	C₂⁴	—	2	4	no	—
232	C₂⁴	—	2	4	no	—
233	C₂⁴	—	2	6	no	—
234	C₂⁴	—	4	4	no	—
235	C₂⁴	—	4	4	no	—
236	C₂⁴	—	4	4	no	—
237	C₂⁴	SD₁₆×C₁₉	1	8	yes	complemented
238	C₂⁴	C₂×D₄×C₁₉	1	6	yes	—
239	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
240	C₂×Q₈	—	2	192	no	—
241	C₂×Q₈	—	2	96	no	—
242	C₂×Q₈	—	2	64	no	—
243	C₂×Q₈	—	2	48	no	—
244	C₂×Q₈	—	2	24	no	—
245	C₂×Q₈	—	2	12	no	—
246	C₂×Q₈	—	2	16	no	—
247	C₂×Q₈	C₂×D₄×C₁₉	1	48	yes	complemented
248	C₂×Q₈	C₂⁴×C₁₉	1	8	yes	—
249	C₂×D₄	—	2	16	no	—
250	C₂×D₄	—	2	24	no	—
251	C₂×D₄	—	2	6	no	—
252	C₂×D₄	—	4	48	no	—
253	C₂×D₄	—	4	12	no	—
254	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
255	C₂²×C₄	—	2	96	no	—
256	C₂²×C₄	—	2	16	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	12	no	—
259	C₂²×C₄	—	2	16	no	—
260	C₂²×C₄	—	2	24	no	—
261	C₂²×C₄	—	2	24	no	—
262	C₂²×C₄	—	2	6	no	—
263	C₂²×C₄	—	4	4	no	—
264	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
265	C₂²×C₄	C₂×D₄×C₁₉	1	12	yes	—
266	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
267	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
268	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
269	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
270	SD₁₆	—	2	64	no	—
271	C₂×C₈	—	2	24	no	—
272	C₂×C₈	C₂⁴×C₁₉	1	8	yes	—
273	C₄⋊C₄	—	2	6	no	—
274	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
275	C₂²⋊C₄	—	2	16	no	—
276	C₂³	—	2	32	no	—
277	C₂³	—	2	12	no	—
278	C₂³	—	2	12	no	—
279	C₂³	—	2	4	no	—
280	C₂³	—	4	12	no	—
281	C₂³	—	4	12	no	—
282	C₂³	—	4	12	no	—
283	C₂³	—	8	16	no	—
284	C₂³	C₁₉×#120	1	4	yes	—
285	C₂³	C₂×SD₁₆×C₁₉	1	4	yes	—
286	C₂³	C₂×SD₁₆×C₁₉	1	24	yes	complemented
287	C₂³	C₁₉×#137	1	4	yes	—
288	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
289	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
290	Q₈	—	2	64	no	—
291	Q₈	—	2	48	no	—
292	Q₈	—	2	8	no	—
293	Q₈	C₂²×D₄×C₁₉	1	16	yes	complemented
294	D₄	—	2	8	no	—
295	D₄	—	4	32	no	—
296	D₄	—	4	12	no	—
297	C₂×C₄	—	2	64	no	—
298	C₂×C₄	—	2	48	no	—
299	C₂×C₄	—	2	12	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	2	24	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	4	12	no	—
305	C₂×C₄	C₁₉×#120	1	12	yes	—
306	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
307	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
308	C₂×C₄	C₂²×D₄×C₁₉	1	12	yes	—
309	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
310	C₈	—	2	8	no	—
311	C₂²	—	2	4	no	—
312	C₂²	—	2	48	no	—
313	C₂²	—	2	4	no	—
314	C₂²	—	4	4	no	—
315	C₂²	—	4	4	no	—
316	C₂²	—	4	4	no	—
317	C₂²	—	8	24	no	—
318	C₂²	C₁₉×#448	1	16	yes	direct product factor
319	C₂²	C₂×C₁₉×#120	1	6	yes	—
320	C₂²	C₂²×SD₁₆×C₁₉	1	6	yes	—
321	C₂²	C₂²×SD₁₆×C₁₉	1	8	yes	complemented
322	C₂²	C₂×C₁₉×#137	1	6	yes	—
323	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
324	C₄	—	2	16	no	—
325	C₄	—	2	4	no	—
326	C₄	—	4	4	no	—
327	C₄	C₂×C₁₉×#120	1	6	yes	—
328	C₄	C₂³×D₄×C₁₉	1	2	yes	—
329	C₂	—	2	8	no	—
330	C₂	—	8	4	no	—
331	C₂	C₂×C₁₉×#448	1	12	yes	direct product factor
332	C₂	C₂²×C₁₉×#120	1	1	yes	characteristic
333	C₂	C₂³×SD₁₆×C₁₉	1	1	yes	characteristic
334	C₂	C₂²×C₁₉×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₂²×C₁₉×#121	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×Q₈×C₁₉	C₂	semidirect
2. C₂³×SD₁₆×C₁₉	C₂	semidirect
4. C₂×C₁₉×#448	C₂	direct (N × H)
5. C₂²×C₁₉×#103	C₂	semidirect
6. C₂²×C₁₉×C₂²⋊C₈	C₂	semidirect
11. C₂³×Q₈×C₁₉	C₂²	semidirect
17. C₂²×SD₁₆×C₁₉	C₂²	semidirect
23. C₁₉×#448	C₂²	direct (N × H)
24. C₂×C₁₉×#103	C₂²	semidirect
25. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
35. C₂²×Q₈×C₁₉	D₄	semidirect
37. C₂²×Q₈×C₁₉	C₂³	semidirect
53. C₂×SD₁₆×C₁₉	C₂³	semidirect
61. C₁₉×#103	C₂³	semidirect
62. C₁₉×C₂²⋊C₈	C₂³	semidirect
69. C₂⁴×C₁₉	SD₁₆	semidirect
79. C₂×Q₈×C₁₉	C₂×D₄	semidirect
108. C₂²×#448	C₁₉	direct (N × H)
119. C₂³×C₁₉	C₂×SD₁₆	semidirect
126. Q₈×C₁₉	C₂²×D₄	semidirect
144. C₂⁴×Q₈	C₂×C₁₉	semidirect
145. C₂³×SD₁₆	C₂×C₁₉	semidirect
147. C₂×#448	C₂×C₁₉	direct (N × H)
148. C₂²×#103	C₂×C₁₉	semidirect
149. C₂²×C₂²⋊C₈	C₂×C₁₉	semidirect
157. C₂²×C₁₉	#448	direct (N × H)
160. C₂²×C₁₉	C₂²×SD₁₆	semidirect
172. C₂³×Q₈	C₂²×C₁₉	semidirect
178. C₂²×SD₁₆	C₂²×C₁₉	semidirect
184. #448	C₂²×C₁₉	direct (N × H)
185. C₂×#103	C₂²×C₁₉	semidirect
186. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
189. C₂×C₁₉	C₂×#448	direct (N × H)
202. C₂²×Q₈	D₄×C₁₉	semidirect
204. C₂²×Q₈	C₂³×C₁₉	semidirect
220. C₂×SD₁₆	C₂³×C₁₉	semidirect
228. #103	C₂³×C₁₉	semidirect
229. C₂²⋊C₈	C₂³×C₁₉	semidirect
230. C₁₉	C₂²×#448	direct (N × H)
237. C₂⁴	SD₁₆×C₁₉	semidirect
247. C₂×Q₈	C₂×D₄×C₁₉	semidirect
286. C₂³	C₂×SD₁₆×C₁₉	semidirect
293. Q₈	C₂²×D₄×C₁₉	semidirect
318. C₂²	C₁₉×#448	direct (N × H)
321. C₂²	C₂²×SD₁₆×C₁₉	semidirect
331. C₂	C₂×C₁₉×#448	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×Q₈×C₁₉	2
C₂³×SD₁₆×C₁₉	2
C₂²×C₁₉×#121	2
C₂×C₁₉×#448	2
C₂²×C₁₉×#103	2
C₂²×C₁₉×C₂²⋊C₈	2
C₂²×#448	19

Subgroups — C22×C19×#448 #18066308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₉×#448 #18066308