Subgroups — C₂²×C₁₉×#342 #18026311

Order 4864.

4334 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₂²⋊C₄×C₁₉	C₂	1	2	yes	maximal
3	C₂×C₁₉×#342	C₂	1	12	yes	maximal, direct product factor
4	C₂⁶×C₁₉	C₂²	1	1	yes	characteristic
5	C₂⁴×C₄×C₁₉	—	2	2	no	—
6	C₂⁴×C₄×C₁₉	C₄	1	2	yes	complemented
7	C₂²×C₂²⋊C₄×C₁₉	—	2	6	no	—
8	C₂²×C₂²⋊C₄×C₁₉	—	2	6	no	—
9	C₂²×C₂²⋊C₄×C₁₉	—	2	8	no	—
10	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
11	C₂²×C₂²⋊C₄×C₁₉	C₄	1	6	yes	complemented
12	C₂²×C₂²⋊C₄×C₁₉	C₄	1	16	yes	complemented
13	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	6	yes	—
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	12	yes	—
15	C₁₉×#342	C₂²	1	16	yes	direct product factor
16	C₂⁵×C₁₉	—	4	8	no	—
17	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂⁵×C₁₉	C₂×C₄	1	8	yes	—
19	C₂⁵×C₁₉	C₂×C₄	1	3	yes	—
20	C₂⁵×C₁₉	D₄	1	2	yes	—
21	C₂⁵×C₁₉	D₄	1	6	yes	—
22	C₂⁵×C₁₉	D₄	1	4	yes	—
23	C₂⁵×C₁₉	Q₈	1	4	yes	—
24	C₂⁵×C₁₉	C₂³	1	3	yes	—
25	C₂³×C₄×C₁₉	—	2	6	no	—
26	C₂³×C₄×C₁₉	—	2	16	no	—
27	C₂³×C₄×C₁₉	—	2	2	no	—
28	C₂³×C₄×C₁₉	—	2	12	no	—
29	C₂³×C₄×C₁₉	—	4	16	no	—
30	C₂³×C₄×C₁₉	—	4	8	no	—
31	C₂³×C₄×C₁₉	C₂×C₄	1	12	yes	complemented
32	C₂×C₂²⋊C₄×C₁₉	—	2	12	no	—
33	C₂×C₂²⋊C₄×C₁₉	—	2	12	no	—
34	C₂×C₂²⋊C₄×C₁₉	—	2	48	no	—
35	C₂×C₂²⋊C₄×C₁₉	—	2	12	no	—
36	C₂×C₂²⋊C₄×C₁₉	—	2	12	no	—
37	C₂×C₂²⋊C₄×C₁₉	—	2	12	no	—
38	C₂×C₂²⋊C₄×C₁₉	—	2	24	no	—
39	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	12	yes	complemented
40	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	48	yes	complemented
41	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
42	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
43	C₂⁴×C₁₉	—	2	8	no	—
44	C₂⁴×C₁₉	—	2	16	no	—
45	C₂⁴×C₁₉	—	4	32	no	—
46	C₂⁴×C₁₉	—	4	12	no	—
47	C₂⁴×C₁₉	—	4	16	no	—
48	C₂⁴×C₁₉	—	4	24	no	—
49	C₂⁴×C₁₉	—	4	16	no	—
50	C₂⁴×C₁₉	—	4	12	no	—
51	C₂⁴×C₁₉	C₄²	1	4	yes	—
52	C₂⁴×C₁₉	C₄²	1	12	yes	—
53	C₂⁴×C₁₉	C₂²⋊C₄	1	6	yes	—
54	C₂⁴×C₁₉	C₂²⋊C₄	1	8	yes	—
55	C₂⁴×C₁₉	C₂²⋊C₄	1	3	yes	—
56	C₂⁴×C₁₉	C₂²⋊C₄	1	24	yes	—
57	C₂⁴×C₁₉	C₂²⋊C₄	1	6	yes	—
58	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂⁴×C₁₉	C₄⋊C₄	1	4	yes	—
60	C₂⁴×C₁₉	C₄⋊C₄	1	8	yes	—
61	C₂⁴×C₁₉	C₄⋊C₄	1	24	yes	—
62	C₂⁴×C₁₉	C₄⋊C₄	1	12	yes	—
63	C₂⁴×C₁₉	C₂²×C₄	1	3	yes	—
64	C₂⁴×C₁₉	C₂²×C₄	1	12	yes	—
65	C₂⁴×C₁₉	C₂²×C₄	1	3	yes	—
66	C₂⁴×C₁₉	C₂×D₄	1	6	yes	—
67	C₂⁴×C₁₉	C₂×D₄	1	6	yes	—
68	C₂⁴×C₁₉	C₂×D₄	1	6	yes	—
69	C₂⁴×C₁₉	C₂×Q₈	1	6	yes	—
70	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	—	2	12	no	—
72	C₂²×C₄×C₁₉	—	2	12	no	—
73	C₂²×C₄×C₁₉	—	2	48	no	—
74	C₂²×C₄×C₁₉	—	2	8	no	—
75	C₂²×C₄×C₁₉	—	4	64	no	—
76	C₂²×C₄×C₁₉	—	4	48	no	—
77	C₂²×C₄×C₁₉	—	4	24	no	—
78	C₂²×C₄×C₁₉	—	4	8	no	—
79	C₂²×C₄×C₁₉	—	4	24	no	—
80	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	complemented
81	C₂²⋊C₄×C₁₉	—	2	24	no	—
82	C₂²⋊C₄×C₁₉	—	2	48	no	—
83	C₂²⋊C₄×C₁₉	—	2	8	no	—
84	C₂²⋊C₄×C₁₉	—	2	8	no	—
85	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	complemented
86	C₂²×#342	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂³×C₁₉	—	2	32	no	—
88	C₂³×C₁₉	—	2	16	no	—
89	C₂³×C₁₉	—	2	16	no	—
90	C₂³×C₁₉	—	2	32	no	—
91	C₂³×C₁₉	—	2	12	no	—
92	C₂³×C₁₉	—	2	12	no	—
93	C₂³×C₁₉	—	2	24	no	—
94	C₂³×C₁₉	—	2	24	no	—
95	C₂³×C₁₉	—	4	24	no	—
96	C₂³×C₁₉	—	4	12	no	—
97	C₂³×C₁₉	—	4	48	no	—
98	C₂³×C₁₉	—	4	24	no	—
99	C₂³×C₁₉	—	4	48	no	—
100	C₂³×C₁₉	—	4	6	no	—
101	C₂³×C₁₉	—	4	24	no	—
102	C₂³×C₁₉	—	4	12	no	—
103	C₂³×C₁₉	—	4	12	no	—
104	C₂³×C₁₉	—	4	12	no	—
105	C₂³×C₁₉	—	4	2	no	—
106	C₂³×C₁₉	#95	1	12	yes	—
107	C₂³×C₁₉	#95	1	24	yes	—
108	C₂³×C₁₉	#95	1	24	yes	—
109	C₂³×C₁₉	#95	1	4	yes	—
110	C₂³×C₁₉	#99	1	8	yes	—
111	C₂³×C₁₉	C₂×C₄²	1	6	yes	—
112	C₂³×C₁₉	C₂×C₄²	1	6	yes	—
113	C₂³×C₁₉	C₂×C₂²⋊C₄	1	6	yes	—
114	C₂³×C₁₉	C₂×C₂²⋊C₄	1	3	yes	—
115	C₂³×C₁₉	C₂×C₂²⋊C₄	1	12	yes	—
116	C₂³×C₁₉	C₂×C₂²⋊C₄	1	12	yes	—
117	C₂³×C₁₉	C₂×C₂²⋊C₄	1	3	yes	—
118	C₂³×C₁₉	C₂×C₄⋊C₄	1	6	yes	—
119	C₂³×C₁₉	C₂×C₄⋊C₄	1	12	yes	—
120	C₂³×C₁₉	C₂×C₄⋊C₄	1	6	yes	—
121	C₂³×C₁₉	C₂×C₄⋊C₄	1	12	yes	—
122	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
123	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
124	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
125	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
126	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
127	C₂×C₄×C₁₉	—	2	8	no	—
128	C₂×C₄×C₁₉	—	2	16	no	—
129	C₂×C₄×C₁₉	—	4	16	no	—
130	C₂×C₄×C₁₉	—	4	96	no	—
131	C₂×C₄×C₁₉	—	4	24	no	—
132	C₂×C₄×C₁₉	—	4	24	no	—
133	C₂×C₄×C₁₉	—	4	8	no	—
134	C₂³×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
135	C₂³×C₂²⋊C₄	C₂×C₁₉	1	2	yes	—
136	C₂×#342	C₂×C₁₉	1	12	yes	direct product factor
137	C₂²×C₁₉	—	2	6	no	—
138	C₂²×C₁₉	—	2	2	no	—
139	C₂²×C₁₉	—	2	4	no	—
140	C₂²×C₁₉	—	2	12	no	—
141	C₂²×C₁₉	—	2	24	no	—
142	C₂²×C₁₉	—	2	48	no	—
143	C₂²×C₁₉	—	2	24	no	—
144	C₂²×C₁₉	—	2	12	no	—
145	C₂²×C₁₉	—	2	12	no	—
146	C₂²×C₁₉	—	2	24	no	—
147	C₂²×C₁₉	—	4	24	no	—
148	C₂²×C₁₉	—	4	6	no	—
149	C₂²×C₁₉	—	4	12	no	—
150	C₂²×C₁₉	—	4	6	no	—
151	C₂²×C₁₉	—	4	12	no	—
152	C₂²×C₁₉	—	4	2	no	—
153	C₂²×C₁₉	—	4	1	no	—
154	C₂²×C₁₉	—	4	1	no	—
155	C₂²×C₁₉	#342	1	16	yes	direct product factor
156	C₂²×C₁₉	C₂×#95	1	6	yes	—
157	C₂²×C₁₉	C₂×#95	1	12	yes	—
158	C₂²×C₁₉	C₂×#95	1	6	yes	—
159	C₂²×C₁₉	C₂×#99	1	12	yes	—
160	C₂²×C₁₉	C₂²×C₄²	1	1	yes	characteristic
161	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	2	yes	—
162	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
164	C₂²×C₁₉	C₂²×C₄⋊C₄	1	2	yes	—
165	C₄×C₁₉	—	4	16	no	—
166	C₄×C₁₉	—	4	8	no	—
167	C₂⁶	C₂²×C₁₉	1	1	yes	characteristic
168	C₂⁴×C₄	—	2	2	no	—
169	C₂⁴×C₄	C₄×C₁₉	1	2	yes	complemented
170	C₂²×C₂²⋊C₄	—	2	6	no	—
171	C₂²×C₂²⋊C₄	—	2	2	no	—
172	C₂²×C₂²⋊C₄	—	2	6	no	—
173	C₂²×C₂²⋊C₄	—	2	8	no	—
174	C₂²×C₂²⋊C₄	C₄×C₁₉	1	6	yes	complemented
175	C₂²×C₂²⋊C₄	C₄×C₁₉	1	16	yes	complemented
176	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	6	yes	—
177	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	12	yes	—
178	#342	C₂²×C₁₉	1	16	yes	direct product factor
179	C₂×C₁₉	—	2	2	no	—
180	C₂×C₁₉	—	2	1	no	—
181	C₂×C₁₉	—	2	2	no	—
182	C₂×C₁₉	—	2	6	no	—
183	C₂×C₁₉	—	2	12	no	—
184	C₂×C₁₉	—	2	1	no	—
185	C₂×C₁₉	C₂×#342	1	12	yes	direct product factor
186	C₂×C₁₉	C₂²×#95	1	1	yes	characteristic
187	C₂×C₁₉	C₂²×#99	1	2	yes	—
188	C₂⁵	—	4	8	no	—
189	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
190	C₂⁵	C₂×C₄×C₁₉	1	8	yes	—
191	C₂⁵	C₂×C₄×C₁₉	1	3	yes	—
192	C₂⁵	D₄×C₁₉	1	2	yes	—
193	C₂⁵	D₄×C₁₉	1	6	yes	—
194	C₂⁵	D₄×C₁₉	1	4	yes	—
195	C₂⁵	Q₈×C₁₉	1	4	yes	—
196	C₂⁵	C₂³×C₁₉	1	3	yes	—
197	C₂³×C₄	—	2	6	no	—
198	C₂³×C₄	—	2	2	no	—
199	C₂³×C₄	—	2	16	no	—
200	C₂³×C₄	—	2	12	no	—
201	C₂³×C₄	—	4	16	no	—
202	C₂³×C₄	—	4	8	no	—
203	C₂³×C₄	C₂×C₄×C₁₉	1	12	yes	complemented
204	C₂×C₂²⋊C₄	—	2	12	no	—
205	C₂×C₂²⋊C₄	—	2	12	no	—
206	C₂×C₂²⋊C₄	—	2	48	no	—
207	C₂×C₂²⋊C₄	—	2	12	no	—
208	C₂×C₂²⋊C₄	—	2	12	no	—
209	C₂×C₂²⋊C₄	—	2	12	no	—
210	C₂×C₂²⋊C₄	—	2	24	no	—
211	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	12	yes	complemented
212	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	48	yes	complemented
213	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
214	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
215	C₁₉	C₂²×#342	1	1	yes	characteristic, direct product factor, Sylow
216	C₂⁴	—	2	8	no	—
217	C₂⁴	—	2	16	no	—
218	C₂⁴	—	4	32	no	—
219	C₂⁴	—	4	12	no	—
220	C₂⁴	—	4	16	no	—
221	C₂⁴	—	4	24	no	—
222	C₂⁴	—	4	16	no	—
223	C₂⁴	—	4	12	no	—
224	C₂⁴	C₄²×C₁₉	1	4	yes	—
225	C₂⁴	C₄²×C₁₉	1	12	yes	—
226	C₂⁴	C₂²⋊C₄×C₁₉	1	6	yes	—
227	C₂⁴	C₂²⋊C₄×C₁₉	1	8	yes	—
228	C₂⁴	C₂²⋊C₄×C₁₉	1	3	yes	—
229	C₂⁴	C₂²⋊C₄×C₁₉	1	6	yes	—
230	C₂⁴	C₂²⋊C₄×C₁₉	1	24	yes	—
231	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
232	C₂⁴	C₄⋊C₄×C₁₉	1	4	yes	—
233	C₂⁴	C₄⋊C₄×C₁₉	1	8	yes	—
234	C₂⁴	C₄⋊C₄×C₁₉	1	12	yes	—
235	C₂⁴	C₄⋊C₄×C₁₉	1	24	yes	—
236	C₂⁴	C₂²×C₄×C₁₉	1	3	yes	—
237	C₂⁴	C₂²×C₄×C₁₉	1	12	yes	—
238	C₂⁴	C₂²×C₄×C₁₉	1	3	yes	—
239	C₂⁴	C₂×D₄×C₁₉	1	6	yes	—
240	C₂⁴	C₂×D₄×C₁₉	1	6	yes	—
241	C₂⁴	C₂×D₄×C₁₉	1	6	yes	—
242	C₂⁴	C₂×Q₈×C₁₉	1	6	yes	—
243	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
244	C₂²×C₄	—	2	12	no	—
245	C₂²×C₄	—	2	12	no	—
246	C₂²×C₄	—	2	48	no	—
247	C₂²×C₄	—	2	8	no	—
248	C₂²×C₄	—	4	64	no	—
249	C₂²×C₄	—	4	48	no	—
250	C₂²×C₄	—	4	24	no	—
251	C₂²×C₄	—	4	8	no	—
252	C₂²×C₄	—	4	24	no	—
253	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	complemented
254	C₂²⋊C₄	—	2	24	no	—
255	C₂²⋊C₄	—	2	48	no	—
256	C₂²⋊C₄	—	2	8	no	—
257	C₂²⋊C₄	—	2	8	no	—
258	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	complemented
259	C₂³	—	2	32	no	—
260	C₂³	—	2	16	no	—
261	C₂³	—	2	16	no	—
262	C₂³	—	2	32	no	—
263	C₂³	—	2	12	no	—
264	C₂³	—	2	12	no	—
265	C₂³	—	2	24	no	—
266	C₂³	—	2	24	no	—
267	C₂³	—	4	24	no	—
268	C₂³	—	4	48	no	—
269	C₂³	—	4	12	no	—
270	C₂³	—	4	24	no	—
271	C₂³	—	4	48	no	—
272	C₂³	—	4	24	no	—
273	C₂³	—	4	6	no	—
274	C₂³	—	4	12	no	—
275	C₂³	—	4	12	no	—
276	C₂³	—	4	12	no	—
277	C₂³	—	4	2	no	—
278	C₂³	C₁₉×#95	1	12	yes	—
279	C₂³	C₁₉×#95	1	24	yes	—
280	C₂³	C₁₉×#95	1	24	yes	—
281	C₂³	C₁₉×#95	1	4	yes	—
282	C₂³	C₁₉×#99	1	8	yes	—
283	C₂³	C₂×C₄²×C₁₉	1	6	yes	—
284	C₂³	C₂×C₄²×C₁₉	1	6	yes	—
285	C₂³	C₂×C₂²⋊C₄×C₁₉	1	6	yes	—
286	C₂³	C₂×C₂²⋊C₄×C₁₉	1	12	yes	—
287	C₂³	C₂×C₂²⋊C₄×C₁₉	1	3	yes	—
288	C₂³	C₂×C₂²⋊C₄×C₁₉	1	12	yes	—
289	C₂³	C₂×C₂²⋊C₄×C₁₉	1	3	yes	—
290	C₂³	C₂×C₄⋊C₄×C₁₉	1	6	yes	—
291	C₂³	C₂×C₄⋊C₄×C₁₉	1	12	yes	—
292	C₂³	C₂×C₄⋊C₄×C₁₉	1	12	yes	—
293	C₂³	C₂×C₄⋊C₄×C₁₉	1	6	yes	—
294	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
295	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
296	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
297	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
298	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	2	16	no	—
301	C₂×C₄	—	4	96	no	—
302	C₂×C₄	—	4	16	no	—
303	C₂×C₄	—	4	24	no	—
304	C₂×C₄	—	4	24	no	—
305	C₂×C₄	—	4	8	no	—
306	C₂²	—	2	24	no	—
307	C₂²	—	2	12	no	—
308	C₂²	—	2	12	no	—
309	C₂²	—	2	24	no	—
310	C₂²	—	2	48	no	—
311	C₂²	—	2	24	no	—
312	C₂²	—	2	6	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	2	4	no	—
315	C₂²	—	2	12	no	—
316	C₂²	—	4	6	no	—
317	C₂²	—	4	12	no	—
318	C₂²	—	4	6	no	—
319	C₂²	—	4	12	no	—
320	C₂²	—	4	2	no	—
321	C₂²	—	4	1	no	—
322	C₂²	—	4	1	no	—
323	C₂²	—	4	24	no	—
324	C₂²	C₁₉×#342	1	16	yes	direct product factor
325	C₂²	C₂×C₁₉×#95	1	6	yes	—
326	C₂²	C₂×C₁₉×#95	1	12	yes	—
327	C₂²	C₂×C₁₉×#95	1	6	yes	—
328	C₂²	C₂×C₁₉×#99	1	12	yes	—
329	C₂²	C₂²×C₄²×C₁₉	1	1	yes	characteristic
330	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	2	yes	—
331	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
332	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
333	C₂²	C₂²×C₄⋊C₄×C₁₉	1	2	yes	—
334	C₄	—	4	16	no	—
335	C₄	—	4	8	no	—
336	C₂	—	2	2	no	—
337	C₂	—	2	12	no	—
338	C₂	—	2	6	no	—
339	C₂	—	2	1	no	—
340	C₂	—	2	1	no	—
341	C₂	—	2	2	no	—
342	C₂	C₂×C₁₉×#342	1	12	yes	direct product factor
343	C₂	C₂²×C₁₉×#95	1	1	yes	characteristic
344	C₂	C₂²×C₁₉×#99	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂²⋊C₄
commutator	C₂²	C₂²×C₄²×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁶×C₁₉	C₂²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂⁶×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₉×#342	C₂	direct (N × H)
6. C₂⁴×C₄×C₁₉	C₄	semidirect
11. C₂²×C₂²⋊C₄×C₁₉	C₄	semidirect
12. C₂²×C₂²⋊C₄×C₁₉	C₄	semidirect
15. C₁₉×#342	C₂²	direct (N × H)
31. C₂³×C₄×C₁₉	C₂×C₄	semidirect
39. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
40. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
80. C₂²×C₄×C₁₉	C₂²×C₄	semidirect
85. C₂²⋊C₄×C₁₉	C₂²×C₄	semidirect
86. C₂²×#342	C₁₉	direct (N × H)
136. C₂×#342	C₂×C₁₉	direct (N × H)
155. C₂²×C₁₉	#342	direct (N × H)
169. C₂⁴×C₄	C₄×C₁₉	semidirect
174. C₂²×C₂²⋊C₄	C₄×C₁₉	semidirect
175. C₂²×C₂²⋊C₄	C₄×C₁₉	semidirect
178. #342	C₂²×C₁₉	direct (N × H)
185. C₂×C₁₉	C₂×#342	direct (N × H)
203. C₂³×C₄	C₂×C₄×C₁₉	semidirect
211. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
212. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
215. C₁₉	C₂²×#342	direct (N × H)
253. C₂²×C₄	C₂²×C₄×C₁₉	semidirect
258. C₂²⋊C₄	C₂²×C₄×C₁₉	semidirect
324. C₂²	C₁₉×#342	direct (N × H)
342. C₂	C₂×C₁₉×#342	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₂²⋊C₄×C₁₉	2
C₂×C₁₉×#342	2
C₂²×#342	19

Subgroups — C22×C19×#342 #18026311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₉×#342 #18026311