Subgroups — C₂×#123×D₁₉ #14576865

Order 2432.

1968 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×D₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597340	C₂	1	2	yes	maximal, complemented
4	C₂×#10597332	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10597375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597329	C₂	1	2	yes	maximal, complemented
7	C₂×#10597381	C₂	1	1	yes	maximal, characteristic, complemented
8	#123×D₁₉	C₂	1	16	yes	maximal, direct product factor
9	C₂×C₄⋊C₄×D₁₉	C₂	1	2	yes	maximal, complemented
10	C₂×C₂²⋊C₄×D₁₉	C₂	1	2	yes	maximal, complemented
11	C₂×C₂²⋊C₄×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#123	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₁₉	C₂²	1	1	yes	characteristic
14	C₂⁴×D₁₉	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
19	C₂³×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
20	C₂×D₄×D₁₉	—	2	8	no	—
21	C₂×D₄×D₁₉	C₂²	1	8	yes	—
22	C₂²×D₇₆	C₂²	1	1	yes	characteristic
23	C₂²×C₄×D₁₉	—	2	8	no	—
24	C₂²×C₄×D₁₉	C₂²	1	2	yes	—
25	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₉	C₂²	1	2	yes	—
27	C₂²×C₄×D₁₉	C₂²	1	8	yes	complemented
28	C₂²×C₄×D₁₉	C₂²	1	2	yes	complemented
29	C₁₉×#123	C₂²	1	8	yes	complemented
30	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
31	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	complemented
32	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	complemented
34	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic, complemented
35	#10597381	C₂²	1	8	yes	complemented
36	#10597375	C₂²	1	8	yes	complemented
37	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
38	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
39	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
40	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	complemented
41	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
42	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
43	#10597340	C₂²	1	16	yes	complemented
44	C₄⋊C₄×D₁₉	C₂²	1	16	yes	complemented
45	#10597332	C₂²	1	8	yes	complemented
46	#10597329	C₂²	1	16	yes	complemented
47	C₂²⋊C₄×D₁₉	C₂²	1	8	yes	complemented
48	C₂²⋊C₄×D₁₉	C₂²	1	16	yes	complemented
49	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
50	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
51	C₂³×D₁₉	—	2	8	no	—
52	C₂³×D₁₉	—	2	4	no	—
53	C₂³×D₁₉	—	2	8	no	—
54	C₂³×D₁₉	D₄	1	8	yes	—
55	C₂³×D₁₉	C₂³	1	1	yes	characteristic
56	C₂³×D₁₉	C₂³	1	4	yes	—
57	C₂³×D₁₉	C₂³	1	1	yes	characteristic
58	C₂³×D₁₉	C₂³	1	4	yes	—
59	C₂³×D₁₉	C₂³	1	1	yes	characteristic
60	C₂×D₄×C₁₉	—	2	4	no	—
61	C₂×D₄×C₁₉	C₂³	1	4	yes	—
62	C₂²×C₄×C₁₉	—	2	4	no	—
63	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
64	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
65	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂³	1	4	yes	complemented
67	C₂×C₂²⋊D₁₉	—	2	4	no	—
68	C₂×C₂²⋊D₁₉	—	2	4	no	—
69	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
70	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
71	C₂²×Dic₁₉	—	2	4	no	—
72	C₂²×Dic₁₉	C₂³	1	2	yes	—
73	C₂²×Dic₁₉	C₂³	1	2	yes	—
74	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
75	C₂²×Dic₁₉	C₂³	1	4	yes	complemented
76	D₄×D₁₉	—	2	32	no	—
77	C₂×D₇₆	—	2	4	no	—
78	C₂×D₇₆	C₂³	1	4	yes	—
79	C₂×C₄×D₁₉	—	2	8	no	—
80	C₂×C₄×D₁₉	—	2	32	no	—
81	C₂×C₄×D₁₉	—	2	8	no	—
82	C₂×C₄×D₁₉	—	2	4	no	—
83	C₂×C₄×D₁₉	—	2	8	no	—
84	C₂×C₄×D₁₉	C₂³	1	8	yes	—
85	C₂×C₄×D₁₉	C₂³	1	4	yes	—
86	C₂×C₄×D₁₉	C₂³	1	8	yes	—
87	C₂×C₄×D₁₉	C₂³	1	8	yes	complemented
88	C₄⋊C₄×C₁₉	C₂³	1	8	yes	complemented
89	C₂²⋊C₄×C₁₉	C₂³	1	8	yes	complemented
90	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	complemented
91	C₂²⋊Dic₁₉	C₂³	1	8	yes	complemented
92	C₂²⋊Dic₁₉	C₂³	1	4	yes	complemented
93	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	complemented
94	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	complemented
95	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	complemented
96	C₄⋊Dic₁₉	C₂³	1	8	yes	complemented
97	Dic₁₉⋊C₄	C₂³	1	8	yes	complemented
98	Dic₁₉⋊C₄	C₂³	1	8	yes	complemented
99	C₂³×C₁₉	—	2	4	no	—
100	C₂³×C₁₉	—	2	2	no	—
101	C₂³×C₁₉	—	2	4	no	—
102	C₂³×C₁₉	C₂×D₄	1	4	yes	—
103	C₂³×C₁₉	C₂⁴	1	2	yes	—
104	C₂³×C₁₉	C₂⁴	1	2	yes	—
105	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
106	C₂²×D₁₉	—	2	4	no	—
107	C₂²×D₁₉	—	2	32	no	—
108	C₂²×D₁₉	—	2	16	no	—
109	C₂²×D₁₉	—	2	2	no	—
110	C₂²×D₁₉	—	2	4	no	—
111	C₂²×D₁₉	—	2	8	no	—
112	C₂²×D₁₉	—	2	16	no	—
113	C₂²×D₁₉	—	4	16	no	—
114	C₂²×D₁₉	C₂×D₄	1	4	yes	—
115	C₂²×D₁₉	C₂×D₄	1	16	yes	—
116	C₂²×D₁₉	C₂×D₄	1	4	yes	—
117	C₂²×D₁₉	#41	1	8	yes	—
118	C₂²×D₁₉	C₂⁴	1	2	yes	—
119	C₂²×D₁₉	C₂⁴	1	2	yes	—
120	C₂²×D₁₉	C₂⁴	1	2	yes	—
121	D₄×C₁₉	—	2	8	no	—
122	C₂×C₄×C₁₉	—	2	4	no	—
123	C₂×C₄×C₁₉	—	2	8	no	—
124	C₂×C₄×C₁₉	—	2	2	no	—
125	C₂×C₄×C₁₉	—	2	4	no	—
126	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
127	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
128	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
129	C₂²⋊D₁₉	—	2	8	no	—
130	C₂²⋊D₁₉	—	2	8	no	—
131	C₂×Dic₁₉	—	2	4	no	—
132	C₂×Dic₁₉	—	2	8	no	—
133	C₂×Dic₁₉	—	2	2	no	—
134	C₂×Dic₁₉	—	2	4	no	—
135	C₂×Dic₁₉	C₂⁴	1	2	yes	—
136	C₂×Dic₁₉	C₂⁴	1	4	yes	—
137	C₂×Dic₁₉	C₂⁴	1	4	yes	—
138	D₇₆	—	2	8	no	—
139	C₄×D₁₉	—	2	16	no	—
140	C₄×D₁₉	—	2	16	no	—
141	C₄×D₁₉	—	2	8	no	—
142	C₄×D₁₉	—	2	16	no	—
143	C₂²×#123	—	19	1	no	maximal, Sylow
144	C₂²×C₁₉	—	2	8	no	—
145	C₂²×C₁₉	—	2	4	no	—
146	C₂²×C₁₉	—	2	2	no	—
147	C₂²×C₁₉	—	2	4	no	—
148	C₂²×C₁₉	—	4	4	no	—
149	C₂²×C₁₉	C₂²×D₄	1	4	yes	—
150	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
151	C₂²×C₁₉	C₂×#41	1	4	yes	—
152	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
153	C₂×D₁₉	—	2	8	no	—
154	C₂×D₁₉	—	2	4	no	—
155	C₂×D₁₉	—	2	32	no	—
156	C₂×D₁₉	—	2	2	no	—
157	C₂×D₁₉	—	2	4	no	—
158	C₂×D₁₉	—	4	4	no	—
159	C₂×D₁₉	—	4	16	no	—
160	C₂×D₁₉	#123	1	16	yes	direct product factor
161	C₂×D₁₉	C₂²×D₄	1	4	yes	—
162	C₂×D₁₉	C₂²×D₄	1	4	yes	—
163	C₂×D₁₉	C₂×#41	1	8	yes	—
164	C₄×C₁₉	—	2	4	no	—
165	C₄×C₁₉	—	2	2	no	—
166	C₄×C₁₉	—	2	4	no	—
167	Dic₁₉	—	2	4	no	—
168	Dic₁₉	—	2	2	no	—
169	Dic₁₉	—	2	4	no	—
170	C₂³×D₄	—	19	1	no	—
171	C₂⁴×C₄	—	19	1	no	—
172	C₂×#123	—	19	1	no	—
173	C₂×#123	—	19	1	no	—
174	C₂×#123	—	19	16	no	—
175	C₂×#123	—	19	2	no	—
176	C₂×#123	—	19	2	no	—
177	C₂×#123	—	19	1	no	—
178	C₂×#123	D₁₉	1	1	yes	characteristic, direct product factor
179	C₂²×C₄⋊C₄	—	19	2	no	—
180	C₂²×C₂²⋊C₄	—	19	1	no	—
181	C₂²×C₂²⋊C₄	—	19	2	no	—
182	C₂×C₁₉	—	2	4	no	—
183	C₂×C₁₉	—	4	2	no	—
184	C₂×C₁₉	C₂×#123	1	4	yes	complemented
185	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
186	C₂×C₁₉	C₂²×#41	1	2	yes	—
187	D₁₉	—	2	4	no	—
188	D₁₉	—	4	2	no	—
189	D₁₉	C₂×#123	1	8	yes	direct product factor
190	C₂⁵	—	19	1	no	—
191	C₂⁵	—	19	1	no	—
192	C₂²×D₄	—	19	1	no	—
193	C₂²×D₄	—	19	1	no	—
194	C₂²×D₄	—	19	8	no	—
195	C₂²×D₄	—	19	1	no	—
196	C₂²×D₄	—	38	8	no	—
197	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
198	C₂³×C₄	—	19	1	no	—
199	C₂³×C₄	—	19	2	no	—
200	C₂³×C₄	—	19	2	no	—
201	C₂³×C₄	—	19	1	no	—
202	C₂³×C₄	—	19	2	no	—
203	C₂³×C₄	—	19	8	no	—
204	C₂³×C₄	—	38	8	no	—
205	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
206	#123	—	19	8	no	—
207	#123	—	19	8	no	—
208	#123	—	19	16	no	—
209	#123	—	19	16	no	—
210	#123	—	19	8	no	—
211	#123	C₂×D₁₉	1	8	yes	direct product factor
212	C₂×C₄⋊C₄	—	19	2	no	—
213	C₂×C₄⋊C₄	—	19	2	no	—
214	C₂×C₄⋊C₄	—	19	2	no	—
215	C₂×C₄⋊C₄	—	19	16	no	—
216	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	complemented
217	C₂×C₂²⋊C₄	—	19	1	no	—
218	C₂×C₂²⋊C₄	—	19	2	no	—
219	C₂×C₂²⋊C₄	—	19	2	no	—
220	C₂×C₂²⋊C₄	—	19	2	no	—
221	C₂×C₂²⋊C₄	—	19	2	no	—
222	C₂×C₂²⋊C₄	—	19	8	no	—
223	C₂×C₂²⋊C₄	—	19	16	no	—
224	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
225	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	complemented
226	C₁₉	C₂²×#123	1	1	yes	characteristic, complemented, Sylow
227	C₂⁴	—	19	1	no	—
228	C₂⁴	—	19	8	no	—
229	C₂⁴	—	19	4	no	—
230	C₂⁴	—	19	1	no	—
231	C₂⁴	—	19	4	no	—
232	C₂⁴	—	19	1	no	—
233	C₂⁴	—	38	8	no	—
234	C₂⁴	—	38	4	no	—
235	C₂⁴	—	38	8	no	—
236	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
237	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
238	C₂×D₄	—	2	4	no	—
239	C₂×D₄	—	19	4	no	—
240	C₂×D₄	—	19	4	no	—
241	C₂×D₄	—	19	4	no	—
242	C₂×D₄	—	38	4	no	—
243	C₂×D₄	—	38	32	no	—
244	C₂×D₄	—	38	4	no	—
245	C₂×D₄	—	38	4	no	—
246	C₂×D₄	C₂²×D₁₉	1	4	yes	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	19	4	no	—
249	C₂²×C₄	—	19	2	no	—
250	C₂²×C₄	—	19	2	no	—
251	C₂²×C₄	—	19	1	no	—
252	C₂²×C₄	—	19	8	no	—
253	C₂²×C₄	—	19	8	no	—
254	C₂²×C₄	—	19	4	no	—
255	C₂²×C₄	—	19	8	no	—
256	C₂²×C₄	—	38	8	no	—
257	C₂²×C₄	—	38	8	no	—
258	C₂²×C₄	—	38	8	no	—
259	C₂²×C₄	—	38	32	no	—
260	C₂²×C₄	—	38	4	no	—
261	C₂²×C₄	—	38	4	no	—
262	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
263	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
264	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
265	C₂²×C₄	C₂²×D₁₉	1	4	yes	complemented
266	C₄⋊C₄	—	19	8	no	—
267	C₄⋊C₄	—	19	8	no	—
268	C₄⋊C₄	—	19	8	no	—
269	C₄⋊C₄	C₂²×D₁₉	1	8	yes	complemented
270	C₂²⋊C₄	—	19	4	no	—
271	C₂²⋊C₄	—	19	8	no	—
272	C₂²⋊C₄	—	19	8	no	—
273	C₂²⋊C₄	—	19	8	no	—
274	C₂²⋊C₄	—	19	8	no	—
275	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	complemented
276	C₂²⋊C₄	C₂²×D₁₉	1	8	yes	complemented
277	C₂³	—	2	4	no	—
278	C₂³	—	2	2	no	—
279	C₂³	—	2	4	no	—
280	C₂³	—	19	4	no	—
281	C₂³	—	19	8	no	—
282	C₂³	—	19	2	no	—
283	C₂³	—	19	16	no	—
284	C₂³	—	19	4	no	—
285	C₂³	—	19	2	no	—
286	C₂³	—	19	2	no	—
287	C₂³	—	38	32	no	—
288	C₂³	—	38	16	no	—
289	C₂³	—	38	8	no	—
290	C₂³	—	38	16	no	—
291	C₂³	—	38	4	no	—
292	C₂³	—	38	2	no	—
293	C₂³	—	38	4	no	—
294	C₂³	—	76	16	no	—
295	C₂³	D₄×D₁₉	1	4	yes	—
296	C₂³	C₂³×D₁₉	1	2	yes	—
297	C₂³	C₂³×D₁₉	1	2	yes	—
298	C₂³	C₂³×D₁₉	1	1	yes	characteristic
299	D₄	—	2	8	no	—
300	D₄	—	38	8	no	—
301	D₄	—	38	8	no	—
302	D₄	—	38	8	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	19	4	no	—
308	C₂×C₄	—	19	4	no	—
309	C₂×C₄	—	19	2	no	—
310	C₂×C₄	—	38	16	no	—
311	C₂×C₄	—	38	16	no	—
312	C₂×C₄	—	38	8	no	—
313	C₂×C₄	—	38	16	no	—
314	C₂×C₄	—	38	8	no	—
315	C₂×C₄	—	38	4	no	—
316	C₂×C₄	—	38	2	no	—
317	C₂×C₄	—	38	4	no	—
318	C₂×C₄	C₂³×D₁₉	1	4	yes	—
319	C₂×C₄	C₂³×D₁₉	1	4	yes	—
320	C₂×C₄	C₂³×D₁₉	1	2	yes	—
321	C₂²	—	2	8	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	2	4	no	—
325	C₂²	—	4	4	no	—
326	C₂²	—	19	16	no	—
327	C₂²	—	19	4	no	—
328	C₂²	—	19	8	no	—
329	C₂²	—	19	4	no	—
330	C₂²	—	38	32	no	—
331	C₂²	—	38	8	no	—
332	C₂²	—	38	4	no	—
333	C₂²	—	38	2	no	—
334	C₂²	—	38	4	no	—
335	C₂²	—	76	16	no	—
336	C₂²	—	76	4	no	—
337	C₂²	C₂×D₄×D₁₉	1	4	yes	—
338	C₂²	C₂×D₄×D₁₉	1	2	yes	—
339	C₂²	#41×D₁₉	1	4	yes	—
340	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
341	C₄	—	2	4	no	—
342	C₄	—	2	2	no	—
343	C₄	—	2	4	no	—
344	C₄	—	38	4	no	—
345	C₄	—	38	2	no	—
346	C₄	—	38	4	no	—
347	C₂	—	2	4	no	—
348	C₂	—	4	2	no	—
349	C₂	—	19	8	no	—
350	C₂	—	38	4	no	—
351	C₂	—	76	2	no	—
352	C₂	#123×D₁₉	1	4	yes	direct product factor
353	C₂	C₂²×D₄×D₁₉	1	1	yes	characteristic
354	C₂	C₂×#41×D₁₉	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂³×D₁₉
commutator, cosocle	C₂²×C₁₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₉
Fitting	C₂×C₁₉×#123	C₂
socle	C₂³×C₁₉	C₂⁴
prime radical	C₂²×D₄×D₁₉	C₂
hypercenter	C₂×#123	D₁₉
hypocenter	C₁₉	C₂²×#123
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×#123

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄×D₁₉	C₂	semidirect
3. C₂×#10597340	C₂	semidirect
4. C₂×#10597332	C₂	semidirect
5. C₂×#10597375	C₂	semidirect
6. C₂×#10597329	C₂	semidirect
7. C₂×#10597381	C₂	semidirect
8. #123×D₁₉	C₂	direct (N × H)
9. C₂×C₄⋊C₄×D₁₉	C₂	semidirect
10. C₂×C₂²⋊C₄×D₁₉	C₂	semidirect
11. C₂×C₂²⋊C₄×D₁₉	C₂	semidirect
12. C₂×C₁₉×#123	C₂	semidirect
16. C₂³×C₄×C₁₉	C₂²	semidirect
19. C₂³×Dic₁₉	C₂²	semidirect
27. C₂²×C₄×D₁₉	C₂²	semidirect
28. C₂²×C₄×D₁₉	C₂²	semidirect
29. C₁₉×#123	C₂²	semidirect
30. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
31. C₂×C₂²⋊C₄×C₁₉	C₂²	semidirect
32. C₂×C₂²⋊C₄×C₁₉	C₂²	semidirect
33. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
34. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
35. #10597381	C₂²	semidirect
36. #10597375	C₂²	semidirect
37. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
38. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
39. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
40. C₂×C₄⋊Dic₁₉	C₂²	semidirect
41. C₂×Dic₁₉⋊C₄	C₂²	semidirect
42. C₂×Dic₁₉⋊C₄	C₂²	semidirect
43. #10597340	C₂²	semidirect
44. C₄⋊C₄×D₁₉	C₂²	semidirect
45. #10597332	C₂²	semidirect
46. #10597329	C₂²	semidirect
47. C₂²⋊C₄×D₁₉	C₂²	semidirect
48. C₂²⋊C₄×D₁₉	C₂²	semidirect
66. C₂²×C₄×C₁₉	C₂³	semidirect
75. C₂²×Dic₁₉	C₂³	semidirect
87. C₂×C₄×D₁₉	C₂³	semidirect
88. C₄⋊C₄×C₁₉	C₂³	semidirect
89. C₂²⋊C₄×C₁₉	C₂³	semidirect
90. C₂²⋊C₄×C₁₉	C₂³	semidirect
91. C₂²⋊Dic₁₉	C₂³	semidirect
92. C₂²⋊Dic₁₉	C₂³	semidirect
93. (C₂×D₁₉)⋊C₄	C₂³	semidirect
94. (C₂×D₁₉)⋊C₄	C₂³	semidirect
95. (C₂×D₁₉)⋊C₄	C₂³	semidirect
96. C₄⋊Dic₁₉	C₂³	semidirect
97. Dic₁₉⋊C₄	C₂³	semidirect
98. Dic₁₉⋊C₄	C₂³	semidirect
160. C₂×D₁₉	#123	direct (N × H)
178. C₂×#123	D₁₉	direct (N × H)
184. C₂×C₁₉	C₂×#123	semidirect
189. D₁₉	C₂×#123	direct (N × H)
205. C₂³×C₄	C₂×D₁₉	semidirect
211. #123	C₂×D₁₉	direct (N × H)
216. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
224. C₂×C₂²⋊C₄	C₂×D₁₉	semidirect
225. C₂×C₂²⋊C₄	C₂×D₁₉	semidirect
226. C₁₉	C₂²×#123	semidirect
265. C₂²×C₄	C₂²×D₁₉	semidirect
269. C₄⋊C₄	C₂²×D₁₉	semidirect
275. C₂²⋊C₄	C₂²×D₁₉	semidirect
276. C₂²⋊C₄	C₂²×D₁₉	semidirect
352. C₂	#123×D₁₉	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×D₄×D₁₉	2
C₂³×C₄×D₁₉	2
C₂×#10597340	2
C₂×#10597332	2
C₂×#10597375	2
C₂×#10597329	2
C₂×#10597381	2
#123×D₁₉	2
C₂×C₄⋊C₄×D₁₉	2
C₂×C₂²⋊C₄×D₁₉	2
C₂×C₁₉×#123	2
C₂²×#123	19

Subgroups — C2×#123×D19 #14576865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#123×D₁₉ #14576865