Subgroups — C₁₉×#60307 #18066266

Order 4864.

1820 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3529	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2995	C₂	1	6	yes	maximal, complemented
3	C₁₉×#2980	C₂	1	3	yes	maximal, complemented
4	C₁₉×#2978	C₂	1	6	yes	maximal, complemented
5	C₁₉×#2966	C₂	1	6	yes	maximal, complemented
6	C₁₉×#2931	C₂	1	3	yes	maximal, complemented
7	C₁₉×#2929	C₂	1	6	yes	maximal, complemented
8	C₂×C₁₉×#131	C₂²	1	3	yes	—
9	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic, complemented
10	C₂³×C₈×C₁₉	C₂²	1	2	yes	complemented
11	C₁₉×#563	C₄	1	3	yes	—
12	C₁₉×#562	C₄	1	6	yes	—
13	C₁₉×H(3,𝔽₄)	C₄	1	1	yes	characteristic
14	C₁₉×#560	C₄	1	6	yes	—
15	C₁₉×#532	C₂²	1	3	yes	—
16	C₁₉×#529	C₂²	1	6	yes	—
17	C₁₉×#525	C₂²	1	6	yes	—
18	C₁₉×#446	C₂²	1	6	yes	complemented
19	C₈×Q₈×C₁₉	C₂²	1	2	yes	complemented
20	C₁₉×#436	C₂²	1	6	yes	—
21	C₁₉×#436	C₂²	1	12	yes	complemented
22	C₁₉×#435	C₂²	1	12	yes	—
23	C₁₉×#435	C₂²	1	12	yes	complemented
24	C₁₉×#435	C₂²	1	12	yes	complemented
25	C₈×D₄×C₁₉	C₂²	1	6	yes	—
26	C₈×D₄×C₁₉	C₂²	1	12	yes	complemented
27	C₁₉×#433	C₂²	1	12	yes	complemented
28	C₁₉×#432	C₂²	1	6	yes	complemented
29	C₁₉×#424	C₂²	1	6	yes	complemented
30	C₁₉×#423	C₂²	1	3	yes	complemented
31	C₁₉×#408	C₂²	1	6	yes	—
32	C₁₉×#408	C₂²	1	3	yes	—
33	C₁₉×#408	C₂²	1	3	yes	complemented
34	C₁₉×#407	C₂²	1	6	yes	complemented
35	C₁₉×#405	C₂²	1	6	yes	complemented
36	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	complemented
37	C₂×#41×C₁₉	C₂³	1	3	yes	—
38	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
40	C₁₉×#131	—	4	6	no	—
41	C₁₉×#131	—	4	2	no	—
42	C₂×M₁₆×C₁₉	C₂³	1	6	yes	—
43	C₂×M₁₆×C₁₉	C₂³	1	6	yes	—
44	C₂×M₁₆×C₁₉	C₂³	1	3	yes	—
45	C₂×M₁₆×C₁₉	C₂³	1	3	yes	—
46	C₂²×C₈×C₁₉	—	4	4	no	—
47	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
48	C₂²×C₈×C₁₉	C₂³	1	6	yes	—
49	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
50	C₂²×C₈×C₁₉	C₂³	1	6	yes	—
51	C₁₉×C₄⋊Q₈	C₂×C₄	1	3	yes	—
52	C₁₉×#127	C₂×C₄	1	3	yes	—
53	C₁₉×#126	C₂×C₄	1	12	yes	—
54	C₁₉×#125	C₂×C₄	1	6	yes	—
55	C₁₉×#124	C₂×C₄	1	6	yes	—
56	C₁₉×#124	C₂×C₄	1	3	yes	—
57	C₁₉×#124	C₂×C₄	1	3	yes	—
58	C₁₉×#123	C₂×C₄	1	6	yes	—
59	C₁₉×#123	C₂×C₄	1	6	yes	—
60	C₁₉×#123	C₂×C₄	1	12	yes	—
61	C₁₉×C₂²⋊Q₈	C₂×C₄	1	12	yes	—
62	C₁₉×C₂²⋊Q₈	C₂×C₄	1	6	yes	—
63	C₁₉×#121	C₂×C₄	1	12	yes	—
64	C₁₉×#121	C₂×C₄	1	6	yes	—
65	C₁₉×#121	C₂×C₄	1	12	yes	—
66	C₁₉×#120	C₂×C₄	1	6	yes	—
67	C₁₉×#120	C₂×C₄	1	6	yes	—
68	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
69	C₄×D₄×C₁₉	C₂³	1	6	yes	—
70	C₄×D₄×C₁₉	C₂³	1	12	yes	—
71	C₁₉×#117	C₂³	1	6	yes	—
72	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
73	C₁₉×C₄⋊C₈	C₂³	1	12	yes	—
74	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
75	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
76	C₁₉×C₂²⋊C₈	C₂³	1	12	yes	—
77	C₁₉×C₂²⋊C₈	C₂³	1	12	yes	—
78	C₁₉×C₂²⋊C₈	C₂³	1	12	yes	—
79	C₁₉×#97	C₂³	1	12	yes	—
80	C₄×C₈×C₁₉	C₂³	1	6	yes	—
81	C₄×C₈×C₁₉	C₂³	1	6	yes	—
82	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
83	#41×C₁₉	—	4	3	no	—
84	#41×C₁₉	—	4	1	no	—
85	#41×C₁₉	—	4	1	no	—
86	#41×C₁₉	—	4	3	no	—
87	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
88	C₂×Q₈×C₁₉	C₂²×C₄	1	3	yes	—
89	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
90	C₂×D₄×C₁₉	C₂²×C₄	1	6	yes	—
91	C₂×D₄×C₁₉	C₂²×C₄	1	12	yes	—
92	C₂×D₄×C₁₉	C₂²×C₄	1	3	yes	—
93	C₂×D₄×C₁₉	C₂²×C₄	1	6	yes	—
94	C₂×D₄×C₁₉	C₂²×C₄	1	3	yes	—
95	C₂²×C₄×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	—	4	2	no	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
98	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
99	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
100	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
101	M₁₆×C₁₉	—	4	6	no	—
102	M₁₆×C₁₉	—	4	3	no	—
103	M₁₆×C₁₉	—	4	6	no	—
104	M₁₆×C₁₉	—	4	3	no	—
105	C₂×C₈×C₁₉	—	2	12	no	—
106	C₂×C₈×C₁₉	—	2	6	no	—
107	C₂×C₈×C₁₉	—	4	6	no	—
108	C₂×C₈×C₁₉	—	4	3	no	—
109	C₂×C₈×C₁₉	C₂⁴	1	6	yes	—
110	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
111	C₂×C₈×C₁₉	C₂⁴	1	6	yes	—
112	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
113	C₄⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
114	C₄⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
115	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
116	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
117	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
118	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
119	C₂²⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
120	C₂²⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
121	C₂²⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
122	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
123	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
124	C₄²×C₁₉	C₂⁴	1	6	yes	—
125	#60307	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₁₉	—	4	2	no	—
127	C₂³×C₁₉	—	4	4	no	—
128	C₂³×C₁₉	C₂³×C₄	1	6	yes	—
129	C₂³×C₁₉	C₂³×C₄	1	3	yes	—
130	Q₈×C₁₉	—	4	2	no	—
131	Q₈×C₁₉	—	4	3	no	—
132	Q₈×C₁₉	—	4	1	no	—
133	D₄×C₁₉	—	4	12	no	—
134	D₄×C₁₉	—	4	6	no	—
135	D₄×C₁₉	—	4	6	no	—
136	D₄×C₁₉	—	4	3	no	—
137	D₄×C₁₉	—	4	3	no	—
138	C₂×C₄×C₁₉	—	2	6	no	—
139	C₂×C₄×C₁₉	—	2	3	no	—
140	C₂×C₄×C₁₉	—	2	3	no	—
141	C₂×C₄×C₁₉	—	2	6	no	—
142	C₂×C₄×C₁₉	—	4	6	no	—
143	C₂×C₄×C₁₉	—	4	6	no	—
144	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
145	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
146	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
147	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
148	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
149	C₈×C₁₉	—	2	6	no	—
150	C₈×C₁₉	—	2	3	no	—
151	C₈×C₁₉	—	2	6	no	—
152	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
153	#3529	C₂×C₁₉	1	1	yes	characteristic
154	#2995	C₂×C₁₉	1	6	yes	complemented
155	#2980	C₂×C₁₉	1	3	yes	complemented
156	#2978	C₂×C₁₉	1	6	yes	complemented
157	#2966	C₂×C₁₉	1	6	yes	complemented
158	#2931	C₂×C₁₉	1	3	yes	complemented
159	#2929	C₂×C₁₉	1	6	yes	complemented
160	C₂²×C₁₉	—	2	6	no	—
161	C₂²×C₁₉	—	2	3	no	—
162	C₂²×C₁₉	—	2	6	no	—
163	C₂²×C₁₉	—	2	12	no	—
164	C₂²×C₁₉	—	4	8	no	—
165	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
166	C₄×C₁₉	—	2	6	no	—
167	C₄×C₁₉	—	2	3	no	—
168	C₄×C₁₉	—	2	6	no	—
169	C₄×C₁₉	—	2	6	no	—
170	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
171	C₄×C₁₉	#585	1	1	yes	characteristic
172	C₂×#131	C₂²×C₁₉	1	3	yes	—
173	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic, complemented
174	C₂³×C₈	C₂²×C₁₉	1	2	yes	complemented
175	#563	C₄×C₁₉	1	3	yes	—
176	#562	C₄×C₁₉	1	6	yes	—
177	H(3,𝔽₄)	C₄×C₁₉	1	1	yes	characteristic
178	#560	C₄×C₁₉	1	6	yes	—
179	#532	C₂²×C₁₉	1	3	yes	—
180	#529	C₂²×C₁₉	1	6	yes	—
181	#525	C₂²×C₁₉	1	6	yes	—
182	#446	C₂²×C₁₉	1	6	yes	complemented
183	C₈×Q₈	C₂²×C₁₉	1	2	yes	complemented
184	#436	C₂²×C₁₉	1	6	yes	—
185	#436	C₂²×C₁₉	1	12	yes	complemented
186	#435	C₂²×C₁₉	1	12	yes	—
187	#435	C₂²×C₁₉	1	12	yes	complemented
188	#435	C₂²×C₁₉	1	12	yes	complemented
189	C₈×D₄	C₂²×C₁₉	1	6	yes	—
190	C₈×D₄	C₂²×C₁₉	1	12	yes	complemented
191	#433	C₂²×C₁₉	1	12	yes	complemented
192	#432	C₂²×C₁₉	1	6	yes	complemented
193	#424	C₂²×C₁₉	1	6	yes	complemented
194	#423	C₂²×C₁₉	1	3	yes	complemented
195	#408	C₂²×C₁₉	1	6	yes	—
196	#408	C₂²×C₁₉	1	3	yes	—
197	#408	C₂²×C₁₉	1	3	yes	complemented
198	#407	C₂²×C₁₉	1	6	yes	complemented
199	#405	C₂²×C₁₉	1	6	yes	complemented
200	C₂×C₄×C₈	C₂²×C₁₉	1	3	yes	complemented
201	C₂×C₁₉	—	4	3	no	—
202	C₂×C₁₉	—	4	6	no	—
203	C₂×C₁₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₁₉	#3573	1	2	yes	—
205	C₂×#41	C₂³×C₁₉	1	3	yes	—
206	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
207	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
208	#131	—	4	6	no	—
209	#131	—	4	2	no	—
210	C₂×M₁₆	C₂³×C₁₉	1	6	yes	—
211	C₂×M₁₆	C₂³×C₁₉	1	3	yes	—
212	C₂×M₁₆	C₂³×C₁₉	1	3	yes	—
213	C₂×M₁₆	C₂³×C₁₉	1	6	yes	—
214	C₂²×C₈	—	4	4	no	—
215	C₂²×C₈	C₂³×C₁₉	1	6	yes	—
216	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
217	C₂²×C₈	C₂³×C₁₉	1	6	yes	—
218	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
219	C₄⋊Q₈	C₂×C₄×C₁₉	1	3	yes	—
220	#127	C₂×C₄×C₁₉	1	3	yes	—
221	#126	C₂×C₄×C₁₉	1	12	yes	—
222	#125	C₂×C₄×C₁₉	1	6	yes	—
223	#124	C₂×C₄×C₁₉	1	6	yes	—
224	#124	C₂×C₄×C₁₉	1	3	yes	—
225	#124	C₂×C₄×C₁₉	1	3	yes	—
226	#123	C₂×C₄×C₁₉	1	6	yes	—
227	#123	C₂×C₄×C₁₉	1	6	yes	—
228	#123	C₂×C₄×C₁₉	1	12	yes	—
229	C₂²⋊Q₈	C₂×C₄×C₁₉	1	12	yes	—
230	C₂²⋊Q₈	C₂×C₄×C₁₉	1	6	yes	—
231	#121	C₂×C₄×C₁₉	1	12	yes	—
232	#121	C₂×C₄×C₁₉	1	6	yes	—
233	#121	C₂×C₄×C₁₉	1	12	yes	—
234	#120	C₂×C₄×C₁₉	1	6	yes	—
235	#120	C₂×C₄×C₁₉	1	6	yes	—
236	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
237	C₄×D₄	C₂³×C₁₉	1	6	yes	—
238	C₄×D₄	C₂³×C₁₉	1	12	yes	—
239	#117	C₂³×C₁₉	1	6	yes	—
240	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
241	C₄⋊C₈	C₂³×C₁₉	1	12	yes	—
242	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
243	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
244	C₂²⋊C₈	C₂³×C₁₉	1	12	yes	—
245	C₂²⋊C₈	C₂³×C₁₉	1	12	yes	—
246	C₂²⋊C₈	C₂³×C₁₉	1	12	yes	—
247	#97	C₂³×C₁₉	1	12	yes	—
248	C₄×C₈	C₂³×C₁₉	1	6	yes	—
249	C₄×C₈	C₂³×C₁₉	1	6	yes	—
250	C₁₉	#60307	1	1	yes	characteristic, direct product factor, Sylow
251	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
252	#41	—	4	3	no	—
253	#41	—	4	1	no	—
254	#41	—	4	1	no	—
255	#41	—	4	3	no	—
256	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
257	C₂×Q₈	C₂²×C₄×C₁₉	1	3	yes	—
258	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
259	C₂×D₄	C₂²×C₄×C₁₉	1	6	yes	—
260	C₂×D₄	C₂²×C₄×C₁₉	1	12	yes	—
261	C₂×D₄	C₂²×C₄×C₁₉	1	3	yes	—
262	C₂×D₄	C₂²×C₄×C₁₉	1	6	yes	—
263	C₂×D₄	C₂²×C₄×C₁₉	1	3	yes	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
267	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
268	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
269	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
270	M₁₆	—	4	6	no	—
271	M₁₆	—	4	3	no	—
272	M₁₆	—	4	6	no	—
273	M₁₆	—	4	3	no	—
274	C₂×C₈	—	2	12	no	—
275	C₂×C₈	—	2	6	no	—
276	C₂×C₈	—	4	6	no	—
277	C₂×C₈	—	4	3	no	—
278	C₂×C₈	C₂⁴×C₁₉	1	6	yes	—
279	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
280	C₂×C₈	C₂⁴×C₁₉	1	6	yes	—
281	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
282	C₄⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
283	C₄⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
284	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
285	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
286	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
287	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
288	C₂²⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
289	C₂²⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
290	C₂²⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
291	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
292	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
293	C₄²	C₂⁴×C₁₉	1	6	yes	—
294	C₂³	—	4	2	no	—
295	C₂³	—	4	4	no	—
296	C₂³	C₂³×C₄×C₁₉	1	6	yes	—
297	C₂³	C₂³×C₄×C₁₉	1	3	yes	—
298	Q₈	—	4	3	no	—
299	Q₈	—	4	1	no	—
300	Q₈	—	4	2	no	—
301	D₄	—	4	6	no	—
302	D₄	—	4	3	no	—
303	D₄	—	4	3	no	—
304	D₄	—	4	12	no	—
305	D₄	—	4	6	no	—
306	C₂×C₄	—	2	6	no	—
307	C₂×C₄	—	2	3	no	—
308	C₂×C₄	—	2	3	no	—
309	C₂×C₄	—	2	6	no	—
310	C₂×C₄	—	4	6	no	—
311	C₂×C₄	—	4	6	no	—
312	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
313	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
314	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
315	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
316	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
317	C₈	—	2	6	no	—
318	C₈	—	2	3	no	—
319	C₈	—	2	6	no	—
320	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
321	C₂²	—	2	6	no	—
322	C₂²	—	2	3	no	—
323	C₂²	—	2	6	no	—
324	C₂²	—	2	12	no	—
325	C₂²	—	4	8	no	—
326	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
327	C₄	—	2	6	no	—
328	C₄	—	2	3	no	—
329	C₄	—	2	6	no	—
330	C₄	—	2	6	no	—
331	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
332	C₄	C₁₉×#585	1	1	yes	characteristic
333	C₂	—	4	6	no	—
334	C₂	—	4	3	no	—
335	C₂	C₄×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
336	C₂	C₁₉×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂⁴×C₄
prime radical	C₁₉×#3529	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2995	C₂	semidirect
3. C₁₉×#2980	C₂	semidirect
4. C₁₉×#2978	C₂	semidirect
5. C₁₉×#2966	C₂	semidirect
6. C₁₉×#2931	C₂	semidirect
7. C₁₉×#2929	C₂	semidirect
9. C₂×C₁₉×#131	C₂²	semidirect
10. C₂³×C₈×C₁₉	C₂²	semidirect
18. C₁₉×#446	C₂²	semidirect
19. C₈×Q₈×C₁₉	C₂²	semidirect
21. C₁₉×#436	C₂²	semidirect
23. C₁₉×#435	C₂²	semidirect
24. C₁₉×#435	C₂²	semidirect
26. C₈×D₄×C₁₉	C₂²	semidirect
27. C₁₉×#433	C₂²	semidirect
28. C₁₉×#432	C₂²	semidirect
29. C₁₉×#424	C₂²	semidirect
30. C₁₉×#423	C₂²	semidirect
33. C₁₉×#408	C₂²	semidirect
34. C₁₉×#407	C₂²	semidirect
35. C₁₉×#405	C₂²	semidirect
36. C₂×C₄×C₈×C₁₉	C₂²	semidirect
125. #60307	C₁₉	direct (N × H)
154. #2995	C₂×C₁₉	semidirect
155. #2980	C₂×C₁₉	semidirect
156. #2978	C₂×C₁₉	semidirect
157. #2966	C₂×C₁₉	semidirect
158. #2931	C₂×C₁₉	semidirect
159. #2929	C₂×C₁₉	semidirect
173. C₂×#131	C₂²×C₁₉	semidirect
174. C₂³×C₈	C₂²×C₁₉	semidirect
182. #446	C₂²×C₁₉	semidirect
183. C₈×Q₈	C₂²×C₁₉	semidirect
185. #436	C₂²×C₁₉	semidirect
187. #435	C₂²×C₁₉	semidirect
188. #435	C₂²×C₁₉	semidirect
190. C₈×D₄	C₂²×C₁₉	semidirect
191. #433	C₂²×C₁₉	semidirect
192. #432	C₂²×C₁₉	semidirect
193. #424	C₂²×C₁₉	semidirect
194. #423	C₂²×C₁₉	semidirect
197. #408	C₂²×C₁₉	semidirect
198. #407	C₂²×C₁₉	semidirect
199. #405	C₂²×C₁₉	semidirect
200. C₂×C₄×C₈	C₂²×C₁₉	semidirect
250. C₁₉	#60307	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×#3529	2
C₁₉×#2995	2
C₁₉×#2980	2
C₁₉×#2978	2
C₁₉×#2966	2
C₁₉×#2931	2
C₁₉×#2929	2
#60307	19

Subgroups — C19×#60307 #18066266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60307 #18066266