Subgroups — C₁₉×#62328 #18068287

Order 4864.

2020 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3549	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3341	C₂	1	4	yes	maximal, complemented
3	C₁₉×#3325	C₂	1	8	yes	maximal, complemented
4	D₄×D₈×C₁₉	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3253	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3199	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3169	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3058	C₂	1	4	yes	maximal, complemented
9	C₁₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₁₉	C₂²	1	4	yes	complemented
11	C₂×C₁₉×#131	C₂²	1	2	yes	complemented
12	C₁₉×H(3,𝔽₄)	—	2	4	no	—
13	C₁₉×#555	—	2	2	no	—
14	C₁₉×#555	C₂²	1	8	yes	complemented
15	D₄²×C₁₉	—	2	2	no	—
16	D₄²×C₁₉	C₂²	1	8	yes	complemented
17	C₁₉×#535	—	2	8	no	—
18	C₁₉×#535	C₂²	1	8	yes	complemented
19	C₁₉×#532	C₂²	1	1	yes	characteristic
20	C₁₉×#532	C₂²	1	4	yes	complemented
21	C₁₉×#500	C₂²	1	2	yes	complemented
22	C₁₉×#493	C₂²	1	2	yes	—
23	C₁₉×#486	C₂²	1	4	yes	complemented
24	C₁₉×#482	C₂²	1	16	yes	complemented
25	C₁₉×#476	C₂²	1	8	yes	complemented
26	C₁₉×#469	C₂²	1	8	yes	complemented
27	C₁₉×#469	C₂²	1	8	yes	complemented
28	C₁₉×#466	C₂²	1	4	yes	complemented
29	C₁₉×#466	C₂²	1	4	yes	complemented
30	C₁₉×#466	C₂²	1	8	yes	complemented
31	C₁₉×#459	C₂²	1	8	yes	complemented
32	C₁₉×#447	C₂²	1	16	yes	complemented
33	C₄×D₈×C₁₉	C₂²	1	4	yes	complemented
34	C₄×D₈×C₁₉	C₂²	1	4	yes	complemented
35	C₁₉×#436	C₂²	1	4	yes	complemented
36	C₈×D₄×C₁₉	C₂²	1	4	yes	complemented
37	C₁₉×#427	C₂²	1	4	yes	complemented
38	C₁₉×#423	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#418	C₂²	1	8	yes	complemented
40	C₁₉×#408	C₂²	1	2	yes	complemented
41	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×#41×C₁₉	—	2	4	no	—
43	C₂×#41×C₁₉	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₉	—	2	8	no	—
45	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
46	C₂×D₈×C₁₉	—	4	8	no	—
47	C₂×D₈×C₁₉	C₂³	1	4	yes	—
48	C₂×D₈×C₁₉	C₂³	1	4	yes	—
49	C₂×D₈×C₁₉	C₂³	1	8	yes	—
50	C₁₉×#131	—	4	4	no	—
51	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
52	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
53	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
55	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
57	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
58	C₁₉×#127	—	2	8	no	—
59	C₁₉×#127	D₄	1	1	yes	characteristic
60	C₁₉×#127	C₂³	1	4	yes	—
61	C₁₉×#124	—	2	8	no	—
62	C₁₉×#124	—	2	16	no	—
63	C₁₉×#124	—	2	4	no	—
64	C₁₉×#124	D₄	1	2	yes	—
65	C₁₉×#121	—	2	8	no	—
66	C₁₉×#121	—	2	4	no	—
67	C₁₉×#121	—	2	8	no	—
68	C₁₉×#121	D₄	1	4	yes	—
69	C₁₉×#121	C₂³	1	16	yes	—
70	C₁₉×#121	C₂³	1	8	yes	—
71	C₁₉×#120	—	2	8	no	—
72	C₁₉×#120	—	2	8	no	—
73	C₁₉×#120	—	2	16	no	—
74	C₄×D₄×C₁₉	—	2	4	no	—
75	C₄×D₄×C₁₉	C₂³	1	8	yes	—
76	C₄×D₄×C₁₉	C₂³	1	4	yes	—
77	C₁₉×#117	—	2	8	no	—
78	C₁₉×#117	C₂³	1	8	yes	—
79	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×#107	C₂³	1	4	yes	—
81	C₁₉×#107	C₂³	1	4	yes	—
82	C₁₉×#106	C₂³	1	8	yes	—
83	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
84	C₁₉×#102	C₂³	1	8	yes	—
85	C₁₉×#102	C₂³	1	16	yes	—
86	C₁₉×#102	C₂³	1	8	yes	—
87	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
88	C₄×C₈×C₁₉	C₂³	1	2	yes	—
89	C₄×C₈×C₁₉	C₂³	1	2	yes	—
90	C₂⁴×C₁₉	—	2	8	no	—
91	#41×C₁₉	—	4	2	no	—
92	#41×C₁₉	—	4	2	no	—
93	#41×C₁₉	—	8	8	no	—
94	C₂×Q₈×C₁₉	—	2	4	no	—
95	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
96	C₂×D₄×C₁₉	—	2	16	no	—
97	C₂×D₄×C₁₉	—	2	8	no	—
98	C₂×D₄×C₁₉	—	2	4	no	—
99	C₂×D₄×C₁₉	—	2	4	no	—
100	C₂×D₄×C₁₉	—	2	8	no	—
101	C₂×D₄×C₁₉	—	4	8	no	—
102	C₂×D₄×C₁₉	—	4	8	no	—
103	C₂×D₄×C₁₉	—	8	16	no	—
104	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
105	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
107	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
108	C₂²×C₄×C₁₉	—	2	8	no	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
112	D₈×C₁₉	—	2	8	no	—
113	D₈×C₁₉	—	4	8	no	—
114	D₈×C₁₉	—	4	4	no	—
115	M₁₆×C₁₉	—	4	4	no	—
116	M₁₆×C₁₉	—	4	2	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	8	no	—
119	C₂×C₈×C₁₉	—	4	1	no	—
120	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
121	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
122	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
123	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
126	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
127	C₂²⋊C₄×C₁₉	—	2	8	no	—
128	C₂²⋊C₄×C₁₉	—	2	16	no	—
129	C₂²⋊C₄×C₁₉	—	2	8	no	—
130	C₂²⋊C₄×C₁₉	—	2	8	no	—
131	C₂²⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
132	C₄²×C₁₉	—	2	8	no	—
133	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₉	C₂⁴	1	2	yes	—
136	#62328	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₁₉	—	2	8	no	—
138	C₂³×C₁₉	—	8	8	no	—
139	C₂³×C₁₉	—	8	16	no	—
140	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
141	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
142	Q₈×C₁₉	—	4	2	no	—
143	Q₈×C₁₉	—	8	4	no	—
144	D₄×C₁₉	—	2	8	no	—
145	D₄×C₁₉	—	2	8	no	—
146	D₄×C₁₉	—	2	8	no	—
147	D₄×C₁₉	—	4	2	no	—
148	D₄×C₁₉	—	4	4	no	—
149	D₄×C₁₉	—	4	8	no	—
150	D₄×C₁₉	—	8	8	no	—
151	D₄×C₁₉	—	8	4	no	—
152	D₄×C₁₉	—	8	16	no	—
153	D₄×C₁₉	—	8	8	no	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	8	no	—
160	C₂×C₄×C₁₉	—	4	16	no	—
161	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
162	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
164	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
165	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
166	C₈×C₁₉	—	2	1	no	—
167	C₈×C₁₉	—	2	4	no	—
168	C₈×C₁₉	—	2	2	no	—
169	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
170	#3549	C₂×C₁₉	1	2	yes	complemented
171	#3341	C₂×C₁₉	1	4	yes	complemented
172	#3325	C₂×C₁₉	1	8	yes	complemented
173	D₄×D₈	C₂×C₁₉	1	4	yes	complemented
174	#3253	C₂×C₁₉	1	2	yes	complemented
175	#3199	C₂×C₁₉	1	4	yes	complemented
176	#3169	C₂×C₁₉	1	2	yes	complemented
177	#3058	C₂×C₁₉	1	4	yes	complemented
178	#2931	C₂×C₁₉	1	1	yes	characteristic, complemented
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	2	4	no	—
181	C₂²×C₁₉	—	2	2	no	—
182	C₂²×C₁₉	—	2	8	no	—
183	C₂²×C₁₉	—	4	8	no	—
184	C₂²×C₁₉	—	4	8	no	—
185	C₂²×C₁₉	—	4	8	no	—
186	C₂²×C₁₉	—	16	16	no	—
187	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
188	C₄×C₁₉	—	2	1	no	—
189	C₄×C₁₉	—	2	4	no	—
190	C₄×C₁₉	—	2	2	no	—
191	C₄×C₁₉	—	4	8	no	—
192	C₄×C₁₉	#576	1	4	yes	—
193	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
194	C₄×C₁₉	#585	1	1	yes	characteristic
195	C₂²×D₈	C₂²×C₁₉	1	4	yes	complemented
196	C₂×#131	C₂²×C₁₉	1	2	yes	complemented
197	H(3,𝔽₄)	—	2	4	no	—
198	#555	—	2	2	no	—
199	#555	C₂²×C₁₉	1	8	yes	complemented
200	D₄²	—	2	2	no	—
201	D₄²	C₂²×C₁₉	1	8	yes	complemented
202	#535	—	2	8	no	—
203	#535	C₂²×C₁₉	1	8	yes	complemented
204	#532	C₂²×C₁₉	1	1	yes	characteristic
205	#532	C₂²×C₁₉	1	4	yes	complemented
206	#500	C₂²×C₁₉	1	2	yes	complemented
207	#493	C₂²×C₁₉	1	2	yes	—
208	#486	C₂²×C₁₉	1	4	yes	complemented
209	#482	C₂²×C₁₉	1	16	yes	complemented
210	#476	C₂²×C₁₉	1	8	yes	complemented
211	#469	C₂²×C₁₉	1	8	yes	complemented
212	#469	C₂²×C₁₉	1	8	yes	complemented
213	#466	C₂²×C₁₉	1	8	yes	complemented
214	#466	C₂²×C₁₉	1	4	yes	complemented
215	#466	C₂²×C₁₉	1	4	yes	complemented
216	#459	C₂²×C₁₉	1	8	yes	complemented
217	#447	C₂²×C₁₉	1	16	yes	complemented
218	C₄×D₈	C₂²×C₁₉	1	4	yes	complemented
219	C₄×D₈	C₂²×C₁₉	1	4	yes	complemented
220	#436	C₂²×C₁₉	1	4	yes	complemented
221	C₈×D₄	C₂²×C₁₉	1	4	yes	complemented
222	#427	C₂²×C₁₉	1	4	yes	complemented
223	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
224	#418	C₂²×C₁₉	1	8	yes	complemented
225	#408	C₂²×C₁₉	1	2	yes	complemented
226	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
227	C₂×C₁₉	—	4	1	no	—
228	C₂×C₁₉	—	4	4	no	—
229	C₂×C₁₉	—	8	8	no	—
230	C₂×C₁₉	#3496	1	1	yes	characteristic
231	C₂×C₁₉	C₂×#576	1	2	yes	—
232	C₂×#41	—	2	4	no	—
233	C₂×#41	C₂³×C₁₉	1	2	yes	—
234	C₂²×D₄	—	2	8	no	—
235	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
236	C₂×D₈	—	4	8	no	—
237	C₂×D₈	C₂³×C₁₉	1	4	yes	—
238	C₂×D₈	C₂³×C₁₉	1	8	yes	—
239	C₂×D₈	C₂³×C₁₉	1	4	yes	—
240	#131	—	4	4	no	—
241	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
242	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
243	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
245	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
246	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
247	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
248	#127	—	2	8	no	—
249	#127	D₄×C₁₉	1	1	yes	characteristic
250	#127	C₂³×C₁₉	1	4	yes	—
251	#124	—	2	8	no	—
252	#124	—	2	16	no	—
253	#124	—	2	4	no	—
254	#124	D₄×C₁₉	1	2	yes	—
255	#121	—	2	8	no	—
256	#121	—	2	4	no	—
257	#121	—	2	8	no	—
258	#121	D₄×C₁₉	1	4	yes	—
259	#121	C₂³×C₁₉	1	8	yes	—
260	#121	C₂³×C₁₉	1	16	yes	—
261	#120	—	2	8	no	—
262	#120	—	2	8	no	—
263	#120	—	2	16	no	—
264	C₄×D₄	—	2	4	no	—
265	C₄×D₄	C₂³×C₁₉	1	8	yes	—
266	C₄×D₄	C₂³×C₁₉	1	4	yes	—
267	#117	—	2	8	no	—
268	#117	C₂³×C₁₉	1	8	yes	—
269	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
270	#107	C₂³×C₁₉	1	4	yes	—
271	#107	C₂³×C₁₉	1	4	yes	—
272	#106	C₂³×C₁₉	1	8	yes	—
273	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
274	#102	C₂³×C₁₉	1	8	yes	—
275	#102	C₂³×C₁₉	1	16	yes	—
276	#102	C₂³×C₁₉	1	8	yes	—
277	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
278	C₄×C₈	C₂³×C₁₉	1	2	yes	—
279	C₄×C₈	C₂³×C₁₉	1	2	yes	—
280	C₁₉	#62328	1	1	yes	characteristic, direct product factor, Sylow
281	C₂⁴	—	2	8	no	—
282	#41	—	4	2	no	—
283	#41	—	4	2	no	—
284	#41	—	8	8	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
287	C₂×D₄	—	2	16	no	—
288	C₂×D₄	—	2	8	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	4	8	no	—
293	C₂×D₄	—	4	8	no	—
294	C₂×D₄	—	8	16	no	—
295	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
296	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
297	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
298	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
301	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
302	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
303	D₈	—	2	8	no	—
304	D₈	—	4	8	no	—
305	D₈	—	4	4	no	—
306	M₁₆	—	4	4	no	—
307	M₁₆	—	4	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	8	no	—
310	C₂×C₈	—	4	1	no	—
311	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
312	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
313	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
314	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
317	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
318	C₂²⋊C₄	—	2	8	no	—
319	C₂²⋊C₄	—	2	16	no	—
320	C₂²⋊C₄	—	2	8	no	—
321	C₂²⋊C₄	—	2	8	no	—
322	C₂²⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
323	C₄²	—	2	8	no	—
324	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
325	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
326	C₄²	C₂⁴×C₁₉	1	2	yes	—
327	C₂³	—	2	8	no	—
328	C₂³	—	8	8	no	—
329	C₂³	—	8	16	no	—
330	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
331	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
332	Q₈	—	4	2	no	—
333	Q₈	—	8	4	no	—
334	D₄	—	2	8	no	—
335	D₄	—	2	8	no	—
336	D₄	—	2	8	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	4	no	—
339	D₄	—	4	8	no	—
340	D₄	—	8	8	no	—
341	D₄	—	8	4	no	—
342	D₄	—	8	16	no	—
343	D₄	—	8	8	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	4	16	no	—
351	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
352	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
353	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
354	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
355	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
356	C₈	—	2	1	no	—
357	C₈	—	2	4	no	—
358	C₈	—	2	2	no	—
359	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	4	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	8	no	—
364	C₂²	—	4	8	no	—
365	C₂²	—	4	8	no	—
366	C₂²	—	4	8	no	—
367	C₂²	—	16	16	no	—
368	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	2	4	no	—
371	C₄	—	2	2	no	—
372	C₄	—	4	8	no	—
373	C₄	C₁₉×#576	1	4	yes	—
374	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
375	C₄	C₁₉×#585	1	1	yes	characteristic
376	C₂	—	4	4	no	—
377	C₂	—	4	1	no	—
378	C₂	—	8	8	no	—
379	C₂	C₁₉×#3496	1	1	yes	characteristic
380	C₂	C₂×C₁₉×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3549	C₂	semidirect
2. C₁₉×#3341	C₂	semidirect
3. C₁₉×#3325	C₂	semidirect
4. D₄×D₈×C₁₉	C₂	semidirect
5. C₁₉×#3253	C₂	semidirect
6. C₁₉×#3199	C₂	semidirect
7. C₁₉×#3169	C₂	semidirect
8. C₁₉×#3058	C₂	semidirect
9. C₁₉×#2931	C₂	semidirect
10. C₂²×D₈×C₁₉	C₂²	semidirect
11. C₂×C₁₉×#131	C₂²	semidirect
14. C₁₉×#555	C₂²	semidirect
16. D₄²×C₁₉	C₂²	semidirect
18. C₁₉×#535	C₂²	semidirect
20. C₁₉×#532	C₂²	semidirect
21. C₁₉×#500	C₂²	semidirect
23. C₁₉×#486	C₂²	semidirect
24. C₁₉×#482	C₂²	semidirect
25. C₁₉×#476	C₂²	semidirect
26. C₁₉×#469	C₂²	semidirect
27. C₁₉×#469	C₂²	semidirect
28. C₁₉×#466	C₂²	semidirect
29. C₁₉×#466	C₂²	semidirect
30. C₁₉×#466	C₂²	semidirect
31. C₁₉×#459	C₂²	semidirect
32. C₁₉×#447	C₂²	semidirect
33. C₄×D₈×C₁₉	C₂²	semidirect
34. C₄×D₈×C₁₉	C₂²	semidirect
35. C₁₉×#436	C₂²	semidirect
36. C₈×D₄×C₁₉	C₂²	semidirect
37. C₁₉×#427	C₂²	semidirect
38. C₁₉×#423	C₂²	semidirect
39. C₁₉×#418	C₂²	semidirect
40. C₁₉×#408	C₂²	semidirect
41. C₂×C₄×C₈×C₁₉	C₂²	semidirect
136. #62328	C₁₉	direct (N × H)
170. #3549	C₂×C₁₉	semidirect
171. #3341	C₂×C₁₉	semidirect
172. #3325	C₂×C₁₉	semidirect
173. D₄×D₈	C₂×C₁₉	semidirect
174. #3253	C₂×C₁₉	semidirect
175. #3199	C₂×C₁₉	semidirect
176. #3169	C₂×C₁₉	semidirect
177. #3058	C₂×C₁₉	semidirect
178. #2931	C₂×C₁₉	semidirect
195. C₂²×D₈	C₂²×C₁₉	semidirect
196. C₂×#131	C₂²×C₁₉	semidirect
199. #555	C₂²×C₁₉	semidirect
201. D₄²	C₂²×C₁₉	semidirect
203. #535	C₂²×C₁₉	semidirect
205. #532	C₂²×C₁₉	semidirect
206. #500	C₂²×C₁₉	semidirect
208. #486	C₂²×C₁₉	semidirect
209. #482	C₂²×C₁₉	semidirect
210. #476	C₂²×C₁₉	semidirect
211. #469	C₂²×C₁₉	semidirect
212. #469	C₂²×C₁₉	semidirect
213. #466	C₂²×C₁₉	semidirect
214. #466	C₂²×C₁₉	semidirect
215. #466	C₂²×C₁₉	semidirect
216. #459	C₂²×C₁₉	semidirect
217. #447	C₂²×C₁₉	semidirect
218. C₄×D₈	C₂²×C₁₉	semidirect
219. C₄×D₈	C₂²×C₁₉	semidirect
220. #436	C₂²×C₁₉	semidirect
221. C₈×D₄	C₂²×C₁₉	semidirect
222. #427	C₂²×C₁₉	semidirect
223. #423	C₂²×C₁₉	semidirect
224. #418	C₂²×C₁₉	semidirect
225. #408	C₂²×C₁₉	semidirect
226. C₂×C₄×C₈	C₂²×C₁₉	semidirect
280. C₁₉	#62328	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×#3549	2
C₁₉×#3341	2
C₁₉×#3325	2
D₄×D₈×C₁₉	2
C₁₉×#3253	2
C₁₉×#3199	2
C₁₉×#3169	2
C₁₉×#3058	2
C₁₉×#2931	2
#62328	19

Subgroups — C19×#62328 #18068287

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62328 #18068287